LMFDB - Embedded newform 1445.2.d.j.866.3

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			866.3
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04505 q^{2} +3.19566i q^{3} +2.18224 q^{4} -1.00000i q^{5} -6.53528i q^{6} +1.17743i q^{7} -0.372688 q^{8} -7.21221 q^{9} +O(q^{10})$	\(q-2.04505 q^{2} +3.19566i q^{3} +2.18224 q^{4} -1.00000i q^{5} -6.53528i q^{6} +1.17743i q^{7} -0.372688 q^{8} -7.21221 q^{9} +2.04505i q^{10} -4.92251i q^{11} +6.97368i q^{12} -2.46296 q^{13} -2.40791i q^{14} +3.19566 q^{15} -3.60231 q^{16} +14.7494 q^{18} -2.04173 q^{19} -2.18224i q^{20} -3.76267 q^{21} +10.0668i q^{22} -0.119023i q^{23} -1.19098i q^{24} -1.00000 q^{25} +5.03689 q^{26} -13.4608i q^{27} +2.56944i q^{28} +1.06541i q^{29} -6.53528 q^{30} +2.79577i q^{31} +8.11229 q^{32} +15.7307 q^{33} +1.17743 q^{35} -15.7388 q^{36} -2.31477i q^{37} +4.17544 q^{38} -7.87078i q^{39} +0.372688i q^{40} -0.717574i q^{41} +7.69485 q^{42} +10.0958 q^{43} -10.7421i q^{44} +7.21221i q^{45} +0.243408i q^{46} -3.39482 q^{47} -11.5117i q^{48} +5.61365 q^{49} +2.04505 q^{50} -5.37477 q^{52} +13.9241 q^{53} +27.5280i q^{54} -4.92251 q^{55} -0.438815i q^{56} -6.52466i q^{57} -2.17882i q^{58} -1.51711 q^{59} +6.97368 q^{60} -8.08120i q^{61} -5.71749i q^{62} -8.49190i q^{63} -9.38544 q^{64} +2.46296i q^{65} -32.1700 q^{66} -4.92534 q^{67} +0.380355 q^{69} -2.40791 q^{70} -6.63635i q^{71} +2.68790 q^{72} -3.66716i q^{73} +4.73382i q^{74} -3.19566i q^{75} -4.45554 q^{76} +5.79593 q^{77} +16.0962i q^{78} -8.18051i q^{79} +3.60231i q^{80} +21.3794 q^{81} +1.46748i q^{82} +6.08874 q^{83} -8.21104 q^{84} -20.6464 q^{86} -3.40468 q^{87} +1.83456i q^{88} +8.46170 q^{89} -14.7494i q^{90} -2.89997i q^{91} -0.259736i q^{92} -8.93431 q^{93} +6.94259 q^{94} +2.04173i q^{95} +25.9241i q^{96} -4.48946i q^{97} -11.4802 q^{98} +35.5022i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.04505	−1.44607	−0.723035	−	0.690811i	$-0.757254\pi$
$2$	−2.04505	−1.44607	−0.723035	+	0.690811i	$0.757254\pi$
$3$	3.19566i	1.84501i	0.385982	+	0.922506i	$0.373863\pi$
$3$	3.19566i	1.84501i	−0.385982	+	0.922506i	$0.626137\pi$
$4$	2.18224	1.09112
$5$	− 1.00000i	− 0.447214i
$5$	− 1.00000i	− 0.447214i
$6$	− 6.53528i	− 2.66802i
$7$	1.17743i	0.445028i	0.974930	+	0.222514i	$0.0714262\pi$
$7$	1.17743i	0.445028i	−0.974930	+	0.222514i	$0.928574\pi$
$8$	−0.372688	−0.131765
$9$	−7.21221	−2.40407
$10$	2.04505i	0.646702i
$11$	− 4.92251i	− 1.48419i	−0.670293	−	0.742097i	$-0.733831\pi$
$11$	− 4.92251i	− 1.48419i	0.670293	−	0.742097i	$-0.266169\pi$
$12$	6.97368i	2.01313i
$13$	−2.46296	−0.683103	−0.341551	−	0.939863i	$-0.610952\pi$
$13$	−2.46296	−0.683103	−0.341551	+	0.939863i	$0.610952\pi$
$14$	− 2.40791i	− 0.643541i
$15$	3.19566	0.825115
$16$	−3.60231	−0.900578
$17$	0	0
$17$	0	0
$18$	14.7494	3.47646
$19$	−2.04173	−0.468405	−0.234202	−	0.972188i	$-0.575248\pi$
$19$	−2.04173	−0.468405	−0.234202	+	0.972188i	$0.575248\pi$
$20$	− 2.18224i	− 0.487963i
$21$	−3.76267	−0.821082
$22$	10.0668i	2.14625i
$23$	− 0.119023i	− 0.0248179i	−0.999923	−	0.0124090i	$-0.996050\pi$
$23$	− 0.119023i	− 0.0248179i	0.999923	−	0.0124090i	$-0.00395000\pi$
$24$	− 1.19098i	− 0.243108i
$25$	−1.00000	−0.200000
$26$	5.03689	0.987815
$27$	− 13.4608i	− 2.59053i
$28$	2.56944i	0.485578i
$29$	1.06541i	0.197841i	0.995095	+	0.0989207i	$0.0315390\pi$
$29$	1.06541i	0.197841i	−0.995095	+	0.0989207i	$0.968461\pi$
$30$	−6.53528	−1.19317
$31$	2.79577i	0.502135i	0.967970	+	0.251067i	$0.0807816\pi$
$31$	2.79577i	0.502135i	−0.967970	+	0.251067i	$0.919218\pi$
$32$	8.11229	1.43406
$33$	15.7307	2.73836
$34$	0	0
$35$	1.17743	0.199022
$36$	−15.7388	−2.62313
$37$	− 2.31477i	− 0.380545i	−0.981731	−	0.190273i	$-0.939063\pi$
$37$	− 2.31477i	− 0.380545i	0.981731	−	0.190273i	$-0.0609372\pi$
$38$	4.17544	0.677346
$39$	− 7.87078i	− 1.26033i
$40$	0.372688i	0.0589271i
$41$	− 0.717574i	− 0.112066i	−0.998429	−	0.0560331i	$-0.982155\pi$
$41$	− 0.717574i	− 0.112066i	0.998429	−	0.0560331i	$-0.0178452\pi$
$42$	7.69485	1.18734
$43$	10.0958	1.53960	0.769798	−	0.638288i	$-0.220357\pi$
$43$	10.0958	1.53960	0.769798	+	0.638288i	$0.220357\pi$
$44$	− 10.7421i	− 1.61943i
$45$	7.21221i	1.07513i
$46$	0.243408i	0.0358885i
$47$	−3.39482	−0.495186	−0.247593	−	0.968864i	$-0.579640\pi$
$47$	−3.39482	−0.495186	−0.247593	+	0.968864i	$0.579640\pi$
$48$	− 11.5117i	− 1.66158i
$49$	5.61365	0.801950
$50$	2.04505	0.289214
$51$	0	0
$52$	−5.37477	−0.745347
$53$	13.9241	1.91262	0.956310	−	0.292355i	$-0.0944390\pi$
$53$	13.9241	1.91262	0.956310	+	0.292355i	$0.0944390\pi$
$54$	27.5280i	3.74609i
$55$	−4.92251	−0.663752
$56$	− 0.438815i	− 0.0586391i
$57$	− 6.52466i	− 0.864213i
$58$	− 2.17882i	− 0.286093i
$59$	−1.51711	−0.197511	−0.0987555	−	0.995112i	$-0.531486\pi$
$59$	−1.51711	−0.197511	−0.0987555	+	0.995112i	$0.531486\pi$
$60$	6.97368	0.900299
$61$	− 8.08120i	− 1.03469i	−0.855776	−	0.517346i	$-0.826920\pi$
$61$	− 8.08120i	− 1.03469i	0.855776	−	0.517346i	$-0.173080\pi$
$62$	− 5.71749i	− 0.726122i
$63$	− 8.49190i	− 1.06988i
$64$	−9.38544	−1.17318
$65$	2.46296i	0.305493i
$66$	−32.1700	−3.95986
$67$	−4.92534	−0.601726	−0.300863	−	0.953667i	$-0.597275\pi$
$67$	−4.92534	−0.601726	−0.300863	+	0.953667i	$0.597275\pi$
$68$	0	0
$69$	0.380355	0.0457894
$70$	−2.40791	−0.287800
$71$	− 6.63635i	− 0.787590i	−0.919198	−	0.393795i	$-0.871162\pi$
$71$	− 6.63635i	− 0.787590i	0.919198	−	0.393795i	$-0.128838\pi$
$72$	2.68790	0.316773
$73$	− 3.66716i	− 0.429209i	−0.976701	−	0.214605i	$-0.931154\pi$
$73$	− 3.66716i	− 0.429209i	0.976701	−	0.214605i	$-0.0688463\pi$
$74$	4.73382i	0.550295i
$75$	− 3.19566i	− 0.369003i
$76$	−4.45554	−0.511086
$77$	5.79593	0.660507
$78$	16.0962i	1.82253i
$79$	− 8.18051i	− 0.920380i	−0.887821	−	0.460190i	$-0.847781\pi$
$79$	− 8.18051i	− 0.920380i	0.887821	−	0.460190i	$-0.152219\pi$
$80$	3.60231i	0.402751i
$81$	21.3794	2.37549
$82$	1.46748i	0.162056i
$83$	6.08874	0.668326	0.334163	−	0.942515i	$-0.391546\pi$
$83$	6.08874	0.668326	0.334163	+	0.942515i	$0.391546\pi$
$84$	−8.21104	−0.895898
$85$	0	0
$86$	−20.6464	−2.22636
$87$	−3.40468	−0.365020
$88$	1.83456i	0.195565i
$89$	8.46170	0.896938	0.448469	−	0.893798i	$-0.351969\pi$
$89$	8.46170	0.896938	0.448469	+	0.893798i	$0.351969\pi$
$90$	− 14.7494i	− 1.55472i
$91$	− 2.89997i	− 0.304000i
$92$	− 0.259736i	− 0.0270793i
$93$	−8.93431	−0.926445
$94$	6.94259	0.716074
$95$	2.04173i	0.209477i
$96$	25.9241i	2.64587i
$97$	− 4.48946i	− 0.455836i	−0.973680	−	0.227918i	$-0.926808\pi$
$97$	− 4.48946i	− 0.455836i	0.973680	−	0.227918i	$-0.0731918\pi$
$98$	−11.4802	−1.15968
$99$	35.5022i	3.56811i
$100$	−2.18224	−0.218224
$101$	17.7855	1.76972	0.884861	−	0.465854i	$-0.154253\pi$
$101$	17.7855	1.76972	0.884861	+	0.465854i	$0.154253\pi$
$102$	0	0
$103$	−11.3352	−1.11689	−0.558445	−	0.829542i	$-0.688602\pi$
$103$	−11.3352	−1.11689	−0.558445	+	0.829542i	$0.688602\pi$
$104$	0.917916	0.0900091
$105$	3.76267i	0.367199i
$106$	−28.4755	−2.76578
$107$	12.8865i	1.24579i	0.782307	+	0.622893i	$0.214043\pi$
$107$	12.8865i	1.24579i	−0.782307	+	0.622893i	$0.785957\pi$
$108$	− 29.3747i	− 2.82658i
$109$	11.3210i	1.08436i	0.840263	+	0.542179i	$0.182401\pi$
$109$	11.3210i	1.08436i	−0.840263	+	0.542179i	$0.817599\pi$
$110$	10.0668	0.959832
$111$	7.39720	0.702111
$112$	− 4.24148i	− 0.400782i
$113$	5.85089i	0.550405i	0.961386	+	0.275203i	$0.0887449\pi$
$113$	5.85089i	0.550405i	−0.961386	+	0.275203i	$0.911255\pi$
$114$	13.3433i	1.24971i
$115$	−0.119023	−0.0110989
$116$	2.32498i	0.215869i
$117$	17.7634	1.64223
$118$	3.10257	0.285615
$119$	0	0
$120$	−1.19098	−0.108721
$121$	−13.2311	−1.20283
$122$	16.5265i	1.49624i
$123$	2.29312	0.206764
$124$	6.10103i	0.547889i
$125$	1.00000i	0.0894427i
$126$	17.3664i	1.54712i
$127$	6.80398	0.603755	0.301878	−	0.953347i	$-0.402387\pi$
$127$	6.80398	0.603755	0.301878	+	0.953347i	$0.402387\pi$
$128$	2.96912	0.262436
$129$	32.2627i	2.84057i
$130$	− 5.03689i	− 0.441764i
$131$	1.90025i	0.166026i	0.996548	+	0.0830128i	$0.0264542\pi$
$131$	1.90025i	0.166026i	−0.996548	+	0.0830128i	$0.973546\pi$
$132$	34.3281	2.98787
$133$	− 2.40400i	− 0.208453i
$134$	10.0726	0.870138
$135$	−13.4608	−1.15852
$136$	0	0
$137$	19.3637	1.65435	0.827174	−	0.561946i	$-0.189947\pi$
$137$	19.3637	1.65435	0.827174	+	0.561946i	$0.189947\pi$
$138$	−0.777847	−0.0662147
$139$	− 8.27692i	− 0.702039i	−0.936368	−	0.351020i	$-0.885835\pi$
$139$	− 8.27692i	− 0.702039i	0.936368	−	0.351020i	$-0.114165\pi$
$140$	2.56944	0.217157
$141$	− 10.8487i	− 0.913624i
$142$	13.5717i	1.13891i
$143$	12.1240i	1.01386i
$144$	25.9806	2.16505
$145$	1.06541	0.0884773
$146$	7.49954i	0.620666i
$147$	17.9393i	1.47961i
$148$	− 5.05137i	− 0.415220i
$149$	4.93485	0.404279	0.202139	−	0.979357i	$-0.435211\pi$
$149$	4.93485	0.404279	0.202139	+	0.979357i	$0.435211\pi$
$150$	6.53528i	0.533604i
$151$	0.712752	0.0580029	0.0290015	−	0.999579i	$-0.490767\pi$
$151$	0.712752	0.0580029	0.0290015	+	0.999579i	$0.490767\pi$
$152$	0.760928	0.0617194
$153$	0	0
$154$	−11.8530	−0.955140
$155$	2.79577	0.224562
$156$	− 17.1759i	− 1.37517i
$157$	5.88566	0.469727	0.234863	−	0.972028i	$-0.424536\pi$
$157$	5.88566	0.469727	0.234863	+	0.972028i	$0.424536\pi$
$158$	16.7296i	1.33093i
$159$	44.4966i	3.52881i
$160$	− 8.11229i	− 0.641333i
$161$	0.140141	0.0110447
$162$	−43.7220	−3.43512
$163$	− 5.89619i	− 0.461826i	−0.972974	−	0.230913i	$-0.925829\pi$
$163$	− 5.89619i	− 0.461826i	0.972974	−	0.230913i	$-0.0741712\pi$
$164$	− 1.56592i	− 0.122278i
$165$	− 15.7307i	− 1.22463i
$166$	−12.4518	−0.966446
$167$	− 10.7684i	− 0.833284i	−0.909071	−	0.416642i	$-0.863207\pi$
$167$	− 10.7684i	− 0.833284i	0.909071	−	0.416642i	$-0.136793\pi$
$168$	1.40230	0.108190
$169$	−6.93382	−0.533371
$170$	0	0
$171$	14.7254	1.12608
$172$	22.0315	1.67988
$173$	− 9.69698i	− 0.737248i	−0.929579	−	0.368624i	$-0.879829\pi$
$173$	− 9.69698i	− 0.737248i	0.929579	−	0.368624i	$-0.120171\pi$
$174$	6.96274	0.527844
$175$	− 1.17743i	− 0.0890055i
$176$	17.7324i	1.33663i
$177$	− 4.84816i	− 0.364410i
$178$	−17.3046	−1.29704
$179$	−15.7156	−1.17464	−0.587319	−	0.809356i	$-0.699817\pi$
$179$	−15.7156	−1.17464	−0.587319	+	0.809356i	$0.699817\pi$
$180$	15.7388i	1.17310i
$181$	3.98916i	0.296512i	0.988949	+	0.148256i	$0.0473659\pi$
$181$	3.98916i	0.296512i	−0.988949	+	0.148256i	$0.952634\pi$
$182$	5.93059i	0.439605i
$183$	25.8247	1.90902
$184$	0.0443583i	0.00327014i
$185$	−2.31477	−0.170185
$186$	18.2711	1.33970
$187$	0	0
$188$	−7.40832	−0.540307
$189$	15.8492	1.15286
$190$	− 4.17544i	− 0.302919i
$191$	19.2007	1.38931	0.694655	−	0.719343i	$-0.255557\pi$
$191$	19.2007	1.38931	0.694655	+	0.719343i	$0.255557\pi$
$192$	− 29.9926i	− 2.16453i
$193$	− 11.7595i	− 0.846466i	−0.906021	−	0.423233i	$-0.860895\pi$
$193$	− 11.7595i	− 0.846466i	0.906021	−	0.423233i	$-0.139105\pi$
$194$	9.18118i	0.659170i
$195$	−7.87078	−0.563638
$196$	12.2503	0.875024
$197$	− 19.1390i	− 1.36360i	−0.731540	−	0.681799i	$-0.761198\pi$
$197$	− 19.1390i	− 1.36360i	0.731540	−	0.681799i	$-0.238802\pi$
$198$	− 72.6039i	− 5.15974i
$199$	10.4492i	0.740723i	0.928888	+	0.370362i	$0.120766\pi$
$199$	10.4492i	0.740723i	−0.928888	+	0.370362i	$0.879234\pi$
$200$	0.372688	0.0263530
$201$	− 15.7397i	− 1.11019i
$202$	−36.3723	−2.55914
$203$	−1.25445	−0.0880449
$204$	0	0
$205$	−0.717574	−0.0501176
$206$	23.1811	1.61510
$207$	0.858417i	0.0596641i
$208$	8.87236	0.615187
$209$	10.0504i	0.695204i
$210$	− 7.69485i	− 0.530995i
$211$	− 21.7830i	− 1.49960i	−0.661663	−	0.749801i	$-0.730149\pi$
$211$	− 21.7830i	− 1.49960i	0.661663	−	0.749801i	$-0.269851\pi$
$212$	30.3857	2.08690
$213$	21.2075	1.45311
$214$	− 26.3536i	− 1.80149i
$215$	− 10.0958i	− 0.688528i
$216$	5.01667i	0.341341i
$217$	−3.29183	−0.223464
$218$	− 23.1521i	− 1.56806i
$219$	11.7190	0.791896
$220$	−10.7421	−0.724232
$221$	0	0
$222$	−15.1277	−1.01530
$223$	−20.0185	−1.34054	−0.670270	−	0.742117i	$-0.733822\pi$
$223$	−20.0185	−1.34054	−0.670270	+	0.742117i	$0.733822\pi$
$224$	9.55167i	0.638198i
$225$	7.21221	0.480814
$226$	− 11.9654i	− 0.795924i
$227$	13.7803i	0.914630i	0.889305	+	0.457315i	$0.151189\pi$
$227$	13.7803i	0.914630i	−0.889305	+	0.457315i	$0.848811\pi$
$228$	− 14.2384i	− 0.942960i
$229$	−3.64022	−0.240553	−0.120276	−	0.992740i	$-0.538378\pi$
$229$	−3.64022	−0.240553	−0.120276	+	0.992740i	$0.538378\pi$
$230$	0.243408	0.0160498
$231$	18.5218i	1.21864i
$232$	− 0.397065i	− 0.0260686i
$233$	14.1608i	0.927703i	0.885913	+	0.463851i	$0.153533\pi$
$233$	14.1608i	0.927703i	−0.885913	+	0.463851i	$0.846467\pi$
$234$	−36.3271	−2.37478
$235$	3.39482i	0.221454i
$236$	−3.31070	−0.215508
$237$	26.1421	1.69811
$238$	0	0
$239$	−22.6621	−1.46589	−0.732944	−	0.680289i	$-0.761854\pi$
$239$	−22.6621	−1.46589	−0.732944	+	0.680289i	$0.761854\pi$
$240$	−11.5117	−0.743080
$241$	− 6.04498i	− 0.389391i	−0.980864	−	0.194696i	$-0.937628\pi$
$241$	− 6.04498i	− 0.389391i	0.980864	−	0.194696i	$-0.0623719\pi$
$242$	27.0584	1.73938
$243$	27.9388i	1.79228i
$244$	− 17.6351i	− 1.12897i
$245$	− 5.61365i	− 0.358643i
$246$	−4.68955	−0.298995
$247$	5.02870	0.319969
$248$	− 1.04195i	− 0.0661638i
$249$	19.4575i	1.23307i
$250$	− 2.04505i	− 0.129340i
$251$	−0.706952	−0.0446224	−0.0223112	−	0.999751i	$-0.507102\pi$
$251$	−0.706952	−0.0446224	−0.0223112	+	0.999751i	$0.507102\pi$
$252$	− 18.5313i	− 1.16736i
$253$	−0.585891	−0.0368346
$254$	−13.9145	−0.873073
$255$	0	0
$256$	12.6989	0.793679
$257$	15.0724	0.940193	0.470096	−	0.882615i	$-0.344219\pi$
$257$	15.0724	0.940193	0.470096	+	0.882615i	$0.344219\pi$
$258$	− 65.9789i	− 4.10767i
$259$	2.72548	0.169353
$260$	5.37477i	0.333329i
$261$	− 7.68395i	− 0.475625i
$262$	− 3.88611i	− 0.240085i
$263$	14.5292	0.895911	0.447955	−	0.894056i	$-0.352152\pi$
$263$	14.5292	0.895911	0.447955	+	0.894056i	$0.352152\pi$
$264$	−5.86262	−0.360820
$265$	− 13.9241i	− 0.855349i
$266$	4.91630i	0.301438i
$267$	27.0407i	1.65486i
$268$	−10.7483	−0.656555
$269$	− 28.3603i	− 1.72916i	−0.502497	−	0.864579i	$-0.667585\pi$
$269$	− 28.3603i	− 1.72916i	0.502497	−	0.864579i	$-0.332415\pi$
$270$	27.5280	1.67530
$271$	9.29673	0.564736	0.282368	−	0.959306i	$-0.408880\pi$
$271$	9.29673	0.564736	0.282368	+	0.959306i	$0.408880\pi$
$272$	0	0
$273$	9.26731	0.560883
$274$	−39.5997	−2.39230
$275$	4.92251i	0.296839i
$276$	0.830026	0.0499617
$277$	22.4063i	1.34627i	0.739522	+	0.673133i	$0.235052\pi$
$277$	22.4063i	1.34627i	−0.739522	+	0.673133i	$0.764948\pi$
$278$	16.9267i	1.01520i
$279$	− 20.1637i	− 1.20717i
$280$	−0.438815	−0.0262242
$281$	−31.2511	−1.86428	−0.932142	−	0.362093i	$-0.882062\pi$
$281$	−31.2511	−1.86428	−0.932142	+	0.362093i	$0.882062\pi$
$282$	22.1861i	1.32117i
$283$	− 11.7455i	− 0.698197i	−0.937086	−	0.349098i	$-0.886488\pi$
$283$	− 11.7455i	− 0.698197i	0.937086	−	0.349098i	$-0.113512\pi$
$284$	− 14.4821i	− 0.859355i
$285$	−6.52466	−0.386488
$286$	− 24.7941i	− 1.46611i
$287$	0.844895	0.0498726
$288$	−58.5076	−3.44759
$289$	0	0
$290$	−2.17882	−0.127944
$291$	14.3468	0.841023
$292$	− 8.00263i	− 0.468318i
$293$	−26.5905	−1.55344	−0.776718	−	0.629848i	$-0.783117\pi$
$293$	−26.5905	−1.55344	−0.776718	+	0.629848i	$0.783117\pi$
$294$	− 36.6868i	− 2.13962i
$295$	1.51711i	0.0883296i
$296$	0.862685i	0.0501426i
$297$	−66.2609	−3.84485
$298$	−10.0920	−0.584616
$299$	0.293148i	0.0169532i
$300$	− 6.97368i	− 0.402626i
$301$	11.8871i	0.685163i
$302$	−1.45761	−0.0838763
$303$	56.8363i	3.26516i
$304$	7.35495	0.421835
$305$	−8.08120	−0.462728
$306$	0	0
$307$	18.6981	1.06715	0.533577	−	0.845751i	$-0.320847\pi$
$307$	18.6981	1.06715	0.533577	+	0.845751i	$0.320847\pi$
$308$	12.6481	0.720692
$309$	− 36.2234i	− 2.06068i
$310$	−5.71749	−0.324732
$311$	− 7.96633i	− 0.451729i	−0.974159	−	0.225865i	$-0.927479\pi$
$311$	− 7.96633i	− 0.451729i	0.974159	−	0.225865i	$-0.0725207\pi$
$312$	2.93334i	0.166068i
$313$	− 7.98760i	− 0.451486i	−0.974187	−	0.225743i	$-0.927519\pi$
$313$	− 7.98760i	− 0.451486i	0.974187	−	0.225743i	$-0.0724809\pi$
$314$	−12.0365	−0.679258
$315$	−8.49190	−0.478464
$316$	− 17.8518i	− 1.00424i
$317$	− 15.6320i	− 0.877981i	−0.898492	−	0.438991i	$-0.855336\pi$
$317$	− 15.6320i	− 0.877981i	0.898492	−	0.438991i	$-0.144664\pi$
$318$	− 90.9978i	− 5.10290i
$319$	5.24449	0.293635
$320$	9.38544i	0.524662i
$321$	−41.1809	−2.29849
$322$	−0.286596	−0.0159714
$323$	0	0
$324$	46.6550	2.59194
$325$	2.46296	0.136621
$326$	12.0580i	0.667832i
$327$	−36.1781	−2.00065
$328$	0.267431i	0.0147664i
$329$	− 3.99718i	− 0.220371i
$330$	32.1700i	1.77090i
$331$	4.43051	0.243523	0.121761	−	0.992559i	$-0.461146\pi$
$331$	4.43051	0.243523	0.121761	+	0.992559i	$0.461146\pi$
$332$	13.2871	0.729223
$333$	16.6946i	0.914858i
$334$	22.0219i	1.20499i
$335$	4.92534i	0.269100i
$336$	13.5543	0.739448
$337$	6.03607i	0.328806i	0.986393	+	0.164403i	$0.0525697\pi$
$337$	6.03607i	0.328806i	−0.986393	+	0.164403i	$0.947430\pi$
$338$	14.1800	0.771291
$339$	−18.6974	−1.01550
$340$	0	0
$341$	13.7622	0.745266
$342$	−30.1142	−1.62839
$343$	14.8517i	0.801918i
$344$	−3.76258	−0.202865
$345$	− 0.380355i	− 0.0204776i
$346$	19.8308i	1.06611i
$347$	0.0930963i	0.00499767i	0.999997	+	0.00249883i	$0.000795405\pi$
$347$	0.0930963i	0.00499767i	−0.999997	+	0.00249883i	$0.999205\pi$
$348$	−7.42982	−0.398280
$349$	−9.54221	−0.510783	−0.255391	−	0.966838i	$-0.582204\pi$
$349$	−9.54221	−0.510783	−0.255391	+	0.966838i	$0.582204\pi$
$350$	2.40791i	0.128708i
$351$	33.1534i	1.76960i
$352$	− 39.9329i	− 2.12843i
$353$	17.2138	0.916197	0.458099	−	0.888901i	$-0.348531\pi$
$353$	17.2138	0.916197	0.458099	+	0.888901i	$0.348531\pi$
$354$	9.91475i	0.526963i
$355$	−6.63635	−0.352221
$356$	18.4655	0.978667
$357$	0	0
$358$	32.1392	1.69861
$359$	17.7449	0.936538	0.468269	−	0.883586i	$-0.344878\pi$
$359$	17.7449	0.936538	0.468269	+	0.883586i	$0.344878\pi$
$360$	− 2.68790i	− 0.141665i
$361$	−14.8313	−0.780597
$362$	− 8.15803i	− 0.428777i
$363$	− 42.2822i	− 2.21924i
$364$	− 6.32843i	− 0.331700i
$365$	−3.66716	−0.191948
$366$	−52.8129	−2.76058
$367$	36.3041i	1.89506i	0.319669	+	0.947529i	$0.396428\pi$
$367$	36.3041i	1.89506i	−0.319669	+	0.947529i	$0.603572\pi$
$368$	0.428757i	0.0223505i
$369$	5.17530i	0.269415i
$370$	4.73382	0.246100
$371$	16.3947i	0.851169i
$372$	−19.4968	−1.01086
$373$	5.89146	0.305048	0.152524	−	0.988300i	$-0.451260\pi$
$373$	5.89146	0.305048	0.152524	+	0.988300i	$0.451260\pi$
$374$	0	0
$375$	−3.19566	−0.165023
$376$	1.26521	0.0652482
$377$	− 2.62406i	− 0.135146i
$378$	−32.4124	−1.66711
$379$	− 29.2735i	− 1.50368i	−0.659347	−	0.751838i	$-0.729167\pi$
$379$	− 29.2735i	− 1.50368i	0.659347	−	0.751838i	$-0.270833\pi$
$380$	4.45554i	0.228564i
$381$	21.7432i	1.11394i
$382$	−39.2663	−2.00904
$383$	−12.3062	−0.628816	−0.314408	−	0.949288i	$-0.601806\pi$
$383$	−12.3062	−0.628816	−0.314408	+	0.949288i	$0.601806\pi$
$384$	9.48830i	0.484198i
$385$	− 5.79593i	− 0.295388i
$386$	24.0488i	1.22405i
$387$	−72.8131	−3.70130
$388$	− 9.79708i	− 0.497371i
$389$	2.12579	0.107782	0.0538910	−	0.998547i	$-0.482838\pi$
$389$	2.12579	0.107782	0.0538910	+	0.998547i	$0.482838\pi$
$390$	16.0962	0.815061
$391$	0	0
$392$	−2.09214	−0.105669
$393$	−6.07254	−0.306319
$394$	39.1403i	1.97186i
$395$	−8.18051	−0.411606
$396$	77.4743i	3.89323i
$397$	− 25.1983i	− 1.26467i	−0.774696	−	0.632334i	$-0.782097\pi$
$397$	− 25.1983i	− 1.26467i	0.774696	−	0.632334i	$-0.217903\pi$
$398$	− 21.3691i	− 1.07114i
$399$	7.68235	0.384599
$400$	3.60231	0.180116
$401$	− 32.8681i	− 1.64135i	−0.571392	−	0.820677i	$-0.693596\pi$
$401$	− 32.8681i	− 1.64135i	0.571392	−	0.820677i	$-0.306404\pi$
$402$	32.1885i	1.60542i
$403$	− 6.88587i	− 0.343010i
$404$	38.8122	1.93098
$405$	− 21.3794i	− 1.06235i
$406$	2.56541	0.127319
$407$	−11.3945	−0.564803
$408$	0	0
$409$	−16.5721	−0.819437	−0.409719	−	0.912212i	$-0.634373\pi$
$409$	−16.5721	−0.819437	−0.409719	+	0.912212i	$0.634373\pi$
$410$	1.46748	0.0724735
$411$	61.8796i	3.05229i
$412$	−24.7361	−1.21866
$413$	− 1.78630i	− 0.0878979i
$414$	− 1.75551i	− 0.0862785i
$415$	− 6.08874i	− 0.298884i
$416$	−19.9803	−0.979613
$417$	26.4502	1.29527
$418$	− 20.5537i	− 1.00531i
$419$	− 5.31866i	− 0.259833i	−0.991525	−	0.129917i	$-0.958529\pi$
$419$	− 5.31866i	− 0.259833i	0.991525	−	0.129917i	$-0.0414710\pi$
$420$	8.21104i	0.400658i
$421$	3.72116	0.181358	0.0906791	−	0.995880i	$-0.471096\pi$
$421$	3.72116	0.181358	0.0906791	+	0.995880i	$0.471096\pi$
$422$	44.5473i	2.16853i
$423$	24.4842	1.19046
$424$	−5.18933	−0.252016
$425$	0	0
$426$	−43.3705	−2.10131
$427$	9.51507	0.460466
$428$	28.1215i	1.35930i
$429$	−38.7440	−1.87058
$430$	20.6464i	0.995660i
$431$	0.652621i	0.0314357i	0.999876	+	0.0157178i	$0.00500335\pi$
$431$	0.652621i	0.0314357i	−0.999876	+	0.0157178i	$0.994997\pi$
$432$	48.4900i	2.33297i
$433$	−5.31477	−0.255411	−0.127706	−	0.991812i	$-0.540761\pi$
$433$	−5.31477	−0.255411	−0.127706	+	0.991812i	$0.540761\pi$
$434$	6.73196	0.323145
$435$	3.40468i	0.163242i
$436$	24.7052i	1.18316i
$437$	0.243012i	0.0116248i
$438$	−23.9660	−1.14514
$439$	− 5.53592i	− 0.264215i	−0.991235	−	0.132107i	$-0.957826\pi$
$439$	− 5.53592i	− 0.264215i	0.991235	−	0.132107i	$-0.0421744\pi$
$440$	1.83456	0.0874593
$441$	−40.4869	−1.92795
$442$	0	0
$443$	14.9894	0.712169	0.356084	−	0.934454i	$-0.384112\pi$
$443$	14.9894	0.712169	0.356084	+	0.934454i	$0.384112\pi$
$444$	16.1425	0.766087
$445$	− 8.46170i	− 0.401123i
$446$	40.9390	1.93852
$447$	15.7701i	0.745900i
$448$	− 11.0507i	− 0.522097i
$449$	− 20.7816i	− 0.980743i	−0.871514	−	0.490371i	$-0.836861\pi$
$449$	− 20.7816i	− 0.980743i	0.871514	−	0.490371i	$-0.163139\pi$
$450$	−14.7494	−0.695291
$451$	−3.53227	−0.166328
$452$	12.7680i	0.600558i
$453$	2.27771i	0.107016i
$454$	− 28.1814i	− 1.32262i
$455$	−2.89997	−0.135953
$456$	2.43166i	0.113873i
$457$	−15.6444	−0.731816	−0.365908	−	0.930651i	$-0.619242\pi$
$457$	−15.6444	−0.731816	−0.365908	+	0.930651i	$0.619242\pi$
$458$	7.44445	0.347856
$459$	0	0
$460$	−0.259736	−0.0121102
$461$	7.39362	0.344355	0.172178	−	0.985066i	$-0.444920\pi$
$461$	7.39362	0.344355	0.172178	+	0.985066i	$0.444920\pi$
$462$	− 37.8780i	− 1.76225i
$463$	17.2150	0.800049	0.400025	−	0.916504i	$-0.369002\pi$
$463$	17.2150	0.800049	0.400025	+	0.916504i	$0.369002\pi$
$464$	− 3.83793i	− 0.178172i
$465$	8.93431i	0.414319i
$466$	− 28.9595i	− 1.34152i
$467$	36.3391	1.68157	0.840787	−	0.541367i	$-0.182093\pi$
$467$	36.3391	1.68157	0.840787	+	0.541367i	$0.182093\pi$
$468$	38.7640	1.79187
$469$	− 5.79925i	− 0.267785i
$470$	− 6.94259i	− 0.320238i
$471$	18.8085i	0.866651i
$472$	0.565409	0.0260250
$473$	− 49.6967i	− 2.28506i
$474$	−53.4620	−2.45559
$475$	2.04173	0.0936810
$476$	0	0
$477$	−100.423	−4.59807
$478$	46.3451	2.11978
$479$	− 30.3678i	− 1.38754i	−0.720196	−	0.693770i	$-0.755948\pi$
$479$	− 30.3678i	− 1.38754i	0.720196	−	0.693770i	$-0.244052\pi$
$480$	25.9241	1.18327
$481$	5.70118i	0.259952i
$482$	12.3623i	0.563087i
$483$	0.447843i	0.0203776i
$484$	−28.8735	−1.31243
$485$	−4.48946	−0.203856
$486$	− 57.1364i	− 2.59176i
$487$	− 25.2832i	− 1.14569i	−0.819663	−	0.572846i	$-0.805839\pi$
$487$	− 25.2832i	− 1.14569i	0.819663	−	0.572846i	$-0.194161\pi$
$488$	3.01176i	0.136336i
$489$	18.8422	0.852074
$490$	11.4802i	0.518623i
$491$	28.7941	1.29946	0.649730	−	0.760165i	$-0.274882\pi$
$491$	28.7941	1.29946	0.649730	+	0.760165i	$0.274882\pi$
$492$	5.00413	0.225604
$493$	0	0
$494$	−10.2840	−0.462697
$495$	35.5022	1.59571
$496$	− 10.0712i	− 0.452212i
$497$	7.81386	0.350500
$498$	− 39.7916i	− 1.78311i
$499$	− 14.9561i	− 0.669527i	−0.942302	−	0.334764i	$-0.891344\pi$
$499$	− 14.9561i	− 0.669527i	0.942302	−	0.334764i	$-0.108656\pi$
$500$	2.18224i	0.0975927i
$501$	34.4121	1.53742
$502$	1.44575	0.0645272
$503$	32.5784i	1.45260i	0.687378	+	0.726300i	$0.258761\pi$
$503$	32.5784i	1.45260i	−0.687378	+	0.726300i	$0.741239\pi$
$504$	3.16483i	0.140973i
$505$	− 17.7855i	− 0.791444i
$506$	1.19818	0.0532655
$507$	− 22.1581i	− 0.984075i
$508$	14.8479	0.658769
$509$	−33.1868	−1.47098	−0.735490	−	0.677535i	$-0.763048\pi$
$509$	−33.1868	−1.47098	−0.735490	+	0.677535i	$0.763048\pi$
$510$	0	0
$511$	4.31784	0.191010
$512$	−31.9081	−1.41015
$513$	27.4833i	1.21342i
$514$	−30.8239	−1.35958
$515$	11.3352i	0.499488i
$516$	70.4049i	3.09940i
$517$	16.7111i	0.734952i
$518$	−5.57375	−0.244897
$519$	30.9882	1.36023
$520$	− 0.917916i	− 0.0402533i
$521$	− 28.6670i	− 1.25593i	−0.778244	−	0.627963i	$-0.783889\pi$
$521$	− 28.6670i	− 1.25593i	0.778244	−	0.627963i	$-0.216111\pi$
$522$	15.7141i	0.687787i
$523$	−42.6141	−1.86338	−0.931692	−	0.363248i	$-0.881668\pi$
$523$	−42.6141	−1.86338	−0.931692	+	0.363248i	$0.881668\pi$
$524$	4.14680i	0.181154i
$525$	3.76267	0.164216
$526$	−29.7130	−1.29555
$527$	0	0
$528$	−56.6667	−2.46610
$529$	22.9858	0.999384
$530$	28.4755i	1.23690i
$531$	10.9417	0.474831
$532$	− 5.24610i	− 0.227447i
$533$	1.76736i	0.0765528i
$534$	− 55.2996i	− 2.39305i
$535$	12.8865	0.557133
$536$	1.83561	0.0792864
$537$	− 50.2216i	− 2.16722i
$538$	57.9983i	2.50048i
$539$	− 27.6333i	− 1.19025i
$540$	−29.3747	−1.26408
$541$	− 22.0963i	− 0.949993i	−0.879988	−	0.474997i	$-0.842449\pi$
$541$	− 22.0963i	− 0.949993i	0.879988	−	0.474997i	$-0.157551\pi$
$542$	−19.0123	−0.816648
$543$	−12.7480	−0.547068
$544$	0	0
$545$	11.3210	0.484940
$546$	−18.9521	−0.811077
$547$	38.6850i	1.65405i	0.562163	+	0.827026i	$0.309969\pi$
$547$	38.6850i	1.65405i	−0.562163	+	0.827026i	$0.690031\pi$
$548$	42.2561	1.80509
$549$	58.2834i	2.48747i
$550$	− 10.0668i	− 0.429250i
$551$	− 2.17528i	− 0.0926699i
$552$	−0.141754	−0.00603344
$553$	9.63200	0.409594
$554$	− 45.8221i	− 1.94679i
$555$	− 7.39720i	− 0.313994i
$556$	− 18.0622i	− 0.766009i
$557$	33.9638	1.43909	0.719546	−	0.694445i	$-0.244350\pi$
$557$	33.9638	1.43909	0.719546	+	0.694445i	$0.244350\pi$
$558$	41.2358i	1.74565i
$559$	−24.8656	−1.05170
$560$	−4.24148	−0.179235
$561$	0	0
$562$	63.9101	2.69589
$563$	2.27374	0.0958267	0.0479133	−	0.998851i	$-0.484743\pi$
$563$	2.27374	0.0958267	0.0479133	+	0.998851i	$0.484743\pi$
$564$	− 23.6744i	− 0.996873i
$565$	5.85089	0.246149
$566$	24.0201i	1.00964i
$567$	25.1728i	1.05716i
$568$	2.47329i	0.103777i
$569$	5.68027	0.238129	0.119065	−	0.992887i	$-0.462010\pi$
$569$	5.68027	0.238129	0.119065	+	0.992887i	$0.462010\pi$
$570$	13.3433	0.558889
$571$	− 12.9627i	− 0.542471i	−0.962513	−	0.271236i	$-0.912568\pi$
$571$	− 12.9627i	− 0.542471i	0.962513	−	0.271236i	$-0.0874323\pi$
$572$	26.4574i	1.10624i
$573$	61.3587i	2.56330i
$574$	−1.72785	−0.0721193
$575$	0.119023i	0.00496359i
$576$	67.6898	2.82041
$577$	27.7816	1.15656	0.578281	−	0.815838i	$-0.303724\pi$
$577$	27.7816	1.15656	0.578281	+	0.815838i	$0.303724\pi$
$578$	0	0
$579$	37.5793	1.56174
$580$	2.32498	0.0965393
$581$	7.16908i	0.297424i
$582$	−29.3399	−1.21618
$583$	− 68.5415i	− 2.83870i
$584$	1.36671i	0.0565547i
$585$	− 17.7634i	− 0.734427i
$586$	54.3791	2.24638
$587$	6.89170	0.284451	0.142226	−	0.989834i	$-0.454574\pi$
$587$	6.89170	0.284451	0.142226	+	0.989834i	$0.454574\pi$
$588$	39.1478i	1.61443i
$589$	− 5.70820i	− 0.235202i
$590$	− 3.10257i	− 0.127731i
$591$	61.1617	2.51585
$592$	8.33851i	0.342711i
$593$	13.9274	0.571930	0.285965	−	0.958240i	$-0.407686\pi$
$593$	13.9274	0.571930	0.285965	+	0.958240i	$0.407686\pi$
$594$	135.507	5.55992
$595$	0	0
$596$	10.7690	0.441117
$597$	−33.3920	−1.36664
$598$	− 0.599504i	− 0.0245155i
$599$	19.3270	0.789681	0.394841	−	0.918750i	$-0.370800\pi$
$599$	19.3270	0.789681	0.394841	+	0.918750i	$0.370800\pi$
$600$	1.19098i	0.0486216i
$601$	− 42.1759i	− 1.72039i	−0.509965	−	0.860195i	$-0.670342\pi$
$601$	− 42.1759i	− 1.72039i	0.509965	−	0.860195i	$-0.329658\pi$
$602$	− 24.3098i	− 0.990793i
$603$	35.5226	1.44659
$604$	1.55539	0.0632881
$605$	13.2311i	0.537923i
$606$	− 116.233i	− 4.72165i
$607$	18.8481i	0.765021i	0.923951	+	0.382511i	$0.124940\pi$
$607$	18.8481i	0.765021i	−0.923951	+	0.382511i	$0.875060\pi$
$608$	−16.5631	−0.671723
$609$	− 4.00878i	− 0.162444i
$610$	16.5265	0.669138
$611$	8.36132	0.338263
$612$	0	0
$613$	16.1284	0.651420	0.325710	−	0.945470i	$-0.394397\pi$
$613$	16.1284	0.651420	0.325710	+	0.945470i	$0.394397\pi$
$614$	−38.2385	−1.54318
$615$	− 2.29312i	− 0.0924675i
$616$	−2.16007	−0.0870318
$617$	− 37.7508i	− 1.51979i	−0.650046	−	0.759894i	$-0.725251\pi$
$617$	− 37.7508i	− 1.51979i	0.650046	−	0.759894i	$-0.274749\pi$
$618$	74.0787i	2.97988i
$619$	48.7190i	1.95818i	0.203425	+	0.979091i	$0.434793\pi$
$619$	48.7190i	1.95818i	−0.203425	+	0.979091i	$0.565207\pi$
$620$	6.10103	0.245023
$621$	−1.60214	−0.0642916
$622$	16.2916i	0.653232i
$623$	9.96308i	0.399162i
$624$	28.3530i	1.13503i
$625$	1.00000	0.0400000
$626$	16.3351i	0.652880i
$627$	−32.1178	−1.28266
$628$	12.8439	0.512528
$629$	0	0
$630$	17.3664	0.691893
$631$	39.1517	1.55861	0.779303	−	0.626647i	$-0.215573\pi$
$631$	39.1517	1.55861	0.779303	+	0.626647i	$0.215573\pi$
$632$	3.04878i	0.121274i
$633$	69.6109	2.76678
$634$	31.9683i	1.26962i
$635$	− 6.80398i	− 0.270008i
$636$	97.1021i	3.85035i
$637$	−13.8262	−0.547815
$638$	−10.7253	−0.424617
$639$	47.8628i	1.89342i
$640$	− 2.96912i	− 0.117365i
$641$	− 49.9352i	− 1.97232i	−0.165793	−	0.986161i	$-0.553018\pi$
$641$	− 49.9352i	− 1.97232i	0.165793	−	0.986161i	$-0.446982\pi$
$642$	84.2170	3.32378
$643$	− 15.6383i	− 0.616714i	−0.951271	−	0.308357i	$-0.900221\pi$
$643$	− 15.6383i	− 0.616714i	0.951271	−	0.308357i	$-0.0997791\pi$
$644$	0.305821	0.0120511
$645$	32.2627	1.27034
$646$	0	0
$647$	−24.8287	−0.976118	−0.488059	−	0.872811i	$-0.662295\pi$
$647$	−24.8287	−0.976118	−0.488059	+	0.872811i	$0.662295\pi$
$648$	−7.96784	−0.313006
$649$	7.46800i	0.293145i
$650$	−5.03689	−0.197563
$651$	− 10.5196i	− 0.412294i
$652$	− 12.8669i	− 0.503907i
$653$	16.8005i	0.657453i	0.944425	+	0.328727i	$0.106619\pi$
$653$	16.8005i	0.657453i	−0.944425	+	0.328727i	$0.893381\pi$
$654$	73.9862	2.89309
$655$	1.90025	0.0742489
$656$	2.58493i	0.100924i
$657$	26.4484i	1.03185i
$658$	8.17443i	0.318673i
$659$	13.1974	0.514097	0.257048	−	0.966399i	$-0.417250\pi$
$659$	13.1974	0.514097	0.257048	+	0.966399i	$0.417250\pi$
$660$	− 34.3281i	− 1.33622i
$661$	38.1892	1.48539	0.742694	−	0.669631i	$-0.233548\pi$
$661$	38.1892	1.48539	0.742694	+	0.669631i	$0.233548\pi$
$662$	−9.06062	−0.352151
$663$	0	0
$664$	−2.26920	−0.0880620
$665$	−2.40400	−0.0932231
$666$	− 34.1413i	− 1.32295i
$667$	0.126808	0.00491001
$668$	− 23.4992i	− 0.909212i
$669$	− 63.9724i	− 2.47331i
$670$	− 10.0726i	− 0.389138i
$671$	−39.7798	−1.53568
$672$	−30.5239	−1.17748
$673$	24.3655i	0.939219i	0.882874	+	0.469610i	$0.155605\pi$
$673$	24.3655i	0.939219i	−0.882874	+	0.469610i	$0.844395\pi$
$674$	− 12.3441i	− 0.475476i
$675$	13.4608i	0.518106i
$676$	−15.1312	−0.581971
$677$	46.2667i	1.77817i	0.457737	+	0.889087i	$0.348660\pi$
$677$	46.2667i	1.77817i	−0.457737	+	0.889087i	$0.651340\pi$
$678$	38.2372	1.46849
$679$	5.28604	0.202859
$680$	0	0
$681$	−44.0371	−1.68750
$682$	−28.1444	−1.07771
$683$	− 16.4922i	− 0.631056i	−0.948916	−	0.315528i	$-0.897818\pi$
$683$	− 16.4922i	− 0.631056i	0.948916	−	0.315528i	$-0.102182\pi$
$684$	32.1343	1.22869
$685$	− 19.3637i	− 0.739847i
$686$	− 30.3726i	− 1.15963i
$687$	− 11.6329i	− 0.443823i
$688$	−36.3682	−1.38653
$689$	−34.2945	−1.30652
$690$	0.777847i	0.0296121i
$691$	25.8554i	0.983584i	0.870713	+	0.491792i	$0.163658\pi$
$691$	25.8554i	0.983584i	−0.870713	+	0.491792i	$0.836342\pi$
$692$	− 21.1611i	− 0.804425i
$693$	−41.8015	−1.58791
$694$	− 0.190387i	− 0.00722698i
$695$	−8.27692	−0.313962
$696$	1.26888	0.0480968
$697$	0	0
$698$	19.5143	0.738628
$699$	−45.2529	−1.71162
$700$	− 2.56944i	− 0.0971157i
$701$	8.67606	0.327690	0.163845	−	0.986486i	$-0.447610\pi$
$701$	8.67606	0.327690	0.163845	+	0.986486i	$0.447610\pi$
$702$	− 67.8005i	− 2.55896i
$703$	4.72613i	0.178249i
$704$	46.1999i	1.74123i
$705$	−10.8487	−0.408585
$706$	−35.2031	−1.32489
$707$	20.9412i	0.787576i
$708$	− 10.5799i	− 0.397615i
$709$	35.9232i	1.34912i	0.738218	+	0.674562i	$0.235667\pi$
$709$	35.9232i	1.34912i	−0.738218	+	0.674562i	$0.764333\pi$
$710$	13.5717	0.509337
$711$	58.9996i	2.21266i
$712$	−3.15357	−0.118185
$713$	0.332760	0.0124620
$714$	0	0
$715$	12.1240	0.453411
$716$	−34.2952	−1.28167
$717$	− 72.4202i	− 2.70458i
$718$	−36.2892	−1.35430
$719$	9.75299i	0.363725i	0.983324	+	0.181863i	$0.0582126\pi$
$719$	9.75299i	0.363725i	−0.983324	+	0.181863i	$0.941787\pi$
$720$	− 25.9806i	− 0.968241i
$721$	− 13.3464i	− 0.497047i
$722$	30.3309	1.12880
$723$	19.3177	0.718432
$724$	8.70529i	0.323530i
$725$	− 1.06541i	− 0.0395683i
$726$	86.4693i	3.20918i
$727$	−11.0694	−0.410542	−0.205271	−	0.978705i	$-0.565808\pi$
$727$	−11.0694	−0.410542	−0.205271	+	0.978705i	$0.565808\pi$
$728$	1.08078i	0.0400565i
$729$	−25.1447	−0.931285
$730$	7.49954	0.277570
$731$	0	0
$732$	56.3557	2.08297
$733$	−42.1634	−1.55734	−0.778670	−	0.627434i	$-0.784105\pi$
$733$	−42.1634	−1.55734	−0.778670	+	0.627434i	$0.784105\pi$
$734$	− 74.2438i	− 2.74039i
$735$	17.9393	0.661701
$736$	− 0.965546i	− 0.0355905i
$737$	24.2451i	0.893078i
$738$	− 10.5838i	− 0.389593i
$739$	−47.1617	−1.73487	−0.867435	−	0.497550i	$-0.834233\pi$
$739$	−47.1617	−1.73487	−0.867435	+	0.497550i	$0.834233\pi$
$740$	−5.05137	−0.185692
$741$	16.0700i	0.590346i
$742$	− 33.5279i	− 1.23085i
$743$	31.7495i	1.16478i	0.812911	+	0.582388i	$0.197882\pi$
$743$	31.7495i	1.16478i	−0.812911	+	0.582388i	$0.802118\pi$
$744$	3.32971	0.122073
$745$	− 4.93485i	− 0.180799i
$746$	−12.0483	−0.441121
$747$	−43.9133	−1.60670
$748$	0	0
$749$	−15.1730	−0.554409
$750$	6.53528	0.238635
$751$	22.1885i	0.809668i	0.914390	+	0.404834i	$0.132671\pi$
$751$	22.1885i	0.809668i	−0.914390	+	0.404834i	$0.867329\pi$
$752$	12.2292	0.445954
$753$	− 2.25918i	− 0.0823289i
$754$	5.36634i	0.195431i
$755$	− 0.712752i	− 0.0259397i
$756$	34.5867	1.25791
$757$	13.0640	0.474821	0.237410	−	0.971409i	$-0.423701\pi$
$757$	13.0640	0.474821	0.237410	+	0.971409i	$0.423701\pi$
$758$	59.8658i	2.17442i
$759$	− 1.87230i	− 0.0679604i
$760$	− 0.760928i	− 0.0276017i
$761$	18.9811	0.688065	0.344033	−	0.938958i	$-0.388207\pi$
$761$	18.9811	0.688065	0.344033	+	0.938958i	$0.388207\pi$
$762$	− 44.4659i	− 1.61083i
$763$	−13.3298	−0.482569
$764$	41.9004	1.51590
$765$	0	0
$766$	25.1668	0.909313
$767$	3.73659	0.134920
$768$	40.5812i	1.46435i
$769$	−22.0057	−0.793544	−0.396772	−	0.917917i	$-0.629870\pi$
$769$	−22.0057	−0.793544	−0.396772	+	0.917917i	$0.629870\pi$
$770$	11.8530i	0.427152i
$771$	48.1663i	1.73467i
$772$	− 25.6620i	− 0.923596i
$773$	13.2410	0.476247	0.238123	−	0.971235i	$-0.423468\pi$
$773$	13.2410	0.476247	0.238123	+	0.971235i	$0.423468\pi$
$774$	148.907	5.35234
$775$	− 2.79577i	− 0.100427i
$776$	1.67317i	0.0600632i
$777$	8.70970i	0.312459i
$778$	−4.34736	−0.155860
$779$	1.46509i	0.0524924i
$780$	−17.1759	−0.614997
$781$	−32.6676	−1.16894
$782$	0	0
$783$	14.3412	0.512514
$784$	−20.2221	−0.722219
$785$	− 5.88566i	− 0.210068i
$786$	12.4187	0.442959
$787$	11.9863i	0.427266i	0.976914	+	0.213633i	$0.0685297\pi$
$787$	11.9863i	0.427266i	−0.976914	+	0.213633i	$0.931470\pi$
$788$	− 41.7659i	− 1.48785i
$789$	46.4304i	1.65297i
$790$	16.7296	0.595212
$791$	−6.88902	−0.244945
$792$	− 13.2312i	− 0.470152i
$793$	19.9037i	0.706801i
$794$	51.5319i	1.82880i
$795$	44.4966	1.57813
$796$	22.8026i	0.808218i
$797$	23.3187	0.825989	0.412995	−	0.910734i	$-0.364483\pi$
$797$	23.3187	0.825989	0.412995	+	0.910734i	$0.364483\pi$
$798$	−15.7108	−0.556157
$799$	0	0
$800$	−8.11229	−0.286813
$801$	−61.0276	−2.15630
$802$	67.2170i	2.37351i
$803$	−18.0517	−0.637030
$804$	− 34.3478i	− 1.21135i
$805$	− 0.140141i	− 0.00493933i
$806$	14.0820i	0.496016i
$807$	90.6298	3.19032
$808$	−6.62844	−0.233188
$809$	30.8141i	1.08337i	0.840583	+	0.541683i	$0.182213\pi$
$809$	30.8141i	1.08337i	−0.840583	+	0.541683i	$0.817787\pi$
$810$	43.7220i	1.53623i
$811$	38.6069i	1.35567i	0.735213	+	0.677836i	$0.237082\pi$
$811$	38.6069i	1.35567i	−0.735213	+	0.677836i	$0.762918\pi$
$812$	−2.73750	−0.0960675
$813$	29.7091i	1.04194i
$814$	23.3023	0.816745
$815$	−5.89619	−0.206535
$816$	0	0
$817$	−20.6129	−0.721154
$818$	33.8908	1.18496
$819$	20.9152i	0.730837i
$820$	−1.56592	−0.0546842
$821$	− 21.5899i	− 0.753493i	−0.926316	−	0.376747i	$-0.877043\pi$
$821$	− 21.5899i	− 0.753493i	0.926316	−	0.376747i	$-0.122957\pi$
$822$	− 126.547i	− 4.41383i
$823$	− 25.4053i	− 0.885573i	−0.896627	−	0.442787i	$-0.853990\pi$
$823$	− 25.4053i	− 0.885573i	0.896627	−	0.442787i	$-0.146010\pi$
$824$	4.22449	0.147167
$825$	−15.7307	−0.547671
$826$	3.65307i	0.127107i
$827$	− 14.8822i	− 0.517506i	−0.965943	−	0.258753i	$-0.916688\pi$
$827$	− 14.8822i	− 0.517506i	0.965943	−	0.258753i	$-0.0833116\pi$
$828$	1.87327i	0.0651007i
$829$	−29.8580	−1.03701	−0.518505	−	0.855075i	$-0.673511\pi$
$829$	−29.8580	−1.03701	−0.518505	+	0.855075i	$0.673511\pi$
$830$	12.4518i	0.432208i
$831$	−71.6029	−2.48388
$832$	23.1160	0.801402
$833$	0	0
$834$	−54.0920	−1.87305
$835$	−10.7684	−0.372656
$836$	21.9325i	0.758550i
$837$	37.6333	1.30080
$838$	10.8769i	0.375737i
$839$	− 32.2189i	− 1.11232i	−0.831075	−	0.556161i	$-0.812274\pi$
$839$	− 32.2189i	− 1.11232i	0.831075	−	0.556161i	$-0.187726\pi$
$840$	− 1.40230i	− 0.0483840i
$841$	27.8649	0.960859
$842$	−7.60996	−0.262257
$843$	− 99.8677i	− 3.43963i
$844$	− 47.5357i	− 1.63624i
$845$	6.93382i	0.238531i
$846$	−50.0715	−1.72149
$847$	− 15.5788i	− 0.535293i
$848$	−50.1589	−1.72246
$849$	37.5345	1.28818
$850$	0	0
$851$	−0.275510	−0.00944435
$852$	46.2798	1.58552
$853$	6.64528i	0.227530i	0.993508	+	0.113765i	$0.0362911\pi$
$853$	6.64528i	0.227530i	−0.993508	+	0.113765i	$0.963709\pi$
$854$	−19.4588	−0.665867
$855$	− 14.7254i	− 0.503598i
$856$	− 4.80265i	− 0.164151i
$857$	− 34.5296i	− 1.17951i	−0.807583	−	0.589754i	$-0.799225\pi$
$857$	− 34.5296i	− 1.17951i	0.807583	−	0.589754i	$-0.200775\pi$
$858$	79.2336	2.70499
$859$	−46.7639	−1.59556	−0.797782	−	0.602946i	$-0.793993\pi$
$859$	−46.7639	−1.59556	−0.797782	+	0.602946i	$0.793993\pi$
$860$	− 22.0315i	− 0.751266i
$861$	2.69999i	0.0920155i
$862$	− 1.33464i	− 0.0454582i
$863$	−40.3468	−1.37342	−0.686711	−	0.726930i	$-0.740946\pi$
$863$	−40.3468	−1.37342	−0.686711	+	0.726930i	$0.740946\pi$
$864$	− 109.198i	− 3.71499i
$865$	−9.69698	−0.329707
$866$	10.8690	0.369343
$867$	0	0
$868$	−7.18356	−0.243826
$869$	−40.2687	−1.36602
$870$	− 6.96274i	− 0.236059i
$871$	12.1309	0.411041
$872$	− 4.21921i	− 0.142880i
$873$	32.3790i	1.09586i
$874$	− 0.496972i	− 0.0168103i
$875$	−1.17743	−0.0398045
$876$	25.5736	0.864053
$877$	− 15.5336i	− 0.524531i	−0.964996	−	0.262266i	$-0.915530\pi$
$877$	− 15.5336i	− 0.524531i	0.964996	−	0.262266i	$-0.0844696\pi$
$878$	11.3212i	0.382073i
$879$	− 84.9742i	− 2.86611i
$880$	17.7324	0.597760
$881$	− 33.1990i	− 1.11850i	−0.828998	−	0.559251i	$-0.811089\pi$
$881$	− 33.1990i	− 1.11850i	0.828998	−	0.559251i	$-0.188911\pi$
$882$	82.7978	2.78795
$883$	34.1078	1.14782	0.573909	−	0.818919i	$-0.305426\pi$
$883$	34.1078	1.14782	0.573909	+	0.818919i	$0.305426\pi$
$884$	0	0
$885$	−4.84816	−0.162969
$886$	−30.6541	−1.02985
$887$	− 32.3508i	− 1.08623i	−0.839658	−	0.543116i	$-0.817244\pi$
$887$	− 32.3508i	− 1.08623i	0.839658	−	0.543116i	$-0.182756\pi$
$888$	−2.75685	−0.0925137
$889$	8.01122i	0.268688i
$890$	17.3046i	0.580052i
$891$	− 105.240i	− 3.52569i
$892$	−43.6852	−1.46269
$893$	6.93131	0.231948
$894$	− 32.2507i	− 1.07862i
$895$	15.7156i	0.525314i
$896$	3.49594i	0.116791i
$897$	−0.936801	−0.0312789
$898$	42.4994i	1.41822i
$899$	−2.97864	−0.0993431
$900$	15.7388	0.524626
$901$	0	0
$902$	7.22367	0.240522
$903$	−37.9872	−1.26413
$904$	− 2.18055i	− 0.0725241i
$905$	3.98916	0.132604
$906$	− 4.65803i	− 0.154753i
$907$	27.9582i	0.928336i	0.885747	+	0.464168i	$0.153647\pi$
$907$	27.9582i	0.928336i	−0.885747	+	0.464168i	$0.846353\pi$
$908$	30.0719i	0.997970i
$909$	−128.273	−4.25454
$910$	5.93059	0.196597
$911$	− 12.3093i	− 0.407826i	−0.978989	−	0.203913i	$-0.934634\pi$
$911$	− 12.3093i	− 0.407826i	0.978989	−	0.203913i	$-0.0653659\pi$
$912$	23.5039i	0.778291i
$913$	− 29.9719i	− 0.991925i
$914$	31.9937	1.05826
$915$	− 25.8247i	− 0.853739i
$916$	−7.94384	−0.262472
$917$	−2.23742	−0.0738860
$918$	0	0
$919$	20.0893	0.662683	0.331342	−	0.943511i	$-0.392499\pi$
$919$	20.0893	0.662683	0.331342	+	0.943511i	$0.392499\pi$
$920$	0.0443583	0.00146245
$921$	59.7526i	1.96891i
$922$	−15.1203	−0.497962
$923$	16.3451i	0.538005i
$924$	40.4190i	1.32969i
$925$	2.31477i	0.0761091i
$926$	−35.2056	−1.15693
$927$	81.7518	2.68508
$928$	8.64290i	0.283717i
$929$	− 6.06146i	− 0.198870i	−0.995044	−	0.0994350i	$-0.968296\pi$
$929$	− 6.06146i	− 0.198870i	0.995044	−	0.0994350i	$-0.0317035\pi$
$930$	− 18.2711i	− 0.599134i
$931$	−11.4616	−0.375638
$932$	30.9022i	1.01223i
$933$	25.4577	0.833446
$934$	−74.3154	−2.43167
$935$	0	0
$936$	−6.62021	−0.216388
$937$	34.1763	1.11649	0.558246	−	0.829675i	$-0.311474\pi$
$937$	34.1763	1.11649	0.558246	+	0.829675i	$0.311474\pi$
$938$	11.8598i	0.387236i
$939$	25.5256	0.832997
$940$	7.40832i	0.241633i
$941$	36.0225i	1.17430i	0.809479	+	0.587149i	$0.199750\pi$
$941$	36.0225i	1.17430i	−0.809479	+	0.587149i	$0.800250\pi$
$942$	− 38.4644i	− 1.25324i
$943$	−0.0854076	−0.00278125
$944$	5.46511	0.177874
$945$	− 15.8492i	− 0.515574i
$946$	101.632i	3.30435i
$947$	− 39.4153i	− 1.28083i	−0.768030	−	0.640413i	$-0.778763\pi$
$947$	− 39.4153i	− 1.28083i	0.768030	−	0.640413i	$-0.221237\pi$
$948$	57.0483	1.85284
$949$	9.03209i	0.293194i
$950$	−4.17544	−0.135469
$951$	49.9545	1.61989
$952$	0	0
$953$	−6.36027	−0.206029	−0.103015	−	0.994680i	$-0.532849\pi$
$953$	−6.36027	−0.206029	−0.103015	+	0.994680i	$0.532849\pi$
$954$	205.371	6.64914
$955$	− 19.2007i	− 0.621319i
$956$	−49.4540	−1.59946
$957$	16.7596i	0.541760i
$958$	62.1038i	2.00648i
$959$	22.7994i	0.736231i
$960$	−29.9926	−0.968008
$961$	23.1837	0.747861
$962$	− 11.6592i	− 0.375908i
$963$	− 92.9403i	− 2.99496i
$964$	− 13.1916i	− 0.424872i
$965$	−11.7595	−0.378551
$966$	− 0.915862i	− 0.0294674i
$967$	−34.3424	−1.10438	−0.552189	−	0.833719i	$-0.686207\pi$
$967$	−34.3424	−1.10438	−0.552189	+	0.833719i	$0.686207\pi$
$968$	4.93109	0.158491
$969$	0	0
$970$	9.18118	0.294790
$971$	7.98605	0.256285	0.128142	−	0.991756i	$-0.459099\pi$
$971$	7.98605	0.256285	0.128142	+	0.991756i	$0.459099\pi$
$972$	60.9692i	1.95559i
$973$	9.74552	0.312427
$974$	51.7055i	1.65675i
$975$	7.87078i	0.252067i
$976$	29.1110i	0.931821i
$977$	15.0989	0.483056	0.241528	−	0.970394i	$-0.422351\pi$
$977$	15.0989	0.483056	0.241528	+	0.970394i	$0.422351\pi$
$978$	−38.5333	−1.23216
$979$	− 41.6528i	− 1.33123i
$980$	− 12.2503i	− 0.391322i
$981$	− 81.6497i	− 2.60688i
$982$	−58.8855	−1.87911
$983$	50.2932i	1.60410i	0.597254	+	0.802052i	$0.296258\pi$
$983$	50.2932i	1.60410i	−0.597254	+	0.802052i	$0.703742\pi$
$984$	−0.854618	−0.0272442
$985$	−19.1390	−0.609819
$986$	0	0
$987$	12.7736	0.406588
$988$	10.9738	0.349124
$989$	− 1.20163i	− 0.0382096i
$990$	−72.6039	−2.30750
$991$	13.0116i	0.413326i	0.978412	+	0.206663i	$0.0662604\pi$
$991$	13.0116i	0.413326i	−0.978412	+	0.206663i	$0.933740\pi$
$992$	22.6801i	0.720094i
$993$	14.1584i	0.449302i
$994$	−15.9798	−0.506847
$995$	10.4492	0.331262
$996$	42.4609i	1.34543i
$997$	− 9.34885i	− 0.296081i	−0.988981	−	0.148040i	$-0.952703\pi$
$997$	− 9.34885i	− 0.296081i	0.988981	−	0.148040i	$-0.0472966\pi$
$998$	30.5860i	0.968183i
$999$	−31.1586	−0.985814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.3		24
17.3	odd	16		85.2.l.a.76.1	yes	24
17.4	even	4		1445.2.a.q.1.11		12
17.11	odd	16		85.2.l.a.66.1	✓	24
17.13	even	4		1445.2.a.p.1.11		12
17.16	even	2	inner	1445.2.d.j.866.4		24
51.11	even	16		765.2.be.b.406.6		24
51.20	even	16		765.2.be.b.586.6		24
85.3	even	16		425.2.n.c.399.6		24
85.4	even	4		7225.2.a.bq.1.2		12
85.28	even	16		425.2.n.f.49.1		24
85.37	even	16		425.2.n.f.399.1		24
85.54	odd	16		425.2.m.b.76.6		24
85.62	even	16		425.2.n.c.49.6		24
85.64	even	4		7225.2.a.bs.1.2		12
85.79	odd	16		425.2.m.b.151.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.1	✓	24	17.11	odd	16
85.2.l.a.76.1	yes	24	17.3	odd	16
425.2.m.b.76.6		24	85.54	odd	16
425.2.m.b.151.6		24	85.79	odd	16
425.2.n.c.49.6		24	85.62	even	16
425.2.n.c.399.6		24	85.3	even	16
425.2.n.f.49.1		24	85.28	even	16
425.2.n.f.399.1		24	85.37	even	16
765.2.be.b.406.6		24	51.11	even	16
765.2.be.b.586.6		24	51.20	even	16
1445.2.a.p.1.11		12	17.13	even	4
1445.2.a.q.1.11		12	17.4	even	4
1445.2.d.j.866.3		24	1.1	even	1	trivial
1445.2.d.j.866.4		24	17.16	even	2	inner
7225.2.a.bq.1.2		12	85.4	even	4
7225.2.a.bs.1.2		12	85.64	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)

\(f(q)\)	\(=\)	\(q-2.04505 q^{2} +3.19566i q^{3} +2.18224 q^{4} -1.00000i q^{5} -6.53528i q^{6} +1.17743i q^{7} -0.372688 q^{8} -7.21221 q^{9} +O(q^{10})\)	\(q-2.04505 q^{2} +3.19566i q^{3} +2.18224 q^{4} -1.00000i q^{5} -6.53528i q^{6} +1.17743i q^{7} -0.372688 q^{8} -7.21221 q^{9} +2.04505i q^{10} -4.92251i q^{11} +6.97368i q^{12} -2.46296 q^{13} -2.40791i q^{14} +3.19566 q^{15} -3.60231 q^{16} +14.7494 q^{18} -2.04173 q^{19} -2.18224i q^{20} -3.76267 q^{21} +10.0668i q^{22} -0.119023i q^{23} -1.19098i q^{24} -1.00000 q^{25} +5.03689 q^{26} -13.4608i q^{27} +2.56944i q^{28} +1.06541i q^{29} -6.53528 q^{30} +2.79577i q^{31} +8.11229 q^{32} +15.7307 q^{33} +1.17743 q^{35} -15.7388 q^{36} -2.31477i q^{37} +4.17544 q^{38} -7.87078i q^{39} +0.372688i q^{40} -0.717574i q^{41} +7.69485 q^{42} +10.0958 q^{43} -10.7421i q^{44} +7.21221i q^{45} +0.243408i q^{46} -3.39482 q^{47} -11.5117i q^{48} +5.61365 q^{49} +2.04505 q^{50} -5.37477 q^{52} +13.9241 q^{53} +27.5280i q^{54} -4.92251 q^{55} -0.438815i q^{56} -6.52466i q^{57} -2.17882i q^{58} -1.51711 q^{59} +6.97368 q^{60} -8.08120i q^{61} -5.71749i q^{62} -8.49190i q^{63} -9.38544 q^{64} +2.46296i q^{65} -32.1700 q^{66} -4.92534 q^{67} +0.380355 q^{69} -2.40791 q^{70} -6.63635i q^{71} +2.68790 q^{72} -3.66716i q^{73} +4.73382i q^{74} -3.19566i q^{75} -4.45554 q^{76} +5.79593 q^{77} +16.0962i q^{78} -8.18051i q^{79} +3.60231i q^{80} +21.3794 q^{81} +1.46748i q^{82} +6.08874 q^{83} -8.21104 q^{84} -20.6464 q^{86} -3.40468 q^{87} +1.83456i q^{88} +8.46170 q^{89} -14.7494i q^{90} -2.89997i q^{91} -0.259736i q^{92} -8.93431 q^{93} +6.94259 q^{94} +2.04173i q^{95} +25.9241i q^{96} -4.48946i q^{97} -11.4802 q^{98} +35.5022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9}+O(q^{10}) \) 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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