LMFDB - Embedded newform 441.2.bg.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			89.2
Character	$\chi$	$=$	441.89
Dual form			441.2.bg.a.332.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73897 + 1.87416i) q^{2} +(-0.339014 - 4.52383i) q^{4} +(0.526440 + 1.34135i) q^{5} +(2.25076 - 1.39071i) q^{7} +(5.07018 + 4.04333i) q^{8} +O(q^{10})$	\(q+(-1.73897 + 1.87416i) q^{2} +(-0.339014 - 4.52383i) q^{4} +(0.526440 + 1.34135i) q^{5} +(2.25076 - 1.39071i) q^{7} +(5.07018 + 4.04333i) q^{8} +(-3.42937 - 1.34593i) q^{10} +(-1.53405 - 4.97326i) q^{11} +(-4.91498 - 1.12181i) q^{13} +(-1.30760 + 6.63670i) q^{14} +(-7.42308 + 1.11885i) q^{16} +(-5.11017 - 3.48405i) q^{17} +(-3.65054 - 2.10764i) q^{19} +(5.88955 - 2.83626i) q^{20} +(11.9884 + 5.77329i) q^{22} +(1.02621 + 1.50518i) q^{23} +(2.14319 - 1.98859i) q^{25} +(10.6495 - 7.26069i) q^{26} +(-7.05436 - 9.71060i) q^{28} +(-2.64083 - 5.48373i) q^{29} +(-2.33940 + 1.35066i) q^{31} +(3.50535 - 5.14140i) q^{32} +(15.4161 - 3.51863i) q^{34} +(3.05031 + 2.28693i) q^{35} +(0.262556 - 3.50357i) q^{37} +(10.2983 - 3.17659i) q^{38} +(-2.75437 + 8.92944i) q^{40} +(-0.957069 + 1.20013i) q^{41} +(6.06849 + 7.60964i) q^{43} +(-21.9781 + 8.62577i) q^{44} +(-4.60550 - 0.694168i) q^{46} +(2.72404 + 2.52754i) q^{47} +(3.13187 - 6.26030i) q^{49} +7.47479i q^{50} +(-3.40864 + 22.6148i) q^{52} +(-2.32824 + 0.174478i) q^{53} +(5.86327 - 4.67580i) q^{55} +(17.0349 + 2.04945i) q^{56} +(14.8697 + 4.58671i) q^{58} +(3.19735 - 8.14670i) q^{59} +(-0.839762 - 0.0629315i) q^{61} +(1.53680 - 6.73318i) q^{62} +(0.199240 + 0.872927i) q^{64} +(-1.08270 - 7.18326i) q^{65} +(1.52304 + 2.63798i) q^{67} +(-14.0288 + 24.2987i) q^{68} +(-9.59048 + 1.73988i) q^{70} +(-3.48850 + 7.24395i) q^{71} +(10.5398 + 11.3592i) q^{73} +(6.10969 + 6.58468i) q^{74} +(-8.29703 + 17.2290i) q^{76} +(-10.3691 - 9.06021i) q^{77} +(1.11008 - 1.92271i) q^{79} +(-5.40857 - 9.36792i) q^{80} +(-0.584920 - 3.88069i) q^{82} +(-2.19378 - 9.61160i) q^{83} +(1.98313 - 8.68865i) q^{85} +(-24.8146 - 1.85960i) q^{86} +(12.3306 - 31.4180i) q^{88} +(1.58636 + 0.489328i) q^{89} +(-12.6226 + 4.31037i) q^{91} +(6.46126 - 5.15269i) q^{92} +(-9.47404 + 0.709981i) q^{94} +(0.905288 - 6.00619i) q^{95} -18.0874i q^{97} +(6.28662 + 16.7561i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{23}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.73897	+	1.87416i	−1.22964	+	1.32523i	−0.301285	+	0.953534i	$0.597416\pi$
$2$	−1.73897	+	1.87416i	−1.22964	+	1.32523i	−0.928353	+	0.371701i	$0.878775\pi$
$3$		0			0
$3$		0			0
$4$	−0.339014	−	4.52383i	−0.169507	−	2.26191i
$5$	0.526440	+	1.34135i	0.235431	+	0.599868i	0.998945	−	0.0459230i	$-0.0146229\pi$
$5$	0.526440	+	1.34135i	0.235431	+	0.599868i	−0.763514	+	0.645791i	$0.776528\pi$
$6$		0			0
$7$	2.25076	−	1.39071i	0.850708	−	0.525638i
$7$	2.25076	−	1.39071i	0.850708	−	0.525638i
$8$	5.07018	+	4.04333i	1.79258	+	1.42953i
$9$		0			0
$10$	−3.42937	−	1.34593i	−1.08446	−	0.425620i
$11$	−1.53405	−	4.97326i	−0.462532	−	1.49949i	−0.823718	−	0.566999i	$-0.808104\pi$
$11$	−1.53405	−	4.97326i	−0.462532	−	1.49949i	0.361186	−	0.932494i	$-0.382372\pi$
$12$		0			0
$13$	−4.91498	−	1.12181i	−1.36317	−	0.311135i	−0.522480	−	0.852651i	$-0.674993\pi$
$13$	−4.91498	−	1.12181i	−1.36317	−	0.311135i	−0.840690	+	0.541517i	$0.817850\pi$
$14$	−1.30760	+	6.63670i	−0.349470	+	1.77373i
$15$		0			0
$16$	−7.42308	+	1.11885i	−1.85577	+	0.279712i
$17$	−5.11017	−	3.48405i	−1.23940	−	0.845007i	−0.247113	−	0.968987i	$-0.579482\pi$
$17$	−5.11017	−	3.48405i	−1.23940	−	0.845007i	−0.992285	+	0.123980i	$0.960434\pi$
$18$		0			0
$19$	−3.65054	−	2.10764i	−0.837492	−	0.483526i	0.0189187	−	0.999821i	$-0.493978\pi$
$19$	−3.65054	−	2.10764i	−0.837492	−	0.483526i	−0.856411	+	0.516295i	$0.827311\pi$
$20$	5.88955	−	2.83626i	1.31694	−	0.634206i
$21$		0			0
$22$	11.9884	+	5.77329i	2.55593	+	1.23087i
$23$	1.02621	+	1.50518i	0.213980	+	0.313851i	0.918190	−	0.396141i	$-0.129651\pi$
$23$	1.02621	+	1.50518i	0.213980	+	0.313851i	−0.704210	+	0.709992i	$0.748698\pi$
$24$		0			0
$25$	2.14319	−	1.98859i	0.428638	−	0.397718i
$26$	10.6495	−	7.26069i	2.08853	−	1.42394i
$27$		0			0
$28$	−7.05436	−	9.71060i	−1.33315	−	1.83513i
$29$	−2.64083	−	5.48373i	−0.490389	−	1.01830i	−0.988504	−	0.151193i	$-0.951689\pi$
$29$	−2.64083	−	5.48373i	−0.490389	−	1.01830i	0.498115	−	0.867111i	$-0.334026\pi$
$30$		0			0
$31$	−2.33940	+	1.35066i	−0.420170	+	0.242585i	−0.695150	−	0.718865i	$-0.744662\pi$
$31$	−2.33940	+	1.35066i	−0.420170	+	0.242585i	0.274980	+	0.961450i	$0.411329\pi$
$32$	3.50535	−	5.14140i	0.619664	−	0.908881i
$33$		0			0
$34$	15.4161	−	3.51863i	2.64384	−	0.603440i
$35$	3.05031	+	2.28693i	0.515597	+	0.386562i
$36$		0			0
$37$	0.262556	−	3.50357i	0.0431640	−	0.575984i	−0.933131	−	0.359538i	$-0.882934\pi$
$37$	0.262556	−	3.50357i	0.0431640	−	0.575984i	0.976295	−	0.216446i	$-0.0694465\pi$
$38$	10.2983	−	3.17659i	1.67060	−	0.515311i
$39$		0			0
$40$	−2.75437	+	8.92944i	−0.435504	+	1.41187i
$41$	−0.957069	+	1.20013i	−0.149469	+	0.187428i	−0.850929	−	0.525280i	$-0.823960\pi$
$41$	−0.957069	+	1.20013i	−0.149469	+	0.187428i	0.701460	+	0.712709i	$0.252532\pi$
$42$		0			0
$43$	6.06849	+	7.60964i	0.925435	+	1.16046i	0.986735	+	0.162340i	$0.0519041\pi$
$43$	6.06849	+	7.60964i	0.925435	+	1.16046i	−0.0612995	+	0.998119i	$0.519524\pi$
$44$	−21.9781	+	8.62577i	−3.31332	+	1.30038i
$45$		0			0
$46$	−4.60550	−	0.694168i	−0.679045	−	0.102349i
$47$	2.72404	+	2.52754i	0.397342	+	0.368679i	0.853387	−	0.521277i	$-0.174544\pi$
$47$	2.72404	+	2.52754i	0.397342	+	0.368679i	−0.456046	+	0.889956i	$0.650735\pi$
$48$		0			0
$49$	3.13187	−	6.26030i	0.447410	−	0.894329i
$50$			7.47479i			1.05709i
$51$		0			0
$52$	−3.40864	+	22.6148i	−0.472693	+	3.13611i
$53$	−2.32824	+	0.174478i	−0.319809	+	0.0239663i	−0.233667	−	0.972317i	$-0.575073\pi$
$53$	−2.32824	+	0.174478i	−0.319809	+	0.0239663i	−0.0861412	+	0.996283i	$0.527454\pi$
$54$		0			0
$55$	5.86327	−	4.67580i	0.790604	−	0.630485i
$56$	17.0349	+	2.04945i	2.27638	+	0.273869i
$57$		0			0
$58$	14.8697	+	4.58671i	1.95249	+	0.602264i
$59$	3.19735	−	8.14670i	0.416259	−	1.06061i	−0.556921	−	0.830565i	$-0.688017\pi$
$59$	3.19735	−	8.14670i	0.416259	−	1.06061i	0.973180	−	0.230045i	$-0.0738874\pi$
$60$		0			0
$61$	−0.839762	−	0.0629315i	−0.107521	−	0.00805755i	0.0208611	−	0.999782i	$-0.493359\pi$
$61$	−0.839762	−	0.0629315i	−0.107521	−	0.00805755i	−0.128382	+	0.991725i	$0.540978\pi$
$62$	1.53680	−	6.73318i	0.195174	−	0.855115i
$63$		0			0
$64$	0.199240	+	0.872927i	0.0249050	+	0.109116i
$65$	−1.08270	−	7.18326i	−0.134293	−	0.890973i
$66$		0			0
$67$	1.52304	+	2.63798i	0.186068	+	0.322280i	0.943936	−	0.330128i	$-0.107092\pi$
$67$	1.52304	+	2.63798i	0.186068	+	0.322280i	−0.757868	+	0.652408i	$0.773759\pi$
$68$	−14.0288	+	24.2987i	−1.70125	+	2.94665i
$69$		0			0
$70$	−9.59048	+	1.73988i	−1.14628	+	0.207956i
$71$	−3.48850	+	7.24395i	−0.414009	+	0.859698i	0.584813	+	0.811168i	$0.301168\pi$
$71$	−3.48850	+	7.24395i	−0.414009	+	0.859698i	−0.998822	+	0.0485299i	$0.984546\pi$
$72$		0			0
$73$	10.5398	+	11.3592i	1.23359	+	1.32949i	0.925787	+	0.378045i	$0.123403\pi$
$73$	10.5398	+	11.3592i	1.23359	+	1.32949i	0.307803	+	0.951450i	$0.400406\pi$
$74$	6.10969	+	6.58468i	0.710237	+	0.765454i
$75$		0			0
$76$	−8.29703	+	17.2290i	−0.951735	+	1.97630i
$77$	−10.3691	−	9.06021i	−1.18167	−	1.03251i
$78$		0			0
$79$	1.11008	−	1.92271i	0.124893	−	0.216322i	−0.796798	−	0.604246i	$-0.793474\pi$
$79$	1.11008	−	1.92271i	0.124893	−	0.216322i	0.921691	+	0.387924i	$0.126808\pi$
$80$	−5.40857	−	9.36792i	−0.604696	−	1.04736i
$81$		0			0
$82$	−0.584920	−	3.88069i	−0.0645936	−	0.428551i
$83$	−2.19378	−	9.61160i	−0.240799	−	1.05501i	−0.940292	−	0.340370i	$-0.889448\pi$
$83$	−2.19378	−	9.61160i	−0.240799	−	1.05501i	0.699492	−	0.714640i	$-0.253409\pi$
$84$		0			0
$85$	1.98313	−	8.68865i	0.215100	−	0.942416i
$86$	−24.8146	−	1.85960i	−2.67583	−	0.200526i
$87$		0			0
$88$	12.3306	−	31.4180i	1.31445	−	3.34917i
$89$	1.58636	+	0.489328i	0.168154	+	0.0518687i	0.377689	−	0.925932i	$-0.376719\pi$
$89$	1.58636	+	0.489328i	0.168154	+	0.0518687i	−0.209535	+	0.977801i	$0.567195\pi$
$90$		0			0
$91$	−12.6226	+	4.31037i	−1.32320	+	0.451849i
$92$	6.46126	−	5.15269i	0.673633	−	0.537205i
$93$		0			0
$94$	−9.47404	+	0.709981i	−0.977173	+	0.0732290i
$95$	0.905288	−	6.00619i	0.0928805	−	0.616222i
$96$		0			0
$97$		−	18.0874i		−	1.83650i	−0.395999	−	0.918251i	$-0.629602\pi$
$97$		−	18.0874i		−	1.83650i	0.395999	−	0.918251i	$-0.370398\pi$
$98$	6.28662	+	16.7561i	0.635044	+	1.69262i
$99$		0			0
$100$	−9.72261	−	9.02126i	−0.972261	−	0.902126i
$101$	10.6165	+	1.60018i	1.05638	+	0.159224i	0.654189	−	0.756331i	$-0.273010\pi$
$101$	10.6165	+	1.60018i	1.05638	+	0.159224i	0.402193	+	0.915555i	$0.368248\pi$
$102$		0			0
$103$	−13.0716	+	5.13024i	−1.28799	+	0.505498i	−0.907797	−	0.419411i	$-0.862237\pi$
$103$	−13.0716	+	5.13024i	−1.28799	+	0.505498i	−0.380190	+	0.924908i	$0.624141\pi$
$104$	−20.3840	−	25.5607i	−1.99881	−	2.50643i
$105$		0			0
$106$	3.72174	−	4.66692i	0.361488	−	0.453291i
$107$	2.17270	−	7.04371i	0.210043	−	0.680941i	−0.787839	−	0.615882i	$-0.788800\pi$
$107$	2.17270	−	7.04371i	0.210043	−	0.680941i	0.997881	−	0.0650599i	$-0.0207238\pi$
$108$		0			0
$109$	−14.7891	+	4.56185i	−1.41654	+	0.436946i	−0.906136	−	0.422987i	$-0.860982\pi$
$109$	−14.7891	+	4.56185i	−1.41654	+	0.436946i	−0.510407	+	0.859933i	$0.670505\pi$
$110$	−1.43283	+	19.1198i	−0.136615	+	1.82300i
$111$		0			0
$112$	−15.1516	+	12.8416i	−1.43169	+	1.21342i
$113$	13.2361	−	3.02106i	1.24515	−	0.284198i	0.451335	−	0.892355i	$-0.350948\pi$
$113$	13.2361	−	3.02106i	1.24515	−	0.284198i	0.793817	+	0.608157i	$0.208091\pi$
$114$		0			0
$115$	−1.47872	+	2.16889i	−0.137892	+	0.202250i
$116$	−23.9122	+	13.8057i	−2.22019	+	1.28183i
$117$		0			0
$118$	9.70818	+	20.1592i	0.893710	+	1.85581i
$119$	−16.3471	−	0.735031i	−1.49853	−	0.0673802i
$120$		0			0
$121$	−13.2913	+	9.06188i	−1.20830	+	0.823808i
$122$	1.57827	−	1.46442i	0.142890	−	0.132582i
$123$		0			0
$124$	6.90323	+	10.1252i	0.619928	+	0.909268i
$125$	10.2869	+	4.95392i	0.920090	+	0.443092i
$126$		0			0
$127$	−2.73325	+	1.31627i	−0.242537	+	0.116800i	−0.551204	−	0.834370i	$-0.685831\pi$
$127$	−2.73325	+	1.31627i	−0.242537	+	0.116800i	0.308667	+	0.951170i	$0.400117\pi$
$128$	8.79549	+	5.07808i	0.777418	+	0.448843i
$129$		0			0
$130$	15.3454	+	10.4623i	1.34588	+	0.917605i
$131$	−20.3855	+	3.07262i	−1.78109	+	0.268456i	−0.955325	−	0.295557i	$-0.904495\pi$
$131$	−20.3855	+	3.07262i	−1.78109	+	0.268456i	−0.825766	+	0.564014i	$0.809257\pi$
$132$		0			0
$133$	−11.1476	+	0.333034i	−0.966622	+	0.0288777i
$134$	−7.59251	−	1.73294i	−0.655893	−	0.149703i
$135$		0			0
$136$	−11.8223	−	38.3269i	−1.01375	−	3.28650i
$137$	17.2919	+	6.78656i	1.47734	+	0.579815i	0.960996	−	0.276563i	$-0.0891956\pi$
$137$	17.2919	+	6.78656i	1.47734	+	0.579815i	0.516349	+	0.856378i	$0.327291\pi$
$138$		0			0
$139$	−0.104900	−	0.0836551i	−0.00889752	−	0.00709553i	0.619031	−	0.785367i	$-0.287526\pi$
$139$	−0.104900	−	0.0836551i	−0.00889752	−	0.00709553i	−0.627928	+	0.778271i	$0.716097\pi$
$140$	9.31158	−	14.5744i	0.786972	−	1.23176i
$141$		0			0
$142$	−7.50995	−	19.1350i	−0.630221	−	1.60578i
$143$	1.96075	+	26.1644i	0.163966	+	2.18797i
$144$		0			0
$145$	5.96535	−	6.42912i	0.495395	−	0.533909i
$146$	−39.6174			−3.27876
$147$		0			0
$148$	−15.9386			−1.31014
$149$	6.61792	−	7.13242i	0.542161	−	0.584311i	−0.401237	−	0.915974i	$-0.631419\pi$
$149$	6.61792	−	7.13242i	0.542161	−	0.584311i	0.943398	+	0.331664i	$0.107610\pi$
$150$		0			0
$151$	−0.120002	−	1.60131i	−0.00976559	−	0.130313i	0.990190	−	0.139727i	$-0.0446224\pi$
$151$	−0.120002	−	1.60131i	−0.00976559	−	0.130313i	−0.999956	+	0.00941402i	$0.997003\pi$
$152$	−9.98702	−	25.4465i	−0.810054	−	2.06398i
$153$		0			0
$154$	35.0119	−	3.67799i	2.82134	−	0.296381i
$155$	−3.04325	−	2.42691i	−0.244440	−	0.194934i
$156$		0			0
$157$	2.15735	+	0.846696i	0.172175	+	0.0675737i	0.449863	−	0.893098i	$-0.351473\pi$
$157$	2.15735	+	0.846696i	0.172175	+	0.0675737i	−0.277688	+	0.960671i	$0.589568\pi$
$158$	1.67308	+	5.42400i	0.133103	+	0.431511i
$159$		0			0
$160$	8.74176	+	1.99525i	0.691097	+	0.157738i
$161$	4.40302	+	1.96064i	0.347007	+	0.154520i
$162$		0			0
$163$	20.5571	−	3.09849i	1.61016	−	0.242692i	0.718541	−	0.695484i	$-0.244810\pi$
$163$	20.5571	−	3.09849i	1.61016	−	0.242692i	0.891616	+	0.452792i	$0.149572\pi$
$164$	5.75363	+	3.92276i	0.449283	+	0.306316i
$165$		0			0
$166$	21.8286	+	12.6028i	1.69423	+	0.978165i
$167$	−14.5294	+	6.99699i	−1.12432	+	0.541443i	−0.901224	−	0.433354i	$-0.857330\pi$
$167$	−14.5294	+	6.99699i	−1.12432	+	0.541443i	−0.223094	+	0.974797i	$0.571616\pi$
$168$		0			0
$169$	11.1860	+	5.38688i	0.860460	+	0.414376i
$170$	12.8354	+	18.8260i	0.984427	+	1.44389i
$171$		0			0
$172$	32.3674	−	30.0326i	2.46799	−	2.28996i
$173$	5.46640	−	3.72693i	0.415603	−	0.283353i	−0.337412	−	0.941357i	$-0.609551\pi$
$173$	5.46640	−	3.72693i	0.415603	−	0.283353i	0.753014	+	0.658004i	$0.228599\pi$
$174$		0			0
$175$	2.05827	−	7.45639i	0.155590	−	0.563650i
$176$	16.9517	+	35.2005i	1.27778	+	2.65334i
$177$		0			0
$178$	−3.67572	+	2.12218i	−0.275507	+	0.159064i
$179$	0.535987	−	0.786149i	0.0400616	−	0.0587595i	−0.805685	−	0.592344i	$-0.798203\pi$
$179$	0.535987	−	0.786149i	0.0400616	−	0.0587595i	0.845747	+	0.533584i	$0.179155\pi$
$180$		0			0
$181$	−22.4411	+	5.12203i	−1.66803	+	0.380718i	−0.949251	−	0.314518i	$-0.898157\pi$
$181$	−22.4411	+	5.12203i	−1.66803	+	0.380718i	−0.718781	+	0.695236i	$0.755300\pi$
$182$	13.8719	−	31.1524i	1.02826	−	2.30917i
$183$		0			0
$184$	−0.882852	+	11.7808i	−0.0650847	+	0.868495i
$185$	4.83772	−	1.49224i	0.355676	−	0.109712i
$186$		0			0
$187$	−9.48785	+	30.7589i	−0.693821	+	2.24931i
$188$	10.5107	−	13.1799i	0.766568	−	0.961246i
$189$		0			0
$190$	9.68232	+	12.1412i	0.702429	+	0.880819i
$191$	16.1144	−	6.32444i	1.16600	−	0.457621i	0.298184	−	0.954509i	$-0.403619\pi$
$191$	16.1144	−	6.32444i	1.16600	−	0.457621i	0.867815	+	0.496888i	$0.165524\pi$
$192$		0			0
$193$	3.96672	+	0.597887i	0.285531	+	0.0430368i	0.290246	−	0.956952i	$-0.406263\pi$
$193$	3.96672	+	0.597887i	0.285531	+	0.0430368i	−0.00471536	+	0.999989i	$0.501501\pi$
$194$	33.8989	+	31.4535i	2.43380	+	2.25823i
$195$		0			0
$196$	−29.3823	−	12.0457i	−2.09874	−	0.860407i
$197$		−	5.93147i		−	0.422600i	−0.977421	−	0.211300i	$-0.932230\pi$
$197$		−	5.93147i		−	0.422600i	0.977421	−	0.211300i	$-0.0677697\pi$
$198$		0			0
$199$	−1.58505	+	10.5161i	−0.112361	+	0.745469i	0.859710	+	0.510783i	$0.170644\pi$
$199$	−1.58505	+	10.5161i	−0.112361	+	0.745469i	−0.972071	+	0.234686i	$0.924594\pi$
$200$	18.9069	−	1.41688i	1.33692	−	0.100188i
$201$		0			0
$202$	−21.4608	+	17.1144i	−1.50998	+	1.20417i
$203$	−13.5701	−	8.66997i	−0.952437	−	0.608512i
$204$		0			0
$205$	−2.11362	−	0.651967i	−0.147622	−	0.0455353i
$206$	13.1163	−	33.4197i	0.913855	−	2.32846i
$207$		0			0
$208$	37.7395	+	2.82818i	2.61676	+	0.196099i
$209$	−4.88174	+	21.3883i	−0.337677	+	1.47946i
$210$		0			0
$211$	−1.97169	−	8.63854i	−0.135737	−	0.594701i	−0.996344	−	0.0854322i	$-0.972773\pi$
$211$	−1.97169	−	8.63854i	−0.135737	−	0.594701i	0.860607	−	0.509269i	$-0.170084\pi$
$212$	1.57861	+	10.4734i	0.108420	+	0.719317i
$213$		0			0
$214$	9.42282	+	16.3208i	0.644131	+	1.11567i
$215$	−7.01247	+	12.1460i	−0.478247	+	0.828347i
$216$		0			0
$217$	−3.38708	+	6.29343i	−0.229930	+	0.427226i
$218$	17.1682	−	35.6502i	1.16278	−	2.41454i
$219$		0			0
$220$	−23.1403	−	24.9393i	−1.56012	−	1.68141i
$221$	21.2079	+	22.8567i	1.42660	+	1.53751i
$222$		0			0
$223$	−3.88182	+	8.06068i	−0.259946	+	0.539783i	−0.989568	−	0.144068i	$-0.953982\pi$
$223$	−3.88182	+	8.06068i	−0.259946	+	0.539783i	0.729622	+	0.683851i	$0.239696\pi$
$224$	0.739524	−	16.4470i	0.0494116	−	1.09891i
$225$		0			0
$226$	−17.3553	+	30.0602i	−1.15446	+	1.99958i
$227$	−4.61812	−	7.99882i	−0.306516	−	0.530900i	0.671082	−	0.741383i	$-0.265830\pi$
$227$	−4.61812	−	7.99882i	−0.306516	−	0.530900i	−0.977598	+	0.210483i	$0.932496\pi$
$228$		0			0
$229$	−1.22211	−	8.10815i	−0.0807591	−	0.535801i	−0.992228	−	0.124433i	$-0.960289\pi$
$229$	−1.22211	−	8.10815i	−0.0807591	−	0.535801i	0.911469	−	0.411369i	$-0.134949\pi$
$230$	−1.49340	−	6.54301i	−0.0984719	−	0.431433i
$231$		0			0
$232$	8.78310	−	38.4813i	0.576639	−	2.52642i
$233$	3.87395	+	0.290313i	0.253791	+	0.0190190i	0.201018	−	0.979588i	$-0.435575\pi$
$233$	3.87395	+	0.290313i	0.253791	+	0.0190190i	0.0527730	+	0.998607i	$0.483194\pi$
$234$		0			0
$235$	−1.95626	+	4.98447i	−0.127612	+	0.325151i
$236$	−37.9382	−	11.7024i	−2.46957	−	0.761761i
$237$		0			0
$238$	29.8047	−	29.3589i	1.93195	−	1.90306i
$239$	11.4957	−	9.16752i	0.743596	−	0.592998i	−0.176680	−	0.984268i	$-0.556536\pi$
$239$	11.4957	−	9.16752i	0.743596	−	0.592998i	0.920276	+	0.391271i	$0.127964\pi$
$240$		0			0
$241$	10.4427	−	0.782569i	0.672670	−	0.0504097i	0.265984	−	0.963977i	$-0.414303\pi$
$241$	10.4427	−	0.782569i	0.672670	−	0.0504097i	0.406686	+	0.913568i	$0.366684\pi$
$242$	6.12979	−	40.6685i	0.394038	−	2.61427i
$243$		0			0
$244$			3.82028i			0.244568i
$245$	10.0460	+	0.905246i	0.641814	+	0.0578341i
$246$		0			0
$247$	15.5780	+	14.4543i	0.991203	+	0.919702i
$248$	−17.3224	−	2.61093i	−1.09997	−	0.165794i
$249$		0			0
$250$	−27.1731	+	10.6647i	−1.71858	+	0.674492i
$251$	5.40095	+	6.77258i	0.340905	+	0.427481i	0.922500	−	0.385997i	$-0.126143\pi$
$251$	5.40095	+	6.77258i	0.340905	+	0.427481i	−0.581595	+	0.813479i	$0.697571\pi$
$252$		0			0
$253$	5.91137	−	7.41263i	0.371645	−	0.466028i
$254$	2.28615	−	7.41151i	0.143446	−	0.465040i
$255$		0			0
$256$	−26.5234	+	8.18140i	−1.65771	+	0.511337i
$257$	0.185401	−	2.47400i	0.0115650	−	0.154324i	−0.988431	−	0.151668i	$-0.951536\pi$
$257$	0.185401	−	2.47400i	0.0115650	−	0.154324i	0.999996	−	0.00265605i	$-0.000845449\pi$
$258$		0			0
$259$	−4.28149	−	8.25085i	−0.266039	−	0.512683i
$260$	−32.1288	+	7.33318i	−1.99254	+	0.454785i
$261$		0			0
$262$	29.6912	−	43.5490i	1.83433	−	2.69047i
$263$	−14.1051	+	8.14361i	−0.869760	+	0.502156i	−0.867268	−	0.497841i	$-0.834126\pi$
$263$	−14.1051	+	8.14361i	−0.869760	+	0.502156i	−0.00249156	+	0.999997i	$0.500793\pi$
$264$		0			0
$265$	−1.45971	−	3.03113i	−0.0896695	−	0.186201i
$266$	18.7612	−	21.4716i	1.15033	−	1.31651i
$267$		0			0
$268$	11.4174	−	7.78426i	0.697430	−	0.475500i
$269$	−2.87605	+	2.66859i	−0.175356	+	0.162707i	−0.762968	−	0.646436i	$-0.776259\pi$
$269$	−2.87605	+	2.66859i	−0.175356	+	0.162707i	0.587612	+	0.809143i	$0.300068\pi$
$270$		0			0
$271$	−8.41985	−	12.3496i	−0.511469	−	0.750188i	0.480455	−	0.877019i	$-0.340472\pi$
$271$	−8.41985	−	12.3496i	−0.511469	−	0.750188i	−0.991924	+	0.126832i	$0.959519\pi$
$272$	41.8313	+	20.1449i	2.53640	+	1.22146i
$273$		0			0
$274$	−42.7892	+	20.6062i	−2.58499	+	1.24487i
$275$	−13.1775	−	7.60804i	−0.794634	−	0.458782i
$276$		0			0
$277$	−11.0372	−	7.52505i	−0.663162	−	0.452136i	0.184387	−	0.982854i	$-0.440970\pi$
$277$	−11.0372	−	7.52505i	−0.663162	−	0.452136i	−0.847549	+	0.530717i	$0.821923\pi$
$278$	0.339202	−	0.0511264i	0.0203440	−	0.00306636i
$279$		0			0
$280$	6.21881	+	23.9286i	0.371645	+	1.43001i
$281$	−26.5427	−	6.05820i	−1.58341	−	0.361402i	−0.661846	−	0.749640i	$-0.730227\pi$
$281$	−26.5427	−	6.05820i	−1.58341	−	0.361402i	−0.921559	+	0.388238i	$0.873084\pi$
$282$		0			0
$283$	−0.703628	−	2.28111i	−0.0418264	−	0.135598i	0.932251	−	0.361811i	$-0.117841\pi$
$283$	−0.703628	−	2.28111i	−0.0418264	−	0.135598i	−0.974078	+	0.226213i	$0.927365\pi$
$284$	33.9530	+	13.3256i	2.01474	+	0.790728i
$285$		0			0
$286$	−52.4460	−	41.8243i	−3.10120	−	2.47312i
$287$	−0.485111	+	4.03220i	−0.0286352	+	0.238013i
$288$		0			0
$289$	7.76439	+	19.7833i	0.456729	+	1.16373i
$290$	1.67566	+	22.3601i	0.0983980	+	1.31303i
$291$		0			0
$292$	47.8140	−	51.5312i	2.79810	−	3.01564i
$293$	10.8221			0.632233			0.316116	−	0.948720i	$-0.397621\pi$
$293$	10.8221			0.632233			0.316116	+	0.948720i	$0.397621\pi$
$294$		0			0
$295$	12.6108			0.734227
$296$	15.4973	−	16.7021i	0.900763	−	0.970792i
$297$		0			0
$298$	1.85896	+	24.8061i	0.107687	+	1.43698i
$299$	−3.35529	−	8.54914i	−0.194041	−	0.494409i
$300$		0			0
$301$	24.2415	+	8.68801i	1.39726	+	0.500769i
$302$	3.20980	+	2.55973i	0.184703	+	0.147296i
$303$		0			0
$304$	29.4564	+	11.5608i	1.68944	+	0.663057i
$305$	−0.357671	−	1.15954i	−0.0204802	−	0.0663952i
$306$		0			0
$307$	13.4713	+	3.07473i	0.768847	+	0.175484i	0.588915	−	0.808195i	$-0.299555\pi$
$307$	13.4713	+	3.07473i	0.768847	+	0.175484i	0.179932	+	0.983679i	$0.442412\pi$
$308$	−37.4716	+	49.9796i	−2.13514	+	2.84785i
$309$		0			0
$310$	9.84056	−	1.48323i	0.558906	−	0.0842416i
$311$	5.81425	+	3.96409i	0.329696	+	0.224783i	0.716842	−	0.697235i	$-0.245587\pi$
$311$	5.81425	+	3.96409i	0.329696	+	0.224783i	−0.387146	+	0.922018i	$0.626539\pi$
$312$		0			0
$313$	−11.6165	−	6.70679i	−0.656603	−	0.379090i	0.134378	−	0.990930i	$-0.457096\pi$
$313$	−11.6165	−	6.70679i	−0.656603	−	0.379090i	−0.790982	+	0.611840i	$0.790430\pi$
$314$	−5.33841	+	2.57084i	−0.301264	+	0.145081i
$315$		0			0
$316$	−9.07434	−	4.36997i	−0.510472	−	0.245830i
$317$	−8.40996	−	12.3351i	−0.472350	−	0.692810i	0.513941	−	0.857826i	$-0.328185\pi$
$317$	−8.40996	−	12.3351i	−0.472350	−	0.692810i	−0.986291	+	0.165015i	$0.947233\pi$
$318$		0			0
$319$	−23.2209	+	21.5458i	−1.30012	+	1.20633i
$320$	−1.06601	+	0.726793i	−0.0595918	+	0.0406290i
$321$		0			0
$322$	−11.3313	+	4.84250i	−0.631468	+	0.269862i
$323$	11.3118	+	23.4891i	0.629403	+	1.30697i
$324$		0			0
$325$	−12.7646	+	7.36962i	−0.708050	+	0.408793i
$326$	−29.9412	+	43.9156i	−1.65829	+	2.43226i
$327$		0			0
$328$	−9.70503	+	2.21511i	−0.535871	+	0.122309i
$329$	9.64622	+	1.90055i	0.531813	+	0.104781i
$330$		0			0
$331$	−0.510332	+	6.80991i	−0.0280504	+	0.374307i	0.965459	+	0.260556i	$0.0839057\pi$
$331$	−0.510332	+	6.80991i	−0.0280504	+	0.374307i	−0.993509	+	0.113751i	$0.963713\pi$
$332$	−42.7375	+	13.1828i	−2.34553	+	0.723499i
$333$		0			0
$334$	12.1527	−	39.3980i	0.664965	−	2.15576i
$335$	−2.73665	+	3.43165i	−0.149519	+	0.187491i
$336$		0			0
$337$	−13.1306	−	16.4652i	−0.715268	−	0.896918i	0.282791	−	0.959181i	$-0.408740\pi$
$337$	−13.1306	−	16.4652i	−0.715268	−	0.896918i	−0.998060	+	0.0622633i	$0.980168\pi$
$338$	−29.5480	+	11.5967i	−1.60720	+	0.630779i
$339$		0			0
$340$	−39.9783	−	6.02575i	−2.16813	−	0.326792i
$341$	10.3059	+	9.56249i	0.558096	+	0.517838i
$342$		0			0
$343$	−1.65716	−	18.4460i	−0.0894782	−	0.995989i
$344$			63.1192i			3.40316i
$345$		0			0
$346$	−2.52103	+	16.7259i	−0.135531	+	0.899193i
$347$	3.31948	−	0.248760i	0.178199	−	0.0133542i	0.0146682	−	0.999892i	$-0.495331\pi$
$347$	3.31948	−	0.248760i	0.178199	−	0.0133542i	0.163531	+	0.986538i	$0.447712\pi$
$348$		0			0
$349$	24.3589	−	19.4256i	1.30390	−	1.03983i	0.307814	−	0.951447i	$-0.400403\pi$
$349$	24.3589	−	19.4256i	1.30390	−	1.03983i	0.996087	−	0.0883794i	$-0.0281688\pi$
$350$	10.3952	+	16.8240i	0.555649	+	0.899279i
$351$		0			0
$352$	−30.9469	−	9.54585i	−1.64947	−	0.508796i
$353$	2.04368	−	5.20722i	0.108774	−	0.277152i	−0.866114	−	0.499846i	$-0.833390\pi$
$353$	2.04368	−	5.20722i	0.108774	−	0.277152i	0.974888	+	0.222694i	$0.0714851\pi$
$354$		0			0
$355$	−11.5531	−	0.865787i	−0.613176	−	0.0459512i
$356$	1.67584	−	7.34232i	0.0888192	−	0.389142i
$357$		0			0
$358$	0.541307	+	2.37162i	0.0286089	+	0.125344i
$359$	−0.664847	−	4.41097i	−0.0350893	−	0.232802i	0.964411	−	0.264407i	$-0.0851763\pi$
$359$	−0.664847	−	4.41097i	−0.0350893	−	0.232802i	−0.999500	+	0.0316049i	$0.989938\pi$
$360$		0			0
$361$	−0.615682	−	1.06639i	−0.0324043	−	0.0561259i
$362$	29.4249	−	50.9654i	1.54654	−	2.67868i
$363$		0			0
$364$	23.7786	+	55.6411i	1.24634	+	2.91638i
$365$	−9.68806	+	20.1175i	−0.507096	+	1.05300i
$366$		0			0
$367$	25.7479	+	27.7497i	1.34403	+	1.44852i	0.785203	+	0.619238i	$0.212558\pi$
$367$	25.7479	+	27.7497i	1.34403	+	1.44852i	0.558828	+	0.829283i	$0.311251\pi$
$368$	−9.30173	−	10.0249i	−0.484886	−	0.522583i
$369$		0			0
$370$	−5.61595	+	11.6616i	−0.291960	+	0.606260i
$371$	−4.99767	+	3.63061i	−0.259466	+	0.188492i
$372$		0			0
$373$	10.4924	−	18.1734i	0.543276	−	0.940981i	−0.455437	−	0.890268i	$-0.650517\pi$
$373$	10.4924	−	18.1734i	0.543276	−	0.940981i	0.998713	−	0.0507135i	$-0.0161495\pi$
$374$	−41.1481	−	71.2706i	−2.12772	−	3.68531i
$375$		0			0
$376$	3.59168	+	23.8293i	0.185227	+	1.22890i
$377$	6.82789	+	29.9150i	0.351654	+	1.54070i
$378$		0			0
$379$	4.89184	−	21.4325i	0.251277	−	1.10092i	−0.679023	−	0.734117i	$-0.737597\pi$
$379$	4.89184	−	21.4325i	0.251277	−	1.10092i	0.930300	−	0.366799i	$-0.119546\pi$
$380$	−27.4779	−	2.05918i	−1.40959	−	0.105634i
$381$		0			0
$382$	−16.1695	+	41.1991i	−0.827301	+	2.10793i
$383$	−14.8908	−	4.59319i	−0.760883	−	0.234701i	−0.110054	−	0.993926i	$-0.535102\pi$
$383$	−14.8908	−	4.59319i	−0.760883	−	0.234701i	−0.650829	+	0.759224i	$0.725579\pi$
$384$		0			0
$385$	6.69416	−	18.6782i	0.341166	−	0.951930i
$386$	−8.01855	+	6.39458i	−0.408133	+	0.325475i
$387$		0			0
$388$	−81.8245	+	6.13190i	−4.15401	+	0.311300i
$389$	1.97603	−	13.1101i	0.100189	−	0.664709i	−0.881209	−	0.472726i	$-0.843270\pi$
$389$	1.97603	−	13.1101i	0.100189	−	0.664709i	0.981398	−	0.191983i	$-0.0614919\pi$
$390$		0			0
$391$		−	11.2671i		−	0.569801i
$392$	41.1916	−	19.0777i	2.08049	−	0.963569i
$393$		0			0
$394$	11.1166	+	10.3147i	0.560044	+	0.519645i
$395$	3.16341	+	0.476807i	0.159168	+	0.0239908i
$396$		0			0
$397$	27.0536	−	10.6178i	1.35778	−	0.532890i	0.428929	−	0.903338i	$-0.358891\pi$
$397$	27.0536	−	10.6178i	1.35778	−	0.532890i	0.928853	+	0.370448i	$0.120796\pi$
$398$	−16.9526	−	21.2579i	−0.849757	−	1.06556i
$399$		0			0
$400$	−13.6841	+	17.1594i	−0.684207	+	0.857968i
$401$	1.37674	−	4.46328i	0.0687512	−	0.222886i	−0.914677	−	0.404187i	$-0.867555\pi$
$401$	1.37674	−	4.46328i	0.0687512	−	0.222886i	0.983428	+	0.181301i	$0.0580308\pi$
$402$		0			0
$403$	13.0133	−	4.01408i	0.648239	−	0.199955i
$404$	3.63980	−	48.5698i	0.181087	−	2.41644i
$405$		0			0
$406$	39.8470	−	10.3559i	1.97757	−	0.513953i
$407$	−17.8269	+	4.06888i	−0.883648	+	0.201687i
$408$		0			0
$409$	3.01014	−	4.41506i	0.148842	−	0.218311i	−0.744576	−	0.667538i	$-0.767348\pi$
$409$	3.01014	−	4.41506i	0.148842	−	0.218311i	0.893418	+	0.449227i	$0.148301\pi$
$410$	4.89742	−	2.82753i	0.241867	−	0.139642i
$411$		0			0
$412$	27.6398	+	57.3946i	1.36172	+	2.82763i
$413$	−4.13321	−	22.7829i	−0.203382	−	1.12107i
$414$		0			0
$415$	11.7376	−	8.00255i	0.576175	−	0.392830i
$416$	−22.9964	+	21.3376i	−1.12749	+	1.04616i
$417$		0			0
$418$	−31.5960	−	46.3428i	−1.54541	−	2.26670i
$419$	−3.22151	−	1.55140i	−0.157381	−	0.0757907i	0.353535	−	0.935421i	$-0.384979\pi$
$419$	−3.22151	−	1.55140i	−0.157381	−	0.0757907i	−0.510916	+	0.859631i	$0.670694\pi$
$420$		0			0
$421$	25.2515	−	12.1605i	1.23068	−	0.592665i	0.298415	−	0.954436i	$-0.403542\pi$
$421$	25.2515	−	12.1605i	1.23068	−	0.592665i	0.932267	+	0.361771i	$0.117828\pi$
$422$	19.6188	+	11.3269i	0.955026	+	0.551384i
$423$		0			0
$424$	−12.5101	−	8.52923i	−0.607543	−	0.414216i
$425$	−17.8804	+	2.69504i	−0.867327	+	0.130728i
$426$		0			0
$427$	−1.97763	+	1.02622i	−0.0957040	+	0.0496623i
$428$	−32.6011	−	7.44099i	−1.57583	−	0.359674i
$429$		0			0
$430$	−10.5690	−	34.2640i	−0.509684	−	1.65236i
$431$	36.6098	+	14.3683i	1.76343	+	0.692096i	0.998869	+	0.0475461i	$0.0151401\pi$
$431$	36.6098	+	14.3683i	1.76343	+	0.692096i	0.764562	+	0.644550i	$0.222955\pi$
$432$		0			0
$433$	−12.9887	−	10.3581i	−0.624197	−	0.497780i	0.259560	−	0.965727i	$-0.416423\pi$
$433$	−12.9887	−	10.3581i	−0.624197	−	0.497780i	−0.883757	+	0.467947i	$0.844994\pi$
$434$	−5.90490	−	17.2920i	−0.283444	−	0.830045i
$435$		0			0
$436$	25.6507	+	65.3570i	1.22845	+	3.13003i
$437$	−0.573858	−	7.65761i	−0.0274514	−	0.366313i
$438$		0			0
$439$	0.169525	−	0.182705i	0.00809099	−	0.00872002i	−0.728993	−	0.684521i	$-0.760012\pi$
$439$	0.169525	−	0.182705i	0.00809099	−	0.00872002i	0.737084	+	0.675801i	$0.236202\pi$
$440$	48.6337			2.31852
$441$		0			0
$442$	−79.7172			−3.79176
$443$	−9.53746	+	10.2789i	−0.453138	+	0.488367i	−0.917756	−	0.397144i	$-0.870001\pi$
$443$	−9.53746	+	10.2789i	−0.453138	+	0.488367i	0.464618	+	0.885511i	$0.346192\pi$
$444$		0			0
$445$	0.178766	+	2.38546i	0.00847431	+	0.113082i
$446$	−8.35667	−	21.2924i	−0.395700	−	1.00823i
$447$		0			0
$448$	1.66243	+	1.68767i	0.0785423	+	0.0797348i
$449$	−9.88630	−	7.88406i	−0.466564	−	0.372072i	0.361807	−	0.932253i	$-0.382160\pi$
$449$	−9.88630	−	7.88406i	−0.466564	−	0.372072i	−0.828370	+	0.560181i	$0.810732\pi$
$450$		0			0
$451$	7.43672	+	2.91870i	0.350182	+	0.137436i
$452$	−18.1540	−	58.8538i	−0.853893	−	2.76825i
$453$		0			0
$454$	23.0219	+	5.25460i	1.08047	+	0.246610i
$455$	−12.4267	−	14.6621i	−0.582573	−	0.687369i
$456$		0			0
$457$	−21.8838	+	3.29845i	−1.02368	+	0.154295i	−0.639362	−	0.768906i	$-0.720801\pi$
$457$	−21.8838	+	3.29845i	−1.02368	+	0.154295i	−0.384318	+	0.923201i	$0.625563\pi$
$458$	17.3212	+	11.8094i	0.809367	+	0.551817i
$459$		0			0
$460$	10.3130	+	5.95421i	0.480846	+	0.277617i
$461$	14.1890	−	6.83305i	0.660846	−	0.318247i	−0.0732289	−	0.997315i	$-0.523330\pi$
$461$	14.1890	−	6.83305i	0.660846	−	0.318247i	0.734075	+	0.679068i	$0.237616\pi$
$462$		0			0
$463$	28.6492	+	13.7967i	1.33144	+	0.641189i	0.958081	−	0.286497i	$-0.0924908\pi$
$463$	28.6492	+	13.7967i	1.33144	+	0.641189i	0.373362	+	0.927686i	$0.378205\pi$
$464$	25.7385	+	37.7515i	1.19488	+	1.75257i
$465$		0			0
$466$	−7.28079	+	6.75558i	−0.337276	+	0.312946i
$467$	8.79170	−	5.99408i	0.406832	−	0.277373i	−0.342565	−	0.939494i	$-0.611296\pi$
$467$	8.79170	−	5.99408i	0.406832	−	0.277373i	0.749397	+	0.662121i	$0.230343\pi$
$468$		0			0
$469$	7.09664	+	3.81936i	0.327693	+	0.176362i
$470$	−5.93984	−	12.3342i	−0.273984	−	0.568934i
$471$		0			0
$472$	49.1510	−	28.3773i	2.26236	−	1.30617i
$473$	28.5353	−	41.8537i	1.31206	−	1.92443i
$474$		0			0
$475$	−12.0150	+	2.74235i	−0.551288	+	0.125828i
$476$	2.21673	+	74.2005i	0.101604	+	3.40098i
$477$		0			0
$478$	−2.80926	+	37.4869i	−0.128492	+	1.71461i
$479$	−34.6322	+	10.6826i	−1.58238	+	0.488101i	−0.956480	−	0.291799i	$-0.905746\pi$
$479$	−34.6322	+	10.6826i	−1.58238	+	0.488101i	−0.625904	+	0.779900i	$0.715270\pi$
$480$		0			0
$481$	−5.22081	+	16.9254i	−0.238048	+	0.771734i
$482$	−16.6928	+	20.9321i	−0.760337	+	0.953432i
$483$		0			0
$484$	45.5004	+	57.0556i	2.06820	+	2.59344i
$485$	24.2615	−	9.52195i	1.10166	−	0.432369i
$486$		0			0
$487$	−13.5513	−	2.04254i	−0.614070	−	0.0925561i	−0.165359	−	0.986233i	$-0.552878\pi$
$487$	−13.5513	−	2.04254i	−0.614070	−	0.0925561i	−0.448710	+	0.893677i	$0.648117\pi$
$488$	−4.00329	−	3.71451i	−0.181221	−	0.168148i
$489$		0			0
$490$	−19.1662	+	17.2536i	−0.865842	+	0.779439i
$491$			11.5276i			0.520234i	0.965577	+	0.260117i	$0.0837612\pi$
$491$			11.5276i			0.520234i	−0.965577	+	0.260117i	$0.916239\pi$
$492$		0			0
$493$	−5.61055	+	37.2236i	−0.252687	+	1.67647i
$494$	−54.1793	+	4.06018i	−2.43764	+	0.182676i
$495$		0			0
$496$	15.8544	−	12.6435i	0.711884	−	0.567709i
$497$	2.22242	+	21.1559i	0.0996891	+	0.948971i
$498$		0			0
$499$	−31.2789	−	9.64825i	−1.40023	−	0.431915i	−0.499511	−	0.866308i	$-0.666487\pi$
$499$	−31.2789	−	9.64825i	−1.40023	−	0.431915i	−0.900724	+	0.434393i	$0.856963\pi$
$500$	18.9233	−	48.2157i	0.846274	−	2.15627i
$501$		0			0
$502$	−22.0850	−	1.65504i	−0.985703	−	0.0738682i
$503$	4.85678	−	21.2790i	0.216553	−	0.948782i	−0.743450	−	0.668792i	$-0.766812\pi$
$503$	4.85678	−	21.2790i	0.216553	−	0.948782i	0.960003	−	0.279990i	$-0.0903312\pi$
$504$		0			0
$505$	3.44255	+	15.0828i	0.153192	+	0.671176i
$506$	3.61278	+	23.9692i	0.160608	+	1.06556i
$507$		0			0
$508$	6.88117	+	11.9185i	0.305303	+	0.528800i
$509$	−14.1326	+	24.4783i	−0.626414	+	1.08498i	0.361851	+	0.932236i	$0.382145\pi$
$509$	−14.1326	+	24.4783i	−0.626414	+	1.08498i	−0.988266	+	0.152746i	$0.951188\pi$
$510$		0			0
$511$	39.5199	+	10.9091i	1.74826	+	0.482590i
$512$	21.9770	−	45.6358i	0.971256	−	2.01683i
$513$		0			0
$514$	4.31429	+	4.64969i	0.190295	+	0.205089i
$515$	−13.7629	−	14.8328i	−0.606464	−	0.653613i
$516$		0			0
$517$	8.39129	−	17.4247i	0.369048	−	0.766337i
$518$	22.9088	+	6.32377i	1.00656	+	0.277850i
$519$		0			0
$520$	23.5548	−	40.7981i	1.03295	−	1.78912i
$521$	17.2330	+	29.8485i	0.754993	+	1.30769i	0.945378	+	0.325976i	$0.105693\pi$
$521$	17.2330	+	29.8485i	0.754993	+	1.30769i	−0.190385	+	0.981709i	$0.560974\pi$
$522$		0			0
$523$	3.83310	+	25.4309i	0.167610	+	1.11202i	0.901509	+	0.432760i	$0.142460\pi$
$523$	3.83310	+	25.4309i	0.167610	+	1.11202i	−0.733900	+	0.679258i	$0.762302\pi$
$524$	20.8110	+	91.1789i	0.909132	+	3.98317i
$525$		0			0
$526$	9.26597	−	40.5968i	0.404015	−	1.77011i
$527$	16.6605	+	1.24853i	0.725743	+	0.0543869i
$528$		0			0
$529$	7.19040	−	18.3208i	0.312626	−	0.796558i
$530$	8.21923	+	2.53530i	0.357020	+	0.110126i
$531$		0			0
$532$	5.28579	+	50.3170i	0.229168	+	2.18152i
$533$	6.05029	−	4.82495i	0.262067	−	0.208992i
$534$		0			0
$535$	10.5919	−	0.793749i	0.457926	−	0.0343168i
$536$	−2.94415	+	19.5332i	−0.127168	+	0.843704i
$537$		0			0
$538$		−	10.0308i		−	0.432458i
$539$	−35.9385	−	5.97198i	−1.54798	−	0.257231i
$540$		0			0
$541$	−15.3893	−	14.2792i	−0.661639	−	0.613912i	0.276151	−	0.961114i	$-0.410941\pi$
$541$	−15.3893	−	14.2792i	−0.661639	−	0.613912i	−0.937790	+	0.347203i	$0.887132\pi$
$542$	37.7871	+	5.69550i	1.62310	+	0.244642i
$543$		0			0
$544$	−35.8259	+	14.0606i	−1.53602	+	0.602844i
$545$	−13.9046	−	17.4358i	−0.595608	−	0.746869i
$546$		0			0
$547$	6.04450	−	7.57956i	0.258444	−	0.324079i	−0.635633	−	0.771991i	$-0.719261\pi$
$547$	6.04450	−	7.57956i	0.258444	−	0.324079i	0.894077	+	0.447912i	$0.147832\pi$
$548$	24.8390	−	80.5262i	1.06107	−	3.43991i
$549$		0			0
$550$	37.1740	−	11.4667i	1.58511	−	0.488940i
$551$	−1.91730	+	25.5845i	−0.0816795	+	1.08994i
$552$		0			0
$553$	−0.175406	−	5.87136i	−0.00745902	−	0.249675i
$554$	33.2966	−	7.59973i	1.41464	−	0.322882i
$555$		0			0
$556$	−0.342879	+	0.502911i	−0.0145413	+	0.0213282i
$557$	−11.3834	+	6.57222i	−0.482331	+	0.278474i	−0.721387	−	0.692532i	$-0.756495\pi$
$557$	−11.3834	+	6.57222i	−0.482331	+	0.278474i	0.239057	+	0.971006i	$0.423162\pi$
$558$		0			0
$559$	−21.2899	−	44.2089i	−0.900467	−	1.86984i
$560$	−25.2014	−	13.5632i	−1.06496	−	0.573151i
$561$		0			0
$562$	57.5111	−	39.2104i	2.42596	−	1.65399i
$563$	−29.0678	+	26.9709i	−1.22506	+	1.13669i	−0.238874	+	0.971051i	$0.576778\pi$
$563$	−29.0678	+	26.9709i	−1.22506	+	1.13669i	−0.986186	+	0.165639i	$0.947031\pi$
$564$		0			0
$565$	11.0203	+	16.1638i	0.463628	+	0.680018i
$566$	5.49876	+	2.64806i	0.231130	+	0.111306i
$567$		0			0
$568$	−46.9770	+	22.6229i	−1.97111	+	0.949238i
$569$	−1.56892	−	0.905818i	−0.0657727	−	0.0379739i	0.466753	−	0.884388i	$-0.345424\pi$
$569$	−1.56892	−	0.905818i	−0.0657727	−	0.0379739i	−0.532526	+	0.846414i	$0.678757\pi$
$570$		0			0
$571$	12.4121	+	8.46246i	0.519432	+	0.354143i	0.794483	−	0.607287i	$-0.207742\pi$
$571$	12.4121	+	8.46246i	0.519432	+	0.354143i	−0.275050	+	0.961430i	$0.588695\pi$
$572$	117.698	−	17.7402i	4.92122	−	0.741754i
$573$		0			0
$574$	−6.71342	−	7.92106i	−0.280213	−	0.330619i
$575$	5.19255	+	1.18516i	0.216544	+	0.0494248i
$576$		0			0
$577$	−11.8691	−	38.4787i	−0.494117	−	1.60189i	−0.768219	−	0.640187i	$-0.778857\pi$
$577$	−11.8691	−	38.4787i	−0.494117	−	1.60189i	0.274102	−	0.961701i	$-0.411619\pi$
$578$	−50.5793	−	19.8509i	−2.10382	−	0.825689i
$579$		0			0
$580$	−31.1066	−	24.8067i	−1.29163	−	1.03004i
$581$	−18.3046	−	18.5825i	−0.759403	−	0.770933i
$582$		0			0
$583$	4.43935	+	11.3113i	0.183859	+	0.468465i
$584$	7.50964	+	100.209i	0.310751	+	4.14669i
$585$		0			0
$586$	−18.8193	+	20.2824i	−0.777418	+	0.837857i
$587$	22.8219			0.941960			0.470980	−	0.882144i	$-0.343900\pi$
$587$	22.8219			0.941960			0.470980	+	0.882144i	$0.343900\pi$
$588$		0			0
$589$	11.3868			0.469185
$590$	−21.9297	+	23.6346i	−0.902833	+	0.973023i
$591$		0			0
$592$	1.97099	+	26.3011i	0.0810073	+	1.08097i
$593$	−3.44606	−	8.78042i	−0.141513	−	0.360568i	0.842493	−	0.538708i	$-0.181087\pi$
$593$	−3.44606	−	8.78042i	−0.141513	−	0.360568i	−0.984005	+	0.178140i	$0.942992\pi$
$594$		0			0
$595$	−7.61981	−	22.3140i	−0.312382	−	0.914786i
$596$	−34.5094	−	27.5203i	−1.41356	−	1.12728i
$597$		0			0
$598$	21.8572	+	8.57833i	0.893809	+	0.350794i
$599$	2.67404	+	8.66903i	0.109258	+	0.354207i	0.993647	−	0.112545i	$-0.0359003\pi$
$599$	2.67404	+	8.66903i	0.109258	+	0.354207i	−0.884388	+	0.466752i	$0.845424\pi$
$600$		0			0
$601$	12.4244	+	2.83578i	0.506800	+	0.115674i	0.468273	−	0.883584i	$-0.344876\pi$
$601$	12.4244	+	2.83578i	0.506800	+	0.115674i	0.0385269	+	0.999258i	$0.487733\pi$
$602$	−58.4380	+	30.3244i	−2.38176	+	1.23593i
$603$		0			0
$604$	−7.20337	+	1.08573i	−0.293101	+	0.0441779i
$605$	−19.1522	−	13.0578i	−0.778648	−	0.530873i
$606$		0			0
$607$	23.9400	+	13.8218i	0.971695	+	0.561009i	0.899753	−	0.436400i	$-0.143747\pi$
$607$	23.9400	+	13.8218i	0.971695	+	0.561009i	0.0719428	+	0.997409i	$0.477080\pi$
$608$	−23.6327	+	11.3809i	−0.958432	+	0.461556i
$609$		0			0
$610$	2.79515	+	1.34607i	0.113172	+	0.0545010i
$611$	−10.5532	−	15.4786i	−0.426935	−	0.626199i
$612$		0			0
$613$	−12.2109	+	11.3300i	−0.493192	+	0.457615i	−0.887129	−	0.461522i	$-0.847303\pi$
$613$	−12.2109	+	11.3300i	−0.493192	+	0.457615i	0.393937	+	0.919138i	$0.371113\pi$
$614$	−29.1887	+	19.9005i	−1.17796	+	0.803121i
$615$		0			0
$616$	−15.9398	−	87.8627i	−0.642234	−	3.54009i
$617$	11.1962	+	23.2491i	0.450741	+	0.935974i	0.995262	+	0.0972268i	$0.0309972\pi$
$617$	11.1962	+	23.2491i	0.450741	+	0.935974i	−0.544521	+	0.838747i	$0.683289\pi$
$618$		0			0
$619$	27.0938	−	15.6426i	1.08899	−	0.628729i	0.155683	−	0.987807i	$-0.450242\pi$
$619$	27.0938	−	15.6426i	1.08899	−	0.628729i	0.933308	+	0.359078i	$0.116909\pi$
$620$	−9.94723	+	14.5899i	−0.399490	+	0.585945i
$621$		0			0
$622$	−17.5402	+	4.00343i	−0.703297	+	0.160523i
$623$	4.25104	−	1.10480i	0.170314	−	0.0442630i
$624$		0			0
$625$	−0.137055	+	1.82887i	−0.00548219	+	0.0731547i
$626$	32.7704	−	10.1083i	1.30977	−	0.404010i
$627$		0			0
$628$	3.09894	−	10.0465i	0.123661	−	0.400899i
$629$	−13.5483	+	16.9891i	−0.540208	+	0.677399i
$630$		0			0
$631$	14.0265	+	17.5886i	0.558385	+	0.700193i	0.978258	−	0.207390i	$-0.0664970\pi$
$631$	14.0265	+	17.5886i	0.558385	+	0.700193i	−0.419873	+	0.907583i	$0.637926\pi$
$632$	13.4024	−	5.26007i	0.533121	−	0.209234i
$633$		0			0
$634$	37.7428	+	5.68880i	1.49896	+	0.225931i
$635$	−3.20446	−	2.97330i	−0.127165	−	0.117992i
$636$		0			0
$637$	−22.4160	+	27.2559i	−0.888152	+	1.07992i
$638$		−	80.9872i		−	3.20632i
$639$		0			0
$640$	−2.18117	+	14.4711i	−0.0862181	+	0.572020i
$641$	35.0911	−	2.62971i	1.38601	−	0.103867i	0.639272	−	0.768981i	$-0.279236\pi$
$641$	35.0911	−	2.62971i	1.38601	−	0.103867i	0.746743	+	0.665113i	$0.231617\pi$
$642$		0			0
$643$	−24.0098	+	19.1472i	−0.946853	+	0.755090i	−0.969611	−	0.244651i	$-0.921327\pi$
$643$	−24.0098	+	19.1472i	−0.946853	+	0.755090i	0.0227579	+	0.999741i	$0.492755\pi$
$644$	7.37690	−	20.5832i	0.290690	−	0.811092i
$645$		0			0
$646$	−63.6933	−	19.6468i	−2.50598	−	0.772992i
$647$	−5.41543	+	13.7983i	−0.212903	+	0.542467i	−0.996933	−	0.0782550i	$-0.975065\pi$
$647$	−5.41543	+	13.7983i	−0.212903	+	0.542467i	0.784031	+	0.620722i	$0.213160\pi$
$648$		0			0
$649$	−45.4205	−	3.40380i	−1.78291	−	0.133611i
$650$	8.38531	−	36.7384i	0.328899	−	1.44100i
$651$		0			0
$652$	−20.9862	−	91.9464i	−0.821882	−	3.60090i
$653$	0.943273	+	6.25820i	0.0369131	+	0.244902i	0.999676	−	0.0254438i	$-0.00809990\pi$
$653$	0.943273	+	6.25820i	0.0369131	+	0.244902i	−0.962763	+	0.270346i	$0.912862\pi$
$654$		0			0
$655$	−14.8532	−	25.7265i	−0.580362	−	1.00522i
$656$	5.76164	−	9.97946i	0.224954	−	0.389632i
$657$		0			0
$658$	−20.3364	+	14.7736i	−0.792797	+	0.575935i
$659$	10.2391	−	21.2617i	0.398858	−	0.828238i	−0.600727	−	0.799454i	$-0.705122\pi$
$659$	10.2391	−	21.2617i	0.398858	−	0.828238i	0.999586	−	0.0287840i	$-0.00916351\pi$
$660$		0			0
$661$	−29.4570	−	31.7471i	−1.14574	−	1.23482i	−0.968056	−	0.250732i	$-0.919329\pi$
$661$	−29.4570	−	31.7471i	−1.14574	−	1.23482i	−0.177688	−	0.984087i	$-0.556862\pi$
$662$	−11.8754	−	12.7987i	−0.461552	−	0.497435i
$663$		0			0
$664$	27.7400	−	57.6027i	1.07652	−	2.23542i
$665$	−6.31526	−	14.7775i	−0.244895	−	0.573047i
$666$		0			0
$667$	5.54394	−	9.60239i	0.214662	−	0.371806i
$668$	36.5788	+	63.3564i	1.41528	+	2.45133i
$669$		0			0
$670$	−1.67253	−	11.0965i	−0.0646153	−	0.428694i
$671$	0.975260	+	4.27289i	0.0376495	+	0.164953i
$672$		0			0
$673$	−4.90014	+	21.4689i	−0.188886	+	0.827565i	0.788319	+	0.615267i	$0.210952\pi$
$673$	−4.90014	+	21.4689i	−0.188886	+	0.827565i	−0.977205	+	0.212298i	$0.931905\pi$
$674$	53.6923	+	4.02368i	2.06815	+	0.154986i
$675$		0			0
$676$	20.5771	−	52.4297i	0.791428	−	2.01653i
$677$	44.1471	+	13.6176i	1.69671	+	0.523366i	0.984011	−	0.178106i	$-0.0569969\pi$
$677$	44.1471	+	13.6176i	1.69671	+	0.523366i	0.712698	+	0.701471i	$0.247473\pi$
$678$		0			0
$679$	−25.1543	−	40.7106i	−0.965335	−	1.56233i
$680$	45.1859	−	36.0346i	1.73280	−	1.38186i
$681$		0			0
$682$	−35.8434	+	2.68609i	−1.37251	+	0.102856i
$683$	−3.35856	+	22.2826i	−0.128512	+	0.852620i	0.827958	+	0.560790i	$0.189502\pi$
$683$	−3.35856	+	22.2826i	−0.128512	+	0.852620i	−0.956470	+	0.291831i	$0.905736\pi$
$684$		0			0
$685$			26.7671i			1.02272i
$686$	37.4525	+	28.9712i	1.42994	+	1.10613i
$687$		0			0
$688$	−53.5609	−	49.6973i	−2.04199	−	1.89469i
$689$	11.6390	+	1.75430i	0.443410	+	0.0668334i
$690$		0			0
$691$	10.1005	−	3.96414i	0.384240	−	0.150803i	−0.165356	−	0.986234i	$-0.552877\pi$
$691$	10.1005	−	3.96414i	0.384240	−	0.150803i	0.549595	+	0.835431i	$0.314782\pi$
$692$	−18.7132	−	23.4656i	−0.711368	−	0.892027i
$693$		0			0
$694$	−5.30625	+	6.65383i	−0.201423	+	0.252576i
$695$	0.0569868	−	0.184747i	0.00216163	−	0.00700784i
$696$		0			0
$697$	9.07209	−	2.79837i	0.343630	−	0.105996i
$698$	−5.95268	+	79.4330i	−0.225312	+	3.00658i
$699$		0			0
$700$	−34.4292	−	6.78342i	−1.30130	−	0.256389i
$701$	−8.35288	+	1.90649i	−0.315484	+	0.0720071i	−0.377331	−	0.926079i	$-0.623158\pi$
$701$	−8.35288	+	1.90649i	−0.315484	+	0.0720071i	0.0618470	+	0.998086i	$0.480301\pi$
$702$		0			0
$703$	−8.34275	+	12.2366i	−0.314653	+	0.461511i
$704$	4.03565	−	2.32998i	0.152099	−	0.0878145i
$705$		0			0
$706$	6.20528	+	12.8854i	0.233539	+	0.484948i
$707$	26.1206	−	11.1628i	0.982368	−	0.419821i
$708$		0			0
$709$	26.2839	−	17.9200i	0.987112	−	0.673001i	0.0417852	−	0.999127i	$-0.486695\pi$
$709$	26.2839	−	17.9200i	0.987112	−	0.673001i	0.945327	+	0.326125i	$0.105743\pi$
$710$	21.7132	−	20.1469i	0.814881	−	0.756099i
$711$		0			0
$712$	6.06463	+	8.89518i	0.227282	+	0.333361i
$713$	−4.43370	−	2.13516i	−0.166043	−	0.0799623i
$714$		0			0
$715$	−34.0633	+	16.4040i	−1.27389	+	0.613475i
$716$	−3.73811	−	2.15820i	−0.139700	−	0.0806557i
$717$		0			0
$718$	9.42304	+	6.42452i	0.351665	+	0.239761i
$719$	−28.0213	+	4.22352i	−1.04502	+	0.157511i	−0.649044	−	0.760751i	$-0.724831\pi$
$719$	−28.0213	+	4.22352i	−1.04502	+	0.157511i	−0.395973	+	0.918262i	$0.629593\pi$
$720$		0			0
$721$	−22.2865	+	29.7258i	−0.829993	+	1.10705i
$722$	3.06925	+	0.700536i	0.114226	+	0.0260713i
$723$		0			0
$724$	30.7790	+	99.7832i	1.14389	+	3.70841i
$725$	−16.5647	−	6.50116i	−0.615197	−	0.241447i
$726$		0			0
$727$	21.5242	+	17.1650i	0.798288	+	0.636613i	0.935260	−	0.353962i	$-0.115166\pi$
$727$	21.5242	+	17.1650i	0.798288	+	0.636613i	−0.136972	+	0.990575i	$0.543737\pi$
$728$	−81.4270	−	29.1829i	−3.01788	−	1.08159i
$729$		0			0
$730$	−20.8562	−	53.1407i	−0.771922	−	1.96683i
$731$	−4.49859	−	60.0295i	−0.166386	−	2.22027i
$732$		0			0
$733$	−22.2069	+	23.9333i	−0.820231	+	0.883998i	−0.994924	−	0.100624i	$-0.967916\pi$
$733$	−22.2069	+	23.9333i	−0.820231	+	0.883998i	0.174694	+	0.984623i	$0.444106\pi$
$734$	−96.7824			−3.57230
$735$		0			0
$736$	11.3360			0.417849
$737$	10.7829	−	11.6212i	0.397194	−	0.428073i
$738$		0			0
$739$	−1.19409	−	15.9340i	−0.0439254	−	0.586143i	−0.975128	−	0.221642i	$-0.928858\pi$
$739$	−1.19409	−	15.9340i	−0.0439254	−	0.586143i	0.931203	−	0.364502i	$-0.118761\pi$
$740$	−8.39069	−	21.3791i	−0.308448	−	0.785913i
$741$		0			0
$742$	1.88645	−	15.6800i	0.0692536	−	0.575630i
$743$	25.5481	+	20.3739i	0.937270	+	0.747448i	0.967704	−	0.252089i	$-0.0811177\pi$
$743$	25.5481	+	20.3739i	0.937270	+	0.747448i	−0.0304345	+	0.999537i	$0.509689\pi$
$744$		0			0
$745$	13.0510	+	5.12213i	0.478151	+	0.187660i
$746$	15.8139	+	51.2674i	0.578988	+	1.87703i
$747$		0			0
$748$	142.364	+	32.4937i	5.20536	+	1.18809i
$749$	−4.90551	−	18.8753i	−0.179244	−	0.689689i
$750$		0			0
$751$	−19.2997	+	2.90896i	−0.704257	+	0.106150i	−0.491400	−	0.870934i	$-0.663515\pi$
$751$	−19.2997	+	2.90896i	−0.704257	+	0.106150i	−0.212856	+	0.977083i	$0.568277\pi$
$752$	−23.0487	−	15.7143i	−0.840499	−	0.573042i
$753$		0			0
$754$	−67.9391	−	39.2246i	−2.47419	−	1.42848i
$755$	2.08474	−	1.00396i	0.0758714	−	0.0365377i
$756$		0			0
$757$	3.89317	+	1.87485i	0.141500	+	0.0681426i	0.503294	−	0.864115i	$-0.332121\pi$
$757$	3.89317	+	1.87485i	0.141500	+	0.0681426i	−0.361794	+	0.932258i	$0.617836\pi$
$758$	31.6613	+	46.4387i	1.14999	+	1.68673i
$759$		0			0
$760$	28.8750	−	26.7921i	1.04741	−	0.971851i
$761$	−24.0556	+	16.4008i	−0.872015	+	0.594530i	−0.914508	−	0.404567i	$-0.867422\pi$
$761$	−24.0556	+	16.4008i	−0.872015	+	0.594530i	0.0424931	+	0.999097i	$0.486470\pi$
$762$		0			0
$763$	−26.9427	+	30.8350i	−0.975390	+	1.11630i
$764$	−34.0737	−	70.7548i	−1.23274	−	2.55982i
$765$		0			0
$766$	34.5030	−	19.9203i	1.24664	−	0.719751i
$767$	−24.8540	+	36.4541i	−0.897425	+	1.31628i
$768$		0			0
$769$	23.5088	−	5.36572i	0.847748	−	0.193493i	0.223485	−	0.974707i	$-0.428257\pi$
$769$	23.5088	−	5.36572i	0.847748	−	0.193493i	0.624263	+	0.781214i	$0.285399\pi$
$770$	23.3651	+	45.0269i	0.842020	+	1.62266i
$771$		0			0
$772$	1.35996	−	18.1474i	0.0489461	−	0.653141i
$773$	25.8671	−	7.97894i	0.930374	−	0.286982i	0.207717	−	0.978189i	$-0.433397\pi$
$773$	25.8671	−	7.97894i	0.930374	−	0.286982i	0.722657	+	0.691207i	$0.242921\pi$
$774$		0			0
$775$	−2.32789	+	7.54682i	−0.0836202	+	0.271090i
$776$	73.1336	−	91.7066i	2.62534	−	3.29208i
$777$		0			0
$778$	21.1343	+	26.5015i	0.757700	+	0.950126i
$779$	6.02326	−	2.36396i	0.215806	−	0.0846975i
$780$		0			0
$781$	41.3775	+	6.23666i	1.48060	+	0.223165i
$782$	21.1164	+	19.5931i	0.755120	+	0.700649i
$783$		0			0
$784$	−16.2438	+	49.9749i	−0.580135	+	1.78482i
$785$			3.33948i			0.119191i
$786$		0			0
$787$	−2.42860	+	16.1127i	−0.0865702	+	0.574356i	0.902926	+	0.429796i	$0.141415\pi$
$787$	−2.42860	+	16.1127i	−0.0865702	+	0.574356i	−0.989496	+	0.144560i	$0.953823\pi$
$788$	−26.8330	+	2.01085i	−0.955884	+	0.0716336i
$789$		0			0
$790$	−6.39469	+	5.09959i	−0.227513	+	0.181435i
$791$	25.5900	−	25.2073i	0.909876	−	0.896268i
$792$		0			0
$793$	4.05682	+	1.25136i	0.144062	+	0.0444372i
$794$	−27.1460	+	69.1669i	−0.963376	+	2.45464i
$795$		0			0
$796$	48.1105	+	3.60539i	1.70523	+	0.127790i
$797$	0.878178	−	3.84755i	0.0311067	−	0.136287i	−0.956990	−	0.290120i	$-0.906305\pi$
$797$	0.878178	−	3.84755i	0.0311067	−	0.136287i	0.988097	+	0.153833i	$0.0491618\pi$
$798$		0			0
$799$	−5.11421	−	22.4068i	−0.180928	−	0.792696i
$800$	−2.71151	−	17.9897i	−0.0958664	−	0.636032i
$801$		0			0
$802$	5.97082	+	10.3418i	0.210837	+	0.365180i
$803$	40.3237	−	69.8427i	1.42299	−	2.46469i
$804$		0			0
$805$	−0.311967	+	6.93813i	−0.0109954	+	0.244537i
$806$	−15.1067	+	31.3695i	−0.532112	+	1.10494i
$807$		0			0
$808$	47.3576	+	51.0393i	1.66603	+	1.79556i
$809$	12.0266	+	12.9616i	0.422832	+	0.455705i	0.908157	−	0.418629i	$-0.137489\pi$
$809$	12.0266	+	12.9616i	0.422832	+	0.455705i	−0.485325	+	0.874334i	$0.661299\pi$
$810$		0			0
$811$	−0.726017	+	1.50759i	−0.0254939	+	0.0529386i	−0.913327	−	0.407227i	$-0.866496\pi$
$811$	−0.726017	+	1.50759i	−0.0254939	+	0.0529386i	0.887833	+	0.460166i	$0.152210\pi$
$812$	−34.6210	+	64.3282i	−1.21496	+	2.25748i
$813$		0			0
$814$	23.3748	−	40.4863i	0.819285	−	1.41904i
$815$	14.9782	+	25.9430i	0.524664	+	0.908745i
$816$		0			0
$817$	−6.11487	−	40.5695i	−0.213932	−	1.41935i
$818$	3.04001	+	13.3192i	0.106291	+	0.465693i
$819$		0			0
$820$	−2.23284	+	9.78270i	−0.0779741	+	0.341627i
$821$	−24.9736	−	1.87151i	−0.871584	−	0.0653162i	−0.368576	−	0.929598i	$-0.620155\pi$
$821$	−24.9736	−	1.87151i	−0.871584	−	0.0653162i	−0.503009	+	0.864281i	$0.667774\pi$
$822$		0			0
$823$	−10.4231	+	26.5576i	−0.363326	+	0.925740i	0.625974	+	0.779844i	$0.284702\pi$
$823$	−10.4231	+	26.5576i	−0.363326	+	0.925740i	−0.989300	+	0.145896i	$0.953393\pi$
$824$	−87.0188	−	26.8418i	−3.03145	−	0.935077i
$825$		0			0
$826$	49.8864	+	31.8724i	1.73577	+	1.10898i
$827$	28.8572	−	23.0128i	1.00346	−	0.800234i	0.0235617	−	0.999722i	$-0.492499\pi$
$827$	28.8572	−	23.0128i	1.00346	−	0.800234i	0.979900	+	0.199488i	$0.0639280\pi$
$828$		0			0
$829$	−2.46374	+	0.184632i	−0.0855691	+	0.00641252i	−0.117446	−	0.993079i	$-0.537471\pi$
$829$	−2.46374	+	0.184632i	−0.0855691	+	0.00641252i	0.0318767	+	0.999492i	$0.489852\pi$
$830$	−5.41322	+	35.9144i	−0.187896	+	1.24661i
$831$		0			0
$832$		−	4.51393i		−	0.156492i
$833$	−37.8156	+	21.0796i	−1.31023	+	0.730365i
$834$		0			0
$835$	−17.0342	−	15.8055i	−0.589494	−	0.546970i
$836$	98.4120	+	14.8332i	3.40365	+	0.513018i
$837$		0			0
$838$	8.50968	−	3.33980i	0.293962	−	0.115372i
$839$	−6.16745	−	7.73374i	−0.212924	−	0.266998i	0.663887	−	0.747832i	$-0.268905\pi$
$839$	−6.16745	−	7.73374i	−0.212924	−	0.266998i	−0.876812	+	0.480834i	$0.840334\pi$
$840$		0			0
$841$	−5.01616	+	6.29006i	−0.172971	+	0.216899i
$842$	−21.1209	+	68.4721i	−0.727873	+	2.35971i
$843$		0			0
$844$	−38.4108	+	11.8482i	−1.32216	+	0.407831i
$845$	−1.33693	+	17.8401i	−0.0459919	+	0.613719i
$846$		0			0
$847$	−17.3132	+	38.8805i	−0.594890	+	1.33595i
$848$	17.0875	−	3.90011i	0.586788	−	0.133930i
$849$		0			0
$850$	26.0426	−	38.1974i	0.893252	−	1.31016i
$851$	5.54294	−	3.20022i	0.190009	−	0.109702i
$852$		0			0
$853$	16.9290	+	35.1534i	0.579637	+	1.20363i	0.960314	+	0.278920i	$0.0899765\pi$
$853$	16.9290	+	35.1534i	0.579637	+	1.20363i	−0.380677	+	0.924708i	$0.624309\pi$
$854$	1.51573	−	5.49096i	0.0518671	−	0.187897i
$855$		0			0
$856$	39.4961	−	26.9280i	1.34995	−	0.920379i
$857$	17.4932	−	16.2313i	0.597557	−	0.554452i	−0.322334	−	0.946626i	$-0.604467\pi$
$857$	17.4932	−	16.2313i	0.597557	−	0.554452i	0.919891	+	0.392174i	$0.128277\pi$
$858$		0			0
$859$	17.1042	+	25.0872i	0.583587	+	0.855965i	0.998548	−	0.0538741i	$-0.0171570\pi$
$859$	17.1042	+	25.0872i	0.583587	+	0.855965i	−0.414960	+	0.909839i	$0.636205\pi$
$860$	57.3235	+	27.6056i	1.95472	+	0.941342i
$861$		0			0
$862$	−90.5919	+	43.6268i	−3.08557	+	1.48593i
$863$	4.90398	+	2.83131i	0.166933	+	0.0963791i	0.581139	−	0.813804i	$-0.302607\pi$
$863$	4.90398	+	2.83131i	0.166933	+	0.0963791i	−0.414206	+	0.910183i	$0.635941\pi$
$864$		0			0
$865$	7.87683	+	5.37033i	0.267820	+	0.182597i
$866$	41.9998	−	6.33045i	1.42721	−	0.215118i
$867$		0			0
$868$	29.6187	+	13.1890i	1.00532	+	0.447664i
$869$	−11.2650	−	2.57117i	−0.382140	−	0.0872210i
$870$		0			0
$871$	−4.52638	−	14.6742i	−0.153370	−	0.497215i
$872$	−93.4287	−	36.6681i	−3.16390	−	1.24174i
$873$		0			0
$874$	15.3495	+	12.2409i	0.519206	+	0.414053i
$875$	30.0429	−	3.15599i	1.01563	−	0.106692i
$876$		0			0
$877$	−13.4665	−	34.3120i	−0.454730	−	1.15863i	−0.956006	−	0.293346i	$-0.905231\pi$
$877$	−13.4665	−	34.3120i	−0.454730	−	1.15863i	0.501276	−	0.865287i	$-0.332864\pi$
$878$	0.0476194	+	0.635436i	0.00160708	+	0.0214449i
$879$		0			0
$880$	−38.2920	+	41.2690i	−1.29082	+	1.39118i
$881$	−0.0685756			−0.00231037			−0.00115518	−	0.999999i	$-0.500368\pi$
$881$	−0.0685756			−0.00231037			−0.00115518	+	0.999999i	$0.500368\pi$
$882$		0			0
$883$	−23.2531			−0.782530			−0.391265	−	0.920278i	$-0.627962\pi$
$883$	−23.2531			−0.782530			−0.391265	+	0.920278i	$0.627962\pi$
$884$	96.2100	−	103.690i	3.23589	−	3.48746i
$885$		0			0
$886$	−2.67906	−	35.7495i	−0.0900047	−	1.20103i
$887$	6.03735	+	15.3829i	0.202714	+	0.516508i	0.995690	−	0.0927459i	$-0.0295644\pi$
$887$	6.03735	+	15.3829i	0.202714	+	0.516508i	−0.792976	+	0.609254i	$0.791469\pi$
$888$		0			0
$889$	−4.32137	+	6.76376i	−0.144934	+	0.226849i
$890$	−4.78162	−	3.81321i	−0.160280	−	0.127819i
$891$		0			0
$892$	37.7811	+	14.8280i	1.26501	+	0.496478i
$893$	−4.61707	−	14.9682i	−0.154504	−	0.500891i
$894$		0			0
$895$	1.33666	+	0.305085i	0.0446797	+	0.0101979i
$896$	26.8587	−	0.802400i	0.897285	−	0.0268063i
$897$		0			0
$898$	31.9680	−	4.81841i	1.06679	−	0.160792i
$899$	13.5846	+	9.26182i	0.453072	+	0.308899i
$900$		0			0
$901$	12.5056	+	7.22011i	0.416622	+	0.240537i
$902$	−18.4024	+	8.86211i	−0.612732	+	0.295076i
$903$		0			0
$904$	79.3248	+	38.2008i	2.63830	+	1.27054i
$905$	−18.6843	−	27.4048i	−0.621087	−	0.910967i
$906$		0			0
$907$	−26.3650	+	24.4631i	−0.875434	+	0.812284i	−0.983321	−	0.181879i	$-0.941782\pi$
$907$	−26.3650	+	24.4631i	−0.875434	+	0.812284i	0.107887	+	0.994163i	$0.465592\pi$
$908$	−34.6197	+	23.6033i	−1.14889	+	0.783303i
$909$		0			0
$910$	49.0889	+	2.20724i	1.62728	+	0.0731692i
$911$	7.16894	+	14.8865i	0.237518	+	0.493210i	0.985321	−	0.170709i	$-0.0546060\pi$
$911$	7.16894	+	14.8865i	0.237518	+	0.493210i	−0.747804	+	0.663920i	$0.768892\pi$
$912$		0			0
$913$	−44.4356	+	25.6549i	−1.47060	+	0.849053i
$914$	31.8734	−	46.7497i	1.05428	−	1.54634i
$915$		0			0
$916$	−36.2656	+	8.27738i	−1.19825	+	0.273492i
$917$	−41.6098	+	35.2660i	−1.37408	+	1.16459i
$918$		0			0
$919$	−0.799459	+	10.6680i	−0.0263717	+	0.351906i	0.968372	+	0.249511i	$0.0802697\pi$
$919$	−0.799459	+	10.6680i	−0.0263717	+	0.351906i	−0.994744	+	0.102395i	$0.967349\pi$
$920$	−16.2670	+	5.01769i	−0.536306	+	0.165428i
$921$		0			0
$922$	−11.8679	+	38.4749i	−0.390850	+	1.26710i
$923$	25.2723	−	31.6904i	0.831846	−	1.04310i
$924$		0			0
$925$	−6.40445	−	8.03093i	−0.210577	−	0.264055i
$926$	−75.6776	+	29.7013i	−2.48692	+	0.976044i
$927$		0			0
$928$	−37.4511	−	5.64485i	−1.22939	−	0.185301i
$929$	−28.1819	−	26.1490i	−0.924619	−	0.857921i	0.0655427	−	0.997850i	$-0.479122\pi$
$929$	−28.1819	−	26.1490i	−0.924619	−	0.857921i	−0.990162	+	0.139929i	$0.955313\pi$
$930$		0			0
$931$	−24.6275	+	16.2527i	−0.807134	+	0.532659i
$932$		−	17.6235i		−	0.577278i
$933$		0			0
$934$	−4.05462	+	26.9006i	−0.132671	+	0.880216i
$935$	−46.2531	+	3.46619i	−1.51264	+	0.113356i
$936$		0			0
$937$	26.0971	−	20.8118i	0.852556	−	0.679890i	−0.0963854	−	0.995344i	$-0.530728\pi$
$937$	26.0971	−	20.8118i	0.852556	−	0.679890i	0.948941	+	0.315454i	$0.102157\pi$
$938$	−19.4990	+	6.65852i	−0.636664	+	0.217408i
$939$		0			0
$940$	23.2121	+	7.15998i	0.757095	+	0.233533i
$941$	1.80947	−	4.61045i	0.0589869	−	0.150296i	−0.898342	−	0.439297i	$-0.855228\pi$
$941$	1.80947	−	4.61045i	0.0589869	−	0.150296i	0.957329	+	0.289000i	$0.0933229\pi$
$942$		0			0
$943$	−2.78856	−	0.208974i	−0.0908080	−	0.00680512i
$944$	−14.6192	+	64.0510i	−0.475815	+	2.08468i
$945$		0			0
$946$	28.8185	+	126.262i	0.936971	+	4.10514i
$947$	5.36349	+	35.5845i	0.174290	+	1.15634i	0.889333	+	0.457259i	$0.151169\pi$
$947$	5.36349	+	35.5845i	0.174290	+	1.15634i	−0.715043	+	0.699080i	$0.753593\pi$
$948$		0			0
$949$	−39.0600	−	67.6540i	−1.26794	−	2.19614i
$950$	15.7542	−	27.2870i	0.511133	−	0.885309i
$951$		0			0
$952$	−79.9106	−	69.8234i	−2.58992	−	2.26299i
$953$	5.84261	−	12.1323i	0.189261	−	0.393004i	−0.784649	−	0.619940i	$-0.787157\pi$
$953$	5.84261	−	12.1323i	0.189261	−	0.393004i	0.973910	+	0.226937i	$0.0728710\pi$
$954$		0			0
$955$	16.9665	+	18.2856i	0.549024	+	0.591707i
$956$	−45.3695	−	48.8967i	−1.46735	−	1.58143i
$957$		0			0
$958$	40.2033	−	83.4831i	1.29891	−	2.69722i
$959$	48.3580	−	8.77299i	1.56156	−	0.283295i
$960$		0			0
$961$	−11.8515	+	20.5273i	−0.382305	+	0.662172i
$962$	−22.6422	−	39.2175i	−0.730015	−	1.26442i
$963$		0			0
$964$	−7.08041	−	46.9755i	−0.228045	−	1.51298i
$965$	1.28626	+	5.63549i	0.0414063	+	0.181413i
$966$		0			0
$967$	1.45197	−	6.36150i	0.0466922	−	0.204572i	−0.946201	−	0.323579i	$-0.895114\pi$
$967$	1.45197	−	6.36150i	0.0466922	−	0.204572i	0.992893	+	0.119007i	$0.0379710\pi$
$968$	−104.030	−	7.79595i	−3.34364	−	0.250571i
$969$		0			0
$970$	−24.3444	+	62.0285i	−0.781651	+	1.99161i
$971$	−32.8415	−	10.1303i	−1.05393	−	0.325096i	−0.281083	−	0.959683i	$-0.590694\pi$
$971$	−32.8415	−	10.1303i	−1.05393	−	0.325096i	−0.772851	+	0.634588i	$0.781170\pi$
$972$		0			0
$973$	−0.352445	−	0.0424024i	−0.0112989	−	0.00135936i
$974$	27.3934	−	21.8455i	0.877742	−	0.699976i
$975$		0			0
$976$	6.30404	−	0.472422i	0.201787	−	0.0151219i
$977$	8.24898	−	54.7284i	0.263908	−	1.75092i	−0.327784	−	0.944753i	$-0.606302\pi$
$977$	8.24898	−	54.7284i	0.263908	−	1.75092i	0.591692	−	0.806164i	$-0.298460\pi$
$978$		0			0
$979$		−	8.64004i		−	0.276137i
$980$	0.689453	−	45.7532i	0.0220238	−	1.46153i
$981$		0			0
$982$	−21.6047	−	20.0462i	−0.689433	−	0.639700i
$983$	9.77828	+	1.47384i	0.311879	+	0.0470082i	0.303117	−	0.952953i	$-0.401973\pi$
$983$	9.77828	+	1.47384i	0.311879	+	0.0470082i	0.00876210	+	0.999962i	$0.497211\pi$
$984$		0			0
$985$	7.95615	−	3.12256i	0.253504	−	0.0994930i
$986$	−60.0065	−	75.2458i	−1.91100	−	2.39631i
$987$		0			0
$988$	60.1074	−	75.3723i	1.91227	−	2.39791i
$989$	−5.22630	+	16.9433i	−0.166187	+	0.538764i
$990$		0			0
$991$	44.9200	−	13.8560i	1.42693	−	0.440150i	0.517385	−	0.855753i	$-0.326905\pi$
$991$	44.9200	−	13.8560i	1.42693	−	0.440150i	0.909546	+	0.415603i	$0.136429\pi$
$992$	−1.25616	+	16.7624i	−0.0398833	+	0.532205i
$993$		0			0
$994$	−43.5143	−	32.6243i	−1.38019	−	1.03478i
$995$	−14.9402	+	3.41000i	−0.473636	+	0.108104i
$996$		0			0
$997$	−4.40039	+	6.45418i	−0.139362	+	0.204406i	−0.889574	−	0.456791i	$-0.848999\pi$
$997$	−4.40039	+	6.45418i	−0.139362	+	0.204406i	0.750213	+	0.661197i	$0.229951\pi$
$998$	72.4754	−	41.8437i	2.29417	−	1.32454i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.89.2	✓	216
3.2	odd	2	inner	441.2.bg.a.89.17	yes	216
49.38	odd	42	inner	441.2.bg.a.332.17	yes	216
147.38	even	42	inner	441.2.bg.a.332.2	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.89.2	✓	216	1.1	even	1	trivial
441.2.bg.a.89.17	yes	216	3.2	odd	2	inner
441.2.bg.a.332.2	yes	216	147.38	even	42	inner
441.2.bg.a.332.17	yes	216	49.38	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73897 + 1.87416i) q^{2} +(-0.339014 - 4.52383i) q^{4} +(0.526440 + 1.34135i) q^{5} +(2.25076 - 1.39071i) q^{7} +(5.07018 + 4.04333i) q^{8} +O(q^{10})\)	\(q+(-1.73897 + 1.87416i) q^{2} +(-0.339014 - 4.52383i) q^{4} +(0.526440 + 1.34135i) q^{5} +(2.25076 - 1.39071i) q^{7} +(5.07018 + 4.04333i) q^{8} +(-3.42937 - 1.34593i) q^{10} +(-1.53405 - 4.97326i) q^{11} +(-4.91498 - 1.12181i) q^{13} +(-1.30760 + 6.63670i) q^{14} +(-7.42308 + 1.11885i) q^{16} +(-5.11017 - 3.48405i) q^{17} +(-3.65054 - 2.10764i) q^{19} +(5.88955 - 2.83626i) q^{20} +(11.9884 + 5.77329i) q^{22} +(1.02621 + 1.50518i) q^{23} +(2.14319 - 1.98859i) q^{25} +(10.6495 - 7.26069i) q^{26} +(-7.05436 - 9.71060i) q^{28} +(-2.64083 - 5.48373i) q^{29} +(-2.33940 + 1.35066i) q^{31} +(3.50535 - 5.14140i) q^{32} +(15.4161 - 3.51863i) q^{34} +(3.05031 + 2.28693i) q^{35} +(0.262556 - 3.50357i) q^{37} +(10.2983 - 3.17659i) q^{38} +(-2.75437 + 8.92944i) q^{40} +(-0.957069 + 1.20013i) q^{41} +(6.06849 + 7.60964i) q^{43} +(-21.9781 + 8.62577i) q^{44} +(-4.60550 - 0.694168i) q^{46} +(2.72404 + 2.52754i) q^{47} +(3.13187 - 6.26030i) q^{49} +7.47479i q^{50} +(-3.40864 + 22.6148i) q^{52} +(-2.32824 + 0.174478i) q^{53} +(5.86327 - 4.67580i) q^{55} +(17.0349 + 2.04945i) q^{56} +(14.8697 + 4.58671i) q^{58} +(3.19735 - 8.14670i) q^{59} +(-0.839762 - 0.0629315i) q^{61} +(1.53680 - 6.73318i) q^{62} +(0.199240 + 0.872927i) q^{64} +(-1.08270 - 7.18326i) q^{65} +(1.52304 + 2.63798i) q^{67} +(-14.0288 + 24.2987i) q^{68} +(-9.59048 + 1.73988i) q^{70} +(-3.48850 + 7.24395i) q^{71} +(10.5398 + 11.3592i) q^{73} +(6.10969 + 6.58468i) q^{74} +(-8.29703 + 17.2290i) q^{76} +(-10.3691 - 9.06021i) q^{77} +(1.11008 - 1.92271i) q^{79} +(-5.40857 - 9.36792i) q^{80} +(-0.584920 - 3.88069i) q^{82} +(-2.19378 - 9.61160i) q^{83} +(1.98313 - 8.68865i) q^{85} +(-24.8146 - 1.85960i) q^{86} +(12.3306 - 31.4180i) q^{88} +(1.58636 + 0.489328i) q^{89} +(-12.6226 + 4.31037i) q^{91} +(6.46126 - 5.15269i) q^{92} +(-9.47404 + 0.709981i) q^{94} +(0.905288 - 6.00619i) q^{95} -18.0874i q^{97} +(6.28662 + 16.7561i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more