LMFDB - Embedded newform 810.2.s.a.773.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [810,2,Mod(17,810)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			773.4
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.209292 + 2.22625i) q^{5} +(-0.734969 - 0.514631i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.402526 - 2.19954i) q^{10} +(-0.457015 + 1.25564i) q^{11} +(0.0942983 + 1.07783i) q^{13} +(0.687319 + 0.576729i) q^{14} +(0.939693 + 0.342020i) q^{16} +(3.60283 - 0.965374i) q^{17} +(-4.47083 + 2.58124i) q^{19} +(-0.592697 + 2.15609i) q^{20} +(0.564712 - 1.21103i) q^{22} +(0.187700 + 0.268064i) q^{23} +(-4.91239 - 0.931873i) q^{25} -1.08195i q^{26} +(-0.634439 - 0.634439i) q^{28} +(-3.73628 + 3.13512i) q^{29} +(-1.54601 + 8.76783i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-3.67325 + 0.647694i) q^{34} +(1.29952 - 1.52852i) q^{35} +(-2.74278 - 10.2362i) q^{37} +(4.67879 - 2.18175i) q^{38} +(0.778357 - 2.09623i) q^{40} +(-0.945418 + 1.12671i) q^{41} +(0.475774 + 1.02030i) q^{43} +(-0.668111 + 1.15720i) q^{44} +(-0.163623 - 0.283403i) q^{46} +(-4.63025 + 6.61269i) q^{47} +(-2.11881 - 5.82137i) q^{49} +(4.81248 + 1.35647i) q^{50} +(-0.0942983 + 1.07783i) q^{52} +(2.08364 - 2.08364i) q^{53} +(-2.69972 - 1.28022i) q^{55} +(0.576729 + 0.687319i) q^{56} +(3.99531 - 2.79755i) q^{58} +(-11.7104 + 4.26225i) q^{59} +(1.05434 + 5.97947i) q^{61} +(2.30429 - 8.59972i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-2.41927 - 0.0156502i) q^{65} +(-9.51755 + 0.832678i) q^{67} +(3.71573 - 0.325084i) q^{68} +(-1.42780 + 1.40944i) q^{70} +(2.95943 + 1.70863i) q^{71} +(-1.15401 + 4.30684i) q^{73} +(1.84020 + 10.4363i) q^{74} +(-4.85114 + 1.76567i) q^{76} +(0.982082 - 0.687661i) q^{77} +(10.7626 + 12.8264i) q^{79} +(-0.958093 + 2.02041i) q^{80} +(1.04002 - 1.04002i) q^{82} +(0.298155 - 3.40793i) q^{83} +(1.39512 + 8.22284i) q^{85} +(-0.385038 - 1.05788i) q^{86} +(0.766425 - 1.09457i) q^{88} +(4.47579 + 7.75230i) q^{89} +(0.485381 - 0.840704i) q^{91} +(0.138300 + 0.296585i) q^{92} +(5.18897 - 6.18397i) q^{94} +(-4.81077 - 10.4934i) q^{95} +(-10.5006 + 4.89650i) q^{97} +(1.60338 + 5.98389i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−0.209292	+	2.22625i	−0.0935982	+	0.995610i
$5$	−0.209292	+	2.22625i	−0.0935982	+	0.995610i
$6$		0			0
$7$	−0.734969	−	0.514631i	−0.277792	−	0.194512i	0.426375	−	0.904547i	$-0.359790\pi$
$7$	−0.734969	−	0.514631i	−0.277792	−	0.194512i	−0.704167	+	0.710034i	$0.748679\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	0.402526	−	2.19954i	0.127290	−	0.695555i
$11$	−0.457015	+	1.25564i	−0.137795	+	0.378589i	−0.989327	−	0.145714i	$-0.953452\pi$
$11$	−0.457015	+	1.25564i	−0.137795	+	0.378589i	0.851532	+	0.524303i	$0.175674\pi$
$12$		0			0
$13$	0.0942983	+	1.07783i	0.0261537	+	0.298938i	0.997995	+	0.0632997i	$0.0201624\pi$
$13$	0.0942983	+	1.07783i	0.0261537	+	0.298938i	−0.971841	+	0.235638i	$0.924282\pi$
$14$	0.687319	+	0.576729i	0.183694	+	0.154137i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	3.60283	−	0.965374i	0.873814	−	0.234138i	0.206077	−	0.978536i	$-0.433930\pi$
$17$	3.60283	−	0.965374i	0.873814	−	0.234138i	0.667736	+	0.744398i	$0.267263\pi$
$18$		0			0
$19$	−4.47083	+	2.58124i	−1.02568	+	0.592176i	−0.915744	−	0.401763i	$-0.868398\pi$
$19$	−4.47083	+	2.58124i	−1.02568	+	0.592176i	−0.109935	+	0.993939i	$0.535064\pi$
$20$	−0.592697	+	2.15609i	−0.132531	+	0.482116i
$21$		0			0
$22$	0.564712	−	1.21103i	0.120397	−	0.258192i
$23$	0.187700	+	0.268064i	0.0391382	+	0.0558952i	0.838244	−	0.545295i	$-0.183582\pi$
$23$	0.187700	+	0.268064i	0.0391382	+	0.0558952i	−0.799106	+	0.601190i	$0.794693\pi$
$24$		0			0
$25$	−4.91239	−	0.931873i	−0.982479	−	0.186375i
$26$		−	1.08195i		−	0.212188i
$27$		0			0
$28$	−0.634439	−	0.634439i	−0.119898	−	0.119898i
$29$	−3.73628	+	3.13512i	−0.693811	+	0.582176i	−0.920005	−	0.391906i	$-0.871816\pi$
$29$	−3.73628	+	3.13512i	−0.693811	+	0.582176i	0.226195	+	0.974082i	$0.427371\pi$
$30$		0			0
$31$	−1.54601	+	8.76783i	−0.277671	+	1.57475i	0.452678	+	0.891674i	$0.350469\pi$
$31$	−1.54601	+	8.76783i	−0.277671	+	1.57475i	−0.730348	+	0.683075i	$0.760642\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	−3.67325	+	0.647694i	−0.629958	+	0.111079i
$35$	1.29952	−	1.52852i	0.219659	−	0.258367i
$36$		0			0
$37$	−2.74278	−	10.2362i	−0.450910	−	1.68282i	−0.699841	−	0.714298i	$-0.746746\pi$
$37$	−2.74278	−	10.2362i	−0.450910	−	1.68282i	0.248931	−	0.968521i	$-0.419921\pi$
$38$	4.67879	−	2.18175i	0.758999	−	0.353927i
$39$		0			0
$40$	0.778357	−	2.09623i	0.123069	−	0.331442i
$41$	−0.945418	+	1.12671i	−0.147649	+	0.175962i	−0.834800	−	0.550553i	$-0.814417\pi$
$41$	−0.945418	+	1.12671i	−0.147649	+	0.175962i	0.687151	+	0.726515i	$0.258861\pi$
$42$		0			0
$43$	0.475774	+	1.02030i	0.0725548	+	0.155594i	0.939240	−	0.343261i	$-0.111532\pi$
$43$	0.475774	+	1.02030i	0.0725548	+	0.155594i	−0.866685	+	0.498855i	$0.833754\pi$
$44$	−0.668111	+	1.15720i	−0.100721	+	0.174455i
$45$		0			0
$46$	−0.163623	−	0.283403i	−0.0241249	−	0.0417855i
$47$	−4.63025	+	6.61269i	−0.675392	+	0.964560i	0.324434	+	0.945908i	$0.394826\pi$
$47$	−4.63025	+	6.61269i	−0.675392	+	0.964560i	−0.999826	+	0.0186513i	$0.994063\pi$
$48$		0			0
$49$	−2.11881	−	5.82137i	−0.302687	−	0.831625i
$50$	4.81248	+	1.35647i	0.680588	+	0.191834i
$51$		0			0
$52$	−0.0942983	+	1.07783i	−0.0130768	+	0.149469i
$53$	2.08364	−	2.08364i	0.286210	−	0.286210i	−0.549369	−	0.835580i	$-0.685132\pi$
$53$	2.08364	−	2.08364i	0.286210	−	0.286210i	0.835580	+	0.549369i	$0.185132\pi$
$54$		0			0
$55$	−2.69972	−	1.28022i	−0.364030	−	0.172625i
$56$	0.576729	+	0.687319i	0.0770687	+	0.0918469i
$57$		0			0
$58$	3.99531	−	2.79755i	0.524610	−	0.367336i
$59$	−11.7104	+	4.26225i	−1.52457	+	0.554898i	−0.962284	−	0.272046i	$-0.912300\pi$
$59$	−11.7104	+	4.26225i	−1.52457	+	0.554898i	−0.562284	+	0.826944i	$0.690077\pi$
$60$		0			0
$61$	1.05434	+	5.97947i	0.134995	+	0.765593i	0.974863	+	0.222803i	$0.0715208\pi$
$61$	1.05434	+	5.97947i	0.134995	+	0.765593i	−0.839869	+	0.542790i	$0.817368\pi$
$62$	2.30429	−	8.59972i	0.292645	−	1.09217i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−2.41927	−	0.0156502i	−0.300073	−	0.00194117i
$66$		0			0
$67$	−9.51755	+	0.832678i	−1.16275	+	0.101728i	−0.652151	−	0.758089i	$-0.726133\pi$
$67$	−9.51755	+	0.832678i	−1.16275	+	0.101728i	−0.510603	+	0.859817i	$0.670578\pi$
$68$	3.71573	−	0.325084i	0.450598	−	0.0394222i
$69$		0			0
$70$	−1.42780	+	1.40944i	−0.170654	+	0.168460i
$71$	2.95943	+	1.70863i	0.351220	+	0.202777i	0.665223	−	0.746645i	$-0.268337\pi$
$71$	2.95943	+	1.70863i	0.351220	+	0.202777i	−0.314002	+	0.949422i	$0.601670\pi$
$72$		0			0
$73$	−1.15401	+	4.30684i	−0.135067	+	0.504077i	0.864931	+	0.501892i	$0.167362\pi$
$73$	−1.15401	+	4.30684i	−0.135067	+	0.504077i	−0.999998	+	0.00218557i	$0.999304\pi$
$74$	1.84020	+	10.4363i	0.213919	+	1.21319i
$75$		0			0
$76$	−4.85114	+	1.76567i	−0.556463	+	0.202536i
$77$	0.982082	−	0.687661i	0.111919	−	0.0783662i
$78$		0			0
$79$	10.7626	+	12.8264i	1.21089	+	1.44308i	0.862747	+	0.505636i	$0.168742\pi$
$79$	10.7626	+	12.8264i	1.21089	+	1.44308i	0.348140	+	0.937443i	$0.386813\pi$
$80$	−0.958093	+	2.02041i	−0.107118	+	0.225889i
$81$		0			0
$82$	1.04002	−	1.04002i	0.114851	−	0.114851i
$83$	0.298155	−	3.40793i	0.0327268	−	0.374069i	−0.962116	−	0.272640i	$-0.912103\pi$
$83$	0.298155	−	3.40793i	0.0327268	−	0.374069i	0.994843	−	0.101429i	$-0.0323414\pi$
$84$		0			0
$85$	1.39512	+	8.22284i	0.151322	+	0.891892i
$86$	−0.385038	−	1.05788i	−0.0415197	−	0.114075i
$87$		0			0
$88$	0.766425	−	1.09457i	0.0817012	−	0.116681i
$89$	4.47579	+	7.75230i	0.474433	+	0.821742i	0.999571	−	0.0292749i	$-0.00931982\pi$
$89$	4.47579	+	7.75230i	0.474433	+	0.821742i	−0.525139	+	0.851017i	$0.675986\pi$
$90$		0			0
$91$	0.485381	−	0.840704i	0.0508817	−	0.0881298i
$92$	0.138300	+	0.296585i	0.0144188	+	0.0309211i
$93$		0			0
$94$	5.18897	−	6.18397i	0.535201	−	0.637828i
$95$	−4.81077	−	10.4934i	−0.493575	−	1.07660i
$96$		0			0
$97$	−10.5006	+	4.89650i	−1.06617	+	0.497164i	−0.874865	−	0.484366i	$-0.839050\pi$
$97$	−10.5006	+	4.89650i	−1.06617	+	0.497164i	−0.191306	+	0.981530i	$0.561272\pi$
$98$	1.60338	+	5.98389i	0.161966	+	0.604464i
$99$		0			0
$100$	−4.67595	−	1.77074i	−0.467595	−	0.177074i
$101$	−16.8242	+	2.96657i	−1.67407	+	0.295184i	−0.928526	−	0.371268i	$-0.878923\pi$
$101$	−16.8242	+	2.96657i	−1.67407	+	0.295184i	−0.745548	+	0.666452i	$0.767812\pi$
$102$		0			0
$103$	7.74438	+	3.61126i	0.763076	+	0.355828i	0.764882	−	0.644170i	$-0.222797\pi$
$103$	7.74438	+	3.61126i	0.763076	+	0.355828i	−0.00180621	+	0.999998i	$0.500575\pi$
$104$	0.187879	−	1.06551i	0.0184231	−	0.104482i
$105$		0			0
$106$	−2.25731	+	1.89411i	−0.219250	+	0.183972i
$107$	4.81383	+	4.81383i	0.465371	+	0.465371i	0.900411	−	0.435040i	$-0.143266\pi$
$107$	4.81383	+	4.81383i	0.465371	+	0.465371i	−0.435040	+	0.900411i	$0.643266\pi$
$108$		0			0
$109$		−	17.8131i		−	1.70618i	−0.521760	−	0.853092i	$-0.674724\pi$
$109$		−	17.8131i		−	1.70618i	0.521760	−	0.853092i	$-0.325276\pi$
$110$	2.57786	+	1.51065i	0.245790	+	0.144035i
$111$		0			0
$112$	−0.514631	−	0.734969i	−0.0486281	−	0.0694481i
$113$	0.287331	−	0.616184i	0.0270299	−	0.0579657i	−0.892329	−	0.451385i	$-0.850930\pi$
$113$	0.287331	−	0.616184i	0.0270299	−	0.0579657i	0.919359	+	0.393419i	$0.128708\pi$
$114$		0			0
$115$	−0.636062	+	0.361765i	−0.0593131	+	0.0337347i
$116$	−4.22393	+	2.43869i	−0.392182	+	0.226426i
$117$		0			0
$118$	12.0374	−	3.22540i	1.10813	−	0.296922i
$119$	−3.14478	−	1.14461i	−0.288281	−	0.104926i
$120$		0			0
$121$	7.05873	+	5.92297i	0.641702	+	0.538452i
$122$	−0.529185	−	6.04861i	−0.0479101	−	0.547616i
$123$		0			0
$124$	−3.04504	+	8.36617i	−0.273452	+	0.751304i
$125$	3.10271	−	10.7412i	0.277515	−	0.960721i
$126$		0			0
$127$	3.40787	+	0.913135i	0.302399	+	0.0810277i	0.406828	−	0.913505i	$-0.366635\pi$
$127$	3.40787	+	0.913135i	0.302399	+	0.0810277i	−0.104429	+	0.994532i	$0.533301\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	2.40870	+	0.226444i	0.211257	+	0.0198604i
$131$	−15.1888	−	2.67820i	−1.32705	−	0.233995i	−0.535209	−	0.844720i	$-0.679767\pi$
$131$	−15.1888	−	2.67820i	−1.32705	−	0.233995i	−0.791843	+	0.610725i	$0.790878\pi$
$132$		0			0
$133$	4.61431	+	0.403699i	0.400111	+	0.0350052i
$134$	9.55391			0.825332
$135$		0			0
$136$	−3.72992			−0.319838
$137$	14.2637	+	1.24791i	1.21863	+	0.106616i	0.678267	−	0.734815i	$-0.262731\pi$
$137$	14.2637	+	1.24791i	1.21863	+	0.106616i	0.540364	+	0.841432i	$0.318287\pi$
$138$		0			0
$139$	10.6457	+	1.87712i	0.902953	+	0.159215i	0.605802	−	0.795616i	$-0.292852\pi$
$139$	10.6457	+	1.87712i	0.902953	+	0.159215i	0.297151	+	0.954831i	$0.403964\pi$
$140$	1.54520	−	1.27964i	0.130593	−	0.108149i
$141$		0			0
$142$	−2.79926	−	1.96006i	−0.234908	−	0.164485i
$143$	−1.39647	−	0.374182i	−0.116778	−	0.0312907i
$144$		0			0
$145$	−6.19758	−	8.97406i	−0.514681	−	0.745255i
$146$	1.52499	−	4.18987i	0.126209	−	0.346756i
$147$		0			0
$148$	−0.923614	−	10.5570i	−0.0759206	−	0.867777i
$149$	−3.34495	−	2.80675i	−0.274029	−	0.229938i	0.495408	−	0.868660i	$-0.335019\pi$
$149$	−3.34495	−	2.80675i	−0.274029	−	0.229938i	−0.769437	+	0.638723i	$0.779463\pi$
$150$		0			0
$151$	4.82495	+	1.75614i	0.392649	+	0.142913i	0.530797	−	0.847499i	$-0.321893\pi$
$151$	4.82495	+	1.75614i	0.392649	+	0.142913i	−0.138148	+	0.990412i	$0.544115\pi$
$152$	4.98656	−	1.33615i	0.404464	−	0.108376i
$153$		0			0
$154$	−1.03828	+	0.599450i	−0.0836668	+	0.0483051i
$155$	−19.1958	−	5.27683i	−1.54185	−	0.423845i
$156$		0			0
$157$	2.73848	−	5.87269i	0.218554	−	0.468691i	−0.766209	−	0.642592i	$-0.777859\pi$
$157$	2.73848	−	5.87269i	0.218554	−	0.468691i	0.984763	+	0.173900i	$0.0556370\pi$
$158$	−9.60375	−	13.7156i	−0.764033	−	1.09115i
$159$		0			0
$160$	1.13054	−	1.92922i	0.0893768	−	0.152518i
$161$		−	0.293615i		−	0.0231401i
$162$		0			0
$163$	−2.98075	−	2.98075i	−0.233470	−	0.233470i	0.580669	−	0.814140i	$-0.302791\pi$
$163$	−2.98075	−	2.98075i	−0.233470	−	0.233470i	−0.814140	+	0.580669i	$0.802791\pi$
$164$	−1.12671	+	0.945418i	−0.0879809	+	0.0738247i
$165$		0			0
$166$	−0.594042	+	3.36898i	−0.0461066	+	0.261483i
$167$	−14.0572	−	6.55497i	−1.08778	−	0.507239i	−0.205831	−	0.978588i	$-0.565990\pi$
$167$	−14.0572	−	6.55497i	−1.08778	−	0.507239i	−0.881947	+	0.471349i	$0.843767\pi$
$168$		0			0
$169$	11.6497	−	2.05415i	0.896128	−	0.158012i
$170$	−0.673147	−	8.31314i	−0.0516280	−	0.637589i
$171$		0			0
$172$	0.291372	+	1.08742i	0.0222169	+	0.0829147i
$173$	22.8491	−	10.6547i	1.73719	−	0.810064i	0.747949	−	0.663756i	$-0.231039\pi$
$173$	22.8491	−	10.6547i	1.73719	−	0.810064i	0.989239	−	0.146308i	$-0.0467390\pi$
$174$		0			0
$175$	3.13089	+	3.21297i	0.236673	+	0.242878i
$176$	−0.858907	+	1.02360i	−0.0647425	+	0.0771571i
$177$		0			0
$178$	−3.78310	−	8.11289i	−0.283555	−	0.608087i
$179$	10.5977	−	18.3558i	0.792112	−	1.37198i	−0.132544	−	0.991177i	$-0.542315\pi$
$179$	10.5977	−	18.3558i	0.792112	−	1.37198i	0.924657	−	0.380802i	$-0.124352\pi$
$180$		0			0
$181$	5.84791	+	10.1289i	0.434672	+	0.752874i	0.997269	−	0.0738575i	$-0.0235310\pi$
$181$	5.84791	+	10.1289i	0.434672	+	0.752874i	−0.562597	+	0.826731i	$0.690198\pi$
$182$	−0.556806	+	0.795201i	−0.0412732	+	0.0589443i
$183$		0			0
$184$	−0.111925	−	0.307510i	−0.00825119	−	0.0226700i
$185$	23.3624	−	3.96377i	1.71764	−	0.291422i
$186$		0			0
$187$	−0.434384	+	4.96503i	−0.0317653	+	0.363079i
$188$	−5.70819	+	5.70819i	−0.416313	+	0.416313i
$189$		0			0
$190$	3.87790	+	10.8728i	0.281333	+	0.788794i
$191$	12.0553	+	14.3669i	0.872288	+	1.03955i	0.998867	+	0.0475957i	$0.0151559\pi$
$191$	12.0553	+	14.3669i	0.872288	+	1.03955i	−0.126579	+	0.991957i	$0.540400\pi$
$192$		0			0
$193$	14.6069	−	10.2279i	1.05143	−	0.736218i	0.0858443	−	0.996309i	$-0.472641\pi$
$193$	14.6069	−	10.2279i	1.05143	−	0.736218i	0.965584	+	0.260090i	$0.0837524\pi$
$194$	10.8874	−	3.96268i	0.781668	−	0.284504i
$195$		0			0
$196$	−1.07575	−	6.10086i	−0.0768390	−	0.435776i
$197$	−0.506253	+	1.88936i	−0.0360691	+	0.134612i	−0.981613	−	0.190884i	$-0.938865\pi$
$197$	−0.506253	+	1.88936i	−0.0360691	+	0.134612i	0.945544	+	0.325496i	$0.105531\pi$
$198$		0			0
$199$	4.22337	+	2.43837i	0.299387	+	0.172851i	0.642168	−	0.766564i	$-0.278035\pi$
$199$	4.22337	+	2.43837i	0.299387	+	0.172851i	−0.342780	+	0.939416i	$0.611369\pi$
$200$	4.50382	+	2.17154i	0.318468	+	0.153551i
$201$		0			0
$202$	17.0188	−	1.48895i	1.19744	−	0.104762i
$203$	4.35948	−	0.381405i	0.305976	−	0.0267694i
$204$		0			0
$205$	−2.31046	−	2.34055i	−0.161370	−	0.163471i
$206$	−7.40016	−	4.27249i	−0.515594	−	0.297678i
$207$		0			0
$208$	−0.280030	+	1.04509i	−0.0194166	+	0.0724636i
$209$	−1.19786	−	6.79340i	−0.0828577	−	0.469910i
$210$		0			0
$211$	−2.69507	+	0.980927i	−0.185537	+	0.0675298i	−0.433118	−	0.901337i	$-0.642587\pi$
$211$	−2.69507	+	0.980927i	−0.185537	+	0.0675298i	0.247581	+	0.968867i	$0.420364\pi$
$212$	2.41381	−	1.69017i	0.165781	−	0.116081i
$213$		0			0
$214$	−4.37596	−	5.21507i	−0.299135	−	0.356495i
$215$	−2.37102	+	0.845651i	−0.161702	+	0.0576729i
$216$		0			0
$217$	5.64846	−	5.64846i	0.383443	−	0.383443i
$218$	−1.55251	+	17.7453i	−0.105149	+	1.20186i
$219$		0			0
$220$	−2.43639	−	1.72958i	−0.164262	−	0.116608i
$221$	1.38025	+	3.79222i	0.0928460	+	0.255092i
$222$		0			0
$223$	8.64537	−	12.3469i	0.578937	−	0.826807i	−0.417714	−	0.908578i	$-0.637169\pi$
$223$	8.64537	−	12.3469i	0.578937	−	0.826807i	0.996651	+	0.0817710i	$0.0260576\pi$
$224$	0.448616	+	0.777025i	0.0299744	+	0.0519172i
$225$		0			0
$226$	−0.339942	+	0.588797i	−0.0226126	+	0.0391662i
$227$	−9.65741	−	20.7104i	−0.640985	−	1.37460i	−0.911267	−	0.411815i	$-0.864895\pi$
$227$	−9.65741	−	20.7104i	−0.640985	−	1.37460i	0.270283	−	0.962781i	$-0.412883\pi$
$228$		0			0
$229$	7.00025	−	8.34257i	0.462589	−	0.551293i	−0.483438	−	0.875378i	$-0.660612\pi$
$229$	7.00025	−	8.34257i	0.462589	−	0.551293i	0.946028	+	0.324086i	$0.105057\pi$
$230$	0.665171	−	0.304952i	0.0438601	−	0.0201079i
$231$		0			0
$232$	4.42040	−	2.06127i	0.290214	−	0.135329i
$233$	2.47423	+	9.23397i	0.162092	+	0.604937i	0.998393	+	0.0566662i	$0.0180471\pi$
$233$	2.47423	+	9.23397i	0.162092	+	0.604937i	−0.836301	+	0.548271i	$0.815286\pi$
$234$		0			0
$235$	−13.7524	−	11.6921i	−0.897110	−	0.762708i
$236$	−12.2727	+	2.16400i	−0.798882	+	0.140864i
$237$		0			0
$238$	3.03305	+	1.41434i	0.196604	+	0.0916777i
$239$	−2.54154	+	14.4138i	−0.164399	+	0.932351i	0.785284	+	0.619136i	$0.212517\pi$
$239$	−2.54154	+	14.4138i	−0.164399	+	0.932351i	−0.949682	+	0.313215i	$0.898594\pi$
$240$		0			0
$241$	−2.57850	+	2.16361i	−0.166095	+	0.139371i	−0.722047	−	0.691844i	$-0.756799\pi$
$241$	−2.57850	+	2.16361i	−0.166095	+	0.139371i	0.555951	+	0.831215i	$0.312354\pi$
$242$	−6.51564	−	6.51564i	−0.418841	−	0.418841i
$243$		0			0
$244$			6.07172i			0.388702i
$245$	13.4033	−	3.49863i	0.856305	−	0.223519i
$246$		0			0
$247$	−3.20374	−	4.57541i	−0.203849	−	0.291126i
$248$	3.76261	−	8.06894i	0.238926	−	0.512378i
$249$		0			0
$250$	−4.02706	+	10.4299i	−0.254693	+	0.659645i
$251$	6.11959	−	3.53315i	0.386265	−	0.223010i	−0.294275	−	0.955721i	$-0.595078\pi$
$251$	6.11959	−	3.53315i	0.386265	−	0.223010i	0.680541	+	0.732710i	$0.261745\pi$
$252$		0			0
$253$	−0.422373	+	0.113174i	−0.0265543	+	0.00711522i
$254$	−3.31531	−	1.20668i	−0.208021	−	0.0757136i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.38920	+	15.8787i	0.0866561	+	0.990484i	0.907700	+	0.419619i	$0.137836\pi$
$257$	1.38920	+	15.8787i	0.0866561	+	0.990484i	−0.821044	+	0.570865i	$0.806608\pi$
$258$		0			0
$259$	−3.25200	+	8.93480i	−0.202070	+	0.555182i
$260$	−2.37980	−	0.435514i	−0.147589	−	0.0270094i
$261$		0			0
$262$	14.8976	+	3.99180i	0.920376	+	0.246614i
$263$	16.3071	+	11.4183i	1.00554	+	0.704085i	0.955600	−	0.294668i	$-0.0952090\pi$
$263$	16.3071	+	11.4183i	1.00554	+	0.704085i	0.0499372	+	0.998752i	$0.484098\pi$
$264$		0			0
$265$	4.20262	+	5.07480i	0.258165	+	0.311743i
$266$	−4.56156	−	0.804327i	−0.279687	−	0.0493164i
$267$		0			0
$268$	−9.51755	−	0.832678i	−0.581377	−	0.0508639i
$269$	23.9757			1.46182			0.730911	−	0.682473i	$-0.239095\pi$
$269$	23.9757			1.46182			0.730911	+	0.682473i	$0.239095\pi$
$270$		0			0
$271$	−31.4527			−1.91061			−0.955307	−	0.295616i	$-0.904475\pi$
$271$	−31.4527			−1.91061			−0.955307	+	0.295616i	$0.904475\pi$
$272$	3.71573	+	0.325084i	0.225299	+	0.0197111i
$273$		0			0
$274$	−14.1007	−	2.48633i	−0.851853	−	0.150205i
$275$	3.41513	−	5.74231i	0.205940	−	0.346274i
$276$		0			0
$277$	−4.77388	−	3.34271i	−0.286835	−	0.200844i	0.421300	−	0.906921i	$-0.361574\pi$
$277$	−4.77388	−	3.34271i	−0.286835	−	0.200844i	−0.708134	+	0.706078i	$0.750463\pi$
$278$	−10.4415	−	2.79780i	−0.626242	−	0.167801i
$279$		0			0
$280$	−1.65085	+	1.14009i	−0.0986572	+	0.0681337i
$281$	−1.23133	+	3.38305i	−0.0734550	+	0.201816i	−0.970986	−	0.239134i	$-0.923136\pi$
$281$	−1.23133	+	3.38305i	−0.0734550	+	0.201816i	0.897531	+	0.440950i	$0.145359\pi$
$282$		0			0
$283$	1.10313	+	12.6089i	0.0655746	+	0.749521i	0.955803	+	0.294007i	$0.0949889\pi$
$283$	1.10313	+	12.6089i	0.0655746	+	0.749521i	−0.890229	+	0.455514i	$0.849456\pi$
$284$	2.61777	+	2.19657i	0.155336	+	0.130343i
$285$		0			0
$286$	1.35854	+	0.494468i	0.0803321	+	0.0292385i
$287$	1.27469	−	0.341552i	0.0752426	−	0.0201612i
$288$		0			0
$289$	−2.67403	+	1.54385i	−0.157296	+	0.0908147i
$290$	5.39186	+	9.48007i	0.316621	+	0.556689i
$291$		0			0
$292$	−1.88436	+	4.04101i	−0.110274	+	0.236482i
$293$	5.36649	+	7.66414i	0.313514	+	0.447744i	0.944723	−	0.327868i	$-0.106330\pi$
$293$	5.36649	+	7.66414i	0.313514	+	0.447744i	−0.631210	+	0.775612i	$0.717441\pi$
$294$		0			0
$295$	−7.03794	−	26.9624i	−0.409765	−	1.56981i
$296$			10.5973i			0.615955i
$297$		0			0
$298$	3.08760	+	3.08760i	0.178860	+	0.178860i
$299$	−0.271229	+	0.227588i	−0.0156856	+	0.0131617i
$300$		0			0
$301$	0.175399	−	0.994737i	0.0101098	−	0.0573357i
$302$	−4.65353	−	2.16998i	−0.267781	−	0.124868i
$303$		0			0
$304$	−5.08404	+	0.896454i	−0.291590	+	0.0514151i
$305$	−13.5325	+	1.09578i	−0.774867	+	0.0627440i
$306$		0			0
$307$	3.31174	+	12.3596i	0.189011	+	0.705398i	0.993736	+	0.111751i	$0.0356458\pi$
$307$	3.31174	+	12.3596i	0.189011	+	0.705398i	−0.804725	+	0.593647i	$0.797687\pi$
$308$	1.08657	−	0.506677i	0.0619132	−	0.0288706i
$309$		0			0
$310$	18.6629	+	6.92978i	1.05998	+	0.393585i
$311$	12.7735	−	15.2229i	0.724319	−	0.863210i	−0.270724	−	0.962657i	$-0.587263\pi$
$311$	12.7735	−	15.2229i	0.724319	−	0.863210i	0.995043	+	0.0994475i	$0.0317075\pi$
$312$		0			0
$313$	−12.8521	−	27.5614i	−0.726444	−	1.55786i	−0.826535	−	0.562886i	$-0.809691\pi$
$313$	−12.8521	−	27.5614i	−0.726444	−	1.55786i	0.100090	−	0.994978i	$-0.468087\pi$
$314$	−3.23990	+	5.61167i	−0.182838	+	0.316685i
$315$		0			0
$316$	8.37181	+	14.5004i	0.470951	+	0.815712i
$317$	−0.425247	+	0.607316i	−0.0238842	+	0.0341102i	−0.830917	−	0.556397i	$-0.812183\pi$
$317$	−0.425247	+	0.607316i	−0.0238842	+	0.0341102i	0.807032	+	0.590507i	$0.201072\pi$
$318$		0			0
$319$	−2.22903	−	6.12421i	−0.124802	−	0.342890i
$320$	−1.29438	+	1.82334i	−0.0723579	+	0.101928i
$321$		0			0
$322$	−0.0255902	+	0.292498i	−0.00142609	+	0.0163003i
$323$	−13.6158	+	13.6158i	−0.757601	+	0.757601i
$324$		0			0
$325$	0.541174	−	5.38262i	0.0300190	−	0.298574i
$326$	2.70962	+	3.22920i	0.150072	+	0.178849i
$327$		0			0
$328$	1.20482	−	0.843622i	0.0665249	−	0.0465812i
$329$	6.80619	−	2.47725i	0.375237	−	0.136575i
$330$		0			0
$331$	−2.86141	−	16.2279i	−0.157278	−	0.891965i	−0.956674	−	0.291161i	$-0.905958\pi$
$331$	−2.86141	−	16.2279i	−0.157278	−	0.891965i	0.799396	−	0.600804i	$-0.205153\pi$
$332$	0.885407	−	3.30438i	0.0485930	−	0.181352i
$333$		0			0
$334$	13.4324	+	7.75519i	0.734988	+	0.424345i
$335$	0.138195	−	21.3627i	0.00755042	−	1.16717i
$336$		0			0
$337$	−31.9721	+	2.79720i	−1.74163	+	0.152373i	−0.913145	−	0.407635i	$-0.866353\pi$
$337$	−31.9721	+	2.79720i	−1.74163	+	0.152373i	−0.828487	+	0.560009i	$0.810798\pi$
$338$	−11.7844	+	1.03100i	−0.640985	+	0.0560789i
$339$		0			0
$340$	−0.0539525	+	8.34018i	−0.00292599	+	0.452310i
$341$	−10.3027	−	5.94825i	−0.557921	−	0.322116i
$342$		0			0
$343$	−3.06415	+	11.4355i	−0.165448	+	0.617462i
$344$	−0.195489	−	1.10867i	−0.0105401	−	0.0597757i
$345$		0			0
$346$	−23.6908	+	8.62275i	−1.27363	+	0.463562i
$347$	−20.6058	+	14.4284i	−1.10618	+	0.774556i	−0.976181	−	0.216959i	$-0.930386\pi$
$347$	−20.6058	+	14.4284i	−1.10618	+	0.774556i	−0.129999	+	0.991514i	$0.541497\pi$
$348$		0			0
$349$	18.1194	+	21.5939i	0.969910	+	1.15589i	0.987749	+	0.156053i	$0.0498770\pi$
$349$	18.1194	+	21.5939i	0.969910	+	1.15589i	−0.0178387	+	0.999841i	$0.505679\pi$
$350$	−2.83895	−	3.47362i	−0.151748	−	0.185673i
$351$		0			0
$352$	0.944851	−	0.944851i	0.0503607	−	0.0503607i
$353$	−0.285255	+	3.26048i	−0.0151826	+	0.173538i	−1.00000		5.56666e-5i	$-0.999982\pi$
$353$	−0.285255	+	3.26048i	−0.0151826	+	0.173538i	0.984817	+	0.173593i	$0.0555378\pi$
$354$		0			0
$355$	−4.42323	+	6.23084i	−0.234760	+	0.330699i
$356$	3.06162	+	8.41174i	0.162266	+	0.445821i
$357$		0			0
$358$	−12.1572	+	17.3623i	−0.642530	+	0.917627i
$359$	10.3345	+	17.8999i	0.545434	+	0.944720i	0.998579	+	0.0532832i	$0.0169686\pi$
$359$	10.3345	+	17.8999i	0.545434	+	0.944720i	−0.453145	+	0.891437i	$0.649698\pi$
$360$		0			0
$361$	3.82555	−	6.62605i	0.201345	−	0.348739i
$362$	−4.94287	−	10.6000i	−0.259791	−	0.557125i
$363$		0			0
$364$	0.623994	−	0.743647i	0.0327062	−	0.0389777i
$365$	−9.34658	−	3.47051i	−0.489222	−	0.181655i
$366$		0			0
$367$	−3.76935	+	1.75767i	−0.196758	+	0.0917499i	−0.518500	−	0.855078i	$-0.673509\pi$
$367$	−3.76935	+	1.75767i	−0.196758	+	0.0917499i	0.321742	+	0.946827i	$0.395732\pi$
$368$	0.0846974	+	0.316095i	0.00441516	+	0.0164776i
$369$		0			0
$370$	−23.6189	+	1.91252i	−1.22789	+	0.0994270i
$371$	−2.60372	+	0.459106i	−0.135178	+	0.0238356i
$372$		0			0
$373$	8.08198	+	3.76869i	0.418469	+	0.195135i	0.620436	−	0.784257i	$-0.286956\pi$
$373$	8.08198	+	3.76869i	0.418469	+	0.195135i	−0.201967	+	0.979392i	$0.564733\pi$
$374$	0.865462	−	4.90828i	0.0447520	−	0.253801i
$375$		0			0
$376$	6.18397	−	5.18897i	0.318914	−	0.267601i
$377$	−3.73146	−	3.73146i	−0.192180	−	0.192180i
$378$		0			0
$379$		−	4.09110i		−	0.210146i	−0.994465	−	0.105073i	$-0.966492\pi$
$379$		−	4.09110i		−	0.210146i	0.994465	−	0.105073i	$-0.0335076\pi$
$380$	−2.91552	−	11.1694i	−0.149563	−	0.572978i
$381$		0			0
$382$	−10.7572	−	15.3629i	−0.550388	−	0.786035i
$383$	−6.45751	+	13.8482i	−0.329963	+	0.707608i	−0.999377	−	0.0352811i	$-0.988767\pi$
$383$	−6.45751	+	13.8482i	−0.329963	+	0.707608i	0.669414	+	0.742889i	$0.266545\pi$
$384$		0			0
$385$	1.32536	+	2.33028i	0.0675468	+	0.118762i
$386$	−15.4427	+	8.91587i	−0.786015	+	0.453806i
$387$		0			0
$388$	−11.1913	+	2.99870i	−0.568153	+	0.152236i
$389$	−26.1240	−	9.50835i	−1.32454	−	0.482092i	−0.419628	−	0.907696i	$-0.637840\pi$
$389$	−26.1240	−	9.50835i	−1.32454	−	0.482092i	−0.904910	+	0.425604i	$0.860062\pi$
$390$		0			0
$391$	0.935033	+	0.784586i	0.0472867	+	0.0396782i
$392$	0.539928	+	6.17140i	0.0272705	+	0.311703i
$393$		0			0
$394$	0.668996	−	1.83805i	0.0337035	−	0.0925997i
$395$	−30.8072	+	21.2758i	−1.55008	+	1.07050i
$396$		0			0
$397$	32.6082	+	8.73733i	1.63656	+	0.438514i	0.955805	−	0.294000i	$-0.0949865\pi$
$397$	32.6082	+	8.73733i	1.63656	+	0.438514i	0.680752	+	0.732514i	$0.261653\pi$
$398$	−3.99479	−	2.79718i	−0.200241	−	0.140210i
$399$		0			0
$400$	−4.29742	−	2.55581i	−0.214871	−	0.127791i
$401$	9.33902	+	1.64672i	0.466368	+	0.0822333i	0.401894	−	0.915686i	$-0.368352\pi$
$401$	9.33902	+	1.64672i	0.466368	+	0.0822333i	0.0644740	+	0.997919i	$0.479463\pi$
$402$		0			0
$403$	−9.59606	−	0.839547i	−0.478014	−	0.0418208i
$404$	−17.0838			−0.849950
$405$		0			0
$406$	−4.37613			−0.217184
$407$	14.1064	+	1.23415i	0.699230	+	0.0611747i
$408$		0			0
$409$	−27.2521	−	4.80528i	−1.34753	−	0.237606i	−0.547118	−	0.837056i	$-0.684275\pi$
$409$	−27.2521	−	4.80528i	−1.34753	−	0.237606i	−0.800412	+	0.599450i	$0.795386\pi$
$410$	2.09768	+	2.53301i	0.103597	+	0.125097i
$411$		0			0
$412$	6.99963	+	4.90120i	0.344847	+	0.241465i
$413$	10.8003	+	2.89393i	0.531448	+	0.142401i
$414$		0			0
$415$	7.52452	+	1.37702i	0.369364	+	0.0675953i
$416$	0.370049	−	1.01670i	0.0181432	−	0.0498479i
$417$		0			0
$418$	0.601218	+	6.87195i	0.0294065	+	0.336118i
$419$	−1.14029	−	0.956820i	−0.0557070	−	0.0467437i	0.614509	−	0.788910i	$-0.289354\pi$
$419$	−1.14029	−	0.956820i	−0.0557070	−	0.0467437i	−0.670216	+	0.742166i	$0.733799\pi$
$420$		0			0
$421$	23.4690	+	8.54203i	1.14381	+	0.416313i	0.843288	−	0.537461i	$-0.180617\pi$
$421$	23.4690	+	8.54203i	1.14381	+	0.416313i	0.300523	+	0.953775i	$0.402839\pi$
$422$	2.77031	−	0.742303i	0.134857	−	0.0361347i
$423$		0			0
$424$	−2.55193	+	1.47336i	−0.123933	+	0.0715526i
$425$	−18.5981	+	1.38492i	−0.902141	+	0.0671787i
$426$		0			0
$427$	2.30231	−	4.93733i	0.111417	−	0.238934i
$428$	3.90479	+	5.57662i	0.188745	+	0.269556i
$429$		0			0
$430$	2.43570	−	0.635785i	0.117460	−	0.0306603i
$431$		−	20.8531i		−	1.00446i	−0.864734	−	0.502230i	$-0.832513\pi$
$431$		−	20.8531i		−	1.00446i	0.864734	−	0.502230i	$-0.167487\pi$
$432$		0			0
$433$	23.9469	+	23.9469i	1.15081	+	1.15081i	0.986390	+	0.164423i	$0.0525761\pi$
$433$	23.9469	+	23.9469i	1.15081	+	1.15081i	0.164423	+	0.986390i	$0.447424\pi$
$434$	−6.11927	+	5.13467i	−0.293734	+	0.246472i
$435$		0			0
$436$	3.09321	−	17.5425i	0.148138	−	0.840132i
$437$	−1.53111	−	0.713969i	−0.0732430	−	0.0341538i
$438$		0			0
$439$	0.464538	−	0.0819106i	0.0221712	−	0.00390938i	−0.162552	−	0.986700i	$-0.551972\pi$
$439$	0.464538	−	0.0819106i	0.0221712	−	0.00390938i	0.184723	+	0.982791i	$0.440861\pi$
$440$	2.27638	+	1.93534i	0.108522	+	0.0922637i
$441$		0			0
$442$	−1.04449	−	3.89808i	−0.0496813	−	0.185413i
$443$	16.1817	−	7.54566i	0.768817	−	0.358505i	0.00168819	−	0.999999i	$-0.499463\pi$
$443$	16.1817	−	7.54566i	0.768817	−	0.358505i	0.767129	+	0.641493i	$0.221685\pi$
$444$		0			0
$445$	−18.1953	+	8.34174i	−0.862541	+	0.395437i
$446$	−9.68857	+	11.5464i	−0.458767	+	0.546737i
$447$		0			0
$448$	−0.379187	−	0.813168i	−0.0179149	−	0.0384186i
$449$	−8.04414	+	13.9329i	−0.379627	+	0.657533i	−0.991008	−	0.133804i	$-0.957281\pi$
$449$	−8.04414	+	13.9329i	−0.379627	+	0.657533i	0.611381	+	0.791336i	$0.290614\pi$
$450$		0			0
$451$	−0.982663	−	1.70202i	−0.0462718	−	0.0801451i
$452$	0.389965	−	0.556928i	0.0183424	−	0.0261957i
$453$		0			0
$454$	7.81563	+	21.4733i	0.366806	+	1.00779i
$455$	1.77003	+	1.25653i	0.0829804	+	0.0589072i
$456$		0			0
$457$	1.39167	−	15.9069i	0.0650995	−	0.744091i	−0.891564	−	0.452895i	$-0.850391\pi$
$457$	1.39167	−	15.9069i	0.0650995	−	0.744091i	0.956663	−	0.291196i	$-0.0940532\pi$
$458$	−7.70071	+	7.70071i	−0.359831	+	0.359831i
$459$		0			0
$460$	−0.689218	+	0.245818i	−0.0321350	+	0.0114613i
$461$	17.3655	+	20.6954i	0.808793	+	0.963881i	0.999843	−	0.0176987i	$-0.00563395\pi$
$461$	17.3655	+	20.6954i	0.808793	+	0.963881i	−0.191051	+	0.981580i	$0.561190\pi$
$462$		0			0
$463$	−0.0655686	+	0.0459116i	−0.00304723	+	0.00213369i	−0.575099	−	0.818084i	$-0.695036\pi$
$463$	−0.0655686	+	0.0459116i	−0.00304723	+	0.00213369i	0.572052	+	0.820217i	$0.306148\pi$
$464$	−4.58323	+	1.66816i	−0.212771	+	0.0774424i
$465$		0			0
$466$	−1.66003	−	9.41447i	−0.0768992	−	0.436117i
$467$	−5.40356	+	20.1664i	−0.250047	+	0.933188i	0.720732	+	0.693214i	$0.243806\pi$
$467$	−5.40356	+	20.1664i	−0.250047	+	0.933188i	−0.970779	+	0.239975i	$0.922861\pi$
$468$		0			0
$469$	7.42363	+	4.28604i	0.342791	+	0.197911i
$470$	12.6811	+	12.8462i	0.584934	+	0.592551i
$471$		0			0
$472$	12.4146	−	1.08613i	0.571426	−	0.0499933i
$473$	−1.49856	+	0.131107i	−0.0689040	+	0.00602832i
$474$		0			0
$475$	24.3679	−	8.51380i	1.11807	−	0.390640i
$476$	−2.89824	−	1.67330i	−0.132841	−	0.0766956i
$477$		0			0
$478$	3.78812	−	14.1374i	0.173264	−	0.646631i
$479$	−2.34496	−	13.2989i	−0.107144	−	0.607644i	−0.990342	−	0.138644i	$-0.955726\pi$
$479$	−2.34496	−	13.2989i	−0.107144	−	0.607644i	0.883198	−	0.469000i	$-0.155386\pi$
$480$		0			0
$481$	10.7743	−	3.92152i	0.491265	−	0.178806i
$482$	2.75725	−	1.93065i	0.125590	−	0.0879387i
$483$		0			0
$484$	5.92297	+	7.05873i	0.269226	+	0.320851i
$485$	−8.70315	−	24.4017i	−0.395190	−	1.10802i
$486$		0			0
$487$	−18.5265	+	18.5265i	−0.839518	+	0.839518i	−0.988795	−	0.149278i	$-0.952305\pi$
$487$	−18.5265	+	18.5265i	−0.839518	+	0.839518i	0.149278	+	0.988795i	$0.452305\pi$
$488$	0.529185	−	6.04861i	0.0239551	−	0.273808i
$489$		0			0
$490$	−13.6572	+	2.31714i	−0.616970	+	0.104678i
$491$	0.472624	+	1.29852i	0.0213292	+	0.0586015i	0.949900	−	0.312553i	$-0.101184\pi$
$491$	0.472624	+	1.29852i	0.0213292	+	0.0586015i	−0.928571	+	0.371155i	$0.878962\pi$
$492$		0			0
$493$	−10.4346	+	14.9022i	−0.469952	+	0.671161i
$494$	2.79277	+	4.83722i	0.125653	+	0.217637i
$495$		0			0
$496$	−4.45155	+	7.71030i	−0.199880	+	0.346203i
$497$	−1.29578	−	2.77881i	−0.0581236	−	0.124647i
$498$		0			0
$499$	−19.6741	+	23.4466i	−0.880732	+	1.04962i	0.117668	+	0.993053i	$0.462458\pi$
$499$	−19.6741	+	23.4466i	−0.880732	+	1.04962i	−0.998399	+	0.0565620i	$0.981986\pi$
$500$	4.92076	−	10.0392i	0.220063	−	0.448968i
$501$		0			0
$502$	−6.40424	+	2.98635i	−0.285835	+	0.133287i
$503$	8.89285	+	33.1886i	0.396513	+	1.47981i	0.819189	+	0.573524i	$0.194424\pi$
$503$	8.89285	+	33.1886i	0.396513	+	1.47981i	−0.422676	+	0.906281i	$0.638909\pi$
$504$		0			0
$505$	−3.08315	−	38.0759i	−0.137198	−	1.69435i
$506$	0.430629	−	0.0759316i	0.0191438	−	0.00337557i
$507$		0			0
$508$	3.19753	+	1.49103i	0.141867	+	0.0661539i
$509$	−4.31600	+	24.4773i	−0.191304	+	1.08494i	0.726282	+	0.687397i	$0.241247\pi$
$509$	−4.31600	+	24.4773i	−0.191304	+	1.08494i	−0.917585	+	0.397539i	$0.869864\pi$
$510$		0			0
$511$	3.06460	−	2.57150i	0.135570	−	0.113757i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	15.9393i		−	0.703053i
$515$	−9.66041	+	16.4851i	−0.425689	+	0.726421i
$516$		0			0
$517$	−6.18704	−	8.83601i	−0.272106	−	0.388607i
$518$	4.01835	−	8.61737i	0.176556	−	0.378626i
$519$		0			0
$520$	2.33278	+	0.641270i	0.102299	+	0.0281215i
$521$	32.7211	−	18.8916i	1.43354	−	0.827654i	0.436150	−	0.899874i	$-0.356342\pi$
$521$	32.7211	−	18.8916i	1.43354	−	0.827654i	0.997389	+	0.0722201i	$0.0230084\pi$
$522$		0			0
$523$	−38.5745	+	10.3360i	−1.68675	+	0.451962i	−0.969547	−	0.244907i	$-0.921243\pi$
$523$	−38.5745	+	10.3360i	−1.68675	+	0.451962i	−0.717199	+	0.696869i	$0.754576\pi$
$524$	−14.4930	−	5.27501i	−0.633129	−	0.230440i
$525$		0			0
$526$	−15.2498	−	12.7961i	−0.664925	−	0.557938i
$527$	2.89425	+	33.0814i	0.126076	+	1.44105i
$528$		0			0
$529$	7.82984	−	21.5123i	0.340428	−	0.935317i
$530$	−3.74433	−	5.42177i	−0.162643	−	0.235507i
$531$		0			0
$532$	4.47410	+	1.19883i	0.193977	+	0.0519760i
$533$	−1.30355	−	0.912758i	−0.0564632	−	0.0395359i
$534$		0			0
$535$	−11.7243	+	9.70931i	−0.506886	+	0.419770i
$536$	9.40876	+	1.65902i	0.406397	+	0.0716587i
$537$		0			0
$538$	−23.8844	−	2.08962i	−1.02973	−	0.0900898i
$539$	8.27786			0.356553
$540$		0			0
$541$	15.8053			0.679525			0.339762	−	0.940511i	$-0.389653\pi$
$541$	15.8053			0.679525			0.339762	+	0.940511i	$0.389653\pi$
$542$	31.3330	+	2.74128i	1.34587	+	0.117748i
$543$		0			0
$544$	−3.67325	−	0.647694i	−0.157489	−	0.0277696i
$545$	39.6564	+	3.72814i	1.69869	+	0.159696i
$546$		0			0
$547$	8.19122	+	5.73556i	0.350231	+	0.245235i	0.735432	−	0.677598i	$-0.236979\pi$
$547$	8.19122	+	5.73556i	0.350231	+	0.245235i	−0.385201	+	0.922833i	$0.625868\pi$
$548$	13.8303	+	3.70582i	0.590802	+	0.158305i
$549$		0			0
$550$	−3.90261	+	5.42281i	−0.166408	+	0.231229i
$551$	8.61183	−	23.6608i	0.366876	−	1.00798i
$552$		0			0
$553$	−1.30933	−	14.9657i	−0.0556785	−	0.636408i
$554$	4.46438	+	3.74606i	0.189673	+	0.159155i
$555$		0			0
$556$	10.1580	+	3.69720i	0.430794	+	0.156796i
$557$	−8.03172	+	2.15209i	−0.340315	+	0.0911871i	−0.424929	−	0.905227i	$-0.639701\pi$
$557$	−8.03172	+	2.15209i	−0.340315	+	0.0911871i	0.0846140	+	0.996414i	$0.473034\pi$
$558$		0			0
$559$	−1.05485	+	0.609018i	−0.0446154	+	0.0257587i
$560$	1.74393	−	0.991875i	0.0736947	−	0.0419144i
$561$		0			0
$562$	1.52150	−	3.26286i	0.0641805	−	0.137635i
$563$	−21.8741	−	31.2395i	−0.921885	−	1.31659i	−0.948445	−	0.316941i	$-0.897344\pi$
$563$	−21.8741	−	31.2395i	−0.921885	−	1.31659i	0.0265602	−	0.999647i	$-0.491545\pi$
$564$		0			0
$565$	1.31164	+	0.768634i	0.0551813	+	0.0323367i
$566$		−	12.6571i		−	0.532016i
$567$		0			0
$568$	−2.41637	−	2.41637i	−0.101389	−	0.101389i
$569$	11.5102	−	9.65816i	0.482531	−	0.404891i	−0.368810	−	0.929505i	$-0.620235\pi$
$569$	11.5102	−	9.65816i	0.482531	−	0.404891i	0.851340	+	0.524614i	$0.175790\pi$
$570$		0			0
$571$	−3.15997	+	17.9211i	−0.132241	+	0.749974i	0.844501	+	0.535554i	$0.179897\pi$
$571$	−3.15997	+	17.9211i	−0.132241	+	0.749974i	−0.976742	+	0.214420i	$0.931214\pi$
$572$	−1.31027	−	0.610991i	−0.0547853	−	0.0255468i
$573$		0			0
$574$	−1.29961	+	0.229156i	−0.0542446	+	0.00956479i
$575$	−0.672256	−	1.49175i	−0.0280350	−	0.0622102i
$576$		0			0
$577$	4.02827	+	15.0337i	0.167699	+	0.625862i	0.997681	+	0.0680705i	$0.0216843\pi$
$577$	4.02827	+	15.0337i	0.167699	+	0.625862i	−0.829981	+	0.557791i	$0.811649\pi$
$578$	2.79841	−	1.30492i	0.116398	−	0.0542775i
$579$		0			0
$580$	−4.54510	−	9.91393i	−0.188725	−	0.411653i
$581$	−1.97296	+	2.35129i	−0.0818523	+	0.0975478i
$582$		0			0
$583$	1.66404	+	3.56855i	0.0689177	+	0.147794i
$584$	2.22938	−	3.86140i	0.0922525	−	0.159786i
$585$		0			0
$586$	−4.67809	−	8.10269i	−0.193250	−	0.334719i
$587$	20.8321	−	29.7513i	0.859831	−	1.22797i	−0.112334	−	0.993671i	$-0.535833\pi$
$587$	20.8321	−	29.7513i	0.859831	−	1.22797i	0.972165	−	0.234296i	$-0.0752785\pi$
$588$		0			0
$589$	−15.7199	−	43.1901i	−0.647728	−	1.77962i
$590$	4.66123	+	27.4732i	0.191900	+	1.13105i
$591$		0			0
$592$	0.923614	−	10.5570i	0.0379603	−	0.433888i
$593$	−7.15045	+	7.15045i	−0.293634	+	0.293634i	−0.838514	−	0.544880i	$-0.816575\pi$
$593$	−7.15045	+	7.15045i	−0.293634	+	0.293634i	0.544880	+	0.838514i	$0.316575\pi$
$594$		0			0
$595$	3.20636	−	6.76151i	0.131448	−	0.277195i
$596$	−2.80675	−	3.34495i	−0.114969	−	0.137014i
$597$		0			0
$598$	0.290032	−	0.203083i	0.0118603	−	0.00830467i
$599$	22.8455	−	8.31508i	0.933442	−	0.339745i	0.169869	−	0.985467i	$-0.445666\pi$
$599$	22.8455	−	8.31508i	0.933442	−	0.339745i	0.763573	+	0.645722i	$0.223443\pi$
$600$		0			0
$601$	5.19436	+	29.4587i	0.211882	+	1.20164i	0.886235	+	0.463236i	$0.153312\pi$
$601$	5.19436	+	29.4587i	0.211882	+	1.20164i	−0.674353	+	0.738409i	$0.735577\pi$
$602$	−0.261429	+	0.975664i	−0.0106550	+	0.0397651i
$603$		0			0
$604$	4.44670	+	2.56730i	0.180934	+	0.104462i
$605$	−14.6634	+	14.4749i	−0.596151	+	0.588487i
$606$		0			0
$607$	−18.8229	+	1.64679i	−0.763996	+	0.0668410i	−0.462492	−	0.886624i	$-0.653044\pi$
$607$	−18.8229	+	1.64679i	−0.763996	+	0.0668410i	−0.301505	+	0.953465i	$0.597489\pi$
$608$	5.14283	−	0.449939i	0.208569	−	0.0182474i
$609$		0			0
$610$	13.5765	+	0.0878262i	0.549696	+	0.00355598i
$611$	−7.56401	−	4.36708i	−0.306007	−	0.176673i
$612$		0			0
$613$	−0.988160	+	3.68786i	−0.0399114	+	0.148951i	−0.983006	−	0.183573i	$-0.941234\pi$
$613$	−0.988160	+	3.68786i	−0.0399114	+	0.148951i	0.943095	+	0.332524i	$0.107900\pi$
$614$	−2.22193	−	12.6012i	−0.0896697	−	0.508542i
$615$		0			0
$616$	−1.12660	+	0.410048i	−0.0453919	+	0.0165213i
$617$	25.3036	−	17.7178i	1.01869	−	0.713292i	0.0601284	−	0.998191i	$-0.480849\pi$
$617$	25.3036	−	17.7178i	1.01869	−	0.713292i	0.958558	+	0.284899i	$0.0919601\pi$
$618$		0			0
$619$	−8.89621	−	10.6021i	−0.357569	−	0.426134i	0.557032	−	0.830491i	$-0.311940\pi$
$619$	−8.89621	−	10.6021i	−0.357569	−	0.426134i	−0.914601	+	0.404357i	$0.867495\pi$
$620$	−17.9879	−	8.52999i	−0.722411	−	0.342573i
$621$		0			0
$622$	−14.0517	+	14.0517i	−0.563420	+	0.563420i
$623$	0.700004	−	8.00108i	0.0280451	−	0.320557i
$624$		0			0
$625$	23.2632	+	9.15545i	0.930529	+	0.366218i
$626$	10.4011	+	28.5767i	0.415710	+	1.14215i
$627$		0			0
$628$	3.71666	−	5.30794i	0.148311	−	0.211810i
$629$	−19.7635	−	34.2314i	−0.788023	−	1.36490i
$630$		0			0
$631$	13.5113	−	23.4023i	0.537878	−	0.931632i	−0.461140	−	0.887327i	$-0.652559\pi$
$631$	13.5113	−	23.4023i	0.537878	−	0.931632i	0.999018	−	0.0443048i	$-0.0141073\pi$
$632$	−7.07616	−	15.1749i	−0.281475	−	0.603624i
$633$		0			0
$634$	0.476560	−	0.567942i	0.0189266	−	0.0225558i
$635$	−2.74611	+	7.39566i	−0.108976	+	0.293488i
$636$		0			0
$637$	6.07468	−	2.83267i	0.240688	−	0.112234i
$638$	1.68679	+	6.29518i	0.0667806	+	0.249229i
$639$		0			0
$640$	1.44837	−	1.70359i	0.0572517	−	0.0673405i
$641$	−41.5970	+	7.33467i	−1.64298	+	0.289702i	−0.917261	−	0.398287i	$-0.869605\pi$
$641$	−41.5970	+	7.33467i	−1.64298	+	0.289702i	−0.725721	+	0.687989i	$0.758494\pi$
$642$		0			0
$643$	−17.6764	−	8.24266i	−0.697091	−	0.325059i	0.0415703	−	0.999136i	$-0.486764\pi$
$643$	−17.6764	−	8.24266i	−0.697091	−	0.325059i	−0.738661	+	0.674077i	$0.764542\pi$
$644$	0.0509857	−	0.289154i	0.00200912	−	0.0113943i
$645$		0			0
$646$	14.7506	−	12.3773i	0.580356	−	0.486977i
$647$	19.5310	+	19.5310i	0.767844	+	0.767844i	0.977727	−	0.209883i	$-0.0673082\pi$
$647$	19.5310	+	19.5310i	0.767844	+	0.767844i	−0.209883	+	0.977727i	$0.567308\pi$
$648$		0			0
$649$		−	16.6520i		−	0.653647i
$650$	−1.00824	+	5.31497i	−0.0395465	+	0.208470i
$651$		0			0
$652$	−2.41786	−	3.45307i	−0.0946909	−	0.135233i
$653$	−0.510177	+	1.09408i	−0.0199648	+	0.0428146i	−0.916037	−	0.401093i	$-0.868630\pi$
$653$	−0.510177	+	1.09408i	−0.0199648	+	0.0428146i	0.896073	+	0.443908i	$0.146408\pi$
$654$		0			0
$655$	9.14123	−	33.2536i	0.357177	−	1.29932i
$656$	−1.27376	+	0.735405i	−0.0497319	+	0.0287127i
$657$		0			0
$658$	−6.99619	+	1.87462i	−0.272740	+	0.0730805i
$659$	8.79668	+	3.20173i	0.342670	+	0.124722i	0.507622	−	0.861580i	$-0.330525\pi$
$659$	8.79668	+	3.20173i	0.342670	+	0.124722i	−0.164952	+	0.986302i	$0.552747\pi$
$660$		0			0
$661$	−20.6324	−	17.3127i	−0.802509	−	0.673385i	0.146298	−	0.989241i	$-0.453264\pi$
$661$	−20.6324	−	17.3127i	−0.802509	−	0.673385i	−0.948807	+	0.315856i	$0.897709\pi$
$662$	1.43617	+	16.4155i	0.0558184	+	0.638007i
$663$		0			0
$664$	−1.17003	+	3.21464i	−0.0454061	+	0.124752i
$665$	−1.86447	+	10.1881i	−0.0723012	+	0.395078i
$666$		0			0
$667$	−1.54171	−	0.413101i	−0.0596954	−	0.0159953i
$668$	−12.7054	−	8.89639i	−0.491585	−	0.344212i
$669$		0			0
$670$	−1.99956	+	21.2694i	−0.0772496	+	0.821709i
$671$	−7.98990	−	1.40883i	−0.308447	−	0.0543875i
$672$		0			0
$673$	−16.9406	−	1.48211i	−0.653013	−	0.0571312i	−0.244165	−	0.969734i	$-0.578514\pi$
$673$	−16.9406	−	1.48211i	−0.653013	−	0.0571312i	−0.408848	+	0.912603i	$0.634069\pi$
$674$	32.0942			1.23622
$675$		0			0
$676$	11.8294			0.454976
$677$	−30.9278	−	2.70584i	−1.18865	−	0.103994i	−0.524381	−	0.851484i	$-0.675703\pi$
$677$	−30.9278	−	2.70584i	−1.18865	−	0.103994i	−0.664273	+	0.747490i	$0.731259\pi$
$678$		0			0
$679$	10.2375	+	1.80514i	0.392879	+	0.0692751i
$680$	0.780642	−	8.30374i	0.0299362	−	0.318434i
$681$		0			0
$682$	9.74504	+	6.82355i	0.373157	+	0.261287i
$683$	−38.6745	−	10.3628i	−1.47984	−	0.396522i	−0.573548	−	0.819172i	$-0.694433\pi$
$683$	−38.6745	−	10.3628i	−1.47984	−	0.396522i	−0.906293	+	0.422650i	$0.861100\pi$
$684$		0			0
$685$	−5.76345	+	31.4934i	−0.220210	+	1.20330i
$686$	4.04916	−	11.1250i	0.154598	−	0.424753i
$687$		0			0
$688$	0.0981179	+	1.12149i	0.00374071	+	0.0427565i
$689$	2.44231	+	2.04934i	0.0930445	+	0.0780736i
$690$		0			0
$691$	17.7490	+	6.46009i	0.675202	+	0.245753i	0.656786	−	0.754077i	$-0.271915\pi$
$691$	17.7490	+	6.46009i	0.675202	+	0.245753i	0.0184160	+	0.999830i	$0.494138\pi$
$692$	24.3522	−	6.52515i	0.925731	−	0.248049i
$693$		0			0
$694$	21.7850	−	12.5775i	0.826946	−	0.477437i
$695$	−6.40698	+	23.3070i	−0.243031	+	0.884087i
$696$		0			0
$697$	−2.31848	+	4.97201i	−0.0878188	+	0.188328i
$698$	−16.1684	−	23.0909i	−0.611984	−	0.874004i
$699$		0			0
$700$	2.52540	+	3.70783i	0.0954510	+	0.140143i
$701$		−	33.0600i		−	1.24866i	−0.781161	−	0.624330i	$-0.785372\pi$
$701$		−	33.0600i		−	1.24866i	0.781161	−	0.624330i	$-0.214628\pi$
$702$		0			0
$703$	38.6845	+	38.6845i	1.45901	+	1.45901i
$704$	−1.02360	+	0.858907i	−0.0385786	+	0.0323713i
$705$		0			0
$706$	0.568339	−	3.22321i	0.0213897	−	0.121307i
$707$	13.8920	+	6.47794i	0.522462	+	0.243628i
$708$		0			0
$709$	−0.912124	+	0.160832i	−0.0342555	+	0.00604018i	−0.190750	−	0.981639i	$-0.561092\pi$
$709$	−0.912124	+	0.160832i	−0.0342555	+	0.00604018i	0.156494	+	0.987679i	$0.449981\pi$
$710$	4.94945	−	5.82162i	0.185749	−	0.218482i
$711$		0			0
$712$	−2.31684	−	8.64656i	−0.0868272	−	0.324044i
$713$	−2.64052	+	1.23130i	−0.0988884	+	0.0461124i
$714$		0			0
$715$	1.12529	−	3.03057i	0.0420835	−	0.113337i
$716$	13.6242	−	16.2367i	0.509160	−	0.606793i
$717$		0			0
$718$	−8.73510	−	18.7325i	−0.325991	−	0.699090i
$719$	10.7184	−	18.5648i	0.399729	−	0.692351i	−0.593963	−	0.804492i	$-0.702438\pi$
$719$	10.7184	−	18.5648i	0.399729	−	0.692351i	0.993692	+	0.112141i	$0.0357709\pi$
$720$		0			0
$721$	−3.83341	−	6.63966i	−0.142764	−	0.247274i
$722$	−4.38849	+	6.26741i	−0.163323	+	0.233249i
$723$		0			0
$724$	4.00021	+	10.9905i	0.148667	+	0.408458i
$725$	21.2756	−	11.9192i	0.790157	−	0.442667i
$726$		0			0
$727$	−0.310319	+	3.54696i	−0.0115091	+	0.131550i	−0.999775	−	0.0211908i	$-0.993254\pi$
$727$	−0.310319	+	3.54696i	−0.0115091	+	0.131550i	0.988266	+	0.152740i	$0.0488098\pi$
$728$	−0.686432	+	0.686432i	−0.0254409	+	0.0254409i
$729$		0			0
$730$	9.00854	+	4.27191i	0.333421	+	0.158111i
$731$	2.69910	+	3.21666i	0.0998298	+	0.118973i
$732$		0			0
$733$	26.0456	−	18.2373i	0.962016	−	0.673611i	0.0167325	−	0.999860i	$-0.494674\pi$
$733$	26.0456	−	18.2373i	0.962016	−	0.673611i	0.945284	+	0.326249i	$0.105785\pi$
$734$	3.90819	−	1.42247i	0.144254	−	0.0525042i
$735$		0			0
$736$	−0.0568256	−	0.322274i	−0.00209462	−	0.0118792i
$737$	3.30412	−	12.3311i	0.121709	−	0.454223i
$738$		0			0
$739$	32.8067	+	18.9409i	1.20681	+	0.696754i	0.962062	−	0.272832i	$-0.0879604\pi$
$739$	32.8067	+	18.9409i	1.20681	+	0.696754i	0.244751	+	0.969586i	$0.421294\pi$
$740$	23.6958	+	0.153288i	0.871073	+	0.00563496i
$741$		0			0
$742$	2.63383	−	0.230430i	0.0966908	−	0.00845935i
$743$	12.6032	−	1.10263i	0.462365	−	0.0404517i	0.146406	−	0.989225i	$-0.453229\pi$
$743$	12.6032	−	1.10263i	0.462365	−	0.0404517i	0.315959	+	0.948773i	$0.397674\pi$
$744$		0			0
$745$	6.94859	−	6.85927i	0.254577	−	0.251304i
$746$	−7.72276	−	4.45874i	−0.282750	−	0.163246i
$747$		0			0
$748$	−1.28995	+	4.81417i	−0.0471654	+	0.176024i
$749$	−1.06067	−	6.01537i	−0.0387561	−	0.219797i
$750$		0			0
$751$	34.1139	−	12.4164i	1.24483	−	0.453082i	0.366181	−	0.930544i	$-0.380665\pi$
$751$	34.1139	−	12.4164i	1.24483	−	0.453082i	0.878653	+	0.477461i	$0.158443\pi$
$752$	−6.61269	+	4.63025i	−0.241140	+	0.168848i
$753$		0			0
$754$	3.39204	+	4.04248i	0.123531	+	0.147218i
$755$	−4.91943	+	10.3740i	−0.179036	+	0.377549i
$756$		0			0
$757$	−1.14349	+	1.14349i	−0.0415609	+	0.0415609i	−0.727582	−	0.686021i	$-0.759356\pi$
$757$	−1.14349	+	1.14349i	−0.0415609	+	0.0415609i	0.686021	+	0.727582i	$0.259356\pi$
$758$	−0.356563	+	4.07554i	−0.0129510	+	0.148030i
$759$		0			0
$760$	1.93095	+	11.3810i	0.0700429	+	0.412832i
$761$	1.01737	+	2.79520i	0.0368796	+	0.101326i	0.956766	−	0.290860i	$-0.0939413\pi$
$761$	1.01737	+	2.79520i	0.0368796	+	0.101326i	−0.919886	+	0.392186i	$0.871719\pi$
$762$		0			0
$763$	−9.16717	+	13.0921i	−0.331874	+	0.473965i
$764$	9.37733	+	16.2420i	0.339260	+	0.587615i
$765$		0			0
$766$	7.63988	−	13.2327i	0.276040	−	0.478115i
$767$	−5.69828	−	12.2200i	−0.205753	−	0.441238i
$768$		0			0
$769$	−12.2665	+	14.6186i	−0.442341	+	0.527162i	−0.940440	−	0.339958i	$-0.889587\pi$
$769$	−12.2665	+	14.6186i	−0.442341	+	0.527162i	0.498099	+	0.867120i	$0.334031\pi$
$770$	−1.11722	−	2.43693i	−0.0402619	−	0.0878208i
$771$		0			0
$772$	16.1611	−	7.53602i	0.581649	−	0.271227i
$773$	−11.1062	−	41.4490i	−0.399463	−	1.49082i	−0.814044	−	0.580804i	$-0.802738\pi$
$773$	−11.1062	−	41.4490i	−0.399463	−	1.49082i	0.414581	−	0.910013i	$-0.363928\pi$
$774$		0			0
$775$	15.7651	−	41.6304i	0.566299	−	1.49541i
$776$	11.4101	−	2.01190i	0.409598	−	0.0722232i
$777$		0			0
$778$	25.1959	+	11.7490i	0.903315	+	0.421223i
$779$	1.31851	−	7.47765i	0.0472406	−	0.267915i
$780$		0			0
$781$	−3.49792	+	2.93511i	−0.125166	+	0.105026i
$782$	−0.863094	−	0.863094i	−0.0308642	−	0.0308642i
$783$		0			0
$784$		−	6.19498i		−	0.221249i
$785$	12.5009	+	7.32565i	0.446178	+	0.261464i
$786$		0			0
$787$	28.1608	+	40.2177i	1.00382	+	1.43361i	0.898399	+	0.439180i	$0.144731\pi$
$787$	28.1608	+	40.2177i	1.00382	+	1.43361i	0.105423	+	0.994427i	$0.466380\pi$
$788$	−0.826647	+	1.77275i	−0.0294481	+	0.0631516i
$789$		0			0
$790$	32.5443	−	18.5098i	1.15787	−	0.658549i
$791$	−0.528287	+	0.305007i	−0.0187837	+	0.0108448i
$792$		0			0
$793$	−6.34546	+	1.70026i	−0.225334	+	0.0603781i
$794$	−31.7226	−	11.5461i	−1.12579	−	0.409755i
$795$		0			0
$796$	3.73579	+	3.13470i	0.132412	+	0.111107i
$797$	1.69288	+	19.3498i	0.0599650	+	0.685404i	0.965375	+	0.260866i	$0.0840079\pi$
$797$	1.69288	+	19.3498i	0.0599650	+	0.685404i	−0.905410	+	0.424538i	$0.860437\pi$
$798$		0			0
$799$	−10.2983	+	28.2943i	−0.364327	+	1.00098i
$800$	4.05831	+	2.92063i	0.143483	+	0.103260i
$801$		0			0
$802$	−9.15996	−	2.45440i	−0.323449	−	0.0866680i
$803$	−4.88042	−	3.41731i	−0.172226	−	0.120594i
$804$		0			0
$805$	0.653661	+	0.0614512i	0.0230385	+	0.00216587i
$806$	9.48637	+	1.67270i	0.334143	+	0.0589185i
$807$		0			0
$808$	17.0188	+	1.48895i	0.598718	+	0.0523810i
$809$	−36.3148			−1.27676			−0.638379	−	0.769722i	$-0.720395\pi$
$809$	−36.3148			−1.27676			−0.638379	+	0.769722i	$0.720395\pi$
$810$		0			0
$811$	−24.5432			−0.861827			−0.430914	−	0.902393i	$-0.641809\pi$
$811$	−24.5432			−0.861827			−0.430914	+	0.902393i	$0.641809\pi$
$812$	4.35948	+	0.381405i	0.152988	+	0.0133847i
$813$		0			0
$814$	−13.9452	−	2.45891i	−0.488779	−	0.0861849i
$815$	7.25975	−	6.01205i	0.254298	−	0.210593i
$816$		0			0
$817$	−4.76074	−	3.33350i	−0.166557	−	0.116625i
$818$	26.7296	+	7.16218i	0.934579	+	0.250420i
$819$		0			0
$820$	−1.86893	−	2.70620i	−0.0652658	−	0.0945045i
$821$	−5.86960	+	16.1266i	−0.204851	+	0.562822i	−0.998991	−	0.0449121i	$-0.985699\pi$
$821$	−5.86960	+	16.1266i	−0.204851	+	0.562822i	0.794140	+	0.607734i	$0.207921\pi$
$822$		0			0
$823$	−1.80668	−	20.6504i	−0.0629768	−	0.719828i	−0.960394	−	0.278645i	$-0.910115\pi$
$823$	−1.80668	−	20.6504i	−0.0629768	−	0.719828i	0.897417	−	0.441183i	$-0.145441\pi$
$824$	−6.54583	−	5.49260i	−0.228035	−	0.191344i
$825$		0			0
$826$	−10.5070	−	3.82422i	−0.365584	−	0.133062i
$827$	−0.200648	+	0.0537636i	−0.00697723	+	0.00186954i	−0.262306	−	0.964985i	$-0.584483\pi$
$827$	−0.200648	+	0.0537636i	−0.00697723	+	0.00186954i	0.255329	+	0.966854i	$0.417816\pi$
$828$		0			0
$829$	−26.1088	+	15.0739i	−0.906795	+	0.523538i	−0.879398	−	0.476086i	$-0.842055\pi$
$829$	−26.1088	+	15.0739i	−0.906795	+	0.523538i	−0.0273963	+	0.999625i	$0.508722\pi$
$830$	−7.37587	−	2.02759i	−0.256020	−	0.0703786i
$831$		0			0
$832$	−0.457253	+	0.980582i	−0.0158524	+	0.0339956i
$833$	−13.2535	−	18.9279i	−0.459206	−	0.655815i
$834$		0			0
$835$	17.5351	−	29.9229i	0.606826	−	1.03553i
$836$		−	6.89820i		−	0.238579i
$837$		0			0
$838$	1.05256	+	1.05256i	0.0363601	+	0.0363601i
$839$	3.20065	−	2.68567i	0.110499	−	0.0927195i	−0.585864	−	0.810409i	$-0.699245\pi$
$839$	3.20065	−	2.68567i	0.110499	−	0.0927195i	0.696363	+	0.717690i	$0.254800\pi$
$840$		0			0
$841$	−0.904920	+	5.13206i	−0.0312042	+	0.176968i
$842$	−22.6352	−	10.5550i	−0.780062	−	0.363749i
$843$		0			0
$844$	−2.82447	+	0.498030i	−0.0972221	+	0.0171429i
$845$	2.13488	+	26.3650i	0.0734420	+	0.906984i
$846$		0			0
$847$	−2.13980	−	7.98584i	−0.0735244	−	0.274397i
$848$	2.67063	−	1.24534i	0.0917098	−	0.0427650i
$849$		0			0
$850$	18.6480	+	0.241278i	0.639622	+	0.00827577i
$851$	2.22913	−	2.65658i	0.0764137	−	0.0910663i
$852$		0			0
$853$	−1.49224	−	3.20011i	−0.0510932	−	0.109570i	0.879104	−	0.476630i	$-0.158142\pi$
$853$	−1.49224	−	3.20011i	−0.0510932	−	0.109570i	−0.930197	+	0.367061i	$0.880364\pi$
$854$	−2.72387	+	4.71788i	−0.0932088	+	0.161442i
$855$		0			0
$856$	−3.40390	−	5.89572i	−0.116343	−	0.201512i
$857$	−6.18309	+	8.83037i	−0.211210	+	0.301640i	−0.910753	−	0.412951i	$-0.864498\pi$
$857$	−6.18309	+	8.83037i	−0.211210	+	0.301640i	0.699543	+	0.714591i	$0.253387\pi$
$858$		0			0
$859$	−4.16152	−	11.4337i	−0.141989	−	0.390113i	0.848231	−	0.529627i	$-0.177668\pi$
$859$	−4.16152	−	11.4337i	−0.141989	−	0.390113i	−0.990220	+	0.139514i	$0.955446\pi$
$860$	−2.48184	+	0.421081i	−0.0846302	+	0.0143587i
$861$		0			0
$862$	−1.81747	+	20.7738i	−0.0619033	+	0.707558i
$863$	−13.6586	+	13.6586i	−0.464945	+	0.464945i	−0.900272	−	0.435328i	$-0.856633\pi$
$863$	−13.6586	+	13.6586i	−0.464945	+	0.464945i	0.435328	+	0.900272i	$0.356633\pi$
$864$		0			0
$865$	18.9380	+	53.0979i	0.643910	+	1.80538i
$866$	−21.7686	−	25.9428i	−0.739728	−	0.881574i
$867$		0			0
$868$	6.54350	−	4.58181i	0.222101	−	0.155517i
$869$	−21.0239	+	7.65208i	−0.713188	+	0.259579i
$870$		0			0
$871$	−1.79498	−	10.1798i	−0.0608205	−	0.344930i
$872$	−4.61037	+	17.2061i	−0.156127	+	0.582673i
$873$		0			0
$874$	1.46306	+	0.844698i	0.0494887	+	0.0285723i
$875$	−7.80814	+	6.29770i	−0.263963	+	0.212901i
$876$		0			0
$877$	−26.0383	+	2.27806i	−0.879251	+	0.0769245i	−0.517835	−	0.855480i	$-0.673262\pi$
$877$	−26.0383	+	2.27806i	−0.879251	+	0.0769245i	−0.361416	+	0.932405i	$0.617706\pi$
$878$	−0.469909	+	0.0411117i	−0.0158587	+	0.00138745i
$879$		0			0
$880$	−2.09904	−	2.12637i	−0.0707586	−	0.0716801i
$881$	19.2790	+	11.1307i	0.649524	+	0.375003i	0.788274	−	0.615324i	$-0.210975\pi$
$881$	19.2790	+	11.1307i	0.649524	+	0.375003i	−0.138750	+	0.990327i	$0.544308\pi$
$882$		0			0
$883$	−5.65042	+	21.0877i	−0.190152	+	0.709656i	0.803317	+	0.595552i	$0.203067\pi$
$883$	−5.65042	+	21.0877i	−0.190152	+	0.709656i	−0.993469	+	0.114104i	$0.963600\pi$
$884$	0.700774	+	3.97428i	0.0235696	+	0.133670i
$885$		0			0
$886$	−16.7778	+	6.10662i	−0.563661	+	0.205156i
$887$	4.18671	−	2.93156i	0.140576	−	0.0984323i	−0.501173	−	0.865347i	$-0.667098\pi$
$887$	4.18671	−	2.93156i	0.140576	−	0.0984323i	0.641749	+	0.766915i	$0.278209\pi$
$888$		0			0
$889$	−2.03475	−	2.42492i	−0.0682433	−	0.0813292i
$890$	18.8531	−	6.72418i	0.631957	−	0.225395i
$891$		0			0
$892$	10.6580	−	10.6580i	0.356857	−	0.356857i
$893$	3.63218	−	41.5160i	0.121546	−	1.38928i
$894$		0			0
$895$	38.6467	+	27.4350i	1.29182	+	0.917050i
$896$	0.306871	+	0.843122i	0.0102519	+	0.0281667i
$897$		0			0
$898$	9.22786	−	13.1788i	0.307938	−	0.439781i
$899$	−21.7118	−	37.6060i	−0.724131	−	1.25423i
$900$		0			0
$901$	5.49551	−	9.51849i	0.183082	−	0.317107i
$902$	0.830583	+	1.78119i	0.0276554	+	0.0593072i
$903$		0			0
$904$	−0.437021	+	0.520821i	−0.0145351	+	0.0173223i
$905$	−23.7734	+	10.8990i	−0.790253	+	0.362296i
$906$		0			0
$907$	−19.7789	+	9.22305i	−0.656747	+	0.306246i	−0.722277	−	0.691604i	$-0.756904\pi$
$907$	−19.7789	+	9.22305i	−0.656747	+	0.306246i	0.0655293	+	0.997851i	$0.479126\pi$
$908$	−5.91437	−	22.0727i	−0.196275	−	0.732509i
$909$		0			0
$910$	−1.65378	−	1.40602i	−0.0548224	−	0.0466091i
$911$	49.7438	−	8.77118i	1.64809	−	0.290602i	0.728957	−	0.684559i	$-0.240005\pi$
$911$	49.7438	−	8.77118i	1.64809	−	0.290602i	0.919129	+	0.393957i	$0.128894\pi$
$912$		0			0
$913$	4.14287	+	1.93185i	0.137109	+	0.0639349i
$914$	−2.77275	+	15.7250i	−0.0917143	+	0.520138i
$915$		0			0
$916$	8.34257	−	7.00025i	0.275646	−	0.231295i
$917$	9.78502	+	9.78502i	0.323130	+	0.323130i
$918$		0			0
$919$		−	28.1849i		−	0.929736i	−0.885380	−	0.464868i	$-0.846102\pi$
$919$		−	28.1849i		−	0.929736i	0.885380	−	0.464868i	$-0.153898\pi$
$920$	0.708020	−	0.184813i	0.0233427	−	0.00609310i
$921$		0			0
$922$	−15.4957	−	22.1302i	−0.510324	−	0.728818i
$923$	−1.56255	+	3.35090i	−0.0514320	+	0.110296i
$924$		0			0
$925$	3.93478	+	52.8401i	0.129375	+	1.73737i
$926$	0.0693205	−	0.0400222i	0.00227801	−	0.00131521i
$927$		0			0
$928$	4.71118	−	1.26236i	0.154652	−	0.0414389i
$929$	37.8692	+	13.7833i	1.24245	+	0.452214i	0.877843	−	0.478948i	$-0.158982\pi$
$929$	37.8692	+	13.7833i	1.24245	+	0.452214i	0.364605	+	0.931162i	$0.381204\pi$
$930$		0			0
$931$	24.4992	+	20.5572i	0.802927	+	0.673736i
$932$	0.833183	+	9.52333i	0.0272918	+	0.311947i
$933$		0			0
$934$	7.14062	−	19.6187i	0.233648	−	0.641943i
$935$	−10.9625	−	2.00619i	−0.358512	−	0.0656094i
$936$		0			0
$937$	42.2493	+	11.3207i	1.38022	+	0.369830i	0.871203	−	0.490923i	$-0.163341\pi$
$937$	42.2493	+	11.3207i	1.38022	+	0.369830i	0.509022	+	0.860754i	$0.330007\pi$
$938$	−7.02183	−	4.91674i	−0.229271	−	0.160537i
$939$		0			0
$940$	−11.5132	−	13.9025i	−0.375519	−	0.453451i
$941$	13.1370	+	2.31641i	0.428255	+	0.0755129i	0.383621	−	0.923491i	$-0.374677\pi$
$941$	13.1370	+	2.31641i	0.428255	+	0.0755129i	0.0446337	+	0.999003i	$0.485788\pi$
$942$		0			0
$943$	−0.479484	−	0.0419494i	−0.0156142	−	0.00136606i
$944$	−12.4620			−0.405603
$945$		0			0
$946$	1.50429			0.0489086
$947$	−17.2503	−	1.50920i	−0.560559	−	0.0490425i	−0.196644	−	0.980475i	$-0.563004\pi$
$947$	−17.2503	−	1.50920i	−0.560559	−	0.0490425i	−0.363914	+	0.931432i	$0.618560\pi$
$948$		0			0
$949$	−4.75088	−	0.837708i	−0.154220	−	0.0271932i
$950$	−25.0172	+	6.35760i	−0.811664	+	0.206268i
$951$		0			0
$952$	2.74138	+	1.91953i	0.0888485	+	0.0622124i
$953$	−23.8444	−	6.38908i	−0.772395	−	0.206963i	−0.148966	−	0.988842i	$-0.547594\pi$
$953$	−23.8444	−	6.38908i	−0.772395	−	0.206963i	−0.623429	+	0.781880i	$0.714261\pi$
$954$		0			0
$955$	−34.5074	+	23.8312i	−1.11663	+	0.771158i
$956$	−5.00586	+	13.7535i	−0.161901	+	0.444820i
$957$		0			0
$958$	1.17696	+	13.4527i	0.0380259	+	0.434638i
$959$	−9.84117	−	8.25772i	−0.317788	−	0.266656i
$960$		0			0
$961$	−45.3543	−	16.5076i	−1.46304	−	0.532503i
$962$	−11.0751	+	2.96756i	−0.357075	+	0.0956778i
$963$		0			0
$964$	−2.91503	+	1.68299i	−0.0938868	+	0.0542056i
$965$	19.7127	+	34.6593i	0.634574	+	1.11572i
$966$		0			0
$967$	10.7948	−	23.1494i	0.347136	−	0.744435i	−0.652778	−	0.757549i	$-0.726397\pi$
$967$	10.7948	−	23.1494i	0.347136	−	0.744435i	0.999914	+	0.0131138i	$0.00417436\pi$
$968$	−5.28523	−	7.54809i	−0.169874	−	0.242605i
$969$		0			0
$970$	6.54328	+	25.0674i	0.210092	+	0.804865i
$971$			31.8579i			1.02237i	0.859471	+	0.511185i	$0.170793\pi$
$971$			31.8579i			1.02237i	−0.859471	+	0.511185i	$0.829207\pi$
$972$		0			0
$973$	−6.85821	−	6.85821i	−0.219864	−	0.219864i
$974$	20.0707	−	16.8413i	0.643108	−	0.539631i
$975$		0			0
$976$	−1.05434	+	5.97947i	−0.0337487	+	0.191398i
$977$	−52.2358	−	24.3580i	−1.67117	−	0.779280i	−0.999253	−	0.0386561i	$-0.987692\pi$
$977$	−52.2358	−	24.3580i	−1.67117	−	0.779280i	−0.671919	−	0.740624i	$-0.734530\pi$
$978$		0			0
$979$	−11.7796	+	2.07706i	−0.376477	+	0.0663830i
$980$	13.8072	−	1.11802i	0.441055	−	0.0357139i
$981$		0			0
$982$	−0.357651	−	1.33477i	−0.0114131	−	0.0425943i
$983$	−2.67813	+	1.24883i	−0.0854189	+	0.0398315i	−0.464858	−	0.885385i	$-0.653895\pi$
$983$	−2.67813	+	1.24883i	−0.0854189	+	0.0398315i	0.379439	+	0.925217i	$0.376117\pi$
$984$		0			0
$985$	−4.10024	−	1.52248i	−0.130645	−	0.0485101i
$986$	11.6937	−	13.9360i	0.372404	−	0.443814i
$987$		0			0
$988$	−2.36055	−	5.06222i	−0.0750992	−	0.161051i
$989$	−0.184203	+	0.319048i	−0.00585730	+	0.0101451i
$990$		0			0
$991$	−21.5167	−	37.2680i	−0.683500	−	1.18386i	−0.973906	−	0.226954i	$-0.927123\pi$
$991$	−21.5167	−	37.2680i	−0.683500	−	1.18386i	0.290405	−	0.956904i	$-0.406210\pi$
$992$	5.10660	−	7.29298i	0.162135	−	0.231552i
$993$		0			0
$994$	1.04866	+	2.88117i	0.0332614	+	0.0913851i
$995$	−6.31234	+	8.89197i	−0.200114	+	0.281894i
$996$		0			0
$997$	−2.60662	+	29.7938i	−0.0825526	+	0.943580i	0.836116	+	0.548552i	$0.184821\pi$
$997$	−2.60662	+	29.7938i	−0.0825526	+	0.943580i	−0.918669	+	0.395028i	$0.870735\pi$
$998$	21.6427	−	21.6427i	0.685088	−	0.685088i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.4		216
3.2	odd	2		270.2.r.a.113.17	✓	216
5.2	odd	4	inner	810.2.s.a.287.16		216
15.2	even	4		270.2.r.a.167.7	yes	216
27.11	odd	18	inner	810.2.s.a.683.16		216
27.16	even	9		270.2.r.a.173.7	yes	216
135.92	even	36	inner	810.2.s.a.197.4		216
135.97	odd	36		270.2.r.a.227.17	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.17	✓	216	3.2	odd	2
270.2.r.a.167.7	yes	216	15.2	even	4
270.2.r.a.173.7	yes	216	27.16	even	9
270.2.r.a.227.17	yes	216	135.97	odd	36
810.2.s.a.197.4		216	135.92	even	36	inner
810.2.s.a.287.16		216	5.2	odd	4	inner
810.2.s.a.683.16		216	27.11	odd	18	inner
810.2.s.a.773.4		216	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.209292 + 2.22625i) q^{5} +(-0.734969 - 0.514631i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.402526 - 2.19954i) q^{10} +(-0.457015 + 1.25564i) q^{11} +(0.0942983 + 1.07783i) q^{13} +(0.687319 + 0.576729i) q^{14} +(0.939693 + 0.342020i) q^{16} +(3.60283 - 0.965374i) q^{17} +(-4.47083 + 2.58124i) q^{19} +(-0.592697 + 2.15609i) q^{20} +(0.564712 - 1.21103i) q^{22} +(0.187700 + 0.268064i) q^{23} +(-4.91239 - 0.931873i) q^{25} -1.08195i q^{26} +(-0.634439 - 0.634439i) q^{28} +(-3.73628 + 3.13512i) q^{29} +(-1.54601 + 8.76783i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-3.67325 + 0.647694i) q^{34} +(1.29952 - 1.52852i) q^{35} +(-2.74278 - 10.2362i) q^{37} +(4.67879 - 2.18175i) q^{38} +(0.778357 - 2.09623i) q^{40} +(-0.945418 + 1.12671i) q^{41} +(0.475774 + 1.02030i) q^{43} +(-0.668111 + 1.15720i) q^{44} +(-0.163623 - 0.283403i) q^{46} +(-4.63025 + 6.61269i) q^{47} +(-2.11881 - 5.82137i) q^{49} +(4.81248 + 1.35647i) q^{50} +(-0.0942983 + 1.07783i) q^{52} +(2.08364 - 2.08364i) q^{53} +(-2.69972 - 1.28022i) q^{55} +(0.576729 + 0.687319i) q^{56} +(3.99531 - 2.79755i) q^{58} +(-11.7104 + 4.26225i) q^{59} +(1.05434 + 5.97947i) q^{61} +(2.30429 - 8.59972i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-2.41927 - 0.0156502i) q^{65} +(-9.51755 + 0.832678i) q^{67} +(3.71573 - 0.325084i) q^{68} +(-1.42780 + 1.40944i) q^{70} +(2.95943 + 1.70863i) q^{71} +(-1.15401 + 4.30684i) q^{73} +(1.84020 + 10.4363i) q^{74} +(-4.85114 + 1.76567i) q^{76} +(0.982082 - 0.687661i) q^{77} +(10.7626 + 12.8264i) q^{79} +(-0.958093 + 2.02041i) q^{80} +(1.04002 - 1.04002i) q^{82} +(0.298155 - 3.40793i) q^{83} +(1.39512 + 8.22284i) q^{85} +(-0.385038 - 1.05788i) q^{86} +(0.766425 - 1.09457i) q^{88} +(4.47579 + 7.75230i) q^{89} +(0.485381 - 0.840704i) q^{91} +(0.138300 + 0.296585i) q^{92} +(5.18897 - 6.18397i) q^{94} +(-4.81077 - 10.4934i) q^{95} +(-10.5006 + 4.89650i) q^{97} +(1.60338 + 5.98389i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 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

Related objects

Downloads

Learn more