LMFDB - Embedded newform 1849.4.a.m.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.08007 q^{2} -3.35274 q^{3} +17.8071 q^{4} -16.0526 q^{5} +17.0322 q^{6} +17.0633 q^{7} -49.8208 q^{8} -15.7591 q^{9} +O(q^{10})$	\(q-5.08007 q^{2} -3.35274 q^{3} +17.8071 q^{4} -16.0526 q^{5} +17.0322 q^{6} +17.0633 q^{7} -49.8208 q^{8} -15.7591 q^{9} +81.5484 q^{10} -11.9512 q^{11} -59.7027 q^{12} -1.30416 q^{13} -86.6828 q^{14} +53.8203 q^{15} +110.636 q^{16} +110.494 q^{17} +80.0575 q^{18} -145.212 q^{19} -285.851 q^{20} -57.2089 q^{21} +60.7127 q^{22} +156.075 q^{23} +167.036 q^{24} +132.686 q^{25} +6.62523 q^{26} +143.360 q^{27} +303.848 q^{28} -59.3589 q^{29} -273.411 q^{30} -309.679 q^{31} -163.474 q^{32} +40.0691 q^{33} -561.317 q^{34} -273.911 q^{35} -280.625 q^{36} -116.479 q^{37} +737.685 q^{38} +4.37251 q^{39} +799.755 q^{40} +394.241 q^{41} +290.625 q^{42} -212.816 q^{44} +252.975 q^{45} -792.874 q^{46} +297.245 q^{47} -370.935 q^{48} -51.8434 q^{49} -674.056 q^{50} -370.458 q^{51} -23.2233 q^{52} -449.259 q^{53} -728.280 q^{54} +191.847 q^{55} -850.108 q^{56} +486.857 q^{57} +301.547 q^{58} +284.675 q^{59} +958.384 q^{60} +42.9199 q^{61} +1573.19 q^{62} -268.903 q^{63} -54.6312 q^{64} +20.9352 q^{65} -203.554 q^{66} +104.873 q^{67} +1967.58 q^{68} -523.281 q^{69} +1391.49 q^{70} +338.009 q^{71} +785.133 q^{72} +441.287 q^{73} +591.722 q^{74} -444.863 q^{75} -2585.80 q^{76} -203.926 q^{77} -22.2127 q^{78} +220.732 q^{79} -1776.00 q^{80} -55.1537 q^{81} -2002.77 q^{82} -344.620 q^{83} -1018.72 q^{84} -1773.72 q^{85} +199.015 q^{87} +595.416 q^{88} -1475.78 q^{89} -1285.13 q^{90} -22.2533 q^{91} +2779.25 q^{92} +1038.27 q^{93} -1510.03 q^{94} +2331.02 q^{95} +548.087 q^{96} -695.274 q^{97} +263.368 q^{98} +188.340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−5.08007	−1.79608	−0.898038	−	0.439918i	$-0.855008\pi$
$2$	−5.08007	−1.79608	−0.898038	+	0.439918i	$0.855008\pi$
$3$	−3.35274	−0.645235	−0.322618	−	0.946529i	$-0.604563\pi$
$3$	−3.35274	−0.645235	−0.322618	+	0.946529i	$0.604563\pi$
$4$	17.8071	2.22589
$5$	−16.0526	−1.43579	−0.717895	−	0.696152i	$-0.754894\pi$
$5$	−16.0526	−1.43579	−0.717895	+	0.696152i	$0.754894\pi$
$6$	17.0322	1.15889
$7$	17.0633	0.921332	0.460666	−	0.887574i	$-0.347611\pi$
$7$	17.0633	0.921332	0.460666	+	0.887574i	$0.347611\pi$
$8$	−49.8208	−2.20179
$9$	−15.7591	−0.583671
$10$	81.5484	2.57879
$11$	−11.9512	−0.327582	−0.163791	−	0.986495i	$-0.552372\pi$
$11$	−11.9512	−0.327582	−0.163791	+	0.986495i	$0.552372\pi$
$12$	−59.7027	−1.43622
$13$	−1.30416	−0.0278238	−0.0139119	−	0.999903i	$-0.504428\pi$
$13$	−1.30416	−0.0278238	−0.0139119	+	0.999903i	$0.504428\pi$
$14$	−86.6828	−1.65478
$15$	53.8203	0.926422
$16$	110.636	1.72869
$17$	110.494	1.57640	0.788198	−	0.615422i	$-0.211014\pi$
$17$	110.494	1.57640	0.788198	+	0.615422i	$0.211014\pi$
$18$	80.0575	1.04832
$19$	−145.212	−1.75336	−0.876679	−	0.481076i	$-0.840246\pi$
$19$	−145.212	−1.75336	−0.876679	+	0.481076i	$0.840246\pi$
$20$	−285.851	−3.19591
$21$	−57.2089	−0.594476
$22$	60.7127	0.588363
$23$	156.075	1.41496	0.707478	−	0.706735i	$-0.249833\pi$
$23$	156.075	1.41496	0.707478	+	0.706735i	$0.249833\pi$
$24$	167.036	1.42067
$25$	132.686	1.06149
$26$	6.62523	0.0499736
$27$	143.360	1.02184
$28$	303.848	2.05078
$29$	−59.3589	−0.380092	−0.190046	−	0.981775i	$-0.560864\pi$
$29$	−59.3589	−0.380092	−0.190046	+	0.981775i	$0.560864\pi$
$30$	−273.411	−1.66392
$31$	−309.679	−1.79419	−0.897097	−	0.441833i	$-0.854328\pi$
$31$	−309.679	−1.79419	−0.897097	+	0.441833i	$0.854328\pi$
$32$	−163.474	−0.903076
$33$	40.0691	0.211368
$34$	−561.317	−2.83133
$35$	−273.911	−1.32284
$36$	−280.625	−1.29919
$37$	−116.479	−0.517542	−0.258771	−	0.965939i	$-0.583317\pi$
$37$	−116.479	−0.517542	−0.258771	+	0.965939i	$0.583317\pi$
$38$	737.685	3.14916
$39$	4.37251	0.0179529
$40$	799.755	3.16131
$41$	394.241	1.50171	0.750855	−	0.660467i	$-0.229642\pi$
$41$	394.241	1.50171	0.750855	+	0.660467i	$0.229642\pi$
$42$	290.625	1.06772
$43$	0	0
$43$	0	0
$44$	−212.816	−0.729162
$45$	252.975	0.838029
$46$	−792.874	−2.54137
$47$	297.245	0.922504	0.461252	−	0.887269i	$-0.347400\pi$
$47$	297.245	0.922504	0.461252	+	0.887269i	$0.347400\pi$
$48$	−370.935	−1.11541
$49$	−51.8434	−0.151147
$50$	−674.056	−1.90652
$51$	−370.458	−1.01715
$52$	−23.2233	−0.0619326
$53$	−449.259	−1.16435	−0.582174	−	0.813064i	$-0.697798\pi$
$53$	−449.259	−1.16435	−0.582174	+	0.813064i	$0.697798\pi$
$54$	−728.280	−1.83530
$55$	191.847	0.470339
$56$	−850.108	−2.02858
$57$	486.857	1.13133
$58$	301.547	0.682674
$59$	284.675	0.628161	0.314080	−	0.949396i	$-0.398304\pi$
$59$	284.675	0.628161	0.314080	+	0.949396i	$0.398304\pi$
$60$	958.384	2.06211
$61$	42.9199	0.0900873	0.0450437	−	0.998985i	$-0.485657\pi$
$61$	42.9199	0.0900873	0.0450437	+	0.998985i	$0.485657\pi$
$62$	1573.19	3.22251
$63$	−268.903	−0.537755
$64$	−54.6312	−0.106702
$65$	20.9352	0.0399491
$66$	−203.554	−0.379633
$67$	104.873	0.191229	0.0956145	−	0.995418i	$-0.469518\pi$
$67$	104.873	0.191229	0.0956145	+	0.995418i	$0.469518\pi$
$68$	1967.58	3.50888
$69$	−523.281	−0.912980
$70$	1391.49	2.37592
$71$	338.009	0.564990	0.282495	−	0.959269i	$-0.408838\pi$
$71$	338.009	0.564990	0.282495	+	0.959269i	$0.408838\pi$
$72$	785.133	1.28512
$73$	441.287	0.707517	0.353758	−	0.935337i	$-0.384904\pi$
$73$	441.287	0.707517	0.353758	+	0.935337i	$0.384904\pi$
$74$	591.722	0.929544
$75$	−444.863	−0.684912
$76$	−2585.80	−3.90278
$77$	−203.926	−0.301812
$78$	−22.2127	−0.0322447
$79$	220.732	0.314358	0.157179	−	0.987570i	$-0.449760\pi$
$79$	220.732	0.314358	0.157179	+	0.987570i	$0.449760\pi$
$80$	−1776.00	−2.48204
$81$	−55.1537	−0.0756566
$82$	−2002.77	−2.69719
$83$	−344.620	−0.455747	−0.227873	−	0.973691i	$-0.573177\pi$
$83$	−344.620	−0.455747	−0.227873	+	0.973691i	$0.573177\pi$
$84$	−1018.72	−1.32324
$85$	−1773.72	−2.26337
$86$	0	0
$87$	199.015	0.245249
$88$	595.416	0.721268
$89$	−1475.78	−1.75766	−0.878832	−	0.477131i	$-0.841677\pi$
$89$	−1475.78	−1.75766	−0.878832	+	0.477131i	$0.841677\pi$
$90$	−1285.13	−1.50516
$91$	−22.2533	−0.0256349
$92$	2779.25	3.14954
$93$	1038.27	1.15768
$94$	−1510.03	−1.65689
$95$	2331.02	2.51745
$96$	548.087	0.582696
$97$	−695.274	−0.727777	−0.363889	−	0.931442i	$-0.618551\pi$
$97$	−695.274	−0.727777	−0.363889	+	0.931442i	$0.618551\pi$
$98$	263.368	0.271472
$99$	188.340	0.191200
$100$	2362.76	2.36276
$101$	−1220.77	−1.20268	−0.601341	−	0.798993i	$-0.705367\pi$
$101$	−1220.77	−1.20268	−0.601341	+	0.798993i	$0.705367\pi$
$102$	1881.95	1.82687
$103$	524.156	0.501423	0.250712	−	0.968062i	$-0.419335\pi$
$103$	524.156	0.501423	0.250712	+	0.968062i	$0.419335\pi$
$104$	64.9744	0.0612621
$105$	918.352	0.853543
$106$	2282.27	2.09126
$107$	−1218.80	−1.10117	−0.550586	−	0.834778i	$-0.685596\pi$
$107$	−1218.80	−1.10117	−0.550586	+	0.834778i	$0.685596\pi$
$108$	2552.83	2.27450
$109$	752.273	0.661052	0.330526	−	0.943797i	$-0.392774\pi$
$109$	752.273	0.661052	0.330526	+	0.943797i	$0.392774\pi$
$110$	−974.597	−0.844765
$111$	390.524	0.333936
$112$	1887.82	1.59270
$113$	857.489	0.713856	0.356928	−	0.934132i	$-0.383824\pi$
$113$	857.489	0.713856	0.356928	+	0.934132i	$0.383824\pi$
$114$	−2473.27	−2.03195
$115$	−2505.42	−2.03158
$116$	−1057.01	−0.846043
$117$	20.5524	0.0162399
$118$	−1446.17	−1.12822
$119$	1885.39	1.45238
$120$	−2681.37	−2.03979
$121$	−1188.17	−0.892690
$122$	−218.036	−0.161804
$123$	−1321.79	−0.968956
$124$	−5514.49	−3.99368
$125$	−123.387	−0.0882885
$126$	1366.05	0.965849
$127$	−297.988	−0.208206	−0.104103	−	0.994567i	$-0.533197\pi$
$127$	−297.988	−0.208206	−0.104103	+	0.994567i	$0.533197\pi$
$128$	1585.32	1.09472
$129$	0	0
$130$	−106.352	−0.0717516
$131$	−144.192	−0.0961689	−0.0480844	−	0.998843i	$-0.515312\pi$
$131$	−144.192	−0.0961689	−0.0480844	+	0.998843i	$0.515312\pi$
$132$	713.515	0.470481
$133$	−2477.79	−1.61543
$134$	−532.765	−0.343462
$135$	−2301.31	−1.46715
$136$	−5504.90	−3.47089
$137$	511.717	0.319117	0.159558	−	0.987189i	$-0.448993\pi$
$137$	511.717	0.319117	0.159558	+	0.987189i	$0.448993\pi$
$138$	2658.30	1.63978
$139$	−264.762	−0.161560	−0.0807800	−	0.996732i	$-0.525741\pi$
$139$	−264.762	−0.161560	−0.0807800	+	0.996732i	$0.525741\pi$
$140$	−4877.56	−2.94449
$141$	−996.586	−0.595232
$142$	−1717.11	−1.01476
$143$	15.5862	0.00911458
$144$	−1743.53	−1.00899
$145$	952.865	0.545732
$146$	−2241.77	−1.27075
$147$	173.818	0.0975254
$148$	−2074.16	−1.15199
$149$	−742.955	−0.408491	−0.204246	−	0.978920i	$-0.565474\pi$
$149$	−742.955	−0.408491	−0.204246	+	0.978920i	$0.565474\pi$
$150$	2259.94	1.23015
$151$	−1557.79	−0.839545	−0.419772	−	0.907629i	$-0.637890\pi$
$151$	−1557.79	−0.839545	−0.419772	+	0.907629i	$0.637890\pi$
$152$	7234.56	3.86053
$153$	−1741.29	−0.920097
$154$	1035.96	0.542078
$155$	4971.16	2.57609
$156$	77.8619	0.0399611
$157$	1945.43	0.988932	0.494466	−	0.869197i	$-0.335364\pi$
$157$	1945.43	0.988932	0.494466	+	0.869197i	$0.335364\pi$
$158$	−1121.34	−0.564612
$159$	1506.25	0.751279
$160$	2624.19	1.29663
$161$	2663.16	1.30364
$162$	280.184	0.135885
$163$	−3029.35	−1.45569	−0.727843	−	0.685744i	$-0.759477\pi$
$163$	−3029.35	−1.45569	−0.727843	+	0.685744i	$0.759477\pi$
$164$	7020.30	3.34264
$165$	−643.214	−0.303480
$166$	1750.70	0.818556
$167$	−592.214	−0.274412	−0.137206	−	0.990543i	$-0.543812\pi$
$167$	−592.214	−0.274412	−0.137206	+	0.990543i	$0.543812\pi$
$168$	2850.19	1.30891
$169$	−2195.30	−0.999226
$170$	9010.61	4.06519
$171$	2288.41	1.02338
$172$	0	0
$173$	−2606.58	−1.14552	−0.572758	−	0.819724i	$-0.694127\pi$
$173$	−2606.58	−1.14552	−0.572758	+	0.819724i	$0.694127\pi$
$174$	−1011.01	−0.440486
$175$	2264.07	0.977986
$176$	−1322.23	−0.566290
$177$	−954.440	−0.405312
$178$	7497.06	3.15690
$179$	−155.202	−0.0648062	−0.0324031	−	0.999475i	$-0.510316\pi$
$179$	−155.202	−0.0648062	−0.0324031	+	0.999475i	$0.510316\pi$
$180$	4504.76	1.86536
$181$	−4154.48	−1.70608	−0.853038	−	0.521849i	$-0.825243\pi$
$181$	−4154.48	−1.70608	−0.853038	+	0.521849i	$0.825243\pi$
$182$	113.048	0.0460423
$183$	−143.899	−0.0581275
$184$	−7775.81	−3.11544
$185$	1869.79	0.743081
$186$	−5274.51	−2.07928
$187$	−1320.53	−0.516400
$188$	5293.08	2.05339
$189$	2446.20	0.941455
$190$	−11841.8	−4.52154
$191$	−3309.84	−1.25388	−0.626942	−	0.779066i	$-0.715694\pi$
$191$	−3309.84	−1.25388	−0.626942	+	0.779066i	$0.715694\pi$
$192$	183.164	0.0688476
$193$	−1803.27	−0.672550	−0.336275	−	0.941764i	$-0.609167\pi$
$193$	−1803.27	−0.672550	−0.336275	+	0.941764i	$0.609167\pi$
$194$	3532.04	1.30714
$195$	−70.1903	−0.0257766
$196$	−923.182	−0.336437
$197$	−3531.58	−1.27723	−0.638616	−	0.769525i	$-0.720493\pi$
$197$	−3531.58	−1.27723	−0.638616	+	0.769525i	$0.720493\pi$
$198$	−956.779	−0.343411
$199$	−1335.69	−0.475800	−0.237900	−	0.971290i	$-0.576459\pi$
$199$	−1335.69	−0.475800	−0.237900	+	0.971290i	$0.576459\pi$
$200$	−6610.55	−2.33718
$201$	−351.614	−0.123388
$202$	6201.58	2.16011
$203$	−1012.86	−0.350191
$204$	−6596.78	−2.26405
$205$	−6328.60	−2.15614
$206$	−2662.75	−0.900595
$207$	−2459.61	−0.825869
$208$	−144.288	−0.0480988
$209$	1735.44	0.574369
$210$	−4665.29	−1.53303
$211$	2489.02	0.812091	0.406046	−	0.913853i	$-0.366907\pi$
$211$	2489.02	0.812091	0.406046	+	0.913853i	$0.366907\pi$
$212$	−8000.01	−2.59171
$213$	−1133.26	−0.364551
$214$	6191.57	1.97779
$215$	0	0
$216$	−7142.33	−2.24988
$217$	−5284.15	−1.65305
$218$	−3821.60	−1.18730
$219$	−1479.52	−0.456515
$220$	3416.25	1.04692
$221$	−144.102	−0.0438613
$222$	−1983.89	−0.599775
$223$	1569.97	0.471449	0.235724	−	0.971820i	$-0.424254\pi$
$223$	1569.97	0.471449	0.235724	+	0.971820i	$0.424254\pi$
$224$	−2789.41	−0.832033
$225$	−2091.02	−0.619562
$226$	−4356.10	−1.28214
$227$	1345.89	0.393523	0.196761	−	0.980451i	$-0.436958\pi$
$227$	1345.89	0.393523	0.196761	+	0.980451i	$0.436958\pi$
$228$	8669.51	2.51821
$229$	−80.1907	−0.0231404	−0.0115702	−	0.999933i	$-0.503683\pi$
$229$	−80.1907	−0.0231404	−0.0115702	+	0.999933i	$0.503683\pi$
$230$	12727.7	3.64887
$231$	683.712	0.194740
$232$	2957.31	0.836883
$233$	1332.17	0.374564	0.187282	−	0.982306i	$-0.440032\pi$
$233$	1332.17	0.374564	0.187282	+	0.982306i	$0.440032\pi$
$234$	−104.408	−0.0291682
$235$	−4771.56	−1.32452
$236$	5069.23	1.39822
$237$	−740.058	−0.202835
$238$	−9577.93	−2.60859
$239$	−180.631	−0.0488873	−0.0244437	−	0.999701i	$-0.507781\pi$
$239$	−180.631	−0.0488873	−0.0244437	+	0.999701i	$0.507781\pi$
$240$	5954.48	1.60150
$241$	2424.62	0.648064	0.324032	−	0.946046i	$-0.394961\pi$
$241$	2424.62	0.648064	0.324032	+	0.946046i	$0.394961\pi$
$242$	6035.99	1.60334
$243$	−3685.81	−0.973024
$244$	764.279	0.200524
$245$	832.223	0.217015
$246$	6714.78	1.74032
$247$	189.379	0.0487850
$248$	15428.5	3.95044
$249$	1155.42	0.294064
$250$	626.814	0.158573
$251$	−7070.47	−1.77803	−0.889013	−	0.457883i	$-0.848608\pi$
$251$	−7070.47	−1.77803	−0.889013	+	0.457883i	$0.848608\pi$
$252$	−4788.38	−1.19698
$253$	−1865.28	−0.463515
$254$	1513.80	0.373954
$255$	5946.81	1.46041
$256$	−7616.51	−1.85950
$257$	−1653.12	−0.401241	−0.200620	−	0.979669i	$-0.564296\pi$
$257$	−1653.12	−0.401241	−0.200620	+	0.979669i	$0.564296\pi$
$258$	0	0
$259$	−1987.52	−0.476828
$260$	372.795	0.0889222
$261$	935.444	0.221849
$262$	732.506	0.172727
$263$	−304.759	−0.0714534	−0.0357267	−	0.999362i	$-0.511375\pi$
$263$	−304.759	−0.0714534	−0.0357267	+	0.999362i	$0.511375\pi$
$264$	−1996.28	−0.465388
$265$	7211.78	1.67176
$266$	12587.3	2.90143
$267$	4947.90	1.13411
$268$	1867.49	0.425654
$269$	6678.36	1.51371	0.756853	−	0.653585i	$-0.226736\pi$
$269$	6678.36	1.51371	0.756853	+	0.653585i	$0.226736\pi$
$270$	11690.8	2.63511
$271$	−671.196	−0.150451	−0.0752255	−	0.997167i	$-0.523968\pi$
$271$	−671.196	−0.150451	−0.0752255	+	0.997167i	$0.523968\pi$
$272$	12224.7	2.72511
$273$	74.6096	0.0165406
$274$	−2599.56	−0.573158
$275$	−1585.76	−0.347726
$276$	−9318.12	−2.03219
$277$	5952.21	1.29110	0.645548	−	0.763720i	$-0.276629\pi$
$277$	5952.21	1.29110	0.645548	+	0.763720i	$0.276629\pi$
$278$	1345.01	0.290174
$279$	4880.27	1.04722
$280$	13646.5	2.91261
$281$	8504.85	1.80554	0.902770	−	0.430124i	$-0.141530\pi$
$281$	8504.85	1.80554	0.902770	+	0.430124i	$0.141530\pi$
$282$	5062.73	1.06908
$283$	−6383.40	−1.34083	−0.670413	−	0.741988i	$-0.733883\pi$
$283$	−6383.40	−1.34083	−0.670413	+	0.741988i	$0.733883\pi$
$284$	6018.96	1.25760
$285$	−7815.32	−1.62435
$286$	−79.1791	−0.0163705
$287$	6727.06	1.38357
$288$	2576.21	0.527099
$289$	7295.91	1.48502
$290$	−4840.62	−0.980176
$291$	2331.07	0.469588
$292$	7858.04	1.57485
$293$	−718.238	−0.143208	−0.0716039	−	0.997433i	$-0.522812\pi$
$293$	−718.238	−0.143208	−0.0716039	+	0.997433i	$0.522812\pi$
$294$	−883.006	−0.175163
$295$	−4569.77	−0.901906
$296$	5803.08	1.13952
$297$	−1713.32	−0.334737
$298$	3774.26	0.733682
$299$	−203.547	−0.0393694
$300$	−7921.73	−1.52454
$301$	0	0
$302$	7913.69	1.50789
$303$	4092.91	0.776013
$304$	−16065.7	−3.03102
$305$	−688.976	−0.129346
$306$	8845.87	1.65256
$307$	1662.99	0.309160	0.154580	−	0.987980i	$-0.450598\pi$
$307$	1662.99	0.309160	0.154580	+	0.987980i	$0.450598\pi$
$308$	−3631.34	−0.671801
$309$	−1757.36	−0.323536
$310$	−25253.8	−4.62685
$311$	5804.06	1.05826	0.529129	−	0.848541i	$-0.322519\pi$
$311$	5804.06	1.05826	0.529129	+	0.848541i	$0.322519\pi$
$312$	−217.842	−0.0395285
$313$	2652.96	0.479086	0.239543	−	0.970886i	$-0.423002\pi$
$313$	2652.96	0.479086	0.239543	+	0.970886i	$0.423002\pi$
$314$	−9882.92	−1.77620
$315$	4316.59	0.772103
$316$	3930.60	0.699727
$317$	7185.34	1.27309	0.636544	−	0.771240i	$-0.280363\pi$
$317$	7185.34	1.27309	0.636544	+	0.771240i	$0.280363\pi$
$318$	−7651.85	−1.34935
$319$	709.407	0.124511
$320$	876.973	0.153201
$321$	4086.31	0.710515
$322$	−13529.1	−2.34144
$323$	−16045.0	−2.76399
$324$	−982.127	−0.168403
$325$	−173.044	−0.0295347
$326$	15389.3	2.61452
$327$	−2522.18	−0.426534
$328$	−19641.4	−3.30645
$329$	5071.99	0.849932
$330$	3267.57	0.545073
$331$	−52.0842	−0.00864896	−0.00432448	−	0.999991i	$-0.501377\pi$
$331$	−52.0842	−0.00864896	−0.00432448	+	0.999991i	$0.501377\pi$
$332$	−6136.69	−1.01444
$333$	1835.61	0.302074
$334$	3008.49	0.492866
$335$	−1683.49	−0.274564
$336$	−6329.38	−1.02767
$337$	7119.45	1.15080	0.575402	−	0.817870i	$-0.304845\pi$
$337$	7119.45	1.15080	0.575402	+	0.817870i	$0.304845\pi$
$338$	11152.3	1.79469
$339$	−2874.94	−0.460605
$340$	−31584.8	−5.03802
$341$	3701.02	0.587747
$342$	−11625.3	−1.83808
$343$	−6737.34	−1.06059
$344$	0	0
$345$	8400.02	1.31085
$346$	13241.6	2.05743
$347$	7966.62	1.23248	0.616240	−	0.787558i	$-0.288655\pi$
$347$	7966.62	1.23248	0.616240	+	0.787558i	$0.288655\pi$
$348$	3543.88	0.545897
$349$	−6786.46	−1.04089	−0.520446	−	0.853895i	$-0.674234\pi$
$349$	−6786.46	−1.04089	−0.520446	+	0.853895i	$0.674234\pi$
$350$	−11501.6	−1.75654
$351$	−186.965	−0.0284315
$352$	1953.70	0.295832
$353$	2970.52	0.447890	0.223945	−	0.974602i	$-0.428106\pi$
$353$	2970.52	0.447890	0.223945	+	0.974602i	$0.428106\pi$
$354$	4848.62	0.727970
$355$	−5425.93	−0.811206
$356$	−26279.4	−3.91237
$357$	−6321.23	−0.937129
$358$	788.435	0.116397
$359$	3501.08	0.514708	0.257354	−	0.966317i	$-0.417149\pi$
$359$	3501.08	0.514708	0.257354	+	0.966317i	$0.417149\pi$
$360$	−12603.4	−1.84516
$361$	14227.4	2.07426
$362$	21105.0	3.06424
$363$	3983.63	0.575995
$364$	−396.267	−0.0570605
$365$	−7083.81	−1.01584
$366$	731.018	0.104401
$367$	−3024.48	−0.430181	−0.215091	−	0.976594i	$-0.569005\pi$
$367$	−3024.48	−0.430181	−0.215091	+	0.976594i	$0.569005\pi$
$368$	17267.6	2.44603
$369$	−6212.89	−0.876505
$370$	−9498.68	−1.33463
$371$	−7665.85	−1.07275
$372$	18488.7	2.57686
$373$	6071.61	0.842831	0.421415	−	0.906868i	$-0.361533\pi$
$373$	6071.61	0.842831	0.421415	+	0.906868i	$0.361533\pi$
$374$	6708.38	0.927493
$375$	413.684	0.0569669
$376$	−14809.0	−2.03116
$377$	77.4135	0.0105756
$378$	−12426.9	−1.69092
$379$	−2063.83	−0.279715	−0.139857	−	0.990172i	$-0.544664\pi$
$379$	−2063.83	−0.279715	−0.139857	+	0.990172i	$0.544664\pi$
$380$	41508.8	5.60357
$381$	999.076	0.134342
$382$	16814.2	2.25207
$383$	−4156.07	−0.554479	−0.277239	−	0.960801i	$-0.589419\pi$
$383$	−4156.07	−0.554479	−0.277239	+	0.960801i	$0.589419\pi$
$384$	−5315.18	−0.706352
$385$	3273.55	0.433339
$386$	9160.73	1.20795
$387$	0	0
$388$	−12380.8	−1.61995
$389$	4996.29	0.651213	0.325607	−	0.945505i	$-0.394431\pi$
$389$	4996.29	0.651213	0.325607	+	0.945505i	$0.394431\pi$
$390$	356.572	0.0462967
$391$	17245.4	2.23053
$392$	2582.88	0.332794
$393$	483.439	0.0620516
$394$	17940.7	2.29401
$395$	−3543.33	−0.451352
$396$	3353.79	0.425591
$397$	8925.97	1.12842	0.564209	−	0.825632i	$-0.309181\pi$
$397$	8925.97	1.12842	0.564209	+	0.825632i	$0.309181\pi$
$398$	6785.38	0.854574
$399$	8307.39	1.04233
$400$	14679.9	1.83499
$401$	−7413.73	−0.923252	−0.461626	−	0.887075i	$-0.652734\pi$
$401$	−7413.73	−0.923252	−0.461626	+	0.887075i	$0.652734\pi$
$402$	1786.22	0.221614
$403$	403.871	0.0499213
$404$	−21738.3	−2.67704
$405$	885.360	0.108627
$406$	5145.40	0.628970
$407$	1392.06	0.169538
$408$	18456.5	2.23954
$409$	1661.17	0.200830	0.100415	−	0.994946i	$-0.467983\pi$
$409$	1661.17	0.200830	0.100415	+	0.994946i	$0.467983\pi$
$410$	32149.7	3.87259
$411$	−1715.66	−0.205905
$412$	9333.70	1.11611
$413$	4857.49	0.578745
$414$	12495.0	1.48332
$415$	5532.06	0.654357
$416$	213.197	0.0251270
$417$	887.680	0.104244
$418$	−8816.18	−1.03161
$419$	5902.39	0.688188	0.344094	−	0.938935i	$-0.388186\pi$
$419$	5902.39	0.688188	0.344094	+	0.938935i	$0.388186\pi$
$420$	16353.2	1.89989
$421$	13346.2	1.54502	0.772510	−	0.635003i	$-0.219001\pi$
$421$	13346.2	1.54502	0.772510	+	0.635003i	$0.219001\pi$
$422$	−12644.4	−1.45858
$423$	−4684.32	−0.538439
$424$	22382.5	2.56365
$425$	14661.0	1.67333
$426$	5757.02	0.654762
$427$	732.355	0.0830003
$428$	−21703.2	−2.45109
$429$	−52.2566	−0.00588105
$430$	0	0
$431$	7381.54	0.824956	0.412478	−	0.910967i	$-0.364663\pi$
$431$	7381.54	0.824956	0.412478	+	0.910967i	$0.364663\pi$
$432$	15860.9	1.76645
$433$	3028.18	0.336085	0.168043	−	0.985780i	$-0.446255\pi$
$433$	3028.18	0.336085	0.168043	+	0.985780i	$0.446255\pi$
$434$	26843.9	2.96900
$435$	−3194.71	−0.352126
$436$	13395.8	1.47143
$437$	−22664.0	−2.48092
$438$	7516.07	0.819935
$439$	13968.2	1.51860	0.759299	−	0.650742i	$-0.225542\pi$
$439$	13968.2	1.51860	0.759299	+	0.650742i	$0.225542\pi$
$440$	−9557.99	−1.03559
$441$	817.007	0.0882202
$442$	732.048	0.0787782
$443$	−471.622	−0.0505812	−0.0252906	−	0.999680i	$-0.508051\pi$
$443$	−471.622	−0.0505812	−0.0252906	+	0.999680i	$0.508051\pi$
$444$	6954.11	0.743305
$445$	23690.1	2.52364
$446$	−7975.57	−0.846758
$447$	2490.94	0.263573
$448$	−932.189	−0.0983076
$449$	−10942.7	−1.15015	−0.575076	−	0.818100i	$-0.695028\pi$
$449$	−10942.7	−1.15015	−0.575076	+	0.818100i	$0.695028\pi$
$450$	10622.5	1.11278
$451$	−4711.63	−0.491934
$452$	15269.4	1.58897
$453$	5222.87	0.541704
$454$	−6837.20	−0.706797
$455$	357.224	0.0368064
$456$	−24255.6	−2.49095
$457$	−7705.67	−0.788744	−0.394372	−	0.918951i	$-0.629038\pi$
$457$	−7705.67	−0.788744	−0.394372	+	0.918951i	$0.629038\pi$
$458$	407.374	0.0415619
$459$	15840.4	1.61083
$460$	−44614.3	−4.52207
$461$	−13188.9	−1.33247	−0.666233	−	0.745744i	$-0.732094\pi$
$461$	−13188.9	−1.33247	−0.666233	+	0.745744i	$0.732094\pi$
$462$	−3473.30	−0.349768
$463$	−13134.9	−1.31842	−0.659212	−	0.751957i	$-0.729110\pi$
$463$	−13134.9	−1.31842	−0.659212	+	0.751957i	$0.729110\pi$
$464$	−6567.26	−0.657063
$465$	−16667.0	−1.66218
$466$	−6767.52	−0.672745
$467$	17817.7	1.76553	0.882765	−	0.469814i	$-0.155679\pi$
$467$	17817.7	1.76553	0.882765	+	0.469814i	$0.155679\pi$
$468$	365.979	0.0361483
$469$	1789.49	0.176185
$470$	24239.9	2.37894
$471$	−6522.53	−0.638094
$472$	−14182.7	−1.38308
$473$	0	0
$474$	3759.55	0.364307
$475$	−19267.6	−1.86117
$476$	33573.4	3.23285
$477$	7079.93	0.679597
$478$	917.620	0.0878054
$479$	−2439.30	−0.232682	−0.116341	−	0.993209i	$-0.537117\pi$
$479$	−2439.30	−0.232682	−0.116341	+	0.993209i	$0.537117\pi$
$480$	−8798.22	−0.836629
$481$	151.907	0.0144000
$482$	−12317.2	−1.16397
$483$	−8928.90	−0.841158
$484$	−21157.9	−1.98703
$485$	11161.0	1.04493
$486$	18724.2	1.74763
$487$	10296.6	0.958075	0.479037	−	0.877794i	$-0.340986\pi$
$487$	10296.6	0.958075	0.479037	+	0.877794i	$0.340986\pi$
$488$	−2138.30	−0.198353
$489$	10156.6	0.939260
$490$	−4227.75	−0.389776
$491$	580.199	0.0533279	0.0266640	−	0.999644i	$-0.491512\pi$
$491$	580.199	0.0533279	0.0266640	+	0.999644i	$0.491512\pi$
$492$	−23537.2	−2.15679
$493$	−6558.80	−0.599175
$494$	−962.059	−0.0876217
$495$	−3023.34	−0.274524
$496$	−34261.8	−3.10161
$497$	5767.55	0.520543
$498$	−5869.63	−0.528161
$499$	−7010.14	−0.628892	−0.314446	−	0.949275i	$-0.601819\pi$
$499$	−7010.14	−0.628892	−0.314446	+	0.949275i	$0.601819\pi$
$500$	−2197.17	−0.196520
$501$	1985.54	0.177061
$502$	35918.5	3.19347
$503$	5698.39	0.505126	0.252563	−	0.967580i	$-0.418726\pi$
$503$	5698.39	0.505126	0.252563	+	0.967580i	$0.418726\pi$
$504$	13397.0	1.18402
$505$	19596.5	1.72680
$506$	9475.76	0.832508
$507$	7360.27	0.644736
$508$	−5306.30	−0.463443
$509$	−9809.56	−0.854226	−0.427113	−	0.904198i	$-0.640469\pi$
$509$	−9809.56	−0.854226	−0.427113	+	0.904198i	$0.640469\pi$
$510$	−30210.2	−2.62300
$511$	7529.81	0.651858
$512$	26009.8	2.24508
$513$	−20817.6	−1.79165
$514$	8397.97	0.720659
$515$	−8414.07	−0.719939
$516$	0	0
$517$	−3552.42	−0.302196
$518$	10096.7	0.856419
$519$	8739.17	0.739128
$520$	−1043.01	−0.0879595
$521$	19025.5	1.59985	0.799927	−	0.600098i	$-0.204872\pi$
$521$	19025.5	1.59985	0.799927	+	0.600098i	$0.204872\pi$
$522$	−4752.12	−0.398457
$523$	19956.4	1.66851	0.834257	−	0.551376i	$-0.185897\pi$
$523$	19956.4	1.66851	0.834257	+	0.551376i	$0.185897\pi$
$524$	−2567.64	−0.214061
$525$	−7590.84	−0.631031
$526$	1548.20	0.128336
$527$	−34217.7	−2.82836
$528$	4433.10	0.365390
$529$	12192.6	1.00210
$530$	−36636.4	−3.00261
$531$	−4486.22	−0.366639
$532$	−44122.3	−3.59576
$533$	−514.154	−0.0417832
$534$	−25135.7	−2.03694
$535$	19564.9	1.58105
$536$	−5224.89	−0.421046
$537$	520.351	0.0418153
$538$	−33926.6	−2.71873
$539$	619.589	0.0495131
$540$	−40979.6	−3.26571
$541$	670.678	0.0532989	0.0266495	−	0.999645i	$-0.491516\pi$
$541$	670.678	0.0532989	0.0266495	+	0.999645i	$0.491516\pi$
$542$	3409.72	0.270222
$543$	13928.9	1.10082
$544$	−18062.9	−1.42360
$545$	−12075.9	−0.949131
$546$	−379.022	−0.0297081
$547$	16722.9	1.30717	0.653584	−	0.756854i	$-0.273265\pi$
$547$	16722.9	1.30717	0.653584	+	0.756854i	$0.273265\pi$
$548$	9112.21	0.710318
$549$	−676.379	−0.0525814
$550$	8055.75	0.624542
$551$	8619.59	0.666437
$552$	26070.3	2.01019
$553$	3766.42	0.289628
$554$	−30237.6	−2.31891
$555$	−6268.93	−0.479462
$556$	−4714.65	−0.359615
$557$	14248.0	1.08385	0.541926	−	0.840426i	$-0.317695\pi$
$557$	14248.0	1.08385	0.541926	+	0.840426i	$0.317695\pi$
$558$	−24792.1	−1.88089
$559$	0	0
$560$	−30304.5	−2.28678
$561$	4427.40	0.333199
$562$	−43205.2	−3.24289
$563$	−7127.30	−0.533534	−0.266767	−	0.963761i	$-0.585955\pi$
$563$	−7127.30	−0.533534	−0.266767	+	0.963761i	$0.585955\pi$
$564$	−17746.3	−1.32492
$565$	−13764.9	−1.02495
$566$	32428.1	2.40822
$567$	−941.104	−0.0697048
$568$	−16839.9	−1.24399
$569$	1332.44	0.0981703	0.0490852	−	0.998795i	$-0.484369\pi$
$569$	1332.44	0.0981703	0.0490852	+	0.998795i	$0.484369\pi$
$570$	39702.4	2.91746
$571$	−15792.8	−1.15745	−0.578727	−	0.815521i	$-0.696450\pi$
$571$	−15792.8	−1.15745	−0.578727	+	0.815521i	$0.696450\pi$
$572$	277.546	0.0202880
$573$	11097.1	0.809050
$574$	−34173.9	−2.48500
$575$	20709.1	1.50196
$576$	860.940	0.0622786
$577$	−20938.5	−1.51071	−0.755357	−	0.655313i	$-0.772537\pi$
$577$	−20938.5	−1.51071	−0.755357	+	0.655313i	$0.772537\pi$
$578$	−37063.8	−2.66721
$579$	6045.89	0.433953
$580$	16967.8	1.21474
$581$	−5880.36	−0.419894
$582$	−11842.0	−0.843415
$583$	5369.16	0.381420
$584$	−21985.3	−1.55780
$585$	−329.920	−0.0233171
$586$	3648.70	0.257212
$587$	8853.01	0.622492	0.311246	−	0.950329i	$-0.399254\pi$
$587$	8853.01	0.622492	0.311246	+	0.950329i	$0.399254\pi$
$588$	3095.19	0.217081
$589$	44969.0	3.14587
$590$	23214.8	1.61989
$591$	11840.5	0.824116
$592$	−12886.8	−0.894671
$593$	−483.779	−0.0335016	−0.0167508	−	0.999860i	$-0.505332\pi$
$593$	−483.779	−0.0335016	−0.0167508	+	0.999860i	$0.505332\pi$
$594$	8703.79	0.601213
$595$	−30265.5	−2.08532
$596$	−13229.9	−0.909257
$597$	4478.21	0.307003
$598$	1034.04	0.0707105
$599$	18897.4	1.28903	0.644514	−	0.764592i	$-0.277060\pi$
$599$	18897.4	1.28903	0.644514	+	0.764592i	$0.277060\pi$
$600$	22163.5	1.50803
$601$	20295.1	1.37746	0.688732	−	0.725016i	$-0.258168\pi$
$601$	20295.1	1.37746	0.688732	+	0.725016i	$0.258168\pi$
$602$	0	0
$603$	−1652.71	−0.111615
$604$	−27739.8	−1.86873
$605$	19073.2	1.28171
$606$	−20792.3	−1.39378
$607$	4083.04	0.273024	0.136512	−	0.990638i	$-0.456411\pi$
$607$	4083.04	0.273024	0.136512	+	0.990638i	$0.456411\pi$
$608$	23738.3	1.58342
$609$	3395.86	0.225956
$610$	3500.05	0.232316
$611$	−387.656	−0.0256675
$612$	−31007.3	−2.04803
$613$	14285.3	0.941237	0.470618	−	0.882337i	$-0.344031\pi$
$613$	14285.3	0.941237	0.470618	+	0.882337i	$0.344031\pi$
$614$	−8448.12	−0.555274
$615$	21218.2	1.39122
$616$	10159.8	0.664527
$617$	−7909.90	−0.516111	−0.258056	−	0.966130i	$-0.583082\pi$
$617$	−7909.90	−0.516111	−0.258056	+	0.966130i	$0.583082\pi$
$618$	8927.51	0.581096
$619$	−12136.4	−0.788053	−0.394027	−	0.919099i	$-0.628918\pi$
$619$	−12136.4	−0.788053	−0.394027	+	0.919099i	$0.628918\pi$
$620$	88522.0	5.73408
$621$	22375.0	1.44586
$622$	−29485.0	−1.90071
$623$	−25181.7	−1.61939
$624$	483.759	0.0310350
$625$	−14605.1	−0.934728
$626$	−13477.2	−0.860475
$627$	−5818.50	−0.370603
$628$	34642.5	2.20125
$629$	−12870.2	−0.815850
$630$	−21928.6	−1.38676
$631$	−26680.6	−1.68326	−0.841630	−	0.540055i	$-0.818404\pi$
$631$	−26680.6	−1.68326	−0.841630	+	0.540055i	$0.818404\pi$
$632$	−10997.1	−0.692151
$633$	−8345.04	−0.523990
$634$	−36502.0	−2.28656
$635$	4783.48	0.298940
$636$	26822.0	1.67226
$637$	67.6122	0.00420548
$638$	−3603.84	−0.223632
$639$	−5326.72	−0.329768
$640$	−25448.6	−1.57179
$641$	−233.934	−0.0144147	−0.00720736	−	0.999974i	$-0.502294\pi$
$641$	−233.934	−0.0144147	−0.00720736	+	0.999974i	$0.502294\pi$
$642$	−20758.7	−1.27614
$643$	−17466.1	−1.07122	−0.535611	−	0.844465i	$-0.679919\pi$
$643$	−17466.1	−1.07122	−0.535611	+	0.844465i	$0.679919\pi$
$644$	47423.3	2.90177
$645$	0	0
$646$	81509.7	4.96433
$647$	−20184.1	−1.22646	−0.613228	−	0.789906i	$-0.710129\pi$
$647$	−20184.1	−1.22646	−0.613228	+	0.789906i	$0.710129\pi$
$648$	2747.80	0.166580
$649$	−3402.19	−0.205774
$650$	879.078	0.0530466
$651$	17716.4	1.06661
$652$	−53944.0	−3.24020
$653$	26195.1	1.56982	0.784912	−	0.619608i	$-0.212708\pi$
$653$	26195.1	1.56982	0.784912	+	0.619608i	$0.212708\pi$
$654$	12812.8	0.766088
$655$	2314.66	0.138078
$656$	43617.4	2.59600
$657$	−6954.29	−0.412957
$658$	−25766.1	−1.52654
$659$	−25883.0	−1.52998	−0.764991	−	0.644041i	$-0.777257\pi$
$659$	−25883.0	−1.52998	−0.764991	+	0.644041i	$0.777257\pi$
$660$	−11453.8	−0.675512
$661$	9885.19	0.581678	0.290839	−	0.956772i	$-0.406066\pi$
$661$	9885.19	0.581678	0.290839	+	0.956772i	$0.406066\pi$
$662$	264.591	0.0155342
$663$	483.136	0.0283008
$664$	17169.3	1.00346
$665$	39775.0	2.31941
$666$	−9325.02	−0.542548
$667$	−9264.47	−0.537813
$668$	−10545.6	−0.610812
$669$	−5263.71	−0.304196
$670$	8552.27	0.493139
$671$	−512.942	−0.0295110
$672$	9352.17	0.536857
$673$	−29734.1	−1.70307	−0.851533	−	0.524301i	$-0.824327\pi$
$673$	−29734.1	−1.70307	−0.851533	+	0.524301i	$0.824327\pi$
$674$	−36167.3	−2.06693
$675$	19022.0	1.08468
$676$	−39091.9	−2.22417
$677$	−7116.16	−0.403983	−0.201991	−	0.979387i	$-0.564741\pi$
$677$	−7116.16	−0.403983	−0.201991	+	0.979387i	$0.564741\pi$
$678$	14604.9	0.827282
$679$	−11863.7	−0.670524
$680$	88368.1	4.98347
$681$	−4512.41	−0.253915
$682$	−18801.5	−1.05564
$683$	20899.7	1.17087	0.585436	−	0.810719i	$-0.300923\pi$
$683$	20899.7	1.17087	0.585436	+	0.810719i	$0.300923\pi$
$684$	40749.9	2.27794
$685$	−8214.40	−0.458184
$686$	34226.1	1.90490
$687$	268.859	0.0149310
$688$	0	0
$689$	585.906	0.0323966
$690$	−42672.7	−2.35438
$691$	11114.8	0.611904	0.305952	−	0.952047i	$-0.401025\pi$
$691$	11114.8	0.611904	0.305952	+	0.952047i	$0.401025\pi$
$692$	−46415.6	−2.54979
$693$	3213.70	0.176159
$694$	−40471.0	−2.21363
$695$	4250.13	0.231966
$696$	−9915.09	−0.539987
$697$	43561.3	2.36729
$698$	34475.7	1.86952
$699$	−4466.42	−0.241682
$700$	40316.5	2.17689
$701$	−33212.3	−1.78946	−0.894730	−	0.446608i	$-0.852632\pi$
$701$	−33212.3	−1.78946	−0.894730	+	0.446608i	$0.852632\pi$
$702$	949.795	0.0510651
$703$	16914.1	0.907436
$704$	652.906	0.0349536
$705$	15997.8	0.854628
$706$	−15090.5	−0.804444
$707$	−20830.3	−1.10807
$708$	−16995.8	−0.902179
$709$	6375.28	0.337699	0.168849	−	0.985642i	$-0.445995\pi$
$709$	6375.28	0.337699	0.168849	+	0.985642i	$0.445995\pi$
$710$	27564.1	1.45699
$711$	−3478.55	−0.183482
$712$	73524.5	3.87001
$713$	−48333.3	−2.53871
$714$	32112.3	1.68316
$715$	−250.200	−0.0130866
$716$	−2763.69	−0.144251
$717$	605.610	0.0315438
$718$	−17785.8	−0.924455
$719$	31330.1	1.62506	0.812528	−	0.582922i	$-0.198091\pi$
$719$	31330.1	1.62506	0.812528	+	0.582922i	$0.198091\pi$
$720$	27988.3	1.44870
$721$	8943.83	0.461978
$722$	−72276.1	−3.72554
$723$	−8129.12	−0.418154
$724$	−73979.2	−3.79754
$725$	−7876.12	−0.403464
$726$	−20237.1	−1.03453
$727$	−35190.2	−1.79523	−0.897616	−	0.440778i	$-0.854703\pi$
$727$	−35190.2	−1.79523	−0.897616	+	0.440778i	$0.854703\pi$
$728$	1108.68	0.0564428
$729$	13846.7	0.703486
$730$	35986.2	1.82453
$731$	0	0
$732$	−2562.43	−0.129385
$733$	−2133.15	−0.107489	−0.0537446	−	0.998555i	$-0.517116\pi$
$733$	−2133.15	−0.107489	−0.0537446	+	0.998555i	$0.517116\pi$
$734$	15364.6	0.772638
$735$	−2790.23	−0.140026
$736$	−25514.3	−1.27781
$737$	−1253.36	−0.0626432
$738$	31561.9	1.57427
$739$	−11405.1	−0.567718	−0.283859	−	0.958866i	$-0.591615\pi$
$739$	−11405.1	−0.567718	−0.283859	+	0.958866i	$0.591615\pi$
$740$	33295.6	1.65402
$741$	−634.939	−0.0314778
$742$	38943.0	1.92674
$743$	−2654.10	−0.131049	−0.0655246	−	0.997851i	$-0.520872\pi$
$743$	−2654.10	−0.131049	−0.0655246	+	0.997851i	$0.520872\pi$
$744$	−51727.7	−2.54896
$745$	11926.4	0.586508
$746$	−30844.2	−1.51379
$747$	5430.91	0.266006
$748$	−23514.8	−1.14945
$749$	−20796.7	−1.01455
$750$	−2101.55	−0.102317
$751$	31031.5	1.50780	0.753899	−	0.656991i	$-0.228171\pi$
$751$	31031.5	1.50780	0.753899	+	0.656991i	$0.228171\pi$
$752$	32886.2	1.59473
$753$	23705.5	1.14724
$754$	−393.266	−0.0189946
$755$	25006.6	1.20541
$756$	43559.8	2.09557
$757$	−1207.14	−0.0579580	−0.0289790	−	0.999580i	$-0.509226\pi$
$757$	−1207.14	−0.0579580	−0.0289790	+	0.999580i	$0.509226\pi$
$758$	10484.4	0.502389
$759$	6253.81	0.299076
$760$	−116134.	−5.54290
$761$	36031.7	1.71636	0.858178	−	0.513352i	$-0.171596\pi$
$761$	36031.7	1.71636	0.858178	+	0.513352i	$0.171596\pi$
$762$	−5075.38	−0.241288
$763$	12836.3	0.609048
$764$	−58938.8	−2.79101
$765$	27952.2	1.32107
$766$	21113.1	0.995886
$767$	−371.261	−0.0174778
$768$	25536.2	1.19981
$769$	7672.75	0.359800	0.179900	−	0.983685i	$-0.442423\pi$
$769$	7672.75	0.359800	0.179900	+	0.983685i	$0.442423\pi$
$770$	−16629.9	−0.778310
$771$	5542.49	0.258895
$772$	−32111.0	−1.49702
$773$	−3228.00	−0.150198	−0.0750990	−	0.997176i	$-0.523927\pi$
$773$	−3228.00	−0.150198	−0.0750990	+	0.997176i	$0.523927\pi$
$774$	0	0
$775$	−41090.2	−1.90452
$776$	34639.1	1.60241
$777$	6663.64	0.307666
$778$	−25381.5	−1.16963
$779$	−57248.3	−2.63304
$780$	−1249.89	−0.0573758
$781$	−4039.59	−0.185081
$782$	−87607.8	−4.00620
$783$	−8509.71	−0.388394
$784$	−5735.77	−0.261287
$785$	−31229.2	−1.41990
$786$	−2455.90	−0.111449
$787$	7667.49	0.347289	0.173644	−	0.984808i	$-0.444446\pi$
$787$	7667.49	0.347289	0.173644	+	0.984808i	$0.444446\pi$
$788$	−62887.3	−2.84298
$789$	1021.78	0.0461043
$790$	18000.4	0.810663
$791$	14631.6	0.657699
$792$	−9383.24	−0.420983
$793$	−55.9744	−0.00250657
$794$	−45344.6	−2.02672
$795$	−24179.2	−1.07868
$796$	−23784.7	−1.05908
$797$	11390.2	0.506224	0.253112	−	0.967437i	$-0.418546\pi$
$797$	11390.2	0.506224	0.253112	+	0.967437i	$0.418546\pi$
$798$	−42202.1	−1.87210
$799$	32843.8	1.45423
$800$	−21690.8	−0.958607
$801$	23257.0	1.02590
$802$	37662.3	1.65823
$803$	−5273.88	−0.231770
$804$	−6261.23	−0.274647
$805$	−42750.7	−1.87176
$806$	−2051.70	−0.0896624
$807$	−22390.8	−0.976697
$808$	60819.6	2.64805
$809$	−25006.2	−1.08674	−0.543369	−	0.839494i	$-0.682852\pi$
$809$	−25006.2	−1.08674	−0.543369	+	0.839494i	$0.682852\pi$
$810$	−4497.69	−0.195102
$811$	−13444.2	−0.582110	−0.291055	−	0.956706i	$-0.594006\pi$
$811$	−13444.2	−0.582110	−0.291055	+	0.956706i	$0.594006\pi$
$812$	−18036.1	−0.779486
$813$	2250.35	0.0970764
$814$	−7071.76	−0.304502
$815$	48629.0	2.09006
$816$	−40986.1	−1.75833
$817$	0	0
$818$	−8438.86	−0.360706
$819$	350.692	0.0149624
$820$	−112694.	−4.79933
$821$	−37756.0	−1.60499	−0.802493	−	0.596661i	$-0.796494\pi$
$821$	−37756.0	−1.60499	−0.802493	+	0.596661i	$0.796494\pi$
$822$	8715.65	0.369822
$823$	14203.6	0.601589	0.300794	−	0.953689i	$-0.402748\pi$
$823$	14203.6	0.601589	0.300794	+	0.953689i	$0.402748\pi$
$824$	−26113.9	−1.10403
$825$	5316.63	0.224365
$826$	−24676.4	−1.03947
$827$	−21947.1	−0.922822	−0.461411	−	0.887186i	$-0.652657\pi$
$827$	−21947.1	−0.922822	−0.461411	+	0.887186i	$0.652657\pi$
$828$	−43798.6	−1.83829
$829$	39551.8	1.65705	0.828523	−	0.559956i	$-0.189182\pi$
$829$	39551.8	1.65705	0.828523	+	0.559956i	$0.189182\pi$
$830$	−28103.2	−1.17527
$831$	−19956.2	−0.833061
$832$	71.2478	0.00296884
$833$	−5728.39	−0.238268
$834$	−4509.47	−0.187231
$835$	9506.58	0.393998
$836$	30903.3	1.27848
$837$	−44395.7	−1.83338
$838$	−29984.6	−1.23604
$839$	−14681.2	−0.604115	−0.302058	−	0.953290i	$-0.597674\pi$
$839$	−14681.2	−0.604115	−0.302058	+	0.953290i	$0.597674\pi$
$840$	−45753.1	−1.87932
$841$	−20865.5	−0.855530
$842$	−67799.5	−2.77497
$843$	−28514.5	−1.16500
$844$	44322.3	1.80762
$845$	35240.3	1.43468
$846$	23796.7	0.967077
$847$	−20274.1	−0.822464
$848$	−49704.4	−2.01280
$849$	21401.9	0.865148
$850$	−74479.1	−3.00543
$851$	−18179.5	−0.732299
$852$	−20180.0	−0.811451
$853$	−29871.6	−1.19904	−0.599521	−	0.800359i	$-0.704642\pi$
$853$	−29871.6	−1.19904	−0.599521	+	0.800359i	$0.704642\pi$
$854$	−3720.41	−0.149075
$855$	−36734.9	−1.46937
$856$	60721.4	2.42455
$857$	−30385.7	−1.21115	−0.605574	−	0.795789i	$-0.707057\pi$
$857$	−30385.7	−1.21115	−0.605574	+	0.795789i	$0.707057\pi$
$858$	265.467	0.0105628
$859$	−5374.75	−0.213486	−0.106743	−	0.994287i	$-0.534042\pi$
$859$	−5374.75	−0.213486	−0.106743	+	0.994287i	$0.534042\pi$
$860$	0	0
$861$	−22554.1	−0.892731
$862$	−37498.7	−1.48168
$863$	15300.2	0.603506	0.301753	−	0.953386i	$-0.402428\pi$
$863$	15300.2	0.603506	0.301753	+	0.953386i	$0.402428\pi$
$864$	−23435.7	−0.922800
$865$	41842.4	1.64472
$866$	−15383.4	−0.603635
$867$	−24461.3	−0.958189
$868$	−94095.5	−3.67950
$869$	−2638.00	−0.102978
$870$	16229.4	0.632445
$871$	−136.772	−0.00532071
$872$	−37478.9	−1.45550
$873$	10956.9	0.424783
$874$	115134.	4.45593
$875$	−2105.39	−0.0813430
$876$	−26346.0	−1.01615
$877$	36106.3	1.39022	0.695111	−	0.718902i	$-0.255355\pi$
$877$	36106.3	1.39022	0.695111	+	0.718902i	$0.255355\pi$
$878$	−70959.3	−2.72752
$879$	2408.07	0.0924028
$880$	21225.3	0.813073
$881$	46814.9	1.79028	0.895139	−	0.445788i	$-0.147076\pi$
$881$	46814.9	1.79028	0.895139	+	0.445788i	$0.147076\pi$
$882$	−4150.45	−0.158450
$883$	10985.0	0.418656	0.209328	−	0.977845i	$-0.432872\pi$
$883$	10985.0	0.418656	0.209328	+	0.977845i	$0.432872\pi$
$884$	−2566.04	−0.0976303
$885$	15321.3	0.581942
$886$	2395.88	0.0908476
$887$	−19578.3	−0.741123	−0.370562	−	0.928808i	$-0.620835\pi$
$887$	−19578.3	−0.741123	−0.370562	+	0.928808i	$0.620835\pi$
$888$	−19456.2	−0.735258
$889$	−5084.66	−0.191827
$890$	−120347.	−4.53264
$891$	659.150	0.0247838
$892$	27956.7	1.04939
$893$	−43163.4	−1.61748
$894$	−12654.1	−0.473397
$895$	2491.39	0.0930481
$896$	27050.9	1.00860
$897$	682.442	0.0254025
$898$	55589.7	2.06576
$899$	18382.2	0.681959
$900$	−37235.1	−1.37908
$901$	−49640.4	−1.83547
$902$	23935.4	0.883551
$903$	0	0
$904$	−42720.8	−1.57176
$905$	66690.2	2.44957
$906$	−26532.6	−0.972942
$907$	11640.9	0.426162	0.213081	−	0.977034i	$-0.431650\pi$
$907$	11640.9	0.426162	0.213081	+	0.977034i	$0.431650\pi$
$908$	23966.4	0.875938
$909$	19238.2	0.701971
$910$	−1814.72	−0.0661070
$911$	42622.7	1.55011	0.775057	−	0.631891i	$-0.217721\pi$
$911$	42622.7	1.55011	0.775057	+	0.631891i	$0.217721\pi$
$912$	53864.1	1.95572
$913$	4118.61	0.149295
$914$	39145.3	1.41664
$915$	2309.96	0.0834589
$916$	−1427.96	−0.0515080
$917$	−2460.39	−0.0886035
$918$	−80470.6	−2.89316
$919$	12388.7	0.444684	0.222342	−	0.974969i	$-0.428630\pi$
$919$	12388.7	0.444684	0.222342	+	0.974969i	$0.428630\pi$
$920$	124822.	4.47311
$921$	−5575.58	−0.199481
$922$	67000.4	2.39321
$923$	−440.818	−0.0157201
$924$	12174.9	0.433470
$925$	−15455.2	−0.549366
$926$	66726.2	2.36799
$927$	−8260.24	−0.292666
$928$	9703.64	0.343252
$929$	18032.2	0.636832	0.318416	−	0.947951i	$-0.396849\pi$
$929$	18032.2	0.636832	0.318416	+	0.947951i	$0.396849\pi$
$930$	84669.6	2.98540
$931$	7528.26	0.265015
$932$	23722.1	0.833738
$933$	−19459.5	−0.682825
$934$	−90515.0	−3.17103
$935$	21198.0	0.741441
$936$	−1023.94	−0.0357569
$937$	−4996.78	−0.174213	−0.0871065	−	0.996199i	$-0.527762\pi$
$937$	−4996.78	−0.174213	−0.0871065	+	0.996199i	$0.527762\pi$
$938$	−9090.73	−0.316442
$939$	−8894.68	−0.309123
$940$	−84967.8	−2.94824
$941$	9105.72	0.315449	0.157725	−	0.987483i	$-0.449584\pi$
$941$	9105.72	0.315449	0.157725	+	0.987483i	$0.449584\pi$
$942$	33134.9	1.14606
$943$	61531.4	2.12485
$944$	31495.4	1.08590
$945$	−39267.9	−1.35173
$946$	0	0
$947$	22281.3	0.764566	0.382283	−	0.924045i	$-0.375138\pi$
$947$	22281.3	0.764566	0.382283	+	0.924045i	$0.375138\pi$
$948$	−13178.3	−0.451489
$949$	−575.509	−0.0196858
$950$	97880.7	3.34281
$951$	−24090.6	−0.821442
$952$	−93931.8	−3.19784
$953$	723.226	0.0245830	0.0122915	−	0.999924i	$-0.496087\pi$
$953$	723.226	0.0245830	0.0122915	+	0.999924i	$0.496087\pi$
$954$	−35966.5	−1.22061
$955$	53131.6	1.80031
$956$	−3216.52	−0.108818
$957$	−2378.46	−0.0803392
$958$	12391.8	0.417914
$959$	8731.59	0.294012
$960$	−2940.27	−0.0988507
$961$	66110.2	2.21913
$962$	−771.700	−0.0258634
$963$	19207.1	0.642722
$964$	43175.4	1.44252
$965$	28947.2	0.965640
$966$	45359.4	1.51078
$967$	31182.0	1.03697	0.518483	−	0.855088i	$-0.326497\pi$
$967$	31182.0	1.03697	0.518483	+	0.855088i	$0.326497\pi$
$968$	59195.6	1.96552
$969$	53794.7	1.78342
$970$	−56698.5	−1.87678
$971$	46308.4	1.53049	0.765246	−	0.643738i	$-0.222617\pi$
$971$	46308.4	1.53049	0.765246	+	0.643738i	$0.222617\pi$
$972$	−65633.7	−2.16584
$973$	−4517.72	−0.148850
$974$	−52307.3	−1.72078
$975$	580.173	0.0190568
$976$	4748.50	0.155733
$977$	23348.6	0.764573	0.382286	−	0.924044i	$-0.375137\pi$
$977$	23348.6	0.764573	0.382286	+	0.924044i	$0.375137\pi$
$978$	−51596.4	−1.68698
$979$	17637.2	0.575780
$980$	14819.5	0.483052
$981$	−11855.2	−0.385837
$982$	−2947.45	−0.0957810
$983$	−13317.5	−0.432109	−0.216055	−	0.976381i	$-0.569319\pi$
$983$	−13317.5	−0.432109	−0.216055	+	0.976381i	$0.569319\pi$
$984$	65852.6	2.13344
$985$	56691.1	1.83384
$986$	33319.2	1.07616
$987$	−17005.1	−0.548406
$988$	3372.30	0.108590
$989$	0	0
$990$	15358.8	0.493065
$991$	22123.5	0.709159	0.354580	−	0.935026i	$-0.384624\pi$
$991$	22123.5	0.709159	0.354580	+	0.935026i	$0.384624\pi$
$992$	50624.6	1.62029
$993$	174.625	0.00558062
$994$	−29299.6	−0.934935
$995$	21441.3	0.683149
$996$	20574.7	0.654554
$997$	−9846.81	−0.312790	−0.156395	−	0.987695i	$-0.549987\pi$
$997$	−9846.81	−0.312790	−0.156395	+	0.987695i	$0.549987\pi$
$998$	35612.0	1.12954
$999$	−16698.5	−0.528845

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.8	✓	110
43.42	odd	2	inner	1849.4.a.m.1.103	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.8	✓	110	1.1	even	1	trivial
1849.4.a.m.1.103	yes	110	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-5.08007 q^{2} -3.35274 q^{3} +17.8071 q^{4} -16.0526 q^{5} +17.0322 q^{6} +17.0633 q^{7} -49.8208 q^{8} -15.7591 q^{9} +O(q^{10})\)	\(q-5.08007 q^{2} -3.35274 q^{3} +17.8071 q^{4} -16.0526 q^{5} +17.0322 q^{6} +17.0633 q^{7} -49.8208 q^{8} -15.7591 q^{9} +81.5484 q^{10} -11.9512 q^{11} -59.7027 q^{12} -1.30416 q^{13} -86.6828 q^{14} +53.8203 q^{15} +110.636 q^{16} +110.494 q^{17} +80.0575 q^{18} -145.212 q^{19} -285.851 q^{20} -57.2089 q^{21} +60.7127 q^{22} +156.075 q^{23} +167.036 q^{24} +132.686 q^{25} +6.62523 q^{26} +143.360 q^{27} +303.848 q^{28} -59.3589 q^{29} -273.411 q^{30} -309.679 q^{31} -163.474 q^{32} +40.0691 q^{33} -561.317 q^{34} -273.911 q^{35} -280.625 q^{36} -116.479 q^{37} +737.685 q^{38} +4.37251 q^{39} +799.755 q^{40} +394.241 q^{41} +290.625 q^{42} -212.816 q^{44} +252.975 q^{45} -792.874 q^{46} +297.245 q^{47} -370.935 q^{48} -51.8434 q^{49} -674.056 q^{50} -370.458 q^{51} -23.2233 q^{52} -449.259 q^{53} -728.280 q^{54} +191.847 q^{55} -850.108 q^{56} +486.857 q^{57} +301.547 q^{58} +284.675 q^{59} +958.384 q^{60} +42.9199 q^{61} +1573.19 q^{62} -268.903 q^{63} -54.6312 q^{64} +20.9352 q^{65} -203.554 q^{66} +104.873 q^{67} +1967.58 q^{68} -523.281 q^{69} +1391.49 q^{70} +338.009 q^{71} +785.133 q^{72} +441.287 q^{73} +591.722 q^{74} -444.863 q^{75} -2585.80 q^{76} -203.926 q^{77} -22.2127 q^{78} +220.732 q^{79} -1776.00 q^{80} -55.1537 q^{81} -2002.77 q^{82} -344.620 q^{83} -1018.72 q^{84} -1773.72 q^{85} +199.015 q^{87} +595.416 q^{88} -1475.78 q^{89} -1285.13 q^{90} -22.2533 q^{91} +2779.25 q^{92} +1038.27 q^{93} -1510.03 q^{94} +2331.02 q^{95} +548.087 q^{96} -695.274 q^{97} +263.368 q^{98} +188.340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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