LMFDB - Embedded newform 1078.2.i.a.1011.2

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			1011.2
Root			$-0.793353 - 0.608761i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.a.901.2

$q$-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} +(-1.89097 - 2.72474i) 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} +(0.297934 + 3.57750i) 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} +(-3.30518 + 0.275255i) 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} +(-2.04677 - 2.94924i) 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} +(2.72474 - 1.89097i) 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	0.204367	−	0.978894i	$-0.434486\pi$
$3$	−0.937379	−	0.541196i	−0.541196	−	0.312460i	−0.745564	+	0.666435i	$0.767820\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.937379	+	0.541196i	−0.419209	+	0.242030i	−0.694739	−	0.719262i	$-0.744480\pi$
$5$	−0.937379	+	0.541196i	−0.419209	+	0.242030i	0.275530	+	0.961292i	$0.411147\pi$
$6$	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
$11$	−1.89097	−	2.72474i	−0.570149	−	0.821541i
$11$	−1.89097	−	2.72474i	−0.570149	−	0.821541i
$12$	−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	$0.0521708\pi$
$29$			1.75736i			0.326333i	−0.986599	+	0.163167i	$0.947829\pi$
$30$	−1.01461	+	0.585786i	−0.185242	+	0.106949i
$31$	−1.21193	−	0.699709i	−0.217669	−	0.125671i	0.387201	−	0.921995i	$-0.373442\pi$
$31$	−1.21193	−	0.699709i	−0.217669	−	0.125671i	−0.604871	+	0.796324i	$0.706775\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.297934	+	3.57750i	0.0518637	+	0.622764i
$34$		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	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$	−3.30518	+	0.275255i	−0.498275	+	0.0414963i
$45$	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	−0.776926	−	0.629592i	$-0.783222\pi$
$47$	−4.25151	+	2.45461i	−0.620147	+	0.358042i	0.156779	+	0.987634i	$0.449889\pi$
$48$			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	0.0354028	−	0.999373i	$-0.488729\pi$
$59$	−6.24000	−	3.60266i	−0.812378	−	0.469027i	−0.847781	+	0.530346i	$0.822062\pi$
$60$	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
$66$	−2.04677	−	2.94924i	−0.251940	−	0.363027i
$67$	−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	−0.852745	−	0.522328i	$-0.825064\pi$
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	0.0259772	+	0.999663i	$0.491730\pi$
$80$	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
$88$	2.72474	−	1.89097i	0.290459	−	0.201578i
$89$	3.08669	−	1.78210i	0.327188	−	0.188902i	−0.327404	−	0.944885i	$-0.606174\pi$
$89$	3.08669	−	1.78210i	0.327188	−	0.188902i	0.654592	+	0.755982i	$0.272840\pi$
$90$	−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	$0.143902\pi$
$97$			8.60474i			0.873679i	−0.899539	+	0.436840i	$0.856098\pi$
$98$		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	−0.748934	−	0.662644i	$-0.769434\pi$
$103$	−5.57717	+	3.21998i	−0.549535	+	0.317274i	0.199400	+	0.979918i	$0.436101\pi$
$104$			2.29610i			0.225151i
$105$		0			0
$106$		−	4.48528i		−	0.435649i
$107$	11.0227	−	6.36396i	1.06561	−	0.615227i	0.138628	−	0.990345i	$-0.455731\pi$
$107$	11.0227	−	6.36396i	1.06561	−	0.615227i	0.926977	+	0.375117i	$0.122398\pi$
$108$	4.52607	+	2.61313i	0.435521	+	0.251448i
$109$	−3.04384	−	1.75736i	−0.291547	−	0.168324i	0.347093	−	0.937831i	$-0.387169\pi$
$109$	−3.04384	−	1.75736i	−0.291547	−	0.168324i	−0.638639	+	0.769506i	$0.720502\pi$
$110$	−3.57750	+	0.297934i	−0.341102	+	0.0284069i
$111$			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
$121$	−3.84847	+	10.3048i	−0.349861	+	0.936802i
$122$	−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	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$	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
$143$	−4.34186	−	6.25629i	−0.363084	−	0.523177i
$144$	−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	−0.241973	−	0.970283i	$-0.577795\pi$
$149$	5.82655	−	3.36396i	0.477330	−	0.275586i	0.719303	+	0.694696i	$0.244461\pi$
$150$	−2.07193	+	3.58869i	−0.169172	+	0.293015i
$151$	5.19615	+	3.00000i	0.422857	+	0.244137i	0.696299	−	0.717752i	$-0.254829\pi$
$151$	5.19615	+	3.00000i	0.422857	+	0.244137i	−0.273442	+	0.961888i	$0.588162\pi$
$152$	−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	0.842509	−	0.538683i	$-0.181078\pi$
$157$	9.98951	+	5.76745i	0.797250	+	0.460292i	−0.0452587	+	0.998975i	$0.514411\pi$
$158$	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
$165$	−2.21541	−	3.19224i	−0.172469	−	0.248515i
$166$	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	$-0.725069\pi$
$181$		−	20.4567i		−	1.52053i	0.649612	−	0.760266i	$-0.274931\pi$
$182$		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	0.420532	−	0.907278i	$-0.361843\pi$
$193$	−2.15232	−	1.24264i	−0.154927	−	0.0894472i	−0.575459	+	0.817830i	$0.695177\pi$
$194$	−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	$0.260367\pi$
$197$			20.4853i			1.45952i	−0.683706	+	0.729758i	$0.739633\pi$
$198$	−0.503284	−	6.04329i	−0.0357668	−	0.429478i
$199$	21.3518	+	12.3275i	1.51359	+	0.873870i	0.999873	+	0.0159092i	$0.00506428\pi$
$199$	21.3518	+	12.3275i	1.51359	+	0.873870i	0.513715	+	0.857961i	$0.328269\pi$
$200$	−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	$-0.675893\pi$
$211$		−	24.7279i		−	1.70234i	0.524890	−	0.851170i	$-0.324107\pi$
$212$	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
$220$	2.94924	−	2.04677i	0.198838	−	0.137993i
$221$		0			0
$222$	−3.24718	−	5.62427i	−0.217936	−	0.377477i
$223$			7.89377i			0.528606i	0.964440	+	0.264303i	$0.0851419\pi$
$223$			7.89377i			0.528606i	−0.964440	+	0.264303i	$0.914858\pi$
$224$		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	$-0.276495\pi$
$229$	24.6659	−	14.2409i	1.62997	−	0.941064i	0.984100	−	0.177616i	$-0.0568386\pi$
$230$	−6.75699			−0.445542
$231$		0			0
$232$	−1.75736			−0.115376
$233$	−7.34847	+	4.24264i	−0.481414	+	0.277945i	−0.721006	−	0.692929i	$-0.756320\pi$
$233$	−7.34847	+	4.24264i	−0.481414	+	0.277945i	0.239591	+	0.970874i	$0.422987\pi$
$234$	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	$0.327425\pi$
$239$			26.4853i			1.71319i	−0.515989	+	0.856595i	$0.672575\pi$
$240$	−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	$0.119414\pi$
$242$	−1.81954	−	10.8485i	−0.116964	−	0.697366i
$243$	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	$-0.874530\pi$
$251$		−	12.1689i		−	0.768097i	0.923313	−	0.384049i	$-0.125470\pi$
$252$		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	−0.958471	−	0.285191i	$-0.907943\pi$
$257$	−19.0888	+	11.0209i	−1.19072	+	0.687465i	−0.232253	+	0.972655i	$0.574610\pi$
$258$			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	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$	−3.57750	+	0.297934i	−0.220180	+	0.0183366i
$265$		−	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	0.404466	−	0.914553i	$-0.367457\pi$
$269$	−3.03958	−	1.75490i	−0.185327	−	0.106998i	−0.589793	+	0.807555i	$0.700791\pi$
$270$	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
$275$	12.6537	−	1.05379i	0.763044	−	0.0635462i
$276$	5.85172	+	3.37849i	0.352232	+	0.203361i
$277$	16.2189	+	9.36396i	0.974497	+	0.562626i	0.900604	−	0.434640i	$-0.143124\pi$
$277$	16.2189	+	9.36396i	0.974497	+	0.562626i	0.0738925	+	0.997266i	$0.476458\pi$
$278$	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	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$	−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
$297$	14.2402	−	9.88268i	0.826300	−	0.573451i
$298$	−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	$-0.937713\pi$
$311$	−28.9174	−	16.6955i	−1.63976	−	0.946714i	−0.658841	−	0.752282i	$-0.728953\pi$
$312$	1.24264	−	2.15232i	0.0703507	−	0.121851i
$313$	8.93841	−	5.16059i	0.505229	−	0.291694i	−0.225641	−	0.974210i	$-0.572448\pi$
$313$	8.93841	−	5.16059i	0.505229	−	0.291694i	0.730870	+	0.682516i	$0.239114\pi$
$314$	−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
$319$	4.78836	−	3.32311i	0.268096	−	0.186059i
$320$	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	$-0.743512\pi$
$337$		−	26.4853i		−	1.44275i	0.692547	−	0.721373i	$-0.256488\pi$
$338$	6.69258	−	3.86396i	0.364028	−	0.210172i
$339$	1.32565	+	0.765367i	0.0719997	+	0.0415690i
$340$		0			0
$341$	0.385197	+	4.62533i	0.0208596	+	0.250476i
$342$			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	0.669364	−	0.742935i	$-0.266567\pi$
$347$	6.71807	+	3.87868i	0.360645	+	0.208218i	−0.308719	+	0.951153i	$0.599900\pi$
$348$	−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
$352$	−0.275255	−	3.30518i	−0.0146711	−	0.176167i
$353$	1.05110	+	0.606854i	0.0559445	+	0.0322996i	0.527711	−	0.849424i	$-0.323050\pi$
$353$	1.05110	+	0.606854i	0.0559445	+	0.0322996i	−0.471767	+	0.881723i	$0.656384\pi$
$354$	−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	−0.555721	−	0.831369i	$-0.687558\pi$
$359$	−2.15232	+	1.24264i	−0.113595	+	0.0655841i	0.442126	+	0.896953i	$0.354224\pi$
$360$	−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	0.226576	−	0.973994i	$-0.427247\pi$
$367$	−9.64834	−	5.57047i	−0.503639	−	0.290776i	−0.730215	+	0.683217i	$0.760580\pi$
$368$	−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	−0.883183	−	0.469029i	$-0.844604\pi$
$373$	−17.7408	+	10.2426i	−0.918582	+	0.530344i	−0.0353999	+	0.999373i	$0.511270\pi$
$374$		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	−0.784655	−	0.619933i	$-0.787160\pi$
$383$	−12.5271	+	7.23252i	−0.640105	+	0.369565i	0.144550	+	0.989497i	$0.453827\pi$
$384$	−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
$396$	3.45750	+	4.98200i	0.173746	+	0.250355i
$397$	−1.48648	+	0.858221i	−0.0746044	+	0.0430729i	−0.536838	−	0.843685i	$-0.680381\pi$
$397$	−1.48648	+	0.858221i	−0.0746044	+	0.0430729i	0.462234	+	0.886758i	$0.347048\pi$
$398$	−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
$418$	1.52582	+	18.3215i	0.0746301	+	0.896136i
$419$			8.47343i			0.413954i	0.978346	+	0.206977i	$0.0663625\pi$
$419$			8.47343i			0.413954i	−0.978346	+	0.206977i	$0.933637\pi$
$420$		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
$429$	0.684086	+	8.21431i	0.0330280	+	0.396591i
$430$	3.97696	+	2.29610i	0.191786	+	0.110728i
$431$	2.15232	+	1.24264i	0.103673	+	0.0598559i	0.550940	−	0.834545i	$-0.314269\pi$
$431$	2.15232	+	1.24264i	0.103673	+	0.0598559i	−0.447267	+	0.894401i	$0.647603\pi$
$432$	4.52607	−	2.61313i	0.217760	−	0.125724i
$433$			22.6758i			1.08973i	0.838523	+	0.544866i	$0.183419\pi$
$433$			22.6758i			1.08973i	−0.838523	+	0.544866i	$0.816581\pi$
$434$		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
$451$	−8.68371	−	12.5126i	−0.408900	−	0.589194i
$452$	−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	−0.975795	−	0.218685i	$-0.929823\pi$
$457$	−27.2416	+	15.7279i	−1.27431	+	0.735721i	−0.298511	+	0.954406i	$0.596490\pi$
$458$	−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	−0.978565	−	0.205938i	$-0.933976\pi$
$467$	−27.8663	+	16.0886i	−1.28950	+	0.744493i	−0.310935	+	0.950431i	$0.600642\pi$
$468$	−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
$473$	11.5601	−	8.02270i	0.531535	−	0.368884i
$474$	−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	$-0.642644\pi$
$491$		−	39.9411i		−	1.80252i	0.433281	−	0.901259i	$-0.357356\pi$
$492$	−4.30463	+	2.48528i	−0.194068	+	0.112045i
$493$		0			0
$494$	−11.0227	−	6.36396i	−0.495935	−	0.286328i
$495$	−0.544751	−	6.54121i	−0.0244847	−	0.294005i
$496$			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
$506$	−1.71832	−	20.6331i	−0.0763886	−	0.917252i
$507$	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	−0.970155	−	0.242485i	$-0.922038\pi$
$509$	−28.0938	+	16.2200i	−1.24523	+	0.718937i	−0.275080	+	0.961421i	$0.588704\pi$
$510$		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	−0.145931	−	0.989295i	$-0.546618\pi$
$521$	−24.5522	−	14.1752i	−1.07565	−	0.621028i	−0.929720	+	0.368267i	$0.879951\pi$
$522$	−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
$528$	2.94924	−	2.04677i	0.128349	−	0.0890743i
$529$	−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	−0.690132	−	0.723683i	$-0.742448\pi$
$541$	−9.50079	+	5.48528i	−0.408471	+	0.235831i	0.281662	+	0.959514i	$0.409114\pi$
$542$	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	$0.171497\pi$
$547$			24.0000i			1.02617i	−0.858339	+	0.513083i	$0.828503\pi$
$548$	−8.48528	−	14.6969i	−0.362473	−	0.627822i
$549$	5.06774	−	8.77758i	0.216286	−	0.374618i
$550$	−10.4315	+	7.23944i	−0.444800	+	0.308691i
$551$	−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	0.606028	−	0.795443i	$-0.292762\pi$
$557$	5.19615	+	3.00000i	0.220168	+	0.127114i	−0.385860	+	0.922557i	$0.626095\pi$
$558$	−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	−0.933355	−	0.358954i	$-0.883134\pi$
$569$	−25.9808	+	15.0000i	−1.08917	+	0.628833i	−0.155815	+	0.987786i	$0.549800\pi$
$570$	−5.62427	−	3.24718i	−0.235575	−	0.136009i
$571$	31.1769	+	18.0000i	1.30471	+	0.753277i	0.981209	−	0.192950i	$-0.0618055\pi$
$571$	31.1769	+	18.0000i	1.30471	+	0.753277i	0.323505	+	0.946227i	$0.395139\pi$
$572$	−7.58903	+	0.632013i	−0.317313	+	0.0264258i
$573$		−	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	0.959919	−	0.280276i	$-0.0904259\pi$
$577$	28.7566	+	16.6026i	1.19715	+	0.691177i	0.237234	+	0.971453i	$0.423759\pi$
$578$	−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
$583$	14.8247	−	1.23460i	0.613975	−	0.0511318i
$584$	−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	$0.276885\pi$
$587$			37.0321i			1.52848i	−0.644933	+	0.764239i	$0.723115\pi$
$588$		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
$605$	−1.96945	−	11.7423i	−0.0800696	−	0.477392i
$606$	−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	0.239710	−	0.970845i	$-0.422948\pi$
$613$	−11.9142	−	6.87868i	−0.481211	−	0.277827i	−0.720921	+	0.693017i	$0.756281\pi$
$614$	−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	0.469829	−	0.882757i	$-0.344316\pi$
$619$	−1.48648	−	0.858221i	−0.0597468	−	0.0344948i	−0.529576	+	0.848263i	$0.677649\pi$
$620$	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
$627$	−16.3485	+	11.3458i	−0.652895	+	0.453108i
$628$	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	$0.0316891\pi$
$643$			5.04054i			0.198780i	−0.995049	+	0.0993898i	$0.968311\pi$
$644$		0			0
$645$			4.97056i			0.195716i
$646$		0			0
$647$	3.08669	+	1.78210i	0.121350	+	0.0700616i	0.559446	−	0.828866i	$-0.311014\pi$
$647$	3.08669	+	1.78210i	0.121350	+	0.0700616i	−0.438096	+	0.898928i	$0.644347\pi$
$648$	0.148586	+	0.0857864i	0.00583703	+	0.00337001i
$649$	1.98330	+	23.8149i	0.0778515	+	0.934818i
$650$		−	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	$0.0574311\pi$
$659$			9.21320i			0.358895i	−0.983768	+	0.179448i	$0.942569\pi$
$660$	−3.87226	+	0.322481i	−0.150728	+	0.0125526i
$661$	−28.9645	−	16.7227i	−1.12659	−	0.650437i	−0.183515	−	0.983017i	$-0.558748\pi$
$661$	−28.9645	−	16.7227i	−1.12659	−	0.650437i	−0.943075	+	0.332580i	$0.892081\pi$
$662$	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	$-0.653850\pi$
$673$		−	45.9411i		−	1.77090i	0.464734	−	0.885450i	$-0.346150\pi$
$674$	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
$682$	−2.64626	−	3.81306i	−0.101330	−	0.146009i
$683$	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	−0.428310	−	0.903632i	$-0.640891\pi$
$691$	3.68290	−	2.12632i	0.140104	−	0.0808891i	0.568414	+	0.822743i	$0.307557\pi$
$692$	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	$0.272013\pi$
$701$			39.9411i			1.50856i	−0.656555	+	0.754278i	$0.727987\pi$
$702$	−6.00000	−	10.3923i	−0.226455	−	0.392232i
$703$	16.6298	−	28.8037i	0.627206	−	1.08635i
$704$	1.89097	+	2.72474i	0.0712686	+	0.102693i
$705$	−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	−0.825453	−	0.564471i	$-0.809080\pi$
$719$	−20.0927	+	11.6006i	−0.749333	+	0.432628i	0.0761198	+	0.997099i	$0.475747\pi$
$720$		−	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
$726$	−4.16555	+	11.1539i	−0.154598	+	0.413958i
$727$			25.9999i			0.964285i	0.876093	+	0.482142i	$0.160141\pi$
$727$			25.9999i			0.964285i	−0.876093	+	0.482142i	$0.839859\pi$
$728$		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
$737$	38.5280	−	3.20861i	1.41920	−	0.118191i
$738$	7.27159	+	4.19825i	0.267671	+	0.154540i
$739$	20.7846	+	12.0000i	0.764574	+	0.441427i	0.830936	−	0.556369i	$-0.187806\pi$
$739$	20.7846	+	12.0000i	0.764574	+	0.441427i	−0.0663614	+	0.997796i	$0.521139\pi$
$740$	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	$0.232925\pi$
$743$			36.4264i			1.33636i	−0.744002	+	0.668178i	$0.767075\pi$
$744$	−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
$759$	18.4111	−	12.7773i	0.668279	−	0.463785i
$760$	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	0.0434768	−	0.999054i	$-0.486157\pi$
$773$	−22.2421	−	12.8415i	−0.799991	−	0.461875i	−0.843468	+	0.537179i	$0.819490\pi$
$774$	−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
$781$	−3.78194	−	5.44949i	−0.135328	−	0.194998i
$782$		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	$-0.847331\pi$
$797$		−	26.0543i		−	0.922892i	0.887168	−	0.461446i	$-0.152669\pi$
$798$		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
$803$	51.8212	−	4.31566i	1.82873	−	0.152296i
$804$		−	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	0.262996	−	0.964797i	$-0.415290\pi$
$809$	−12.5446	−	7.24264i	−0.441045	−	0.254638i	−0.704041	+	0.710159i	$0.748623\pi$
$810$	−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
$814$	−1.65153	−	19.8311i	−0.0578861	−	0.695080i
$815$	−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	−0.693283	−	0.720666i	$-0.743836\pi$
$821$	−11.9142	+	6.87868i	−0.415809	+	0.240068i	0.277473	+	0.960733i	$0.410503\pi$
$822$	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	$0.0953404\pi$
$827$			16.9706i			0.590124i	−0.955478	+	0.295062i	$0.904660\pi$
$828$	5.70711	+	9.88500i	0.198336	+	0.343527i
$829$	19.0416	+	10.9937i	0.661344	+	0.381827i	0.792789	−	0.609496i	$-0.208628\pi$
$829$	19.0416	+	10.9937i	0.661344	+	0.381827i	−0.131445	+	0.991323i	$0.541962\pi$
$830$	−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
$836$	−10.4822	−	15.1040i	−0.362533	−	0.522383i
$837$	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	$-0.845157\pi$
$839$		−	27.0823i		−	0.934986i	0.883997	−	0.467493i	$-0.154843\pi$
$840$		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	$0.177010\pi$
$858$	−4.69959	−	6.77176i	−0.160441	−	0.231184i
$859$	−9.98951	+	5.76745i	−0.340838	+	0.196783i	−0.660642	−	0.750701i	$-0.729716\pi$
$859$	−9.98951	+	5.76745i	−0.340838	+	0.196783i	0.319805	+	0.947483i	$0.396383\pi$
$860$	−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	$-0.301417\pi$
$877$	46.7654	−	27.0000i	1.57915	−	0.911725i	0.994977	−	0.100099i	$-0.0319159\pi$
$878$	5.62427	+	3.24718i	0.189810	+	0.109587i
$879$	−0.891519	−	0.514719i	−0.0300702	−	0.0173610i
$880$	−0.297934	−	3.57750i	−0.0100434	−	0.120598i
$881$		−	31.4888i		−	1.06089i	−0.847721	−	0.530443i	$-0.822026\pi$
$881$		−	31.4888i		−	1.06089i	0.847721	−	0.530443i	$-0.177974\pi$
$882$		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
$891$	−0.567080	+	0.0472263i	−0.0189979	+	0.00158214i
$892$	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
$913$	25.3062	+	36.4643i	0.837513	+	1.20679i
$914$	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	−0.867085	−	0.498160i	$-0.834009\pi$
$919$	−26.3500	+	15.2132i	−0.869208	+	0.501837i	−0.00212280	+	0.999998i	$0.500676\pi$
$920$	−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	0.238790	−	0.971071i	$-0.423249\pi$
$929$	36.5497	−	21.1020i	1.19916	−	0.692334i	0.960367	+	0.278738i	$0.0899160\pi$
$930$	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	$-0.732884\pi$
$953$		−	45.9411i		−	1.48818i	0.668080	−	0.744090i	$-0.267116\pi$
$954$	−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
$957$	−6.28696	+	0.523577i	−0.203229	+	0.0169248i
$958$		−	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	$-0.898723\pi$
$967$		−	19.4558i		−	0.625658i	0.949810	−	0.312829i	$-0.101277\pi$
$968$	−10.3048	−	3.84847i	−0.331209	−	0.123694i
$969$		0			0
$970$	8.06591	+	4.65685i	0.258981	+	0.149523i
$971$	31.3884	−	18.1221i	1.00730	−	0.581566i	0.0969013	−	0.995294i	$-0.469107\pi$
$971$	31.3884	−	18.1221i	1.00730	−	0.581566i	0.910401	+	0.413728i	$0.135774\pi$
$972$		−	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	0.969717	−	0.244232i	$-0.0785359\pi$
$983$	38.9736	+	22.5014i	1.24306	+	0.717683i	0.273347	+	0.961915i	$0.411869\pi$
$984$	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
$990$	3.74237	+	5.39248i	0.118940	+	0.171384i
$991$	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.1011.2		16
7.2	even	3	inner	1078.2.i.a.901.7		16
7.3	odd	6		1078.2.c.a.1077.2	✓	8
7.4	even	3		1078.2.c.a.1077.3	yes	8
7.5	odd	6	inner	1078.2.i.a.901.6		16
7.6	odd	2	inner	1078.2.i.a.1011.3		16
11.10	odd	2	inner	1078.2.i.a.1011.6		16
77.10	even	6		1078.2.c.a.1077.6	yes	8
77.32	odd	6		1078.2.c.a.1077.7	yes	8
77.54	even	6	inner	1078.2.i.a.901.2		16
77.65	odd	6	inner	1078.2.i.a.901.3		16
77.76	even	2	inner	1078.2.i.a.1011.7		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
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} +(-1.89097 - 2.72474i) 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} +(0.297934 + 3.57750i) 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} +(-3.30518 + 0.275255i) 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} +(-2.04677 - 2.94924i) 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} +(2.72474 - 1.89097i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more