LMFDB - Embedded newform 1445.2.d.j.866.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (of order $2$, degree $1$, not 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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.23
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73061 q^{2} +1.54691i q^{3} +5.45623 q^{4} +1.00000i q^{5} +4.22400i q^{6} +1.26445i q^{7} +9.43761 q^{8} +0.607075 q^{9} +O(q^{10})$	\(q+2.73061 q^{2} +1.54691i q^{3} +5.45623 q^{4} +1.00000i q^{5} +4.22400i q^{6} +1.26445i q^{7} +9.43761 q^{8} +0.607075 q^{9} +2.73061i q^{10} -0.417956i q^{11} +8.44028i q^{12} -5.66390 q^{13} +3.45273i q^{14} -1.54691 q^{15} +14.8580 q^{16} +1.65769 q^{18} +0.134144 q^{19} +5.45623i q^{20} -1.95600 q^{21} -1.14127i q^{22} -6.81922i q^{23} +14.5991i q^{24} -1.00000 q^{25} -15.4659 q^{26} +5.57981i q^{27} +6.89915i q^{28} +0.329510i q^{29} -4.22400 q^{30} -0.605659i q^{31} +21.6961 q^{32} +0.646540 q^{33} -1.26445 q^{35} +3.31234 q^{36} -8.83716i q^{37} +0.366294 q^{38} -8.76154i q^{39} +9.43761i q^{40} -1.63371i q^{41} -5.34106 q^{42} +1.99751 q^{43} -2.28046i q^{44} +0.607075i q^{45} -18.6206i q^{46} -5.06253 q^{47} +22.9839i q^{48} +5.40115 q^{49} -2.73061 q^{50} -30.9036 q^{52} +1.54296 q^{53} +15.2363i q^{54} +0.417956 q^{55} +11.9334i q^{56} +0.207508i q^{57} +0.899762i q^{58} +1.41104 q^{59} -8.44028 q^{60} +7.80498i q^{61} -1.65382i q^{62} +0.767619i q^{63} +29.5276 q^{64} -5.66390i q^{65} +1.76545 q^{66} -12.1014 q^{67} +10.5487 q^{69} -3.45273 q^{70} +4.82493i q^{71} +5.72934 q^{72} -2.90042i q^{73} -24.1308i q^{74} -1.54691i q^{75} +0.731919 q^{76} +0.528486 q^{77} -23.9243i q^{78} -4.33770i q^{79} +14.8580i q^{80} -6.81023 q^{81} -4.46102i q^{82} +4.39202 q^{83} -10.6724 q^{84} +5.45443 q^{86} -0.509721 q^{87} -3.94451i q^{88} +4.98704 q^{89} +1.65769i q^{90} -7.16175i q^{91} -37.2072i q^{92} +0.936899 q^{93} -13.8238 q^{94} +0.134144i q^{95} +33.5619i q^{96} -0.635381i q^{97} +14.7484 q^{98} -0.253731i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43} - 64 q^{47} - 40 q^{49} - 8 q^{50} - 48 q^{52} - 32 q^{55} - 16 q^{59} + 32 q^{60} + 72 q^{64} - 80 q^{66} - 16 q^{67} + 96 q^{69} - 32 q^{70} + 24 q^{72} - 32 q^{76} - 48 q^{77} + 72 q^{81} + 80 q^{83} + 64 q^{84} - 16 q^{86} + 64 q^{87} + 16 q^{89} - 48 q^{93} + 32 q^{94} - 120 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	2.73061	1.93083	0.965416	−	0.260713i	$-0.0839577\pi$
$2$	2.73061	1.93083	0.965416	+	0.260713i	$0.0839577\pi$
$3$	1.54691i	0.893108i	0.894757	+	0.446554i	$0.147349\pi$
$3$	1.54691i	0.893108i	−0.894757	+	0.446554i	$0.852651\pi$
$4$	5.45623	2.72811
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	4.22400i	1.72444i
$7$	1.26445i	0.477919i	0.971030	+	0.238959i	$0.0768063\pi$
$7$	1.26445i	0.477919i	−0.971030	+	0.238959i	$0.923194\pi$
$8$	9.43761	3.33670
$9$	0.607075	0.202358
$10$	2.73061i	0.863495i
$11$	− 0.417956i	− 0.126018i	−0.998013	−	0.0630092i	$-0.979930\pi$
$11$	− 0.417956i	− 0.126018i	0.998013	−	0.0630092i	$-0.0200698\pi$
$12$	8.44028i	2.43650i
$13$	−5.66390	−1.57088	−0.785442	−	0.618935i	$-0.787564\pi$
$13$	−5.66390	−1.57088	−0.785442	+	0.618935i	$0.787564\pi$
$14$	3.45273i	0.922781i
$15$	−1.54691	−0.399410
$16$	14.8580	3.71449
$17$	0	0
$17$	0	0
$18$	1.65769	0.390720
$19$	0.134144	0.0307747	0.0153873	−	0.999882i	$-0.495102\pi$
$19$	0.134144	0.0307747	0.0153873	+	0.999882i	$0.495102\pi$
$20$	5.45623i	1.22005i
$21$	−1.95600	−0.426833
$22$	− 1.14127i	− 0.243321i
$23$	− 6.81922i	− 1.42191i	−0.703239	−	0.710953i	$-0.748264\pi$
$23$	− 6.81922i	− 1.42191i	0.703239	−	0.710953i	$-0.251736\pi$
$24$	14.5991i	2.98003i
$25$	−1.00000	−0.200000
$26$	−15.4659	−3.03311
$27$	5.57981i	1.07384i
$28$	6.89915i	1.30382i
$29$	0.329510i	0.0611884i	0.999532	+	0.0305942i	$0.00973995\pi$
$29$	0.329510i	0.0611884i	−0.999532	+	0.0305942i	$0.990260\pi$
$30$	−4.22400	−0.771194
$31$	− 0.605659i	− 0.108780i	−0.998520	−	0.0543898i	$-0.982679\pi$
$31$	− 0.605659i	− 0.108780i	0.998520	−	0.0543898i	$-0.0173214\pi$
$32$	21.6961	3.83537
$33$	0.646540	0.112548
$34$	0	0
$35$	−1.26445	−0.213732
$36$	3.31234	0.552057
$37$	− 8.83716i	− 1.45282i	−0.687261	−	0.726410i	$-0.741187\pi$
$37$	− 8.83716i	− 1.45282i	0.687261	−	0.726410i	$-0.258813\pi$
$38$	0.366294	0.0594207
$39$	− 8.76154i	− 1.40297i
$40$	9.43761i	1.49222i
$41$	− 1.63371i	− 0.255143i	−0.991829	−	0.127571i	$-0.959282\pi$
$41$	− 1.63371i	− 0.255143i	0.991829	−	0.127571i	$-0.0407182\pi$
$42$	−5.34106	−0.824143
$43$	1.99751	0.304618	0.152309	−	0.988333i	$-0.451329\pi$
$43$	1.99751	0.304618	0.152309	+	0.988333i	$0.451329\pi$
$44$	− 2.28046i	− 0.343793i
$45$	0.607075i	0.0904974i
$46$	− 18.6206i	− 2.74546i
$47$	−5.06253	−0.738445	−0.369223	−	0.929341i	$-0.620376\pi$
$47$	−5.06253	−0.738445	−0.369223	+	0.929341i	$0.620376\pi$
$48$	22.9839i	3.31744i
$49$	5.40115	0.771594
$50$	−2.73061	−0.386167
$51$	0	0
$52$	−30.9036	−4.28555
$53$	1.54296	0.211942	0.105971	−	0.994369i	$-0.466205\pi$
$53$	1.54296	0.211942	0.105971	+	0.994369i	$0.466205\pi$
$54$	15.2363i	2.07340i
$55$	0.417956	0.0563572
$56$	11.9334i	1.59467i
$57$	0.207508i	0.0274851i
$58$	0.899762i	0.118145i
$59$	1.41104	0.183702	0.0918510	−	0.995773i	$-0.470722\pi$
$59$	1.41104	0.183702	0.0918510	+	0.995773i	$0.470722\pi$
$60$	−8.44028	−1.08964
$61$	7.80498i	0.999325i	0.866220	+	0.499663i	$0.166543\pi$
$61$	7.80498i	0.999325i	−0.866220	+	0.499663i	$0.833457\pi$
$62$	− 1.65382i	− 0.210035i
$63$	0.767619i	0.0967109i
$64$	29.5276	3.69095
$65$	− 5.66390i	− 0.702521i
$66$	1.76545	0.217312
$67$	−12.1014	−1.47842	−0.739209	−	0.673477i	$-0.764800\pi$
$67$	−12.1014	−1.47842	−0.739209	+	0.673477i	$0.764800\pi$
$68$	0	0
$69$	10.5487	1.26992
$70$	−3.45273	−0.412680
$71$	4.82493i	0.572614i	0.958138	+	0.286307i	$0.0924278\pi$
$71$	4.82493i	0.572614i	−0.958138	+	0.286307i	$0.907572\pi$
$72$	5.72934	0.675209
$73$	− 2.90042i	− 0.339468i	−0.985490	−	0.169734i	$-0.945709\pi$
$73$	− 2.90042i	− 0.339468i	0.985490	−	0.169734i	$-0.0542909\pi$
$74$	− 24.1308i	− 2.80515i
$75$	− 1.54691i	− 0.178622i
$76$	0.731919	0.0839568
$77$	0.528486	0.0602266
$78$	− 23.9243i	− 2.70890i
$79$	− 4.33770i	− 0.488029i	−0.969772	−	0.244015i	$-0.921535\pi$
$79$	− 4.33770i	− 0.488029i	0.969772	−	0.244015i	$-0.0784645\pi$
$80$	14.8580i	1.66117i
$81$	−6.81023	−0.756693
$82$	− 4.46102i	− 0.492638i
$83$	4.39202	0.482087	0.241043	−	0.970514i	$-0.422510\pi$
$83$	4.39202	0.482087	0.241043	+	0.970514i	$0.422510\pi$
$84$	−10.6724	−1.16445
$85$	0	0
$86$	5.45443	0.588167
$87$	−0.509721	−0.0546478
$88$	− 3.94451i	− 0.420486i
$89$	4.98704	0.528625	0.264313	−	0.964437i	$-0.414855\pi$
$89$	4.98704	0.528625	0.264313	+	0.964437i	$0.414855\pi$
$90$	1.65769i	0.174735i
$91$	− 7.16175i	− 0.750755i
$92$	− 37.2072i	− 3.87912i
$93$	0.936899	0.0971519
$94$	−13.8238	−1.42581
$95$	0.134144i	0.0137628i
$96$	33.5619i	3.42539i
$97$	− 0.635381i	− 0.0645131i	−0.999480	−	0.0322566i	$-0.989731\pi$
$97$	− 0.635381i	− 0.0645131i	0.999480	−	0.0322566i	$-0.0102694\pi$
$98$	14.7484	1.48982
$99$	− 0.253731i	− 0.0255009i
$100$	−5.45623	−0.545623
$101$	−7.45004	−0.741307	−0.370653	−	0.928771i	$-0.620866\pi$
$101$	−7.45004	−0.741307	−0.370653	+	0.928771i	$0.620866\pi$
$102$	0	0
$103$	13.5860	1.33866	0.669332	−	0.742963i	$-0.266580\pi$
$103$	13.5860	1.33866	0.669332	+	0.742963i	$0.266580\pi$
$104$	−53.4537	−5.24157
$105$	− 1.95600i	− 0.190886i
$106$	4.21322	0.409224
$107$	− 9.27421i	− 0.896572i	−0.893890	−	0.448286i	$-0.852035\pi$
$107$	− 9.27421i	− 0.896572i	0.893890	−	0.448286i	$-0.147965\pi$
$108$	30.4447i	2.92955i
$109$	15.7066i	1.50442i	0.658925	+	0.752209i	$0.271012\pi$
$109$	15.7066i	1.50442i	−0.658925	+	0.752209i	$0.728988\pi$
$110$	1.14127	0.108816
$111$	13.6703	1.29753
$112$	18.7872i	1.77523i
$113$	1.24680i	0.117289i	0.998279	+	0.0586447i	$0.0186779\pi$
$113$	1.24680i	0.117289i	−0.998279	+	0.0586447i	$0.981322\pi$
$114$	0.566623i	0.0530691i
$115$	6.81922	0.635896
$116$	1.79788i	0.166929i
$117$	−3.43842	−0.317882
$118$	3.85301	0.354698
$119$	0	0
$120$	−14.5991	−1.33271
$121$	10.8253	0.984119
$122$	21.3124i	1.92953i
$123$	2.52720	0.227870
$124$	− 3.30461i	− 0.296763i
$125$	− 1.00000i	− 0.0894427i
$126$	2.09607i	0.186733i
$127$	−17.8153	−1.58085	−0.790427	−	0.612556i	$-0.790141\pi$
$127$	−17.8153	−1.58085	−0.790427	+	0.612556i	$0.790141\pi$
$128$	37.2362	3.29125
$129$	3.08997i	0.272057i
$130$	− 15.4659i	− 1.35645i
$131$	− 4.47235i	− 0.390751i	−0.980729	−	0.195375i	$-0.937407\pi$
$131$	− 4.47235i	− 0.390751i	0.980729	−	0.195375i	$-0.0625925\pi$
$132$	3.52767	0.307044
$133$	0.169619i	0.0147078i
$134$	−33.0441	−2.85458
$135$	−5.57981	−0.480234
$136$	0	0
$137$	9.04916	0.773122	0.386561	−	0.922264i	$-0.373663\pi$
$137$	9.04916	0.773122	0.386561	+	0.922264i	$0.373663\pi$
$138$	28.8044	2.45199
$139$	− 4.70076i	− 0.398713i	−0.979927	−	0.199357i	$-0.936115\pi$
$139$	− 4.70076i	− 0.398713i	0.979927	−	0.199357i	$-0.0638852\pi$
$140$	−6.89915	−0.583085
$141$	− 7.83126i	− 0.659511i
$142$	13.1750i	1.10562i
$143$	2.36726i	0.197960i
$144$	9.01991	0.751659
$145$	−0.329510	−0.0273643
$146$	− 7.91990i	− 0.655456i
$147$	8.35509i	0.689116i
$148$	− 48.2176i	− 3.96346i
$149$	−0.775949	−0.0635683	−0.0317841	−	0.999495i	$-0.510119\pi$
$149$	−0.775949	−0.0635683	−0.0317841	+	0.999495i	$0.510119\pi$
$150$	− 4.22400i	− 0.344888i
$151$	2.28712	0.186123	0.0930617	−	0.995660i	$-0.470335\pi$
$151$	2.28712	0.186123	0.0930617	+	0.995660i	$0.470335\pi$
$152$	1.26600	0.102686
$153$	0	0
$154$	1.44309	0.116288
$155$	0.605659	0.0486477
$156$	− 47.8050i	− 3.82746i
$157$	−19.1134	−1.52541	−0.762707	−	0.646745i	$-0.776130\pi$
$157$	−19.1134	−1.52541	−0.762707	+	0.646745i	$0.776130\pi$
$158$	− 11.8446i	− 0.942303i
$159$	2.38682i	0.189287i
$160$	21.6961i	1.71523i
$161$	8.62260	0.679556
$162$	−18.5961	−1.46105
$163$	18.3295i	1.43568i	0.696209	+	0.717839i	$0.254869\pi$
$163$	18.3295i	1.43568i	−0.696209	+	0.717839i	$0.745131\pi$
$164$	− 8.91389i	− 0.696058i
$165$	0.646540i	0.0503330i
$166$	11.9929	0.930829
$167$	− 20.1484i	− 1.55913i	−0.626322	−	0.779564i	$-0.715441\pi$
$167$	− 20.1484i	− 1.55913i	0.626322	−	0.779564i	$-0.284559\pi$
$168$	−18.4599	−1.42421
$169$	19.0798	1.46768
$170$	0	0
$171$	0.0814353	0.00622751
$172$	10.8989	0.831033
$173$	− 19.1144i	− 1.45324i	−0.687041	−	0.726619i	$-0.741091\pi$
$173$	− 19.1144i	− 1.45324i	0.687041	−	0.726619i	$-0.258909\pi$
$174$	−1.39185	−0.105516
$175$	− 1.26445i	− 0.0955838i
$176$	− 6.20998i	− 0.468095i
$177$	2.18275i	0.164066i
$178$	13.6177	1.02069
$179$	−19.8154	−1.48107	−0.740535	−	0.672018i	$-0.765428\pi$
$179$	−19.8154	−1.48107	−0.740535	+	0.672018i	$0.765428\pi$
$180$	3.31234i	0.246887i
$181$	− 8.86555i	− 0.658971i	−0.944161	−	0.329485i	$-0.893125\pi$
$181$	− 8.86555i	− 0.658971i	0.944161	−	0.329485i	$-0.106875\pi$
$182$	− 19.5559i	− 1.44958i
$183$	−12.0736	−0.892505
$184$	− 64.3572i	− 4.74447i
$185$	8.83716	0.649721
$186$	2.55831	0.187584
$187$	0	0
$188$	−27.6223	−2.01456
$189$	−7.05542	−0.513206
$190$	0.366294i	0.0265738i
$191$	10.6081	0.767576	0.383788	−	0.923421i	$-0.374619\pi$
$191$	10.6081	0.767576	0.383788	+	0.923421i	$0.374619\pi$
$192$	45.6765i	3.29642i
$193$	− 9.72535i	− 0.700046i	−0.936741	−	0.350023i	$-0.886174\pi$
$193$	− 9.72535i	− 0.700046i	0.936741	−	0.350023i	$-0.113826\pi$
$194$	− 1.73498i	− 0.124564i
$195$	8.76154	0.627427
$196$	29.4699	2.10500
$197$	− 23.7953i	− 1.69534i	−0.530521	−	0.847671i	$-0.678004\pi$
$197$	− 23.7953i	− 1.69534i	0.530521	−	0.847671i	$-0.321996\pi$
$198$	− 0.692839i	− 0.0492380i
$199$	13.2078i	0.936276i	0.883655	+	0.468138i	$0.155075\pi$
$199$	13.2078i	0.936276i	−0.883655	+	0.468138i	$0.844925\pi$
$200$	−9.43761	−0.667340
$201$	− 18.7197i	− 1.32039i
$202$	−20.3431	−1.43134
$203$	−0.416650	−0.0292431
$204$	0	0
$205$	1.63371	0.114103
$206$	37.0979	2.58474
$207$	− 4.13978i	− 0.287735i
$208$	−84.1541	−5.83504
$209$	− 0.0560662i	− 0.00387818i
$210$	− 5.34106i	− 0.368568i
$211$	19.8864i	1.36904i	0.728996	+	0.684518i	$0.239987\pi$
$211$	19.8864i	1.36904i	−0.728996	+	0.684518i	$0.760013\pi$
$212$	8.41873	0.578201
$213$	−7.46373	−0.511406
$214$	− 25.3243i	− 1.73113i
$215$	1.99751i	0.136229i
$216$	52.6601i	3.58307i
$217$	0.765828	0.0519878
$218$	42.8885i	2.90478i
$219$	4.48668	0.303182
$220$	2.28046	0.153749
$221$	0	0
$222$	37.3282	2.50530
$223$	−6.36311	−0.426106	−0.213053	−	0.977041i	$-0.568341\pi$
$223$	−6.36311	−0.426106	−0.213053	+	0.977041i	$0.568341\pi$
$224$	27.4337i	1.83299i
$225$	−0.607075	−0.0404717
$226$	3.40453i	0.226466i
$227$	26.5359i	1.76125i	0.473814	+	0.880625i	$0.342877\pi$
$227$	26.5359i	1.76125i	−0.473814	+	0.880625i	$0.657123\pi$
$228$	1.13221i	0.0749825i
$229$	−15.5455	−1.02728	−0.513639	−	0.858006i	$-0.671703\pi$
$229$	−15.5455	−1.02728	−0.513639	+	0.858006i	$0.671703\pi$
$230$	18.6206	1.22781
$231$	0.817520i	0.0537889i
$232$	3.10978i	0.204167i
$233$	3.80274i	0.249126i	0.992212	+	0.124563i	$0.0397528\pi$
$233$	3.80274i	0.249126i	−0.992212	+	0.124563i	$0.960247\pi$
$234$	−9.38897	−0.613776
$235$	− 5.06253i	− 0.330243i
$236$	7.69897	0.501160
$237$	6.71002	0.435863
$238$	0	0
$239$	−5.80679	−0.375610	−0.187805	−	0.982206i	$-0.560137\pi$
$239$	−5.80679	−0.375610	−0.187805	+	0.982206i	$0.560137\pi$
$240$	−22.9839	−1.48361
$241$	− 8.72796i	− 0.562218i	−0.959676	−	0.281109i	$-0.909298\pi$
$241$	− 8.72796i	− 0.562218i	0.959676	−	0.281109i	$-0.0907022\pi$
$242$	29.5597	1.90017
$243$	6.20463i	0.398027i
$244$	42.5858i	2.72627i
$245$	5.40115i	0.345067i
$246$	6.90079	0.439979
$247$	−0.759777	−0.0483434
$248$	− 5.71597i	− 0.362965i
$249$	6.79405i	0.430556i
$250$	− 2.73061i	− 0.172699i
$251$	15.2424	0.962093	0.481047	−	0.876695i	$-0.340257\pi$
$251$	15.2424	0.962093	0.481047	+	0.876695i	$0.340257\pi$
$252$	4.18830i	0.263838i
$253$	−2.85014	−0.179186
$254$	−48.6467	−3.05236
$255$	0	0
$256$	42.6224	2.66390
$257$	−14.5342	−0.906620	−0.453310	−	0.891353i	$-0.649757\pi$
$257$	−14.5342	−0.906620	−0.453310	+	0.891353i	$0.649757\pi$
$258$	8.43751i	0.525296i
$259$	11.1742	0.694331
$260$	− 30.9036i	− 1.91656i
$261$	0.200037i	0.0123820i
$262$	− 12.2122i	− 0.754474i
$263$	−19.0283	−1.17333	−0.586666	−	0.809829i	$-0.699560\pi$
$263$	−19.0283	−1.17333	−0.586666	+	0.809829i	$0.699560\pi$
$264$	6.10179	0.375539
$265$	1.54296i	0.0947832i
$266$	0.463162i	0.0283983i
$267$	7.71449i	0.472119i
$268$	−66.0278	−4.03329
$269$	22.6849i	1.38312i	0.722319	+	0.691560i	$0.243076\pi$
$269$	22.6849i	1.38312i	−0.722319	+	0.691560i	$0.756924\pi$
$270$	−15.2363	−0.927251
$271$	−9.96764	−0.605491	−0.302745	−	0.953071i	$-0.597903\pi$
$271$	−9.96764	−0.605491	−0.302745	+	0.953071i	$0.597903\pi$
$272$	0	0
$273$	11.0786	0.670506
$274$	24.7097	1.49277
$275$	0.417956i	0.0252037i
$276$	57.5562	3.46448
$277$	− 11.7071i	− 0.703412i	−0.936110	−	0.351706i	$-0.885602\pi$
$277$	− 11.7071i	− 0.703412i	0.936110	−	0.351706i	$-0.114398\pi$
$278$	− 12.8359i	− 0.769848i
$279$	− 0.367681i	− 0.0220125i
$280$	−11.9334	−0.713159
$281$	1.18521	0.0707038	0.0353519	−	0.999375i	$-0.488745\pi$
$281$	1.18521	0.0707038	0.0353519	+	0.999375i	$0.488745\pi$
$282$	− 21.3841i	− 1.27341i
$283$	− 4.61084i	− 0.274086i	−0.990565	−	0.137043i	$-0.956240\pi$
$283$	− 4.61084i	− 0.274086i	0.990565	−	0.137043i	$-0.0437598\pi$
$284$	26.3259i	1.56216i
$285$	−0.207508	−0.0122917
$286$	6.46407i	0.382229i
$287$	2.06575	0.121937
$288$	13.1712	0.776118
$289$	0	0
$290$	−0.899762	−0.0528358
$291$	0.982876	0.0576172
$292$	− 15.8253i	− 0.926108i
$293$	−3.09527	−0.180828	−0.0904138	−	0.995904i	$-0.528819\pi$
$293$	−3.09527	−0.180828	−0.0904138	+	0.995904i	$0.528819\pi$
$294$	22.8145i	1.33057i
$295$	1.41104i	0.0821541i
$296$	− 83.4017i	− 4.84763i
$297$	2.33212	0.135323
$298$	−2.11882	−0.122740
$299$	38.6234i	2.23365i
$300$	− 8.44028i	− 0.487300i
$301$	2.52577i	0.145583i
$302$	6.24524	0.359373
$303$	− 11.5245i	− 0.662067i
$304$	1.99310	0.114312
$305$	−7.80498	−0.446912
$306$	0	0
$307$	11.8387	0.675668	0.337834	−	0.941206i	$-0.390306\pi$
$307$	11.8387	0.675668	0.337834	+	0.941206i	$0.390306\pi$
$308$	2.88354	0.164305
$309$	21.0162i	1.19557i
$310$	1.65382	0.0939306
$311$	23.4500i	1.32973i	0.746965	+	0.664863i	$0.231510\pi$
$311$	23.4500i	1.32973i	−0.746965	+	0.664863i	$0.768490\pi$
$312$	− 82.6880i	− 4.68129i
$313$	− 27.6083i	− 1.56051i	−0.625459	−	0.780257i	$-0.715088\pi$
$313$	− 27.6083i	− 1.56051i	0.625459	−	0.780257i	$-0.284912\pi$
$314$	−52.1912	−2.94532
$315$	−0.767619	−0.0432504
$316$	− 23.6675i	− 1.33140i
$317$	31.8609i	1.78949i	0.446580	+	0.894744i	$0.352642\pi$
$317$	31.8609i	1.78949i	−0.446580	+	0.894744i	$0.647358\pi$
$318$	6.51746i	0.365481i
$319$	0.137720	0.00771087
$320$	29.5276i	1.65065i
$321$	14.3464	0.800736
$322$	23.5449	1.31211
$323$	0	0
$324$	−37.1582	−2.06434
$325$	5.66390	0.314177
$326$	50.0507i	2.77205i
$327$	−24.2966	−1.34361
$328$	− 15.4183i	− 0.851334i
$329$	− 6.40133i	− 0.352917i
$330$	1.76545i	0.0971847i
$331$	26.0748	1.43320	0.716600	−	0.697484i	$-0.245697\pi$
$331$	26.0748	1.43320	0.716600	+	0.697484i	$0.245697\pi$
$332$	23.9639	1.31519
$333$	− 5.36482i	− 0.293990i
$334$	− 55.0174i	− 3.01042i
$335$	− 12.1014i	− 0.661168i
$336$	−29.0621	−1.58547
$337$	16.5187i	0.899833i	0.893071	+	0.449917i	$0.148546\pi$
$337$	16.5187i	0.899833i	−0.893071	+	0.449917i	$0.851454\pi$
$338$	52.0995	2.83384
$339$	−1.92869	−0.104752
$340$	0	0
$341$	−0.253139	−0.0137082
$342$	0.222368	0.0120243
$343$	15.6807i	0.846678i
$344$	18.8518	1.01642
$345$	10.5487i	0.567924i
$346$	− 52.1938i	− 2.80596i
$347$	20.3246i	1.09108i	0.838085	+	0.545540i	$0.183675\pi$
$347$	20.3246i	1.09108i	−0.838085	+	0.545540i	$0.816325\pi$
$348$	−2.78115	−0.149086
$349$	−4.88555	−0.261517	−0.130759	−	0.991414i	$-0.541741\pi$
$349$	−4.88555	−0.261517	−0.130759	+	0.991414i	$0.541741\pi$
$350$	− 3.45273i	− 0.184556i
$351$	− 31.6035i	− 1.68687i
$352$	− 9.06802i	− 0.483327i
$353$	22.6733	1.20678	0.603389	−	0.797447i	$-0.293817\pi$
$353$	22.6733	1.20678	0.603389	+	0.797447i	$0.293817\pi$
$354$	5.96025i	0.316783i
$355$	−4.82493	−0.256081
$356$	27.2104	1.44215
$357$	0	0
$358$	−54.1080	−2.85970
$359$	−13.4808	−0.711490	−0.355745	−	0.934583i	$-0.615773\pi$
$359$	−13.4808	−0.711490	−0.355745	+	0.934583i	$0.615773\pi$
$360$	5.72934i	0.301963i
$361$	−18.9820	−0.999053
$362$	− 24.2083i	− 1.27236i
$363$	16.7458i	0.878925i
$364$	− 39.0761i	− 2.04815i
$365$	2.90042	0.151815
$366$	−32.9683	−1.72328
$367$	− 1.91088i	− 0.0997470i	−0.998756	−	0.0498735i	$-0.984118\pi$
$367$	− 1.91088i	− 0.0997470i	0.998756	−	0.0498735i	$-0.0158818\pi$
$368$	− 101.320i	− 5.28166i
$369$	− 0.991785i	− 0.0516302i
$370$	24.1308	1.25450
$371$	1.95100i	0.101291i
$372$	5.11193	0.265041
$373$	24.9357	1.29112	0.645562	−	0.763708i	$-0.276623\pi$
$373$	24.9357	1.29112	0.645562	+	0.763708i	$0.276623\pi$
$374$	0	0
$375$	1.54691	0.0798820
$376$	−47.7781	−2.46397
$377$	− 1.86631i	− 0.0961199i
$378$	−19.2656	−0.990916
$379$	− 16.6020i	− 0.852789i	−0.904537	−	0.426394i	$-0.859784\pi$
$379$	− 16.6020i	− 0.852789i	0.904537	−	0.426394i	$-0.140216\pi$
$380$	0.731919i	0.0375466i
$381$	− 27.5587i	− 1.41187i
$382$	28.9666	1.48206
$383$	20.0900	1.02655	0.513277	−	0.858223i	$-0.328432\pi$
$383$	20.0900	1.02655	0.513277	+	0.858223i	$0.328432\pi$
$384$	57.6010i	2.93944i
$385$	0.528486i	0.0269342i
$386$	− 26.5561i	− 1.35167i
$387$	1.21264	0.0616420
$388$	− 3.46678i	− 0.175999i
$389$	22.2783	1.12955	0.564777	−	0.825244i	$-0.308962\pi$
$389$	22.2783	1.12955	0.564777	+	0.825244i	$0.308962\pi$
$390$	23.9243	1.21146
$391$	0	0
$392$	50.9740	2.57458
$393$	6.91831	0.348983
$394$	− 64.9756i	− 3.27342i
$395$	4.33770	0.218253
$396$	− 1.38441i	− 0.0695694i
$397$	− 26.2699i	− 1.31845i	−0.751947	−	0.659223i	$-0.770885\pi$
$397$	− 26.2699i	− 1.31845i	0.751947	−	0.659223i	$-0.229115\pi$
$398$	36.0653i	1.80779i
$399$	−0.262384	−0.0131356
$400$	−14.8580	−0.742899
$401$	38.1569i	1.90547i	0.303807	+	0.952733i	$0.401742\pi$
$401$	38.1569i	1.90547i	−0.303807	+	0.952733i	$0.598258\pi$
$402$	− 51.1162i	− 2.54944i
$403$	3.43040i	0.170880i
$404$	−40.6491	−2.02237
$405$	− 6.81023i	− 0.338403i
$406$	−1.13771	−0.0564635
$407$	−3.69355	−0.183082
$408$	0	0
$409$	−19.0995	−0.944411	−0.472206	−	0.881488i	$-0.656542\pi$
$409$	−19.0995	−0.944411	−0.472206	+	0.881488i	$0.656542\pi$
$410$	4.46102	0.220314
$411$	13.9982i	0.690481i
$412$	74.1281	3.65203
$413$	1.78420i	0.0877947i
$414$	− 11.3041i	− 0.555567i
$415$	4.39202i	0.215596i
$416$	−122.885	−6.02492
$417$	7.27164	0.356094
$418$	− 0.153095i	− 0.00748811i
$419$	33.5509i	1.63907i	0.573032	+	0.819533i	$0.305767\pi$
$419$	33.5509i	1.63907i	−0.573032	+	0.819533i	$0.694233\pi$
$420$	− 10.6724i	− 0.520758i
$421$	−18.9396	−0.923058	−0.461529	−	0.887125i	$-0.652699\pi$
$421$	−18.9396	−0.923058	−0.461529	+	0.887125i	$0.652699\pi$
$422$	54.3020i	2.64338i
$423$	−3.07333	−0.149431
$424$	14.5618	0.707186
$425$	0	0
$426$	−20.3805	−0.987440
$427$	−9.86904	−0.477596
$428$	− 50.6022i	− 2.44595i
$429$	−3.66194	−0.176800
$430$	5.45443i	0.263036i
$431$	24.3871i	1.17469i	0.809338	+	0.587343i	$0.199826\pi$
$431$	24.3871i	1.17469i	−0.809338	+	0.587343i	$0.800174\pi$
$432$	82.9047i	3.98876i
$433$	−9.69125	−0.465732	−0.232866	−	0.972509i	$-0.574810\pi$
$433$	−9.69125	−0.465732	−0.232866	+	0.972509i	$0.574810\pi$
$434$	2.09118	0.100380
$435$	− 0.509721i	− 0.0244392i
$436$	85.6987i	4.10422i
$437$	− 0.914756i	− 0.0437587i
$438$	12.2514	0.585393
$439$	3.22352i	0.153850i	0.997037	+	0.0769251i	$0.0245102\pi$
$439$	3.22352i	0.153850i	−0.997037	+	0.0769251i	$0.975490\pi$
$440$	3.94451	0.188047
$441$	3.27891	0.156138
$442$	0	0
$443$	−17.5623	−0.834412	−0.417206	−	0.908812i	$-0.636991\pi$
$443$	−17.5623	−0.834412	−0.417206	+	0.908812i	$0.636991\pi$
$444$	74.5882	3.53980
$445$	4.98704i	0.236408i
$446$	−17.3752	−0.822739
$447$	− 1.20032i	− 0.0567733i
$448$	37.3364i	1.76398i
$449$	− 18.5233i	− 0.874169i	−0.899421	−	0.437084i	$-0.856011\pi$
$449$	− 18.5233i	− 0.874169i	0.899421	−	0.437084i	$-0.143989\pi$
$450$	−1.65769	−0.0781440
$451$	−0.682819	−0.0321527
$452$	6.80284i	0.319979i
$453$	3.53797i	0.166228i
$454$	72.4592i	3.40068i
$455$	7.16175	0.335748
$456$	1.95838i	0.0917095i
$457$	−14.7077	−0.687997	−0.343998	−	0.938970i	$-0.611781\pi$
$457$	−14.7077	−0.687997	−0.343998	+	0.938970i	$0.611781\pi$
$458$	−42.4488	−1.98350
$459$	0	0
$460$	37.2072	1.73480
$461$	−17.9494	−0.835985	−0.417992	−	0.908451i	$-0.637266\pi$
$461$	−17.9494	−0.835985	−0.417992	+	0.908451i	$0.637266\pi$
$462$	2.23233i	0.103857i
$463$	35.5792	1.65350	0.826752	−	0.562567i	$-0.190186\pi$
$463$	35.5792	1.65350	0.826752	+	0.562567i	$0.190186\pi$
$464$	4.89584i	0.227284i
$465$	0.936899i	0.0434476i
$466$	10.3838i	0.481020i
$467$	−29.4411	−1.36237	−0.681185	−	0.732111i	$-0.738535\pi$
$467$	−29.4411	−1.36237	−0.681185	+	0.732111i	$0.738535\pi$
$468$	−18.7608	−0.867217
$469$	− 15.3016i	− 0.706564i
$470$	− 13.8238i	− 0.637643i
$471$	− 29.5666i	− 1.36236i
$472$	13.3169	0.612959
$473$	− 0.834873i	− 0.0383875i
$474$	18.3225	0.841578
$475$	−0.134144	−0.00615493
$476$	0	0
$477$	0.936692	0.0428882
$478$	−15.8561	−0.725240
$479$	16.7360i	0.764685i	0.924021	+	0.382343i	$0.124883\pi$
$479$	16.7360i	0.764685i	−0.924021	+	0.382343i	$0.875117\pi$
$480$	−33.5619	−1.53188
$481$	50.0529i	2.28221i
$482$	− 23.8327i	− 1.08555i
$483$	13.3384i	0.606917i
$484$	59.0654	2.68479
$485$	0.635381	0.0288512
$486$	16.9424i	0.768524i
$487$	23.4424i	1.06228i	0.847285	+	0.531138i	$0.178235\pi$
$487$	23.4424i	1.06228i	−0.847285	+	0.531138i	$0.821765\pi$
$488$	73.6604i	3.33445i
$489$	−28.3541	−1.28222
$490$	14.7484i	0.666267i
$491$	−25.4877	−1.15025	−0.575123	−	0.818067i	$-0.695046\pi$
$491$	−25.4877	−1.15025	−0.575123	+	0.818067i	$0.695046\pi$
$492$	13.7890	0.621655
$493$	0	0
$494$	−2.07465	−0.0933431
$495$	0.253731	0.0114043
$496$	− 8.99887i	− 0.404061i
$497$	−6.10091	−0.273663
$498$	18.5519i	0.831331i
$499$	28.7421i	1.28667i	0.765584	+	0.643336i	$0.222450\pi$
$499$	28.7421i	1.28667i	−0.765584	+	0.643336i	$0.777550\pi$
$500$	− 5.45623i	− 0.244010i
$501$	31.1677	1.39247
$502$	41.6211	1.85764
$503$	0.0102855i	0 0.000458606i	1.00000		0.000229303i	$7.29894e-5\pi$
$503$	0.0102855i	0 0.000458606i	−1.00000		0.000229303i	$0.999927\pi$
$504$	7.24449i	0.322695i
$505$	− 7.45004i	− 0.331522i
$506$	−7.78261	−0.345979
$507$	29.5147i	1.31079i
$508$	−97.2044	−4.31275
$509$	26.8066	1.18818	0.594091	−	0.804398i	$-0.297512\pi$
$509$	26.8066	1.18818	0.594091	+	0.804398i	$0.297512\pi$
$510$	0	0
$511$	3.66744	0.162238
$512$	41.9126	1.85229
$513$	0.748497i	0.0330469i
$514$	−39.6873	−1.75053
$515$	13.5860i	0.598669i
$516$	16.8596i	0.742202i
$517$	2.11591i	0.0930578i
$518$	30.5124	1.34064
$519$	29.5681	1.29790
$520$	− 53.4537i	− 2.34410i
$521$	− 10.1427i	− 0.444359i	−0.975006	−	0.222180i	$-0.928683\pi$
$521$	− 10.1427i	− 0.444359i	0.975006	−	0.222180i	$-0.0713172\pi$
$522$	0.546223i	0.0239075i
$523$	−16.7568	−0.732724	−0.366362	−	0.930472i	$-0.619397\pi$
$523$	−16.7568	−0.732724	−0.366362	+	0.930472i	$0.619397\pi$
$524$	− 24.4021i	− 1.06601i
$525$	1.95600	0.0853666
$526$	−51.9587	−2.26551
$527$	0	0
$528$	9.60627	0.418059
$529$	−23.5018	−1.02182
$530$	4.21322i	0.183010i
$531$	0.856609	0.0371736
$532$	0.925478i	0.0401245i
$533$	9.25318i	0.400800i
$534$	21.0653i	0.911583i
$535$	9.27421	0.400959
$536$	−114.208	−4.93303
$537$	− 30.6525i	− 1.32275i
$538$	61.9435i	2.67057i
$539$	− 2.25745i	− 0.0972351i
$540$	−30.4447	−1.31013
$541$	− 18.1364i	− 0.779745i	−0.920869	−	0.389873i	$-0.872519\pi$
$541$	− 18.1364i	− 0.779745i	0.920869	−	0.389873i	$-0.127481\pi$
$542$	−27.2177	−1.16910
$543$	13.7142	0.588532
$544$	0	0
$545$	−15.7066	−0.672796
$546$	30.2512	1.29463
$547$	− 22.5759i	− 0.965277i	−0.875820	−	0.482638i	$-0.839679\pi$
$547$	− 22.5759i	− 0.965277i	0.875820	−	0.482638i	$-0.160321\pi$
$548$	49.3743	2.10916
$549$	4.73821i	0.202222i
$550$	1.14127i	0.0486641i
$551$	0.0442016i	0.00188305i
$552$	99.5546	4.23733
$553$	5.48483	0.233239
$554$	− 31.9676i	− 1.35817i
$555$	13.6703i	0.580271i
$556$	− 25.6484i	− 1.08774i
$557$	5.97545	0.253188	0.126594	−	0.991955i	$-0.459595\pi$
$557$	5.97545	0.253188	0.126594	+	0.991955i	$0.459595\pi$
$558$	− 1.00399i	− 0.0425024i
$559$	−11.3137	−0.478520
$560$	−18.7872	−0.793905
$561$	0	0
$562$	3.23635	0.136517
$563$	3.56804	0.150375	0.0751874	−	0.997169i	$-0.476045\pi$
$563$	3.56804	0.150375	0.0751874	+	0.997169i	$0.476045\pi$
$564$	− 42.7292i	− 1.79922i
$565$	−1.24680	−0.0524534
$566$	− 12.5904i	− 0.529214i
$567$	− 8.61123i	− 0.361638i
$568$	45.5358i	1.91064i
$569$	44.1186	1.84955	0.924773	−	0.380518i	$-0.124254\pi$
$569$	44.1186	1.84955	0.924773	+	0.380518i	$0.124254\pi$
$570$	−0.566623	−0.0237332
$571$	− 12.5732i	− 0.526171i	−0.964773	−	0.263085i	$-0.915260\pi$
$571$	− 12.5732i	− 0.526171i	0.964773	−	0.263085i	$-0.0847401\pi$
$572$	12.9163i	0.540059i
$573$	16.4098i	0.685528i
$574$	5.64076	0.235441
$575$	6.81922i	0.284381i
$576$	17.9255	0.746896
$577$	−14.5344	−0.605075	−0.302538	−	0.953137i	$-0.597834\pi$
$577$	−14.5344	−0.605075	−0.302538	+	0.953137i	$0.597834\pi$
$578$	0	0
$579$	15.0442	0.625217
$580$	−1.79788	−0.0746529
$581$	5.55351i	0.230398i
$582$	2.68385	0.111249
$583$	− 0.644889i	− 0.0267086i
$584$	− 27.3730i	− 1.13270i
$585$	− 3.43842i	− 0.142161i
$586$	−8.45197	−0.349148
$587$	−12.2048	−0.503745	−0.251872	−	0.967760i	$-0.581046\pi$
$587$	−12.2048	−0.503745	−0.251872	+	0.967760i	$0.581046\pi$
$588$	45.5873i	1.87999i
$589$	− 0.0812453i	− 0.00334766i
$590$	3.85301i	0.158626i
$591$	36.8091	1.51412
$592$	− 131.302i	− 5.39649i
$593$	11.4292	0.469343	0.234671	−	0.972075i	$-0.424599\pi$
$593$	11.4292	0.469343	0.234671	+	0.972075i	$0.424599\pi$
$594$	6.36810	0.261286
$595$	0	0
$596$	−4.23376	−0.173421
$597$	−20.4312	−0.836195
$598$	105.465i	4.31280i
$599$	−27.2578	−1.11372	−0.556861	−	0.830606i	$-0.687994\pi$
$599$	−27.2578	−1.11372	−0.556861	+	0.830606i	$0.687994\pi$
$600$	− 14.5991i	− 0.596006i
$601$	− 11.2039i	− 0.457016i	−0.973542	−	0.228508i	$-0.926615\pi$
$601$	− 11.2039i	− 0.457016i	0.973542	−	0.228508i	$-0.0733848\pi$
$602$	6.89688i	0.281096i
$603$	−7.34644	−0.299170
$604$	12.4791	0.507766
$605$	10.8253i	0.440112i
$606$	− 31.4690i	− 1.27834i
$607$	40.0476i	1.62548i	0.582624	+	0.812742i	$0.302026\pi$
$607$	40.0476i	1.62548i	−0.582624	+	0.812742i	$0.697974\pi$
$608$	2.91039	0.118032
$609$	− 0.644519i	− 0.0261172i
$610$	−21.3124	−0.862912
$611$	28.6737	1.16001
$612$	0	0
$613$	29.1043	1.17551	0.587755	−	0.809039i	$-0.300012\pi$
$613$	29.1043	1.17551	0.587755	+	0.809039i	$0.300012\pi$
$614$	32.3268	1.30460
$615$	2.52720i	0.101907i
$616$	4.98765	0.200958
$617$	16.4653i	0.662869i	0.943478	+	0.331435i	$0.107533\pi$
$617$	16.4653i	0.662869i	−0.943478	+	0.331435i	$0.892467\pi$
$618$	57.3871i	2.30845i
$619$	− 7.61375i	− 0.306023i	−0.988224	−	0.153011i	$-0.951103\pi$
$619$	− 7.61375i	− 0.306023i	0.988224	−	0.153011i	$-0.0488971\pi$
$620$	3.30461	0.132717
$621$	38.0500	1.52689
$622$	64.0327i	2.56748i
$623$	6.30589i	0.252640i
$624$	− 130.179i	− 5.21132i
$625$	1.00000	0.0400000
$626$	− 75.3875i	− 3.01309i
$627$	0.0867292	0.00346363
$628$	−104.287	−4.16150
$629$	0	0
$630$	−2.09607	−0.0835093
$631$	37.1952	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$631$	37.1952	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$632$	− 40.9375i	− 1.62841i
$633$	−30.7624	−1.22270
$634$	86.9997i	3.45520i
$635$	− 17.8153i	− 0.706979i
$636$	13.0230i	0.516396i
$637$	−30.5916	−1.21208
$638$	0.376061	0.0148884
$639$	2.92910i	0.115873i
$640$	37.2362i	1.47189i
$641$	− 8.61170i	− 0.340142i	−0.985432	−	0.170071i	$-0.945600\pi$
$641$	− 8.61170i	− 0.340142i	0.985432	−	0.170071i	$-0.0543997\pi$
$642$	39.1743	1.54609
$643$	19.1230i	0.754136i	0.926186	+	0.377068i	$0.123068\pi$
$643$	19.1230i	0.754136i	−0.926186	+	0.377068i	$0.876932\pi$
$644$	47.0469	1.85391
$645$	−3.08997	−0.121668
$646$	0	0
$647$	−25.5972	−1.00633	−0.503164	−	0.864191i	$-0.667831\pi$
$647$	−25.5972	−1.00633	−0.503164	+	0.864191i	$0.667831\pi$
$648$	−64.2723	−2.52486
$649$	− 0.589754i	− 0.0231499i
$650$	15.4659	0.606623
$651$	1.18467i	0.0464307i
$652$	100.010i	3.91669i
$653$	− 8.67406i	− 0.339442i	−0.985492	−	0.169721i	$-0.945713\pi$
$653$	− 8.67406i	− 0.339442i	0.985492	−	0.169721i	$-0.0542867\pi$
$654$	−66.3446	−2.59428
$655$	4.47235	0.174749
$656$	− 24.2736i	− 0.947726i
$657$	− 1.76077i	− 0.0686942i
$658$	− 17.4795i	− 0.681424i
$659$	36.0328	1.40364	0.701819	−	0.712355i	$-0.252372\pi$
$659$	36.0328	1.40364	0.701819	+	0.712355i	$0.252372\pi$
$660$	3.52767i	0.137314i
$661$	9.40443	0.365790	0.182895	−	0.983132i	$-0.441453\pi$
$661$	9.40443	0.365790	0.182895	+	0.983132i	$0.441453\pi$
$662$	71.2001	2.76727
$663$	0	0
$664$	41.4502	1.60858
$665$	−0.169619	−0.00657753
$666$	− 14.6492i	− 0.567646i
$667$	2.24700	0.0870041
$668$	− 109.934i	− 4.25348i
$669$	− 9.84315i	− 0.380558i
$670$	− 33.0441i	− 1.27661i
$671$	3.26214	0.125933
$672$	−42.4375	−1.63706
$673$	− 4.55958i	− 0.175759i	−0.996131	−	0.0878794i	$-0.971991\pi$
$673$	− 4.55958i	− 0.175759i	0.996131	−	0.0878794i	$-0.0280090\pi$
$674$	45.1062i	1.73743i
$675$	− 5.57981i	− 0.214767i
$676$	104.104	4.00399
$677$	35.6013i	1.36827i	0.729355	+	0.684135i	$0.239820\pi$
$677$	35.6013i	1.36827i	−0.729355	+	0.684135i	$0.760180\pi$
$678$	−5.26650	−0.202259
$679$	0.803410	0.0308321
$680$	0	0
$681$	−41.0486	−1.57299
$682$	−0.691223	−0.0264683
$683$	11.9719i	0.458092i	0.973416	+	0.229046i	$0.0735606\pi$
$683$	11.9719i	0.458092i	−0.973416	+	0.229046i	$0.926439\pi$
$684$	0.444329	0.0169894
$685$	9.04916i	0.345751i
$686$	42.8179i	1.63479i
$687$	− 24.0475i	− 0.917470i
$688$	29.6790	1.13150
$689$	−8.73917	−0.332936
$690$	28.8044i	1.09657i
$691$	− 20.7951i	− 0.791082i	−0.918448	−	0.395541i	$-0.870557\pi$
$691$	− 20.7951i	− 0.791082i	0.918448	−	0.395541i	$-0.129443\pi$
$692$	− 104.292i	− 3.96460i
$693$	0.320831	0.0121874
$694$	55.4984i	2.10669i
$695$	4.70076	0.178310
$696$	−4.81055	−0.182343
$697$	0	0
$698$	−13.3405	−0.504946
$699$	−5.88249	−0.222496
$700$	− 6.89915i	− 0.260763i
$701$	−13.1645	−0.497215	−0.248607	−	0.968604i	$-0.579973\pi$
$701$	−13.1645	−0.497215	−0.248607	+	0.968604i	$0.579973\pi$
$702$	− 86.2969i	− 3.25707i
$703$	− 1.18545i	− 0.0447101i
$704$	− 12.3413i	− 0.465129i
$705$	7.83126	0.294942
$706$	61.9119	2.33009
$707$	− 9.42024i	− 0.354284i
$708$	11.9096i	0.447590i
$709$	− 20.3126i	− 0.762854i	−0.924399	−	0.381427i	$-0.875433\pi$
$709$	− 20.3126i	− 0.762854i	0.924399	−	0.381427i	$-0.124567\pi$
$710$	−13.1750	−0.494449
$711$	− 2.63331i	− 0.0987568i
$712$	47.0657	1.76386
$713$	−4.13012	−0.154674
$714$	0	0
$715$	−2.36726	−0.0885306
$716$	−108.117	−4.04053
$717$	− 8.98257i	− 0.335460i
$718$	−36.8108	−1.37377
$719$	− 29.1456i	− 1.08695i	−0.839426	−	0.543474i	$-0.817109\pi$
$719$	− 29.1456i	− 1.08695i	0.839426	−	0.543474i	$-0.182891\pi$
$720$	9.01991i	0.336152i
$721$	17.1788i	0.639773i
$722$	−51.8324	−1.92900
$723$	13.5014	0.502121
$724$	− 48.3724i	− 1.79775i
$725$	− 0.329510i	− 0.0122377i
$726$	45.7261i	1.69706i
$727$	−18.9928	−0.704402	−0.352201	−	0.935924i	$-0.614567\pi$
$727$	−18.9928	−0.704402	−0.352201	+	0.935924i	$0.614567\pi$
$728$	− 67.5898i	− 2.50505i
$729$	−30.0287	−1.11217
$730$	7.91990	0.293129
$731$	0	0
$732$	−65.8762	−2.43486
$733$	−32.5640	−1.20278	−0.601390	−	0.798956i	$-0.705386\pi$
$733$	−32.5640	−1.20278	−0.601390	+	0.798956i	$0.705386\pi$
$734$	− 5.21786i	− 0.192595i
$735$	−8.35509	−0.308182
$736$	− 147.951i	− 5.45353i
$737$	5.05784i	0.186308i
$738$	− 2.70818i	− 0.0996894i
$739$	−30.7452	−1.13098	−0.565489	−	0.824756i	$-0.691313\pi$
$739$	−30.7452	−1.13098	−0.565489	+	0.824756i	$0.691313\pi$
$740$	48.2176	1.77251
$741$	− 1.17531i	− 0.0431759i
$742$	5.32742i	0.195576i
$743$	9.77413i	0.358578i	0.983796	+	0.179289i	$0.0573798\pi$
$743$	9.77413i	0.358578i	−0.983796	+	0.179289i	$0.942620\pi$
$744$	8.84209	0.324167
$745$	− 0.775949i	− 0.0284286i
$746$	68.0898	2.49294
$747$	2.66629	0.0975543
$748$	0	0
$749$	11.7268	0.428489
$750$	4.22400	0.154239
$751$	− 12.9774i	− 0.473551i	−0.971564	−	0.236776i	$-0.923909\pi$
$751$	− 12.9774i	− 0.473551i	0.971564	−	0.236776i	$-0.0760906\pi$
$752$	−75.2189	−2.74295
$753$	23.5786i	0.859253i
$754$	− 5.09616i	− 0.185591i
$755$	2.28712i	0.0832369i
$756$	−38.4960	−1.40009
$757$	−35.5081	−1.29057	−0.645283	−	0.763944i	$-0.723260\pi$
$757$	−35.5081	−1.29057	−0.645283	+	0.763944i	$0.723260\pi$
$758$	− 45.3337i	− 1.64659i
$759$	− 4.40890i	− 0.160033i
$760$	1.26600i	0.0459225i
$761$	23.6745	0.858200	0.429100	−	0.903257i	$-0.358831\pi$
$761$	23.6745	0.858200	0.429100	+	0.903257i	$0.358831\pi$
$762$	− 75.2519i	− 2.72609i
$763$	−19.8603	−0.718990
$764$	57.8802	2.09403
$765$	0	0
$766$	54.8581	1.98210
$767$	−7.99201	−0.288575
$768$	65.9329i	2.37915i
$769$	5.83645	0.210468	0.105234	−	0.994447i	$-0.466441\pi$
$769$	5.83645	0.210468	0.105234	+	0.994447i	$0.466441\pi$
$770$	1.44309i	0.0520054i
$771$	− 22.4831i	− 0.809709i
$772$	− 53.0637i	− 1.90981i
$773$	30.6187	1.10128	0.550639	−	0.834743i	$-0.314384\pi$
$773$	30.6187	1.10128	0.550639	+	0.834743i	$0.314384\pi$
$774$	3.31125	0.119020
$775$	0.605659i	0.0217559i
$776$	− 5.99648i	− 0.215261i
$777$	17.2855i	0.620112i
$778$	60.8333	2.18098
$779$	− 0.219152i	− 0.00785193i
$780$	47.8050	1.71169
$781$	2.01661	0.0721600
$782$	0	0
$783$	−1.83860	−0.0657063
$784$	80.2502	2.86608
$785$	− 19.1134i	− 0.682186i
$786$	18.8912	0.673827
$787$	37.8438i	1.34898i	0.738282	+	0.674492i	$0.235637\pi$
$787$	37.8438i	1.34898i	−0.738282	+	0.674492i	$0.764363\pi$
$788$	− 129.832i	− 4.62509i
$789$	− 29.4350i	− 1.04791i
$790$	11.8446	0.421411
$791$	−1.57653	−0.0560548
$792$	− 2.39461i	− 0.0850888i
$793$	− 44.2067i	− 1.56982i
$794$	− 71.7327i	− 2.54570i
$795$	−2.38682	−0.0846516
$796$	72.0647i	2.55427i
$797$	7.46090	0.264279	0.132139	−	0.991231i	$-0.457815\pi$
$797$	7.46090	0.264279	0.132139	+	0.991231i	$0.457815\pi$
$798$	−0.716469	−0.0253627
$799$	0	0
$800$	−21.6961	−0.767073
$801$	3.02751	0.106972
$802$	104.192i	3.67914i
$803$	−1.21225	−0.0427793
$804$	− 102.139i	− 3.60216i
$805$	8.62260i	0.303907i
$806$	9.36707i	0.329941i
$807$	−35.0914	−1.23528
$808$	−70.3106	−2.47352
$809$	− 37.6824i	− 1.32484i	−0.749132	−	0.662421i	$-0.769529\pi$
$809$	− 37.6824i	− 1.32484i	0.749132	−	0.662421i	$-0.230471\pi$
$810$	− 18.5961i	− 0.653400i
$811$	6.87611i	0.241453i	0.992686	+	0.120726i	$0.0385224\pi$
$811$	6.87611i	0.241453i	−0.992686	+	0.120726i	$0.961478\pi$
$812$	−2.27334	−0.0797785
$813$	− 15.4190i	− 0.540769i
$814$	−10.0856	−0.353501
$815$	−18.3295	−0.642055
$816$	0	0
$817$	0.267954	0.00937452
$818$	−52.1534	−1.82350
$819$	− 4.34772i	− 0.151922i
$820$	8.91389	0.311287
$821$	23.5090i	0.820471i	0.911980	+	0.410236i	$0.134554\pi$
$821$	23.5090i	0.820471i	−0.911980	+	0.410236i	$0.865446\pi$
$822$	38.2237i	1.33320i
$823$	− 54.8707i	− 1.91267i	−0.292268	−	0.956336i	$-0.594410\pi$
$823$	− 54.8707i	− 1.91267i	0.292268	−	0.956336i	$-0.405590\pi$
$824$	128.219	4.46672
$825$	−0.646540	−0.0225096
$826$	4.87195i	0.169517i
$827$	17.6179i	0.612634i	0.951930	+	0.306317i	$0.0990967\pi$
$827$	17.6179i	0.612634i	−0.951930	+	0.306317i	$0.900903\pi$
$828$	− 22.5876i	− 0.784973i
$829$	11.9207	0.414022	0.207011	−	0.978339i	$-0.433626\pi$
$829$	11.9207	0.414022	0.207011	+	0.978339i	$0.433626\pi$
$830$	11.9929i	0.416279i
$831$	18.1098	0.628223
$832$	−167.242	−5.79806
$833$	0	0
$834$	19.8560	0.687558
$835$	20.1484	0.697263
$836$	− 0.305910i	− 0.0105801i
$837$	3.37946	0.116811
$838$	91.6143i	3.16476i
$839$	42.3385i	1.46169i	0.682545	+	0.730844i	$0.260873\pi$
$839$	42.3385i	1.46169i	−0.682545	+	0.730844i	$0.739127\pi$
$840$	− 18.4599i	− 0.636928i
$841$	28.8914	0.996256
$842$	−51.7166	−1.78227
$843$	1.83341i	0.0631461i
$844$	108.505i	3.73489i
$845$	19.0798i	0.656366i
$846$	−8.39207	−0.288525
$847$	13.6881i	0.470329i
$848$	22.9252	0.787256
$849$	7.13254	0.244788
$850$	0	0
$851$	−60.2626	−2.06578
$852$	−40.7238	−1.39517
$853$	− 33.1729i	− 1.13582i	−0.823091	−	0.567909i	$-0.807753\pi$
$853$	− 33.1729i	− 1.13582i	0.823091	−	0.567909i	$-0.192247\pi$
$854$	−26.9485	−0.922159
$855$	0.0814353i	0.00278503i
$856$	− 87.5264i	− 2.99159i
$857$	15.3710i	0.525062i	0.964924	+	0.262531i	$0.0845572\pi$
$857$	15.3710i	0.525062i	−0.964924	+	0.262531i	$0.915443\pi$
$858$	−9.99932	−0.341371
$859$	42.8054	1.46050	0.730250	−	0.683180i	$-0.239404\pi$
$859$	42.8054	1.46050	0.730250	+	0.683180i	$0.239404\pi$
$860$	10.8989i	0.371649i
$861$	3.19553i	0.108903i
$862$	66.5917i	2.26812i
$863$	31.3841	1.06833	0.534163	−	0.845382i	$-0.320627\pi$
$863$	31.3841	1.06833	0.534163	+	0.845382i	$0.320627\pi$
$864$	121.060i	4.11855i
$865$	19.1144	0.649907
$866$	−26.4630	−0.899250
$867$	0	0
$868$	4.17853	0.141829
$869$	−1.81297	−0.0615007
$870$	− 1.39185i	− 0.0471881i
$871$	68.5410	2.32242
$872$	148.233i	5.01979i
$873$	− 0.385724i	− 0.0130548i
$874$	− 2.49784i	− 0.0844907i
$875$	1.26445	0.0427464
$876$	24.4803	0.827114
$877$	− 29.2384i	− 0.987310i	−0.869658	−	0.493655i	$-0.835661\pi$
$877$	− 29.2384i	− 0.987310i	0.869658	−	0.493655i	$-0.164339\pi$
$878$	8.80217i	0.297059i
$879$	− 4.78810i	− 0.161499i
$880$	6.20998	0.209338
$881$	− 22.9441i	− 0.773006i	−0.922288	−	0.386503i	$-0.873683\pi$
$881$	− 22.9441i	− 0.773006i	0.922288	−	0.386503i	$-0.126317\pi$
$882$	8.95341	0.301477
$883$	−21.1206	−0.710766	−0.355383	−	0.934721i	$-0.615649\pi$
$883$	−21.1206	−0.710766	−0.355383	+	0.934721i	$0.615649\pi$
$884$	0	0
$885$	−2.18275	−0.0733724
$886$	−47.9559	−1.61111
$887$	17.9732i	0.603482i	0.953390	+	0.301741i	$0.0975677\pi$
$887$	17.9732i	0.603482i	−0.953390	+	0.301741i	$0.902432\pi$
$888$	129.015	4.32945
$889$	− 22.5267i	− 0.755520i
$890$	13.6177i	0.456465i
$891$	2.84638i	0.0953573i
$892$	−34.7186	−1.16246
$893$	−0.679106	−0.0227254
$894$	− 3.27761i	− 0.109620i
$895$	− 19.8154i	− 0.662354i
$896$	47.0835i	1.57295i
$897$	−59.7469	−1.99489
$898$	− 50.5799i	− 1.68787i
$899$	0.199570	0.00665605
$900$	−3.31234	−0.110411
$901$	0	0
$902$	−1.86451	−0.0620815
$903$	−3.90713	−0.130021
$904$	11.7668i	0.391359i
$905$	8.86555	0.294701
$906$	9.66081i	0.320959i
$907$	55.8990i	1.85610i	0.372461	+	0.928048i	$0.378514\pi$
$907$	55.8990i	1.85610i	−0.372461	+	0.928048i	$0.621486\pi$
$908$	144.786i	4.80489i
$909$	−4.52273	−0.150010
$910$	19.5559	0.648273
$911$	0.561306i	0.0185969i	0.999957	+	0.00929845i	$0.00295983\pi$
$911$	0.561306i	0.0185969i	−0.999957	+	0.00929845i	$0.997040\pi$
$912$	3.08315i	0.102093i
$913$	− 1.83567i	− 0.0607519i
$914$	−40.1610	−1.32841
$915$	− 12.0736i	− 0.399140i
$916$	−84.8200	−2.80253
$917$	5.65508	0.186747
$918$	0	0
$919$	4.29583	0.141706	0.0708531	−	0.997487i	$-0.477428\pi$
$919$	4.29583	0.141706	0.0708531	+	0.997487i	$0.477428\pi$
$920$	64.3572	2.12179
$921$	18.3133i	0.603445i
$922$	−49.0127	−1.61415
$923$	− 27.3280i	− 0.899511i
$924$	4.46058i	0.146742i
$925$	8.83716i	0.290564i
$926$	97.1528	3.19264
$927$	8.24769	0.270890
$928$	7.14907i	0.234680i
$929$	− 9.55355i	− 0.313442i	−0.987643	−	0.156721i	$-0.949908\pi$
$929$	− 9.55355i	− 0.313442i	0.987643	−	0.156721i	$-0.0500923\pi$
$930$	2.55831i	0.0838901i
$931$	0.724531	0.0237455
$932$	20.7486i	0.679643i
$933$	−36.2750	−1.18759
$934$	−80.3921	−2.63051
$935$	0	0
$936$	−32.4504	−1.06068
$937$	55.7449	1.82111	0.910553	−	0.413392i	$-0.135656\pi$
$937$	55.7449	1.82111	0.910553	+	0.413392i	$0.135656\pi$
$938$	− 41.7828i	− 1.36426i
$939$	42.7075	1.39371
$940$	− 27.6223i	− 0.900940i
$941$	− 29.4430i	− 0.959813i	−0.877320	−	0.479906i	$-0.840671\pi$
$941$	− 29.4430i	− 0.959813i	0.877320	−	0.479906i	$-0.159329\pi$
$942$	− 80.7349i	− 2.63049i
$943$	−11.1406	−0.362789
$944$	20.9652	0.682360
$945$	− 7.05542i	− 0.229513i
$946$	− 2.27971i	− 0.0741199i
$947$	31.5924i	1.02662i	0.858205	+	0.513308i	$0.171580\pi$
$947$	31.5924i	1.02662i	−0.858205	+	0.513308i	$0.828420\pi$
$948$	36.6114	1.18908
$949$	16.4277i	0.533265i
$950$	−0.366294	−0.0118841
$951$	−49.2859	−1.59821
$952$	0	0
$953$	−18.4486	−0.597610	−0.298805	−	0.954314i	$-0.596588\pi$
$953$	−18.4486	−0.597610	−0.298805	+	0.954314i	$0.596588\pi$
$954$	2.55774	0.0828099
$955$	10.6081i	0.343270i
$956$	−31.6832	−1.02471
$957$	0.213041i	0.00688664i
$958$	45.6994i	1.47648i
$959$	11.4422i	0.369490i
$960$	−45.6765	−1.47420
$961$	30.6332	0.988167
$962$	136.675i	4.40657i
$963$	− 5.63014i	− 0.181429i
$964$	− 47.6218i	− 1.53379i
$965$	9.72535	0.313070
$966$	36.4219i	1.17185i
$967$	38.3638	1.23370	0.616848	−	0.787083i	$-0.288409\pi$
$967$	38.3638	1.23370	0.616848	+	0.787083i	$0.288409\pi$
$968$	102.165	3.28371
$969$	0	0
$970$	1.73498	0.0557067
$971$	52.5632	1.68683	0.843417	−	0.537260i	$-0.180541\pi$
$971$	52.5632	1.68683	0.843417	+	0.537260i	$0.180541\pi$
$972$	33.8539i	1.08586i
$973$	5.94390	0.190553
$974$	64.0120i	2.05108i
$975$	8.76154i	0.280594i
$976$	115.966i	3.71199i
$977$	34.3771	1.09982	0.549911	−	0.835224i	$-0.314662\pi$
$977$	34.3771	1.09982	0.549911	+	0.835224i	$0.314662\pi$
$978$	−77.4239	−2.47574
$979$	− 2.08436i	− 0.0666166i
$980$	29.4699i	0.941382i
$981$	9.53507i	0.304431i
$982$	−69.5971	−2.22093
$983$	28.7282i	0.916288i	0.888878	+	0.458144i	$0.151486\pi$
$983$	28.7282i	0.916288i	−0.888878	+	0.458144i	$0.848514\pi$
$984$	23.8507	0.760333
$985$	23.7953	0.758180
$986$	0	0
$987$	9.90228	0.315193
$988$	−4.14552	−0.131886
$989$	− 13.6215i	− 0.433138i
$990$	0.692839	0.0220199
$991$	− 47.8330i	− 1.51946i	−0.650236	−	0.759732i	$-0.725330\pi$
$991$	− 47.8330i	− 1.51946i	0.650236	−	0.759732i	$-0.274670\pi$
$992$	− 13.1404i	− 0.417209i
$993$	40.3353i	1.28000i
$994$	−16.6592	−0.528398
$995$	−13.2078	−0.418715
$996$	37.0699i	1.17460i
$997$	− 7.81193i	− 0.247406i	−0.992319	−	0.123703i	$-0.960523\pi$
$997$	− 7.81193i	− 0.247406i	0.992319	−	0.123703i	$-0.0394771\pi$
$998$	78.4833i	2.48435i
$999$	49.3097	1.56009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.23		24
17.4	even	4		1445.2.a.p.1.1		12
17.5	odd	16		85.2.l.a.26.1	✓	24
17.10	odd	16		85.2.l.a.36.1	yes	24
17.13	even	4		1445.2.a.q.1.1		12
17.16	even	2	inner	1445.2.d.j.866.24		24
51.5	even	16		765.2.be.b.451.6		24
51.44	even	16		765.2.be.b.631.6		24
85.4	even	4		7225.2.a.bs.1.12		12
85.22	even	16		425.2.n.f.349.1		24
85.27	even	16		425.2.n.c.274.6		24
85.39	odd	16		425.2.m.b.26.6		24
85.44	odd	16		425.2.m.b.376.6		24
85.64	even	4		7225.2.a.bq.1.12		12
85.73	even	16		425.2.n.c.349.6		24
85.78	even	16		425.2.n.f.274.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.1	✓	24	17.5	odd	16
85.2.l.a.36.1	yes	24	17.10	odd	16
425.2.m.b.26.6		24	85.39	odd	16
425.2.m.b.376.6		24	85.44	odd	16
425.2.n.c.274.6		24	85.27	even	16
425.2.n.c.349.6		24	85.73	even	16
425.2.n.f.274.1		24	85.78	even	16
425.2.n.f.349.1		24	85.22	even	16
765.2.be.b.451.6		24	51.5	even	16
765.2.be.b.631.6		24	51.44	even	16
1445.2.a.p.1.1		12	17.4	even	4
1445.2.a.q.1.1		12	17.13	even	4
1445.2.d.j.866.23		24	1.1	even	1	trivial
1445.2.d.j.866.24		24	17.16	even	2	inner
7225.2.a.bq.1.12		12	85.64	even	4
7225.2.a.bs.1.12		12	85.4	even	4

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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.73061 q^{2} +1.54691i q^{3} +5.45623 q^{4} +1.00000i q^{5} +4.22400i q^{6} +1.26445i q^{7} +9.43761 q^{8} +0.607075 q^{9} +O(q^{10})\)	\(q+2.73061 q^{2} +1.54691i q^{3} +5.45623 q^{4} +1.00000i q^{5} +4.22400i q^{6} +1.26445i q^{7} +9.43761 q^{8} +0.607075 q^{9} +2.73061i q^{10} -0.417956i q^{11} +8.44028i q^{12} -5.66390 q^{13} +3.45273i q^{14} -1.54691 q^{15} +14.8580 q^{16} +1.65769 q^{18} +0.134144 q^{19} +5.45623i q^{20} -1.95600 q^{21} -1.14127i q^{22} -6.81922i q^{23} +14.5991i q^{24} -1.00000 q^{25} -15.4659 q^{26} +5.57981i q^{27} +6.89915i q^{28} +0.329510i q^{29} -4.22400 q^{30} -0.605659i q^{31} +21.6961 q^{32} +0.646540 q^{33} -1.26445 q^{35} +3.31234 q^{36} -8.83716i q^{37} +0.366294 q^{38} -8.76154i q^{39} +9.43761i q^{40} -1.63371i q^{41} -5.34106 q^{42} +1.99751 q^{43} -2.28046i q^{44} +0.607075i q^{45} -18.6206i q^{46} -5.06253 q^{47} +22.9839i q^{48} +5.40115 q^{49} -2.73061 q^{50} -30.9036 q^{52} +1.54296 q^{53} +15.2363i q^{54} +0.417956 q^{55} +11.9334i q^{56} +0.207508i q^{57} +0.899762i q^{58} +1.41104 q^{59} -8.44028 q^{60} +7.80498i q^{61} -1.65382i q^{62} +0.767619i q^{63} +29.5276 q^{64} -5.66390i q^{65} +1.76545 q^{66} -12.1014 q^{67} +10.5487 q^{69} -3.45273 q^{70} +4.82493i q^{71} +5.72934 q^{72} -2.90042i q^{73} -24.1308i q^{74} -1.54691i q^{75} +0.731919 q^{76} +0.528486 q^{77} -23.9243i q^{78} -4.33770i q^{79} +14.8580i q^{80} -6.81023 q^{81} -4.46102i q^{82} +4.39202 q^{83} -10.6724 q^{84} +5.45443 q^{86} -0.509721 q^{87} -3.94451i q^{88} +4.98704 q^{89} +1.65769i q^{90} -7.16175i q^{91} -37.2072i q^{92} +0.936899 q^{93} -13.8238 q^{94} +0.134144i q^{95} +33.5619i q^{96} -0.635381i q^{97} +14.7484 q^{98} -0.253731i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43} - 64 q^{47} - 40 q^{49} - 8 q^{50} - 48 q^{52} - 32 q^{55} - 16 q^{59} + 32 q^{60} + 72 q^{64} - 80 q^{66} - 16 q^{67} + 96 q^{69} - 32 q^{70} + 24 q^{72} - 32 q^{76} - 48 q^{77} + 72 q^{81} + 80 q^{83} + 64 q^{84} - 16 q^{86} + 64 q^{87} + 16 q^{89} - 48 q^{93} + 32 q^{94} - 120 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

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