LMFDB - Embedded newform 392.2.p.a.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(165,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("392.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.p (of order $6$, degree $2$, not 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	392.373
Dual form			392.2.p.a.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.22474 - 0.707107i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.22474 + 0.707107i) q^{5} -2.00000 q^{6} -2.82843i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.22474 - 0.707107i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.22474 + 0.707107i) q^{5} -2.00000 q^{6} -2.82843i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(2.44949 - 1.41421i) q^{11} +(2.44949 + 1.41421i) q^{12} -4.24264i q^{13} +2.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(1.22474 - 0.707107i) q^{18} +(3.67423 + 2.12132i) q^{19} +2.82843i q^{20} -4.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(-1.50000 - 2.59808i) q^{25} +(-3.00000 + 5.19615i) q^{26} +5.65685i q^{27} +2.82843i q^{29} +(-2.44949 - 1.41421i) q^{30} +(2.00000 + 3.46410i) q^{31} +(4.89898 - 2.82843i) q^{32} +(2.00000 - 3.46410i) q^{33} -8.48528i q^{34} -2.00000 q^{36} +(-7.34847 - 4.24264i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(2.00000 - 3.46410i) q^{40} +6.00000 q^{41} -8.48528i q^{43} +(4.89898 + 2.82843i) q^{44} +(-1.22474 + 0.707107i) q^{45} +(-7.34847 + 4.24264i) q^{46} +5.65685i q^{48} +4.24264i q^{50} +(7.34847 + 4.24264i) q^{51} +(7.34847 - 4.24264i) q^{52} +(-4.89898 + 2.82843i) q^{53} +(4.00000 - 6.92820i) q^{54} +4.00000 q^{55} +6.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-1.22474 + 0.707107i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-11.0227 - 6.36396i) q^{61} -5.65685i q^{62} -8.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(-4.89898 + 2.82843i) q^{66} +(-6.00000 + 10.3923i) q^{68} -8.48528i q^{69} +(2.44949 + 1.41421i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(6.00000 + 10.3923i) q^{74} +(-3.67423 - 2.12132i) q^{75} +8.48528i q^{76} +8.48528i q^{78} +(-4.00000 + 6.92820i) q^{79} +(-4.89898 + 2.82843i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-7.34847 - 4.24264i) q^{82} +15.5563i q^{83} +8.48528i q^{85} +(-6.00000 + 10.3923i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-4.00000 - 6.92820i) q^{88} +(-3.00000 + 5.19615i) q^{89} +2.00000 q^{90} +12.0000 q^{92} +(4.89898 + 2.82843i) q^{93} +(3.00000 + 5.19615i) q^{95} +(4.00000 - 6.92820i) q^{96} -10.0000 q^{97} +2.82843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 8 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 - 8 * q^6 - 2 * q^9	$ 4 q + 4 q^{4} - 8 q^{6} - 2 q^{9} - 4 q^{10} + 8 q^{15} - 8 q^{16} + 12 q^{17} - 16 q^{22} + 12 q^{23} - 8 q^{24} - 6 q^{25} - 12 q^{26} + 8 q^{31} + 8 q^{33} - 8 q^{36} - 12 q^{38} - 12 q^{39} + 8 q^{40} + 24 q^{41} + 16 q^{54} + 16 q^{55} + 24 q^{57} + 8 q^{58} + 8 q^{60} - 32 q^{64} + 12 q^{65} - 24 q^{68} - 4 q^{73} + 24 q^{74} - 16 q^{79} + 10 q^{81} - 24 q^{86} + 8 q^{87} - 16 q^{88} - 12 q^{89} + 8 q^{90} + 48 q^{92} + 12 q^{95} + 16 q^{96} - 40 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 - 8 * q^6 - 2 * q^9 - 4 * q^10 + 8 * q^15 - 8 * q^16 + 12 * q^17 - 16 * q^22 + 12 * q^23 - 8 * q^24 - 6 * q^25 - 12 * q^26 + 8 * q^31 + 8 * q^33 - 8 * q^36 - 12 * q^38 - 12 * q^39 + 8 * q^40 + 24 * q^41 + 16 * q^54 + 16 * q^55 + 24 * q^57 + 8 * q^58 + 8 * q^60 - 32 * q^64 + 12 * q^65 - 24 * q^68 - 4 * q^73 + 24 * q^74 - 16 * q^79 + 10 * q^81 - 24 * q^86 + 8 * q^87 - 16 * q^88 - 12 * q^89 + 8 * q^90 + 48 * q^92 + 12 * q^95 + 16 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$3$	1.22474	−	0.707107i	0.707107	−	0.408248i	−0.102882	−	0.994694i	$-0.532806\pi$
$3$	1.22474	−	0.707107i	0.707107	−	0.408248i	0.809989	+	0.586445i	$0.199473\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	0.748203	−	0.663470i	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	1.00000i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	0.821541	+	0.570149i	$0.193114\pi$
$12$	2.44949	+	1.41421i	0.707107	+	0.408248i
$13$		−	4.24264i		−	1.17670i	−0.808608	−	0.588348i	$-0.799778\pi$
$13$		−	4.24264i		−	1.17670i	0.808608	−	0.588348i	$-0.200222\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	1.22474	−	0.707107i	0.288675	−	0.166667i
$19$	3.67423	+	2.12132i	0.842927	+	0.486664i	0.858258	−	0.513218i	$-0.171547\pi$
$19$	3.67423	+	2.12132i	0.842927	+	0.486664i	−0.0153309	+	0.999882i	$0.504880\pi$
$20$			2.82843i			0.632456i
$21$		0			0
$22$	−4.00000			−0.852803
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−2.00000	−	3.46410i	−0.408248	−	0.707107i
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$			5.65685i			1.08866i
$28$		0			0
$29$			2.82843i			0.525226i	0.964901	+	0.262613i	$0.0845842\pi$
$29$			2.82843i			0.525226i	−0.964901	+	0.262613i	$0.915416\pi$
$30$	−2.44949	−	1.41421i	−0.447214	−	0.258199i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	4.89898	−	2.82843i	0.866025	−	0.500000i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$		−	8.48528i		−	1.45521i
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−7.34847	−	4.24264i	−1.20808	−	0.697486i	−0.245741	−	0.969335i	$-0.579031\pi$
$37$	−7.34847	−	4.24264i	−1.20808	−	0.697486i	−0.962340	+	0.271850i	$0.912365\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$	2.00000	−	3.46410i	0.316228	−	0.547723i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$		−	8.48528i		−	1.29399i	−0.762493	−	0.646997i	$-0.776025\pi$
$43$		−	8.48528i		−	1.29399i	0.762493	−	0.646997i	$-0.223975\pi$
$44$	4.89898	+	2.82843i	0.738549	+	0.426401i
$45$	−1.22474	+	0.707107i	−0.182574	+	0.105409i
$46$	−7.34847	+	4.24264i	−1.08347	+	0.625543i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$			5.65685i			0.816497i
$49$		0			0
$50$			4.24264i			0.600000i
$51$	7.34847	+	4.24264i	1.02899	+	0.594089i
$52$	7.34847	−	4.24264i	1.01905	−	0.588348i
$53$	−4.89898	+	2.82843i	−0.672927	+	0.388514i	−0.797185	−	0.603736i	$-0.793678\pi$
$53$	−4.89898	+	2.82843i	−0.672927	+	0.388514i	0.124258	+	0.992250i	$0.460345\pi$
$54$	4.00000	−	6.92820i	0.544331	−	0.942809i
$55$	4.00000			0.539360
$56$		0			0
$57$	6.00000			0.794719
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	−1.22474	+	0.707107i	−0.159448	+	0.0920575i	−0.577601	−	0.816319i	$-0.696011\pi$
$59$	−1.22474	+	0.707107i	−0.159448	+	0.0920575i	0.418153	+	0.908377i	$0.362678\pi$
$60$	2.00000	+	3.46410i	0.258199	+	0.447214i
$61$	−11.0227	−	6.36396i	−1.41131	−	0.814822i	−0.415800	−	0.909456i	$-0.636499\pi$
$61$	−11.0227	−	6.36396i	−1.41131	−	0.814822i	−0.995512	+	0.0946341i	$0.969832\pi$
$62$		−	5.65685i		−	0.718421i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$	−4.89898	+	2.82843i	−0.603023	+	0.348155i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−6.00000	+	10.3923i	−0.727607	+	1.26025i
$69$		−	8.48528i		−	1.02151i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	2.44949	+	1.41421i	0.288675	+	0.166667i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	6.00000	+	10.3923i	0.697486	+	1.20808i
$75$	−3.67423	−	2.12132i	−0.424264	−	0.244949i
$76$			8.48528i			0.973329i
$77$		0			0
$78$			8.48528i			0.960769i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−4.89898	+	2.82843i	−0.547723	+	0.316228i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−7.34847	−	4.24264i	−0.811503	−	0.468521i
$83$			15.5563i			1.70753i	0.520658	+	0.853766i	$0.325687\pi$
$83$			15.5563i			1.70753i	−0.520658	+	0.853766i	$0.674313\pi$
$84$		0			0
$85$			8.48528i			0.920358i
$86$	−6.00000	+	10.3923i	−0.646997	+	1.12063i
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$	−4.00000	−	6.92820i	−0.426401	−	0.738549i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	12.0000			1.25109
$93$	4.89898	+	2.82843i	0.508001	+	0.293294i
$94$		0			0
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	4.00000	−	6.92820i	0.408248	−	0.707107i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$			2.82843i			0.284268i
$100$	3.00000	−	5.19615i	0.300000	−	0.519615i
$101$	−8.57321	+	4.94975i	−0.853067	+	0.492518i	−0.861684	−	0.507445i	$-0.830590\pi$
$101$	−8.57321	+	4.94975i	−0.853067	+	0.492518i	0.00861771	+	0.999963i	$0.497257\pi$
$102$	−6.00000	−	10.3923i	−0.594089	−	1.02899i
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−12.0000			−1.17670
$105$		0			0
$106$	8.00000			0.777029
$107$	4.89898	+	2.82843i	0.473602	+	0.273434i	0.717746	−	0.696305i	$-0.245174\pi$
$107$	4.89898	+	2.82843i	0.473602	+	0.273434i	−0.244144	+	0.969739i	$0.578507\pi$
$108$	−9.79796	+	5.65685i	−0.942809	+	0.544331i
$109$	−7.34847	+	4.24264i	−0.703856	+	0.406371i	−0.808782	−	0.588109i	$-0.799873\pi$
$109$	−7.34847	+	4.24264i	−0.703856	+	0.406371i	0.104926	+	0.994480i	$0.466539\pi$
$110$	−4.89898	−	2.82843i	−0.467099	−	0.269680i
$111$	−12.0000			−1.13899
$112$		0			0
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	−7.34847	−	4.24264i	−0.688247	−	0.397360i
$115$	7.34847	−	4.24264i	0.685248	−	0.395628i
$116$	−4.89898	+	2.82843i	−0.454859	+	0.262613i
$117$	3.67423	+	2.12132i	0.339683	+	0.196116i
$118$	2.00000			0.184115
$119$		0			0
$120$		−	5.65685i		−	0.516398i
$121$	−1.50000	+	2.59808i	−0.136364	+	0.236189i
$122$	9.00000	+	15.5885i	0.814822	+	1.41131i
$123$	7.34847	−	4.24264i	0.662589	−	0.382546i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	9.79796	+	5.65685i	0.866025	+	0.500000i
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$	−7.34847	+	4.24264i	−0.644503	+	0.372104i
$131$	1.22474	+	0.707107i	0.107006	+	0.0617802i	0.552548	−	0.833481i	$-0.313656\pi$
$131$	1.22474	+	0.707107i	0.107006	+	0.0617802i	−0.445542	+	0.895261i	$0.646989\pi$
$132$	8.00000			0.696311
$133$		0			0
$134$		0			0
$135$	−4.00000	+	6.92820i	−0.344265	+	0.596285i
$136$	14.6969	−	8.48528i	1.26025	−	0.727607i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$	−6.00000	+	10.3923i	−0.510754	+	0.884652i
$139$		−	4.24264i		−	0.359856i	−0.983680	−	0.179928i	$-0.942414\pi$
$139$		−	4.24264i		−	0.359856i	0.983680	−	0.179928i	$-0.0575865\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$			2.82843i			0.234082i
$147$		0			0
$148$		−	16.9706i		−	1.39497i
$149$	−9.79796	−	5.65685i	−0.802680	−	0.463428i	0.0417274	−	0.999129i	$-0.486714\pi$
$149$	−9.79796	−	5.65685i	−0.802680	−	0.463428i	−0.844407	+	0.535701i	$0.820047\pi$
$150$	3.00000	+	5.19615i	0.244949	+	0.424264i
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	6.00000	−	10.3923i	0.486664	−	0.842927i
$153$	−6.00000			−0.485071
$154$		0			0
$155$			5.65685i			0.454369i
$156$	6.00000	−	10.3923i	0.480384	−	0.832050i
$157$	11.0227	−	6.36396i	0.879708	−	0.507899i	0.00914557	−	0.999958i	$-0.497089\pi$
$157$	11.0227	−	6.36396i	0.879708	−	0.507899i	0.870562	+	0.492059i	$0.163756\pi$
$158$	9.79796	−	5.65685i	0.779484	−	0.450035i
$159$	−4.00000	+	6.92820i	−0.317221	+	0.549442i
$160$	8.00000			0.632456
$161$		0			0
$162$		−	7.07107i		−	0.555556i
$163$	−7.34847	−	4.24264i	−0.575577	−	0.332309i	0.183797	−	0.982964i	$-0.441161\pi$
$163$	−7.34847	−	4.24264i	−0.575577	−	0.332309i	−0.759374	+	0.650655i	$0.774494\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	4.89898	−	2.82843i	0.381385	−	0.220193i
$166$	11.0000	−	19.0526i	0.853766	−	1.47877i
$167$	24.0000			1.85718			0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000			1.85718			0.928588	+	0.371113i	$0.121024\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	6.00000	−	10.3923i	0.460179	−	0.797053i
$171$	−3.67423	+	2.12132i	−0.280976	+	0.162221i
$172$	14.6969	−	8.48528i	1.12063	−	0.646997i
$173$	8.57321	+	4.94975i	0.651809	+	0.376322i	0.789149	−	0.614202i	$-0.210522\pi$
$173$	8.57321	+	4.94975i	0.651809	+	0.376322i	−0.137340	+	0.990524i	$0.543855\pi$
$174$		−	5.65685i		−	0.428845i
$175$		0			0
$176$			11.3137i			0.852803i
$177$	−1.00000	+	1.73205i	−0.0751646	+	0.130189i
$178$	7.34847	−	4.24264i	0.550791	−	0.317999i
$179$	−4.89898	+	2.82843i	−0.366167	+	0.211407i	−0.671783	−	0.740748i	$-0.734471\pi$
$179$	−4.89898	+	2.82843i	−0.366167	+	0.211407i	0.305616	+	0.952155i	$0.401138\pi$
$180$	−2.44949	−	1.41421i	−0.182574	−	0.105409i
$181$			12.7279i			0.946059i	0.881047	+	0.473029i	$0.156840\pi$
$181$			12.7279i			0.946059i	−0.881047	+	0.473029i	$0.843160\pi$
$182$		0			0
$183$	−18.0000			−1.33060
$184$	−14.6969	−	8.48528i	−1.08347	−	0.625543i
$185$	−6.00000	−	10.3923i	−0.441129	−	0.764057i
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	14.6969	+	8.48528i	1.07475	+	0.620505i
$188$		0			0
$189$		0			0
$190$		−	8.48528i		−	0.615587i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−9.79796	+	5.65685i	−0.707107	+	0.408248i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	12.2474	+	7.07107i	0.879316	+	0.507673i
$195$		−	8.48528i		−	0.607644i
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	−7.34847	+	4.24264i	−0.519615	+	0.300000i
$201$		0			0
$202$	14.0000			0.985037
$203$		0			0
$204$			16.9706i			1.18818i
$205$	7.34847	+	4.24264i	0.513239	+	0.296319i
$206$	−4.89898	+	2.82843i	−0.341328	+	0.197066i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	14.6969	+	8.48528i	1.01905	+	0.588348i
$209$	12.0000			0.830057
$210$		0			0
$211$		−	16.9706i		−	1.16830i	−0.811645	−	0.584151i	$-0.801428\pi$
$211$		−	16.9706i		−	1.16830i	0.811645	−	0.584151i	$-0.198572\pi$
$212$	−9.79796	−	5.65685i	−0.672927	−	0.388514i
$213$		0			0
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$	16.0000			1.08866
$217$		0			0
$218$	12.0000			0.812743
$219$	−2.44949	−	1.41421i	−0.165521	−	0.0955637i
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$	22.0454	−	12.7279i	1.48293	−	0.856173i
$222$	14.6969	+	8.48528i	0.986394	+	0.569495i
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	14.6969	+	8.48528i	0.977626	+	0.564433i
$227$	−8.57321	+	4.94975i	−0.569024	+	0.328526i	−0.756760	−	0.653693i	$-0.773219\pi$
$227$	−8.57321	+	4.94975i	−0.569024	+	0.328526i	0.187735	+	0.982220i	$0.439885\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	−3.67423	−	2.12132i	−0.242800	−	0.140181i	0.373663	−	0.927565i	$-0.378102\pi$
$229$	−3.67423	−	2.12132i	−0.242800	−	0.140181i	−0.616463	+	0.787384i	$0.711435\pi$
$230$	−12.0000			−0.791257
$231$		0			0
$232$	8.00000			0.525226
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$		0			0
$236$	−2.44949	−	1.41421i	−0.159448	−	0.0920575i
$237$			11.3137i			0.734904i
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−4.00000	+	6.92820i	−0.258199	+	0.447214i
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	3.67423	−	2.12132i	0.236189	−	0.136364i
$243$	−8.57321	−	4.94975i	−0.549972	−	0.317526i
$244$		−	25.4558i		−	1.62964i
$245$		0			0
$246$	−12.0000			−0.765092
$247$	9.00000	−	15.5885i	0.572656	−	0.991870i
$248$	9.79796	−	5.65685i	0.622171	−	0.359211i
$249$	11.0000	+	19.0526i	0.697097	+	1.20741i
$250$	−8.00000	+	13.8564i	−0.505964	+	0.876356i
$251$		−	18.3848i		−	1.16044i	−0.814461	−	0.580218i	$-0.802967\pi$
$251$		−	18.3848i		−	1.16044i	0.814461	−	0.580218i	$-0.197033\pi$
$252$		0			0
$253$		−	16.9706i		−	1.06693i
$254$	−2.44949	−	1.41421i	−0.153695	−	0.0887357i
$255$	6.00000	+	10.3923i	0.375735	+	0.650791i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$			16.9706i			1.05654i
$259$		0			0
$260$	12.0000			0.744208
$261$	−2.44949	−	1.41421i	−0.151620	−	0.0875376i
$262$	−1.00000	−	1.73205i	−0.0617802	−	0.107006i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	−9.79796	−	5.65685i	−0.603023	−	0.348155i
$265$	−8.00000			−0.491436
$266$		0			0
$267$			8.48528i			0.519291i
$268$		0			0
$269$	6.12372	−	3.53553i	0.373370	−	0.215565i	−0.301560	−	0.953447i	$-0.597507\pi$
$269$	6.12372	−	3.53553i	0.373370	−	0.215565i	0.674930	+	0.737882i	$0.264174\pi$
$270$	9.79796	−	5.65685i	0.596285	−	0.344265i
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$	−24.0000			−1.45521
$273$		0			0
$274$			8.48528i			0.512615i
$275$	−7.34847	−	4.24264i	−0.443129	−	0.255841i
$276$	14.6969	−	8.48528i	0.884652	−	0.510754i
$277$	−14.6969	+	8.48528i	−0.883053	+	0.509831i	−0.871664	−	0.490104i	$-0.836959\pi$
$277$	−14.6969	+	8.48528i	−0.883053	+	0.509831i	−0.0113895	+	0.999935i	$0.503625\pi$
$278$	−3.00000	+	5.19615i	−0.179928	+	0.311645i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	11.0227	−	6.36396i	0.655232	−	0.378298i	−0.135226	−	0.990815i	$-0.543176\pi$
$283$	11.0227	−	6.36396i	0.655232	−	0.378298i	0.790458	+	0.612517i	$0.209843\pi$
$284$		0			0
$285$	7.34847	+	4.24264i	0.435286	+	0.251312i
$286$			16.9706i			1.00349i
$287$		0			0
$288$			5.65685i			0.333333i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	4.89898	−	2.82843i	0.287678	−	0.166091i
$291$	−12.2474	+	7.07107i	−0.717958	+	0.414513i
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$			24.0416i			1.40453i	0.711917	+	0.702264i	$0.247827\pi$
$293$			24.0416i			1.40453i	−0.711917	+	0.702264i	$0.752173\pi$
$294$		0			0
$295$	−2.00000			−0.116445
$296$	−12.0000	+	20.7846i	−0.697486	+	1.20808i
$297$	8.00000	+	13.8564i	0.464207	+	0.804030i
$298$	8.00000	+	13.8564i	0.463428	+	0.802680i
$299$	−22.0454	−	12.7279i	−1.27492	−	0.736075i
$300$		−	8.48528i		−	0.489898i
$301$		0			0
$302$		−	14.1421i		−	0.813788i
$303$	−7.00000	+	12.1244i	−0.402139	+	0.696526i
$304$	−14.6969	+	8.48528i	−0.842927	+	0.486664i
$305$	−9.00000	−	15.5885i	−0.515339	−	0.892592i
$306$	7.34847	+	4.24264i	0.420084	+	0.242536i
$307$		−	12.7279i		−	0.726421i	−0.931707	−	0.363210i	$-0.881681\pi$
$307$		−	12.7279i		−	0.726421i	0.931707	−	0.363210i	$-0.118319\pi$
$308$		0			0
$309$		−	5.65685i		−	0.321807i
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	−14.6969	+	8.48528i	−0.832050	+	0.480384i
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	−18.0000			−1.01580
$315$		0			0
$316$	−16.0000			−0.900070
$317$	19.5959	+	11.3137i	1.10062	+	0.635441i	0.936383	−	0.350980i	$-0.114152\pi$
$317$	19.5959	+	11.3137i	1.10062	+	0.635441i	0.164234	+	0.986421i	$0.447485\pi$
$318$	9.79796	−	5.65685i	0.549442	−	0.317221i
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	−9.79796	−	5.65685i	−0.547723	−	0.316228i
$321$	8.00000			0.446516
$322$		0			0
$323$			25.4558i			1.41640i
$324$	−5.00000	+	8.66025i	−0.277778	+	0.481125i
$325$	−11.0227	+	6.36396i	−0.611430	+	0.353009i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	−6.00000	+	10.3923i	−0.331801	+	0.574696i
$328$		−	16.9706i		−	0.937043i
$329$		0			0
$330$	−8.00000			−0.440386
$331$	−22.0454	−	12.7279i	−1.21173	−	0.699590i	−0.248590	−	0.968609i	$-0.579967\pi$
$331$	−22.0454	−	12.7279i	−1.21173	−	0.699590i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	−26.9444	+	15.5563i	−1.47877	+	0.853766i
$333$	7.34847	−	4.24264i	0.402694	−	0.232495i
$334$	−29.3939	−	16.9706i	−1.60836	−	0.928588i
$335$		0			0
$336$		0			0
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$	6.12372	+	3.53553i	0.333087	+	0.192308i
$339$	−14.6969	+	8.48528i	−0.798228	+	0.460857i
$340$	−14.6969	+	8.48528i	−0.797053	+	0.460179i
$341$	9.79796	+	5.65685i	0.530589	+	0.306336i
$342$	6.00000			0.324443
$343$		0			0
$344$	−24.0000			−1.29399
$345$	6.00000	−	10.3923i	0.323029	−	0.559503i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	−12.2474	+	7.07107i	−0.657477	+	0.379595i	−0.791315	−	0.611408i	$-0.790603\pi$
$347$	−12.2474	+	7.07107i	−0.657477	+	0.379595i	0.133838	+	0.991003i	$0.457270\pi$
$348$	−4.00000	+	6.92820i	−0.214423	+	0.371391i
$349$			4.24264i			0.227103i	0.993532	+	0.113552i	$0.0362227\pi$
$349$			4.24264i			0.227103i	−0.993532	+	0.113552i	$0.963777\pi$
$350$		0			0
$351$	24.0000			1.28103
$352$	8.00000	−	13.8564i	0.426401	−	0.738549i
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	2.44949	−	1.41421i	0.130189	−	0.0751646i
$355$		0			0
$356$	−12.0000			−0.635999
$357$		0			0
$358$	8.00000			0.422813
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	−0.133263	−	0.991081i	$-0.542545\pi$
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	0.924932	−	0.380131i	$-0.124121\pi$
$360$	2.00000	+	3.46410i	0.105409	+	0.182574i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	9.00000	−	15.5885i	0.473029	−	0.819311i
$363$			4.24264i			0.222681i
$364$		0			0
$365$		−	2.82843i		−	0.148047i
$366$	22.0454	+	12.7279i	1.15233	+	0.665299i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	12.0000	+	20.7846i	0.625543	+	1.08347i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$			16.9706i			0.882258i
$371$		0			0
$372$			11.3137i			0.586588i
$373$	29.3939	+	16.9706i	1.52196	+	0.878702i	0.999664	+	0.0259367i	$0.00825685\pi$
$373$	29.3939	+	16.9706i	1.52196	+	0.878702i	0.522294	+	0.852766i	$0.325076\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$	−8.00000	−	13.8564i	−0.413118	−	0.715542i
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$			25.4558i			1.30758i	0.756677	+	0.653789i	$0.226822\pi$
$379$			25.4558i			1.30758i	−0.756677	+	0.653789i	$0.773178\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$	2.44949	−	1.41421i	0.125491	−	0.0724524i
$382$		0			0
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$	16.0000			0.816497
$385$		0			0
$386$		−	5.65685i		−	0.287926i
$387$	7.34847	+	4.24264i	0.373544	+	0.215666i
$388$	−10.0000	−	17.3205i	−0.507673	−	0.879316i
$389$	2.44949	−	1.41421i	0.124194	−	0.0717035i	−0.436616	−	0.899648i	$-0.643823\pi$
$389$	2.44949	−	1.41421i	0.124194	−	0.0717035i	0.560810	+	0.827945i	$0.310490\pi$
$390$	−6.00000	+	10.3923i	−0.303822	+	0.526235i
$391$	36.0000			1.82060
$392$		0			0
$393$	2.00000			0.100887
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	−9.79796	+	5.65685i	−0.492989	+	0.284627i
$396$	−4.89898	+	2.82843i	−0.246183	+	0.142134i
$397$	−18.3712	−	10.6066i	−0.922023	−	0.532330i	−0.0377429	−	0.999287i	$-0.512017\pi$
$397$	−18.3712	−	10.6066i	−0.922023	−	0.532330i	−0.884280	+	0.466957i	$0.845350\pi$
$398$			28.2843i			1.41776i
$399$		0			0
$400$	12.0000			0.600000
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$		0			0
$403$	14.6969	−	8.48528i	0.732107	−	0.422682i
$404$	−17.1464	−	9.89949i	−0.853067	−	0.492518i
$405$			7.07107i			0.351364i
$406$		0			0
$407$	−24.0000			−1.18964
$408$	12.0000	−	20.7846i	0.594089	−	1.02899i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	−7.34847	−	4.24264i	−0.362473	−	0.209274i
$412$	8.00000			0.394132
$413$		0			0
$414$		−	8.48528i		−	0.417029i
$415$	−11.0000	+	19.0526i	−0.539969	+	0.935253i
$416$	−12.0000	−	20.7846i	−0.588348	−	1.01905i
$417$	−3.00000	−	5.19615i	−0.146911	−	0.254457i
$418$	−14.6969	−	8.48528i	−0.718851	−	0.415029i
$419$		−	26.8701i		−	1.31269i	−0.754462	−	0.656344i	$-0.772102\pi$
$419$		−	26.8701i		−	1.31269i	0.754462	−	0.656344i	$-0.227898\pi$
$420$		0			0
$421$			16.9706i			0.827095i	0.910483	+	0.413547i	$0.135710\pi$
$421$			16.9706i			0.827095i	−0.910483	+	0.413547i	$0.864290\pi$
$422$	−12.0000	+	20.7846i	−0.584151	+	1.01178i
$423$		0			0
$424$	8.00000	+	13.8564i	0.388514	+	0.672927i
$425$	9.00000	−	15.5885i	0.436564	−	0.756151i
$426$		0			0
$427$		0			0
$428$			11.3137i			0.546869i
$429$	−14.6969	−	8.48528i	−0.709575	−	0.409673i
$430$	−14.6969	+	8.48528i	−0.708749	+	0.409197i
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	−19.5959	−	11.3137i	−0.942809	−	0.544331i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$			5.65685i			0.271225i
$436$	−14.6969	−	8.48528i	−0.703856	−	0.406371i
$437$	22.0454	−	12.7279i	1.05457	−	0.608859i
$438$	2.00000	+	3.46410i	0.0955637	+	0.165521i
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		−	11.3137i		−	0.539360i
$441$		0			0
$442$	−36.0000			−1.71235
$443$	19.5959	+	11.3137i	0.931030	+	0.537531i	0.887137	−	0.461506i	$-0.152691\pi$
$443$	19.5959	+	11.3137i	0.931030	+	0.537531i	0.0438929	+	0.999036i	$0.486024\pi$
$444$	−12.0000	−	20.7846i	−0.569495	−	0.986394i
$445$	−7.34847	+	4.24264i	−0.348351	+	0.201120i
$446$	34.2929	+	19.7990i	1.62381	+	0.937509i
$447$	−16.0000			−0.756774
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	−3.67423	−	2.12132i	−0.173205	−	0.100000i
$451$	14.6969	−	8.48528i	0.692052	−	0.399556i
$452$	−12.0000	−	20.7846i	−0.564433	−	0.977626i
$453$	12.2474	+	7.07107i	0.575435	+	0.332228i
$454$	14.0000			0.657053
$455$		0			0
$456$		−	16.9706i		−	0.794719i
$457$	14.0000	−	24.2487i	0.654892	−	1.13431i	−0.327028	−	0.945015i	$-0.606047\pi$
$457$	14.0000	−	24.2487i	0.654892	−	1.13431i	0.981921	−	0.189292i	$-0.0606194\pi$
$458$	3.00000	+	5.19615i	0.140181	+	0.242800i
$459$	−29.3939	+	16.9706i	−1.37199	+	0.792118i
$460$	14.6969	+	8.48528i	0.685248	+	0.395628i
$461$			15.5563i			0.724531i	0.932075	+	0.362266i	$0.117997\pi$
$461$			15.5563i			0.724531i	−0.932075	+	0.362266i	$0.882003\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	−9.79796	−	5.65685i	−0.454859	−	0.262613i
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$	7.34847	−	4.24264i	0.340411	−	0.196537i
$467$	−6.12372	−	3.53553i	−0.283372	−	0.163605i	0.351577	−	0.936159i	$-0.385646\pi$
$467$	−6.12372	−	3.53553i	−0.283372	−	0.163605i	−0.634949	+	0.772554i	$0.718979\pi$
$468$			8.48528i			0.392232i
$469$		0			0
$470$		0			0
$471$	9.00000	−	15.5885i	0.414698	−	0.718278i
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	−12.0000	−	20.7846i	−0.551761	−	0.955677i
$474$	8.00000	−	13.8564i	0.367452	−	0.636446i
$475$		−	12.7279i		−	0.583997i
$476$		0			0
$477$		−	5.65685i		−	0.259010i
$478$	−7.34847	−	4.24264i	−0.336111	−	0.194054i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$	9.79796	−	5.65685i	0.447214	−	0.258199i
$481$	−18.0000	+	31.1769i	−0.820729	+	1.42154i
$482$		−	14.1421i		−	0.644157i
$483$		0			0
$484$	−6.00000			−0.272727
$485$	−12.2474	−	7.07107i	−0.556128	−	0.321081i
$486$	7.00000	+	12.1244i	0.317526	+	0.549972i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	−18.0000	+	31.1769i	−0.814822	+	1.41131i
$489$	−12.0000			−0.542659
$490$		0			0
$491$		−	39.5980i		−	1.78703i	−0.449032	−	0.893516i	$-0.648231\pi$
$491$		−	39.5980i		−	1.78703i	0.449032	−	0.893516i	$-0.351769\pi$
$492$	14.6969	+	8.48528i	0.662589	+	0.382546i
$493$	−14.6969	+	8.48528i	−0.661917	+	0.382158i
$494$	−22.0454	+	12.7279i	−0.991870	+	0.572656i
$495$	−2.00000	+	3.46410i	−0.0898933	+	0.155700i
$496$	−16.0000			−0.718421
$497$		0			0
$498$		−	31.1127i		−	1.39419i
$499$	−14.6969	−	8.48528i	−0.657925	−	0.379853i	0.133561	−	0.991041i	$-0.457359\pi$
$499$	−14.6969	−	8.48528i	−0.657925	−	0.379853i	−0.791486	+	0.611187i	$0.790692\pi$
$500$	19.5959	−	11.3137i	0.876356	−	0.505964i
$501$	29.3939	−	16.9706i	1.31322	−	0.758189i
$502$	−13.0000	+	22.5167i	−0.580218	+	1.00497i
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$	−12.0000	+	20.7846i	−0.533465	+	0.923989i
$507$	−6.12372	+	3.53553i	−0.271964	+	0.157019i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	1.22474	+	0.707107i	0.0542859	+	0.0313420i	0.526897	−	0.849929i	$-0.323355\pi$
$509$	1.22474	+	0.707107i	0.0542859	+	0.0313420i	−0.472611	+	0.881271i	$0.656689\pi$
$510$		−	16.9706i		−	0.751469i
$511$		0			0
$512$			22.6274i			1.00000i
$513$	−12.0000	+	20.7846i	−0.529813	+	0.917663i
$514$	−7.34847	+	4.24264i	−0.324127	+	0.187135i
$515$	4.89898	−	2.82843i	0.215875	−	0.124635i
$516$	12.0000	−	20.7846i	0.528271	−	0.914991i
$517$		0			0
$518$		0			0
$519$	14.0000			0.614532
$520$	−14.6969	−	8.48528i	−0.644503	−	0.372104i
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	0.924229	−	0.381839i	$-0.124709\pi$
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	−0.792797	+	0.609486i	$0.791376\pi$
$522$	2.00000	+	3.46410i	0.0875376	+	0.151620i
$523$	25.7196	+	14.8492i	1.12464	+	0.649312i	0.942582	−	0.333975i	$-0.108390\pi$
$523$	25.7196	+	14.8492i	1.12464	+	0.649312i	0.182060	+	0.983287i	$0.441724\pi$
$524$			2.82843i			0.123560i
$525$		0			0
$526$			33.9411i			1.47990i
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$	8.00000	+	13.8564i	0.348155	+	0.603023i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	9.79796	+	5.65685i	0.425596	+	0.245718i
$531$		−	1.41421i		−	0.0613716i
$532$		0			0
$533$		−	25.4558i		−	1.10262i
$534$	6.00000	−	10.3923i	0.259645	−	0.449719i
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$		0			0
$537$	−4.00000	+	6.92820i	−0.172613	+	0.298974i
$538$	−10.0000			−0.431131
$539$		0			0
$540$	−16.0000			−0.688530
$541$	14.6969	+	8.48528i	0.631871	+	0.364811i	0.781476	−	0.623935i	$-0.214467\pi$
$541$	14.6969	+	8.48528i	0.631871	+	0.364811i	−0.149605	+	0.988746i	$0.547800\pi$
$542$	24.4949	−	14.1421i	1.05215	−	0.607457i
$543$	9.00000	+	15.5885i	0.386227	+	0.668965i
$544$	29.3939	+	16.9706i	1.26025	+	0.727607i
$545$	−12.0000			−0.514024
$546$		0			0
$547$		−	8.48528i		−	0.362804i	−0.983409	−	0.181402i	$-0.941936\pi$
$547$		−	8.48528i		−	0.362804i	0.983409	−	0.181402i	$-0.0580636\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	11.0227	−	6.36396i	0.470438	−	0.271607i
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$	−24.0000			−1.02151
$553$		0			0
$554$	24.0000			1.01966
$555$	−14.6969	−	8.48528i	−0.623850	−	0.360180i
$556$	7.34847	−	4.24264i	0.311645	−	0.179928i
$557$	−4.89898	+	2.82843i	−0.207576	+	0.119844i	−0.600185	−	0.799862i	$-0.704906\pi$
$557$	−4.89898	+	2.82843i	−0.207576	+	0.119844i	0.392608	+	0.919706i	$0.371573\pi$
$558$	4.89898	+	2.82843i	0.207390	+	0.119737i
$559$	−36.0000			−1.52264
$560$		0			0
$561$	24.0000			1.01328
$562$	7.34847	+	4.24264i	0.309976	+	0.178965i
$563$	−1.22474	+	0.707107i	−0.0516168	+	0.0298010i	−0.525586	−	0.850740i	$-0.676154\pi$
$563$	−1.22474	+	0.707107i	−0.0516168	+	0.0298010i	0.473970	+	0.880541i	$0.342821\pi$
$564$		0			0
$565$	−14.6969	−	8.48528i	−0.618305	−	0.356978i
$566$	−18.0000			−0.756596
$567$		0			0
$568$		0			0
$569$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$	−6.00000	−	10.3923i	−0.251312	−	0.435286i
$571$	22.0454	−	12.7279i	0.922572	−	0.532647i	0.0381170	−	0.999273i	$-0.487864\pi$
$571$	22.0454	−	12.7279i	0.922572	−	0.532647i	0.884455	+	0.466626i	$0.154531\pi$
$572$	12.0000	−	20.7846i	0.501745	−	0.869048i
$573$		0			0
$574$		0			0
$575$	−18.0000			−0.750652
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−19.0000	−	32.9090i	−0.790980	−	1.37002i	−0.925361	−	0.379088i	$-0.876238\pi$
$577$	−19.0000	−	32.9090i	−0.790980	−	1.37002i	0.134380	−	0.990930i	$-0.457096\pi$
$578$	23.2702	−	13.4350i	0.967911	−	0.558824i
$579$	4.89898	+	2.82843i	0.203595	+	0.117545i
$580$	−8.00000			−0.332182
$581$		0			0
$582$	20.0000			0.829027
$583$	−8.00000	+	13.8564i	−0.331326	+	0.573874i
$584$	−4.89898	+	2.82843i	−0.202721	+	0.117041i
$585$	3.00000	+	5.19615i	0.124035	+	0.214834i
$586$	17.0000	−	29.4449i	0.702264	−	1.21636i
$587$			41.0122i			1.69275i	0.532584	+	0.846377i	$0.321221\pi$
$587$			41.0122i			1.69275i	−0.532584	+	0.846377i	$0.678779\pi$
$588$		0			0
$589$			16.9706i			0.699260i
$590$	2.44949	+	1.41421i	0.100844	+	0.0582223i
$591$	−4.00000	−	6.92820i	−0.164538	−	0.284988i
$592$	29.3939	−	16.9706i	1.20808	−	0.697486i
$593$	15.0000	−	25.9808i	0.615976	−	1.06690i	−0.374236	−	0.927333i	$-0.622095\pi$
$593$	15.0000	−	25.9808i	0.615976	−	1.06690i	0.990212	−	0.139569i	$-0.0445716\pi$
$594$		−	22.6274i		−	0.928414i
$595$		0			0
$596$		−	22.6274i		−	0.926855i
$597$	−24.4949	−	14.1421i	−1.00251	−	0.578799i
$598$	18.0000	+	31.1769i	0.736075	+	1.27492i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	−6.00000	+	10.3923i	−0.244949	+	0.424264i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−3.67423	+	2.12132i	−0.149379	+	0.0862439i
$606$	17.1464	−	9.89949i	0.696526	−	0.402139i
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	24.0000			0.973329
$609$		0			0
$610$			25.4558i			1.03068i
$611$		0			0
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−7.34847	+	4.24264i	−0.296802	+	0.171359i	−0.641005	−	0.767536i	$-0.721482\pi$
$613$	−7.34847	+	4.24264i	−0.296802	+	0.171359i	0.344203	+	0.938895i	$0.388149\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$	12.0000			0.483887
$616$		0			0
$617$	24.0000			0.966204			0.483102	−	0.875564i	$-0.339510\pi$
$617$	24.0000			0.966204			0.483102	+	0.875564i	$0.339510\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	−3.67423	+	2.12132i	−0.147680	+	0.0852631i	−0.572019	−	0.820240i	$-0.693840\pi$
$619$	−3.67423	+	2.12132i	−0.147680	+	0.0852631i	0.424339	+	0.905503i	$0.360506\pi$
$620$	−9.79796	+	5.65685i	−0.393496	+	0.227185i
$621$	29.3939	+	16.9706i	1.17954	+	0.681005i
$622$		0			0
$623$		0			0
$624$	24.0000			0.960769
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−12.2474	+	7.07107i	−0.489506	+	0.282617i
$627$	14.6969	−	8.48528i	0.586939	−	0.338869i
$628$	22.0454	+	12.7279i	0.879708	+	0.507899i
$629$		−	50.9117i		−	2.02998i
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	19.5959	+	11.3137i	0.779484	+	0.450035i
$633$	−12.0000	−	20.7846i	−0.476957	−	0.826114i
$634$	−16.0000	−	27.7128i	−0.635441	−	1.10062i
$635$	2.44949	+	1.41421i	0.0972050	+	0.0561214i
$636$	−16.0000			−0.634441
$637$		0			0
$638$		−	11.3137i		−	0.447914i
$639$		0			0
$640$	8.00000	+	13.8564i	0.316228	+	0.547723i
$641$	24.0000	+	41.5692i	0.947943	+	1.64189i	0.749749	+	0.661723i	$0.230174\pi$
$641$	24.0000	+	41.5692i	0.947943	+	1.64189i	0.198194	+	0.980163i	$0.436492\pi$
$642$	−9.79796	−	5.65685i	−0.386695	−	0.223258i
$643$			21.2132i			0.836567i	0.908317	+	0.418284i	$0.137368\pi$
$643$			21.2132i			0.836567i	−0.908317	+	0.418284i	$0.862632\pi$
$644$		0			0
$645$		−	16.9706i		−	0.668215i
$646$	18.0000	−	31.1769i	0.708201	−	1.22664i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	12.2474	−	7.07107i	0.481125	−	0.277778i
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$	18.0000			0.706018
$651$		0			0
$652$		−	16.9706i		−	0.664619i
$653$	−31.8434	−	18.3848i	−1.24613	−	0.719452i	−0.275792	−	0.961217i	$-0.588940\pi$
$653$	−31.8434	−	18.3848i	−1.24613	−	0.719452i	−0.970335	+	0.241765i	$0.922274\pi$
$654$	14.6969	−	8.48528i	0.574696	−	0.331801i
$655$	1.00000	+	1.73205i	0.0390732	+	0.0676768i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	2.00000			0.0780274
$658$		0			0
$659$			2.82843i			0.110180i	0.998481	+	0.0550899i	$0.0175446\pi$
$659$			2.82843i			0.110180i	−0.998481	+	0.0550899i	$0.982455\pi$
$660$	9.79796	+	5.65685i	0.381385	+	0.220193i
$661$	−33.0681	+	19.0919i	−1.28620	+	0.742588i	−0.977974	−	0.208725i	$-0.933069\pi$
$661$	−33.0681	+	19.0919i	−1.28620	+	0.742588i	−0.308226	+	0.951313i	$0.599735\pi$
$662$	18.0000	+	31.1769i	0.699590	+	1.21173i
$663$	18.0000	−	31.1769i	0.699062	−	1.21081i
$664$	44.0000			1.70753
$665$		0			0
$666$	−12.0000			−0.464991
$667$	14.6969	+	8.48528i	0.569068	+	0.328551i
$668$	24.0000	+	41.5692i	0.928588	+	1.60836i
$669$	−34.2929	+	19.7990i	−1.32584	+	0.765473i
$670$		0			0
$671$	−36.0000			−1.38976
$672$		0			0
$673$	−46.0000			−1.77317			−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000			−1.77317			−0.886585	+	0.462566i	$0.846929\pi$
$674$	−39.1918	−	22.6274i	−1.50961	−	0.871576i
$675$	14.6969	−	8.48528i	0.565685	−	0.326599i
$676$	−5.00000	−	8.66025i	−0.192308	−	0.333087i
$677$	8.57321	+	4.94975i	0.329495	+	0.190234i	0.655617	−	0.755094i	$-0.272409\pi$
$677$	8.57321	+	4.94975i	0.329495	+	0.190234i	−0.326122	+	0.945328i	$0.605742\pi$
$678$	24.0000			0.921714
$679$		0			0
$680$	24.0000			0.920358
$681$	−7.00000	+	12.1244i	−0.268241	+	0.464606i
$682$	−8.00000	−	13.8564i	−0.306336	−	0.530589i
$683$	−4.89898	+	2.82843i	−0.187454	+	0.108227i	−0.590790	−	0.806825i	$-0.701184\pi$
$683$	−4.89898	+	2.82843i	−0.187454	+	0.108227i	0.403336	+	0.915052i	$0.367851\pi$
$684$	−7.34847	−	4.24264i	−0.280976	−	0.162221i
$685$		−	8.48528i		−	0.324206i
$686$		0			0
$687$	−6.00000			−0.228914
$688$	29.3939	+	16.9706i	1.12063	+	0.646997i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$	−14.6969	+	8.48528i	−0.559503	+	0.323029i
$691$	11.0227	+	6.36396i	0.419323	+	0.242096i	0.694788	−	0.719215i	$-0.255498\pi$
$691$	11.0227	+	6.36396i	0.419323	+	0.242096i	−0.275464	+	0.961311i	$0.588832\pi$
$692$			19.7990i			0.752645i
$693$		0			0
$694$	20.0000			0.759190
$695$	3.00000	−	5.19615i	0.113796	−	0.197101i
$696$	9.79796	−	5.65685i	0.371391	−	0.214423i
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	3.00000	−	5.19615i	0.113552	−	0.196677i
$699$			8.48528i			0.320943i
$700$		0			0
$701$			19.7990i			0.747798i	0.927470	+	0.373899i	$0.121979\pi$
$701$			19.7990i			0.747798i	−0.927470	+	0.373899i	$0.878021\pi$
$702$	−29.3939	−	16.9706i	−1.10940	−	0.640513i
$703$	−18.0000	−	31.1769i	−0.678883	−	1.17586i
$704$	−19.5959	+	11.3137i	−0.738549	+	0.426401i
$705$		0			0
$706$			8.48528i			0.319348i
$707$		0			0
$708$	−4.00000			−0.150329
$709$	22.0454	+	12.7279i	0.827933	+	0.478007i	0.853144	−	0.521675i	$-0.174693\pi$
$709$	22.0454	+	12.7279i	0.827933	+	0.478007i	−0.0252116	+	0.999682i	$0.508026\pi$
$710$		0			0
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	14.6969	+	8.48528i	0.550791	+	0.317999i
$713$	24.0000			0.898807
$714$		0			0
$715$		−	16.9706i		−	0.634663i
$716$	−9.79796	−	5.65685i	−0.366167	−	0.211407i
$717$	7.34847	−	4.24264i	0.274434	−	0.158444i
$718$	−36.7423	+	21.2132i	−1.37121	+	0.791670i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$		−	5.65685i		−	0.210819i
$721$		0			0
$722$			1.41421i			0.0526316i
$723$	12.2474	+	7.07107i	0.455488	+	0.262976i
$724$	−22.0454	+	12.7279i	−0.819311	+	0.473029i
$725$	7.34847	−	4.24264i	0.272915	−	0.157568i
$726$	3.00000	−	5.19615i	0.111340	−	0.192847i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	−29.0000			−1.07407
$730$	−2.00000	+	3.46410i	−0.0740233	+	0.128212i
$731$	44.0908	−	25.4558i	1.63076	−	0.941518i
$732$	−18.0000	−	31.1769i	−0.665299	−	1.15233i
$733$	−25.7196	−	14.8492i	−0.949977	−	0.548469i	−0.0569030	−	0.998380i	$-0.518123\pi$
$733$	−25.7196	−	14.8492i	−0.949977	−	0.548469i	−0.893074	+	0.449910i	$0.851456\pi$
$734$		−	39.5980i		−	1.46159i
$735$		0			0
$736$		−	33.9411i		−	1.25109i
$737$		0			0
$738$	7.34847	−	4.24264i	0.270501	−	0.156174i
$739$	36.7423	−	21.2132i	1.35159	−	0.780340i	0.363117	−	0.931744i	$-0.381713\pi$
$739$	36.7423	−	21.2132i	1.35159	−	0.780340i	0.988472	+	0.151403i	$0.0483792\pi$
$740$	12.0000	−	20.7846i	0.441129	−	0.764057i
$741$		−	25.4558i		−	0.935144i
$742$		0			0
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$	8.00000	−	13.8564i	0.293294	−	0.508001i
$745$	−8.00000	−	13.8564i	−0.293097	−	0.507659i
$746$	−24.0000	−	41.5692i	−0.878702	−	1.52196i
$747$	−13.4722	−	7.77817i	−0.492922	−	0.284589i
$748$			33.9411i			1.24101i
$749$		0			0
$750$			22.6274i			0.826236i
$751$	11.0000	−	19.0526i	0.401396	−	0.695238i	−0.592499	−	0.805571i	$-0.701859\pi$
$751$	11.0000	−	19.0526i	0.401396	−	0.695238i	0.993895	+	0.110333i	$0.0351919\pi$
$752$		0			0
$753$	−13.0000	−	22.5167i	−0.473746	−	0.820553i
$754$	−14.6969	−	8.48528i	−0.535231	−	0.309016i
$755$			14.1421i			0.514685i
$756$		0			0
$757$			25.4558i			0.925208i	0.886565	+	0.462604i	$0.153085\pi$
$757$			25.4558i			0.925208i	−0.886565	+	0.462604i	$0.846915\pi$
$758$	18.0000	−	31.1769i	0.653789	−	1.13240i
$759$	−12.0000	−	20.7846i	−0.435572	−	0.754434i
$760$	14.6969	−	8.48528i	0.533114	−	0.307794i
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	0.454935	+	0.890525i	$0.349663\pi$
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	−0.998684	+	0.0512772i	$0.983671\pi$
$762$	−4.00000			−0.144905
$763$		0			0
$764$		0			0
$765$	−7.34847	−	4.24264i	−0.265684	−	0.153393i
$766$	−29.3939	+	16.9706i	−1.06204	+	0.613171i
$767$	3.00000	+	5.19615i	0.108324	+	0.187622i
$768$	−19.5959	−	11.3137i	−0.707107	−	0.408248i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		−	8.48528i		−	0.305590i
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	28.1691	−	16.2635i	1.01317	−	0.584956i	0.101054	−	0.994881i	$-0.467778\pi$
$773$	28.1691	−	16.2635i	1.01317	−	0.584956i	0.912119	+	0.409925i	$0.134445\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$	6.00000	−	10.3923i	0.215526	−	0.373303i
$776$			28.2843i			1.01535i
$777$		0			0
$778$	−4.00000			−0.143407
$779$	22.0454	+	12.7279i	0.789859	+	0.456025i
$780$	14.6969	−	8.48528i	0.526235	−	0.303822i
$781$		0			0
$782$	−44.0908	−	25.4558i	−1.57668	−	0.910299i
$783$	−16.0000			−0.571793
$784$		0			0
$785$	18.0000			0.642448
$786$	−2.44949	−	1.41421i	−0.0873704	−	0.0504433i
$787$	−33.0681	+	19.0919i	−1.17875	+	0.680552i	−0.955725	−	0.294260i	$-0.904927\pi$
$787$	−33.0681	+	19.0919i	−1.17875	+	0.680552i	−0.223026	+	0.974813i	$0.571593\pi$
$788$	9.79796	−	5.65685i	0.349038	−	0.201517i
$789$	−29.3939	−	16.9706i	−1.04645	−	0.604168i
$790$	16.0000			0.569254
$791$		0			0
$792$	8.00000			0.284268
$793$	−27.0000	+	46.7654i	−0.958798	+	1.66069i
$794$	15.0000	+	25.9808i	0.532330	+	0.922023i
$795$	−9.79796	+	5.65685i	−0.347498	+	0.200628i
$796$	20.0000	−	34.6410i	0.708881	−	1.22782i
$797$		−	26.8701i		−	0.951786i	−0.879503	−	0.475893i	$-0.842125\pi$
$797$		−	26.8701i		−	0.951786i	0.879503	−	0.475893i	$-0.157875\pi$
$798$		0			0
$799$		0			0
$800$	−14.6969	−	8.48528i	−0.519615	−	0.300000i
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−29.3939	+	16.9706i	−1.03793	+	0.599251i
$803$	−4.89898	−	2.82843i	−0.172881	−	0.0998130i
$804$		0			0
$805$		0			0
$806$	−24.0000			−0.845364
$807$	5.00000	−	8.66025i	0.176008	−	0.304855i
$808$	14.0000	+	24.2487i	0.492518	+	0.853067i
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$	5.00000	−	8.66025i	0.175682	−	0.304290i
$811$			12.7279i			0.446938i	0.974711	+	0.223469i	$0.0717381\pi$
$811$			12.7279i			0.446938i	−0.974711	+	0.223469i	$0.928262\pi$
$812$		0			0
$813$			28.2843i			0.991973i
$814$	29.3939	+	16.9706i	1.03025	+	0.594818i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$	−29.3939	+	16.9706i	−1.02899	+	0.594089i
$817$	18.0000	−	31.1769i	0.629740	−	1.09074i
$818$		−	31.1127i		−	1.08783i
$819$		0			0
$820$			16.9706i			0.592638i
$821$	19.5959	+	11.3137i	0.683902	+	0.394851i	0.801324	−	0.598231i	$-0.204129\pi$
$821$	19.5959	+	11.3137i	0.683902	+	0.394851i	−0.117421	+	0.993082i	$0.537463\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	−9.79796	−	5.65685i	−0.341328	−	0.197066i
$825$	−12.0000			−0.417786
$826$		0			0
$827$			45.2548i			1.57366i	0.617167	+	0.786832i	$0.288280\pi$
$827$			45.2548i			1.57366i	−0.617167	+	0.786832i	$0.711720\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−18.3712	+	10.6066i	−0.638057	+	0.368383i	−0.783866	−	0.620930i	$-0.786755\pi$
$829$	−18.3712	+	10.6066i	−0.638057	+	0.368383i	0.145809	+	0.989313i	$0.453422\pi$
$830$	26.9444	−	15.5563i	0.935253	−	0.539969i
$831$	−12.0000	+	20.7846i	−0.416275	+	0.721010i
$832$			33.9411i			1.17670i
$833$		0			0
$834$			8.48528i			0.293821i
$835$	29.3939	+	16.9706i	1.01722	+	0.587291i
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	−19.5959	+	11.3137i	−0.677334	+	0.391059i
$838$	−19.0000	+	32.9090i	−0.656344	+	1.13682i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	12.0000	−	20.7846i	0.413547	−	0.716285i
$843$	−7.34847	+	4.24264i	−0.253095	+	0.146124i
$844$	29.3939	−	16.9706i	1.01178	−	0.584151i
$845$	−6.12372	−	3.53553i	−0.210663	−	0.121626i
$846$		0			0
$847$		0			0
$848$		−	22.6274i		−	0.777029i
$849$	9.00000	−	15.5885i	0.308879	−	0.534994i
$850$	−22.0454	+	12.7279i	−0.756151	+	0.436564i
$851$	−44.0908	+	25.4558i	−1.51141	+	0.872615i
$852$		0			0
$853$			4.24264i			0.145265i	0.997359	+	0.0726326i	$0.0231401\pi$
$853$			4.24264i			0.145265i	−0.997359	+	0.0726326i	$0.976860\pi$
$854$		0			0
$855$	−6.00000			−0.205196
$856$	8.00000	−	13.8564i	0.273434	−	0.473602i
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$	12.0000	+	20.7846i	0.409673	+	0.709575i
$859$	40.4166	+	23.3345i	1.37900	+	0.796164i	0.992039	−	0.125934i	$-0.0401927\pi$
$859$	40.4166	+	23.3345i	1.37900	+	0.796164i	0.386957	+	0.922098i	$0.373526\pi$
$860$	24.0000			0.818393
$861$		0			0
$862$		−	8.48528i		−	0.289010i
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	16.0000	+	27.7128i	0.544331	+	0.942809i
$865$	7.00000	+	12.1244i	0.238007	+	0.412240i
$866$	−2.44949	−	1.41421i	−0.0832370	−	0.0480569i
$867$			26.8701i			0.912555i
$868$		0			0
$869$			22.6274i			0.767583i
$870$	4.00000	−	6.92820i	0.135613	−	0.234888i
$871$		0			0
$872$	12.0000	+	20.7846i	0.406371	+	0.703856i
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$	−36.0000			−1.21772
$875$		0			0
$876$		−	5.65685i		−	0.191127i
$877$	−36.7423	−	21.2132i	−1.24070	−	0.716319i	−0.271464	−	0.962449i	$-0.587508\pi$
$877$	−36.7423	−	21.2132i	−1.24070	−	0.716319i	−0.969237	+	0.246130i	$0.920841\pi$
$878$	−34.2929	+	19.7990i	−1.15733	+	0.668184i
$879$	17.0000	+	29.4449i	0.573396	+	0.993151i
$880$	−8.00000	+	13.8564i	−0.269680	+	0.467099i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$		−	50.9117i		−	1.71331i	−0.515886	−	0.856657i	$-0.672537\pi$
$883$		−	50.9117i		−	1.71331i	0.515886	−	0.856657i	$-0.327463\pi$
$884$	44.0908	+	25.4558i	1.48293	+	0.856173i
$885$	−2.44949	+	1.41421i	−0.0823387	+	0.0475383i
$886$	−16.0000	−	27.7128i	−0.537531	−	0.931030i
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$			33.9411i			1.13899i
$889$		0			0
$890$	12.0000			0.402241
$891$	12.2474	+	7.07107i	0.410305	+	0.236890i
$892$	−28.0000	−	48.4974i	−0.937509	−	1.62381i
$893$		0			0
$894$	19.5959	+	11.3137i	0.655386	+	0.378387i
$895$	−8.00000			−0.267411
$896$		0			0
$897$	−36.0000			−1.20201
$898$	22.0454	+	12.7279i	0.735665	+	0.424736i
$899$	−9.79796	+	5.65685i	−0.326780	+	0.188667i
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$	−29.3939	−	16.9706i	−0.979252	−	0.565371i
$902$	−24.0000			−0.799113
$903$		0			0
$904$			33.9411i			1.12887i
$905$	−9.00000	+	15.5885i	−0.299170	+	0.518178i
$906$	−10.0000	−	17.3205i	−0.332228	−	0.575435i
$907$	29.3939	−	16.9706i	0.976008	−	0.563498i	0.0749452	−	0.997188i	$-0.476122\pi$
$907$	29.3939	−	16.9706i	0.976008	−	0.563498i	0.901062	+	0.433689i	$0.142788\pi$
$908$	−17.1464	−	9.89949i	−0.569024	−	0.328526i
$909$		−	9.89949i		−	0.328346i
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−12.0000	+	20.7846i	−0.397360	+	0.688247i
$913$	22.0000	+	38.1051i	0.728094	+	1.26110i
$914$	−34.2929	+	19.7990i	−1.13431	+	0.654892i
$915$	−22.0454	−	12.7279i	−0.728799	−	0.420772i
$916$		−	8.48528i		−	0.280362i
$917$		0			0
$918$	48.0000			1.58424
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	−12.0000	−	20.7846i	−0.395628	−	0.685248i
$921$	−9.00000	−	15.5885i	−0.296560	−	0.513657i
$922$	11.0000	−	19.0526i	0.362266	−	0.627463i
$923$		0			0
$924$		0			0
$925$			25.4558i			0.836983i
$926$	−39.1918	−	22.6274i	−1.28792	−	0.743583i
$927$	2.00000	+	3.46410i	0.0656886	+	0.113776i
$928$	8.00000	+	13.8564i	0.262613	+	0.454859i
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$		−	11.3137i		−	0.370991i
$931$		0			0
$932$	−12.0000			−0.393073
$933$		0			0
$934$	5.00000	+	8.66025i	0.163605	+	0.283372i
$935$	12.0000	+	20.7846i	0.392442	+	0.679729i
$936$	6.00000	−	10.3923i	0.196116	−	0.339683i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$		−	14.1421i		−	0.461511i
$940$		0			0
$941$	−45.3156	+	26.1630i	−1.47725	+	0.852888i	−0.999670	−	0.0257029i	$-0.991818\pi$
$941$	−45.3156	+	26.1630i	−1.47725	+	0.852888i	−0.477575	+	0.878591i	$0.658484\pi$
$942$	−22.0454	+	12.7279i	−0.718278	+	0.414698i
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$		−	5.65685i		−	0.184115i
$945$		0			0
$946$			33.9411i			1.10352i
$947$	−2.44949	−	1.41421i	−0.0795977	−	0.0459558i	0.459673	−	0.888088i	$-0.347967\pi$
$947$	−2.44949	−	1.41421i	−0.0795977	−	0.0459558i	−0.539271	+	0.842133i	$0.681300\pi$
$948$	−19.5959	+	11.3137i	−0.636446	+	0.367452i
$949$	−7.34847	+	4.24264i	−0.238541	+	0.137722i
$950$	−9.00000	+	15.5885i	−0.291999	+	0.505756i
$951$	32.0000			1.03767
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	9.79796	+	5.65685i	0.316723	+	0.182860i
$958$		−	16.9706i		−	0.548294i
$959$		0			0
$960$	−16.0000			−0.516398
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	44.0908	−	25.4558i	1.42154	−	0.820729i
$963$	−4.89898	+	2.82843i	−0.157867	+	0.0911448i
$964$	−10.0000	+	17.3205i	−0.322078	+	0.557856i
$965$			5.65685i			0.182101i
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$	7.34847	+	4.24264i	0.236189	+	0.136364i
$969$	18.0000	+	31.1769i	0.578243	+	1.00155i
$970$	10.0000	+	17.3205i	0.321081	+	0.556128i
$971$	−28.1691	−	16.2635i	−0.903990	−	0.521919i	−0.0254978	−	0.999675i	$-0.508117\pi$
$971$	−28.1691	−	16.2635i	−0.903990	−	0.521919i	−0.878493	+	0.477756i	$0.841450\pi$
$972$		−	19.7990i		−	0.635053i
$973$		0			0
$974$			2.82843i			0.0906287i
$975$	−9.00000	+	15.5885i	−0.288231	+	0.499230i
$976$	44.0908	−	25.4558i	1.41131	−	0.814822i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$	14.6969	+	8.48528i	0.469956	+	0.271329i
$979$			16.9706i			0.542382i
$980$		0			0
$981$		−	8.48528i		−	0.270914i
$982$	−28.0000	+	48.4974i	−0.893516	+	1.54761i
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	0.945705	−	0.325027i	$-0.105374\pi$
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	−0.754334	+	0.656490i	$0.772040\pi$
$984$	−12.0000	−	20.7846i	−0.382546	−	0.662589i
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$	24.0000			0.764316
$987$		0			0
$988$	36.0000			1.14531
$989$	−44.0908	−	25.4558i	−1.40201	−	0.809449i
$990$	4.89898	−	2.82843i	0.155700	−	0.0898933i
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$	19.5959	+	11.3137i	0.622171	+	0.359211i
$993$	−36.0000			−1.14243
$994$		0			0
$995$		−	28.2843i		−	0.896672i
$996$	−22.0000	+	38.1051i	−0.697097	+	1.20741i
$997$	18.3712	−	10.6066i	0.581821	−	0.335914i	−0.180036	−	0.983660i	$-0.557621\pi$
$997$	18.3712	−	10.6066i	0.581821	−	0.335914i	0.761857	+	0.647746i	$0.224288\pi$
$998$	12.0000	+	20.7846i	0.379853	+	0.657925i
$999$	24.0000	−	41.5692i	0.759326	−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.p.a.373.1		4
4.3	odd	2		1568.2.t.c.177.1		4
7.2	even	3		56.2.b.a.29.2	yes	2
7.3	odd	6		392.2.p.b.165.2		4
7.4	even	3	inner	392.2.p.a.165.2		4
7.5	odd	6		392.2.b.b.197.2		2
7.6	odd	2		392.2.p.b.373.1		4
8.3	odd	2		1568.2.t.c.177.2		4
8.5	even	2	inner	392.2.p.a.373.2		4
21.2	odd	6		504.2.c.a.253.1		2
28.3	even	6		1568.2.t.b.753.1		4
28.11	odd	6		1568.2.t.c.753.2		4
28.19	even	6		1568.2.b.a.785.2		2
28.23	odd	6		224.2.b.a.113.1		2
28.27	even	2		1568.2.t.b.177.2		4
56.3	even	6		1568.2.t.b.753.2		4
56.5	odd	6		392.2.b.b.197.1		2
56.11	odd	6		1568.2.t.c.753.1		4
56.13	odd	2		392.2.p.b.373.2		4
56.19	even	6		1568.2.b.a.785.1		2
56.27	even	2		1568.2.t.b.177.1		4
56.37	even	6		56.2.b.a.29.1	✓	2
56.45	odd	6		392.2.p.b.165.1		4
56.51	odd	6		224.2.b.a.113.2		2
56.53	even	6	inner	392.2.p.a.165.1		4
84.23	even	6		2016.2.c.a.1009.2		2
112.37	even	12		1792.2.a.n.1.2		2
112.51	odd	12		1792.2.a.p.1.2		2
112.93	even	12		1792.2.a.n.1.1		2
112.107	odd	12		1792.2.a.p.1.1		2
168.107	even	6		2016.2.c.a.1009.1		2
168.149	odd	6		504.2.c.a.253.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.b.a.29.1	✓	2	56.37	even	6
56.2.b.a.29.2	yes	2	7.2	even	3
224.2.b.a.113.1		2	28.23	odd	6
224.2.b.a.113.2		2	56.51	odd	6
392.2.b.b.197.1		2	56.5	odd	6
392.2.b.b.197.2		2	7.5	odd	6
392.2.p.a.165.1		4	56.53	even	6	inner
392.2.p.a.165.2		4	7.4	even	3	inner
392.2.p.a.373.1		4	1.1	even	1	trivial
392.2.p.a.373.2		4	8.5	even	2	inner
392.2.p.b.165.1		4	56.45	odd	6
392.2.p.b.165.2		4	7.3	odd	6
392.2.p.b.373.1		4	7.6	odd	2
392.2.p.b.373.2		4	56.13	odd	2
504.2.c.a.253.1		2	21.2	odd	6
504.2.c.a.253.2		2	168.149	odd	6
1568.2.b.a.785.1		2	56.19	even	6
1568.2.b.a.785.2		2	28.19	even	6
1568.2.t.b.177.1		4	56.27	even	2
1568.2.t.b.177.2		4	28.27	even	2
1568.2.t.b.753.1		4	28.3	even	6
1568.2.t.b.753.2		4	56.3	even	6
1568.2.t.c.177.1		4	4.3	odd	2
1568.2.t.c.177.2		4	8.3	odd	2
1568.2.t.c.753.1		4	56.11	odd	6
1568.2.t.c.753.2		4	28.11	odd	6
1792.2.a.n.1.1		2	112.93	even	12
1792.2.a.n.1.2		2	112.37	even	12
1792.2.a.p.1.1		2	112.107	odd	12
1792.2.a.p.1.2		2	112.51	odd	12
2016.2.c.a.1009.1		2	168.107	even	6
2016.2.c.a.1009.2		2	84.23	even	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.22474 - 0.707107i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.22474 + 0.707107i) q^{5} -2.00000 q^{6} -2.82843i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.22474 - 0.707107i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.22474 + 0.707107i) q^{5} -2.00000 q^{6} -2.82843i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(2.44949 - 1.41421i) q^{11} +(2.44949 + 1.41421i) q^{12} -4.24264i q^{13} +2.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(1.22474 - 0.707107i) q^{18} +(3.67423 + 2.12132i) q^{19} +2.82843i q^{20} -4.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(-1.50000 - 2.59808i) q^{25} +(-3.00000 + 5.19615i) q^{26} +5.65685i q^{27} +2.82843i q^{29} +(-2.44949 - 1.41421i) q^{30} +(2.00000 + 3.46410i) q^{31} +(4.89898 - 2.82843i) q^{32} +(2.00000 - 3.46410i) q^{33} -8.48528i q^{34} -2.00000 q^{36} +(-7.34847 - 4.24264i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(2.00000 - 3.46410i) q^{40} +6.00000 q^{41} -8.48528i q^{43} +(4.89898 + 2.82843i) q^{44} +(-1.22474 + 0.707107i) q^{45} +(-7.34847 + 4.24264i) q^{46} +5.65685i q^{48} +4.24264i q^{50} +(7.34847 + 4.24264i) q^{51} +(7.34847 - 4.24264i) q^{52} +(-4.89898 + 2.82843i) q^{53} +(4.00000 - 6.92820i) q^{54} +4.00000 q^{55} +6.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-1.22474 + 0.707107i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-11.0227 - 6.36396i) q^{61} -5.65685i q^{62} -8.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(-4.89898 + 2.82843i) q^{66} +(-6.00000 + 10.3923i) q^{68} -8.48528i q^{69} +(2.44949 + 1.41421i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(6.00000 + 10.3923i) q^{74} +(-3.67423 - 2.12132i) q^{75} +8.48528i q^{76} +8.48528i q^{78} +(-4.00000 + 6.92820i) q^{79} +(-4.89898 + 2.82843i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-7.34847 - 4.24264i) q^{82} +15.5563i q^{83} +8.48528i q^{85} +(-6.00000 + 10.3923i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-4.00000 - 6.92820i) q^{88} +(-3.00000 + 5.19615i) q^{89} +2.00000 q^{90} +12.0000 q^{92} +(4.89898 + 2.82843i) q^{93} +(3.00000 + 5.19615i) q^{95} +(4.00000 - 6.92820i) q^{96} -10.0000 q^{97} +2.82843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 - 8 * q^6 - 2 * q^9	\( 4 q + 4 q^{4} - 8 q^{6} - 2 q^{9} - 4 q^{10} + 8 q^{15} - 8 q^{16} + 12 q^{17} - 16 q^{22} + 12 q^{23} - 8 q^{24} - 6 q^{25} - 12 q^{26} + 8 q^{31} + 8 q^{33} - 8 q^{36} - 12 q^{38} - 12 q^{39} + 8 q^{40} + 24 q^{41} + 16 q^{54} + 16 q^{55} + 24 q^{57} + 8 q^{58} + 8 q^{60} - 32 q^{64} + 12 q^{65} - 24 q^{68} - 4 q^{73} + 24 q^{74} - 16 q^{79} + 10 q^{81} - 24 q^{86} + 8 q^{87} - 16 q^{88} - 12 q^{89} + 8 q^{90} + 48 q^{92} + 12 q^{95} + 16 q^{96} - 40 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 - 8 * q^6 - 2 * q^9 - 4 * q^10 + 8 * q^15 - 8 * q^16 + 12 * q^17 - 16 * q^22 + 12 * q^23 - 8 * q^24 - 6 * q^25 - 12 * q^26 + 8 * q^31 + 8 * q^33 - 8 * q^36 - 12 * q^38 - 12 * q^39 + 8 * q^40 + 24 * q^41 + 16 * q^54 + 16 * q^55 + 24 * q^57 + 8 * q^58 + 8 * q^60 - 32 * q^64 + 12 * q^65 - 24 * q^68 - 4 * q^73 + 24 * q^74 - 16 * q^79 + 10 * q^81 - 24 * q^86 + 8 * q^87 - 16 * q^88 - 12 * q^89 + 8 * q^90 + 48 * q^92 + 12 * q^95 + 16 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more