LMFDB - Embedded newform 75.9.k.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.6671 + 3.59011i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(257.437 - 83.6462i) q^{4} +(-191.814 + 594.838i) q^{5} +(331.652 - 1020.72i) q^{6} +(-1074.42 + 1074.42i) q^{7} +(-300.281 + 153.001i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-22.6671 + 3.59011i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(257.437 - 83.6462i) q^{4} +(-191.814 + 594.838i) q^{5} +(331.652 - 1020.72i) q^{6} +(-1074.42 + 1074.42i) q^{7} +(-300.281 + 153.001i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(2212.32 - 14171.9i) q^{10} +(3327.98 + 2417.92i) q^{11} +(-1980.25 + 12502.8i) q^{12} +(12826.7 + 2031.55i) q^{13} +(20496.7 - 28211.3i) q^{14} +(-20713.5 - 20621.6i) q^{15} +(-49803.9 + 36184.7i) q^{16} +(-20078.4 - 39406.0i) q^{17} +(35490.3 + 35490.3i) q^{18} +(-211149. - 68606.6i) q^{19} +(376.107 + 169178. i) q^{20} +(-21958.2 - 67580.4i) q^{21} +(-84116.2 - 42859.4i) q^{22} +(-42411.3 - 267774. i) q^{23} -15760.6i q^{24} +(-317040. - 228196. i) q^{25} -298037. q^{26} +(101017. - 15999.5i) q^{27} +(-186724. + 366467. i) q^{28} +(-520892. + 169248. i) q^{29} +(543547. + 393067. i) q^{30} +(-193560. + 595716. i) q^{31} +(1.06001e6 - 1.06001e6i) q^{32} +(-171407. + 87336.3i) q^{33} +(596590. + 821135. i) q^{34} +(-433019. - 845197. i) q^{35} +(-478928. - 347962. i) q^{36} +(102186. - 645174. i) q^{37} +(5.03245e6 + 797061. i) q^{38} +(-356975. + 491334. i) q^{39} +(-33412.7 - 207966. i) q^{40} +(3.69204e6 - 2.68243e6i) q^{41} +(740350. + 1.45302e6i) q^{42} +(166529. + 166529. i) q^{43} +(1.05899e6 + 344088. i) q^{44} +(1.29903e6 - 425277. i) q^{45} +(1.92268e6 + 5.91740e6i) q^{46} +(6.14580e6 + 3.13144e6i) q^{47} +(-450363. - 2.84348e6i) q^{48} +3.45603e6i q^{49} +(8.00562e6 + 4.03433e6i) q^{50} +2.06826e6 q^{51} +(3.47199e6 - 549910. i) q^{52} +(2.96871e6 - 5.82643e6i) q^{53} +(-2.23231e6 + 725322. i) q^{54} +(-2.07662e6 + 1.51582e6i) q^{55} +(158241. - 487017. i) q^{56} +(7.34164e6 - 7.34164e6i) q^{57} +(1.11995e7 - 5.70642e6i) q^{58} +(-1.37097e7 - 1.88698e7i) q^{59} +(-7.05732e6 - 3.57615e6i) q^{60} +(9.10341e6 + 6.61402e6i) q^{61} +(2.24875e6 - 1.41980e7i) q^{62} +(3.28215e6 + 519842. i) q^{63} +(-1.09584e7 + 1.50830e7i) q^{64} +(-3.66878e6 + 7.24013e6i) q^{65} +(3.57175e6 - 2.59503e6i) q^{66} +(2.91498e6 + 5.72097e6i) q^{67} +(-8.46507e6 - 8.46507e6i) q^{68} +(1.20581e7 + 3.91792e6i) q^{69} +(1.28496e7 + 1.76036e7i) q^{70} +(9.44467e6 + 2.90677e7i) q^{71} +(656715. + 334613. i) q^{72} +(-770966. - 4.86769e6i) q^{73} +1.49911e7i q^{74} +(1.62396e7 - 8.36566e6i) q^{75} -6.00963e7 q^{76} +(-6.17353e6 + 977791. i) q^{77} +(6.32764e6 - 1.24187e7i) q^{78} +(-1.68692e7 + 5.48113e6i) q^{79} +(-1.19709e7 - 3.65660e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-7.40576e7 + 7.40576e7i) q^{82} +(2.31829e7 - 1.18123e7i) q^{83} +(-1.13057e7 - 1.55610e7i) q^{84} +(2.72915e7 - 4.38477e6i) q^{85} +(-4.37258e6 - 3.17687e6i) q^{86} +(4.00681e6 - 2.52980e7i) q^{87} +(-1.36927e6 - 216872. i) q^{88} +(-3.50800e7 + 4.82834e7i) q^{89} +(-2.79185e7 + 1.43034e7i) q^{90} +(-1.59640e7 + 1.15986e7i) q^{91} +(-3.33165e7 - 6.53874e7i) q^{92} +(-2.07130e7 - 2.07130e7i) q^{93} +(-1.50549e8 - 4.89165e7i) q^{94} +(8.13112e7 - 1.12440e8i) q^{95} +(2.16636e7 + 6.66737e7i) q^{96} +(-6.00315e7 - 3.05876e7i) q^{97} +(-1.24075e7 - 7.83381e7i) q^{98} -8.99647e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−22.6671	+	3.59011i	−1.41669	+	0.224382i	−0.817364	−	0.576122i	$-0.804565\pi$
$2$	−22.6671	+	3.59011i	−1.41669	+	0.224382i	−0.599328	+	0.800504i	$0.704565\pi$
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$4$	257.437	−	83.6462i	1.00561	−	0.326743i
$5$	−191.814	+	594.838i	−0.306902	+	0.951741i
$5$	−191.814	+	594.838i	−0.306902	+	0.951741i
$6$	331.652	−	1020.72i	0.255904	−	0.787592i
$7$	−1074.42	+	1074.42i	−0.447490	+	0.447490i	−0.894519	−	0.447029i	$-0.852482\pi$
$7$	−1074.42	+	1074.42i	−0.447490	+	0.447490i	0.447029	+	0.894519i	$0.352482\pi$
$8$	−300.281	+	153.001i	−0.0733108	+	0.0373537i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	2212.32	−	14171.9i	0.221232	−	1.41719i
$11$	3327.98	+	2417.92i	0.227306	+	0.165147i	0.695609	−	0.718420i	$-0.255135\pi$
$11$	3327.98	+	2417.92i	0.227306	+	0.165147i	−0.468303	+	0.883568i	$0.655135\pi$
$12$	−1980.25	+	12502.8i	−0.0954984	+	0.602953i
$13$	12826.7	+	2031.55i	0.449098	+	0.0711302i	0.376887	−	0.926259i	$-0.376994\pi$
$13$	12826.7	+	2031.55i	0.449098	+	0.0711302i	0.0722112	+	0.997389i	$0.476994\pi$
$14$	20496.7	−	28211.3i	0.533547	−	0.734364i
$15$	−20713.5	−	20621.6i	−0.409155	−	0.407340i
$16$	−49803.9	+	36184.7i	−0.759947	+	0.552134i
$17$	−20078.4	−	39406.0i	−0.240399	−	0.471810i	0.739010	−	0.673694i	$-0.235293\pi$
$17$	−20078.4	−	39406.0i	−0.240399	−	0.471810i	−0.979409	+	0.201884i	$0.935293\pi$
$18$	35490.3	+	35490.3i	0.338080	+	0.338080i
$19$	−211149.	−	68606.6i	−1.62023	−	0.526443i	−0.648231	−	0.761444i	$-0.724491\pi$
$19$	−211149.	−	68606.6i	−1.62023	−	0.526443i	−0.971995	+	0.235001i	$0.924491\pi$
$20$	376.107	+	169178.i	0.00235067	+	1.05736i
$21$	−21958.2	−	67580.4i	−0.112907	−	0.347491i
$22$	−84116.2	−	42859.4i	−0.359078	−	0.182960i
$23$	−42411.3	−	267774.i	−0.151555	−	0.956880i	−0.939851	−	0.341584i	$-0.889037\pi$
$23$	−42411.3	−	267774.i	−0.151555	−	0.956880i	0.788296	−	0.615296i	$-0.210963\pi$
$24$		−	15760.6i		−	0.0475036i
$25$	−317040.	−	228196.i	−0.811622	−	0.584182i
$26$	−298037.			−0.652194
$27$	101017.	−	15999.5i	0.190081	−	0.0301058i
$28$	−186724.	+	366467.i	−0.303787	+	0.596215i
$29$	−520892.	+	169248.i	−0.736471	+	0.239294i	−0.653150	−	0.757229i	$-0.726553\pi$
$29$	−520892.	+	169248.i	−0.736471	+	0.239294i	−0.0833215	+	0.996523i	$0.526553\pi$
$30$	543547.	+	393067.i	0.671046	+	0.485268i
$31$	−193560.	+	595716.i	−0.209589	+	0.645048i	0.789905	+	0.613230i	$0.210130\pi$
$31$	−193560.	+	595716.i	−0.209589	+	0.645048i	−0.999494	+	0.0318189i	$0.989870\pi$
$32$	1.06001e6	−	1.06001e6i	1.01090	−	1.01090i
$33$	−171407.	+	87336.3i	−0.144535	+	0.0736443i
$34$	596590.	+	821135.i	0.446437	+	0.614468i
$35$	−433019.	−	845197.i	−0.288559	−	0.563230i
$36$	−478928.	−	347962.i	−0.285142	−	0.207167i
$37$	102186.	−	645174.i	0.0545233	−	0.344247i	−0.945313	−	0.326164i	$-0.894244\pi$
$37$	102186.	−	645174.i	0.0545233	−	0.344247i	0.999836	−	0.0180827i	$-0.00575622\pi$
$38$	5.03245e6	+	797061.i	2.41349	+	0.382259i
$39$	−356975.	+	491334.i	−0.154305	+	0.212382i
$40$	−33412.7	−	207966.i	−0.0130519	−	0.0812369i
$41$	3.69204e6	−	2.68243e6i	1.30657	−	0.949275i	0.306569	−	0.951849i	$-0.400819\pi$
$41$	3.69204e6	−	2.68243e6i	1.30657	−	0.949275i	0.999997	+	0.00257325i	$0.000819091\pi$
$42$	740350.	+	1.45302e6i	0.237925	+	0.466954i
$43$	166529.	+	166529.i	0.0487098	+	0.0487098i	0.731042	−	0.682332i	$-0.239034\pi$
$43$	166529.	+	166529.i	0.0487098	+	0.0487098i	−0.682332	+	0.731042i	$0.739034\pi$
$44$	1.05899e6	+	344088.i	0.282542	+	0.0918035i
$45$	1.29903e6	−	425277.i	0.316789	−	0.103710i
$46$	1.92268e6	+	5.91740e6i	0.429413	+	1.32160i
$47$	6.14580e6	+	3.13144e6i	1.25947	+	0.641731i	0.950908	−	0.309474i	$-0.100153\pi$
$47$	6.14580e6	+	3.13144e6i	1.25947	+	0.641731i	0.308560	+	0.951205i	$0.400153\pi$
$48$	−450363.	−	2.84348e6i	−0.0848394	−	0.535655i
$49$			3.45603e6i			0.599506i
$50$	8.00562e6	+	4.03433e6i	1.28090	+	0.645493i
$51$	2.06826e6			0.305721
$52$	3.47199e6	−	549910.i	0.474860	−	0.0752104i
$53$	2.96871e6	−	5.82643e6i	0.376240	−	0.738412i	−0.622793	−	0.782387i	$-0.714002\pi$
$53$	2.96871e6	−	5.82643e6i	0.376240	−	0.738412i	0.999033	+	0.0439747i	$0.0140021\pi$
$54$	−2.23231e6	+	725322.i	−0.262531	+	0.0853014i
$55$	−2.07662e6	+	1.51582e6i	−0.226938	+	0.165652i
$56$	158241.	−	487017.i	0.0160904	−	0.0495213i
$57$	7.34164e6	−	7.34164e6i	0.695494	−	0.695494i
$58$	1.11995e7	−	5.70642e6i	0.989660	−	0.504257i
$59$	−1.37097e7	−	1.88698e7i	−1.13141	−	1.55725i	−0.785360	−	0.619039i	$-0.787522\pi$
$59$	−1.37097e7	−	1.88698e7i	−1.13141	−	1.55725i	−0.346051	−	0.938216i	$-0.612478\pi$
$60$	−7.05732e6	−	3.57615e6i	−0.544546	−	0.275937i
$61$	9.10341e6	+	6.61402e6i	0.657484	+	0.477690i	0.865812	−	0.500369i	$-0.166802\pi$
$61$	9.10341e6	+	6.61402e6i	0.657484	+	0.477690i	−0.208329	+	0.978059i	$0.566802\pi$
$62$	2.24875e6	−	1.41980e7i	0.152186	−	0.960863i
$63$	3.28215e6	+	519842.i	0.208352	+	0.0329997i
$64$	−1.09584e7	+	1.50830e7i	−0.653174	+	0.899017i
$65$	−3.66878e6	+	7.24013e6i	−0.205527	+	0.405595i
$66$	3.57175e6	−	2.59503e6i	0.188237	−	0.136762i
$67$	2.91498e6	+	5.72097e6i	0.144656	+	0.283903i	0.951954	−	0.306240i	$-0.0990711\pi$
$67$	2.91498e6	+	5.72097e6i	0.144656	+	0.283903i	−0.807298	+	0.590144i	$0.799071\pi$
$68$	−8.46507e6	−	8.46507e6i	−0.395909	−	0.395909i
$69$	1.20581e7	+	3.91792e6i	0.531965	+	0.172846i
$70$	1.28496e7	+	1.76036e7i	0.535178	+	0.733176i
$71$	9.44467e6	+	2.90677e7i	0.371667	+	1.14387i	0.945700	+	0.325040i	$0.105378\pi$
$71$	9.44467e6	+	2.90677e7i	0.371667	+	1.14387i	−0.574034	+	0.818832i	$0.694622\pi$
$72$	656715.	+	334613.i	0.0244369	+	0.0124512i
$73$	−770966.	−	4.86769e6i	−0.0271484	−	0.171408i	0.970389	−	0.241548i	$-0.0776553\pi$
$73$	−770966.	−	4.86769e6i	−0.0271484	−	0.171408i	−0.997537	+	0.0701404i	$0.977655\pi$
$74$			1.49911e7i			0.499926i
$75$	1.62396e7	−	8.36566e6i	0.513252	−	0.264396i
$76$	−6.00963e7			−1.80133
$77$	−6.17353e6	+	977791.i	−0.175619	+	0.0278153i
$78$	6.32764e6	−	1.24187e7i	0.170948	−	0.335504i
$79$	−1.68692e7	+	5.48113e6i	−0.433098	+	0.140722i	−0.517449	−	0.855714i	$-0.673118\pi$
$79$	−1.68692e7	+	5.48113e6i	−0.433098	+	0.140722i	0.0843512	+	0.996436i	$0.473118\pi$
$80$	−1.19709e7	−	3.65660e7i	−0.292259	−	0.892724i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	−7.40576e7	+	7.40576e7i	−1.63800	+	1.63800i
$83$	2.31829e7	−	1.18123e7i	0.488489	−	0.248898i	−0.192356	−	0.981325i	$-0.561613\pi$
$83$	2.31829e7	−	1.18123e7i	0.488489	−	0.248898i	0.680845	+	0.732428i	$0.261613\pi$
$84$	−1.13057e7	−	1.55610e7i	−0.227081	−	0.312550i
$85$	2.72915e7	−	4.38477e6i	0.522820	−	0.0839984i
$86$	−4.37258e6	−	3.17687e6i	−0.0799363	−	0.0580771i
$87$	4.00681e6	−	2.52980e7i	0.0699393	−	0.441579i
$88$	−1.36927e6	−	216872.i	−0.0228328	−	0.00361637i
$89$	−3.50800e7	+	4.82834e7i	−0.559112	+	0.769552i	−0.991213	−	0.132273i	$-0.957772\pi$
$89$	−3.50800e7	+	4.82834e7i	−0.559112	+	0.769552i	0.432101	+	0.901825i	$0.357772\pi$
$90$	−2.79185e7	+	1.43034e7i	−0.425522	+	0.218007i
$91$	−1.59640e7	+	1.15986e7i	−0.232797	+	0.169137i
$92$	−3.33165e7	−	6.53874e7i	−0.465060	−	0.912731i
$93$	−2.07130e7	−	2.07130e7i	−0.276892	−	0.276892i
$94$	−1.50549e8	−	4.89165e7i	−1.92827	−	0.626533i
$95$	8.13112e7	−	1.12440e8i	0.998288	−	1.38047i
$96$	2.16636e7	+	6.66737e7i	0.255062	+	0.785000i
$97$	−6.00315e7	−	3.05876e7i	−0.678098	−	0.345508i	0.0807883	−	0.996731i	$-0.474256\pi$
$97$	−6.00315e7	−	3.05876e7i	−0.678098	−	0.345508i	−0.758886	+	0.651223i	$0.774256\pi$
$98$	−1.24075e7	−	7.83381e7i	−0.134518	−	0.849315i
$99$		−	8.99647e6i		−	0.0936551i
$100$	−1.00705e8	−	3.22269e7i	−1.00705	−	0.322269i
$101$	−8.79065e6			−0.0844764			−0.0422382	−	0.999108i	$-0.513449\pi$
$101$	−8.79065e6			−0.0844764			−0.0422382	+	0.999108i	$0.513449\pi$
$102$	−4.68815e7	+	7.42530e6i	−0.433113	+	0.0685983i
$103$	−1.20524e7	+	2.36542e7i	−0.107084	+	0.210165i	−0.938330	−	0.345740i	$-0.887628\pi$
$103$	−1.20524e7	+	2.36542e7i	−0.107084	+	0.210165i	0.831246	+	0.555905i	$0.187628\pi$
$104$	−4.16244e6	+	1.35246e6i	−0.0355808	+	0.0115609i
$105$	4.44113e7	−	98733.1i	0.365373	−	0.000812279i
$106$	−4.63745e7	+	1.42726e8i	−0.367329	+	1.13052i
$107$	8.12257e7	−	8.12257e7i	0.619667	−	0.619667i	−0.325779	−	0.945446i	$-0.605627\pi$
$107$	8.12257e7	−	8.12257e7i	0.619667	−	0.619667i	0.945446	+	0.325779i	$0.105627\pi$
$108$	2.46671e7	−	1.25685e7i	0.181311	−	0.0923823i
$109$	7.41617e7	+	1.02075e8i	0.525380	+	0.723124i	0.986418	−	0.164257i	$-0.0525226\pi$
$109$	7.41617e7	+	1.02075e8i	0.525380	+	0.723124i	−0.461037	+	0.887381i	$0.652523\pi$
$110$	4.16290e7	−	4.18145e7i	0.284332	−	0.285599i
$111$	2.47138e7	+	1.79556e7i	0.162797	+	0.118279i
$112$	1.46328e7	−	9.23881e7i	0.0929943	−	0.587143i
$113$	2.90228e8	+	4.59675e7i	1.78002	+	0.281928i	0.957841	−	0.287300i	$-0.0927578\pi$
$113$	2.90228e8	+	4.59675e7i	1.78002	+	0.281928i	0.822180	+	0.569228i	$0.192758\pi$
$114$	−1.40056e8	+	1.92771e8i	−0.829245	+	1.14136i
$115$	1.67417e8	+	2.61349e7i	0.957215	+	0.149427i
$116$	−1.19940e8	+	8.71413e7i	−0.662417	+	0.481274i
$117$	−1.28941e7	−	2.53061e7i	−0.0688093	−	0.135046i
$118$	3.78504e8	+	3.78504e8i	1.95228	+	1.95228i
$119$	6.39114e7	+	2.07661e7i	0.318706	+	0.103554i
$120$	9.37498e6	+	3.02309e6i	0.0452111	+	0.0145789i
$121$	−6.10114e7	−	1.87774e8i	−0.284623	−	0.875979i
$122$	−2.30093e8	−	1.17238e8i	−1.03864	−	0.529212i
$123$	3.33861e7	+	2.10792e8i	0.145863	+	0.920943i
$124$			1.69550e8i			0.717150i
$125$	1.96552e8	−	1.44816e8i	0.805079	−	0.593168i
$126$	−7.62631e7			−0.302575
$127$	−2.54128e8	+	4.02499e7i	−0.976871	+	0.154721i	−0.624403	−	0.781103i	$-0.714657\pi$
$127$	−2.54128e8	+	4.02499e7i	−0.976871	+	0.154721i	−0.352468	+	0.935824i	$0.614657\pi$
$128$	2.00211e7	−	3.92937e7i	0.0745846	−	0.146380i
$129$	−1.04746e7	+	3.40339e6i	−0.0378248	+	0.0122900i
$130$	5.71676e7	−	1.77284e8i	0.200160	−	0.620720i
$131$	2.91846e6	−	8.98211e6i	0.00990990	−	0.0304995i	−0.945979	−	0.324227i	$-0.894896\pi$
$131$	2.91846e6	−	8.98211e6i	0.00990990	−	0.0304995i	0.955889	+	0.293727i	$0.0948958\pi$
$132$	−3.68211e7	+	3.68211e7i	−0.121283	+	0.121283i
$133$	3.00576e8	−	1.53151e8i	0.960613	−	0.489457i
$134$	−8.66130e7	−	1.19213e8i	−0.268636	−	0.369745i
$135$	−9.85929e6	+	6.31575e7i	−0.0296832	+	0.190147i
$136$	1.20583e7	+	8.76088e6i	0.0352477	+	0.0256090i
$137$	5.77238e7	−	3.64454e8i	0.163860	−	1.03457i	−0.759464	−	0.650549i	$-0.774539\pi$
$137$	5.77238e7	−	3.64454e8i	0.163860	−	1.03457i	0.923324	−	0.384021i	$-0.125461\pi$
$138$	−2.87388e8	−	4.55178e7i	−0.792415	−	0.125506i
$139$	−5.82977e7	+	8.02399e7i	−0.156168	+	0.214947i	−0.879931	−	0.475102i	$-0.842411\pi$
$139$	−5.82977e7	+	8.02399e7i	−0.156168	+	0.214947i	0.723763	+	0.690049i	$0.242411\pi$
$140$	−1.82172e8	−	1.81364e8i	−0.474210	−	0.472106i
$141$	−2.60963e8	+	1.89601e8i	−0.660242	+	0.479694i
$142$	−3.18439e8	−	6.24972e8i	−0.783201	−	1.53712i
$143$	3.77749e7	+	3.77749e7i	0.0903357	+	0.0903357i
$144$	1.28044e8	+	4.16042e7i	0.297791	+	0.0967580i
$145$	−761008.	−	3.42311e8i	−0.00172154	−	0.774370i
$146$	3.49511e7	+	1.07568e8i	0.0769217	+	0.236741i
$147$	−1.44007e8	−	7.33751e7i	−0.308399	−	0.157137i
$148$	−2.76601e7	−	1.74639e8i	−0.0576510	−	0.363994i
$149$			6.98684e8i			1.41754i	0.705439	+	0.708770i	$0.250750\pi$
$149$			6.98684e8i			1.41754i	−0.705439	+	0.708770i	$0.749250\pi$
$150$	−3.38071e8	+	2.47927e8i	−0.667795	+	0.489733i
$151$	4.41413e8			0.849059			0.424529	−	0.905414i	$-0.360440\pi$
$151$	4.41413e8			0.849059			0.424529	+	0.905414i	$0.360440\pi$
$152$	7.39011e7	−	1.17048e7i	0.138445	−	0.0219275i
$153$	−4.39114e7	+	8.61810e7i	−0.0801330	+	0.157270i
$154$	1.36426e8	−	4.43273e7i	0.242556	−	0.0788113i
$155$	−3.17227e8	−	2.29403e8i	−0.549596	−	0.397441i
$156$	−5.08002e7	+	1.56347e8i	−0.0857763	+	0.263992i
$157$	−1.63111e8	+	1.63111e8i	−0.268464	+	0.268464i	−0.828481	−	0.560017i	$-0.810795\pi$
$157$	−1.63111e8	+	1.63111e8i	−0.268464	+	0.268464i	0.560017	+	0.828481i	$0.310795\pi$
$158$	3.62697e8	−	1.84803e8i	0.581991	−	0.296539i
$159$	1.79748e8	+	2.47402e8i	0.281239	+	0.387093i
$160$	4.27209e8	+	8.33857e8i	0.651869	+	1.27236i
$161$	3.33271e8	+	2.42135e8i	0.496013	+	0.360375i
$162$	1.71714e7	−	1.08416e8i	0.0249313	−	0.157410i
$163$	1.03380e9	+	1.63737e8i	1.46448	+	0.231951i	0.837225	−	0.546859i	$-0.184177\pi$
$163$	1.03380e9	+	1.63737e8i	1.46448	+	0.231951i	0.627259	+	0.778811i	$0.284177\pi$
$164$	7.26092e8	−	9.99380e8i	1.00373	−	1.38151i
$165$	−1.90727e7	−	1.18712e8i	−0.0257322	−	0.160161i
$166$	−4.83080e8	+	3.50978e8i	−0.636190	+	0.462219i
$167$	−1.27575e8	−	2.50380e8i	−0.164021	−	0.321909i	0.794338	−	0.607476i	$-0.207818\pi$
$167$	−1.27575e8	−	2.50380e8i	−0.164021	−	0.321909i	−0.958359	+	0.285567i	$0.907818\pi$
$168$	1.69335e7	+	1.69335e7i	0.0212574	+	0.0212574i
$169$	−6.15409e8	−	1.99959e8i	−0.754427	−	0.245128i
$170$	−6.02877e8	+	1.97369e8i	−0.721827	+	0.236311i
$171$	1.50043e8	+	4.61784e8i	0.175481	+	0.540075i
$172$	5.68002e7	+	2.89411e7i	0.0648987	+	0.0330675i
$173$	7.35865e6	+	4.64607e7i	0.00821512	+	0.0518682i	0.991455	−	0.130446i	$-0.0416411\pi$
$173$	7.35865e6	+	4.64607e7i	0.00821512	+	0.0518682i	−0.983240	+	0.182315i	$0.941641\pi$
$174$			5.87816e8i			0.641275i
$175$	5.85814e8	−	9.54558e7i	0.624608	−	0.101777i
$176$	−2.53238e8			−0.263924
$177$	1.07734e9	−	1.70634e8i	1.09764	−	0.173850i
$178$	6.21817e8	−	1.22038e9i	0.619416	−	1.21567i
$179$	8.94175e8	−	2.90535e8i	0.870985	−	0.283000i	0.160776	−	0.986991i	$-0.448600\pi$
$179$	8.94175e8	−	2.90535e8i	0.870985	−	0.283000i	0.710209	+	0.703991i	$0.248600\pi$
$180$	2.98846e8	−	2.18141e8i	0.284680	−	0.207801i
$181$	4.41585e8	−	1.35906e9i	0.411434	−	1.26626i	−0.503968	−	0.863722i	$-0.668127\pi$
$181$	4.41585e8	−	1.35906e9i	0.411434	−	1.26626i	0.915402	−	0.402541i	$-0.131873\pi$
$182$	3.20218e8	−	3.20218e8i	0.291850	−	0.291850i
$183$	−4.68869e8	+	2.38901e8i	−0.418069	+	0.213017i
$184$	5.37050e7	+	7.39186e7i	0.0468537	+	0.0644885i
$185$	3.64174e8	+	1.84537e8i	0.310901	+	0.157542i
$186$	5.43864e8	+	3.95140e8i	0.454400	+	0.330141i
$187$	2.84602e7	−	1.79691e8i	0.0232740	−	0.146946i
$188$	1.84409e9	+	2.92075e8i	1.47622	+	0.233810i
$189$	−9.13445e7	+	1.25725e8i	−0.0715871	+	0.0985312i
$190$	−1.43941e9	+	2.84060e9i	−1.10451	+	2.17970i
$191$	−1.69997e9	+	1.23510e9i	−1.27734	+	0.928043i	−0.999469	−	0.0325746i	$-0.989629\pi$
$191$	−1.69997e9	+	1.23510e9i	−1.27734	+	0.928043i	−0.277873	+	0.960618i	$0.589629\pi$
$192$	−3.95823e8	−	7.76847e8i	−0.291271	−	0.571651i
$193$	−9.02746e8	−	9.02746e8i	−0.650634	−	0.650634i	0.302512	−	0.953146i	$-0.402175\pi$
$193$	−9.02746e8	−	9.02746e8i	−0.650634	−	0.650634i	−0.953146	+	0.302512i	$0.902175\pi$
$194$	1.47055e9	+	4.77811e8i	1.03818	+	0.337326i
$195$	−2.23792e8	−	3.06587e8i	−0.154777	−	0.212039i
$196$	2.89084e8	+	8.89709e8i	0.195884	+	0.602870i
$197$	−8.63067e8	−	4.39754e8i	−0.573033	−	0.291975i	0.143362	−	0.989670i	$-0.454209\pi$
$197$	−8.63067e8	−	4.39754e8i	−0.573033	−	0.291975i	−0.716394	+	0.697696i	$0.754209\pi$
$198$	3.22983e7	+	2.03924e8i	0.0210145	+	0.132680i
$199$		−	1.01112e9i		−	0.644746i	−0.946613	−	0.322373i	$-0.895519\pi$
$199$		−	1.01112e9i		−	0.644746i	0.946613	−	0.322373i	$-0.104481\pi$
$200$	1.30115e8	+	2.00156e7i	0.0813221	+	0.0125098i
$201$	−3.00271e8			−0.183962
$202$	1.99258e8	−	3.15594e7i	0.119677	−	0.0189550i
$203$	3.77814e8	−	7.41503e8i	0.222482	−	0.436645i
$204$	5.32447e8	−	1.73003e8i	0.307437	−	0.0998923i
$205$	8.87425e8	+	2.71069e9i	0.502477	+	1.53485i
$206$	1.88272e8	−	5.79442e8i	0.104548	−	0.321767i
$207$	−4.19259e8	+	4.19259e8i	−0.228350	+	0.228350i
$208$	−7.12331e8	+	3.62951e8i	−0.380564	+	0.193907i
$209$	−5.36816e8	−	7.38865e8i	−0.281346	−	0.387240i
$210$	−1.00632e9	+	1.61680e8i	−0.517439	+	0.0831339i
$211$	−3.81379e7	−	2.77088e7i	−0.0192410	−	0.0139794i	0.578123	−	0.815949i	$-0.303785\pi$
$211$	−3.81379e7	−	2.77088e7i	−0.0192410	−	0.0139794i	−0.597364	+	0.801970i	$0.703785\pi$
$212$	2.76897e8	−	1.74826e9i	0.137080	−	0.865490i
$213$	−1.41172e9	−	2.23595e8i	−0.685852	−	0.108628i
$214$	−1.54954e9	+	2.13276e9i	−0.738835	+	1.01692i
$215$	−1.31000e8	+	6.71153e7i	−0.0613082	+	0.0314100i
$216$	−2.78855e7	+	2.02600e7i	−0.0128104	+	0.00930731i
$217$	−4.32086e8	−	8.48016e8i	−0.194864	−	0.382442i
$218$	−2.04749e9	−	2.04749e9i	−0.906558	−	0.906558i
$219$	2.19196e8	+	7.12212e7i	0.0952921	+	0.0309623i
$220$	−4.07807e8	+	5.63930e8i	−0.174086	+	0.240732i
$221$	−1.77484e8	−	5.46239e8i	−0.0744029	−	0.228989i
$222$	−6.24651e8	−	3.18276e8i	−0.257173	−	0.131036i
$223$	−4.72419e6	−	2.98274e7i	−0.00191033	−	0.0120613i	0.986715	−	0.162462i	$-0.0519436\pi$
$223$	−4.72419e6	−	2.98274e7i	−0.00191033	−	0.0120613i	−0.988625	+	0.150401i	$0.951944\pi$
$224$			2.27779e9i			0.904737i
$225$	3.79844e6	+	8.54288e8i	0.00148209	+	0.333330i
$226$	−6.74364e9			−2.58500
$227$	2.84916e9	−	4.51263e8i	1.07303	−	0.169952i	0.405175	−	0.914239i	$-0.367211\pi$
$227$	2.84916e9	−	4.51263e8i	1.07303	−	0.169952i	0.667859	+	0.744287i	$0.267211\pi$
$228$	1.27591e9	−	2.50411e9i	0.472149	−	0.926646i
$229$	1.43417e7	−	4.65990e6i	0.00521505	−	0.00169447i	−0.306408	−	0.951900i	$-0.599127\pi$
$229$	1.43417e7	−	4.65990e6i	0.00521505	−	0.00169447i	0.311623	+	0.950206i	$0.399127\pi$
$230$	−3.88869e9	+	8.64515e6i	−1.38961	+	0.00308931i
$231$	9.03276e7	−	2.78000e8i	0.0317229	−	0.0976330i
$232$	1.30519e8	−	1.30519e8i	0.0450528	−	0.0450528i
$233$	3.58702e8	−	1.82768e8i	0.121705	−	0.0620120i	−0.392078	−	0.919932i	$-0.628244\pi$
$233$	3.58702e8	−	1.82768e8i	0.121705	−	0.0620120i	0.513783	+	0.857920i	$0.328244\pi$
$234$	3.83123e8	+	5.27323e8i	0.127783	+	0.175879i
$235$	−3.04155e9	+	3.05510e9i	−0.997294	+	1.00174i
$236$	−5.10777e9	−	3.71102e9i	−1.64658	−	1.19631i
$237$	1.29761e8	−	8.19280e8i	0.0411293	−	0.259680i
$238$	−1.52324e9	−	2.41257e8i	−0.474744	−	0.0751921i
$239$	2.12127e9	−	2.91968e9i	0.650137	−	0.894837i	−0.348968	−	0.937135i	$-0.613468\pi$
$239$	2.12127e9	−	2.91968e9i	0.650137	−	0.894837i	0.999105	+	0.0422975i	$0.0134677\pi$
$240$	1.77780e9	+	2.77525e8i	0.535842	+	0.0836484i
$241$	3.58553e9	−	2.60504e9i	1.06288	−	0.772229i	0.0882623	−	0.996097i	$-0.471869\pi$
$241$	3.58553e9	−	2.60504e9i	1.06288	−	0.772229i	0.974619	+	0.223869i	$0.0718686\pi$
$242$	2.05708e9	+	4.03724e9i	0.599776	+	1.17713i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	2.89679e9	+	9.41224e8i	0.817255	+	0.265542i
$245$	−2.05578e9	−	6.62914e8i	−0.570574	−	0.183989i
$246$	−1.51353e9	−	4.65817e9i	−0.413286	−	1.27196i
$247$	−2.56897e9	−	1.30896e9i	−0.690195	−	0.351672i
$248$	−3.30227e7	−	2.08497e8i	−0.00872983	−	0.0551180i
$249$			1.21678e9i			0.316529i
$250$	−3.93536e9	+	3.98821e9i	−1.00745	+	1.02098i
$251$	−5.95004e9			−1.49908			−0.749540	−	0.661959i	$-0.769725\pi$
$251$	−5.95004e9			−1.49908			−0.749540	+	0.661959i	$0.769725\pi$
$252$	8.88430e8	−	1.40713e8i	0.220303	−	0.0348926i
$253$	5.06313e8	−	9.93696e8i	0.123577	−	0.242533i
$254$	5.61583e9	−	1.82469e9i	1.34921	−	0.438384i
$255$	−3.96721e8	+	1.23028e9i	−0.0938264	+	0.290967i
$256$	1.16211e9	−	3.57662e9i	0.270576	−	0.832747i
$257$	−4.38481e9	+	4.38481e9i	−1.00512	+	1.00512i	−0.00513428	+	0.999987i	$0.501634\pi$
$257$	−4.38481e9	+	4.38481e9i	−1.00512	+	1.00512i	−0.999987	+	0.00513428i	$0.998366\pi$
$258$	2.25209e8	−	1.14750e8i	0.0508284	−	0.0258984i
$259$	5.83399e8	+	8.02980e8i	0.129648	+	0.178446i
$260$	−3.38869e8	+	2.17075e9i	−0.0741546	+	0.475026i
$261$	9.69054e8	+	7.04059e8i	0.208827	+	0.151721i
$262$	−3.39063e7	+	2.14076e8i	−0.00719573	+	0.0454320i
$263$	4.98905e9	+	7.90188e8i	1.04279	+	0.165161i	0.654254	−	0.756275i	$-0.272983\pi$
$263$	4.98905e9	+	7.90188e8i	1.04279	+	0.165161i	0.388531	+	0.921436i	$0.372983\pi$
$264$	3.81078e7	−	5.24509e7i	0.00784509	−	0.0107978i
$265$	2.89634e9	+	2.88349e9i	0.587308	+	0.584703i
$266$	−6.26336e9	+	4.55059e9i	−1.25107	+	0.908953i
$267$	−1.26710e9	−	2.48683e9i	−0.249325	−	0.489329i
$268$	1.22896e9	+	1.22896e9i	0.238231	+	0.238231i
$269$	6.58182e9	+	2.13856e9i	1.25700	+	0.408426i	0.860426	−	0.509575i	$-0.170197\pi$
$269$	6.58182e9	+	2.13856e9i	1.25700	+	0.408426i	0.396578	+	0.918001i	$0.370197\pi$
$270$	−3.26134e6	−	1.46699e9i	−0.000613679	−	0.276040i
$271$	−2.46262e9	−	7.57917e9i	−0.456584	−	1.40522i	−0.869266	−	0.494345i	$-0.835408\pi$
$271$	−2.46262e9	−	7.57917e9i	−0.456584	−	1.40522i	0.412682	−	0.910875i	$-0.364592\pi$
$272$	2.42587e9	+	1.23604e9i	0.443193	+	0.225818i
$273$	−1.44358e8	−	9.11443e8i	−0.0259891	−	0.164089i
$274$			8.46833e9i			1.50243i
$275$	−5.03343e8	−	1.52601e9i	−0.0880103	−	0.266825i
$276$	3.43192e9			0.591427
$277$	7.12412e9	−	1.12835e9i	1.21007	−	0.191657i	0.481390	−	0.876507i	$-0.340132\pi$
$277$	7.12412e9	−	1.12835e9i	1.21007	−	0.191657i	0.728684	+	0.684850i	$0.240132\pi$
$278$	1.03337e9	−	2.02810e9i	0.173012	−	0.339555i
$279$	1.30283e9	−	4.23315e8i	0.215016	−	0.0698630i
$280$	2.59343e8	+	1.87544e8i	0.0421932	+	0.0305121i
$281$	1.16330e9	−	3.58027e9i	0.186580	−	0.574236i	−0.813392	−	0.581717i	$-0.802381\pi$
$281$	1.16330e9	−	3.58027e9i	0.186580	−	0.574236i	0.999972	+	0.00748101i	$0.00238130\pi$
$282$	5.23459e9	−	5.23459e9i	0.827725	−	0.827725i
$283$	−3.37813e9	+	1.72124e9i	−0.526661	+	0.268347i	−0.697041	−	0.717031i	$-0.745500\pi$
$283$	−3.37813e9	+	1.72124e9i	−0.526661	+	0.268347i	0.170380	+	0.985378i	$0.445500\pi$
$284$	4.86281e9	+	6.69308e9i	0.747505	+	1.02885i
$285$	2.95886e9	+	5.77531e9i	0.448482	+	0.875379i
$286$	−9.91863e8	−	7.20630e8i	−0.148248	−	0.107708i
$287$	−1.08476e9	+	6.84887e9i	−0.159884	+	1.00947i
$288$	−3.23812e9	−	5.12868e8i	−0.470677	−	0.0745479i
$289$	2.95055e9	−	4.06109e9i	0.422973	−	0.582172i
$290$	1.24618e9	+	7.75645e9i	0.176194	+	1.09666i
$291$	2.54906e9	−	1.85200e9i	0.355475	−	0.258267i
$292$	−6.05638e8	−	1.18863e9i	−0.0833071	−	0.163499i
$293$	6.61627e9	+	6.61627e9i	0.897724	+	0.897724i	0.995235	−	0.0975103i	$-0.0310879\pi$
$293$	6.61627e9	+	6.61627e9i	0.897724	+	0.897724i	−0.0975103	+	0.995235i	$0.531088\pi$
$294$	3.52764e9	+	1.14620e9i	0.472166	+	0.153416i
$295$	1.38542e10	−	4.53558e9i	1.82934	−	0.598887i
$296$	6.80278e7	+	2.09368e8i	0.00886175	+	0.0272737i
$297$	3.74867e8	+	1.91004e8i	0.0481783	+	0.0245481i
$298$	−2.50835e9	−	1.58371e10i	−0.318071	−	2.00822i
$299$		−	3.52082e9i		−	0.440513i
$300$	3.48092e9	−	3.51201e9i	0.429743	−	0.433582i
$301$	−3.57845e8			−0.0435942
$302$	−1.00055e10	+	1.58472e9i	−1.20285	+	0.190513i
$303$	1.86635e8	−	3.66291e8i	0.0221422	−	0.0434566i
$304$	1.29986e10	−	4.22349e9i	1.52195	−	0.494513i
$305$	−5.68043e9	+	4.14640e9i	−0.656420	+	0.479150i
$306$	6.85943e8	−	2.11112e9i	0.0782353	−	0.240783i
$307$	5.80489e9	−	5.80489e9i	0.653493	−	0.653493i	−0.300340	−	0.953832i	$-0.597100\pi$
$307$	5.80489e9	−	5.80489e9i	0.653493	−	0.653493i	0.953832	+	0.300340i	$0.0971000\pi$
$308$	−1.50751e9	+	7.68112e8i	−0.167516	+	0.0853536i
$309$	−7.29745e8	−	1.00441e9i	−0.0800456	−	0.110173i
$310$	8.01419e9	+	4.06102e9i	0.867787	+	0.439732i
$311$	6.79126e9	+	4.93414e9i	0.725954	+	0.527436i	0.888281	−	0.459301i	$-0.151900\pi$
$311$	6.79126e9	+	4.93414e9i	0.725954	+	0.527436i	−0.162327	+	0.986737i	$0.551900\pi$
$312$	3.20184e7	−	2.02156e8i	0.00337894	−	0.0213338i
$313$	1.46143e10	+	2.31468e9i	1.52265	+	0.241165i	0.860984	−	0.508631i	$-0.169848\pi$
$313$	1.46143e10	+	2.31468e9i	1.52265	+	0.241165i	0.661669	+	0.749796i	$0.269848\pi$
$314$	3.11167e9	−	4.28285e9i	0.320092	−	0.440569i
$315$	−9.38784e8	+	1.85264e9i	−0.0953506	+	0.188169i
$316$	−3.88427e9	+	2.82209e9i	−0.389548	+	0.283023i
$317$	3.56134e9	+	6.98952e9i	0.352676	+	0.692166i	0.997386	−	0.0722619i	$-0.0230217\pi$
$317$	3.56134e9	+	6.98952e9i	0.352676	+	0.692166i	−0.644710	+	0.764428i	$0.723022\pi$
$318$	−4.96256e9	−	4.96256e9i	−0.485286	−	0.485286i
$319$	−2.14275e9	−	6.96221e8i	−0.206923	−	0.0672333i
$320$	−6.86997e9	−	9.41163e9i	−0.655171	−	0.897563i
$321$	1.66003e9	+	5.10904e9i	0.156349	+	0.481192i
$322$	−8.42356e9	−	4.29202e9i	−0.783560	−	0.399244i
$323$	1.53602e9	+	9.69807e9i	0.141120	+	0.890995i
$324$			1.29468e9i			0.117485i
$325$	−3.60298e9	−	3.57109e9i	−0.322945	−	0.320086i
$326$	−2.40210e10			−2.12677
$327$	−5.82781e9	+	9.23034e8i	−0.509700	+	0.0807285i
$328$	−6.98237e8	+	1.37037e9i	−0.0603264	+	0.118397i
$329$	−9.96768e9	+	3.23870e9i	−0.850767	+	0.276431i
$330$	8.58511e8	+	2.62237e9i	0.0723919	+	0.221126i
$331$	−2.08137e9	+	6.40581e9i	−0.173396	+	0.533657i	−0.999557	−	0.0297775i	$-0.990520\pi$
$331$	−2.08137e9	+	6.40581e9i	−0.173396	+	0.533657i	0.826161	+	0.563434i	$0.190520\pi$
$332$	4.98007e9	−	4.98007e9i	0.409905	−	0.409905i
$333$	−1.27288e9	+	6.48563e8i	−0.103517	+	0.0527443i
$334$	3.79064e9	+	5.21737e9i	0.304598	+	0.419243i
$335$	−3.96218e9	+	6.36581e8i	−0.314598	+	0.0505446i
$336$	3.53898e9	+	2.57122e9i	0.277665	+	0.201735i
$337$	3.16957e9	−	2.00119e10i	0.245743	−	1.55156i	−0.488434	−	0.872601i	$-0.662432\pi$
$337$	3.16957e9	−	2.00119e10i	0.245743	−	1.55156i	0.734177	−	0.678959i	$-0.237568\pi$
$338$	1.46674e10	+	2.32309e9i	1.12379	+	0.177991i
$339$	−8.07722e9	+	1.11173e10i	−0.611594	+	0.841787i
$340$	6.65907e9	−	3.41163e9i	0.498308	−	0.255298i
$341$	−2.08456e9	+	1.51452e9i	−0.154169	+	0.112010i
$342$	−5.05888e9	−	9.92862e9i	−0.369786	−	0.725746i
$343$	−9.90707e9	−	9.90707e9i	−0.715763	−	0.715763i
$344$	−7.54846e7	−	2.45264e7i	−0.00539045	−	0.00175146i
$345$	−4.64344e9	+	6.42112e9i	−0.327766	+	0.453247i
$346$	−3.33598e8	−	1.02671e9i	−0.0232766	−	0.0716380i
$347$	−2.01437e10	−	1.02637e10i	−1.38938	−	0.707925i	−0.410406	−	0.911903i	$-0.634613\pi$
$347$	−2.01437e10	−	1.02637e10i	−1.38938	−	0.707925i	−0.978976	+	0.203977i	$0.934613\pi$
$348$	−1.08458e9	−	6.84778e9i	−0.0739512	−	0.466910i
$349$		−	1.30747e10i		−	0.881312i	−0.897676	−	0.440656i	$-0.854746\pi$
$349$		−	1.30747e10i		−	0.881312i	0.897676	−	0.440656i	$-0.145254\pi$
$350$	−1.29360e10	+	4.26684e9i	−0.862041	+	0.284338i
$351$	1.32821e9			0.0875064
$352$	6.09070e9	−	9.64672e8i	0.396732	−	0.0628361i
$353$	9.91024e9	−	1.94499e10i	0.638242	−	1.25262i	−0.314620	−	0.949218i	$-0.601877\pi$
$353$	9.91024e9	−	1.94499e10i	0.638242	−	1.25262i	0.952862	−	0.303403i	$-0.0981228\pi$
$354$	−2.38076e10	+	7.73557e9i	−1.51601	+	0.492583i
$355$	−1.91022e10	+	4.24671e7i	−1.20274	+	0.00267386i
$356$	−4.99214e9	+	1.53642e10i	−0.310804	+	0.956557i
$357$	−2.22219e9	+	2.22219e9i	−0.136807	+	0.136807i
$358$	−1.92253e10	+	9.79577e9i	−1.17042	+	0.596357i
$359$	−1.37681e10	−	1.89502e10i	−0.828891	−	1.14087i	−0.988128	−	0.153631i	$-0.950903\pi$
$359$	−1.37681e10	−	1.89502e10i	−0.828891	−	1.14087i	0.159237	−	0.987240i	$-0.449097\pi$
$360$	−3.25007e8	+	3.26456e8i	−0.0193501	+	0.0194363i
$361$	2.61372e10	+	1.89898e10i	1.53897	+	1.11813i
$362$	−5.13027e9	+	3.23912e10i	−0.298748	+	1.88622i
$363$	9.11954e9	+	1.44439e9i	0.525226	+	0.0831877i
$364$	−3.13955e9	+	4.32123e9i	−0.178839	+	0.246151i
$365$	3.04337e9	+	4.75089e8i	0.171468	+	0.0267672i
$366$	9.77021e9	−	7.09848e9i	0.544477	−	0.395586i
$367$	−6.39971e9	−	1.25601e10i	−0.352774	−	0.692357i	0.644621	−	0.764503i	$-0.277015\pi$
$367$	−6.39971e9	−	1.25601e10i	−0.352774	−	0.692357i	−0.997394	+	0.0721456i	$0.977015\pi$
$368$	1.18016e10	+	1.18016e10i	0.643500	+	0.643500i
$369$	−9.49214e9	−	3.08418e9i	−0.511987	−	0.166355i
$370$	−8.91726e9	−	2.87549e9i	−0.475800	−	0.153428i
$371$	3.07039e9	+	9.44970e9i	0.162068	+	0.498795i
$372$	−7.06484e9	−	3.59971e9i	−0.368918	−	0.187973i
$373$	3.48540e9	+	2.20059e10i	0.180060	+	1.13685i	0.897755	+	0.440495i	$0.145197\pi$
$373$	3.48540e9	+	2.20059e10i	0.180060	+	1.13685i	−0.717695	+	0.696358i	$0.754803\pi$
$374$			4.17523e9i			0.213400i
$375$	1.86123e9	+	1.12646e10i	0.0941186	+	0.569627i
$376$	−2.32458e9			−0.116304
$377$	−7.02516e9	+	1.11268e9i	−0.347769	+	0.0550812i
$378$	1.61914e9	−	3.17775e9i	0.0793083	−	0.155651i
$379$	−3.64574e10	+	1.18457e10i	−1.76697	+	0.574123i	−0.997884	−	0.0650234i	$-0.979288\pi$
$379$	−3.64574e10	+	1.18457e10i	−1.76697	+	0.574123i	−0.769085	+	0.639146i	$0.779288\pi$
$380$	1.15273e10	−	3.57476e10i	0.552832	−	1.71440i
$381$	3.71825e9	−	1.14436e10i	0.176457	−	0.543079i
$382$	3.40991e10	−	3.40991e10i	1.60136	−	1.60136i
$383$	1.43541e10	−	7.31378e9i	0.667084	−	0.339896i	−0.0874388	−	0.996170i	$-0.527868\pi$
$383$	1.43541e10	−	7.31378e9i	0.667084	−	0.339896i	0.754523	+	0.656273i	$0.227868\pi$
$384$	1.21223e9	+	1.66849e9i	0.0557520	+	0.0767360i
$385$	6.02540e8	−	3.85981e9i	0.0274248	−	0.175680i
$386$	2.37036e10	+	1.72217e10i	1.06774	+	0.775757i
$387$	8.05724e7	−	5.08714e8i	0.00359205	−	0.0226793i
$388$	−1.80129e10	−	2.85296e9i	−0.794796	−	0.125883i
$389$	8.37069e9	−	1.15213e10i	0.365563	−	0.503155i	−0.586125	−	0.810221i	$-0.699347\pi$
$389$	8.37069e9	−	1.15213e10i	0.365563	−	0.503155i	0.951688	+	0.307066i	$0.0993472\pi$
$390$	6.17338e9	+	6.14599e9i	0.266848	+	0.265665i
$391$	−9.70037e9	+	7.04773e9i	−0.415032	+	0.301538i
$392$	−5.28776e8	−	1.03778e9i	−0.0223938	−	0.0439503i
$393$	3.12307e8	+	3.12307e8i	0.0130922	+	0.0130922i
$394$	2.11420e10	+	6.86944e9i	0.877325	+	0.285060i
$395$	−2.46454e7	−	1.10858e10i	−0.00101239	−	0.455385i
$396$	−7.52521e8	−	2.31602e9i	−0.0306012	−	0.0941807i
$397$	−1.01201e10	−	5.15646e9i	−0.407403	−	0.207582i	0.238266	−	0.971200i	$-0.423421\pi$
$397$	−1.01201e10	−	5.15646e9i	−0.407403	−	0.207582i	−0.645668	+	0.763618i	$0.723421\pi$
$398$	3.63002e9	+	2.29190e10i	0.144669	+	0.913407i
$399$			1.57761e10i			0.622453i
$400$	2.40470e10	−	1.06921e8i	0.939337	−	0.00417660i
$401$	−4.33625e10			−1.67701			−0.838507	−	0.544891i	$-0.816571\pi$
$401$	−4.33625e10			−1.67701			−0.838507	+	0.544891i	$0.816571\pi$
$402$	6.80626e9	−	1.07801e9i	0.260618	−	0.0412778i
$403$	−3.69296e9	+	7.24784e9i	−0.140008	+	0.274782i
$404$	−2.26304e9	+	7.35305e8i	−0.0849505	+	0.0276021i
$405$	−2.42234e9	−	1.75172e9i	−0.0900357	−	0.0651095i
$406$	−5.90187e9	+	1.81641e10i	−0.217213	+	0.668512i
$407$	1.90005e9	−	1.90005e9i	0.0692449	−	0.0692449i
$408$	−6.21061e8	+	3.16446e8i	−0.0224127	+	0.0114198i
$409$	−9.26642e9	−	1.27541e10i	−0.331146	−	0.455783i	0.610684	−	0.791875i	$-0.290895\pi$
$409$	−9.26642e9	−	1.27541e10i	−0.331146	−	0.455783i	−0.941829	+	0.336092i	$0.890895\pi$
$410$	−2.98470e10	−	5.82575e10i	−1.05625	−	2.06166i
$411$	1.39606e10	+	1.01430e10i	0.489257	+	0.355466i
$412$	−1.12415e9	+	7.09761e9i	−0.0390154	+	0.246333i
$413$	3.50042e10	+	5.54412e9i	1.20315	+	0.190560i
$414$	7.99819e9	−	1.10086e10i	0.272264	−	0.374740i
$415$	2.57959e9	+	1.60558e10i	0.0869679	+	0.541302i
$416$	1.57499e10	−	1.14429e10i	0.525900	−	0.382089i
$417$	−2.10574e9	−	4.13274e9i	−0.0696402	−	0.136677i
$418$	1.48207e10	+	1.48207e10i	0.485470	+	0.485470i
$419$	−2.09140e10	−	6.79538e9i	−0.678549	−	0.220474i	−0.0505891	−	0.998720i	$-0.516110\pi$
$419$	−2.09140e10	−	6.79538e9i	−0.678549	−	0.220474i	−0.627960	+	0.778246i	$0.716110\pi$
$420$	1.14248e10	−	3.74026e9i	0.367158	−	0.120200i
$421$	−3.60223e9	−	1.10865e10i	−0.114668	−	0.352912i	0.877210	−	0.480108i	$-0.159402\pi$
$421$	−3.60223e9	−	1.10865e10i	−0.114668	−	0.352912i	−0.991878	+	0.127196i	$0.959402\pi$
$422$	9.63953e8	+	4.91158e8i	0.0303953	+	0.0154872i
$423$	−2.35982e9	−	1.48993e10i	−0.0737084	−	0.465377i
$424$			2.20378e9i			0.0681876i
$425$	−2.62666e9	+	1.70751e10i	−0.0805096	+	0.523368i
$426$	3.28023e10			0.996015
$427$	−1.68872e10	+	2.67466e9i	−0.507979	+	0.0804559i
$428$	1.41162e10	−	2.77047e10i	0.420672	−	0.825616i
$429$	−2.37601e9	+	7.72014e8i	−0.0701488	+	0.0227927i
$430$	2.72844e9	−	1.99161e9i	0.0798070	−	0.0582547i
$431$	1.32579e9	−	4.08035e9i	0.0384206	−	0.118247i	−0.930007	−	0.367543i	$-0.880199\pi$
$431$	1.32579e9	−	4.08035e9i	0.0384206	−	0.118247i	0.968427	+	0.249296i	$0.0801992\pi$
$432$	−4.45209e9	+	4.45209e9i	−0.127829	+	0.127829i
$433$	−3.99125e10	+	2.03364e10i	−1.13542	+	0.578527i	−0.917617	−	0.397465i	$-0.869890\pi$
$433$	−3.99125e10	+	2.03364e10i	−1.13542	+	0.578527i	−0.217806	+	0.975992i	$0.569890\pi$
$434$	1.28386e10	+	1.76708e10i	0.361875	+	0.498078i
$435$	1.42796e10	+	7.23590e9i	0.398805	+	0.202086i
$436$	2.76301e10	+	2.00745e10i	0.764604	+	0.555518i
$437$	−9.41597e9	+	5.94501e10i	−0.258190	+	1.63015i
$438$	−5.22423e9	−	8.27437e8i	−0.141947	−	0.0224822i
$439$	−3.08296e10	+	4.24332e10i	−0.830059	+	1.14248i	0.157853	+	0.987463i	$0.449543\pi$
$439$	−3.08296e10	+	4.24332e10i	−0.830059	+	1.14248i	−0.987912	+	0.155016i	$0.950457\pi$
$440$	3.91649e8	−	7.72898e8i	0.0104493	−	0.0206211i
$441$	6.11483e9	−	4.44268e9i	0.161670	−	0.117460i
$442$	5.98410e9	+	1.17445e10i	0.156787	+	0.307712i
$443$	2.45994e9	+	2.45994e9i	0.0638718	+	0.0638718i	0.738321	−	0.674449i	$-0.235619\pi$
$443$	2.45994e9	+	2.45994e9i	0.0638718	+	0.0638718i	−0.674449	+	0.738321i	$0.735619\pi$
$444$	7.86415e9	+	2.55522e9i	0.202358	+	0.0657500i
$445$	−2.19920e10	−	3.01283e10i	−0.560822	−	0.768307i
$446$	2.14167e8	+	6.59138e8i	0.00541269	+	0.0166585i
$447$	−2.91129e10	−	1.48338e10i	−0.729215	−	0.371554i
$448$	−4.43152e9	−	2.79795e10i	−0.110012	−	0.694590i
$449$		−	6.29413e10i		−	1.54864i	−0.632795	−	0.774320i	$-0.718092\pi$
$449$		−	6.29413e10i		−	1.54864i	0.632795	−	0.774320i	$-0.281908\pi$
$450$	−3.15309e9	−	1.93506e10i	−0.0768929	−	0.471893i
$451$	1.87729e10			0.453760
$452$	7.85602e10	−	1.24427e10i	1.88213	−	0.298100i
$453$	−9.37166e9	+	1.83929e10i	−0.222548	+	0.436775i
$454$	−6.29620e10	+	2.04576e10i	−1.48202	+	0.481539i
$455$	−3.83714e9	−	1.17208e10i	−0.0895287	−	0.273471i
$456$	−1.08128e9	+	3.32783e9i	−0.0250080	+	0.0769666i
$457$	−1.34531e10	+	1.34531e10i	−0.308432	+	0.308432i	−0.844301	−	0.535869i	$-0.819984\pi$
$457$	−1.34531e10	+	1.34531e10i	−0.308432	+	0.308432i	0.535869	+	0.844301i	$0.319984\pi$
$458$	−3.08355e8	+	1.57114e8i	−0.00700791	+	0.00357071i
$459$	−2.65873e9	−	3.65942e9i	−0.0598995	−	0.0824445i
$460$	4.52855e10	−	7.27575e9i	1.01141	−	0.162497i
$461$	−7.01580e9	−	5.09728e9i	−0.155336	−	0.112859i	0.507402	−	0.861709i	$-0.330606\pi$
$461$	−7.01580e9	−	5.09728e9i	−0.155336	−	0.112859i	−0.662739	+	0.748851i	$0.730606\pi$
$462$	−1.04941e9	+	6.62573e9i	−0.0230345	+	0.145434i
$463$	−1.57676e10	−	2.49735e9i	−0.343117	−	0.0543445i	−0.0175022	−	0.999847i	$-0.505571\pi$
$463$	−1.57676e10	−	2.49735e9i	−0.343117	−	0.0543445i	−0.325615	+	0.945502i	$0.605571\pi$
$464$	1.98183e10	−	2.72775e10i	0.427557	−	0.588482i
$465$	1.62939e10	−	8.34783e9i	0.348508	−	0.178551i
$466$	−7.47456e9	+	5.43059e9i	−0.158505	+	0.115160i
$467$	−1.54652e10	−	3.03522e10i	−0.325154	−	0.638151i	0.669339	−	0.742957i	$-0.266578\pi$
$467$	−1.54652e10	−	3.03522e10i	−0.325154	−	0.638151i	−0.994493	+	0.104807i	$0.966578\pi$
$468$	−5.43617e9	−	5.43617e9i	−0.113321	−	0.113321i
$469$	−9.27866e9	−	3.01482e9i	−0.191776	−	0.0623118i
$470$	5.79748e10	−	8.01697e10i	1.18809	−	1.64293i
$471$	−3.33354e9	−	1.02596e10i	−0.0677365	−	0.208471i
$472$	7.00387e9	+	3.56865e9i	0.141114	+	0.0719012i
$473$	1.51552e8	+	9.56860e8i	0.00302772	+	0.0191163i
$474$			1.90365e10i			0.377116i
$475$	5.12871e10	+	6.99346e10i	1.00747	+	1.37378i
$476$	1.81901e10			0.354330
$477$	−1.41251e10	+	2.23719e9i	−0.272845	+	0.0432145i
$478$	−3.76011e10	+	7.37963e10i	−0.720259	+	1.41359i
$479$	5.59529e10	−	1.81802e10i	1.06287	−	0.345348i	0.275164	−	0.961397i	$-0.411268\pi$
$479$	5.59529e10	−	1.81802e10i	1.06287	−	0.345348i	0.787708	+	0.616049i	$0.211268\pi$
$480$	−4.38155e10	+	9.74084e7i	−0.825396	+	0.00183498i
$481$	2.62141e9	−	8.06786e9i	0.0489727	−	0.150722i
$482$	−7.19210e10	+	7.19210e10i	−1.33250	+	1.33250i
$483$	−1.71650e10	+	8.74602e9i	−0.315396	+	0.160702i
$484$	−3.14131e10	−	4.32365e10i	−0.572440	−	0.787896i
$485$	2.97095e10	−	2.98419e10i	0.536944	−	0.539337i
$486$	4.15293e9	+	3.01728e9i	0.0744406	+	0.0540843i
$487$	−1.46181e10	+	9.22950e10i	−0.259881	+	1.64083i	0.420015	+	0.907517i	$0.362025\pi$
$487$	−1.46181e10	+	9.22950e10i	−0.259881	+	1.64083i	−0.679897	+	0.733308i	$0.737975\pi$
$488$	−3.74553e9	−	5.93234e8i	−0.0660442	−	0.0104604i
$489$	−2.87712e10	+	3.96002e10i	−0.503179	+	0.692567i
$490$	4.89784e10	+	7.64584e9i	0.849612	+	0.132630i
$491$	5.85507e10	−	4.25396e10i	1.00741	−	0.731926i	0.0437458	−	0.999043i	$-0.486071\pi$
$491$	5.85507e10	−	4.25396e10i	1.00741	−	0.731926i	0.963664	+	0.267116i	$0.0860708\pi$
$492$	2.62267e10	+	5.14729e10i	0.447593	+	0.878452i
$493$	1.71281e10	+	1.71281e10i	0.289948	+	0.289948i
$494$	6.29304e10	+	2.04473e10i	1.05670	+	0.343343i
$495$	5.35145e9	+	1.72565e9i	0.0891354	+	0.0287429i
$496$	−1.19157e10	−	3.66729e10i	−0.196877	−	0.605924i
$497$	−4.13786e10	−	2.10834e10i	−0.678188	−	0.345554i
$498$	−4.36836e9	−	2.75807e10i	−0.0710233	−	0.448424i
$499$		−	2.31958e10i		−	0.374117i	−0.982349	−	0.187058i	$-0.940105\pi$
$499$		−	2.31958e10i		−	0.374117i	0.982349	−	0.187058i	$-0.0598954\pi$
$500$	3.84865e10	−	5.37219e10i	0.615783	−	0.859551i
$501$	1.31414e10			0.208589
$502$	1.34870e11	−	2.13613e10i	2.12373	−	0.336367i
$503$	−2.96435e10	+	5.81786e10i	−0.463081	+	0.908848i	0.534874	+	0.844932i	$0.320359\pi$
$503$	−2.96435e10	+	5.81786e10i	−0.463081	+	0.908848i	−0.997955	+	0.0639165i	$0.979641\pi$
$504$	−1.06511e9	+	3.46074e8i	−0.0165071	+	0.00536348i
$505$	1.68617e9	−	5.22901e9i	0.0259260	−	0.0803997i
$506$	−7.90916e9	+	2.43419e10i	−0.120650	+	0.371323i
$507$	2.13977e10	−	2.13977e10i	0.323843	−	0.323843i
$508$	−6.20550e10	+	3.16186e10i	−0.931799	+	0.474775i
$509$	−3.96278e10	−	5.45430e10i	−0.590377	−	0.812584i	0.404408	−	0.914579i	$-0.367477\pi$
$509$	−3.96278e10	−	5.45430e10i	−0.590377	−	0.812584i	−0.994785	+	0.101995i	$0.967477\pi$
$510$	4.57566e9	−	2.93112e10i	0.0676353	−	0.433264i
$511$	6.05830e9	+	4.40161e9i	0.0888520	+	0.0645547i
$512$	−1.52674e10	+	9.63943e10i	−0.222169	+	1.40272i
$513$	−2.24273e10	−	3.55213e9i	−0.323823	−	0.0512885i
$514$	8.36489e10	−	1.15133e11i	1.19842	−	1.64948i
$515$	−1.17586e10	−	1.17065e10i	−0.167158	−	0.166417i
$516$	−2.41185e9	+	1.75231e9i	−0.0340214	+	0.0247180i
$517$	1.28815e10	+	2.52814e10i	0.180304	+	0.353867i
$518$	−1.61067e10	−	1.61067e10i	−0.223712	−	0.223712i
$519$	−2.09217e9	−	6.79787e8i	−0.0288355	−	0.00936921i
$520$	−6.08121e6	−	2.73540e9i	−8.31719e−5	−	0.0374117i
$521$	−3.08969e10	−	9.50908e10i	−0.419337	−	1.29059i	−0.908313	−	0.418290i	$-0.862629\pi$
$521$	−3.08969e10	−	9.50908e10i	−0.419337	−	1.29059i	0.488976	−	0.872297i	$-0.337371\pi$
$522$	−2.44933e10	−	1.24799e10i	−0.329887	−	0.168086i
$523$	3.55110e9	+	2.24208e10i	0.0474632	+	0.299671i	0.999989	−	0.00478863i	$-0.00152427\pi$
$523$	3.55110e9	+	2.24208e10i	0.0474632	+	0.299671i	−0.952525	+	0.304459i	$0.901524\pi$
$524$		−	2.55644e9i		−	0.0339087i
$525$	−8.45997e9	+	2.64365e10i	−0.111361	+	0.347990i
$526$	−1.15924e11			−1.51436
$527$	2.73612e10	−	4.33358e9i	0.354725	−	0.0561829i
$528$	5.37651e9	−	1.05520e10i	0.0691775	−	0.135768i
$529$	4.57380e9	−	1.48612e9i	0.0584056	−	0.0189771i
$530$	−7.60036e10	−	5.49621e10i	−0.963232	−	0.696562i
$531$	−1.57631e10	+	4.85138e10i	−0.198273	+	0.610221i
$532$	6.45689e10	−	6.45689e10i	0.806077	−	0.806077i
$533$	5.28062e10	−	2.69061e10i	0.654298	−	0.333382i
$534$	3.76495e10	+	5.18201e10i	0.463014	+	0.637284i
$535$	3.27359e10	+	6.38963e10i	0.399585	+	0.779939i
$536$	−1.75063e9	−	1.27191e9i	−0.0212097	−	0.0154097i
$537$	−6.87817e9	+	4.34271e10i	−0.0827134	+	0.522232i
$538$	−1.56868e11	−	2.48455e10i	−1.87243	−	0.296564i
$539$	−8.35641e9	+	1.15016e10i	−0.0990067	+	0.136271i
$540$	2.74475e9	+	1.70837e10i	0.0322795	+	0.200913i
$541$	1.37887e11	−	1.00181e11i	1.60967	−	1.16949i	0.745128	−	0.666922i	$-0.232389\pi$
$541$	1.37887e11	−	1.00181e11i	1.60967	−	1.16949i	0.864538	−	0.502568i	$-0.167611\pi$
$542$	8.30304e10	+	1.62956e11i	0.962144	+	1.88831i
$543$	4.72543e10	+	4.72543e10i	0.543553	+	0.543553i
$544$	−6.30539e10	−	2.04875e10i	−0.719973	−	0.233934i
$545$	−7.49432e10	+	2.45349e10i	−0.849467	+	0.278098i
$546$	6.54436e9	+	2.01415e10i	0.0736371	+	0.226632i
$547$	−9.84209e9	−	5.01479e9i	−0.109936	−	0.0560149i	0.398158	−	0.917317i	$-0.369650\pi$
$547$	−9.84209e9	−	5.01479e9i	−0.109936	−	0.0560149i	−0.508094	+	0.861302i	$0.669650\pi$
$548$	−1.56250e10	−	9.86521e10i	−0.173259	−	1.09392i
$549$		−	2.46091e10i		−	0.270898i
$550$	1.68879e10	+	3.27831e10i	0.184554	+	0.358261i
$551$	1.21598e11			1.31922
$552$	−4.22027e9	+	6.68426e8i	−0.0454553	+	0.00719941i
$553$	1.22356e10	−	2.40137e10i	0.130835	−	0.256778i
$554$	−1.57432e11	+	5.11528e10i	−1.67130	+	0.543038i
$555$	−1.54211e10	+	1.12566e10i	−0.162534	+	0.118641i
$556$	−8.29620e9	+	2.55331e10i	−0.0868121	+	0.267180i
$557$	9.54786e10	−	9.54786e10i	0.991940	−	0.991940i	−0.00802815	−	0.999968i	$-0.502555\pi$
$557$	9.54786e10	−	9.54786e10i	0.991940	−	0.991940i	0.999968	+	0.00802815i	$0.00255547\pi$
$558$	−2.80116e10	+	1.42726e10i	−0.288936	+	0.147220i
$559$	1.79771e9	+	2.47433e9i	0.0184107	+	0.0253402i
$560$	5.21492e10	+	2.64255e10i	0.530268	+	0.268702i
$561$	6.88315e9	+	5.00090e9i	0.0694922	+	0.0504890i
$562$	−1.35150e10	+	8.53305e10i	−0.135479	+	0.855380i
$563$	−3.87103e10	−	6.13111e9i	−0.385295	−	0.0610247i	−0.0392174	−	0.999231i	$-0.512486\pi$
$563$	−3.87103e10	−	6.13111e9i	−0.385295	−	0.0610247i	−0.346077	+	0.938206i	$0.612486\pi$
$564$	−5.13221e10	+	7.06388e10i	−0.507210	+	0.698115i
$565$	−8.30129e10	+	1.63821e11i	−0.814614	+	1.60759i
$566$	7.03929e10	−	5.11434e10i	0.685904	−	0.498338i
$567$	−3.29940e9	−	6.47543e9i	−0.0319229	−	0.0626522i
$568$	−7.28344e9	−	7.28344e9i	−0.0699751	−	0.0699751i
$569$	1.13062e11	+	3.67361e10i	1.07862	+	0.350465i	0.793839	−	0.608128i	$-0.208079\pi$
$569$	1.13062e11	+	3.67361e10i	1.07862	+	0.350465i	0.284781	+	0.958593i	$0.408079\pi$
$570$	−8.78027e10	−	1.20287e11i	−0.831780	−	1.13951i
$571$	−4.04364e10	−	1.24451e11i	−0.380389	−	1.17072i	−0.939770	−	0.341807i	$-0.888961\pi$
$571$	−4.04364e10	−	1.24451e11i	−0.380389	−	1.17072i	0.559381	−	0.828911i	$-0.311039\pi$
$572$	1.28844e10	+	6.56492e9i	0.120359	+	0.0613261i
$573$	−1.53723e10	−	9.70571e10i	−0.142601	−	0.900345i
$574$		−	1.59138e11i		−	1.46598i
$575$	−4.76590e10	+	9.45733e10i	−0.435987	+	0.865161i
$576$	4.07736e10			0.370416
$577$	1.46103e11	−	2.31405e10i	1.31812	−	0.208770i	0.542548	−	0.840025i	$-0.317460\pi$
$577$	1.46103e11	−	2.31405e10i	1.31812	−	0.208770i	0.775576	+	0.631255i	$0.217460\pi$
$578$	−5.23006e10	+	1.02646e11i	−0.468593	+	0.919665i
$579$	5.67821e10	−	1.84496e10i	0.505239	−	0.164162i
$580$	−2.88289e10	−	8.80597e10i	−0.254751	−	0.778153i
$581$	−1.22168e10	+	3.75996e10i	−0.107215	+	0.329973i
$582$	−5.11309e10	+	5.11309e10i	−0.445647	+	0.445647i
$583$	2.39677e10	−	1.22121e10i	0.207468	−	0.105710i
$584$	9.76267e8	+	1.34372e9i	0.00839300	+	0.0115520i
$585$	1.75263e10	−	2.81584e9i	0.149646	−	0.0240428i
$586$	−1.73725e11	−	1.26218e11i	−1.47323	−	1.07037i
$587$	−1.63367e10	+	1.03146e11i	−0.137598	+	0.868758i	0.818243	+	0.574873i	$0.194948\pi$
$587$	−1.63367e10	+	1.03146e11i	−0.137598	+	0.868758i	−0.955841	+	0.293885i	$0.905052\pi$
$588$	−4.32102e10	−	6.84382e9i	−0.361474	−	0.0572518i
$589$	8.17401e10	−	1.12506e11i	0.679163	−	0.934788i
$590$	−2.97751e11	+	1.52546e11i	−2.45723	+	1.25891i
$591$	3.66476e10	−	2.66260e10i	0.300397	−	0.218251i
$592$	1.82562e10	+	3.58297e10i	0.148636	+	0.291714i
$593$	−1.51774e11	−	1.51774e11i	−1.22738	−	1.22738i	−0.964951	−	0.262428i	$-0.915477\pi$
$593$	−1.51774e11	−	1.51774e11i	−1.22738	−	1.22738i	−0.262428	−	0.964951i	$-0.584523\pi$
$594$	−9.18287e9	−	2.98370e9i	−0.0737620	−	0.0239667i
$595$	−2.46115e10	+	3.40337e10i	−0.196368	+	0.271545i
$596$	5.84423e10	+	1.79867e11i	0.463172	+	1.42550i
$597$	4.21315e10	+	2.14670e10i	0.331672	+	0.168995i
$598$	1.26401e10	+	7.98067e10i	0.0988433	+	0.624072i
$599$			4.04563e10i			0.314252i	0.987579	+	0.157126i	$0.0502229\pi$
$599$			4.04563e10i			0.314252i	−0.987579	+	0.157126i	$0.949777\pi$
$600$	−3.59650e9	+	4.99673e9i	−0.0277508	+	0.0385550i
$601$	7.99996e10			0.613183			0.306591	−	0.951841i	$-0.400812\pi$
$601$	7.99996e10			0.613183			0.306591	+	0.951841i	$0.400812\pi$
$602$	8.11130e9	−	1.28470e9i	0.0617596	−	0.00978176i
$603$	6.37506e9	−	1.25118e10i	0.0482187	−	0.0946344i
$604$	1.13636e11	−	3.69226e10i	0.853824	−	0.277424i
$605$	1.23398e11	−	2.74332e8i	0.921056	−	0.00204765i
$606$	−2.91543e9	+	8.97278e9i	−0.0216179	+	0.0665329i
$607$	−4.28476e10	+	4.28476e10i	−0.315625	+	0.315625i	−0.847084	−	0.531459i	$-0.821644\pi$
$607$	−4.28476e10	+	4.28476e10i	−0.315625	+	0.315625i	0.531459	+	0.847084i	$0.321644\pi$
$608$	−2.96544e11	+	1.51097e11i	−2.17007	+	1.10571i
$609$	2.28757e10	+	3.14857e10i	0.166305	+	0.228899i
$610$	1.13873e11	−	1.14380e11i	0.822432	−	0.826097i
$611$	7.24686e10	+	5.26515e10i	0.519978	+	0.377786i
$612$	−4.09569e9	+	2.58592e10i	−0.0291959	+	0.184335i
$613$	4.24948e10	+	6.73052e9i	0.300950	+	0.0476657i	0.305083	−	0.952326i	$-0.401316\pi$
$613$	4.24948e10	+	6.73052e9i	0.300950	+	0.0476657i	−0.00413348	+	0.999991i	$0.501316\pi$
$614$	−1.10740e11	+	1.52420e11i	−0.779166	+	1.07243i
$615$	−1.31791e11	−	2.05734e10i	−0.921265	−	0.143815i
$616$	1.70419e9	−	1.23817e9i	0.0118358	−	0.00859918i
$617$	−9.25537e10	−	1.81647e11i	−0.638636	−	1.25339i	−0.952677	−	0.303984i	$-0.901683\pi$
$617$	−9.25537e10	−	1.81647e11i	−0.638636	−	1.25339i	0.314042	−	0.949409i	$-0.398317\pi$
$618$	2.01471e10	+	2.01471e10i	0.138121	+	0.138121i
$619$	−2.72596e11	−	8.85717e10i	−1.85676	−	0.603298i	−0.995457	−	0.0952089i	$-0.969648\pi$
$619$	−2.72596e11	−	8.85717e10i	−1.85676	−	0.603298i	−0.861304	−	0.508090i	$-0.830352\pi$
$620$	−1.00855e11	−	3.25219e10i	−0.682541	−	0.220095i
$621$	−8.56849e9	−	2.63711e10i	−0.0576153	−	0.177322i
$622$	−1.71652e11	−	8.74611e10i	−1.14680	−	0.584324i
$623$	−1.41861e10	−	8.95676e10i	−0.0941697	−	0.594564i
$624$		−	3.73874e10i		−	0.246596i
$625$	4.84409e10	+	1.44695e11i	0.317462	+	0.948271i
$626$	−3.39574e11			−2.21124
$627$	4.21844e10	−	6.68135e9i	0.272949	−	0.0432309i
$628$	−2.83472e10	+	5.56345e10i	−0.182252	+	0.357689i
$629$	−2.74755e10	+	8.92732e9i	−0.175526	+	0.0570320i
$630$	1.46283e10	−	4.53642e10i	0.0928607	−	0.287973i
$631$	−1.69910e10	+	5.22928e10i	−0.107177	+	0.329856i	−0.990235	−	0.139407i	$-0.955480\pi$
$631$	−1.69910e10	+	5.22928e10i	−0.107177	+	0.329856i	0.883058	+	0.469263i	$0.155480\pi$
$632$	4.22688e9	−	4.22688e9i	0.0264943	−	0.0264943i
$633$	1.96429e9	−	1.00085e9i	0.0122346	−	0.00623384i
$634$	−1.05818e11	−	1.45646e11i	−0.654943	−	0.901451i
$635$	2.48030e10	−	1.58885e11i	0.152549	−	0.977212i
$636$	6.69680e10	+	4.86551e10i	0.409297	+	0.297372i
$637$	−7.02110e9	+	4.43295e10i	−0.0426430	+	0.269237i
$638$	5.10694e10	+	8.08859e9i	0.308232	+	0.0488191i
$639$	3.92891e10	−	5.40768e10i	0.235651	−	0.324345i
$640$	1.95331e10	+	1.94464e10i	0.116426	+	0.115910i
$641$	2.40748e11	−	1.74913e11i	1.42603	−	1.03607i	0.435295	−	0.900288i	$-0.356644\pi$
$641$	2.40748e11	−	1.74913e11i	1.42603	−	1.03607i	0.990738	−	0.135786i	$-0.0433560\pi$
$642$	−5.59699e10	−	1.09847e11i	−0.329469	−	0.646620i
$643$	1.59281e11	+	1.59281e11i	0.931797	+	0.931797i	0.997818	−	0.0660212i	$-0.0210305\pi$
$643$	1.59281e11	+	1.59281e11i	0.931797	+	0.931797i	−0.0660212	+	0.997818i	$0.521030\pi$
$644$	1.06050e11	+	3.44577e10i	0.616547	+	0.200328i
$645$	−1.53030e7	−	6.88348e9i	−8.84175e−5	−	0.0397713i
$646$	−6.96343e10	−	2.14312e11i	−0.399846	−	1.23060i
$647$	−2.22607e11	−	1.13424e11i	−1.27035	−	0.647273i	−0.316792	−	0.948495i	$-0.602606\pi$
$647$	−2.22607e11	−	1.13424e11i	−1.27035	−	0.647273i	−0.953554	+	0.301222i	$0.902606\pi$
$648$	−2.52161e8	−	1.59208e9i	−0.00143014	−	0.00902952i
$649$		−	9.59475e10i		−	0.540822i
$650$	9.44897e10	+	6.80109e10i	0.529336	+	0.381000i
$651$	4.45090e10			0.247813
$652$	2.79833e11	−	4.43212e10i	1.54849	−	0.245257i
$653$	7.34366e9	−	1.44128e10i	0.0403887	−	0.0792673i	−0.869930	−	0.493175i	$-0.835836\pi$
$653$	7.34366e9	−	1.44128e10i	0.0403887	−	0.0792673i	0.910319	+	0.413907i	$0.135836\pi$
$654$	1.28786e11	−	4.18450e10i	0.703973	−	0.228735i
$655$	4.78310e9	+	3.45891e9i	0.0259863	+	0.0187920i
$656$	−8.68155e10	+	2.67190e11i	−0.468794	+	1.44280i
$657$	−7.62143e9	+	7.62143e9i	−0.0409049	+	0.0409049i
$658$	2.14311e11	−	1.09197e11i	1.14325	−	0.582514i
$659$	−4.89862e10	−	6.74237e10i	−0.259736	−	0.357496i	0.659155	−	0.752007i	$-0.270914\pi$
$659$	−4.89862e10	−	6.74237e10i	−0.259736	−	0.357496i	−0.918891	+	0.394511i	$0.870914\pi$
$660$	−1.48398e10	−	2.89654e10i	−0.0782083	−	0.152652i
$661$	5.55582e10	+	4.03654e10i	0.291033	+	0.211448i	0.723716	−	0.690098i	$-0.242433\pi$
$661$	5.55582e10	+	4.03654e10i	0.291033	+	0.211448i	−0.432682	+	0.901546i	$0.642433\pi$
$662$	2.41811e10	−	1.52673e11i	0.125905	−	0.794934i
$663$	2.65290e10	+	4.20178e9i	0.137299	+	0.0217460i
$664$	−5.15409e9	+	7.09400e9i	−0.0265143	+	0.0364938i
$665$	3.34456e10	+	2.08171e11i	0.171022	+	1.06447i
$666$	2.65240e10	−	1.92708e10i	0.134816	−	0.0979497i
$667$	6.74120e10	+	1.32304e11i	0.340592	+	0.668449i
$668$	−5.37858e10	−	5.37858e10i	−0.270123	−	0.270123i
$669$	1.34315e9	+	4.36417e8i	0.00670534	+	0.00217870i
$670$	8.75257e10	−	2.86541e10i	0.434347	−	0.142196i
$671$	1.43038e10	+	4.40227e10i	0.0705606	+	0.217163i
$672$	−9.49117e10	−	4.83599e10i	−0.465417	−	0.237142i
$673$	1.99602e10	+	1.26024e11i	0.0972981	+	0.614316i	0.987362	+	0.158481i	$0.0506595\pi$
$673$	1.99602e10	+	1.26024e11i	0.0972981	+	0.614316i	−0.890064	+	0.455836i	$0.849340\pi$
$674$			4.64990e11i			2.25322i
$675$	−3.56773e10	−	1.79792e10i	−0.171861	−	0.0866072i
$676$	−1.75155e11			−0.838754
$677$	2.27022e11	−	3.59568e10i	1.08072	−	0.171170i	0.409415	−	0.912348i	$-0.365733\pi$
$677$	2.27022e11	−	3.59568e10i	1.08072	−	0.171170i	0.671308	+	0.741179i	$0.265733\pi$
$678$	1.43174e11	−	2.80996e11i	0.677558	−	1.32978i
$679$	9.73633e10	−	3.16352e10i	0.458053	−	0.148831i
$680$	−7.52425e9	+	5.49229e9i	−0.0351907	+	0.0256873i
$681$	−4.16873e10	+	1.28300e11i	−0.193827	+	0.596540i
$682$	4.18135e10	−	4.18135e10i	0.193277	−	0.193277i
$683$	3.25224e11	−	1.65710e11i	1.49451	−	0.761493i	0.499993	−	0.866030i	$-0.333336\pi$
$683$	3.25224e11	−	1.65710e11i	1.49451	−	0.761493i	0.994521	+	0.104537i	$0.0333360\pi$
$684$	7.72530e10	+	1.06330e11i	0.352932	+	0.485769i
$685$	2.05719e11	+	1.04244e11i	0.934354	+	0.473464i
$686$	2.60132e11	+	1.88997e11i	1.17462	+	0.853411i
$687$	−1.10319e8	+	6.96528e8i	−0.000495249	+	0.00312688i
$688$	−1.43196e10	−	2.26800e9i	−0.0639112	−	0.0101225i
$689$	4.99154e10	−	6.87027e10i	0.221492	−	0.304858i
$690$	8.22007e10	−	1.62218e11i	0.362643	−	0.715655i
$691$	−2.64303e11	+	1.92028e11i	−1.15929	+	0.842270i	−0.989687	−	0.143243i	$-0.954247\pi$
$691$	−2.64303e11	+	1.92028e11i	−1.15929	+	0.842270i	−0.169598	+	0.985513i	$0.554247\pi$
$692$	5.78065e9	+	1.13452e10i	0.0252088	+	0.0494751i
$693$	9.66602e9	+	9.66602e9i	0.0419097	+	0.0419097i
$694$	4.93447e11	+	1.60331e11i	2.12717	+	0.691160i
$695$	−3.65475e10	−	5.00688e10i	−0.156646	−	0.214599i
$696$	2.66744e9	+	8.20955e9i	0.0113673	+	0.0349850i
$697$	−1.79834e11	−	9.16299e10i	−0.761974	−	0.388245i
$698$	4.69396e10	+	2.96365e11i	0.197751	+	1.24855i
$699$			1.88268e10i			0.0788621i
$700$	1.42826e11	−	7.35750e10i	0.594859	−	0.306435i
$701$	4.58029e11			1.89680			0.948399	−	0.317078i	$-0.102702\pi$
$701$	4.58029e11			1.89680			0.948399	+	0.317078i	$0.102702\pi$
$702$	−3.01067e10	+	4.76844e9i	−0.123970	+	0.0196348i
$703$	−6.58396e10	+	1.29218e11i	−0.269567	+	0.529054i
$704$	−7.29391e10	+	2.36993e10i	−0.296941	+	0.0964818i
$705$	−6.27256e10	−	1.91599e11i	−0.253915	−	0.775598i
$706$	−1.54809e11	+	4.76452e11i	−0.623127	+	1.91779i
$707$	9.44488e9	−	9.44488e9i	0.0378023	−	0.0378023i
$708$	2.63075e11	−	1.34043e11i	1.04700	−	0.533473i
$709$	−1.19019e9	−	1.63815e9i	−0.00471010	−	0.00648290i	0.806655	−	0.591022i	$-0.201275\pi$
$709$	−1.19019e9	−	1.63815e9i	−0.00471010	−	0.00648290i	−0.811366	+	0.584539i	$0.801275\pi$
$710$	4.32838e11	−	6.95416e10i	1.70331	−	0.273660i
$711$	3.13830e10	+	2.28011e10i	0.122805	+	0.0892230i
$712$	3.14644e9	−	1.98659e10i	0.0122433	−	0.0773014i
$713$	1.67727e11	+	2.65653e10i	0.648998	+	0.102791i
$714$	4.23927e10	−	5.83485e10i	0.163116	−	0.224511i
$715$	−2.97157e10	+	1.52242e10i	−0.113700	+	0.0582520i
$716$	2.05891e11	−	1.49589e11i	0.783404	−	0.569177i
$717$	7.66212e10	+	1.50378e11i	0.289916	+	0.568993i
$718$	3.80117e11	+	3.80117e11i	1.43027	+	1.43027i
$719$	1.10297e10	+	3.58378e9i	0.0412714	+	0.0134099i	0.329580	−	0.944128i	$-0.393093\pi$
$719$	1.10297e10	+	3.58378e9i	0.0412714	+	0.0134099i	−0.288309	+	0.957538i	$0.593093\pi$
$720$	−4.93084e10	+	6.81855e10i	−0.183481	+	0.253724i
$721$	−1.24652e10	−	3.83641e10i	−0.0461275	−	0.141966i
$722$	−6.60630e11	−	3.36608e11i	−2.43114	−	1.23873i
$723$	3.24229e10	+	2.04710e11i	0.118659	+	0.749181i
$724$		−	3.86809e11i		−	1.40780i
$725$	2.03765e11	+	6.52072e10i	0.737528	+	0.236017i
$726$	−2.11899e11			−0.762750
$727$	−7.48957e10	+	1.18623e10i	−0.268114	+	0.0424651i	−0.289044	−	0.957316i	$-0.593337\pi$
$727$	−7.48957e10	+	1.18623e10i	−0.268114	+	0.0424651i	0.0209299	+	0.999781i	$0.493337\pi$
$728$	3.01911e9	−	5.92534e9i	0.0107486	−	0.0210954i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	−7.06898e10	+	1.57154e8i	−0.248923	+	0.000553394i
$731$	3.21861e9	−	9.90588e9i	0.0112720	−	0.0346915i
$732$	−1.00721e11	+	1.00721e11i	−0.350813	+	0.350813i
$733$	−2.10603e11	+	1.07308e11i	−0.729540	+	0.371719i	−0.778972	−	0.627058i	$-0.784259\pi$
$733$	−2.10603e11	+	1.07308e11i	−0.729540	+	0.371719i	0.0494323	+	0.998777i	$0.484259\pi$
$734$	1.90155e11	+	2.61726e11i	0.655124	+	0.901700i
$735$	7.12688e10	−	7.15864e10i	0.244202	−	0.245291i
$736$	−3.28799e11	−	2.38887e11i	−1.12052	−	0.814105i
$737$	−4.13185e9	+	2.60875e10i	−0.0140047	+	0.0884224i
$738$	2.26232e11	+	3.58315e10i	0.762654	+	0.120793i
$739$	−3.24787e11	+	4.47031e11i	−1.08898	+	1.49886i	−0.239752	+	0.970834i	$0.577066\pi$
$739$	−3.24787e11	+	4.47031e11i	−1.08898	+	1.49886i	−0.849231	+	0.528022i	$0.822934\pi$
$740$	1.09187e11	+	1.70449e10i	0.364121	+	0.0568416i
$741$	1.09084e11	−	7.92541e10i	0.361816	−	0.262875i
$742$	−1.03522e11	−	2.03174e11i	−0.341522	−	0.670274i
$743$	−4.24473e11	−	4.24473e11i	−1.39282	−	1.39282i	−0.818937	−	0.573884i	$-0.805436\pi$
$743$	−4.24473e11	−	4.24473e11i	−1.39282	−	1.39282i	−0.573884	−	0.818937i	$-0.694564\pi$
$744$	9.38881e9	+	3.05061e9i	0.0306421	+	0.00995623i
$745$	−4.15604e11	−	1.34017e11i	−1.34913	−	0.435046i
$746$	−1.58007e11	−	4.86297e11i	−0.510179	−	1.57017i
$747$	−5.07009e10	−	2.58334e10i	−0.162830	−	0.0829658i
$748$	−7.70374e9	−	4.86395e10i	−0.0246091	−	0.155376i
$749$			1.74541e11i			0.554589i
$750$	−8.26299e10	−	2.48653e11i	−0.261151	−	0.785868i
$751$	−5.92011e11			−1.86110			−0.930551	−	0.366163i	$-0.880671\pi$
$751$	−5.92011e11			−1.86110			−0.930551	+	0.366163i	$0.880671\pi$
$752$	−4.19395e11	+	6.64256e10i	−1.31145	+	0.207713i
$753$	1.26325e11	−	2.47928e11i	0.392926	−	0.771161i
$754$	1.55245e11	−	5.04422e10i	0.480322	−	0.156066i
$755$	−8.46691e10	+	2.62570e11i	−0.260578	+	0.808084i
$756$	−1.29990e10	+	4.00068e10i	−0.0397945	+	0.122475i
$757$	4.32242e11	−	4.32242e11i	1.31626	−	1.31626i	0.399556	−	0.916709i	$-0.369164\pi$
$757$	4.32242e11	−	4.32242e11i	1.31626	−	1.31626i	0.916709	−	0.399556i	$-0.130836\pi$
$758$	7.83855e11	−	3.99394e11i	2.37443	−	1.20983i
$759$	3.06560e10	+	4.21944e10i	0.0923737	+	0.127142i
$760$	−7.21279e9	+	4.62043e10i	−0.0216197	+	0.138493i
$761$	−8.32524e10	−	6.04864e10i	−0.248232	−	0.180351i	0.456711	−	0.889615i	$-0.349027\pi$
$761$	−8.32524e10	−	6.04864e10i	−0.248232	−	0.180351i	−0.704943	+	0.709264i	$0.749027\pi$
$762$	−4.31981e10	+	2.72742e11i	−0.128128	+	0.808969i
$763$	−1.89353e11	−	2.99905e10i	−0.558693	−	0.0884882i
$764$	−3.34323e11	+	4.60156e11i	−0.981279	+	1.35061i
$765$	−4.28409e10	−	4.26509e10i	−0.125087	−	0.124532i
$766$	−2.99108e11	+	2.17315e11i	−0.868786	+	0.631210i
$767$	−1.37516e11	−	2.69889e11i	−0.397347	−	0.779838i
$768$	1.24359e11	+	1.24359e11i	0.357463	+	0.357463i
$769$	7.50263e10	+	2.43775e10i	0.214540	+	0.0697083i	0.414315	−	0.910134i	$-0.364021\pi$
$769$	7.50263e10	+	2.43775e10i	0.214540	+	0.0697083i	−0.199775	+	0.979842i	$0.564021\pi$
$770$	1.99314e8	+	8.96537e10i	0.000566989	+	0.255038i
$771$	−8.96133e10	−	2.75801e11i	−0.253603	−	0.780511i
$772$	−3.07911e11	−	1.56889e11i	−0.866875	−	0.441695i
$773$	−3.94561e10	−	2.49116e11i	−0.110509	−	0.697725i	−0.979280	−	0.202511i	$-0.935090\pi$
$773$	−3.94561e10	−	2.49116e11i	−0.110509	−	0.697725i	0.868771	−	0.495214i	$-0.164910\pi$
$774$			1.18203e10i			0.0329356i
$775$	1.97306e11	−	1.44696e11i	0.546933	−	0.401098i
$776$	2.27063e10			0.0626180
$777$	−4.58450e10	+	7.26113e9i	−0.125779	+	0.0199214i
$778$	−1.48376e11	+	2.91205e11i	−0.404992	+	0.794841i
$779$	−9.63605e11	+	3.13094e11i	−2.61667	+	0.850208i
$780$	−8.32570e10	−	6.02074e10i	−0.224927	−	0.162657i
$781$	−3.88517e10	+	1.19573e11i	−0.104425	+	0.321388i
$782$	1.94577e11	−	1.94577e11i	0.520312	−	0.520312i
$783$	−4.99109e10	+	2.54309e10i	−0.132785	+	0.0676573i
$784$	−1.25055e11	−	1.72124e11i	−0.331007	−	0.455593i
$785$	−6.57379e10	−	1.28312e11i	−0.173116	−	0.337900i
$786$	−8.20030e9	−	5.95786e9i	−0.0214852	−	0.0156099i
$787$	3.37265e10	−	2.12941e11i	0.0879168	−	0.555085i	−0.903933	−	0.427674i	$-0.859333\pi$
$787$	3.37265e10	−	2.12941e11i	0.0879168	−	0.555085i	0.991850	−	0.127411i	$-0.0406668\pi$
$788$	−2.58969e11	−	4.10166e10i	−0.671649	−	0.106379i
$789$	−1.38848e11	+	1.91109e11i	−0.358289	+	0.493142i
$790$	4.03579e10	+	2.51194e11i	0.103614	+	0.644913i
$791$	−3.61216e11	+	2.62439e11i	−0.922701	+	0.670381i
$792$	1.37647e9	+	2.70147e9i	0.00349837	+	0.00686593i
$793$	1.03330e11	+	1.03330e11i	0.261297	+	0.261297i
$794$	2.47906e11	+	8.05495e10i	0.623741	+	0.202666i
$795$	−1.81642e11	+	5.94660e10i	−0.454725	+	0.148868i
$796$	−8.45761e10	−	2.60298e11i	−0.210666	−	0.648365i
$797$	−4.90685e11	−	2.50016e11i	−1.21610	−	0.619634i	−0.276205	−	0.961099i	$-0.589077\pi$
$797$	−4.90685e11	−	2.50016e11i	−1.21610	−	0.619634i	−0.939895	+	0.341465i	$0.889077\pi$
$798$	−5.66378e10	−	3.57597e11i	−0.139667	−	0.881825i
$799$		−	3.05056e11i		−	0.748501i
$800$	−5.77955e11	+	9.41751e10i	−1.41102	+	0.229920i
$801$	1.30524e11			0.317073
$802$	9.82900e11	−	1.55676e11i	2.37581	−	0.376291i
$803$	9.20392e9	−	1.80637e10i	0.0221366	−	0.0434455i
$804$	−7.73007e10	+	2.51165e10i	−0.184995	+	0.0601084i
$805$	−2.07957e11	+	1.51797e11i	−0.495211	+	0.361477i
$806$	5.76880e10	−	1.77545e11i	0.136693	−	0.420697i
$807$	−2.28849e11	+	2.28849e11i	−0.539579	+	0.539579i
$808$	2.63967e9	−	1.34498e9i	0.00619304	−	0.00315551i
$809$	1.90901e11	+	2.62752e11i	0.445670	+	0.613413i	0.971460	−	0.237202i	$-0.0762303\pi$
$809$	1.90901e11	+	2.62752e11i	0.445670	+	0.613413i	−0.525790	+	0.850614i	$0.676230\pi$
$810$	6.11962e10	+	3.10099e10i	0.142162	+	0.0720377i
$811$	4.54746e11	+	3.30392e11i	1.05120	+	0.763742i	0.972440	−	0.233152i	$-0.0749038\pi$
$811$	4.54746e11	+	3.30392e11i	1.05120	+	0.763742i	0.0787602	+	0.996894i	$0.474904\pi$
$812$	3.52394e10	−	2.22493e11i	0.0810596	−	0.511790i
$813$	3.68095e11	+	5.83004e10i	0.842553	+	0.133447i
$814$	−3.62472e10	+	4.98900e10i	−0.0825614	+	0.113636i
$815$	−2.95693e11	+	5.83535e11i	−0.670211	+	1.32262i
$816$	−1.03008e11	+	7.48394e10i	−0.232332	+	0.168799i
$817$	−2.37375e10	−	4.65875e10i	−0.0532779	−	0.104564i
$818$	2.55831e11	+	2.55831e11i	0.571401	+	0.571401i
$819$	4.10431e10	+	1.33357e10i	0.0912231	+	0.0296402i
$820$	4.55195e11	+	6.23602e11i	1.00680	+	1.37928i
$821$	1.78605e11	+	5.49690e11i	0.393116	+	1.20989i	0.930419	+	0.366498i	$0.119443\pi$
$821$	1.78605e11	+	5.49690e11i	0.393116	+	1.20989i	−0.537303	+	0.843390i	$0.680557\pi$
$822$	−3.52861e11	−	1.79791e11i	−0.772887	−	0.393805i
$823$	−1.29628e11	−	8.18442e11i	−0.282554	−	1.78397i	−0.565408	−	0.824811i	$-0.691281\pi$
$823$	−1.29628e11	−	8.18442e11i	−0.282554	−	1.78397i	0.282854	−	0.959163i	$-0.408719\pi$
$824$		−	8.94696e9i		−	0.0194074i
$825$	7.42727e10	+	1.14254e10i	0.160330	+	0.0246635i
$826$	−8.13347e11			−1.74725
$827$	5.97916e11	−	9.47006e10i	1.27826	−	0.202456i	0.519861	−	0.854251i	$-0.325984\pi$
$827$	5.97916e11	−	9.47006e10i	1.27826	−	0.202456i	0.758396	+	0.651795i	$0.225984\pi$
$828$	−7.28633e10	+	1.43002e11i	−0.155020	+	0.304244i
$829$	8.94741e10	−	2.90719e10i	0.189443	−	0.0615538i	−0.212759	−	0.977105i	$-0.568245\pi$
$829$	8.94741e10	−	2.90719e10i	0.189443	−	0.0615538i	0.402202	+	0.915551i	$0.368245\pi$
$830$	−1.16114e11	−	3.54677e11i	−0.244665	−	0.747344i
$831$	−1.04236e11	+	3.20806e11i	−0.218582	+	0.672725i
$832$	−1.71203e11	+	1.71203e11i	−0.357287	+	0.357287i
$833$	1.36188e11	−	6.93915e10i	0.282853	−	0.144121i
$834$	6.25679e10	+	8.61173e10i	0.129326	+	0.178002i
$835$	1.73406e11	−	2.78601e10i	0.356713	−	0.0573109i
$836$	−1.99999e11	−	1.45308e11i	−0.409453	−	0.297485i
$837$	−1.00216e10	+	6.32741e10i	−0.0204191	+	0.128921i
$838$	4.98456e11	+	7.89476e10i	1.01077	+	0.160090i
$839$	−1.09670e11	+	1.50948e11i	−0.221330	+	0.304635i	−0.905214	−	0.424956i	$-0.860290\pi$
$839$	−1.09670e11	+	1.50948e11i	−0.221330	+	0.304635i	0.683884	+	0.729591i	$0.260290\pi$
$840$	−1.33208e10	+	6.82462e9i	−0.0267555	+	0.0137076i
$841$	−1.62024e11	+	1.17717e11i	−0.323889	+	0.235319i
$842$	1.21454e11	+	2.38366e11i	0.241637	+	0.474238i
$843$	1.24485e11	+	1.24485e11i	0.246495	+	0.246495i
$844$	−1.21358e10	−	3.94317e9i	−0.0239166	−	0.00777098i
$845$	2.36987e11	−	3.27714e11i	0.464833	−	0.642789i
$846$	1.06980e11	+	3.29252e11i	0.208844	+	0.642757i
$847$	2.67301e11	+	1.36196e11i	0.519357	+	0.264626i
$848$	6.29737e10	+	3.97601e11i	0.121780	+	0.768889i
$849$		−	1.77305e11i		−	0.341263i
$850$	−1.76284e9	−	3.96472e11i	−0.00337706	−	0.759517i
$851$	−1.77095e11			−0.337666
$852$	−3.82132e11	+	6.05237e10i	−0.725194	+	0.114860i
$853$	2.44033e11	−	4.78941e11i	0.460948	−	0.904661i	−0.537178	−	0.843469i	$-0.680510\pi$
$853$	2.44033e11	−	4.78941e11i	0.460948	−	0.904661i	0.998126	−	0.0611923i	$-0.0194903\pi$
$854$	3.73180e11	−	1.21254e11i	0.701596	−	0.227962i
$855$	−3.03467e11	+	6.74653e8i	−0.567867	+	0.00126246i
$856$	−1.19629e10	+	3.68181e10i	−0.0222814	+	0.0685751i
$857$	4.69355e10	−	4.69355e10i	0.0870119	−	0.0870119i	−0.662261	−	0.749273i	$-0.730403\pi$
$857$	4.69355e10	−	4.69355e10i	0.0870119	−	0.0870119i	0.749273	+	0.662261i	$0.230403\pi$
$858$	5.10857e10	−	2.60295e10i	0.0942649	−	0.0480304i
$859$	4.51318e11	+	6.21185e11i	0.828914	+	1.14090i	0.988124	+	0.153658i	$0.0491054\pi$
$859$	4.51318e11	+	6.21185e11i	0.828914	+	1.14090i	−0.159210	+	0.987245i	$0.550895\pi$
$860$	−2.81104e10	+	2.82356e10i	−0.0513893	+	0.0516183i
$861$	−2.62350e11	−	1.90609e11i	−0.477385	−	0.346840i
$862$	−1.54028e10	+	9.72494e10i	−0.0278978	+	0.176140i
$863$	−8.14669e11	−	1.29031e11i	−1.46872	−	0.232622i	−0.629747	−	0.776800i	$-0.716842\pi$
$863$	−8.14669e11	−	1.29031e11i	−1.46872	−	0.232622i	−0.838970	+	0.544178i	$0.816842\pi$
$864$	9.01189e10	−	1.24038e11i	0.161719	−	0.222587i
$865$	−2.90481e10	−	4.53459e9i	−0.0518864	−	0.00809979i
$866$	8.31690e11	−	6.04258e11i	1.47873	−	1.07436i
$867$	1.06575e11	+	2.09166e11i	0.188616	+	0.370181i
$868$	−1.82168e11	−	1.82168e11i	−0.320917	−	0.320917i
$869$	−6.93933e10	−	2.25473e10i	−0.121685	−	0.0395380i
$870$	−3.49655e11	−	1.12751e11i	−0.610328	−	0.196809i
$871$	2.57671e10	+	7.93031e10i	0.0447707	+	0.137790i
$872$	−3.78869e10	−	1.93043e10i	−0.0655274	−	0.0333879i
$873$	2.30505e10	+	1.45535e11i	0.0396847	+	0.250559i
$874$		−	1.38136e12i		−	2.36735i
$875$	−5.55864e10	+	3.66775e11i	−0.0948280	+	0.625701i
$876$	6.23866e10			0.105944
$877$	3.41408e11	−	5.40737e10i	0.577132	−	0.0914087i	0.138957	−	0.990298i	$-0.455625\pi$
$877$	3.41408e11	−	5.40737e10i	0.577132	−	0.0914087i	0.438175	+	0.898890i	$0.355625\pi$
$878$	5.46476e11	−	1.07252e12i	0.919587	−	1.80479i
$879$	−4.16159e11	+	1.35218e11i	−0.697114	+	0.226506i
$880$	4.85746e10	−	1.50636e11i	0.0809987	−	0.251187i
$881$	8.49961e10	−	2.61591e11i	0.141090	−	0.434230i	−0.855398	−	0.517972i	$-0.826687\pi$
$881$	8.49961e10	−	2.61591e11i	0.141090	−	0.434230i	0.996487	+	0.0837421i	$0.0266872\pi$
$882$	−1.22655e11	+	1.22655e11i	−0.202681	+	0.202681i
$883$	−2.80840e11	+	1.43095e11i	−0.461972	+	0.235387i	−0.669456	−	0.742852i	$-0.733473\pi$
$883$	−2.80840e11	+	1.43095e11i	−0.461972	+	0.235387i	0.207484	+	0.978239i	$0.433473\pi$
$884$	−9.13817e10	−	1.25776e11i	−0.149641	−	0.205963i
$885$	−1.05149e11	+	6.73575e11i	−0.171409	+	1.09803i
$886$	−6.45910e10	−	4.69281e10i	−0.104818	−	0.0761549i
$887$	4.77505e10	−	3.01485e11i	0.0771408	−	0.487048i	−0.918626	−	0.395129i	$-0.870700\pi$
$887$	4.77505e10	−	3.01485e11i	0.0771408	−	0.487048i	0.995767	−	0.0919188i	$-0.0293000\pi$
$888$	−1.01683e10	−	1.61050e9i	−0.0163530	−	0.00259006i
$889$	2.29795e11	−	3.16286e11i	0.367904	−	0.506376i
$890$	6.06659e11	+	6.03967e11i	0.966906	+	0.962616i
$891$	−1.59176e10	+	1.15648e10i	−0.0252562	+	0.0183497i
$892$	−3.71113e9	−	7.28349e9i	−0.00586201	−	0.0115048i
$893$	−1.08284e12	−	1.08284e12i	−1.70279	−	1.70279i
$894$	7.13160e11	+	2.31720e11i	1.11644	+	0.362754i
$895$	1.30636e9	+	5.87618e11i	0.00203597	+	0.915805i
$896$	2.07069e10	+	6.37292e10i	0.0321279	+	0.0988796i
$897$	1.46706e11	+	7.47507e10i	0.226610	+	0.115464i
$898$	2.25966e11	+	1.42669e12i	0.347487	+	2.19394i
$899$		−	3.43063e11i		−	0.525213i
$900$	7.24359e10	+	2.19607e11i	0.110404	+	0.334716i
$901$	−2.89203e11			−0.438838
$902$	−4.25528e11	+	6.73970e10i	−0.642838	+	0.101816i
$903$	7.59742e9	−	1.49108e10i	0.0114266	−	0.0224259i
$904$	−9.41830e10	+	3.06019e10i	−0.141026	+	0.0458221i
$905$	7.23718e11	+	5.23358e11i	1.07888	+	0.780197i
$906$	1.46395e11	−	4.50559e11i	0.217278	−	0.668712i
$907$	6.92063e11	−	6.92063e11i	1.02263	−	1.02263i	0.0228876	−	0.999738i	$-0.492714\pi$
$907$	6.92063e11	−	6.92063e11i	1.02263	−	1.02263i	0.999738	−	0.0228876i	$-0.00728598\pi$
$908$	6.95732e11	−	3.54493e11i	1.02353	−	0.521512i
$909$	1.13003e10	+	1.55535e10i	0.0165513	+	0.0227809i
$910$	1.29056e11	+	2.51900e11i	0.188197	+	0.367335i
$911$	7.81827e11	+	5.68031e11i	1.13511	+	0.824704i	0.986430	−	0.164181i	$-0.0524982\pi$
$911$	7.81827e11	+	5.68031e11i	1.13511	+	0.824704i	0.148678	+	0.988886i	$0.452498\pi$
$912$	−9.99876e10	+	6.31297e11i	−0.144533	+	0.912545i
$913$	1.05713e11	+	1.67433e10i	0.152141	+	0.0240968i
$914$	2.56645e11	−	3.53242e11i	0.367746	−	0.506159i
$915$	−5.21718e10	−	3.24726e11i	−0.0744306	−	0.463268i
$916$	3.30229e9	−	2.39926e9i	0.00469066	−	0.00340796i
$917$	6.51492e9	+	1.27863e10i	0.00921365	+	0.0180828i
$918$	7.34033e10	+	7.34033e10i	0.103358	+	0.103358i
$919$	−2.99056e10	−	9.71693e9i	−0.0419267	−	0.0136228i	0.287979	−	0.957637i	$-0.407017\pi$
$919$	−2.99056e10	−	9.71693e9i	−0.0419267	−	0.0136228i	−0.329905	+	0.944014i	$0.607017\pi$
$920$	−5.42710e10	+	1.77672e10i	−0.0757559	+	0.0248009i
$921$	1.18636e11	+	3.65124e11i	0.164884	+	0.507460i
$922$	1.77327e11	+	9.03528e10i	0.245387	+	0.125031i
$923$	6.20915e10	+	3.92030e11i	0.0855510	+	0.540148i
$924$		−	7.91229e10i		−	0.108546i
$925$	−1.79623e11	+	1.81228e11i	−0.245355	+	0.247547i
$926$	3.66372e11			0.498286
$927$	5.73452e10	−	9.08258e9i	0.0776565	−	0.0122996i
$928$	−3.72745e11	+	7.31554e11i	−0.502597	+	0.986403i
$929$	1.50591e11	−	4.89299e10i	0.202179	−	0.0656919i	−0.206177	−	0.978515i	$-0.566102\pi$
$929$	1.50591e11	−	4.89299e10i	0.202179	−	0.0656919i	0.408356	+	0.912823i	$0.366102\pi$
$930$	−3.39365e11	+	2.47718e11i	−0.453665	+	0.331150i
$931$	2.37107e11	−	7.29739e11i	0.315606	−	0.971335i
$932$	7.70552e10	−	7.70552e10i	0.102126	−	0.102126i
$933$	−3.49783e11	+	1.78223e11i	−0.461606	+	0.235200i
$934$	4.59520e11	+	6.32474e11i	0.603832	+	0.831104i
$935$	1.01428e11	+	5.13963e10i	0.132712	+	0.0672489i
$936$	7.74370e9	+	5.62613e9i	0.0100889	+	0.00733004i
$937$	9.28091e10	−	5.85974e11i	0.120402	−	0.760186i	−0.851423	−	0.524480i	$-0.824260\pi$
$937$	9.28091e10	−	5.85974e11i	0.120402	−	0.760186i	0.971824	−	0.235706i	$-0.0757402\pi$
$938$	2.21144e11	+	3.50257e10i	0.285669	+	0.0452455i
$939$	−4.06726e11	+	5.59810e11i	−0.523166	+	0.720076i
$940$	−5.27458e11	+	1.04091e12i	−0.675580	+	1.33322i
$941$	−8.86439e10	+	6.44035e10i	−0.113055	+	0.0821393i	−0.642876	−	0.765970i	$-0.722259\pi$
$941$	−8.86439e10	+	6.44035e10i	−0.113055	+	0.0821393i	0.529821	+	0.848109i	$0.322259\pi$
$942$	1.12395e11	+	2.20587e11i	0.142739	+	0.280141i
$943$	−8.74869e11	−	8.74869e11i	−1.10636	−	1.10636i
$944$	1.36560e12	+	4.43709e11i	1.71963	+	0.558740i
$945$	−5.72648e10	−	7.84509e10i	−0.0718060	−	0.0983718i
$946$	−6.87047e9	−	2.11451e10i	−0.00857870	−	0.0264025i
$947$	6.16405e11	+	3.14074e11i	0.766419	+	0.390510i	0.793066	−	0.609135i	$-0.208483\pi$
$947$	6.16405e11	+	3.14074e11i	0.766419	+	0.390510i	−0.0266478	+	0.999645i	$0.508483\pi$
$948$	−3.51244e10	−	2.21767e11i	−0.0434886	−	0.274576i
$949$		−	6.40026e10i		−	0.0789101i
$950$	−1.41360e12	−	1.40109e12i	−1.73553	−	1.72017i
$951$	−3.66852e11			−0.448506
$952$	−2.23686e10	+	3.54284e9i	−0.0272327	+	0.00431324i
$953$	−3.02396e11	+	5.93486e11i	−0.366610	+	0.719513i	−0.998454	−	0.0555827i	$-0.982298\pi$
$953$	−3.02396e11	+	5.93486e11i	−0.366610	+	0.719513i	0.631844	+	0.775096i	$0.282298\pi$
$954$	3.12142e11	−	1.01421e11i	0.376841	−	0.122443i
$955$	−4.08607e11	−	1.24811e12i	−0.491238	−	1.50052i
$956$	3.01873e11	−	9.29070e11i	0.361404	−	1.11229i
$957$	7.45031e10	−	7.45031e10i	0.0888232	−	0.0888232i
$958$	−1.20302e12	+	6.12969e11i	−1.42827	+	0.727741i
$959$	3.29558e11	+	4.53597e11i	0.389634	+	0.536285i
$960$	5.38023e11	−	8.64410e10i	0.633455	−	0.101774i
$961$	3.72591e11	+	2.70704e11i	0.436857	+	0.317395i
$962$	−3.04551e10	+	1.92286e11i	−0.0355598	+	0.224516i
$963$	−2.48129e11	−	3.92997e10i	−0.288517	−	0.0456966i
$964$	7.05145e11	−	9.70548e11i	0.816526	−	1.12385i
$965$	7.10147e11	−	3.63829e11i	0.818915	−	0.419554i
$966$	3.57682e11	−	2.59871e11i	0.410760	−	0.298435i
$967$	2.53858e11	+	4.98224e11i	0.290325	+	0.569795i	0.989394	−	0.145260i	$-0.0464018\pi$
$967$	2.53858e11	+	4.98224e11i	0.290325	+	0.569795i	−0.699069	+	0.715055i	$0.746402\pi$
$968$	4.70501e10	+	4.70501e10i	0.0535870	+	0.0535870i
$969$	−4.36713e11	−	1.41897e11i	−0.495337	−	0.160945i
$970$	−5.66292e11	+	7.83090e11i	−0.639667	+	0.884554i
$971$	−4.08966e11	−	1.25867e12i	−0.460056	−	1.41591i	−0.865096	−	0.501607i	$-0.832742\pi$
$971$	−4.08966e11	−	1.25867e12i	−0.460056	−	1.41591i	0.405040	−	0.914299i	$-0.367258\pi$
$972$	−5.39470e10	−	2.74873e10i	−0.0604369	−	0.0307941i
$973$	−2.35752e10	−	1.48848e11i	−0.0263029	−	0.166070i
$974$		−	2.14454e12i		−	2.38286i
$975$	2.25296e11	−	7.43122e10i	0.249307	−	0.0822322i
$976$	−6.92711e11			−0.763402
$977$	2.63102e11	−	4.16712e10i	0.288765	−	0.0457359i	−0.0103713	−	0.999946i	$-0.503301\pi$
$977$	2.63102e11	−	4.16712e10i	0.288765	−	0.0457359i	0.299137	+	0.954210i	$0.403301\pi$
$978$	5.09990e11	−	1.00091e12i	0.557450	−	1.09406i
$979$	−2.33491e11	+	7.58658e10i	−0.254179	+	0.0825877i
$980$	−5.84683e11	+	1.29984e9i	−0.633894	+	0.00140924i
$981$	8.52692e10	−	2.62432e11i	0.0920696	−	0.283361i
$982$	−1.17445e12	+	1.17445e12i	−1.26296	+	1.26296i
$983$	−4.20424e11	+	2.14217e11i	−0.450270	+	0.229424i	−0.664394	−	0.747382i	$-0.731310\pi$
$983$	−4.20424e11	+	2.14217e11i	−0.450270	+	0.229424i	0.214124	+	0.976807i	$0.431310\pi$
$984$	−4.22765e10	−	5.81886e10i	−0.0450940	−	0.0620666i
$985$	4.27131e11	−	4.29034e11i	0.453749	−	0.455771i
$986$	−4.49735e11	−	3.26751e11i	−0.475827	−	0.345708i
$987$	7.66734e10	−	4.84097e11i	0.0807934	−	0.510110i
$988$	−7.70837e11	−	1.22089e11i	−0.808974	−	0.128129i
$989$	3.75295e10	−	5.16549e10i	0.0392272	−	0.0539916i
$990$	−1.27497e11	−	1.99031e10i	−0.132727	−	0.0207195i
$991$	−7.42931e11	+	5.39771e11i	−0.770290	+	0.559648i	−0.902049	−	0.431634i	$-0.857937\pi$
$991$	−7.42931e11	+	5.39771e11i	−0.770290	+	0.559648i	0.131759	+	0.991282i	$0.457937\pi$
$992$	4.26288e11	+	8.36638e11i	0.440207	+	0.863955i
$993$	−2.22729e11	−	2.22729e11i	−0.229076	−	0.229076i
$994$	1.01362e12	+	3.29346e11i	1.03832	+	0.337370i
$995$	6.01451e11	+	1.93946e11i	0.613632	+	0.197874i
$996$	1.01779e11	+	3.13243e11i	0.103424	+	0.318305i
$997$	9.95616e11	+	5.07292e11i	1.00765	+	0.513425i	0.878268	−	0.478169i	$-0.158699\pi$
$997$	9.95616e11	+	5.07292e11i	1.00765	+	0.513425i	0.129386	+	0.991594i	$0.458699\pi$
$998$	8.32755e10	+	5.25781e11i	0.0839450	+	0.530008i
$999$		−	6.68083e10i		−	0.0670762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.7	✓	320
25.2	odd	20	inner	75.9.k.a.52.7	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.7	✓	320	1.1	even	1	trivial
75.9.k.a.52.7	yes	320	25.2	odd	20	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.6671 + 3.59011i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(257.437 - 83.6462i) q^{4} +(-191.814 + 594.838i) q^{5} +(331.652 - 1020.72i) q^{6} +(-1074.42 + 1074.42i) q^{7} +(-300.281 + 153.001i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-22.6671 + 3.59011i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(257.437 - 83.6462i) q^{4} +(-191.814 + 594.838i) q^{5} +(331.652 - 1020.72i) q^{6} +(-1074.42 + 1074.42i) q^{7} +(-300.281 + 153.001i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(2212.32 - 14171.9i) q^{10} +(3327.98 + 2417.92i) q^{11} +(-1980.25 + 12502.8i) q^{12} +(12826.7 + 2031.55i) q^{13} +(20496.7 - 28211.3i) q^{14} +(-20713.5 - 20621.6i) q^{15} +(-49803.9 + 36184.7i) q^{16} +(-20078.4 - 39406.0i) q^{17} +(35490.3 + 35490.3i) q^{18} +(-211149. - 68606.6i) q^{19} +(376.107 + 169178. i) q^{20} +(-21958.2 - 67580.4i) q^{21} +(-84116.2 - 42859.4i) q^{22} +(-42411.3 - 267774. i) q^{23} -15760.6i q^{24} +(-317040. - 228196. i) q^{25} -298037. q^{26} +(101017. - 15999.5i) q^{27} +(-186724. + 366467. i) q^{28} +(-520892. + 169248. i) q^{29} +(543547. + 393067. i) q^{30} +(-193560. + 595716. i) q^{31} +(1.06001e6 - 1.06001e6i) q^{32} +(-171407. + 87336.3i) q^{33} +(596590. + 821135. i) q^{34} +(-433019. - 845197. i) q^{35} +(-478928. - 347962. i) q^{36} +(102186. - 645174. i) q^{37} +(5.03245e6 + 797061. i) q^{38} +(-356975. + 491334. i) q^{39} +(-33412.7 - 207966. i) q^{40} +(3.69204e6 - 2.68243e6i) q^{41} +(740350. + 1.45302e6i) q^{42} +(166529. + 166529. i) q^{43} +(1.05899e6 + 344088. i) q^{44} +(1.29903e6 - 425277. i) q^{45} +(1.92268e6 + 5.91740e6i) q^{46} +(6.14580e6 + 3.13144e6i) q^{47} +(-450363. - 2.84348e6i) q^{48} +3.45603e6i q^{49} +(8.00562e6 + 4.03433e6i) q^{50} +2.06826e6 q^{51} +(3.47199e6 - 549910. i) q^{52} +(2.96871e6 - 5.82643e6i) q^{53} +(-2.23231e6 + 725322. i) q^{54} +(-2.07662e6 + 1.51582e6i) q^{55} +(158241. - 487017. i) q^{56} +(7.34164e6 - 7.34164e6i) q^{57} +(1.11995e7 - 5.70642e6i) q^{58} +(-1.37097e7 - 1.88698e7i) q^{59} +(-7.05732e6 - 3.57615e6i) q^{60} +(9.10341e6 + 6.61402e6i) q^{61} +(2.24875e6 - 1.41980e7i) q^{62} +(3.28215e6 + 519842. i) q^{63} +(-1.09584e7 + 1.50830e7i) q^{64} +(-3.66878e6 + 7.24013e6i) q^{65} +(3.57175e6 - 2.59503e6i) q^{66} +(2.91498e6 + 5.72097e6i) q^{67} +(-8.46507e6 - 8.46507e6i) q^{68} +(1.20581e7 + 3.91792e6i) q^{69} +(1.28496e7 + 1.76036e7i) q^{70} +(9.44467e6 + 2.90677e7i) q^{71} +(656715. + 334613. i) q^{72} +(-770966. - 4.86769e6i) q^{73} +1.49911e7i q^{74} +(1.62396e7 - 8.36566e6i) q^{75} -6.00963e7 q^{76} +(-6.17353e6 + 977791. i) q^{77} +(6.32764e6 - 1.24187e7i) q^{78} +(-1.68692e7 + 5.48113e6i) q^{79} +(-1.19709e7 - 3.65660e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-7.40576e7 + 7.40576e7i) q^{82} +(2.31829e7 - 1.18123e7i) q^{83} +(-1.13057e7 - 1.55610e7i) q^{84} +(2.72915e7 - 4.38477e6i) q^{85} +(-4.37258e6 - 3.17687e6i) q^{86} +(4.00681e6 - 2.52980e7i) q^{87} +(-1.36927e6 - 216872. i) q^{88} +(-3.50800e7 + 4.82834e7i) q^{89} +(-2.79185e7 + 1.43034e7i) q^{90} +(-1.59640e7 + 1.15986e7i) q^{91} +(-3.33165e7 - 6.53874e7i) q^{92} +(-2.07130e7 - 2.07130e7i) q^{93} +(-1.50549e8 - 4.89165e7i) q^{94} +(8.13112e7 - 1.12440e8i) q^{95} +(2.16636e7 + 6.66737e7i) q^{96} +(-6.00315e7 - 3.05876e7i) q^{97} +(-1.24075e7 - 7.83381e7i) q^{98} -8.99647e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

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