LMFDB - Embedded newform 9409.2.a.q.1.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9409,2,Mod(1,9409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9409, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9409.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 9409 = 97^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9409.a (trivial)

Newform invariants

comment:select newform

sage:traces = [168,0,0,168,42] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$75.1312432618$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
Character	$\chi$	$=$	9409.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.73548 q^{2} -3.39646 q^{3} +1.01188 q^{4} -2.86049 q^{5} +5.89447 q^{6} -0.942308 q^{7} +1.71486 q^{8} +8.53591 q^{9} +4.96432 q^{10} -3.33425 q^{11} -3.43680 q^{12} -1.74775 q^{13} +1.63535 q^{14} +9.71553 q^{15} -4.99986 q^{16} +3.59451 q^{17} -14.8139 q^{18} +1.93989 q^{19} -2.89447 q^{20} +3.20051 q^{21} +5.78651 q^{22} -2.66109 q^{23} -5.82445 q^{24} +3.18242 q^{25} +3.03318 q^{26} -18.8025 q^{27} -0.953502 q^{28} -7.36263 q^{29} -16.8611 q^{30} +3.74428 q^{31} +5.24742 q^{32} +11.3246 q^{33} -6.23819 q^{34} +2.69546 q^{35} +8.63731 q^{36} +0.721516 q^{37} -3.36664 q^{38} +5.93616 q^{39} -4.90534 q^{40} +5.04402 q^{41} -5.55440 q^{42} +6.72602 q^{43} -3.37386 q^{44} -24.4169 q^{45} +4.61826 q^{46} +7.87110 q^{47} +16.9818 q^{48} -6.11206 q^{49} -5.52301 q^{50} -12.2086 q^{51} -1.76851 q^{52} +2.72580 q^{53} +32.6312 q^{54} +9.53759 q^{55} -1.61593 q^{56} -6.58876 q^{57} +12.7777 q^{58} +7.83008 q^{59} +9.83095 q^{60} +5.40424 q^{61} -6.49812 q^{62} -8.04345 q^{63} +0.892947 q^{64} +4.99943 q^{65} -19.6536 q^{66} +8.28669 q^{67} +3.63721 q^{68} +9.03827 q^{69} -4.67792 q^{70} +12.6912 q^{71} +14.6379 q^{72} -3.27219 q^{73} -1.25217 q^{74} -10.8089 q^{75} +1.96294 q^{76} +3.14189 q^{77} -10.3021 q^{78} +0.714972 q^{79} +14.3021 q^{80} +38.2540 q^{81} -8.75378 q^{82} +4.45725 q^{83} +3.23853 q^{84} -10.2821 q^{85} -11.6729 q^{86} +25.0069 q^{87} -5.71777 q^{88} +15.6316 q^{89} +42.3750 q^{90} +1.64692 q^{91} -2.69270 q^{92} -12.7173 q^{93} -13.6601 q^{94} -5.54905 q^{95} -17.8226 q^{96} +10.6073 q^{98} -28.4608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 168 q^{4} + 42 q^{5} + 42 q^{7} + 168 q^{9} + 42 q^{10} + 42 q^{13} + 70 q^{14} + 84 q^{15} + 140 q^{16} + 49 q^{17} - 49 q^{18} + 84 q^{19} + 98 q^{20} + 84 q^{21} - 35 q^{22} + 126 q^{23} + 168 q^{25}+ \cdots - 84 q^{99}+O(q^{100}) $ 168 * q + 168 * q^4 + 42 * q^5 + 42 * q^7 + 168 * q^9 + 42 * q^10 + 42 * q^13 + 70 * q^14 + 84 * q^15 + 140 * q^16 + 49 * q^17 - 49 * q^18 + 84 * q^19 + 98 * q^20 + 84 * q^21 - 35 * q^22 + 126 * q^23 + 168 * q^25 + 105 * q^26 + 84 * q^28 + 126 * q^29 + 84 * q^30 + 84 * q^34 + 168 * q^36 + 42 * q^37 + 112 * q^38 + 168 * q^39 + 126 * q^40 + 154 * q^41 + 28 * q^42 - 63 * q^44 + 91 * q^45 - 21 * q^46 - 42 * q^47 - 56 * q^48 + 126 * q^49 - 28 * q^50 + 168 * q^51 + 63 * q^52 - 28 * q^53 - 42 * q^54 + 168 * q^55 + 140 * q^56 + 56 * q^57 - 77 * q^58 + 238 * q^59 + 168 * q^60 - 56 * q^61 - 91 * q^62 + 210 * q^63 + 112 * q^64 - 49 * q^65 - 133 * q^66 + 28 * q^67 + 126 * q^68 + 105 * q^69 - 147 * q^70 + 252 * q^71 - 98 * q^72 + 77 * q^73 + 147 * q^74 + 14 * q^75 + 196 * q^76 + 77 * q^77 - 63 * q^78 + 56 * q^79 + 133 * q^80 + 168 * q^81 + 56 * q^82 + 203 * q^83 + 252 * q^84 - 56 * q^85 - 56 * q^86 + 182 * q^87 - 182 * q^88 + 84 * q^90 - 42 * q^91 + 189 * q^92 + 84 * q^93 - 154 * q^94 - 28 * q^95 - 21 * q^96 + 84 * q^98 - 84 * q^99

Coefficient data

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

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

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

$2$	−1.73548	−1.22717	−0.613584	−	0.789630i	$-0.710273\pi$
$2$	−1.73548	−1.22717	−0.613584	+	0.789630i	$0.710273\pi$
$3$	−3.39646	−1.96094	−0.980472	−	0.196658i	$-0.936991\pi$
$3$	−3.39646	−1.96094	−0.980472	+	0.196658i	$0.936991\pi$
$4$	1.01188	0.505940
$5$	−2.86049	−1.27925	−0.639626	−	0.768687i	$-0.720911\pi$
$5$	−2.86049	−1.27925	−0.639626	+	0.768687i	$0.720911\pi$
$6$	5.89447	2.40641
$7$	−0.942308	−0.356159	−0.178079	−	0.984016i	$-0.556988\pi$
$7$	−0.942308	−0.356159	−0.178079	+	0.984016i	$0.556988\pi$
$8$	1.71486	0.606295
$9$	8.53591	2.84530
$10$	4.96432	1.56986
$11$	−3.33425	−1.00531	−0.502657	−	0.864486i	$-0.667644\pi$
$11$	−3.33425	−1.00531	−0.502657	+	0.864486i	$0.667644\pi$
$12$	−3.43680	−0.992120
$13$	−1.74775	−0.484739	−0.242369	−	0.970184i	$-0.577925\pi$
$13$	−1.74775	−0.484739	−0.242369	+	0.970184i	$0.577925\pi$
$14$	1.63535	0.437067
$15$	9.71553	2.50854
$16$	−4.99986	−1.24996
$17$	3.59451	0.871798	0.435899	−	0.899996i	$-0.356431\pi$
$17$	3.59451	0.871798	0.435899	+	0.899996i	$0.356431\pi$
$18$	−14.8139	−3.49166
$19$	1.93989	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$19$	1.93989	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$20$	−2.89447	−0.647224
$21$	3.20051	0.698408
$22$	5.78651	1.23369
$23$	−2.66109	−0.554875	−0.277438	−	0.960744i	$-0.589485\pi$
$23$	−2.66109	−0.554875	−0.277438	+	0.960744i	$0.589485\pi$
$24$	−5.82445	−1.18891
$25$	3.18242	0.636483
$26$	3.03318	0.594856
$27$	−18.8025	−3.61854
$28$	−0.953502	−0.180195
$29$	−7.36263	−1.36721	−0.683603	−	0.729854i	$-0.739588\pi$
$29$	−7.36263	−1.36721	−0.683603	+	0.729854i	$0.739588\pi$
$30$	−16.8611	−3.07840
$31$	3.74428	0.672493	0.336246	−	0.941774i	$-0.390842\pi$
$31$	3.74428	0.672493	0.336246	+	0.941774i	$0.390842\pi$
$32$	5.24742	0.927621
$33$	11.3246	1.97136
$34$	−6.23819	−1.06984
$35$	2.69546	0.455617
$36$	8.63731	1.43955
$37$	0.721516	0.118616	0.0593082	−	0.998240i	$-0.481111\pi$
$37$	0.721516	0.118616	0.0593082	+	0.998240i	$0.481111\pi$
$38$	−3.36664	−0.546141
$39$	5.93616	0.950546
$40$	−4.90534	−0.775603
$41$	5.04402	0.787744	0.393872	−	0.919165i	$-0.371135\pi$
$41$	5.04402	0.787744	0.393872	+	0.919165i	$0.371135\pi$
$42$	−5.55440	−0.857063
$43$	6.72602	1.02571	0.512855	−	0.858476i	$-0.328588\pi$
$43$	6.72602	1.02571	0.512855	+	0.858476i	$0.328588\pi$
$44$	−3.37386	−0.508628
$45$	−24.4169	−3.63986
$46$	4.61826	0.680925
$47$	7.87110	1.14812	0.574059	−	0.818814i	$-0.305368\pi$
$47$	7.87110	1.14812	0.574059	+	0.818814i	$0.305368\pi$
$48$	16.9818	2.45111
$49$	−6.11206	−0.873151
$50$	−5.52301	−0.781071
$51$	−12.2086	−1.70955
$52$	−1.76851	−0.245249
$53$	2.72580	0.374417	0.187208	−	0.982320i	$-0.440056\pi$
$53$	2.72580	0.374417	0.187208	+	0.982320i	$0.440056\pi$
$54$	32.6312	4.44055
$55$	9.53759	1.28605
$56$	−1.61593	−0.215937
$57$	−6.58876	−0.872703
$58$	12.7777	1.67779
$59$	7.83008	1.01939	0.509695	−	0.860355i	$-0.329758\pi$
$59$	7.83008	1.01939	0.509695	+	0.860355i	$0.329758\pi$
$60$	9.83095	1.26917
$61$	5.40424	0.691943	0.345971	−	0.938245i	$-0.387549\pi$
$61$	5.40424	0.691943	0.345971	+	0.938245i	$0.387549\pi$
$62$	−6.49812	−0.825261
$63$	−8.04345	−1.01338
$64$	0.892947	0.111618
$65$	4.99943	0.620103
$66$	−19.6536	−2.41919
$67$	8.28669	1.01238	0.506190	−	0.862422i	$-0.331053\pi$
$67$	8.28669	1.01238	0.506190	+	0.862422i	$0.331053\pi$
$68$	3.63721	0.441077
$69$	9.03827	1.08808
$70$	−4.67792	−0.559118
$71$	12.6912	1.50616	0.753082	−	0.657927i	$-0.228566\pi$
$71$	12.6912	1.50616	0.753082	+	0.657927i	$0.228566\pi$
$72$	14.6379	1.72509
$73$	−3.27219	−0.382981	−0.191491	−	0.981494i	$-0.561332\pi$
$73$	−3.27219	−0.382981	−0.191491	+	0.981494i	$0.561332\pi$
$74$	−1.25217	−0.145562
$75$	−10.8089	−1.24811
$76$	1.96294	0.225164
$77$	3.14189	0.358052
$78$	−10.3021	−1.16648
$79$	0.714972	0.0804406	0.0402203	−	0.999191i	$-0.487194\pi$
$79$	0.714972	0.0804406	0.0402203	+	0.999191i	$0.487194\pi$
$80$	14.3021	1.59902
$81$	38.2540	4.25045
$82$	−8.75378	−0.966693
$83$	4.45725	0.489247	0.244623	−	0.969618i	$-0.421336\pi$
$83$	4.45725	0.489247	0.244623	+	0.969618i	$0.421336\pi$
$84$	3.23853	0.353352
$85$	−10.2821	−1.11525
$86$	−11.6729	−1.25872
$87$	25.0069	2.68102
$88$	−5.71777	−0.609517
$89$	15.6316	1.65694	0.828471	−	0.560032i	$-0.189211\pi$
$89$	15.6316	1.65694	0.828471	+	0.560032i	$0.189211\pi$
$90$	42.3750	4.46671
$91$	1.64692	0.172644
$92$	−2.69270	−0.280733
$93$	−12.7173	−1.31872
$94$	−13.6601	−1.40893
$95$	−5.54905	−0.569320
$96$	−17.8226	−1.81901
$97$	0	0
$97$	0	0
$98$	10.6073	1.07150
$99$	−28.4608	−2.86042
$100$	3.22022	0.322022
$101$	−2.01374	−0.200374	−0.100187	−	0.994969i	$-0.531944\pi$
$101$	−2.01374	−0.200374	−0.100187	+	0.994969i	$0.531944\pi$
$102$	21.1878	2.09790
$103$	−15.9245	−1.56909	−0.784546	−	0.620071i	$-0.787104\pi$
$103$	−15.9245	−1.56909	−0.784546	+	0.620071i	$0.787104\pi$
$104$	−2.99715	−0.293895
$105$	−9.15502	−0.893439
$106$	−4.73055	−0.459472
$107$	7.74763	0.748992	0.374496	−	0.927229i	$-0.377816\pi$
$107$	7.74763	0.748992	0.374496	+	0.927229i	$0.377816\pi$
$108$	−19.0258	−1.83076
$109$	−0.292450	−0.0280116	−0.0140058	−	0.999902i	$-0.504458\pi$
$109$	−0.292450	−0.0280116	−0.0140058	+	0.999902i	$0.504458\pi$
$110$	−16.5523	−1.57820
$111$	−2.45060	−0.232600
$112$	4.71141	0.445186
$113$	−6.81974	−0.641547	−0.320773	−	0.947156i	$-0.603943\pi$
$113$	−6.81974	−0.641547	−0.320773	+	0.947156i	$0.603943\pi$
$114$	11.4346	1.07095
$115$	7.61202	0.709825
$116$	−7.45010	−0.691724
$117$	−14.9186	−1.37923
$118$	−13.5889	−1.25096
$119$	−3.38714	−0.310498
$120$	16.6608	1.52091
$121$	0.117218	0.0106562
$122$	−9.37894	−0.849129
$123$	−17.1318	−1.54472
$124$	3.78876	0.340241
$125$	5.19919	0.465029
$126$	13.9592	1.24359
$127$	−2.03854	−0.180891	−0.0904454	−	0.995901i	$-0.528829\pi$
$127$	−2.03854	−0.180891	−0.0904454	+	0.995901i	$0.528829\pi$
$128$	−12.0445	−1.06460
$129$	−22.8446	−2.01136
$130$	−8.67639	−0.760970
$131$	−15.7227	−1.37370	−0.686848	−	0.726801i	$-0.741006\pi$
$131$	−15.7227	−1.37370	−0.686848	+	0.726801i	$0.741006\pi$
$132$	11.4592	0.997392
$133$	−1.82798	−0.158506
$134$	−14.3814	−1.24236
$135$	53.7843	4.62902
$136$	6.16409	0.528566
$137$	17.1501	1.46523	0.732614	−	0.680644i	$-0.238300\pi$
$137$	17.1501	1.46523	0.732614	+	0.680644i	$0.238300\pi$
$138$	−15.6857	−1.33526
$139$	−8.30958	−0.704809	−0.352405	−	0.935848i	$-0.614636\pi$
$139$	−8.30958	−0.704809	−0.352405	+	0.935848i	$0.614636\pi$
$140$	2.72748	0.230515
$141$	−26.7338	−2.25139
$142$	−22.0252	−1.84832
$143$	5.82744	0.487315
$144$	−42.6783	−3.55653
$145$	21.0608	1.74900
$146$	5.67881	0.469982
$147$	20.7593	1.71220
$148$	0.730087	0.0600128
$149$	5.76701	0.472451	0.236226	−	0.971698i	$-0.424090\pi$
$149$	5.76701	0.472451	0.236226	+	0.971698i	$0.424090\pi$
$150$	18.7587	1.53164
$151$	−2.77811	−0.226079	−0.113040	−	0.993590i	$-0.536059\pi$
$151$	−2.77811	−0.226079	−0.113040	+	0.993590i	$0.536059\pi$
$152$	3.32665	0.269827
$153$	30.6824	2.48053
$154$	−5.45268	−0.439389
$155$	−10.7105	−0.860287
$156$	6.00668	0.480919
$157$	−15.4848	−1.23582	−0.617911	−	0.786248i	$-0.712021\pi$
$157$	−15.4848	−1.23582	−0.617911	+	0.786248i	$0.712021\pi$
$158$	−1.24082	−0.0987141
$159$	−9.25804	−0.734211
$160$	−15.0102	−1.18666
$161$	2.50756	0.197624
$162$	−66.3889	−5.21601
$163$	3.65715	0.286450	0.143225	−	0.989690i	$-0.454253\pi$
$163$	3.65715	0.286450	0.143225	+	0.989690i	$0.454253\pi$
$164$	5.10394	0.398551
$165$	−32.3940	−2.52187
$166$	−7.73545	−0.600388
$167$	−6.74844	−0.522210	−0.261105	−	0.965310i	$-0.584087\pi$
$167$	−6.74844	−0.522210	−0.261105	+	0.965310i	$0.584087\pi$
$168$	5.48842	0.423441
$169$	−9.94537	−0.765028
$170$	17.8443	1.36860
$171$	16.5588	1.26628
$172$	6.80592	0.518947
$173$	−2.01940	−0.153532	−0.0767659	−	0.997049i	$-0.524459\pi$
$173$	−2.01940	−0.153532	−0.0767659	+	0.997049i	$0.524459\pi$
$174$	−43.3988	−3.29006
$175$	−2.99882	−0.226689
$176$	16.6708	1.25661
$177$	−26.5945	−1.99897
$178$	−27.1282	−2.03334
$179$	9.53477	0.712662	0.356331	−	0.934360i	$-0.384027\pi$
$179$	9.53477	0.712662	0.356331	+	0.934360i	$0.384027\pi$
$180$	−24.7070	−1.84155
$181$	5.34716	0.397451	0.198726	−	0.980055i	$-0.436320\pi$
$181$	5.34716	0.397451	0.198726	+	0.980055i	$0.436320\pi$
$182$	−2.85819	−0.211863
$183$	−18.3553	−1.35686
$184$	−4.56339	−0.336418
$185$	−2.06389	−0.151740
$186$	22.0706	1.61829
$187$	−11.9850	−0.876430
$188$	7.96460	0.580878
$189$	17.7177	1.28877
$190$	9.63025	0.698652
$191$	23.3916	1.69256	0.846279	−	0.532739i	$-0.178837\pi$
$191$	23.3916	1.69256	0.846279	+	0.532739i	$0.178837\pi$
$192$	−3.03285	−0.218877
$193$	3.96645	0.285512	0.142756	−	0.989758i	$-0.454404\pi$
$193$	3.96645	0.285512	0.142756	+	0.989758i	$0.454404\pi$
$194$	0	0
$195$	−16.9803	−1.21599
$196$	−6.18466	−0.441762
$197$	12.5988	0.897630	0.448815	−	0.893625i	$-0.351846\pi$
$197$	12.5988	0.897630	0.448815	+	0.893625i	$0.351846\pi$
$198$	49.3931	3.51022
$199$	4.91759	0.348599	0.174299	−	0.984693i	$-0.444234\pi$
$199$	4.91759	0.348599	0.174299	+	0.984693i	$0.444234\pi$
$200$	5.45740	0.385896
$201$	−28.1454	−1.98522
$202$	3.49480	0.245893
$203$	6.93787	0.486943
$204$	−12.3536	−0.864927
$205$	−14.4284	−1.00772
$206$	27.6367	1.92554
$207$	−22.7148	−1.57879
$208$	8.73851	0.605907
$209$	−6.46809	−0.447407
$210$	15.8883	1.09640
$211$	23.0844	1.58920	0.794598	−	0.607136i	$-0.207682\pi$
$211$	23.0844	1.58920	0.794598	+	0.607136i	$0.207682\pi$
$212$	2.75818	0.189432
$213$	−43.1050	−2.95350
$214$	−13.4458	−0.919138
$215$	−19.2397	−1.31214
$216$	−32.2436	−2.19390
$217$	−3.52827	−0.239514
$218$	0.507540	0.0343749
$219$	11.1139	0.751005
$220$	9.65089	0.650663
$221$	−6.28232	−0.422594
$222$	4.25295	0.285439
$223$	0.545584	0.0365350	0.0182675	−	0.999833i	$-0.494185\pi$
$223$	0.545584	0.0365350	0.0182675	+	0.999833i	$0.494185\pi$
$224$	−4.94468	−0.330381
$225$	27.1648	1.81099
$226$	11.8355	0.787285
$227$	−27.2803	−1.81066	−0.905328	−	0.424712i	$-0.860375\pi$
$227$	−27.2803	−1.81066	−0.905328	+	0.424712i	$0.860375\pi$
$228$	−6.66703	−0.441535
$229$	−18.4163	−1.21698	−0.608492	−	0.793560i	$-0.708225\pi$
$229$	−18.4163	−1.21698	−0.608492	+	0.793560i	$0.708225\pi$
$230$	−13.2105	−0.871074
$231$	−10.6713	−0.702119
$232$	−12.6259	−0.828930
$233$	−12.7989	−0.838486	−0.419243	−	0.907874i	$-0.637705\pi$
$233$	−12.7989	−0.838486	−0.419243	+	0.907874i	$0.637705\pi$
$234$	25.8910	1.69254
$235$	−22.5152	−1.46873
$236$	7.92310	0.515750
$237$	−2.42837	−0.157740
$238$	5.87830	0.381034
$239$	24.9198	1.61193	0.805963	−	0.591966i	$-0.201648\pi$
$239$	24.9198	1.61193	0.805963	+	0.591966i	$0.201648\pi$
$240$	−48.5763	−3.13559
$241$	24.2385	1.56134	0.780668	−	0.624946i	$-0.214879\pi$
$241$	24.2385	1.56134	0.780668	+	0.624946i	$0.214879\pi$
$242$	−0.203430	−0.0130770
$243$	−73.5206	−4.71635
$244$	5.46844	0.350081
$245$	17.4835	1.11698
$246$	29.7318	1.89563
$247$	−3.39045	−0.215729
$248$	6.42092	0.407729
$249$	−15.1388	−0.959386
$250$	−9.02307	−0.570669
$251$	5.19850	0.328127	0.164063	−	0.986450i	$-0.447540\pi$
$251$	5.19850	0.328127	0.164063	+	0.986450i	$0.447540\pi$
$252$	−8.13900	−0.512709
$253$	8.87273	0.557824
$254$	3.53783	0.221983
$255$	34.9226	2.18694
$256$	19.1171	1.19482
$257$	−16.4146	−1.02392	−0.511958	−	0.859011i	$-0.671080\pi$
$257$	−16.4146	−1.02392	−0.511958	+	0.859011i	$0.671080\pi$
$258$	39.6463	2.46827
$259$	−0.679890	−0.0422463
$260$	5.05882	0.313735
$261$	−62.8468	−3.89012
$262$	27.2863	1.68575
$263$	−15.2376	−0.939589	−0.469795	−	0.882776i	$-0.655672\pi$
$263$	−15.2376	−0.939589	−0.469795	+	0.882776i	$0.655672\pi$
$264$	19.4202	1.19523
$265$	−7.79712	−0.478973
$266$	3.17241	0.194513
$267$	−53.0919	−3.24917
$268$	8.38513	0.512204
$269$	−18.9641	−1.15626	−0.578131	−	0.815944i	$-0.696218\pi$
$269$	−18.9641	−1.15626	−0.578131	+	0.815944i	$0.696218\pi$
$270$	−93.3414	−5.68058
$271$	20.3997	1.23919	0.619597	−	0.784920i	$-0.287296\pi$
$271$	20.3997	1.23919	0.619597	+	0.784920i	$0.287296\pi$
$272$	−17.9721	−1.08972
$273$	−5.59369	−0.338545
$274$	−29.7635	−1.79808
$275$	−10.6110	−0.639865
$276$	9.14564	0.550503
$277$	−25.5622	−1.53588	−0.767941	−	0.640521i	$-0.778719\pi$
$277$	−25.5622	−1.53588	−0.767941	+	0.640521i	$0.778719\pi$
$278$	14.4211	0.864919
$279$	31.9609	1.91345
$280$	4.62235	0.276238
$281$	−28.6097	−1.70671	−0.853355	−	0.521331i	$-0.825436\pi$
$281$	−28.6097	−1.70671	−0.853355	+	0.521331i	$0.825436\pi$
$282$	46.3959	2.76284
$283$	−8.12628	−0.483057	−0.241529	−	0.970394i	$-0.577649\pi$
$283$	−8.12628	−0.483057	−0.241529	+	0.970394i	$0.577649\pi$
$284$	12.8419	0.762028
$285$	18.8471	1.11641
$286$	−10.1134	−0.598017
$287$	−4.75302	−0.280562
$288$	44.7915	2.63936
$289$	−4.07947	−0.239969
$290$	−36.5505	−2.14632
$291$	0	0
$292$	−3.31106	−0.193765
$293$	−5.71365	−0.333795	−0.166897	−	0.985974i	$-0.553375\pi$
$293$	−5.71365	−0.333795	−0.166897	+	0.985974i	$0.553375\pi$
$294$	−36.0273	−2.10116
$295$	−22.3979	−1.30406
$296$	1.23730	0.0719165
$297$	62.6921	3.63777
$298$	−10.0085	−0.579777
$299$	4.65092	0.268970
$300$	−10.9373	−0.631467
$301$	−6.33799	−0.365315
$302$	4.82134	0.277437
$303$	6.83957	0.392923
$304$	−9.69919	−0.556287
$305$	−15.4588	−0.885168
$306$	−53.2487	−3.04402
$307$	8.65650	0.494053	0.247026	−	0.969009i	$-0.420547\pi$
$307$	8.65650	0.494053	0.247026	+	0.969009i	$0.420547\pi$
$308$	3.17921	0.181152
$309$	54.0870	3.07690
$310$	18.5878	1.05572
$311$	34.1650	1.93732	0.968661	−	0.248388i	$-0.0799007\pi$
$311$	34.1650	1.93732	0.968661	+	0.248388i	$0.0799007\pi$
$312$	10.1797	0.576311
$313$	−4.80055	−0.271343	−0.135672	−	0.990754i	$-0.543319\pi$
$313$	−4.80055	−0.271343	−0.135672	+	0.990754i	$0.543319\pi$
$314$	26.8735	1.51656
$315$	23.0082	1.29637
$316$	0.723465	0.0406981
$317$	−14.5022	−0.814524	−0.407262	−	0.913311i	$-0.633516\pi$
$317$	−14.5022	−0.814524	−0.407262	+	0.913311i	$0.633516\pi$
$318$	16.0671	0.900999
$319$	24.5489	1.37447
$320$	−2.55427	−0.142788
$321$	−26.3145	−1.46873
$322$	−4.35182	−0.242517
$323$	6.97297	0.387987
$324$	38.7084	2.15047
$325$	−5.56207	−0.308528
$326$	−6.34690	−0.351522
$327$	0.993292	0.0549292
$328$	8.64979	0.477605
$329$	−7.41700	−0.408912
$330$	56.2191	3.09476
$331$	−16.7465	−0.920469	−0.460234	−	0.887798i	$-0.652235\pi$
$331$	−16.7465	−0.920469	−0.460234	+	0.887798i	$0.652235\pi$
$332$	4.51020	0.247529
$333$	6.15879	0.337500
$334$	11.7118	0.640839
$335$	−23.7040	−1.29509
$336$	−16.0021	−0.872985
$337$	−19.6797	−1.07202	−0.536010	−	0.844211i	$-0.680069\pi$
$337$	−19.6797	−1.07202	−0.536010	+	0.844211i	$0.680069\pi$
$338$	17.2600	0.938818
$339$	23.1629	1.25804
$340$	−10.4042	−0.564248
$341$	−12.4844	−0.676067
$342$	−28.7373	−1.55394
$343$	12.3556	0.667139
$344$	11.5342	0.621882
$345$	−25.8539	−1.39193
$346$	3.50462	0.188409
$347$	−25.3801	−1.36247	−0.681237	−	0.732063i	$-0.738558\pi$
$347$	−25.3801	−1.36247	−0.681237	+	0.732063i	$0.738558\pi$
$348$	25.3039	1.35643
$349$	32.6491	1.74767	0.873834	−	0.486224i	$-0.161626\pi$
$349$	32.6491	1.74767	0.873834	+	0.486224i	$0.161626\pi$
$350$	5.20437	0.278186
$351$	32.8620	1.75405
$352$	−17.4962	−0.932551
$353$	3.48296	0.185379	0.0926896	−	0.995695i	$-0.470454\pi$
$353$	3.48296	0.185379	0.0926896	+	0.995695i	$0.470454\pi$
$354$	46.1542	2.45307
$355$	−36.3030	−1.92676
$356$	15.8173	0.838313
$357$	11.5043	0.608870
$358$	−16.5474	−0.874556
$359$	25.6900	1.35587	0.677933	−	0.735123i	$-0.262876\pi$
$359$	25.6900	1.35587	0.677933	+	0.735123i	$0.262876\pi$
$360$	−41.8716	−2.20683
$361$	−15.2368	−0.801938
$362$	−9.27987	−0.487739
$363$	−0.398127	−0.0208963
$364$	1.66648	0.0873475
$365$	9.36008	0.489929
$366$	31.8552	1.66510
$367$	−7.79766	−0.407035	−0.203517	−	0.979071i	$-0.565237\pi$
$367$	−7.79766	−0.407035	−0.203517	+	0.979071i	$0.565237\pi$
$368$	13.3051	0.693574
$369$	43.0553	2.24137
$370$	3.58183	0.186211
$371$	−2.56854	−0.133352
$372$	−12.8684	−0.667193
$373$	0.469987	0.0243350	0.0121675	−	0.999926i	$-0.496127\pi$
$373$	0.469987	0.0243350	0.0121675	+	0.999926i	$0.496127\pi$
$374$	20.7997	1.07553
$375$	−17.6588	−0.911897
$376$	13.4978	0.696098
$377$	12.8681	0.662738
$378$	−30.7487	−1.58154
$379$	13.8394	0.710883	0.355441	−	0.934699i	$-0.384331\pi$
$379$	13.8394	0.710883	0.355441	+	0.934699i	$0.384331\pi$
$380$	−5.61497	−0.288042
$381$	6.92380	0.354717
$382$	−40.5956	−2.07705
$383$	2.52866	0.129209	0.0646043	−	0.997911i	$-0.479421\pi$
$383$	2.52866	0.129209	0.0646043	+	0.997911i	$0.479421\pi$
$384$	40.9087	2.08761
$385$	−8.98735	−0.458038
$386$	−6.88369	−0.350371
$387$	57.4127	2.91845
$388$	0	0
$389$	−25.5869	−1.29731	−0.648653	−	0.761084i	$-0.724667\pi$
$389$	−25.5869	−1.29731	−0.648653	+	0.761084i	$0.724667\pi$
$390$	29.4690	1.49222
$391$	−9.56532	−0.483739
$392$	−10.4813	−0.529387
$393$	53.4013	2.69374
$394$	−21.8650	−1.10154
$395$	−2.04517	−0.102904
$396$	−28.7989	−1.44720
$397$	11.9865	0.601583	0.300792	−	0.953690i	$-0.402749\pi$
$397$	11.9865	0.601583	0.300792	+	0.953690i	$0.402749\pi$
$398$	−8.53437	−0.427789
$399$	6.20864	0.310821
$400$	−15.9116	−0.795581
$401$	0.0336991	0.00168286	0.000841428	−	1.00000i	$-0.499732\pi$
$401$	0.0336991	0.00168286	0.000841428		1.00000i	$0.499732\pi$
$402$	48.8457	2.43620
$403$	−6.54407	−0.325984
$404$	−2.03766	−0.101377
$405$	−109.425	−5.43739
$406$	−12.0405	−0.597560
$407$	−2.40571	−0.119247
$408$	−20.9361	−1.03649
$409$	−15.9489	−0.788624	−0.394312	−	0.918977i	$-0.629017\pi$
$409$	−15.9489	−0.788624	−0.394312	+	0.918977i	$0.629017\pi$
$410$	25.0401	1.23664
$411$	−58.2494	−2.87323
$412$	−16.1137	−0.793866
$413$	−7.37835	−0.363065
$414$	39.4210	1.93744
$415$	−12.7499	−0.625869
$416$	−9.17118	−0.449654
$417$	28.2231	1.38209
$418$	11.2252	0.549043
$419$	−17.1414	−0.837410	−0.418705	−	0.908122i	$-0.637516\pi$
$419$	−17.1414	−0.837410	−0.418705	+	0.908122i	$0.637516\pi$
$420$	−9.26378	−0.452026
$421$	11.9712	0.583443	0.291721	−	0.956503i	$-0.405772\pi$
$421$	11.9712	0.583443	0.291721	+	0.956503i	$0.405772\pi$
$422$	−40.0625	−1.95021
$423$	67.1870	3.26674
$424$	4.67436	0.227007
$425$	11.4392	0.554885
$426$	74.8077	3.62444
$427$	−5.09246	−0.246442
$428$	7.83967	0.378945
$429$	−19.7926	−0.955597
$430$	33.3901	1.61021
$431$	−30.9215	−1.48943	−0.744717	−	0.667380i	$-0.767416\pi$
$431$	−30.9215	−1.48943	−0.744717	+	0.667380i	$0.767416\pi$
$432$	94.0097	4.52304
$433$	−8.24602	−0.396279	−0.198139	−	0.980174i	$-0.563490\pi$
$433$	−8.24602	−0.396279	−0.198139	+	0.980174i	$0.563490\pi$
$434$	6.12322	0.293924
$435$	−71.5319	−3.42969
$436$	−0.295924	−0.0141722
$437$	−5.16223	−0.246943
$438$	−19.2878	−0.921609
$439$	10.1541	0.484628	0.242314	−	0.970198i	$-0.422094\pi$
$439$	10.1541	0.484628	0.242314	+	0.970198i	$0.422094\pi$
$440$	16.3556	0.779725
$441$	−52.1719	−2.48438
$442$	10.9028	0.518594
$443$	7.57735	0.360011	0.180005	−	0.983666i	$-0.442388\pi$
$443$	7.57735	0.360011	0.180005	+	0.983666i	$0.442388\pi$
$444$	−2.47971	−0.117682
$445$	−44.7140	−2.11964
$446$	−0.946848	−0.0448345
$447$	−19.5874	−0.926451
$448$	−0.841431	−0.0397539
$449$	6.34626	0.299498	0.149749	−	0.988724i	$-0.452153\pi$
$449$	6.34626	0.299498	0.149749	+	0.988724i	$0.452153\pi$
$450$	−47.1439	−2.22238
$451$	−16.8180	−0.791930
$452$	−6.90075	−0.324584
$453$	9.43572	0.443329
$454$	47.3443	2.22198
$455$	−4.71100	−0.220855
$456$	−11.2988	−0.529115
$457$	3.14530	0.147131	0.0735654	−	0.997290i	$-0.476562\pi$
$457$	3.14530	0.147131	0.0735654	+	0.997290i	$0.476562\pi$
$458$	31.9610	1.49344
$459$	−67.5857	−3.15463
$460$	7.70245	0.359128
$461$	20.5233	0.955863	0.477932	−	0.878397i	$-0.341387\pi$
$461$	20.5233	0.955863	0.477932	+	0.878397i	$0.341387\pi$
$462$	18.5198	0.861618
$463$	8.19203	0.380716	0.190358	−	0.981715i	$-0.439035\pi$
$463$	8.19203	0.380716	0.190358	+	0.981715i	$0.439035\pi$
$464$	36.8121	1.70896
$465$	36.3777	1.68698
$466$	22.2123	1.02896
$467$	−4.62621	−0.214075	−0.107038	−	0.994255i	$-0.534137\pi$
$467$	−4.62621	−0.214075	−0.107038	+	0.994255i	$0.534137\pi$
$468$	−15.0959	−0.697807
$469$	−7.80862	−0.360568
$470$	39.0746	1.80238
$471$	52.5935	2.42338
$472$	13.4275	0.618050
$473$	−22.4262	−1.03116
$474$	4.21438	0.193573
$475$	6.17355	0.283262
$476$	−3.42738	−0.157094
$477$	23.2671	1.06533
$478$	−43.2477	−1.97810
$479$	−13.0994	−0.598527	−0.299264	−	0.954170i	$-0.596741\pi$
$479$	−13.0994	−0.598527	−0.299264	+	0.954170i	$0.596741\pi$
$480$	50.9815	2.32697
$481$	−1.26103	−0.0574980
$482$	−42.0653	−1.91602
$483$	−8.51683	−0.387529
$484$	0.118611	0.00539141
$485$	0	0
$486$	127.593	5.78775
$487$	−29.5431	−1.33872	−0.669362	−	0.742937i	$-0.733432\pi$
$487$	−29.5431	−1.33872	−0.669362	+	0.742937i	$0.733432\pi$
$488$	9.26753	0.419521
$489$	−12.4213	−0.561713
$490$	−30.3422	−1.37072
$491$	24.2470	1.09425	0.547125	−	0.837051i	$-0.315722\pi$
$491$	24.2470	1.09425	0.547125	+	0.837051i	$0.315722\pi$
$492$	−17.3353	−0.781536
$493$	−26.4651	−1.19193
$494$	5.88405	0.264736
$495$	81.4120	3.65920
$496$	−18.7209	−0.840593
$497$	−11.9590	−0.536434
$498$	26.2731	1.17733
$499$	6.00068	0.268627	0.134314	−	0.990939i	$-0.457117\pi$
$499$	6.00068	0.268627	0.134314	+	0.990939i	$0.457117\pi$
$500$	5.26095	0.235277
$501$	22.9208	1.02402
$502$	−9.02188	−0.402666
$503$	37.7592	1.68360	0.841799	−	0.539792i	$-0.181497\pi$
$503$	37.7592	1.68360	0.841799	+	0.539792i	$0.181497\pi$
$504$	−13.7934	−0.614407
$505$	5.76028	0.256329
$506$	−15.3984	−0.684543
$507$	33.7790	1.50018
$508$	−2.06275	−0.0915198
$509$	5.07395	0.224899	0.112449	−	0.993657i	$-0.464130\pi$
$509$	5.07395	0.224899	0.112449	+	0.993657i	$0.464130\pi$
$510$	−60.6074	−2.68374
$511$	3.08341	0.136402
$512$	−9.08823	−0.401647
$513$	−36.4748	−1.61040
$514$	28.4872	1.25652
$515$	45.5520	2.00726
$516$	−23.1160	−1.01763
$517$	−26.2442	−1.15422
$518$	1.17993	0.0518433
$519$	6.85879	0.301067
$520$	8.57332	0.375965
$521$	21.2407	0.930573	0.465287	−	0.885160i	$-0.345951\pi$
$521$	21.2407	0.930573	0.465287	+	0.885160i	$0.345951\pi$
$522$	109.069	4.77383
$523$	−12.1208	−0.530005	−0.265003	−	0.964248i	$-0.585373\pi$
$523$	−12.1208	−0.530005	−0.265003	+	0.964248i	$0.585373\pi$
$524$	−15.9094	−0.695007
$525$	10.1853	0.444525
$526$	26.4445	1.15303
$527$	13.4589	0.586278
$528$	−56.6215	−2.46414
$529$	−15.9186	−0.692113
$530$	13.5317	0.587780
$531$	66.8368	2.90047
$532$	−1.84969	−0.0801943
$533$	−8.81569	−0.381850
$534$	92.1397	3.98728
$535$	−22.1620	−0.958148
$536$	14.2105	0.613801
$537$	−32.3844	−1.39749
$538$	32.9118	1.41893
$539$	20.3791	0.877791
$540$	54.4232	2.34200
$541$	−17.4681	−0.751013	−0.375507	−	0.926820i	$-0.622531\pi$
$541$	−17.4681	−0.751013	−0.375507	+	0.926820i	$0.622531\pi$
$542$	−35.4032	−1.52070
$543$	−18.1614	−0.779380
$544$	18.8619	0.808698
$545$	0.836550	0.0358339
$546$	9.70772	0.415452
$547$	−14.0282	−0.599802	−0.299901	−	0.953970i	$-0.596954\pi$
$547$	−14.0282	−0.599802	−0.299901	+	0.953970i	$0.596954\pi$
$548$	17.3538	0.741317
$549$	46.1301	1.96879
$550$	18.4151	0.785222
$551$	−14.2827	−0.608465
$552$	15.4994	0.659697
$553$	−0.673723	−0.0286496
$554$	44.3625	1.88478
$555$	7.00991	0.297554
$556$	−8.40829	−0.356591
$557$	−35.4605	−1.50251	−0.751255	−	0.660012i	$-0.770551\pi$
$557$	−35.4605	−1.50251	−0.751255	+	0.660012i	$0.770551\pi$
$558$	−55.4673	−2.34812
$559$	−11.7554	−0.497201
$560$	−13.4769	−0.569505
$561$	40.7065	1.71863
$562$	49.6514	2.09442
$563$	−37.1657	−1.56635	−0.783173	−	0.621804i	$-0.786400\pi$
$563$	−37.1657	−1.56635	−0.783173	+	0.621804i	$0.786400\pi$
$564$	−27.0514	−1.13907
$565$	19.5078	0.820700
$566$	14.1030	0.592792
$567$	−36.0471	−1.51383
$568$	21.7636	0.913179
$569$	35.6166	1.49312	0.746562	−	0.665316i	$-0.231703\pi$
$569$	35.6166	1.49312	0.746562	+	0.665316i	$0.231703\pi$
$570$	−32.7087	−1.37002
$571$	−4.08957	−0.171143	−0.0855717	−	0.996332i	$-0.527272\pi$
$571$	−4.08957	−0.171143	−0.0855717	+	0.996332i	$0.527272\pi$
$572$	5.89666	0.246552
$573$	−79.4486	−3.31901
$574$	8.24876	0.344296
$575$	−8.46869	−0.353169
$576$	7.62211	0.317588
$577$	−45.1541	−1.87979	−0.939896	−	0.341461i	$-0.889078\pi$
$577$	−45.1541	−1.87979	−0.939896	+	0.341461i	$0.889078\pi$
$578$	7.07983	0.294482
$579$	−13.4719	−0.559872
$580$	21.3109	0.884889
$581$	−4.20010	−0.174250
$582$	0	0
$583$	−9.08848	−0.376406
$584$	−5.61135	−0.232199
$585$	42.6747	1.76438
$586$	9.91590	0.409622
$587$	−13.3063	−0.549209	−0.274605	−	0.961557i	$-0.588547\pi$
$587$	−13.3063	−0.549209	−0.274605	+	0.961557i	$0.588547\pi$
$588$	21.0059	0.866270
$589$	7.26351	0.299288
$590$	38.8710	1.60029
$591$	−42.7914	−1.76020
$592$	−3.60748	−0.148266
$593$	16.0790	0.660284	0.330142	−	0.943931i	$-0.392903\pi$
$593$	16.0790	0.660284	0.330142	+	0.943931i	$0.392903\pi$
$594$	−108.801	−4.46415
$595$	9.68888	0.397206
$596$	5.83551	0.239032
$597$	−16.7024	−0.683583
$598$	−8.07156	−0.330071
$599$	−4.19878	−0.171558	−0.0857788	−	0.996314i	$-0.527338\pi$
$599$	−4.19878	−0.171558	−0.0857788	+	0.996314i	$0.527338\pi$
$600$	−18.5358	−0.756721
$601$	46.3079	1.88894	0.944468	−	0.328602i	$-0.106578\pi$
$601$	46.3079	1.88894	0.944468	+	0.328602i	$0.106578\pi$
$602$	10.9994	0.448303
$603$	70.7344	2.88053
$604$	−2.81111	−0.114382
$605$	−0.335302	−0.0136320
$606$	−11.8699	−0.482182
$607$	30.0832	1.22104	0.610519	−	0.792001i	$-0.290961\pi$
$607$	30.0832	1.22104	0.610519	+	0.792001i	$0.290961\pi$
$608$	10.1794	0.412830
$609$	−23.5642	−0.954868
$610$	26.8284	1.08625
$611$	−13.7567	−0.556537
$612$	31.0469	1.25500
$613$	−16.5116	−0.666897	−0.333448	−	0.942768i	$-0.608212\pi$
$613$	−16.5116	−0.666897	−0.333448	+	0.942768i	$0.608212\pi$
$614$	−15.0232	−0.606285
$615$	49.0054	1.97609
$616$	5.38790	0.217085
$617$	−19.2819	−0.776260	−0.388130	−	0.921605i	$-0.626879\pi$
$617$	−19.2819	−0.776260	−0.388130	+	0.921605i	$0.626879\pi$
$618$	−93.8667	−3.77587
$619$	35.4780	1.42598	0.712990	−	0.701174i	$-0.247340\pi$
$619$	35.4780	1.42598	0.712990	+	0.701174i	$0.247340\pi$
$620$	−10.8377	−0.435253
$621$	50.0350	2.00784
$622$	−59.2926	−2.37742
$623$	−14.7297	−0.590135
$624$	−29.6800	−1.18815
$625$	−30.7843	−1.23137
$626$	8.33124	0.332983
$627$	21.9686	0.877340
$628$	−15.6688	−0.625251
$629$	2.59350	0.103410
$630$	−39.9303	−1.59086
$631$	17.4790	0.695829	0.347914	−	0.937526i	$-0.386890\pi$
$631$	17.4790	0.695829	0.347914	+	0.937526i	$0.386890\pi$
$632$	1.22608	0.0487707
$633$	−78.4052	−3.11633
$634$	25.1682	0.999557
$635$	5.83122	0.231405
$636$	−9.36802	−0.371466
$637$	10.6824	0.423250
$638$	−42.6040	−1.68671
$639$	108.331	4.28549
$640$	34.4533	1.36188
$641$	22.3284	0.881920	0.440960	−	0.897527i	$-0.354638\pi$
$641$	22.3284	0.881920	0.440960	+	0.897527i	$0.354638\pi$
$642$	45.6682	1.80238
$643$	−23.5306	−0.927955	−0.463978	−	0.885847i	$-0.653578\pi$
$643$	−23.5306	−0.927955	−0.463978	+	0.885847i	$0.653578\pi$
$644$	2.53735	0.0999857
$645$	65.3469	2.57303
$646$	−12.1014	−0.476124
$647$	8.99761	0.353732	0.176866	−	0.984235i	$-0.443404\pi$
$647$	8.99761	0.353732	0.176866	+	0.984235i	$0.443404\pi$
$648$	65.6003	2.57702
$649$	−26.1074	−1.02481
$650$	9.65284	0.378616
$651$	11.9836	0.469674
$652$	3.70060	0.144927
$653$	16.8628	0.659893	0.329947	−	0.944000i	$-0.392969\pi$
$653$	16.8628	0.659893	0.329947	+	0.944000i	$0.392969\pi$
$654$	−1.72384	−0.0674073
$655$	44.9745	1.75730
$656$	−25.2194	−0.984652
$657$	−27.9311	−1.08970
$658$	12.8720	0.501804
$659$	−21.2538	−0.827932	−0.413966	−	0.910292i	$-0.635857\pi$
$659$	−21.2538	−0.827932	−0.413966	+	0.910292i	$0.635857\pi$
$660$	−32.7788	−1.27591
$661$	−29.5558	−1.14959	−0.574794	−	0.818298i	$-0.694918\pi$
$661$	−29.5558	−1.14959	−0.574794	+	0.818298i	$0.694918\pi$
$662$	29.0631	1.12957
$663$	21.3376	0.828684
$664$	7.64356	0.296628
$665$	5.22891	0.202769
$666$	−10.6884	−0.414169
$667$	19.5926	0.758629
$668$	−6.82860	−0.264207
$669$	−1.85305	−0.0716431
$670$	41.1378	1.58929
$671$	−18.0191	−0.695620
$672$	16.7944	0.647858
$673$	4.42959	0.170748	0.0853741	−	0.996349i	$-0.472791\pi$
$673$	4.42959	0.170748	0.0853741	+	0.996349i	$0.472791\pi$
$674$	34.1536	1.31555
$675$	−59.8373	−2.30314
$676$	−10.0635	−0.387058
$677$	38.3577	1.47421	0.737103	−	0.675780i	$-0.236193\pi$
$677$	38.3577	1.47421	0.737103	+	0.675780i	$0.236193\pi$
$678$	−40.1987	−1.54382
$679$	0	0
$680$	−17.6323	−0.676169
$681$	92.6563	3.55060
$682$	21.6663	0.829647
$683$	18.8900	0.722804	0.361402	−	0.932410i	$-0.382298\pi$
$683$	18.8900	0.722804	0.361402	+	0.932410i	$0.382298\pi$
$684$	16.7555	0.640661
$685$	−49.0576	−1.87439
$686$	−21.4428	−0.818692
$687$	62.5501	2.38644
$688$	−33.6292	−1.28210
$689$	−4.76401	−0.181494
$690$	44.8688	1.70813
$691$	8.39288	0.319280	0.159640	−	0.987175i	$-0.448967\pi$
$691$	8.39288	0.319280	0.159640	+	0.987175i	$0.448967\pi$
$692$	−2.04339	−0.0776779
$693$	26.8189	1.01877
$694$	44.0465	1.67198
$695$	23.7695	0.901628
$696$	42.8833	1.62549
$697$	18.1308	0.686753
$698$	−56.6618	−2.14468
$699$	43.4710	1.64423
$700$	−3.03444	−0.114691
$701$	10.3167	0.389656	0.194828	−	0.980837i	$-0.437585\pi$
$701$	10.3167	0.389656	0.194828	+	0.980837i	$0.437585\pi$
$702$	−57.0313	−2.15251
$703$	1.39966	0.0527893
$704$	−2.97731	−0.112211
$705$	76.4719	2.88010
$706$	−6.04459	−0.227491
$707$	1.89756	0.0713651
$708$	−26.9104	−1.01136
$709$	−46.8155	−1.75819	−0.879097	−	0.476644i	$-0.841853\pi$
$709$	−46.8155	−1.75819	−0.879097	+	0.476644i	$0.841853\pi$
$710$	63.0030	2.36446
$711$	6.10293	0.228878
$712$	26.8059	1.00460
$713$	−9.96387	−0.373150
$714$	−19.9654	−0.747186
$715$	−16.6693	−0.623398
$716$	9.64804	0.360564
$717$	−84.6389	−3.16090
$718$	−44.5844	−1.66388
$719$	0.967369	0.0360768	0.0180384	−	0.999837i	$-0.494258\pi$
$719$	0.967369	0.0360768	0.0180384	+	0.999837i	$0.494258\pi$
$720$	122.081	4.54969
$721$	15.0058	0.558846
$722$	26.4431	0.984112
$723$	−82.3248	−3.06169
$724$	5.41068	0.201086
$725$	−23.4310	−0.870204
$726$	0.690941	0.0256432
$727$	46.9288	1.74049	0.870247	−	0.492615i	$-0.163959\pi$
$727$	46.9288	1.74049	0.870247	+	0.492615i	$0.163959\pi$
$728$	2.82424	0.104673
$729$	134.948	4.99806
$730$	−16.2442	−0.601225
$731$	24.1768	0.894211
$732$	−18.5733	−0.686490
$733$	44.2879	1.63581	0.817906	−	0.575351i	$-0.195135\pi$
$733$	44.2879	1.63581	0.817906	+	0.575351i	$0.195135\pi$
$734$	13.5327	0.499500
$735$	−59.3819	−2.19033
$736$	−13.9638	−0.514714
$737$	−27.6299	−1.01776
$738$	−74.7215	−2.75054
$739$	−10.2807	−0.378180	−0.189090	−	0.981960i	$-0.560554\pi$
$739$	−10.2807	−0.378180	−0.189090	+	0.981960i	$0.560554\pi$
$740$	−2.08841	−0.0767714
$741$	11.5155	0.423033
$742$	4.45764	0.163645
$743$	10.1513	0.372414	0.186207	−	0.982510i	$-0.440380\pi$
$743$	10.1513	0.372414	0.186207	+	0.982510i	$0.440380\pi$
$744$	−21.8084	−0.799534
$745$	−16.4965	−0.604384
$746$	−0.815652	−0.0298631
$747$	38.0467	1.39206
$748$	−12.1274	−0.443421
$749$	−7.30065	−0.266760
$750$	30.6464	1.11905
$751$	−14.9074	−0.543977	−0.271989	−	0.962300i	$-0.587681\pi$
$751$	−14.9074	−0.543977	−0.271989	+	0.962300i	$0.587681\pi$
$752$	−39.3544	−1.43511
$753$	−17.6565	−0.643438
$754$	−22.3322	−0.813291
$755$	7.94675	0.289212
$756$	17.9282	0.652042
$757$	18.0524	0.656125	0.328062	−	0.944656i	$-0.393604\pi$
$757$	18.0524	0.656125	0.328062	+	0.944656i	$0.393604\pi$
$758$	−24.0180	−0.872372
$759$	−30.1358	−1.09386
$760$	−9.51585	−0.345176
$761$	42.1081	1.52642	0.763208	−	0.646153i	$-0.223623\pi$
$761$	42.1081	1.52642	0.763208	+	0.646153i	$0.223623\pi$
$762$	−12.0161	−0.435297
$763$	0.275578	0.00997658
$764$	23.6695	0.856333
$765$	−87.7669	−3.17322
$766$	−4.38844	−0.158561
$767$	−13.6850	−0.494138
$768$	−64.9304	−2.34297
$769$	11.5808	0.417615	0.208807	−	0.977957i	$-0.433042\pi$
$769$	11.5808	0.417615	0.208807	+	0.977957i	$0.433042\pi$
$770$	15.5973	0.562089
$771$	55.7515	2.00784
$772$	4.01357	0.144452
$773$	35.3702	1.27218	0.636089	−	0.771616i	$-0.280551\pi$
$773$	35.3702	1.27218	0.636089	+	0.771616i	$0.280551\pi$
$774$	−99.6384	−3.58143
$775$	11.9159	0.428030
$776$	0	0
$777$	2.30922	0.0828427
$778$	44.4054	1.59201
$779$	9.78486	0.350579
$780$	−17.1821	−0.615216
$781$	−42.3155	−1.51417
$782$	16.6004	0.593629
$783$	138.436	4.94729
$784$	30.5594	1.09141
$785$	44.2942	1.58093
$786$	−92.6767	−3.30567
$787$	8.09748	0.288644	0.144322	−	0.989531i	$-0.453900\pi$
$787$	8.09748	0.288644	0.144322	+	0.989531i	$0.453900\pi$
$788$	12.7485	0.454147
$789$	51.7537	1.84248
$790$	3.54935	0.126280
$791$	6.42629	0.228493
$792$	−48.8064	−1.73426
$793$	−9.44527	−0.335412
$794$	−20.8022	−0.738243
$795$	26.4826	0.939240
$796$	4.97601	0.176370
$797$	22.7696	0.806540	0.403270	−	0.915081i	$-0.367874\pi$
$797$	22.7696	0.806540	0.403270	+	0.915081i	$0.367874\pi$
$798$	−10.7750	−0.381429
$799$	28.2928	1.00093
$800$	16.6995	0.590415
$801$	133.430	4.71450
$802$	−0.0584841	−0.00206514
$803$	10.9103	0.385016
$804$	−28.4797	−1.00440
$805$	−7.17287	−0.252810
$806$	11.3571	0.400036
$807$	64.4108	2.26737
$808$	−3.45328	−0.121486
$809$	−49.8706	−1.75336	−0.876678	−	0.481077i	$-0.840246\pi$
$809$	−49.8706	−1.75336	−0.876678	+	0.481077i	$0.840246\pi$
$810$	189.905	6.67258
$811$	−34.5496	−1.21320	−0.606600	−	0.795007i	$-0.707467\pi$
$811$	−34.5496	−1.21320	−0.606600	+	0.795007i	$0.707467\pi$
$812$	7.02029	0.246364
$813$	−69.2867	−2.42999
$814$	4.17506	0.146336
$815$	−10.4613	−0.366442
$816$	61.0413	2.13687
$817$	13.0478	0.456484
$818$	27.6790	0.967773
$819$	14.0580	0.491225
$820$	−14.5998	−0.509846
$821$	−8.47879	−0.295912	−0.147956	−	0.988994i	$-0.547269\pi$
$821$	−8.47879	−0.295912	−0.147956	+	0.988994i	$0.547269\pi$
$822$	101.090	3.52594
$823$	11.3704	0.396348	0.198174	−	0.980167i	$-0.436499\pi$
$823$	11.3704	0.396348	0.198174	+	0.980167i	$0.436499\pi$
$824$	−27.3084	−0.951332
$825$	36.0397	1.25474
$826$	12.8049	0.445541
$827$	4.30863	0.149826	0.0749129	−	0.997190i	$-0.476132\pi$
$827$	4.30863	0.149826	0.0749129	+	0.997190i	$0.476132\pi$
$828$	−22.9846	−0.798772
$829$	−40.5319	−1.40773	−0.703866	−	0.710333i	$-0.748544\pi$
$829$	−40.5319	−1.40773	−0.703866	+	0.710333i	$0.748544\pi$
$830$	22.1272	0.768046
$831$	86.8208	3.01178
$832$	−1.56065	−0.0541057
$833$	−21.9699	−0.761211
$834$	−48.9805	−1.69606
$835$	19.3038	0.668037
$836$	−6.54492	−0.226361
$837$	−70.4017	−2.43344
$838$	29.7484	1.02764
$839$	13.7517	0.474760	0.237380	−	0.971417i	$-0.423711\pi$
$839$	13.7517	0.474760	0.237380	+	0.971417i	$0.423711\pi$
$840$	−15.6996	−0.541687
$841$	25.2084	0.869255
$842$	−20.7758	−0.715982
$843$	97.1715	3.34676
$844$	23.3586	0.804038
$845$	28.4486	0.978663
$846$	−116.601	−4.00884
$847$	−0.110456	−0.00379531
$848$	−13.6286	−0.468008
$849$	27.6006	0.947249
$850$	−19.8525	−0.680936
$851$	−1.92002	−0.0658173
$852$	−43.6170	−1.49429
$853$	1.18274	0.0404962	0.0202481	−	0.999795i	$-0.493554\pi$
$853$	1.18274	0.0404962	0.0202481	+	0.999795i	$0.493554\pi$
$854$	8.83785	0.302425
$855$	−47.3662	−1.61989
$856$	13.2861	0.454110
$857$	−44.4945	−1.51990	−0.759951	−	0.649980i	$-0.774777\pi$
$857$	−44.4945	−1.51990	−0.759951	+	0.649980i	$0.774777\pi$
$858$	34.3497	1.17268
$859$	−26.7028	−0.911086	−0.455543	−	0.890214i	$-0.650555\pi$
$859$	−26.7028	−0.911086	−0.455543	+	0.890214i	$0.650555\pi$
$860$	−19.4683	−0.663863
$861$	16.1434	0.550166
$862$	53.6635	1.82779
$863$	49.8431	1.69668	0.848339	−	0.529453i	$-0.177603\pi$
$863$	49.8431	1.69668	0.848339	+	0.529453i	$0.177603\pi$
$864$	−98.6644	−3.35663
$865$	5.77647	0.196406
$866$	14.3108	0.486300
$867$	13.8557	0.470566
$868$	−3.57018	−0.121180
$869$	−2.38389	−0.0808681
$870$	124.142	4.20881
$871$	−14.4831	−0.490740
$872$	−0.501510	−0.0169833
$873$	0	0
$874$	8.95892	0.303040
$875$	−4.89923	−0.165624
$876$	11.2459	0.379963
$877$	53.6507	1.81166	0.905828	−	0.423646i	$-0.139250\pi$
$877$	53.6507	1.81166	0.905828	+	0.423646i	$0.139250\pi$
$878$	−17.6222	−0.594719
$879$	19.4061	0.654553
$880$	−47.6866	−1.60752
$881$	−3.83856	−0.129324	−0.0646622	−	0.997907i	$-0.520597\pi$
$881$	−3.83856	−0.129324	−0.0646622	+	0.997907i	$0.520597\pi$
$882$	90.5432	3.04875
$883$	6.63424	0.223260	0.111630	−	0.993750i	$-0.464393\pi$
$883$	6.63424	0.223260	0.111630	+	0.993750i	$0.464393\pi$
$884$	−6.35695	−0.213807
$885$	76.0734	2.55718
$886$	−13.1503	−0.441794
$887$	56.2809	1.88973	0.944864	−	0.327463i	$-0.106194\pi$
$887$	56.2809	1.88973	0.944864	+	0.327463i	$0.106194\pi$
$888$	−4.20243	−0.141024
$889$	1.92093	0.0644259
$890$	77.6000	2.60116
$891$	−127.548	−4.27303
$892$	0.552065	0.0184845
$893$	15.2691	0.510961
$894$	33.9934	1.13691
$895$	−27.2741	−0.911674
$896$	11.3496	0.379165
$897$	−15.7966	−0.527434
$898$	−11.0138	−0.367535
$899$	−27.5678	−0.919437
$900$	27.4875	0.916250
$901$	9.79791	0.326416
$902$	29.1873	0.971830
$903$	21.5267	0.716363
$904$	−11.6949	−0.388967
$905$	−15.2955	−0.508440
$906$	−16.3755	−0.544038
$907$	−11.3747	−0.377691	−0.188845	−	0.982007i	$-0.560474\pi$
$907$	−11.3747	−0.377691	−0.188845	+	0.982007i	$0.560474\pi$
$908$	−27.6044	−0.916083
$909$	−17.1891	−0.570126
$910$	8.17583	0.271026
$911$	−30.2350	−1.00173	−0.500865	−	0.865526i	$-0.666985\pi$
$911$	−30.2350	−1.00173	−0.500865	+	0.865526i	$0.666985\pi$
$912$	32.9429	1.09085
$913$	−14.8616	−0.491847
$914$	−5.45859	−0.180554
$915$	52.5051	1.73577
$916$	−18.6351	−0.615720
$917$	14.8156	0.489254
$918$	117.293	3.87126
$919$	−52.0463	−1.71685	−0.858424	−	0.512941i	$-0.828556\pi$
$919$	−52.0463	−1.71685	−0.858424	+	0.512941i	$0.828556\pi$
$920$	13.0536	0.430363
$921$	−29.4014	−0.968810
$922$	−35.6176	−1.17300
$923$	−22.1810	−0.730096
$924$	−10.7981	−0.355230
$925$	2.29616	0.0754974
$926$	−14.2171	−0.467202
$927$	−135.930	−4.46454
$928$	−38.6348	−1.26825
$929$	16.1368	0.529430	0.264715	−	0.964327i	$-0.414722\pi$
$929$	16.1368	0.529430	0.264715	+	0.964327i	$0.414722\pi$
$930$	−63.1327	−2.07020
$931$	−11.8567	−0.388589
$932$	−12.9510	−0.424224
$933$	−116.040	−3.79898
$934$	8.02868	0.262706
$935$	34.2830	1.12117
$936$	−25.5834	−0.836219
$937$	−53.2295	−1.73893	−0.869466	−	0.493992i	$-0.835537\pi$
$937$	−53.2295	−1.73893	−0.869466	+	0.493992i	$0.835537\pi$
$938$	13.5517	0.442478
$939$	16.3049	0.532089
$940$	−22.7827	−0.743089
$941$	−0.731285	−0.0238392	−0.0119196	−	0.999929i	$-0.503794\pi$
$941$	−0.731285	−0.0238392	−0.0119196	+	0.999929i	$0.503794\pi$
$942$	−91.2747	−2.97389
$943$	−13.4226	−0.437099
$944$	−39.1493	−1.27420
$945$	−50.6814	−1.64867
$946$	38.9202	1.26541
$947$	20.0528	0.651628	0.325814	−	0.945434i	$-0.394362\pi$
$947$	20.0528	0.651628	0.325814	+	0.945434i	$0.394362\pi$
$948$	−2.45722	−0.0798067
$949$	5.71898	0.185646
$950$	−10.7140	−0.347610
$951$	49.2560	1.59724
$952$	−5.80847	−0.188254
$953$	27.8089	0.900817	0.450409	−	0.892823i	$-0.351278\pi$
$953$	27.8089	0.900817	0.450409	+	0.892823i	$0.351278\pi$
$954$	−40.3796	−1.30734
$955$	−66.9116	−2.16521
$956$	25.2158	0.815537
$957$	−83.3791	−2.69526
$958$	22.7337	0.734493
$959$	−16.1606	−0.521854
$960$	8.67545	0.279999
$961$	−16.9803	−0.547753
$962$	2.18849	0.0705597
$963$	66.1330	2.13111
$964$	24.5264	0.789942
$965$	−11.3460	−0.365241
$966$	14.7808	0.475563
$967$	−25.0008	−0.803973	−0.401986	−	0.915646i	$-0.631680\pi$
$967$	−25.0008	−0.803973	−0.401986	+	0.915646i	$0.631680\pi$
$968$	0.201013	0.00646081
$969$	−23.6834	−0.760820
$970$	0	0
$971$	−3.44575	−0.110579	−0.0552897	−	0.998470i	$-0.517608\pi$
$971$	−3.44575	−0.110579	−0.0552897	+	0.998470i	$0.517608\pi$
$972$	−74.3940	−2.38619
$973$	7.83018	0.251024
$974$	51.2713	1.64284
$975$	18.8913	0.605007
$976$	−27.0205	−0.864904
$977$	−37.3759	−1.19576	−0.597880	−	0.801585i	$-0.703990\pi$
$977$	−37.3759	−1.19576	−0.597880	+	0.801585i	$0.703990\pi$
$978$	21.5570	0.689316
$979$	−52.1195	−1.66575
$980$	17.6912	0.565124
$981$	−2.49632	−0.0797015
$982$	−42.0800	−1.34283
$983$	22.3176	0.711822	0.355911	−	0.934520i	$-0.384171\pi$
$983$	22.3176	0.711822	0.355911	+	0.934520i	$0.384171\pi$
$984$	−29.3786	−0.936556
$985$	−36.0389	−1.14829
$986$	45.9295	1.46269
$987$	25.1915	0.801854
$988$	−3.43073	−0.109146
$989$	−17.8985	−0.569141
$990$	−141.289	−4.49045
$991$	−37.6583	−1.19626	−0.598128	−	0.801401i	$-0.704089\pi$
$991$	−37.6583	−1.19626	−0.598128	+	0.801401i	$0.704089\pi$
$992$	19.6478	0.623819
$993$	56.8786	1.80499
$994$	20.7545	0.658294
$995$	−14.0667	−0.445946
$996$	−15.3187	−0.485391
$997$	−9.14953	−0.289769	−0.144884	−	0.989449i	$-0.546281\pi$
$997$	−9.14953	−0.289769	−0.144884	+	0.989449i	$0.546281\pi$
$998$	−10.4140	−0.329650
$999$	−13.5663	−0.429218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9409.2.a.q.1.37	yes	168
97.96	even	2		9409.2.a.p.1.37	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9409.2.a.p.1.37	✓	168	97.96	even	2
9409.2.a.q.1.37	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9409 = 97^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9409.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73548 q^{2} -3.39646 q^{3} +1.01188 q^{4} -2.86049 q^{5} +5.89447 q^{6} -0.942308 q^{7} +1.71486 q^{8} +8.53591 q^{9} +4.96432 q^{10} -3.33425 q^{11} -3.43680 q^{12} -1.74775 q^{13} +1.63535 q^{14} +9.71553 q^{15} -4.99986 q^{16} +3.59451 q^{17} -14.8139 q^{18} +1.93989 q^{19} -2.89447 q^{20} +3.20051 q^{21} +5.78651 q^{22} -2.66109 q^{23} -5.82445 q^{24} +3.18242 q^{25} +3.03318 q^{26} -18.8025 q^{27} -0.953502 q^{28} -7.36263 q^{29} -16.8611 q^{30} +3.74428 q^{31} +5.24742 q^{32} +11.3246 q^{33} -6.23819 q^{34} +2.69546 q^{35} +8.63731 q^{36} +0.721516 q^{37} -3.36664 q^{38} +5.93616 q^{39} -4.90534 q^{40} +5.04402 q^{41} -5.55440 q^{42} +6.72602 q^{43} -3.37386 q^{44} -24.4169 q^{45} +4.61826 q^{46} +7.87110 q^{47} +16.9818 q^{48} -6.11206 q^{49} -5.52301 q^{50} -12.2086 q^{51} -1.76851 q^{52} +2.72580 q^{53} +32.6312 q^{54} +9.53759 q^{55} -1.61593 q^{56} -6.58876 q^{57} +12.7777 q^{58} +7.83008 q^{59} +9.83095 q^{60} +5.40424 q^{61} -6.49812 q^{62} -8.04345 q^{63} +0.892947 q^{64} +4.99943 q^{65} -19.6536 q^{66} +8.28669 q^{67} +3.63721 q^{68} +9.03827 q^{69} -4.67792 q^{70} +12.6912 q^{71} +14.6379 q^{72} -3.27219 q^{73} -1.25217 q^{74} -10.8089 q^{75} +1.96294 q^{76} +3.14189 q^{77} -10.3021 q^{78} +0.714972 q^{79} +14.3021 q^{80} +38.2540 q^{81} -8.75378 q^{82} +4.45725 q^{83} +3.23853 q^{84} -10.2821 q^{85} -11.6729 q^{86} +25.0069 q^{87} -5.71777 q^{88} +15.6316 q^{89} +42.3750 q^{90} +1.64692 q^{91} -2.69270 q^{92} -12.7173 q^{93} -13.6601 q^{94} -5.54905 q^{95} -17.8226 q^{96} +10.6073 q^{98} -28.4608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 168 q^{4} + 42 q^{5} + 42 q^{7} + 168 q^{9} + 42 q^{10} + 42 q^{13} + 70 q^{14} + 84 q^{15} + 140 q^{16} + 49 q^{17} - 49 q^{18} + 84 q^{19} + 98 q^{20} + 84 q^{21} - 35 q^{22} + 126 q^{23} + 168 q^{25}+ \cdots - 84 q^{99}+O(q^{100}) \) 168 * q + 168 * q^4 + 42 * q^5 + 42 * q^7 + 168 * q^9 + 42 * q^10 + 42 * q^13 + 70 * q^14 + 84 * q^15 + 140 * q^16 + 49 * q^17 - 49 * q^18 + 84 * q^19 + 98 * q^20 + 84 * q^21 - 35 * q^22 + 126 * q^23 + 168 * q^25 + 105 * q^26 + 84 * q^28 + 126 * q^29 + 84 * q^30 + 84 * q^34 + 168 * q^36 + 42 * q^37 + 112 * q^38 + 168 * q^39 + 126 * q^40 + 154 * q^41 + 28 * q^42 - 63 * q^44 + 91 * q^45 - 21 * q^46 - 42 * q^47 - 56 * q^48 + 126 * q^49 - 28 * q^50 + 168 * q^51 + 63 * q^52 - 28 * q^53 - 42 * q^54 + 168 * q^55 + 140 * q^56 + 56 * q^57 - 77 * q^58 + 238 * q^59 + 168 * q^60 - 56 * q^61 - 91 * q^62 + 210 * q^63 + 112 * q^64 - 49 * q^65 - 133 * q^66 + 28 * q^67 + 126 * q^68 + 105 * q^69 - 147 * q^70 + 252 * q^71 - 98 * q^72 + 77 * q^73 + 147 * q^74 + 14 * q^75 + 196 * q^76 + 77 * q^77 - 63 * q^78 + 56 * q^79 + 133 * q^80 + 168 * q^81 + 56 * q^82 + 203 * q^83 + 252 * q^84 - 56 * q^85 - 56 * q^86 + 182 * q^87 - 182 * q^88 + 84 * q^90 - 42 * q^91 + 189 * q^92 + 84 * q^93 - 154 * q^94 - 28 * q^95 - 21 * q^96 + 84 * q^98 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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