LMFDB - Embedded newform 6.31.b.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,31,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 31, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 31);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 31 $
Character orbit:	$[\chi]$	$=$	6.b (of order $2$, degree $1$, 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:	$34.2085571416$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + \cdots + 17\!\cdots\!00 $ x^10 + 8552062877595970390x^8 + 25392807796994293834069533242559594025x^6 + 31363214047445929775687291161211122208644643150843750000x^4 + 14997479733093492468171154918719535444710088825890735887189931640625000000x^2 + 1779211874045772876005913493072356377360261727229346754892124420427761840820312500000000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{104}\cdot 3^{53}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Root			$1.19483e9i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.31.b.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23170.5i q^{2} +(7.57629e6 + 1.21857e7i) q^{3} -5.36871e8 q^{4} +2.86759e10i q^{5} +(2.82348e11 - 1.75546e11i) q^{6} -3.86992e12 q^{7} +1.24396e13i q^{8} +(-9.10907e13 + 1.84645e14i) q^{9} +O(q^{10})$	\(q-23170.5i q^{2} +(7.57629e6 + 1.21857e7i) q^{3} -5.36871e8 q^{4} +2.86759e10i q^{5} +(2.82348e11 - 1.75546e11i) q^{6} -3.86992e12 q^{7} +1.24396e13i q^{8} +(-9.10907e13 + 1.84645e14i) q^{9} +6.64434e14 q^{10} +1.21973e15i q^{11} +(-4.06749e15 - 6.54214e15i) q^{12} -5.72073e16 q^{13} +8.96678e16i q^{14} +(-3.49435e17 + 2.17257e17i) q^{15} +2.88230e17 q^{16} -4.94792e18i q^{17} +(4.27830e18 + 2.11061e18i) q^{18} +2.15233e19 q^{19} -1.53953e19i q^{20} +(-2.93196e19 - 4.71576e19i) q^{21} +2.82618e19 q^{22} -1.53583e20i q^{23} +(-1.51584e20 + 9.42457e19i) q^{24} +1.09015e20 q^{25} +1.32552e21i q^{26} +(-2.94015e21 + 2.88919e20i) q^{27} +2.07765e21 q^{28} -8.01754e21i q^{29} +(5.03395e21 + 8.09659e21i) q^{30} -2.10460e22 q^{31} -6.67843e21i q^{32} +(-1.48633e22 + 9.24105e21i) q^{33} -1.14646e23 q^{34} -1.10973e23i q^{35} +(4.89040e22 - 9.91303e22i) q^{36} -1.99779e23 q^{37} -4.98704e23i q^{38} +(-4.33419e23 - 6.97110e23i) q^{39} -3.56715e23 q^{40} +2.99372e23i q^{41} +(-1.09266e24 + 6.79349e23i) q^{42} -5.08423e24 q^{43} -6.54839e23i q^{44} +(-5.29485e24 - 2.61211e24i) q^{45} -3.55858e24 q^{46} -5.51797e24i q^{47} +(2.18372e24 + 3.51228e24i) q^{48} -7.56309e24 q^{49} -2.52594e24i q^{50} +(6.02937e25 - 3.74869e25i) q^{51} +3.07129e25 q^{52} +2.02634e25i q^{53} +(6.69440e24 + 6.81247e25i) q^{54} -3.49769e25 q^{55} -4.81400e25i q^{56} +(1.63067e26 + 2.62276e26i) q^{57} -1.85770e26 q^{58} +4.17852e26i q^{59} +(1.87602e26 - 1.16639e26i) q^{60} +1.01948e27 q^{61} +4.87646e26i q^{62} +(3.52513e26 - 7.14559e26i) q^{63} -1.54743e26 q^{64} -1.64047e27i q^{65} +(2.14120e26 + 3.44389e26i) q^{66} -4.41872e27 q^{67} +2.65639e27i q^{68} +(1.87151e27 - 1.16359e27i) q^{69} -2.57130e27 q^{70} -8.92058e27i q^{71} +(-2.29690e27 - 1.13313e27i) q^{72} -4.52229e27 q^{73} +4.62897e27i q^{74} +(8.25933e26 + 1.32843e27i) q^{75} -1.15552e28 q^{76} -4.72026e27i q^{77} +(-1.61524e28 + 1.00425e28i) q^{78} +3.16027e28 q^{79} +8.26526e27i q^{80} +(-2.57961e28 - 3.36388e28i) q^{81} +6.93660e27 q^{82} +2.37093e27i q^{83} +(1.57409e28 + 2.53175e28i) q^{84} +1.41886e29 q^{85} +1.17804e29i q^{86} +(9.76992e28 - 6.07432e28i) q^{87} -1.51729e28 q^{88} -5.31121e28i q^{89} +(-6.05238e28 + 1.22684e29i) q^{90} +2.21387e29 q^{91} +8.24540e28i q^{92} +(-1.59451e29 - 2.56460e29i) q^{93} -1.27854e29 q^{94} +6.17199e29i q^{95} +(8.13813e28 - 5.05978e28i) q^{96} -6.93514e29 q^{97} +1.75240e29i q^{98} +(-2.25217e29 - 1.11106e29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) $ 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9	$ 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) $ 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9 - 1111538175836160 * q^10 - 7591226920402944 * q^12 + 11241857908456580 * q^13 - 1208370750576105600 * q^15 + 2882303761517117440 * q^16 + 4378961453216956416 * q^18 - 406434941012438620 * q^19 + 189341373476724706020 * q^21 - 175966920878069907456 * q^22 + 78269746773932113920 * q^24 - 538750688835772733030 * q^25 - 509686212259700532126 * q^27 + 783474298257252810752 * q^28 + 3618734882327478927360 * q^30 - 3850790055930904811020 * q^31 + 13877514934601873876352 * q^33 - 21974427701517892976640 * q^34 - 22394560921038760181760 * q^36 + 691786417224189171658916 * q^37 + 264189297409049008449300 * q^39 + 596752514183975581777920 * q^40 + 2551733261187619598893056 * q^42 - 10594373354873893550389372 * q^43 + 21961398854703004532478720 * q^45 - 14905926072892021549301760 * q^46 + 4075508919955679952764928 * q^48 - 14303693611422252234715650 * q^49 + 100757981401326611204590080 * q^51 - 6035426507887496617000960 * q^52 + 186364360915292902942310400 * q^54 - 905529883473273884900970240 * q^55 + 1357830109447011748343825076 * q^57 - 1026862318649343581985177600 * q^58 + 648739106895918338880307200 * q^60 - 2949272535924647913201299260 * q^61 + 5088794127795653673352888692 * q^63 - 1547425049106725343623905280 * q^64 + 3787402697011447732654571520 * q^66 - 10556251754234326335356822044 * q^67 + 15764240424701154050198334720 * q^69 - 8691440888931957213379952640 * q^70 - 2350937029001432724922171392 * q^72 + 12106003505184711607130189300 * q^73 - 7500206691267464218185712830 * q^75 + 218203097450014125263421440 * q^76 - 23839067108381696719249735680 * q^78 + 68719005124237783442983312820 * q^79 - 111620808361643664456575921430 * q^81 + 18283730424263848186657898496 * q^82 - 101651875857781803693889290240 * q^84 + 403836274868708986530058828800 * q^85 - 512433611792960206983797969280 * q^87 + 94471521293641232015658319872 * q^88 - 426164288449255115819581440000 * q^90 + 1222541373056582384854822798600 * q^91 - 983623123086267594817934884284 * q^93 - 80746046881825464175401369600 * q^94 - 42020750332529991826318295040 * q^96 - 1391585232259866867438139103212 * q^97 + 2707446209006624257844338302720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$		−	23170.5i		−	0.707107i
$2$		−	23170.5i		−	0.707107i
$3$	7.57629e6	+	1.21857e7i	0.528005	+	0.849241i
$3$	7.57629e6	+	1.21857e7i	0.528005	+	0.849241i
$4$	−5.36871e8			−0.500000
$5$			2.86759e10i			0.939652i	0.882759	+	0.469826i	$0.155683\pi$
$5$			2.86759e10i			0.939652i	−0.882759	+	0.469826i	$0.844317\pi$
$6$	2.82348e11	−	1.75546e11i	0.600504	−	0.373356i
$7$	−3.86992e12			−0.815138			−0.407569	−	0.913174i	$-0.633623\pi$
$7$	−3.86992e12			−0.815138			−0.407569	+	0.913174i	$0.633623\pi$
$8$			1.24396e13i			0.353553i
$9$	−9.10907e13	+	1.84645e14i	−0.442422	+	0.896807i
$10$	6.64434e14			0.664434
$11$			1.21973e15i			0.291994i	0.989285	+	0.145997i	$0.0466390\pi$
$11$			1.21973e15i			0.291994i	−0.989285	+	0.145997i	$0.953361\pi$
$12$	−4.06749e15	−	6.54214e15i	−0.264002	−	0.424621i
$13$	−5.72073e16			−1.11764			−0.558819	−	0.829290i	$-0.688745\pi$
$13$	−5.72073e16			−1.11764			−0.558819	+	0.829290i	$0.688745\pi$
$14$			8.96678e16i			0.576389i
$15$	−3.49435e17	+	2.17257e17i	−0.797991	+	0.496141i
$16$	2.88230e17			0.250000
$17$		−	4.94792e18i		−	1.72858i	−0.502997	−	0.864288i	$-0.667769\pi$
$17$		−	4.94792e18i		−	1.72858i	0.502997	−	0.864288i	$-0.332231\pi$
$18$	4.27830e18	+	2.11061e18i	0.634138	+	0.312839i
$19$	2.15233e19			1.41776			0.708882	−	0.705327i	$-0.249200\pi$
$19$	2.15233e19			1.41776			0.708882	+	0.705327i	$0.249200\pi$
$20$		−	1.53953e19i		−	0.469826i
$21$	−2.93196e19	−	4.71576e19i	−0.430397	−	0.692249i
$22$	2.82618e19			0.206471
$23$		−	1.53583e20i		−	0.576003i	−0.957630	−	0.288001i	$-0.907009\pi$
$23$		−	1.53583e20i		−	0.576003i	0.957630	−	0.288001i	$-0.0929907\pi$
$24$	−1.51584e20	+	9.42457e19i	−0.300252	+	0.186678i
$25$	1.09015e20			0.117054
$26$			1.32552e21i			0.790289i
$27$	−2.94015e21	+	2.88919e20i	−0.995207	+	0.0977957i
$28$	2.07765e21			0.407569
$29$		−	8.01754e21i		−	0.929119i	−0.885542	−	0.464559i	$-0.846213\pi$
$29$		−	8.01754e21i		−	0.929119i	0.885542	−	0.464559i	$-0.153787\pi$
$30$	5.03395e21	+	8.09659e21i	0.350824	+	0.564265i
$31$	−2.10460e22			−0.896900			−0.448450	−	0.893808i	$-0.648024\pi$
$31$	−2.10460e22			−0.896900			−0.448450	+	0.893808i	$0.648024\pi$
$32$		−	6.67843e21i		−	0.176777i
$33$	−1.48633e22	+	9.24105e21i	−0.247974	+	0.154174i
$34$	−1.14646e23			−1.22229
$35$		−	1.10973e23i		−	0.765946i
$36$	4.89040e22	−	9.91303e22i	0.221211	−	0.448404i
$37$	−1.99779e23			−0.599134			−0.299567	−	0.954075i	$-0.596842\pi$
$37$	−1.99779e23			−0.599134			−0.299567	+	0.954075i	$0.596842\pi$
$38$		−	4.98704e23i		−	1.00251i
$39$	−4.33419e23	−	6.97110e23i	−0.590118	−	0.949144i
$40$	−3.56715e23			−0.332217
$41$			2.99372e23i			0.192510i	0.995357	+	0.0962551i	$0.0306865\pi$
$41$			2.99372e23i			0.192510i	−0.995357	+	0.0962551i	$0.969314\pi$
$42$	−1.09266e24	+	6.79349e23i	−0.489494	+	0.304336i
$43$	−5.08423e24			−1.60029			−0.800144	−	0.599808i	$-0.795244\pi$
$43$	−5.08423e24			−1.60029			−0.800144	+	0.599808i	$0.795244\pi$
$44$		−	6.54839e23i		−	0.145997i
$45$	−5.29485e24	−	2.61211e24i	−0.842686	−	0.415722i
$46$	−3.55858e24			−0.407295
$47$		−	5.51797e24i		−	0.457416i	−0.973495	−	0.228708i	$-0.926550\pi$
$47$		−	5.51797e24i		−	0.457416i	0.973495	−	0.228708i	$-0.0734501\pi$
$48$	2.18372e24	+	3.51228e24i	0.132001	+	0.212310i
$49$	−7.56309e24			−0.335551
$50$		−	2.52594e24i		−	0.0827700i
$51$	6.02937e25	−	3.74869e25i	1.46798	−	0.912696i
$52$	3.07129e25			0.558819
$53$			2.02634e25i			0.277060i	0.990358	+	0.138530i	$0.0442378\pi$
$53$			2.02634e25i			0.277060i	−0.990358	+	0.138530i	$0.955762\pi$
$54$	6.69440e24	+	6.81247e25i	0.0691520	+	0.703717i
$55$	−3.49769e25			−0.274373
$56$		−	4.81400e25i		−	0.288195i
$57$	1.63067e26	+	2.62276e26i	0.748587	+	1.20402i
$58$	−1.85770e26			−0.656986
$59$			4.17852e26i			1.14352i	0.820422	+	0.571759i	$0.193739\pi$
$59$			4.17852e26i			1.14352i	−0.820422	+	0.571759i	$0.806261\pi$
$60$	1.87602e26	−	1.16639e26i	0.398996	−	0.248070i
$61$	1.01948e27			1.69212			0.846062	−	0.533085i	$-0.178967\pi$
$61$	1.01948e27			1.69212			0.846062	+	0.533085i	$0.178967\pi$
$62$			4.87646e26i			0.634204i
$63$	3.52513e26	−	7.14559e26i	0.360635	−	0.731021i
$64$	−1.54743e26			−0.125000
$65$		−	1.64047e27i		−	1.05019i
$66$	2.14120e26	+	3.44389e26i	0.109018	+	0.175344i
$67$	−4.41872e27			−1.79546			−0.897728	−	0.440550i	$-0.854783\pi$
$67$	−4.41872e27			−1.79546			−0.897728	+	0.440550i	$0.854783\pi$
$68$			2.65639e27i			0.864288i
$69$	1.87151e27	−	1.16359e27i	0.489165	−	0.304132i
$70$	−2.57130e27			−0.541605
$71$		−	8.92058e27i		−	1.51886i	−0.650589	−	0.759430i	$-0.725478\pi$
$71$		−	8.92058e27i		−	1.51886i	0.650589	−	0.759430i	$-0.274522\pi$
$72$	−2.29690e27	−	1.13313e27i	−0.317069	−	0.156420i
$73$	−4.52229e27			−0.507592			−0.253796	−	0.967258i	$-0.581679\pi$
$73$	−4.52229e27			−0.507592			−0.253796	+	0.967258i	$0.581679\pi$
$74$			4.62897e27i			0.423652i
$75$	8.25933e26	+	1.32843e27i	0.0618053	+	0.0994075i
$76$	−1.15552e28			−0.708882
$77$		−	4.72026e27i		−	0.238016i
$78$	−1.61524e28	+	1.00425e28i	−0.671146	+	0.417277i
$79$	3.16027e28			1.08472			0.542360	−	0.840146i	$-0.317531\pi$
$79$	3.16027e28			1.08472			0.542360	+	0.840146i	$0.317531\pi$
$80$			8.26526e27i			0.234913i
$81$	−2.57961e28	−	3.36388e28i	−0.608526	−	0.793534i
$82$	6.93660e27			0.136125
$83$			2.37093e27i			0.0387925i	0.999812	+	0.0193962i	$0.00617440\pi$
$83$			2.37093e27i			0.0387925i	−0.999812	+	0.0193962i	$0.993826\pi$
$84$	1.57409e28	+	2.53175e28i	0.215198	+	0.346124i
$85$	1.41886e29			1.62426
$86$			1.17804e29i			1.13157i
$87$	9.76992e28	−	6.07432e28i	0.789046	−	0.490579i
$88$	−1.51729e28			−0.103236
$89$		−	5.31121e28i		−	0.305030i	−0.988301	−	0.152515i	$-0.951263\pi$
$89$		−	5.31121e28i		−	0.305030i	0.988301	−	0.152515i	$-0.0487373\pi$
$90$	−6.05238e28	+	1.22684e29i	−0.293960	+	0.595869i
$91$	2.21387e29			0.911029
$92$			8.24540e28i			0.288001i
$93$	−1.59451e29	−	2.56460e29i	−0.473568	−	0.761685i
$94$	−1.27854e29			−0.323442
$95$			6.17199e29i			1.33221i
$96$	8.13813e28	−	5.05978e28i	0.150126	−	0.0933390i
$97$	−6.93514e29			−1.09516			−0.547582	−	0.836752i	$-0.684452\pi$
$97$	−6.93514e29			−1.09516			−0.547582	+	0.836752i	$0.684452\pi$
$98$			1.75240e29i			0.237270i
$99$	−2.25217e29	−	1.11106e29i	−0.261863	−	0.129185i
$100$	−5.85272e28			−0.0585272
$101$		−	1.84054e30i		−	1.58534i	−0.609648	−	0.792672i	$-0.708689\pi$
$101$		−	1.84054e30i		−	1.58534i	0.609648	−	0.792672i	$-0.291311\pi$
$102$	−8.68588e29	−	1.39703e30i	−0.645374	−	1.03802i
$103$	1.62174e28			0.0104093			0.00520467	−	0.999986i	$-0.498343\pi$
$103$	1.62174e28			0.0104093			0.00520467	+	0.999986i	$0.498343\pi$
$104$		−	7.11633e29i		−	0.395145i
$105$	1.35229e30	−	8.40766e29i	0.650473	−	0.404423i
$106$	4.69512e29			0.195911
$107$			4.15310e30i			1.50527i	0.658436	+	0.752636i	$0.271218\pi$
$107$			4.15310e30i			1.50527i	−0.658436	+	0.752636i	$0.728782\pi$
$108$	1.57848e30	−	1.55112e29i	0.497603	−	0.0488979i
$109$	−6.16347e30			−1.69211			−0.846054	−	0.533098i	$-0.821028\pi$
$109$	−6.16347e30			−1.69211			−0.846054	+	0.533098i	$0.821028\pi$
$110$			8.10432e29i			0.194011i
$111$	−1.51358e30	−	2.43444e30i	−0.316346	−	0.508809i
$112$	−1.11543e30			−0.203784
$113$			1.15650e31i			1.84914i	0.381009	+	0.924571i	$0.375577\pi$
$113$			1.15650e31i			1.84914i	−0.381009	+	0.924571i	$0.624423\pi$
$114$	6.07705e30	−	3.77833e30i	0.851374	−	0.529331i
$115$	4.40412e30			0.541242
$116$			4.30438e30i			0.464559i
$117$	5.21105e30	−	1.05630e31i	0.494467	−	1.00231i
$118$	9.68184e30			0.808589
$119$			1.91480e31i			1.40903i
$120$	−2.70258e30	−	4.34682e30i	−0.175412	−	0.282132i
$121$	1.59617e31			0.914739
$122$		−	2.36219e31i		−	1.19651i
$123$	−3.64806e30	+	2.26813e30i	−0.163488	+	0.101646i
$124$	1.12990e31			0.448450
$125$			2.98326e31i			1.04964i
$126$	−1.65567e31	−	8.16790e30i	−0.516910	−	0.255007i
$127$	−4.86678e30			−0.134954			−0.0674770	−	0.997721i	$-0.521495\pi$
$127$	−4.86678e30			−0.134954			−0.0674770	+	0.997721i	$0.521495\pi$
$128$			3.58546e30i			0.0883883i
$129$	−3.85196e31	−	6.19548e31i	−0.844960	−	1.35903i
$130$	−3.80105e31			−0.742597
$131$			2.76358e31i			0.481285i	0.970614	+	0.240643i	$0.0773581\pi$
$131$			2.76358e31i			0.481285i	−0.970614	+	0.240643i	$0.922642\pi$
$132$	7.97966e30	−	4.96125e30i	0.123987	−	0.0770872i
$133$	−8.32932e31			−1.15567
$134$			1.02384e32i			1.26958i
$135$	−8.28502e30	−	8.43115e31i	−0.0918939	−	0.935148i
$136$	6.15499e31			0.611144
$137$		−	7.46283e31i		−	0.663888i	−0.943299	−	0.331944i	$-0.892295\pi$
$137$		−	7.46283e31i		−	0.663888i	0.943299	−	0.331944i	$-0.107705\pi$
$138$	−2.69609e31	−	4.33637e31i	−0.215054	−	0.345892i
$139$	6.63178e31			0.474688			0.237344	−	0.971426i	$-0.423723\pi$
$139$	6.63178e31			0.474688			0.237344	+	0.971426i	$0.423723\pi$
$140$			5.95783e31i			0.382973i
$141$	6.72402e31	−	4.18057e31i	0.388457	−	0.241518i
$142$	−2.06694e32			−1.07400
$143$		−	6.97776e31i		−	0.326344i
$144$	−2.62551e31	+	5.32202e31i	−0.110605	+	0.224202i
$145$	2.29910e32			0.873048
$146$			1.04784e32i			0.358922i
$147$	−5.73002e31	−	9.21614e31i	−0.177172	−	0.284963i
$148$	1.07256e32			0.299567
$149$			3.27988e32i			0.828064i	0.910262	+	0.414032i	$0.135880\pi$
$149$			3.27988e32i			0.828064i	−0.910262	+	0.414032i	$0.864120\pi$
$150$	3.07803e31	−	1.91373e31i	0.0702917	−	0.0437030i
$151$	3.88035e32			0.802077			0.401039	−	0.916061i	$-0.368649\pi$
$151$	3.88035e32			0.802077			0.401039	+	0.916061i	$0.368649\pi$
$152$			2.67740e32i			0.501256i
$153$	9.13606e32	+	4.50709e32i	1.55020	+	0.764759i
$154$	−1.09371e32			−0.168302
$155$		−	6.03513e32i		−	0.842774i
$156$	2.32690e32	+	3.74258e32i	0.295059	+	0.474572i
$157$	−8.67424e32			−0.999394			−0.499697	−	0.866200i	$-0.666555\pi$
$157$	−8.67424e32			−0.999394			−0.499697	+	0.866200i	$0.666555\pi$
$158$		−	7.32250e32i		−	0.767013i
$159$	−2.46923e32	+	1.53521e32i	−0.235291	+	0.146289i
$160$	1.91510e32			0.166109
$161$			5.94352e32i			0.469521i
$162$	−7.79427e32	+	5.97708e32i	−0.561113	+	0.430293i
$163$	−1.77971e33			−1.16825			−0.584123	−	0.811665i	$-0.698562\pi$
$163$	−1.77971e33			−1.16825			−0.584123	+	0.811665i	$0.698562\pi$
$164$		−	1.60724e32i		−	0.0962551i
$165$	−2.64995e32	−	4.26218e32i	−0.144870	−	0.233009i
$166$	5.49356e31			0.0274304
$167$		−	3.79418e33i		−	1.73130i	−0.500653	−	0.865648i	$-0.666907\pi$
$167$		−	3.79418e33i		−	1.73130i	0.500653	−	0.865648i	$-0.333093\pi$
$168$	5.86619e32	−	3.64723e32i	0.244747	−	0.152168i
$169$	6.52679e32			0.249114
$170$		−	3.28756e33i		−	1.14852i
$171$	−1.96057e33	+	3.97416e33i	−0.627250	+	1.27146i
$172$	2.72957e33			0.800144
$173$		−	2.80895e32i		−	0.0754836i	−0.999288	−	0.0377418i	$-0.987984\pi$
$173$		−	2.80895e32i		−	0.0754836i	0.999288	−	0.0377418i	$-0.0120164\pi$
$174$	−1.40745e33	−	2.26374e33i	−0.346892	−	0.557940i
$175$	−4.21881e32			−0.0954155
$176$			3.51564e32i			0.0729986i
$177$	−5.09182e33	+	3.16577e33i	−0.971122	+	0.603783i
$178$	−1.23063e33			−0.215689
$179$			5.13277e33i			0.827097i	0.910482	+	0.413549i	$0.135711\pi$
$179$			5.13277e33i			0.827097i	−0.910482	+	0.413549i	$0.864289\pi$
$180$	2.84265e33	+	1.40236e33i	0.421343	+	0.207861i
$181$	2.23718e33			0.305156			0.152578	−	0.988291i	$-0.451242\pi$
$181$	2.23718e33			0.305156			0.152578	+	0.988291i	$0.451242\pi$
$182$		−	5.12965e33i		−	0.644195i
$183$	7.72389e33	+	1.24231e34i	0.893449	+	1.43702i
$184$	1.91050e33			0.203648
$185$		−	5.72884e33i		−	0.562977i
$186$	−5.94230e33	+	3.69455e33i	−0.538593	+	0.334863i
$187$	6.03513e33			0.504734
$188$			2.96244e33i			0.228708i
$189$	1.13781e34	−	1.11809e33i	0.811230	−	0.0797170i
$190$	1.43008e34			0.942011
$191$		−	1.52021e34i		−	0.925560i	−0.886473	−	0.462780i	$-0.846852\pi$
$191$		−	1.52021e34i		−	0.925560i	0.886473	−	0.462780i	$-0.153148\pi$
$192$	−1.17237e33	−	1.88564e33i	−0.0660006	−	0.106155i
$193$	−1.75011e34			−0.911390			−0.455695	−	0.890136i	$-0.650609\pi$
$193$	−1.75011e34			−0.911390			−0.455695	+	0.890136i	$0.650609\pi$
$194$			1.60690e34i			0.774398i
$195$	1.99903e34	−	1.24287e34i	0.891865	−	0.554506i
$196$	4.06040e33			0.167775
$197$			3.12038e33i			0.119458i	0.998215	+	0.0597289i	$0.0190236\pi$
$197$			3.12038e33i			0.119458i	−0.998215	+	0.0597289i	$0.980976\pi$
$198$	−2.57439e33	+	5.21839e33i	−0.0913473	+	0.185165i
$199$	−1.07600e34			−0.354011			−0.177006	−	0.984210i	$-0.556641\pi$
$199$	−1.07600e34			−0.354011			−0.177006	+	0.984210i	$0.556641\pi$
$200$			1.35610e33i			0.0413850i
$201$	−3.34775e34	−	5.38452e34i	−0.948009	−	1.52478i
$202$	−4.26461e34			−1.12101
$203$			3.10272e34i			0.757360i
$204$	−3.23700e34	+	2.01256e34i	−0.733989	+	0.456348i
$205$	−8.58477e33			−0.180893
$206$		−	3.75765e32i		−	0.00736051i
$207$	2.83582e34	+	1.39899e34i	0.516563	+	0.254836i
$208$	−1.64889e34			−0.279409
$209$			2.62526e34i			0.413979i
$210$	−1.94810e34	−	3.13331e34i	−0.285970	−	0.459954i
$211$	−8.62877e34			−1.17954			−0.589769	−	0.807572i	$-0.700781\pi$
$211$	−8.62877e34			−1.17954			−0.589769	+	0.807572i	$0.700781\pi$
$212$		−	1.08788e34i		−	0.138530i
$213$	1.08703e35	−	6.75849e34i	1.28988	−	0.801966i
$214$	9.62292e34			1.06439
$215$		−	1.45795e35i		−	1.50371i
$216$	−3.59403e33	−	3.65742e34i	−0.0345760	−	0.351859i
$217$	8.14463e34			0.731097
$218$			1.42811e35i			1.19650i
$219$	−3.42622e34	−	5.51072e34i	−0.268011	−	0.431069i
$220$	1.87781e34			0.137186
$221$			2.83057e35i			1.93192i
$222$	−5.64072e34	+	3.50705e34i	−0.359783	+	0.223690i
$223$	5.24908e34			0.312975			0.156488	−	0.987680i	$-0.449983\pi$
$223$	5.24908e34			0.312975			0.156488	+	0.987680i	$0.449983\pi$
$224$			2.58450e34i			0.144097i
$225$	−9.93030e33	+	2.01291e34i	−0.0517874	+	0.104975i
$226$	2.67967e35			1.30754
$227$			1.84843e35i			0.844142i	0.906563	+	0.422071i	$0.138697\pi$
$227$			1.84843e35i			0.844142i	−0.906563	+	0.422071i	$0.861303\pi$
$228$	−8.75457e34	−	1.40808e35i	−0.374293	−	0.602012i
$229$	−1.69646e35			−0.679220			−0.339610	−	0.940566i	$-0.610295\pi$
$229$	−1.69646e35			−0.679220			−0.339610	+	0.940566i	$0.610295\pi$
$230$		−	1.02046e35i		−	0.382716i
$231$	5.75196e34	−	3.57621e34i	0.202133	−	0.125673i
$232$	9.97346e34			0.328493
$233$			1.72603e35i			0.532977i	0.963838	+	0.266489i	$0.0858635\pi$
$233$			1.72603e35i			0.532977i	−0.963838	+	0.266489i	$0.914137\pi$
$234$	−2.44750e35	−	1.20743e35i	−0.708737	−	0.349641i
$235$	1.58233e35			0.429812
$236$		−	2.24333e35i		−	0.571759i
$237$	2.39431e35	+	3.85101e35i	0.572738	+	0.921190i
$238$	4.43669e35			0.996333
$239$		−	1.65172e34i		−	0.0348312i	−0.999848	−	0.0174156i	$-0.994456\pi$
$239$		−	1.65172e34i		−	0.0348312i	0.999848	−	0.0174156i	$-0.00554384\pi$
$240$	−1.00718e35	+	6.26201e34i	−0.199498	+	0.124035i
$241$	−1.05445e36			−1.96232			−0.981158	−	0.193206i	$-0.938111\pi$
$241$	−1.05445e36			−1.96232			−0.981158	+	0.193206i	$0.938111\pi$
$242$		−	3.69839e35i		−	0.646818i
$243$	2.14473e35	−	5.69201e35i	0.352597	−	0.935775i
$244$	−5.47330e35			−0.846062
$245$		−	2.16878e35i		−	0.315301i
$246$	5.25537e34	+	8.45272e34i	0.0718748	+	0.115603i
$247$	−1.23129e36			−1.58455
$248$		−	2.61803e35i		−	0.317102i
$249$	−2.88914e34	+	1.79629e34i	−0.0329442	+	0.0204826i
$250$	6.91236e35			0.742209
$251$		−	1.07540e36i		−	1.08759i	−0.839219	−	0.543794i	$-0.816987\pi$
$251$		−	1.07540e36i		−	1.08759i	0.839219	−	0.543794i	$-0.183013\pi$
$252$	−1.89254e35	+	3.83626e35i	−0.180317	+	0.365511i
$253$	1.87330e35			0.168189
$254$			1.12766e35i			0.0954268i
$255$	1.07497e36	+	1.72898e36i	0.857617	+	1.37939i
$256$	8.30767e34			0.0625000
$257$		−	7.39792e35i		−	0.524944i	−0.964940	−	0.262472i	$-0.915462\pi$
$257$		−	7.39792e35i		−	0.524944i	0.964940	−	0.262472i	$-0.0845377\pi$
$258$	−1.43552e36	+	8.92517e35i	−0.960980	+	0.597477i
$259$	7.73128e35			0.488377
$260$			8.80721e35i			0.525095i
$261$	1.48040e36	+	7.30323e35i	0.833240	+	0.411062i
$262$	6.40334e35			0.340320
$263$		−	1.37844e36i		−	0.691913i	−0.938250	−	0.345957i	$-0.887554\pi$
$263$		−	1.37844e36i		−	0.691913i	0.938250	−	0.345957i	$-0.112446\pi$
$264$	−1.14955e35	−	1.84893e35i	−0.0545089	−	0.0876719i
$265$	−5.81071e35			−0.260340
$266$			1.92994e36i			0.817185i
$267$	6.47207e35	−	4.02393e35i	0.259044	−	0.161058i
$268$	2.37228e36			0.897728
$269$		−	1.32713e35i		−	0.0474929i	−0.999718	−	0.0237465i	$-0.992441\pi$
$269$		−	1.32713e35i		−	0.0474929i	0.999718	−	0.0237465i	$-0.00755945\pi$
$270$	−1.95354e36	+	1.91968e35i	−0.661249	+	0.0649788i
$271$	1.66897e36			0.534453			0.267227	−	0.963634i	$-0.413893\pi$
$271$	1.66897e36			0.534453			0.267227	+	0.963634i	$0.413893\pi$
$272$		−	1.42614e36i		−	0.432144i
$273$	1.67730e36	+	2.69776e36i	0.481028	+	0.773683i
$274$	−1.72917e36			−0.469440
$275$			1.32970e35i			0.0341792i
$276$	−1.00476e36	+	6.24696e35i	−0.244583	+	0.152066i
$277$	−1.56374e36			−0.360552			−0.180276	−	0.983616i	$-0.557699\pi$
$277$	−1.56374e36			−0.360552			−0.180276	+	0.983616i	$0.557699\pi$
$278$		−	1.53662e36i		−	0.335655i
$279$	1.91710e36	−	3.88603e36i	0.396808	−	0.804347i
$280$	1.38046e36			0.270803
$281$		−	5.33172e36i		−	0.991455i	−0.868478	−	0.495727i	$-0.834902\pi$
$281$		−	5.33172e36i		−	0.991455i	0.868478	−	0.495727i	$-0.165098\pi$
$282$	−9.68659e35	−	1.55799e36i	−0.170779	−	0.274680i
$283$	5.81215e36			0.971718			0.485859	−	0.874037i	$-0.338507\pi$
$283$	5.81215e36			0.971718			0.485859	+	0.874037i	$0.338507\pi$
$284$			4.78920e36i			0.759430i
$285$	−7.52099e36	+	4.67608e36i	−1.13136	+	0.703411i
$286$	−1.61678e36			−0.230760
$287$		−	1.15855e36i		−	0.156922i
$288$	1.23314e36	+	6.08343e35i	0.158535	+	0.0782098i
$289$	−1.62884e37			−1.98797
$290$		−	5.32713e36i		−	0.617338i
$291$	−5.25426e36	−	8.45094e36i	−0.578252	−	0.930058i
$292$	2.42788e36			0.253796
$293$			1.35292e37i			1.34357i	0.740748	+	0.671784i	$0.234471\pi$
$293$			1.35292e37i			1.34357i	−0.740748	+	0.671784i	$0.765529\pi$
$294$	−2.13542e36	+	1.32767e36i	−0.201500	+	0.125280i
$295$	−1.19823e37			−1.07451
$296$		−	2.48516e36i		−	0.211826i
$297$	−3.52404e35	−	3.58620e36i	−0.0285558	−	0.290595i
$298$	7.59964e36			0.585530
$299$			8.78604e36i			0.643762i
$300$	−4.43419e35	−	7.13194e35i	−0.0309027	−	0.0497037i
$301$	1.96755e37			1.30445
$302$		−	8.99094e36i		−	0.567154i
$303$	2.24282e37	−	1.39444e37i	1.34634	−	0.837069i
$304$	6.20366e36			0.354441
$305$			2.92346e37i			1.59001i
$306$	1.04431e37	−	2.11687e37i	0.540767	−	1.09616i
$307$	5.01508e36			0.247287			0.123644	−	0.992327i	$-0.460542\pi$
$307$	5.01508e36			0.247287			0.123644	+	0.992327i	$0.460542\pi$
$308$			2.53417e36i			0.119008i
$309$	1.22868e35	+	1.97620e35i	0.00549618	+	0.00884004i
$310$	−1.39837e37			−0.595931
$311$		−	2.91851e36i		−	0.118510i	−0.998243	−	0.0592550i	$-0.981127\pi$
$311$		−	2.91851e36i		−	0.118510i	0.998243	−	0.0592550i	$-0.0188725\pi$
$312$	8.67174e36	−	5.39154e36i	0.335573	−	0.208638i
$313$	−9.64574e36			−0.355771			−0.177885	−	0.984051i	$-0.556926\pi$
$313$	−9.64574e36			−0.355771			−0.177885	+	0.984051i	$0.556926\pi$
$314$			2.00986e37i			0.706678i
$315$	2.04906e37	+	1.01086e37i	0.686905	+	0.338871i
$316$	−1.69666e37			−0.542360
$317$			5.68761e37i			1.73397i	0.498336	+	0.866984i	$0.333944\pi$
$317$			5.68761e37i			1.73397i	−0.498336	+	0.866984i	$0.666056\pi$
$318$	3.55716e36	+	5.72133e36i	0.103442	+	0.166376i
$319$	9.77925e36			0.271297
$320$		−	4.43738e36i		−	0.117456i
$321$	−5.06083e37	+	3.14651e37i	−1.27834	+	0.794791i
$322$	1.37714e37			0.332002
$323$		−	1.06495e38i		−	2.45071i
$324$	1.38492e37	+	1.80597e37i	0.304263	+	0.396767i
$325$	−6.23648e36			−0.130825
$326$			4.12367e37i			0.826075i
$327$	−4.66963e37	−	7.51061e37i	−0.893441	−	1.43701i
$328$	−3.72406e36			−0.0680626
$329$			2.13541e37i			0.372857i
$330$	−9.87567e36	+	6.14007e36i	−0.164762	+	0.102439i
$331$	7.41026e37			1.18144			0.590722	−	0.806875i	$-0.298843\pi$
$331$	7.41026e37			1.18144			0.590722	+	0.806875i	$0.298843\pi$
$332$		−	1.27288e36i		−	0.0193962i
$333$	1.81980e37	−	3.68881e37i	0.265070	−	0.537308i
$334$	−8.79131e37			−1.22421
$335$		−	1.26711e38i		−	1.68710i
$336$	−8.45080e36	−	1.35922e37i	−0.107599	−	0.173062i
$337$	3.15483e37			0.384174			0.192087	−	0.981378i	$-0.438474\pi$
$337$	3.15483e37			0.384174			0.192087	+	0.981378i	$0.438474\pi$
$338$		−	1.51229e37i		−	0.176150i
$339$	−1.40928e38	+	8.76201e37i	−1.57037	+	0.976356i
$340$	−7.61744e37			−0.812130
$341$		−	2.56705e37i		−	0.261890i
$342$	9.20831e37	+	4.54273e37i	0.899059	+	0.443533i
$343$	1.16494e38			1.08866
$344$		−	6.32455e37i		−	0.565787i
$345$	3.33669e37	+	5.36672e37i	0.285778	+	0.459645i
$346$	−6.50847e36			−0.0533750
$347$			5.36870e37i			0.421626i	0.977526	+	0.210813i	$0.0676111\pi$
$347$			5.36870e37i			0.421626i	−0.977526	+	0.210813i	$0.932389\pi$
$348$	−5.24519e37	+	3.26113e37i	−0.394523	+	0.245290i
$349$	−2.32592e38			−1.67577			−0.837883	−	0.545850i	$-0.816207\pi$
$349$	−2.32592e38			−1.67577			−0.837883	+	0.545850i	$0.816207\pi$
$350$			9.77518e36i			0.0674690i
$351$	1.68198e38	−	1.65283e37i	1.11228	−	0.109300i
$352$	8.14590e36			0.0516178
$353$			7.00642e37i			0.425476i	0.977109	+	0.212738i	$0.0682381\pi$
$353$			7.00642e37i			0.425476i	−0.977109	+	0.212738i	$0.931762\pi$
$354$	7.33524e37	+	1.17980e38i	0.426939	+	0.686687i
$355$	2.55806e38			1.42720
$356$			2.85143e37i			0.152515i
$357$	−2.33332e38	+	1.45071e38i	−1.19660	+	0.743973i
$358$	1.18929e38			0.584846
$359$		−	1.17608e38i		−	0.554651i	−0.960776	−	0.277325i	$-0.910552\pi$
$359$		−	1.17608e38i		−	0.554651i	0.960776	−	0.277325i	$-0.0894480\pi$
$360$	3.24935e37	−	6.58656e37i	0.146980	−	0.297935i
$361$	2.32784e38			1.01006
$362$		−	5.18366e37i		−	0.215778i
$363$	1.20930e38	+	1.94504e38i	0.482987	+	0.776834i
$364$	−1.18856e38			−0.455514
$365$		−	1.29681e38i		−	0.476960i
$366$	2.87849e38	−	1.78966e38i	1.01613	−	0.631764i
$367$	2.25103e37			0.0762764			0.0381382	−	0.999272i	$-0.487857\pi$
$367$	2.25103e37			0.0762764			0.0381382	+	0.999272i	$0.487857\pi$
$368$		−	4.42672e37i		−	0.144001i
$369$	−5.52775e37	−	2.72700e37i	−0.172645	−	0.0851707i
$370$	−1.32740e38			−0.398085
$371$		−	7.84176e37i		−	0.225842i
$372$	8.56044e37	+	1.37686e38i	0.236784	+	0.380842i
$373$	−5.22609e38			−1.38849			−0.694247	−	0.719736i	$-0.744263\pi$
$373$	−5.22609e38			−1.38849			−0.694247	+	0.719736i	$0.744263\pi$
$374$		−	1.39837e38i		−	0.356901i
$375$	−3.63531e38	+	2.26021e38i	−0.891400	+	0.554216i
$376$	6.86411e37			0.161721
$377$			4.58662e38i			1.03842i
$378$	−2.59067e37	−	2.63637e38i	−0.0563684	−	0.573626i
$379$	−2.47822e38			−0.518265			−0.259132	−	0.965842i	$-0.583437\pi$
$379$	−2.47822e38			−0.518265			−0.259132	+	0.965842i	$0.583437\pi$
$380$		−	3.31356e38i		−	0.666103i
$381$	−3.68721e37	−	5.93050e37i	−0.0712563	−	0.114608i
$382$	−3.52241e38			−0.654469
$383$		−	5.97260e38i		−	1.06704i	−0.845786	−	0.533522i	$-0.820868\pi$
$383$		−	5.97260e38i		−	1.06704i	0.845786	−	0.533522i	$-0.179132\pi$
$384$	−4.36913e37	+	2.71645e37i	−0.0750630	+	0.0466695i
$385$	1.35358e38			0.223652
$386$			4.05508e38i			0.644450i
$387$	4.63126e38	−	9.38775e38i	0.708002	−	1.43515i
$388$	3.72327e38			0.547582
$389$			1.09279e39i			1.54629i	0.634227	+	0.773147i	$0.281318\pi$
$389$			1.09279e39i			1.54629i	−0.634227	+	0.773147i	$0.718682\pi$
$390$	−2.87979e38	−	4.63184e38i	−0.392095	−	0.630644i
$391$	−7.59914e38			−0.995664
$392$		−	9.40815e37i		−	0.118635i
$393$	−3.36761e38	+	2.09377e38i	−0.408727	+	0.254121i
$394$	7.23007e37			0.0844694
$395$			9.06236e38i			1.01926i
$396$	1.20912e38	+	5.96497e37i	0.130931	+	0.0645923i
$397$	1.15132e39			1.20043			0.600217	−	0.799838i	$-0.295081\pi$
$397$	1.15132e39			1.20043			0.600217	+	0.799838i	$0.295081\pi$
$398$			2.49315e38i			0.250324i
$399$	−6.31054e38	−	1.01499e39i	−0.610201	−	0.981446i
$400$	3.14216e37			0.0292636
$401$		−	4.37389e38i		−	0.392376i	−0.980566	−	0.196188i	$-0.937144\pi$
$401$		−	4.37389e38i		−	0.392376i	0.980566	−	0.196188i	$-0.0628563\pi$
$402$	−1.24762e39	+	7.75690e38i	−1.07818	+	0.670344i
$403$	1.20398e39			1.00241
$404$			9.88130e38i			0.792672i
$405$	9.64623e38	−	7.39727e38i	0.745646	−	0.571803i
$406$	7.18915e38			0.535534
$407$		−	2.43677e38i		−	0.174944i
$408$	4.66320e38	+	7.50027e38i	0.322687	+	0.519009i
$409$	5.72484e38			0.381868			0.190934	−	0.981603i	$-0.438848\pi$
$409$	5.72484e38			0.381868			0.190934	+	0.981603i	$0.438848\pi$
$410$			1.98913e38i			0.127910i
$411$	9.09397e38	−	5.65406e38i	0.563801	−	0.350536i
$412$	−8.70666e36			−0.00520467
$413$		−	1.61705e39i		−	0.932124i
$414$	3.24154e38	−	6.57073e38i	0.180196	−	0.365265i
$415$	−6.79885e37			−0.0364514
$416$			3.82055e38i			0.197572i
$417$	5.02443e38	+	8.08128e38i	0.250638	+	0.403125i
$418$	6.08286e38			0.292727
$419$			3.73146e39i			1.73248i	0.499627	+	0.866240i	$0.333470\pi$
$419$			3.73146e39i			1.73248i	−0.499627	+	0.866240i	$0.666530\pi$
$420$	−7.26003e38	+	4.51383e38i	−0.325236	+	0.202212i
$421$	−1.26887e39			−0.548511			−0.274256	−	0.961657i	$-0.588431\pi$
$421$	−1.26887e39			−0.548511			−0.274256	+	0.961657i	$0.588431\pi$
$422$			1.99933e39i			0.834060i
$423$	1.01886e39	+	5.02636e38i	0.410214	+	0.202371i
$424$	−2.52068e38			−0.0979555
$425$		−	5.39399e38i		−	0.202338i
$426$	−1.56598e39	−	2.51871e39i	−0.567075	−	0.912082i
$427$	−3.94531e39			−1.37931
$428$		−	2.22968e39i		−	0.752636i
$429$	8.50288e38	−	5.28655e38i	0.277145	−	0.172311i
$430$	−3.37813e39			−1.06329
$431$		−	3.46093e39i		−	1.05204i	−0.850471	−	0.526022i	$-0.823683\pi$
$431$		−	3.46093e39i		−	1.05204i	0.850471	−	0.526022i	$-0.176317\pi$
$432$	−8.47441e38	+	8.32753e37i	−0.248802	+	0.0244489i
$433$	−3.72282e39			−1.05573			−0.527865	−	0.849328i	$-0.677007\pi$
$433$	−3.72282e39			−1.05573			−0.527865	+	0.849328i	$0.677007\pi$
$434$		−	1.88715e39i		−	0.516964i
$435$	1.74187e39	+	2.80161e39i	0.460974	+	0.741428i
$436$	3.30899e39			0.846054
$437$		−	3.30560e39i		−	0.816636i
$438$	−1.27686e39	+	7.93871e38i	−0.304811	+	0.189513i
$439$	−2.34741e39			−0.541528			−0.270764	−	0.962646i	$-0.587276\pi$
$439$	−2.34741e39			−0.541528			−0.270764	+	0.962646i	$0.587276\pi$
$440$		−	4.35097e38i		−	0.0970055i
$441$	6.88927e38	−	1.39648e39i	0.148455	−	0.300924i
$442$	6.55856e39			1.36607
$443$			4.24715e39i			0.855150i	0.903980	+	0.427575i	$0.140632\pi$
$443$			4.24715e39i			0.855150i	−0.903980	+	0.427575i	$0.859368\pi$
$444$	8.12599e38	+	1.30698e39i	0.158173	+	0.254405i
$445$	1.52304e39			0.286622
$446$		−	1.21624e39i		−	0.221307i
$447$	−3.99676e39	+	2.48493e39i	−0.703226	+	0.437222i
$448$	5.98841e38			0.101892
$449$		−	1.05305e40i		−	1.73281i	−0.499339	−	0.866407i	$-0.666424\pi$
$449$		−	1.05305e40i		−	1.73281i	0.499339	−	0.866407i	$-0.333576\pi$
$450$	4.66401e38	+	2.30090e38i	0.0742287	+	0.0366193i
$451$	−3.65154e38			−0.0562119
$452$		−	6.20893e39i		−	0.924571i
$453$	2.93986e39	+	4.72847e39i	0.423501	+	0.681157i
$454$	4.28290e39			0.596899
$455$			6.34848e39i			0.856050i
$456$	−3.26259e39	+	2.02848e39i	−0.425687	+	0.264665i
$457$	−2.58352e39			−0.326189			−0.163095	−	0.986610i	$-0.552148\pi$
$457$	−2.58352e39			−0.326189			−0.163095	+	0.986610i	$0.552148\pi$
$458$			3.93077e39i			0.480281i
$459$	1.42955e39	+	1.45476e40i	0.169047	+	1.72029i
$460$	−2.36444e39			−0.270621
$461$			4.73290e39i			0.524341i	0.965022	+	0.262170i	$0.0844382\pi$
$461$			4.73290e39i			0.524341i	−0.965022	+	0.262170i	$0.915562\pi$
$462$	−8.28625e38	−	1.33276e39i	−0.0888645	−	0.142929i
$463$	−8.07016e38			−0.0837851			−0.0418926	−	0.999122i	$-0.513339\pi$
$463$	−8.07016e38			−0.0837851			−0.0418926	+	0.999122i	$0.513339\pi$
$464$		−	2.31090e39i		−	0.232280i
$465$	7.35422e39	−	4.57239e39i	0.715719	−	0.444989i
$466$	3.99928e39			0.376872
$467$			1.19493e40i			1.09041i	0.838303	+	0.545205i	$0.183548\pi$
$467$			1.19493e40i			1.09041i	−0.838303	+	0.545205i	$0.816452\pi$
$468$	−2.79766e39	+	5.67098e39i	−0.247234	+	0.501153i
$469$	1.71001e40			1.46354
$470$		−	3.66633e39i		−	0.303923i
$471$	−6.57186e39	−	1.05702e40i	−0.527685	−	0.848727i
$472$	−5.19790e39			−0.404294
$473$		−	6.20140e39i		−	0.467275i
$474$	8.92297e39	−	5.54774e39i	0.651380	−	0.404987i
$475$	2.34637e39			0.165956
$476$		−	1.02800e40i		−	0.704514i
$477$	−3.74153e39	−	1.84581e39i	−0.248469	−	0.122577i
$478$	−3.82712e38			−0.0246294
$479$		−	1.92274e40i		−	1.19919i	−0.800305	−	0.599594i	$-0.795329\pi$
$479$		−	1.92274e40i		−	1.19919i	0.800305	−	0.599594i	$-0.204671\pi$
$480$	1.45094e39	+	2.33368e39i	0.0877061	+	0.141066i
$481$	1.14288e40			0.669615
$482$			2.44320e40i			1.38757i
$483$	−7.24258e39	+	4.50298e39i	−0.398737	+	0.247910i
$484$	−8.56935e39			−0.457370
$485$		−	1.98871e40i		−	1.02907i
$486$	−1.31887e40	−	4.96944e39i	−0.661693	−	0.249324i
$487$	−1.67856e40			−0.816588			−0.408294	−	0.912851i	$-0.633876\pi$
$487$	−1.67856e40			−0.816588			−0.408294	+	0.912851i	$0.633876\pi$
$488$			1.26819e40i			0.598256i
$489$	−1.34836e40	−	2.16870e40i	−0.616840	−	0.992124i
$490$	−5.02517e39			−0.222951
$491$			2.80498e39i			0.120700i	0.998177	+	0.0603500i	$0.0192217\pi$
$491$			2.80498e39i			0.120700i	−0.998177	+	0.0603500i	$0.980778\pi$
$492$	1.95854e39	−	1.21769e39i	0.0817438	−	0.0508232i
$493$	−3.96701e40			−1.60605
$494$			2.85295e40i			1.12044i
$495$	3.18607e39	−	6.45830e39i	0.121389	−	0.246060i
$496$	−6.06610e39			−0.224225
$497$			3.45219e40i			1.23808i
$498$	4.16208e38	+	6.69428e38i	0.0144834	+	0.0232950i
$499$	−1.89055e39			−0.0638382			−0.0319191	−	0.999490i	$-0.510162\pi$
$499$	−1.89055e39			−0.0638382			−0.0319191	+	0.999490i	$0.510162\pi$
$500$		−	1.60163e40i		−	0.524821i
$501$	4.62347e40	−	2.87459e40i	1.47029	−	0.914133i
$502$	−2.49175e40			−0.769041
$503$		−	7.58402e39i		−	0.227185i	−0.993527	−	0.113592i	$-0.963764\pi$
$503$		−	7.58402e39i		−	0.227185i	0.993527	−	0.113592i	$-0.0362358\pi$
$504$	8.88880e39	+	4.38511e39i	0.258455	+	0.127504i
$505$	5.27790e40			1.48967
$506$		−	4.34052e39i		−	0.118928i
$507$	4.94488e39	+	7.95334e39i	0.131534	+	0.211558i
$508$	2.61283e39			0.0674770
$509$			3.20015e40i			0.802424i	0.915985	+	0.401212i	$0.131411\pi$
$509$			3.20015e40i			0.802424i	−0.915985	+	0.401212i	$0.868589\pi$
$510$	4.00612e40	−	2.49075e40i	0.975375	−	0.606427i
$511$	1.75009e40			0.413758
$512$		−	1.92493e39i		−	0.0441942i
$513$	−6.32817e40	+	6.21848e39i	−1.41097	+	0.138651i
$514$	−1.71413e40			−0.371191
$515$			4.65049e38i			0.00978115i
$516$	2.06801e40	+	3.32617e40i	0.422480	+	0.679515i
$517$	6.73045e39			0.133563
$518$		−	1.79137e40i		−	0.345334i
$519$	3.42290e39	−	2.12814e39i	0.0641038	−	0.0398557i
$520$	2.04067e40			0.371298
$521$			3.79285e40i			0.670502i	0.942129	+	0.335251i	$0.108821\pi$
$521$			3.79285e40i			0.670502i	−0.942129	+	0.335251i	$0.891179\pi$
$522$	1.69219e40	−	3.43015e40i	0.290665	−	0.589190i
$523$	8.20827e40			1.37002			0.685009	−	0.728534i	$-0.259798\pi$
$523$	8.20827e40			1.37002			0.685009	+	0.728534i	$0.259798\pi$
$524$		−	1.48368e40i		−	0.240643i
$525$	−3.19629e39	−	5.14091e39i	−0.0503799	−	0.0810308i
$526$	−3.19391e40			−0.489257
$527$			1.04134e41i			1.55036i
$528$	−4.28405e39	+	2.66355e39i	−0.0619934	+	0.0385436i
$529$	4.75067e40			0.668221
$530$			1.34637e40i			0.184088i
$531$	−7.71542e40	−	3.80625e40i	−1.02551	−	0.505917i
$532$	4.47177e40			0.577837
$533$		−	1.71263e40i		−	0.215157i
$534$	−9.32363e39	−	1.49961e40i	−0.113885	−	0.183172i
$535$	−1.19094e41			−1.41443
$536$		−	5.49669e40i		−	0.634790i
$537$	−6.25464e40	+	3.88874e40i	−0.702405	+	0.436711i
$538$	−3.07502e39			−0.0335826
$539$		−	9.22494e39i		−	0.0979788i
$540$	4.44798e39	+	4.52644e40i	0.0459470	+	0.467574i
$541$	2.65153e40			0.266402			0.133201	−	0.991089i	$-0.457474\pi$
$541$	2.65153e40			0.266402			0.133201	+	0.991089i	$0.457474\pi$
$542$		−	3.86709e40i		−	0.377916i
$543$	1.69495e40	+	2.72616e40i	0.161124	+	0.259151i
$544$	−3.30443e40			−0.305572
$545$		−	1.76743e41i		−	1.58999i
$546$	6.25083e40	−	3.88637e40i	0.547077	−	0.340138i
$547$	−7.29141e40			−0.620871			−0.310436	−	0.950594i	$-0.600475\pi$
$547$	−7.29141e40			−0.620871			−0.310436	+	0.950594i	$0.600475\pi$
$548$			4.00658e40i			0.331944i
$549$	−9.28653e40	+	1.88242e41i	−0.748632	+	1.51751i
$550$	3.08097e39			0.0241684
$551$		−	1.72564e41i		−	1.31727i
$552$	1.44745e40	+	2.32807e40i	0.107527	+	0.172946i
$553$	−1.22300e41			−0.884197
$554$			3.62326e40i			0.254949i
$555$	6.98099e40	−	4.34034e40i	0.478104	−	0.297255i
$556$	−3.56041e40			−0.237344
$557$		−	5.46804e40i		−	0.354816i	−0.984137	−	0.177408i	$-0.943229\pi$
$557$		−	5.46804e40i		−	0.354816i	0.984137	−	0.177408i	$-0.0567713\pi$
$558$	−9.00412e40	−	4.44200e40i	−0.568759	−	0.280586i
$559$	2.90855e41			1.78854
$560$		−	3.19859e40i		−	0.191486i
$561$	4.57239e40	+	7.35422e40i	0.266502	+	0.428641i
$562$	−1.23539e41			−0.701064
$563$		−	1.20100e41i		−	0.663618i	−0.943347	−	0.331809i	$-0.892341\pi$
$563$		−	1.20100e41i		−	0.663618i	0.943347	−	0.331809i	$-0.107659\pi$
$564$	−3.60993e40	+	2.24443e40i	−0.194228	+	0.120759i
$565$	−3.31638e41			−1.73755
$566$		−	1.34670e41i		−	0.687108i
$567$	9.98288e40	+	1.30179e41i	0.496033	+	0.646839i
$568$	1.10968e41			0.536998
$569$			2.51057e41i			1.18328i	0.806201	+	0.591641i	$0.201520\pi$
$569$			2.51057e41i			1.18328i	−0.806201	+	0.591641i	$0.798480\pi$
$570$	1.08347e41	+	1.74265e41i	0.497387	+	0.799995i
$571$	4.11578e41			1.84039			0.920196	−	0.391458i	$-0.128029\pi$
$571$	4.11578e41			1.84039			0.920196	+	0.391458i	$0.128029\pi$
$572$			3.74616e40i			0.163172i
$573$	1.85249e41	−	1.15176e41i	0.786023	−	0.488700i
$574$	−2.68441e40			−0.110961
$575$		−	1.67429e40i		−	0.0674237i
$576$	1.40956e40	−	2.85724e40i	0.0553027	−	0.112101i
$577$	2.11665e41			0.809118			0.404559	−	0.914512i	$-0.367425\pi$
$577$	2.11665e41			0.809118			0.404559	+	0.914512i	$0.367425\pi$
$578$			3.77410e41i			1.40571i
$579$	−1.32593e41	−	2.13262e41i	−0.481219	−	0.773990i
$580$	−1.23432e41			−0.436524
$581$		−	9.17530e39i		−	0.0316212i
$582$	−1.95812e41	+	1.21744e41i	−0.657651	+	0.408886i
$583$	−2.47159e40			−0.0809000
$584$		−	5.62552e40i		−	0.179461i
$585$	3.02904e41	+	1.49432e41i	0.941818	+	0.464627i
$586$	3.13479e41			0.950045
$587$		−	2.25157e41i		−	0.665142i	−0.943078	−	0.332571i	$-0.892084\pi$
$587$		−	2.25157e41i		−	0.665142i	0.943078	−	0.332571i	$-0.107916\pi$
$588$	3.07628e40	+	4.94788e40i	0.0885862	+	0.142482i
$589$	−4.52979e41			−1.27159
$590$			2.77635e41i			0.759792i
$591$	−3.80240e40	+	2.36409e40i	−0.101448	+	0.0630743i
$592$	−5.75824e40			−0.149783
$593$			2.43336e41i			0.617142i	0.951201	+	0.308571i	$0.0998508\pi$
$593$			2.43336e41i			0.617142i	−0.951201	+	0.308571i	$0.900149\pi$
$594$	−8.30939e40	+	8.16537e39i	−0.205481	+	0.0201920i
$595$	−5.49087e41			−1.32400
$596$		−	1.76087e41i		−	0.414032i
$597$	−8.15211e40	−	1.31118e41i	−0.186920	−	0.300641i
$598$	2.03577e41			0.455209
$599$		−	3.21497e41i		−	0.701091i	−0.936546	−	0.350545i	$-0.885996\pi$
$599$		−	3.21497e41i		−	0.701091i	0.936546	−	0.350545i	$-0.114004\pi$
$600$	−1.65251e40	+	1.02742e40i	−0.0351459	+	0.0218515i
$601$	4.02428e40			0.0834778			0.0417389	−	0.999129i	$-0.486710\pi$
$601$	4.02428e40			0.0834778			0.0417389	+	0.999129i	$0.486710\pi$
$602$		−	4.55891e41i		−	0.922389i
$603$	4.02505e41	−	8.15893e41i	0.794349	−	1.61018i
$604$	−2.08324e41			−0.401039
$605$			4.57715e41i			0.859537i
$606$	−3.23099e41	−	5.19672e41i	−0.591897	−	0.952006i
$607$	1.10635e41			0.197726			0.0988630	−	0.995101i	$-0.468479\pi$
$607$	1.10635e41			0.197726			0.0988630	+	0.995101i	$0.468479\pi$
$608$		−	1.43742e41i		−	0.250628i
$609$	−3.78088e41	+	2.35071e41i	−0.643181	+	0.399890i
$610$	6.77379e41			1.12430
$611$			3.15668e41i			0.511225i
$612$	−4.90488e41	−	2.41973e41i	−0.775100	−	0.382380i
$613$	4.11390e41			0.634375			0.317188	−	0.948363i	$-0.397262\pi$
$613$	4.11390e41			0.634375			0.317188	+	0.948363i	$0.397262\pi$
$614$		−	1.16202e41i		−	0.174859i
$615$	−6.50407e40	−	1.04611e41i	−0.0955122	−	0.153621i
$616$	5.87180e40			0.0841512
$617$			5.52119e41i			0.772246i	0.922447	+	0.386123i	$0.126186\pi$
$617$			5.52119e41i			0.772246i	−0.922447	+	0.386123i	$0.873814\pi$
$618$	4.57896e39	−	2.84691e39i	0.00625085	−	0.00388639i
$619$	−1.19123e42			−1.58722			−0.793610	−	0.608427i	$-0.791801\pi$
$619$	−1.19123e42			−1.58722			−0.793610	+	0.608427i	$0.791801\pi$
$620$			3.24009e41i			0.421387i
$621$	4.43730e40	+	4.51556e41i	0.0563306	+	0.573241i
$622$	−6.76232e40			−0.0837992
$623$			2.05539e41i			0.248642i
$624$	−1.24925e41	−	2.00928e41i	−0.147530	−	0.237286i
$625$	−7.53949e41			−0.869244
$626$			2.23496e41i			0.251568i
$627$	−3.19906e41	+	1.98898e41i	−0.351568	+	0.218583i
$628$	4.65695e41			0.499697
$629$			9.88489e41i			1.03565i
$630$	2.34222e41	−	4.74778e41i	0.239618	−	0.485716i
$631$	9.47177e41			0.946217			0.473108	−	0.881004i	$-0.343132\pi$
$631$	9.47177e41			0.946217			0.473108	+	0.881004i	$0.343132\pi$
$632$			3.93124e41i			0.383507i
$633$	−6.53741e41	−	1.05147e42i	−0.622802	−	1.00171i
$634$	1.31785e42			1.22610
$635$		−	1.39559e41i		−	0.126810i
$636$	1.32566e41	−	8.24212e40i	0.117645	−	0.0731445i
$637$	4.32664e41			0.375024
$638$		−	2.26590e41i		−	0.191836i
$639$	1.64714e42	+	8.12582e41i	1.36213	+	0.671977i
$640$	−1.02816e41			−0.0830543
$641$		−	1.13236e42i		−	0.893539i	−0.894649	−	0.446769i	$-0.852574\pi$
$641$		−	1.13236e42i		−	0.893539i	0.894649	−	0.446769i	$-0.147426\pi$
$642$	7.29061e41	+	1.17262e42i	0.562002	+	0.903923i
$643$	9.03304e41			0.680251			0.340126	−	0.940380i	$-0.389530\pi$
$643$	9.03304e41			0.680251			0.340126	+	0.940380i	$0.389530\pi$
$644$		−	3.19090e41i		−	0.234761i
$645$	1.77661e42	−	1.10458e42i	1.27702	−	0.793968i
$646$	−2.46755e42			−1.73292
$647$			1.18663e42i			0.814238i	0.913375	+	0.407119i	$0.133467\pi$
$647$			1.18663e42i			0.814238i	−0.913375	+	0.407119i	$0.866533\pi$
$648$	4.18452e41	−	3.20892e41i	0.280557	−	0.215146i
$649$	−5.09668e41			−0.333900
$650$			1.44502e41i			0.0925069i
$651$	6.17061e41	+	9.92479e41i	0.386023	+	0.620878i
$652$	9.55473e41			0.584123
$653$		−	5.07689e41i		−	0.303319i	−0.988433	−	0.151660i	$-0.951538\pi$
$653$		−	5.07689e41i		−	0.303319i	0.988433	−	0.151660i	$-0.0484618\pi$
$654$	−1.74024e42	+	1.08197e42i	−1.01612	+	0.631758i
$655$	−7.92481e41			−0.452240
$656$			8.62882e40i			0.0481276i
$657$	4.11938e41	−	8.35016e41i	0.224570	−	0.455213i
$658$	4.94784e41			0.263650
$659$		−	1.51159e42i		−	0.787322i	−0.919256	−	0.393661i	$-0.871208\pi$
$659$		−	1.51159e42i		−	0.787322i	0.919256	−	0.393661i	$-0.128792\pi$
$660$	1.42268e41	+	2.28824e41i	0.0724351	+	0.116504i
$661$	−1.63741e42			−0.814958			−0.407479	−	0.913215i	$-0.633592\pi$
$661$	−1.63741e42			−0.814958			−0.407479	+	0.913215i	$0.633592\pi$
$662$		−	1.71699e42i		−	0.835407i
$663$	−3.44924e42	+	2.14452e42i	−1.64067	+	1.02006i
$664$	−2.94933e40			−0.0137152
$665$		−	2.38851e42i		−	1.08593i
$666$	−8.54715e41	−	4.21656e41i	−0.379934	−	0.187433i
$667$	−1.23135e42			−0.535175
$668$			2.03699e42i			0.865648i
$669$	3.97686e41	+	6.39636e41i	0.165253	+	0.265792i
$670$	−2.93595e42			−1.19296
$671$			1.24350e42i			0.494090i
$672$	−3.14939e41	+	1.95809e41i	−0.122373	+	0.0760841i
$673$	2.18036e42			0.828520			0.414260	−	0.910159i	$-0.364040\pi$
$673$	2.18036e42			0.828520			0.414260	+	0.910159i	$0.364040\pi$
$674$		−	7.30989e41i		−	0.271652i
$675$	−3.20522e41	+	3.14967e40i	−0.116493	+	0.0114474i
$676$	−3.50404e41			−0.124557
$677$		−	5.03764e42i		−	1.75145i	−0.482811	−	0.875724i	$-0.660384\pi$
$677$		−	5.03764e42i		−	1.75145i	0.482811	−	0.875724i	$-0.339616\pi$
$678$	2.03020e42	+	3.26537e42i	0.690388	+	1.11042i
$679$	2.68384e42			0.892709
$680$			1.76500e42i			0.574262i
$681$	−2.25244e42	+	1.40043e42i	−0.716880	+	0.445711i
$682$	−5.94798e41			−0.185184
$683$		−	2.27267e42i		−	0.692191i	−0.938199	−	0.346095i	$-0.887507\pi$
$683$		−	2.27267e42i		−	0.692191i	0.938199	−	0.346095i	$-0.112493\pi$
$684$	1.05257e42	−	2.13361e42i	0.313625	−	0.635731i
$685$	2.14003e42			0.623824
$686$		−	2.69922e42i		−	0.769797i
$687$	−1.28528e42	−	2.06725e42i	−0.358631	−	0.576822i
$688$	−1.46543e42			−0.400072
$689$		−	1.15921e42i		−	0.309653i
$690$	1.24349e42	−	7.73127e41i	0.325018	−	0.202076i
$691$	1.33919e42			0.342507			0.171254	−	0.985227i	$-0.445218\pi$
$691$	1.33919e42			0.342507			0.171254	+	0.985227i	$0.445218\pi$
$692$			1.50804e41i			0.0377418i
$693$	8.71571e41	+	4.29972e41i	0.213454	+	0.105303i
$694$	1.24395e42			0.298134
$695$			1.90172e42i			0.446041i
$696$	7.55619e41	+	1.21533e42i	0.173446	+	0.278970i
$697$	1.48127e42			0.332769
$698$			5.38927e42i			1.18495i
$699$	−2.10328e42	+	1.30769e42i	−0.452626	+	0.281415i
$700$	2.26496e41			0.0477078
$701$			4.38736e42i			0.904550i	0.891878	+	0.452275i	$0.149387\pi$
$701$			4.38736e42i			0.904550i	−0.891878	+	0.452275i	$0.850613\pi$
$702$	−3.82968e41	−	3.89723e42i	−0.0772869	−	0.786501i
$703$	−4.29990e42			−0.849431
$704$		−	1.88744e41i		−	0.0364993i
$705$	1.19882e42	+	1.92817e42i	0.226943	+	0.365014i
$706$	1.62342e42			0.300857
$707$			7.12272e42i			1.29227i
$708$	2.73365e42	−	1.69961e42i	0.485561	−	0.301891i
$709$	8.42700e42			1.46548			0.732739	−	0.680509i	$-0.238241\pi$
$709$	8.42700e42			1.46548			0.732739	+	0.680509i	$0.238241\pi$
$710$		−	5.92714e42i		−	1.00918i
$711$	−2.87871e42	+	5.83527e42i	−0.479904	+	0.972785i
$712$	6.60691e41			0.107845
$713$			3.23230e42i			0.516617i
$714$	3.36136e42	+	5.40641e42i	0.526069	+	0.846127i
$715$	2.00093e42			0.306650
$716$		−	2.75564e42i		−	0.413549i
$717$	2.01274e41	−	1.25139e41i	0.0295801	−	0.0183911i
$718$	−2.72503e42			−0.392197
$719$		−	4.45533e42i		−	0.627982i	−0.949426	−	0.313991i	$-0.898334\pi$
$719$		−	4.45533e42i		−	0.627982i	0.949426	−	0.313991i	$-0.101666\pi$
$720$	−1.52614e42	−	7.52889e41i	−0.210672	−	0.103931i
$721$	−6.27600e40			−0.00848504
$722$		−	5.39373e42i		−	0.714218i
$723$	−7.98880e42	−	1.28492e43i	−1.03611	−	1.66648i
$724$	−1.20108e42			−0.152578
$725$		−	8.74036e41i		−	0.108757i
$726$	4.50674e42	−	2.80201e42i	0.549305	−	0.341523i
$727$	−2.06925e42			−0.247057			−0.123529	−	0.992341i	$-0.539421\pi$
$727$	−2.06925e42			−0.247057			−0.123529	+	0.992341i	$0.539421\pi$
$728$			2.75396e42i			0.322097i
$729$	8.56101e42	−	1.69893e42i	0.980872	−	0.194654i
$730$	−3.00476e42			−0.337262
$731$			2.51563e43i			2.76622i
$732$	−4.14673e42	−	6.66959e42i	−0.446725	−	0.718510i
$733$	−1.66650e43			−1.75892			−0.879461	−	0.475971i	$-0.842097\pi$
$733$	−1.66650e43			−1.75892			−0.879461	+	0.475971i	$0.842097\pi$
$734$		−	5.21574e41i		−	0.0539356i
$735$	2.64281e42	−	1.64313e42i	0.267766	−	0.166480i
$736$	−1.02569e42			−0.101824
$737$		−	5.38966e42i		−	0.524263i
$738$	−6.31860e41	+	1.28081e42i	−0.0602248	+	0.122078i
$739$	1.92289e42			0.179593			0.0897963	−	0.995960i	$-0.471378\pi$
$739$	1.92289e42			0.179593			0.0897963	+	0.995960i	$0.471378\pi$
$740$			3.07565e42i			0.281489i
$741$	−9.32860e42	−	1.50041e43i	−0.836649	−	1.34566i
$742$	−1.81697e42			−0.159695
$743$		−	1.26232e43i		−	1.08727i	−0.839322	−	0.543635i	$-0.817047\pi$
$743$		−	1.26232e43i		−	1.08727i	0.839322	−	0.543635i	$-0.182953\pi$
$744$	3.19025e42	−	1.98350e42i	0.269296	−	0.167432i
$745$	−9.40535e42			−0.778092
$746$			1.21091e43i			0.981814i
$747$	−4.37780e41	−	2.15970e41i	−0.0347894	−	0.0171626i
$748$	−3.24009e42			−0.252367
$749$		−	1.60721e43i		−	1.22700i
$750$	5.23701e42	+	8.42319e42i	0.391890	+	0.630315i
$751$	3.21315e42			0.235685			0.117842	−	0.993032i	$-0.462402\pi$
$751$	3.21315e42			0.235685			0.117842	+	0.993032i	$0.462402\pi$
$752$		−	1.59045e42i		−	0.114354i
$753$	1.31045e43	−	8.14755e42i	0.923625	−	0.574252i
$754$	1.06274e43			0.734273
$755$			1.11272e43i			0.753673i
$756$	−6.10859e42	+	6.00272e41i	−0.405615	+	0.0398585i
$757$	1.05705e42			0.0688108			0.0344054	−	0.999408i	$-0.489046\pi$
$757$	1.05705e42			0.0688108			0.0344054	+	0.999408i	$0.489046\pi$
$758$			5.74215e42i			0.366468i
$759$	1.41926e42	+	2.28274e42i	0.0888048	+	0.142833i
$760$	−7.67768e42			−0.471006
$761$			2.10209e43i			1.26439i	0.774808	+	0.632197i	$0.217847\pi$
$761$			2.10209e43i			1.26439i	−0.774808	+	0.632197i	$0.782153\pi$
$762$	−1.37413e42	+	8.54345e41i	−0.0810404	+	0.0503858i
$763$	2.38521e43			1.37930
$764$			8.16159e42i			0.462780i
$765$	−1.29245e43	+	2.61985e43i	−0.718608	+	1.45665i
$766$	−1.38388e43			−0.754513
$767$		−	2.39042e43i		−	1.27804i
$768$	6.29414e41	+	1.01235e42i	0.0330003	+	0.0530776i
$769$	2.15488e43			1.10797			0.553986	−	0.832526i	$-0.313106\pi$
$769$	2.15488e43			1.10797			0.553986	+	0.832526i	$0.313106\pi$
$770$		−	3.13630e42i		−	0.158146i
$771$	9.01488e42	−	5.60488e42i	0.445804	−	0.277173i
$772$	9.39581e42			0.455695
$773$			3.92653e42i			0.186774i	0.995630	+	0.0933870i	$0.0297694\pi$
$773$			3.92653e42i			0.186774i	−0.995630	+	0.0933870i	$0.970231\pi$
$774$	−2.17519e43	−	1.07308e43i	−1.01480	−	0.500633i
$775$	−2.29434e42			−0.104986
$776$		−	8.62700e42i		−	0.387199i
$777$	5.85744e42	+	9.42109e42i	0.257865	+	0.414750i
$778$	2.53204e43			1.09339
$779$			6.44347e42i			0.272934i
$780$	−1.07322e43	+	6.67260e42i	−0.445933	+	0.277253i
$781$	1.08807e43			0.443499
$782$			1.76076e43i			0.704041i
$783$	2.31642e42	+	2.35728e43i	0.0908638	+	0.924665i
$784$	−2.17991e42			−0.0838876
$785$		−	2.48742e43i		−	0.939082i
$786$	4.85136e42	+	7.80291e42i	0.179691	+	0.289014i
$787$	5.16355e42			0.187641			0.0938204	−	0.995589i	$-0.470092\pi$
$787$	5.16355e42			0.187641			0.0938204	+	0.995589i	$0.470092\pi$
$788$		−	1.67524e42i		−	0.0597289i
$789$	1.67972e43	−	1.04435e43i	0.587601	−	0.365334i
$790$	2.09979e43			0.720726
$791$		−	4.47557e43i		−	1.50731i
$792$	1.38211e42	−	2.80160e42i	0.0456736	−	0.0925824i
$793$	−5.83218e43			−1.89118
$794$		−	2.66766e43i		−	0.848834i
$795$	−4.40236e42	−	7.08075e42i	−0.137461	−	0.221092i
$796$	5.77674e42			0.177006
$797$			4.51648e42i			0.135808i	0.997692	+	0.0679040i	$0.0216312\pi$
$797$			4.51648e42i			0.135808i	−0.997692	+	0.0679040i	$0.978369\pi$
$798$	−2.35177e43	+	1.46218e43i	−0.693987	+	0.431477i
$799$	−2.73024e43			−0.790678
$800$		−	7.28053e41i		−	0.0206925i
$801$	9.80686e42	+	4.83802e42i	0.273554	+	0.134952i
$802$	−1.01345e43			−0.277452
$803$		−	5.51598e42i		−	0.148214i
$804$	1.79731e43	+	2.89079e43i	0.474005	+	0.762388i
$805$	−1.70436e43			−0.441187
$806$		−	2.78969e43i		−	0.708811i
$807$	1.61720e42	−	1.00547e42i	0.0403330	−	0.0250765i
$808$	2.28954e43			0.560504
$809$			6.23427e43i			1.49816i	0.662480	+	0.749079i	$0.269504\pi$
$809$			6.23427e43i			1.49816i	−0.662480	+	0.749079i	$0.730496\pi$
$810$	−1.71398e43	−	2.23508e43i	−0.404326	−	0.527251i
$811$	−3.68446e43			−0.853219			−0.426610	−	0.904436i	$-0.640292\pi$
$811$	−3.68446e43			−0.853219			−0.426610	+	0.904436i	$0.640292\pi$
$812$		−	1.66576e43i		−	0.378680i
$813$	1.26446e43	+	2.03376e43i	0.282194	+	0.453880i
$814$	−5.64611e42			−0.123704
$815$		−	5.10347e43i		−	1.09775i
$816$	1.73785e43	−	1.08049e43i	0.366995	−	0.228174i
$817$	−1.09429e44			−2.26883
$818$		−	1.32647e43i		−	0.270022i
$819$	−2.01663e43	+	4.08780e43i	−0.403059	+	0.817017i
$820$	4.60891e42			0.0904463
$821$			5.33120e43i			1.02725i	0.858014	+	0.513626i	$0.171698\pi$
$821$			5.33120e43i			1.02725i	−0.858014	+	0.513626i	$0.828302\pi$
$822$	−1.31007e43	−	2.10712e43i	−0.247867	−	0.398668i
$823$	9.76425e43			1.81402			0.907009	−	0.421112i	$-0.138360\pi$
$823$	9.76425e43			1.81402			0.907009	+	0.421112i	$0.138360\pi$
$824$			2.01737e41i			0.00368026i
$825$	−1.62033e42	+	1.00742e42i	−0.0290264	+	0.0180468i
$826$	−3.74679e43			−0.659111
$827$		−	3.49263e43i		−	0.603351i	−0.953411	−	0.301675i	$-0.902454\pi$
$827$		−	3.49263e43i		−	0.603351i	0.953411	−	0.301675i	$-0.0975459\pi$
$828$	−1.52247e43	−	7.51079e42i	−0.258282	−	0.127418i
$829$	−3.39016e42			−0.0564810			−0.0282405	−	0.999601i	$-0.508990\pi$
$829$	−3.39016e42			−0.0564810			−0.0282405	+	0.999601i	$0.508990\pi$
$830$			1.57533e42i			0.0257750i
$831$	−1.18474e43	−	1.90552e43i	−0.190373	−	0.306196i
$832$	8.85240e42			0.139705
$833$			3.74215e43i			0.580025i
$834$	1.87247e43	−	1.16419e43i	0.285052	−	0.177228i
$835$	1.08802e44			1.62682
$836$		−	1.40943e43i		−	0.206990i
$837$	6.18784e43	−	6.08059e42i	0.892601	−	0.0877130i
$838$	8.64597e43			1.22505
$839$		−	6.60631e42i		−	0.0919453i	−0.998943	−	0.0459727i	$-0.985361\pi$
$839$		−	6.60631e42i		−	0.0919453i	0.998943	−	0.0459727i	$-0.0146387\pi$
$840$	1.04588e43	+	1.68218e43i	0.142985	+	0.229977i
$841$	1.01819e43			0.136738
$842$			2.94003e43i			0.387856i
$843$	6.49707e43	−	4.03947e43i	0.841984	−	0.523493i
$844$	4.63254e43			0.589769
$845$			1.87161e43i			0.234081i
$846$	1.16463e43	−	2.36075e43i	0.143098	−	0.290065i
$847$	−6.17703e43			−0.745639
$848$			5.84052e42i			0.0692650i
$849$	4.40345e43	+	7.08250e43i	0.513072	+	0.825223i
$850$	−1.24981e43			−0.143074
$851$			3.06826e43i			0.345103i
$852$	−5.83597e43	+	3.62844e43i	−0.644940	+	0.400983i
$853$	−1.01467e43			−0.110176			−0.0550882	−	0.998481i	$-0.517544\pi$
$853$	−1.01467e43			−0.110176			−0.0550882	+	0.998481i	$0.517544\pi$
$854$			9.14147e43i			0.975322i
$855$	−1.13962e44	−	5.62211e43i	−1.19473	−	0.589397i
$856$	−5.16627e43			−0.532194
$857$		−	3.63018e43i		−	0.367465i	−0.982976	−	0.183733i	$-0.941182\pi$
$857$		−	3.63018e43i		−	0.367465i	0.982976	−	0.183733i	$-0.0588181\pi$
$858$	−1.22492e43	−	1.97016e43i	−0.121842	−	0.195971i
$859$	−8.30869e42			−0.0812148			−0.0406074	−	0.999175i	$-0.512929\pi$
$859$	−8.30869e42			−0.0812148			−0.0406074	+	0.999175i	$0.512929\pi$
$860$			7.82730e43i			0.751857i
$861$	1.41177e43	−	8.77748e42i	0.133265	−	0.0828558i
$862$	−8.01914e43			−0.743907
$863$			1.07396e44i			0.979098i	0.871976	+	0.489549i	$0.162839\pi$
$863$			1.07396e44i			0.979098i	−0.871976	+	0.489549i	$0.837161\pi$
$864$	1.92953e42	+	1.96356e43i	0.0172880	+	0.175929i
$865$	8.05492e42			0.0709283
$866$			8.62594e43i			0.746514i
$867$	−1.23406e44	−	1.98485e44i	−1.04966	−	1.68827i
$868$	−4.37261e43			−0.365549
$869$			3.85469e43i			0.316732i
$870$	6.49147e43	−	4.03599e43i	0.524269	−	0.325958i
$871$	2.52783e44			2.00667
$872$		−	7.66708e43i		−	0.598250i
$873$	6.31727e43	−	1.28054e44i	0.484524	−	0.982151i
$874$	−7.65923e43			−0.577449
$875$		−	1.15450e44i		−	0.855603i
$876$	1.83944e43	+	2.95854e43i	0.134006	+	0.215534i
$877$	−1.31951e44			−0.944968			−0.472484	−	0.881339i	$-0.656643\pi$
$877$	−1.31951e44			−0.944968			−0.472484	+	0.881339i	$0.656643\pi$
$878$			5.43906e43i			0.382918i
$879$	−1.64863e44	+	1.02502e44i	−1.14101	+	0.709410i
$880$	−1.00814e43			−0.0685932
$881$		−	1.64057e44i		−	1.09738i	−0.836026	−	0.548690i	$-0.815127\pi$
$881$		−	1.64057e44i		−	1.09738i	0.836026	−	0.548690i	$-0.184873\pi$
$882$	−3.23572e43	−	1.59628e43i	−0.212786	−	0.104973i
$883$	1.30275e44			0.842267			0.421133	−	0.906999i	$-0.361632\pi$
$883$	1.30275e44			0.842267			0.421133	+	0.906999i	$0.361632\pi$
$884$		−	1.51965e44i		−	0.965961i
$885$	−9.07814e43	−	1.46012e44i	−0.567346	−	0.912517i
$886$	9.84086e43			0.604682
$887$			2.26334e44i			1.36740i	0.729764	+	0.683699i	$0.239630\pi$
$887$			2.26334e44i			1.36740i	−0.729764	+	0.683699i	$0.760370\pi$
$888$	3.02834e43	−	1.88283e43i	0.179891	−	0.111845i
$889$	1.88340e43			0.110006
$890$		−	3.52895e43i		−	0.202673i
$891$	4.10304e43	−	3.14644e43i	0.231707	−	0.177686i
$892$	−2.81808e43			−0.156488
$893$		−	1.18765e44i		−	0.648508i
$894$	5.75771e43	+	9.26068e43i	0.309163	+	0.497256i
$895$	−1.47187e44			−0.777184
$896$		−	1.38754e43i		−	0.0720487i
$897$	−1.07064e44	+	6.65656e43i	−0.546710	+	0.339910i
$898$	−2.43996e44			−1.22528
$899$			1.68737e44i			0.833327i
$900$	5.33129e42	−	1.08067e43i	0.0258937	−	0.0524876i
$901$	1.00262e44			0.478919
$902$			8.46080e42i			0.0397478i
$903$	1.49068e44	+	2.39760e44i	0.688759	+	1.10780i
$904$	−1.43864e44			−0.653771
$905$			6.41532e43i			0.286741i
$906$	1.09561e44	−	6.81180e43i	0.481651	−	0.299460i
$907$	−2.24502e44			−0.970758			−0.485379	−	0.874304i	$-0.661318\pi$
$907$	−2.24502e44			−0.970758			−0.485379	+	0.874304i	$0.661318\pi$
$908$		−	9.92369e43i		−	0.422071i
$909$	3.39845e44	+	1.67656e44i	1.42175	+	0.701391i
$910$	1.47097e44			0.605319
$911$		−	3.05583e44i		−	1.23695i	−0.785803	−	0.618476i	$-0.787750\pi$
$911$		−	3.05583e44i		−	1.23695i	0.785803	−	0.618476i	$-0.212250\pi$
$912$	4.70007e43	+	7.55958e43i	0.187147	+	0.301006i
$913$	−2.89190e42			−0.0113272
$914$			5.98615e43i			0.230650i
$915$	−3.56243e44	+	2.21490e44i	−1.35030	+	0.839531i
$916$	9.10778e43			0.339610
$917$		−	1.06948e44i		−	0.392314i
$918$	3.37075e44	−	3.31233e43i	1.21643	−	0.119535i
$919$	5.25879e44			1.86704			0.933519	−	0.358529i	$-0.116722\pi$
$919$	5.25879e44			1.86704			0.933519	+	0.358529i	$0.116722\pi$
$920$			5.47853e43i			0.191358i
$921$	3.79957e43	+	6.11121e43i	0.130569	+	0.210007i
$922$	1.09664e44			0.370765
$923$			5.10322e44i			1.69754i
$924$	−3.08806e43	+	1.91996e43i	−0.101066	+	0.0628367i
$925$	−2.17790e43			−0.0701313
$926$			1.86989e43i			0.0592450i
$927$	−1.47726e42	+	2.99446e42i	−0.00460532	+	0.00933517i
$928$	−5.35446e43			−0.164247
$929$		−	1.82729e44i		−	0.551532i	−0.961225	−	0.275766i	$-0.911068\pi$
$929$		−	1.82729e44i		−	0.551532i	0.961225	−	0.275766i	$-0.0889316\pi$
$930$	−1.05944e44	−	1.70401e44i	−0.314655	−	0.506090i
$931$	−1.62782e44			−0.475732
$932$		−	9.26653e43i		−	0.266489i
$933$	3.55640e43	−	2.21115e43i	0.100644	−	0.0625738i
$934$	2.76871e44			0.771037
$935$			1.73063e44i			0.474274i
$936$	1.31399e44	+	6.48232e43i	0.354369	+	0.174821i
$937$	−3.69894e44			−0.981710			−0.490855	−	0.871241i	$-0.663316\pi$
$937$	−3.69894e44			−0.981710			−0.490855	+	0.871241i	$0.663316\pi$
$938$		−	3.96217e44i		−	1.03488i
$939$	−7.30789e43	−	1.17540e44i	−0.187849	−	0.302135i
$940$	−8.49505e43			−0.214906
$941$		−	6.36599e44i		−	1.58497i	−0.609889	−	0.792487i	$-0.708786\pi$
$941$		−	6.36599e44i		−	1.58497i	0.609889	−	0.792487i	$-0.291214\pi$
$942$	−2.44916e44	+	1.52273e44i	−0.600140	+	0.373130i
$943$	4.59784e43			0.110886
$944$			1.20438e44i			0.285879i
$945$	3.20623e43	+	3.26278e44i	0.0749062	+	0.762274i
$946$	−1.43689e44			−0.330413
$947$		−	7.96444e44i		−	1.80263i	−0.433169	−	0.901313i	$-0.642605\pi$
$947$		−	7.96444e44i		−	1.80263i	0.433169	−	0.901313i	$-0.357395\pi$
$948$	−1.28544e44	−	2.06749e44i	−0.286369	−	0.460595i
$949$	2.58708e44			0.567305
$950$		−	5.43665e43i		−	0.117348i
$951$	−6.93074e44	+	4.30910e44i	−1.47256	+	0.915543i
$952$	−2.38193e44			−0.498166
$953$			5.94488e44i			1.22391i	0.790892	+	0.611955i	$0.209617\pi$
$953$			5.94488e44i			1.22391i	−0.790892	+	0.611955i	$0.790383\pi$
$954$	−4.27682e43	+	8.66929e43i	−0.0866753	+	0.175694i
$955$	4.35935e44			0.869704
$956$			8.86762e42i			0.0174156i
$957$	7.40905e43	+	1.19167e44i	0.143246	+	0.230397i
$958$	−4.45507e44			−0.847953
$959$			2.88805e44i			0.541160i
$960$	5.40725e43	−	3.36189e43i	0.0997489	−	0.0620176i
$961$	−1.07684e44			−0.195570
$962$		−	2.64811e44i		−	0.473489i
$963$	−7.66847e44	−	3.78308e44i	−1.34994	−	0.665965i
$964$	5.66102e44			0.981158
$965$		−	5.01858e44i		−	0.856390i
$966$	1.04336e44	+	1.67814e44i	0.175299	+	0.281950i
$967$	−3.95331e44			−0.653980			−0.326990	−	0.945028i	$-0.606034\pi$
$967$	−3.95331e44			−0.653980			−0.326990	+	0.945028i	$0.606034\pi$
$968$			1.98556e44i			0.323409i
$969$	1.29772e45	−	8.06840e44i	2.08125	−	1.29399i
$970$	−4.60794e44			−0.727664
$971$			3.18022e44i			0.494502i	0.968951	+	0.247251i	$0.0795272\pi$
$971$			3.18022e44i			0.494502i	−0.968951	+	0.247251i	$0.920473\pi$
$972$	−1.15144e44	+	3.05587e44i	−0.176299	+	0.467888i
$973$	−2.56644e44			−0.386936
$974$			3.88931e44i			0.577415i
$975$	−4.72494e43	−	7.59958e43i	−0.0690760	−	0.111102i
$976$	2.93846e44			0.423031
$977$			9.00792e43i			0.127704i	0.997959	+	0.0638522i	$0.0203386\pi$
$977$			9.00792e43i			0.127704i	−0.997959	+	0.0638522i	$0.979661\pi$
$978$	−5.02497e44	+	3.12421e44i	−0.701537	+	0.436172i
$979$	6.47825e43			0.0890671
$980$			1.16436e44i			0.157650i
$981$	5.61435e44	−	1.13805e45i	0.748625	−	1.51749i
$982$	6.49927e43			0.0853477
$983$		−	3.50700e44i		−	0.453559i	−0.973946	−	0.226779i	$-0.927180\pi$
$983$		−	3.50700e44i		−	0.453559i	0.973946	−	0.226779i	$-0.0728196\pi$
$984$	−2.82146e43	−	4.53802e43i	−0.0359374	−	0.0578016i
$985$	−8.94797e43			−0.112249
$986$			9.19175e44i			1.13565i
$987$	−2.60214e44	+	1.61785e44i	−0.316646	+	0.196870i
$988$	6.61043e44			0.792274
$989$			7.80849e44i			0.921770i
$990$	−1.49642e44	−	7.38228e43i	−0.173990	−	0.0858347i
$991$	6.33121e44			0.725074			0.362537	−	0.931969i	$-0.381911\pi$
$991$	6.33121e44			0.725074			0.362537	+	0.931969i	$0.381911\pi$
$992$			1.40554e44i			0.158551i
$993$	5.61423e44	+	9.02991e44i	0.623809	+	1.00333i
$994$	7.99889e44			0.875455
$995$		−	3.08553e44i		−	0.332647i
$996$	1.55110e43	−	9.64374e42i	0.0164721	−	0.0102413i
$997$	−1.68352e45			−1.76112			−0.880562	−	0.473930i	$-0.842835\pi$
$997$	−1.68352e45			−1.76112			−0.880562	+	0.473930i	$0.842835\pi$
$998$			4.38050e43i			0.0451404i
$999$	5.87380e44	−	5.77200e43i	0.596262	−	0.0585927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.31.b.a.5.4	✓	10
3.2	odd	2	inner	6.31.b.a.5.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.31.b.a.5.4	✓	10	1.1	even	1	trivial
6.31.b.a.5.9	yes	10	3.2	odd	2	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 31 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-23170.5i q^{2} +(7.57629e6 + 1.21857e7i) q^{3} -5.36871e8 q^{4} +2.86759e10i q^{5} +(2.82348e11 - 1.75546e11i) q^{6} -3.86992e12 q^{7} +1.24396e13i q^{8} +(-9.10907e13 + 1.84645e14i) q^{9} +O(q^{10})\)	\(q-23170.5i q^{2} +(7.57629e6 + 1.21857e7i) q^{3} -5.36871e8 q^{4} +2.86759e10i q^{5} +(2.82348e11 - 1.75546e11i) q^{6} -3.86992e12 q^{7} +1.24396e13i q^{8} +(-9.10907e13 + 1.84645e14i) q^{9} +6.64434e14 q^{10} +1.21973e15i q^{11} +(-4.06749e15 - 6.54214e15i) q^{12} -5.72073e16 q^{13} +8.96678e16i q^{14} +(-3.49435e17 + 2.17257e17i) q^{15} +2.88230e17 q^{16} -4.94792e18i q^{17} +(4.27830e18 + 2.11061e18i) q^{18} +2.15233e19 q^{19} -1.53953e19i q^{20} +(-2.93196e19 - 4.71576e19i) q^{21} +2.82618e19 q^{22} -1.53583e20i q^{23} +(-1.51584e20 + 9.42457e19i) q^{24} +1.09015e20 q^{25} +1.32552e21i q^{26} +(-2.94015e21 + 2.88919e20i) q^{27} +2.07765e21 q^{28} -8.01754e21i q^{29} +(5.03395e21 + 8.09659e21i) q^{30} -2.10460e22 q^{31} -6.67843e21i q^{32} +(-1.48633e22 + 9.24105e21i) q^{33} -1.14646e23 q^{34} -1.10973e23i q^{35} +(4.89040e22 - 9.91303e22i) q^{36} -1.99779e23 q^{37} -4.98704e23i q^{38} +(-4.33419e23 - 6.97110e23i) q^{39} -3.56715e23 q^{40} +2.99372e23i q^{41} +(-1.09266e24 + 6.79349e23i) q^{42} -5.08423e24 q^{43} -6.54839e23i q^{44} +(-5.29485e24 - 2.61211e24i) q^{45} -3.55858e24 q^{46} -5.51797e24i q^{47} +(2.18372e24 + 3.51228e24i) q^{48} -7.56309e24 q^{49} -2.52594e24i q^{50} +(6.02937e25 - 3.74869e25i) q^{51} +3.07129e25 q^{52} +2.02634e25i q^{53} +(6.69440e24 + 6.81247e25i) q^{54} -3.49769e25 q^{55} -4.81400e25i q^{56} +(1.63067e26 + 2.62276e26i) q^{57} -1.85770e26 q^{58} +4.17852e26i q^{59} +(1.87602e26 - 1.16639e26i) q^{60} +1.01948e27 q^{61} +4.87646e26i q^{62} +(3.52513e26 - 7.14559e26i) q^{63} -1.54743e26 q^{64} -1.64047e27i q^{65} +(2.14120e26 + 3.44389e26i) q^{66} -4.41872e27 q^{67} +2.65639e27i q^{68} +(1.87151e27 - 1.16359e27i) q^{69} -2.57130e27 q^{70} -8.92058e27i q^{71} +(-2.29690e27 - 1.13313e27i) q^{72} -4.52229e27 q^{73} +4.62897e27i q^{74} +(8.25933e26 + 1.32843e27i) q^{75} -1.15552e28 q^{76} -4.72026e27i q^{77} +(-1.61524e28 + 1.00425e28i) q^{78} +3.16027e28 q^{79} +8.26526e27i q^{80} +(-2.57961e28 - 3.36388e28i) q^{81} +6.93660e27 q^{82} +2.37093e27i q^{83} +(1.57409e28 + 2.53175e28i) q^{84} +1.41886e29 q^{85} +1.17804e29i q^{86} +(9.76992e28 - 6.07432e28i) q^{87} -1.51729e28 q^{88} -5.31121e28i q^{89} +(-6.05238e28 + 1.22684e29i) q^{90} +2.21387e29 q^{91} +8.24540e28i q^{92} +(-1.59451e29 - 2.56460e29i) q^{93} -1.27854e29 q^{94} +6.17199e29i q^{95} +(8.13813e28 - 5.05978e28i) q^{96} -6.93514e29 q^{97} +1.75240e29i q^{98} +(-2.25217e29 - 1.11106e29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) \) 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9	\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) \) 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9 - 1111538175836160 * q^10 - 7591226920402944 * q^12 + 11241857908456580 * q^13 - 1208370750576105600 * q^15 + 2882303761517117440 * q^16 + 4378961453216956416 * q^18 - 406434941012438620 * q^19 + 189341373476724706020 * q^21 - 175966920878069907456 * q^22 + 78269746773932113920 * q^24 - 538750688835772733030 * q^25 - 509686212259700532126 * q^27 + 783474298257252810752 * q^28 + 3618734882327478927360 * q^30 - 3850790055930904811020 * q^31 + 13877514934601873876352 * q^33 - 21974427701517892976640 * q^34 - 22394560921038760181760 * q^36 + 691786417224189171658916 * q^37 + 264189297409049008449300 * q^39 + 596752514183975581777920 * q^40 + 2551733261187619598893056 * q^42 - 10594373354873893550389372 * q^43 + 21961398854703004532478720 * q^45 - 14905926072892021549301760 * q^46 + 4075508919955679952764928 * q^48 - 14303693611422252234715650 * q^49 + 100757981401326611204590080 * q^51 - 6035426507887496617000960 * q^52 + 186364360915292902942310400 * q^54 - 905529883473273884900970240 * q^55 + 1357830109447011748343825076 * q^57 - 1026862318649343581985177600 * q^58 + 648739106895918338880307200 * q^60 - 2949272535924647913201299260 * q^61 + 5088794127795653673352888692 * q^63 - 1547425049106725343623905280 * q^64 + 3787402697011447732654571520 * q^66 - 10556251754234326335356822044 * q^67 + 15764240424701154050198334720 * q^69 - 8691440888931957213379952640 * q^70 - 2350937029001432724922171392 * q^72 + 12106003505184711607130189300 * q^73 - 7500206691267464218185712830 * q^75 + 218203097450014125263421440 * q^76 - 23839067108381696719249735680 * q^78 + 68719005124237783442983312820 * q^79 - 111620808361643664456575921430 * q^81 + 18283730424263848186657898496 * q^82 - 101651875857781803693889290240 * q^84 + 403836274868708986530058828800 * q^85 - 512433611792960206983797969280 * q^87 + 94471521293641232015658319872 * q^88 - 426164288449255115819581440000 * q^90 + 1222541373056582384854822798600 * q^91 - 983623123086267594817934884284 * q^93 - 80746046881825464175401369600 * q^94 - 42020750332529991826318295040 * q^96 - 1391585232259866867438139103212 * q^97 + 2707446209006624257844338302720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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