LMFDB - Embedded newform 91.10.q.a.36.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, 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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$124$
Relative dimension:	$62$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.12
Character	$\chi$	$=$	91.36
Dual form			91.10.q.a.43.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.9451 + 15.5567i) q^{2} +(20.0545 + 34.7353i) q^{3} +(228.024 - 394.949i) q^{4} -2230.19i q^{5} +(-1080.74 - 623.963i) q^{6} +(-2079.33 - 1200.50i) q^{7} -1740.87i q^{8} +(9037.14 - 15652.8i) q^{9} +O(q^{10})$	\(q+(-26.9451 + 15.5567i) q^{2} +(20.0545 + 34.7353i) q^{3} +(228.024 - 394.949i) q^{4} -2230.19i q^{5} +(-1080.74 - 623.963i) q^{6} +(-2079.33 - 1200.50i) q^{7} -1740.87i q^{8} +(9037.14 - 15652.8i) q^{9} +(34694.4 + 60092.5i) q^{10} +(22261.2 - 12852.5i) q^{11} +18291.6 q^{12} +(29969.6 - 98520.7i) q^{13} +74703.4 q^{14} +(77466.2 - 44725.1i) q^{15} +(143830. + 249122. i) q^{16} +(343843. - 595554. i) q^{17} +562353. i q^{18} +(181218. + 104626. i) q^{19} +(-880809. - 508535. i) q^{20} -96301.5i q^{21} +(-399885. + 692622. i) q^{22} +(-1.04516e6 - 1.81027e6i) q^{23} +(60469.7 - 34912.2i) q^{24} -3.02060e6 q^{25} +(725127. + 3.12087e6i) q^{26} +1.51440e6 q^{27} +(-948272. + 547485. i) q^{28} +(3.04370e6 + 5.27185e6i) q^{29} +(-1.39155e6 + 2.41024e6i) q^{30} -838297. i q^{31} +(-6.97913e6 - 4.02940e6i) q^{32} +(892870. + 515499. i) q^{33} +2.13963e7i q^{34} +(-2.67734e6 + 4.63729e6i) q^{35} +(-4.12137e6 - 7.13841e6i) q^{36} +(-4.53854e6 + 2.62033e6i) q^{37} -6.51057e6 q^{38} +(4.02317e6 - 934774. i) q^{39} -3.88247e6 q^{40} +(2.06519e7 - 1.19234e7i) q^{41} +(1.49814e6 + 2.59485e6i) q^{42} +(-1.45264e7 + 2.51605e7i) q^{43} -1.17227e7i q^{44} +(-3.49086e7 - 2.01545e7i) q^{45} +(5.63238e7 + 3.25186e7i) q^{46} -3.03084e7i q^{47} +(-5.76888e6 + 9.99200e6i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(8.13903e7 - 4.69907e7i) q^{50} +2.75823e7 q^{51} +(-3.20768e7 - 3.43015e7i) q^{52} +3.67401e7 q^{53} +(-4.08057e7 + 2.35592e7i) q^{54} +(-2.86634e7 - 4.96465e7i) q^{55} +(-2.08992e6 + 3.61984e6i) q^{56} +8.39288e6i q^{57} +(-1.64025e8 - 9.47002e7i) q^{58} +(-7.05944e7 - 4.07577e7i) q^{59} -4.07936e7i q^{60} +(1.33085e7 - 2.30510e7i) q^{61} +(1.30412e7 + 2.25880e7i) q^{62} +(-3.75823e7 + 2.16982e7i) q^{63} +1.03455e8 q^{64} +(-2.19719e8 - 6.68378e7i) q^{65} -3.20779e7 q^{66} +(1.94032e8 - 1.12025e8i) q^{67} +(-1.56809e8 - 2.71601e8i) q^{68} +(4.19202e7 - 7.26080e7i) q^{69} -1.66603e8i q^{70} +(1.22027e8 + 7.04521e7i) q^{71} +(-2.72495e7 - 1.57325e7i) q^{72} -2.61883e8i q^{73} +(8.15275e7 - 1.41210e8i) q^{74} +(-6.05765e7 - 1.04922e8i) q^{75} +(8.26440e7 - 4.77145e7i) q^{76} -6.17176e7 q^{77} +(-9.38625e7 + 8.77749e7i) q^{78} +4.67397e8 q^{79} +(5.55588e8 - 3.20769e8i) q^{80} +(-1.47507e8 - 2.55490e8i) q^{81} +(-3.70977e8 + 6.42551e8i) q^{82} +2.60202e8i q^{83} +(-3.80342e7 - 2.19590e7i) q^{84} +(-1.32820e9 - 7.66834e8i) q^{85} -9.03934e8i q^{86} +(-1.22080e8 + 2.11448e8i) q^{87} +(-2.23745e7 - 3.87538e7i) q^{88} +(1.95058e8 - 1.12617e8i) q^{89} +1.25415e9 q^{90} +(-1.80591e8 + 1.68878e8i) q^{91} -9.53286e8 q^{92} +(2.91185e7 - 1.68116e7i) q^{93} +(4.71500e8 + 8.16661e8i) q^{94} +(2.33336e8 - 4.04150e8i) q^{95} -3.23230e8i q^{96} +(-1.62485e8 - 9.38109e7i) q^{97} +(-1.55333e8 - 8.96815e7i) q^{98} -4.64599e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9}+O(q^{10}) $ 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9	\( 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9} - 47368 q^{10} + 18420 q^{11} + 434316 q^{12} - 103730 q^{13} - 307328 q^{14} - 994308 q^{15} - 4327304 q^{16} + 826226 q^{17} - 832512 q^{20} - 2238874 q^{22} - 5178348 q^{23} + 13060272 q^{24} - 56263016 q^{25} + 12486810 q^{26} - 16794384 q^{27} + 8409710 q^{29} - 18091000 q^{30} + 30354048 q^{32} + 36508140 q^{33} + 8902908 q^{35} + 42350446 q^{36} + 26865678 q^{37} - 7473860 q^{38} - 21470652 q^{39} - 112860988 q^{40} - 109829778 q^{41} + 12446784 q^{42} - 53384856 q^{43} - 84576450 q^{45} + 160042176 q^{46} - 39524126 q^{48} + 357417662 q^{49} + 35767422 q^{50} + 121877584 q^{51} + 61751010 q^{52} - 252868460 q^{53} + 951692088 q^{54} - 414833028 q^{55} - 118013952 q^{56} - 342666540 q^{58} - 440088588 q^{59} + 264060146 q^{61} + 995887736 q^{62} - 383747028 q^{63} - 2239569444 q^{64} - 501903354 q^{65} + 304284804 q^{66} + 392937636 q^{67} - 3665660 q^{68} - 249969892 q^{69} - 375620748 q^{71} - 2829560808 q^{72} + 1336479018 q^{74} + 1306893216 q^{75} + 1652559990 q^{76} + 823754288 q^{77} + 857091302 q^{78} - 2357982776 q^{79} + 1107773136 q^{80} - 1492992434 q^{81} - 1984241462 q^{82} - 2156016366 q^{84} + 3060837654 q^{85} - 1286987624 q^{87} + 1904443442 q^{88} + 887446752 q^{89} + 7601525656 q^{90} - 86522436 q^{91} - 8365653336 q^{92} - 776657196 q^{93} + 6270763420 q^{94} - 6325568332 q^{95} - 5522676732 q^{97}+O(q^{100}) \) 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9 - 47368 * q^10 + 18420 * q^11 + 434316 * q^12 - 103730 * q^13 - 307328 * q^14 - 994308 * q^15 - 4327304 * q^16 + 826226 * q^17 - 832512 * q^20 - 2238874 * q^22 - 5178348 * q^23 + 13060272 * q^24 - 56263016 * q^25 + 12486810 * q^26 - 16794384 * q^27 + 8409710 * q^29 - 18091000 * q^30 + 30354048 * q^32 + 36508140 * q^33 + 8902908 * q^35 + 42350446 * q^36 + 26865678 * q^37 - 7473860 * q^38 - 21470652 * q^39 - 112860988 * q^40 - 109829778 * q^41 + 12446784 * q^42 - 53384856 * q^43 - 84576450 * q^45 + 160042176 * q^46 - 39524126 * q^48 + 357417662 * q^49 + 35767422 * q^50 + 121877584 * q^51 + 61751010 * q^52 - 252868460 * q^53 + 951692088 * q^54 - 414833028 * q^55 - 118013952 * q^56 - 342666540 * q^58 - 440088588 * q^59 + 264060146 * q^61 + 995887736 * q^62 - 383747028 * q^63 - 2239569444 * q^64 - 501903354 * q^65 + 304284804 * q^66 + 392937636 * q^67 - 3665660 * q^68 - 249969892 * q^69 - 375620748 * q^71 - 2829560808 * q^72 + 1336479018 * q^74 + 1306893216 * q^75 + 1652559990 * q^76 + 823754288 * q^77 + 857091302 * q^78 - 2357982776 * q^79 + 1107773136 * q^80 - 1492992434 * q^81 - 1984241462 * q^82 - 2156016366 * q^84 + 3060837654 * q^85 - 1286987624 * q^87 + 1904443442 * q^88 + 887446752 * q^89 + 7601525656 * q^90 - 86522436 * q^91 - 8365653336 * q^92 - 776657196 * q^93 + 6270763420 * q^94 - 6325568332 * q^95 - 5522676732 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−26.9451	+	15.5567i	−1.19081	+	0.687517i	−0.958491	−	0.285122i	$-0.907966\pi$
$2$	−26.9451	+	15.5567i	−1.19081	+	0.687517i	−0.232323	+	0.972639i	$0.574633\pi$
$3$	20.0545	+	34.7353i	0.142944	+	0.247586i	0.928604	−	0.371073i	$-0.121010\pi$
$3$	20.0545	+	34.7353i	0.142944	+	0.247586i	−0.785660	+	0.618658i	$0.787677\pi$
$4$	228.024	−	394.949i	0.445359	−	0.771384i
$5$		−	2230.19i		−	1.59579i	−0.602796	−	0.797895i	$-0.705947\pi$
$5$		−	2230.19i		−	1.59579i	0.602796	−	0.797895i	$-0.294053\pi$
$6$	−1080.74	−	623.963i	−0.340439	−	0.196552i
$7$	−2079.33	−	1200.50i	−0.327327	−	0.188982i
$7$	−2079.33	−	1200.50i	−0.327327	−	0.188982i
$8$		−	1740.87i		−	0.150266i
$9$	9037.14	−	15652.8i	0.459134	−	0.795244i
$10$	34694.4	+	60092.5i	1.09713	+	1.90029i
$11$	22261.2	−	12852.5i	0.458438	−	0.264679i	−0.252949	−	0.967480i	$-0.581401\pi$
$11$	22261.2	−	12852.5i	0.458438	−	0.264679i	0.711387	+	0.702800i	$0.248067\pi$
$12$	18291.6			0.254645
$13$	29969.6	−	98520.7i	0.291029	−	0.956714i
$13$	29969.6	−	98520.7i	0.291029	−	0.956714i
$14$	74703.4			0.519714
$15$	77466.2	−	44725.1i	0.395095	−	0.228108i
$16$	143830.	+	249122.i	0.548670	+	0.950324i
$17$	343843.	−	595554.i	0.998482	−	1.72942i	0.451535	−	0.892254i	$-0.350877\pi$
$17$	343843.	−	595554.i	0.998482	−	1.72942i	0.546947	−	0.837167i	$-0.315790\pi$
$18$			562353.i			1.26265i
$19$	181218.	+	104626.i	0.319014	+	0.184183i	0.650953	−	0.759118i	$-0.274369\pi$
$19$	181218.	+	104626.i	0.319014	+	0.184183i	−0.331939	+	0.943301i	$0.607703\pi$
$20$	−880809.	−	508535.i	−1.23097	−	0.710700i
$21$		−	96301.5i		−	0.108055i
$22$	−399885.	+	692622.i	−0.363943	+	0.630368i
$23$	−1.04516e6	−	1.81027e6i	−0.778767	−	1.34886i	−0.932653	−	0.360775i	$-0.882512\pi$
$23$	−1.04516e6	−	1.81027e6i	−0.778767	−	1.34886i	0.153886	−	0.988089i	$-0.450821\pi$
$24$	60469.7	−	34912.2i	0.0372038	−	0.0214796i
$25$	−3.02060e6			−1.54655
$26$	725127.	+	3.12087e6i	0.311196	+	1.33936i
$27$	1.51440e6			0.548409
$28$	−948272.	+	547485.i	−0.291556	+	0.168330i
$29$	3.04370e6	+	5.27185e6i	0.799119	+	1.38411i	0.920191	+	0.391471i	$0.128034\pi$
$29$	3.04370e6	+	5.27185e6i	0.799119	+	1.38411i	−0.121072	+	0.992644i	$0.538633\pi$
$30$	−1.39155e6	+	2.41024e6i	−0.313657	+	0.543269i
$31$		−	838297.i		−	0.163031i	−0.996672	−	0.0815155i	$-0.974024\pi$
$31$		−	838297.i		−	0.163031i	0.996672	−	0.0815155i	$-0.0259760\pi$
$32$	−6.97913e6	−	4.02940e6i	−1.17659	−	0.679306i
$33$	892870.	+	515499.i	0.131062	+	0.0756685i
$34$			2.13963e7i			2.74589i
$35$	−2.67734e6	+	4.63729e6i	−0.301576	+	0.522345i
$36$	−4.12137e6	−	7.13841e6i	−0.408959	−	0.708338i
$37$	−4.53854e6	+	2.62033e6i	−0.398115	+	0.229852i	−0.685670	−	0.727912i	$-0.740491\pi$
$37$	−4.53854e6	+	2.62033e6i	−0.398115	+	0.229852i	0.287555	+	0.957764i	$0.407157\pi$
$38$	−6.51057e6			−0.506515
$39$	4.02317e6	−	934774.i	0.278470	−	0.0647017i
$40$	−3.88247e6			−0.239794
$41$	2.06519e7	−	1.19234e7i	1.14138	−	0.658978i	0.194611	−	0.980880i	$-0.437656\pi$
$41$	2.06519e7	−	1.19234e7i	1.14138	−	0.658978i	0.946773	+	0.321902i	$0.104322\pi$
$42$	1.49814e6	+	2.59485e6i	0.0742899	+	0.128674i
$43$	−1.45264e7	+	2.51605e7i	−0.647963	+	1.12230i	0.335646	+	0.941988i	$0.391045\pi$
$43$	−1.45264e7	+	2.51605e7i	−0.647963	+	1.12230i	−0.983609	+	0.180316i	$0.942288\pi$
$44$		−	1.17227e7i		−	0.471509i
$45$	−3.49086e7	−	2.01545e7i	−1.26904	−	0.732682i
$46$	5.63238e7	+	3.25186e7i	1.85473	+	1.07083i
$47$		−	3.03084e7i		−	0.905988i	−0.891513	−	0.452994i	$-0.850356\pi$
$47$		−	3.03084e7i		−	0.905988i	0.891513	−	0.452994i	$-0.149644\pi$
$48$	−5.76888e6	+	9.99200e6i	−0.156858	+	0.271686i
$49$	2.88240e6	+	4.99246e6i	0.0714286	+	0.123718i
$50$	8.13903e7	−	4.69907e7i	1.84165	−	1.06328i
$51$	2.75823e7			0.570907
$52$	−3.20768e7	−	3.43015e7i	−0.608382	−	0.650576i
$53$	3.67401e7			0.639586			0.319793	−	0.947487i	$-0.396387\pi$
$53$	3.67401e7			0.639586			0.319793	+	0.947487i	$0.396387\pi$
$54$	−4.08057e7	+	2.35592e7i	−0.653053	+	0.377040i
$55$	−2.86634e7	−	4.96465e7i	−0.422373	−	0.731571i
$56$	−2.08992e6	+	3.61984e6i	−0.0283977	+	0.0491862i
$57$			8.39288e6i			0.105311i
$58$	−1.64025e8	−	9.47002e7i	−1.90320	−	1.09882i
$59$	−7.05944e7	−	4.07577e7i	−0.758467	−	0.437901i	0.0702784	−	0.997527i	$-0.477611\pi$
$59$	−7.05944e7	−	4.07577e7i	−0.758467	−	0.437901i	−0.828745	+	0.559627i	$0.810945\pi$
$60$		−	4.07936e7i		−	0.406360i
$61$	1.33085e7	−	2.30510e7i	0.123068	−	0.213160i	−0.797908	−	0.602779i	$-0.794060\pi$
$61$	1.33085e7	−	2.30510e7i	0.123068	−	0.213160i	0.920976	+	0.389619i	$0.127393\pi$
$62$	1.30412e7	+	2.25880e7i	0.112087	+	0.194140i
$63$	−3.75823e7	+	2.16982e7i	−0.300574	+	0.173536i
$64$	1.03455e8			0.770799
$65$	−2.19719e8	−	6.68378e7i	−1.52672	−	0.464421i
$66$	−3.20779e7			−0.208093
$67$	1.94032e8	−	1.12025e8i	1.17635	−	0.679167i	0.221184	−	0.975232i	$-0.429008\pi$
$67$	1.94032e8	−	1.12025e8i	1.17635	−	0.679167i	0.955168	+	0.296065i	$0.0956744\pi$
$68$	−1.56809e8	−	2.71601e8i	−0.889366	−	1.54043i
$69$	4.19202e7	−	7.26080e7i	0.222640	−	0.385623i
$70$		−	1.66603e8i		−	0.829355i
$71$	1.22027e8	+	7.04521e7i	0.569892	+	0.329027i	0.757106	−	0.653292i	$-0.226613\pi$
$71$	1.22027e8	+	7.04521e7i	0.569892	+	0.329027i	−0.187214	+	0.982319i	$0.559946\pi$
$72$	−2.72495e7	−	1.57325e7i	−0.119498	−	0.0689924i
$73$		−	2.61883e8i		−	1.07933i	−0.841880	−	0.539664i	$-0.818551\pi$
$73$		−	2.61883e8i		−	1.07933i	0.841880	−	0.539664i	$-0.181449\pi$
$74$	8.15275e7	−	1.41210e8i	0.316054	−	0.547422i
$75$	−6.05765e7	−	1.04922e8i	−0.221069	−	0.382904i
$76$	8.26440e7	−	4.77145e7i	0.284152	−	0.164055i
$77$	−6.17176e7			−0.200079
$78$	−9.38625e7	+	8.77749e7i	−0.287122	+	0.268500i
$79$	4.67397e8			1.35009			0.675047	−	0.737774i	$-0.264123\pi$
$79$	4.67397e8			1.35009			0.675047	+	0.737774i	$0.264123\pi$
$80$	5.55588e8	−	3.20769e8i	1.51652	−	0.875562i
$81$	−1.47507e8	−	2.55490e8i	−0.380743	−	0.659465i
$82$	−3.70977e8	+	6.42551e8i	−0.906118	+	1.56944i
$83$			2.60202e8i			0.601811i	0.953654	+	0.300905i	$0.0972888\pi$
$83$			2.60202e8i			0.601811i	−0.953654	+	0.300905i	$0.902711\pi$
$84$	−3.80342e7	−	2.19590e7i	−0.0833522	−	0.0481234i
$85$	−1.32820e9	−	7.66834e8i	−2.75979	−	1.59337i
$86$		−	9.03934e8i		−	1.78194i
$87$	−1.22080e8	+	2.11448e8i	−0.228458	+	0.395701i
$88$	−2.23745e7	−	3.87538e7i	−0.0397724	−	0.0688878i
$89$	1.95058e8	−	1.12617e8i	0.329541	−	0.190261i	−0.326096	−	0.945337i	$-0.605733\pi$
$89$	1.95058e8	−	1.12617e8i	0.329541	−	0.190261i	0.655637	+	0.755076i	$0.272400\pi$
$90$	1.25415e9			2.01493
$91$	−1.80591e8	+	1.68878e8i	−0.276064	+	0.258159i
$92$	−9.53286e8			−1.38732
$93$	2.91185e7	−	1.68116e7i	0.0403642	−	0.0233043i
$94$	4.71500e8	+	8.16661e8i	0.622882	+	1.07886i
$95$	2.33336e8	−	4.04150e8i	0.293917	−	0.509080i
$96$		−	3.23230e8i		−	0.388410i
$97$	−1.62485e8	−	9.38109e7i	−0.186355	−	0.107592i	0.403920	−	0.914794i	$-0.367647\pi$
$97$	−1.62485e8	−	9.38109e7i	−0.186355	−	0.107592i	−0.590275	+	0.807202i	$0.700981\pi$
$98$	−1.55333e8	−	8.96815e7i	−0.170116	−	0.0982167i
$99$		−	4.64599e8i		−	0.486093i
$100$	−6.88770e8	+	1.19298e9i	−0.688770	+	1.19298i
$101$	3.99331e8	+	6.91661e8i	0.381845	+	0.661374i	0.991326	−	0.131426i	$-0.0419556\pi$
$101$	3.99331e8	+	6.91661e8i	0.381845	+	0.661374i	−0.609481	+	0.792800i	$0.708622\pi$
$102$	−7.43207e8	+	4.29091e8i	−0.679844	+	0.392508i
$103$	1.81523e9			1.58915			0.794573	−	0.607169i	$-0.207695\pi$
$103$	1.81523e9			1.58915			0.794573	+	0.607169i	$0.207695\pi$
$104$	−1.71512e8	−	5.21732e7i	−0.143762	−	0.0437318i
$105$	−2.14770e8			−0.172434
$106$	−9.89964e8	+	5.71556e8i	−0.761629	+	0.439726i
$107$	−3.31418e7	−	5.74033e7i	−0.0244427	−	0.0423360i	0.853545	−	0.521019i	$-0.174448\pi$
$107$	−3.31418e7	−	5.74033e7i	−0.0244427	−	0.0423360i	−0.877988	+	0.478683i	$0.841114\pi$
$108$	3.45320e8	−	5.98112e8i	0.244239	−	0.423034i
$109$			1.53871e9i			1.04409i	0.852919	+	0.522044i	$0.174830\pi$
$109$			1.53871e9i			1.04409i	−0.852919	+	0.522044i	$0.825170\pi$
$110$	1.54467e9	+	8.91818e8i	1.00594	+	0.580777i
$111$	−1.82036e8	−	1.05098e8i	−0.113816	−	0.0657117i
$112$		−	6.90674e8i		−	0.414755i
$113$	−4.77436e8	+	8.26944e8i	−0.275463	+	0.477115i	−0.970252	−	0.242098i	$-0.922164\pi$
$113$	−4.77436e8	+	8.26944e8i	−0.275463	+	0.477115i	0.694789	+	0.719213i	$0.255498\pi$
$114$	−1.30566e8	−	2.26147e8i	−0.0724032	−	0.125406i
$115$	−4.03724e9	+	2.33090e9i	−2.15251	+	1.24275i
$116$	2.77615e9			1.42358
$117$	−1.27128e9	−	1.35945e9i	−0.627200	−	0.670699i
$118$	2.53623e9			1.20426
$119$	−1.42992e9	+	8.25567e8i	−0.653660	+	0.377391i
$120$	−7.78607e7	−	1.34859e8i	−0.0342770	−	0.0593695i
$121$	−8.48601e8	+	1.46982e9i	−0.359890	+	0.623347i
$122$			8.28148e8i			0.338445i
$123$	8.28323e8	+	4.78233e8i	0.326307	+	0.188394i
$124$	−3.31084e8	−	1.91152e8i	−0.125760	−	0.0726074i
$125$			2.38067e9i			0.872178i
$126$	6.75105e8	−	1.16932e9i	0.238618	−	0.413299i
$127$	1.36151e9	+	2.35821e9i	0.464413	+	0.804387i	0.999175	−	0.0406159i	$-0.0129320\pi$
$127$	1.36151e9	+	2.35821e9i	0.464413	+	0.804387i	−0.534762	+	0.845003i	$0.679599\pi$
$128$	7.85717e8	−	4.53634e8i	0.258715	−	0.149369i
$129$	−1.16528e9			−0.370489
$130$	6.96013e9	−	1.61717e9i	2.13733	−	0.496604i
$131$	−4.19933e9			−1.24583			−0.622916	−	0.782289i	$-0.714052\pi$
$131$	−4.19933e9			−1.24583			−0.622916	+	0.782289i	$0.714052\pi$
$132$	4.07191e8	−	2.35092e8i	0.116739	−	0.0673993i
$133$	−2.51208e8	−	4.35104e8i	−0.0696146	−	0.120576i
$134$	−3.48547e9	+	6.03702e9i	−0.933878	+	1.61752i
$135$		−	3.37740e9i		−	0.875146i
$136$	−1.03678e9	−	5.98586e8i	−0.259874	−	0.150038i
$137$	3.11037e8	+	1.79577e8i	0.0754344	+	0.0435521i	0.537243	−	0.843428i	$-0.319466\pi$
$137$	3.11037e8	+	1.79577e8i	0.0754344	+	0.0435521i	−0.461808	+	0.886980i	$0.652799\pi$
$138$			2.60857e9i			0.612274i
$139$	9.06419e8	−	1.56996e9i	0.205950	−	0.356716i	−0.744485	−	0.667639i	$-0.767305\pi$
$139$	9.06419e8	−	1.56996e9i	0.205950	−	0.356716i	0.950435	+	0.310923i	$0.100638\pi$
$140$	1.22099e9	+	2.11482e9i	0.268619	+	0.465262i
$141$	1.05277e9	−	6.07818e8i	0.224310	−	0.129505i
$142$	−4.38402e9			−0.904847
$143$	−5.99077e8	−	2.57837e9i	−0.119804	−	0.515623i
$144$	5.19926e9			1.00765
$145$	1.17572e10	−	6.78802e9i	2.20876	−	1.27523i
$146$	4.07404e9	+	7.05644e9i	0.742057	+	1.28528i
$147$	−1.15610e8	+	2.00242e8i	−0.0204205	+	0.0353694i
$148$			2.38999e9i			0.409466i
$149$	−4.27116e9	−	2.46595e9i	−0.709917	−	0.409871i	0.101113	−	0.994875i	$-0.467760\pi$
$149$	−4.27116e9	−	2.46595e9i	−0.709917	−	0.409871i	−0.811030	+	0.585004i	$0.801093\pi$
$150$	3.26448e9	+	1.88475e9i	0.526505	+	0.303978i
$151$		−	3.01134e9i		−	0.471371i	−0.971829	−	0.235686i	$-0.924266\pi$
$151$		−	3.01134e9i		−	0.471371i	0.971829	−	0.235686i	$-0.0757335\pi$
$152$	1.82141e8	−	3.15477e8i	0.0276765	−	0.0479371i
$153$	−6.21471e9	−	1.07642e10i	−0.916874	−	1.58807i
$154$	1.66298e9	−	9.60125e8i	0.238257	−	0.137558i
$155$	−1.86956e9			−0.260163
$156$	5.48191e8	−	1.80210e9i	0.0741091	−	0.243623i
$157$	−1.30305e10			−1.71164			−0.855820	−	0.517275i	$-0.826947\pi$
$157$	−1.30305e10			−1.71164			−0.855820	+	0.517275i	$0.826947\pi$
$158$	−1.25940e10	+	7.27117e9i	−1.60771	+	0.928213i
$159$	7.36803e8	+	1.27618e9i	0.0914249	+	0.158352i
$160$	−8.98631e9	+	1.55648e10i	−1.08403	+	1.87760i
$161$			5.01886e9i			0.588693i
$162$	7.94919e9	+	4.58947e9i	0.906787	+	0.523534i
$163$	−2.82149e9	−	1.62899e9i	−0.313065	−	0.180748i	0.335232	−	0.942135i	$-0.391185\pi$
$163$	−2.82149e9	−	1.62899e9i	−0.313065	−	0.180748i	−0.648297	+	0.761387i	$0.724519\pi$
$164$		−	1.08752e10i		−	1.17393i
$165$	1.14966e9	−	1.99127e9i	0.120751	−	0.209147i
$166$	−4.04790e9	−	7.01117e9i	−0.413755	−	0.716645i
$167$	1.53473e10	−	8.86076e9i	1.52689	−	0.881550i	0.527400	−	0.849617i	$-0.323167\pi$
$167$	1.53473e10	−	8.86076e9i	1.52689	−	0.881550i	0.999490	−	0.0319328i	$-0.0101663\pi$
$168$	−1.67648e8			−0.0162371
$169$	−8.80814e9	−	5.90525e9i	−0.830604	−	0.556863i
$170$	4.77177e10			4.38187
$171$	3.27538e9	−	1.89104e9i	0.292941	−	0.169129i
$172$	6.62473e9	+	1.14744e10i	0.577152	+	0.999657i
$173$	2.37769e9	−	4.11827e9i	0.201812	−	0.349549i	−0.747300	−	0.664486i	$-0.768650\pi$
$173$	2.37769e9	−	4.11827e9i	0.201812	−	0.349549i	0.949112	+	0.314938i	$0.101984\pi$
$174$		−	7.59664e9i		−	0.628275i
$175$	6.28082e9	+	3.62623e9i	0.506227	+	0.292270i
$176$	6.40366e9	+	3.69716e9i	0.503062	+	0.290443i
$177$		−	3.26949e9i		−	0.250381i
$178$	−3.50391e9	+	6.06894e9i	−0.261615	+	0.453130i
$179$	1.70866e9	+	2.95948e9i	0.124399	+	0.215465i	0.921498	−	0.388384i	$-0.126966\pi$
$179$	1.70866e9	+	2.95948e9i	0.124399	+	0.215465i	−0.797099	+	0.603849i	$0.793633\pi$
$180$	−1.59200e10	+	9.19141e9i	−1.13036	+	0.652613i
$181$	−1.35893e10			−0.941115			−0.470558	−	0.882369i	$-0.655947\pi$
$181$	−1.35893e10			−0.941115			−0.470558	+	0.882369i	$0.655947\pi$
$182$	2.23883e9	−	7.35983e9i	0.151252	−	0.497218i
$183$	1.06758e9			0.0703672
$184$	−3.15145e9	+	1.81949e9i	−0.202689	+	0.117022i
$185$	5.84382e9	+	1.01218e10i	0.366795	+	0.635308i
$186$	−5.23067e8	+	9.05978e8i	−0.0320442	+	0.0555021i
$187$		−	1.76769e10i		−	1.05711i
$188$	−1.19703e10	−	6.91104e9i	−0.698865	−	0.403490i
$189$	−3.14894e9	−	1.81804e9i	−0.179509	−	0.103640i
$190$			1.45198e10i			0.808293i
$191$	−1.31414e10	+	2.27615e10i	−0.714480	+	1.23752i	0.248679	+	0.968586i	$0.420004\pi$
$191$	−1.31414e10	+	2.27615e10i	−0.714480	+	1.23752i	−0.963160	+	0.268931i	$0.913330\pi$
$192$	2.07473e9	+	3.59354e9i	0.110181	+	0.190839i
$193$	−1.07459e10	+	6.20415e9i	−0.557487	+	0.321865i	−0.752136	−	0.659008i	$-0.770977\pi$
$193$	−1.07459e10	+	6.20415e9i	−0.557487	+	0.321865i	0.194649	+	0.980873i	$0.437643\pi$
$194$	5.83756e9			0.295886
$195$	−2.08472e9	−	8.97242e9i	−0.103250	−	0.444379i
$196$	2.62902e9			0.127245
$197$	−2.65096e10	+	1.53053e10i	−1.25402	+	0.724011i	−0.971906	−	0.235369i	$-0.924370\pi$
$197$	−2.65096e10	+	1.53053e10i	−1.25402	+	0.724011i	−0.282117	+	0.959380i	$0.591037\pi$
$198$	7.22764e9	+	1.25186e10i	0.334197	+	0.578847i
$199$	−3.30733e9	+	5.72847e9i	−0.149499	+	0.258940i	−0.931042	−	0.364911i	$-0.881099\pi$
$199$	−3.30733e9	+	5.72847e9i	−0.149499	+	0.258940i	0.781543	+	0.623851i	$0.214433\pi$
$200$			5.25848e9i			0.232394i
$201$	7.78242e9	+	4.49318e9i	0.336304	+	0.194165i
$202$	−2.15200e10	−	1.24246e10i	−0.909412	−	0.525049i
$203$		−	1.46159e10i		−	0.604077i
$204$	6.28943e9	−	1.08936e10i	0.254258	−	0.440389i
$205$	−2.65913e10	−	4.60575e10i	−1.05159	−	1.82141i
$206$	−4.89114e10	+	2.82390e10i	−1.89238	+	1.09256i
$207$	−3.77810e10			−1.43023
$208$	2.88542e10	−	6.70419e9i	1.06887	−	0.248349i
$209$	5.37883e9			0.194998
$210$	5.78699e9	−	3.34112e9i	0.205336	−	0.118551i
$211$	1.64358e10	+	2.84677e10i	0.570848	+	0.988738i	0.996479	+	0.0838412i	$0.0267189\pi$
$211$	1.64358e10	+	2.84677e10i	0.570848	+	0.988738i	−0.425631	+	0.904897i	$0.639948\pi$
$212$	8.37762e9	−	1.45105e10i	0.284846	−	0.493367i
$213$			5.65152e9i			0.188129i
$214$	1.78602e9	+	1.03116e9i	0.0582134	+	0.0336095i
$215$	5.61125e10	+	3.23966e10i	1.79096	+	1.03401i
$216$		−	2.63638e9i		−	0.0824074i
$217$	−1.00638e9	+	1.74309e9i	−0.0308100	+	0.0533644i
$218$	−2.39373e10	−	4.14605e10i	−0.717828	−	1.24331i
$219$	9.09658e9	−	5.25191e9i	0.267227	−	0.154283i
$220$	−2.61438e10			−0.752430
$221$	−4.83695e10	−	5.17242e10i	−1.36397	−	1.45857i
$222$	6.53995e9			0.180712
$223$	1.06584e10	−	6.15364e9i	0.288616	−	0.166633i	−0.348701	−	0.937234i	$-0.613377\pi$
$223$	1.06584e10	−	6.15364e9i	0.288616	−	0.166633i	0.637318	+	0.770601i	$0.280044\pi$
$224$	9.67459e9	+	1.67569e10i	0.256754	+	0.444710i
$225$	−2.72976e10	+	4.72808e10i	−0.710073	+	1.22988i
$226$		−	2.97094e10i		−	0.757541i
$227$	1.84348e10	+	1.06433e10i	0.460810	+	0.266049i	0.712385	−	0.701789i	$-0.247615\pi$
$227$	1.84348e10	+	1.06433e10i	0.460810	+	0.266049i	−0.251575	+	0.967838i	$0.580949\pi$
$228$	3.31476e9	+	1.91378e9i	0.0812354	+	0.0469013i
$229$		−	5.87533e10i		−	1.41180i	−0.708312	−	0.705899i	$-0.750543\pi$
$229$		−	5.87533e10i		−	1.41180i	0.708312	−	0.705899i	$-0.249457\pi$
$230$	7.25224e10	−	1.25612e11i	1.70882	−	2.95977i
$231$	−1.23771e9	−	2.14378e9i	−0.0286000	−	0.0495367i
$232$	9.17761e9	−	5.29870e9i	0.207986	−	0.120081i
$233$	6.36543e10			1.41490			0.707451	−	0.706763i	$-0.249845\pi$
$233$	6.36543e10			1.41490			0.707451	+	0.706763i	$0.249845\pi$
$234$	5.54034e10	+	1.68535e10i	1.20800	+	0.367468i
$235$	−6.75934e10			−1.44577
$236$	−3.21944e10	+	1.85875e10i	−0.675580	+	0.390046i
$237$	9.37339e9	+	1.62352e10i	0.192988	+	0.334264i
$238$	2.56863e10	−	4.44899e10i	0.518925	−	0.898804i
$239$			6.39141e10i			1.26709i	0.773707	+	0.633543i	$0.218400\pi$
$239$			6.39141e10i			1.26709i	−0.773707	+	0.633543i	$0.781600\pi$
$240$	2.22840e10	+	1.28657e10i	0.433554	+	0.250312i
$241$	−3.33417e10	−	1.92499e10i	−0.636666	−	0.367579i	0.146663	−	0.989186i	$-0.453147\pi$
$241$	−3.33417e10	−	1.92499e10i	−0.636666	−	0.367579i	−0.783329	+	0.621607i	$0.786480\pi$
$242$		−	5.28058e10i		−	0.989721i
$243$	2.08204e10	−	3.60619e10i	0.383054	−	0.663469i
$244$	−6.06932e9	−	1.05124e10i	−0.109619	−	0.189866i
$245$	1.11341e10	−	6.42829e9i	0.197428	−	0.113985i
$246$	−2.97590e10			−0.518095
$247$	1.57389e10	−	1.47181e10i	0.269053	−	0.251603i
$248$	−1.45937e9			−0.0244981
$249$	−9.03822e9	+	5.21822e9i	−0.149000	+	0.0860251i
$250$	−3.70355e10	−	6.41474e10i	−0.599637	−	1.03860i
$251$	−2.69817e10	+	4.67336e10i	−0.429079	+	0.743187i	−0.996792	−	0.0800402i	$-0.974495\pi$
$251$	−2.69817e10	+	4.67336e10i	−0.429079	+	0.743187i	0.567713	+	0.823227i	$0.307828\pi$
$252$			1.97908e10i			0.309144i
$253$	−4.65329e10	−	2.68658e10i	−0.714033	−	0.412247i
$254$	−7.33720e10	−	4.23613e10i	−1.10606	−	0.638584i
$255$		−	6.15137e10i		−	0.911048i
$256$	−4.05986e10	+	7.03188e10i	−0.590787	+	1.02327i
$257$	1.09951e10	+	1.90440e10i	0.157217	+	0.272308i	0.933864	−	0.357628i	$-0.116414\pi$
$257$	1.09951e10	+	1.90440e10i	0.157217	+	0.272308i	−0.776647	+	0.629936i	$0.783081\pi$
$258$	3.13984e10	−	1.81279e10i	0.441183	−	0.254717i
$259$	1.25828e10			0.173752
$260$	−7.64988e10	+	7.15373e10i	−1.03818	+	0.970851i
$261$	1.10025e11			1.46761
$262$	1.13151e11	−	6.53279e10i	1.48355	−	0.856530i
$263$	5.36292e10	+	9.28885e10i	0.691195	+	1.19718i	0.971447	+	0.237258i	$0.0762486\pi$
$263$	5.36292e10	+	9.28885e10i	0.691195	+	1.19718i	−0.280252	+	0.959926i	$0.590418\pi$
$264$	8.97417e8	−	1.55437e9i	0.0113704	−	0.0196942i
$265$		−	8.19373e10i		−	1.02065i
$266$	1.35376e10	+	7.81594e9i	0.165796	+	0.0957224i
$267$	7.82358e9	+	4.51695e9i	0.0942117	+	0.0543932i
$268$		−	1.02177e11i		−	1.20989i
$269$	−7.35633e10	+	1.27415e11i	−0.856596	+	1.48367i	0.0185609	+	0.999828i	$0.494092\pi$
$269$	−7.35633e10	+	1.27415e11i	−0.856596	+	1.48367i	−0.875157	+	0.483840i	$0.839242\pi$
$270$	5.25413e10	+	9.10042e10i	0.601678	+	1.04214i
$271$	3.23906e10	−	1.87007e10i	0.364802	−	0.210618i	−0.306383	−	0.951908i	$-0.599119\pi$
$271$	3.23906e10	−	1.87007e10i	0.364802	−	0.210618i	0.671185	+	0.741290i	$0.265786\pi$
$272$	1.97820e11			2.19135
$273$	−9.48769e9	−	2.88612e9i	−0.103378	−	0.0314472i
$274$	−1.11745e10			−0.119771
$275$	−6.72421e10	+	3.88222e10i	−0.708997	+	0.409339i
$276$	−1.91176e10	−	3.31127e10i	−0.198309	−	0.343482i
$277$	−4.13475e10	+	7.16159e10i	−0.421978	+	0.730888i	−0.996133	−	0.0878592i	$-0.971997\pi$
$277$	−4.13475e10	+	7.16159e10i	−0.421978	+	0.730888i	0.574155	+	0.818747i	$0.305331\pi$
$278$			5.64037e10i			0.566377i
$279$	−1.31217e10	−	7.57581e9i	−0.129649	−	0.0748531i
$280$	8.07292e9	+	4.66090e9i	0.0784909	+	0.0453167i
$281$			1.21644e10i			0.116389i	0.998305	+	0.0581946i	$0.0185344\pi$
$281$			1.21644e10i			0.116389i	−0.998305	+	0.0581946i	$0.981466\pi$
$282$	−1.89113e10	+	3.27554e10i	−0.178074	+	0.308434i
$283$	−4.90881e10	−	8.50231e10i	−0.454923	−	0.787949i	0.543761	−	0.839240i	$-0.317000\pi$
$283$	−4.90881e10	−	8.50231e10i	−0.454923	−	0.787949i	−0.998684	+	0.0512910i	$0.983666\pi$
$284$	5.56500e10	−	3.21295e10i	0.507613	−	0.293070i
$285$	1.87177e10			0.168055
$286$	5.62531e10	+	6.01546e10i	0.497164	+	0.531645i
$287$	−5.72560e10			−0.498141
$288$	−1.26143e11	+	7.28285e10i	−1.08043	+	0.623785i
$289$	−1.77162e11	−	3.06854e11i	−1.49393	−	2.58756i
$290$	−2.11199e11	+	3.65807e11i	−1.75348	+	3.03712i
$291$		−	7.52530e9i		−	0.0615185i
$292$	−1.03430e11	−	5.97155e10i	−0.832578	−	0.480689i
$293$	1.36646e11	+	7.88926e10i	1.08316	+	0.625363i	0.931747	−	0.363108i	$-0.118284\pi$
$293$	1.36646e11	+	7.88926e10i	1.08316	+	0.625363i	0.151413	+	0.988471i	$0.451618\pi$
$294$		−	7.19405e9i		−	0.0561579i
$295$	−9.08973e10	+	1.57439e11i	−0.698798	+	1.21035i
$296$	4.56165e9	+	7.90101e9i	0.0345390	+	0.0598233i
$297$	3.37124e10	−	1.94638e10i	0.251411	−	0.145152i
$298$	1.53449e11			1.12717
$299$	−2.09672e11	+	4.87168e10i	−1.51712	+	0.352499i
$300$	−5.52516e10			−0.393821
$301$	6.04103e10	−	3.48779e10i	0.424191	−	0.244907i
$302$	4.68465e10	+	8.11406e10i	0.324076	+	0.561315i
$303$	−1.60167e10	+	2.77418e10i	−0.109165	+	0.189079i
$304$			6.01937e10i			0.404222i
$305$	−5.14081e10	−	2.96805e10i	−0.340159	−	0.196391i
$306$	3.34912e11	+	1.93361e11i	2.18365	+	1.26073i
$307$			2.13226e11i			1.36999i	0.728546	+	0.684997i	$0.240196\pi$
$307$			2.13226e11i			1.36999i	−0.728546	+	0.684997i	$0.759804\pi$
$308$	−1.40731e10	+	2.43753e10i	−0.0891069	+	0.154338i
$309$	3.64034e10	+	6.30525e10i	0.227158	+	0.393450i
$310$	5.03753e10	−	2.90842e10i	0.309806	−	0.178867i
$311$	1.79869e11			1.09027			0.545136	−	0.838348i	$-0.316478\pi$
$311$	1.79869e11			1.09027			0.545136	+	0.838348i	$0.316478\pi$
$312$	−1.62732e9	−	7.00382e9i	−0.00972249	−	0.0418446i
$313$	4.39706e10			0.258948			0.129474	−	0.991583i	$-0.458671\pi$
$313$	4.39706e10			0.258948			0.129474	+	0.991583i	$0.458671\pi$
$314$	3.51107e11	−	2.02712e11i	2.03824	−	1.17678i
$315$	4.83909e10	+	8.38156e10i	0.276928	+	0.479653i
$316$	1.06578e11	−	1.84598e11i	0.601277	−	1.04144i
$317$			9.89318e10i			0.550262i	0.961407	+	0.275131i	$0.0887212\pi$
$317$			9.89318e10i			0.550262i	−0.961407	+	0.275131i	$0.911279\pi$
$318$	−3.97064e10	−	2.29245e10i	−0.217740	−	0.125712i
$319$	1.35513e11	+	7.82383e10i	0.732693	+	0.423020i
$320$		−	2.30724e11i		−	1.23003i
$321$	1.32928e9	−	2.30238e9i	0.00698786	−	0.0121033i
$322$	−7.80770e10	−	1.35233e11i	−0.404736	−	0.701023i
$323$	1.24621e11	−	7.19500e10i	0.637059	−	0.367806i
$324$	−1.34541e11			−0.678269
$325$	−9.05263e10	+	2.97592e11i	−0.450090	+	1.47961i
$326$	1.01367e11			0.497069
$327$	−5.34475e10	+	3.08579e10i	−0.258501	+	0.149246i
$328$	−2.07570e10	−	3.59522e10i	−0.0990223	−	0.171512i
$329$	−3.63852e10	+	6.30211e10i	−0.171216	+	0.296554i
$330$			7.15397e10i			0.332074i
$331$	3.26220e11	+	1.88343e11i	1.49377	+	0.862430i	0.999974	−	0.00714573i	$-0.00227458\pi$
$331$	3.26220e11	+	1.88343e11i	1.49377	+	0.862430i	0.493799	+	0.869576i	$0.335608\pi$
$332$	1.02767e11	+	5.93324e10i	0.464228	+	0.268022i
$333$			9.47211e10i			0.422131i
$334$	−2.75689e11	+	4.77507e11i	−1.21216	+	2.09952i
$335$	−2.49836e11	−	4.32728e11i	−1.08381	−	1.87721i
$336$	2.39908e10	−	1.38511e10i	0.102688	−	0.0592867i
$337$	−3.88791e11			−1.64203			−0.821015	−	0.570906i	$-0.806592\pi$
$337$	−3.88791e11			−1.64203			−0.821015	+	0.570906i	$0.806592\pi$
$338$	3.29202e11	+	2.20914e10i	1.37195	+	0.0920656i
$339$	−3.82989e10			−0.157503
$340$	−6.05720e11	+	3.49713e11i	−2.45820	+	1.41924i
$341$	−1.07742e10	−	1.86615e10i	−0.0431509	−	0.0747396i
$342$	−5.88369e10	+	1.01908e11i	−0.232559	+	0.402803i
$343$		−	1.38413e10i		−	0.0539949i
$344$	4.38011e10	+	2.52886e10i	0.168645	+	0.0973670i
$345$	−1.61929e11	−	9.34899e10i	−0.615374	−	0.355286i
$346$			1.47956e11i			0.554997i
$347$	−8.37843e10	+	1.45119e11i	−0.310227	+	0.537330i	−0.978411	−	0.206666i	$-0.933739\pi$
$347$	−8.37843e10	+	1.45119e11i	−0.310227	+	0.537330i	0.668184	+	0.743996i	$0.267072\pi$
$348$	5.56741e10	+	9.64304e10i	0.203492	+	0.352458i
$349$	1.20851e11	−	6.97736e10i	0.436051	−	0.251754i	−0.265870	−	0.964009i	$-0.585659\pi$
$349$	1.20851e11	−	6.97736e10i	0.436051	−	0.251754i	0.701921	+	0.712255i	$0.252326\pi$
$350$	−2.25649e11			−0.803763
$351$	4.53861e10	−	1.49200e11i	0.159603	−	0.524671i
$352$	−2.07151e11			−0.719193
$353$	2.14198e11	−	1.23667e11i	0.734224	−	0.423905i	−0.0857413	−	0.996317i	$-0.527326\pi$
$353$	2.14198e11	−	1.23667e11i	0.734224	−	0.423905i	0.819966	+	0.572413i	$0.193993\pi$
$354$	5.08627e10	+	8.80967e10i	0.172141	+	0.298157i
$355$	1.57121e11	−	2.72142e11i	0.525058	−	0.909428i
$356$		−	1.02717e11i		−	0.338937i
$357$	−5.73527e10	−	3.31126e10i	−0.186873	−	0.107891i
$358$	−9.20796e10	−	5.31622e10i	−0.296272	−	0.171052i
$359$		−	4.19720e11i		−	1.33363i	−0.745225	−	0.666813i	$-0.767658\pi$
$359$		−	4.19720e11i		−	1.33363i	0.745225	−	0.666813i	$-0.232342\pi$
$360$	−3.50864e10	+	6.07714e10i	−0.110097	+	0.190694i
$361$	−1.39451e11	−	2.41535e11i	−0.432153	−	0.748512i
$362$	3.66164e11	−	2.11405e11i	1.12069	−	0.647033i
$363$	−6.80729e10			−0.205776
$364$	2.55193e10	+	1.09832e11i	0.0761924	+	0.327925i
$365$	−5.84047e11			−1.72238
$366$	−2.87660e10	+	1.66081e10i	−0.0837943	+	0.0483787i
$367$	2.26397e11	+	3.92131e11i	0.651439	+	1.12832i	0.982774	+	0.184812i	$0.0591675\pi$
$367$	2.26397e11	+	3.92131e11i	0.651439	+	1.12832i	−0.331335	+	0.943513i	$0.607499\pi$
$368$	3.00652e11	−	5.20744e11i	0.854572	−	1.48016i
$369$		−	4.31012e11i		−	1.21024i
$370$	−3.14924e11	−	1.81821e11i	−0.873570	−	0.504356i
$371$	−7.63947e10	−	4.41065e10i	−0.209354	−	0.120870i
$372$		−	1.53338e10i		−	0.0415151i
$373$	3.10044e11	−	5.37012e11i	0.829342	−	1.43646i	−0.0692127	−	0.997602i	$-0.522049\pi$
$373$	3.10044e11	−	5.37012e11i	0.829342	−	1.43646i	0.898555	−	0.438861i	$-0.144618\pi$
$374$	2.74996e11	+	4.76306e11i	0.726781	+	1.25882i
$375$	−8.26935e10	+	4.77431e10i	−0.215939	+	0.124672i
$376$	−5.27630e10			−0.136140
$377$	6.10605e11	−	1.41872e11i	1.55677	−	0.361711i
$378$	1.13131e11			0.285016
$379$	−4.53039e10	+	2.61562e10i	−0.112787	+	0.0651176i	−0.555332	−	0.831629i	$-0.687409\pi$
$379$	−4.53039e10	+	2.61562e10i	−0.112787	+	0.0651176i	0.442545	+	0.896746i	$0.354076\pi$
$380$	−1.06412e11	−	1.84311e11i	−0.261798	−	0.453447i
$381$	−5.46087e10	+	9.45851e10i	−0.132770	+	0.229964i
$382$		−	8.17747e11i		−	1.96487i
$383$	2.17861e11	+	1.25782e11i	0.517351	+	0.298693i	0.735850	−	0.677144i	$-0.236783\pi$
$383$	2.17861e11	+	1.25782e11i	0.517351	+	0.298693i	−0.218499	+	0.975837i	$0.570116\pi$
$384$	3.15142e10	+	1.81948e10i	0.0739633	+	0.0427027i
$385$			1.37642e11i			0.319284i
$386$	1.93033e11	−	3.34342e11i	0.442576	−	0.766564i
$387$	2.62554e11	+	4.54757e11i	0.595004	+	1.03058i
$388$	−7.41010e10	+	4.27822e10i	−0.165990	+	0.0958343i
$389$	4.10275e11			0.908451			0.454226	−	0.890887i	$-0.349916\pi$
$389$	4.10275e11			0.908451			0.454226	+	0.890887i	$0.349916\pi$
$390$	1.95754e11	+	2.09331e11i	0.428470	+	0.458187i
$391$	−1.43748e12			−3.11034
$392$	8.69124e9	−	5.01789e9i	0.0185906	−	0.0107333i
$393$	−8.42153e10	−	1.45865e11i	−0.178084	−	0.308450i
$394$	4.76202e11	−	8.24806e11i	0.995539	−	1.72432i
$395$		−	1.04238e12i		−	2.15447i
$396$	−1.83493e11	−	1.05940e11i	−0.374965	−	0.216486i
$397$	−3.53061e11	−	2.03840e11i	−0.713333	−	0.411843i	0.0989607	−	0.995091i	$-0.468448\pi$
$397$	−3.53061e11	−	2.03840e11i	−0.713333	−	0.411843i	−0.812294	+	0.583248i	$0.801782\pi$
$398$		−	2.05805e11i		−	0.411133i
$399$	1.00757e10	−	1.74516e10i	0.0199019	−	0.0344712i
$400$	−4.34455e11	−	7.52498e11i	−0.848544	−	1.46972i
$401$	5.08350e11	−	2.93496e11i	0.981777	−	0.566829i	0.0789712	−	0.996877i	$-0.474836\pi$
$401$	5.08350e11	−	2.93496e11i	0.981777	−	0.566829i	0.902806	+	0.430047i	$0.141503\pi$
$402$	−2.79597e11			−0.533968
$403$	−8.25896e10	−	2.51234e10i	−0.155974	−	0.0474467i
$404$	3.64228e11			0.680232
$405$	−5.69791e11	+	3.28969e11i	−1.05237	+	0.607586i
$406$	2.27375e11	+	3.93825e11i	0.415313	+	0.719344i
$407$	−6.73554e10	+	1.16663e11i	−0.121674	+	0.210746i
$408$		−	4.80173e10i		−	0.0857881i
$409$	−2.98279e11	−	1.72212e11i	−0.527070	−	0.304304i	0.212752	−	0.977106i	$-0.431757\pi$
$409$	−2.98279e11	−	1.72212e11i	−0.527070	−	0.304304i	−0.739823	+	0.672802i	$0.765091\pi$
$410$	1.43301e12	+	8.27347e11i	2.50450	+	1.44597i
$411$			1.44053e10i			0.0249020i
$412$	4.13915e11	−	7.16922e11i	0.707740	−	1.22584i
$413$	9.78593e10	+	1.69497e11i	0.165511	+	0.286673i
$414$	1.01801e12	−	5.87749e11i	1.70314	−	0.983310i
$415$	5.80300e11			0.960364
$416$	−6.06141e11	+	5.66829e11i	−0.992324	+	0.927966i
$417$	7.27110e10			0.117757
$418$	−1.44933e11	+	8.36770e10i	−0.232206	+	0.134064i
$419$	−5.32794e10	−	9.22827e10i	−0.0844494	−	0.146271i	0.820707	−	0.571349i	$-0.193580\pi$
$419$	−5.32794e10	−	9.22827e10i	−0.0844494	−	0.146271i	−0.905156	+	0.425079i	$0.860246\pi$
$420$	−4.89727e10	+	8.48232e10i	−0.0767949	+	0.133013i
$421$			3.24462e11i			0.503378i	0.967808	+	0.251689i	$0.0809860\pi$
$421$			3.24462e11i			0.503378i	−0.967808	+	0.251689i	$0.919014\pi$
$422$	−8.85729e11	−	5.11376e11i	−1.35955	−	0.784936i
$423$	−4.74411e11	−	2.73901e11i	−0.720482	−	0.415970i
$424$		−	6.39598e10i		−	0.0961083i
$425$	−1.03861e12	+	1.79893e12i	−1.54420	+	2.67463i
$426$	−8.79191e10	−	1.52280e11i	−0.129342	−	0.224027i
$427$	−5.53455e10	+	3.19537e10i	−0.0805670	+	0.0465154i
$428$	−3.02285e10			−0.0435431
$429$	7.75463e10	−	7.25169e10i	0.110536	−	0.103367i
$430$	−2.01594e12			−2.84361
$431$	−1.05643e12	+	6.09932e11i	−1.47467	+	0.851401i	−0.999593	−	0.0285439i	$-0.990913\pi$
$431$	−1.05643e12	+	6.09932e11i	−1.47467	+	0.851401i	−0.475077	+	0.879944i	$0.657580\pi$
$432$	2.17817e11	+	3.77271e11i	0.300895	+	0.521166i
$433$	−4.45457e11	+	7.71555e11i	−0.608991	+	1.05480i	0.382416	+	0.923990i	$0.375092\pi$
$433$	−4.45457e11	+	7.71555e11i	−0.608991	+	1.05480i	−0.991407	+	0.130813i	$0.958241\pi$
$434$		−	6.26237e10i		−	0.0847295i
$435$	4.71568e11	+	2.72260e11i	0.631456	+	0.364571i
$436$	6.07711e11	+	3.50862e11i	0.805393	+	0.464994i
$437$		−	4.37405e11i		−	0.573742i
$438$	−1.63405e11	+	2.83026e11i	−0.212145	+	0.367446i
$439$	−4.79600e10	−	8.30691e10i	−0.0616295	−	0.106745i	0.833564	−	0.552422i	$-0.186296\pi$
$439$	−4.79600e10	−	8.30691e10i	−0.0616295	−	0.106745i	−0.895194	+	0.445677i	$0.852963\pi$
$440$	−8.64282e10	+	4.98993e10i	−0.109931	+	0.0634684i
$441$	1.04195e11			0.131181
$442$	2.10798e12	+	6.41239e11i	2.62703	+	0.799134i
$443$	−7.76735e11			−0.958199			−0.479100	−	0.877761i	$-0.659037\pi$
$443$	−7.76735e11			−0.958199			−0.479100	+	0.877761i	$0.659037\pi$
$444$	−8.30170e10	+	4.79299e10i	−0.101378	+	0.0585306i
$445$	−2.51157e11	−	4.35017e11i	−0.303616	−	0.525879i
$446$	−1.91461e11	+	3.31620e11i	−0.229126	+	0.396857i
$447$		−	1.97813e11i		−	0.234354i
$448$	−2.15116e11	−	1.24198e11i	−0.252303	−	0.145667i
$449$	2.49182e11	+	1.43865e11i	0.289340	+	0.167051i	0.637644	−	0.770331i	$-0.279909\pi$
$449$	2.49182e11	+	1.43865e11i	0.289340	+	0.167051i	−0.348304	+	0.937382i	$0.613242\pi$
$450$		−	1.69865e12i		−	1.95275i
$451$	3.06489e11	−	5.30855e11i	0.348836	−	0.604201i
$452$	2.17734e11	+	3.77126e11i	0.245359	+	0.424975i
$453$	1.04600e11	−	6.03907e10i	0.116705	−	0.0673795i
$454$	−6.62301e11			−0.731652
$455$	3.76630e11	+	4.02751e11i	0.411968	+	0.440540i
$456$	1.46109e10			0.0158247
$457$	1.41523e9	−	8.17082e8i	0.00151776	−	0.000876280i	−0.499241	−	0.866463i	$-0.666388\pi$
$457$	1.41523e9	−	8.17082e8i	0.00151776	−	0.000876280i	0.500759	+	0.865587i	$0.333054\pi$
$458$	9.14009e11	+	1.58311e12i	0.970635	+	1.68119i
$459$	5.20717e11	−	9.01908e11i	0.547576	−	0.948430i
$460$			2.12600e12i			2.21388i
$461$	8.62849e11	+	4.98166e11i	0.889776	+	0.513712i	0.873869	−	0.486161i	$-0.161603\pi$
$461$	8.62849e11	+	4.98166e11i	0.889776	+	0.513712i	0.0159065	+	0.999873i	$0.494937\pi$
$462$	6.67005e10	+	3.85095e10i	0.0681146	+	0.0393260i
$463$		−	7.47888e11i		−	0.756349i	−0.925734	−	0.378175i	$-0.876552\pi$
$463$		−	7.47888e11i		−	0.756349i	0.925734	−	0.378175i	$-0.123448\pi$
$464$	−8.75555e11	+	1.51651e12i	−0.876905	+	1.51884i
$465$	−3.74930e10	−	6.49397e10i	−0.0371887	−	0.0644128i
$466$	−1.71517e12	+	9.90253e11i	−1.68488	+	0.972769i
$467$	−5.29734e11			−0.515385			−0.257693	−	0.966227i	$-0.582962\pi$
$467$	−5.29734e11			−0.515385			−0.257693	+	0.966227i	$0.582962\pi$
$468$	−8.26797e11	+	1.92104e11i	−0.796696	+	0.185110i
$469$	−5.37942e11			−0.513402
$470$	1.82131e12	−	1.05153e12i	1.72164	−	0.993990i
$471$	−2.61319e11	−	4.52618e11i	−0.244668	−	0.423778i
$472$	−7.09539e10	+	1.22896e11i	−0.0658018	+	0.113972i
$473$			7.46801e11i			0.686009i
$474$	−5.05133e11	−	2.91639e11i	−0.459625	−	0.265364i
$475$	−5.47387e11	−	3.16034e11i	−0.493371	−	0.284848i
$476$			7.52996e11i			0.672297i
$477$	3.32026e11	−	5.75085e11i	0.293656	−	0.508627i
$478$	−9.94295e11	−	1.72217e12i	−0.871143	−	1.50886i
$479$	1.17876e12	−	6.80555e11i	1.02309	−	0.590682i	0.108093	−	0.994141i	$-0.465525\pi$
$479$	1.17876e12	−	6.80555e11i	1.02309	−	0.590682i	0.914998	+	0.403459i	$0.132192\pi$
$480$	−7.20862e11			−0.619822
$481$	1.22138e11	+	5.25670e11i	0.104040	+	0.447776i
$482$	1.19786e12			1.01087
$483$	−1.74332e11	+	1.00650e11i	−0.145752	+	0.0841499i
$484$	3.87003e11	+	6.70308e11i	0.320560	+	0.555227i
$485$	−2.09216e11	+	3.62372e11i	−0.171695	+	0.297384i
$486$			1.29559e12i			1.05342i
$487$	1.56700e12	+	9.04709e11i	1.26238	+	0.728834i	0.973534	−	0.228542i	$-0.0733958\pi$
$487$	1.56700e12	+	9.04709e11i	1.26238	+	0.728834i	0.288844	+	0.957376i	$0.406729\pi$
$488$	−4.01289e10	−	2.31684e10i	−0.0320308	−	0.0184930i
$489$		−	1.30674e11i		−	0.103347i
$490$	−2.00006e11	+	3.46421e11i	−0.156733	+	0.271470i
$491$	1.63423e11	+	2.83056e11i	0.126895	+	0.219789i	0.922472	−	0.386064i	$-0.126165\pi$
$491$	1.63423e11	+	2.83056e11i	0.126895	+	0.219789i	−0.795577	+	0.605853i	$0.792832\pi$
$492$	3.77755e11	−	2.18097e11i	0.290648	−	0.167806i
$493$	4.18622e12			3.19162
$494$	−1.95119e11	+	6.41425e11i	−0.147411	+	0.484591i
$495$	−1.03614e12			−0.775703
$496$	2.08838e11	−	1.20573e11i	0.154932	−	0.0894502i
$497$	−1.69156e11	−	2.92986e11i	−0.124361	−	0.215399i
$498$	1.62357e11	−	2.81210e11i	0.118287	−	0.204880i
$499$		−	9.33504e11i		−	0.674006i	−0.941504	−	0.337003i	$-0.890587\pi$
$499$		−	9.33504e11i		−	0.674006i	0.941504	−	0.337003i	$-0.109413\pi$
$500$	9.40245e11	+	5.42851e11i	0.672784	+	0.388432i
$501$	6.15563e11	+	3.55395e11i	0.436519	+	0.252024i
$502$		−	1.67899e12i		−	1.18000i
$503$	4.80505e11	−	8.32259e11i	0.334689	−	0.579699i	−0.648736	−	0.761014i	$-0.724702\pi$
$503$	4.80505e11	−	8.32259e11i	0.334689	−	0.579699i	0.983425	+	0.181315i	$0.0580353\pi$
$504$	3.77737e10	+	6.54260e10i	0.0260767	+	0.0451661i
$505$	1.54253e12	−	8.90582e11i	1.05541	−	0.609344i
$506$	1.67178e12			1.13371
$507$	2.84783e10	−	4.24380e11i	0.0191416	−	0.285246i
$508$	1.24183e12			0.827322
$509$	−1.31362e12	+	7.58422e11i	−0.867444	+	0.500819i	−0.866498	−	0.499181i	$-0.833634\pi$
$509$	−1.31362e12	+	7.58422e11i	−0.867444	+	0.500819i	−0.000945810		1.00000i	$0.500301\pi$
$510$	9.56952e11	+	1.65749e12i	0.626361	+	1.08489i
$511$	−3.14390e11	+	5.44540e11i	−0.203974	+	0.353293i
$512$		−	2.06180e12i		−	1.32597i
$513$	2.74437e11	+	1.58446e11i	0.174950	+	0.101008i
$514$	−5.92526e11	−	3.42095e11i	−0.374432	−	0.216179i
$515$		−	4.04830e12i		−	2.53594i
$516$	−2.65711e11	+	4.60225e11i	−0.165001	+	0.285789i
$517$	−3.89538e11	−	6.74700e11i	−0.239796	−	0.415340i
$518$	−3.39045e11	+	1.95747e11i	−0.206906	+	0.119457i
$519$	1.90733e11			0.115391
$520$	−1.16356e11	+	3.82503e11i	−0.0697869	+	0.229414i
$521$	3.28300e11			0.195209			0.0976047	−	0.995225i	$-0.468882\pi$
$521$	3.28300e11			0.195209			0.0976047	+	0.995225i	$0.468882\pi$
$522$	−2.96464e12	+	1.71164e12i	−1.74765	+	1.00901i
$523$	1.35536e12	+	2.34756e12i	0.792132	+	1.37201i	0.924644	+	0.380832i	$0.124362\pi$
$523$	1.35536e12	+	2.34756e12i	0.792132	+	1.37201i	−0.132512	+	0.991181i	$0.542304\pi$
$524$	−9.57547e11	+	1.65852e12i	−0.554842	+	0.961015i
$525$			2.90889e11i			0.167113i
$526$	−2.89008e12	−	1.66859e12i	−1.64617	−	0.950416i
$527$	−4.99251e11	−	2.88243e11i	−0.281949	−	0.162784i
$528$			2.96578e11i			0.166068i
$529$	−1.28414e12	+	2.22420e12i	−0.712956	+	1.23488i
$530$	1.27468e12	+	2.20780e12i	0.701711	+	1.21540i
$531$	−1.27594e12	+	7.36666e11i	−0.696476	+	0.402111i
$532$	−2.29125e11			−0.124014
$533$	−5.55769e11	−	2.39197e12i	−0.298278	−	1.28376i
$534$	−2.81076e11			−0.149585
$535$	−1.28020e11	+	7.39124e10i	−0.0675594	+	0.0390054i
$536$	−1.95020e11	−	3.37785e11i	−0.102056	−	0.176766i
$537$	−6.85323e10	+	1.18701e11i	−0.0355640	+	0.0615987i
$538$		−	4.57762e12i		−	2.35570i
$539$	1.28331e11	+	7.40920e10i	0.0654911	+	0.0378113i
$540$	−1.33390e12	−	7.70128e11i	−0.675074	−	0.389754i
$541$		−	7.26363e11i		−	0.364558i	−0.983247	−	0.182279i	$-0.941653\pi$
$541$		−	7.26363e11i		−	0.364558i	0.983247	−	0.182279i	$-0.0583473\pi$
$542$	−5.81844e11	+	1.00778e12i	−0.289607	+	0.501614i
$543$	−2.72526e11	−	4.72028e11i	−0.134527	−	0.233007i
$544$	−4.79945e12	+	2.77096e12i	−2.34961	+	1.35655i
$545$	3.43160e12			1.66614
$546$	3.00545e11	−	6.98308e10i	0.144725	−	0.0336264i
$547$	−2.86606e11			−0.136881			−0.0684405	−	0.997655i	$-0.521802\pi$
$547$	−2.86606e11			−0.136881			−0.0684405	+	0.997655i	$0.521802\pi$
$548$	1.41848e11	−	8.18958e10i	0.0671908	−	0.0387926i
$549$	−2.40542e11	−	4.16631e11i	−0.113010	−	0.195738i
$550$	1.20789e12	−	2.09213e12i	0.562856	−	0.974894i
$551$			1.27380e12i			0.588736i
$552$	−1.26401e11	−	7.29777e10i	−0.0579462	−	0.0334553i
$553$	−9.71872e11	−	5.61110e11i	−0.441922	−	0.255144i
$554$		−	2.57293e12i		−	1.16047i
$555$	−2.34389e11	+	4.05974e11i	−0.104862	+	0.181627i
$556$	−4.13370e11	−	7.15978e11i	−0.183444	−	0.317734i
$557$	−6.32143e11	+	3.64968e11i	−0.278270	+	0.160660i	−0.632640	−	0.774446i	$-0.718029\pi$
$557$	−6.32143e11	+	3.64968e11i	−0.278270	+	0.160660i	0.354370	+	0.935105i	$0.384695\pi$
$558$	4.71419e11			0.205851
$559$	2.04348e12	+	2.18520e12i	0.885149	+	0.946538i
$560$	−1.54033e12			−0.661863
$561$	6.14015e11	−	3.54501e11i	0.261725	−	0.151107i
$562$	−1.89238e11	−	3.27770e11i	−0.0800195	−	0.138598i
$563$	−1.53006e12	+	2.65013e12i	−0.641829	+	1.11168i	0.343195	+	0.939264i	$0.388491\pi$
$563$	−1.53006e12	+	2.65013e12i	−0.641829	+	1.11168i	−0.985024	+	0.172416i	$0.944843\pi$
$564$		−	5.54388e11i		−	0.230706i
$565$	1.84424e12	+	1.06477e12i	0.761376	+	0.439581i
$566$	2.64536e12	+	1.52730e12i	1.08346	+	0.625534i
$567$			7.08331e11i			0.287814i
$568$	1.22648e11	−	2.12433e11i	0.0494417	−	0.0856355i
$569$	−1.08178e12	−	1.87370e12i	−0.432647	−	0.749366i	0.564454	−	0.825465i	$-0.309087\pi$
$569$	−1.08178e12	−	1.87370e12i	−0.432647	−	0.749366i	−0.997100	+	0.0760990i	$0.975754\pi$
$570$	−5.04349e11	+	2.91186e11i	−0.200122	+	0.115540i
$571$	5.38072e10			0.0211825			0.0105913	−	0.999944i	$-0.496629\pi$
$571$	5.38072e10			0.0211825			0.0105913	+	0.999944i	$0.496629\pi$
$572$	−1.15493e12	−	3.51324e11i	−0.451100	−	0.137223i
$573$	−1.05417e12			−0.408522
$574$	1.54276e12	−	8.90716e11i	0.593193	−	0.342480i
$575$	3.15701e12	+	5.46811e12i	1.20440	+	2.08608i
$576$	9.34936e11	−	1.61936e12i	0.353900	−	0.612973i
$577$			3.41636e12i			1.28314i	0.767066	+	0.641569i	$0.221716\pi$
$577$			3.41636e12i			1.28314i	−0.767066	+	0.641569i	$0.778284\pi$
$578$	9.54728e12	+	5.51213e12i	3.55799	+	2.05421i
$579$	−4.31006e11	−	2.48842e11i	−0.159379	−	0.0920173i
$580$		−	6.19132e12i		−	2.27173i
$581$	3.12373e11	−	5.41046e11i	0.113732	−	0.196989i
$582$	1.17069e11	+	2.02770e11i	0.0422950	+	0.0732571i
$583$	8.17877e11	−	4.72202e11i	0.293211	−	0.169285i
$584$	−4.55904e11			−0.162187
$585$	−3.03183e12	+	2.83520e12i	−1.07030	+	1.00088i
$586$	−4.90925e12			−1.71979
$587$	3.38848e12	−	1.95634e12i	1.17797	−	0.680100i	0.222424	−	0.974950i	$-0.428603\pi$
$587$	3.38848e12	−	1.95634e12i	1.17797	−	0.680100i	0.955543	+	0.294850i	$0.0952698\pi$
$588$	5.27236e10	+	9.13200e10i	0.0181889	+	0.0315042i
$589$	8.77078e10	−	1.51914e11i	0.0300275	−	0.0520092i
$590$		−	5.65626e12i		−	1.92174i
$591$	−1.06327e12	−	6.13880e11i	−0.358509	−	0.206986i
$592$	−1.30556e12	−	7.53766e11i	−0.436867	−	0.252225i
$593$		−	1.05143e12i		−	0.349169i	−0.984642	−	0.174585i	$-0.944142\pi$
$593$		−	1.05143e12i		−	0.349169i	0.984642	−	0.174585i	$-0.0558583\pi$
$594$	−6.05587e11	+	1.04891e12i	−0.199590	+	0.345699i
$595$	1.84117e12	+	3.18900e12i	0.602236	+	1.04310i
$596$	−1.94785e12	+	1.12459e12i	−0.632336	+	0.365079i
$597$	−2.65307e11			−0.0854799
$598$	4.89175e12	−	4.57449e12i	1.56426	−	1.46281i
$599$	−7.36868e11			−0.233867			−0.116934	−	0.993140i	$-0.537306\pi$
$599$	−7.36868e11			−0.233867			−0.116934	+	0.993140i	$0.537306\pi$
$600$	−1.82655e11	+	1.05456e11i	−0.0575375	+	0.0332193i
$601$	3.05264e12	+	5.28732e12i	0.954422	+	1.65311i	0.735686	+	0.677322i	$0.236860\pi$
$601$	3.05264e12	+	5.28732e12i	0.954422	+	1.65311i	0.218735	+	0.975784i	$0.429807\pi$
$602$	−1.08517e12	+	1.87957e12i	−0.336755	+	0.583277i
$603$		−	4.04953e12i		−	1.24732i
$604$	−1.18932e12	−	6.86656e11i	−0.363608	−	0.209929i
$605$	3.27797e12	+	1.89254e12i	0.994732	+	0.574309i
$606$		−	9.96671e11i		−	0.300210i
$607$	1.72685e12	−	2.99099e12i	0.516304	−	0.894264i	−0.483517	−	0.875335i	$-0.660641\pi$
$607$	1.72685e12	−	2.99099e12i	0.516304	−	0.894264i	0.999821	−	0.0189292i	$-0.00602571\pi$
$608$	−8.43162e11	−	1.46040e12i	−0.250233	−	0.433417i
$609$	5.07687e11	−	2.93113e11i	0.149561	−	0.0863490i
$610$	1.84692e12			0.540088
$611$	−2.98600e12	−	9.08331e11i	−0.866772	−	0.263669i
$612$	−5.66841e12			−1.63335
$613$	1.97513e12	−	1.14034e12i	0.564966	−	0.326183i	−0.190170	−	0.981751i	$-0.560904\pi$
$613$	1.97513e12	−	1.14034e12i	0.564966	−	0.326183i	0.755136	+	0.655568i	$0.227571\pi$
$614$	−3.31711e12	−	5.74540e12i	−0.941894	−	1.63141i
$615$	1.06655e12	−	1.84732e12i	0.300637	−	0.520718i
$616$			1.07442e11i			0.0300651i
$617$	−3.23362e12	−	1.86693e12i	−0.898267	−	0.518615i	−0.0216298	−	0.999766i	$-0.506886\pi$
$617$	−3.23362e12	−	1.86693e12i	−0.898267	−	0.518615i	−0.876638	+	0.481151i	$0.840219\pi$
$618$	−1.96178e12	−	1.13264e12i	−0.541007	−	0.312350i
$619$			5.28384e12i			1.44658i	0.690545	+	0.723289i	$0.257371\pi$
$619$			5.28384e12i			1.44658i	−0.690545	+	0.723289i	$0.742629\pi$
$620$	−4.26304e11	+	7.38380e11i	−0.115866	+	0.200686i
$621$	−1.58279e12	−	2.74148e12i	−0.427083	−	0.739729i
$622$	−4.84658e12	+	2.79818e12i	−1.29831	+	0.749580i
$623$	−5.40787e11			−0.143824
$624$	8.11527e11	+	8.67810e11i	0.214275	+	0.229136i
$625$	−5.90269e11			−0.154736
$626$	−1.18479e12	+	6.84039e11i	−0.308359	+	0.178031i
$627$	1.07869e11	+	1.86835e11i	0.0278737	+	0.0482786i
$628$	−2.97126e12	+	5.14638e12i	−0.762294	+	1.32033i
$629$			3.60393e12i			0.918011i
$630$	−2.60779e12	−	1.50561e12i	−0.659539	−	0.380785i
$631$	5.63742e12	+	3.25477e12i	1.41563	+	0.817312i	0.995911	−	0.0903446i	$-0.0287968\pi$
$631$	5.63742e12	+	3.25477e12i	1.41563	+	0.817312i	0.419715	+	0.907656i	$0.362130\pi$
$632$		−	8.13678e11i		−	0.202874i
$633$	−6.59223e11	+	1.14181e12i	−0.163198	+	0.282668i
$634$	−1.53906e12	−	2.66572e12i	−0.378314	−	0.655259i
$635$	5.25924e12	−	3.03642e12i	1.28363	−	0.741106i
$636$	6.72035e11			0.162868
$637$	5.78245e11	−	1.34354e11i	0.139150	−	0.0323313i
$638$	−4.86853e12			−1.16333
$639$	2.20554e12	−	1.27337e12i	0.523313	−	0.302135i
$640$	−1.01169e12	−	1.75229e12i	−0.238362	−	0.412855i
$641$	7.99311e11	−	1.38445e12i	0.187006	−	0.323903i	−0.757245	−	0.653131i	$-0.773455\pi$
$641$	7.99311e11	−	1.38445e12i	0.187006	−	0.323903i	0.944250	+	0.329228i	$0.106788\pi$
$642$			8.27171e10i			0.0192171i
$643$	−3.94291e12	−	2.27644e12i	−0.909636	−	0.525179i	−0.0293221	−	0.999570i	$-0.509335\pi$
$643$	−3.94291e12	−	2.27644e12i	−0.909636	−	0.525179i	−0.880314	+	0.474391i	$0.842668\pi$
$644$	1.98219e12	+	1.14442e12i	0.454108	+	0.262180i
$645$			2.59878e12i			0.591223i
$646$	−2.23861e12	+	3.87739e12i	−0.505746	+	0.875978i
$647$	−1.52959e12	−	2.64932e12i	−0.343167	−	0.594382i	0.641852	−	0.766828i	$-0.278166\pi$
$647$	−1.52959e12	−	2.64932e12i	−0.343167	−	0.594382i	−0.985019	+	0.172446i	$0.944833\pi$
$648$	−4.44776e11	+	2.56791e11i	−0.0990954	+	0.0572128i
$649$	−2.09535e12			−0.463613
$650$	−2.19032e12	−	9.42692e12i	−0.481280	−	2.07138i
$651$	−8.07292e10			−0.0176164
$652$	−1.28673e12	+	7.42896e11i	−0.278852	+	0.160996i
$653$	3.03013e12	+	5.24833e12i	0.652156	+	1.12957i	0.982599	+	0.185741i	$0.0594687\pi$
$653$	3.03013e12	+	5.24833e12i	0.652156	+	1.12957i	−0.330443	+	0.943826i	$0.607198\pi$
$654$	9.60097e11	−	1.66294e12i	0.205218	−	0.355448i
$655$			9.36529e12i			1.98809i
$656$	5.94073e12	+	3.42988e12i	1.25249	+	0.723123i
$657$	−4.09919e12	−	2.36667e12i	−0.858330	−	0.495557i
$658$		−	2.26414e12i		−	0.470855i
$659$	1.61062e11	−	2.78968e11i	0.0332667	−	0.0576196i	−0.848913	−	0.528533i	$-0.822742\pi$
$659$	1.61062e11	−	2.78968e11i	0.0332667	−	0.0576196i	0.882179	+	0.470913i	$0.156076\pi$
$660$	−5.24299e11	−	9.08113e11i	−0.107555	−	0.186291i
$661$	−3.88875e12	+	2.24517e12i	−0.792325	+	0.457449i	−0.840780	−	0.541376i	$-0.817903\pi$
$661$	−3.88875e12	+	2.24517e12i	−0.792325	+	0.457449i	0.0484556	+	0.998825i	$0.484570\pi$
$662$	−1.17200e13			−2.37174
$663$	8.26632e11	−	2.71743e12i	0.166150	−	0.546195i
$664$	4.52979e11			0.0904319
$665$	−9.70363e11	+	5.60239e11i	−0.192414	+	0.111090i
$666$	−1.47355e12	−	2.55226e12i	−0.290222	−	0.502680i
$667$	6.36231e12	−	1.10199e13i	1.24465	−	2.15581i
$668$		−	8.08186e12i		−	1.57043i
$669$	4.27498e11	+	2.46816e11i	0.0825118	+	0.0476382i
$670$	1.34637e13	+	7.77325e12i	2.58123	+	1.49027i
$671$		−	6.84190e11i		−	0.130294i
$672$	−3.88037e11	+	6.72100e11i	−0.0734026	+	0.127137i
$673$	−5.28169e10	−	9.14815e10i	−0.00992441	−	0.0171896i	0.861021	−	0.508570i	$-0.169826\pi$
$673$	−5.28169e10	−	9.14815e10i	−0.00992441	−	0.0171896i	−0.870945	+	0.491381i	$0.836492\pi$
$674$	1.04760e13	−	6.04831e12i	1.95535	−	1.12892i
$675$	−4.57441e12			−0.848141
$676$	−4.34074e12	+	2.13223e12i	−0.799473	+	0.392712i
$677$	1.01810e13			1.86270			0.931348	−	0.364131i	$-0.118634\pi$
$677$	1.01810e13			1.86270			0.931348	+	0.364131i	$0.118634\pi$
$678$	1.03197e12	−	5.95806e11i	0.187556	−	0.108286i
$679$	2.25240e11	+	3.90127e11i	0.0406660	+	0.0704356i
$680$	−1.33496e12	+	2.31222e12i	−0.239430	+	0.414704i
$681$			8.53784e11i			0.152120i
$682$	5.80623e11	+	3.35223e11i	0.102770	+	0.0593340i
$683$	4.14895e12	+	2.39540e12i	0.729533	+	0.421196i	0.818251	−	0.574861i	$-0.194944\pi$
$683$	4.14895e12	+	2.39540e12i	0.729533	+	0.421196i	−0.0887181	+	0.996057i	$0.528277\pi$
$684$		−	1.72481e12i		−	0.301293i
$685$	4.00491e11	−	6.93670e11i	0.0695000	−	0.120378i
$686$	2.15325e11	+	3.72954e11i	0.0371224	+	0.0642979i
$687$	2.04082e12	−	1.17827e12i	0.349541	−	0.201808i
$688$	−8.35736e12			−1.42207
$689$	1.10109e12	−	3.61966e12i	0.186138	−	0.611901i
$690$	5.81759e12			0.977062
$691$	−8.44866e12	+	4.87784e12i	−1.40973	+	0.813909i	−0.995362	−	0.0961989i	$-0.969331\pi$
$691$	−8.44866e12	+	4.87784e12i	−1.40973	+	0.813909i	−0.414370	+	0.910108i	$0.635998\pi$
$692$	−1.08434e12	−	1.87813e12i	−0.179758	−	0.311349i
$693$	−5.57751e11	+	9.66052e11i	−0.0918630	+	0.159111i
$694$		−	5.21364e12i		−	0.853146i
$695$	−3.50131e12	−	2.02148e12i	−0.569245	−	0.328654i
$696$	3.68104e11	+	2.12525e11i	0.0594605	+	0.0343296i
$697$		−	1.63991e13i		−	2.63191i
$698$	−2.17090e12	+	3.76011e12i	−0.346171	+	0.599585i
$699$	1.27655e12	+	2.21105e12i	0.202251	+	0.350309i
$700$	2.86435e12	−	1.65374e12i	0.450905	−	0.260330i
$701$	−4.35722e12			−0.681519			−0.340760	−	0.940150i	$-0.610684\pi$
$701$	−4.35722e12			−0.681519			−0.340760	+	0.940150i	$0.610684\pi$
$702$	1.09813e12	+	4.72626e12i	0.170663	+	0.734515i
$703$	−1.09662e12			−0.169339
$704$	2.30302e12	−	1.32965e12i	0.353363	−	0.204014i
$705$	−1.35555e12	−	2.34788e12i	−0.206664	−	0.357952i
$706$	−3.84771e12	+	6.66443e12i	−0.582883	+	1.00958i
$707$		−	1.91759e12i		−	0.288647i
$708$	−1.29128e12	−	7.45523e11i	−0.193140	−	0.111509i
$709$	8.88677e12	+	5.13078e12i	1.32080	+	0.762562i	0.983856	−	0.178963i	$-0.0572744\pi$
$709$	8.88677e12	+	5.13078e12i	1.32080	+	0.762562i	0.336941	+	0.941526i	$0.390608\pi$
$710$			9.77718e12i			1.44395i
$711$	4.22393e12	−	7.31607e12i	0.619875	−	1.07365i
$712$	−1.96052e11	−	3.39572e11i	−0.0285898	−	0.0495189i
$713$	−1.51754e12	+	8.76155e11i	−0.219907	+	0.126963i
$714$	2.06049e12			0.296708
$715$	−5.75024e12	+	1.33605e12i	−0.822827	+	0.191182i
$716$	1.55846e12			0.221608
$717$	−2.22008e12	+	1.28176e12i	−0.313713	+	0.181122i
$718$	6.52947e12	+	1.13094e13i	0.916891	+	1.58810i
$719$	4.55941e12	−	7.89714e12i	0.636252	−	1.10202i	−0.349997	−	0.936751i	$-0.613817\pi$
$719$	4.55941e12	−	7.89714e12i	0.636252	−	1.10202i	0.986248	−	0.165270i	$-0.0528494\pi$
$720$		−	1.15953e13i		−	1.60800i
$721$	−3.77445e12	−	2.17918e12i	−0.520170	−	0.300320i
$722$	7.51501e12	+	4.33879e12i	1.02923	+	0.594225i
$723$		−	1.54418e12i		−	0.210173i
$724$	−3.09868e12	+	5.36707e12i	−0.419134	+	0.725962i
$725$	−9.19382e12	−	1.59242e13i	−1.23588	−	2.14060i
$726$	1.83423e12	−	1.05899e12i	0.245041	−	0.141474i
$727$	5.34518e12			0.709671			0.354836	−	0.934929i	$-0.384537\pi$
$727$	5.34518e12			0.709671			0.354836	+	0.934929i	$0.384537\pi$
$728$	2.93995e11	+	3.14385e11i	0.0387926	+	0.0414831i
$729$	−4.13662e12			−0.542464
$730$	1.57372e13	−	9.08586e12i	2.05104	−	1.18417i
$731$	9.98961e12	+	1.73025e13i	1.29396	+	2.24120i
$732$	2.43434e11	−	4.21639e11i	0.0313387	−	0.0542802i
$733$		−	2.32950e12i		−	0.298054i	−0.988833	−	0.149027i	$-0.952386\pi$
$733$		−	2.32950e12i		−	0.298054i	0.988833	−	0.149027i	$-0.0476141\pi$
$734$	−1.22006e13	−	7.04400e12i	−1.55148	−	0.895750i
$735$	4.46577e11	+	2.57832e11i	0.0564422	+	0.0325869i
$736$			1.68455e13i			2.11609i
$737$	2.87959e12	−	4.98759e12i	0.359523	−	0.622712i
$738$	6.70514e12	+	1.16136e13i	0.832059	+	1.44117i
$739$	7.49713e12	−	4.32847e12i	0.924687	−	0.533868i	0.0395598	−	0.999217i	$-0.487404\pi$
$739$	7.49713e12	−	4.32847e12i	0.924687	−	0.533868i	0.885127	+	0.465349i	$0.154071\pi$
$740$	5.33012e12			0.653423
$741$	8.26873e11	+	2.51531e11i	0.100753	+	0.0306486i
$742$	2.74461e12			0.332402
$743$	−8.87724e10	+	5.12527e10i	−0.0106863	+	0.00616975i	−0.505334	−	0.862924i	$-0.668631\pi$
$743$	−8.87724e10	+	5.12527e10i	−0.0106863	+	0.00616975i	0.494647	+	0.869094i	$0.335297\pi$
$744$	−2.92668e10	−	5.06916e10i	−0.00350185	−	0.00606538i
$745$	−5.49954e12	+	9.52548e12i	−0.654068	+	1.13288i
$746$			1.92931e13i			2.28075i
$747$	4.07289e12	+	2.35149e12i	0.478586	+	0.276312i
$748$	−6.98149e12	−	4.03076e12i	−0.815438	−	0.470793i
$749$			1.59147e11i			0.0184769i
$750$	1.48545e12	−	2.57288e12i	0.171429	−	0.296923i
$751$	5.88136e12	+	1.01868e13i	0.674680	+	1.16858i	0.976562	+	0.215235i	$0.0690516\pi$
$751$	5.88136e12	+	1.01868e13i	0.674680	+	1.16858i	−0.301882	+	0.953345i	$0.597615\pi$
$752$	7.55048e12	−	4.35927e12i	0.860982	−	0.497088i
$753$	−2.16441e12			−0.245337
$754$	−1.42457e13	+	1.33218e13i	−1.60514	+	1.50104i
$755$	−6.71584e12			−0.752210
$756$	−1.43607e12	+	8.29113e11i	−0.159892	+	0.0923136i
$757$	−2.18094e12	−	3.77750e12i	−0.241386	−	0.418094i	0.719723	−	0.694261i	$-0.244269\pi$
$757$	−2.18094e12	−	3.77750e12i	−0.241386	−	0.418094i	−0.961109	+	0.276168i	$0.910935\pi$
$758$	8.13811e11	−	1.40956e12i	0.0895389	−	0.155086i
$759$		−	2.15512e12i		−	0.235712i
$760$	−7.03572e11	−	4.06208e11i	−0.0764976	−	0.0441659i
$761$	−8.95960e12	−	5.17283e12i	−0.968406	−	0.559110i	−0.0696564	−	0.997571i	$-0.522190\pi$
$761$	−8.95960e12	−	5.17283e12i	−0.968406	−	0.559110i	−0.898750	+	0.438461i	$0.855524\pi$
$762$		−	3.39813e12i		−	0.365126i
$763$	1.84722e12	−	3.19948e12i	0.197314	−	0.341758i
$764$	5.99309e12	+	1.03803e13i	0.636401	+	1.10228i
$765$	−2.40062e13	+	1.38600e13i	−2.53423	+	1.46314i
$766$	−7.82704e12			−0.821426
$767$	−6.13117e12	+	5.73352e12i	−0.639682	+	0.598194i
$768$	−3.25673e12			−0.337797
$769$	5.23619e12	−	3.02312e12i	0.539942	−	0.311736i	−0.205113	−	0.978738i	$-0.565756\pi$
$769$	5.23619e12	−	3.02312e12i	0.539942	−	0.311736i	0.745056	+	0.667002i	$0.232423\pi$
$770$	−2.14126e12	−	3.70876e12i	−0.219513	−	0.380208i
$771$	−4.41001e11	+	7.63835e11i	−0.0449463	+	0.0778494i
$772$			5.65878e12i			0.573383i
$773$	−1.60449e13	−	9.26354e12i	−1.61633	−	0.933188i	−0.987859	−	0.155355i	$-0.950348\pi$
$773$	−1.60449e13	−	9.26354e12i	−1.61633	−	0.933188i	−0.628471	−	0.777833i	$-0.716319\pi$
$774$	−1.41491e13	−	8.16897e12i	−1.41708	−	0.818150i
$775$			2.53216e12i			0.252135i
$776$	−1.63313e11	+	2.82866e11i	−0.0161675	+	0.0280029i
$777$	2.52341e11	+	4.37068e11i	0.0248367	+	0.0430184i
$778$	−1.10549e13	+	6.38254e12i	−1.08180	+	0.624576i
$779$	4.98998e12			0.485490
$780$	−4.01901e12	−	1.22257e12i	−0.388771	−	0.118263i
$781$	3.62194e12			0.348347
$782$	3.87331e13	−	2.23626e13i	3.70383	−	2.13841i
$783$	4.60939e12	+	7.98370e12i	0.438244	+	0.759061i
$784$	−8.29154e11	+	1.43614e12i	−0.0783814	+	0.135761i
$785$			2.90604e13i			2.73142i
$786$	4.53837e12	+	2.62023e12i	0.424129	+	0.244871i
$787$	2.71092e12	+	1.56515e12i	0.251901	+	0.145435i	0.620635	−	0.784100i	$-0.286875\pi$
$787$	2.71092e12	+	1.56515e12i	0.251901	+	0.145435i	−0.368733	+	0.929535i	$0.620208\pi$
$788$			1.39599e13i			1.28978i
$789$	−2.15101e12	+	3.72565e12i	−0.197604	+	0.342260i
$790$	1.62161e13	+	2.80871e13i	1.48123	+	2.56557i
$791$	1.98549e12	−	1.14632e12i	0.180333	−	0.104115i
$792$	−8.08806e11			−0.0730434
$793$	−1.87215e12	−	2.00199e12i	−0.168117	−	0.179777i
$794$	1.26843e13			1.13260
$795$	2.84612e12	−	1.64321e12i	0.252697	−	0.145895i
$796$	1.50830e12	+	2.61245e12i	0.133162	+	0.230643i
$797$	−8.78888e11	+	1.52228e12i	−0.0771562	+	0.133639i	−0.902022	−	0.431690i	$-0.857917\pi$
$797$	−8.78888e11	+	1.52228e12i	−0.0771562	+	0.133639i	0.824866	+	0.565329i	$0.191251\pi$
$798$			6.26977e11i			0.0547317i
$799$	−1.80503e13	−	1.04213e13i	−1.56684	−	0.904613i
$800$	2.10812e13	+	1.21712e13i	1.81966	+	1.05058i
$801$		−	4.07094e12i		−	0.349421i
$802$	−9.13168e12	+	1.58165e13i	−0.779410	+	1.34998i
$803$	−3.36584e12	−	5.82981e12i	−0.285676	−	0.494805i
$804$	3.54916e12	−	2.04911e12i	0.299552	−	0.172947i
$805$	1.11930e13			0.939430
$806$	2.61622e12	−	6.07872e11i	0.218357	−	0.0507346i
$807$	−5.90109e12			−0.489780
$808$	1.20409e12	−	6.95183e11i	0.0993823	−	0.0573784i
$809$	−5.47062e12	−	9.47539e12i	−0.449022	−	0.777730i	0.549300	−	0.835625i	$-0.314894\pi$
$809$	−5.47062e12	−	9.47539e12i	−0.449022	−	0.777730i	−0.998323	+	0.0578955i	$0.981561\pi$
$810$	1.02354e13	−	1.77282e13i	0.835451	−	1.44704i
$811$			1.40650e12i			0.114168i	0.998369	+	0.0570840i	$0.0181803\pi$
$811$			1.40650e12i			0.114168i	−0.998369	+	0.0570840i	$0.981820\pi$
$812$	−5.77252e12	−	3.33277e12i	−0.465976	−	0.269031i
$813$	1.29915e12	+	7.50065e11i	0.104292	+	0.0602131i
$814$		−	4.19132e12i		−	0.334612i
$815$	−3.63294e12	+	6.29244e12i	−0.288436	+	0.499586i
$816$	3.96718e12	+	6.87136e12i	0.313239	+	0.542546i
$817$	−5.26489e12	+	3.03969e12i	−0.413419	+	0.238687i
$818$	1.07162e13			0.836857
$819$	1.01139e12	+	4.35292e12i	0.0785491	+	0.338067i
$820$	−2.42538e13			−1.87334
$821$	3.64612e12	−	2.10509e12i	0.280083	−	0.161706i	−0.353378	−	0.935481i	$-0.614967\pi$
$821$	3.64612e12	−	2.10509e12i	0.280083	−	0.161706i	0.633461	+	0.773775i	$0.281634\pi$
$822$	−2.24099e11	−	3.88152e11i	−0.0171205	−	0.0296536i
$823$	9.41980e12	−	1.63156e13i	0.715719	−	1.23966i	−0.246963	−	0.969025i	$-0.579433\pi$
$823$	9.41980e12	−	1.63156e13i	0.715719	−	1.23966i	0.962682	−	0.270636i	$-0.0872340\pi$
$824$		−	3.16008e12i		−	0.238795i
$825$	−2.69701e12	−	1.55712e12i	−0.202693	−	0.117025i
$826$	−5.27365e12	−	3.04474e12i	−0.394186	−	0.227583i
$827$			1.18007e12i			0.0877268i	0.999038	+	0.0438634i	$0.0139666\pi$
$827$			1.18007e12i			0.0877268i	−0.999038	+	0.0438634i	$0.986033\pi$
$828$	−8.61497e12	+	1.49216e13i	−0.636968	+	1.10326i
$829$	9.35384e12	+	1.62013e13i	0.687852	+	1.19139i	0.972532	+	0.232771i	$0.0747793\pi$
$829$	9.35384e12	+	1.62013e13i	0.687852	+	1.19139i	−0.284680	+	0.958623i	$0.591887\pi$
$830$	−1.56362e13	+	9.02757e12i	−1.14362	+	0.660267i
$831$	−3.31680e12			−0.241277
$832$	3.10050e12	−	1.01924e13i	0.224325	−	0.737434i
$833$	3.96437e12			0.285280
$834$	−1.95920e12	+	1.13114e12i	−0.140227	+	0.0809601i
$835$	−1.97611e13	−	3.42273e13i	−1.40677	−	2.43660i
$836$	1.22650e12	−	2.12436e12i	0.0868439	−	0.150418i
$837$		−	1.26952e12i		−	0.0894077i
$838$	2.87123e12	+	1.65771e12i	0.201127	+	0.116121i
$839$	−3.49809e12	−	2.01962e12i	−0.243726	−	0.140715i	0.373162	−	0.927766i	$-0.378274\pi$
$839$	−3.49809e12	−	2.01962e12i	−0.243726	−	0.140715i	−0.616888	+	0.787051i	$0.711607\pi$
$840$			3.73887e11i			0.0259110i
$841$	−1.12747e13	+	1.95283e13i	−0.777182	+	1.34612i
$842$	−5.04756e12	−	8.74264e12i	−0.346081	−	0.599429i
$843$	−4.22535e11	+	2.43950e11i	−0.0288163	+	0.0166371i
$844$	1.49910e13			1.01693
$845$	−1.31698e13	+	1.96438e13i	−0.888637	+	1.32547i
$846$	1.70440e13			1.14395
$847$	3.52904e12	−	2.03749e12i	0.235603	−	0.136026i
$848$	5.28435e12	+	9.15276e12i	0.350922	+	0.607814i
$849$	1.96887e12	−	3.41018e12i	0.130057	−	0.225265i
$850$		−	6.46297e13i		−	4.24666i
$851$	9.48700e12	+	5.47732e12i	0.620078	+	0.358002i
$852$	2.23206e12	+	1.28868e12i	0.145120	+	0.0837852i
$853$			1.14206e13i			0.738613i	0.929308	+	0.369307i	$0.120405\pi$
$853$			1.14206e13i			0.738613i	−0.929308	+	0.369307i	$0.879595\pi$
$854$	9.94192e11	−	1.72199e12i	0.0639602	−	0.110782i
$855$	−4.21738e12	−	7.30471e12i	−0.269895	−	0.467472i
$856$	−9.99318e10	+	5.76956e10i	−0.00636168	+	0.00367292i
$857$	−1.77228e13			−1.12232			−0.561161	−	0.827707i	$-0.689645\pi$
$857$	−1.77228e13			−1.12232			−0.561161	+	0.827707i	$0.689645\pi$
$858$	−9.61363e11	+	3.16034e12i	−0.0605612	+	0.199086i
$859$	−1.04325e13			−0.653764			−0.326882	−	0.945065i	$-0.605998\pi$
$859$	−1.04325e13			−0.653764			−0.326882	+	0.945065i	$0.605998\pi$
$860$	2.55900e13	−	1.47744e13i	1.59524	−	0.921014i
$861$	−1.14824e12	−	1.98880e12i	−0.0712061	−	0.123333i
$862$	1.89771e13	−	3.28693e13i	1.17070	−	2.02772i
$863$			1.17430e13i			0.720660i	0.932825	+	0.360330i	$0.117336\pi$
$863$			1.17430e13i			0.720660i	−0.932825	+	0.360330i	$0.882664\pi$
$864$	−1.05692e13	−	6.10214e12i	−0.645254	−	0.372538i
$865$	−9.18451e12	−	5.30268e12i	−0.557807	−	0.322050i
$866$		−	2.77194e13i		−	1.67477i
$867$	7.10578e12	−	1.23076e13i	0.427096	−	0.739752i
$868$	4.58955e11	+	7.94934e11i	0.0274430	+	0.0475327i
$869$	1.04048e13	−	6.00721e12i	0.618935	−	0.357342i
$870$	−1.69419e13			−1.00260
$871$	−5.22167e12	−	2.24735e13i	−0.307417	−	1.32309i
$872$	2.67869e12			0.156891
$873$	−2.93680e12	+	1.69556e12i	−0.171124	+	0.0987985i
$874$	6.80458e12	+	1.17859e13i	0.394457	+	0.683220i
$875$	2.85800e12	−	4.95020e12i	0.164826	−	0.285487i
$876$		−	4.79024e12i		−	0.274846i
$877$	7.74263e11	+	4.47021e11i	0.0441968	+	0.0255170i	0.521936	−	0.852985i	$-0.325210\pi$
$877$	7.74263e11	+	4.47021e11i	0.0441968	+	0.0255170i	−0.477739	+	0.878502i	$0.658543\pi$
$878$	2.58457e12	+	1.49220e12i	0.146779	+	0.0847427i
$879$			6.32859e12i			0.357567i
$880$	8.24535e12	−	1.42814e13i	0.463486	−	0.802782i
$881$	3.79488e12	+	6.57292e12i	0.212230	+	0.367593i	0.952412	−	0.304814i	$-0.0985942\pi$
$881$	3.79488e12	+	6.57292e12i	0.212230	+	0.367593i	−0.740182	+	0.672406i	$0.765261\pi$
$882$	−2.80753e12	+	1.62093e12i	−0.156212	+	0.0901893i
$883$	−2.66101e13			−1.47307			−0.736535	−	0.676400i	$-0.763539\pi$
$883$	−2.66101e13			−1.47307			−0.736535	+	0.676400i	$0.763539\pi$
$884$	−3.14578e13	+	7.30914e12i	−1.73258	+	0.402560i
$885$	−7.29158e12			−0.399555
$886$	2.09292e13	−	1.20835e13i	1.14104	−	0.658778i
$887$	−5.74961e12	−	9.95862e12i	−0.311876	−	0.540185i	0.666892	−	0.745154i	$-0.267624\pi$
$887$	−5.74961e12	−	9.95862e12i	−0.311876	−	0.540185i	−0.978769	+	0.204969i	$0.934291\pi$
$888$	−1.82963e11	+	3.16901e11i	−0.00987426	+	0.0171027i
$889$		−	6.53798e12i		−	0.351063i
$890$	1.35349e13	+	7.81436e12i	0.723101	+	0.417483i
$891$	−6.56737e12	−	3.79167e12i	−0.349094	−	0.201549i
$892$		−	5.61271e12i		−	0.296846i
$893$	3.17105e12	−	5.49242e12i	0.166868	−	0.289023i
$894$	3.07733e12	+	5.33009e12i	0.161122	+	0.279072i
$895$	6.60019e12	−	3.81062e12i	0.343837	−	0.198514i
$896$	−2.17835e12			−0.112912
$897$	−5.89705e12	−	6.30604e12i	−0.304137	−	0.325230i
$898$	−8.95231e12			−0.459400
$899$	4.41938e12	−	2.55153e12i	0.225654	−	0.130281i
$900$	1.24490e13	+	2.15623e13i	0.632475	+	1.09548i
$901$	1.26328e13	−	2.18807e13i	0.638615	−	1.10611i
$902$			1.90719e13i			0.959322i
$903$	2.42299e12	+	1.39891e12i	0.121271	+	0.0700158i
$904$	1.43960e12	+	8.31155e11i	0.0716943	+	0.0413927i
$905$			3.03066e13i			1.50182i
$906$	−1.87896e12	+	3.25446e12i	−0.0926492	+	0.160473i
$907$	−1.40534e13	−	2.43412e13i	−0.689524	−	1.19429i	−0.971992	−	0.235013i	$-0.924487\pi$
$907$	−1.40534e13	−	2.43412e13i	−0.689524	−	1.19429i	0.282469	−	0.959277i	$-0.408847\pi$
$908$	8.40714e12	−	4.85386e12i	0.410451	−	0.236974i
$909$	1.44352e13			0.701272
$910$	−1.64138e13	−	4.99301e12i	−0.793456	−	0.241366i
$911$	4.04598e13			1.94622			0.973108	−	0.230349i	$-0.0739869\pi$
$911$	4.04598e13			1.94622			0.973108	+	0.230349i	$0.0739869\pi$
$912$	−2.09085e12	+	1.20715e12i	−0.100080	+	0.0577810i
$913$	3.34425e12	+	5.79241e12i	0.159287	+	0.275893i
$914$	−2.54222e10	+	4.40326e10i	−0.00120491	+	0.00208697i
$915$		−	2.38090e12i		−	0.112291i
$916$	−2.32045e13	−	1.33972e13i	−1.08904	−	0.628757i
$917$	8.73178e12	+	5.04130e12i	0.407794	+	0.235440i
$918$			3.24026e13i			1.50587i
$919$	5.06672e12	−	8.77582e12i	0.234319	−	0.405852i	−0.724756	−	0.689006i	$-0.758047\pi$
$919$	5.06672e12	−	8.77582e12i	0.234319	−	0.405852i	0.959075	+	0.283154i	$0.0913807\pi$
$920$	4.05780e12	+	7.02831e12i	0.186743	+	0.323449i
$921$	−7.40649e12	+	4.27614e12i	−0.339191	+	0.195832i
$922$	−3.09993e13			−1.41274
$923$	1.05981e13	−	9.91073e12i	0.480640	−	0.449467i
$924$	−1.12891e12			−0.0509491
$925$	1.37091e13	−	7.91497e12i	0.615704	−	0.355477i
$926$	1.16347e13	+	2.01519e13i	0.520003	+	0.900671i
$927$	1.64045e13	−	2.84134e13i	0.729631	−	1.26376i
$928$		−	4.90572e13i		−	2.17139i
$929$	−3.21975e13	−	1.85892e13i	−1.41824	−	0.818824i	−0.422099	−	0.906550i	$-0.638707\pi$
$929$	−3.21975e13	−	1.85892e13i	−1.41824	−	0.818824i	−0.996145	+	0.0877261i	$0.972040\pi$
$930$	2.02050e12	+	1.16654e12i	0.0885698	+	0.0511358i
$931$			1.20630e12i			0.0526237i
$932$	1.45147e13	−	2.51402e13i	0.630139	−	1.09143i
$933$	3.60718e12	+	6.24781e12i	0.155848	+	0.269936i
$934$	1.42737e13	−	8.24093e12i	0.613728	−	0.354336i
$935$	−3.94229e13			−1.68693
$936$	−2.36663e12	+	2.21314e12i	−0.100783	+	0.0942470i
$937$	−9.84555e12			−0.417265			−0.208632	−	0.977994i	$-0.566901\pi$
$937$	−9.84555e12			−0.417265			−0.208632	+	0.977994i	$0.566901\pi$
$938$	1.44949e13	−	8.36862e12i	0.611367	−	0.352973i
$939$	8.81806e11	+	1.52733e12i	0.0370150	+	0.0641119i
$940$	−1.54129e13	+	2.66959e13i	−0.643886	+	1.11524i
$941$			1.53291e13i			0.637329i	0.947868	+	0.318665i	$0.103234\pi$
$941$			1.53291e13i			0.637329i	−0.947868	+	0.318665i	$0.896766\pi$
$942$	1.40825e13	+	8.13055e12i	0.582708	+	0.336427i
$943$	−4.31690e13	−	2.49236e13i	−1.77774	−	1.02638i
$944$		−	2.34488e13i		−	0.961052i
$945$	−4.05457e12	+	7.02272e12i	−0.165387	+	0.286459i
$946$	−1.16178e13	−	2.01226e13i	−0.471643	−	0.816910i
$947$	−1.30806e13	+	7.55211e12i	−0.528511	+	0.305136i	−0.740410	−	0.672156i	$-0.765369\pi$
$947$	−1.30806e13	+	7.55211e12i	−0.528511	+	0.305136i	0.211899	+	0.977292i	$0.432035\pi$
$948$	8.54943e12			0.343795
$949$	−2.58008e13	−	7.84852e12i	−1.03261	−	0.314116i
$950$	1.96658e13			0.783351
$951$	−3.43643e12	+	1.98402e12i	−0.136237	+	0.0786565i
$952$	1.43721e12	+	2.48931e12i	0.0567091	+	0.0982230i
$953$	−2.25442e12	+	3.90477e12i	−0.0885354	+	0.153348i	−0.906892	−	0.421363i	$-0.861552\pi$
$953$	−2.25442e12	+	3.90477e12i	−0.0885354	+	0.153348i	0.818357	+	0.574710i	$0.194885\pi$
$954$			2.06609e13i			0.807574i
$955$	5.07624e13	+	2.93077e13i	1.97482	+	1.14016i
$956$	2.52428e13	+	1.45739e13i	0.977411	+	0.564308i
$957$			6.27610e12i			0.241872i
$958$	−2.11744e13	+	3.66752e13i	−0.812208	+	1.40679i
$959$	−4.31165e11	−	7.46800e11i	−0.0164611	−	0.0285115i
$960$	8.01426e12	−	4.62703e12i	0.304539	−	0.175826i
$961$	2.57369e13			0.973421
$962$	−1.14687e13	−	1.22641e13i	−0.431745	−	0.461689i
$963$	−1.19803e12			−0.0448899
$964$	−1.52054e13	+	8.77885e12i	−0.567090	+	0.327409i
$965$	1.38364e13	+	2.39654e13i	0.513630	+	0.889633i
$966$	3.13158e12	−	5.42406e12i	0.115709	−	0.200414i
$967$		−	4.27573e13i		−	1.57250i	−0.617907	−	0.786251i	$-0.712019\pi$
$967$		−	4.27573e13i		−	1.57250i	0.617907	−	0.786251i	$-0.287981\pi$
$968$	2.55877e12	+	1.47731e12i	0.0936681	+	0.0540793i
$969$	4.99841e12	+	2.88583e12i	0.182127	+	0.105151i
$970$		−	1.30189e13i		−	0.472172i
$971$	−1.55156e13	+	2.68739e13i	−0.560123	+	0.970161i	0.437362	+	0.899285i	$0.355913\pi$
$971$	−1.55156e13	+	2.68739e13i	−0.560123	+	0.970161i	−0.997485	+	0.0708759i	$0.977421\pi$
$972$	−9.49508e12	−	1.64460e13i	−0.341193	−	0.590964i
$973$	−3.76948e12	+	2.17631e12i	−0.134826	+	0.0778419i
$974$	−5.62973e13			−2.00434
$975$	−1.21524e13	+	2.82358e12i	−0.430667	+	0.100064i
$976$	7.65668e12			0.270095
$977$	1.02500e13	−	5.91785e12i	0.359915	−	0.207797i	−0.309129	−	0.951020i	$-0.600037\pi$
$977$	1.02500e13	−	5.91785e12i	0.359915	−	0.207797i	0.669043	+	0.743223i	$0.266704\pi$
$978$	2.03286e12	+	3.52101e12i	0.0710529	+	0.123067i
$979$	2.89482e12	−	5.01397e12i	0.100716	−	0.174445i
$980$		−	5.86321e12i		−	0.203057i
$981$	2.40851e13	+	1.39055e13i	0.830304	+	0.479376i
$982$	−8.80686e12	−	5.08464e12i	−0.302217	−	0.174485i
$983$			7.91414e12i			0.270342i	0.990822	+	0.135171i	$0.0431583\pi$
$983$			7.91414e12i			0.270342i	−0.990822	+	0.135171i	$0.956842\pi$
$984$	8.32542e11	−	1.44200e12i	0.0283092	−	0.0490330i
$985$	3.41337e13	+	5.91214e13i	1.15537	+	2.00116i
$986$	−1.12798e14	+	6.51240e13i	−3.80063	+	2.19429i
$987$	−2.91874e12			−0.0978969
$988$	−2.22406e12	−	9.57213e12i	−0.0742575	−	0.319597i
$989$	6.07297e13			2.01845
$990$	2.79189e13	−	1.61190e13i	0.923718	−	0.533309i
$991$	1.55953e13	+	2.70119e13i	0.513644	+	0.889658i	0.999875	+	0.0158275i	$0.00503826\pi$
$991$	1.55953e13	+	2.70119e13i	0.513644	+	0.889658i	−0.486230	+	0.873831i	$0.661628\pi$
$992$	−3.37784e12	+	5.85058e12i	−0.110748	+	0.191821i
$993$			1.51085e13i			0.493116i
$994$	9.11581e12	+	5.26302e12i	0.296181	+	0.171000i
$995$	1.27755e13	+	7.37596e12i	0.413214	+	0.238569i
$996$			4.75951e12i			0.153248i
$997$	2.66552e13	−	4.61682e13i	0.854387	−	1.47984i	−0.0228260	−	0.999739i	$-0.507266\pi$
$997$	2.66552e13	−	4.61682e13i	0.854387	−	1.47984i	0.877213	−	0.480102i	$-0.159400\pi$
$998$	1.45223e13	+	2.51533e13i	0.463391	+	0.802616i
$999$	−6.87318e12	+	3.96823e12i	−0.218330	+	0.126053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.q.a.36.12	✓	124
13.4	even	6	inner	91.10.q.a.43.12	yes	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.q.a.36.12	✓	124	1.1	even	1	trivial
91.10.q.a.43.12	yes	124	13.4	even	6	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-26.9451 + 15.5567i) q^{2} +(20.0545 + 34.7353i) q^{3} +(228.024 - 394.949i) q^{4} -2230.19i q^{5} +(-1080.74 - 623.963i) q^{6} +(-2079.33 - 1200.50i) q^{7} -1740.87i q^{8} +(9037.14 - 15652.8i) q^{9} +O(q^{10})\)	\(q+(-26.9451 + 15.5567i) q^{2} +(20.0545 + 34.7353i) q^{3} +(228.024 - 394.949i) q^{4} -2230.19i q^{5} +(-1080.74 - 623.963i) q^{6} +(-2079.33 - 1200.50i) q^{7} -1740.87i q^{8} +(9037.14 - 15652.8i) q^{9} +(34694.4 + 60092.5i) q^{10} +(22261.2 - 12852.5i) q^{11} +18291.6 q^{12} +(29969.6 - 98520.7i) q^{13} +74703.4 q^{14} +(77466.2 - 44725.1i) q^{15} +(143830. + 249122. i) q^{16} +(343843. - 595554. i) q^{17} +562353. i q^{18} +(181218. + 104626. i) q^{19} +(-880809. - 508535. i) q^{20} -96301.5i q^{21} +(-399885. + 692622. i) q^{22} +(-1.04516e6 - 1.81027e6i) q^{23} +(60469.7 - 34912.2i) q^{24} -3.02060e6 q^{25} +(725127. + 3.12087e6i) q^{26} +1.51440e6 q^{27} +(-948272. + 547485. i) q^{28} +(3.04370e6 + 5.27185e6i) q^{29} +(-1.39155e6 + 2.41024e6i) q^{30} -838297. i q^{31} +(-6.97913e6 - 4.02940e6i) q^{32} +(892870. + 515499. i) q^{33} +2.13963e7i q^{34} +(-2.67734e6 + 4.63729e6i) q^{35} +(-4.12137e6 - 7.13841e6i) q^{36} +(-4.53854e6 + 2.62033e6i) q^{37} -6.51057e6 q^{38} +(4.02317e6 - 934774. i) q^{39} -3.88247e6 q^{40} +(2.06519e7 - 1.19234e7i) q^{41} +(1.49814e6 + 2.59485e6i) q^{42} +(-1.45264e7 + 2.51605e7i) q^{43} -1.17227e7i q^{44} +(-3.49086e7 - 2.01545e7i) q^{45} +(5.63238e7 + 3.25186e7i) q^{46} -3.03084e7i q^{47} +(-5.76888e6 + 9.99200e6i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(8.13903e7 - 4.69907e7i) q^{50} +2.75823e7 q^{51} +(-3.20768e7 - 3.43015e7i) q^{52} +3.67401e7 q^{53} +(-4.08057e7 + 2.35592e7i) q^{54} +(-2.86634e7 - 4.96465e7i) q^{55} +(-2.08992e6 + 3.61984e6i) q^{56} +8.39288e6i q^{57} +(-1.64025e8 - 9.47002e7i) q^{58} +(-7.05944e7 - 4.07577e7i) q^{59} -4.07936e7i q^{60} +(1.33085e7 - 2.30510e7i) q^{61} +(1.30412e7 + 2.25880e7i) q^{62} +(-3.75823e7 + 2.16982e7i) q^{63} +1.03455e8 q^{64} +(-2.19719e8 - 6.68378e7i) q^{65} -3.20779e7 q^{66} +(1.94032e8 - 1.12025e8i) q^{67} +(-1.56809e8 - 2.71601e8i) q^{68} +(4.19202e7 - 7.26080e7i) q^{69} -1.66603e8i q^{70} +(1.22027e8 + 7.04521e7i) q^{71} +(-2.72495e7 - 1.57325e7i) q^{72} -2.61883e8i q^{73} +(8.15275e7 - 1.41210e8i) q^{74} +(-6.05765e7 - 1.04922e8i) q^{75} +(8.26440e7 - 4.77145e7i) q^{76} -6.17176e7 q^{77} +(-9.38625e7 + 8.77749e7i) q^{78} +4.67397e8 q^{79} +(5.55588e8 - 3.20769e8i) q^{80} +(-1.47507e8 - 2.55490e8i) q^{81} +(-3.70977e8 + 6.42551e8i) q^{82} +2.60202e8i q^{83} +(-3.80342e7 - 2.19590e7i) q^{84} +(-1.32820e9 - 7.66834e8i) q^{85} -9.03934e8i q^{86} +(-1.22080e8 + 2.11448e8i) q^{87} +(-2.23745e7 - 3.87538e7i) q^{88} +(1.95058e8 - 1.12617e8i) q^{89} +1.25415e9 q^{90} +(-1.80591e8 + 1.68878e8i) q^{91} -9.53286e8 q^{92} +(2.91185e7 - 1.68116e7i) q^{93} +(4.71500e8 + 8.16661e8i) q^{94} +(2.33336e8 - 4.04150e8i) q^{95} -3.23230e8i q^{96} +(-1.62485e8 - 9.38109e7i) q^{97} +(-1.55333e8 - 8.96815e7i) q^{98} -4.64599e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9}+O(q^{10}) \) 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9	\( 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9} - 47368 q^{10} + 18420 q^{11} + 434316 q^{12} - 103730 q^{13} - 307328 q^{14} - 994308 q^{15} - 4327304 q^{16} + 826226 q^{17} - 832512 q^{20} - 2238874 q^{22} - 5178348 q^{23} + 13060272 q^{24} - 56263016 q^{25} + 12486810 q^{26} - 16794384 q^{27} + 8409710 q^{29} - 18091000 q^{30} + 30354048 q^{32} + 36508140 q^{33} + 8902908 q^{35} + 42350446 q^{36} + 26865678 q^{37} - 7473860 q^{38} - 21470652 q^{39} - 112860988 q^{40} - 109829778 q^{41} + 12446784 q^{42} - 53384856 q^{43} - 84576450 q^{45} + 160042176 q^{46} - 39524126 q^{48} + 357417662 q^{49} + 35767422 q^{50} + 121877584 q^{51} + 61751010 q^{52} - 252868460 q^{53} + 951692088 q^{54} - 414833028 q^{55} - 118013952 q^{56} - 342666540 q^{58} - 440088588 q^{59} + 264060146 q^{61} + 995887736 q^{62} - 383747028 q^{63} - 2239569444 q^{64} - 501903354 q^{65} + 304284804 q^{66} + 392937636 q^{67} - 3665660 q^{68} - 249969892 q^{69} - 375620748 q^{71} - 2829560808 q^{72} + 1336479018 q^{74} + 1306893216 q^{75} + 1652559990 q^{76} + 823754288 q^{77} + 857091302 q^{78} - 2357982776 q^{79} + 1107773136 q^{80} - 1492992434 q^{81} - 1984241462 q^{82} - 2156016366 q^{84} + 3060837654 q^{85} - 1286987624 q^{87} + 1904443442 q^{88} + 887446752 q^{89} + 7601525656 q^{90} - 86522436 q^{91} - 8365653336 q^{92} - 776657196 q^{93} + 6270763420 q^{94} - 6325568332 q^{95} - 5522676732 q^{97}+O(q^{100}) \) 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9 - 47368 * q^10 + 18420 * q^11 + 434316 * q^12 - 103730 * q^13 - 307328 * q^14 - 994308 * q^15 - 4327304 * q^16 + 826226 * q^17 - 832512 * q^20 - 2238874 * q^22 - 5178348 * q^23 + 13060272 * q^24 - 56263016 * q^25 + 12486810 * q^26 - 16794384 * q^27 + 8409710 * q^29 - 18091000 * q^30 + 30354048 * q^32 + 36508140 * q^33 + 8902908 * q^35 + 42350446 * q^36 + 26865678 * q^37 - 7473860 * q^38 - 21470652 * q^39 - 112860988 * q^40 - 109829778 * q^41 + 12446784 * q^42 - 53384856 * q^43 - 84576450 * q^45 + 160042176 * q^46 - 39524126 * q^48 + 357417662 * q^49 + 35767422 * q^50 + 121877584 * q^51 + 61751010 * q^52 - 252868460 * q^53 + 951692088 * q^54 - 414833028 * q^55 - 118013952 * q^56 - 342666540 * q^58 - 440088588 * q^59 + 264060146 * q^61 + 995887736 * q^62 - 383747028 * q^63 - 2239569444 * q^64 - 501903354 * q^65 + 304284804 * q^66 + 392937636 * q^67 - 3665660 * q^68 - 249969892 * q^69 - 375620748 * q^71 - 2829560808 * q^72 + 1336479018 * q^74 + 1306893216 * q^75 + 1652559990 * q^76 + 823754288 * q^77 + 857091302 * q^78 - 2357982776 * q^79 + 1107773136 * q^80 - 1492992434 * q^81 - 1984241462 * q^82 - 2156016366 * q^84 + 3060837654 * q^85 - 1286987624 * q^87 + 1904443442 * q^88 + 887446752 * q^89 + 7601525656 * q^90 - 86522436 * q^91 - 8365653336 * q^92 - 776657196 * q^93 + 6270763420 * q^94 - 6325568332 * q^95 - 5522676732 * q^97

Introduction

L-functions

Modular forms

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