LMFDB - Embedded newform 418.2.e.g.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(45,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("418.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.e (of order $3$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	418.45
Dual form			418.2.e.g.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.22474 - 2.12132i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{6} +2.44949 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.22474 - 2.12132i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{6} +2.44949 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{9} -1.00000 q^{11} +2.44949 q^{12} +(2.94949 - 5.10867i) q^{13} +(1.22474 + 2.12132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.224745 - 0.389270i) q^{17} -3.00000 q^{18} +(-3.17423 - 2.98735i) q^{19} +(-3.00000 - 5.19615i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(4.44949 - 7.70674i) q^{23} +(1.22474 + 2.12132i) q^{24} +(2.50000 - 4.33013i) q^{25} +5.89898 q^{26} +(-1.22474 + 2.12132i) q^{28} +(-3.94949 + 6.84072i) q^{29} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.22474 + 2.12132i) q^{33} +(0.224745 - 0.389270i) q^{34} +(-1.50000 - 2.59808i) q^{36} +3.55051 q^{37} +(1.00000 - 4.24264i) q^{38} -14.4495 q^{39} +(6.22474 + 10.7816i) q^{41} +(3.00000 - 5.19615i) q^{42} +(-2.27526 - 3.94086i) q^{43} +(0.500000 - 0.866025i) q^{44} +8.89898 q^{46} +(5.72474 - 9.91555i) q^{47} +(-1.22474 + 2.12132i) q^{48} -1.00000 q^{49} +5.00000 q^{50} +(-0.550510 + 0.953512i) q^{51} +(2.94949 + 5.10867i) q^{52} +(-5.89898 + 10.2173i) q^{53} -2.44949 q^{56} +(-2.44949 + 10.3923i) q^{57} -7.89898 q^{58} +(3.44949 + 5.97469i) q^{59} +(0.949490 - 1.64456i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-3.67423 + 6.36396i) q^{63} +1.00000 q^{64} +(-1.22474 + 2.12132i) q^{66} +(-7.22474 + 12.5136i) q^{67} +0.449490 q^{68} -21.7980 q^{69} +(-1.27526 - 2.20881i) q^{71} +(1.50000 - 2.59808i) q^{72} +(4.77526 + 8.27098i) q^{73} +(1.77526 + 3.07483i) q^{74} -12.2474 q^{75} +(4.17423 - 1.25529i) q^{76} -2.44949 q^{77} +(-7.22474 - 12.5136i) q^{78} +(0.224745 + 0.389270i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-6.22474 + 10.7816i) q^{82} -0.550510 q^{83} +6.00000 q^{84} +(2.27526 - 3.94086i) q^{86} +19.3485 q^{87} +1.00000 q^{88} +(4.50000 - 7.79423i) q^{89} +(7.22474 - 12.5136i) q^{91} +(4.44949 + 7.70674i) q^{92} +(-2.44949 - 4.24264i) q^{93} +11.4495 q^{94} -2.44949 q^{96} +(2.94949 + 5.10867i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{9} - 4 q^{11} + 2 q^{13} - 2 q^{16} + 4 q^{17} - 12 q^{18} + 2 q^{19} - 12 q^{21} - 2 q^{22} + 8 q^{23} + 10 q^{25} + 4 q^{26} - 6 q^{29} + 8 q^{31} + 2 q^{32} - 4 q^{34} - 6 q^{36} + 24 q^{37} + 4 q^{38} - 48 q^{39} + 20 q^{41} + 12 q^{42} - 14 q^{43} + 2 q^{44} + 16 q^{46} + 18 q^{47} - 4 q^{49} + 20 q^{50} - 12 q^{51} + 2 q^{52} - 4 q^{53} - 12 q^{58} + 4 q^{59} - 6 q^{61} + 4 q^{62} + 4 q^{64} - 24 q^{67} - 8 q^{68} - 48 q^{69} - 10 q^{71} + 6 q^{72} + 24 q^{73} + 12 q^{74} + 2 q^{76} - 24 q^{78} - 4 q^{79} + 18 q^{81} - 20 q^{82} - 12 q^{83} + 24 q^{84} + 14 q^{86} + 48 q^{87} + 4 q^{88} + 18 q^{89} + 24 q^{91} + 8 q^{92} + 36 q^{94} + 2 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 6 * q^9 - 4 * q^11 + 2 * q^13 - 2 * q^16 + 4 * q^17 - 12 * q^18 + 2 * q^19 - 12 * q^21 - 2 * q^22 + 8 * q^23 + 10 * q^25 + 4 * q^26 - 6 * q^29 + 8 * q^31 + 2 * q^32 - 4 * q^34 - 6 * q^36 + 24 * q^37 + 4 * q^38 - 48 * q^39 + 20 * q^41 + 12 * q^42 - 14 * q^43 + 2 * q^44 + 16 * q^46 + 18 * q^47 - 4 * q^49 + 20 * q^50 - 12 * q^51 + 2 * q^52 - 4 * q^53 - 12 * q^58 + 4 * q^59 - 6 * q^61 + 4 * q^62 + 4 * q^64 - 24 * q^67 - 8 * q^68 - 48 * q^69 - 10 * q^71 + 6 * q^72 + 24 * q^73 + 12 * q^74 + 2 * q^76 - 24 * q^78 - 4 * q^79 + 18 * q^81 - 20 * q^82 - 12 * q^83 + 24 * q^84 + 14 * q^86 + 48 * q^87 + 4 * q^88 + 18 * q^89 + 24 * q^91 + 8 * q^92 + 36 * q^94 + 2 * q^97 - 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.22474	−	2.12132i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$3$	−1.22474	−	2.12132i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	1.22474	−	2.12132i	0.500000	−	0.866025i
$7$	2.44949			0.925820			0.462910	−	0.886405i	$-0.346805\pi$
$7$	2.44949			0.925820			0.462910	+	0.886405i	$0.346805\pi$
$8$	−1.00000			−0.353553
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$		0			0
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	2.44949			0.707107
$13$	2.94949	−	5.10867i	0.818041	−	1.41689i	−0.0890821	−	0.996024i	$-0.528393\pi$
$13$	2.94949	−	5.10867i	0.818041	−	1.41689i	0.907123	−	0.420865i	$-0.138273\pi$
$14$	1.22474	+	2.12132i	0.327327	+	0.566947i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.224745	−	0.389270i	−0.0545086	−	0.0944117i	0.837484	−	0.546463i	$-0.184026\pi$
$17$	−0.224745	−	0.389270i	−0.0545086	−	0.0944117i	−0.891992	+	0.452051i	$0.850693\pi$
$18$	−3.00000			−0.707107
$19$	−3.17423	−	2.98735i	−0.728219	−	0.685344i
$19$	−3.17423	−	2.98735i	−0.728219	−	0.685344i
$20$		0			0
$21$	−3.00000	−	5.19615i	−0.654654	−	1.13389i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	4.44949	−	7.70674i	0.927783	−	1.60697i	0.140759	−	0.990044i	$-0.455046\pi$
$23$	4.44949	−	7.70674i	0.927783	−	1.60697i	0.787024	−	0.616923i	$-0.211621\pi$
$24$	1.22474	+	2.12132i	0.250000	+	0.433013i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	5.89898			1.15689
$27$		0			0
$28$	−1.22474	+	2.12132i	−0.231455	+	0.400892i
$29$	−3.94949	+	6.84072i	−0.733402	+	1.27029i	0.222019	+	0.975042i	$0.428735\pi$
$29$	−3.94949	+	6.84072i	−0.733402	+	1.27029i	−0.955421	+	0.295247i	$0.904598\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.22474	+	2.12132i	0.213201	+	0.369274i
$34$	0.224745	−	0.389270i	0.0385434	−	0.0667592i
$35$		0			0
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	3.55051			0.583700			0.291850	−	0.956464i	$-0.405729\pi$
$37$	3.55051			0.583700			0.291850	+	0.956464i	$0.405729\pi$
$38$	1.00000	−	4.24264i	0.162221	−	0.688247i
$39$	−14.4495			−2.31377
$40$		0			0
$41$	6.22474	+	10.7816i	0.972142	+	1.68380i	0.689062	+	0.724703i	$0.258023\pi$
$41$	6.22474	+	10.7816i	0.972142	+	1.68380i	0.283080	+	0.959096i	$0.408644\pi$
$42$	3.00000	−	5.19615i	0.462910	−	0.801784i
$43$	−2.27526	−	3.94086i	−0.346973	−	0.600975i	0.638737	−	0.769425i	$-0.279457\pi$
$43$	−2.27526	−	3.94086i	−0.346973	−	0.600975i	−0.985710	+	0.168450i	$0.946124\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	8.89898			1.31208
$47$	5.72474	−	9.91555i	0.835040	−	1.44633i	−0.0589581	−	0.998260i	$-0.518778\pi$
$47$	5.72474	−	9.91555i	0.835040	−	1.44633i	0.893998	−	0.448071i	$-0.147889\pi$
$48$	−1.22474	+	2.12132i	−0.176777	+	0.306186i
$49$	−1.00000			−0.142857
$50$	5.00000			0.707107
$51$	−0.550510	+	0.953512i	−0.0770869	+	0.133518i
$52$	2.94949	+	5.10867i	0.409021	+	0.708445i
$53$	−5.89898	+	10.2173i	−0.810287	+	1.40346i	0.102376	+	0.994746i	$0.467356\pi$
$53$	−5.89898	+	10.2173i	−0.810287	+	1.40346i	−0.912663	+	0.408713i	$0.865978\pi$
$54$		0			0
$55$		0			0
$56$	−2.44949			−0.327327
$57$	−2.44949	+	10.3923i	−0.324443	+	1.37649i
$58$	−7.89898			−1.03719
$59$	3.44949	+	5.97469i	0.449085	+	0.777839i	0.998327	−	0.0578252i	$-0.0184166\pi$
$59$	3.44949	+	5.97469i	0.449085	+	0.777839i	−0.549241	+	0.835664i	$0.685083\pi$
$60$		0			0
$61$	0.949490	−	1.64456i	0.121570	−	0.210565i	−0.798817	−	0.601574i	$-0.794541\pi$
$61$	0.949490	−	1.64456i	0.121570	−	0.210565i	0.920387	+	0.391009i	$0.127874\pi$
$62$	1.00000	+	1.73205i	0.127000	+	0.219971i
$63$	−3.67423	+	6.36396i	−0.462910	+	0.801784i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.22474	+	2.12132i	−0.150756	+	0.261116i
$67$	−7.22474	+	12.5136i	−0.882643	+	1.52878i	−0.0342516	+	0.999413i	$0.510905\pi$
$67$	−7.22474	+	12.5136i	−0.882643	+	1.52878i	−0.848391	+	0.529369i	$0.822429\pi$
$68$	0.449490			0.0545086
$69$	−21.7980			−2.62417
$70$		0			0
$71$	−1.27526	−	2.20881i	−0.151345	−	0.262137i	0.780377	−	0.625309i	$-0.215027\pi$
$71$	−1.27526	−	2.20881i	−0.151345	−	0.262137i	−0.931722	+	0.363172i	$0.881694\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	4.77526	+	8.27098i	0.558901	+	0.968046i	0.997589	+	0.0694057i	$0.0221103\pi$
$73$	4.77526	+	8.27098i	0.558901	+	0.968046i	−0.438687	+	0.898640i	$0.644556\pi$
$74$	1.77526	+	3.07483i	0.206369	+	0.357442i
$75$	−12.2474			−1.41421
$76$	4.17423	−	1.25529i	0.478818	−	0.143992i
$77$	−2.44949			−0.279145
$78$	−7.22474	−	12.5136i	−0.818041	−	1.41689i
$79$	0.224745	+	0.389270i	0.0252858	+	0.0437962i	0.878391	−	0.477942i	$-0.158617\pi$
$79$	0.224745	+	0.389270i	0.0252858	+	0.0437962i	−0.853106	+	0.521738i	$0.825284\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−6.22474	+	10.7816i	−0.687408	+	1.19063i
$83$	−0.550510			−0.0604264			−0.0302132	−	0.999543i	$-0.509619\pi$
$83$	−0.550510			−0.0604264			−0.0302132	+	0.999543i	$0.509619\pi$
$84$	6.00000			0.654654
$85$		0			0
$86$	2.27526	−	3.94086i	0.245347	−	0.424954i
$87$	19.3485			2.07437
$88$	1.00000			0.106600
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$		0			0
$91$	7.22474	−	12.5136i	0.757359	−	1.31178i
$92$	4.44949	+	7.70674i	0.463891	+	0.803483i
$93$	−2.44949	−	4.24264i	−0.254000	−	0.439941i
$94$	11.4495			1.18092
$95$		0			0
$96$	−2.44949			−0.250000
$97$	2.94949	+	5.10867i	0.299475	+	0.518706i	0.976016	−	0.217699i	$-0.0698550\pi$
$97$	2.94949	+	5.10867i	0.299475	+	0.518706i	−0.676541	+	0.736405i	$0.736522\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	−2.50000	+	4.33013i	−0.248759	+	0.430864i	−0.963182	−	0.268851i	$-0.913356\pi$
$101$	−2.50000	+	4.33013i	−0.248759	+	0.430864i	0.714423	+	0.699715i	$0.246689\pi$
$102$	−1.10102			−0.109017
$103$	6.34847			0.625533			0.312767	−	0.949830i	$-0.398744\pi$
$103$	6.34847			0.625533			0.312767	+	0.949830i	$0.398744\pi$
$104$	−2.94949	+	5.10867i	−0.289221	+	0.500946i
$105$		0			0
$106$	−11.7980			−1.14592
$107$	−4.34847			−0.420382			−0.210191	−	0.977660i	$-0.567409\pi$
$107$	−4.34847			−0.420382			−0.210191	+	0.977660i	$0.567409\pi$
$108$		0			0
$109$	−3.05051	−	5.28364i	−0.292186	−	0.506081i	0.682140	−	0.731221i	$-0.261049\pi$
$109$	−3.05051	−	5.28364i	−0.292186	−	0.506081i	−0.974326	+	0.225140i	$0.927716\pi$
$110$		0			0
$111$	−4.34847	−	7.53177i	−0.412738	−	0.714884i
$112$	−1.22474	−	2.12132i	−0.115728	−	0.200446i
$113$	−13.6969			−1.28850			−0.644250	−	0.764815i	$-0.722830\pi$
$113$	−13.6969			−1.28850			−0.644250	+	0.764815i	$0.722830\pi$
$114$	−10.2247	+	3.07483i	−0.957635	+	0.287984i
$115$		0			0
$116$	−3.94949	−	6.84072i	−0.366701	−	0.635145i
$117$	8.84847	+	15.3260i	0.818041	+	1.41689i
$118$	−3.44949	+	5.97469i	−0.317551	+	0.550015i
$119$	−0.550510	−	0.953512i	−0.0504652	−	0.0874083i
$120$		0			0
$121$	1.00000			0.0909091
$122$	1.89898			0.171926
$123$	15.2474	−	26.4094i	1.37482	−	2.38125i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	−7.34847			−0.654654
$127$	8.34847	−	14.4600i	0.740807	−	1.28312i	−0.211322	−	0.977417i	$-0.567777\pi$
$127$	8.34847	−	14.4600i	0.740807	−	1.28312i	0.952128	−	0.305699i	$-0.0988900\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−5.57321	+	9.65309i	−0.490694	+	0.849907i
$130$		0			0
$131$	5.17423	+	8.96204i	0.452075	+	0.783017i	0.998515	−	0.0544816i	$-0.0173506\pi$
$131$	5.17423	+	8.96204i	0.452075	+	0.783017i	−0.546440	+	0.837498i	$0.684017\pi$
$132$	−2.44949			−0.213201
$133$	−7.77526	−	7.31747i	−0.674200	−	0.634505i
$134$	−14.4495			−1.24825
$135$		0			0
$136$	0.224745	+	0.389270i	0.0192717	+	0.0333796i
$137$	−0.949490	+	1.64456i	−0.0811204	+	0.140505i	−0.903731	−	0.428100i	$-0.859183\pi$
$137$	−0.949490	+	1.64456i	−0.0811204	+	0.140505i	0.822611	+	0.568604i	$0.192516\pi$
$138$	−10.8990	−	18.8776i	−0.927783	−	1.60697i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	−28.0454			−2.36185
$142$	1.27526	−	2.20881i	0.107017	−	0.185359i
$143$	−2.94949	+	5.10867i	−0.246649	+	0.427208i
$144$	3.00000			0.250000
$145$		0			0
$146$	−4.77526	+	8.27098i	−0.395203	+	0.684512i
$147$	1.22474	+	2.12132i	0.101015	+	0.174964i
$148$	−1.77526	+	3.07483i	−0.145925	+	0.252750i
$149$	5.34847	+	9.26382i	0.438164	+	0.758922i	0.997548	−	0.0699867i	$-0.0222957\pi$
$149$	5.34847	+	9.26382i	0.438164	+	0.758922i	−0.559384	+	0.828908i	$0.688962\pi$
$150$	−6.12372	−	10.6066i	−0.500000	−	0.866025i
$151$	−3.55051			−0.288936			−0.144468	−	0.989509i	$-0.546147\pi$
$151$	−3.55051			−0.288936			−0.144468	+	0.989509i	$0.546147\pi$
$152$	3.17423	+	2.98735i	0.257464	+	0.242306i
$153$	1.34847			0.109017
$154$	−1.22474	−	2.12132i	−0.0986928	−	0.170941i
$155$		0			0
$156$	7.22474	−	12.5136i	0.578443	−	1.00189i
$157$	3.00000	+	5.19615i	0.239426	+	0.414698i	0.960550	−	0.278108i	$-0.0897074\pi$
$157$	3.00000	+	5.19615i	0.239426	+	0.414698i	−0.721124	+	0.692806i	$0.756374\pi$
$158$	−0.224745	+	0.389270i	−0.0178797	+	0.0309686i
$159$	28.8990			2.29184
$160$		0			0
$161$	10.8990	−	18.8776i	0.858960	−	1.48776i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	−6.89898			−0.540370			−0.270185	−	0.962808i	$-0.587085\pi$
$163$	−6.89898			−0.540370			−0.270185	+	0.962808i	$0.587085\pi$
$164$	−12.4495			−0.972142
$165$		0			0
$166$	−0.275255	−	0.476756i	−0.0213639	−	0.0370034i
$167$	−10.5732	+	18.3133i	−0.818180	+	1.41713i	0.0888421	+	0.996046i	$0.471683\pi$
$167$	−10.5732	+	18.3133i	−0.818180	+	1.41713i	−0.907022	+	0.421083i	$0.861650\pi$
$168$	3.00000	+	5.19615i	0.231455	+	0.400892i
$169$	−10.8990	−	18.8776i	−0.838383	−	1.45212i
$170$		0			0
$171$	12.5227	−	3.76588i	0.957635	−	0.287984i
$172$	4.55051			0.346973
$173$	4.89898	+	8.48528i	0.372463	+	0.645124i	0.989944	−	0.141462i	$-0.0451802\pi$
$173$	4.89898	+	8.48528i	0.372463	+	0.645124i	−0.617481	+	0.786586i	$0.711847\pi$
$174$	9.67423	+	16.7563i	0.733402	+	1.27029i
$175$	6.12372	−	10.6066i	0.462910	−	0.801784i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	8.44949	−	14.6349i	0.635103	−	1.10003i
$178$	9.00000			0.674579
$179$	9.79796			0.732334			0.366167	−	0.930549i	$-0.380670\pi$
$179$	9.79796			0.732334			0.366167	+	0.930549i	$0.380670\pi$
$180$		0			0
$181$	10.1237	−	17.5348i	0.752491	−	1.30335i	−0.194122	−	0.980977i	$-0.562186\pi$
$181$	10.1237	−	17.5348i	0.752491	−	1.30335i	0.946612	−	0.322374i	$-0.104481\pi$
$182$	14.4495			1.07107
$183$	−4.65153			−0.343851
$184$	−4.44949	+	7.70674i	−0.328021	+	0.568149i
$185$		0			0
$186$	2.44949	−	4.24264i	0.179605	−	0.311086i
$187$	0.224745	+	0.389270i	0.0164350	+	0.0284662i
$188$	5.72474	+	9.91555i	0.417520	+	0.723166i
$189$		0			0
$190$		0			0
$191$	−22.3485			−1.61708			−0.808539	−	0.588442i	$-0.799741\pi$
$191$	−22.3485			−1.61708			−0.808539	+	0.588442i	$0.799741\pi$
$192$	−1.22474	−	2.12132i	−0.0883883	−	0.153093i
$193$	4.32577	+	7.49245i	0.311375	+	0.539318i	0.978660	−	0.205484i	$-0.0658770\pi$
$193$	4.32577	+	7.49245i	0.311375	+	0.539318i	−0.667285	+	0.744803i	$0.732544\pi$
$194$	−2.94949	+	5.10867i	−0.211761	+	0.366781i
$195$		0			0
$196$	0.500000	−	0.866025i	0.0357143	−	0.0618590i
$197$	15.8990			1.13276			0.566378	−	0.824146i	$-0.308344\pi$
$197$	15.8990			1.13276			0.566378	+	0.824146i	$0.308344\pi$
$198$	3.00000			0.213201
$199$	−2.82577	+	4.89437i	−0.200313	+	0.346953i	−0.948629	−	0.316390i	$-0.897529\pi$
$199$	−2.82577	+	4.89437i	−0.200313	+	0.346953i	0.748316	+	0.663342i	$0.230863\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$	35.3939			2.49649
$202$	−5.00000			−0.351799
$203$	−9.67423	+	16.7563i	−0.678998	+	1.17606i
$204$	−0.550510	−	0.953512i	−0.0385434	−	0.0667592i
$205$		0			0
$206$	3.17423	+	5.49794i	0.221159	+	0.383059i
$207$	13.3485	+	23.1202i	0.927783	+	1.60697i
$208$	−5.89898			−0.409021
$209$	3.17423	+	2.98735i	0.219566	+	0.206639i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	−5.89898	−	10.2173i	−0.405144	−	0.701729i
$213$	−3.12372	+	5.41045i	−0.214034	+	0.370718i
$214$	−2.17423	−	3.76588i	−0.148628	−	0.257431i
$215$		0			0
$216$		0			0
$217$	4.89898			0.332564
$218$	3.05051	−	5.28364i	0.206607	−	0.357853i
$219$	11.6969	−	20.2597i	0.790406	−	1.36902i
$220$		0			0
$221$	−2.65153			−0.178361
$222$	4.34847	−	7.53177i	0.291850	−	0.505499i
$223$	11.6237	+	20.1329i	0.778382	+	1.34820i	0.932874	+	0.360203i	$0.117293\pi$
$223$	11.6237	+	20.1329i	0.778382	+	1.34820i	−0.154492	+	0.987994i	$0.549374\pi$
$224$	1.22474	−	2.12132i	0.0818317	−	0.141737i
$225$	7.50000	+	12.9904i	0.500000	+	0.866025i
$226$	−6.84847	−	11.8619i	−0.455553	−	0.789042i
$227$	23.7980			1.57953			0.789763	−	0.613412i	$-0.210204\pi$
$227$	23.7980			1.57953			0.789763	+	0.613412i	$0.210204\pi$
$228$	−7.77526	−	7.31747i	−0.514929	−	0.484611i
$229$	−15.3485			−1.01426			−0.507128	−	0.861871i	$-0.669293\pi$
$229$	−15.3485			−1.01426			−0.507128	+	0.861871i	$0.669293\pi$
$230$		0			0
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	3.94949	−	6.84072i	0.259297	−	0.449115i
$233$	2.77526	+	4.80688i	0.181813	+	0.314909i	0.942498	−	0.334212i	$-0.108470\pi$
$233$	2.77526	+	4.80688i	0.181813	+	0.314909i	−0.760685	+	0.649121i	$0.775137\pi$
$234$	−8.84847	+	15.3260i	−0.578443	+	1.00189i
$235$		0			0
$236$	−6.89898			−0.449085
$237$	0.550510	−	0.953512i	0.0357595	−	0.0619372i
$238$	0.550510	−	0.953512i	0.0356843	−	0.0618070i
$239$	2.20204			0.142438			0.0712191	−	0.997461i	$-0.477311\pi$
$239$	2.20204			0.142438			0.0712191	+	0.997461i	$0.477311\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	11.0227	−	19.0919i	0.707107	−	1.22474i
$244$	0.949490	+	1.64456i	0.0607849	+	0.105282i
$245$		0			0
$246$	30.4949			1.94428
$247$	−24.6237	+	7.40496i	−1.56677	+	0.471166i
$248$	−2.00000			−0.127000
$249$	0.674235	+	1.16781i	0.0427279	+	0.0740069i
$250$		0			0
$251$	0.123724	−	0.214297i	0.00780941	−	0.0135263i	−0.862094	−	0.506748i	$-0.830847\pi$
$251$	0.123724	−	0.214297i	0.00780941	−	0.0135263i	0.869904	+	0.493222i	$0.164181\pi$
$252$	−3.67423	−	6.36396i	−0.231455	−	0.400892i
$253$	−4.44949	+	7.70674i	−0.279737	+	0.484519i
$254$	16.6969			1.04766
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.0000	−	19.0526i	0.686161	−	1.18847i	−0.286909	−	0.957958i	$-0.592628\pi$
$257$	11.0000	−	19.0526i	0.686161	−	1.18847i	0.973070	−	0.230508i	$-0.0740389\pi$
$258$	−11.1464			−0.693946
$259$	8.69694			0.540401
$260$		0			0
$261$	−11.8485	−	20.5222i	−0.733402	−	1.27029i
$262$	−5.17423	+	8.96204i	−0.319665	+	0.553677i
$263$	8.89898	+	15.4135i	0.548735	+	0.950436i	0.998362	+	0.0572198i	$0.0182236\pi$
$263$	8.89898	+	15.4135i	0.548735	+	0.950436i	−0.449627	+	0.893216i	$0.648443\pi$
$264$	−1.22474	−	2.12132i	−0.0753778	−	0.130558i
$265$		0			0
$266$	2.44949	−	10.3923i	0.150188	−	0.637193i
$267$	−22.0454			−1.34916
$268$	−7.22474	−	12.5136i	−0.441322	−	0.764391i
$269$	−7.77526	−	13.4671i	−0.474066	−	0.821106i	0.525493	−	0.850798i	$-0.323881\pi$
$269$	−7.77526	−	13.4671i	−0.474066	−	0.821106i	−0.999559	+	0.0296918i	$0.990547\pi$
$270$		0			0
$271$	2.34847	+	4.06767i	0.142659	+	0.247093i	0.928497	−	0.371339i	$-0.121101\pi$
$271$	2.34847	+	4.06767i	0.142659	+	0.247093i	−0.785838	+	0.618433i	$0.787768\pi$
$272$	−0.224745	+	0.389270i	−0.0136272	+	0.0236029i
$273$	−35.3939			−2.14213
$274$	−1.89898			−0.114722
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$	10.8990	−	18.8776i	0.656041	−	1.13630i
$277$	17.4949			1.05117			0.525583	−	0.850742i	$-0.323847\pi$
$277$	17.4949			1.05117			0.525583	+	0.850742i	$0.323847\pi$
$278$	4.00000			0.239904
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$		0			0
$281$	−8.57321	+	14.8492i	−0.511435	+	0.885832i	0.488477	+	0.872577i	$0.337553\pi$
$281$	−8.57321	+	14.8492i	−0.511435	+	0.885832i	−0.999912	+	0.0132548i	$0.995781\pi$
$282$	−14.0227	−	24.2880i	−0.835040	−	1.44633i
$283$	−6.44949	−	11.1708i	−0.383382	−	0.664038i	0.608161	−	0.793814i	$-0.291908\pi$
$283$	−6.44949	−	11.1708i	−0.383382	−	0.664038i	−0.991543	+	0.129776i	$0.958574\pi$
$284$	2.55051			0.151345
$285$		0			0
$286$	−5.89898			−0.348814
$287$	15.2474	+	26.4094i	0.900028	+	1.55889i
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	8.39898	−	14.5475i	0.494058	−	0.855733i
$290$		0			0
$291$	7.22474	−	12.5136i	0.423522	−	0.733562i
$292$	−9.55051			−0.558901
$293$	1.89898			0.110940			0.0554698	−	0.998460i	$-0.482334\pi$
$293$	1.89898			0.110940			0.0554698	+	0.998460i	$0.482334\pi$
$294$	−1.22474	+	2.12132i	−0.0714286	+	0.123718i
$295$		0			0
$296$	−3.55051			−0.206369
$297$		0			0
$298$	−5.34847	+	9.26382i	−0.309829	+	0.536639i
$299$	−26.2474	−	45.4619i	−1.51793	−	2.62913i
$300$	6.12372	−	10.6066i	0.353553	−	0.612372i
$301$	−5.57321	−	9.65309i	−0.321235	−	0.556395i
$302$	−1.77526	−	3.07483i	−0.102154	−	0.176937i
$303$	12.2474			0.703598
$304$	−1.00000	+	4.24264i	−0.0573539	+	0.243332i
$305$		0			0
$306$	0.674235	+	1.16781i	0.0385434	+	0.0667592i
$307$	−2.62372	−	4.54442i	−0.149744	−	0.259364i	0.781389	−	0.624044i	$-0.214512\pi$
$307$	−2.62372	−	4.54442i	−0.149744	−	0.259364i	−0.931133	+	0.364680i	$0.881178\pi$
$308$	1.22474	−	2.12132i	0.0697863	−	0.120873i
$309$	−7.77526	−	13.4671i	−0.442319	−	0.766119i
$310$		0			0
$311$	−17.2474			−0.978013			−0.489007	−	0.872280i	$-0.662641\pi$
$311$	−17.2474			−0.978013			−0.489007	+	0.872280i	$0.662641\pi$
$312$	14.4495			0.818041
$313$	−4.84847	+	8.39780i	−0.274052	+	0.474671i	−0.969895	−	0.243522i	$-0.921697\pi$
$313$	−4.84847	+	8.39780i	−0.274052	+	0.474671i	0.695844	+	0.718193i	$0.255031\pi$
$314$	−3.00000	+	5.19615i	−0.169300	+	0.293236i
$315$		0			0
$316$	−0.449490			−0.0252858
$317$	−10.0227	+	17.3598i	−0.562931	+	0.975025i	0.434308	+	0.900765i	$0.356993\pi$
$317$	−10.0227	+	17.3598i	−0.562931	+	0.975025i	−0.997239	+	0.0742608i	$0.976340\pi$
$318$	14.4495	+	25.0273i	0.810287	+	1.40346i
$319$	3.94949	−	6.84072i	0.221129	−	0.383007i
$320$		0			0
$321$	5.32577	+	9.22450i	0.297255	+	0.514861i
$322$	21.7980			1.21475
$323$	−0.449490	+	1.90702i	−0.0250103	+	0.106110i
$324$	−9.00000			−0.500000
$325$	−14.7474	−	25.5433i	−0.818041	−	1.41689i
$326$	−3.44949	−	5.97469i	−0.191050	−	0.330908i
$327$	−7.47219	+	12.9422i	−0.413213	+	0.715706i
$328$	−6.22474	−	10.7816i	−0.343704	−	0.595313i
$329$	14.0227	−	24.2880i	0.773097	−	1.33904i
$330$		0			0
$331$	−9.34847			−0.513838			−0.256919	−	0.966433i	$-0.582707\pi$
$331$	−9.34847			−0.513838			−0.256919	+	0.966433i	$0.582707\pi$
$332$	0.275255	−	0.476756i	0.0151066	−	0.0261654i
$333$	−5.32577	+	9.22450i	−0.291850	+	0.505499i
$334$	−21.1464			−1.15708
$335$		0			0
$336$	−3.00000	+	5.19615i	−0.163663	+	0.283473i
$337$	−15.8990	−	27.5378i	−0.866073	−	1.50008i	−0.865978	−	0.500082i	$-0.833303\pi$
$337$	−15.8990	−	27.5378i	−0.866073	−	1.50008i	−9.43983e−5	−	1.00000i	$-0.500030\pi$
$338$	10.8990	−	18.8776i	0.592826	−	1.02681i
$339$	16.7753	+	29.0556i	0.911107	+	1.57808i
$340$		0			0
$341$	−2.00000			−0.108306
$342$	9.52270	+	8.96204i	0.514929	+	0.484611i
$343$	−19.5959			−1.05808
$344$	2.27526	+	3.94086i	0.122674	+	0.212477i
$345$		0			0
$346$	−4.89898	+	8.48528i	−0.263371	+	0.456172i
$347$	1.27526	+	2.20881i	0.0684593	+	0.118575i	0.898223	−	0.439539i	$-0.144858\pi$
$347$	1.27526	+	2.20881i	0.0684593	+	0.118575i	−0.829764	+	0.558114i	$0.811525\pi$
$348$	−9.67423	+	16.7563i	−0.518593	+	0.898230i
$349$	31.0000			1.65939			0.829696	−	0.558216i	$-0.188514\pi$
$349$	31.0000			1.65939			0.829696	+	0.558216i	$0.188514\pi$
$350$	12.2474			0.654654
$351$		0			0
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−21.4949			−1.14406			−0.572029	−	0.820233i	$-0.693844\pi$
$353$	−21.4949			−1.14406			−0.572029	+	0.820233i	$0.693844\pi$
$354$	16.8990			0.898171
$355$		0			0
$356$	4.50000	+	7.79423i	0.238500	+	0.413093i
$357$	−1.34847	+	2.33562i	−0.0713686	+	0.123614i
$358$	4.89898	+	8.48528i	0.258919	+	0.448461i
$359$	2.34847	+	4.06767i	0.123947	+	0.214683i	0.921321	−	0.388803i	$-0.127111\pi$
$359$	2.34847	+	4.06767i	0.123947	+	0.214683i	−0.797374	+	0.603486i	$0.793778\pi$
$360$		0			0
$361$	1.15153	+	18.9651i	0.0606069	+	0.998162i
$362$	20.2474			1.06418
$363$	−1.22474	−	2.12132i	−0.0642824	−	0.111340i
$364$	7.22474	+	12.5136i	0.378680	+	0.655892i
$365$		0			0
$366$	−2.32577	−	4.02834i	−0.121570	−	0.210565i
$367$	10.2753	−	17.7973i	0.536364	−	0.929010i	−0.462732	−	0.886498i	$-0.653131\pi$
$367$	10.2753	−	17.7973i	0.536364	−	0.929010i	0.999096	−	0.0425114i	$-0.0135359\pi$
$368$	−8.89898			−0.463891
$369$	−37.3485			−1.94428
$370$		0			0
$371$	−14.4495	+	25.0273i	−0.750180	+	1.29935i
$372$	4.89898			0.254000
$373$	1.79796			0.0930948			0.0465474	−	0.998916i	$-0.485178\pi$
$373$	1.79796			0.0930948			0.0465474	+	0.998916i	$0.485178\pi$
$374$	−0.224745	+	0.389270i	−0.0116213	+	0.0201286i
$375$		0			0
$376$	−5.72474	+	9.91555i	−0.295231	+	0.511355i
$377$	23.2980	+	40.3532i	1.19991	+	2.07830i
$378$		0			0
$379$	11.3485			0.582932			0.291466	−	0.956581i	$-0.405857\pi$
$379$	11.3485			0.582932			0.291466	+	0.956581i	$0.405857\pi$
$380$		0			0
$381$	−40.8990			−2.09532
$382$	−11.1742	−	19.3543i	−0.571724	−	0.990254i
$383$	−1.34847	−	2.33562i	−0.0689036	−	0.119344i	0.829515	−	0.558484i	$-0.188617\pi$
$383$	−1.34847	−	2.33562i	−0.0689036	−	0.119344i	−0.898419	+	0.439139i	$0.855283\pi$
$384$	1.22474	−	2.12132i	0.0625000	−	0.108253i
$385$		0			0
$386$	−4.32577	+	7.49245i	−0.220176	+	0.381355i
$387$	13.6515			0.693946
$388$	−5.89898			−0.299475
$389$	−8.12372	+	14.0707i	−0.411889	+	0.713413i	−0.995096	−	0.0989105i	$-0.968464\pi$
$389$	−8.12372	+	14.0707i	−0.411889	+	0.713413i	0.583207	+	0.812323i	$0.301798\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	1.00000			0.0505076
$393$	12.6742	−	21.9524i	0.639331	−	1.10735i
$394$	7.94949	+	13.7689i	0.400490	+	0.693668i
$395$		0			0
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	5.32577	+	9.22450i	0.267293	+	0.462964i	0.968162	−	0.250326i	$-0.0805377\pi$
$397$	5.32577	+	9.22450i	0.267293	+	0.462964i	−0.700869	+	0.713290i	$0.747204\pi$
$398$	−5.65153			−0.283286
$399$	−6.00000	+	25.4558i	−0.300376	+	1.27439i
$400$	−5.00000			−0.250000
$401$	−4.65153	−	8.05669i	−0.232286	−	0.402332i	0.726194	−	0.687490i	$-0.241287\pi$
$401$	−4.65153	−	8.05669i	−0.232286	−	0.402332i	−0.958481	+	0.285158i	$0.907954\pi$
$402$	17.6969	+	30.6520i	0.882643	+	1.52878i
$403$	5.89898	−	10.2173i	0.293849	−	0.508962i
$404$	−2.50000	−	4.33013i	−0.124380	−	0.215432i
$405$		0			0
$406$	−19.3485			−0.960248
$407$	−3.55051			−0.175992
$408$	0.550510	−	0.953512i	0.0272543	−	0.0472059i
$409$	−15.4722	+	26.7986i	−0.765051	+	1.32511i	0.175169	+	0.984538i	$0.443953\pi$
$409$	−15.4722	+	26.7986i	−0.765051	+	1.32511i	−0.940220	+	0.340568i	$0.889381\pi$
$410$		0			0
$411$	4.65153			0.229443
$412$	−3.17423	+	5.49794i	−0.156383	+	0.270864i
$413$	8.44949	+	14.6349i	0.415772	+	0.720139i
$414$	−13.3485	+	23.1202i	−0.656041	+	1.13630i
$415$		0			0
$416$	−2.94949	−	5.10867i	−0.144611	−	0.250473i
$417$	−9.79796			−0.479808
$418$	−1.00000	+	4.24264i	−0.0489116	+	0.207514i
$419$	−2.65153			−0.129536			−0.0647679	−	0.997900i	$-0.520631\pi$
$419$	−2.65153			−0.129536			−0.0647679	+	0.997900i	$0.520631\pi$
$420$		0			0
$421$	10.3258	+	17.8848i	0.503247	+	0.871649i	0.999993	+	0.00375339i	$0.00119475\pi$
$421$	10.3258	+	17.8848i	0.503247	+	0.871649i	−0.496746	+	0.867896i	$0.665472\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$	17.1742	+	29.7466i	0.835040	+	1.44633i
$424$	5.89898	−	10.2173i	0.286480	−	0.496198i
$425$	−2.24745			−0.109017
$426$	−6.24745			−0.302690
$427$	2.32577	−	4.02834i	0.112552	−	0.194945i
$428$	2.17423	−	3.76588i	0.105096	−	0.182031i
$429$	14.4495			0.697628
$430$		0			0
$431$	14.0227	−	24.2880i	0.675450	−	1.16991i	−0.300887	−	0.953660i	$-0.597283\pi$
$431$	14.0227	−	24.2880i	0.675450	−	1.16991i	0.976337	−	0.216254i	$-0.0693839\pi$
$432$		0			0
$433$	−1.15153	+	1.99451i	−0.0553390	+	0.0958500i	−0.892368	−	0.451309i	$-0.850957\pi$
$433$	−1.15153	+	1.99451i	−0.0553390	+	0.0958500i	0.837029	+	0.547159i	$0.184291\pi$
$434$	2.44949	+	4.24264i	0.117579	+	0.203653i
$435$		0			0
$436$	6.10102			0.292186
$437$	−37.1464	+	11.1708i	−1.77695	+	0.534374i
$438$	23.3939			1.11780
$439$	13.7980	+	23.8988i	0.658541	+	1.14063i	0.980994	+	0.194040i	$0.0621593\pi$
$439$	13.7980	+	23.8988i	0.658541	+	1.14063i	−0.322453	+	0.946586i	$0.604507\pi$
$440$		0			0
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$	−1.32577	−	2.29629i	−0.0630602	−	0.109224i
$443$	3.32577	−	5.76039i	0.158012	−	0.273685i	−0.776140	−	0.630561i	$-0.782825\pi$
$443$	3.32577	−	5.76039i	0.158012	−	0.273685i	0.934152	+	0.356876i	$0.116158\pi$
$444$	8.69694			0.412738
$445$		0			0
$446$	−11.6237	+	20.1329i	−0.550399	+	0.953320i
$447$	13.1010	−	22.6916i	0.619657	−	1.07328i
$448$	2.44949			0.115728
$449$	29.7980			1.40625			0.703126	−	0.711065i	$-0.251787\pi$
$449$	29.7980			1.40625			0.703126	+	0.711065i	$0.251787\pi$
$450$	−7.50000	+	12.9904i	−0.353553	+	0.612372i
$451$	−6.22474	−	10.7816i	−0.293112	−	0.507685i
$452$	6.84847	−	11.8619i	0.322125	−	0.557937i
$453$	4.34847	+	7.53177i	0.204309	+	0.353873i
$454$	11.8990	+	20.6096i	0.558447	+	0.967258i
$455$		0			0
$456$	2.44949	−	10.3923i	0.114708	−	0.486664i
$457$	30.9444			1.44752			0.723759	−	0.690053i	$-0.242413\pi$
$457$	30.9444			1.44752			0.723759	+	0.690053i	$0.242413\pi$
$458$	−7.67423	−	13.2922i	−0.358593	−	0.621102i
$459$		0			0
$460$		0			0
$461$	−3.39898	−	5.88721i	−0.158306	−	0.274194i	0.775952	−	0.630792i	$-0.217270\pi$
$461$	−3.39898	−	5.88721i	−0.158306	−	0.274194i	−0.934258	+	0.356598i	$0.883937\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	5.85357			0.272039			0.136019	−	0.990706i	$-0.456569\pi$
$463$	5.85357			0.272039			0.136019	+	0.990706i	$0.456569\pi$
$464$	7.89898			0.366701
$465$		0			0
$466$	−2.77526	+	4.80688i	−0.128561	+	0.222675i
$467$	−21.3485			−0.987889			−0.493945	−	0.869493i	$-0.664445\pi$
$467$	−21.3485			−0.987889			−0.493945	+	0.869493i	$0.664445\pi$
$468$	−17.6969			−0.818041
$469$	−17.6969	+	30.6520i	−0.817169	+	1.41538i
$470$		0			0
$471$	7.34847	−	12.7279i	0.338600	−	0.586472i
$472$	−3.44949	−	5.97469i	−0.158776	−	0.275007i
$473$	2.27526	+	3.94086i	0.104616	+	0.181201i
$474$	1.10102			0.0505715
$475$	−20.8712	+	6.27647i	−0.957635	+	0.287984i
$476$	1.10102			0.0504652
$477$	−17.6969	−	30.6520i	−0.810287	−	1.40346i
$478$	1.10102	+	1.90702i	0.0503595	+	0.0872252i
$479$	4.42679	−	7.66742i	0.202265	−	0.350333i	−0.746993	−	0.664832i	$-0.768503\pi$
$479$	4.42679	−	7.66742i	0.202265	−	0.350333i	0.949258	+	0.314499i	$0.101836\pi$
$480$		0			0
$481$	10.4722	−	18.1384i	0.477491	−	0.827039i
$482$	−10.0000			−0.455488
$483$	−53.3939			−2.42951
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$		0			0
$486$	22.0454			1.00000
$487$	−22.3485			−1.01271			−0.506353	−	0.862326i	$-0.669007\pi$
$487$	−22.3485			−1.01271			−0.506353	+	0.862326i	$0.669007\pi$
$488$	−0.949490	+	1.64456i	−0.0429814	+	0.0744459i
$489$	8.44949	+	14.6349i	0.382099	+	0.661815i
$490$		0			0
$491$	−2.89898	−	5.02118i	−0.130829	−	0.226603i	0.793167	−	0.609004i	$-0.208431\pi$
$491$	−2.89898	−	5.02118i	−0.130829	−	0.226603i	−0.923996	+	0.382401i	$0.875097\pi$
$492$	15.2474	+	26.4094i	0.687408	+	1.19063i
$493$	3.55051			0.159907
$494$	−18.7247	−	17.6223i	−0.842466	−	0.792864i
$495$		0			0
$496$	−1.00000	−	1.73205i	−0.0449013	−	0.0777714i
$497$	−3.12372	−	5.41045i	−0.140118	−	0.242692i
$498$	−0.674235	+	1.16781i	−0.0302132	+	0.0523308i
$499$	−14.3485	−	24.8523i	−0.642326	−	1.11254i	−0.984912	−	0.173054i	$-0.944636\pi$
$499$	−14.3485	−	24.8523i	−0.642326	−	1.11254i	0.342587	−	0.939486i	$-0.388697\pi$
$500$		0			0
$501$	51.7980			2.31416
$502$	0.247449			0.0110442
$503$	0.550510	−	0.953512i	0.0245460	−	0.0425150i	−0.853491	−	0.521107i	$-0.825519\pi$
$503$	0.550510	−	0.953512i	0.0245460	−	0.0425150i	0.878037	+	0.478592i	$0.158853\pi$
$504$	3.67423	−	6.36396i	0.163663	−	0.283473i
$505$		0			0
$506$	−8.89898			−0.395608
$507$	−26.6969	+	46.2405i	−1.18565	+	2.05361i
$508$	8.34847	+	14.4600i	0.370403	+	0.641558i
$509$	7.79796	−	13.5065i	0.345638	−	0.598663i	−0.639831	−	0.768516i	$-0.720996\pi$
$509$	7.79796	−	13.5065i	0.345638	−	0.598663i	0.985470	+	0.169852i	$0.0543290\pi$
$510$		0			0
$511$	11.6969	+	20.2597i	0.517442	+	0.896236i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	22.0000			0.970378
$515$		0			0
$516$	−5.57321	−	9.65309i	−0.245347	−	0.424954i
$517$	−5.72474	+	9.91555i	−0.251774	+	0.436085i
$518$	4.34847	+	7.53177i	0.191061	+	0.330927i
$519$	12.0000	−	20.7846i	0.526742	−	0.912343i
$520$		0			0
$521$	−12.3031			−0.539007			−0.269503	−	0.962999i	$-0.586860\pi$
$521$	−12.3031			−0.539007			−0.269503	+	0.962999i	$0.586860\pi$
$522$	11.8485	−	20.5222i	0.518593	−	0.898230i
$523$	6.82577	−	11.8226i	0.298470	−	0.516965i	−0.677316	−	0.735692i	$-0.736857\pi$
$523$	6.82577	−	11.8226i	0.298470	−	0.516965i	0.975786	+	0.218727i	$0.0701904\pi$
$524$	−10.3485			−0.452075
$525$	−30.0000			−1.30931
$526$	−8.89898	+	15.4135i	−0.388014	+	0.672060i
$527$	−0.449490	−	0.778539i	−0.0195801	−	0.0339137i
$528$	1.22474	−	2.12132i	0.0533002	−	0.0923186i
$529$	−28.0959	−	48.6636i	−1.22156	−	2.11581i
$530$		0			0
$531$	−20.6969			−0.898171
$532$	10.2247	−	3.07483i	0.443299	−	0.133311i
$533$	73.4393			3.18101
$534$	−11.0227	−	19.0919i	−0.476999	−	0.826187i
$535$		0			0
$536$	7.22474	−	12.5136i	0.312061	−	0.540506i
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$	7.77526	−	13.4671i	0.335215	−	0.580610i
$539$	1.00000			0.0430730
$540$		0			0
$541$	−9.10102	+	15.7634i	−0.391283	+	0.677723i	−0.992619	−	0.121274i	$-0.961302\pi$
$541$	−9.10102	+	15.7634i	−0.391283	+	0.677723i	0.601336	+	0.798997i	$0.294635\pi$
$542$	−2.34847	+	4.06767i	−0.100875	+	0.174721i
$543$	−49.5959			−2.12836
$544$	−0.449490			−0.0192717
$545$		0			0
$546$	−17.6969	−	30.6520i	−0.757359	−	1.31178i
$547$	−15.1742	+	26.2825i	−0.648803	+	1.12376i	0.334606	+	0.942358i	$0.391397\pi$
$547$	−15.1742	+	26.2825i	−0.648803	+	1.12376i	−0.983409	+	0.181402i	$0.941936\pi$
$548$	−0.949490	−	1.64456i	−0.0405602	−	0.0702523i
$549$	2.84847	+	4.93369i	0.121570	+	0.210565i
$550$	−5.00000			−0.213201
$551$	32.9722	−	9.91555i	1.40466	−	0.422417i
$552$	21.7980			0.927783
$553$	0.550510	+	0.953512i	0.0234101	+	0.0405474i
$554$	8.74745	+	15.1510i	0.371643	+	0.643705i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	11.2980	−	19.5686i	0.478710	−	0.829150i	−0.520992	−	0.853561i	$-0.674438\pi$
$557$	11.2980	−	19.5686i	0.478710	−	0.829150i	0.999702	+	0.0244117i	$0.00777124\pi$
$558$	−6.00000			−0.254000
$559$	−26.8434			−1.13535
$560$		0			0
$561$	0.550510	−	0.953512i	0.0232426	−	0.0402573i
$562$	−17.1464			−0.723278
$563$	−8.89898			−0.375047			−0.187524	−	0.982260i	$-0.560046\pi$
$563$	−8.89898			−0.375047			−0.187524	+	0.982260i	$0.560046\pi$
$564$	14.0227	−	24.2880i	0.590462	−	1.02271i
$565$		0			0
$566$	6.44949	−	11.1708i	0.271092	−	0.469546i
$567$	11.0227	+	19.0919i	0.462910	+	0.801784i
$568$	1.27526	+	2.20881i	0.0535085	+	0.0926795i
$569$	5.59592			0.234593			0.117297	−	0.993097i	$-0.462577\pi$
$569$	5.59592			0.234593			0.117297	+	0.993097i	$0.462577\pi$
$570$		0			0
$571$	33.9444			1.42053			0.710264	−	0.703935i	$-0.248575\pi$
$571$	33.9444			1.42053			0.710264	+	0.703935i	$0.248575\pi$
$572$	−2.94949	−	5.10867i	−0.123324	−	0.213604i
$573$	27.3712	+	47.4083i	1.14345	+	1.98051i
$574$	−15.2474	+	26.4094i	−0.636416	+	1.10231i
$575$	−22.2474	−	38.5337i	−0.927783	−	1.60697i
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	−18.2020			−0.757761			−0.378880	−	0.925446i	$-0.623691\pi$
$577$	−18.2020			−0.757761			−0.378880	+	0.925446i	$0.623691\pi$
$578$	16.7980			0.698703
$579$	10.5959	−	18.3527i	0.440351	−	0.762711i
$580$		0			0
$581$	−1.34847			−0.0559439
$582$	14.4495			0.598951
$583$	5.89898	−	10.2173i	0.244311	−	0.423159i
$584$	−4.77526	−	8.27098i	−0.197601	−	0.342256i
$585$		0			0
$586$	0.949490	+	1.64456i	0.0392231	+	0.0679363i
$587$	6.32577	+	10.9565i	0.261092	+	0.452225i	0.966532	−	0.256544i	$-0.0825840\pi$
$587$	6.32577	+	10.9565i	0.261092	+	0.452225i	−0.705440	+	0.708769i	$0.749251\pi$
$588$	−2.44949			−0.101015
$589$	−6.34847	−	5.97469i	−0.261584	−	0.246183i
$590$		0			0
$591$	−19.4722	−	33.7268i	−0.800979	−	1.38734i
$592$	−1.77526	−	3.07483i	−0.0729625	−	0.126375i
$593$	16.6969	−	28.9199i	0.685661	−	1.18760i	−0.287567	−	0.957760i	$-0.592847\pi$
$593$	16.6969	−	28.9199i	0.685661	−	1.18760i	0.973229	−	0.229839i	$-0.0738201\pi$
$594$		0			0
$595$		0			0
$596$	−10.6969			−0.438164
$597$	13.8434			0.566571
$598$	26.2474	−	45.4619i	1.07334	−	1.85908i
$599$	−9.82577	+	17.0187i	−0.401470	+	0.695366i	−0.993904	−	0.110253i	$-0.964834\pi$
$599$	−9.82577	+	17.0187i	−0.401470	+	0.695366i	0.592434	+	0.805619i	$0.298167\pi$
$600$	12.2474			0.500000
$601$	43.5959			1.77831			0.889157	−	0.457602i	$-0.151291\pi$
$601$	43.5959			1.77831			0.889157	+	0.457602i	$0.151291\pi$
$602$	5.57321	−	9.65309i	0.227147	−	0.393431i
$603$	−21.6742	−	37.5409i	−0.882643	−	1.52878i
$604$	1.77526	−	3.07483i	0.0722341	−	0.125113i
$605$		0			0
$606$	6.12372	+	10.6066i	0.248759	+	0.430864i
$607$	15.1464			0.614775			0.307387	−	0.951585i	$-0.400545\pi$
$607$	15.1464			0.614775			0.307387	+	0.951585i	$0.400545\pi$
$608$	−4.17423	+	1.25529i	−0.169288	+	0.0509089i
$609$	47.3939			1.92050
$610$		0			0
$611$	−33.7702	−	58.4916i	−1.36619	−	2.36632i
$612$	−0.674235	+	1.16781i	−0.0272543	+	0.0472059i
$613$	3.60102	+	6.23715i	0.145444	+	0.251916i	0.929538	−	0.368725i	$-0.120206\pi$
$613$	3.60102	+	6.23715i	0.145444	+	0.251916i	−0.784095	+	0.620641i	$0.786872\pi$
$614$	2.62372	−	4.54442i	0.105885	−	0.183398i
$615$		0			0
$616$	2.44949			0.0986928
$617$	−10.1969	+	17.6616i	−0.410513	+	0.711030i	−0.994946	−	0.100412i	$-0.967984\pi$
$617$	−10.1969	+	17.6616i	−0.410513	+	0.711030i	0.584433	+	0.811442i	$0.301317\pi$
$618$	7.77526	−	13.4671i	0.312767	−	0.541728i
$619$	4.69694			0.188786			0.0943929	−	0.995535i	$-0.469909\pi$
$619$	4.69694			0.188786			0.0943929	+	0.995535i	$0.469909\pi$
$620$		0			0
$621$		0			0
$622$	−8.62372	−	14.9367i	−0.345780	−	0.598908i
$623$	11.0227	−	19.0919i	0.441615	−	0.764900i
$624$	7.22474	+	12.5136i	0.289221	+	0.500946i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−9.69694			−0.387568
$627$	2.44949	−	10.3923i	0.0978232	−	0.415029i
$628$	−6.00000			−0.239426
$629$	−0.797959	−	1.38211i	−0.0318167	−	0.0551082i
$630$		0			0
$631$	−22.5227	+	39.0105i	−0.896615	+	1.55298i	−0.0648212	+	0.997897i	$0.520648\pi$
$631$	−22.5227	+	39.0105i	−0.896615	+	1.55298i	−0.831793	+	0.555085i	$0.812686\pi$
$632$	−0.224745	−	0.389270i	−0.00893987	−	0.0154843i
$633$	−24.4949	+	42.4264i	−0.973585	+	1.68630i
$634$	−20.0454			−0.796105
$635$		0			0
$636$	−14.4495	+	25.0273i	−0.572960	+	0.992395i
$637$	−2.94949	+	5.10867i	−0.116863	+	0.202413i
$638$	7.89898			0.312724
$639$	7.65153			0.302690
$640$		0			0
$641$	−2.74745	−	4.75872i	−0.108518	−	0.187958i	0.806652	−	0.591026i	$-0.201277\pi$
$641$	−2.74745	−	4.75872i	−0.108518	−	0.187958i	−0.915170	+	0.403068i	$0.867944\pi$
$642$	−5.32577	+	9.22450i	−0.210191	+	0.364062i
$643$	−5.67423	−	9.82806i	−0.223770	−	0.387581i	0.732180	−	0.681111i	$-0.238503\pi$
$643$	−5.67423	−	9.82806i	−0.223770	−	0.387581i	−0.955950	+	0.293531i	$0.905170\pi$
$644$	10.8990	+	18.8776i	0.429480	+	0.743881i
$645$		0			0
$646$	−1.87628	+	0.564242i	−0.0738211	+	0.0221998i
$647$	−14.7526			−0.579983			−0.289991	−	0.957029i	$-0.593652\pi$
$647$	−14.7526			−0.579983			−0.289991	+	0.957029i	$0.593652\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−3.44949	−	5.97469i	−0.135404	−	0.234527i
$650$	14.7474	−	25.5433i	0.578443	−	1.00189i
$651$	−6.00000	−	10.3923i	−0.235159	−	0.407307i
$652$	3.44949	−	5.97469i	0.135092	−	0.233987i
$653$	−11.3485			−0.444100			−0.222050	−	0.975035i	$-0.571275\pi$
$653$	−11.3485			−0.444100			−0.222050	+	0.975035i	$0.571275\pi$
$654$	−14.9444			−0.584372
$655$		0			0
$656$	6.22474	−	10.7816i	0.243035	−	0.420950i
$657$	−28.6515			−1.11780
$658$	28.0454			1.09332
$659$	−15.9722	+	27.6647i	−0.622188	+	1.07766i	0.366889	+	0.930265i	$0.380423\pi$
$659$	−15.9722	+	27.6647i	−0.622188	+	1.07766i	−0.989077	+	0.147397i	$0.952910\pi$
$660$		0			0
$661$	12.5732	−	21.7774i	0.489041	−	0.847044i	−0.510879	−	0.859653i	$-0.670680\pi$
$661$	12.5732	−	21.7774i	0.489041	−	0.847044i	0.999921	+	0.0126081i	$0.00401338\pi$
$662$	−4.67423	−	8.09601i	−0.181669	−	0.314660i
$663$	3.24745	+	5.62475i	0.126120	+	0.218447i
$664$	0.550510			0.0213639
$665$		0			0
$666$	−10.6515			−0.412738
$667$	35.1464	+	60.8754i	1.36088	+	2.35710i
$668$	−10.5732	−	18.3133i	−0.409090	−	0.708565i
$669$	28.4722	−	49.3153i	1.10080	−	1.90664i
$670$		0			0
$671$	−0.949490	+	1.64456i	−0.0366546	+	0.0634877i
$672$	−6.00000			−0.231455
$673$	30.7423			1.18503			0.592515	−	0.805559i	$-0.298135\pi$
$673$	30.7423			1.18503			0.592515	+	0.805559i	$0.298135\pi$
$674$	15.8990	−	27.5378i	0.612406	−	1.06072i
$675$		0			0
$676$	21.7980			0.838383
$677$	−15.6969			−0.603282			−0.301641	−	0.953422i	$-0.597534\pi$
$677$	−15.6969			−0.603282			−0.301641	+	0.953422i	$0.597534\pi$
$678$	−16.7753	+	29.0556i	−0.644250	+	1.11587i
$679$	7.22474	+	12.5136i	0.277260	+	0.480229i
$680$		0			0
$681$	−29.1464	−	50.4831i	−1.11689	−	1.93452i
$682$	−1.00000	−	1.73205i	−0.0382920	−	0.0663237i
$683$	−0.853572			−0.0326610			−0.0163305	−	0.999867i	$-0.505198\pi$
$683$	−0.853572			−0.0326610			−0.0163305	+	0.999867i	$0.505198\pi$
$684$	−3.00000	+	12.7279i	−0.114708	+	0.486664i
$685$		0			0
$686$	−9.79796	−	16.9706i	−0.374088	−	0.647939i
$687$	18.7980	+	32.5590i	0.717187	+	1.24220i
$688$	−2.27526	+	3.94086i	−0.0867433	+	0.150244i
$689$	34.7980	+	60.2718i	1.32570	+	2.29617i
$690$		0			0
$691$	43.6413			1.66019			0.830097	−	0.557619i	$-0.188285\pi$
$691$	43.6413			1.66019			0.830097	+	0.557619i	$0.188285\pi$
$692$	−9.79796			−0.372463
$693$	3.67423	−	6.36396i	0.139573	−	0.241747i
$694$	−1.27526	+	2.20881i	−0.0484080	+	0.0838452i
$695$		0			0
$696$	−19.3485			−0.733402
$697$	2.79796	−	4.84621i	0.105980	−	0.183563i
$698$	15.5000	+	26.8468i	0.586684	+	1.01617i
$699$	6.79796	−	11.7744i	0.257122	−	0.445349i
$700$	6.12372	+	10.6066i	0.231455	+	0.400892i
$701$	3.70204	+	6.41212i	0.139824	+	0.242183i	0.927430	−	0.373997i	$-0.122013\pi$
$701$	3.70204	+	6.41212i	0.139824	+	0.242183i	−0.787606	+	0.616179i	$0.788680\pi$
$702$		0			0
$703$	−11.2702	−	10.6066i	−0.425062	−	0.400036i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	−10.7474	−	18.6151i	−0.404486	−	0.700590i
$707$	−6.12372	+	10.6066i	−0.230306	+	0.398902i
$708$	8.44949	+	14.6349i	0.317551	+	0.550015i
$709$	21.6969	−	37.5802i	0.814846	−	1.41135i	−0.0945931	−	0.995516i	$-0.530155\pi$
$709$	21.6969	−	37.5802i	0.814846	−	1.41135i	0.909439	−	0.415838i	$-0.136512\pi$
$710$		0			0
$711$	−1.34847			−0.0505715
$712$	−4.50000	+	7.79423i	−0.168645	+	0.292101i
$713$	8.89898	−	15.4135i	0.333269	−	0.577240i
$714$	−2.69694			−0.100930
$715$		0			0
$716$	−4.89898	+	8.48528i	−0.183083	+	0.317110i
$717$	−2.69694	−	4.67123i	−0.100719	−	0.174450i
$718$	−2.34847	+	4.06767i	−0.0876441	+	0.151804i
$719$	20.0732	+	34.7678i	0.748605	+	1.29662i	0.948492	+	0.316802i	$0.102609\pi$
$719$	20.0732	+	34.7678i	0.748605	+	1.29662i	−0.199887	+	0.979819i	$0.564058\pi$
$720$		0			0
$721$	15.5505			0.579131
$722$	−15.8485	+	10.4798i	−0.589819	+	0.390017i
$723$	24.4949			0.910975
$724$	10.1237	+	17.5348i	0.376245	+	0.651676i
$725$	19.7474	+	34.2036i	0.733402	+	1.27029i
$726$	1.22474	−	2.12132i	0.0454545	−	0.0787296i
$727$	21.9722	+	38.0570i	0.814904	+	1.41145i	0.909397	+	0.415929i	$0.136543\pi$
$727$	21.9722	+	38.0570i	0.814904	+	1.41145i	−0.0944936	+	0.995525i	$0.530123\pi$
$728$	−7.22474	+	12.5136i	−0.267767	+	0.463786i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.02270	+	1.77138i	−0.0378261	+	0.0655167i
$732$	2.32577	−	4.02834i	0.0859628	−	0.148892i
$733$	40.8990			1.51064			0.755319	−	0.655357i	$-0.227482\pi$
$733$	40.8990			1.51064			0.755319	+	0.655357i	$0.227482\pi$
$734$	20.5505			0.758533
$735$		0			0
$736$	−4.44949	−	7.70674i	−0.164010	−	0.284074i
$737$	7.22474	−	12.5136i	0.266127	−	0.460945i
$738$	−18.6742	−	32.3447i	−0.687408	−	1.19063i
$739$	20.8712	+	36.1499i	0.767759	+	1.32980i	0.938776	+	0.344529i	$0.111961\pi$
$739$	20.8712	+	36.1499i	0.767759	+	1.32980i	−0.171017	+	0.985268i	$0.554705\pi$
$740$		0			0
$741$	45.8661	+	43.1656i	1.68493	+	1.58573i
$742$	−28.8990			−1.06091
$743$	1.42679	+	2.47127i	0.0523437	+	0.0906619i	0.891010	−	0.453984i	$-0.149998\pi$
$743$	1.42679	+	2.47127i	0.0523437	+	0.0906619i	−0.838666	+	0.544646i	$0.816664\pi$
$744$	2.44949	+	4.24264i	0.0898027	+	0.155543i
$745$		0			0
$746$	0.898979	+	1.55708i	0.0329140	+	0.0570087i
$747$	0.825765	−	1.43027i	0.0302132	−	0.0523308i
$748$	−0.449490			−0.0164350
$749$	−10.6515			−0.389198
$750$		0			0
$751$	−22.7702	+	39.4391i	−0.830895	+	1.43915i	0.0664350	+	0.997791i	$0.478838\pi$
$751$	−22.7702	+	39.4391i	−0.830895	+	1.43915i	−0.897330	+	0.441361i	$0.854496\pi$
$752$	−11.4495			−0.417520
$753$	−0.606123			−0.0220884
$754$	−23.2980	+	40.3532i	−0.848462	+	1.46958i
$755$		0			0
$756$		0			0
$757$	−17.8990	−	31.0019i	−0.650549	−	1.12678i	−0.982990	−	0.183660i	$-0.941205\pi$
$757$	−17.8990	−	31.0019i	−0.650549	−	1.12678i	0.332440	−	0.943124i	$-0.392128\pi$
$758$	5.67423	+	9.82806i	0.206097	+	0.356971i
$759$	21.7980			0.791216
$760$		0			0
$761$	−47.1918			−1.71070			−0.855351	−	0.518048i	$-0.826659\pi$
$761$	−47.1918			−1.71070			−0.855351	+	0.518048i	$0.826659\pi$
$762$	−20.4495	−	35.4196i	−0.740807	−	1.28312i
$763$	−7.47219	−	12.9422i	−0.270512	−	0.468540i
$764$	11.1742	−	19.3543i	0.404270	−	0.700216i
$765$		0			0
$766$	1.34847	−	2.33562i	0.0487222	−	0.0843893i
$767$	40.6969			1.46948
$768$	2.44949			0.0883883
$769$	−9.69694	+	16.7956i	−0.349681	+	0.605664i	−0.986193	−	0.165602i	$-0.947043\pi$
$769$	−9.69694	+	16.7956i	−0.349681	+	0.605664i	0.636512	+	0.771267i	$0.280377\pi$
$770$		0			0
$771$	−53.8888			−1.94076
$772$	−8.65153			−0.311375
$773$	11.5732	−	20.0454i	0.416260	−	0.720983i	−0.579300	−	0.815114i	$-0.696674\pi$
$773$	11.5732	−	20.0454i	0.416260	−	0.720983i	0.995560	+	0.0941315i	$0.0300074\pi$
$774$	6.82577	+	11.8226i	0.245347	+	0.424954i
$775$	5.00000	−	8.66025i	0.179605	−	0.311086i
$776$	−2.94949	−	5.10867i	−0.105881	−	0.183390i
$777$	−10.6515	−	18.4490i	−0.382122	−	0.661854i
$778$	−16.2474			−0.582499
$779$	12.4495	−	52.8187i	0.446049	−	1.89243i
$780$		0			0
$781$	1.27526	+	2.20881i	0.0456322	+	0.0790373i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$		0			0
$786$	25.3485			0.904150
$787$	0.752551			0.0268256			0.0134128	−	0.999910i	$-0.495730\pi$
$787$	0.752551			0.0268256			0.0134128	+	0.999910i	$0.495730\pi$
$788$	−7.94949	+	13.7689i	−0.283189	+	0.490497i
$789$	21.7980	−	37.7552i	0.776028	−	1.34412i
$790$		0			0
$791$	−33.5505			−1.19292
$792$	−1.50000	+	2.59808i	−0.0533002	+	0.0923186i
$793$	−5.60102	−	9.70125i	−0.198898	−	0.344502i
$794$	−5.32577	+	9.22450i	−0.189004	+	0.327365i
$795$		0			0
$796$	−2.82577	−	4.89437i	−0.100157	−	0.173476i
$797$	−42.0454			−1.48932			−0.744662	−	0.667441i	$-0.767389\pi$
$797$	−42.0454			−1.48932			−0.744662	+	0.667441i	$0.767389\pi$
$798$	−25.0454	+	7.53177i	−0.886598	+	0.266622i
$799$	−5.14643			−0.182068
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	13.5000	+	23.3827i	0.476999	+	0.826187i
$802$	4.65153	−	8.05669i	0.164251	−	0.284492i
$803$	−4.77526	−	8.27098i	−0.168515	−	0.291877i
$804$	−17.6969	+	30.6520i	−0.624123	+	1.08101i
$805$		0			0
$806$	11.7980			0.415565
$807$	−19.0454	+	32.9876i	−0.670430	+	1.16122i
$808$	2.50000	−	4.33013i	0.0879497	−	0.152333i
$809$	35.1464			1.23568			0.617841	−	0.786303i	$-0.288007\pi$
$809$	35.1464			1.23568			0.617841	+	0.786303i	$0.288007\pi$
$810$		0			0
$811$	3.72474	−	6.45145i	0.130793	−	0.226541i	−0.793189	−	0.608975i	$-0.791581\pi$
$811$	3.72474	−	6.45145i	0.130793	−	0.226541i	0.923983	+	0.382434i	$0.124914\pi$
$812$	−9.67423	−	16.7563i	−0.339499	−	0.588030i
$813$	5.75255	−	9.96371i	0.201751	−	0.349443i
$814$	−1.77526	−	3.07483i	−0.0622227	−	0.107773i
$815$		0			0
$816$	1.10102			0.0385434
$817$	−4.55051	+	19.3062i	−0.159202	+	0.675438i
$818$	−30.9444			−1.08195
$819$	21.6742	+	37.5409i	0.757359	+	1.31178i
$820$		0			0
$821$	11.1464	−	19.3062i	0.389013	−	0.673790i	−0.603304	−	0.797511i	$-0.706149\pi$
$821$	11.1464	−	19.3062i	0.389013	−	0.673790i	0.992317	+	0.123721i	$0.0394828\pi$
$822$	2.32577	+	4.02834i	0.0811204	+	0.140505i
$823$	2.27526	−	3.94086i	0.0793104	−	0.137370i	−0.823642	−	0.567110i	$-0.808062\pi$
$823$	2.27526	−	3.94086i	0.0793104	−	0.137370i	0.902953	+	0.429740i	$0.141395\pi$
$824$	−6.34847			−0.221159
$825$	12.2474			0.426401
$826$	−8.44949	+	14.6349i	−0.293995	+	0.509215i
$827$	−17.4217	+	30.1752i	−0.605811	+	1.04930i	0.386111	+	0.922452i	$0.373818\pi$
$827$	−17.4217	+	30.1752i	−0.605811	+	1.04930i	−0.991923	+	0.126844i	$0.959515\pi$
$828$	−26.6969			−0.927783
$829$	−31.1464			−1.08176			−0.540880	−	0.841100i	$-0.681909\pi$
$829$	−31.1464			−1.08176			−0.540880	+	0.841100i	$0.681909\pi$
$830$		0			0
$831$	−21.4268	−	37.1123i	−0.743287	−	1.28741i
$832$	2.94949	−	5.10867i	0.102255	−	0.177111i
$833$	0.224745	+	0.389270i	0.00778695	+	0.0134874i
$834$	−4.89898	−	8.48528i	−0.169638	−	0.293821i
$835$		0			0
$836$	−4.17423	+	1.25529i	−0.144369	+	0.0434153i
$837$		0			0
$838$	−1.32577	−	2.29629i	−0.0457978	−	0.0793241i
$839$	−22.6237	−	39.1854i	−0.781058	−	1.35283i	−0.931326	−	0.364186i	$-0.881347\pi$
$839$	−22.6237	−	39.1854i	−0.781058	−	1.35283i	0.150268	−	0.988645i	$-0.451986\pi$
$840$		0			0
$841$	−16.6969	−	28.9199i	−0.575756	−	0.997240i
$842$	−10.3258	+	17.8848i	−0.355849	+	0.616349i
$843$	42.0000			1.44656
$844$	20.0000			0.688428
$845$		0			0
$846$	−17.1742	+	29.7466i	−0.590462	+	1.02271i
$847$	2.44949			0.0841655
$848$	11.7980			0.405144
$849$	−15.7980	+	27.3629i	−0.542185	+	0.939091i
$850$	−1.12372	−	1.94635i	−0.0385434	−	0.0667592i
$851$	15.7980	−	27.3629i	0.541547	−	0.937987i
$852$	−3.12372	−	5.41045i	−0.107017	−	0.185359i
$853$	−13.3485	−	23.1202i	−0.457043	−	0.791621i	0.541760	−	0.840533i	$-0.317758\pi$
$853$	−13.3485	−	23.1202i	−0.457043	−	0.791621i	−0.998803	+	0.0489116i	$0.984425\pi$
$854$	4.65153			0.159172
$855$		0			0
$856$	4.34847			0.148628
$857$	11.5732	+	20.0454i	0.395333	+	0.684738i	0.993144	−	0.116900i	$-0.0372957\pi$
$857$	11.5732	+	20.0454i	0.395333	+	0.684738i	−0.597810	+	0.801638i	$0.703962\pi$
$858$	7.22474	+	12.5136i	0.246649	+	0.427208i
$859$	5.44949	−	9.43879i	0.185934	−	0.322047i	−0.757957	−	0.652305i	$-0.773802\pi$
$859$	5.44949	−	9.43879i	0.185934	−	0.322047i	0.943891	+	0.330257i	$0.107136\pi$
$860$		0			0
$861$	37.3485	−	64.6894i	1.27283	−	2.20461i
$862$	28.0454			0.955230
$863$	−26.3485			−0.896912			−0.448456	−	0.893805i	$-0.648026\pi$
$863$	−26.3485			−0.896912			−0.448456	+	0.893805i	$0.648026\pi$
$864$		0			0
$865$		0			0
$866$	−2.30306			−0.0782612
$867$	−41.1464			−1.39741
$868$	−2.44949	+	4.24264i	−0.0831411	+	0.144005i
$869$	−0.224745	−	0.389270i	−0.00762395	−	0.0132051i
$870$		0			0
$871$	42.6186	+	73.8176i	1.44408	+	2.50121i
$872$	3.05051	+	5.28364i	0.103303	+	0.178927i
$873$	−17.6969			−0.598951
$874$	−28.2474	−	26.5843i	−0.955484	−	0.899228i
$875$		0			0
$876$	11.6969	+	20.2597i	0.395203	+	0.684512i
$877$	0.797959	+	1.38211i	0.0269452	+	0.0466704i	0.879184	−	0.476483i	$-0.158089\pi$
$877$	0.797959	+	1.38211i	0.0269452	+	0.0466704i	−0.852238	+	0.523154i	$0.824755\pi$
$878$	−13.7980	+	23.8988i	−0.465659	+	0.806544i
$879$	−2.32577	−	4.02834i	−0.0784461	−	0.135873i
$880$		0			0
$881$	3.10102			0.104476			0.0522380	−	0.998635i	$-0.483365\pi$
$881$	3.10102			0.104476			0.0522380	+	0.998635i	$0.483365\pi$
$882$	3.00000			0.101015
$883$	3.77526	−	6.53893i	0.127047	−	0.220053i	−0.795484	−	0.605975i	$-0.792783\pi$
$883$	3.77526	−	6.53893i	0.127047	−	0.220053i	0.922531	+	0.385922i	$0.126117\pi$
$884$	1.32577	−	2.29629i	0.0445903	−	0.0772327i
$885$		0			0
$886$	6.65153			0.223463
$887$	0.674235	−	1.16781i	0.0226386	−	0.0392112i	−0.854484	−	0.519477i	$-0.826127\pi$
$887$	0.674235	−	1.16781i	0.0226386	−	0.0392112i	0.877123	+	0.480266i	$0.159460\pi$
$888$	4.34847	+	7.53177i	0.145925	+	0.252750i
$889$	20.4495	−	35.4196i	0.685854	−	1.18793i
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	−23.2474			−0.778382
$893$	−47.7929	+	14.3725i	−1.59933	+	0.480957i
$894$	26.2020			0.876327
$895$		0			0
$896$	1.22474	+	2.12132i	0.0409159	+	0.0708683i
$897$	−64.2929	+	111.358i	−2.14668	+	3.71815i
$898$	14.8990	+	25.8058i	0.497185	+	0.861150i
$899$	−7.89898	+	13.6814i	−0.263446	+	0.456301i
$900$	−15.0000			−0.500000
$901$	5.30306			0.176671
$902$	6.22474	−	10.7816i	0.207261	−	0.358987i
$903$	−13.6515	+	23.6451i	−0.454294	+	0.786861i
$904$	13.6969			0.455553
$905$		0			0
$906$	−4.34847	+	7.53177i	−0.144468	+	0.250226i
$907$	−14.5505	−	25.2022i	−0.483142	−	0.836826i	0.516671	−	0.856184i	$-0.327171\pi$
$907$	−14.5505	−	25.2022i	−0.483142	−	0.836826i	−0.999813	+	0.0193580i	$0.993838\pi$
$908$	−11.8990	+	20.6096i	−0.394882	+	0.683955i
$909$	−7.50000	−	12.9904i	−0.248759	−	0.430864i
$910$		0			0
$911$	24.4949			0.811552			0.405776	−	0.913973i	$-0.367001\pi$
$911$	24.4949			0.811552			0.405776	+	0.913973i	$0.367001\pi$
$912$	10.2247	−	3.07483i	0.338575	−	0.101818i
$913$	0.550510			0.0182192
$914$	15.4722	+	26.7986i	0.511775	+	0.886420i
$915$		0			0
$916$	7.67423	−	13.2922i	0.253564	−	0.439185i
$917$	12.6742	+	21.9524i	0.418540	+	0.724933i
$918$		0			0
$919$	−10.6515			−0.351362			−0.175681	−	0.984447i	$-0.556213\pi$
$919$	−10.6515			−0.351362			−0.175681	+	0.984447i	$0.556213\pi$
$920$		0			0
$921$	−6.42679	+	11.1315i	−0.211770	+	0.366796i
$922$	3.39898	−	5.88721i	0.111939	−	0.193885i
$923$	−15.0454			−0.495226
$924$	−6.00000			−0.197386
$925$	8.87628	−	15.3742i	0.291850	−	0.505499i
$926$	2.92679	+	5.06934i	0.0961802	+	0.166589i
$927$	−9.52270	+	16.4938i	−0.312767	+	0.541728i
$928$	3.94949	+	6.84072i	0.129648	+	0.224558i
$929$	−5.74745	−	9.95487i	−0.188568	−	0.326609i	0.756205	−	0.654334i	$-0.227051\pi$
$929$	−5.74745	−	9.95487i	−0.188568	−	0.326609i	−0.944773	+	0.327726i	$0.893718\pi$
$930$		0			0
$931$	3.17423	+	2.98735i	0.104031	+	0.0979063i
$932$	−5.55051			−0.181813
$933$	21.1237	+	36.5874i	0.691560	+	1.19782i
$934$	−10.6742	−	18.4883i	−0.349272	−	0.604956i
$935$		0			0
$936$	−8.84847	−	15.3260i	−0.289221	−	0.500946i
$937$	−2.89898	+	5.02118i	−0.0947055	+	0.164035i	−0.909486	−	0.415735i	$-0.863524\pi$
$937$	−2.89898	+	5.02118i	−0.0947055	+	0.164035i	0.814780	+	0.579770i	$0.196858\pi$
$938$	−35.3939			−1.15565
$939$	23.7526			0.775135
$940$		0			0
$941$	13.1010	−	22.6916i	0.427081	−	0.739726i	−0.569531	−	0.821970i	$-0.692875\pi$
$941$	13.1010	−	22.6916i	0.427081	−	0.739726i	0.996612	+	0.0822436i	$0.0262086\pi$
$942$	14.6969			0.478852
$943$	110.788			3.60775
$944$	3.44949	−	5.97469i	0.112271	−	0.194460i
$945$		0			0
$946$	−2.27526	+	3.94086i	−0.0739749	+	0.128128i
$947$	−10.1464	−	17.5741i	−0.329715	−	0.571082i	0.652741	−	0.757582i	$-0.273619\pi$
$947$	−10.1464	−	17.5741i	−0.329715	−	0.571082i	−0.982455	+	0.186499i	$0.940286\pi$
$948$	0.550510	+	0.953512i	0.0178797	+	0.0309686i
$949$	56.3383			1.82882
$950$	−15.8712	−	14.9367i	−0.514929	−	0.484611i
$951$	49.1010			1.59221
$952$	0.550510	+	0.953512i	0.0178421	+	0.0309035i
$953$	−20.0000	−	34.6410i	−0.647864	−	1.12213i	−0.983632	−	0.180188i	$-0.942329\pi$
$953$	−20.0000	−	34.6410i	−0.647864	−	1.12213i	0.335769	−	0.941944i	$-0.391004\pi$
$954$	17.6969	−	30.6520i	0.572960	−	0.992395i
$955$		0			0
$956$	−1.10102	+	1.90702i	−0.0356095	+	0.0616775i
$957$	−19.3485			−0.625447
$958$	8.85357			0.286046
$959$	−2.32577	+	4.02834i	−0.0751029	+	0.130082i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	20.9444			0.675274
$963$	6.52270	−	11.2977i	0.210191	−	0.364062i
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$		0			0
$966$	−26.6969	−	46.2405i	−0.858960	−	1.48776i
$967$	9.10102	+	15.7634i	0.292669	+	0.506918i	0.974440	−	0.224648i	$-0.0721232\pi$
$967$	9.10102	+	15.7634i	0.292669	+	0.506918i	−0.681771	+	0.731566i	$0.738790\pi$
$968$	−1.00000			−0.0321412
$969$	4.59592	−	1.38211i	0.147642	−	0.0443996i
$970$		0			0
$971$	−9.92168	−	17.1849i	−0.318402	−	0.551488i	0.661753	−	0.749722i	$-0.269813\pi$
$971$	−9.92168	−	17.1849i	−0.318402	−	0.551488i	−0.980155	+	0.198234i	$0.936480\pi$
$972$	11.0227	+	19.0919i	0.353553	+	0.612372i
$973$	4.89898	−	8.48528i	0.157054	−	0.272026i
$974$	−11.1742	−	19.3543i	−0.358046	−	0.620153i
$975$	−36.1237	+	62.5681i	−1.15689	+	2.00378i
$976$	−1.89898			−0.0607849
$977$	−57.0000			−1.82359			−0.911796	−	0.410644i	$-0.865304\pi$
$977$	−57.0000			−1.82359			−0.911796	+	0.410644i	$0.865304\pi$
$978$	−8.44949	+	14.6349i	−0.270185	+	0.467974i
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$		0			0
$981$	18.3031			0.584372
$982$	2.89898	−	5.02118i	0.0925102	−	0.160232i
$983$	13.8712	+	24.0256i	0.442422	+	0.766297i	0.997869	−	0.0652551i	$-0.0207861\pi$
$983$	13.8712	+	24.0256i	0.442422	+	0.766297i	−0.555447	+	0.831552i	$0.687453\pi$
$984$	−15.2474	+	26.4094i	−0.486071	+	0.841900i
$985$		0			0
$986$	1.77526	+	3.07483i	0.0565356	+	0.0979226i
$987$	−68.6969			−2.18665
$988$	5.89898	−	25.0273i	0.187672	−	0.796223i
$989$	−40.4949			−1.28766
$990$		0			0
$991$	1.72474	+	2.98735i	0.0547883	+	0.0948962i	0.892119	−	0.451801i	$-0.149218\pi$
$991$	1.72474	+	2.98735i	0.0547883	+	0.0948962i	−0.837330	+	0.546697i	$0.815885\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	11.4495	+	19.8311i	0.363339	+	0.629321i
$994$	3.12372	−	5.41045i	0.0990785	−	0.171609i
$995$		0			0
$996$	−1.34847			−0.0427279
$997$	−24.5959	+	42.6014i	−0.778961	+	1.34920i	0.153581	+	0.988136i	$0.450919\pi$
$997$	−24.5959	+	42.6014i	−0.778961	+	1.34920i	−0.932541	+	0.361063i	$0.882414\pi$
$998$	14.3485	−	24.8523i	0.454193	−	0.786685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.e.g.45.1	✓	4
19.7	even	3		7942.2.a.v.1.2		2
19.11	even	3	inner	418.2.e.g.353.1	yes	4
19.12	odd	6		7942.2.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.g.45.1	✓	4	1.1	even	1	trivial
418.2.e.g.353.1	yes	4	19.11	even	3	inner
7942.2.a.v.1.2		2	19.7	even	3
7942.2.a.y.1.1		2	19.12	odd	6

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.22474 - 2.12132i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{6} +2.44949 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.22474 - 2.12132i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{6} +2.44949 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{9} -1.00000 q^{11} +2.44949 q^{12} +(2.94949 - 5.10867i) q^{13} +(1.22474 + 2.12132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.224745 - 0.389270i) q^{17} -3.00000 q^{18} +(-3.17423 - 2.98735i) q^{19} +(-3.00000 - 5.19615i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(4.44949 - 7.70674i) q^{23} +(1.22474 + 2.12132i) q^{24} +(2.50000 - 4.33013i) q^{25} +5.89898 q^{26} +(-1.22474 + 2.12132i) q^{28} +(-3.94949 + 6.84072i) q^{29} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.22474 + 2.12132i) q^{33} +(0.224745 - 0.389270i) q^{34} +(-1.50000 - 2.59808i) q^{36} +3.55051 q^{37} +(1.00000 - 4.24264i) q^{38} -14.4495 q^{39} +(6.22474 + 10.7816i) q^{41} +(3.00000 - 5.19615i) q^{42} +(-2.27526 - 3.94086i) q^{43} +(0.500000 - 0.866025i) q^{44} +8.89898 q^{46} +(5.72474 - 9.91555i) q^{47} +(-1.22474 + 2.12132i) q^{48} -1.00000 q^{49} +5.00000 q^{50} +(-0.550510 + 0.953512i) q^{51} +(2.94949 + 5.10867i) q^{52} +(-5.89898 + 10.2173i) q^{53} -2.44949 q^{56} +(-2.44949 + 10.3923i) q^{57} -7.89898 q^{58} +(3.44949 + 5.97469i) q^{59} +(0.949490 - 1.64456i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-3.67423 + 6.36396i) q^{63} +1.00000 q^{64} +(-1.22474 + 2.12132i) q^{66} +(-7.22474 + 12.5136i) q^{67} +0.449490 q^{68} -21.7980 q^{69} +(-1.27526 - 2.20881i) q^{71} +(1.50000 - 2.59808i) q^{72} +(4.77526 + 8.27098i) q^{73} +(1.77526 + 3.07483i) q^{74} -12.2474 q^{75} +(4.17423 - 1.25529i) q^{76} -2.44949 q^{77} +(-7.22474 - 12.5136i) q^{78} +(0.224745 + 0.389270i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-6.22474 + 10.7816i) q^{82} -0.550510 q^{83} +6.00000 q^{84} +(2.27526 - 3.94086i) q^{86} +19.3485 q^{87} +1.00000 q^{88} +(4.50000 - 7.79423i) q^{89} +(7.22474 - 12.5136i) q^{91} +(4.44949 + 7.70674i) q^{92} +(-2.44949 - 4.24264i) q^{93} +11.4495 q^{94} -2.44949 q^{96} +(2.94949 + 5.10867i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{9} - 4 q^{11} + 2 q^{13} - 2 q^{16} + 4 q^{17} - 12 q^{18} + 2 q^{19} - 12 q^{21} - 2 q^{22} + 8 q^{23} + 10 q^{25} + 4 q^{26} - 6 q^{29} + 8 q^{31} + 2 q^{32} - 4 q^{34} - 6 q^{36} + 24 q^{37} + 4 q^{38} - 48 q^{39} + 20 q^{41} + 12 q^{42} - 14 q^{43} + 2 q^{44} + 16 q^{46} + 18 q^{47} - 4 q^{49} + 20 q^{50} - 12 q^{51} + 2 q^{52} - 4 q^{53} - 12 q^{58} + 4 q^{59} - 6 q^{61} + 4 q^{62} + 4 q^{64} - 24 q^{67} - 8 q^{68} - 48 q^{69} - 10 q^{71} + 6 q^{72} + 24 q^{73} + 12 q^{74} + 2 q^{76} - 24 q^{78} - 4 q^{79} + 18 q^{81} - 20 q^{82} - 12 q^{83} + 24 q^{84} + 14 q^{86} + 48 q^{87} + 4 q^{88} + 18 q^{89} + 24 q^{91} + 8 q^{92} + 36 q^{94} + 2 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 6 * q^9 - 4 * q^11 + 2 * q^13 - 2 * q^16 + 4 * q^17 - 12 * q^18 + 2 * q^19 - 12 * q^21 - 2 * q^22 + 8 * q^23 + 10 * q^25 + 4 * q^26 - 6 * q^29 + 8 * q^31 + 2 * q^32 - 4 * q^34 - 6 * q^36 + 24 * q^37 + 4 * q^38 - 48 * q^39 + 20 * q^41 + 12 * q^42 - 14 * q^43 + 2 * q^44 + 16 * q^46 + 18 * q^47 - 4 * q^49 + 20 * q^50 - 12 * q^51 + 2 * q^52 - 4 * q^53 - 12 * q^58 + 4 * q^59 - 6 * q^61 + 4 * q^62 + 4 * q^64 - 24 * q^67 - 8 * q^68 - 48 * q^69 - 10 * q^71 + 6 * q^72 + 24 * q^73 + 12 * q^74 + 2 * q^76 - 24 * q^78 - 4 * q^79 + 18 * q^81 - 20 * q^82 - 12 * q^83 + 24 * q^84 + 14 * q^86 + 48 * q^87 + 4 * q^88 + 18 * q^89 + 24 * q^91 + 8 * q^92 + 36 * q^94 + 2 * q^97 - 2 * q^98 + 6 * q^99

Introduction

L-functions

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Database

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