LMFDB - Embedded newform 9409.2.a.p.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:	$1$
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	$-0.279089\pi$
$5$	2.86049	1.27925	0.639626	+	0.768687i	$0.279089\pi$
$6$	5.89447	2.40641
$7$	0.942308	0.356159	0.178079	−	0.984016i	$-0.443012\pi$
$7$	0.942308	0.356159	0.178079	+	0.984016i	$0.443012\pi$
$8$	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	$-0.422075\pi$
$13$	1.74775	0.484739	0.242369	+	0.970184i	$0.422075\pi$
$14$	−1.63535	−0.437067
$15$	−9.71553	−2.50854
$16$	−4.99986	−1.24996
$17$	−3.59451	−0.871798	−0.435899	−	0.899996i	$-0.643569\pi$
$17$	−3.59451	−0.871798	−0.435899	+	0.899996i	$0.643569\pi$
$18$	−14.8139	−3.49166
$19$	−1.93989	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$19$	−1.93989	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$20$	2.89447	0.647224
$21$	−3.20051	−0.698408
$22$	5.78651	1.23369
$23$	2.66109	0.554875	0.277438	−	0.960744i	$-0.410515\pi$
$23$	2.66109	0.554875	0.277438	+	0.960744i	$0.410515\pi$
$24$	−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	$-0.260412\pi$
$29$	7.36263	1.36721	0.683603	+	0.729854i	$0.260412\pi$
$30$	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	$-0.518889\pi$
$37$	−0.721516	−0.118616	−0.0593082	+	0.998240i	$0.518889\pi$
$38$	3.36664	0.546141
$39$	−5.93616	−0.950546
$40$	4.90534	0.775603
$41$	−5.04402	−0.787744	−0.393872	−	0.919165i	$-0.628865\pi$
$41$	−5.04402	−0.787744	−0.393872	+	0.919165i	$0.628865\pi$
$42$	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	$-0.670242\pi$
$59$	−7.83008	−1.01939	−0.509695	+	0.860355i	$0.670242\pi$
$60$	−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	$-0.668947\pi$
$67$	−8.28669	−1.01238	−0.506190	+	0.862422i	$0.668947\pi$
$68$	−3.63721	−0.441077
$69$	−9.03827	−1.08808
$70$	−4.67792	−0.559118
$71$	−12.6912	−1.50616	−0.753082	−	0.657927i	$-0.771434\pi$
$71$	−12.6912	−1.50616	−0.753082	+	0.657927i	$0.771434\pi$
$72$	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	$-0.578664\pi$
$83$	−4.45725	−0.489247	−0.244623	+	0.969618i	$0.578664\pi$
$84$	−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	$-0.622184\pi$
$107$	−7.74763	−0.748992	−0.374496	+	0.927229i	$0.622184\pi$
$108$	−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	$-0.471171\pi$
$127$	2.03854	0.180891	0.0904454	+	0.995901i	$0.471171\pi$
$128$	−12.0445	−1.06460
$129$	−22.8446	−2.01136
$130$	−8.67639	−0.760970
$131$	15.7227	1.37370	0.686848	−	0.726801i	$-0.258994\pi$
$131$	15.7227	1.37370	0.686848	+	0.726801i	$0.258994\pi$
$132$	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	$-0.761700\pi$
$137$	−17.1501	−1.46523	−0.732614	+	0.680644i	$0.761700\pi$
$138$	15.6857	1.33526
$139$	8.30958	0.704809	0.352405	−	0.935848i	$-0.385364\pi$
$139$	8.30958	0.704809	0.352405	+	0.935848i	$0.385364\pi$
$140$	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	$-0.575910\pi$
$149$	−5.76701	−0.472451	−0.236226	+	0.971698i	$0.575910\pi$
$150$	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	$-0.287979\pi$
$157$	15.4848	1.23582	0.617911	+	0.786248i	$0.287979\pi$
$158$	−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	$-0.475541\pi$
$173$	2.01940	0.153532	0.0767659	+	0.997049i	$0.475541\pi$
$174$	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	$-0.615973\pi$
$179$	−9.53477	−0.712662	−0.356331	+	0.934360i	$0.615973\pi$
$180$	24.7070	1.84155
$181$	−5.34716	−0.397451	−0.198726	−	0.980055i	$-0.563680\pi$
$181$	−5.34716	−0.397451	−0.198726	+	0.980055i	$0.563680\pi$
$182$	−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	$-0.555766\pi$
$199$	−4.91759	−0.348599	−0.174299	+	0.984693i	$0.555766\pi$
$200$	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	$-0.792318\pi$
$211$	−23.0844	−1.58920	−0.794598	+	0.607136i	$0.792318\pi$
$212$	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	$-0.505815\pi$
$223$	−0.545584	−0.0365350	−0.0182675	+	0.999833i	$0.505815\pi$
$224$	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	$-0.362295\pi$
$233$	12.7989	0.838486	0.419243	+	0.907874i	$0.362295\pi$
$234$	−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	$-0.798352\pi$
$239$	−24.9198	−1.61193	−0.805963	+	0.591966i	$0.798352\pi$
$240$	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	$-0.552460\pi$
$251$	−5.19850	−0.328127	−0.164063	+	0.986450i	$0.552460\pi$
$252$	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	$-0.328920\pi$
$257$	16.4146	1.02392	0.511958	+	0.859011i	$0.328920\pi$
$258$	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	$-0.344328\pi$
$263$	15.2376	0.939589	0.469795	+	0.882776i	$0.344328\pi$
$264$	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	$-0.712704\pi$
$271$	−20.3997	−1.23919	−0.619597	+	0.784920i	$0.712704\pi$
$272$	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	$-0.221281\pi$
$277$	25.5622	1.53588	0.767941	+	0.640521i	$0.221281\pi$
$278$	−14.4211	−0.864919
$279$	31.9609	1.91345
$280$	4.62235	0.276238
$281$	28.6097	1.70671	0.853355	−	0.521331i	$-0.174564\pi$
$281$	28.6097	1.70671	0.853355	+	0.521331i	$0.174564\pi$
$282$	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	$-0.920099\pi$
$311$	−34.1650	−1.93732	−0.968661	+	0.248388i	$0.920099\pi$
$312$	−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	$-0.366484\pi$
$317$	14.5022	0.814524	0.407262	+	0.913311i	$0.366484\pi$
$318$	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	$-0.347765\pi$
$331$	16.7465	0.920469	0.460234	+	0.887798i	$0.347765\pi$
$332$	−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	$-0.319931\pi$
$337$	19.6797	1.07202	0.536010	+	0.844211i	$0.319931\pi$
$338$	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	$-0.261442\pi$
$347$	25.3801	1.36247	0.681237	+	0.732063i	$0.261442\pi$
$348$	−25.3039	−1.35643
$349$	−32.6491	−1.74767	−0.873834	−	0.486224i	$-0.838374\pi$
$349$	−32.6491	−1.74767	−0.873834	+	0.486224i	$0.838374\pi$
$350$	−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	$-0.737124\pi$
$359$	−25.6900	−1.35587	−0.677933	+	0.735123i	$0.737124\pi$
$360$	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	$-0.434763\pi$
$367$	7.79766	0.407035	0.203517	+	0.979071i	$0.434763\pi$
$368$	−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	$-0.503873\pi$
$373$	−0.469987	−0.0243350	−0.0121675	+	0.999926i	$0.503873\pi$
$374$	−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	$-0.520579\pi$
$383$	−2.52866	−0.129209	−0.0646043	+	0.997911i	$0.520579\pi$
$384$	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	$-0.500268\pi$
$401$	−0.0336991	−0.00168286	−0.000841428		1.00000i	$0.500268\pi$
$402$	−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	$-0.370983\pi$
$409$	15.9489	0.788624	0.394312	+	0.918977i	$0.370983\pi$
$410$	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	$-0.436510\pi$
$433$	8.24602	0.396279	0.198139	+	0.980174i	$0.436510\pi$
$434$	−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	$-0.577906\pi$
$439$	−10.1541	−0.484628	−0.242314	+	0.970198i	$0.577906\pi$
$440$	−16.3556	−0.779725
$441$	−52.1719	−2.48438
$442$	10.9028	0.518594
$443$	−7.57735	−0.360011	−0.180005	−	0.983666i	$-0.557612\pi$
$443$	−7.57735	−0.360011	−0.180005	+	0.983666i	$0.557612\pi$
$444$	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	$-0.523438\pi$
$457$	−3.14530	−0.147131	−0.0735654	+	0.997290i	$0.523438\pi$
$458$	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	$-0.542883\pi$
$499$	−6.00068	−0.268627	−0.134314	+	0.990939i	$0.542883\pi$
$500$	−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	$-0.414627\pi$
$523$	12.1208	0.530005	0.265003	+	0.964248i	$0.414627\pi$
$524$	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	$-0.377469\pi$
$541$	17.4681	0.751013	0.375507	+	0.926820i	$0.377469\pi$
$542$	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	$-0.213600\pi$
$563$	37.1657	1.56635	0.783173	+	0.621804i	$0.213600\pi$
$564$	−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	$-0.768297\pi$
$569$	−35.6166	−1.49312	−0.746562	+	0.665316i	$0.768297\pi$
$570$	−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	$-0.110922\pi$
$577$	45.1541	1.87979	0.939896	+	0.341461i	$0.110922\pi$
$578$	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	$-0.411453\pi$
$587$	13.3063	0.549209	0.274605	+	0.961557i	$0.411453\pi$
$588$	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	$-0.472662\pi$
$599$	4.19878	0.171558	0.0857788	+	0.996314i	$0.472662\pi$
$600$	−18.5358	−0.756721
$601$	−46.3079	−1.88894	−0.944468	−	0.328602i	$-0.893422\pi$
$601$	−46.3079	−1.88894	−0.944468	+	0.328602i	$0.893422\pi$
$602$	−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	$-0.752660\pi$
$619$	−35.4780	−1.42598	−0.712990	+	0.701174i	$0.752660\pi$
$620$	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	$-0.645362\pi$
$641$	−22.3284	−0.881920	−0.440960	+	0.897527i	$0.645362\pi$
$642$	−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	$-0.607031\pi$
$653$	−16.8628	−0.659893	−0.329947	+	0.944000i	$0.607031\pi$
$654$	−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	$-0.364143\pi$
$659$	21.2538	0.827932	0.413966	+	0.910292i	$0.364143\pi$
$660$	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	$-0.158147\pi$
$709$	46.8155	1.75819	0.879097	+	0.476644i	$0.158147\pi$
$710$	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	$-0.505742\pi$
$719$	−0.967369	−0.0360768	−0.0180384	+	0.999837i	$0.505742\pi$
$720$	−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	$-0.439446\pi$
$739$	10.2807	0.378180	0.189090	+	0.981960i	$0.439446\pi$
$740$	−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	$-0.606396\pi$
$757$	−18.0524	−0.656125	−0.328062	+	0.944656i	$0.606396\pi$
$758$	−24.0180	−0.872372
$759$	30.1358	1.09386
$760$	−9.51585	−0.345176
$761$	−42.1081	−1.52642	−0.763208	−	0.646153i	$-0.776377\pi$
$761$	−42.1081	−1.52642	−0.763208	+	0.646153i	$0.776377\pi$
$762$	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	$-0.566958\pi$
$769$	−11.5808	−0.417615	−0.208807	+	0.977957i	$0.566958\pi$
$770$	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	$-0.632126\pi$
$797$	−22.7696	−0.806540	−0.403270	+	0.915081i	$0.632126\pi$
$798$	−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	$-0.452731\pi$
$821$	8.47879	0.295912	0.147956	+	0.988994i	$0.452731\pi$
$822$	−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	$-0.523868\pi$
$827$	−4.30863	−0.149826	−0.0749129	+	0.997190i	$0.523868\pi$
$828$	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	$-0.576289\pi$
$839$	−13.7517	−0.474760	−0.237380	+	0.971417i	$0.576289\pi$
$840$	−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	$-0.506446\pi$
$853$	−1.18274	−0.0404962	−0.0202481	+	0.999795i	$0.506446\pi$
$854$	−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	$-0.349445\pi$
$859$	26.7028	0.911086	0.455543	+	0.890214i	$0.349445\pi$
$860$	19.4683	0.663863
$861$	16.1434	0.550166
$862$	53.6635	1.82779
$863$	−49.8431	−1.69668	−0.848339	−	0.529453i	$-0.822397\pi$
$863$	−49.8431	−1.69668	−0.848339	+	0.529453i	$0.822397\pi$
$864$	−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	$-0.535607\pi$
$883$	−6.63424	−0.223260	−0.111630	+	0.993750i	$0.535607\pi$
$884$	−6.35695	−0.213807
$885$	76.0734	2.55718
$886$	13.1503	0.441794
$887$	−56.2809	−1.88973	−0.944864	−	0.327463i	$-0.893806\pi$
$887$	−56.2809	−1.88973	−0.944864	+	0.327463i	$0.893806\pi$
$888$	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	$-0.439526\pi$
$907$	11.3747	0.377691	0.188845	+	0.982007i	$0.439526\pi$
$908$	−27.6044	−0.916083
$909$	−17.1891	−0.570126
$910$	−8.17583	−0.271026
$911$	30.2350	1.00173	0.500865	−	0.865526i	$-0.333015\pi$
$911$	30.2350	1.00173	0.500865	+	0.865526i	$0.333015\pi$
$912$	−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	$-0.171444\pi$
$919$	52.0463	1.71685	0.858424	+	0.512941i	$0.171444\pi$
$920$	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	$-0.585278\pi$
$929$	−16.1368	−0.529430	−0.264715	+	0.964327i	$0.585278\pi$
$930$	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	$-0.496206\pi$
$941$	0.731285	0.0238392	0.0119196	+	0.999929i	$0.496206\pi$
$942$	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	$-0.605638\pi$
$947$	−20.0528	−0.651628	−0.325814	+	0.945434i	$0.605638\pi$
$948$	−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	$-0.648722\pi$
$953$	−27.8089	−0.900817	−0.450409	+	0.892823i	$0.648722\pi$
$954$	−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	$-0.296010\pi$
$977$	37.3759	1.19576	0.597880	+	0.801585i	$0.296010\pi$
$978$	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	$-0.615829\pi$
$983$	−22.3176	−0.711822	−0.355911	+	0.934520i	$0.615829\pi$
$984$	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	$-0.295911\pi$
$991$	37.6583	1.19626	0.598128	+	0.801401i	$0.295911\pi$
$992$	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.p.1.37	✓	168
97.96	even	2		9409.2.a.q.1.37	yes	168

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

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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