LMFDB - Embedded newform 1445.2.d.j.866.20

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			866.20
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.80583 q^{2} -0.687917i q^{3} +1.26102 q^{4} -1.00000i q^{5} -1.24226i q^{6} -4.34193i q^{7} -1.33447 q^{8} +2.52677 q^{9} +O(q^{10})$	\(q+1.80583 q^{2} -0.687917i q^{3} +1.26102 q^{4} -1.00000i q^{5} -1.24226i q^{6} -4.34193i q^{7} -1.33447 q^{8} +2.52677 q^{9} -1.80583i q^{10} -0.0525004i q^{11} -0.867478i q^{12} +3.02508 q^{13} -7.84078i q^{14} -0.687917 q^{15} -4.93187 q^{16} +4.56292 q^{18} -7.82043 q^{19} -1.26102i q^{20} -2.98689 q^{21} -0.0948069i q^{22} +1.04197i q^{23} +0.918004i q^{24} -1.00000 q^{25} +5.46278 q^{26} -3.80196i q^{27} -5.47526i q^{28} +0.420754i q^{29} -1.24226 q^{30} -1.38429i q^{31} -6.23717 q^{32} -0.0361159 q^{33} -4.34193 q^{35} +3.18631 q^{36} -0.336949i q^{37} -14.1224 q^{38} -2.08100i q^{39} +1.33447i q^{40} -6.59268i q^{41} -5.39381 q^{42} +9.99466 q^{43} -0.0662042i q^{44} -2.52677i q^{45} +1.88162i q^{46} -6.13168 q^{47} +3.39272i q^{48} -11.8523 q^{49} -1.80583 q^{50} +3.81469 q^{52} +12.0629 q^{53} -6.86569i q^{54} -0.0525004 q^{55} +5.79417i q^{56} +5.37981i q^{57} +0.759811i q^{58} +5.09779 q^{59} -0.867478 q^{60} -5.97063i q^{61} -2.49979i q^{62} -10.9711i q^{63} -1.39954 q^{64} -3.02508i q^{65} -0.0652192 q^{66} -0.916040 q^{67} +0.716788 q^{69} -7.84078 q^{70} -4.17986i q^{71} -3.37190 q^{72} +5.39059i q^{73} -0.608473i q^{74} +0.687917i q^{75} -9.86173 q^{76} -0.227953 q^{77} -3.75794i q^{78} -9.98296i q^{79} +4.93187i q^{80} +4.96488 q^{81} -11.9053i q^{82} -6.53008 q^{83} -3.76653 q^{84} +18.0487 q^{86} +0.289444 q^{87} +0.0700602i q^{88} +10.2159 q^{89} -4.56292i q^{90} -13.1347i q^{91} +1.31395i q^{92} -0.952278 q^{93} -11.0728 q^{94} +7.82043i q^{95} +4.29066i q^{96} +19.2238i q^{97} -21.4033 q^{98} -0.132657i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.80583	1.27691	0.638457	−	0.769657i	$-0.279573\pi$
$2$	1.80583	1.27691	0.638457	+	0.769657i	$0.279573\pi$
$3$	− 0.687917i	− 0.397169i	−0.980084	−	0.198585i	$-0.936366\pi$
$3$	− 0.687917i	− 0.397169i	0.980084	−	0.198585i	$-0.0636344\pi$
$4$	1.26102	0.630511
$5$	− 1.00000i	− 0.447214i
$5$	− 1.00000i	− 0.447214i
$6$	− 1.24226i	− 0.507151i
$7$	− 4.34193i	− 1.64109i	−0.571579	−	0.820547i	$-0.693669\pi$
$7$	− 4.34193i	− 1.64109i	0.571579	−	0.820547i	$-0.306331\pi$
$8$	−1.33447	−0.471806
$9$	2.52677	0.842257
$10$	− 1.80583i	− 0.571054i
$11$	− 0.0525004i	− 0.0158295i	−0.999969	−	0.00791474i	$-0.997481\pi$
$11$	− 0.0525004i	− 0.0158295i	0.999969	−	0.00791474i	$-0.00251937\pi$
$12$	− 0.867478i	− 0.250419i
$13$	3.02508	0.839006	0.419503	−	0.907754i	$-0.362204\pi$
$13$	3.02508	0.839006	0.419503	+	0.907754i	$0.362204\pi$
$14$	− 7.84078i	− 2.09554i
$15$	−0.687917	−0.177619
$16$	−4.93187	−1.23297
$17$	0	0
$17$	0	0
$18$	4.56292	1.07549
$19$	−7.82043	−1.79413	−0.897065	−	0.441898i	$-0.854305\pi$
$19$	−7.82043	−1.79413	−0.897065	+	0.441898i	$0.854305\pi$
$20$	− 1.26102i	− 0.281973i
$21$	−2.98689	−0.651792
$22$	− 0.0948069i	− 0.0202129i
$23$	1.04197i	0.217266i	0.994082	+	0.108633i	$0.0346473\pi$
$23$	1.04197i	0.217266i	−0.994082	+	0.108633i	$0.965353\pi$
$24$	0.918004i	0.187387i
$25$	−1.00000	−0.200000
$26$	5.46278	1.07134
$27$	− 3.80196i	− 0.731687i
$28$	− 5.47526i	− 1.03473i
$29$	0.420754i	0.0781321i	0.999237	+	0.0390661i	$0.0124383\pi$
$29$	0.420754i	0.0781321i	−0.999237	+	0.0390661i	$0.987562\pi$
$30$	−1.24226	−0.226805
$31$	− 1.38429i	− 0.248626i	−0.992243	−	0.124313i	$-0.960327\pi$
$31$	− 1.38429i	− 0.248626i	0.992243	−	0.124313i	$-0.0396727\pi$
$32$	−6.23717	−1.10259
$33$	−0.0361159	−0.00628698
$34$	0	0
$35$	−4.34193	−0.733920
$36$	3.18631	0.531052
$37$	− 0.336949i	− 0.0553941i	−0.999616	−	0.0276971i	$-0.991183\pi$
$37$	− 0.336949i	− 0.0553941i	0.999616	−	0.0276971i	$-0.00881738\pi$
$38$	−14.1224	−2.29095
$39$	− 2.08100i	− 0.333227i
$40$	1.33447i	0.210998i
$41$	− 6.59268i	− 1.02960i	−0.857309	−	0.514802i	$-0.827865\pi$
$41$	− 6.59268i	− 1.02960i	0.857309	−	0.514802i	$-0.172135\pi$
$42$	−5.39381	−0.832283
$43$	9.99466	1.52417	0.762086	−	0.647476i	$-0.224175\pi$
$43$	9.99466	1.52417	0.762086	+	0.647476i	$0.224175\pi$
$44$	− 0.0662042i	− 0.00998065i
$45$	− 2.52677i	− 0.376669i
$46$	1.88162i	0.277430i
$47$	−6.13168	−0.894398	−0.447199	−	0.894435i	$-0.647578\pi$
$47$	−6.13168	−0.894398	−0.447199	+	0.894435i	$0.647578\pi$
$48$	3.39272i	0.489696i
$49$	−11.8523	−1.69319
$50$	−1.80583	−0.255383
$51$	0	0
$52$	3.81469	0.529002
$53$	12.0629	1.65696	0.828482	−	0.560016i	$-0.189205\pi$
$53$	12.0629	1.65696	0.828482	+	0.560016i	$0.189205\pi$
$54$	− 6.86569i	− 0.934302i
$55$	−0.0525004	−0.00707916
$56$	5.79417i	0.774279i
$57$	5.37981i	0.712573i
$58$	0.759811i	0.0997681i
$59$	5.09779	0.663676	0.331838	−	0.943336i	$-0.392331\pi$
$59$	5.09779	0.663676	0.331838	+	0.943336i	$0.392331\pi$
$60$	−0.867478	−0.111991
$61$	− 5.97063i	− 0.764461i	−0.924067	−	0.382230i	$-0.875156\pi$
$61$	− 5.97063i	− 0.764461i	0.924067	−	0.382230i	$-0.124844\pi$
$62$	− 2.49979i	− 0.317474i
$63$	− 10.9711i	− 1.38222i
$64$	−1.39954	−0.174943
$65$	− 3.02508i	− 0.375215i
$66$	−0.0652192	−0.00802793
$67$	−0.916040	−0.111912	−0.0559561	−	0.998433i	$-0.517821\pi$
$67$	−0.916040	−0.111912	−0.0559561	+	0.998433i	$0.517821\pi$
$68$	0	0
$69$	0.716788	0.0862912
$70$	−7.84078	−0.937153
$71$	− 4.17986i	− 0.496058i	−0.968753	−	0.248029i	$-0.920217\pi$
$71$	− 4.17986i	− 0.496058i	0.968753	−	0.248029i	$-0.0797829\pi$
$72$	−3.37190	−0.397382
$73$	5.39059i	0.630920i	0.948939	+	0.315460i	$0.102159\pi$
$73$	5.39059i	0.630920i	−0.948939	+	0.315460i	$0.897841\pi$
$74$	− 0.608473i	− 0.0707336i
$75$	0.687917i	0.0794338i
$76$	−9.86173	−1.13122
$77$	−0.227953	−0.0259777
$78$	− 3.75794i	− 0.425503i
$79$	− 9.98296i	− 1.12317i	−0.827419	−	0.561585i	$-0.810192\pi$
$79$	− 9.98296i	− 1.12317i	0.827419	−	0.561585i	$-0.189808\pi$
$80$	4.93187i	0.551400i
$81$	4.96488	0.551653
$82$	− 11.9053i	− 1.31472i
$83$	−6.53008	−0.716770	−0.358385	−	0.933574i	$-0.616672\pi$
$83$	−6.53008	−0.716770	−0.358385	+	0.933574i	$0.616672\pi$
$84$	−3.76653	−0.410962
$85$	0	0
$86$	18.0487	1.94624
$87$	0.289444	0.0310317
$88$	0.0700602i	0.00746845i
$89$	10.2159	1.08289	0.541443	−	0.840738i	$-0.317878\pi$
$89$	10.2159	1.08289	0.541443	+	0.840738i	$0.317878\pi$
$90$	− 4.56292i	− 0.480974i
$91$	− 13.1347i	− 1.37689i
$92$	1.31395i	0.136988i
$93$	−0.952278	−0.0987466
$94$	−11.0728	−1.14207
$95$	7.82043i	0.802359i
$96$	4.29066i	0.437914i
$97$	19.2238i	1.95188i	0.218037	+	0.975940i	$0.430035\pi$
$97$	19.2238i	1.95188i	−0.218037	+	0.975940i	$0.569965\pi$
$98$	−21.4033	−2.16206
$99$	− 0.132657i	− 0.0133325i
$100$	−1.26102	−0.126102
$101$	13.2926	1.32266	0.661331	−	0.750094i	$-0.269992\pi$
$101$	13.2926	1.32266	0.661331	+	0.750094i	$0.269992\pi$
$102$	0	0
$103$	−6.91299	−0.681157	−0.340579	−	0.940216i	$-0.610623\pi$
$103$	−6.91299	−0.681157	−0.340579	+	0.940216i	$0.610623\pi$
$104$	−4.03687	−0.395848
$105$	2.98689i	0.291490i
$106$	21.7835	2.11580
$107$	14.7407i	1.42504i	0.701651	+	0.712520i	$0.252446\pi$
$107$	14.7407i	1.42504i	−0.701651	+	0.712520i	$0.747554\pi$
$108$	− 4.79435i	− 0.461337i
$109$	4.74828i	0.454803i	0.973801	+	0.227402i	$0.0730230\pi$
$109$	4.74828i	0.454803i	−0.973801	+	0.227402i	$0.926977\pi$
$110$	−0.0948069	−0.00903948
$111$	−0.231793	−0.0220008
$112$	21.4138i	2.02342i
$113$	− 3.01331i	− 0.283468i	−0.989905	−	0.141734i	$-0.954732\pi$
$113$	− 3.01331i	− 0.283468i	0.989905	−	0.141734i	$-0.0452678\pi$
$114$	9.71502i	0.909895i
$115$	1.04197	0.0971641
$116$	0.530580i	0.0492631i
$117$	7.64368	0.706658
$118$	9.20574	0.847457
$119$	0	0
$120$	0.918004	0.0838020
$121$	10.9972	0.999749
$122$	− 10.7819i	− 0.976151i
$123$	−4.53522	−0.408927
$124$	− 1.74562i	− 0.156761i
$125$	1.00000i	0.0894427i
$126$	− 19.8119i	− 1.76498i
$127$	0.00828706	0.000735358 0	0.000367679	−	1.00000i	$-0.499883\pi$
$127$	0.00828706	0.000735358 0	0.000367679		1.00000i	$0.499883\pi$
$128$	9.94702	0.879200
$129$	− 6.87550i	− 0.605354i
$130$	− 5.46278i	− 0.479117i
$131$	− 8.18458i	− 0.715090i	−0.933896	−	0.357545i	$-0.883614\pi$
$131$	− 8.18458i	− 0.715090i	0.933896	−	0.357545i	$-0.116386\pi$
$132$	−0.0455430	−0.00396401
$133$	33.9558i	2.94434i
$134$	−1.65421	−0.142902
$135$	−3.80196	−0.327221
$136$	0	0
$137$	−2.23387	−0.190852	−0.0954260	−	0.995437i	$-0.530421\pi$
$137$	−2.23387	−0.190852	−0.0954260	+	0.995437i	$0.530421\pi$
$138$	1.29440	0.110186
$139$	19.7358i	1.67397i	0.547225	+	0.836985i	$0.315684\pi$
$139$	19.7358i	1.67397i	−0.547225	+	0.836985i	$0.684316\pi$
$140$	−5.47526	−0.462744
$141$	4.21809i	0.355227i
$142$	− 7.54812i	− 0.633424i
$143$	− 0.158818i	− 0.0132810i
$144$	−12.4617	−1.03847
$145$	0.420754	0.0349418
$146$	9.73448i	0.805632i
$147$	8.15343i	0.672483i
$148$	− 0.424900i	− 0.0349266i
$149$	10.1835	0.834263	0.417132	−	0.908846i	$-0.363035\pi$
$149$	10.1835	0.834263	0.417132	+	0.908846i	$0.363035\pi$
$150$	1.24226i	0.101430i
$151$	15.3484	1.24903	0.624516	−	0.781012i	$-0.285296\pi$
$151$	15.3484	1.24903	0.624516	+	0.781012i	$0.285296\pi$
$152$	10.4361	0.846482
$153$	0	0
$154$	−0.411645	−0.0331713
$155$	−1.38429	−0.111189
$156$	− 2.62419i	− 0.210103i
$157$	9.41222	0.751177	0.375588	−	0.926787i	$-0.377441\pi$
$157$	9.41222	0.751177	0.375588	+	0.926787i	$0.377441\pi$
$158$	− 18.0275i	− 1.43419i
$159$	− 8.29826i	− 0.658095i
$160$	6.23717i	0.493092i
$161$	4.52415	0.356553
$162$	8.96572	0.704414
$163$	− 12.4453i	− 0.974793i	−0.873181	−	0.487397i	$-0.837947\pi$
$163$	− 12.4453i	− 0.974793i	0.873181	−	0.487397i	$-0.162053\pi$
$164$	− 8.31351i	− 0.649176i
$165$	0.0361159i	0.00281162i
$166$	−11.7922	−0.915253
$167$	12.6025i	0.975211i	0.873064	+	0.487605i	$0.162130\pi$
$167$	12.6025i	0.975211i	−0.873064	+	0.487605i	$0.837870\pi$
$168$	3.98591	0.307520
$169$	−3.84890	−0.296069
$170$	0	0
$171$	−19.7604	−1.51112
$172$	12.6035	0.961007
$173$	− 12.1965i	− 0.927284i	−0.886023	−	0.463642i	$-0.846542\pi$
$173$	− 12.1965i	− 0.927284i	0.886023	−	0.463642i	$-0.153458\pi$
$174$	0.522687	0.0396248
$175$	4.34193i	0.328219i
$176$	0.258925i	0.0195172i
$177$	− 3.50686i	− 0.263592i
$178$	18.4482	1.38275
$179$	−13.8608	−1.03600	−0.518002	−	0.855379i	$-0.673324\pi$
$179$	−13.8608	−1.03600	−0.518002	+	0.855379i	$0.673324\pi$
$180$	− 3.18631i	− 0.237494i
$181$	− 2.04424i	− 0.151947i	−0.997110	−	0.0759736i	$-0.975794\pi$
$181$	− 2.04424i	− 0.151947i	0.997110	−	0.0759736i	$-0.0242065\pi$
$182$	− 23.7190i	− 1.75817i
$183$	−4.10730	−0.303620
$184$	− 1.39048i	− 0.102507i
$185$	−0.336949	−0.0247730
$186$	−1.71965	−0.126091
$187$	0	0
$188$	−7.73218	−0.563927
$189$	−16.5078	−1.20077
$190$	14.1224i	1.02454i
$191$	−3.08056	−0.222902	−0.111451	−	0.993770i	$-0.535550\pi$
$191$	−3.08056	−0.222902	−0.111451	+	0.993770i	$0.535550\pi$
$192$	0.962768i	0.0694818i
$193$	20.6419i	1.48584i	0.669382	+	0.742918i	$0.266559\pi$
$193$	20.6419i	1.48584i	−0.669382	+	0.742918i	$0.733441\pi$
$194$	34.7149i	2.49239i
$195$	−2.08100	−0.149024
$196$	−14.9461	−1.06758
$197$	− 18.2365i	− 1.29930i	−0.760235	−	0.649649i	$-0.774916\pi$
$197$	− 18.2365i	− 1.29930i	0.760235	−	0.649649i	$-0.225084\pi$
$198$	− 0.239555i	− 0.0170244i
$199$	26.6677i	1.89042i	0.326463	+	0.945210i	$0.394143\pi$
$199$	26.6677i	1.89042i	−0.326463	+	0.945210i	$0.605857\pi$
$200$	1.33447	0.0943613
$201$	0.630160i	0.0444480i
$202$	24.0041	1.68893
$203$	1.82689	0.128222
$204$	0	0
$205$	−6.59268	−0.460453
$206$	−12.4837	−0.869779
$207$	2.63282i	0.182993i
$208$	−14.9193	−1.03447
$209$	0.410576i	0.0284001i
$210$	5.39381i	0.372208i
$211$	− 7.80566i	− 0.537364i	−0.963229	−	0.268682i	$-0.913412\pi$
$211$	− 7.80566i	− 0.537364i	0.963229	−	0.268682i	$-0.0865881\pi$
$212$	15.2115	1.04473
$213$	−2.87540	−0.197019
$214$	26.6193i	1.81966i
$215$	− 9.99466i	− 0.681630i
$216$	5.07360i	0.345215i
$217$	−6.01049	−0.408019
$218$	8.57459i	0.580745i
$219$	3.70828	0.250582
$220$	−0.0662042	−0.00446348
$221$	0	0
$222$	−0.418579	−0.0280932
$223$	−4.76891	−0.319350	−0.159675	−	0.987170i	$-0.551045\pi$
$223$	−4.76891	−0.319350	−0.159675	+	0.987170i	$0.551045\pi$
$224$	27.0814i	1.80945i
$225$	−2.52677	−0.168451
$226$	− 5.44152i	− 0.361964i
$227$	− 11.2111i	− 0.744105i	−0.928212	−	0.372053i	$-0.878654\pi$
$227$	− 11.2111i	− 0.744105i	0.928212	−	0.372053i	$-0.121346\pi$
$228$	6.78405i	0.449285i
$229$	−20.6484	−1.36449	−0.682244	−	0.731125i	$-0.738996\pi$
$229$	−20.6484	−1.36449	−0.682244	+	0.731125i	$0.738996\pi$
$230$	1.88162	0.124070
$231$	0.156813i	0.0103175i
$232$	− 0.561484i	− 0.0368632i
$233$	3.05851i	0.200370i	0.994969	+	0.100185i	$0.0319434\pi$
$233$	3.05851i	0.200370i	−0.994969	+	0.100185i	$0.968057\pi$
$234$	13.8032	0.902342
$235$	6.13168i	0.399987i
$236$	6.42842	0.418455
$237$	−6.86745	−0.446089
$238$	0	0
$239$	4.94072	0.319588	0.159794	−	0.987150i	$-0.448917\pi$
$239$	4.94072	0.319588	0.159794	+	0.987150i	$0.448917\pi$
$240$	3.39272	0.218999
$241$	− 1.66176i	− 0.107043i	−0.998567	−	0.0535217i	$-0.982955\pi$
$241$	− 1.66176i	− 0.107043i	0.998567	−	0.0535217i	$-0.0170446\pi$
$242$	19.8592	1.27659
$243$	− 14.8213i	− 0.950787i
$244$	− 7.52909i	− 0.482001i
$245$	11.8523i	0.757218i
$246$	−8.18983	−0.522165
$247$	−23.6574	−1.50529
$248$	1.84729i	0.117303i
$249$	4.49215i	0.284679i
$250$	1.80583i	0.114211i
$251$	9.14240	0.577063	0.288531	−	0.957470i	$-0.406833\pi$
$251$	9.14240	0.577063	0.288531	+	0.957470i	$0.406833\pi$
$252$	− 13.8347i	− 0.871506i
$253$	0.0547038	0.00343920
$254$	0.0149650	0.000938989 0
$255$	0	0
$256$	20.7617	1.29761
$257$	16.6522	1.03874	0.519369	−	0.854550i	$-0.326167\pi$
$257$	16.6522	1.03874	0.519369	+	0.854550i	$0.326167\pi$
$258$	− 12.4160i	− 0.772985i
$259$	−1.46301	−0.0909070
$260$	− 3.81469i	− 0.236577i
$261$	1.06315i	0.0658073i
$262$	− 14.7800i	− 0.913109i
$263$	21.7280	1.33981	0.669903	−	0.742448i	$-0.266335\pi$
$263$	21.7280	1.33981	0.669903	+	0.742448i	$0.266335\pi$
$264$	0.0481956	0.00296624
$265$	− 12.0629i	− 0.741017i
$266$	61.3183i	3.75967i
$267$	− 7.02771i	− 0.430089i
$268$	−1.15515	−0.0705618
$269$	− 23.1721i	− 1.41283i	−0.707799	−	0.706414i	$-0.750312\pi$
$269$	− 23.1721i	− 1.41283i	0.707799	−	0.706414i	$-0.249688\pi$
$270$	−6.86569	−0.417833
$271$	3.95595	0.240307	0.120153	−	0.992755i	$-0.461661\pi$
$271$	3.95595	0.240307	0.120153	+	0.992755i	$0.461661\pi$
$272$	0	0
$273$	−9.03556	−0.546857
$274$	−4.03398	−0.243702
$275$	0.0525004i	0.00316590i
$276$	0.903885	0.0544075
$277$	− 16.9099i	− 1.01602i	−0.861352	−	0.508009i	$-0.830382\pi$
$277$	− 16.9099i	− 1.01602i	0.861352	−	0.508009i	$-0.169618\pi$
$278$	35.6395i	2.13752i
$279$	− 3.49779i	− 0.209407i
$280$	5.79417	0.346268
$281$	−4.66987	−0.278581	−0.139291	−	0.990252i	$-0.544482\pi$
$281$	−4.66987	−0.278581	−0.139291	+	0.990252i	$0.544482\pi$
$282$	7.61715i	0.453595i
$283$	8.70036i	0.517183i	0.965987	+	0.258591i	$0.0832583\pi$
$283$	8.70036i	0.517183i	−0.965987	+	0.258591i	$0.916742\pi$
$284$	− 5.27089i	− 0.312770i
$285$	5.37981	0.318672
$286$	− 0.286798i	− 0.0169587i
$287$	−28.6250	−1.68968
$288$	−15.7599	−0.928661
$289$	0	0
$290$	0.759811	0.0446176
$291$	13.2244	0.775227
$292$	6.79765i	0.397802i
$293$	0.739100	0.0431787	0.0215893	−	0.999767i	$-0.493127\pi$
$293$	0.739100	0.0431787	0.0215893	+	0.999767i	$0.493127\pi$
$294$	14.7237i	0.858704i
$295$	− 5.09779i	− 0.296805i
$296$	0.449649i	0.0261353i
$297$	−0.199605	−0.0115822
$298$	18.3896	1.06528
$299$	3.15204i	0.182287i
$300$	0.867478i	0.0500839i
$301$	− 43.3961i	− 2.50131i
$302$	27.7165	1.59491
$303$	− 9.14419i	− 0.525320i
$304$	38.5693	2.21210
$305$	−5.97063	−0.341877
$306$	0	0
$307$	−2.86108	−0.163290	−0.0816451	−	0.996661i	$-0.526017\pi$
$307$	−2.86108	−0.163290	−0.0816451	+	0.996661i	$0.526017\pi$
$308$	−0.287454	−0.0163792
$309$	4.75556i	0.270535i
$310$	−2.49979	−0.141979
$311$	20.4980i	1.16233i	0.813784	+	0.581167i	$0.197404\pi$
$311$	20.4980i	1.16233i	−0.813784	+	0.581167i	$0.802596\pi$
$312$	2.77703i	0.157219i
$313$	− 8.46543i	− 0.478494i	−0.970959	−	0.239247i	$-0.923099\pi$
$313$	− 8.46543i	− 0.478494i	0.970959	−	0.239247i	$-0.0769006\pi$
$314$	16.9969	0.959189
$315$	−10.9711	−0.618149
$316$	− 12.5887i	− 0.708171i
$317$	21.0918i	1.18463i	0.805705	+	0.592317i	$0.201787\pi$
$317$	21.0918i	1.18463i	−0.805705	+	0.592317i	$0.798213\pi$
$318$	− 14.9852i	− 0.840331i
$319$	0.0220898	0.00123679
$320$	1.39954i	0.0782367i
$321$	10.1404	0.565982
$322$	8.16985	0.455288
$323$	0	0
$324$	6.26082	0.347823
$325$	−3.02508	−0.167801
$326$	− 22.4741i	− 1.24473i
$327$	3.26643	0.180634
$328$	8.79773i	0.485774i
$329$	26.6233i	1.46779i
$330$	0.0652192i	0.00359020i
$331$	15.2261	0.836903	0.418451	−	0.908239i	$-0.362573\pi$
$331$	15.2261	0.836903	0.418451	+	0.908239i	$0.362573\pi$
$332$	−8.23457	−0.451931
$333$	− 0.851393i	− 0.0466561i
$334$	22.7580i	1.24526i
$335$	0.916040i	0.0500486i
$336$	14.7309	0.803638
$337$	11.4737i	0.625011i	0.949916	+	0.312506i	$0.101168\pi$
$337$	11.4737i	0.625011i	−0.949916	+	0.312506i	$0.898832\pi$
$338$	−6.95046	−0.378055
$339$	−2.07290	−0.112585
$340$	0	0
$341$	−0.0726759	−0.00393562
$342$	−35.6840	−1.92957
$343$	21.0685i	1.13759i
$344$	−13.3376	−0.719114
$345$	− 0.716788i	− 0.0385906i
$346$	− 22.0248i	− 1.18406i
$347$	14.9843i	0.804399i	0.915552	+	0.402199i	$0.131754\pi$
$347$	14.9843i	0.804399i	−0.915552	+	0.402199i	$0.868246\pi$
$348$	0.364995	0.0195658
$349$	4.53667	0.242842	0.121421	−	0.992601i	$-0.461255\pi$
$349$	4.53667	0.242842	0.121421	+	0.992601i	$0.461255\pi$
$350$	7.84078i	0.419108i
$351$	− 11.5012i	− 0.613890i
$352$	0.327454i	0.0174534i
$353$	−7.71469	−0.410612	−0.205306	−	0.978698i	$-0.565819\pi$
$353$	−7.71469	−0.410612	−0.205306	+	0.978698i	$0.565819\pi$
$354$	− 6.33279i	− 0.336584i
$355$	−4.17986	−0.221844
$356$	12.8825	0.682771
$357$	0	0
$358$	−25.0302	−1.32289
$359$	11.0284	0.582057	0.291029	−	0.956714i	$-0.406003\pi$
$359$	11.0284	0.582057	0.291029	+	0.956714i	$0.406003\pi$
$360$	3.37190i	0.177715i
$361$	42.1592	2.21890
$362$	− 3.69155i	− 0.194023i
$363$	− 7.56519i	− 0.397070i
$364$	− 16.5631i	− 0.868142i
$365$	5.39059	0.282156
$366$	−7.41708	−0.387697
$367$	− 16.0285i	− 0.836683i	−0.908290	−	0.418342i	$-0.862611\pi$
$367$	− 16.0285i	− 0.836683i	0.908290	−	0.418342i	$-0.137389\pi$
$368$	− 5.13885i	− 0.267881i
$369$	− 16.6582i	− 0.867191i
$370$	−0.608473	−0.0316330
$371$	− 52.3761i	− 2.71923i
$372$	−1.20084	−0.0622608
$373$	10.2501	0.530732	0.265366	−	0.964148i	$-0.414507\pi$
$373$	10.2501	0.530732	0.265366	+	0.964148i	$0.414507\pi$
$374$	0	0
$375$	0.687917	0.0355239
$376$	8.18254	0.421982
$377$	1.27281i	0.0655533i
$378$	−29.8103	−1.53328
$379$	− 13.9520i	− 0.716664i	−0.933594	−	0.358332i	$-0.883346\pi$
$379$	− 13.9520i	− 0.716664i	0.933594	−	0.358332i	$-0.116654\pi$
$380$	9.86173i	0.505896i
$381$	− 0.00570081i	0 0.000292061i
$382$	−5.56297	−0.284626
$383$	5.62186	0.287264	0.143632	−	0.989631i	$-0.454122\pi$
$383$	5.62186	0.287264	0.143632	+	0.989631i	$0.454122\pi$
$384$	− 6.84272i	− 0.349191i
$385$	0.227953i	0.0116176i
$386$	37.2757i	1.89729i
$387$	25.2542	1.28374
$388$	24.2416i	1.23068i
$389$	−35.8157	−1.81593	−0.907965	−	0.419047i	$-0.862364\pi$
$389$	−35.8157	−1.81593	−0.907965	+	0.419047i	$0.862364\pi$
$390$	−3.75794	−0.190291
$391$	0	0
$392$	15.8166	0.798858
$393$	−5.63032	−0.284012
$394$	− 32.9320i	− 1.65909i
$395$	−9.98296	−0.502297
$396$	− 0.167283i	− 0.00840627i
$397$	3.89017i	0.195242i	0.995224	+	0.0976211i	$0.0311233\pi$
$397$	3.89017i	0.195242i	−0.995224	+	0.0976211i	$0.968877\pi$
$398$	48.1573i	2.41390i
$399$	23.3587	1.16940
$400$	4.93187	0.246593
$401$	36.7386i	1.83464i	0.398156	+	0.917318i	$0.369650\pi$
$401$	36.7386i	1.83464i	−0.398156	+	0.917318i	$0.630350\pi$
$402$	1.13796i	0.0567564i
$403$	− 4.18759i	− 0.208599i
$404$	16.7622	0.833952
$405$	− 4.96488i	− 0.246707i
$406$	3.29904	0.163729
$407$	−0.0176900	−0.000876860 0
$408$	0	0
$409$	−22.3529	−1.10528	−0.552641	−	0.833419i	$-0.686380\pi$
$409$	−22.3529	−1.10528	−0.552641	+	0.833419i	$0.686380\pi$
$410$	−11.9053	−0.587959
$411$	1.53671i	0.0758005i
$412$	−8.71743	−0.429477
$413$	− 22.1342i	− 1.08915i
$414$	4.75442i	0.233667i
$415$	6.53008i	0.320549i
$416$	−18.8679	−0.925077
$417$	13.5766	0.664849
$418$	0.741431i	0.0362646i
$419$	− 21.8658i	− 1.06821i	−0.845417	−	0.534107i	$-0.820648\pi$
$419$	− 21.8658i	− 1.06821i	0.845417	−	0.534107i	$-0.179352\pi$
$420$	3.76653i	0.183788i
$421$	20.6111	1.00453	0.502263	−	0.864715i	$-0.332501\pi$
$421$	20.6111	1.00453	0.502263	+	0.864715i	$0.332501\pi$
$422$	− 14.0957i	− 0.686168i
$423$	−15.4934	−0.753313
$424$	−16.0975	−0.781766
$425$	0	0
$426$	−5.19248	−0.251576
$427$	−25.9241	−1.25455
$428$	18.5884i	0.898503i
$429$	−0.109254	−0.00527481
$430$	− 18.0487i	− 0.870384i
$431$	22.3052i	1.07441i	0.843453	+	0.537203i	$0.180519\pi$
$431$	22.3052i	1.07441i	−0.843453	+	0.537203i	$0.819481\pi$
$432$	18.7508i	0.902146i
$433$	−8.93127	−0.429210	−0.214605	−	0.976701i	$-0.568846\pi$
$433$	−8.93127	−0.429210	−0.214605	+	0.976701i	$0.568846\pi$
$434$	−10.8539	−0.521005
$435$	− 0.289444i	− 0.0138778i
$436$	5.98769i	0.286758i
$437$	− 8.14865i	− 0.389803i
$438$	6.69652	0.319972
$439$	22.2643i	1.06262i	0.847179	+	0.531308i	$0.178299\pi$
$439$	22.2643i	1.06262i	−0.847179	+	0.531308i	$0.821701\pi$
$440$	0.0700602	0.00333999
$441$	−29.9481	−1.42610
$442$	0	0
$443$	−6.17421	−0.293346	−0.146673	−	0.989185i	$-0.546856\pi$
$443$	−6.17421	−0.293346	−0.146673	+	0.989185i	$0.546856\pi$
$444$	−0.292296	−0.0138718
$445$	− 10.2159i	− 0.484281i
$446$	−8.61184	−0.407783
$447$	− 7.00539i	− 0.331344i
$448$	6.07671i	0.287097i
$449$	− 30.2985i	− 1.42988i	−0.699188	−	0.714938i	$-0.746455\pi$
$449$	− 30.2985i	− 1.42988i	0.699188	−	0.714938i	$-0.253545\pi$
$450$	−4.56292	−0.215098
$451$	−0.346119	−0.0162981
$452$	− 3.79984i	− 0.178730i
$453$	− 10.5584i	− 0.496077i
$454$	− 20.2453i	− 0.950159i
$455$	−13.1347	−0.615763
$456$	− 7.17919i	− 0.336196i
$457$	25.5756	1.19638	0.598188	−	0.801356i	$-0.295888\pi$
$457$	25.5756	1.19638	0.598188	+	0.801356i	$0.295888\pi$
$458$	−37.2876	−1.74233
$459$	0	0
$460$	1.31395	0.0612630
$461$	14.0565	0.654677	0.327338	−	0.944907i	$-0.393848\pi$
$461$	14.0565	0.654677	0.327338	+	0.944907i	$0.393848\pi$
$462$	0.283177i	0.0131746i
$463$	−25.1233	−1.16758	−0.583789	−	0.811905i	$-0.698431\pi$
$463$	−25.1233	−1.16758	−0.583789	+	0.811905i	$0.698431\pi$
$464$	− 2.07511i	− 0.0963343i
$465$	0.952278i	0.0441608i
$466$	5.52315i	0.255855i
$467$	−22.2900	−1.03146	−0.515730	−	0.856751i	$-0.672479\pi$
$467$	−22.2900	−1.03146	−0.515730	+	0.856751i	$0.672479\pi$
$468$	9.63884	0.445556
$469$	3.97738i	0.183658i
$470$	11.0728i	0.510749i
$471$	− 6.47483i	− 0.298344i
$472$	−6.80285	−0.313126
$473$	− 0.524724i	− 0.0241268i
$474$	−12.4014	−0.569617
$475$	7.82043	0.358826
$476$	0	0
$477$	30.4801	1.39559
$478$	8.92209	0.408087
$479$	− 26.7496i	− 1.22222i	−0.791545	−	0.611111i	$-0.790723\pi$
$479$	− 26.7496i	− 1.22222i	0.791545	−	0.611111i	$-0.209277\pi$
$480$	4.29066	0.195841
$481$	− 1.01930i	− 0.0464760i
$482$	− 3.00086i	− 0.136685i
$483$	− 3.11224i	− 0.141612i
$484$	13.8678	0.630353
$485$	19.2238	0.872908
$486$	− 26.7647i	− 1.21407i
$487$	23.1460i	1.04885i	0.851458	+	0.524423i	$0.175719\pi$
$487$	23.1460i	1.04885i	−0.851458	+	0.524423i	$0.824281\pi$
$488$	7.96763i	0.360677i
$489$	−8.56135	−0.387158
$490$	21.4033i	0.966903i
$491$	−7.78981	−0.351549	−0.175775	−	0.984430i	$-0.556243\pi$
$491$	−7.78981	−0.351549	−0.175775	+	0.984430i	$0.556243\pi$
$492$	−5.71901	−0.257833
$493$	0	0
$494$	−42.7213	−1.92212
$495$	−0.132657	−0.00596247
$496$	6.82714i	0.306548i
$497$	−18.1487	−0.814079
$498$	8.11207i	0.363510i
$499$	− 8.79764i	− 0.393837i	−0.980420	−	0.196918i	$-0.936907\pi$
$499$	− 8.79764i	− 0.393837i	0.980420	−	0.196918i	$-0.0630934\pi$
$500$	1.26102i	0.0563946i
$501$	8.66948	0.387324
$502$	16.5096	0.736860
$503$	− 7.83946i	− 0.349544i	−0.984609	−	0.174772i	$-0.944081\pi$
$503$	− 7.83946i	− 0.349544i	0.984609	−	0.174772i	$-0.0559188\pi$
$504$	14.6405i	0.652141i
$505$	− 13.2926i	− 0.591512i
$506$	0.0987858	0.00439156
$507$	2.64773i	0.117590i
$508$	0.0104502	0.000463651 0
$509$	−2.52868	−0.112082	−0.0560409	−	0.998428i	$-0.517848\pi$
$509$	−2.52868	−0.112082	−0.0560409	+	0.998428i	$0.517848\pi$
$510$	0	0
$511$	23.4055	1.03540
$512$	17.5981	0.777732
$513$	29.7330i	1.31274i
$514$	30.0711	1.32638
$515$	6.91299i	0.304623i
$516$	− 8.67015i	− 0.381682i
$517$	0.321916i	0.0141578i
$518$	−2.64195	−0.116080
$519$	−8.39019	−0.368289
$520$	4.03687i	0.177029i
$521$	− 10.1083i	− 0.442853i	−0.975177	−	0.221426i	$-0.928929\pi$
$521$	− 10.1083i	− 0.442853i	0.975177	−	0.221426i	$-0.0710712\pi$
$522$	1.91987i	0.0840303i
$523$	−5.80494	−0.253833	−0.126916	−	0.991913i	$-0.540508\pi$
$523$	−5.80494	−0.253833	−0.126916	+	0.991913i	$0.540508\pi$
$524$	− 10.3209i	− 0.450872i
$525$	2.98689	0.130358
$526$	39.2371	1.71082
$527$	0	0
$528$	0.178119	0.00775164
$529$	21.9143	0.952796
$530$	− 21.7835i	− 0.946215i
$531$	12.8809	0.558985
$532$	42.8189i	1.85644i
$533$	− 19.9434i	− 0.863844i
$534$	− 12.6908i	− 0.549187i
$535$	14.7407	0.637298
$536$	1.22243	0.0528009
$537$	9.53508i	0.411469i
$538$	− 41.8449i	− 1.80406i
$539$	0.622253i	0.0268023i
$540$	−4.79435	−0.206316
$541$	42.3404i	1.82035i	0.414219	+	0.910177i	$0.364055\pi$
$541$	42.3404i	1.82035i	−0.414219	+	0.910177i	$0.635945\pi$
$542$	7.14377	0.306851
$543$	−1.40627	−0.0603487
$544$	0	0
$545$	4.74828	0.203394
$546$	−16.3167	−0.698290
$547$	− 20.0061i	− 0.855398i	−0.903921	−	0.427699i	$-0.859324\pi$
$547$	− 20.0061i	− 0.855398i	0.903921	−	0.427699i	$-0.140676\pi$
$548$	−2.81695	−0.120334
$549$	− 15.0864i	− 0.643872i
$550$	0.0948069i	0.00404258i
$551$	− 3.29048i	− 0.140179i
$552$	−0.956532	−0.0407127
$553$	−43.3453	−1.84323
$554$	− 30.5364i	− 1.29737i
$555$	0.231793i	0.00983907i
$556$	24.8873i	1.05546i
$557$	−25.8965	−1.09727	−0.548636	−	0.836062i	$-0.684853\pi$
$557$	−25.8965	−1.09727	−0.548636	+	0.836062i	$0.684853\pi$
$558$	− 6.31641i	− 0.267395i
$559$	30.2346	1.27879
$560$	21.4138	0.904899
$561$	0	0
$562$	−8.43299	−0.355724
$563$	−28.0309	−1.18136	−0.590681	−	0.806905i	$-0.701141\pi$
$563$	−28.0309	−1.18136	−0.590681	+	0.806905i	$0.701141\pi$
$564$	5.31910i	0.223975i
$565$	−3.01331	−0.126771
$566$	15.7114i	0.660398i
$567$	− 21.5571i	− 0.905315i
$568$	5.57790i	0.234043i
$569$	−39.1921	−1.64302	−0.821509	−	0.570195i	$-0.806868\pi$
$569$	−39.1921	−1.64302	−0.821509	+	0.570195i	$0.806868\pi$
$570$	9.71502	0.406917
$571$	3.86762i	0.161855i	0.996720	+	0.0809275i	$0.0257882\pi$
$571$	3.86762i	0.161855i	−0.996720	+	0.0809275i	$0.974212\pi$
$572$	− 0.200273i	− 0.00837383i
$573$	2.11917i	0.0885297i
$574$	−51.6918	−2.15757
$575$	− 1.04197i	− 0.0434531i
$576$	−3.53632	−0.147347
$577$	−14.4808	−0.602845	−0.301423	−	0.953491i	$-0.597461\pi$
$577$	−14.4808	−0.602845	−0.301423	+	0.953491i	$0.597461\pi$
$578$	0	0
$579$	14.1999	0.590128
$580$	0.530580	0.0220311
$581$	28.3531i	1.17629i
$582$	23.8810	0.989898
$583$	− 0.633306i	− 0.0262289i
$584$	− 7.19357i	− 0.297672i
$585$	− 7.64368i	− 0.316027i
$586$	1.33469	0.0551355
$587$	−31.2452	−1.28963	−0.644814	−	0.764339i	$-0.723065\pi$
$587$	−31.2452	−1.28963	−0.644814	+	0.764339i	$0.723065\pi$
$588$	10.2816i	0.424008i
$589$	10.8258i	0.446068i
$590$	− 9.20574i	− 0.378994i
$591$	−12.5452	−0.516041
$592$	1.66179i	0.0682991i
$593$	2.00543	0.0823530	0.0411765	−	0.999152i	$-0.486889\pi$
$593$	2.00543	0.0823530	0.0411765	+	0.999152i	$0.486889\pi$
$594$	−0.360452	−0.0147895
$595$	0	0
$596$	12.8416	0.526012
$597$	18.3451	0.750816
$598$	5.69204i	0.232765i
$599$	36.0451	1.47276	0.736381	−	0.676567i	$-0.236533\pi$
$599$	36.0451	1.47276	0.736381	+	0.676567i	$0.236533\pi$
$600$	− 0.918004i	− 0.0374774i
$601$	− 38.7948i	− 1.58247i	−0.611510	−	0.791237i	$-0.709438\pi$
$601$	− 38.7948i	− 1.58247i	0.611510	−	0.791237i	$-0.290562\pi$
$602$	− 78.3660i	− 3.19396i
$603$	−2.31462	−0.0942588
$604$	19.3546	0.787529
$605$	− 10.9972i	− 0.447102i
$606$	− 16.5129i	− 0.670789i
$607$	28.9535i	1.17519i	0.809156	+	0.587594i	$0.199925\pi$
$607$	28.9535i	1.17519i	−0.809156	+	0.587594i	$0.800075\pi$
$608$	48.7774	1.97818
$609$	− 1.25675i	− 0.0509259i
$610$	−10.7819	−0.436548
$611$	−18.5488	−0.750405
$612$	0	0
$613$	9.10707	0.367831	0.183915	−	0.982942i	$-0.441123\pi$
$613$	9.10707	0.367831	0.183915	+	0.982942i	$0.441123\pi$
$614$	−5.16662	−0.208508
$615$	4.53522i	0.182878i
$616$	0.304197	0.0122564
$617$	− 5.05551i	− 0.203527i	−0.994809	−	0.101764i	$-0.967551\pi$
$617$	− 5.05551i	− 0.203527i	0.994809	−	0.101764i	$-0.0324485\pi$
$618$	8.58774i	0.345450i
$619$	− 16.8593i	− 0.677632i	−0.940853	−	0.338816i	$-0.889974\pi$
$619$	− 16.8593i	− 0.677632i	0.940853	−	0.338816i	$-0.110026\pi$
$620$	−1.74562	−0.0701058
$621$	3.96152	0.158970
$622$	37.0159i	1.48420i
$623$	− 44.3568i	− 1.77712i
$624$	10.2632i	0.410858i
$625$	1.00000	0.0400000
$626$	− 15.2871i	− 0.610996i
$627$	0.282442	0.0112797
$628$	11.8690	0.473625
$629$	0	0
$630$	−19.8119	−0.789323
$631$	−2.71309	−0.108007	−0.0540033	−	0.998541i	$-0.517198\pi$
$631$	−2.71309	−0.108007	−0.0540033	+	0.998541i	$0.517198\pi$
$632$	13.3220i	0.529919i
$633$	−5.36965	−0.213424
$634$	38.0882i	1.51268i
$635$	− 0.00828706i	0 0.000328862i
$636$	− 10.4643i	− 0.414936i
$637$	−35.8543	−1.42060
$638$	0.0398904	0.00157928
$639$	− 10.5615i	− 0.417808i
$640$	− 9.94702i	− 0.393190i
$641$	22.8123i	0.901030i	0.892769	+	0.450515i	$0.148760\pi$
$641$	22.8123i	0.901030i	−0.892769	+	0.450515i	$0.851240\pi$
$642$	18.3118	0.722711
$643$	− 19.2771i	− 0.760214i	−0.924942	−	0.380107i	$-0.875887\pi$
$643$	− 19.2771i	− 0.760214i	0.924942	−	0.380107i	$-0.124113\pi$
$644$	5.70506	0.224811
$645$	−6.87550	−0.270722
$646$	0	0
$647$	12.8098	0.503606	0.251803	−	0.967778i	$-0.418976\pi$
$647$	12.8098	0.503606	0.251803	+	0.967778i	$0.418976\pi$
$648$	−6.62548	−0.260273
$649$	− 0.267636i	− 0.0105056i
$650$	−5.46278	−0.214268
$651$	4.13472i	0.162052i
$652$	− 15.6938i	− 0.614618i
$653$	41.7200i	1.63263i	0.577607	+	0.816315i	$0.303987\pi$
$653$	41.7200i	1.63263i	−0.577607	+	0.816315i	$0.696013\pi$
$654$	5.89861	0.230654
$655$	−8.18458	−0.319798
$656$	32.5142i	1.26947i
$657$	13.6208i	0.531397i
$658$	48.0772i	1.87424i
$659$	−34.3290	−1.33727	−0.668633	−	0.743592i	$-0.733120\pi$
$659$	−34.3290	−1.33727	−0.668633	+	0.743592i	$0.733120\pi$
$660$	0.0455430i	0.00177276i
$661$	−27.7009	−1.07744	−0.538720	−	0.842485i	$-0.681092\pi$
$661$	−27.7009	−1.07744	−0.538720	+	0.842485i	$0.681092\pi$
$662$	27.4958	1.06865
$663$	0	0
$664$	8.71419	0.338176
$665$	33.9558	1.31675
$666$	− 1.53747i	− 0.0595758i
$667$	−0.438413	−0.0169754
$668$	15.8920i	0.614881i
$669$	3.28062i	0.126836i
$670$	1.65421i	0.0639078i
$671$	−0.313461	−0.0121010
$672$	18.6297	0.718658
$673$	36.2078i	1.39571i	0.716240	+	0.697854i	$0.245862\pi$
$673$	36.2078i	1.39571i	−0.716240	+	0.697854i	$0.754138\pi$
$674$	20.7195i	0.798086i
$675$	3.80196i	0.146337i
$676$	−4.85355	−0.186675
$677$	17.1158i	0.657812i	0.944363	+	0.328906i	$0.106680\pi$
$677$	17.1158i	0.657812i	−0.944363	+	0.328906i	$0.893320\pi$
$678$	−3.74331	−0.143761
$679$	83.4684	3.20322
$680$	0	0
$681$	−7.71229	−0.295536
$682$	−0.131240	−0.00502545
$683$	− 8.85022i	− 0.338644i	−0.985561	−	0.169322i	$-0.945842\pi$
$683$	− 8.85022i	− 0.338644i	0.985561	−	0.169322i	$-0.0541578\pi$
$684$	−24.9183	−0.952776
$685$	2.23387i	0.0853516i
$686$	38.0462i	1.45261i
$687$	14.2044i	0.541932i
$688$	−49.2924	−1.87925
$689$	36.4911	1.39020
$690$	− 1.29440i	− 0.0492769i
$691$	− 1.39834i	− 0.0531953i	−0.999646	−	0.0265977i	$-0.991533\pi$
$691$	− 1.39834i	− 0.0531953i	0.999646	−	0.0265977i	$-0.00846730\pi$
$692$	− 15.3801i	− 0.584663i
$693$	−0.575985	−0.0218799
$694$	27.0591i	1.02715i
$695$	19.7358	0.748622
$696$	−0.386254	−0.0146409
$697$	0	0
$698$	8.19245	0.310089
$699$	2.10400	0.0795806
$700$	5.47526i	0.206946i
$701$	2.36331	0.0892608	0.0446304	−	0.999004i	$-0.485789\pi$
$701$	2.36331	0.0892608	0.0446304	+	0.999004i	$0.485789\pi$
$702$	− 20.7693i	− 0.783885i
$703$	2.63509i	0.0993843i
$704$	0.0734765i	0.00276925i
$705$	4.21809	0.158862
$706$	−13.9314	−0.524316
$707$	− 57.7154i	− 2.17061i
$708$	− 4.42222i	− 0.166197i
$709$	− 32.5266i	− 1.22156i	−0.791799	−	0.610782i	$-0.790855\pi$
$709$	− 32.5266i	− 1.22156i	0.791799	−	0.610782i	$-0.209145\pi$
$710$	−7.54812	−0.283276
$711$	− 25.2247i	− 0.945998i
$712$	−13.6328	−0.510912
$713$	1.44239	0.0540179
$714$	0	0
$715$	−0.158818	−0.00593945
$716$	−17.4788	−0.653212
$717$	− 3.39880i	− 0.126931i
$718$	19.9154	0.743237
$719$	− 16.4302i	− 0.612744i	−0.951912	−	0.306372i	$-0.900885\pi$
$719$	− 16.4302i	− 0.612744i	0.951912	−	0.306372i	$-0.0991152\pi$
$720$	12.4617i	0.464420i
$721$	30.0157i	1.11784i
$722$	76.1323	2.83335
$723$	−1.14315	−0.0425143
$724$	− 2.57783i	− 0.0958043i
$725$	− 0.420754i	− 0.0156264i
$726$	− 13.6614i	− 0.507024i
$727$	−32.4709	−1.20428	−0.602139	−	0.798391i	$-0.705685\pi$
$727$	−32.4709	−1.20428	−0.602139	+	0.798391i	$0.705685\pi$
$728$	17.5278i	0.649624i
$729$	4.69881	0.174030
$730$	9.73448	0.360289
$731$	0	0
$732$	−5.17939	−0.191436
$733$	8.63424	0.318913	0.159456	−	0.987205i	$-0.449026\pi$
$733$	8.63424	0.318913	0.159456	+	0.987205i	$0.449026\pi$
$734$	− 28.9448i	− 1.06837i
$735$	8.15343	0.300744
$736$	− 6.49894i	− 0.239554i
$737$	0.0480925i	0.00177151i
$738$	− 30.0819i	− 1.10733i
$739$	−10.6026	−0.390022	−0.195011	−	0.980801i	$-0.562474\pi$
$739$	−10.6026	−0.390022	−0.195011	+	0.980801i	$0.562474\pi$
$740$	−0.424900	−0.0156196
$741$	16.2743i	0.597853i
$742$	− 94.5824i	− 3.47223i
$743$	22.3424i	0.819665i	0.912161	+	0.409832i	$0.134413\pi$
$743$	22.3424i	0.819665i	−0.912161	+	0.409832i	$0.865587\pi$
$744$	1.27079	0.0465893
$745$	− 10.1835i	− 0.373094i
$746$	18.5100	0.677700
$747$	−16.5000	−0.603704
$748$	0	0
$749$	64.0032	2.33863
$750$	1.24226	0.0453610
$751$	− 7.13989i	− 0.260538i	−0.991479	−	0.130269i	$-0.958416\pi$
$751$	− 7.13989i	− 0.260538i	0.991479	−	0.130269i	$-0.0415841\pi$
$752$	30.2406	1.10276
$753$	− 6.28921i	− 0.229192i
$754$	2.29849i	0.0837060i
$755$	− 15.3484i	− 0.558584i
$756$	−20.8167	−0.757097
$757$	−18.0266	−0.655186	−0.327593	−	0.944819i	$-0.606238\pi$
$757$	−18.0266	−0.655186	−0.327593	+	0.944819i	$0.606238\pi$
$758$	− 25.1949i	− 0.915119i
$759$	− 0.0376317i	− 0.00136594i
$760$	− 10.4361i	− 0.378558i
$761$	−49.9437	−1.81046	−0.905230	−	0.424923i	$-0.860301\pi$
$761$	−49.9437	−1.81046	−0.905230	+	0.424923i	$0.860301\pi$
$762$	− 0.0102947i	0 0.000372937i
$763$	20.6167	0.746375
$764$	−3.88466	−0.140542
$765$	0	0
$766$	10.1521	0.366811
$767$	15.4212	0.556828
$768$	− 14.2823i	− 0.515369i
$769$	−43.9115	−1.58349	−0.791745	−	0.610852i	$-0.790827\pi$
$769$	−43.9115	−1.58349	−0.791745	+	0.610852i	$0.790827\pi$
$770$	0.411645i	0.0148346i
$771$	− 11.4554i	− 0.412554i
$772$	26.0299i	0.936836i
$773$	9.67759	0.348079	0.174039	−	0.984739i	$-0.444318\pi$
$773$	9.67759	0.348079	0.174039	+	0.984739i	$0.444318\pi$
$774$	45.6048	1.63923
$775$	1.38429i	0.0497252i
$776$	− 25.6536i	− 0.920910i
$777$	1.00643i	0.0361055i
$778$	−64.6771	−2.31879
$779$	51.5576i	1.84724i
$780$	−2.62419	−0.0939610
$781$	−0.219445	−0.00785234
$782$	0	0
$783$	1.59969	0.0571683
$784$	58.4542	2.08765
$785$	− 9.41222i	− 0.335937i
$786$	−10.1674	−0.362659
$787$	19.8384i	0.707161i	0.935404	+	0.353581i	$0.115036\pi$
$787$	19.8384i	0.707161i	−0.935404	+	0.353581i	$0.884964\pi$
$788$	− 22.9966i	− 0.819221i
$789$	− 14.9471i	− 0.532130i
$790$	−18.0275	−0.641391
$791$	−13.0836	−0.465198
$792$	0.177026i	0.00629035i
$793$	− 18.0616i	− 0.641387i
$794$	7.02499i	0.249308i
$795$	−8.29826	−0.294309
$796$	33.6285i	1.19193i
$797$	−5.56111	−0.196984	−0.0984922	−	0.995138i	$-0.531402\pi$
$797$	−5.56111	−0.196984	−0.0984922	+	0.995138i	$0.531402\pi$
$798$	42.1819	1.49322
$799$	0	0
$800$	6.23717	0.220517
$801$	25.8133	0.912068
$802$	66.3436i	2.34267i
$803$	0.283008	0.00998714
$804$	0.794645i	0.0280250i
$805$	− 4.52415i	− 0.159455i
$806$	− 7.56207i	− 0.266363i
$807$	−15.9405	−0.561132
$808$	−17.7385	−0.624040
$809$	31.0442i	1.09146i	0.837962	+	0.545729i	$0.183747\pi$
$809$	31.0442i	1.09146i	−0.837962	+	0.545729i	$0.816253\pi$
$810$	− 8.96572i	− 0.315023i
$811$	46.9708i	1.64937i	0.565595	+	0.824683i	$0.308647\pi$
$811$	46.9708i	1.64937i	−0.565595	+	0.824683i	$0.691353\pi$
$812$	2.30374	0.0808455
$813$	− 2.72136i	− 0.0954424i
$814$	−0.0319451	−0.00111968
$815$	−12.4453	−0.435941
$816$	0	0
$817$	−78.1626	−2.73456
$818$	−40.3656	−1.41135
$819$	− 33.1883i	− 1.15969i
$820$	−8.31351	−0.290320
$821$	16.7433i	0.584346i	0.956366	+	0.292173i	$0.0943783\pi$
$821$	16.7433i	0.584346i	−0.956366	+	0.292173i	$0.905622\pi$
$822$	2.77505i	0.0967908i
$823$	26.5996i	0.927205i	0.886043	+	0.463602i	$0.153443\pi$
$823$	26.5996i	0.927205i	−0.886043	+	0.463602i	$0.846557\pi$
$824$	9.22517	0.321374
$825$	0.0361159	0.00125740
$826$	− 39.9707i	− 1.39076i
$827$	− 34.4855i	− 1.19918i	−0.800307	−	0.599590i	$-0.795330\pi$
$827$	− 34.4855i	− 1.19918i	0.800307	−	0.599590i	$-0.204670\pi$
$828$	3.32004i	0.115379i
$829$	−7.29346	−0.253312	−0.126656	−	0.991947i	$-0.540424\pi$
$829$	−7.29346	−0.253312	−0.126656	+	0.991947i	$0.540424\pi$
$830$	11.7922i	0.409314i
$831$	−11.6326	−0.403531
$832$	−4.23372	−0.146778
$833$	0	0
$834$	24.5170	0.848956
$835$	12.6025	0.436128
$836$	0.517745i	0.0179066i
$837$	−5.26302	−0.181917
$838$	− 39.4859i	− 1.36402i
$839$	− 35.5082i	− 1.22588i	−0.790129	−	0.612940i	$-0.789987\pi$
$839$	− 35.5082i	− 1.22588i	0.790129	−	0.612940i	$-0.210013\pi$
$840$	− 3.98591i	− 0.137527i
$841$	28.8230	0.993895
$842$	37.2202	1.28269
$843$	3.21248i	0.110644i
$844$	− 9.84311i	− 0.338814i
$845$	3.84890i	0.132406i
$846$	−27.9784	−0.961916
$847$	− 47.7492i	− 1.64068i
$848$	−59.4925	−2.04298
$849$	5.98513	0.205409
$850$	0	0
$851$	0.351091	0.0120352
$852$	−3.62594	−0.124223
$853$	− 0.238822i	− 0.00817712i	−0.999992	−	0.00408856i	$-0.998699\pi$
$853$	− 0.238822i	− 0.00817712i	0.999992	−	0.00408856i	$-0.00130143\pi$
$854$	−46.8144	−1.60196
$855$	19.7604i	0.675793i
$856$	− 19.6711i	− 0.672343i
$857$	18.1950i	0.621528i	0.950487	+	0.310764i	$0.100585\pi$
$857$	18.1950i	0.621528i	−0.950487	+	0.310764i	$0.899415\pi$
$858$	−0.197293	−0.00673548
$859$	20.1560	0.687715	0.343857	−	0.939022i	$-0.388266\pi$
$859$	20.1560	0.687715	0.343857	+	0.939022i	$0.388266\pi$
$860$	− 12.6035i	− 0.429775i
$861$	19.6916i	0.671088i
$862$	40.2795i	1.37192i
$863$	14.7597	0.502424	0.251212	−	0.967932i	$-0.419171\pi$
$863$	14.7597	0.502424	0.251212	+	0.967932i	$0.419171\pi$
$864$	23.7135i	0.806749i
$865$	−12.1965	−0.414694
$866$	−16.1284	−0.548064
$867$	0	0
$868$	−7.57936	−0.257260
$869$	−0.524110	−0.0177792
$870$	− 0.522687i	− 0.0177207i
$871$	−2.77109	−0.0938949
$872$	− 6.33644i	− 0.214579i
$873$	48.5741i	1.64398i
$874$	− 14.7151i	− 0.497745i
$875$	4.34193	0.146784
$876$	4.67622	0.157995
$877$	42.7577i	1.44382i	0.691984	+	0.721912i	$0.256737\pi$
$877$	42.7577i	1.44382i	−0.691984	+	0.721912i	$0.743263\pi$
$878$	40.2055i	1.35687i
$879$	− 0.508439i	− 0.0171492i
$880$	0.258925	0.00872837
$881$	− 43.6832i	− 1.47172i	−0.677131	−	0.735862i	$-0.736777\pi$
$881$	− 43.6832i	− 1.47172i	0.677131	−	0.735862i	$-0.263223\pi$
$882$	−54.0813	−1.82101
$883$	−41.4824	−1.39599	−0.697997	−	0.716101i	$-0.745925\pi$
$883$	−41.4824	−1.39599	−0.697997	+	0.716101i	$0.745925\pi$
$884$	0	0
$885$	−3.50686	−0.117882
$886$	−11.1496	−0.374577
$887$	− 32.8798i	− 1.10400i	−0.833845	−	0.551998i	$-0.813866\pi$
$887$	− 32.8798i	− 1.10400i	0.833845	−	0.551998i	$-0.186134\pi$
$888$	0.309321	0.0103801
$889$	− 0.0359818i	− 0.00120679i
$890$	− 18.4482i	− 0.618386i
$891$	− 0.260658i	− 0.00873238i
$892$	−6.01370	−0.201354
$893$	47.9524	1.60467
$894$	− 12.6505i	− 0.423097i
$895$	13.8608i	0.463315i
$896$	− 43.1892i	− 1.44285i
$897$	2.16834	0.0723988
$898$	− 54.7140i	− 1.82583i
$899$	0.582447	0.0194257
$900$	−3.18631	−0.106210
$901$	0	0
$902$	−0.625031	−0.0208113
$903$	−29.8529	−0.993443
$904$	4.02116i	0.133742i
$905$	−2.04424	−0.0679528
$906$	− 19.0667i	− 0.633448i
$907$	36.4475i	1.21022i	0.796142	+	0.605110i	$0.206871\pi$
$907$	36.4475i	1.21022i	−0.796142	+	0.605110i	$0.793129\pi$
$908$	− 14.1374i	− 0.469166i
$909$	33.5873	1.11402
$910$	−23.7190	−0.786277
$911$	− 29.8739i	− 0.989767i	−0.868959	−	0.494883i	$-0.835211\pi$
$911$	− 29.8739i	− 0.989767i	0.868959	−	0.494883i	$-0.164789\pi$
$912$	− 26.5325i	− 0.878579i
$913$	0.342832i	0.0113461i
$914$	46.1852	1.52767
$915$	4.10730i	0.135783i
$916$	−26.0381	−0.860324
$917$	−35.5369	−1.17353
$918$	0	0
$919$	11.6218	0.383368	0.191684	−	0.981457i	$-0.438605\pi$
$919$	11.6218	0.383368	0.191684	+	0.981457i	$0.438605\pi$
$920$	−1.39048	−0.0458426
$921$	1.96818i	0.0648539i
$922$	25.3837	0.835966
$923$	− 12.6444i	− 0.416196i
$924$	0.197744i	0.00650531i
$925$	0.336949i	0.0110788i
$926$	−45.3684	−1.49090
$927$	−17.4675	−0.573709
$928$	− 2.62432i	− 0.0861475i
$929$	5.04232i	0.165433i	0.996573	+	0.0827165i	$0.0263596\pi$
$929$	5.04232i	0.165433i	−0.996573	+	0.0827165i	$0.973640\pi$
$930$	1.71965i	0.0563896i
$931$	92.6904	3.03781
$932$	3.85685i	0.126335i
$933$	14.1009	0.461643
$934$	−40.2520	−1.31709
$935$	0	0
$936$	−10.2003	−0.333406
$937$	−34.9116	−1.14051	−0.570257	−	0.821466i	$-0.693156\pi$
$937$	−34.9116	−1.14051	−0.570257	+	0.821466i	$0.693156\pi$
$938$	7.18248i	0.234516i
$939$	−5.82351	−0.190043
$940$	7.73218i	0.252196i
$941$	11.0586i	0.360502i	0.983621	+	0.180251i	$0.0576909\pi$
$941$	11.0586i	0.360502i	−0.983621	+	0.180251i	$0.942309\pi$
$942$	− 11.6924i	− 0.380960i
$943$	6.86937	0.223697
$944$	−25.1416	−0.818290
$945$	16.5078i	0.537000i
$946$	− 0.947562i	− 0.0308079i
$947$	− 11.4918i	− 0.373435i	−0.982414	−	0.186717i	$-0.940215\pi$
$947$	− 11.4918i	− 0.373435i	0.982414	−	0.186717i	$-0.0597848\pi$
$948$	−8.66000	−0.281264
$949$	16.3069i	0.529346i
$950$	14.1224	0.458190
$951$	14.5094	0.470500
$952$	0	0
$953$	−0.704896	−0.0228338	−0.0114169	−	0.999935i	$-0.503634\pi$
$953$	−0.704896	−0.0228338	−0.0114169	+	0.999935i	$0.503634\pi$
$954$	55.0419	1.78205
$955$	3.08056i	0.0996847i
$956$	6.23035	0.201504
$957$	− 0.0151959i	0 0.000491215i
$958$	− 48.3053i	− 1.56067i
$959$	9.69929i	0.313206i
$960$	0.962768	0.0310732
$961$	29.0837	0.938185
$962$	− 1.84068i	− 0.0593459i
$963$	37.2465i	1.20025i
$964$	− 2.09552i	− 0.0674920i
$965$	20.6419	0.664486
$966$	− 5.62018i	− 0.180826i
$967$	39.9545	1.28485	0.642425	−	0.766348i	$-0.277928\pi$
$967$	39.9545	1.28485	0.642425	+	0.766348i	$0.277928\pi$
$968$	−14.6755	−0.471688
$969$	0	0
$970$	34.7149	1.11463
$971$	−43.2538	−1.38808	−0.694040	−	0.719936i	$-0.744171\pi$
$971$	−43.2538	−1.38808	−0.694040	+	0.719936i	$0.744171\pi$
$972$	− 18.6900i	− 0.599481i
$973$	85.6915	2.74714
$974$	41.7978i	1.33929i
$975$	2.08100i	0.0666454i
$976$	29.4464i	0.942555i
$977$	−48.8671	−1.56340	−0.781699	−	0.623656i	$-0.785647\pi$
$977$	−48.8671	−1.56340	−0.781699	+	0.623656i	$0.785647\pi$
$978$	−15.4603	−0.494367
$979$	− 0.536340i	− 0.0171415i
$980$	14.9461i	0.477434i
$981$	11.9978i	0.383061i
$982$	−14.0671	−0.448898
$983$	− 48.8832i	− 1.55913i	−0.626321	−	0.779565i	$-0.715440\pi$
$983$	− 48.8832i	− 1.55913i	0.626321	−	0.779565i	$-0.284560\pi$
$984$	6.05211	0.192934
$985$	−18.2365	−0.581063
$986$	0	0
$987$	18.3146	0.582961
$988$	−29.8325	−0.949099
$989$	10.4141i	0.331150i
$990$	−0.239555	−0.00761356
$991$	14.5340i	0.461687i	0.972991	+	0.230843i	$0.0741485\pi$
$991$	14.5340i	0.461687i	−0.972991	+	0.230843i	$0.925851\pi$
$992$	8.63407i	0.274132i
$993$	− 10.4743i	− 0.332392i
$994$	−32.7734	−1.03951
$995$	26.6677	0.845422
$996$	5.66470i	0.179493i
$997$	44.2040i	1.39995i	0.714165	+	0.699977i	$0.246807\pi$
$997$	44.2040i	1.39995i	−0.714165	+	0.699977i	$0.753193\pi$
$998$	− 15.8870i	− 0.502896i
$999$	−1.28107	−0.0405312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.20		24
17.4	even	4		1445.2.a.q.1.3		12
17.5	odd	16		85.2.l.a.26.2	✓	24
17.10	odd	16		85.2.l.a.36.2	yes	24
17.13	even	4		1445.2.a.p.1.3		12
17.16	even	2	inner	1445.2.d.j.866.19		24
51.5	even	16		765.2.be.b.451.5		24
51.44	even	16		765.2.be.b.631.5		24
85.4	even	4		7225.2.a.bq.1.10		12
85.22	even	16		425.2.n.f.349.2		24
85.27	even	16		425.2.n.c.274.5		24
85.39	odd	16		425.2.m.b.26.5		24
85.44	odd	16		425.2.m.b.376.5		24
85.64	even	4		7225.2.a.bs.1.10		12
85.73	even	16		425.2.n.c.349.5		24
85.78	even	16		425.2.n.f.274.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.2	✓	24	17.5	odd	16
85.2.l.a.36.2	yes	24	17.10	odd	16
425.2.m.b.26.5		24	85.39	odd	16
425.2.m.b.376.5		24	85.44	odd	16
425.2.n.c.274.5		24	85.27	even	16
425.2.n.c.349.5		24	85.73	even	16
425.2.n.f.274.2		24	85.78	even	16
425.2.n.f.349.2		24	85.22	even	16
765.2.be.b.451.5		24	51.5	even	16
765.2.be.b.631.5		24	51.44	even	16
1445.2.a.p.1.3		12	17.13	even	4
1445.2.a.q.1.3		12	17.4	even	4
1445.2.d.j.866.19		24	17.16	even	2	inner
1445.2.d.j.866.20		24	1.1	even	1	trivial
7225.2.a.bq.1.10		12	85.4	even	4
7225.2.a.bs.1.10		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)

\(f(q)\)	\(=\)	\(q+1.80583 q^{2} -0.687917i q^{3} +1.26102 q^{4} -1.00000i q^{5} -1.24226i q^{6} -4.34193i q^{7} -1.33447 q^{8} +2.52677 q^{9} +O(q^{10})\)	\(q+1.80583 q^{2} -0.687917i q^{3} +1.26102 q^{4} -1.00000i q^{5} -1.24226i q^{6} -4.34193i q^{7} -1.33447 q^{8} +2.52677 q^{9} -1.80583i q^{10} -0.0525004i q^{11} -0.867478i q^{12} +3.02508 q^{13} -7.84078i q^{14} -0.687917 q^{15} -4.93187 q^{16} +4.56292 q^{18} -7.82043 q^{19} -1.26102i q^{20} -2.98689 q^{21} -0.0948069i q^{22} +1.04197i q^{23} +0.918004i q^{24} -1.00000 q^{25} +5.46278 q^{26} -3.80196i q^{27} -5.47526i q^{28} +0.420754i q^{29} -1.24226 q^{30} -1.38429i q^{31} -6.23717 q^{32} -0.0361159 q^{33} -4.34193 q^{35} +3.18631 q^{36} -0.336949i q^{37} -14.1224 q^{38} -2.08100i q^{39} +1.33447i q^{40} -6.59268i q^{41} -5.39381 q^{42} +9.99466 q^{43} -0.0662042i q^{44} -2.52677i q^{45} +1.88162i q^{46} -6.13168 q^{47} +3.39272i q^{48} -11.8523 q^{49} -1.80583 q^{50} +3.81469 q^{52} +12.0629 q^{53} -6.86569i q^{54} -0.0525004 q^{55} +5.79417i q^{56} +5.37981i q^{57} +0.759811i q^{58} +5.09779 q^{59} -0.867478 q^{60} -5.97063i q^{61} -2.49979i q^{62} -10.9711i q^{63} -1.39954 q^{64} -3.02508i q^{65} -0.0652192 q^{66} -0.916040 q^{67} +0.716788 q^{69} -7.84078 q^{70} -4.17986i q^{71} -3.37190 q^{72} +5.39059i q^{73} -0.608473i q^{74} +0.687917i q^{75} -9.86173 q^{76} -0.227953 q^{77} -3.75794i q^{78} -9.98296i q^{79} +4.93187i q^{80} +4.96488 q^{81} -11.9053i q^{82} -6.53008 q^{83} -3.76653 q^{84} +18.0487 q^{86} +0.289444 q^{87} +0.0700602i q^{88} +10.2159 q^{89} -4.56292i q^{90} -13.1347i q^{91} +1.31395i q^{92} -0.952278 q^{93} -11.0728 q^{94} +7.82043i q^{95} +4.29066i q^{96} +19.2238i q^{97} -21.4033 q^{98} -0.132657i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9}+O(q^{10}) \) 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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