LMFDB - Embedded newform 756.2.bx.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60018 + 0.662888i) q^{3} +(1.50391 + 1.26193i) q^{5} +(-2.43356 - 1.03816i) q^{7} +(2.12116 - 2.12148i) q^{9} +O(q^{10})$	\(q+(-1.60018 + 0.662888i) q^{3} +(1.50391 + 1.26193i) q^{5} +(-2.43356 - 1.03816i) q^{7} +(2.12116 - 2.12148i) q^{9} +(-1.84654 - 2.20062i) q^{11} +(5.10557 + 0.900250i) q^{13} +(-3.24305 - 1.02239i) q^{15} +(1.89933 - 3.28974i) q^{17} +(1.67851 - 0.969089i) q^{19} +(4.58232 + 0.0480554i) q^{21} +(2.48687 + 6.83262i) q^{23} +(-0.198964 - 1.12838i) q^{25} +(-1.98793 + 4.80085i) q^{27} +(0.278395 - 0.0490886i) q^{29} +(2.13090 + 5.85459i) q^{31} +(4.41355 + 2.29734i) q^{33} +(-2.34978 - 4.63228i) q^{35} +(0.779265 - 1.34973i) q^{37} +(-8.76661 + 1.94386i) q^{39} +(-0.786563 + 4.46082i) q^{41} +(7.64536 - 6.41522i) q^{43} +(5.86719 - 0.513764i) q^{45} +(9.49663 + 3.45649i) q^{47} +(4.84447 + 5.05283i) q^{49} +(-0.858544 + 6.52322i) q^{51} +0.0240181i q^{53} -5.63972i q^{55} +(-2.04352 + 2.66338i) q^{57} +(-2.86867 - 2.40710i) q^{59} +(-3.06689 + 8.42621i) q^{61} +(-7.36440 + 2.96067i) q^{63} +(6.54227 + 7.79677i) q^{65} +(2.31196 - 13.1118i) q^{67} +(-8.50870 - 9.28490i) q^{69} +(12.7474 + 7.35971i) q^{71} +(6.18283 - 3.56966i) q^{73} +(1.06637 + 1.67372i) q^{75} +(2.20908 + 7.27233i) q^{77} +(-1.27491 - 7.23036i) q^{79} +(-0.00137476 - 9.00000i) q^{81} +(0.183414 + 1.04019i) q^{83} +(7.00784 - 2.55064i) q^{85} +(-0.412942 + 0.263096i) q^{87} +(4.91491 + 8.51288i) q^{89} +(-11.4901 - 7.49119i) q^{91} +(-7.29075 - 7.95585i) q^{93} +(3.74725 + 0.660741i) q^{95} +(-8.45008 - 10.0704i) q^{97} +(-8.58536 - 0.750461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.60018	+	0.662888i	−0.923865	+	0.382719i
$3$	−1.60018	+	0.662888i	−0.923865	+	0.382719i
$4$		0			0
$5$	1.50391	+	1.26193i	0.672569	+	0.564352i	0.913824	−	0.406109i	$-0.133115\pi$
$5$	1.50391	+	1.26193i	0.672569	+	0.564352i	−0.241256	+	0.970462i	$0.577559\pi$
$6$		0			0
$7$	−2.43356	−	1.03816i	−0.919801	−	0.392386i
$7$	−2.43356	−	1.03816i	−0.919801	−	0.392386i
$8$		0			0
$9$	2.12116	−	2.12148i	0.707053	−	0.707161i
$10$		0			0
$11$	−1.84654	−	2.20062i	−0.556751	−	0.663510i	0.412104	−	0.911137i	$-0.364794\pi$
$11$	−1.84654	−	2.20062i	−0.556751	−	0.663510i	−0.968856	+	0.247626i	$0.920349\pi$
$12$		0			0
$13$	5.10557	+	0.900250i	1.41603	+	0.249685i	0.828714	−	0.559672i	$-0.189073\pi$
$13$	5.10557	+	0.900250i	1.41603	+	0.249685i	0.587317	+	0.809357i	$0.300184\pi$
$14$		0			0
$15$	−3.24305	−	1.02239i	−0.837351	−	0.263981i
$16$		0			0
$17$	1.89933	−	3.28974i	0.460655	−	0.797878i	−0.538339	−	0.842729i	$-0.680948\pi$
$17$	1.89933	−	3.28974i	0.460655	−	0.797878i	0.998994	+	0.0448506i	$0.0142812\pi$
$18$		0			0
$19$	1.67851	−	0.969089i	0.385077	−	0.222324i	−0.294948	−	0.955513i	$-0.595302\pi$
$19$	1.67851	−	0.969089i	0.385077	−	0.222324i	0.680025	+	0.733189i	$0.261969\pi$
$20$		0			0
$21$	4.58232	+	0.0480554i	0.999945	+	0.0104865i
$22$		0			0
$23$	2.48687	+	6.83262i	0.518548	+	1.42470i	0.872120	+	0.489292i	$0.162745\pi$
$23$	2.48687	+	6.83262i	0.518548	+	1.42470i	−0.353572	+	0.935407i	$0.615033\pi$
$24$		0			0
$25$	−0.198964	−	1.12838i	−0.0397928	−	0.225676i
$26$		0			0
$27$	−1.98793	+	4.80085i	−0.382578	+	0.923923i
$28$		0			0
$29$	0.278395	−	0.0490886i	0.0516967	−	0.00911552i	−0.147740	−	0.989026i	$-0.547200\pi$
$29$	0.278395	−	0.0490886i	0.0516967	−	0.00911552i	0.199437	+	0.979911i	$0.436089\pi$
$30$		0			0
$31$	2.13090	+	5.85459i	0.382720	+	1.05151i	0.970206	+	0.242281i	$0.0778954\pi$
$31$	2.13090	+	5.85459i	0.382720	+	1.05151i	−0.587486	+	0.809234i	$0.699882\pi$
$32$		0			0
$33$	4.41355	+	2.29734i	0.768301	+	0.399915i
$34$		0			0
$35$	−2.34978	−	4.63228i	−0.397185	−	0.782998i
$36$		0			0
$37$	0.779265	−	1.34973i	0.128110	−	0.221894i	−0.794834	−	0.606827i	$-0.792442\pi$
$37$	0.779265	−	1.34973i	0.128110	−	0.221894i	0.922944	+	0.384933i	$0.125775\pi$
$38$		0			0
$39$	−8.76661	+	1.94386i	−1.40378	+	0.311267i
$40$		0			0
$41$	−0.786563	+	4.46082i	−0.122841	+	0.696663i	0.859726	+	0.510755i	$0.170634\pi$
$41$	−0.786563	+	4.46082i	−0.122841	+	0.696663i	−0.982567	+	0.185909i	$0.940477\pi$
$42$		0			0
$43$	7.64536	−	6.41522i	1.16591	−	0.978312i	0.165938	−	0.986136i	$-0.446935\pi$
$43$	7.64536	−	6.41522i	1.16591	−	0.978312i	0.999969	+	0.00782407i	$0.00249050\pi$
$44$		0			0
$45$	5.86719	−	0.513764i	0.874629	−	0.0765875i
$46$		0			0
$47$	9.49663	+	3.45649i	1.38523	+	0.504181i	0.923758	−	0.382976i	$-0.125101\pi$
$47$	9.49663	+	3.45649i	1.38523	+	0.504181i	0.461468	+	0.887157i	$0.347323\pi$
$48$		0			0
$49$	4.84447	+	5.05283i	0.692067	+	0.721834i
$50$		0			0
$51$	−0.858544	+	6.52322i	−0.120220	+	0.913433i
$52$		0			0
$53$			0.0240181i			0.00329914i	0.999999	+	0.00164957i	$0.000525074\pi$
$53$			0.0240181i			0.00329914i	−0.999999	+	0.00164957i	$0.999475\pi$
$54$		0			0
$55$		−	5.63972i		−	0.760460i
$56$		0			0
$57$	−2.04352	+	2.66338i	−0.270671	+	0.352774i
$58$		0			0
$59$	−2.86867	−	2.40710i	−0.373468	−	0.313377i	0.436663	−	0.899625i	$-0.356160\pi$
$59$	−2.86867	−	2.40710i	−0.373468	−	0.313377i	−0.810132	+	0.586248i	$0.800605\pi$
$60$		0			0
$61$	−3.06689	+	8.42621i	−0.392675	+	1.07887i	0.573100	+	0.819485i	$0.305741\pi$
$61$	−3.06689	+	8.42621i	−0.392675	+	1.07887i	−0.965775	+	0.259380i	$0.916482\pi$
$62$		0			0
$63$	−7.36440	+	2.96067i	−0.927828	+	0.373010i
$64$		0			0
$65$	6.54227	+	7.79677i	0.811468	+	0.967070i
$66$		0			0
$67$	2.31196	−	13.1118i	0.282451	−	1.60186i	−0.431801	−	0.901969i	$-0.642122\pi$
$67$	2.31196	−	13.1118i	0.282451	−	1.60186i	0.714252	−	0.699889i	$-0.246767\pi$
$68$		0			0
$69$	−8.50870	−	9.28490i	−1.02433	−	1.11777i
$70$		0			0
$71$	12.7474	+	7.35971i	1.51284	+	0.873437i	0.999887	+	0.0150179i	$0.00478051\pi$
$71$	12.7474	+	7.35971i	1.51284	+	0.873437i	0.512949	+	0.858419i	$0.328553\pi$
$72$		0			0
$73$	6.18283	−	3.56966i	0.723645	−	0.417797i	−0.0924478	−	0.995718i	$-0.529469\pi$
$73$	6.18283	−	3.56966i	0.723645	−	0.417797i	0.816093	+	0.577921i	$0.196136\pi$
$74$		0			0
$75$	1.06637	+	1.67372i	0.123134	+	0.193265i
$76$		0			0
$77$	2.20908	+	7.27233i	0.251748	+	0.828759i
$78$		0			0
$79$	−1.27491	−	7.23036i	−0.143438	−	0.813479i	−0.968608	−	0.248594i	$-0.920032\pi$
$79$	−1.27491	−	7.23036i	−0.143438	−	0.813479i	0.825170	−	0.564885i	$-0.191080\pi$
$80$		0			0
$81$	−0.00137476	−	9.00000i	−0.000152751	−	1.00000i
$82$		0			0
$83$	0.183414	+	1.04019i	0.0201323	+	0.114176i	0.993218	−	0.116268i	$-0.0370933\pi$
$83$	0.183414	+	1.04019i	0.0201323	+	0.114176i	−0.973086	+	0.230444i	$0.925982\pi$
$84$		0			0
$85$	7.00784	−	2.55064i	0.760106	−	0.276656i
$86$		0			0
$87$	−0.412942	+	0.263096i	−0.0442721	+	0.0282068i
$88$		0			0
$89$	4.91491	+	8.51288i	0.520980	+	0.902364i	0.999702	+	0.0243973i	$0.00776667\pi$
$89$	4.91491	+	8.51288i	0.520980	+	0.902364i	−0.478723	+	0.877966i	$0.658900\pi$
$90$		0			0
$91$	−11.4901	−	7.49119i	−1.20449	−	0.785291i
$92$		0			0
$93$	−7.29075	−	7.95585i	−0.756016	−	0.824983i
$94$		0			0
$95$	3.74725	+	0.660741i	0.384460	+	0.0677906i
$96$		0			0
$97$	−8.45008	−	10.0704i	−0.857976	−	1.02250i	−0.999470	−	0.0325568i	$-0.989635\pi$
$97$	−8.45008	−	10.0704i	−0.857976	−	1.02250i	0.141494	−	0.989939i	$-0.454809\pi$
$98$		0			0
$99$	−8.58536	−	0.750461i	−0.862861	−	0.0754242i
$100$		0			0
$101$	8.47670	+	3.08527i	0.843463	+	0.306995i	0.727372	−	0.686243i	$-0.240741\pi$
$101$	8.47670	+	3.08527i	0.843463	+	0.306995i	0.116091	+	0.993239i	$0.462964\pi$
$102$		0			0
$103$	4.99940	−	5.95806i	0.492606	−	0.587065i	−0.461272	−	0.887259i	$-0.652607\pi$
$103$	4.99940	−	5.95806i	0.492606	−	0.587065i	0.953878	+	0.300194i	$0.0970513\pi$
$104$		0			0
$105$	6.83076	+	5.85484i	0.666614	+	0.571374i
$106$		0			0
$107$			6.79908i			0.657292i	0.944453	+	0.328646i	$0.106592\pi$
$107$			6.79908i			0.657292i	−0.944453	+	0.328646i	$0.893408\pi$
$108$		0			0
$109$	−12.3551			−1.18341			−0.591704	−	0.806155i	$-0.701545\pi$
$109$	−12.3551			−1.18341			−0.591704	+	0.806155i	$0.701545\pi$
$110$		0			0
$111$	−0.352247	+	2.67637i	−0.0334338	+	0.254030i
$112$		0			0
$113$	−0.105597	+	0.125845i	−0.00993369	+	0.0118385i	−0.770988	−	0.636849i	$-0.780237\pi$
$113$	−0.105597	+	0.125845i	−0.00993369	+	0.0118385i	0.761055	+	0.648688i	$0.224682\pi$
$114$		0			0
$115$	−4.88226	+	13.4139i	−0.455273	+	1.25085i
$116$		0			0
$117$	12.7396	−	8.92181i	1.17778	−	0.824822i
$118$		0			0
$119$	−8.03740	+	6.03398i	−0.736787	+	0.553134i
$120$		0			0
$121$	0.477116	−	2.70586i	0.0433742	−	0.245987i
$122$		0			0
$123$	−1.69838	−	7.65953i	−0.153138	−	0.690636i
$124$		0			0
$125$	6.03275	−	10.4490i	0.539586	−	0.934590i
$126$		0			0
$127$	−6.17139	−	10.6892i	−0.547622	−	0.948509i	−0.998437	−	0.0558919i	$-0.982200\pi$
$127$	−6.17139	−	10.6892i	−0.547622	−	0.948509i	0.450815	−	0.892618i	$-0.351134\pi$
$128$		0			0
$129$	−7.98139	+	15.3335i	−0.702722	+	1.35004i
$130$		0			0
$131$	−19.4949	+	7.09556i	−1.70328	+	0.619942i	−0.996192	−	0.0871855i	$-0.972213\pi$
$131$	−19.4949	+	7.09556i	−1.70328	+	0.619942i	−0.707086	+	0.707128i	$0.749990\pi$
$132$		0			0
$133$	−5.09083	+	0.615784i	−0.441431	+	0.0533953i
$134$		0			0
$135$	−9.04800	+	4.71141i	−0.778728	+	0.405493i
$136$		0			0
$137$	−8.50383	+	1.49945i	−0.726531	+	0.128107i	−0.524668	−	0.851307i	$-0.675811\pi$
$137$	−8.50383	+	1.49945i	−0.726531	+	0.128107i	−0.201863	+	0.979414i	$0.564699\pi$
$138$		0			0
$139$	−1.00678	−	2.76611i	−0.0853942	−	0.234619i	0.889644	−	0.456654i	$-0.150952\pi$
$139$	−1.00678	−	2.76611i	−0.0853942	−	0.234619i	−0.975039	+	0.222035i	$0.928730\pi$
$140$		0			0
$141$	−17.4876	+	0.764194i	−1.47272	+	0.0643567i
$142$		0			0
$143$	−7.44652	−	12.8977i	−0.622709	−	1.07856i
$144$		0			0
$145$	0.480627	+	0.277490i	0.0399139	+	0.0230443i
$146$		0			0
$147$	−11.1015	−	4.87411i	−0.915635	−	0.402010i
$148$		0			0
$149$	−13.4016	−	2.36307i	−1.09790	−	0.193590i	−0.404784	−	0.914412i	$-0.632653\pi$
$149$	−13.4016	−	2.36307i	−1.09790	−	0.193590i	−0.693120	+	0.720822i	$0.743765\pi$
$150$		0			0
$151$	−1.86536	+	1.56523i	−0.151801	+	0.127376i	−0.715525	−	0.698587i	$-0.753813\pi$
$151$	−1.86536	+	1.56523i	−0.151801	+	0.127376i	0.563724	+	0.825963i	$0.309368\pi$
$152$		0			0
$153$	−2.95034	−	11.0074i	−0.238521	−	0.889899i
$154$		0			0
$155$	−4.18340	+	11.4938i	−0.336019	+	0.923205i
$156$		0			0
$157$	1.13835	−	1.35664i	0.0908504	−	0.108271i	−0.718704	−	0.695316i	$-0.755264\pi$
$157$	1.13835	−	1.35664i	0.0908504	−	0.108271i	0.809554	+	0.587045i	$0.199709\pi$
$158$		0			0
$159$	−0.0159213	−	0.0384333i	−0.00126264	−	0.00304796i
$160$		0			0
$161$	1.04136	−	19.2094i	0.0820708	−	1.51391i
$162$		0			0
$163$	19.8197			1.55240			0.776201	−	0.630485i	$-0.217144\pi$
$163$	19.8197			1.55240			0.776201	+	0.630485i	$0.217144\pi$
$164$		0			0
$165$	3.73851	+	9.02458i	0.291042	+	0.702563i
$166$		0			0
$167$	−18.0526	−	15.1479i	−1.39695	−	1.17218i	−0.962433	−	0.271520i	$-0.912474\pi$
$167$	−18.0526	−	15.1479i	−1.39695	−	1.17218i	−0.434520	−	0.900662i	$-0.643082\pi$
$168$		0			0
$169$	13.0404	+	4.74633i	1.00311	+	0.365102i
$170$		0			0
$171$	1.50448	−	5.61652i	0.115051	−	0.429506i
$172$		0			0
$173$	−4.54111	+	3.81044i	−0.345254	+	0.289702i	−0.798881	−	0.601489i	$-0.794574\pi$
$173$	−4.54111	+	3.81044i	−0.345254	+	0.289702i	0.453627	+	0.891192i	$0.350130\pi$
$174$		0			0
$175$	−0.687244	+	2.95255i	−0.0519507	+	0.223192i
$176$		0			0
$177$	6.18602	+	1.95019i	0.464970	+	0.146585i
$178$		0			0
$179$	9.25732	+	5.34472i	0.691925	+	0.399483i	0.804333	−	0.594179i	$-0.202523\pi$
$179$	9.25732	+	5.34472i	0.691925	+	0.399483i	−0.112408	+	0.993662i	$0.535856\pi$
$180$		0			0
$181$	−10.5542	+	6.09345i	−0.784485	+	0.452923i	−0.838018	−	0.545643i	$-0.816285\pi$
$181$	−10.5542	+	6.09345i	−0.784485	+	0.452923i	0.0535322	+	0.998566i	$0.482952\pi$
$182$		0			0
$183$	−0.678057	−	15.5165i	−0.0501234	−	1.14701i
$184$		0			0
$185$	2.87520	−	1.04649i	0.211389	−	0.0769394i
$186$		0			0
$187$	−10.7466	+	1.89492i	−0.785871	+	0.138570i
$188$		0			0
$189$	9.82178	−	9.61939i	0.714430	−	0.699707i
$190$		0			0
$191$	19.5202	−	3.44193i	1.41243	−	0.249049i	0.585188	−	0.810897i	$-0.301021\pi$
$191$	19.5202	−	3.44193i	1.41243	−	0.249049i	0.827240	+	0.561848i	$0.189909\pi$
$192$		0			0
$193$	−5.98892	+	2.17979i	−0.431092	+	0.156905i	−0.548447	−	0.836185i	$-0.684781\pi$
$193$	−5.98892	+	2.17979i	−0.431092	+	0.156905i	0.117355	+	0.993090i	$0.462559\pi$
$194$		0			0
$195$	−15.6372	−	8.13945i	−1.11980	−	0.582878i
$196$		0			0
$197$	−15.7838	+	9.11276i	−1.12455	+	0.649258i	−0.942558	−	0.334043i	$-0.891587\pi$
$197$	−15.7838	+	9.11276i	−1.12455	+	0.649258i	−0.181989	+	0.983301i	$0.558254\pi$
$198$		0			0
$199$	−1.00287	−	0.579005i	−0.0710913	−	0.0410446i	0.464033	−	0.885818i	$-0.346402\pi$
$199$	−1.00287	−	0.579005i	−0.0710913	−	0.0410446i	−0.535124	+	0.844773i	$0.679735\pi$
$200$		0			0
$201$	4.99209	+	22.5138i	0.352115	+	1.58800i
$202$		0			0
$203$	−0.728454	−	0.169557i	−0.0511274	−	0.0119006i
$204$		0			0
$205$	−6.81216	+	5.71608i	−0.475782	+	0.399229i
$206$		0			0
$207$	19.7703	+	9.21721i	1.37413	+	0.640640i
$208$		0			0
$209$	−5.23202	−	1.90430i	−0.361906	−	0.131723i
$210$		0			0
$211$	−8.77128	−	7.35998i	−0.603840	−	0.506682i	0.288838	−	0.957378i	$-0.406731\pi$
$211$	−8.77128	−	7.35998i	−0.603840	−	0.506682i	−0.892677	+	0.450696i	$0.851176\pi$
$212$		0			0
$213$	−25.2768	−	3.32677i	−1.73194	−	0.227947i
$214$		0			0
$215$	19.5935			1.33627
$216$		0			0
$217$	0.892300	−	16.4597i	0.0605733	−	1.11736i
$218$		0			0
$219$	−7.52736	+	9.81062i	−0.508652	+	0.662940i
$220$		0			0
$221$	12.6588	−	15.0861i	0.851520	−	1.01480i
$222$		0			0
$223$	−5.67779	+	15.5996i	−0.380213	+	1.04463i	0.591054	+	0.806632i	$0.298712\pi$
$223$	−5.67779	+	15.5996i	−0.380213	+	1.04463i	−0.971267	+	0.237994i	$0.923510\pi$
$224$		0			0
$225$	−2.81588	−	1.97138i	−0.187725	−	0.131425i
$226$		0			0
$227$	4.49457	−	3.77139i	0.298315	−	0.250316i	−0.481327	−	0.876541i	$-0.659845\pi$
$227$	4.49457	−	3.77139i	0.298315	−	0.250316i	0.779643	+	0.626225i	$0.215401\pi$
$228$		0			0
$229$	22.6023	+	3.98539i	1.49360	+	0.263362i	0.859998	−	0.510297i	$-0.170465\pi$
$229$	22.6023	+	3.98539i	1.49360	+	0.263362i	0.633602	+	0.773659i	$0.281576\pi$
$230$		0			0
$231$	−8.35567	−	10.1727i	−0.549763	−	0.669312i
$232$		0			0
$233$	−2.09433	−	1.20916i	−0.137204	−	0.0792147i	0.429827	−	0.902911i	$-0.358575\pi$
$233$	−2.09433	−	1.20916i	−0.137204	−	0.0792147i	−0.567031	+	0.823697i	$0.691908\pi$
$234$		0			0
$235$	9.92022	+	17.1823i	0.647124	+	1.12085i
$236$		0			0
$237$	6.83300	+	10.7248i	0.443851	+	0.696648i
$238$		0			0
$239$	8.10459	+	22.2672i	0.524242	+	1.44034i	0.865755	+	0.500467i	$0.166838\pi$
$239$	8.10459	+	22.2672i	0.524242	+	1.44034i	−0.341513	+	0.939877i	$0.610939\pi$
$240$		0			0
$241$	23.6052	−	4.16223i	1.52054	−	0.268113i	0.649897	−	0.760022i	$-0.274812\pi$
$241$	23.6052	−	4.16223i	1.52054	−	0.268113i	0.870647	+	0.491909i	$0.163701\pi$
$242$		0			0
$243$	5.96819	+	14.4007i	0.382860	+	0.923806i
$244$		0			0
$245$	0.909317	+	13.7124i	0.0580941	+	0.876052i
$246$		0			0
$247$	9.44218	−	3.43667i	0.600792	−	0.218670i
$248$		0			0
$249$	−0.983024	−	1.54291i	−0.0622966	−	0.0977779i
$250$		0			0
$251$	−4.77696	−	8.27393i	−0.301519	−	0.522246i	0.674961	−	0.737853i	$-0.264160\pi$
$251$	−4.77696	−	8.27393i	−0.301519	−	0.522246i	−0.976480	+	0.215607i	$0.930827\pi$
$252$		0			0
$253$	10.4439	−	18.0893i	0.656600	−	1.13726i
$254$		0			0
$255$	−9.52301	+	8.72690i	−0.596354	+	0.546500i
$256$		0			0
$257$	3.50702	−	19.8893i	0.218762	−	1.24066i	−0.655496	−	0.755199i	$-0.727540\pi$
$257$	3.50702	−	19.8893i	0.218762	−	1.24066i	0.874258	−	0.485462i	$-0.161349\pi$
$258$		0			0
$259$	−3.29762	+	2.47565i	−0.204904	+	0.153829i
$260$		0			0
$261$	0.486380	−	0.694735i	0.0301061	−	0.0430030i
$262$		0			0
$263$	2.34860	−	6.45271i	0.144821	−	0.397891i	−0.845981	−	0.533213i	$-0.820984\pi$
$263$	2.34860	−	6.45271i	0.144821	−	0.397891i	0.990802	+	0.135321i	$0.0432067\pi$
$264$		0			0
$265$	−0.0303091	+	0.0361210i	−0.00186187	+	0.00221890i
$266$		0			0
$267$	−13.5078	−	10.3641i	−0.826666	−	0.634273i
$268$		0			0
$269$	−1.32387			−0.0807178			−0.0403589	−	0.999185i	$-0.512850\pi$
$269$	−1.32387			−0.0807178			−0.0403589	+	0.999185i	$0.512850\pi$
$270$		0			0
$271$		−	17.3159i		−	1.05187i	−0.850526	−	0.525933i	$-0.823716\pi$
$271$		−	17.3159i		−	1.05187i	0.850526	−	0.525933i	$-0.176284\pi$
$272$		0			0
$273$	23.3521	+	4.37059i	1.41334	+	0.264520i
$274$		0			0
$275$	−2.11574	+	2.52144i	−0.127584	+	0.152049i
$276$		0			0
$277$	5.82840	+	2.12136i	0.350194	+	0.127460i	0.511127	−	0.859505i	$-0.329228\pi$
$277$	5.82840	+	2.12136i	0.350194	+	0.127460i	−0.160933	+	0.986965i	$0.551450\pi$
$278$		0			0
$279$	16.9404	+	7.89785i	1.01419	+	0.472832i
$280$		0			0
$281$	3.44330	+	4.10357i	0.205410	+	0.244798i	0.858908	−	0.512130i	$-0.171144\pi$
$281$	3.44330	+	4.10357i	0.205410	+	0.244798i	−0.653498	+	0.756929i	$0.726699\pi$
$282$		0			0
$283$	1.64911	+	0.290783i	0.0980294	+	0.0172852i	0.222448	−	0.974945i	$-0.428595\pi$
$283$	1.64911	+	0.290783i	0.0980294	+	0.0172852i	−0.124418	+	0.992230i	$0.539706\pi$
$284$		0			0
$285$	−6.43428	+	1.42670i	−0.381134	+	0.0845106i
$286$		0			0
$287$	6.54518	−	10.0391i	0.386350	−	0.592591i
$288$		0			0
$289$	1.28509	+	2.22585i	0.0755937	+	0.130932i
$290$		0			0
$291$	20.1972	+	10.5130i	1.18398	+	0.616285i
$292$		0			0
$293$	−12.8885	+	4.69103i	−0.752953	+	0.274053i	−0.689848	−	0.723954i	$-0.742323\pi$
$293$	−12.8885	+	4.69103i	−0.752953	+	0.274053i	−0.0631054	+	0.998007i	$0.520100\pi$
$294$		0			0
$295$	−1.27663	−	7.24011i	−0.0743281	−	0.421536i
$296$		0			0
$297$	14.2356	−	4.49026i	0.826033	−	0.260551i
$298$		0			0
$299$	6.54583	+	37.1232i	0.378555	+	2.14689i
$300$		0			0
$301$	−25.2655	+	7.67478i	−1.45628	+	0.442367i
$302$		0			0
$303$	−15.6094	+	0.682120i	−0.896739	+	0.0391868i
$304$		0			0
$305$	−15.2456	+	8.80206i	−0.872961	+	0.504004i
$306$		0			0
$307$	−4.15779	−	2.40050i	−0.237297	−	0.137004i	0.376637	−	0.926361i	$-0.377081\pi$
$307$	−4.15779	−	2.40050i	−0.237297	−	0.137004i	−0.613934	+	0.789357i	$0.710414\pi$
$308$		0			0
$309$	−4.05042	+	12.8480i	−0.230421	+	0.730898i
$310$		0			0
$311$	−3.65409	+	20.7233i	−0.207204	+	1.17511i	0.686729	+	0.726913i	$0.259046\pi$
$311$	−3.65409	+	20.7233i	−0.207204	+	1.17511i	−0.893933	+	0.448200i	$0.852065\pi$
$312$		0			0
$313$	12.9357	+	15.4162i	0.731169	+	0.871373i	0.995665	−	0.0930139i	$-0.0296501\pi$
$313$	12.9357	+	15.4162i	0.731169	+	0.871373i	−0.264496	+	0.964387i	$0.585206\pi$
$314$		0			0
$315$	−14.8116	−	4.84078i	−0.834537	−	0.272747i
$316$		0			0
$317$	5.24089	−	14.3992i	0.294358	−	0.808741i	−0.701059	−	0.713104i	$-0.747289\pi$
$317$	5.24089	−	14.3992i	0.294358	−	0.808741i	0.995416	−	0.0956371i	$-0.0304888\pi$
$318$		0			0
$319$	−0.622092	−	0.521997i	−0.0348304	−	0.0292262i
$320$		0			0
$321$	−4.50703	−	10.8798i	−0.251558	−	0.607249i
$322$		0			0
$323$		−	7.36248i		−	0.409659i
$324$		0			0
$325$		−	5.94016i		−	0.329501i
$326$		0			0
$327$	19.7705	−	8.19008i	1.09331	−	0.452913i
$328$		0			0
$329$	−19.5223	−	18.2706i	−1.07630	−	1.00729i
$330$		0			0
$331$	−15.6828	−	5.70809i	−0.862007	−	0.313745i	−0.127081	−	0.991892i	$-0.540561\pi$
$331$	−15.6828	−	5.70809i	−0.862007	−	0.313745i	−0.734926	+	0.678148i	$0.762783\pi$
$332$		0			0
$333$	−1.21048	−	4.51618i	−0.0663337	−	0.247485i
$334$		0			0
$335$	20.0231	−	16.8014i	1.09398	−	0.917958i
$336$		0			0
$337$	−3.56515	+	20.2190i	−0.194206	+	1.10140i	0.719339	+	0.694659i	$0.244445\pi$
$337$	−3.56515	+	20.2190i	−0.194206	+	1.10140i	−0.913545	+	0.406738i	$0.866666\pi$
$338$		0			0
$339$	0.0855524	−	0.271374i	0.00464657	−	0.0147390i
$340$		0			0
$341$	8.94892	−	15.5000i	0.484611	−	0.839371i
$342$		0			0
$343$	−6.54369	−	17.3257i	−0.353326	−	0.935500i
$344$		0			0
$345$	−1.07942	−	24.7010i	−0.0581138	−	1.32986i
$346$		0			0
$347$	−7.81405	−	21.4689i	−0.419480	−	1.15251i	−0.952001	−	0.306095i	$-0.900977\pi$
$347$	−7.81405	−	21.4689i	−0.419480	−	1.15251i	0.532521	−	0.846417i	$-0.321245\pi$
$348$		0			0
$349$	−21.3328	+	3.76154i	−1.14192	+	0.201351i	−0.712444	−	0.701729i	$-0.752412\pi$
$349$	−21.3328	+	3.76154i	−1.14192	+	0.201351i	−0.429473	+	0.903080i	$0.641301\pi$
$350$		0			0
$351$	−14.4715	+	22.7214i	−0.772431	+	1.21278i
$352$		0			0
$353$	2.32691	+	13.1966i	0.123849	+	0.702383i	0.981985	+	0.188960i	$0.0605116\pi$
$353$	2.32691	+	13.1966i	0.123849	+	0.702383i	−0.858136	+	0.513423i	$0.828377\pi$
$354$		0			0
$355$	9.88348	+	27.1546i	0.524561	+	1.44122i
$356$		0			0
$357$	8.86143	−	14.9834i	0.468997	−	0.793004i
$358$		0			0
$359$	−27.3405	+	15.7851i	−1.44298	+	0.833104i	−0.998047	−	0.0624603i	$-0.980105\pi$
$359$	−27.3405	+	15.7851i	−1.44298	+	0.833104i	−0.444932	+	0.895565i	$0.646772\pi$
$360$		0			0
$361$	−7.62173	+	13.2012i	−0.401144	+	0.694802i
$362$		0			0
$363$	1.03021	+	4.64614i	0.0540720	+	0.243859i
$364$		0			0
$365$	13.8031	+	2.43385i	0.722485	+	0.127394i
$366$		0			0
$367$	−15.8291	−	18.8644i	−0.826273	−	0.984713i	0.173727	−	0.984794i	$-0.444419\pi$
$367$	−15.8291	−	18.8644i	−0.826273	−	0.984713i	−1.00000		8.03765e-5i	$0.999974\pi$
$368$		0			0
$369$	7.79513	+	11.1308i	0.405798	+	0.579446i
$370$		0			0
$371$	0.0249345	−	0.0584495i	0.00129453	−	0.00303455i
$372$		0			0
$373$	−11.8486	−	9.94219i	−0.613499	−	0.514787i	0.282253	−	0.959340i	$-0.408918\pi$
$373$	−11.8486	−	9.94219i	−0.613499	−	0.514787i	−0.895753	+	0.444553i	$0.853363\pi$
$374$		0			0
$375$	−2.72695	+	20.7194i	−0.140819	+	1.06994i
$376$		0			0
$377$	1.46556			0.0754801
$378$		0			0
$379$	−7.38456			−0.379319			−0.189660	−	0.981850i	$-0.560738\pi$
$379$	−7.38456			−0.379319			−0.189660	+	0.981850i	$0.560738\pi$
$380$		0			0
$381$	16.9611	+	13.0136i	0.868941	+	0.666709i
$382$		0			0
$383$	23.0237	+	19.3192i	1.17645	+	0.987163i	0.999996	+	0.00285464i	$0.000908661\pi$
$383$	23.0237	+	19.3192i	1.17645	+	0.987163i	0.176459	+	0.984308i	$0.443536\pi$
$384$		0			0
$385$	−5.85491	+	13.7246i	−0.298394	+	0.699472i
$386$		0			0
$387$	2.60725	−	29.8272i	0.132534	−	1.51620i
$388$		0			0
$389$	−2.93148	−	3.49360i	−0.148632	−	0.177133i	0.686591	−	0.727043i	$-0.259106\pi$
$389$	−2.93148	−	3.49360i	−0.148632	−	0.177133i	−0.835223	+	0.549911i	$0.814662\pi$
$390$		0			0
$391$	27.2009	+	4.79625i	1.37561	+	0.242557i
$392$		0			0
$393$	26.4918	−	24.2771i	1.33633	−	1.22462i
$394$		0			0
$395$	7.20686	−	12.4827i	0.362617	−	0.628070i
$396$		0			0
$397$	−6.35806	+	3.67083i	−0.319102	+	0.184234i	−0.650992	−	0.759084i	$-0.725647\pi$
$397$	−6.35806	+	3.67083i	−0.319102	+	0.184234i	0.331890	+	0.943318i	$0.392314\pi$
$398$		0			0
$399$	7.73805	−	4.36002i	0.387387	−	0.218274i
$400$		0			0
$401$	−12.7406	−	35.0044i	−0.636233	−	1.74804i	−0.663246	−	0.748402i	$-0.730822\pi$
$401$	−12.7406	−	35.0044i	−0.636233	−	1.74804i	0.0270125	−	0.999635i	$-0.491401\pi$
$402$		0			0
$403$	5.60885	+	31.8094i	0.279397	+	1.58454i
$404$		0			0
$405$	11.3553	−	13.5369i	0.564249	−	0.672655i
$406$		0			0
$407$	−4.40917	+	0.777455i	−0.218554	+	0.0385370i
$408$		0			0
$409$	9.16167	+	25.1715i	0.453016	+	1.24465i	0.930591	+	0.366059i	$0.119293\pi$
$409$	9.16167	+	25.1715i	0.453016	+	1.24465i	−0.477576	+	0.878590i	$0.658484\pi$
$410$		0			0
$411$	12.6137	−	8.03648i	0.622187	−	0.396411i
$412$		0			0
$413$	4.48214	+	8.83594i	0.220552	+	0.434788i
$414$		0			0
$415$	−1.03681	+	1.79581i	−0.0508950	+	0.0881527i
$416$		0			0
$417$	3.44466	+	3.75890i	0.168686	+	0.184074i
$418$		0			0
$419$	−4.32004	+	24.5002i	−0.211048	+	1.19691i	0.676586	+	0.736363i	$0.263458\pi$
$419$	−4.32004	+	24.5002i	−0.211048	+	1.19691i	−0.887634	+	0.460549i	$0.847653\pi$
$420$		0			0
$421$	9.36234	−	7.85594i	0.456293	−	0.382875i	−0.385472	−	0.922720i	$-0.625961\pi$
$421$	9.36234	−	7.85594i	0.456293	−	0.382875i	0.841765	+	0.539844i	$0.181517\pi$
$422$		0			0
$423$	27.4767	−	12.8152i	1.33596	−	0.623095i
$424$		0			0
$425$	−4.08998	−	1.48863i	−0.198393	−	0.0722092i
$426$		0			0
$427$	16.2112	−	17.3218i	0.784514	−	0.838261i
$428$		0			0
$429$	20.4655	+	15.7025i	0.988086	+	0.758125i
$430$		0			0
$431$		−	39.6357i		−	1.90918i	−0.297918	−	0.954591i	$-0.596292\pi$
$431$		−	39.6357i		−	1.90918i	0.297918	−	0.954591i	$-0.403708\pi$
$432$		0			0
$433$		−	9.19588i		−	0.441926i	−0.975282	−	0.220963i	$-0.929080\pi$
$433$		−	9.19588i		−	0.441926i	0.975282	−	0.220963i	$-0.0709199\pi$
$434$		0			0
$435$	−0.953036	−	0.125433i	−0.0456946	−	0.00601403i
$436$		0			0
$437$	10.7956	+	9.05862i	0.516426	+	0.433333i
$438$		0			0
$439$	−5.41133	+	14.8675i	−0.258269	+	0.709587i	0.741006	+	0.671499i	$0.234349\pi$
$439$	−5.41133	+	14.8675i	−0.258269	+	0.709587i	−0.999274	+	0.0380885i	$0.987873\pi$
$440$		0			0
$441$	20.9954	+	0.440410i	0.999780	+	0.0209719i
$442$		0			0
$443$	5.34477	+	6.36965i	0.253938	+	0.302631i	0.877920	−	0.478807i	$-0.158931\pi$
$443$	5.34477	+	6.36965i	0.253938	+	0.302631i	−0.623982	+	0.781438i	$0.714486\pi$
$444$		0			0
$445$	−3.35107	+	19.0049i	−0.158856	+	0.900918i
$446$		0			0
$447$	23.0115	−	5.10245i	1.08841	−	0.241337i
$448$		0			0
$449$	10.6884	+	6.17097i	0.504418	+	0.291226i	0.730536	−	0.682874i	$-0.239270\pi$
$449$	10.6884	+	6.17097i	0.504418	+	0.291226i	−0.226118	+	0.974100i	$0.572604\pi$
$450$		0			0
$451$	11.2690	−	6.50614i	0.530635	−	0.306362i
$452$		0			0
$453$	1.94735	−	3.74117i	0.0914945	−	0.175776i
$454$		0			0
$455$	−7.82677	−	25.7658i	−0.366925	−	1.20792i
$456$		0			0
$457$	5.76582	+	32.6996i	0.269714	+	1.52962i	0.755269	+	0.655415i	$0.227506\pi$
$457$	5.76582	+	32.6996i	0.269714	+	1.52962i	−0.485555	+	0.874206i	$0.661382\pi$
$458$		0			0
$459$	12.0178	+	15.6582i	0.560942	+	0.730860i
$460$		0			0
$461$	1.63480	+	9.27140i	0.0761401	+	0.431812i	0.998919	+	0.0464825i	$0.0148012\pi$
$461$	1.63480	+	9.27140i	0.0761401	+	0.431812i	−0.922779	+	0.385330i	$0.874088\pi$
$462$		0			0
$463$	39.5178	−	14.3833i	1.83655	−	0.668449i	0.845669	−	0.533708i	$-0.179202\pi$
$463$	39.5178	−	14.3833i	1.83655	−	0.668449i	0.990881	−	0.134741i	$-0.0430202\pi$
$464$		0			0
$465$	−0.924907	−	21.1653i	−0.0428915	−	0.981517i
$466$		0			0
$467$	−7.16601	−	12.4119i	−0.331604	−	0.574354i	0.651223	−	0.758886i	$-0.274256\pi$
$467$	−7.16601	−	12.4119i	−0.331604	−	0.574354i	−0.982826	+	0.184532i	$0.940923\pi$
$468$		0			0
$469$	−19.2384	+	29.5082i	−0.888345	+	1.36256i
$470$		0			0
$471$	−0.922272	+	2.92546i	−0.0424961	+	0.134798i
$472$		0			0
$473$	−28.2349	−	4.97857i	−1.29824	−	0.228915i
$474$		0			0
$475$	−1.42747	−	1.70119i	−0.0654966	−	0.0780559i
$476$		0			0
$477$	0.0509539	+	0.0509461i	0.00233302	+	0.00233266i
$478$		0			0
$479$	24.7802	+	9.01926i	1.13224	+	0.412100i	0.839104	−	0.543971i	$-0.183080\pi$
$479$	24.7802	+	9.01926i	1.13224	+	0.412100i	0.293133	+	0.956072i	$0.405302\pi$
$480$		0			0
$481$	5.19369	−	6.18959i	0.236812	−	0.282221i
$482$		0			0
$483$	11.0673	+	31.4288i	0.503579	+	1.43006i
$484$		0			0
$485$		−	25.8084i		−	1.17190i
$486$		0			0
$487$	−15.2304			−0.690154			−0.345077	−	0.938574i	$-0.612147\pi$
$487$	−15.2304			−0.690154			−0.345077	+	0.938574i	$0.612147\pi$
$488$		0			0
$489$	−31.7152	+	13.1383i	−1.43421	+	0.594133i
$490$		0			0
$491$	−16.4365	+	19.5882i	−0.741768	+	0.884005i	−0.996550	−	0.0829937i	$-0.973552\pi$
$491$	−16.4365	+	19.5882i	−0.741768	+	0.884005i	0.254782	+	0.966999i	$0.417996\pi$
$492$		0			0
$493$	0.367276	−	1.00908i	0.0165413	−	0.0454468i
$494$		0			0
$495$	−11.9646	−	11.9627i	−0.537768	−	0.537686i
$496$		0			0
$497$	−23.3811	−	31.1441i	−1.04878	−	1.39700i
$498$		0			0
$499$	2.07058	−	11.7429i	0.0926920	−	0.525683i	−0.902738	−	0.430190i	$-0.858446\pi$
$499$	2.07058	−	11.7429i	0.0926920	−	0.525683i	0.995430	−	0.0954921i	$-0.0304425\pi$
$500$		0			0
$501$	38.9288	+	12.2726i	1.73921	+	0.548298i
$502$		0			0
$503$	−3.24888	+	5.62722i	−0.144860	+	0.250905i	−0.929321	−	0.369273i	$-0.879607\pi$
$503$	−3.24888	+	5.62722i	−0.144860	+	0.250905i	0.784461	+	0.620179i	$0.212940\pi$
$504$		0			0
$505$	8.85480	+	15.3370i	0.394033	+	0.682486i
$506$		0			0
$507$	−24.0133	+	1.04936i	−1.06647	+	0.0466039i
$508$		0			0
$509$	−18.7472	+	6.82341i	−0.830954	+	0.302443i	−0.722250	−	0.691632i	$-0.756892\pi$
$509$	−18.7472	+	6.82341i	−0.830954	+	0.302443i	−0.108704	+	0.994074i	$0.534670\pi$
$510$		0			0
$511$	−18.7522	+	2.26825i	−0.829547	+	0.100342i
$512$		0			0
$513$	1.31568	+	9.98476i	0.0580888	+	0.440838i
$514$		0			0
$515$	15.0373	−	2.65148i	0.662623	−	0.116838i
$516$		0			0
$517$	−9.92946	−	27.2810i	−0.436697	−	1.19982i
$518$		0			0
$519$	4.74069	−	9.10764i	0.208093	−	0.399781i
$520$		0			0
$521$	−1.84181	−	3.19011i	−0.0806911	−	0.139761i	0.822856	−	0.568250i	$-0.192379\pi$
$521$	−1.84181	−	3.19011i	−0.0806911	−	0.139761i	−0.903547	+	0.428489i	$0.859046\pi$
$522$		0			0
$523$	−31.2135	−	18.0211i	−1.36487	−	0.788009i	−0.374604	−	0.927185i	$-0.622221\pi$
$523$	−31.2135	−	18.0211i	−1.36487	−	0.788009i	−0.990268	+	0.139176i	$0.955555\pi$
$524$		0			0
$525$	−0.857494	−	5.18017i	−0.0374241	−	0.226081i
$526$		0			0
$527$	23.3073	+	4.10971i	1.01528	+	0.179022i
$528$		0			0
$529$	−22.8811	+	19.1995i	−0.994830	+	0.834762i
$530$		0			0
$531$	−11.1915	+	0.979991i	−0.485670	+	0.0425280i
$532$		0			0
$533$	−8.03171	+	22.0670i	−0.347892	+	0.955826i
$534$		0			0
$535$	−8.57997	+	10.2252i	−0.370944	+	0.442074i
$536$		0			0
$537$	−18.3563	−	2.41594i	−0.792134	−	0.104256i
$538$		0			0
$539$	2.17386	−	19.9910i	0.0936350	−	0.861075i
$540$		0			0
$541$	2.97654			0.127971			0.0639856	−	0.997951i	$-0.479619\pi$
$541$	2.97654			0.127971			0.0639856	+	0.997951i	$0.479619\pi$
$542$		0			0
$543$	12.8493	−	16.7469i	0.551416	−	0.718677i
$544$		0			0
$545$	−18.5810	−	15.5913i	−0.795924	−	0.667859i
$546$		0			0
$547$	6.88632	+	2.50642i	0.294438	+	0.107167i	0.485016	−	0.874506i	$-0.338814\pi$
$547$	6.88632	+	2.50642i	0.294438	+	0.107167i	−0.190578	+	0.981672i	$0.561036\pi$
$548$		0			0
$549$	11.3707	+	24.3797i	0.485289	+	1.04050i
$550$		0			0
$551$	0.419718	−	0.352185i	0.0178806	−	0.0150036i
$552$		0			0
$553$	−4.40367	+	18.9191i	−0.187263	+	0.804522i
$554$		0			0
$555$	−3.90714	+	3.58051i	−0.165849	+	0.151984i
$556$		0			0
$557$	7.89939	+	4.56071i	0.334708	+	0.193244i	0.657929	−	0.753080i	$-0.271433\pi$
$557$	7.89939	+	4.56071i	0.334708	+	0.193244i	−0.323222	+	0.946323i	$0.604766\pi$
$558$		0			0
$559$	44.8093	−	25.8706i	1.89523	−	1.09421i
$560$		0			0
$561$	15.9404	−	10.1560i	0.673005	−	0.428788i
$562$		0			0
$563$	−33.4088	+	12.1598i	−1.40801	+	0.512474i	−0.930546	−	0.366176i	$-0.880667\pi$
$563$	−33.4088	+	12.1598i	−1.40801	+	0.512474i	−0.477466	+	0.878650i	$0.658445\pi$
$564$		0			0
$565$	−0.317615	+	0.0560042i	−0.0133622	+	0.00235611i
$566$		0			0
$567$	−9.34005	+	21.9035i	−0.392245	+	0.919861i
$568$		0			0
$569$	−41.8695	+	7.38273i	−1.75526	+	0.309500i	−0.956410	−	0.292028i	$-0.905670\pi$
$569$	−41.8695	+	7.38273i	−1.75526	+	0.309500i	−0.798852	+	0.601528i	$0.794559\pi$
$570$		0			0
$571$	−40.1251	+	14.6043i	−1.67918	+	0.611173i	−0.993197	−	0.116442i	$-0.962851\pi$
$571$	−40.1251	+	14.6043i	−1.67918	+	0.611173i	−0.685986	+	0.727615i	$0.740629\pi$
$572$		0			0
$573$	−28.9542	+	18.4474i	−1.20958	+	0.770651i
$574$		0			0
$575$	7.21500	−	4.16558i	0.300886	−	0.173717i
$576$		0			0
$577$	18.3401	+	10.5887i	0.763508	+	0.440812i	0.830554	−	0.556938i	$-0.188024\pi$
$577$	18.3401	+	10.5887i	0.763508	+	0.440812i	−0.0670457	+	0.997750i	$0.521357\pi$
$578$		0			0
$579$	8.13840	−	7.45804i	0.338220	−	0.309946i
$580$		0			0
$581$	0.633530	−	2.72178i	0.0262833	−	0.112918i
$582$		0			0
$583$	0.0528545	−	0.0443502i	0.00218901	−	0.00183680i
$584$		0			0
$585$	30.4179	+	2.65888i	1.25763	+	0.109931i
$586$		0			0
$587$	26.5668	+	9.66951i	1.09653	+	0.399103i	0.826035	−	0.563619i	$-0.190591\pi$
$587$	26.5668	+	9.66951i	1.09653	+	0.399103i	0.270493	+	0.962722i	$0.412813\pi$
$588$		0			0
$589$	9.25034	+	7.76196i	0.381154	+	0.319826i
$590$		0			0
$591$	19.2161	−	25.0449i	0.790447	−	1.03021i
$592$		0			0
$593$	10.4080			0.427407			0.213703	−	0.976899i	$-0.431447\pi$
$593$	10.4080			0.427407			0.213703	+	0.976899i	$0.431447\pi$
$594$		0			0
$595$	−19.7020	−	1.06807i	−0.807702	−	0.0437865i
$596$		0			0
$597$	1.98858	+	0.261725i	0.0813873	+	0.0107117i
$598$		0			0
$599$	−11.1106	+	13.2411i	−0.453969	+	0.541019i	−0.943677	−	0.330867i	$-0.892659\pi$
$599$	−11.1106	+	13.2411i	−0.453969	+	0.541019i	0.489709	+	0.871886i	$0.337103\pi$
$600$		0			0
$601$	3.65246	−	10.0351i	0.148987	−	0.409338i	−0.842639	−	0.538478i	$-0.818999\pi$
$601$	3.65246	−	10.0351i	0.148987	−	0.409338i	0.991626	+	0.129140i	$0.0412216\pi$
$602$		0			0
$603$	−22.9124	−	32.7169i	−0.933063	−	1.33234i
$604$		0			0
$605$	4.13214	−	3.46728i	0.167995	−	0.140965i
$606$		0			0
$607$	38.8906	+	6.85746i	1.57852	+	0.278336i	0.893116	−	0.449827i	$-0.148515\pi$
$607$	38.8906	+	6.85746i	1.57852	+	0.278336i	0.685404	+	0.728163i	$0.259626\pi$
$608$		0			0
$609$	1.27806	−	0.211561i	0.0517894	−	0.00857290i
$610$		0			0
$611$	45.3740	+	26.1967i	1.83564	+	1.05981i
$612$		0			0
$613$	1.77421	+	3.07302i	0.0716595	+	0.124118i	0.899629	−	0.436656i	$-0.143837\pi$
$613$	1.77421	+	3.07302i	0.0716595	+	0.124118i	−0.827969	+	0.560774i	$0.810504\pi$
$614$		0			0
$615$	7.11157	−	13.6625i	0.286766	−	0.550924i
$616$		0			0
$617$	7.91190	+	21.7378i	0.318521	+	0.875130i	0.990861	+	0.134887i	$0.0430671\pi$
$617$	7.91190	+	21.7378i	0.318521	+	0.875130i	−0.672340	+	0.740243i	$0.734711\pi$
$618$		0			0
$619$	−42.3380	+	7.46533i	−1.70171	+	0.300057i	−0.938290	−	0.345849i	$-0.887591\pi$
$619$	−42.3380	+	7.46533i	−1.70171	+	0.300057i	−0.763417	+	0.645906i	$0.776480\pi$
$620$		0			0
$621$	−37.7461	−	1.64370i	−1.51470	−	0.0659593i
$622$		0			0
$623$	−3.12307	−	25.8191i	−0.125123	−	1.03442i
$624$		0			0
$625$	16.8752	−	6.14207i	0.675008	−	0.245683i
$626$		0			0
$627$	9.63452	−	0.421021i	0.384766	−	0.0168140i
$628$		0			0
$629$	−2.96016	−	5.12715i	−0.118029	−	0.204433i
$630$		0			0
$631$	0.305419	−	0.529001i	0.0121585	−	0.0210592i	−0.859882	−	0.510493i	$-0.829463\pi$
$631$	0.305419	−	0.529001i	0.0121585	−	0.0210592i	0.872041	+	0.489433i	$0.162796\pi$
$632$		0			0
$633$	18.9145	+	5.96292i	0.751783	+	0.237005i
$634$		0			0
$635$	4.20776	−	23.8634i	0.166980	−	0.946990i
$636$		0			0
$637$	20.1850	+	30.1589i	0.799757	+	1.19494i
$638$		0			0
$639$	42.6527	−	11.4323i	1.68732	−	0.452253i
$640$		0			0
$641$	11.5302	−	31.6788i	0.455414	−	1.25124i	−0.473451	−	0.880820i	$-0.656992\pi$
$641$	11.5302	−	31.6788i	0.455414	−	1.25124i	0.928865	−	0.370419i	$-0.120786\pi$
$642$		0			0
$643$	−19.5837	+	23.3390i	−0.772307	+	0.920400i	−0.998559	−	0.0536693i	$-0.982908\pi$
$643$	−19.5837	+	23.3390i	−0.772307	+	0.920400i	0.226252	+	0.974069i	$0.427353\pi$
$644$		0			0
$645$	−31.3531	+	12.9883i	−1.23453	+	0.511414i
$646$		0			0
$647$	−45.7165			−1.79730			−0.898652	−	0.438663i	$-0.855452\pi$
$647$	−45.7165			−1.79730			−0.898652	+	0.438663i	$0.855452\pi$
$648$		0			0
$649$			10.7576i			0.422273i
$650$		0			0
$651$	9.48311	+	26.9300i	0.371672	+	1.05547i
$652$		0			0
$653$	1.54785	−	1.84465i	0.0605719	−	0.0721868i	−0.734908	−	0.678167i	$-0.762775\pi$
$653$	1.54785	−	1.84465i	0.0605719	−	0.0721868i	0.795480	+	0.605980i	$0.207219\pi$
$654$		0			0
$655$	−38.2727	−	13.9301i	−1.49544	−	0.544295i
$656$		0			0
$657$	5.54179	−	20.6886i	0.216206	−	0.807138i
$658$		0			0
$659$	−8.07269	−	9.62066i	−0.314467	−	0.374768i	0.585539	−	0.810644i	$-0.300883\pi$
$659$	−8.07269	−	9.62066i	−0.314467	−	0.374768i	−0.900006	+	0.435877i	$0.856438\pi$
$660$		0			0
$661$	−42.6620	−	7.52247i	−1.65936	−	0.292590i	−0.736131	−	0.676839i	$-0.763349\pi$
$661$	−42.6620	−	7.52247i	−1.65936	−	0.292590i	−0.923230	+	0.384249i	$0.874461\pi$
$662$		0			0
$663$	−10.2559	+	32.5319i	−0.398306	+	1.26343i
$664$		0			0
$665$	−8.43322	−	5.49818i	−0.327026	−	0.213210i
$666$		0			0
$667$	1.02774	+	1.78009i	0.0397941	+	0.0689254i
$668$		0			0
$669$	−1.25530	−	28.7259i	−0.0485327	−	1.11061i
$670$		0			0
$671$	24.2060	−	8.81025i	0.934461	−	0.340116i
$672$		0			0
$673$	−4.34857	−	24.6620i	−0.167625	−	0.950650i	−0.946316	−	0.323242i	$-0.895227\pi$
$673$	−4.34857	−	24.6620i	−0.167625	−	0.950650i	0.778691	−	0.627407i	$-0.215884\pi$
$674$		0			0
$675$	5.81272	+	1.28795i	0.223732	+	0.0495732i
$676$		0			0
$677$	−2.53470	−	14.3750i	−0.0974164	−	0.552476i	−0.993980	−	0.109561i	$-0.965055\pi$
$677$	−2.53470	−	14.3750i	−0.0974164	−	0.552476i	0.896564	−	0.442915i	$-0.146056\pi$
$678$		0			0
$679$	10.1092	+	33.2795i	0.387954	+	1.27715i
$680$		0			0
$681$	−4.69211	+	9.01431i	−0.179802	+	0.345429i
$682$		0			0
$683$	−24.6100	+	14.2086i	−0.941675	+	0.543676i	−0.890485	−	0.455013i	$-0.849635\pi$
$683$	−24.6100	+	14.2086i	−0.941675	+	0.543676i	−0.0511899	+	0.998689i	$0.516301\pi$
$684$		0			0
$685$	−14.6812	−	8.47619i	−0.560939	−	0.323859i
$686$		0			0
$687$	−38.8096	+	8.60543i	−1.48068	+	0.328318i
$688$		0			0
$689$	−0.0216223	+	0.122626i	−0.000823743	+	0.00467168i
$690$		0			0
$691$	9.85945	+	11.7500i	0.375071	+	0.446993i	0.920252	−	0.391326i	$-0.127983\pi$
$691$	9.85945	+	11.7500i	0.375071	+	0.446993i	−0.545181	+	0.838318i	$0.683539\pi$
$692$		0			0
$693$	20.1139	+	10.7392i	0.764065	+	0.407950i
$694$		0			0
$695$	1.97653	−	5.43047i	0.0749741	−	0.205990i
$696$		0			0
$697$	13.1810	+	11.0602i	0.499265	+	0.418933i
$698$		0			0
$699$	4.15284	+	0.546570i	0.157075	+	0.0206732i
$700$		0			0
$701$		−	22.5056i		−	0.850024i	−0.905188	−	0.425012i	$-0.860270\pi$
$701$		−	22.5056i		−	0.850024i	0.905188	−	0.425012i	$-0.139730\pi$
$702$		0			0
$703$		−	3.02071i		−	0.113928i
$704$		0			0
$705$	−27.2641	−	20.9188i	−1.02683	−	0.787849i
$706$		0			0
$707$	−17.4256	−	16.3083i	−0.655357	−	0.613338i
$708$		0			0
$709$	0.511648	+	0.186224i	0.0192153	+	0.00699381i	0.351610	−	0.936147i	$-0.385634\pi$
$709$	0.511648	+	0.186224i	0.0192153	+	0.00699381i	−0.332395	+	0.943140i	$0.607857\pi$
$710$		0			0
$711$	−18.0434	−	12.6320i	−0.676679	−	0.473739i
$712$		0			0
$713$	−34.7029	+	29.1192i	−1.29963	+	1.09052i
$714$		0			0
$715$	5.07716	−	28.7940i	0.189875	−	1.07684i
$716$		0			0
$717$	−27.7295	−	30.2591i	−1.03558	−	1.13005i
$718$		0			0
$719$	7.69559	−	13.3291i	0.286997	−	0.497093i	−0.686095	−	0.727512i	$-0.740676\pi$
$719$	7.69559	−	13.3291i	0.286997	−	0.497093i	0.973091	+	0.230419i	$0.0740097\pi$
$720$		0			0
$721$	−18.3518	+	9.30916i	−0.683455	+	0.346691i
$722$		0			0
$723$	−35.0135	+	22.3079i	−1.30217	+	0.829641i
$724$		0			0
$725$	−0.110781	−	0.304369i	−0.00411432	−	0.0113040i
$726$		0			0
$727$	19.2782	−	3.39927i	0.714989	−	0.126072i	0.195691	−	0.980666i	$-0.437305\pi$
$727$	19.2782	−	3.39927i	0.714989	−	0.126072i	0.519297	+	0.854594i	$0.326194\pi$
$728$		0			0
$729$	−19.0963	−	19.0875i	−0.707269	−	0.706945i
$730$		0			0
$731$	−6.58332	−	37.3358i	−0.243493	−	1.38092i
$732$		0			0
$733$	−15.4059	−	42.3272i	−0.569028	−	1.56339i	−0.806025	−	0.591882i	$-0.798385\pi$
$733$	−15.4059	−	42.3272i	−0.569028	−	1.56339i	0.236997	−	0.971510i	$-0.423837\pi$
$734$		0			0
$735$	−10.5449	−	21.3395i	−0.388953	−	0.787120i
$736$		0			0
$737$	−33.1231	+	19.1236i	−1.22010	+	0.704428i
$738$		0			0
$739$	15.4028	−	26.6784i	0.566600	−	0.981380i	−0.430299	−	0.902686i	$-0.641592\pi$
$739$	15.4028	−	26.6784i	0.566600	−	0.981380i	0.996899	−	0.0786932i	$-0.0250748\pi$
$740$		0			0
$741$	−12.8311	+	11.7584i	−0.471361	+	0.431956i
$742$		0			0
$743$	24.3422	+	4.29219i	0.893030	+	0.157465i	0.601289	−	0.799032i	$-0.294654\pi$
$743$	24.3422	+	4.29219i	0.893030	+	0.157465i	0.291741	+	0.956497i	$0.405765\pi$
$744$		0			0
$745$	−17.1728	−	20.4658i	−0.629163	−	0.749808i
$746$		0			0
$747$	2.59579	+	1.81730i	0.0949751	+	0.0664915i
$748$		0			0
$749$	7.05850	−	16.5460i	0.257912	−	0.604578i
$750$		0			0
$751$	3.40791	+	2.85958i	0.124356	+	0.104347i	0.702845	−	0.711343i	$-0.251913\pi$
$751$	3.40791	+	2.85958i	0.124356	+	0.104347i	−0.578489	+	0.815691i	$0.696357\pi$
$752$		0			0
$753$	13.1287	+	10.0732i	0.478436	+	0.367088i
$754$		0			0
$755$	−4.78054			−0.173982
$756$		0			0
$757$	24.3023			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$757$	24.3023			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$758$		0			0
$759$	−4.72089	+	35.8693i	−0.171357	+	1.30197i
$760$		0			0
$761$	−30.4826	−	25.5780i	−1.10499	−	0.927201i	−0.107244	−	0.994233i	$-0.534203\pi$
$761$	−30.4826	−	25.5780i	−1.10499	−	0.927201i	−0.997751	+	0.0670320i	$0.978647\pi$
$762$		0			0
$763$	30.0670	+	12.8266i	1.08850	+	0.464353i
$764$		0			0
$765$	9.45358	−	20.2773i	0.341795	−	0.733128i
$766$		0			0
$767$	−12.4792	−	14.8721i	−0.450598	−	0.537001i
$768$		0			0
$769$	−16.2697	−	2.86879i	−0.586702	−	0.103451i	−0.127586	−	0.991828i	$-0.540723\pi$
$769$	−16.2697	−	2.86879i	−0.586702	−	0.103451i	−0.459116	+	0.888376i	$0.651834\pi$
$770$		0			0
$771$	7.57252	+	34.1512i	0.272718	+	1.22993i
$772$		0			0
$773$	−7.34991	+	12.7304i	−0.264358	+	0.457881i	−0.967395	−	0.253272i	$-0.918493\pi$
$773$	−7.34991	+	12.7304i	−0.264358	+	0.457881i	0.703037	+	0.711153i	$0.251827\pi$
$774$		0			0
$775$	6.18224	−	3.56932i	0.222073	−	0.128214i
$776$		0			0
$777$	3.63571	−	6.14744i	0.130430	−	0.220538i
$778$		0			0
$779$	3.00268	+	8.24979i	0.107582	+	0.295579i
$780$		0			0
$781$	−7.34262	−	41.6421i	−0.262740	−	1.49007i
$782$		0			0
$783$	−0.317764	+	1.43412i	−0.0113560	+	0.0512512i
$784$		0			0
$785$	3.42396	−	0.603736i	0.122206	−	0.0215483i
$786$		0			0
$787$	−6.79081	−	18.6576i	−0.242066	−	0.665071i	−0.999920	−	0.0126468i	$-0.995974\pi$
$787$	−6.79081	−	18.6576i	−0.242066	−	0.665071i	0.757854	−	0.652424i	$-0.226248\pi$
$788$		0			0
$789$	0.519250	+	11.8824i	0.0184858	+	0.423023i
$790$		0			0
$791$	0.387623	−	0.196626i	0.0137823	−	0.00699123i
$792$		0			0
$793$	−23.2439	+	40.2597i	−0.825416	+	1.42966i
$794$		0			0
$795$	0.0245559	−	0.0778917i	0.000870908	−	0.00276253i
$796$		0			0
$797$	−1.48037	+	8.39557i	−0.0524372	+	0.297386i	−0.999736	−	0.0229642i	$-0.992690\pi$
$797$	−1.48037	+	8.39557i	−0.0524372	+	0.297386i	0.947299	+	0.320351i	$0.103801\pi$
$798$		0			0
$799$	29.4082	−	24.6764i	1.04039	−	0.872988i
$800$		0			0
$801$	28.4852	+	7.63026i	1.00648	+	0.269602i
$802$		0			0
$803$	−19.2722	−	7.01452i	−0.680103	−	0.247537i
$804$		0			0
$805$	25.8070	−	27.5750i	0.909577	−	0.971892i
$806$		0			0
$807$	2.11843	−	0.877578i	0.0745724	−	0.0308922i
$808$		0			0
$809$		−	45.3488i		−	1.59438i	−0.603730	−	0.797189i	$-0.706320\pi$
$809$		−	45.3488i		−	1.59438i	0.603730	−	0.797189i	$-0.293680\pi$
$810$		0			0
$811$			25.7719i			0.904973i	0.891771	+	0.452486i	$0.149463\pi$
$811$			25.7719i			0.904973i	−0.891771	+	0.452486i	$0.850537\pi$
$812$		0			0
$813$	11.4785	+	27.7086i	0.402569	+	0.971782i
$814$		0			0
$815$	29.8071	+	25.0111i	1.04410	+	0.876102i
$816$		0			0
$817$	6.61591	−	18.1771i	0.231461	−	0.635935i
$818$		0			0
$819$	−40.2648	+	8.48612i	−1.40697	+	0.296529i
$820$		0			0
$821$	16.7812	+	19.9991i	0.585669	+	0.697974i	0.974767	−	0.223223i	$-0.0716577\pi$
$821$	16.7812	+	19.9991i	0.585669	+	0.697974i	−0.389098	+	0.921196i	$0.627213\pi$
$822$		0			0
$823$	−6.96464	+	39.4984i	−0.242772	+	1.37683i	0.582838	+	0.812588i	$0.301942\pi$
$823$	−6.96464	+	39.4984i	−0.242772	+	1.37683i	−0.825610	+	0.564241i	$0.809169\pi$
$824$		0			0
$825$	1.71413	−	5.43726i	0.0596785	−	0.189301i
$826$		0			0
$827$	27.2928	+	15.7575i	0.949064	+	0.547942i	0.892790	−	0.450473i	$-0.148745\pi$
$827$	27.2928	+	15.7575i	0.949064	+	0.547942i	0.0562739	+	0.998415i	$0.482078\pi$
$828$		0			0
$829$	−32.2170	+	18.6005i	−1.11894	+	0.646021i	−0.941131	−	0.338043i	$-0.890235\pi$
$829$	−32.2170	+	18.6005i	−1.11894	+	0.646021i	−0.177811	+	0.984065i	$0.556902\pi$
$830$		0			0
$831$	−10.7327	+	0.469011i	−0.372314	+	0.0162698i
$832$		0			0
$833$	25.8237	−	6.34002i	0.894739	−	0.219669i
$834$		0			0
$835$	−8.03385	−	45.5622i	−0.278023	−	1.57675i
$836$		0			0
$837$	−32.3430	−	1.40842i	−1.11794	−	0.0486820i
$838$		0			0
$839$	0.750998	+	4.25912i	0.0259273	+	0.147041i	0.995023	−	0.0996431i	$-0.0317701\pi$
$839$	0.750998	+	4.25912i	0.0259273	+	0.147041i	−0.969096	+	0.246684i	$0.920659\pi$
$840$		0			0
$841$	−27.1760	+	9.89125i	−0.937103	+	0.341078i
$842$		0			0
$843$	−8.23011	−	4.28392i	−0.283460	−	0.147546i
$844$		0			0
$845$	13.6221	+	23.5941i	0.468614	+	0.811663i
$846$		0			0
$847$	−3.97019	+	6.08956i	−0.136417	+	0.209240i
$848$		0			0
$849$	−2.83163	+	0.627871i	−0.0971813	+	0.0215485i
$850$		0			0
$851$	11.1601	+	1.96783i	0.382563	+	0.0674562i
$852$		0			0
$853$	15.0308	+	17.9131i	0.514646	+	0.613332i	0.959306	−	0.282368i	$-0.0911199\pi$
$853$	15.0308	+	17.9131i	0.514646	+	0.613332i	−0.444660	+	0.895700i	$0.646675\pi$
$854$		0			0
$855$	9.35026	−	6.54819i	0.319772	−	0.223943i
$856$		0			0
$857$	−15.3161	−	5.57460i	−0.523187	−	0.190425i	0.0669065	−	0.997759i	$-0.478687\pi$
$857$	−15.3161	−	5.57460i	−0.523187	−	0.190425i	−0.590094	+	0.807335i	$0.700909\pi$
$858$		0			0
$859$	−1.62975	+	1.94226i	−0.0556065	+	0.0662692i	−0.793131	−	0.609051i	$-0.791550\pi$
$859$	−1.62975	+	1.94226i	−0.0556065	+	0.0662692i	0.737524	+	0.675321i	$0.235995\pi$
$860$		0			0
$861$	−3.81865	+	20.4031i	−0.130139	+	0.695337i
$862$		0			0
$863$			11.2774i			0.383886i	0.981406	+	0.191943i	$0.0614789\pi$
$863$			11.2774i			0.383886i	−0.981406	+	0.191943i	$0.938521\pi$
$864$		0			0
$865$	−11.6379			−0.395701
$866$		0			0
$867$	−3.53187	−	2.70988i	−0.119949	−	0.0920325i
$868$		0			0
$869$	−13.5571	+	16.1567i	−0.459892	+	0.548078i
$870$		0			0
$871$	23.6078	−	64.8618i	0.799918	−	2.19776i
$872$		0			0
$873$	−39.2882	−	3.43425i	−1.32970	−	0.116232i
$874$		0			0
$875$	−25.5288	+	19.1655i	−0.863031	+	0.647911i
$876$		0			0
$877$	5.51629	−	31.2844i	0.186272	−	1.05640i	−0.738038	−	0.674759i	$-0.764248\pi$
$877$	5.51629	−	31.2844i	0.186272	−	1.05640i	0.924310	−	0.381642i	$-0.124641\pi$
$878$		0			0
$879$	17.5143	−	16.0501i	0.590742	−	0.541357i
$880$		0			0
$881$	−3.95021	+	6.84196i	−0.133086	+	0.230512i	−0.924865	−	0.380296i	$-0.875822\pi$
$881$	−3.95021	+	6.84196i	−0.133086	+	0.230512i	0.791779	+	0.610808i	$0.209155\pi$
$882$		0			0
$883$	−0.282051	−	0.488526i	−0.00949176	−	0.0164402i	0.861241	−	0.508198i	$-0.169688\pi$
$883$	−0.282051	−	0.488526i	−0.00949176	−	0.0164402i	−0.870732	+	0.491757i	$0.836355\pi$
$884$		0			0
$885$	6.84222	+	10.7392i	0.229999	+	0.360995i
$886$		0			0
$887$	7.36835	−	2.68186i	0.247405	−	0.0900480i	−0.215341	−	0.976539i	$-0.569086\pi$
$887$	7.36835	−	2.68186i	0.247405	−	0.0900480i	0.462746	+	0.886491i	$0.346864\pi$
$888$		0			0
$889$	3.92146	+	32.4196i	0.131522	+	1.08732i
$890$		0			0
$891$	−19.8030	+	16.6218i	−0.663425	+	0.556853i
$892$		0			0
$893$	19.2898	−	3.40132i	0.645510	−	0.113821i
$894$		0			0
$895$	7.17751	+	19.7201i	0.239918	+	0.659169i
$896$		0			0
$897$	−35.0831	−	55.0647i	−1.17139	−	1.83856i
$898$		0			0
$899$	0.880624	+	1.52529i	0.0293705	+	0.0508711i
$900$		0			0
$901$	0.0790131	+	0.0456182i	0.00263231	+	0.00151976i
$902$		0			0
$903$	35.3418	−	29.0292i	1.17610	−	0.966032i
$904$		0			0
$905$	−23.5620	−	4.15462i	−0.783228	−	0.138104i
$906$		0			0
$907$	−14.7624	+	12.3871i	−0.490176	+	0.411307i	−0.854089	−	0.520126i	$-0.825885\pi$
$907$	−14.7624	+	12.3871i	−0.490176	+	0.411307i	0.363913	+	0.931433i	$0.381440\pi$
$908$		0			0
$909$	24.5258	−	11.4388i	0.813468	−	0.379402i
$910$		0			0
$911$	−14.5751	+	40.0448i	−0.482896	+	1.32674i	0.424104	+	0.905613i	$0.360589\pi$
$911$	−14.5751	+	40.0448i	−0.482896	+	1.32674i	−0.907000	+	0.421131i	$0.861633\pi$
$912$		0			0
$913$	1.95038	−	2.32437i	0.0645481	−	0.0769254i
$914$		0			0
$915$	18.5610	−	24.1910i	0.613606	−	0.799730i
$916$		0			0
$917$	54.8084	+	2.97123i	1.80993	+	0.0981186i
$918$		0			0
$919$	9.95811			0.328488			0.164244	−	0.986420i	$-0.447482\pi$
$919$	9.95811			0.328488			0.164244	+	0.986420i	$0.447482\pi$
$920$		0			0
$921$	8.24447	+	1.08508i	0.271665	+	0.0357548i
$922$		0			0
$923$	58.4571	+	49.0514i	1.92414	+	1.61455i
$924$		0			0
$925$	−1.67805	−	0.610761i	−0.0551741	−	0.0200817i
$926$		0			0
$927$	−2.03539	−	23.2441i	−0.0668509	−	0.763437i
$928$		0			0
$929$	−42.0726	+	35.3031i	−1.38036	+	1.15826i	−0.411277	+	0.911511i	$0.634917\pi$
$929$	−42.0726	+	35.3031i	−1.38036	+	1.15826i	−0.969080	+	0.246746i	$0.920639\pi$
$930$		0			0
$931$	13.0281	+	3.78652i	0.426980	+	0.124098i
$932$		0			0
$933$	−7.89007	−	35.5834i	−0.258309	−	1.16495i
$934$		0			0
$935$	−18.5532	−	10.7117i	−0.606755	−	0.350310i
$936$		0			0
$937$	−39.1160	+	22.5836i	−1.27786	+	0.737775i	−0.976455	−	0.215720i	$-0.930790\pi$
$937$	−39.1160	+	22.5836i	−1.27786	+	0.737775i	−0.301408	+	0.953495i	$0.597457\pi$
$938$		0			0
$939$	−30.9186	−	16.0937i	−1.00899	−	0.525199i
$940$		0			0
$941$	−10.5522	+	3.84069i	−0.343992	+	0.125203i	−0.508238	−	0.861216i	$-0.669703\pi$
$941$	−10.5522	+	3.84069i	−0.343992	+	0.125203i	0.164246	+	0.986419i	$0.447481\pi$
$942$		0			0
$943$	−32.4352	+	5.71919i	−1.05623	+	0.186243i
$944$		0			0
$945$	26.9101	−	2.07228i	0.875384	−	0.0674114i
$946$		0			0
$947$	−2.43115	+	0.428676i	−0.0790016	+	0.0139301i	−0.213009	−	0.977050i	$-0.568326\pi$
$947$	−2.43115	+	0.428676i	−0.0790016	+	0.0139301i	0.134008	+	0.990980i	$0.457215\pi$
$948$		0			0
$949$	34.7805	−	12.6590i	1.12902	−	0.410930i
$950$		0			0
$951$	1.15871	+	26.5155i	0.0375736	+	0.859823i
$952$		0			0
$953$	−33.0119	+	19.0594i	−1.06936	+	0.617396i	−0.928007	−	0.372563i	$-0.878479\pi$
$953$	−33.0119	+	19.0594i	−1.06936	+	0.617396i	−0.141354	+	0.989959i	$0.545146\pi$
$954$		0			0
$955$	33.7000	+	19.4567i	1.09051	+	0.629605i
$956$		0			0
$957$	1.34148	+	0.422912i	0.0433640	+	0.0136708i
$958$		0			0
$959$	22.2513	+	5.17927i	0.718531	+	0.167248i
$960$		0			0
$961$	−5.98809	+	5.02460i	−0.193164	+	0.162084i
$962$		0			0
$963$	14.4241	+	14.4219i	0.464811	+	0.464740i
$964$		0			0
$965$	−11.7575	−	4.27939i	−0.378489	−	0.137759i
$966$		0			0
$967$	23.1300	+	19.4084i	0.743810	+	0.624131i	0.933858	−	0.357644i	$-0.116420\pi$
$967$	23.1300	+	19.4084i	0.743810	+	0.624131i	−0.190048	+	0.981775i	$0.560864\pi$
$968$		0			0
$969$	4.88050	+	11.7813i	0.156784	+	0.378470i
$970$		0			0
$971$	−13.5761			−0.435678			−0.217839	−	0.975985i	$-0.569901\pi$
$971$	−13.5761			−0.435678			−0.217839	+	0.975985i	$0.569901\pi$
$972$		0			0
$973$	−0.421584	+	7.77671i	−0.0135154	+	0.249310i
$974$		0			0
$975$	3.93766	+	9.50532i	0.126106	+	0.304414i
$976$		0			0
$977$	−11.6721	+	13.9103i	−0.373425	+	0.445031i	−0.919728	−	0.392557i	$-0.871590\pi$
$977$	−11.6721	+	13.9103i	−0.373425	+	0.445031i	0.546302	+	0.837588i	$0.316035\pi$
$978$		0			0
$979$	9.65801	−	26.5352i	0.308671	−	0.848068i
$980$		0			0
$981$	−26.2072	+	26.2112i	−0.836732	+	0.836860i
$982$		0			0
$983$	41.2689	−	34.6287i	1.31627	−	1.10449i	0.329194	−	0.944262i	$-0.393223\pi$
$983$	41.2689	−	34.6287i	1.31627	−	1.10449i	0.987081	−	0.160223i	$-0.0512213\pi$
$984$		0			0
$985$	−35.2370	−	6.21324i	−1.12275	−	0.197970i
$986$		0			0
$987$	43.3505	+	16.2951i	1.37986	+	0.518679i
$988$		0			0
$989$	62.8458	+	36.2840i	1.99838	+	1.15376i
$990$		0			0
$991$	0.129714	+	0.224671i	0.00412051	+	0.00713692i	0.868078	−	0.496427i	$-0.165355\pi$
$991$	0.129714	+	0.224671i	0.00412051	+	0.00713692i	−0.863958	+	0.503564i	$0.832022\pi$
$992$		0			0
$993$	28.8792	−	1.26200i	0.916454	−	0.0400483i
$994$		0			0
$995$	−0.777556	−	2.13632i	−0.0246502	−	0.0677258i
$996$		0			0
$997$	49.0006	−	8.64014i	1.55187	−	0.273636i	0.669001	−	0.743262i	$-0.266722\pi$
$997$	49.0006	−	8.64014i	1.55187	−	0.273636i	0.882865	+	0.469626i	$0.155611\pi$
$998$		0			0
$999$	4.93070	+	6.42430i	0.156001	+	0.203256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.4	✓	144
7.6	odd	2	inner	756.2.bx.a.41.21	yes	144
27.2	odd	18	inner	756.2.bx.a.461.21	yes	144
189.83	even	18	inner	756.2.bx.a.461.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.4	✓	144	1.1	even	1	trivial
756.2.bx.a.41.21	yes	144	7.6	odd	2	inner
756.2.bx.a.461.4	yes	144	189.83	even	18	inner
756.2.bx.a.461.21	yes	144	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60018 + 0.662888i) q^{3} +(1.50391 + 1.26193i) q^{5} +(-2.43356 - 1.03816i) q^{7} +(2.12116 - 2.12148i) q^{9} +O(q^{10})\)	\(q+(-1.60018 + 0.662888i) q^{3} +(1.50391 + 1.26193i) q^{5} +(-2.43356 - 1.03816i) q^{7} +(2.12116 - 2.12148i) q^{9} +(-1.84654 - 2.20062i) q^{11} +(5.10557 + 0.900250i) q^{13} +(-3.24305 - 1.02239i) q^{15} +(1.89933 - 3.28974i) q^{17} +(1.67851 - 0.969089i) q^{19} +(4.58232 + 0.0480554i) q^{21} +(2.48687 + 6.83262i) q^{23} +(-0.198964 - 1.12838i) q^{25} +(-1.98793 + 4.80085i) q^{27} +(0.278395 - 0.0490886i) q^{29} +(2.13090 + 5.85459i) q^{31} +(4.41355 + 2.29734i) q^{33} +(-2.34978 - 4.63228i) q^{35} +(0.779265 - 1.34973i) q^{37} +(-8.76661 + 1.94386i) q^{39} +(-0.786563 + 4.46082i) q^{41} +(7.64536 - 6.41522i) q^{43} +(5.86719 - 0.513764i) q^{45} +(9.49663 + 3.45649i) q^{47} +(4.84447 + 5.05283i) q^{49} +(-0.858544 + 6.52322i) q^{51} +0.0240181i q^{53} -5.63972i q^{55} +(-2.04352 + 2.66338i) q^{57} +(-2.86867 - 2.40710i) q^{59} +(-3.06689 + 8.42621i) q^{61} +(-7.36440 + 2.96067i) q^{63} +(6.54227 + 7.79677i) q^{65} +(2.31196 - 13.1118i) q^{67} +(-8.50870 - 9.28490i) q^{69} +(12.7474 + 7.35971i) q^{71} +(6.18283 - 3.56966i) q^{73} +(1.06637 + 1.67372i) q^{75} +(2.20908 + 7.27233i) q^{77} +(-1.27491 - 7.23036i) q^{79} +(-0.00137476 - 9.00000i) q^{81} +(0.183414 + 1.04019i) q^{83} +(7.00784 - 2.55064i) q^{85} +(-0.412942 + 0.263096i) q^{87} +(4.91491 + 8.51288i) q^{89} +(-11.4901 - 7.49119i) q^{91} +(-7.29075 - 7.95585i) q^{93} +(3.74725 + 0.660741i) q^{95} +(-8.45008 - 10.0704i) q^{97} +(-8.58536 - 0.750461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more