LMFDB - Embedded newform 91.10.q.a.36.9

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			36.9
Character	$\chi$	$=$	91.36
Dual form			91.10.q.a.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-30.7856 + 17.7740i) q^{2} +(-47.1433 - 81.6546i) q^{3} +(375.833 - 650.963i) q^{4} -1486.53i q^{5} +(2902.67 + 1675.85i) q^{6} +(-2079.33 - 1200.50i) q^{7} +8519.70i q^{8} +(5396.52 - 9347.04i) q^{9} +O(q^{10})$	\(q+(-30.7856 + 17.7740i) q^{2} +(-47.1433 - 81.6546i) q^{3} +(375.833 - 650.963i) q^{4} -1486.53i q^{5} +(2902.67 + 1675.85i) q^{6} +(-2079.33 - 1200.50i) q^{7} +8519.70i q^{8} +(5396.52 - 9347.04i) q^{9} +(26421.7 + 45763.7i) q^{10} +(-4147.10 + 2394.33i) q^{11} -70872.1 q^{12} +(-73976.1 + 71638.2i) q^{13} +85351.0 q^{14} +(-121382. + 70080.0i) q^{15} +(40997.1 + 71009.1i) q^{16} +(-217122. + 376067. i) q^{17} +383672. i q^{18} +(-374209. - 216050. i) q^{19} +(-967676. - 558688. i) q^{20} +226382. i q^{21} +(85113.9 - 147422. i) q^{22} +(520568. + 901650. i) q^{23} +(695673. - 401647. i) q^{24} -256648. q^{25} +(1.00410e6 - 3.52028e6i) q^{26} -2.87348e6 q^{27} +(-1.56296e6 + 902376. i) q^{28} +(-333564. - 577750. i) q^{29} +(2.49121e6 - 4.31490e6i) q^{30} -4.44419e6i q^{31} +(-6.30192e6 - 3.63841e6i) q^{32} +(391016. + 225753. i) q^{33} -1.54366e7i q^{34} +(-1.78458e6 + 3.09098e6i) q^{35} +(-4.05638e6 - 7.02586e6i) q^{36} +(6.01958e6 - 3.47540e6i) q^{37} +1.53603e7 q^{38} +(9.33707e6 + 2.66323e6i) q^{39} +1.26648e7 q^{40} +(8.26079e6 - 4.76937e6i) q^{41} +(-4.02373e6 - 6.96930e6i) q^{42} +(-9.93298e6 + 1.72044e7i) q^{43} +3.59948e6i q^{44} +(-1.38947e7 - 8.02209e6i) q^{45} +(-3.20519e7 - 1.85052e7i) q^{46} +2.90659e7i q^{47} +(3.86548e6 - 6.69521e6i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(7.90104e6 - 4.56167e6i) q^{50} +4.09434e7 q^{51} +(1.88311e7 + 7.50797e7i) q^{52} -9.15252e7 q^{53} +(8.84617e7 - 5.10734e7i) q^{54} +(3.55925e6 + 6.16479e6i) q^{55} +(1.02279e7 - 1.77153e7i) q^{56} +4.07412e7i q^{57} +(2.05379e7 + 1.18576e7i) q^{58} +(3.60990e7 + 2.08417e7i) q^{59} +1.05354e8i q^{60} +(-5.29113e7 + 9.16450e7i) q^{61} +(7.89912e7 + 1.36817e8i) q^{62} +(-2.24423e7 + 1.29570e7i) q^{63} +2.16696e8 q^{64} +(1.06492e8 + 1.09968e8i) q^{65} -1.60502e7 q^{66} +(6.54476e7 - 3.77862e7i) q^{67} +(1.63204e8 + 2.82677e8i) q^{68} +(4.90826e7 - 8.50135e7i) q^{69} -1.26877e8i q^{70} +(5.74235e7 + 3.31535e7i) q^{71} +(7.96341e7 + 4.59767e7i) q^{72} +3.59382e7i q^{73} +(-1.23544e8 + 2.13984e8i) q^{74} +(1.20992e7 + 2.09565e7i) q^{75} +(-2.81281e8 + 1.62398e8i) q^{76} +1.14976e7 q^{77} +(-3.34783e8 + 8.39684e7i) q^{78} +1.63853e8 q^{79} +(1.05557e8 - 6.09435e7i) q^{80} +(2.92458e7 + 5.06551e7i) q^{81} +(-1.69542e8 + 2.93655e8i) q^{82} +3.78823e8i q^{83} +(1.47366e8 + 8.50820e7i) q^{84} +(5.59034e8 + 3.22759e8i) q^{85} -7.06197e8i q^{86} +(-3.14506e7 + 5.44741e7i) q^{87} +(-2.03990e7 - 3.53321e7i) q^{88} +(3.44689e7 - 1.99006e7i) q^{89} +5.70340e8 q^{90} +(2.39822e8 - 6.01509e7i) q^{91} +7.82587e8 q^{92} +(-3.62889e8 + 2.09514e8i) q^{93} +(-5.16619e8 - 8.94811e8i) q^{94} +(-3.21165e8 + 5.56274e8i) q^{95} +6.86107e8i q^{96} +(5.79302e8 + 3.34460e8i) q^{97} +(-1.77473e8 - 1.02464e8i) q^{98} +5.16842e7i 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 $

$2$	−30.7856	+	17.7740i	−1.36054	+	0.785509i	−0.989696	−	0.143185i	$-0.954266\pi$
$2$	−30.7856	+	17.7740i	−1.36054	+	0.785509i	−0.370846	+	0.928694i	$0.620932\pi$
$3$	−47.1433	−	81.6546i	−0.336027	−	0.582016i	0.647654	−	0.761934i	$-0.275750\pi$
$3$	−47.1433	−	81.6546i	−0.336027	−	0.582016i	−0.983682	+	0.179918i	$0.942417\pi$
$4$	375.833	−	650.963i	0.734050	−	1.27141i
$5$		−	1486.53i		−	1.06367i	−0.846847	−	0.531837i	$-0.821502\pi$
$5$		−	1486.53i		−	1.06367i	0.846847	−	0.531837i	$-0.178498\pi$
$6$	2902.67	+	1675.85i	0.914358	+	0.527905i
$7$	−2079.33	−	1200.50i	−0.327327	−	0.188982i
$7$	−2079.33	−	1200.50i	−0.327327	−	0.188982i
$8$			8519.70i			0.735393i
$9$	5396.52	−	9347.04i	0.274172	−	0.474879i
$10$	26421.7	+	45763.7i	0.835526	+	1.44717i
$11$	−4147.10	+	2394.33i	−0.0854039	+	0.0493080i	−0.542094	−	0.840318i	$-0.682368\pi$
$11$	−4147.10	+	2394.33i	−0.0854039	+	0.0493080i	0.456690	+	0.889626i	$0.349035\pi$
$12$	−70872.1			−0.986643
$13$	−73976.1	+	71638.2i	−0.718367	+	0.695664i
$13$	−73976.1	+	71638.2i	−0.718367	+	0.695664i
$14$	85351.0			0.593789
$15$	−121382.	+	70080.0i	−0.619076	+	0.357424i
$16$	40997.1	+	71009.1i	0.156392	+	0.270878i
$17$	−217122.	+	376067.i	−0.630498	+	1.09206i	0.356952	+	0.934123i	$0.383816\pi$
$17$	−217122.	+	376067.i	−0.630498	+	1.09206i	−0.987450	+	0.157932i	$0.949517\pi$
$18$			383672.i			0.861457i
$19$	−374209.	−	216050.i	−0.658754	−	0.380332i	0.133048	−	0.991110i	$-0.457524\pi$
$19$	−374209.	−	216050.i	−0.658754	−	0.380332i	−0.791802	+	0.610778i	$0.790857\pi$
$20$	−967676.	−	558688.i	−1.35237	−	0.780790i
$21$			226382.i			0.254013i
$22$	85113.9	−	147422.i	0.0774637	−	0.134171i
$23$	520568.	+	901650.i	0.387884	+	0.671835i	0.992165	−	0.124937i	$-0.0398728\pi$
$23$	520568.	+	901650.i	0.387884	+	0.671835i	−0.604281	+	0.796771i	$0.706539\pi$
$24$	695673.	−	401647.i	0.428011	−	0.247112i
$25$	−256648.			−0.131404
$26$	1.00410e6	−	3.52028e6i	0.430918	−	1.51076i
$27$	−2.87348e6			−1.04057
$28$	−1.56296e6	+	902376.i	−0.480548	+	0.277445i
$29$	−333564.	−	577750.i	−0.0875766	−	0.151687i	0.818910	−	0.573922i	$-0.194579\pi$
$29$	−333564.	−	577750.i	−0.0875766	−	0.151687i	−0.906486	+	0.422235i	$0.861246\pi$
$30$	2.49121e6	−	4.31490e6i	0.561519	−	0.972580i
$31$		−	4.44419e6i		−	0.864301i	−0.901801	−	0.432151i	$-0.857755\pi$
$31$		−	4.44419e6i		−	0.864301i	0.901801	−	0.432151i	$-0.142245\pi$
$32$	−6.30192e6	−	3.63841e6i	−1.06242	−	0.613391i
$33$	391016.	+	225753.i	0.0573961	+	0.0331376i
$34$		−	1.54366e7i		−	1.98105i
$35$	−1.78458e6	+	3.09098e6i	−0.201016	+	0.348169i
$36$	−4.05638e6	−	7.02586e6i	−0.402511	−	0.697170i
$37$	6.01958e6	−	3.47540e6i	0.528029	−	0.304858i	−0.212184	−	0.977230i	$-0.568058\pi$
$37$	6.01958e6	−	3.47540e6i	0.528029	−	0.304858i	0.740214	+	0.672372i	$0.234724\pi$
$38$	1.53603e7			1.19502
$39$	9.33707e6	+	2.66323e6i	0.646279	+	0.184339i
$40$	1.26648e7			0.782219
$41$	8.26079e6	−	4.76937e6i	0.456556	−	0.263593i	−0.254039	−	0.967194i	$-0.581759\pi$
$41$	8.26079e6	−	4.76937e6i	0.456556	−	0.263593i	0.710595	+	0.703601i	$0.248426\pi$
$42$	−4.02373e6	−	6.96930e6i	−0.199529	−	0.345595i
$43$	−9.93298e6	+	1.72044e7i	−0.443069	+	0.767418i	−0.997915	−	0.0645348i	$-0.979444\pi$
$43$	−9.93298e6	+	1.72044e7i	−0.443069	+	0.767418i	0.554847	+	0.831953i	$0.312777\pi$
$44$			3.59948e6i			0.144778i
$45$	−1.38947e7	−	8.02209e6i	−0.505117	−	0.291629i
$46$	−3.20519e7	−	1.85052e7i	−1.05547	−	0.609373i
$47$			2.90659e7i			0.868848i	0.900709	+	0.434424i	$0.143048\pi$
$47$			2.90659e7i			0.868848i	−0.900709	+	0.434424i	$0.856952\pi$
$48$	3.86548e6	−	6.69521e6i	0.105104	−	0.182045i
$49$	2.88240e6	+	4.99246e6i	0.0714286	+	0.123718i
$50$	7.90104e6	−	4.56167e6i	0.178780	−	0.103219i
$51$	4.09434e7			0.847458
$52$	1.88311e7	+	7.50797e7i	0.357158	+	1.42399i
$53$	−9.15252e7			−1.59331			−0.796653	−	0.604437i	$-0.793398\pi$
$53$	−9.15252e7			−1.59331			−0.796653	+	0.604437i	$0.793398\pi$
$54$	8.84617e7	−	5.10734e7i	1.41574	−	0.817378i
$55$	3.55925e6	+	6.16479e6i	0.0524476	+	0.0908420i
$56$	1.02279e7	−	1.77153e7i	0.138976	−	0.240714i
$57$			4.07412e7i			0.511207i
$58$	2.05379e7	+	1.18576e7i	0.238303	+	0.137585i
$59$	3.60990e7	+	2.08417e7i	0.387847	+	0.223924i	0.681227	−	0.732072i	$-0.261447\pi$
$59$	3.60990e7	+	2.08417e7i	0.387847	+	0.223924i	−0.293380	+	0.955996i	$0.594780\pi$
$60$			1.05354e8i			1.04947i
$61$	−5.29113e7	+	9.16450e7i	−0.489287	+	0.847470i	−0.999924	−	0.0123263i	$-0.996076\pi$
$61$	−5.29113e7	+	9.16450e7i	−0.489287	+	0.847470i	0.510637	+	0.859796i	$0.329410\pi$
$62$	7.89912e7	+	1.36817e8i	0.678917	+	1.17592i
$63$	−2.24423e7	+	1.29570e7i	−0.179487	+	0.103627i
$64$	2.16696e8			1.61451
$65$	1.06492e8	+	1.09968e8i	0.739960	+	0.764109i
$66$	−1.60502e7			−0.104120
$67$	6.54476e7	−	3.77862e7i	0.396787	−	0.229085i	−0.288310	−	0.957537i	$-0.593093\pi$
$67$	6.54476e7	−	3.77862e7i	0.396787	−	0.229085i	0.685096	+	0.728452i	$0.259760\pi$
$68$	1.63204e8	+	2.82677e8i	0.925634	+	1.60325i
$69$	4.90826e7	−	8.50135e7i	0.260679	−	0.451509i
$70$		−	1.26877e8i		−	0.631599i
$71$	5.74235e7	+	3.31535e7i	0.268180	+	0.154834i	0.628060	−	0.778165i	$-0.283849\pi$
$71$	5.74235e7	+	3.31535e7i	0.268180	+	0.154834i	−0.359880	+	0.932999i	$0.617182\pi$
$72$	7.96341e7	+	4.59767e7i	0.349223	+	0.201624i
$73$			3.59382e7i			0.148116i	0.997254	+	0.0740582i	$0.0235951\pi$
$73$			3.59382e7i			0.148116i	−0.997254	+	0.0740582i	$0.976405\pi$
$74$	−1.23544e8	+	2.13984e8i	−0.478938	+	0.829544i
$75$	1.20992e7	+	2.09565e7i	0.0441552	+	0.0764790i
$76$	−2.81281e8	+	1.62398e8i	−0.967117	+	0.558365i
$77$	1.14976e7			0.0372733
$78$	−3.34783e8	+	8.39684e7i	−1.02409	+	0.256856i
$79$	1.63853e8			0.473295			0.236648	−	0.971596i	$-0.423951\pi$
$79$	1.63853e8			0.473295			0.236648	+	0.971596i	$0.423951\pi$
$80$	1.05557e8	−	6.09435e7i	0.288126	−	0.166350i
$81$	2.92458e7	+	5.06551e7i	0.0754884	+	0.130750i
$82$	−1.69542e8	+	2.93655e8i	−0.414109	+	0.717258i
$83$			3.78823e8i			0.876162i	0.898935	+	0.438081i	$0.144342\pi$
$83$			3.78823e8i			0.876162i	−0.898935	+	0.438081i	$0.855658\pi$
$84$	1.47366e8	+	8.50820e7i	0.322955	+	0.186458i
$85$	5.59034e8	+	3.22759e8i	1.16159	+	0.670645i
$86$		−	7.06197e8i		−	1.39214i
$87$	−3.14506e7	+	5.44741e7i	−0.0588563	+	0.101942i
$88$	−2.03990e7	−	3.53321e7i	−0.0362607	−	0.0628054i
$89$	3.44689e7	−	1.99006e7i	0.0582335	−	0.0336211i	−0.470601	−	0.882346i	$-0.655963\pi$
$89$	3.44689e7	−	1.99006e7i	0.0582335	−	0.0336211i	0.528834	+	0.848725i	$0.322629\pi$
$90$	5.70340e8			0.916310
$91$	2.39822e8	−	6.01509e7i	0.366609	−	0.0919508i
$92$	7.82587e8			1.13890
$93$	−3.62889e8	+	2.09514e8i	−0.503037	+	0.290429i
$94$	−5.16619e8	−	8.94811e8i	−0.682488	−	1.18210i
$95$	−3.21165e8	+	5.56274e8i	−0.404549	+	0.700700i
$96$			6.86107e8i			0.824464i
$97$	5.79302e8	+	3.34460e8i	0.664404	+	0.383594i	0.793953	−	0.607979i	$-0.208020\pi$
$97$	5.79302e8	+	3.34460e8i	0.664404	+	0.383594i	−0.129549	+	0.991573i	$0.541353\pi$
$98$	−1.77473e8	−	1.02464e8i	−0.194363	−	0.112216i
$99$			5.16842e7i			0.0540754i
$100$	−9.64568e7	+	1.67068e8i	−0.0964568	+	0.167068i
$101$	−8.96188e8	−	1.55224e9i	−0.856945	−	1.48427i	−0.874828	−	0.484433i	$-0.839026\pi$
$101$	−8.96188e8	−	1.55224e9i	−0.856945	−	1.48427i	0.0178829	−	0.999840i	$-0.494307\pi$
$102$	−1.26047e9	+	7.27730e8i	−1.15300	+	0.665686i
$103$	1.63783e9			1.43384			0.716921	−	0.697154i	$-0.245551\pi$
$103$	1.63783e9			1.43384			0.716921	+	0.697154i	$0.245551\pi$
$104$	−6.10336e8	−	6.30255e8i	−0.511587	−	0.528282i
$105$	3.36524e8			0.270187
$106$	2.81765e9	−	1.62677e9i	2.16776	−	1.25156i
$107$	−4.74571e8	−	8.21981e8i	−0.350005	−	0.606226i	0.636245	−	0.771487i	$-0.280487\pi$
$107$	−4.74571e8	−	8.21981e8i	−0.350005	−	0.606226i	−0.986250	+	0.165261i	$0.947153\pi$
$108$	−1.07995e9	+	1.87053e9i	−0.763831	+	1.32299i
$109$			5.47366e8i			0.371414i	0.982605	+	0.185707i	$0.0594576\pi$
$109$			5.47366e8i			0.371414i	−0.982605	+	0.185707i	$0.940542\pi$
$110$	−2.19147e8	−	1.26524e8i	−0.142714	−	0.0823962i
$111$	−5.67565e8	−	3.27684e8i	−0.354864	−	0.204881i
$112$		−	1.96868e8i		−	0.118221i
$113$	1.54870e9	−	2.68243e9i	0.893541	−	1.54766i	0.0579404	−	0.998320i	$-0.481547\pi$
$113$	1.54870e9	−	2.68243e9i	0.893541	−	1.54766i	0.835600	−	0.549338i	$-0.185120\pi$
$114$	−7.24136e8	−	1.25424e9i	−0.401558	−	0.695519i
$115$	1.34033e9	−	7.73840e8i	0.714614	−	0.412582i
$116$	−5.01458e8			−0.257142
$117$	2.70392e8	+	1.07805e9i	0.133400	+	0.531869i
$118$	−1.48177e9			−0.703577
$119$	9.02936e8	−	5.21310e8i	0.412758	−	0.238306i
$120$	−5.97061e8	−	1.03414e9i	−0.262847	−	0.455264i
$121$	−1.16751e9	+	2.02218e9i	−0.495137	+	0.857603i
$122$		−	3.76179e9i		−	1.53736i
$123$	−7.78882e8	−	4.49688e8i	−0.306831	−	0.177149i
$124$	−2.89300e9	−	1.67028e9i	−1.09888	−	0.634440i
$125$		−	2.52187e9i		−	0.923904i
$126$	4.60598e8	−	7.97779e8i	0.162800	−	0.281978i
$127$	−4.26156e8	−	7.38124e8i	−0.145362	−	0.251775i	0.784146	−	0.620577i	$-0.213101\pi$
$127$	−4.26156e8	−	7.38124e8i	−0.145362	−	0.251775i	−0.929508	+	0.368802i	$0.879768\pi$
$128$	−3.44453e9	+	1.98870e9i	−1.13419	+	0.654825i
$129$	1.87309e9			0.595533
$130$	−5.23300e9	−	1.49262e9i	−1.60696	−	0.458357i
$131$	−4.91870e9			−1.45925			−0.729625	−	0.683847i	$-0.760305\pi$
$131$	−4.91870e9			−1.45925			−0.729625	+	0.683847i	$0.760305\pi$
$132$	2.93914e8	−	1.69691e8i	0.0842631	−	0.0486493i
$133$	5.18736e8	+	8.98477e8i	0.143752	+	0.248986i
$134$	−1.34323e9	+	2.32654e9i	−0.359896	+	0.623359i
$135$			4.27152e9i			1.10683i
$136$	−3.20398e9	−	1.84982e9i	−0.803090	−	0.463664i
$137$	2.88215e9	+	1.66401e9i	0.698996	+	0.403566i	0.806973	−	0.590588i	$-0.201104\pi$
$137$	2.88215e9	+	1.66401e9i	0.698996	+	0.403566i	−0.107977	+	0.994153i	$0.534437\pi$
$138$			3.48958e9i			0.819063i
$139$	1.26864e9	−	2.19734e9i	0.288251	−	0.499265i	−0.685142	−	0.728410i	$-0.740260\pi$
$139$	1.26864e9	−	2.19734e9i	0.288251	−	0.499265i	0.973392	+	0.229145i	$0.0735930\pi$
$140$	1.34141e9	+	2.32339e9i	0.295111	+	0.511147i
$141$	2.37337e9	−	1.37026e9i	0.505683	−	0.291956i
$142$	−2.35708e9			−0.486494
$143$	1.35261e8	−	4.74214e8i	0.0270496	−	0.0948337i
$144$	8.84967e8			0.171512
$145$	−8.58843e8	+	4.95853e8i	−0.161346	+	0.0931531i
$146$	−6.38767e8	−	1.10638e9i	−0.116347	−	0.201519i
$147$	2.71772e8	−	4.70722e8i	0.0480039	−	0.0831452i
$148$		−	5.22469e9i		−	0.895124i
$149$	6.67605e9	+	3.85442e9i	1.10964	+	0.640650i	0.938736	−	0.344638i	$-0.111998\pi$
$149$	6.67605e9	+	3.85442e9i	1.10964	+	0.640650i	0.170903	+	0.985288i	$0.445332\pi$
$150$	−7.44963e8	−	4.30104e8i	−0.120150	−	0.0693686i
$151$			7.58645e9i			1.18752i	0.804641	+	0.593762i	$0.202358\pi$
$151$			7.58645e9i			1.18752i	−0.804641	+	0.593762i	$0.797642\pi$
$152$	1.84068e9	−	3.18815e9i	0.279693	−	0.484443i
$153$	2.34341e9	+	4.05890e9i	0.345729	+	0.598821i
$154$	−3.53959e8	+	2.04358e8i	−0.0507119	+	0.0292785i
$155$	−6.60642e9			−0.919335
$156$	5.24285e9	−	5.07715e9i	0.708772	−	0.686372i
$157$	1.28933e10			1.69362			0.846812	−	0.531893i	$-0.178519\pi$
$157$	1.28933e10			1.69362			0.846812	+	0.531893i	$0.178519\pi$
$158$	−5.04430e9	+	2.91233e9i	−0.643938	+	0.371778i
$159$	4.31480e9	+	7.47345e9i	0.535394	+	0.927330i
$160$	−5.40861e9	+	9.36799e9i	−0.652448	+	1.13007i
$161$		−	2.49977e9i		−	0.293213i
$162$	−1.80069e9	−	1.03963e9i	−0.205410	−	0.118594i
$163$	1.12018e10	+	6.46735e9i	1.24292	+	0.717599i	0.969687	−	0.244349i	$-0.0785743\pi$
$163$	1.12018e10	+	6.46735e9i	1.24292	+	0.717599i	0.273231	+	0.961948i	$0.411908\pi$
$164$		−	7.16996e9i		−	0.773961i
$165$	3.35589e8	−	5.81258e8i	0.0352477	−	0.0610507i
$166$	−6.73321e9	−	1.16623e10i	−0.688234	−	1.19206i
$167$	9.34139e8	−	5.39326e8i	0.0929368	−	0.0536571i	−0.452811	−	0.891606i	$-0.649579\pi$
$167$	9.34139e8	−	5.39326e8i	0.0929368	−	0.0536571i	0.545748	+	0.837949i	$0.316246\pi$
$168$	−1.92871e9			−0.186799
$169$	3.40439e8	−	1.05990e10i	0.0321032	−	0.999485i
$170$	−2.29469e10			−2.10719
$171$	−4.03885e9	+	2.33183e9i	−0.361223	+	0.208552i
$172$	7.46629e9	+	1.29320e10i	0.650469	+	1.12665i
$173$	−9.91063e9	+	1.71657e10i	−0.841189	+	1.45698i	0.0477006	+	0.998862i	$0.484811\pi$
$173$	−9.91063e9	+	1.71657e10i	−0.841189	+	1.45698i	−0.888890	+	0.458121i	$0.848523\pi$
$174$		−	2.23602e9i		−	0.184929i
$175$	5.33655e8	+	3.08106e8i	0.0430119	+	0.0248330i
$176$	−3.40039e8	−	1.96321e8i	−0.0267129	−	0.0154227i
$177$		−	3.93020e9i		−	0.300978i
$178$	−7.07430e8	+	1.22530e9i	−0.0528194	+	0.0914858i
$179$	−5.91251e9	−	1.02408e10i	−0.430460	−	0.745579i	0.566453	−	0.824094i	$-0.308315\pi$
$179$	−5.91251e9	−	1.02408e10i	−0.430460	−	0.745579i	−0.996913	+	0.0785151i	$0.974982\pi$
$180$	−1.04442e10	+	6.02994e9i	−0.741562	+	0.428141i
$181$	6.07946e9			0.421028			0.210514	−	0.977591i	$-0.432486\pi$
$181$	6.07946e9			0.421028			0.210514	+	0.977591i	$0.432486\pi$
$182$	−6.31394e9	+	6.11439e9i	−0.426559	+	0.413078i
$183$	9.97764e9			0.657655
$184$	−7.68179e9	+	4.43508e9i	−0.494063	+	0.285247i
$185$	−5.16629e9	−	8.94828e9i	−0.324270	−	0.561652i
$186$	7.44782e9	−	1.29000e10i	0.456269	−	0.790281i
$187$		−	2.07945e9i		−	0.124354i
$188$	1.89208e10	+	1.09239e10i	1.10466	+	0.637778i
$189$	5.97491e9	+	3.44962e9i	0.340607	+	0.196649i
$190$		−	2.28336e10i		−	1.27111i
$191$	8.90248e9	−	1.54195e10i	0.484017	−	0.838342i	−0.515814	−	0.856700i	$-0.672511\pi$
$191$	8.90248e9	−	1.54195e10i	0.484017	−	0.838342i	0.999831	+	0.0183582i	$0.00584393\pi$
$192$	−1.02158e10	−	1.76942e10i	−0.542520	−	0.939673i
$193$	2.33613e10	−	1.34876e10i	1.21196	−	0.699725i	0.248774	−	0.968562i	$-0.419972\pi$
$193$	2.33613e10	−	1.34876e10i	1.21196	−	0.699725i	0.963186	+	0.268836i	$0.0866391\pi$
$194$	−2.37788e10			−1.20527
$195$	3.95897e9	−	1.38798e10i	0.196077	−	0.687430i
$196$	4.33321e9			0.209729
$197$	2.00902e10	−	1.15991e10i	0.950356	−	0.548688i	0.0571647	−	0.998365i	$-0.481794\pi$
$197$	2.00902e10	−	1.15991e10i	0.950356	−	0.548688i	0.893192	+	0.449676i	$0.148461\pi$
$198$	−9.18637e8	−	1.59113e9i	−0.0424767	−	0.0735718i
$199$	9.26970e9	−	1.60556e10i	0.419012	−	0.725751i	−0.576828	−	0.816866i	$-0.695710\pi$
$199$	9.26970e9	−	1.60556e10i	0.419012	−	0.725751i	0.995840	+	0.0911150i	$0.0290431\pi$
$200$		−	2.18656e9i		−	0.0966334i
$201$	−6.17083e9	−	3.56273e9i	−0.266662	−	0.153957i
$202$	5.51793e10	+	3.18578e10i	2.33182	+	1.34628i
$203$			1.60177e9i			0.0662017i
$204$	1.53879e10	−	2.66526e10i	0.622077	−	1.07747i
$205$	−7.08981e9	−	1.22799e10i	−0.280377	−	0.485627i
$206$	−5.04215e10	+	2.91109e10i	−1.95080	+	1.12630i
$207$	1.12370e10			0.425387
$208$	−8.11977e9	−	2.31602e9i	−0.300787	−	0.0857940i
$209$	2.06918e9			0.0750136
$210$	−1.03601e10	+	5.98139e9i	−0.367600	+	0.212234i
$211$	7.84230e9	+	1.35833e10i	0.272378	+	0.471773i	0.969470	−	0.245209i	$-0.0788564\pi$
$211$	7.84230e9	+	1.35833e10i	0.272378	+	0.471773i	−0.697092	+	0.716982i	$0.745523\pi$
$212$	−3.43982e10	+	5.95795e10i	−1.16957	+	2.02575i
$213$		−	6.25185e9i		−	0.208114i
$214$	2.92198e10	+	1.68701e10i	0.952392	+	0.549864i
$215$	2.55749e10	+	1.47657e10i	0.816283	+	0.471281i
$216$		−	2.44812e10i		−	0.765229i
$217$	−5.33525e9	+	9.24093e9i	−0.163338	+	0.282909i
$218$	−9.72891e9	−	1.68510e10i	−0.291749	−	0.505325i
$219$	2.93452e9	−	1.69424e9i	0.0862061	−	0.0497711i
$220$	5.35074e9			0.153997
$221$	−1.08789e10	−	4.33742e10i	−0.306774	−	1.22311i
$222$	2.32971e10			0.643744
$223$	−5.44687e10	+	3.14475e10i	−1.47494	+	0.851559i	−0.999601	−	0.0282414i	$-0.991009\pi$
$223$	−5.44687e10	+	3.14475e10i	−1.47494	+	0.851559i	−0.475343	+	0.879801i	$0.657676\pi$
$224$	8.73583e9	+	1.51309e10i	0.231840	+	0.401558i
$225$	−1.38500e9	+	2.39890e9i	−0.0360271	+	0.0624008i
$226$			1.10107e11i			2.80754i
$227$	−3.39081e10	−	1.95769e10i	−0.847593	−	0.489358i	0.0122450	−	0.999925i	$-0.496102\pi$
$227$	−3.39081e10	−	1.95769e10i	−0.847593	−	0.489358i	−0.859838	+	0.510567i	$0.829436\pi$
$228$	2.65210e10	+	1.53119e10i	0.649955	+	0.375252i
$229$			3.26121e10i			0.783645i	0.920041	+	0.391822i	$0.128155\pi$
$229$			3.26121e10i			0.783645i	−0.920041	+	0.391822i	$0.871845\pi$
$230$	−2.75085e10	+	4.76462e10i	−0.648175	+	1.12267i
$231$	−5.42034e8	−	9.38830e8i	−0.0125248	−	0.0216937i
$232$	4.92226e9	−	2.84187e9i	0.111550	−	0.0644033i
$233$	7.93493e9			0.176377			0.0881884	−	0.996104i	$-0.471892\pi$
$233$	7.93493e9			0.176377			0.0881884	+	0.996104i	$0.471892\pi$
$234$	−2.74856e10	−	2.83826e10i	−0.599285	−	0.618843i
$235$	4.32074e10			0.924172
$236$	2.71344e10	−	1.56661e10i	0.569398	−	0.328742i
$237$	−7.72457e9	−	1.33793e10i	−0.159040	−	0.275466i
$238$	−1.85316e10	+	3.20976e10i	−0.374383	+	0.648451i
$239$		−	3.23563e10i		−	0.641459i	−0.947171	−	0.320729i	$-0.896072\pi$
$239$		−	3.23563e10i		−	0.641459i	0.947171	−	0.320729i	$-0.103928\pi$
$240$	−9.95263e9	−	5.74615e9i	−0.193636	−	0.111796i
$241$	2.84487e10	+	1.64249e10i	0.543233	+	0.313636i	0.746388	−	0.665511i	$-0.231786\pi$
$241$	2.84487e10	+	1.64249e10i	0.543233	+	0.313636i	−0.203155	+	0.979147i	$0.565120\pi$
$242$		−	8.30054e10i		−	1.55574i
$243$	−2.55219e10	+	4.42052e10i	−0.469553	+	0.813290i
$244$	3.97716e10	+	6.88865e10i	0.718322	+	1.24417i
$245$	7.42145e9	−	4.28478e9i	0.131596	−	0.0759768i
$246$	3.19711e10			0.556608
$247$	4.31600e10	−	1.08251e10i	0.737811	−	0.185054i
$248$	3.78632e10			0.635601
$249$	3.09326e10	−	1.78590e10i	0.509941	−	0.294414i
$250$	4.48237e10	+	7.76370e10i	0.725735	+	1.25701i
$251$	−5.25010e10	+	9.09344e10i	−0.834902	+	1.44609i	0.0592074	+	0.998246i	$0.481143\pi$
$251$	−5.25010e10	+	9.09344e10i	−0.834902	+	1.44609i	−0.894110	+	0.447848i	$0.852191\pi$
$252$			1.94788e10i			0.304270i
$253$	−4.31769e9	−	2.49282e9i	−0.0662536	−	0.0382515i
$254$	2.62389e10	+	1.51490e10i	0.395543	+	0.228367i
$255$		−	6.08636e10i		−	0.901420i
$256$	1.52203e10	−	2.63624e10i	0.221485	−	0.383623i
$257$	2.50607e10	+	4.34064e10i	0.358339	+	0.620662i	0.987684	−	0.156465i	$-0.0500098\pi$
$257$	2.50607e10	+	4.34064e10i	0.358339	+	0.620662i	−0.629344	+	0.777127i	$0.716676\pi$
$258$	−5.76642e10	+	3.32924e10i	−0.810247	+	0.467797i
$259$	−1.66889e10			−0.230451
$260$	1.11608e11	−	2.79930e10i	1.51466	−	0.379900i
$261$	−7.20034e9			−0.0960441
$262$	1.51425e11	−	8.74253e10i	1.98537	−	1.14625i
$263$	−3.73366e10	−	6.46688e10i	−0.481209	−	0.833478i	0.518559	−	0.855042i	$-0.326469\pi$
$263$	−3.73366e10	−	6.46688e10i	−0.481209	−	0.833478i	−0.999767	+	0.0215642i	$0.993135\pi$
$264$	−1.92335e9	+	3.33134e9i	−0.0243692	+	0.0422087i
$265$			1.36055e11i			1.69476i
$266$	−3.19391e10	−	1.84401e10i	−0.391161	−	0.225837i
$267$	−3.24996e9	−	1.87636e9i	−0.0391360	−	0.0225952i
$268$		−	5.68052e10i		−	0.672639i
$269$	−3.94772e10	+	6.83766e10i	−0.459686	+	0.796200i	−0.998944	−	0.0459409i	$-0.985371\pi$
$269$	−3.94772e10	+	6.83766e10i	−0.459686	+	0.796200i	0.539258	+	0.842141i	$0.318705\pi$
$270$	−7.59222e10	−	1.31501e11i	−0.869424	−	1.50589i
$271$	6.25913e10	−	3.61371e10i	0.704940	−	0.406997i	−0.104245	−	0.994552i	$-0.533243\pi$
$271$	6.25913e10	−	3.61371e10i	0.704940	−	0.406997i	0.809185	+	0.587555i	$0.199909\pi$
$272$	−3.56055e10			−0.394419
$273$	−1.62176e10	−	1.67469e10i	−0.176707	−	0.182474i
$274$	−1.18305e11			−1.26802
$275$	1.06434e9	−	6.14500e8i	0.0112224	−	0.00647925i
$276$	−3.68937e10	−	6.39018e10i	−0.382703	−	0.662861i
$277$	−7.31606e9	+	1.26718e10i	−0.0746652	+	0.129324i	−0.900941	−	0.433942i	$-0.857122\pi$
$277$	−7.31606e9	+	1.26718e10i	−0.0746652	+	0.129324i	0.826275	+	0.563266i	$0.190455\pi$
$278$			9.01952e10i			0.905695i
$279$	−4.15400e10	−	2.39832e10i	−0.410438	−	0.236967i
$280$	−2.63343e10	−	1.52041e10i	−0.256041	−	0.147826i
$281$		−	1.57029e11i		−	1.50245i	−0.660045	−	0.751226i	$-0.729463\pi$
$281$		−	1.57029e11i		−	1.50245i	0.660045	−	0.751226i	$-0.270537\pi$
$282$	−4.87103e10	+	8.43686e10i	−0.458669	+	0.794438i
$283$	1.86898e10	+	3.23717e10i	0.173207	+	0.300004i	0.939539	−	0.342441i	$-0.111254\pi$
$283$	1.86898e10	+	3.23717e10i	0.173207	+	0.300004i	−0.766332	+	0.642444i	$0.777920\pi$
$284$	4.31633e10	−	2.49204e10i	0.393715	−	0.227312i
$285$	6.05631e10			0.543758
$286$	4.26462e9	+	1.70031e10i	0.0376906	+	0.150273i
$287$	−2.29025e10			−0.199257
$288$	−6.80168e10	+	3.92695e10i	−0.582573	+	0.336349i
$289$	−3.49901e10	−	6.06046e10i	−0.295056	−	0.511053i
$290$	1.76266e10	−	3.05302e10i	0.146345	−	0.253477i
$291$		−	6.30702e10i		−	0.515591i
$292$	2.33944e10	+	1.35068e10i	0.188317	+	0.108725i
$293$	−4.67039e10	−	2.69645e10i	−0.370210	−	0.213741i	0.303340	−	0.952882i	$-0.401898\pi$
$293$	−4.67039e10	−	2.69645e10i	−0.370210	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$294$			1.93219e10i			0.150830i
$295$	3.09819e10	−	5.36622e10i	0.238182	−	0.412543i
$296$	2.96094e10	+	5.12850e10i	0.224190	+	0.388309i
$297$	1.19166e10	−	6.88007e9i	0.0888688	−	0.0513084i
$298$	−2.74035e11			−2.01295
$299$	−1.03102e11	−	2.94080e10i	−0.746014	−	0.212787i
$300$	1.81892e10			0.129648
$301$	4.13078e10	−	2.38491e10i	0.290057	−	0.167464i
$302$	−1.34842e11	−	2.33553e11i	−0.932811	−	1.61568i
$303$	−8.44986e10	+	1.46356e11i	−0.575914	+	0.997512i
$304$		−	3.54297e10i		−	0.237923i
$305$	1.36233e11	+	7.86542e10i	0.901432	+	0.520442i
$306$	−1.44286e11	−	8.33037e10i	−0.940759	−	0.543147i
$307$		−	7.69410e10i		−	0.494351i	−0.968971	−	0.247175i	$-0.920498\pi$
$307$		−	7.69410e10i		−	0.494351i	0.968971	−	0.247175i	$-0.0795024\pi$
$308$	4.32117e9	−	7.48449e9i	0.0273605	−	0.0473897i
$309$	−7.72127e10	−	1.33736e11i	−0.481810	−	0.834519i
$310$	2.03382e11	−	1.17423e11i	1.25079	−	0.722146i
$311$	7.73257e10			0.468708			0.234354	−	0.972151i	$-0.424703\pi$
$311$	7.73257e10			0.468708			0.234354	+	0.972151i	$0.424703\pi$
$312$	−2.26899e10	+	7.95491e10i	−0.135562	+	0.475269i
$313$	−1.80033e11			−1.06024			−0.530118	−	0.847924i	$-0.677852\pi$
$313$	−1.80033e11			−1.06024			−0.530118	+	0.847924i	$0.677852\pi$
$314$	−3.96928e11	+	2.29167e11i	−2.30425	+	1.33036i
$315$	1.92610e10	+	3.33611e10i	0.110226	+	0.190916i
$316$	6.15814e10	−	1.06662e11i	0.347422	−	0.601753i
$317$			4.73851e10i			0.263557i	0.991279	+	0.131779i	$0.0420688\pi$
$317$			4.73851e10i			0.263557i	−0.991279	+	0.131779i	$0.957931\pi$
$318$	−2.65667e11	−	1.53383e11i	−1.45685	−	0.841114i
$319$	2.76665e9	+	1.59733e9i	0.0149588	+	0.00863645i
$320$		−	3.22126e11i		−	1.71732i
$321$	−4.47457e10	+	7.75018e10i	−0.235222	+	0.407417i
$322$	4.44310e10	+	7.69567e10i	0.230321	+	0.398928i
$323$	1.62498e11	−	9.38184e10i	0.830687	−	0.479597i
$324$	4.39662e10			0.221649
$325$	1.89858e10	−	1.83858e10i	0.0943961	−	0.0914128i
$326$	−4.59804e11			−2.25472
$327$	4.46950e10	−	2.58046e10i	0.216169	−	0.124805i
$328$	4.06336e10	+	7.03795e10i	0.193844	+	0.335748i
$329$	3.48936e10	−	6.04376e10i	0.164197	−	0.284397i
$330$			2.38591e10i			0.110749i
$331$	3.58385e11	+	2.06913e11i	1.64106	+	0.947464i	0.980459	+	0.196722i	$0.0630298\pi$
$331$	3.58385e11	+	2.06913e11i	1.64106	+	0.947464i	0.660596	+	0.750741i	$0.270304\pi$
$332$	2.46599e11	+	1.42374e11i	1.11396	+	0.643147i
$333$		−	7.50203e10i		−	0.334333i
$334$	−1.91720e10	+	3.32069e10i	−0.0842963	+	0.146005i
$335$	−5.61703e10	−	9.72898e10i	−0.243672	−	0.422052i
$336$	−1.60752e10	+	9.28101e9i	−0.0688065	+	0.0397254i
$337$	4.47938e10			0.189183			0.0945917	−	0.995516i	$-0.469845\pi$
$337$	4.47938e10			0.189183			0.0945917	+	0.995516i	$0.469845\pi$
$338$	1.77907e11	+	3.32348e11i	0.741427	+	1.38506i
$339$	−2.92043e11			−1.20102
$340$	4.20208e11	−	2.42607e11i	1.70533	−	0.984574i
$341$	1.06409e10	+	1.84305e10i	0.0426169	+	0.0738147i
$342$	8.28922e10	−	1.43574e11i	0.327640	−	0.567489i
$343$		−	1.38413e10i		−	0.0539949i
$344$	−1.46577e11	−	8.46260e10i	−0.564354	−	0.325830i
$345$	−1.26375e11	−	7.29627e10i	−0.480259	−	0.277278i
$346$		−	7.04608e11i		−	2.64305i
$347$	−1.05695e11	+	1.83069e11i	−0.391356	+	0.677848i	−0.992629	−	0.121196i	$-0.961327\pi$
$347$	−1.05695e11	+	1.83069e11i	−0.391356	+	0.677848i	0.601273	+	0.799044i	$0.294661\pi$
$348$	2.36404e10	+	4.09464e10i	0.0864069	+	0.149661i
$349$	3.39465e11	−	1.95990e11i	1.22484	−	0.707163i	0.258896	−	0.965905i	$-0.416641\pi$
$349$	3.39465e11	−	1.95990e11i	1.22484	−	0.707163i	0.965946	+	0.258743i	$0.0833081\pi$
$350$	−2.19051e10			−0.0780261
$351$	2.12569e11	−	2.05851e11i	0.747512	−	0.723887i
$352$	3.48463e10			0.120980
$353$	8.76364e9	−	5.05969e9i	0.0300399	−	0.0173435i	−0.484905	−	0.874567i	$-0.661146\pi$
$353$	8.76364e9	−	5.05969e9i	0.0300399	−	0.0173435i	0.514945	+	0.857223i	$0.327812\pi$
$354$	6.98555e10	+	1.20993e11i	0.236421	+	0.409493i
$355$	4.92836e10	−	8.53617e10i	0.164693	−	0.285257i
$356$		−	2.99173e10i		−	0.0987182i
$357$	−8.51348e10	−	4.91526e10i	−0.277396	−	0.160155i
$358$	3.64040e11	+	2.10178e11i	1.17132	+	0.676261i
$359$			2.53070e11i			0.804110i	0.915616	+	0.402055i	$0.131704\pi$
$359$			2.53070e11i			0.804110i	−0.915616	+	0.402055i	$0.868296\pi$
$360$	6.83458e10	−	1.18378e11i	0.214462	−	0.371459i
$361$	−6.79888e10	−	1.17760e11i	−0.210695	−	0.364935i
$362$	−1.87160e11	+	1.08057e11i	−0.572827	+	0.330722i
$363$	2.20161e11			0.665518
$364$	5.09773e10	−	1.78722e11i	0.152202	−	0.533607i
$365$	5.34232e10			0.157548
$366$	−3.07167e11	+	1.77343e11i	−0.894767	+	0.516594i
$367$	1.48977e11	+	2.58036e11i	0.428670	+	0.742478i	0.996755	−	0.0804916i	$-0.0256490\pi$
$367$	1.48977e11	+	2.58036e11i	0.428670	+	0.742478i	−0.568085	+	0.822970i	$0.692316\pi$
$368$	−4.26835e10	+	7.39301e10i	−0.121324	+	0.210139i
$369$		−	1.02952e11i		−	0.289079i
$370$	3.18094e11	+	1.83652e11i	0.882365	+	0.509434i
$371$	1.90311e11	+	1.09876e11i	0.521532	+	0.301107i
$372$			3.14969e11i			0.852756i
$373$	−7.90301e10	+	1.36884e11i	−0.211399	+	0.366153i	−0.952153	−	0.305623i	$-0.901135\pi$
$373$	−7.90301e10	+	1.36884e11i	−0.211399	+	0.366153i	0.740754	+	0.671777i	$0.234469\pi$
$374$	3.69602e10	+	6.40170e10i	0.0976815	+	0.169189i
$375$	−2.05922e11	+	1.18889e11i	−0.537727	+	0.310457i
$376$	−2.47633e11			−0.638945
$377$	6.60647e10	+	1.88438e10i	0.168436	+	0.0480432i
$378$	−2.45254e11			−0.617880
$379$	9.30230e10	−	5.37069e10i	0.231587	−	0.133707i	−0.379717	−	0.925103i	$-0.623979\pi$
$379$	9.30230e10	−	5.37069e10i	0.231587	−	0.133707i	0.611304	+	0.791396i	$0.290645\pi$
$380$	2.41409e11	+	4.18132e11i	0.593919	+	1.02870i
$381$	−4.01808e10	+	6.95952e10i	−0.0976914	+	0.169207i
$382$			6.32932e11i			1.52080i
$383$	2.02160e11	+	1.16717e11i	0.480065	+	0.277166i	0.720444	−	0.693513i	$-0.243938\pi$
$383$	2.02160e11	+	1.16717e11i	0.480065	+	0.277166i	−0.240378	+	0.970679i	$0.577272\pi$
$384$	3.24773e11	+	1.87508e11i	0.762237	+	0.440078i
$385$		−	1.70915e10i		−	0.0396467i
$386$	−4.79459e11	+	8.30448e11i	−1.09928	+	1.90401i
$387$	1.07207e11	+	1.85688e11i	0.242954	+	0.420808i
$388$	4.35442e11	−	2.51403e11i	0.975411	−	0.563154i
$389$	−3.89273e11			−0.861949			−0.430974	−	0.902364i	$-0.641830\pi$
$389$	−3.89273e11			−0.861949			−0.430974	+	0.902364i	$0.641830\pi$
$390$	1.24822e11	+	4.97665e11i	0.273212	+	1.08930i
$391$	−4.52107e11			−0.978241
$392$	−4.25343e10	+	2.45572e10i	−0.0909813	+	0.0525281i
$393$	2.31884e11	+	4.01635e11i	0.490348	+	0.849307i
$394$	−4.12325e11	+	7.14169e11i	−0.862000	+	1.49303i
$395$		−	2.43572e11i		−	0.503432i
$396$	3.36445e10	+	1.94247e10i	0.0687520	+	0.0396940i
$397$	1.28852e11	+	7.43927e10i	0.260336	+	0.150305i	0.624488	−	0.781035i	$-0.285308\pi$
$397$	1.28852e11	+	7.43927e10i	0.260336	+	0.150305i	−0.364152	+	0.931340i	$0.618641\pi$
$398$			6.59040e11i			1.31655i
$399$	4.89098e10	−	8.47143e10i	0.0966091	−	0.167332i
$400$	−1.05218e10	−	1.82243e10i	−0.0205504	−	0.0355944i
$401$	5.22771e11	−	3.01822e11i	1.00963	−	0.582909i	0.0985454	−	0.995133i	$-0.468581\pi$
$401$	5.22771e11	−	3.01822e11i	1.00963	−	0.582909i	0.911083	+	0.412223i	$0.135248\pi$
$402$	2.53297e11			0.483740
$403$	3.18374e11	+	3.28764e11i	0.601263	+	0.620886i
$404$	−1.34727e12			−2.51616
$405$	7.53004e10	−	4.34747e10i	0.139075	−	0.0802951i
$406$	−2.84700e10	−	4.93115e10i	−0.0520021	−	0.0900702i
$407$	−1.66425e10	+	2.88257e10i	−0.0300639	+	0.0520721i
$408$			3.48826e11i			0.623215i
$409$	3.17045e11	+	1.83046e11i	0.560230	+	0.323449i	0.753238	−	0.657748i	$-0.228491\pi$
$409$	3.17045e11	+	1.83046e11i	0.560230	+	0.323449i	−0.193008	+	0.981197i	$0.561824\pi$
$410$	4.36528e11	+	2.52029e11i	0.762930	+	0.440478i
$411$		−	3.13788e11i		−	0.542436i
$412$	6.15551e11	−	1.06617e12i	1.05251	−	1.82300i
$413$	−5.00410e10	−	8.66736e10i	−0.0846352	−	0.146592i
$414$	−3.45938e11	+	1.99727e11i	−0.578757	+	0.334145i
$415$	5.63132e11			0.931952
$416$	7.26841e11	−	1.82302e11i	1.18992	−	0.298450i
$417$	−2.39231e11			−0.387440
$418$	−6.37008e10	+	3.67777e10i	−0.102059	+	0.0589239i
$419$	2.81727e11	+	4.87965e11i	0.446545	+	0.773438i	0.998158	−	0.0606615i	$-0.0193210\pi$
$419$	2.81727e11	+	4.87965e11i	0.446545	+	0.773438i	−0.551614	+	0.834100i	$0.685988\pi$
$420$	1.26477e11	−	2.19065e11i	0.198331	−	0.343519i
$421$		−	1.03298e12i		−	1.60259i	−0.598273	−	0.801293i	$-0.704146\pi$
$421$		−	1.03298e12i		−	1.60259i	0.598273	−	0.801293i	$-0.295854\pi$
$422$	−4.82859e11	−	2.78779e11i	−0.741164	−	0.427911i
$423$	2.71680e11	+	1.56855e11i	0.412598	+	0.238213i
$424$		−	7.79768e11i		−	1.17171i
$425$	5.57239e10	−	9.65166e10i	0.0828498	−	0.143500i
$426$	1.11121e11	+	1.92467e11i	0.163475	+	0.283147i
$427$	2.20040e11	−	1.27040e11i	0.320314	−	0.184933i
$428$	−7.13438e11			−1.02768
$429$	−4.50984e10	+	1.13113e10i	−0.0642841	+	0.0161234i
$430$	−1.04978e12			−1.48078
$431$	−3.75311e11	+	2.16686e11i	−0.523894	+	0.302470i	−0.738526	−	0.674225i	$-0.764478\pi$
$431$	−3.75311e11	+	2.16686e11i	−0.523894	+	0.302470i	0.214633	+	0.976695i	$0.431145\pi$
$432$	−1.17804e11	−	2.04043e11i	−0.162736	−	0.281868i
$433$	7.42135e10	−	1.28542e11i	0.101458	−	0.175731i	−0.810827	−	0.585285i	$-0.800983\pi$
$433$	7.42135e10	−	1.28542e11i	0.101458	−	0.175731i	0.912286	+	0.409554i	$0.134316\pi$
$434$		−	3.79316e11i		−	0.513213i
$435$	8.09774e10	+	4.67523e10i	0.108433	+	0.0626039i
$436$	3.56315e11	+	2.05719e11i	0.472220	+	0.272637i
$437$		−	4.49874e11i		−	0.590099i
$438$	−6.02271e10	+	1.04316e11i	−0.0781914	+	0.135431i
$439$	−2.13471e11	−	3.69743e11i	−0.274315	−	0.475127i	0.695647	−	0.718384i	$-0.255118\pi$
$439$	−2.13471e11	−	3.69743e11i	−0.274315	−	0.475127i	−0.969962	+	0.243256i	$0.921784\pi$
$440$	−5.25222e10	+	3.03237e10i	−0.0668046	+	0.0385696i
$441$	6.22197e10			0.0783347
$442$	1.10585e12	+	1.14194e12i	1.37814	+	1.42312i
$443$	−1.65250e11			−0.203856			−0.101928	−	0.994792i	$-0.532501\pi$
$443$	−1.65250e11			−0.203856			−0.101928	+	0.994792i	$0.532501\pi$
$444$	−4.26620e11	+	2.46309e11i	−0.520976	+	0.300786i
$445$	−2.95829e10	−	5.12391e10i	−0.0357619	−	0.0619414i
$446$	1.11790e12	−	1.93626e12i	1.33782	−	2.31716i
$447$		−	7.26841e11i		−	0.861104i
$448$	−4.50582e11	−	2.60144e11i	−0.528474	−	0.305114i
$449$	−2.84890e11	−	1.64481e11i	−0.330803	−	0.190989i	0.325395	−	0.945578i	$-0.394503\pi$
$449$	−2.84890e11	−	1.64481e11i	−0.330803	−	0.190989i	−0.656197	+	0.754589i	$0.727836\pi$
$450$		−	9.84685e10i		−	0.113199i
$451$	−2.28389e10	+	3.95581e10i	−0.0259945	+	0.0450237i
$452$	−1.16411e12	−	2.01629e12i	−1.31181	−	2.27212i
$453$	6.19469e11	−	3.57650e11i	0.691158	−	0.399040i
$454$	1.39184e12			1.53758
$455$	−8.94161e10	−	3.56503e11i	−0.0978058	−	0.389953i
$456$	−3.47103e11			−0.375938
$457$	−1.14047e12	+	6.58452e11i	−1.22310	+	0.706157i	−0.965578	−	0.260115i	$-0.916239\pi$
$457$	−1.14047e12	+	6.58452e11i	−1.22310	+	0.706157i	−0.257522	+	0.966272i	$0.582906\pi$
$458$	−5.79649e11	−	1.00398e12i	−0.615560	−	1.06618i
$459$	6.23897e11	−	1.08062e12i	0.656078	−	1.13636i
$460$		−	1.16334e12i		−	1.21142i
$461$	−8.40592e11	−	4.85316e11i	−0.866824	−	0.500461i	−0.000532520	−	1.00000i	$-0.500170\pi$
$461$	−8.40592e11	−	4.85316e11i	−0.866824	−	0.500461i	−0.866292	+	0.499539i	$0.833503\pi$
$462$	3.33736e10	+	1.92683e10i	0.0340812	+	0.0196768i
$463$			1.18378e12i			1.19717i	0.801058	+	0.598587i	$0.204271\pi$
$463$			1.18378e12i			1.19717i	−0.801058	+	0.598587i	$0.795729\pi$
$464$	2.73503e10	−	4.73722e10i	0.0273925	−	0.0474452i
$465$	3.11449e11	+	5.39445e11i	0.308922	+	0.535068i
$466$	−2.44281e11	+	1.41036e11i	−0.239968	+	0.138546i
$467$	1.73365e12			1.68669			0.843347	−	0.537369i	$-0.180582\pi$
$467$	1.73365e12			1.68669			0.843347	+	0.537369i	$0.180582\pi$
$468$	8.03396e11	+	2.29154e11i	0.774147	+	0.220811i
$469$	−1.81449e11			−0.173172
$470$	−1.33016e12	+	7.67970e11i	−1.25737	+	0.725945i
$471$	−6.07834e11	−	1.05280e12i	−0.569103	−	0.985716i
$472$	−1.77566e11	+	3.07553e11i	−0.164672	+	0.285220i
$473$		−	9.51313e10i		−	0.0873873i
$474$	4.75610e11	+	2.74594e11i	0.432762	+	0.249855i
$475$	9.60400e10	+	5.54487e10i	0.0865627	+	0.0499770i
$476$		−	7.83703e11i		−	0.699714i
$477$	−4.93917e11	+	8.55490e11i	−0.436839	+	0.756628i
$478$	5.75103e11	+	9.96108e11i	0.503872	+	0.872732i
$479$	−1.44662e12	+	8.35204e11i	−1.25558	+	0.724908i	−0.972212	−	0.234104i	$-0.924784\pi$
$479$	−1.44662e12	+	8.35204e11i	−1.25558	+	0.724908i	−0.283366	+	0.959012i	$0.591451\pi$
$480$	1.01992e12			0.876961
$481$	−1.96333e11	+	6.88329e11i	−0.167240	+	0.586331i
$482$	−1.16775e12			−0.985455
$483$	−2.04117e11	+	1.17847e11i	−0.170655	+	0.0985274i
$484$	8.77577e11	+	1.52001e12i	0.726911	+	1.25905i
$485$	4.97185e11	−	8.61150e11i	0.408019	−	0.706709i
$486$		−	1.81451e12i		−	1.47535i
$487$	1.88900e12	+	1.09061e12i	1.52178	+	0.878599i	0.999669	+	0.0257192i	$0.00818757\pi$
$487$	1.88900e12	+	1.09061e12i	1.52178	+	0.878599i	0.522108	+	0.852879i	$0.325146\pi$
$488$	−7.80788e11	−	4.50788e11i	−0.623224	−	0.359818i
$489$		−	1.21957e12i		−	0.964531i
$490$	−1.52316e11	+	2.63818e11i	−0.119361	+	0.206739i
$491$	9.73242e11	+	1.68571e12i	0.755709	+	1.30893i	0.945021	+	0.327009i	$0.106041\pi$
$491$	9.73242e11	+	1.68571e12i	0.755709	+	1.30893i	−0.189313	+	0.981917i	$0.560626\pi$
$492$	−5.85460e11	+	3.38015e11i	−0.450458	+	0.260072i
$493$	2.89697e11			0.220868
$494$	−1.13630e12	+	1.10039e12i	−0.858461	+	0.831330i
$495$	7.68301e10			0.0575186
$496$	3.15578e11	−	1.82199e11i	0.234120	−	0.135169i
$497$	−7.96014e10	−	1.37874e11i	−0.0585217	−	0.101363i
$498$	−6.34852e11	+	1.09960e12i	−0.462530	+	0.801126i
$499$			1.67803e12i			1.21157i	0.795630	+	0.605783i	$0.207140\pi$
$499$			1.67803e12i			1.21157i	−0.795630	+	0.605783i	$0.792860\pi$
$500$	−1.64164e12	−	9.47801e11i	−1.17466	−	0.678191i
$501$	−8.80768e10	−	5.08512e10i	−0.0624586	−	0.0360605i
$502$		−	3.73262e12i		−	2.62329i
$503$	−9.84304e11	+	1.70486e12i	−0.685604	+	1.18750i	0.287643	+	0.957738i	$0.407128\pi$
$503$	−9.84304e11	+	1.70486e12i	−0.685604	+	1.18750i	−0.973247	+	0.229763i	$0.926205\pi$
$504$	−1.10390e11	−	1.91201e11i	−0.0762067	−	0.131994i
$505$	−2.30746e12	+	1.33221e12i	−1.57878	+	0.911511i
$506$	1.77230e11			0.120188
$507$	−8.81509e11	+	4.71875e11i	−0.592504	+	0.317169i
$508$	−6.40655e11			−0.426813
$509$	−1.55437e12	+	8.97416e11i	−1.02642	+	0.592603i	−0.915957	−	0.401277i	$-0.868566\pi$
$509$	−1.55437e12	+	8.97416e11i	−1.02642	+	0.592603i	−0.110462	+	0.993880i	$0.535233\pi$
$510$	1.08179e12	+	1.87372e12i	0.708074	+	1.22642i
$511$	4.31438e10	−	7.47272e10i	0.0279914	−	0.0484825i
$512$		−	9.54324e11i		−	0.613735i
$513$	1.07528e12	+	6.20815e11i	0.685480	+	0.395762i
$514$	−1.54302e12	−	8.90860e11i	−0.975071	−	0.562957i
$515$		−	2.43468e12i		−	1.52514i
$516$	7.03971e11	−	1.21931e12i	0.437151	−	0.757167i
$517$	−6.95934e10	−	1.20539e11i	−0.0428411	−	0.0742030i
$518$	5.13777e11	−	2.96629e11i	0.313538	−	0.181021i
$519$	1.86888e12			1.13065
$520$	−9.36893e11	+	9.07283e11i	−0.561921	+	0.544162i
$521$	−1.58518e12			−0.942558			−0.471279	−	0.881984i	$-0.656208\pi$
$521$	−1.58518e12			−0.942558			−0.471279	+	0.881984i	$0.656208\pi$
$522$	2.21666e11	−	1.27979e11i	0.130672	−	0.0754435i
$523$	2.42280e11	+	4.19641e11i	0.141599	+	0.245257i	0.928099	−	0.372334i	$-0.121442\pi$
$523$	2.42280e11	+	4.19641e11i	0.141599	+	0.245257i	−0.786500	+	0.617590i	$0.788109\pi$
$524$	−1.84861e12	+	3.20189e12i	−1.07116	+	1.85531i
$525$		−	5.81005e10i		−	0.0333782i
$526$	2.29885e12	+	1.32724e12i	1.30941	+	0.755988i
$527$	1.67131e12	+	9.64932e11i	0.943864	+	0.544940i
$528$			3.70209e10i			0.0207298i
$529$	3.58595e11	−	6.21105e11i	0.199092	−	0.344837i
$530$	−2.41825e12	−	4.18853e12i	−1.33125	−	2.30579i
$531$	3.89617e11	−	2.24946e11i	0.212673	−	0.122787i
$532$	7.79833e11			0.422084
$533$	−2.69432e11	+	9.44608e11i	−0.144603	+	0.506966i
$534$	1.33402e11			0.0709950
$535$	−1.22190e12	+	7.05464e11i	−0.644827	+	0.372291i
$536$	3.21927e11	+	5.57594e11i	0.168467	+	0.291794i
$537$	−5.57470e11	+	9.65567e11i	−0.289293	+	0.501070i
$538$		−	2.80668e12i		−	1.44435i
$539$	−2.39072e10	−	1.38028e10i	−0.0122006	−	0.00704400i
$540$	2.78060e12	+	1.60538e12i	1.40723	+	0.812467i
$541$		−	3.57352e12i		−	1.79353i	−0.442507	−	0.896765i	$-0.645911\pi$
$541$		−	3.57352e12i		−	1.79353i	0.442507	−	0.896765i	$-0.354089\pi$
$542$	−1.28460e12	+	2.22500e12i	−0.639400	+	1.10747i
$543$	−2.86606e11	−	4.96416e11i	−0.141477	−	0.245045i
$544$	2.73657e12	−	1.57996e12i	1.33971	−	0.773484i
$545$	8.13676e11			0.395064
$546$	7.96928e11	+	2.27309e11i	0.383753	+	0.109459i
$547$	−2.47035e12			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$547$	−2.47035e12			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$548$	2.16642e12	−	1.25078e12i	1.02620	−	0.592474i
$549$	5.71073e11	+	9.89128e11i	0.268297	+	0.464704i
$550$	−2.18443e10	+	3.78354e10i	−0.0101790	+	0.0176306i
$551$			2.88266e11i			0.133233i
$552$	7.24290e11	+	4.18169e11i	0.332037	+	0.191702i
$553$	−3.40704e11	−	1.96705e11i	−0.154922	−	0.0894444i
$554$		−	5.20144e11i		−	0.234601i
$555$	−4.87112e11	+	8.43703e11i	−0.217927	+	0.377460i
$556$	−9.53592e11	−	1.65167e12i	−0.423181	−	0.732971i
$557$	5.60797e11	−	3.23776e11i	0.246864	−	0.142527i	−0.371464	−	0.928448i	$-0.621144\pi$
$557$	5.60797e11	−	3.23776e11i	0.246864	−	0.142527i	0.618327	+	0.785921i	$0.287811\pi$
$558$	1.70511e12			0.744558
$559$	−4.97690e11	−	1.98430e12i	−0.215579	−	0.859515i
$560$	−2.92650e11			−0.125749
$561$	−1.69797e11	+	9.80321e10i	−0.0723762	+	0.0417864i
$562$	2.79104e12	+	4.83422e12i	1.18019	+	2.04415i
$563$	−1.27129e12	+	2.20194e12i	−0.533282	+	0.923671i	0.465963	+	0.884804i	$0.345708\pi$
$563$	−1.27129e12	+	2.20194e12i	−0.533282	+	0.923671i	−0.999244	+	0.0388667i	$0.987625\pi$
$564$		−	2.05996e12i		−	0.857242i
$565$	−3.98751e12	−	2.30219e12i	−1.64620	−	0.950437i
$566$	−1.15075e12	−	6.64387e11i	−0.471311	−	0.272112i
$567$		−	1.40438e11i		−	0.0570639i
$568$	−2.82458e11	+	4.89231e11i	−0.113864	+	0.197218i
$569$	3.90692e11	+	6.76698e11i	0.156253	+	0.270639i	0.933515	−	0.358539i	$-0.116725\pi$
$569$	3.90692e11	+	6.76698e11i	0.156253	+	0.270639i	−0.777261	+	0.629178i	$0.783392\pi$
$570$	−1.86447e12	+	1.07645e12i	−0.739806	+	0.427127i
$571$	2.17941e11			0.0857978			0.0428989	−	0.999079i	$-0.486341\pi$
$571$	2.17941e11			0.0857978			0.0428989	+	0.999079i	$0.486341\pi$
$572$	−2.57860e11	−	2.66276e11i	−0.100717	−	0.104004i
$573$	−1.67877e12			−0.650571
$574$	7.05067e11	−	4.07070e11i	0.271098	−	0.156519i
$575$	−1.33603e11	−	2.31406e11i	−0.0509694	−	0.0882816i
$576$	1.16941e12	−	2.02547e12i	0.442654	−	0.766698i
$577$		−	3.38318e12i		−	1.27067i	−0.772235	−	0.635337i	$-0.780861\pi$
$577$		−	3.38318e12i		−	1.27067i	0.772235	−	0.635337i	$-0.219139\pi$
$578$	2.15438e12	+	1.24383e12i	0.802873	+	0.463539i
$579$	−2.20265e12	−	1.27170e12i	−0.814503	−	0.470253i
$580$			7.45433e11i			0.273516i
$581$	4.54777e11	−	7.87696e11i	0.165579	−	0.286791i
$582$	1.12101e12	+	1.94165e12i	0.405002	+	0.701484i
$583$	3.79564e11	−	2.19142e11i	0.136075	−	0.0785627i
$584$	−3.06183e11			−0.108924
$585$	1.60256e12	−	4.01946e11i	0.565735	−	0.141895i
$586$	1.91707e12			0.671582
$587$	−1.18728e12	+	6.85477e11i	−0.412745	+	0.238299i	−0.691969	−	0.721928i	$-0.743256\pi$
$587$	−1.18728e12	+	6.85477e11i	−0.412745	+	0.238299i	0.279223	+	0.960226i	$0.409923\pi$
$588$	−2.04282e11	−	3.53827e11i	−0.0704745	−	0.122065i
$589$	−9.60167e11	+	1.66306e12i	−0.328721	+	0.569362i
$590$			2.20269e12i			0.748377i
$591$	−1.89424e12	−	1.09364e12i	−0.638691	−	0.368748i
$592$	4.93571e11	+	2.84963e11i	0.165159	+	0.0953544i
$593$			1.37862e12i			0.457825i	0.973447	+	0.228913i	$0.0735170\pi$
$593$			1.37862e12i			0.457825i	−0.973447	+	0.228913i	$0.926483\pi$
$594$	−2.44573e11	+	4.23613e11i	−0.0806065	+	0.139615i
$595$	−7.74944e11	−	1.34224e12i	−0.253480	−	0.439040i
$596$	5.01817e12	−	2.89724e12i	1.62906	−	0.940538i
$597$	−1.74802e12			−0.563198
$598$	3.69676e12	−	9.27200e11i	1.18213	−	0.296495i
$599$	2.85786e12			0.907026			0.453513	−	0.891250i	$-0.350170\pi$
$599$	2.85786e12			0.907026			0.453513	+	0.891250i	$0.350170\pi$
$600$	−1.78543e11	+	1.03082e11i	−0.0562422	+	0.0324714i
$601$	1.06072e12	+	1.83721e12i	0.331638	+	0.574413i	0.982833	−	0.184497i	$-0.0590655\pi$
$601$	1.06072e12	+	1.83721e12i	0.331638	+	0.574413i	−0.651196	+	0.758910i	$0.725732\pi$
$602$	−8.47789e11	+	1.46841e12i	−0.263090	+	0.455684i
$603$		−	8.15655e11i		−	0.251234i
$604$	4.93850e12	+	2.85124e12i	1.50983	+	0.871702i
$605$	3.00604e12	+	1.73554e12i	0.912211	+	0.526665i
$606$		−	6.00753e12i		−	1.80954i
$607$	−1.40868e12	+	2.43991e12i	−0.421177	+	0.729499i	−0.996055	−	0.0887397i	$-0.971716\pi$
$607$	−1.40868e12	+	2.43991e12i	−0.421177	+	0.729499i	0.574878	+	0.818239i	$0.305049\pi$
$608$	1.57216e12	+	2.72306e12i	0.466584	+	0.808147i
$609$	1.30792e11	−	7.55130e10i	0.0385305	−	0.0222456i
$610$	−5.59201e12			−1.63525
$611$	−2.08223e12	−	2.15018e12i	−0.604426	−	0.624152i
$612$	3.52292e12			1.01513
$613$	−4.98356e12	+	2.87726e12i	−1.42550	+	0.823013i	−0.996761	−	0.0804147i	$-0.974376\pi$
$613$	−4.98356e12	+	2.87726e12i	−1.42550	+	0.823013i	−0.428740	+	0.903428i	$0.641042\pi$
$614$	1.36755e12	+	2.36867e12i	0.388317	+	0.672585i
$615$	−6.68474e11	+	1.15783e12i	−0.188429	+	0.326368i
$616$			9.79560e10i			0.0274105i
$617$	−1.89078e12	−	1.09164e12i	−0.525239	−	0.303247i	0.213836	−	0.976870i	$-0.431404\pi$
$617$	−1.89078e12	−	1.09164e12i	−0.525239	−	0.303247i	−0.739076	+	0.673622i	$0.764737\pi$
$618$	4.75407e12	+	2.74476e12i	1.31105	+	0.756932i
$619$		−	6.15285e11i		−	0.168449i	−0.996447	−	0.0842246i	$-0.973159\pi$
$619$		−	6.15285e11i		−	0.168449i	0.996447	−	0.0842246i	$-0.0268413\pi$
$620$	−2.48292e12	+	4.30054e12i	−0.674838	+	1.16885i
$621$	−1.49584e12	−	2.59087e12i	−0.403621	−	0.699092i
$622$	−2.38051e12	+	1.37439e12i	−0.637697	+	0.368174i
$623$	−9.55629e10			−0.0254152
$624$	1.93679e11	+	7.72201e11i	0.0511390	+	0.203892i
$625$	−4.25009e12			−1.11414
$626$	5.54242e12	−	3.19992e12i	1.44250	−	0.832825i
$627$	−9.75479e10	−	1.68958e11i	−0.0252066	−	0.0436591i
$628$	4.84575e12	−	8.39308e12i	1.24320	−	2.15329i
$629$			3.01835e12i			0.768850i
$630$	−1.18592e12	−	6.84693e11i	−0.299933	−	0.173166i
$631$	−4.06951e12	−	2.34953e12i	−1.02190	−	0.589996i	−0.107248	−	0.994232i	$-0.534204\pi$
$631$	−4.06951e12	−	2.34953e12i	−1.02190	−	0.589996i	−0.914655	+	0.404236i	$0.867537\pi$
$632$			1.39598e12i			0.348058i
$633$	7.39424e11	−	1.28072e12i	0.183053	−	0.317057i
$634$	−8.42225e11	−	1.45878e12i	−0.207027	−	0.358581i
$635$	−1.09724e12	+	6.33494e11i	−0.267807	+	0.154618i
$636$	6.48658e12			1.57202
$637$	−5.70880e11	−	1.62833e11i	−0.137378	−	0.0391846i
$638$	−1.13564e11			−0.0271361
$639$	6.19774e11	−	3.57826e11i	0.147055	−	0.0849021i
$640$	2.95627e12	+	5.12040e12i	0.696520	+	1.20641i
$641$	1.35033e12	−	2.33884e12i	0.315921	−	0.547191i	−0.663712	−	0.747988i	$-0.731020\pi$
$641$	1.35033e12	−	2.33884e12i	0.315921	−	0.547191i	0.979633	+	0.200797i	$0.0643532\pi$
$642$		−	3.18125e12i		−	0.739077i
$643$	−4.74492e12	−	2.73948e12i	−1.09466	−	0.632003i	−0.159848	−	0.987142i	$-0.551100\pi$
$643$	−4.74492e12	−	2.73948e12i	−1.09466	−	0.632003i	−0.934814	+	0.355139i	$0.884434\pi$
$644$	−1.62725e12	−	9.39496e11i	−0.372794	−	0.215233i
$645$		−	2.78441e12i		−	0.633453i
$646$	−3.33507e12	+	5.77650e12i	−0.753456	+	1.30502i
$647$	−3.38633e12	−	5.86530e12i	−0.759732	−	1.31589i	−0.942987	−	0.332829i	$-0.891997\pi$
$647$	−3.38633e12	−	5.86530e12i	−0.759732	−	1.31589i	0.183255	−	0.983065i	$-0.441337\pi$
$648$	−4.31567e11	+	2.49165e11i	−0.0961525	+	0.0555137i
$649$	−1.99608e11			−0.0441649
$650$	−2.57699e11	+	9.03471e11i	−0.0566243	+	0.198520i
$651$	1.00609e12			0.219543
$652$	8.42000e12	−	4.86129e12i	1.82473	−	1.05351i
$653$	3.43137e12	+	5.94332e12i	0.738514	+	1.27914i	0.953164	+	0.302453i	$0.0978055\pi$
$653$	3.43137e12	+	5.94332e12i	0.738514	+	1.27914i	−0.214650	+	0.976691i	$0.568861\pi$
$654$	−9.17306e11	+	1.58882e12i	−0.196071	+	0.339606i
$655$			7.31180e12i			1.55217i
$656$	6.77337e11	+	3.91061e11i	0.142803	+	0.0824474i
$657$	3.35916e11	+	1.93941e11i	0.0703374	+	0.0406093i
$658$			2.48080e12i			0.515913i
$659$	−1.65958e12	+	2.87447e12i	−0.342778	+	0.593710i	−0.984948	−	0.172853i	$-0.944701\pi$
$659$	−1.65958e12	+	2.87447e12i	−0.342778	+	0.593710i	0.642169	+	0.766563i	$0.278035\pi$
$660$	−2.52251e11	−	4.36912e11i	−0.0517471	−	0.0896286i
$661$	7.18367e12	−	4.14749e12i	1.46366	−	0.845044i	0.464481	−	0.885583i	$-0.346241\pi$
$661$	7.18367e12	−	4.14749e12i	1.46366	−	0.845044i	0.999178	+	0.0405395i	$0.0129077\pi$
$662$	−1.47108e13			−2.97697
$663$	−3.02884e12	+	2.93311e12i	−0.608786	+	0.589546i
$664$	−3.22746e12			−0.644324
$665$	1.33561e12	−	7.71116e11i	0.264840	−	0.152905i
$666$	1.33341e12	+	2.30954e12i	0.262622	+	0.454875i
$667$	3.47285e11	−	6.01516e11i	0.0679392	−	0.117674i
$668$		−	8.10787e11i		−	0.157548i
$669$	5.13567e12	+	2.96508e12i	0.991242	+	0.572294i
$670$	3.45847e12	+	1.99675e12i	0.663051	+	0.382813i
$671$		−	5.06748e11i		−	0.0965030i
$672$	8.23672e11	−	1.42664e12i	0.155809	−	0.269869i
$673$	−8.25391e11	−	1.42962e12i	−0.155093	−	0.268629i	0.778000	−	0.628264i	$-0.216234\pi$
$673$	−8.25391e11	−	1.42962e12i	−0.155093	−	0.268629i	−0.933093	+	0.359636i	$0.882901\pi$
$674$	−1.37900e12	+	7.96167e11i	−0.257392	+	0.148605i
$675$	7.37473e11			0.136735
$676$	−6.77163e12	−	4.20508e12i	−1.24719	−	0.774488i
$677$	1.04939e13			1.91994			0.959968	−	0.280111i	$-0.0903712\pi$
$677$	1.04939e13			1.91994			0.959968	+	0.280111i	$0.0903712\pi$
$678$	8.99072e12	−	5.19079e12i	1.63403	−	0.943409i
$679$	−8.03038e11	−	1.39090e12i	−0.144985	−	0.251121i
$680$	−2.74981e12	+	4.76281e12i	−0.493188	+	0.854226i
$681$			3.69167e12i			0.657750i
$682$	−6.55170e11	−	3.78262e11i	−0.115964	−	0.0669520i
$683$	5.10590e12	+	2.94789e12i	0.897800	+	0.518345i	0.876486	−	0.481428i	$-0.159882\pi$
$683$	5.10590e12	+	2.94789e12i	0.897800	+	0.518345i	0.0213139	+	0.999773i	$0.493215\pi$
$684$			3.50553e12i			0.612351i
$685$	2.47361e12	−	4.28441e12i	0.429262	−	0.743504i
$686$	2.46016e11	+	4.26112e11i	0.0424135	+	0.0734624i
$687$	2.66293e12	−	1.53744e12i	0.456094	−	0.263326i
$688$	−1.62889e12			−0.277169
$689$	6.77068e12	−	6.55670e12i	1.14458	−	1.10841i
$690$	5.18737e12			0.871217
$691$	−6.51107e12	+	3.75917e12i	−1.08643	+	0.627250i	−0.932623	−	0.360852i	$-0.882486\pi$
$691$	−6.51107e12	+	3.75917e12i	−1.08643	+	0.627250i	−0.153805	+	0.988101i	$0.549153\pi$
$692$	7.44949e12	+	1.29029e13i	1.23495	+	2.13900i
$693$	6.20469e10	−	1.07468e11i	0.0102193	−	0.0177003i
$694$		−	7.51451e12i		−	1.22965i
$695$	−3.26642e12	−	1.88587e12i	−0.531055	−	0.306605i
$696$	−4.64103e11	−	2.67950e11i	−0.0749675	−	0.0432825i
$697$			4.14214e12i			0.664780i
$698$	−6.96707e12	+	1.20673e13i	−1.11097	+	1.92425i
$699$	−3.74079e11	−	6.47924e11i	−0.0592674	−	0.102654i
$700$	4.01131e11	−	2.31593e11i	0.0631458	−	0.0364573i
$701$	−7.28791e12			−1.13991			−0.569957	−	0.821675i	$-0.693040\pi$
$701$	−7.28791e12			−1.13991			−0.569957	+	0.821675i	$0.693040\pi$
$702$	−2.88525e12	+	1.01155e13i	−0.448401	+	1.57206i
$703$	−3.00344e12			−0.463789
$704$	−8.98662e11	+	5.18843e11i	−0.137886	+	0.0796084i
$705$	−2.03694e12	−	3.52808e12i	−0.310547	−	0.537883i
$706$	−1.79862e11	+	3.11531e11i	−0.0272470	+	0.0471932i
$707$			4.30350e12i			0.647790i
$708$	−2.55841e12	−	1.47710e12i	−0.382667	−	0.220933i
$709$	2.56967e12	+	1.48360e12i	0.381917	+	0.220500i	0.678652	−	0.734460i	$-0.262564\pi$
$709$	2.56967e12	+	1.48360e12i	0.381917	+	0.220500i	−0.296735	+	0.954960i	$0.595898\pi$
$710$			3.50388e12i			0.517471i
$711$	8.84235e11	−	1.53154e12i	0.129764	−	0.224758i
$712$	1.69548e11	+	2.93665e11i	0.0247247	+	0.0428245i
$713$	4.00710e12	−	2.31350e12i	0.580668	−	0.335249i
$714$	3.49456e12			0.503212
$715$	−7.04934e11	−	2.01070e11i	−0.100872	−	0.0287720i
$716$	−8.88848e12			−1.26392
$717$	−2.64204e12	+	1.52538e12i	−0.373339	+	0.215548i
$718$	−4.49808e12	−	7.79090e12i	−0.631636	−	1.09403i
$719$	−4.49124e12	+	7.77905e12i	−0.626738	+	1.08554i	0.361464	+	0.932386i	$0.382277\pi$
$719$	−4.49124e12	+	7.77905e12i	−0.626738	+	1.08554i	−0.988202	+	0.153156i	$0.951056\pi$
$720$		−	1.31553e12i		−	0.182433i
$721$	−3.40558e12	−	1.96621e12i	−0.469335	−	0.270971i
$722$	4.18614e12	+	2.41687e12i	0.573320	+	0.331006i
$723$		−	3.09729e12i		−	0.421560i
$724$	2.28486e12	−	3.95750e12i	0.309056	−	0.535300i
$725$	8.56085e10	+	1.48278e11i	0.0115079	+	0.0199323i
$726$	−6.77777e12	+	3.91315e12i	−0.905466	+	0.522771i
$727$	1.95672e12			0.259791			0.129895	−	0.991528i	$-0.458536\pi$
$727$	1.95672e12			0.259791			0.129895	+	0.991528i	$0.458536\pi$
$728$	5.12468e11	+	2.04321e12i	0.0676200	+	0.269602i
$729$	5.96403e12			0.782107
$730$	−1.64466e12	+	9.49546e11i	−0.214350	+	0.123755i
$731$	−4.31334e12	−	7.47092e12i	−0.558708	−	0.967711i
$732$	3.74993e12	−	6.49507e12i	0.482752	−	0.836150i
$733$			9.41659e12i			1.20483i	0.798183	+	0.602415i	$0.205795\pi$
$733$			9.41659e12i			1.20483i	−0.798183	+	0.602415i	$0.794205\pi$
$734$	−9.17270e12	−	5.29586e12i	−1.16645	−	0.673448i
$735$	−6.99743e11	−	4.03997e11i	−0.0884394	−	0.0510605i
$736$		−	7.57616e12i		−	0.951698i
$737$	−1.80945e11	+	3.13406e11i	−0.0225914	+	0.0391295i
$738$	1.82987e12	+	3.16943e12i	0.227074	+	0.393304i
$739$	−9.03438e12	+	5.21600e12i	−1.11429	+	0.643336i	−0.939937	−	0.341347i	$-0.889117\pi$
$739$	−9.03438e12	+	5.21600e12i	−1.11429	+	0.643336i	−0.174353	+	0.984683i	$0.555783\pi$
$740$	−7.76667e12			−0.952120
$741$	−2.91863e12	−	3.01388e12i	−0.355629	−	0.367235i
$742$	−7.81176e12			−0.946088
$743$	6.69468e12	−	3.86517e12i	0.805898	−	0.465285i	−0.0396316	−	0.999214i	$-0.512618\pi$
$743$	6.69468e12	−	3.86517e12i	0.805898	−	0.465285i	0.845529	+	0.533929i	$0.179285\pi$
$744$	−1.78500e12	−	3.09170e12i	−0.213579	−	0.369930i
$745$	5.72972e12	−	9.92416e12i	0.681443	−	1.18029i
$746$		−	5.61874e12i		−	0.664223i
$747$	3.54087e12	+	2.04432e12i	0.416071	+	0.240219i
$748$	−1.35364e12	−	7.81527e11i	−0.158106	−	0.0912823i
$749$			2.27889e12i			0.264579i
$750$	4.22628e12	−	7.32013e12i	0.487733	−	0.844779i
$751$	4.63589e12	+	8.02959e12i	0.531806	+	0.921115i	0.999311	+	0.0371245i	$0.0118198\pi$
$751$	4.63589e12	+	8.02959e12i	0.531806	+	0.921115i	−0.467505	+	0.883991i	$0.654847\pi$
$752$	−2.06394e12	+	1.19162e12i	−0.235352	+	0.135881i
$753$	9.90028e12			1.12220
$754$	−2.36877e12	+	5.94122e11i	−0.266902	+	0.0669429i
$755$	1.12775e13			1.26314
$756$	4.49114e12	−	2.59296e12i	0.500045	−	0.288701i
$757$	4.42410e12	+	7.66277e12i	0.489659	+	0.848115i	0.999929	−	0.0118996i	$-0.00378785\pi$
$757$	4.42410e12	+	7.66277e12i	0.489659	+	0.848115i	−0.510270	+	0.860014i	$0.670455\pi$
$758$	−1.90918e12	+	3.30679e12i	−0.210056	+	0.363827i
$759$			4.70079e11i			0.0514142i
$760$	−4.73929e12	−	2.73623e12i	−0.515290	−	0.297503i
$761$	1.27341e13	+	7.35203e12i	1.37638	+	0.794651i	0.991721	−	0.128410i	$-0.0409873\pi$
$761$	1.27341e13	+	7.35203e12i	1.37638	+	0.794651i	0.384655	+	0.923061i	$0.374321\pi$
$762$		−	2.85670e12i		−	0.306950i
$763$	6.57113e11	−	1.13815e12i	0.0701907	−	0.121574i
$764$	−6.69170e12	−	1.15904e13i	−0.710585	−	1.23077i
$765$	6.03368e12	−	3.48355e12i	0.636951	−	0.367744i
$766$	−8.29813e12			−0.870865
$767$	−4.16353e12	+	1.04427e12i	−0.434392	+	0.108952i
$768$	−2.87015e12			−0.297700
$769$	−5.82163e11	+	3.36112e11i	−0.0600310	+	0.0346589i	−0.529715	−	0.848176i	$-0.677701\pi$
$769$	−5.82163e11	+	3.36112e11i	−0.0600310	+	0.0346589i	0.469684	+	0.882835i	$0.344368\pi$
$770$	3.03785e11	+	5.26171e11i	0.0311428	+	0.0539410i
$771$	2.36289e12	−	4.09264e12i	0.240823	−	0.417118i
$772$		−	2.02764e13i		−	2.05453i
$773$	−1.21310e13	−	7.00382e12i	−1.22205	−	0.705549i	−0.256692	−	0.966493i	$-0.582633\pi$
$773$	−1.21310e13	−	7.00382e12i	−1.22205	−	0.705549i	−0.965354	+	0.260945i	$0.915966\pi$
$774$	−6.60085e12	−	3.81100e12i	−0.661098	−	0.381685i
$775$			1.14059e12i			0.113572i
$776$	−2.84950e12	+	4.93548e12i	−0.282092	+	0.488598i
$777$	7.86769e11	+	1.36272e12i	0.0774378	+	0.134126i
$778$	1.19840e13	−	6.91896e12i	1.17272	−	0.677069i
$779$	−4.12169e12			−0.401011
$780$	−7.54734e12	−	7.79365e12i	−0.730076	−	0.753903i
$781$	−3.17521e11			−0.0305382
$782$	1.39184e13	−	8.03577e12i	1.33094	−	0.768417i
$783$	9.58490e11	+	1.66015e12i	0.0911297	+	0.157841i
$784$	−2.36340e11	+	4.09353e11i	−0.0223417	+	0.0386969i
$785$		−	1.91663e13i		−	1.80146i
$786$	−1.42774e13	−	8.24303e12i	−1.33428	−	0.770346i
$787$	6.14240e12	+	3.54632e12i	0.570758	+	0.329527i	0.757452	−	0.652891i	$-0.226444\pi$
$787$	6.14240e12	+	3.54632e12i	0.570758	+	0.329527i	−0.186694	+	0.982418i	$0.559777\pi$
$788$		−	1.74373e13i		−	1.61106i
$789$	−3.52034e12	+	6.09740e12i	−0.323398	+	0.560142i
$790$	4.32927e12	+	7.49851e12i	0.395451	+	0.684941i
$791$	−6.44051e12	+	3.71843e12i	−0.584960	+	0.337727i
$792$	−4.40334e11			−0.0397667
$793$	−2.65111e12	−	1.05700e13i	−0.238067	−	0.949174i
$794$	−5.28904e12			−0.472264
$795$	1.11095e13	−	6.41408e12i	0.986377	−	0.569485i
$796$	−6.96773e12	−	1.20685e13i	−0.615152	−	1.06547i
$797$	−7.88160e12	+	1.36513e13i	−0.691914	+	1.19843i	0.279296	+	0.960205i	$0.409899\pi$
$797$	−7.88160e12	+	1.36513e13i	−0.691914	+	1.19843i	−0.971210	+	0.238225i	$0.923434\pi$
$798$			3.47730e12i			0.303549i
$799$	−1.09307e13	−	6.31086e12i	−0.948830	−	0.547807i
$800$	1.61737e12	+	9.33791e11i	0.139606	+	0.0806018i
$801$		−	4.29577e11i		−	0.0368718i
$802$	−1.07292e13	+	1.85835e13i	−0.915761	+	1.58614i
$803$	−8.60479e10	−	1.49039e11i	−0.00730332	−	0.0126497i
$804$	−4.63841e12	+	2.67799e12i	−0.391486	+	0.226025i
$805$	−3.71598e12			−0.311883
$806$	−1.56448e13	−	4.46239e12i	−1.30576	−	0.372443i
$807$	7.44435e12			0.617868
$808$	1.32247e13	−	7.63526e12i	1.09152	−	0.630192i
$809$	−6.21712e11	−	1.07684e12i	−0.0510295	−	0.0883857i	0.839382	−	0.543541i	$-0.182917\pi$
$809$	−6.21712e11	−	1.07684e12i	−0.0510295	−	0.0883857i	−0.890412	+	0.455156i	$0.849584\pi$
$810$	−1.54544e12	+	2.67679e12i	−0.126145	+	0.218490i
$811$			2.68896e12i			0.218269i	0.994027	+	0.109134i	$0.0348078\pi$
$811$			2.68896e12i			0.218269i	−0.994027	+	0.109134i	$0.965192\pi$
$812$	1.04270e12	+	6.02001e11i	0.0841696	+	0.0485954i
$813$	−5.90152e12	−	3.40724e12i	−0.473758	−	0.273524i
$814$		−	1.18322e12i		−	0.0944617i
$815$	9.61391e12	−	1.66518e13i	0.763292	−	1.32206i
$816$	1.67856e12	+	2.90735e12i	0.132535	+	0.229558i
$817$	7.43402e12	−	4.29204e12i	0.583747	−	0.337027i
$818$	−1.30139e13			−1.01629
$819$	7.31972e11	−	2.56623e12i	0.0568482	−	0.199305i
$820$	−1.06584e13			−0.823243
$821$	2.46857e12	−	1.42523e12i	0.189628	−	0.109482i	−0.402181	−	0.915560i	$-0.631748\pi$
$821$	2.46857e12	−	1.42523e12i	0.189628	−	0.109482i	0.591808	+	0.806079i	$0.298414\pi$
$822$	5.57729e12	+	9.66014e12i	0.426088	+	0.738007i
$823$	1.00773e13	−	1.74544e13i	0.765678	−	1.32619i	−0.174210	−	0.984709i	$-0.555737\pi$
$823$	1.00773e13	−	1.74544e13i	0.765678	−	1.32619i	0.939888	−	0.341484i	$-0.110930\pi$
$824$			1.39538e13i			1.05444i
$825$	−1.00353e11	−	5.79391e10i	−0.00754205	−	0.00435441i
$826$	3.08108e12	+	1.77886e12i	0.230300	+	0.132963i
$827$			1.70111e13i			1.26462i	0.774717	+	0.632308i	$0.217892\pi$
$827$			1.70111e13i			1.26462i	−0.774717	+	0.632308i	$0.782108\pi$
$828$	4.22324e12	−	7.31487e12i	0.312255	−	0.540842i
$829$	1.17817e13	+	2.04064e13i	0.866386	+	1.50062i	0.865665	+	0.500624i	$0.166896\pi$
$829$	1.17817e13	+	2.04064e13i	0.866386	+	1.50062i	0.000720831		1.00000i	$0.499771\pi$
$830$	−1.73363e13	+	1.00091e13i	−1.26796	+	0.732057i
$831$	1.37961e12			0.100358
$832$	−1.60304e13	+	1.55237e13i	−1.15981	+	1.12316i
$833$	−2.50333e12			−0.180142
$834$	7.36485e12	−	4.25210e12i	0.527129	−	0.304338i
$835$	−8.01724e11	−	1.38863e12i	−0.0570737	−	0.0988545i
$836$	7.77667e11	−	1.34696e12i	0.0550637	−	0.0953731i
$837$			1.27703e13i			0.899366i
$838$	−1.73462e13	−	1.00149e13i	−1.21509	−	0.701530i
$839$	−6.38819e12	−	3.68823e12i	−0.445092	−	0.256974i	0.260663	−	0.965430i	$-0.416059\pi$
$839$	−6.38819e12	−	3.68823e12i	−0.445092	−	0.256974i	−0.705755	+	0.708456i	$0.749392\pi$
$840$			2.86708e12i			0.198694i
$841$	7.03104e12	−	1.21781e13i	0.484661	−	0.839457i
$842$	1.83602e13	+	3.18008e13i	1.25885	+	2.18038i
$843$	−1.28221e13	+	7.40285e12i	−0.874451	+	0.504865i
$844$	1.17896e13			0.799757
$845$	−1.57558e13	−	5.06073e11i	−1.06313	−	0.0341474i
$846$	−1.11518e13			−0.748475
$847$	4.85526e12	−	2.80319e12i	0.324144	−	0.187144i
$848$	−3.75227e12	−	6.49912e12i	−0.249180	−	0.431592i
$849$	1.76220e12	−	3.05222e12i	0.116405	−	0.201619i
$850$			3.96176e12i			0.260317i
$851$	6.26719e12	+	3.61837e12i	0.409628	+	0.236499i
$852$	−4.06972e12	−	2.34966e12i	−0.264598	−	0.152766i
$853$		−	1.39402e12i		−	0.0901566i	−0.998983	−	0.0450783i	$-0.985646\pi$
$853$		−	1.39402e12i		−	0.0901566i	0.998983	−	0.0450783i	$-0.0143537\pi$
$854$	−4.51603e12	+	7.82199e12i	−0.290533	+	0.503219i
$855$	3.46634e12	+	6.00388e12i	0.221832	+	0.384224i
$856$	7.00303e12	−	4.04320e12i	0.445815	−	0.257391i
$857$	−8.65932e11			−0.0548366			−0.0274183	−	0.999624i	$-0.508729\pi$
$857$	−8.65932e11			−0.0548366			−0.0274183	+	0.999624i	$0.508729\pi$
$858$	1.18733e12	−	1.14981e12i	0.0747962	−	0.0724323i
$859$	2.31704e13			1.45199			0.725996	−	0.687699i	$-0.241379\pi$
$859$	2.31704e13			1.45199			0.725996	+	0.687699i	$0.241379\pi$
$860$	1.92238e13	−	1.10989e13i	1.19838	−	0.691888i
$861$	1.07970e12	+	1.87010e12i	0.0669559	+	0.115971i
$862$	7.70276e12	−	1.33416e13i	0.475186	−	0.823047i
$863$			6.74319e12i			0.413825i	0.978359	+	0.206912i	$0.0663415\pi$
$863$			6.74319e12i			0.413825i	−0.978359	+	0.206912i	$0.933658\pi$
$864$	1.81084e13	+	1.04549e13i	1.10553	+	0.638276i
$865$	2.55174e13	+	1.47325e13i	1.54976	+	0.894752i
$866$			5.27630e12i			0.318786i
$867$	−3.29910e12	+	5.71421e12i	−0.198294	+	0.343455i
$868$	4.01033e12	+	6.94610e12i	0.239796	+	0.415338i
$869$	−6.79515e11	+	3.92318e11i	−0.0404213	+	0.0233372i
$870$	−3.32391e12			−0.196704
$871$	−2.13463e12	+	7.48382e12i	−0.125672	+	0.440597i
$872$	−4.66340e12			−0.273136
$873$	6.25242e12	−	3.60984e12i	0.364321	−	0.210341i
$874$	7.99609e12	+	1.38496e13i	0.463528	+	0.802854i
$875$	−3.02750e12	+	5.24378e12i	−0.174601	+	0.302419i
$876$		−	2.54701e12i		−	0.146138i
$877$	2.22329e13	+	1.28361e13i	1.26910	+	0.732717i	0.974818	−	0.223000i	$-0.0715851\pi$
$877$	2.22329e13	+	1.28361e13i	1.26910	+	0.732717i	0.294285	+	0.955718i	$0.404918\pi$
$878$	1.31437e13	+	7.58850e12i	0.746434	+	0.430954i
$879$			5.08478e12i			0.287291i
$880$	−2.91838e11	+	5.05478e11i	−0.0164047	+	0.0284138i
$881$	−1.25245e13	−	2.16931e13i	−0.700437	−	1.21319i	−0.968313	−	0.249738i	$-0.919655\pi$
$881$	−1.25245e13	−	2.16931e13i	−0.700437	−	1.21319i	0.267877	−	0.963453i	$-0.413678\pi$
$882$	−1.91547e12	+	1.10590e12i	−0.106578	+	0.0615327i
$883$	1.41878e13			0.785401			0.392701	−	0.919666i	$-0.371541\pi$
$883$	1.41878e13			0.785401			0.392701	+	0.919666i	$0.371541\pi$
$884$	−3.23236e13	−	9.21973e12i	−1.78027	−	0.507789i
$885$	−5.84235e12			−0.320142
$886$	5.08731e12	−	2.93716e12i	0.277355	−	0.160131i
$887$	1.19007e13	+	2.06125e13i	0.645527	+	1.11809i	0.984179	+	0.177174i	$0.0566956\pi$
$887$	1.19007e13	+	2.06125e13i	0.645527	+	1.11809i	−0.338652	+	0.940912i	$0.609971\pi$
$888$	2.79177e12	−	4.83549e12i	0.150668	−	0.260965i
$889$			2.04640e12i			0.109884i
$890$	1.82145e12	+	1.05162e12i	0.0973112	+	0.0561826i
$891$	−2.42570e11	−	1.40048e11i	−0.0128940	−	0.00744436i
$892$			4.72762e13i			2.50035i
$893$	6.27969e12	−	1.08767e13i	0.330451	−	0.572357i
$894$	1.29189e13	+	2.23762e13i	0.676405	+	1.17157i
$895$	−1.52232e13	+	8.78913e12i	−0.793054	+	0.457870i
$896$	9.54975e12			0.495001
$897$	2.45927e12	+	9.80515e12i	0.126836	+	0.505695i
$898$	1.16940e13			0.600095
$899$	−2.56763e12	+	1.48242e12i	−0.131103	+	0.0756926i
$900$	1.04106e12	+	1.80317e12i	0.0528914	+	0.0916106i
$901$	1.98721e13	−	3.44196e13i	1.00458	−	1.73998i
$902$		−	1.62376e12i		−	0.0816756i
$903$	−3.89477e12	−	2.24865e12i	−0.194934	−	0.112545i
$904$	2.28535e13	+	1.31945e13i	1.13814	+	0.657104i
$905$		−	9.03730e12i		−	0.447837i
$906$	−1.27138e13	+	2.20209e13i	−0.626900	+	1.08582i
$907$	1.36167e13	+	2.35847e13i	0.668094	+	1.15717i	0.978436	+	0.206548i	$0.0662230\pi$
$907$	1.36167e13	+	2.35847e13i	0.668094	+	1.15717i	−0.310342	+	0.950625i	$0.600444\pi$
$908$	−2.54876e13	+	1.47153e13i	−1.24435	+	0.718426i
$909$	−1.93452e13			−0.939800
$910$	9.08923e12	+	9.38586e12i	0.439380	+	0.453720i
$911$	−5.74828e12			−0.276506			−0.138253	−	0.990397i	$-0.544149\pi$
$911$	−5.74828e12			−0.276506			−0.138253	+	0.990397i	$0.544149\pi$
$912$	−2.89300e12	+	1.67027e12i	−0.138475	+	0.0799485i
$913$	−9.07027e11	−	1.57102e12i	−0.0432018	−	0.0748277i
$914$	2.34067e13	−	4.05416e13i	1.10939	−	1.92151i
$915$		−	1.48321e13i		−	0.699531i
$916$	2.12293e13	+	1.22567e13i	0.996335	+	0.575234i
$917$	1.02276e13	+	5.90490e12i	0.477652	+	0.275772i
$918$			4.43567e13i			2.06142i
$919$	−1.06964e12	+	1.85267e12i	−0.0494672	+	0.0856796i	−0.889699	−	0.456548i	$-0.849086\pi$
$919$	−1.06964e12	+	1.85267e12i	−0.0494672	+	0.0856796i	0.840232	+	0.542228i	$0.182419\pi$
$920$	6.59288e12	+	1.14192e13i	0.303410	+	0.525522i
$921$	−6.28259e12	+	3.62725e12i	−0.287720	+	0.166115i
$922$	3.45041e13			1.57247
$923$	−6.62302e12	+	1.66115e12i	−0.300364	+	0.0753357i
$924$	−8.14858e11			−0.0367754
$925$	−1.54491e12	+	8.91955e11i	−0.0693850	+	0.0400595i
$926$	−2.10406e13	−	3.64434e13i	−0.940391	−	1.62881i
$927$	8.83858e12	−	1.53089e13i	0.393119	−	0.680901i
$928$			4.85458e12i			0.214875i
$929$	−2.57774e12	−	1.48826e12i	−0.113545	−	0.0655552i	0.442152	−	0.896940i	$-0.354215\pi$
$929$	−2.57774e12	−	1.48826e12i	−0.113545	−	0.0655552i	−0.555697	+	0.831385i	$0.687549\pi$
$930$	−1.91762e13	−	1.10714e13i	−0.840601	−	0.485321i
$931$		−	2.49097e12i		−	0.108666i
$932$	2.98221e12	−	5.16535e12i	0.129469	−	0.224248i
$933$	−3.64539e12	−	6.31400e12i	−0.157499	−	0.272795i
$934$	−5.33715e13	+	3.08140e13i	−2.29482	+	1.32491i
$935$	−3.09116e12			−0.132273
$936$	−9.18471e12	+	2.30366e12i	−0.391133	+	0.0981017i
$937$	−7.54662e12			−0.319834			−0.159917	−	0.987130i	$-0.551123\pi$
$937$	−7.54662e12			−0.319834			−0.159917	+	0.987130i	$0.551123\pi$
$938$	5.58601e12	−	3.22509e12i	0.235608	−	0.136028i
$939$	8.48735e12	+	1.47005e13i	0.356268	+	0.617075i
$940$	1.62388e13	−	2.81264e13i	0.678388	−	1.17500i
$941$		−	2.47347e13i		−	1.02838i	−0.857676	−	0.514191i	$-0.828092\pi$
$941$		−	2.47347e13i		−	1.02838i	0.857676	−	0.514191i	$-0.171908\pi$
$942$	3.74250e13	+	2.16074e13i	1.54858	+	0.894072i
$943$	8.60060e12	+	4.96556e12i	0.354182	+	0.204487i
$944$			3.41781e12i			0.140079i
$945$	5.12796e12	−	8.88188e12i	0.209171	−	0.362295i
$946$	1.69087e12	+	2.92867e12i	0.0686435	+	0.118894i
$947$	9.79854e12	−	5.65719e12i	0.395901	−	0.228573i	−0.288813	−	0.957386i	$-0.593261\pi$
$947$	9.79854e12	−	5.65719e12i	0.395901	−	0.228573i	0.684714	+	0.728812i	$0.259927\pi$
$948$	−1.16126e13			−0.466973
$949$	−2.57455e12	−	2.65857e12i	−0.103039	−	0.106402i
$950$	−3.94219e12			−0.157030
$951$	3.86921e12	−	2.23389e12i	0.153395	−	0.0885624i
$952$	4.44141e12	+	7.69275e12i	0.175249	+	0.303539i
$953$	1.53018e13	−	2.65036e13i	0.600933	−	1.04085i	−0.391748	−	0.920073i	$-0.628129\pi$
$953$	1.53018e13	−	2.65036e13i	0.600933	−	1.04085i	0.992680	−	0.120773i	$-0.0385373\pi$
$954$		−	3.51156e13i		−	1.37256i
$955$	−2.29216e13	−	1.32338e13i	−0.891723	−	0.514837i
$956$	−2.10628e13	−	1.21606e13i	−0.815558	−	0.470863i
$957$		−	3.01213e11i		−	0.0116083i
$958$	2.96899e13	−	5.14244e13i	1.13884	−	1.97254i
$959$	−3.99529e12	−	6.92005e12i	−0.152533	−	0.264196i
$960$	−2.63030e13	+	1.51861e13i	−0.999506	+	0.577065i
$961$	6.68879e12			0.252984
$962$	−6.19015e12	−	2.46802e13i	−0.233031	−	0.929097i
$963$	−1.02441e13			−0.383845
$964$	2.13840e13	−	1.23460e13i	0.797520	−	0.460448i
$965$	−2.00498e13	−	3.47272e13i	−0.744280	−	1.28913i
$966$	4.18924e12	−	7.25598e12i	0.154788	−	0.268101i
$967$			4.36340e13i			1.60474i	0.596824	+	0.802372i	$0.296429\pi$
$967$			4.36340e13i			1.60474i	−0.596824	+	0.802372i	$0.703571\pi$
$968$	−1.72284e13	−	9.94683e12i	−0.630676	−	0.364121i
$969$	−1.53214e13	−	8.84582e12i	−0.558267	−	0.322315i
$970$			3.53480e13i			1.28201i
$971$	−1.19342e13	+	2.06707e13i	−0.430832	+	0.746224i	−0.996945	−	0.0781042i	$-0.975113\pi$
$971$	−1.19342e13	+	2.06707e13i	−0.430832	+	0.746224i	0.566113	+	0.824328i	$0.308447\pi$
$972$	1.91840e13	+	3.32276e13i	0.689351	+	1.19399i
$973$	−5.27582e12	+	3.04600e12i	−0.188704	+	0.108949i
$974$	−7.75384e13			−2.76059
$975$	−2.39634e12	−	6.83512e11i	−0.0849234	−	0.0242229i
$976$	−8.67683e12			−0.306082
$977$	4.52773e13	−	2.61408e13i	1.58984	−	0.917897i	0.596513	−	0.802603i	$-0.296552\pi$
$977$	4.52773e13	−	2.61408e13i	1.58984	−	0.917897i	0.993331	−	0.115294i	$-0.0367810\pi$
$978$	2.16767e13	+	3.75451e13i	0.757648	+	1.31229i
$979$	−9.52974e10	+	1.65060e11i	−0.00331558	+	0.00574275i
$980$		−	6.44145e12i		−	0.223083i
$981$	5.11625e12	+	2.95387e12i	0.176377	+	0.101831i
$982$	−5.99236e13	−	3.45969e13i	−2.05635	−	1.18723i
$983$			2.13702e11i			0.00729993i	0.999993	+	0.00364996i	$0.00116182\pi$
$983$			2.13702e11i			0.00729993i	−0.999993	+	0.00364996i	$0.998838\pi$
$984$	3.83121e12	−	6.63584e12i	0.130274	−	0.225641i
$985$	−1.72424e13	−	2.98647e13i	−0.583626	−	1.01087i
$986$	−8.91847e12	+	5.14908e12i	−0.300500	+	0.173494i
$987$	−6.58001e12			−0.220698
$988$	9.17420e12	−	3.21640e13i	0.306311	−	1.07390i
$989$	−2.06831e13			−0.687437
$990$	−2.36526e12	+	1.36558e12i	−0.0782565	+	0.0451814i
$991$	2.12598e13	+	3.68231e13i	0.700210	+	1.21280i	0.968392	+	0.249431i	$0.0802437\pi$
$991$	2.12598e13	+	3.68231e13i	0.700210	+	1.21280i	−0.268182	+	0.963368i	$0.586423\pi$
$992$	−1.61698e13	+	2.80069e13i	−0.530154	+	0.918254i
$993$		−	3.90183e13i		−	1.27349i
$994$	4.90115e12	+	2.82968e12i	0.159243	+	0.0919387i
$995$	−2.38671e13	−	1.37797e13i	−0.771962	−	0.445693i
$996$		−	2.68480e13i		−	0.864459i
$997$	−2.28244e13	+	3.95329e13i	−0.731594	+	1.26716i	0.224607	+	0.974449i	$0.427890\pi$
$997$	−2.28244e13	+	3.95329e13i	−0.731594	+	1.26716i	−0.956201	+	0.292709i	$0.905443\pi$
$998$	−2.98254e13	−	5.16591e13i	−0.951696	−	1.64839i
$999$	−1.72971e13	+	9.98651e12i	−0.549452	+	0.317226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.q.a.36.9	✓	124
13.4	even	6	inner	91.10.q.a.43.9	yes	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.q.a.36.9	✓	124	1.1	even	1	trivial
91.10.q.a.43.9	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)

\(f(q)\)	\(=\)	\(q+(-30.7856 + 17.7740i) q^{2} +(-47.1433 - 81.6546i) q^{3} +(375.833 - 650.963i) q^{4} -1486.53i q^{5} +(2902.67 + 1675.85i) q^{6} +(-2079.33 - 1200.50i) q^{7} +8519.70i q^{8} +(5396.52 - 9347.04i) q^{9} +O(q^{10})\)	\(q+(-30.7856 + 17.7740i) q^{2} +(-47.1433 - 81.6546i) q^{3} +(375.833 - 650.963i) q^{4} -1486.53i q^{5} +(2902.67 + 1675.85i) q^{6} +(-2079.33 - 1200.50i) q^{7} +8519.70i q^{8} +(5396.52 - 9347.04i) q^{9} +(26421.7 + 45763.7i) q^{10} +(-4147.10 + 2394.33i) q^{11} -70872.1 q^{12} +(-73976.1 + 71638.2i) q^{13} +85351.0 q^{14} +(-121382. + 70080.0i) q^{15} +(40997.1 + 71009.1i) q^{16} +(-217122. + 376067. i) q^{17} +383672. i q^{18} +(-374209. - 216050. i) q^{19} +(-967676. - 558688. i) q^{20} +226382. i q^{21} +(85113.9 - 147422. i) q^{22} +(520568. + 901650. i) q^{23} +(695673. - 401647. i) q^{24} -256648. q^{25} +(1.00410e6 - 3.52028e6i) q^{26} -2.87348e6 q^{27} +(-1.56296e6 + 902376. i) q^{28} +(-333564. - 577750. i) q^{29} +(2.49121e6 - 4.31490e6i) q^{30} -4.44419e6i q^{31} +(-6.30192e6 - 3.63841e6i) q^{32} +(391016. + 225753. i) q^{33} -1.54366e7i q^{34} +(-1.78458e6 + 3.09098e6i) q^{35} +(-4.05638e6 - 7.02586e6i) q^{36} +(6.01958e6 - 3.47540e6i) q^{37} +1.53603e7 q^{38} +(9.33707e6 + 2.66323e6i) q^{39} +1.26648e7 q^{40} +(8.26079e6 - 4.76937e6i) q^{41} +(-4.02373e6 - 6.96930e6i) q^{42} +(-9.93298e6 + 1.72044e7i) q^{43} +3.59948e6i q^{44} +(-1.38947e7 - 8.02209e6i) q^{45} +(-3.20519e7 - 1.85052e7i) q^{46} +2.90659e7i q^{47} +(3.86548e6 - 6.69521e6i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(7.90104e6 - 4.56167e6i) q^{50} +4.09434e7 q^{51} +(1.88311e7 + 7.50797e7i) q^{52} -9.15252e7 q^{53} +(8.84617e7 - 5.10734e7i) q^{54} +(3.55925e6 + 6.16479e6i) q^{55} +(1.02279e7 - 1.77153e7i) q^{56} +4.07412e7i q^{57} +(2.05379e7 + 1.18576e7i) q^{58} +(3.60990e7 + 2.08417e7i) q^{59} +1.05354e8i q^{60} +(-5.29113e7 + 9.16450e7i) q^{61} +(7.89912e7 + 1.36817e8i) q^{62} +(-2.24423e7 + 1.29570e7i) q^{63} +2.16696e8 q^{64} +(1.06492e8 + 1.09968e8i) q^{65} -1.60502e7 q^{66} +(6.54476e7 - 3.77862e7i) q^{67} +(1.63204e8 + 2.82677e8i) q^{68} +(4.90826e7 - 8.50135e7i) q^{69} -1.26877e8i q^{70} +(5.74235e7 + 3.31535e7i) q^{71} +(7.96341e7 + 4.59767e7i) q^{72} +3.59382e7i q^{73} +(-1.23544e8 + 2.13984e8i) q^{74} +(1.20992e7 + 2.09565e7i) q^{75} +(-2.81281e8 + 1.62398e8i) q^{76} +1.14976e7 q^{77} +(-3.34783e8 + 8.39684e7i) q^{78} +1.63853e8 q^{79} +(1.05557e8 - 6.09435e7i) q^{80} +(2.92458e7 + 5.06551e7i) q^{81} +(-1.69542e8 + 2.93655e8i) q^{82} +3.78823e8i q^{83} +(1.47366e8 + 8.50820e7i) q^{84} +(5.59034e8 + 3.22759e8i) q^{85} -7.06197e8i q^{86} +(-3.14506e7 + 5.44741e7i) q^{87} +(-2.03990e7 - 3.53321e7i) q^{88} +(3.44689e7 - 1.99006e7i) q^{89} +5.70340e8 q^{90} +(2.39822e8 - 6.01509e7i) q^{91} +7.82587e8 q^{92} +(-3.62889e8 + 2.09514e8i) q^{93} +(-5.16619e8 - 8.94811e8i) q^{94} +(-3.21165e8 + 5.56274e8i) q^{95} +6.86107e8i q^{96} +(5.79302e8 + 3.34460e8i) q^{97} +(-1.77473e8 - 1.02464e8i) q^{98} +5.16842e7i 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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Representations

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Database

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