LMFDB - Embedded newform 1078.2.i.a.1011.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.7
Root			$-0.130526 - 0.991445i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.a.901.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.937379 + 0.541196i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.937379 - 0.541196i) q^{5} +1.08239 q^{6} -1.00000i q^{8} +(-0.914214 - 1.58346i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.937379 + 0.541196i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.937379 - 0.541196i) q^{5} +1.08239 q^{6} -1.00000i q^{8} +(-0.914214 - 1.58346i) q^{9} +(0.541196 - 0.937379i) q^{10} +(3.30518 + 0.275255i) q^{11} +(0.937379 - 0.541196i) q^{12} +2.29610 q^{13} +1.17157 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.58346 - 0.914214i) q^{18} +(2.77164 + 4.80062i) q^{19} -1.08239i q^{20} +(3.00000 - 1.41421i) q^{22} +(-3.12132 - 5.40629i) q^{23} +(0.541196 - 0.937379i) q^{24} +(-1.91421 + 3.31552i) q^{25} +(1.98848 - 1.14805i) q^{26} -5.22625i q^{27} -1.75736i q^{29} +(1.01461 - 0.585786i) q^{30} +(1.21193 + 0.699709i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.94924 + 2.04677i) q^{33} -1.82843 q^{36} +(-3.00000 - 5.19615i) q^{37} +(4.80062 + 2.77164i) q^{38} +(2.15232 + 1.24264i) q^{39} +(-0.541196 - 0.937379i) q^{40} +4.59220 q^{41} -4.24264i q^{43} +(1.89097 - 2.72474i) q^{44} +(-1.71393 - 0.989538i) q^{45} +(-5.40629 - 3.12132i) q^{46} +(4.25151 - 2.45461i) q^{47} -1.08239i q^{48} +3.82843i q^{50} +(1.14805 - 1.98848i) q^{52} +(-2.24264 + 3.88437i) q^{53} +(-2.61313 - 4.52607i) q^{54} +(3.24718 - 1.53073i) q^{55} +6.00000i q^{57} +(-0.878680 - 1.52192i) q^{58} +(6.24000 + 3.60266i) q^{59} +(0.585786 - 1.01461i) q^{60} +(2.77164 + 4.80062i) q^{61} +1.39942 q^{62} -1.00000 q^{64} +(2.15232 - 1.24264i) q^{65} +(3.57750 + 0.297934i) q^{66} +(-5.82843 + 10.0951i) q^{67} -6.75699i q^{69} +2.00000 q^{71} +(-1.58346 + 0.914214i) q^{72} +(-7.83938 + 13.5782i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(-3.58869 + 2.07193i) q^{75} +5.54328 q^{76} +2.48528 q^{78} +(7.34847 - 4.24264i) q^{79} +(-0.937379 - 0.541196i) q^{80} +(0.0857864 - 0.148586i) q^{81} +(3.97696 - 2.29610i) q^{82} -13.3827 q^{83} +(-2.12132 - 3.67423i) q^{86} +(0.951076 - 1.64731i) q^{87} +(0.275255 - 3.30518i) q^{88} +(-3.08669 + 1.78210i) q^{89} -1.97908 q^{90} -6.24264 q^{92} +(0.757359 + 1.31178i) q^{93} +(2.45461 - 4.25151i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-0.541196 - 0.937379i) q^{96} -8.60474i q^{97} +(-2.58579 - 5.48528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^9	$ 16 q + 8 q^{4} + 8 q^{9} + 64 q^{15} - 8 q^{16} + 48 q^{22} - 16 q^{23} - 8 q^{25} + 16 q^{36} - 48 q^{37} + 32 q^{53} - 48 q^{58} + 32 q^{60} - 16 q^{64} - 48 q^{67} + 32 q^{71} - 96 q^{78} + 24 q^{81} + 24 q^{88} - 32 q^{92} + 80 q^{93} - 64 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^9 + 64 * q^15 - 8 * q^16 + 48 * q^22 - 16 * q^23 - 8 * q^25 + 16 * q^36 - 48 * q^37 + 32 * q^53 - 48 * q^58 + 32 * q^60 - 16 * q^64 - 48 * q^67 + 32 * q^71 - 96 * q^78 + 24 * q^81 + 24 * q^88 - 32 * q^92 + 80 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.937379	+	0.541196i	0.541196	+	0.312460i	0.745564	−	0.666435i	$-0.232180\pi$
$3$	0.937379	+	0.541196i	0.541196	+	0.312460i	−0.204367	+	0.978894i	$0.565514\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.937379	−	0.541196i	0.419209	−	0.242030i	−0.275530	−	0.961292i	$-0.588853\pi$
$5$	0.937379	−	0.541196i	0.419209	−	0.242030i	0.694739	+	0.719262i	$0.255520\pi$
$6$	1.08239			0.441885
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−0.914214	−	1.58346i	−0.304738	−	0.527821i
$10$	0.541196	−	0.937379i	0.171141	−	0.296425i
$11$	3.30518	+	0.275255i	0.996550	+	0.0829925i
$11$	3.30518	+	0.275255i	0.996550	+	0.0829925i
$12$	0.937379	−	0.541196i	0.270598	−	0.156230i
$13$	2.29610			0.636824			0.318412	−	0.947952i	$-0.396851\pi$
$13$	2.29610			0.636824			0.318412	+	0.947952i	$0.396851\pi$
$14$		0			0
$15$	1.17157			0.302499
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−1.58346	−	0.914214i	−0.373226	−	0.215482i
$19$	2.77164	+	4.80062i	0.635858	+	1.10134i	0.986333	+	0.164766i	$0.0526867\pi$
$19$	2.77164	+	4.80062i	0.635858	+	1.10134i	−0.350475	+	0.936572i	$0.613980\pi$
$20$		−	1.08239i		−	0.242030i
$21$		0			0
$22$	3.00000	−	1.41421i	0.639602	−	0.301511i
$23$	−3.12132	−	5.40629i	−0.650840	−	1.12729i	−0.982919	−	0.184037i	$-0.941083\pi$
$23$	−3.12132	−	5.40629i	−0.650840	−	1.12729i	0.332079	−	0.943252i	$-0.392250\pi$
$24$	0.541196	−	0.937379i	0.110471	−	0.191342i
$25$	−1.91421	+	3.31552i	−0.382843	+	0.663103i
$26$	1.98848	−	1.14805i	0.389973	−	0.225151i
$27$		−	5.22625i		−	1.00579i
$28$		0			0
$29$		−	1.75736i		−	0.326333i	−0.986599	−	0.163167i	$-0.947829\pi$
$29$		−	1.75736i		−	0.326333i	0.986599	−	0.163167i	$-0.0521708\pi$
$30$	1.01461	−	0.585786i	0.185242	−	0.106949i
$31$	1.21193	+	0.699709i	0.217669	+	0.125671i	0.604871	−	0.796324i	$-0.293225\pi$
$31$	1.21193	+	0.699709i	0.217669	+	0.125671i	−0.387201	+	0.921995i	$0.626558\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.94924	+	2.04677i	0.513397	+	0.356297i
$34$		0			0
$35$		0			0
$36$	−1.82843			−0.304738
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	4.80062	+	2.77164i	0.778763	+	0.449619i
$39$	2.15232	+	1.24264i	0.344647	+	0.198982i
$40$	−0.541196	−	0.937379i	−0.0855706	−	0.148213i
$41$	4.59220			0.717181			0.358591	−	0.933495i	$-0.383257\pi$
$41$	4.59220			0.717181			0.358591	+	0.933495i	$0.383257\pi$
$42$		0			0
$43$		−	4.24264i		−	0.646997i	−0.946229	−	0.323498i	$-0.895141\pi$
$43$		−	4.24264i		−	0.646997i	0.946229	−	0.323498i	$-0.104859\pi$
$44$	1.89097	−	2.72474i	0.285074	−	0.410771i
$45$	−1.71393	−	0.989538i	−0.255498	−	0.147512i
$46$	−5.40629	−	3.12132i	−0.797113	−	0.460214i
$47$	4.25151	−	2.45461i	0.620147	−	0.358042i	−0.156779	−	0.987634i	$-0.550111\pi$
$47$	4.25151	−	2.45461i	0.620147	−	0.358042i	0.776926	+	0.629592i	$0.216778\pi$
$48$		−	1.08239i		−	0.156230i
$49$		0			0
$50$			3.82843i			0.541421i
$51$		0			0
$52$	1.14805	−	1.98848i	0.159206	−	0.275753i
$53$	−2.24264	+	3.88437i	−0.308050	+	0.533559i	−0.977936	−	0.208906i	$-0.933010\pi$
$53$	−2.24264	+	3.88437i	−0.308050	+	0.533559i	0.669885	+	0.742464i	$0.266343\pi$
$54$	−2.61313	−	4.52607i	−0.355601	−	0.615920i
$55$	3.24718	−	1.53073i	0.437849	−	0.206404i
$56$		0			0
$57$			6.00000i			0.794719i
$58$	−0.878680	−	1.52192i	−0.115376	−	0.199838i
$59$	6.24000	+	3.60266i	0.812378	+	0.469027i	0.847781	−	0.530346i	$-0.177938\pi$
$59$	6.24000	+	3.60266i	0.812378	+	0.469027i	−0.0354028	+	0.999373i	$0.511271\pi$
$60$	0.585786	−	1.01461i	0.0756247	−	0.130986i
$61$	2.77164	+	4.80062i	0.354872	+	0.614656i	0.987096	−	0.160129i	$-0.0511911\pi$
$61$	2.77164	+	4.80062i	0.354872	+	0.614656i	−0.632224	+	0.774786i	$0.717858\pi$
$62$	1.39942			0.177726
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.15232	−	1.24264i	0.266962	−	0.154131i
$66$	3.57750	+	0.297934i	0.440360	+	0.0366731i
$67$	−5.82843	+	10.0951i	−0.712056	+	1.23332i	0.252028	+	0.967720i	$0.418902\pi$
$67$	−5.82843	+	10.0951i	−0.712056	+	1.23332i	−0.964084	+	0.265597i	$0.914431\pi$
$68$		0			0
$69$		−	6.75699i		−	0.813445i
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−1.58346	+	0.914214i	−0.186613	+	0.107741i
$73$	−7.83938	+	13.5782i	−0.917530	+	1.58921i	−0.114375	+	0.993438i	$0.536487\pi$
$73$	−7.83938	+	13.5782i	−0.917530	+	1.58921i	−0.803155	+	0.595771i	$0.796847\pi$
$74$	−5.19615	−	3.00000i	−0.604040	−	0.348743i
$75$	−3.58869	+	2.07193i	−0.414386	+	0.239246i
$76$	5.54328			0.635858
$77$		0			0
$78$	2.48528			0.281403
$79$	7.34847	−	4.24264i	0.826767	−	0.477334i	−0.0259772	−	0.999663i	$-0.508270\pi$
$79$	7.34847	−	4.24264i	0.826767	−	0.477334i	0.852745	+	0.522328i	$0.174936\pi$
$80$	−0.937379	−	0.541196i	−0.104802	−	0.0605076i
$81$	0.0857864	−	0.148586i	0.00953183	−	0.0165096i
$82$	3.97696	−	2.29610i	0.439182	−	0.253562i
$83$	−13.3827			−1.46894			−0.734469	−	0.678643i	$-0.762569\pi$
$83$	−13.3827			−1.46894			−0.734469	+	0.678643i	$0.762569\pi$
$84$		0			0
$85$		0			0
$86$	−2.12132	−	3.67423i	−0.228748	−	0.396203i
$87$	0.951076	−	1.64731i	0.101966	−	0.176610i
$88$	0.275255	−	3.30518i	0.0293423	−	0.352334i
$89$	−3.08669	+	1.78210i	−0.327188	+	0.188902i	−0.654592	−	0.755982i	$-0.727160\pi$
$89$	−3.08669	+	1.78210i	−0.327188	+	0.188902i	0.327404	+	0.944885i	$0.393826\pi$
$90$	−1.97908			−0.208613
$91$		0			0
$92$	−6.24264			−0.650840
$93$	0.757359	+	1.31178i	0.0785345	+	0.136026i
$94$	2.45461	−	4.25151i	0.253174	−	0.438510i
$95$	5.19615	+	3.00000i	0.533114	+	0.307794i
$96$	−0.541196	−	0.937379i	−0.0552356	−	0.0956709i
$97$		−	8.60474i		−	0.873679i	−0.899539	−	0.436840i	$-0.856098\pi$
$97$		−	8.60474i		−	0.873679i	0.899539	−	0.436840i	$-0.143902\pi$
$98$		0			0
$99$	−2.58579	−	5.48528i	−0.259881	−	0.551292i
$100$	1.91421	+	3.31552i	0.191421	+	0.331552i
$101$	−8.31492	+	14.4019i	−0.827365	+	1.43304i	0.0727333	+	0.997351i	$0.476828\pi$
$101$	−8.31492	+	14.4019i	−0.827365	+	1.43304i	−0.900098	+	0.435687i	$0.856506\pi$
$102$		0			0
$103$	5.57717	−	3.21998i	0.549535	−	0.317274i	−0.199400	−	0.979918i	$-0.563899\pi$
$103$	5.57717	−	3.21998i	0.549535	−	0.317274i	0.748934	+	0.662644i	$0.230566\pi$
$104$		−	2.29610i		−	0.225151i
$105$		0			0
$106$			4.48528i			0.435649i
$107$	−11.0227	+	6.36396i	−1.06561	+	0.615227i	−0.926977	−	0.375117i	$-0.877602\pi$
$107$	−11.0227	+	6.36396i	−1.06561	+	0.615227i	−0.138628	+	0.990345i	$0.544269\pi$
$108$	−4.52607	−	2.61313i	−0.435521	−	0.251448i
$109$	3.04384	+	1.75736i	0.291547	+	0.168324i	0.638639	−	0.769506i	$-0.279498\pi$
$109$	3.04384	+	1.75736i	0.291547	+	0.168324i	−0.347093	+	0.937831i	$0.612831\pi$
$110$	2.04677	−	2.94924i	0.195152	−	0.281199i
$111$		−	6.49435i		−	0.616417i
$112$		0			0
$113$	−1.41421			−0.133038			−0.0665190	−	0.997785i	$-0.521189\pi$
$113$	−1.41421			−0.133038			−0.0665190	+	0.997785i	$0.521189\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−5.85172	−	3.37849i	−0.545676	−	0.315046i
$116$	−1.52192	−	0.878680i	−0.141307	−	0.0815834i
$117$	−2.09913	−	3.63579i	−0.194064	−	0.336129i
$118$	7.20533			0.663304
$119$		0			0
$120$		−	1.17157i		−	0.106949i
$121$	10.8485	+	1.81954i	0.986224	+	0.165412i
$122$	4.80062	+	2.77164i	0.434628	+	0.250932i
$123$	4.30463	+	2.48528i	0.388136	+	0.224090i
$124$	1.21193	−	0.699709i	0.108835	−	0.0628357i
$125$			9.55582i			0.854699i
$126$		0			0
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.29610	−	3.97696i	0.202160	−	0.350152i
$130$	1.24264	−	2.15232i	0.108987	−	0.188771i
$131$	−3.44415	−	5.96544i	−0.300917	−	0.521203i	0.675427	−	0.737427i	$-0.263959\pi$
$131$	−3.44415	−	5.96544i	−0.300917	−	0.521203i	−0.976344	+	0.216224i	$0.930626\pi$
$132$	3.24718	−	1.53073i	0.282630	−	0.133233i
$133$		0			0
$134$			11.6569i			1.00700i
$135$	−2.82843	−	4.89898i	−0.243432	−	0.421637i
$136$		0			0
$137$	8.48528	−	14.6969i	0.724947	−	1.25564i	−0.234050	−	0.972225i	$-0.575198\pi$
$137$	8.48528	−	14.6969i	0.724947	−	1.25564i	0.958996	−	0.283420i	$-0.0914689\pi$
$138$	−3.37849	−	5.85172i	−0.287596	−	0.498132i
$139$	−13.3827			−1.13510			−0.567551	−	0.823338i	$-0.692109\pi$
$139$	−13.3827			−1.13510			−0.567551	+	0.823338i	$0.692109\pi$
$140$		0			0
$141$	5.31371			0.447495
$142$	1.73205	−	1.00000i	0.145350	−	0.0839181i
$143$	7.58903	+	0.632013i	0.634627	+	0.0528516i
$144$	−0.914214	+	1.58346i	−0.0761845	+	0.131955i
$145$	−0.951076	−	1.64731i	−0.0789826	−	0.136802i
$146$			15.6788i			1.29758i
$147$		0			0
$148$	−6.00000			−0.493197
$149$	−5.82655	+	3.36396i	−0.477330	+	0.275586i	−0.719303	−	0.694696i	$-0.755539\pi$
$149$	−5.82655	+	3.36396i	−0.477330	+	0.275586i	0.241973	+	0.970283i	$0.422205\pi$
$150$	−2.07193	+	3.58869i	−0.169172	+	0.293015i
$151$	−5.19615	−	3.00000i	−0.422857	−	0.244137i	0.273442	−	0.961888i	$-0.411838\pi$
$151$	−5.19615	−	3.00000i	−0.422857	−	0.244137i	−0.696299	+	0.717752i	$0.745171\pi$
$152$	4.80062	−	2.77164i	0.389382	−	0.224810i
$153$		0			0
$154$		0			0
$155$	1.51472			0.121665
$156$	2.15232	−	1.24264i	0.172323	−	0.0994909i
$157$	−9.98951	−	5.76745i	−0.797250	−	0.460292i	0.0452587	−	0.998975i	$-0.485589\pi$
$157$	−9.98951	−	5.76745i	−0.797250	−	0.460292i	−0.842509	+	0.538683i	$0.818922\pi$
$158$	4.24264	−	7.34847i	0.337526	−	0.584613i
$159$	−4.20441	+	2.42742i	−0.333431	+	0.192507i
$160$	−1.08239			−0.0855706
$161$		0			0
$162$		−	0.171573i		−	0.0134800i
$163$	4.07107	+	7.05130i	0.318871	+	0.552300i	0.980253	−	0.197749i	$-0.0633631\pi$
$163$	4.07107	+	7.05130i	0.318871	+	0.552300i	−0.661382	+	0.750049i	$0.730030\pi$
$164$	2.29610	−	3.97696i	0.179295	−	0.310549i
$165$	3.87226	+	0.322481i	0.301455	+	0.0251051i
$166$	−11.5897	+	6.69133i	−0.899537	+	0.519348i
$167$	−20.2710			−1.56861			−0.784307	−	0.620373i	$-0.786981\pi$
$167$	−20.2710			−1.56861			−0.784307	+	0.620373i	$0.786981\pi$
$168$		0			0
$169$	−7.72792			−0.594456
$170$		0			0
$171$	5.06774	−	8.77758i	0.387540	−	0.671238i
$172$	−3.67423	−	2.12132i	−0.280158	−	0.161749i
$173$	12.9071	+	22.3558i	0.981310	+	1.69968i	0.657308	+	0.753622i	$0.271695\pi$
$173$	12.9071	+	22.3558i	0.981310	+	1.69968i	0.324002	+	0.946056i	$0.394971\pi$
$174$		−	1.90215i		−	0.144202i
$175$		0			0
$176$	−1.41421	−	3.00000i	−0.106600	−	0.226134i
$177$	3.89949	+	6.75412i	0.293104	+	0.507671i
$178$	−1.78210	+	3.08669i	−0.133574	+	0.231357i
$179$	2.82843	−	4.89898i	0.211407	−	0.366167i	−0.740748	−	0.671783i	$-0.765529\pi$
$179$	2.82843	−	4.89898i	0.211407	−	0.366167i	0.952155	+	0.305616i	$0.0988623\pi$
$180$	−1.71393	+	0.989538i	−0.127749	+	0.0737558i
$181$			20.4567i			1.52053i	0.649612	+	0.760266i	$0.274931\pi$
$181$			20.4567i			1.52053i	−0.649612	+	0.760266i	$0.725069\pi$
$182$		0			0
$183$			6.00000i			0.443533i
$184$	−5.40629	+	3.12132i	−0.398557	+	0.230107i
$185$	−5.62427	−	3.24718i	−0.413505	−	0.238737i
$186$	1.31178	+	0.757359i	0.0961847	+	0.0555323i
$187$		0			0
$188$		−	4.90923i		−	0.358042i
$189$		0			0
$190$	6.00000			0.435286
$191$	0.878680	+	1.52192i	0.0635790	+	0.110122i	0.896063	−	0.443927i	$-0.146415\pi$
$191$	0.878680	+	1.52192i	0.0635790	+	0.110122i	−0.832484	+	0.554049i	$0.813082\pi$
$192$	−0.937379	−	0.541196i	−0.0676495	−	0.0390575i
$193$	2.15232	+	1.24264i	0.154927	+	0.0894472i	0.575459	−	0.817830i	$-0.304823\pi$
$193$	2.15232	+	1.24264i	0.154927	+	0.0894472i	−0.420532	+	0.907278i	$0.638157\pi$
$194$	−4.30237	−	7.45193i	−0.308892	−	0.535017i
$195$	2.69005			0.192638
$196$		0			0
$197$		−	20.4853i		−	1.45952i	−0.683706	−	0.729758i	$-0.739633\pi$
$197$		−	20.4853i		−	1.45952i	0.683706	−	0.729758i	$-0.260367\pi$
$198$	−4.98200	−	3.45750i	−0.354055	−	0.245714i
$199$	−21.3518	−	12.3275i	−1.51359	−	0.873870i	−0.999873	−	0.0159092i	$-0.994936\pi$
$199$	−21.3518	−	12.3275i	−1.51359	−	0.873870i	−0.513715	−	0.857961i	$-0.671731\pi$
$200$	3.31552	+	1.91421i	0.234442	+	0.135355i
$201$	−10.9269	+	6.30864i	−0.770724	+	0.444977i
$202$			16.6298i			1.17007i
$203$		0			0
$204$		0			0
$205$	4.30463	−	2.48528i	0.300649	−	0.173580i
$206$	3.21998	−	5.57717i	0.224347	−	0.388580i
$207$	−5.70711	+	9.88500i	−0.396671	+	0.687055i
$208$	−1.14805	−	1.98848i	−0.0796030	−	0.137876i
$209$	7.83938	+	16.6298i	0.542261	+	1.15031i
$210$		0			0
$211$			24.7279i			1.70234i	0.524890	+	0.851170i	$0.324107\pi$
$211$			24.7279i			1.70234i	−0.524890	+	0.851170i	$0.675893\pi$
$212$	2.24264	+	3.88437i	0.154025	+	0.266779i
$213$	1.87476	+	1.08239i	0.128456	+	0.0741643i
$214$	−6.36396	+	11.0227i	−0.435031	+	0.753497i
$215$	−2.29610	−	3.97696i	−0.156593	−	0.271227i
$216$	−5.22625			−0.355601
$217$		0			0
$218$	3.51472			0.238047
$219$	−14.6969	+	8.48528i	−0.993127	+	0.573382i
$220$	0.297934	−	3.57750i	0.0200867	−	0.241195i
$221$		0			0
$222$	−3.24718	−	5.62427i	−0.217936	−	0.377477i
$223$		−	7.89377i		−	0.528606i	−0.964440	−	0.264303i	$-0.914858\pi$
$223$		−	7.89377i		−	0.528606i	0.964440	−	0.264303i	$-0.0851419\pi$
$224$		0			0
$225$	7.00000			0.466667
$226$	−1.22474	+	0.707107i	−0.0814688	+	0.0470360i
$227$	0.475538	−	0.823656i	0.0315626	−	0.0546680i	−0.849813	−	0.527085i	$-0.823285\pi$
$227$	0.475538	−	0.823656i	0.0315626	−	0.0546680i	0.881375	+	0.472417i	$0.156618\pi$
$228$	5.19615	+	3.00000i	0.344124	+	0.198680i
$229$	−24.6659	+	14.2409i	−1.62997	+	0.941064i	−0.645870	+	0.763447i	$0.723505\pi$
$229$	−24.6659	+	14.2409i	−1.62997	+	0.941064i	−0.984100	+	0.177616i	$0.943161\pi$
$230$	−6.75699			−0.445542
$231$		0			0
$232$	−1.75736			−0.115376
$233$	7.34847	−	4.24264i	0.481414	−	0.277945i	−0.239591	−	0.970874i	$-0.577013\pi$
$233$	7.34847	−	4.24264i	0.481414	−	0.277945i	0.721006	+	0.692929i	$0.243680\pi$
$234$	−3.63579	−	2.09913i	−0.237679	−	0.137224i
$235$	2.65685	−	4.60181i	0.173314	−	0.300189i
$236$	6.24000	−	3.60266i	0.406189	−	0.234513i
$237$	9.18440			0.596591
$238$		0			0
$239$		−	26.4853i		−	1.71319i	−0.515989	−	0.856595i	$-0.672575\pi$
$239$		−	26.4853i		−	1.71319i	0.515989	−	0.856595i	$-0.327425\pi$
$240$	−0.585786	−	1.01461i	−0.0378124	−	0.0654929i
$241$	2.29610	−	3.97696i	0.147905	−	0.256179i	−0.782548	−	0.622590i	$-0.786080\pi$
$241$	2.29610	−	3.97696i	0.147905	−	0.256179i	0.930453	+	0.366411i	$0.119414\pi$
$242$	10.3048	−	3.84847i	0.662419	−	0.247389i
$243$	−13.4174	+	7.74652i	−0.860725	+	0.496940i
$244$	5.54328			0.354872
$245$		0			0
$246$	4.97056			0.316912
$247$	6.36396	+	11.0227i	0.404929	+	0.701358i
$248$	0.699709	−	1.21193i	0.0444316	−	0.0769577i
$249$	−12.5446	−	7.24264i	−0.794983	−	0.458984i
$250$	4.77791	+	8.27558i	0.302182	+	0.523394i
$251$			12.1689i			0.768097i	0.923313	+	0.384049i	$0.125470\pi$
$251$			12.1689i			0.768097i	−0.923313	+	0.384049i	$0.874530\pi$
$252$		0			0
$253$	−8.82843	−	18.7279i	−0.555038	−	1.17741i
$254$	3.00000	+	5.19615i	0.188237	+	0.326036i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	19.0888	−	11.0209i	1.19072	−	0.687465i	0.232253	−	0.972655i	$-0.425390\pi$
$257$	19.0888	−	11.0209i	1.19072	−	0.687465i	0.958471	+	0.285191i	$0.0920570\pi$
$258$		−	4.59220i		−	0.285898i
$259$		0			0
$260$		−	2.48528i		−	0.154131i
$261$	−2.78272	+	1.60660i	−0.172246	+	0.0994461i
$262$	−5.96544	−	3.44415i	−0.368546	−	0.212780i
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.977147	−	0.212565i	$-0.0681817\pi$
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.304487	+	0.952517i	$0.401515\pi$
$264$	2.04677	−	2.94924i	0.125970	−	0.181513i
$265$			4.85483i			0.298230i
$266$		0			0
$267$	−3.85786			−0.236097
$268$	5.82843	+	10.0951i	0.356028	+	0.616658i
$269$	3.03958	+	1.75490i	0.185327	+	0.106998i	0.589793	−	0.807555i	$-0.299209\pi$
$269$	3.03958	+	1.75490i	0.185327	+	0.106998i	−0.404466	+	0.914553i	$0.632543\pi$
$270$	−4.89898	−	2.82843i	−0.298142	−	0.172133i
$271$	−13.3827	−	23.1794i	−0.812938	−	1.40805i	−0.910799	−	0.412850i	$-0.864533\pi$
$271$	−13.3827	−	23.1794i	−0.812938	−	1.40805i	0.0978604	−	0.995200i	$-0.468800\pi$
$272$		0			0
$273$		0			0
$274$		−	16.9706i		−	1.02523i
$275$	−7.23944	+	10.4315i	−0.436555	+	0.629042i
$276$	−5.85172	−	3.37849i	−0.352232	−	0.203361i
$277$	−16.2189	−	9.36396i	−0.974497	−	0.562626i	−0.0738925	−	0.997266i	$-0.523542\pi$
$277$	−16.2189	−	9.36396i	−0.974497	−	0.562626i	−0.900604	+	0.434640i	$0.856876\pi$
$278$	−11.5897	+	6.69133i	−0.695105	+	0.401319i
$279$		−	2.55873i		−	0.153187i
$280$		0			0
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$	4.60181	−	2.65685i	0.274034	−	0.158213i
$283$	11.2835	−	19.5436i	0.670736	−	1.16175i	−0.306960	−	0.951723i	$-0.599312\pi$
$283$	11.2835	−	19.5436i	0.670736	−	1.16175i	0.977696	−	0.210027i	$-0.0673550\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	3.24718	+	5.62427i	0.192346	+	0.333153i
$286$	6.88830	−	3.24718i	0.407314	−	0.192010i
$287$		0			0
$288$			1.82843i			0.107741i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−1.64731	−	0.951076i	−0.0967335	−	0.0558491i
$291$	4.65685	−	8.06591i	0.272990	−	0.472832i
$292$	7.83938	+	13.5782i	0.458765	+	0.794604i
$293$	0.951076			0.0555625			0.0277812	−	0.999614i	$-0.491156\pi$
$293$	0.951076			0.0555625			0.0277812	+	0.999614i	$0.491156\pi$
$294$		0			0
$295$	7.79899			0.454075
$296$	−5.19615	+	3.00000i	−0.302020	+	0.174371i
$297$	1.43855	−	17.2737i	0.0834733	−	1.00232i
$298$	−3.36396	+	5.82655i	−0.194869	+	0.337523i
$299$	−7.16687	−	12.4134i	−0.414471	−	0.717884i
$300$			4.14386i			0.239246i
$301$		0			0
$302$	−6.00000			−0.345261
$303$	−15.5885	+	9.00000i	−0.895533	+	0.517036i
$304$	2.77164	−	4.80062i	0.158964	−	0.275334i
$305$	5.19615	+	3.00000i	0.297531	+	0.171780i
$306$		0			0
$307$	7.44543			0.424933			0.212467	−	0.977168i	$-0.431850\pi$
$307$	7.44543			0.424933			0.212467	+	0.977168i	$0.431850\pi$
$308$		0			0
$309$	6.97056			0.396541
$310$	1.31178	−	0.757359i	0.0745044	−	0.0430151i
$311$	28.9174	+	16.6955i	1.63976	+	0.946714i	0.980916	+	0.194433i	$0.0622865\pi$
$311$	28.9174	+	16.6955i	1.63976	+	0.946714i	0.658841	+	0.752282i	$0.271047\pi$
$312$	1.24264	−	2.15232i	0.0703507	−	0.121851i
$313$	−8.93841	+	5.16059i	−0.505229	+	0.291694i	−0.730870	−	0.682516i	$-0.760886\pi$
$313$	−8.93841	+	5.16059i	−0.505229	+	0.291694i	0.225641	+	0.974210i	$0.427552\pi$
$314$	−11.5349			−0.650952
$315$		0			0
$316$		−	8.48528i		−	0.477334i
$317$	11.4853	+	19.8931i	0.645078	+	1.11731i	0.984284	+	0.176595i	$0.0565083\pi$
$317$	11.4853	+	19.8931i	0.645078	+	1.11731i	−0.339206	+	0.940712i	$0.610158\pi$
$318$	−2.42742	+	4.20441i	−0.136123	+	0.235772i
$319$	0.483722	−	5.80839i	0.0270832	−	0.325208i
$320$	−0.937379	+	0.541196i	−0.0524011	+	0.0302538i
$321$	−13.7766			−0.768935
$322$		0			0
$323$		0			0
$324$	−0.0857864	−	0.148586i	−0.00476591	−	0.00825480i
$325$	−4.39523	+	7.61276i	−0.243803	+	0.422280i
$326$	7.05130	+	4.07107i	0.390535	+	0.225476i
$327$	1.90215	+	3.29462i	0.105189	+	0.182193i
$328$		−	4.59220i		−	0.253562i
$329$		0			0
$330$	3.51472	−	1.65685i	0.193479	−	0.0912068i
$331$	−10.2426	−	17.7408i	−0.562986	−	0.975121i	−0.997234	−	0.0743275i	$-0.976319\pi$
$331$	−10.2426	−	17.7408i	−0.562986	−	0.975121i	0.434247	−	0.900794i	$-0.357014\pi$
$332$	−6.69133	+	11.5897i	−0.367234	+	0.636068i
$333$	−5.48528	+	9.50079i	−0.300592	+	0.520640i
$334$	−17.5552	+	10.1355i	−0.960576	+	0.554589i
$335$			12.6173i			0.689356i
$336$		0			0
$337$			26.4853i			1.44275i	0.692547	+	0.721373i	$0.256488\pi$
$337$			26.4853i			1.44275i	−0.692547	+	0.721373i	$0.743512\pi$
$338$	−6.69258	+	3.86396i	−0.364028	+	0.210172i
$339$	−1.32565	−	0.765367i	−0.0719997	−	0.0415690i
$340$		0			0
$341$	3.81306	+	2.64626i	0.206489	+	0.143303i
$342$		−	10.1355i		−	0.548064i
$343$		0			0
$344$	−4.24264			−0.228748
$345$	−3.65685	−	6.33386i	−0.196878	−	0.341003i
$346$	22.3558	+	12.9071i	1.20185	+	0.693891i
$347$	−6.71807	−	3.87868i	−0.360645	−	0.208218i	0.308719	−	0.951153i	$-0.400100\pi$
$347$	−6.71807	−	3.87868i	−0.360645	−	0.208218i	−0.669364	+	0.742935i	$0.733433\pi$
$348$	−0.951076	−	1.64731i	−0.0509830	−	0.0883052i
$349$	29.0614			1.55562			0.777811	−	0.628498i	$-0.216330\pi$
$349$	29.0614			1.55562			0.777811	+	0.628498i	$0.216330\pi$
$350$		0			0
$351$		−	12.0000i		−	0.640513i
$352$	−2.72474	−	1.89097i	−0.145229	−	0.100789i
$353$	−1.05110	−	0.606854i	−0.0559445	−	0.0322996i	0.471767	−	0.881723i	$-0.343616\pi$
$353$	−1.05110	−	0.606854i	−0.0559445	−	0.0322996i	−0.527711	+	0.849424i	$0.676950\pi$
$354$	6.75412	+	3.89949i	0.358978	+	0.207256i
$355$	1.87476	−	1.08239i	0.0995018	−	0.0574474i
$356$			3.56420i			0.188902i
$357$		0			0
$358$		−	5.65685i		−	0.298974i
$359$	2.15232	−	1.24264i	0.113595	−	0.0655841i	−0.442126	−	0.896953i	$-0.645776\pi$
$359$	2.15232	−	1.24264i	0.113595	−	0.0655841i	0.555721	+	0.831369i	$0.312442\pi$
$360$	−0.989538	+	1.71393i	−0.0521532	+	0.0903320i
$361$	−5.86396	+	10.1567i	−0.308630	+	0.534562i
$362$	10.2283	+	17.7160i	0.537589	+	0.931132i
$363$	9.18440	+	7.57675i	0.482056	+	0.397676i
$364$		0			0
$365$			16.9706i			0.888280i
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	9.64834	+	5.57047i	0.503639	+	0.290776i	0.730215	−	0.683217i	$-0.239420\pi$
$367$	9.64834	+	5.57047i	0.503639	+	0.290776i	−0.226576	+	0.973994i	$0.572753\pi$
$368$	−3.12132	+	5.40629i	−0.162710	+	0.281822i
$369$	−4.19825	−	7.27159i	−0.218552	−	0.378544i
$370$	−6.49435			−0.337625
$371$		0			0
$372$	1.51472			0.0785345
$373$	17.7408	−	10.2426i	0.918582	−	0.530344i	0.0353999	−	0.999373i	$-0.488730\pi$
$373$	17.7408	−	10.2426i	0.918582	−	0.530344i	0.883183	+	0.469029i	$0.155396\pi$
$374$		0			0
$375$	−5.17157	+	8.95743i	−0.267059	+	0.462560i
$376$	−2.45461	−	4.25151i	−0.126587	−	0.219255i
$377$		−	4.03507i		−	0.207817i
$378$		0			0
$379$	−11.6569			−0.598772			−0.299386	−	0.954132i	$-0.596782\pi$
$379$	−11.6569			−0.598772			−0.299386	+	0.954132i	$0.596782\pi$
$380$	5.19615	−	3.00000i	0.266557	−	0.153897i
$381$	−3.24718	+	5.62427i	−0.166358	+	0.288140i
$382$	1.52192	+	0.878680i	0.0778681	+	0.0449572i
$383$	12.5271	−	7.23252i	0.640105	−	0.369565i	−0.144550	−	0.989497i	$-0.546173\pi$
$383$	12.5271	−	7.23252i	0.640105	−	0.369565i	0.784655	+	0.619933i	$0.212840\pi$
$384$	−1.08239			−0.0552356
$385$		0			0
$386$	2.48528			0.126497
$387$	−6.71807	+	3.87868i	−0.341499	+	0.197164i
$388$	−7.45193	−	4.30237i	−0.378314	−	0.218420i
$389$	16.0000	−	27.7128i	0.811232	−	1.40510i	−0.100770	−	0.994910i	$-0.532131\pi$
$389$	16.0000	−	27.7128i	0.811232	−	1.40510i	0.912002	−	0.410186i	$-0.134536\pi$
$390$	2.32965	−	1.34502i	0.117966	−	0.0681080i
$391$		0			0
$392$		0			0
$393$		−	7.45584i		−	0.376098i
$394$	−10.2426	−	17.7408i	−0.516017	−	0.893767i
$395$	4.59220	−	7.95393i	0.231059	−	0.400205i
$396$	−6.04329	−	0.503284i	−0.303687	−	0.0252910i
$397$	1.48648	−	0.858221i	0.0746044	−	0.0430729i	−0.462234	−	0.886758i	$-0.652952\pi$
$397$	1.48648	−	0.858221i	0.0746044	−	0.0430729i	0.536838	+	0.843685i	$0.319619\pi$
$398$	−24.6549			−1.23584
$399$		0			0
$400$	3.82843			0.191421
$401$	−0.242641	−	0.420266i	−0.0121169	−	0.0209871i	0.859903	−	0.510457i	$-0.170524\pi$
$401$	−0.242641	−	0.420266i	−0.0121169	−	0.0209871i	−0.872020	+	0.489470i	$0.837190\pi$
$402$	−6.30864	+	10.9269i	−0.314647	+	0.544984i
$403$	2.78272	+	1.60660i	0.138617	+	0.0800305i
$404$	8.31492	+	14.4019i	0.413683	+	0.716519i
$405$		−	0.185709i		−	0.00922796i
$406$		0			0
$407$	−8.48528	−	18.0000i	−0.420600	−	0.892227i
$408$		0			0
$409$	−18.9259	+	32.7807i	−0.935827	+	1.62090i	−0.162675	+	0.986680i	$0.552012\pi$
$409$	−18.9259	+	32.7807i	−0.935827	+	1.62090i	−0.773152	+	0.634220i	$0.781321\pi$
$410$	2.48528	−	4.30463i	0.122739	−	0.212591i
$411$	15.9079	−	9.18440i	0.784676	−	0.453033i
$412$		−	6.43996i		−	0.317274i
$413$		0			0
$414$			11.4142i			0.560978i
$415$	−12.5446	+	7.24264i	−0.615791	+	0.355527i
$416$	−1.98848	−	1.14805i	−0.0974933	−	0.0562878i
$417$	−12.5446	−	7.24264i	−0.614313	−	0.354674i
$418$	15.1040	+	10.4822i	0.738762	+	0.512700i
$419$		−	8.47343i		−	0.413954i	−0.978346	−	0.206977i	$-0.933637\pi$
$419$		−	8.47343i		−	0.413954i	0.978346	−	0.206977i	$-0.0663625\pi$
$420$		0			0
$421$	17.6569			0.860542			0.430271	−	0.902700i	$-0.358418\pi$
$421$	17.6569			0.860542			0.430271	+	0.902700i	$0.358418\pi$
$422$	12.3640	+	21.4150i	0.601868	+	1.04247i
$423$	−7.77359	−	4.48808i	−0.377965	−	0.218218i
$424$	3.88437	+	2.24264i	0.188642	+	0.108912i
$425$		0			0
$426$	2.16478			0.104884
$427$		0			0
$428$			12.7279i			0.615227i
$429$	6.77176	+	4.69959i	0.326944	+	0.226898i
$430$	−3.97696	−	2.29610i	−0.191786	−	0.110728i
$431$	−2.15232	−	1.24264i	−0.103673	−	0.0598559i	0.447267	−	0.894401i	$-0.352397\pi$
$431$	−2.15232	−	1.24264i	−0.103673	−	0.0598559i	−0.550940	+	0.834545i	$0.685731\pi$
$432$	−4.52607	+	2.61313i	−0.217760	+	0.125724i
$433$		−	22.6758i		−	1.08973i	−0.838523	−	0.544866i	$-0.816581\pi$
$433$		−	22.6758i		−	1.08973i	0.838523	−	0.544866i	$-0.183419\pi$
$434$		0			0
$435$		−	2.05887i		−	0.0987155i
$436$	3.04384	−	1.75736i	0.145773	−	0.0841622i
$437$	17.3023	−	29.9685i	0.827683	−	1.43359i
$438$	−8.48528	+	14.6969i	−0.405442	+	0.702247i
$439$	−3.24718	−	5.62427i	−0.154979	−	0.268432i	0.778072	−	0.628175i	$-0.216198\pi$
$439$	−3.24718	−	5.62427i	−0.154979	−	0.268432i	−0.933051	+	0.359743i	$0.882864\pi$
$440$	−1.53073	−	3.24718i	−0.0729749	−	0.154803i
$441$		0			0
$442$		0			0
$443$	−11.3137	−	19.5959i	−0.537531	−	0.931030i	−0.999036	−	0.0438929i	$-0.986024\pi$
$443$	−11.3137	−	19.5959i	−0.537531	−	0.931030i	0.461506	−	0.887137i	$-0.347309\pi$
$444$	−5.62427	−	3.24718i	−0.266916	−	0.154104i
$445$	−1.92893	+	3.34101i	−0.0914402	+	0.158379i
$446$	−3.94689	−	6.83621i	−0.186890	−	0.323704i
$447$	−7.28225			−0.344439
$448$		0			0
$449$	−40.7279			−1.92207			−0.961035	−	0.276428i	$-0.910849\pi$
$449$	−40.7279			−1.92207			−0.961035	+	0.276428i	$0.910849\pi$
$450$	6.06218	−	3.50000i	0.285774	−	0.164992i
$451$	15.1781	+	1.26403i	0.714707	+	0.0595207i
$452$	−0.707107	+	1.22474i	−0.0332595	+	0.0576072i
$453$	−3.24718	−	5.62427i	−0.152566	−	0.264251i
$454$		−	0.951076i		−	0.0446362i
$455$		0			0
$456$	6.00000			0.280976
$457$	27.2416	−	15.7279i	1.27431	−	0.735721i	0.298511	−	0.954406i	$-0.403510\pi$
$457$	27.2416	−	15.7279i	1.27431	−	0.735721i	0.975795	+	0.218685i	$0.0701767\pi$
$458$	−14.2409	+	24.6659i	−0.665432	+	1.15256i
$459$		0			0
$460$	−5.85172	+	3.37849i	−0.272838	+	0.157523i
$461$	29.0614			1.35352			0.676762	−	0.736201i	$-0.263382\pi$
$461$	29.0614			1.35352			0.676762	+	0.736201i	$0.263382\pi$
$462$		0			0
$463$	−5.31371			−0.246949			−0.123474	−	0.992348i	$-0.539404\pi$
$463$	−5.31371			−0.246949			−0.123474	+	0.992348i	$0.539404\pi$
$464$	−1.52192	+	0.878680i	−0.0706533	+	0.0407917i
$465$	1.41987	+	0.819760i	0.0658447	+	0.0380155i
$466$	4.24264	−	7.34847i	0.196537	−	0.340411i
$467$	27.8663	−	16.0886i	1.28950	−	0.744493i	0.310935	−	0.950431i	$-0.399358\pi$
$467$	27.8663	−	16.0886i	1.28950	−	0.744493i	0.978565	+	0.205938i	$0.0660245\pi$
$468$	−4.19825			−0.194064
$469$		0			0
$470$		−	5.31371i		−	0.245103i
$471$	−6.24264	−	10.8126i	−0.287646	−	0.498217i
$472$	3.60266	−	6.24000i	0.165826	−	0.287219i
$473$	1.16781	−	14.0227i	0.0536959	−	0.644765i
$474$	7.95393	−	4.59220i	0.365336	−	0.210927i
$475$	−21.2220			−0.973734
$476$		0			0
$477$	8.20101			0.375498
$478$	−13.2426	−	22.9369i	−0.605704	−	1.04911i
$479$	−4.59220	+	7.95393i	−0.209823	+	0.363424i	−0.951659	−	0.307158i	$-0.900622\pi$
$479$	−4.59220	+	7.95393i	−0.209823	+	0.363424i	0.741836	+	0.670582i	$0.233955\pi$
$480$	−1.01461	−	0.585786i	−0.0463105	−	0.0267374i
$481$	−6.88830	−	11.9309i	−0.314080	−	0.544002i
$482$		−	4.59220i		−	0.209169i
$483$		0			0
$484$	7.00000	−	8.48528i	0.318182	−	0.385695i
$485$	−4.65685	−	8.06591i	−0.211457	−	0.366254i
$486$	−7.74652	+	13.4174i	−0.351389	+	0.608624i
$487$	1.22183	−	2.11626i	0.0553662	−	0.0958971i	−0.837014	−	0.547182i	$-0.815701\pi$
$487$	1.22183	−	2.11626i	0.0553662	−	0.0958971i	0.892380	+	0.451285i	$0.149034\pi$
$488$	4.80062	−	2.77164i	0.217314	−	0.125466i
$489$			8.81298i			0.398537i
$490$		0			0
$491$			39.9411i			1.80252i	0.433281	+	0.901259i	$0.357356\pi$
$491$			39.9411i			1.80252i	−0.433281	+	0.901259i	$0.642644\pi$
$492$	4.30463	−	2.48528i	0.194068	−	0.112045i
$493$		0			0
$494$	11.0227	+	6.36396i	0.495935	+	0.286328i
$495$	−5.39248	−	3.74237i	−0.242374	−	0.168207i
$496$		−	1.39942i		−	0.0628357i
$497$		0			0
$498$	−14.4853			−0.649101
$499$	−14.3137	−	24.7921i	−0.640770	−	1.10985i	−0.985261	−	0.171056i	$-0.945282\pi$
$499$	−14.3137	−	24.7921i	−0.640770	−	1.10985i	0.344492	−	0.938789i	$-0.388051\pi$
$500$	8.27558	+	4.77791i	0.370095	+	0.213675i
$501$	−19.0016	−	10.9706i	−0.848928	−	0.490129i
$502$	6.08447	+	10.5386i	0.271563	+	0.470361i
$503$	6.49435			0.289569			0.144784	−	0.989463i	$-0.453751\pi$
$503$	6.49435			0.289569			0.144784	+	0.989463i	$0.453751\pi$
$504$		0			0
$505$			18.0000i			0.800989i
$506$	−17.0096	−	11.8046i	−0.756169	−	0.524780i
$507$	−7.24399	−	4.18232i	−0.321717	−	0.185743i
$508$	5.19615	+	3.00000i	0.230542	+	0.133103i
$509$	28.0938	−	16.2200i	1.24523	−	0.718937i	0.275080	−	0.961421i	$-0.411296\pi$
$509$	28.0938	−	16.2200i	1.24523	−	0.718937i	0.970155	+	0.242485i	$0.0779624\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	25.0892	−	14.4853i	1.10772	−	0.639541i
$514$	11.0209	−	19.0888i	0.486111	−	0.841969i
$515$	3.48528	−	6.03668i	0.153580	−	0.266008i
$516$	−2.29610	−	3.97696i	−0.101080	−	0.175076i
$517$	14.7277	−	6.94269i	0.647723	−	0.305339i
$518$		0			0
$519$			27.9411i			1.22648i
$520$	−1.24264	−	2.15232i	−0.0544934	−	0.0943853i
$521$	24.5522	+	14.1752i	1.07565	+	0.621028i	0.929720	−	0.368267i	$-0.120049\pi$
$521$	24.5522	+	14.1752i	1.07565	+	0.621028i	0.145931	+	0.989295i	$0.453382\pi$
$522$	−1.60660	+	2.78272i	−0.0703190	+	0.121796i
$523$	−0.475538	−	0.823656i	−0.0207938	−	0.0360160i	0.855441	−	0.517900i	$-0.173286\pi$
$523$	−0.475538	−	0.823656i	−0.0207938	−	0.0360160i	−0.876235	+	0.481884i	$0.839953\pi$
$524$	−6.88830			−0.300917
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	0.297934	−	3.57750i	0.0129659	−	0.155691i
$529$	−7.98528	+	13.8309i	−0.347186	+	0.601344i
$530$	2.42742	+	4.20441i	0.105440	+	0.182628i
$531$		−	13.1744i		−	0.571721i
$532$		0			0
$533$	10.5442			0.456718
$534$	−3.34101	+	1.92893i	−0.144580	+	0.0834731i
$535$	−6.88830	+	11.9309i	−0.297807	+	0.515817i
$536$	10.0951	+	5.82843i	0.436043	+	0.251750i
$537$	5.30262	−	3.06147i	0.228825	−	0.132112i
$538$	3.50981			0.151319
$539$		0			0
$540$	−5.65685			−0.243432
$541$	9.50079	−	5.48528i	0.408471	−	0.235831i	−0.281662	−	0.959514i	$-0.590886\pi$
$541$	9.50079	−	5.48528i	0.408471	−	0.235831i	0.690132	+	0.723683i	$0.257552\pi$
$542$	−23.1794	−	13.3827i	−0.995642	−	0.574834i
$543$	−11.0711	+	19.1757i	−0.475105	+	0.822906i
$544$		0			0
$545$	3.80430			0.162958
$546$		0			0
$547$		−	24.0000i		−	1.02617i	−0.858339	−	0.513083i	$-0.828503\pi$
$547$		−	24.0000i		−	1.02617i	0.858339	−	0.513083i	$-0.171497\pi$
$548$	−8.48528	−	14.6969i	−0.362473	−	0.627822i
$549$	5.06774	−	8.77758i	0.216286	−	0.374618i
$550$	−1.05379	+	12.6537i	−0.0449339	+	0.539554i
$551$	8.43641	−	4.87076i	0.359403	−	0.207502i
$552$	−6.75699			−0.287596
$553$		0			0
$554$	−18.7279			−0.795673
$555$	−3.51472	−	6.08767i	−0.149191	−	0.258407i
$556$	−6.69133	+	11.5897i	−0.283775	+	0.491514i
$557$	−5.19615	−	3.00000i	−0.220168	−	0.127114i	0.385860	−	0.922557i	$-0.373905\pi$
$557$	−5.19615	−	3.00000i	−0.220168	−	0.127114i	−0.606028	+	0.795443i	$0.707238\pi$
$558$	−1.27937	−	2.21593i	−0.0541599	−	0.0938077i
$559$		−	9.74153i		−	0.412023i
$560$		0			0
$561$		0			0
$562$	6.00000	+	10.3923i	0.253095	+	0.438373i
$563$	−13.5796	+	23.5206i	−0.572313	+	0.991275i	0.424015	+	0.905655i	$0.360620\pi$
$563$	−13.5796	+	23.5206i	−0.572313	+	0.991275i	−0.996328	+	0.0856201i	$0.972713\pi$
$564$	2.65685	−	4.60181i	0.111874	−	0.193771i
$565$	−1.32565	+	0.765367i	−0.0557707	+	0.0321992i
$566$		−	22.5671i		−	0.948564i
$567$		0			0
$568$		−	2.00000i		−	0.0839181i
$569$	25.9808	−	15.0000i	1.08917	−	0.628833i	0.155815	−	0.987786i	$-0.450200\pi$
$569$	25.9808	−	15.0000i	1.08917	−	0.628833i	0.933355	+	0.358954i	$0.116866\pi$
$570$	5.62427	+	3.24718i	0.235575	+	0.136009i
$571$	−31.1769	−	18.0000i	−1.30471	−	0.753277i	−0.323505	−	0.946227i	$-0.604861\pi$
$571$	−31.1769	−	18.0000i	−1.30471	−	0.753277i	−0.981209	+	0.192950i	$0.938194\pi$
$572$	4.34186	−	6.25629i	0.181542	−	0.261589i
$573$			1.90215i			0.0794635i
$574$		0			0
$575$	23.8995			0.996678
$576$	0.914214	+	1.58346i	0.0380922	+	0.0659777i
$577$	−28.7566	−	16.6026i	−1.19715	−	0.691177i	−0.237234	−	0.971453i	$-0.576241\pi$
$577$	−28.7566	−	16.6026i	−1.19715	−	0.691177i	−0.959919	+	0.280276i	$0.909574\pi$
$578$	14.7224	+	8.50000i	0.612372	+	0.353553i
$579$	1.34502	+	2.32965i	0.0558973	+	0.0968170i
$580$	−1.90215			−0.0789826
$581$		0			0
$582$		−	9.31371i		−	0.386066i
$583$	−8.48153	+	12.2212i	−0.351269	+	0.506152i
$584$	13.5782	+	7.83938i	0.561870	+	0.324396i
$585$	−3.93535	−	2.27208i	−0.162707	−	0.0939389i
$586$	0.823656	−	0.475538i	0.0340249	−	0.0196443i
$587$		−	37.0321i		−	1.52848i	−0.644933	−	0.764239i	$-0.723115\pi$
$587$		−	37.0321i		−	1.52848i	0.644933	−	0.764239i	$-0.276885\pi$
$588$		0			0
$589$			7.75736i			0.319636i
$590$	6.75412	−	3.89949i	0.278063	−	0.160540i
$591$	11.0866	−	19.2025i	0.456040	−	0.789884i
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	14.3337	+	24.8268i	0.588616	+	1.01951i	0.994414	+	0.105550i	$0.0336602\pi$
$593$	14.3337	+	24.8268i	0.588616	+	1.01951i	−0.405798	+	0.913963i	$0.633006\pi$
$594$	−7.39104	−	15.6788i	−0.303258	−	0.643307i
$595$		0			0
$596$			6.72792i			0.275586i
$597$	−13.3431	−	23.1110i	−0.546099	−	0.945871i
$598$	−12.4134	−	7.16687i	−0.507621	−	0.293075i
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	−0.468173	−	0.883637i	$-0.655088\pi$
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	0.999338	−	0.0363689i	$-0.0115791\pi$
$600$	2.07193	+	3.58869i	0.0845862	+	0.146508i
$601$	−35.9497			−1.46642			−0.733210	−	0.680003i	$-0.761979\pi$
$601$	−35.9497			−1.46642			−0.733210	+	0.680003i	$0.761979\pi$
$602$		0			0
$603$	21.3137			0.867961
$604$	−5.19615	+	3.00000i	−0.211428	+	0.122068i
$605$	11.1539	−	4.16555i	0.453469	−	0.169354i
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	−23.1242	−	40.0523i	−0.938582	−	1.62567i	−0.768119	−	0.640307i	$-0.778807\pi$
$607$	−23.1242	−	40.0523i	−0.938582	−	1.62567i	−0.170463	−	0.985364i	$-0.554526\pi$
$608$		−	5.54328i		−	0.224810i
$609$		0			0
$610$	6.00000			0.242933
$611$	9.76191	−	5.63604i	0.394924	−	0.228010i
$612$		0			0
$613$	11.9142	+	6.87868i	0.481211	+	0.277827i	0.720921	−	0.693017i	$-0.243719\pi$
$613$	11.9142	+	6.87868i	0.481211	+	0.277827i	−0.239710	+	0.970845i	$0.577052\pi$
$614$	6.44793	−	3.72271i	0.260217	−	0.150237i
$615$	5.38010			0.216947
$616$		0			0
$617$	1.41421			0.0569341			0.0284670	−	0.999595i	$-0.490937\pi$
$617$	1.41421			0.0569341			0.0284670	+	0.999595i	$0.490937\pi$
$618$	6.03668	−	3.48528i	0.242831	−	0.140199i
$619$	1.48648	+	0.858221i	0.0597468	+	0.0344948i	0.529576	−	0.848263i	$-0.322351\pi$
$619$	1.48648	+	0.858221i	0.0597468	+	0.0344948i	−0.469829	+	0.882757i	$0.655684\pi$
$620$	0.757359	−	1.31178i	0.0304163	−	0.0526825i
$621$	−28.2546	+	16.3128i	−1.13382	+	0.654610i
$622$	33.3910			1.33886
$623$		0			0
$624$		−	2.48528i		−	0.0994909i
$625$	−4.39949	−	7.62015i	−0.175980	−	0.304806i
$626$	−5.16059	+	8.93841i	−0.206259	+	0.357251i
$627$	−1.65153	+	19.8311i	−0.0659558	+	0.791978i
$628$	−9.98951	+	5.76745i	−0.398625	+	0.230146i
$629$		0			0
$630$		0			0
$631$	15.2132			0.605628			0.302814	−	0.953050i	$-0.402074\pi$
$631$	15.2132			0.605628			0.302814	+	0.953050i	$0.402074\pi$
$632$	−4.24264	−	7.34847i	−0.168763	−	0.292306i
$633$	−13.3827	+	23.1794i	−0.531913	+	0.921300i
$634$	19.8931	+	11.4853i	0.790056	+	0.456139i
$635$	3.24718	+	5.62427i	0.128860	+	0.223193i
$636$			4.85483i			0.192507i
$637$		0			0
$638$	−2.48528	−	5.27208i	−0.0983932	−	0.208724i
$639$	−1.82843	−	3.16693i	−0.0723315	−	0.125282i
$640$	−0.541196	+	0.937379i	−0.0213927	+	0.0370532i
$641$	−1.39340	+	2.41344i	−0.0550359	+	0.0953250i	−0.892231	−	0.451580i	$-0.850861\pi$
$641$	−1.39340	+	2.41344i	−0.0550359	+	0.0953250i	0.837195	+	0.546905i	$0.184194\pi$
$642$	−11.9309	+	6.88830i	−0.470875	+	0.271860i
$643$		−	5.04054i		−	0.198780i	−0.995049	−	0.0993898i	$-0.968311\pi$
$643$		−	5.04054i		−	0.198780i	0.995049	−	0.0993898i	$-0.0316891\pi$
$644$		0			0
$645$		−	4.97056i		−	0.195716i
$646$		0			0
$647$	−3.08669	−	1.78210i	−0.121350	−	0.0700616i	0.438096	−	0.898928i	$-0.355653\pi$
$647$	−3.08669	−	1.78210i	−0.121350	−	0.0700616i	−0.559446	+	0.828866i	$0.688986\pi$
$648$	−0.148586	−	0.0857864i	−0.00583703	−	0.00337001i
$649$	19.6327	+	13.6251i	0.770650	+	0.534830i
$650$			8.79045i			0.344790i
$651$		0			0
$652$	8.14214			0.318871
$653$	−10.7279	−	18.5813i	−0.419816	−	0.727143i	0.576105	−	0.817376i	$-0.304572\pi$
$653$	−10.7279	−	18.5813i	−0.419816	−	0.727143i	−0.995921	+	0.0902333i	$0.971239\pi$
$654$	3.29462	+	1.90215i	0.128830	+	0.0743800i
$655$	−6.45695	−	3.72792i	−0.252294	−	0.145662i
$656$	−2.29610	−	3.97696i	−0.0896477	−	0.155274i
$657$	28.6675			1.11842
$658$		0			0
$659$		−	9.21320i		−	0.358895i	−0.983768	−	0.179448i	$-0.942569\pi$
$659$		−	9.21320i		−	0.358895i	0.983768	−	0.179448i	$-0.0574311\pi$
$660$	2.21541	−	3.19224i	0.0862347	−	0.124258i
$661$	28.9645	+	16.7227i	1.12659	+	0.650437i	0.943075	−	0.332580i	$-0.107919\pi$
$661$	28.9645	+	16.7227i	1.12659	+	0.650437i	0.183515	+	0.983017i	$0.441252\pi$
$662$	−17.7408	−	10.2426i	−0.689515	−	0.398092i
$663$		0			0
$664$			13.3827i			0.519348i
$665$		0			0
$666$			10.9706i			0.425101i
$667$	−9.50079	+	5.48528i	−0.367872	+	0.212391i
$668$	−10.1355	+	17.5552i	−0.392153	+	0.679230i
$669$	4.27208	−	7.39946i	0.165168	−	0.286079i
$670$	6.30864	+	10.9269i	0.243724	+	0.422143i
$671$	7.83938	+	16.6298i	0.302636	+	0.641988i
$672$		0			0
$673$			45.9411i			1.77090i	0.464734	+	0.885450i	$0.346150\pi$
$673$			45.9411i			1.77090i	−0.464734	+	0.885450i	$0.653850\pi$
$674$	13.2426	+	22.9369i	0.510087	+	0.883497i
$675$	17.3277	+	10.0042i	0.666944	+	0.385060i
$676$	−3.86396	+	6.69258i	−0.148614	+	0.257407i
$677$	9.93850	+	17.2140i	0.381968	+	0.661588i	0.991343	−	0.131294i	$-0.0419132\pi$
$677$	9.93850	+	17.2140i	0.381968	+	0.661588i	−0.609376	+	0.792882i	$0.708580\pi$
$678$	−1.53073			−0.0587875
$679$		0			0
$680$		0			0
$681$	0.891519	−	0.514719i	0.0341631	−	0.0197241i
$682$	4.62533	+	0.385197i	0.177113	+	0.0147499i
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$	−5.06774	−	8.77758i	−0.193770	−	0.335619i
$685$		−	18.3688i		−	0.701836i
$686$		0			0
$687$	−30.8284			−1.17618
$688$	−3.67423	+	2.12132i	−0.140079	+	0.0808746i
$689$	−5.14933	+	8.91890i	−0.196174	+	0.339783i
$690$	−6.33386	−	3.65685i	−0.241126	−	0.139214i
$691$	−3.68290	+	2.12632i	−0.140104	+	0.0808891i	−0.568414	−	0.822743i	$-0.692443\pi$
$691$	−3.68290	+	2.12632i	−0.140104	+	0.0808891i	0.428310	+	0.903632i	$0.359109\pi$
$692$	25.8142			0.981310
$693$		0			0
$694$	−7.75736			−0.294465
$695$	−12.5446	+	7.24264i	−0.475845	+	0.274729i
$696$	−1.64731	−	0.951076i	−0.0624412	−	0.0360504i
$697$		0			0
$698$	25.1679	−	14.5307i	0.952620	−	0.549995i
$699$	9.18440			0.347386
$700$		0			0
$701$		−	39.9411i		−	1.50856i	−0.656555	−	0.754278i	$-0.727987\pi$
$701$		−	39.9411i		−	1.50856i	0.656555	−	0.754278i	$-0.272013\pi$
$702$	−6.00000	−	10.3923i	−0.226455	−	0.392232i
$703$	16.6298	−	28.8037i	0.627206	−	1.08635i
$704$	−3.30518	−	0.275255i	−0.124569	−	0.0103741i
$705$	4.98096	−	2.87576i	0.187594	−	0.108307i
$706$	−1.21371			−0.0456785
$707$		0			0
$708$	7.79899			0.293104
$709$	11.6569	+	20.1903i	0.437782	+	0.758261i	0.997518	−	0.0704099i	$-0.0224307\pi$
$709$	11.6569	+	20.1903i	0.437782	+	0.758261i	−0.559736	+	0.828671i	$0.689097\pi$
$710$	1.08239	−	1.87476i	0.0406215	−	0.0703584i
$711$	−13.4361	−	7.75736i	−0.503895	−	0.290924i
$712$	1.78210	+	3.08669i	0.0667871	+	0.115679i
$713$		−	8.73606i		−	0.327168i
$714$		0			0
$715$	7.45584	−	3.51472i	0.278833	−	0.131443i
$716$	−2.82843	−	4.89898i	−0.105703	−	0.183083i
$717$	14.3337	−	24.8268i	0.535303	−	0.927172i
$718$	1.24264	−	2.15232i	0.0463749	−	0.0803237i
$719$	20.0927	−	11.6006i	0.749333	−	0.432628i	−0.0761198	−	0.997099i	$-0.524253\pi$
$719$	20.0927	−	11.6006i	0.749333	−	0.432628i	0.825453	+	0.564471i	$0.190920\pi$
$720$			1.97908i			0.0737558i
$721$		0			0
$722$			11.7279i			0.436468i
$723$	4.30463	−	2.48528i	0.160091	−	0.0924286i
$724$	17.7160	+	10.2283i	0.658410	+	0.380133i
$725$	5.82655	+	3.36396i	0.216393	+	0.124934i
$726$	11.7423	+	1.96945i	0.435798	+	0.0730932i
$727$		−	25.9999i		−	0.964285i	−0.876093	−	0.482142i	$-0.839859\pi$
$727$		−	25.9999i		−	0.964285i	0.876093	−	0.482142i	$-0.160141\pi$
$728$		0			0
$729$	−17.2843			−0.640158
$730$	8.48528	+	14.6969i	0.314054	+	0.543958i
$731$		0			0
$732$	5.19615	+	3.00000i	0.192055	+	0.110883i
$733$	0.475538	+	0.823656i	0.0175644	+	0.0304224i	0.874674	−	0.484712i	$-0.161075\pi$
$733$	0.475538	+	0.823656i	0.0175644	+	0.0304224i	−0.857110	+	0.515134i	$0.827742\pi$
$734$	11.1409			0.411220
$735$		0			0
$736$			6.24264i			0.230107i
$737$	−22.0428	+	31.7620i	−0.811955	+	1.16997i
$738$	−7.27159	−	4.19825i	−0.267671	−	0.154540i
$739$	−20.7846	−	12.0000i	−0.764574	−	0.441427i	0.0663614	−	0.997796i	$-0.478861\pi$
$739$	−20.7846	−	12.0000i	−0.764574	−	0.441427i	−0.830936	+	0.556369i	$0.812194\pi$
$740$	−5.62427	+	3.24718i	−0.206752	+	0.119369i
$741$			13.7766i			0.506096i
$742$		0			0
$743$		−	36.4264i		−	1.33636i	−0.744002	−	0.668178i	$-0.767075\pi$
$743$		−	36.4264i		−	1.33636i	0.744002	−	0.668178i	$-0.232925\pi$
$744$	1.31178	−	0.757359i	0.0480924	−	0.0277661i
$745$	−3.64113	+	6.30661i	−0.133401	+	0.231056i
$746$	10.2426	−	17.7408i	0.375010	−	0.649536i
$747$	12.2346	+	21.1910i	0.447641	+	0.775337i
$748$		0			0
$749$		0			0
$750$			10.3431i			0.377678i
$751$	−9.70711	−	16.8132i	−0.354217	−	0.613522i	0.632766	−	0.774343i	$-0.281919\pi$
$751$	−9.70711	−	16.8132i	−0.354217	−	0.613522i	−0.986984	+	0.160820i	$0.948586\pi$
$752$	−4.25151	−	2.45461i	−0.155037	−	0.0895105i
$753$	−6.58579	+	11.4069i	−0.239999	+	0.415691i
$754$	−2.01754	−	3.49448i	−0.0734744	−	0.127261i
$755$	−6.49435			−0.236354
$756$		0			0
$757$	−38.1421			−1.38630			−0.693150	−	0.720794i	$-0.743778\pi$
$757$	−38.1421			−1.38630			−0.693150	+	0.720794i	$0.743778\pi$
$758$	−10.0951	+	5.82843i	−0.366672	+	0.211698i
$759$	1.85989	−	22.3331i	0.0675099	−	0.810639i
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	−14.3337	−	24.8268i	−0.519597	−	0.899969i	−0.999741	−	0.0227789i	$-0.992749\pi$
$761$	−14.3337	−	24.8268i	−0.519597	−	0.899969i	0.480143	−	0.877190i	$-0.340585\pi$
$762$			6.49435i			0.235266i
$763$		0			0
$764$	1.75736			0.0635790
$765$		0			0
$766$	7.23252	−	12.5271i	0.261322	−	0.452622i
$767$	14.3277	+	8.27208i	0.517342	+	0.298687i
$768$	−0.937379	+	0.541196i	−0.0338248	+	0.0195287i
$769$	−6.49435			−0.234192			−0.117096	−	0.993121i	$-0.537359\pi$
$769$	−6.49435			−0.234192			−0.117096	+	0.993121i	$0.537359\pi$
$770$		0			0
$771$	23.8579			0.859220
$772$	2.15232	−	1.24264i	0.0774636	−	0.0447236i
$773$	22.2421	+	12.8415i	0.799991	+	0.461875i	0.843468	−	0.537179i	$-0.180510\pi$
$773$	22.2421	+	12.8415i	0.799991	+	0.461875i	−0.0434768	+	0.999054i	$0.513843\pi$
$774$	−3.87868	+	6.71807i	−0.139416	+	0.241476i
$775$	−4.63979	+	2.67878i	−0.166666	+	0.0962248i
$776$	−8.60474			−0.308892
$777$		0			0
$778$		−	32.0000i		−	1.14726i
$779$	12.7279	+	22.0454i	0.456025	+	0.789859i
$780$	1.34502	−	2.32965i	0.0481596	−	0.0834149i
$781$	6.61037	+	0.550510i	0.236537	+	0.0196988i
$782$		0			0
$783$	−9.18440			−0.328224
$784$		0			0
$785$	−12.4853			−0.445619
$786$	−3.72792	−	6.45695i	−0.132971	−	0.230312i
$787$	−4.39523	+	7.61276i	−0.156673	+	0.271365i	−0.933667	−	0.358143i	$-0.883410\pi$
$787$	−4.39523	+	7.61276i	−0.156673	+	0.271365i	0.776994	+	0.629508i	$0.216744\pi$
$788$	−17.7408	−	10.2426i	−0.631989	−	0.364879i
$789$	12.9887	+	22.4971i	0.462410	+	0.800918i
$790$		−	9.18440i		−	0.326766i
$791$		0			0
$792$	−5.48528	+	2.58579i	−0.194911	+	0.0918819i
$793$	6.36396	+	11.0227i	0.225991	+	0.391428i
$794$	0.858221	−	1.48648i	0.0304571	−	0.0527533i
$795$	−2.62742	+	4.55082i	−0.0931849	+	0.161401i
$796$	−21.3518	+	12.3275i	−0.756794	+	0.436935i
$797$			26.0543i			0.922892i	0.887168	+	0.461446i	$0.152669\pi$
$797$			26.0543i			0.922892i	−0.887168	+	0.461446i	$0.847331\pi$
$798$		0			0
$799$		0			0
$800$	3.31552	−	1.91421i	0.117221	−	0.0676777i
$801$	5.64379	+	3.25844i	0.199413	+	0.115131i
$802$	−0.420266	−	0.242641i	−0.0148401	−	0.00856794i
$803$	−29.6480	+	42.7206i	−1.04626	+	1.50758i
$804$			12.6173i			0.444977i
$805$		0			0
$806$	3.21320			0.113180
$807$	1.89949	+	3.29002i	0.0668654	+	0.115814i
$808$	14.4019	+	8.31492i	0.506656	+	0.292518i
$809$	12.5446	+	7.24264i	0.441045	+	0.254638i	0.704041	−	0.710159i	$-0.251377\pi$
$809$	12.5446	+	7.24264i	0.441045	+	0.254638i	−0.262996	+	0.964797i	$0.584710\pi$
$810$	−0.0928546	−	0.160829i	−0.00326258	−	0.00565095i
$811$	−6.88830			−0.241881			−0.120940	−	0.992660i	$-0.538591\pi$
$811$	−6.88830			−0.241881			−0.120940	+	0.992660i	$0.538591\pi$
$812$		0			0
$813$		−	28.9706i		−	1.01604i
$814$	−16.3485	−	11.3458i	−0.573014	−	0.397671i
$815$	7.63227	+	4.40649i	0.267347	+	0.154353i
$816$		0			0
$817$	20.3673	−	11.7591i	0.712562	−	0.411398i
$818$			37.8519i			1.32346i
$819$		0			0
$820$		−	4.97056i		−	0.173580i
$821$	11.9142	−	6.87868i	0.415809	−	0.240068i	−0.277473	−	0.960733i	$-0.589497\pi$
$821$	11.9142	−	6.87868i	0.415809	−	0.240068i	0.693283	+	0.720666i	$0.256164\pi$
$822$	9.18440	−	15.9079i	0.320343	−	0.554850i
$823$	−4.39340	+	7.60959i	−0.153144	+	0.265254i	−0.932382	−	0.361475i	$-0.882273\pi$
$823$	−4.39340	+	7.60959i	−0.153144	+	0.265254i	0.779238	+	0.626729i	$0.215607\pi$
$824$	−3.21998	−	5.57717i	−0.112173	−	0.194290i
$825$	−12.4316	+	5.86030i	−0.432812	+	0.204030i
$826$		0			0
$827$		−	16.9706i		−	0.590124i	−0.955478	−	0.295062i	$-0.904660\pi$
$827$		−	16.9706i		−	0.590124i	0.955478	−	0.295062i	$-0.0953404\pi$
$828$	5.70711	+	9.88500i	0.198336	+	0.343527i
$829$	−19.0416	−	10.9937i	−0.661344	−	0.381827i	0.131445	−	0.991323i	$-0.458038\pi$
$829$	−19.0416	−	10.9937i	−0.661344	−	0.381827i	−0.792789	+	0.609496i	$0.791372\pi$
$830$	−7.24264	+	12.5446i	−0.251396	+	0.435430i
$831$	−10.1355	−	17.5552i	−0.351596	−	0.608982i
$832$	−2.29610			−0.0796030
$833$		0			0
$834$	−14.4853			−0.501584
$835$	−19.0016	+	10.9706i	−0.657577	+	0.379652i
$836$	18.3215	+	1.52582i	0.633664	+	0.0527714i
$837$	3.65685	−	6.33386i	0.126399	−	0.218930i
$838$	−4.23671	−	7.33820i	−0.146355	−	0.253494i
$839$			27.0823i			0.934986i	0.883997	+	0.467493i	$0.154843\pi$
$839$			27.0823i			0.934986i	−0.883997	+	0.467493i	$0.845157\pi$
$840$		0			0
$841$	25.9117			0.893506
$842$	15.2913	−	8.82843i	0.526972	−	0.304248i
$843$	−6.49435	+	11.2485i	−0.223677	+	0.387421i
$844$	21.4150	+	12.3640i	0.737135	+	0.425585i
$845$	−7.24399	+	4.18232i	−0.249201	+	0.143876i
$846$	−8.97616			−0.308607
$847$		0			0
$848$	4.48528			0.154025
$849$	21.1539	−	12.2132i	0.726000	−	0.419156i
$850$		0			0
$851$	−18.7279	+	32.4377i	−0.641985	+	1.11195i
$852$	1.87476	−	1.08239i	0.0642282	−	0.0370821i
$853$	5.54328			0.189798			0.0948991	−	0.995487i	$-0.469747\pi$
$853$	5.54328			0.189798			0.0948991	+	0.995487i	$0.469747\pi$
$854$		0			0
$855$		−	10.9706i		−	0.375185i
$856$	6.36396	+	11.0227i	0.217516	+	0.376748i
$857$	−0.951076	+	1.64731i	−0.0324881	+	0.0562711i	−0.881812	−	0.471601i	$-0.843676\pi$
$857$	−0.951076	+	1.64731i	−0.0324881	+	0.0562711i	0.849324	+	0.527872i	$0.177010\pi$
$858$	8.21431	+	0.684086i	0.280432	+	0.0233543i
$859$	9.98951	−	5.76745i	0.340838	−	0.196783i	−0.319805	−	0.947483i	$-0.603617\pi$
$859$	9.98951	−	5.76745i	0.340838	−	0.196783i	0.660642	+	0.750701i	$0.270284\pi$
$860$	−4.59220			−0.156593
$861$		0			0
$862$	−2.48528			−0.0846490
$863$	15.3640	+	26.6112i	0.522995	+	0.905854i	0.999642	+	0.0267595i	$0.00851881\pi$
$863$	15.3640	+	26.6112i	0.522995	+	0.905854i	−0.476647	+	0.879095i	$0.658148\pi$
$864$	−2.61313	+	4.52607i	−0.0889003	+	0.153980i
$865$	24.1977	+	13.9706i	0.822747	+	0.475013i
$866$	−11.3379	−	19.6379i	−0.385278	−	0.667322i
$867$			18.4007i			0.624919i
$868$		0			0
$869$	25.4558	−	12.0000i	0.863530	−	0.407072i
$870$	−1.02944	−	1.78304i	−0.0349012	−	0.0604506i
$871$	−13.3827	+	23.1794i	−0.453454	+	0.785405i
$872$	1.75736	−	3.04384i	0.0595117	−	0.103077i
$873$	−13.6253	+	7.86657i	−0.461147	+	0.266243i
$874$		−	34.6047i		−	1.17052i
$875$		0			0
$876$			16.9706i			0.573382i
$877$	−46.7654	+	27.0000i	−1.57915	+	0.911725i	−0.584177	+	0.811626i	$0.698583\pi$
$877$	−46.7654	+	27.0000i	−1.57915	+	0.911725i	−0.994977	+	0.100099i	$0.968084\pi$
$878$	−5.62427	−	3.24718i	−0.189810	−	0.109587i
$879$	0.891519	+	0.514719i	0.0300702	+	0.0173610i
$880$	−2.94924	−	2.04677i	−0.0994189	−	0.0689966i
$881$			31.4888i			1.06089i	0.847721	+	0.530443i	$0.177974\pi$
$881$			31.4888i			1.06089i	−0.847721	+	0.530443i	$0.822026\pi$
$882$		0			0
$883$	−42.4264			−1.42776			−0.713881	−	0.700267i	$-0.753064\pi$
$883$	−42.4264			−1.42776			−0.713881	+	0.700267i	$0.753064\pi$
$884$		0			0
$885$	7.31061	+	4.22078i	0.245743	+	0.141880i
$886$	−19.5959	−	11.3137i	−0.658338	−	0.380091i
$887$	4.59220	+	7.95393i	0.154191	+	0.267067i	0.932764	−	0.360487i	$-0.117390\pi$
$887$	4.59220	+	7.95393i	0.154191	+	0.267067i	−0.778573	+	0.627554i	$0.784056\pi$
$888$	−6.49435			−0.217936
$889$		0			0
$890$			3.85786i			0.129316i
$891$	0.324439	−	0.467492i	0.0108691	−	0.0156616i
$892$	−6.83621	−	3.94689i	−0.228893	−	0.132151i
$893$	23.5673	+	13.6066i	0.788650	+	0.455328i
$894$	−6.30661	+	3.64113i	−0.210925	+	0.121777i
$895$		−	6.12293i		−	0.204667i
$896$		0			0
$897$		−	15.5147i		−	0.518021i
$898$	−35.2714	+	20.3640i	−1.17702	+	0.679554i
$899$	1.22964	−	2.12980i	0.0410108	−	0.0710328i
$900$	3.50000	−	6.06218i	0.116667	−	0.202073i
$901$		0			0
$902$	13.7766	−	6.49435i	0.458711	−	0.216238i
$903$		0			0
$904$			1.41421i			0.0470360i
$905$	11.0711	+	19.1757i	0.368015	+	0.637420i
$906$	−5.62427	−	3.24718i	−0.186854	−	0.107880i
$907$	0.899495	−	1.55797i	0.0298672	−	0.0517316i	−0.850705	−	0.525643i	$-0.823825\pi$
$907$	0.899495	−	1.55797i	0.0298672	−	0.0517316i	0.880573	+	0.473911i	$0.157158\pi$
$908$	−0.475538	−	0.823656i	−0.0157813	−	0.0273340i
$909$	30.4064			1.00852
$910$		0			0
$911$	38.2426			1.26704			0.633518	−	0.773728i	$-0.281610\pi$
$911$	38.2426			1.26704			0.633518	+	0.773728i	$0.281610\pi$
$912$	5.19615	−	3.00000i	0.172062	−	0.0993399i
$913$	−44.2321	−	3.68364i	−1.46387	−	0.121911i
$914$	15.7279	−	27.2416i	0.520233	−	0.901071i
$915$	3.24718	+	5.62427i	0.107348	+	0.185933i
$916$			28.4818i			0.941064i
$917$		0			0
$918$		0			0
$919$	26.3500	−	15.2132i	0.869208	−	0.501837i	0.00212280	−	0.999998i	$-0.499324\pi$
$919$	26.3500	−	15.2132i	0.869208	−	0.501837i	0.867085	+	0.498160i	$0.165991\pi$
$920$	−3.37849	+	5.85172i	−0.111386	+	0.192926i
$921$	6.97919	+	4.02944i	0.229972	+	0.132774i
$922$	25.1679	−	14.5307i	0.828861	−	0.478543i
$923$	4.59220			0.151154
$924$		0			0
$925$	22.9706			0.755267
$926$	−4.60181	+	2.65685i	−0.151225	+	0.0873096i
$927$	−10.1974	−	5.88750i	−0.334928	−	0.193371i
$928$	−0.878680	+	1.52192i	−0.0288441	+	0.0499594i
$929$	−36.5497	+	21.1020i	−1.19916	+	0.692334i	−0.960367	−	0.278738i	$-0.910084\pi$
$929$	−36.5497	+	21.1020i	−1.19916	+	0.692334i	−0.238790	+	0.971071i	$0.576751\pi$
$930$	1.63952			0.0537620
$931$		0			0
$932$		−	8.48528i		−	0.277945i
$933$	18.0711	+	31.3000i	0.591620	+	1.02472i
$934$	16.0886	−	27.8663i	0.526436	−	0.911814i
$935$		0			0
$936$	−3.63579	+	2.09913i	−0.118840	+	0.0686121i
$937$	−35.9497			−1.17443			−0.587213	−	0.809432i	$-0.699775\pi$
$937$	−35.9497			−1.17443			−0.587213	+	0.809432i	$0.699775\pi$
$938$		0			0
$939$	−11.1716			−0.364571
$940$	−2.65685	−	4.60181i	−0.0866570	−	0.150094i
$941$	20.0740	−	34.7692i	0.654393	−	1.13344i	−0.327652	−	0.944798i	$-0.606258\pi$
$941$	20.0740	−	34.7692i	0.654393	−	1.13344i	0.982046	−	0.188644i	$-0.0604092\pi$
$942$	−10.8126	−	6.24264i	−0.352293	−	0.203396i
$943$	−14.3337	−	24.8268i	−0.466771	−	0.808470i
$944$		−	7.20533i		−	0.234513i
$945$		0			0
$946$	−6.00000	−	12.7279i	−0.195077	−	0.413820i
$947$	1.75736	+	3.04384i	0.0571065	+	0.0989114i	0.893165	−	0.449728i	$-0.148479\pi$
$947$	1.75736	+	3.04384i	0.0571065	+	0.0989114i	−0.836059	+	0.548640i	$0.815146\pi$
$948$	4.59220	−	7.95393i	0.149148	−	0.258331i
$949$	−18.0000	+	31.1769i	−0.584305	+	1.01205i
$950$	−18.3788	+	10.6110i	−0.596288	+	0.344267i
$951$			24.8632i			0.806243i
$952$		0			0
$953$			45.9411i			1.48818i	0.668080	+	0.744090i	$0.267116\pi$
$953$			45.9411i			1.48818i	−0.668080	+	0.744090i	$0.732884\pi$
$954$	7.10228	−	4.10051i	0.229945	−	0.132759i
$955$	1.64731	+	0.951076i	0.0533058	+	0.0307761i
$956$	−22.9369	−	13.2426i	−0.741833	−	0.428298i
$957$	3.59691	−	5.18288i	0.116272	−	0.167539i
$958$			9.18440i			0.296735i
$959$		0			0
$960$	−1.17157			−0.0378124
$961$	−14.5208	−	25.1508i	−0.468413	−	0.811316i
$962$	−11.9309	−	6.88830i	−0.384667	−	0.222088i
$963$	20.1542	+	11.6360i	0.649460	+	0.374966i
$964$	−2.29610	−	3.97696i	−0.0739524	−	0.128089i
$965$	2.69005			0.0865957
$966$		0			0
$967$			19.4558i			0.625658i	0.949810	+	0.312829i	$0.101277\pi$
$967$			19.4558i			0.625658i	−0.949810	+	0.312829i	$0.898723\pi$
$968$	1.81954	−	10.8485i	0.0584821	−	0.348683i
$969$		0			0
$970$	−8.06591	−	4.65685i	−0.258981	−	0.149523i
$971$	−31.3884	+	18.1221i	−1.00730	+	0.581566i	−0.910401	−	0.413728i	$-0.864226\pi$
$971$	−31.3884	+	18.1221i	−1.00730	+	0.581566i	−0.0969013	+	0.995294i	$0.530893\pi$
$972$			15.4930i			0.496940i
$973$		0			0
$974$		−	2.44365i		−	0.0782996i
$975$	−8.23999	+	4.75736i	−0.263891	+	0.152357i
$976$	2.77164	−	4.80062i	0.0887180	−	0.153664i
$977$	22.1213	−	38.3153i	0.707724	−	1.22581i	−0.257976	−	0.966151i	$-0.583055\pi$
$977$	22.1213	−	38.3153i	0.707724	−	1.22581i	0.965700	−	0.259662i	$-0.0836112\pi$
$978$	4.40649	+	7.63227i	0.140904	+	0.244053i
$979$	−10.6926	+	5.04054i	−0.341737	+	0.161096i
$980$		0			0
$981$		−	6.42641i		−	0.205179i
$982$	19.9706	+	34.5900i	0.637286	+	1.10381i
$983$	−38.9736	−	22.5014i	−1.24306	−	0.717683i	−0.273347	−	0.961915i	$-0.588131\pi$
$983$	−38.9736	−	22.5014i	−1.24306	−	0.717683i	−0.969717	+	0.244232i	$0.921464\pi$
$984$	2.48528	−	4.30463i	0.0792279	−	0.137227i
$985$	−11.0866	−	19.2025i	−0.353247	−	0.611842i
$986$		0			0
$987$		0			0
$988$	12.7279			0.404929
$989$	−22.9369	+	13.2426i	−0.729352	+	0.421091i
$990$	−6.54121	−	0.544751i	−0.207893	−	0.0173133i
$991$	28.7990	−	49.8813i	0.914830	−	1.58453i	0.107680	−	0.994186i	$-0.465658\pi$
$991$	28.7990	−	49.8813i	0.914830	−	1.58453i	0.807150	−	0.590347i	$-0.201009\pi$
$992$	−0.699709	−	1.21193i	−0.0222158	−	0.0384789i
$993$		−	22.1731i		−	0.703642i
$994$		0			0
$995$	−26.6863			−0.846012
$996$	−12.5446	+	7.24264i	−0.397492	+	0.229492i
$997$	3.05020	−	5.28311i	0.0966009	−	0.167318i	−0.813675	−	0.581320i	$-0.802536\pi$
$997$	3.05020	−	5.28311i	0.0966009	−	0.167318i	0.910276	+	0.414003i	$0.135870\pi$
$998$	−24.7921	−	14.3137i	−0.784779	−	0.453093i
$999$	−27.1564	+	15.6788i	−0.859191	+	0.496054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.a.1011.7		16
7.2	even	3	inner	1078.2.i.a.901.2		16
7.3	odd	6		1078.2.c.a.1077.7	yes	8
7.4	even	3		1078.2.c.a.1077.6	yes	8
7.5	odd	6	inner	1078.2.i.a.901.3		16
7.6	odd	2	inner	1078.2.i.a.1011.6		16
11.10	odd	2	inner	1078.2.i.a.1011.3		16
77.10	even	6		1078.2.c.a.1077.3	yes	8
77.32	odd	6		1078.2.c.a.1077.2	✓	8
77.54	even	6	inner	1078.2.i.a.901.7		16
77.65	odd	6	inner	1078.2.i.a.901.6		16
77.76	even	2	inner	1078.2.i.a.1011.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.a.1077.2	✓	8	77.32	odd	6
1078.2.c.a.1077.3	yes	8	77.10	even	6
1078.2.c.a.1077.6	yes	8	7.4	even	3
1078.2.c.a.1077.7	yes	8	7.3	odd	6
1078.2.i.a.901.2		16	7.2	even	3	inner
1078.2.i.a.901.3		16	7.5	odd	6	inner
1078.2.i.a.901.6		16	77.65	odd	6	inner
1078.2.i.a.901.7		16	77.54	even	6	inner
1078.2.i.a.1011.2		16	77.76	even	2	inner
1078.2.i.a.1011.3		16	11.10	odd	2	inner
1078.2.i.a.1011.6		16	7.6	odd	2	inner
1078.2.i.a.1011.7		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.937379 + 0.541196i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.937379 - 0.541196i) q^{5} +1.08239 q^{6} -1.00000i q^{8} +(-0.914214 - 1.58346i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.937379 + 0.541196i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.937379 - 0.541196i) q^{5} +1.08239 q^{6} -1.00000i q^{8} +(-0.914214 - 1.58346i) q^{9} +(0.541196 - 0.937379i) q^{10} +(3.30518 + 0.275255i) q^{11} +(0.937379 - 0.541196i) q^{12} +2.29610 q^{13} +1.17157 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.58346 - 0.914214i) q^{18} +(2.77164 + 4.80062i) q^{19} -1.08239i q^{20} +(3.00000 - 1.41421i) q^{22} +(-3.12132 - 5.40629i) q^{23} +(0.541196 - 0.937379i) q^{24} +(-1.91421 + 3.31552i) q^{25} +(1.98848 - 1.14805i) q^{26} -5.22625i q^{27} -1.75736i q^{29} +(1.01461 - 0.585786i) q^{30} +(1.21193 + 0.699709i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.94924 + 2.04677i) q^{33} -1.82843 q^{36} +(-3.00000 - 5.19615i) q^{37} +(4.80062 + 2.77164i) q^{38} +(2.15232 + 1.24264i) q^{39} +(-0.541196 - 0.937379i) q^{40} +4.59220 q^{41} -4.24264i q^{43} +(1.89097 - 2.72474i) q^{44} +(-1.71393 - 0.989538i) q^{45} +(-5.40629 - 3.12132i) q^{46} +(4.25151 - 2.45461i) q^{47} -1.08239i q^{48} +3.82843i q^{50} +(1.14805 - 1.98848i) q^{52} +(-2.24264 + 3.88437i) q^{53} +(-2.61313 - 4.52607i) q^{54} +(3.24718 - 1.53073i) q^{55} +6.00000i q^{57} +(-0.878680 - 1.52192i) q^{58} +(6.24000 + 3.60266i) q^{59} +(0.585786 - 1.01461i) q^{60} +(2.77164 + 4.80062i) q^{61} +1.39942 q^{62} -1.00000 q^{64} +(2.15232 - 1.24264i) q^{65} +(3.57750 + 0.297934i) q^{66} +(-5.82843 + 10.0951i) q^{67} -6.75699i q^{69} +2.00000 q^{71} +(-1.58346 + 0.914214i) q^{72} +(-7.83938 + 13.5782i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(-3.58869 + 2.07193i) q^{75} +5.54328 q^{76} +2.48528 q^{78} +(7.34847 - 4.24264i) q^{79} +(-0.937379 - 0.541196i) q^{80} +(0.0857864 - 0.148586i) q^{81} +(3.97696 - 2.29610i) q^{82} -13.3827 q^{83} +(-2.12132 - 3.67423i) q^{86} +(0.951076 - 1.64731i) q^{87} +(0.275255 - 3.30518i) q^{88} +(-3.08669 + 1.78210i) q^{89} -1.97908 q^{90} -6.24264 q^{92} +(0.757359 + 1.31178i) q^{93} +(2.45461 - 4.25151i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-0.541196 - 0.937379i) q^{96} -8.60474i q^{97} +(-2.58579 - 5.48528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^9	\( 16 q + 8 q^{4} + 8 q^{9} + 64 q^{15} - 8 q^{16} + 48 q^{22} - 16 q^{23} - 8 q^{25} + 16 q^{36} - 48 q^{37} + 32 q^{53} - 48 q^{58} + 32 q^{60} - 16 q^{64} - 48 q^{67} + 32 q^{71} - 96 q^{78} + 24 q^{81} + 24 q^{88} - 32 q^{92} + 80 q^{93} - 64 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^9 + 64 * q^15 - 8 * q^16 + 48 * q^22 - 16 * q^23 - 8 * q^25 + 16 * q^36 - 48 * q^37 + 32 * q^53 - 48 * q^58 + 32 * q^60 - 16 * q^64 - 48 * q^67 + 32 * q^71 - 96 * q^78 + 24 * q^81 + 24 * q^88 - 32 * q^92 + 80 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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