LMFDB - Embedded newform 1011.4.a.c.1.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1011,4,Mod(1,1011)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1011.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1011 = 3 \cdot 337 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1011.a (trivial)

Newform invariants

comment:select newform

sage:traces = [46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$59.6509310158$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1011.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.34241 q^{2} -3.00000 q^{3} -6.19794 q^{4} +12.1140 q^{5} +4.02723 q^{6} -29.9968 q^{7} +19.0594 q^{8} +9.00000 q^{9} -16.2620 q^{10} -69.4805 q^{11} +18.5938 q^{12} -87.1823 q^{13} +40.2679 q^{14} -36.3421 q^{15} +23.9980 q^{16} +35.5007 q^{17} -12.0817 q^{18} -6.22423 q^{19} -75.0821 q^{20} +89.9903 q^{21} +93.2712 q^{22} -101.725 q^{23} -57.1783 q^{24} +21.7499 q^{25} +117.034 q^{26} -27.0000 q^{27} +185.918 q^{28} -190.141 q^{29} +48.7860 q^{30} -291.491 q^{31} -184.691 q^{32} +208.441 q^{33} -47.6565 q^{34} -363.382 q^{35} -55.7815 q^{36} +177.937 q^{37} +8.35547 q^{38} +261.547 q^{39} +230.887 q^{40} -285.777 q^{41} -120.804 q^{42} +337.844 q^{43} +430.636 q^{44} +109.026 q^{45} +136.557 q^{46} +347.892 q^{47} -71.9939 q^{48} +556.806 q^{49} -29.1972 q^{50} -106.502 q^{51} +540.350 q^{52} -99.4021 q^{53} +36.2450 q^{54} -841.689 q^{55} -571.722 q^{56} +18.6727 q^{57} +255.246 q^{58} -827.088 q^{59} +225.246 q^{60} -657.687 q^{61} +391.300 q^{62} -269.971 q^{63} +55.9464 q^{64} -1056.13 q^{65} -279.813 q^{66} -237.729 q^{67} -220.031 q^{68} +305.176 q^{69} +487.807 q^{70} -871.171 q^{71} +171.535 q^{72} -308.793 q^{73} -238.864 q^{74} -65.2497 q^{75} +38.5774 q^{76} +2084.19 q^{77} -351.103 q^{78} +188.201 q^{79} +290.712 q^{80} +81.0000 q^{81} +383.629 q^{82} -1092.18 q^{83} -557.755 q^{84} +430.057 q^{85} -453.525 q^{86} +570.422 q^{87} -1324.26 q^{88} +488.104 q^{89} -146.358 q^{90} +2615.19 q^{91} +630.488 q^{92} +874.474 q^{93} -467.013 q^{94} -75.4006 q^{95} +554.072 q^{96} -263.482 q^{97} -747.462 q^{98} -625.324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) $ 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * q^99

Coefficient data

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

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

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

$2$	−1.34241	−0.474613	−0.237307	−	0.971435i	$-0.576265\pi$
$2$	−1.34241	−0.474613	−0.237307	+	0.971435i	$0.576265\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.19794	−0.774742
$5$	12.1140	1.08351	0.541756	−	0.840536i	$-0.317760\pi$
$5$	12.1140	1.08351	0.541756	+	0.840536i	$0.317760\pi$
$6$	4.02723	0.274018
$7$	−29.9968	−1.61967	−0.809837	−	0.586655i	$-0.800444\pi$
$7$	−29.9968	−1.61967	−0.809837	+	0.586655i	$0.800444\pi$
$8$	19.0594	0.842316
$9$	9.00000	0.333333
$10$	−16.2620	−0.514249
$11$	−69.4805	−1.90447	−0.952234	−	0.305369i	$-0.901220\pi$
$11$	−69.4805	−1.90447	−0.952234	+	0.305369i	$0.901220\pi$
$12$	18.5938	0.447298
$13$	−87.1823	−1.86000	−0.930000	−	0.367559i	$-0.880194\pi$
$13$	−87.1823	−1.86000	−0.930000	+	0.367559i	$0.880194\pi$
$14$	40.2679	0.768718
$15$	−36.3421	−0.625566
$16$	23.9980	0.374968
$17$	35.5007	0.506482	0.253241	−	0.967403i	$-0.418503\pi$
$17$	35.5007	0.506482	0.253241	+	0.967403i	$0.418503\pi$
$18$	−12.0817	−0.158204
$19$	−6.22423	−0.0751546	−0.0375773	−	0.999294i	$-0.511964\pi$
$19$	−6.22423	−0.0751546	−0.0375773	+	0.999294i	$0.511964\pi$
$20$	−75.0821	−0.839443
$21$	89.9903	0.935119
$22$	93.2712	0.903885
$23$	−101.725	−0.922227	−0.461114	−	0.887341i	$-0.652550\pi$
$23$	−101.725	−0.922227	−0.461114	+	0.887341i	$0.652550\pi$
$24$	−57.1783	−0.486311
$25$	21.7499	0.173999
$26$	117.034	0.882780
$27$	−27.0000	−0.192450
$28$	185.918	1.25483
$29$	−190.141	−1.21753	−0.608763	−	0.793352i	$-0.708334\pi$
$29$	−190.141	−1.21753	−0.608763	+	0.793352i	$0.708334\pi$
$30$	48.7860	0.296902
$31$	−291.491	−1.68882	−0.844409	−	0.535699i	$-0.820048\pi$
$31$	−291.491	−1.68882	−0.844409	+	0.535699i	$0.820048\pi$
$32$	−184.691	−1.02028
$33$	208.441	1.09955
$34$	−47.6565	−0.240383
$35$	−363.382	−1.75494
$36$	−55.7815	−0.258247
$37$	177.937	0.790613	0.395307	−	0.918549i	$-0.370638\pi$
$37$	177.937	0.790613	0.395307	+	0.918549i	$0.370638\pi$
$38$	8.35547	0.0356694
$39$	261.547	1.07387
$40$	230.887	0.912660
$41$	−285.777	−1.08856	−0.544279	−	0.838905i	$-0.683197\pi$
$41$	−285.777	−1.08856	−0.544279	+	0.838905i	$0.683197\pi$
$42$	−120.804	−0.443820
$43$	337.844	1.19816	0.599079	−	0.800690i	$-0.295534\pi$
$43$	337.844	1.19816	0.599079	+	0.800690i	$0.295534\pi$
$44$	430.636	1.47547
$45$	109.026	0.361171
$46$	136.557	0.437701
$47$	347.892	1.07969	0.539843	−	0.841766i	$-0.318484\pi$
$47$	347.892	1.07969	0.539843	+	0.841766i	$0.318484\pi$
$48$	−71.9939	−0.216488
$49$	556.806	1.62334
$50$	−29.1972	−0.0825823
$51$	−106.502	−0.292417
$52$	540.350	1.44102
$53$	−99.4021	−0.257621	−0.128811	−	0.991669i	$-0.541116\pi$
$53$	−99.4021	−0.257621	−0.128811	+	0.991669i	$0.541116\pi$
$54$	36.2450	0.0913393
$55$	−841.689	−2.06351
$56$	−571.722	−1.36428
$57$	18.6727	0.0433905
$58$	255.246	0.577853
$59$	−827.088	−1.82505	−0.912523	−	0.409025i	$-0.865869\pi$
$59$	−827.088	−1.82505	−0.912523	+	0.409025i	$0.865869\pi$
$60$	225.246	0.484653
$61$	−657.687	−1.38046	−0.690231	−	0.723589i	$-0.742491\pi$
$61$	−657.687	−1.38046	−0.690231	+	0.723589i	$0.742491\pi$
$62$	391.300	0.801535
$63$	−269.971	−0.539891
$64$	55.9464	0.109270
$65$	−1056.13	−2.01533
$66$	−279.813	−0.521858
$67$	−237.729	−0.433480	−0.216740	−	0.976229i	$-0.569542\pi$
$67$	−237.729	−0.433480	−0.216740	+	0.976229i	$0.569542\pi$
$68$	−220.031	−0.392393
$69$	305.176	0.532448
$70$	487.807	0.832916
$71$	−871.171	−1.45618	−0.728092	−	0.685480i	$-0.759592\pi$
$71$	−871.171	−1.45618	−0.728092	+	0.685480i	$0.759592\pi$
$72$	171.535	0.280772
$73$	−308.793	−0.495088	−0.247544	−	0.968877i	$-0.579624\pi$
$73$	−308.793	−0.495088	−0.247544	+	0.968877i	$0.579624\pi$
$74$	−238.864	−0.375235
$75$	−65.2497	−0.100458
$76$	38.5774	0.0582255
$77$	2084.19	3.08462
$78$	−351.103	−0.509674
$79$	188.201	0.268029	0.134014	−	0.990979i	$-0.457213\pi$
$79$	188.201	0.268029	0.134014	+	0.990979i	$0.457213\pi$
$80$	290.712	0.406283
$81$	81.0000	0.111111
$82$	383.629	0.516643
$83$	−1092.18	−1.44437	−0.722186	−	0.691699i	$-0.756863\pi$
$83$	−1092.18	−1.44437	−0.722186	+	0.691699i	$0.756863\pi$
$84$	−557.755	−0.724476
$85$	430.057	0.548779
$86$	−453.525	−0.568661
$87$	570.422	0.702939
$88$	−1324.26	−1.60416
$89$	488.104	0.581336	0.290668	−	0.956824i	$-0.406123\pi$
$89$	488.104	0.581336	0.290668	+	0.956824i	$0.406123\pi$
$90$	−146.358	−0.171416
$91$	2615.19	3.01259
$92$	630.488	0.714489
$93$	874.474	0.975040
$94$	−467.013	−0.512433
$95$	−75.4006	−0.0814309
$96$	554.072	0.589059
$97$	−263.482	−0.275799	−0.137899	−	0.990446i	$-0.544035\pi$
$97$	−263.482	−0.275799	−0.137899	+	0.990446i	$0.544035\pi$
$98$	−747.462	−0.770460
$99$	−625.324	−0.634823
$100$	−134.805	−0.134805
$101$	−13.7034	−0.0135004	−0.00675022	−	0.999977i	$-0.502149\pi$
$101$	−13.7034	−0.0135004	−0.00675022	+	0.999977i	$0.502149\pi$
$102$	142.969	0.138785
$103$	−867.497	−0.829874	−0.414937	−	0.909850i	$-0.636196\pi$
$103$	−867.497	−0.829874	−0.414937	+	0.909850i	$0.636196\pi$
$104$	−1661.64	−1.56671
$105$	1090.15	1.01321
$106$	133.438	0.122270
$107$	1476.00	1.33356	0.666778	−	0.745256i	$-0.267673\pi$
$107$	1476.00	1.33356	0.666778	+	0.745256i	$0.267673\pi$
$108$	167.344	0.149099
$109$	−912.433	−0.801791	−0.400895	−	0.916124i	$-0.631301\pi$
$109$	−912.433	−0.801791	−0.400895	+	0.916124i	$0.631301\pi$
$110$	1129.89	0.979371
$111$	−533.811	−0.456461
$112$	−719.862	−0.607326
$113$	646.940	0.538575	0.269287	−	0.963060i	$-0.413212\pi$
$113$	646.940	0.538575	0.269287	+	0.963060i	$0.413212\pi$
$114$	−25.0664	−0.0205937
$115$	−1232.31	−0.999245
$116$	1178.48	0.943269
$117$	−784.640	−0.620000
$118$	1110.29	0.866191
$119$	−1064.91	−0.820335
$120$	−692.660	−0.526924
$121$	3496.54	2.62700
$122$	882.884	0.655185
$123$	857.331	0.628479
$124$	1806.64	1.30840
$125$	−1250.78	−0.894982
$126$	362.411	0.256239
$127$	489.275	0.341859	0.170930	−	0.985283i	$-0.445323\pi$
$127$	489.275	0.341859	0.170930	+	0.985283i	$0.445323\pi$
$128$	1402.42	0.968420
$129$	−1013.53	−0.691757
$130$	1417.76	0.956504
$131$	−66.4457	−0.0443159	−0.0221580	−	0.999754i	$-0.507054\pi$
$131$	−66.4457	−0.0443159	−0.0221580	+	0.999754i	$0.507054\pi$
$132$	−1291.91	−0.851864
$133$	186.707	0.121726
$134$	319.129	0.205735
$135$	−327.079	−0.208522
$136$	676.624	0.426618
$137$	259.736	0.161976	0.0809881	−	0.996715i	$-0.474192\pi$
$137$	259.736	0.161976	0.0809881	+	0.996715i	$0.474192\pi$
$138$	−409.671	−0.252707
$139$	1018.37	0.621418	0.310709	−	0.950505i	$-0.399434\pi$
$139$	1018.37	0.621418	0.310709	+	0.950505i	$0.399434\pi$
$140$	2252.22	1.35962
$141$	−1043.67	−0.623357
$142$	1169.47	0.691124
$143$	6057.46	3.54231
$144$	215.982	0.124989
$145$	−2303.37	−1.31920
$146$	414.526	0.234975
$147$	−1670.42	−0.937237
$148$	−1102.84	−0.612522
$149$	2490.24	1.36918	0.684592	−	0.728926i	$-0.259980\pi$
$149$	2490.24	1.36918	0.684592	+	0.728926i	$0.259980\pi$
$150$	87.5917	0.0476789
$151$	2397.91	1.29231	0.646155	−	0.763206i	$-0.276376\pi$
$151$	2397.91	1.29231	0.646155	+	0.763206i	$0.276376\pi$
$152$	−118.630	−0.0633039
$153$	319.507	0.168827
$154$	−2797.83	−1.46400
$155$	−3531.14	−1.82986
$156$	−1621.05	−0.831974
$157$	3004.75	1.52742	0.763712	−	0.645558i	$-0.223375\pi$
$157$	3004.75	1.52742	0.763712	+	0.645558i	$0.223375\pi$
$158$	−252.643	−0.127210
$159$	298.206	0.148738
$160$	−2237.35	−1.10549
$161$	3051.44	1.49371
$162$	−108.735	−0.0527348
$163$	−2158.96	−1.03744	−0.518721	−	0.854944i	$-0.673592\pi$
$163$	−2158.96	−1.03744	−0.518721	+	0.854944i	$0.673592\pi$
$164$	1771.23	0.843351
$165$	2525.07	1.19137
$166$	1466.16	0.685518
$167$	−3254.32	−1.50794	−0.753972	−	0.656906i	$-0.771865\pi$
$167$	−3254.32	−1.50794	−0.753972	+	0.656906i	$0.771865\pi$
$168$	1715.16	0.787666
$169$	5403.75	2.45960
$170$	−577.312	−0.260458
$171$	−56.0181	−0.0250515
$172$	−2093.94	−0.928264
$173$	1682.34	0.739342	0.369671	−	0.929163i	$-0.379470\pi$
$173$	1682.34	0.739342	0.369671	+	0.929163i	$0.379470\pi$
$174$	−765.739	−0.333624
$175$	−652.427	−0.281822
$176$	−1667.39	−0.714115
$177$	2481.27	1.05369
$178$	−655.234	−0.275910
$179$	451.358	0.188470	0.0942349	−	0.995550i	$-0.469960\pi$
$179$	451.358	0.188470	0.0942349	+	0.995550i	$0.469960\pi$
$180$	−675.739	−0.279814
$181$	2835.14	1.16428	0.582138	−	0.813090i	$-0.302216\pi$
$181$	2835.14	1.16428	0.582138	+	0.813090i	$0.302216\pi$
$182$	−3510.65	−1.42982
$183$	1973.06	0.797010
$184$	−1938.83	−0.776807
$185$	2155.54	0.856639
$186$	−1173.90	−0.462767
$187$	−2466.61	−0.964578
$188$	−2156.21	−0.836478
$189$	809.913	0.311706
$190$	101.218	0.0386482
$191$	1918.87	0.726933	0.363467	−	0.931607i	$-0.381593\pi$
$191$	1918.87	0.726933	0.363467	+	0.931607i	$0.381593\pi$
$192$	−167.839	−0.0630872
$193$	−2908.50	−1.08476	−0.542379	−	0.840134i	$-0.682476\pi$
$193$	−2908.50	−1.08476	−0.542379	+	0.840134i	$0.682476\pi$
$194$	353.700	0.130898
$195$	3168.39	1.16355
$196$	−3451.05	−1.25767
$197$	−757.805	−0.274068	−0.137034	−	0.990566i	$-0.543757\pi$
$197$	−757.805	−0.274068	−0.137034	+	0.990566i	$0.543757\pi$
$198$	839.440	0.301295
$199$	790.988	0.281767	0.140884	−	0.990026i	$-0.455006\pi$
$199$	790.988	0.281767	0.140884	+	0.990026i	$0.455006\pi$
$200$	414.541	0.146562
$201$	713.186	0.250270
$202$	18.3956	0.00640748
$203$	5703.61	1.97199
$204$	660.094	0.226548
$205$	−3461.91	−1.17947
$206$	1164.54	0.393869
$207$	−915.529	−0.307409
$208$	−2092.20	−0.697441
$209$	432.463	0.143130
$210$	−1463.42	−0.480884
$211$	10.3337	0.00337156	0.00168578	−	0.999999i	$-0.499463\pi$
$211$	10.3337	0.00337156	0.00168578	+	0.999999i	$0.499463\pi$
$212$	616.088	0.199590
$213$	2613.51	0.840728
$214$	−1981.40	−0.632923
$215$	4092.66	1.29822
$216$	−514.605	−0.162104
$217$	8743.80	2.73533
$218$	1224.86	0.380540
$219$	926.378	0.285839
$220$	5216.74	1.59869
$221$	−3095.03	−0.942056
$222$	716.593	0.216642
$223$	−4984.39	−1.49677	−0.748384	−	0.663266i	$-0.769170\pi$
$223$	−4984.39	−1.49677	−0.748384	+	0.663266i	$0.769170\pi$
$224$	5540.12	1.65252
$225$	195.749	0.0579997
$226$	−868.457	−0.255615
$227$	−4896.81	−1.43178	−0.715888	−	0.698216i	$-0.753978\pi$
$227$	−4896.81	−1.43178	−0.715888	+	0.698216i	$0.753978\pi$
$228$	−115.732	−0.0336165
$229$	−2997.38	−0.864946	−0.432473	−	0.901647i	$-0.642359\pi$
$229$	−2997.38	−0.864946	−0.432473	+	0.901647i	$0.642359\pi$
$230$	1654.26	0.474255
$231$	−6252.57	−1.78090
$232$	−3623.97	−1.02554
$233$	3159.51	0.888354	0.444177	−	0.895939i	$-0.353496\pi$
$233$	3159.51	0.888354	0.444177	+	0.895939i	$0.353496\pi$
$234$	1053.31	0.294260
$235$	4214.37	1.16985
$236$	5126.24	1.41394
$237$	−564.603	−0.154746
$238$	1429.54	0.389342
$239$	223.747	0.0605566	0.0302783	−	0.999542i	$-0.490361\pi$
$239$	223.747	0.0605566	0.0302783	+	0.999542i	$0.490361\pi$
$240$	−872.137	−0.234568
$241$	−2612.37	−0.698246	−0.349123	−	0.937077i	$-0.613520\pi$
$241$	−2612.37	−0.698246	−0.349123	+	0.937077i	$0.613520\pi$
$242$	−4693.78	−1.24681
$243$	−243.000	−0.0641500
$244$	4076.30	1.06950
$245$	6745.17	1.75891
$246$	−1150.89	−0.298284
$247$	542.643	0.139788
$248$	−5555.66	−1.42252
$249$	3276.55	0.833909
$250$	1679.05	0.424770
$251$	1610.97	0.405114	0.202557	−	0.979270i	$-0.435075\pi$
$251$	1610.97	0.405114	0.202557	+	0.979270i	$0.435075\pi$
$252$	1673.26	0.418277
$253$	7067.94	1.75635
$254$	−656.806	−0.162251
$255$	−1290.17	−0.316838
$256$	−2330.19	−0.568895
$257$	−4936.17	−1.19809	−0.599047	−	0.800714i	$-0.704454\pi$
$257$	−4936.17	−1.19809	−0.599047	+	0.800714i	$0.704454\pi$
$258$	1360.58	0.328317
$259$	−5337.54	−1.28054
$260$	6545.82	1.56136
$261$	−1711.27	−0.405842
$262$	89.1973	0.0210329
$263$	1327.34	0.311205	0.155603	−	0.987820i	$-0.450268\pi$
$263$	1327.34	0.311205	0.155603	+	0.987820i	$0.450268\pi$
$264$	3972.78	0.926164
$265$	−1204.16	−0.279136
$266$	−250.637	−0.0577727
$267$	−1464.31	−0.335634
$268$	1473.43	0.335836
$269$	8351.21	1.89287	0.946435	−	0.322894i	$-0.104656\pi$
$269$	8351.21	1.89287	0.946435	+	0.322894i	$0.104656\pi$
$270$	439.074	0.0989673
$271$	−3726.99	−0.835419	−0.417709	−	0.908581i	$-0.637167\pi$
$271$	−3726.99	−0.835419	−0.417709	+	0.908581i	$0.637167\pi$
$272$	851.945	0.189915
$273$	−7845.56	−1.73932
$274$	−348.672	−0.0768760
$275$	−1511.19	−0.331376
$276$	−1891.47	−0.412510
$277$	−7111.92	−1.54265	−0.771324	−	0.636442i	$-0.780405\pi$
$277$	−7111.92	−1.54265	−0.771324	+	0.636442i	$0.780405\pi$
$278$	−1367.07	−0.294933
$279$	−2623.42	−0.562939
$280$	−6925.86	−1.47821
$281$	−1497.37	−0.317885	−0.158942	−	0.987288i	$-0.550808\pi$
$281$	−1497.37	−0.317885	−0.158942	+	0.987288i	$0.550808\pi$
$282$	1401.04	0.295853
$283$	−2974.87	−0.624869	−0.312434	−	0.949939i	$-0.601144\pi$
$283$	−2974.87	−0.624869	−0.312434	+	0.949939i	$0.601144\pi$
$284$	5399.47	1.12817
$285$	226.202	0.0470142
$286$	−8131.59	−1.68123
$287$	8572.38	1.76311
$288$	−1662.21	−0.340094
$289$	−3652.70	−0.743476
$290$	3092.06	0.626111
$291$	790.445	0.159233
$292$	1913.88	0.383566
$293$	−2500.94	−0.498656	−0.249328	−	0.968419i	$-0.580210\pi$
$293$	−2500.94	−0.498656	−0.249328	+	0.968419i	$0.580210\pi$
$294$	2242.39	0.444825
$295$	−10019.4	−1.97746
$296$	3391.38	0.665946
$297$	1875.97	0.366515
$298$	−3342.92	−0.649833
$299$	8868.66	1.71534
$300$	404.414	0.0778294
$301$	−10134.2	−1.94062
$302$	−3218.97	−0.613347
$303$	41.1103	0.00779448
$304$	−149.369	−0.0281806
$305$	−7967.24	−1.49575
$306$	−428.908	−0.0801276
$307$	−6043.40	−1.12350	−0.561751	−	0.827307i	$-0.689872\pi$
$307$	−6043.40	−1.12350	−0.561751	+	0.827307i	$0.689872\pi$
$308$	−12917.7	−2.38978
$309$	2602.49	0.479128
$310$	4740.23	0.868473
$311$	−3121.96	−0.569228	−0.284614	−	0.958642i	$-0.591866\pi$
$311$	−3121.96	−0.569228	−0.284614	+	0.958642i	$0.591866\pi$
$312$	4984.93	0.904539
$313$	1095.54	0.197839	0.0989193	−	0.995095i	$-0.468461\pi$
$313$	1095.54	0.197839	0.0989193	+	0.995095i	$0.468461\pi$
$314$	−4033.61	−0.724935
$315$	−3270.44	−0.584979
$316$	−1166.46	−0.207653
$317$	9615.47	1.70365	0.851827	−	0.523823i	$-0.175495\pi$
$317$	9615.47	1.70365	0.851827	+	0.523823i	$0.175495\pi$
$318$	−400.314	−0.0705928
$319$	13211.1	2.31874
$320$	677.736	0.118396
$321$	−4428.01	−0.769929
$322$	−4096.27	−0.708933
$323$	−220.965	−0.0380644
$324$	−502.033	−0.0860825
$325$	−1896.20	−0.323638
$326$	2898.21	0.492384
$327$	2737.30	0.462914
$328$	−5446.74	−0.916909
$329$	−10435.6	−1.74874
$330$	−3389.67	−0.565440
$331$	11503.7	1.91027	0.955137	−	0.296164i	$-0.0957075\pi$
$331$	11503.7	1.91027	0.955137	+	0.296164i	$0.0957075\pi$
$332$	6769.30	1.11902
$333$	1601.43	0.263538
$334$	4368.62	0.715690
$335$	−2879.85	−0.469681
$336$	2159.59	0.350640
$337$	−337.000	−0.0544735
$337$	−337.000	−0.0544735
$338$	−7254.03	−1.16736
$339$	−1940.82	−0.310946
$340$	−2665.47	−0.425163
$341$	20252.9	3.21630
$342$	75.1992	0.0118898
$343$	−6413.50	−1.00961
$344$	6439.12	1.00923
$345$	3696.92	0.576914
$346$	−2258.39	−0.350901
$347$	−8974.64	−1.38843	−0.694213	−	0.719770i	$-0.744247\pi$
$347$	−8974.64	−1.38843	−0.694213	+	0.719770i	$0.744247\pi$
$348$	−3535.44	−0.544596
$349$	−2003.54	−0.307298	−0.153649	−	0.988125i	$-0.549102\pi$
$349$	−2003.54	−0.307298	−0.153649	+	0.988125i	$0.549102\pi$
$350$	875.823	0.133756
$351$	2353.92	0.357957
$352$	12832.4	1.94309
$353$	−8053.02	−1.21422	−0.607109	−	0.794619i	$-0.707671\pi$
$353$	−8053.02	−1.21422	−0.607109	+	0.794619i	$0.707671\pi$
$354$	−3330.87	−0.500095
$355$	−10553.4	−1.57779
$356$	−3025.24	−0.450385
$357$	3194.72	0.473621
$358$	−605.907	−0.0894503
$359$	−11942.4	−1.75570	−0.877850	−	0.478935i	$-0.841023\pi$
$359$	−11942.4	−1.75570	−0.877850	+	0.478935i	$0.841023\pi$
$360$	2077.98	0.304220
$361$	−6820.26	−0.994352
$362$	−3805.91	−0.552581
$363$	−10489.6	−1.51670
$364$	−16208.8	−2.33398
$365$	−3740.72	−0.536434
$366$	−2648.65	−0.378271
$367$	−4427.03	−0.629670	−0.314835	−	0.949146i	$-0.601949\pi$
$367$	−4427.03	−0.629670	−0.314835	+	0.949146i	$0.601949\pi$
$368$	−2441.21	−0.345806
$369$	−2571.99	−0.362852
$370$	−2893.61	−0.406572
$371$	2981.74	0.417262
$372$	−5419.93	−0.755405
$373$	12835.7	1.78179	0.890896	−	0.454208i	$-0.150078\pi$
$373$	12835.7	1.78179	0.890896	+	0.454208i	$0.150078\pi$
$374$	3311.19	0.457801
$375$	3752.33	0.516718
$376$	6630.62	0.909436
$377$	16576.9	2.26460
$378$	−1087.23	−0.147940
$379$	−6995.26	−0.948080	−0.474040	−	0.880503i	$-0.657205\pi$
$379$	−6995.26	−0.948080	−0.474040	+	0.880503i	$0.657205\pi$
$380$	467.328	0.0630880
$381$	−1467.82	−0.197372
$382$	−2575.90	−0.345012
$383$	−6310.56	−0.841918	−0.420959	−	0.907080i	$-0.638306\pi$
$383$	−6310.56	−0.841918	−0.420959	+	0.907080i	$0.638306\pi$
$384$	−4207.26	−0.559117
$385$	25248.0	3.34222
$386$	3904.40	0.514841
$387$	3040.60	0.399386
$388$	1633.04	0.213673
$389$	804.581	0.104869	0.0524343	−	0.998624i	$-0.483302\pi$
$389$	804.581	0.104869	0.0524343	+	0.998624i	$0.483302\pi$
$390$	−4253.27	−0.552238
$391$	−3611.33	−0.467091
$392$	10612.4	1.36737
$393$	199.337	0.0255858
$394$	1017.28	0.130076
$395$	2279.87	0.290412
$396$	3875.72	0.491824
$397$	−5647.08	−0.713901	−0.356951	−	0.934123i	$-0.616184\pi$
$397$	−5647.08	−0.713901	−0.356951	+	0.934123i	$0.616184\pi$
$398$	−1061.83	−0.133730
$399$	−560.121	−0.0702785
$400$	521.953	0.0652442
$401$	−7121.98	−0.886920	−0.443460	−	0.896294i	$-0.646249\pi$
$401$	−7121.98	−0.886920	−0.443460	+	0.896294i	$0.646249\pi$
$402$	−957.387	−0.118781
$403$	25412.9	3.14120
$404$	84.9331	0.0104594
$405$	981.237	0.120390
$406$	−7656.57	−0.935934
$407$	−12363.2	−1.50570
$408$	−2029.87	−0.246308
$409$	5989.22	0.724078	0.362039	−	0.932163i	$-0.382081\pi$
$409$	5989.22	0.724078	0.362039	+	0.932163i	$0.382081\pi$
$410$	4647.30	0.559790
$411$	−779.207	−0.0935169
$412$	5376.69	0.642938
$413$	24810.0	2.95598
$414$	1229.01	0.145900
$415$	−13230.8	−1.56499
$416$	16101.7	1.89772
$417$	−3055.11	−0.358776
$418$	−580.542	−0.0679311
$419$	−13695.5	−1.59683	−0.798414	−	0.602110i	$-0.794327\pi$
$419$	−13695.5	−1.59683	−0.798414	+	0.602110i	$0.794327\pi$
$420$	−6756.66	−0.784979
$421$	10907.5	1.26270	0.631350	−	0.775498i	$-0.282501\pi$
$421$	10907.5	1.26270	0.631350	+	0.775498i	$0.282501\pi$
$422$	−13.8720	−0.00160019
$423$	3131.02	0.359895
$424$	−1894.55	−0.216998
$425$	772.137	0.0881274
$426$	−3508.40	−0.399020
$427$	19728.5	2.23590
$428$	−9148.17	−1.03316
$429$	−18172.4	−2.04515
$430$	−5494.02	−0.616151
$431$	−8364.30	−0.934789	−0.467394	−	0.884049i	$-0.654807\pi$
$431$	−8364.30	−0.934789	−0.467394	+	0.884049i	$0.654807\pi$
$432$	−647.945	−0.0721627
$433$	−4468.44	−0.495934	−0.247967	−	0.968768i	$-0.579763\pi$
$433$	−4468.44	−0.495934	−0.247967	+	0.968768i	$0.579763\pi$
$434$	−11737.7	−1.29823
$435$	6910.11	0.761643
$436$	5655.20	0.621182
$437$	633.163	0.0693096
$438$	−1243.58	−0.135663
$439$	6787.27	0.737901	0.368951	−	0.929449i	$-0.379717\pi$
$439$	6787.27	0.737901	0.368951	+	0.929449i	$0.379717\pi$
$440$	−16042.1	−1.73813
$441$	5011.26	0.541114
$442$	4154.80	0.447112
$443$	−3252.95	−0.348876	−0.174438	−	0.984668i	$-0.555811\pi$
$443$	−3252.95	−0.348876	−0.174438	+	0.984668i	$0.555811\pi$
$444$	3308.53	0.353639
$445$	5912.91	0.629885
$446$	6691.08	0.710385
$447$	−7470.73	−0.790499
$448$	−1678.21	−0.176982
$449$	11894.2	1.25016	0.625079	−	0.780562i	$-0.285067\pi$
$449$	11894.2	1.25016	0.625079	+	0.780562i	$0.285067\pi$
$450$	−262.775	−0.0275274
$451$	19855.9	2.07312
$452$	−4009.69	−0.417257
$453$	−7193.72	−0.746116
$454$	6573.52	0.679539
$455$	31680.5	3.26418
$456$	355.891	0.0365485
$457$	−8808.13	−0.901591	−0.450795	−	0.892627i	$-0.648860\pi$
$457$	−8808.13	−0.901591	−0.450795	+	0.892627i	$0.648860\pi$
$458$	4023.71	0.410514
$459$	−958.520	−0.0974725
$460$	7637.76	0.774157
$461$	5879.71	0.594025	0.297013	−	0.954874i	$-0.404010\pi$
$461$	5879.71	0.594025	0.297013	+	0.954874i	$0.404010\pi$
$462$	8393.50	0.845240
$463$	−4277.60	−0.429367	−0.214684	−	0.976684i	$-0.568872\pi$
$463$	−4277.60	−0.429367	−0.214684	+	0.976684i	$0.568872\pi$
$464$	−4562.99	−0.456533
$465$	10593.4	1.05647
$466$	−4241.36	−0.421625
$467$	−5701.47	−0.564952	−0.282476	−	0.959274i	$-0.591156\pi$
$467$	−5701.47	−0.564952	−0.282476	+	0.959274i	$0.591156\pi$
$468$	4863.15	0.480340
$469$	7131.09	0.702097
$470$	−5657.41	−0.555227
$471$	−9014.26	−0.881858
$472$	−15763.8	−1.53727
$473$	−23473.6	−2.28185
$474$	757.928	0.0734447
$475$	−135.376	−0.0130768
$476$	6600.23	0.635548
$477$	−894.618	−0.0858737
$478$	−300.361	−0.0287409
$479$	2191.74	0.209067	0.104533	−	0.994521i	$-0.466665\pi$
$479$	2191.74	0.209067	0.104533	+	0.994521i	$0.466665\pi$
$480$	6712.04	0.638253
$481$	−15513.0	−1.47054
$482$	3506.86	0.331397
$483$	−9154.31	−0.862392
$484$	−21671.3	−2.03525
$485$	−3191.83	−0.298832
$486$	326.205	0.0304464
$487$	6949.86	0.646670	0.323335	−	0.946285i	$-0.395196\pi$
$487$	6949.86	0.646670	0.323335	+	0.946285i	$0.395196\pi$
$488$	−12535.1	−1.16278
$489$	6476.89	0.598967
$490$	−9054.78	−0.834802
$491$	−4846.12	−0.445423	−0.222711	−	0.974884i	$-0.571491\pi$
$491$	−4846.12	−0.445423	−0.222711	+	0.974884i	$0.571491\pi$
$492$	−5313.68	−0.486909
$493$	−6750.13	−0.616654
$494$	−728.448	−0.0663450
$495$	−7575.20	−0.687838
$496$	−6995.20	−0.633253
$497$	26132.3	2.35854
$498$	−4398.47	−0.395784
$499$	−5100.46	−0.457571	−0.228786	−	0.973477i	$-0.573476\pi$
$499$	−5100.46	−0.457571	−0.228786	+	0.973477i	$0.573476\pi$
$500$	7752.23	0.693381
$501$	9762.95	0.870612
$502$	−2162.58	−0.192272
$503$	1129.97	0.100165	0.0500826	−	0.998745i	$-0.484052\pi$
$503$	1129.97	0.100165	0.0500826	+	0.998745i	$0.484052\pi$
$504$	−5145.49	−0.454759
$505$	−166.004	−0.0146279
$506$	−9488.06	−0.833588
$507$	−16211.2	−1.42005
$508$	−3032.49	−0.264853
$509$	8755.93	0.762475	0.381237	−	0.924477i	$-0.375498\pi$
$509$	8755.93	0.762475	0.381237	+	0.924477i	$0.375498\pi$
$510$	1731.94	0.150375
$511$	9262.78	0.801881
$512$	−8091.30	−0.698415
$513$	168.054	0.0144635
$514$	6626.36	0.568631
$515$	−10508.9	−0.899179
$516$	6281.82	0.535933
$517$	−24171.7	−2.05623
$518$	7165.16	0.607759
$519$	−5047.03	−0.426859
$520$	−20129.2	−1.69755
$521$	−1646.47	−0.138451	−0.0692256	−	0.997601i	$-0.522053\pi$
$521$	−1646.47	−0.138451	−0.0692256	+	0.997601i	$0.522053\pi$
$522$	2297.22	0.192618
$523$	10277.1	0.859251	0.429626	−	0.903007i	$-0.358646\pi$
$523$	10277.1	0.859251	0.429626	+	0.903007i	$0.358646\pi$
$524$	411.827	0.0343334
$525$	1957.28	0.162710
$526$	−1781.83	−0.147702
$527$	−10348.1	−0.855356
$528$	5002.17	0.412295
$529$	−1818.92	−0.149496
$530$	1616.47	0.132481
$531$	−7443.80	−0.608349
$532$	−1157.20	−0.0943062
$533$	24914.7	2.02472
$534$	1965.70	0.159296
$535$	17880.3	1.44492
$536$	−4530.97	−0.365127
$537$	−1354.07	−0.108813
$538$	−11210.7	−0.898381
$539$	−38687.2	−3.09160
$540$	2027.22	0.161551
$541$	13415.1	1.06610	0.533050	−	0.846084i	$-0.321046\pi$
$541$	13415.1	1.06610	0.533050	+	0.846084i	$0.321046\pi$
$542$	5003.14	0.396501
$543$	−8505.41	−0.672195
$544$	−6556.65	−0.516754
$545$	−11053.2	−0.868750
$546$	10531.9	0.825505
$547$	−6975.72	−0.545265	−0.272633	−	0.962118i	$-0.587894\pi$
$547$	−6975.72	−0.545265	−0.272633	+	0.962118i	$0.587894\pi$
$548$	−1609.83	−0.125490
$549$	−5919.18	−0.460154
$550$	2028.64	0.157275
$551$	1183.48	0.0915026
$552$	5816.49	0.448490
$553$	−5645.42	−0.434119
$554$	9547.10	0.732161
$555$	−6466.61	−0.494581
$556$	−6311.80	−0.481439
$557$	11985.4	0.911741	0.455870	−	0.890046i	$-0.349328\pi$
$557$	11985.4	0.911741	0.455870	+	0.890046i	$0.349328\pi$
$558$	3521.70	0.267178
$559$	−29454.0	−2.22857
$560$	−8720.43	−0.658046
$561$	7399.82	0.556900
$562$	2010.08	0.150872
$563$	−354.616	−0.0265458	−0.0132729	−	0.999912i	$-0.504225\pi$
$563$	−354.616	−0.0265458	−0.0132729	+	0.999912i	$0.504225\pi$
$564$	6468.63	0.482941
$565$	7837.05	0.583553
$566$	3993.49	0.296571
$567$	−2429.74	−0.179964
$568$	−16604.0	−1.22657
$569$	−1274.82	−0.0939246	−0.0469623	−	0.998897i	$-0.514954\pi$
$569$	−1274.82	−0.0939246	−0.0469623	+	0.998897i	$0.514954\pi$
$570$	−303.655	−0.0223135
$571$	−22145.5	−1.62305	−0.811525	−	0.584318i	$-0.801362\pi$
$571$	−22145.5	−1.62305	−0.811525	+	0.584318i	$0.801362\pi$
$572$	−37543.8	−2.74438
$573$	−5756.60	−0.419695
$574$	−11507.6	−0.836794
$575$	−2212.52	−0.160467
$576$	503.517	0.0364234
$577$	−15098.2	−1.08934	−0.544668	−	0.838652i	$-0.683344\pi$
$577$	−15098.2	−1.08934	−0.544668	+	0.838652i	$0.683344\pi$
$578$	4903.41	0.352864
$579$	8725.50	0.626286
$580$	14276.2	1.02204
$581$	32762.0	2.33941
$582$	−1061.10	−0.0755739
$583$	6906.50	0.490631
$584$	−5885.41	−0.417021
$585$	−9505.16	−0.671778
$586$	3357.28	0.236669
$587$	−27927.4	−1.96369	−0.981846	−	0.189681i	$-0.939255\pi$
$587$	−27927.4	−1.96369	−0.981846	+	0.189681i	$0.939255\pi$
$588$	10353.2	0.726117
$589$	1814.31	0.126922
$590$	13450.1	0.938528
$591$	2273.41	0.158233
$592$	4270.13	0.296455
$593$	−5027.62	−0.348161	−0.174081	−	0.984731i	$-0.555695\pi$
$593$	−5027.62	−0.348161	−0.174081	+	0.984731i	$0.555695\pi$
$594$	−2518.32	−0.173953
$595$	−12900.3	−0.888843
$596$	−15434.4	−1.06077
$597$	−2372.97	−0.162678
$598$	−11905.4	−0.814124
$599$	7596.56	0.518175	0.259088	−	0.965854i	$-0.416578\pi$
$599$	7596.56	0.518175	0.259088	+	0.965854i	$0.416578\pi$
$600$	−1243.62	−0.0846178
$601$	15089.4	1.02414	0.512071	−	0.858943i	$-0.328879\pi$
$601$	15089.4	1.02414	0.512071	+	0.858943i	$0.328879\pi$
$602$	13604.3	0.921046
$603$	−2139.56	−0.144493
$604$	−14862.1	−1.00121
$605$	42357.2	2.84639
$606$	−55.1869	−0.00369936
$607$	−172.631	−0.0115435	−0.00577173	−	0.999983i	$-0.501837\pi$
$607$	−172.631	−0.0115435	−0.00577173	+	0.999983i	$0.501837\pi$
$608$	1149.56	0.0766788
$609$	−17110.8	−1.13853
$610$	10695.3	0.709901
$611$	−30330.0	−2.00822
$612$	−1980.28	−0.130798
$613$	−6661.19	−0.438896	−0.219448	−	0.975624i	$-0.570426\pi$
$613$	−6661.19	−0.438896	−0.219448	+	0.975624i	$0.570426\pi$
$614$	8112.71	0.533229
$615$	10385.7	0.680965
$616$	39723.5	2.59822
$617$	7878.39	0.514055	0.257028	−	0.966404i	$-0.417257\pi$
$617$	7878.39	0.514055	0.257028	+	0.966404i	$0.417257\pi$
$618$	−3493.61	−0.227400
$619$	−15153.5	−0.983957	−0.491979	−	0.870607i	$-0.663726\pi$
$619$	−15153.5	−0.983957	−0.491979	+	0.870607i	$0.663726\pi$
$620$	21885.8	1.41767
$621$	2746.59	0.177483
$622$	4190.94	0.270163
$623$	−14641.5	−0.941574
$624$	6276.59	0.402668
$625$	−17870.7	−1.14372
$626$	−1470.66	−0.0938968
$627$	−1297.39	−0.0826359
$628$	−18623.3	−1.18336
$629$	6316.90	0.400431
$630$	4390.26	0.277639
$631$	15566.8	0.982102	0.491051	−	0.871131i	$-0.336613\pi$
$631$	15566.8	0.982102	0.491051	+	0.871131i	$0.336613\pi$
$632$	3587.00	0.225765
$633$	−31.0010	−0.00194657
$634$	−12907.9	−0.808577
$635$	5927.09	0.370409
$636$	−1848.26	−0.115233
$637$	−48543.6	−3.01942
$638$	−17734.6	−1.10050
$639$	−7840.54	−0.485394
$640$	16989.0	1.04929
$641$	−30078.1	−1.85338	−0.926688	−	0.375831i	$-0.877357\pi$
$641$	−30078.1	−1.85338	−0.926688	+	0.375831i	$0.877357\pi$
$642$	5944.19	0.365418
$643$	21515.5	1.31958	0.659790	−	0.751450i	$-0.270645\pi$
$643$	21515.5	1.31958	0.659790	+	0.751450i	$0.270645\pi$
$644$	−18912.6	−1.15724
$645$	−12278.0	−0.749527
$646$	296.625	0.0180659
$647$	12175.7	0.739838	0.369919	−	0.929064i	$-0.379385\pi$
$647$	12175.7	0.739838	0.369919	+	0.929064i	$0.379385\pi$
$648$	1543.81	0.0935907
$649$	57466.5	3.47574
$650$	2545.48	0.153603
$651$	−26231.4	−1.57925
$652$	13381.1	0.803750
$653$	−15615.8	−0.935822	−0.467911	−	0.883775i	$-0.654993\pi$
$653$	−15615.8	−0.935822	−0.467911	+	0.883775i	$0.654993\pi$
$654$	−3674.57	−0.219705
$655$	−804.926	−0.0480169
$656$	−6858.06	−0.408174
$657$	−2779.13	−0.165029
$658$	14008.9	0.829974
$659$	7235.86	0.427722	0.213861	−	0.976864i	$-0.431396\pi$
$659$	7235.86	0.427722	0.213861	+	0.976864i	$0.431396\pi$
$660$	−15650.2	−0.923006
$661$	−15772.9	−0.928131	−0.464065	−	0.885801i	$-0.653610\pi$
$661$	−15772.9	−0.928131	−0.464065	+	0.885801i	$0.653610\pi$
$662$	−15442.7	−0.906641
$663$	9285.10	0.543896
$664$	−20816.4	−1.21662
$665$	2261.78	0.131892
$666$	−2149.78	−0.125078
$667$	19342.2	1.12284
$668$	20170.1	1.16827
$669$	14953.2	0.864159
$670$	3865.94	0.222917
$671$	45696.4	2.62904
$672$	−16620.4	−0.954084
$673$	−2763.32	−0.158274	−0.0791368	−	0.996864i	$-0.525216\pi$
$673$	−2763.32	−0.158274	−0.0791368	+	0.996864i	$0.525216\pi$
$674$	452.392	0.0258538
$675$	−587.247	−0.0334861
$676$	−33492.1	−1.90556
$677$	16000.3	0.908331	0.454165	−	0.890917i	$-0.349938\pi$
$677$	16000.3	0.908331	0.454165	+	0.890917i	$0.349938\pi$
$678$	2605.37	0.147579
$679$	7903.60	0.446704
$680$	8196.64	0.462246
$681$	14690.4	0.826636
$682$	−27187.7	−1.52650
$683$	19766.2	1.10737	0.553683	−	0.832727i	$-0.313222\pi$
$683$	19766.2	1.10737	0.553683	+	0.832727i	$0.313222\pi$
$684$	347.197	0.0194085
$685$	3146.45	0.175503
$686$	8609.54	0.479175
$687$	8992.14	0.499377
$688$	8107.58	0.449271
$689$	8666.10	0.479176
$690$	−4962.78	−0.273811
$691$	406.016	0.0223525	0.0111762	−	0.999938i	$-0.496442\pi$
$691$	406.016	0.0223525	0.0111762	+	0.999938i	$0.496442\pi$
$692$	−10427.1	−0.572800
$693$	18757.7	1.02821
$694$	12047.6	0.658965
$695$	12336.6	0.673314
$696$	10871.9	0.592096
$697$	−10145.3	−0.551334
$698$	2689.57	0.145848
$699$	−9478.54	−0.512892
$700$	4043.70	0.218339
$701$	8241.31	0.444037	0.222019	−	0.975042i	$-0.428735\pi$
$701$	8241.31	0.444037	0.222019	+	0.975042i	$0.428735\pi$
$702$	−3159.92	−0.169891
$703$	−1107.52	−0.0594182
$704$	−3887.18	−0.208102
$705$	−12643.1	−0.675415
$706$	10810.4	0.576284
$707$	411.059	0.0218663
$708$	−15378.7	−0.816339
$709$	−33227.1	−1.76004	−0.880022	−	0.474934i	$-0.842472\pi$
$709$	−33227.1	−1.76004	−0.880022	+	0.474934i	$0.842472\pi$
$710$	14167.0	0.748841
$711$	1693.81	0.0893429
$712$	9302.98	0.489668
$713$	29652.1	1.55747
$714$	−4288.62	−0.224787
$715$	73380.3	3.83814
$716$	−2797.49	−0.146016
$717$	−671.242	−0.0349624
$718$	16031.6	0.833279
$719$	16537.9	0.857803	0.428901	−	0.903351i	$-0.358901\pi$
$719$	16537.9	0.857803	0.428901	+	0.903351i	$0.358901\pi$
$720$	2616.41	0.135428
$721$	26022.1	1.34412
$722$	9155.57	0.471932
$723$	7837.10	0.403133
$724$	−17572.0	−0.902014
$725$	−4135.54	−0.211848
$726$	14081.3	0.719845
$727$	10475.4	0.534405	0.267203	−	0.963640i	$-0.413901\pi$
$727$	10475.4	0.534405	0.267203	+	0.963640i	$0.413901\pi$
$728$	49844.0	2.53756
$729$	729.000	0.0370370
$730$	5021.58	0.254599
$731$	11993.7	0.606845
$732$	−12228.9	−0.617477
$733$	−11111.7	−0.559917	−0.279958	−	0.960012i	$-0.590321\pi$
$733$	−11111.7	−0.559917	−0.279958	+	0.960012i	$0.590321\pi$
$734$	5942.88	0.298850
$735$	−20235.5	−1.01551
$736$	18787.7	0.940931
$737$	16517.5	0.825549
$738$	3452.66	0.172214
$739$	22630.9	1.12651	0.563254	−	0.826283i	$-0.309549\pi$
$739$	22630.9	1.12651	0.563254	+	0.826283i	$0.309549\pi$
$740$	−13359.9	−0.663675
$741$	−1627.93	−0.0807064
$742$	−4002.71	−0.198038
$743$	−23438.8	−1.15731	−0.578657	−	0.815571i	$-0.696423\pi$
$743$	−23438.8	−1.15731	−0.578657	+	0.815571i	$0.696423\pi$
$744$	16667.0	0.821291
$745$	30166.9	1.48353
$746$	−17230.8	−0.845661
$747$	−9829.66	−0.481457
$748$	15287.9	0.747300
$749$	−44275.3	−2.15993
$750$	−5037.16	−0.245241
$751$	1928.93	0.0937254	0.0468627	−	0.998901i	$-0.485078\pi$
$751$	1928.93	0.0937254	0.0468627	+	0.998901i	$0.485078\pi$
$752$	8348.69	0.404848
$753$	−4832.91	−0.233893
$754$	−22253.0	−1.07481
$755$	29048.3	1.40023
$756$	−5019.79	−0.241492
$757$	10573.0	0.507639	0.253820	−	0.967252i	$-0.418313\pi$
$757$	10573.0	0.507639	0.253820	+	0.967252i	$0.418313\pi$
$758$	9390.50	0.449971
$759$	−21203.8	−1.01403
$760$	−1437.09	−0.0685906
$761$	−23685.4	−1.12825	−0.564123	−	0.825691i	$-0.690786\pi$
$761$	−23685.4	−1.12825	−0.564123	+	0.825691i	$0.690786\pi$
$762$	1970.42	0.0936755
$763$	27370.0	1.29864
$764$	−11893.0	−0.563186
$765$	3870.51	0.182926
$766$	8471.35	0.399585
$767$	72107.4	3.39459
$768$	6990.58	0.328452
$769$	−32885.3	−1.54210	−0.771050	−	0.636775i	$-0.780268\pi$
$769$	−32885.3	−1.54210	−0.771050	+	0.636775i	$0.780268\pi$
$770$	−33893.1	−1.58626
$771$	14808.5	0.691720
$772$	18026.7	0.840409
$773$	−10521.8	−0.489578	−0.244789	−	0.969576i	$-0.578719\pi$
$773$	−10521.8	−0.489578	−0.244789	+	0.969576i	$0.578719\pi$
$774$	−4081.73	−0.189554
$775$	−6339.90	−0.293853
$776$	−5021.81	−0.232310
$777$	16012.6	0.739317
$778$	−1080.08	−0.0497720
$779$	1778.74	0.0818101
$780$	−19637.5	−0.901454
$781$	60529.4	2.77325
$782$	4847.88	0.221688
$783$	5133.80	0.234313
$784$	13362.2	0.608702
$785$	36399.7	1.65498
$786$	−267.592	−0.0121434
$787$	−27581.8	−1.24928	−0.624641	−	0.780912i	$-0.714755\pi$
$787$	−27581.8	−1.24928	−0.624641	+	0.780912i	$0.714755\pi$
$788$	4696.83	0.212332
$789$	−3982.01	−0.179674
$790$	−3060.52	−0.137833
$791$	−19406.1	−0.872316
$792$	−11918.3	−0.534721
$793$	57338.6	2.56766
$794$	7580.69	0.338827
$795$	3612.48	0.161159
$796$	−4902.50	−0.218297
$797$	−467.263	−0.0207670	−0.0103835	−	0.999946i	$-0.503305\pi$
$797$	−467.263	−0.0207670	−0.0103835	+	0.999946i	$0.503305\pi$
$798$	751.911	0.0333551
$799$	12350.4	0.546841
$800$	−4017.00	−0.177528
$801$	4392.93	0.193779
$802$	9560.61	0.420944
$803$	21455.1	0.942880
$804$	−4420.28	−0.193895
$805$	36965.2	1.61845
$806$	−34114.4	−1.49086
$807$	−25053.6	−1.09285
$808$	−261.180	−0.0113716
$809$	−18801.0	−0.817068	−0.408534	−	0.912743i	$-0.633960\pi$
$809$	−18801.0	−0.817068	−0.408534	+	0.912743i	$0.633960\pi$
$810$	−1317.22	−0.0571388
$811$	−768.197	−0.0332615	−0.0166307	−	0.999862i	$-0.505294\pi$
$811$	−768.197	−0.0332615	−0.0166307	+	0.999862i	$0.505294\pi$
$812$	−35350.6	−1.52779
$813$	11181.0	0.482329
$814$	16596.4	0.714624
$815$	−26153.8	−1.12408
$816$	−2555.84	−0.109647
$817$	−2102.82	−0.0900471
$818$	−8039.98	−0.343657
$819$	23536.7	1.00420
$820$	21456.7	0.913782
$821$	−24759.2	−1.05250	−0.526249	−	0.850330i	$-0.676402\pi$
$821$	−24759.2	−1.05250	−0.526249	+	0.850330i	$0.676402\pi$
$822$	1046.01	0.0443844
$823$	33400.5	1.41467	0.707333	−	0.706881i	$-0.249898\pi$
$823$	33400.5	1.41467	0.707333	+	0.706881i	$0.249898\pi$
$824$	−16534.0	−0.699016
$825$	4533.58	0.191320
$826$	−33305.1	−1.40295
$827$	−42365.6	−1.78138	−0.890688	−	0.454616i	$-0.849777\pi$
$827$	−42365.6	−1.78138	−0.890688	+	0.454616i	$0.849777\pi$
$828$	5674.40	0.238163
$829$	−2213.76	−0.0927469	−0.0463735	−	0.998924i	$-0.514766\pi$
$829$	−2213.76	−0.0927469	−0.0463735	+	0.998924i	$0.514766\pi$
$830$	17761.1	0.742767
$831$	21335.8	0.890649
$832$	−4877.53	−0.203243
$833$	19767.0	0.822193
$834$	4101.21	0.170280
$835$	−39422.9	−1.63388
$836$	−2680.38	−0.110889
$837$	7870.26	0.325013
$838$	18385.0	0.757875
$839$	−25581.3	−1.05264	−0.526319	−	0.850287i	$-0.676428\pi$
$839$	−25581.3	−1.05264	−0.526319	+	0.850287i	$0.676428\pi$
$840$	20777.6	0.853445
$841$	11764.5	0.482368
$842$	−14642.3	−0.599294
$843$	4492.11	0.183531
$844$	−64.0475	−0.00261209
$845$	65461.2	2.66501
$846$	−4203.11	−0.170811
$847$	−104885.	−4.25488
$848$	−2385.45	−0.0965998
$849$	8924.62	0.360768
$850$	−1036.52	−0.0418264
$851$	−18100.7	−0.729125
$852$	−16198.4	−0.651347
$853$	−48112.0	−1.93121	−0.965605	−	0.260013i	$-0.916273\pi$
$853$	−48112.0	−1.93121	−0.965605	+	0.260013i	$0.916273\pi$
$854$	−26483.7	−1.06119
$855$	−678.605	−0.0271436
$856$	28131.8	1.12328
$857$	−18720.2	−0.746172	−0.373086	−	0.927797i	$-0.621700\pi$
$857$	−18720.2	−0.746172	−0.373086	+	0.927797i	$0.621700\pi$
$858$	24394.8	0.970657
$859$	−1989.65	−0.0790292	−0.0395146	−	0.999219i	$-0.512581\pi$
$859$	−1989.65	−0.0790292	−0.0395146	+	0.999219i	$0.512581\pi$
$860$	−25366.1	−1.00579
$861$	−25717.1	−1.01793
$862$	11228.3	0.443663
$863$	−20736.1	−0.817921	−0.408960	−	0.912552i	$-0.634109\pi$
$863$	−20736.1	−0.817921	−0.408960	+	0.912552i	$0.634109\pi$
$864$	4986.64	0.196353
$865$	20380.0	0.801086
$866$	5998.47	0.235377
$867$	10958.1	0.429246
$868$	−54193.5	−2.11918
$869$	−13076.3	−0.510452
$870$	−9276.19	−0.361486
$871$	20725.7	0.806274
$872$	−17390.5	−0.675361
$873$	−2371.33	−0.0919330
$874$	−849.964	−0.0328953
$875$	37519.2	1.44958
$876$	−5741.63	−0.221452
$877$	−46349.3	−1.78461	−0.892306	−	0.451430i	$-0.850914\pi$
$877$	−46349.3	−1.78461	−0.892306	+	0.451430i	$0.850914\pi$
$878$	−9111.28	−0.350217
$879$	7502.81	0.287899
$880$	−20198.8	−0.773753
$881$	−12201.1	−0.466590	−0.233295	−	0.972406i	$-0.574951\pi$
$881$	−12201.1	−0.466590	−0.233295	+	0.972406i	$0.574951\pi$
$882$	−6727.16	−0.256820
$883$	−25393.0	−0.967773	−0.483887	−	0.875131i	$-0.660775\pi$
$883$	−25393.0	−0.967773	−0.483887	+	0.875131i	$0.660775\pi$
$884$	19182.8	0.729851
$885$	30058.1	1.14169
$886$	4366.78	0.165581
$887$	1362.08	0.0515607	0.0257803	−	0.999668i	$-0.491793\pi$
$887$	1362.08	0.0515607	0.0257803	+	0.999668i	$0.491793\pi$
$888$	−10174.1	−0.384484
$889$	−14676.7	−0.553700
$890$	−7937.53	−0.298951
$891$	−5627.92	−0.211608
$892$	30892.9	1.15961
$893$	−2165.36	−0.0811433
$894$	10028.8	0.375181
$895$	5467.77	0.204209
$896$	−42068.1	−1.56852
$897$	−26606.0	−0.990354
$898$	−15966.8	−0.593341
$899$	55424.3	2.05618
$900$	−1213.24	−0.0449348
$901$	−3528.84	−0.130480
$902$	−26654.7	−0.983931
$903$	30402.7	1.12042
$904$	12330.3	0.453650
$905$	34344.9	1.26151
$906$	9656.91	0.354116
$907$	−46545.5	−1.70399	−0.851994	−	0.523552i	$-0.824607\pi$
$907$	−46545.5	−1.70399	−0.851994	+	0.523552i	$0.824607\pi$
$908$	30350.2	1.10926
$909$	−123.331	−0.00450014
$910$	−42528.1	−1.54922
$911$	−555.003	−0.0201845	−0.0100922	−	0.999949i	$-0.503213\pi$
$911$	−555.003	−0.0201845	−0.0100922	+	0.999949i	$0.503213\pi$
$912$	448.107	0.0162701
$913$	75885.5	2.75076
$914$	11824.1	0.427907
$915$	23901.7	0.863570
$916$	18577.6	0.670110
$917$	1993.16	0.0717774
$918$	1286.72	0.0462617
$919$	18763.0	0.673486	0.336743	−	0.941597i	$-0.390675\pi$
$919$	18763.0	0.673486	0.336743	+	0.941597i	$0.390675\pi$
$920$	−23487.1	−0.841680
$921$	18130.2	0.648654
$922$	−7892.98	−0.281932
$923$	75950.7	2.70850
$924$	38753.0	1.37974
$925$	3870.11	0.137566
$926$	5742.29	0.203783
$927$	−7807.47	−0.276625
$928$	35117.2	1.24222
$929$	−27203.0	−0.960712	−0.480356	−	0.877074i	$-0.659493\pi$
$929$	−27203.0	−0.960712	−0.480356	+	0.877074i	$0.659493\pi$
$930$	−14220.7	−0.501413
$931$	−3465.69	−0.122002
$932$	−19582.5	−0.688246
$933$	9365.88	0.328644
$934$	7653.71	0.268134
$935$	−29880.6	−1.04513
$936$	−14954.8	−0.522236
$937$	−28889.8	−1.00725	−0.503623	−	0.863924i	$-0.668000\pi$
$937$	−28889.8	−1.00725	−0.503623	+	0.863924i	$0.668000\pi$
$938$	−9572.84	−0.333224
$939$	−3286.61	−0.114222
$940$	−26120.4	−0.906334
$941$	27867.8	0.965425	0.482712	−	0.875779i	$-0.339652\pi$
$941$	27867.8	0.965425	0.482712	+	0.875779i	$0.339652\pi$
$942$	12100.8	0.418541
$943$	29070.8	1.00390
$944$	−19848.4	−0.684335
$945$	9811.31	0.337738
$946$	31511.1	1.08300
$947$	27727.4	0.951445	0.475722	−	0.879595i	$-0.342187\pi$
$947$	27727.4	0.951445	0.475722	+	0.879595i	$0.342187\pi$
$948$	3499.37	0.119889
$949$	26921.2	0.920864
$950$	181.730	0.00620644
$951$	−28846.4	−0.983605
$952$	−20296.5	−0.690981
$953$	7462.86	0.253668	0.126834	−	0.991924i	$-0.459518\pi$
$953$	7462.86	0.253668	0.126834	+	0.991924i	$0.459518\pi$
$954$	1200.94	0.0407568
$955$	23245.2	0.787641
$956$	−1386.77	−0.0469158
$957$	−39633.2	−1.33872
$958$	−2942.21	−0.0992259
$959$	−7791.24	−0.262348
$960$	−2033.21	−0.0683558
$961$	55176.1	1.85211
$962$	20824.7	0.697938
$963$	13284.0	0.444519
$964$	16191.3	0.540961
$965$	−35233.7	−1.17535
$966$	12288.8	0.409303
$967$	49419.6	1.64346	0.821730	−	0.569877i	$-0.193009\pi$
$967$	49419.6	1.64346	0.821730	+	0.569877i	$0.193009\pi$
$968$	66642.0	2.21276
$969$	662.894	0.0219765
$970$	4284.73	0.141829
$971$	20757.1	0.686021	0.343011	−	0.939332i	$-0.388553\pi$
$971$	20757.1	0.686021	0.343011	+	0.939332i	$0.388553\pi$
$972$	1506.10	0.0496998
$973$	−30547.8	−1.00649
$974$	−9329.55	−0.306918
$975$	5688.61	0.186853
$976$	−15783.1	−0.517629
$977$	15254.1	0.499510	0.249755	−	0.968309i	$-0.419650\pi$
$977$	15254.1	0.499510	0.249755	+	0.968309i	$0.419650\pi$
$978$	−8694.63	−0.284278
$979$	−33913.7	−1.10714
$980$	−41806.2	−1.36270
$981$	−8211.90	−0.267264
$982$	6505.48	0.211403
$983$	−3303.04	−0.107173	−0.0535863	−	0.998563i	$-0.517065\pi$
$983$	−3303.04	−0.107173	−0.0535863	+	0.998563i	$0.517065\pi$
$984$	16340.2	0.529378
$985$	−9180.07	−0.296956
$986$	9061.43	0.292672
$987$	31306.9	1.00963
$988$	−3363.27	−0.108299
$989$	−34367.4	−1.10497
$990$	10169.0	0.326457
$991$	−31497.2	−1.00963	−0.504814	−	0.863228i	$-0.668439\pi$
$991$	−31497.2	−1.00963	−0.504814	+	0.863228i	$0.668439\pi$
$992$	53835.7	1.72307
$993$	−34511.1	−1.10290
$994$	−35080.3	−1.11939
$995$	9582.06	0.305298
$996$	−20307.9	−0.646064
$997$	1822.10	0.0578800	0.0289400	−	0.999581i	$-0.490787\pi$
$997$	1822.10	0.0578800	0.0289400	+	0.999581i	$0.490787\pi$
$998$	6846.91	0.217169
$999$	−4804.30	−0.152154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1011.4.a.c.1.18	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1011.4.a.c.1.18	✓	46	1.1	even	1	trivial

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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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.34241 q^{2} -3.00000 q^{3} -6.19794 q^{4} +12.1140 q^{5} +4.02723 q^{6} -29.9968 q^{7} +19.0594 q^{8} +9.00000 q^{9} -16.2620 q^{10} -69.4805 q^{11} +18.5938 q^{12} -87.1823 q^{13} +40.2679 q^{14} -36.3421 q^{15} +23.9980 q^{16} +35.5007 q^{17} -12.0817 q^{18} -6.22423 q^{19} -75.0821 q^{20} +89.9903 q^{21} +93.2712 q^{22} -101.725 q^{23} -57.1783 q^{24} +21.7499 q^{25} +117.034 q^{26} -27.0000 q^{27} +185.918 q^{28} -190.141 q^{29} +48.7860 q^{30} -291.491 q^{31} -184.691 q^{32} +208.441 q^{33} -47.6565 q^{34} -363.382 q^{35} -55.7815 q^{36} +177.937 q^{37} +8.35547 q^{38} +261.547 q^{39} +230.887 q^{40} -285.777 q^{41} -120.804 q^{42} +337.844 q^{43} +430.636 q^{44} +109.026 q^{45} +136.557 q^{46} +347.892 q^{47} -71.9939 q^{48} +556.806 q^{49} -29.1972 q^{50} -106.502 q^{51} +540.350 q^{52} -99.4021 q^{53} +36.2450 q^{54} -841.689 q^{55} -571.722 q^{56} +18.6727 q^{57} +255.246 q^{58} -827.088 q^{59} +225.246 q^{60} -657.687 q^{61} +391.300 q^{62} -269.971 q^{63} +55.9464 q^{64} -1056.13 q^{65} -279.813 q^{66} -237.729 q^{67} -220.031 q^{68} +305.176 q^{69} +487.807 q^{70} -871.171 q^{71} +171.535 q^{72} -308.793 q^{73} -238.864 q^{74} -65.2497 q^{75} +38.5774 q^{76} +2084.19 q^{77} -351.103 q^{78} +188.201 q^{79} +290.712 q^{80} +81.0000 q^{81} +383.629 q^{82} -1092.18 q^{83} -557.755 q^{84} +430.057 q^{85} -453.525 q^{86} +570.422 q^{87} -1324.26 q^{88} +488.104 q^{89} -146.358 q^{90} +2615.19 q^{91} +630.488 q^{92} +874.474 q^{93} -467.013 q^{94} -75.4006 q^{95} +554.072 q^{96} -263.482 q^{97} -747.462 q^{98} -625.324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) \) 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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