LMFDB - Embedded newform 1183.2.c.g.337.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(337,1183)] 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("1183.337"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.11667456256.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 13x^{6} + 44x^{4} + 21x^{2} + 1 $ x^8 + 13x^6 + 44x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$-2.74108i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.g.337.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.74108i q^{2} +1.36482 q^{3} -5.51353 q^{4} +0.741082i q^{5} -3.74108i q^{6} +1.00000i q^{7} +9.63087i q^{8} -1.13727 q^{9} +2.03137 q^{10} +1.36482i q^{11} -7.52497 q^{12} +2.74108 q^{14} +1.01144i q^{15} +15.3720 q^{16} +4.14871 q^{17} +3.11734i q^{18} +7.26606i q^{19} -4.08598i q^{20} +1.36482i q^{21} +3.74108 q^{22} +2.33345 q^{23} +13.1444i q^{24} +4.45080 q^{25} -5.64662 q^{27} -5.51353i q^{28} -0.407629 q^{29} +2.77245 q^{30} -2.77245i q^{31} -22.8740i q^{32} +1.86273i q^{33} -11.3720i q^{34} -0.741082 q^{35} +6.27036 q^{36} +6.10590i q^{37} +19.9169 q^{38} -7.13727 q^{40} +1.25461i q^{41} +3.74108 q^{42} +1.74108 q^{43} -7.52497i q^{44} -0.842809i q^{45} -6.39619i q^{46} +5.85843i q^{47} +20.9799 q^{48} -1.00000 q^{49} -12.2000i q^{50} +5.66224 q^{51} +4.56778 q^{53} +15.4779i q^{54} -1.01144 q^{55} -9.63087 q^{56} +9.91685i q^{57} +1.11734i q^{58} +10.9843i q^{59} -5.57662i q^{60} +6.52497 q^{61} -7.59951 q^{62} -1.13727i q^{63} -31.9557 q^{64} +5.10590 q^{66} -13.7597i q^{67} -22.8740 q^{68} +3.18474 q^{69} +2.03137i q^{70} -4.81526i q^{71} -10.9529i q^{72} -6.06987i q^{73} +16.7368 q^{74} +6.07453 q^{75} -40.0616i q^{76} -1.36482 q^{77} -9.12582 q^{79} +11.3919i q^{80} -4.29482 q^{81} +3.43900 q^{82} +11.7368i q^{83} -7.52497i q^{84} +3.07453i q^{85} -4.77245i q^{86} -0.556340 q^{87} -13.1444 q^{88} +1.76101i q^{89} -2.31021 q^{90} -12.8656 q^{92} -3.78389i q^{93} +16.0584 q^{94} -5.38474 q^{95} -31.2189i q^{96} +9.53381i q^{97} +2.74108i q^{98} -1.55217i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 10 q^{4} + 14 q^{9} + 22 q^{10} - 24 q^{12} + 2 q^{14} + 38 q^{16} + 8 q^{17} + 10 q^{22} + 4 q^{23} - 10 q^{25} - 52 q^{27} + 2 q^{29} + 8 q^{30} + 14 q^{35} + 68 q^{36} + 46 q^{38} - 34 q^{40}+ \cdots - 42 q^{95}+O(q^{100}) $ 8 * q + 2 * q^3 - 10 * q^4 + 14 * q^9 + 22 * q^10 - 24 * q^12 + 2 * q^14 + 38 * q^16 + 8 * q^17 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 52 * q^27 + 2 * q^29 + 8 * q^30 + 14 * q^35 + 68 * q^36 + 46 * q^38 - 34 * q^40 + 10 * q^42 - 6 * q^43 + 22 * q^48 - 8 * q^49 - 14 * q^51 + 4 * q^53 - 6 * q^55 - 12 * q^56 + 16 * q^61 + 10 * q^62 - 28 * q^64 + 12 * q^66 - 66 * q^68 + 36 * q^69 + 40 * q^74 + 14 * q^75 - 2 * q^77 - 52 * q^79 + 48 * q^81 + 28 * q^82 + 26 * q^87 - 6 * q^88 - 52 * q^90 + 24 * q^92 + 66 * q^94 - 42 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.74108i	− 1.93824i	−0.246594	−	0.969119i	$-0.579311\pi$
$2$	− 2.74108i	− 1.93824i	0.246594	−	0.969119i	$-0.420689\pi$
$3$	1.36482	0.787979	0.393989	−	0.919115i	$-0.371095\pi$
$3$	1.36482	0.787979	0.393989	+	0.919115i	$0.371095\pi$
$4$	−5.51353	−2.75677
$5$	0.741082i	0.331422i	0.986174	+	0.165711i	$0.0529919\pi$
$5$	0.741082i	0.331422i	−0.986174	+	0.165711i	$0.947008\pi$
$6$	− 3.74108i	− 1.52729i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	9.63087i	3.40503i
$9$	−1.13727	−0.379089
$10$	2.03137	0.642374
$11$	1.36482i	0.411509i	0.978604	+	0.205754i	$0.0659648\pi$
$11$	1.36482i	0.411509i	−0.978604	+	0.205754i	$0.934035\pi$
$12$	−7.52497	−2.17227
$13$	0	0
$13$	0	0
$14$	2.74108	0.732585
$15$	1.01144i	0.261153i
$16$	15.3720	3.84299
$17$	4.14871	1.00621	0.503105	−	0.864225i	$-0.332191\pi$
$17$	4.14871	1.00621	0.503105	+	0.864225i	$0.332191\pi$
$18$	3.11734i	0.734765i
$19$	7.26606i	1.66695i	0.552559	+	0.833474i	$0.313651\pi$
$19$	7.26606i	1.66695i	−0.552559	+	0.833474i	$0.686349\pi$
$20$	− 4.08598i	− 0.913652i
$21$	1.36482i	0.297828i
$22$	3.74108	0.797601
$23$	2.33345	0.486559	0.243279	−	0.969956i	$-0.421777\pi$
$23$	2.33345	0.486559	0.243279	+	0.969956i	$0.421777\pi$
$24$	13.1444i	2.68309i
$25$	4.45080	0.890159
$26$	0	0
$27$	−5.64662	−1.08669
$28$	− 5.51353i	− 1.04196i
$29$	−0.407629	−0.0756948	−0.0378474	−	0.999284i	$-0.512050\pi$
$29$	−0.407629	−0.0756948	−0.0378474	+	0.999284i	$0.512050\pi$
$30$	2.77245	0.506178
$31$	− 2.77245i	− 0.497946i	−0.968510	−	0.248973i	$-0.919907\pi$
$31$	− 2.77245i	− 0.497946i	0.968510	−	0.248973i	$-0.0800931\pi$
$32$	− 22.8740i	− 4.04360i
$33$	1.86273i	0.324260i
$34$	− 11.3720i	− 1.95027i
$35$	−0.741082	−0.125266
$36$	6.27036	1.04506
$37$	6.10590i	1.00380i	0.864924	+	0.501902i	$0.167366\pi$
$37$	6.10590i	1.00380i	−0.864924	+	0.501902i	$0.832634\pi$
$38$	19.9169	3.23094
$39$	0	0
$40$	−7.13727	−1.12850
$41$	1.25461i	0.195938i	0.995189	+	0.0979688i	$0.0312345\pi$
$41$	1.25461i	0.195938i	−0.995189	+	0.0979688i	$0.968765\pi$
$42$	3.74108	0.577261
$43$	1.74108	0.265513	0.132756	−	0.991149i	$-0.457617\pi$
$43$	1.74108	0.265513	0.132756	+	0.991149i	$0.457617\pi$
$44$	− 7.52497i	− 1.13443i
$45$	− 0.842809i	− 0.125639i
$46$	− 6.39619i	− 0.943066i
$47$	5.85843i	0.854539i	0.904124	+	0.427270i	$0.140525\pi$
$47$	5.85843i	0.854539i	−0.904124	+	0.427270i	$0.859475\pi$
$48$	20.9799	3.02819
$49$	−1.00000	−0.142857
$50$	− 12.2000i	− 1.72534i
$51$	5.66224	0.792872
$52$	0	0
$53$	4.56778	0.627433	0.313717	−	0.949517i	$-0.398426\pi$
$53$	4.56778	0.627433	0.313717	+	0.949517i	$0.398426\pi$
$54$	15.4779i	2.10627i
$55$	−1.01144	−0.136383
$56$	−9.63087	−1.28698
$57$	9.91685i	1.31352i
$58$	1.11734i	0.146715i
$59$	10.9843i	1.43003i	0.699110	+	0.715014i	$0.253580\pi$
$59$	10.9843i	1.43003i	−0.699110	+	0.715014i	$0.746420\pi$
$60$	− 5.57662i	− 0.719939i
$61$	6.52497	0.835437	0.417719	−	0.908576i	$-0.362830\pi$
$61$	6.52497	0.835437	0.417719	+	0.908576i	$0.362830\pi$
$62$	−7.59951	−0.965139
$63$	− 1.13727i	− 0.143282i
$64$	−31.9557	−3.99446
$65$	0	0
$66$	5.10590	0.628493
$67$	− 13.7597i	− 1.68101i	−0.541804	−	0.840505i	$-0.682258\pi$
$67$	− 13.7597i	− 1.68101i	0.541804	−	0.840505i	$-0.317742\pi$
$68$	−22.8740	−2.77389
$69$	3.18474	0.383398
$70$	2.03137i	0.242795i
$71$	− 4.81526i	− 0.571466i	−0.958309	−	0.285733i	$-0.907763\pi$
$71$	− 4.81526i	− 0.571466i	0.958309	−	0.285733i	$-0.0922370\pi$
$72$	− 10.9529i	− 1.29081i
$73$	− 6.06987i	− 0.710425i	−0.934786	−	0.355212i	$-0.884409\pi$
$73$	− 6.06987i	− 0.710425i	0.934786	−	0.355212i	$-0.115591\pi$
$74$	16.7368	1.94561
$75$	6.07453	0.701427
$76$	− 40.0616i	− 4.59538i
$77$	−1.36482	−0.155536
$78$	0	0
$79$	−9.12582	−1.02674	−0.513368	−	0.858169i	$-0.671602\pi$
$79$	−9.12582	−1.02674	−0.513368	+	0.858169i	$0.671602\pi$
$80$	11.3919i	1.27365i
$81$	−4.29482	−0.477202
$82$	3.43900	0.379774
$83$	11.7368i	1.28828i	0.764908	+	0.644139i	$0.222784\pi$
$83$	11.7368i	1.28828i	−0.764908	+	0.644139i	$0.777216\pi$
$84$	− 7.52497i	− 0.821042i
$85$	3.07453i	0.333480i
$86$	− 4.77245i	− 0.514626i
$87$	−0.556340	−0.0596459
$88$	−13.1444	−1.40120
$89$	1.76101i	0.186666i	0.995635	+	0.0933331i	$0.0297522\pi$
$89$	1.76101i	0.186666i	−0.995635	+	0.0933331i	$0.970248\pi$
$90$	−2.31021	−0.243517
$91$	0	0
$92$	−12.8656	−1.34133
$93$	− 3.78389i	− 0.392371i
$94$	16.0584	1.65630
$95$	−5.38474	−0.552463
$96$	− 31.2189i	− 3.18627i
$97$	9.53381i	0.968012i	0.875065	+	0.484006i	$0.160819\pi$
$97$	9.53381i	0.968012i	−0.875065	+	0.484006i	$0.839181\pi$
$98$	2.74108i	0.276891i
$99$	− 1.55217i	− 0.155998i
$100$	−24.5396	−2.45396
$101$	7.49361	0.745642	0.372821	−	0.927903i	$-0.378391\pi$
$101$	7.49361	0.745642	0.372821	+	0.927903i	$0.378391\pi$
$102$	− 15.5207i	− 1.53678i
$103$	−2.80848	−0.276728	−0.138364	−	0.990381i	$-0.544184\pi$
$103$	−2.80848	−0.276728	−0.138364	+	0.990381i	$0.544184\pi$
$104$	0	0
$105$	−1.01144	−0.0987067
$106$	− 12.5207i	− 1.21611i
$107$	1.48647	0.143702	0.0718512	−	0.997415i	$-0.477109\pi$
$107$	1.48647	0.143702	0.0718512	+	0.997415i	$0.477109\pi$
$108$	31.1328	2.99576
$109$	2.87121i	0.275012i	0.990501	+	0.137506i	$0.0439087\pi$
$109$	2.87121i	0.275012i	−0.990501	+	0.137506i	$0.956091\pi$
$110$	2.77245i	0.264343i
$111$	8.33345i	0.790976i
$112$	15.3720i	1.45251i
$113$	−12.4194	−1.16832	−0.584161	−	0.811638i	$-0.698576\pi$
$113$	−12.4194	−1.16832	−0.584161	+	0.811638i	$0.698576\pi$
$114$	27.1829	2.54591
$115$	1.72928i	0.161256i
$116$	2.24747	0.208673
$117$	0	0
$118$	30.1087	2.77173
$119$	4.14871i	0.380312i
$120$	−9.74108	−0.889235
$121$	9.13727	0.830661
$122$	− 17.8855i	− 1.61928i
$123$	1.71232i	0.154395i
$124$	15.2860i	1.37272i
$125$	7.00382i	0.626440i
$126$	−3.11734	−0.277715
$127$	−5.43052	−0.481880	−0.240940	−	0.970540i	$-0.577456\pi$
$127$	−5.43052	−0.481880	−0.240940	+	0.970540i	$0.577456\pi$
$128$	41.8452i	3.69862i
$129$	2.37626	0.209218
$130$	0	0
$131$	−11.3220	−0.989209	−0.494604	−	0.869118i	$-0.664687\pi$
$131$	−11.3220	−0.989209	−0.494604	+	0.869118i	$0.664687\pi$
$132$	− 10.2702i	− 0.893909i
$133$	−7.26606	−0.630047
$134$	−37.7164	−3.25820
$135$	− 4.18461i	− 0.360154i
$136$	39.9557i	3.42617i
$137$	13.9754i	1.19400i	0.802241	+	0.597000i	$0.203641\pi$
$137$	13.9754i	1.19400i	−0.802241	+	0.597000i	$0.796359\pi$
$138$	− 8.72964i	− 0.743116i
$139$	10.4309	0.884735	0.442368	−	0.896834i	$-0.354139\pi$
$139$	10.4309	0.884735	0.442368	+	0.896834i	$0.354139\pi$
$140$	4.08598	0.345328
$141$	7.99569i	0.673359i
$142$	−13.1990	−1.10764
$143$	0	0
$144$	−17.4820	−1.45684
$145$	− 0.302087i	− 0.0250869i
$146$	−16.6380	−1.37697
$147$	−1.36482	−0.112568
$148$	− 33.6651i	− 2.76725i
$149$	8.16433i	0.668848i	0.942423	+	0.334424i	$0.108542\pi$
$149$	8.16433i	0.668848i	−0.942423	+	0.334424i	$0.891458\pi$
$150$	− 16.6508i	− 1.35953i
$151$	2.46188i	0.200345i	0.994970	+	0.100173i	$0.0319395\pi$
$151$	2.46188i	0.200345i	−0.994970	+	0.100173i	$0.968061\pi$
$152$	−69.9785	−5.67600
$153$	−4.71820	−0.381444
$154$	3.74108i	0.301465i
$155$	2.05461	0.165030
$156$	0	0
$157$	−12.9198	−1.03111	−0.515557	−	0.856855i	$-0.672415\pi$
$157$	−12.9198	−1.03111	−0.515557	+	0.856855i	$0.672415\pi$
$158$	25.0146i	1.99006i
$159$	6.23420	0.494404
$160$	16.9515	1.34014
$161$	2.33345i	0.183902i
$162$	11.7724i	0.924931i
$163$	6.02742i	0.472104i	0.971740	+	0.236052i	$0.0758536\pi$
$163$	6.02742i	0.472104i	−0.971740	+	0.236052i	$0.924146\pi$
$164$	− 6.91734i	− 0.540154i
$165$	−1.38044	−0.107467
$166$	32.1715	2.49699
$167$	− 7.65116i	− 0.592064i	−0.955178	−	0.296032i	$-0.904336\pi$
$167$	− 7.65116i	− 0.592064i	0.955178	−	0.296032i	$-0.0956636\pi$
$168$	−13.1444	−1.01411
$169$	0	0
$170$	8.42755	0.646364
$171$	− 8.26345i	− 0.631922i
$172$	−9.59951	−0.731956
$173$	0.164460	0.0125036	0.00625182	−	0.999980i	$-0.498010\pi$
$173$	0.164460	0.0125036	0.00625182	+	0.999980i	$0.498010\pi$
$174$	1.52497i	0.115608i
$175$	4.45080i	0.336449i
$176$	20.9799i	1.58142i
$177$	14.9915i	1.12683i
$178$	4.82706	0.361803
$179$	−0.768633	−0.0574503	−0.0287252	−	0.999587i	$-0.509145\pi$
$179$	−0.768633	−0.0574503	−0.0287252	+	0.999587i	$0.509145\pi$
$180$	4.64685i	0.346356i
$181$	9.92152	0.737461	0.368730	−	0.929536i	$-0.379793\pi$
$181$	9.92152	0.737461	0.368730	+	0.929536i	$0.379793\pi$
$182$	0	0
$183$	8.90541	0.658307
$184$	22.4732i	1.65675i
$185$	−4.52497	−0.332683
$186$	−10.3720	−0.760509
$187$	5.66224i	0.414064i
$188$	− 32.3006i	− 2.35576i
$189$	− 5.64662i	− 0.410731i
$190$	14.7600i	1.07080i
$191$	9.89693	0.716117	0.358058	−	0.933699i	$-0.383439\pi$
$191$	9.89693	0.716117	0.358058	+	0.933699i	$0.383439\pi$
$192$	−43.6138	−3.14755
$193$	− 8.70075i	− 0.626293i	−0.949705	−	0.313147i	$-0.898617\pi$
$193$	− 8.70075i	− 0.626293i	0.949705	−	0.313147i	$-0.101383\pi$
$194$	26.1330	1.87624
$195$	0	0
$196$	5.51353	0.393824
$197$	− 26.0186i	− 1.85375i	−0.375374	−	0.926874i	$-0.622486\pi$
$197$	− 26.0186i	− 1.85375i	0.375374	−	0.926874i	$-0.377514\pi$
$198$	−4.25461	−0.302362
$199$	−10.1330	−0.718307	−0.359153	−	0.933279i	$-0.616934\pi$
$199$	−10.1330	−0.718307	−0.359153	+	0.933279i	$0.616934\pi$
$200$	42.8651i	3.03102i
$201$	− 18.7795i	− 1.32460i
$202$	− 20.5406i	− 1.44523i
$203$	− 0.407629i	− 0.0286099i
$204$	−31.2189	−2.18576
$205$	−0.929771	−0.0649380
$206$	7.69827i	0.536364i
$207$	−2.65376	−0.184449
$208$	0	0
$209$	−9.91685	−0.685963
$210$	2.77245i	0.191317i
$211$	16.6782	1.14818	0.574088	−	0.818794i	$-0.305357\pi$
$211$	16.6782	1.14818	0.574088	+	0.818794i	$0.305357\pi$
$212$	−25.1846	−1.72969
$213$	− 6.57196i	− 0.450303i
$214$	− 4.07453i	− 0.278529i
$215$	1.29028i	0.0879967i
$216$	− 54.3819i	− 3.70022i
$217$	2.77245	0.188206
$218$	7.87023	0.533039
$219$	− 8.28428i	− 0.559800i
$220$	5.57662	0.375976
$221$	0	0
$222$	22.8427	1.53310
$223$	1.07036i	0.0716766i	0.999358	+	0.0358383i	$0.0114101\pi$
$223$	1.07036i	0.0716766i	−0.999358	+	0.0358383i	$0.988590\pi$
$224$	22.8740	1.52834
$225$	−5.06175	−0.337450
$226$	34.0427i	2.26449i
$227$	− 24.4664i	− 1.62389i	−0.583732	−	0.811947i	$-0.698408\pi$
$227$	− 24.4664i	− 1.62389i	0.583732	−	0.811947i	$-0.301592\pi$
$228$	− 54.6769i	− 3.62106i
$229$	− 4.72964i	− 0.312543i	−0.987714	−	0.156272i	$-0.950052\pi$
$229$	− 4.72964i	− 0.312543i	0.987714	−	0.156272i	$-0.0499475\pi$
$230$	4.74010	0.312553
$231$	−1.86273	−0.122559
$232$	− 3.92582i	− 0.257743i
$233$	−20.5507	−1.34632	−0.673160	−	0.739497i	$-0.735064\pi$
$233$	−20.5507	−1.34632	−0.673160	+	0.739497i	$0.735064\pi$
$234$	0	0
$235$	−4.34157	−0.283213
$236$	− 60.5620i	− 3.94225i
$237$	−12.4551	−0.809046
$238$	11.3720	0.737134
$239$	6.25461i	0.404577i	0.979326	+	0.202289i	$0.0648379\pi$
$239$	6.25461i	0.404577i	−0.979326	+	0.202289i	$0.935162\pi$
$240$	15.5479i	1.00361i
$241$	12.1444i	0.782290i	0.920329	+	0.391145i	$0.127921\pi$
$241$	12.1444i	0.782290i	−0.920329	+	0.391145i	$0.872079\pi$
$242$	− 25.0460i	− 1.61002i
$243$	11.0782	0.710668
$244$	−35.9756	−2.30310
$245$	− 0.741082i	− 0.0473460i
$246$	4.69361	0.299254
$247$	0	0
$248$	26.7011	1.69552
$249$	16.0186i	1.01514i
$250$	19.1980	1.21419
$251$	6.31438	0.398560	0.199280	−	0.979943i	$-0.436140\pi$
$251$	6.31438	0.398560	0.199280	+	0.979943i	$0.436140\pi$
$252$	6.27036i	0.394996i
$253$	3.18474i	0.200223i
$254$	14.8855i	0.933999i
$255$	4.19619i	0.262775i
$256$	50.7896	3.17435
$257$	−24.3562	−1.51930	−0.759649	−	0.650333i	$-0.774629\pi$
$257$	−24.3562	−1.51930	−0.759649	+	0.650333i	$0.774629\pi$
$258$	− 6.51353i	− 0.405515i
$259$	−6.10590	−0.379402
$260$	0	0
$261$	0.463583	0.0286951
$262$	31.0346i	1.91732i
$263$	−9.57910	−0.590672	−0.295336	−	0.955393i	$-0.595432\pi$
$263$	−9.57910	−0.590672	−0.295336	+	0.955393i	$0.595432\pi$
$264$	−17.9397	−1.10411
$265$	3.38510i	0.207945i
$266$	19.9169i	1.22118i
$267$	2.40345i	0.147089i
$268$	75.8643i	4.63415i
$269$	29.3990	1.79249	0.896245	−	0.443560i	$-0.146285\pi$
$269$	29.3990	1.79249	0.896245	+	0.443560i	$0.146285\pi$
$270$	−11.4704	−0.698064
$271$	0.300385i	0.0182471i	0.999958	+	0.00912354i	$0.00290415\pi$
$271$	0.300385i	0.0182471i	−0.999958	+	0.00912354i	$0.997096\pi$
$272$	63.7738	3.86686
$273$	0	0
$274$	38.3078	2.31426
$275$	6.07453i	0.366308i
$276$	−17.5592	−1.05694
$277$	32.7710	1.96902	0.984509	−	0.175337i	$-0.0561014\pi$
$277$	32.7710	1.96902	0.984509	+	0.175337i	$0.0561014\pi$
$278$	− 28.5919i	− 1.71483i
$279$	3.15302i	0.188766i
$280$	− 7.13727i	− 0.426533i
$281$	− 4.29482i	− 0.256207i	−0.991761	−	0.128104i	$-0.959111\pi$
$281$	− 4.29482i	− 0.256207i	0.991761	−	0.128104i	$-0.0408890\pi$
$282$	21.9169	1.30513
$283$	21.1003	1.25428	0.627140	−	0.778907i	$-0.284225\pi$
$283$	21.1003	1.25428	0.627140	+	0.778907i	$0.284225\pi$
$284$	26.5491i	1.57540i
$285$	−7.34920	−0.435329
$286$	0	0
$287$	−1.25461	−0.0740574
$288$	26.0139i	1.53288i
$289$	0.211803	0.0124590
$290$	−0.828044	−0.0486244
$291$	13.0119i	0.762773i
$292$	33.4664i	1.95847i
$293$	− 17.7638i	− 1.03777i	−0.854843	−	0.518887i	$-0.826346\pi$
$293$	− 17.7638i	− 1.03777i	0.854843	−	0.518887i	$-0.173654\pi$
$294$	3.74108i	0.218184i
$295$	−8.14023	−0.473943
$296$	−58.8052	−3.41798
$297$	− 7.70662i	− 0.447184i
$298$	22.3791	1.29639
$299$	0	0
$300$	−33.4921	−1.93367
$301$	1.74108i	0.100354i
$302$	6.74822	0.388316
$303$	10.2274	0.587550
$304$	111.693i	6.40606i
$305$	4.83554i	0.276882i
$306$	12.9330i	0.739328i
$307$	− 18.0156i	− 1.02821i	−0.857729	−	0.514103i	$-0.828125\pi$
$307$	− 18.0156i	− 1.02821i	0.857729	−	0.514103i	$-0.171875\pi$
$308$	7.52497	0.428775
$309$	−3.83307	−0.218056
$310$	− 5.63186i	− 0.319868i
$311$	−17.2545	−0.978412	−0.489206	−	0.872168i	$-0.662713\pi$
$311$	−17.2545	−0.978412	−0.489206	+	0.872168i	$0.662713\pi$
$312$	0	0
$313$	6.81526	0.385221	0.192611	−	0.981275i	$-0.438305\pi$
$313$	6.81526	0.385221	0.192611	+	0.981275i	$0.438305\pi$
$314$	35.4143i	1.99854i
$315$	0.842809	0.0474869
$316$	50.3155	2.83047
$317$	− 25.0770i	− 1.40847i	−0.709969	−	0.704233i	$-0.751291\pi$
$317$	− 25.0770i	− 1.40847i	0.709969	−	0.704233i	$-0.248709\pi$
$318$	− 17.0885i	− 0.958273i
$319$	− 0.556340i	− 0.0311491i
$320$	− 23.6818i	− 1.32385i
$321$	2.02876	0.113234
$322$	6.39619	0.356446
$323$	30.1448i	1.67730i
$324$	23.6796	1.31553
$325$	0	0
$326$	16.5217	0.915050
$327$	3.91869i	0.216704i
$328$	−12.0830	−0.667173
$329$	−5.85843	−0.322986
$330$	3.78389i	0.208296i
$331$	− 2.99534i	− 0.164639i	−0.996606	−	0.0823193i	$-0.973767\pi$
$331$	− 2.99534i	− 0.164639i	0.996606	−	0.0823193i	$-0.0262327\pi$
$332$	− 64.7111i	− 3.55148i
$333$	− 6.94405i	− 0.380531i
$334$	−20.9724	−1.14756
$335$	10.1970	0.557124
$336$	20.9799i	1.14455i
$337$	29.4888	1.60636	0.803179	−	0.595738i	$-0.203140\pi$
$337$	29.4888	1.60636	0.803179	+	0.595738i	$0.203140\pi$
$338$	0	0
$339$	−16.9503	−0.920613
$340$	− 16.9515i	− 0.919326i
$341$	3.78389	0.204909
$342$	−22.6508	−1.22481
$343$	− 1.00000i	− 0.0539949i
$344$	16.7681i	0.904078i
$345$	2.36015i	0.127066i
$346$	− 0.450797i	− 0.0242350i
$347$	−5.98686	−0.321391	−0.160696	−	0.987004i	$-0.551374\pi$
$347$	−5.98686	−0.321391	−0.160696	+	0.987004i	$0.551374\pi$
$348$	3.06740	0.164430
$349$	30.3362i	1.62386i	0.583757	+	0.811929i	$0.301582\pi$
$349$	30.3362i	1.62386i	−0.583757	+	0.811929i	$0.698418\pi$
$350$	12.2000	0.652117
$351$	0	0
$352$	31.2189	1.66398
$353$	− 28.6063i	− 1.52256i	−0.648424	−	0.761280i	$-0.724572\pi$
$353$	− 28.6063i	− 1.52256i	0.648424	−	0.761280i	$-0.275428\pi$
$354$	41.0930	2.18407
$355$	3.56850	0.189396
$356$	− 9.70936i	− 0.514595i
$357$	5.66224i	0.299678i
$358$	2.10689i	0.111352i
$359$	− 23.4618i	− 1.23826i	−0.785287	−	0.619132i	$-0.787485\pi$
$359$	− 23.4618i	− 1.23826i	0.785287	−	0.619132i	$-0.212515\pi$
$360$	8.11699	0.427803
$361$	−33.7956	−1.77871
$362$	− 27.1957i	− 1.42937i
$363$	12.4707	0.654543
$364$	0	0
$365$	4.49827	0.235450
$366$	− 24.4105i	− 1.27596i
$367$	36.5197	1.90631	0.953156	−	0.302479i	$-0.0978143\pi$
$367$	36.5197	1.90631	0.953156	+	0.302479i	$0.0978143\pi$
$368$	35.8697	1.86984
$369$	− 1.42683i	− 0.0742778i
$370$	12.4033i	0.644818i
$371$	4.56778i	0.237147i
$372$	20.8626i	1.08168i
$373$	−13.0498	−0.675694	−0.337847	−	0.941201i	$-0.609699\pi$
$373$	−13.0498	−0.675694	−0.337847	+	0.941201i	$0.609699\pi$
$374$	15.5207	0.802555
$375$	9.55894i	0.493622i
$376$	−56.4218	−2.90973
$377$	0	0
$378$	−15.4779	−0.796095
$379$	30.6037i	1.57201i	0.618223	+	0.786003i	$0.287853\pi$
$379$	30.6037i	1.57201i	−0.618223	+	0.786003i	$0.712147\pi$
$380$	29.6889	1.52301
$381$	−7.41167	−0.379711
$382$	− 27.1283i	− 1.38800i
$383$	− 4.88598i	− 0.249662i	−0.992178	−	0.124831i	$-0.960161\pi$
$383$	− 4.88598i	− 0.249662i	0.992178	−	0.124831i	$-0.0398388\pi$
$384$	57.1111i	2.91444i
$385$	− 1.01144i	− 0.0515479i
$386$	−23.8495	−1.21391
$387$	−1.98008	−0.100653
$388$	− 52.5650i	− 2.66858i
$389$	1.85425	0.0940143	0.0470072	−	0.998895i	$-0.485032\pi$
$389$	1.85425	0.0940143	0.0470072	+	0.998895i	$0.485032\pi$
$390$	0	0
$391$	9.68082	0.489580
$392$	− 9.63087i	− 0.486433i
$393$	−15.4525	−0.779475
$394$	−71.3191	−3.59300
$395$	− 6.76298i	− 0.340283i
$396$	8.55791i	0.430051i
$397$	− 21.5134i	− 1.07973i	−0.841753	−	0.539863i	$-0.818476\pi$
$397$	− 21.5134i	− 1.07973i	0.841753	−	0.539863i	$-0.181524\pi$
$398$	27.7753i	1.39225i
$399$	−9.91685	−0.496464
$400$	68.4175	3.42087
$401$	14.5653i	0.727357i	0.931525	+	0.363678i	$0.118479\pi$
$401$	14.5653i	0.727357i	−0.931525	+	0.363678i	$0.881521\pi$
$402$	−51.4760	−2.56739
$403$	0	0
$404$	−41.3162	−2.05556
$405$	− 3.18281i	− 0.158155i
$406$	−1.11734	−0.0554529
$407$	−8.33345	−0.413074
$408$	54.5323i	2.69975i
$409$	− 22.1290i	− 1.09421i	−0.837064	−	0.547105i	$-0.815730\pi$
$409$	− 22.1290i	− 1.09421i	0.837064	−	0.547105i	$-0.184270\pi$
$410$	2.54858i	0.125865i
$411$	19.0739i	0.940847i
$412$	15.4846	0.762873
$413$	−10.9843	−0.540500
$414$	7.27418i	0.357506i
$415$	−8.69791	−0.426964
$416$	0	0
$417$	14.2363	0.697153
$418$	27.1829i	1.32956i
$419$	3.37590	0.164924	0.0824618	−	0.996594i	$-0.473722\pi$
$419$	3.37590	0.164924	0.0824618	+	0.996594i	$0.473722\pi$
$420$	5.57662	0.272111
$421$	− 25.1101i	− 1.22379i	−0.790939	−	0.611895i	$-0.790407\pi$
$421$	− 25.1101i	− 1.22379i	0.790939	−	0.611895i	$-0.209593\pi$
$422$	− 45.7164i	− 2.22544i
$423$	− 6.66260i	− 0.323947i
$424$	43.9917i	2.13643i
$425$	18.4651	0.895688
$426$	−18.0143	−0.872794
$427$	6.52497i	0.315766i
$428$	−8.19570	−0.396154
$429$	0	0
$430$	3.53678	0.170558
$431$	10.7948i	0.519969i	0.965613	+	0.259985i	$0.0837175\pi$
$431$	10.7948i	0.519969i	−0.965613	+	0.259985i	$0.916282\pi$
$432$	−86.7997	−4.17615
$433$	14.5182	0.697700	0.348850	−	0.937179i	$-0.386572\pi$
$433$	14.5182	0.697700	0.348850	+	0.937179i	$0.386572\pi$
$434$	− 7.59951i	− 0.364788i
$435$	− 0.412294i	− 0.0197680i
$436$	− 15.8305i	− 0.758144i
$437$	16.9550i	0.811068i
$438$	−22.7079	−1.08502
$439$	14.4309	0.688748	0.344374	−	0.938833i	$-0.388091\pi$
$439$	14.4309	0.688748	0.344374	+	0.938833i	$0.388091\pi$
$440$	− 9.74108i	− 0.464388i
$441$	1.13727	0.0541556
$442$	0	0
$443$	−30.2430	−1.43689	−0.718445	−	0.695584i	$-0.755146\pi$
$443$	−30.2430	−1.43689	−0.718445	+	0.695584i	$0.755146\pi$
$444$	− 45.9467i	− 2.18054i
$445$	−1.30505	−0.0618653
$446$	2.93395	0.138926
$447$	11.1428i	0.527038i
$448$	− 31.9557i	− 1.50977i
$449$	− 31.2760i	− 1.47601i	−0.674797	−	0.738003i	$-0.735769\pi$
$449$	− 31.2760i	− 1.47601i	0.674797	−	0.738003i	$-0.264231\pi$
$450$	13.8747i	0.654058i
$451$	−1.71232	−0.0806300
$452$	68.4749	3.22079
$453$	3.36002i	0.157868i
$454$	−67.0645	−3.14749
$455$	0	0
$456$	−95.5080	−4.47257
$457$	20.6466i	0.965808i	0.875673	+	0.482904i	$0.160418\pi$
$457$	20.6466i	0.965808i	−0.875673	+	0.482904i	$0.839582\pi$
$458$	−12.9643	−0.605783
$459$	−23.4262	−1.09344
$460$	− 9.53444i	− 0.444545i
$461$	27.2961i	1.27131i	0.771975	+	0.635653i	$0.219269\pi$
$461$	27.2961i	1.27131i	−0.771975	+	0.635653i	$0.780731\pi$
$462$	5.10590i	0.237548i
$463$	− 5.65977i	− 0.263032i	−0.991314	−	0.131516i	$-0.958016\pi$
$463$	− 5.65977i	− 0.263032i	0.991314	−	0.131516i	$-0.0419844\pi$
$464$	−6.26606	−0.290894
$465$	2.80417	0.130040
$466$	56.3311i	2.60949i
$467$	−42.2145	−1.95345	−0.976727	−	0.214486i	$-0.931192\pi$
$467$	−42.2145	−1.95345	−0.976727	+	0.214486i	$0.931192\pi$
$468$	0	0
$469$	13.7597	0.635362
$470$	11.9006i	0.548934i
$471$	−17.6332	−0.812496
$472$	−105.788	−4.86929
$473$	2.37626i	0.109261i
$474$	34.1405i	1.56812i
$475$	32.3397i	1.48385i
$476$	− 22.8740i	− 1.04843i
$477$	−5.19479	−0.237853
$478$	17.1444	0.784167
$479$	− 32.5316i	− 1.48641i	−0.669065	−	0.743204i	$-0.733305\pi$
$479$	− 32.5316i	− 1.48641i	0.669065	−	0.743204i	$-0.266695\pi$
$480$	23.1358	1.05600
$481$	0	0
$482$	33.2888	1.51626
$483$	3.18474i	0.144911i
$484$	−50.3786	−2.28994
$485$	−7.06534	−0.320820
$486$	− 30.3663i	− 1.37744i
$487$	26.8583i	1.21707i	0.793529	+	0.608533i	$0.208242\pi$
$487$	26.8583i	1.21707i	−0.793529	+	0.608533i	$0.791758\pi$
$488$	62.8412i	2.84469i
$489$	8.22634i	0.372008i
$490$	−2.03137	−0.0917678
$491$	−43.6878	−1.97160	−0.985802	−	0.167912i	$-0.946298\pi$
$491$	−43.6878	−1.97160	−0.985802	+	0.167912i	$0.946298\pi$
$492$	− 9.44093i	− 0.425630i
$493$	−1.69113	−0.0761649
$494$	0	0
$495$	1.15028	0.0517013
$496$	− 42.6180i	− 1.91360i
$497$	4.81526	0.215994
$498$	43.9082	1.96758
$499$	− 18.1020i	− 0.810355i	−0.914238	−	0.405177i	$-0.867210\pi$
$499$	− 18.1020i	− 0.810355i	0.914238	−	0.405177i	$-0.132790\pi$
$500$	− 38.6158i	− 1.72695i
$501$	− 10.4424i	− 0.466534i
$502$	− 17.3082i	− 0.772505i
$503$	−28.4155	−1.26698	−0.633492	−	0.773749i	$-0.718379\pi$
$503$	−28.4155	−1.26698	−0.633492	+	0.773749i	$0.718379\pi$
$504$	10.9529	0.487880
$505$	5.55338i	0.247122i
$506$	8.72964	0.388080
$507$	0	0
$508$	29.9413	1.32843
$509$	17.4791i	0.774748i	0.921923	+	0.387374i	$0.126618\pi$
$509$	17.4791i	0.774748i	−0.921923	+	0.387374i	$0.873382\pi$
$510$	11.5021	0.509321
$511$	6.06987	0.268515
$512$	− 55.5280i	− 2.45402i
$513$	− 41.0287i	− 1.81146i
$514$	66.7624i	2.94476i
$515$	− 2.08131i	− 0.0917136i
$516$	−13.1016	−0.576766
$517$	−7.99569	−0.351650
$518$	16.7368i	0.735372i
$519$	0.224458	0.00985260
$520$	0	0
$521$	19.3087	0.845931	0.422966	−	0.906146i	$-0.360989\pi$
$521$	19.3087	0.845931	0.422966	+	0.906146i	$0.360989\pi$
$522$	− 1.27072i	− 0.0556179i
$523$	−10.0229	−0.438270	−0.219135	−	0.975695i	$-0.570324\pi$
$523$	−10.0229	−0.438270	−0.219135	+	0.975695i	$0.570324\pi$
$524$	62.4242	2.72702
$525$	6.07453i	0.265114i
$526$	26.2571i	1.14486i
$527$	− 11.5021i	− 0.501039i
$528$	28.6338i	1.24613i
$529$	−17.5550	−0.763261
$530$	9.27884	0.403047
$531$	− 12.4920i	− 0.542108i
$532$	40.0616	1.73689
$533$	0	0
$534$	6.58807	0.285093
$535$	1.10160i	0.0476261i
$536$	132.518	5.72389
$537$	−1.04904	−0.0452696
$538$	− 80.5851i	− 3.47427i
$539$	− 1.36482i	− 0.0587869i
$540$	23.0720i	0.992860i
$541$	− 17.6153i	− 0.757339i	−0.925532	−	0.378670i	$-0.876382\pi$
$541$	− 17.6153i	− 0.757339i	0.925532	−	0.378670i	$-0.123618\pi$
$542$	0.823379	0.0353672
$543$	13.5411	0.581103
$544$	− 94.8978i	− 4.06871i
$545$	−2.12780	−0.0911451
$546$	0	0
$547$	2.98425	0.127597	0.0637987	−	0.997963i	$-0.479678\pi$
$547$	2.98425	0.127597	0.0637987	+	0.997963i	$0.479678\pi$
$548$	− 77.0539i	− 3.29158i
$549$	−7.42064	−0.316705
$550$	16.6508	0.709992
$551$	− 2.96185i	− 0.126179i
$552$	30.6719i	1.30548i
$553$	− 9.12582i	− 0.388070i
$554$	− 89.8279i	− 3.81642i
$555$	−6.17577	−0.262147
$556$	−57.5109	−2.43901
$557$	− 7.25596i	− 0.307445i	−0.988114	−	0.153722i	$-0.950874\pi$
$557$	− 7.25596i	− 0.307445i	0.988114	−	0.153722i	$-0.0491261\pi$
$558$	8.64268	0.365874
$559$	0	0
$560$	−11.3919	−0.481395
$561$	7.72794i	0.326274i
$562$	−11.7724	−0.496591
$563$	−4.27933	−0.180352	−0.0901762	−	0.995926i	$-0.528743\pi$
$563$	−4.27933	−0.180352	−0.0901762	+	0.995926i	$0.528743\pi$
$564$	− 44.0845i	− 1.85629i
$565$	− 9.20382i	− 0.387207i
$566$	− 57.8375i	− 2.43109i
$567$	− 4.29482i	− 0.180365i
$568$	46.3751	1.94586
$569$	19.7626	0.828492	0.414246	−	0.910165i	$-0.364045\pi$
$569$	19.7626	0.828492	0.414246	+	0.910165i	$0.364045\pi$
$570$	20.1448i	0.843771i
$571$	19.9236	0.833778	0.416889	−	0.908957i	$-0.363120\pi$
$571$	19.9236	0.833778	0.416889	+	0.908957i	$0.363120\pi$
$572$	0	0
$573$	13.5075	0.564285
$574$	3.43900i	0.143541i
$575$	10.3857	0.433115
$576$	36.3422	1.51426
$577$	− 28.7300i	− 1.19605i	−0.801479	−	0.598023i	$-0.795953\pi$
$577$	− 28.7300i	− 1.19605i	0.801479	−	0.598023i	$-0.204047\pi$
$578$	− 0.580569i	− 0.0241485i
$579$	− 11.8749i	− 0.493506i
$580$	1.66556i	0.0691587i
$581$	−11.7368	−0.486924
$582$	35.6668	1.47844
$583$	6.23420i	0.258194i
$584$	58.4582	2.41902
$585$	0	0
$586$	−48.6921	−2.01145
$587$	31.5388i	1.30174i	0.759188	+	0.650872i	$0.225597\pi$
$587$	31.5388i	1.30174i	−0.759188	+	0.650872i	$0.774403\pi$
$588$	7.52497	0.310325
$589$	20.1448	0.830051
$590$	22.3130i	0.918613i
$591$	− 35.5107i	− 1.46071i
$592$	93.8597i	3.85761i
$593$	11.1181i	0.456564i	0.973595	+	0.228282i	$0.0733108\pi$
$593$	11.1181i	0.456564i	−0.973595	+	0.228282i	$0.926689\pi$
$594$	−21.1245	−0.866748
$595$	−3.07453	−0.126044
$596$	− 45.0143i	− 1.84386i
$597$	−13.8297	−0.566010
$598$	0	0
$599$	−7.29572	−0.298095	−0.149048	−	0.988830i	$-0.547621\pi$
$599$	−7.29572	−0.298095	−0.149048	+	0.988830i	$0.547621\pi$
$600$	58.5031i	2.38838i
$601$	−1.17258	−0.0478306	−0.0239153	−	0.999714i	$-0.507613\pi$
$601$	−1.17258	−0.0478306	−0.0239153	+	0.999714i	$0.507613\pi$
$602$	4.77245	0.194510
$603$	15.6484i	0.637253i
$604$	− 13.5737i	− 0.552304i
$605$	6.77146i	0.275299i
$606$	− 28.0342i	− 1.13881i
$607$	0.633838	0.0257267	0.0128633	−	0.999917i	$-0.495905\pi$
$607$	0.633838	0.0257267	0.0128633	+	0.999917i	$0.495905\pi$
$608$	166.204	6.74047
$609$	− 0.556340i	− 0.0225440i
$610$	13.2546	0.536664
$611$	0	0
$612$	26.0139	1.05155
$613$	− 30.8550i	− 1.24622i	−0.782134	−	0.623110i	$-0.785869\pi$
$613$	− 30.8550i	− 1.24622i	0.782134	−	0.623110i	$-0.214131\pi$
$614$	−49.3823	−1.99291
$615$	−1.26897	−0.0511698
$616$	− 13.1444i	− 0.529603i
$617$	33.8209i	1.36158i	0.732479	+	0.680790i	$0.238363\pi$
$617$	33.8209i	1.36158i	−0.732479	+	0.680790i	$0.761637\pi$
$618$	10.5068i	0.422644i
$619$	0.404797i	0.0162702i	0.999967	+	0.00813509i	$0.00258951\pi$
$619$	0.404797i	0.0162702i	−0.999967	+	0.00813509i	$0.997410\pi$
$620$	−11.3282	−0.454950
$621$	−13.1761	−0.528740
$622$	47.2959i	1.89639i
$623$	−1.76101	−0.0705532
$624$	0	0
$625$	17.0636	0.682543
$626$	− 18.6812i	− 0.746650i
$627$	−13.5347	−0.540524
$628$	71.2338	2.84254
$629$	25.3316i	1.01004i
$630$	− 2.31021i	− 0.0920409i
$631$	− 30.4508i	− 1.21223i	−0.795378	−	0.606114i	$-0.792728\pi$
$631$	− 30.4508i	− 1.21223i	0.795378	−	0.606114i	$-0.207272\pi$
$632$	− 87.8897i	− 3.49606i
$633$	22.7628	0.904738
$634$	−68.7381	−2.72994
$635$	− 4.02446i	− 0.159706i
$636$	−34.3724	−1.36296
$637$	0	0
$638$	−1.52497	−0.0603743
$639$	5.47624i	0.216637i
$640$	−31.0107	−1.22581
$641$	−9.64564	−0.380980	−0.190490	−	0.981689i	$-0.561008\pi$
$641$	−9.64564	−0.380980	−0.190490	+	0.981689i	$0.561008\pi$
$642$	− 5.56100i	− 0.219475i
$643$	8.13296i	0.320733i	0.987058	+	0.160366i	$0.0512676\pi$
$643$	8.13296i	0.320733i	−0.987058	+	0.160366i	$0.948732\pi$
$644$	− 12.8656i	− 0.506974i
$645$	1.76101i	0.0693395i
$646$	82.6293	3.25101
$647$	11.5227	0.453005	0.226503	−	0.974011i	$-0.427271\pi$
$647$	11.5227	0.453005	0.226503	+	0.974011i	$0.427271\pi$
$648$	− 41.3629i	− 1.62489i
$649$	−14.9915	−0.588469
$650$	0	0
$651$	3.78389	0.148302
$652$	− 33.2324i	− 1.30148i
$653$	42.4039	1.65939	0.829697	−	0.558215i	$-0.188513\pi$
$653$	42.4039	1.65939	0.829697	+	0.558215i	$0.188513\pi$
$654$	10.7414	0.420024
$655$	− 8.39054i	− 0.327845i
$656$	19.2858i	0.752986i
$657$	6.90307i	0.269314i
$658$	16.0584i	0.626023i
$659$	−2.50088	−0.0974203	−0.0487101	−	0.998813i	$-0.515511\pi$
$659$	−2.50088	−0.0974203	−0.0487101	+	0.998813i	$0.515511\pi$
$660$	7.61108	0.296261
$661$	− 14.8394i	− 0.577184i	−0.957452	−	0.288592i	$-0.906813\pi$
$661$	− 14.8394i	− 0.577184i	0.957452	−	0.288592i	$-0.0931871\pi$
$662$	−8.21046	−0.319109
$663$	0	0
$664$	−113.035	−4.38663
$665$	− 5.38474i	− 0.208811i
$666$	−19.0342	−0.737560
$667$	−0.951183	−0.0368300
$668$	42.1849i	1.63218i
$669$	1.46085i	0.0564797i
$670$	− 27.9509i	− 1.07984i
$671$	8.90541i	0.343790i
$672$	31.2189	1.20430
$673$	−39.6091	−1.52682	−0.763410	−	0.645915i	$-0.776476\pi$
$673$	−39.6091	−1.52682	−0.763410	+	0.645915i	$0.776476\pi$
$674$	− 80.8313i	− 3.11350i
$675$	−25.1320	−0.967330
$676$	0	0
$677$	17.0321	0.654596	0.327298	−	0.944921i	$-0.393862\pi$
$677$	17.0321	0.654596	0.327298	+	0.944921i	$0.393862\pi$
$678$	46.4621i	1.78437i
$679$	−9.53381	−0.365874
$680$	−29.6105	−1.13551
$681$	− 33.3922i	− 1.27959i
$682$	− 10.3720i	− 0.397163i
$683$	− 32.8912i	− 1.25854i	−0.777185	−	0.629272i	$-0.783353\pi$
$683$	− 32.8912i	− 1.25854i	0.777185	−	0.629272i	$-0.216647\pi$
$684$	45.5608i	1.74206i
$685$	−10.3569	−0.395718
$686$	−2.74108	−0.104655
$687$	− 6.45510i	− 0.246278i
$688$	26.7638	1.02036
$689$	0	0
$690$	6.46938	0.246285
$691$	− 23.7922i	− 0.905099i	−0.891739	−	0.452550i	$-0.850514\pi$
$691$	− 23.7922i	− 0.905099i	0.891739	−	0.452550i	$-0.149486\pi$
$692$	−0.906754	−0.0344696
$693$	1.55217	0.0589619
$694$	16.4105i	0.622933i
$695$	7.73013i	0.293221i
$696$	− 5.35804i	− 0.203096i
$697$	5.20502i	0.197154i
$698$	83.1539	3.14742
$699$	−28.0480	−1.06087
$700$	− 24.5396i	− 0.927510i
$701$	−29.7796	−1.12476	−0.562380	−	0.826879i	$-0.690114\pi$
$701$	−29.7796	−1.12476	−0.562380	+	0.826879i	$0.690114\pi$
$702$	0	0
$703$	−44.3658	−1.67329
$704$	− 43.6138i	− 1.64376i
$705$	−5.92547	−0.223166
$706$	−78.4122	−2.95108
$707$	7.49361i	0.281826i
$708$	− 82.6562i	− 3.10641i
$709$	− 11.9304i	− 0.448054i	−0.974583	−	0.224027i	$-0.928080\pi$
$709$	− 11.9304i	− 0.448054i	0.974583	−	0.224027i	$-0.0719204\pi$
$710$	− 9.78155i	− 0.367095i
$711$	10.3785	0.389224
$712$	−16.9600	−0.635604
$713$	− 6.46938i	− 0.242280i
$714$	15.5207	0.580846
$715$	0	0
$716$	4.23788	0.158377
$717$	8.53642i	0.318798i
$718$	−64.3106	−2.40005
$719$	−32.3638	−1.20697	−0.603484	−	0.797375i	$-0.706221\pi$
$719$	−32.3638	−1.20697	−0.603484	+	0.797375i	$0.706221\pi$
$720$	− 12.9556i	− 0.482827i
$721$	− 2.80848i	− 0.104593i
$722$	92.6364i	3.44757i
$723$	16.5749i	0.616428i
$724$	−54.7026	−2.03301
$725$	−1.81427	−0.0673805
$726$	− 34.1833i	− 1.26866i
$727$	31.4897	1.16789	0.583943	−	0.811794i	$-0.301509\pi$
$727$	31.4897	1.16789	0.583943	+	0.811794i	$0.301509\pi$
$728$	0	0
$729$	28.0042	1.03719
$730$	− 12.3301i	− 0.456359i
$731$	7.22325	0.267161
$732$	−49.1003	−1.81480
$733$	2.66224i	0.0983321i	0.998791	+	0.0491661i	$0.0156564\pi$
$733$	2.66224i	0.0983321i	−0.998791	+	0.0491661i	$0.984344\pi$
$734$	− 100.103i	− 3.69489i
$735$	− 1.01144i	− 0.0373076i
$736$	− 53.3755i	− 1.96745i
$737$	18.7795	0.691750
$738$	−3.91106	−0.143968
$739$	35.5828i	1.30893i	0.756091	+	0.654467i	$0.227107\pi$
$739$	35.5828i	1.30893i	−0.756091	+	0.654467i	$0.772893\pi$
$740$	24.9486	0.917128
$741$	0	0
$742$	12.5207	0.459648
$743$	24.2406i	0.889300i	0.895704	+	0.444650i	$0.146672\pi$
$743$	24.2406i	0.889300i	−0.895704	+	0.444650i	$0.853328\pi$
$744$	36.4422	1.33604
$745$	−6.05044	−0.221671
$746$	35.7706i	1.30966i
$747$	− 13.3479i	− 0.488373i
$748$	− 31.2189i	− 1.14148i
$749$	1.48647i	0.0543144i
$750$	26.2018	0.956756
$751$	29.1410	1.06337	0.531684	−	0.846943i	$-0.321559\pi$
$751$	29.1410	1.06337	0.531684	+	0.846943i	$0.321559\pi$
$752$	90.0555i	3.28399i
$753$	8.61799	0.314057
$754$	0	0
$755$	−1.82446	−0.0663988
$756$	31.1328i	1.13229i
$757$	−4.98990	−0.181361	−0.0906805	−	0.995880i	$-0.528904\pi$
$757$	−4.98990	−0.181361	−0.0906805	+	0.995880i	$0.528904\pi$
$758$	83.8872	3.04692
$759$	4.34660i	0.157772i
$760$	− 51.8598i	− 1.88115i
$761$	11.8372i	0.429097i	0.976713	+	0.214548i	$0.0688280\pi$
$761$	11.8372i	0.429097i	−0.976713	+	0.214548i	$0.931172\pi$
$762$	20.3160i	0.735971i
$763$	−2.87121	−0.103945
$764$	−54.5670	−1.97417
$765$	− 3.49657i	− 0.126419i
$766$	−13.3929	−0.483904
$767$	0	0
$768$	69.3186	2.50132
$769$	− 35.8183i	− 1.29164i	−0.763489	−	0.645821i	$-0.776515\pi$
$769$	− 35.8183i	− 1.29164i	0.763489	−	0.645821i	$-0.223485\pi$
$770$	−2.77245	−0.0999121
$771$	−33.2418	−1.19718
$772$	47.9718i	1.72654i
$773$	− 19.9534i	− 0.717673i	−0.933400	−	0.358837i	$-0.883174\pi$
$773$	− 19.9534i	− 0.717673i	0.933400	−	0.358837i	$-0.116826\pi$
$774$	5.42755i	0.195089i
$775$	− 12.3396i	− 0.443252i
$776$	−91.8190	−3.29611
$777$	−8.33345	−0.298961
$778$	− 5.08266i	− 0.182222i
$779$	−9.11608	−0.326618
$780$	0	0
$781$	6.57196	0.235163
$782$	− 26.5359i	− 0.948923i
$783$	2.30173	0.0822570
$784$	−15.3720	−0.548998
$785$	− 9.57464i	− 0.341734i
$786$	42.3566i	1.51081i
$787$	− 2.79619i	− 0.0996733i	−0.998757	−	0.0498367i	$-0.984130\pi$
$787$	− 2.79619i	− 0.0996733i	0.998757	−	0.0498367i	$-0.0158701\pi$
$788$	143.454i	5.11035i
$789$	−13.0737	−0.465437
$790$	−18.5379	−0.659549
$791$	− 12.4194i	− 0.441584i
$792$	14.9487	0.531179
$793$	0	0
$794$	−58.9700	−2.09277
$795$	4.62005i	0.163856i
$796$	55.8684	1.98020
$797$	−1.68562	−0.0597076	−0.0298538	−	0.999554i	$-0.509504\pi$
$797$	−1.68562	−0.0597076	−0.0298538	+	0.999554i	$0.509504\pi$
$798$	27.1829i	0.962265i
$799$	24.3049i	0.859846i
$800$	− 101.808i	− 3.59945i
$801$	− 2.00273i	− 0.0707632i
$802$	39.9247	1.40979
$803$	8.28428	0.292346
$804$	103.541i	3.65161i
$805$	−1.72928	−0.0609491
$806$	0	0
$807$	40.1244	1.41244
$808$	72.1700i	2.53893i
$809$	−43.4372	−1.52717	−0.763585	−	0.645708i	$-0.776562\pi$
$809$	−43.4372	−1.52717	−0.763585	+	0.645708i	$0.776562\pi$
$810$	−8.72435	−0.306542
$811$	5.60812i	0.196928i	0.995141	+	0.0984639i	$0.0313929\pi$
$811$	5.60812i	0.196928i	−0.995141	+	0.0984639i	$0.968607\pi$
$812$	2.24747i	0.0788709i
$813$	0.409971i	0.0143783i
$814$	22.8427i	0.800635i
$815$	−4.46681	−0.156466
$816$	87.0397	3.04700
$817$	12.6508i	0.442595i
$818$	−60.6574	−2.12084
$819$	0	0
$820$	5.12632	0.179019
$821$	− 23.9448i	− 0.835678i	−0.908521	−	0.417839i	$-0.862788\pi$
$821$	− 23.9448i	− 0.835678i	0.908521	−	0.417839i	$-0.137212\pi$
$822$	52.2832	1.82358
$823$	−35.4117	−1.23437	−0.617187	−	0.786817i	$-0.711728\pi$
$823$	−35.4117	−1.23437	−0.617187	+	0.786817i	$0.711728\pi$
$824$	− 27.0481i	− 0.942266i
$825$	8.29064i	0.288643i
$826$	30.1087i	1.04762i
$827$	16.1563i	0.561811i	0.959735	+	0.280905i	$0.0906347\pi$
$827$	16.1563i	0.561811i	−0.959735	+	0.280905i	$0.909365\pi$
$828$	14.6316	0.508483
$829$	52.7010	1.83038	0.915190	−	0.403022i	$-0.132040\pi$
$829$	52.7010	1.83038	0.915190	+	0.403022i	$0.132040\pi$
$830$	23.8417i	0.827557i
$831$	44.7265	1.55154
$832$	0	0
$833$	−4.14871	−0.143744
$834$	− 39.0228i	− 1.35125i
$835$	5.67013	0.196223
$836$	54.6769	1.89104
$837$	15.6550i	0.541115i
$838$	− 9.25363i	− 0.319661i
$839$	22.4338i	0.774502i	0.921974	+	0.387251i	$0.126575\pi$
$839$	22.4338i	0.774502i	−0.921974	+	0.387251i	$0.873425\pi$
$840$	− 9.74108i	− 0.336099i
$841$	−28.8338	−0.994270
$842$	−68.8288	−2.37200
$843$	− 5.86165i	− 0.201886i
$844$	−91.9559	−3.16525
$845$	0	0
$846$	−18.2627	−0.627886
$847$	9.13727i	0.313960i
$848$	70.2158	2.41122
$849$	28.7980	0.988346
$850$	− 50.6143i	− 1.73606i
$851$	14.2478i	0.488409i
$852$	36.2347i	1.24138i
$853$	− 30.8521i	− 1.05635i	−0.849134	−	0.528177i	$-0.822876\pi$
$853$	− 30.8521i	− 1.05635i	0.849134	−	0.528177i	$-0.177124\pi$
$854$	17.8855	0.612029
$855$	6.12390	0.209433
$856$	14.3160i	0.489311i
$857$	−26.7400	−0.913420	−0.456710	−	0.889616i	$-0.650972\pi$
$857$	−26.7400	−0.913420	−0.456710	+	0.889616i	$0.650972\pi$
$858$	0	0
$859$	−5.15804	−0.175990	−0.0879950	−	0.996121i	$-0.528046\pi$
$859$	−5.15804	−0.175990	−0.0879950	+	0.996121i	$0.528046\pi$
$860$	− 7.11402i	− 0.242586i
$861$	−1.71232	−0.0583557
$862$	29.5896	1.00782
$863$	8.16814i	0.278047i	0.990289	+	0.139023i	$0.0443963\pi$
$863$	8.16814i	0.278047i	−0.990289	+	0.139023i	$0.955604\pi$
$864$	129.161i	4.39415i
$865$	0.121878i	0.00414398i
$866$	− 39.7956i	− 1.35231i
$867$	0.289073	0.00981742
$868$	−15.2860	−0.518840
$869$	− 12.4551i	− 0.422510i
$870$	−1.13013	−0.0383150
$871$	0	0
$872$	−27.6523	−0.936425
$873$	− 10.8425i	− 0.366963i
$874$	46.4750	1.57204
$875$	−7.00382	−0.236772
$876$	45.6756i	1.54324i
$877$	15.6184i	0.527398i	0.964605	+	0.263699i	$0.0849425\pi$
$877$	15.6184i	0.527398i	−0.964605	+	0.263699i	$0.915058\pi$
$878$	− 39.5562i	− 1.33496i
$879$	− 24.2444i	− 0.817744i
$880$	−15.5479	−0.524118
$881$	46.4375	1.56452	0.782260	−	0.622952i	$-0.214067\pi$
$881$	46.4375	1.56452	0.782260	+	0.622952i	$0.214067\pi$
$882$	− 3.11734i	− 0.104966i
$883$	−15.6588	−0.526960	−0.263480	−	0.964665i	$-0.584870\pi$
$883$	−15.6588	−0.526960	−0.263480	+	0.964665i	$0.584870\pi$
$884$	0	0
$885$	−11.1099	−0.373457
$886$	82.8986i	2.78503i
$887$	31.5107	1.05803	0.529013	−	0.848614i	$-0.322562\pi$
$887$	31.5107	1.05803	0.529013	+	0.848614i	$0.322562\pi$
$888$	−80.2584	−2.69330
$889$	− 5.43052i	− 0.182134i
$890$	3.57725i	0.119910i
$891$	− 5.86165i	− 0.196373i
$892$	− 5.90146i	− 0.197596i
$893$	−42.5677	−1.42447
$894$	30.5434	1.02152
$895$	− 0.569620i	− 0.0190403i
$896$	−41.8452	−1.39795
$897$	0	0
$898$	−85.7301	−2.86085
$899$	1.13013i	0.0376920i
$900$	27.9081	0.930270
$901$	18.9504	0.631330
$902$	4.69361i	0.156280i
$903$	2.37626i	0.0790771i
$904$	− 119.610i	− 3.97817i
$905$	7.35266i	0.244411i
$906$	9.21010	0.305985
$907$	0.747991	0.0248366	0.0124183	−	0.999923i	$-0.496047\pi$
$907$	0.747991	0.0248366	0.0124183	+	0.999923i	$0.496047\pi$
$908$	134.896i	4.47669i
$909$	−8.52224	−0.282665
$910$	0	0
$911$	24.9000	0.824973	0.412486	−	0.910964i	$-0.364660\pi$
$911$	24.9000	0.824973	0.412486	+	0.910964i	$0.364660\pi$
$912$	152.441i	5.04784i
$913$	−16.0186	−0.530138
$914$	56.5941	1.87197
$915$	6.59964i	0.218177i
$916$	26.0770i	0.861609i
$917$	− 11.3220i	− 0.373886i
$918$	64.2132i	2.11935i
$919$	0.586495	0.0193467	0.00967334	−	0.999953i	$-0.496921\pi$
$919$	0.586495	0.0193467	0.00967334	+	0.999953i	$0.496921\pi$
$920$	−16.6545	−0.549082
$921$	− 24.5881i	− 0.810204i
$922$	74.8208	2.46409
$923$	0	0
$924$	10.2702	0.337866
$925$	27.1761i	0.893546i
$926$	−15.5139	−0.509818
$927$	3.19399	0.104905
$928$	9.32412i	0.306079i
$929$	− 50.1949i	− 1.64684i	−0.567431	−	0.823421i	$-0.692062\pi$
$929$	− 50.1949i	− 1.64684i	0.567431	−	0.823421i	$-0.307938\pi$
$930$	− 7.68647i	− 0.252049i
$931$	− 7.26606i	− 0.238135i
$932$	113.307	3.71149
$933$	−23.5493	−0.770968
$934$	115.713i	3.78626i
$935$	−4.19619	−0.137230
$936$	0	0
$937$	22.7130	0.742003	0.371001	−	0.928632i	$-0.379015\pi$
$937$	22.7130	0.742003	0.371001	+	0.928632i	$0.379015\pi$
$938$	− 37.7164i	− 1.23148i
$939$	9.30160	0.303546
$940$	23.9374	0.780752
$941$	− 49.8734i	− 1.62583i	−0.582384	−	0.812914i	$-0.697880\pi$
$941$	− 49.8734i	− 1.62583i	0.582384	−	0.812914i	$-0.302120\pi$
$942$	48.3341i	1.57481i
$943$	2.92758i	0.0953351i
$944$	168.849i	5.49558i
$945$	4.18461	0.136125
$946$	6.51353	0.211773
$947$	− 0.266414i	− 0.00865731i	−0.999991	−	0.00432865i	$-0.998622\pi$
$947$	− 0.266414i	− 0.00865731i	0.999991	−	0.00432865i	$-0.00137786\pi$
$948$	68.6716	2.23035
$949$	0	0
$950$	88.6459	2.87605
$951$	− 34.2256i	− 1.10984i
$952$	−39.9557	−1.29497
$953$	−7.82029	−0.253324	−0.126662	−	0.991946i	$-0.540426\pi$
$953$	−7.82029	−0.253324	−0.126662	+	0.991946i	$0.540426\pi$
$954$	14.2394i	0.461016i
$955$	7.33444i	0.237337i
$956$	− 34.4850i	− 1.11532i
$957$	− 0.759304i	− 0.0245448i
$958$	−89.1718	−2.88101
$959$	−13.9754	−0.451290
$960$	− 32.3214i	− 1.04317i
$961$	23.3135	0.752049
$962$	0	0
$963$	−1.69051	−0.0544761
$964$	− 66.9585i	− 2.15659i
$965$	6.44797	0.207567
$966$	8.72964	0.280872
$967$	39.8224i	1.28060i	0.768124	+	0.640301i	$0.221190\pi$
$967$	39.8224i	1.28060i	−0.768124	+	0.640301i	$0.778810\pi$
$968$	87.9999i	2.82842i
$969$	41.1422i	1.32168i
$970$	19.3667i	0.621826i
$971$	−45.9295	−1.47395	−0.736974	−	0.675921i	$-0.763746\pi$
$971$	−45.9295	−1.47395	−0.736974	+	0.675921i	$0.763746\pi$
$972$	−61.0801	−1.95915
$973$	10.4309i	0.334398i
$974$	73.6208	2.35896
$975$	0	0
$976$	100.302	3.21058
$977$	− 28.6627i	− 0.917002i	−0.888694	−	0.458501i	$-0.848387\pi$
$977$	− 28.6627i	− 0.917002i	0.888694	−	0.458501i	$-0.151613\pi$
$978$	22.5491	0.721040
$979$	−2.40345	−0.0768147
$980$	4.08598i	0.130522i
$981$	− 3.26534i	− 0.104254i
$982$	119.752i	3.82144i
$983$	46.1200i	1.47100i	0.677524	+	0.735500i	$0.263053\pi$
$983$	46.1200i	1.47100i	−0.677524	+	0.735500i	$0.736947\pi$
$984$	−16.4911	−0.525718
$985$	19.2819	0.614372
$986$	4.63554i	0.147626i
$987$	−7.99569	−0.254506
$988$	0	0
$989$	4.06273	0.129187
$990$	− 3.15302i	− 0.100209i
$991$	37.8249	1.20155	0.600773	−	0.799419i	$-0.294859\pi$
$991$	37.8249	1.20155	0.600773	+	0.799419i	$0.294859\pi$
$992$	−63.4171	−2.01350
$993$	− 4.08809i	− 0.129732i
$994$	− 13.1990i	− 0.418647i
$995$	− 7.50936i	− 0.238063i
$996$	− 88.3189i	− 2.79849i
$997$	38.3748	1.21534	0.607671	−	0.794189i	$-0.292104\pi$
$997$	38.3748	1.21534	0.607671	+	0.794189i	$0.292104\pi$
$998$	−49.6189	−1.57066
$999$	− 34.4777i	− 1.09083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.g.337.1		8
13.2	odd	12		91.2.f.c.22.4	✓	8
13.5	odd	4		1183.2.a.k.1.1		4
13.6	odd	12		91.2.f.c.29.4	yes	8
13.8	odd	4		1183.2.a.l.1.4		4
13.12	even	2	inner	1183.2.c.g.337.8		8
39.2	even	12		819.2.o.h.568.1		8
39.32	even	12		819.2.o.h.757.1		8
52.15	even	12		1456.2.s.q.113.3		8
52.19	even	12		1456.2.s.q.1121.3		8
91.2	odd	12		637.2.h.h.165.1		8
91.6	even	12		637.2.f.i.393.4		8
91.19	even	12		637.2.g.j.263.4		8
91.32	odd	12		637.2.h.h.471.1		8
91.34	even	4		8281.2.a.bt.1.4		4
91.41	even	12		637.2.f.i.295.4		8
91.45	even	12		637.2.h.i.471.1		8
91.54	even	12		637.2.h.i.165.1		8
91.58	odd	12		637.2.g.k.263.4		8
91.67	odd	12		637.2.g.k.373.4		8
91.80	even	12		637.2.g.j.373.4		8
91.83	even	4		8281.2.a.bp.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.4	✓	8	13.2	odd	12
91.2.f.c.29.4	yes	8	13.6	odd	12
637.2.f.i.295.4		8	91.41	even	12
637.2.f.i.393.4		8	91.6	even	12
637.2.g.j.263.4		8	91.19	even	12
637.2.g.j.373.4		8	91.80	even	12
637.2.g.k.263.4		8	91.58	odd	12
637.2.g.k.373.4		8	91.67	odd	12
637.2.h.h.165.1		8	91.2	odd	12
637.2.h.h.471.1		8	91.32	odd	12
637.2.h.i.165.1		8	91.54	even	12
637.2.h.i.471.1		8	91.45	even	12
819.2.o.h.568.1		8	39.2	even	12
819.2.o.h.757.1		8	39.32	even	12
1183.2.a.k.1.1		4	13.5	odd	4
1183.2.a.l.1.4		4	13.8	odd	4
1183.2.c.g.337.1		8	1.1	even	1	trivial
1183.2.c.g.337.8		8	13.12	even	2	inner
1456.2.s.q.113.3		8	52.15	even	12
1456.2.s.q.1121.3		8	52.19	even	12
8281.2.a.bp.1.1		4	91.83	even	4
8281.2.a.bt.1.4		4	91.34	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.74108i q^{2} +1.36482 q^{3} -5.51353 q^{4} +0.741082i q^{5} -3.74108i q^{6} +1.00000i q^{7} +9.63087i q^{8} -1.13727 q^{9} +2.03137 q^{10} +1.36482i q^{11} -7.52497 q^{12} +2.74108 q^{14} +1.01144i q^{15} +15.3720 q^{16} +4.14871 q^{17} +3.11734i q^{18} +7.26606i q^{19} -4.08598i q^{20} +1.36482i q^{21} +3.74108 q^{22} +2.33345 q^{23} +13.1444i q^{24} +4.45080 q^{25} -5.64662 q^{27} -5.51353i q^{28} -0.407629 q^{29} +2.77245 q^{30} -2.77245i q^{31} -22.8740i q^{32} +1.86273i q^{33} -11.3720i q^{34} -0.741082 q^{35} +6.27036 q^{36} +6.10590i q^{37} +19.9169 q^{38} -7.13727 q^{40} +1.25461i q^{41} +3.74108 q^{42} +1.74108 q^{43} -7.52497i q^{44} -0.842809i q^{45} -6.39619i q^{46} +5.85843i q^{47} +20.9799 q^{48} -1.00000 q^{49} -12.2000i q^{50} +5.66224 q^{51} +4.56778 q^{53} +15.4779i q^{54} -1.01144 q^{55} -9.63087 q^{56} +9.91685i q^{57} +1.11734i q^{58} +10.9843i q^{59} -5.57662i q^{60} +6.52497 q^{61} -7.59951 q^{62} -1.13727i q^{63} -31.9557 q^{64} +5.10590 q^{66} -13.7597i q^{67} -22.8740 q^{68} +3.18474 q^{69} +2.03137i q^{70} -4.81526i q^{71} -10.9529i q^{72} -6.06987i q^{73} +16.7368 q^{74} +6.07453 q^{75} -40.0616i q^{76} -1.36482 q^{77} -9.12582 q^{79} +11.3919i q^{80} -4.29482 q^{81} +3.43900 q^{82} +11.7368i q^{83} -7.52497i q^{84} +3.07453i q^{85} -4.77245i q^{86} -0.556340 q^{87} -13.1444 q^{88} +1.76101i q^{89} -2.31021 q^{90} -12.8656 q^{92} -3.78389i q^{93} +16.0584 q^{94} -5.38474 q^{95} -31.2189i q^{96} +9.53381i q^{97} +2.74108i q^{98} -1.55217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 10 q^{4} + 14 q^{9} + 22 q^{10} - 24 q^{12} + 2 q^{14} + 38 q^{16} + 8 q^{17} + 10 q^{22} + 4 q^{23} - 10 q^{25} - 52 q^{27} + 2 q^{29} + 8 q^{30} + 14 q^{35} + 68 q^{36} + 46 q^{38} - 34 q^{40}+ \cdots - 42 q^{95}+O(q^{100}) \) 8 * q + 2 * q^3 - 10 * q^4 + 14 * q^9 + 22 * q^10 - 24 * q^12 + 2 * q^14 + 38 * q^16 + 8 * q^17 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 52 * q^27 + 2 * q^29 + 8 * q^30 + 14 * q^35 + 68 * q^36 + 46 * q^38 - 34 * q^40 + 10 * q^42 - 6 * q^43 + 22 * q^48 - 8 * q^49 - 14 * q^51 + 4 * q^53 - 6 * q^55 - 12 * q^56 + 16 * q^61 + 10 * q^62 - 28 * q^64 + 12 * q^66 - 66 * q^68 + 36 * q^69 + 40 * q^74 + 14 * q^75 - 2 * q^77 - 52 * q^79 + 48 * q^81 + 28 * q^82 + 26 * q^87 - 6 * q^88 - 52 * q^90 + 24 * q^92 + 66 * q^94 - 42 * q^95

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