LMFDB - Embedded newform 37.10.f.a.7.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(7,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.15
Character	$\chi$	$=$	37.7
Dual form			37.10.f.a.16.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.13813 - 1.87013i) q^{2} +(-174.502 - 63.5134i) q^{3} +(-369.312 + 309.889i) q^{4} +(226.866 + 1286.62i) q^{5} -1015.39 q^{6} +(674.322 + 3824.27i) q^{7} +(-2717.82 + 4707.40i) q^{8} +(11338.8 + 9514.40i) q^{9} +O(q^{10})$	\(q+(5.13813 - 1.87013i) q^{2} +(-174.502 - 63.5134i) q^{3} +(-369.312 + 309.889i) q^{4} +(226.866 + 1286.62i) q^{5} -1015.39 q^{6} +(674.322 + 3824.27i) q^{7} +(-2717.82 + 4707.40i) q^{8} +(11338.8 + 9514.40i) q^{9} +(3571.81 + 6186.56i) q^{10} +(-4503.19 + 7799.76i) q^{11} +(84127.6 - 30620.0i) q^{12} +(-46670.8 + 39161.5i) q^{13} +(10616.6 + 18388.5i) q^{14} +(42129.2 - 238927. i) q^{15} +(37701.6 - 213816. i) q^{16} +(-150019. - 125881. i) q^{17} +(76053.5 + 27681.2i) q^{18} +(-609739. - 221927. i) q^{19} +(-482495. - 404861. i) q^{20} +(125222. - 710170. i) q^{21} +(-8551.46 + 48497.7i) q^{22} +(60356.1 + 104540. i) q^{23} +(773247. - 648831. i) q^{24} +(231411. - 84226.6i) q^{25} +(-166564. + 288497. i) q^{26} +(453223. + 785005. i) q^{27} +(-1.43414e6 - 1.20338e6i) q^{28} +(1.20095e6 - 2.08010e6i) q^{29} +(-230358. - 1.30642e6i) q^{30} +3.26346e6 q^{31} +(-689419. - 3.90989e6i) q^{32} +(1.28120e6 - 1.07506e6i) q^{33} +(-1.00623e6 - 366237. i) q^{34} +(-4.76741e6 + 1.73520e6i) q^{35} -7.13597e6 q^{36} +(-3.00122e6 - 1.09979e7i) q^{37} -3.54795e6 q^{38} +(1.06314e7 - 3.86952e6i) q^{39} +(-6.67322e6 - 2.42885e6i) q^{40} +(1.15765e7 - 9.71380e6i) q^{41} +(-684701. - 3.88313e6i) q^{42} +1.72403e6 q^{43} +(-753980. - 4.27603e6i) q^{44} +(-9.66904e6 + 1.67473e7i) q^{45} +(505621. + 424266. i) q^{46} +(330134. + 571810. i) q^{47} +(-2.01592e7 + 3.49168e7i) q^{48} +(2.37496e7 - 8.64416e6i) q^{49} +(1.03150e6 - 865535. i) q^{50} +(1.81834e7 + 3.14946e7i) q^{51} +(5.10036e6 - 2.89256e7i) q^{52} +(-6.90155e6 + 3.91406e7i) q^{53} +(3.79678e6 + 3.18587e6i) q^{54} +(-1.10570e7 - 4.02440e6i) q^{55} +(-1.98351e7 - 7.21937e6i) q^{56} +(9.23052e7 + 7.74532e7i) q^{57} +(2.28057e6 - 1.29337e7i) q^{58} +(-2.42491e7 + 1.37524e8i) q^{59} +(5.84820e7 + 1.01294e8i) q^{60} +(-4.45382e7 + 3.73720e7i) q^{61} +(1.67681e7 - 6.10309e6i) q^{62} +(-2.87396e7 + 4.97785e7i) q^{63} +(4.47271e7 + 7.74696e7i) q^{64} +(-6.09740e7 - 5.11633e7i) q^{65} +(4.57250e6 - 7.91980e6i) q^{66} +(-4.75516e7 - 2.69678e8i) q^{67} +9.44128e7 q^{68} +(-3.89256e6 - 2.20758e7i) q^{69} +(-2.12505e7 + 1.78313e7i) q^{70} +(-3.50421e8 - 1.27543e8i) q^{71} +(-7.56050e7 + 2.75180e7i) q^{72} +4.48383e7 q^{73} +(-3.59882e7 - 5.08961e7i) q^{74} -4.57311e7 q^{75} +(2.93957e8 - 1.06991e8i) q^{76} +(-3.28650e7 - 1.19619e7i) q^{77} +(4.73891e7 - 3.97642e7i) q^{78} +(4.87563e6 + 2.76511e7i) q^{79} +2.83654e8 q^{80} +(-7.98211e7 - 4.52688e8i) q^{81} +(4.13153e7 - 7.15602e7i) q^{82} +(1.98728e8 + 1.66752e8i) q^{83} +(1.73828e8 + 3.01079e8i) q^{84} +(1.27927e8 - 2.21575e8i) q^{85} +(8.85830e6 - 3.22416e6i) q^{86} +(-3.41681e8 + 2.86704e8i) q^{87} +(-2.44777e7 - 4.23966e7i) q^{88} +(5.14621e7 - 2.91856e8i) q^{89} +(-1.83613e7 + 1.04132e8i) q^{90} +(-1.81235e8 - 1.52074e8i) q^{91} +(-5.46860e7 - 1.99041e7i) q^{92} +(-5.69479e8 - 2.07274e8i) q^{93} +(2.76563e6 + 2.32064e6i) q^{94} +(1.47207e8 - 8.34851e8i) q^{95} +(-1.28026e8 + 7.26069e8i) q^{96} +(-2.01930e8 - 3.49753e8i) q^{97} +(1.05863e8 - 8.88297e7i) q^{98} +(-1.25271e8 + 4.55949e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9}+O(q^{10}) $ 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9	\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9} + 59997 q^{10} + 175689 q^{11} - 147411 q^{12} + 713586 q^{13} - 96867 q^{14} - 143316 q^{15} + 556665 q^{16} - 119334 q^{17} - 711948 q^{18} + 1752348 q^{19} + 4774248 q^{20} + 57972 q^{21} + 1413495 q^{22} - 5098719 q^{23} + 3891975 q^{24} + 10869768 q^{25} + 5518221 q^{26} + 13281609 q^{27} + 9017757 q^{28} - 2782023 q^{29} - 10231020 q^{30} + 8407836 q^{31} + 6197838 q^{32} - 8252229 q^{33} - 49656453 q^{34} - 23563824 q^{35} + 151165428 q^{36} - 23634336 q^{37} - 12277422 q^{38} + 100476834 q^{39} + 165006327 q^{40} + 74094072 q^{41} - 3662109 q^{42} - 90803088 q^{43} - 350087604 q^{44} - 184820799 q^{45} - 114643110 q^{46} + 158694333 q^{47} + 359750805 q^{48} + 36118224 q^{49} - 259200273 q^{50} + 176035647 q^{51} - 203883429 q^{52} - 31488120 q^{53} - 109796865 q^{54} + 23137227 q^{55} + 37371291 q^{56} - 12449808 q^{57} - 840994983 q^{58} - 77893794 q^{59} + 244178580 q^{60} - 980597586 q^{61} - 586588080 q^{62} - 48634623 q^{63} - 917012376 q^{64} + 1432770144 q^{65} - 177475497 q^{66} - 302695398 q^{67} + 1615796082 q^{68} + 699674787 q^{69} + 2092804794 q^{70} - 774435768 q^{71} - 2899807611 q^{72} - 2505680652 q^{73} + 1161236205 q^{74} - 2302474524 q^{75} + 1445475621 q^{76} - 1374645213 q^{77} + 2942410749 q^{78} - 29533980 q^{79} + 9154934064 q^{80} - 2232253221 q^{81} + 707552205 q^{82} - 392438496 q^{83} - 1388366664 q^{84} - 556053567 q^{85} + 852383496 q^{86} - 6650019951 q^{87} + 3660093510 q^{88} + 100313124 q^{89} + 12897388398 q^{90} + 684844038 q^{91} + 621259308 q^{92} + 2212599060 q^{93} + 3136220628 q^{94} + 1257937926 q^{95} - 6811500039 q^{96} + 70258497 q^{97} - 8202052869 q^{98} - 2679000153 q^{99}+O(q^{100}) \) 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9 + 59997 * q^10 + 175689 * q^11 - 147411 * q^12 + 713586 * q^13 - 96867 * q^14 - 143316 * q^15 + 556665 * q^16 - 119334 * q^17 - 711948 * q^18 + 1752348 * q^19 + 4774248 * q^20 + 57972 * q^21 + 1413495 * q^22 - 5098719 * q^23 + 3891975 * q^24 + 10869768 * q^25 + 5518221 * q^26 + 13281609 * q^27 + 9017757 * q^28 - 2782023 * q^29 - 10231020 * q^30 + 8407836 * q^31 + 6197838 * q^32 - 8252229 * q^33 - 49656453 * q^34 - 23563824 * q^35 + 151165428 * q^36 - 23634336 * q^37 - 12277422 * q^38 + 100476834 * q^39 + 165006327 * q^40 + 74094072 * q^41 - 3662109 * q^42 - 90803088 * q^43 - 350087604 * q^44 - 184820799 * q^45 - 114643110 * q^46 + 158694333 * q^47 + 359750805 * q^48 + 36118224 * q^49 - 259200273 * q^50 + 176035647 * q^51 - 203883429 * q^52 - 31488120 * q^53 - 109796865 * q^54 + 23137227 * q^55 + 37371291 * q^56 - 12449808 * q^57 - 840994983 * q^58 - 77893794 * q^59 + 244178580 * q^60 - 980597586 * q^61 - 586588080 * q^62 - 48634623 * q^63 - 917012376 * q^64 + 1432770144 * q^65 - 177475497 * q^66 - 302695398 * q^67 + 1615796082 * q^68 + 699674787 * q^69 + 2092804794 * q^70 - 774435768 * q^71 - 2899807611 * q^72 - 2505680652 * q^73 + 1161236205 * q^74 - 2302474524 * q^75 + 1445475621 * q^76 - 1374645213 * q^77 + 2942410749 * q^78 - 29533980 * q^79 + 9154934064 * q^80 - 2232253221 * q^81 + 707552205 * q^82 - 392438496 * q^83 - 1388366664 * q^84 - 556053567 * q^85 + 852383496 * q^86 - 6650019951 * q^87 + 3660093510 * q^88 + 100313124 * q^89 + 12897388398 * q^90 + 684844038 * q^91 + 621259308 * q^92 + 2212599060 * q^93 + 3136220628 * q^94 + 1257937926 * q^95 - 6811500039 * q^96 + 70258497 * q^97 - 8202052869 * q^98 - 2679000153 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	5.13813	−	1.87013i	0.227075	−	0.0826487i	−0.225977	−	0.974133i	$-0.572557\pi$
$2$	5.13813	−	1.87013i	0.227075	−	0.0826487i	0.453052	+	0.891484i	$0.350335\pi$
$3$	−174.502	−	63.5134i	−1.24381	−	0.452710i	−0.365504	−	0.930810i	$-0.619103\pi$
$3$	−174.502	−	63.5134i	−1.24381	−	0.452710i	−0.878305	+	0.478100i	$0.841326\pi$
$4$	−369.312	+	309.889i	−0.721312	+	0.605253i
$5$	226.866	+	1286.62i	0.162332	+	0.920631i	0.951773	+	0.306804i	$0.0992597\pi$
$5$	226.866	+	1286.62i	0.162332	+	0.920631i	−0.789441	+	0.613827i	$0.789629\pi$
$6$	−1015.39			−0.319855
$7$	674.322	+	3824.27i	0.106152	+	0.602015i	0.990754	+	0.135670i	$0.0433186\pi$
$7$	674.322	+	3824.27i	0.106152	+	0.602015i	−0.884603	+	0.466346i	$0.845570\pi$
$8$	−2717.82	+	4707.40i	−0.234593	+	0.406327i
$9$	11338.8	+	9514.40i	0.576072	+	0.483382i
$10$	3571.81	+	6186.56i	0.112951	+	0.195636i
$11$	−4503.19	+	7799.76i	−0.0927371	+	0.160625i	−0.908662	−	0.417533i	$-0.862895\pi$
$11$	−4503.19	+	7799.76i	−0.0927371	+	0.160625i	0.815925	+	0.578158i	$0.196228\pi$
$12$	84127.6	−	30620.0i	1.17118	−	0.426274i
$13$	−46670.8	+	39161.5i	−0.453211	+	0.380289i	−0.840626	−	0.541616i	$-0.817813\pi$
$13$	−46670.8	+	39161.5i	−0.453211	+	0.380289i	0.387415	+	0.921905i	$0.373368\pi$
$14$	10616.6	+	18388.5i	0.0738602	+	0.127930i
$15$	42129.2	−	238927.i	0.214868	−	1.21858i
$16$	37701.6	−	213816.i	0.143820	−	0.815645i
$17$	−150019.	−	125881.i	−0.435638	−	0.365543i	0.398436	−	0.917196i	$-0.369553\pi$
$17$	−150019.	−	125881.i	−0.435638	−	0.365543i	−0.834074	+	0.551653i	$0.813997\pi$
$18$	76053.5	+	27681.2i	0.170763	+	0.0621525i
$19$	−609739.	−	221927.i	−1.07338	−	0.390678i	−0.255939	−	0.966693i	$-0.582385\pi$
$19$	−609739.	−	221927.i	−1.07338	−	0.390678i	−0.817439	+	0.576015i	$0.804607\pi$
$20$	−482495.	−	404861.i	−0.674307	−	0.565810i
$21$	125222.	−	710170.i	0.140506	−	0.796848i
$22$	−8551.46	+	48497.7i	−0.00778284	+	0.0441387i
$23$	60356.1	+	104540.i	0.0449724	+	0.0778945i	0.887635	−	0.460547i	$-0.152347\pi$
$23$	60356.1	+	104540.i	0.0449724	+	0.0778945i	−0.842663	+	0.538441i	$0.819013\pi$
$24$	773247.	−	648831.i	0.475738	−	0.399191i
$25$	231411.	−	84226.6i	0.118482	−	0.0431240i
$26$	−166564.	+	288497.i	−0.0714827	+	0.123812i
$27$	453223.	+	785005.i	0.164125	+	0.284273i
$28$	−1.43414e6	−	1.20338e6i	−0.440940	−	0.369992i
$29$	1.20095e6	−	2.08010e6i	0.315306	−	0.546126i	−0.664196	−	0.747558i	$-0.731226\pi$
$29$	1.20095e6	−	2.08010e6i	0.315306	−	0.546126i	0.979503	+	0.201432i	$0.0645595\pi$
$30$	−230358.	−	1.30642e6i	−0.0519227	−	0.294468i
$31$	3.26346e6			0.634674			0.317337	−	0.948313i	$-0.397211\pi$
$31$	3.26346e6			0.634674			0.317337	+	0.948313i	$0.397211\pi$
$32$	−689419.	−	3.90989e6i	−0.116227	−	0.659158i
$33$	1.28120e6	−	1.07506e6i	0.188064	−	0.157804i
$34$	−1.00623e6	−	366237.i	−0.129134	−	0.0470010i
$35$	−4.76741e6	+	1.73520e6i	−0.537002	+	0.195453i
$36$	−7.13597e6			−0.708096
$37$	−3.00122e6	−	1.09979e7i	−0.263263	−	0.964724i
$37$	−3.00122e6	−	1.09979e7i	−0.263263	−	0.964724i
$38$	−3.54795e6			−0.276027
$39$	1.06314e7	−	3.86952e6i	0.735869	−	0.267834i
$40$	−6.67322e6	−	2.42885e6i	−0.412160	−	0.150014i
$41$	1.15765e7	−	9.71380e6i	0.639806	−	0.536861i	−0.264153	−	0.964481i	$-0.585092\pi$
$41$	1.15765e7	−	9.71380e6i	0.639806	−	0.536861i	0.903959	+	0.427620i	$0.140648\pi$
$42$	−684701.	−	3.88313e6i	−0.0339531	−	0.192557i
$43$	1.72403e6			0.0769019			0.0384510	−	0.999260i	$-0.487758\pi$
$43$	1.72403e6			0.0769019			0.0384510	+	0.999260i	$0.487758\pi$
$44$	−753980.	−	4.27603e6i	−0.0303265	−	0.171990i
$45$	−9.66904e6	+	1.67473e7i	−0.351501	+	0.608818i
$46$	505621.	+	424266.i	0.0166500	+	0.0139710i
$47$	330134.	+	571810.i	0.00986849	+	0.0170927i	0.870917	−	0.491429i	$-0.163525\pi$
$47$	330134.	+	571810.i	0.00986849	+	0.0170927i	−0.861049	+	0.508522i	$0.830192\pi$
$48$	−2.01592e7	+	3.49168e7i	−0.548135	+	0.949398i
$49$	2.37496e7	−	8.64416e6i	0.588538	−	0.214210i
$50$	1.03150e6	−	865535.i	0.0233403	−	0.0195848i
$51$	1.81834e7	+	3.14946e7i	0.376365	+	0.651884i
$52$	5.10036e6	−	2.89256e7i	0.0967355	−	0.548614i
$53$	−6.90155e6	+	3.91406e7i	−0.120145	+	0.681375i	0.863929	+	0.503614i	$0.167997\pi$
$53$	−6.90155e6	+	3.91406e7i	−0.120145	+	0.681375i	−0.984074	+	0.177761i	$0.943115\pi$
$54$	3.79678e6	+	3.18587e6i	0.0607636	+	0.0509867i
$55$	−1.10570e7	−	4.02440e6i	−0.162931	−	0.0593020i
$56$	−1.98351e7	−	7.21937e6i	−0.269518	−	0.0980965i
$57$	9.23052e7	+	7.74532e7i	1.15821	+	0.971858i
$58$	2.28057e6	−	1.29337e7i	0.0264616	−	0.150071i
$59$	−2.42491e7	+	1.37524e8i	−0.260533	+	1.47755i	0.520929	+	0.853600i	$0.325586\pi$
$59$	−2.42491e7	+	1.37524e8i	−0.260533	+	1.47755i	−0.781461	+	0.623954i	$0.785525\pi$
$60$	5.84820e7	+	1.01294e8i	0.582561	+	1.00903i
$61$	−4.45382e7	+	3.73720e7i	−0.411859	+	0.345590i	−0.825056	−	0.565051i	$-0.808856\pi$
$61$	−4.45382e7	+	3.73720e7i	−0.411859	+	0.345590i	0.413197	+	0.910642i	$0.364412\pi$
$62$	1.67681e7	−	6.10309e6i	0.144119	−	0.0524550i
$63$	−2.87396e7	+	4.97785e7i	−0.229852	+	0.398116i
$64$	4.47271e7	+	7.74696e7i	0.333243	+	0.577194i
$65$	−6.09740e7	−	5.11633e7i	−0.423677	−	0.355507i
$66$	4.57250e6	−	7.91980e6i	0.0296624	−	0.0513767i
$67$	−4.75516e7	−	2.69678e8i	−0.288289	−	1.63497i	−0.693294	−	0.720655i	$-0.743841\pi$
$67$	−4.75516e7	−	2.69678e8i	−0.288289	−	1.63497i	0.405005	−	0.914315i	$-0.367270\pi$
$68$	9.44128e7			0.535477
$69$	−3.89256e6	−	2.20758e7i	−0.0206735	−	0.117245i
$70$	−2.12505e7	+	1.78313e7i	−0.105786	+	0.0887651i
$71$	−3.50421e8	−	1.27543e8i	−1.63654	−	0.595653i	−0.650114	−	0.759837i	$-0.725279\pi$
$71$	−3.50421e8	−	1.27543e8i	−1.63654	−	0.595653i	−0.986430	+	0.164184i	$0.947501\pi$
$72$	−7.56050e7	+	2.75180e7i	−0.331554	+	0.120676i
$73$	4.48383e7			0.184798			0.0923989	−	0.995722i	$-0.470547\pi$
$73$	4.48383e7			0.184798			0.0923989	+	0.995722i	$0.470547\pi$
$74$	−3.59882e7	−	5.08961e7i	−0.139514	−	0.197307i
$75$	−4.57311e7			−0.166892
$76$	2.93957e8	−	1.06991e8i	1.01070	−	0.367865i
$77$	−3.28650e7	−	1.19619e7i	−0.106543	−	0.0387785i
$78$	4.73891e7	−	3.97642e7i	0.144962	−	0.121637i
$79$	4.87563e6	+	2.76511e7i	0.0140834	+	0.0798712i	0.991039	−	0.133570i	$-0.0426440\pi$
$79$	4.87563e6	+	2.76511e7i	0.0140834	+	0.0798712i	−0.976956	+	0.213441i	$0.931533\pi$
$80$	2.83654e8			0.774255
$81$	−7.98211e7	−	4.52688e8i	−0.206032	−	1.16847i
$82$	4.13153e7	−	7.15602e7i	0.100913	−	0.174787i
$83$	1.98728e8	+	1.66752e8i	0.459629	+	0.385674i	0.842994	−	0.537922i	$-0.180791\pi$
$83$	1.98728e8	+	1.66752e8i	0.459629	+	0.385674i	−0.383366	+	0.923597i	$0.625235\pi$
$84$	1.73828e8	+	3.01079e8i	0.380946	+	0.659818i
$85$	1.27927e8	−	2.21575e8i	0.265813	−	0.460401i
$86$	8.85830e6	−	3.22416e6i	0.0174625	−	0.00635585i
$87$	−3.41681e8	+	2.86704e8i	−0.639417	+	0.536535i
$88$	−2.44777e7	−	4.23966e7i	−0.0435110	−	0.0753632i
$89$	5.14621e7	−	2.91856e8i	0.0869425	−	0.493076i	−0.909978	−	0.414657i	$-0.863902\pi$
$89$	5.14621e7	−	2.91856e8i	0.0869425	−	0.493076i	0.996920	−	0.0784190i	$-0.0249872\pi$
$90$	−1.83613e7	+	1.04132e8i	−0.0294993	+	0.167299i
$91$	−1.81235e8	−	1.52074e8i	−0.277049	−	0.232472i
$92$	−5.46860e7	−	1.99041e7i	−0.0795850	−	0.0289666i
$93$	−5.69479e8	−	2.07274e8i	−0.789414	−	0.287323i
$94$	2.76563e6	+	2.32064e6i	0.00365358	+	0.00306572i
$95$	1.47207e8	−	8.34851e8i	0.185426	−	1.05161i
$96$	−1.28026e8	+	7.26069e8i	−0.153843	+	0.872484i
$97$	−2.01930e8	−	3.49753e8i	−0.231594	−	0.401133i	0.726683	−	0.686973i	$-0.241061\pi$
$97$	−2.01930e8	−	3.49753e8i	−0.231594	−	0.401133i	−0.958277	+	0.285840i	$0.907727\pi$
$98$	1.05863e8	−	8.88297e7i	0.115938	−	0.0972838i
$99$	−1.25271e8	+	4.55949e7i	−0.131067	+	0.0477043i
$100$	−5.93618e7	+	1.02818e8i	−0.0593618	+	0.102818i
$101$	−8.03772e8	−	1.39217e9i	−0.768576	−	1.33121i	−0.938335	−	0.345726i	$-0.887633\pi$
$101$	−8.03772e8	−	1.39217e9i	−0.768576	−	1.33121i	0.169760	−	0.985485i	$-0.445701\pi$
$102$	1.52328e8	+	1.27818e8i	0.139341	+	0.116921i
$103$	1.56773e8	−	2.71538e8i	0.137247	−	0.237719i	−0.789207	−	0.614128i	$-0.789508\pi$
$103$	1.56773e8	−	2.71538e8i	0.137247	−	0.237719i	0.926454	+	0.376409i	$0.122841\pi$
$104$	−5.75059e7	−	3.26132e8i	−0.0482017	−	0.273365i
$105$	9.42129e8			0.756412
$106$	3.77369e7	+	2.14016e8i	0.0290328	+	0.164653i
$107$	−5.83087e8	+	4.89268e8i	−0.430037	+	0.360844i	−0.831966	−	0.554827i	$-0.812784\pi$
$107$	−5.83087e8	+	4.89268e8i	−0.430037	+	0.360844i	0.401929	+	0.915671i	$0.368340\pi$
$108$	−4.10645e8	−	1.49463e8i	−0.290442	−	0.105712i
$109$	9.35049e8	−	3.40330e8i	0.634476	−	0.230930i	−0.00470255	−	0.999989i	$-0.501497\pi$
$109$	9.35049e8	−	3.40330e8i	0.634476	−	0.230930i	0.639178	+	0.769059i	$0.279275\pi$
$110$	−6.43382e7			−0.0418988
$111$	−1.74797e8	+	2.10977e9i	−0.109290	+	1.31911i
$112$	8.43115e8			0.506298
$113$	4.01387e8	−	1.46093e8i	0.231585	−	0.0842901i	−0.223621	−	0.974676i	$-0.571788\pi$
$113$	4.01387e8	−	1.46093e8i	0.231585	−	0.0842901i	0.455206	+	0.890386i	$0.349566\pi$
$114$	6.19123e8	+	2.25342e8i	0.343325	+	0.124960i
$115$	−1.20810e8	+	1.01372e8i	−0.0644116	+	0.0540478i
$116$	2.01077e8	+	1.14036e9i	0.103110	+	0.584767i
$117$	−9.01790e8			−0.444907
$118$	1.32591e8	+	7.51964e8i	0.0629574	+	0.357049i
$119$	3.80241e8	−	6.58597e8i	0.173819	−	0.301064i
$120$	1.01022e9	+	8.47678e8i	0.444736	+	0.373177i
$121$	1.13842e9	+	1.97179e9i	0.482800	+	0.836234i
$122$	−1.58953e8	+	2.75314e8i	−0.0649604	+	0.112515i
$123$	−2.63707e9	+	9.59814e8i	−1.03884	+	0.378107i
$124$	−1.20523e9	+	1.01131e9i	−0.457798	+	0.384138i
$125$	1.43672e9	+	2.48847e9i	0.526352	+	0.911668i
$126$	−5.45759e7	+	3.09515e8i	−0.0192901	+	0.109399i
$127$	−4.28530e8	+	2.43031e9i	−0.146172	+	0.828983i	0.820247	+	0.572010i	$0.193836\pi$
$127$	−4.28530e8	+	2.43031e9i	−0.146172	+	0.828983i	−0.966419	+	0.256973i	$0.917275\pi$
$128$	1.93186e9	+	1.62103e9i	0.636109	+	0.533759i
$129$	−3.00846e8	−	1.09499e8i	−0.0956514	−	0.0348142i
$130$	−4.08974e8	−	1.48854e8i	−0.125589	−	0.0457106i
$131$	−1.10153e9	−	9.24298e8i	−0.326797	−	0.274215i	0.464597	−	0.885522i	$-0.346199\pi$
$131$	−1.10153e9	−	9.24298e8i	−0.326797	−	0.274215i	−0.791393	+	0.611308i	$0.790644\pi$
$132$	−1.40015e8	+	7.94063e8i	−0.0401413	+	0.227652i
$133$	4.37548e8	−	2.48146e9i	0.121253	−	0.687662i
$134$	−7.48659e8	−	1.29672e9i	−0.200592	−	0.347435i
$135$	−9.07183e8	+	7.61217e8i	−0.235068	+	0.197245i
$136$	1.00029e9	−	3.64077e8i	0.250728	−	0.0912575i
$137$	2.82002e9	−	4.88442e9i	0.683928	−	1.18460i	−0.289845	−	0.957074i	$-0.593604\pi$
$137$	2.82002e9	−	4.88442e9i	0.683928	−	1.18460i	0.973773	−	0.227524i	$-0.0730629\pi$
$138$	−6.12850e7	−	1.06149e8i	−0.0143846	−	0.0249149i
$139$	−3.33751e9	−	2.80050e9i	−0.758326	−	0.636311i	0.179364	−	0.983783i	$-0.442596\pi$
$139$	−3.33751e9	−	2.80050e9i	−0.758326	−	0.636311i	−0.937691	+	0.347472i	$0.887040\pi$
$140$	1.22294e9	−	2.11820e9i	0.269048	−	0.466005i
$141$	−2.12914e7	−	1.20750e8i	−0.00453648	−	0.0257276i
$142$	−2.03903e9			−0.420849
$143$	−9.52823e7	−	5.40373e8i	−0.0190546	−	0.108064i
$144$	2.46183e9	−	2.06572e9i	0.477119	−	0.400350i
$145$	2.94875e9	+	1.07326e9i	0.553965	+	0.201627i
$146$	2.30385e8	−	8.38534e7i	0.0419630	−	0.0152733i
$147$	−4.69337e9			−0.829005
$148$	4.51653e9	+	3.13162e9i	0.773797	+	0.536526i
$149$	3.10867e9			0.516698			0.258349	−	0.966052i	$-0.416822\pi$
$149$	3.10867e9			0.516698			0.258349	+	0.966052i	$0.416822\pi$
$150$	−2.34972e8	+	8.55229e7i	−0.0378971	+	0.0137934i
$151$	−9.42516e9	−	3.43048e9i	−1.47534	−	0.536980i	−0.525796	−	0.850611i	$-0.676232\pi$
$151$	−9.42516e9	−	3.43048e9i	−1.47534	−	0.536980i	−0.949545	+	0.313631i	$0.898455\pi$
$152$	2.70186e9	−	2.26713e9i	0.410550	−	0.344493i
$153$	−5.03357e8	−	2.85468e9i	−0.0742616	−	0.421158i
$154$	−1.91235e8			−0.0273983
$155$	7.40369e8	+	4.19884e9i	0.103028	+	0.584301i
$156$	−2.72718e9	+	4.72362e9i	−0.368684	+	0.638579i
$157$	−7.50856e9	−	6.30043e9i	−0.986298	−	0.827602i	−0.00127035	−	0.999999i	$-0.500404\pi$
$157$	−7.50856e9	−	6.30043e9i	−0.986298	−	0.827602i	−0.985028	+	0.172397i	$0.944849\pi$
$158$	7.67626e7	+	1.32957e8i	0.00979925	+	0.0169728i
$159$	3.69029e9	−	6.39176e9i	0.457903	−	0.793110i
$160$	4.87414e9	−	1.77404e9i	0.587974	−	0.214005i
$161$	−3.59090e8	+	3.01312e8i	−0.0421198	+	0.0353427i
$162$	−1.25671e9	−	2.17669e9i	−0.143357	−	0.248302i
$163$	−8.00898e8	+	4.54212e9i	−0.0888654	+	0.503981i	0.907590	+	0.419858i	$0.137920\pi$
$163$	−8.00898e8	+	4.54212e9i	−0.0888654	+	0.503981i	−0.996455	+	0.0841232i	$0.973191\pi$
$164$	−1.26512e9	+	7.17484e9i	−0.136563	+	0.774489i
$165$	1.67385e9	+	1.40453e9i	0.175808	+	0.147521i
$166$	1.33294e9	+	4.85149e8i	0.136246	+	0.0495894i
$167$	−1.97067e9	−	7.17264e8i	−0.196060	−	0.0713600i	0.242124	−	0.970245i	$-0.422156\pi$
$167$	−1.97067e9	−	7.17264e8i	−0.196060	−	0.0713600i	−0.438184	+	0.898885i	$0.644378\pi$
$168$	3.00272e9	+	2.51958e9i	0.290820	+	0.244027i
$169$	−1.19691e9	+	6.78800e9i	−0.112868	+	0.640105i
$170$	2.42930e8	−	1.37772e9i	0.0223080	−	0.126515i
$171$	−4.80222e9	−	8.31769e9i	−0.429497	−	0.743910i
$172$	−6.36705e8	+	5.34259e8i	−0.0554703	+	0.0465451i
$173$	3.43603e9	−	1.25061e9i	0.291641	−	0.106149i	−0.192056	−	0.981384i	$-0.561516\pi$
$173$	3.43603e9	−	1.25061e9i	0.291641	−	0.106149i	0.483698	+	0.875235i	$0.339293\pi$
$174$	−1.21943e9	+	2.11211e9i	−0.100852	+	0.174681i
$175$	4.78151e8	+	8.28182e8i	0.0385384	+	0.0667505i
$176$	1.49794e9	+	1.25692e9i	0.117676	+	0.0987417i
$177$	1.29661e10	−	2.24580e10i	0.992956	−	1.71985i
$178$	−2.81389e8	−	1.59584e9i	−0.0210095	−	0.119151i
$179$	−1.30635e10			−0.951085			−0.475543	−	0.879693i	$-0.657748\pi$
$179$	−1.30635e10			−0.951085			−0.475543	+	0.879693i	$0.657748\pi$
$180$	−1.61891e9	−	9.18129e9i	−0.114947	−	0.651895i
$181$	5.01599e9	−	4.20891e9i	0.347378	−	0.291485i	−0.452358	−	0.891836i	$-0.649417\pi$
$181$	5.01599e9	−	4.20891e9i	0.347378	−	0.291485i	0.799736	+	0.600351i	$0.204973\pi$
$182$	−1.21561e9	−	4.42446e8i	−0.0821245	−	0.0298909i
$183$	1.01456e10	−	3.69270e9i	0.668726	−	0.243396i
$184$	−6.56148e8			−0.0422009
$185$	1.34693e10	−	6.35649e9i	0.845419	−	0.398974i
$186$	−3.31369e9			−0.203003
$187$	1.65740e9	−	6.03245e8i	0.0991153	−	0.0360750i
$188$	−2.99120e8	−	1.08871e8i	−0.0174637	−	0.00635626i
$189$	−2.69646e9	+	2.26259e9i	−0.153715	+	0.128982i
$190$	−8.04910e8	−	4.56487e9i	−0.0448080	−	0.254119i
$191$	−1.05247e10			−0.572214			−0.286107	−	0.958198i	$-0.592361\pi$
$191$	−1.05247e10			−0.572214			−0.286107	+	0.958198i	$0.592361\pi$
$192$	−2.88459e9	−	1.63593e10i	−0.153190	−	0.868781i
$193$	−1.59578e10	+	2.76398e10i	−0.827877	+	1.43392i	0.0718240	+	0.997417i	$0.477118\pi$
$193$	−1.59578e10	+	2.76398e10i	−0.827877	+	1.43392i	−0.899701	+	0.436507i	$0.856215\pi$
$194$	−1.69162e9	−	1.41944e9i	−0.0857424	−	0.0719465i
$195$	7.39051e9	+	1.28007e10i	0.366032	+	0.633986i
$196$	−6.09229e9	+	1.05522e10i	−0.294868	+	0.510727i
$197$	−5.99215e9	+	2.18097e9i	−0.283455	+	0.103169i	−0.479835	−	0.877359i	$-0.659304\pi$
$197$	−5.99215e9	+	2.18097e9i	−0.283455	+	0.103169i	0.196380	+	0.980528i	$0.437081\pi$
$198$	−5.58390e8	+	4.68545e8i	−0.0258193	+	0.0216650i
$199$	5.95058e9	+	1.03067e10i	0.268980	+	0.465887i	0.968599	−	0.248629i	$-0.0799801\pi$
$199$	5.95058e9	+	1.03067e10i	0.268980	+	0.465887i	−0.699619	+	0.714517i	$0.746647\pi$
$200$	−2.32444e8	+	1.31826e9i	−0.0102727	+	0.0582592i
$201$	−8.83037e9	+	5.00795e10i	−0.381590	+	2.16410i
$202$	−6.73343e9	−	5.65001e9i	−0.284548	−	0.238764i
$203$	8.76469e9	+	3.19009e9i	0.362247	+	0.131847i
$204$	−1.64752e10	−	5.99648e9i	−0.666031	−	0.242415i
$205$	1.51243e10	+	1.26908e10i	0.598112	+	0.501876i
$206$	2.97707e8	−	1.68838e9i	0.0115183	−	0.0653233i
$207$	−3.10267e8	+	1.75961e9i	−0.0117454	+	0.0666117i
$208$	6.61380e9	+	1.14554e10i	0.245000	+	0.424353i
$209$	4.47675e9	−	3.75644e9i	0.162295	−	0.136181i
$210$	4.84078e9	−	1.76190e9i	0.171763	−	0.0625165i
$211$	−9.72178e9	+	1.68386e10i	−0.337656	+	0.584838i	−0.983991	−	0.178216i	$-0.942967\pi$
$211$	−9.72178e9	+	1.68386e10i	−0.337656	+	0.584838i	0.646335	+	0.763054i	$0.276301\pi$
$212$	−9.58044e9	−	1.65938e10i	−0.325742	−	0.564202i
$213$	5.30484e10	+	4.45129e10i	1.76589	+	1.48176i
$214$	−2.08098e9	+	3.60437e9i	−0.0678276	+	0.117481i
$215$	3.91124e8	+	2.21818e9i	0.0124837	+	0.0707983i
$216$	−4.92711e9			−0.154011
$217$	2.20063e9	+	1.24804e10i	0.0673717	+	0.382084i
$218$	4.16794e9	−	3.49732e9i	0.124988	−	0.104877i
$219$	−7.82437e9	−	2.84784e9i	−0.229853	−	0.0836597i
$220$	5.33058e9	−	1.94017e9i	0.153417	−	0.0558391i
$221$	1.19312e10			0.336448
$222$	3.04741e9	+	1.11672e10i	0.0842060	+	0.308571i
$223$	3.93102e10			1.06447			0.532235	−	0.846597i	$-0.321352\pi$
$223$	3.93102e10			1.06447			0.532235	+	0.846597i	$0.321352\pi$
$224$	1.44876e10	−	5.27305e9i	0.384486	−	0.139941i
$225$	3.42529e9	+	1.24670e9i	0.0890997	+	0.0324296i
$226$	1.78917e9	−	1.50129e9i	0.0456208	−	0.0382804i
$227$	−5.61170e9	−	3.18255e10i	−0.140274	−	0.795535i	−0.971041	−	0.238914i	$-0.923209\pi$
$227$	−5.61170e9	−	3.18255e10i	−0.140274	−	0.795535i	0.830767	−	0.556621i	$-0.187902\pi$
$228$	−5.80913e10			−1.42365
$229$	−6.10861e7	−	3.46436e8i	−0.00146785	−	0.00832461i	0.984065	−	0.177809i	$-0.0569009\pi$
$229$	−6.10861e7	−	3.46436e8i	−0.00146785	−	0.00832461i	−0.985533	+	0.169484i	$0.945790\pi$
$230$	−4.31162e8	+	7.46794e8i	−0.0101593	+	0.0175965i
$231$	4.97526e9	+	4.17474e9i	0.114964	+	0.0964662i
$232$	6.52790e9	+	1.13067e10i	0.147937	+	0.256235i
$233$	3.35775e10	−	5.81580e10i	0.746358	−	1.29273i	−0.203200	−	0.979137i	$-0.565134\pi$
$233$	3.35775e10	−	5.81580e10i	0.746358	−	1.29273i	0.949558	−	0.313592i	$-0.101532\pi$
$234$	−4.63352e9	+	1.68646e9i	−0.101027	+	0.0367710i
$235$	−6.60806e8	+	5.54482e8i	−0.0141341	+	0.0118599i
$236$	−3.36616e10	−	5.83037e10i	−0.706368	−	1.22347i
$237$	9.05408e8	−	5.13483e9i	0.0186413	−	0.105720i
$238$	7.22069e8	−	4.09505e9i	0.0145875	−	0.0827301i
$239$	−4.06195e10	−	3.40838e10i	−0.805274	−	0.675705i	0.144201	−	0.989548i	$-0.453939\pi$
$239$	−4.06195e10	−	3.40838e10i	−0.805274	−	0.675705i	−0.949475	+	0.313844i	$0.898383\pi$
$240$	−4.94981e10	−	1.80158e10i	−0.963026	−	0.350513i
$241$	−8.93027e10	−	3.25035e10i	−1.70525	−	0.620660i	−0.708843	−	0.705366i	$-0.750783\pi$
$241$	−8.93027e10	−	3.25035e10i	−1.70525	−	0.620660i	−0.996406	+	0.0847063i	$0.973005\pi$
$242$	9.53684e9	+	8.00236e9i	0.178746	+	0.149985i
$243$	−1.17247e10	+	6.64940e10i	−0.215711	+	1.22336i
$244$	4.86730e9	−	2.76038e10i	0.0879090	−	0.498557i
$245$	1.65097e10	+	2.85957e10i	0.292747	+	0.507053i
$246$	−1.17546e10	+	9.86330e9i	−0.204645	+	0.171717i
$247$	3.71480e10	−	1.35208e10i	0.635037	−	0.231135i
$248$	−8.86950e9	+	1.53624e10i	−0.148890	+	0.257886i
$249$	−2.40873e10	−	4.17204e10i	−0.397092	−	0.687784i
$250$	1.20358e10	+	1.00992e10i	0.194870	+	0.163515i
$251$	4.86400e10	−	8.42470e10i	0.773503	−	1.33975i	−0.162129	−	0.986770i	$-0.551836\pi$
$251$	4.86400e10	−	8.42470e10i	0.773503	−	1.33975i	0.935632	−	0.352977i	$-0.114831\pi$
$252$	−4.81195e9	−	2.72899e10i	−0.0751655	−	0.426285i
$253$	−1.08718e9			−0.0166824
$254$	2.34315e9	+	1.32887e10i	0.0353223	+	0.200323i
$255$	−3.63964e10	+	3.05402e10i	−0.539048	+	0.452315i
$256$	−3.00807e10	−	1.09485e10i	−0.437732	−	0.159322i
$257$	8.46531e10	−	3.08112e10i	1.21044	−	0.440565i	0.343585	−	0.939122i	$-0.388359\pi$
$257$	8.46531e10	−	3.08112e10i	1.21044	−	0.440565i	0.866857	+	0.498557i	$0.166136\pi$
$258$	−1.75057e9			−0.0245974
$259$	4.00353e10	−	1.88936e10i	0.552833	−	0.260896i
$260$	3.83734e10			0.520775
$261$	3.34082e10	−	1.21596e10i	0.445626	−	0.162195i
$262$	−7.38838e9	−	2.68915e9i	−0.0968710	−	0.0352582i
$263$	9.59684e10	−	8.05271e10i	1.23688	−	1.03787i	0.239118	−	0.970990i	$-0.423142\pi$
$263$	9.59684e10	−	8.05271e10i	1.23688	−	1.03787i	0.997761	−	0.0668748i	$-0.0213028\pi$
$264$	1.57865e9	+	8.95295e9i	0.0200017	+	0.113435i
$265$	−5.19249e10			−0.646799
$266$	−2.39246e9	−	1.35683e10i	−0.0293007	−	0.166172i
$267$	−2.75170e10	+	4.76608e10i	−0.331360	+	0.573933i
$268$	1.01132e11	+	8.48597e10i	1.19752	+	1.00484i
$269$	2.67437e9	+	4.63214e9i	0.0311413	+	0.0539382i	0.881176	−	0.472788i	$-0.156752\pi$
$269$	2.67437e9	+	4.63214e9i	0.0311413	+	0.0539382i	−0.850035	+	0.526727i	$0.823419\pi$
$270$	−3.23765e9	+	5.60778e9i	−0.0370761	+	0.0642176i
$271$	−1.42381e11	+	5.18224e10i	−1.60358	+	0.583654i	−0.980155	−	0.198232i	$-0.936480\pi$
$271$	−1.42381e11	+	5.18224e10i	−1.60358	+	0.583654i	−0.623421	+	0.781886i	$0.714258\pi$
$272$	−3.25713e10	+	2.73306e10i	−0.360807	+	0.302753i
$273$	2.19671e10	+	3.80481e10i	0.239354	+	0.414573i
$274$	5.35516e9	−	3.03706e10i	0.0573977	−	0.325519i
$275$	−3.85140e8	+	2.18424e9i	−0.00406089	+	0.0230305i
$276$	8.27863e9	+	6.94659e9i	0.0858751	+	0.0720578i
$277$	−8.79503e10	−	3.20113e10i	−0.897590	−	0.326696i	−0.148304	−	0.988942i	$-0.547381\pi$
$277$	−8.79503e10	−	3.20113e10i	−0.897590	−	0.326696i	−0.749287	+	0.662246i	$0.769603\pi$
$278$	−2.23859e10	−	8.14779e9i	−0.224788	−	0.0818160i
$279$	3.70038e10	+	3.10499e10i	0.365618	+	0.306790i
$280$	4.78870e9	−	2.71580e10i	0.0465593	−	0.264051i
$281$	2.53135e10	−	1.43560e11i	0.242199	−	1.37358i	−0.584708	−	0.811244i	$-0.698791\pi$
$281$	2.53135e10	−	1.43560e11i	0.242199	−	1.37358i	0.826908	−	0.562338i	$-0.190098\pi$
$282$	−3.35215e8	−	5.80610e8i	−0.00315648	−	0.00546718i
$283$	−1.35704e11	+	1.13870e11i	−1.25764	+	1.05528i	−0.261706	+	0.965148i	$0.584285\pi$
$283$	−1.35704e11	+	1.13870e11i	−1.25764	+	1.05528i	−0.995930	+	0.0901344i	$0.971270\pi$
$284$	1.68939e11	−	6.14887e10i	1.54098	−	0.560871i
$285$	−7.87121e10	+	1.36333e11i	−0.706707	+	1.22405i
$286$	−1.50014e9	−	2.59832e9i	−0.0132582	−	0.0229639i
$287$	4.49545e10	+	3.77213e10i	0.391115	+	0.328185i
$288$	2.93831e10	−	5.08929e10i	0.251670	−	0.435905i
$289$	−1.39329e10	−	7.90173e10i	−0.117490	−	0.666319i
$290$	1.71582e10			0.142456
$291$	1.30231e10	+	7.38577e10i	0.106462	+	0.603778i
$292$	−1.65593e10	+	1.38949e10i	−0.133297	+	0.111849i
$293$	8.49057e10	+	3.09031e10i	0.673027	+	0.244962i	0.655851	−	0.754891i	$-0.272310\pi$
$293$	8.49057e10	+	3.09031e10i	0.673027	+	0.244962i	0.0171763	+	0.999852i	$0.494532\pi$
$294$	−2.41152e10	+	8.77720e9i	−0.188247	+	0.0685162i
$295$	−1.82442e11			−1.40258
$296$	5.99284e10	+	1.57624e10i	0.453754	+	0.119347i
$297$	−8.16380e9			−0.0608819
$298$	1.59728e10	−	5.81361e9i	0.117329	−	0.0427044i
$299$	−6.91081e9	−	2.51533e9i	−0.0500044	−	0.0182001i
$300$	1.68890e10	−	1.41716e10i	0.120381	−	0.101012i
$301$	1.16255e9	+	6.59317e9i	0.00816326	+	0.0462962i
$302$	−5.48431e10			−0.379394
$303$	5.18378e10	+	2.93987e11i	0.353309	+	2.00372i
$304$	−7.04398e10	+	1.22005e11i	−0.473028	+	0.819308i
$305$	−5.81878e10	−	4.88253e10i	−0.385019	−	0.323069i
$306$	−7.92492e9	−	1.37264e10i	−0.0516712	−	0.0894971i
$307$	1.05921e11	−	1.83461e11i	0.680550	−	1.17875i	−0.294263	−	0.955725i	$-0.595074\pi$
$307$	1.05921e11	−	1.83461e11i	0.680550	−	1.17875i	0.974813	−	0.223023i	$-0.0715925\pi$
$308$	1.58443e10	−	5.76685e9i	0.100322	−	0.0365141i
$309$	−4.46034e10	+	3.74267e10i	−0.278326	+	0.233544i
$310$	1.16565e10	+	2.01896e10i	0.0716869	+	0.124165i
$311$	2.76421e10	−	1.56766e11i	0.167552	−	0.950234i	−0.778842	−	0.627220i	$-0.784193\pi$
$311$	2.76421e10	−	1.56766e11i	0.167552	−	0.950234i	0.946394	−	0.323014i	$-0.104696\pi$
$312$	−1.06789e10	+	6.05630e10i	−0.0638014	+	0.361836i
$313$	1.55718e11	+	1.30663e11i	0.917041	+	0.769489i	0.973445	−	0.228919i	$-0.0735192\pi$
$313$	1.55718e11	+	1.30663e11i	0.917041	+	0.769489i	−0.0564046	+	0.998408i	$0.517964\pi$
$314$	−5.03626e10	−	1.83305e10i	−0.292364	−	0.106412i
$315$	−7.05662e10	−	2.56840e10i	−0.403830	−	0.146982i
$316$	−1.03694e10	−	8.70096e9i	−0.0585008	−	0.0490880i
$317$	−4.70261e9	+	2.66698e10i	−0.0261560	+	0.148338i	−0.995089	−	0.0989859i	$-0.968440\pi$
$317$	−4.70261e9	+	2.66698e10i	−0.0261560	+	0.148338i	0.968933	+	0.247324i	$0.0795513\pi$
$318$	7.00777e9	−	3.97430e10i	0.0384289	−	0.217941i
$319$	1.08162e10	+	1.87342e10i	0.0584811	+	0.101292i
$320$	−8.95270e10	+	7.51221e10i	−0.477286	+	0.400491i
$321$	1.32825e11	−	4.83442e10i	0.698242	−	0.254139i
$322$	−1.28156e9	+	2.21972e9i	−0.00664334	+	0.0115066i
$323$	6.35360e10	+	1.10048e11i	0.324794	+	0.562560i
$324$	1.69762e11	+	1.42447e11i	0.855831	+	0.718127i
$325$	−7.50169e9	+	1.29933e10i	−0.0372979	+	0.0646018i
$326$	4.37922e9	+	2.48358e10i	0.0214742	+	0.121786i
$327$	−1.84783e11			−0.893711
$328$	1.42640e10	+	8.08954e10i	0.0680472	+	0.385915i
$329$	−1.96414e9	+	1.64811e9i	−0.00924253	+	0.00775540i
$330$	1.12271e10	+	4.08634e9i	0.0521142	+	0.0189680i
$331$	1.97689e11	−	7.19530e10i	0.905226	−	0.329475i	0.152881	−	0.988245i	$-0.451145\pi$
$331$	1.97689e11	−	7.19530e10i	0.905226	−	0.329475i	0.752345	+	0.658769i	$0.228923\pi$
$332$	−1.25067e11			−0.564966
$333$	7.06084e10	−	1.53258e11i	0.314671	−	0.683007i
$334$	−1.14669e10			−0.0504182
$335$	3.36186e11	−	1.22362e11i	1.45841	−	0.530816i
$336$	−1.47125e11	−	5.35491e10i	−0.629738	−	0.229206i
$337$	−9.82795e10	+	8.24663e10i	−0.415077	+	0.348291i	−0.826286	−	0.563250i	$-0.809551\pi$
$337$	−9.82795e10	+	8.24663e10i	−0.415077	+	0.348291i	0.411210	+	0.911541i	$0.365106\pi$
$338$	6.54455e9	+	3.71160e10i	0.0272744	+	0.154681i
$339$	−7.93216e10			−0.326207
$340$	2.14190e10	+	1.21473e11i	0.0869251	+	0.492977i
$341$	−1.46960e10	+	2.54542e10i	−0.0588578	+	0.101945i
$342$	−4.02296e10	−	3.37566e10i	−0.159011	−	0.133426i
$343$	1.27424e11	+	2.20706e11i	0.497083	+	0.860974i
$344$	−4.68561e9	+	8.11571e9i	−0.0180407	+	0.0312474i
$345$	2.75201e10	−	1.00165e10i	0.104584	−	0.0380654i
$346$	1.53160e10	−	1.28516e10i	0.0574515	−	0.0482076i
$347$	−2.54874e11	−	4.41454e11i	−0.943718	−	1.63457i	−0.758298	−	0.651908i	$-0.773969\pi$
$347$	−2.54874e11	−	4.41454e11i	−0.943718	−	1.63457i	−0.185419	−	0.982659i	$-0.559364\pi$
$348$	3.73402e10	−	2.11767e11i	0.136480	−	0.774018i
$349$	−6.57010e10	+	3.72609e11i	−0.237059	+	1.34443i	0.601173	+	0.799119i	$0.294700\pi$
$349$	−6.57010e10	+	3.72609e11i	−0.237059	+	1.34443i	−0.838233	+	0.545312i	$0.816411\pi$
$350$	4.00561e9	+	3.36110e9i	0.0142680	+	0.0119723i
$351$	−5.18942e10	−	1.88880e10i	−0.182489	−	0.0664206i
$352$	3.36008e10	+	1.22297e10i	0.116656	+	0.0424593i
$353$	−4.05104e11	−	3.39922e11i	−1.38861	−	1.16518i	−0.965900	−	0.258917i	$-0.916635\pi$
$353$	−4.05104e11	−	3.39922e11i	−1.38861	−	1.16518i	−0.422710	−	0.906265i	$-0.638921\pi$
$354$	2.46223e10	−	1.39640e11i	0.0833325	−	0.472602i
$355$	8.46007e10	−	4.79794e11i	0.282713	−	1.60335i
$356$	7.14375e10	+	1.23733e11i	0.235723	+	0.408284i
$357$	−1.08182e11	+	9.07758e10i	−0.352492	+	0.295776i
$358$	−6.71218e10	+	2.44303e10i	−0.215968	+	0.0786060i
$359$	−1.54731e11	+	2.68002e11i	−0.491645	+	0.851555i	−0.999954	−	0.00962033i	$-0.996938\pi$
$359$	−1.54731e11	+	2.68002e11i	−0.491645	+	0.851555i	0.508308	+	0.861175i	$0.330271\pi$
$360$	−5.25574e10	−	9.10321e10i	−0.164920	−	0.285649i
$361$	7.53372e10	+	6.32154e10i	0.233468	+	0.195903i
$362$	1.79016e10	−	3.10065e10i	0.0547903	−	0.0948995i
$363$	−7.34201e10	−	4.16386e11i	−0.221940	−	1.25868i
$364$	1.14059e11			0.340543
$365$	1.01723e10	+	5.76900e10i	0.0299986	+	0.170131i
$366$	4.52236e10	−	3.79471e10i	0.131735	−	0.110539i
$367$	4.28761e10	+	1.56056e10i	0.123372	+	0.0449039i	0.402969	−	0.915214i	$-0.367978\pi$
$367$	4.28761e10	+	1.56056e10i	0.123372	+	0.0449039i	−0.279596	+	0.960118i	$0.590201\pi$
$368$	2.46279e10	−	8.96381e9i	0.0700022	−	0.0254787i
$369$	2.23684e11			0.628083
$370$	5.73195e10	−	5.78498e10i	0.158999	−	0.160470i
$371$	−1.54338e11			−0.422952
$372$	2.74547e11	−	9.99270e10i	0.743317	−	0.270545i
$373$	4.80672e10	+	1.74950e10i	0.128576	+	0.0467977i	0.405507	−	0.914092i	$-0.367095\pi$
$373$	4.80672e10	+	1.74950e10i	0.128576	+	0.0467977i	−0.276931	+	0.960890i	$0.589317\pi$
$374$	7.38780e9	−	6.19910e9i	0.0195251	−	0.0163835i
$375$	−9.26584e10	−	5.25492e11i	−0.241960	−	1.37223i
$376$	−3.58898e9			−0.00926032
$377$	2.54106e10	+	1.44111e11i	0.0647857	+	0.367418i
$378$	−9.62340e9	+	1.66682e10i	−0.0242446	+	0.0419929i
$379$	−4.92415e11	−	4.13185e11i	−1.22590	−	1.02865i	−0.998495	−	0.0548504i	$-0.982532\pi$
$379$	−4.92415e11	−	4.13185e11i	−1.22590	−	1.02865i	−0.227404	−	0.973801i	$-0.573024\pi$
$380$	2.04346e11	+	3.53938e11i	0.502737	+	0.870765i
$381$	2.29137e11	−	3.96876e11i	0.557099	−	0.964924i
$382$	−5.40772e10	+	1.96825e10i	−0.129936	+	0.0472927i
$383$	−1.33938e11	+	1.12388e11i	−0.318061	+	0.266885i	−0.787814	−	0.615913i	$-0.788787\pi$
$383$	−1.33938e11	+	1.12388e11i	−0.318061	+	0.266885i	0.469753	+	0.882798i	$0.344343\pi$
$384$	−2.34157e11	−	4.05571e11i	−0.549561	−	0.951868i
$385$	7.93446e9	−	4.49986e10i	0.0184054	−	0.104382i
$386$	−3.03035e10	+	1.71860e11i	−0.0694785	+	0.394032i
$387$	1.95485e10	+	1.64031e10i	0.0443010	+	0.0371730i
$388$	1.82960e11	+	6.65919e10i	0.409838	+	0.149169i
$389$	−5.43715e11	−	1.97896e11i	−1.20392	−	0.438192i	−0.339331	−	0.940667i	$-0.610201\pi$
$389$	−5.43715e11	−	1.97896e11i	−1.20392	−	0.438192i	−0.864592	+	0.502475i	$0.832423\pi$
$390$	6.19124e10	+	5.19507e10i	0.135515	+	0.113711i
$391$	4.10500e9	−	2.32806e10i	0.00888214	−	0.0503731i
$392$	−2.38557e10	+	1.35292e11i	−0.0510275	+	0.289391i
$393$	1.33514e11	+	2.31254e11i	0.282333	+	0.489015i
$394$	−2.67098e10	+	2.24122e10i	−0.0558390	+	0.0468545i
$395$	−3.44703e10	+	1.25462e10i	−0.0712457	+	0.0259313i
$396$	3.21347e10	−	5.56589e10i	0.0656667	−	0.113738i
$397$	3.40176e11	+	5.89202e11i	0.687300	+	1.19044i	0.972708	+	0.232032i	$0.0745374\pi$
$397$	3.40176e11	+	5.89202e11i	0.687300	+	1.19044i	−0.285408	+	0.958406i	$0.592129\pi$
$398$	4.98497e10	+	4.18289e10i	0.0995838	+	0.0835607i
$399$	−2.33959e11	+	4.05229e11i	−0.462127	+	0.800427i
$400$	−9.28448e9	−	5.26549e10i	−0.0181338	−	0.102842i
$401$	3.09750e11			0.598220			0.299110	−	0.954219i	$-0.403310\pi$
$401$	3.09750e11			0.598220			0.299110	+	0.954219i	$0.403310\pi$
$402$	4.82834e10	+	2.73829e11i	0.0922106	+	0.522952i
$403$	−1.52308e11	+	1.27802e11i	−0.287641	+	0.241360i
$404$	7.28262e11	+	2.65066e11i	1.36010	+	0.495037i
$405$	5.64329e11	−	2.05399e11i	1.04228	−	0.379359i
$406$	5.10000e10			0.0931543
$407$	9.92963e10	+	2.61170e10i	0.179373	+	0.0471789i
$408$	−1.97677e11			−0.353171
$409$	5.73475e11	−	2.08728e11i	1.01335	−	0.368829i	0.218631	−	0.975808i	$-0.429841\pi$
$409$	5.73475e11	−	2.08728e11i	1.01335	−	0.368829i	0.794718	+	0.606978i	$0.207619\pi$
$410$	1.01444e11	+	3.69226e10i	0.177296	+	0.0645305i
$411$	−8.02325e11	+	6.73231e11i	−1.38695	+	1.16379i
$412$	2.62488e10	+	1.48864e11i	0.0448820	+	0.254538i
$413$	−5.42280e11			−0.917166
$414$	1.69650e9	+	9.62136e9i	0.00283827	+	0.0160966i
$415$	−1.69463e11	+	2.93518e11i	−0.280451	+	0.485756i
$416$	1.85293e11	+	1.55479e11i	0.303346	+	0.254538i
$417$	4.04532e11	+	7.00669e11i	0.655149	+	1.13475i
$418$	1.59771e10	−	2.76732e10i	0.0255979	−	0.0443369i
$419$	1.22633e11	−	4.46348e10i	0.194377	−	0.0707475i	−0.242997	−	0.970027i	$-0.578131\pi$
$419$	1.22633e11	−	4.46348e10i	0.194377	−	0.0707475i	0.437374	+	0.899279i	$0.355908\pi$
$420$	−3.47939e11	+	2.91956e11i	−0.545609	+	0.457821i
$421$	−4.73673e11	−	8.20426e11i	−0.734868	−	1.27283i	−0.954781	−	0.297309i	$-0.903911\pi$
$421$	−4.73673e11	−	8.20426e11i	−0.734868	−	1.27283i	0.219913	−	0.975519i	$-0.429423\pi$
$422$	−1.84614e10	+	1.04700e11i	−0.0283374	+	0.160709i
$423$	−1.69709e9	+	9.62468e9i	−0.00257735	+	0.0146169i
$424$	−1.65493e11	−	1.38865e11i	−0.248676	−	0.208664i
$425$	−4.53185e10	−	1.64946e10i	−0.0673791	−	0.0245240i
$426$	3.55814e11	+	1.29506e11i	0.523456	+	0.190522i
$427$	−1.72954e11	−	1.45125e11i	−0.251770	−	0.211260i
$428$	6.37219e10	−	3.61385e11i	0.0917892	−	0.520562i
$429$	−1.76940e10	+	1.00348e11i	−0.0252213	+	0.143037i
$430$	6.15792e9	+	1.06658e10i	0.00868612	+	0.0150448i
$431$	−1.05682e11	+	8.86778e10i	−0.147521	+	0.123785i	−0.713561	−	0.700593i	$-0.752919\pi$
$431$	−1.05682e11	+	8.86778e10i	−0.147521	+	0.123785i	0.566040	+	0.824377i	$0.308475\pi$
$432$	1.84934e11	−	6.73106e10i	0.255470	−	0.0929836i
$433$	1.65513e11	−	2.86677e11i	0.226275	−	0.391920i	−0.730426	−	0.682992i	$-0.760679\pi$
$433$	1.65513e11	−	2.86677e11i	0.226275	−	0.391920i	0.956701	+	0.291072i	$0.0940119\pi$
$434$	3.46470e10	+	6.00103e10i	0.0468772	+	0.0811936i
$435$	−4.46396e11	−	3.74571e11i	−0.597749	−	0.501571i
$436$	−2.39860e11	+	4.15449e11i	−0.317884	+	0.550591i
$437$	−1.36013e10	−	7.71367e10i	−0.0178408	−	0.101180i
$438$	−4.55284e10			−0.0591084
$439$	8.64547e10	+	4.90309e11i	0.111096	+	0.630057i	0.988609	+	0.150504i	$0.0480898\pi$
$439$	8.64547e10	+	4.90309e11i	0.111096	+	0.630057i	−0.877513	+	0.479552i	$0.840799\pi$
$440$	4.89953e10	−	4.11119e10i	0.0623185	−	0.0522914i
$441$	3.51537e11	+	1.27949e11i	0.442586	+	0.161088i
$442$	6.13039e10	−	2.23128e10i	0.0763991	−	0.0278070i
$443$	−9.81038e11			−1.21023			−0.605116	−	0.796137i	$-0.706873\pi$
$443$	−9.81038e11			−1.21023			−0.605116	+	0.796137i	$0.706873\pi$
$444$	−5.89242e11	−	8.33332e11i	−0.719565	−	1.01764i
$445$	3.87183e11			0.468055
$446$	2.01981e11	−	7.35151e10i	0.241715	−	0.0879771i
$447$	−5.42469e11	−	1.97442e11i	−0.642674	−	0.233914i
$448$	−2.66104e11	+	2.23288e11i	−0.312105	+	0.261887i
$449$	7.03967e10	+	3.99239e11i	0.0817417	+	0.463580i	0.998012	+	0.0630202i	$0.0200732\pi$
$449$	7.03967e10	+	3.99239e11i	0.0817417	+	0.463580i	−0.916271	+	0.400560i	$0.868816\pi$
$450$	1.99311e10			0.0229126
$451$	2.36343e10	+	1.34037e11i	0.0268997	+	0.152556i
$452$	−1.02964e11	+	1.78339e11i	−0.116028	+	0.200967i
$453$	1.42682e12	+	1.19725e12i	1.59195	+	1.33580i
$454$	−8.83514e10	−	1.53029e11i	−0.0976028	−	0.169053i
$455$	1.54546e11	−	2.67682e11i	0.169047	−	0.292798i
$456$	−6.15472e11	+	2.24013e11i	−0.666602	+	0.242623i
$457$	1.06602e12	−	8.94497e11i	1.14325	−	0.959303i	0.143712	−	0.989619i	$-0.454096\pi$
$457$	1.06602e12	−	8.94497e11i	1.14325	−	0.959303i	0.999540	+	0.0303165i	$0.00965153\pi$
$458$	−9.61748e8	−	1.66580e9i	−0.00102133	−	0.00176900i
$459$	3.08250e10	−	1.74817e11i	0.0324150	−	0.183835i
$460$	1.32026e10	−	7.48758e10i	0.0137483	−	0.0779706i
$461$	1.00910e12	+	8.46739e11i	1.04060	+	0.873163i	0.992074	−	0.125659i	$-0.0401045\pi$
$461$	1.00910e12	+	8.46739e11i	1.04060	+	0.873163i	0.0485219	+	0.998822i	$0.484549\pi$
$462$	3.33708e10	+	1.21460e10i	0.0340783	+	0.0124035i
$463$	−1.17979e12	−	4.29410e11i	−1.19314	−	0.434268i	−0.332315	−	0.943168i	$-0.607830\pi$
$463$	−1.17979e12	−	4.29410e11i	−1.19314	−	0.434268i	−0.860825	+	0.508901i	$0.830052\pi$
$464$	−3.99482e11	−	3.35205e11i	−0.400098	−	0.335722i
$465$	1.37487e11	−	7.79728e11i	0.136371	−	0.773401i
$466$	6.37629e10	−	3.61618e11i	0.0626371	−	0.355233i
$467$	7.62762e11	+	1.32114e12i	0.742101	+	1.28536i	0.951537	+	0.307535i	$0.0995041\pi$
$467$	7.62762e11	+	1.32114e12i	0.742101	+	1.28536i	−0.209435	+	0.977823i	$0.567163\pi$
$468$	3.33042e11	−	2.79455e11i	0.320917	−	0.269281i
$469$	9.99259e11	−	3.63700e11i	0.953675	−	0.347109i
$470$	−2.35836e9	+	4.08479e9i	−0.00222930	+	0.00386127i
$471$	9.10094e11	+	1.57633e12i	0.852103	+	1.47589i
$472$	−5.81474e11	−	4.87915e11i	−0.539252	−	0.452486i
$473$	−7.76365e9	+	1.34470e10i	−0.00713166	+	0.0123524i
$474$	−4.95067e9	−	2.80766e10i	−0.00450465	−	0.0255472i
$475$	−1.59792e11			−0.144024
$476$	6.36646e10	+	3.61060e11i	0.0568417	+	0.322365i
$477$	−4.50655e11	+	3.78145e11i	−0.398576	+	0.334445i
$478$	−2.72449e11	−	9.91633e10i	−0.238704	−	0.0868812i
$479$	−1.01829e12	+	3.70628e11i	−0.883817	+	0.321683i	−0.743749	−	0.668459i	$-0.766954\pi$
$479$	−1.01829e12	+	3.70628e11i	−0.883817	+	0.321683i	−0.140068	+	0.990142i	$0.544732\pi$
$480$	−9.63221e11			−0.828210
$481$	5.70765e11	+	3.95750e11i	0.486188	+	0.337107i
$482$	−5.19635e11			−0.438517
$483$	8.17991e10	−	2.97724e10i	0.0683890	−	0.0248916i
$484$	−1.03147e12	−	3.75424e11i	−0.854382	−	0.310970i
$485$	4.04188e11	−	3.39154e11i	0.331700	−	0.278330i
$486$	6.41092e10	+	3.63581e11i	0.0521263	+	0.295623i
$487$	7.97907e11			0.642794			0.321397	−	0.946945i	$-0.395848\pi$
$487$	7.97907e11			0.642794			0.321397	+	0.946945i	$0.395848\pi$
$488$	−5.48781e10	−	3.11229e11i	−0.0438036	−	0.248423i
$489$	4.28243e11	−	7.41739e11i	0.338689	−	0.586626i
$490$	1.38307e11	+	1.16053e11i	0.108383	+	0.0909442i
$491$	−5.43854e11	−	9.41983e11i	−0.422295	−	0.731436i	0.573869	−	0.818947i	$-0.305442\pi$
$491$	−5.43854e11	−	9.41983e11i	−0.422295	−	0.731436i	−0.996164	+	0.0875115i	$0.972109\pi$
$492$	6.76464e11	−	1.17167e12i	0.520477	−	0.901493i
$493$	−4.42008e11	+	1.60878e11i	−0.336992	+	0.122655i
$494$	1.65586e11	−	1.38943e11i	0.125098	−	0.104970i
$495$	−8.70831e10	−	1.50832e11i	−0.0651944	−	0.112920i
$496$	1.23038e11	−	6.97782e11i	0.0912790	−	0.517669i
$497$	2.51462e11	−	1.42611e12i	0.184871	−	1.04845i
$498$	−2.01786e11	−	1.69319e11i	−0.147014	−	0.123360i
$499$	−1.88132e12	−	6.84746e11i	−1.35835	−	0.494399i	−0.442805	−	0.896618i	$-0.646017\pi$
$499$	−1.88132e12	−	6.84746e11i	−1.35835	−	0.494399i	−0.915543	+	0.402219i	$0.868239\pi$
$500$	−1.30175e12	−	4.73796e11i	−0.931453	−	0.339021i
$501$	2.98329e11	+	2.50327e11i	0.211556	+	0.177516i
$502$	9.23662e10	−	5.23835e11i	0.0649152	−	0.368153i
$503$	−1.29468e11	+	7.34250e11i	−0.0901793	+	0.511432i	0.905939	+	0.423408i	$0.139166\pi$
$503$	−1.29468e11	+	7.34250e11i	−0.0901793	+	0.511432i	−0.996118	+	0.0880242i	$0.971945\pi$
$504$	−1.56218e11	−	2.70578e11i	−0.107844	−	0.186791i
$505$	1.60885e12	−	1.34999e12i	1.10079	−	0.923673i
$506$	−5.58608e9	+	2.03317e9i	−0.00378817	+	0.00137878i
$507$	6.39991e11	−	1.10850e12i	0.430168	−	0.745073i
$508$	−5.94867e11	−	1.03034e12i	−0.396308	−	0.686426i
$509$	−3.55099e11	−	2.97963e11i	−0.234487	−	0.196758i	0.517971	−	0.855398i	$-0.326688\pi$
$509$	−3.55099e11	−	2.97963e11i	−0.234487	−	0.196758i	−0.752458	+	0.658640i	$0.771132\pi$
$510$	−1.29895e11	+	2.24986e11i	−0.0850214	+	0.147261i
$511$	3.02355e10	+	1.71474e11i	0.0196166	+	0.111251i
$512$	−1.46623e12			−0.942948
$513$	−1.02134e11	−	5.79231e11i	−0.0651092	−	0.369253i
$514$	3.77338e11	−	3.16624e11i	0.238450	−	0.200083i
$515$	3.84933e11	+	1.40104e11i	0.241131	+	0.0877644i
$516$	1.45039e11	−	5.27898e10i	0.0900659	−	0.0327813i
$517$	−5.94664e9			−0.00366070
$518$	1.70373e11	−	1.71949e11i	0.103972	−	0.104934i
$519$	−6.79023e11			−0.410801
$520$	4.06562e11	−	1.47977e11i	0.243844	−	0.0887519i
$521$	1.10318e12	+	4.01525e11i	0.655960	+	0.238750i	0.648491	−	0.761222i	$-0.275400\pi$
$521$	1.10318e12	+	4.01525e11i	0.655960	+	0.238750i	0.00746895	+	0.999972i	$0.497623\pi$
$522$	1.48916e11	−	1.24955e11i	0.0877856	−	0.0736609i
$523$	4.34379e11	+	2.46349e12i	0.253870	+	1.43977i	0.798956	+	0.601389i	$0.205386\pi$
$523$	4.34379e11	+	2.46349e12i	0.253870	+	1.43977i	−0.545086	+	0.838380i	$0.683503\pi$
$524$	6.93240e11			0.401692
$525$	−3.08375e10	−	1.74888e11i	−0.0177159	−	0.100472i
$526$	3.42502e11	−	5.93232e11i	0.195087	−	0.337900i
$527$	−4.89580e11	−	4.10807e11i	−0.276488	−	0.232001i
$528$	−1.81562e11	−	3.14474e11i	−0.101665	−	0.176089i
$529$	8.93291e11	−	1.54722e12i	0.495955	−	0.859019i
$530$	−2.66797e11	+	9.71061e10i	−0.146872	+	0.0534571i
$531$	−1.58341e12	+	1.32864e12i	−0.864308	+	0.725241i
$532$	6.07386e11	+	1.05202e12i	0.328747	+	0.569407i
$533$	−1.59876e11	+	9.06702e11i	−0.0858047	+	0.486623i
$534$	−5.22541e10	+	2.96348e11i	−0.0278090	+	0.157712i
$535$	−7.61785e11	−	6.39213e11i	−0.402013	−	0.337329i
$536$	1.39872e12	+	5.09093e11i	0.731964	+	0.266413i
$537$	2.27960e12	+	8.29705e11i	1.18297	+	0.430566i
$538$	2.24040e10	+	1.87991e10i	0.0115293	+	0.00967426i
$539$	−3.95268e10	+	2.24168e11i	−0.0201717	+	0.114399i
$540$	9.91404e10	−	5.62253e11i	0.0501740	−	0.284551i
$541$	1.52223e12	+	2.63658e12i	0.763999	+	1.32328i	0.940774	+	0.339033i	$0.110100\pi$
$541$	1.52223e12	+	2.63658e12i	0.763999	+	1.32328i	−0.176776	+	0.984251i	$0.556567\pi$
$542$	−6.34657e11	+	5.32540e11i	−0.315895	+	0.265067i
$543$	−1.14262e12	+	4.15880e11i	−0.564031	+	0.205290i
$544$	−3.88754e11	+	6.73341e11i	−0.190318	+	0.329640i
$545$	6.50006e11	+	1.12584e12i	0.315597	+	0.546631i
$546$	1.84025e11	+	1.54415e11i	0.0886154	+	0.0743571i
$547$	−5.86276e11	+	1.01546e12i	−0.280001	+	0.484976i	−0.971385	−	0.237512i	$-0.923668\pi$
$547$	−5.86276e11	+	1.01546e12i	−0.280001	+	0.484976i	0.691384	+	0.722488i	$0.257001\pi$
$548$	4.72163e11	+	2.67777e12i	0.223655	+	1.26841i
$549$	−8.60582e11			−0.404312
$550$	2.10590e9	+	1.19432e10i	0.000981309	+	0.00556528i
$551$	−1.19389e12	+	1.00180e12i	−0.551802	+	0.463017i
$552$	1.14499e11	+	4.16742e10i	0.0524899	+	0.0191048i
$553$	−1.02457e11	+	3.72915e10i	−0.0465887	+	0.0169569i
$554$	−5.11765e11			−0.230822
$555$	−2.75414e12	+	2.53738e11i	−1.23216	+	0.113519i
$556$	2.10043e12			0.932119
$557$	−2.11668e12	+	7.70407e11i	−0.931764	+	0.339134i	−0.762908	−	0.646506i	$-0.776229\pi$
$557$	−2.11668e12	+	7.70407e11i	−0.931764	+	0.339134i	−0.168855	+	0.985641i	$0.554007\pi$
$558$	2.48198e11	+	9.03366e10i	0.108379	+	0.0394466i
$559$	−8.04620e10	+	6.75156e10i	−0.0348528	+	0.0292450i
$560$	1.91274e11	+	1.08477e12i	0.0821884	+	0.466113i
$561$	−3.27534e11			−0.139612
$562$	−1.38411e11	−	7.84968e11i	−0.0585272	−	0.331924i
$563$	−3.66997e11	+	6.35658e11i	−0.153948	+	0.266646i	−0.932676	−	0.360716i	$-0.882532\pi$
$563$	−3.66997e11	+	6.35658e11i	−0.153948	+	0.266646i	0.778727	+	0.627363i	$0.215866\pi$
$564$	4.52822e10	+	3.79963e10i	0.0188439	+	0.0158119i
$565$	2.79027e11	+	4.83290e11i	0.115194	+	0.199521i
$566$	−4.84317e11	+	8.38861e11i	−0.198361	+	0.343571i
$567$	1.67738e12	−	6.10515e11i	0.681564	−	0.248069i
$568$	1.55278e12	−	1.30293e12i	0.625952	−	0.525236i
$569$	1.89174e10	+	3.27659e10i	0.00756582	+	0.0131044i	0.869784	−	0.493433i	$-0.164258\pi$
$569$	1.89174e10	+	3.27659e10i	0.00756582	+	0.0131044i	−0.862218	+	0.506538i	$0.830925\pi$
$570$	−1.49472e11	+	8.47700e11i	−0.0593095	+	0.336361i
$571$	−2.04021e11	+	1.15706e12i	−0.0803178	+	0.455505i	0.917951	+	0.396693i	$0.129842\pi$
$571$	−2.04021e11	+	1.15706e12i	−0.0803178	+	0.455505i	−0.998269	+	0.0588118i	$0.981269\pi$
$572$	2.02645e11	+	1.70039e11i	0.0791504	+	0.0664151i
$573$	1.83657e12	+	6.68458e11i	0.711725	+	0.259047i
$574$	3.01526e11	+	1.09746e11i	0.115937	+	0.0421975i
$575$	2.27721e10	+	1.91081e10i	0.00868756	+	0.00728973i
$576$	−2.29924e11	+	1.30397e12i	−0.0870330	+	0.493589i
$577$	2.33630e11	−	1.32498e12i	0.0877480	−	0.497643i	−0.908982	−	0.416836i	$-0.863139\pi$
$577$	2.33630e11	−	1.32498e12i	0.0877480	−	0.497643i	0.996730	−	0.0808075i	$-0.0257499\pi$
$578$	−2.19361e11	−	3.79945e11i	−0.0817495	−	0.141594i
$579$	4.54016e12	−	3.80965e12i	1.67887	−	1.40874i
$580$	−1.42160e12	+	5.17420e11i	−0.521617	+	0.189853i
$581$	−5.03700e11	+	8.72434e11i	−0.183392	+	0.317643i
$582$	2.05038e11	+	3.55135e11i	0.0740764	+	0.128304i
$583$	−2.74208e11	−	2.30088e11i	−0.0983042	−	0.0824871i
$584$	−1.21862e11	+	2.11072e11i	−0.0433523	+	0.0750884i
$585$	−2.04586e11	−	1.16026e12i	−0.0722227	−	0.409595i
$586$	4.94049e11			0.173074
$587$	7.00013e10	+	3.96997e11i	0.0243352	+	0.138012i	0.994555	−	0.104215i	$-0.0332332\pi$
$587$	7.00013e10	+	3.96997e11i	0.0243352	+	0.138012i	−0.970220	+	0.242227i	$0.922122\pi$
$588$	1.73332e12	−	1.45443e12i	0.597971	−	0.501757i
$589$	−1.98986e12	−	7.24250e11i	−0.681246	−	0.247953i
$590$	−9.37412e11	+	3.41190e11i	−0.318490	+	0.115921i
$591$	1.18416e12			0.399270
$592$	−2.46469e12	+	2.27071e11i	−0.824735	+	0.0759827i
$593$	−1.16375e12			−0.386468			−0.193234	−	0.981153i	$-0.561898\pi$
$593$	−1.16375e12			−0.386468			−0.193234	+	0.981153i	$0.561898\pi$
$594$	−4.19467e10	+	1.52673e10i	−0.0138248	+	0.00503181i
$595$	9.33628e11	+	3.39813e11i	0.305385	+	0.111151i
$596$	−1.14807e12	+	9.63345e11i	−0.372701	+	0.312733i
$597$	−3.83772e11	−	2.17648e12i	−0.123648	−	0.701245i
$598$	−4.02126e10			−0.0128590
$599$	−9.07649e11	−	5.14754e12i	−0.288070	−	1.63372i	−0.694110	−	0.719869i	$-0.744202\pi$
$599$	−9.07649e11	−	5.14754e12i	−0.288070	−	1.63372i	0.406041	−	0.913855i	$-0.366909\pi$
$600$	1.24289e11	−	2.15274e11i	0.0391518	−	0.0678128i
$601$	−3.13074e11	−	2.62701e11i	−0.0978841	−	0.0821345i	0.592532	−	0.805547i	$-0.298128\pi$
$601$	−3.13074e11	−	2.62701e11i	−0.0978841	−	0.0821345i	−0.690416	+	0.723412i	$0.742573\pi$
$602$	1.83034e10	+	3.17024e10i	0.00567999	+	0.00983804i
$603$	2.02665e12	−	3.51026e12i	0.624239	−	1.08121i
$604$	4.54389e12	−	1.65384e12i	1.38919	−	0.505624i
$605$	−2.27869e12	+	1.91204e12i	−0.691489	+	0.580228i
$606$	8.16142e11	+	1.41360e12i	0.245832	+	0.425794i
$607$	−4.80371e10	+	2.72432e11i	−0.0143624	+	0.0814534i	−0.991146	−	0.132773i	$-0.957612\pi$
$607$	−4.80371e10	+	2.72432e11i	−0.0143624	+	0.0814534i	0.976784	+	0.214226i	$0.0687230\pi$
$608$	−4.47344e11	+	2.53701e12i	−0.132762	+	0.752933i
$609$	−1.32684e12	−	1.11335e12i	−0.390877	−	0.327985i
$610$	−3.90286e11	−	1.42052e11i	−0.114130	−	0.0415398i
$611$	−3.78006e10	−	1.37583e10i	−0.0109727	−	0.00399373i
$612$	1.07053e12	+	8.98281e11i	0.308473	+	0.258840i
$613$	−6.02028e11	+	3.41427e12i	−0.172204	+	0.976620i	0.769117	+	0.639108i	$0.220696\pi$
$613$	−6.02028e11	+	3.41427e12i	−0.172204	+	0.976620i	−0.941321	+	0.337512i	$0.890415\pi$
$614$	2.01142e11	−	1.14073e12i	0.0571143	−	0.323911i
$615$	−1.83318e12	−	3.17516e12i	−0.516734	−	0.895009i
$616$	1.45630e11	−	1.22198e11i	0.0407511	−	0.0341942i
$617$	−2.13093e12	+	7.75596e11i	−0.591952	+	0.215453i	−0.620588	−	0.784137i	$-0.713106\pi$
$617$	−2.13093e12	+	7.75596e11i	−0.591952	+	0.215453i	0.0286360	+	0.999590i	$0.490884\pi$
$618$	−1.59185e11	+	2.75717e11i	−0.0438990	+	0.0760353i
$619$	−1.04540e12	−	1.81068e12i	−0.286202	−	0.495717i	0.686698	−	0.726943i	$-0.259060\pi$
$619$	−1.04540e12	−	1.81068e12i	−0.286202	−	0.495717i	−0.972900	+	0.231226i	$0.925726\pi$
$620$	−1.57460e12	−	1.32125e12i	−0.427965	−	0.359105i
$621$	−5.47096e10	+	9.47597e10i	−0.0147622	+	0.0255689i
$622$	−1.51144e11	−	8.57179e11i	−0.0404887	−	0.229623i
$623$	1.15084e12			0.306068
$624$	−4.26545e11	−	2.41906e12i	−0.112625	−	0.638728i
$625$	−2.50732e12	+	2.10389e12i	−0.657278	+	0.551522i
$626$	1.04445e12	+	3.80150e11i	0.271835	+	0.0989397i
$627$	−1.01978e12	+	3.71171e11i	−0.263514	+	0.0959114i
$628$	4.72543e12			1.21234
$629$	−9.34187e11	+	2.02769e12i	−0.237961	+	0.516504i
$630$	−4.10610e11			−0.103848
$631$	−4.35383e12	+	1.58466e12i	−1.09330	+	0.397928i	−0.824842	−	0.565363i	$-0.808736\pi$
$631$	−4.35383e12	+	1.58466e12i	−1.09330	+	0.397928i	−0.268457	+	0.963292i	$0.586514\pi$
$632$	−1.43416e11	−	5.21991e10i	−0.0357577	−	0.0130147i
$633$	2.76595e12	−	2.32090e12i	0.684742	−	0.574567i
$634$	2.57133e10	+	1.45827e11i	0.00632057	+	0.0358457i
$635$	−3.22411e12			−0.786916
$636$	6.17873e11	+	3.50413e12i	0.149742	+	0.849227i
$637$	−7.69897e11	+	1.33350e12i	−0.185270	+	0.320897i
$638$	9.06102e10	+	7.60310e10i	0.0216513	+	0.0181676i
$639$	−2.75987e12	−	4.78023e12i	−0.654839	−	1.13421i
$640$	−1.64737e12	+	2.85333e12i	−0.388134	+	0.672269i
$641$	7.67427e12	−	2.79320e12i	1.79546	−	0.653494i	0.796664	−	0.604422i	$-0.206596\pi$
$641$	7.67427e12	−	2.79320e12i	1.79546	−	0.653494i	0.998795	−	0.0490721i	$-0.0156264\pi$
$642$	5.92061e11	−	4.96798e11i	0.137549	−	0.115418i
$643$	2.92550e12	+	5.06712e12i	0.674918	+	1.16899i	0.976493	+	0.215550i	$0.0691544\pi$
$643$	2.92550e12	+	5.06712e12i	0.674918	+	1.16899i	−0.301575	+	0.953443i	$0.597512\pi$
$644$	3.92426e10	−	2.22556e11i	0.00899025	−	0.0509862i
$645$	7.26321e10	−	4.11917e11i	0.0165238	−	0.0937111i
$646$	5.32259e11	+	4.46618e11i	0.120248	+	0.100900i
$647$	7.90947e12	+	2.87881e12i	1.77451	+	0.645868i	0.999910	+	0.0134159i	$0.00427055\pi$
$647$	7.90947e12	+	2.87881e12i	1.77451	+	0.645868i	0.774599	+	0.632453i	$0.217952\pi$
$648$	2.34792e12	+	8.54573e11i	0.523114	+	0.190398i
$649$	−9.63453e11	−	8.08433e11i	−0.213172	−	0.178872i
$650$	−1.42455e10	+	8.07905e10i	−0.00313018	+	0.0177521i
$651$	4.08658e11	−	2.31761e12i	0.0891755	−	0.505739i
$652$	−1.11177e12	−	1.92565e12i	−0.240936	−	0.417313i
$653$	−9.06345e11	+	7.60514e11i	−0.195067	+	0.163681i	−0.735090	−	0.677970i	$-0.762860\pi$
$653$	−9.06345e11	+	7.60514e11i	−0.195067	+	0.163681i	0.540023	+	0.841650i	$0.318416\pi$
$654$	−9.49439e11	+	3.45568e11i	−0.202940	+	0.0738641i
$655$	9.39320e11	−	1.62695e12i	0.199401	−	0.345373i
$656$	−1.64052e12	−	2.84146e12i	−0.345871	−	0.599066i
$657$	5.08414e11	+	4.26610e11i	0.106457	+	0.0893279i
$658$	−7.00983e9	+	1.21414e10i	−0.00145778	+	0.00252494i
$659$	−5.15306e11	−	2.92244e12i	−0.106434	−	0.603618i	−0.990638	−	0.136516i	$-0.956409\pi$
$659$	−5.15306e11	−	2.92244e12i	−0.106434	−	0.603618i	0.884204	−	0.467101i	$-0.154702\pi$
$660$	−1.05342e12			−0.216100
$661$	−1.50894e12	−	8.55763e12i	−0.307444	−	1.74360i	−0.611773	−	0.791033i	$-0.709543\pi$
$661$	−1.50894e12	−	8.55763e12i	−0.307444	−	1.74360i	0.304329	−	0.952567i	$-0.401568\pi$
$662$	8.81192e11	−	7.39408e11i	0.178324	−	0.149632i
$663$	−2.08201e12	−	7.57789e11i	−0.418477	−	0.152313i
$664$	−1.32508e12	+	4.82288e11i	−0.264536	+	0.0962831i
$665$	3.29196e12			0.652766
$666$	7.61824e10	−	9.19508e11i	0.0150045	−	0.181101i
$667$	2.89938e11			0.0567203
$668$	9.50062e11	−	3.45794e11i	0.184611	−	0.0671930i
$669$	−6.85970e12	−	2.49673e12i	−1.32400	−	0.481896i
$670$	1.49854e12	−	1.25742e12i	0.287297	−	0.241071i
$671$	−9.09283e10	−	5.15680e11i	−0.0173160	−	0.0982039i
$672$	−2.86302e12			−0.541580
$673$	−9.45140e11	−	5.36016e12i	−0.177594	−	1.00719i	−0.935107	−	0.354366i	$-0.884697\pi$
$673$	−9.45140e11	−	5.36016e12i	−0.177594	−	1.00719i	0.757513	−	0.652820i	$-0.226414\pi$
$674$	−3.50750e11	+	6.07518e11i	−0.0654679	+	0.113394i
$675$	1.70999e11	+	1.43485e11i	0.0317049	+	0.0266036i
$676$	−1.66150e12	−	2.87780e12i	−0.306012	−	0.530029i
$677$	−1.58202e12	+	2.74015e12i	−0.289444	+	0.501331i	−0.973677	−	0.227932i	$-0.926804\pi$
$677$	−1.58202e12	+	2.74015e12i	−0.289444	+	0.501331i	0.684233	+	0.729263i	$0.260137\pi$
$678$	−4.07565e11	+	1.48341e11i	−0.0740735	+	0.0269606i
$679$	1.20138e12	−	1.00808e12i	0.216904	−	0.182004i
$680$	6.95362e11	+	1.20440e12i	0.124716	+	0.216014i
$681$	−1.04210e12	+	5.91002e12i	−0.185672	+	1.05300i
$682$	−2.79073e10	+	1.58270e11i	−0.00493957	+	0.0280137i
$683$	3.44973e12	+	2.89467e12i	0.606586	+	0.508986i	0.893555	−	0.448954i	$-0.148203\pi$
$683$	3.44973e12	+	2.89467e12i	0.606586	+	0.508986i	−0.286969	+	0.957940i	$0.592648\pi$
$684$	4.35108e12	+	1.58366e12i	0.760055	+	0.276637i
$685$	6.92417e12	+	2.52019e12i	1.20160	+	0.437347i
$686$	1.06747e12	+	8.95715e11i	0.184034	+	0.154423i
$687$	−1.13437e10	+	6.43335e10i	−0.00194290	+	0.0110187i
$688$	6.49988e10	−	3.68626e11i	0.0110601	−	0.0627247i
$689$	−1.21070e12	−	2.09700e12i	−0.204669	−	0.354497i
$690$	1.22670e11	−	1.02932e11i	0.0206024	−	0.0172874i
$691$	−5.44232e12	+	1.98084e12i	−0.908099	+	0.330521i	−0.753494	−	0.657455i	$-0.771633\pi$
$691$	−5.44232e12	+	1.98084e12i	−0.908099	+	0.330521i	−0.154605	+	0.987976i	$0.549411\pi$
$692$	−8.81414e11	+	1.52665e12i	−0.146118	+	0.253083i
$693$	−2.58840e11	−	4.48325e11i	−0.0426317	−	0.0738402i
$694$	−2.13515e12	−	1.79160e12i	−0.349390	−	0.293173i
$695$	2.84602e12	−	4.92945e12i	0.462707	−	0.801432i
$696$	−4.21005e11	−	2.38764e12i	−0.0680058	−	0.385680i
$697$	−2.95947e12			−0.474970
$698$	3.59245e11	+	2.03738e12i	0.0572851	+	0.324880i
$699$	−9.55315e12	+	8.01604e12i	−1.51356	+	1.27003i
$700$	−4.33232e11	−	1.57683e11i	−0.0681991	−	0.0248225i
$701$	−5.41822e12	+	1.97207e12i	−0.847472	+	0.308454i	−0.729009	−	0.684504i	$-0.760019\pi$
$701$	−5.41822e12	+	1.97207e12i	−0.847472	+	0.308454i	−0.118463	+	0.992959i	$0.537797\pi$
$702$	−3.01962e11			−0.0469284
$703$	−6.10773e11	+	7.37192e12i	−0.0943150	+	1.13837i
$704$	−8.05659e11			−0.123616
$705$	1.50529e11	−	5.47880e10i	0.0229493	−	0.00835285i
$706$	−2.71717e12	−	9.88971e11i	−0.411620	−	0.149817i
$707$	4.78205e12	−	4.01262e12i	0.719825	−	0.604005i
$708$	2.17095e12	+	1.23120e13i	0.324713	+	1.84154i
$709$	−2.85052e12			−0.423658			−0.211829	−	0.977307i	$-0.567942\pi$
$709$	−2.85052e12			−0.423658			−0.211829	+	0.977307i	$0.567942\pi$
$710$	−4.62587e11	−	2.62346e12i	−0.0683173	−	0.387447i
$711$	−2.07800e11	+	3.59919e11i	−0.0304952	+	0.0528192i
$712$	1.23402e12	+	1.03546e12i	0.179954	+	0.150999i
$713$	1.96970e11	+	3.41162e11i	0.0285428	+	0.0494376i
$714$	−3.86093e11	+	6.68733e11i	−0.0555968	+	0.0962965i
$715$	6.73639e11	−	2.45184e11i	0.0963940	−	0.0350845i
$716$	4.82449e12	−	4.04823e12i	0.686029	−	0.575647i
$717$	4.92339e12	+	8.52755e12i	0.695709	+	1.20500i
$718$	−2.93830e11	+	1.66639e12i	−0.0412607	+	0.234001i
$719$	1.74616e12	−	9.90299e12i	0.243672	−	1.38193i	−0.579886	−	0.814698i	$-0.696903\pi$
$719$	1.74616e12	−	9.90299e12i	0.243672	−	1.38193i	0.823557	−	0.567233i	$-0.191986\pi$
$720$	3.21630e12	+	2.69880e12i	0.446027	+	0.374261i
$721$	1.14415e12	+	4.16437e11i	0.157679	+	0.0573905i
$722$	5.05313e11	+	1.83919e11i	0.0692059	+	0.0251889i
$723$	1.35191e13	+	1.13438e13i	1.84003	+	1.54397i
$724$	−5.48166e11	+	3.10880e12i	−0.0741461	+	0.420503i
$725$	1.02712e11	−	5.82509e11i	0.0138070	−	0.0783036i
$726$	−1.15594e12	−	2.00214e12i	−0.154426	−	0.267473i
$727$	−2.52260e12	+	2.11671e12i	−0.334922	+	0.281033i	−0.794702	−	0.607000i	$-0.792373\pi$
$727$	−2.52260e12	+	2.11671e12i	−0.334922	+	0.281033i	0.459780	+	0.888033i	$0.347928\pi$
$728$	1.20844e12	−	4.39836e11i	0.159453	−	0.0580363i
$729$	1.74538e12	−	3.02309e12i	0.228884	−	0.396439i
$730$	1.60154e11	+	2.77395e11i	0.0208730	+	0.0361531i
$731$	−2.58637e11	−	2.17022e11i	−0.0335014	−	0.0281110i
$732$	−2.60256e12	+	4.50777e12i	−0.335044	+	0.580313i
$733$	8.28211e11	+	4.69702e12i	0.105968	+	0.600972i	0.990829	+	0.135119i	$0.0431415\pi$
$733$	8.28211e11	+	4.69702e12i	0.105968	+	0.600972i	−0.884862	+	0.465854i	$0.845747\pi$
$734$	2.49488e11			0.0317261
$735$	−1.06477e12	−	6.03859e12i	−0.134574	−	0.763208i
$736$	3.67129e11	−	3.08058e11i	0.0461178	−	0.0386974i
$737$	2.31756e12	+	8.43523e11i	0.289353	+	0.105316i
$738$	1.14932e12	−	4.18318e11i	0.142622	−	0.0519103i
$739$	5.00506e12			0.617319			0.308660	−	0.951173i	$-0.400120\pi$
$739$	5.00506e12			0.617319			0.308660	+	0.951173i	$0.400120\pi$
$740$	−3.00456e12	+	6.52152e12i	−0.368331	+	0.799477i
$741$	−7.34114e12			−0.894503
$742$	−7.93010e11	+	2.88632e11i	−0.0960420	+	0.0349564i
$743$	9.95707e12	+	3.62408e12i	1.19862	+	0.436263i	0.862743	−	0.505643i	$-0.168745\pi$
$743$	9.95707e12	+	3.62408e12i	1.19862	+	0.436263i	0.335879	+	0.941905i	$0.390967\pi$
$744$	2.52346e12	−	2.11744e12i	0.301938	−	0.253356i
$745$	7.05252e11	+	3.99969e12i	0.0838767	+	0.475688i
$746$	2.79693e11			0.0330641
$747$	6.66790e11	+	3.78155e12i	0.0783513	+	0.444352i
$748$	−4.25159e11	+	7.36397e11i	−0.0496585	+	0.0860111i
$749$	−2.26428e12	−	1.89996e12i	−0.262883	−	0.220585i
$750$	−1.45883e12	−	2.52676e12i	−0.168356	−	0.291601i
$751$	−3.90305e11	+	6.76028e11i	−0.0447738	+	0.0775506i	−0.887544	−	0.460723i	$-0.847590\pi$
$751$	−3.90305e11	+	6.76028e11i	−0.0447738	+	0.0775506i	0.842770	+	0.538274i	$0.180923\pi$
$752$	1.34709e11	−	4.90300e10i	0.0153609	−	0.00559090i
$753$	−1.38386e13	+	1.16119e13i	−1.56861	+	1.31622i
$754$	4.00068e11	+	6.92939e11i	0.0450778	+	0.0780771i
$755$	2.27548e12	−	1.29049e13i	0.254865	−	1.44541i
$756$	2.94679e11	−	1.67121e12i	0.0328096	−	0.186072i
$757$	3.11891e12	+	2.61707e12i	0.345200	+	0.289657i	0.798859	−	0.601518i	$-0.205437\pi$
$757$	3.11891e12	+	2.61707e12i	0.345200	+	0.289657i	−0.453659	+	0.891175i	$0.649882\pi$
$758$	−3.30280e12	−	1.20212e12i	−0.363388	−	0.132262i
$759$	1.89715e11	+	6.90506e10i	0.0207498	+	0.00755230i
$760$	3.52990e12	+	2.96193e12i	0.383796	+	0.322043i
$761$	2.11820e12	−	1.20129e13i	0.228948	−	1.29843i	−0.626045	−	0.779787i	$-0.715327\pi$
$761$	2.11820e12	−	1.20129e13i	0.228948	−	1.29843i	0.854992	−	0.518640i	$-0.173562\pi$
$762$	4.35125e11	−	2.46772e12i	0.0467538	−	0.265154i
$763$	1.93204e12	+	3.34639e12i	0.206374	+	0.357450i
$764$	3.88689e12	−	3.26148e12i	0.412745	−	0.346334i
$765$	3.55869e12	−	1.29526e12i	0.375677	−	0.136735i
$766$	−4.78013e11	+	8.27943e11i	−0.0501661	+	0.0868903i
$767$	−4.25390e12	−	7.36798e12i	−0.443822	−	0.768722i
$768$	4.55376e12	+	3.82106e12i	0.472329	+	0.396331i
$769$	3.51393e12	−	6.08630e12i	0.362346	−	0.627603i	−0.626000	−	0.779823i	$-0.715309\pi$
$769$	3.51393e12	−	6.08630e12i	0.362346	−	0.627603i	0.988347	+	0.152220i	$0.0486424\pi$
$770$	−4.33847e10	−	2.46047e11i	−0.00444763	−	0.0252238i
$771$	−1.67290e13			−1.70501
$772$	−2.67186e12	−	1.51528e13i	−0.270729	−	1.53538i
$773$	−9.75194e12	+	8.18285e12i	−0.982388	+	0.824322i	−0.984448	−	0.175676i	$-0.943789\pi$
$773$	−9.75194e12	+	8.18285e12i	−0.982388	+	0.824322i	0.00205979	+	0.999998i	$0.499344\pi$
$774$	1.31119e11	+	4.77233e10i	0.0131320	+	0.00477965i
$775$	7.55200e11	−	2.74870e11i	0.0751977	−	0.0273697i
$776$	2.19523e12			0.217322
$777$	−8.18622e12	+	7.54195e11i	−0.805729	+	0.0742317i
$778$	−3.16377e12			−0.309597
$779$	−9.21437e12	+	3.35376e12i	−0.896494	+	0.326297i
$780$	−6.69622e12	−	2.43722e12i	−0.647745	−	0.235760i
$781$	2.57282e12	−	2.15885e12i	0.247445	−	0.207631i
$782$	−2.24457e10	−	1.27296e11i	−0.00214636	−	0.0121726i
$783$	2.17718e12			0.206998
$784$	−9.52864e11	−	5.40396e12i	−0.0900759	−	0.510846i
$785$	6.40283e12	−	1.10900e13i	0.601809	−	1.04236i
$786$	1.11849e12	+	9.38523e11i	0.104527	+	0.0877089i
$787$	1.59455e12	+	2.76184e12i	0.148167	+	0.256633i	0.930550	−	0.366165i	$-0.119329\pi$
$787$	1.59455e12	+	2.76184e12i	0.148167	+	0.256633i	−0.782383	+	0.622798i	$0.785996\pi$
$788$	1.53711e12	−	2.66236e12i	0.142016	−	0.245979i
$789$	−2.18612e13	+	7.95682e12i	−2.00829	+	0.730959i
$790$	−1.53650e11	+	1.28928e11i	−0.0140350	+	0.0117767i
$791$	8.29364e11	+	1.43650e12i	0.0753270	+	0.130470i
$792$	1.25830e11	−	7.13619e11i	0.0113638	−	0.0644471i
$793$	6.15092e11	−	3.48836e12i	0.0552345	−	0.313251i
$794$	2.84975e12	+	2.39122e12i	0.254457	+	0.213515i
$795$	9.06098e12	+	3.29793e12i	0.804495	+	0.292812i
$796$	−5.39156e12	−	1.96237e12i	−0.475998	−	0.173249i
$797$	9.54915e12	+	8.01269e12i	0.838305	+	0.703422i	0.957182	−	0.289488i	$-0.0934849\pi$
$797$	9.54915e12	+	8.01269e12i	0.838305	+	0.703422i	−0.118877	+	0.992909i	$0.537929\pi$
$798$	−4.44282e11	+	2.51965e12i	−0.0387834	+	0.219952i
$799$	2.24534e10	−	1.27340e11i	0.00194905	−	0.0110536i
$800$	−4.88856e11	−	8.46723e11i	−0.0421964	−	0.0730864i
$801$	3.36036e12	−	2.81967e12i	0.288429	−	0.242021i
$802$	1.59153e12	−	5.79271e11i	0.135841	−	0.0494421i
$803$	−2.01916e11	+	3.49728e11i	−0.0171376	+	0.0296832i
$804$	−1.22579e13	−	2.12314e13i	−1.03458	−	1.79195i
$805$	−4.69140e11	−	3.93655e11i	−0.0393750	−	0.0330395i
$806$	−5.43575e11	+	9.41499e11i	−0.0453682	+	0.0785801i
$807$	−1.72479e11	−	9.78175e11i	−0.0143154	−	0.0811868i
$808$	8.73802e12			0.721210
$809$	−3.67608e12	−	2.08481e13i	−0.301728	−	1.71119i	−0.638518	−	0.769607i	$-0.720452\pi$
$809$	−3.67608e12	−	2.08481e13i	−0.301728	−	1.71119i	0.336790	−	0.941580i	$-0.390659\pi$
$810$	2.51547e12	−	2.11073e12i	0.205323	−	0.172286i
$811$	1.58466e13	+	5.76770e12i	1.28630	+	0.468175i	0.892511	−	0.451025i	$-0.148941\pi$
$811$	1.58466e13	+	5.76770e12i	1.28630	+	0.468175i	0.393790	+	0.919200i	$0.371164\pi$
$812$	−4.22548e12	+	1.53795e12i	−0.341093	+	0.124148i
$813$	2.81371e13			2.25877
$814$	5.59039e11	−	5.15042e10i	0.0446306	−	0.00411181i
$815$	−6.02568e12			−0.478406
$816$	7.41960e12	−	2.70051e12i	0.585835	−	0.213226i
$817$	−1.05121e12	−	3.82609e11i	−0.0825449	−	0.0300439i
$818$	2.55624e12	−	2.14494e12i	0.199624	−	0.167504i
$819$	−6.08097e11	−	3.44869e12i	−0.0472276	−	0.267841i
$820$	−9.51832e12			−0.735187
$821$	−2.16474e12	−	1.22768e13i	−0.166288	−	0.943067i	−0.947726	−	0.319084i	$-0.896625\pi$
$821$	−2.16474e12	−	1.22768e13i	−0.166288	−	0.943067i	0.781438	−	0.623982i	$-0.214486\pi$
$822$	−2.86342e12	+	4.95960e12i	−0.218757	+	0.378899i
$823$	5.24918e11	+	4.40459e11i	0.0398834	+	0.0334662i	0.662511	−	0.749052i	$-0.269491\pi$
$823$	5.24918e11	+	4.40459e11i	0.0398834	+	0.0334662i	−0.622628	+	0.782518i	$0.713935\pi$
$824$	8.52158e11	+	1.47598e12i	0.0643944	+	0.111534i
$825$	2.05936e11	−	3.56691e11i	0.0154771	−	0.0268071i
$826$	−2.78630e12	+	1.01413e12i	−0.208266	+	0.0758026i
$827$	1.56130e13	−	1.31009e13i	1.16068	−	0.973923i	0.160762	−	0.986993i	$-0.448605\pi$
$827$	1.56130e13	−	1.31009e13i	1.16068	−	0.973923i	0.999915	+	0.0130701i	$0.00416045\pi$
$828$	−4.30700e11	−	7.45994e11i	−0.0318448	−	0.0551568i
$829$	−7.62582e11	+	4.32482e12i	−0.0560779	+	0.318033i	−0.999924	−	0.0123529i	$-0.996068\pi$
$829$	−7.62582e11	+	4.32482e12i	−0.0560779	+	0.318033i	0.943846	+	0.330386i	$0.107179\pi$
$830$	−3.21805e11	+	1.82505e12i	−0.0235365	+	0.133482i
$831$	1.33143e13	+	1.11720e13i	0.968533	+	0.812696i
$832$	−5.12128e12	−	1.86399e12i	−0.370530	−	0.134862i
$833$	−4.65102e12	−	1.69283e12i	−0.334693	−	0.121818i
$834$	3.38888e12	+	2.84360e12i	0.242554	+	0.203527i
$835$	4.75770e11	−	2.69822e12i	0.0338694	−	0.192083i
$836$	−4.89236e11	+	2.77459e12i	−0.0346410	+	0.196459i
$837$	1.47908e12	+	2.56183e12i	0.104166	+	0.180421i
$838$	5.46633e11	−	4.58679e11i	0.0382911	−	0.0321300i
$839$	−1.73209e13	+	6.30427e12i	−1.20681	+	0.439244i	−0.865598	−	0.500740i	$-0.833061\pi$
$839$	−1.73209e13	+	6.30427e12i	−1.20681	+	0.439244i	−0.341217	+	0.939985i	$0.610839\pi$
$840$	−2.56054e12	+	4.43498e12i	−0.177449	+	0.307351i
$841$	4.36903e12	+	7.56739e12i	0.301164	+	0.521632i
$842$	−3.96810e12	−	3.32963e12i	−0.272068	−	0.228292i
$843$	−1.35352e13	+	2.34437e13i	−0.923084	+	1.59883i
$844$	−1.62774e12	−	9.23138e12i	−0.110419	−	0.626218i
$845$	−9.00512e12			−0.607623
$846$	9.27950e9	+	5.26267e10i	0.000622813	+	0.00353215i
$847$	−6.77302e12	+	5.68324e12i	−0.452176	+	0.379420i
$848$	8.10871e12	+	2.95133e12i	0.538481	+	0.195991i
$849$	3.09129e13	−	1.12514e13i	2.04200	−	0.743226i
$850$	−2.63699e11			−0.0173270
$851$	9.68580e11	−	9.77540e11i	0.0633071	−	0.0638927i
$852$	−3.33855e13			−2.17060
$853$	2.16347e11	−	7.87438e10i	0.0139920	−	0.00509267i	−0.335015	−	0.942213i	$-0.608741\pi$
$853$	2.16347e11	−	7.87438e10i	0.0139920	−	0.00509267i	0.349007	+	0.937120i	$0.386519\pi$
$854$	−1.16006e12	−	4.22228e11i	−0.0746312	−	0.0271635i
$855$	9.61226e12	−	8.06565e12i	0.615146	−	0.516169i
$856$	−7.18455e11	−	4.07456e12i	−0.0457370	−	0.259387i
$857$	−1.43478e12			−0.0908595			−0.0454298	−	0.998968i	$-0.514466\pi$
$857$	−1.43478e12			−0.0908595			−0.0454298	+	0.998968i	$0.514466\pi$
$858$	9.67487e10	+	5.48689e11i	0.00609470	+	0.0345648i
$859$	−3.74561e12	+	6.48758e12i	−0.234721	+	0.406550i	−0.959192	−	0.282757i	$-0.908751\pi$
$859$	−3.74561e12	+	6.48758e12i	−0.234721	+	0.406550i	0.724470	+	0.689306i	$0.242084\pi$
$860$	−8.31836e11	−	6.97993e11i	−0.0518555	−	0.0435119i
$861$	−5.44882e12	−	9.43764e12i	−0.337900	−	0.585261i
$862$	−3.77170e11	+	6.53277e11i	−0.0232677	+	0.0403009i
$863$	9.55978e12	−	3.47948e12i	0.586678	−	0.213533i	−0.0315899	−	0.999501i	$-0.510057\pi$
$863$	9.55978e12	−	3.47948e12i	0.586678	−	0.213533i	0.618268	+	0.785968i	$0.287835\pi$
$864$	2.75682e12	−	2.31325e12i	0.168305	−	0.141225i
$865$	2.38858e12	+	4.13714e12i	0.145067	+	0.251263i
$866$	3.14305e11	−	1.78251e12i	0.0189898	−	0.107697i
$867$	−2.58735e12	+	1.46736e13i	−0.155514	+	0.881963i
$868$	−4.68025e12	−	3.92720e12i	−0.279853	−	0.234825i
$869$	−2.37628e11	−	8.64894e10i	−0.0141354	−	0.00514486i
$870$	−2.99414e12	−	1.08978e12i	−0.177188	−	0.0644912i
$871$	1.27803e13	+	1.07239e13i	0.752417	+	0.631353i
$872$	−9.39224e11	+	5.32660e12i	−0.0550104	+	0.311979i
$873$	1.03804e12	−	5.88702e12i	0.0604854	−	0.343030i
$874$	−2.14141e11	−	3.70902e11i	−0.0124136	−	0.0215010i
$875$	−8.54776e12	+	7.17242e12i	−0.492965	+	0.413647i
$876$	3.77214e12	−	1.37295e12i	0.216431	−	0.0787745i
$877$	−1.39219e13	+	2.41135e13i	−0.794697	+	1.37646i	0.128334	+	0.991731i	$0.459037\pi$
$877$	−1.39219e13	+	2.41135e13i	−0.794697	+	1.37646i	−0.923031	+	0.384725i	$0.874296\pi$
$878$	1.36116e12	+	2.35759e12i	0.0773005	+	0.133888i
$879$	−1.28534e13	−	1.07853e13i	−0.726221	−	0.609372i
$880$	−1.27735e12	+	2.21243e12i	−0.0718021	+	0.124365i
$881$	−7.19453e11	−	4.08022e12i	−0.0402356	−	0.228188i	0.958059	−	0.286573i	$-0.0925160\pi$
$881$	−7.19453e11	−	4.08022e12i	−0.0402356	−	0.228188i	−0.998294	+	0.0583851i	$0.981405\pi$
$882$	2.04552e12			0.113814
$883$	1.48957e12	+	8.44778e12i	0.0824590	+	0.467648i	0.997876	+	0.0651415i	$0.0207499\pi$
$883$	1.48957e12	+	8.44778e12i	0.0824590	+	0.467648i	−0.915417	+	0.402507i	$0.868139\pi$
$884$	−4.40632e12	+	3.69734e12i	−0.242684	+	0.203636i
$885$	3.18365e13	+	1.15875e13i	1.74454	+	0.634960i
$886$	−5.04070e12	+	1.83466e12i	−0.274814	+	0.100024i
$887$	1.84062e13			0.998409			0.499204	−	0.866484i	$-0.333626\pi$
$887$	1.84062e13			0.998409			0.499204	+	0.866484i	$0.333626\pi$
$888$	−9.45648e12	−	6.55682e12i	−0.510354	−	0.353863i
$889$	−9.58315e12			−0.514577
$890$	1.98940e12	−	7.24082e11i	0.106284	−	0.0386841i
$891$	3.89030e12	+	1.41596e12i	0.206792	+	0.0752662i
$892$	−1.45177e13	+	1.21818e13i	−0.767815	+	0.644273i
$893$	−7.43960e10	−	4.21921e11i	−0.00391487	−	0.0222024i
$894$	−3.15652e12			−0.165268
$895$	−2.96366e12	−	1.68077e13i	−0.154392	−	0.875599i
$896$	−4.89655e12	+	8.48107e12i	−0.253807	+	0.439607i
$897$	1.04619e12	+	8.77858e11i	0.0539566	+	0.0452750i
$898$	1.10834e12	+	1.91969e12i	0.0568758	+	0.0985118i
$899$	3.91924e12	−	6.78832e12i	0.200117	−	0.346612i
$900$	−1.65134e12	+	6.01039e11i	−0.0838968	+	0.0305359i
$901$	5.96241e12	−	5.00306e12i	0.301412	−	0.252915i
$902$	3.72102e11	+	6.44499e11i	0.0187168	+	0.0324185i
$903$	2.15887e11	−	1.22436e12i	0.0108052	−	0.0612792i
$904$	−4.03179e11	+	2.28654e12i	−0.0200789	+	0.113873i
$905$	6.55324e12	+	5.49882e12i	0.324741	+	0.272490i
$906$	9.57021e12	+	3.48327e12i	0.471894	+	0.171755i
$907$	1.84914e12	+	6.73031e11i	0.0907270	+	0.0330219i	0.386985	−	0.922086i	$-0.373517\pi$
$907$	1.84914e12	+	6.73031e11i	0.0907270	+	0.0330219i	−0.296258	+	0.955108i	$0.595739\pi$
$908$	1.19349e13	+	1.00145e13i	0.582681	+	0.488927i
$909$	4.13187e12	−	2.34330e13i	0.200729	−	1.13839i
$910$	2.93480e11	−	1.66440e12i	0.0141870	−	0.0804586i
$911$	2.02044e13	+	3.49951e13i	0.971883	+	1.68335i	0.689859	+	0.723944i	$0.257673\pi$
$911$	2.02044e13	+	3.49951e13i	0.971883	+	1.68335i	0.282024	+	0.959407i	$0.408994\pi$
$912$	2.00408e13	−	1.68163e13i	0.959266	−	0.804919i
$913$	−2.19554e12	+	7.99110e11i	−0.104574	+	0.0380617i
$914$	3.80453e12	−	6.58963e12i	0.180319	−	0.312323i
$915$	7.05280e12	+	1.22158e13i	0.332634	+	0.576139i
$916$	1.29917e11	+	1.09013e11i	0.00609727	+	0.00511622i
$917$	2.79198e12	−	4.83584e12i	0.130392	−	0.225845i
$918$	−1.68548e11	−	9.55882e11i	−0.00783305	−	0.0444234i
$919$	−3.11038e13			−1.43845			−0.719224	−	0.694778i	$-0.755503\pi$
$919$	−3.11038e13			−1.43845			−0.719224	+	0.694778i	$0.755503\pi$
$920$	−1.48858e11	−	8.44214e11i	−0.00685056	−	0.0388515i
$921$	−3.01357e13	+	2.52868e13i	−1.38011	+	1.15805i
$922$	6.76842e12	+	2.46350e12i	0.308459	+	0.112270i
$923$	2.13492e13	−	7.77048e12i	0.968220	−	0.352403i
$924$	−3.13113e12			−0.141311
$925$	−1.62083e12	−	2.29226e12i	−0.0727949	−	0.102950i
$926$	−6.86499e12			−0.306825
$927$	4.36114e12	−	1.58732e12i	0.193973	−	0.0706003i
$928$	−8.96091e12	−	3.26150e12i	−0.396631	−	0.144362i
$929$	−1.71478e13	+	1.43887e13i	−0.755333	+	0.633800i	−0.936908	−	0.349577i	$-0.886325\pi$
$929$	−1.71478e13	+	1.43887e13i	−0.755333	+	0.633800i	0.181574	+	0.983377i	$0.441881\pi$
$930$	−7.51763e11	−	4.26346e12i	−0.0329540	−	0.186891i
$931$	−1.63995e13			−0.715411
$932$	5.62196e12	+	3.18837e13i	0.244071	+	1.38420i
$933$	−1.47803e13	+	2.56003e13i	−0.638583	+	1.10606i
$934$	6.38988e12	+	5.36174e12i	0.274746	+	0.230539i
$935$	1.15216e12	+	1.99559e12i	0.0493014	+	0.0853925i
$936$	2.45090e12	−	4.24509e12i	0.104372	−	0.180778i
$937$	3.43316e12	−	1.24957e12i	0.145501	−	0.0529580i	−0.268243	−	0.963351i	$-0.586443\pi$
$937$	3.43316e12	−	1.24957e12i	0.145501	−	0.0529580i	0.413744	+	0.910393i	$0.364221\pi$
$938$	4.45416e12	−	3.73748e12i	0.187868	−	0.157640i
$939$	−1.88742e13	−	3.26910e13i	−0.792269	−	1.37225i
$940$	7.22154e10	−	4.09554e11i	0.00301685	−	0.0171094i
$941$	−5.44594e12	+	3.08854e13i	−0.226422	+	1.28410i	0.633525	+	0.773722i	$0.281607\pi$
$941$	−5.44594e12	+	3.08854e13i	−0.226422	+	1.28410i	−0.859947	+	0.510383i	$0.829504\pi$
$942$	7.62412e12	+	6.39740e12i	0.315472	+	0.264712i
$943$	1.71419e12	+	6.23914e11i	0.0705921	+	0.0256934i
$944$	2.84906e13	+	1.03697e13i	1.16769	+	0.425004i
$945$	−3.52284e12	−	2.95601e12i	−0.143698	−	0.120577i
$946$	−1.47430e10	+	8.36116e10i	−0.000598515	+	0.00339435i
$947$	7.75440e12	−	4.39774e13i	0.313309	−	1.77687i	−0.268237	−	0.963353i	$-0.586441\pi$
$947$	7.75440e12	−	4.39774e13i	0.313309	−	1.77687i	0.581547	−	0.813513i	$-0.302448\pi$
$948$	1.25685e12	+	2.17693e12i	0.0505412	+	0.0875400i
$949$	−2.09264e12	+	1.75594e12i	−0.0837524	+	0.0702766i
$950$	−8.21034e11	+	2.98832e11i	−0.0327043	+	0.0119034i
$951$	2.51450e12	−	4.35525e12i	0.0996873	−	0.172664i
$952$	2.06685e12	+	3.57989e12i	0.0815536	+	0.141255i
$953$	−1.35752e13	−	1.13909e13i	−0.533123	−	0.447343i	0.336056	−	0.941842i	$-0.390907\pi$
$953$	−1.35752e13	−	1.13909e13i	−0.533123	−	0.447343i	−0.869178	+	0.494499i	$0.835351\pi$
$954$	−1.60835e12	+	2.78574e12i	−0.0628655	+	0.108886i
$955$	−2.38769e12	−	1.35413e13i	−0.0928887	−	0.526798i
$956$	2.55634e13			0.989826
$957$	−6.97570e11	−	3.95612e12i	−0.0268834	−	0.152463i
$958$	−4.53899e12	+	3.80867e12i	−0.174106	+	0.146093i
$959$	2.05810e13	+	7.49086e12i	0.785746	+	0.285988i
$960$	2.03939e13	−	7.42276e12i	0.774960	−	0.282062i
$961$	−1.57894e13			−0.597189
$962$	3.67277e12	+	9.66013e11i	0.138263	+	0.0363660i
$963$	−1.12666e13			−0.422158
$964$	4.30530e13	−	1.56700e13i	1.60567	−	0.584417i
$965$	−3.91822e13	−	1.42611e13i	−1.45451	−	0.529397i
$966$	3.64616e11	−	3.05949e11i	0.0134722	−	0.0113045i
$967$	4.88792e12	+	2.77208e13i	0.179765	+	1.01950i	0.932499	+	0.361173i	$0.117624\pi$
$967$	4.88792e12	+	2.77208e13i	0.179765	+	1.01950i	−0.752734	+	0.658325i	$0.771265\pi$
$968$	−1.23760e13			−0.453046
$969$	−4.09764e12	−	2.32389e13i	−0.149306	−	0.846755i
$970$	1.44251e12	−	2.49850e12i	0.0523174	−	0.0906164i
$971$	−2.65615e13	−	2.22877e13i	−0.958883	−	0.804598i	0.0218882	−	0.999760i	$-0.493032\pi$
$971$	−2.65615e13	−	2.22877e13i	−0.958883	−	0.804598i	−0.980771	+	0.195162i	$0.937477\pi$
$972$	−1.62757e13	−	2.81904e13i	−0.584846	−	1.01298i
$973$	8.45933e12	−	1.46520e13i	0.302572	−	0.524069i
$974$	4.09975e12	−	1.49219e12i	0.145963	−	0.0531261i
$975$	2.13431e12	−	1.79090e12i	0.0756373	−	0.0634673i
$976$	6.31158e12	+	1.09320e13i	0.222645	+	0.385633i
$977$	2.63765e12	−	1.49589e13i	0.0926172	−	0.525258i	−0.902834	−	0.429989i	$-0.858518\pi$
$977$	2.63765e12	−	1.49589e13i	0.0926172	−	0.525258i	0.995451	−	0.0952697i	$-0.0303714\pi$
$978$	8.13224e11	−	4.61202e12i	0.0284240	−	0.161201i
$979$	2.04466e12	+	1.71568e12i	0.0711376	+	0.0596916i
$980$	−1.49588e13	−	5.44454e12i	−0.518058	−	0.188558i
$981$	1.38404e13	+	5.03749e12i	0.477131	+	0.173661i
$982$	−4.55602e12	−	3.82295e12i	−0.156345	−	0.131189i
$983$	4.24875e12	−	2.40959e13i	0.145134	−	0.823098i	−0.822125	−	0.569307i	$-0.807211\pi$
$983$	4.24875e12	−	2.40959e13i	0.145134	−	0.823098i	0.967259	−	0.253791i	$-0.0816774\pi$
$984$	2.64884e12	−	1.50223e13i	0.0900696	−	0.510810i
$985$	−4.16549e12	−	7.21484e12i	−0.140995	−	0.244210i
$986$	−1.97024e12	+	1.65322e12i	−0.0663853	+	0.0557039i
$987$	4.47422e11	−	1.62848e11i	0.0150069	−	0.00546206i
$988$	−9.52926e12	+	1.65052e13i	−0.318165	+	0.551078i
$989$	1.04056e11	+	1.80230e11i	0.00345847	+	0.00599024i
$990$	−7.29520e11	−	6.12140e11i	−0.0241367	−	0.0202531i
$991$	4.21550e12	−	7.30146e12i	0.138841	−	0.240480i	−0.788217	−	0.615397i	$-0.788996\pi$
$991$	4.21550e12	−	7.30146e12i	0.138841	−	0.240480i	0.927058	+	0.374918i	$0.122329\pi$
$992$	−2.24989e12	−	1.27598e13i	−0.0737665	−	0.418351i
$993$	−3.90671e13			−1.27509
$994$	−1.37496e12	−	7.79781e12i	−0.0446738	−	0.253358i
$995$	−1.19108e13	+	9.99438e12i	−0.385246	+	0.323260i
$996$	2.18244e13	+	7.94345e12i	0.702710	+	0.255766i
$997$	9.75592e12	−	3.55087e12i	0.312709	−	0.113817i	−0.180898	−	0.983502i	$-0.557900\pi$
$997$	9.75592e12	−	3.55087e12i	0.312709	−	0.113817i	0.493607	+	0.869685i	$0.335678\pi$
$998$	−1.09471e13			−0.349309
$999$	7.27321e12	−	7.34049e12i	0.231037	−	0.233174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.f.a.7.15	✓	162
37.16	even	9	inner	37.10.f.a.16.15	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.f.a.7.15	✓	162	1.1	even	1	trivial
37.10.f.a.16.15	yes	162	37.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(5.13813 - 1.87013i) q^{2} +(-174.502 - 63.5134i) q^{3} +(-369.312 + 309.889i) q^{4} +(226.866 + 1286.62i) q^{5} -1015.39 q^{6} +(674.322 + 3824.27i) q^{7} +(-2717.82 + 4707.40i) q^{8} +(11338.8 + 9514.40i) q^{9} +O(q^{10})\)	\(q+(5.13813 - 1.87013i) q^{2} +(-174.502 - 63.5134i) q^{3} +(-369.312 + 309.889i) q^{4} +(226.866 + 1286.62i) q^{5} -1015.39 q^{6} +(674.322 + 3824.27i) q^{7} +(-2717.82 + 4707.40i) q^{8} +(11338.8 + 9514.40i) q^{9} +(3571.81 + 6186.56i) q^{10} +(-4503.19 + 7799.76i) q^{11} +(84127.6 - 30620.0i) q^{12} +(-46670.8 + 39161.5i) q^{13} +(10616.6 + 18388.5i) q^{14} +(42129.2 - 238927. i) q^{15} +(37701.6 - 213816. i) q^{16} +(-150019. - 125881. i) q^{17} +(76053.5 + 27681.2i) q^{18} +(-609739. - 221927. i) q^{19} +(-482495. - 404861. i) q^{20} +(125222. - 710170. i) q^{21} +(-8551.46 + 48497.7i) q^{22} +(60356.1 + 104540. i) q^{23} +(773247. - 648831. i) q^{24} +(231411. - 84226.6i) q^{25} +(-166564. + 288497. i) q^{26} +(453223. + 785005. i) q^{27} +(-1.43414e6 - 1.20338e6i) q^{28} +(1.20095e6 - 2.08010e6i) q^{29} +(-230358. - 1.30642e6i) q^{30} +3.26346e6 q^{31} +(-689419. - 3.90989e6i) q^{32} +(1.28120e6 - 1.07506e6i) q^{33} +(-1.00623e6 - 366237. i) q^{34} +(-4.76741e6 + 1.73520e6i) q^{35} -7.13597e6 q^{36} +(-3.00122e6 - 1.09979e7i) q^{37} -3.54795e6 q^{38} +(1.06314e7 - 3.86952e6i) q^{39} +(-6.67322e6 - 2.42885e6i) q^{40} +(1.15765e7 - 9.71380e6i) q^{41} +(-684701. - 3.88313e6i) q^{42} +1.72403e6 q^{43} +(-753980. - 4.27603e6i) q^{44} +(-9.66904e6 + 1.67473e7i) q^{45} +(505621. + 424266. i) q^{46} +(330134. + 571810. i) q^{47} +(-2.01592e7 + 3.49168e7i) q^{48} +(2.37496e7 - 8.64416e6i) q^{49} +(1.03150e6 - 865535. i) q^{50} +(1.81834e7 + 3.14946e7i) q^{51} +(5.10036e6 - 2.89256e7i) q^{52} +(-6.90155e6 + 3.91406e7i) q^{53} +(3.79678e6 + 3.18587e6i) q^{54} +(-1.10570e7 - 4.02440e6i) q^{55} +(-1.98351e7 - 7.21937e6i) q^{56} +(9.23052e7 + 7.74532e7i) q^{57} +(2.28057e6 - 1.29337e7i) q^{58} +(-2.42491e7 + 1.37524e8i) q^{59} +(5.84820e7 + 1.01294e8i) q^{60} +(-4.45382e7 + 3.73720e7i) q^{61} +(1.67681e7 - 6.10309e6i) q^{62} +(-2.87396e7 + 4.97785e7i) q^{63} +(4.47271e7 + 7.74696e7i) q^{64} +(-6.09740e7 - 5.11633e7i) q^{65} +(4.57250e6 - 7.91980e6i) q^{66} +(-4.75516e7 - 2.69678e8i) q^{67} +9.44128e7 q^{68} +(-3.89256e6 - 2.20758e7i) q^{69} +(-2.12505e7 + 1.78313e7i) q^{70} +(-3.50421e8 - 1.27543e8i) q^{71} +(-7.56050e7 + 2.75180e7i) q^{72} +4.48383e7 q^{73} +(-3.59882e7 - 5.08961e7i) q^{74} -4.57311e7 q^{75} +(2.93957e8 - 1.06991e8i) q^{76} +(-3.28650e7 - 1.19619e7i) q^{77} +(4.73891e7 - 3.97642e7i) q^{78} +(4.87563e6 + 2.76511e7i) q^{79} +2.83654e8 q^{80} +(-7.98211e7 - 4.52688e8i) q^{81} +(4.13153e7 - 7.15602e7i) q^{82} +(1.98728e8 + 1.66752e8i) q^{83} +(1.73828e8 + 3.01079e8i) q^{84} +(1.27927e8 - 2.21575e8i) q^{85} +(8.85830e6 - 3.22416e6i) q^{86} +(-3.41681e8 + 2.86704e8i) q^{87} +(-2.44777e7 - 4.23966e7i) q^{88} +(5.14621e7 - 2.91856e8i) q^{89} +(-1.83613e7 + 1.04132e8i) q^{90} +(-1.81235e8 - 1.52074e8i) q^{91} +(-5.46860e7 - 1.99041e7i) q^{92} +(-5.69479e8 - 2.07274e8i) q^{93} +(2.76563e6 + 2.32064e6i) q^{94} +(1.47207e8 - 8.34851e8i) q^{95} +(-1.28026e8 + 7.26069e8i) q^{96} +(-2.01930e8 - 3.49753e8i) q^{97} +(1.05863e8 - 8.88297e7i) q^{98} +(-1.25271e8 + 4.55949e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9}+O(q^{10}) \) 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9	\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9} + 59997 q^{10} + 175689 q^{11} - 147411 q^{12} + 713586 q^{13} - 96867 q^{14} - 143316 q^{15} + 556665 q^{16} - 119334 q^{17} - 711948 q^{18} + 1752348 q^{19} + 4774248 q^{20} + 57972 q^{21} + 1413495 q^{22} - 5098719 q^{23} + 3891975 q^{24} + 10869768 q^{25} + 5518221 q^{26} + 13281609 q^{27} + 9017757 q^{28} - 2782023 q^{29} - 10231020 q^{30} + 8407836 q^{31} + 6197838 q^{32} - 8252229 q^{33} - 49656453 q^{34} - 23563824 q^{35} + 151165428 q^{36} - 23634336 q^{37} - 12277422 q^{38} + 100476834 q^{39} + 165006327 q^{40} + 74094072 q^{41} - 3662109 q^{42} - 90803088 q^{43} - 350087604 q^{44} - 184820799 q^{45} - 114643110 q^{46} + 158694333 q^{47} + 359750805 q^{48} + 36118224 q^{49} - 259200273 q^{50} + 176035647 q^{51} - 203883429 q^{52} - 31488120 q^{53} - 109796865 q^{54} + 23137227 q^{55} + 37371291 q^{56} - 12449808 q^{57} - 840994983 q^{58} - 77893794 q^{59} + 244178580 q^{60} - 980597586 q^{61} - 586588080 q^{62} - 48634623 q^{63} - 917012376 q^{64} + 1432770144 q^{65} - 177475497 q^{66} - 302695398 q^{67} + 1615796082 q^{68} + 699674787 q^{69} + 2092804794 q^{70} - 774435768 q^{71} - 2899807611 q^{72} - 2505680652 q^{73} + 1161236205 q^{74} - 2302474524 q^{75} + 1445475621 q^{76} - 1374645213 q^{77} + 2942410749 q^{78} - 29533980 q^{79} + 9154934064 q^{80} - 2232253221 q^{81} + 707552205 q^{82} - 392438496 q^{83} - 1388366664 q^{84} - 556053567 q^{85} + 852383496 q^{86} - 6650019951 q^{87} + 3660093510 q^{88} + 100313124 q^{89} + 12897388398 q^{90} + 684844038 q^{91} + 621259308 q^{92} + 2212599060 q^{93} + 3136220628 q^{94} + 1257937926 q^{95} - 6811500039 q^{96} + 70258497 q^{97} - 8202052869 q^{98} - 2679000153 q^{99}+O(q^{100}) \) 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9 + 59997 * q^10 + 175689 * q^11 - 147411 * q^12 + 713586 * q^13 - 96867 * q^14 - 143316 * q^15 + 556665 * q^16 - 119334 * q^17 - 711948 * q^18 + 1752348 * q^19 + 4774248 * q^20 + 57972 * q^21 + 1413495 * q^22 - 5098719 * q^23 + 3891975 * q^24 + 10869768 * q^25 + 5518221 * q^26 + 13281609 * q^27 + 9017757 * q^28 - 2782023 * q^29 - 10231020 * q^30 + 8407836 * q^31 + 6197838 * q^32 - 8252229 * q^33 - 49656453 * q^34 - 23563824 * q^35 + 151165428 * q^36 - 23634336 * q^37 - 12277422 * q^38 + 100476834 * q^39 + 165006327 * q^40 + 74094072 * q^41 - 3662109 * q^42 - 90803088 * q^43 - 350087604 * q^44 - 184820799 * q^45 - 114643110 * q^46 + 158694333 * q^47 + 359750805 * q^48 + 36118224 * q^49 - 259200273 * q^50 + 176035647 * q^51 - 203883429 * q^52 - 31488120 * q^53 - 109796865 * q^54 + 23137227 * q^55 + 37371291 * q^56 - 12449808 * q^57 - 840994983 * q^58 - 77893794 * q^59 + 244178580 * q^60 - 980597586 * q^61 - 586588080 * q^62 - 48634623 * q^63 - 917012376 * q^64 + 1432770144 * q^65 - 177475497 * q^66 - 302695398 * q^67 + 1615796082 * q^68 + 699674787 * q^69 + 2092804794 * q^70 - 774435768 * q^71 - 2899807611 * q^72 - 2505680652 * q^73 + 1161236205 * q^74 - 2302474524 * q^75 + 1445475621 * q^76 - 1374645213 * q^77 + 2942410749 * q^78 - 29533980 * q^79 + 9154934064 * q^80 - 2232253221 * q^81 + 707552205 * q^82 - 392438496 * q^83 - 1388366664 * q^84 - 556053567 * q^85 + 852383496 * q^86 - 6650019951 * q^87 + 3660093510 * q^88 + 100313124 * q^89 + 12897388398 * q^90 + 684844038 * q^91 + 621259308 * q^92 + 2212599060 * q^93 + 3136220628 * q^94 + 1257937926 * q^95 - 6811500039 * q^96 + 70258497 * q^97 - 8202052869 * q^98 - 2679000153 * q^99

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