LMFDB - Embedded newform 9409.2.a.q.1.88

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			1.88
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)

$f(q)$	$=$	\(q+0.182861 q^{2} +0.212177 q^{3} -1.96656 q^{4} +1.31754 q^{5} +0.0387989 q^{6} -0.932372 q^{7} -0.725328 q^{8} -2.95498 q^{9} +0.240927 q^{10} -0.156648 q^{11} -0.417260 q^{12} -5.64631 q^{13} -0.170494 q^{14} +0.279553 q^{15} +3.80049 q^{16} +4.23788 q^{17} -0.540350 q^{18} -6.19567 q^{19} -2.59103 q^{20} -0.197828 q^{21} -0.0286448 q^{22} +8.05860 q^{23} -0.153898 q^{24} -3.26408 q^{25} -1.03249 q^{26} -1.26351 q^{27} +1.83357 q^{28} -4.32772 q^{29} +0.0511193 q^{30} +1.97001 q^{31} +2.14562 q^{32} -0.0332372 q^{33} +0.774941 q^{34} -1.22844 q^{35} +5.81115 q^{36} -3.36489 q^{37} -1.13295 q^{38} -1.19802 q^{39} -0.955651 q^{40} +4.91958 q^{41} -0.0361750 q^{42} -7.62311 q^{43} +0.308058 q^{44} -3.89331 q^{45} +1.47360 q^{46} +5.05439 q^{47} +0.806378 q^{48} -6.13068 q^{49} -0.596872 q^{50} +0.899182 q^{51} +11.1038 q^{52} -1.53542 q^{53} -0.231047 q^{54} -0.206390 q^{55} +0.676276 q^{56} -1.31458 q^{57} -0.791371 q^{58} -3.79302 q^{59} -0.549758 q^{60} -0.386484 q^{61} +0.360237 q^{62} +2.75514 q^{63} -7.20863 q^{64} -7.43926 q^{65} -0.00607778 q^{66} -2.31208 q^{67} -8.33405 q^{68} +1.70985 q^{69} -0.224633 q^{70} -9.43418 q^{71} +2.14333 q^{72} -6.50580 q^{73} -0.615306 q^{74} -0.692565 q^{75} +12.1842 q^{76} +0.146054 q^{77} -0.219071 q^{78} +5.96451 q^{79} +5.00731 q^{80} +8.59685 q^{81} +0.899598 q^{82} -12.1863 q^{83} +0.389042 q^{84} +5.58358 q^{85} -1.39397 q^{86} -0.918245 q^{87} +0.113621 q^{88} +13.8185 q^{89} -0.711934 q^{90} +5.26447 q^{91} -15.8477 q^{92} +0.417991 q^{93} +0.924249 q^{94} -8.16306 q^{95} +0.455252 q^{96} -1.12106 q^{98} +0.462892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.182861	0.129302	0.0646510	−	0.997908i	$-0.479407\pi$
$2$	0.182861	0.129302	0.0646510	+	0.997908i	$0.479407\pi$
$3$	0.212177	0.122501	0.0612504	−	0.998122i	$-0.480491\pi$
$3$	0.212177	0.122501	0.0612504	+	0.998122i	$0.480491\pi$
$4$	−1.96656	−0.983281
$5$	1.31754	0.589223	0.294612	−	0.955617i	$-0.404810\pi$
$5$	1.31754	0.589223	0.294612	+	0.955617i	$0.404810\pi$
$6$	0.0387989	0.0158396
$7$	−0.932372	−0.352404	−0.176202	−	0.984354i	$-0.556381\pi$
$7$	−0.932372	−0.352404	−0.176202	+	0.984354i	$0.556381\pi$
$8$	−0.725328	−0.256442
$9$	−2.95498	−0.984994
$10$	0.240927	0.0761878
$11$	−0.156648	−0.0472312	−0.0236156	−	0.999721i	$-0.507518\pi$
$11$	−0.156648	−0.0472312	−0.0236156	+	0.999721i	$0.507518\pi$
$12$	−0.417260	−0.120453
$13$	−5.64631	−1.56601	−0.783003	−	0.622018i	$-0.786313\pi$
$13$	−5.64631	−1.56601	−0.783003	+	0.622018i	$0.786313\pi$
$14$	−0.170494	−0.0455665
$15$	0.279553	0.0721803
$16$	3.80049	0.950122
$17$	4.23788	1.02784	0.513918	−	0.857839i	$-0.328194\pi$
$17$	4.23788	1.02784	0.513918	+	0.857839i	$0.328194\pi$
$18$	−0.540350	−0.127362
$19$	−6.19567	−1.42139	−0.710693	−	0.703503i	$-0.751618\pi$
$19$	−6.19567	−1.42139	−0.710693	+	0.703503i	$0.751618\pi$
$20$	−2.59103	−0.579372
$21$	−0.197828	−0.0431697
$22$	−0.0286448	−0.00610709
$23$	8.05860	1.68033	0.840167	−	0.542327i	$-0.182457\pi$
$23$	8.05860	1.68033	0.840167	+	0.542327i	$0.182457\pi$
$24$	−0.153898	−0.0314144
$25$	−3.26408	−0.652816
$26$	−1.03249	−0.202488
$27$	−1.26351	−0.243163
$28$	1.83357	0.346512
$29$	−4.32772	−0.803638	−0.401819	−	0.915719i	$-0.631622\pi$
$29$	−4.32772	−0.803638	−0.401819	+	0.915719i	$0.631622\pi$
$30$	0.0511193	0.00933306
$31$	1.97001	0.353824	0.176912	−	0.984227i	$-0.443389\pi$
$31$	1.97001	0.353824	0.176912	+	0.984227i	$0.443389\pi$
$32$	2.14562	0.379295
$33$	−0.0332372	−0.00578585
$34$	0.774941	0.132901
$35$	−1.22844	−0.207644
$36$	5.81115	0.968525
$37$	−3.36489	−0.553184	−0.276592	−	0.960987i	$-0.589205\pi$
$37$	−3.36489	−0.553184	−0.276592	+	0.960987i	$0.589205\pi$
$38$	−1.13295	−0.183788
$39$	−1.19802	−0.191837
$40$	−0.955651	−0.151102
$41$	4.91958	0.768309	0.384155	−	0.923269i	$-0.374493\pi$
$41$	4.91958	0.768309	0.384155	+	0.923269i	$0.374493\pi$
$42$	−0.0361750	−0.00558193
$43$	−7.62311	−1.16251	−0.581257	−	0.813720i	$-0.697439\pi$
$43$	−7.62311	−1.16251	−0.581257	+	0.813720i	$0.697439\pi$
$44$	0.308058	0.0464415
$45$	−3.89331	−0.580381
$46$	1.47360	0.217271
$47$	5.05439	0.737258	0.368629	−	0.929577i	$-0.379827\pi$
$47$	5.05439	0.737258	0.368629	+	0.929577i	$0.379827\pi$
$48$	0.806378	0.116391
$49$	−6.13068	−0.875812
$50$	−0.596872	−0.0844105
$51$	0.899182	0.125911
$52$	11.1038	1.53982
$53$	−1.53542	−0.210907	−0.105453	−	0.994424i	$-0.533629\pi$
$53$	−1.53542	−0.210907	−0.105453	+	0.994424i	$0.533629\pi$
$54$	−0.231047	−0.0314415
$55$	−0.206390	−0.0278297
$56$	0.676276	0.0903712
$57$	−1.31458	−0.174121
$58$	−0.791371	−0.103912
$59$	−3.79302	−0.493809	−0.246904	−	0.969040i	$-0.579413\pi$
$59$	−3.79302	−0.493809	−0.246904	+	0.969040i	$0.579413\pi$
$60$	−0.549758	−0.0709735
$61$	−0.386484	−0.0494843	−0.0247421	−	0.999694i	$-0.507876\pi$
$61$	−0.386484	−0.0494843	−0.0247421	+	0.999694i	$0.507876\pi$
$62$	0.360237	0.0457501
$63$	2.75514	0.347115
$64$	−7.20863	−0.901079
$65$	−7.43926	−0.922727
$66$	−0.00607778	−0.000748123 0
$67$	−2.31208	−0.282465	−0.141233	−	0.989976i	$-0.545107\pi$
$67$	−2.31208	−0.282465	−0.141233	+	0.989976i	$0.545107\pi$
$68$	−8.33405	−1.01065
$69$	1.70985	0.205842
$70$	−0.224633	−0.0268488
$71$	−9.43418	−1.11963	−0.559816	−	0.828617i	$-0.689128\pi$
$71$	−9.43418	−1.11963	−0.559816	+	0.828617i	$0.689128\pi$
$72$	2.14333	0.252594
$73$	−6.50580	−0.761446	−0.380723	−	0.924689i	$-0.624325\pi$
$73$	−6.50580	−0.761446	−0.380723	+	0.924689i	$0.624325\pi$
$74$	−0.615306	−0.0715278
$75$	−0.692565	−0.0799705
$76$	12.1842	1.39762
$77$	0.146054	0.0166444
$78$	−0.219071	−0.0248049
$79$	5.96451	0.671060	0.335530	−	0.942030i	$-0.391085\pi$
$79$	5.96451	0.671060	0.335530	+	0.942030i	$0.391085\pi$
$80$	5.00731	0.559834
$81$	8.59685	0.955206
$82$	0.899598	0.0993439
$83$	−12.1863	−1.33762	−0.668810	−	0.743433i	$-0.733196\pi$
$83$	−12.1863	−1.33762	−0.668810	+	0.743433i	$0.733196\pi$
$84$	0.389042	0.0424479
$85$	5.58358	0.605625
$86$	−1.39397	−0.150315
$87$	−0.918245	−0.0984462
$88$	0.113621	0.0121121
$89$	13.8185	1.46476	0.732380	−	0.680896i	$-0.238410\pi$
$89$	13.8185	1.46476	0.732380	+	0.680896i	$0.238410\pi$
$90$	−0.711934	−0.0750444
$91$	5.26447	0.551866
$92$	−15.8477	−1.65224
$93$	0.417991	0.0433437
$94$	0.924249	0.0953290
$95$	−8.16306	−0.837513
$96$	0.455252	0.0464639
$97$	0	0
$97$	0	0
$98$	−1.12106	−0.113244
$99$	0.462892	0.0465224
$100$	6.41902	0.641902
$101$	14.4677	1.43959	0.719795	−	0.694186i	$-0.244236\pi$
$101$	14.4677	1.43959	0.719795	+	0.694186i	$0.244236\pi$
$102$	0.164425	0.0162805
$103$	−2.03065	−0.200086	−0.100043	−	0.994983i	$-0.531898\pi$
$103$	−2.03065	−0.200086	−0.100043	+	0.994983i	$0.531898\pi$
$104$	4.09543	0.401590
$105$	−0.260647	−0.0254366
$106$	−0.280769	−0.0272707
$107$	−16.6070	−1.60546	−0.802730	−	0.596343i	$-0.796620\pi$
$107$	−16.6070	−1.60546	−0.802730	+	0.596343i	$0.796620\pi$
$108$	2.48478	0.239098
$109$	14.7502	1.41281	0.706406	−	0.707806i	$-0.250315\pi$
$109$	14.7502	1.41281	0.706406	+	0.707806i	$0.250315\pi$
$110$	−0.0377407	−0.00359844
$111$	−0.713953	−0.0677654
$112$	−3.54347	−0.334827
$113$	−14.9769	−1.40891	−0.704453	−	0.709751i	$-0.748807\pi$
$113$	−14.9769	−1.40891	−0.704453	+	0.709751i	$0.748807\pi$
$114$	−0.240386	−0.0225142
$115$	10.6176	0.990092
$116$	8.51074	0.790202
$117$	16.6847	1.54251
$118$	−0.693594	−0.0638505
$119$	−3.95128	−0.362213
$120$	−0.202768	−0.0185101
$121$	−10.9755	−0.997769
$122$	−0.0706728	−0.00639842
$123$	1.04382	0.0941184
$124$	−3.87414	−0.347908
$125$	−10.8883	−0.973877
$126$	0.503807	0.0448827
$127$	9.80034	0.869639	0.434820	−	0.900518i	$-0.356812\pi$
$127$	9.80034	0.869639	0.434820	+	0.900518i	$0.356812\pi$
$128$	−5.60941	−0.495806
$129$	−1.61745	−0.142409
$130$	−1.36035	−0.119310
$131$	14.3773	1.25615	0.628076	−	0.778152i	$-0.283843\pi$
$131$	14.3773	1.25615	0.628076	+	0.778152i	$0.283843\pi$
$132$	0.0653630	0.00568912
$133$	5.77667	0.500901
$134$	−0.422788	−0.0365233
$135$	−1.66473	−0.143277
$136$	−3.07385	−0.263581
$137$	3.10358	0.265157	0.132578	−	0.991173i	$-0.457674\pi$
$137$	3.10358	0.265157	0.132578	+	0.991173i	$0.457674\pi$
$138$	0.312665	0.0266158
$139$	9.93757	0.842894	0.421447	−	0.906853i	$-0.361522\pi$
$139$	9.93757	0.842894	0.421447	+	0.906853i	$0.361522\pi$
$140$	2.41580	0.204173
$141$	1.07243	0.0903147
$142$	−1.72514	−0.144771
$143$	0.884484	0.0739643
$144$	−11.2304	−0.935865
$145$	−5.70196	−0.473522
$146$	−1.18965	−0.0984565
$147$	−1.30079	−0.107288
$148$	6.61726	0.543935
$149$	7.01173	0.574423	0.287212	−	0.957867i	$-0.407272\pi$
$149$	7.01173	0.574423	0.287212	+	0.957867i	$0.407272\pi$
$150$	−0.126643	−0.0103403
$151$	13.7266	1.11705	0.558526	−	0.829487i	$-0.311367\pi$
$151$	13.7266	1.11705	0.558526	+	0.829487i	$0.311367\pi$
$152$	4.49390	0.364503
$153$	−12.5228	−1.01241
$154$	0.0267076	0.00215216
$155$	2.59557	0.208481
$156$	2.35598	0.188630
$157$	9.67217	0.771923	0.385962	−	0.922515i	$-0.373870\pi$
$157$	9.67217	0.771923	0.385962	+	0.922515i	$0.373870\pi$
$158$	1.09067	0.0867694
$159$	−0.325782	−0.0258362
$160$	2.82694	0.223489
$161$	−7.51362	−0.592156
$162$	1.57203	0.123510
$163$	17.4563	1.36728	0.683640	−	0.729819i	$-0.260396\pi$
$163$	17.4563	1.36728	0.683640	+	0.729819i	$0.260396\pi$
$164$	−9.67466	−0.755464
$165$	−0.0437914	−0.00340916
$166$	−2.22840	−0.172957
$167$	−16.9851	−1.31434	−0.657172	−	0.753741i	$-0.728247\pi$
$167$	−16.9851	−1.31434	−0.657172	+	0.753741i	$0.728247\pi$
$168$	0.143491	0.0110705
$169$	18.8809	1.45237
$170$	1.02102	0.0783085
$171$	18.3081	1.40006
$172$	14.9913	1.14308
$173$	12.0005	0.912384	0.456192	−	0.889881i	$-0.349213\pi$
$173$	12.0005	0.912384	0.456192	+	0.889881i	$0.349213\pi$
$174$	−0.167911	−0.0127293
$175$	3.04334	0.230055
$176$	−0.595339	−0.0448754
$177$	−0.804792	−0.0604919
$178$	2.52686	0.189396
$179$	23.7165	1.77265	0.886326	−	0.463062i	$-0.153249\pi$
$179$	23.7165	1.77265	0.886326	+	0.463062i	$0.153249\pi$
$180$	7.65644	0.570677
$181$	10.3002	0.765605	0.382803	−	0.923830i	$-0.374959\pi$
$181$	10.3002	0.765605	0.382803	+	0.923830i	$0.374959\pi$
$182$	0.962664	0.0713574
$183$	−0.0820033	−0.00606186
$184$	−5.84513	−0.430909
$185$	−4.43338	−0.325949
$186$	0.0764342	0.00560442
$187$	−0.663855	−0.0485459
$188$	−9.93977	−0.724932
$189$	1.17806	0.0856916
$190$	−1.49270	−0.108292
$191$	−17.0133	−1.23104	−0.615521	−	0.788121i	$-0.711054\pi$
$191$	−17.0133	−1.23104	−0.615521	+	0.788121i	$0.711054\pi$
$192$	−1.52951	−0.110383
$193$	19.6564	1.41490	0.707449	−	0.706764i	$-0.249846\pi$
$193$	19.6564	1.41490	0.707449	+	0.706764i	$0.249846\pi$
$194$	0	0
$195$	−1.57844	−0.113035
$196$	12.0564	0.861169
$197$	−9.39677	−0.669492	−0.334746	−	0.942308i	$-0.608651\pi$
$197$	−9.39677	−0.669492	−0.334746	+	0.942308i	$0.608651\pi$
$198$	0.0846448	0.00601544
$199$	3.82942	0.271460	0.135730	−	0.990746i	$-0.456662\pi$
$199$	3.82942	0.271460	0.135730	+	0.990746i	$0.456662\pi$
$200$	2.36753	0.167410
$201$	−0.490571	−0.0346022
$202$	2.64558	0.186142
$203$	4.03505	0.283205
$204$	−1.76830	−0.123806
$205$	6.48175	0.452705
$206$	−0.371327	−0.0258716
$207$	−23.8130	−1.65512
$208$	−21.4588	−1.48790
$209$	0.970540	0.0671337
$210$	−0.0476622	−0.00328900
$211$	12.0717	0.831048	0.415524	−	0.909582i	$-0.363598\pi$
$211$	12.0717	0.831048	0.415524	+	0.909582i	$0.363598\pi$
$212$	3.01950	0.207380
$213$	−2.00172	−0.137156
$214$	−3.03677	−0.207589
$215$	−10.0438	−0.684980
$216$	0.916462	0.0623573
$217$	−1.83678	−0.124689
$218$	2.69723	0.182680
$219$	−1.38038	−0.0932777
$220$	0.405880	0.0273644
$221$	−23.9284	−1.60960
$222$	−0.130554	−0.00876221
$223$	−17.7555	−1.18899	−0.594497	−	0.804097i	$-0.702649\pi$
$223$	−17.7555	−1.18899	−0.594497	+	0.804097i	$0.702649\pi$
$224$	−2.00051	−0.133665
$225$	9.64530	0.643020
$226$	−2.73868	−0.182174
$227$	−3.70215	−0.245720	−0.122860	−	0.992424i	$-0.539207\pi$
$227$	−3.70215	−0.245720	−0.122860	+	0.992424i	$0.539207\pi$
$228$	2.58521	0.171210
$229$	−21.0058	−1.38810	−0.694052	−	0.719925i	$-0.744176\pi$
$229$	−21.0058	−1.38810	−0.694052	+	0.719925i	$0.744176\pi$
$230$	1.94153	0.128021
$231$	0.0309894	0.00203895
$232$	3.13902	0.206087
$233$	−4.16366	−0.272770	−0.136385	−	0.990656i	$-0.543548\pi$
$233$	−4.16366	−0.272770	−0.136385	+	0.990656i	$0.543548\pi$
$234$	3.05099	0.199449
$235$	6.65937	0.434410
$236$	7.45920	0.485553
$237$	1.26553	0.0822053
$238$	−0.722534	−0.0468349
$239$	−1.24051	−0.0802419	−0.0401209	−	0.999195i	$-0.512774\pi$
$239$	−1.24051	−0.0802419	−0.0401209	+	0.999195i	$0.512774\pi$
$240$	1.06244	0.0685801
$241$	−13.5826	−0.874932	−0.437466	−	0.899235i	$-0.644124\pi$
$241$	−13.5826	−0.874932	−0.437466	+	0.899235i	$0.644124\pi$
$242$	−2.00698	−0.129014
$243$	5.61460	0.360177
$244$	0.760045	0.0486569
$245$	−8.07744	−0.516048
$246$	0.190874	0.0121697
$247$	34.9827	2.22590
$248$	−1.42890	−0.0907354
$249$	−2.58566	−0.163859
$250$	−1.99104	−0.125924
$251$	22.2238	1.40275	0.701376	−	0.712792i	$-0.252570\pi$
$251$	22.2238	1.40275	0.701376	+	0.712792i	$0.252570\pi$
$252$	−5.41816	−0.341312
$253$	−1.26236	−0.0793642
$254$	1.79210	0.112446
$255$	1.18471	0.0741895
$256$	13.3915	0.836970
$257$	26.9559	1.68146	0.840731	−	0.541452i	$-0.182125\pi$
$257$	26.9559	1.68146	0.840731	+	0.541452i	$0.182125\pi$
$258$	−0.295769	−0.0184138
$259$	3.13733	0.194944
$260$	14.6298	0.907300
$261$	12.7883	0.791578
$262$	2.62905	0.162423
$263$	7.72216	0.476169	0.238084	−	0.971244i	$-0.423480\pi$
$263$	7.72216	0.476169	0.238084	+	0.971244i	$0.423480\pi$
$264$	0.0241079	0.00148374
$265$	−2.02299	−0.124271
$266$	1.05633	0.0647676
$267$	2.93198	0.179434
$268$	4.54684	0.277743
$269$	6.56976	0.400565	0.200283	−	0.979738i	$-0.435814\pi$
$269$	6.56976	0.400565	0.200283	+	0.979738i	$0.435814\pi$
$270$	−0.304414	−0.0185261
$271$	10.2463	0.622419	0.311209	−	0.950341i	$-0.399266\pi$
$271$	10.2463	0.622419	0.311209	+	0.950341i	$0.399266\pi$
$272$	16.1060	0.976570
$273$	1.11700	0.0676040
$274$	0.567523	0.0342853
$275$	0.511312	0.0308333
$276$	−3.36253	−0.202401
$277$	7.79839	0.468560	0.234280	−	0.972169i	$-0.424727\pi$
$277$	7.79839	0.468560	0.234280	+	0.972169i	$0.424727\pi$
$278$	1.81719	0.108988
$279$	−5.82133	−0.348514
$280$	0.891023	0.0532488
$281$	30.5323	1.82141	0.910703	−	0.413062i	$-0.135541\pi$
$281$	30.5323	1.82141	0.910703	+	0.413062i	$0.135541\pi$
$282$	0.196105	0.0116779
$283$	4.04559	0.240486	0.120243	−	0.992745i	$-0.461633\pi$
$283$	4.04559	0.240486	0.120243	+	0.992745i	$0.461633\pi$
$284$	18.5529	1.10091
$285$	−1.73202	−0.102596
$286$	0.161737	0.00956373
$287$	−4.58688	−0.270755
$288$	−6.34026	−0.373603
$289$	0.959606	0.0564474
$290$	−1.04266	−0.0612274
$291$	0	0
$292$	12.7941	0.748715
$293$	−20.9258	−1.22250	−0.611250	−	0.791437i	$-0.709333\pi$
$293$	−20.9258	−1.22250	−0.611250	+	0.791437i	$0.709333\pi$
$294$	−0.237864	−0.0138725
$295$	−4.99746	−0.290963
$296$	2.44065	0.141860
$297$	0.197927	0.0114849
$298$	1.28217	0.0742741
$299$	−45.5014	−2.63141
$300$	1.36197	0.0786334
$301$	7.10758	0.409674
$302$	2.51005	0.144437
$303$	3.06972	0.176351
$304$	−23.5466	−1.35049
$305$	−0.509210	−0.0291573
$306$	−2.28994	−0.130907
$307$	9.32737	0.532341	0.266171	−	0.963926i	$-0.414242\pi$
$307$	9.32737	0.532341	0.266171	+	0.963926i	$0.414242\pi$
$308$	−0.287225	−0.0163662
$309$	−0.430859	−0.0245107
$310$	0.474628	0.0269570
$311$	−29.4308	−1.66887	−0.834434	−	0.551108i	$-0.814205\pi$
$311$	−29.4308	−1.66887	−0.834434	+	0.551108i	$0.814205\pi$
$312$	0.868959	0.0491951
$313$	9.74302	0.550708	0.275354	−	0.961343i	$-0.411205\pi$
$313$	9.74302	0.550708	0.275354	+	0.961343i	$0.411205\pi$
$314$	1.76866	0.0998112
$315$	3.63002	0.204528
$316$	−11.7296	−0.659840
$317$	27.7899	1.56083	0.780417	−	0.625260i	$-0.215007\pi$
$317$	27.7899	1.56083	0.780417	+	0.625260i	$0.215007\pi$
$318$	−0.0595728	−0.00334068
$319$	0.677929	0.0379568
$320$	−9.49768	−0.530936
$321$	−3.52363	−0.196670
$322$	−1.37395	−0.0765670
$323$	−26.2565	−1.46095
$324$	−16.9062	−0.939236
$325$	18.4300	1.02231
$326$	3.19207	0.176792
$327$	3.12966	0.173071
$328$	−3.56831	−0.197027
$329$	−4.71257	−0.259812
$330$	−0.00800773	−0.000440811 0
$331$	25.4454	1.39861	0.699304	−	0.714825i	$-0.253494\pi$
$331$	25.4454	1.39861	0.699304	+	0.714825i	$0.253494\pi$
$332$	23.9651	1.31526
$333$	9.94317	0.544883
$334$	−3.10590	−0.169947
$335$	−3.04626	−0.166435
$336$	−0.751845	−0.0410165
$337$	23.3206	1.27035	0.635177	−	0.772366i	$-0.280927\pi$
$337$	23.3206	1.27035	0.635177	+	0.772366i	$0.280927\pi$
$338$	3.45257	0.187795
$339$	−3.17775	−0.172592
$340$	−10.9805	−0.595499
$341$	−0.308598	−0.0167115
$342$	3.34783	0.181030
$343$	12.2427	0.661043
$344$	5.52926	0.298118
$345$	2.25281	0.121287
$346$	2.19443	0.117973
$347$	22.2963	1.19693	0.598463	−	0.801150i	$-0.295778\pi$
$347$	22.2963	1.19693	0.598463	+	0.801150i	$0.295778\pi$
$348$	1.80579	0.0968003
$349$	−29.0495	−1.55498	−0.777492	−	0.628892i	$-0.783509\pi$
$349$	−29.0495	−1.55498	−0.777492	+	0.628892i	$0.783509\pi$
$350$	0.556507	0.0297466
$351$	7.13419	0.380795
$352$	−0.336107	−0.0179146
$353$	9.11949	0.485382	0.242691	−	0.970104i	$-0.421970\pi$
$353$	9.11949	0.485382	0.242691	+	0.970104i	$0.421970\pi$
$354$	−0.147165	−0.00782173
$355$	−12.4299	−0.659713
$356$	−27.1750	−1.44027
$357$	−0.838372	−0.0443714
$358$	4.33681	0.229208
$359$	−14.7337	−0.777617	−0.388809	−	0.921319i	$-0.627113\pi$
$359$	−14.7337	−0.777617	−0.388809	+	0.921319i	$0.627113\pi$
$360$	2.82393	0.148834
$361$	19.3864	1.02034
$362$	1.88350	0.0989943
$363$	−2.32875	−0.122227
$364$	−10.3529	−0.542639
$365$	−8.57167	−0.448662
$366$	−0.0149952	−0.000783811 0
$367$	−6.73927	−0.351787	−0.175893	−	0.984409i	$-0.556281\pi$
$367$	−6.73927	−0.351787	−0.175893	+	0.984409i	$0.556281\pi$
$368$	30.6266	1.59652
$369$	−14.5373	−0.756779
$370$	−0.810691	−0.0421458
$371$	1.43159	0.0743242
$372$	−0.822005	−0.0426190
$373$	4.99549	0.258657	0.129328	−	0.991602i	$-0.458718\pi$
$373$	4.99549	0.258657	0.129328	+	0.991602i	$0.458718\pi$
$374$	−0.121393	−0.00627709
$375$	−2.31025	−0.119301
$376$	−3.66609	−0.189064
$377$	24.4357	1.25850
$378$	0.215422	0.0110801
$379$	−31.3682	−1.61128	−0.805638	−	0.592409i	$-0.798177\pi$
$379$	−31.3682	−1.61128	−0.805638	+	0.592409i	$0.798177\pi$
$380$	16.0532	0.823510
$381$	2.07941	0.106531
$382$	−3.11107	−0.159176
$383$	−21.3109	−1.08894	−0.544468	−	0.838782i	$-0.683268\pi$
$383$	−21.3109	−1.08894	−0.544468	+	0.838782i	$0.683268\pi$
$384$	−1.19019	−0.0607367
$385$	0.192433	0.00980728
$386$	3.59438	0.182949
$387$	22.5262	1.14507
$388$	0	0
$389$	12.9660	0.657402	0.328701	−	0.944434i	$-0.393389\pi$
$389$	12.9660	0.657402	0.328701	+	0.944434i	$0.393389\pi$
$390$	−0.288635	−0.0146156
$391$	34.1514	1.72711
$392$	4.44676	0.224595
$393$	3.05054	0.153879
$394$	−1.71830	−0.0865667
$395$	7.85849	0.395404
$396$	−0.910306	−0.0457446
$397$	31.8619	1.59910	0.799551	−	0.600598i	$-0.205071\pi$
$397$	31.8619	1.59910	0.799551	+	0.600598i	$0.205071\pi$
$398$	0.700251	0.0351004
$399$	1.22568	0.0613608
$400$	−12.4051	−0.620255
$401$	26.4108	1.31889	0.659446	−	0.751752i	$-0.270791\pi$
$401$	26.4108	1.31889	0.659446	+	0.751752i	$0.270791\pi$
$402$	−0.0897061	−0.00447414
$403$	−11.1233	−0.554090
$404$	−28.4516	−1.41552
$405$	11.3267	0.562829
$406$	0.737852	0.0366190
$407$	0.527103	0.0261275
$408$	−0.652202	−0.0322888
$409$	22.0013	1.08789	0.543947	−	0.839120i	$-0.316929\pi$
$409$	22.0013	1.08789	0.543947	+	0.839120i	$0.316929\pi$
$410$	1.18526	0.0585357
$411$	0.658510	0.0324819
$412$	3.99341	0.196741
$413$	3.53650	0.174020
$414$	−4.35447	−0.214010
$415$	−16.0560	−0.788157
$416$	−12.1148	−0.593978
$417$	2.10853	0.103255
$418$	0.177474	0.00868052
$419$	−30.8265	−1.50597	−0.752987	−	0.658035i	$-0.771388\pi$
$419$	−30.8265	−1.50597	−0.752987	+	0.658035i	$0.771388\pi$
$420$	0.512579	0.0250113
$421$	−23.9820	−1.16881	−0.584406	−	0.811461i	$-0.698672\pi$
$421$	−23.9820	−1.16881	−0.584406	+	0.811461i	$0.698672\pi$
$422$	2.20743	0.107456
$423$	−14.9356	−0.726195
$424$	1.11369	0.0540854
$425$	−13.8328	−0.670988
$426$	−0.366036	−0.0177345
$427$	0.360347	0.0174384
$428$	32.6587	1.57862
$429$	0.187668	0.00906068
$430$	−1.83661	−0.0885693
$431$	−7.62142	−0.367111	−0.183555	−	0.983009i	$-0.558761\pi$
$431$	−7.62142	−0.367111	−0.183555	+	0.983009i	$0.558761\pi$
$432$	−4.80197	−0.231035
$433$	−26.2279	−1.26043	−0.630216	−	0.776419i	$-0.717034\pi$
$433$	−26.2279	−1.26043	−0.630216	+	0.776419i	$0.717034\pi$
$434$	−0.335875	−0.0161225
$435$	−1.20983	−0.0580068
$436$	−29.0072	−1.38919
$437$	−49.9285	−2.38840
$438$	−0.252418	−0.0120610
$439$	−7.14303	−0.340918	−0.170459	−	0.985365i	$-0.554525\pi$
$439$	−7.14303	−0.340918	−0.170459	+	0.985365i	$0.554525\pi$
$440$	0.149701	0.00713671
$441$	18.1160	0.862669
$442$	−4.37556	−0.208124
$443$	1.98411	0.0942681	0.0471341	−	0.998889i	$-0.484991\pi$
$443$	1.98411	0.0942681	0.0471341	+	0.998889i	$0.484991\pi$
$444$	1.40403	0.0666325
$445$	18.2065	0.863070
$446$	−3.24678	−0.153740
$447$	1.48773	0.0703673
$448$	6.72113	0.317543
$449$	−13.2638	−0.625958	−0.312979	−	0.949760i	$-0.601327\pi$
$449$	−13.2638	−0.625958	−0.312979	+	0.949760i	$0.601327\pi$
$450$	1.76375	0.0831438
$451$	−0.770642	−0.0362881
$452$	29.4529	1.38535
$453$	2.91247	0.136840
$454$	−0.676978	−0.0317721
$455$	6.93616	0.325172
$456$	0.953504	0.0446519
$457$	29.0979	1.36114	0.680571	−	0.732683i	$-0.261732\pi$
$457$	29.0979	1.36114	0.680571	+	0.732683i	$0.261732\pi$
$458$	−3.84114	−0.179485
$459$	−5.35461	−0.249932
$460$	−20.8801	−0.973539
$461$	−27.4520	−1.27857	−0.639283	−	0.768971i	$-0.720769\pi$
$461$	−27.4520	−1.27857	−0.639283	+	0.768971i	$0.720769\pi$
$462$	0.00566675	0.000263641 0
$463$	20.0811	0.933250	0.466625	−	0.884455i	$-0.345470\pi$
$463$	20.0811	0.933250	0.466625	+	0.884455i	$0.345470\pi$
$464$	−16.4475	−0.763554
$465$	0.550721	0.0255391
$466$	−0.761370	−0.0352698
$467$	−0.351390	−0.0162604	−0.00813020	−	0.999967i	$-0.502588\pi$
$467$	−0.351390	−0.0162604	−0.00813020	+	0.999967i	$0.502588\pi$
$468$	−32.8116	−1.51672
$469$	2.15572	0.0995417
$470$	1.21774	0.0561700
$471$	2.05222	0.0945611
$472$	2.75118	0.126633
$473$	1.19415	0.0549069
$474$	0.231417	0.0106293
$475$	20.2232	0.927903
$476$	7.77043	0.356157
$477$	4.53715	0.207742
$478$	−0.226840	−0.0103754
$479$	−7.94575	−0.363051	−0.181525	−	0.983386i	$-0.558103\pi$
$479$	−7.94575	−0.363051	−0.181525	+	0.983386i	$0.558103\pi$
$480$	0.599814	0.0273776
$481$	18.9992	0.866289
$482$	−2.48372	−0.113131
$483$	−1.59422	−0.0725395
$484$	21.5839	0.981087
$485$	0	0
$486$	1.02669	0.0465716
$487$	−26.3079	−1.19212	−0.596062	−	0.802938i	$-0.703269\pi$
$487$	−26.3079	−1.19212	−0.596062	+	0.802938i	$0.703269\pi$
$488$	0.280328	0.0126899
$489$	3.70383	0.167493
$490$	−1.47705	−0.0667261
$491$	−25.3483	−1.14395	−0.571976	−	0.820270i	$-0.693823\pi$
$491$	−25.3483	−1.14395	−0.571976	+	0.820270i	$0.693823\pi$
$492$	−2.05274	−0.0925449
$493$	−18.3404	−0.826008
$494$	6.39697	0.287813
$495$	0.609880	0.0274121
$496$	7.48699	0.336176
$497$	8.79617	0.394562
$498$	−0.472816	−0.0211874
$499$	−11.7544	−0.526198	−0.263099	−	0.964769i	$-0.584745\pi$
$499$	−11.7544	−0.526198	−0.263099	+	0.964769i	$0.584745\pi$
$500$	21.4125	0.957595
$501$	−3.60385	−0.161008
$502$	4.06385	0.181379
$503$	40.0929	1.78765	0.893826	−	0.448414i	$-0.148011\pi$
$503$	40.0929	1.78765	0.893826	+	0.448414i	$0.148011\pi$
$504$	−1.99838	−0.0890150
$505$	19.0618	0.848240
$506$	−0.230837	−0.0102620
$507$	4.00609	0.177917
$508$	−19.2730	−0.855100
$509$	9.10217	0.403447	0.201723	−	0.979443i	$-0.435346\pi$
$509$	9.10217	0.403447	0.201723	+	0.979443i	$0.435346\pi$
$510$	0.216637	0.00959285
$511$	6.06582	0.268336
$512$	13.6676	0.604028
$513$	7.82831	0.345628
$514$	4.92918	0.217417
$515$	−2.67547	−0.117895
$516$	3.18082	0.140028
$517$	−0.791760	−0.0348216
$518$	0.573694	0.0252067
$519$	2.54624	0.111768
$520$	5.39591	0.236626
$521$	27.6045	1.20937	0.604687	−	0.796463i	$-0.293298\pi$
$521$	27.6045	1.20937	0.604687	+	0.796463i	$0.293298\pi$
$522$	2.33848	0.102353
$523$	13.6360	0.596260	0.298130	−	0.954525i	$-0.403637\pi$
$523$	13.6360	0.596260	0.298130	+	0.954525i	$0.403637\pi$
$524$	−28.2739	−1.23515
$525$	0.645728	0.0281819
$526$	1.41208	0.0615696
$527$	8.34865	0.363673
$528$	−0.126318	−0.00549727
$529$	41.9411	1.82353
$530$	−0.369925	−0.0160685
$531$	11.2083	0.486398
$532$	−11.3602	−0.492527
$533$	−27.7775	−1.20318
$534$	0.536144	0.0232012
$535$	−21.8804	−0.945974
$536$	1.67702	0.0724360
$537$	5.03210	0.217151
$538$	1.20135	0.0517939
$539$	0.960359	0.0413656
$540$	3.27380	0.140882
$541$	−42.4095	−1.82333	−0.911664	−	0.410936i	$-0.865202\pi$
$541$	−42.4095	−1.82333	−0.911664	+	0.410936i	$0.865202\pi$
$542$	1.87365	0.0804801
$543$	2.18546	0.0937872
$544$	9.09286	0.389853
$545$	19.4340	0.832462
$546$	0.204256	0.00874134
$547$	1.42544	0.0609474	0.0304737	−	0.999536i	$-0.490298\pi$
$547$	1.42544	0.0609474	0.0304737	+	0.999536i	$0.490298\pi$
$548$	−6.10339	−0.260724
$549$	1.14205	0.0487417
$550$	0.0934989	0.00398681
$551$	26.8132	1.14228
$552$	−1.24021	−0.0527867
$553$	−5.56114	−0.236484
$554$	1.42602	0.0605858
$555$	−0.940664	−0.0399290
$556$	−19.5428	−0.828801
$557$	5.34346	0.226410	0.113205	−	0.993572i	$-0.463888\pi$
$557$	5.34346	0.226410	0.113205	+	0.993572i	$0.463888\pi$
$558$	−1.06449	−0.0450636
$559$	43.0425	1.82050
$560$	−4.66867	−0.197287
$561$	−0.140855	−0.00594691
$562$	5.58316	0.235512
$563$	3.93120	0.165680	0.0828401	−	0.996563i	$-0.473601\pi$
$563$	3.93120	0.165680	0.0828401	+	0.996563i	$0.473601\pi$
$564$	−2.10899	−0.0888047
$565$	−19.7327	−0.830159
$566$	0.739780	0.0310953
$567$	−8.01547	−0.336618
$568$	6.84288	0.287121
$569$	−2.93293	−0.122955	−0.0614773	−	0.998108i	$-0.519581\pi$
$569$	−2.93293	−0.122955	−0.0614773	+	0.998108i	$0.519581\pi$
$570$	−0.316718	−0.0132659
$571$	−3.69849	−0.154777	−0.0773886	−	0.997001i	$-0.524658\pi$
$571$	−3.69849	−0.154777	−0.0773886	+	0.997001i	$0.524658\pi$
$572$	−1.73939	−0.0727277
$573$	−3.60985	−0.150804
$574$	−0.838760	−0.0350092
$575$	−26.3039	−1.09695
$576$	21.3014	0.887557
$577$	−45.3394	−1.88750	−0.943752	−	0.330654i	$-0.892731\pi$
$577$	−45.3394	−1.88750	−0.943752	+	0.330654i	$0.892731\pi$
$578$	0.175474	0.00729877
$579$	4.17064	0.173326
$580$	11.2133	0.465605
$581$	11.3622	0.471382
$582$	0	0
$583$	0.240521	0.00996136
$584$	4.71884	0.195267
$585$	21.9829	0.908880
$586$	−3.82651	−0.158072
$587$	44.4538	1.83480	0.917402	−	0.397963i	$-0.130283\pi$
$587$	44.4538	1.83480	0.917402	+	0.397963i	$0.130283\pi$
$588$	2.55809	0.105494
$589$	−12.2055	−0.502920
$590$	−0.913839	−0.0376222
$591$	−1.99378	−0.0820133
$592$	−12.7882	−0.525592
$593$	22.3143	0.916339	0.458169	−	0.888865i	$-0.348505\pi$
$593$	22.3143	0.916339	0.458169	+	0.888865i	$0.348505\pi$
$594$	0.0361930	0.00148502
$595$	−5.20598	−0.213424
$596$	−13.7890	−0.564820
$597$	0.812517	0.0332541
$598$	−8.32042	−0.340247
$599$	−8.73460	−0.356886	−0.178443	−	0.983950i	$-0.557106\pi$
$599$	−8.73460	−0.356886	−0.178443	+	0.983950i	$0.557106\pi$
$600$	0.502337	0.0205078
$601$	11.3824	0.464299	0.232150	−	0.972680i	$-0.425424\pi$
$601$	11.3824	0.464299	0.232150	+	0.972680i	$0.425424\pi$
$602$	1.29970	0.0529717
$603$	6.83214	0.278226
$604$	−26.9941	−1.09838
$605$	−14.4606	−0.587909
$606$	0.561332	0.0228025
$607$	30.7774	1.24922	0.624608	−	0.780938i	$-0.285259\pi$
$607$	30.7774	1.24922	0.624608	+	0.780938i	$0.285259\pi$
$608$	−13.2935	−0.539124
$609$	0.856146	0.0346928
$610$	−0.0931145	−0.00377009
$611$	−28.5387	−1.15455
$612$	24.6270	0.995486
$613$	−12.4603	−0.503268	−0.251634	−	0.967822i	$-0.580968\pi$
$613$	−12.4603	−0.503268	−0.251634	+	0.967822i	$0.580968\pi$
$614$	1.70561	0.0688328
$615$	1.37528	0.0554567
$616$	−0.105937	−0.00426834
$617$	−35.2061	−1.41734	−0.708672	−	0.705538i	$-0.750706\pi$
$617$	−35.2061	−1.41734	−0.708672	+	0.705538i	$0.750706\pi$
$618$	−0.0787872	−0.00316929
$619$	27.4490	1.10327	0.551635	−	0.834086i	$-0.314004\pi$
$619$	27.4490	1.10327	0.551635	+	0.834086i	$0.314004\pi$
$620$	−5.10435	−0.204995
$621$	−10.1821	−0.408596
$622$	−5.38174	−0.215788
$623$	−12.8840	−0.516186
$624$	−4.55307	−0.182269
$625$	1.97463	0.0789853
$626$	1.78162	0.0712077
$627$	0.205927	0.00822392
$628$	−19.0209	−0.759017
$629$	−14.2600	−0.568582
$630$	0.663788	0.0264459
$631$	10.0579	0.400400	0.200200	−	0.979755i	$-0.435841\pi$
$631$	10.0579	0.400400	0.200200	+	0.979755i	$0.435841\pi$
$632$	−4.32623	−0.172088
$633$	2.56134	0.101804
$634$	5.08167	0.201819
$635$	12.9124	0.512411
$636$	0.640671	0.0254043
$637$	34.6158	1.37153
$638$	0.123967	0.00490789
$639$	27.8778	1.10283
$640$	−7.39064	−0.292141
$641$	5.82995	0.230269	0.115135	−	0.993350i	$-0.463270\pi$
$641$	5.82995	0.230269	0.115135	+	0.993350i	$0.463270\pi$
$642$	−0.644334	−0.0254298
$643$	16.6517	0.656678	0.328339	−	0.944560i	$-0.393511\pi$
$643$	16.6517	0.656678	0.328339	+	0.944560i	$0.393511\pi$
$644$	14.7760	0.582256
$645$	−2.13106	−0.0839105
$646$	−4.80128	−0.188904
$647$	34.3676	1.35113	0.675564	−	0.737301i	$-0.263900\pi$
$647$	34.3676	1.35113	0.675564	+	0.737301i	$0.263900\pi$
$648$	−6.23554	−0.244955
$649$	0.594168	0.0233232
$650$	3.37013	0.132187
$651$	−0.389723	−0.0152745
$652$	−34.3288	−1.34442
$653$	2.96803	0.116148	0.0580740	−	0.998312i	$-0.481504\pi$
$653$	2.96803	0.116148	0.0580740	+	0.998312i	$0.481504\pi$
$654$	0.572292	0.0223784
$655$	18.9427	0.740153
$656$	18.6968	0.729988
$657$	19.2245	0.750019
$658$	−0.861744	−0.0335943
$659$	28.8214	1.12272	0.561362	−	0.827570i	$-0.310278\pi$
$659$	28.8214	1.12272	0.561362	+	0.827570i	$0.310278\pi$
$660$	0.0861185	0.00335216
$661$	22.6402	0.880600	0.440300	−	0.897851i	$-0.354872\pi$
$661$	22.6402	0.880600	0.440300	+	0.897851i	$0.354872\pi$
$662$	4.65297	0.180843
$663$	−5.07707	−0.197177
$664$	8.83907	0.343022
$665$	7.61101	0.295142
$666$	1.81822	0.0704544
$667$	−34.8754	−1.35038
$668$	33.4022	1.29237
$669$	−3.76731	−0.145653
$670$	−0.557042	−0.0215204
$671$	0.0605420	0.00233720
$672$	−0.424464	−0.0163741
$673$	−33.5848	−1.29460	−0.647299	−	0.762236i	$-0.724102\pi$
$673$	−33.5848	−1.29460	−0.647299	+	0.762236i	$0.724102\pi$
$674$	4.26442	0.164259
$675$	4.12421	0.158741
$676$	−37.1304	−1.42809
$677$	−24.8589	−0.955403	−0.477702	−	0.878522i	$-0.658530\pi$
$677$	−24.8589	−0.955403	−0.477702	+	0.878522i	$0.658530\pi$
$678$	−0.581086	−0.0223165
$679$	0	0
$680$	−4.04993	−0.155308
$681$	−0.785513	−0.0301009
$682$	−0.0564304	−0.00216083
$683$	9.31225	0.356323	0.178162	−	0.984001i	$-0.442985\pi$
$683$	9.31225	0.356323	0.178162	+	0.984001i	$0.442985\pi$
$684$	−36.0040	−1.37665
$685$	4.08910	0.156237
$686$	2.23871	0.0854742
$687$	−4.45696	−0.170044
$688$	−28.9716	−1.10453
$689$	8.66948	0.330281
$690$	0.411950	0.0156827
$691$	−28.2328	−1.07403	−0.537014	−	0.843574i	$-0.680448\pi$
$691$	−28.2328	−1.07403	−0.537014	+	0.843574i	$0.680448\pi$
$692$	−23.5998	−0.897129
$693$	−0.431588	−0.0163947
$694$	4.07711	0.154765
$695$	13.0932	0.496652
$696$	0.666030	0.0252458
$697$	20.8486	0.789696
$698$	−5.31202	−0.201063
$699$	−0.883435	−0.0334146
$700$	−5.98491	−0.226208
$701$	−42.4683	−1.60400	−0.802002	−	0.597321i	$-0.796232\pi$
$701$	−42.4683	−1.60400	−0.802002	+	0.597321i	$0.796232\pi$
$702$	1.30456	0.0492376
$703$	20.8477	0.786287
$704$	1.12922	0.0425590
$705$	1.41297	0.0532155
$706$	1.66760	0.0627608
$707$	−13.4893	−0.507317
$708$	1.58267	0.0594805
$709$	−23.7389	−0.891533	−0.445767	−	0.895149i	$-0.647069\pi$
$709$	−23.7389	−0.891533	−0.445767	+	0.895149i	$0.647069\pi$
$710$	−2.27295	−0.0853022
$711$	−17.6250	−0.660989
$712$	−10.0230	−0.375626
$713$	15.8755	0.594542
$714$	−0.153305	−0.00573731
$715$	1.16535	0.0435815
$716$	−46.6399	−1.74301
$717$	−0.263208	−0.00982969
$718$	−2.69422	−0.100547
$719$	−0.996105	−0.0371485	−0.0185742	−	0.999827i	$-0.505913\pi$
$719$	−0.996105	−0.0371485	−0.0185742	+	0.999827i	$0.505913\pi$
$720$	−14.7965	−0.551433
$721$	1.89332	0.0705111
$722$	3.54501	0.131931
$723$	−2.88192	−0.107180
$724$	−20.2559	−0.752805
$725$	14.1260	0.524628
$726$	−0.425836	−0.0158043
$727$	41.3342	1.53300	0.766500	−	0.642244i	$-0.221996\pi$
$727$	41.3342	1.53300	0.766500	+	0.642244i	$0.221996\pi$
$728$	−3.81847	−0.141522
$729$	−24.5993	−0.911084
$730$	−1.56742	−0.0580129
$731$	−32.3058	−1.19487
$732$	0.161265	0.00596051
$733$	15.4984	0.572446	0.286223	−	0.958163i	$-0.407600\pi$
$733$	15.4984	0.572446	0.286223	+	0.958163i	$0.407600\pi$
$734$	−1.23235	−0.0454868
$735$	−1.71385	−0.0632163
$736$	17.2907	0.637343
$737$	0.362182	0.0133412
$738$	−2.65829	−0.0978532
$739$	23.5971	0.868034	0.434017	−	0.900905i	$-0.357096\pi$
$739$	23.5971	0.868034	0.434017	+	0.900905i	$0.357096\pi$
$740$	8.71852	0.320499
$741$	7.42255	0.272674
$742$	0.261781	0.00961028
$743$	−41.8985	−1.53711	−0.768553	−	0.639786i	$-0.779023\pi$
$743$	−41.8985	−1.53711	−0.768553	+	0.639786i	$0.779023\pi$
$744$	−0.303181	−0.0111151
$745$	9.23826	0.338463
$746$	0.913479	0.0334448
$747$	36.0103	1.31755
$748$	1.30551	0.0477343
$749$	15.4839	0.565770
$750$	−0.422454	−0.0154258
$751$	45.9340	1.67616	0.838078	−	0.545550i	$-0.183679\pi$
$751$	45.9340	1.67616	0.838078	+	0.545550i	$0.183679\pi$
$752$	19.2091	0.700486
$753$	4.71538	0.171838
$754$	4.46833	0.162727
$755$	18.0853	0.658193
$756$	−2.31674	−0.0842589
$757$	7.24377	0.263279	0.131640	−	0.991298i	$-0.457976\pi$
$757$	7.24377	0.263279	0.131640	+	0.991298i	$0.457976\pi$
$758$	−5.73601	−0.208341
$759$	−0.267845	−0.00972217
$760$	5.92090	0.214774
$761$	26.6515	0.966116	0.483058	−	0.875588i	$-0.339526\pi$
$761$	26.6515	0.966116	0.483058	+	0.875588i	$0.339526\pi$
$762$	0.380243	0.0137747
$763$	−13.7527	−0.497880
$764$	33.4578	1.21046
$765$	−16.4994	−0.596537
$766$	−3.89692	−0.140802
$767$	21.4166	0.773307
$768$	2.84138	0.102529
$769$	35.5378	1.28153	0.640763	−	0.767739i	$-0.278618\pi$
$769$	35.5378	1.28153	0.640763	+	0.767739i	$0.278618\pi$
$770$	0.0351884	0.00126810
$771$	5.71943	0.205980
$772$	−38.6555	−1.39124
$773$	5.82505	0.209513	0.104756	−	0.994498i	$-0.466594\pi$
$773$	5.82505	0.209513	0.104756	+	0.994498i	$0.466594\pi$
$774$	4.11915	0.148060
$775$	−6.43026	−0.230982
$776$	0	0
$777$	0.665670	0.0238808
$778$	2.37097	0.0850035
$779$	−30.4801	−1.09206
$780$	3.10411	0.111145
$781$	1.47785	0.0528815
$782$	6.24495	0.223319
$783$	5.46813	0.195415
$784$	−23.2996	−0.832128
$785$	12.7435	0.454835
$786$	0.557824	0.0198969
$787$	−17.8872	−0.637611	−0.318806	−	0.947820i	$-0.603282\pi$
$787$	−17.8872	−0.637611	−0.318806	+	0.947820i	$0.603282\pi$
$788$	18.4793	0.658299
$789$	1.63847	0.0583310
$790$	1.43701	0.0511265
$791$	13.9640	0.496503
$792$	−0.335749	−0.0119303
$793$	2.18221	0.0774926
$794$	5.82629	0.206767
$795$	−0.429232	−0.0152233
$796$	−7.53079	−0.266922
$797$	−5.46970	−0.193747	−0.0968734	−	0.995297i	$-0.530884\pi$
$797$	−5.46970	−0.193747	−0.0968734	+	0.995297i	$0.530884\pi$
$798$	0.224129	0.00793407
$799$	21.4199	0.757781
$800$	−7.00347	−0.247610
$801$	−40.8334	−1.44278
$802$	4.82950	0.170536
$803$	1.01912	0.0359640
$804$	0.964738	0.0340237
$805$	−9.89951	−0.348912
$806$	−2.03401	−0.0716450
$807$	1.39395	0.0490695
$808$	−10.4938	−0.369172
$809$	10.6533	0.374552	0.187276	−	0.982307i	$-0.440034\pi$
$809$	10.6533	0.374552	0.187276	+	0.982307i	$0.440034\pi$
$810$	2.07121	0.0727750
$811$	24.2231	0.850586	0.425293	−	0.905056i	$-0.360171\pi$
$811$	24.2231	0.850586	0.425293	+	0.905056i	$0.360171\pi$
$812$	−7.93517	−0.278470
$813$	2.17404	0.0762468
$814$	0.0963864	0.00337834
$815$	22.9994	0.805633
$816$	3.41733	0.119631
$817$	47.2303	1.65238
$818$	4.02317	0.140667
$819$	−15.5564	−0.543584
$820$	−12.7468	−0.445137
$821$	26.5303	0.925915	0.462957	−	0.886381i	$-0.346788\pi$
$821$	26.5303	0.925915	0.462957	+	0.886381i	$0.346788\pi$
$822$	0.120416	0.00419998
$823$	4.33414	0.151079	0.0755394	−	0.997143i	$-0.475932\pi$
$823$	4.33414	0.151079	0.0755394	+	0.997143i	$0.475932\pi$
$824$	1.47289	0.0513106
$825$	0.108489	0.00377710
$826$	0.646687	0.0225011
$827$	−20.2227	−0.703211	−0.351606	−	0.936148i	$-0.614364\pi$
$827$	−20.2227	−0.703211	−0.351606	+	0.936148i	$0.614364\pi$
$828$	46.8298	1.62745
$829$	−10.2305	−0.355319	−0.177660	−	0.984092i	$-0.556853\pi$
$829$	−10.2305	−0.355319	−0.177660	+	0.984092i	$0.556853\pi$
$830$	−2.93601	−0.101910
$831$	1.65464	0.0573989
$832$	40.7022	1.41109
$833$	−25.9811	−0.900191
$834$	0.385567	0.0133511
$835$	−22.3786	−0.774442
$836$	−1.90863	−0.0660113
$837$	−2.48913	−0.0860369
$838$	−5.63696	−0.194726
$839$	44.0117	1.51945	0.759727	−	0.650242i	$-0.225333\pi$
$839$	44.0117	1.51945	0.759727	+	0.650242i	$0.225333\pi$
$840$	0.189055	0.00652301
$841$	−10.2708	−0.354166
$842$	−4.38537	−0.151130
$843$	6.47827	0.223124
$844$	−23.7397	−0.817153
$845$	24.8763	0.855772
$846$	−2.73114	−0.0938985
$847$	10.2332	0.351617
$848$	−5.83536	−0.200387
$849$	0.858384	0.0294597
$850$	−2.52947	−0.0867602
$851$	−27.1163	−0.929534
$852$	3.93651	0.134863
$853$	−52.1267	−1.78478	−0.892392	−	0.451261i	$-0.850974\pi$
$853$	−52.1267	−1.78478	−0.892392	+	0.451261i	$0.850974\pi$
$854$	0.0658934	0.00225482
$855$	24.1217	0.824945
$856$	12.0455	0.411708
$857$	−5.12483	−0.175061	−0.0875304	−	0.996162i	$-0.527897\pi$
$857$	−5.12483	−0.175061	−0.0875304	+	0.996162i	$0.527897\pi$
$858$	0.0343170	0.00117156
$859$	−28.4960	−0.972272	−0.486136	−	0.873883i	$-0.661594\pi$
$859$	−28.4960	−0.972272	−0.486136	+	0.873883i	$0.661594\pi$
$860$	19.7517	0.673528
$861$	−0.973232	−0.0331677
$862$	−1.39366	−0.0474682
$863$	14.5738	0.496099	0.248050	−	0.968747i	$-0.420210\pi$
$863$	14.5738	0.496099	0.248050	+	0.968747i	$0.420210\pi$
$864$	−2.71102	−0.0922306
$865$	15.8112	0.537597
$866$	−4.79606	−0.162977
$867$	0.203607	0.00691485
$868$	3.61214	0.122604
$869$	−0.934329	−0.0316949
$870$	−0.221230	−0.00750040
$871$	13.0547	0.442342
$872$	−10.6987	−0.362305
$873$	0	0
$874$	−9.12996	−0.308825
$875$	10.1519	0.343198
$876$	2.71461	0.0917182
$877$	14.5979	0.492937	0.246469	−	0.969151i	$-0.420730\pi$
$877$	14.5979	0.492937	0.246469	+	0.969151i	$0.420730\pi$
$878$	−1.30618	−0.0440814
$879$	−4.43999	−0.149757
$880$	−0.784385	−0.0264416
$881$	35.7782	1.20540	0.602699	−	0.797968i	$-0.294092\pi$
$881$	35.7782	1.20540	0.602699	+	0.797968i	$0.294092\pi$
$882$	3.31271	0.111545
$883$	−31.8575	−1.07209	−0.536045	−	0.844189i	$-0.680082\pi$
$883$	−31.8575	−1.07209	−0.536045	+	0.844189i	$0.680082\pi$
$884$	47.0567	1.58269
$885$	−1.06035	−0.0356432
$886$	0.362817	0.0121891
$887$	−21.9678	−0.737607	−0.368804	−	0.929507i	$-0.620232\pi$
$887$	−21.9678	−0.737607	−0.368804	+	0.929507i	$0.620232\pi$
$888$	0.517851	0.0173779
$889$	−9.13756	−0.306464
$890$	3.32925	0.111597
$891$	−1.34668	−0.0451155
$892$	34.9173	1.16912
$893$	−31.3153	−1.04793
$894$	0.272048	0.00909864
$895$	31.2475	1.04449
$896$	5.23006	0.174724
$897$	−9.65437	−0.322350
$898$	−2.42543	−0.0809377
$899$	−8.52564	−0.284346
$900$	−18.9681	−0.632269
$901$	−6.50694	−0.216777
$902$	−0.140920	−0.00469213
$903$	1.50807	0.0501854
$904$	10.8631	0.361303
$905$	13.5709	0.451112
$906$	0.532576	0.0176937
$907$	23.4800	0.779641	0.389821	−	0.920891i	$-0.372537\pi$
$907$	23.4800	0.779641	0.389821	+	0.920891i	$0.372537\pi$
$908$	7.28050	0.241612
$909$	−42.7518	−1.41799
$910$	1.26835	0.0420454
$911$	−16.3674	−0.542276	−0.271138	−	0.962541i	$-0.587400\pi$
$911$	−16.3674	−0.542276	−0.271138	+	0.962541i	$0.587400\pi$
$912$	−4.99606	−0.165436
$913$	1.90896	0.0631774
$914$	5.32086	0.175998
$915$	−0.108043	−0.00357179
$916$	41.3093	1.36490
$917$	−13.4050	−0.442672
$918$	−0.979149	−0.0323167
$919$	33.0446	1.09004	0.545021	−	0.838423i	$-0.316522\pi$
$919$	33.0446	1.09004	0.545021	+	0.838423i	$0.316522\pi$
$920$	−7.70121	−0.253902
$921$	1.97906	0.0652122
$922$	−5.01989	−0.165321
$923$	53.2684	1.75335
$924$	−0.0609426	−0.00200487
$925$	10.9833	0.361127
$926$	3.67205	0.120671
$927$	6.00054	0.197084
$928$	−9.28564	−0.304816
$929$	−12.2805	−0.402911	−0.201456	−	0.979498i	$-0.564567\pi$
$929$	−12.2805	−0.402911	−0.201456	+	0.979498i	$0.564567\pi$
$930$	0.100705	0.00330226
$931$	37.9837	1.24487
$932$	8.18809	0.268210
$933$	−6.24455	−0.204438
$934$	−0.0642555	−0.00210250
$935$	−0.874658	−0.0286044
$936$	−12.1019	−0.395564
$937$	15.5314	0.507389	0.253695	−	0.967284i	$-0.418354\pi$
$937$	15.5314	0.507389	0.253695	+	0.967284i	$0.418354\pi$
$938$	0.394196	0.0128710
$939$	2.06725	0.0674622
$940$	−13.0961	−0.427147
$941$	−27.7528	−0.904717	−0.452358	−	0.891836i	$-0.649417\pi$
$941$	−27.7528	−0.904717	−0.452358	+	0.891836i	$0.649417\pi$
$942$	0.375270	0.0122270
$943$	39.6449	1.29102
$944$	−14.4153	−0.469179
$945$	1.55215	0.0504914
$946$	0.218362	0.00709957
$947$	−22.6268	−0.735273	−0.367636	−	0.929970i	$-0.619833\pi$
$947$	−22.6268	−0.735273	−0.367636	+	0.929970i	$0.619833\pi$
$948$	−2.48875	−0.0808309
$949$	36.7338	1.19243
$950$	3.69803	0.119980
$951$	5.89638	0.191203
$952$	2.86598	0.0928868
$953$	20.0799	0.650452	0.325226	−	0.945636i	$-0.394560\pi$
$953$	20.0799	0.650452	0.325226	+	0.945636i	$0.394560\pi$
$954$	0.829666	0.0268614
$955$	−22.4158	−0.725358
$956$	2.43954	0.0789003
$957$	0.143841	0.00464973
$958$	−1.45297	−0.0469432
$959$	−2.89369	−0.0934423
$960$	−2.01519	−0.0650401
$961$	−27.1191	−0.874809
$962$	3.47421	0.112013
$963$	49.0734	1.58137
$964$	26.7110	0.860304
$965$	25.8981	0.833691
$966$	−0.291520	−0.00937951
$967$	36.9832	1.18930	0.594650	−	0.803984i	$-0.297291\pi$
$967$	36.9832	1.18930	0.594650	+	0.803984i	$0.297291\pi$
$968$	7.96081	0.255870
$969$	−5.57104	−0.178968
$970$	0	0
$971$	31.8536	1.02223	0.511115	−	0.859512i	$-0.329233\pi$
$971$	31.8536	1.02223	0.511115	+	0.859512i	$0.329233\pi$
$972$	−11.0415	−0.354155
$973$	−9.26551	−0.297039
$974$	−4.81068	−0.154144
$975$	3.91044	0.125234
$976$	−1.46883	−0.0470161
$977$	18.4394	0.589928	0.294964	−	0.955508i	$-0.404692\pi$
$977$	18.4394	0.589928	0.294964	+	0.955508i	$0.404692\pi$
$978$	0.677285	0.0216572
$979$	−2.16464	−0.0691823
$980$	15.8848	0.507421
$981$	−43.5866	−1.39161
$982$	−4.63521	−0.147915
$983$	−21.5151	−0.686225	−0.343112	−	0.939294i	$-0.611481\pi$
$983$	−21.5151	−0.686225	−0.343112	+	0.939294i	$0.611481\pi$
$984$	−0.757115	−0.0241359
$985$	−12.3806	−0.394480
$986$	−3.35373	−0.106805
$987$	−0.999901	−0.0318272
$988$	−68.7957	−2.18868
$989$	−61.4316	−1.95341
$990$	0.111523	0.00354444
$991$	−36.7480	−1.16734	−0.583670	−	0.811991i	$-0.698384\pi$
$991$	−36.7480	−1.16734	−0.583670	+	0.811991i	$0.698384\pi$
$992$	4.22688	0.134204
$993$	5.39895	0.171330
$994$	1.60847	0.0510177
$995$	5.04543	0.159951
$996$	5.08486	0.161120
$997$	−33.6178	−1.06469	−0.532344	−	0.846528i	$-0.678689\pi$
$997$	−33.6178	−1.06469	−0.532344	+	0.846528i	$0.678689\pi$
$998$	−2.14942	−0.0680385
$999$	4.25158	0.134514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9409.2.a.q.1.88	yes	168
97.96	even	2		9409.2.a.p.1.88	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9409.2.a.p.1.88	✓	168	97.96	even	2
9409.2.a.q.1.88	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)

\(f(q)\)	\(=\)	\(q+0.182861 q^{2} +0.212177 q^{3} -1.96656 q^{4} +1.31754 q^{5} +0.0387989 q^{6} -0.932372 q^{7} -0.725328 q^{8} -2.95498 q^{9} +0.240927 q^{10} -0.156648 q^{11} -0.417260 q^{12} -5.64631 q^{13} -0.170494 q^{14} +0.279553 q^{15} +3.80049 q^{16} +4.23788 q^{17} -0.540350 q^{18} -6.19567 q^{19} -2.59103 q^{20} -0.197828 q^{21} -0.0286448 q^{22} +8.05860 q^{23} -0.153898 q^{24} -3.26408 q^{25} -1.03249 q^{26} -1.26351 q^{27} +1.83357 q^{28} -4.32772 q^{29} +0.0511193 q^{30} +1.97001 q^{31} +2.14562 q^{32} -0.0332372 q^{33} +0.774941 q^{34} -1.22844 q^{35} +5.81115 q^{36} -3.36489 q^{37} -1.13295 q^{38} -1.19802 q^{39} -0.955651 q^{40} +4.91958 q^{41} -0.0361750 q^{42} -7.62311 q^{43} +0.308058 q^{44} -3.89331 q^{45} +1.47360 q^{46} +5.05439 q^{47} +0.806378 q^{48} -6.13068 q^{49} -0.596872 q^{50} +0.899182 q^{51} +11.1038 q^{52} -1.53542 q^{53} -0.231047 q^{54} -0.206390 q^{55} +0.676276 q^{56} -1.31458 q^{57} -0.791371 q^{58} -3.79302 q^{59} -0.549758 q^{60} -0.386484 q^{61} +0.360237 q^{62} +2.75514 q^{63} -7.20863 q^{64} -7.43926 q^{65} -0.00607778 q^{66} -2.31208 q^{67} -8.33405 q^{68} +1.70985 q^{69} -0.224633 q^{70} -9.43418 q^{71} +2.14333 q^{72} -6.50580 q^{73} -0.615306 q^{74} -0.692565 q^{75} +12.1842 q^{76} +0.146054 q^{77} -0.219071 q^{78} +5.96451 q^{79} +5.00731 q^{80} +8.59685 q^{81} +0.899598 q^{82} -12.1863 q^{83} +0.389042 q^{84} +5.58358 q^{85} -1.39397 q^{86} -0.918245 q^{87} +0.113621 q^{88} +13.8185 q^{89} -0.711934 q^{90} +5.26447 q^{91} -15.8477 q^{92} +0.417991 q^{93} +0.924249 q^{94} -8.16306 q^{95} +0.455252 q^{96} -1.12106 q^{98} +0.462892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 168 q^{4} + 42 q^{5} + 42 q^{7} + 168 q^{9} + 42 q^{10} + 42 q^{13} + 70 q^{14} + 84 q^{15} + 140 q^{16} + 49 q^{17} - 49 q^{18} + 84 q^{19} + 98 q^{20} + 84 q^{21} - 35 q^{22} + 126 q^{23} + 168 q^{25}+ \cdots - 84 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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