LMFDB - Embedded newform 37.10.h.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(3,37)]

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([13]))

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

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

chi := DirichletCharacter("37.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.h (of order $18$, 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:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	37.25
Dual form			37.10.h.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.1667 - 26.4172i) q^{2} +(114.438 + 96.0253i) q^{3} +(-117.600 + 666.941i) q^{4} +(92.1806 + 253.264i) q^{5} -5151.70i q^{6} +(-10964.7 + 3990.81i) q^{7} +(4934.58 - 2848.98i) q^{8} +(457.392 + 2594.00i) q^{9} +O(q^{10})$	\(q+(-22.1667 - 26.4172i) q^{2} +(114.438 + 96.0253i) q^{3} +(-117.600 + 666.941i) q^{4} +(92.1806 + 253.264i) q^{5} -5151.70i q^{6} +(-10964.7 + 3990.81i) q^{7} +(4934.58 - 2848.98i) q^{8} +(457.392 + 2594.00i) q^{9} +(4647.19 - 8049.17i) q^{10} +(-30835.8 - 53409.1i) q^{11} +(-77501.1 + 65031.1i) q^{12} +(173861. + 30656.4i) q^{13} +(348476. + 201193. i) q^{14} +(-13770.7 + 37834.8i) q^{15} +(141185. + 51387.1i) q^{16} +(106598. - 18796.0i) q^{17} +(58387.3 - 69583.3i) q^{18} +(513265. - 611685. i) q^{19} +(-179752. + 31695.2i) q^{20} +(-1.63800e6 - 596183. i) q^{21} +(-727393. + 1.99850e6i) q^{22} +(320300. + 184925. i) q^{23} +(838280. + 147811. i) q^{24} +(1.44054e6 - 1.20875e6i) q^{25} +(-3.04406e6 - 5.27247e6i) q^{26} +(1.27346e6 - 2.20570e6i) q^{27} +(-1.37219e6 - 7.78210e6i) q^{28} +(1.15718e6 - 668100. i) q^{29} +(1.30474e6 - 474887. i) q^{30} +6.64232e6i q^{31} +(-2.76989e6 - 7.61021e6i) q^{32} +(1.59983e6 - 9.07307e6i) q^{33} +(-2.85945e6 - 2.39936e6i) q^{34} +(-2.02146e6 - 2.40908e6i) q^{35} -1.78383e6 q^{36} +(9.56068e6 + 6.20928e6i) q^{37} -2.75364e7 q^{38} +(1.69526e7 + 2.02033e7i) q^{39} +(1.17642e6 + 987131. i) q^{40} +(4.54407e6 - 2.57707e7i) q^{41} +(2.05595e7 + 5.64867e7i) q^{42} -634604. i q^{43} +(3.92470e7 - 1.42847e7i) q^{44} +(-614804. + 354957. i) q^{45} +(-2.21477e6 - 1.25606e7i) q^{46} +(-2.70566e7 + 4.68634e7i) q^{47} +(1.12225e7 + 1.94380e7i) q^{48} +(7.33847e7 - 6.15771e7i) q^{49} +(-6.38637e7 - 1.12609e7i) q^{50} +(1.40038e7 + 8.08507e6i) q^{51} +(-4.08920e7 + 1.12350e8i) q^{52} +(-3.15846e7 - 1.14958e7i) q^{53} +(-8.64970e7 + 1.52517e7i) q^{54} +(1.06841e7 - 1.27329e7i) q^{55} +(-4.27363e7 + 5.09311e7i) q^{56} +(1.17474e8 - 2.07139e7i) q^{57} +(-4.33002e7 - 1.57600e7i) q^{58} +(3.82364e7 - 1.05054e8i) q^{59} +(-2.36141e7 - 1.36336e7i) q^{60} +(-7.92355e7 - 1.39714e7i) q^{61} +(1.75472e8 - 1.47238e8i) q^{62} +(-1.53673e7 - 2.66170e7i) q^{63} +(-1.01178e8 + 1.75246e8i) q^{64} +(8.26245e6 + 4.68587e7i) q^{65} +(-2.75148e8 + 1.58857e8i) q^{66} +(-1.82037e7 + 6.62562e6i) q^{67} +7.33047e7i q^{68} +(1.88971e7 + 5.19194e7i) q^{69} +(-1.88322e7 + 1.06803e8i) q^{70} +(-1.71720e7 - 1.44090e7i) q^{71} +(9.64729e6 + 1.14972e7i) q^{72} -1.75252e8 q^{73} +(-4.78964e7 - 3.90205e8i) q^{74} +2.80923e8 q^{75} +(3.47598e8 + 4.14251e8i) q^{76} +(5.51249e8 + 4.62553e8i) q^{77} +(1.57933e8 - 8.95681e8i) q^{78} +(-3.26973e6 - 8.98351e6i) q^{79} +4.04940e7i q^{80} +(4.06255e8 - 1.47865e8i) q^{81} +(-7.81516e8 + 4.51208e8i) q^{82} +(1.66216e7 + 9.42660e7i) q^{83} +(5.90246e8 - 1.02234e9i) q^{84} +(1.45866e7 + 2.52647e7i) q^{85} +(-1.67645e7 + 1.40670e7i) q^{86} +(1.96581e8 + 3.46625e7i) q^{87} +(-3.04323e8 - 1.75701e8i) q^{88} +(1.77490e8 - 4.87651e8i) q^{89} +(2.30051e7 + 8.37318e6i) q^{90} +(-2.02867e9 + 3.57710e8i) q^{91} +(-1.61001e8 + 1.91874e8i) q^{92} +(-6.37831e8 + 7.60137e8i) q^{93} +(1.83775e9 - 3.24046e8i) q^{94} +(2.02231e8 + 7.36060e7i) q^{95} +(4.13791e8 - 1.13688e9i) q^{96} +(-4.53730e8 - 2.61961e8i) q^{97} +(-3.25339e9 - 5.73660e8i) q^{98} +(1.24439e8 - 1.04417e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9}+O(q^{10}) $ 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9	\( 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9} - 60003 q^{10} + 175689 q^{11} - 307257 q^{12} - 713598 q^{13} + 290583 q^{14} - 385260 q^{15} + 292473 q^{16} + 951645 q^{17} - 2634174 q^{18} + 87108 q^{19} - 6701172 q^{20} + 1892136 q^{21} - 1410435 q^{22} - 9 q^{23} + 6919605 q^{24} - 1830519 q^{25} - 12361155 q^{26} + 12227553 q^{27} - 14971305 q^{28} - 8346069 q^{29} + 32076480 q^{30} + 25901316 q^{32} + 29661003 q^{33} + 17761257 q^{34} - 25104648 q^{35} - 302330892 q^{36} - 89711496 q^{37} + 137852370 q^{38} + 3073230 q^{39} + 72127485 q^{40} + 40690731 q^{41} + 229015377 q^{42} + 187195086 q^{44} - 293199021 q^{45} - 286926930 q^{46} - 134086527 q^{47} + 86156133 q^{48} + 67568640 q^{49} + 134153859 q^{50} - 528106959 q^{51} + 402280539 q^{52} + 147470676 q^{53} + 422122437 q^{54} - 55011861 q^{55} - 616228263 q^{56} - 449072832 q^{57} + 529606191 q^{58} + 773443290 q^{59} + 1433547972 q^{60} + 469275144 q^{61} - 914552304 q^{62} - 673379979 q^{63} + 1146585192 q^{64} - 243884745 q^{65} + 1805055381 q^{66} + 214516206 q^{67} + 722409993 q^{69} - 2605801512 q^{70} - 1455384636 q^{71} - 4689293691 q^{72} + 930909090 q^{73} - 1261741251 q^{74} + 3013150476 q^{75} + 195486513 q^{76} + 1827454371 q^{77} + 1710012453 q^{78} + 1230271476 q^{79} + 2262925611 q^{81} - 3346032141 q^{82} - 2122951164 q^{83} - 6124511730 q^{84} - 39169146 q^{85} - 2603533938 q^{86} + 1185003879 q^{87} - 261497646 q^{88} + 1603969074 q^{89} + 7288796094 q^{90} - 4883515182 q^{91} - 7533267018 q^{92} + 1209552852 q^{93} + 1712695200 q^{94} + 2036912394 q^{95} + 7661250639 q^{96} - 7583351877 q^{97} - 10074558573 q^{98} - 7520510685 q^{99}+O(q^{100}) \) 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9 - 60003 * q^10 + 175689 * q^11 - 307257 * q^12 - 713598 * q^13 + 290583 * q^14 - 385260 * q^15 + 292473 * q^16 + 951645 * q^17 - 2634174 * q^18 + 87108 * q^19 - 6701172 * q^20 + 1892136 * q^21 - 1410435 * q^22 - 9 * q^23 + 6919605 * q^24 - 1830519 * q^25 - 12361155 * q^26 + 12227553 * q^27 - 14971305 * q^28 - 8346069 * q^29 + 32076480 * q^30 + 25901316 * q^32 + 29661003 * q^33 + 17761257 * q^34 - 25104648 * q^35 - 302330892 * q^36 - 89711496 * q^37 + 137852370 * q^38 + 3073230 * q^39 + 72127485 * q^40 + 40690731 * q^41 + 229015377 * q^42 + 187195086 * q^44 - 293199021 * q^45 - 286926930 * q^46 - 134086527 * q^47 + 86156133 * q^48 + 67568640 * q^49 + 134153859 * q^50 - 528106959 * q^51 + 402280539 * q^52 + 147470676 * q^53 + 422122437 * q^54 - 55011861 * q^55 - 616228263 * q^56 - 449072832 * q^57 + 529606191 * q^58 + 773443290 * q^59 + 1433547972 * q^60 + 469275144 * q^61 - 914552304 * q^62 - 673379979 * q^63 + 1146585192 * q^64 - 243884745 * q^65 + 1805055381 * q^66 + 214516206 * q^67 + 722409993 * q^69 - 2605801512 * q^70 - 1455384636 * q^71 - 4689293691 * q^72 + 930909090 * q^73 - 1261741251 * q^74 + 3013150476 * q^75 + 195486513 * q^76 + 1827454371 * q^77 + 1710012453 * q^78 + 1230271476 * q^79 + 2262925611 * q^81 - 3346032141 * q^82 - 2122951164 * q^83 - 6124511730 * q^84 - 39169146 * q^85 - 2603533938 * q^86 + 1185003879 * q^87 - 261497646 * q^88 + 1603969074 * q^89 + 7288796094 * q^90 - 4883515182 * q^91 - 7533267018 * q^92 + 1209552852 * q^93 + 1712695200 * q^94 + 2036912394 * q^95 + 7661250639 * q^96 - 7583351877 * q^97 - 10074558573 * q^98 - 7520510685 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−22.1667	−	26.4172i	−0.979637	−	1.16749i	−0.985871	−	0.167506i	$-0.946429\pi$
$2$	−22.1667	−	26.4172i	−0.979637	−	1.16749i	0.00623384	−	0.999981i	$-0.498016\pi$
$3$	114.438	+	96.0253i	0.815692	+	0.684447i	0.951959	−	0.306225i	$-0.0990660\pi$
$3$	114.438	+	96.0253i	0.815692	+	0.684447i	−0.136267	+	0.990672i	$0.543510\pi$
$4$	−117.600	+	666.941i	−0.229687	+	1.30262i
$5$	92.1806	+	253.264i	0.0659590	+	0.181221i	0.968293	−	0.249816i	$-0.0803701\pi$
$5$	92.1806	+	253.264i	0.0659590	+	0.181221i	−0.902334	+	0.431037i	$0.858148\pi$
$6$		−	5151.70i		−	1.62282i
$7$	−10964.7	+	3990.81i	−1.72605	+	0.628232i	−0.998337	−	0.0576457i	$-0.981641\pi$
$7$	−10964.7	+	3990.81i	−1.72605	+	0.628232i	−0.727717	+	0.685878i	$0.759418\pi$
$8$	4934.58	−	2848.98i	0.425937	−	0.245915i
$9$	457.392	+	2594.00i	0.0232379	+	0.131789i
$10$	4647.19	−	8049.17i	0.146957	−	0.254537i
$11$	−30835.8	−	53409.1i	−0.635020	−	1.09989i	−0.986511	−	0.163696i	$-0.947658\pi$
$11$	−30835.8	−	53409.1i	−0.635020	−	1.09989i	0.351491	−	0.936191i	$-0.385675\pi$
$12$	−77501.1	+	65031.1i	−1.07893	+	0.905327i
$13$	173861.	+	30656.4i	1.68833	+	0.297698i	0.933594	−	0.358332i	$-0.116654\pi$
$13$	173861.	+	30656.4i	1.68833	+	0.297698i	0.754735	+	0.656030i	$0.227765\pi$
$14$	348476.	+	201193.i	2.42436	+	1.39970i
$15$	−13770.7	+	37834.8i	−0.0702339	+	0.192966i
$16$	141185.	+	51387.1i	0.538578	+	0.196026i
$17$	106598.	−	18796.0i	0.309547	−	0.0545816i	−0.0167165	−	0.999860i	$-0.505321\pi$
$17$	106598.	−	18796.0i	0.309547	−	0.0545816i	0.326264	+	0.945279i	$0.394210\pi$
$18$	58387.3	−	69583.3i	0.131097	−	0.156235i
$19$	513265.	−	611685.i	0.903546	−	1.07680i	−0.0931556	−	0.995652i	$-0.529695\pi$
$19$	513265.	−	611685.i	0.903546	−	1.07680i	0.996702	−	0.0811528i	$-0.0258602\pi$
$20$	−179752.	+	31695.2i	−0.251212	+	0.0442954i
$21$	−1.63800e6	−	596183.i	−1.83792	−	0.668948i
$22$	−727393.	+	1.99850e6i	−0.662014	+	1.81887i
$23$	320300.	+	184925.i	0.238661	+	0.137791i	0.614561	−	0.788869i	$-0.289333\pi$
$23$	320300.	+	184925.i	0.238661	+	0.137791i	−0.375900	+	0.926660i	$0.622666\pi$
$24$	838280.	+	147811.i	0.515749	+	0.0909405i
$25$	1.44054e6	−	1.20875e6i	0.737554	−	0.618881i
$26$	−3.04406e6	−	5.27247e6i	−1.30639	−	2.26274i
$27$	1.27346e6	−	2.20570e6i	0.461158	−	0.798749i
$28$	−1.37219e6	−	7.78210e6i	−0.421895	−	2.39269i
$29$	1.15718e6	−	668100.i	0.303817	−	0.175409i	−0.340340	−	0.940303i	$-0.610542\pi$
$29$	1.15718e6	−	668100.i	0.303817	−	0.175409i	0.644156	+	0.764894i	$0.277209\pi$
$30$	1.30474e6	−	474887.i	0.294089	−	0.107040i
$31$			6.64232e6i			1.29179i	0.763426	+	0.645896i	$0.223516\pi$
$31$			6.64232e6i			1.29179i	−0.763426	+	0.645896i	$0.776484\pi$
$32$	−2.76989e6	−	7.61021e6i	−0.466969	−	1.28299i
$33$	1.59983e6	−	9.07307e6i	0.234834	−	1.33181i
$34$	−2.85945e6	−	2.39936e6i	−0.366967	−	0.307922i
$35$	−2.02146e6	−	2.40908e6i	−0.227698	−	0.271360i
$36$	−1.78383e6			−0.177008
$37$	9.56068e6	+	6.20928e6i	0.838650	+	0.544670i
$37$	9.56068e6	+	6.20928e6i	0.838650	+	0.544670i
$38$	−2.75364e7			−2.14230
$39$	1.69526e7	+	2.02033e7i	1.17340	+	1.39840i
$40$	1.17642e6	+	987131.i	0.0726593	+	0.0609684i
$41$	4.54407e6	−	2.57707e7i	0.251141	−	1.42429i	−0.554647	−	0.832086i	$-0.687147\pi$
$41$	4.54407e6	−	2.57707e7i	0.251141	−	1.42429i	0.805788	−	0.592204i	$-0.201742\pi$
$42$	2.05595e7	+	5.64867e7i	1.01951	+	2.80107i
$43$		−	634604.i		−	0.0283070i	−0.999900	−	0.0141535i	$-0.995495\pi$
$43$		−	634604.i		−	0.0283070i	0.999900	−	0.0141535i	$-0.00450536\pi$
$44$	3.92470e7	−	1.42847e7i	1.57859	−	0.574559i
$45$	−614804.	+	354957.i	−0.0223501	+	0.0129039i
$46$	−2.21477e6	−	1.25606e7i	−0.0729321	−	0.413619i
$47$	−2.70566e7	+	4.68634e7i	−0.808785	+	1.40086i	0.104922	+	0.994481i	$0.466541\pi$
$47$	−2.70566e7	+	4.68634e7i	−0.808785	+	1.40086i	−0.913706	+	0.406376i	$0.866792\pi$
$48$	1.12225e7	+	1.94380e7i	0.305144	+	0.528525i
$49$	7.33847e7	−	6.15771e7i	1.81854	−	1.52594i
$50$	−6.38637e7	−	1.12609e7i	−1.44507	−	0.254805i
$51$	1.40038e7	+	8.08507e6i	0.289854	+	0.167347i
$52$	−4.08920e7	+	1.12350e8i	−0.775574	+	2.13087i
$53$	−3.15846e7	−	1.14958e7i	−0.549836	−	0.200124i	0.0521374	−	0.998640i	$-0.483397\pi$
$53$	−3.15846e7	−	1.14958e7i	−0.549836	−	0.200124i	−0.601974	+	0.798516i	$0.705619\pi$
$54$	−8.64970e7	+	1.52517e7i	−1.38430	+	0.244089i
$55$	1.06841e7	−	1.27329e7i	0.157437	−	0.187626i
$56$	−4.27363e7	+	5.09311e7i	−0.580698	+	0.692049i
$57$	1.17474e8	−	2.07139e7i	1.47403	−	0.259911i
$58$	−4.33002e7	−	1.57600e7i	−0.502417	−	0.182865i
$59$	3.82364e7	−	1.05054e8i	0.410811	−	1.12869i	−0.545949	−	0.837818i	$-0.683831\pi$
$59$	3.82364e7	−	1.05054e8i	0.410811	−	1.12869i	0.956761	−	0.290877i	$-0.0939469\pi$
$60$	−2.36141e7	−	1.36336e7i	−0.235229	−	0.135810i
$61$	−7.92355e7	−	1.39714e7i	−0.732716	−	0.129198i	−0.205173	−	0.978726i	$-0.565776\pi$
$61$	−7.92355e7	−	1.39714e7i	−0.732716	−	0.129198i	−0.527543	+	0.849528i	$0.676887\pi$
$62$	1.75472e8	−	1.47238e8i	1.50815	−	1.26549i
$63$	−1.53673e7	−	2.66170e7i	−0.122904	−	0.212876i
$64$	−1.01178e8	+	1.75246e8i	−0.753837	+	1.30568i
$65$	8.26245e6	+	4.68587e7i	0.0574115	+	0.325597i
$66$	−2.75148e8	+	1.58857e8i	−1.78492	+	1.03052i
$67$	−1.82037e7	+	6.62562e6i	−0.110363	+	0.0401689i	−0.396611	−	0.917987i	$-0.629814\pi$
$67$	−1.82037e7	+	6.62562e6i	−0.110363	+	0.0401689i	0.286248	+	0.958155i	$0.407592\pi$
$68$			7.33047e7i			0.415759i
$69$	1.88971e7	+	5.19194e7i	0.100363	+	0.275746i
$70$	−1.88322e7	+	1.06803e8i	−0.0937474	+	0.531668i
$71$	−1.71720e7	−	1.44090e7i	−0.0801972	−	0.0672934i	0.601808	−	0.798641i	$-0.294447\pi$
$71$	−1.71720e7	−	1.44090e7i	−0.0801972	−	0.0672934i	−0.682005	+	0.731348i	$0.738892\pi$
$72$	9.64729e6	+	1.14972e7i	0.0423067	+	0.0504191i
$73$	−1.75252e8			−0.722289			−0.361144	−	0.932510i	$-0.617614\pi$
$73$	−1.75252e8			−0.722289			−0.361144	+	0.932510i	$0.617614\pi$
$74$	−4.78964e7	−	3.90205e8i	−0.185678	−	1.51269i
$75$	2.80923e8			1.02521
$76$	3.47598e8	+	4.14251e8i	1.19513	+	1.42430i
$77$	5.51249e8	+	4.62553e8i	1.78706	+	1.49952i
$78$	1.57933e8	−	8.95681e8i	0.483110	−	2.73985i
$79$	−3.26973e6	−	8.98351e6i	−0.00944475	−	0.0259492i	0.934881	−	0.354962i	$-0.115506\pi$
$79$	−3.26973e6	−	8.98351e6i	−0.00944475	−	0.0259492i	−0.944325	+	0.329013i	$0.893284\pi$
$80$			4.04940e7i			0.110531i
$81$	4.06255e8	−	1.47865e8i	1.04862	−	0.381665i
$82$	−7.81516e8	+	4.51208e8i	−1.90887	+	1.10208i
$83$	1.66216e7	+	9.42660e7i	0.0384435	+	0.218024i	0.997977	−	0.0635692i	$-0.0202484\pi$
$83$	1.66216e7	+	9.42660e7i	0.0384435	+	0.218024i	−0.959534	+	0.281593i	$0.909137\pi$
$84$	5.90246e8	−	1.02234e9i	1.29353	−	2.24046i
$85$	1.45866e7	+	2.52647e7i	0.0303088	+	0.0524964i
$86$	−1.67645e7	+	1.40670e7i	−0.0330481	+	0.0277306i
$87$	1.96581e8	+	3.46625e7i	0.367879	+	0.0648669i
$88$	−3.04323e8	−	1.75701e8i	−0.540957	−	0.312322i
$89$	1.77490e8	−	4.87651e8i	0.299861	−	0.823861i	−0.694662	−	0.719337i	$-0.744446\pi$
$89$	1.77490e8	−	4.87651e8i	0.299861	−	0.823861i	0.994522	−	0.104524i	$-0.0333319\pi$
$90$	2.30051e7	+	8.37318e6i	0.0369601	+	0.0134524i
$91$	−2.02867e9	+	3.57710e8i	−3.10117	+	0.546820i
$92$	−1.61001e8	+	1.91874e8i	−0.234306	+	0.279235i
$93$	−6.37831e8	+	7.60137e8i	−0.884163	+	1.05370i
$94$	1.83775e9	−	3.24046e8i	2.42780	−	0.428086i
$95$	2.02231e8	+	7.36060e7i	0.254737	+	0.0927165i
$96$	4.13791e8	−	1.13688e9i	0.497233	−	1.36614i
$97$	−4.53730e8	−	2.61961e8i	−0.520385	−	0.300444i	0.216707	−	0.976237i	$-0.430468\pi$
$97$	−4.53730e8	−	2.61961e8i	−0.520385	−	0.300444i	−0.737092	+	0.675792i	$0.763802\pi$
$98$	−3.25339e9	−	5.73660e8i	−3.56302	−	0.628257i
$99$	1.24439e8	−	1.04417e8i	0.130196	−	0.109248i
$100$	6.36760e8	+	1.10290e9i	0.636760	+	1.10290i
$101$	5.94209e8	−	1.02920e9i	0.568189	−	0.984133i	−0.428556	−	0.903515i	$-0.640977\pi$
$101$	5.94209e8	−	1.02920e9i	0.568189	−	0.984133i	0.996745	−	0.0806176i	$-0.0256892\pi$
$102$	−9.68316e7	−	5.49159e8i	−0.0885760	−	0.502340i
$103$	1.55586e9	−	8.98275e8i	1.36208	−	0.786397i	0.372179	−	0.928161i	$-0.378611\pi$
$103$	1.55586e9	−	8.98275e8i	1.36208	−	0.786397i	0.989901	+	0.141764i	$0.0452773\pi$
$104$	9.45271e8	−	3.44050e8i	0.792330	−	0.288385i
$105$		−	4.69803e8i		−	0.377193i
$106$	3.96436e8	+	1.08920e9i	0.304998	+	0.837976i
$107$	5.98715e7	−	3.39548e8i	0.0441563	−	0.250423i	−0.954737	−	0.297450i	$-0.903864\pi$
$107$	5.98715e7	−	3.39548e8i	0.0441563	−	0.250423i	0.998894	+	0.0470274i	$0.0149748\pi$
$108$	1.32131e9	+	1.10871e9i	0.934543	+	0.784175i
$109$	6.69978e8	+	7.98449e8i	0.454612	+	0.541786i	0.943854	−	0.330362i	$-0.107171\pi$
$109$	6.69978e8	+	7.98449e8i	0.454612	+	0.541786i	−0.489242	+	0.872148i	$0.662726\pi$
$110$	−5.73198e8			−0.373283
$111$	4.97861e8	+	1.62865e9i	0.311282	+	1.01830i
$112$	−1.75312e9			−1.05276
$113$	1.24922e9	+	1.48876e9i	0.720751	+	0.858957i	0.994704	−	0.102786i	$-0.0327756\pi$
$113$	1.24922e9	+	1.48876e9i	0.720751	+	0.858957i	−0.273953	+	0.961743i	$0.588331\pi$
$114$	−3.15122e9	−	2.64419e9i	−1.74746	−	1.46629i
$115$	−1.73095e7	+	9.81669e7i	−0.00922877	+	0.0523389i
$116$	3.09499e8	+	8.50341e8i	0.158708	+	0.436046i
$117$			4.65017e8i			0.229421i
$118$	−3.62279e9	+	1.31859e9i	−1.72018	+	0.626095i
$119$	−1.09380e9	+	6.31503e8i	−0.500006	+	0.288678i
$120$	3.98378e7	+	2.25932e8i	0.0175380	+	0.0994629i
$121$	−7.22713e8	+	1.25178e9i	−0.306501	+	0.530875i
$122$	1.38730e9	+	2.40288e9i	0.566959	+	0.982002i
$123$	2.99465e9	−	2.51281e9i	1.17970	−	0.989890i
$124$	−4.43004e9	−	7.81135e8i	−1.68271	−	0.296707i
$125$	8.94801e8	+	5.16613e8i	0.327817	+	0.189265i
$126$	−3.62504e8	+	9.95970e8i	−0.128128	+	0.352029i
$127$	4.41646e8	+	1.60746e8i	0.150646	+	0.0548306i	0.416243	−	0.909254i	$-0.363347\pi$
$127$	4.41646e8	+	1.60746e8i	0.150646	+	0.0548306i	−0.265597	+	0.964084i	$0.585569\pi$
$128$	2.78879e9	−	4.91740e8i	0.918272	−	0.161916i
$129$	6.09380e7	−	7.26231e7i	0.0193747	−	0.0230898i
$130$	1.05472e9	−	1.25697e9i	0.323887	−	0.385994i
$131$	2.39378e9	−	4.22088e8i	0.710172	−	0.125222i	0.193118	−	0.981175i	$-0.438140\pi$
$131$	2.39378e9	−	4.22088e8i	0.710172	−	0.125222i	0.517054	+	0.855953i	$0.327029\pi$
$132$	5.86306e9	+	2.13398e9i	1.68090	+	0.611797i
$133$	−3.18666e9	+	8.75527e9i	−0.883086	+	2.42626i
$134$	5.78546e8	+	3.34024e8i	0.155012	+	0.0894965i
$135$	6.76014e8	+	1.19200e8i	0.175168	+	0.0308868i
$136$	4.72465e8	−	3.96445e8i	0.118425	−	0.0993706i
$137$	−4.16556e8	−	7.21496e8i	−0.101026	−	0.174981i	0.811082	−	0.584933i	$-0.198879\pi$
$137$	−4.16556e8	−	7.21496e8i	−0.101026	−	0.174981i	−0.912107	+	0.409951i	$0.865546\pi$
$138$	9.52680e8	−	1.65009e9i	0.223610	−	0.387304i
$139$	9.46835e8	+	5.36977e9i	0.215133	+	1.22008i	0.880675	+	0.473721i	$0.157089\pi$
$139$	9.46835e8	+	5.36977e9i	0.215133	+	1.22008i	−0.665542	+	0.746361i	$0.731800\pi$
$140$	1.84444e9	−	1.06489e9i	0.405777	−	0.234275i
$141$	−7.59639e9	+	2.76486e9i	−1.61853	+	0.589097i
$142$			7.73037e8i			0.159552i
$143$	−3.72381e9	−	1.02311e10i	−0.744689	−	2.04602i
$144$	−6.87213e7	+	3.89738e8i	−0.0133186	+	0.0755338i
$145$	2.75876e8	+	2.31487e8i	0.0518272	+	0.0434881i
$146$	3.88476e9	+	4.62968e9i	0.707581	+	0.843262i
$147$	1.43110e10			2.52779
$148$	−5.26556e9	+	5.64619e9i	−0.902124	+	0.967338i
$149$	5.53829e9			0.920528			0.460264	−	0.887782i	$-0.347755\pi$
$149$	5.53829e9			0.920528			0.460264	+	0.887782i	$0.347755\pi$
$150$	−6.22713e9	−	7.42121e9i	−1.00433	−	1.19692i
$151$	−8.73205e9	−	7.32706e9i	−1.36685	−	1.14692i	−0.973801	−	0.227401i	$-0.926977\pi$
$151$	−8.73205e9	−	7.32706e9i	−1.36685	−	1.14692i	−0.393045	−	0.919519i	$-0.628579\pi$
$152$	7.90067e8	−	4.48069e9i	0.120052	−	0.680846i
$153$	9.75137e7	+	2.67917e8i	0.0143865	+	0.0395265i
$154$		−	2.48157e10i		−	3.55536i
$155$	−1.68226e9	+	6.12293e8i	−0.234100	+	0.0852053i
$156$	−1.54680e10	+	8.93048e9i	−2.09110	+	1.20730i
$157$	−1.25600e9	−	7.12311e9i	−0.164983	−	0.935667i	−0.949082	−	0.315030i	$-0.897985\pi$
$157$	−1.25600e9	−	7.12311e9i	−0.164983	−	0.935667i	0.784098	−	0.620636i	$-0.213126\pi$
$158$	−1.64840e8	+	2.85512e8i	−0.0210429	+	0.0364474i
$159$	−2.51060e9	−	4.34848e9i	−0.311523	−	0.539574i
$160$	1.67206e9	−	1.40303e9i	0.201703	−	0.169249i
$161$	−4.24998e9	−	7.49387e8i	−0.498506	−	0.0879001i
$162$	−1.29115e10	−	7.45446e9i	−1.47285	−	0.850351i
$163$	−2.49988e8	+	6.86837e8i	−0.0277380	+	0.0762096i	−0.952789	−	0.303634i	$-0.901800\pi$
$163$	−2.49988e8	+	6.86837e8i	−0.0277380	+	0.0762096i	0.925051	+	0.379844i	$0.124022\pi$
$164$	1.66531e10	+	6.06124e9i	1.79762	+	0.654281i
$165$	2.44535e9	−	4.31182e8i	0.256841	−	0.0452880i
$166$	2.12180e9	−	2.52866e9i	0.216879	−	0.258466i
$167$	4.01781e9	−	4.78824e9i	0.399729	−	0.476378i	−0.528208	−	0.849115i	$-0.677136\pi$
$167$	4.01781e9	−	4.78824e9i	0.399729	−	0.476378i	0.927937	+	0.372737i	$0.121580\pi$
$168$	−9.78135e9	+	1.72472e9i	−0.947343	+	0.167042i
$169$	1.93229e10	+	7.03295e9i	1.82214	+	0.663205i
$170$	3.44087e8	−	9.45371e8i	0.0315972	−	0.0868125i
$171$	1.82147e9	+	1.05163e9i	0.162907	+	0.0940545i
$172$	4.23243e8	+	7.46292e7i	0.0368733	+	0.00650175i
$173$	5.09725e9	−	4.27710e9i	0.432642	−	0.363030i	−0.400306	−	0.916382i	$-0.631096\pi$
$173$	5.09725e9	−	4.27710e9i	0.432642	−	0.363030i	0.832948	+	0.553352i	$0.186652\pi$
$174$	−3.44185e9	−	5.96147e9i	−0.284656	−	0.493039i
$175$	−1.09711e10	+	1.90025e10i	−0.884257	+	1.53158i
$176$	−1.60901e9	−	9.12512e9i	−0.126401	−	0.716856i
$177$	1.44635e10	−	8.35051e9i	1.10763	−	0.639489i
$178$	−1.68167e10	+	6.12079e9i	−1.25560	+	0.457001i
$179$		−	1.35159e10i		−	0.984023i	−0.870589	−	0.492011i	$-0.836262\pi$
$179$		−	1.35159e10i		−	0.984023i	0.870589	−	0.492011i	$-0.163738\pi$
$180$	−1.64435e8	−	4.51780e8i	−0.0116753	−	0.0320775i
$181$	−3.40624e9	+	1.93177e10i	−0.235896	+	1.33784i	0.604821	+	0.796361i	$0.293245\pi$
$181$	−3.40624e9	+	1.93177e10i	−0.235896	+	1.33784i	−0.840718	+	0.541474i	$0.817867\pi$
$182$	5.44186e10	+	4.56626e10i	3.67643	+	3.08489i
$183$	−7.72599e9	−	9.20747e9i	−0.509242	−	0.606891i
$184$	2.10739e9			0.135539
$185$	−6.91280e8	+	2.99375e9i	−0.0433891	+	0.187907i
$186$	3.42193e10			2.09634
$187$	−4.29090e9	−	5.11369e9i	−0.256602	−	0.305807i
$188$	−2.80733e10	−	2.35563e10i	−1.63901	−	1.37530i
$189$	−5.16056e9	+	2.92670e10i	−0.294184	+	1.66840i
$190$	−2.53832e9	−	6.97397e9i	−0.141304	−	0.388230i
$191$		−	1.24954e10i		−	0.679359i	−0.940541	−	0.339680i	$-0.889681\pi$
$191$		−	1.24954e10i		−	0.679359i	0.940541	−	0.339680i	$-0.110319\pi$
$192$	−2.84067e10	+	1.03392e10i	−1.50857	+	0.549075i
$193$	1.32590e10	−	7.65510e9i	0.687865	−	0.397139i	−0.114947	−	0.993372i	$-0.536670\pi$
$193$	1.32590e10	−	7.65510e9i	0.687865	−	0.397139i	0.802812	+	0.596233i	$0.203336\pi$
$194$	3.13740e9	+	1.77931e10i	0.159024	+	0.901869i
$195$	−3.55407e9	+	6.15584e9i	−0.176024	+	0.304882i
$196$	3.24382e10	+	5.61847e10i	1.57002	+	2.71935i
$197$	2.41595e10	−	2.02722e10i	1.14285	−	0.958966i	0.143323	−	0.989676i	$-0.454221\pi$
$197$	2.41595e10	−	2.02722e10i	1.14285	−	0.958966i	0.999528	+	0.0307098i	$0.00977677\pi$
$198$	−5.51680e9	−	9.72760e8i	−0.255090	−	0.0449793i
$199$	−4.81009e9	−	2.77711e9i	−0.217428	−	0.125532i	0.387331	−	0.921941i	$-0.373397\pi$
$199$	−4.81009e9	−	2.77711e9i	−0.217428	−	0.125532i	−0.604759	+	0.796409i	$0.706730\pi$
$200$	3.66472e9	−	1.00687e10i	0.161959	−	0.444980i
$201$	−2.71943e9	−	9.89793e8i	−0.117516	−	0.0427723i
$202$	−4.03602e10	+	7.11660e9i	−1.70558	+	0.300740i
$203$	−1.00219e10	+	1.19436e10i	−0.414206	+	0.493632i
$204$	−7.03910e9	+	8.38887e9i	−0.284565	+	0.339131i
$205$	6.94566e9	−	1.22471e9i	0.274676	−	0.0484328i
$206$	−5.82181e10	−	2.11897e10i	−2.25245	−	0.819825i
$207$	−3.33193e8	+	9.15440e8i	−0.0126133	+	0.0346548i
$208$	2.29712e10	+	1.32624e10i	0.850941	+	0.491291i
$209$	−4.84965e10	−	8.55123e9i	−1.75813	−	0.310006i
$210$	−1.24109e10	+	1.04140e10i	−0.440368	+	0.369512i
$211$	1.02473e10	+	1.77489e10i	0.355909	+	0.616453i	0.987273	−	0.159034i	$-0.0508379\pi$
$211$	1.02473e10	+	1.77489e10i	0.355909	+	0.616453i	−0.631364	+	0.775487i	$0.717505\pi$
$212$	1.13814e10	−	1.97131e10i	0.386975	−	0.670261i
$213$	−5.81508e8	−	3.29790e9i	−0.0193574	−	0.109781i
$214$	−1.02971e10	+	5.94501e9i	−0.335623	+	0.193772i
$215$	1.60722e8	−	5.84981e7i	0.00512983	−	0.00186711i
$216$		−	1.45123e10i		−	0.453622i
$217$	−2.65083e10	−	7.28309e10i	−0.811545	−	2.22970i
$218$	6.24160e9	−	3.53979e10i	0.187172	−	1.06151i
$219$	−2.00556e10	−	1.68287e10i	−0.589166	−	0.494369i
$220$	7.23561e9	+	8.62307e9i	0.208244	+	0.248176i
$221$	1.91094e10			0.538867
$222$	3.19884e10	−	4.92538e10i	0.883902	−	1.36098i
$223$	−2.29730e10			−0.622079			−0.311040	−	0.950397i	$-0.600677\pi$
$223$	−2.29730e10			−0.622079			−0.311040	+	0.950397i	$0.600677\pi$
$224$	6.07419e10	+	7.23893e10i	1.61203	+	1.92114i
$225$	3.79439e9	+	3.18387e9i	0.0987008	+	0.0828198i
$226$	1.16379e10	−	6.60017e10i	0.296747	−	1.68293i
$227$	3.43041e9	+	9.42496e9i	0.0857490	+	0.235593i	0.975155	−	0.221525i	$-0.0711036\pi$
$227$	3.43041e9	+	9.42496e9i	0.0857490	+	0.235593i	−0.889406	+	0.457119i	$0.848881\pi$
$228$			8.07844e10i			1.97980i
$229$	−3.79452e10	+	1.38109e10i	−0.911794	+	0.331866i	−0.754969	−	0.655761i	$-0.772348\pi$
$229$	−3.79452e10	+	1.38109e10i	−0.911794	+	0.331866i	−0.156825	+	0.987626i	$0.550126\pi$
$230$	2.97699e9	−	1.71876e9i	0.0701458	−	0.0404987i
$231$	1.86673e10	+	1.05868e11i	0.431349	+	2.44630i
$232$	3.80681e9	−	6.59359e9i	0.0862711	−	0.149426i
$233$	−1.34526e10	−	2.33006e10i	−0.299024	−	0.517924i	0.676889	−	0.736085i	$-0.263328\pi$
$233$	−1.34526e10	−	2.33006e10i	−0.299024	−	0.517924i	−0.975913	+	0.218161i	$0.929994\pi$
$234$	1.22844e10	−	1.03079e10i	0.267845	−	0.224749i
$235$	−1.43629e10	−	2.53257e9i	−0.307211	−	0.0541696i
$236$	6.55679e10	+	3.78556e10i	1.37590	+	0.794377i
$237$	4.88461e8	−	1.34204e9i	0.0100569	−	0.0276310i
$238$	4.09284e10	+	1.48967e10i	0.826852	+	0.300950i
$239$	−6.40824e10	+	1.12995e10i	−1.27042	+	0.224010i	−0.767909	−	0.640559i	$-0.778703\pi$
$239$	−6.40824e10	+	1.12995e10i	−1.27042	+	0.224010i	−0.502514	+	0.864569i	$0.667592\pi$
$240$	−3.88845e9	+	4.63407e9i	−0.0756529	+	0.0901596i
$241$	5.04014e9	−	6.00660e9i	0.0962422	−	0.114697i	−0.715774	−	0.698332i	$-0.753926\pi$
$241$	5.04014e9	−	6.00660e9i	0.0962422	−	0.114697i	0.812016	+	0.583635i	$0.198370\pi$
$242$	4.90886e10	−	8.65564e9i	0.920050	−	0.162230i
$243$	1.35821e10	+	4.94347e9i	0.249884	+	0.0909503i
$244$	1.86361e10	−	5.12023e10i	0.336590	−	0.924774i
$245$	2.23599e10	+	1.29095e10i	0.396481	+	0.228908i
$246$	−1.32763e11	−	2.34097e10i	−2.31137	−	0.407556i
$247$	1.07989e11	−	9.06134e10i	1.84605	−	1.54902i
$248$	1.89239e10	+	3.27771e10i	0.317671	+	0.550222i
$249$	−7.14976e9	+	1.23838e10i	−0.117868	+	0.204153i
$250$	−6.18726e9	−	3.50897e10i	−0.100177	−	0.568133i
$251$	−5.67101e10	+	3.27416e10i	−0.901839	+	0.520677i	−0.877796	−	0.479034i	$-0.840987\pi$
$251$	−5.67101e10	+	3.27416e10i	−0.901839	+	0.520677i	−0.0240426	+	0.999711i	$0.507654\pi$
$252$	1.95591e10	−	7.11894e9i	0.305525	−	0.111202i
$253$		−	2.28092e10i		−	0.350000i
$254$	−5.54335e9	−	1.52302e10i	−0.0835643	−	0.229591i
$255$	−7.56784e8	+	4.29194e9i	−0.0112083	+	0.0635656i
$256$	4.55862e9	+	3.82513e9i	0.0663366	+	0.0556630i
$257$	7.42437e10	+	8.84802e10i	1.06160	+	1.26516i	0.962845	+	0.270053i	$0.0870413\pi$
$257$	7.42437e10	+	8.84802e10i	1.06160	+	1.26516i	0.0987540	+	0.995112i	$0.468514\pi$
$258$	−3.26929e9			−0.0459372
$259$	−1.29610e11	−	2.99279e10i	−1.78973	−	0.413263i
$260$	−3.22236e10			−0.437315
$261$	2.26234e9	+	2.69615e9i	0.0301769	+	0.0359635i
$262$	−6.42125e10	−	5.38807e10i	−0.841906	−	0.706443i
$263$	−3.29303e9	+	1.86757e10i	−0.0424420	+	0.240700i	−0.998647	−	0.0519965i	$-0.983442\pi$
$263$	−3.29303e9	+	1.86757e10i	−0.0424420	+	0.240700i	0.956205	+	0.292697i	$0.0945527\pi$
$264$	−1.79545e10	−	4.93297e10i	−0.227487	−	0.625015i
$265$		−	9.05893e9i		−	0.112842i
$266$	3.01927e11	−	1.09893e11i	3.69773	−	1.34586i
$267$	6.71385e10	−	3.87624e10i	0.808483	−	0.466778i
$268$	−2.27814e9	−	1.29200e10i	−0.0269758	−	0.152987i
$269$	−7.32582e10	+	1.26887e11i	−0.853043	+	1.47751i	0.0254063	+	0.999677i	$0.491912\pi$
$269$	−7.32582e10	+	1.26887e11i	−0.853043	+	1.47751i	−0.878449	+	0.477836i	$0.841421\pi$
$270$	−1.18361e10	−	2.05007e10i	−0.135541	−	0.234764i
$271$	5.00893e10	−	4.20299e10i	0.564136	−	0.473366i	−0.315558	−	0.948906i	$-0.602192\pi$
$271$	5.00893e10	−	4.20299e10i	0.564136	−	0.473366i	0.879694	+	0.475540i	$0.157747\pi$
$272$	1.60159e10	+	2.82403e9i	0.177415	+	0.0312830i
$273$	−2.66507e11	−	1.53868e11i	−2.90387	−	1.67655i
$274$	−9.82626e9	+	2.69974e10i	−0.105320	+	0.289364i
$275$	−1.08978e11	−	3.96649e10i	−1.14906	−	0.418224i
$276$	−3.68495e10	+	6.49756e9i	−0.382244	+	0.0673999i
$277$	2.69751e10	−	3.21477e10i	0.275299	−	0.328088i	−0.610624	−	0.791920i	$-0.709081\pi$
$277$	2.69751e10	−	3.21477e10i	0.275299	−	0.328088i	0.885923	+	0.463832i	$0.153526\pi$
$278$	1.20866e11	−	1.44042e11i	1.21368	−	1.44640i
$279$	−1.72302e10	+	3.03814e9i	−0.170244	+	0.0300185i
$280$	−1.68385e10	−	6.12870e9i	−0.163716	−	0.0595878i
$281$	3.70668e10	−	1.01840e11i	0.354656	−	0.974408i	−0.626198	−	0.779664i	$-0.715390\pi$
$281$	3.70668e10	−	1.01840e11i	0.354656	−	0.974408i	0.980854	−	0.194745i	$-0.0623878\pi$
$282$	2.41426e11	+	1.39388e11i	2.27334	+	1.31251i
$283$	1.31709e10	+	2.32239e9i	0.122061	+	0.0215227i	0.234345	−	0.972153i	$-0.424705\pi$
$283$	1.31709e10	+	2.32239e9i	0.122061	+	0.0215227i	−0.112284	+	0.993676i	$0.535817\pi$
$284$	1.16294e10	−	9.75822e9i	0.106078	−	0.0890099i
$285$	1.60750e10	+	2.78426e10i	0.144327	+	0.249982i
$286$	−1.87732e11	+	3.25161e11i	−1.65917	+	2.87377i
$287$	5.30218e10	+	3.00701e11i	0.461302	+	2.61618i
$288$	1.84739e10	−	1.06659e10i	0.158232	−	0.0913551i
$289$	−1.00426e11	+	3.65522e10i	−0.846852	+	0.308229i
$290$		−	1.24192e10i		−	0.103110i
$291$	−2.67693e10	−	7.35480e10i	−0.218836	−	0.601246i
$292$	2.06096e10	−	1.16883e11i	0.165900	−	0.940867i
$293$	−5.97949e10	−	5.01738e10i	−0.473980	−	0.397716i	0.374264	−	0.927322i	$-0.377895\pi$
$293$	−5.97949e10	−	5.01738e10i	−0.473980	−	0.397716i	−0.848244	+	0.529606i	$0.822340\pi$
$294$	−3.17227e11	−	3.78056e11i	−2.47632	−	2.95116i
$295$	3.01309e10			0.231640
$296$	6.48681e10	+	3.40202e9i	0.491155	+	0.0257587i
$297$	−1.57073e11			−1.17138
$298$	−1.22765e11	−	1.46306e11i	−0.901784	−	1.07470i
$299$	5.00185e10	+	4.19705e10i	0.361918	+	0.303685i
$300$	−3.30365e10	+	1.87359e11i	−0.235477	+	1.33546i
$301$	2.53258e9	+	6.95822e9i	0.0177834	+	0.0488595i
$302$			3.93093e11i			2.71934i
$303$	1.66830e11	−	6.07210e10i	1.13705	−	0.413854i
$304$	1.03898e11	−	5.99856e10i	0.697712	−	0.402824i
$305$	−3.76553e9	−	2.13554e10i	−0.0249159	−	0.141305i
$306$	4.91606e9	−	8.51486e9i	0.0320531	−	0.0555176i
$307$	1.13479e11	+	1.96552e11i	0.729110	+	1.26286i	0.957260	+	0.289230i	$0.0933991\pi$
$307$	1.13479e11	+	1.96552e11i	0.729110	+	1.26286i	−0.228150	+	0.973626i	$0.573268\pi$
$308$	−3.73322e11	+	3.13255e11i	−2.36377	+	1.98344i
$309$	2.64307e11	+	4.66045e10i	1.64929	+	0.290813i
$310$	5.34652e10	+	3.08681e10i	0.328809	+	0.189838i
$311$	−1.95235e9	+	5.36404e9i	−0.0118341	+	0.0325140i	−0.945469	−	0.325712i	$-0.894396\pi$
$311$	−1.95235e9	+	5.36404e9i	−0.0118341	+	0.0325140i	0.933635	+	0.358226i	$0.116618\pi$
$312$	1.41213e11	+	5.13973e10i	0.843682	+	0.307075i
$313$	2.11490e11	−	3.72913e10i	1.24549	−	0.219613i	0.488222	−	0.872719i	$-0.337646\pi$
$313$	2.11490e11	−	3.72913e10i	1.24549	−	0.219613i	0.757266	+	0.653106i	$0.226535\pi$
$314$	−1.60331e11	+	1.91075e11i	−0.930754	+	1.10923i
$315$	5.32455e9	−	6.34555e9i	0.0304709	−	0.0363138i
$316$	6.37599e9	−	1.12426e9i	0.0359713	−	0.00634271i
$317$	2.57876e11	+	9.38591e10i	1.43431	+	0.522047i	0.938164	−	0.346190i	$-0.112525\pi$
$317$	2.57876e11	+	9.38591e10i	1.43431	+	0.522047i	0.496149	+	0.868238i	$0.334747\pi$
$318$	−5.92232e10	+	1.62714e11i	−0.324765	+	0.892285i
$319$	−7.13653e10	−	4.12028e10i	−0.385859	−	0.222776i
$320$	−5.37102e10	−	9.47055e9i	−0.286340	−	0.0504894i
$321$	3.94568e10	−	3.31082e10i	0.207419	−	0.174045i
$322$	7.44112e10	+	1.28884e11i	0.385733	+	0.668110i
$323$	4.32155e10	−	7.48515e10i	0.220917	−	0.382639i
$324$	5.08416e10	+	2.88337e11i	0.256311	+	1.45361i
$325$	2.87509e11	−	1.65993e11i	1.42947	−	0.825307i
$326$	2.36857e10	−	8.62089e9i	0.116147	−	0.0422740i
$327$			1.55708e11i			0.753089i
$328$	−5.09971e10	−	1.40113e11i	−0.243284	−	0.668417i
$329$	1.09644e11	−	6.21820e11i	0.515943	−	2.92606i
$330$	−6.55959e10	−	5.50415e10i	−0.304484	−	0.255492i
$331$	8.02398e10	+	9.56261e10i	0.367421	+	0.437875i	0.917802	−	0.397038i	$-0.129962\pi$
$331$	8.02398e10	+	9.56261e10i	0.367421	+	0.437875i	−0.550381	+	0.834914i	$0.685518\pi$
$332$	−6.48245e10			−0.292832
$333$	−1.17339e10	+	2.76404e10i	−0.0522929	+	0.123182i
$334$	−2.15553e11			−0.947754
$335$	−3.35606e9	−	3.99960e9i	−0.0145589	−	0.0173506i
$336$	−2.00625e11	−	1.68344e11i	−0.858732	−	0.720562i
$337$	1.44062e10	−	8.17013e10i	0.0608434	−	0.345060i	−0.939155	−	0.343493i	$-0.888390\pi$
$337$	1.44062e10	−	8.17013e10i	0.0608434	−	0.345060i	0.999999	−	0.00156740i	$-0.000498918\pi$
$338$	−2.42533e11	−	6.66354e11i	−1.01075	−	2.77702i
$339$			2.90328e11i			1.19396i
$340$	−1.85654e10	+	6.75727e9i	−0.0753442	+	0.0274231i
$341$	3.54760e11	−	2.04821e11i	1.42082	−	0.820314i
$342$	−1.25949e10	−	7.14293e10i	−0.0497826	−	0.282331i
$343$	−3.23466e11	+	5.60260e11i	−1.26184	+	2.18558i
$344$	−1.80797e9	−	3.13150e9i	−0.00696112	−	0.0120570i
$345$	−1.14074e10	+	9.57192e9i	−0.0433511	+	0.0363759i
$346$	−2.25978e11	−	3.98460e10i	−0.847664	−	0.149466i
$347$	−9.42646e10	−	5.44237e10i	−0.349033	−	0.201514i	0.315226	−	0.949016i	$-0.397920\pi$
$347$	−9.42646e10	−	5.44237e10i	−0.349033	−	0.201514i	−0.664259	+	0.747502i	$0.731253\pi$
$348$	−4.62357e10	+	1.27031e11i	−0.168994	+	0.464306i
$349$	9.57134e10	+	3.48368e10i	0.345349	+	0.125697i	0.508871	−	0.860843i	$-0.330063\pi$
$349$	9.57134e10	+	3.48368e10i	0.345349	+	0.125697i	−0.163522	+	0.986540i	$0.552285\pi$
$350$	7.45184e11	−	1.31396e11i	2.65435	−	0.468033i
$351$	2.89025e11	−	3.44446e11i	1.01637	−	1.21127i
$352$	−3.21043e11	+	3.82604e11i	−1.11461	+	1.32833i
$353$	−4.72106e11	+	8.32450e10i	−1.61828	+	0.285346i	−0.908125	−	0.418700i	$-0.862486\pi$
$353$	−4.72106e11	+	8.32450e10i	−1.61828	+	0.285346i	−0.710154	+	0.704046i	$0.751375\pi$
$354$	−5.41205e11	−	1.96982e11i	−1.83167	−	0.666673i
$355$	2.06636e9	−	5.67729e9i	0.00690525	−	0.0189720i
$356$	3.04361e11	+	1.75723e11i	1.00430	+	0.579834i
$357$	−1.85813e11	−	3.27638e10i	−0.605436	−	0.106755i
$358$	−3.57051e11	+	2.99602e11i	−1.14883	+	0.963985i
$359$	−1.32088e11	−	2.28783e11i	−0.419699	−	0.726940i	0.576210	−	0.817302i	$-0.304531\pi$
$359$	−1.32088e11	−	2.28783e11i	−0.419699	−	0.726940i	−0.995909	+	0.0903618i	$0.971198\pi$
$360$	−2.02253e9	+	3.50313e9i	−0.00634650	+	0.0109925i
$361$	−5.46839e10	−	3.10128e11i	−0.169464	−	0.961077i
$362$	5.85825e11	−	3.38226e11i	1.79300	−	1.03519i
$363$	−2.02908e11	+	7.38526e10i	−0.613367	+	0.223247i
$364$		−	1.39507e12i		−	4.16524i
$365$	−1.61549e10	−	4.43851e10i	−0.0476415	−	0.130894i
$366$	−7.19763e10	+	4.08198e11i	−0.209664	+	1.18907i
$367$	3.45996e11	+	2.90325e11i	0.995575	+	0.835387i	0.986365	−	0.164571i	$-0.0526239\pi$
$367$	3.45996e11	+	2.90325e11i	0.995575	+	0.835387i	0.00920996	+	0.999958i	$0.497068\pi$
$368$	3.57188e10	+	4.25680e10i	0.101527	+	0.120995i
$369$	6.89275e10			0.193541
$370$	9.44099e10	−	4.80998e10i	0.261884	−	0.133424i
$371$	3.92192e11			1.07477
$372$	−4.31958e11	−	5.14787e11i	−1.16949	−	1.39375i
$373$	1.28043e11	+	1.07441e11i	0.342504	+	0.287395i	0.797772	−	0.602959i	$-0.206012\pi$
$373$	1.28043e11	+	1.07441e11i	0.342504	+	0.287395i	−0.455268	+	0.890355i	$0.650456\pi$
$374$	−3.99745e10	+	2.26707e11i	−0.105648	+	0.599160i
$375$	5.27917e10	+	1.45044e11i	0.137856	+	0.378755i
$376$			3.08335e11i			0.795568i
$377$	2.21671e11	−	8.06816e10i	0.565161	−	0.205702i
$378$	8.87544e11	−	5.12424e11i	2.23602	−	1.29097i
$379$	5.29843e9	+	3.00489e10i	0.0131908	+	0.0748087i	0.990693	−	0.136119i	$-0.0434628\pi$
$379$	5.29843e9	+	3.00489e10i	0.0131908	+	0.0748087i	−0.977502	+	0.210927i	$0.932352\pi$
$380$	−7.28731e10	+	1.26220e11i	−0.179284	+	0.310529i
$381$	3.51056e10	+	6.08047e10i	0.0853520	+	0.147834i
$382$	−3.30093e11	+	2.76981e11i	−0.793142	+	0.665526i
$383$	−6.94902e11	−	1.22530e11i	−1.65017	−	0.290970i	−0.730281	−	0.683147i	$-0.760611\pi$
$383$	−6.94902e11	−	1.22530e11i	−1.65017	−	0.290970i	−0.919890	+	0.392177i	$0.871722\pi$
$384$	3.66365e11	+	2.11521e11i	0.859851	+	0.496435i
$385$	−6.63336e10	+	1.82250e11i	−0.153872	+	0.422761i
$386$	−4.96134e11	−	1.80578e11i	−1.13751	−	0.414021i
$387$	1.64616e9	−	2.90262e8i	0.00373055	−	0.000657797i
$388$	2.28071e11	−	2.71804e11i	0.510890	−	0.608855i
$389$	4.23063e11	−	5.04187e11i	0.936768	−	1.11640i	−0.0562483	−	0.998417i	$-0.517914\pi$
$389$	4.23063e11	−	5.04187e11i	0.936768	−	1.11640i	0.993016	−	0.117979i	$-0.0376417\pi$
$390$	2.41402e11	−	4.25657e10i	0.528385	−	0.0931684i
$391$	3.76191e10	+	1.36922e10i	0.0813978	+	0.0296264i
$392$	1.86691e11	−	5.12929e11i	0.399333	−	1.09716i
$393$	3.14472e11	+	1.81560e11i	0.664990	+	0.383932i
$394$	−1.07107e12	−	1.88859e11i	−2.23916	−	0.394824i
$395$	1.97380e9	−	1.65621e9i	0.00407958	−	0.00342317i
$396$	5.50058e10	+	9.52728e10i	0.112404	+	0.194689i
$397$	7.29031e10	−	1.26272e11i	0.147295	−	0.255123i	−0.782932	−	0.622108i	$-0.786277\pi$
$397$	7.29031e10	−	1.26272e11i	0.147295	−	0.255123i	0.930227	+	0.366985i	$0.119610\pi$
$398$	3.32603e10	+	1.88628e11i	0.0664434	+	0.376819i
$399$	−1.20540e12	+	6.95940e11i	−2.38097	+	1.37465i
$400$	2.65496e11	−	9.66327e10i	0.518547	−	0.188736i
$401$			3.64114e11i			0.703214i	0.936148	+	0.351607i	$0.114365\pi$
$401$			3.64114e11i			0.703214i	−0.936148	+	0.351607i	$0.885635\pi$
$402$	3.41332e10	+	9.37802e10i	0.0651868	+	0.179099i
$403$	−2.03630e11	+	1.15484e12i	−0.384564	+	2.18097i
$404$	6.16537e11	+	5.17336e11i	1.15144	+	0.966176i
$405$	7.48977e10	+	8.92596e10i	0.138331	+	0.164857i
$406$	5.37668e11			0.982080
$407$	3.68216e10	−	7.02095e11i	0.0665162	−	1.26830i
$408$	9.21369e10			0.164613
$409$	−1.95901e11	−	2.33466e11i	−0.346164	−	0.412543i	0.564669	−	0.825318i	$-0.309004\pi$
$409$	−1.95901e11	−	2.33466e11i	−0.346164	−	0.412543i	−0.910833	+	0.412775i	$0.864560\pi$
$410$	−1.86315e11	−	1.56337e11i	−0.325628	−	0.273234i
$411$	2.16118e10	−	1.22567e11i	0.0373597	−	0.211878i
$412$	4.16128e11	+	1.14330e12i	0.711524	+	1.95490i
$413$			1.30447e12i			2.20627i
$414$	3.15691e10	−	1.14902e10i	0.0528155	−	0.0192233i
$415$	−2.23420e10	+	1.28992e10i	−0.0369748	+	0.0213474i
$416$	−2.48274e11	−	1.40803e12i	−0.406455	−	2.30512i
$417$	−4.07279e11	+	7.05428e11i	−0.659599	+	1.14246i
$418$	8.49105e11	+	1.47069e12i	1.36040	+	2.35629i
$419$	−1.56067e10	+	1.30956e10i	−0.0247371	+	0.0207569i	−0.655072	−	0.755566i	$-0.727362\pi$
$419$	−1.56067e10	+	1.30956e10i	−0.0247371	+	0.0207569i	0.630335	+	0.776323i	$0.282917\pi$
$420$	3.13330e11	+	5.52486e10i	0.491338	+	0.0866362i
$421$	−7.33775e11	−	4.23645e11i	−1.13840	−	0.657254i	−0.192364	−	0.981324i	$-0.561615\pi$
$421$	−7.33775e11	−	4.23645e11i	−1.13840	−	0.657254i	−0.946033	+	0.324070i	$0.894949\pi$
$422$	2.41727e11	−	6.64139e11i	0.371038	−	1.01942i
$423$	−1.33939e11	−	4.87498e10i	−0.203411	−	0.0740357i
$424$	−1.88608e11	+	3.32567e10i	−0.283409	+	0.0499727i
$425$	1.30838e11	−	1.55926e11i	0.194528	−	0.231830i
$426$	−7.42311e10	+	8.84652e10i	−0.109205	+	0.130145i
$427$	9.24548e11	−	1.63023e11i	1.34587	−	0.237314i
$428$	2.19418e11	+	7.98614e10i	0.316064	+	0.115038i
$429$	5.56295e11	−	1.52841e12i	0.792953	−	2.17862i
$430$	−5.10803e9	−	2.94912e9i	−0.00720519	−	0.00415992i
$431$	−1.03463e12	−	1.82433e11i	−1.44423	−	0.254658i	−0.604045	−	0.796950i	$-0.706445\pi$
$431$	−1.03463e12	−	1.82433e11i	−1.44423	−	0.254658i	−0.840190	+	0.542293i	$0.817556\pi$
$432$	2.93139e11	−	2.45973e11i	0.404945	−	0.339790i
$433$	−4.31938e11	−	7.48139e11i	−0.590509	−	1.02279i	−0.994164	−	0.107880i	$-0.965594\pi$
$433$	−4.31938e11	−	7.48139e11i	−0.590509	−	1.02279i	0.403655	−	0.914911i	$-0.367739\pi$
$434$	−1.33639e12	+	2.31469e12i	−1.80813	+	3.13177i
$435$	9.34217e9	+	5.29821e10i	0.0125097	+	0.0709459i
$436$	−6.11307e11	+	3.52938e11i	−0.810159	+	0.467745i
$437$	2.77515e11	−	1.01007e11i	0.364015	−	0.132491i
$438$			9.02848e11i			1.17214i
$439$	1.99294e11	+	5.47555e11i	0.256096	+	0.703618i	0.999399	+	0.0346634i	$0.0110359\pi$
$439$	1.99294e11	+	5.47555e11i	0.256096	+	0.703618i	−0.743303	+	0.668955i	$0.766742\pi$
$440$	1.64461e10	−	9.32703e10i	0.0209182	−	0.118633i
$441$	1.93296e11	+	1.62195e11i	0.243360	+	0.204204i
$442$	−4.23591e11	−	5.04817e11i	−0.527894	−	0.629120i
$443$	5.89157e11			0.726799			0.363400	−	0.931633i	$-0.381616\pi$
$443$	5.89157e11			0.726799			0.363400	+	0.931633i	$0.381616\pi$
$444$	−1.14476e12	+	1.40515e11i	−1.39795	+	0.171593i
$445$	1.39866e11			0.169079
$446$	5.09235e11	+	6.06882e11i	0.609412	+	0.726269i
$447$	6.33793e11	+	5.31815e11i	0.750868	+	0.630053i
$448$	4.10013e11	−	2.32530e12i	0.480891	−	2.72727i
$449$	4.91272e11	+	1.34976e12i	0.570445	+	1.56729i	0.803804	+	0.594895i	$0.202806\pi$
$449$	4.91272e11	+	1.34976e12i	0.570445	+	1.56729i	−0.233359	+	0.972391i	$0.574972\pi$
$450$		−	1.70813e11i		−	0.196365i
$451$	−1.51651e12	+	5.51964e11i	−1.72604	+	0.628226i
$452$	−1.13982e12	+	6.58076e11i	−1.28444	+	0.741572i
$453$	−2.95699e11	−	1.67699e12i	−0.329920	−	1.87107i
$454$	1.72940e11	−	2.99542e11i	0.191049	−	0.330907i
$455$	−2.77599e11	−	4.80816e11i	−0.303646	−	0.525930i
$456$	5.20674e11	−	4.36897e11i	0.563928	−	0.473192i
$457$	−1.56941e11	−	2.76729e10i	−0.168311	−	0.0296778i	0.0888574	−	0.996044i	$-0.471678\pi$
$457$	−1.56941e11	−	2.76729e10i	−0.168311	−	0.0296778i	−0.257169	+	0.966367i	$0.582790\pi$
$458$	1.20596e12	+	6.96263e11i	1.28068	+	0.739399i
$459$	9.42897e10	−	2.59059e11i	0.0991533	−	0.272421i
$460$	−6.34359e10	−	2.30888e10i	−0.0660579	−	0.0240431i
$461$	−1.33747e12	+	2.35832e11i	−1.37921	+	0.243191i	−0.813571	−	0.581465i	$-0.802480\pi$
$461$	−1.33747e12	+	2.35832e11i	−1.37921	+	0.243191i	−0.565634	+	0.824656i	$0.691369\pi$
$462$	2.38294e12	−	2.83987e12i	2.43346	−	2.90008i
$463$	−6.31668e11	+	7.52793e11i	−0.638814	+	0.761309i	−0.984182	−	0.177158i	$-0.943310\pi$
$463$	−6.31668e11	+	7.52793e11i	−0.638814	+	0.761309i	0.345368	+	0.938467i	$0.387754\pi$
$464$	1.97709e11	−	3.48614e10i	0.198014	−	0.0349151i
$465$	−2.51311e11	−	9.14697e10i	−0.249272	−	0.0907275i
$466$	−3.17338e11	+	8.71878e11i	−0.311735	+	0.856484i
$467$	−1.03983e12	−	6.00346e11i	−1.01166	−	0.584084i	−0.0999855	−	0.994989i	$-0.531880\pi$
$467$	−1.03983e12	−	6.00346e11i	−1.01166	−	0.584084i	−0.911678	+	0.410904i	$0.865213\pi$
$468$	−3.10139e11	−	5.46858e10i	−0.298848	−	0.0526949i
$469$	1.73156e11	−	1.45295e11i	0.165257	−	0.138667i
$470$	2.51474e11	+	4.35566e11i	0.237713	+	0.411731i
$471$	5.40264e11	−	9.35765e11i	0.505839	−	0.876138i
$472$	−1.10615e11	−	6.27330e11i	−0.102583	−	0.581777i
$473$	−3.38936e10	+	1.95685e10i	−0.0311346	+	0.0179755i
$474$	−4.62804e10	+	1.68447e10i	−0.0421109	+	0.0153271i
$475$		−	1.50156e12i		−	1.35339i
$476$	−2.92545e11	−	8.03761e11i	−0.261193	−	0.717622i
$477$	1.53737e10	−	8.71884e10i	0.0135971	−	0.0771127i
$478$	1.71899e12	+	1.44241e12i	1.50608	+	1.26375i
$479$	−4.78679e11	−	5.70467e11i	−0.415465	−	0.495132i	0.517206	−	0.855861i	$-0.326972\pi$
$479$	−4.78679e11	−	5.70467e11i	−0.415465	−	0.495132i	−0.932670	+	0.360729i	$0.882528\pi$
$480$	3.26074e11			0.280370
$481$	1.47188e12	+	1.37265e12i	1.25377	+	1.16925i
$482$	−2.70400e11			−0.228190
$483$	−4.14401e11	−	4.93864e11i	−0.346465	−	0.412901i
$484$	−7.49870e11	−	6.29215e11i	−0.621129	−	0.521189i
$485$	2.45202e10	−	1.39061e11i	0.0201227	−	0.114122i
$486$	−1.70477e11	−	4.68381e11i	−0.138612	−	0.380834i
$487$			9.16521e11i			0.738350i	0.929360	+	0.369175i	$0.120360\pi$
$487$			9.16521e11i			0.738350i	−0.929360	+	0.369175i	$0.879640\pi$
$488$	−4.30798e11	+	1.56798e11i	−0.343862	+	0.125156i
$489$	−9.45620e10	+	5.45954e10i	−0.0747871	+	0.0431783i
$490$	−1.54612e11	−	8.76846e11i	−0.121160	−	0.687134i
$491$	6.52283e10	−	1.12979e11i	0.0506488	−	0.0877263i	−0.839589	−	0.543221i	$-0.817204\pi$
$491$	6.52283e10	−	1.12979e11i	0.0506488	−	0.0877263i	0.890238	+	0.455495i	$0.150538\pi$
$492$	1.32373e12	+	2.29276e12i	1.01849	+	1.76407i
$493$	1.10795e11	−	9.29684e10i	0.0844716	−	0.0708801i
$494$	−4.78750e12	−	8.44166e11i	−3.61691	−	0.637759i
$495$	3.79159e10	+	2.18907e10i	0.0283856	+	0.0163884i
$496$	−3.41330e11	+	9.37797e11i	−0.253225	+	0.695731i
$497$	2.45789e11	+	8.94600e10i	0.180700	+	0.0657696i
$498$	4.85630e11	−	8.56298e10i	0.353813	−	0.0623868i
$499$	7.54756e11	−	8.99483e11i	0.544946	−	0.649442i	−0.421343	−	0.906902i	$-0.638441\pi$
$499$	7.54756e11	−	8.99483e11i	0.544946	−	0.649442i	0.966289	+	0.257460i	$0.0828854\pi$
$500$	−4.49779e11	+	5.36025e11i	−0.321835	+	0.383548i
$501$	9.19584e11	−	1.62147e11i	0.652111	−	0.114985i
$502$	2.12202e12	+	7.72351e11i	1.49136	+	0.542810i
$503$	3.78467e11	−	1.03983e12i	0.263617	−	0.724280i	−0.735300	−	0.677742i	$-0.762959\pi$
$503$	3.78467e11	−	1.03983e12i	0.263617	−	0.724280i	0.998916	−	0.0465387i	$-0.0148191\pi$
$504$	−1.51662e11	−	8.75623e10i	−0.104699	−	0.0604477i
$505$	3.15434e11	+	5.56195e10i	0.215823	+	0.0380554i
$506$	−6.02556e11	+	5.05604e11i	−0.408620	+	0.342873i
$507$	1.53594e12	+	2.66033e12i	1.03238	+	1.78813i
$508$	−1.59145e11	+	2.75648e11i	−0.106025	+	0.183640i
$509$	5.06905e11	+	2.87480e12i	0.334732	+	1.89836i	0.429866	+	0.902892i	$0.358561\pi$
$509$	5.06905e11	+	2.87480e12i	0.334732	+	1.89836i	−0.0951349	+	0.995464i	$0.530328\pi$
$510$	1.30156e11	−	7.51458e10i	0.0851921	−	0.0491857i
$511$	1.92158e12	−	6.99399e11i	1.24671	−	0.453765i
$512$		−	1.65511e12i		−	1.06441i
$513$	−6.95572e11	−	1.91107e12i	−0.443419	−	1.21828i
$514$	6.91664e11	−	3.92262e12i	0.437080	−	2.47881i
$515$	3.70921e11	+	3.11239e11i	0.232353	+	0.194967i
$516$	4.12690e10	+	4.91825e10i	0.0256271	+	0.0305412i
$517$	3.33724e12			2.05438
$518$	2.08240e12	+	4.08733e12i	1.27081	+	2.49434i
$519$	9.94032e11			0.601377
$520$	1.74271e11	+	2.07688e11i	0.104523	+	0.124565i
$521$	−1.06387e12	−	8.92691e11i	−0.632584	−	0.530801i	0.269147	−	0.963099i	$-0.413258\pi$
$521$	−1.06387e12	−	8.92691e11i	−0.632584	−	0.530801i	−0.901731	+	0.432298i	$0.857703\pi$
$522$	2.10762e10	−	1.19529e11i	0.0124244	−	0.0704623i
$523$	3.48213e11	+	9.56707e11i	0.203511	+	0.559141i	0.998897	−	0.0469623i	$-0.0149541\pi$
$523$	3.48213e11	+	9.56707e11i	0.203511	+	0.559141i	−0.795386	+	0.606103i	$0.792732\pi$
$524$			1.64615e12i			0.953845i
$525$	−3.08023e12	+	1.12111e12i	−1.76957	+	0.644069i
$526$	5.66356e11	−	3.26986e11i	0.322592	−	0.186249i
$527$	1.24849e11	+	7.08056e11i	0.0705080	+	0.399871i
$528$	6.92110e11	−	1.19877e12i	0.387546	−	0.671248i
$529$	−8.32182e11	−	1.44138e12i	−0.462027	−	0.800255i
$530$	−2.39311e11	+	2.00806e11i	−0.131741	+	0.110544i
$531$	2.89998e11	+	5.11344e10i	0.158296	+	0.0279118i
$532$	−5.46449e12	−	3.15493e12i	−2.95766	−	1.70760i
$533$	1.58007e12	−	4.34121e12i	0.848017	−	2.32991i
$534$	−2.51223e12	−	9.14378e11i	−1.33698	−	0.486620i
$535$	9.15143e10	−	1.61364e10i	0.0482944	−	0.00851561i
$536$	−7.09515e10	+	8.45568e10i	−0.0371296	+	0.0442493i
$537$	1.29786e12	−	1.54673e12i	0.673511	−	0.802660i
$538$	4.97588e12	−	8.77383e11i	2.56065	−	0.451511i
$539$	−5.55165e12	−	2.02063e12i	−2.83317	−	1.03119i
$540$	−1.58998e11	+	4.36843e11i	−0.0804674	+	0.221082i
$541$	−2.28554e12	−	1.31956e12i	−1.14710	−	0.662278i	−0.198920	−	0.980016i	$-0.563743\pi$
$541$	−2.28554e12	−	1.31956e12i	−1.14710	−	0.662278i	−0.948179	+	0.317738i	$0.897077\pi$
$542$	−2.22063e12	−	3.91556e11i	−1.10530	−	0.194894i
$543$	−2.24480e12	+	1.88361e12i	−1.10810	+	0.929803i
$544$	−4.38306e11	−	7.59167e11i	−0.214576	−	0.371657i
$545$	−1.40459e11	+	2.43283e11i	−0.0681972	+	0.118121i
$546$	1.84281e12	+	1.04511e13i	0.887390	+	5.03264i
$547$	−1.72523e12	+	9.96061e11i	−0.823955	+	0.475711i	−0.851778	−	0.523902i	$-0.824476\pi$
$547$	−1.72523e12	+	9.96061e11i	−0.823955	+	0.475711i	0.0278235	+	0.999613i	$0.491142\pi$
$548$	5.30182e11	−	1.92971e11i	0.251138	−	0.0914068i
$549$		−	2.11927e11i		−	0.0995660i
$550$	1.36785e12	+	3.75814e12i	0.637392	+	1.75122i
$551$	1.85275e11	−	1.05074e12i	0.0856315	−	0.485641i
$552$	2.41167e11	+	2.02363e11i	0.110558	+	0.0927695i
$553$	7.17031e10	+	8.54524e10i	0.0326043	+	0.0388563i
$554$	−1.44720e12			−0.652731
$555$	−3.66585e11	+	2.76220e11i	−0.164005	+	0.123577i
$556$	−3.69266e12			−1.63871
$557$	−1.71520e12	−	2.04409e12i	−0.755032	−	0.899813i	0.242491	−	0.970154i	$-0.422036\pi$
$557$	−1.71520e12	−	2.04409e12i	−0.755032	−	0.899813i	−0.997523	+	0.0703412i	$0.977591\pi$
$558$	4.62195e11	+	3.87827e11i	0.201823	+	0.169350i
$559$	1.94547e10	−	1.10333e11i	0.00842695	−	0.0477916i
$560$	−1.61604e11	−	4.44003e11i	−0.0694394	−	0.190783i
$561$		−	9.97237e11i		−	0.425075i
$562$	−3.51198e12	+	1.27826e12i	−1.48504	+	0.540511i
$563$	−1.26505e12	+	7.30378e11i	−0.530665	+	0.306380i	−0.741287	−	0.671188i	$-0.765784\pi$
$563$	−1.26505e12	+	7.30378e11i	−0.530665	+	0.306380i	0.210622	+	0.977568i	$0.432451\pi$
$564$	−9.50664e11	−	5.39149e12i	−0.395614	−	2.24364i
$565$	−2.61896e11	+	4.53617e11i	−0.108121	+	0.187271i
$566$	−2.30605e11	−	3.99419e11i	−0.0944483	−	0.163589i
$567$	−3.86435e12	+	3.24258e12i	−1.57019	+	1.31755i
$568$	−1.25788e11	−	2.21798e10i	−0.0507074	−	0.00894108i
$569$	2.64325e12	+	1.52608e12i	1.05714	+	0.610342i	0.924641	−	0.380841i	$-0.124365\pi$
$569$	2.64325e12	+	1.52608e12i	1.05714	+	0.610342i	0.132502	+	0.991183i	$0.457699\pi$
$570$	3.79196e11	−	1.04183e12i	0.150462	−	0.413391i
$571$	2.26357e12	+	8.23870e11i	0.891108	+	0.324337i	0.746684	−	0.665179i	$-0.231645\pi$
$571$	2.26357e12	+	8.23870e11i	0.891108	+	0.324337i	0.144424	+	0.989516i	$0.453867\pi$
$572$	7.26144e12	−	1.28039e12i	2.83622	−	0.500103i
$573$	1.19987e12	−	1.42995e12i	0.464985	−	0.554148i
$574$	6.76837e12	−	8.06623e12i	2.60244	−	3.10147i
$575$	6.84932e11	−	1.20772e11i	0.261302	−	0.0460745i
$576$	−5.00866e11	−	1.82300e11i	−0.189592	−	0.0690059i
$577$	−1.20611e12	+	3.31377e12i	−0.452998	+	1.24460i	0.477606	+	0.878574i	$0.341505\pi$
$577$	−1.20611e12	+	3.31377e12i	−0.452998	+	1.24460i	−0.930604	+	0.366028i	$0.880717\pi$
$578$	3.19173e12	+	1.84274e12i	1.18946	+	0.686736i
$579$	2.25242e12	+	3.97163e11i	0.832907	+	0.146864i
$580$	−1.86831e11	+	1.56770e11i	−0.0685525	+	0.0575223i
$581$	−5.58449e11	−	9.67262e11i	−0.203325	−	0.352169i
$582$	−1.34955e12	+	2.33748e12i	−0.487567	+	0.844491i
$583$	3.59951e11	+	2.04139e12i	0.129043	+	0.731841i
$584$	−8.64797e11	+	4.99291e11i	−0.307650	+	0.177622i
$585$	−1.17772e11	+	4.28655e10i	−0.0415758	+	0.0151324i
$586$			2.69180e12i			0.942982i
$587$	2.50246e11	+	6.87544e11i	0.0869951	+	0.239017i	0.975560	−	0.219734i	$-0.0705191\pi$
$587$	2.50246e11	+	6.87544e11i	0.0869951	+	0.239017i	−0.888565	+	0.458751i	$0.848297\pi$
$588$	−1.68297e12	+	9.54458e12i	−0.580601	+	3.29275i
$589$	4.06301e12	+	3.40927e12i	1.39101	+	1.16719i
$590$	−6.67902e11	−	7.95975e11i	−0.226923	−	0.270436i
$591$	4.71142e12			1.58858
$592$	1.03075e12	+	1.36795e12i	0.344909	+	0.457745i
$593$	2.67881e12			0.889601			0.444801	−	0.895630i	$-0.353275\pi$
$593$	2.67881e12			0.889601			0.444801	+	0.895630i	$0.353275\pi$
$594$	3.48178e12	+	4.14942e12i	1.14753	+	1.36757i
$595$	−2.60764e11	−	2.18807e11i	−0.0852945	−	0.0715706i
$596$	−6.51300e11	+	3.69371e12i	−0.211433	+	1.19910i
$597$	−2.83787e11	−	7.79699e11i	−0.0914341	−	0.251213i
$598$		−	2.25170e12i		−	0.720036i
$599$	−4.01990e12	+	1.46312e12i	−1.27583	+	0.464365i	−0.889052	−	0.457806i	$-0.848635\pi$
$599$	−4.01990e12	+	1.46312e12i	−1.27583	+	0.464365i	−0.386781	+	0.922171i	$0.626413\pi$
$600$	1.38624e12	−	8.00346e11i	0.436674	−	0.252114i
$601$	−4.22181e11	−	2.39431e12i	−0.131997	−	0.748591i	−0.976904	−	0.213678i	$-0.931456\pi$
$601$	−4.22181e11	−	2.39431e12i	−0.131997	−	0.748591i	0.844907	−	0.534913i	$-0.179655\pi$
$602$	1.27678e11	−	2.21144e11i	0.0396215	−	0.0686264i
$603$	−2.55131e10	−	4.41899e10i	−0.00785841	−	0.0136112i
$604$	5.91360e12	−	4.96210e12i	1.80795	−	1.51705i
$605$	−3.83650e11	−	6.76479e10i	−0.116422	−	0.0205284i
$606$	−5.30213e12	−	3.06119e12i	−1.59707	−	0.922069i
$607$	−1.47337e10	+	4.04805e10i	−0.00440516	+	0.0121031i	−0.941876	−	0.335962i	$-0.890939\pi$
$607$	−1.47337e10	+	4.04805e10i	−0.00440516	+	0.0121031i	0.937471	+	0.348065i	$0.113161\pi$
$608$	−6.07674e12	−	2.21175e12i	−1.80345	−	0.656403i
$609$	−2.29378e12	+	4.04455e11i	−0.675730	+	0.119149i
$610$	−4.80680e11	+	5.72852e11i	−0.140563	+	0.167517i
$611$	−6.14075e12	+	7.31826e12i	−1.78253	+	2.12433i
$612$	−1.90152e11	+	3.35290e10i	−0.0547923	+	0.00966137i
$613$	−4.13744e11	−	1.50591e11i	−0.118348	−	0.0430750i	0.282168	−	0.959365i	$-0.408947\pi$
$613$	−4.13744e11	−	1.50591e11i	−0.118348	−	0.0430750i	−0.400515	+	0.916290i	$0.631169\pi$
$614$	2.67689e12	−	7.35469e12i	0.760103	−	2.08837i
$615$	9.12453e11	+	5.26805e11i	0.257201	+	0.148495i
$616$	4.03799e12	+	7.12007e11i	1.12993	+	0.199237i
$617$	−6.51364e11	+	5.46559e11i	−0.180942	+	0.151829i	−0.728760	−	0.684769i	$-0.759903\pi$
$617$	−6.51364e11	+	5.46559e11i	−0.180942	+	0.151829i	0.547818	+	0.836598i	$0.315459\pi$
$618$	−4.62765e12	−	8.01532e12i	−1.27618	−	2.21041i
$619$	−3.35558e12	+	5.81204e12i	−0.918671	+	1.59118i	−0.117234	+	0.993104i	$0.537403\pi$
$619$	−3.35558e12	+	5.81204e12i	−0.918671	+	1.59118i	−0.801436	+	0.598080i	$0.795930\pi$
$620$	−2.10530e11	−	1.19397e12i	−0.0572204	−	0.324513i
$621$	8.15780e11	−	4.70991e11i	0.220121	−	0.127087i
$622$	1.84980e11	−	6.73272e10i	0.0495527	−	0.0180357i
$623$			6.05526e12i			1.61041i
$624$	1.35526e12	+	3.72355e12i	0.357843	+	0.983166i
$625$	5.89423e11	−	3.34278e12i	0.154514	−	0.876290i
$626$	−5.67315e12	−	4.76034e12i	−1.47652	−	1.23895i
$627$	−4.72873e12	−	5.63548e12i	−1.22191	−	1.45622i
$628$	4.89839e12			1.25671
$629$	1.13586e12	+	4.82192e11i	0.289331	+	0.122827i
$630$	−2.85659e11			−0.0722463
$631$	−2.87379e12	−	3.42485e12i	−0.721643	−	0.860021i	0.273146	−	0.961973i	$-0.411936\pi$
$631$	−2.87379e12	−	3.42485e12i	−0.721643	−	0.860021i	−0.994789	+	0.101951i	$0.967491\pi$
$632$	−4.17286e10	−	3.50145e10i	−0.0104042	−	0.00873013i
$633$	−5.31653e11	+	3.01515e12i	−0.131617	+	0.746437i
$634$	−3.23675e12	−	8.89290e12i	−0.795623	−	2.18596i
$635$			1.26671e11i			0.0309168i
$636$	3.19543e12	−	1.16304e12i	0.774411	−	0.281863i
$637$	1.46465e13	−	8.45615e12i	3.52457	−	2.03491i
$638$	4.93468e11	+	2.79860e12i	0.117914	+	0.668725i
$639$	2.95227e10	−	5.11348e10i	0.00700490	−	0.0121328i
$640$	3.81613e11	+	6.60972e11i	0.0899110	+	0.155730i
$641$	1.38502e12	−	1.16217e12i	0.324038	−	0.271900i	−0.466227	−	0.884665i	$-0.654387\pi$
$641$	1.38502e12	−	1.16217e12i	0.324038	−	0.271900i	0.790265	+	0.612765i	$0.209943\pi$
$642$	−1.74925e12	−	3.08440e11i	−0.406391	−	0.0716578i
$643$	6.12540e12	+	3.53650e12i	1.41314	+	0.815876i	0.995683	−	0.0928210i	$-0.0295884\pi$
$643$	6.12540e12	+	3.53650e12i	1.41314	+	0.815876i	0.417456	+	0.908697i	$0.362922\pi$
$644$	9.99593e11	−	2.74636e12i	0.229001	−	0.629174i
$645$	2.40101e10	+	8.73896e9i	0.00546230	+	0.00198811i
$646$	−2.93531e12	+	5.17575e11i	−0.663144	+	0.116930i
$647$	3.37865e12	−	4.02652e12i	0.758009	−	0.903359i	−0.239712	−	0.970844i	$-0.577053\pi$
$647$	3.37865e12	−	4.02652e12i	0.758009	−	0.903359i	0.997720	+	0.0674847i	$0.0214974\pi$
$648$	1.58344e12	−	1.88706e12i	0.352787	−	0.420435i
$649$	−6.78986e12	+	1.19724e12i	−1.50231	+	0.264898i
$650$	−1.07582e13	−	3.91566e12i	−2.36390	−	0.860390i
$651$	3.96004e12	−	1.08801e13i	0.864142	−	2.37421i
$652$	−4.28681e11	−	2.47499e11i	−0.0929009	−	0.0536364i
$653$	−2.59572e12	−	4.57695e11i	−0.558661	−	0.0985070i	−0.112814	−	0.993616i	$-0.535986\pi$
$653$	−2.59572e12	−	4.57695e11i	−0.558661	−	0.0985070i	−0.445847	+	0.895109i	$0.647098\pi$
$654$	4.11337e12	−	3.45153e12i	0.879221	−	0.737754i
$655$	3.27560e11	+	5.67350e11i	0.0695352	+	0.120438i
$656$	1.96584e12	−	3.40493e12i	0.414457	−	0.717861i
$657$	−8.01590e10	−	4.54604e11i	−0.0167845	−	0.0951895i
$658$	−1.88572e13	+	1.08872e13i	−3.92157	+	2.26412i
$659$	4.50826e12	−	1.64087e12i	0.931160	−	0.338914i	0.168491	−	0.985703i	$-0.446111\pi$
$659$	4.50826e12	−	1.64087e12i	0.931160	−	0.338914i	0.762669	+	0.646789i	$0.223888\pi$
$660$			1.68161e12i			0.344968i
$661$	−6.36477e11	−	1.74870e12i	−0.129681	−	0.356295i	0.857811	−	0.513965i	$-0.171824\pi$
$661$	−6.36477e11	−	1.74870e12i	−0.129681	−	0.356295i	−0.987492	+	0.157670i	$0.949602\pi$
$662$	7.47524e11	−	4.23942e12i	0.151274	−	0.857918i
$663$	2.18685e12	+	1.83498e12i	0.439550	+	0.368826i
$664$	3.50583e11	+	4.17808e11i	0.0699897	+	0.0834105i
$665$	−2.51114e12			−0.497937
$666$	9.90284e11	−	3.02720e11i	0.195041	−	0.0596220i
$667$	4.94194e11			0.0966789
$668$	2.72098e12	+	3.24274e12i	0.528727	+	0.630112i
$669$	−2.62899e12	−	2.20599e12i	−0.507425	−	0.425780i
$670$	−3.12655e10	+	1.77315e11i	−0.00599417	+	0.0339946i
$671$	1.69709e12	+	4.66271e12i	0.323187	+	0.887948i
$672$			1.41169e13i			2.67040i
$673$	7.47173e11	−	2.71949e11i	0.140396	−	0.0510998i	−0.270867	−	0.962617i	$-0.587310\pi$
$673$	7.47173e11	−	2.71949e11i	0.140396	−	0.0510998i	0.411262	+	0.911517i	$0.365088\pi$
$674$	−2.47766e12	+	1.43048e12i	−0.462457	+	0.267000i
$675$	−8.31681e11	−	4.71670e12i	−0.154202	−	0.874522i
$676$	−6.96293e12	+	1.20601e13i	−1.28242	+	2.22122i
$677$	5.01934e12	+	8.69376e12i	0.918328	+	1.59059i	0.801954	+	0.597386i	$0.203794\pi$
$677$	5.01934e12	+	8.69376e12i	0.918328	+	1.59059i	0.116374	+	0.993205i	$0.462873\pi$
$678$	7.66965e12	−	6.43560e12i	1.39393	−	1.16965i
$679$	6.02044e12	+	1.06157e12i	1.08696	+	0.191661i
$680$	1.43957e11	+	8.31138e10i	0.0258193	+	0.0149068i
$681$	−5.12464e11	+	1.40798e12i	−0.0913065	+	0.250862i
$682$	−1.32747e13	−	4.83158e12i	−2.34960	−	0.855184i
$683$	6.74840e12	−	1.18992e12i	1.18661	−	0.209231i	0.454707	−	0.890641i	$-0.349744\pi$
$683$	6.74840e12	−	1.18992e12i	1.18661	−	0.209231i	0.731902	+	0.681410i	$0.238633\pi$
$684$	−9.15578e11	+	1.09114e12i	−0.159935	+	0.190603i
$685$	1.44331e11	−	1.72007e11i	0.0250467	−	0.0298495i
$686$	2.19707e13	−	3.87402e12i	3.78778	−	0.667888i
$687$	−5.66858e12	−	2.06319e12i	−0.970888	−	0.353374i
$688$	3.26105e10	−	8.95965e10i	0.00554893	−	0.0152456i
$689$	−5.13891e12	−	2.96695e12i	−0.868729	−	0.501561i
$690$	5.05727e11	+	8.91733e10i	0.0849366	+	0.0149766i
$691$	−2.27314e12	+	1.90739e12i	−0.379293	+	0.318265i	−0.812425	−	0.583066i	$-0.801853\pi$
$691$	−2.27314e12	+	1.90739e12i	−0.379293	+	0.318265i	0.433132	+	0.901331i	$0.357409\pi$
$692$	2.25314e12	+	3.90255e12i	0.373517	+	0.646950i
$693$	−9.47725e11	+	1.64151e12i	−0.156093	+	0.270361i
$694$	6.51810e11	+	3.69660e12i	0.106660	+	0.604902i
$695$	−1.27269e12	+	7.34787e11i	−0.206914	+	0.119462i
$696$	1.06880e12	−	3.89010e11i	0.172645	−	0.0628376i
$697$		−	2.83250e12i		−	0.454593i
$698$	−1.20136e12	−	3.30070e12i	−0.191568	−	0.526328i
$699$	6.97952e11	−	3.95828e12i	0.110580	−	0.627133i
$700$	−1.13833e13	−	9.55175e12i	−1.79196	−	1.50363i
$701$	3.57733e11	+	4.26330e11i	0.0559536	+	0.0666829i	0.793295	−	0.608837i	$-0.208364\pi$
$701$	3.57733e11	+	4.26330e11i	0.0559536	+	0.0666829i	−0.737342	+	0.675520i	$0.763919\pi$
$702$	−1.55060e13			−2.40981
$703$	8.70529e12	−	2.66112e12i	1.34426	−	0.410927i
$704$	1.24796e13			1.91481
$705$	−1.40048e12	−	1.66903e12i	−0.213514	−	0.254456i
$706$	1.26641e13	+	1.06265e13i	1.91846	+	1.60978i
$707$	−2.40796e12	+	1.36562e13i	−0.362461	+	2.05562i
$708$	3.86839e12	+	1.06283e13i	0.578603	+	1.58970i
$709$			6.67978e12i			0.992783i	0.868099	+	0.496392i	$0.165342\pi$
$709$			6.67978e12i			0.992783i	−0.868099	+	0.496392i	$0.834658\pi$
$710$	−1.95782e11	+	7.12590e10i	−0.0289142	+	0.0105239i
$711$	2.18077e10	−	1.25907e10i	0.00320034	−	0.00184772i
$712$	−5.13467e11	−	2.91202e12i	−0.0748778	−	0.424653i
$713$	−1.22833e12	+	2.12753e12i	−0.177997	+	0.308300i
$714$	3.25332e12	+	5.63491e12i	0.468473	+	0.811419i
$715$	2.24790e12	−	1.88621e12i	0.321662	−	0.269907i
$716$	9.01428e12	+	1.58946e12i	1.28181	+	0.226017i
$717$	−8.41853e12	−	4.86044e12i	−1.18960	−	0.686814i
$718$	−3.11586e12	+	8.56074e12i	−0.437540	+	1.20213i
$719$	1.22674e13	+	4.46498e12i	1.71188	+	0.623074i	0.997088	−	0.0762620i	$-0.0242985\pi$
$719$	1.22674e13	+	4.46498e12i	1.71188	+	0.623074i	0.714793	+	0.699336i	$0.246521\pi$
$720$	−1.05041e11	+	1.85216e10i	−0.0145668	+	0.00256852i
$721$	−1.34746e13	+	1.60584e13i	−1.85698	+	2.21307i
$722$	−6.98055e12	+	8.31909e12i	−0.956031	+	1.13935i
$723$	1.15357e12	−	2.03406e11i	0.157008	−	0.0276848i
$724$	−1.24832e13	−	4.54352e12i	−1.68851	−	0.614566i
$725$	8.59396e11	−	2.36117e12i	0.115524	−	0.317400i
$726$	6.44878e12	+	3.72320e12i	0.861515	+	0.497396i
$727$	−7.14106e12	−	1.25916e12i	−0.948108	−	0.167177i	−0.321848	−	0.946791i	$-0.604304\pi$
$727$	−7.14106e12	−	1.25916e12i	−0.948108	−	0.167177i	−0.626260	+	0.779614i	$0.715415\pi$
$728$	−8.99154e12	+	7.54480e12i	−1.18643	+	0.995535i
$729$	−3.17514e12	−	5.49950e12i	−0.416379	−	0.721190i
$730$	−8.14431e11	+	1.41064e12i	−0.106145	+	0.183849i
$731$	−1.19280e10	−	6.76472e10i	−0.00154504	−	0.00876238i
$732$	7.04941e12	−	4.06998e12i	0.907513	−	0.523953i
$733$	1.35308e13	−	4.92480e12i	1.73123	−	0.630116i	0.732512	−	0.680755i	$-0.238348\pi$
$733$	1.35308e13	−	4.92480e12i	1.73123	−	0.630116i	0.998717	+	0.0506389i	$0.0161258\pi$
$734$		−	1.55758e13i		−	1.98070i
$735$	1.31919e12	+	3.62446e12i	0.166731	+	0.458089i
$736$	5.20124e11	−	2.94977e12i	0.0653367	−	0.370543i
$737$	9.15194e11	+	7.67939e11i	0.114264	+	0.0958789i
$738$	−1.52789e12	−	1.82087e12i	−0.189600	−	0.225957i
$739$	3.90155e12			0.481213			0.240606	−	0.970623i	$-0.422654\pi$
$739$	3.90155e12			0.481213			0.240606	+	0.970623i	$0.422654\pi$
$740$	−1.91536e12	−	8.13106e11i	−0.234805	−	0.0996792i
$741$	2.10593e13			2.56603
$742$	−8.69359e12	−	1.03606e13i	−1.05289	−	1.25478i
$743$	−9.05399e12	−	7.59720e12i	−1.08991	−	0.914543i	−0.0932038	−	0.995647i	$-0.529711\pi$
$743$	−9.05399e12	−	7.59720e12i	−1.08991	−	0.914543i	−0.996706	+	0.0811045i	$0.974155\pi$
$744$	−9.81811e11	+	5.56813e12i	−0.117476	+	0.666240i
$745$	5.10522e11	+	1.40265e12i	0.0607172	+	0.166819i
$746$		−	5.76414e12i		−	0.681412i
$747$	−2.36923e11	+	8.62330e10i	−0.0278397	+	0.0101328i
$748$	3.91514e12	−	2.26040e12i	0.457288	−	0.264015i
$749$	6.98602e11	+	3.96197e12i	0.0811076	+	0.459984i
$750$	2.66144e12	−	4.60975e12i	0.307143	−	0.531987i
$751$	−9.14950e11	−	1.58474e12i	−0.104958	−	0.181793i	0.808763	−	0.588135i	$-0.200138\pi$
$751$	−9.14950e11	−	1.58474e12i	−0.104958	−	0.181793i	−0.913721	+	0.406342i	$0.866804\pi$
$752$	−6.22816e12	+	5.22605e12i	−0.710198	+	0.595927i
$753$	−9.63384e12	−	1.69871e12i	−1.09200	−	0.192549i
$754$	−7.04508e12	−	4.06748e12i	−0.793807	−	0.458305i
$755$	1.05075e12	−	2.88693e12i	0.117690	−	0.323351i
$756$	−1.89124e13	−	6.88357e12i	−2.10572	−	0.766418i
$757$	−5.58745e12	+	9.85218e11i	−0.618418	+	0.109044i	−0.474076	−	0.880484i	$-0.657218\pi$
$757$	−5.58745e12	+	9.85218e11i	−0.618418	+	0.109044i	−0.144342	+	0.989528i	$0.546107\pi$
$758$	6.76359e11	−	8.06054e11i	0.0744160	−	0.0886855i
$759$	2.19026e12	−	2.61025e12i	0.239557	−	0.285492i
$760$	1.20763e12	−	2.12937e11i	0.131302	−	0.0231521i
$761$	1.37516e13	+	5.00519e12i	1.48636	+	0.540990i	0.952488	−	0.304577i	$-0.0985150\pi$
$761$	1.37516e13	+	5.00519e12i	1.48636	+	0.540990i	0.533870	+	0.845567i	$0.320737\pi$
$762$	8.28115e11	−	2.27523e12i	0.0889802	−	0.244471i
$763$	−1.05325e13	−	6.08097e12i	−1.12505	−	0.649550i
$764$	8.33368e12	+	1.46945e12i	0.884946	+	0.156040i
$765$	−5.88648e10	+	4.93934e10i	−0.00621411	+	0.00521426i
$766$	1.21668e13	+	2.10734e13i	1.27687	+	2.21160i
$767$	9.86837e12	−	1.70925e13i	1.02960	−	1.78331i
$768$	1.54372e11	+	8.75485e11i	0.0160119	+	0.0908078i
$769$	1.48821e12	−	8.59220e11i	0.153460	−	0.0886004i	−0.421303	−	0.906920i	$-0.638427\pi$
$769$	1.48821e12	−	8.59220e11i	0.153460	−	0.0886004i	0.574764	+	0.818319i	$0.305094\pi$
$770$	6.28493e12	−	2.28753e12i	0.644306	−	0.234508i
$771$			1.72548e13i			1.75859i
$772$	3.54624e12	+	9.74321e12i	0.359327	+	0.987243i
$773$	−7.52617e11	+	4.26830e12i	−0.0758169	+	0.429979i	0.923146	+	0.384449i	$0.125609\pi$
$773$	−7.52617e11	+	4.26830e12i	−0.0758169	+	0.429979i	−0.998963	+	0.0455298i	$0.985502\pi$
$774$	−4.41578e10	−	3.70528e10i	−0.00442255	−	0.00371096i
$775$	8.02893e12	+	9.56850e12i	0.799466	+	0.952766i
$776$	−2.98529e12			−0.295535
$777$	−1.19585e13	−	1.58707e13i	−1.17702	−	1.56207i
$778$	−2.26971e13			−2.22107
$779$	−1.34312e13	−	1.60067e13i	−1.30676	−	1.55734i
$780$	−3.68762e12	−	3.09428e12i	−0.356714	−	0.299319i
$781$	−2.40061e11	+	1.36146e12i	−0.0230883	+	0.130940i
$782$	−4.72179e11	−	1.29730e12i	−0.0451519	−	0.124054i
$783$		−	3.40321e12i		−	0.323564i
$784$	1.35251e13	−	4.92273e12i	1.27855	−	0.465354i
$785$	1.68825e12	−	9.74711e11i	0.158680	−	0.0916141i
$786$	−2.17447e12	−	1.23320e13i	−0.203213	−	1.15248i
$787$	−1.95328e12	+	3.38319e12i	−0.181501	+	0.314369i	−0.942392	−	0.334511i	$-0.891429\pi$
$787$	−1.95328e12	+	3.38319e12i	−0.181501	+	0.314369i	0.760891	+	0.648880i	$0.224762\pi$
$788$	1.06792e13	+	1.84970e13i	0.986669	+	1.70896i
$789$	−2.17019e12	+	1.82101e12i	−0.199366	+	0.167288i
$790$	−8.75049e10	−	1.54295e10i	−0.00799301	−	0.00140938i
$791$	−1.96386e13	−	1.13384e13i	−1.78368	−	1.02981i
$792$	3.16573e11	−	8.69777e11i	0.0285898	−	0.0785497i
$793$	−1.33477e13	−	4.85815e12i	−1.19860	−	0.436256i
$794$	−4.95177e12	+	8.73131e11i	−0.442148	+	0.0779627i
$795$	8.69886e11	−	1.03669e12i	0.0772343	−	0.0920443i
$796$	2.41783e12	−	2.88146e12i	0.213460	−	0.254392i
$797$	−6.94604e12	+	1.22477e12i	−0.609782	+	0.107521i	−0.470008	−	0.882662i	$-0.655749\pi$
$797$	−6.94604e12	+	1.22477e12i	−0.609782	+	0.107521i	−0.139775	+	0.990183i	$0.544638\pi$
$798$	4.51045e13	+	1.64167e13i	3.93738	+	1.43309i
$799$	−2.00332e12	+	5.50408e12i	−0.173896	+	0.477776i
$800$	−1.31890e13	−	7.61467e12i	−1.13843	−	0.657273i
$801$	1.34615e12	+	2.37362e11i	0.115544	+	0.0203735i
$802$	9.61886e12	−	8.07118e12i	0.820992	−	0.688894i
$803$	5.40404e12	+	9.36007e12i	0.458668	+	0.794436i
$804$	9.79938e11	−	1.69730e12i	0.0827077	−	0.143254i
$805$	−2.01973e11	−	1.14545e12i	−0.0169517	−	0.0961376i
$806$	3.50215e13	−	2.02197e13i	2.92299	−	1.68759i
$807$	−2.05679e13	+	7.48610e12i	−1.70710	+	0.621334i
$808$		−	6.77156e12i		−	0.558905i
$809$	6.50561e11	+	1.78740e12i	0.0533974	+	0.146708i	0.963524	−	0.267622i	$-0.0862380\pi$
$809$	6.50561e11	+	1.78740e12i	0.0533974	+	0.146708i	−0.910126	+	0.414331i	$0.864016\pi$
$810$	6.97756e11	−	3.95717e12i	0.0569536	−	0.323000i
$811$	−1.08125e13	−	9.07276e12i	−0.877671	−	0.736454i	0.0880277	−	0.996118i	$-0.471944\pi$
$811$	−1.08125e13	−	9.07276e12i	−0.877671	−	0.736454i	−0.965699	+	0.259664i	$0.916388\pi$
$812$	−6.78711e12	−	8.08856e12i	−0.547876	−	0.652933i
$813$	9.76808e12			0.784155
$814$	−1.93636e13	+	1.45904e13i	−1.54588	+	1.16481i
$815$	−1.96995e11			−0.0156403
$816$	1.56165e12	+	1.86110e12i	0.123304	+	0.146948i
$817$	−3.88178e11	−	3.25720e11i	−0.0304811	−	0.0255767i
$818$	−1.82504e12	+	1.03503e13i	−0.142522	+	0.808284i
$819$	−1.85580e12	−	5.09876e12i	−0.144129	−	0.395992i
$820$			4.77637e12i			0.368923i
$821$	5.26716e12	−	1.91709e12i	0.404606	−	0.147265i	−0.131697	−	0.991290i	$-0.542043\pi$
$821$	5.26716e12	−	1.91709e12i	0.404606	−	0.147265i	0.536303	+	0.844025i	$0.319820\pi$
$822$	−3.71694e12	+	2.14597e12i	−0.283963	+	0.163946i
$823$	−1.02111e11	−	5.79100e11i	−0.00775842	−	0.0440002i	0.980683	−	0.195605i	$-0.0626670\pi$
$823$	−1.02111e11	−	5.79100e11i	−0.00775842	−	0.0440002i	−0.988441	+	0.151605i	$0.951556\pi$
$824$	5.11834e12	−	8.86522e12i	0.386773	−	0.669911i
$825$	−8.66248e12	−	1.50039e13i	−0.651028	−	1.12761i
$826$	3.44605e13	−	2.89158e13i	2.57579	−	2.16135i
$827$	1.61524e13	+	2.84810e12i	1.20077	+	0.211729i	0.738033	−	0.674765i	$-0.235755\pi$
$827$	1.61524e13	+	2.84810e12i	1.20077	+	0.211729i	0.462741	+	0.886494i	$0.346866\pi$
$828$	−5.71361e11	−	3.29875e11i	−0.0422449	−	0.0243901i
$829$	−8.37945e12	+	2.30224e13i	−0.616198	+	1.69299i	0.0999068	+	0.994997i	$0.468146\pi$
$829$	−8.37945e12	+	2.30224e13i	−0.616198	+	1.69299i	−0.716105	+	0.697993i	$0.754077\pi$
$830$	8.36007e11	+	3.04282e11i	0.0611447	+	0.0222548i
$831$	6.17398e12	−	1.08864e12i	0.449118	−	0.0791916i
$832$	−2.29634e13	+	2.73667e13i	−1.66143	+	1.98001i
$833$	6.66523e12	−	7.94331e12i	0.479637	−	0.571609i
$834$	2.76634e13	−	4.87781e12i	1.97997	−	0.349122i
$835$	1.58305e12	+	5.76184e11i	0.112695	+	0.0410178i
$836$	1.14063e13	−	3.13386e13i	0.807640	−	2.21897i
$837$	1.46510e13	+	8.45876e12i	1.03182	+	0.595720i
$838$	6.91899e11	+	1.22000e11i	0.0484668	+	0.00854601i
$839$	4.49898e12	−	3.77509e12i	0.313462	−	0.263026i	−0.472459	−	0.881353i	$-0.656634\pi$
$839$	4.49898e12	−	3.77509e12i	0.313462	−	0.263026i	0.785921	+	0.618327i	$0.212189\pi$
$840$	−1.33846e12	−	2.31828e12i	−0.0927573	−	0.160660i
$841$	−6.36086e12	+	1.10173e13i	−0.438464	+	0.759441i
$842$	5.07383e12	+	2.87751e13i	0.347881	+	1.97293i
$843$	1.40211e13	−	8.09509e12i	0.956221	−	0.552074i
$844$	−1.30425e13	+	4.74709e12i	−0.884750	+	0.322023i
$845$			5.54209e12i			0.373954i
$846$	1.68115e12	+	4.61891e12i	0.112834	+	0.310008i
$847$	2.92871e12	−	1.66095e13i	0.195524	−	1.10887i
$848$	−3.86853e12	−	3.24608e12i	−0.256900	−	0.215565i
$849$	1.28425e12	+	1.53051e12i	0.0848333	+	0.101100i
$850$	−7.01938e12			−0.461226
$851$	1.91403e12	+	3.75684e12i	0.125102	+	0.245550i
$852$	2.26789e12			0.147449
$853$	4.66966e12	+	5.56508e12i	0.302005	+	0.359916i	0.895609	−	0.444841i	$-0.146740\pi$
$853$	4.66966e12	+	5.56508e12i	0.302005	+	0.359916i	−0.593604	+	0.804757i	$0.702296\pi$
$854$	−2.48007e13	−	2.08103e13i	−1.59553	−	1.33881i
$855$	−9.84351e10	+	5.58253e11i	−0.00629945	+	0.0357259i
$856$	−6.71926e11	−	1.84610e12i	−0.0427749	−	0.117523i
$857$		−	2.64666e12i		−	0.167604i	−0.996482	−	0.0838021i	$-0.973294\pi$
$857$		−	2.64666e12i		−	0.167604i	0.996482	−	0.0838021i	$-0.0267064\pi$
$858$	−5.27075e13	+	1.91839e13i	−3.32031	+	1.20850i
$859$	5.71421e12	−	3.29910e12i	0.358086	−	0.206741i	−0.310155	−	0.950686i	$-0.600381\pi$
$859$	5.71421e12	−	3.29910e12i	0.358086	−	0.206741i	0.668241	+	0.743945i	$0.267048\pi$
$860$	2.01139e10	+	1.14072e11i	0.00125387	+	0.00711106i
$861$	−2.28072e13	+	3.95032e13i	−1.41435	+	2.44973i
$862$	1.81149e13	+	3.13760e13i	1.11752	+	1.93560i
$863$	−2.03611e12	+	1.70850e12i	−0.124955	+	0.104849i	−0.703124	−	0.711068i	$-0.748212\pi$
$863$	−2.03611e12	+	1.70850e12i	−0.124955	+	0.104849i	0.578169	+	0.815917i	$0.303767\pi$
$864$	−2.03132e13	−	3.58177e12i	−1.24013	−	0.218668i
$865$	1.55310e12	+	8.96685e11i	0.0943252	+	0.0544587i
$866$	−1.01891e13	+	2.79943e13i	−0.615610	+	1.69137i
$867$	−1.50026e13	−	5.46049e12i	−0.901737	−	0.328205i
$868$	5.16912e13	−	9.11456e12i	3.09085	−	0.545000i
$869$	−3.78977e11	+	4.51647e11i	−0.0225436	+	0.0268664i
$870$	1.19255e12	−	1.42123e12i	0.0705734	−	0.0841061i
$871$	−3.36804e12	+	5.93876e11i	−0.198287	+	0.0349634i
$872$	5.58083e12	+	2.03125e12i	0.326869	+	0.118971i
$873$	4.71994e11	−	1.29679e12i	0.0275025	−	0.0755626i
$874$	−8.81990e12	−	5.09217e12i	−0.511284	−	0.295190i
$875$	−1.18729e13	−	2.09351e12i	−0.684732	−	0.120737i
$876$	1.35822e13	−	1.13969e13i	0.779297	−	0.653908i
$877$	−1.33119e13	−	2.30568e13i	−0.759873	−	1.31614i	−0.942915	−	0.333033i	$-0.891928\pi$
$877$	−1.33119e13	−	2.30568e13i	−0.759873	−	1.31614i	0.183043	−	0.983105i	$-0.441405\pi$
$878$	1.00472e13	−	1.74022e13i	0.570584	−	0.988280i
$879$	−2.02487e12	−	1.14836e13i	−0.114406	−	0.648828i
$880$	2.16275e12	−	1.24866e12i	0.121572	−	0.0701896i
$881$	−1.78274e13	+	6.48866e12i	−0.997005	+	0.362880i	−0.788429	−	0.615126i	$-0.789105\pi$
$881$	−1.78274e13	+	6.48866e12i	−0.997005	+	0.362880i	−0.208576	+	0.978006i	$0.566883\pi$
$882$		−	8.70167e12i		−	0.484165i
$883$	5.09882e12	+	1.40089e13i	0.282258	+	0.775497i	0.997092	+	0.0762034i	$0.0242798\pi$
$883$	5.09882e12	+	1.40089e13i	0.282258	+	0.775497i	−0.714834	+	0.699294i	$0.753498\pi$
$884$	−2.24726e12	+	1.27448e13i	−0.123771	+	0.701938i
$885$	3.44814e12	+	2.89333e12i	0.188947	+	0.158545i
$886$	−1.30597e13	−	1.55639e13i	−0.712000	−	0.848528i
$887$	−1.49495e13			−0.810904			−0.405452	−	0.914116i	$-0.632886\pi$
$887$	−1.49495e13			−0.810904			−0.405452	+	0.914116i	$0.632886\pi$
$888$	7.09672e12	+	6.61830e12i	0.383001	+	0.357181i
$889$	−5.48400e12			−0.294469
$890$	−3.10035e12	−	3.69486e12i	−0.165636	−	0.197398i
$891$	−2.04245e13	−	1.71382e13i	−1.08568	−	0.910994i
$892$	2.70162e12	−	1.53216e13i	0.142883	−	0.810332i
$893$	1.47785e13	+	4.06035e13i	0.777674	+	2.13664i
$894$		−	2.85316e13i		−	1.49385i
$895$	3.42308e12	−	1.24590e12i	0.178326	−	0.0649052i
$896$	−2.86158e13	+	1.65213e13i	−1.48327	+	0.856364i
$897$	1.69381e12	+	9.60608e12i	0.0873573	+	0.495428i
$898$	2.47670e13	−	4.28977e13i	1.27095	−	2.20136i
$899$	4.43774e12	+	7.68639e12i	0.226591	+	0.392468i
$900$	−2.56967e12	+	2.15621e12i	−0.130553	+	0.109547i
$901$	−3.58292e12	−	6.31765e11i	−0.181124	−	0.0319370i
$902$	4.81973e13	+	2.78267e13i	2.42434	+	1.39969i
$903$	−3.78340e11	+	1.03948e12i	−0.0189360	+	0.0520261i
$904$	1.04058e13	+	3.78741e12i	0.518225	+	0.188618i
$905$	−5.20648e12	+	9.18042e11i	−0.258003	+	0.0454929i
$906$	−3.77468e13	+	4.49849e13i	−1.86124	+	2.21815i
$907$	3.50185e12	−	4.17335e12i	0.171817	−	0.204763i	−0.673264	−	0.739402i	$-0.735108\pi$
$907$	3.50185e12	−	4.17335e12i	0.171817	−	0.204763i	0.845080	+	0.534639i	$0.179553\pi$
$908$	−6.68930e12	+	1.17950e12i	−0.326584	+	0.0575855i
$909$	2.94153e12	+	1.07063e12i	0.142901	+	0.0520118i
$910$	−6.54836e12	+	1.79915e13i	−0.316553	+	0.869722i
$911$	1.63575e13	+	9.44403e12i	0.786838	+	0.454281i	0.838848	−	0.544365i	$-0.183230\pi$
$911$	1.63575e13	+	9.44403e12i	0.786838	+	0.454281i	−0.0520102	+	0.998647i	$0.516563\pi$
$912$	1.76501e13	+	3.11218e12i	0.844830	+	0.148966i
$913$	4.52212e12	−	3.79451e12i	0.215389	−	0.180733i
$914$	2.74781e12	+	4.75935e12i	0.130236	+	0.225575i
$915$	1.61974e12	−	2.80546e12i	0.0763922	−	0.132315i
$916$	−4.74872e12	−	2.69313e13i	−0.222868	−	1.26394i
$917$	−2.45625e13	+	1.41812e13i	−1.14713	+	0.662293i
$918$	−8.93370e12	+	3.25160e12i	−0.415183	+	0.151114i
$919$		−	3.98170e13i		−	1.84140i	−0.390266	−	0.920702i	$-0.627617\pi$
$919$		−	3.98170e13i		−	1.84140i	0.390266	−	0.920702i	$-0.372383\pi$
$920$	1.94261e11	+	5.33727e11i	0.00894005	+	0.0245626i
$921$	−5.88754e12	+	3.33899e13i	−0.269628	+	1.52914i
$922$	3.58772e13	+	3.01045e13i	1.63504	+	1.37196i
$923$	−2.54382e12	−	3.03160e12i	−0.115366	−	0.137488i
$924$	−7.28028e13			−3.28567
$925$	2.12780e13	−	2.61180e12i	0.955636	−	0.117301i
$926$	3.38887e13			1.51462
$927$	3.04176e12	+	3.62503e12i	0.135290	+	0.161233i
$928$	−8.28966e12	−	6.95585e12i	−0.366919	−	0.307882i
$929$	3.28950e12	−	1.86557e13i	0.144897	−	0.821752i	−0.822553	−	0.568689i	$-0.807451\pi$
$929$	3.28950e12	−	1.86557e13i	0.144897	−	0.821752i	0.967450	−	0.253063i	$-0.0814381\pi$
$930$	3.15435e12	+	8.66651e12i	0.138273	+	0.379902i
$931$		−	7.64937e13i		−	3.33697i
$932$	1.71222e13	−	6.23196e12i	0.743340	−	0.270553i
$933$	−7.38507e11	+	4.26377e11i	−0.0319071	+	0.0184216i
$934$	7.19009e12	+	4.07771e13i	0.309153	+	1.75329i
$935$	8.99577e11	−	1.55811e12i	0.0384934	−	0.0666725i
$936$	1.32483e12	+	2.29466e12i	0.0564179	+	0.0977187i
$937$	2.35900e13	−	1.97944e13i	0.999771	−	0.838907i	0.0128179	−	0.999918i	$-0.495920\pi$
$937$	2.35900e13	−	1.97944e13i	0.999771	−	0.838907i	0.986953	+	0.161011i	$0.0514754\pi$
$938$	−7.67659e12	−	1.35359e12i	−0.323784	−	0.0570919i
$939$	2.77835e13	+	1.60408e13i	1.16625	+	0.673334i
$940$	3.37814e12	−	9.28138e12i	0.141125	−	0.387737i
$941$	2.08668e13	+	7.59488e12i	0.867564	+	0.315767i	0.737180	−	0.675696i	$-0.236157\pi$
$941$	2.08668e13	+	7.59488e12i	0.867564	+	0.315767i	0.130384	+	0.991464i	$0.458379\pi$
$942$	−3.66961e13	+	6.47052e12i	−1.51842	+	0.267738i
$943$	6.22111e12	−	7.41403e12i	0.256192	−	0.305318i
$944$	1.07968e13	−	1.28671e13i	0.442508	−	0.527360i
$945$	−7.88797e12	+	1.39086e12i	−0.321753	+	0.0567337i
$946$	1.26825e12	+	4.61606e11i	0.0514868	+	0.0187397i
$947$	−1.31477e12	+	3.61230e12i	−0.0531220	+	0.145952i	−0.963416	−	0.268011i	$-0.913633\pi$
$947$	−1.31477e12	+	3.61230e12i	−0.0531220	+	0.145952i	0.910294	+	0.413963i	$0.135856\pi$
$948$	8.37616e11	+	4.83598e11i	0.0336827	+	0.0194467i
$949$	−3.04696e13	−	5.37261e12i	−1.21946	−	0.215024i
$950$	−3.96671e13	+	3.32847e13i	−1.58006	+	1.32583i
$951$	2.04981e13	+	3.55037e13i	0.812644	+	1.40754i
$952$	−3.59828e12	+	6.23241e12i	−0.141981	+	0.245918i
$953$	3.64648e11	+	2.06802e12i	0.0143204	+	0.0812151i	0.991130	−	0.132893i	$-0.0424267\pi$
$953$	3.64648e11	+	2.06802e12i	0.0143204	+	0.0812151i	−0.976810	+	0.214108i	$0.931316\pi$
$954$	−2.64406e12	+	1.52655e12i	−0.103348	+	0.0596681i
$955$	3.16463e12	−	1.15183e12i	0.123114	−	0.0448099i
$956$		−	4.40680e13i		−	1.70633i
$957$	−4.21043e12	−	1.15680e13i	−0.162264	−	0.445817i
$958$	−4.45943e12	+	2.52907e13i	−0.171055	+	0.970099i
$959$	7.44676e12	+	6.24857e12i	0.284304	+	0.238560i
$960$	−5.23710e12	−	6.24133e12i	−0.199008	−	0.237168i
$961$	−1.76808e13			−0.668725
$962$	3.63497e12	−	6.93098e13i	0.136840	−	2.60920i
$963$	9.08172e11			0.0340290
$964$	3.41333e12	+	4.06784e12i	0.127301	+	0.151711i
$965$	3.16098e12	+	2.65238e12i	0.117341	+	0.0984607i
$966$	−3.86062e12	+	2.18946e13i	−0.142646	+	0.808986i
$967$	6.44353e12	+	1.77034e13i	0.236976	+	0.651086i	0.999989	+	0.00470307i	$0.00149704\pi$
$967$	6.44353e12	+	1.77034e13i	0.236976	+	0.651086i	−0.763013	+	0.646383i	$0.776281\pi$
$968$			8.23599e12i			0.301493i
$969$	1.21332e13	−	4.41611e12i	0.442096	−	0.160910i
$970$	−4.21714e12	+	2.43477e12i	−0.152948	+	0.0883048i
$971$	2.64228e12	+	1.49851e13i	0.0953875	+	0.540970i	0.994628	+	0.103515i	$0.0330089\pi$
$971$	2.64228e12	+	1.49851e13i	0.0953875	+	0.540970i	−0.899240	+	0.437455i	$0.855880\pi$
$972$	−4.89425e12	+	8.47709e12i	−0.175868	+	0.304613i
$973$	−3.18115e13	−	5.50991e13i	−1.13783	−	1.97077i
$974$	2.42119e13	−	2.03162e13i	0.862013	−	0.723315i
$975$	4.88416e13	+	8.61210e12i	1.73089	+	0.305203i
$976$	−1.04689e13	−	6.04423e12i	−0.369299	−	0.213215i
$977$	−1.15322e13	+	3.16844e13i	−0.404935	+	1.11255i	0.554883	+	0.831928i	$0.312763\pi$
$977$	−1.15322e13	+	3.16844e13i	−0.404935	+	1.11255i	−0.959818	+	0.280622i	$0.909459\pi$
$978$	3.53838e12	+	1.28786e12i	0.123674	+	0.0450138i
$979$	−3.15180e13	+	5.55748e12i	−1.09657	+	0.193355i
$980$	−1.12394e13	+	1.33946e13i	−0.389247	+	0.463886i
$981$	−1.76473e12	+	2.10313e12i	−0.0608370	+	0.0725028i
$982$	−4.43047e12	+	7.81212e11i	−0.152037	+	0.0268082i
$983$	−2.62007e13	−	9.53629e12i	−0.895000	−	0.325753i	−0.146752	−	0.989173i	$-0.546882\pi$
$983$	−2.62007e13	−	9.53629e12i	−0.895000	−	0.325753i	−0.748247	+	0.663420i	$0.769104\pi$
$984$	7.61840e12	−	2.09314e13i	0.259051	−	0.711738i
$985$	7.36126e12	+	4.25002e12i	0.249166	+	0.143856i
$986$	−4.91193e12	−	8.66105e11i	−0.165503	−	0.0291826i
$987$	7.22578e13	−	6.06315e13i	2.42358	−	2.03363i
$988$	4.77343e13	+	8.26782e13i	1.59377	+	2.76048i
$989$	1.17354e11	−	2.03263e11i	0.00390046	−	0.00675579i
$990$	−2.62176e11	−	1.48688e12i	−0.00867431	−	0.0491945i
$991$	−6.66734e12	+	3.84939e12i	−0.219594	+	0.126783i	−0.605762	−	0.795646i	$-0.707132\pi$
$991$	−6.66734e12	+	3.84939e12i	−0.219594	+	0.126783i	0.386168	+	0.922428i	$0.373798\pi$
$992$	5.05495e13	−	1.83985e13i	1.65735	−	0.603226i
$993$			1.86483e13i			0.608652i
$994$	−3.08505e12	−	8.47609e12i	−0.100236	−	0.275396i
$995$	2.59945e11	−	1.47422e12i	0.00840769	−	0.0476824i
$996$	−7.41842e12	−	6.22479e12i	−0.238860	−	0.200428i
$997$	−1.52831e13	−	1.82137e13i	−0.489872	−	0.583807i	0.463313	−	0.886195i	$-0.346661\pi$
$997$	−1.52831e13	−	1.82137e13i	−0.489872	−	0.583807i	−0.953185	+	0.302388i	$0.902216\pi$
$998$	−4.04922e13			−1.29206
$999$	2.58710e13	−	1.31807e13i	0.821805	−	0.418692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.h.a.25.6	yes	168
37.3	even	18	inner	37.10.h.a.3.6	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.h.a.3.6	✓	168	37.3	even	18	inner
37.10.h.a.25.6	yes	168	1.1	even	1	trivial

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.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.1667 - 26.4172i) q^{2} +(114.438 + 96.0253i) q^{3} +(-117.600 + 666.941i) q^{4} +(92.1806 + 253.264i) q^{5} -5151.70i q^{6} +(-10964.7 + 3990.81i) q^{7} +(4934.58 - 2848.98i) q^{8} +(457.392 + 2594.00i) q^{9} +O(q^{10})\)	\(q+(-22.1667 - 26.4172i) q^{2} +(114.438 + 96.0253i) q^{3} +(-117.600 + 666.941i) q^{4} +(92.1806 + 253.264i) q^{5} -5151.70i q^{6} +(-10964.7 + 3990.81i) q^{7} +(4934.58 - 2848.98i) q^{8} +(457.392 + 2594.00i) q^{9} +(4647.19 - 8049.17i) q^{10} +(-30835.8 - 53409.1i) q^{11} +(-77501.1 + 65031.1i) q^{12} +(173861. + 30656.4i) q^{13} +(348476. + 201193. i) q^{14} +(-13770.7 + 37834.8i) q^{15} +(141185. + 51387.1i) q^{16} +(106598. - 18796.0i) q^{17} +(58387.3 - 69583.3i) q^{18} +(513265. - 611685. i) q^{19} +(-179752. + 31695.2i) q^{20} +(-1.63800e6 - 596183. i) q^{21} +(-727393. + 1.99850e6i) q^{22} +(320300. + 184925. i) q^{23} +(838280. + 147811. i) q^{24} +(1.44054e6 - 1.20875e6i) q^{25} +(-3.04406e6 - 5.27247e6i) q^{26} +(1.27346e6 - 2.20570e6i) q^{27} +(-1.37219e6 - 7.78210e6i) q^{28} +(1.15718e6 - 668100. i) q^{29} +(1.30474e6 - 474887. i) q^{30} +6.64232e6i q^{31} +(-2.76989e6 - 7.61021e6i) q^{32} +(1.59983e6 - 9.07307e6i) q^{33} +(-2.85945e6 - 2.39936e6i) q^{34} +(-2.02146e6 - 2.40908e6i) q^{35} -1.78383e6 q^{36} +(9.56068e6 + 6.20928e6i) q^{37} -2.75364e7 q^{38} +(1.69526e7 + 2.02033e7i) q^{39} +(1.17642e6 + 987131. i) q^{40} +(4.54407e6 - 2.57707e7i) q^{41} +(2.05595e7 + 5.64867e7i) q^{42} -634604. i q^{43} +(3.92470e7 - 1.42847e7i) q^{44} +(-614804. + 354957. i) q^{45} +(-2.21477e6 - 1.25606e7i) q^{46} +(-2.70566e7 + 4.68634e7i) q^{47} +(1.12225e7 + 1.94380e7i) q^{48} +(7.33847e7 - 6.15771e7i) q^{49} +(-6.38637e7 - 1.12609e7i) q^{50} +(1.40038e7 + 8.08507e6i) q^{51} +(-4.08920e7 + 1.12350e8i) q^{52} +(-3.15846e7 - 1.14958e7i) q^{53} +(-8.64970e7 + 1.52517e7i) q^{54} +(1.06841e7 - 1.27329e7i) q^{55} +(-4.27363e7 + 5.09311e7i) q^{56} +(1.17474e8 - 2.07139e7i) q^{57} +(-4.33002e7 - 1.57600e7i) q^{58} +(3.82364e7 - 1.05054e8i) q^{59} +(-2.36141e7 - 1.36336e7i) q^{60} +(-7.92355e7 - 1.39714e7i) q^{61} +(1.75472e8 - 1.47238e8i) q^{62} +(-1.53673e7 - 2.66170e7i) q^{63} +(-1.01178e8 + 1.75246e8i) q^{64} +(8.26245e6 + 4.68587e7i) q^{65} +(-2.75148e8 + 1.58857e8i) q^{66} +(-1.82037e7 + 6.62562e6i) q^{67} +7.33047e7i q^{68} +(1.88971e7 + 5.19194e7i) q^{69} +(-1.88322e7 + 1.06803e8i) q^{70} +(-1.71720e7 - 1.44090e7i) q^{71} +(9.64729e6 + 1.14972e7i) q^{72} -1.75252e8 q^{73} +(-4.78964e7 - 3.90205e8i) q^{74} +2.80923e8 q^{75} +(3.47598e8 + 4.14251e8i) q^{76} +(5.51249e8 + 4.62553e8i) q^{77} +(1.57933e8 - 8.95681e8i) q^{78} +(-3.26973e6 - 8.98351e6i) q^{79} +4.04940e7i q^{80} +(4.06255e8 - 1.47865e8i) q^{81} +(-7.81516e8 + 4.51208e8i) q^{82} +(1.66216e7 + 9.42660e7i) q^{83} +(5.90246e8 - 1.02234e9i) q^{84} +(1.45866e7 + 2.52647e7i) q^{85} +(-1.67645e7 + 1.40670e7i) q^{86} +(1.96581e8 + 3.46625e7i) q^{87} +(-3.04323e8 - 1.75701e8i) q^{88} +(1.77490e8 - 4.87651e8i) q^{89} +(2.30051e7 + 8.37318e6i) q^{90} +(-2.02867e9 + 3.57710e8i) q^{91} +(-1.61001e8 + 1.91874e8i) q^{92} +(-6.37831e8 + 7.60137e8i) q^{93} +(1.83775e9 - 3.24046e8i) q^{94} +(2.02231e8 + 7.36060e7i) q^{95} +(4.13791e8 - 1.13688e9i) q^{96} +(-4.53730e8 - 2.61961e8i) q^{97} +(-3.25339e9 - 5.73660e8i) q^{98} +(1.24439e8 - 1.04417e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9}+O(q^{10}) \) 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9	\( 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9} - 60003 q^{10} + 175689 q^{11} - 307257 q^{12} - 713598 q^{13} + 290583 q^{14} - 385260 q^{15} + 292473 q^{16} + 951645 q^{17} - 2634174 q^{18} + 87108 q^{19} - 6701172 q^{20} + 1892136 q^{21} - 1410435 q^{22} - 9 q^{23} + 6919605 q^{24} - 1830519 q^{25} - 12361155 q^{26} + 12227553 q^{27} - 14971305 q^{28} - 8346069 q^{29} + 32076480 q^{30} + 25901316 q^{32} + 29661003 q^{33} + 17761257 q^{34} - 25104648 q^{35} - 302330892 q^{36} - 89711496 q^{37} + 137852370 q^{38} + 3073230 q^{39} + 72127485 q^{40} + 40690731 q^{41} + 229015377 q^{42} + 187195086 q^{44} - 293199021 q^{45} - 286926930 q^{46} - 134086527 q^{47} + 86156133 q^{48} + 67568640 q^{49} + 134153859 q^{50} - 528106959 q^{51} + 402280539 q^{52} + 147470676 q^{53} + 422122437 q^{54} - 55011861 q^{55} - 616228263 q^{56} - 449072832 q^{57} + 529606191 q^{58} + 773443290 q^{59} + 1433547972 q^{60} + 469275144 q^{61} - 914552304 q^{62} - 673379979 q^{63} + 1146585192 q^{64} - 243884745 q^{65} + 1805055381 q^{66} + 214516206 q^{67} + 722409993 q^{69} - 2605801512 q^{70} - 1455384636 q^{71} - 4689293691 q^{72} + 930909090 q^{73} - 1261741251 q^{74} + 3013150476 q^{75} + 195486513 q^{76} + 1827454371 q^{77} + 1710012453 q^{78} + 1230271476 q^{79} + 2262925611 q^{81} - 3346032141 q^{82} - 2122951164 q^{83} - 6124511730 q^{84} - 39169146 q^{85} - 2603533938 q^{86} + 1185003879 q^{87} - 261497646 q^{88} + 1603969074 q^{89} + 7288796094 q^{90} - 4883515182 q^{91} - 7533267018 q^{92} + 1209552852 q^{93} + 1712695200 q^{94} + 2036912394 q^{95} + 7661250639 q^{96} - 7583351877 q^{97} - 10074558573 q^{98} - 7520510685 q^{99}+O(q^{100}) \) 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9 - 60003 * q^10 + 175689 * q^11 - 307257 * q^12 - 713598 * q^13 + 290583 * q^14 - 385260 * q^15 + 292473 * q^16 + 951645 * q^17 - 2634174 * q^18 + 87108 * q^19 - 6701172 * q^20 + 1892136 * q^21 - 1410435 * q^22 - 9 * q^23 + 6919605 * q^24 - 1830519 * q^25 - 12361155 * q^26 + 12227553 * q^27 - 14971305 * q^28 - 8346069 * q^29 + 32076480 * q^30 + 25901316 * q^32 + 29661003 * q^33 + 17761257 * q^34 - 25104648 * q^35 - 302330892 * q^36 - 89711496 * q^37 + 137852370 * q^38 + 3073230 * q^39 + 72127485 * q^40 + 40690731 * q^41 + 229015377 * q^42 + 187195086 * q^44 - 293199021 * q^45 - 286926930 * q^46 - 134086527 * q^47 + 86156133 * q^48 + 67568640 * q^49 + 134153859 * q^50 - 528106959 * q^51 + 402280539 * q^52 + 147470676 * q^53 + 422122437 * q^54 - 55011861 * q^55 - 616228263 * q^56 - 449072832 * q^57 + 529606191 * q^58 + 773443290 * q^59 + 1433547972 * q^60 + 469275144 * q^61 - 914552304 * q^62 - 673379979 * q^63 + 1146585192 * q^64 - 243884745 * q^65 + 1805055381 * q^66 + 214516206 * q^67 + 722409993 * q^69 - 2605801512 * q^70 - 1455384636 * q^71 - 4689293691 * q^72 + 930909090 * q^73 - 1261741251 * q^74 + 3013150476 * q^75 + 195486513 * q^76 + 1827454371 * q^77 + 1710012453 * q^78 + 1230271476 * q^79 + 2262925611 * q^81 - 3346032141 * q^82 - 2122951164 * q^83 - 6124511730 * q^84 - 39169146 * q^85 - 2603533938 * q^86 + 1185003879 * q^87 - 261497646 * q^88 + 1603969074 * q^89 + 7288796094 * q^90 - 4883515182 * q^91 - 7533267018 * q^92 + 1209552852 * q^93 + 1712695200 * q^94 + 2036912394 * q^95 + 7661250639 * q^96 - 7583351877 * q^97 - 10074558573 * q^98 - 7520510685 * q^99

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