LMFDB - Embedded newform 603.2.v.a.8.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(8,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("603.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.v (of order $22$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			8.19
Character	$\chi$	$=$	603.8
Dual form			603.2.v.a.377.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222573 - 1.54803i) q^{2} +(-0.427866 - 0.125633i) q^{4} +(-0.138128 - 0.0887696i) q^{5} +(0.350805 + 0.0504381i) q^{7} +(1.00966 - 2.21085i) q^{8} +O(q^{10})$	\(q+(0.222573 - 1.54803i) q^{2} +(-0.427866 - 0.125633i) q^{4} +(-0.138128 - 0.0887696i) q^{5} +(0.350805 + 0.0504381i) q^{7} +(1.00966 - 2.21085i) q^{8} +(-0.168161 + 0.194069i) q^{10} +(-4.59943 - 2.95588i) q^{11} +(4.21165 - 1.92340i) q^{13} +(0.156159 - 0.531830i) q^{14} +(-3.94801 - 2.53723i) q^{16} +(0.803590 + 2.73678i) q^{17} +(0.193755 + 1.34760i) q^{19} +(0.0479480 + 0.0553349i) q^{20} +(-5.59949 + 6.46215i) q^{22} +(5.08820 - 4.40895i) q^{23} +(-2.06588 - 4.52364i) q^{25} +(-2.04007 - 6.94785i) q^{26} +(-0.143761 - 0.0656533i) q^{28} -10.4491i q^{29} +(5.90648 + 2.69740i) q^{31} +(-1.62317 + 1.87323i) q^{32} +(4.41546 - 0.634848i) q^{34} +(-0.0439787 - 0.0381078i) q^{35} -6.49059 q^{37} +2.12924 q^{38} +(-0.335719 + 0.215753i) q^{40} +(-3.69254 + 1.08423i) q^{41} +(1.97683 + 6.73245i) q^{43} +(1.59658 + 1.84256i) q^{44} +(-5.69268 - 8.85799i) q^{46} +(-8.23014 + 7.13146i) q^{47} +(-6.59593 - 1.93674i) q^{49} +(-7.46252 + 2.19119i) q^{50} +(-2.04366 + 0.293834i) q^{52} +(5.32650 + 1.56400i) q^{53} +(0.372920 + 0.816580i) q^{55} +(0.465705 - 0.724650i) q^{56} +(-16.1755 - 2.32568i) q^{58} +(13.1778 + 6.01811i) q^{59} +(4.15833 + 6.47049i) q^{61} +(5.49027 - 8.54303i) q^{62} +(-3.60799 - 4.16384i) q^{64} +(-0.752487 - 0.108191i) q^{65} +(5.43774 + 6.11809i) q^{67} -1.27193i q^{68} +(-0.0687803 + 0.0595985i) q^{70} +(-0.403473 + 1.37410i) q^{71} +(4.59776 - 2.95480i) q^{73} +(-1.44463 + 10.0476i) q^{74} +(0.0864012 - 0.600933i) q^{76} +(-1.46441 - 1.26892i) q^{77} +(2.03355 - 0.928690i) q^{79} +(0.320102 + 0.700926i) q^{80} +(0.856556 + 5.95748i) q^{82} +(-7.71031 + 11.9975i) q^{83} +(0.131944 - 0.449361i) q^{85} +(10.8620 - 1.56172i) q^{86} +(-11.1788 + 7.18421i) q^{88} +(0.884896 + 0.766767i) q^{89} +(1.57448 - 0.462309i) q^{91} +(-2.73097 + 1.24719i) q^{92} +(9.20789 + 14.3278i) q^{94} +(0.0928627 - 0.203341i) q^{95} -8.19939i q^{97} +(-4.46620 + 9.77962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 28 q^{4}+O(q^{10}) $ 240 * q - 28 * q^4	$ 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) $ 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

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 $

$2$	0.222573	−	1.54803i	0.157383	−	1.09462i	−0.746050	−	0.665890i	$-0.768052\pi$
$2$	0.222573	−	1.54803i	0.157383	−	1.09462i	0.903432	−	0.428731i	$-0.141039\pi$
$3$		0			0
$3$		0			0
$4$	−0.427866	−	0.125633i	−0.213933	−	0.0628164i
$5$	−0.138128	−	0.0887696i	−0.0617728	−	0.0396990i	0.509390	−	0.860536i	$-0.329871\pi$
$5$	−0.138128	−	0.0887696i	−0.0617728	−	0.0396990i	−0.571163	+	0.820837i	$0.693507\pi$
$6$		0			0
$7$	0.350805	+	0.0504381i	0.132592	+	0.0190638i	0.208291	−	0.978067i	$-0.433210\pi$
$7$	0.350805	+	0.0504381i	0.132592	+	0.0190638i	−0.0756994	+	0.997131i	$0.524119\pi$
$8$	1.00966	−	2.21085i	0.356969	−	0.781652i
$9$		0			0
$10$	−0.168161	+	0.194069i	−0.0531773	+	0.0613699i
$11$	−4.59943	−	2.95588i	−1.38678	−	0.891230i	−0.387254	−	0.921973i	$-0.626576\pi$
$11$	−4.59943	−	2.95588i	−1.38678	−	0.891230i	−0.999527	+	0.0307433i	$0.990213\pi$
$12$		0			0
$13$	4.21165	−	1.92340i	1.16810	−	0.533454i	0.265576	−	0.964090i	$-0.414438\pi$
$13$	4.21165	−	1.92340i	1.16810	−	0.533454i	0.902526	+	0.430636i	$0.141711\pi$
$14$	0.156159	−	0.531830i	0.0417353	−	0.142137i
$15$		0			0
$16$	−3.94801	−	2.53723i	−0.987002	−	0.634308i
$17$	0.803590	+	2.73678i	0.194899	+	0.663766i	0.997717	+	0.0675406i	$0.0215152\pi$
$17$	0.803590	+	2.73678i	0.194899	+	0.663766i	−0.802817	+	0.596225i	$0.796667\pi$
$18$		0			0
$19$	0.193755	+	1.34760i	0.0444505	+	0.309160i	0.999902	+	0.0140115i	$0.00446014\pi$
$19$	0.193755	+	1.34760i	0.0444505	+	0.309160i	−0.955451	+	0.295149i	$0.904631\pi$
$20$	0.0479480	+	0.0553349i	0.0107215	+	0.0123733i
$21$		0			0
$22$	−5.59949	+	6.46215i	−1.19381	+	1.37774i
$23$	5.08820	−	4.40895i	1.06096	−	0.919330i	0.0640579	−	0.997946i	$-0.479596\pi$
$23$	5.08820	−	4.40895i	1.06096	−	0.919330i	0.996905	+	0.0786166i	$0.0250503\pi$
$24$		0			0
$25$	−2.06588	−	4.52364i	−0.413175	−	0.904727i
$26$	−2.04007	−	6.94785i	−0.400091	−	1.36259i
$27$		0			0
$28$	−0.143761	−	0.0656533i	−0.0271682	−	0.0124073i
$29$		−	10.4491i		−	1.94035i	−0.242415	−	0.970173i	$-0.577939\pi$
$29$		−	10.4491i		−	1.94035i	0.242415	−	0.970173i	$-0.422061\pi$
$30$		0			0
$31$	5.90648	+	2.69740i	1.06084	+	0.484467i	0.867897	−	0.496744i	$-0.165471\pi$
$31$	5.90648	+	2.69740i	1.06084	+	0.484467i	0.192938	+	0.981211i	$0.438198\pi$
$32$	−1.62317	+	1.87323i	−0.286938	+	0.331144i
$33$		0			0
$34$	4.41546	−	0.634848i	0.757246	−	0.108875i
$35$	−0.0439787	−	0.0381078i	−0.00743376	−	0.00644139i
$36$		0			0
$37$	−6.49059			−1.06705			−0.533523	−	0.845785i	$-0.679132\pi$
$37$	−6.49059			−1.06705			−0.533523	+	0.845785i	$0.679132\pi$
$38$	2.12924			0.345409
$39$		0			0
$40$	−0.335719	+	0.215753i	−0.0530818	+	0.0341136i
$41$	−3.69254	+	1.08423i	−0.576678	+	0.169328i	−0.557049	−	0.830479i	$-0.688067\pi$
$41$	−3.69254	+	1.08423i	−0.576678	+	0.169328i	−0.0196287	+	0.999807i	$0.506248\pi$
$42$		0			0
$43$	1.97683	+	6.73245i	0.301463	+	1.02669i	0.961351	+	0.275325i	$0.0887855\pi$
$43$	1.97683	+	6.73245i	0.301463	+	1.02669i	−0.659888	+	0.751364i	$0.729396\pi$
$44$	1.59658	+	1.84256i	0.240694	+	0.277776i
$45$		0			0
$46$	−5.69268	−	8.85799i	−0.839340	−	1.30604i
$47$	−8.23014	+	7.13146i	−1.20049	+	1.04023i	−0.202346	+	0.979314i	$0.564857\pi$
$47$	−8.23014	+	7.13146i	−1.20049	+	1.04023i	−0.998143	+	0.0609158i	$0.980598\pi$
$48$		0			0
$49$	−6.59593	−	1.93674i	−0.942276	−	0.276677i
$50$	−7.46252	+	2.19119i	−1.05536	+	0.309882i
$51$		0			0
$52$	−2.04366	+	0.293834i	−0.283405	+	0.0407475i
$53$	5.32650	+	1.56400i	0.731652	+	0.214832i	0.626277	−	0.779600i	$-0.284578\pi$
$53$	5.32650	+	1.56400i	0.731652	+	0.214832i	0.105374	+	0.994433i	$0.466396\pi$
$54$		0			0
$55$	0.372920	+	0.816580i	0.0502845	+	0.110108i
$56$	0.465705	−	0.724650i	0.0622324	−	0.0968355i
$57$		0			0
$58$	−16.1755	−	2.32568i	−2.12394	−	0.305377i
$59$	13.1778	+	6.01811i	1.71561	+	0.783491i	0.996024	+	0.0890823i	$0.0283934\pi$
$59$	13.1778	+	6.01811i	1.71561	+	0.783491i	0.719581	+	0.694408i	$0.244334\pi$
$60$		0			0
$61$	4.15833	+	6.47049i	0.532420	+	0.828461i	0.998412	−	0.0563272i	$-0.0179390\pi$
$61$	4.15833	+	6.47049i	0.532420	+	0.828461i	−0.465993	+	0.884789i	$0.654303\pi$
$62$	5.49027	−	8.54303i	0.697265	−	1.08497i
$63$		0			0
$64$	−3.60799	−	4.16384i	−0.450998	−	0.520480i
$65$	−0.752487	−	0.108191i	−0.0933346	−	0.0134195i
$66$		0			0
$67$	5.43774	+	6.11809i	0.664326	+	0.747443i
$67$	5.43774	+	6.11809i	0.664326	+	0.747443i
$68$		−	1.27193i		−	0.154244i
$69$		0			0
$70$	−0.0687803	+	0.0595985i	−0.00822082	+	0.00712338i
$71$	−0.403473	+	1.37410i	−0.0478835	+	0.163076i	−0.979964	−	0.199175i	$-0.936174\pi$
$71$	−0.403473	+	1.37410i	−0.0478835	+	0.163076i	0.932080	+	0.362251i	$0.117992\pi$
$72$		0			0
$73$	4.59776	−	2.95480i	0.538127	−	0.345833i	−0.243179	−	0.969981i	$-0.578190\pi$
$73$	4.59776	−	2.95480i	0.538127	−	0.345833i	0.781306	+	0.624148i	$0.214554\pi$
$74$	−1.44463	+	10.0476i	−0.167935	+	1.16801i
$75$		0			0
$76$	0.0864012	−	0.600933i	0.00991089	−	0.0689318i
$77$	−1.46441	−	1.26892i	−0.166886	−	0.144607i
$78$		0			0
$79$	2.03355	−	0.928690i	0.228792	−	0.104486i	−0.297721	−	0.954653i	$-0.596226\pi$
$79$	2.03355	−	0.928690i	0.228792	−	0.104486i	0.526513	+	0.850167i	$0.323499\pi$
$80$	0.320102	+	0.700926i	0.0357885	+	0.0783660i
$81$		0			0
$82$	0.856556	+	5.95748i	0.0945908	+	0.657893i
$83$	−7.71031	+	11.9975i	−0.846316	+	1.31689i	0.100440	+	0.994943i	$0.467975\pi$
$83$	−7.71031	+	11.9975i	−0.846316	+	1.31689i	−0.946756	+	0.321951i	$0.895661\pi$
$84$		0			0
$85$	0.131944	−	0.449361i	0.0143114	−	0.0487400i
$86$	10.8620	−	1.56172i	1.17128	−	0.168405i
$87$		0			0
$88$	−11.1788	+	7.18421i	−1.19167	+	0.765839i
$89$	0.884896	+	0.766767i	0.0937988	+	0.0812771i	0.700498	−	0.713654i	$-0.252961\pi$
$89$	0.884896	+	0.766767i	0.0937988	+	0.0812771i	−0.606699	+	0.794932i	$0.707507\pi$
$90$		0			0
$91$	1.57448	−	0.462309i	0.165050	−	0.0484632i
$92$	−2.73097	+	1.24719i	−0.284724	+	0.130029i
$93$		0			0
$94$	9.20789	+	14.3278i	0.949721	+	1.47779i
$95$	0.0928627	−	0.203341i	0.00952752	−	0.0208624i
$96$		0			0
$97$		−	8.19939i		−	0.832522i	−0.909245	−	0.416261i	$-0.863340\pi$
$97$		−	8.19939i		−	0.832522i	0.909245	−	0.416261i	$-0.136660\pi$
$98$	−4.46620	+	9.77962i	−0.451155	+	0.987891i
$99$		0			0
$100$	0.315601	+	2.19505i	0.0315601	+	0.219505i
$101$	0.471330	+	3.27817i	0.0468991	+	0.326190i	0.999742	+	0.0227254i	$0.00723435\pi$
$101$	0.471330	+	3.27817i	0.0468991	+	0.326190i	−0.952843	+	0.303465i	$0.901857\pi$
$102$		0			0
$103$	3.60827	−	7.90100i	0.355533	−	0.778509i	−0.644372	−	0.764712i	$-0.722881\pi$
$103$	3.60827	−	7.90100i	0.355533	−	0.778509i	0.999905	−	0.0137966i	$-0.00439173\pi$
$104$		−	11.2533i		−	1.10348i
$105$		0			0
$106$	3.60665	−	7.89747i	0.350309	−	0.767070i
$107$	6.05116	+	9.41579i	0.584988	+	0.910259i	1.00000		0.000443055i	$0.000141029\pi$
$107$	6.05116	+	9.41579i	0.584988	+	0.910259i	−0.415012	+	0.909816i	$0.636223\pi$
$108$		0			0
$109$	10.3941	−	4.74681i	0.995571	−	0.454662i	0.150093	−	0.988672i	$-0.452043\pi$
$109$	10.3941	−	4.74681i	0.995571	−	0.454662i	0.845478	+	0.534010i	$0.179315\pi$
$110$	1.34709	−	0.395541i	0.128440	−	0.0377134i
$111$		0			0
$112$	−1.25701	−	1.08920i	−0.118776	−	0.102920i
$113$	−9.82989	+	6.31729i	−0.924719	+	0.594281i	−0.914023	−	0.405662i	$-0.867041\pi$
$113$	−9.82989	+	6.31729i	−0.924719	+	0.594281i	−0.0106955	+	0.999943i	$0.503405\pi$
$114$		0			0
$115$	−1.09420	+	0.157323i	−0.102035	+	0.0146704i
$116$	−1.31275	+	4.47080i	−0.121885	+	0.415104i
$117$		0			0
$118$	12.2492	−	19.0602i	1.12763	−	1.75463i
$119$	0.143865	+	1.00061i	0.0131881	+	0.0917254i
$120$		0			0
$121$	7.84801	+	17.1847i	0.713455	+	1.56225i
$122$	10.9420	−	4.99706i	0.990645	−	0.452412i
$123$		0			0
$124$	−2.18830	−	1.89617i	−0.196515	−	0.170281i
$125$	−0.233042	+	1.62084i	−0.0208439	+	0.144972i
$126$		0			0
$127$	2.88185	−	20.0437i	0.255723	−	1.77859i	−0.306765	−	0.951785i	$-0.599247\pi$
$127$	2.88185	−	20.0437i	0.255723	−	1.77859i	0.562488	−	0.826806i	$-0.309844\pi$
$128$	−11.4191	+	7.33862i	−1.00932	+	0.648648i
$129$		0			0
$130$	−0.334966	+	1.14079i	−0.0293785	+	0.100054i
$131$	−0.179245	+	0.155317i	−0.0156607	+	0.0135701i	−0.662656	−	0.748924i	$-0.730571\pi$
$131$	−0.179245	+	0.155317i	−0.0156607	+	0.0135701i	0.646995	+	0.762494i	$0.276025\pi$
$132$		0			0
$133$			0.482517i			0.0418395i
$134$	10.6813	−	7.05605i	0.922720	−	0.609550i
$135$		0			0
$136$	6.86194	+	0.986598i	0.588407	+	0.0846001i
$137$	−1.97004	−	2.27355i	−0.168312	−	0.194242i	0.665327	−	0.746552i	$-0.268292\pi$
$137$	−1.97004	−	2.27355i	−0.168312	−	0.194242i	−0.833639	+	0.552310i	$0.813747\pi$
$138$		0			0
$139$	−9.27780	+	14.4365i	−0.786933	+	1.22449i	0.183476	+	0.983024i	$0.441265\pi$
$139$	−9.27780	+	14.4365i	−0.786933	+	1.22449i	−0.970409	+	0.241467i	$0.922371\pi$
$140$	0.0140294	+	0.0218302i	0.00118570	+	0.00184499i
$141$		0			0
$142$	2.03735	+	0.930426i	0.170971	+	0.0780796i
$143$	−25.0565	−	3.60258i	−2.09533	−	0.301263i
$144$		0			0
$145$	−0.927561	+	1.44331i	−0.0770298	+	0.119861i
$146$	−3.55078	−	7.77512i	−0.293864	−	0.643473i
$147$		0			0
$148$	2.77710	+	0.815431i	0.228276	+	0.0670280i
$149$	10.4324	−	1.49996i	0.854658	−	0.122881i	0.298960	−	0.954266i	$-0.403360\pi$
$149$	10.4324	−	1.49996i	0.854658	−	0.122881i	0.555698	+	0.831384i	$0.312451\pi$
$150$		0			0
$151$	9.67031	−	2.83946i	0.786958	−	0.231072i	0.136527	−	0.990636i	$-0.456406\pi$
$151$	9.67031	−	2.83946i	0.786958	−	0.231072i	0.650432	+	0.759565i	$0.274588\pi$
$152$	3.17496	+	0.932252i	0.257523	+	0.0756157i
$153$		0			0
$154$	−2.29027	+	1.98453i	−0.184555	+	0.159918i
$155$	−0.576405	−	0.896903i	−0.0462979	−	0.0720410i
$156$		0			0
$157$	9.04316	+	10.4364i	0.721723	+	0.832913i	0.991513	−	0.130007i	$-0.0414998\pi$
$157$	9.04316	+	10.4364i	0.721723	+	0.832913i	−0.269790	+	0.962919i	$0.586954\pi$
$158$	−0.985026	−	3.35469i	−0.0783644	−	0.266885i
$159$		0			0
$160$	0.390491	−	0.114659i	0.0308710	−	0.00906455i
$161$	2.00734	−	1.29004i	0.158201	−	0.101670i
$162$		0			0
$163$	0.659709			0.0516724			0.0258362	−	0.999666i	$-0.491775\pi$
$163$	0.659709			0.0516724			0.0258362	+	0.999666i	$0.491775\pi$
$164$	1.71613			0.134007
$165$		0			0
$166$	16.8563	+	14.6061i	1.30830	+	1.13365i
$167$	15.9250	−	2.28968i	1.23232	−	0.177180i	0.504780	−	0.863248i	$-0.331574\pi$
$167$	15.9250	−	2.28968i	1.23232	−	0.177180i	0.727538	+	0.686068i	$0.240665\pi$
$168$		0			0
$169$	5.52536	−	6.37661i	0.425028	−	0.490508i
$170$	−0.666255	−	0.304269i	−0.0510995	−	0.0233363i
$171$		0			0
$172$		−	3.12894i		−	0.238579i
$173$	10.1819	+	4.64990i	0.774112	+	0.353525i	0.762988	−	0.646413i	$-0.223732\pi$
$173$	10.1819	+	4.64990i	0.774112	+	0.353525i	0.0111245	+	0.999938i	$0.496459\pi$
$174$		0			0
$175$	−0.496556	−	1.69111i	−0.0375361	−	0.127836i
$176$	10.6589	+	23.3396i	0.803441	+	1.75929i
$177$		0			0
$178$	1.38393	−	1.19918i	0.103730	−	0.0898825i
$179$	−7.17935	+	8.28542i	−0.536610	+	0.619281i	−0.957711	−	0.287733i	$-0.907098\pi$
$179$	−7.17935	+	8.28542i	−0.536610	+	0.619281i	0.421101	+	0.907014i	$0.361644\pi$
$180$		0			0
$181$	3.68822	+	4.25643i	0.274143	+	0.316378i	0.876080	−	0.482165i	$-0.160150\pi$
$181$	3.68822	+	4.25643i	0.274143	+	0.316378i	−0.601937	+	0.798544i	$0.705604\pi$
$182$	−0.365231	−	2.54024i	−0.0270727	−	0.188295i
$183$		0			0
$184$	−4.61016	−	15.7008i	−0.339865	−	1.15748i
$185$	0.896534	+	0.576168i	0.0659145	+	0.0423607i
$186$		0			0
$187$	4.39351	−	14.9629i	0.321285	−	1.09420i
$188$	4.41734	−	2.01733i	0.322168	−	0.147129i
$189$		0			0
$190$	−0.294109	−	0.189012i	−0.0213369	−	0.0137124i
$191$	−8.13356	+	9.38663i	−0.588524	+	0.679193i	−0.969415	−	0.245427i	$-0.921072\pi$
$191$	−8.13356	+	9.38663i	−0.588524	+	0.679193i	0.380891	+	0.924620i	$0.375617\pi$
$192$		0			0
$193$	−2.52710	+	5.53359i	−0.181905	+	0.398316i	−0.978515	−	0.206178i	$-0.933897\pi$
$193$	−2.52710	+	5.53359i	−0.181905	+	0.398316i	0.796610	+	0.604494i	$0.206625\pi$
$194$	−12.6929	−	1.82496i	−0.911296	−	0.131025i
$195$		0			0
$196$	2.57886	+	1.65733i	0.184204	+	0.118381i
$197$	−2.10198	−	0.617198i	−0.149760	−	0.0439735i	0.205993	−	0.978553i	$-0.433958\pi$
$197$	−2.10198	−	0.617198i	−0.149760	−	0.0439735i	−0.355753	+	0.934580i	$0.615776\pi$
$198$		0			0
$199$	−1.09329	+	7.60403i	−0.0775015	+	0.539035i	0.913671	+	0.406455i	$0.133235\pi$
$199$	−1.09329	+	7.60403i	−0.0775015	+	0.539035i	−0.991172	+	0.132580i	$0.957674\pi$
$200$	−12.0869			−0.854673
$201$		0			0
$202$	5.17960			0.364436
$203$	0.527032	−	3.66559i	0.0369904	−	0.257274i
$204$		0			0
$205$	0.606291	+	0.178023i	0.0423452	+	0.0124337i
$206$	−11.4279	−	7.34425i	−0.796218	−	0.511698i
$207$		0			0
$208$	−21.5077	−	3.09234i	−1.49129	−	0.214416i
$209$	3.09217	−	6.77090i	0.213890	−	0.468353i
$210$		0			0
$211$	−4.63806	+	5.35261i	−0.319298	+	0.368489i	−0.892596	−	0.450858i	$-0.851118\pi$
$211$	−4.63806	+	5.35261i	−0.319298	+	0.368489i	0.573298	+	0.819347i	$0.305664\pi$
$212$	−2.08254	−	1.33837i	−0.143029	−	0.0919194i
$213$		0			0
$214$	15.9227	−	7.27167i	1.08846	−	0.497081i
$215$	0.324582	−	1.10542i	0.0221363	−	0.0753893i
$216$		0			0
$217$	1.93597	+	1.24417i	0.131422	+	0.0844600i
$218$	−5.03476	−	17.1468i	−0.340997	−	1.16133i
$219$		0			0
$220$	−0.0569703	−	0.396237i	−0.00384094	−	0.0267143i
$221$	8.64835	+	9.98072i	0.581751	+	0.671376i
$222$		0			0
$223$	14.4686	−	16.6977i	0.968890	−	1.11816i	−0.0240703	−	0.999710i	$-0.507663\pi$
$223$	14.4686	−	16.6977i	0.968890	−	1.11816i	0.992960	−	0.118448i	$-0.0377920\pi$
$224$	−0.663897	+	0.575270i	−0.0443585	+	0.0384368i
$225$		0			0
$226$	7.59147	+	16.6230i	0.504977	+	1.10575i
$227$	2.42288	+	8.25158i	0.160812	+	0.547677i	0.999993	+	0.00382349i	$0.00121706\pi$
$227$	2.42288	+	8.25158i	0.160812	+	0.547677i	−0.839180	+	0.543853i	$0.816965\pi$
$228$		0			0
$229$	−23.0590	−	10.5307i	−1.52378	−	0.695888i	−0.534946	−	0.844887i	$-0.679668\pi$
$229$	−23.0590	−	10.5307i	−1.52378	−	0.695888i	−0.988837	+	0.148998i	$0.952395\pi$
$230$			1.72888i			0.113999i
$231$		0			0
$232$	−23.1013	−	10.5500i	−1.51668	−	0.692642i
$233$	7.10126	−	8.19529i	0.465219	−	0.536892i	−0.473856	−	0.880602i	$-0.657138\pi$
$233$	7.10126	−	8.19529i	0.465219	−	0.536892i	0.939076	+	0.343711i	$0.111684\pi$
$234$		0			0
$235$	1.76987	−	0.254469i	0.115454	−	0.0165997i
$236$	−4.88226	−	4.23051i	−0.317808	−	0.275383i
$237$		0			0
$238$	1.58099			0.102480
$239$	−7.73696			−0.500462			−0.250231	−	0.968186i	$-0.580507\pi$
$239$	−7.73696			−0.500462			−0.250231	+	0.968186i	$0.580507\pi$
$240$		0			0
$241$	−21.4283	+	13.7711i	−1.38032	+	0.887077i	−0.999297	−	0.0374891i	$-0.988064\pi$
$241$	−21.4283	+	13.7711i	−1.38032	+	0.887077i	−0.381022	+	0.924566i	$0.624428\pi$
$242$	28.3492	−	8.32408i	1.82236	−	0.535092i
$243$		0			0
$244$	−0.966302	−	3.29092i	−0.0618612	−	0.210680i
$245$	0.739161	+	0.853037i	0.0472232	+	0.0544985i
$246$		0			0
$247$	3.40800	+	5.30295i	0.216846	+	0.337418i
$248$	11.9271	−	10.3349i	0.757370	−	0.656264i
$249$		0			0
$250$	2.45724	+	0.721510i	0.155409	+	0.0456323i
$251$	1.53315	−	0.450174i	0.0967716	−	0.0284147i	−0.232988	−	0.972480i	$-0.574850\pi$
$251$	1.53315	−	0.450174i	0.0967716	−	0.0284147i	0.329760	+	0.944065i	$0.393032\pi$
$252$		0			0
$253$	−36.4351	+	5.23858i	−2.29066	+	0.329347i
$254$	−30.3868	−	8.92237i	−1.90664	−	0.559839i
$255$		0			0
$256$	4.24130	+	9.28716i	0.265081	+	0.580447i
$257$	12.6329	−	19.6571i	0.788017	−	1.22618i	−0.182037	−	0.983292i	$-0.558269\pi$
$257$	12.6329	−	19.6571i	0.788017	−	1.22618i	0.970055	−	0.242887i	$-0.0780945\pi$
$258$		0			0
$259$	−2.27693	−	0.327373i	−0.141482	−	0.0203420i
$260$	0.308371	+	0.140828i	0.0191244	+	0.00873381i
$261$		0			0
$262$	0.200540	+	0.312046i	0.0123894	+	0.0192782i
$263$	−9.79134	+	15.2356i	−0.603760	+	0.939468i	0.396015	+	0.918244i	$0.370393\pi$
$263$	−9.79134	+	15.2356i	−0.603760	+	0.939468i	−0.999775	+	0.0212243i	$0.993244\pi$
$264$		0			0
$265$	−0.596905	−	0.688865i	−0.0366676	−	0.0423166i
$266$	0.746950	+	0.107395i	0.0457984	+	0.00658482i
$267$		0			0
$268$	−1.55799	−	3.30088i	−0.0951695	−	0.201633i
$269$			9.47302i			0.577580i	0.957392	+	0.288790i	$0.0932530\pi$
$269$			9.47302i			0.577580i	−0.957392	+	0.288790i	$0.906747\pi$
$270$		0			0
$271$	−3.14870	+	2.72836i	−0.191270	+	0.165736i	−0.745231	−	0.666806i	$-0.767661\pi$
$271$	−3.14870	+	2.72836i	−0.191270	+	0.165736i	0.553962	+	0.832542i	$0.313115\pi$
$272$	3.77125	−	12.8437i	0.228666	−	0.778764i
$273$		0			0
$274$	−3.95799	+	2.54365i	−0.239111	+	0.153667i
$275$	−3.86945	+	26.9126i	−0.233337	+	1.62289i
$276$		0			0
$277$	1.12197	−	7.80348i	0.0674127	−	0.468866i	−0.927952	−	0.372699i	$-0.878433\pi$
$277$	1.12197	−	7.80348i	0.0674127	−	0.468866i	0.995365	−	0.0961672i	$-0.0306584\pi$
$278$	20.2832	+	17.5755i	1.21650	+	1.05411i
$279$		0			0
$280$	−0.128654	+	0.0587543i	−0.00768854	+	0.00351124i
$281$	0.896186	+	1.96237i	0.0534620	+	0.117065i	0.934478	−	0.356021i	$-0.115867\pi$
$281$	0.896186	+	1.96237i	0.0534620	+	0.117065i	−0.881016	+	0.473087i	$0.843140\pi$
$282$		0			0
$283$	1.00440	+	6.98578i	0.0597056	+	0.415262i	0.997652	+	0.0684823i	$0.0218157\pi$
$283$	1.00440	+	6.98578i	0.0597056	+	0.415262i	−0.937947	+	0.346779i	$0.887275\pi$
$284$	0.345265	−	0.537242i	0.0204877	−	0.0318795i
$285$		0			0
$286$	−11.1538	+	37.9864i	−0.659538	+	2.24618i
$287$	−1.35005	+	0.194108i	−0.0796908	+	0.0114578i
$288$		0			0
$289$	7.45712	−	4.79240i	0.438654	−	0.281906i
$290$	2.02784	+	1.75713i	0.119079	+	0.103182i
$291$		0			0
$292$	−2.33844	+	0.686629i	−0.136847	+	0.0401819i
$293$	−22.2265	+	10.1505i	−1.29849	+	0.592999i	−0.940203	−	0.340614i	$-0.889365\pi$
$293$	−22.2265	+	10.1505i	−1.29849	+	0.592999i	−0.358283	+	0.933613i	$0.616638\pi$
$294$		0			0
$295$	−1.28600	−	2.00106i	−0.0748740	−	0.116506i
$296$	−6.55329	+	14.3497i	−0.380902	+	0.834059i
$297$		0			0
$298$		−	16.4835i		−	0.954866i
$299$	12.9496	−	28.3556i	0.748892	−	1.63985i
$300$		0			0
$301$	0.353908	+	2.46148i	0.0203989	+	0.141878i
$302$	−2.24321	−	15.6019i	−0.129082	−	0.897788i
$303$		0			0
$304$	2.65422	−	5.81193i	0.152230	−	0.333337i
$305$		−	1.26289i		−	0.0723129i
$306$		0			0
$307$	−2.78945	+	6.10805i	−0.159202	+	0.348605i	−0.972377	−	0.233415i	$-0.925010\pi$
$307$	−2.78945	+	6.10805i	−0.159202	+	0.348605i	0.813175	+	0.582020i	$0.197737\pi$
$308$	0.467155	+	0.726907i	0.0266186	+	0.0414194i
$309$		0			0
$310$	−1.51672	+	0.692664i	−0.0861441	+	0.0393407i
$311$	−14.8485	+	4.35991i	−0.841980	+	0.247228i	−0.674156	−	0.738589i	$-0.735492\pi$
$311$	−14.8485	+	4.35991i	−0.841980	+	0.247228i	−0.167825	+	0.985817i	$0.553674\pi$
$312$		0			0
$313$	−22.9386	−	19.8764i	−1.29657	−	1.12348i	−0.984869	−	0.173298i	$-0.944557\pi$
$313$	−22.9386	−	19.8764i	−1.29657	−	1.12348i	−0.311696	−	0.950182i	$-0.600897\pi$
$314$	18.1685	−	11.6762i	1.02531	−	0.658927i
$315$		0			0
$316$	−0.986759	+	0.141875i	−0.0555096	+	0.00798107i
$317$	5.96229	−	20.3057i	0.334875	−	1.14048i	−0.604218	−	0.796819i	$-0.706514\pi$
$317$	5.96229	−	20.3057i	0.334875	−	1.14048i	0.939093	−	0.343662i	$-0.111667\pi$
$318$		0			0
$319$	−30.8862	+	48.0598i	−1.72929	+	2.69083i
$320$	0.128742	+	0.895423i	0.00719692	+	0.0500557i
$321$		0			0
$322$	−1.55024	−	3.39455i	−0.0863915	−	0.189171i
$323$	−3.53238	+	1.61318i	−0.196547	+	0.0897598i
$324$		0			0
$325$	−17.4015	−	15.0785i	−0.965261	−	0.836404i
$326$	0.146833	−	1.02125i	0.00813234	−	0.0565617i
$327$		0			0
$328$	−1.33115	+	9.25834i	−0.0735004	+	0.511206i
$329$	−3.24687	+	2.08664i	−0.179006	+	0.115040i
$330$		0			0
$331$	−2.56205	+	8.72555i	−0.140823	+	0.479600i	−0.999456	−	0.0329921i	$-0.989496\pi$
$331$	−2.56205	+	8.72555i	−0.140823	+	0.479600i	0.858632	+	0.512592i	$0.171315\pi$
$332$	4.80625	−	4.16464i	0.263777	−	0.228564i
$333$		0			0
$334$		−	25.1620i		−	1.37681i
$335$	−0.208005	−	1.32779i	−0.0113645	−	0.0725447i
$336$		0			0
$337$	−32.1176	−	4.61781i	−1.74956	−	0.251548i	−0.808187	−	0.588926i	$-0.799551\pi$
$337$	−32.1176	−	4.61781i	−1.74956	−	0.251548i	−0.941369	+	0.337378i	$0.890460\pi$
$338$	−8.64137	−	9.97268i	−0.470029	−	0.542442i
$339$		0			0
$340$	−0.112909	+	0.175689i	−0.00612334	+	0.00952810i
$341$	−19.1933	−	29.8653i	−1.03937	−	1.61730i
$342$		0			0
$343$	−4.47289	−	2.04270i	−0.241514	−	0.110296i
$344$	16.8803	+	2.42703i	0.910126	+	0.130856i
$345$		0			0
$346$	9.46438	−	14.7269i	0.508808	−	0.791721i
$347$	−4.54515	−	9.95249i	−0.243996	−	0.534278i	0.747523	−	0.664236i	$-0.231243\pi$
$347$	−4.54515	−	9.95249i	−0.243996	−	0.534278i	−0.991519	+	0.129958i	$0.958516\pi$
$348$		0			0
$349$	−7.75142	−	2.27602i	−0.414924	−	0.121833i	0.0676059	−	0.997712i	$-0.478464\pi$
$349$	−7.75142	−	2.27602i	−0.414924	−	0.121833i	−0.482530	+	0.875879i	$0.660282\pi$
$350$	−2.72841	+	0.392286i	−0.145840	+	0.0209686i
$351$		0			0
$352$	13.0027	−	3.81793i	0.693045	−	0.203496i
$353$	20.3761	+	5.98297i	1.08451	+	0.318441i	0.774682	−	0.632351i	$-0.217910\pi$
$353$	20.3761	+	5.98297i	1.08451	+	0.318441i	0.309829	+	0.950792i	$0.399728\pi$
$354$		0			0
$355$	0.177710	−	0.153986i	0.00943185	−	0.00817275i
$356$	−0.282286	−	0.439245i	−0.0149611	−	0.0232799i
$357$		0			0
$358$	11.2281	+	12.9579i	0.593425	+	0.684849i
$359$	6.91941	+	23.5653i	0.365193	+	1.24373i	0.913288	+	0.407315i	$0.133535\pi$
$359$	6.91941	+	23.5653i	0.365193	+	1.24373i	−0.548095	+	0.836416i	$0.684647\pi$
$360$		0			0
$361$	16.4519	−	4.83071i	0.865889	−	0.254248i
$362$	7.40998	−	4.76210i	0.389460	−	0.250291i
$363$		0			0
$364$	−0.731748			−0.0383540
$365$	−0.897377			−0.0469708
$366$		0			0
$367$	−15.5832	−	13.5030i	−0.813438	−	0.704848i	0.145223	−	0.989399i	$-0.453610\pi$
$367$	−15.5832	−	13.5030i	−0.813438	−	0.704848i	−0.958661	+	0.284551i	$0.908156\pi$
$368$	−31.2748	+	4.49663i	−1.63031	+	0.234403i
$369$		0			0
$370$	1.09147	−	1.25962i	0.0567427	−	0.0654846i
$371$	1.78968	+	0.817319i	0.0929155	+	0.0424331i
$372$		0			0
$373$		−	33.3121i		−	1.72483i	−0.506199	−	0.862417i	$-0.668950\pi$
$373$		−	33.3121i		−	1.72483i	0.506199	−	0.862417i	$-0.331050\pi$
$374$	−22.1852	−	10.1316i	−1.14717	−	0.523894i
$375$		0			0
$376$	7.45691	+	25.3959i	0.384561	+	1.30969i
$377$	−20.0977	−	44.0079i	−1.03509	−	2.26652i
$378$		0			0
$379$	17.0574	−	14.7803i	0.876181	−	0.759215i	−0.0955205	−	0.995427i	$-0.530452\pi$
$379$	17.0574	−	14.7803i	0.876181	−	0.759215i	0.971701	+	0.236212i	$0.0759061\pi$
$380$	−0.0652791	+	0.0753361i	−0.00334875	+	0.00386466i
$381$		0			0
$382$	12.7205	+	14.6802i	0.650835	+	0.751104i
$383$	0.0815547	+	0.567225i	0.00416725	+	0.0289839i	0.991799	−	0.127808i	$-0.0407940\pi$
$383$	0.0815547	+	0.567225i	0.00416725	+	0.0289839i	−0.987632	+	0.156792i	$0.949885\pi$
$384$		0			0
$385$	0.0896352	+	0.305270i	0.00456823	+	0.0155580i
$386$	8.00368	+	5.14365i	0.407377	+	0.261805i
$387$		0			0
$388$	−1.03011	+	3.50824i	−0.0522960	+	0.178104i
$389$	1.31321	−	0.599723i	0.0665824	−	0.0304072i	−0.381845	−	0.924226i	$-0.624711\pi$
$389$	1.31321	−	0.599723i	0.0665824	−	0.0304072i	0.448428	+	0.893819i	$0.351984\pi$
$390$		0			0
$391$	16.1551	+	10.3823i	0.817000	+	0.525054i
$392$	−10.9415	+	12.6271i	−0.552628	+	0.637767i
$393$		0			0
$394$	−1.42328	+	3.11656i	−0.0717040	+	0.157010i
$395$	−0.363330	−	0.0522390i	−0.0182811	−	0.00262843i
$396$		0			0
$397$	11.3803	+	7.31366i	0.571160	+	0.367062i	0.794116	−	0.607766i	$-0.207934\pi$
$397$	11.3803	+	7.31366i	0.571160	+	0.367062i	−0.222956	+	0.974829i	$0.571571\pi$
$398$	11.5279	+	3.38490i	0.577842	+	0.169670i
$399$		0			0
$400$	−3.32142	+	23.1010i	−0.166071	+	1.15505i
$401$	22.4700			1.12210			0.561049	−	0.827783i	$-0.310398\pi$
$401$	22.4700			1.12210			0.561049	+	0.827783i	$0.310398\pi$
$402$		0			0
$403$	30.0642			1.49760
$404$	0.210180	−	1.46183i	0.0104568	−	0.0727288i
$405$		0			0
$406$	−5.55713	−	1.63172i	−0.275796	−	0.0809809i
$407$	29.8530	+	19.1854i	1.47976	+	0.950984i
$408$		0			0
$409$	19.1910	+	2.75925i	0.948935	+	0.136436i	0.599367	−	0.800474i	$-0.295419\pi$
$409$	19.1910	+	2.75925i	0.948935	+	0.136436i	0.349569	+	0.936911i	$0.386328\pi$
$410$	0.410528	−	0.898932i	0.0202746	−	0.0443951i
$411$		0			0
$412$	−2.53648	+	2.92725i	−0.124963	+	0.144215i
$413$	4.31930	+	2.77585i	0.212539	+	0.136590i
$414$		0			0
$415$	2.13002	−	0.972749i	0.104559	−	0.0477504i
$416$	−3.23324	+	11.0114i	−0.158522	+	0.539878i
$417$		0			0
$418$	−9.79332	−	6.29378i	−0.479007	−	0.307839i
$419$	−7.70527	−	26.2417i	−0.376427	−	1.28199i	−0.902182	−	0.431356i	$-0.858035\pi$
$419$	−7.70527	−	26.2417i	−0.376427	−	1.28199i	0.525755	−	0.850636i	$-0.323783\pi$
$420$		0			0
$421$	1.25757	+	8.74660i	0.0612903	+	0.426283i	0.997246	+	0.0741654i	$0.0236293\pi$
$421$	1.25757	+	8.74660i	0.0612903	+	0.426283i	−0.935956	+	0.352118i	$0.885462\pi$
$422$	7.25369	+	8.37120i	0.353104	+	0.407504i
$423$		0			0
$424$	8.83572	−	10.1970i	0.429101	−	0.495209i
$425$	10.7201	−	9.28899i	0.519999	−	0.450582i
$426$		0			0
$427$	1.13240	+	2.47962i	0.0548009	+	0.119997i
$428$	−1.40615	−	4.78892i	−0.0679690	−	0.231481i
$429$		0			0
$430$	−1.63898	−	0.748499i	−0.0790388	−	0.0360958i
$431$		−	9.76897i		−	0.470555i	−0.971928	−	0.235277i	$-0.924400\pi$
$431$		−	9.76897i		−	0.470555i	0.971928	−	0.235277i	$-0.0755999\pi$
$432$		0			0
$433$	−14.7653	−	6.74308i	−0.709575	−	0.324052i	0.0277269	−	0.999616i	$-0.491173\pi$
$433$	−14.7653	−	6.74308i	−0.709575	−	0.324052i	−0.737302	+	0.675564i	$0.763900\pi$
$434$	2.35691	−	2.72002i	0.113135	−	0.130565i
$435$		0			0
$436$	−5.04362	+	0.725163i	−0.241546	+	0.0347290i
$437$	6.92736	+	6.00259i	0.331381	+	0.287143i
$438$		0			0
$439$	2.68724			0.128255			0.0641275	−	0.997942i	$-0.479574\pi$
$439$	2.68724			0.128255			0.0641275	+	0.997942i	$0.479574\pi$
$440$	2.18185			0.104016
$441$		0			0
$442$	17.3753	−	11.1664i	0.826460	−	0.531134i
$443$	−9.02501	+	2.64998i	−0.428791	+	0.125904i	−0.489005	−	0.872281i	$-0.662640\pi$
$443$	−9.02501	+	2.64998i	−0.428791	+	0.125904i	0.0602138	+	0.998186i	$0.480822\pi$
$444$		0			0
$445$	−0.0541635	−	0.184464i	−0.00256760	−	0.00874443i
$446$	−22.6281	−	26.1143i	−1.07147	−	1.23655i
$447$		0			0
$448$	−1.05568	−	1.64268i	−0.0498763	−	0.0776091i
$449$	18.1117	−	15.6938i	0.854742	−	0.740638i	−0.112727	−	0.993626i	$-0.535959\pi$
$449$	18.1117	−	15.6938i	0.854742	−	0.740638i	0.967470	+	0.252988i	$0.0814132\pi$
$450$		0			0
$451$	20.1884	+	5.92786i	0.950636	+	0.279132i
$452$	4.99953	−	1.46800i	0.235158	−	0.0690487i
$453$		0			0
$454$	13.3130	−	1.91411i	0.624808	−	0.0898338i
$455$	−0.258519	−	0.0759081i	−0.0121196	−	0.00355863i
$456$		0			0
$457$	−0.946292	−	2.07209i	−0.0442657	−	0.0969283i	0.886207	−	0.463289i	$-0.153331\pi$
$457$	−0.946292	−	2.07209i	−0.0442657	−	0.0969283i	−0.930473	+	0.366361i	$0.880604\pi$
$458$	−21.4341	+	33.3522i	−1.00155	+	1.55844i
$459$		0			0
$460$	0.487938	+	0.0701549i	0.0227502	+	0.00327099i
$461$	−28.6745	−	13.0952i	−1.33550	−	0.609903i	−0.385662	−	0.922640i	$-0.626027\pi$
$461$	−28.6745	−	13.0952i	−1.33550	−	0.609903i	−0.949840	+	0.312736i	$0.898754\pi$
$462$		0			0
$463$	−6.98678	−	10.8716i	−0.324703	−	0.505248i	0.640075	−	0.768312i	$-0.278903\pi$
$463$	−6.98678	−	10.8716i	−0.324703	−	0.505248i	−0.964778	+	0.263064i	$0.915267\pi$
$464$	−26.5117	+	41.2530i	−1.23078	+	1.91512i
$465$		0			0
$466$	−11.1060	−	12.8170i	−0.514475	−	0.593736i
$467$	−25.7942	−	3.70865i	−1.19361	−	0.171616i	−0.483271	−	0.875471i	$-0.660551\pi$
$467$	−25.7942	−	3.70865i	−1.19361	−	0.171616i	−0.710343	+	0.703855i	$0.751460\pi$
$468$		0			0
$469$	1.59900	+	2.42052i	0.0738350	+	0.111769i
$470$		−	2.79645i		−	0.128991i
$471$		0			0
$472$	26.6102	−	23.0579i	1.22483	−	1.06133i
$473$	10.8080	−	36.8087i	0.496953	−	1.69247i
$474$		0			0
$475$	5.69577	−	3.66045i	0.261340	−	0.167953i
$476$	0.0641538	−	0.446199i	0.00294048	−	0.0204515i
$477$		0			0
$478$	−1.72204	+	11.9770i	−0.0787641	+	0.547816i
$479$	20.0434	+	17.3677i	0.915807	+	0.793551i	0.978875	−	0.204458i	$-0.0655431\pi$
$479$	20.0434	+	17.3677i	0.915807	+	0.793551i	−0.0630682	+	0.998009i	$0.520089\pi$
$480$		0			0
$481$	−27.3361	+	12.4840i	−1.24642	+	0.569221i
$482$	16.5487	+	36.2367i	0.753775	+	1.65054i
$483$		0			0
$484$	−1.19893	−	8.33873i	−0.0544967	−	0.379033i
$485$	−0.727857	+	1.13257i	−0.0330503	+	0.0514272i
$486$		0			0
$487$	−7.63197	+	25.9921i	−0.345837	+	1.17781i	0.584587	+	0.811331i	$0.301256\pi$
$487$	−7.63197	+	25.9921i	−0.345837	+	1.17781i	−0.930425	+	0.366483i	$0.880562\pi$
$488$	18.5038	−	2.66044i	0.837626	−	0.120432i
$489$		0			0
$490$	1.48504	−	0.954379i	0.0670874	−	0.0431144i
$491$	−9.05167	−	7.84332i	−0.408496	−	0.353964i	0.426244	−	0.904608i	$-0.359837\pi$
$491$	−9.05167	−	7.84332i	−0.408496	−	0.353964i	−0.834740	+	0.550644i	$0.814382\pi$
$492$		0			0
$493$	28.5968	−	8.39678i	1.28793	−	0.378172i
$494$	8.96764	−	4.09538i	0.403473	−	0.184260i
$495$		0			0
$496$	−16.4749	−	25.6355i	−0.739745	−	1.15107i
$497$	−0.210848	+	0.461692i	−0.00945781	+	0.0207097i
$498$		0			0
$499$			21.0318i			0.941513i	0.882263	+	0.470756i	$0.156019\pi$
$499$			21.0318i			0.941513i	−0.882263	+	0.470756i	$0.843981\pi$
$500$	0.303341	−	0.664224i	0.0135658	−	0.0297050i
$501$		0			0
$502$	−0.355644	−	2.47356i	−0.0158732	−	0.110400i
$503$	−2.18094	−	15.1687i	−0.0972432	−	0.676341i	−0.978883	−	0.204419i	$-0.934469\pi$
$503$	−2.18094	−	15.1687i	−0.0972432	−	0.676341i	0.881640	−	0.471922i	$-0.156440\pi$
$504$		0			0
$505$	0.225898	−	0.494648i	0.0100523	−	0.0220115i
$506$			57.5686i			2.55923i
$507$		0			0
$508$	−3.75119	+	8.21396i	−0.166432	+	0.364435i
$509$	9.34541	+	14.5417i	0.414228	+	0.644551i	0.984189	−	0.177120i	$-0.0566782\pi$
$509$	9.34541	+	14.5417i	0.414228	+	0.644551i	−0.569961	+	0.821672i	$0.693042\pi$
$510$		0			0
$511$	1.76195	−	0.804656i	0.0779441	−	0.0355959i
$512$	−10.7274	+	3.14985i	−0.474088	+	0.139205i
$513$		0			0
$514$	−27.6181	−	23.9312i	−1.21818	−	1.05556i
$515$	−1.19977	+	0.771047i	−0.0528683	+	0.0339764i
$516$		0			0
$517$	58.9337	−	8.47338i	2.59190	−	0.372659i
$518$	−1.01357	+	3.45189i	−0.0445335	+	0.151667i
$519$		0			0
$520$	−0.998950	+	1.55440i	−0.0438069	+	0.0681648i
$521$	−3.76161	−	26.1626i	−0.164799	−	1.14620i	−0.889432	−	0.457068i	$-0.848899\pi$
$521$	−3.76161	−	26.1626i	−0.164799	−	1.14620i	0.724632	−	0.689136i	$-0.242010\pi$
$522$		0			0
$523$	−6.42225	−	14.0628i	−0.280825	−	0.614922i	0.715682	−	0.698426i	$-0.246116\pi$
$523$	−6.42225	−	14.0628i	−0.280825	−	0.614922i	−0.996507	+	0.0835044i	$0.973389\pi$
$524$	0.0962057	−	0.0439357i	0.00420276	−	0.00191934i
$525$		0			0
$526$	21.4059	+	18.5483i	0.933340	+	0.808744i
$527$	−2.63579	+	18.3323i	−0.114817	+	0.798568i
$528$		0			0
$529$	3.17769	−	22.1013i	0.138161	−	0.960928i
$530$	−1.19924	+	0.770703i	−0.0520915	+	0.0334772i
$531$		0			0
$532$	0.0606199	−	0.206452i	0.00262821	−	0.00895085i
$533$	−13.4663	+	11.6686i	−0.583290	+	0.505424i
$534$		0			0
$535$		−	1.83775i		−	0.0794527i
$536$	19.0164	−	5.84482i	0.821384	−	0.252458i
$537$		0			0
$538$	14.6645	+	2.10844i	0.632232	+	0.0909012i
$539$	24.6128	+	28.4047i	1.06015	+	1.22347i
$540$		0			0
$541$	−13.0798	+	20.3525i	−0.562344	+	0.875024i	−0.999706	−	0.0242616i	$-0.992277\pi$
$541$	−13.0798	+	20.3525i	−0.562344	+	0.875024i	0.437362	+	0.899286i	$0.355913\pi$
$542$	3.52276	+	5.48153i	0.151316	+	0.235452i
$543$		0			0
$544$	−6.43098	−	2.93693i	−0.275726	−	0.125920i
$545$	−1.85709	−	0.267009i	−0.0795489	−	0.0114374i
$546$		0			0
$547$	−5.81387	+	9.04656i	−0.248583	+	0.386803i	−0.943012	−	0.332758i	$-0.892021\pi$
$547$	−5.81387	+	9.04656i	−0.248583	+	0.386803i	0.694429	+	0.719561i	$0.255657\pi$
$548$	0.557280	+	1.22027i	0.0238058	+	0.0521275i
$549$		0			0
$550$	40.8003	+	11.9800i	1.73973	+	0.510831i
$551$	14.0812	−	2.02457i	0.599878	−	0.0862494i
$552$		0			0
$553$	0.760220	−	0.223221i	0.0323278	−	0.00949231i
$554$	−11.8303	−	3.47369i	−0.502621	−	0.147583i
$555$		0			0
$556$	5.78335	−	5.01130i	0.245269	−	0.212527i
$557$	−0.546821	−	0.850870i	−0.0231695	−	0.0360525i	0.829476	−	0.558543i	$-0.188639\pi$
$557$	−0.546821	−	0.850870i	−0.0231695	−	0.0360525i	−0.852645	+	0.522490i	$0.825003\pi$
$558$		0			0
$559$	21.2749	+	24.5525i	0.899831	+	1.03846i
$560$	0.0769401	+	0.262034i	0.00325131	+	0.0110729i
$561$		0			0
$562$	3.23727	−	0.950550i	0.136556	−	0.0400965i
$563$	−0.0104498	+	0.00671569i	−0.000440407	+	0.000283033i	−0.540861	−	0.841112i	$-0.681902\pi$
$563$	−0.0104498	+	0.00671569i	−0.000440407	+	0.000283033i	0.540421	+	0.841395i	$0.318265\pi$
$564$		0			0
$565$	1.91857			0.0807148
$566$	11.0377			0.463951
$567$		0			0
$568$	2.63056	+	2.27939i	0.110376	+	0.0956413i
$569$	16.9953	−	2.44356i	0.712481	−	0.102439i	0.223462	−	0.974713i	$-0.428264\pi$
$569$	16.9953	−	2.44356i	0.712481	−	0.102439i	0.489019	+	0.872273i	$0.337355\pi$
$570$		0			0
$571$	16.8488	−	19.4446i	0.705102	−	0.813731i	−0.284330	−	0.958726i	$-0.591771\pi$
$571$	16.8488	−	19.4446i	0.705102	−	0.813731i	0.989432	+	0.144995i	$0.0463167\pi$
$572$	10.2682	+	4.68934i	0.429336	+	0.196071i
$573$		0			0
$574$			2.13312i			0.0890345i
$575$	−30.4561	−	13.9088i	−1.27011	−	0.580038i
$576$		0			0
$577$	3.65774	+	12.4571i	0.152274	+	0.518597i	0.999929	−	0.0119511i	$-0.00380424\pi$
$577$	3.65774	+	12.4571i	0.152274	+	0.518597i	−0.847655	+	0.530548i	$0.821986\pi$
$578$	−5.75902	−	12.6105i	−0.239544	−	0.524527i
$579$		0			0
$580$	0.578199	−	0.501012i	0.0240084	−	0.0208034i
$581$	−3.30994	+	3.81988i	−0.137320	+	0.158475i
$582$		0			0
$583$	−19.8759	−	22.9380i	−0.823175	−	0.949995i
$584$	−1.89044	−	13.1483i	−0.0782268	−	0.544080i
$585$		0			0
$586$	10.7662	+	36.6665i	0.444750	+	1.51468i
$587$	13.7702	+	8.84959i	0.568358	+	0.365262i	0.793039	−	0.609171i	$-0.208498\pi$
$587$	13.7702	+	8.84959i	0.568358	+	0.365262i	−0.224681	+	0.974432i	$0.572134\pi$
$588$		0			0
$589$	−2.49060	+	8.48220i	−0.102623	+	0.349503i
$590$	−3.38393	+	1.54539i	−0.139314	+	0.0636226i
$591$		0			0
$592$	25.6249	+	16.4681i	1.05318	+	0.676836i
$593$	−22.6710	+	26.1638i	−0.930987	+	1.07442i	0.0660744	+	0.997815i	$0.478953\pi$
$593$	−22.6710	+	26.1638i	−0.930987	+	1.07442i	−0.997062	+	0.0766019i	$0.975593\pi$
$594$		0			0
$595$	0.0689516	−	0.150983i	0.00282674	−	0.00618969i
$596$	−4.65212	−	0.668874i	−0.190558	−	0.0273982i
$597$		0			0
$598$	−41.0130	−	26.3575i	−1.67715	−	1.07784i
$599$	−0.612977	−	0.179986i	−0.0250455	−	0.00735404i	0.269186	−	0.963088i	$-0.413245\pi$
$599$	−0.612977	−	0.179986i	−0.0250455	−	0.00735404i	−0.294231	+	0.955734i	$0.595064\pi$
$600$		0			0
$601$	6.52206	−	45.3619i	0.266040	−	1.85035i	−0.218826	−	0.975764i	$-0.570223\pi$
$601$	6.52206	−	45.3619i	0.266040	−	1.85035i	0.484867	−	0.874588i	$-0.338868\pi$
$602$	3.88922			0.158513
$603$		0			0
$604$	−4.49432			−0.182871
$605$	0.441452	−	3.07036i	0.0179476	−	0.124828i
$606$		0			0
$607$	−14.2945	−	4.19724i	−0.580195	−	0.170361i	−0.0215503	−	0.999768i	$-0.506860\pi$
$607$	−14.2945	−	4.19724i	−0.580195	−	0.170361i	−0.558645	+	0.829407i	$0.688678\pi$
$608$	−2.83886	−	1.82443i	−0.115131	−	0.0739903i
$609$		0			0
$610$	−1.95499	−	0.281085i	−0.0791553	−	0.0113808i
$611$	−20.9459	+	45.8650i	−0.847379	+	1.85550i
$612$		0			0
$613$	−24.5072	+	28.2828i	−0.989837	+	1.14233i	−1.84242e−5		1.00000i	$0.500006\pi$
$613$	−24.5072	+	28.2828i	−0.989837	+	1.14233i	−0.989819	+	0.142333i	$0.954540\pi$
$614$	8.83458	+	5.67764i	0.356534	+	0.229131i
$615$		0			0
$616$	−4.28395	+	1.95642i	−0.172605	+	0.0788262i
$617$	−3.35168	+	11.4148i	−0.134934	+	0.459542i	−0.999042	−	0.0437641i	$-0.986065\pi$
$617$	−3.35168	+	11.4148i	−0.134934	+	0.459542i	0.864108	+	0.503306i	$0.167883\pi$
$618$		0			0
$619$	13.3959	+	8.60900i	0.538426	+	0.346025i	0.781423	−	0.624002i	$-0.214494\pi$
$619$	13.3959	+	8.60900i	0.538426	+	0.346025i	−0.242997	+	0.970027i	$0.578131\pi$
$620$	0.133943	+	0.456169i	0.00537930	+	0.0183202i
$621$		0			0
$622$	3.44439	+	23.9563i	0.138108	+	0.960559i
$623$	0.271752	+	0.313618i	0.0108875	+	0.0125648i
$624$		0			0
$625$	−16.1072	+	18.5887i	−0.644287	+	0.743547i
$626$	−35.8747	+	31.0856i	−1.43384	+	1.24243i
$627$		0			0
$628$	−2.55811	−	5.60148i	−0.102080	−	0.223523i
$629$	−5.21577	−	17.7633i	−0.207967	−	0.708269i
$630$		0			0
$631$	31.3865	+	14.3337i	1.24948	+	0.570616i	0.926680	−	0.375852i	$-0.122650\pi$
$631$	31.3865	+	14.3337i	1.24948	+	0.570616i	0.322796	+	0.946469i	$0.395377\pi$
$632$		−	5.43352i		−	0.216134i
$633$		0			0
$634$	−30.1067	−	13.7493i	−1.19569	−	0.546054i
$635$	−2.17734	+	2.51278i	−0.0864050	+	0.0997167i
$636$		0			0
$637$	−31.5049	+	4.52972i	−1.24827	+	0.179474i
$638$	67.5235	+	58.5095i	2.67328	+	2.31641i
$639$		0			0
$640$	2.22875			0.0880990
$641$	40.8530			1.61359			0.806797	−	0.590828i	$-0.201199\pi$
$641$	40.8530			1.61359			0.806797	+	0.590828i	$0.201199\pi$
$642$		0			0
$643$	−23.5703	+	15.1477i	−0.929523	+	0.597368i	−0.915406	−	0.402532i	$-0.868130\pi$
$643$	−23.5703	+	15.1477i	−0.929523	+	0.597368i	−0.0141170	+	0.999900i	$0.504494\pi$
$644$	−1.02095	+	0.299777i	−0.0402309	+	0.0118129i
$645$		0			0
$646$	1.71104	+	5.82727i	0.0673200	+	0.229271i
$647$	−16.9407	−	19.5506i	−0.666008	−	0.768614i	0.317739	−	0.948178i	$-0.397077\pi$
$647$	−16.9407	−	19.5506i	−0.666008	−	0.768614i	−0.983746	+	0.179565i	$0.942531\pi$
$648$		0			0
$649$	−42.8217	−	66.6318i	−1.68090	−	2.61553i
$650$	−27.2150	+	23.5819i	−1.06746	+	0.924960i
$651$		0			0
$652$	−0.282267	−	0.0828810i	−0.0110544	−	0.00324587i
$653$	4.28834	−	1.25917i	0.167816	−	0.0492751i	−0.196745	−	0.980455i	$-0.563037\pi$
$653$	4.28834	−	1.25917i	0.167816	−	0.0492751i	0.364561	+	0.931179i	$0.381219\pi$
$654$		0			0
$655$	0.0385462	−	0.00554211i	0.00150613	−	0.000216548i
$656$	17.3291	+	5.08829i	0.676588	+	0.198664i
$657$		0			0
$658$	2.50751	+	5.49068i	0.0977528	+	0.214049i
$659$	19.5491	−	30.4190i	0.761526	−	1.18496i	−0.216461	−	0.976291i	$-0.569451\pi$
$659$	19.5491	−	30.4190i	0.761526	−	1.18496i	0.977987	−	0.208666i	$-0.0669122\pi$
$660$		0			0
$661$	49.7906	+	7.15881i	1.93663	+	0.278445i	0.997820	−	0.0659908i	$-0.0210208\pi$
$661$	49.7906	+	7.15881i	1.93663	+	0.278445i	0.938810	+	0.344436i	$0.111930\pi$
$662$	12.9372	+	5.90820i	0.502817	+	0.229629i
$663$		0			0
$664$	18.7398	+	29.1597i	0.727244	+	1.13161i
$665$	0.0428329	−	0.0666492i	0.00166099	−	0.00258455i
$666$		0			0
$667$	−46.0695	−	53.1670i	−1.78382	−	2.05863i
$668$	−7.10144	−	1.02103i	−0.274763	−	0.0395050i
$669$		0			0
$670$	−2.10175	+	0.0264688i	−0.0811976	+	0.00102258i
$671$		−	42.0521i		−	1.62340i
$672$		0			0
$673$	−2.30211	+	1.99479i	−0.0887400	+	0.0768936i	−0.698101	−	0.715999i	$-0.745971\pi$
$673$	−2.30211	+	1.99479i	−0.0887400	+	0.0768936i	0.609361	+	0.792893i	$0.291426\pi$
$674$	−14.2970	+	48.6911i	−0.550700	+	1.87551i
$675$		0			0
$676$	−3.16522	+	2.03417i	−0.121739	+	0.0782372i
$677$	1.76154	−	12.2518i	0.0677014	−	0.470874i	−0.927563	−	0.373667i	$-0.878100\pi$
$677$	1.76154	−	12.2518i	0.0677014	−	0.470874i	0.995264	−	0.0972065i	$-0.0309907\pi$
$678$		0			0
$679$	0.413562	−	2.87639i	0.0158710	−	0.110386i
$680$	−0.860248	−	0.745409i	−0.0329890	−	0.0285851i
$681$		0			0
$682$	−50.5043	+	23.0645i	−1.93391	+	0.883186i
$683$	2.96652	+	6.49577i	0.113511	+	0.248554i	0.957858	−	0.287243i	$-0.0927387\pi$
$683$	2.96652	+	6.49577i	0.113511	+	0.248554i	−0.844347	+	0.535797i	$0.820011\pi$
$684$		0			0
$685$	0.0702962	+	0.488921i	0.00268588	+	0.0186807i
$686$	−4.15770	+	6.46951i	−0.158742	+	0.247007i
$687$		0			0
$688$	9.27725	−	31.5954i	0.353692	−	1.20456i
$689$	25.4416	−	3.65795i	0.969247	−	0.139357i
$690$		0			0
$691$	−6.21782	+	3.99595i	−0.236537	+	0.152013i	−0.653540	−	0.756892i	$-0.726717\pi$
$691$	−6.21782	+	3.99595i	−0.236537	+	0.152013i	0.417003	+	0.908905i	$0.363080\pi$
$692$	−3.77229	−	3.26871i	−0.143401	−	0.124258i
$693$		0			0
$694$	−16.4184	+	4.82086i	−0.623232	+	0.182997i
$695$	2.56305	−	1.17051i	0.0972221	−	0.0443999i
$696$		0			0
$697$	−5.93458	−	9.23438i	−0.224788	−	0.349777i
$698$	−5.24860	+	11.4928i	−0.198663	+	0.435010i
$699$		0			0
$700$			0.785953i			0.0297062i
$701$	−18.9777	+	41.5553i	−0.716777	+	1.56952i	0.101589	+	0.994826i	$0.467607\pi$
$701$	−18.9777	+	41.5553i	−0.716777	+	1.56952i	−0.818366	+	0.574697i	$0.805120\pi$
$702$		0			0
$703$	−1.25759	−	8.74671i	−0.0474308	−	0.329889i
$704$	4.28690	+	29.8160i	0.161569	+	1.12373i
$705$		0			0
$706$	13.7970	−	30.2112i	0.519256	−	1.13701i
$707$			1.17377i			0.0441442i
$708$		0			0
$709$	−4.96867	+	10.8799i	−0.186602	+	0.408602i	−0.979693	−	0.200501i	$-0.935743\pi$
$709$	−4.96867	+	10.8799i	−0.186602	+	0.408602i	0.793091	+	0.609103i	$0.208470\pi$
$710$	−0.198822	−	0.309373i	−0.00746165	−	0.0116106i
$711$		0			0
$712$	2.58865	−	1.18220i	0.0970136	−	0.0443046i
$713$	41.9460	−	12.3165i	1.57089	−	0.461255i
$714$		0			0
$715$	3.14121	+	2.72188i	0.117475	+	0.101792i
$716$	4.11272	−	2.64308i	0.153700	−	0.0987767i
$717$		0			0
$718$	38.0199	−	5.46644i	1.41889	−	0.204006i
$719$	1.29904	−	4.42413i	0.0484461	−	0.164992i	−0.931717	−	0.363185i	$-0.881689\pi$
$719$	1.29904	−	4.42413i	0.0484461	−	0.164992i	0.980163	+	0.198193i	$0.0635074\pi$
$720$		0			0
$721$	1.66431	−	2.58972i	0.0619821	−	0.0964461i
$722$	−3.81633	−	26.5432i	−0.142029	−	0.987834i
$723$		0			0
$724$	−1.04332	−	2.28454i	−0.0387745	−	0.0849044i
$725$	−47.2678	+	21.5865i	−1.75548	+	0.801703i
$726$		0			0
$727$	34.9328	+	30.2695i	1.29559	+	1.12263i	0.985086	+	0.172060i	$0.0550423\pi$
$727$	34.9328	+	30.2695i	1.29559	+	1.12263i	0.310501	+	0.950573i	$0.399503\pi$
$728$	0.567595	−	3.94771i	0.0210365	−	0.146312i
$729$		0			0
$730$	−0.199732	+	1.38916i	−0.00739240	+	0.0514153i
$731$	−16.8367	+	10.8203i	−0.622726	+	0.400202i
$732$		0			0
$733$	−12.0208	+	40.9391i	−0.443998	+	1.51212i	0.368764	+	0.929523i	$0.379781\pi$
$733$	−12.0208	+	40.9391i	−0.443998	+	1.51212i	−0.812762	+	0.582596i	$0.802037\pi$
$734$	−24.3714	+	21.1179i	−0.899563	+	0.779476i
$735$		0			0
$736$			16.6878i			0.615122i
$737$	−6.92622	−	44.2130i	−0.255130	−	1.62861i
$738$		0			0
$739$	47.7751	+	6.86902i	1.75743	+	0.252681i	0.944227	−	0.329294i	$-0.106811\pi$
$739$	47.7751	+	6.86902i	1.75743	+	0.252681i	0.813206	+	0.581975i	$0.197720\pi$
$740$	−0.311211	−	0.359156i	−0.0114403	−	0.0132029i
$741$		0			0
$742$	1.66357	−	2.58856i	0.0610714	−	0.0950290i
$743$	−15.9329	−	24.7921i	−0.584521	−	0.909532i	0.415479	−	0.909603i	$-0.363614\pi$
$743$	−15.9329	−	24.7921i	−0.584521	−	0.909532i	−1.00000		7.04229e-5i	$0.999978\pi$
$744$		0			0
$745$	−1.57416	−	0.718897i	−0.0576729	−	0.0263383i
$746$	−51.5680	−	7.41436i	−1.88804	−	0.271459i
$747$		0			0
$748$	−3.75967	+	5.85016i	−0.137467	+	0.213903i
$749$	1.64786	+	3.60832i	0.0602116	+	0.131845i
$750$		0			0
$751$	29.2366	+	8.58464i	1.06686	+	0.313258i	0.767610	−	0.640917i	$-0.221446\pi$
$751$	29.2366	+	8.58464i	1.06686	+	0.313258i	0.299249	+	0.954175i	$0.403264\pi$
$752$	50.5868	−	7.27328i	1.84471	−	0.265229i
$753$		0			0
$754$	−72.5986	+	21.3169i	−2.64389	+	0.776315i
$755$	−1.58780	−	0.466220i	−0.0577860	−	0.0169675i
$756$		0			0
$757$	−21.7613	+	18.8562i	−0.790927	+	0.685342i	−0.953513	−	0.301353i	$-0.902562\pi$
$757$	−21.7613	+	18.8562i	−0.790927	+	0.685342i	0.162586	+	0.986694i	$0.448016\pi$
$758$	−19.0839	−	29.6951i	−0.693157	−	1.07857i
$759$		0			0
$760$	−0.355796	−	0.410610i	−0.0129061	−	0.0148944i
$761$	9.70746	+	33.0606i	0.351895	+	1.19844i	0.925320	+	0.379187i	$0.123796\pi$
$761$	9.70746	+	33.0606i	0.351895	+	1.19844i	−0.573425	+	0.819258i	$0.694386\pi$
$762$		0			0
$763$	3.88571	−	1.14095i	0.140672	−	0.0413051i
$764$	4.65934	−	2.99438i	0.168569	−	0.108333i
$765$		0			0
$766$	0.896232			0.0323822
$767$	67.0756			2.42196
$768$		0			0
$769$	2.35305	+	2.03893i	0.0848532	+	0.0735258i	0.696255	−	0.717795i	$-0.254848\pi$
$769$	2.35305	+	2.03893i	0.0848532	+	0.0735258i	−0.611401	+	0.791321i	$0.709394\pi$
$770$	0.492516	−	0.0708131i	0.0177491	−	0.00255193i
$771$		0			0
$772$	1.77646	−	2.05015i	0.0639362	−	0.0737864i
$773$	−8.39688	−	3.83473i	−0.302015	−	0.137926i	0.258643	−	0.965973i	$-0.416725\pi$
$773$	−8.39688	−	3.83473i	−0.302015	−	0.137926i	−0.560658	+	0.828047i	$0.689452\pi$
$774$		0			0
$775$		−	32.2913i		−	1.15994i
$776$	−18.1276	−	8.27859i	−0.650742	−	0.297184i
$777$		0			0
$778$	−0.636103	−	2.16637i	−0.0228054	−	0.0776681i
$779$	−2.17655	−	4.76599i	−0.0779831	−	0.170759i
$780$		0			0
$781$	5.91743	−	5.12748i	0.211742	−	0.183476i
$782$	19.6677	−	22.6978i	0.703317	−	0.811671i
$783$		0			0
$784$	21.1268	+	24.3817i	0.754530	+	0.870774i
$785$	−0.322684	−	2.24432i	−0.0115171	−	0.0801030i
$786$		0			0
$787$	−10.2080	−	34.7653i	−0.363877	−	1.23925i	−0.914531	−	0.404517i	$-0.867440\pi$
$787$	−10.2080	−	34.7653i	−0.363877	−	1.23925i	0.550654	−	0.834734i	$-0.314378\pi$
$788$	0.821827	+	0.528156i	0.0292764	+	0.0188148i
$789$		0			0
$790$	−0.161735	+	0.550818i	−0.00575426	+	0.0195972i
$791$	−3.76701	+	1.72033i	−0.133939	+	0.0611681i
$792$		0			0
$793$	29.9588	+	19.2533i	1.06387	+	0.683706i
$794$	13.8547	−	15.9892i	0.491685	−	0.567434i
$795$		0			0
$796$	1.42310	−	3.11615i	0.0504404	−	0.110449i
$797$	42.9139	+	6.17008i	1.52009	+	0.218556i	0.851213	−	0.524820i	$-0.175867\pi$
$797$	42.9139	+	6.17008i	1.52009	+	0.218556i	0.668874	+	0.743376i	$0.266777\pi$
$798$		0			0
$799$	−26.1309	−	16.7933i	−0.924443	−	0.594104i
$800$	11.8271	+	3.47274i	0.418150	+	0.122780i
$801$		0			0
$802$	5.00121	−	34.7842i	0.176599	−	1.22827i
$803$	−29.8811			−1.05448
$804$		0			0
$805$	−0.391788			−0.0138087
$806$	6.69147	−	46.5402i	0.235697	−	1.63931i
$807$		0			0
$808$	7.72341	+	2.26780i	0.271709	+	0.0797809i
$809$	−12.3967	−	7.96688i	−0.435845	−	0.280101i	0.304264	−	0.952588i	$-0.401590\pi$
$809$	−12.3967	−	7.96688i	−0.435845	−	0.280101i	−0.740109	+	0.672487i	$0.765226\pi$
$810$		0			0
$811$	2.80904	+	0.403879i	0.0986387	+	0.0141821i	0.191457	−	0.981501i	$-0.438679\pi$
$811$	2.80904	+	0.403879i	0.0986387	+	0.0141821i	−0.0928187	+	0.995683i	$0.529588\pi$
$812$	−0.686017	+	1.50217i	−0.0240745	+	0.0527157i
$813$		0			0
$814$	36.3440	−	41.9432i	1.27386	−	1.47011i
$815$	−0.0911244	−	0.0585621i	−0.00319195	−	0.00205134i
$816$		0			0
$817$	−8.68962	+	3.96842i	−0.304011	+	0.138837i
$818$	8.54280	−	29.0941i	0.298692	−	1.01725i
$819$		0			0
$820$	−0.237046	−	0.152340i	−0.00827799	−	0.00531994i
$821$	−8.79431	−	29.9507i	−0.306924	−	1.04529i	−0.958118	−	0.286375i	$-0.907550\pi$
$821$	−8.79431	−	29.9507i	−0.306924	−	1.04529i	0.651194	−	0.758911i	$-0.274268\pi$
$822$		0			0
$823$	0.559867	+	3.89396i	0.0195157	+	0.135735i	0.997250	−	0.0741125i	$-0.0236124\pi$
$823$	0.559867	+	3.89396i	0.0195157	+	0.135735i	−0.977734	+	0.209847i	$0.932703\pi$
$824$	−13.8248	−	15.9546i	−0.481609	−	0.555807i
$825$		0			0
$826$	5.25845	−	6.06857i	0.182965	−	0.211153i
$827$	3.51982	−	3.04994i	0.122396	−	0.106057i	−0.591512	−	0.806296i	$-0.701469\pi$
$827$	3.51982	−	3.04994i	0.122396	−	0.106057i	0.713908	+	0.700239i	$0.246923\pi$
$828$		0			0
$829$	10.9159	+	23.9026i	0.379126	+	0.830170i	0.998967	+	0.0454427i	$0.0144698\pi$
$829$	10.9159	+	23.9026i	0.379126	+	0.830170i	−0.619841	+	0.784727i	$0.712803\pi$
$830$	−1.03176	−	3.51384i	−0.0358128	−	0.121967i
$831$		0			0
$832$	−23.2043	−	10.5970i	−0.804464	−	0.367386i
$833$		−	19.6079i		−	0.679375i
$834$		0			0
$835$	−2.40295	−	1.09739i	−0.0831576	−	0.0379768i
$836$	−2.17368	+	2.50856i	−0.0751783	+	0.0867604i
$837$		0			0
$838$	−42.3379	+	6.08727i	−1.46254	+	0.210281i
$839$	4.04797	+	3.50759i	0.139751	+	0.121095i	0.721931	−	0.691965i	$-0.243255\pi$
$839$	4.04797	+	3.50759i	0.139751	+	0.121095i	−0.582180	+	0.813060i	$0.697800\pi$
$840$		0			0
$841$	−80.1833			−2.76494
$842$	13.8199			0.476265
$843$		0			0
$844$	2.65693	−	1.70751i	0.0914554	−	0.0587748i
$845$	−1.32926	+	0.390305i	−0.0457279	+	0.0134269i
$846$		0			0
$847$	1.88635	+	6.42433i	0.0648159	+	0.220743i
$848$	−17.0608	−	19.6893i	−0.585872	−	0.676132i
$849$		0			0
$850$	−11.9936	−	18.6624i	−0.411378	−	0.640116i
$851$	−33.0254	+	28.6167i	−1.13210	+	0.980968i
$852$		0			0
$853$	34.3803	+	10.0950i	1.17716	+	0.345645i	0.811078	−	0.584937i	$-0.198881\pi$
$853$	34.3803	+	10.0950i	1.17716	+	0.345645i	0.366082	+	0.930583i	$0.380699\pi$
$854$	4.09056	−	1.20110i	0.139976	−	0.0411007i
$855$		0			0
$856$	26.9265	−	3.87144i	0.920328	−	0.132323i
$857$	−36.6032	−	10.7477i	−1.25034	−	0.367134i	−0.411451	−	0.911432i	$-0.634978\pi$
$857$	−36.6032	−	10.7477i	−1.25034	−	0.367134i	−0.838892	+	0.544298i	$0.816796\pi$
$858$		0			0
$859$	−11.0844	−	24.2714i	−0.378194	−	0.828130i	−0.999023	−	0.0441838i	$-0.985931\pi$
$859$	−11.0844	−	24.2714i	−0.378194	−	0.828130i	0.620829	−	0.783946i	$-0.286796\pi$
$860$	−0.277755	+	0.432195i	−0.00947136	+	0.0147377i
$861$		0			0
$862$	−15.1226	−	2.17431i	−0.515079	−	0.0740572i
$863$	7.33807	+	3.35118i	0.249791	+	0.114076i	0.536376	−	0.843979i	$-0.319793\pi$
$863$	7.33807	+	3.35118i	0.249791	+	0.114076i	−0.286585	+	0.958055i	$0.592520\pi$
$864$		0			0
$865$	−0.993632	−	1.54612i	−0.0337845	−	0.0525697i
$866$	−13.7248	+	21.3563i	−0.466389	+	0.725715i
$867$		0			0
$868$	−0.672027	−	0.775560i	−0.0228101	−	0.0263242i
$869$	−12.0983	−	1.73947i	−0.410405	−	0.0590074i
$870$		0			0
$871$	34.6694	+	15.3083i	1.17473	+	0.518702i
$872$		−	27.7723i		−	0.940490i
$873$		0			0
$874$	10.8340	−	9.38773i	0.366466	−	0.317545i
$875$	−0.163504	+	0.556844i	−0.00552745	+	0.0188248i
$876$		0			0
$877$	4.80876	−	3.09040i	0.162380	−	0.104355i	−0.456927	−	0.889504i	$-0.651050\pi$
$877$	4.80876	−	3.09040i	0.162380	−	0.104355i	0.619307	+	0.785149i	$0.287414\pi$
$878$	0.598107	−	4.15992i	0.0201851	−	0.140391i
$879$		0			0
$880$	0.599562	−	4.17005i	0.0202112	−	0.140572i
$881$	12.3378	+	10.6908i	0.415671	+	0.360181i	0.837447	−	0.546519i	$-0.184047\pi$
$881$	12.3378	+	10.6908i	0.415671	+	0.360181i	−0.421775	+	0.906700i	$0.638593\pi$
$882$		0			0
$883$	−31.8636	+	14.5516i	−1.07230	+	0.489702i	−0.871734	−	0.489979i	$-0.837004\pi$
$883$	−31.8636	+	14.5516i	−1.07230	+	0.489702i	−0.200563	+	0.979681i	$0.564277\pi$
$884$	−2.44643	−	5.35693i	−0.0822822	−	0.180173i
$885$		0			0
$886$	2.09352	+	14.5608i	0.0703333	+	0.489179i
$887$	−7.11673	+	11.0738i	−0.238956	+	0.371823i	−0.939932	−	0.341362i	$-0.889112\pi$
$887$	−7.11673	+	11.0738i	−0.238956	+	0.371823i	0.700976	+	0.713185i	$0.252748\pi$
$888$		0			0
$889$	2.02193	−	6.88607i	0.0678135	−	0.230952i
$890$	−0.297611	+	0.0427900i	−0.00997593	+	0.00143432i
$891$		0			0
$892$	−8.28840	+	5.32663i	−0.277516	+	0.178349i
$893$	−11.2050	−	9.70917i	−0.374960	−	0.324905i
$894$		0			0
$895$	1.72717	−	0.507141i	0.0577328	−	0.0169519i
$896$	−4.37603	+	1.99846i	−0.146193	+	0.0667640i
$897$		0			0
$898$	−20.2633	−	31.5304i	−0.676197	−	1.05218i
$899$	28.1853	−	61.7173i	0.940034	−	2.05839i
$900$		0			0
$901$			15.8343i			0.527516i
$902$	13.6699	−	29.9329i	0.455157	−	0.996656i
$903$		0			0
$904$	4.04171	+	28.1107i	0.134425	+	0.934948i
$905$	−0.131605	−	0.915336i	−0.00437471	−	0.0304268i
$906$		0			0
$907$	6.90648	−	15.1231i	0.229326	−	0.502153i	−0.759632	−	0.650354i	$-0.774621\pi$
$907$	6.90648	−	15.1231i	0.229326	−	0.502153i	0.988957	+	0.148200i	$0.0473480\pi$
$908$		−	3.83496i		−	0.127268i
$909$		0			0
$910$	−0.175047	+	0.383300i	−0.00580276	+	0.0127063i
$911$	11.2822	+	17.5554i	0.373795	+	0.581637i	0.976285	−	0.216490i	$-0.0694609\pi$
$911$	11.2822	+	17.5554i	0.373795	+	0.581637i	−0.602490	+	0.798127i	$0.705825\pi$
$912$		0			0
$913$	70.9261	−	32.3908i	2.34731	−	1.07198i
$914$	−3.41827	+	1.00370i	−0.113066	+	0.0331993i
$915$		0			0
$916$	8.54316	+	7.40269i	0.282274	+	0.244592i
$917$	−0.0707139	+	0.0454451i	−0.00233518	+	0.00150073i
$918$		0			0
$919$	−15.8048	+	2.27239i	−0.521352	+	0.0749591i	−0.397967	−	0.917400i	$-0.630284\pi$
$919$	−15.8048	+	2.27239i	−0.521352	+	0.0749591i	−0.123385	+	0.992359i	$0.539375\pi$
$920$	−0.756958	+	2.57796i	−0.0249562	+	0.0849929i
$921$		0			0
$922$	−26.6539	+	41.4742i	−0.877798	+	1.36588i
$923$	0.943658	+	6.56329i	0.0310609	+	0.216033i
$924$		0			0
$925$	13.4088	+	29.3611i	0.440877	+	0.965386i
$926$	−18.3847	+	8.39600i	−0.604158	+	0.275910i
$927$		0			0
$928$	19.5736	+	16.9606i	0.642533	+	0.556758i
$929$	6.56309	−	45.6473i	0.215328	−	1.49764i	−0.539650	−	0.841890i	$-0.681443\pi$
$929$	6.56309	−	45.6473i	0.215328	−	1.49764i	0.754978	−	0.655750i	$-0.227648\pi$
$930$		0			0
$931$	1.33195	−	9.26392i	0.0436529	−	0.303613i
$932$	−4.06798	+	2.61433i	−0.133251	+	0.0856354i
$933$		0			0
$934$	−11.4822	+	39.1047i	−0.375708	+	1.27955i
$935$	−1.93512	+	1.67679i	−0.0632852	+	0.0548370i
$936$		0			0
$937$		−	6.72232i		−	0.219609i	−0.993953	−	0.109804i	$-0.964978\pi$
$937$		−	6.72232i		−	0.219609i	0.993953	−	0.109804i	$-0.0350224\pi$
$938$	4.10293	−	1.93656i	0.133966	−	0.0632308i
$939$		0			0
$940$	−0.789237	−	0.113475i	−0.0257421	−	0.00370115i
$941$	−21.3745	−	24.6675i	−0.696789	−	0.804137i	0.291526	−	0.956563i	$-0.405837\pi$
$941$	−21.3745	−	24.6675i	−0.696789	−	0.804137i	−0.988315	+	0.152426i	$0.951292\pi$
$942$		0			0
$943$	−14.0081	+	21.7970i	−0.456166	+	0.709808i
$944$	−36.7568	−	57.1947i	−1.19633	−	1.86153i
$945$		0			0
$946$	−54.5753	−	24.9237i	−1.77440	−	0.810340i
$947$	−35.9683	−	5.17146i	−1.16881	−	0.168050i	−0.469544	−	0.882909i	$-0.655582\pi$
$947$	−35.9683	−	5.17146i	−1.16881	−	0.168050i	−0.699268	+	0.714859i	$0.746491\pi$
$948$		0			0
$949$	13.6809	−	21.2879i	0.444101	−	0.691034i
$950$	−4.39876	−	9.63193i	−0.142714	−	0.312501i
$951$		0			0
$952$	2.35744	+	0.692207i	0.0764051	+	0.0224346i
$953$	32.3297	−	4.64831i	1.04726	−	0.150573i	0.402861	−	0.915261i	$-0.368016\pi$
$953$	32.3297	−	4.64831i	1.04726	−	0.150573i	0.644401	+	0.764688i	$0.277107\pi$
$954$		0			0
$955$	1.95672	−	0.574546i	0.0633181	−	0.0185919i
$956$	3.31038	+	0.972015i	0.107065	+	0.0314372i
$957$		0			0
$958$	31.3468	−	27.1622i	1.01277	−	0.877571i
$959$	−0.576426	−	0.896936i	−0.0186138	−	0.0289636i
$960$		0			0
$961$	7.30986	+	8.43603i	0.235802	+	0.272130i
$962$	13.2413	+	45.0957i	0.426916	+	1.45394i
$963$		0			0
$964$	10.8985	−	3.20010i	0.351019	−	0.103068i
$965$	0.840279	−	0.540015i	0.0270495	−	0.0173837i
$966$		0			0
$967$	−39.8635			−1.28193			−0.640963	−	0.767572i	$-0.721465\pi$
$967$	−39.8635			−1.28193			−0.640963	+	0.767572i	$0.721465\pi$
$968$	45.9166			1.47582
$969$		0			0
$970$	1.59124	+	1.37882i	0.0510918	+	0.0442713i
$971$	1.82792	−	0.262815i	0.0586607	−	0.00843413i	−0.112922	−	0.993604i	$-0.536021\pi$
$971$	1.82792	−	0.262815i	0.0586607	−	0.00843413i	0.171583	+	0.985170i	$0.445112\pi$
$972$		0			0
$973$	−3.98285	+	4.59645i	−0.127684	+	0.147356i
$974$	38.5378	+	17.5996i	1.23483	+	0.563928i
$975$		0			0
$976$		−	36.0962i		−	1.15541i
$977$	1.47553	+	0.673850i	0.0472063	+	0.0215584i	0.438878	−	0.898547i	$-0.355376\pi$
$977$	1.47553	+	0.673850i	0.0472063	+	0.0215584i	−0.391672	+	0.920105i	$0.628103\pi$
$978$		0			0
$979$	−1.80355	−	6.14233i	−0.0576417	−	0.196310i
$980$	−0.209092	−	0.457848i	−0.00667921	−	0.0146254i
$981$		0			0
$982$	−14.1563	+	12.2665i	−0.451747	+	0.391441i
$983$	−12.5350	+	14.4662i	−0.399806	+	0.461400i	−0.919580	−	0.392903i	$-0.871471\pi$
$983$	−12.5350	+	14.4662i	−0.399806	+	0.461400i	0.519774	+	0.854304i	$0.326016\pi$
$984$		0			0
$985$	0.235555	+	0.271845i	0.00750540	+	0.00866170i
$986$	−6.63357	−	46.1375i	−0.211256	−	1.46932i
$987$		0			0
$988$	−0.791942	−	2.69711i	−0.0251950	−	0.0858064i
$989$	39.7415	+	25.5403i	1.26371	+	0.812135i
$990$		0			0
$991$	−13.7440	+	46.8077i	−0.436592	+	1.48690i	0.388262	+	0.921549i	$0.373076\pi$
$991$	−13.7440	+	46.8077i	−0.436592	+	1.48690i	−0.824854	+	0.565346i	$0.808743\pi$
$992$	−14.6400	+	6.68589i	−0.464822	+	0.212277i
$993$		0			0
$994$	0.667783	+	0.429158i	0.0211808	+	0.0136121i
$995$	0.826021	−	0.953280i	0.0261866	−	0.0302210i
$996$		0			0
$997$	25.9738	−	56.8747i	0.822598	−	1.80124i	0.283569	−	0.958952i	$-0.408481\pi$
$997$	25.9738	−	56.8747i	0.822598	−	1.80124i	0.539029	−	0.842287i	$-0.318791\pi$
$998$	32.5578	+	4.68111i	1.03060	+	0.148178i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.v.a.8.19	yes	240
3.2	odd	2	inner	603.2.v.a.8.6	✓	240
67.42	odd	22	inner	603.2.v.a.377.6	yes	240
201.176	even	22	inner	603.2.v.a.377.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.v.a.8.6	✓	240	3.2	odd	2	inner
603.2.v.a.8.19	yes	240	1.1	even	1	trivial
603.2.v.a.377.6	yes	240	67.42	odd	22	inner
603.2.v.a.377.19	yes	240	201.176	even	22	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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222573 - 1.54803i) q^{2} +(-0.427866 - 0.125633i) q^{4} +(-0.138128 - 0.0887696i) q^{5} +(0.350805 + 0.0504381i) q^{7} +(1.00966 - 2.21085i) q^{8} +O(q^{10})\)	\(q+(0.222573 - 1.54803i) q^{2} +(-0.427866 - 0.125633i) q^{4} +(-0.138128 - 0.0887696i) q^{5} +(0.350805 + 0.0504381i) q^{7} +(1.00966 - 2.21085i) q^{8} +(-0.168161 + 0.194069i) q^{10} +(-4.59943 - 2.95588i) q^{11} +(4.21165 - 1.92340i) q^{13} +(0.156159 - 0.531830i) q^{14} +(-3.94801 - 2.53723i) q^{16} +(0.803590 + 2.73678i) q^{17} +(0.193755 + 1.34760i) q^{19} +(0.0479480 + 0.0553349i) q^{20} +(-5.59949 + 6.46215i) q^{22} +(5.08820 - 4.40895i) q^{23} +(-2.06588 - 4.52364i) q^{25} +(-2.04007 - 6.94785i) q^{26} +(-0.143761 - 0.0656533i) q^{28} -10.4491i q^{29} +(5.90648 + 2.69740i) q^{31} +(-1.62317 + 1.87323i) q^{32} +(4.41546 - 0.634848i) q^{34} +(-0.0439787 - 0.0381078i) q^{35} -6.49059 q^{37} +2.12924 q^{38} +(-0.335719 + 0.215753i) q^{40} +(-3.69254 + 1.08423i) q^{41} +(1.97683 + 6.73245i) q^{43} +(1.59658 + 1.84256i) q^{44} +(-5.69268 - 8.85799i) q^{46} +(-8.23014 + 7.13146i) q^{47} +(-6.59593 - 1.93674i) q^{49} +(-7.46252 + 2.19119i) q^{50} +(-2.04366 + 0.293834i) q^{52} +(5.32650 + 1.56400i) q^{53} +(0.372920 + 0.816580i) q^{55} +(0.465705 - 0.724650i) q^{56} +(-16.1755 - 2.32568i) q^{58} +(13.1778 + 6.01811i) q^{59} +(4.15833 + 6.47049i) q^{61} +(5.49027 - 8.54303i) q^{62} +(-3.60799 - 4.16384i) q^{64} +(-0.752487 - 0.108191i) q^{65} +(5.43774 + 6.11809i) q^{67} -1.27193i q^{68} +(-0.0687803 + 0.0595985i) q^{70} +(-0.403473 + 1.37410i) q^{71} +(4.59776 - 2.95480i) q^{73} +(-1.44463 + 10.0476i) q^{74} +(0.0864012 - 0.600933i) q^{76} +(-1.46441 - 1.26892i) q^{77} +(2.03355 - 0.928690i) q^{79} +(0.320102 + 0.700926i) q^{80} +(0.856556 + 5.95748i) q^{82} +(-7.71031 + 11.9975i) q^{83} +(0.131944 - 0.449361i) q^{85} +(10.8620 - 1.56172i) q^{86} +(-11.1788 + 7.18421i) q^{88} +(0.884896 + 0.766767i) q^{89} +(1.57448 - 0.462309i) q^{91} +(-2.73097 + 1.24719i) q^{92} +(9.20789 + 14.3278i) q^{94} +(0.0928627 - 0.203341i) q^{95} -8.19939i q^{97} +(-4.46620 + 9.77962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 28 q^{4}+O(q^{10}) \) 240 * q - 28 * q^4	\( 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) \) 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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