LMFDB - Embedded newform 576.2.bd.a.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			181.3
Character	$\chi$	$=$	576.181
Dual form			576.2.bd.a.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.325482 + 1.37625i) q^{2} +(-1.78812 - 0.895889i) q^{4} +(0.967135 + 1.44742i) q^{5} +(4.53283 + 1.87756i) q^{7} +(1.81497 - 2.16931i) q^{8} +O(q^{10})$	\(q+(-0.325482 + 1.37625i) q^{2} +(-1.78812 - 0.895889i) q^{4} +(0.967135 + 1.44742i) q^{5} +(4.53283 + 1.87756i) q^{7} +(1.81497 - 2.16931i) q^{8} +(-2.30680 + 0.859909i) q^{10} +(0.540778 - 2.71867i) q^{11} +(1.42546 - 2.13334i) q^{13} +(-4.05935 + 5.62719i) q^{14} +(2.39477 + 3.20392i) q^{16} +(2.43954 - 2.43954i) q^{17} +(-1.88371 - 1.25865i) q^{19} +(-0.432628 - 3.45461i) q^{20} +(3.56556 + 1.62913i) q^{22} +(0.690956 + 1.66811i) q^{23} +(0.753743 - 1.81970i) q^{25} +(2.47205 + 2.65615i) q^{26} +(-6.42318 - 7.41822i) q^{28} +(1.50522 + 7.56726i) q^{29} +3.63299i q^{31} +(-5.18884 + 2.25298i) q^{32} +(2.56339 + 4.15144i) q^{34} +(1.66624 + 8.37677i) q^{35} +(-5.55115 + 3.70916i) q^{37} +(2.34533 - 2.18278i) q^{38} +(4.89522 + 0.529009i) q^{40} +(0.926510 + 2.23679i) q^{41} +(-6.41133 - 1.27529i) q^{43} +(-3.40261 + 4.37685i) q^{44} +(-2.52064 + 0.407986i) q^{46} +(-3.58669 + 3.58669i) q^{47} +(12.0716 + 12.0716i) q^{49} +(2.25903 + 1.62962i) q^{50} +(-4.46013 + 2.53763i) q^{52} +(0.513941 - 2.58375i) q^{53} +(4.45807 - 1.84659i) q^{55} +(12.3000 - 6.42539i) q^{56} +(-10.9044 - 0.391449i) q^{58} +(-5.40361 - 8.08707i) q^{59} +(13.1016 - 2.60608i) q^{61} +(-4.99991 - 1.18248i) q^{62} +(-1.41178 - 7.87444i) q^{64} +4.46645 q^{65} +(-2.72425 + 0.541887i) q^{67} +(-6.54775 + 2.17664i) q^{68} +(-12.0708 - 0.433324i) q^{70} +(-4.17620 - 1.72984i) q^{71} +(-5.46867 + 2.26520i) q^{73} +(-3.29793 - 8.84703i) q^{74} +(2.24069 + 3.93822i) q^{76} +(7.55573 - 11.3080i) q^{77} +(-5.71185 - 5.71185i) q^{79} +(-2.32135 + 6.56485i) q^{80} +(-3.37995 + 0.547072i) q^{82} +(-10.3786 - 6.93477i) q^{83} +(5.89040 + 1.17167i) q^{85} +(3.84189 - 8.40850i) q^{86} +(-4.91614 - 6.10742i) q^{88} +(-3.49372 + 8.43458i) q^{89} +(10.4668 - 6.99371i) q^{91} +(0.258932 - 3.60181i) q^{92} +(-3.76877 - 6.10358i) q^{94} -3.94381i q^{95} -9.58124i q^{97} +(-20.5426 + 12.6844i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	−0.325482	+	1.37625i	−0.230151	+	0.973155i
$2$	−0.325482	+	1.37625i	−0.230151	+	0.973155i
$3$		0			0
$3$		0			0
$4$	−1.78812	−	0.895889i	−0.894061	−	0.447945i
$5$	0.967135	+	1.44742i	0.432516	+	0.647306i	0.982150	−	0.188100i	$-0.0602328\pi$
$5$	0.967135	+	1.44742i	0.432516	+	0.647306i	−0.549634	+	0.835406i	$0.685233\pi$
$6$		0			0
$7$	4.53283	+	1.87756i	1.71325	+	0.709651i	0.999961	+	0.00878062i	$0.00279499\pi$
$7$	4.53283	+	1.87756i	1.71325	+	0.709651i	0.713288	+	0.700871i	$0.247205\pi$
$8$	1.81497	−	2.16931i	0.641688	−	0.766966i
$9$		0			0
$10$	−2.30680	+	0.859909i	−0.729473	+	0.271927i
$11$	0.540778	−	2.71867i	0.163051	−	0.819711i	−0.809518	−	0.587095i	$-0.800271\pi$
$11$	0.540778	−	2.71867i	0.163051	−	0.819711i	0.972569	−	0.232616i	$-0.0747286\pi$
$12$		0			0
$13$	1.42546	−	2.13334i	0.395350	−	0.591683i	−0.579383	−	0.815055i	$-0.696706\pi$
$13$	1.42546	−	2.13334i	0.395350	−	0.591683i	0.974733	+	0.223372i	$0.0717065\pi$
$14$	−4.05935	+	5.62719i	−1.08491	+	1.50393i
$15$		0			0
$16$	2.39477	+	3.20392i	0.598691	+	0.800980i
$17$	2.43954	−	2.43954i	0.591675	−	0.591675i	−0.346409	−	0.938084i	$-0.612599\pi$
$17$	2.43954	−	2.43954i	0.591675	−	0.591675i	0.938084	+	0.346409i	$0.112599\pi$
$18$		0			0
$19$	−1.88371	−	1.25865i	−0.432152	−	0.288755i	0.320406	−	0.947280i	$-0.396181\pi$
$19$	−1.88371	−	1.25865i	−0.432152	−	0.288755i	−0.752559	+	0.658525i	$0.771181\pi$
$20$	−0.432628	−	3.45461i	−0.0967387	−	0.772474i
$21$		0			0
$22$	3.56556	+	1.62913i	0.760180	+	0.347331i
$23$	0.690956	+	1.66811i	0.144074	+	0.347826i	0.979400	−	0.201929i	$-0.0647211\pi$
$23$	0.690956	+	1.66811i	0.144074	+	0.347826i	−0.835326	+	0.549755i	$0.814721\pi$
$24$		0			0
$25$	0.753743	−	1.81970i	0.150749	−	0.363939i
$26$	2.47205	+	2.65615i	0.484809	+	0.520913i
$27$		0			0
$28$	−6.42318	−	7.41822i	−1.21387	−	1.40191i
$29$	1.50522	+	7.56726i	0.279513	+	1.40521i	0.824073	+	0.566483i	$0.191697\pi$
$29$	1.50522	+	7.56726i	0.279513	+	1.40521i	−0.544560	+	0.838722i	$0.683303\pi$
$30$		0			0
$31$			3.63299i			0.652505i	0.945283	+	0.326253i	$0.105786\pi$
$31$			3.63299i			0.652505i	−0.945283	+	0.326253i	$0.894214\pi$
$32$	−5.18884	+	2.25298i	−0.917267	+	0.398273i
$33$		0			0
$34$	2.56339	+	4.15144i	0.439617	+	0.711966i
$35$	1.66624	+	8.37677i	0.281646	+	1.41593i
$36$		0			0
$37$	−5.55115	+	3.70916i	−0.912603	+	0.609782i	−0.920737	−	0.390185i	$-0.872411\pi$
$37$	−5.55115	+	3.70916i	−0.912603	+	0.609782i	0.00813317	+	0.999967i	$0.497411\pi$
$38$	2.34533	−	2.18278i	0.380464	−	0.354094i
$39$		0			0
$40$	4.89522	+	0.529009i	0.774002	+	0.0836437i
$41$	0.926510	+	2.23679i	0.144697	+	0.349328i	0.979567	−	0.201118i	$-0.0644575\pi$
$41$	0.926510	+	2.23679i	0.144697	+	0.349328i	−0.834870	+	0.550446i	$0.814458\pi$
$42$		0			0
$43$	−6.41133	−	1.27529i	−0.977718	−	0.194480i	−0.319730	−	0.947509i	$-0.603592\pi$
$43$	−6.41133	−	1.27529i	−0.977718	−	0.194480i	−0.657988	+	0.753028i	$0.728592\pi$
$44$	−3.40261	+	4.37685i	−0.512962	+	0.659834i
$45$		0			0
$46$	−2.52064	+	0.407986i	−0.371647	+	0.0601542i
$47$	−3.58669	+	3.58669i	−0.523172	+	0.523172i	−0.918528	−	0.395356i	$-0.870621\pi$
$47$	−3.58669	+	3.58669i	−0.523172	+	0.523172i	0.395356	+	0.918528i	$0.370621\pi$
$48$		0			0
$49$	12.0716	+	12.0716i	1.72451	+	1.72451i
$50$	2.25903	+	1.62962i	0.319475	+	0.230463i
$51$		0			0
$52$	−4.46013	+	2.53763i	−0.618509	+	0.351906i
$53$	0.513941	−	2.58375i	0.0705952	−	0.354906i	−0.929301	−	0.369324i	$-0.879589\pi$
$53$	0.513941	−	2.58375i	0.0705952	−	0.354906i	0.999896	+	0.0144176i	$0.00458942\pi$
$54$		0			0
$55$	4.45807	−	1.84659i	0.601126	−	0.248994i
$56$	12.3000	−	6.42539i	1.64365	−	0.858629i
$57$		0			0
$58$	−10.9044	−	0.391449i	−1.43181	−	0.0513997i
$59$	−5.40361	−	8.08707i	−0.703490	−	1.05285i	−0.995344	−	0.0963843i	$-0.969272\pi$
$59$	−5.40361	−	8.08707i	−0.703490	−	1.05285i	0.291854	−	0.956463i	$-0.405728\pi$
$60$		0			0
$61$	13.1016	−	2.60608i	1.67749	−	0.333674i	0.737624	−	0.675211i	$-0.235948\pi$
$61$	13.1016	−	2.60608i	1.67749	−	0.333674i	0.939868	+	0.341537i	$0.110948\pi$
$62$	−4.99991	−	1.18248i	−0.634989	−	0.150174i
$63$		0			0
$64$	−1.41178	−	7.87444i	−0.176472	−	0.984306i
$65$	4.46645			0.553995
$66$		0			0
$67$	−2.72425	+	0.541887i	−0.332820	+	0.0662021i	−0.358672	−	0.933464i	$-0.616770\pi$
$67$	−2.72425	+	0.541887i	−0.332820	+	0.0662021i	0.0258515	+	0.999666i	$0.491770\pi$
$68$	−6.54775	+	2.17664i	−0.794031	+	0.263956i
$69$		0			0
$70$	−12.0708	−	0.433324i	−1.44274	−	0.0517921i
$71$	−4.17620	−	1.72984i	−0.495623	−	0.205294i	0.120848	−	0.992671i	$-0.461439\pi$
$71$	−4.17620	−	1.72984i	−0.495623	−	0.205294i	−0.616472	+	0.787377i	$0.711439\pi$
$72$		0			0
$73$	−5.46867	+	2.26520i	−0.640059	+	0.265121i	−0.679020	−	0.734119i	$-0.737595\pi$
$73$	−5.46867	+	2.26520i	−0.640059	+	0.265121i	0.0389610	+	0.999241i	$0.487595\pi$
$74$	−3.29793	−	8.84703i	−0.383376	−	1.02845i
$75$		0			0
$76$	2.24069	+	3.93822i	0.257025	+	0.451745i
$77$	7.55573	−	11.3080i	0.861056	−	1.28866i
$78$		0			0
$79$	−5.71185	−	5.71185i	−0.642633	−	0.642633i	0.308569	−	0.951202i	$-0.400150\pi$
$79$	−5.71185	−	5.71185i	−0.642633	−	0.642633i	−0.951202	+	0.308569i	$0.900150\pi$
$80$	−2.32135	+	6.56485i	−0.259535	+	0.733973i
$81$		0			0
$82$	−3.37995	+	0.547072i	−0.373253	+	0.0604140i
$83$	−10.3786	−	6.93477i	−1.13920	−	0.761189i	−0.164871	−	0.986315i	$-0.552721\pi$
$83$	−10.3786	−	6.93477i	−1.13920	−	0.761189i	−0.974330	+	0.225126i	$0.927721\pi$
$84$		0			0
$85$	5.89040	+	1.17167i	0.638903	+	0.127086i
$86$	3.84189	−	8.40850i	0.414282	−	0.906712i
$87$		0			0
$88$	−4.91614	−	6.10742i	−0.524063	−	0.651053i
$89$	−3.49372	+	8.43458i	−0.370333	+	0.894064i	0.623360	+	0.781935i	$0.285767\pi$
$89$	−3.49372	+	8.43458i	−0.370333	+	0.894064i	−0.993694	+	0.112129i	$0.964233\pi$
$90$		0			0
$91$	10.4668	−	6.99371i	1.09722	−	0.733141i
$92$	0.258932	−	3.60181i	0.0269955	−	0.375515i
$93$		0			0
$94$	−3.76877	−	6.10358i	−0.388719	−	0.629536i
$95$		−	3.94381i		−	0.404626i
$96$		0			0
$97$		−	9.58124i		−	0.972828i	−0.873728	−	0.486414i	$-0.838305\pi$
$97$		−	9.58124i		−	0.972828i	0.873728	−	0.486414i	$-0.161695\pi$
$98$	−20.5426	+	12.6844i	−2.07512	+	1.28132i
$99$		0			0
$100$	−2.97803	+	2.57857i	−0.297803	+	0.257857i
$101$	3.78774	−	2.53089i	0.376894	−	0.251833i	−0.352666	−	0.935749i	$-0.614725\pi$
$101$	3.78774	−	2.53089i	0.376894	−	0.251833i	0.729560	+	0.683917i	$0.239725\pi$
$102$		0			0
$103$	−0.503843	+	1.21638i	−0.0496451	+	0.119854i	−0.946756	−	0.321951i	$-0.895662\pi$
$103$	−0.503843	+	1.21638i	−0.0496451	+	0.119854i	0.897111	+	0.441804i	$0.145662\pi$
$104$	−2.04072	−	6.96420i	−0.200109	−	0.682896i
$105$		0			0
$106$	3.38861	+	1.54828i	0.329131	+	0.150382i
$107$	3.54726	+	0.705594i	0.342927	+	0.0682124i	0.363549	−	0.931575i	$-0.381565\pi$
$107$	3.54726	+	0.705594i	0.342927	+	0.0682124i	−0.0206225	+	0.999787i	$0.506565\pi$
$108$		0			0
$109$	−7.61993	−	5.09147i	−0.729857	−	0.487675i	0.134272	−	0.990944i	$-0.457130\pi$
$109$	−7.61993	−	5.09147i	−0.729857	−	0.487675i	−0.864129	+	0.503270i	$0.832130\pi$
$110$	1.09035	+	6.73645i	0.103961	+	0.642295i
$111$		0			0
$112$	4.83952	+	19.0191i	0.457292	+	1.79714i
$113$	9.25522	+	9.25522i	0.870658	+	0.870658i	0.992544	−	0.121886i	$-0.0388944\pi$
$113$	9.25522	+	9.25522i	0.870658	+	0.870658i	−0.121886	+	0.992544i	$0.538894\pi$
$114$		0			0
$115$	−1.74621	+	2.61340i	−0.162835	+	0.243700i
$116$	4.08791	−	14.8797i	0.379552	−	1.38155i
$117$		0			0
$118$	12.8886	−	4.80451i	1.18649	−	0.442291i
$119$	15.6384	−	6.47764i	1.43357	−	0.593804i
$120$		0			0
$121$	3.06392	+	1.26912i	0.278539	+	0.115374i
$122$	−0.677738	+	18.8793i	−0.0613595	+	1.70926i
$123$		0			0
$124$	3.25476	−	6.49624i	0.292286	−	0.583380i
$125$	11.8996	−	2.36697i	1.06433	−	0.211709i
$126$		0			0
$127$	8.28837			0.735474			0.367737	−	0.929930i	$-0.380133\pi$
$127$	8.28837			0.735474			0.367737	+	0.929930i	$0.380133\pi$
$128$	11.2967	+	0.620033i	0.998497	+	0.0548037i
$129$		0			0
$130$	−1.45375	+	6.14695i	−0.127502	+	0.539123i
$131$	−12.8274	+	2.55153i	−1.12074	+	0.222928i	−0.720480	−	0.693475i	$-0.756079\pi$
$131$	−12.8274	+	2.55153i	−1.12074	+	0.222928i	−0.400256	+	0.916404i	$0.631079\pi$
$132$		0			0
$133$	−6.17534	−	9.24205i	−0.535470	−	0.801387i
$134$	0.140923	−	3.92562i	0.0121739	−	0.339122i
$135$		0			0
$136$	−0.864420	−	9.71979i	−0.0741234	−	0.833465i
$137$	3.42304	−	1.41787i	0.292450	−	0.121137i	−0.231635	−	0.972803i	$-0.574407\pi$
$137$	3.42304	−	1.41787i	0.292450	−	0.121137i	0.524085	+	0.851666i	$0.324407\pi$
$138$		0			0
$139$	−3.82451	+	19.2271i	−0.324391	+	1.63082i	0.382822	+	0.923822i	$0.374952\pi$
$139$	−3.82451	+	19.2271i	−0.324391	+	1.63082i	−0.707213	+	0.707001i	$0.750048\pi$
$140$	4.52521	−	16.4715i	0.382450	−	1.39209i
$141$		0			0
$142$	3.73996	−	5.18446i	0.313851	−	0.435070i
$143$	−5.02901	−	5.02901i	−0.420547	−	0.420547i
$144$		0			0
$145$	−9.49725	+	9.49725i	−0.788704	+	0.788704i
$146$	−1.33752	−	8.26353i	−0.110694	−	0.683895i
$147$		0			0
$148$	13.2491	−	1.65922i	1.08907	−	0.136387i
$149$	−9.20724	−	1.83143i	−0.754287	−	0.150037i	−0.197053	−	0.980393i	$-0.563137\pi$
$149$	−9.20724	−	1.83143i	−0.754287	−	0.150037i	−0.557234	+	0.830356i	$0.688137\pi$
$150$		0			0
$151$	−6.60900	−	15.9555i	−0.537833	−	1.29844i	−0.926233	−	0.376952i	$-0.876972\pi$
$151$	−6.60900	−	15.9555i	−0.537833	−	1.29844i	0.388400	−	0.921491i	$-0.373028\pi$
$152$	−6.14928	+	1.80192i	−0.498772	+	0.146155i
$153$		0			0
$154$	13.1033	+	14.0791i	1.05589	+	1.13453i
$155$	−5.25847	+	3.51360i	−0.422370	+	0.282219i
$156$		0			0
$157$	−0.838120	−	4.21351i	−0.0668893	−	0.336275i	0.932821	−	0.360340i	$-0.117339\pi$
$157$	−0.838120	−	4.21351i	−0.0668893	−	0.336275i	−0.999710	+	0.0240647i	$0.992339\pi$
$158$	9.72003	−	6.00182i	0.773284	−	0.477479i
$159$		0			0
$160$	−8.27931	−	5.33150i	−0.654537	−	0.421492i
$161$			8.85860i			0.698155i
$162$		0			0
$163$	1.20061	+	6.03588i	0.0940391	+	0.472766i	0.998893	+	0.0470438i	$0.0149800\pi$
$163$	1.20061	+	6.03588i	0.0940391	+	0.472766i	−0.904854	+	0.425723i	$0.860020\pi$
$164$	0.347205	−	4.82971i	0.0271121	−	0.377137i
$165$		0			0
$166$	12.9220	−	12.0264i	1.00294	−	0.933430i
$167$	2.59281	−	6.25960i	0.200638	−	0.484382i	−0.791251	−	0.611492i	$-0.790570\pi$
$167$	2.59281	−	6.25960i	0.200638	−	0.484382i	0.991889	+	0.127109i	$0.0405698\pi$
$168$		0			0
$169$	2.45565	+	5.92846i	0.188896	+	0.456035i
$170$	−3.52973	+	7.72530i	−0.270718	+	0.592503i
$171$		0			0
$172$	10.3217	+	8.02422i	0.787024	+	0.611841i
$173$	−13.9780	−	9.33980i	−1.06273	−	0.710092i	−0.104046	−	0.994572i	$-0.533179\pi$
$173$	−13.9780	−	9.33980i	−1.06273	−	0.710092i	−0.958682	+	0.284480i	$0.908179\pi$
$174$		0			0
$175$	6.83318	−	6.83318i	0.516540	−	0.516540i
$176$	10.0055	−	4.77798i	0.754189	−	0.360154i
$177$		0			0
$178$	−10.4709	−	7.55353i	−0.784830	−	0.566161i
$179$	10.0942	−	15.1070i	0.754476	−	1.12915i	−0.233167	−	0.972437i	$-0.574909\pi$
$179$	10.0942	−	15.1070i	0.754476	−	1.12915i	0.987644	−	0.156717i	$-0.0500911\pi$
$180$		0			0
$181$	1.33053	−	6.68904i	0.0988977	−	0.497192i	−0.899308	−	0.437316i	$-0.855929\pi$
$181$	1.33053	−	6.68904i	0.0988977	−	0.497192i	0.998206	−	0.0598766i	$-0.0190707\pi$
$182$	6.21833	+	16.6813i	0.460933	+	1.23650i
$183$		0			0
$184$	4.87271	+	1.52868i	0.359221	+	0.112696i
$185$	−10.7374	−	4.44759i	−0.789431	−	0.326993i
$186$		0			0
$187$	−5.31306	−	7.95156i	−0.388530	−	0.581476i
$188$	9.62672	−	3.20016i	0.702100	−	0.233396i
$189$		0			0
$190$	5.42766	+	1.28364i	0.393764	+	0.0931249i
$191$	−4.13034			−0.298861			−0.149430	−	0.988772i	$-0.547744\pi$
$191$	−4.13034			−0.298861			−0.149430	+	0.988772i	$0.547744\pi$
$192$		0			0
$193$	2.74997			0.197947			0.0989737	−	0.995090i	$-0.468444\pi$
$193$	2.74997			0.197947			0.0989737	+	0.995090i	$0.468444\pi$
$194$	13.1862	+	3.11852i	0.946712	+	0.223897i
$195$		0			0
$196$	−10.7707	−	32.4003i	−0.769334	−	2.31431i
$197$	1.52669	+	2.28486i	0.108772	+	0.162789i	0.881862	−	0.471507i	$-0.156290\pi$
$197$	1.52669	+	2.28486i	0.108772	+	0.162789i	−0.773090	+	0.634296i	$0.781290\pi$
$198$		0			0
$199$	0.831551	+	0.344440i	0.0589471	+	0.0244167i	0.411962	−	0.911201i	$-0.364844\pi$
$199$	0.831551	+	0.344440i	0.0589471	+	0.0244167i	−0.353015	+	0.935618i	$0.614844\pi$
$200$	−2.57946	−	4.93779i	−0.182395	−	0.349155i
$201$		0			0
$202$	2.25029	+	6.03663i	0.158330	+	0.424736i
$203$	−7.38507	+	37.1273i	−0.518331	+	2.60582i
$204$		0			0
$205$	−2.34152	+	3.50433i	−0.163539	+	0.244753i
$206$	−1.51006	−	1.08932i	−0.105211	−	0.0758968i
$207$		0			0
$208$	10.2487	−	0.541817i	0.710619	−	0.0375682i
$209$	−4.44054	+	4.44054i	−0.307158	+	0.307158i
$210$		0			0
$211$	−11.5419	−	7.71208i	−0.794581	−	0.530922i	0.0907556	−	0.995873i	$-0.471072\pi$
$211$	−11.5419	−	7.71208i	−0.794581	−	0.530922i	−0.885336	+	0.464951i	$0.846072\pi$
$212$	−3.23375	+	4.15964i	−0.222095	+	0.285685i
$213$		0			0
$214$	−2.12564	+	4.65226i	−0.145306	+	0.318022i
$215$	−4.35474	−	10.5133i	−0.296991	−	0.716999i
$216$		0			0
$217$	−6.82117	+	16.4678i	−0.463051	+	1.11790i
$218$	9.48729	−	8.82974i	0.642560	−	0.598025i
$219$		0			0
$220$	−9.62592	−	0.692001i	−0.648979	−	0.0466547i
$221$	−1.72692	−	8.68183i	−0.116165	−	0.584003i
$222$		0			0
$223$			6.30327i			0.422098i	0.977475	+	0.211049i	$0.0676880\pi$
$223$			6.30327i			0.422098i	−0.977475	+	0.211049i	$0.932312\pi$
$224$	−27.7503	+	0.469989i	−1.85414	+	0.0314025i
$225$		0			0
$226$	−15.7499	+	9.72508i	−1.04767	+	0.646902i
$227$	−3.46768	−	17.4332i	−0.230158	−	1.15708i	−0.907057	−	0.421007i	$-0.861677\pi$
$227$	−3.46768	−	17.4332i	−0.230158	−	1.15708i	0.676899	−	0.736076i	$-0.263323\pi$
$228$		0			0
$229$	7.65290	−	5.11350i	0.505718	−	0.337910i	−0.276398	−	0.961043i	$-0.589141\pi$
$229$	7.65290	−	5.11350i	0.505718	−	0.337910i	0.782115	+	0.623134i	$0.214141\pi$
$230$	−3.02832	−	3.25384i	−0.199682	−	0.214552i
$231$		0			0
$232$	19.1476	+	10.4691i	1.25710	+	0.687327i
$233$	−5.24399	−	12.6601i	−0.343545	−	0.829391i	−0.997352	−	0.0727295i	$-0.976829\pi$
$233$	−5.24399	−	12.6601i	−0.343545	−	0.829391i	0.653807	−	0.756662i	$-0.273171\pi$
$234$		0			0
$235$	−8.66026	−	1.72263i	−0.564933	−	0.112372i
$236$	2.41720	+	19.3017i	0.157346	+	1.25643i
$237$		0			0
$238$	3.82482	+	23.6307i	0.247926	+	1.53175i
$239$	−8.39091	+	8.39091i	−0.542763	+	0.542763i	−0.924338	−	0.381575i	$-0.875382\pi$
$239$	−8.39091	+	8.39091i	−0.542763	+	0.542763i	0.381575	+	0.924338i	$0.375382\pi$
$240$		0			0
$241$	3.97755	+	3.97755i	0.256217	+	0.256217i	0.823513	−	0.567297i	$-0.192011\pi$
$241$	3.97755	+	3.97755i	0.256217	+	0.256217i	−0.567297	+	0.823513i	$0.692011\pi$
$242$	−2.74388	+	3.80365i	−0.176383	+	0.244508i
$243$		0			0
$244$	−25.7621	−	7.07763i	−1.64925	−	0.453099i
$245$	−5.79780	+	29.1475i	−0.370408	+	1.86217i
$246$		0			0
$247$	−5.37028	+	2.22444i	−0.341703	+	0.141538i
$248$	7.88108	+	6.59377i	0.500449	+	0.418705i
$249$		0			0
$250$	−0.615556	+	17.1472i	−0.0389312	+	1.08448i
$251$	10.0908	+	15.1019i	0.636924	+	0.953224i	0.999772	+	0.0213753i	$0.00680450\pi$
$251$	10.0908	+	15.1019i	0.636924	+	0.953224i	−0.362848	+	0.931848i	$0.618196\pi$
$252$		0			0
$253$	4.90871	−	0.976404i	0.308608	−	0.0613860i
$254$	−2.69772	+	11.4069i	−0.169270	+	0.715730i
$255$		0			0
$256$	−4.53020	+	15.3453i	−0.283137	+	0.959079i
$257$	15.1836			0.947128			0.473564	−	0.880760i	$-0.342967\pi$
$257$	15.1836			0.947128			0.473564	+	0.880760i	$0.342967\pi$
$258$		0			0
$259$	−32.1266	+	6.39038i	−1.99625	+	0.397079i
$260$	−7.98656	−	4.00145i	−0.495306	−	0.248159i
$261$		0			0
$262$	0.663552	−	18.4842i	0.0409944	−	1.14196i
$263$	19.1921	+	7.94964i	1.18344	+	0.490196i	0.885613	−	0.464425i	$-0.153739\pi$
$263$	19.1921	+	7.94964i	1.18344	+	0.490196i	0.297825	+	0.954620i	$0.403739\pi$
$264$		0			0
$265$	4.23683	−	1.75495i	0.260266	−	0.107806i
$266$	14.7293	−	5.49068i	0.903112	−	0.336655i
$267$		0			0
$268$	5.35677	+	1.47167i	0.327217	+	0.0898963i
$269$	3.71107	−	5.55401i	0.226268	−	0.338634i	−0.700914	−	0.713246i	$-0.747224\pi$
$269$	3.71107	−	5.55401i	0.226268	−	0.338634i	0.927182	+	0.374612i	$0.122224\pi$
$270$		0			0
$271$	2.68097	+	2.68097i	0.162858	+	0.162858i	0.783831	−	0.620974i	$-0.213263\pi$
$271$	2.68097	+	2.68097i	0.162858	+	0.162858i	−0.620974	+	0.783831i	$0.713263\pi$
$272$	13.6582	+	1.97396i	0.828150	+	0.119689i
$273$		0			0
$274$	0.837203	+	5.17245i	0.0505773	+	0.312479i
$275$	−4.53956	−	3.03323i	−0.273746	−	0.182911i
$276$		0			0
$277$	−7.35826	−	1.46365i	−0.442115	−	0.0879421i	−0.0309870	−	0.999520i	$-0.509865\pi$
$277$	−7.35826	−	1.46365i	−0.442115	−	0.0879421i	−0.411128	+	0.911578i	$0.634865\pi$
$278$	−25.2165	−	11.5216i	−1.51238	−	0.691018i
$279$		0			0
$280$	21.1959	+	11.5890i	1.26670	+	0.692574i
$281$	8.64142	−	20.8622i	0.515504	−	1.24454i	−0.425136	−	0.905130i	$-0.639774\pi$
$281$	8.64142	−	20.8622i	0.515504	−	1.24454i	0.940640	−	0.339407i	$-0.110226\pi$
$282$		0			0
$283$	−26.0256	+	17.3898i	−1.54706	+	1.03371i	−0.569776	+	0.821800i	$0.692970\pi$
$283$	−26.0256	+	17.3898i	−1.54706	+	1.03371i	−0.977288	+	0.211915i	$0.932030\pi$
$284$	5.91781	+	6.83457i	0.351157	+	0.405557i
$285$		0			0
$286$	8.55803	−	5.28432i	0.506047	−	0.312468i
$287$			11.8786i			0.701171i
$288$		0			0
$289$			5.09731i			0.299842i
$290$	−9.97940	−	16.1618i	−0.586010	−	0.949052i
$291$		0			0
$292$	11.8080	+	0.848871i	0.691012	+	0.0496764i
$293$	−16.4610	+	10.9989i	−0.961661	+	0.642561i	−0.934082	−	0.357058i	$-0.883780\pi$
$293$	−16.4610	+	10.9989i	−0.961661	+	0.642561i	−0.0275790	+	0.999620i	$0.508780\pi$
$294$		0			0
$295$	6.47937	−	15.6426i	0.377243	−	0.910746i
$296$	−2.02886	+	18.7742i	−0.117925	+	1.09123i
$297$		0			0
$298$	5.51730	−	12.0754i	0.319609	−	0.699507i
$299$	4.54359	+	0.903776i	0.262763	+	0.0522667i
$300$		0			0
$301$	−26.6670	−	17.8183i	−1.53706	−	1.02703i
$302$	24.1099	−	3.90238i	1.38737	−	0.224557i
$303$		0			0
$304$	−0.478415	−	9.04943i	−0.0274390	−	0.519020i
$305$	16.4431	+	16.4431i	0.941531	+	0.941531i
$306$		0			0
$307$	14.1044	−	21.1087i	0.804981	−	1.20474i	−0.170652	−	0.985331i	$-0.554587\pi$
$307$	14.1044	−	21.1087i	0.804981	−	1.20474i	0.975633	−	0.219408i	$-0.0704126\pi$
$308$	−23.6413	+	13.4509i	−1.34709	+	0.766437i
$309$		0			0
$310$	−3.12405	−	8.38057i	−0.177434	−	0.475985i
$311$	−13.9327	+	5.77111i	−0.790051	+	0.327250i	−0.740964	−	0.671545i	$-0.765631\pi$
$311$	−13.9327	+	5.77111i	−0.790051	+	0.327250i	−0.0490867	+	0.998795i	$0.515631\pi$
$312$		0			0
$313$	5.08075	+	2.10452i	0.287181	+	0.118954i	0.521624	−	0.853176i	$-0.325327\pi$
$313$	5.08075	+	2.10452i	0.287181	+	0.118954i	−0.234443	+	0.972130i	$0.575327\pi$
$314$	6.07164	+	0.217962i	0.342642	+	0.0123003i
$315$		0			0
$316$	5.09630	+	15.3307i	0.286689	+	0.862417i
$317$	4.93180	−	0.980996i	0.276997	−	0.0550982i	−0.0546367	−	0.998506i	$-0.517400\pi$
$317$	4.93180	−	0.980996i	0.276997	−	0.0550982i	0.331634	+	0.943408i	$0.392400\pi$
$318$		0			0
$319$	21.3869			1.19744
$320$	10.0322	−	9.65909i	0.560820	−	0.539959i
$321$		0			0
$322$	−12.1916	−	2.88332i	−0.679413	−	0.160681i
$323$	−7.66591	+	1.52484i	−0.426543	+	0.0848446i
$324$		0			0
$325$	−2.80761	−	4.20189i	−0.155738	−	0.233079i
$326$	−8.69765	−	0.312231i	−0.481718	−	0.0172929i
$327$		0			0
$328$	6.53387	+	2.04982i	0.360773	+	0.113183i
$329$	−22.9921	+	9.52364i	−1.26760	+	0.525055i
$330$		0			0
$331$	−1.36801	+	6.87743i	−0.0751924	+	0.378018i	−0.999997	−	0.00242459i	$-0.999228\pi$
$331$	−1.36801	+	6.87743i	−0.0751924	+	0.378018i	0.924805	+	0.380442i	$0.124228\pi$
$332$	12.3454	+	21.6983i	0.677544	+	1.19085i
$333$		0			0
$334$	7.77085	+	5.60574i	0.425202	+	0.306733i
$335$	−3.41906	−	3.41906i	−0.186803	−	0.186803i
$336$		0			0
$337$	−11.6065	+	11.6065i	−0.632248	+	0.632248i	−0.948631	−	0.316383i	$-0.897531\pi$
$337$	−11.6065	+	11.6065i	−0.632248	+	0.632248i	0.316383	+	0.948631i	$0.397531\pi$
$338$	−8.95831	+	1.44998i	−0.487268	+	0.0788683i
$339$		0			0
$340$	−9.48307	−	7.37224i	−0.514291	−	0.399816i
$341$	9.87693	+	1.96464i	0.534866	+	0.106391i
$342$		0			0
$343$	18.9104	+	45.6538i	1.02107	+	2.46507i
$344$	−14.4029	+	11.5935i	−0.776550	+	0.625081i
$345$		0			0
$346$	17.4035	−	16.1973i	0.935617	−	0.870771i
$347$	−14.1994	+	9.48772i	−0.762262	+	0.509327i	−0.874897	−	0.484309i	$-0.839071\pi$
$347$	−14.1994	+	9.48772i	−0.762262	+	0.509327i	0.112635	+	0.993636i	$0.464071\pi$
$348$		0			0
$349$	−2.26631	−	11.3935i	−0.121313	−	0.609881i	−0.992832	−	0.119519i	$-0.961865\pi$
$349$	−2.26631	−	11.3935i	−0.121313	−	0.609881i	0.871519	−	0.490362i	$-0.163135\pi$
$350$	7.18008	+	11.6282i	0.383792	+	0.621556i
$351$		0			0
$352$	3.31909	+	15.3251i	0.176908	+	0.816833i
$353$		−	11.5221i		−	0.613261i	−0.951829	−	0.306631i	$-0.900798\pi$
$353$		−	11.5221i		−	0.613261i	0.951829	−	0.306631i	$-0.0992016\pi$
$354$		0			0
$355$	−1.53515	−	7.71770i	−0.0814770	−	0.409613i
$356$	13.8036	−	11.9521i	0.731592	−	0.633459i
$357$		0			0
$358$	17.5056	+	18.8092i	0.925198	+	0.994098i
$359$	1.31387	−	3.17197i	0.0693435	−	0.167410i	−0.885408	−	0.464815i	$-0.846121\pi$
$359$	1.31387	−	3.17197i	0.0693435	−	0.167410i	0.954752	+	0.297405i	$0.0961210\pi$
$360$		0			0
$361$	−5.30684	−	12.8118i	−0.279307	−	0.674307i
$362$	8.77271	+	4.00831i	0.461084	+	0.210672i
$363$		0			0
$364$	−24.9816	+	3.12850i	−1.30939	+	0.163978i
$365$	−8.56763	−	5.72471i	−0.448450	−	0.299645i
$366$		0			0
$367$	−22.5749	+	22.5749i	−1.17840	+	1.17840i	−0.198245	+	0.980152i	$0.563524\pi$
$367$	−22.5749	+	22.5749i	−1.17840	+	1.17840i	−0.980152	+	0.198245i	$0.936476\pi$
$368$	−3.68983	+	6.20851i	−0.192346	+	0.323641i
$369$		0			0
$370$	9.61582	−	13.3298i	0.499903	−	0.692981i
$371$	7.18076	−	10.7468i	0.372807	−	0.557945i
$372$		0			0
$373$	−6.61395	+	33.2506i	−0.342457	+	1.72165i	0.298793	+	0.954318i	$0.403416\pi$
$373$	−6.61395	+	33.2506i	−0.342457	+	1.72165i	−0.641250	+	0.767332i	$0.721584\pi$
$374$	12.6726	−	4.72400i	0.655286	−	0.244272i
$375$		0			0
$376$	1.27090	+	14.2904i	0.0655416	+	0.736969i
$377$	18.2892	+	7.57563i	0.941942	+	0.390165i
$378$		0			0
$379$	−11.6484	−	17.4330i	−0.598337	−	0.895474i	0.401455	−	0.915879i	$-0.368505\pi$
$379$	−11.6484	−	17.4330i	−0.598337	−	0.895474i	−0.999792	+	0.0204046i	$0.993505\pi$
$380$	−3.53321	+	7.05201i	−0.181250	+	0.361760i
$381$		0			0
$382$	1.34435	−	5.68437i	0.0687830	−	0.290838i
$383$	−0.0590227			−0.00301592			−0.00150796	−	0.999999i	$-0.500480\pi$
$383$	−0.0590227			−0.00301592			−0.00150796	+	0.999999i	$0.500480\pi$
$384$		0			0
$385$	23.6748			1.20658
$386$	−0.895067	+	3.78465i	−0.0455577	+	0.192633i
$387$		0			0
$388$	−8.58373	+	17.1324i	−0.435773	+	0.869768i
$389$	1.79208	+	2.68204i	0.0908621	+	0.135985i	0.874116	−	0.485717i	$-0.161442\pi$
$389$	1.79208	+	2.68204i	0.0908621	+	0.135985i	−0.783254	+	0.621702i	$0.786442\pi$
$390$		0			0
$391$	5.75504	+	2.38382i	0.291045	+	0.120555i
$392$	48.0965	−	4.27742i	2.42924	−	0.216042i
$393$		0			0
$394$	−3.64144	+	1.35743i	−0.183453	+	0.0683863i
$395$	2.74331	−	13.7916i	0.138031	−	0.693929i
$396$		0			0
$397$	3.22276	−	4.82320i	0.161746	−	0.242069i	−0.741740	−	0.670687i	$-0.765999\pi$
$397$	3.22276	−	4.82320i	0.161746	−	0.242069i	0.903486	+	0.428618i	$0.140999\pi$
$398$	−0.744690	+	1.03231i	−0.0373279	+	0.0517451i
$399$		0			0
$400$	7.63520	−	1.94282i	0.381760	−	0.0971408i
$401$	−18.2413	+	18.2413i	−0.910926	+	0.910926i	−0.996345	−	0.0854187i	$-0.972777\pi$
$401$	−18.2413	+	18.2413i	−0.910926	+	0.910926i	0.0854187	+	0.996345i	$0.472777\pi$
$402$		0			0
$403$	7.75043	+	5.17867i	0.386076	+	0.257968i
$404$	−9.04034	+	1.13214i	−0.449774	+	0.0563261i
$405$		0			0
$406$	−48.6927	−	22.2480i	−2.41658	−	1.10415i
$407$	7.08206	+	17.0976i	0.351045	+	0.847497i
$408$		0			0
$409$	3.91775	−	9.45829i	0.193720	−	0.467682i	−0.796936	−	0.604064i	$-0.793547\pi$
$409$	3.91775	−	9.45829i	0.193720	−	0.467682i	0.990656	+	0.136381i	$0.0435473\pi$
$410$	−4.06071	−	4.36311i	−0.200544	−	0.215479i
$411$		0			0
$412$	1.99068	−	1.72366i	0.0980737	−	0.0849185i
$413$	−9.30969	−	46.8030i	−0.458100	−	2.30302i
$414$		0			0
$415$		−	21.7291i		−	1.06664i
$416$	−2.59009	+	14.2811i	−0.126990	+	0.700189i
$417$		0			0
$418$	−4.66597	−	7.55660i	−0.228220	−	0.369606i
$419$	−6.22515	−	31.2959i	−0.304119	−	1.52891i	−0.766511	−	0.642232i	$-0.778009\pi$
$419$	−6.22515	−	31.2959i	−0.304119	−	1.52891i	0.462392	−	0.886676i	$-0.346991\pi$
$420$		0			0
$421$	9.43550	−	6.30460i	0.459858	−	0.307268i	−0.303976	−	0.952680i	$-0.598314\pi$
$421$	9.43550	−	6.30460i	0.459858	−	0.307268i	0.763835	+	0.645412i	$0.223314\pi$
$422$	14.3704	−	13.3745i	0.699542	−	0.651058i
$423$		0			0
$424$	−4.67217	−	5.80433i	−0.226901	−	0.281883i
$425$	−2.60044	−	6.27801i	−0.126140	−	0.304528i
$426$		0			0
$427$	64.2806	+	12.7862i	3.11076	+	0.618768i
$428$	−5.71081	−	4.43964i	−0.276042	−	0.214598i
$429$		0			0
$430$	15.8863	−	2.57132i	0.766103	−	0.124000i
$431$	19.4613	−	19.4613i	0.937417	−	0.937417i	−0.0607373	−	0.998154i	$-0.519345\pi$
$431$	19.4613	−	19.4613i	0.937417	−	0.937417i	0.998154	+	0.0607373i	$0.0193452\pi$
$432$		0			0
$433$	−25.2269	−	25.2269i	−1.21233	−	1.21233i	−0.970259	−	0.242069i	$-0.922174\pi$
$433$	−25.2269	−	25.2269i	−1.21233	−	1.21233i	−0.242069	−	0.970259i	$-0.577826\pi$
$434$	−20.4436	−	14.7476i	−0.981323	−	0.707907i
$435$		0			0
$436$	9.06397	+	15.9308i	0.434086	+	0.762947i
$437$	0.798020	−	4.01192i	0.0381745	−	0.191916i
$438$		0			0
$439$	26.5392	−	10.9929i	1.26665	−	0.524662i	0.354704	−	0.934979i	$-0.384582\pi$
$439$	26.5392	−	10.9929i	1.26665	−	0.524662i	0.911943	+	0.410316i	$0.134582\pi$
$440$	4.08543	−	13.0224i	0.194765	−	0.620820i
$441$		0			0
$442$	12.5104	+	0.449104i	0.595061	+	0.0213617i
$443$	−0.00461809	−	0.00691146i	−0.000219412	−	0.000328373i	0.831360	−	0.555734i	$-0.187563\pi$
$443$	−0.00461809	−	0.00691146i	−0.000219412	−	0.000328373i	−0.831579	+	0.555406i	$0.812563\pi$
$444$		0			0
$445$	−15.5873	+	3.10050i	−0.738908	+	0.146978i
$446$	−8.67487	−	2.05160i	−0.410767	−	0.0971462i
$447$		0			0
$448$	8.38539	−	38.3442i	0.396173	−	1.81160i
$449$	−13.9393			−0.657838			−0.328919	−	0.944358i	$-0.606684\pi$
$449$	−13.9393			−0.657838			−0.328919	+	0.944358i	$0.606684\pi$
$450$		0			0
$451$	6.58215	−	1.30927i	0.309941	−	0.0616511i
$452$	−8.25782	−	24.8411i	−0.388415	−	1.16843i
$453$		0			0
$454$	25.1211	+	0.901807i	1.17899	+	0.0423239i
$455$	20.2457	+	8.38604i	0.949132	+	0.393143i
$456$		0			0
$457$	−13.6237	+	5.64312i	−0.637290	+	0.263974i	−0.677847	−	0.735203i	$-0.737087\pi$
$457$	−13.6237	+	5.64312i	−0.637290	+	0.263974i	0.0405569	+	0.999177i	$0.487087\pi$
$458$	4.54657	+	12.1966i	0.212447	+	0.569912i
$459$		0			0
$460$	5.46376	−	3.10866i	0.254749	−	0.144942i
$461$	−16.5649	+	24.7911i	−0.771504	+	1.15464i	0.212616	+	0.977136i	$0.431802\pi$
$461$	−16.5649	+	24.7911i	−0.771504	+	1.15464i	−0.984120	+	0.177502i	$0.943198\pi$
$462$		0			0
$463$	−7.31500	−	7.31500i	−0.339957	−	0.339957i	0.516394	−	0.856351i	$-0.327274\pi$
$463$	−7.31500	−	7.31500i	−0.339957	−	0.339957i	−0.856351	+	0.516394i	$0.827274\pi$
$464$	−20.6402	+	22.9444i	−0.958199	+	1.06517i
$465$		0			0
$466$	19.1303	−	3.09639i	0.886193	−	0.143438i
$467$	26.6310	+	17.7943i	1.23233	+	0.823420i	0.989200	−	0.146573i	$-0.0468242\pi$
$467$	26.6310	+	17.7943i	1.23233	+	0.823420i	0.243135	+	0.969992i	$0.421824\pi$
$468$		0			0
$469$	−13.3660	−	2.65866i	−0.617185	−	0.122766i
$470$	5.18953	−	11.3580i	0.239375	−	0.523905i
$471$		0			0
$472$	−27.3507	−	2.95570i	−1.25892	−	0.136047i
$473$	−6.93421	+	16.7407i	−0.318835	+	0.769737i
$474$		0			0
$475$	−3.71020	+	2.47908i	−0.170236	+	0.113748i
$476$	−33.7666	−	2.42746i	−1.54769	−	0.111262i
$477$		0			0
$478$	−8.81689	−	14.2791i	−0.403275	−	0.653110i
$479$			24.2263i			1.10693i	0.832873	+	0.553465i	$0.186695\pi$
$479$			24.2263i			1.10693i	−0.832873	+	0.553465i	$0.813305\pi$
$480$		0			0
$481$			17.1298i			0.781050i
$482$	−6.76873	+	4.17948i	−0.308307	+	0.190370i
$483$		0			0
$484$	−4.34168	−	5.01428i	−0.197349	−	0.227922i
$485$	13.8681	−	9.26636i	0.629717	−	0.420764i
$486$		0			0
$487$	12.2953	−	29.6835i	0.557153	−	1.34509i	−0.354857	−	0.934921i	$-0.615470\pi$
$487$	12.2953	−	29.6835i	0.557153	−	1.34509i	0.912011	−	0.410167i	$-0.134530\pi$
$488$	18.1257	−	33.1514i	0.820511	−	1.50069i
$489$		0			0
$490$	−38.2272	−	17.4662i	−1.72693	−	0.789043i
$491$	17.7528	+	3.53125i	0.801173	+	0.159363i	0.578663	−	0.815567i	$-0.303575\pi$
$491$	17.7528	+	3.53125i	0.801173	+	0.159363i	0.222510	+	0.974930i	$0.428575\pi$
$492$		0			0
$493$	22.1327	+	14.7886i	0.996805	+	0.666044i
$494$	−1.31346	−	8.11487i	−0.0590953	−	0.365105i
$495$		0			0
$496$	−11.6398	+	8.70017i	−0.522643	+	0.390649i
$497$	−15.6821	−	15.6821i	−0.703440	−	0.703440i
$498$		0			0
$499$	15.7545	−	23.5782i	0.705267	−	1.05551i	−0.289875	−	0.957064i	$-0.593614\pi$
$499$	15.7545	−	23.5782i	0.705267	−	1.05551i	0.995143	−	0.0984427i	$-0.0313861\pi$
$500$	−23.3984	−	6.42826i	−1.04641	−	0.287481i
$501$		0			0
$502$	−24.0683	+	8.97201i	−1.07422	+	0.400440i
$503$	29.1486	−	12.0738i	1.29967	−	0.538342i	0.377819	−	0.925880i	$-0.376674\pi$
$503$	29.1486	−	12.0738i	1.29967	−	0.538342i	0.921854	+	0.387538i	$0.126674\pi$
$504$		0			0
$505$	7.32651	+	3.03474i	0.326025	+	0.135044i
$506$	−0.253924	+	7.07342i	−0.0112883	+	0.314452i
$507$		0			0
$508$	−14.8206	−	7.42546i	−0.657559	−	0.329452i
$509$	−5.86884	+	1.16739i	−0.260132	+	0.0517435i	−0.323433	−	0.946251i	$-0.604837\pi$
$509$	−5.86884	+	1.16739i	−0.260132	+	0.0517435i	0.0633013	+	0.997994i	$0.479837\pi$
$510$		0			0
$511$	−29.0416			−1.28473
$512$	−19.6444	−	11.2293i	−0.868169	−	0.496269i
$513$		0			0
$514$	−4.94199	+	20.8964i	−0.217982	+	0.921702i
$515$	−2.24790	+	0.447136i	−0.0990544	+	0.0197031i
$516$		0			0
$517$	7.81144	+	11.6906i	0.343547	+	0.514154i
$518$	1.66188	−	46.2942i	0.0730190	−	2.03405i
$519$		0			0
$520$	8.10647	−	9.68910i	0.355492	−	0.424895i
$521$	−26.1756	+	10.8423i	−1.14678	+	0.475010i	−0.873451	−	0.486912i	$-0.838123\pi$
$521$	−26.1756	+	10.8423i	−1.14678	+	0.475010i	−0.273325	+	0.961922i	$0.588123\pi$
$522$		0			0
$523$	−1.00914	+	5.07326i	−0.0441264	+	0.221838i	−0.996556	−	0.0829195i	$-0.973576\pi$
$523$	−1.00914	+	5.07326i	−0.0441264	+	0.221838i	0.952430	+	0.304758i	$0.0985756\pi$
$524$	25.2229	+	6.92949i	1.10187	+	0.302716i
$525$		0			0
$526$	−17.1874	+	23.8257i	−0.749406	+	1.03885i
$527$	8.86283	+	8.86283i	0.386071	+	0.386071i
$528$		0			0
$529$	13.9583	−	13.9583i	0.606881	−	0.606881i
$530$	1.03624	+	6.40213i	0.0450113	+	0.278091i
$531$		0			0
$532$	2.76241	+	22.0583i	0.119766	+	0.956350i
$533$	6.09255	+	1.21188i	0.263898	+	0.0524925i
$534$		0			0
$535$	2.40939	+	5.81678i	0.104167	+	0.251481i
$536$	−3.76891	+	6.89324i	−0.162792	+	0.297743i
$537$		0			0
$538$	6.43581	+	6.91508i	0.277467	+	0.298130i
$539$	39.3468	−	26.2907i	1.69479	−	1.13242i
$540$		0			0
$541$	0.217556	+	1.09373i	0.00935346	+	0.0470230i	0.985180	−	0.171523i	$-0.0548687\pi$
$541$	0.217556	+	1.09373i	0.00935346	+	0.0470230i	−0.975827	+	0.218546i	$0.929869\pi$
$542$	−4.56230	+	2.81708i	−0.195967	+	0.121004i
$543$		0			0
$544$	−7.16216	+	18.1546i	−0.307075	+	0.778372i
$545$		−	15.9534i		−	0.683368i
$546$		0			0
$547$	−1.95857	−	9.84642i	−0.0837426	−	0.421002i	−0.999801	−	0.0199572i	$-0.993647\pi$
$547$	−1.95857	−	9.84642i	−0.0837426	−	0.421002i	0.916058	−	0.401045i	$-0.131353\pi$
$548$	−7.39107	−	0.531339i	−0.315731	−	0.0226977i
$549$		0			0
$550$	5.65203	−	5.26030i	0.241003	−	0.224300i
$551$	6.68916	−	16.1491i	0.284968	−	0.687973i
$552$		0			0
$553$	−15.1665	−	36.6152i	−0.644946	−	1.55704i
$554$	4.40933	−	9.65040i	0.187334	−	0.410006i
$555$		0			0
$556$	24.0641	−	30.9541i	1.02054	−	1.31275i
$557$	20.7214	+	13.8456i	0.877994	+	0.586657i	0.910820	−	0.412804i	$-0.135451\pi$
$557$	20.7214	+	13.8456i	0.877994	+	0.586657i	−0.0328255	+	0.999461i	$0.510451\pi$
$558$		0			0
$559$	−11.8597	+	11.8597i	−0.501612	+	0.501612i
$560$	−22.8482	+	25.3989i	−0.965514	+	1.07330i
$561$		0			0
$562$	25.8990	+	18.6830i	1.09248	+	0.788096i
$563$	−22.4818	+	33.6463i	−0.947493	+	1.41802i	−0.0394146	+	0.999223i	$0.512549\pi$
$563$	−22.4818	+	33.6463i	−0.947493	+	1.41802i	−0.908078	+	0.418800i	$0.862451\pi$
$564$		0			0
$565$	−4.44514	+	22.3472i	−0.187008	+	0.940155i
$566$	−15.4618	−	41.4778i	−0.649907	−	1.74344i
$567$		0			0
$568$	−11.3322	+	5.91985i	−0.475489	+	0.248391i
$569$	−21.2575	−	8.80516i	−0.891163	−	0.369132i	−0.110347	−	0.993893i	$-0.535196\pi$
$569$	−21.2575	−	8.80516i	−0.891163	−	0.369132i	−0.780816	+	0.624762i	$0.785196\pi$
$570$		0			0
$571$	21.4891	+	32.1606i	0.899289	+	1.34588i	0.938002	+	0.346631i	$0.112674\pi$
$571$	21.4891	+	32.1606i	0.899289	+	1.34588i	−0.0387126	+	0.999250i	$0.512326\pi$
$572$	4.48706	+	13.4979i	0.187613	+	0.564377i
$573$		0			0
$574$	−16.3479	−	3.86627i	−0.682348	−	0.161375i
$575$	3.55627			0.148307
$576$		0			0
$577$	12.9731			0.540076			0.270038	−	0.962850i	$-0.412964\pi$
$577$	12.9731			0.540076			0.270038	+	0.962850i	$0.412964\pi$
$578$	−7.01517	−	1.65908i	−0.291792	−	0.0690088i
$579$		0			0
$580$	25.4907	−	8.47377i	1.05845	−	0.351854i
$581$	−34.0241	−	50.9206i	−1.41156	−	2.11254i
$582$		0			0
$583$	−6.74646	−	2.79448i	−0.279410	−	0.115735i
$584$	−5.01156	+	15.9745i	−0.207380	+	0.661029i
$585$		0			0
$586$	−9.77944	−	26.2344i	−0.403985	−	1.08373i
$587$	−0.438329	+	2.20363i	−0.0180918	+	0.0909534i	−0.988776	−	0.149404i	$-0.952265\pi$
$587$	−0.438329	+	2.20363i	−0.0180918	+	0.0909534i	0.970685	+	0.240357i	$0.0772646\pi$
$588$		0			0
$589$	4.57268	−	6.84350i	0.188414	−	0.281982i
$590$	19.4192	+	14.0086i	0.799474	+	0.576725i
$591$		0			0
$592$	−25.1775	−	8.90287i	−1.03479	−	0.365906i
$593$	25.5913	−	25.5913i	1.05091	−	1.05091i	0.0522765	−	0.998633i	$-0.483352\pi$
$593$	25.5913	−	25.5913i	1.05091	−	1.05091i	0.998633	−	0.0522765i	$-0.0166477\pi$
$594$		0			0
$595$	24.5003	+	16.3706i	1.00441	+	0.671128i
$596$	14.8229	+	11.5235i	0.607170	+	0.472021i
$597$		0			0
$598$	−2.72268	+	5.95895i	−0.111339	+	0.243679i
$599$	−4.71217	−	11.3762i	−0.192534	−	0.464819i	0.797903	−	0.602786i	$-0.205943\pi$
$599$	−4.71217	−	11.3762i	−0.192534	−	0.464819i	−0.990437	+	0.137968i	$0.955943\pi$
$600$		0			0
$601$	−8.85882	+	21.3871i	−0.361359	+	0.872397i	0.633743	+	0.773543i	$0.281518\pi$
$601$	−8.85882	+	21.3871i	−0.361359	+	0.872397i	−0.995102	+	0.0988537i	$0.968482\pi$
$602$	33.2021	−	30.9009i	1.35322	−	1.25943i
$603$		0			0
$604$	−2.47669	+	34.4514i	−0.100775	+	1.40181i
$605$	1.12628	+	5.66219i	0.0457898	+	0.230201i
$606$		0			0
$607$			11.3561i			0.460929i	0.973081	+	0.230465i	$0.0740246\pi$
$607$			11.3561i			0.460929i	−0.973081	+	0.230465i	$0.925975\pi$
$608$	12.6100	+	2.28701i	0.511402	+	0.0927505i
$609$		0			0
$610$	−27.9818	+	17.2779i	−1.13295	+	0.699562i
$611$	2.53898	+	12.7643i	0.102716	+	0.516389i
$612$		0			0
$613$	20.5529	−	13.7330i	0.830122	−	0.554670i	−0.0663364	−	0.997797i	$-0.521131\pi$
$613$	20.5529	−	13.7330i	0.830122	−	0.554670i	0.896459	+	0.443127i	$0.146131\pi$
$614$	24.4601	+	26.2817i	0.987131	+	1.06064i
$615$		0			0
$616$	−10.8170	−	36.9143i	−0.435829	−	1.48732i
$617$	1.48976	+	3.59660i	0.0599754	+	0.144793i	0.951026	−	0.309110i	$-0.100031\pi$
$617$	1.48976	+	3.59660i	0.0599754	+	0.144793i	−0.891051	+	0.453903i	$0.850031\pi$
$618$		0			0
$619$	−0.987852	−	0.196496i	−0.0397051	−	0.00789784i	0.175198	−	0.984533i	$-0.443944\pi$
$619$	−0.987852	−	0.196496i	−0.0397051	−	0.00789784i	−0.214903	+	0.976635i	$0.568944\pi$
$620$	12.5506	−	1.57174i	0.504043	−	0.0631225i
$621$		0			0
$622$	−3.40764	−	21.0532i	−0.136634	−	0.844158i
$623$	−31.6729	+	31.6729i	−1.26895	+	1.26895i
$624$		0			0
$625$	7.97082	+	7.97082i	0.318833	+	0.318833i
$626$	−4.55003	+	6.30739i	−0.181856	+	0.252094i
$627$		0			0
$628$	−2.27618	+	8.28514i	−0.0908295	+	0.330613i
$629$	−4.49360	+	22.5909i	−0.179172	+	0.900757i
$630$		0			0
$631$	−24.1540	+	10.0049i	−0.961554	+	0.398289i	−0.807561	−	0.589783i	$-0.799213\pi$
$631$	−24.1540	+	10.0049i	−0.961554	+	0.398289i	−0.153992	+	0.988072i	$0.549213\pi$
$632$	−22.7576	+	2.02392i	−0.905248	+	0.0805073i
$633$		0			0
$634$	−0.255118	+	7.10668i	−0.0101320	+	0.282242i
$635$	8.01597	+	11.9968i	0.318104	+	0.476077i
$636$		0			0
$637$	42.9604	−	8.54535i	1.70215	−	0.338579i
$638$	−6.96106	+	29.4337i	−0.275591	+	1.16529i
$639$		0			0
$640$	10.0280	+	16.9507i	0.396391	+	0.670036i
$641$	6.97029			0.275310			0.137655	−	0.990480i	$-0.456044\pi$
$641$	6.97029			0.275310			0.137655	+	0.990480i	$0.456044\pi$
$642$		0			0
$643$	−10.2606	+	2.04096i	−0.404638	+	0.0804875i	−0.393214	−	0.919447i	$-0.628637\pi$
$643$	−10.2606	+	2.04096i	−0.404638	+	0.0804875i	−0.0114247	+	0.999935i	$0.503637\pi$
$644$	7.93632	−	15.8403i	0.312735	−	0.624194i
$645$		0			0
$646$	0.396552	−	11.0465i	0.0156021	−	0.434619i
$647$	−2.38405	−	0.987505i	−0.0937266	−	0.0388228i	0.335328	−	0.942102i	$-0.391153\pi$
$647$	−2.38405	−	0.987505i	−0.0937266	−	0.0388228i	−0.429054	+	0.903279i	$0.641153\pi$
$648$		0			0
$649$	−24.9083	+	10.3173i	−0.977735	+	0.404991i
$650$	6.69668	−	2.49633i	0.262665	−	0.0979143i
$651$		0			0
$652$	3.26064	−	11.8685i	0.127696	−	0.464806i
$653$	4.66186	−	6.97696i	0.182433	−	0.273030i	−0.728970	−	0.684546i	$-0.760001\pi$
$653$	4.66186	−	6.97696i	0.182433	−	0.273030i	0.911403	+	0.411516i	$0.135001\pi$
$654$		0			0
$655$	−16.0990	−	16.0990i	−0.629039	−	0.629039i
$656$	−4.94773	+	8.32506i	−0.193176	+	0.325039i
$657$		0			0
$658$	−5.62338	−	34.7426i	−0.219222	−	1.35441i
$659$	1.71040	+	1.14285i	0.0666278	+	0.0445192i	0.588438	−	0.808542i	$-0.299743\pi$
$659$	1.71040	+	1.14285i	0.0666278	+	0.0445192i	−0.521810	+	0.853062i	$0.674743\pi$
$660$		0			0
$661$	−2.70170	−	0.537402i	−0.105084	−	0.0209025i	0.142268	−	0.989828i	$-0.454560\pi$
$661$	−2.70170	−	0.537402i	−0.105084	−	0.0209025i	−0.247352	+	0.968926i	$0.579560\pi$
$662$	−9.01979	−	4.12120i	−0.350564	−	0.160175i
$663$		0			0
$664$	−33.8805	+	9.92800i	−1.31482	+	0.385281i
$665$	7.40473	−	17.8766i	0.287143	−	0.693225i
$666$		0			0
$667$	−11.5830	+	7.73953i	−0.448496	+	0.299676i
$668$	−10.2442	+	8.87006i	−0.396359	+	0.343193i
$669$		0			0
$670$	5.81832	−	3.59263i	0.224781	−	0.138795i
$671$		−	37.0284i		−	1.42947i
$672$		0			0
$673$		−	6.84519i		−	0.263863i	−0.991259	−	0.131931i	$-0.957882\pi$
$673$		−	6.84519i		−	0.263863i	0.991259	−	0.131931i	$-0.0421178\pi$
$674$	−12.1958	−	19.7512i	−0.469763	−	0.760788i
$675$		0			0
$676$	0.920242	−	12.8008i	0.0353939	−	0.492339i
$677$	−15.3133	+	10.2320i	−0.588539	+	0.393249i	−0.813882	−	0.581030i	$-0.802650\pi$
$677$	−15.3133	+	10.2320i	−0.588539	+	0.393249i	0.225343	+	0.974280i	$0.427650\pi$
$678$		0			0
$679$	17.9894	−	43.4302i	0.690369	−	1.66670i
$680$	13.2326	−	10.6515i	0.507447	−	0.408467i
$681$		0			0
$682$	−5.91860	+	12.9537i	−0.226635	+	0.496021i
$683$	−16.5246	−	3.28694i	−0.632296	−	0.125771i	−0.131471	−	0.991320i	$-0.541970\pi$
$683$	−16.5246	−	3.28694i	−0.632296	−	0.125771i	−0.500825	+	0.865549i	$0.666970\pi$
$684$		0			0
$685$	5.36279	+	3.58330i	0.204902	+	0.136911i
$686$	−68.9860	+	11.1660i	−2.63390	+	0.426318i
$687$		0			0
$688$	−11.2677	−	23.5954i	−0.429577	−	0.899566i
$689$	−4.77944	−	4.77944i	−0.182082	−	0.182082i
$690$		0			0
$691$	−6.27571	+	9.39227i	−0.238739	+	0.357299i	−0.931420	−	0.363945i	$-0.881429\pi$
$691$	−6.27571	+	9.39227i	−0.238739	+	0.357299i	0.692681	+	0.721244i	$0.256429\pi$
$692$	16.6270	+	29.2235i	0.632062	+	1.11091i
$693$		0			0
$694$	−8.43582	−	22.6300i	−0.320219	−	0.859021i
$695$	−31.5285	+	13.0595i	−1.19595	+	0.495377i
$696$		0			0
$697$	7.71700	+	3.19648i	0.292302	+	0.121075i
$698$	16.4180	+	0.589378i	0.621429	+	0.0223083i
$699$		0			0
$700$	−18.3403	+	6.09680i	−0.693200	+	0.230437i
$701$	28.6261	−	5.69409i	1.08119	−	0.215063i	0.377817	−	0.925880i	$-0.376675\pi$
$701$	28.6261	−	5.69409i	1.08119	−	0.215063i	0.703377	+	0.710817i	$0.251675\pi$
$702$		0			0
$703$	15.1253			0.570461
$704$	−22.1715	−	0.420160i	−0.835620	−	0.0158354i
$705$		0			0
$706$	15.8573	+	3.75025i	0.596798	+	0.141143i
$707$	21.9211	−	4.36037i	0.824427	−	0.163989i
$708$		0			0
$709$	−26.7046	−	39.9663i	−1.00291	−	1.50097i	−0.859390	−	0.511320i	$-0.829157\pi$
$709$	−26.7046	−	39.9663i	−1.00291	−	1.50097i	−0.143524	−	0.989647i	$-0.545843\pi$
$710$	11.1211	+	0.399231i	0.417369	+	0.0149829i
$711$		0			0
$712$	11.9562	+	22.8874i	0.448078	+	0.857743i
$713$	−6.06025	+	2.51024i	−0.226958	+	0.0940092i
$714$		0			0
$715$	2.41536	−	12.1428i	0.0903293	−	0.454116i
$716$	−31.5839	+	17.9700i	−1.18035	+	0.671569i
$717$		0			0
$718$	3.93778	+	2.84063i	0.146956	+	0.106012i
$719$	−17.7608	−	17.7608i	−0.662368	−	0.662368i	0.293570	−	0.955938i	$-0.405157\pi$
$719$	−17.7608	−	17.7608i	−0.662368	−	0.662368i	−0.955938	+	0.293570i	$0.905157\pi$
$720$		0			0
$721$	−4.56767	+	4.56767i	−0.170109	+	0.170109i
$722$	19.3596	−	3.13350i	0.720488	−	0.116617i
$723$		0			0
$724$	−8.37179	+	10.7688i	−0.311135	+	0.400220i
$725$	14.9047	+	2.96472i	0.553546	+	0.110107i
$726$		0			0
$727$	19.6348	+	47.4026i	0.728214	+	1.75806i	0.648459	+	0.761250i	$0.275414\pi$
$727$	19.6348	+	47.4026i	0.728214	+	1.75806i	0.0797551	+	0.996814i	$0.474586\pi$
$728$	3.82547	−	35.3991i	0.141781	−	1.31198i
$729$		0			0
$730$	10.6672	−	9.92790i	0.394812	−	0.367448i
$731$	−18.7518	+	12.5296i	−0.693560	+	0.463422i
$732$		0			0
$733$	−0.665236	−	3.34437i	−0.0245710	−	0.123527i	0.966553	−	0.256467i	$-0.0825584\pi$
$733$	−0.665236	−	3.34437i	−0.0245710	−	0.123527i	−0.991124	+	0.132940i	$0.957558\pi$
$734$	−23.7209	−	38.4163i	−0.875555	−	1.41797i
$735$		0			0
$736$	−7.34348	−	7.09888i	−0.270684	−	0.261668i
$737$			7.69939i			0.283611i
$738$		0			0
$739$	4.70308	+	23.6440i	0.173006	+	0.869758i	0.965605	+	0.260015i	$0.0837274\pi$
$739$	4.70308	+	23.6440i	0.173006	+	0.869758i	−0.792599	+	0.609743i	$0.791273\pi$
$740$	15.2153	+	17.5724i	0.559325	+	0.645973i
$741$		0			0
$742$	12.4530	+	13.3804i	0.457165	+	0.491210i
$743$	16.2703	−	39.2800i	0.596899	−	1.44104i	−0.279826	−	0.960051i	$-0.590277\pi$
$743$	16.2703	−	39.2800i	0.596899	−	1.44104i	0.876725	−	0.480992i	$-0.159723\pi$
$744$		0			0
$745$	−6.25379	−	15.0980i	−0.229121	−	0.553148i
$746$	−43.6084	−	19.9249i	−1.59662	−	0.729503i
$747$		0			0
$748$	2.37669	+	18.9783i	0.0869004	+	0.693914i
$749$	14.7544	+	9.85854i	0.539112	+	0.360223i
$750$		0			0
$751$	1.57525	−	1.57525i	0.0574817	−	0.0574817i	−0.677782	−	0.735263i	$-0.737059\pi$
$751$	1.57525	−	1.57525i	0.0574817	−	0.0574817i	0.735263	+	0.677782i	$0.237059\pi$
$752$	−20.0807	−	2.90218i	−0.732269	−	0.105832i
$753$		0			0
$754$	−16.3788	+	22.7048i	−0.596480	+	0.826859i
$755$	16.7026	−	24.9971i	0.607868	−	0.909739i
$756$		0			0
$757$	−3.61478	+	18.1727i	−0.131382	+	0.660500i	0.857821	+	0.513948i	$0.171817\pi$
$757$	−3.61478	+	18.1727i	−0.131382	+	0.660500i	−0.989203	+	0.146552i	$0.953183\pi$
$758$	27.7835	−	10.3569i	1.00914	−	0.376180i
$759$		0			0
$760$	−8.55532	−	7.15788i	−0.310334	−	0.259644i
$761$	25.7162	+	10.6520i	0.932211	+	0.386135i	0.796517	−	0.604616i	$-0.206673\pi$
$761$	25.7162	+	10.6520i	0.932211	+	0.386135i	0.135694	+	0.990751i	$0.456673\pi$
$762$		0			0
$763$	−24.9803	−	37.3857i	−0.904348	−	1.35345i
$764$	7.38555	+	3.70032i	0.267200	+	0.133873i
$765$		0			0
$766$	0.0192108	−	0.0812300i	0.000694116	−	0.00293496i
$767$	−24.9551			−0.901077
$768$		0			0
$769$	9.14052			0.329615			0.164808	−	0.986326i	$-0.447300\pi$
$769$	9.14052			0.329615			0.164808	+	0.986326i	$0.447300\pi$
$770$	−7.70572	+	32.5824i	−0.277695	+	1.17419i
$771$		0			0
$772$	−4.91729	−	2.46367i	−0.176977	−	0.0886694i
$773$	21.6826	+	32.4503i	0.779869	+	1.16716i	0.982200	+	0.187839i	$0.0601482\pi$
$773$	21.6826	+	32.4503i	0.779869	+	1.16716i	−0.202331	+	0.979317i	$0.564852\pi$
$774$		0			0
$775$	6.61095	+	2.73835i	0.237472	+	0.0983643i
$776$	−20.7847	−	17.3897i	−0.746126	−	0.624252i
$777$		0			0
$778$	−4.27444	+	1.59339i	−0.153246	+	0.0571259i
$779$	1.07007	−	5.37962i	0.0383393	−	0.192745i
$780$		0			0
$781$	−6.96126	+	10.4183i	−0.249093	+	0.372795i
$782$	−5.15389	+	7.14448i	−0.184303	+	0.255486i
$783$		0			0
$784$	−9.76777	+	67.5850i	−0.348849	+	2.41375i
$785$	5.28815	−	5.28815i	0.188742	−	0.188742i
$786$		0			0
$787$	−5.88104	−	3.92959i	−0.209637	−	0.140075i	0.446320	−	0.894874i	$-0.352734\pi$
$787$	−5.88104	−	3.92959i	−0.209637	−	0.140075i	−0.655956	+	0.754799i	$0.727734\pi$
$788$	−0.682935	−	5.45335i	−0.0243286	−	0.194268i
$789$		0			0
$790$	18.0877	+	8.26439i	0.643533	+	0.294034i
$791$	24.5751	+	59.3296i	0.873791	+	2.10952i
$792$		0			0
$793$	13.1161	−	31.6651i	0.465768	−	1.12446i
$794$	5.58897	+	6.00518i	0.198345	+	0.213116i
$795$		0			0
$796$	−1.17834	−	1.36088i	−0.0417650	−	0.0482350i
$797$	6.94836	+	34.9318i	0.246124	+	1.23735i	0.884103	+	0.467293i	$0.154771\pi$
$797$	6.94836	+	34.9318i	0.246124	+	1.23735i	−0.637979	+	0.770054i	$0.720229\pi$
$798$		0			0
$799$			17.4997i			0.619096i
$800$	0.188676	+	11.1403i	0.00667071	+	0.393869i
$801$		0			0
$802$	−19.1673	−	31.0418i	−0.676822	−	1.09612i
$803$	3.20100	+	16.0925i	0.112961	+	0.567892i
$804$		0			0
$805$	−12.8221	+	8.56746i	−0.451920	+	0.301963i
$806$	−9.64977	+	8.98095i	−0.339899	+	0.316341i
$807$		0			0
$808$	1.38436	−	12.8102i	0.0487016	−	0.450663i
$809$	−20.3911	−	49.2285i	−0.716913	−	1.73078i	−0.681958	−	0.731392i	$-0.738871\pi$
$809$	−20.3911	−	49.2285i	−0.716913	−	1.73078i	−0.0349550	−	0.999389i	$-0.511129\pi$
$810$		0			0
$811$	20.2159	+	4.02118i	0.709875	+	0.141203i	0.536804	−	0.843707i	$-0.319631\pi$
$811$	20.2159	+	4.02118i	0.709875	+	0.141203i	0.173070	+	0.984910i	$0.444631\pi$
$812$	46.4673	−	59.7719i	1.63068	−	2.09758i
$813$		0			0
$814$	−25.8356	+	4.18171i	−0.905539	+	0.146569i
$815$	−7.57529	+	7.57529i	−0.265351	+	0.265351i
$816$		0			0
$817$	10.4719	+	10.4719i	0.366366	+	0.366366i
$818$	11.7418	+	8.47031i	0.410542	+	0.296157i
$819$		0			0
$820$	7.32641	−	4.16843i	0.255849	−	0.145568i
$821$	1.78916	−	8.99472i	0.0624421	−	0.313918i	−0.936923	−	0.349535i	$-0.886340\pi$
$821$	1.78916	−	8.99472i	0.0624421	−	0.313918i	0.999366	+	0.0356170i	$0.0113397\pi$
$822$		0			0
$823$	−27.9325	+	11.5700i	−0.973664	+	0.403305i	−0.812075	−	0.583553i	$-0.801662\pi$
$823$	−27.9325	+	11.5700i	−0.973664	+	0.403305i	−0.161589	+	0.986858i	$0.551662\pi$
$824$	1.72425	+	3.30069i	0.0600671	+	0.114985i
$825$		0			0
$826$	67.4427	+	2.42108i	2.34663	+	0.0842402i
$827$	−2.65323	−	3.97084i	−0.0922619	−	0.138080i	0.782467	−	0.622692i	$-0.213961\pi$
$827$	−2.65323	−	3.97084i	−0.0922619	−	0.138080i	−0.874729	+	0.484612i	$0.838961\pi$
$828$		0			0
$829$	22.9462	−	4.56428i	0.796953	−	0.158524i	0.220213	−	0.975452i	$-0.429325\pi$
$829$	22.9462	−	4.56428i	0.796953	−	0.158524i	0.576740	+	0.816928i	$0.304325\pi$
$830$	29.9046	+	7.07242i	1.03800	+	0.245487i
$831$		0			0
$832$	−18.8113	−	8.21286i	−0.652165	−	0.284730i
$833$	58.8982			2.04070
$834$		0			0
$835$	11.5679	−	2.30099i	0.400323	−	0.0796291i
$836$	11.9185	−	3.96200i	0.412208	−	0.137029i
$837$		0			0
$838$	45.0972	+	1.61892i	1.55786	+	0.0559245i
$839$	−15.5489	−	6.44058i	−0.536809	−	0.222354i	0.0977736	−	0.995209i	$-0.468828\pi$
$839$	−15.5489	−	6.44058i	−0.536809	−	0.222354i	−0.634582	+	0.772855i	$0.718828\pi$
$840$		0			0
$841$	−28.2052	+	11.6830i	−0.972595	+	0.402862i
$842$	5.60561	+	15.0376i	0.193182	+	0.518231i
$843$		0			0
$844$	13.7292	+	24.1305i	0.472580	+	0.830605i
$845$	−6.20603	+	9.28798i	−0.213494	+	0.319516i
$846$		0			0
$847$	11.5054	+	11.5054i	0.395331	+	0.395331i
$848$	9.50891	−	4.54086i	0.326537	−	0.155934i
$849$		0			0
$850$	9.48649	−	1.53547i	0.325384	−	0.0526661i
$851$	−10.0229	−	6.69709i	−0.343581	−	0.229573i
$852$		0			0
$853$	42.7816	+	8.50979i	1.46481	+	0.291370i	0.862161	−	0.506634i	$-0.169110\pi$
$853$	42.7816	+	8.50979i	1.46481	+	0.291370i	0.602653	+	0.798003i	$0.294110\pi$
$854$	−38.5192	+	84.3044i	−1.31810	+	2.88484i
$855$		0			0
$856$	7.96882	−	6.41447i	0.272369	−	0.219242i
$857$	−21.1682	+	51.1045i	−0.723091	+	1.74570i	−0.0587410	+	0.998273i	$0.518709\pi$
$857$	−21.1682	+	51.1045i	−0.723091	+	1.74570i	−0.664350	+	0.747422i	$0.731291\pi$
$858$		0			0
$859$	30.3027	−	20.2476i	1.03392	−	0.690840i	0.0818217	−	0.996647i	$-0.473926\pi$
$859$	30.3027	−	20.2476i	1.03392	−	0.690840i	0.952094	+	0.305807i	$0.0989262\pi$
$860$	−1.63191	+	22.7004i	−0.0556478	+	0.774076i
$861$		0			0
$862$	20.4493	+	33.1179i	0.696505	+	1.12800i
$863$			45.1415i			1.53663i	0.640070	+	0.768317i	$0.278905\pi$
$863$			45.1415i			1.53663i	−0.640070	+	0.768317i	$0.721095\pi$
$864$		0			0
$865$		−	29.2649i		−	0.995036i
$866$	42.9294	−	26.5076i	1.45880	−	0.900765i
$867$		0			0
$868$	26.9504	−	23.3354i	0.914755	−	0.792054i
$869$	−18.6175	+	12.4398i	−0.631555	+	0.421992i
$870$		0			0
$871$	−2.72727	+	6.58420i	−0.0924099	+	0.223097i
$872$	−24.8749	+	7.28910i	−0.842370	+	0.246840i
$873$		0			0
$874$	5.26165	+	2.40408i	0.177978	+	0.0813193i
$875$	58.3829	+	11.6131i	1.97370	+	0.392594i
$876$		0			0
$877$	−8.73879	−	5.83907i	−0.295088	−	0.197171i	0.399209	−	0.916860i	$-0.369285\pi$
$877$	−8.73879	−	5.83907i	−0.295088	−	0.197171i	−0.694297	+	0.719688i	$0.744285\pi$
$878$	6.49093	+	40.1026i	0.219058	+	1.35340i
$879$		0			0
$880$	16.5924	+	9.86114i	0.559328	+	0.332419i
$881$	22.1067	+	22.1067i	0.744795	+	0.744795i	0.973496	−	0.228702i	$-0.0734481\pi$
$881$	22.1067	+	22.1067i	0.744795	+	0.744795i	−0.228702	+	0.973496i	$0.573448\pi$
$882$		0			0
$883$	0.0585565	−	0.0876360i	0.00197058	−	0.00294919i	−0.830483	−	0.557044i	$-0.811935\pi$
$883$	0.0585565	−	0.0876360i	0.00197058	−	0.00294919i	0.832454	+	0.554095i	$0.186935\pi$
$884$	−4.69000	+	17.0713i	−0.157742	+	0.574170i
$885$		0			0
$886$	0.0110150	−	0.00410608i	0.000370056	−	0.000137947i
$887$	14.2474	−	5.90145i	0.478380	−	0.198151i	−0.130446	−	0.991455i	$-0.541641\pi$
$887$	14.2474	−	5.90145i	0.478380	−	0.198151i	0.608826	+	0.793304i	$0.291641\pi$
$888$		0			0
$889$	37.5698	+	15.5619i	1.26005	+	0.521930i
$890$	0.806318	−	22.4611i	0.0270278	−	0.752899i
$891$		0			0
$892$	5.64703	−	11.2710i	0.189077	−	0.377382i
$893$	11.2707	−	2.24188i	0.377159	−	0.0750216i
$894$		0			0
$895$	31.6287			1.05723
$896$	50.0419	+	24.0208i	1.67178	+	0.802477i
$897$		0			0
$898$	4.53701	−	19.1840i	0.151402	−	0.640178i
$899$	−27.4918	+	5.46846i	−0.916904	+	0.182383i
$900$		0			0
$901$	−5.04939	−	7.55695i	−0.168220	−	0.251758i
$902$	−0.340489	+	9.48482i	−0.0113371	+	0.315810i
$903$		0			0
$904$	36.8753	−	3.27947i	1.22646	−	0.109074i
$905$	10.9686	−	4.54336i	0.364610	−	0.151026i
$906$		0			0
$907$	−4.20851	+	21.1576i	−0.139741	+	0.702527i	0.845855	+	0.533413i	$0.179091\pi$
$907$	−4.20851	+	21.1576i	−0.139741	+	0.702527i	−0.985596	+	0.169114i	$0.945909\pi$
$908$	−9.41759	+	34.2794i	−0.312534	+	1.13760i
$909$		0			0
$910$	−18.1309	+	25.1336i	−0.601033	+	0.833171i
$911$	−29.1379	−	29.1379i	−0.965382	−	0.965382i	0.0340388	−	0.999421i	$-0.489163\pi$
$911$	−29.1379	−	29.1379i	−0.965382	−	0.965382i	−0.999421	+	0.0340388i	$0.989163\pi$
$912$		0			0
$913$	−24.4659	+	24.4659i	−0.809703	+	0.809703i
$914$	−3.33207	−	20.5863i	−0.110215	−	0.680936i
$915$		0			0
$916$	−18.2654	+	2.28742i	−0.603507	+	0.0755786i
$917$	−62.9352	−	12.5186i	−2.07830	−	0.413400i
$918$		0			0
$919$	−15.4221	−	37.2322i	−0.508727	−	1.22818i	−0.944617	−	0.328176i	$-0.893566\pi$
$919$	−15.4221	−	37.2322i	−0.508727	−	1.22818i	0.435889	−	0.900000i	$-0.356434\pi$
$920$	2.49993	+	8.53130i	0.0824202	+	0.281269i
$921$		0			0
$922$	−28.7272	−	30.8665i	−0.946079	−	1.01653i
$923$	−9.64332	+	6.44346i	−0.317414	+	0.212089i
$924$		0			0
$925$	2.56541	+	12.8972i	0.0843500	+	0.424056i
$926$	12.4482	−	7.68636i	0.409072	−	0.252590i
$927$		0			0
$928$	−24.8592	−	35.8741i	−0.816044	−	1.17763i
$929$			9.25514i			0.303651i	0.988407	+	0.151826i	$0.0485152\pi$
$929$			9.25514i			0.303651i	−0.988407	+	0.151826i	$0.951485\pi$
$930$		0			0
$931$	−7.54541	−	37.9333i	−0.247291	−	1.24321i
$932$	−1.96516	+	27.3359i	−0.0643709	+	0.895416i
$933$		0			0
$934$	−33.1572	+	30.8591i	−1.08494	+	1.00974i
$935$	6.37080	−	15.3805i	0.208347	−	0.502995i
$936$		0			0
$937$	2.35348	+	5.68181i	0.0768850	+	0.185617i	0.957649	−	0.287939i	$-0.0929701\pi$
$937$	2.35348	+	5.68181i	0.0768850	+	0.185617i	−0.880764	+	0.473556i	$0.842970\pi$
$938$	8.00938	−	17.5296i	0.261515	−	0.572362i
$939$		0			0
$940$	13.9423	+	10.8389i	0.454748	+	0.353526i
$941$	−34.8411	−	23.2801i	−1.13579	−	0.758908i	−0.162094	−	0.986775i	$-0.551825\pi$
$941$	−34.8411	−	23.2801i	−1.13579	−	0.758908i	−0.973692	+	0.227867i	$0.926825\pi$
$942$		0			0
$943$	−3.09105	+	3.09105i	−0.100658	+	0.100658i
$944$	12.9699	−	36.6794i	0.422136	−	1.19381i
$945$		0			0
$946$	−20.7824	−	14.9920i	−0.675693	−	0.487432i
$947$	13.4472	−	20.1252i	0.436975	−	0.653980i	−0.545986	−	0.837795i	$-0.683845\pi$
$947$	13.4472	−	20.1252i	0.436975	−	0.653980i	0.982961	+	0.183815i	$0.0588447\pi$
$948$		0			0
$949$	−2.96290	+	14.8955i	−0.0961797	+	0.483528i
$950$	−2.20422	−	5.91306i	−0.0715144	−	0.191845i
$951$		0			0
$952$	14.3312	−	45.6812i	0.464478	−	1.48054i
$953$	−20.7537	−	8.59648i	−0.672279	−	0.278467i	0.0203159	−	0.999794i	$-0.493533\pi$
$953$	−20.7537	−	8.59648i	−0.672279	−	0.278467i	−0.692595	+	0.721326i	$0.743533\pi$
$954$		0			0
$955$	−3.99459	−	5.97833i	−0.129262	−	0.193454i
$956$	22.5213	−	7.48665i	0.728391	−	0.242136i
$957$		0			0
$958$	−33.3415	−	7.88524i	−1.07721	−	0.254761i
$959$	18.1782			0.587005
$960$		0			0
$961$	17.8013			0.574237
$962$	−23.5748	−	5.57543i	−0.760082	−	0.179759i
$963$		0			0
$964$	−3.54891	−	10.6758i	−0.114303	−	0.343844i
$965$	2.65959	+	3.98036i	0.0856154	+	0.128132i
$966$		0			0
$967$	−28.9735	−	12.0012i	−0.931724	−	0.385933i	−0.135392	−	0.990792i	$-0.543229\pi$
$967$	−28.9735	−	12.0012i	−0.931724	−	0.385933i	−0.796332	+	0.604859i	$0.793229\pi$
$968$	8.31403	−	4.34318i	0.267223	−	0.139595i
$969$		0			0
$970$	8.23900	+	22.1020i	0.264538	+	0.709651i
$971$	−5.69005	+	28.6058i	−0.182602	+	0.918004i	0.775450	+	0.631409i	$0.217523\pi$
$971$	−5.69005	+	28.6058i	−0.182602	+	0.918004i	−0.958052	+	0.286595i	$0.907477\pi$
$972$		0			0
$973$	−53.4360	+	79.9726i	−1.71308	+	2.56380i
$974$	36.8500	+	26.5828i	1.18075	+	0.851769i
$975$		0			0
$976$	39.7250	+	35.7356i	1.27157	+	1.14387i
$977$	−36.4851	+	36.4851i	−1.16726	+	1.16726i	−0.184412	+	0.982849i	$0.559038\pi$
$977$	−36.4851	+	36.4851i	−1.16726	+	1.16726i	−0.982849	+	0.184412i	$0.940962\pi$
$978$		0			0
$979$	21.0416	+	14.0595i	0.672491	+	0.449344i
$980$	36.4801	−	46.9252i	1.16531	−	1.49897i
$981$		0			0
$982$	−10.6381	+	23.2829i	−0.339476	+	0.742988i
$983$	−1.68976	−	4.07944i	−0.0538950	−	0.130114i	0.894639	−	0.446790i	$-0.147433\pi$
$983$	−1.68976	−	4.07944i	−0.0538950	−	0.130114i	−0.948534	+	0.316676i	$0.897433\pi$
$984$		0			0
$985$	−1.83063	+	4.41953i	−0.0583287	+	0.140818i
$986$	−27.5565	+	25.6466i	−0.877579	+	0.816755i
$987$		0			0
$988$	11.5956	+	0.833599i	0.368905	+	0.0265203i
$989$	−2.30261	−	11.5760i	−0.0732187	−	0.368095i
$990$		0			0
$991$			21.8887i			0.695318i	0.937621	+	0.347659i	$0.113023\pi$
$991$			21.8887i			0.695318i	−0.937621	+	0.347659i	$0.886977\pi$
$992$	−8.18505	−	18.8510i	−0.259875	−	0.598521i
$993$		0			0
$994$	26.6868	−	16.4783i	0.846453	−	0.522659i
$995$	0.305673	+	1.53672i	0.00969049	+	0.0487174i
$996$		0			0
$997$	−24.5633	+	16.4127i	−0.777927	+	0.519794i	−0.879995	−	0.474983i	$-0.842454\pi$
$997$	−24.5633	+	16.4127i	−0.777927	+	0.519794i	0.102068	+	0.994777i	$0.467454\pi$
$998$	27.3217	+	29.3564i	0.864854	+	0.929260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.181.3		56
3.2	odd	2		64.2.i.a.53.5	yes	56
12.11	even	2		256.2.i.a.49.4		56
24.5	odd	2		512.2.i.b.353.4		56
24.11	even	2		512.2.i.a.353.4		56
64.29	even	16	inner	576.2.bd.a.541.3		56
192.29	odd	16		64.2.i.a.29.5	✓	56
192.35	even	16		256.2.i.a.209.4		56
192.125	odd	16		512.2.i.b.161.4		56
192.131	even	16		512.2.i.a.161.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.5	✓	56	192.29	odd	16
64.2.i.a.53.5	yes	56	3.2	odd	2
256.2.i.a.49.4		56	12.11	even	2
256.2.i.a.209.4		56	192.35	even	16
512.2.i.a.161.4		56	192.131	even	16
512.2.i.a.353.4		56	24.11	even	2
512.2.i.b.161.4		56	192.125	odd	16
512.2.i.b.353.4		56	24.5	odd	2
576.2.bd.a.181.3		56	1.1	even	1	trivial
576.2.bd.a.541.3		56	64.29	even	16	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.325482 + 1.37625i) q^{2} +(-1.78812 - 0.895889i) q^{4} +(0.967135 + 1.44742i) q^{5} +(4.53283 + 1.87756i) q^{7} +(1.81497 - 2.16931i) q^{8} +O(q^{10})\)	\(q+(-0.325482 + 1.37625i) q^{2} +(-1.78812 - 0.895889i) q^{4} +(0.967135 + 1.44742i) q^{5} +(4.53283 + 1.87756i) q^{7} +(1.81497 - 2.16931i) q^{8} +(-2.30680 + 0.859909i) q^{10} +(0.540778 - 2.71867i) q^{11} +(1.42546 - 2.13334i) q^{13} +(-4.05935 + 5.62719i) q^{14} +(2.39477 + 3.20392i) q^{16} +(2.43954 - 2.43954i) q^{17} +(-1.88371 - 1.25865i) q^{19} +(-0.432628 - 3.45461i) q^{20} +(3.56556 + 1.62913i) q^{22} +(0.690956 + 1.66811i) q^{23} +(0.753743 - 1.81970i) q^{25} +(2.47205 + 2.65615i) q^{26} +(-6.42318 - 7.41822i) q^{28} +(1.50522 + 7.56726i) q^{29} +3.63299i q^{31} +(-5.18884 + 2.25298i) q^{32} +(2.56339 + 4.15144i) q^{34} +(1.66624 + 8.37677i) q^{35} +(-5.55115 + 3.70916i) q^{37} +(2.34533 - 2.18278i) q^{38} +(4.89522 + 0.529009i) q^{40} +(0.926510 + 2.23679i) q^{41} +(-6.41133 - 1.27529i) q^{43} +(-3.40261 + 4.37685i) q^{44} +(-2.52064 + 0.407986i) q^{46} +(-3.58669 + 3.58669i) q^{47} +(12.0716 + 12.0716i) q^{49} +(2.25903 + 1.62962i) q^{50} +(-4.46013 + 2.53763i) q^{52} +(0.513941 - 2.58375i) q^{53} +(4.45807 - 1.84659i) q^{55} +(12.3000 - 6.42539i) q^{56} +(-10.9044 - 0.391449i) q^{58} +(-5.40361 - 8.08707i) q^{59} +(13.1016 - 2.60608i) q^{61} +(-4.99991 - 1.18248i) q^{62} +(-1.41178 - 7.87444i) q^{64} +4.46645 q^{65} +(-2.72425 + 0.541887i) q^{67} +(-6.54775 + 2.17664i) q^{68} +(-12.0708 - 0.433324i) q^{70} +(-4.17620 - 1.72984i) q^{71} +(-5.46867 + 2.26520i) q^{73} +(-3.29793 - 8.84703i) q^{74} +(2.24069 + 3.93822i) q^{76} +(7.55573 - 11.3080i) q^{77} +(-5.71185 - 5.71185i) q^{79} +(-2.32135 + 6.56485i) q^{80} +(-3.37995 + 0.547072i) q^{82} +(-10.3786 - 6.93477i) q^{83} +(5.89040 + 1.17167i) q^{85} +(3.84189 - 8.40850i) q^{86} +(-4.91614 - 6.10742i) q^{88} +(-3.49372 + 8.43458i) q^{89} +(10.4668 - 6.99371i) q^{91} +(0.258932 - 3.60181i) q^{92} +(-3.76877 - 6.10358i) q^{94} -3.94381i q^{95} -9.58124i q^{97} +(-20.5426 + 12.6844i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more