LMFDB - Embedded newform 431.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [431,2,Mod(1,431)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(431, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("431.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	431.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$3.44155232712$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.762826 q^{2} -0.504361 q^{3} -1.41810 q^{4} -3.90060 q^{5} +0.384740 q^{6} +0.799887 q^{7} +2.60741 q^{8} -2.74562 q^{9} +2.97548 q^{10} -2.94608 q^{11} +0.715233 q^{12} +7.03930 q^{13} -0.610175 q^{14} +1.96731 q^{15} +0.847190 q^{16} +0.393953 q^{17} +2.09443 q^{18} -4.94861 q^{19} +5.53142 q^{20} -0.403432 q^{21} +2.24735 q^{22} +7.39242 q^{23} -1.31508 q^{24} +10.2147 q^{25} -5.36976 q^{26} +2.89787 q^{27} -1.13432 q^{28} -0.760089 q^{29} -1.50072 q^{30} +5.60540 q^{31} -5.86108 q^{32} +1.48589 q^{33} -0.300517 q^{34} -3.12004 q^{35} +3.89355 q^{36} +7.29977 q^{37} +3.77493 q^{38} -3.55035 q^{39} -10.1705 q^{40} -10.8923 q^{41} +0.307749 q^{42} +2.29761 q^{43} +4.17782 q^{44} +10.7096 q^{45} -5.63913 q^{46} +2.26168 q^{47} -0.427290 q^{48} -6.36018 q^{49} -7.79201 q^{50} -0.198694 q^{51} -9.98241 q^{52} +0.453054 q^{53} -2.21057 q^{54} +11.4915 q^{55} +2.08564 q^{56} +2.49589 q^{57} +0.579816 q^{58} +12.8185 q^{59} -2.78984 q^{60} -1.86472 q^{61} -4.27595 q^{62} -2.19619 q^{63} +2.77661 q^{64} -27.4575 q^{65} -1.13347 q^{66} -12.3240 q^{67} -0.558663 q^{68} -3.72845 q^{69} +2.38005 q^{70} +7.05470 q^{71} -7.15896 q^{72} +15.1804 q^{73} -5.56846 q^{74} -5.15188 q^{75} +7.01760 q^{76} -2.35653 q^{77} +2.70830 q^{78} -0.886279 q^{79} -3.30455 q^{80} +6.77529 q^{81} +8.30893 q^{82} +4.38957 q^{83} +0.572106 q^{84} -1.53665 q^{85} -1.75268 q^{86} +0.383359 q^{87} -7.68165 q^{88} +3.93084 q^{89} -8.16953 q^{90} +5.63065 q^{91} -10.4832 q^{92} -2.82715 q^{93} -1.72527 q^{94} +19.3025 q^{95} +2.95610 q^{96} +18.8451 q^{97} +4.85171 q^{98} +8.08881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + q^{3} + 33 q^{4} + 13 q^{5} + 17 q^{6} + 8 q^{7} - 3 q^{8} + 31 q^{9} - 6 q^{10} + 15 q^{11} - 12 q^{12} + 11 q^{13} + 16 q^{14} - 5 q^{15} + 43 q^{16} + 6 q^{17} - 8 q^{18} + 18 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) $ 24 * q + q^2 + q^3 + 33 * q^4 + 13 * q^5 + 17 * q^6 + 8 * q^7 - 3 * q^8 + 31 * q^9 - 6 * q^10 + 15 * q^11 - 12 * q^12 + 11 * q^13 + 16 * q^14 - 5 * q^15 + 43 * q^16 + 6 * q^17 - 8 * q^18 + 18 * q^19 - 10 * q^20 - 7 * q^21 - 5 * q^22 - 8 * q^23 + 15 * q^24 + 51 * q^25 + 5 * q^26 + 13 * q^27 + 2 * q^28 + 17 * q^29 - 54 * q^30 + 37 * q^31 - 20 * q^32 + 16 * q^33 + 50 * q^34 + 3 * q^35 + 54 * q^36 + 7 * q^37 - 25 * q^38 - 38 * q^39 + 2 * q^40 + 24 * q^41 + 18 * q^42 + 10 * q^43 + 78 * q^45 + 9 * q^46 - 6 * q^47 - 25 * q^48 + 84 * q^49 - 65 * q^50 - 21 * q^51 - 31 * q^52 - 22 * q^53 + 23 * q^54 + 12 * q^55 - 45 * q^56 + 9 * q^57 - 12 * q^58 + 21 * q^59 - 82 * q^60 + 46 * q^61 - 68 * q^62 - 47 * q^63 + 53 * q^64 - 42 * q^65 - 56 * q^66 - 25 * q^67 + 3 * q^68 - 33 * q^69 - 18 * q^70 - 6 * q^71 - 115 * q^72 + 86 * q^73 - 60 * q^74 - 34 * q^75 + 48 * q^76 - 31 * q^77 - 84 * q^78 - 6 * q^79 - 24 * q^80 + 44 * q^81 - 3 * q^82 - 49 * q^83 - 126 * q^84 + 75 * q^85 - 56 * q^86 - 31 * q^87 - 91 * q^88 + 61 * q^89 - 161 * q^90 + 32 * q^91 - 130 * q^92 - 6 * q^93 + 8 * q^94 - 23 * q^95 - 5 * q^96 + 88 * q^97 - 120 * q^98 - 9 * 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 $

$2$	−0.762826	−0.539400	−0.269700	−	0.962944i	$-0.586924\pi$
$2$	−0.762826	−0.539400	−0.269700	+	0.962944i	$0.586924\pi$
$3$	−0.504361	−0.291193	−0.145597	−	0.989344i	$-0.546510\pi$
$3$	−0.504361	−0.291193	−0.145597	+	0.989344i	$0.546510\pi$
$4$	−1.41810	−0.709048
$5$	−3.90060	−1.74440	−0.872200	−	0.489149i	$-0.837307\pi$
$5$	−3.90060	−1.74440	−0.872200	+	0.489149i	$0.837307\pi$
$6$	0.384740	0.157069
$7$	0.799887	0.302329	0.151164	−	0.988509i	$-0.451698\pi$
$7$	0.799887	0.302329	0.151164	+	0.988509i	$0.451698\pi$
$8$	2.60741	0.921860
$9$	−2.74562	−0.915207
$10$	2.97548	0.940929
$11$	−2.94608	−0.888276	−0.444138	−	0.895958i	$-0.646490\pi$
$11$	−2.94608	−0.888276	−0.444138	+	0.895958i	$0.646490\pi$
$12$	0.715233	0.206470
$13$	7.03930	1.95235	0.976176	−	0.216982i	$-0.0696214\pi$
$13$	7.03930	1.95235	0.976176	+	0.216982i	$0.0696214\pi$
$14$	−0.610175	−0.163076
$15$	1.96731	0.507957
$16$	0.847190	0.211797
$17$	0.393953	0.0955475	0.0477738	−	0.998858i	$-0.484787\pi$
$17$	0.393953	0.0955475	0.0477738	+	0.998858i	$0.484787\pi$
$18$	2.09443	0.493662
$19$	−4.94861	−1.13529	−0.567644	−	0.823274i	$-0.692145\pi$
$19$	−4.94861	−1.13529	−0.567644	+	0.823274i	$0.692145\pi$
$20$	5.53142	1.23686
$21$	−0.403432	−0.0880361
$22$	2.24735	0.479136
$23$	7.39242	1.54143	0.770713	−	0.637183i	$-0.219900\pi$
$23$	7.39242	1.54143	0.770713	+	0.637183i	$0.219900\pi$
$24$	−1.31508	−0.268439
$25$	10.2147	2.04293
$26$	−5.36976	−1.05310
$27$	2.89787	0.557695
$28$	−1.13432	−0.214366
$29$	−0.760089	−0.141145	−0.0705725	−	0.997507i	$-0.522483\pi$
$29$	−0.760089	−0.141145	−0.0705725	+	0.997507i	$0.522483\pi$
$30$	−1.50072	−0.273992
$31$	5.60540	1.00676	0.503380	−	0.864065i	$-0.332090\pi$
$31$	5.60540	1.00676	0.503380	+	0.864065i	$0.332090\pi$
$32$	−5.86108	−1.03610
$33$	1.48589	0.258660
$34$	−0.300517	−0.0515383
$35$	−3.12004	−0.527383
$36$	3.89355	0.648925
$37$	7.29977	1.20008	0.600038	−	0.799972i	$-0.295152\pi$
$37$	7.29977	1.20008	0.600038	+	0.799972i	$0.295152\pi$
$38$	3.77493	0.612374
$39$	−3.55035	−0.568511
$40$	−10.1705	−1.60809
$41$	−10.8923	−1.70109	−0.850545	−	0.525902i	$-0.823728\pi$
$41$	−10.8923	−1.70109	−0.850545	+	0.525902i	$0.823728\pi$
$42$	0.307749	0.0474867
$43$	2.29761	0.350383	0.175191	−	0.984534i	$-0.443946\pi$
$43$	2.29761	0.350383	0.175191	+	0.984534i	$0.443946\pi$
$44$	4.17782	0.629831
$45$	10.7096	1.59649
$46$	−5.63913	−0.831444
$47$	2.26168	0.329901	0.164950	−	0.986302i	$-0.447254\pi$
$47$	2.26168	0.329901	0.164950	+	0.986302i	$0.447254\pi$
$48$	−0.427290	−0.0616740
$49$	−6.36018	−0.908597
$50$	−7.79201	−1.10196
$51$	−0.198694	−0.0278228
$52$	−9.98241	−1.38431
$53$	0.453054	0.0622317	0.0311158	−	0.999516i	$-0.490094\pi$
$53$	0.453054	0.0622317	0.0311158	+	0.999516i	$0.490094\pi$
$54$	−2.21057	−0.300820
$55$	11.4915	1.54951
$56$	2.08564	0.278705
$57$	2.49589	0.330588
$58$	0.579816	0.0761335
$59$	12.8185	1.66883	0.834415	−	0.551137i	$-0.185806\pi$
$59$	12.8185	1.66883	0.834415	+	0.551137i	$0.185806\pi$
$60$	−2.78984	−0.360166
$61$	−1.86472	−0.238753	−0.119377	−	0.992849i	$-0.538090\pi$
$61$	−1.86472	−0.238753	−0.119377	+	0.992849i	$0.538090\pi$
$62$	−4.27595	−0.543046
$63$	−2.19619	−0.276693
$64$	2.77661	0.347076
$65$	−27.4575	−3.40568
$66$	−1.13347	−0.139521
$67$	−12.3240	−1.50562	−0.752811	−	0.658237i	$-0.771303\pi$
$67$	−12.3240	−1.50562	−0.752811	+	0.658237i	$0.771303\pi$
$68$	−0.558663	−0.0677478
$69$	−3.72845	−0.448853
$70$	2.38005	0.284470
$71$	7.05470	0.837239	0.418620	−	0.908162i	$-0.362514\pi$
$71$	7.05470	0.837239	0.418620	+	0.908162i	$0.362514\pi$
$72$	−7.15896	−0.843692
$73$	15.1804	1.77674	0.888368	−	0.459132i	$-0.151839\pi$
$73$	15.1804	1.77674	0.888368	+	0.459132i	$0.151839\pi$
$74$	−5.56846	−0.647320
$75$	−5.15188	−0.594888
$76$	7.01760	0.804974
$77$	−2.35653	−0.268552
$78$	2.70830	0.306655
$79$	−0.886279	−0.0997142	−0.0498571	−	0.998756i	$-0.515877\pi$
$79$	−0.886279	−0.0997142	−0.0498571	+	0.998756i	$0.515877\pi$
$80$	−3.30455	−0.369459
$81$	6.77529	0.752810
$82$	8.30893	0.917568
$83$	4.38957	0.481817	0.240909	−	0.970548i	$-0.422555\pi$
$83$	4.38957	0.481817	0.240909	+	0.970548i	$0.422555\pi$
$84$	0.572106	0.0624219
$85$	−1.53665	−0.166673
$86$	−1.75268	−0.188996
$87$	0.383359	0.0411005
$88$	−7.68165	−0.818866
$89$	3.93084	0.416668	0.208334	−	0.978058i	$-0.433196\pi$
$89$	3.93084	0.416668	0.208334	+	0.978058i	$0.433196\pi$
$90$	−8.16953	−0.861144
$91$	5.63065	0.590252
$92$	−10.4832	−1.09295
$93$	−2.82715	−0.293162
$94$	−1.72527	−0.177948
$95$	19.3025	1.98040
$96$	2.95610	0.301706
$97$	18.8451	1.91343	0.956715	−	0.291027i	$-0.0939969\pi$
$97$	18.8451	1.91343	0.956715	+	0.291027i	$0.0939969\pi$
$98$	4.85171	0.490097
$99$	8.08881	0.812956
$100$	−14.4854	−1.44854
$101$	0.354180	0.0352422	0.0176211	−	0.999845i	$-0.494391\pi$
$101$	0.354180	0.0352422	0.0176211	+	0.999845i	$0.494391\pi$
$102$	0.151569	0.0150076
$103$	−15.9391	−1.57052	−0.785261	−	0.619165i	$-0.787471\pi$
$103$	−15.9391	−1.57052	−0.785261	+	0.619165i	$0.787471\pi$
$104$	18.3544	1.79979
$105$	1.57363	0.153570
$106$	−0.345601	−0.0335677
$107$	−15.0957	−1.45935	−0.729676	−	0.683793i	$-0.760329\pi$
$107$	−15.0957	−1.45935	−0.729676	+	0.683793i	$0.760329\pi$
$108$	−4.10946	−0.395433
$109$	−6.98888	−0.669413	−0.334707	−	0.942322i	$-0.608637\pi$
$109$	−6.98888	−0.669413	−0.334707	+	0.942322i	$0.608637\pi$
$110$	−8.76599	−0.835805
$111$	−3.68172	−0.349454
$112$	0.677656	0.0640325
$113$	4.05349	0.381320	0.190660	−	0.981656i	$-0.438937\pi$
$113$	4.05349	0.381320	0.190660	+	0.981656i	$0.438937\pi$
$114$	−1.90393	−0.178319
$115$	−28.8348	−2.68886
$116$	1.07788	0.100079
$117$	−19.3272	−1.78680
$118$	−9.77830	−0.900166
$119$	0.315118	0.0288868
$120$	5.12959	0.468266
$121$	−2.32062	−0.210965
$122$	1.42246	0.128783
$123$	5.49365	0.495346
$124$	−7.94900	−0.713842
$125$	−20.3403	−1.81929
$126$	1.67531	0.149248
$127$	14.2960	1.26856	0.634281	−	0.773102i	$-0.281296\pi$
$127$	14.2960	1.26856	0.634281	+	0.773102i	$0.281296\pi$
$128$	9.60410	0.848890
$129$	−1.15883	−0.102029
$130$	20.9453	1.83702
$131$	−17.3988	−1.52014	−0.760069	−	0.649843i	$-0.774835\pi$
$131$	−17.3988	−1.52014	−0.760069	+	0.649843i	$0.774835\pi$
$132$	−2.10713	−0.183402
$133$	−3.95833	−0.343231
$134$	9.40110	0.812132
$135$	−11.3034	−0.972843
$136$	1.02720	0.0880814
$137$	11.2993	0.965361	0.482681	−	0.875796i	$-0.339663\pi$
$137$	11.2993	0.965361	0.482681	+	0.875796i	$0.339663\pi$
$138$	2.84416	0.242111
$139$	8.93862	0.758164	0.379082	−	0.925363i	$-0.376240\pi$
$139$	8.93862	0.758164	0.379082	+	0.925363i	$0.376240\pi$
$140$	4.42451	0.373940
$141$	−1.14071	−0.0960648
$142$	−5.38151	−0.451606
$143$	−20.7383	−1.73423
$144$	−2.32606	−0.193838
$145$	2.96480	0.246213
$146$	−11.5800	−0.958371
$147$	3.20783	0.264577
$148$	−10.3518	−0.850911
$149$	−0.514437	−0.0421444	−0.0210722	−	0.999778i	$-0.506708\pi$
$149$	−0.514437	−0.0421444	−0.0210722	+	0.999778i	$0.506708\pi$
$150$	3.92999	0.320882
$151$	10.4431	0.849851	0.424926	−	0.905228i	$-0.360300\pi$
$151$	10.4431	0.849851	0.424926	+	0.905228i	$0.360300\pi$
$152$	−12.9031	−1.04658
$153$	−1.08164	−0.0874457
$154$	1.79762	0.144857
$155$	−21.8644	−1.75619
$156$	5.03474	0.403102
$157$	3.33465	0.266134	0.133067	−	0.991107i	$-0.457517\pi$
$157$	3.33465	0.266134	0.133067	+	0.991107i	$0.457517\pi$
$158$	0.676077	0.0537858
$159$	−0.228503	−0.0181214
$160$	22.8617	1.80738
$161$	5.91310	0.466018
$162$	−5.16836	−0.406065
$163$	15.7960	1.23724	0.618619	−	0.785691i	$-0.287692\pi$
$163$	15.7960	1.23724	0.618619	+	0.785691i	$0.287692\pi$
$164$	15.4463	1.20616
$165$	−5.79585	−0.451207
$166$	−3.34848	−0.259892
$167$	5.43655	0.420693	0.210346	−	0.977627i	$-0.432541\pi$
$167$	5.43655	0.420693	0.210346	+	0.977627i	$0.432541\pi$
$168$	−1.05191	−0.0811570
$169$	36.5518	2.81167
$170$	1.17220	0.0899034
$171$	13.5870	1.03902
$172$	−3.25824	−0.248438
$173$	16.3463	1.24279	0.621394	−	0.783498i	$-0.286567\pi$
$173$	16.3463	1.24279	0.621394	+	0.783498i	$0.286567\pi$
$174$	−0.292437	−0.0221696
$175$	8.17058	0.617637
$176$	−2.49589	−0.188135
$177$	−6.46517	−0.485952
$178$	−2.99854	−0.224750
$179$	5.85712	0.437782	0.218891	−	0.975749i	$-0.429756\pi$
$179$	5.85712	0.437782	0.218891	+	0.975749i	$0.429756\pi$
$180$	−15.1872	−1.13199
$181$	1.87539	0.139396	0.0696982	−	0.997568i	$-0.477796\pi$
$181$	1.87539	0.139396	0.0696982	+	0.997568i	$0.477796\pi$
$182$	−4.29521	−0.318382
$183$	0.940494	0.0695233
$184$	19.2751	1.42098
$185$	−28.4735	−2.09341
$186$	2.15662	0.158131
$187$	−1.16062	−0.0848726
$188$	−3.20729	−0.233915
$189$	2.31797	0.168607
$190$	−14.7245	−1.06823
$191$	2.27837	0.164857	0.0824285	−	0.996597i	$-0.473732\pi$
$191$	2.27837	0.164857	0.0824285	+	0.996597i	$0.473732\pi$
$192$	−1.40041	−0.101066
$193$	13.7983	0.993223	0.496611	−	0.867973i	$-0.334577\pi$
$193$	13.7983	0.993223	0.496611	+	0.867973i	$0.334577\pi$
$194$	−14.3755	−1.03210
$195$	13.8485	0.991711
$196$	9.01935	0.644239
$197$	2.57148	0.183210	0.0916052	−	0.995795i	$-0.470800\pi$
$197$	2.57148	0.183210	0.0916052	+	0.995795i	$0.470800\pi$
$198$	−6.17036	−0.438508
$199$	5.05421	0.358284	0.179142	−	0.983823i	$-0.442668\pi$
$199$	5.05421	0.358284	0.179142	+	0.983823i	$0.442668\pi$
$200$	26.6338	1.88330
$201$	6.21577	0.438427
$202$	−0.270178	−0.0190096
$203$	−0.607985	−0.0426722
$204$	0.281768	0.0197277
$205$	42.4865	2.96738
$206$	12.1587	0.847139
$207$	−20.2968	−1.41072
$208$	5.96362	0.413503
$209$	14.5790	1.00845
$210$	−1.20040	−0.0828357
$211$	−16.1262	−1.11018	−0.555088	−	0.831792i	$-0.687315\pi$
$211$	−16.1262	−1.11018	−0.555088	+	0.831792i	$0.687315\pi$
$212$	−0.642474	−0.0441253
$213$	−3.55812	−0.243798
$214$	11.5154	0.787174
$215$	−8.96206	−0.611207
$216$	7.55594	0.514117
$217$	4.48369	0.304373
$218$	5.33130	0.361081
$219$	−7.65643	−0.517374
$220$	−16.2960	−1.09868
$221$	2.77315	0.186542
$222$	2.80852	0.188495
$223$	8.42872	0.564429	0.282214	−	0.959351i	$-0.408931\pi$
$223$	8.42872	0.564429	0.282214	+	0.959351i	$0.408931\pi$
$224$	−4.68821	−0.313244
$225$	−28.0456	−1.86970
$226$	−3.09211	−0.205684
$227$	−16.3902	−1.08786	−0.543930	−	0.839131i	$-0.683064\pi$
$227$	−16.3902	−1.08786	−0.543930	+	0.839131i	$0.683064\pi$
$228$	−3.53941	−0.234403
$229$	12.4044	0.819703	0.409851	−	0.912152i	$-0.365581\pi$
$229$	12.4044	0.819703	0.409851	+	0.912152i	$0.365581\pi$
$230$	21.9960	1.45037
$231$	1.18854	0.0782004
$232$	−1.98187	−0.130116
$233$	17.4908	1.14586	0.572929	−	0.819605i	$-0.305807\pi$
$233$	17.4908	1.14586	0.572929	+	0.819605i	$0.305807\pi$
$234$	14.7433	0.963802
$235$	−8.82192	−0.575479
$236$	−18.1779	−1.18328
$237$	0.447005	0.0290361
$238$	−0.240380	−0.0155815
$239$	−18.2611	−1.18121	−0.590606	−	0.806960i	$-0.701111\pi$
$239$	−18.2611	−1.18121	−0.590606	+	0.806960i	$0.701111\pi$
$240$	1.66669	0.107584
$241$	15.3425	0.988297	0.494148	−	0.869378i	$-0.335480\pi$
$241$	15.3425	0.988297	0.494148	+	0.869378i	$0.335480\pi$
$242$	1.77023	0.113794
$243$	−12.1108	−0.776908
$244$	2.64436	0.169288
$245$	24.8085	1.58496
$246$	−4.19070	−0.267189
$247$	−34.8348	−2.21648
$248$	14.6156	0.928092
$249$	−2.21393	−0.140302
$250$	15.5161	0.981324
$251$	11.2782	0.711875	0.355938	−	0.934510i	$-0.384162\pi$
$251$	11.2782	0.711875	0.355938	+	0.934510i	$0.384162\pi$
$252$	3.11440	0.196189
$253$	−21.7787	−1.36921
$254$	−10.9053	−0.684262
$255$	0.775027	0.0485341
$256$	−12.8795	−0.804967
$257$	3.90455	0.243559	0.121780	−	0.992557i	$-0.461140\pi$
$257$	3.90455	0.243559	0.121780	+	0.992557i	$0.461140\pi$
$258$	0.883984	0.0550344
$259$	5.83900	0.362818
$260$	38.9374	2.41479
$261$	2.08691	0.129177
$262$	13.2722	0.819961
$263$	−12.1398	−0.748571	−0.374285	−	0.927314i	$-0.622112\pi$
$263$	−12.1398	−0.748571	−0.374285	+	0.927314i	$0.622112\pi$
$264$	3.87433	0.238448
$265$	−1.76718	−0.108557
$266$	3.01952	0.185138
$267$	−1.98256	−0.121331
$268$	17.4767	1.06756
$269$	12.8549	0.783779	0.391889	−	0.920012i	$-0.371822\pi$
$269$	12.8549	0.783779	0.391889	+	0.920012i	$0.371822\pi$
$270$	8.62254	0.524751
$271$	11.4276	0.694176	0.347088	−	0.937832i	$-0.387170\pi$
$271$	11.4276	0.694176	0.347088	+	0.937832i	$0.387170\pi$
$272$	0.333753	0.0202367
$273$	−2.83988	−0.171877
$274$	−8.61937	−0.520715
$275$	−30.0932	−1.81469
$276$	5.28730	0.318258
$277$	−10.4286	−0.626593	−0.313296	−	0.949655i	$-0.601433\pi$
$277$	−10.4286	−0.626593	−0.313296	+	0.949655i	$0.601433\pi$
$278$	−6.81861	−0.408953
$279$	−15.3903	−0.921394
$280$	−8.13523	−0.486173
$281$	8.64987	0.516008	0.258004	−	0.966144i	$-0.416935\pi$
$281$	8.64987	0.516008	0.258004	+	0.966144i	$0.416935\pi$
$282$	0.870161	0.0518173
$283$	−22.5505	−1.34049	−0.670245	−	0.742140i	$-0.733811\pi$
$283$	−22.5505	−1.34049	−0.670245	+	0.742140i	$0.733811\pi$
$284$	−10.0042	−0.593643
$285$	−9.73545	−0.576678
$286$	15.8198	0.935441
$287$	−8.71261	−0.514289
$288$	16.0923	0.948248
$289$	−16.8448	−0.990871
$290$	−2.26163	−0.132807
$291$	−9.50474	−0.557178
$292$	−21.5273	−1.25979
$293$	−10.6374	−0.621444	−0.310722	−	0.950501i	$-0.600571\pi$
$293$	−10.6374	−0.621444	−0.310722	+	0.950501i	$0.600571\pi$
$294$	−2.44702	−0.142713
$295$	−49.9999	−2.91111
$296$	19.0335	1.10630
$297$	−8.53735	−0.495387
$298$	0.392426	0.0227326
$299$	52.0375	3.00940
$300$	7.30586	0.421804
$301$	1.83783	0.105931
$302$	−7.96630	−0.458409
$303$	−0.178635	−0.0102623
$304$	−4.19241	−0.240451
$305$	7.27353	0.416481
$306$	0.825106	0.0471682
$307$	10.2742	0.586382	0.293191	−	0.956054i	$-0.405283\pi$
$307$	10.2742	0.586382	0.293191	+	0.956054i	$0.405283\pi$
$308$	3.34179	0.190416
$309$	8.03904	0.457325
$310$	16.6788	0.947290
$311$	−24.5952	−1.39467	−0.697334	−	0.716746i	$-0.745630\pi$
$311$	−24.5952	−1.39467	−0.697334	+	0.716746i	$0.745630\pi$
$312$	−9.25724	−0.524088
$313$	16.2399	0.917932	0.458966	−	0.888454i	$-0.348220\pi$
$313$	16.2399	0.917932	0.458966	+	0.888454i	$0.348220\pi$
$314$	−2.54376	−0.143553
$315$	8.56644	0.482664
$316$	1.25683	0.0707022
$317$	19.8258	1.11353	0.556763	−	0.830672i	$-0.312043\pi$
$317$	19.8258	1.11353	0.556763	+	0.830672i	$0.312043\pi$
$318$	0.174308	0.00977470
$319$	2.23928	0.125376
$320$	−10.8304	−0.605440
$321$	7.61367	0.424954
$322$	−4.51067	−0.251370
$323$	−1.94952	−0.108474
$324$	−9.60801	−0.533778
$325$	71.9041	3.98852
$326$	−12.0496	−0.667366
$327$	3.52492	0.194929
$328$	−28.4007	−1.56817
$329$	1.80909	0.0997385
$330$	4.42123	0.243381
$331$	−17.3716	−0.954830	−0.477415	−	0.878678i	$-0.658426\pi$
$331$	−17.3716	−0.954830	−0.477415	+	0.878678i	$0.658426\pi$
$332$	−6.22483	−0.341632
$333$	−20.0424	−1.09832
$334$	−4.14714	−0.226921
$335$	48.0711	2.62641
$336$	−0.341784	−0.0186458
$337$	−7.36233	−0.401052	−0.200526	−	0.979688i	$-0.564265\pi$
$337$	−7.36233	−0.401052	−0.200526	+	0.979688i	$0.564265\pi$
$338$	−27.8826	−1.51662
$339$	−2.04442	−0.111038
$340$	2.17912	0.118179
$341$	−16.5140	−0.894281
$342$	−10.3645	−0.560449
$343$	−10.6866	−0.577024
$344$	5.99082	0.323004
$345$	14.5432	0.782979
$346$	−12.4694	−0.670359
$347$	4.81358	0.258407	0.129203	−	0.991618i	$-0.458758\pi$
$347$	4.81358	0.258407	0.129203	+	0.991618i	$0.458758\pi$
$348$	−0.543641	−0.0291422
$349$	−32.5237	−1.74096	−0.870478	−	0.492207i	$-0.836190\pi$
$349$	−32.5237	−1.74096	−0.870478	+	0.492207i	$0.836190\pi$
$350$	−6.23273	−0.333153
$351$	20.3990	1.08882
$352$	17.2672	0.920346
$353$	16.3793	0.871782	0.435891	−	0.899999i	$-0.356433\pi$
$353$	16.3793	0.871782	0.435891	+	0.899999i	$0.356433\pi$
$354$	4.93180	0.262122
$355$	−27.5176	−1.46048
$356$	−5.57430	−0.295438
$357$	−0.158933	−0.00841164
$358$	−4.46796	−0.236139
$359$	−19.1765	−1.01210	−0.506050	−	0.862504i	$-0.668895\pi$
$359$	−19.1765	−1.01210	−0.506050	+	0.862504i	$0.668895\pi$
$360$	27.9242	1.47174
$361$	5.48873	0.288881
$362$	−1.43059	−0.0751903
$363$	1.17043	0.0614316
$364$	−7.98480	−0.418517
$365$	−59.2128	−3.09934
$366$	−0.717433	−0.0375008
$367$	−2.40715	−0.125652	−0.0628261	−	0.998024i	$-0.520011\pi$
$367$	−2.40715	−0.125652	−0.0628261	+	0.998024i	$0.520011\pi$
$368$	6.26278	0.326470
$369$	29.9061	1.55685
$370$	21.7203	1.12919
$371$	0.362392	0.0188144
$372$	4.00917	0.207866
$373$	9.44701	0.489147	0.244574	−	0.969631i	$-0.421352\pi$
$373$	9.44701	0.489147	0.244574	+	0.969631i	$0.421352\pi$
$374$	0.885348	0.0457802
$375$	10.2589	0.529765
$376$	5.89715	0.304122
$377$	−5.35050	−0.275565
$378$	−1.76821	−0.0909468
$379$	−2.99284	−0.153732	−0.0768660	−	0.997041i	$-0.524491\pi$
$379$	−2.99284	−0.153732	−0.0768660	+	0.997041i	$0.524491\pi$
$380$	−27.3728	−1.40420
$381$	−7.21034	−0.369397
$382$	−1.73800	−0.0889238
$383$	33.2120	1.69706	0.848528	−	0.529151i	$-0.177490\pi$
$383$	33.2120	1.69706	0.848528	+	0.529151i	$0.177490\pi$
$384$	−4.84394	−0.247191
$385$	9.19188	0.468462
$386$	−10.5257	−0.535744
$387$	−6.30837	−0.320672
$388$	−26.7242	−1.35671
$389$	−3.81911	−0.193636	−0.0968182	−	0.995302i	$-0.530867\pi$
$389$	−3.81911	−0.193636	−0.0968182	+	0.995302i	$0.530867\pi$
$390$	−10.5640	−0.534929
$391$	2.91226	0.147279
$392$	−16.5836	−0.837599
$393$	8.77527	0.442654
$394$	−1.96159	−0.0988236
$395$	3.45702	0.173942
$396$	−11.4707	−0.576425
$397$	−16.0408	−0.805066	−0.402533	−	0.915405i	$-0.631870\pi$
$397$	−16.0408	−0.805066	−0.402533	+	0.915405i	$0.631870\pi$
$398$	−3.85548	−0.193258
$399$	1.99643	0.0999464
$400$	8.65375	0.432688
$401$	−4.17536	−0.208508	−0.104254	−	0.994551i	$-0.533245\pi$
$401$	−4.17536	−0.208508	−0.104254	+	0.994551i	$0.533245\pi$
$402$	−4.74155	−0.236487
$403$	39.4581	1.96555
$404$	−0.502261	−0.0249884
$405$	−26.4277	−1.31320
$406$	0.463787	0.0230174
$407$	−21.5057	−1.06600
$408$	−0.518079	−0.0256487
$409$	−31.2424	−1.54484	−0.772419	−	0.635114i	$-0.780953\pi$
$409$	−31.2424	−1.54484	−0.772419	+	0.635114i	$0.780953\pi$
$410$	−32.4098	−1.60061
$411$	−5.69891	−0.281107
$412$	22.6031	1.11358
$413$	10.2534	0.504535
$414$	15.4829	0.760943
$415$	−17.1219	−0.840482
$416$	−41.2579	−2.02284
$417$	−4.50829	−0.220772
$418$	−11.1212	−0.543958
$419$	−10.1795	−0.497301	−0.248651	−	0.968593i	$-0.579987\pi$
$419$	−10.1795	−0.497301	−0.248651	+	0.968593i	$0.579987\pi$
$420$	−2.23155	−0.108889
$421$	9.33687	0.455051	0.227525	−	0.973772i	$-0.426936\pi$
$421$	9.33687	0.455051	0.227525	+	0.973772i	$0.426936\pi$
$422$	12.3015	0.598828
$423$	−6.20973	−0.301927
$424$	1.18130	0.0573689
$425$	4.02409	0.195197
$426$	2.71423	0.131505
$427$	−1.49157	−0.0721820
$428$	21.4071	1.03475
$429$	10.4596	0.504995
$430$	6.83649	0.329685
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	2.45504	0.118118
$433$	5.94715	0.285802	0.142901	−	0.989737i	$-0.454357\pi$
$433$	5.94715	0.285802	0.142901	+	0.989737i	$0.454357\pi$
$434$	−3.42028	−0.164179
$435$	−1.49533	−0.0716956
$436$	9.91091	0.474646
$437$	−36.5822	−1.74996
$438$	5.84052	0.279071
$439$	−21.4239	−1.02251	−0.511253	−	0.859430i	$-0.670819\pi$
$439$	−21.4239	−1.02251	−0.511253	+	0.859430i	$0.670819\pi$
$440$	29.9630	1.42843
$441$	17.4626	0.831554
$442$	−2.11543	−0.100621
$443$	−16.4937	−0.783640	−0.391820	−	0.920042i	$-0.628154\pi$
$443$	−16.4937	−0.783640	−0.391820	+	0.920042i	$0.628154\pi$
$444$	5.22104	0.247780
$445$	−15.3326	−0.726835
$446$	−6.42965	−0.304453
$447$	0.259462	0.0122721
$448$	2.22097	0.104931
$449$	5.97396	0.281929	0.140964	−	0.990015i	$-0.454980\pi$
$449$	5.97396	0.281929	0.140964	+	0.990015i	$0.454980\pi$
$450$	21.3939	1.00852
$451$	32.0896	1.51104
$452$	−5.74823	−0.270374
$453$	−5.26712	−0.247471
$454$	12.5029	0.586791
$455$	−21.9629	−1.02964
$456$	6.50781	0.304756
$457$	−5.59547	−0.261745	−0.130873	−	0.991399i	$-0.541778\pi$
$457$	−5.59547	−0.261745	−0.130873	+	0.991399i	$0.541778\pi$
$458$	−9.46236	−0.442147
$459$	1.14162	0.0532864
$460$	40.8906	1.90653
$461$	25.6839	1.19622	0.598109	−	0.801415i	$-0.295919\pi$
$461$	25.6839	1.19622	0.598109	+	0.801415i	$0.295919\pi$
$462$	−0.906652	−0.0421813
$463$	−10.4231	−0.484401	−0.242201	−	0.970226i	$-0.577869\pi$
$463$	−10.4231	−0.484401	−0.242201	+	0.970226i	$0.577869\pi$
$464$	−0.643939	−0.0298941
$465$	11.0276	0.511391
$466$	−13.3424	−0.618075
$467$	8.80090	0.407257	0.203629	−	0.979048i	$-0.434727\pi$
$467$	8.80090	0.407257	0.203629	+	0.979048i	$0.434727\pi$
$468$	27.4079	1.26693
$469$	−9.85785	−0.455193
$470$	6.72959	0.310413
$471$	−1.68187	−0.0774965
$472$	33.4232	1.53843
$473$	−6.76895	−0.311237
$474$	−0.340987	−0.0156621
$475$	−50.5483	−2.31932
$476$	−0.446867	−0.0204821
$477$	−1.24391	−0.0569548
$478$	13.9300	0.637145
$479$	−12.8610	−0.587636	−0.293818	−	0.955861i	$-0.594926\pi$
$479$	−12.8610	−0.587636	−0.293818	+	0.955861i	$0.594926\pi$
$480$	−11.5306	−0.526296
$481$	51.3853	2.34297
$482$	−11.7037	−0.533087
$483$	−2.98234	−0.135701
$484$	3.29086	0.149584
$485$	−73.5071	−3.33779
$486$	9.23843	0.419064
$487$	−12.1808	−0.551965	−0.275982	−	0.961163i	$-0.589003\pi$
$487$	−12.1808	−0.551965	−0.275982	+	0.961163i	$0.589003\pi$
$488$	−4.86210	−0.220097
$489$	−7.96689	−0.360275
$490$	−18.9246	−0.854925
$491$	14.1471	0.638451	0.319225	−	0.947679i	$-0.396577\pi$
$491$	14.1471	0.638451	0.319225	+	0.947679i	$0.396577\pi$
$492$	−7.79053	−0.351224
$493$	−0.299439	−0.0134861
$494$	26.5729	1.19557
$495$	−31.5512	−1.41812
$496$	4.74884	0.213229
$497$	5.64297	0.253122
$498$	1.68884	0.0756788
$499$	−12.6940	−0.568261	−0.284130	−	0.958786i	$-0.591705\pi$
$499$	−12.6940	−0.568261	−0.284130	+	0.958786i	$0.591705\pi$
$500$	28.8445	1.28996
$501$	−2.74198	−0.122503
$502$	−8.60332	−0.383985
$503$	29.4917	1.31497	0.657486	−	0.753467i	$-0.271620\pi$
$503$	29.4917	1.31497	0.657486	+	0.753467i	$0.271620\pi$
$504$	−5.72637	−0.255073
$505$	−1.38151	−0.0614766
$506$	16.6133	0.738552
$507$	−18.4353	−0.818741
$508$	−20.2731	−0.899472
$509$	11.2544	0.498843	0.249421	−	0.968395i	$-0.419760\pi$
$509$	11.2544	0.498843	0.249421	+	0.968395i	$0.419760\pi$
$510$	−0.591211	−0.0261793
$511$	12.1426	0.537159
$512$	−9.38340	−0.414691
$513$	−14.3404	−0.633145
$514$	−2.97850	−0.131376
$515$	62.1718	2.73962
$516$	1.64333	0.0723435
$517$	−6.66310	−0.293043
$518$	−4.45414	−0.195704
$519$	−8.24445	−0.361891
$520$	−71.5930	−3.13956
$521$	43.1760	1.89158	0.945788	−	0.324786i	$-0.105292\pi$
$521$	43.1760	1.89158	0.945788	+	0.324786i	$0.105292\pi$
$522$	−1.59195	−0.0696779
$523$	30.6334	1.33951	0.669753	−	0.742584i	$-0.266400\pi$
$523$	30.6334	1.33951	0.669753	+	0.742584i	$0.266400\pi$
$524$	24.6731	1.07785
$525$	−4.12092	−0.179852
$526$	9.26054	0.403779
$527$	2.20826	0.0961935
$528$	1.25883	0.0547835
$529$	31.6478	1.37599
$530$	1.34805	0.0585556
$531$	−35.1948	−1.52732
$532$	5.61329	0.243367
$533$	−76.6742	−3.32113
$534$	1.51235	0.0654458
$535$	58.8821	2.54569
$536$	−32.1339	−1.38797
$537$	−2.95410	−0.127479
$538$	−9.80607	−0.422770
$539$	18.7376	0.807085
$540$	16.0293	0.689793
$541$	−21.0763	−0.906139	−0.453070	−	0.891475i	$-0.649671\pi$
$541$	−21.0763	−0.906139	−0.453070	+	0.891475i	$0.649671\pi$
$542$	−8.71726	−0.374438
$543$	−0.945872	−0.0405913
$544$	−2.30899	−0.0989971
$545$	27.2608	1.16772
$546$	2.16634	0.0927106
$547$	13.7175	0.586519	0.293260	−	0.956033i	$-0.405260\pi$
$547$	13.7175	0.586519	0.293260	+	0.956033i	$0.405260\pi$
$548$	−16.0234	−0.684488
$549$	5.11982	0.218509
$550$	22.9559	0.978842
$551$	3.76138	0.160240
$552$	−9.72161	−0.413779
$553$	−0.708924	−0.0301465
$554$	7.95520	0.337984
$555$	14.3609	0.609587
$556$	−12.6758	−0.537575
$557$	−35.0576	−1.48544	−0.742720	−	0.669602i	$-0.766465\pi$
$557$	−35.0576	−1.48544	−0.742720	+	0.669602i	$0.766465\pi$
$558$	11.7401	0.496999
$559$	16.1736	0.684070
$560$	−2.64326	−0.111698
$561$	0.585370	0.0247143
$562$	−6.59835	−0.278334
$563$	−29.3929	−1.23876	−0.619381	−	0.785090i	$-0.712617\pi$
$563$	−29.3929	−1.23876	−0.619381	+	0.785090i	$0.712617\pi$
$564$	1.61763	0.0681146
$565$	−15.8110	−0.665174
$566$	17.2021	0.723059
$567$	5.41946	0.227596
$568$	18.3945	0.771817
$569$	−17.7677	−0.744860	−0.372430	−	0.928060i	$-0.621475\pi$
$569$	−17.7677	−0.744860	−0.372430	+	0.928060i	$0.621475\pi$
$570$	7.42646	0.311060
$571$	−39.7364	−1.66292	−0.831459	−	0.555587i	$-0.812494\pi$
$571$	−39.7364	−1.66292	−0.831459	+	0.555587i	$0.812494\pi$
$572$	29.4090	1.22965
$573$	−1.14912	−0.0480053
$574$	6.64621	0.277407
$575$	75.5110	3.14903
$576$	−7.62351	−0.317646
$577$	−10.1482	−0.422477	−0.211238	−	0.977435i	$-0.567750\pi$
$577$	−10.1482	−0.422477	−0.211238	+	0.977435i	$0.567750\pi$
$578$	12.8497	0.534475
$579$	−6.95932	−0.289220
$580$	−4.20437	−0.174577
$581$	3.51116	0.145667
$582$	7.25046	0.300541
$583$	−1.33473	−0.0552789
$584$	39.5817	1.63790
$585$	75.3878	3.11690
$586$	8.11449	0.335206
$587$	26.6622	1.10047	0.550234	−	0.835011i	$-0.314539\pi$
$587$	26.6622	1.10047	0.550234	+	0.835011i	$0.314539\pi$
$588$	−4.54901	−0.187598
$589$	−27.7390	−1.14296
$590$	38.1412	1.57025
$591$	−1.29696	−0.0533496
$592$	6.18429	0.254173
$593$	4.64555	0.190770	0.0953849	−	0.995440i	$-0.469592\pi$
$593$	4.64555	0.190770	0.0953849	+	0.995440i	$0.469592\pi$
$594$	6.51251	0.267212
$595$	−1.22915	−0.0503901
$596$	0.729522	0.0298824
$597$	−2.54915	−0.104330
$598$	−39.6955	−1.62327
$599$	−24.7553	−1.01147	−0.505736	−	0.862688i	$-0.668779\pi$
$599$	−24.7553	−1.01147	−0.505736	+	0.862688i	$0.668779\pi$
$600$	−13.4331	−0.548403
$601$	−37.3762	−1.52461	−0.762304	−	0.647219i	$-0.775932\pi$
$601$	−37.3762	−1.52461	−0.762304	+	0.647219i	$0.775932\pi$
$602$	−1.40195	−0.0571390
$603$	33.8371	1.37795
$604$	−14.8094	−0.602585
$605$	9.05179	0.368008
$606$	0.136267	0.00553548
$607$	26.9871	1.09537	0.547686	−	0.836684i	$-0.315509\pi$
$607$	26.9871	1.09537	0.547686	+	0.836684i	$0.315509\pi$
$608$	29.0042	1.17628
$609$	0.306644	0.0124259
$610$	−5.54844	−0.224650
$611$	15.9207	0.644082
$612$	1.53388	0.0620032
$613$	−16.4687	−0.665165	−0.332583	−	0.943074i	$-0.607920\pi$
$613$	−16.4687	−0.665165	−0.332583	+	0.943074i	$0.607920\pi$
$614$	−7.83746	−0.316294
$615$	−21.4285	−0.864082
$616$	−6.14445	−0.247567
$617$	17.0863	0.687868	0.343934	−	0.938994i	$-0.388240\pi$
$617$	17.0863	0.687868	0.343934	+	0.938994i	$0.388240\pi$
$618$	−6.13239	−0.246681
$619$	17.2504	0.693350	0.346675	−	0.937985i	$-0.387311\pi$
$619$	17.2504	0.693350	0.346675	+	0.937985i	$0.387311\pi$
$620$	31.0059	1.24523
$621$	21.4223	0.859646
$622$	18.7619	0.752283
$623$	3.14423	0.125971
$624$	−3.00782	−0.120409
$625$	28.2660	1.13064
$626$	−12.3882	−0.495132
$627$	−7.35308	−0.293654
$628$	−4.72886	−0.188702
$629$	2.87576	0.114664
$630$	−6.53470	−0.260349
$631$	−22.2393	−0.885334	−0.442667	−	0.896686i	$-0.645968\pi$
$631$	−22.2393	−0.885334	−0.442667	+	0.896686i	$0.645968\pi$
$632$	−2.31090	−0.0919225
$633$	8.13345	0.323275
$634$	−15.1236	−0.600635
$635$	−55.7628	−2.21288
$636$	0.324039	0.0128490
$637$	−44.7712	−1.77390
$638$	−1.70818	−0.0676276
$639$	−19.3695	−0.766247
$640$	−37.4617	−1.48080
$641$	9.62162	0.380031	0.190016	−	0.981781i	$-0.439146\pi$
$641$	9.62162	0.380031	0.190016	+	0.981781i	$0.439146\pi$
$642$	−5.80791	−0.229220
$643$	−22.9895	−0.906619	−0.453310	−	0.891353i	$-0.649757\pi$
$643$	−22.9895	−0.906619	−0.453310	+	0.891353i	$0.649757\pi$
$644$	−8.38535	−0.330429
$645$	4.52012	0.177979
$646$	1.48714	0.0585108
$647$	17.6777	0.694983	0.347491	−	0.937683i	$-0.387034\pi$
$647$	17.6777	0.694983	0.347491	+	0.937683i	$0.387034\pi$
$648$	17.6660	0.693985
$649$	−37.7644	−1.48238
$650$	−54.8503	−2.15141
$651$	−2.26140	−0.0886313
$652$	−22.4002	−0.877261
$653$	30.7840	1.20467	0.602336	−	0.798243i	$-0.294237\pi$
$653$	30.7840	1.20467	0.602336	+	0.798243i	$0.294237\pi$
$654$	−2.68890	−0.105144
$655$	67.8656	2.65173
$656$	−9.22784	−0.360287
$657$	−41.6797	−1.62608
$658$	−1.38002	−0.0537989
$659$	−17.1562	−0.668310	−0.334155	−	0.942518i	$-0.608451\pi$
$659$	−17.1562	−0.668310	−0.334155	+	0.942518i	$0.608451\pi$
$660$	8.21908	0.319927
$661$	24.4127	0.949546	0.474773	−	0.880108i	$-0.342530\pi$
$661$	24.4127	0.949546	0.474773	+	0.880108i	$0.342530\pi$
$662$	13.2515	0.515035
$663$	−1.39867	−0.0543199
$664$	11.4454	0.444168
$665$	15.4398	0.598732
$666$	15.2889	0.592432
$667$	−5.61889	−0.217564
$668$	−7.70955	−0.298291
$669$	−4.25112	−0.164358
$670$	−36.6699	−1.41668
$671$	5.49362	0.212079
$672$	2.36455	0.0912145
$673$	27.1193	1.04537	0.522686	−	0.852525i	$-0.324930\pi$
$673$	27.1193	1.04537	0.522686	+	0.852525i	$0.324930\pi$
$674$	5.61618	0.216327
$675$	29.6007	1.13933
$676$	−51.8339	−1.99361
$677$	41.0355	1.57712	0.788562	−	0.614956i	$-0.210826\pi$
$677$	41.0355	1.57712	0.788562	+	0.614956i	$0.210826\pi$
$678$	1.55954	0.0598937
$679$	15.0740	0.578485
$680$	−4.00668	−0.153649
$681$	8.26661	0.316777
$682$	12.5973	0.482375
$683$	7.57432	0.289823	0.144912	−	0.989445i	$-0.453710\pi$
$683$	7.57432	0.289823	0.144912	+	0.989445i	$0.453710\pi$
$684$	−19.2677	−0.736718
$685$	−44.0739	−1.68398
$686$	8.15205	0.311247
$687$	−6.25628	−0.238692
$688$	1.94651	0.0742101
$689$	3.18918	0.121498
$690$	−11.0939	−0.422338
$691$	−5.85472	−0.222724	−0.111362	−	0.993780i	$-0.535521\pi$
$691$	−5.85472	−0.222724	−0.111362	+	0.993780i	$0.535521\pi$
$692$	−23.1807	−0.881196
$693$	6.47014	0.245780
$694$	−3.67193	−0.139384
$695$	−34.8659	−1.32254
$696$	0.999577	0.0378889
$697$	−4.29105	−0.162535
$698$	24.8100	0.939071
$699$	−8.82167	−0.333666
$700$	−11.5867	−0.437935
$701$	−3.77528	−0.142590	−0.0712952	−	0.997455i	$-0.522713\pi$
$701$	−3.77528	−0.142590	−0.0712952	+	0.997455i	$0.522713\pi$
$702$	−15.5609	−0.587307
$703$	−36.1237	−1.36243
$704$	−8.18011	−0.308300
$705$	4.44944	0.167575
$706$	−12.4946	−0.470239
$707$	0.283304	0.0106547
$708$	9.16823	0.344563
$709$	5.58035	0.209574	0.104787	−	0.994495i	$-0.466584\pi$
$709$	5.58035	0.209574	0.104787	+	0.994495i	$0.466584\pi$
$710$	20.9911	0.787782
$711$	2.43339	0.0912591
$712$	10.2493	0.384109
$713$	41.4375	1.55185
$714$	0.121238	0.00453723
$715$	80.8919	3.02519
$716$	−8.30596	−0.310408
$717$	9.21018	0.343961
$718$	14.6284	0.545926
$719$	36.4226	1.35833	0.679167	−	0.733984i	$-0.262341\pi$
$719$	36.4226	1.35833	0.679167	+	0.733984i	$0.262341\pi$
$720$	9.07303	0.338132
$721$	−12.7494	−0.474814
$722$	−4.18695	−0.155822
$723$	−7.73816	−0.287785
$724$	−2.65948	−0.0988387
$725$	−7.76405	−0.288350
$726$	−0.892834	−0.0331362
$727$	−18.5317	−0.687303	−0.343651	−	0.939097i	$-0.611664\pi$
$727$	−18.5317	−0.687303	−0.343651	+	0.939097i	$0.611664\pi$
$728$	14.6814	0.544130
$729$	−14.2176	−0.526579
$730$	45.1691	1.67178
$731$	0.905150	0.0334782
$732$	−1.33371	−0.0492954
$733$	35.1901	1.29978	0.649889	−	0.760030i	$-0.274816\pi$
$733$	35.1901	1.29978	0.649889	+	0.760030i	$0.274816\pi$
$734$	1.83624	0.0677768
$735$	−12.5125	−0.461529
$736$	−43.3276	−1.59708
$737$	36.3076	1.33741
$738$	−22.8132	−0.839764
$739$	12.0692	0.443973	0.221986	−	0.975050i	$-0.428746\pi$
$739$	12.0692	0.443973	0.221986	+	0.975050i	$0.428746\pi$
$740$	40.3781	1.48433
$741$	17.5693	0.645425
$742$	−0.276442	−0.0101485
$743$	−21.7032	−0.796213	−0.398106	−	0.917339i	$-0.630333\pi$
$743$	−21.7032	−0.796213	−0.398106	+	0.917339i	$0.630333\pi$
$744$	−7.37155	−0.270254
$745$	2.00661	0.0735166
$746$	−7.20642	−0.263846
$747$	−12.0521	−0.440963
$748$	1.64586	0.0601788
$749$	−12.0748	−0.441205
$750$	−7.82572	−0.285755
$751$	42.9590	1.56760	0.783798	−	0.621016i	$-0.213280\pi$
$751$	42.9590	1.56760	0.783798	+	0.621016i	$0.213280\pi$
$752$	1.91608	0.0698721
$753$	−5.68830	−0.207293
$754$	4.08150	0.148639
$755$	−40.7345	−1.48248
$756$	−3.28710	−0.119551
$757$	−37.1921	−1.35177	−0.675886	−	0.737007i	$-0.736239\pi$
$757$	−37.1921	−1.35177	−0.675886	+	0.737007i	$0.736239\pi$
$758$	2.28302	0.0829229
$759$	10.9843	0.398705
$760$	50.3297	1.82565
$761$	30.4030	1.10211	0.551053	−	0.834470i	$-0.314226\pi$
$761$	30.4030	1.10211	0.551053	+	0.834470i	$0.314226\pi$
$762$	5.50023	0.199252
$763$	−5.59032	−0.202383
$764$	−3.23095	−0.116892
$765$	4.21906	0.152540
$766$	−25.3350	−0.915391
$767$	90.2334	3.25814
$768$	6.49591	0.234401
$769$	7.02764	0.253423	0.126712	−	0.991940i	$-0.459558\pi$
$769$	7.02764	0.253423	0.126712	+	0.991940i	$0.459558\pi$
$770$	−7.01181	−0.252688
$771$	−1.96931	−0.0709228
$772$	−19.5673	−0.704243
$773$	30.2946	1.08962	0.544811	−	0.838559i	$-0.316602\pi$
$773$	30.2946	1.08962	0.544811	+	0.838559i	$0.316602\pi$
$774$	4.81219	0.172971
$775$	57.2573	2.05674
$776$	49.1370	1.76391
$777$	−2.94496	−0.105650
$778$	2.91331	0.104447
$779$	53.9017	1.93123
$780$	−19.6385	−0.703171
$781$	−20.7837	−0.743700
$782$	−2.22155	−0.0794424
$783$	−2.20264	−0.0787159
$784$	−5.38828	−0.192439
$785$	−13.0071	−0.464245
$786$	−6.69400	−0.238767
$787$	21.4271	0.763794	0.381897	−	0.924205i	$-0.375271\pi$
$787$	21.4271	0.763794	0.381897	+	0.924205i	$0.375271\pi$
$788$	−3.64661	−0.129905
$789$	6.12283	0.217979
$790$	−2.63710	−0.0938240
$791$	3.24233	0.115284
$792$	21.0909	0.749432
$793$	−13.1263	−0.466130
$794$	12.2364	0.434252
$795$	0.891297	0.0316110
$796$	−7.16736	−0.254040
$797$	−18.2989	−0.648181	−0.324091	−	0.946026i	$-0.605058\pi$
$797$	−18.2989	−0.648181	−0.324091	+	0.946026i	$0.605058\pi$
$798$	−1.52293	−0.0539111
$799$	0.890996	0.0315212
$800$	−59.8690	−2.11669
$801$	−10.7926	−0.381337
$802$	3.18507	0.112469
$803$	−44.7228	−1.57823
$804$	−8.81456	−0.310866
$805$	−23.0646	−0.812921
$806$	−30.0997	−1.06022
$807$	−6.48353	−0.228231
$808$	0.923494	0.0324884
$809$	2.59577	0.0912624	0.0456312	−	0.998958i	$-0.485470\pi$
$809$	2.59577	0.0912624	0.0456312	+	0.998958i	$0.485470\pi$
$810$	20.1597	0.708340
$811$	39.0518	1.37129	0.685646	−	0.727935i	$-0.259520\pi$
$811$	39.0518	1.37129	0.685646	+	0.727935i	$0.259520\pi$
$812$	0.862182	0.0302567
$813$	−5.76363	−0.202139
$814$	16.4051	0.574999
$815$	−61.6138	−2.15824
$816$	−0.168332	−0.00589279
$817$	−11.3700	−0.397785
$818$	23.8325	0.833284
$819$	−15.4596	−0.540203
$820$	−60.2499	−2.10402
$821$	24.0702	0.840057	0.420028	−	0.907511i	$-0.362020\pi$
$821$	24.0702	0.840057	0.420028	+	0.907511i	$0.362020\pi$
$822$	4.34728	0.151629
$823$	−14.1358	−0.492744	−0.246372	−	0.969175i	$-0.579238\pi$
$823$	−14.1358	−0.492744	−0.246372	+	0.969175i	$0.579238\pi$
$824$	−41.5597	−1.44780
$825$	15.1778	0.528425
$826$	−7.82154	−0.272146
$827$	−8.20230	−0.285222	−0.142611	−	0.989779i	$-0.545550\pi$
$827$	−8.20230	−0.285222	−0.142611	+	0.989779i	$0.545550\pi$
$828$	28.7828	1.00027
$829$	29.4740	1.02368	0.511838	−	0.859082i	$-0.328965\pi$
$829$	29.4740	1.02368	0.511838	+	0.859082i	$0.328965\pi$
$830$	13.0611	0.453356
$831$	5.25978	0.182460
$832$	19.5454	0.677615
$833$	−2.50561	−0.0868142
$834$	3.43904	0.119084
$835$	−21.2058	−0.733856
$836$	−20.6744	−0.715040
$837$	16.2437	0.561465
$838$	7.76519	0.268244
$839$	30.8066	1.06356	0.531781	−	0.846882i	$-0.321523\pi$
$839$	30.8066	1.06356	0.531781	+	0.846882i	$0.321523\pi$
$840$	4.10310	0.141570
$841$	−28.4223	−0.980078
$842$	−7.12240	−0.245454
$843$	−4.36266	−0.150258
$844$	22.8685	0.787168
$845$	−142.574	−4.90469
$846$	4.73694	0.162859
$847$	−1.85623	−0.0637809
$848$	0.383822	0.0131805
$849$	11.3736	0.390341
$850$	−3.06968	−0.105289
$851$	53.9630	1.84983
$852$	5.04576	0.172865
$853$	52.7834	1.80727	0.903634	−	0.428305i	$-0.140889\pi$
$853$	52.7834	1.80727	0.903634	+	0.428305i	$0.140889\pi$
$854$	1.13781	0.0389350
$855$	−52.9974	−1.81247
$856$	−39.3606	−1.34532
$857$	−17.7549	−0.606497	−0.303249	−	0.952911i	$-0.598071\pi$
$857$	−17.7549	−0.606497	−0.303249	+	0.952911i	$0.598071\pi$
$858$	−7.97887	−0.272394
$859$	−45.5665	−1.55471	−0.777355	−	0.629063i	$-0.783439\pi$
$859$	−45.5665	−1.55471	−0.777355	+	0.629063i	$0.783439\pi$
$860$	12.7091	0.433375
$861$	4.39430	0.149757
$862$	−0.762826	−0.0259820
$863$	1.71146	0.0582587	0.0291294	−	0.999576i	$-0.490727\pi$
$863$	1.71146	0.0582587	0.0291294	+	0.999576i	$0.490727\pi$
$864$	−16.9847	−0.577830
$865$	−63.7604	−2.16792
$866$	−4.53664	−0.154161
$867$	8.49587	0.288535
$868$	−6.35831	−0.215815
$869$	2.61105	0.0885738
$870$	1.14068	0.0386726
$871$	−86.7527	−2.93950
$872$	−18.2229	−0.617105
$873$	−51.7415	−1.75118
$874$	27.9058	0.943929
$875$	−16.2699	−0.550024
$876$	10.8576	0.366843
$877$	42.5013	1.43517	0.717584	−	0.696472i	$-0.245248\pi$
$877$	42.5013	1.43517	0.717584	+	0.696472i	$0.245248\pi$
$878$	16.3427	0.551540
$879$	5.36510	0.180960
$880$	9.73545	0.328182
$881$	47.3462	1.59513	0.797567	−	0.603231i	$-0.206120\pi$
$881$	47.3462	1.59513	0.797567	+	0.603231i	$0.206120\pi$
$882$	−13.3210	−0.448540
$883$	−44.0352	−1.48190	−0.740951	−	0.671559i	$-0.765625\pi$
$883$	−44.0352	−1.48190	−0.740951	+	0.671559i	$0.765625\pi$
$884$	−3.93259	−0.132267
$885$	25.2180	0.847694
$886$	12.5818	0.422695
$887$	15.6633	0.525923	0.262962	−	0.964806i	$-0.415301\pi$
$887$	15.6633	0.525923	0.262962	+	0.964806i	$0.415301\pi$
$888$	−9.59978	−0.322147
$889$	11.4352	0.383523
$890$	11.6961	0.392055
$891$	−19.9605	−0.668703
$892$	−11.9527	−0.400207
$893$	−11.1922	−0.374532
$894$	−0.197925	−0.00661959
$895$	−22.8463	−0.763666
$896$	7.68220	0.256644
$897$	−26.2457	−0.876318
$898$	−4.55709	−0.152072
$899$	−4.26061	−0.142099
$900$	39.7713	1.32571
$901$	0.178482	0.00594608
$902$	−24.4788	−0.815054
$903$	−0.926931	−0.0308463
$904$	10.5691	0.351523
$905$	−7.31512	−0.243163
$906$	4.01790	0.133486
$907$	−4.05621	−0.134684	−0.0673421	−	0.997730i	$-0.521452\pi$
$907$	−4.05621	−0.134684	−0.0673421	+	0.997730i	$0.521452\pi$
$908$	23.2430	0.771344
$909$	−0.972444	−0.0322539
$910$	16.7539	0.555385
$911$	−21.0079	−0.696022	−0.348011	−	0.937491i	$-0.613143\pi$
$911$	−21.0079	−0.696022	−0.348011	+	0.937491i	$0.613143\pi$
$912$	2.11449	0.0700178
$913$	−12.9320	−0.427987
$914$	4.26837	0.141185
$915$	−3.66849	−0.121276
$916$	−17.5906	−0.581209
$917$	−13.9171	−0.459582
$918$	−0.870860	−0.0287427
$919$	−1.82444	−0.0601826	−0.0300913	−	0.999547i	$-0.509580\pi$
$919$	−1.82444	−0.0601826	−0.0300913	+	0.999547i	$0.509580\pi$
$920$	−75.1844	−2.47875
$921$	−5.18193	−0.170750
$922$	−19.5923	−0.645239
$923$	49.6602	1.63458
$924$	−1.68547	−0.0554479
$925$	74.5647	2.45167
$926$	7.95099	0.261286
$927$	43.7626	1.43735
$928$	4.45495	0.146241
$929$	18.4341	0.604805	0.302402	−	0.953180i	$-0.402211\pi$
$929$	18.4341	0.604805	0.302402	+	0.953180i	$0.402211\pi$
$930$	−8.41212	−0.275844
$931$	31.4740	1.03152
$932$	−24.8036	−0.812469
$933$	12.4049	0.406118
$934$	−6.71356	−0.219674
$935$	4.52709	0.148052
$936$	−50.3941	−1.64718
$937$	−5.62021	−0.183604	−0.0918021	−	0.995777i	$-0.529263\pi$
$937$	−5.62021	−0.183604	−0.0918021	+	0.995777i	$0.529263\pi$
$938$	7.51982	0.245531
$939$	−8.19077	−0.267296
$940$	12.5103	0.408042
$941$	39.8933	1.30049	0.650243	−	0.759727i	$-0.274667\pi$
$941$	39.8933	1.30049	0.650243	+	0.759727i	$0.274667\pi$
$942$	1.28298	0.0418016
$943$	−80.5204	−2.62211
$944$	10.8597	0.353454
$945$	−9.04146	−0.294119
$946$	5.16353	0.167881
$947$	−1.90270	−0.0618294	−0.0309147	−	0.999522i	$-0.509842\pi$
$947$	−1.90270	−0.0618294	−0.0309147	+	0.999522i	$0.509842\pi$
$948$	−0.633896	−0.0205880
$949$	106.860	3.46881
$950$	38.5596	1.25104
$951$	−9.99934	−0.324251
$952$	0.821642	0.0266296
$953$	23.2751	0.753954	0.376977	−	0.926223i	$-0.376964\pi$
$953$	23.2751	0.753954	0.376977	+	0.926223i	$0.376964\pi$
$954$	0.948889	0.0307214
$955$	−8.88700	−0.287577
$956$	25.8960	0.837536
$957$	−1.12941	−0.0365086
$958$	9.81074	0.316971
$959$	9.03814	0.291857
$960$	5.46245	0.176300
$961$	0.420559	0.0135664
$962$	−39.1981	−1.26380
$963$	41.4469	1.33561
$964$	−21.7571	−0.700750
$965$	−53.8216	−1.73258
$966$	2.27501	0.0731972
$967$	−10.2236	−0.328768	−0.164384	−	0.986396i	$-0.552564\pi$
$967$	−10.2236	−0.328768	−0.164384	+	0.986396i	$0.552564\pi$
$968$	−6.05080	−0.194480
$969$	0.983261	0.0315869
$970$	56.0732	1.80040
$971$	0.885195	0.0284073	0.0142036	−	0.999899i	$-0.495479\pi$
$971$	0.885195	0.0284073	0.0142036	+	0.999899i	$0.495479\pi$
$972$	17.1743	0.550865
$973$	7.14989	0.229215
$974$	9.29183	0.297730
$975$	−36.2656	−1.16143
$976$	−1.57977	−0.0505673
$977$	−50.3194	−1.60986	−0.804930	−	0.593370i	$-0.797797\pi$
$977$	−50.3194	−1.60986	−0.804930	+	0.593370i	$0.797797\pi$
$978$	6.07735	0.194332
$979$	−11.5806	−0.370116
$980$	−35.1808	−1.12381
$981$	19.1888	0.612652
$982$	−10.7918	−0.344380
$983$	32.5727	1.03891	0.519454	−	0.854499i	$-0.326136\pi$
$983$	32.5727	1.03891	0.519454	+	0.854499i	$0.326136\pi$
$984$	14.3242	0.456640
$985$	−10.0303	−0.319592
$986$	0.228420	0.00727437
$987$	−0.912437	−0.0290432
$988$	49.3990	1.57159
$989$	16.9849	0.540089
$990$	24.0681	0.764934
$991$	42.2425	1.34188	0.670938	−	0.741513i	$-0.265892\pi$
$991$	42.2425	1.34188	0.670938	+	0.741513i	$0.265892\pi$
$992$	−32.8538	−1.04311
$993$	8.76157	0.278040
$994$	−4.30460	−0.136534
$995$	−19.7144	−0.624990
$996$	3.13956	0.0994809
$997$	−32.2633	−1.02179	−0.510894	−	0.859644i	$-0.670686\pi$
$997$	−32.2633	−1.02179	−0.510894	+	0.859644i	$0.670686\pi$
$998$	9.68330	0.306520
$999$	21.1538	0.669276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.2.a.f.1.9	✓	24
3.2	odd	2		3879.2.a.r.1.16		24
4.3	odd	2		6896.2.a.w.1.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.2.a.f.1.9	✓	24	1.1	even	1	trivial
3879.2.a.r.1.16		24	3.2	odd	2
6896.2.a.w.1.13		24	4.3	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	431.a (trivial)

\(f(q)\)	\(=\)	\(q-0.762826 q^{2} -0.504361 q^{3} -1.41810 q^{4} -3.90060 q^{5} +0.384740 q^{6} +0.799887 q^{7} +2.60741 q^{8} -2.74562 q^{9} +2.97548 q^{10} -2.94608 q^{11} +0.715233 q^{12} +7.03930 q^{13} -0.610175 q^{14} +1.96731 q^{15} +0.847190 q^{16} +0.393953 q^{17} +2.09443 q^{18} -4.94861 q^{19} +5.53142 q^{20} -0.403432 q^{21} +2.24735 q^{22} +7.39242 q^{23} -1.31508 q^{24} +10.2147 q^{25} -5.36976 q^{26} +2.89787 q^{27} -1.13432 q^{28} -0.760089 q^{29} -1.50072 q^{30} +5.60540 q^{31} -5.86108 q^{32} +1.48589 q^{33} -0.300517 q^{34} -3.12004 q^{35} +3.89355 q^{36} +7.29977 q^{37} +3.77493 q^{38} -3.55035 q^{39} -10.1705 q^{40} -10.8923 q^{41} +0.307749 q^{42} +2.29761 q^{43} +4.17782 q^{44} +10.7096 q^{45} -5.63913 q^{46} +2.26168 q^{47} -0.427290 q^{48} -6.36018 q^{49} -7.79201 q^{50} -0.198694 q^{51} -9.98241 q^{52} +0.453054 q^{53} -2.21057 q^{54} +11.4915 q^{55} +2.08564 q^{56} +2.49589 q^{57} +0.579816 q^{58} +12.8185 q^{59} -2.78984 q^{60} -1.86472 q^{61} -4.27595 q^{62} -2.19619 q^{63} +2.77661 q^{64} -27.4575 q^{65} -1.13347 q^{66} -12.3240 q^{67} -0.558663 q^{68} -3.72845 q^{69} +2.38005 q^{70} +7.05470 q^{71} -7.15896 q^{72} +15.1804 q^{73} -5.56846 q^{74} -5.15188 q^{75} +7.01760 q^{76} -2.35653 q^{77} +2.70830 q^{78} -0.886279 q^{79} -3.30455 q^{80} +6.77529 q^{81} +8.30893 q^{82} +4.38957 q^{83} +0.572106 q^{84} -1.53665 q^{85} -1.75268 q^{86} +0.383359 q^{87} -7.68165 q^{88} +3.93084 q^{89} -8.16953 q^{90} +5.63065 q^{91} -10.4832 q^{92} -2.82715 q^{93} -1.72527 q^{94} +19.3025 q^{95} +2.95610 q^{96} +18.8451 q^{97} +4.85171 q^{98} +8.08881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + q^{3} + 33 q^{4} + 13 q^{5} + 17 q^{6} + 8 q^{7} - 3 q^{8} + 31 q^{9} - 6 q^{10} + 15 q^{11} - 12 q^{12} + 11 q^{13} + 16 q^{14} - 5 q^{15} + 43 q^{16} + 6 q^{17} - 8 q^{18} + 18 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 24 * q + q^2 + q^3 + 33 * q^4 + 13 * q^5 + 17 * q^6 + 8 * q^7 - 3 * q^8 + 31 * q^9 - 6 * q^10 + 15 * q^11 - 12 * q^12 + 11 * q^13 + 16 * q^14 - 5 * q^15 + 43 * q^16 + 6 * q^17 - 8 * q^18 + 18 * q^19 - 10 * q^20 - 7 * q^21 - 5 * q^22 - 8 * q^23 + 15 * q^24 + 51 * q^25 + 5 * q^26 + 13 * q^27 + 2 * q^28 + 17 * q^29 - 54 * q^30 + 37 * q^31 - 20 * q^32 + 16 * q^33 + 50 * q^34 + 3 * q^35 + 54 * q^36 + 7 * q^37 - 25 * q^38 - 38 * q^39 + 2 * q^40 + 24 * q^41 + 18 * q^42 + 10 * q^43 + 78 * q^45 + 9 * q^46 - 6 * q^47 - 25 * q^48 + 84 * q^49 - 65 * q^50 - 21 * q^51 - 31 * q^52 - 22 * q^53 + 23 * q^54 + 12 * q^55 - 45 * q^56 + 9 * q^57 - 12 * q^58 + 21 * q^59 - 82 * q^60 + 46 * q^61 - 68 * q^62 - 47 * q^63 + 53 * q^64 - 42 * q^65 - 56 * q^66 - 25 * q^67 + 3 * q^68 - 33 * q^69 - 18 * q^70 - 6 * q^71 - 115 * q^72 + 86 * q^73 - 60 * q^74 - 34 * q^75 + 48 * q^76 - 31 * q^77 - 84 * q^78 - 6 * q^79 - 24 * q^80 + 44 * q^81 - 3 * q^82 - 49 * q^83 - 126 * q^84 + 75 * q^85 - 56 * q^86 - 31 * q^87 - 91 * q^88 + 61 * q^89 - 161 * q^90 + 32 * q^91 - 130 * q^92 - 6 * q^93 + 8 * q^94 - 23 * q^95 - 5 * q^96 + 88 * q^97 - 120 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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