LMFDB - Embedded newform 845.2.c.h.506.14

Error: table mf_hecke_newspace_traces does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(506,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.506"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,14,-34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 34x^{16} + 407x^{14} + 2175x^{12} + 5555x^{10} + 6664x^{8} + 3544x^{6} + 681x^{4} + 47x^{2} + 1 $ x^18 + 34x^16 + 407x^14 + 2175x^12 + 5555x^10 + 6664x^8 + 3544x^6 + 681x^4 + 47x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			506.14
Root			$-1.76052i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.h.506.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.20556i q^{2} -0.0130567 q^{3} -2.86449 q^{4} +1.00000i q^{5} -0.0287972i q^{6} -4.60897i q^{7} -1.90669i q^{8} -2.99983 q^{9} -2.20556 q^{10} -2.93232i q^{11} +0.0374007 q^{12} +10.1654 q^{14} -0.0130567i q^{15} -1.52367 q^{16} +3.35206 q^{17} -6.61630i q^{18} -2.46021i q^{19} -2.86449i q^{20} +0.0601778i q^{21} +6.46741 q^{22} +1.58329 q^{23} +0.0248950i q^{24} -1.00000 q^{25} +0.0783378 q^{27} +13.2024i q^{28} +8.26322 q^{29} +0.0287972 q^{30} -9.77959i q^{31} -7.17392i q^{32} +0.0382863i q^{33} +7.39317i q^{34} +4.60897 q^{35} +8.59299 q^{36} -4.12917i q^{37} +5.42613 q^{38} +1.90669 q^{40} +7.26508i q^{41} -0.132726 q^{42} +0.705329 q^{43} +8.39961i q^{44} -2.99983i q^{45} +3.49204i q^{46} -8.57322i q^{47} +0.0198940 q^{48} -14.2426 q^{49} -2.20556i q^{50} -0.0437667 q^{51} -12.4639 q^{53} +0.172779i q^{54} +2.93232 q^{55} -8.78787 q^{56} +0.0321221i q^{57} +18.2250i q^{58} +5.33445i q^{59} +0.0374007i q^{60} +1.92092 q^{61} +21.5695 q^{62} +13.8261i q^{63} +12.7752 q^{64} -0.0844427 q^{66} -7.29793i q^{67} -9.60195 q^{68} -0.0206725 q^{69} +10.1654i q^{70} -6.68083i q^{71} +5.71974i q^{72} +12.4541i q^{73} +9.10713 q^{74} +0.0130567 q^{75} +7.04724i q^{76} -13.5150 q^{77} +0.984840 q^{79} -1.52367i q^{80} +8.99847 q^{81} -16.0236 q^{82} -7.84405i q^{83} -0.172379i q^{84} +3.35206i q^{85} +1.55565i q^{86} -0.107890 q^{87} -5.59102 q^{88} +0.412834i q^{89} +6.61630 q^{90} -4.53532 q^{92} +0.127689i q^{93} +18.9087 q^{94} +2.46021 q^{95} +0.0936675i q^{96} -3.38416i q^{97} -31.4129i q^{98} +8.79646i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$1$

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 $

$2$	2.20556i	1.55957i	0.626050	+	0.779783i	$0.284671\pi$
$2$	2.20556i	1.55957i	−0.626050	+	0.779783i	$0.715329\pi$
$3$	−0.0130567	−0.00753827	−0.00376913	−	0.999993i	$-0.501200\pi$
$3$	−0.0130567	−0.00753827	−0.00376913	+	0.999993i	$0.501200\pi$
$4$	−2.86449	−1.43225
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 0.0287972i	− 0.0117564i
$7$	− 4.60897i	− 1.74203i	−0.491259	−	0.871013i	$-0.663463\pi$
$7$	− 4.60897i	− 1.74203i	0.491259	−	0.871013i	$-0.336537\pi$
$8$	− 1.90669i	− 0.674116i
$9$	−2.99983	−0.999943
$10$	−2.20556	−0.697459
$11$	− 2.93232i	− 0.884128i	−0.896984	−	0.442064i	$-0.854246\pi$
$11$	− 2.93232i	− 0.884128i	0.896984	−	0.442064i	$-0.145754\pi$
$12$	0.0374007	0.0107967
$13$	0	0
$13$	0	0
$14$	10.1654	2.71681
$15$	− 0.0130567i	− 0.00337122i
$16$	−1.52367	−0.380917
$17$	3.35206	0.812994	0.406497	−	0.913652i	$-0.366750\pi$
$17$	3.35206	0.812994	0.406497	+	0.913652i	$0.366750\pi$
$18$	− 6.61630i	− 1.55948i
$19$	− 2.46021i	− 0.564410i	−0.959354	−	0.282205i	$-0.908934\pi$
$19$	− 2.46021i	− 0.564410i	0.959354	−	0.282205i	$-0.0910659\pi$
$20$	− 2.86449i	− 0.640520i
$21$	0.0601778i	0.0131319i
$22$	6.46741	1.37886
$23$	1.58329	0.330139	0.165069	−	0.986282i	$-0.447215\pi$
$23$	1.58329	0.330139	0.165069	+	0.986282i	$0.447215\pi$
$24$	0.0248950i	0.00508167i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	0.0783378	0.0150761
$28$	13.2024i	2.49501i
$29$	8.26322	1.53444	0.767221	−	0.641383i	$-0.221639\pi$
$29$	8.26322	1.53444	0.767221	+	0.641383i	$0.221639\pi$
$30$	0.0287972	0.00525763
$31$	− 9.77959i	− 1.75647i	−0.478233	−	0.878233i	$-0.658723\pi$
$31$	− 9.77959i	− 1.75647i	0.478233	−	0.878233i	$-0.341277\pi$
$32$	− 7.17392i	− 1.26818i
$33$	0.0382863i	0.00666479i
$34$	7.39317i	1.26792i
$35$	4.60897	0.779058
$36$	8.59299	1.43216
$37$	− 4.12917i	− 0.678831i	−0.940637	−	0.339416i	$-0.889771\pi$
$37$	− 4.12917i	− 0.678831i	0.940637	−	0.339416i	$-0.110229\pi$
$38$	5.42613	0.880235
$39$	0	0
$40$	1.90669	0.301474
$41$	7.26508i	1.13462i	0.823506	+	0.567308i	$0.192015\pi$
$41$	7.26508i	1.13462i	−0.823506	+	0.567308i	$0.807985\pi$
$42$	−0.132726	−0.0204800
$43$	0.705329	0.107562	0.0537809	−	0.998553i	$-0.482873\pi$
$43$	0.705329	0.107562	0.0537809	+	0.998553i	$0.482873\pi$
$44$	8.39961i	1.26629i
$45$	− 2.99983i	− 0.447188i
$46$	3.49204i	0.514873i
$47$	− 8.57322i	− 1.25053i	−0.780411	−	0.625266i	$-0.784990\pi$
$47$	− 8.57322i	− 1.25053i	0.780411	−	0.625266i	$-0.215010\pi$
$48$	0.0198940	0.00287146
$49$	−14.2426	−2.03466
$50$	− 2.20556i	− 0.311913i
$51$	−0.0437667	−0.00612857
$52$	0	0
$53$	−12.4639	−1.71204	−0.856022	−	0.516940i	$-0.827071\pi$
$53$	−12.4639	−1.71204	−0.856022	+	0.516940i	$0.827071\pi$
$54$	0.172779i	0.0235122i
$55$	2.93232	0.395394
$56$	−8.78787	−1.17433
$57$	0.0321221i	0.00425467i
$58$	18.2250i	2.39306i
$59$	5.33445i	0.694487i	0.937775	+	0.347243i	$0.112882\pi$
$59$	5.33445i	0.694487i	−0.937775	+	0.347243i	$0.887118\pi$
$60$	0.0374007i	0.00482841i
$61$	1.92092	0.245949	0.122974	−	0.992410i	$-0.460757\pi$
$61$	1.92092	0.245949	0.122974	+	0.992410i	$0.460757\pi$
$62$	21.5695	2.73932
$63$	13.8261i	1.74193i
$64$	12.7752	1.59690
$65$	0	0
$66$	−0.0844427	−0.0103942
$67$	− 7.29793i	− 0.891584i	−0.895137	−	0.445792i	$-0.852922\pi$
$67$	− 7.29793i	− 0.891584i	0.895137	−	0.445792i	$-0.147078\pi$
$68$	−9.60195	−1.16441
$69$	−0.0206725	−0.00248867
$70$	10.1654i	1.21499i
$71$	− 6.68083i	− 0.792868i	−0.918063	−	0.396434i	$-0.870248\pi$
$71$	− 6.68083i	− 0.792868i	0.918063	−	0.396434i	$-0.129752\pi$
$72$	5.71974i	0.674078i
$73$	12.4541i	1.45765i	0.684702	+	0.728824i	$0.259933\pi$
$73$	12.4541i	1.45765i	−0.684702	+	0.728824i	$0.740067\pi$
$74$	9.10713	1.05868
$75$	0.0130567	0.00150765
$76$	7.04724i	0.808374i
$77$	−13.5150	−1.54017
$78$	0	0
$79$	0.984840	0.110803	0.0554016	−	0.998464i	$-0.482356\pi$
$79$	0.984840	0.110803	0.0554016	+	0.998464i	$0.482356\pi$
$80$	− 1.52367i	− 0.170351i
$81$	8.99847	0.999830
$82$	−16.0236	−1.76951
$83$	− 7.84405i	− 0.860997i	−0.902591	−	0.430498i	$-0.858338\pi$
$83$	− 7.84405i	− 0.860997i	0.902591	−	0.430498i	$-0.141662\pi$
$84$	− 0.172379i	− 0.0188081i
$85$	3.35206i	0.363582i
$86$	1.55565i	0.167750i
$87$	−0.107890	−0.0115670
$88$	−5.59102	−0.596005
$89$	0.412834i	0.0437604i	0.999761	+	0.0218802i	$0.00696523\pi$
$89$	0.412834i	0.0437604i	−0.999761	+	0.0218802i	$0.993035\pi$
$90$	6.61630	0.697419
$91$	0	0
$92$	−4.53532	−0.472840
$93$	0.127689i	0.0132407i
$94$	18.9087	1.95029
$95$	2.46021	0.252412
$96$	0.0936675i	0.00955989i
$97$	− 3.38416i	− 0.343609i	−0.985131	−	0.171805i	$-0.945040\pi$
$97$	− 3.38416i	− 0.343609i	0.985131	−	0.171805i	$-0.0549598\pi$
$98$	− 31.4129i	− 3.17318i
$99$	8.79646i	0.884077i
$100$	2.86449	0.286449
$101$	10.5432	1.04909	0.524545	−	0.851383i	$-0.324235\pi$
$101$	10.5432	1.04909	0.524545	+	0.851383i	$0.324235\pi$
$102$	− 0.0965301i	− 0.00955790i
$103$	−14.1152	−1.39081	−0.695404	−	0.718619i	$-0.744774\pi$
$103$	−14.1152	−1.39081	−0.695404	+	0.718619i	$0.744774\pi$
$104$	0	0
$105$	−0.0601778	−0.00587275
$106$	− 27.4898i	− 2.67004i
$107$	−3.97165	−0.383954	−0.191977	−	0.981399i	$-0.561490\pi$
$107$	−3.97165	−0.383954	−0.191977	+	0.981399i	$0.561490\pi$
$108$	−0.224398	−0.0215927
$109$	10.1737i	0.974460i	0.873274	+	0.487230i	$0.161993\pi$
$109$	10.1737i	0.974460i	−0.873274	+	0.487230i	$0.838007\pi$
$110$	6.46741i	0.616643i
$111$	0.0539132i	0.00511721i
$112$	7.02254i	0.663568i
$113$	−2.59984	−0.244572	−0.122286	−	0.992495i	$-0.539023\pi$
$113$	−2.59984	−0.244572	−0.122286	+	0.992495i	$0.539023\pi$
$114$	−0.0708472	−0.00663545
$115$	1.58329i	0.147642i
$116$	−23.6699	−2.19770
$117$	0	0
$118$	−11.7655	−1.08310
$119$	− 15.4495i	− 1.41626i
$120$	−0.0248950	−0.00227259
$121$	2.40150	0.218318
$122$	4.23670i	0.383573i
$123$	− 0.0948578i	− 0.00855304i
$124$	28.0135i	2.51569i
$125$	− 1.00000i	− 0.0894427i
$126$	−30.4943	−2.71665
$127$	−19.9719	−1.77222	−0.886109	−	0.463476i	$-0.846602\pi$
$127$	−19.9719	−1.77222	−0.886109	+	0.463476i	$0.846602\pi$
$128$	13.8286i	1.22228i
$129$	−0.00920925	−0.000810829 0
$130$	0	0
$131$	−11.4400	−0.999514	−0.499757	−	0.866166i	$-0.666577\pi$
$131$	−11.4400	−0.999514	−0.499757	+	0.866166i	$0.666577\pi$
$132$	− 0.109671i	− 0.00954562i
$133$	−11.3390	−0.983217
$134$	16.0960	1.39048
$135$	0.0783378i	0.00674224i
$136$	− 6.39133i	− 0.548052i
$137$	− 3.12520i	− 0.267004i	−0.991049	−	0.133502i	$-0.957378\pi$
$137$	− 3.12520i	− 0.267004i	0.991049	−	0.133502i	$-0.0426222\pi$
$138$	− 0.0455944i	− 0.00388125i
$139$	6.09526	0.516993	0.258497	−	0.966012i	$-0.416773\pi$
$139$	6.09526	0.516993	0.258497	+	0.966012i	$0.416773\pi$
$140$	−13.2024	−1.11580
$141$	0.111938i	0.00942685i
$142$	14.7350	1.23653
$143$	0	0
$144$	4.57075	0.380896
$145$	8.26322i	0.686223i
$146$	−27.4684	−2.27330
$147$	0.185961	0.0153378
$148$	11.8280i	0.972253i
$149$	− 14.6196i	− 1.19769i	−0.800866	−	0.598844i	$-0.795627\pi$
$149$	− 14.6196i	− 1.19769i	0.800866	−	0.598844i	$-0.204373\pi$
$150$	0.0287972i	0.00235129i
$151$	− 12.2510i	− 0.996973i	−0.866897	−	0.498487i	$-0.833889\pi$
$151$	− 12.2510i	− 0.996973i	0.866897	−	0.498487i	$-0.166111\pi$
$152$	−4.69085	−0.380478
$153$	−10.0556	−0.812948
$154$	− 29.8081i	− 2.40200i
$155$	9.77959	0.785515
$156$	0	0
$157$	7.13991	0.569827	0.284914	−	0.958553i	$-0.408035\pi$
$157$	7.13991	0.569827	0.284914	+	0.958553i	$0.408035\pi$
$158$	2.17212i	0.172805i
$159$	0.162736	0.0129058
$160$	7.17392	0.567148
$161$	− 7.29733i	− 0.575110i
$162$	19.8467i	1.55930i
$163$	− 2.39002i	− 0.187201i	−0.995610	−	0.0936004i	$-0.970162\pi$
$163$	− 2.39002i	− 0.187201i	0.995610	−	0.0936004i	$-0.0298376\pi$
$164$	− 20.8108i	− 1.62505i
$165$	−0.0382863	−0.00298059
$166$	17.3005	1.34278
$167$	7.43841i	0.575601i	0.957690	+	0.287801i	$0.0929240\pi$
$167$	7.43841i	0.575601i	−0.957690	+	0.287801i	$0.907076\pi$
$168$	0.114740	0.00885240
$169$	0	0
$170$	−7.39317	−0.567030
$171$	7.38020i	0.564378i
$172$	−2.02041	−0.154055
$173$	−2.54119	−0.193203	−0.0966015	−	0.995323i	$-0.530797\pi$
$173$	−2.54119	−0.193203	−0.0966015	+	0.995323i	$0.530797\pi$
$174$	− 0.237958i	− 0.0180396i
$175$	4.60897i	0.348405i
$176$	4.46788i	0.336779i
$177$	− 0.0696502i	− 0.00523523i
$178$	−0.910531	−0.0682472
$179$	10.6913	0.799105	0.399553	−	0.916710i	$-0.369165\pi$
$179$	10.6913	0.799105	0.399553	+	0.916710i	$0.369165\pi$
$180$	8.59299i	0.640484i
$181$	11.7908	0.876402	0.438201	−	0.898877i	$-0.355616\pi$
$181$	11.7908	0.876402	0.438201	+	0.898877i	$0.355616\pi$
$182$	0	0
$183$	−0.0250808	−0.00185403
$184$	− 3.01884i	− 0.222552i
$185$	4.12917	0.303583
$186$	−0.281625	−0.0206498
$187$	− 9.82931i	− 0.718790i
$188$	24.5579i	1.79107i
$189$	− 0.361056i	− 0.0262630i
$190$	5.42613i	0.393653i
$191$	13.4746	0.974990	0.487495	−	0.873126i	$-0.337911\pi$
$191$	13.4746	0.974990	0.487495	+	0.873126i	$0.337911\pi$
$192$	−0.166801	−0.0120378
$193$	− 6.98737i	− 0.502962i	−0.967862	−	0.251481i	$-0.919082\pi$
$193$	− 6.98737i	− 0.502962i	0.967862	−	0.251481i	$-0.0809176\pi$
$194$	7.46397	0.535882
$195$	0	0
$196$	40.7978	2.91413
$197$	1.43795i	0.102450i	0.998687	+	0.0512248i	$0.0163125\pi$
$197$	1.43795i	0.102450i	−0.998687	+	0.0512248i	$0.983687\pi$
$198$	−19.4011	−1.37878
$199$	2.42852	0.172153	0.0860765	−	0.996289i	$-0.472567\pi$
$199$	2.42852	0.172153	0.0860765	+	0.996289i	$0.472567\pi$
$200$	1.90669i	0.134823i
$201$	0.0952866i	0.00672100i
$202$	23.2537i	1.63613i
$203$	− 38.0849i	− 2.67304i
$204$	0.125369	0.00877761
$205$	−7.26508	−0.507415
$206$	− 31.1318i	− 2.16906i
$207$	−4.74960	−0.330120
$208$	0	0
$209$	−7.21411	−0.499011
$210$	− 0.132726i	− 0.00915894i
$211$	18.2640	1.25735	0.628674	−	0.777669i	$-0.283598\pi$
$211$	18.2640	1.25735	0.628674	+	0.777669i	$0.283598\pi$
$212$	35.7026	2.45207
$213$	0.0872293i	0.00597685i
$214$	− 8.75970i	− 0.598801i
$215$	0.705329i	0.0481031i
$216$	− 0.149366i	− 0.0101631i
$217$	−45.0738	−3.05981
$218$	−22.4386	−1.51973
$219$	− 0.162610i	− 0.0109881i
$220$	−8.39961	−0.566301
$221$	0	0
$222$	−0.118909	−0.00798063
$223$	15.5841i	1.04359i	0.853072	+	0.521793i	$0.174737\pi$
$223$	15.5841i	1.04359i	−0.853072	+	0.521793i	$0.825263\pi$
$224$	−33.0644	−2.20921
$225$	2.99983	0.199989
$226$	− 5.73409i	− 0.381426i
$227$	− 4.03380i	− 0.267733i	−0.990999	−	0.133866i	$-0.957261\pi$
$227$	− 4.03380i	− 0.267733i	0.990999	−	0.133866i	$-0.0427393\pi$
$228$	− 0.0920135i	− 0.00609374i
$229$	− 22.5147i	− 1.48781i	−0.668284	−	0.743906i	$-0.732971\pi$
$229$	− 22.5147i	− 1.48781i	0.668284	−	0.743906i	$-0.267029\pi$
$230$	−3.49204	−0.230258
$231$	0.176460	0.0116102
$232$	− 15.7554i	− 1.03439i
$233$	7.69759	0.504286	0.252143	−	0.967690i	$-0.418865\pi$
$233$	7.69759	0.504286	0.252143	+	0.967690i	$0.418865\pi$
$234$	0	0
$235$	8.57322	0.559255
$236$	− 15.2805i	− 0.994676i
$237$	−0.0128587	−0.000835264 0
$238$	34.0749	2.20875
$239$	18.7203i	1.21092i	0.795877	+	0.605459i	$0.207010\pi$
$239$	18.7203i	1.21092i	−0.795877	+	0.605459i	$0.792990\pi$
$240$	0.0198940i	0.00128415i
$241$	22.6183i	1.45697i	0.685061	+	0.728486i	$0.259775\pi$
$241$	22.6183i	1.45697i	−0.685061	+	0.728486i	$0.740225\pi$
$242$	5.29665i	0.340482i
$243$	−0.352503	−0.0226131
$244$	−5.50246	−0.352259
$245$	− 14.2426i	− 0.909926i
$246$	0.209214	0.0133390
$247$	0	0
$248$	−18.6466	−1.18406
$249$	0.102417i	0.00649042i
$250$	2.20556	0.139492
$251$	−1.78412	−0.112612	−0.0563062	−	0.998414i	$-0.517932\pi$
$251$	−1.78412	−0.112612	−0.0563062	+	0.998414i	$0.517932\pi$
$252$	− 39.6048i	− 2.49487i
$253$	− 4.64271i	− 0.291885i
$254$	− 44.0492i	− 2.76389i
$255$	− 0.0437667i	− 0.00274078i
$256$	−4.94936	−0.309335
$257$	4.59847	0.286845	0.143422	−	0.989662i	$-0.454189\pi$
$257$	4.59847	0.286845	0.143422	+	0.989662i	$0.454189\pi$
$258$	− 0.0203115i	− 0.00126454i
$259$	−19.0312	−1.18254
$260$	0	0
$261$	−24.7883	−1.53435
$262$	− 25.2315i	− 1.55881i
$263$	18.8127	1.16004	0.580022	−	0.814601i	$-0.303044\pi$
$263$	18.8127	1.16004	0.580022	+	0.814601i	$0.303044\pi$
$264$	0.0730001	0.00449284
$265$	− 12.4639i	− 0.765649i
$266$	− 25.0089i	− 1.53339i
$267$	− 0.00539024i	0 0.000329877i
$268$	20.9049i	1.27697i
$269$	1.85412	0.113048	0.0565238	−	0.998401i	$-0.481998\pi$
$269$	1.85412	0.113048	0.0565238	+	0.998401i	$0.481998\pi$
$270$	−0.172779	−0.0105150
$271$	− 0.149698i	− 0.00909352i	−0.999990	−	0.00454676i	$-0.998553\pi$
$271$	− 0.149698i	− 0.00909352i	0.999990	−	0.00454676i	$-0.00144728\pi$
$272$	−5.10743	−0.309683
$273$	0	0
$274$	6.89281	0.416410
$275$	2.93232i	0.176826i
$276$	0.0592161	0.00356439
$277$	−22.0184	−1.32296	−0.661478	−	0.749965i	$-0.730071\pi$
$277$	−22.0184	−1.32296	−0.661478	+	0.749965i	$0.730071\pi$
$278$	13.4435i	0.806285i
$279$	29.3371i	1.75637i
$280$	− 8.78787i	− 0.525176i
$281$	0.438029i	0.0261306i	0.999915	+	0.0130653i	$0.00415894\pi$
$281$	0.438029i	0.0261306i	−0.999915	+	0.0130653i	$0.995841\pi$
$282$	−0.246885	−0.0147018
$283$	−13.8290	−0.822049	−0.411025	−	0.911624i	$-0.634829\pi$
$283$	−13.8290	−0.822049	−0.411025	+	0.911624i	$0.634829\pi$
$284$	19.1372i	1.13558i
$285$	−0.0321221	−0.00190275
$286$	0	0
$287$	33.4845	1.97653
$288$	21.5205i	1.26811i
$289$	−5.76370	−0.339041
$290$	−18.2250	−1.07021
$291$	0.0441858i	0.00259022i
$292$	− 35.6748i	− 2.08771i
$293$	− 14.5656i	− 0.850929i	−0.904975	−	0.425464i	$-0.860111\pi$
$293$	− 14.5656i	− 0.850929i	0.904975	−	0.425464i	$-0.139889\pi$
$294$	0.410148i	0.0239203i
$295$	−5.33445	−0.310584
$296$	−7.87304	−0.457611
$297$	− 0.229711i	− 0.0133292i
$298$	32.2445	1.86787
$299$	0	0
$300$	−0.0374007	−0.00215933
$301$	− 3.25084i	− 0.187375i
$302$	27.0203	1.55485
$303$	−0.137659	−0.00790833
$304$	3.74854i	0.214994i
$305$	1.92092i	0.109992i
$306$	− 22.1782i	− 1.26785i
$307$	9.05062i	0.516546i	0.966072	+	0.258273i	$0.0831535\pi$
$307$	9.05062i	0.516546i	−0.966072	+	0.258273i	$0.916847\pi$
$308$	38.7135	2.20591
$309$	0.184297	0.0104843
$310$	21.5695i	1.22506i
$311$	−7.28812	−0.413272	−0.206636	−	0.978418i	$-0.566252\pi$
$311$	−7.28812	−0.413272	−0.206636	+	0.978418i	$0.566252\pi$
$312$	0	0
$313$	12.9725	0.733250	0.366625	−	0.930369i	$-0.380513\pi$
$313$	12.9725	0.733250	0.366625	+	0.930369i	$0.380513\pi$
$314$	15.7475i	0.888683i
$315$	−13.8261	−0.779014
$316$	−2.82107	−0.158697
$317$	15.5048i	0.870838i	0.900228	+	0.435419i	$0.143400\pi$
$317$	15.5048i	0.870838i	−0.900228	+	0.435419i	$0.856600\pi$
$318$	0.358925i	0.0201275i
$319$	− 24.2304i	− 1.35664i
$320$	12.7752i	0.714154i
$321$	0.0518565	0.00289434
$322$	16.0947	0.896922
$323$	− 8.24676i	− 0.458862i
$324$	−25.7760	−1.43200
$325$	0	0
$326$	5.27133	0.291952
$327$	− 0.132834i	− 0.00734574i
$328$	13.8523	0.764863
$329$	−39.5137	−2.17846
$330$	− 0.0844427i	− 0.00464842i
$331$	26.0853i	1.43378i	0.697186	+	0.716890i	$0.254435\pi$
$331$	26.0853i	1.43378i	−0.697186	+	0.716890i	$0.745565\pi$
$332$	22.4692i	1.23316i
$333$	12.3868i	0.678793i
$334$	−16.4058	−0.897688
$335$	7.29793	0.398728
$336$	− 0.0916910i	− 0.00500215i
$337$	14.4785	0.788697	0.394348	−	0.918961i	$-0.370970\pi$
$337$	14.4785	0.788697	0.394348	+	0.918961i	$0.370970\pi$
$338$	0	0
$339$	0.0339452	0.00184365
$340$	− 9.60195i	− 0.520739i
$341$	−28.6769	−1.55294
$342$	−16.2775	−0.880185
$343$	33.3809i	1.80240i
$344$	− 1.34484i	− 0.0725091i
$345$	− 0.0206725i	− 0.00111297i
$346$	− 5.60474i	− 0.301313i
$347$	6.81412	0.365801	0.182901	−	0.983131i	$-0.441451\pi$
$347$	6.81412	0.365801	0.182901	+	0.983131i	$0.441451\pi$
$348$	0.309050	0.0165668
$349$	33.7357i	1.80583i	0.429818	+	0.902915i	$0.358578\pi$
$349$	33.7357i	1.80583i	−0.429818	+	0.902915i	$0.641422\pi$
$350$	−10.1654	−0.543361
$351$	0	0
$352$	−21.0362	−1.12123
$353$	− 18.7215i	− 0.996447i	−0.867049	−	0.498223i	$-0.833986\pi$
$353$	− 18.7215i	− 0.996447i	0.867049	−	0.498223i	$-0.166014\pi$
$354$	0.153618	0.00816468
$355$	6.68083	0.354581
$356$	− 1.18256i	− 0.0626756i
$357$	0.201719i	0.0106761i
$358$	23.5803i	1.24626i
$359$	27.9262i	1.47389i	0.675952	+	0.736945i	$0.263732\pi$
$359$	27.9262i	1.47389i	−0.675952	+	0.736945i	$0.736268\pi$
$360$	−5.71974	−0.301457
$361$	12.9474	0.681441
$362$	26.0053i	1.36681i
$363$	−0.0313556	−0.00164574
$364$	0	0
$365$	−12.4541	−0.651880
$366$	− 0.0553172i	− 0.00289148i
$367$	2.50988	0.131015	0.0655074	−	0.997852i	$-0.479133\pi$
$367$	2.50988	0.131015	0.0655074	+	0.997852i	$0.479133\pi$
$368$	−2.41241	−0.125755
$369$	− 21.7940i	− 1.13455i
$370$	9.10713i	0.473457i
$371$	57.4456i	2.98243i
$372$	− 0.365763i	− 0.0189640i
$373$	22.1779	1.14833	0.574165	−	0.818739i	$-0.305327\pi$
$373$	22.1779	1.14833	0.574165	+	0.818739i	$0.305327\pi$
$374$	21.6791	1.12100
$375$	0.0130567i	0 0.000674243i
$376$	−16.3465	−0.843005
$377$	0	0
$378$	0.796331	0.0409589
$379$	− 1.42116i	− 0.0730001i	−0.999334	−	0.0365001i	$-0.988379\pi$
$379$	− 1.42116i	− 0.0730001i	0.999334	−	0.0365001i	$-0.0116209\pi$
$380$	−7.04724	−0.361516
$381$	0.260766	0.0133595
$382$	29.7191i	1.52056i
$383$	21.0733i	1.07679i	0.842691	+	0.538397i	$0.180970\pi$
$383$	21.0733i	1.07679i	−0.842691	+	0.538397i	$0.819030\pi$
$384$	− 0.180555i	− 0.00921390i
$385$	− 13.5150i	− 0.688787i
$386$	15.4111	0.784402
$387$	−2.11587	−0.107556
$388$	9.69390i	0.492133i
$389$	−13.4713	−0.683021	−0.341511	−	0.939878i	$-0.610939\pi$
$389$	−13.4713	−0.683021	−0.341511	+	0.939878i	$0.610939\pi$
$390$	0	0
$391$	5.30728	0.268401
$392$	27.1562i	1.37160i
$393$	0.149368	0.00753461
$394$	−3.17148	−0.159777
$395$	0.984840i	0.0495527i
$396$	− 25.1974i	− 1.26622i
$397$	− 27.1859i	− 1.36442i	−0.731156	−	0.682210i	$-0.761019\pi$
$397$	− 27.1859i	− 1.36442i	0.731156	−	0.682210i	$-0.238981\pi$
$398$	5.35624i	0.268484i
$399$	0.148050	0.00741176
$400$	1.52367	0.0761834
$401$	3.27520i	0.163556i	0.996651	+	0.0817779i	$0.0260598\pi$
$401$	3.27520i	0.163556i	−0.996651	+	0.0817779i	$0.973940\pi$
$402$	−0.210160	−0.0104818
$403$	0	0
$404$	−30.2010	−1.50256
$405$	8.99847i	0.447137i
$406$	83.9986	4.16878
$407$	−12.1080	−0.600173
$408$	0.0834495i	0.00413137i
$409$	− 19.1677i	− 0.947782i	−0.880583	−	0.473891i	$-0.842849\pi$
$409$	− 19.1677i	− 0.947782i	0.880583	−	0.473891i	$-0.157151\pi$
$410$	− 16.0236i	− 0.791348i
$411$	0.0408047i	0.00201275i
$412$	40.4327	1.99198
$413$	24.5863	1.20981
$414$	− 10.4755i	− 0.514844i
$415$	7.84405	0.385049
$416$	0	0
$417$	−0.0795837	−0.00389723
$418$	− 15.9112i	− 0.778240i
$419$	0.392463	0.0191731	0.00958653	−	0.999954i	$-0.496948\pi$
$419$	0.392463	0.0191731	0.00958653	+	0.999954i	$0.496948\pi$
$420$	0.172379	0.00841122
$421$	35.1816i	1.71465i	0.514779	+	0.857323i	$0.327874\pi$
$421$	35.1816i	1.71465i	−0.514779	+	0.857323i	$0.672126\pi$
$422$	40.2824i	1.96092i
$423$	25.7182i	1.25046i
$424$	23.7647i	1.15412i
$425$	−3.35206	−0.162599
$426$	−0.192389	−0.00932130
$427$	− 8.85346i	− 0.428449i
$428$	11.3768	0.549916
$429$	0	0
$430$	−1.55565	−0.0750199
$431$	2.27454i	0.109561i	0.998498	+	0.0547803i	$0.0174459\pi$
$431$	2.27454i	0.109561i	−0.998498	+	0.0547803i	$0.982554\pi$
$432$	−0.119361	−0.00574275
$433$	−11.8827	−0.571048	−0.285524	−	0.958372i	$-0.592168\pi$
$433$	−11.8827	−0.571048	−0.285524	+	0.958372i	$0.592168\pi$
$434$	− 99.4130i	− 4.77197i
$435$	− 0.107890i	− 0.00517293i
$436$	− 29.1424i	− 1.39567i
$437$	− 3.89522i	− 0.186334i
$438$	0.358645	0.0171367
$439$	35.7273	1.70517	0.852585	−	0.522588i	$-0.175033\pi$
$439$	35.7273	1.70517	0.852585	+	0.522588i	$0.175033\pi$
$440$	− 5.59102i	− 0.266541i
$441$	42.7254	2.03454
$442$	0	0
$443$	4.98904	0.237036	0.118518	−	0.992952i	$-0.462186\pi$
$443$	4.98904	0.237036	0.118518	+	0.992952i	$0.462186\pi$
$444$	− 0.154434i	− 0.00732911i
$445$	−0.412834	−0.0195702
$446$	−34.3716	−1.62754
$447$	0.190884i	0.00902849i
$448$	− 58.8804i	− 2.78184i
$449$	23.4886i	1.10850i	0.832352	+	0.554248i	$0.186994\pi$
$449$	23.4886i	1.10850i	−0.832352	+	0.554248i	$0.813006\pi$
$450$	6.61630i	0.311895i
$451$	21.3035	1.00314
$452$	7.44721	0.350287
$453$	0.159957i	0.00751545i
$454$	8.89679	0.417547
$455$	0	0
$456$	0.0612468	0.00286815
$457$	40.2510i	1.88286i	0.337208	+	0.941430i	$0.390518\pi$
$457$	40.2510i	1.88286i	−0.337208	+	0.941430i	$0.609482\pi$
$458$	49.6575	2.32034
$459$	0.262593	0.0122568
$460$	− 4.53532i	− 0.211460i
$461$	− 31.2140i	− 1.45378i	−0.686754	−	0.726890i	$-0.740965\pi$
$461$	− 31.2140i	− 1.45378i	0.686754	−	0.726890i	$-0.259035\pi$
$462$	0.389194i	0.0181069i
$463$	17.7491i	0.824872i	0.910987	+	0.412436i	$0.135322\pi$
$463$	17.7491i	0.824872i	−0.910987	+	0.412436i	$0.864678\pi$
$464$	−12.5904	−0.584495
$465$	−0.127689	−0.00592142
$466$	16.9775i	0.786467i
$467$	−26.6645	−1.23389	−0.616944	−	0.787007i	$-0.711630\pi$
$467$	−26.6645	−1.23389	−0.616944	+	0.787007i	$0.711630\pi$
$468$	0	0
$469$	−33.6359	−1.55316
$470$	18.9087i	0.872196i
$471$	−0.0932234	−0.00429551
$472$	10.1711	0.468165
$473$	− 2.06825i	− 0.0950983i
$474$	− 0.0283607i	− 0.00130265i
$475$	2.46021i	0.112882i
$476$	44.2551i	2.02843i
$477$	37.3895	1.71195
$478$	−41.2888	−1.88851
$479$	20.4630i	0.934980i	0.883998	+	0.467490i	$0.154842\pi$
$479$	20.4630i	0.934980i	−0.883998	+	0.467490i	$0.845158\pi$
$480$	−0.0936675	−0.00427531
$481$	0	0
$482$	−49.8860	−2.27224
$483$	0.0952788i	0.00433534i
$484$	−6.87908	−0.312686
$485$	3.38416	0.153667
$486$	− 0.777467i	− 0.0352666i
$487$	− 8.11789i	− 0.367857i	−0.982940	−	0.183928i	$-0.941119\pi$
$487$	− 8.11789i	− 0.367857i	0.982940	−	0.183928i	$-0.0588815\pi$
$488$	− 3.66260i	− 0.165798i
$489$	0.0312057i	0.00141117i
$490$	31.4129	1.41909
$491$	−3.26996	−0.147571	−0.0737857	−	0.997274i	$-0.523508\pi$
$491$	−3.26996	−0.147571	−0.0737857	+	0.997274i	$0.523508\pi$
$492$	0.271719i	0.0122501i
$493$	27.6988	1.24749
$494$	0	0
$495$	−8.79646	−0.395371
$496$	14.9008i	0.669068i
$497$	−30.7917	−1.38120
$498$	−0.225887	−0.0101222
$499$	− 8.89340i	− 0.398123i	−0.979987	−	0.199062i	$-0.936211\pi$
$499$	− 8.89340i	− 0.398123i	0.979987	−	0.199062i	$-0.0637894\pi$
$500$	2.86449i	0.128104i
$501$	− 0.0971208i	− 0.00433904i
$502$	− 3.93498i	− 0.175627i
$503$	−23.7974	−1.06107	−0.530537	−	0.847662i	$-0.678010\pi$
$503$	−23.7974	−1.06107	−0.530537	+	0.847662i	$0.678010\pi$
$504$	26.3621	1.17426
$505$	10.5432i	0.469168i
$506$	10.2398	0.455213
$507$	0	0
$508$	57.2093	2.53825
$509$	1.26770i	0.0561898i	0.999605	+	0.0280949i	$0.00894406\pi$
$509$	1.26770i	0.0561898i	−0.999605	+	0.0280949i	$0.991056\pi$
$510$	0.0965301	0.00427442
$511$	57.4008	2.53926
$512$	16.7410i	0.739855i
$513$	− 0.192727i	− 0.00850911i
$514$	10.1422i	0.447354i
$515$	− 14.1152i	− 0.621988i
$516$	0.0263798	0.00116131
$517$	−25.1394	−1.10563
$518$	− 41.9745i	− 1.84425i
$519$	0.0331794	0.00145642
$520$	0	0
$521$	14.3916	0.630506	0.315253	−	0.949008i	$-0.397911\pi$
$521$	14.3916	0.630506	0.315253	+	0.949008i	$0.397911\pi$
$522$	− 54.6720i	− 2.39293i
$523$	19.0185	0.831622	0.415811	−	0.909451i	$-0.363498\pi$
$523$	19.0185	0.831622	0.415811	+	0.909451i	$0.363498\pi$
$524$	32.7697	1.43155
$525$	− 0.0601778i	− 0.00262637i
$526$	41.4926i	1.80916i
$527$	− 32.7818i	− 1.42800i
$528$	− 0.0583357i	− 0.00253873i
$529$	−20.4932	−0.891008
$530$	27.4898	1.19408
$531$	− 16.0024i	− 0.694447i
$532$	32.4805	1.40821
$533$	0	0
$534$	0.0118885	0.000514465 0
$535$	− 3.97165i	− 0.171709i
$536$	−13.9149	−0.601031
$537$	−0.139593	−0.00602387
$538$	4.08937i	0.176305i
$539$	41.7638i	1.79890i
$540$	− 0.224398i	− 0.00965655i
$541$	− 13.8969i	− 0.597475i	−0.954335	−	0.298738i	$-0.903434\pi$
$541$	− 13.8969i	− 0.597475i	0.954335	−	0.298738i	$-0.0965656\pi$
$542$	0.330168	0.0141819
$543$	−0.153948	−0.00660656
$544$	− 24.0474i	− 1.03102i
$545$	−10.1737	−0.435792
$546$	0	0
$547$	37.0840	1.58560	0.792798	−	0.609484i	$-0.208623\pi$
$547$	37.0840	1.58560	0.792798	+	0.609484i	$0.208623\pi$
$548$	8.95211i	0.382415i
$549$	−5.76243	−0.245935
$550$	−6.46741	−0.275771
$551$	− 20.3292i	− 0.866054i
$552$	0.0394160i	0.00167766i
$553$	− 4.53910i	− 0.193022i
$554$	− 48.5628i	− 2.06324i
$555$	−0.0539132	−0.00228849
$556$	−17.4598	−0.740461
$557$	− 31.8065i	− 1.34768i	−0.738875	−	0.673842i	$-0.764643\pi$
$557$	− 31.8065i	− 1.34768i	0.738875	−	0.673842i	$-0.235357\pi$
$558$	−64.7047	−2.73917
$559$	0	0
$560$	−7.02254	−0.296757
$561$	0.128338i	0.00541843i
$562$	−0.966100	−0.0407525
$563$	−26.3595	−1.11092	−0.555461	−	0.831543i	$-0.687458\pi$
$563$	−26.3595	−1.11092	−0.555461	+	0.831543i	$0.687458\pi$
$564$	− 0.320645i	− 0.0135016i
$565$	− 2.59984i	− 0.109376i
$566$	− 30.5007i	− 1.28204i
$567$	− 41.4736i	− 1.74173i
$568$	−12.7383	−0.534485
$569$	−17.7846	−0.745569	−0.372785	−	0.927918i	$-0.621597\pi$
$569$	−17.7846	−0.745569	−0.372785	+	0.927918i	$0.621597\pi$
$570$	− 0.0708472i	− 0.00296746i
$571$	−19.6399	−0.821903	−0.410952	−	0.911657i	$-0.634804\pi$
$571$	−19.6399	−0.821903	−0.410952	+	0.911657i	$0.634804\pi$
$572$	0	0
$573$	−0.175934	−0.00734974
$574$	73.8522i	3.08253i
$575$	−1.58329	−0.0660277
$576$	−38.3233	−1.59681
$577$	18.1454i	0.755403i	0.925927	+	0.377701i	$0.123285\pi$
$577$	18.1454i	0.755403i	−0.925927	+	0.377701i	$0.876715\pi$
$578$	− 12.7122i	− 0.528757i
$579$	0.0912317i	0.00379146i
$580$	− 23.6699i	− 0.982840i
$581$	−36.1530	−1.49988
$582$	−0.0974545	−0.00403962
$583$	36.5480i	1.51366i
$584$	23.7462	0.982624
$585$	0	0
$586$	32.1252	1.32708
$587$	− 0.423843i	− 0.0174939i	−0.999962	−	0.00874694i	$-0.997216\pi$
$587$	− 0.423843i	− 0.0174939i	0.999962	−	0.00874694i	$-0.00278427\pi$
$588$	−0.532683	−0.0219675
$589$	−24.0598	−0.991367
$590$	− 11.7655i	− 0.484376i
$591$	− 0.0187748i	0 0.000772293i
$592$	6.29149i	0.258578i
$593$	47.5064i	1.95085i	0.220327	+	0.975426i	$0.429288\pi$
$593$	47.5064i	1.95085i	−0.220327	+	0.975426i	$0.570712\pi$
$594$	0.506642	0.0207878
$595$	15.4495	0.633369
$596$	41.8778i	1.71538i
$597$	−0.0317083	−0.00129774
$598$	0	0
$599$	25.7871	1.05363	0.526816	−	0.849979i	$-0.323386\pi$
$599$	25.7871	1.05363	0.526816	+	0.849979i	$0.323386\pi$
$600$	− 0.0248950i	− 0.00101633i
$601$	−12.6776	−0.517130	−0.258565	−	0.965994i	$-0.583250\pi$
$601$	−12.6776	−0.517130	−0.258565	+	0.965994i	$0.583250\pi$
$602$	7.16992	0.292224
$603$	21.8925i	0.891533i
$604$	35.0929i	1.42791i
$605$	2.40150i	0.0976349i
$606$	− 0.303616i	− 0.0123336i
$607$	−4.40448	−0.178772	−0.0893862	−	0.995997i	$-0.528491\pi$
$607$	−4.40448	−0.178772	−0.0893862	+	0.995997i	$0.528491\pi$
$608$	−17.6493	−0.715775
$609$	0.497262i	0.0201501i
$610$	−4.23670	−0.171539
$611$	0	0
$612$	28.8042	1.16434
$613$	− 33.3599i	− 1.34739i	−0.739008	−	0.673696i	$-0.764706\pi$
$613$	− 33.3599i	− 1.34739i	0.739008	−	0.673696i	$-0.235294\pi$
$614$	−19.9617	−0.805588
$615$	0.0948578	0.00382503
$616$	25.7688i	1.03826i
$617$	− 32.5535i	− 1.31055i	−0.755389	−	0.655277i	$-0.772552\pi$
$617$	− 32.5535i	− 1.31055i	0.755389	−	0.655277i	$-0.227448\pi$
$618$	0.406477i	0.0163509i
$619$	35.5813i	1.43013i	0.699056	+	0.715067i	$0.253604\pi$
$619$	35.5813i	1.43013i	−0.699056	+	0.715067i	$0.746396\pi$
$620$	−28.0135	−1.12505
$621$	0.124031	0.00497721
$622$	− 16.0744i	− 0.644524i
$623$	1.90274	0.0762317
$624$	0	0
$625$	1.00000	0.0400000
$626$	28.6116i	1.14355i
$627$	0.0941922	0.00376168
$628$	−20.4522	−0.816133
$629$	− 13.8412i	− 0.551886i
$630$	− 30.4943i	− 1.21492i
$631$	− 25.4117i	− 1.01162i	−0.862644	−	0.505812i	$-0.831193\pi$
$631$	− 25.4117i	− 1.01162i	0.862644	−	0.505812i	$-0.168807\pi$
$632$	− 1.87778i	− 0.0746942i
$633$	−0.238467	−0.00947822
$634$	−34.1968	−1.35813
$635$	− 19.9719i	− 0.792560i
$636$	−0.466157	−0.0184843
$637$	0	0
$638$	53.4416	2.11577
$639$	20.0413i	0.792823i
$640$	−13.8286	−0.546622
$641$	10.1479	0.400817	0.200408	−	0.979712i	$-0.435773\pi$
$641$	10.1479	0.400817	0.200408	+	0.979712i	$0.435773\pi$
$642$	0.114372i	0.00451392i
$643$	1.85439i	0.0731298i	0.999331	+	0.0365649i	$0.0116416\pi$
$643$	1.85439i	0.0731298i	−0.999331	+	0.0365649i	$0.988358\pi$
$644$	20.9032i	0.823700i
$645$	− 0.00920925i	0 0.000362614i
$646$	18.1887	0.715626
$647$	29.6034	1.16383	0.581914	−	0.813250i	$-0.302304\pi$
$647$	29.6034	1.16383	0.581914	+	0.813250i	$0.302304\pi$
$648$	− 17.1573i	− 0.674001i
$649$	15.6423	0.614015
$650$	0	0
$651$	0.588514	0.0230657
$652$	6.84619i	0.268118i
$653$	6.78882	0.265667	0.132834	−	0.991138i	$-0.457592\pi$
$653$	6.78882	0.265667	0.132834	+	0.991138i	$0.457592\pi$
$654$	0.292973	0.0114562
$655$	− 11.4400i	− 0.446996i
$656$	− 11.0696i	− 0.432195i
$657$	− 37.3603i	− 1.45756i
$658$	− 87.1498i	− 3.39745i
$659$	7.94959	0.309672	0.154836	−	0.987940i	$-0.450515\pi$
$659$	7.94959	0.309672	0.154836	+	0.987940i	$0.450515\pi$
$660$	0.109671	0.00426893
$661$	− 40.3832i	− 1.57072i	−0.619038	−	0.785361i	$-0.712477\pi$
$661$	− 40.3832i	− 1.57072i	0.619038	−	0.785361i	$-0.287523\pi$
$662$	−57.5328	−2.23607
$663$	0	0
$664$	−14.9562	−0.580412
$665$	− 11.3390i	− 0.439708i
$666$	−27.3198	−1.05862
$667$	13.0831	0.506579
$668$	− 21.3073i	− 0.824402i
$669$	− 0.203476i	− 0.00786684i
$670$	16.0960i	0.621843i
$671$	− 5.63275i	− 0.217450i
$672$	0.431710	0.0166536
$673$	−9.63920	−0.371564	−0.185782	−	0.982591i	$-0.559482\pi$
$673$	−9.63920	−0.371564	−0.185782	+	0.982591i	$0.559482\pi$
$674$	31.9333i	1.23002i
$675$	−0.0783378	−0.00301522
$676$	0	0
$677$	51.1565	1.96610	0.983051	−	0.183330i	$-0.0586878\pi$
$677$	51.1565	1.96610	0.983051	+	0.183330i	$0.0586878\pi$
$678$	0.0748681i	0.00287529i
$679$	−15.5975	−0.598577
$680$	6.39133	0.245097
$681$	0.0526680i	0.00201824i
$682$	− 63.2485i	− 2.42191i
$683$	8.34502i	0.319313i	0.987173	+	0.159657i	$0.0510387\pi$
$683$	8.34502i	0.319313i	−0.987173	+	0.159657i	$0.948961\pi$
$684$	− 21.1405i	− 0.808328i
$685$	3.12520	0.119408
$686$	−73.6236	−2.81096
$687$	0.293967i	0.0112155i
$688$	−1.07469	−0.0409721
$689$	0	0
$690$	0.0455944	0.00173575
$691$	− 36.1243i	− 1.37423i	−0.726547	−	0.687117i	$-0.758876\pi$
$691$	− 36.1243i	− 1.37423i	0.726547	−	0.687117i	$-0.241124\pi$
$692$	7.27921	0.276714
$693$	40.5426	1.54009
$694$	15.0289i	0.570491i
$695$	6.09526i	0.231206i
$696$	0.205713i	0.00779753i
$697$	24.3530i	0.922435i
$698$	−74.4061	−2.81631
$699$	−0.100505	−0.00380144
$700$	− 13.2024i	− 0.499002i
$701$	45.9823	1.73673	0.868364	−	0.495928i	$-0.165172\pi$
$701$	45.9823	1.73673	0.868364	+	0.495928i	$0.165172\pi$
$702$	0	0
$703$	−10.1586	−0.383139
$704$	− 37.4609i	− 1.41186i
$705$	−0.111938	−0.00421582
$706$	41.2915	1.55402
$707$	− 48.5934i	− 1.82754i
$708$	0.199512i	0.00749813i
$709$	− 38.0949i	− 1.43069i	−0.698774	−	0.715343i	$-0.746271\pi$
$709$	− 38.0949i	− 1.43069i	0.698774	−	0.715343i	$-0.253729\pi$
$710$	14.7350i	0.552993i
$711$	−2.95435	−0.110797
$712$	0.787147	0.0294996
$713$	− 15.4839i	− 0.579877i
$714$	−0.444904	−0.0166501
$715$	0	0
$716$	−30.6251	−1.14452
$717$	− 0.244425i	− 0.00912822i
$718$	−61.5930	−2.29863
$719$	27.8672	1.03927	0.519635	−	0.854388i	$-0.326068\pi$
$719$	27.8672	1.03927	0.519635	+	0.854388i	$0.326068\pi$
$720$	4.57075i	0.170342i
$721$	65.0563i	2.42282i
$722$	28.5562i	1.06275i
$723$	− 0.295319i	− 0.0109830i
$724$	−33.7746	−1.25522
$725$	−8.26322	−0.306888
$726$	− 0.0691566i	− 0.00256664i
$727$	13.7750	0.510885	0.255443	−	0.966824i	$-0.417779\pi$
$727$	13.7750	0.510885	0.255443	+	0.966824i	$0.417779\pi$
$728$	0	0
$729$	−26.9908	−0.999659
$730$	− 27.4684i	− 1.01665i
$731$	2.36431	0.0874470
$732$	0.0718438	0.00265542
$733$	− 6.58392i	− 0.243183i	−0.992580	−	0.121591i	$-0.961200\pi$
$733$	− 6.58392i	− 0.243183i	0.992580	−	0.121591i	$-0.0387997\pi$
$734$	5.53570i	0.204326i
$735$	0.185961i	0.00685927i
$736$	− 11.3584i	− 0.418676i
$737$	−21.3999	−0.788274
$738$	48.0680	1.76941
$739$	− 5.47501i	− 0.201401i	−0.994917	−	0.100701i	$-0.967892\pi$
$739$	− 5.47501i	− 0.201401i	0.994917	−	0.100701i	$-0.0321085\pi$
$740$	−11.8280	−0.434805
$741$	0	0
$742$	−126.700	−4.65129
$743$	− 26.6714i	− 0.978479i	−0.872150	−	0.489239i	$-0.837274\pi$
$743$	− 26.6714i	− 0.978479i	0.872150	−	0.489239i	$-0.162726\pi$
$744$	0.243463	0.00892578
$745$	14.6196	0.535622
$746$	48.9148i	1.79090i
$747$	23.5308i	0.860948i
$748$	28.1560i	1.02948i
$749$	18.3052i	0.668857i
$750$	−0.0287972	−0.00105153
$751$	−21.8067	−0.795740	−0.397870	−	0.917442i	$-0.630250\pi$
$751$	−21.8067	−0.795740	−0.397870	+	0.917442i	$0.630250\pi$
$752$	13.0627i	0.476349i
$753$	0.0232946	0.000848903 0
$754$	0	0
$755$	12.2510	0.445860
$756$	1.03424i	0.0376151i
$757$	−8.33422	−0.302912	−0.151456	−	0.988464i	$-0.548396\pi$
$757$	−8.33422	−0.302912	−0.151456	+	0.988464i	$0.548396\pi$
$758$	3.13446	0.113849
$759$	0.0606183i	0.00220031i
$760$	− 4.69085i	− 0.170155i
$761$	7.33096i	0.265747i	0.991133	+	0.132874i	$0.0424204\pi$
$761$	7.33096i	0.265747i	−0.991133	+	0.132874i	$0.957580\pi$
$762$	0.575135i	0.0208350i
$763$	46.8901	1.69753
$764$	−38.5980	−1.39643
$765$	− 10.0556i	− 0.363561i
$766$	−46.4783	−1.67933
$767$	0	0
$768$	0.0646221	0.00233185
$769$	− 22.3346i	− 0.805407i	−0.915331	−	0.402703i	$-0.868071\pi$
$769$	− 22.3346i	− 0.805407i	0.915331	−	0.402703i	$-0.131929\pi$
$770$	29.8081	1.07421
$771$	−0.0600407	−0.00216231
$772$	20.0153i	0.720365i
$773$	− 27.1591i	− 0.976844i	−0.872608	−	0.488422i	$-0.837573\pi$
$773$	− 27.1591i	− 0.976844i	0.872608	−	0.488422i	$-0.162427\pi$
$774$	− 4.66667i	− 0.167740i
$775$	9.77959i	0.351293i
$776$	−6.45254	−0.231633
$777$	0.248484	0.00891432
$778$	− 29.7117i	− 1.06522i
$779$	17.8736	0.640388
$780$	0	0
$781$	−19.5903	−0.700997
$782$	11.7055i	0.418589i
$783$	0.647322	0.0231334
$784$	21.7010	0.775036
$785$	7.13991i	0.254834i
$786$	0.329440i	0.0117507i
$787$	− 11.5806i	− 0.412805i	−0.978467	−	0.206403i	$-0.933824\pi$
$787$	− 11.5806i	− 0.412805i	0.978467	−	0.206403i	$-0.0661756\pi$
$788$	− 4.11899i	− 0.146733i
$789$	−0.245632	−0.00874472
$790$	−2.17212	−0.0772807
$791$	11.9826i	0.426051i
$792$	16.7721	0.595971
$793$	0	0
$794$	59.9601	2.12790
$795$	0.162736i	0.00577167i
$796$	−6.95647	−0.246566
$797$	47.7004	1.68963	0.844817	−	0.535055i	$-0.179709\pi$
$797$	47.7004	1.68963	0.844817	+	0.535055i	$0.179709\pi$
$798$	0.326532i	0.0115591i
$799$	− 28.7379i	− 1.01668i
$800$	7.17392i	0.253636i
$801$	− 1.23843i	− 0.0437579i
$802$	−7.22365	−0.255076
$803$	36.5195	1.28875
$804$	− 0.272948i	− 0.00962612i
$805$	7.29733	0.257197
$806$	0	0
$807$	−0.0242086	−0.000852184 0
$808$	− 20.1027i	− 0.707209i
$809$	36.3910	1.27944	0.639720	−	0.768608i	$-0.279050\pi$
$809$	36.3910	1.27944	0.639720	+	0.768608i	$0.279050\pi$
$810$	−19.8467	−0.697340
$811$	− 36.8088i	− 1.29253i	−0.763112	−	0.646266i	$-0.776330\pi$
$811$	− 36.8088i	− 1.29253i	0.763112	−	0.646266i	$-0.223670\pi$
$812$	109.094i	3.82845i
$813$	0.00195456i	0 6.85494e-5i
$814$	− 26.7050i	− 0.936010i
$815$	2.39002	0.0837188
$816$	0.0666860	0.00233448
$817$	− 1.73526i	− 0.0607089i
$818$	42.2755	1.47813
$819$	0	0
$820$	20.8108	0.726744
$821$	33.6668i	1.17498i	0.809231	+	0.587491i	$0.199884\pi$
$821$	33.6668i	1.17498i	−0.809231	+	0.587491i	$0.800116\pi$
$822$	−0.0899971	−0.00313901
$823$	−31.8809	−1.11130	−0.555649	−	0.831417i	$-0.687530\pi$
$823$	−31.8809	−1.11130	−0.555649	+	0.831417i	$0.687530\pi$
$824$	26.9132i	0.937566i
$825$	− 0.0382863i	− 0.00133296i
$826$	54.2266i	1.88678i
$827$	18.4625i	0.642003i	0.947079	+	0.321002i	$0.104019\pi$
$827$	18.4625i	0.642003i	−0.947079	+	0.321002i	$0.895981\pi$
$828$	13.6052	0.472813
$829$	34.9663	1.21443	0.607214	−	0.794538i	$-0.292287\pi$
$829$	34.9663	1.21443	0.607214	+	0.794538i	$0.292287\pi$
$830$	17.3005i	0.600510i
$831$	0.287487	0.00997280
$832$	0	0
$833$	−47.7420	−1.65416
$834$	− 0.175527i	− 0.00607799i
$835$	−7.43841	−0.257417
$836$	20.6648	0.714706
$837$	− 0.766111i	− 0.0264807i
$838$	0.865600i	0.0299017i
$839$	28.7234i	0.991641i	0.868425	+	0.495820i	$0.165133\pi$
$839$	28.7234i	0.991641i	−0.868425	+	0.495820i	$0.834867\pi$
$840$	0.114740i	0.00395892i
$841$	39.2808	1.35451
$842$	−77.5951	−2.67410
$843$	− 0.00571920i	0 0.000196980i
$844$	−52.3172	−1.80083
$845$	0	0
$846$	−56.7230	−1.95018
$847$	− 11.0684i	− 0.380316i
$848$	18.9908	0.652147
$849$	0.180561	0.00619683
$850$	− 7.39317i	− 0.253584i
$851$	− 6.53767i	− 0.224108i
$852$	− 0.249868i	− 0.00856032i
$853$	13.7453i	0.470629i	0.971919	+	0.235315i	$0.0756121\pi$
$853$	13.7453i	0.470629i	−0.971919	+	0.235315i	$0.924388\pi$
$854$	19.5268	0.668195
$855$	−7.38020	−0.252398
$856$	7.57269i	0.258829i
$857$	12.6495	0.432099	0.216049	−	0.976382i	$-0.430683\pi$
$857$	12.6495	0.432099	0.216049	+	0.976382i	$0.430683\pi$
$858$	0	0
$859$	−11.0929	−0.378485	−0.189243	−	0.981930i	$-0.560603\pi$
$859$	−11.0929	−0.378485	−0.189243	+	0.981930i	$0.560603\pi$
$860$	− 2.02041i	− 0.0688954i
$861$	−0.437196	−0.0148996
$862$	−5.01663	−0.170867
$863$	− 33.0295i	− 1.12434i	−0.827022	−	0.562169i	$-0.809967\pi$
$863$	− 33.0295i	− 1.12434i	0.827022	−	0.562169i	$-0.190033\pi$
$864$	− 0.561989i	− 0.0191192i
$865$	− 2.54119i	− 0.0864030i
$866$	− 26.2081i	− 0.890587i
$867$	0.0752546	0.00255578
$868$	129.114	4.38240
$869$	− 2.88787i	− 0.0979641i
$870$	0.237958	0.00806753
$871$	0	0
$872$	19.3980	0.656899
$873$	10.1519i	0.343590i
$874$	8.59114	0.290600
$875$	−4.60897	−0.155812
$876$	0.465794i	0.0157377i
$877$	15.4397i	0.521362i	0.965425	+	0.260681i	$0.0839471\pi$
$877$	15.4397i	0.521362i	−0.965425	+	0.260681i	$0.916053\pi$
$878$	78.7987i	2.65933i
$879$	0.190178i	0.00641453i
$880$	−4.46788	−0.150612
$881$	16.6260	0.560143	0.280072	−	0.959979i	$-0.409642\pi$
$881$	16.6260	0.560143	0.280072	+	0.959979i	$0.409642\pi$
$882$	94.2333i	3.17300i
$883$	−57.2845	−1.92778	−0.963888	−	0.266309i	$-0.914196\pi$
$883$	−57.2845	−1.92778	−0.963888	+	0.266309i	$0.914196\pi$
$884$	0	0
$885$	0.0696502	0.00234126
$886$	11.0036i	0.369674i
$887$	18.4657	0.620018	0.310009	−	0.950734i	$-0.399668\pi$
$887$	18.4657	0.620018	0.310009	+	0.950734i	$0.399668\pi$
$888$	0.102796	0.00344960
$889$	92.0498i	3.08725i
$890$	− 0.910531i	− 0.0305211i
$891$	− 26.3864i	− 0.883977i
$892$	− 44.6405i	− 1.49467i
$893$	−21.0919	−0.705813
$894$	−0.421005	−0.0140805
$895$	10.6913i	0.357371i
$896$	63.7354	2.12925
$897$	0	0
$898$	−51.8055	−1.72877
$899$	− 80.8109i	− 2.69519i
$900$	−8.59299	−0.286433
$901$	−41.7796	−1.39188
$902$	46.9862i	1.56447i
$903$	0.0424451i	0.00141249i
$904$	4.95708i	0.164870i
$905$	11.7908i	0.391939i
$906$	−0.352795	−0.0117208
$907$	−44.9489	−1.49250	−0.746251	−	0.665664i	$-0.768148\pi$
$907$	−44.9489	−1.49250	−0.746251	+	0.665664i	$0.768148\pi$
$908$	11.5548i	0.383459i
$909$	−31.6279	−1.04903
$910$	0	0
$911$	−44.3728	−1.47014	−0.735069	−	0.677992i	$-0.762850\pi$
$911$	−44.3728	−1.47014	−0.735069	+	0.677992i	$0.762850\pi$
$912$	− 0.0489434i	− 0.00162068i
$913$	−23.0013	−0.761231
$914$	−88.7759	−2.93645
$915$	− 0.0250808i	0 0.000829146i
$916$	64.4931i	2.13091i
$917$	52.7264i	1.74118i
$918$	0.579164i	0.0191153i
$919$	25.1680	0.830217	0.415108	−	0.909772i	$-0.363744\pi$
$919$	25.1680	0.830217	0.415108	+	0.909772i	$0.363744\pi$
$920$	3.01884	0.0995282
$921$	− 0.118171i	− 0.00389386i
$922$	68.8443	2.26726
$923$	0	0
$924$	−0.505469	−0.0166287
$925$	4.12917i	0.135766i
$926$	−39.1468	−1.28644
$927$	42.3430	1.39073
$928$	− 59.2797i	− 1.94595i
$929$	− 37.5601i	− 1.23231i	−0.787626	−	0.616153i	$-0.788690\pi$
$929$	− 37.5601i	− 1.23231i	0.787626	−	0.616153i	$-0.211310\pi$
$930$	− 0.281625i	− 0.00923485i
$931$	35.0397i	1.14838i
$932$	−22.0497	−0.722262
$933$	0.0951586	0.00311535
$934$	− 58.8102i	− 1.92433i
$935$	9.82931	0.321453
$936$	0	0
$937$	−17.1212	−0.559326	−0.279663	−	0.960098i	$-0.590223\pi$
$937$	−17.1212	−0.559326	−0.279663	+	0.960098i	$0.590223\pi$
$938$	− 74.1860i	− 2.42226i
$939$	−0.169378	−0.00552743
$940$	−24.5579	−0.800991
$941$	0.208568i	0.00679913i	0.999994	+	0.00339956i	$0.00108212\pi$
$941$	0.208568i	0.00679913i	−0.999994	+	0.00339956i	$0.998918\pi$
$942$	− 0.205610i	− 0.00669913i
$943$	11.5027i	0.374580i
$944$	− 8.12794i	− 0.264542i
$945$	0.361056	0.0117452
$946$	4.56165	0.148312
$947$	0.414059i	0.0134551i	0.999977	+	0.00672755i	$0.00214146\pi$
$947$	0.414059i	0.0134551i	−0.999977	+	0.00672755i	$0.997859\pi$
$948$	0.0368337	0.00119630
$949$	0	0
$950$	−5.42613	−0.176047
$951$	− 0.202441i	− 0.00656461i
$952$	−29.4575	−0.954722
$953$	33.8593	1.09681	0.548404	−	0.836213i	$-0.315235\pi$
$953$	33.8593	1.09681	0.548404	+	0.836213i	$0.315235\pi$
$954$	82.4647i	2.66989i
$955$	13.4746i	0.436029i
$956$	− 53.6243i	− 1.73433i
$957$	0.316368i	0.0102267i
$958$	−45.1324	−1.45816
$959$	−14.4039	−0.465128
$960$	− 0.166801i	− 0.00538348i
$961$	−64.6403	−2.08517
$962$	0	0
$963$	11.9143	0.383932
$964$	− 64.7899i	− 2.08674i
$965$	6.98737	0.224931
$966$	−0.210143	−0.00676124
$967$	− 13.2125i	− 0.424885i	−0.977174	−	0.212442i	$-0.931858\pi$
$967$	− 13.2125i	− 0.424885i	0.977174	−	0.212442i	$-0.0681417\pi$
$968$	− 4.57892i	− 0.147172i
$969$	0.107675i	0.00345902i
$970$	7.46397i	0.239654i
$971$	−17.6019	−0.564872	−0.282436	−	0.959286i	$-0.591142\pi$
$971$	−17.6019	−0.564872	−0.282436	+	0.959286i	$0.591142\pi$
$972$	1.00974	0.0323875
$973$	− 28.0929i	− 0.900616i
$974$	17.9045	0.573697
$975$	0	0
$976$	−2.92685	−0.0936861
$977$	11.7812i	0.376913i	0.982082	+	0.188457i	$0.0603485\pi$
$977$	11.7812i	0.376913i	−0.982082	+	0.188457i	$0.939652\pi$
$978$	−0.0688260	−0.00220081
$979$	1.21056	0.0386897
$980$	40.7978i	1.30324i
$981$	− 30.5192i	− 0.974404i
$982$	− 7.21210i	− 0.230147i
$983$	− 45.4985i	− 1.45118i	−0.688128	−	0.725589i	$-0.741567\pi$
$983$	− 45.4985i	− 1.45118i	0.688128	−	0.725589i	$-0.258433\pi$
$984$	−0.180864	−0.00576574
$985$	−1.43795	−0.0458169
$986$	61.0914i	1.94555i
$987$	0.515917	0.0164218
$988$	0	0
$989$	1.11674	0.0355103
$990$	− 19.4011i	− 0.616608i
$991$	33.2685	1.05681	0.528405	−	0.848993i	$-0.322790\pi$
$991$	33.2685	1.05681	0.528405	+	0.848993i	$0.322790\pi$
$992$	−70.1580	−2.22752
$993$	− 0.340588i	− 0.0108082i
$994$	− 67.9130i	− 2.15407i
$995$	2.42852i	0.0769892i
$996$	− 0.293373i	− 0.00929589i
$997$	−39.7870	−1.26007	−0.630033	−	0.776568i	$-0.716959\pi$
$997$	−39.7870	−1.26007	−0.630033	+	0.776568i	$0.716959\pi$
$998$	19.6149	0.620899
$999$	− 0.323470i	− 0.0102341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.h.506.14		18
13.2	odd	12		845.2.e.o.191.3		18
13.3	even	3		845.2.m.j.316.5		36
13.4	even	6		845.2.m.j.361.5		36
13.5	odd	4		845.2.a.o.1.7	yes	9
13.6	odd	12		845.2.e.o.146.3		18
13.7	odd	12		845.2.e.p.146.7		18
13.8	odd	4		845.2.a.n.1.3	✓	9
13.9	even	3		845.2.m.j.361.14		36
13.10	even	6		845.2.m.j.316.14		36
13.11	odd	12		845.2.e.p.191.7		18
13.12	even	2	inner	845.2.c.h.506.5		18
39.5	even	4		7605.2.a.cp.1.3		9
39.8	even	4		7605.2.a.cs.1.7		9
65.34	odd	4		4225.2.a.bt.1.7		9
65.44	odd	4		4225.2.a.bs.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.3	✓	9	13.8	odd	4
845.2.a.o.1.7	yes	9	13.5	odd	4
845.2.c.h.506.5		18	13.12	even	2	inner
845.2.c.h.506.14		18	1.1	even	1	trivial
845.2.e.o.146.3		18	13.6	odd	12
845.2.e.o.191.3		18	13.2	odd	12
845.2.e.p.146.7		18	13.7	odd	12
845.2.e.p.191.7		18	13.11	odd	12
845.2.m.j.316.5		36	13.3	even	3
845.2.m.j.316.14		36	13.10	even	6
845.2.m.j.361.5		36	13.4	even	6
845.2.m.j.361.14		36	13.9	even	3
4225.2.a.bs.1.3		9	65.44	odd	4
4225.2.a.bt.1.7		9	65.34	odd	4
7605.2.a.cp.1.3		9	39.5	even	4
7605.2.a.cs.1.7		9	39.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.20556i q^{2} -0.0130567 q^{3} -2.86449 q^{4} +1.00000i q^{5} -0.0287972i q^{6} -4.60897i q^{7} -1.90669i q^{8} -2.99983 q^{9} -2.20556 q^{10} -2.93232i q^{11} +0.0374007 q^{12} +10.1654 q^{14} -0.0130567i q^{15} -1.52367 q^{16} +3.35206 q^{17} -6.61630i q^{18} -2.46021i q^{19} -2.86449i q^{20} +0.0601778i q^{21} +6.46741 q^{22} +1.58329 q^{23} +0.0248950i q^{24} -1.00000 q^{25} +0.0783378 q^{27} +13.2024i q^{28} +8.26322 q^{29} +0.0287972 q^{30} -9.77959i q^{31} -7.17392i q^{32} +0.0382863i q^{33} +7.39317i q^{34} +4.60897 q^{35} +8.59299 q^{36} -4.12917i q^{37} +5.42613 q^{38} +1.90669 q^{40} +7.26508i q^{41} -0.132726 q^{42} +0.705329 q^{43} +8.39961i q^{44} -2.99983i q^{45} +3.49204i q^{46} -8.57322i q^{47} +0.0198940 q^{48} -14.2426 q^{49} -2.20556i q^{50} -0.0437667 q^{51} -12.4639 q^{53} +0.172779i q^{54} +2.93232 q^{55} -8.78787 q^{56} +0.0321221i q^{57} +18.2250i q^{58} +5.33445i q^{59} +0.0374007i q^{60} +1.92092 q^{61} +21.5695 q^{62} +13.8261i q^{63} +12.7752 q^{64} -0.0844427 q^{66} -7.29793i q^{67} -9.60195 q^{68} -0.0206725 q^{69} +10.1654i q^{70} -6.68083i q^{71} +5.71974i q^{72} +12.4541i q^{73} +9.10713 q^{74} +0.0130567 q^{75} +7.04724i q^{76} -13.5150 q^{77} +0.984840 q^{79} -1.52367i q^{80} +8.99847 q^{81} -16.0236 q^{82} -7.84405i q^{83} -0.172379i q^{84} +3.35206i q^{85} +1.55565i q^{86} -0.107890 q^{87} -5.59102 q^{88} +0.412834i q^{89} +6.61630 q^{90} -4.53532 q^{92} +0.127689i q^{93} +18.9087 q^{94} +2.46021 q^{95} +0.0936675i q^{96} -3.38416i q^{97} -31.4129i q^{98} +8.79646i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

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