LMFDB - Embedded newform 810.2.s.a.557.2

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			557.2
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.07008 + 0.845439i) q^{5} +(0.101570 + 0.217817i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.07008 + 0.845439i) q^{5} +(0.101570 + 0.217817i) q^{7} +(0.258819 - 0.965926i) q^{8} +(2.18063 + 0.494807i) q^{10} +(-2.07374 - 2.47139i) q^{11} +(1.10564 + 1.57902i) q^{13} +(0.0417336 - 0.236683i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.935037 - 3.48961i) q^{17} +(1.18424 - 0.683723i) q^{19} +(-1.50246 - 1.65608i) q^{20} +(0.281179 + 3.21390i) q^{22} +(6.16839 + 2.87637i) q^{23} +(3.57047 - 3.50025i) q^{25} -1.92762i q^{26} +(-0.169942 + 0.169942i) q^{28} +(0.340130 + 1.92898i) q^{29} +(2.42139 - 0.881313i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-1.23562 + 3.39483i) q^{34} +(-0.394408 - 0.365027i) q^{35} +(5.53629 - 1.48345i) q^{37} +(-1.36224 - 0.119181i) q^{38} +(0.280855 + 2.21836i) q^{40} +(-0.258116 - 0.0455128i) q^{41} +(0.573015 - 6.54960i) q^{43} +(1.61309 - 2.79395i) q^{44} +(-3.40303 - 5.89422i) q^{46} +(11.9311 - 5.56356i) q^{47} +(4.46239 - 5.31806i) q^{49} +(-4.93242 + 0.819303i) q^{50} +(-1.10564 + 1.57902i) q^{52} +(9.15736 + 9.15736i) q^{53} +(6.38223 + 3.36276i) q^{55} +(0.236683 - 0.0417336i) q^{56} +(0.827796 - 1.77522i) q^{58} +(4.98299 + 4.18123i) q^{59} +(-14.0977 - 5.13113i) q^{61} +(-2.48899 - 0.666922i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.62373 - 2.33394i) q^{65} +(-3.34324 + 2.34096i) q^{67} +(2.95936 - 2.07216i) q^{68} +(0.113709 + 0.525236i) q^{70} +(-9.56731 - 5.52369i) q^{71} +(2.32572 + 0.623174i) q^{73} +(-5.38594 - 1.96032i) q^{74} +(1.04752 + 0.878977i) q^{76} +(0.327681 - 0.702714i) q^{77} +(2.06587 - 0.364269i) q^{79} +(1.04234 - 1.97827i) q^{80} +(0.185331 + 0.185331i) q^{82} +(5.39056 - 7.69851i) q^{83} +(4.88585 + 6.43325i) q^{85} +(-4.22608 + 5.03645i) q^{86} +(-2.92390 + 1.36344i) q^{88} +(-1.90193 - 3.29423i) q^{89} +(-0.231637 + 0.401207i) q^{91} +(-0.593187 + 6.78016i) q^{92} +(-12.9645 - 2.28599i) q^{94} +(-1.87343 + 2.41657i) q^{95} +(-7.17216 - 0.627483i) q^{97} +(-6.70569 + 1.79678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.07008	+	0.845439i	−0.925768	+	0.378092i
$5$	−2.07008	+	0.845439i	−0.925768	+	0.378092i
$6$		0			0
$7$	0.101570	+	0.217817i	0.0383897	+	0.0823270i	0.924567	−	0.381019i	$-0.124427\pi$
$7$	0.101570	+	0.217817i	0.0383897	+	0.0823270i	−0.886178	+	0.463346i	$0.846649\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	2.18063	+	0.494807i	0.689577	+	0.156472i
$11$	−2.07374	−	2.47139i	−0.625257	−	0.745152i	0.356708	−	0.934216i	$-0.383899\pi$
$11$	−2.07374	−	2.47139i	−0.625257	−	0.745152i	−0.981965	+	0.189064i	$0.939455\pi$
$12$		0			0
$13$	1.10564	+	1.57902i	0.306649	+	0.437941i	0.942668	−	0.333733i	$-0.108309\pi$
$13$	1.10564	+	1.57902i	0.306649	+	0.437941i	−0.636018	+	0.771674i	$0.719420\pi$
$14$	0.0417336	−	0.236683i	0.0111538	−	0.0632562i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.935037	−	3.48961i	−0.226780	−	0.846354i	−0.981684	−	0.190518i	$-0.938983\pi$
$17$	−0.935037	−	3.48961i	−0.226780	−	0.846354i	0.754904	−	0.655836i	$-0.227684\pi$
$18$		0			0
$19$	1.18424	−	0.683723i	0.271684	−	0.156857i	−0.357969	−	0.933734i	$-0.616531\pi$
$19$	1.18424	−	0.683723i	0.271684	−	0.156857i	0.629653	+	0.776877i	$0.283197\pi$
$20$	−1.50246	−	1.65608i	−0.335961	−	0.370311i
$21$		0			0
$22$	0.281179	+	3.21390i	0.0599477	+	0.685205i
$23$	6.16839	+	2.87637i	1.28620	+	0.599764i	0.940886	−	0.338724i	$-0.109995\pi$
$23$	6.16839	+	2.87637i	1.28620	+	0.599764i	0.345312	+	0.938488i	$0.387773\pi$
$24$		0			0
$25$	3.57047	−	3.50025i	0.714093	−	0.700050i
$26$		−	1.92762i		−	0.378038i
$27$		0			0
$28$	−0.169942	+	0.169942i	−0.0321160	+	0.0321160i
$29$	0.340130	+	1.92898i	0.0631606	+	0.358202i	0.999965	+	0.00834852i	$0.00265745\pi$
$29$	0.340130	+	1.92898i	0.0631606	+	0.358202i	−0.936805	+	0.349853i	$0.886231\pi$
$30$		0			0
$31$	2.42139	−	0.881313i	0.434894	−	0.158288i	−0.115290	−	0.993332i	$-0.536780\pi$
$31$	2.42139	−	0.881313i	0.434894	−	0.158288i	0.550184	+	0.835043i	$0.314558\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$		0			0
$34$	−1.23562	+	3.39483i	−0.211907	+	0.582209i
$35$	−0.394408	−	0.365027i	−0.0666671	−	0.0617009i
$36$		0			0
$37$	5.53629	−	1.48345i	0.910161	−	0.243877i	0.226786	−	0.973945i	$-0.427178\pi$
$37$	5.53629	−	1.48345i	0.910161	−	0.243877i	0.683375	+	0.730068i	$0.260511\pi$
$38$	−1.36224	−	0.119181i	−0.220985	−	0.0193337i
$39$		0			0
$40$	0.280855	+	2.21836i	0.0444070	+	0.350753i
$41$	−0.258116	−	0.0455128i	−0.0403110	−	0.00710791i	0.153456	−	0.988155i	$-0.450960\pi$
$41$	−0.258116	−	0.0455128i	−0.0403110	−	0.00710791i	−0.193767	+	0.981048i	$0.562071\pi$
$42$		0			0
$43$	0.573015	−	6.54960i	0.0873840	−	0.998804i	−0.818283	−	0.574815i	$-0.805074\pi$
$43$	0.573015	−	6.54960i	0.0873840	−	0.998804i	0.905667	−	0.423989i	$-0.139370\pi$
$44$	1.61309	−	2.79395i	0.243182	−	0.421203i
$45$		0			0
$46$	−3.40303	−	5.89422i	−0.501750	−	0.869056i
$47$	11.9311	−	5.56356i	1.74033	−	0.811528i	0.752005	−	0.659158i	$-0.229087\pi$
$47$	11.9311	−	5.56356i	1.74033	−	0.811528i	0.988323	−	0.152370i	$-0.0486907\pi$
$48$		0			0
$49$	4.46239	−	5.31806i	0.637484	−	0.759723i
$50$	−4.93242	+	0.819303i	−0.697549	+	0.115867i
$51$		0			0
$52$	−1.10564	+	1.57902i	−0.153325	+	0.218970i
$53$	9.15736	+	9.15736i	1.25786	+	1.25786i	0.952113	+	0.305748i	$0.0989064\pi$
$53$	9.15736	+	9.15736i	1.25786	+	1.25786i	0.305748	+	0.952113i	$0.401094\pi$
$54$		0			0
$55$	6.38223	+	3.36276i	0.860579	+	0.453434i
$56$	0.236683	−	0.0417336i	0.0316281	−	0.00557689i
$57$		0			0
$58$	0.827796	−	1.77522i	0.108695	−	0.233097i
$59$	4.98299	+	4.18123i	0.648731	+	0.544350i	0.906685	−	0.421807i	$-0.138604\pi$
$59$	4.98299	+	4.18123i	0.648731	+	0.544350i	−0.257955	+	0.966157i	$0.583049\pi$
$60$		0			0
$61$	−14.0977	−	5.13113i	−1.80502	−	0.656974i	−0.997769	−	0.0667682i	$-0.978731\pi$
$61$	−14.0977	−	5.13113i	−1.80502	−	0.656974i	−0.807253	−	0.590206i	$-0.799047\pi$
$62$	−2.48899	−	0.666922i	−0.316101	−	0.0846991i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−3.62373	−	2.33394i	−0.449468	−	0.289490i
$66$		0			0
$67$	−3.34324	+	2.34096i	−0.408442	+	0.285994i	−0.759686	−	0.650290i	$-0.774648\pi$
$67$	−3.34324	+	2.34096i	−0.408442	+	0.285994i	0.351244	+	0.936284i	$0.385759\pi$
$68$	2.95936	−	2.07216i	0.358875	−	0.251287i
$69$		0			0
$70$	0.113709	+	0.525236i	0.0135908	+	0.0627777i
$71$	−9.56731	−	5.52369i	−1.13543	−	0.655541i	−0.190136	−	0.981758i	$-0.560893\pi$
$71$	−9.56731	−	5.52369i	−1.13543	−	0.655541i	−0.945295	+	0.326217i	$0.894226\pi$
$72$		0			0
$73$	2.32572	+	0.623174i	0.272205	+	0.0729370i	0.392339	−	0.919821i	$-0.371666\pi$
$73$	2.32572	+	0.623174i	0.272205	+	0.0729370i	−0.120135	+	0.992758i	$0.538333\pi$
$74$	−5.38594	−	1.96032i	−0.626102	−	0.227883i
$75$		0			0
$76$	1.04752	+	0.878977i	0.120159	+	0.100826i
$77$	0.327681	−	0.702714i	0.0373427	−	0.0800817i
$78$		0			0
$79$	2.06587	−	0.364269i	0.232429	−	0.0409835i	−0.0562205	−	0.998418i	$-0.517905\pi$
$79$	2.06587	−	0.364269i	0.232429	−	0.0409835i	0.288649	+	0.957435i	$0.406794\pi$
$80$	1.04234	−	1.97827i	0.116537	−	0.221177i
$81$		0			0
$82$	0.185331	+	0.185331i	0.0204664	+	0.0204664i
$83$	5.39056	−	7.69851i	0.591690	−	0.845022i	−0.405934	−	0.913902i	$-0.633054\pi$
$83$	5.39056	−	7.69851i	0.591690	−	0.845022i	0.997625	+	0.0688806i	$0.0219428\pi$
$84$		0			0
$85$	4.88585	+	6.43325i	0.529945	+	0.697784i
$86$	−4.22608	+	5.03645i	−0.455710	+	0.543094i
$87$		0			0
$88$	−2.92390	+	1.36344i	−0.311689	+	0.145343i
$89$	−1.90193	−	3.29423i	−0.201604	−	0.349188i	0.747441	−	0.664328i	$-0.231282\pi$
$89$	−1.90193	−	3.29423i	−0.201604	−	0.349188i	−0.949045	+	0.315139i	$0.897949\pi$
$90$		0			0
$91$	−0.231637	+	0.401207i	−0.0242822	+	0.0420579i
$92$	−0.593187	+	6.78016i	−0.0618441	+	0.706881i
$93$		0			0
$94$	−12.9645	−	2.28599i	−1.33719	−	0.235782i
$95$	−1.87343	+	2.41657i	−0.192210	+	0.247934i
$96$		0			0
$97$	−7.17216	−	0.627483i	−0.728223	−	0.0637112i	−0.282986	−	0.959124i	$-0.591325\pi$
$97$	−7.17216	−	0.627483i	−0.728223	−	0.0637112i	−0.445237	+	0.895413i	$0.646880\pi$
$98$	−6.70569	+	1.79678i	−0.677377	+	0.181503i
$99$		0			0
$100$	4.51033	+	2.15798i	0.451033	+	0.215798i
$101$	6.07255	−	16.6842i	0.604242	−	1.66014i	−0.138340	−	0.990385i	$-0.544177\pi$
$101$	6.07255	−	16.6842i	0.604242	−	1.66014i	0.742581	−	0.669756i	$-0.233601\pi$
$102$		0			0
$103$	17.9043	−	1.56642i	1.76416	−	0.154344i	0.841577	−	0.540137i	$-0.181628\pi$
$103$	17.9043	−	1.56642i	1.76416	−	0.154344i	0.922585	+	0.385793i	$0.126072\pi$
$104$	1.81137	−	0.659287i	0.177620	−	0.0646484i
$105$		0			0
$106$	−2.24882	−	12.7537i	−0.218425	−	1.23875i
$107$	−7.07022	+	7.07022i	−0.683504	+	0.683504i	−0.960788	−	0.277284i	$-0.910566\pi$
$107$	−7.07022	+	7.07022i	−0.683504	+	0.683504i	0.277284	+	0.960788i	$0.410566\pi$
$108$		0			0
$109$			1.47414i			0.141197i	0.997505	+	0.0705987i	$0.0224910\pi$
$109$			1.47414i			0.141197i	−0.997505	+	0.0705987i	$0.977509\pi$
$110$	−3.29922	−	6.41530i	−0.314568	−	0.611675i
$111$		0			0
$112$	−0.217817	−	0.101570i	−0.0205817	−	0.00959743i
$113$	−0.582064	−	6.65302i	−0.0547560	−	0.625864i	−0.973146	−	0.230188i	$-0.926066\pi$
$113$	−0.582064	−	6.65302i	−0.0547560	−	0.625864i	0.918390	−	0.395676i	$-0.129490\pi$
$114$		0			0
$115$	−15.2009	−	0.739316i	−1.41749	−	0.0689416i
$116$	−1.69631	+	0.979367i	−0.157499	+	0.0909319i
$117$		0			0
$118$	−1.68358	−	6.28319i	−0.154986	−	0.578415i
$119$	0.665123	−	0.558105i	0.0609718	−	0.0511614i
$120$		0			0
$121$	0.102767	−	0.582822i	0.00934248	−	0.0529839i
$122$	8.60504	+	12.2893i	0.779063	+	1.11262i
$123$		0			0
$124$	1.65633	+	1.97393i	0.148743	+	0.177264i
$125$	−4.43190	+	10.2644i	−0.396402	+	0.918077i
$126$		0			0
$127$	−1.05518	+	3.93800i	−0.0936325	+	0.349441i	−0.996809	−	0.0798291i	$-0.974563\pi$
$127$	−1.05518	+	3.93800i	−0.0936325	+	0.349441i	0.903176	+	0.429270i	$0.141229\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$		0			0
$130$	1.62969	+	3.99034i	0.142933	+	0.349976i
$131$	5.12096	+	14.0697i	0.447421	+	1.22928i	0.934513	+	0.355928i	$0.115835\pi$
$131$	5.12096	+	14.0697i	0.447421	+	1.22928i	−0.487093	+	0.873350i	$0.661943\pi$
$132$		0			0
$133$	0.269209	+	0.188502i	0.0233434	+	0.0163452i
$134$	4.08134			0.352574
$135$		0			0
$136$	−3.61271			−0.309787
$137$	8.21123	+	5.74956i	0.701533	+	0.491218i	0.869096	−	0.494643i	$-0.164701\pi$
$137$	8.21123	+	5.74956i	0.701533	+	0.491218i	−0.167564	+	0.985861i	$0.553590\pi$
$138$		0			0
$139$	−0.704970	−	1.93689i	−0.0597947	−	0.164285i	0.906198	−	0.422853i	$-0.138971\pi$
$139$	−0.704970	−	1.93689i	−0.0597947	−	0.164285i	−0.965993	+	0.258569i	$0.916749\pi$
$140$	0.208118	−	0.495469i	0.0175892	−	0.0418748i
$141$		0			0
$142$	4.66882	+	10.0123i	0.391799	+	0.840215i
$143$	1.60956	−	6.00695i	0.134598	−	0.502326i
$144$		0			0
$145$	−2.33493	−	3.70558i	−0.193905	−	0.307731i
$146$	−1.54768	−	1.84445i	−0.128087	−	0.152648i
$147$		0			0
$148$	3.28751	+	4.69505i	0.270231	+	0.385930i
$149$	0.807636	−	4.58033i	0.0661641	−	0.375235i	−0.933689	−	0.358086i	$-0.883430\pi$
$149$	0.807636	−	4.58033i	0.0661641	−	0.375235i	0.999853	−	0.0171499i	$-0.00545926\pi$
$150$		0			0
$151$	−10.8548	+	9.10825i	−0.883350	+	0.741219i	−0.966865	−	0.255288i	$-0.917830\pi$
$151$	−10.8548	+	9.10825i	−0.883350	+	0.741219i	0.0835152	+	0.996507i	$0.473385\pi$
$152$	−0.353921	−	1.32085i	−0.0287068	−	0.107135i
$153$		0			0
$154$	−0.671481	+	0.387680i	−0.0541095	+	0.0312401i
$155$	−4.26737	+	3.87152i	−0.342764	+	0.310968i
$156$		0			0
$157$	0.185801	+	2.12372i	0.0148285	+	0.169491i	0.999998	−	0.00209430i	$-0.000666636\pi$
$157$	0.185801	+	2.12372i	0.0148285	+	0.169491i	−0.985169	+	0.171585i	$0.945111\pi$
$158$	−1.90120	−	0.886544i	−0.151251	−	0.0705296i
$159$		0			0
$160$	−1.98852	+	1.02264i	−0.157206	+	0.0808469i
$161$			1.63573i			0.128914i
$162$		0			0
$163$	4.26565	−	4.26565i	0.334112	−	0.334112i	−0.520034	−	0.854146i	$-0.674081\pi$
$163$	4.26565	−	4.26565i	0.334112	−	0.334112i	0.854146	+	0.520034i	$0.174081\pi$
$164$	−0.0455128	−	0.258116i	−0.00355396	−	0.0201555i
$165$		0			0
$166$	−8.83137	+	3.21436i	−0.685447	+	0.249482i
$167$	−9.93568	+	0.869259i	−0.768846	+	0.0672653i	−0.464828	−	0.885401i	$-0.653884\pi$
$167$	−9.93568	+	0.869259i	−0.768846	+	0.0672653i	−0.304018	+	0.952666i	$0.598328\pi$
$168$		0			0
$169$	3.17540	−	8.72435i	0.244262	−	0.671104i
$170$	−0.312294	−	8.07222i	−0.0239519	−	0.619111i
$171$		0			0
$172$	6.35059	−	1.70164i	0.484228	−	0.129748i
$173$	13.9858	+	1.22360i	1.06332	+	0.0930285i	0.605366	−	0.795947i	$-0.293027\pi$
$173$	13.9858	+	1.22360i	1.06332	+	0.0930285i	0.457955	+	0.888976i	$0.348582\pi$
$174$		0			0
$175$	1.12506	+	0.422188i	0.0850469	+	0.0319144i
$176$	3.17716	+	0.560219i	0.239487	+	0.0422281i
$177$		0			0
$178$	−0.331528	+	3.78938i	−0.0248491	+	0.284026i
$179$	−11.3133	+	19.5952i	−0.845596	+	1.46461i	0.0395073	+	0.999219i	$0.487421\pi$
$179$	−11.3133	+	19.5952i	−0.845596	+	1.46461i	−0.885103	+	0.465395i	$0.845912\pi$
$180$		0			0
$181$	−2.35398	−	4.07721i	−0.174970	−	0.303057i	0.765181	−	0.643815i	$-0.222650\pi$
$181$	−2.35398	−	4.07721i	−0.174970	−	0.303057i	−0.940151	+	0.340758i	$0.889316\pi$
$182$	0.419869	−	0.195788i	0.0311228	−	0.0145128i
$183$		0			0
$184$	4.37485	−	5.21375i	0.322518	−	0.384363i
$185$	−10.2064	+	7.75145i	−0.750390	+	0.569898i
$186$		0			0
$187$	−6.68516	+	9.54739i	−0.488867	+	0.698174i
$188$	9.30871	+	9.30871i	0.678907	+	0.678907i
$189$		0			0
$190$	2.92071	−	0.904978i	0.211891	−	0.0656540i
$191$	−3.59944	+	0.634678i	−0.260446	+	0.0459237i	−0.302346	−	0.953198i	$-0.597770\pi$
$191$	−3.59944	+	0.634678i	−0.260446	+	0.0459237i	0.0419002	+	0.999122i	$0.486659\pi$
$192$		0			0
$193$	−8.47458	+	18.1738i	−0.610014	+	1.30818i	0.322337	+	0.946625i	$0.395532\pi$
$193$	−8.47458	+	18.1738i	−0.610014	+	1.30818i	−0.932351	+	0.361554i	$0.882246\pi$
$194$	5.51518	+	4.62779i	0.395967	+	0.332256i
$195$		0			0
$196$	6.52357	+	2.37439i	0.465969	+	0.169599i
$197$	−19.5332	−	5.23391i	−1.39168	−	0.372901i	−0.516333	−	0.856388i	$-0.672703\pi$
$197$	−19.5332	−	5.23391i	−1.39168	−	0.372901i	−0.875352	+	0.483487i	$0.839370\pi$
$198$		0			0
$199$	−3.12299	−	1.80306i	−0.221383	−	0.127816i	0.385208	−	0.922830i	$-0.374130\pi$
$199$	−3.12299	−	1.80306i	−0.221383	−	0.127816i	−0.606590	+	0.795014i	$0.707463\pi$
$200$	−2.45688	−	4.35474i	−0.173728	−	0.307926i
$201$		0			0
$202$	−14.5440	+	10.1838i	−1.02331	+	0.716532i
$203$	−0.385616	+	0.270011i	−0.0270650	+	0.0189511i
$204$		0			0
$205$	0.572799	−	0.124006i	0.0400060	−	0.00866096i
$206$	−15.5648	−	8.98634i	−1.08445	−	0.626108i
$207$		0			0
$208$	−1.86194	−	0.498906i	−0.129102	−	0.0345929i
$209$	−4.14556	−	1.50886i	−0.286754	−	0.104370i
$210$		0			0
$211$	8.53894	+	7.16502i	0.587845	+	0.493260i	0.887513	−	0.460783i	$-0.152431\pi$
$211$	8.53894	+	7.16502i	0.587845	+	0.493260i	−0.299668	+	0.954044i	$0.596876\pi$
$212$	−5.47310	+	11.7371i	−0.375894	+	0.806108i
$213$		0			0
$214$	9.84689	−	1.73627i	0.673120	−	0.118689i
$215$	4.35109	+	14.0426i	0.296742	+	0.957700i
$216$		0			0
$217$	0.437904	+	0.437904i	0.0297269	+	0.0297269i
$218$	0.845534	−	1.20755i	0.0572668	−	0.0817855i
$219$		0			0
$220$	−0.977107	+	7.14746i	−0.0658765	+	0.481882i
$221$	4.47634	−	5.33469i	0.301111	−	0.358850i
$222$		0			0
$223$	17.0332	−	7.94271i	1.14063	−	0.531883i	0.241860	−	0.970311i	$-0.422242\pi$
$223$	17.0332	−	7.94271i	1.14063	−	0.531883i	0.898766	+	0.438428i	$0.144465\pi$
$224$	0.120167	+	0.208136i	0.00802900	+	0.0139066i
$225$		0			0
$226$	−3.33922	+	5.78370i	−0.222121	+	0.384726i
$227$	−2.00487	+	22.9157i	−0.133068	+	1.52097i	0.576945	+	0.816783i	$0.304245\pi$
$227$	−2.00487	+	22.9157i	−0.133068	+	1.52097i	−0.710013	+	0.704189i	$0.751311\pi$
$228$		0			0
$229$	−25.0466	−	4.41639i	−1.65512	−	0.291843i	−0.733431	−	0.679764i	$-0.762082\pi$
$229$	−25.0466	−	4.41639i	−1.65512	−	0.291843i	−0.921693	+	0.387921i	$0.873193\pi$
$230$	12.0278	+	9.32446i	0.793087	+	0.614837i
$231$		0			0
$232$	1.95128	+	0.170715i	0.128108	+	0.0112080i
$233$	−13.3281	+	3.57124i	−0.873150	+	0.233960i	−0.667450	−	0.744655i	$-0.732614\pi$
$233$	−13.3281	+	3.57124i	−0.873150	+	0.233960i	−0.205701	+	0.978615i	$0.565947\pi$
$234$		0			0
$235$	−19.9947	+	21.6040i	−1.30431	+	1.40929i
$236$	−2.22479	+	6.11255i	−0.144821	+	0.397893i
$237$		0			0
$238$	−0.864953	+	0.0756736i	−0.0560666	+	0.00490519i
$239$	20.6508	−	7.51627i	1.33579	−	0.486187i	0.427304	−	0.904108i	$-0.359463\pi$
$239$	20.6508	−	7.51627i	1.33579	−	0.486187i	0.908483	+	0.417921i	$0.137241\pi$
$240$		0			0
$241$	4.30767	+	24.4300i	0.277481	+	1.57368i	0.730968	+	0.682412i	$0.239069\pi$
$241$	4.30767	+	24.4300i	0.277481	+	1.57368i	−0.453486	+	0.891263i	$0.649820\pi$
$242$	−0.418475	+	0.418475i	−0.0269006	+	0.0269006i
$243$		0			0
$244$		−	15.0024i		−	0.960432i
$245$	−4.74140	+	14.7815i	−0.302917	+	0.944355i
$246$		0			0
$247$	2.38896	+	1.11399i	0.152006	+	0.0708814i
$248$	−0.224582	−	2.56698i	−0.0142610	−	0.163003i
$249$		0			0
$250$	9.51783	−	5.86608i	0.601960	−	0.371004i
$251$	13.2807	−	7.66761i	0.838270	−	0.483975i	−0.0184059	−	0.999831i	$-0.505859\pi$
$251$	13.2807	−	7.66761i	0.838270	−	0.483975i	0.856676	+	0.515855i	$0.172526\pi$
$252$		0			0
$253$	−5.68303	−	21.2093i	−0.357289	−	1.33342i
$254$	3.12310	−	2.62059i	0.195961	−	0.164431i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−11.7141	−	16.7295i	−0.730705	−	1.04356i	−0.996826	−	0.0796157i	$-0.974631\pi$
$257$	−11.7141	−	16.7295i	−0.730705	−	1.04356i	0.266120	−	0.963940i	$-0.414258\pi$
$258$		0			0
$259$	0.885439	+	1.05522i	0.0550185	+	0.0655685i
$260$	0.953801	−	4.20345i	0.0591523	−	0.260687i
$261$		0			0
$262$	3.87522	−	14.4625i	0.239412	−	0.893497i
$263$	10.3818	+	22.2638i	0.640169	+	1.37285i	0.911876	+	0.410466i	$0.134634\pi$
$263$	10.3818	+	22.2638i	0.640169	+	1.37285i	−0.271707	+	0.962380i	$0.587588\pi$
$264$		0			0
$265$	−26.6985	−	11.2145i	−1.64007	−	0.688900i
$266$	−0.112403	−	0.308824i	−0.00689186	−	0.0189352i
$267$		0			0
$268$	−3.34324	−	2.34096i	−0.204221	−	0.142997i
$269$	10.0313			0.611621			0.305811	−	0.952092i	$-0.401073\pi$
$269$	10.0313			0.611621			0.305811	+	0.952092i	$0.401073\pi$
$270$		0			0
$271$	−0.774034			−0.0470192			−0.0235096	−	0.999724i	$-0.507484\pi$
$271$	−0.774034			−0.0470192			−0.0235096	+	0.999724i	$0.507484\pi$
$272$	2.95936	+	2.07216i	0.179437	+	0.125643i
$273$		0			0
$274$	−3.42843	−	9.41954i	−0.207119	−	0.569055i
$275$	−16.0547	−	1.56539i	−0.968136	−	0.0943969i
$276$		0			0
$277$	−5.28136	−	11.3259i	−0.317326	−	0.680508i	0.681349	−	0.731958i	$-0.261393\pi$
$277$	−5.28136	−	11.3259i	−0.317326	−	0.680508i	−0.998676	+	0.0514503i	$0.983616\pi$
$278$	−0.533476	+	1.99096i	−0.0319958	+	0.119410i
$279$		0			0
$280$	−0.454670	+	0.286493i	−0.0271717	+	0.0171212i
$281$	−17.3303	−	20.6535i	−1.03384	−	1.23208i	−0.972241	−	0.233981i	$-0.924825\pi$
$281$	−17.3303	−	20.6535i	−1.03384	−	1.23208i	−0.0615979	−	0.998101i	$-0.519620\pi$
$282$		0			0
$283$	9.58970	+	13.6955i	0.570048	+	0.814114i	0.995879	−	0.0906893i	$-0.0289070\pi$
$283$	9.58970	+	13.6955i	0.570048	+	0.814114i	−0.425831	+	0.904803i	$0.640018\pi$
$284$	1.91836	−	10.8795i	0.113834	−	0.645582i
$285$		0			0
$286$	−4.76392	+	3.99740i	−0.281696	+	0.236371i
$287$	−0.0163033	−	0.0608447i	−0.000962353	−	0.00359155i
$288$		0			0
$289$	3.41937	−	1.97418i	0.201140	−	0.116128i
$290$	−0.212770	+	4.37469i	−0.0124943	+	0.256891i
$291$		0			0
$292$	0.209850	+	2.39860i	0.0122806	+	0.140367i
$293$	−16.4218	−	7.65762i	−0.959373	−	0.447363i	−0.121116	−	0.992638i	$-0.538647\pi$
$293$	−16.4218	−	7.65762i	−0.959373	−	0.447363i	−0.838257	+	0.545275i	$0.816425\pi$
$294$		0			0
$295$	−13.8502	−	4.44266i	−0.806388	−	0.258662i
$296$		−	5.73159i		−	0.333142i
$297$		0			0
$298$	−3.28875	+	3.28875i	−0.190512	+	0.190512i
$299$	2.27818	+	12.9202i	0.131751	+	0.747196i
$300$		0			0
$301$	1.48481	−	0.540428i	0.0855832	−	0.0311497i
$302$	14.1160	−	1.23499i	0.812284	−	0.0710657i
$303$		0			0
$304$	−0.467694	+	1.28498i	−0.0268241	+	0.0736986i
$305$	33.5214	−	1.29686i	1.91943	−	0.0742579i
$306$		0			0
$307$	13.0517	−	3.49720i	0.744902	−	0.199596i	0.133646	−	0.991029i	$-0.457331\pi$
$307$	13.0517	−	3.49720i	0.744902	−	0.199596i	0.611255	+	0.791433i	$0.290665\pi$
$308$	0.772409	+	0.0675770i	0.0440121	+	0.00385056i
$309$		0			0
$310$	5.71624	−	0.723703i	0.324661	−	0.0411036i
$311$	13.2793	+	2.34149i	0.752998	+	0.132774i	0.536956	−	0.843610i	$-0.319574\pi$
$311$	13.2793	+	2.34149i	0.752998	+	0.132774i	0.216042	+	0.976384i	$0.430685\pi$
$312$		0			0
$313$	1.39088	−	15.8978i	0.0786172	−	0.898599i	−0.849811	−	0.527087i	$-0.823284\pi$
$313$	1.39088	−	15.8978i	0.0786172	−	0.898599i	0.928428	−	0.371512i	$-0.121160\pi$
$314$	1.06591	−	1.84622i	0.0601530	−	0.104188i
$315$		0			0
$316$	1.04887	+	1.81670i	0.0590036	+	0.102197i
$317$	−2.80390	+	1.30748i	−0.157483	+	0.0734354i	−0.499762	−	0.866163i	$-0.666579\pi$
$317$	−2.80390	+	1.30748i	−0.157483	+	0.0734354i	0.342279	+	0.939598i	$0.388801\pi$
$318$		0			0
$319$	4.06191	−	4.84080i	0.227423	−	0.271033i
$320$	2.21546	+	0.302869i	0.123848	+	0.0169309i
$321$		0			0
$322$	0.938216	−	1.33991i	0.0522847	−	0.0746703i
$323$	−3.49323	−	3.49323i	−0.194369	−	0.194369i
$324$		0			0
$325$	9.47461	+	1.76781i	0.525557	+	0.0980605i
$326$	−5.94089	+	1.04754i	−0.329036	+	0.0580179i
$327$		0			0
$328$	−0.110767	+	0.237541i	−0.00611611	+	0.0131160i
$329$	2.42367	+	2.03370i	0.133621	+	0.112122i
$330$		0			0
$331$	−9.25843	−	3.36979i	−0.508890	−	0.185221i	0.0747985	−	0.997199i	$-0.476169\pi$
$331$	−9.25843	−	3.36979i	−0.508890	−	0.185221i	−0.583688	+	0.811978i	$0.698391\pi$
$332$	9.07791	+	2.43242i	0.498215	+	0.133496i
$333$		0			0
$334$	8.63742	+	4.98682i	0.472618	+	0.272866i
$335$	4.94164	−	7.67249i	0.269991	−	0.419193i
$336$		0			0
$337$	28.4103	−	19.8931i	1.54761	−	1.08365i	0.585610	−	0.810593i	$-0.300855\pi$
$337$	28.4103	−	19.8931i	1.54761	−	1.08365i	0.961999	−	0.273054i	$-0.0880337\pi$
$338$	−7.60522	+	5.32523i	−0.413670	+	0.289655i
$339$		0			0
$340$	−4.37422	+	6.79150i	−0.237225	+	0.368321i
$341$	−7.19941	−	4.15658i	−0.389870	−	0.225091i
$342$		0			0
$343$	3.23662	+	0.867250i	0.174761	+	0.0468271i
$344$	−6.17812	−	2.24865i	−0.333102	−	0.121239i
$345$		0			0
$346$	−10.7547	−	9.02424i	−0.578175	−	0.485146i
$347$	0.925787	−	1.98536i	0.0496989	−	0.106580i	−0.879890	−	0.475177i	$-0.842384\pi$
$347$	0.925787	−	1.98536i	0.0496989	−	0.106580i	0.929589	+	0.368597i	$0.120162\pi$
$348$		0			0
$349$	−3.94897	+	0.696310i	−0.211384	+	0.0372726i	−0.278337	−	0.960483i	$-0.589783\pi$
$349$	−3.94897	+	0.696310i	−0.211384	+	0.0372726i	0.0669534	+	0.997756i	$0.478672\pi$
$350$	−0.679442	−	0.991147i	−0.0363177	−	0.0529790i
$351$		0			0
$352$	−2.28125	−	2.28125i	−0.121591	−	0.121591i
$353$	14.8237	−	21.1704i	0.788986	−	1.12679i	−0.200148	−	0.979766i	$-0.564142\pi$
$353$	14.8237	−	21.1704i	0.788986	−	1.12679i	0.989133	−	0.147022i	$-0.0469689\pi$
$354$		0			0
$355$	24.4750	+	3.34591i	1.29900	+	0.177582i
$356$	2.44507	−	2.91392i	0.129588	−	0.154438i
$357$		0			0
$358$	20.5067	−	9.56241i	1.08381	−	0.505389i
$359$	−15.1015	−	26.1567i	−0.797029	−	1.38050i	−0.921543	−	0.388277i	$-0.873070\pi$
$359$	−15.1015	−	26.1567i	−0.797029	−	1.38050i	0.124513	−	0.992218i	$-0.460263\pi$
$360$		0			0
$361$	−8.56505	+	14.8351i	−0.450792	+	0.780795i
$362$	−0.410326	+	4.69005i	−0.0215662	+	0.246503i
$363$		0			0
$364$	−0.456236	−	0.0804467i	−0.0239133	−	0.00421655i
$365$	−5.34128	+	0.676231i	−0.279575	+	0.0353956i
$366$		0			0
$367$	36.6920	+	3.21013i	1.91531	+	0.167568i	0.981661	−	0.190634i	$-0.0610544\pi$
$367$	36.6920	+	3.21013i	1.91531	+	0.167568i	0.933644	+	0.358202i	$0.116610\pi$
$368$	−6.57415	+	1.76154i	−0.342701	+	0.0918266i
$369$		0			0
$370$	12.8067	−	0.495458i	0.665786	−	0.0257576i
$371$	−1.06452	+	2.92474i	−0.0552670	+	0.151845i
$372$		0			0
$373$	−29.7977	+	2.60696i	−1.54287	+	0.134984i	−0.826579	−	0.562820i	$-0.809716\pi$
$373$	−29.7977	+	2.60696i	−1.54287	+	0.134984i	−0.716289	+	0.697804i	$0.754161\pi$
$374$	10.9523	−	3.98632i	0.566331	−	0.206128i
$375$		0			0
$376$	−2.28599	−	12.9645i	−0.117891	−	0.668593i
$377$	−2.66983	+	2.66983i	−0.137503	+	0.137503i
$378$		0			0
$379$			17.6628i			0.907278i	0.891185	+	0.453639i	$0.149874\pi$
$379$			17.6628i			0.907278i	−0.891185	+	0.453639i	$0.850126\pi$
$380$	−2.91158	−	0.933936i	−0.149361	−	0.0479099i
$381$		0			0
$382$	3.31253	+	1.54466i	0.169484	+	0.0790315i
$383$	−1.69852	−	19.4142i	−0.0867905	−	0.992020i	−0.907327	−	0.420426i	$-0.861881\pi$
$383$	−1.69852	−	19.4142i	−0.0867905	−	0.992020i	0.820536	−	0.571594i	$-0.193675\pi$
$384$		0			0
$385$	−0.0842243	+	1.73171i	−0.00429247	+	0.0882561i
$386$	17.3660	−	10.0263i	0.883908	−	0.510325i
$387$		0			0
$388$	−1.86338	−	6.95424i	−0.0945989	−	0.353048i
$389$	10.6757	−	8.95799i	0.541280	−	0.454188i	−0.330695	−	0.943738i	$-0.607283\pi$
$389$	10.6757	−	8.95799i	0.541280	−	0.454188i	0.871975	+	0.489550i	$0.162839\pi$
$390$		0			0
$391$	4.26971	−	24.2148i	0.215929	−	1.22459i
$392$	−3.98190	−	5.68675i	−0.201117	−	0.287224i
$393$		0			0
$394$	12.9986	+	15.4912i	0.654862	+	0.780434i
$395$	−3.96855	+	2.50063i	−0.199680	+	0.125821i
$396$		0			0
$397$	6.67595	−	24.9150i	0.335056	−	1.25045i	−0.568752	−	0.822509i	$-0.692573\pi$
$397$	6.67595	−	24.9150i	0.335056	−	1.25045i	0.903808	−	0.427938i	$-0.140760\pi$
$398$	1.52401	+	3.26825i	0.0763918	+	0.163823i
$399$		0			0
$400$	−0.485217	+	4.97640i	−0.0242609	+	0.248820i
$401$	−12.1213	−	33.3030i	−0.605309	−	1.66307i	−0.740340	−	0.672232i	$-0.765336\pi$
$401$	−12.1213	−	33.3030i	−0.605309	−	1.66307i	0.135031	−	0.990841i	$-0.456887\pi$
$402$		0			0
$403$	4.06879	+	2.84900i	0.202681	+	0.141919i
$404$	17.7550			0.883342
$405$		0			0
$406$	0.470751			0.0233630
$407$	−15.1470	−	10.6061i	−0.750810	−	0.525723i
$408$		0			0
$409$	3.49946	+	9.61469i	0.173037	+	0.475416i	0.995649	−	0.0931882i	$-0.0297058\pi$
$409$	3.49946	+	9.61469i	0.173037	+	0.475416i	−0.822611	+	0.568604i	$0.807484\pi$
$410$	−0.540337	−	0.226964i	−0.0266853	−	0.0112090i
$411$		0			0
$412$	7.59558	+	16.2888i	0.374208	+	0.802491i
$413$	−0.404621	+	1.51007i	−0.0199101	+	0.0743055i
$414$		0			0
$415$	−4.65027	+	20.4939i	−0.228273	+	1.00601i
$416$	1.23905	+	1.47665i	0.0607496	+	0.0723985i
$417$		0			0
$418$	2.53040	+	3.61378i	0.123766	+	0.176756i
$419$	1.94413	−	11.0257i	0.0949771	−	0.538642i	−0.899777	−	0.436350i	$-0.856271\pi$
$419$	1.94413	−	11.0257i	0.0949771	−	0.538642i	0.994754	−	0.102293i	$-0.0326178\pi$
$420$		0			0
$421$	−0.765760	+	0.642549i	−0.0373208	+	0.0313159i	−0.661257	−	0.750159i	$-0.729977\pi$
$421$	−0.765760	+	0.642549i	−0.0373208	+	0.0313159i	0.623936	+	0.781475i	$0.285532\pi$
$422$	−2.88500	−	10.7670i	−0.140440	−	0.524128i
$423$		0			0
$424$	11.2154	−	6.47523i	0.544669	−	0.314465i
$425$	−15.5530	−	9.18666i	−0.754432	−	0.445618i
$426$		0			0
$427$	−0.314248	−	3.59187i	−0.0152075	−	0.173823i
$428$	−9.06199	−	4.22567i	−0.438028	−	0.204256i
$429$		0			0
$430$	4.49032	−	13.9987i	0.216542	−	0.675079i
$431$			23.7841i			1.14564i	0.819680	+	0.572821i	$0.194151\pi$
$431$			23.7841i			1.14564i	−0.819680	+	0.572821i	$0.805849\pi$
$432$		0			0
$433$	−16.6701	+	16.6701i	−0.801116	+	0.801116i	−0.983270	−	0.182154i	$-0.941693\pi$
$433$	−16.6701	+	16.6701i	−0.801116	+	0.801116i	0.182154	+	0.983270i	$0.441693\pi$
$434$	−0.107539	−	0.609882i	−0.00516202	−	0.0292753i
$435$		0			0
$436$	−1.38524	+	0.504187i	−0.0663411	+	0.0241462i
$437$	9.27150	−	0.811151i	0.443516	−	0.0388026i
$438$		0			0
$439$	−4.44858	+	12.2224i	−0.212319	+	0.583342i	−0.999440	−	0.0334563i	$-0.989349\pi$
$439$	−4.44858	+	12.2224i	−0.212319	+	0.583342i	0.787121	+	0.616799i	$0.211571\pi$
$440$	4.90001	−	5.29441i	0.233599	−	0.252401i
$441$		0			0
$442$	−6.72665	+	1.80240i	−0.319954	+	0.0857315i
$443$	3.57624	+	0.312881i	0.169913	+	0.0148654i	0.171794	−	0.985133i	$-0.445043\pi$
$443$	3.57624	+	0.312881i	0.169913	+	0.0148654i	−0.00188197	+	0.999998i	$0.500599\pi$
$444$		0			0
$445$	6.72222	+	5.21137i	0.318664	+	0.247043i
$446$	−18.5085	−	3.26355i	−0.876404	−	0.154534i
$447$		0			0
$448$	0.0209465	−	0.239420i	0.000989629	−	0.0113115i
$449$	1.08484	−	1.87900i	0.0511968	−	0.0886755i	−0.839291	−	0.543682i	$-0.817030\pi$
$449$	1.08484	−	1.87900i	0.0511968	−	0.0886755i	0.890488	+	0.455007i	$0.150363\pi$
$450$		0			0
$451$	0.422787	+	0.732288i	0.0199082	+	0.0344821i
$452$	6.05272	−	2.82243i	0.284696	−	0.132756i
$453$		0			0
$454$	14.7862	−	17.6215i	0.693952	−	0.827020i
$455$	0.140311	−	1.02637i	0.00657790	−	0.0481168i
$456$		0			0
$457$	3.01442	−	4.30504i	0.141009	−	0.201381i	−0.742436	−	0.669917i	$-0.766329\pi$
$457$	3.01442	−	4.30504i	0.141009	−	0.201381i	0.883444	+	0.468536i	$0.155218\pi$
$458$	17.9838	+	17.9838i	0.840328	+	0.840328i
$459$		0			0
$460$	−4.50427	−	14.5370i	−0.210013	−	0.677791i
$461$	27.5583	−	4.85926i	1.28352	−	0.226318i	0.510044	−	0.860149i	$-0.329629\pi$
$461$	27.5583	−	4.85926i	1.28352	−	0.226318i	0.773472	+	0.633830i	$0.218518\pi$
$462$		0			0
$463$	3.48237	−	7.46797i	0.161840	−	0.347066i	−0.808619	−	0.588332i	$-0.799785\pi$
$463$	3.48237	−	7.46797i	0.161840	−	0.347066i	0.970459	+	0.241266i	$0.0775626\pi$
$464$	−1.50048	−	1.25905i	−0.0696579	−	0.0584499i
$465$		0			0
$466$	12.9661	+	4.71927i	0.600642	+	0.218616i
$467$	−10.2047	−	2.73435i	−0.472219	−	0.126531i	0.0148581	−	0.999890i	$-0.495270\pi$
$467$	−10.2047	−	2.73435i	−0.472219	−	0.126531i	−0.487077	+	0.873359i	$0.661937\pi$
$468$		0			0
$469$	−0.849473	−	0.490443i	−0.0392250	−	0.0226466i
$470$	28.7702	−	6.22850i	1.32707	−	0.287300i
$471$		0			0
$472$	5.32845	−	3.73102i	0.245262	−	0.171734i
$473$	−17.3749	+	12.1660i	−0.798899	+	0.559395i
$474$		0			0
$475$	1.83510	−	6.58636i	0.0842000	−	0.302203i
$476$	0.751933	+	0.434128i	0.0344648	+	0.0198982i
$477$		0			0
$478$	−21.2273	−	5.68783i	−0.970913	−	0.260155i
$479$	0.0205101	+	0.00746508i	0.000937133	+	0.000341088i	0.342489	−	0.939522i	$-0.388730\pi$
$479$	0.0205101	+	0.00746508i	0.000937133	+	0.000341088i	−0.341552	+	0.939863i	$0.610952\pi$
$480$		0			0
$481$	8.46354	+	7.10175i	0.385904	+	0.323812i
$482$	10.4838	−	22.4827i	0.477526	−	1.02406i
$483$		0			0
$484$	0.582822	−	0.102767i	0.0264919	−	0.00467124i
$485$	15.3774	−	4.76468i	0.698254	−	0.216353i
$486$		0			0
$487$	−18.8277	−	18.8277i	−0.853166	−	0.853166i	0.137355	−	0.990522i	$-0.456140\pi$
$487$	−18.8277	−	18.8277i	−0.853166	−	0.853166i	−0.990522	+	0.137355i	$0.956140\pi$
$488$	−8.60504	+	12.2893i	−0.389532	+	0.556309i
$489$		0			0
$490$	12.3622	−	9.38874i	0.558469	−	0.424140i
$491$	−10.6744	+	12.7213i	−0.481729	+	0.574102i	−0.951094	−	0.308902i	$-0.900039\pi$
$491$	−10.6744	+	12.7213i	−0.481729	+	0.574102i	0.469365	+	0.883004i	$0.344483\pi$
$492$		0			0
$493$	6.41333	−	2.99059i	0.288842	−	0.134689i
$494$	−1.31796	−	2.28277i	−0.0592979	−	0.102707i
$495$		0			0
$496$	−1.28839	+	2.23156i	−0.0578506	+	0.100200i
$497$	0.231404	−	2.64496i	0.0103799	−	0.118643i
$498$		0			0
$499$	−15.6197	−	2.75418i	−0.699236	−	0.123294i	−0.187281	−	0.982306i	$-0.559967\pi$
$499$	−15.6197	−	2.75418i	−0.699236	−	0.123294i	−0.511955	+	0.859012i	$0.671079\pi$
$500$	−11.1612	−	0.653992i	−0.499144	−	0.0292474i
$501$		0			0
$502$	−15.2769	−	1.33655i	−0.681840	−	0.0596533i
$503$	−1.07505	+	0.288059i	−0.0479342	+	0.0128439i	−0.282706	−	0.959206i	$-0.591232\pi$
$503$	−1.07505	+	0.288059i	−0.0479342	+	0.0128439i	0.234772	+	0.972050i	$0.424566\pi$
$504$		0			0
$505$	1.53480	+	39.6716i	0.0682976	+	1.76536i
$506$	−7.50992	+	20.6333i	−0.333857	+	0.917263i
$507$		0			0
$508$	−4.06141	+	0.355327i	−0.180196	+	0.0157651i
$509$	8.42858	−	3.06775i	0.373590	−	0.135976i	−0.148400	−	0.988927i	$-0.547412\pi$
$509$	8.42858	−	3.06775i	0.373590	−	0.135976i	0.521990	+	0.852952i	$0.325190\pi$
$510$		0			0
$511$	0.100485	+	0.569876i	0.00444517	+	0.0252098i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			20.4229i			0.900816i
$515$	−35.7390	+	18.3796i	−1.57485	+	0.809902i
$516$		0			0
$517$	−38.4917	−	17.9490i	−1.69286	−	0.789396i
$518$	−0.120057	−	1.37226i	−0.00527500	−	0.0602935i
$519$		0			0
$520$	−3.19231	+	2.89618i	−0.139992	+	0.127006i
$521$	19.1924	−	11.0808i	0.840836	−	0.485457i	−0.0167122	−	0.999860i	$-0.505320\pi$
$521$	19.1924	−	11.0808i	0.840836	−	0.485457i	0.857548	+	0.514403i	$0.171987\pi$
$522$		0			0
$523$	8.81487	+	32.8975i	0.385447	+	1.43851i	0.837461	+	0.546497i	$0.184039\pi$
$523$	8.81487	+	32.8975i	0.385447	+	1.43851i	−0.452014	+	0.892011i	$0.649294\pi$
$524$	−11.4698	+	9.62426i	−0.501058	+	0.420438i
$525$		0			0
$526$	4.26574	−	24.1922i	0.185995	−	1.05483i
$527$	−5.33952	−	7.62563i	−0.232593	−	0.332178i
$528$		0			0
$529$	14.9914	+	17.8661i	0.651800	+	0.776785i
$530$	15.4377	+	24.5000i	0.670572	+	1.06421i
$531$		0			0
$532$	−0.0850593	+	0.317446i	−0.00368779	+	0.0137630i
$533$	−0.213518	−	0.457891i	−0.00924849	−	0.0198335i
$534$		0			0
$535$	8.65848	−	20.6134i	0.374339	−	0.891193i
$536$	1.39590	+	3.83521i	0.0602938	+	0.165656i
$537$		0			0
$538$	−8.21719	−	5.75374i	−0.354268	−	0.248061i
$539$	−22.3969			−0.964701
$540$		0			0
$541$	11.3812			0.489314			0.244657	−	0.969610i	$-0.421325\pi$
$541$	11.3812			0.489314			0.244657	+	0.969610i	$0.421325\pi$
$542$	0.634052	+	0.443968i	0.0272349	+	0.0190700i
$543$		0			0
$544$	−1.23562	−	3.39483i	−0.0529767	−	0.145552i
$545$	−1.24630	−	3.05160i	−0.0533855	−	0.130716i
$546$		0			0
$547$	9.32837	+	20.0048i	0.398852	+	0.855341i	0.998483	+	0.0550645i	$0.0175364\pi$
$547$	9.32837	+	20.0048i	0.398852	+	0.855341i	−0.599631	+	0.800277i	$0.704686\pi$
$548$	−2.59442	+	9.68250i	−0.110828	+	0.413616i
$549$		0			0
$550$	12.2534	+	10.4909i	0.522486	+	0.447334i
$551$	1.72168	+	2.05182i	0.0733461	+	0.0874105i
$552$		0			0
$553$	0.289174	+	0.412983i	0.0122969	+	0.0175618i
$554$	−2.17004	+	12.3069i	−0.0921961	+	0.522870i
$555$		0			0
$556$	1.57897	−	1.32491i	0.0669630	−	0.0561887i
$557$	0.213989	+	0.798617i	0.00906700	+	0.0338385i	0.970311	−	0.241860i	$-0.0777575\pi$
$557$	0.213989	+	0.798617i	0.00906700	+	0.0338385i	−0.961244	+	0.275699i	$0.911091\pi$
$558$		0			0
$559$	10.9755	−	6.33669i	0.464213	−	0.268014i
$560$	0.536769	+	0.0261066i	0.0226826	+	0.00110320i
$561$		0			0
$562$	2.34982	+	26.8586i	0.0991212	+	1.13296i
$563$	−35.3533	−	16.4855i	−1.48997	−	0.694782i	−0.504306	−	0.863525i	$-0.668252\pi$
$563$	−35.3533	−	16.4855i	−1.48997	−	0.694782i	−0.985660	+	0.168743i	$0.946029\pi$
$564$		0			0
$565$	6.82964	+	13.2802i	0.287325	+	0.558702i
$566$		−	16.7191i		−	0.702757i
$567$		0			0
$568$	−7.81167	+	7.81167i	−0.327771	+	0.327771i
$569$	−0.170803	−	0.968674i	−0.00716045	−	0.0406089i	0.981018	−	0.193916i	$-0.0621188\pi$
$569$	−0.170803	−	0.968674i	−0.00716045	−	0.0406089i	−0.988179	+	0.153307i	$0.951008\pi$
$570$		0			0
$571$	14.5969	−	5.31284i	0.610861	−	0.222335i	−0.0180189	−	0.999838i	$-0.505736\pi$
$571$	14.5969	−	5.31284i	0.610861	−	0.222335i	0.628880	+	0.777502i	$0.283514\pi$
$572$	6.19519	−	0.542008i	0.259034	−	0.0226625i
$573$		0			0
$574$	−0.0215442	+	0.0591923i	−0.000899239	+	0.00247064i
$575$	32.0920	−	11.3209i	1.33833	−	0.472116i
$576$		0			0
$577$	−26.9888	+	7.23164i	−1.12356	+	0.301057i	−0.772323	−	0.635229i	$-0.780906\pi$
$577$	−26.9888	+	7.23164i	−1.12356	+	0.301057i	−0.351237	+	0.936287i	$0.614239\pi$
$578$	−3.93333	−	0.344121i	−0.163605	−	0.0143136i
$579$		0			0
$580$	2.68351	−	3.46150i	0.111427	−	0.143731i
$581$	2.22438	+	0.392219i	0.0922829	+	0.0162720i
$582$		0			0
$583$	3.64140	−	41.6214i	0.150812	−	1.72378i
$584$	1.20388	−	2.08518i	0.0498169	−	0.0862855i
$585$		0			0
$586$	9.05974	+	15.6919i	0.374254	+	0.648228i
$587$	−3.87371	+	1.80634i	−0.159885	+	0.0745557i	−0.500914	−	0.865497i	$-0.667003\pi$
$587$	−3.87371	+	1.80634i	−0.159885	+	0.0745557i	0.341028	+	0.940053i	$0.389225\pi$
$588$		0			0
$589$	2.26494	−	2.69925i	0.0933251	−	0.111220i
$590$	8.79719	+	11.5833i	0.362175	+	0.476879i
$591$		0			0
$592$	−3.28751	+	4.69505i	−0.135116	+	0.192965i
$593$	18.4908	+	18.4908i	0.759325	+	0.759325i	0.976199	−	0.216875i	$-0.0695863\pi$
$593$	18.4908	+	18.4908i	0.759325	+	0.759325i	−0.216875	+	0.976199i	$0.569586\pi$
$594$		0			0
$595$	−0.905016	+	1.71764i	−0.0371020	+	0.0704165i
$596$	4.58033	−	0.807636i	0.187618	−	0.0330821i
$597$		0			0
$598$	5.54456	−	11.8903i	0.226734	−	0.486232i
$599$	26.2752	+	22.0475i	1.07358	+	0.900837i	0.995372	−	0.0961008i	$-0.0306371\pi$
$599$	26.2752	+	22.0475i	1.07358	+	0.900837i	0.0782037	+	0.996937i	$0.475082\pi$
$600$		0			0
$601$	2.23759	+	0.814415i	0.0912731	+	0.0332207i	0.387253	−	0.921973i	$-0.373424\pi$
$601$	2.23759	+	0.814415i	0.0912731	+	0.0332207i	−0.295980	+	0.955194i	$0.595646\pi$
$602$	−1.52626	−	0.408961i	−0.0622059	−	0.0166680i
$603$		0			0
$604$	−12.2715	−	7.08496i	−0.499321	−	0.288283i
$605$	0.280004	+	1.29337i	0.0113838	+	0.0525831i
$606$		0			0
$607$	9.61996	−	6.73597i	0.390462	−	0.273404i	−0.361817	−	0.932249i	$-0.617843\pi$
$607$	9.61996	−	6.73597i	0.390462	−	0.273404i	0.752279	+	0.658845i	$0.228955\pi$
$608$	1.12015	−	0.784334i	0.0454279	−	0.0318090i
$609$		0			0
$610$	−28.2029	−	18.1647i	−1.14190	−	0.735469i
$611$	21.9764	+	12.6881i	0.889072	+	0.513306i
$612$		0			0
$613$	−19.7628	−	5.29543i	−0.798212	−	0.213880i	−0.163413	−	0.986558i	$-0.552250\pi$
$613$	−19.7628	−	5.29543i	−0.798212	−	0.213880i	−0.634799	+	0.772677i	$0.718917\pi$
$614$	−12.6973	−	4.62143i	−0.512420	−	0.186506i
$615$		0			0
$616$	−0.593960	−	0.498391i	−0.0239313	−	0.0200808i
$617$	7.02782	−	15.0712i	0.282929	−	0.606744i	−0.712561	−	0.701611i	$-0.752465\pi$
$617$	7.02782	−	15.0712i	0.282929	−	0.606744i	0.995490	+	0.0948664i	$0.0302424\pi$
$618$		0			0
$619$	−10.8338	+	1.91029i	−0.435447	+	0.0767810i	−0.387075	−	0.922048i	$-0.626514\pi$
$619$	−10.8338	+	1.91029i	−0.435447	+	0.0767810i	−0.0483720	+	0.998829i	$0.515403\pi$
$620$	−5.09757	−	2.68588i	−0.204723	−	0.107867i
$621$		0			0
$622$	−9.53472	−	9.53472i	−0.382307	−	0.382307i
$623$	0.524361	−	0.748866i	0.0210081	−	0.0300027i
$624$		0			0
$625$	0.496466	−	24.9951i	0.0198586	−	0.999803i
$626$	−10.2580	+	12.2250i	−0.409991	+	0.488608i
$627$		0			0
$628$	−1.93209	+	0.900950i	−0.0770989	+	0.0359518i
$629$	−10.3533	−	17.9324i	−0.412812	−	0.715012i
$630$		0			0
$631$	−3.43478	+	5.94921i	−0.136736	+	0.236834i	−0.926259	−	0.376887i	$-0.876995\pi$
$631$	−3.43478	+	5.94921i	−0.136736	+	0.236834i	0.789523	+	0.613721i	$0.210328\pi$
$632$	0.182830	−	2.08976i	0.00727260	−	0.0831261i
$633$		0			0
$634$	3.04676	+	0.537226i	0.121002	+	0.0213360i
$635$	−1.14502	−	9.04407i	−0.0454388	−	0.358903i
$636$		0			0
$637$	13.3311	+	1.16632i	0.528198	+	0.0462113i
$638$	−6.10389	+	1.63553i	−0.241655	+	0.0647513i
$639$		0			0
$640$	−1.64108	−	1.51883i	−0.0648694	−	0.0600371i
$641$	−10.0003	+	27.4757i	−0.394990	+	1.08523i	0.569704	+	0.821850i	$0.307058\pi$
$641$	−10.0003	+	27.4757i	−0.394990	+	1.08523i	−0.964694	+	0.263375i	$0.915164\pi$
$642$		0			0
$643$	−11.9257	+	1.04336i	−0.470303	+	0.0411462i	−0.319845	−	0.947470i	$-0.603631\pi$
$643$	−11.9257	+	1.04336i	−0.470303	+	0.0411462i	−0.150459	+	0.988616i	$0.548075\pi$
$644$	−1.53708	+	0.559452i	−0.0605696	+	0.0220455i
$645$		0			0
$646$	0.857853	+	4.86513i	0.0337518	+	0.191416i
$647$	23.8770	−	23.8770i	0.938701	−	0.938701i	−0.0595255	−	0.998227i	$-0.518959\pi$
$647$	23.8770	−	23.8770i	0.938701	−	0.938701i	0.998227	+	0.0595255i	$0.0189588\pi$
$648$		0			0
$649$		−	20.9857i		−	0.823762i
$650$	−6.74717	−	6.88252i	−0.264646	−	0.269955i
$651$		0			0
$652$	5.46734	+	2.54946i	0.214118	+	0.0998447i
$653$	2.32621	+	26.5887i	0.0910317	+	1.04050i	0.895072	+	0.445922i	$0.147124\pi$
$653$	2.32621	+	26.5887i	0.0910317	+	1.04050i	−0.804040	+	0.594575i	$0.797320\pi$
$654$		0			0
$655$	−22.4959	−	24.7960i	−0.878988	−	0.968861i
$656$	0.226983	−	0.131049i	0.00886222	−	0.00511660i
$657$		0			0
$658$	−0.818872	−	3.05607i	−0.0319230	−	0.119138i
$659$	−31.8707	+	26.7427i	−1.24151	+	1.04175i	−0.244101	+	0.969750i	$0.578493\pi$
$659$	−31.8707	+	26.7427i	−1.24151	+	1.04175i	−0.997405	+	0.0719972i	$0.977063\pi$
$660$		0			0
$661$	2.79132	−	15.8304i	0.108570	−	0.615730i	−0.881164	−	0.472810i	$-0.843240\pi$
$661$	2.79132	−	15.8304i	0.108570	−	0.615730i	0.989734	−	0.142920i	$-0.0456492\pi$
$662$	5.65123	+	8.07079i	0.219641	+	0.313680i
$663$		0			0
$664$	−6.04101	−	7.19940i	−0.234437	−	0.279391i
$665$	−0.716652	−	0.162615i	−0.0277906	−	0.00630594i
$666$		0			0
$667$	−3.45038	+	12.8770i	−0.133599	+	0.498600i
$668$	−4.21504	−	9.03918i	−0.163085	−	0.349736i
$669$		0			0
$670$	−8.44871	+	3.45053i	−0.326402	+	0.133305i
$671$	16.5539	+	45.4815i	0.639057	+	1.75579i
$672$		0			0
$673$	25.9838	+	18.1941i	1.00160	+	0.701330i	0.954700	−	0.297570i	$-0.0961761\pi$
$673$	25.9838	+	18.1941i	1.00160	+	0.701330i	0.0469026	+	0.998899i	$0.485065\pi$
$674$	−34.6826			−1.33592
$675$		0			0
$676$	9.28426			0.357087
$677$	−6.45041	−	4.51663i	−0.247910	−	0.173588i	0.443017	−	0.896513i	$-0.353908\pi$
$677$	−6.45041	−	4.51663i	−0.247910	−	0.173588i	−0.690926	+	0.722925i	$0.742797\pi$
$678$		0			0
$679$	−0.591797	−	1.62595i	−0.0227111	−	0.0623982i
$680$	7.47859	−	3.05432i	0.286791	−	0.117128i
$681$		0			0
$682$	3.51329	+	7.53428i	0.134531	+	0.288503i
$683$	3.68379	−	13.7481i	0.140956	−	0.526057i	−0.858946	−	0.512067i	$-0.828880\pi$
$683$	3.68379	−	13.7481i	0.140956	−	0.526057i	0.999902	−	0.0139900i	$-0.00445330\pi$
$684$		0			0
$685$	−21.8588	−	4.95997i	−0.835182	−	0.189511i
$686$	−2.15385	−	2.56686i	−0.0822344	−	0.0980031i
$687$		0			0
$688$	3.77104	+	5.38561i	0.143770	+	0.205324i
$689$	−4.33489	+	24.5844i	−0.165146	+	0.936590i
$690$		0			0
$691$	26.0895	−	21.8917i	0.992492	−	0.832800i	0.00656535	−	0.999978i	$-0.497910\pi$
$691$	26.0895	−	21.8917i	0.992492	−	0.832800i	0.985927	+	0.167179i	$0.0534657\pi$
$692$	3.63362	+	13.5608i	0.138129	+	0.515506i
$693$		0			0
$694$	−1.89711	+	1.09530i	−0.0720135	+	0.0415770i
$695$	3.09686	+	3.41351i	0.117471	+	0.129482i
$696$		0			0
$697$	0.0825263	+	0.943280i	0.00312591	+	0.0357293i
$698$	3.63420	+	1.69465i	0.137556	+	0.0641436i
$699$		0			0
$700$	−0.0119324	+	1.20161i	−0.000451001	+	0.0454167i
$701$			39.3013i			1.48439i	0.670183	+	0.742195i	$0.266215\pi$
$701$			39.3013i			1.48439i	−0.670183	+	0.742195i	$0.733785\pi$
$702$		0			0
$703$	5.54205	−	5.54205i	0.209022	−	0.209022i
$704$	0.560219	+	3.17716i	0.0211140	+	0.119744i
$705$		0			0
$706$	−24.2857	+	8.83928i	−0.914005	+	0.332671i
$707$	4.25089	−	0.371904i	0.159871	−	0.0139869i
$708$		0			0
$709$	−14.7719	+	40.5855i	−0.554771	+	1.52422i	0.272350	+	0.962198i	$0.412199\pi$
$709$	−14.7719	+	40.5855i	−0.554771	+	1.52422i	−0.827121	+	0.562023i	$0.810023\pi$
$710$	−18.1296	−	16.7791i	−0.680393	−	0.629709i
$711$		0			0
$712$	−3.67424	+	0.984510i	−0.137698	+	0.0368961i
$713$	17.4710	+	1.52852i	0.654296	+	0.0572434i
$714$		0			0
$715$	1.74659	+	13.7956i	0.0653189	+	0.515928i
$716$	−22.2828	−	3.92907i	−0.832749	−	0.146836i
$717$		0			0
$718$	−2.63237	+	30.0882i	−0.0982393	+	1.12288i
$719$	−10.0133	+	17.3435i	−0.373432	+	0.646804i	−0.990091	−	0.140427i	$-0.955152\pi$
$719$	−10.0133	+	17.3435i	−0.373432	+	0.646804i	0.616659	+	0.787231i	$0.288486\pi$
$720$		0			0
$721$	2.15973	+	3.74075i	0.0804324	+	0.139313i
$722$	15.5251	−	7.23949i	0.577786	−	0.269426i
$723$		0			0
$724$	3.02622	−	3.60651i	0.112469	−	0.134035i
$725$	7.96633	+	5.69680i	0.295862	+	0.211574i
$726$		0			0
$727$	−13.1646	+	18.8010i	−0.488247	+	0.697289i	−0.985377	−	0.170387i	$-0.945498\pi$
$727$	−13.1646	+	18.8010i	−0.488247	+	0.697289i	0.497130	+	0.867676i	$0.334387\pi$
$728$	0.327584	+	0.327584i	0.0121411	+	0.0121411i
$729$		0			0
$730$	4.76319	+	2.50970i	0.176294	+	0.0928880i
$731$	−23.3913	+	4.12452i	−0.865159	+	0.152551i
$732$		0			0
$733$	−12.7041	+	27.2441i	−0.469238	+	1.00628i	0.519200	+	0.854653i	$0.326230\pi$
$733$	−12.7041	+	27.2441i	−0.469238	+	1.00628i	−0.988437	+	0.151630i	$0.951548\pi$
$734$	−28.2150	−	23.6752i	−1.04144	−	0.873869i
$735$		0			0
$736$	6.39561	+	2.32781i	0.235745	+	0.0858042i
$737$	12.7185	+	3.40790i	0.468490	+	0.125532i
$738$		0			0
$739$	37.0093	+	21.3673i	1.36141	+	0.786009i	0.989811	−	0.142385i	$-0.0454771\pi$
$739$	37.0093	+	21.3673i	1.36141	+	0.786009i	0.371597	+	0.928394i	$0.378810\pi$
$740$	−10.7748	−	6.93974i	−0.396089	−	0.255110i
$741$		0			0
$742$	2.54956	−	1.78522i	0.0935973	−	0.0655376i
$743$	2.70180	−	1.89182i	0.0991194	−	0.0694041i	−0.522966	−	0.852354i	$-0.675175\pi$
$743$	2.70180	−	1.89182i	0.0991194	−	0.0694041i	0.622085	+	0.782949i	$0.286286\pi$
$744$		0			0
$745$	2.20052	+	10.1645i	0.0806208	+	0.372397i
$746$	25.9042	+	14.9558i	0.948419	+	0.547570i
$747$		0			0
$748$	−11.2581	−	3.01659i	−0.411636	−	0.110297i
$749$	−2.25813	−	0.821892i	−0.0825103	−	0.0300313i
$750$		0			0
$751$	8.80887	+	7.39152i	0.321440	+	0.269720i	0.789201	−	0.614135i	$-0.210495\pi$
$751$	8.80887	+	7.39152i	0.321440	+	0.269720i	−0.467761	+	0.883855i	$0.654939\pi$
$752$	−5.56356	+	11.9311i	−0.202882	+	0.435082i
$753$		0			0
$754$	3.71834	−	0.655644i	0.135414	−	0.0238771i
$755$	14.7698	−	28.0319i	0.537529	−	1.02018i
$756$		0			0
$757$	−5.86658	−	5.86658i	−0.213224	−	0.213224i	0.592411	−	0.805636i	$-0.298176\pi$
$757$	−5.86658	−	5.86658i	−0.213224	−	0.213224i	−0.805636	+	0.592411i	$0.798176\pi$
$758$	10.1310	−	14.4685i	0.367974	−	0.525521i
$759$		0			0
$760$	1.84934	+	2.43505i	0.0670827	+	0.0883285i
$761$	−1.90580	+	2.27124i	−0.0690852	+	0.0823325i	−0.799480	−	0.600693i	$-0.794892\pi$
$761$	−1.90580	+	2.27124i	−0.0690852	+	0.0823325i	0.730395	+	0.683025i	$0.239336\pi$
$762$		0			0
$763$	−0.321093	+	0.149728i	−0.0116244	+	0.00542053i
$764$	−1.82748	−	3.16529i	−0.0661160	−	0.114516i
$765$		0			0
$766$	−9.74419	+	16.8774i	−0.352072	+	0.609806i
$767$	−1.09284	+	12.4912i	−0.0394600	+	0.451030i
$768$		0			0
$769$	−10.4760	−	1.84719i	−0.377773	−	0.0666115i	−0.0184621	−	0.999830i	$-0.505877\pi$
$769$	−10.4760	−	1.84719i	−0.377773	−	0.0666115i	−0.359311	+	0.933218i	$0.616988\pi$
$770$	1.06226	−	1.37022i	0.0382812	−	0.0493795i
$771$		0			0
$772$	−19.9763	−	1.74770i	−0.718962	−	0.0629010i
$773$	−1.33913	+	0.358818i	−0.0481650	+	0.0129058i	−0.282821	−	0.959173i	$-0.591270\pi$
$773$	−1.33913	+	0.358818i	−0.0481650	+	0.0129058i	0.234656	+	0.972078i	$0.424604\pi$
$774$		0			0
$775$	5.56067	−	11.6222i	0.199745	−	0.417481i
$776$	−2.46239	+	6.76537i	−0.0883948	+	0.242863i
$777$		0			0
$778$	−13.8831	+	1.21462i	−0.497734	+	0.0435461i
$779$	−0.336790	+	0.122582i	−0.0120668	+	0.00439194i
$780$		0			0
$781$	6.18895	+	35.0993i	0.221458	+	1.25595i
$782$	−17.3866	+	17.3866i	−0.621742	+	0.621742i
$783$		0			0
$784$			6.94224i			0.247937i
$785$	−2.18010	−	4.23918i	−0.0778109	−	0.151303i
$786$		0			0
$787$	−35.2269	−	16.4266i	−1.25570	−	0.585545i	−0.323073	−	0.946374i	$-0.604716\pi$
$787$	−35.2269	−	16.4266i	−1.25570	−	0.585545i	−0.932632	+	0.360830i	$0.882494\pi$
$788$	−1.76249	−	20.1453i	−0.0627860	−	0.717648i
$789$		0			0
$790$	4.68515	+	0.227870i	0.166690	+	0.00810724i
$791$	1.39002	−	0.802528i	0.0494234	−	0.0285346i
$792$		0			0
$793$	−7.48480	−	27.9337i	−0.265793	−	0.991953i
$794$	−19.7593	+	16.5800i	−0.701230	+	0.588402i
$795$		0			0
$796$	0.626196	−	3.55133i	0.0221949	−	0.125874i
$797$	6.14276	+	8.77276i	0.217588	+	0.310747i	0.913076	−	0.407791i	$-0.133701\pi$
$797$	6.14276	+	8.77276i	0.217588	+	0.310747i	−0.695488	+	0.718538i	$0.744812\pi$
$798$		0			0
$799$	−30.5706	−	36.4327i	−1.08151	−	1.28890i
$800$	3.25181	−	3.79812i	0.114969	−	0.134284i
$801$		0			0
$802$	−9.17263	+	34.2327i	−0.323897	+	1.20880i
$803$	−3.28284	−	7.04006i	−0.115849	−	0.248438i
$804$		0			0
$805$	−1.38291	−	3.38609i	−0.0487411	−	0.119344i
$806$	−1.69884	−	4.66753i	−0.0598391	−	0.164407i
$807$		0			0
$808$	−14.5440	−	10.1838i	−0.511657	−	0.358266i
$809$	0.139320			0.00489823			0.00244912	−	0.999997i	$-0.499220\pi$
$809$	0.139320			0.00489823			0.00244912	+	0.999997i	$0.499220\pi$
$810$		0			0
$811$	−31.6077			−1.10990			−0.554948	−	0.831885i	$-0.687262\pi$
$811$	−31.6077			−1.10990			−0.554948	+	0.831885i	$0.687262\pi$
$812$	−0.385616	−	0.270011i	−0.0135325	−	0.00947554i
$813$		0			0
$814$	6.32433	+	17.3760i	0.221668	+	0.609027i
$815$	−5.22390	+	12.4366i	−0.182985	+	0.435635i
$816$		0			0
$817$	−3.79952	−	8.14809i	−0.132928	−	0.285066i
$818$	2.64817	−	9.88311i	0.0925911	−	0.345555i
$819$		0			0
$820$	0.312437	+	0.495843i	0.0109108	+	0.0173156i
$821$	2.58425	+	3.07979i	0.0901909	+	0.107485i	0.809252	−	0.587461i	$-0.199872\pi$
$821$	2.58425	+	3.07979i	0.0901909	+	0.107485i	−0.719061	+	0.694946i	$0.755428\pi$
$822$		0			0
$823$	26.5517	+	37.9198i	0.925535	+	1.32180i	0.946731	+	0.322025i	$0.104364\pi$
$823$	26.5517	+	37.9198i	0.925535	+	1.32180i	−0.0211966	+	0.999775i	$0.506748\pi$
$824$	3.12092	−	17.6996i	0.108723	−	0.616596i
$825$		0			0
$826$	1.19758	−	1.00489i	0.0416693	−	0.0349647i
$827$	−6.81107	−	25.4192i	−0.236844	−	0.883914i	−0.977309	−	0.211819i	$-0.932061\pi$
$827$	−6.81107	−	25.4192i	−0.236844	−	0.883914i	0.740465	−	0.672095i	$-0.234605\pi$
$828$		0			0
$829$	35.2516	−	20.3525i	1.22434	−	0.706872i	0.258499	−	0.966012i	$-0.416772\pi$
$829$	35.2516	−	20.3525i	1.22434	−	0.706872i	0.965840	+	0.259139i	$0.0834389\pi$
$830$	15.5641	−	14.1204i	0.540238	−	0.490125i
$831$		0			0
$832$	−0.168004	−	1.92029i	−0.00582448	−	0.0665741i
$833$	−22.7304	−	10.5994i	−0.787563	−	0.367247i
$834$		0			0
$835$	19.8327	−	10.1994i	0.686341	−	0.352966i
$836$		−	4.41161i		−	0.152579i
$837$		0			0
$838$	−7.91664	+	7.91664i	−0.273476	+	0.273476i
$839$	2.37885	+	13.4912i	0.0821272	+	0.465766i	0.997940	+	0.0641601i	$0.0204368\pi$
$839$	2.37885	+	13.4912i	0.0821272	+	0.465766i	−0.915812	+	0.401606i	$0.868452\pi$
$840$		0			0
$841$	23.6458	−	8.60638i	0.815373	−	0.296772i
$842$	0.995824	−	0.0871233i	0.0343184	−	0.00300247i
$843$		0			0
$844$	−3.81243	+	10.4746i	−0.131229	+	0.360549i
$845$	0.802562	+	20.7447i	0.0276090	+	0.713640i
$846$		0			0
$847$	0.137387	−	0.0368126i	0.00472066	−	0.00126490i
$848$	−12.9012	−	1.12871i	−0.443028	−	0.0387600i
$849$		0			0
$850$	7.47104	+	16.4461i	0.256255	+	0.564097i
$851$	38.4169	+	6.77394i	1.31692	+	0.232208i
$852$		0			0
$853$	1.17036	−	13.3773i	0.0400723	−	0.458029i	−0.949477	−	0.313836i	$-0.898386\pi$
$853$	1.17036	−	13.3773i	0.0400723	−	0.458029i	0.989550	−	0.144193i	$-0.0460586\pi$
$854$	−1.80280	+	3.12254i	−0.0616905	+	0.106851i
$855$		0			0
$856$	4.99940	+	8.65921i	0.170876	+	0.295966i
$857$	−15.1632	+	7.07071i	−0.517965	+	0.241531i	−0.663979	−	0.747752i	$-0.731133\pi$
$857$	−15.1632	+	7.07071i	−0.517965	+	0.241531i	0.146014	+	0.989283i	$0.453356\pi$
$858$		0			0
$859$	−17.3720	+	20.7031i	−0.592724	+	0.706381i	−0.976127	−	0.217200i	$-0.930307\pi$
$859$	−17.3720	+	20.7031i	−0.592724	+	0.706381i	0.383403	+	0.923581i	$0.374752\pi$
$860$	−11.7076	+	8.89156i	−0.399226	+	0.303200i
$861$		0			0
$862$	13.6420	−	19.4828i	0.464649	−	0.663588i
$863$	−9.90332	−	9.90332i	−0.337113	−	0.337113i	0.518167	−	0.855280i	$-0.326615\pi$
$863$	−9.90332	−	9.90332i	−0.337113	−	0.337113i	−0.855280	+	0.518167i	$0.826615\pi$
$864$		0			0
$865$	−29.9862	+	9.29119i	−1.01956	+	0.315910i
$866$	23.2170	−	4.09378i	0.788945	−	0.139112i
$867$		0			0
$868$	−0.261723	+	0.561267i	−0.00888347	+	0.0190507i
$869$	−5.18434	−	4.35018i	−0.175867	−	0.147570i
$870$		0			0
$871$	−7.39284	−	2.69078i	−0.250497	−	0.0911734i
$872$	1.42391	+	0.381536i	0.0482198	+	0.0129205i
$873$		0			0
$874$	−8.06003	−	4.65346i	−0.272634	−	0.157406i
$875$	−2.68591	+	0.0772096i	−0.0908003	+	0.00261016i
$876$		0			0
$877$	−34.6972	+	24.2953i	−1.17164	+	0.820393i	−0.986731	−	0.162363i	$-0.948089\pi$
$877$	−34.6972	+	24.2953i	−1.17164	+	0.820393i	−0.184911	+	0.982755i	$0.559200\pi$
$878$	10.6545	−	7.46039i	0.359573	−	0.251776i
$879$		0			0
$880$	−7.05061	+	1.52640i	−0.237676	+	0.0514548i
$881$	17.4797	+	10.0919i	0.588905	+	0.340004i	0.764664	−	0.644429i	$-0.222905\pi$
$881$	17.4797	+	10.0919i	0.588905	+	0.340004i	−0.175760	+	0.984433i	$0.556238\pi$
$882$		0			0
$883$	2.17639	+	0.583163i	0.0732415	+	0.0196250i	0.295254	−	0.955419i	$-0.404596\pi$
$883$	2.17639	+	0.583163i	0.0732415	+	0.0196250i	−0.222012	+	0.975044i	$0.571262\pi$
$884$	6.54397	+	2.38181i	0.220097	+	0.0801089i
$885$		0			0
$886$	−2.75003	−	2.30755i	−0.0923890	−	0.0775236i
$887$	11.4763	−	24.6110i	0.385336	−	0.826356i	−0.613978	−	0.789323i	$-0.710432\pi$
$887$	11.4763	−	24.6110i	0.385336	−	0.826356i	0.999314	−	0.0370330i	$-0.0117907\pi$
$888$		0			0
$889$	−0.964937	+	0.170144i	−0.0323630	+	0.00570646i
$890$	−2.51740	−	8.12461i	−0.0843834	−	0.272337i
$891$		0			0
$892$	13.2894	+	13.2894i	0.444962	+	0.444962i
$893$	10.3254	−	14.7462i	0.345525	−	0.493461i
$894$		0			0
$895$	6.85289	−	50.1284i	0.229067	−	1.67561i
$896$	−0.154484	+	0.184107i	−0.00516094	+	0.00615057i
$897$		0			0
$898$	−1.96640	+	0.916947i	−0.0656196	+	0.0305989i
$899$	2.52362	+	4.37104i	0.0841674	+	0.145782i
$900$		0			0
$901$	23.3931	−	40.5181i	0.779338	−	1.34985i
$902$	0.0736966	−	0.842355i	0.00245383	−	0.0280474i
$903$		0			0
$904$	−6.57698	−	1.15970i	−0.218747	−	0.0385710i
$905$	8.31996	+	6.45001i	0.276565	+	0.214406i
$906$		0			0
$907$	5.99333	+	0.524348i	0.199005	+	0.0174107i	0.186222	−	0.982508i	$-0.440375\pi$
$907$	5.99333	+	0.524348i	0.199005	+	0.0174107i	0.0127827	+	0.999918i	$0.495931\pi$
$908$	−22.2195	+	5.95369i	−0.737379	+	0.197580i
$909$		0			0
$910$	−0.703636	+	0.760271i	−0.0233253	+	0.0252027i
$911$	−7.15714	+	19.6641i	−0.237126	+	0.651500i	0.762861	+	0.646562i	$0.223794\pi$
$911$	−7.15714	+	19.6641i	−0.237126	+	0.651500i	−0.999988	+	0.00493753i	$0.998428\pi$
$912$		0			0
$913$	−30.2047	+	2.64257i	−0.999629	+	0.0874562i
$914$	−4.93854	+	1.79748i	−0.163353	+	0.0594555i
$915$		0			0
$916$	−4.41639	−	25.0466i	−0.145922	−	0.827562i
$917$	−2.54449	+	2.54449i	−0.0840264	+	0.0840264i
$918$		0			0
$919$		−	9.67644i		−	0.319196i	−0.987182	−	0.159598i	$-0.948980\pi$
$919$		−	9.67644i		−	0.319196i	0.987182	−	0.159598i	$-0.0510198\pi$
$920$	−4.64839	+	14.4915i	−0.153253	+	0.477772i
$921$		0			0
$922$	−25.3616	−	11.8263i	−0.835238	−	0.389478i
$923$	−1.85600	−	21.2142i	−0.0610909	−	0.698273i
$924$		0			0
$925$	14.5747	−	24.6750i	0.479214	−	0.811310i
$926$	−7.13604	+	4.12000i	−0.234505	+	0.135392i
$927$		0			0
$928$	0.506957	+	1.89199i	0.0166417	+	0.0621076i
$929$	13.5294	−	11.3525i	0.443887	−	0.372465i	−0.393275	−	0.919421i	$-0.628658\pi$
$929$	13.5294	−	11.3525i	0.443887	−	0.372465i	0.837161	+	0.546956i	$0.184213\pi$
$930$		0			0
$931$	1.64847	−	9.34891i	0.0540263	−	0.306398i
$932$	−7.91434	−	11.3028i	−0.259243	−	0.370237i
$933$		0			0
$934$	6.79088	+	8.09305i	0.222204	+	0.264813i
$935$	5.76708	−	25.4158i	0.188604	−	0.831184i
$936$		0			0
$937$	11.5162	−	42.9791i	0.376218	−	1.40406i	−0.475339	−	0.879803i	$-0.657675\pi$
$937$	11.5162	−	42.9791i	0.376218	−	1.40406i	0.851557	−	0.524262i	$-0.175659\pi$
$938$	0.414541	+	0.888985i	0.0135352	+	0.0290264i
$939$		0			0
$940$	−27.1397	−	11.3998i	−0.885200	−	0.371822i
$941$	4.65295	+	12.7839i	0.151682	+	0.416743i	0.992140	−	0.125134i	$-0.0399361\pi$
$941$	4.65295	+	12.7839i	0.151682	+	0.416743i	−0.840458	+	0.541877i	$0.817714\pi$
$942$		0			0
$943$	−1.46125	−	1.02318i	−0.0475848	−	0.0333192i
$944$	−6.50484			−0.211714
$945$		0			0
$946$	21.2108			0.689624
$947$	14.7106	+	10.3005i	0.478029	+	0.334720i	0.787632	−	0.616146i	$-0.211307\pi$
$947$	14.7106	+	10.3005i	0.478029	+	0.334720i	−0.309602	+	0.950866i	$0.600196\pi$
$948$		0			0
$949$	1.58740	+	4.36136i	0.0515293	+	0.141576i
$950$	−5.28100	+	4.34266i	−0.171338	+	0.140894i
$951$		0			0
$952$	−0.366941	−	0.786908i	−0.0118926	−	0.0255038i
$953$	−14.2887	+	53.3261i	−0.462856	+	1.72740i	0.201045	+	0.979582i	$0.435566\pi$
$953$	−14.2887	+	53.3261i	−0.462856	+	1.72740i	−0.663901	+	0.747821i	$0.731100\pi$
$954$		0			0
$955$	6.91455	−	4.35694i	0.223750	−	0.140987i
$956$	14.1260	+	16.8347i	0.456866	+	0.544472i
$957$		0			0
$958$	−0.0125191	−	0.0178792i	−0.000404475	−	0.000577650i
$959$	−0.418340	+	2.37252i	−0.0135089	+	0.0766128i
$960$		0			0
$961$	−18.6610	+	15.6584i	−0.601967	+	0.505110i
$962$	−2.85953	−	10.6719i	−0.0921948	−	0.344076i
$963$		0			0
$964$	−21.4834	+	12.4034i	−0.691933	+	0.399488i
$965$	2.17823	−	44.7860i	0.0701198	−	1.44171i
$966$		0			0
$967$	4.80317	+	54.9005i	0.154459	+	1.76548i	0.538938	+	0.842346i	$0.318826\pi$
$967$	4.80317	+	54.9005i	0.154459	+	1.76548i	−0.384478	+	0.923134i	$0.625619\pi$
$968$	−0.536365	−	0.250111i	−0.0172394	−	0.00803888i
$969$		0			0
$970$	−15.3294	−	4.91714i	−0.492197	−	0.157880i
$971$		−	28.5223i		−	0.915326i	−0.889126	−	0.457663i	$-0.848687\pi$
$971$		−	28.5223i		−	0.915326i	0.889126	−	0.457663i	$-0.151313\pi$
$972$		0			0
$973$	0.350283	−	0.350283i	0.0112296	−	0.0112296i
$974$	4.62363	+	26.2219i	0.148151	+	0.840205i
$975$		0			0
$976$	14.0977	−	5.13113i	0.451255	−	0.164244i
$977$	−5.20188	+	0.455106i	−0.166423	+	0.0145601i	−0.170063	−	0.985433i	$-0.554397\pi$
$977$	−5.20188	+	0.455106i	−0.166423	+	0.0145601i	0.00363966	+	0.999993i	$0.498841\pi$
$978$		0			0
$979$	−4.19723	+	11.5318i	−0.134144	+	0.368558i
$980$	−15.5117	+	0.600110i	−0.495504	+	0.0191698i
$981$		0			0
$982$	16.0406	−	4.29806i	0.511875	−	0.137157i
$983$	7.36268	+	0.644151i	0.234833	+	0.0205452i	0.203965	−	0.978978i	$-0.434617\pi$
$983$	7.36268	+	0.644151i	0.234833	+	0.0205452i	0.0308682	+	0.999523i	$0.490173\pi$
$984$		0			0
$985$	44.8603	−	5.67953i	1.42937	−	0.180965i
$986$	−6.96882	−	1.22879i	−0.221933	−	0.0391327i
$987$		0			0
$988$	−0.229736	+	2.62589i	−0.00730887	+	0.0835407i
$989$	22.3736	−	38.7522i	0.711440	−	1.23225i
$990$		0			0
$991$	−13.5114	−	23.4024i	−0.429204	−	0.743403i	0.567599	−	0.823305i	$-0.307872\pi$
$991$	−13.5114	−	23.4024i	−0.429204	−	0.743403i	−0.996803	+	0.0799026i	$0.974539\pi$
$992$	2.33536	−	1.08900i	0.0741478	−	0.0345757i
$993$		0			0
$994$	−1.70664	+	2.03390i	−0.0541314	+	0.0645112i
$995$	7.98922	+	1.09218i	0.253275	+	0.0346245i
$996$		0			0
$997$	19.7330	−	28.1816i	0.624949	−	0.892520i	−0.374447	−	0.927248i	$-0.622168\pi$
$997$	19.7330	−	28.1816i	0.624949	−	0.892520i	0.999397	+	0.0347279i	$0.0110565\pi$
$998$	11.2152	+	11.2152i	0.355011	+	0.355011i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.2		216
3.2	odd	2		270.2.r.a.257.10	yes	216
5.3	odd	4	inner	810.2.s.a.233.4		216
15.8	even	4		270.2.r.a.203.14	yes	216
27.2	odd	18	inner	810.2.s.a.737.4		216
27.25	even	9		270.2.r.a.137.14	yes	216
135.83	even	36	inner	810.2.s.a.413.2		216
135.133	odd	36		270.2.r.a.83.10	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.10	✓	216	135.133	odd	36
270.2.r.a.137.14	yes	216	27.25	even	9
270.2.r.a.203.14	yes	216	15.8	even	4
270.2.r.a.257.10	yes	216	3.2	odd	2
810.2.s.a.233.4		216	5.3	odd	4	inner
810.2.s.a.413.2		216	135.83	even	36	inner
810.2.s.a.557.2		216	1.1	even	1	trivial
810.2.s.a.737.4		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)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.07008 + 0.845439i) q^{5} +(0.101570 + 0.217817i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.07008 + 0.845439i) q^{5} +(0.101570 + 0.217817i) q^{7} +(0.258819 - 0.965926i) q^{8} +(2.18063 + 0.494807i) q^{10} +(-2.07374 - 2.47139i) q^{11} +(1.10564 + 1.57902i) q^{13} +(0.0417336 - 0.236683i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.935037 - 3.48961i) q^{17} +(1.18424 - 0.683723i) q^{19} +(-1.50246 - 1.65608i) q^{20} +(0.281179 + 3.21390i) q^{22} +(6.16839 + 2.87637i) q^{23} +(3.57047 - 3.50025i) q^{25} -1.92762i q^{26} +(-0.169942 + 0.169942i) q^{28} +(0.340130 + 1.92898i) q^{29} +(2.42139 - 0.881313i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-1.23562 + 3.39483i) q^{34} +(-0.394408 - 0.365027i) q^{35} +(5.53629 - 1.48345i) q^{37} +(-1.36224 - 0.119181i) q^{38} +(0.280855 + 2.21836i) q^{40} +(-0.258116 - 0.0455128i) q^{41} +(0.573015 - 6.54960i) q^{43} +(1.61309 - 2.79395i) q^{44} +(-3.40303 - 5.89422i) q^{46} +(11.9311 - 5.56356i) q^{47} +(4.46239 - 5.31806i) q^{49} +(-4.93242 + 0.819303i) q^{50} +(-1.10564 + 1.57902i) q^{52} +(9.15736 + 9.15736i) q^{53} +(6.38223 + 3.36276i) q^{55} +(0.236683 - 0.0417336i) q^{56} +(0.827796 - 1.77522i) q^{58} +(4.98299 + 4.18123i) q^{59} +(-14.0977 - 5.13113i) q^{61} +(-2.48899 - 0.666922i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.62373 - 2.33394i) q^{65} +(-3.34324 + 2.34096i) q^{67} +(2.95936 - 2.07216i) q^{68} +(0.113709 + 0.525236i) q^{70} +(-9.56731 - 5.52369i) q^{71} +(2.32572 + 0.623174i) q^{73} +(-5.38594 - 1.96032i) q^{74} +(1.04752 + 0.878977i) q^{76} +(0.327681 - 0.702714i) q^{77} +(2.06587 - 0.364269i) q^{79} +(1.04234 - 1.97827i) q^{80} +(0.185331 + 0.185331i) q^{82} +(5.39056 - 7.69851i) q^{83} +(4.88585 + 6.43325i) q^{85} +(-4.22608 + 5.03645i) q^{86} +(-2.92390 + 1.36344i) q^{88} +(-1.90193 - 3.29423i) q^{89} +(-0.231637 + 0.401207i) q^{91} +(-0.593187 + 6.78016i) q^{92} +(-12.9645 - 2.28599i) q^{94} +(-1.87343 + 2.41657i) q^{95} +(-7.17216 - 0.627483i) q^{97} +(-6.70569 + 1.79678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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