LMFDB - Embedded newform 810.2.s.a.557.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.5
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.334065 + 2.21097i) q^{5} +(-1.37151 - 2.94121i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.334065 + 2.21097i) q^{5} +(-1.37151 - 2.94121i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.994512 - 2.00273i) q^{10} +(-0.631072 - 0.752082i) q^{11} +(-1.82331 - 2.60396i) q^{13} +(-0.563535 + 3.19597i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.889378 + 3.31920i) q^{17} +(4.66256 - 2.69193i) q^{19} +(-1.96338 + 1.07012i) q^{20} +(0.0855672 + 0.978038i) q^{22} +(-7.99560 - 3.72841i) q^{23} +(-4.77680 + 1.47722i) q^{25} +3.17885i q^{26} +(2.29475 - 2.29475i) q^{28} +(-1.14076 - 6.46960i) q^{29} +(4.97961 - 1.81243i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.17528 - 3.22906i) q^{34} +(6.04477 - 4.01493i) q^{35} +(-0.374016 + 0.100217i) q^{37} +(-5.36338 - 0.469235i) q^{38} +(2.22210 + 0.249560i) q^{40} +(5.80755 + 1.02403i) q^{41} +(0.538395 - 6.15389i) q^{43} +(0.490887 - 0.850241i) q^{44} +(4.41109 + 7.64023i) q^{46} +(7.38791 - 3.44504i) q^{47} +(-2.27018 + 2.70550i) q^{49} +(4.76022 + 1.52979i) q^{50} +(1.82331 - 2.60396i) q^{52} +(-8.75993 - 8.75993i) q^{53} +(1.45201 - 1.64653i) q^{55} +(-3.19597 + 0.563535i) q^{56} +(-2.77635 + 5.95390i) q^{58} +(-1.28340 - 1.07690i) q^{59} +(0.743093 + 0.270464i) q^{61} +(-5.11863 - 1.37153i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(5.14819 - 4.90119i) q^{65} +(7.92964 - 5.55239i) q^{67} +(-2.81485 + 1.97098i) q^{68} +(-7.25445 - 0.178300i) q^{70} +(-9.04122 - 5.21995i) q^{71} +(-4.64706 - 1.24518i) q^{73} +(0.363858 + 0.132433i) q^{74} +(4.12428 + 3.46068i) q^{76} +(-1.34651 + 2.88761i) q^{77} +(-12.8715 + 2.26960i) q^{79} +(-1.67709 - 1.47897i) q^{80} +(-4.16991 - 4.16991i) q^{82} +(4.49978 - 6.42635i) q^{83} +(-7.04156 + 3.07522i) q^{85} +(-3.97075 + 4.73216i) q^{86} +(-0.889789 + 0.414916i) q^{88} +(1.77673 + 3.07739i) q^{89} +(-5.15812 + 8.93412i) q^{91} +(0.768903 - 8.78860i) q^{92} +(-8.02782 - 1.41552i) q^{94} +(7.50939 + 9.40952i) q^{95} +(-4.77946 - 0.418149i) q^{97} +(3.41143 - 0.914091i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	0.334065	+	2.21097i	0.149398	+	0.988777i
$5$	0.334065	+	2.21097i	0.149398	+	0.988777i
$6$		0			0
$7$	−1.37151	−	2.94121i	−0.518382	−	1.11167i	−0.975040	−	0.222031i	$-0.928731\pi$
$7$	−1.37151	−	2.94121i	−0.518382	−	1.11167i	0.456657	−	0.889643i	$-0.349047\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	0.994512	−	2.00273i	0.314492	−	0.633320i
$11$	−0.631072	−	0.752082i	−0.190275	−	0.226761i	0.662470	−	0.749089i	$-0.269508\pi$
$11$	−0.631072	−	0.752082i	−0.190275	−	0.226761i	−0.852745	+	0.522327i	$0.825064\pi$
$12$		0			0
$13$	−1.82331	−	2.60396i	−0.505697	−	0.722210i	0.482416	−	0.875942i	$-0.339759\pi$
$13$	−1.82331	−	2.60396i	−0.505697	−	0.722210i	−0.988112	+	0.153733i	$0.950871\pi$
$14$	−0.563535	+	3.19597i	−0.150611	+	0.854158i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	0.889378	+	3.31920i	0.215706	+	0.805025i	0.985917	+	0.167236i	$0.0534841\pi$
$17$	0.889378	+	3.31920i	0.215706	+	0.805025i	−0.770211	+	0.637789i	$0.779849\pi$
$18$		0			0
$19$	4.66256	−	2.69193i	1.06967	−	0.617572i	0.141575	−	0.989927i	$-0.454783\pi$
$19$	4.66256	−	2.69193i	1.06967	−	0.617572i	0.928090	+	0.372356i	$0.121450\pi$
$20$	−1.96338	+	1.07012i	−0.439025	+	0.239285i
$21$		0			0
$22$	0.0855672	+	0.978038i	0.0182430	+	0.208518i
$23$	−7.99560	−	3.72841i	−1.66720	−	0.777427i	−0.999454	−	0.0330369i	$-0.989482\pi$
$23$	−7.99560	−	3.72841i	−1.66720	−	0.777427i	−0.667744	−	0.744391i	$-0.732740\pi$
$24$		0			0
$25$	−4.77680	+	1.47722i	−0.955360	+	0.295444i
$26$			3.17885i			0.623424i
$27$		0			0
$28$	2.29475	−	2.29475i	0.433667	−	0.433667i
$29$	−1.14076	−	6.46960i	−0.211835	−	1.20137i	−0.886315	−	0.463082i	$-0.846744\pi$
$29$	−1.14076	−	6.46960i	−0.211835	−	1.20137i	0.674481	−	0.738292i	$-0.264368\pi$
$30$		0			0
$31$	4.97961	−	1.81243i	0.894365	−	0.325522i	0.146373	−	0.989230i	$-0.453240\pi$
$31$	4.97961	−	1.81243i	0.894365	−	0.325522i	0.747992	+	0.663707i	$0.231018\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$		0			0
$34$	1.17528	−	3.22906i	0.201559	−	0.553779i
$35$	6.04477	−	4.01493i	1.02175	−	0.678647i
$36$		0			0
$37$	−0.374016	+	0.100217i	−0.0614878	+	0.0164756i	−0.289432	−	0.957199i	$-0.593466\pi$
$37$	−0.374016	+	0.100217i	−0.0614878	+	0.0164756i	0.227944	+	0.973674i	$0.426800\pi$
$38$	−5.36338	−	0.469235i	−0.870055	−	0.0761199i
$39$		0			0
$40$	2.22210	+	0.249560i	0.351345	+	0.0394589i
$41$	5.80755	+	1.02403i	0.906987	+	0.159926i	0.607635	−	0.794217i	$-0.292118\pi$
$41$	5.80755	+	1.02403i	0.906987	+	0.159926i	0.299352	+	0.954143i	$0.403230\pi$
$42$		0			0
$43$	0.538395	−	6.15389i	0.0821045	−	0.938459i	−0.837713	−	0.546111i	$-0.816107\pi$
$43$	0.538395	−	6.15389i	0.0821045	−	0.938459i	0.919817	−	0.392348i	$-0.128337\pi$
$44$	0.490887	−	0.850241i	0.0740040	−	0.128179i
$45$		0			0
$46$	4.41109	+	7.64023i	0.650379	+	1.12649i
$47$	7.38791	−	3.44504i	1.07764	−	0.502511i	0.199000	−	0.980000i	$-0.436231\pi$
$47$	7.38791	−	3.44504i	1.07764	−	0.502511i	0.878638	+	0.477489i	$0.158453\pi$
$48$		0			0
$49$	−2.27018	+	2.70550i	−0.324312	+	0.386500i
$50$	4.76022	+	1.52979i	0.673197	+	0.216346i
$51$		0			0
$52$	1.82331	−	2.60396i	0.252848	−	0.361105i
$53$	−8.75993	−	8.75993i	−1.20327	−	1.20327i	−0.973166	−	0.230102i	$-0.926094\pi$
$53$	−8.75993	−	8.75993i	−1.20327	−	1.20327i	−0.230102	−	0.973166i	$-0.573906\pi$
$54$		0			0
$55$	1.45201	−	1.64653i	0.195790	−	0.222018i
$56$	−3.19597	+	0.563535i	−0.427079	+	0.0753056i
$57$		0			0
$58$	−2.77635	+	5.95390i	−0.364553	+	0.781786i
$59$	−1.28340	−	1.07690i	−0.167084	−	0.140200i	0.555412	−	0.831576i	$-0.312561\pi$
$59$	−1.28340	−	1.07690i	−0.167084	−	0.140200i	−0.722496	+	0.691375i	$0.757005\pi$
$60$		0			0
$61$	0.743093	+	0.270464i	0.0951434	+	0.0346294i	0.389153	−	0.921173i	$-0.372768\pi$
$61$	0.743093	+	0.270464i	0.0951434	+	0.0346294i	−0.294010	+	0.955802i	$0.594990\pi$
$62$	−5.11863	−	1.37153i	−0.650066	−	0.174185i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	5.14819	−	4.90119i	0.638554	−	0.607918i
$66$		0			0
$67$	7.92964	−	5.55239i	0.968760	−	0.678333i	0.0218259	−	0.999762i	$-0.493052\pi$
$67$	7.92964	−	5.55239i	0.968760	−	0.678333i	0.946934	+	0.321429i	$0.104163\pi$
$68$	−2.81485	+	1.97098i	−0.341350	+	0.239016i
$69$		0			0
$70$	−7.25445	−	0.178300i	−0.867073	−	0.0213109i
$71$	−9.04122	−	5.21995i	−1.07300	−	0.619494i	−0.143997	−	0.989578i	$-0.545996\pi$
$71$	−9.04122	−	5.21995i	−1.07300	−	0.619494i	−0.928998	+	0.370084i	$0.879329\pi$
$72$		0			0
$73$	−4.64706	−	1.24518i	−0.543897	−	0.145737i	−0.0235990	−	0.999722i	$-0.507512\pi$
$73$	−4.64706	−	1.24518i	−0.543897	−	0.145737i	−0.520298	+	0.853985i	$0.674179\pi$
$74$	0.363858	+	0.132433i	0.0422976	+	0.0153951i
$75$		0			0
$76$	4.12428	+	3.46068i	0.473087	+	0.396967i
$77$	−1.34651	+	2.88761i	−0.153449	+	0.329073i
$78$		0			0
$79$	−12.8715	+	2.26960i	−1.44816	+	0.255350i	−0.841778	−	0.539824i	$-0.818491\pi$
$79$	−12.8715	+	2.26960i	−1.44816	+	0.255350i	−0.606381	+	0.795174i	$0.707380\pi$
$80$	−1.67709	−	1.47897i	−0.187505	−	0.165354i
$81$		0			0
$82$	−4.16991	−	4.16991i	−0.460489	−	0.460489i
$83$	4.49978	−	6.42635i	0.493915	−	0.705383i	−0.492379	−	0.870381i	$-0.663873\pi$
$83$	4.49978	−	6.42635i	0.493915	−	0.705383i	0.986294	+	0.164997i	$0.0527616\pi$
$84$		0			0
$85$	−7.04156	+	3.07522i	−0.763764	+	0.333554i
$86$	−3.97075	+	4.73216i	−0.428177	+	0.510282i
$87$		0			0
$88$	−0.889789	+	0.414916i	−0.0948519	+	0.0442301i
$89$	1.77673	+	3.07739i	0.188333	+	0.326202i	0.944695	−	0.327951i	$-0.106358\pi$
$89$	1.77673	+	3.07739i	0.188333	+	0.326202i	−0.756362	+	0.654154i	$0.773025\pi$
$90$		0			0
$91$	−5.15812	+	8.93412i	−0.540718	+	0.936550i
$92$	0.768903	−	8.78860i	0.0801637	−	0.916275i
$93$		0			0
$94$	−8.02782	−	1.41552i	−0.828006	−	0.146000i
$95$	7.50939	+	9.40952i	0.770447	+	0.965396i
$96$		0			0
$97$	−4.77946	−	0.418149i	−0.485281	−	0.0424566i	−0.158109	−	0.987422i	$-0.550540\pi$
$97$	−4.77946	−	0.418149i	−0.485281	−	0.0424566i	−0.327171	+	0.944965i	$0.606095\pi$
$98$	3.41143	−	0.914091i	0.344607	−	0.0923371i
$99$		0			0
$100$	−3.02189	−	3.98349i	−0.302189	−	0.398349i
$101$	−2.83636	+	7.79284i	−0.282228	+	0.775416i	0.714867	+	0.699260i	$0.246487\pi$
$101$	−2.83636	+	7.79284i	−0.282228	+	0.775416i	−0.997096	+	0.0761563i	$0.975735\pi$
$102$		0			0
$103$	8.76860	−	0.767153i	0.863996	−	0.0755898i	0.353463	−	0.935448i	$-0.385004\pi$
$103$	8.76860	−	0.767153i	0.863996	−	0.0755898i	0.510532	+	0.859859i	$0.329448\pi$
$104$	−2.98714	+	1.08723i	−0.292914	+	0.106612i
$105$		0			0
$106$	2.15122	+	12.2002i	0.208945	+	1.18499i
$107$	−13.1135	+	13.1135i	−1.26773	+	1.26773i	−0.320469	+	0.947259i	$0.603841\pi$
$107$	−13.1135	+	13.1135i	−1.26773	+	1.26773i	−0.947259	+	0.320469i	$0.896159\pi$
$108$		0			0
$109$			8.00687i			0.766919i	0.923558	+	0.383459i	$0.125267\pi$
$109$			8.00687i			0.766919i	−0.923558	+	0.383459i	$0.874733\pi$
$110$	−2.13383	+	0.515915i	−0.203453	+	0.0491906i
$111$		0			0
$112$	2.94121	+	1.37151i	0.277919	+	0.129596i
$113$	0.303321	+	3.46698i	0.0285341	+	0.326146i	0.997024	+	0.0770928i	$0.0245638\pi$
$113$	0.303321	+	3.46698i	0.0285341	+	0.326146i	−0.968490	+	0.249053i	$0.919881\pi$
$114$		0			0
$115$	5.57236	−	18.9236i	0.519626	−	1.76463i
$116$	5.68927	−	3.28470i	0.528235	−	0.304977i
$117$		0			0
$118$	0.433614	+	1.61827i	0.0399174	+	0.148974i
$119$	8.54269	−	7.16817i	0.783107	−	0.657105i
$120$		0			0
$121$	1.74275	−	9.88365i	0.158432	−	0.898514i
$122$	−0.453575	−	0.647772i	−0.0410647	−	0.0586465i
$123$		0			0
$124$	3.40626	+	4.05942i	0.305891	+	0.364547i
$125$	−4.86185	−	10.0679i	−0.434857	−	0.900499i
$126$		0			0
$127$	4.38712	−	16.3729i	0.389294	−	1.45286i	−0.441992	−	0.897019i	$-0.645728\pi$
$127$	4.38712	−	16.3729i	0.389294	−	1.45286i	0.831286	−	0.555845i	$-0.187605\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$		0			0
$130$	−7.02836	+	1.06194i	−0.616428	+	0.0931386i
$131$	0.968013	+	2.65959i	0.0845757	+	0.232370i	0.974770	−	0.223211i	$-0.0716539\pi$
$131$	0.968013	+	2.65959i	0.0845757	+	0.232370i	−0.890194	+	0.455581i	$0.849432\pi$
$132$		0			0
$133$	−14.3123	−	10.0216i	−1.24103	−	0.868981i
$134$	−9.68030			−0.836251
$135$		0			0
$136$	3.43629			0.294660
$137$	−0.616116	−	0.431409i	−0.0526383	−	0.0368577i	0.546961	−	0.837158i	$-0.315785\pi$
$137$	−0.616116	−	0.431409i	−0.0526383	−	0.0368577i	−0.599599	+	0.800300i	$0.704673\pi$
$138$		0			0
$139$	6.64862	+	18.2669i	0.563928	+	1.54938i	0.813826	+	0.581108i	$0.197381\pi$
$139$	6.64862	+	18.2669i	0.563928	+	1.54938i	−0.249898	+	0.968272i	$0.580397\pi$
$140$	5.84023	+	4.30704i	0.493590	+	0.364011i
$141$		0			0
$142$	4.41209	+	9.46177i	0.370255	+	0.794014i
$143$	−0.807752	+	3.01457i	−0.0675476	+	0.252091i
$144$		0			0
$145$	13.9230	−	4.68347i	1.15624	−	0.388941i
$146$	3.09244	+	3.68543i	0.255932	+	0.305008i
$147$		0			0
$148$	−0.222094	−	0.317183i	−0.0182560	−	0.0260723i
$149$	1.50387	−	8.52888i	0.123202	−	0.698713i	−0.859158	−	0.511711i	$-0.829012\pi$
$149$	1.50387	−	8.52888i	0.123202	−	0.698713i	0.982360	−	0.187002i	$-0.0598771\pi$
$150$		0			0
$151$	1.49298	−	1.25276i	0.121497	−	0.101948i	−0.580015	−	0.814606i	$-0.696953\pi$
$151$	1.49298	−	1.25276i	0.121497	−	0.101948i	0.701512	+	0.712658i	$0.252509\pi$
$152$	−1.39345	−	5.20041i	−0.113023	−	0.421809i
$153$		0			0
$154$	2.75926	−	1.59306i	0.222348	−	0.128372i
$155$	5.67075	+	10.4043i	0.455486	+	0.835695i
$156$		0			0
$157$	1.52545	+	17.4360i	0.121745	+	1.39155i	0.773826	+	0.633398i	$0.218340\pi$
$157$	1.52545	+	17.4360i	0.121745	+	1.39155i	−0.652082	+	0.758149i	$0.726104\pi$
$158$	11.8455	+	5.52366i	0.942379	+	0.439438i
$159$		0			0
$160$	0.525493	+	2.17344i	0.0415439	+	0.171826i
$161$			28.6303i			2.25639i
$162$		0			0
$163$	−8.23978	+	8.23978i	−0.645389	+	0.645389i	−0.951875	−	0.306486i	$-0.900847\pi$
$163$	−8.23978	+	8.23978i	−0.645389	+	0.645389i	0.306486	+	0.951875i	$0.400847\pi$
$164$	1.02403	+	5.80755i	0.0799631	+	0.453493i
$165$		0			0
$166$	−7.37200	+	2.68319i	−0.572179	+	0.208256i
$167$	17.4945	−	1.53057i	1.35376	−	0.118439i	0.612934	−	0.790134i	$-0.289989\pi$
$167$	17.4945	−	1.53057i	1.35376	−	0.118439i	0.740828	+	0.671695i	$0.234434\pi$
$168$		0			0
$169$	0.990113	−	2.72031i	0.0761626	−	0.209255i
$170$	7.53198	+	1.51980i	0.577676	+	0.116563i
$171$		0			0
$172$	5.96690	−	1.59883i	0.454972	−	0.121909i
$173$	6.64864	+	0.581681i	0.505487	+	0.0442244i	0.337048	−	0.941488i	$-0.390572\pi$
$173$	6.64864	+	0.581681i	0.505487	+	0.0442244i	0.168439	+	0.985712i	$0.446127\pi$
$174$		0			0
$175$	10.8962	+	12.0236i	0.823679	+	0.908896i
$176$	0.966859	+	0.170483i	0.0728797	+	0.0128507i
$177$		0			0
$178$	0.309705	−	3.53994i	0.0232133	−	0.265330i
$179$	−0.0163761	+	0.0283642i	−0.00122401	+	0.00212004i	−0.866637	−	0.498940i	$-0.833723\pi$
$179$	−0.0163761	+	0.0283642i	−0.00122401	+	0.00212004i	0.865413	+	0.501060i	$0.167056\pi$
$180$		0			0
$181$	−0.251411	−	0.435457i	−0.0186873	−	0.0323673i	0.856531	−	0.516096i	$-0.172615\pi$
$181$	−0.251411	−	0.435457i	−0.0186873	−	0.0323673i	−0.875218	+	0.483729i	$0.839282\pi$
$182$	9.34968	−	4.35983i	0.693045	−	0.323172i
$183$		0			0
$184$	−5.67078	+	6.75818i	−0.418056	+	0.498219i
$185$	−0.346523	−	0.793459i	−0.0254769	−	0.0583363i
$186$		0			0
$187$	1.93505	−	2.76354i	0.141505	−	0.202090i
$188$	5.76409	+	5.76409i	0.420390	+	0.420390i
$189$		0			0
$190$	−0.754252	−	12.0150i	−0.0547192	−	0.871662i
$191$	0.613647	−	0.108203i	0.0444019	−	0.00782926i	−0.151403	−	0.988472i	$-0.548379\pi$
$191$	0.613647	−	0.108203i	0.0444019	−	0.00782926i	0.195805	+	0.980643i	$0.437268\pi$
$192$		0			0
$193$	−0.432821	+	0.928188i	−0.0311551	+	0.0668124i	−0.921269	−	0.388925i	$-0.872847\pi$
$193$	−0.432821	+	0.928188i	−0.0311551	+	0.0668124i	0.890114	+	0.455737i	$0.150624\pi$
$194$	3.67526	+	3.08391i	0.263869	+	0.221412i
$195$		0			0
$196$	−3.31878	−	1.20794i	−0.237056	−	0.0862813i
$197$	17.7079	+	4.74481i	1.26163	+	0.338054i	0.826820	−	0.562467i	$-0.190148\pi$
$197$	17.7079	+	4.74481i	1.26163	+	0.338054i	0.434813	+	0.900521i	$0.356814\pi$
$198$		0			0
$199$	11.4533	+	6.61256i	0.811902	+	0.468752i	0.847616	−	0.530610i	$-0.178037\pi$
$199$	11.4533	+	6.61256i	0.811902	+	0.468752i	−0.0357137	+	0.999362i	$0.511370\pi$
$200$	0.190556	+	4.99637i	0.0134743	+	0.353297i
$201$		0			0
$202$	6.79320	−	4.75665i	0.477968	−	0.334677i
$203$	−17.4639	+	12.2284i	−1.22573	+	0.858262i
$204$		0			0
$205$	−0.323997	+	13.1824i	−0.0226290	+	0.920700i
$206$	−7.62284	−	4.40105i	−0.531108	−	0.306635i
$207$		0			0
$208$	3.07054	+	0.822748i	0.212903	+	0.0570473i
$209$	−4.96697	−	1.80783i	−0.343572	−	0.125050i
$210$		0			0
$211$	7.56955	+	6.35161i	0.521110	+	0.437263i	0.865018	−	0.501740i	$-0.167307\pi$
$211$	7.56955	+	6.35161i	0.521110	+	0.437263i	−0.343909	+	0.939003i	$0.611751\pi$
$212$	5.23557	−	11.2277i	0.359580	−	0.771122i
$213$		0			0
$214$	18.2635	−	3.22035i	1.24847	−	0.220139i
$215$	13.7859	−	0.865422i	0.940193	−	0.0590213i
$216$		0			0
$217$	−12.1603	−	12.1603i	−0.825497	−	0.825497i
$218$	4.59255	−	6.55884i	0.311047	−	0.444221i
$219$		0			0
$220$	2.04385	+	0.801302i	0.137796	+	0.0540238i
$221$	7.02147	−	8.36786i	0.472315	−	0.562883i
$222$		0			0
$223$	−24.5468	+	11.4464i	−1.64378	+	0.766506i	−0.643778	+	0.765212i	$0.722634\pi$
$223$	−24.5468	+	11.4464i	−1.64378	+	0.766506i	−0.999999	+	0.00129399i	$0.999588\pi$
$224$	−1.62263	−	2.81049i	−0.108417	−	0.187783i
$225$		0			0
$226$	1.74011	−	3.01396i	0.115750	−	0.200486i
$227$	−0.0836433	+	0.956047i	−0.00555160	+	0.0634551i	−0.998465	−	0.0553840i	$-0.982362\pi$
$227$	−0.0836433	+	0.956047i	−0.00555160	+	0.0634551i	0.992914	+	0.118839i	$0.0379173\pi$
$228$		0			0
$229$	−23.9533	−	4.22361i	−1.58288	−	0.279104i	−0.688101	−	0.725615i	$-0.741555\pi$
$229$	−23.9533	−	4.22361i	−1.58288	−	0.279104i	−0.894778	+	0.446511i	$0.852666\pi$
$230$	−15.4187	+	12.3051i	−1.01668	+	0.811376i
$231$		0			0
$232$	−6.54440	−	0.572561i	−0.429661	−	0.0375905i
$233$	−4.75690	+	1.27461i	−0.311635	+	0.0835022i	−0.411247	−	0.911524i	$-0.634906\pi$
$233$	−4.75690	+	1.27461i	−0.311635	+	0.0835022i	0.0996120	+	0.995026i	$0.468240\pi$
$234$		0			0
$235$	10.0849	+	15.1836i	0.657868	+	0.990469i
$236$	0.573006	−	1.57432i	0.0372995	−	0.102479i
$237$		0			0
$238$	−11.1093	+	0.971934i	−0.720106	+	0.0630011i
$239$	10.1139	−	3.68115i	0.654212	−	0.238114i	0.00647648	−	0.999979i	$-0.497938\pi$
$239$	10.1139	−	3.68115i	0.654212	−	0.238114i	0.647735	+	0.761865i	$0.275716\pi$
$240$		0			0
$241$	2.84672	+	16.1446i	0.183374	+	1.03996i	0.928027	+	0.372512i	$0.121504\pi$
$241$	2.84672	+	16.1446i	0.183374	+	1.03996i	−0.744654	+	0.667451i	$0.767385\pi$
$242$	−7.09661	+	7.09661i	−0.456187	+	0.456187i
$243$		0			0
$244$			0.790784i			0.0506247i
$245$	−6.74017	−	4.11550i	−0.430614	−	0.262929i
$246$		0			0
$247$	−15.5110	−	7.23290i	−0.986942	−	0.460219i
$248$	−0.461855	−	5.27903i	−0.0293278	−	0.335219i
$249$		0			0
$250$	−1.79211	+	11.0358i	−0.113343	+	0.697964i
$251$	−5.23231	+	3.02087i	−0.330260	+	0.190676i	−0.655957	−	0.754799i	$-0.727735\pi$
$251$	−5.23231	+	3.02087i	−0.330260	+	0.190676i	0.325696	+	0.945474i	$0.394401\pi$
$252$		0			0
$253$	2.24173	+	8.36625i	0.140936	+	0.525982i
$254$	−12.9849	+	10.8956i	−0.814742	+	0.683650i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−7.00634	−	10.0061i	−0.437043	−	0.624163i	0.538852	−	0.842400i	$-0.318858\pi$
$257$	−7.00634	−	10.0061i	−0.437043	−	0.624163i	−0.975896	+	0.218238i	$0.929969\pi$
$258$		0			0
$259$	0.807726	+	0.962611i	0.0501897	+	0.0598137i
$260$	6.36640	+	3.16141i	0.394827	+	0.196062i
$261$		0			0
$262$	0.732531	−	2.73384i	0.0452559	−	0.168897i
$263$	−3.74663	−	8.03468i	−0.231027	−	0.495440i	0.756283	−	0.654245i	$-0.227014\pi$
$263$	−3.74663	−	8.03468i	−0.231027	−	0.495440i	−0.987310	+	0.158805i	$0.949236\pi$
$264$		0			0
$265$	16.4416	−	22.2943i	1.01000	−	1.36953i
$266$	5.97581	+	16.4184i	0.366400	+	1.00668i
$267$		0			0
$268$	7.92964	+	5.55239i	0.484380	+	0.339166i
$269$	−25.4358			−1.55085			−0.775425	−	0.631440i	$-0.782464\pi$
$269$	−25.4358			−1.55085			−0.775425	+	0.631440i	$0.782464\pi$
$270$		0			0
$271$	9.27007			0.563117			0.281558	−	0.959544i	$-0.409149\pi$
$271$	9.27007			0.563117			0.281558	+	0.959544i	$0.409149\pi$
$272$	−2.81485	−	1.97098i	−0.170675	−	0.119508i
$273$		0			0
$274$	0.257246	+	0.706779i	0.0155408	+	0.0426981i
$275$	4.12550	+	2.66032i	0.248777	+	0.160423i
$276$		0			0
$277$	11.7700	+	25.2408i	0.707189	+	1.51657i	0.849978	+	0.526819i	$0.176615\pi$
$277$	11.7700	+	25.2408i	0.707189	+	1.51657i	−0.142789	+	0.989753i	$0.545607\pi$
$278$	5.03125	−	18.7769i	0.301754	−	1.12616i
$279$		0			0
$280$	−2.31362	−	6.87794i	−0.138265	−	0.411035i
$281$	−4.33779	−	5.16958i	−0.258771	−	0.308391i	0.620980	−	0.783827i	$-0.286735\pi$
$281$	−4.33779	−	5.16958i	−0.258771	−	0.308391i	−0.879751	+	0.475435i	$0.842291\pi$
$282$		0			0
$283$	9.16374	+	13.0872i	0.544728	+	0.777952i	0.993272	−	0.115809i	$-0.0369460\pi$
$283$	9.16374	+	13.0872i	0.544728	+	0.777952i	−0.448543	+	0.893761i	$0.648057\pi$
$284$	1.81287	−	10.2813i	0.107574	−	0.610083i
$285$		0			0
$286$	2.39076	−	2.00609i	0.141369	−	0.118622i
$287$	−4.95323	−	18.4857i	−0.292380	−	1.09118i
$288$		0			0
$289$	4.49632	−	2.59595i	0.264489	−	0.152703i
$290$	−14.0914	−	4.14944i	−0.827475	−	0.243664i
$291$		0			0
$292$	−0.419305	−	4.79268i	−0.0245380	−	0.280470i
$293$	−17.3461	−	8.08860i	−1.01337	−	0.472541i	−0.156281	−	0.987713i	$-0.549951\pi$
$293$	−17.3461	−	8.08860i	−1.01337	−	0.472541i	−0.857087	+	0.515171i	$0.827728\pi$
$294$		0			0
$295$	1.95225	−	3.19731i	0.113665	−	0.186155i
$296$			0.387209i			0.0225061i
$297$		0			0
$298$	−6.12386	+	6.12386i	−0.354746	+	0.354746i
$299$	4.86986	+	27.6183i	0.281631	+	1.59721i
$300$		0			0
$301$	−18.8383	+	6.85658i	−1.08582	+	0.395207i
$302$	−1.94153	+	0.169862i	−0.111722	+	0.00977445i
$303$		0			0
$304$	−1.84139	+	5.05918i	−0.105611	+	0.290164i
$305$	−0.349747	+	1.73331i	−0.0200264	+	0.0992492i
$306$		0			0
$307$	−21.4627	+	5.75092i	−1.22494	+	0.328222i	−0.812608	−	0.582811i	$-0.801953\pi$
$307$	−21.4627	+	5.75092i	−1.22494	+	0.328222i	−0.412334	+	0.911033i	$0.635286\pi$
$308$	−3.17400	−	0.277689i	−0.180855	−	0.0158228i
$309$		0			0
$310$	1.32247	−	11.7753i	0.0751110	−	0.668794i
$311$	5.69818	+	1.00474i	0.323114	+	0.0569738i	0.332853	−	0.942979i	$-0.391989\pi$
$311$	5.69818	+	1.00474i	0.323114	+	0.0569738i	−0.00973845	+	0.999953i	$0.503100\pi$
$312$		0			0
$313$	2.07910	−	23.7642i	0.117518	−	1.34323i	−0.676997	−	0.735986i	$-0.736719\pi$
$313$	2.07910	−	23.7642i	0.117518	−	1.34323i	0.794514	−	0.607246i	$-0.207726\pi$
$314$	8.75132	−	15.1577i	0.493865	−	0.855400i
$315$		0			0
$316$	−6.53504	−	11.3190i	−0.367625	−	0.636745i
$317$	28.0773	−	13.0927i	1.57698	−	0.735358i	0.580120	−	0.814531i	$-0.303006\pi$
$317$	28.0773	−	13.0927i	1.57698	−	0.735358i	0.996861	+	0.0791730i	$0.0252280\pi$
$318$		0			0
$319$	−4.14577	+	4.94073i	−0.232118	+	0.276628i
$320$	0.816177	−	2.08179i	0.0456257	−	0.116376i
$321$		0			0
$322$	16.4217	−	23.4526i	0.915145	−	1.30696i
$323$	13.0818	+	13.0818i	0.727894	+	0.727894i
$324$		0			0
$325$	12.5562	+	9.74518i	0.696495	+	0.540565i
$326$	11.4758	−	2.02349i	0.635585	−	0.112071i
$327$		0			0
$328$	2.49224	−	5.34462i	0.137611	−	0.295107i
$329$	−20.2652	−	17.0045i	−1.11726	−	0.937489i
$330$		0			0
$331$	9.13678	+	3.32551i	0.502203	+	0.182787i	0.580684	−	0.814129i	$-0.302785\pi$
$331$	9.13678	+	3.32551i	0.502203	+	0.182787i	−0.0784818	+	0.996916i	$0.525007\pi$
$332$	7.57781	+	2.03047i	0.415886	+	0.111436i
$333$		0			0
$334$	−15.2085	−	8.78064i	−0.832173	−	0.480455i
$335$	14.9252	+	15.6774i	0.815451	+	0.856545i
$336$		0			0
$337$	−19.5600	+	13.6961i	−1.06550	+	0.746072i	−0.968450	−	0.249207i	$-0.919830\pi$
$337$	−19.5600	+	13.6961i	−1.06550	+	0.746072i	−0.0970516	+	0.995279i	$0.530941\pi$
$338$	−2.37136	+	1.66044i	−0.128985	+	0.0903163i
$339$		0			0
$340$	−5.29812	−	5.56511i	−0.287331	−	0.301811i
$341$	−4.50559	−	2.60131i	−0.243992	−	0.140869i
$342$		0			0
$343$	−10.8718	−	2.91309i	−0.587023	−	0.157292i
$344$	−5.80485	−	2.11279i	−0.312977	−	0.113914i
$345$		0			0
$346$	−5.11261	−	4.28999i	−0.274856	−	0.230631i
$347$	−3.00821	+	6.45113i	−0.161489	+	0.346315i	−0.970357	−	0.241676i	$-0.922303\pi$
$347$	−3.00821	+	6.45113i	−0.161489	+	0.346315i	0.808868	+	0.587991i	$0.200081\pi$
$348$		0			0
$349$	7.99946	−	1.41052i	0.428201	−	0.0755035i	0.0446059	−	0.999005i	$-0.485797\pi$
$349$	7.99946	−	1.41052i	0.428201	−	0.0755035i	0.383596	+	0.923501i	$0.374686\pi$
$350$	−2.02924	−	16.0990i	−0.108468	−	0.860526i
$351$		0			0
$352$	−0.694219	−	0.694219i	−0.0370020	−	0.0370020i
$353$	11.9396	−	17.0515i	0.635478	−	0.907557i	−0.364240	−	0.931305i	$-0.618671\pi$
$353$	11.9396	−	17.0515i	0.635478	−	0.907557i	0.999718	+	0.0237481i	$0.00755997\pi$
$354$		0			0
$355$	8.52081	−	21.7337i	0.452238	−	1.15350i
$356$	−2.28412	+	2.72211i	−0.121058	+	0.144272i
$357$		0			0
$358$	0.0296836	−	0.0138417i	0.00156883	−	0.000731555i
$359$	10.3277	+	17.8881i	0.545074	+	0.944096i	0.998602	+	0.0528540i	$0.0168318\pi$
$359$	10.3277	+	17.8881i	0.545074	+	0.944096i	−0.453528	+	0.891242i	$0.649835\pi$
$360$		0			0
$361$	4.99300	−	8.64813i	0.262789	−	0.455165i
$362$	−0.0438239	+	0.500909i	−0.00230333	+	0.0263272i
$363$		0			0
$364$	−10.1595	−	1.79140i	−0.532503	−	0.0938946i
$365$	1.20063	−	10.6905i	0.0628438	−	0.559566i
$366$		0			0
$367$	18.4729	+	1.61617i	0.964279	+	0.0843635i	0.558407	−	0.829567i	$-0.311413\pi$
$367$	18.4729	+	1.61617i	0.964279	+	0.0843635i	0.405871	+	0.913930i	$0.366968\pi$
$368$	8.52156	−	2.28335i	0.444217	−	0.119028i
$369$		0			0
$370$	−0.171254	+	0.848721i	−0.00890310	+	0.0441229i
$371$	−13.7505	+	37.7791i	−0.713890	+	1.96140i
$372$		0			0
$373$	20.2699	−	1.77338i	1.04953	−	0.0918223i	0.450684	−	0.892684i	$-0.351180\pi$
$373$	20.2699	−	1.77338i	1.04953	−	0.0918223i	0.598850	+	0.800862i	$0.295625\pi$
$374$	−3.17020	+	1.15386i	−0.163927	+	0.0596647i
$375$		0			0
$376$	−1.41552	−	8.02782i	−0.0729999	−	0.414003i
$377$	−14.7666	+	14.7666i	−0.760520	+	0.760520i
$378$		0			0
$379$		−	22.7317i		−	1.16765i	−0.811879	−	0.583825i	$-0.801555\pi$
$379$		−	22.7317i		−	1.16765i	0.811879	−	0.583825i	$-0.198445\pi$
$380$	−6.27369	+	10.2748i	−0.321834	+	0.527084i
$381$		0			0
$382$	−0.564733	−	0.263339i	−0.0288942	−	0.0134736i
$383$	0.0141846	+	0.162131i	0.000724799	+	0.00828449i	0.996548	−	0.0830127i	$-0.0264542\pi$
$383$	0.0141846	+	0.162131i	0.000724799	+	0.00828449i	−0.995824	+	0.0912972i	$0.970899\pi$
$384$		0			0
$385$	−6.83424	−	2.01245i	−0.348305	−	0.102564i
$386$	0.886933	−	0.512071i	0.0451437	−	0.0260637i
$387$		0			0
$388$	−1.24174	−	4.63424i	−0.0630398	−	0.235268i
$389$	−10.6597	+	8.94454i	−0.540467	+	0.453506i	−0.871698	−	0.490044i	$-0.836981\pi$
$389$	−10.6597	+	8.94454i	−0.540467	+	0.453506i	0.331230	+	0.943550i	$0.392536\pi$
$390$		0			0
$391$	5.26424	−	29.8550i	0.266224	−	1.50983i
$392$	2.02574	+	2.89306i	0.102315	+	0.146122i
$393$		0			0
$394$	−11.7839	−	14.0435i	−0.593666	−	0.707503i
$395$	−9.31794	−	27.7004i	−0.468836	−	1.39376i
$396$		0			0
$397$	−7.18060	+	26.7984i	−0.360384	+	1.34497i	0.513188	+	0.858276i	$0.328464\pi$
$397$	−7.18060	+	26.7984i	−0.360384	+	1.34497i	−0.873572	+	0.486695i	$0.838202\pi$
$398$	−5.58918	−	11.9860i	−0.280160	−	0.600806i
$399$		0			0
$400$	2.70970	−	4.20208i	0.135485	−	0.210104i
$401$	−1.03015	−	2.83031i	−0.0514432	−	0.141339i	0.911310	−	0.411721i	$-0.135072\pi$
$401$	−1.03015	−	2.83031i	−0.0514432	−	0.141339i	−0.962753	+	0.270382i	$0.912850\pi$
$402$		0			0
$403$	−13.7989	−	9.66210i	−0.687373	−	0.481303i
$404$	−8.29296			−0.412590
$405$		0			0
$406$	21.3195			1.05807
$407$	0.311402	+	0.218046i	0.0154356	+	0.0108082i
$408$		0			0
$409$	−2.46064	−	6.76054i	−0.121671	−	0.334287i	0.863873	−	0.503710i	$-0.168032\pi$
$409$	−2.46064	−	6.76054i	−0.121671	−	0.334287i	−0.985543	+	0.169423i	$0.945810\pi$
$410$	7.82653	−	10.6126i	0.386525	−	0.524118i
$411$		0			0
$412$	3.71993	+	7.97741i	0.183268	+	0.393019i
$413$	−1.40719	+	5.25172i	−0.0692435	+	0.258420i
$414$		0			0
$415$	15.7117	+	7.80207i	0.771257	+	0.382988i
$416$	−2.04333	−	2.43514i	−0.100182	−	0.119393i
$417$		0			0
$418$	3.03177	+	4.32982i	0.148289	+	0.211779i
$419$	5.89503	−	33.4324i	0.287991	−	1.63328i	−0.406410	−	0.913691i	$-0.633219\pi$
$419$	5.89503	−	33.4324i	0.287991	−	1.63328i	0.694401	−	0.719588i	$-0.255670\pi$
$420$		0			0
$421$	15.2836	−	12.8245i	0.744879	−	0.625028i	−0.189264	−	0.981926i	$-0.560610\pi$
$421$	15.2836	−	12.8245i	0.744879	−	0.625028i	0.934143	+	0.356899i	$0.116166\pi$
$422$	−2.55748	−	9.54465i	−0.124496	−	0.464626i
$423$		0			0
$424$	−10.7287	+	6.19420i	−0.521031	+	0.300817i
$425$	−9.15157	−	14.5414i	−0.443916	−	0.705360i
$426$		0			0
$427$	−0.223668	−	2.55654i	−0.0108241	−	0.123720i
$428$	−16.8077	−	7.83757i	−0.812432	−	0.378843i
$429$		0			0
$430$	−11.7892	−	7.19838i	−0.568524	−	0.347137i
$431$		−	20.6806i		−	0.996151i	−0.867134	−	0.498075i	$-0.834040\pi$
$431$		−	20.6806i		−	0.996151i	0.867134	−	0.498075i	$-0.165960\pi$
$432$		0			0
$433$	−19.4571	+	19.4571i	−0.935049	+	0.935049i	−0.998016	−	0.0629671i	$-0.979944\pi$
$433$	−19.4571	+	19.4571i	−0.935049	+	0.935049i	0.0629671	+	0.998016i	$0.479944\pi$
$434$	2.98628	+	16.9360i	0.143346	+	0.812956i
$435$		0			0
$436$	−7.52399	+	2.73851i	−0.360334	+	0.131151i
$437$	−47.3166	+	4.13967i	−2.26346	+	0.198027i
$438$		0			0
$439$	11.5262	−	31.6680i	0.550115	−	1.51143i	−0.283438	−	0.958991i	$-0.591475\pi$
$439$	11.5262	−	31.6680i	0.550115	−	1.51143i	0.833553	−	0.552439i	$-0.186303\pi$
$440$	−1.21461	−	1.82869i	−0.0579045	−	0.0871794i
$441$		0			0
$442$	−10.5513	+	2.82720i	−0.501872	+	0.134476i
$443$	2.32186	+	0.203137i	0.110315	+	0.00965132i	0.142180	−	0.989841i	$-0.454589\pi$
$443$	2.32186	+	0.203137i	0.110315	+	0.00965132i	−0.0318645	+	0.999492i	$0.510145\pi$
$444$		0			0
$445$	−6.21048	+	4.95635i	−0.294405	+	0.234954i
$446$	26.6730	+	4.70316i	1.26300	+	0.222701i
$447$		0			0
$448$	−0.282844	+	3.23292i	−0.0133631	+	0.152741i
$449$	−14.7685	+	25.5798i	−0.696970	+	1.20719i	0.272542	+	0.962144i	$0.412136\pi$
$449$	−14.7685	+	25.5798i	−0.696970	+	1.20719i	−0.969512	+	0.245044i	$0.921198\pi$
$450$		0			0
$451$	−2.89483	−	5.01399i	−0.136312	−	0.236100i
$452$	−3.15415	+	1.47080i	−0.148359	+	0.0691808i
$453$		0			0
$454$	0.616883	−	0.735172i	0.0289517	−	0.0345033i
$455$	−21.4762	−	8.41988i	−1.00682	−	0.394730i
$456$		0			0
$457$	−8.79851	+	12.5656i	−0.411577	+	0.587793i	−0.970403	−	0.241492i	$-0.922363\pi$
$457$	−8.79851	+	12.5656i	−0.411577	+	0.587793i	0.558826	+	0.829285i	$0.311252\pi$
$458$	17.1988	+	17.1988i	0.803649	+	0.803649i
$459$		0			0
$460$	19.6882	−	1.23594i	0.917968	−	0.0576261i
$461$	−34.0563	+	6.00504i	−1.58616	+	0.279683i	−0.896027	−	0.444000i	$-0.853559\pi$
$461$	−34.0563	+	6.00504i	−1.58616	+	0.279683i	−0.690133	+	0.723683i	$0.742448\pi$
$462$		0			0
$463$	12.4543	−	26.7084i	0.578802	−	1.24124i	−0.371070	−	0.928605i	$-0.621009\pi$
$463$	12.4543	−	26.7084i	0.578802	−	1.24124i	0.949872	−	0.312639i	$-0.101213\pi$
$464$	5.03246	+	4.22273i	0.233626	+	0.196035i
$465$		0			0
$466$	4.62770	+	1.68435i	0.214374	+	0.0780259i
$467$	3.55757	+	0.953247i	0.164625	+	0.0441110i	0.340190	−	0.940357i	$-0.389509\pi$
$467$	3.55757	+	0.953247i	0.164625	+	0.0441110i	−0.175565	+	0.984468i	$0.556175\pi$
$468$		0			0
$469$	−27.2063	−	15.7076i	−1.25627	−	0.725309i
$470$	0.447864	−	18.2222i	0.0206584	−	0.840525i
$471$		0			0
$472$	−1.37237	+	0.960945i	−0.0631685	+	0.0442311i
$473$	−4.96800	+	3.47863i	−0.228429	+	0.159948i
$474$		0			0
$475$	−18.2956	+	19.7464i	−0.839458	+	0.906029i
$476$	9.65765	+	5.57585i	0.442658	+	0.255568i
$477$		0			0
$478$	−10.3962	−	2.78566i	−0.475512	−	0.127413i
$479$	−18.0421	−	6.56679i	−0.824365	−	0.300044i	−0.104821	−	0.994491i	$-0.533427\pi$
$479$	−18.0421	−	6.56679i	−0.824365	−	0.300044i	−0.719544	+	0.694447i	$0.755649\pi$
$480$		0			0
$481$	0.942910	+	0.791196i	0.0429930	+	0.0360754i
$482$	6.92825	−	14.8577i	0.315573	−	0.676748i
$483$		0			0
$484$	9.88365	−	1.74275i	0.449257	−	0.0792161i
$485$	−0.672136	−	10.7069i	−0.0305201	−	0.486177i
$486$		0			0
$487$	2.98027	+	2.98027i	0.135049	+	0.135049i	0.771400	−	0.636351i	$-0.219557\pi$
$487$	2.98027	+	2.98027i	0.135049	+	0.135049i	−0.636351	+	0.771400i	$0.719557\pi$
$488$	0.453575	−	0.647772i	0.0205324	−	0.0293233i
$489$		0			0
$490$	3.16067	+	7.23722i	0.142785	+	0.326944i
$491$	8.03058	−	9.57048i	0.362415	−	0.431910i	−0.553767	−	0.832672i	$-0.686810\pi$
$491$	8.03058	−	9.57048i	0.362415	−	0.431910i	0.916182	+	0.400762i	$0.131255\pi$
$492$		0			0
$493$	20.4593	−	9.54035i	0.921442	−	0.429676i
$494$	8.55726	+	14.8216i	0.385009	+	0.666855i
$495$		0			0
$496$	−2.64960	+	4.58924i	−0.118970	+	0.206063i
$497$	−2.95286	+	33.7514i	−0.132454	+	1.51396i
$498$		0			0
$499$	8.50126	+	1.49900i	0.380569	+	0.0671045i	0.360660	−	0.932697i	$-0.382551\pi$
$499$	8.50126	+	1.49900i	0.380569	+	0.0671045i	0.0199084	+	0.999802i	$0.493663\pi$
$500$	7.79787	−	8.01207i	0.348731	−	0.358311i
$501$		0			0
$502$	6.01876	+	0.526573i	0.268630	+	0.0235021i
$503$	1.85263	−	0.496411i	0.0826048	−	0.0221339i	−0.217280	−	0.976109i	$-0.569718\pi$
$503$	1.85263	−	0.496411i	0.0826048	−	0.0221339i	0.299885	+	0.953975i	$0.403052\pi$
$504$		0			0
$505$	−18.1773	−	3.66780i	−0.808878	−	0.163215i
$506$	2.96237	−	8.13903i	0.131693	−	0.361824i
$507$		0			0
$508$	16.8860	−	1.47734i	0.749196	−	0.0655462i
$509$	18.7827	−	6.83634i	0.832528	−	0.303016i	0.109632	−	0.993972i	$-0.465033\pi$
$509$	18.7827	−	6.83634i	0.832528	−	0.303016i	0.722896	+	0.690957i	$0.242810\pi$
$510$		0			0
$511$	2.71116	+	15.3758i	0.119935	+	0.680184i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			12.2152i			0.538788i
$515$	4.62544	+	19.1309i	0.203821	+	0.843006i
$516$		0			0
$517$	−7.25326	−	3.38225i	−0.318998	−	0.148751i
$518$	−0.109520	−	1.25182i	−0.00481203	−	0.0550017i
$519$		0			0
$520$	−3.40174	−	6.24129i	−0.149176	−	0.273699i
$521$	29.3037	−	16.9185i	1.28382	−	0.741213i	0.306274	−	0.951943i	$-0.400918\pi$
$521$	29.3037	−	16.9185i	1.28382	−	0.741213i	0.977544	+	0.210730i	$0.0675842\pi$
$522$		0			0
$523$	−5.43026	−	20.2660i	−0.237449	−	0.886171i	−0.977030	−	0.213103i	$-0.931643\pi$
$523$	−5.43026	−	20.2660i	−0.237449	−	0.886171i	0.739581	−	0.673068i	$-0.235024\pi$
$524$	−2.16812	+	1.81927i	−0.0947148	+	0.0794752i
$525$		0			0
$526$	−1.53944	+	8.73061i	−0.0671228	+	0.380673i
$527$	10.4446	+	14.9164i	0.454973	+	0.649769i
$528$		0			0
$529$	35.2445	+	42.0028i	1.53237	+	1.82621i
$530$	−26.2557	+	8.83196i	−1.14047	+	0.383636i
$531$		0			0
$532$	4.52211	−	16.8767i	0.196058	−	0.731700i
$533$	−7.92246	−	16.9898i	−0.343160	−	0.735909i
$534$		0			0
$535$	−33.3743	−	24.6128i	−1.44290	−	1.06410i
$536$	−3.31086	−	9.09651i	−0.143007	−	0.392909i
$537$		0			0
$538$	20.8358	+	14.5894i	0.898295	+	0.628993i
$539$	3.46740			0.149352
$540$		0			0
$541$	−26.9613			−1.15916			−0.579578	−	0.814917i	$-0.696783\pi$
$541$	−26.9613			−1.15916			−0.579578	+	0.814917i	$0.696783\pi$
$542$	−7.59360	−	5.31709i	−0.326173	−	0.228389i
$543$		0			0
$544$	1.17528	+	3.22906i	0.0503898	+	0.138445i
$545$	−17.7030	+	2.67482i	−0.758312	+	0.114577i
$546$		0			0
$547$	−14.0704	−	30.1741i	−0.601608	−	1.29015i	−0.937413	−	0.348221i	$-0.886786\pi$
$547$	−14.0704	−	30.1741i	−0.601608	−	1.29015i	0.335805	−	0.941932i	$-0.390992\pi$
$548$	0.194668	−	0.726510i	0.00831579	−	0.0310350i
$549$		0			0
$550$	−1.85351	−	4.54549i	−0.0790341	−	0.193820i
$551$	−22.7346	−	27.0941i	−0.968527	−	1.15425i
$552$		0			0
$553$	24.3288	+	34.7451i	1.03457	+	1.47751i
$554$	4.83612	−	27.4270i	0.205467	−	1.16526i
$555$		0			0
$556$	−14.8913	+	12.4953i	−0.631533	+	0.529919i
$557$	0.447062	+	1.66846i	0.0189426	+	0.0706948i	0.974750	−	0.223298i	$-0.0716824\pi$
$557$	0.447062	+	1.66846i	0.0189426	+	0.0706948i	−0.955808	+	0.293993i	$0.905016\pi$
$558$		0			0
$559$	−17.0062	+	9.81851i	−0.719284	+	0.415279i
$560$	−2.04981	+	6.96112i	−0.0866205	+	0.294161i
$561$		0			0
$562$	0.588163	+	6.72273i	0.0248101	+	0.283581i
$563$	27.2475	+	12.7057i	1.14834	+	0.535482i	0.901160	−	0.433486i	$-0.142717\pi$
$563$	27.2475	+	12.7057i	1.14834	+	0.535482i	0.247185	+	0.968968i	$0.420495\pi$
$564$		0			0
$565$	−7.56406	+	1.82883i	−0.318223	+	0.0769395i
$566$		−	15.9765i		−	0.671542i
$567$		0			0
$568$	−7.38213	+	7.38213i	−0.309747	+	0.309747i
$569$	0.862418	+	4.89101i	0.0361544	+	0.205042i	0.997534	−	0.0701837i	$-0.0223585\pi$
$569$	0.862418	+	4.89101i	0.0361544	+	0.205042i	−0.961380	+	0.275226i	$0.911247\pi$
$570$		0			0
$571$	20.6171	−	7.50400i	0.862798	−	0.314033i	0.127551	−	0.991832i	$-0.459288\pi$
$571$	20.6171	−	7.50400i	0.862798	−	0.314033i	0.735247	+	0.677799i	$0.237066\pi$
$572$	−3.10904	+	0.272006i	−0.129995	+	0.0113731i
$573$		0			0
$574$	−6.54552	+	17.9837i	−0.273205	+	0.750623i
$575$	43.7011	+	5.99863i	1.82246	+	0.250160i
$576$		0			0
$577$	18.6265	−	4.99096i	0.775432	−	0.207777i	0.150662	−	0.988585i	$-0.451859\pi$
$577$	18.6265	−	4.99096i	0.775432	−	0.207777i	0.624770	+	0.780809i	$0.285193\pi$
$578$	−5.17215	−	0.452504i	−0.215133	−	0.0188217i
$579$		0			0
$580$	9.16297	+	11.4815i	0.380472	+	0.476744i
$581$	−25.0728	−	4.42100i	−1.04019	−	0.183414i
$582$		0			0
$583$	−1.06004	+	12.1163i	−0.0439024	+	0.501807i
$584$	−2.40549	+	4.16644i	−0.0995401	+	0.172408i
$585$		0			0
$586$	9.56963	+	16.5751i	0.395318	+	0.684711i
$587$	−15.2887	+	7.12922i	−0.631030	+	0.294254i	−0.711697	−	0.702487i	$-0.752073\pi$
$587$	−15.2887	+	7.12922i	−0.631030	+	0.294254i	0.0806664	+	0.996741i	$0.474295\pi$
$588$		0			0
$589$	18.3388	−	21.8554i	0.755638	−	0.900534i
$590$	−3.43310	+	1.49932i	−0.141338	+	0.0617259i
$591$		0			0
$592$	0.222094	−	0.317183i	0.00912802	−	0.0130362i
$593$	30.8880	+	30.8880i	1.26842	+	1.26842i	0.946905	+	0.321513i	$0.104191\pi$
$593$	30.8880	+	30.8880i	1.26842	+	1.26842i	0.321513	+	0.946905i	$0.395809\pi$
$594$		0			0
$595$	18.7024	+	16.4930i	0.766725	+	0.676148i
$596$	8.52888	−	1.50387i	0.349357	−	0.0616010i
$597$		0			0
$598$	11.8521	−	25.4168i	0.484667	−	1.03937i
$599$	−4.18053	−	3.50788i	−0.170812	−	0.143328i	0.553374	−	0.832933i	$-0.313340\pi$
$599$	−4.18053	−	3.50788i	−0.170812	−	0.143328i	−0.724186	+	0.689605i	$0.757784\pi$
$600$		0			0
$601$	−2.11991	−	0.771584i	−0.0864730	−	0.0314736i	0.298421	−	0.954434i	$-0.403540\pi$
$601$	−2.11991	−	0.771584i	−0.0864730	−	0.0314736i	−0.384894	+	0.922961i	$0.625762\pi$
$602$	19.3642	+	5.18863i	0.789226	+	0.211473i
$603$		0			0
$604$	1.68784	+	0.974473i	0.0686771	+	0.0396507i
$605$	22.4347	+	0.551399i	0.912099	+	0.0224176i
$606$		0			0
$607$	13.9051	−	9.73644i	0.564389	−	0.395190i	−0.256272	−	0.966605i	$-0.582494\pi$
$607$	13.9051	−	9.73644i	0.564389	−	0.395190i	0.820661	+	0.571415i	$0.193605\pi$
$608$	4.41020	−	3.08806i	0.178857	−	0.125237i
$609$		0			0
$610$	1.28068	−	1.21924i	0.0518533	−	0.0493656i
$611$	−22.4412	−	12.9565i	−0.907876	−	0.524162i
$612$		0			0
$613$	37.9733	+	10.1749i	1.53373	+	0.410961i	0.924233	−	0.381830i	$-0.124706\pi$
$613$	37.9733	+	10.1749i	1.53373	+	0.410961i	0.609494	+	0.792791i	$0.291373\pi$
$614$	20.8798	+	7.59963i	0.842641	+	0.306696i
$615$		0			0
$616$	2.44071	+	2.04800i	0.0983390	+	0.0825162i
$617$	−7.80496	+	16.7378i	−0.314216	+	0.673838i	−0.998464	−	0.0554116i	$-0.982353\pi$
$617$	−7.80496	+	16.7378i	−0.314216	+	0.673838i	0.684248	+	0.729250i	$0.260131\pi$
$618$		0			0
$619$	23.0444	−	4.06335i	0.926233	−	0.163320i	0.309867	−	0.950780i	$-0.399715\pi$
$619$	23.0444	−	4.06335i	0.926233	−	0.163320i	0.616366	+	0.787460i	$0.288604\pi$
$620$	−7.83735	+	8.88725i	−0.314756	+	0.356921i
$621$		0			0
$622$	−4.09138	−	4.09138i	−0.164049	−	0.164049i
$623$	6.61445	−	9.44641i	0.265002	−	0.378463i
$624$		0			0
$625$	20.6357	−	14.1128i	0.825426	−	0.564510i
$626$	−15.3337	+	18.2740i	−0.612857	+	0.730375i
$627$		0			0
$628$	−15.8628	+	7.39693i	−0.632993	+	0.295170i
$629$	−0.665282	−	1.15230i	−0.0265265	−	0.0459453i
$630$		0			0
$631$	−13.3868	+	23.1867i	−0.532922	+	0.923048i	0.466339	+	0.884606i	$0.345573\pi$
$631$	−13.3868	+	23.1867i	−0.532922	+	0.923048i	−0.999261	+	0.0384417i	$0.987761\pi$
$632$	−1.13913	+	13.0203i	−0.0453123	+	0.517922i
$633$		0			0
$634$	−30.5093	−	5.37961i	−1.21168	−	0.213651i
$635$	37.6657	+	4.23017i	1.49472	+	0.167869i
$636$		0			0
$637$	11.1843	+	0.978497i	0.443137	+	0.0387695i
$638$	6.22990	−	1.66930i	0.246644	−	0.0660881i
$639$		0			0
$640$	−1.86264	+	1.23716i	−0.0736273	+	0.0489032i
$641$	12.5163	−	34.3884i	0.494366	−	1.35826i	−0.402282	−	0.915516i	$-0.631783\pi$
$641$	12.5163	−	34.3884i	0.494366	−	1.35826i	0.896648	−	0.442744i	$-0.145995\pi$
$642$		0			0
$643$	−14.1939	+	1.24180i	−0.559753	+	0.0489720i	−0.363522	−	0.931586i	$-0.618426\pi$
$643$	−14.1939	+	1.24180i	−0.559753	+	0.0489720i	−0.196231	+	0.980558i	$0.562870\pi$
$644$	−26.9037	+	9.79215i	−1.06015	+	0.385865i
$645$		0			0
$646$	−3.21258	−	18.2195i	−0.126397	−	0.716835i
$647$	7.19324	−	7.19324i	0.282795	−	0.282795i	−0.551427	−	0.834223i	$-0.685917\pi$
$647$	7.19324	−	7.19324i	0.282795	−	0.282795i	0.834223	+	0.551427i	$0.185917\pi$
$648$		0			0
$649$			1.64482i			0.0645649i
$650$	−4.69586	−	15.1847i	−0.184187	−	0.595595i
$651$		0			0
$652$	−10.5610	−	4.92469i	−0.413602	−	0.192866i
$653$	1.84123	+	21.0453i	0.0720528	+	0.823567i	0.943131	+	0.332422i	$0.107866\pi$
$653$	1.84123	+	21.0453i	0.0720528	+	0.823567i	−0.871078	+	0.491145i	$0.836579\pi$
$654$		0			0
$655$	−5.55691	+	3.02873i	−0.217126	+	0.118342i
$656$	−5.10707	+	2.94857i	−0.199398	+	0.115122i
$657$		0			0
$658$	6.84688	+	25.5529i	0.266919	+	0.996156i
$659$	4.06330	−	3.40951i	0.158284	−	0.132816i	−0.560206	−	0.828353i	$-0.689278\pi$
$659$	4.06330	−	3.40951i	0.158284	−	0.132816i	0.718490	+	0.695537i	$0.244834\pi$
$660$		0			0
$661$	4.36403	−	24.7496i	0.169741	−	0.962649i	−0.774299	−	0.632819i	$-0.781898\pi$
$661$	4.36403	−	24.7496i	0.169741	−	0.962649i	0.944040	−	0.329830i	$-0.106991\pi$
$662$	−5.57697	−	7.96474i	−0.216755	−	0.309558i
$663$		0			0
$664$	−5.04275	−	6.00971i	−0.195697	−	0.233222i
$665$	17.3762	−	34.9920i	0.673820	−	1.35693i
$666$		0			0
$667$	−15.0002	+	55.9816i	−0.580811	+	2.16762i
$668$	7.42172	+	15.9159i	0.287155	+	0.615806i
$669$		0			0
$670$	−3.23385	−	21.4029i	−0.124935	−	0.826865i
$671$	−0.265534	−	0.729550i	−0.0102508	−	0.0281640i
$672$		0			0
$673$	−19.0735	−	13.3554i	−0.735230	−	0.514813i	0.144959	−	0.989438i	$-0.453695\pi$
$673$	−19.0735	−	13.3554i	−0.735230	−	0.514813i	−0.880188	+	0.474624i	$0.842584\pi$
$674$	23.8784			0.919760
$675$		0			0
$676$	2.89490			0.111342
$677$	25.8572	+	18.1054i	0.993772	+	0.695847i	0.952890	−	0.303317i	$-0.0980942\pi$
$677$	25.8572	+	18.1054i	0.993772	+	0.695847i	0.0408825	+	0.999164i	$0.486983\pi$
$678$		0			0
$679$	5.32521	+	14.6309i	0.204363	+	0.561483i
$680$	1.14795	+	7.59755i	0.0440217	+	0.291353i
$681$		0			0
$682$	2.19872	+	4.71517i	0.0841933	+	0.180553i
$683$	−5.50658	+	20.5509i	−0.210704	+	0.786357i	0.776931	+	0.629585i	$0.216775\pi$
$683$	−5.50658	+	20.5509i	−0.210704	+	0.786357i	−0.987635	+	0.156771i	$0.949891\pi$
$684$		0			0
$685$	0.748010	−	1.50633i	0.0285800	−	0.0575541i
$686$	7.23478	+	8.62208i	0.276225	+	0.329193i
$687$		0			0
$688$	3.54321	+	5.06023i	0.135084	+	0.192919i
$689$	−6.83843	+	38.7826i	−0.260523	+	1.47750i
$690$		0			0
$691$	−22.3654	+	18.7668i	−0.850820	+	0.713923i	−0.959970	−	0.280102i	$-0.909632\pi$
$691$	−22.3654	+	18.7668i	−0.850820	+	0.713923i	0.109150	+	0.994025i	$0.465187\pi$
$692$	1.72737	+	6.44663i	0.0656647	+	0.245064i
$693$		0			0
$694$	6.16440	−	3.55902i	0.233998	−	0.135099i
$695$	−38.1666	+	20.8023i	−1.44774	+	0.789075i
$696$		0			0
$697$	1.76615	+	20.1872i	0.0668977	+	0.764644i
$698$	−7.36182	−	3.43287i	−0.278649	−	0.129936i
$699$		0			0
$700$	−7.57173	+	14.3514i	−0.286184	+	0.542433i
$701$		−	3.07620i		−	0.116187i	−0.998311	−	0.0580933i	$-0.981498\pi$
$701$		−	3.07620i		−	0.116187i	0.998311	−	0.0580933i	$-0.0185021\pi$
$702$		0			0
$703$	−1.47409	+	1.47409i	−0.0555965	+	0.0555965i
$704$	0.170483	+	0.966859i	0.00642533	+	0.0364399i
$705$		0			0
$706$	−19.5606	+	7.11948i	−0.736174	+	0.267945i
$707$	26.8105	−	2.34561i	1.00831	−	0.0882159i
$708$		0			0
$709$	−4.50615	+	12.3805i	−0.169232	+	0.464961i	−0.995097	−	0.0989073i	$-0.968465\pi$
$709$	−4.50615	+	12.3805i	−0.169232	+	0.464961i	0.825865	+	0.563868i	$0.190687\pi$
$710$	−19.4458	+	12.9159i	−0.729787	+	0.484724i
$711$		0			0
$712$	3.43238	−	0.919703i	0.128634	−	0.0344673i
$713$	−46.5725	−	4.07457i	−1.74415	−	0.152594i
$714$		0			0
$715$	−6.93498	−	0.778854i	−0.259353	−	0.0291275i
$716$	−0.0322546	−	0.00568736i	−0.00120541	−	0.000212547i
$717$		0			0
$718$	1.80023	−	20.5768i	0.0671841	−	0.767918i
$719$	13.3172	−	23.0661i	0.496649	−	0.860220i	−0.503344	−	0.864086i	$-0.667897\pi$
$719$	13.3172	−	23.0661i	0.496649	−	0.860220i	0.999993	+	0.00386565i	$0.00123048\pi$
$720$		0			0
$721$	−14.2826	−	24.7382i	−0.531911	−	0.921297i
$722$	−9.05039	+	4.22027i	−0.336821	+	0.157062i
$723$		0			0
$724$	0.323208	−	0.385184i	0.0120119	−	0.0143153i
$725$	15.0062	+	29.2188i	0.557317	+	1.08516i
$726$		0			0
$727$	14.2239	−	20.3138i	0.527534	−	0.753397i	−0.463631	−	0.886028i	$-0.653454\pi$
$727$	14.2239	−	20.3138i	0.527534	−	0.753397i	0.991165	+	0.132631i	$0.0423425\pi$
$728$	7.29468	+	7.29468i	0.270359	+	0.270359i
$729$		0			0
$730$	−7.11531	+	8.06848i	−0.263349	+	0.298628i
$731$	20.9048	−	3.68609i	0.773193	−	0.136335i
$732$		0			0
$733$	−11.5231	+	24.7114i	−0.425615	+	0.912735i	0.570214	+	0.821496i	$0.306860\pi$
$733$	−11.5231	+	24.7114i	−0.425615	+	0.912735i	−0.995829	+	0.0912386i	$0.970917\pi$
$734$	−14.2051	−	11.9195i	−0.524321	−	0.439958i
$735$		0			0
$736$	−8.29013	−	3.01736i	−0.305578	−	0.111221i
$737$	−9.18003	−	2.45978i	−0.338151	−	0.0906072i
$738$		0			0
$739$	−0.239048	−	0.138015i	−0.00879354	−	0.00507695i	0.495597	−	0.868553i	$-0.334949\pi$
$739$	−0.239048	−	0.138015i	−0.00879354	−	0.00507695i	−0.504390	+	0.863476i	$0.668283\pi$
$740$	0.627090	−	0.597004i	0.0230523	−	0.0219463i
$741$		0			0
$742$	32.9330	−	23.0599i	1.20901	−	0.846556i
$743$	−10.2041	+	7.14498i	−0.374352	+	0.262124i	−0.745578	−	0.666419i	$-0.767826\pi$
$743$	−10.2041	+	7.14498i	−0.374352	+	0.262124i	0.371226	+	0.928543i	$0.378938\pi$
$744$		0			0
$745$	19.3595	+	0.475818i	0.709278	+	0.0174326i
$746$	−17.6213	−	10.1736i	−0.645160	−	0.372483i
$747$		0			0
$748$	3.25871	+	0.873168i	0.119150	+	0.0319262i
$749$	56.5548	+	20.5843i	2.06647	+	0.752133i
$750$		0			0
$751$	−21.9810	−	18.4443i	−0.802099	−	0.673041i	0.146609	−	0.989195i	$-0.453164\pi$
$751$	−21.9810	−	18.4443i	−0.802099	−	0.673041i	−0.948708	+	0.316153i	$0.897609\pi$
$752$	−3.44504	+	7.38791i	−0.125628	+	0.269409i
$753$		0			0
$754$	20.5659	−	3.62632i	0.748966	−	0.132063i
$755$	3.26857	+	2.88243i	0.118955	+	0.104902i
$756$		0			0
$757$	−15.1203	−	15.1203i	−0.549557	−	0.549557i	0.376756	−	0.926313i	$-0.377040\pi$
$757$	−15.1203	−	15.1203i	−0.549557	−	0.549557i	−0.926313	+	0.376756i	$0.877040\pi$
$758$	−13.0384	+	18.6207i	−0.473576	+	0.676336i
$759$		0			0
$760$	11.0325	−	4.81815i	0.400190	−	0.174773i
$761$	8.46260	−	10.0853i	0.306769	−	0.365593i	−0.590530	−	0.807015i	$-0.701081\pi$
$761$	8.46260	−	10.0853i	0.306769	−	0.365593i	0.897300	+	0.441422i	$0.145526\pi$
$762$		0			0
$763$	23.5499	−	10.9815i	0.852564	−	0.397557i
$764$	0.311557	+	0.539632i	0.0112717	+	0.0195232i
$765$		0			0
$766$	0.0813750	−	0.140946i	0.00294020	−	0.00509257i
$767$	−0.464166	+	5.30544i	−0.0167601	+	0.191568i
$768$		0			0
$769$	−26.9094	−	4.74485i	−0.970377	−	0.171104i	−0.334077	−	0.942546i	$-0.608425\pi$
$769$	−26.9094	−	4.74485i	−0.970377	−	0.171104i	−0.636300	+	0.771442i	$0.719536\pi$
$770$	4.44399	+	5.56847i	0.160150	+	0.200674i
$771$		0			0
$772$	−1.02024	−	0.0892598i	−0.0367194	−	0.00321253i
$773$	49.3328	−	13.2187i	1.77438	−	0.475443i	0.784837	−	0.619702i	$-0.212747\pi$
$773$	49.3328	−	13.2187i	1.77438	−	0.475443i	0.989540	+	0.144259i	$0.0460799\pi$
$774$		0			0
$775$	−21.1093	+	16.0136i	−0.758267	+	0.575225i
$776$	−1.64092	+	4.50838i	−0.0589054	+	0.161841i
$777$		0			0
$778$	13.8623	−	1.21279i	0.496987	−	0.0434807i
$779$	29.8347	−	10.8589i	1.06894	−	0.389062i
$780$		0			0
$781$	1.77983	+	10.0939i	0.0636873	+	0.361189i
$782$	−21.4363	+	21.4363i	−0.766562	+	0.766562i
$783$		0			0
$784$		−	3.53178i		−	0.126135i
$785$	−38.0410	+	9.19751i	−1.35774	+	0.328273i
$786$		0			0
$787$	2.12670	+	0.991695i	0.0758086	+	0.0353501i	0.460153	−	0.887840i	$-0.347795\pi$
$787$	2.12670	+	0.991695i	0.0758086	+	0.0353501i	−0.384344	+	0.923190i	$0.625572\pi$
$788$	1.59779	+	18.2628i	0.0569188	+	0.650584i
$789$		0			0
$790$	−8.25548	+	28.0354i	−0.293717	+	0.997454i
$791$	9.78111	−	5.64713i	0.347776	−	0.200789i
$792$		0			0
$793$	−0.650615	−	2.42813i	−0.0231040	−	0.0862254i
$794$	21.2529	−	17.8333i	0.754238	−	0.632881i
$795$		0			0
$796$	−2.29652	+	13.0242i	−0.0813979	+	0.461631i
$797$	−24.2652	−	34.6543i	−0.859517	−	1.22752i	−0.972262	−	0.233893i	$-0.924853\pi$
$797$	−24.2652	−	34.6543i	−0.859517	−	1.22752i	0.112746	−	0.993624i	$-0.464035\pi$
$798$		0			0
$799$	18.0054	+	21.4580i	0.636986	+	0.759131i
$800$	−4.62988	+	1.88792i	−0.163691	+	0.0667481i
$801$		0			0
$802$	−0.779551	+	2.90933i	−0.0275269	+	0.102732i
$803$	1.99615	+	4.28077i	0.0704428	+	0.151065i
$804$		0			0
$805$	−63.3009	+	9.56439i	−2.23106	+	0.337101i
$806$	5.76145	+	15.8295i	0.202938	+	0.557569i
$807$		0			0
$808$	6.79320	+	4.75665i	0.238984	+	0.167338i
$809$	29.4845			1.03662			0.518310	−	0.855193i	$-0.326561\pi$
$809$	29.4845			1.03662			0.518310	+	0.855193i	$0.326561\pi$
$810$		0			0
$811$	50.9167			1.78793			0.893963	−	0.448140i	$-0.147913\pi$
$811$	50.9167			1.78793			0.893963	+	0.448140i	$0.147913\pi$
$812$	−17.4639	−	12.2284i	−0.612863	−	0.429131i
$813$		0			0
$814$	−0.130020	−	0.357226i	−0.00455719	−	0.0125208i
$815$	−20.9706	−	15.4653i	−0.734567	−	0.541726i
$816$		0			0
$817$	−14.0555	−	30.1422i	−0.491741	−	1.05454i
$818$	−1.86205	+	6.94927i	−0.0651051	+	0.242976i
$819$		0			0
$820$	−12.4982	+	4.20420i	−0.436457	+	0.146817i
$821$	−5.43833	−	6.48115i	−0.189799	−	0.226194i	0.662750	−	0.748840i	$-0.269389\pi$
$821$	−5.43833	−	6.48115i	−0.189799	−	0.226194i	−0.852549	+	0.522647i	$0.824945\pi$
$822$		0			0
$823$	5.74618	+	8.20640i	0.200299	+	0.286057i	0.906718	−	0.421737i	$-0.138579\pi$
$823$	5.74618	+	8.20640i	0.200299	+	0.286057i	−0.706419	+	0.707794i	$0.749690\pi$
$824$	1.52847	−	8.66837i	0.0532467	−	0.301977i
$825$		0			0
$826$	4.16497	−	3.49483i	0.144918	−	0.121601i
$827$	6.75265	+	25.2012i	0.234813	+	0.876333i	0.978233	+	0.207508i	$0.0665355\pi$
$827$	6.75265	+	25.2012i	0.234813	+	0.876333i	−0.743421	+	0.668824i	$0.766798\pi$
$828$		0			0
$829$	36.2687	−	20.9398i	1.25966	−	0.727268i	0.286655	−	0.958034i	$-0.407457\pi$
$829$	36.2687	−	20.9398i	1.25966	−	0.727268i	0.973009	+	0.230766i	$0.0741232\pi$
$830$	−8.39519	−	15.4029i	−0.291401	−	0.534644i
$831$		0			0
$832$	0.277055	+	3.16676i	0.00960516	+	0.109788i
$833$	−10.9991	−	5.12898i	−0.381098	−	0.177709i
$834$		0			0
$835$	9.22833	+	38.1685i	0.319359	+	1.32087i
$836$		−	5.28574i		−	0.182811i
$837$		0			0
$838$	−24.0050	+	24.0050i	−0.829238	+	0.829238i
$839$	−3.66223	−	20.7696i	−0.126434	−	0.717045i	−0.980446	−	0.196790i	$-0.936948\pi$
$839$	−3.66223	−	20.7696i	−0.126434	−	0.717045i	0.854011	−	0.520254i	$-0.174163\pi$
$840$		0			0
$841$	−13.3033	+	4.84200i	−0.458734	+	0.166966i
$842$	−19.8755	+	1.73888i	−0.684953	+	0.0599257i
$843$		0			0
$844$	−3.37962	+	9.28543i	−0.116331	+	0.319618i
$845$	6.34530	+	1.28035i	0.218285	+	0.0440454i
$846$		0			0
$847$	−31.4601	+	8.42971i	−1.08098	+	0.289648i
$848$	12.3413	+	1.07972i	0.423801	+	0.0370778i
$849$		0			0
$850$	−0.844061	+	17.1607i	−0.0289511	+	0.588608i
$851$	3.36413	+	0.593187i	0.115321	+	0.0203342i
$852$		0			0
$853$	−2.39573	+	27.3833i	−0.0820282	+	0.937586i	0.837984	+	0.545695i	$0.183734\pi$
$853$	−2.39573	+	27.3833i	−0.0820282	+	0.937586i	−0.920012	+	0.391891i	$0.871821\pi$
$854$	−1.28315	+	2.22249i	−0.0439086	+	0.0760519i
$855$		0			0
$856$	9.27263	+	16.0607i	0.316932	+	0.548942i
$857$	24.7370	−	11.5350i	0.844999	−	0.394030i	0.0486128	−	0.998818i	$-0.484520\pi$
$857$	24.7370	−	11.5350i	0.844999	−	0.394030i	0.796386	+	0.604788i	$0.206742\pi$
$858$		0			0
$859$	18.6553	−	22.2325i	0.636510	−	0.758563i	−0.347305	−	0.937752i	$-0.612903\pi$
$859$	18.6553	−	22.2325i	0.636510	−	0.758563i	0.983815	+	0.179190i	$0.0573476\pi$
$860$	5.52830	+	12.6586i	0.188513	+	0.431653i
$861$		0			0
$862$	−11.8619	+	16.9406i	−0.404019	+	0.576998i
$863$	−38.2424	−	38.2424i	−1.30178	−	1.30178i	−0.927188	−	0.374597i	$-0.877781\pi$
$863$	−38.2424	−	38.2424i	−1.30178	−	1.30178i	−0.374597	−	0.927188i	$-0.622219\pi$
$864$		0			0
$865$	0.934999	+	14.8943i	0.0317909	+	0.506421i
$866$	27.0985	−	4.77819i	0.920843	−	0.162369i
$867$		0			0
$868$	7.26790	−	15.5861i	0.246689	−	0.529025i
$869$	9.82978	+	8.24816i	0.333452	+	0.279800i
$870$		0			0
$871$	−28.9165	−	10.5247i	−0.979797	−	0.356617i
$872$	7.73404	+	2.07233i	0.261908	+	0.0701779i
$873$		0			0
$874$	41.1339	+	23.7487i	1.39138	+	0.803311i
$875$	−22.9437	+	28.1080i	−0.775640	+	0.950222i
$876$		0			0
$877$	−7.95866	+	5.57271i	−0.268745	+	0.188177i	−0.700179	−	0.713967i	$-0.746897\pi$
$877$	−7.95866	+	5.57271i	−0.268745	+	0.188177i	0.431434	+	0.902144i	$0.358008\pi$
$878$	−27.6057	+	19.3297i	−0.931647	+	0.652347i
$879$		0			0
$880$	−0.0539401	+	2.19465i	−0.00181832	+	0.0739817i
$881$	25.0262	+	14.4489i	0.843155	+	0.486796i	0.858335	−	0.513089i	$-0.171499\pi$
$881$	25.0262	+	14.4489i	0.843155	+	0.486796i	−0.0151804	+	0.999885i	$0.504832\pi$
$882$		0			0
$883$	−37.4186	−	10.0263i	−1.25924	−	0.337411i	−0.433338	−	0.901231i	$-0.642665\pi$
$883$	−37.4186	−	10.0263i	−1.25924	−	0.337411i	−0.825898	+	0.563820i	$0.809331\pi$
$884$	10.2647	+	3.73604i	0.345239	+	0.125657i
$885$		0			0
$886$	−1.78545	−	1.49817i	−0.0599832	−	0.0503319i
$887$	9.73928	−	20.8860i	0.327013	−	0.701282i	−0.672224	−	0.740348i	$-0.734661\pi$
$887$	9.73928	−	20.8860i	0.327013	−	0.701282i	0.999237	+	0.0390665i	$0.0124384\pi$
$888$		0			0
$889$	−54.1733	+	9.55222i	−1.81691	+	0.320371i
$890$	7.93017	−	0.497822i	0.265820	−	0.0166870i
$891$		0			0
$892$	−19.1516	−	19.1516i	−0.641243	−	0.641243i
$893$	25.1728	−	35.9505i	0.842375	−	1.20304i
$894$		0			0
$895$	−0.0681832	−	0.0267316i	−0.00227911	−	0.000893539i
$896$	2.08602	−	2.48602i	0.0696890	−	0.0830521i
$897$		0			0
$898$	26.7697	−	12.4829i	0.893315	−	0.416560i
$899$	−17.4063	−	30.1485i	−0.580532	−	1.00551i
$900$		0			0
$901$	21.2851	−	36.8669i	0.709109	−	1.22821i
$902$	−0.504602	+	5.76763i	−0.0168014	+	0.192041i
$903$		0			0
$904$	3.42735	+	0.604334i	0.113992	+	0.0200998i
$905$	0.878796	−	0.701335i	0.0292122	−	0.0233132i
$906$		0			0
$907$	44.7790	+	3.91765i	1.48686	+	0.130084i	0.801445	−	0.598068i	$-0.204065\pi$
$907$	44.7790	+	3.91765i	1.48686	+	0.130084i	0.685416	+	0.728151i	$0.259620\pi$
$908$	−0.926998	+	0.248388i	−0.0307635	+	0.00824306i
$909$		0			0
$910$	12.7629	+	19.2154i	0.423085	+	0.636985i
$911$	−4.72266	+	12.9754i	−0.156469	+	0.429895i	−0.993013	−	0.118005i	$-0.962350\pi$
$911$	−4.72266	+	12.9754i	−0.156469	+	0.429895i	0.836544	+	0.547899i	$0.184572\pi$
$912$		0			0
$913$	−7.67283	+	0.671286i	−0.253934	+	0.0222163i
$914$	14.4146	−	5.24650i	0.476794	−	0.173539i
$915$		0			0
$916$	−4.22361	−	23.9533i	−0.139552	−	0.791440i
$917$	6.49479	−	6.49479i	0.214477	−	0.214477i
$918$		0			0
$919$		−	26.0919i		−	0.860693i	−0.902664	−	0.430346i	$-0.858391\pi$
$919$		−	26.0919i		−	0.860693i	0.902664	−	0.430346i	$-0.141609\pi$
$920$	−16.8366	−	10.2803i	−0.555085	−	0.338931i
$921$		0			0
$922$	31.3416	+	14.6148i	1.03218	+	0.481314i
$923$	2.89243	+	33.0606i	0.0952055	+	1.08820i
$924$		0			0
$925$	1.63856	−	1.03122i	0.0538754	−	0.0339063i
$926$	−25.5213	+	14.7347i	−0.838682	+	0.484213i
$927$		0			0
$928$	−1.70029	−	6.34556i	−0.0558146	−	0.208303i
$929$	27.4347	−	23.0205i	0.900104	−	0.755277i	−0.0701070	−	0.997539i	$-0.522334\pi$
$929$	27.4347	−	23.0205i	0.900104	−	0.755277i	0.970211	+	0.242263i	$0.0778896\pi$
$930$		0			0
$931$	−3.30185	+	18.7257i	−0.108214	+	0.613711i
$932$	−2.82469	−	4.03408i	−0.0925259	−	0.132141i
$933$		0			0
$934$	−2.36743	−	2.82139i	−0.0774646	−	0.0923188i
$935$	6.75655	+	3.35515i	0.220963	+	0.109725i
$936$		0			0
$937$	12.9314	−	48.2608i	0.422452	−	1.57661i	−0.346973	−	0.937875i	$-0.612791\pi$
$937$	12.9314	−	48.2608i	0.422452	−	1.57661i	0.769425	−	0.638737i	$-0.220543\pi$
$938$	13.2766	+	28.4718i	0.433497	+	0.929638i
$939$		0			0
$940$	−10.8187	+	14.6698i	−0.352866	+	0.478477i
$941$	−4.24509	−	11.6633i	−0.138386	−	0.380213i	0.851069	−	0.525054i	$-0.175955\pi$
$941$	−4.24509	−	11.6633i	−0.138386	−	0.380213i	−0.989455	+	0.144842i	$0.953733\pi$
$942$		0			0
$943$	−42.6169	−	29.8406i	−1.38780	−	0.971745i
$944$	1.67536			0.0545282
$945$		0			0
$946$	6.06480			0.197184
$947$	−28.2015	−	19.7469i	−0.916426	−	0.641688i	0.0172332	−	0.999851i	$-0.494514\pi$
$947$	−28.2015	−	19.7469i	−0.916426	−	0.641688i	−0.933659	+	0.358163i	$0.883403\pi$
$948$		0			0
$949$	5.23066	+	14.3711i	0.169794	+	0.466506i
$950$	26.3129	−	5.68144i	0.853705	−	0.184330i
$951$		0			0
$952$	−4.71291	−	10.1069i	−0.152746	−	0.327565i
$953$	−3.36111	+	12.5438i	−0.108877	+	0.406335i	−0.998756	−	0.0498615i	$-0.984122\pi$
$953$	−3.36111	+	12.5438i	−0.108877	+	0.406335i	0.889879	+	0.456197i	$0.150789\pi$
$954$		0			0
$955$	0.444231	+	1.32061i	0.0143750	+	0.0427339i
$956$	6.91829	+	8.24490i	0.223754	+	0.266659i
$957$		0			0
$958$	11.0127	+	15.7277i	0.355804	+	0.508140i
$959$	−0.423856	+	2.40381i	−0.0136870	+	0.0776231i
$960$		0			0
$961$	−2.23573	+	1.87600i	−0.0721204	+	0.0605162i
$962$	−0.318576	−	1.18894i	−0.0102713	−	0.0383330i
$963$		0			0
$964$	−14.1973	+	8.19681i	−0.457264	+	0.264002i
$965$	−2.19679	−	0.646880i	−0.0707171	−	0.0208238i
$966$		0			0
$967$	3.19646	+	36.5357i	0.102791	+	1.17491i	0.855946	+	0.517065i	$0.172976\pi$
$967$	3.19646	+	36.5357i	0.102791	+	1.17491i	−0.753155	+	0.657843i	$0.771469\pi$
$968$	−9.09581	−	4.24145i	−0.292351	−	0.136325i
$969$		0			0
$970$	−5.59067	+	9.15614i	−0.179506	+	0.293986i
$971$			24.7329i			0.793715i	0.917880	+	0.396858i	$0.129899\pi$
$971$			24.7329i			0.793715i	−0.917880	+	0.396858i	$0.870101\pi$
$972$		0			0
$973$	44.6083	−	44.6083i	1.43008	−	1.43008i
$974$	−0.731882	−	4.15071i	−0.0234510	−	0.132997i
$975$		0			0
$976$	−0.743093	+	0.270464i	−0.0237858	+	0.00865734i
$977$	20.3161	−	1.77743i	0.649969	−	0.0568649i	0.242597	−	0.970127i	$-0.422001\pi$
$977$	20.3161	−	1.77743i	0.649969	−	0.0568649i	0.407372	+	0.913262i	$0.366445\pi$
$978$		0			0
$979$	1.19320	−	3.27830i	0.0381350	−	0.104775i
$980$	1.56203	−	7.74127i	0.0498972	−	0.247286i
$981$		0			0
$982$	−12.0677	+	3.23352i	−0.385095	+	0.103186i
$983$	−16.3946	−	1.43434i	−0.522906	−	0.0457484i	−0.177353	−	0.984147i	$-0.556753\pi$
$983$	−16.3946	−	1.43434i	−0.522906	−	0.0457484i	−0.345554	+	0.938399i	$0.612309\pi$
$984$		0			0
$985$	−4.57506	+	40.7367i	−0.145774	+	1.29798i
$986$	−22.2314	−	3.92000i	−0.707993	−	0.124838i
$987$		0			0
$988$	1.49163	−	17.0494i	0.0474550	−	0.542413i
$989$	−27.2490	+	47.1967i	−0.866468	+	1.50077i
$990$		0			0
$991$	−9.52713	−	16.5015i	−0.302639	−	0.524187i	0.674094	−	0.738646i	$-0.264534\pi$
$991$	−9.52713	−	16.5015i	−0.302639	−	0.524187i	−0.976733	+	0.214459i	$0.931201\pi$
$992$	4.80270	−	2.23954i	0.152486	−	0.0711053i
$993$		0			0
$994$	21.7778	−	25.9538i	0.690751	−	0.823205i
$995$	−10.7940	+	27.5319i	−0.342194	+	0.872821i
$996$		0			0
$997$	−2.18275	+	3.11729i	−0.0691285	+	0.0987257i	−0.852228	−	0.523171i	$-0.824749\pi$
$997$	−2.18275	+	3.11729i	−0.0691285	+	0.0987257i	0.783099	+	0.621897i	$0.213638\pi$
$998$	−6.10403	−	6.10403i	−0.193220	−	0.193220i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.5		216
3.2	odd	2		270.2.r.a.257.12	yes	216
5.3	odd	4	inner	810.2.s.a.233.1		216
15.8	even	4		270.2.r.a.203.17	yes	216
27.2	odd	18	inner	810.2.s.a.737.1		216
27.25	even	9		270.2.r.a.137.17	yes	216
135.83	even	36	inner	810.2.s.a.413.5		216
135.133	odd	36		270.2.r.a.83.12	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.12	✓	216	135.133	odd	36
270.2.r.a.137.17	yes	216	27.25	even	9
270.2.r.a.203.17	yes	216	15.8	even	4
270.2.r.a.257.12	yes	216	3.2	odd	2
810.2.s.a.233.1		216	5.3	odd	4	inner
810.2.s.a.413.5		216	135.83	even	36	inner
810.2.s.a.557.5		216	1.1	even	1	trivial
810.2.s.a.737.1		216	27.2	odd	18	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.334065 + 2.21097i) q^{5} +(-1.37151 - 2.94121i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.334065 + 2.21097i) q^{5} +(-1.37151 - 2.94121i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.994512 - 2.00273i) q^{10} +(-0.631072 - 0.752082i) q^{11} +(-1.82331 - 2.60396i) q^{13} +(-0.563535 + 3.19597i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.889378 + 3.31920i) q^{17} +(4.66256 - 2.69193i) q^{19} +(-1.96338 + 1.07012i) q^{20} +(0.0855672 + 0.978038i) q^{22} +(-7.99560 - 3.72841i) q^{23} +(-4.77680 + 1.47722i) q^{25} +3.17885i q^{26} +(2.29475 - 2.29475i) q^{28} +(-1.14076 - 6.46960i) q^{29} +(4.97961 - 1.81243i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.17528 - 3.22906i) q^{34} +(6.04477 - 4.01493i) q^{35} +(-0.374016 + 0.100217i) q^{37} +(-5.36338 - 0.469235i) q^{38} +(2.22210 + 0.249560i) q^{40} +(5.80755 + 1.02403i) q^{41} +(0.538395 - 6.15389i) q^{43} +(0.490887 - 0.850241i) q^{44} +(4.41109 + 7.64023i) q^{46} +(7.38791 - 3.44504i) q^{47} +(-2.27018 + 2.70550i) q^{49} +(4.76022 + 1.52979i) q^{50} +(1.82331 - 2.60396i) q^{52} +(-8.75993 - 8.75993i) q^{53} +(1.45201 - 1.64653i) q^{55} +(-3.19597 + 0.563535i) q^{56} +(-2.77635 + 5.95390i) q^{58} +(-1.28340 - 1.07690i) q^{59} +(0.743093 + 0.270464i) q^{61} +(-5.11863 - 1.37153i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(5.14819 - 4.90119i) q^{65} +(7.92964 - 5.55239i) q^{67} +(-2.81485 + 1.97098i) q^{68} +(-7.25445 - 0.178300i) q^{70} +(-9.04122 - 5.21995i) q^{71} +(-4.64706 - 1.24518i) q^{73} +(0.363858 + 0.132433i) q^{74} +(4.12428 + 3.46068i) q^{76} +(-1.34651 + 2.88761i) q^{77} +(-12.8715 + 2.26960i) q^{79} +(-1.67709 - 1.47897i) q^{80} +(-4.16991 - 4.16991i) q^{82} +(4.49978 - 6.42635i) q^{83} +(-7.04156 + 3.07522i) q^{85} +(-3.97075 + 4.73216i) q^{86} +(-0.889789 + 0.414916i) q^{88} +(1.77673 + 3.07739i) q^{89} +(-5.15812 + 8.93412i) q^{91} +(0.768903 - 8.78860i) q^{92} +(-8.02782 - 1.41552i) q^{94} +(7.50939 + 9.40952i) q^{95} +(-4.77946 - 0.418149i) q^{97} +(3.41143 - 0.914091i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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