LMFDB - Embedded newform 91.10.q.a.36.16

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			36.16
Character	$\chi$	$=$	91.36
Dual form			91.10.q.a.43.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.5135 + 12.4208i) q^{2} +(94.2787 + 163.295i) q^{3} +(52.5525 - 91.0236i) q^{4} +179.352i q^{5} +(-4056.52 - 2342.03i) q^{6} +(2079.33 + 1200.50i) q^{7} -10107.9i q^{8} +(-7935.43 + 13744.6i) q^{9} +O(q^{10})$	\(q+(-21.5135 + 12.4208i) q^{2} +(94.2787 + 163.295i) q^{3} +(52.5525 - 91.0236i) q^{4} +179.352i q^{5} +(-4056.52 - 2342.03i) q^{6} +(2079.33 + 1200.50i) q^{7} -10107.9i q^{8} +(-7935.43 + 13744.6i) q^{9} +(-2227.69 - 3858.47i) q^{10} +(28843.8 - 16653.0i) q^{11} +19818.3 q^{12} +(-16112.7 - 101710. i) q^{13} -59644.7 q^{14} +(-29287.3 + 16909.0i) q^{15} +(152455. + 264060. i) q^{16} +(28110.2 - 48688.2i) q^{17} -394258. i q^{18} +(671811. + 387870. i) q^{19} +(16325.2 + 9425.38i) q^{20} +452726. i q^{21} +(-413687. + 716527. i) q^{22} +(470610. + 815120. i) q^{23} +(1.65058e6 - 952961. i) q^{24} +1.92096e6 q^{25} +(1.60996e6 + 1.98800e6i) q^{26} +718805. q^{27} +(218548. - 126179. i) q^{28} +(-1.47684e6 - 2.55796e6i) q^{29} +(420048. - 727544. i) q^{30} -3.96060e6i q^{31} +(-2.07778e6 - 1.19961e6i) q^{32} +(5.43872e6 + 3.14004e6i) q^{33} +1.39660e6i q^{34} +(-215312. + 372931. i) q^{35} +(834054. + 1.44462e6i) q^{36} +(3.44285e6 - 1.98773e6i) q^{37} -1.92706e7 q^{38} +(1.50897e7 - 1.22202e7i) q^{39} +1.81287e6 q^{40} +(2.35320e7 - 1.35862e7i) q^{41} +(-5.62322e6 - 9.73970e6i) q^{42} +(8.19194e6 - 1.41889e7i) q^{43} -3.50063e6i q^{44} +(-2.46511e6 - 1.42323e6i) q^{45} +(-2.02489e7 - 1.16907e7i) q^{46} +1.41261e7i q^{47} +(-2.87466e7 + 4.97905e7i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(-4.13264e7 + 2.38598e7i) q^{50} +1.06008e7 q^{51} +(-1.01048e7 - 3.87847e6i) q^{52} -3.70160e7 q^{53} +(-1.54640e7 + 8.92814e6i) q^{54} +(2.98674e6 + 5.17319e6i) q^{55} +(1.21346e7 - 2.10177e7i) q^{56} +1.46272e8i q^{57} +(6.35438e7 + 3.66870e7i) q^{58} +(1.82814e7 + 1.05548e7i) q^{59} +3.55445e6i q^{60} +(-3.39364e7 + 5.87795e7i) q^{61} +(4.91938e7 + 8.52061e7i) q^{62} +(-3.30007e7 + 1.90530e7i) q^{63} -9.65140e7 q^{64} +(1.82418e7 - 2.88984e6i) q^{65} -1.56007e8 q^{66} +(6.11092e7 - 3.52814e7i) q^{67} +(-2.95452e6 - 5.11737e6i) q^{68} +(-8.87369e7 + 1.53697e8i) q^{69} -1.06974e7i q^{70} +(1.09852e8 + 6.34232e7i) q^{71} +(1.38929e8 + 8.02108e7i) q^{72} +1.21937e8i q^{73} +(-4.93783e7 + 8.55258e7i) q^{74} +(1.81105e8 + 3.13684e8i) q^{75} +(7.06107e7 - 4.07671e7i) q^{76} +7.99677e7 q^{77} +(-1.72846e8 + 4.50324e8i) q^{78} -2.15732e8 q^{79} +(-4.73597e7 + 2.73431e7i) q^{80} +(2.23961e8 + 3.87912e8i) q^{81} +(-3.37503e8 + 5.84571e8i) q^{82} +1.37807e8i q^{83} +(4.12088e7 + 2.37919e7i) q^{84} +(8.73232e6 + 5.04160e6i) q^{85} +4.07002e8i q^{86} +(2.78469e8 - 4.82322e8i) q^{87} +(-1.68327e8 - 2.91551e8i) q^{88} +(-7.44888e8 + 4.30061e8i) q^{89} +7.07108e7 q^{90} +(8.85990e7 - 2.30831e8i) q^{91} +9.89269e7 q^{92} +(6.46747e8 - 3.73400e8i) q^{93} +(-1.75457e8 - 3.03901e8i) q^{94} +(-6.95652e7 + 1.20490e8i) q^{95} -4.52389e8i q^{96} +(1.56553e8 + 9.03860e7i) q^{97} +(-1.24021e8 - 7.16034e7i) q^{98} +5.28595e8i 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 $

$2$	−21.5135	+	12.4208i	−0.950769	+	0.548927i	−0.893320	−	0.449421i	$-0.851630\pi$
$2$	−21.5135	+	12.4208i	−0.950769	+	0.548927i	−0.0574495	+	0.998348i	$0.518297\pi$
$3$	94.2787	+	163.295i	0.671998	+	1.16393i	0.977337	+	0.211690i	$0.0678969\pi$
$3$	94.2787	+	163.295i	0.671998	+	1.16393i	−0.305339	+	0.952244i	$0.598770\pi$
$4$	52.5525	−	91.0236i	0.102642	−	0.177780i
$5$			179.352i			0.128334i	0.997939	+	0.0641668i	$0.0204390\pi$
$5$			179.352i			0.128334i	−0.997939	+	0.0641668i	$0.979561\pi$
$6$	−4056.52	−	2342.03i	−1.27783	−	0.737755i
$7$	2079.33	+	1200.50i	0.327327	+	0.188982i
$7$	2079.33	+	1200.50i	0.327327	+	0.188982i
$8$		−	10107.9i		−	0.872483i
$9$	−7935.43	+	13744.6i	−0.403162	+	0.698297i
$10$	−2227.69	−	3858.47i	−0.0704458	−	0.122016i
$11$	28843.8	−	16653.0i	0.593999	−	0.342946i	−0.172678	−	0.984978i	$-0.555242\pi$
$11$	28843.8	−	16653.0i	0.593999	−	0.342946i	0.766677	+	0.642033i	$0.221909\pi$
$12$	19818.3			0.275900
$13$	−16112.7	−	101710.i	−0.156467	−	0.987683i
$13$	−16112.7	−	101710.i	−0.156467	−	0.987683i
$14$	−59644.7			−0.414950
$15$	−29287.3	+	16909.0i	−0.149372	+	0.0862399i
$16$	152455.	+	264060.i	0.581571	+	1.00731i
$17$	28110.2	−	48688.2i	0.0816287	−	0.141385i	−0.822321	−	0.569024i	$-0.807321\pi$
$17$	28110.2	−	48688.2i	0.0816287	−	0.141385i	0.903950	+	0.427639i	$0.140654\pi$
$18$		−	394258.i		−	0.885226i
$19$	671811.	+	387870.i	1.18265	+	0.682803i	0.956626	−	0.291319i	$-0.0940941\pi$
$19$	671811.	+	387870.i	1.18265	+	0.682803i	0.226023	+	0.974122i	$0.427427\pi$
$20$	16325.2	+	9425.38i	0.0228152	+	0.0131724i
$21$			452726.i			0.507983i
$22$	−413687.	+	716527.i	−0.376504	+	0.652124i
$23$	470610.	+	815120.i	0.350660	+	0.607360i	0.986365	−	0.164571i	$-0.0526241\pi$
$23$	470610.	+	815120.i	0.350660	+	0.607360i	−0.635706	+	0.771932i	$0.719291\pi$
$24$	1.65058e6	−	952961.i	1.01551	−	0.586307i
$25$	1.92096e6			0.983530
$26$	1.60996e6	+	1.98800e6i	0.690930	+	0.853170i
$27$	718805.			0.260300
$28$	218548.	−	126179.i	0.0671947	−	0.0387949i
$29$	−1.47684e6	−	2.55796e6i	−0.387741	−	0.671587i	0.604404	−	0.796678i	$-0.293411\pi$
$29$	−1.47684e6	−	2.55796e6i	−0.387741	−	0.671587i	−0.992145	+	0.125091i	$0.960078\pi$
$30$	420048.	−	727544.i	0.0946788	−	0.163989i
$31$		−	3.96060e6i		−	0.770252i	−0.922864	−	0.385126i	$-0.874158\pi$
$31$		−	3.96060e6i		−	0.770252i	0.922864	−	0.385126i	$-0.125842\pi$
$32$	−2.07778e6	−	1.19961e6i	−0.350287	−	0.202239i
$33$	5.43872e6	+	3.14004e6i	0.798332	+	0.460917i
$34$			1.39660e6i			0.179233i
$35$	−215312.	+	372931.i	−0.0242528	+	0.0420070i
$36$	834054.	+	1.44462e6i	0.0827623	+	0.143349i
$37$	3.44285e6	−	1.98773e6i	0.302002	−	0.174361i	−0.341340	−	0.939940i	$-0.610881\pi$
$37$	3.44285e6	−	1.98773e6i	0.302002	−	0.174361i	0.643342	+	0.765579i	$0.277547\pi$
$38$	−1.92706e7			−1.49924
$39$	1.50897e7	−	1.22202e7i	1.04445	−	0.845838i
$40$	1.81287e6			0.111969
$41$	2.35320e7	−	1.35862e7i	1.30056	−	0.750879i	0.320061	−	0.947397i	$-0.396297\pi$
$41$	2.35320e7	−	1.35862e7i	1.30056	−	0.750879i	0.980500	+	0.196518i	$0.0629633\pi$
$42$	−5.62322e6	−	9.73970e6i	−0.278845	−	0.482974i
$43$	8.19194e6	−	1.41889e7i	0.365409	−	0.632906i	−0.623433	−	0.781877i	$-0.714263\pi$
$43$	8.19194e6	−	1.41889e7i	0.365409	−	0.632906i	0.988842	+	0.148970i	$0.0475959\pi$
$44$		−	3.50063e6i		−	0.140802i
$45$	−2.46511e6	−	1.42323e6i	−0.0896150	−	0.0517392i
$46$	−2.02489e7	−	1.16907e7i	−0.666793	−	0.384973i
$47$			1.41261e7i			0.422261i	0.977458	+	0.211131i	$0.0677145\pi$
$47$			1.41261e7i			0.422261i	−0.977458	+	0.211131i	$0.932285\pi$
$48$	−2.87466e7	+	4.97905e7i	−0.781629	+	1.35382i
$49$	2.88240e6	+	4.99246e6i	0.0714286	+	0.123718i
$50$	−4.13264e7	+	2.38598e7i	−0.935111	+	0.539886i
$51$	1.06008e7			0.219417
$52$	−1.01048e7	−	3.87847e6i	−0.191651	−	0.0735606i
$53$	−3.70160e7			−0.644390			−0.322195	−	0.946673i	$-0.604421\pi$
$53$	−3.70160e7			−0.644390			−0.322195	+	0.946673i	$0.604421\pi$
$54$	−1.54640e7	+	8.92814e6i	−0.247485	+	0.142886i
$55$	2.98674e6	+	5.17319e6i	0.0440115	+	0.0762301i
$56$	1.21346e7	−	2.10177e7i	0.164884	−	0.285587i
$57$			1.46272e8i			1.83537i
$58$	6.35438e7	+	3.66870e7i	0.737305	+	0.425683i
$59$	1.82814e7	+	1.05548e7i	0.196416	+	0.113401i	0.594982	−	0.803739i	$-0.297159\pi$
$59$	1.82814e7	+	1.05548e7i	0.196416	+	0.113401i	−0.398567	+	0.917139i	$0.630492\pi$
$60$			3.55445e6i			0.0354072i
$61$	−3.39364e7	+	5.87795e7i	−0.313820	+	0.543553i	−0.979186	−	0.202965i	$-0.934942\pi$
$61$	−3.39364e7	+	5.87795e7i	−0.313820	+	0.543553i	0.665366	+	0.746518i	$0.268276\pi$
$62$	4.91938e7	+	8.52061e7i	0.422812	+	0.732332i
$63$	−3.30007e7	+	1.90530e7i	−0.263931	+	0.152381i
$64$	−9.65140e7			−0.719085
$65$	1.82418e7	−	2.88984e6i	0.126753	−	0.0200800i
$66$	−1.56007e8			−1.01204
$67$	6.11092e7	−	3.52814e7i	0.370485	−	0.213899i	−0.303185	−	0.952932i	$-0.598050\pi$
$67$	6.11092e7	−	3.52814e7i	0.370485	−	0.213899i	0.673670	+	0.739032i	$0.264717\pi$
$68$	−2.95452e6	−	5.11737e6i	−0.0167570	−	0.0290240i
$69$	−8.87369e7	+	1.53697e8i	−0.471285	+	0.816289i
$70$		−	1.06974e7i		−	0.0532520i
$71$	1.09852e8	+	6.34232e7i	0.513034	+	0.296201i	0.734080	−	0.679063i	$-0.237614\pi$
$71$	1.09852e8	+	6.34232e7i	0.513034	+	0.296201i	−0.221046	+	0.975263i	$0.570947\pi$
$72$	1.38929e8	+	8.02108e7i	0.609252	+	0.351752i
$73$			1.21937e8i			0.502555i	0.967915	+	0.251278i	$0.0808507\pi$
$73$			1.21937e8i			0.502555i	−0.967915	+	0.251278i	$0.919149\pi$
$74$	−4.93783e7	+	8.55258e7i	−0.191423	+	0.331554i
$75$	1.81105e8	+	3.13684e8i	0.660930	+	1.14476i
$76$	7.06107e7	−	4.07671e7i	0.242778	−	0.140168i
$77$	7.99677e7			0.259243
$78$	−1.72846e8	+	4.50324e8i	−0.528730	+	1.37753i
$79$	−2.15732e8			−0.623149			−0.311575	−	0.950222i	$-0.600856\pi$
$79$	−2.15732e8			−0.623149			−0.311575	+	0.950222i	$0.600856\pi$
$80$	−4.73597e7	+	2.73431e7i	−0.129272	+	0.0746351i
$81$	2.23961e8	+	3.87912e8i	0.578083	+	1.00127i
$82$	−3.37503e8	+	5.84571e8i	−0.824356	+	1.42783i
$83$			1.37807e8i			0.318728i	0.987220	+	0.159364i	$0.0509444\pi$
$83$			1.37807e8i			0.318728i	−0.987220	+	0.159364i	$0.949056\pi$
$84$	4.12088e7	+	2.37919e7i	0.0903094	+	0.0521401i
$85$	8.73232e6	+	5.04160e6i	0.0181445	+	0.0104757i
$86$			4.07002e8i			0.802331i
$87$	2.78469e8	−	4.82322e8i	0.521122	−	0.902610i
$88$	−1.68327e8	−	2.91551e8i	−0.299214	−	0.518254i
$89$	−7.44888e8	+	4.30061e8i	−1.25845	+	0.726567i	−0.972773	−	0.231759i	$-0.925552\pi$
$89$	−7.44888e8	+	4.30061e8i	−1.25845	+	0.726567i	−0.285677	+	0.958326i	$0.592218\pi$
$90$	7.07108e7			0.113604
$91$	8.85990e7	−	2.30831e8i	0.135439	−	0.352865i
$92$	9.89269e7			0.143969
$93$	6.46747e8	−	3.73400e8i	0.896523	−	0.517608i
$94$	−1.75457e8	−	3.03901e8i	−0.231791	−	0.401473i
$95$	−6.95652e7	+	1.20490e8i	−0.0876266	+	0.151774i
$96$		−	4.52389e8i		−	0.543615i
$97$	1.56553e8	+	9.03860e7i	0.179552	+	0.103664i	0.587082	−	0.809528i	$-0.300277\pi$
$97$	1.56553e8	+	9.03860e7i	0.179552	+	0.103664i	−0.407530	+	0.913192i	$0.633610\pi$
$98$	−1.24021e8	−	7.16034e7i	−0.135824	−	0.0784181i
$99$			5.28595e8i			0.553050i
$100$	1.00951e8	−	1.74852e8i	0.100951	−	0.174852i
$101$	−7.40051e8	−	1.28181e9i	−0.707645	−	1.22568i	−0.965728	−	0.259554i	$-0.916424\pi$
$101$	−7.40051e8	−	1.28181e9i	−0.707645	−	1.22568i	0.258083	−	0.966123i	$-0.416909\pi$
$102$	−2.28059e8	+	1.31670e8i	−0.208615	+	0.120444i
$103$	1.19119e9			1.04283			0.521413	−	0.853304i	$-0.325405\pi$
$103$	1.19119e9			1.04283			0.521413	+	0.853304i	$0.325405\pi$
$104$	−1.02807e9	+	1.62866e8i	−0.861737	+	0.136515i
$105$	−8.11972e7			−0.0651912
$106$	7.96343e8	−	4.59769e8i	0.612666	−	0.353723i
$107$	−9.52294e8	−	1.64942e9i	−0.702335	−	1.21648i	−0.967645	−	0.252316i	$-0.918808\pi$
$107$	−9.52294e8	−	1.64942e9i	−0.702335	−	1.21648i	0.265310	−	0.964163i	$-0.414526\pi$
$108$	3.77750e7	−	6.54282e7i	0.0267176	−	0.0462763i
$109$		−	2.30405e9i		−	1.56341i	−0.623647	−	0.781706i	$-0.714350\pi$
$109$		−	2.30405e9i		−	1.56341i	0.623647	−	0.781706i	$-0.285650\pi$
$110$	−1.28510e8	−	7.41955e7i	−0.0836895	−	0.0483182i
$111$	6.49174e8	+	3.74801e8i	0.405889	+	0.234340i
$112$			7.32091e8i			0.439626i
$113$	−2.06446e8	+	3.57574e8i	−0.119111	+	0.206307i	−0.919416	−	0.393287i	$-0.871338\pi$
$113$	−2.06446e8	+	3.57574e8i	−0.119111	+	0.206307i	0.800304	+	0.599594i	$0.204671\pi$
$114$	−1.81681e9	−	3.14681e9i	−1.00748	−	1.74501i
$115$	−1.46193e8	+	8.44047e7i	−0.0779447	+	0.0450014i
$116$	−3.10446e8			−0.159193
$117$	1.52582e9	+	5.85649e8i	0.752778	+	0.288936i
$118$	−5.24395e8			−0.248995
$119$	1.16900e8	−	6.74925e7i	0.0534386	−	0.0308528i
$120$	1.70915e8	+	2.96034e8i	0.0752428	+	0.130324i
$121$	−6.24329e8	+	1.08137e9i	−0.264777	+	0.458606i
$122$		−	1.68607e9i		−	0.689058i
$123$	4.43712e9	+	2.56177e9i	1.74795	+	1.00918i
$124$	−3.60508e8	−	2.08139e8i	−0.136936	−	0.0790599i
$125$			6.94823e8i			0.254554i
$126$	4.73306e8	−	8.19791e8i	0.167292	−	0.289758i
$127$	1.38747e9	+	2.40317e9i	0.473269	+	0.819726i	0.999532	−	0.0305961i	$-0.00974056\pi$
$127$	1.38747e9	+	2.40317e9i	0.473269	+	0.819726i	−0.526263	+	0.850322i	$0.676407\pi$
$128$	3.14017e9	−	1.81298e9i	1.03397	−	0.596964i
$129$	3.08930e9			0.982215
$130$	−3.56551e8	+	2.88748e8i	−0.109490	+	0.0886696i
$131$	7.42377e8			0.220244			0.110122	−	0.993918i	$-0.464876\pi$
$131$	7.42377e8			0.220244			0.110122	+	0.993918i	$0.464876\pi$
$132$	5.71636e8	−	3.30034e8i	0.163884	−	0.0946186i
$133$	9.31277e8	+	1.61302e9i	0.258075	+	0.446999i
$134$	−8.76447e8	+	1.51805e9i	−0.234830	+	0.406738i
$135$			1.28919e8i			0.0334053i
$136$	−4.92137e8	−	2.84135e8i	−0.123356	−	0.0712197i
$137$	2.78855e9	+	1.60997e9i	0.676295	+	0.390459i	0.798458	−	0.602051i	$-0.205650\pi$
$137$	2.78855e9	+	1.60997e9i	0.676295	+	0.390459i	−0.122163	+	0.992510i	$0.538983\pi$
$138$		−	4.40873e9i		−	1.03480i
$139$	2.65438e9	−	4.59753e9i	0.603111	−	1.04462i	−0.389236	−	0.921138i	$-0.627261\pi$
$139$	2.65438e9	−	4.59753e9i	0.603111	−	1.04462i	0.992347	−	0.123481i	$-0.0394057\pi$
$140$	2.26303e7	+	3.91969e7i	0.00497869	+	0.00862334i
$141$	−2.30672e9	+	1.33179e9i	−0.491484	+	0.283759i
$142$	−3.15107e9			−0.650370
$143$	−2.15852e9	−	2.66538e9i	−0.431663	−	0.533023i
$144$	−4.83920e9			−0.937869
$145$	4.58774e8	−	2.64873e8i	0.0861872	−	0.0497602i
$146$	−1.51456e9	−	2.62329e9i	−0.275866	−	0.477814i
$147$	−5.43498e8	+	9.41366e8i	−0.0959997	+	0.166276i
$148$		−	4.17840e8i		−	0.0715867i
$149$	−1.36200e9	−	7.86354e8i	−0.226381	−	0.130701i	0.382520	−	0.923947i	$-0.375056\pi$
$149$	−1.36200e9	−	7.86354e8i	−0.226381	−	0.130701i	−0.608902	+	0.793246i	$0.708390\pi$
$150$	−7.79240e9	−	4.49895e9i	−1.25678	−	0.725605i
$151$			1.07279e10i			1.67926i	0.543160	+	0.839629i	$0.317228\pi$
$151$			1.07279e10i			1.67926i	−0.543160	+	0.839629i	$0.682772\pi$
$152$	3.92056e9	−	6.79061e9i	0.595734	−	1.03184i
$153$	4.46133e8	+	7.72724e8i	0.0658192	+	0.114002i
$154$	−1.72038e9	+	9.93263e8i	−0.246480	+	0.142305i
$155$	7.10339e8			0.0988492
$156$	−3.19326e8	−	2.01572e9i	−0.0431692	−	0.272501i
$157$	−1.22289e10			−1.60634			−0.803172	−	0.595747i	$-0.796856\pi$
$157$	−1.22289e10			−1.60634			−0.803172	+	0.595747i	$0.796856\pi$
$158$	4.64113e9	−	2.67956e9i	0.592471	−	0.342063i
$159$	−3.48982e9	−	6.04455e9i	−0.433028	−	0.750027i
$160$	2.15151e8	−	3.72653e8i	0.0259540	−	0.0449536i
$161$			2.25987e9i			0.265074i
$162$	−9.63636e9	−	5.56355e9i	−1.09925	−	0.634651i
$163$	9.42727e9	+	5.44283e9i	1.04602	+	0.603922i	0.921534	−	0.388299i	$-0.126937\pi$
$163$	9.42727e9	+	5.44283e9i	1.04602	+	0.603922i	0.124490	+	0.992221i	$0.460270\pi$
$164$		−	2.85595e9i		−	0.308286i
$165$	−5.63172e8	+	9.75443e8i	−0.0591512	+	0.102453i
$166$	−1.71168e9	−	2.96471e9i	−0.174959	−	0.303037i
$167$	2.88274e9	−	1.66435e9i	0.286801	−	0.165585i	−0.349697	−	0.936863i	$-0.613716\pi$
$167$	2.88274e9	−	1.66435e9i	0.286801	−	0.165585i	0.636498	+	0.771278i	$0.280382\pi$
$168$	4.57612e9			0.443206
$169$	−1.00853e10	+	3.27764e9i	−0.951036	+	0.309080i
$170$	−2.50483e8			−0.0230016
$171$	−1.06622e10	+	6.15584e9i	−0.953598	+	0.550560i
$172$	−8.61014e8	−	1.49132e9i	−0.0750123	−	0.129925i
$173$	8.39876e9	−	1.45471e10i	0.712866	−	1.23472i	−0.250911	−	0.968010i	$-0.580730\pi$
$173$	8.39876e9	−	1.45471e10i	0.712866	−	1.23472i	0.963777	−	0.266709i	$-0.0859364\pi$
$174$			1.38352e10i			1.14423i
$175$	3.99430e9	+	2.30611e9i	0.321936	+	0.185870i
$176$	8.79479e9	+	5.07768e9i	0.690906	+	0.398895i
$177$			3.98036e9i			0.304820i
$178$	1.06834e10	−	1.85042e10i	0.797664	−	1.38159i
$179$	6.73556e9	+	1.16663e10i	0.490382	+	0.849367i	0.999939	−	0.0110701i	$-0.00352379\pi$
$179$	6.73556e9	+	1.16663e10i	0.490382	+	0.849367i	−0.509556	+	0.860437i	$0.670190\pi$
$180$	−2.59096e8	+	1.49589e8i	−0.0183964	+	0.0106212i
$181$	1.41355e10			0.978944			0.489472	−	0.872019i	$-0.337190\pi$
$181$	1.41355e10			0.978944			0.489472	+	0.872019i	$0.337190\pi$
$182$	9.61036e8	+	6.06645e9i	0.0649260	+	0.409839i
$183$	−1.27979e10			−0.843546
$184$	8.23917e9	−	4.75689e9i	0.529911	−	0.305944i
$185$	3.56502e8	+	6.17480e8i	0.0223764	+	0.0387570i
$186$	−9.27584e9	+	1.60662e10i	−0.568257	+	0.984251i
$187$		−	1.87247e9i		−	0.111977i
$188$	1.28581e9	+	7.42360e8i	0.0750698	+	0.0433416i
$189$	1.49463e9	+	8.62926e8i	0.0852032	+	0.0491921i
$190$		−	3.45622e9i		−	0.192402i
$191$	1.07557e10	−	1.86294e10i	0.584773	−	1.01286i	−0.410131	−	0.912027i	$-0.634517\pi$
$191$	1.07557e10	−	1.86294e10i	0.584773	−	1.01286i	0.994904	−	0.100830i	$-0.0321498\pi$
$192$	−9.09921e9	−	1.57603e10i	−0.483224	−	0.836968i
$193$	−2.93633e10	+	1.69529e10i	−1.52334	+	0.879500i	−0.523720	+	0.851891i	$0.675456\pi$
$193$	−2.93633e10	+	1.69529e10i	−1.52334	+	0.879500i	−0.999619	+	0.0276090i	$0.991211\pi$
$194$	−4.49067e9			−0.227616
$195$	2.19171e9	+	2.70636e9i	0.108549	+	0.134038i
$196$	6.05909e8			0.0293262
$197$	−1.00353e10	+	5.79387e9i	−0.474714	+	0.274076i	−0.718211	−	0.695826i	$-0.755039\pi$
$197$	−1.00353e10	+	5.79387e9i	−0.474714	+	0.274076i	0.243497	+	0.969902i	$0.421705\pi$
$198$	−6.56557e9	−	1.13719e10i	−0.303584	−	0.525823i
$199$	9.28759e9	−	1.60866e10i	0.419821	−	0.727151i	−0.576100	−	0.817379i	$-0.695426\pi$
$199$	9.28759e9	−	1.60866e10i	0.419821	−	0.727151i	0.995921	+	0.0902278i	$0.0287595\pi$
$200$		−	1.94169e10i		−	0.858114i
$201$	1.15226e10	+	6.65257e9i	0.497930	+	0.287480i
$202$	3.18421e10	+	1.83840e10i	1.34561	+	0.776891i
$203$		−	7.09178e9i		−	0.293105i
$204$	5.57096e8	−	9.64919e8i	0.0225213	−	0.0390081i
$205$	2.43671e9	+	4.22050e9i	0.0963631	+	0.166906i
$206$	−2.56265e10	+	1.47955e10i	−0.991487	+	0.572436i
$207$	−1.49380e10			−0.565490
$208$	2.44011e10	−	1.97609e10i	0.903907	−	0.732019i
$209$	2.58368e10			0.936657
$210$	1.74683e9	−	1.00853e9i	0.0619818	−	0.0357852i
$211$	1.81734e10	+	3.14773e10i	0.631199	+	1.09327i	0.987307	+	0.158824i	$0.0507702\pi$
$211$	1.81734e10	+	3.14773e10i	0.631199	+	1.09327i	−0.356108	+	0.934445i	$0.615897\pi$
$212$	−1.94529e9	+	3.36933e9i	−0.0661412	+	0.114560i
$213$			2.39178e10i			0.796184i
$214$	4.09743e10	+	2.36565e10i	1.33552	+	0.771061i
$215$	2.54480e9	+	1.46924e9i	0.0812232	+	0.0468942i
$216$		−	7.26563e9i		−	0.227107i
$217$	4.75469e9	−	8.23537e9i	0.145564	−	0.252124i
$218$	2.86182e10	+	4.95682e10i	0.858199	+	1.48644i
$219$	−1.99118e10	+	1.14961e10i	−0.584941	+	0.337716i
$220$	6.27843e8			0.0180696
$221$	−5.40500e9	−	2.07458e9i	−0.152416	−	0.0585012i
$222$	−1.86213e10			−0.514543
$223$	−6.07597e9	+	3.50796e9i	−0.164529	+	0.0949911i	−0.580004	−	0.814614i	$-0.696949\pi$
$223$	−6.07597e9	+	3.50796e9i	−0.164529	+	0.0949911i	0.415474	+	0.909605i	$0.363616\pi$
$224$	−2.88025e9	−	4.98875e9i	−0.0764390	−	0.132396i
$225$	−1.52436e10	+	2.64028e10i	−0.396522	+	0.686796i
$226$		−	1.02569e10i		−	0.261533i
$227$	−3.07432e10	−	1.77496e10i	−0.768479	−	0.443682i	0.0638527	−	0.997959i	$-0.479661\pi$
$227$	−3.07432e10	−	1.77496e10i	−0.768479	−	0.443682i	−0.832332	+	0.554278i	$0.812995\pi$
$228$	1.33142e10	+	7.68694e9i	0.326293	+	0.188385i
$229$			6.74077e10i			1.61976i	0.586597	+	0.809879i	$0.300467\pi$
$229$			6.74077e10i			1.61976i	−0.586597	+	0.809879i	$0.699533\pi$
$230$	2.09675e9	−	3.63167e9i	0.0494050	−	0.0855719i
$231$	7.53925e9	+	1.30584e10i	0.174210	+	0.301741i
$232$	−2.58556e10	+	1.49278e10i	−0.585948	+	0.338297i
$233$	4.69023e10			1.04254			0.521269	−	0.853392i	$-0.325459\pi$
$233$	4.69023e10			1.04254			0.521269	+	0.853392i	$0.325459\pi$
$234$	−4.00999e10	+	6.35255e9i	−0.874322	+	0.138509i
$235$	−2.53354e9			−0.0541903
$236$	1.92147e9	−	1.10936e9i	0.0403208	−	0.0232792i
$237$	−2.03389e10	−	3.52280e10i	−0.418755	−	0.725305i
$238$	−1.67662e9	+	2.90399e9i	−0.0338718	+	0.0586677i
$239$			4.82918e10i			0.957377i	0.877985	+	0.478689i	$0.158888\pi$
$239$			4.82918e10i			0.957377i	−0.877985	+	0.478689i	$0.841112\pi$
$240$	−8.93002e9	−	5.15575e9i	−0.173741	−	0.100309i
$241$	4.16243e10	+	2.40318e10i	0.794823	+	0.458891i	0.841658	−	0.540011i	$-0.181580\pi$
$241$	4.16243e10	+	2.40318e10i	0.794823	+	0.458891i	−0.0468345	+	0.998903i	$0.514913\pi$
$242$		−	3.10187e10i		−	0.581372i
$243$	−3.51554e10	+	6.08909e10i	−0.646791	+	1.12027i
$244$	3.56688e9	+	6.17802e9i	0.0644221	+	0.111582i
$245$	−8.95407e8	+	5.16963e8i	−0.0158772	+	0.00916669i
$246$	−1.27277e11			−2.21586
$247$	2.86255e10	−	7.45794e10i	0.489347	−	1.27492i
$248$	−4.00334e10			−0.672032
$249$	−2.25033e10	+	1.29923e10i	−0.370979	+	0.214185i
$250$	−8.63026e9	−	1.49481e10i	−0.139731	−	0.242022i
$251$	3.33259e10	−	5.77221e10i	0.529968	−	0.917932i	−0.469421	−	0.882975i	$-0.655537\pi$
$251$	3.33259e10	−	5.77221e10i	0.529968	−	0.917932i	0.999389	−	0.0349571i	$-0.0111295\pi$
$252$			4.00513e9i			0.0625624i
$253$	2.71484e10	+	1.56741e10i	0.416583	+	0.240514i
$254$	−5.96987e10	−	3.44671e10i	−0.899939	−	0.519580i
$255$			1.90126e9i			0.0281586i
$256$	−2.03297e10	+	3.52121e10i	−0.295836	+	0.512404i
$257$	2.94389e10	+	5.09896e10i	0.420942	+	0.729093i	0.996032	−	0.0889974i	$-0.0283663\pi$
$257$	2.94389e10	+	5.09896e10i	0.420942	+	0.729093i	−0.575090	+	0.818090i	$0.695033\pi$
$258$	−6.64616e10	+	3.83716e10i	−0.933860	+	0.539164i
$259$	9.54507e9			0.131805
$260$	6.95610e8	−	1.81230e9i	0.00944030	−	0.0245952i
$261$	4.68774e10			0.625290
$262$	−1.59711e10	+	9.22091e9i	−0.209401	+	0.120898i
$263$	−5.01357e10	−	8.68375e10i	−0.646169	−	1.11920i	−0.984030	−	0.178001i	$-0.943037\pi$
$263$	−5.01357e10	−	8.68375e10i	−0.646169	−	1.11920i	0.337862	−	0.941196i	$-0.390296\pi$
$264$	3.17393e10	−	5.49741e10i	0.402143	−	0.696531i
$265$		−	6.63889e9i		−	0.0826969i
$266$	−4.00700e10	−	2.31344e10i	−0.490740	−	0.283329i
$267$	−1.40454e11	−	8.10912e10i	−1.69135	−	0.976502i
$268$		−	7.41651e9i		−	0.0878199i
$269$	1.03540e9	−	1.79337e9i	0.0120565	−	0.0208826i	−0.859934	−	0.510405i	$-0.829496\pi$
$269$	1.03540e9	−	1.79337e9i	0.0120565	−	0.0208826i	0.871991	+	0.489522i	$0.162829\pi$
$270$	−1.60128e9	−	2.77349e9i	−0.0183370	−	0.0317607i
$271$	1.04635e11	−	6.04109e10i	1.17846	−	0.680383i	0.222801	−	0.974864i	$-0.428480\pi$
$271$	1.04635e11	−	6.04109e10i	1.17846	−	0.680383i	0.955657	+	0.294481i	$0.0951467\pi$
$272$	1.71422e10			0.189892
$273$	4.60467e10	−	7.29464e9i	0.501726	−	0.0794826i
$274$	−7.99885e10			−0.857334
$275$	5.54078e10	−	3.19897e10i	0.584216	−	0.337298i
$276$	9.32669e9	+	1.61543e10i	0.0967468	+	0.167570i
$277$	9.62472e9	−	1.66705e10i	0.0982267	−	0.170134i	−0.812724	−	0.582649i	$-0.802016\pi$
$277$	9.62472e9	−	1.66705e10i	0.0982267	−	0.170134i	0.910951	+	0.412515i	$0.135350\pi$
$278$			1.31878e11i			1.32426i
$279$	5.44367e10	+	3.14290e10i	0.537864	+	0.310536i
$280$	3.76956e9	+	2.17635e9i	0.0366504	+	0.0211601i
$281$		−	1.18984e11i		−	1.13844i	−0.822186	−	0.569219i	$-0.807246\pi$
$281$		−	1.18984e11i		−	1.13844i	0.822186	−	0.569219i	$-0.192754\pi$
$282$	3.30837e10	−	5.73027e10i	0.311525	−	0.539578i
$283$	7.84531e10	+	1.35885e11i	0.727062	+	1.25931i	0.958120	+	0.286368i	$0.0924479\pi$
$283$	7.84531e10	+	1.35885e11i	0.727062	+	1.25931i	−0.231058	+	0.972940i	$0.574219\pi$
$284$	1.15460e10	−	6.66610e9i	0.105317	−	0.0608050i
$285$	−2.62341e10			−0.235539
$286$	7.95434e10	+	3.05308e10i	0.703003	+	0.269831i
$287$	6.52409e10			0.567611
$288$	3.29762e10	−	1.90388e10i	0.282445	−	0.163070i
$289$	5.77136e10	+	9.99628e10i	0.486673	+	0.842943i
$290$	−6.57988e9	+	1.13967e10i	−0.0546295	+	0.0946210i
$291$			3.40859e10i			0.278648i
$292$	1.10992e10	+	6.40811e9i	0.0893445	+	0.0515831i
$293$	−3.41957e10	−	1.97429e10i	−0.271061	−	0.156497i	0.358309	−	0.933603i	$-0.383354\pi$
$293$	−3.41957e10	−	1.97429e10i	−0.271061	−	0.156497i	−0.629370	+	0.777106i	$0.716687\pi$
$294$		−	2.70027e10i		−	0.210787i
$295$	−1.89302e9	+	3.27880e9i	−0.0145531	+	0.0252067i
$296$	−2.00918e10	−	3.48000e10i	−0.152127	−	0.263492i
$297$	2.07331e10	−	1.19703e10i	0.154618	−	0.0892688i
$298$	3.90686e10			0.286982
$299$	7.53229e10	−	6.09994e10i	0.545013	−	0.441372i
$300$	3.80702e10			0.271356
$301$	3.40675e10	−	1.96689e10i	0.239216	−	0.138112i
$302$	−1.33249e11	−	2.30794e11i	−0.921790	−	1.59659i
$303$	1.39542e11	−	2.41694e11i	0.951072	−	1.64730i
$304$			2.36532e11i			1.58839i
$305$	−1.05422e10	−	6.08655e9i	−0.0697561	−	0.0402737i
$306$	−1.91957e10	−	1.10826e10i	−0.125158	−	0.0722599i
$307$		−	1.18385e11i		−	0.760629i	−0.924857	−	0.380315i	$-0.875816\pi$
$307$		−	1.18385e11i		−	0.760629i	0.924857	−	0.380315i	$-0.124184\pi$
$308$	4.20250e9	−	7.27895e9i	0.0266091	−	0.0460883i
$309$	1.12303e11	+	1.94515e11i	0.700777	+	1.21378i
$310$	−1.52819e10	+	8.82298e9i	−0.0939828	+	0.0542610i
$311$	−2.73459e11			−1.65757			−0.828783	−	0.559571i	$-0.810966\pi$
$311$	−2.73459e11			−1.65757			−0.828783	+	0.559571i	$0.810966\pi$
$312$	−1.23521e11	−	1.52525e11i	−0.737979	−	0.911267i
$313$	−8.06225e10			−0.474796			−0.237398	−	0.971413i	$-0.576294\pi$
$313$	−8.06225e10			−0.474796			−0.237398	+	0.971413i	$0.576294\pi$
$314$	2.63086e11	−	1.51893e11i	1.52726	−	0.881766i
$315$	−3.41718e9	−	5.91874e9i	−0.0195556	−	0.0338713i
$316$	−1.13372e10	+	1.96367e10i	−0.0639610	+	0.110784i
$317$			1.55394e11i			0.864309i	0.901800	+	0.432154i	$0.142246\pi$
$317$			1.55394e11i			0.864309i	−0.901800	+	0.432154i	$0.857754\pi$
$318$	1.50156e11	+	8.66928e10i	0.823420	+	0.475402i
$319$	−8.51953e10	−	4.91876e10i	−0.460636	−	0.265948i
$320$		−	1.73100e10i		−	0.0922828i
$321$	1.79562e11	−	3.11011e11i	0.943934	−	1.63494i
$322$	−2.80694e10	−	4.86176e10i	−0.145506	−	0.252024i
$323$	3.77694e10	−	2.18062e10i	0.193076	−	0.111473i
$324$	4.70789e10			0.237341
$325$	−3.09518e10	−	1.95380e11i	−0.153890	−	0.971417i
$326$	−2.70417e11			−1.32604
$327$	3.76242e11	−	2.17223e11i	1.81971	−	1.05061i
$328$	−1.37328e11	−	2.37859e11i	−0.655129	−	1.13472i
$329$	−1.69584e10	+	2.93727e10i	−0.0797999	+	0.138217i
$330$		−	2.79802e10i		−	0.129879i
$331$	2.85400e11	+	1.64776e11i	1.30686	+	0.754515i	0.981571	−	0.191100i	$-0.0612056\pi$
$331$	2.85400e11	+	1.64776e11i	1.30686	+	0.754515i	0.325288	+	0.945615i	$0.394539\pi$
$332$	1.25437e10	+	7.24211e9i	0.0566637	+	0.0327148i
$333$			6.30939e10i			0.281183i
$334$	−4.13451e10	+	7.16118e10i	−0.181788	+	0.314866i
$335$	6.32779e9	+	1.09600e10i	0.0274505	+	0.0475457i
$336$	−1.19547e11	+	6.90205e10i	−0.511696	+	0.295428i
$337$	−5.63355e10			−0.237929			−0.118965	−	0.992898i	$-0.537958\pi$
$337$	−5.63355e10			−0.237929			−0.118965	+	0.992898i	$0.537958\pi$
$338$	1.76258e11	−	1.95780e11i	0.734554	−	0.815913i
$339$	−7.78537e10			−0.320170
$340$	9.17810e8	−	5.29898e8i	0.00372475	−	0.00215049i
$341$	−6.59558e10	−	1.14239e11i	−0.264155	−	0.457529i
$342$	1.52921e11	−	2.64867e11i	0.604435	−	1.04691i
$343$			1.38413e10i			0.0539949i
$344$	−1.43420e11	−	8.28035e10i	−0.552200	−	0.318813i
$345$	−2.75658e10	−	1.59151e10i	−0.104757	−	0.0604817i
$346$			4.17277e11i			1.56524i
$347$	7.73291e10	−	1.33938e11i	0.286326	−	0.495931i	−0.686604	−	0.727031i	$-0.740899\pi$
$347$	7.73291e10	−	1.33938e11i	0.286326	−	0.495931i	0.972930	+	0.231101i	$0.0742328\pi$
$348$	−2.92684e10	−	5.06944e10i	−0.106978	−	0.185291i
$349$	−2.56584e11	+	1.48139e11i	−0.925794	+	0.534508i	−0.885479	−	0.464679i	$-0.846170\pi$
$349$	−2.56584e11	+	1.48139e11i	−0.925794	+	0.534508i	−0.0403154	+	0.999187i	$0.512836\pi$
$350$	−1.14575e11			−0.408116
$351$	−1.15819e10	−	7.31095e10i	−0.0407284	−	0.257094i
$352$	−7.99082e10			−0.277427
$353$	−2.91882e11	+	1.68518e11i	−1.00051	+	0.577644i	−0.908399	−	0.418105i	$-0.862694\pi$
$353$	−2.91882e11	+	1.68518e11i	−1.00051	+	0.577644i	−0.0921095	+	0.995749i	$0.529361\pi$
$354$	−4.94393e10	−	8.56314e10i	−0.167324	−	0.289813i
$355$	−1.13751e10	+	1.97022e10i	−0.0380125	+	0.0658396i
$356$			9.04032e10i			0.298304i
$357$	2.20424e10	+	1.27262e10i	0.0718212	+	0.0414660i
$358$	−2.89810e11	−	1.67322e11i	−0.932481	−	0.538368i
$359$			2.54543e11i			0.808791i	0.914584	+	0.404395i	$0.132518\pi$
$359$			2.54543e11i			0.808791i	−0.914584	+	0.404395i	$0.867482\pi$
$360$	−1.43859e10	+	2.49172e10i	−0.0451416	+	0.0781875i
$361$	1.39543e11	+	2.41695e11i	0.432440	+	0.749007i
$362$	−3.04104e11	+	1.75574e11i	−0.930750	+	0.537369i
$363$	−2.35444e11			−0.711717
$364$	−1.63550e10	−	2.01954e10i	−0.0488308	−	0.0602969i
$365$	−2.18697e10			−0.0644948
$366$	2.75327e11	−	1.58960e11i	0.802018	−	0.463045i
$367$	2.22980e11	+	3.86213e11i	0.641607	+	1.11130i	0.985074	+	0.172131i	$0.0550653\pi$
$367$	2.22980e11	+	3.86213e11i	0.641607	+	1.11130i	−0.343467	+	0.939165i	$0.611601\pi$
$368$	−1.43494e11	+	2.48539e11i	−0.407867	+	0.706446i
$369$			4.31249e11i			1.21090i
$370$	−1.53392e10	−	8.85609e9i	−0.0425495	−	0.0245660i
$371$	−7.69685e10	−	4.44378e10i	−0.210926	−	0.121778i
$372$		−	7.84923e10i		−	0.212512i
$373$	−1.23250e11	+	2.13475e11i	−0.329683	+	0.571028i	−0.982449	−	0.186532i	$-0.940275\pi$
$373$	−1.23250e11	+	2.13475e11i	−0.329683	+	0.571028i	0.652766	+	0.757560i	$0.273609\pi$
$374$	2.32576e10	+	4.02834e10i	0.0614671	+	0.106464i
$375$	−1.13461e11	+	6.55070e10i	−0.296284	+	0.171059i
$376$	1.42785e11			0.368416
$377$	−2.36374e11	+	1.91424e11i	−0.602647	+	0.488047i
$378$	−4.28729e10			−0.108011
$379$	1.01984e11	−	5.88806e10i	0.253896	−	0.146587i	−0.367651	−	0.929964i	$-0.619838\pi$
$379$	1.01984e11	−	5.88806e10i	0.253896	−	0.146587i	0.621547	+	0.783377i	$0.286504\pi$
$380$	7.31165e9	+	1.26641e10i	0.0179883	+	0.0311566i
$381$	−2.61618e11	+	4.53136e11i	−0.636071	+	1.10171i
$382$			5.34376e11i			1.28399i
$383$	−3.22113e11	−	1.85972e11i	−0.764916	−	0.441625i	0.0661418	−	0.997810i	$-0.478931\pi$
$383$	−3.22113e11	−	1.85972e11i	−0.764916	−	0.441625i	−0.831058	+	0.556186i	$0.812264\pi$
$384$	5.92103e11	+	3.41851e11i	1.38965	+	0.802317i
$385$			1.43423e10i			0.0332695i
$386$	4.21137e11	−	7.29430e11i	0.965562	−	1.67240i
$387$	1.30013e11	+	2.25190e11i	0.294638	+	0.510327i
$388$	1.64545e10	−	9.50002e9i	0.0368589	−	0.0212805i
$389$	1.12200e11			0.248439			0.124219	−	0.992255i	$-0.460357\pi$
$389$	1.12200e11			0.248439			0.124219	+	0.992255i	$0.460357\pi$
$390$	−8.07664e10	−	3.10003e10i	−0.176783	−	0.0678539i
$391$	5.29157e10			0.114496
$392$	5.04634e10	−	2.91351e10i	0.107942	−	0.0623202i
$393$	6.99903e10	+	1.21227e11i	0.148003	+	0.256349i
$394$	1.43929e11	−	2.49292e11i	0.300895	−	0.521166i
$395$		−	3.86918e10i		−	0.0799710i
$396$	4.81146e10	+	2.77790e10i	0.0983215	+	0.0567660i
$397$	−1.12431e11	−	6.49121e10i	−0.227159	−	0.131150i	0.382102	−	0.924120i	$-0.375200\pi$
$397$	−1.12431e11	−	6.49121e10i	−0.227159	−	0.131150i	−0.609261	+	0.792970i	$0.708534\pi$
$398$			4.61437e11i			0.921804i
$399$	−1.75599e11	+	3.04146e11i	−0.346852	+	0.600765i
$400$	2.92860e11	+	5.07249e11i	0.571993	+	0.990721i
$401$	2.50050e11	−	1.44367e11i	0.482923	−	0.278816i	−0.238711	−	0.971091i	$-0.576725\pi$
$401$	2.50050e11	−	1.44367e11i	0.482923	−	0.278816i	0.721634	+	0.692275i	$0.243391\pi$
$402$	−3.30521e11			−0.631222
$403$	−4.02831e11	+	6.38159e10i	−0.760765	+	0.120519i
$404$	−1.55566e11			−0.290535
$405$	−6.95727e10	+	4.01678e10i	−0.128496	+	0.0741875i
$406$	8.80855e10	+	1.52569e11i	0.160893	+	0.278675i
$407$	6.62033e10	−	1.14667e11i	0.119593	−	0.207141i
$408$		−	1.07152e11i		−	0.191438i
$409$	6.96200e11	+	4.01951e11i	1.23021	+	0.710262i	0.967074	−	0.254497i	$-0.0819099\pi$
$409$	6.96200e11	+	4.01951e11i	1.23021	+	0.710262i	0.263136	+	0.964759i	$0.415243\pi$
$410$	−1.04844e11	−	6.05317e10i	−0.183238	−	0.105793i
$411$			6.07143e11i			1.04955i
$412$	6.25998e10	−	1.08426e11i	0.107037	−	0.185394i
$413$	2.53420e10	+	4.38937e10i	0.0428614	+	0.0742381i
$414$	3.21367e11	−	1.85542e11i	0.537651	−	0.310413i
$415$	−2.47160e10			−0.0409036
$416$	−8.85331e10	+	2.30659e11i	−0.144939	+	0.377617i
$417$	1.00101e12			1.62116
$418$	−5.55839e11	+	3.20914e11i	−0.890545	+	0.514156i
$419$	−3.90822e11	−	6.76924e11i	−0.619464	−	1.07294i	−0.989584	−	0.143960i	$-0.954016\pi$
$419$	−3.90822e11	−	6.76924e11i	−0.619464	−	1.07294i	0.370119	−	0.928984i	$-0.379317\pi$
$420$	−4.26712e9	+	7.39086e9i	−0.00669133	+	0.0115897i
$421$			5.08786e11i			0.789343i	0.918822	+	0.394672i	$0.129142\pi$
$421$			5.08786e11i			0.789343i	−0.918822	+	0.394672i	$0.870858\pi$
$422$	−7.81947e11	−	4.51457e11i	−1.20025	−	0.692964i
$423$	−1.94157e11	−	1.12097e11i	−0.294864	−	0.170240i
$424$			3.74155e11i			0.562219i
$425$	5.39984e10	−	9.35280e10i	0.0802844	−	0.139057i
$426$	−2.97079e11	−	5.14555e11i	−0.437047	−	0.756988i
$427$	−1.41130e11	+	8.14812e10i	−0.205444	+	0.118613i
$428$	−2.00182e11			−0.288355
$429$	2.31741e11	−	6.03765e11i	0.330328	−	0.860618i
$430$	−7.29965e10			−0.102966
$431$	2.67522e11	−	1.54454e11i	0.373432	−	0.215601i	−0.301525	−	0.953458i	$-0.597496\pi$
$431$	2.67522e11	−	1.54454e11i	0.373432	−	0.215601i	0.674957	+	0.737857i	$0.264162\pi$
$432$	1.09586e11	+	1.89808e11i	0.151383	+	0.262203i
$433$	−5.17838e10	+	8.96921e10i	−0.0707943	+	0.122619i	−0.899250	−	0.437436i	$-0.855887\pi$
$433$	−5.17838e10	+	8.96921e10i	−0.0707943	+	0.122619i	0.828455	+	0.560055i	$0.189220\pi$
$434$			2.36228e11i			0.319616i
$435$	8.65052e10	+	4.99438e10i	0.115835	+	0.0668775i
$436$	−2.09723e11	−	1.21084e11i	−0.277944	−	0.160471i
$437$			7.30142e11i			0.957725i
$438$	2.85581e11	−	4.94641e11i	0.370763	−	0.642180i
$439$	4.95893e11	+	8.58911e11i	0.637231	+	1.10372i	0.986038	+	0.166522i	$0.0532538\pi$
$439$	4.95893e11	+	8.58911e11i	0.637231	+	1.10372i	−0.348806	+	0.937195i	$0.613413\pi$
$440$	5.22902e10	−	3.01898e10i	0.0665095	−	0.0383993i
$441$	−9.14924e10			−0.115189
$442$	1.42048e11	−	2.25030e10i	0.177025	−	0.0280440i
$443$	9.88866e11			1.21989			0.609945	−	0.792444i	$-0.291191\pi$
$443$	9.88866e11			1.21989			0.609945	+	0.792444i	$0.291191\pi$
$444$	6.82314e10	−	3.93934e10i	0.0833223	−	0.0481061i
$445$	−7.71322e10	−	1.33597e11i	−0.0932429	−	0.161501i
$446$	8.71434e10	−	1.50937e11i	0.104286	−	0.180629i
$447$		−	2.96546e11i		−	0.351324i
$448$	−2.00684e11	−	1.15865e11i	−0.235376	−	0.135894i
$449$	3.22299e11	+	1.86079e11i	0.374240	+	0.216067i	0.675309	−	0.737535i	$-0.264010\pi$
$449$	3.22299e11	+	1.86079e11i	0.374240	+	0.216067i	−0.301069	+	0.953602i	$0.597344\pi$
$450$		−	7.57353e11i		−	0.870646i
$451$	4.52501e11	−	7.83755e11i	0.515022	−	0.892044i
$452$	2.16985e10	+	3.75828e10i	0.0244515	+	0.0423513i
$453$	−1.75181e12	+	1.01141e12i	−1.95455	+	1.12846i
$454$	8.81855e11			0.974195
$455$	4.14000e10	+	1.58904e10i	0.0452844	+	0.0173813i
$456$	1.47850e12			1.60133
$457$	1.03654e12	−	5.98449e11i	1.11164	−	0.641807i	0.172388	−	0.985029i	$-0.444852\pi$
$457$	1.03654e12	−	5.98449e11i	1.11164	−	0.641807i	0.939254	+	0.343222i	$0.111518\pi$
$458$	−8.37258e11	−	1.45017e12i	−0.889129	−	1.54002i
$459$	2.02057e10	−	3.49974e10i	0.0212480	−	0.0368026i
$460$			1.77427e10i			0.0184761i
$461$	−1.02864e12	−	5.93887e11i	−1.06074	−	0.612420i	−0.135105	−	0.990831i	$-0.543137\pi$
$461$	−1.02864e12	−	5.93887e11i	−1.06074	−	0.612420i	−0.925638	+	0.378411i	$0.876470\pi$
$462$	−3.24391e11	−	1.87287e11i	−0.331268	−	0.191258i
$463$		−	1.03412e11i		−	0.104582i	−0.998632	−	0.0522911i	$-0.983348\pi$
$463$		−	1.03412e11i		−	0.104582i	0.998632	−	0.0522911i	$-0.0166524\pi$
$464$	4.50304e11	−	7.79949e11i	0.450998	−	0.781151i
$465$	6.69699e10	+	1.15995e11i	0.0664265	+	0.115054i
$466$	−1.00903e12	+	5.82564e11i	−0.991214	+	0.572278i
$467$	−1.38377e12			−1.34628			−0.673142	−	0.739513i	$-0.735056\pi$
$467$	−1.38377e12			−1.34628			−0.673142	+	0.739513i	$0.735056\pi$
$468$	1.33493e11	−	1.08108e11i	0.128633	−	0.104172i
$469$	1.69421e11			0.161693
$470$	5.45051e10	−	3.14685e10i	0.0515225	−	0.0297465i
$471$	−1.15292e12	−	1.99692e12i	−1.07946	−	1.86968i
$472$	1.06687e11	−	1.84787e11i	0.0989401	−	0.171369i
$473$		−	5.45682e11i		−	0.501261i
$474$	8.75120e11	+	5.05251e11i	0.796279	+	0.459732i
$475$	1.29052e12	+	7.45083e11i	1.16317	+	0.671557i
$476$		−	1.41876e10i		−	0.0126671i
$477$	2.93738e11	−	5.08770e11i	0.259793	−	0.449975i
$478$	−5.99823e11	−	1.03892e12i	−0.525530	−	0.910245i
$479$	1.10418e11	−	6.37496e10i	0.0958359	−	0.0553309i	−0.451316	−	0.892364i	$-0.649045\pi$
$479$	1.10418e11	−	6.37496e10i	0.0958359	−	0.0553309i	0.547152	+	0.837033i	$0.315712\pi$
$480$	8.11368e10			0.0697641
$481$	−2.57645e11	−	3.18144e11i	−0.219467	−	0.271001i
$482$	−1.19398e12			−1.00759
$483$	−3.69026e11	+	2.13057e11i	−0.308528	+	0.178129i
$484$	6.56201e10	+	1.13657e11i	0.0543542	+	0.0941442i
$485$	−1.62109e10	+	2.80781e10i	−0.0133036	+	0.0230425i
$486$		−	1.74663e12i		−	1.42016i
$487$	−1.26207e12	−	7.28658e11i	−1.01673	−	0.587008i	−0.103573	−	0.994622i	$-0.533027\pi$
$487$	−1.26207e12	−	7.28658e11i	−1.01673	−	0.587008i	−0.913154	+	0.407614i	$0.866361\pi$
$488$	5.94139e11	+	3.43026e11i	0.474241	+	0.273803i
$489$			2.05257e12i			1.62334i
$490$	1.28422e10	−	2.22433e10i	0.0100637	−	0.0174308i
$491$	−2.17927e11	−	3.77461e11i	−0.169217	−	0.293093i	0.768928	−	0.639336i	$-0.220791\pi$
$491$	−2.17927e11	−	3.77461e11i	−0.169217	−	0.293093i	−0.938145	+	0.346243i	$0.887457\pi$
$492$	4.66364e11	−	2.69255e11i	0.358824	−	0.207167i
$493$	−1.66057e11			−0.126603
$494$	3.10502e11	+	1.96001e12i	0.234581	+	1.48077i
$495$	−9.48044e10			−0.0709750
$496$	1.04584e12	−	6.03814e11i	0.775883	−	0.447956i
$497$	1.52279e11	+	2.63755e11i	0.111953	+	0.193909i
$498$	3.22749e11	−	5.59018e11i	0.235143	−	0.407280i
$499$		−	1.47555e12i		−	1.06537i	−0.846314	−	0.532685i	$-0.821183\pi$
$499$		−	1.47555e12i		−	1.06537i	0.846314	−	0.532685i	$-0.178817\pi$
$500$	6.32453e10	+	3.65147e10i	0.0452547	+	0.0261278i
$501$	5.43561e11	+	3.13825e11i	0.385459	+	0.222545i
$502$			1.65574e12i			1.16366i
$503$	6.94999e11	−	1.20377e12i	0.484093	−	0.838473i	−0.515740	−	0.856745i	$-0.672483\pi$
$503$	6.94999e11	−	1.20377e12i	0.484093	−	0.838473i	0.999833	+	0.0182718i	$0.00581642\pi$
$504$	1.92586e11	+	3.33569e11i	0.132950	+	0.230276i
$505$	2.29894e11	−	1.32729e11i	0.157296	−	0.0908147i
$506$	−7.78741e11			−0.528099
$507$	−1.48605e12	−	1.33787e12i	−0.998843	−	0.899242i
$508$	2.91661e11			0.194308
$509$	−2.00164e12	+	1.15565e12i	−1.32177	+	0.763124i	−0.984011	−	0.178108i	$-0.943002\pi$
$509$	−2.00164e12	+	1.15565e12i	−1.32177	+	0.763124i	−0.337759	+	0.941233i	$0.609669\pi$
$510$	−2.36152e10	−	4.09027e10i	−0.0154570	−	0.0267724i
$511$	−1.46386e11	+	2.53548e11i	−0.0949740	+	0.164500i
$512$			8.46445e11i			0.544357i
$513$	4.82901e11	+	2.78803e11i	0.307844	+	0.177734i
$514$	−1.26666e12	−	7.31309e11i	−0.800437	−	0.462133i
$515$			2.13641e11i			0.133830i
$516$	1.62351e11	−	2.81199e11i	0.100816	−	0.174619i
$517$	2.35241e11	+	4.07450e11i	0.144813	+	0.250823i
$518$	−2.05347e11	+	1.18557e11i	−0.125316	+	0.0723510i
$519$	3.16729e12			1.91618
$520$	−2.92103e10	−	1.84387e11i	−0.0175195	−	0.110590i
$521$	7.07284e11			0.420556			0.210278	−	0.977642i	$-0.432563\pi$
$521$	7.07284e11			0.420556			0.210278	+	0.977642i	$0.432563\pi$
$522$	−1.00849e12	+	5.82255e11i	−0.594506	+	0.343238i
$523$	−1.08997e12	−	1.88789e12i	−0.637028	−	1.10337i	−0.986082	−	0.166262i	$-0.946830\pi$
$523$	−1.08997e12	−	1.88789e12i	−0.637028	−	1.10337i	0.349053	−	0.937103i	$-0.386503\pi$
$524$	3.90138e10	−	6.75738e10i	0.0226062	−	0.0391550i
$525$			8.69668e11i			0.499616i
$526$	2.15718e12	+	1.24545e12i	1.22871	+	0.709399i
$527$	−1.92834e11	−	1.11333e11i	−0.108902	−	0.0628747i
$528$			1.91487e12i			1.07222i
$529$	4.57629e11	−	7.92637e11i	0.254076	−	0.440072i
$530$	8.24603e10	+	1.42825e11i	0.0453945	+	0.0786257i
$531$	−2.90142e11	+	1.67514e11i	−0.158375	+	0.0914376i
$532$	1.95764e11			0.105957
$533$	−1.76101e12	−	2.17452e12i	−0.945126	−	1.16705i
$534$	4.02887e12			2.14411
$535$	2.95827e11	−	1.70796e11i	0.156115	−	0.0901331i
$536$	−3.56622e11	−	6.17688e11i	−0.186624	−	0.323242i
$537$	−1.27004e12	+	2.19977e12i	−0.659072	+	1.14155i
$538$			5.14420e10i			0.0264727i
$539$	1.66279e11	+	9.60012e10i	0.0848570	+	0.0489922i
$540$	1.17347e10	+	6.77501e9i	0.00593880	+	0.00342877i
$541$		−	3.38096e11i		−	0.169689i	−0.996394	−	0.0848443i	$-0.972961\pi$
$541$		−	3.38096e11i		−	0.169689i	0.996394	−	0.0848443i	$-0.0270393\pi$
$542$	−1.50070e12	+	2.59930e12i	−0.746961	+	1.29378i
$543$	1.33268e12	+	2.30826e12i	0.657848	+	1.13943i
$544$	−1.16813e11	+	6.74422e10i	−0.0571870	+	0.0330170i
$545$	4.13236e11			0.200638
$546$	−9.00018e11	+	7.28869e11i	−0.433395	+	0.350980i
$547$	1.70003e12			0.811919			0.405960	−	0.913891i	$-0.366937\pi$
$547$	1.70003e12			0.811919			0.405960	+	0.913891i	$0.366937\pi$
$548$	2.93091e11	−	1.69216e11i	0.138832	−	0.0801546i
$549$	−5.38600e11	−	9.32882e11i	−0.253041	−	0.438280i
$550$	−7.94675e11	+	1.37642e12i	−0.370303	+	0.641384i
$551$		−	2.29129e12i		−	1.05900i
$552$	1.55356e12	+	8.96946e11i	0.712198	+	0.411188i
$553$	−4.48577e11	−	2.58986e11i	−0.203973	−	0.117764i
$554$			4.78187e11i			0.215677i
$555$	−6.72212e10	+	1.16430e11i	−0.0300737	+	0.0520893i
$556$	−2.78989e11	−	4.83223e11i	−0.123808	−	0.214443i
$557$	1.97569e12	−	1.14066e12i	0.869701	−	0.502122i	0.00245229	−	0.999997i	$-0.499219\pi$
$557$	1.97569e12	−	1.14066e12i	0.869701	−	0.502122i	0.867249	+	0.497875i	$0.165886\pi$
$558$	−1.56150e12			−0.681847
$559$	−1.57514e12	−	6.04580e11i	−0.682285	−	0.261879i
$560$	−1.31302e11			−0.0564188
$561$	3.05766e11	−	1.76534e11i	0.130334	−	0.0752482i
$562$	1.47787e12	+	2.55975e12i	0.624919	+	1.08239i
$563$	6.97767e11	−	1.20857e12i	0.292700	−	0.506971i	−0.681747	−	0.731588i	$-0.738780\pi$
$563$	6.97767e11	−	1.20857e12i	0.292700	−	0.506971i	0.974447	+	0.224617i	$0.0721130\pi$
$564$			2.79955e11i			0.116502i
$565$	−6.41316e10	−	3.70264e10i	−0.0264761	−	0.0152860i
$566$	−3.37560e12	−	1.94890e12i	−1.38254	−	0.798208i
$567$			1.07546e12i			0.436990i
$568$	6.41077e11	−	1.11038e12i	0.258430	−	0.447614i
$569$	−1.87466e12	−	3.24701e12i	−0.749752	−	1.29861i	−0.947942	−	0.318444i	$-0.896840\pi$
$569$	−1.87466e12	−	3.24701e12i	−0.749752	−	1.29861i	0.198190	−	0.980164i	$-0.436494\pi$
$570$	5.64385e11	−	3.25848e11i	0.223944	−	0.129294i
$571$	−1.70668e12			−0.671877			−0.335938	−	0.941884i	$-0.609053\pi$
$571$	−1.70668e12			−0.671877			−0.335938	+	0.941884i	$0.609053\pi$
$572$	−3.56048e11	+	5.64045e10i	−0.139068	+	0.0220309i
$573$	4.05612e12			1.57186
$574$	−1.40356e12	+	8.10344e11i	−0.539668	+	0.311577i
$575$	9.04022e11	+	1.56581e12i	0.344884	+	0.597357i
$576$	7.65880e11	−	1.32654e12i	0.289908	−	0.502135i
$577$			1.74487e12i			0.655349i	0.944791	+	0.327675i	$0.106265\pi$
$577$			1.74487e12i			0.655349i	−0.944791	+	0.327675i	$0.893735\pi$
$578$	−2.48324e12	−	1.43370e12i	−0.925428	−	0.534296i
$579$	−5.53666e12	−	3.19659e12i	−2.04736	−	1.18204i
$580$		−	5.56790e10i		−	0.0204299i
$581$	−1.65438e11	+	2.86546e11i	−0.0602340	+	0.104328i
$582$	−4.23374e11	−	7.33305e11i	−0.152958	−	0.264930i
$583$	−1.06768e12	+	6.16428e11i	−0.382767	+	0.220991i
$584$	1.23253e12			0.438471
$585$	−1.05037e11	+	2.73658e11i	−0.0370802	+	0.0966067i
$586$	9.80889e11			0.343622
$587$	−1.81591e12	+	1.04842e12i	−0.631283	+	0.364471i	−0.781249	−	0.624220i	$-0.785417\pi$
$587$	−1.81591e12	+	1.04842e12i	−0.631283	+	0.364471i	0.149966	+	0.988691i	$0.452084\pi$
$588$	5.71243e10	+	9.89422e10i	0.0197071	+	0.0341337i
$589$	1.53620e12	−	2.66077e12i	0.525930	−	0.910938i
$590$		−	9.40512e10i		−	0.0319544i
$591$	−1.89223e12	−	1.09248e12i	−0.638013	−	0.368357i
$592$	1.04976e12	+	6.06080e11i	0.351271	+	0.202807i
$593$		−	3.25580e12i		−	1.08121i	−0.841275	−	0.540607i	$-0.818195\pi$
$593$		−	3.25580e12i		−	1.08121i	0.841275	−	0.540607i	$-0.181805\pi$
$594$	−2.97360e11	+	5.15043e11i	−0.0980041	+	0.169748i
$595$	1.21049e10	+	2.09663e10i	0.00395945	+	0.00685796i
$596$	−1.43154e11	+	8.26497e10i	−0.0464723	+	0.0268308i
$597$	3.50249e12			1.12848
$598$	−8.62794e11	+	2.24788e12i	−0.275900	+	0.718816i
$599$	2.64369e12			0.839054			0.419527	−	0.907743i	$-0.362196\pi$
$599$	2.64369e12			0.839054			0.419527	+	0.907743i	$0.362196\pi$
$600$	3.17069e12	−	1.83060e12i	0.998788	−	0.576650i
$601$	−2.13281e12	−	3.69413e12i	−0.666832	−	1.15499i	−0.978785	−	0.204890i	$-0.934316\pi$
$601$	−2.13281e12	−	3.69413e12i	−0.666832	−	1.15499i	0.311953	−	0.950098i	$-0.399017\pi$
$602$	−4.88606e11	+	8.46290e11i	−0.151626	+	0.262624i
$603$			1.11989e12i			0.344944i
$604$	9.76490e11	+	5.63777e11i	0.298539	+	0.172362i
$605$	−1.93946e11	−	1.11975e11i	−0.0588546	−	0.0339797i
$606$			6.93289e12i			2.08828i
$607$	−6.60554e11	+	1.14411e12i	−0.197496	+	0.342074i	−0.947716	−	0.319115i	$-0.896614\pi$
$607$	−6.60554e11	+	1.14411e12i	−0.197496	+	0.342074i	0.750220	+	0.661189i	$0.229948\pi$
$608$	−9.30583e11	−	1.61182e12i	−0.276178	−	0.478354i
$609$	1.15805e12	−	6.68603e11i	0.341155	−	0.196966i
$610$	3.02399e11			0.0884293
$611$	1.43676e12	−	2.27609e11i	0.417060	−	0.0660700i
$612$	9.37815e10			0.0270231
$613$	−3.15104e12	+	1.81925e12i	−0.901325	+	0.520380i	−0.877630	−	0.479339i	$-0.840876\pi$
$613$	−3.15104e12	+	1.81925e12i	−0.901325	+	0.520380i	−0.0236952	+	0.999719i	$0.507543\pi$
$614$	1.47043e12	+	2.54686e12i	0.417530	+	0.723183i
$615$	−4.59459e11	+	7.95806e11i	−0.129512	+	0.224321i
$616$		−	8.08307e11i		−	0.226185i
$617$	−4.66851e12	−	2.69537e12i	−1.29687	−	0.748747i	−0.317005	−	0.948424i	$-0.602677\pi$
$617$	−4.66851e12	−	2.69537e12i	−1.29687	−	0.748747i	−0.979862	+	0.199677i	$0.936011\pi$
$618$	−4.83207e12	−	2.78980e12i	−1.33255	−	0.769351i
$619$			3.11485e12i			0.852766i	0.904543	+	0.426383i	$0.140212\pi$
$619$			3.11485e12i			0.852766i	−0.904543	+	0.426383i	$0.859788\pi$
$620$	3.73301e10	−	6.46576e10i	0.0101460	−	0.0175735i
$621$	3.38277e11	+	5.85913e11i	0.0912767	+	0.158096i
$622$	5.88305e12	−	3.39658e12i	1.57596	−	0.909882i
$623$	−2.06515e12			−0.549233
$624$	5.52737e12	+	2.12155e12i	1.45945	+	0.560173i
$625$	3.62725e12			0.950863
$626$	1.73447e12	−	1.00140e12i	0.451421	−	0.260628i
$627$	2.43586e12	+	4.21903e12i	0.629432	+	1.09021i
$628$	−6.42659e11	+	1.11312e12i	−0.164878	+	0.285577i
$629$		−	2.23501e11i		−	0.0569315i
$630$	1.47031e11	+	8.48883e10i	0.0371857	+	0.0214692i
$631$	−2.59795e12	−	1.49993e12i	−0.652377	−	0.376650i	0.136989	−	0.990573i	$-0.456257\pi$
$631$	−2.59795e12	−	1.49993e12i	−0.652377	−	0.376650i	−0.789366	+	0.613923i	$0.789591\pi$
$632$			2.18060e12i			0.543687i
$633$	−3.42674e12	+	5.93528e12i	−0.848328	+	1.46935i
$634$	−1.93012e12	−	3.34307e12i	−0.474442	−	0.821758i
$635$	−4.31013e11	+	2.48846e11i	−0.105198	+	0.0607363i
$636$	−7.33596e11			−0.177787
$637$	4.61339e11	−	3.73610e11i	0.111018	−	0.0899066i
$638$	2.44379e12			0.583945
$639$	−1.74345e12	+	1.00658e12i	−0.413672	+	0.238834i
$640$	3.25161e11	+	5.63195e11i	0.0766105	+	0.132693i
$641$	9.28950e11	−	1.60899e12i	0.217336	−	0.376437i	−0.736657	−	0.676267i	$-0.763597\pi$
$641$	9.28950e11	−	1.60899e12i	0.217336	−	0.376437i	0.953993	+	0.299830i	$0.0969300\pi$
$642$			8.92121e12i			2.07260i
$643$	−1.50634e12	−	8.69685e11i	−0.347515	−	0.200638i	0.316075	−	0.948734i	$-0.397635\pi$
$643$	−1.50634e12	−	8.69685e11i	−0.347515	−	0.200638i	−0.663590	+	0.748096i	$0.730968\pi$
$644$	2.05701e11	+	1.18762e11i	0.0471249	+	0.0272076i
$645$			5.54072e11i			0.126051i
$646$	−5.41701e11	+	9.38253e11i	−0.122381	+	0.211970i
$647$	2.63367e12	+	4.56166e12i	0.590871	+	1.02342i	0.994115	+	0.108327i	$0.0345492\pi$
$647$	2.63367e12	+	4.56166e12i	0.590871	+	1.02342i	−0.403244	+	0.915092i	$0.632117\pi$
$648$	3.92099e12	−	2.26378e12i	0.873590	−	0.504367i
$649$	7.03075e11			0.155561
$650$	3.09266e12	+	3.81886e12i	0.679551	+	0.839119i
$651$	1.79306e12			0.391275
$652$	9.90853e11	−	5.72069e11i	0.214731	−	0.123975i
$653$	−1.15555e12	−	2.00147e12i	−0.248702	−	0.430765i	0.714464	−	0.699673i	$-0.246671\pi$
$653$	−1.15555e12	−	2.00147e12i	−0.248702	−	0.430765i	−0.963166	+	0.268907i	$0.913337\pi$
$654$	−5.39617e12	+	9.34644e12i	−1.15342	+	1.99777i
$655$			1.33147e11i			0.0282647i
$656$	7.17515e12	+	4.14257e12i	1.51274	+	0.873379i
$657$	−1.67598e12	−	9.67626e11i	−0.350933	−	0.202611i
$658$		−	8.42545e11i		−	0.175217i
$659$	−9.55399e11	+	1.65480e12i	−0.197333	+	0.341791i	−0.947663	−	0.319273i	$-0.896561\pi$
$659$	−9.55399e11	+	1.65480e12i	−0.197333	+	0.341791i	0.750330	+	0.661064i	$0.229895\pi$
$660$	5.91922e10	+	1.02524e11i	0.0121427	+	0.0210319i
$661$	4.25986e12	−	2.45943e12i	0.867938	−	0.501104i	0.00127545	−	0.999999i	$-0.499594\pi$
$661$	4.25986e12	−	2.45943e12i	0.867938	−	0.501104i	0.866662	+	0.498895i	$0.166261\pi$
$662$	−8.18659e12			−1.65669
$663$	−1.70807e11	−	1.07820e12i	−0.0343316	−	0.216715i
$664$	1.39294e12			0.278085
$665$	−2.89298e11	+	1.67026e11i	−0.0573651	+	0.0331197i
$666$	−7.83677e11	−	1.35737e12i	−0.154349	−	0.267340i
$667$	1.39003e12	−	2.40760e12i	0.271930	−	0.470997i
$668$		−	3.49863e11i		−	0.0679835i
$669$	−1.14567e12	−	6.61452e11i	−0.221127	−	0.127668i
$670$	−2.72265e11	−	1.57192e11i	−0.0521982	−	0.0301366i
$671$			2.26057e12i			0.430493i
$672$	5.43093e11	−	9.40665e11i	0.102734	−	0.177940i
$673$	−4.73852e12	−	8.20736e12i	−0.890379	−	1.54218i	−0.839422	−	0.543481i	$-0.817106\pi$
$673$	−4.73852e12	−	8.20736e12i	−0.890379	−	1.54218i	−0.0509571	−	0.998701i	$-0.516227\pi$
$674$	1.21197e12	−	6.99732e11i	0.226216	−	0.130606i
$675$	1.38079e12			0.256013
$676$	−2.31663e11	+	1.09024e12i	−0.0426675	+	0.200800i
$677$	1.61057e12			0.294666			0.147333	−	0.989087i	$-0.452931\pi$
$677$	1.61057e12			0.294666			0.147333	+	0.989087i	$0.452931\pi$
$678$	1.67490e12	−	9.67005e11i	0.304408	−	0.175750i
$679$	2.17017e11	+	3.75884e11i	0.0391814	+	0.0678641i
$680$	5.09601e10	−	8.82656e10i	0.00913988	−	0.0158307i
$681$		−	6.69362e12i		−	1.19261i
$682$	2.83787e12	+	1.63845e12i	0.502300	+	0.290003i
$683$	−5.07533e12	−	2.93024e12i	−0.892424	−	0.515241i	−0.0176895	−	0.999844i	$-0.505631\pi$
$683$	−5.07533e12	−	2.93024e12i	−0.892424	−	0.515241i	−0.874735	+	0.484602i	$0.838964\pi$
$684$			1.29402e12i			0.226041i
$685$	−2.88751e11	+	5.00131e11i	−0.0501090	+	0.0867914i
$686$	−1.71920e11	−	2.97774e11i	−0.0296393	−	0.0513367i
$687$	−1.10074e13	+	6.35511e12i	−1.88529	+	1.08847i
$688$	4.99562e12			0.850044
$689$	5.96428e11	+	3.76489e12i	0.100826	+	0.636453i
$690$	7.90714e11			0.132800
$691$	−5.90091e12	+	3.40689e12i	−0.984619	+	0.568470i	−0.903661	−	0.428248i	$-0.859131\pi$
$691$	−5.90091e12	+	3.40689e12i	−0.984619	+	0.568470i	−0.0809572	+	0.996718i	$0.525798\pi$
$692$	−8.82751e11	−	1.52897e12i	−0.146339	−	0.253467i
$693$	−6.34578e11	+	1.09912e12i	−0.104517	+	0.181028i
$694$			3.84196e12i			0.628687i
$695$	8.24574e11	+	4.76068e11i	0.134060	+	0.0773994i
$696$	−4.87527e12	−	2.81474e12i	−0.787512	−	0.454670i
$697$		−	1.52764e12i		−	0.245173i
$698$	3.68000e12	−	6.37395e12i	0.586811	−	1.01639i
$699$	4.42188e12	+	7.65893e12i	0.700584	+	1.21345i
$700$	4.19821e11	−	2.42384e11i	0.0660880	−	0.0381559i
$701$	−7.49605e12			−1.17247			−0.586235	−	0.810141i	$-0.699390\pi$
$701$	−7.49605e12			−1.17247			−0.586235	+	0.810141i	$0.699390\pi$
$702$	1.15725e12	+	1.42898e12i	0.179849	+	0.222080i
$703$	3.08392e12			0.476217
$704$	−2.78383e12	+	1.60725e12i	−0.427136	+	0.246607i
$705$	−2.38858e11	−	4.13715e11i	−0.0364158	−	0.0630740i
$706$	4.18625e12	−	7.25081e12i	0.634168	−	1.09841i
$707$		−	3.55372e12i		−	0.534929i
$708$	3.62307e11	+	2.09178e11i	0.0541910	+	0.0312872i
$709$	5.34843e12	+	3.08792e12i	0.794910	+	0.458942i	0.841688	−	0.539964i	$-0.181562\pi$
$709$	5.34843e12	+	3.08792e12i	0.794910	+	0.458942i	−0.0467782	+	0.998905i	$0.514895\pi$
$710$		−	5.65150e11i		−	0.0834643i
$711$	1.71192e12	−	2.96514e12i	0.251230	−	0.435143i
$712$	4.34703e12	+	7.52927e12i	0.633917	+	1.09798i
$713$	3.22836e12	−	1.86389e12i	0.467820	−	0.270096i
$714$	−6.32278e11			−0.0910472
$715$	4.78040e11	−	3.87135e11i	0.0684048	−	0.0553969i
$716$	1.41588e12			0.201335
$717$	−7.88583e12	+	4.55289e12i	−1.11432	+	0.643355i
$718$	−3.16163e12	−	5.47610e12i	−0.443967	−	0.768973i
$719$	−4.59596e12	+	7.96043e12i	−0.641351	+	1.11085i	0.343780	+	0.939050i	$0.388293\pi$
$719$	−4.59596e12	+	7.96043e12i	−0.641351	+	1.11085i	−0.985131	+	0.171803i	$0.945041\pi$
$720$		−	8.67918e11i		−	0.120360i
$721$	2.47686e12	+	1.43002e12i	0.341345	+	0.197076i
$722$	−6.00410e12	−	3.46647e12i	−0.822301	−	0.474756i
$723$			9.06275e12i			1.23350i
$724$	7.42856e11	−	1.28666e12i	0.100480	−	0.174037i
$725$	−2.83694e12	−	4.91373e12i	−0.381355	−	0.660527i
$726$	5.06521e12	−	2.92440e12i	0.676679	−	0.390681i
$727$	−6.24570e12			−0.829233			−0.414616	−	0.909996i	$-0.636084\pi$
$727$	−6.24570e12			−0.829233			−0.414616	+	0.909996i	$0.636084\pi$
$728$	−2.33322e12	−	8.95552e11i	−0.307868	−	0.118168i
$729$	−4.44116e12			−0.582402
$730$	4.70492e11	−	2.71639e11i	0.0613196	−	0.0354029i
$731$	−4.60554e11	−	7.97702e11i	−0.0596557	−	0.103327i
$732$	−6.72562e11	+	1.16491e12i	−0.0865830	+	0.149966i
$733$			8.32814e11i			0.106557i	0.998580	+	0.0532783i	$0.0169670\pi$
$733$			8.32814e11i			0.106557i	−0.998580	+	0.0532783i	$0.983033\pi$
$734$	−9.59415e12	−	5.53919e12i	−1.22004	−	0.704391i
$735$	−1.68836e11	−	9.74772e10i	−0.0213388	−	0.0123200i
$736$		−	2.25819e12i		−	0.283667i
$737$	1.17508e12	−	2.03530e12i	0.146712	−	0.254112i
$738$	−5.35646e12	−	9.27766e12i	−0.664698	−	1.15129i
$739$	5.93478e12	−	3.42645e12i	0.731989	−	0.422614i	−0.0871604	−	0.996194i	$-0.527779\pi$
$739$	5.93478e12	−	3.42645e12i	0.731989	−	0.422614i	0.819149	+	0.573580i	$0.194446\pi$
$740$	7.49404e10			0.00918699
$741$	1.48773e13	−	2.35683e12i	1.81276	−	0.287175i
$742$	2.20781e12			0.267389
$743$	−5.56578e12	+	3.21340e12i	−0.670002	+	0.386826i	−0.796077	−	0.605195i	$-0.793095\pi$
$743$	−5.56578e12	+	3.21340e12i	−0.670002	+	0.386826i	0.126075	+	0.992021i	$0.459762\pi$
$744$	−3.77429e12	−	6.53727e12i	−0.451604	−	0.782201i
$745$	1.41034e11	−	2.44278e11i	0.0167734	−	0.0290523i
$746$		−	6.12345e12i		−	0.723888i
$747$	−1.89410e12	−	1.09356e12i	−0.222567	−	0.128499i
$748$	−1.70439e11	−	9.84032e10i	−0.0199073	−	0.0114935i
$749$		−	4.57292e12i		−	0.530915i
$750$	1.62730e12	−	2.81856e12i	0.187798	−	0.325276i
$751$	−4.75086e12	−	8.22873e12i	−0.544995	−	0.943958i	−0.998607	−	0.0527594i	$-0.983198\pi$
$751$	−4.75086e12	−	8.22873e12i	−0.544995	−	0.943958i	0.453613	−	0.891199i	$-0.350135\pi$
$752$	−3.73014e12	+	2.15360e12i	−0.425348	+	0.245575i
$753$	1.25677e13			1.42455
$754$	2.70757e12	−	7.05415e12i	0.305076	−	0.794829i
$755$	−1.92406e12			−0.215505
$756$	1.57093e11	−	9.06978e10i	0.0174908	−	0.0100983i
$757$	−3.11333e12	−	5.39245e12i	−0.344583	−	0.596835i	0.640695	−	0.767796i	$-0.278646\pi$
$757$	−3.11333e12	−	5.39245e12i	−0.344583	−	0.596835i	−0.985278	+	0.170960i	$0.945313\pi$
$758$	−1.46269e12	+	2.53345e12i	−0.160931	+	0.278741i
$759$			5.91094e12i			0.646500i
$760$	1.21791e12	+	7.03160e11i	0.132420	+	0.0764527i
$761$	5.91816e12	+	3.41685e12i	0.639670	+	0.369313i	0.784487	−	0.620145i	$-0.212926\pi$
$761$	5.91816e12	+	3.41685e12i	0.639670	+	0.369313i	−0.144818	+	0.989458i	$0.546260\pi$
$762$		−	1.29980e13i		−	1.39663i
$763$	2.76602e12	−	4.79088e12i	0.295457	−	0.511747i
$764$	−1.13047e12	−	1.95804e12i	−0.120044	−	0.207922i
$765$	−1.38589e11	+	8.00146e10i	−0.0146303	+	0.00844682i
$766$	9.23969e12			0.969679
$767$	7.78962e11	−	2.02947e12i	0.0812713	−	0.211740i
$768$	−7.66664e12			−0.795205
$769$	−1.62515e12	+	9.38282e11i	−0.167581	+	0.0967531i	−0.581445	−	0.813586i	$-0.697512\pi$
$769$	−1.62515e12	+	9.38282e11i	−0.167581	+	0.0967531i	0.413864	+	0.910339i	$0.364179\pi$
$770$	−1.78143e11	−	3.08553e11i	−0.0182625	−	0.0316317i
$771$	−5.55092e12	+	9.61447e12i	−0.565744	+	0.979897i
$772$			3.56367e12i			0.361093i
$773$	2.79331e12	+	1.61272e12i	0.281391	+	0.162461i	0.634053	−	0.773290i	$-0.281390\pi$
$773$	2.79331e12	+	1.61272e12i	0.281391	+	0.162461i	−0.352662	+	0.935751i	$0.614723\pi$
$774$	−5.59407e12	−	3.22974e12i	−0.560265	−	0.323469i
$775$		−	7.60814e12i		−	0.757566i
$776$	9.13615e11	−	1.58243e12i	0.0904452	−	0.156656i
$777$	8.99897e11	+	1.55867e12i	0.0885723	+	0.153412i
$778$	−2.41381e12	+	1.39361e12i	−0.236208	+	0.136375i
$779$	2.10787e13			2.05081
$780$	3.61522e11	−	5.72717e10i	0.0349711	−	0.00554006i
$781$	4.22475e12			0.406323
$782$	−1.13840e12	+	6.57255e11i	−0.108859	+	0.0628497i
$783$	−1.06156e12	−	1.83867e12i	−0.100929	−	0.174814i
$784$	−8.78875e11	+	1.52226e12i	−0.0830816	+	0.143902i
$785$		−	2.19327e12i		−	0.206148i
$786$	−3.01147e12	−	1.73867e12i	−0.281434	−	0.162486i
$787$	−6.56224e11	−	3.78871e11i	−0.0609770	−	0.0352051i	0.469202	−	0.883091i	$-0.344542\pi$
$787$	−6.56224e11	−	3.78871e11i	−0.0609770	−	0.0352051i	−0.530179	+	0.847886i	$0.677875\pi$
$788$			1.21793e12i			0.112526i
$789$	9.45345e12	−	1.63739e13i	0.868448	−	1.50420i
$790$	4.80584e11	+	8.32395e11i	0.0438982	+	0.0760340i
$791$	−8.58536e11	+	4.95676e11i	−0.0779766	+	0.0450198i
$792$	5.34300e12			0.482527
$793$	6.52526e12	+	2.50457e12i	0.585961	+	0.224907i
$794$	3.22504e12			0.287967
$795$	1.08410e12	−	6.25906e11i	0.0962537	−	0.0555721i
$796$	−9.76172e11	−	1.69078e12i	−0.0861822	−	0.149272i
$797$	3.88621e12	−	6.73112e12i	0.341165	−	0.590915i	−0.643485	−	0.765459i	$-0.722512\pi$
$797$	3.88621e12	−	6.73112e12i	0.341165	−	0.590915i	0.984649	+	0.174544i	$0.0558452\pi$
$798$		−	8.72432e12i		−	0.761586i
$799$	6.87773e11	+	3.97086e11i	0.0597015	+	0.0344686i
$800$	−3.99133e12	−	2.30439e12i	−0.344518	−	0.198908i
$801$		−	1.36509e13i		−	1.17170i
$802$	−3.58630e12	+	6.21165e12i	−0.306099	+	0.530179i
$803$	2.03062e12	+	3.51714e12i	0.172349	+	0.298518i
$804$	1.21108e12	−	6.99219e11i	0.102217	−	0.0590148i
$805$	−4.05311e11			−0.0340179
$806$	7.87365e12	−	6.37639e12i	0.657156	−	0.532190i
$807$	3.90465e11			0.0324079
$808$	−1.29564e13	+	7.48038e12i	−1.06938	+	0.617408i
$809$	−4.17529e12	−	7.23182e12i	−0.342703	−	0.593580i	0.642230	−	0.766512i	$-0.278009\pi$
$809$	−4.17529e12	−	7.23182e12i	−0.342703	−	0.593580i	−0.984934	+	0.172932i	$0.944676\pi$
$810$	9.97833e11	−	1.72830e12i	0.0814470	−	0.141070i
$811$			1.57249e13i			1.27642i	0.769861	+	0.638212i	$0.220326\pi$
$811$			1.57249e13i			1.27642i	−0.769861	+	0.638212i	$0.779674\pi$
$812$	−6.45519e11	−	3.72690e11i	−0.0521083	−	0.0300847i
$813$	1.97297e13	+	1.13909e13i	1.58384	+	0.914432i
$814$			3.28919e12i			0.262591i
$815$	−9.76182e11	+	1.69080e12i	−0.0775035	+	0.134240i
$816$	1.61614e12	+	2.79924e12i	0.127607	+	0.221021i
$817$	1.10069e13	−	6.35482e12i	0.864301	−	0.499004i
$818$	−1.99702e13			−1.55953
$819$	2.46960e12	+	3.04950e12i	0.191801	+	0.236838i
$820$	5.12220e11			0.0395634
$821$	6.04398e12	−	3.48950e12i	0.464279	−	0.268052i	−0.249563	−	0.968359i	$-0.580287\pi$
$821$	6.04398e12	−	3.48950e12i	0.464279	−	0.268052i	0.713842	+	0.700307i	$0.246954\pi$
$822$	−7.54121e12	−	1.30618e13i	−0.576126	−	0.997880i
$823$	−2.80591e12	+	4.85998e12i	−0.213194	+	0.369262i	−0.952712	−	0.303874i	$-0.901720\pi$
$823$	−2.80591e12	+	4.85998e12i	−0.213194	+	0.369262i	0.739519	+	0.673136i	$0.235053\pi$
$824$		−	1.20404e13i		−	0.909848i
$825$	1.04475e13	+	6.03189e12i	0.785184	+	0.453326i
$826$	−1.09039e12	−	6.29537e11i	−0.0815026	−	0.0470555i
$827$			1.18516e13i			0.881053i	0.897740	+	0.440526i	$0.145208\pi$
$827$			1.18516e13i			0.881053i	−0.897740	+	0.440526i	$0.854792\pi$
$828$	−7.85028e11	+	1.35971e12i	−0.0580428	+	0.100533i
$829$	1.13143e13	+	1.95969e13i	0.832015	+	1.44109i	0.896438	+	0.443170i	$0.146146\pi$
$829$	1.13143e13	+	1.95969e13i	0.832015	+	1.44109i	−0.0644228	+	0.997923i	$0.520521\pi$
$830$	5.31726e11	−	3.06992e11i	0.0388899	−	0.0224531i
$831$	3.62962e12			0.264032
$832$	1.55510e12	+	9.81642e12i	0.112513	+	0.710228i
$833$	3.24099e11			0.0233225
$834$	−2.15351e13	+	1.24333e13i	−1.54135	+	0.889896i
$835$	2.98504e11	+	5.17024e11i	0.0212501	+	0.0368062i
$836$	1.35779e12	−	2.35176e12i	0.0961400	−	0.166519i
$837$		−	2.84690e12i		−	0.200497i
$838$	1.68159e13	+	9.70865e12i	1.17794	+	0.680081i
$839$	1.82164e13	+	1.05173e13i	1.26921	+	0.732780i	0.974839	−	0.222910i	$-0.0715556\pi$
$839$	1.82164e13	+	1.05173e13i	1.26921	+	0.732780i	0.294374	+	0.955690i	$0.404889\pi$
$840$			8.20735e11i			0.0568782i
$841$	2.89147e12	−	5.00818e12i	0.199314	−	0.345221i
$842$	−6.31953e12	−	1.09458e13i	−0.433292	−	0.750483i
$843$	1.94295e13	−	1.12176e13i	1.32507	−	0.765028i
$844$	3.82024e12			0.259149
$845$	−5.87850e11	−	1.80881e12i	−0.0396653	−	0.122050i
$846$	5.56931e12			0.373796
$847$	−2.59637e12	+	1.49901e12i	−0.173337	+	0.100076i
$848$	−5.64329e12	−	9.77447e12i	−0.374758	−	0.649101i
$849$	−1.47929e13	+	2.56221e13i	−0.977168	+	1.69250i
$850$			2.68281e12i			0.176281i
$851$	3.24047e12	+	1.87089e12i	0.211800	+	0.122283i
$852$	2.17709e12	+	1.25694e12i	0.141546	+	0.0817216i
$853$			1.53468e13i			0.992540i	0.868168	+	0.496270i	$0.165297\pi$
$853$			1.53468e13i			0.992540i	−0.868168	+	0.496270i	$0.834703\pi$
$854$	2.02412e12	−	3.50589e12i	0.130220	−	0.225547i
$855$	−1.10406e12	−	1.91229e12i	−0.0706554	−	0.122379i
$856$	−1.66722e13	+	9.62571e12i	−1.06136	+	0.612775i
$857$	−4.83134e12			−0.305952			−0.152976	−	0.988230i	$-0.548886\pi$
$857$	−4.83134e12			−0.305952			−0.152976	+	0.988230i	$0.548886\pi$
$858$	2.51370e12	+	1.58675e13i	0.158351	+	0.999575i
$859$	−2.11836e13			−1.32749			−0.663744	−	0.747960i	$-0.731034\pi$
$859$	−2.11836e13			−1.32749			−0.663744	+	0.747960i	$0.731034\pi$
$860$	2.67471e11	−	1.54424e11i	0.0166738	−	0.00962660i
$861$	6.15082e12	+	1.06535e13i	0.381434	+	0.660662i
$862$	−3.83688e12	+	6.64567e12i	−0.236699	+	0.409974i
$863$			2.07145e13i			1.27124i	0.772003	+	0.635619i	$0.219255\pi$
$863$			2.07145e13i			1.27124i	−0.772003	+	0.635619i	$0.780745\pi$
$864$	−1.49352e12	−	8.62283e11i	−0.0911798	−	0.0526427i
$865$	2.60904e12	+	1.50633e12i	0.158456	+	0.0914846i
$866$		−	2.57278e12i		−	0.155444i
$867$	−1.08823e13	+	1.88487e13i	−0.654087	+	1.13291i
$868$	−4.99742e11	−	8.65579e11i	−0.0298818	−	0.0517568i
$869$	−6.22253e12	+	3.59258e12i	−0.370150	+	0.213706i
$870$	−2.48137e12			−0.146843
$871$	−4.57310e12	−	5.64693e12i	−0.269234	−	0.332453i
$872$	−2.32892e13			−1.36405
$873$	−2.48464e12	+	1.43450e12i	−0.144777	+	0.0835868i
$874$	−9.06895e12	−	1.57079e13i	−0.525721	−	0.910576i
$875$	−8.34135e11	+	1.44477e12i	−0.0481061	+	0.0833222i
$876$			2.41659e12i			0.138655i
$877$	−8.12181e12	−	4.68913e12i	−0.463612	−	0.267667i	0.249950	−	0.968259i	$-0.419586\pi$
$877$	−8.12181e12	−	4.68913e12i	−0.463612	−	0.267667i	−0.713562	+	0.700592i	$0.752919\pi$
$878$	−2.13367e13	−	1.23188e13i	−1.21172	−	0.699587i
$879$		−	7.44533e12i		−	0.420663i
$880$	−9.10690e11	+	1.57736e12i	−0.0511916	+	0.0886664i
$881$	−1.39375e13	−	2.41405e13i	−0.779460	−	1.35007i	−0.932253	−	0.361807i	$-0.882160\pi$
$881$	−1.39375e13	−	2.41405e13i	−0.779460	−	1.35007i	0.152793	−	0.988258i	$-0.451173\pi$
$882$	1.96832e12	−	1.13641e12i	0.109518	−	0.0632304i
$883$	−5.70300e12			−0.315704			−0.157852	−	0.987463i	$-0.550457\pi$
$883$	−5.70300e12			−0.315704			−0.157852	+	0.987463i	$0.550457\pi$
$884$	−4.72882e11	+	3.82958e11i	−0.0260446	+	0.0210919i
$885$	−7.13885e11			−0.0391186
$886$	−2.12739e13	+	1.22825e13i	−1.15983	+	0.669631i
$887$	−1.70873e13	−	2.95961e13i	−0.926866	−	1.60538i	−0.788532	−	0.614994i	$-0.789159\pi$
$887$	−1.70873e13	−	2.95961e13i	−0.926866	−	1.60538i	−0.138334	−	0.990386i	$-0.544175\pi$
$888$	3.78846e12	−	6.56180e12i	0.204458	−	0.354132i
$889$			6.66265e12i			0.357758i
$890$	3.31876e12	+	1.91609e12i	0.177305	+	0.102367i
$891$	1.29198e13	+	7.45925e12i	0.686762	+	0.396502i
$892$			7.37409e11i			0.0390002i
$893$	−5.47909e12	+	9.49005e12i	−0.288321	+	0.499387i
$894$	3.68333e12	+	6.37972e12i	0.192851	+	0.334028i
$895$	−2.09238e12	+	1.20803e12i	−0.109002	+	0.0629326i
$896$	8.70593e12			0.451262
$897$	1.70623e13	+	6.54894e12i	0.879976	+	0.337758i
$898$	−9.24501e12			−0.474421
$899$	−1.01310e13	+	5.84916e12i	−0.517291	+	0.298658i
$900$	1.60218e12	+	2.77506e12i	0.0813993	+	0.140988i
$901$	−1.04053e12	+	1.80225e12i	−0.0526007	+	0.0911071i
$902$			2.24817e13i			1.13084i
$903$	6.42367e12	+	3.70871e12i	0.321505	+	0.185621i
$904$	3.61433e12	+	2.08674e12i	0.179999	+	0.103923i
$905$			2.53523e12i			0.125631i
$906$	2.51250e13	−	4.35178e13i	1.23888	−	2.14581i
$907$	−9.51725e11	−	1.64844e12i	−0.0466959	−	0.0808797i	0.841733	−	0.539894i	$-0.181536\pi$
$907$	−9.51725e11	−	1.64844e12i	−0.0466959	−	0.0808797i	−0.888429	+	0.459015i	$0.848203\pi$
$908$	−3.23126e12	+	1.86557e12i	−0.157756	+	0.0910804i
$909$	2.34905e13			1.14118
$910$	−1.08803e12	+	1.72364e11i	−0.0525961	+	0.00833219i
$911$	−2.08032e13			−1.00068			−0.500342	−	0.865828i	$-0.666792\pi$
$911$	−2.08032e13			−1.00068			−0.500342	+	0.865828i	$0.666792\pi$
$912$	−3.86245e13	+	2.22999e13i	−1.84879	+	1.06740i
$913$	2.29490e12	+	3.97489e12i	0.109306	+	0.189324i
$914$	−1.48664e13	+	2.57494e13i	−0.704610	+	1.22042i
$915$		−	2.29533e12i		−	0.108255i
$916$	6.13569e12	+	3.54244e12i	0.287961	+	0.166254i
$917$	1.54364e12	+	8.91223e11i	0.0720917	+	0.0416222i
$918$			1.00389e12i			0.0466543i
$919$	−1.43745e13	+	2.48973e13i	−0.664770	+	1.15142i	0.314578	+	0.949232i	$0.398137\pi$
$919$	−1.43745e13	+	2.48973e13i	−0.664770	+	1.15142i	−0.979348	+	0.202184i	$0.935196\pi$
$920$	8.53156e11	+	1.47771e12i	0.0392630	+	0.0680055i
$921$	1.93317e13	−	1.11612e13i	0.885322	−	0.511141i
$922$	2.95062e13			1.34470
$923$	4.68075e12	−	1.21950e13i	0.212279	−	0.553061i
$924$	1.58483e12			0.0715249
$925$	6.61356e12	−	3.81834e12i	0.297028	−	0.171489i
$926$	1.28446e12	+	2.22476e12i	0.0574080	+	0.0994336i
$927$	−9.45258e12	+	1.63723e13i	−0.420428	+	0.728202i
$928$			7.08650e12i			0.313665i
$929$	1.90096e13	+	1.09752e13i	0.837342	+	0.483439i	0.856360	−	0.516380i	$-0.172721\pi$
$929$	1.90096e13	+	1.09752e13i	0.837342	+	0.483439i	−0.0190181	+	0.999819i	$0.506054\pi$
$930$	−2.88151e12	−	1.66364e12i	−0.126312	−	0.0729265i
$931$			4.47199e12i			0.195087i
$932$	2.46483e12	−	4.26921e12i	0.107008	−	0.185343i
$933$	−2.57814e13	−	4.46546e13i	−1.11388	−	1.92930i
$934$	2.97696e13	−	1.71875e13i	1.28001	−	0.739011i
$935$	3.35831e11			0.0143704
$936$	5.91970e12	−	1.54229e13i	0.252091	−	0.656786i
$937$	−3.27433e13			−1.38770			−0.693848	−	0.720122i	$-0.744086\pi$
$937$	−3.27433e13			−1.38770			−0.693848	+	0.720122i	$0.744086\pi$
$938$	−3.64484e12	+	2.10435e12i	−0.153733	+	0.0887575i
$939$	−7.60098e12	−	1.31653e13i	−0.319062	−	0.552631i
$940$	−1.33144e11	+	2.30611e11i	−0.00556218	+	0.00963398i
$941$		−	2.24756e13i		−	0.934452i	−0.884138	−	0.467226i	$-0.845253\pi$
$941$		−	2.24756e13i		−	0.934452i	0.884138	−	0.467226i	$-0.154747\pi$
$942$	4.96068e13	+	2.86405e13i	2.05264	+	1.18509i
$943$	2.21487e13	+	1.27876e13i	0.912108	+	0.526606i
$944$			6.43653e12i			0.263802i
$945$	−1.54767e11	+	2.68065e11i	−0.00631300	+	0.0109344i
$946$	6.77780e12	+	1.17395e13i	0.275156	+	0.476584i
$947$	−4.01303e13	+	2.31692e13i	−1.62143	+	0.936131i	−0.634888	+	0.772604i	$0.718954\pi$
$947$	−4.01303e13	+	2.31692e13i	−1.62143	+	0.936131i	−0.986539	+	0.163527i	$0.947713\pi$
$948$	−4.27544e12			−0.171927
$949$	1.24022e13	−	1.96474e12i	0.496366	−	0.0786334i
$950$	−3.70181e13			−1.47454
$951$	−2.53752e13	+	1.46504e13i	−1.00600	+	0.580814i
$952$	−6.82209e11	−	1.18162e12i	−0.0269185	−	0.0466242i
$953$	−1.48359e13	+	2.56965e13i	−0.582634	+	1.00915i	0.412532	+	0.910943i	$0.364644\pi$
$953$	−1.48359e13	+	2.56965e13i	−0.582634	+	1.00915i	−0.995166	+	0.0982084i	$0.968689\pi$
$954$			1.45939e13i			0.570430i
$955$	3.34121e12	+	1.92905e12i	0.129984	+	0.0750461i
$956$	4.39569e12	+	2.53786e12i	0.170203	+	0.0982667i
$957$		−	1.85493e13i		−	0.714866i
$958$	−1.58364e12	+	2.74295e12i	−0.0607452	+	0.105214i
$959$	3.86554e12	+	6.69531e12i	0.147580	+	0.255615i
$960$	2.82664e12	−	1.63196e12i	0.107411	−	0.0620139i
$961$	1.07533e13			0.406712
$962$	9.49443e12	+	3.64421e12i	0.357422	+	0.137188i
$963$	3.02275e13			1.13262
$964$	4.37492e12	−	2.52586e12i	0.163164	−	0.0942027i
$965$	−3.04053e12	−	5.26635e12i	−0.112869	−	0.195496i
$966$	5.29268e12	−	9.16720e12i	0.195560	−	0.338719i
$967$			5.02375e13i			1.84761i	0.382869	+	0.923803i	$0.374936\pi$
$967$			5.02375e13i			1.84761i	−0.382869	+	0.923803i	$0.625064\pi$
$968$	1.09304e13	+	6.31067e12i	0.400126	+	0.231013i
$969$	7.12170e12	+	4.11172e12i	0.259494	+	0.149819i
$970$		−	8.05409e11i		−	0.0292108i
$971$	1.94547e13	−	3.36966e13i	0.702325	−	1.21646i	−0.265323	−	0.964160i	$-0.585479\pi$
$971$	1.94547e13	−	3.36966e13i	0.702325	−	1.21646i	0.967648	−	0.252304i	$-0.0811882\pi$
$972$	3.69501e12	+	6.39994e12i	0.132775	+	0.229973i
$973$	1.10387e13	−	6.37318e12i	0.394829	−	0.227954i
$974$	3.62021e13			1.28890
$975$	2.89866e13	−	2.34745e13i	1.02725	−	0.831908i
$976$	−2.06951e13			−0.730035
$977$	1.96870e13	−	1.13663e13i	0.691280	−	0.399111i	−0.112812	−	0.993616i	$-0.535986\pi$
$977$	1.96870e13	−	1.13663e13i	0.691280	−	0.399111i	0.804091	+	0.594506i	$0.202652\pi$
$978$	−2.54946e13	−	4.41579e13i	−0.891093	−	1.54342i
$979$	−1.43236e13	+	2.48092e13i	−0.498346	+	0.863160i
$980$			1.08671e11i			0.00376353i
$981$	3.16683e13	+	1.82837e13i	1.09173	+	0.630308i
$982$	9.37673e12	+	5.41366e12i	0.321773	+	0.185776i
$983$		−	2.94588e13i		−	1.00629i	−0.864201	−	0.503146i	$-0.832176\pi$
$983$		−	2.94588e13i		−	1.00629i	0.864201	−	0.503146i	$-0.167824\pi$
$984$	2.58942e13	−	4.48501e13i	0.880491	−	1.52505i
$985$	−1.03914e12	−	1.79985e12i	−0.0351732	−	0.0609217i
$986$	3.57245e12	−	2.06256e12i	0.120371	−	0.0694959i
$987$	−6.39524e12			−0.214501
$988$	−5.28414e12	−	6.52493e12i	−0.176428	−	0.217856i
$989$	1.54208e13			0.512536
$990$	2.03957e12	−	1.17755e12i	0.0674808	−	0.0389601i
$991$	−2.06408e13	−	3.57509e13i	−0.679821	−	1.17748i	−0.975035	−	0.222053i	$-0.928724\pi$
$991$	−2.06408e13	−	3.57509e13i	−0.679821	−	1.17748i	0.295214	−	0.955431i	$-0.404609\pi$
$992$	−4.75115e12	+	8.22924e12i	−0.155775	+	0.269810i
$993$			6.21394e13i			2.02813i
$994$	−6.55210e12	−	3.78286e12i	−0.212884	−	0.122908i
$995$	2.88516e12	+	1.66575e12i	0.0933180	+	0.0538772i
$996$			2.73111e12i			0.0879370i
$997$	1.03024e13	−	1.78443e13i	0.330225	−	0.571967i	−0.652330	−	0.757935i	$-0.726209\pi$
$997$	1.03024e13	−	1.78443e13i	0.330225	−	0.571967i	0.982556	+	0.185967i	$0.0595419\pi$
$998$	1.83275e13	+	3.17441e13i	0.584810	+	1.01292i
$999$	2.47474e12	−	1.42879e12i	0.0786112	−	0.0453862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.q.a.36.16	✓	124
13.4	even	6	inner	91.10.q.a.43.16	yes	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.q.a.36.16	✓	124	1.1	even	1	trivial
91.10.q.a.43.16	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)

\(f(q)\)	\(=\)	\(q+(-21.5135 + 12.4208i) q^{2} +(94.2787 + 163.295i) q^{3} +(52.5525 - 91.0236i) q^{4} +179.352i q^{5} +(-4056.52 - 2342.03i) q^{6} +(2079.33 + 1200.50i) q^{7} -10107.9i q^{8} +(-7935.43 + 13744.6i) q^{9} +O(q^{10})\)	\(q+(-21.5135 + 12.4208i) q^{2} +(94.2787 + 163.295i) q^{3} +(52.5525 - 91.0236i) q^{4} +179.352i q^{5} +(-4056.52 - 2342.03i) q^{6} +(2079.33 + 1200.50i) q^{7} -10107.9i q^{8} +(-7935.43 + 13744.6i) q^{9} +(-2227.69 - 3858.47i) q^{10} +(28843.8 - 16653.0i) q^{11} +19818.3 q^{12} +(-16112.7 - 101710. i) q^{13} -59644.7 q^{14} +(-29287.3 + 16909.0i) q^{15} +(152455. + 264060. i) q^{16} +(28110.2 - 48688.2i) q^{17} -394258. i q^{18} +(671811. + 387870. i) q^{19} +(16325.2 + 9425.38i) q^{20} +452726. i q^{21} +(-413687. + 716527. i) q^{22} +(470610. + 815120. i) q^{23} +(1.65058e6 - 952961. i) q^{24} +1.92096e6 q^{25} +(1.60996e6 + 1.98800e6i) q^{26} +718805. q^{27} +(218548. - 126179. i) q^{28} +(-1.47684e6 - 2.55796e6i) q^{29} +(420048. - 727544. i) q^{30} -3.96060e6i q^{31} +(-2.07778e6 - 1.19961e6i) q^{32} +(5.43872e6 + 3.14004e6i) q^{33} +1.39660e6i q^{34} +(-215312. + 372931. i) q^{35} +(834054. + 1.44462e6i) q^{36} +(3.44285e6 - 1.98773e6i) q^{37} -1.92706e7 q^{38} +(1.50897e7 - 1.22202e7i) q^{39} +1.81287e6 q^{40} +(2.35320e7 - 1.35862e7i) q^{41} +(-5.62322e6 - 9.73970e6i) q^{42} +(8.19194e6 - 1.41889e7i) q^{43} -3.50063e6i q^{44} +(-2.46511e6 - 1.42323e6i) q^{45} +(-2.02489e7 - 1.16907e7i) q^{46} +1.41261e7i q^{47} +(-2.87466e7 + 4.97905e7i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(-4.13264e7 + 2.38598e7i) q^{50} +1.06008e7 q^{51} +(-1.01048e7 - 3.87847e6i) q^{52} -3.70160e7 q^{53} +(-1.54640e7 + 8.92814e6i) q^{54} +(2.98674e6 + 5.17319e6i) q^{55} +(1.21346e7 - 2.10177e7i) q^{56} +1.46272e8i q^{57} +(6.35438e7 + 3.66870e7i) q^{58} +(1.82814e7 + 1.05548e7i) q^{59} +3.55445e6i q^{60} +(-3.39364e7 + 5.87795e7i) q^{61} +(4.91938e7 + 8.52061e7i) q^{62} +(-3.30007e7 + 1.90530e7i) q^{63} -9.65140e7 q^{64} +(1.82418e7 - 2.88984e6i) q^{65} -1.56007e8 q^{66} +(6.11092e7 - 3.52814e7i) q^{67} +(-2.95452e6 - 5.11737e6i) q^{68} +(-8.87369e7 + 1.53697e8i) q^{69} -1.06974e7i q^{70} +(1.09852e8 + 6.34232e7i) q^{71} +(1.38929e8 + 8.02108e7i) q^{72} +1.21937e8i q^{73} +(-4.93783e7 + 8.55258e7i) q^{74} +(1.81105e8 + 3.13684e8i) q^{75} +(7.06107e7 - 4.07671e7i) q^{76} +7.99677e7 q^{77} +(-1.72846e8 + 4.50324e8i) q^{78} -2.15732e8 q^{79} +(-4.73597e7 + 2.73431e7i) q^{80} +(2.23961e8 + 3.87912e8i) q^{81} +(-3.37503e8 + 5.84571e8i) q^{82} +1.37807e8i q^{83} +(4.12088e7 + 2.37919e7i) q^{84} +(8.73232e6 + 5.04160e6i) q^{85} +4.07002e8i q^{86} +(2.78469e8 - 4.82322e8i) q^{87} +(-1.68327e8 - 2.91551e8i) q^{88} +(-7.44888e8 + 4.30061e8i) q^{89} +7.07108e7 q^{90} +(8.85990e7 - 2.30831e8i) q^{91} +9.89269e7 q^{92} +(6.46747e8 - 3.73400e8i) q^{93} +(-1.75457e8 - 3.03901e8i) q^{94} +(-6.95652e7 + 1.20490e8i) q^{95} -4.52389e8i q^{96} +(1.56553e8 + 9.03860e7i) q^{97} +(-1.24021e8 - 7.16034e7i) q^{98} +5.28595e8i 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

Varieties

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Database

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