LMFDB - Embedded newform 414.2.j.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(17,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

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

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

chi := DirichletCharacter("414.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.j (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	414.53
Dual form			414.2.j.a.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755750 - 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(-0.922959 - 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(0.540641 - 0.841254i) q^{8} +O(q^{10})$	\(q+(-0.755750 - 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(-0.922959 - 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(0.540641 - 0.841254i) q^{8} +(-0.625947 + 2.13178i) q^{10} +(-1.74253 - 2.01098i) q^{11} +(-1.51348 - 0.444397i) q^{13} +(0.0193125 - 0.0422885i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.0331173 - 0.230336i) q^{17} +(-2.25463 + 0.324167i) q^{19} +(1.86908 - 1.20118i) q^{20} +2.66091i q^{22} +(-3.05411 - 3.69763i) q^{23} +(0.0417212 - 0.0481489i) q^{25} +(0.852791 + 1.32697i) q^{26} +(-0.0422885 + 0.0193125i) q^{28} +(-6.02540 - 0.866322i) q^{29} +(-6.37932 - 4.09974i) q^{31} +(0.909632 + 0.415415i) q^{32} +(-0.175866 + 0.152389i) q^{34} +(0.0780612 - 0.0676404i) q^{35} +(2.80691 + 1.28187i) q^{37} +(1.91622 + 1.23148i) q^{38} +(-2.19916 - 0.316192i) q^{40} +(0.764300 - 0.349044i) q^{41} +(-1.64454 - 2.55895i) q^{43} +(1.74253 - 2.01098i) q^{44} +(-0.113292 + 4.79449i) q^{46} +3.61065i q^{47} +(5.88696 - 3.78332i) q^{49} +(-0.0630616 + 0.00906689i) q^{50} +(0.224483 - 1.56132i) q^{52} +(-6.15867 + 1.80835i) q^{53} +(-2.45591 + 5.37770i) q^{55} +(0.0446065 + 0.0130977i) q^{56} +(3.98638 + 4.60052i) q^{58} +(-0.296092 + 1.00840i) q^{59} +(5.09375 - 7.92604i) q^{61} +(2.13641 + 7.27594i) q^{62} +(-0.415415 - 0.909632i) q^{64} +(0.498752 + 3.46889i) q^{65} +(-4.92015 - 4.26333i) q^{67} +0.232705 q^{68} -0.103290 q^{70} +(9.95203 + 8.62348i) q^{71} +(0.982079 + 6.83051i) q^{73} +(-1.28187 - 2.80691i) q^{74} +(-0.641735 - 2.18555i) q^{76} +(0.0668799 - 0.104067i) q^{77} +(1.88074 - 6.40520i) q^{79} +(1.45495 + 1.67911i) q^{80} +(-0.806195 - 0.236720i) q^{82} +(-3.50663 + 7.67846i) q^{83} +(-0.496075 + 0.145661i) q^{85} +(-0.432898 + 3.01087i) q^{86} +(-2.63383 + 0.378687i) q^{88} +(14.0917 - 9.05622i) q^{89} -0.0733315i q^{91} +(3.22535 - 3.54925i) q^{92} +(2.36447 - 2.72875i) q^{94} +(2.73608 + 4.25742i) q^{95} +(12.6502 - 5.77716i) q^{97} +(-6.92661 - 0.995896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) $ 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{19}{22}\right)$

Coefficient data

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

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

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

$2$	−0.755750	−	0.654861i	−0.534396	−	0.463056i
$2$	−0.755750	−	0.654861i	−0.534396	−	0.463056i
$3$		0			0
$3$		0			0
$4$	0.142315	+	0.989821i	0.0711574	+	0.494911i
$5$	−0.922959	−	2.02100i	−0.412760	−	0.903818i	−0.995816	−	0.0913859i	$-0.970870\pi$
$5$	−0.922959	−	2.02100i	−0.412760	−	0.903818i	0.583056	−	0.812432i	$-0.301857\pi$
$6$		0			0
$7$	0.0130977	+	0.0446065i	0.00495045	+	0.0168597i	0.961931	−	0.273292i	$-0.0881125\pi$
$7$	0.0130977	+	0.0446065i	0.00495045	+	0.0168597i	−0.956981	+	0.290152i	$0.906294\pi$
$8$	0.540641	−	0.841254i	0.191145	−	0.297428i
$9$		0			0
$10$	−0.625947	+	2.13178i	−0.197942	+	0.674128i
$11$	−1.74253	−	2.01098i	−0.525391	−	0.606334i	0.429581	−	0.903028i	$-0.358661\pi$
$11$	−1.74253	−	2.01098i	−0.525391	−	0.606334i	−0.954973	+	0.296694i	$0.904116\pi$
$12$		0			0
$13$	−1.51348	−	0.444397i	−0.419763	−	0.123253i	0.0650284	−	0.997883i	$-0.479286\pi$
$13$	−1.51348	−	0.444397i	−0.419763	−	0.123253i	−0.484791	+	0.874630i	$0.661104\pi$
$14$	0.0193125	−	0.0422885i	0.00516149	−	0.0113021i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.0331173	−	0.230336i	0.00803213	−	0.0558647i	−0.985411	−	0.170191i	$-0.945562\pi$
$17$	0.0331173	−	0.230336i	0.00803213	−	0.0558647i	0.993443	+	0.114326i	$0.0364708\pi$
$18$		0			0
$19$	−2.25463	+	0.324167i	−0.517248	+	0.0743691i	−0.395995	−	0.918253i	$-0.629600\pi$
$19$	−2.25463	+	0.324167i	−0.517248	+	0.0743691i	−0.121253	+	0.992622i	$0.538691\pi$
$20$	1.86908	−	1.20118i	0.417938	−	0.268593i
$21$		0			0
$22$			2.66091i			0.567308i
$23$	−3.05411	−	3.69763i	−0.636825	−	0.771008i
$23$	−3.05411	−	3.69763i	−0.636825	−	0.771008i
$24$		0			0
$25$	0.0417212	−	0.0481489i	0.00834425	−	0.00962978i
$26$	0.852791	+	1.32697i	0.167246	+	0.260240i
$27$		0			0
$28$	−0.0422885	+	0.0193125i	−0.00799178	+	0.00364972i
$29$	−6.02540	−	0.866322i	−1.11889	−	0.160872i	−0.442041	−	0.896995i	$-0.645746\pi$
$29$	−6.02540	−	0.866322i	−1.11889	−	0.160872i	−0.676848	+	0.736123i	$0.736655\pi$
$30$		0			0
$31$	−6.37932	−	4.09974i	−1.14576	−	0.736335i	−0.176969	−	0.984216i	$-0.556629\pi$
$31$	−6.37932	−	4.09974i	−1.14576	−	0.736335i	−0.968790	+	0.247881i	$0.920266\pi$
$32$	0.909632	+	0.415415i	0.160802	+	0.0734357i
$33$		0			0
$34$	−0.175866	+	0.152389i	−0.0301608	+	0.0261345i
$35$	0.0780612	−	0.0676404i	0.0131947	−	0.0114333i
$36$		0			0
$37$	2.80691	+	1.28187i	0.461452	+	0.210738i	0.632556	−	0.774515i	$-0.282006\pi$
$37$	2.80691	+	1.28187i	0.461452	+	0.210738i	−0.171103	+	0.985253i	$0.554733\pi$
$38$	1.91622	+	1.23148i	0.310852	+	0.199773i
$39$		0			0
$40$	−2.19916	−	0.316192i	−0.347718	−	0.0499943i
$41$	0.764300	−	0.349044i	0.119364	−	0.0545116i	−0.354838	−	0.934928i	$-0.615464\pi$
$41$	0.764300	−	0.349044i	0.119364	−	0.0545116i	0.474202	+	0.880416i	$0.342737\pi$
$42$		0			0
$43$	−1.64454	−	2.55895i	−0.250790	−	0.390237i	0.692918	−	0.721016i	$-0.256325\pi$
$43$	−1.64454	−	2.55895i	−0.250790	−	0.390237i	−0.943708	+	0.330779i	$0.892688\pi$
$44$	1.74253	−	2.01098i	0.262696	−	0.303167i
$45$		0			0
$46$	−0.113292	+	4.79449i	−0.0167039	+	0.706909i
$47$			3.61065i			0.526667i	0.964705	+	0.263334i	$0.0848220\pi$
$47$			3.61065i			0.526667i	−0.964705	+	0.263334i	$0.915178\pi$
$48$		0			0
$49$	5.88696	−	3.78332i	0.840994	−	0.540474i
$50$	−0.0630616	+	0.00906689i	−0.00891826	+	0.00128225i
$51$		0			0
$52$	0.224483	−	1.56132i	0.0311302	−	0.216515i
$53$	−6.15867	+	1.80835i	−0.845958	+	0.248396i	−0.675859	−	0.737031i	$-0.736227\pi$
$53$	−6.15867	+	1.80835i	−0.845958	+	0.248396i	−0.170099	+	0.985427i	$0.554409\pi$
$54$		0			0
$55$	−2.45591	+	5.37770i	−0.331155	+	0.725129i
$56$	0.0446065	+	0.0130977i	0.00596080	+	0.00175025i
$57$		0			0
$58$	3.98638	+	4.60052i	0.523437	+	0.604078i
$59$	−0.296092	+	1.00840i	−0.0385479	+	0.131282i	−0.976519	−	0.215431i	$-0.930884\pi$
$59$	−0.296092	+	1.00840i	−0.0385479	+	0.131282i	0.937971	+	0.346714i	$0.112702\pi$
$60$		0			0
$61$	5.09375	−	7.92604i	0.652188	−	1.01482i	−0.344905	−	0.938638i	$-0.612089\pi$
$61$	5.09375	−	7.92604i	0.652188	−	1.01482i	0.997094	−	0.0761874i	$-0.0242747\pi$
$62$	2.13641	+	7.27594i	0.271324	+	0.924046i
$63$		0			0
$64$	−0.415415	−	0.909632i	−0.0519269	−	0.113704i
$65$	0.498752	+	3.46889i	0.0618625	+	0.430263i
$66$		0			0
$67$	−4.92015	−	4.26333i	−0.601092	−	0.520849i	0.300305	−	0.953843i	$-0.402912\pi$
$67$	−4.92015	−	4.26333i	−0.601092	−	0.520849i	−0.901397	+	0.432994i	$0.857457\pi$
$68$	0.232705			0.0282196
$69$		0			0
$70$	−0.103290			−0.0123455
$71$	9.95203	+	8.62348i	1.18109	+	1.02342i	0.999196	+	0.0401004i	$0.0127678\pi$
$71$	9.95203	+	8.62348i	1.18109	+	1.02342i	0.181893	+	0.983318i	$0.441778\pi$
$72$		0			0
$73$	0.982079	+	6.83051i	0.114944	+	0.799451i	0.962992	+	0.269531i	$0.0868687\pi$
$73$	0.982079	+	6.83051i	0.114944	+	0.799451i	−0.848048	+	0.529919i	$0.822222\pi$
$74$	−1.28187	−	2.80691i	−0.149014	−	0.326296i
$75$		0			0
$76$	−0.641735	−	2.18555i	−0.0736121	−	0.250700i
$77$	0.0668799	−	0.104067i	0.00762168	−	0.0118596i
$78$		0			0
$79$	1.88074	−	6.40520i	0.211599	−	0.720641i	−0.783467	−	0.621433i	$-0.786551\pi$
$79$	1.88074	−	6.40520i	0.211599	−	0.720641i	0.995067	−	0.0992080i	$-0.0316309\pi$
$80$	1.45495	+	1.67911i	0.162669	+	0.187730i
$81$		0			0
$82$	−0.806195	−	0.236720i	−0.0890293	−	0.0261414i
$83$	−3.50663	+	7.67846i	−0.384903	+	0.842820i	0.613677	+	0.789557i	$0.289690\pi$
$83$	−3.50663	+	7.67846i	−0.384903	+	0.842820i	−0.998581	+	0.0532633i	$0.983038\pi$
$84$		0			0
$85$	−0.496075	+	0.145661i	−0.0538069	+	0.0157991i
$86$	−0.432898	+	3.01087i	−0.0466806	+	0.324671i
$87$		0			0
$88$	−2.63383	+	0.378687i	−0.280767	+	0.0403682i
$89$	14.0917	−	9.05622i	1.49372	−	0.959957i	0.498038	−	0.867155i	$-0.334054\pi$
$89$	14.0917	−	9.05622i	1.49372	−	0.959957i	0.995685	−	0.0928018i	$-0.0295823\pi$
$90$		0			0
$91$		−	0.0733315i		−	0.00768723i
$92$	3.22535	−	3.54925i	0.336266	−	0.370034i
$93$		0			0
$94$	2.36447	−	2.72875i	0.243877	−	0.281449i
$95$	2.73608	+	4.25742i	0.280715	+	0.436802i
$96$		0			0
$97$	12.6502	−	5.77716i	1.28443	−	0.586581i	0.348023	−	0.937486i	$-0.386853\pi$
$97$	12.6502	−	5.77716i	1.28443	−	0.586581i	0.936411	+	0.350905i	$0.114126\pi$
$98$	−6.92661	−	0.995896i	−0.699693	−	0.100601i
$99$		0			0
$100$	0.0535964	+	0.0344443i	0.00535964	+	0.00344443i
$101$	9.27293	+	4.23481i	0.922691	+	0.421379i	0.819367	−	0.573269i	$-0.194325\pi$
$101$	9.27293	+	4.23481i	0.922691	+	0.421379i	0.103324	+	0.994648i	$0.467052\pi$
$102$		0			0
$103$	6.72255	−	5.82513i	0.662393	−	0.573967i	−0.257432	−	0.966296i	$-0.582876\pi$
$103$	6.72255	−	5.82513i	0.662393	−	0.573967i	0.919825	+	0.392330i	$0.128331\pi$
$104$	−1.19210	+	1.03296i	−0.116895	+	0.101290i
$105$		0			0
$106$	5.83863	+	2.66641i	0.567098	+	0.258985i
$107$	2.28174	+	1.46638i	0.220584	+	0.141761i	0.646266	−	0.763112i	$-0.276330\pi$
$107$	2.28174	+	1.46638i	0.220584	+	0.141761i	−0.425682	+	0.904873i	$0.639966\pi$
$108$		0			0
$109$	8.05101	+	1.15756i	0.771147	+	0.110874i	0.516647	−	0.856198i	$-0.327180\pi$
$109$	8.05101	+	1.15756i	0.771147	+	0.110874i	0.254500	+	0.967073i	$0.418089\pi$
$110$	5.37770	−	2.45591i	0.512743	−	0.234162i
$111$		0			0
$112$	−0.0251342	−	0.0391096i	−0.00237496	−	0.00369551i
$113$	4.42961	−	5.11204i	0.416703	−	0.480900i	−0.508127	−	0.861282i	$-0.669662\pi$
$113$	4.42961	−	5.11204i	0.416703	−	0.480900i	0.924830	+	0.380382i	$0.124207\pi$
$114$		0			0
$115$	−4.65408	+	9.58510i	−0.433996	+	0.893815i
$116$		−	6.08737i		−	0.565198i
$117$		0			0
$118$	0.884130	−	0.568196i	0.0813908	−	0.0523067i
$119$	0.0107083	−	0.00153961i	0.000981624	−	0.000141136i
$120$		0			0
$121$	0.557811	−	3.87966i	0.0507101	−	0.352696i
$122$	−9.04005	+	2.65440i	−0.818448	+	0.240318i
$123$		0			0
$124$	3.15014	−	6.89784i	0.282891	−	0.619444i
$125$	−10.7947	−	3.16961i	−0.965508	−	0.283499i
$126$		0			0
$127$	11.6507	+	13.4457i	1.03384	+	1.19311i	0.980900	+	0.194513i	$0.0623128\pi$
$127$	11.6507	+	13.4457i	1.03384	+	1.19311i	0.0529370	+	0.998598i	$0.483142\pi$
$128$	−0.281733	+	0.959493i	−0.0249019	+	0.0848080i
$129$		0			0
$130$	1.89471	−	2.94823i	0.166177	−	0.258577i
$131$	−0.364203	−	1.24036i	−0.0318205	−	0.108371i	0.942051	−	0.335468i	$-0.108895\pi$
$131$	−0.364203	−	1.24036i	−0.0318205	−	0.108371i	−0.973872	+	0.227098i	$0.927076\pi$
$132$		0			0
$133$	−0.0439904	−	0.0963255i	−0.00381445	−	0.00835248i
$134$	0.926511	+	6.44403i	0.0800384	+	0.556679i
$135$		0			0
$136$	−0.175866	−	0.152389i	−0.0150804	−	0.0130673i
$137$	9.19016			0.785169			0.392584	−	0.919716i	$-0.371581\pi$
$137$	9.19016			0.785169			0.392584	+	0.919716i	$0.371581\pi$
$138$		0			0
$139$	4.56062			0.386827			0.193414	−	0.981117i	$-0.438044\pi$
$139$	4.56062			0.386827			0.193414	+	0.981117i	$0.438044\pi$
$140$	0.0780612	+	0.0676404i	0.00659737	+	0.00571665i
$141$		0			0
$142$	−1.87406	−	13.0344i	−0.157268	−	1.09382i
$143$	1.74360	+	3.81795i	0.145807	+	0.319273i
$144$		0			0
$145$	3.81037	+	12.9769i	0.316434	+	1.07767i
$146$	3.73083	−	5.80528i	0.308765	−	0.480448i
$147$		0			0
$148$	−0.869359	+	2.96076i	−0.0714609	+	0.243373i
$149$	−15.2836	−	17.6382i	−1.25208	−	1.44497i	−0.847780	−	0.530347i	$-0.822062\pi$
$149$	−15.2836	−	17.6382i	−1.25208	−	1.44497i	−0.404297	−	0.914628i	$-0.632484\pi$
$150$		0			0
$151$	−22.0386	−	6.47112i	−1.79348	−	0.526612i	−0.796523	−	0.604608i	$-0.793330\pi$
$151$	−22.0386	−	6.47112i	−1.79348	−	0.526612i	−0.996954	+	0.0779956i	$0.975148\pi$
$152$	−0.946240	+	2.07198i	−0.0767502	+	0.168059i
$153$		0			0
$154$	−0.118694	+	0.0348517i	−0.00956464	+	0.00280843i
$155$	−2.39772	+	16.6765i	−0.192589	+	1.33949i
$156$		0			0
$157$	−8.54975	+	1.22927i	−0.682344	+	0.0981062i	−0.474766	−	0.880112i	$-0.657467\pi$
$157$	−8.54975	+	1.22927i	−0.682344	+	0.0981062i	−0.207578	+	0.978218i	$0.566558\pi$
$158$	−5.61588	+	3.60910i	−0.446775	+	0.287125i
$159$		0			0
$160$		−	2.22178i		−	0.175647i
$161$	0.124937	−	0.184663i	0.00984639	−	0.0145535i
$162$		0			0
$163$	−12.6243	+	14.5692i	−0.988809	+	1.14115i	0.00117993	+	0.999999i	$0.499624\pi$
$163$	−12.6243	+	14.5692i	−0.988809	+	1.14115i	−0.989989	+	0.141147i	$0.954921\pi$
$164$	0.454263	+	0.706847i	0.0354720	+	0.0551954i
$165$		0			0
$166$	7.67846	−	3.50663i	0.595964	−	0.272168i
$167$	−8.15470	−	1.17247i	−0.631029	−	0.0907283i	−0.180624	−	0.983552i	$-0.557812\pi$
$167$	−8.15470	−	1.17247i	−0.631029	−	0.0907283i	−0.450406	+	0.892824i	$0.648721\pi$
$168$		0			0
$169$	−8.84317	−	5.68316i	−0.680244	−	0.437166i
$170$	0.470296	+	0.214777i	0.0360700	+	0.0164726i
$171$		0			0
$172$	2.29887	−	1.99198i	0.175287	−	0.151887i
$173$	5.65069	−	4.89635i	0.429614	−	0.372263i	−0.413045	−	0.910711i	$-0.635535\pi$
$173$	5.65069	−	4.89635i	0.429614	−	0.372263i	0.842659	+	0.538448i	$0.180989\pi$
$174$		0			0
$175$	0.00269421	+	0.00123040i	0.000203663	+	9.30097e-5i
$176$	2.23850	+	1.43860i	0.168733	+	0.108438i
$177$		0			0
$178$	−16.5804	−	2.38390i	−1.24275	−	0.178681i
$179$	2.24912	−	1.02714i	0.168107	−	0.0767720i	−0.329584	−	0.944126i	$-0.606909\pi$
$179$	2.24912	−	1.02714i	0.168107	−	0.0767720i	0.497691	+	0.867354i	$0.334181\pi$
$180$		0			0
$181$	3.22755	+	5.02217i	0.239902	+	0.373295i	0.940238	−	0.340519i	$-0.110603\pi$
$181$	3.22755	+	5.02217i	0.239902	+	0.373295i	−0.700336	+	0.713814i	$0.746966\pi$
$182$	−0.0480219	+	0.0554202i	−0.00355962	+	0.00410802i
$183$		0			0
$184$	−4.76182	+	0.570189i	−0.351046	+	0.0420349i
$185$		−	6.85587i		−	0.504053i
$186$		0			0
$187$	−0.520910	+	0.334768i	−0.0380927	+	0.0244807i
$188$	−3.57390	+	0.513849i	−0.260653	+	0.0374763i
$189$		0			0
$190$	0.720227	−	5.00929i	0.0522508	−	0.363412i
$191$	−4.15448	+	1.21987i	−0.300608	+	0.0882663i	−0.428558	−	0.903514i	$-0.640978\pi$
$191$	−4.15448	+	1.21987i	−0.300608	+	0.0882663i	0.127951	+	0.991781i	$0.459160\pi$
$192$		0			0
$193$	−10.6531	+	23.3270i	−0.766826	+	1.67911i	−0.0333064	+	0.999445i	$0.510604\pi$
$193$	−10.6531	+	23.3270i	−0.766826	+	1.67911i	−0.733519	+	0.679669i	$0.762124\pi$
$194$	−13.3436	−	3.91804i	−0.958016	−	0.281299i
$195$		0			0
$196$	4.58261	+	5.28861i	0.327329	+	0.377758i
$197$	1.04505	−	3.55911i	0.0744567	−	0.253576i	−0.913851	−	0.406050i	$-0.866906\pi$
$197$	1.04505	−	3.55911i	0.0744567	−	0.253576i	0.988307	+	0.152474i	$0.0487240\pi$
$198$		0			0
$199$	−7.22510	+	11.2425i	−0.512174	+	0.796958i	−0.996980	−	0.0776638i	$-0.975254\pi$
$199$	−7.22510	+	11.2425i	−0.512174	+	0.796958i	0.484806	+	0.874622i	$0.338890\pi$
$200$	−0.0179492	−	0.0611294i	−0.00126920	−	0.00432250i
$201$		0			0
$202$	−4.23481	−	9.27293i	−0.297960	−	0.652441i
$203$	−0.0402751	−	0.280119i	−0.00282676	−	0.0196605i
$204$		0			0
$205$	−1.41084	−	1.22250i	−0.0985371	−	0.0853828i
$206$	−8.89521			−0.619759
$207$		0			0
$208$	1.57737			0.109371
$209$	4.58065	+	3.96916i	0.316850	+	0.274552i
$210$		0			0
$211$	−0.449420	−	3.12578i	−0.0309393	−	0.215188i	0.968487	−	0.249065i	$-0.0801234\pi$
$211$	−0.449420	−	3.12578i	−0.0309393	−	0.215188i	−0.999426	+	0.0338777i	$0.989214\pi$
$212$	−2.66641	−	5.83863i	−0.183130	−	0.400999i
$213$		0			0
$214$	−0.764145	−	2.60244i	−0.0522359	−	0.177899i
$215$	−3.65380	+	5.68542i	−0.249187	+	0.387743i
$216$		0			0
$217$	0.0993210	−	0.338256i	0.00674235	−	0.0229623i
$218$	−5.32651	−	6.14712i	−0.360757	−	0.416335i
$219$		0			0
$220$	−5.67247	−	1.66559i	−0.382438	−	0.112294i
$221$	−0.152483	+	0.333891i	−0.0102571	+	0.0224599i
$222$		0			0
$223$	−23.9599	+	7.03527i	−1.60447	+	0.471116i	−0.956787	−	0.290790i	$-0.906082\pi$
$223$	−23.9599	+	7.03527i	−1.60447	+	0.471116i	−0.647688	+	0.761906i	$0.724264\pi$
$224$	−0.00661617	+	0.0460165i	−0.000442062	+	0.00307461i
$225$		0			0
$226$	−6.69535	+	0.962646i	−0.445368	+	0.0640343i
$227$	9.18821	−	5.90491i	0.609843	−	0.391922i	−0.198955	−	0.980009i	$-0.563755\pi$
$227$	9.18821	−	5.90491i	0.609843	−	0.391922i	0.808798	+	0.588086i	$0.200118\pi$
$228$		0			0
$229$		−	19.8476i		−	1.31156i	−0.754950	−	0.655782i	$-0.772339\pi$
$229$		−	19.8476i		−	1.31156i	0.754950	−	0.655782i	$-0.227661\pi$
$230$	9.79423	−	4.19616i	0.645812	−	0.276687i
$231$		0			0
$232$	−3.98638	+	4.60052i	−0.261718	+	0.302039i
$233$	−5.10411	−	7.94216i	−0.334382	−	0.520308i	0.632826	−	0.774294i	$-0.281895\pi$
$233$	−5.10411	−	7.94216i	−0.334382	−	0.520308i	−0.967208	+	0.253986i	$0.918258\pi$
$234$		0			0
$235$	7.29712	−	3.33248i	0.476012	−	0.217387i
$236$	−1.04027	−	0.149568i	−0.0677158	−	0.00973607i
$237$		0			0
$238$	−0.00910099	−	0.00584885i	−0.000589930	−	0.000379125i
$239$	4.78747	+	2.18637i	0.309676	+	0.141424i	0.564190	−	0.825645i	$-0.309188\pi$
$239$	4.78747	+	2.18637i	0.309676	+	0.141424i	−0.254515	+	0.967069i	$0.581916\pi$
$240$		0			0
$241$	14.4634	−	12.5326i	0.931668	−	0.807295i	−0.0498318	−	0.998758i	$-0.515869\pi$
$241$	14.4634	−	12.5326i	0.931668	−	0.807295i	0.981500	+	0.191463i	$0.0613231\pi$
$242$	−2.96220	+	2.56676i	−0.190417	+	0.164998i
$243$		0			0
$244$	8.57028	+	3.91391i	0.548656	+	0.250563i
$245$	−13.0795	−	8.40568i	−0.835619	−	0.537019i
$246$		0			0
$247$	3.55639	+	0.511332i	0.226288	+	0.0325353i
$248$	−6.89784	+	3.15014i	−0.438013	+	0.200034i
$249$		0			0
$250$	6.08244	+	9.46446i	0.384687	+	0.598585i
$251$	9.71762	−	11.2147i	0.613371	−	0.707868i	−0.361063	−	0.932541i	$-0.617586\pi$
$251$	9.71762	−	11.2147i	0.613371	−	0.707868i	0.974434	+	0.224674i	$0.0721316\pi$
$252$		0			0
$253$	−2.11400	+	12.5850i	−0.132906	+	0.791210i
$254$		−	17.7912i		−	1.11632i
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	24.1042	−	3.46566i	1.50358	−	0.216182i	0.659215	−	0.751955i	$-0.270889\pi$
$257$	24.1042	−	3.46566i	1.50358	−	0.216182i	0.844362	+	0.535773i	$0.179980\pi$
$258$		0			0
$259$	−0.0204159	+	0.141996i	−0.00126858	+	0.00882319i
$260$	−3.36261	+	0.987350i	−0.208540	+	0.0612329i
$261$		0			0
$262$	−0.537017	+	1.17590i	−0.0331770	+	0.0726476i
$263$	−24.7861	−	7.27785i	−1.52838	−	0.448772i	−0.593823	−	0.804596i	$-0.702382\pi$
$263$	−24.7861	−	7.27785i	−1.52838	−	0.448772i	−0.934553	+	0.355824i	$0.884200\pi$
$264$		0			0
$265$	9.33887	+	10.7776i	0.573682	+	0.662064i
$266$	−0.0298341	+	0.101606i	−0.00182925	+	0.00622984i
$267$		0			0
$268$	3.51973	−	5.47681i	0.215002	−	0.334549i
$269$	−3.35103	−	11.4126i	−0.204316	−	0.695837i	−0.996350	−	0.0853598i	$-0.972796\pi$
$269$	−3.35103	−	11.4126i	−0.204316	−	0.695837i	0.792034	−	0.610477i	$-0.209022\pi$
$270$		0			0
$271$	−4.35859	−	9.54397i	−0.264765	−	0.579755i	0.729825	−	0.683634i	$-0.239602\pi$
$271$	−4.35859	−	9.54397i	−0.264765	−	0.579755i	−0.994590	+	0.103879i	$0.966874\pi$
$272$	0.0331173	+	0.230336i	0.00200803	+	0.0139662i
$273$		0			0
$274$	−6.94546	−	6.01828i	−0.419591	−	0.363577i
$275$	−0.169527			−0.0102229
$276$		0			0
$277$	6.40498			0.384838			0.192419	−	0.981313i	$-0.438367\pi$
$277$	6.40498			0.384838			0.192419	+	0.981313i	$0.438367\pi$
$278$	−3.44669	−	2.98657i	−0.206719	−	0.179123i
$279$		0			0
$280$	−0.0146997	−	0.102238i	−0.000878473	−	0.00610991i
$281$	3.21066	+	7.03036i	0.191532	+	0.419396i	0.980897	−	0.194528i	$-0.0623174\pi$
$281$	3.21066	+	7.03036i	0.191532	+	0.419396i	−0.789365	+	0.613924i	$0.789590\pi$
$282$		0			0
$283$	0.995499	+	3.39036i	0.0591763	+	0.201536i	0.983775	−	0.179407i	$-0.0574178\pi$
$283$	0.995499	+	3.39036i	0.0591763	+	0.201536i	−0.924599	+	0.380942i	$0.875600\pi$
$284$	−7.11938	+	11.0780i	−0.422458	+	0.657357i
$285$		0			0
$286$	1.18250	−	4.02723i	0.0699227	−	0.238135i
$287$	0.0255802	+	0.0295211i	0.00150995	+	0.00174258i
$288$		0			0
$289$	16.2594	+	4.77420i	0.956437	+	0.280835i
$290$	5.61839	−	12.3026i	0.329923	−	0.722431i
$291$		0			0
$292$	−6.62122	+	1.94417i	−0.387478	+	0.113774i
$293$	−3.52663	+	24.5283i	−0.206028	+	1.43296i	0.579925	+	0.814670i	$0.303082\pi$
$293$	−3.52663	+	24.5283i	−0.206028	+	1.43296i	−0.785953	+	0.618286i	$0.787827\pi$
$294$		0			0
$295$	2.31125	−	0.332307i	0.134566	−	0.0193477i
$296$	2.59591	−	1.66829i	0.150884	−	0.0969672i
$297$		0			0
$298$			23.3386i			1.35197i
$299$	2.97910	+	6.95350i	0.172286	+	0.402132i
$300$		0			0
$301$	0.0926065	−	0.106874i	0.00533775	−	0.00616009i
$302$	12.4180	+	19.3228i	0.714575	+	1.11190i
$303$		0			0
$304$	2.07198	−	0.946240i	0.118836	−	0.0542706i
$305$	−20.7198	−	2.97906i	−1.18641	−	0.170581i
$306$		0			0
$307$	−21.9621	−	14.1142i	−1.25344	−	0.805537i	−0.266068	−	0.963954i	$-0.585725\pi$
$307$	−21.9621	−	14.1142i	−1.25344	−	0.805537i	−0.987372	+	0.158417i	$0.949361\pi$
$308$	0.112526	+	0.0513889i	0.00641176	+	0.00292815i
$309$		0			0
$310$	12.7329	−	11.0331i	0.723177	−	0.626637i
$311$	25.6741	−	22.2467i	1.45585	−	1.26150i	0.551857	−	0.833939i	$-0.313919\pi$
$311$	25.6741	−	22.2467i	1.45585	−	1.26150i	0.903988	−	0.427558i	$-0.140626\pi$
$312$		0			0
$313$	14.4536	+	6.60075i	0.816968	+	0.373097i	0.779657	−	0.626207i	$-0.215394\pi$
$313$	14.4536	+	6.60075i	0.816968	+	0.373097i	0.0373109	+	0.999304i	$0.488121\pi$
$314$	7.26647	+	4.66987i	0.410070	+	0.263536i
$315$		0			0
$316$	6.60766	+	0.950038i	0.371710	+	0.0534438i
$317$	−15.7635	+	7.19897i	−0.885369	+	0.404334i	−0.805587	−	0.592478i	$-0.798150\pi$
$317$	−15.7635	+	7.19897i	−0.885369	+	0.404334i	−0.0797822	+	0.996812i	$0.525422\pi$
$318$		0			0
$319$	8.75727	+	13.6266i	0.490313	+	0.762942i
$320$	−1.45495	+	1.67911i	−0.0813344	+	0.0938649i
$321$		0			0
$322$	−0.215350	+	0.0577431i	−0.0120010	+	0.00321790i
$323$			0.530059i			0.0294933i
$324$		0			0
$325$	−0.0845413	+	0.0543314i	−0.00468951	+	0.00301376i
$326$	19.0816	−	2.74351i	1.05683	−	0.151949i
$327$		0			0
$328$	0.119577	−	0.831678i	0.00660255	−	0.0459217i
$329$	−0.161059	+	0.0472911i	−0.00887945	+	0.00260724i
$330$		0			0
$331$	−2.79260	+	6.11495i	−0.153495	+	0.336108i	−0.970721	−	0.240210i	$-0.922784\pi$
$331$	−2.79260	+	6.11495i	−0.153495	+	0.336108i	0.817226	+	0.576318i	$0.195511\pi$
$332$	−8.09935	−	2.37818i	−0.444509	−	0.130520i
$333$		0			0
$334$	5.39511	+	6.22628i	0.295207	+	0.340687i
$335$	−4.07510	+	13.8785i	−0.222646	+	0.758264i
$336$		0			0
$337$	−5.30057	+	8.24784i	−0.288740	+	0.449289i	−0.955075	−	0.296364i	$-0.904226\pi$
$337$	−5.30057	+	8.24784i	−0.288740	+	0.449289i	0.666335	+	0.745653i	$0.267862\pi$
$338$	2.96154	+	10.0861i	0.161087	+	0.548611i
$339$		0			0
$340$	−0.214777	−	0.470296i	−0.0116479	−	0.0255054i
$341$	2.87163	+	19.9726i	0.155507	+	1.08158i
$342$		0			0
$343$	0.491808	+	0.426154i	0.0265551	+	0.0230102i
$344$	−3.04184			−0.164005
$345$		0			0
$346$	−7.47694			−0.401963
$347$	8.35372	+	7.23854i	0.448451	+	0.388585i	0.849600	−	0.527428i	$-0.176843\pi$
$347$	8.35372	+	7.23854i	0.448451	+	0.388585i	−0.401149	+	0.916013i	$0.631389\pi$
$348$		0			0
$349$	−2.95525	−	20.5542i	−0.158191	−	1.10024i	−0.901965	−	0.431810i	$-0.857875\pi$
$349$	−2.95525	−	20.5542i	−0.158191	−	1.10024i	0.743774	−	0.668431i	$-0.233034\pi$
$350$	−0.00123040	−	0.00269421i	−6.57678e−5	−	0.000144011i
$351$		0			0
$352$	−0.749665	−	2.55313i	−0.0399573	−	0.136082i
$353$	−6.65538	+	10.3560i	−0.354230	+	0.551193i	−0.971945	−	0.235209i	$-0.924422\pi$
$353$	−6.65538	+	10.3560i	−0.354230	+	0.551193i	0.617714	+	0.786403i	$0.288059\pi$
$354$		0			0
$355$	8.24273	−	28.0722i	0.437479	−	1.48992i
$356$	10.9695	+	12.6595i	0.581382	+	0.670951i
$357$		0			0
$358$	−2.37241	−	0.696601i	−0.125386	−	0.0368165i
$359$	8.01543	−	17.5514i	0.423038	−	0.926325i	−0.571367	−	0.820695i	$-0.693587\pi$
$359$	8.01543	−	17.5514i	0.423038	−	0.926325i	0.994405	−	0.105630i	$-0.0336860\pi$
$360$		0			0
$361$	−13.2521	+	3.89116i	−0.697478	+	0.204798i
$362$	0.849601	−	5.90910i	0.0446540	−	0.310576i
$363$		0			0
$364$	0.0725851	−	0.0104362i	0.00380449	−	0.000547003i
$365$	12.8980	−	8.28906i	0.675114	−	0.433869i
$366$		0			0
$367$		−	7.81117i		−	0.407740i	−0.978998	−	0.203870i	$-0.934648\pi$
$367$		−	7.81117i		−	0.407740i	0.978998	−	0.203870i	$-0.0653519\pi$
$368$	3.97213	+	2.68741i	0.207062	+	0.140091i
$369$		0			0
$370$	−4.48964	+	5.18132i	−0.233405	+	0.269364i
$371$	−0.161328	−	0.251032i	−0.00837575	−	0.0130329i
$372$		0			0
$373$	24.0981	−	11.0052i	1.24775	−	0.569829i	0.321563	−	0.946888i	$-0.395792\pi$
$373$	24.0981	−	11.0052i	1.24775	−	0.569829i	0.926189	+	0.377059i	$0.123065\pi$
$374$	0.612904	+	0.0881223i	0.0316925	+	0.00455669i
$375$		0			0
$376$	3.03747	+	1.95206i	0.156646	+	0.100670i
$377$	8.73432	+	3.98883i	0.449840	+	0.205435i
$378$		0			0
$379$	21.9220	−	18.9955i	1.12606	−	0.975736i	0.126191	−	0.992006i	$-0.459725\pi$
$379$	21.9220	−	18.9955i	1.12606	−	0.975736i	0.999868	+	0.0162702i	$0.00517918\pi$
$380$	−3.82470	+	3.31412i	−0.196203	+	0.170011i
$381$		0			0
$382$	3.93859	+	1.79869i	0.201516	+	0.0920291i
$383$	−8.72079	−	5.60451i	−0.445612	−	0.286377i	0.298529	−	0.954401i	$-0.403504\pi$
$383$	−8.72079	−	5.60451i	−0.445612	−	0.286377i	−0.744140	+	0.668024i	$0.767141\pi$
$384$		0			0
$385$	−0.272047	−	0.0391145i	−0.0138648	−	0.00199346i
$386$	23.3270	−	10.6531i	1.18731	−	0.542228i
$387$		0			0
$388$	7.51867	+	11.6993i	0.381702	+	0.593941i
$389$	−10.2330	+	11.8096i	−0.518836	+	0.598769i	−0.953339	−	0.301902i	$-0.902379\pi$
$389$	−10.2330	+	11.8096i	−0.518836	+	0.598769i	0.434503	+	0.900670i	$0.356924\pi$
$390$		0			0
$391$	−0.952841	+	0.581015i	−0.0481872	+	0.0293832i
$392$		−	6.99784i		−	0.353444i
$393$		0			0
$394$	−3.12052	+	2.00544i	−0.157209	+	0.101032i
$395$	−14.6807	+	2.11077i	−0.738668	+	0.106204i
$396$		0			0
$397$	4.07936	−	28.3726i	0.204737	−	1.42398i	−0.585249	−	0.810853i	$-0.699003\pi$
$397$	4.07936	−	28.3726i	0.204737	−	1.42398i	0.789986	−	0.613124i	$-0.210088\pi$
$398$	12.8226	−	3.76506i	0.642740	−	0.188725i
$399$		0			0
$400$	−0.0264661	+	0.0579528i	−0.00132331	+	0.00289764i
$401$	17.3212	+	5.08596i	0.864979	+	0.253981i	0.683978	−	0.729502i	$-0.260248\pi$
$401$	17.3212	+	5.08596i	0.864979	+	0.253981i	0.181000	+	0.983483i	$0.442066\pi$
$402$		0			0
$403$	7.83304	+	9.03981i	0.390191	+	0.450305i
$404$	−2.87203	+	9.78122i	−0.142889	+	0.486634i
$405$		0			0
$406$	−0.153001	+	0.238075i	−0.00759332	+	0.0118154i
$407$	−2.31329	−	7.87833i	−0.114665	−	0.390514i
$408$		0			0
$409$	8.38050	+	18.3507i	0.414389	+	0.907385i	0.995606	+	0.0936368i	$0.0298493\pi$
$409$	8.38050	+	18.3507i	0.414389	+	0.907385i	−0.581218	+	0.813748i	$0.697423\pi$
$410$	0.265674	+	1.84780i	0.0131207	+	0.0912564i
$411$		0			0
$412$	6.72255	+	5.82513i	0.331196	+	0.286983i
$413$	−0.0488592			−0.00240420
$414$		0			0
$415$	18.7546			0.920629
$416$	−1.19210	−	1.03296i	−0.0584474	−	0.0506449i
$417$		0			0
$418$	−0.862580	−	5.99938i	−0.0421902	−	0.293439i
$419$	3.45220	+	7.55927i	0.168651	+	0.369295i	0.975020	−	0.222119i	$-0.0712973\pi$
$419$	3.45220	+	7.55927i	0.168651	+	0.369295i	−0.806368	+	0.591414i	$0.798570\pi$
$420$		0			0
$421$	−10.4846	−	35.7073i	−0.510989	−	1.74027i	−0.659839	−	0.751407i	$-0.729375\pi$
$421$	−10.4846	−	35.7073i	−0.510989	−	1.74027i	0.148850	−	0.988860i	$-0.452443\pi$
$422$	−1.70730	+	2.65662i	−0.0831102	+	0.129322i
$423$		0			0
$424$	−1.80835	+	6.15867i	−0.0878211	+	0.299091i
$425$	−0.00970873	−	0.0112045i	−0.000470943	−	0.000543497i
$426$		0			0
$427$	0.420269	+	0.123402i	0.0203383	+	0.00597185i
$428$	−1.12673	+	2.46720i	−0.0544627	+	0.119257i
$429$		0			0
$430$	6.48452	−	1.90403i	0.312711	−	0.0918203i
$431$	−4.59850	+	31.9833i	−0.221502	+	1.54058i	0.510860	+	0.859664i	$0.329327\pi$
$431$	−4.59850	+	31.9833i	−0.221502	+	1.54058i	−0.732362	+	0.680916i	$0.761582\pi$
$432$		0			0
$433$	−38.4655	+	5.53050i	−1.84853	+	0.265779i	−0.975197	−	0.221340i	$-0.928957\pi$
$433$	−38.4655	+	5.53050i	−1.84853	+	0.265779i	−0.873336	+	0.487118i	$0.838048\pi$
$434$	−0.296573	+	0.190596i	−0.0142359	+	0.00914888i
$435$		0			0
$436$			8.13381i			0.389539i
$437$	8.08453	+	7.34675i	0.386736	+	0.351443i
$438$		0			0
$439$	14.7903	−	17.0690i	0.705905	−	0.814657i	−0.283633	−	0.958933i	$-0.591540\pi$
$439$	14.7903	−	17.0690i	0.705905	−	0.814657i	0.989538	+	0.144276i	$0.0460852\pi$
$440$	3.19624	+	4.97345i	0.152375	+	0.237100i
$441$		0			0
$442$	0.333891	−	0.152483i	0.0158816	−	0.00725287i
$443$	−31.8548	−	4.58002i	−1.51347	−	0.217604i	−0.664996	−	0.746847i	$-0.731567\pi$
$443$	−31.8548	−	4.58002i	−1.51347	−	0.217604i	−0.848470	+	0.529244i	$0.822476\pi$
$444$		0			0
$445$	−31.3087	−	20.1209i	−1.48418	−	0.953822i
$446$	22.7148	+	10.3735i	1.07558	+	0.491200i
$447$		0			0
$448$	0.0351346	−	0.0304443i	0.00165995	−	0.00143836i
$449$	8.21808	−	7.12100i	0.387835	−	0.336061i	−0.439019	−	0.898478i	$-0.644674\pi$
$449$	8.21808	−	7.12100i	0.387835	−	0.336061i	0.826854	+	0.562417i	$0.190128\pi$
$450$		0			0
$451$	−2.03373	−	0.928776i	−0.0957648	−	0.0437343i
$452$	5.69041	+	3.65700i	0.267654	+	0.172011i
$453$		0			0
$454$	−10.8109	−	1.55437i	−0.507380	−	0.0729502i
$455$	−0.148203	+	0.0676820i	−0.00694786	+	0.00317298i
$456$		0			0
$457$	19.0245	+	29.6027i	0.889929	+	1.38476i	0.922792	+	0.385297i	$0.125901\pi$
$457$	19.0245	+	29.6027i	0.889929	+	1.38476i	−0.0328630	+	0.999460i	$0.510463\pi$
$458$	−12.9974	+	14.9998i	−0.607329	+	0.700895i
$459$		0			0
$460$	−10.1499	−	3.24261i	−0.473241	−	0.151187i
$461$			13.6098i			0.633870i	0.948447	+	0.316935i	$0.102654\pi$
$461$			13.6098i			0.633870i	−0.948447	+	0.316935i	$0.897346\pi$
$462$		0			0
$463$	−0.904694	+	0.581412i	−0.0420447	+	0.0270205i	−0.561494	−	0.827481i	$-0.689773\pi$
$463$	−0.904694	+	0.581412i	−0.0420447	+	0.0270205i	0.519450	+	0.854501i	$0.326137\pi$
$464$	6.02540	−	0.866322i	0.279722	−	0.0402180i
$465$		0			0
$466$	−1.34357	+	9.34477i	−0.0622399	+	0.432888i
$467$	38.0188	−	11.1633i	1.75930	−	0.516577i	0.767133	−	0.641488i	$-0.221682\pi$
$467$	38.0188	−	11.1633i	1.75930	−	0.516577i	0.992168	+	0.124910i	$0.0398643\pi$
$468$		0			0
$469$	0.125730	−	0.275311i	0.00580568	−	0.0127127i
$470$	−7.69711	−	2.26007i	−0.355041	−	0.104249i
$471$		0			0
$472$	0.688238	+	0.794269i	0.0316787	+	0.0365592i
$473$	−2.28036	+	7.76619i	−0.104851	+	0.357090i
$474$		0			0
$475$	−0.0784578	+	0.122083i	−0.00359989	+	0.00560154i
$476$	0.00304789	+	0.0103801i	0.000139700	+	0.000475773i
$477$		0			0
$478$	−2.18637	−	4.78747i	−0.100002	−	0.218974i
$479$	1.73581	+	12.0728i	0.0793113	+	0.551622i	0.990274	+	0.139133i	$0.0444315\pi$
$479$	1.73581	+	12.0728i	0.0793113	+	0.551622i	−0.910962	+	0.412489i	$0.864659\pi$
$480$		0			0
$481$	−3.67853	−	3.18746i	−0.167726	−	0.145336i
$482$	−19.1378			−0.871703
$483$		0			0
$484$	3.91955			0.178162
$485$	−23.3513	−	20.2340i	−1.06033	−	0.918778i
$486$		0			0
$487$	−0.876975	−	6.09950i	−0.0397395	−	0.276395i	0.960257	−	0.279118i	$-0.0900421\pi$
$487$	−0.876975	−	6.09950i	−0.0397395	−	0.276395i	−0.999996	+	0.00272360i	$0.999133\pi$
$488$	−3.91391	−	8.57028i	−0.177175	−	0.387958i
$489$		0			0
$490$	4.38027	+	14.9178i	0.197881	+	0.673919i
$491$	−15.0559	+	23.4275i	−0.679465	+	1.05727i	0.314678	+	0.949199i	$0.398104\pi$
$491$	−15.0559	+	23.4275i	−0.679465	+	1.05727i	−0.994143	+	0.108070i	$0.965533\pi$
$492$		0			0
$493$	−0.399091	+	1.35918i	−0.0179741	+	0.0612143i
$494$	−2.35289	−	2.71538i	−0.105862	−	0.122171i
$495$		0			0
$496$	7.27594	+	2.13641i	0.326699	+	0.0959276i
$497$	−0.254315	+	0.556873i	−0.0114076	+	0.0249792i
$498$		0			0
$499$	−35.1176	+	10.3115i	−1.57208	+	0.461605i	−0.947606	−	0.319440i	$-0.896505\pi$
$499$	−35.1176	+	10.3115i	−1.57208	+	0.461605i	−0.624475	+	0.781045i	$0.714687\pi$
$500$	1.60110	−	11.1359i	0.0716035	−	0.498013i
$501$		0			0
$502$	−14.6882	+	2.11184i	−0.655566	+	0.0942561i
$503$	15.9099	−	10.2247i	0.709387	−	0.455896i	−0.135543	−	0.990771i	$-0.543278\pi$
$503$	15.9099	−	10.2247i	0.709387	−	0.455896i	0.844931	+	0.534876i	$0.179642\pi$
$504$		0			0
$505$		−	22.6491i		−	1.00787i
$506$	9.83905	−	8.12670i	0.437399	−	0.361276i
$507$		0			0
$508$	−11.6507	+	13.4457i	−0.516918	+	0.596556i
$509$	14.9080	+	23.1972i	0.660784	+	1.02820i	0.996281	+	0.0861587i	$0.0274592\pi$
$509$	14.9080	+	23.1972i	0.660784	+	1.02820i	−0.335498	+	0.942041i	$0.608904\pi$
$510$		0			0
$511$	−0.291822	+	0.133271i	−0.0129095	+	0.00589555i
$512$	−0.989821	−	0.142315i	−0.0437443	−	0.00628949i
$513$		0			0
$514$	−20.4862	−	13.1657i	−0.903609	−	0.580714i
$515$	−17.9772	−	8.20992i	−0.792171	−	0.361772i
$516$		0			0
$517$	7.26095	−	6.29165i	0.319336	−	0.276707i
$518$	0.108417	−	0.0939437i	0.00476356	−	0.00412765i
$519$		0			0
$520$	3.18786	+	1.45585i	0.139797	+	0.0638432i
$521$	−10.2834	−	6.60872i	−0.450523	−	0.289533i	0.295637	−	0.955300i	$-0.404468\pi$
$521$	−10.2834	−	6.60872i	−0.450523	−	0.289533i	−0.746160	+	0.665767i	$0.768105\pi$
$522$		0			0
$523$	20.5461	+	2.95408i	0.898418	+	0.129173i	0.576024	−	0.817433i	$-0.304603\pi$
$523$	20.5461	+	2.95408i	0.898418	+	0.129173i	0.322394	+	0.946606i	$0.395512\pi$
$524$	1.17590	−	0.537017i	0.0513696	−	0.0234597i
$525$		0			0
$526$	13.9661	+	21.7317i	0.608951	+	0.947546i
$527$	−1.15558	+	1.33362i	−0.0503380	+	0.0580932i
$528$		0			0
$529$	−4.34488	+	22.5859i	−0.188908	+	0.981995i
$530$		−	14.2608i		−	0.619452i
$531$		0			0
$532$	0.0890846	−	0.0572512i	0.00386231	−	0.00248215i
$533$	−1.31186	+	0.188618i	−0.0568232	+	0.00816994i
$534$		0			0
$535$	0.857609	−	5.96480i	0.0370777	−	0.257881i
$536$	−6.24658	+	1.83416i	−0.269811	+	0.0792237i
$537$		0			0
$538$	−4.94110	+	10.8195i	−0.213026	+	0.466462i
$539$	−17.8664	−	5.24604i	−0.769559	−	0.225963i
$540$		0			0
$541$	−10.3296	−	11.9209i	−0.444102	−	0.512521i	0.488926	−	0.872325i	$-0.337389\pi$
$541$	−10.3296	−	11.9209i	−0.444102	−	0.512521i	−0.933028	+	0.359804i	$0.882843\pi$
$542$	−2.95597	+	10.0671i	−0.126970	+	0.432420i
$543$		0			0
$544$	0.125810	−	0.195764i	0.00539404	−	0.00839330i
$545$	−5.09133	−	17.3395i	−0.218089	−	0.742741i
$546$		0			0
$547$	2.26144	+	4.95187i	0.0966923	+	0.211727i	0.951797	−	0.306729i	$-0.0992345\pi$
$547$	2.26144	+	4.95187i	0.0966923	+	0.211727i	−0.855105	+	0.518455i	$0.826507\pi$
$548$	1.30790	+	9.09662i	0.0558706	+	0.388588i
$549$		0			0
$550$	0.128120	+	0.111017i	0.00546305	+	0.00473376i
$551$	13.8659			0.590708
$552$		0			0
$553$	0.310347			0.0131973
$554$	−4.84056	−	4.19437i	−0.205656	−	0.178202i
$555$		0			0
$556$	0.649044	+	4.51420i	0.0275256	+	0.191445i
$557$	−2.75063	−	6.02305i	−0.116548	−	0.255205i	0.842363	−	0.538910i	$-0.181164\pi$
$557$	−2.75063	−	6.02305i	−0.116548	−	0.255205i	−0.958912	+	0.283705i	$0.908436\pi$
$558$		0			0
$559$	1.35178	+	4.60375i	0.0571743	+	0.194718i
$560$	−0.0558426	+	0.0868928i	−0.00235978	+	0.00367189i
$561$		0			0
$562$	2.17745	−	7.41573i	0.0918504	−	0.312814i
$563$	−23.6142	−	27.2522i	−0.995219	−	1.14854i	−0.988903	−	0.148564i	$-0.952535\pi$
$563$	−23.6142	−	27.2522i	−0.995219	−	1.14854i	−0.00631647	−	0.999980i	$-0.502011\pi$
$564$		0			0
$565$	−14.4198	−	4.23403i	−0.606645	−	0.178127i
$566$	1.46786	−	3.21417i	0.0616989	−	0.135102i
$567$		0			0
$568$	12.6350	−	3.70997i	0.530153	−	0.155667i
$569$	1.13089	−	7.86552i	0.0474094	−	0.329740i	−0.952289	−	0.305197i	$-0.901278\pi$
$569$	1.13089	−	7.86552i	0.0474094	−	0.329740i	0.999699	−	0.0245431i	$-0.00781309\pi$
$570$		0			0
$571$	14.7693	−	2.12350i	0.618076	−	0.0888658i	0.173837	−	0.984774i	$-0.444383\pi$
$571$	14.7693	−	2.12350i	0.618076	−	0.0888658i	0.444238	+	0.895909i	$0.353474\pi$
$572$	−3.53095	+	2.26920i	−0.147636	+	0.0948801i
$573$		0			0
$574$		−	0.0390620i		−	0.00163042i
$575$	−0.305458	−	0.00721782i	−0.0127385	−	0.000301004i
$576$		0			0
$577$	−11.2189	+	12.9472i	−0.467047	+	0.539001i	−0.939588	−	0.342308i	$-0.888791\pi$
$577$	−11.2189	+	12.9472i	−0.467047	+	0.539001i	0.472541	+	0.881309i	$0.343337\pi$
$578$	−9.16162	−	14.2558i	−0.381073	−	0.592961i
$579$		0			0
$580$	−12.3026	+	5.61839i	−0.510836	+	0.233291i
$581$	−0.388438	−	0.0558490i	−0.0161151	−	0.00231701i
$582$		0			0
$583$	14.3682	+	9.23388i	0.595070	+	0.382428i
$584$	6.27714	+	2.86667i	0.259750	+	0.118624i
$585$		0			0
$586$	18.7278	−	16.2278i	0.773640	−	0.670363i
$587$	19.9192	−	17.2601i	0.822152	−	0.712399i	−0.138437	−	0.990371i	$-0.544208\pi$
$587$	19.9192	−	17.2601i	0.822152	−	0.712399i	0.960589	+	0.277973i	$0.0896625\pi$
$588$		0			0
$589$	15.7120	+	7.17544i	0.647403	+	0.295659i
$590$	−1.96434	−	1.26240i	−0.0808706	−	0.0519724i
$591$		0			0
$592$	−3.05435	−	0.439149i	−0.125533	−	0.0180489i
$593$	−20.4544	+	9.34121i	−0.839961	+	0.383597i	−0.788468	−	0.615076i	$-0.789125\pi$
$593$	−20.4544	+	9.34121i	−0.839961	+	0.383597i	−0.0514932	+	0.998673i	$0.516398\pi$
$594$		0			0
$595$	−0.0129948	−	0.0202204i	−0.000532737	−	0.000828954i
$596$	15.2836	−	17.6382i	0.626039	−	0.722487i
$597$		0			0
$598$	2.30212	−	7.20601i	0.0941407	−	0.294675i
$599$		−	7.97019i		−	0.325653i	−0.986655	−	0.162826i	$-0.947939\pi$
$599$		−	7.97019i		−	0.325653i	0.986655	−	0.162826i	$-0.0520611\pi$
$600$		0			0
$601$	−20.4910	+	13.1688i	−0.835845	+	0.537165i	−0.887130	−	0.461519i	$-0.847305\pi$
$601$	−20.4910	+	13.1688i	−0.835845	+	0.537165i	0.0512850	+	0.998684i	$0.483668\pi$
$602$	−0.139975	+	0.0201253i	−0.00570494	+	0.000820246i
$603$		0			0
$604$	3.26883	−	22.7352i	0.133007	−	0.925083i
$605$	−8.35562	+	2.45343i	−0.339704	+	0.0997462i
$606$		0			0
$607$	−3.23374	+	7.08091i	−0.131254	+	0.287405i	−0.963836	−	0.266496i	$-0.914134\pi$
$607$	−3.23374	+	7.08091i	−0.131254	+	0.287405i	0.832582	+	0.553901i	$0.186861\pi$
$608$	−2.18555	−	0.641735i	−0.0886358	−	0.0260258i
$609$		0			0
$610$	13.7081	+	15.8200i	0.555026	+	0.640534i
$611$	1.60456	−	5.46463i	0.0649136	−	0.221075i
$612$		0			0
$613$	−3.62934	+	5.64736i	−0.146588	+	0.228095i	−0.906781	−	0.421602i	$-0.861468\pi$
$613$	−3.62934	+	5.64736i	−0.146588	+	0.228095i	0.760193	+	0.649697i	$0.225104\pi$
$614$	7.35501	+	25.0489i	0.296824	+	1.01089i
$615$		0			0
$616$	−0.0513889	−	0.112526i	−0.00207052	−	0.00453380i
$617$	−3.54534	−	24.6584i	−0.142730	−	0.992710i	−0.927740	−	0.373227i	$-0.878251\pi$
$617$	−3.54534	−	24.6584i	−0.142730	−	0.992710i	0.785010	−	0.619483i	$-0.212658\pi$
$618$		0			0
$619$	18.2505	+	15.8141i	0.733548	+	0.635623i	0.939346	−	0.342972i	$-0.111434\pi$
$619$	18.2505	+	15.8141i	0.733548	+	0.635623i	−0.205798	+	0.978594i	$0.565979\pi$
$620$	−16.8480			−0.676631
$621$		0			0
$622$	−33.9717			−1.36214
$623$	0.588535	+	0.509969i	0.0235792	+	0.0204315i
$624$		0			0
$625$	3.51196	+	24.4262i	0.140478	+	0.977048i
$626$	−6.60075	−	14.4536i	−0.263819	−	0.577683i
$627$		0			0
$628$	−2.43351	−	8.28778i	−0.0971077	−	0.330718i
$629$	0.388218	−	0.604079i	0.0154793	−	0.0240862i
$630$		0			0
$631$	11.0207	−	37.5330i	0.438726	−	1.49417i	−0.382712	−	0.923868i	$-0.625010\pi$
$631$	11.0207	−	37.5330i	0.438726	−	1.49417i	0.821438	−	0.570297i	$-0.193172\pi$
$632$	−4.37159	−	5.04509i	−0.173893	−	0.200683i
$633$		0			0
$634$	16.6276	+	4.88231i	0.660367	+	0.193901i
$635$	16.4205	−	35.9560i	0.651629	−	1.42687i
$636$		0			0
$637$	−10.5911	+	3.10982i	−0.419633	+	0.123215i
$638$	2.30521	−	16.0331i	0.0912640	−	0.634755i
$639$		0			0
$640$	2.19916	−	0.316192i	0.0869295	−	0.0124986i
$641$	27.7530	−	17.8358i	1.09618	−	0.704471i	0.137939	−	0.990441i	$-0.455952\pi$
$641$	27.7530	−	17.8358i	1.09618	−	0.704471i	0.958239	+	0.285970i	$0.0923157\pi$
$642$		0			0
$643$			26.1154i			1.02989i	0.857223	+	0.514946i	$0.172188\pi$
$643$			26.1154i			1.02989i	−0.857223	+	0.514946i	$0.827812\pi$
$644$	0.200564	+	0.0973847i	0.00790333	+	0.00383749i
$645$		0			0
$646$	0.347115	−	0.400592i	0.0136570	−	0.0157611i
$647$	−17.6026	−	27.3901i	−0.692028	−	1.07682i	−0.992407	−	0.122997i	$-0.960750\pi$
$647$	−17.6026	−	27.3901i	−0.692028	−	1.07682i	0.300379	−	0.953820i	$-0.402887\pi$
$648$		0			0
$649$	2.54381	−	1.16172i	0.0998535	−	0.0456016i
$650$	0.0994716	+	0.0143019i	0.00390160	+	0.000560965i
$651$		0			0
$652$	−16.2175	−	10.4224i	−0.635127	−	0.408171i
$653$	−17.4974	−	7.99081i	−0.684728	−	0.312705i	0.0425043	−	0.999096i	$-0.486466\pi$
$653$	−17.4974	−	7.99081i	−0.684728	−	0.312705i	−0.727232	+	0.686392i	$0.759194\pi$
$654$		0			0
$655$	−2.17062	+	1.88086i	−0.0848132	+	0.0734911i
$656$	−0.635004	+	0.550234i	−0.0247927	+	0.0214830i
$657$		0			0
$658$	0.152689	+	0.0697308i	0.00595244	+	0.00271839i
$659$	−8.88254	−	5.70846i	−0.346014	−	0.222370i	0.356077	−	0.934457i	$-0.384114\pi$
$659$	−8.88254	−	5.70846i	−0.346014	−	0.222370i	−0.702092	+	0.712087i	$0.747750\pi$
$660$		0			0
$661$	−44.7385	−	6.43243i	−1.74013	−	0.250192i	−0.802207	−	0.597046i	$-0.796341\pi$
$661$	−44.7385	−	6.43243i	−1.74013	−	0.250192i	−0.937919	+	0.346853i	$0.887250\pi$
$662$	6.11495	−	2.79260i	0.237664	−	0.108538i
$663$		0			0
$664$	4.56370	+	7.10126i	0.177106	+	0.275582i
$665$	−0.154072	+	0.177809i	−0.00597467	+	0.00689514i
$666$		0			0
$667$	15.1989	+	24.9255i	0.588503	+	0.965121i
$668$		−	8.23855i		−	0.318759i
$669$		0			0
$670$	12.1682	−	7.82005i	0.470100	−	0.302115i
$671$	−24.8151	+	3.56788i	−0.957977	+	0.137736i
$672$		0			0
$673$	−3.15628	+	21.9524i	−0.121666	+	0.846204i	0.834003	+	0.551760i	$0.186043\pi$
$673$	−3.15628	+	21.9524i	−0.121666	+	0.846204i	−0.955669	+	0.294444i	$0.904866\pi$
$674$	9.40709	−	2.76217i	0.362348	−	0.106395i
$675$		0			0
$676$	4.36680	−	9.56196i	0.167954	−	0.367768i
$677$	21.1861	+	6.22079i	0.814246	+	0.239084i	0.662237	−	0.749295i	$-0.269607\pi$
$677$	21.1861	+	6.22079i	0.814246	+	0.239084i	0.152010	+	0.988379i	$0.451426\pi$
$678$		0			0
$679$	0.423387	+	0.488615i	0.0162481	+	0.0187513i
$680$	−0.145661	+	0.496075i	−0.00558583	+	0.0190236i
$681$		0			0
$682$	10.9090	−	16.9748i	0.417729	−	0.649999i
$683$	1.23411	+	4.20298i	0.0472218	+	0.160823i	0.979728	−	0.200330i	$-0.0642015\pi$
$683$	1.23411	+	4.20298i	0.0472218	+	0.160823i	−0.932507	+	0.361153i	$0.882383\pi$
$684$		0			0
$685$	−8.48215	−	18.5733i	−0.324086	−	0.709650i
$686$	−0.0926121	−	0.644132i	−0.00353595	−	0.0245931i
$687$		0			0
$688$	2.29887	+	1.99198i	0.0876434	+	0.0759435i
$689$	10.1246			0.385717
$690$		0			0
$691$	14.0177			0.533259			0.266629	−	0.963799i	$-0.414090\pi$
$691$	14.0177			0.533259			0.266629	+	0.963799i	$0.414090\pi$
$692$	5.65069	+	4.89635i	0.214807	+	0.186131i
$693$		0			0
$694$	−1.57309	−	10.9411i	−0.0597135	−	0.415317i
$695$	−4.20927	−	9.21702i	−0.159667	−	0.349621i
$696$		0			0
$697$	−0.0550859	−	0.187605i	−0.00208653	−	0.00710606i
$698$	−11.2267	+	17.4691i	−0.424937	+	0.661215i
$699$		0			0
$700$	−0.000834453		0.00284189i	−3.15394e−5		0.000107413i
$701$	−11.8434	−	13.6680i	−0.447319	−	0.516234i	0.486645	−	0.873600i	$-0.338220\pi$
$701$	−11.8434	−	13.6680i	−0.447319	−	0.516234i	−0.933964	+	0.357366i	$0.883675\pi$
$702$		0			0
$703$	−6.74408	−	1.98024i	−0.254358	−	0.0746862i
$704$	−1.10538	+	2.42045i	−0.0416607	+	0.0912241i
$705$		0			0
$706$	11.8115	−	3.46818i	0.444533	−	0.130527i
$707$	−0.0674463	+	0.469099i	−0.00253658	+	0.0176423i
$708$		0			0
$709$	−26.8646	+	3.86254i	−1.00892	+	0.145061i	−0.626905	−	0.779096i	$-0.715679\pi$
$709$	−26.8646	+	3.86254i	−1.00892	+	0.145061i	−0.382014	+	0.924156i	$0.624770\pi$
$710$	−24.6128	+	15.8177i	−0.923702	+	0.593627i
$711$		0			0
$712$		−	16.7509i		−	0.627766i
$713$	4.32381	+	36.1094i	0.161928	+	1.35231i
$714$		0			0
$715$	6.10680	−	7.04762i	0.228381	−	0.263566i
$716$	1.33677	+	2.08005i	0.0499573	+	0.0777351i
$717$		0			0
$718$	−17.5514	+	8.01543i	−0.655011	+	0.299133i
$719$	30.2496	+	4.34924i	1.12812	+	0.162199i	0.681006	−	0.732278i	$-0.261543\pi$
$719$	30.2496	+	4.34924i	1.12812	+	0.162199i	0.447114	+	0.894477i	$0.352452\pi$
$720$		0			0
$721$	0.347888	+	0.223574i	0.0129560	+	0.00832634i
$722$	12.5634	+	5.73752i	0.467562	+	0.213529i
$723$		0			0
$724$	−4.51172	+	3.90943i	−0.167677	+	0.145293i
$725$	−0.293100	+	0.253972i	−0.0108855	+	0.00943230i
$726$		0			0
$727$	34.3027	+	15.6655i	1.27222	+	0.581002i	0.933058	−	0.359727i	$-0.117130\pi$
$727$	34.3027	+	15.6655i	1.27222	+	0.581002i	0.339159	+	0.940729i	$0.389857\pi$
$728$	−0.0616904	−	0.0396460i	−0.00228640	−	0.00146938i
$729$		0			0
$730$	−15.1759	−	2.18196i	−0.561684	−	0.0807579i
$731$	−0.643882	+	0.294051i	−0.0238148	+	0.0108759i
$732$		0			0
$733$	0.757727	+	1.17905i	0.0279873	+	0.0435491i	0.854965	−	0.518685i	$-0.173578\pi$
$733$	0.757727	+	1.17905i	0.0279873	+	0.0435491i	−0.826978	+	0.562234i	$0.809942\pi$
$734$	−5.11523	+	5.90329i	−0.188806	+	0.217894i
$735$		0			0
$736$	−1.24206	−	4.63220i	−0.0457830	−	0.170745i
$737$			17.3233i			0.638112i
$738$		0			0
$739$	−32.5071	+	20.8911i	−1.19579	+	0.768491i	−0.978224	−	0.207554i	$-0.933450\pi$
$739$	−32.5071	+	20.8911i	−1.19579	+	0.768491i	−0.217571	+	0.976044i	$0.569813\pi$
$740$	6.78608	−	0.975692i	0.249461	−	0.0358671i
$741$		0			0
$742$	−0.0424670	+	0.295365i	−0.00155901	+	0.0108432i
$743$	−32.0517	+	9.41123i	−1.17586	+	0.345264i	−0.810578	−	0.585631i	$-0.800847\pi$
$743$	−32.0517	+	9.41123i	−1.17586	+	0.345264i	−0.365285	+	0.930896i	$0.619029\pi$
$744$		0			0
$745$	−21.5406	+	47.1674i	−0.789187	+	1.72808i
$746$	−25.4190	−	7.46370i	−0.930656	−	0.273265i
$747$		0			0
$748$	−0.405494	−	0.467965i	−0.0148263	−	0.0171105i
$749$	−0.0355249	+	0.120987i	−0.00129805	+	0.00442076i
$750$		0			0
$751$	−3.33228	+	5.18512i	−0.121596	+	0.189208i	−0.896715	−	0.442607i	$-0.854054\pi$
$751$	−3.33228	+	5.18512i	−0.121596	+	0.189208i	0.775119	+	0.631815i	$0.217690\pi$
$752$	−1.01724	−	3.46439i	−0.0370948	−	0.126333i
$753$		0			0
$754$	−3.98883	−	8.73432i	−0.145265	−	0.318085i
$755$	7.26261	+	50.5126i	0.264314	+	1.83834i
$756$		0			0
$757$	−17.0984	−	14.8159i	−0.621454	−	0.538493i	0.286223	−	0.958163i	$-0.407600\pi$
$757$	−17.0984	−	14.8159i	−0.621454	−	0.538493i	−0.907677	+	0.419670i	$0.862146\pi$
$758$	−29.0070			−1.05358
$759$		0			0
$760$	5.06080			0.183575
$761$	25.3619	+	21.9762i	0.919369	+	0.796637i	0.979477	−	0.201554i	$-0.0645993\pi$
$761$	25.3619	+	21.9762i	0.919369	+	0.796637i	−0.0601087	+	0.998192i	$0.519145\pi$
$762$		0			0
$763$	0.0538147	+	0.374289i	0.00194822	+	0.0135502i
$764$	−1.79869	−	3.93859i	−0.0650744	−	0.142493i
$765$		0			0
$766$	2.92056	+	9.94651i	0.105524	+	0.359382i
$767$	0.896256	−	1.39460i	0.0323619	−	0.0503561i
$768$		0			0
$769$	1.72019	−	5.85842i	0.0620316	−	0.211260i	−0.922645	−	0.385650i	$-0.873977\pi$
$769$	1.72019	−	5.85842i	0.0620316	−	0.211260i	0.984677	+	0.174390i	$0.0557954\pi$
$770$	0.179985	+	0.207714i	0.00648621	+	0.00748548i
$771$		0			0
$772$	−24.6057	−	7.22487i	−0.885577	−	0.260029i
$773$	1.49152	−	3.26598i	0.0536463	−	0.117469i	−0.880911	−	0.473283i	$-0.843069\pi$
$773$	1.49152	−	3.26598i	0.0536463	−	0.117469i	0.934557	+	0.355814i	$0.115796\pi$
$774$		0			0
$775$	−0.463551	+	0.136111i	−0.0166512	+	0.00488925i
$776$	1.97917	−	13.7654i	0.0710479	−	0.494149i
$777$		0			0
$778$	15.4672	−	2.22385i	0.554527	−	0.0797290i
$779$	−1.61007	+	1.03473i	−0.0576867	+	0.0370730i
$780$		0			0
$781$		−	35.0400i		−	1.25383i
$782$	1.10059	+	0.184876i	0.0393571	+	0.00661115i
$783$		0			0
$784$	−4.58261	+	5.28861i	−0.163665	+	0.188879i
$785$	10.3754	+	16.1445i	0.370314	+	0.576221i
$786$		0			0
$787$	12.3070	−	5.62042i	0.438697	−	0.200346i	−0.183808	−	0.982962i	$-0.558842\pi$
$787$	12.3070	−	5.62042i	0.438697	−	0.200346i	0.622505	+	0.782616i	$0.286115\pi$
$788$	3.67161	+	0.527898i	0.130796	+	0.0188056i
$789$		0			0
$790$	12.4772	+	8.01862i	0.443920	+	0.285290i
$791$	0.286048	+	0.130634i	0.0101707	+	0.00464480i
$792$		0			0
$793$	−11.2316	+	9.73222i	−0.398845	+	0.345601i
$794$	−21.6630	+	18.7711i	−0.768793	+	0.666163i
$795$		0			0
$796$	−12.1563	−	5.55159i	−0.430868	−	0.196771i
$797$	13.6739	+	8.78766i	0.484353	+	0.311275i	0.759931	−	0.650004i	$-0.225233\pi$
$797$	13.6739	+	8.78766i	0.484353	+	0.311275i	−0.275578	+	0.961279i	$0.588869\pi$
$798$		0			0
$799$	0.831663	+	0.119575i	0.0294221	+	0.00423026i
$800$	0.0579528	−	0.0264661i	0.00204894	−	0.000935719i
$801$		0			0
$802$	−9.75988	−	15.1867i	−0.344633	−	0.536260i
$803$	12.0247	−	13.8773i	0.424344	−	0.489719i
$804$		0			0
$805$	−0.488516	−	0.0820602i	−0.0172179	−	0.00289224i
$806$		−	11.9614i		−	0.421322i
$807$		0			0
$808$	8.57587	−	5.51138i	0.301698	−	0.193890i
$809$	−21.0765	+	3.03034i	−0.741009	+	0.106541i	−0.502473	−	0.864593i	$-0.667576\pi$
$809$	−21.0765	+	3.03034i	−0.741009	+	0.106541i	−0.238536	+	0.971134i	$0.576667\pi$
$810$		0			0
$811$	6.58878	−	45.8259i	0.231363	−	1.60917i	−0.460853	−	0.887476i	$-0.652456\pi$
$811$	6.58878	−	45.8259i	0.231363	−	1.60917i	0.692216	−	0.721690i	$-0.256634\pi$
$812$	0.271536	−	0.0797303i	0.00952906	−	0.00279798i
$813$		0			0
$814$	−3.41094	+	7.46892i	−0.119554	+	0.261786i
$815$	41.0960	+	12.0669i	1.43953	+	0.422684i
$816$		0			0
$817$	4.53736	+	5.23640i	0.158742	+	0.183198i
$818$	5.68361	−	19.3566i	0.198723	−	0.676788i
$819$		0			0
$820$	1.00927	−	1.57046i	0.0352452	−	0.0548427i
$821$	8.19118	+	27.8966i	0.285874	+	0.973598i	0.969770	+	0.244019i	$0.0784659\pi$
$821$	8.19118	+	27.8966i	0.285874	+	0.973598i	−0.683896	+	0.729579i	$0.739716\pi$
$822$		0			0
$823$	4.58165	+	10.0324i	0.159706	+	0.349708i	0.972521	−	0.232814i	$-0.0747933\pi$
$823$	4.58165	+	10.0324i	0.159706	+	0.349708i	−0.812815	+	0.582522i	$0.802066\pi$
$824$	−1.26592	−	8.80467i	−0.0441004	−	0.306725i
$825$		0			0
$826$	0.0369253	+	0.0319960i	0.00128480	+	0.00111328i
$827$	29.3931			1.02210			0.511050	−	0.859551i	$-0.329257\pi$
$827$	29.3931			1.02210			0.511050	+	0.859551i	$0.329257\pi$
$828$		0			0
$829$	48.0938			1.67037			0.835184	−	0.549971i	$-0.185361\pi$
$829$	48.0938			1.67037			0.835184	+	0.549971i	$0.185361\pi$
$830$	−14.1738	−	12.2817i	−0.491980	−	0.426303i
$831$		0			0
$832$	0.224483	+	1.56132i	0.00778256	+	0.0541289i
$833$	−0.676474	−	1.48127i	−0.0234384	−	0.0513230i
$834$		0			0
$835$	5.15690	+	17.5628i	0.178462	+	0.607785i
$836$	−3.27686	+	5.09890i	−0.113333	+	0.176349i
$837$		0			0
$838$	2.34127	−	7.97363i	0.0808778	−	0.275444i
$839$	−1.97573	−	2.28011i	−0.0682097	−	0.0787181i	0.720619	−	0.693331i	$-0.243858\pi$
$839$	−1.97573	−	2.28011i	−0.0682097	−	0.0787181i	−0.788829	+	0.614613i	$0.789312\pi$
$840$		0			0
$841$	7.72969	+	2.26964i	0.266541	+	0.0782636i
$842$	−15.4596	+	33.8517i	−0.532772	+	1.16661i
$843$		0			0
$844$	3.03001	−	0.889690i	0.104297	−	0.0306244i
$845$	−3.32378	+	23.1174i	−0.114341	+	0.795262i
$846$		0			0
$847$	0.180364	−	0.0259324i	0.00619739	−	0.000891049i
$848$	5.39973	−	3.47019i	0.185427	−	0.119167i
$849$		0			0
$850$			0.0148256i			0.000508515i
$851$	−3.83271	−	14.2939i	−0.131383	−	0.489987i
$852$		0			0
$853$	−2.74102	+	3.16330i	−0.0938507	+	0.108309i	−0.800732	−	0.599023i	$-0.795556\pi$
$853$	−2.74102	+	3.16330i	−0.0938507	+	0.108309i	0.706881	+	0.707332i	$0.250101\pi$
$854$	−0.236807	−	0.368479i	−0.00810337	−	0.0126091i
$855$		0			0
$856$	2.46720	−	1.12673i	0.0843272	−	0.0385109i
$857$	25.1870	+	3.62134i	0.860372	+	0.123703i	0.558357	−	0.829601i	$-0.311432\pi$
$857$	25.1870	+	3.62134i	0.860372	+	0.123703i	0.302014	+	0.953303i	$0.402341\pi$
$858$		0			0
$859$	13.4173	+	8.62274i	0.457791	+	0.294204i	0.749139	−	0.662413i	$-0.230467\pi$
$859$	13.4173	+	8.62274i	0.457791	+	0.294204i	−0.291348	+	0.956617i	$0.594104\pi$
$860$	−6.14755	−	2.80749i	−0.209630	−	0.0957346i
$861$		0			0
$862$	24.4199	−	21.1600i	0.831745	−	0.720711i
$863$	22.9264	−	19.8658i	0.780422	−	0.676240i	−0.170608	−	0.985339i	$-0.554573\pi$
$863$	22.9264	−	19.8658i	0.780422	−	0.676240i	0.951030	+	0.309099i	$0.100028\pi$
$864$		0			0
$865$	−15.1109	−	6.90091i	−0.513785	−	0.234638i
$866$	32.6920	+	21.0099i	1.11092	+	0.713944i
$867$		0			0
$868$	0.348948	+	0.0501712i	0.0118441	+	0.00170292i
$869$	−16.1580	+	7.37910i	−0.548121	+	0.250319i
$870$		0			0
$871$	5.55192	+	8.63895i	0.188120	+	0.292720i
$872$	5.32651	−	6.14712i	0.180378	−	0.208168i
$873$		0			0
$874$	−1.29879	−	10.8465i	−0.0439321	−	0.366890i
$875$		−	0.523029i		−	0.0176816i
$876$		0			0
$877$	−7.40709	+	4.76025i	−0.250120	+	0.160742i	−0.659693	−	0.751535i	$-0.729314\pi$
$877$	−7.40709	+	4.76025i	−0.250120	+	0.160742i	0.409574	+	0.912277i	$0.365677\pi$
$878$	−22.3556	+	3.21425i	−0.754465	+	0.108476i
$879$		0			0
$880$	0.841358	−	5.85177i	0.0283622	−	0.197263i
$881$	2.67146	−	0.784410i	0.0900037	−	0.0264275i	−0.236421	−	0.971651i	$-0.575974\pi$
$881$	2.67146	−	0.784410i	0.0900037	−	0.0264275i	0.326424	+	0.945223i	$0.394156\pi$
$882$		0			0
$883$	22.1435	−	48.4874i	0.745187	−	1.63173i	−0.0296411	−	0.999561i	$-0.509436\pi$
$883$	22.1435	−	48.4874i	0.745187	−	1.63173i	0.774828	−	0.632172i	$-0.217836\pi$
$884$	−0.352193	−	0.103413i	−0.0118455	−	0.00347816i
$885$		0			0
$886$	21.0750	+	24.3218i	0.708027	+	0.817107i
$887$	0.102799	−	0.350102i	0.00345166	−	0.0117553i	−0.957749	−	0.287605i	$-0.907141\pi$
$887$	0.102799	−	0.350102i	0.00345166	−	0.0117553i	0.961201	+	0.275850i	$0.0889592\pi$
$888$		0			0
$889$	−0.447168	+	0.695807i	−0.0149975	+	0.0233366i
$890$	10.4852	+	35.7092i	0.351464	+	1.19698i
$891$		0			0
$892$	−10.3735	−	22.7148i	−0.347331	−	0.760548i
$893$	−1.17045	−	8.14069i	−0.0391678	−	0.272418i
$894$		0			0
$895$	−4.15169	−	3.59746i	−0.138776	−	0.120250i
$896$	−0.0464897			−0.00155311
$897$		0			0
$898$	−10.8741			−0.362873
$899$	34.8863	+	30.2291i	1.16352	+	1.00820i
$900$		0			0
$901$	0.212569	+	1.47845i	0.00708171	+	0.0492543i
$902$	0.928776	+	2.03373i	0.0309248	+	0.0677160i
$903$		0			0
$904$	−1.90570	−	6.49020i	−0.0633825	−	0.215861i
$905$	7.17090	−	11.1581i	0.238369	−	0.370909i
$906$		0			0
$907$	4.21833	−	14.3663i	0.140067	−	0.477025i	−0.859342	−	0.511402i	$-0.829126\pi$
$907$	4.21833	−	14.3663i	0.140067	−	0.477025i	0.999409	+	0.0343766i	$0.0109446\pi$
$908$	7.15242	+	8.25433i	0.237361	+	0.273930i
$909$		0			0
$910$	0.156327	+	0.0459016i	0.00518217	+	0.00152162i
$911$	−4.67853	+	10.2446i	−0.155007	+	0.339417i	−0.971164	−	0.238412i	$-0.923373\pi$
$911$	−4.67853	+	10.2446i	−0.155007	+	0.339417i	0.816157	+	0.577830i	$0.196100\pi$
$912$		0			0
$913$	21.5516	−	6.32813i	0.713255	−	0.209431i
$914$	5.00789	−	34.8307i	0.165646	−	1.15210i
$915$		0			0
$916$	19.6456	−	2.82460i	0.649107	−	0.0933276i
$917$	0.0505580	−	0.0324916i	0.00166957	−	0.00107297i
$918$		0			0
$919$			11.6487i			0.384255i	0.981370	+	0.192128i	$0.0615388\pi$
$919$			11.6487i			0.384255i	−0.981370	+	0.192128i	$0.938461\pi$
$920$	5.54731	+	9.09736i	0.182889	+	0.299931i
$921$		0			0
$922$	8.91250	−	10.2856i	0.293518	−	0.338737i
$923$	−11.2299	−	17.4741i	−0.369637	−	0.575166i
$924$		0			0
$925$	0.178828	−	0.0816681i	0.00587984	−	0.00268523i
$926$	1.06447	+	0.153047i	0.0349805	+	0.00502944i
$927$		0			0
$928$	−5.12102	−	3.29108i	−0.168106	−	0.108035i
$929$	27.6642	+	12.6338i	0.907633	+	0.414502i	0.813839	−	0.581090i	$-0.197373\pi$
$929$	27.6642	+	12.6338i	0.907633	+	0.414502i	0.0937931	+	0.995592i	$0.470101\pi$
$930$		0			0
$931$	−12.0465	+	10.4383i	−0.394808	+	0.342103i
$932$	7.13493	−	6.18245i	0.233712	−	0.202513i
$933$		0			0
$934$	−36.0431	−	16.4603i	−1.17937	−	0.538599i
$935$	1.15734	+	0.743780i	0.0378492	+	0.0243242i
$936$		0			0
$937$	−4.54428	−	0.653369i	−0.148455	−	0.0213446i	0.0676865	−	0.997707i	$-0.478438\pi$
$937$	−4.54428	−	0.653369i	−0.148455	−	0.0213446i	−0.216142	+	0.976362i	$0.569347\pi$
$938$	−0.275311	+	0.125730i	−0.00898921	+	0.00410523i
$939$		0			0
$940$	4.33705	+	6.74858i	0.141459	+	0.220115i
$941$	−32.8534	+	37.9149i	−1.07099	+	1.23599i	−0.100479	+	0.994939i	$0.532038\pi$
$941$	−32.8534	+	37.9149i	−1.07099	+	1.23599i	−0.970512	+	0.241051i	$0.922508\pi$
$942$		0			0
$943$	−3.62489	−	1.76008i	−0.118043	−	0.0573161i
$944$		−	1.05097i		−	0.0342061i
$945$		0			0
$946$	6.80915	−	4.37598i	0.221385	−	0.142275i
$947$	−56.0261	+	8.05534i	−1.82060	+	0.261763i	−0.966190	−	0.257831i	$-0.916992\pi$
$947$	−56.0261	+	8.05534i	−1.82060	+	0.261763i	−0.854413	+	0.519594i	$0.826083\pi$
$948$		0			0
$949$	1.54910	−	10.7742i	0.0502860	−	0.349747i
$950$	0.139242	−	0.0408850i	0.00451759	−	0.00132649i
$951$		0			0
$952$	0.00449411	−	0.00984074i	0.000145655	−	0.000318940i
$953$	11.8900	+	3.49123i	0.385156	+	0.113092i	0.468578	−	0.883422i	$-0.344767\pi$
$953$	11.8900	+	3.49123i	0.385156	+	0.113092i	−0.0834216	+	0.996514i	$0.526585\pi$
$954$		0			0
$955$	6.29976	+	7.27031i	0.203855	+	0.235262i
$956$	−1.48278	+	5.04990i	−0.0479566	+	0.163325i
$957$		0			0
$958$	6.59419	−	10.2608i	0.213049	−	0.331510i
$959$	0.120370	+	0.409941i	0.00388694	+	0.0132377i
$960$		0			0
$961$	11.0100	+	24.1085i	0.355161	+	0.777694i
$962$	0.692701	+	4.81784i	0.0223336	+	0.155334i
$963$		0			0
$964$	14.4634	+	12.5326i	0.465834	+	0.403648i
$965$	56.9762			1.83413
$966$		0			0
$967$	31.5553			1.01475			0.507374	−	0.861726i	$-0.330616\pi$
$967$	31.5553			1.01475			0.507374	+	0.861726i	$0.330616\pi$
$968$	−2.96220	−	2.56676i	−0.0952087	−	0.0824988i
$969$		0			0
$970$	4.39726	+	30.5836i	0.141188	+	0.981981i
$971$	−1.00035	−	2.19046i	−0.0321028	−	0.0702953i	0.892901	−	0.450252i	$-0.148666\pi$
$971$	−1.00035	−	2.19046i	−0.0321028	−	0.0702953i	−0.925004	+	0.379957i	$0.875939\pi$
$972$		0			0
$973$	0.0597335	+	0.203434i	0.00191497	+	0.00652178i
$974$	−3.33155	+	5.18399i	−0.106750	+	0.166106i
$975$		0			0
$976$	−2.65440	+	9.04005i	−0.0849652	+	0.289365i
$977$	−25.8096	−	29.7859i	−0.825723	−	0.952935i	0.173770	−	0.984786i	$-0.444405\pi$
$977$	−25.8096	−	29.7859i	−0.825723	−	0.952935i	−0.999493	+	0.0318515i	$0.989860\pi$
$978$		0			0
$979$	−42.7671	−	12.5576i	−1.36684	−	0.401341i
$980$	6.45872	−	14.1426i	0.206316	−	0.451770i
$981$		0			0
$982$	26.7203	−	7.84578i	0.852679	−	0.250369i
$983$	1.75178	−	12.1839i	0.0558732	−	0.388606i	−0.942627	−	0.333849i	$-0.891652\pi$
$983$	1.75178	−	12.1839i	0.0558732	−	0.388606i	0.998500	−	0.0547573i	$-0.0174385\pi$
$984$		0			0
$985$	−8.15750	+	1.17287i	−0.259920	+	0.0373708i
$986$	1.19168	−	0.765849i	0.0379510	−	0.0243896i
$987$		0			0
$988$			3.59296i			0.114307i
$989$	−4.43946	+	13.8962i	−0.141167	+	0.441874i
$990$		0			0
$991$	5.85703	−	6.75938i	0.186055	−	0.214719i	−0.655058	−	0.755579i	$-0.727356\pi$
$991$	5.85703	−	6.75938i	0.186055	−	0.214719i	0.841113	+	0.540860i	$0.181901\pi$
$992$	−4.09974	−	6.37932i	−0.130167	−	0.202544i
$993$		0			0
$994$	0.556873	−	0.254315i	0.0176629	−	0.00806639i
$995$	29.3895	+	4.22557i	0.931710	+	0.133960i
$996$		0			0
$997$	32.3793	+	20.8089i	1.02546	+	0.659024i	0.941350	−	0.337432i	$-0.109558\pi$
$997$	32.3793	+	20.8089i	1.02546	+	0.659024i	0.0841114	+	0.996456i	$0.473195\pi$
$998$	33.2927	+	15.2043i	1.05386	+	0.481283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.53.2	✓	80
3.2	odd	2	inner	414.2.j.a.53.7	yes	80
23.10	odd	22	inner	414.2.j.a.125.7	yes	80
69.56	even	22	inner	414.2.j.a.125.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.53.2	✓	80	1.1	even	1	trivial
414.2.j.a.53.7	yes	80	3.2	odd	2	inner
414.2.j.a.125.2	yes	80	69.56	even	22	inner
414.2.j.a.125.7	yes	80	23.10	odd	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755750 - 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(-0.922959 - 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(0.540641 - 0.841254i) q^{8} +O(q^{10})\)	\(q+(-0.755750 - 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(-0.922959 - 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(0.540641 - 0.841254i) q^{8} +(-0.625947 + 2.13178i) q^{10} +(-1.74253 - 2.01098i) q^{11} +(-1.51348 - 0.444397i) q^{13} +(0.0193125 - 0.0422885i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.0331173 - 0.230336i) q^{17} +(-2.25463 + 0.324167i) q^{19} +(1.86908 - 1.20118i) q^{20} +2.66091i q^{22} +(-3.05411 - 3.69763i) q^{23} +(0.0417212 - 0.0481489i) q^{25} +(0.852791 + 1.32697i) q^{26} +(-0.0422885 + 0.0193125i) q^{28} +(-6.02540 - 0.866322i) q^{29} +(-6.37932 - 4.09974i) q^{31} +(0.909632 + 0.415415i) q^{32} +(-0.175866 + 0.152389i) q^{34} +(0.0780612 - 0.0676404i) q^{35} +(2.80691 + 1.28187i) q^{37} +(1.91622 + 1.23148i) q^{38} +(-2.19916 - 0.316192i) q^{40} +(0.764300 - 0.349044i) q^{41} +(-1.64454 - 2.55895i) q^{43} +(1.74253 - 2.01098i) q^{44} +(-0.113292 + 4.79449i) q^{46} +3.61065i q^{47} +(5.88696 - 3.78332i) q^{49} +(-0.0630616 + 0.00906689i) q^{50} +(0.224483 - 1.56132i) q^{52} +(-6.15867 + 1.80835i) q^{53} +(-2.45591 + 5.37770i) q^{55} +(0.0446065 + 0.0130977i) q^{56} +(3.98638 + 4.60052i) q^{58} +(-0.296092 + 1.00840i) q^{59} +(5.09375 - 7.92604i) q^{61} +(2.13641 + 7.27594i) q^{62} +(-0.415415 - 0.909632i) q^{64} +(0.498752 + 3.46889i) q^{65} +(-4.92015 - 4.26333i) q^{67} +0.232705 q^{68} -0.103290 q^{70} +(9.95203 + 8.62348i) q^{71} +(0.982079 + 6.83051i) q^{73} +(-1.28187 - 2.80691i) q^{74} +(-0.641735 - 2.18555i) q^{76} +(0.0668799 - 0.104067i) q^{77} +(1.88074 - 6.40520i) q^{79} +(1.45495 + 1.67911i) q^{80} +(-0.806195 - 0.236720i) q^{82} +(-3.50663 + 7.67846i) q^{83} +(-0.496075 + 0.145661i) q^{85} +(-0.432898 + 3.01087i) q^{86} +(-2.63383 + 0.378687i) q^{88} +(14.0917 - 9.05622i) q^{89} -0.0733315i q^{91} +(3.22535 - 3.54925i) q^{92} +(2.36447 - 2.72875i) q^{94} +(2.73608 + 4.25742i) q^{95} +(12.6502 - 5.77716i) q^{97} +(-6.92661 - 0.995896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more