LMFDB - Embedded newform 819.2.fn.e.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.2
Character	$\chi$	$=$	819.577
Dual form			819.2.fn.e.775.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53492 - 0.411280i) q^{2} +(0.454770 + 0.262561i) q^{4} +(0.0206096 - 0.0769162i) q^{5} +(-2.16435 + 1.52171i) q^{7} +(1.65723 + 1.65723i) q^{8} +O(q^{10})$	\(q+(-1.53492 - 0.411280i) q^{2} +(0.454770 + 0.262561i) q^{4} +(0.0206096 - 0.0769162i) q^{5} +(-2.16435 + 1.52171i) q^{7} +(1.65723 + 1.65723i) q^{8} +(-0.0632682 + 0.109584i) q^{10} +(-4.08225 + 1.09384i) q^{11} +(-0.565867 + 3.56087i) q^{13} +(3.94794 - 1.44555i) q^{14} +(-2.38725 - 4.13483i) q^{16} +(2.90357 - 5.02912i) q^{17} +(1.36980 - 5.11216i) q^{19} +(0.0295679 - 0.0295679i) q^{20} +6.71579 q^{22} +(0.755405 - 0.436133i) q^{23} +(4.32464 + 2.49683i) q^{25} +(2.33307 - 5.23291i) q^{26} +(-1.38382 + 0.123754i) q^{28} -0.362759 q^{29} +(-1.34748 + 0.361057i) q^{31} +(0.750478 + 2.80082i) q^{32} +(-6.52511 + 6.52511i) q^{34} +(0.0724379 + 0.197835i) q^{35} +(1.00978 - 3.76857i) q^{37} +(-4.20506 + 7.28338i) q^{38} +(0.161623 - 0.0933128i) q^{40} +(-7.70995 - 7.70995i) q^{41} +2.65570i q^{43} +(-2.14368 - 0.574398i) q^{44} +(-1.33886 + 0.358745i) q^{46} +(2.79467 + 0.748829i) q^{47} +(2.36879 - 6.58702i) q^{49} +(-5.61106 - 5.61106i) q^{50} +(-1.19229 + 1.47080i) q^{52} +(5.26830 - 9.12497i) q^{53} +0.336535i q^{55} +(-6.10864 - 1.06499i) q^{56} +(0.556806 + 0.149196i) q^{58} +(0.573890 + 2.14179i) q^{59} +(3.63628 - 2.09941i) q^{61} +2.21677 q^{62} +4.94130i q^{64} +(0.262226 + 0.116913i) q^{65} +(-2.61773 - 9.76951i) q^{67} +(2.64091 - 1.52473i) q^{68} +(-0.0298205 - 0.333453i) q^{70} +(-3.65698 + 3.65698i) q^{71} +(-3.08002 - 11.4948i) q^{73} +(-3.09987 + 5.36914i) q^{74} +(1.96520 - 1.96520i) q^{76} +(7.17090 - 8.57944i) q^{77} +(-4.27671 - 7.40747i) q^{79} +(-0.367236 + 0.0984006i) q^{80} +(8.66319 + 15.0051i) q^{82} +(4.91372 + 4.91372i) q^{83} +(-0.326980 - 0.326980i) q^{85} +(1.09224 - 4.07628i) q^{86} +(-8.57795 - 4.95248i) q^{88} +(7.78209 + 2.08520i) q^{89} +(-4.19388 - 8.56804i) q^{91} +0.458047 q^{92} +(-3.98161 - 2.29878i) q^{94} +(-0.364977 - 0.210720i) q^{95} +(-6.04128 - 6.04128i) q^{97} +(-6.34501 + 9.13630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.53492	−	0.411280i	−1.08535	−	0.290819i	−0.328565	−	0.944482i	$-0.606565\pi$
$2$	−1.53492	−	0.411280i	−1.08535	−	0.290819i	−0.756786	+	0.653663i	$0.773232\pi$
$3$		0			0
$3$		0			0
$4$	0.454770	+	0.262561i	0.227385	+	0.131281i
$5$	0.0206096	−	0.0769162i	0.00921691	−	0.0343980i	−0.961164	−	0.275977i	$-0.910999\pi$
$5$	0.0206096	−	0.0769162i	0.00921691	−	0.0343980i	0.970381	+	0.241579i	$0.0776653\pi$
$6$		0			0
$7$	−2.16435	+	1.52171i	−0.818046	+	0.575153i
$7$	−2.16435	+	1.52171i	−0.818046	+	0.575153i
$8$	1.65723	+	1.65723i	0.585918	+	0.585918i
$9$		0			0
$10$	−0.0632682	+	0.109584i	−0.0200072	+	0.0346534i
$11$	−4.08225	+	1.09384i	−1.23084	+	0.329804i	−0.814908	−	0.579590i	$-0.803213\pi$
$11$	−4.08225	+	1.09384i	−1.23084	+	0.329804i	−0.415936	+	0.909394i	$0.636546\pi$
$12$		0			0
$13$	−0.565867	+	3.56087i	−0.156943	+	0.987608i
$13$	−0.565867	+	3.56087i	−0.156943	+	0.987608i
$14$	3.94794	−	1.44555i	1.05513	−	0.386339i
$15$		0			0
$16$	−2.38725	−	4.13483i	−0.596811	−	1.03371i
$17$	2.90357	−	5.02912i	0.704218	−	1.21974i	−0.262755	−	0.964863i	$-0.584631\pi$
$17$	2.90357	−	5.02912i	0.704218	−	1.21974i	0.966973	−	0.254879i	$-0.0820357\pi$
$18$		0			0
$19$	1.36980	−	5.11216i	0.314254	−	1.17281i	−0.610429	−	0.792071i	$-0.709003\pi$
$19$	1.36980	−	5.11216i	0.314254	−	1.17281i	0.924682	−	0.380740i	$-0.124331\pi$
$20$	0.0295679	−	0.0295679i	0.00661158	−	0.00661158i
$21$		0			0
$22$	6.71579			1.43181
$23$	0.755405	−	0.436133i	0.157513	−	0.0909400i	−0.419172	−	0.907907i	$-0.637680\pi$
$23$	0.755405	−	0.436133i	0.157513	−	0.0909400i	0.576685	+	0.816967i	$0.304346\pi$
$24$		0			0
$25$	4.32464	+	2.49683i	0.864927	+	0.499366i
$26$	2.33307	−	5.23291i	0.457553	−	1.02626i
$27$		0			0
$28$	−1.38382	+	0.123754i	−0.261518	+	0.0233873i
$29$	−0.362759			−0.0673627			−0.0336814	−	0.999433i	$-0.510723\pi$
$29$	−0.362759			−0.0673627			−0.0336814	+	0.999433i	$0.510723\pi$
$30$		0			0
$31$	−1.34748	+	0.361057i	−0.242015	+	0.0648477i	−0.377787	−	0.925892i	$-0.623315\pi$
$31$	−1.34748	+	0.361057i	−0.242015	+	0.0648477i	0.135773	+	0.990740i	$0.456648\pi$
$32$	0.750478	+	2.80082i	0.132667	+	0.495120i
$33$		0			0
$34$	−6.52511	+	6.52511i	−1.11905	+	1.11905i
$35$	0.0724379	+	0.197835i	0.0122442	+	0.0334403i
$36$		0			0
$37$	1.00978	−	3.76857i	0.166008	−	0.619549i	−0.831902	−	0.554923i	$-0.812748\pi$
$37$	1.00978	−	3.76857i	0.166008	−	0.619549i	0.997910	−	0.0646262i	$-0.0205855\pi$
$38$	−4.20506	+	7.28338i	−0.682151	+	1.18152i
$39$		0			0
$40$	0.161623	−	0.0933128i	0.0255548	−	0.0147541i
$41$	−7.70995	−	7.70995i	−1.20409	−	1.20409i	−0.972911	−	0.231182i	$-0.925741\pi$
$41$	−7.70995	−	7.70995i	−1.20409	−	1.20409i	−0.231182	−	0.972911i	$-0.574259\pi$
$42$		0			0
$43$			2.65570i			0.404990i	0.979283	+	0.202495i	$0.0649050\pi$
$43$			2.65570i			0.404990i	−0.979283	+	0.202495i	$0.935095\pi$
$44$	−2.14368	−	0.574398i	−0.323172	−	0.0865938i
$45$		0			0
$46$	−1.33886	+	0.358745i	−0.197404	+	0.0528941i
$47$	2.79467	+	0.748829i	0.407644	+	0.109228i	0.456813	−	0.889563i	$-0.348991\pi$
$47$	2.79467	+	0.748829i	0.407644	+	0.109228i	−0.0491692	+	0.998790i	$0.515657\pi$
$48$		0			0
$49$	2.36879	−	6.58702i	0.338399	−	0.941003i
$50$	−5.61106	−	5.61106i	−0.793524	−	0.793524i
$51$		0			0
$52$	−1.19229	+	1.47080i	−0.165340	+	0.203963i
$53$	5.26830	−	9.12497i	0.723657	−	1.25341i	−0.235868	−	0.971785i	$-0.575793\pi$
$53$	5.26830	−	9.12497i	0.723657	−	1.25341i	0.959524	−	0.281625i	$-0.0908735\pi$
$54$		0			0
$55$			0.336535i			0.0453784i
$56$	−6.10864	−	1.06499i	−0.816301	−	0.142316i
$57$		0			0
$58$	0.556806	+	0.149196i	0.0731122	+	0.0195903i
$59$	0.573890	+	2.14179i	0.0747142	+	0.278837i	0.993168	−	0.116690i	$-0.0372285\pi$
$59$	0.573890	+	2.14179i	0.0747142	+	0.278837i	−0.918454	+	0.395527i	$0.870562\pi$
$60$		0			0
$61$	3.63628	−	2.09941i	0.465578	−	0.268802i	−0.248809	−	0.968553i	$-0.580039\pi$
$61$	3.63628	−	2.09941i	0.465578	−	0.268802i	0.714387	+	0.699751i	$0.246706\pi$
$62$	2.21677			0.281530
$63$		0			0
$64$			4.94130i			0.617662i
$65$	0.262226	+	0.116913i	0.0325252	+	0.0145012i
$66$		0			0
$67$	−2.61773	−	9.76951i	−0.319807	−	1.19354i	−0.919430	−	0.393253i	$-0.871350\pi$
$67$	−2.61773	−	9.76951i	−0.319807	−	1.19354i	0.599623	−	0.800282i	$-0.295317\pi$
$68$	2.64091	−	1.52473i	0.320257	−	0.184901i
$69$		0			0
$70$	−0.0298205	−	0.333453i	−0.00356423	−	0.0398553i
$71$	−3.65698	+	3.65698i	−0.434004	+	0.434004i	−0.889988	−	0.455984i	$-0.849287\pi$
$71$	−3.65698	+	3.65698i	−0.434004	+	0.434004i	0.455984	+	0.889988i	$0.349287\pi$
$72$		0			0
$73$	−3.08002	−	11.4948i	−0.360489	−	1.34536i	−0.873434	−	0.486942i	$-0.838112\pi$
$73$	−3.08002	−	11.4948i	−0.360489	−	1.34536i	0.512945	−	0.858421i	$-0.328554\pi$
$74$	−3.09987	+	5.36914i	−0.360353	+	0.624150i
$75$		0			0
$76$	1.96520	−	1.96520i	0.225424	−	0.225424i
$77$	7.17090	−	8.57944i	0.817200	−	0.977718i
$78$		0			0
$79$	−4.27671	−	7.40747i	−0.481167	−	0.833406i	0.518599	−	0.855017i	$-0.326454\pi$
$79$	−4.27671	−	7.40747i	−0.481167	−	0.833406i	−0.999766	+	0.0216116i	$0.993120\pi$
$80$	−0.367236	+	0.0984006i	−0.0410582	+	0.0110015i
$81$		0			0
$82$	8.66319	+	15.0051i	0.956690	+	1.65703i
$83$	4.91372	+	4.91372i	0.539351	+	0.539351i	0.923338	−	0.383987i	$-0.125449\pi$
$83$	4.91372	+	4.91372i	0.539351	+	0.539351i	−0.383987	+	0.923338i	$0.625449\pi$
$84$		0			0
$85$	−0.326980	−	0.326980i	−0.0354659	−	0.0354659i
$86$	1.09224	−	4.07628i	0.117779	−	0.439557i
$87$		0			0
$88$	−8.57795	−	4.95248i	−0.914413	−	0.527936i
$89$	7.78209	+	2.08520i	0.824899	+	0.221031i	0.646487	−	0.762925i	$-0.276237\pi$
$89$	7.78209	+	2.08520i	0.824899	+	0.221031i	0.178412	+	0.983956i	$0.442904\pi$
$90$		0			0
$91$	−4.19388	−	8.56804i	−0.439638	−	0.898175i
$92$	0.458047			0.0477547
$93$		0			0
$94$	−3.98161	−	2.29878i	−0.410671	−	0.237101i
$95$	−0.364977	−	0.210720i	−0.0374459	−	0.0216194i
$96$		0			0
$97$	−6.04128	−	6.04128i	−0.613399	−	0.613399i	0.330431	−	0.943830i	$-0.392806\pi$
$97$	−6.04128	−	6.04128i	−0.613399	−	0.613399i	−0.943830	+	0.330431i	$0.892806\pi$
$98$	−6.34501	+	9.13630i	−0.640943	+	0.922905i
$99$		0			0
$100$	1.31114	+	2.27096i	0.131114	+	0.227096i
$101$	5.60987	−	9.71658i	0.558203	−	0.966836i	−0.439444	−	0.898270i	$-0.644824\pi$
$101$	5.60987	−	9.71658i	0.558203	−	0.966836i	0.997647	−	0.0685657i	$-0.0218423\pi$
$102$		0			0
$103$	−4.82752	−	8.36150i	−0.475669	−	0.823883i	0.523942	−	0.851754i	$-0.324461\pi$
$103$	−4.82752	−	8.36150i	−0.475669	−	0.823883i	−0.999612	+	0.0278704i	$0.991127\pi$
$104$	−6.83894	+	4.96340i	−0.670613	+	0.486701i
$105$		0			0
$106$	−11.8393	+	11.8393i	−1.14994	+	1.14994i
$107$	−8.81408	−	15.2664i	−0.852089	−	1.47586i	−0.879319	−	0.476232i	$-0.842002\pi$
$107$	−8.81408	−	15.2664i	−0.852089	−	1.47586i	0.0272305	−	0.999629i	$-0.491331\pi$
$108$		0			0
$109$	3.53114	+	13.1784i	0.338222	+	1.26226i	0.900334	+	0.435199i	$0.143322\pi$
$109$	3.53114	+	13.1784i	0.338222	+	1.26226i	−0.562113	+	0.827061i	$0.690011\pi$
$110$	0.138410	−	0.516553i	0.0131969	−	0.0492514i
$111$		0			0
$112$	11.4588	+	5.31651i	1.08276	+	0.502363i
$113$	6.02917			0.567176			0.283588	−	0.958946i	$-0.408475\pi$
$113$	6.02917			0.567176			0.283588	+	0.958946i	$0.408475\pi$
$114$		0			0
$115$	−0.0179771	−	0.0670914i	−0.00167637	−	0.00625631i
$116$	−0.164972	−	0.0952466i	−0.0153173	−	0.00884343i
$117$		0			0
$118$		−	3.52350i		−	0.324364i
$119$	1.36855	+	15.3032i	0.125455	+	1.40284i
$120$		0			0
$121$	5.94201	−	3.43062i	0.540183	−	0.311875i
$122$	−6.44484	+	1.72689i	−0.583488	+	0.156345i
$123$		0			0
$124$	−0.707593	−	0.189599i	−0.0635438	−	0.0170265i
$125$	0.562709	−	0.562709i	0.0503302	−	0.0503302i
$126$		0			0
$127$		−	0.259825i		−	0.0230558i	−0.999934	−	0.0115279i	$-0.996330\pi$
$127$		−	0.259825i		−	0.0230558i	0.999934	−	0.0115279i	$-0.00366952\pi$
$128$	3.53321	−	13.1861i	0.312295	−	1.16550i
$129$		0			0
$130$	−0.354412	−	0.287300i	−0.0310840	−	0.0251979i
$131$	−0.679285	+	0.392185i	−0.0593494	+	0.0342654i	−0.529381	−	0.848384i	$-0.677576\pi$
$131$	−0.679285	+	0.392185i	−0.0593494	+	0.0342654i	0.470032	+	0.882650i	$0.344242\pi$
$132$		0			0
$133$	4.81451	+	13.1489i	0.417471	+	1.14016i
$134$			16.0720i			1.38841i
$135$		0			0
$136$	13.1463	−	3.52253i	1.12728	−	0.302055i
$137$	−13.3251	+	3.57044i	−1.13844	+	0.305044i	−0.778323	−	0.627864i	$-0.783929\pi$
$137$	−13.3251	+	3.57044i	−1.13844	+	0.305044i	−0.360115	+	0.932908i	$0.617263\pi$
$138$		0			0
$139$			3.12982i			0.265468i	0.991152	+	0.132734i	$0.0423755\pi$
$139$			3.12982i			0.265468i	−0.991152	+	0.132734i	$0.957624\pi$
$140$	−0.0190014	+	0.108989i	−0.00160591	+	0.00921124i
$141$		0			0
$142$	7.11720	−	4.10912i	0.597262	−	0.344830i
$143$	−1.58499	−	15.1553i	−0.132544	−	1.26735i
$144$		0			0
$145$	−0.00747634	+	0.0279021i	−0.000620876	+	0.00231714i
$146$			18.9103i			1.56503i
$147$		0			0
$148$	1.44870	−	1.44870i	0.119082	−	0.119082i
$149$	3.27187	+	0.876694i	0.268042	+	0.0718216i	0.390337	−	0.920672i	$-0.372359\pi$
$149$	3.27187	+	0.876694i	0.268042	+	0.0718216i	−0.122295	+	0.992494i	$0.539025\pi$
$150$		0			0
$151$	15.7142	−	4.21062i	1.27881	−	0.342655i	0.445408	−	0.895328i	$-0.353059\pi$
$151$	15.7142	−	4.21062i	1.27881	−	0.342655i	0.833398	+	0.552673i	$0.186392\pi$
$152$	10.7421	−	6.20195i	0.871299	−	0.503044i
$153$		0			0
$154$	−14.5353	+	10.2195i	−1.17129	+	0.823510i
$155$			0.111084i			0.00892252i
$156$		0			0
$157$	16.6451	+	9.61006i	1.32842	+	0.766966i	0.985056	−	0.172235i	$-0.0550988\pi$
$157$	16.6451	+	9.61006i	1.32842	+	0.766966i	0.343368	+	0.939201i	$0.388432\pi$
$158$	3.51785	+	13.1288i	0.279865	+	1.04447i
$159$		0			0
$160$	0.230896			0.0182539
$161$	−0.971289	+	2.09345i	−0.0765483	+	0.164987i
$162$		0			0
$163$	0.321549	−	1.20004i	0.0251857	−	0.0939942i	−0.952189	−	0.305510i	$-0.901173\pi$
$163$	0.321549	−	1.20004i	0.0251857	−	0.0939942i	0.977375	+	0.211515i	$0.0678399\pi$
$164$	−1.48192	−	5.53059i	−0.115718	−	0.431866i
$165$		0			0
$166$	−5.52124	−	9.56307i	−0.428532	−	0.742239i
$167$	−7.31443	+	7.31443i	−0.566007	+	0.566007i	−0.931007	−	0.365000i	$-0.881069\pi$
$167$	−7.31443	+	7.31443i	−0.566007	+	0.566007i	0.365000	+	0.931007i	$0.381069\pi$
$168$		0			0
$169$	−12.3596	−	4.02996i	−0.950738	−	0.309997i
$170$	0.367407	+	0.636367i	0.0281788	+	0.0488071i
$171$		0			0
$172$	−0.697284	+	1.20773i	−0.0531674	+	0.0920887i
$173$	1.58153	+	2.73929i	0.120241	+	0.208264i	0.919863	−	0.392240i	$-0.128300\pi$
$173$	1.58153	+	2.73929i	0.120241	+	0.208264i	−0.799621	+	0.600504i	$0.794966\pi$
$174$		0			0
$175$	−13.1595	+	1.17684i	−0.994762	+	0.0889608i
$176$	14.2682	+	14.2682i	1.07550	+	1.07550i
$177$		0			0
$178$	−11.0873	−	6.40123i	−0.831025	−	0.479793i
$179$	−5.02551	−	2.90148i	−0.375624	−	0.216867i	0.300289	−	0.953848i	$-0.402917\pi$
$179$	−5.02551	−	2.90148i	−0.375624	−	0.216867i	−0.675913	+	0.736982i	$0.736250\pi$
$180$		0			0
$181$	−13.7005			−1.01835			−0.509176	−	0.860662i	$-0.670050\pi$
$181$	−13.7005			−1.01835			−0.509176	+	0.860662i	$0.670050\pi$
$182$	2.91340	+	14.8761i	0.215955	+	1.10269i
$183$		0			0
$184$	1.97465	+	0.529106i	0.145573	+	0.0390062i
$185$	−0.269053	−	0.155338i	−0.0197812	−	0.0114207i
$186$		0			0
$187$	−6.35205	+	23.7062i	−0.464508	+	1.73357i
$188$	1.07432	+	1.07432i	0.0783526	+	0.0783526i
$189$		0			0
$190$	0.473545	+	0.473545i	0.0343546	+	0.0343546i
$191$	−4.22861	−	7.32417i	−0.305972	−	0.529958i	0.671506	−	0.740999i	$-0.265648\pi$
$191$	−4.22861	−	7.32417i	−0.305972	−	0.529958i	−0.977477	+	0.211041i	$0.932315\pi$
$192$		0			0
$193$	−0.476941	+	0.127796i	−0.0343310	+	0.00919896i	−0.275944	−	0.961174i	$-0.588990\pi$
$193$	−0.476941	+	0.127796i	−0.0343310	+	0.00919896i	0.241613	+	0.970373i	$0.422324\pi$
$194$	6.78820	+	11.7575i	0.487365	+	0.844140i
$195$		0			0
$196$	2.80675	−	2.37362i	0.200482	−	0.169545i
$197$	2.77899	−	2.77899i	0.197995	−	0.197995i	−0.601145	−	0.799140i	$-0.705289\pi$
$197$	2.77899	−	2.77899i	0.197995	−	0.197995i	0.799140	+	0.601145i	$0.205289\pi$
$198$		0			0
$199$	−8.03206	+	13.9119i	−0.569377	+	0.986191i	0.427250	+	0.904133i	$0.359482\pi$
$199$	−8.03206	+	13.9119i	−0.569377	+	0.986191i	−0.996628	+	0.0820571i	$0.973851\pi$
$200$	3.02909	+	11.3047i	0.214189	+	0.799364i
$201$		0			0
$202$	−12.6069	+	12.6069i	−0.887020	+	0.887020i
$203$	0.785137	−	0.552015i	0.0551058	−	0.0387439i
$204$		0			0
$205$	−0.751920	+	0.434121i	−0.0525164	+	0.0303203i
$206$	3.97092	+	14.8197i	0.276667	+	1.03254i
$207$		0			0
$208$	16.0745	−	6.16091i	1.11456	−	0.427182i
$209$			22.3675i			1.54719i
$210$		0			0
$211$	21.0547			1.44947			0.724734	−	0.689029i	$-0.241963\pi$
$211$	21.0547			1.44947			0.724734	+	0.689029i	$0.241963\pi$
$212$	4.79173	−	2.76651i	0.329097	−	0.190004i
$213$		0			0
$214$	7.25011	+	27.0578i	0.495607	+	1.84963i
$215$	0.204266	+	0.0547330i	0.0139309	+	0.00373276i
$216$		0			0
$217$	2.36699	−	2.83193i	0.160682	−	0.192244i
$218$		−	21.6800i		−	1.46836i
$219$		0			0
$220$	−0.0883611	+	0.153046i	−0.00595730	+	0.0103183i
$221$	16.2650	+	13.1850i	1.09410	+	0.886922i
$222$		0			0
$223$	19.3108	+	19.3108i	1.29314	+	1.29314i	0.932832	+	0.360311i	$0.117330\pi$
$223$	19.3108	+	19.3108i	1.29314	+	1.29314i	0.360311	+	0.932832i	$0.382670\pi$
$224$	−5.88633	−	4.91994i	−0.393297	−	0.328727i
$225$		0			0
$226$	−9.25428	−	2.47968i	−0.615585	−	0.164946i
$227$	−3.34823	+	0.897156i	−0.222230	+	0.0595463i	−0.368216	−	0.929740i	$-0.620031\pi$
$227$	−3.34823	+	0.897156i	−0.222230	+	0.0595463i	0.145986	+	0.989287i	$0.453365\pi$
$228$		0			0
$229$	18.6186	+	4.98883i	1.23035	+	0.329671i	0.814715	−	0.579861i	$-0.196893\pi$
$229$	18.6186	+	4.98883i	1.23035	+	0.329671i	0.415633	+	0.909532i	$0.363560\pi$
$230$			0.110373i			0.00727781i
$231$		0			0
$232$	−0.601175	−	0.601175i	−0.0394691	−	0.0394691i
$233$	4.47705	−	2.58482i	0.293301	−	0.169337i	−0.346129	−	0.938187i	$-0.612504\pi$
$233$	4.47705	−	2.58482i	0.293301	−	0.169337i	0.639430	+	0.768850i	$0.279171\pi$
$234$		0			0
$235$	0.115194	−	0.199522i	0.00751444	−	0.0130154i
$236$	−0.301363	+	1.12470i	−0.0196171	+	0.0732119i
$237$		0			0
$238$	4.19327	−	24.0519i	0.271809	−	1.55906i
$239$	−6.85569	+	6.85569i	−0.443458	+	0.443458i	−0.893172	−	0.449715i	$-0.851526\pi$
$239$	−6.85569	+	6.85569i	−0.443458	+	0.443458i	0.449715	+	0.893172i	$0.351526\pi$
$240$		0			0
$241$	−0.578684	−	2.15968i	−0.0372763	−	0.139117i	0.944780	−	0.327706i	$-0.106275\pi$
$241$	−0.578684	−	2.15968i	−0.0372763	−	0.139117i	−0.982056	+	0.188589i	$0.939609\pi$
$242$	−10.5314	+	2.82189i	−0.676986	+	0.181398i
$243$		0			0
$244$	2.20490			0.141154
$245$	−0.457829	−	0.317955i	−0.0292496	−	0.0203134i
$246$		0			0
$247$	17.4286	+	7.77049i	1.10896	+	0.494424i
$248$	−2.83144	−	1.63473i	−0.179796	−	0.103805i
$249$		0			0
$250$	−1.09514	+	0.632281i	−0.0692629	+	0.0399890i
$251$	24.8342			1.56752			0.783759	−	0.621064i	$-0.213300\pi$
$251$	24.8342			1.56752			0.783759	+	0.621064i	$0.213300\pi$
$252$		0			0
$253$	−2.60669	+	2.60669i	−0.163881	+	0.163881i
$254$	−0.106861	+	0.398810i	−0.00670505	+	0.0250236i
$255$		0			0
$256$	−5.90508	+	10.2279i	−0.369067	+	0.639244i
$257$	−6.67557	−	11.5624i	−0.416411	−	0.721244i	0.579165	−	0.815210i	$-0.303379\pi$
$257$	−6.67557	−	11.5624i	−0.416411	−	0.721244i	−0.995575	+	0.0939662i	$0.970045\pi$
$258$		0			0
$259$	3.54915	+	9.69309i	0.220533	+	0.602299i
$260$	0.0885559	+	0.122019i	0.00549200	+	0.00756729i
$261$		0			0
$262$	1.20394	−	0.322596i	0.0743799	−	0.0199300i
$263$	−0.211897	+	0.367017i	−0.0130662	+	0.0226312i	−0.872485	−	0.488642i	$-0.837493\pi$
$263$	−0.211897	+	0.367017i	−0.0130662	+	0.0226312i	0.859418	+	0.511273i	$0.170826\pi$
$264$		0			0
$265$	−0.593280	−	0.593280i	−0.0364449	−	0.0364449i
$266$	−1.98199	−	22.1626i	−0.121524	−	1.35888i
$267$		0			0
$268$	1.37463	−	5.13019i	0.0839689	−	0.313376i
$269$	12.5697	+	7.25714i	0.766390	+	0.442476i	0.831585	−	0.555397i	$-0.187434\pi$
$269$	12.5697	+	7.25714i	0.766390	+	0.442476i	−0.0651951	+	0.997873i	$0.520767\pi$
$270$		0			0
$271$	−19.1090	−	5.12023i	−1.16079	−	0.311032i	−0.373506	−	0.927628i	$-0.621845\pi$
$271$	−19.1090	−	5.12023i	−1.16079	−	0.311032i	−0.787280	+	0.616596i	$0.788511\pi$
$272$	−27.7261			−1.68114
$273$		0			0
$274$	21.9213			1.32432
$275$	−20.3854	−	5.46224i	−1.22928	−	0.329386i
$276$		0			0
$277$	−20.5717	−	11.8771i	−1.23603	−	0.713623i	−0.267751	−	0.963488i	$-0.586281\pi$
$277$	−20.5717	−	11.8771i	−1.23603	−	0.713623i	−0.968281	+	0.249865i	$0.919614\pi$
$278$	1.28723	−	4.80401i	0.0772030	−	0.288125i
$279$		0			0
$280$	−0.207812	+	0.447904i	−0.0124191	+	0.0267674i
$281$	−9.66092	−	9.66092i	−0.576322	−	0.576322i	0.357566	−	0.933888i	$-0.383607\pi$
$281$	−9.66092	−	9.66092i	−0.576322	−	0.576322i	−0.933888	+	0.357566i	$0.883607\pi$
$282$		0			0
$283$	13.3825	−	23.1791i	0.795506	−	1.37786i	−0.127011	−	0.991901i	$-0.540538\pi$
$283$	13.3825	−	23.1791i	0.795506	−	1.37786i	0.922517	−	0.385956i	$-0.126128\pi$
$284$	−2.62326	+	0.702902i	−0.155662	+	0.0417095i
$285$		0			0
$286$	−3.80025	+	23.9141i	−0.224713	+	1.41407i
$287$	28.4193	+	4.95469i	1.67754	+	0.292466i
$288$		0			0
$289$	−8.36139	−	14.4824i	−0.491847	−	0.851903i
$290$	0.0229511	−	0.0397525i	0.00134774	−	0.00233435i
$291$		0			0
$292$	1.61739	−	6.03618i	0.0946505	−	0.353241i
$293$	21.8755	−	21.8755i	1.27798	−	1.27798i	0.336181	−	0.941797i	$-0.390864\pi$
$293$	21.8755	−	21.8755i	1.27798	−	1.27798i	0.941797	−	0.336181i	$-0.109136\pi$
$294$		0			0
$295$	0.176566			0.0102801
$296$	7.91882	−	4.57193i	0.460272	−	0.265738i
$297$		0			0
$298$	−4.66148	−	2.69131i	−0.270032	−	0.155903i
$299$	1.12555	+	2.93669i	0.0650925	+	0.169833i
$300$		0			0
$301$	−4.04121	−	5.74785i	−0.232931	−	0.331301i
$302$	−25.8518			−1.48760
$303$		0			0
$304$	−24.4080	+	6.54010i	−1.39989	+	0.375100i
$305$	−0.0865362	−	0.322957i	−0.00495505	−	0.0184925i
$306$		0			0
$307$	−2.49534	+	2.49534i	−0.142417	+	0.142417i	−0.774720	−	0.632304i	$-0.782109\pi$
$307$	−2.49534	+	2.49534i	−0.142417	+	0.142417i	0.632304	+	0.774720i	$0.282109\pi$
$308$	5.51374	−	2.01887i	0.314174	−	0.115036i
$309$		0			0
$310$	0.0456868	−	0.170505i	0.00259484	−	0.00968406i
$311$	−15.1553	+	26.2497i	−0.859378	+	1.48849i	0.0131458	+	0.999914i	$0.495815\pi$
$311$	−15.1553	+	26.2497i	−0.859378	+	1.48849i	−0.872523	+	0.488572i	$0.837518\pi$
$312$		0			0
$313$	16.8628	−	9.73575i	0.953143	−	0.550297i	0.0590869	−	0.998253i	$-0.481181\pi$
$313$	16.8628	−	9.73575i	0.953143	−	0.550297i	0.894056	+	0.447956i	$0.147848\pi$
$314$	−21.5964	−	21.5964i	−1.21876	−	1.21876i
$315$		0			0
$316$		−	4.49159i		−	0.252672i
$317$	−4.84229	−	1.29749i	−0.271970	−	0.0728741i	0.120256	−	0.992743i	$-0.461628\pi$
$317$	−4.84229	−	1.29749i	−0.271970	−	0.0728741i	−0.392226	+	0.919869i	$0.628295\pi$
$318$		0			0
$319$	1.48087	−	0.396799i	0.0829131	−	0.0222165i
$320$	0.380066	+	0.101838i	0.0212463	+	0.00569294i
$321$		0			0
$322$	2.35184	−	2.81380i	0.131063	−	0.156807i
$323$	−21.7324	−	21.7324i	−1.20922	−	1.20922i
$324$		0			0
$325$	−11.3381	+	13.9866i	−0.628922	+	0.775836i
$326$	−0.987103	+	1.70971i	−0.0546706	+	0.0946922i
$327$		0			0
$328$		−	25.5543i		−	1.41100i
$329$	−7.18813	+	2.63195i	−0.396294	+	0.145104i
$330$		0			0
$331$	−18.5252	−	4.96381i	−1.01824	−	0.272835i	−0.289169	−	0.957278i	$-0.593379\pi$
$331$	−18.5252	−	4.96381i	−1.01824	−	0.272835i	−0.729067	+	0.684443i	$0.760046\pi$
$332$	0.944458	+	3.52477i	0.0518339	+	0.193447i
$333$		0			0
$334$	14.2353	−	8.21877i	0.778922	−	0.449711i
$335$	−0.805384			−0.0440029
$336$		0			0
$337$			3.01241i			0.164097i	0.996628	+	0.0820483i	$0.0261462\pi$
$337$			3.01241i			0.164097i	−0.996628	+	0.0820483i	$0.973854\pi$
$338$	17.3135	+	11.2689i	0.941731	+	0.612948i
$339$		0			0
$340$	−0.0628482	−	0.234553i	−0.00340842	−	0.0127204i
$341$	5.10582	−	2.94785i	0.276496	−	0.159635i
$342$		0			0
$343$	4.89665	+	17.8612i	0.264394	+	0.964415i
$344$	−4.40110	+	4.40110i	−0.237291	+	0.237291i
$345$		0			0
$346$	−1.30090	−	4.85503i	−0.0699369	−	0.261008i
$347$	−4.11910	+	7.13449i	−0.221125	+	0.382999i	−0.955150	−	0.296123i	$-0.904306\pi$
$347$	−4.11910	+	7.13449i	−0.221125	+	0.382999i	0.734025	+	0.679122i	$0.237639\pi$
$348$		0			0
$349$	8.06122	−	8.06122i	0.431507	−	0.431507i	−0.457634	−	0.889141i	$-0.651303\pi$
$349$	8.06122	−	8.06122i	0.431507	−	0.431507i	0.889141	+	0.457634i	$0.151303\pi$
$350$	20.6827	+	3.60587i	1.10554	+	0.192742i
$351$		0			0
$352$	−6.12728	−	10.6128i	−0.326585	−	0.565662i
$353$	−16.3265	+	4.37468i	−0.868974	+	0.232841i	−0.665644	−	0.746270i	$-0.731843\pi$
$353$	−16.3265	+	4.37468i	−0.868974	+	0.232841i	−0.203330	+	0.979110i	$0.565176\pi$
$354$		0			0
$355$	0.205912	+	0.356650i	0.0109287	+	0.0189290i
$356$	2.99156	+	2.99156i	0.158553	+	0.158553i
$357$		0			0
$358$	6.52042	+	6.52042i	0.344615	+	0.344615i
$359$	5.84652	−	21.8195i	0.308568	−	1.15159i	−0.621263	−	0.783602i	$-0.713380\pi$
$359$	5.84652	−	21.8195i	0.308568	−	1.15159i	0.929831	−	0.367988i	$-0.119953\pi$
$360$		0			0
$361$	−7.80339	−	4.50529i	−0.410705	−	0.237120i
$362$	21.0292	+	5.63475i	1.10527	+	0.296156i
$363$		0			0
$364$	0.342387	−	4.99764i	0.0179460	−	0.261947i
$365$	−0.947614			−0.0496004
$366$		0			0
$367$	−22.2369	−	12.8385i	−1.16076	−	0.670163i	−0.209271	−	0.977858i	$-0.567109\pi$
$367$	−22.2369	−	12.8385i	−1.16076	−	0.670163i	−0.951485	+	0.307695i	$0.900442\pi$
$368$	−3.60667	−	2.08231i	−0.188011	−	0.108548i
$369$		0			0
$370$	0.349087	+	0.349087i	0.0181481	+	0.0181481i
$371$	2.48313	+	27.7664i	0.128918	+	1.44156i
$372$		0			0
$373$	−8.31200	−	14.3968i	−0.430379	−	0.745439i	0.566527	−	0.824043i	$-0.308287\pi$
$373$	−8.31200	−	14.3968i	−0.430379	−	0.745439i	−0.996906	+	0.0786048i	$0.974953\pi$
$374$	19.4997	−	33.7745i	1.00831	−	1.74644i
$375$		0			0
$376$	3.39042	+	5.87238i	0.174848	+	0.302845i
$377$	0.205274	−	1.29174i	0.0105721	−	0.0665279i
$378$		0			0
$379$	−27.0566	+	27.0566i	−1.38980	+	1.38980i	−0.564094	+	0.825711i	$0.690774\pi$
$379$	−27.0566	+	27.0566i	−1.38980	+	1.38980i	−0.825711	+	0.564094i	$0.809226\pi$
$380$	−0.110654	−	0.191658i	−0.00567642	−	0.00983184i
$381$		0			0
$382$	3.47829	+	12.9811i	0.177965	+	0.664173i
$383$	6.99065	−	26.0895i	0.357206	−	1.33311i	−0.520480	−	0.853874i	$-0.674247\pi$
$383$	6.99065	−	26.0895i	0.357206	−	1.33311i	0.877686	−	0.479236i	$-0.159086\pi$
$384$		0			0
$385$	−0.512109	−	0.728378i	−0.0260995	−	0.0371216i
$386$	0.784626			0.0399364
$387$		0			0
$388$	−1.16118	−	4.33359i	−0.0589501	−	0.220005i
$389$	−16.4981	−	9.52520i	−0.836488	−	0.482947i	0.0195807	−	0.999808i	$-0.493767\pi$
$389$	−16.4981	−	9.52520i	−0.836488	−	0.482947i	−0.856069	+	0.516862i	$0.827100\pi$
$390$		0			0
$391$		−	5.06536i		−	0.256166i
$392$	14.8418	−	6.99056i	0.749625	−	0.353077i
$393$		0			0
$394$	−5.40846	+	3.12258i	−0.272474	+	0.157313i
$395$	−0.657896	+	0.176283i	−0.0331024	+	0.00886975i
$396$		0			0
$397$	−3.28902	−	0.881290i	−0.165071	−	0.0442307i	0.175337	−	0.984508i	$-0.443899\pi$
$397$	−3.28902	−	0.881290i	−0.165071	−	0.0442307i	−0.340408	+	0.940278i	$0.610565\pi$
$398$	18.0502	−	18.0502i	0.904777	−	0.904777i
$399$		0			0
$400$		−	23.8422i		−	1.19211i
$401$	−9.54948	+	35.6391i	−0.476878	+	1.77973i	0.137260	+	0.990535i	$0.456170\pi$
$401$	−9.54948	+	35.6391i	−0.476878	+	1.77973i	−0.614138	+	0.789198i	$0.710496\pi$
$402$		0			0
$403$	−0.523180	−	5.00252i	−0.0260614	−	0.249193i
$404$	5.10240	−	2.94587i	0.253854	−	0.146563i
$405$		0			0
$406$	−1.43215	+	0.524386i	−0.0710766	+	0.0260249i
$407$			16.4888i			0.817318i
$408$		0			0
$409$	5.42540	−	1.45373i	0.268269	−	0.0718824i	−0.122177	−	0.992508i	$-0.538988\pi$
$409$	5.42540	−	1.45373i	0.268269	−	0.0718824i	0.390446	+	0.920626i	$0.372321\pi$
$410$	1.33268	−	0.357091i	0.0658164	−	0.0176354i
$411$		0			0
$412$		−	5.07008i		−	0.249785i
$413$	−4.50128	−	3.76228i	−0.221494	−	0.185130i
$414$		0			0
$415$	0.479215	−	0.276675i	0.0235237	−	0.0135814i
$416$	−10.3980	+	1.08746i	−0.509805	+	0.0533171i
$417$		0			0
$418$	9.19929	−	34.3322i	0.449952	−	1.67924i
$419$		−	17.2554i		−	0.842980i	−0.906833	−	0.421490i	$-0.861507\pi$
$419$		−	17.2554i		−	0.842980i	0.906833	−	0.421490i	$-0.138493\pi$
$420$		0			0
$421$	5.55993	−	5.55993i	0.270974	−	0.270974i	−0.558518	−	0.829492i	$-0.688630\pi$
$421$	5.55993	−	5.55993i	0.270974	−	0.270974i	0.829492	+	0.558518i	$0.188630\pi$
$422$	−32.3173	−	8.65939i	−1.57318	−	0.421533i
$423$		0			0
$424$	23.8529	−	6.39137i	1.15840	−	0.310392i
$425$	25.1137	−	14.4994i	1.21819	−	0.703325i
$426$		0			0
$427$	−4.67548	+	10.0772i	−0.226263	+	0.487671i
$428$		−	9.25695i		−	0.447451i
$429$		0			0
$430$	−0.291021	−	0.168021i	−0.0140343	−	0.00810271i
$431$	2.11538	+	7.89471i	0.101894	+	0.380275i	0.997974	−	0.0636179i	$-0.0202639\pi$
$431$	2.11538	+	7.89471i	0.101894	+	0.380275i	−0.896080	+	0.443892i	$0.853597\pi$
$432$		0			0
$433$	6.91474			0.332301			0.166151	−	0.986100i	$-0.446866\pi$
$433$	6.91474			0.332301			0.166151	+	0.986100i	$0.446866\pi$
$434$	−4.79785	+	3.37328i	−0.230304	+	0.161923i
$435$		0			0
$436$	−1.85428	+	6.92027i	−0.0888039	+	0.331421i
$437$	−1.19483	−	4.45917i	−0.0571565	−	0.213311i
$438$		0			0
$439$	2.14789	+	3.72026i	0.102513	+	0.177558i	0.912719	−	0.408587i	$-0.133978\pi$
$439$	2.14789	+	3.72026i	0.102513	+	0.177558i	−0.810206	+	0.586145i	$0.800645\pi$
$440$	−0.557715	+	0.557715i	−0.0265880	+	0.0265880i
$441$		0			0
$442$	−19.5427	−	26.9274i	−0.929553	−	1.28081i
$443$	−11.5068	−	19.9303i	−0.546702	−	0.946916i	−0.998498	−	0.0547947i	$-0.982550\pi$
$443$	−11.5068	−	19.9303i	−0.546702	−	0.946916i	0.451795	−	0.892122i	$-0.350784\pi$
$444$		0			0
$445$	0.320772	−	0.555593i	0.0152061	−	0.0263377i
$446$	−21.6983	−	37.5825i	−1.02744	−	1.77958i
$447$		0			0
$448$	−7.51923	−	10.6947i	−0.355250	−	0.505276i
$449$	7.20816	+	7.20816i	0.340174	+	0.340174i	0.856433	−	0.516259i	$-0.172676\pi$
$449$	7.20816	+	7.20816i	0.340174	+	0.340174i	−0.516259	+	0.856433i	$0.672676\pi$
$450$		0			0
$451$	39.9074	+	23.0405i	1.87916	+	1.08494i
$452$	2.74188	+	1.58303i	0.128967	+	0.0744593i
$453$		0			0
$454$	5.50824			0.258515
$455$	−0.745456	+	0.145993i	−0.0349475	+	0.00684427i
$456$		0			0
$457$	−15.0670	−	4.03718i	−0.704803	−	0.188851i	−0.111422	−	0.993773i	$-0.535540\pi$
$457$	−15.0670	−	4.03718i	−0.704803	−	0.188851i	−0.593381	+	0.804922i	$0.702207\pi$
$458$	−26.5261	−	15.3149i	−1.23949	−	0.715617i
$459$		0			0
$460$	0.00944018	−	0.0352312i	0.000440151	−	0.00164266i
$461$	−10.2849	−	10.2849i	−0.479017	−	0.479017i	0.425800	−	0.904817i	$-0.359993\pi$
$461$	−10.2849	−	10.2849i	−0.479017	−	0.479017i	−0.904817	+	0.425800i	$0.859993\pi$
$462$		0			0
$463$	−15.2514	−	15.2514i	−0.708792	−	0.708792i	0.257489	−	0.966281i	$-0.417105\pi$
$463$	−15.2514	−	15.2514i	−0.708792	−	0.708792i	−0.966281	+	0.257489i	$0.917105\pi$
$464$	0.865996	+	1.49995i	0.0402028	+	0.0696334i
$465$		0			0
$466$	−7.93498	+	2.12617i	−0.367581	+	0.0984930i
$467$	8.90667	+	15.4268i	0.412152	+	0.713868i	0.995125	−	0.0986238i	$-0.0314441\pi$
$467$	8.90667	+	15.4268i	0.412152	+	0.713868i	−0.582973	+	0.812491i	$0.698111\pi$
$468$		0			0
$469$	20.5321	+	17.1612i	0.948082	+	0.792429i
$470$	−0.258873	+	0.258873i	−0.0119409	+	0.0119409i
$471$		0			0
$472$	−2.59836	+	4.50050i	−0.119599	+	0.207152i
$473$	−2.90490	−	10.8412i	−0.133567	−	0.498480i
$474$		0			0
$475$	18.6881	−	18.6881i	0.857468	−	0.857468i
$476$	−3.39564	+	7.31874i	−0.155639	+	0.335454i
$477$		0			0
$478$	13.3425	−	7.70331i	0.610273	−	0.352341i
$479$	−6.55934	−	24.4798i	−0.299704	−	1.11851i	−0.937409	−	0.348229i	$-0.886783\pi$
$479$	−6.55934	−	24.4798i	−0.299704	−	1.11851i	0.637706	−	0.770280i	$-0.279884\pi$
$480$		0			0
$481$	12.8480	+	5.72822i	0.585817	+	0.261184i
$482$			3.55293i			0.161832i
$483$		0			0
$484$	3.60299			0.163772
$485$	−0.589181	+	0.340164i	−0.0267533	+	0.0154460i
$486$		0			0
$487$	−8.64006	−	32.2452i	−0.391519	−	1.46117i	−0.827630	−	0.561275i	$-0.810311\pi$
$487$	−8.64006	−	32.2452i	−0.391519	−	1.46117i	0.436111	−	0.899893i	$-0.356355\pi$
$488$	9.50535	+	2.54695i	0.430287	+	0.115295i
$489$		0			0
$490$	0.571961	+	0.676330i	0.0258386	+	0.0305535i
$491$		−	14.4968i		−	0.654231i	−0.944984	−	0.327115i	$-0.893923\pi$
$491$		−	14.4968i		−	0.654231i	0.944984	−	0.327115i	$-0.106077\pi$
$492$		0			0
$493$	−1.05330	+	1.82436i	−0.0474381	+	0.0821651i
$494$	−23.5557	−	19.0951i	−1.05982	−	0.859129i
$495$		0			0
$496$	4.70968	+	4.70968i	0.211471	+	0.211471i
$497$	2.35010	−	13.4798i	0.105417	−	0.604653i
$498$		0			0
$499$	−9.55534	−	2.56035i	−0.427756	−	0.114617i	0.0385167	−	0.999258i	$-0.487737\pi$
$499$	−9.55534	−	2.56035i	−0.427756	−	0.114617i	−0.466273	+	0.884641i	$0.654403\pi$
$500$	0.403649	−	0.108157i	0.0180517	−	0.00483694i
$501$		0			0
$502$	−38.1184	−	10.2138i	−1.70131	−	0.455864i
$503$			32.9620i			1.46970i	0.678229	+	0.734851i	$0.262748\pi$
$503$			32.9620i			1.46970i	−0.678229	+	0.734851i	$0.737252\pi$
$504$		0			0
$505$	−0.631745	−	0.631745i	−0.0281123	−	0.0281123i
$506$	5.07314	−	2.92898i	0.225528	−	0.130209i
$507$		0			0
$508$	0.0682200	−	0.118161i	0.00302678	−	0.00524253i
$509$	−8.92421	+	33.3056i	−0.395559	+	1.47624i	0.425268	+	0.905067i	$0.360180\pi$
$509$	−8.92421	+	33.3056i	−0.395559	+	1.47624i	−0.820827	+	0.571177i	$0.806487\pi$
$510$		0			0
$511$	24.1580	+	20.1918i	1.06869	+	0.893233i
$512$	−6.03549	+	6.03549i	−0.266733	+	0.266733i
$513$		0			0
$514$	5.49105	+	20.4929i	0.242200	+	0.903903i
$515$	−0.742629	+	0.198987i	−0.0327241	+	0.00876840i
$516$		0			0
$517$	−12.2276			−0.537770
$518$	−1.46108	−	16.3378i	−0.0641960	−	0.717841i
$519$		0			0
$520$	0.240818	+	0.628320i	0.0105606	+	0.0275536i
$521$	28.0062	+	16.1694i	1.22697	+	0.708393i	0.966395	−	0.257060i	$-0.0827538\pi$
$521$	28.0062	+	16.1694i	1.22697	+	0.708393i	0.260577	+	0.965453i	$0.416087\pi$
$522$		0			0
$523$	−16.8623	+	9.73548i	−0.737339	+	0.425703i	−0.821101	−	0.570783i	$-0.806640\pi$
$523$	−16.8623	+	9.73548i	−0.737339	+	0.425703i	0.0837622	+	0.996486i	$0.473306\pi$
$524$	−0.411891			−0.0179935
$525$		0			0
$526$	0.476192	−	0.476192i	0.0207629	−	0.0207629i
$527$	−2.09670	+	7.82500i	−0.0913338	+	0.340863i
$528$		0			0
$529$	−11.1196	+	19.2597i	−0.483460	+	0.837377i
$530$	0.666632	+	1.15464i	0.0289566	+	0.0501544i
$531$		0			0
$532$	−1.26291	+	7.24384i	−0.0547540	+	0.314060i
$533$	31.8169	−	23.0913i	1.37815	−	1.00020i
$534$		0			0
$535$	−1.35589	+	0.363310i	−0.0586203	+	0.0157073i
$536$	11.8521	−	20.5285i	0.511934	−	0.886695i
$537$		0			0
$538$	−16.3088	−	16.3088i	−0.703122	−	0.703122i
$539$	−2.46488	+	29.4809i	−0.106170	+	1.26983i
$540$		0			0
$541$	−1.98308	+	7.40097i	−0.0852594	+	0.318193i	−0.995363	−	0.0961879i	$-0.969335\pi$
$541$	−1.98308	+	7.40097i	−0.0852594	+	0.318193i	0.910104	+	0.414380i	$0.136002\pi$
$542$	27.2248	+	15.7183i	1.16941	+	0.675157i
$543$		0			0
$544$	16.2647	+	4.35812i	0.697345	+	0.186853i
$545$	1.08641			0.0465366
$546$		0			0
$547$	−17.3075			−0.740016			−0.370008	−	0.929029i	$-0.620645\pi$
$547$	−17.3075			−0.740016			−0.370008	+	0.929029i	$0.620645\pi$
$548$	−6.99730	−	1.87492i	−0.298910	−	0.0800927i
$549$		0			0
$550$	29.0433	+	16.7682i	1.23841	+	0.714998i
$551$	−0.496908	+	1.85449i	−0.0211690	+	0.0790037i
$552$		0			0
$553$	20.5283	+	9.52443i	0.872952	+	0.405020i
$554$	26.6910	+	26.6910i	1.13399	+	1.13399i
$555$		0			0
$556$	−0.821769	+	1.42335i	−0.0348508	+	0.0603633i
$557$	16.0740	−	4.30702i	0.681078	−	0.182494i	0.0983379	−	0.995153i	$-0.468647\pi$
$557$	16.0740	−	4.30702i	0.681078	−	0.182494i	0.582740	+	0.812659i	$0.301981\pi$
$558$		0			0
$559$	−9.45660	−	1.50277i	−0.399972	−	0.0635605i
$560$	0.645089	−	0.771800i	0.0272600	−	0.0326145i
$561$		0			0
$562$	10.8554	+	18.8021i	0.457906	+	0.793117i
$563$	−1.95468	+	3.38561i	−0.0823800	+	0.142686i	−0.904272	−	0.426957i	$-0.859585\pi$
$563$	−1.95468	+	3.38561i	−0.0823800	+	0.142686i	0.821892	+	0.569644i	$0.192919\pi$
$564$		0			0
$565$	0.124259	−	0.463741i	0.00522762	−	0.0195097i
$566$	−30.0741	+	30.0741i	−1.26411	+	1.26411i
$567$		0			0
$568$	−12.1209			−0.508581
$569$	2.28143	−	1.31718i	0.0956424	−	0.0552192i	−0.451416	−	0.892314i	$-0.649081\pi$
$569$	2.28143	−	1.31718i	0.0956424	−	0.0552192i	0.547058	+	0.837094i	$0.315748\pi$
$570$		0			0
$571$	−16.2796	−	9.39903i	−0.681280	−	0.393337i	0.119057	−	0.992887i	$-0.462013\pi$
$571$	−16.2796	−	9.39903i	−0.681280	−	0.393337i	−0.800337	+	0.599550i	$0.795346\pi$
$572$	3.25840	−	7.30834i	0.136240	−	0.305577i
$573$		0			0
$574$	−41.5836	−	19.2933i	−1.73566	−	0.805288i
$575$	4.35580			0.181649
$576$		0			0
$577$	43.2935	−	11.6005i	1.80233	−	0.482934i	0.807994	−	0.589190i	$-0.200553\pi$
$577$	43.2935	−	11.6005i	1.80233	−	0.482934i	0.994339	+	0.106257i	$0.0338865\pi$
$578$	6.87775	+	25.6681i	0.286076	+	1.06765i
$579$		0			0
$580$	−0.0107260	+	0.0107260i	−0.000445374	+	0.000445374i
$581$	−18.1123	−	3.15773i	−0.751423	−	0.131005i
$582$		0			0
$583$	−11.5253	+	43.0130i	−0.477330	+	1.78142i
$584$	13.9452	−	24.1538i	0.577056	−	0.999491i
$585$		0			0
$586$	−42.5740	+	24.5801i	−1.75872	+	1.01539i
$587$	21.2468	+	21.2468i	0.876947	+	0.876947i	0.993218	−	0.116270i	$-0.0370939\pi$
$587$	21.2468	+	21.2468i	0.876947	+	0.876947i	−0.116270	+	0.993218i	$0.537094\pi$
$588$		0			0
$589$			7.38312i			0.304216i
$590$	−0.271014	−	0.0726180i	−0.0111575	−	0.00298964i
$591$		0			0
$592$	−17.9930	+	4.82121i	−0.739508	+	0.198151i
$593$	−34.9791	−	9.37263i	−1.43642	−	0.384888i	−0.545142	−	0.838344i	$-0.683524\pi$
$593$	−34.9791	−	9.37263i	−1.43642	−	0.384888i	−0.891279	+	0.453456i	$0.850191\pi$
$594$		0			0
$595$	1.20527	+	0.210129i	0.0494111	+	0.00861444i
$596$	1.25776	+	1.25776i	0.0515198	+	0.0515198i
$597$		0			0
$598$	−0.519831	−	4.97050i	−0.0212575	−	0.203259i
$599$	−1.01128	+	1.75158i	−0.0413196	+	0.0715677i	−0.885946	−	0.463789i	$-0.846490\pi$
$599$	−1.01128	+	1.75158i	−0.0413196	+	0.0715677i	0.844626	+	0.535357i	$0.179823\pi$
$600$		0			0
$601$		−	16.8573i		−	0.687623i	−0.939039	−	0.343811i	$-0.888282\pi$
$601$		−	16.8573i		−	0.687623i	0.939039	−	0.343811i	$-0.111718\pi$
$602$	3.83894	+	10.4845i	0.156464	+	0.427318i
$603$		0			0
$604$	8.25190	+	2.21109i	0.335765	+	0.0899680i
$605$	−0.141408	−	0.527741i	−0.00574904	−	0.0214557i
$606$		0			0
$607$	20.1392	−	11.6274i	0.817424	−	0.471940i	−0.0321030	−	0.999485i	$-0.510220\pi$
$607$	20.1392	−	11.6274i	0.817424	−	0.471940i	0.849528	+	0.527544i	$0.176887\pi$
$608$	15.3463			0.622373
$609$		0			0
$610$			0.531303i			0.0215118i
$611$	−4.24789	+	9.52771i	−0.171851	+	0.385450i
$612$		0			0
$613$	−0.603323	−	2.25163i	−0.0243680	−	0.0909426i	0.952671	−	0.304003i	$-0.0983234\pi$
$613$	−0.603323	−	2.25163i	−0.0243680	−	0.0909426i	−0.977039	+	0.213061i	$0.931657\pi$
$614$	4.85642	−	2.80386i	0.195989	−	0.113155i
$615$		0			0
$616$	26.1019	−	2.33427i	1.05168	−	0.0940506i
$617$	8.67485	−	8.67485i	0.349236	−	0.349236i	−0.510589	−	0.859825i	$-0.670572\pi$
$617$	8.67485	−	8.67485i	0.349236	−	0.349236i	0.859825	+	0.510589i	$0.170572\pi$
$618$		0			0
$619$	6.89158	+	25.7197i	0.276996	+	1.03376i	0.954492	+	0.298237i	$0.0963986\pi$
$619$	6.89158	+	25.7197i	0.276996	+	1.03376i	−0.677496	+	0.735527i	$0.736935\pi$
$620$	−0.0291665	+	0.0505178i	−0.00117135	+	0.00202885i
$621$		0			0
$622$	34.0581	−	34.0581i	1.36561	−	1.36561i
$623$	−20.0162	+	7.32898i	−0.801932	+	0.293629i
$624$		0			0
$625$	12.4525	+	21.5683i	0.498099	+	0.862732i
$626$	−29.8871	+	8.00824i	−1.19453	+	0.320074i
$627$		0			0
$628$	5.04646	+	8.74072i	0.201376	+	0.348793i
$629$	−16.0206	−	16.0206i	−0.638784	−	0.638784i
$630$		0			0
$631$	−2.58488	−	2.58488i	−0.102903	−	0.102903i	0.653781	−	0.756684i	$-0.273182\pi$
$631$	−2.58488	−	2.58488i	−0.102903	−	0.102903i	−0.756684	+	0.653781i	$0.773182\pi$
$632$	5.18839	−	19.3633i	0.206383	−	0.770232i
$633$		0			0
$634$	6.89888	+	3.98307i	0.273989	+	0.158188i
$635$	−0.0199848	−	0.00535490i	−0.000793071	−	0.000212503i
$636$		0			0
$637$	22.1151	+	12.1623i	0.876232	+	0.481889i
$638$	−2.43622			−0.0964507
$639$		0			0
$640$	−0.941409	−	0.543523i	−0.0372125	−	0.0214846i
$641$	−26.8165	−	15.4825i	−1.05919	−	0.611523i	−0.133981	−	0.990984i	$-0.542776\pi$
$641$	−26.8165	−	15.4825i	−1.05919	−	0.611523i	−0.925208	+	0.379461i	$0.876109\pi$
$642$		0			0
$643$	9.81258	+	9.81258i	0.386970	+	0.386970i	0.873605	−	0.486635i	$-0.161776\pi$
$643$	9.81258	+	9.81258i	0.386970	+	0.386970i	−0.486635	+	0.873605i	$0.661776\pi$
$644$	−0.991372	+	0.697015i	−0.0390655	+	0.0274662i
$645$		0			0
$646$	24.4193	+	42.2955i	0.960766	+	1.66410i
$647$	−13.7400	+	23.7983i	−0.540174	+	0.935608i	0.458720	+	0.888581i	$0.348308\pi$
$647$	−13.7400	+	23.7983i	−0.540174	+	0.935608i	−0.998894	+	0.0470275i	$0.985025\pi$
$648$		0			0
$649$	−4.68553	−	8.11557i	−0.183923	−	0.318564i
$650$	23.1554	−	16.8051i	0.908229	−	0.659152i
$651$		0			0
$652$	0.461314	−	0.461314i	0.0180665	−	0.0180665i
$653$	5.05778	+	8.76034i	0.197926	+	0.342819i	0.947856	−	0.318699i	$-0.103246\pi$
$653$	5.05778	+	8.76034i	0.197926	+	0.342819i	−0.749930	+	0.661518i	$0.769913\pi$
$654$		0			0
$655$	0.0161656	+	0.0603308i	0.000631642	+	0.00235732i
$656$	−13.4738	+	50.2849i	−0.526063	+	1.96330i
$657$		0			0
$658$	12.1157	−	1.08349i	0.472317	−	0.0422390i
$659$	−39.4336			−1.53612			−0.768058	−	0.640380i	$-0.778777\pi$
$659$	−39.4336			−1.53612			−0.768058	+	0.640380i	$0.778777\pi$
$660$		0			0
$661$	−6.57200	−	24.5270i	−0.255621	−	0.953992i	−0.967744	−	0.251936i	$-0.918933\pi$
$661$	−6.57200	−	24.5270i	−0.255621	−	0.953992i	0.712123	−	0.702055i	$-0.247734\pi$
$662$	26.3931	+	15.2381i	1.02580	+	0.592244i
$663$		0			0
$664$			16.2863i			0.632032i
$665$	1.11059	−	0.0993194i	0.0430669	−	0.00385144i
$666$		0			0
$667$	−0.274030	+	0.158211i	−0.0106105	+	0.00612597i
$668$	−5.24687	+	1.40589i	−0.203007	+	0.0543957i
$669$		0			0
$670$	1.23620	+	0.331238i	0.0477585	+	0.0127969i
$671$	−12.5478	+	12.5478i	−0.484403	+	0.484403i
$672$		0			0
$673$		−	20.9026i		−	0.805734i	−0.915258	−	0.402867i	$-0.868014\pi$
$673$		−	20.9026i		−	0.805734i	0.915258	−	0.402867i	$-0.131986\pi$
$674$	1.23894	−	4.62380i	0.0477224	−	0.178102i
$675$		0			0
$676$	−4.56265	−	5.07785i	−0.175487	−	0.195302i
$677$	13.6905	−	7.90421i	0.526169	−	0.303784i	−0.213286	−	0.976990i	$-0.568417\pi$
$677$	13.6905	−	7.90421i	0.526169	−	0.303784i	0.739455	+	0.673206i	$0.235083\pi$
$678$		0			0
$679$	22.2685	+	3.88234i	0.854586	+	0.148990i
$680$		−	1.08376i		−	0.0415603i
$681$		0			0
$682$	−9.04940	+	2.42478i	−0.346520	+	0.0928496i
$683$	11.2605	−	3.01723i	0.430870	−	0.115451i	−0.0368647	−	0.999320i	$-0.511737\pi$
$683$	11.2605	−	3.01723i	0.430870	−	0.115451i	0.467734	+	0.883869i	$0.345070\pi$
$684$		0			0
$685$			1.09850i			0.0419715i
$686$	−0.170005	−	29.4294i	−0.00649081	−	1.12362i
$687$		0			0
$688$	10.9809	−	6.33981i	0.418642	−	0.241703i
$689$	29.5117	+	23.9233i	1.12430	+	0.911403i
$690$		0			0
$691$	−2.70856	+	10.1085i	−0.103038	+	0.384545i	−0.998115	−	0.0613673i	$-0.980454\pi$
$691$	−2.70856	+	10.1085i	−0.103038	+	0.384545i	0.895077	+	0.445912i	$0.147121\pi$
$692$			1.66099i			0.0631415i
$693$		0			0
$694$	9.25675	−	9.25675i	0.351381	−	0.351381i
$695$	0.240734	+	0.0645044i	0.00913155	+	0.00244679i
$696$		0			0
$697$	−61.1607	+	16.3880i	−2.31663	+	0.620738i
$698$	−15.6887	+	9.05789i	−0.593827	+	0.342846i
$699$		0			0
$700$	−6.29352	−	2.91998i	−0.237873	−	0.110365i
$701$		−	36.2902i		−	1.37066i	−0.728232	−	0.685331i	$-0.759657\pi$
$701$		−	36.2902i		−	1.37066i	0.728232	−	0.685331i	$-0.240343\pi$
$702$		0			0
$703$	−17.8823	−	10.3244i	−0.674445	−	0.389391i
$704$	−5.40497	−	20.1716i	−0.203707	−	0.760246i
$705$		0			0
$706$	26.8591			1.01086
$707$	2.64412	+	29.5666i	0.0994425	+	1.11197i
$708$		0			0
$709$	1.66812	−	6.22549i	0.0626474	−	0.233803i	−0.927502	−	0.373818i	$-0.878048\pi$
$709$	1.66812	−	6.22549i	0.0626474	−	0.233803i	0.990149	+	0.140015i	$0.0447151\pi$
$710$	−0.169375	−	0.632116i	−0.00635653	−	0.0237229i
$711$		0			0
$712$	9.44103	+	16.3523i	0.353818	+	0.612830i
$713$	−0.860425	+	0.860425i	−0.0322232	+	0.0322232i
$714$		0			0
$715$	−1.19836	−	0.190434i	−0.0448160	−	0.00712183i
$716$	−1.52363	−	2.63901i	−0.0569408	−	0.0986244i
$717$		0			0
$718$	−17.9479	+	31.0866i	−0.669808	+	1.16014i
$719$	−2.59436	−	4.49357i	−0.0967533	−	0.167582i	0.813586	−	0.581445i	$-0.197512\pi$
$719$	−2.59436	−	4.49357i	−0.0967533	−	0.167582i	−0.910339	+	0.413863i	$0.864179\pi$
$720$		0			0
$721$	23.1722	+	10.7511i	0.862978	+	0.400392i
$722$	10.1246	+	10.1246i	0.376799	+	0.376799i
$723$		0			0
$724$	−6.23059	−	3.59723i	−0.231558	−	0.133690i
$725$	−1.56880	−	0.905748i	−0.0582639	−	0.0336387i
$726$		0			0
$727$	23.5345			0.872848			0.436424	−	0.899741i	$-0.356245\pi$
$727$	23.5345			0.872848			0.436424	+	0.899741i	$0.356245\pi$
$728$	7.24898	−	21.1494i	0.268665	−	0.783849i
$729$		0			0
$730$	1.45451	+	0.389735i	0.0538338	+	0.0144247i
$731$	13.3558	+	7.71100i	0.493984	+	0.285202i
$732$		0			0
$733$	−0.491030	+	1.83255i	−0.0181366	+	0.0676867i	−0.974401	−	0.224817i	$-0.927822\pi$
$733$	−0.491030	+	1.83255i	−0.0181366	+	0.0676867i	0.956264	+	0.292503i	$0.0944883\pi$
$734$	28.8516	+	28.8516i	1.06493	+	1.06493i
$735$		0			0
$736$	1.78844	+	1.78844i	0.0659230	+	0.0659230i
$737$	21.3725	+	37.0182i	0.787265	+	1.36358i
$738$		0			0
$739$	−6.31322	+	1.69162i	−0.232236	+	0.0622274i	−0.373060	−	0.927807i	$-0.621691\pi$
$739$	−6.31322	+	1.69162i	−0.232236	+	0.0622274i	0.140824	+	0.990035i	$0.455025\pi$
$740$	−0.0815714	−	0.141286i	−0.00299862	−	0.00519377i
$741$		0			0
$742$	7.60837	−	43.6404i	0.279312	−	1.60209i
$743$	−12.2516	+	12.2516i	−0.449468	+	0.449468i	−0.895178	−	0.445709i	$-0.852951\pi$
$743$	−12.2516	+	12.2516i	−0.449468	+	0.449468i	0.445709	+	0.895178i	$0.352951\pi$
$744$		0			0
$745$	0.134864	−	0.233591i	0.00494103	−	0.00855812i
$746$	6.83712	+	25.5165i	0.250325	+	0.934225i
$747$		0			0
$748$	−9.11304	+	9.11304i	−0.333206	+	0.333206i
$749$	42.3078	+	19.6294i	1.54589	+	0.717241i
$750$		0			0
$751$	−35.4951	+	20.4931i	−1.29524	+	0.747805i	−0.979577	−	0.201068i	$-0.935559\pi$
$751$	−35.4951	+	20.4931i	−1.29524	+	0.747805i	−0.315659	+	0.948873i	$0.602225\pi$
$752$	−3.57528	−	13.3431i	−0.130377	−	0.486573i
$753$		0			0
$754$	−0.846344	+	1.89829i	−0.0308220	+	0.0691316i
$755$		−	1.29546i		−	0.0471466i
$756$		0			0
$757$	−25.7292			−0.935142			−0.467571	−	0.883955i	$-0.654871\pi$
$757$	−25.7292			−0.935142			−0.467571	+	0.883955i	$0.654871\pi$
$758$	52.6575	−	30.4018i	1.91261	−	1.10424i
$759$		0			0
$760$	−0.255640	−	0.954061i	−0.00927303	−	0.0346074i
$761$	−27.4299	−	7.34981i	−0.994332	−	0.266430i	−0.275263	−	0.961369i	$-0.588765\pi$
$761$	−27.4299	−	7.34981i	−0.994332	−	0.266430i	−0.719069	+	0.694939i	$0.755432\pi$
$762$		0			0
$763$	−27.6963	−	23.1492i	−1.00267	−	0.838058i
$764$		−	4.44108i		−	0.160673i
$765$		0			0
$766$	−21.4601	+	37.1701i	−0.775387	+	1.34301i
$767$	−7.95138	+	0.831581i	−0.287108	+	0.0300267i
$768$		0			0
$769$	20.7240	+	20.7240i	0.747328	+	0.747328i	0.973977	−	0.226649i	$-0.0727770\pi$
$769$	20.7240	+	20.7240i	0.747328	+	0.747328i	−0.226649	+	0.973977i	$0.572777\pi$
$770$	0.486477	+	1.32862i	0.0175314	+	0.0478802i
$771$		0			0
$772$	−0.250453	−	0.0671086i	−0.00901399	−	0.00241529i
$773$	−5.88696	+	1.57741i	−0.211739	+	0.0567353i	−0.363129	−	0.931739i	$-0.618292\pi$
$773$	−5.88696	+	1.57741i	−0.211739	+	0.0567353i	0.151390	+	0.988474i	$0.451625\pi$
$774$		0			0
$775$	−6.72886	−	1.80299i	−0.241708	−	0.0647654i
$776$		−	20.0235i		−	0.718803i
$777$		0			0
$778$	21.4057	+	21.4057i	0.767433	+	0.767433i
$779$	−49.9756	+	28.8535i	−1.79056	+	1.03378i
$780$		0			0
$781$	10.9286	−	18.9288i	0.391055	−	0.677327i
$782$	−2.08328	+	7.77492i	−0.0744980	+	0.278030i
$783$		0			0
$784$	−32.8911	+	5.93028i	−1.17468	+	0.211796i
$785$	1.08222	−	1.08222i	0.0386261	−	0.0386261i
$786$		0			0
$787$	−3.40865	−	12.7213i	−0.121505	−	0.453464i	0.878186	−	0.478320i	$-0.158754\pi$
$787$	−3.40865	−	12.7213i	−0.121505	−	0.453464i	−0.999691	+	0.0248556i	$0.992087\pi$
$788$	1.99346	−	0.534145i	0.0710139	−	0.0190281i
$789$		0			0
$790$	1.08232			0.0385071
$791$	−13.0492	+	9.17465i	−0.463976	+	0.326213i
$792$		0			0
$793$	5.41807	+	14.1363i	0.192401	+	0.501995i
$794$	4.68591	+	2.70541i	0.166297	+	0.0960115i
$795$		0			0
$796$	−7.30547	+	4.21782i	−0.258936	+	0.149497i
$797$	32.0204			1.13422			0.567111	−	0.823642i	$-0.308061\pi$
$797$	32.0204			1.13422			0.567111	+	0.823642i	$0.308061\pi$
$798$		0			0
$799$	11.8805	−	11.8805i	0.420300	−	0.420300i
$800$	−3.74763	+	13.9863i	−0.132499	+	0.494492i
$801$		0			0
$802$	29.3153	−	50.7756i	1.03516	−	1.79295i
$803$	25.1468	+	43.5556i	0.887412	+	1.53704i
$804$		0			0
$805$	0.141002	+	0.117853i	0.00496968	+	0.00415378i
$806$	−1.25440	+	7.89362i	−0.0441842	+	0.278041i
$807$		0			0
$808$	25.3994	−	6.80575i	0.893548	−	0.239426i
$809$	−16.2002	+	28.0596i	−0.569570	+	0.986524i	0.427039	+	0.904233i	$0.359557\pi$
$809$	−16.2002	+	28.0596i	−0.569570	+	0.986524i	−0.996608	+	0.0822903i	$0.973777\pi$
$810$		0			0
$811$	−36.2274	−	36.2274i	−1.27212	−	1.27212i	−0.944975	−	0.327142i	$-0.893915\pi$
$811$	−36.2274	−	36.2274i	−1.27212	−	1.27212i	−0.327142	−	0.944975i	$-0.606085\pi$
$812$	0.501994	−	0.0448930i	0.0176165	−	0.00157544i
$813$		0			0
$814$	6.78150	−	25.3089i	0.237692	−	0.887077i
$815$	−0.0856754	−	0.0494647i	−0.00300108	−	0.00173267i
$816$		0			0
$817$	13.5764	+	3.63778i	0.474977	+	0.127270i
$818$	−8.92543			−0.312070
$819$		0			0
$820$	−0.455934			−0.0159219
$821$	−5.16554	−	1.38410i	−0.180279	−	0.0483055i	0.167550	−	0.985864i	$-0.446414\pi$
$821$	−5.16554	−	1.38410i	−0.180279	−	0.0483055i	−0.347829	+	0.937558i	$0.613081\pi$
$822$		0			0
$823$	−13.0985	−	7.56245i	−0.456587	−	0.263610i	0.254021	−	0.967199i	$-0.418247\pi$
$823$	−13.0985	−	7.56245i	−0.456587	−	0.263610i	−0.710608	+	0.703588i	$0.751580\pi$
$824$	5.85662	−	21.8572i	0.204025	−	0.761432i
$825$		0			0
$826$	5.36175	+	7.62607i	0.186559	+	0.265345i
$827$	−18.6451	−	18.6451i	−0.648353	−	0.648353i	0.304242	−	0.952595i	$-0.401597\pi$
$827$	−18.6451	−	18.6451i	−0.648353	−	0.648353i	−0.952595	+	0.304242i	$0.901597\pi$
$828$		0			0
$829$	−8.43417	+	14.6084i	−0.292931	+	0.507371i	−0.974501	−	0.224381i	$-0.927964\pi$
$829$	−8.43417	+	14.6084i	−0.292931	+	0.507371i	0.681571	+	0.731752i	$0.261297\pi$
$830$	−0.849347	+	0.227582i	−0.0294813	+	0.00789948i
$831$		0			0
$832$	−17.5953	−	2.79612i	−0.610008	−	0.0969380i
$833$	−26.2490	−	31.0388i	−0.909474	−	1.07543i
$834$		0			0
$835$	0.411851	+	0.713346i	0.0142527	+	0.0246864i
$836$	−5.87283	+	10.1720i	−0.203116	+	0.351808i
$837$		0			0
$838$	−7.09679	+	26.4856i	−0.245155	+	0.914929i
$839$	21.4556	−	21.4556i	0.740729	−	0.740729i	−0.231989	−	0.972718i	$-0.574523\pi$
$839$	21.4556	−	21.4556i	0.740729	−	0.740729i	0.972718	+	0.231989i	$0.0745235\pi$
$840$		0			0
$841$	−28.8684			−0.995462
$842$	−10.8207	+	6.24735i	−0.372907	+	0.215298i
$843$		0			0
$844$	9.57506	+	5.52816i	0.329587	+	0.190287i
$845$	−0.564696	+	0.867597i	−0.0194261	+	0.0298462i
$846$		0			0
$847$	−7.64015	+	16.4671i	−0.262519	+	0.565815i
$848$	−50.3069			−1.72755
$849$		0			0
$850$	−44.5108	+	11.9266i	−1.52671	+	0.409080i
$851$	−0.880801	−	3.28719i	−0.0301935	−	0.112684i
$852$		0			0
$853$	32.1950	−	32.1950i	1.10234	−	1.10234i	0.108209	−	0.994128i	$-0.465488\pi$
$853$	32.1950	−	32.1950i	1.10234	−	1.10234i	0.994128	−	0.108209i	$-0.0345116\pi$
$854$	11.3210	−	13.5448i	0.387398	−	0.463493i
$855$		0			0
$856$	10.6930	−	39.9069i	0.365480	−	1.36399i
$857$	5.85701	−	10.1446i	0.200071	−	0.346534i	−0.748480	−	0.663158i	$-0.769216\pi$
$857$	5.85701	−	10.1446i	0.200071	−	0.346534i	0.948551	+	0.316624i	$0.102549\pi$
$858$		0			0
$859$	−13.9161	+	8.03444i	−0.474810	+	0.274132i	−0.718251	−	0.695784i	$-0.755057\pi$
$859$	−13.9161	+	8.03444i	−0.474810	+	0.274132i	0.243441	+	0.969916i	$0.421724\pi$
$860$	0.0785234	+	0.0785234i	0.00267763	+	0.00267763i
$861$		0			0
$862$		−	12.9877i		−	0.442364i
$863$	43.5369	+	11.6657i	1.48201	+	0.397104i	0.907032	−	0.421063i	$-0.138343\pi$
$863$	43.5369	+	11.6657i	1.48201	+	0.397104i	0.574981	+	0.818167i	$0.305009\pi$
$864$		0			0
$865$	0.243290	−	0.0651894i	0.00827212	−	0.00221651i
$866$	−10.6136	−	2.84389i	−0.360663	−	0.0966395i
$867$		0			0
$868$	1.81999	−	0.666394i	0.0617746	−	0.0226189i
$869$	25.5611	+	25.5611i	0.867102	+	0.867102i
$870$		0			0
$871$	36.2692	−	3.79316i	1.22894	−	0.128526i
$872$	−15.9877	+	27.6915i	−0.541411	+	0.937752i
$873$		0			0
$874$			7.33586i			0.248139i
$875$	−0.361617	+	2.07418i	−0.0122249	+	0.0701200i
$876$		0			0
$877$	4.23796	+	1.13556i	0.143106	+	0.0383451i	0.329661	−	0.944099i	$-0.393066\pi$
$877$	4.23796	+	1.13556i	0.143106	+	0.0383451i	−0.186555	+	0.982445i	$0.559732\pi$
$878$	−1.76677	−	6.59367i	−0.0596255	−	0.222526i
$879$		0			0
$880$	1.39151	−	0.803391i	0.0469080	−	0.0270823i
$881$	38.4369			1.29497			0.647487	−	0.762077i	$-0.275820\pi$
$881$	38.4369			1.29497			0.647487	+	0.762077i	$0.275820\pi$
$882$		0			0
$883$		−	20.7346i		−	0.697776i	−0.937164	−	0.348888i	$-0.886559\pi$
$883$		−	20.7346i		−	0.697776i	0.937164	−	0.348888i	$-0.113441\pi$
$884$	3.93496	+	10.2667i	0.132347	+	0.345307i
$885$		0			0
$886$	9.46499	+	35.3238i	0.317983	+	1.18673i
$887$	−36.7173	+	21.1987i	−1.23285	+	0.711784i	−0.967622	−	0.252403i	$-0.918779\pi$
$887$	−36.7173	+	21.1987i	−1.23285	+	0.711784i	−0.265223	+	0.964187i	$0.585446\pi$
$888$		0			0
$889$	0.395379	+	0.562352i	0.0132606	+	0.0188607i
$890$	−0.720863	+	0.720863i	−0.0241634	+	0.0241634i
$891$		0			0
$892$	3.71169	+	13.8522i	0.124276	+	0.463806i
$893$	7.65627	−	13.2611i	0.256207	−	0.443764i
$894$		0			0
$895$	−0.326745	+	0.326745i	−0.0109219	+	0.0109219i
$896$	12.4184	+	33.9159i	0.414869	+	1.13305i
$897$		0			0
$898$	−8.09936	−	14.0285i	−0.270279	−	0.468137i
$899$	0.488812	−	0.130977i	0.0163028	−	0.00436832i
$900$		0			0
$901$	−30.5937	−	52.9899i	−1.01922	−	1.76535i
$902$	−51.7784	−	51.7784i	−1.72403	−	1.72403i
$903$		0			0
$904$	9.99170	+	9.99170i	0.332319	+	0.332319i
$905$	−0.282363	+	1.05379i	−0.00938607	+	0.0350293i
$906$		0			0
$907$	51.6892	+	29.8428i	1.71631	+	0.990912i	0.925410	+	0.378968i	$0.123721\pi$
$907$	51.6892	+	29.8428i	1.71631	+	0.990912i	0.790901	+	0.611944i	$0.209612\pi$
$908$	−1.75823	−	0.471117i	−0.0583490	−	0.0156346i
$909$		0			0
$910$	1.20426	+	0.0825034i	0.0399208	+	0.00273496i
$911$	21.0872			0.698649			0.349325	−	0.937002i	$-0.386411\pi$
$911$	21.0872			0.698649			0.349325	+	0.937002i	$0.386411\pi$
$912$		0			0
$913$	−25.4339	−	14.6842i	−0.841738	−	0.485977i
$914$	21.4661	+	12.3935i	0.710037	+	0.409940i
$915$		0			0
$916$	7.15728	+	7.15728i	0.236483	+	0.236483i
$917$	0.873415	−	1.88250i	0.0288427	−	0.0621656i
$918$		0			0
$919$	−7.62853	−	13.2130i	−0.251642	−	0.435857i	0.712336	−	0.701839i	$-0.247637\pi$
$919$	−7.62853	−	13.2130i	−0.251642	−	0.435857i	−0.963978	+	0.265982i	$0.914304\pi$
$920$	0.0813936	−	0.140978i	0.00268347	−	0.00464790i
$921$		0			0
$922$	11.5565	+	20.0165i	0.380595	+	0.659209i
$923$	−10.9527	−	15.0914i	−0.360511	−	0.496739i
$924$		0			0
$925$	13.7764	−	13.7764i	0.452966	−	0.452966i
$926$	17.1370	+	29.6822i	0.563158	+	0.975418i
$927$		0			0
$928$	−0.272243	−	1.01602i	−0.00893681	−	0.0333526i
$929$	2.56954	−	9.58965i	0.0843039	−	0.314626i	−0.910878	−	0.412677i	$-0.864594\pi$
$929$	2.56954	−	9.58965i	0.0843039	−	0.314626i	0.995181	+	0.0980503i	$0.0312606\pi$
$930$		0			0
$931$	−30.4292	−	21.1326i	−0.997275	−	0.692591i
$932$	2.71470			0.0889230
$933$		0			0
$934$	−7.32627	−	27.3420i	−0.239723	−	0.894658i
$935$	1.69248	+	0.977151i	0.0553499	+	0.0319563i
$936$		0			0
$937$			55.6823i			1.81906i	0.415636	+	0.909531i	$0.363559\pi$
$937$			55.6823i			1.81906i	−0.415636	+	0.909531i	$0.636441\pi$
$938$	−24.4570	−	34.7854i	−0.798548	−	1.13578i
$939$		0			0
$940$	0.104774	−	0.0604911i	0.00341734	−	0.00197300i
$941$	−13.8086	+	3.70000i	−0.450147	+	0.120616i	−0.476768	−	0.879029i	$-0.658192\pi$
$941$	−13.8086	+	3.70000i	−0.450147	+	0.120616i	0.0266213	+	0.999646i	$0.491525\pi$
$942$		0			0
$943$	−9.18670	−	2.46157i	−0.299160	−	0.0801597i
$944$	7.48592	−	7.48592i	0.243646	−	0.243646i
$945$		0			0
$946$			17.8351i			0.579870i
$947$	−6.44026	+	24.0354i	−0.209280	+	0.781044i	0.778822	+	0.627245i	$0.215818\pi$
$947$	−6.44026	+	24.0354i	−0.209280	+	0.781044i	−0.988102	+	0.153799i	$0.950849\pi$
$948$		0			0
$949$	42.6743	−	4.46302i	1.38527	−	0.144876i
$950$	−36.3707	+	20.9986i	−1.18002	+	0.681286i
$951$		0			0
$952$	−23.0928	+	27.6288i	−0.748442	+	0.895455i
$953$			0.410134i			0.0132855i	0.999978	+	0.00664276i	$0.00211447\pi$
$953$			0.410134i			0.0132855i	−0.999978	+	0.00664276i	$0.997886\pi$
$954$		0			0
$955$	−0.650498	+	0.174300i	−0.0210496	+	0.00564023i
$956$	−4.91780	+	1.31772i	−0.159053	+	0.0426181i
$957$		0			0
$958$			40.2722i			1.30113i
$959$	23.4069	−	28.0046i	0.755848	−	0.904316i
$960$		0			0
$961$	−25.1614	+	14.5270i	−0.811659	+	0.468612i
$962$	−17.3647	−	14.0765i	−0.559860	−	0.453843i
$963$		0			0
$964$	0.303880	−	1.13410i	0.00978733	−	0.0365268i
$965$			0.0393184i			0.00126570i
$966$		0			0
$967$	24.7994	−	24.7994i	0.797497	−	0.797497i	−0.185204	−	0.982700i	$-0.559294\pi$
$967$	24.7994	−	24.7994i	0.797497	−	0.797497i	0.982700	+	0.185204i	$0.0592945\pi$
$968$	15.5326	+	4.16194i	0.499236	+	0.133770i
$969$		0			0
$970$	1.04425	−	0.279805i	0.0335287	−	0.00898400i
$971$	12.5905	−	7.26911i	0.404047	−	0.233277i	−0.284182	−	0.958770i	$-0.591722\pi$
$971$	12.5905	−	7.26911i	0.404047	−	0.233277i	0.688229	+	0.725494i	$0.258388\pi$
$972$		0			0
$973$	−4.76268	−	6.77401i	−0.152684	−	0.217165i
$974$			53.0471i			1.69974i
$975$		0			0
$976$	−17.3614	−	10.0236i	−0.555725	−	0.320848i
$977$	−8.88774	−	33.1695i	−0.284344	−	1.06119i	−0.949317	−	0.314319i	$-0.898224\pi$
$977$	−8.88774	−	33.1695i	−0.284344	−	1.06119i	0.664973	−	0.746867i	$-0.268443\pi$
$978$		0			0
$979$	−34.0493			−1.08822
$980$	−0.124724	−	0.264804i	−0.00398416	−	0.00845886i
$981$		0			0
$982$	−5.96224	+	22.2514i	−0.190263	+	0.710070i
$983$	−5.84114	−	21.7994i	−0.186304	−	0.695294i	−0.994348	−	0.106172i	$-0.966140\pi$
$983$	−5.84114	−	21.7994i	−0.186304	−	0.695294i	0.808044	−	0.589122i	$-0.200526\pi$
$984$		0			0
$985$	−0.156475	−	0.271023i	−0.00498572	−	0.00863552i
$986$	2.36705	−	2.36705i	0.0753821	−	0.0753821i
$987$		0			0
$988$	5.88578	+	8.10987i	0.187252	+	0.258009i
$989$	1.15824	+	2.00613i	0.0368298	+	0.0637911i
$990$		0			0
$991$	28.4614	−	49.2966i	0.904106	−	1.56596i	0.0819923	−	0.996633i	$-0.473872\pi$
$991$	28.4614	−	49.2966i	0.904106	−	1.56596i	0.822113	−	0.569324i	$-0.192795\pi$
$992$	−2.02251	−	3.50309i	−0.0642148	−	0.111223i
$993$		0			0
$994$	−9.15120	+	19.7239i	−0.290258	+	0.625604i
$995$	0.904515	+	0.904515i	0.0286751	+	0.0286751i
$996$		0			0
$997$	20.0782	+	11.5922i	0.635884	+	0.367128i	0.783027	−	0.621987i	$-0.213674\pi$
$997$	20.0782	+	11.5922i	0.635884	+	0.367128i	−0.147143	+	0.989115i	$0.547008\pi$
$998$	13.6136	+	7.85984i	0.430932	+	0.248799i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.577.2		32
3.2	odd	2		91.2.bb.a.31.7	yes	32
7.5	odd	6	inner	819.2.fn.e.460.7		32
13.8	odd	4	inner	819.2.fn.e.73.7		32
21.2	odd	6		637.2.bc.b.460.2		32
21.5	even	6		91.2.bb.a.5.2	✓	32
21.11	odd	6		637.2.i.a.538.3		32
21.17	even	6		637.2.i.a.538.4		32
21.20	even	2		637.2.bc.b.31.7		32
39.8	even	4		91.2.bb.a.73.2	yes	32
91.47	even	12	inner	819.2.fn.e.775.2		32
273.47	odd	12		91.2.bb.a.47.7	yes	32
273.86	even	12		637.2.bc.b.411.7		32
273.125	odd	4		637.2.bc.b.619.2		32
273.164	odd	12		637.2.i.a.489.4		32
273.242	even	12		637.2.i.a.489.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.2	✓	32	21.5	even	6
91.2.bb.a.31.7	yes	32	3.2	odd	2
91.2.bb.a.47.7	yes	32	273.47	odd	12
91.2.bb.a.73.2	yes	32	39.8	even	4
637.2.i.a.489.3		32	273.242	even	12
637.2.i.a.489.4		32	273.164	odd	12
637.2.i.a.538.3		32	21.11	odd	6
637.2.i.a.538.4		32	21.17	even	6
637.2.bc.b.31.7		32	21.20	even	2
637.2.bc.b.411.7		32	273.86	even	12
637.2.bc.b.460.2		32	21.2	odd	6
637.2.bc.b.619.2		32	273.125	odd	4
819.2.fn.e.73.7		32	13.8	odd	4	inner
819.2.fn.e.460.7		32	7.5	odd	6	inner
819.2.fn.e.577.2		32	1.1	even	1	trivial
819.2.fn.e.775.2		32	91.47	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53492 - 0.411280i) q^{2} +(0.454770 + 0.262561i) q^{4} +(0.0206096 - 0.0769162i) q^{5} +(-2.16435 + 1.52171i) q^{7} +(1.65723 + 1.65723i) q^{8} +O(q^{10})\)	\(q+(-1.53492 - 0.411280i) q^{2} +(0.454770 + 0.262561i) q^{4} +(0.0206096 - 0.0769162i) q^{5} +(-2.16435 + 1.52171i) q^{7} +(1.65723 + 1.65723i) q^{8} +(-0.0632682 + 0.109584i) q^{10} +(-4.08225 + 1.09384i) q^{11} +(-0.565867 + 3.56087i) q^{13} +(3.94794 - 1.44555i) q^{14} +(-2.38725 - 4.13483i) q^{16} +(2.90357 - 5.02912i) q^{17} +(1.36980 - 5.11216i) q^{19} +(0.0295679 - 0.0295679i) q^{20} +6.71579 q^{22} +(0.755405 - 0.436133i) q^{23} +(4.32464 + 2.49683i) q^{25} +(2.33307 - 5.23291i) q^{26} +(-1.38382 + 0.123754i) q^{28} -0.362759 q^{29} +(-1.34748 + 0.361057i) q^{31} +(0.750478 + 2.80082i) q^{32} +(-6.52511 + 6.52511i) q^{34} +(0.0724379 + 0.197835i) q^{35} +(1.00978 - 3.76857i) q^{37} +(-4.20506 + 7.28338i) q^{38} +(0.161623 - 0.0933128i) q^{40} +(-7.70995 - 7.70995i) q^{41} +2.65570i q^{43} +(-2.14368 - 0.574398i) q^{44} +(-1.33886 + 0.358745i) q^{46} +(2.79467 + 0.748829i) q^{47} +(2.36879 - 6.58702i) q^{49} +(-5.61106 - 5.61106i) q^{50} +(-1.19229 + 1.47080i) q^{52} +(5.26830 - 9.12497i) q^{53} +0.336535i q^{55} +(-6.10864 - 1.06499i) q^{56} +(0.556806 + 0.149196i) q^{58} +(0.573890 + 2.14179i) q^{59} +(3.63628 - 2.09941i) q^{61} +2.21677 q^{62} +4.94130i q^{64} +(0.262226 + 0.116913i) q^{65} +(-2.61773 - 9.76951i) q^{67} +(2.64091 - 1.52473i) q^{68} +(-0.0298205 - 0.333453i) q^{70} +(-3.65698 + 3.65698i) q^{71} +(-3.08002 - 11.4948i) q^{73} +(-3.09987 + 5.36914i) q^{74} +(1.96520 - 1.96520i) q^{76} +(7.17090 - 8.57944i) q^{77} +(-4.27671 - 7.40747i) q^{79} +(-0.367236 + 0.0984006i) q^{80} +(8.66319 + 15.0051i) q^{82} +(4.91372 + 4.91372i) q^{83} +(-0.326980 - 0.326980i) q^{85} +(1.09224 - 4.07628i) q^{86} +(-8.57795 - 4.95248i) q^{88} +(7.78209 + 2.08520i) q^{89} +(-4.19388 - 8.56804i) q^{91} +0.458047 q^{92} +(-3.98161 - 2.29878i) q^{94} +(-0.364977 - 0.210720i) q^{95} +(-6.04128 - 6.04128i) q^{97} +(-6.34501 + 9.13630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more