LMFDB - Embedded newform 435.4.a.j.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] 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("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 $ x^7 - x^6 - 35x^5 + 18x^4 + 329x^3 - 167x^2 - 767*x + 638
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.07921$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.07921 q^{2} +3.00000 q^{3} +1.48151 q^{4} -5.00000 q^{5} -9.23762 q^{6} +23.1532 q^{7} +20.0718 q^{8} +9.00000 q^{9} +15.3960 q^{10} -43.1165 q^{11} +4.44453 q^{12} -74.6173 q^{13} -71.2934 q^{14} -15.0000 q^{15} -73.6572 q^{16} +82.7951 q^{17} -27.7129 q^{18} -88.2501 q^{19} -7.40754 q^{20} +69.4596 q^{21} +132.765 q^{22} +175.920 q^{23} +60.2153 q^{24} +25.0000 q^{25} +229.762 q^{26} +27.0000 q^{27} +34.3016 q^{28} -29.0000 q^{29} +46.1881 q^{30} +14.1415 q^{31} +66.2315 q^{32} -129.350 q^{33} -254.943 q^{34} -115.766 q^{35} +13.3336 q^{36} -176.503 q^{37} +271.740 q^{38} -223.852 q^{39} -100.359 q^{40} -138.356 q^{41} -213.880 q^{42} +64.7784 q^{43} -63.8775 q^{44} -45.0000 q^{45} -541.695 q^{46} -101.341 q^{47} -220.972 q^{48} +193.070 q^{49} -76.9801 q^{50} +248.385 q^{51} -110.546 q^{52} +265.178 q^{53} -83.1386 q^{54} +215.583 q^{55} +464.726 q^{56} -264.750 q^{57} +89.2970 q^{58} -645.434 q^{59} -22.2226 q^{60} -386.696 q^{61} -43.5447 q^{62} +208.379 q^{63} +385.317 q^{64} +373.087 q^{65} +398.294 q^{66} -737.103 q^{67} +122.662 q^{68} +527.761 q^{69} +356.467 q^{70} -1014.53 q^{71} +180.646 q^{72} -1158.89 q^{73} +543.489 q^{74} +75.0000 q^{75} -130.743 q^{76} -998.285 q^{77} +689.286 q^{78} +714.039 q^{79} +368.286 q^{80} +81.0000 q^{81} +426.027 q^{82} +747.521 q^{83} +102.905 q^{84} -413.976 q^{85} -199.466 q^{86} -87.0000 q^{87} -865.426 q^{88} -518.363 q^{89} +138.564 q^{90} -1727.63 q^{91} +260.628 q^{92} +42.4246 q^{93} +312.051 q^{94} +441.250 q^{95} +198.694 q^{96} -946.328 q^{97} -594.502 q^{98} -388.049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) $ 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * 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 $

$2$	−3.07921	−1.08866	−0.544332	−	0.838870i	$-0.683217\pi$
$2$	−3.07921	−1.08866	−0.544332	+	0.838870i	$0.683217\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	1.48151	0.185189
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−9.23762	−0.628540
$7$	23.1532	1.25015	0.625077	−	0.780563i	$-0.285067\pi$
$7$	23.1532	1.25015	0.625077	+	0.780563i	$0.285067\pi$
$8$	20.0718	0.887056
$9$	9.00000	0.333333
$10$	15.3960	0.486865
$11$	−43.1165	−1.18183	−0.590915	−	0.806734i	$-0.701233\pi$
$11$	−43.1165	−1.18183	−0.590915	+	0.806734i	$0.701233\pi$
$12$	4.44453	0.106919
$13$	−74.6173	−1.59193	−0.795966	−	0.605341i	$-0.793037\pi$
$13$	−74.6173	−1.59193	−0.795966	+	0.605341i	$0.793037\pi$
$14$	−71.2934	−1.36100
$15$	−15.0000	−0.258199
$16$	−73.6572	−1.15089
$17$	82.7951	1.18122	0.590611	−	0.806956i	$-0.298887\pi$
$17$	82.7951	1.18122	0.590611	+	0.806956i	$0.298887\pi$
$18$	−27.7129	−0.362888
$19$	−88.2501	−1.06558	−0.532788	−	0.846248i	$-0.678856\pi$
$19$	−88.2501	−1.06558	−0.532788	+	0.846248i	$0.678856\pi$
$20$	−7.40754	−0.0828188
$21$	69.4596	0.721777
$22$	132.765	1.28662
$23$	175.920	1.59487	0.797434	−	0.603407i	$-0.206190\pi$
$23$	175.920	1.59487	0.797434	+	0.603407i	$0.206190\pi$
$24$	60.2153	0.512142
$25$	25.0000	0.200000
$26$	229.762	1.73308
$27$	27.0000	0.192450
$28$	34.3016	0.231514
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	46.1881	0.281092
$31$	14.1415	0.0819321	0.0409661	−	0.999161i	$-0.486956\pi$
$31$	14.1415	0.0819321	0.0409661	+	0.999161i	$0.486956\pi$
$32$	66.2315	0.365881
$33$	−129.350	−0.682330
$34$	−254.943	−1.28595
$35$	−115.766	−0.559086
$36$	13.3336	0.0617295
$37$	−176.503	−0.784241	−0.392120	−	0.919914i	$-0.628258\pi$
$37$	−176.503	−0.784241	−0.392120	+	0.919914i	$0.628258\pi$
$38$	271.740	1.16005
$39$	−223.852	−0.919103
$40$	−100.359	−0.396703
$41$	−138.356	−0.527015	−0.263508	−	0.964657i	$-0.584879\pi$
$41$	−138.356	−0.527015	−0.263508	+	0.964657i	$0.584879\pi$
$42$	−213.880	−0.785772
$43$	64.7784	0.229735	0.114868	−	0.993381i	$-0.463356\pi$
$43$	64.7784	0.229735	0.114868	+	0.993381i	$0.463356\pi$
$44$	−63.8775	−0.218861
$45$	−45.0000	−0.149071
$46$	−541.695	−1.73627
$47$	−101.341	−0.314514	−0.157257	−	0.987558i	$-0.550265\pi$
$47$	−101.341	−0.314514	−0.157257	+	0.987558i	$0.550265\pi$
$48$	−220.972	−0.664469
$49$	193.070	0.562886
$50$	−76.9801	−0.217733
$51$	248.385	0.681979
$52$	−110.546	−0.294808
$53$	265.178	0.687265	0.343633	−	0.939104i	$-0.388343\pi$
$53$	265.178	0.687265	0.343633	+	0.939104i	$0.388343\pi$
$54$	−83.1386	−0.209513
$55$	215.583	0.528530
$56$	464.726	1.10896
$57$	−264.750	−0.615211
$58$	89.2970	0.202160
$59$	−645.434	−1.42421	−0.712105	−	0.702073i	$-0.752258\pi$
$59$	−645.434	−1.42421	−0.712105	+	0.702073i	$0.752258\pi$
$60$	−22.2226	−0.0478155
$61$	−386.696	−0.811662	−0.405831	−	0.913948i	$-0.633018\pi$
$61$	−386.696	−0.811662	−0.405831	+	0.913948i	$0.633018\pi$
$62$	−43.5447	−0.0891966
$63$	208.379	0.416718
$64$	385.317	0.752573
$65$	373.087	0.711934
$66$	398.294	0.742828
$67$	−737.103	−1.34405	−0.672026	−	0.740528i	$-0.734576\pi$
$67$	−737.103	−1.34405	−0.672026	+	0.740528i	$0.734576\pi$
$68$	122.662	0.218749
$69$	527.761	0.920797
$70$	356.467	0.608657
$71$	−1014.53	−1.69580	−0.847902	−	0.530152i	$-0.822135\pi$
$71$	−1014.53	−1.69580	−0.847902	+	0.530152i	$0.822135\pi$
$72$	180.646	0.295685
$73$	−1158.89	−1.85805	−0.929025	−	0.370016i	$-0.879352\pi$
$73$	−1158.89	−1.85805	−0.929025	+	0.370016i	$0.879352\pi$
$74$	543.489	0.853775
$75$	75.0000	0.115470
$76$	−130.743	−0.197333
$77$	−998.285	−1.47747
$78$	689.286	1.00059
$79$	714.039	1.01691	0.508453	−	0.861089i	$-0.330217\pi$
$79$	714.039	1.01691	0.508453	+	0.861089i	$0.330217\pi$
$80$	368.286	0.514695
$81$	81.0000	0.111111
$82$	426.027	0.573742
$83$	747.521	0.988567	0.494284	−	0.869301i	$-0.335430\pi$
$83$	747.521	0.988567	0.494284	+	0.869301i	$0.335430\pi$
$84$	102.905	0.133665
$85$	−413.976	−0.528258
$86$	−199.466	−0.250104
$87$	−87.0000	−0.107211
$88$	−865.426	−1.04835
$89$	−518.363	−0.617375	−0.308688	−	0.951163i	$-0.599890\pi$
$89$	−518.363	−0.617375	−0.308688	+	0.951163i	$0.599890\pi$
$90$	138.564	0.162288
$91$	−1727.63	−1.99016
$92$	260.628	0.295351
$93$	42.4246	0.0473035
$94$	312.051	0.342400
$95$	441.250	0.476540
$96$	198.694	0.211241
$97$	−946.328	−0.990568	−0.495284	−	0.868731i	$-0.664936\pi$
$97$	−946.328	−0.990568	−0.495284	+	0.868731i	$0.664936\pi$
$98$	−594.502	−0.612794
$99$	−388.049	−0.393943
$100$	37.0377	0.0370377
$101$	864.251	0.851448	0.425724	−	0.904853i	$-0.360019\pi$
$101$	864.251	0.851448	0.425724	+	0.904853i	$0.360019\pi$
$102$	−764.830	−0.742445
$103$	−1385.74	−1.32564	−0.662819	−	0.748780i	$-0.730640\pi$
$103$	−1385.74	−1.32564	−0.662819	+	0.748780i	$0.730640\pi$
$104$	−1497.70	−1.41213
$105$	−347.298	−0.322788
$106$	−816.539	−0.748201
$107$	−335.496	−0.303118	−0.151559	−	0.988448i	$-0.548429\pi$
$107$	−335.496	−0.303118	−0.151559	+	0.988448i	$0.548429\pi$
$108$	40.0007	0.0356396
$109$	−769.498	−0.676189	−0.338094	−	0.941112i	$-0.609782\pi$
$109$	−769.498	−0.676189	−0.338094	+	0.941112i	$0.609782\pi$
$110$	−663.824	−0.575392
$111$	−529.509	−0.452782
$112$	−1705.40	−1.43879
$113$	1066.98	0.888261	0.444131	−	0.895962i	$-0.353513\pi$
$113$	1066.98	0.888261	0.444131	+	0.895962i	$0.353513\pi$
$114$	815.221	0.669758
$115$	−879.602	−0.713246
$116$	−42.9637	−0.0343887
$117$	−671.556	−0.530644
$118$	1987.43	1.55049
$119$	1916.97	1.47671
$120$	−301.077	−0.229037
$121$	528.036	0.396722
$122$	1190.72	0.883627
$123$	−415.069	−0.304272
$124$	20.9508	0.0151729
$125$	−125.000	−0.0894427
$126$	−641.641	−0.453666
$127$	−1071.24	−0.748482	−0.374241	−	0.927332i	$-0.622097\pi$
$127$	−1071.24	−0.748482	−0.374241	+	0.927332i	$0.622097\pi$
$128$	−1716.32	−1.18518
$129$	194.335	0.132638
$130$	−1148.81	−0.775057
$131$	−2192.32	−1.46217	−0.731083	−	0.682288i	$-0.760985\pi$
$131$	−2192.32	−1.46217	−0.731083	+	0.682288i	$0.760985\pi$
$132$	−191.633	−0.126360
$133$	−2043.27	−1.33214
$134$	2269.69	1.46322
$135$	−135.000	−0.0860663
$136$	1661.85	1.04781
$137$	592.283	0.369359	0.184679	−	0.982799i	$-0.440875\pi$
$137$	592.283	0.369359	0.184679	+	0.982799i	$0.440875\pi$
$138$	−1625.09	−1.00244
$139$	1980.19	1.20833	0.604164	−	0.796860i	$-0.293507\pi$
$139$	1980.19	1.20833	0.604164	+	0.796860i	$0.293507\pi$
$140$	−171.508	−0.103536
$141$	−304.024	−0.181585
$142$	3123.94	1.84616
$143$	3217.24	1.88139
$144$	−662.915	−0.383631
$145$	145.000	0.0830455
$146$	3568.46	2.02279
$147$	579.210	0.324982
$148$	−261.491	−0.145232
$149$	1366.49	0.751326	0.375663	−	0.926756i	$-0.377415\pi$
$149$	1366.49	0.751326	0.375663	+	0.926756i	$0.377415\pi$
$150$	−230.940	−0.125708
$151$	−2204.75	−1.18821	−0.594105	−	0.804387i	$-0.702494\pi$
$151$	−2204.75	−1.18821	−0.594105	+	0.804387i	$0.702494\pi$
$152$	−1771.34	−0.945226
$153$	745.156	0.393741
$154$	3073.93	1.60847
$155$	−70.7077	−0.0366412
$156$	−331.639	−0.170207
$157$	−1798.31	−0.914144	−0.457072	−	0.889430i	$-0.651102\pi$
$157$	−1798.31	−0.914144	−0.457072	+	0.889430i	$0.651102\pi$
$158$	−2198.67	−1.10707
$159$	795.535	0.396793
$160$	−331.157	−0.163627
$161$	4073.12	1.99383
$162$	−249.416	−0.120963
$163$	358.581	0.172308	0.0861540	−	0.996282i	$-0.472542\pi$
$163$	358.581	0.172308	0.0861540	+	0.996282i	$0.472542\pi$
$164$	−204.976	−0.0975972
$165$	646.748	0.305147
$166$	−2301.77	−1.07622
$167$	−3993.78	−1.85059	−0.925293	−	0.379253i	$-0.876181\pi$
$167$	−3993.78	−1.85059	−0.925293	+	0.379253i	$0.876181\pi$
$168$	1394.18	0.640256
$169$	3370.75	1.53425
$170$	1274.72	0.575096
$171$	−794.251	−0.355192
$172$	95.9698	0.0425443
$173$	902.727	0.396723	0.198362	−	0.980129i	$-0.436438\pi$
$173$	902.727	0.396723	0.198362	+	0.980129i	$0.436438\pi$
$174$	267.891	0.116717
$175$	578.830	0.250031
$176$	3175.84	1.36016
$177$	−1936.30	−0.822268
$178$	1596.15	0.672114
$179$	438.007	0.182895	0.0914474	−	0.995810i	$-0.470851\pi$
$179$	438.007	0.182895	0.0914474	+	0.995810i	$0.470851\pi$
$180$	−66.6679	−0.0276063
$181$	4385.45	1.80093	0.900464	−	0.434930i	$-0.143227\pi$
$181$	4385.45	1.80093	0.900464	+	0.434930i	$0.143227\pi$
$182$	5319.72	2.16662
$183$	−1160.09	−0.468613
$184$	3531.04	1.41474
$185$	882.515	0.350723
$186$	−130.634	−0.0514977
$187$	−3569.84	−1.39600
$188$	−150.138	−0.0582444
$189$	625.136	0.240592
$190$	−1358.70	−0.518792
$191$	1188.68	0.450313	0.225156	−	0.974323i	$-0.427711\pi$
$191$	1188.68	0.450313	0.225156	+	0.974323i	$0.427711\pi$
$192$	1155.95	0.434498
$193$	2256.44	0.841565	0.420782	−	0.907162i	$-0.361756\pi$
$193$	2256.44	0.841565	0.420782	+	0.907162i	$0.361756\pi$
$194$	2913.94	1.07840
$195$	1119.26	0.411035
$196$	286.035	0.104240
$197$	−944.551	−0.341606	−0.170803	−	0.985305i	$-0.554636\pi$
$197$	−944.551	−0.341606	−0.170803	+	0.985305i	$0.554636\pi$
$198$	1194.88	0.428872
$199$	−172.934	−0.0616030	−0.0308015	−	0.999526i	$-0.509806\pi$
$199$	−172.934	−0.0616030	−0.0308015	+	0.999526i	$0.509806\pi$
$200$	501.794	0.177411
$201$	−2211.31	−0.775989
$202$	−2661.21	−0.926940
$203$	−671.442	−0.232148
$204$	367.985	0.126295
$205$	691.781	0.235688
$206$	4266.97	1.44317
$207$	1583.28	0.531622
$208$	5496.10	1.83215
$209$	3805.04	1.25933
$210$	1069.40	0.351408
$211$	−3980.90	−1.29885	−0.649423	−	0.760427i	$-0.724990\pi$
$211$	−3980.90	−1.29885	−0.649423	+	0.760427i	$0.724990\pi$
$212$	392.864	0.127274
$213$	−3043.58	−0.979073
$214$	1033.06	0.329994
$215$	−323.892	−0.102741
$216$	541.938	0.170714
$217$	327.422	0.102428
$218$	2369.44	0.736142
$219$	−3476.67	−1.07275
$220$	319.388	0.0978778
$221$	−6177.95	−1.88043
$222$	1630.47	0.492927
$223$	1939.43	0.582392	0.291196	−	0.956663i	$-0.405947\pi$
$223$	1939.43	0.582392	0.291196	+	0.956663i	$0.405947\pi$
$224$	1533.47	0.457407
$225$	225.000	0.0666667
$226$	−3285.47	−0.967017
$227$	−6457.84	−1.88820	−0.944101	−	0.329656i	$-0.893067\pi$
$227$	−6457.84	−1.88820	−0.944101	+	0.329656i	$0.893067\pi$
$228$	−392.230	−0.113930
$229$	−1271.99	−0.367054	−0.183527	−	0.983015i	$-0.558751\pi$
$229$	−1271.99	−0.367054	−0.183527	+	0.983015i	$0.558751\pi$
$230$	2708.48	0.776485
$231$	−2994.86	−0.853018
$232$	−582.082	−0.164722
$233$	1029.14	0.289361	0.144681	−	0.989478i	$-0.453785\pi$
$233$	1029.14	0.289361	0.144681	+	0.989478i	$0.453785\pi$
$234$	2067.86	0.577693
$235$	506.706	0.140655
$236$	−956.216	−0.263747
$237$	2142.12	0.587112
$238$	−5902.75	−1.60764
$239$	2592.45	0.701639	0.350819	−	0.936443i	$-0.385903\pi$
$239$	2592.45	0.701639	0.350819	+	0.936443i	$0.385903\pi$
$240$	1104.86	0.297159
$241$	−5132.31	−1.37179	−0.685894	−	0.727701i	$-0.740589\pi$
$241$	−5132.31	−1.37179	−0.685894	+	0.727701i	$0.740589\pi$
$242$	−1625.93	−0.431896
$243$	243.000	0.0641500
$244$	−572.894	−0.150311
$245$	−965.350	−0.251730
$246$	1278.08	0.331250
$247$	6584.99	1.69633
$248$	283.846	0.0726784
$249$	2242.56	0.570749
$250$	384.901	0.0973730
$251$	96.4840	0.0242630	0.0121315	−	0.999926i	$-0.496138\pi$
$251$	96.4840	0.0242630	0.0121315	+	0.999926i	$0.496138\pi$
$252$	308.715	0.0771714
$253$	−7585.08	−1.88486
$254$	3298.57	0.814845
$255$	−1241.93	−0.304990
$256$	2202.37	0.537689
$257$	1022.96	0.248290	0.124145	−	0.992264i	$-0.460381\pi$
$257$	1022.96	0.248290	0.124145	+	0.992264i	$0.460381\pi$
$258$	−598.398	−0.144398
$259$	−4086.61	−0.980422
$260$	552.731	0.131842
$261$	−261.000	−0.0618984
$262$	6750.60	1.59181
$263$	2925.05	0.685805	0.342902	−	0.939371i	$-0.388590\pi$
$263$	2925.05	0.685805	0.342902	+	0.939371i	$0.388590\pi$
$264$	−2596.28	−0.605264
$265$	−1325.89	−0.307354
$266$	6291.65	1.45025
$267$	−1555.09	−0.356442
$268$	−1092.02	−0.248903
$269$	3935.68	0.892055	0.446028	−	0.895019i	$-0.352838\pi$
$269$	3935.68	0.892055	0.446028	+	0.895019i	$0.352838\pi$
$270$	415.693	0.0936972
$271$	7099.87	1.59146	0.795731	−	0.605650i	$-0.207087\pi$
$271$	7099.87	1.59146	0.795731	+	0.605650i	$0.207087\pi$
$272$	−6098.46	−1.35946
$273$	−5182.89	−1.14902
$274$	−1823.76	−0.402107
$275$	−1077.91	−0.236366
$276$	781.883	0.170521
$277$	5100.47	1.10634	0.553172	−	0.833067i	$-0.313417\pi$
$277$	5100.47	1.10634	0.553172	+	0.833067i	$0.313417\pi$
$278$	−6097.41	−1.31546
$279$	127.274	0.0273107
$280$	−2323.63	−0.495940
$281$	7835.19	1.66337	0.831687	−	0.555245i	$-0.187375\pi$
$281$	7835.19	1.66337	0.831687	+	0.555245i	$0.187375\pi$
$282$	936.152	0.197685
$283$	7148.56	1.50155	0.750773	−	0.660560i	$-0.229681\pi$
$283$	7148.56	1.50155	0.750773	+	0.660560i	$0.229681\pi$
$284$	−1503.03	−0.314044
$285$	1323.75	0.275131
$286$	−9906.55	−2.04820
$287$	−3203.39	−0.658850
$288$	596.083	0.121960
$289$	1942.04	0.395285
$290$	−446.485	−0.0904086
$291$	−2838.98	−0.571905
$292$	−1716.90	−0.344090
$293$	−6053.67	−1.20703	−0.603514	−	0.797352i	$-0.706233\pi$
$293$	−6053.67	−1.20703	−0.603514	+	0.797352i	$0.706233\pi$
$294$	−1783.51	−0.353797
$295$	3227.17	0.636926
$296$	−3542.73	−0.695665
$297$	−1164.15	−0.227443
$298$	−4207.72	−0.817941
$299$	−13126.7	−2.53892
$300$	111.113	0.0213837
$301$	1499.83	0.287204
$302$	6788.87	1.29356
$303$	2592.75	0.491584
$304$	6500.25	1.22637
$305$	1933.48	0.362986
$306$	−2294.49	−0.428651
$307$	5697.09	1.05912	0.529560	−	0.848272i	$-0.322357\pi$
$307$	5697.09	1.05912	0.529560	+	0.848272i	$0.322357\pi$
$308$	−1478.97	−0.273611
$309$	−4157.21	−0.765357
$310$	217.724	0.0398899
$311$	−10242.2	−1.86747	−0.933737	−	0.357960i	$-0.883472\pi$
$311$	−10242.2	−1.86747	−0.933737	+	0.357960i	$0.883472\pi$
$312$	−4493.11	−0.815295
$313$	3018.38	0.545077	0.272539	−	0.962145i	$-0.412137\pi$
$313$	3018.38	0.545077	0.272539	+	0.962145i	$0.412137\pi$
$314$	5537.36	0.995195
$315$	−1041.89	−0.186362
$316$	1057.85	0.188320
$317$	3757.10	0.665678	0.332839	−	0.942984i	$-0.391993\pi$
$317$	3757.10	0.665678	0.332839	+	0.942984i	$0.391993\pi$
$318$	−2449.62	−0.431974
$319$	1250.38	0.219460
$320$	−1926.59	−0.336561
$321$	−1006.49	−0.175005
$322$	−12542.0	−2.17061
$323$	−7306.68	−1.25868
$324$	120.002	0.0205765
$325$	−1865.43	−0.318386
$326$	−1104.14	−0.187585
$327$	−2308.50	−0.390398
$328$	−2777.06	−0.467492
$329$	−2346.37	−0.393191
$330$	−1991.47	−0.332203
$331$	2883.87	0.478888	0.239444	−	0.970910i	$-0.423035\pi$
$331$	2883.87	0.478888	0.239444	+	0.970910i	$0.423035\pi$
$332$	1107.46	0.183071
$333$	−1588.53	−0.261414
$334$	12297.7	2.01467
$335$	3685.52	0.601078
$336$	−5116.20	−0.830689
$337$	−1692.21	−0.273532	−0.136766	−	0.990603i	$-0.543671\pi$
$337$	−1692.21	−0.273532	−0.136766	+	0.990603i	$0.543671\pi$
$338$	−10379.2	−1.67028
$339$	3200.95	0.512838
$340$	−613.309	−0.0978274
$341$	−609.735	−0.0968298
$342$	2445.66	0.386685
$343$	−3471.36	−0.546460
$344$	1300.22	0.203788
$345$	−2638.81	−0.411793
$346$	−2779.68	−0.431898
$347$	4744.08	0.733935	0.366967	−	0.930234i	$-0.380396\pi$
$347$	4744.08	0.733935	0.366967	+	0.930234i	$0.380396\pi$
$348$	−128.891	−0.0198543
$349$	−6690.03	−1.02610	−0.513050	−	0.858359i	$-0.671485\pi$
$349$	−6690.03	−1.02610	−0.513050	+	0.858359i	$0.671485\pi$
$350$	−1782.34	−0.272200
$351$	−2014.67	−0.306368
$352$	−2855.67	−0.432409
$353$	2218.76	0.334541	0.167270	−	0.985911i	$-0.446505\pi$
$353$	2218.76	0.334541	0.167270	+	0.985911i	$0.446505\pi$
$354$	5962.28	0.895173
$355$	5072.63	0.758387
$356$	−767.959	−0.114331
$357$	5750.91	0.852579
$358$	−1348.71	−0.199111
$359$	−2749.37	−0.404195	−0.202098	−	0.979365i	$-0.564776\pi$
$359$	−2749.37	−0.404195	−0.202098	+	0.979365i	$0.564776\pi$
$360$	−903.230	−0.132234
$361$	929.079	0.135454
$362$	−13503.7	−1.96061
$363$	1584.11	0.229047
$364$	−2559.50	−0.368555
$365$	5794.44	0.830945
$366$	3572.15	0.510162
$367$	8213.16	1.16818	0.584092	−	0.811687i	$-0.301451\pi$
$367$	8213.16	1.16818	0.584092	+	0.811687i	$0.301451\pi$
$368$	−12957.8	−1.83552
$369$	−1245.21	−0.175672
$370$	−2717.45	−0.381820
$371$	6139.73	0.859188
$372$	62.8525	0.00876008
$373$	−8062.31	−1.11917	−0.559585	−	0.828773i	$-0.689039\pi$
$373$	−8062.31	−1.11917	−0.559585	+	0.828773i	$0.689039\pi$
$374$	10992.3	1.51978
$375$	−375.000	−0.0516398
$376$	−2034.10	−0.278991
$377$	2163.90	0.295614
$378$	−1924.92	−0.261924
$379$	−5523.37	−0.748593	−0.374296	−	0.927309i	$-0.622116\pi$
$379$	−5523.37	−0.748593	−0.374296	+	0.927309i	$0.622116\pi$
$380$	653.716	0.0882498
$381$	−3213.72	−0.432136
$382$	−3660.18	−0.490239
$383$	10435.1	1.39219	0.696095	−	0.717950i	$-0.254919\pi$
$383$	10435.1	1.39219	0.696095	+	0.717950i	$0.254919\pi$
$384$	−5148.97	−0.684264
$385$	4991.43	0.660745
$386$	−6948.04	−0.916181
$387$	583.006	0.0765784
$388$	−1401.99	−0.183442
$389$	−4033.70	−0.525749	−0.262875	−	0.964830i	$-0.584671\pi$
$389$	−4033.70	−0.525749	−0.262875	+	0.964830i	$0.584671\pi$
$390$	−3446.43	−0.447479
$391$	14565.4	1.88389
$392$	3875.26	0.499311
$393$	−6576.96	−0.844182
$394$	2908.47	0.371894
$395$	−3570.19	−0.454775
$396$	−574.898	−0.0729538
$397$	−14474.2	−1.82982	−0.914911	−	0.403655i	$-0.867740\pi$
$397$	−14474.2	−1.82982	−0.914911	+	0.403655i	$0.867740\pi$
$398$	532.500	0.0670649
$399$	−6129.81	−0.769109
$400$	−1841.43	−0.230179
$401$	−3695.34	−0.460191	−0.230095	−	0.973168i	$-0.573904\pi$
$401$	−3695.34	−0.460191	−0.230095	+	0.973168i	$0.573904\pi$
$402$	6809.08	0.844791
$403$	−1055.20	−0.130430
$404$	1280.40	0.157678
$405$	−405.000	−0.0496904
$406$	2067.51	0.252731
$407$	7610.20	0.926839
$408$	4985.54	0.604953
$409$	5880.15	0.710892	0.355446	−	0.934697i	$-0.384329\pi$
$409$	5880.15	0.710892	0.355446	+	0.934697i	$0.384329\pi$
$410$	−2130.14	−0.256585
$411$	1776.85	0.213249
$412$	−2052.98	−0.245493
$413$	−14943.9	−1.78048
$414$	−4875.26	−0.578758
$415$	−3737.60	−0.442101
$416$	−4942.01	−0.582457
$417$	5940.57	0.697628
$418$	−11716.5	−1.37099
$419$	−10799.8	−1.25921	−0.629603	−	0.776917i	$-0.716782\pi$
$419$	−10799.8	−1.25921	−0.629603	+	0.776917i	$0.716782\pi$
$420$	−514.525	−0.0597767
$421$	5520.52	0.639083	0.319541	−	0.947572i	$-0.396471\pi$
$421$	5520.52	0.639083	0.319541	+	0.947572i	$0.396471\pi$
$422$	12258.0	1.41401
$423$	−912.072	−0.104838
$424$	5322.60	0.609642
$425$	2069.88	0.236244
$426$	9371.81	1.06588
$427$	−8953.25	−1.01470
$428$	−497.040	−0.0561340
$429$	9651.72	1.08622
$430$	997.330	0.111850
$431$	−3360.04	−0.375516	−0.187758	−	0.982215i	$-0.560122\pi$
$431$	−3360.04	−0.375516	−0.187758	+	0.982215i	$0.560122\pi$
$432$	−1988.74	−0.221490
$433$	−5326.35	−0.591150	−0.295575	−	0.955320i	$-0.595511\pi$
$433$	−5326.35	−0.591150	−0.295575	+	0.955320i	$0.595511\pi$
$434$	−1008.20	−0.111509
$435$	435.000	0.0479463
$436$	−1140.02	−0.125222
$437$	−15525.0	−1.69945
$438$	10705.4	1.16786
$439$	−2837.77	−0.308518	−0.154259	−	0.988030i	$-0.549299\pi$
$439$	−2837.77	−0.308518	−0.154259	+	0.988030i	$0.549299\pi$
$440$	4327.13	0.468836
$441$	1737.63	0.187629
$442$	19023.2	2.04715
$443$	10702.1	1.14779	0.573896	−	0.818928i	$-0.305431\pi$
$443$	10702.1	1.14779	0.573896	+	0.818928i	$0.305431\pi$
$444$	−784.472	−0.0838500
$445$	2591.82	0.276099
$446$	−5971.89	−0.634029
$447$	4099.48	0.433778
$448$	8921.32	0.940832
$449$	7956.43	0.836275	0.418137	−	0.908384i	$-0.362683\pi$
$449$	7956.43	0.836275	0.418137	+	0.908384i	$0.362683\pi$
$450$	−692.821	−0.0725776
$451$	5965.44	0.622842
$452$	1580.75	0.164496
$453$	−6614.24	−0.686014
$454$	19885.0	2.05562
$455$	8638.14	0.890027
$456$	−5314.01	−0.545726
$457$	7365.10	0.753884	0.376942	−	0.926237i	$-0.376976\pi$
$457$	7365.10	0.753884	0.376942	+	0.926237i	$0.376976\pi$
$458$	3916.71	0.399598
$459$	2235.47	0.227326
$460$	−1303.14	−0.132085
$461$	15891.5	1.60551	0.802754	−	0.596310i	$-0.203367\pi$
$461$	15891.5	1.60551	0.802754	+	0.596310i	$0.203367\pi$
$462$	9221.78	0.928649
$463$	14456.8	1.45111	0.725555	−	0.688164i	$-0.241583\pi$
$463$	14456.8	1.45111	0.725555	+	0.688164i	$0.241583\pi$
$464$	2136.06	0.213716
$465$	−212.123	−0.0211548
$466$	−3168.93	−0.315017
$467$	−14908.2	−1.47724	−0.738618	−	0.674124i	$-0.764521\pi$
$467$	−14908.2	−1.47724	−0.738618	+	0.674124i	$0.764521\pi$
$468$	−994.916	−0.0982692
$469$	−17066.3	−1.68027
$470$	−1560.25	−0.153126
$471$	−5394.92	−0.527781
$472$	−12955.0	−1.26335
$473$	−2793.02	−0.271508
$474$	−6596.02	−0.639167
$475$	−2206.25	−0.213115
$476$	2840.01	0.273470
$477$	2386.61	0.229088
$478$	−7982.68	−0.763848
$479$	11758.0	1.12158	0.560791	−	0.827957i	$-0.310497\pi$
$479$	11758.0	1.12158	0.560791	+	0.827957i	$0.310497\pi$
$480$	−993.472	−0.0944700
$481$	13170.2	1.24846
$482$	15803.4	1.49342
$483$	12219.4	1.15114
$484$	782.290	0.0734683
$485$	4731.64	0.442995
$486$	−748.247	−0.0698378
$487$	−8795.82	−0.818433	−0.409216	−	0.912437i	$-0.634198\pi$
$487$	−8795.82	−0.818433	−0.409216	+	0.912437i	$0.634198\pi$
$488$	−7761.68	−0.719989
$489$	1075.74	0.0994821
$490$	2972.51	0.274050
$491$	−14778.8	−1.35837	−0.679185	−	0.733967i	$-0.737667\pi$
$491$	−14778.8	−1.35837	−0.679185	+	0.733967i	$0.737667\pi$
$492$	−614.928	−0.0563477
$493$	−2401.06	−0.219347
$494$	−20276.5	−1.84673
$495$	1940.24	0.176177
$496$	−1041.63	−0.0942952
$497$	−23489.5	−2.12002
$498$	−6905.31	−0.621354
$499$	10941.0	0.981538	0.490769	−	0.871290i	$-0.336716\pi$
$499$	10941.0	0.981538	0.490769	+	0.871290i	$0.336716\pi$
$500$	−185.189	−0.0165638
$501$	−11981.3	−1.06844
$502$	−297.094	−0.0264143
$503$	−7424.36	−0.658123	−0.329062	−	0.944308i	$-0.606732\pi$
$503$	−7424.36	−0.658123	−0.329062	+	0.944308i	$0.606732\pi$
$504$	4182.53	0.369652
$505$	−4321.26	−0.380779
$506$	23356.0	2.05198
$507$	10112.2	0.885799
$508$	−1587.05	−0.138610
$509$	3745.37	0.326151	0.163075	−	0.986614i	$-0.447859\pi$
$509$	3745.37	0.326151	0.163075	+	0.986614i	$0.447859\pi$
$510$	3824.15	0.332032
$511$	−26832.0	−2.32285
$512$	6949.02	0.599817
$513$	−2382.75	−0.205070
$514$	−3149.91	−0.270305
$515$	6928.68	0.592843
$516$	287.909	0.0245630
$517$	4369.49	0.371702
$518$	12583.5	1.06735
$519$	2708.18	0.229048
$520$	7488.51	0.631525
$521$	19900.9	1.67346	0.836730	−	0.547616i	$-0.184464\pi$
$521$	19900.9	1.67346	0.836730	+	0.547616i	$0.184464\pi$
$522$	803.673	0.0673866
$523$	−4230.73	−0.353722	−0.176861	−	0.984236i	$-0.556594\pi$
$523$	−4230.73	−0.353722	−0.176861	+	0.984236i	$0.556594\pi$
$524$	−3247.94	−0.270777
$525$	1736.49	0.144355
$526$	−9006.84	−0.746610
$527$	1170.85	0.0967800
$528$	9527.53	0.785289
$529$	18781.0	1.54360
$530$	4082.69	0.334606
$531$	−5808.91	−0.474737
$532$	−3027.12	−0.246696
$533$	10323.8	0.838972
$534$	4788.44	0.388045
$535$	1677.48	0.135558
$536$	−14795.0	−1.19225
$537$	1314.02	0.105594
$538$	−12118.8	−0.971148
$539$	−8324.51	−0.665236
$540$	−200.004	−0.0159385
$541$	−20053.9	−1.59368	−0.796842	−	0.604188i	$-0.793498\pi$
$541$	−20053.9	−1.59368	−0.796842	+	0.604188i	$0.793498\pi$
$542$	−21862.0	−1.73257
$543$	13156.4	1.03977
$544$	5483.64	0.432186
$545$	3847.49	0.302401
$546$	15959.2	1.25090
$547$	753.829	0.0589240	0.0294620	−	0.999566i	$-0.490621\pi$
$547$	753.829	0.0589240	0.0294620	+	0.999566i	$0.490621\pi$
$548$	877.472	0.0684010
$549$	−3480.27	−0.270554
$550$	3319.12	0.257323
$551$	2559.25	0.197873
$552$	10593.1	0.816798
$553$	16532.3	1.27129
$554$	−15705.4	−1.20444
$555$	2647.54	0.202490
$556$	2933.67	0.223769
$557$	14038.4	1.06791	0.533953	−	0.845514i	$-0.320706\pi$
$557$	14038.4	1.06791	0.533953	+	0.845514i	$0.320706\pi$
$558$	−391.903	−0.0297322
$559$	−4833.59	−0.365723
$560$	8526.99	0.643449
$561$	−10709.5	−0.805983
$562$	−24126.2	−1.81085
$563$	−11290.9	−0.845211	−0.422606	−	0.906314i	$-0.638884\pi$
$563$	−11290.9	−0.845211	−0.422606	+	0.906314i	$0.638884\pi$
$564$	−450.414	−0.0336274
$565$	−5334.92	−0.397242
$566$	−22011.9	−1.63468
$567$	1875.41	0.138906
$568$	−20363.3	−1.50427
$569$	−24522.4	−1.80674	−0.903369	−	0.428864i	$-0.858914\pi$
$569$	−24522.4	−1.80674	−0.903369	+	0.428864i	$0.858914\pi$
$570$	−4076.10	−0.299525
$571$	9525.67	0.698138	0.349069	−	0.937097i	$-0.386498\pi$
$571$	9525.67	0.698138	0.349069	+	0.937097i	$0.386498\pi$
$572$	4766.37	0.348413
$573$	3566.03	0.259988
$574$	9863.89	0.717266
$575$	4398.01	0.318973
$576$	3467.86	0.250858
$577$	2493.72	0.179922	0.0899610	−	0.995945i	$-0.471326\pi$
$577$	2493.72	0.179922	0.0899610	+	0.995945i	$0.471326\pi$
$578$	−5979.93	−0.430332
$579$	6769.31	0.485878
$580$	214.819	0.0153791
$581$	17307.5	1.23586
$582$	8741.82	0.622612
$583$	−11433.6	−0.812231
$584$	−23261.0	−1.64819
$585$	3357.78	0.237311
$586$	18640.5	1.31405
$587$	17081.6	1.20108	0.600539	−	0.799595i	$-0.294953\pi$
$587$	17081.6	1.20108	0.600539	+	0.799595i	$0.294953\pi$
$588$	858.104	0.0601830
$589$	−1247.99	−0.0873050
$590$	−9937.13	−0.693398
$591$	−2833.65	−0.197227
$592$	13000.7	0.902578
$593$	−9633.41	−0.667111	−0.333556	−	0.942730i	$-0.608248\pi$
$593$	−9633.41	−0.667111	−0.333556	+	0.942730i	$0.608248\pi$
$594$	3584.65	0.247609
$595$	−9584.86	−0.660405
$596$	2024.47	0.139137
$597$	−518.803	−0.0355665
$598$	40419.8	2.76403
$599$	11572.5	0.789379	0.394690	−	0.918814i	$-0.370852\pi$
$599$	11572.5	0.789379	0.394690	+	0.918814i	$0.370852\pi$
$600$	1505.38	0.102428
$601$	−27804.0	−1.88710	−0.943552	−	0.331225i	$-0.892538\pi$
$601$	−27804.0	−1.88710	−0.943552	+	0.331225i	$0.892538\pi$
$602$	−4618.27	−0.312669
$603$	−6633.93	−0.448017
$604$	−3266.35	−0.220043
$605$	−2640.18	−0.177419
$606$	−7983.62	−0.535169
$607$	2573.81	0.172105	0.0860526	−	0.996291i	$-0.472575\pi$
$607$	2573.81	0.172105	0.0860526	+	0.996291i	$0.472575\pi$
$608$	−5844.93	−0.389874
$609$	−2014.33	−0.134031
$610$	−5953.59	−0.395170
$611$	7561.82	0.500685
$612$	1103.96	0.0729163
$613$	11274.0	0.742824	0.371412	−	0.928468i	$-0.378874\pi$
$613$	11274.0	0.742824	0.371412	+	0.928468i	$0.378874\pi$
$614$	−17542.5	−1.15303
$615$	2075.34	0.136075
$616$	−20037.4	−1.31060
$617$	−1684.94	−0.109940	−0.0549701	−	0.998488i	$-0.517506\pi$
$617$	−1684.94	−0.109940	−0.0549701	+	0.998488i	$0.517506\pi$
$618$	12800.9	0.833216
$619$	14779.1	0.959647	0.479824	−	0.877365i	$-0.340701\pi$
$619$	14779.1	0.959647	0.479824	+	0.877365i	$0.340701\pi$
$620$	−104.754	−0.00678553
$621$	4749.85	0.306932
$622$	31538.0	2.03305
$623$	−12001.8	−0.771814
$624$	16488.3	1.05779
$625$	625.000	0.0400000
$626$	−9294.22	−0.593406
$627$	11415.1	0.727075
$628$	−2664.21	−0.169289
$629$	−14613.6	−0.926362
$630$	3208.20	0.202886
$631$	6631.39	0.418370	0.209185	−	0.977876i	$-0.432919\pi$
$631$	6631.39	0.418370	0.209185	+	0.977876i	$0.432919\pi$
$632$	14332.0	0.902053
$633$	−11942.7	−0.749889
$634$	−11568.9	−0.724699
$635$	5356.20	0.334731
$636$	1178.59	0.0734815
$637$	−14406.4	−0.896077
$638$	−3850.18	−0.238918
$639$	−9130.74	−0.565268
$640$	8581.61	0.530028
$641$	−22946.8	−1.41395	−0.706977	−	0.707237i	$-0.749941\pi$
$641$	−22946.8	−1.41395	−0.706977	+	0.707237i	$0.749941\pi$
$642$	3099.18	0.190522
$643$	−366.544	−0.0224807	−0.0112404	−	0.999937i	$-0.503578\pi$
$643$	−366.544	−0.0224807	−0.0112404	+	0.999937i	$0.503578\pi$
$644$	6034.36	0.369235
$645$	−971.676	−0.0593174
$646$	22498.8	1.37028
$647$	16832.6	1.02281	0.511404	−	0.859340i	$-0.329126\pi$
$647$	16832.6	1.02281	0.511404	+	0.859340i	$0.329126\pi$
$648$	1625.81	0.0985617
$649$	27828.9	1.68317
$650$	5744.05	0.346616
$651$	982.265	0.0591367
$652$	531.240	0.0319095
$653$	−5342.33	−0.320156	−0.160078	−	0.987104i	$-0.551175\pi$
$653$	−5342.33	−0.320156	−0.160078	+	0.987104i	$0.551175\pi$
$654$	7108.33	0.425012
$655$	10961.6	0.653901
$656$	10190.9	0.606538
$657$	−10430.0	−0.619350
$658$	7224.97	0.428052
$659$	27709.9	1.63798	0.818988	−	0.573811i	$-0.194536\pi$
$659$	27709.9	1.63798	0.818988	+	0.573811i	$0.194536\pi$
$660$	958.163	0.0565098
$661$	−32828.4	−1.93174	−0.965868	−	0.259036i	$-0.916595\pi$
$661$	−32828.4	−1.93174	−0.965868	+	0.259036i	$0.916595\pi$
$662$	−8880.03	−0.521348
$663$	−18533.9	−1.08566
$664$	15004.1	0.876914
$665$	10216.4	0.595749
$666$	4891.40	0.284592
$667$	−5101.69	−0.296159
$668$	−5916.82	−0.342707
$669$	5818.28	0.336244
$670$	−11348.5	−0.654372
$671$	16673.0	0.959246
$672$	4600.41	0.264084
$673$	32414.7	1.85660	0.928302	−	0.371827i	$-0.121269\pi$
$673$	32414.7	1.85660	0.928302	+	0.371827i	$0.121269\pi$
$674$	5210.66	0.297785
$675$	675.000	0.0384900
$676$	4993.79	0.284125
$677$	−24783.8	−1.40697	−0.703485	−	0.710710i	$-0.748374\pi$
$677$	−24783.8	−1.40697	−0.703485	+	0.710710i	$0.748374\pi$
$678$	−9856.40	−0.558308
$679$	−21910.5	−1.23836
$680$	−8309.23	−0.468595
$681$	−19373.5	−1.09015
$682$	1877.50	0.105415
$683$	14097.9	0.789811	0.394906	−	0.918722i	$-0.370777\pi$
$683$	14097.9	0.789811	0.394906	+	0.918722i	$0.370777\pi$
$684$	−1176.69	−0.0657776
$685$	−2961.41	−0.165182
$686$	10689.0	0.594911
$687$	−3815.96	−0.211919
$688$	−4771.40	−0.264401
$689$	−19786.9	−1.09408
$690$	8125.43	0.448304
$691$	12672.4	0.697657	0.348829	−	0.937186i	$-0.386579\pi$
$691$	12672.4	0.697657	0.348829	+	0.937186i	$0.386579\pi$
$692$	1337.40	0.0734686
$693$	−8984.57	−0.492490
$694$	−14608.0	−0.799008
$695$	−9900.95	−0.540381
$696$	−1746.24	−0.0951023
$697$	−11455.2	−0.622522
$698$	20600.0	1.11708
$699$	3087.42	0.167063
$700$	857.541	0.0463029
$701$	28508.3	1.53601	0.768005	−	0.640444i	$-0.221250\pi$
$701$	28508.3	1.53601	0.768005	+	0.640444i	$0.221250\pi$
$702$	6203.58	0.333531
$703$	15576.4	0.835669
$704$	−16613.5	−0.889413
$705$	1520.12	0.0812071
$706$	−6832.03	−0.364202
$707$	20010.2	1.06444
$708$	−2868.65	−0.152275
$709$	14243.6	0.754484	0.377242	−	0.926115i	$-0.376873\pi$
$709$	14243.6	0.754484	0.377242	+	0.926115i	$0.376873\pi$
$710$	−15619.7	−0.825628
$711$	6426.35	0.338969
$712$	−10404.5	−0.547646
$713$	2487.79	0.130671
$714$	−17708.2	−0.928172
$715$	−16086.2	−0.841385
$716$	648.911	0.0338700
$717$	7777.35	0.405091
$718$	8465.87	0.440033
$719$	−24710.0	−1.28168	−0.640839	−	0.767675i	$-0.721413\pi$
$719$	−24710.0	−1.28168	−0.640839	+	0.767675i	$0.721413\pi$
$720$	3314.57	0.171565
$721$	−32084.2	−1.65725
$722$	−2860.82	−0.147464
$723$	−15396.9	−0.792003
$724$	6497.08	0.333511
$725$	−725.000	−0.0371391
$726$	−4877.80	−0.249355
$727$	27341.9	1.39485	0.697425	−	0.716658i	$-0.254329\pi$
$727$	27341.9	1.39485	0.697425	+	0.716658i	$0.254329\pi$
$728$	−34676.6	−1.76538
$729$	729.000	0.0370370
$730$	−17842.3	−0.904620
$731$	5363.34	0.271368
$732$	−1718.68	−0.0867818
$733$	18543.0	0.934379	0.467190	−	0.884157i	$-0.345267\pi$
$733$	18543.0	0.934379	0.467190	+	0.884157i	$0.345267\pi$
$734$	−25290.0	−1.27176
$735$	−2896.05	−0.145337
$736$	11651.5	0.583531
$737$	31781.3	1.58844
$738$	3834.25	0.191247
$739$	12155.7	0.605082	0.302541	−	0.953136i	$-0.402165\pi$
$739$	12155.7	0.605082	0.302541	+	0.953136i	$0.402165\pi$
$740$	1307.45	0.0649499
$741$	19755.0	0.979374
$742$	−18905.5	−0.935366
$743$	16802.2	0.829627	0.414814	−	0.909906i	$-0.363847\pi$
$743$	16802.2	0.829627	0.414814	+	0.909906i	$0.363847\pi$
$744$	851.538	0.0419609
$745$	−6832.47	−0.336003
$746$	24825.5	1.21840
$747$	6727.69	0.329522
$748$	−5288.75	−0.258524
$749$	−7767.80	−0.378944
$750$	1154.70	0.0562183
$751$	−19768.5	−0.960538	−0.480269	−	0.877121i	$-0.659461\pi$
$751$	−19768.5	−0.960538	−0.480269	+	0.877121i	$0.659461\pi$
$752$	7464.52	0.361972
$753$	289.452	0.0140083
$754$	−6663.10	−0.321825
$755$	11023.7	0.531384
$756$	926.144	0.0445550
$757$	−21503.5	−1.03244	−0.516221	−	0.856456i	$-0.672662\pi$
$757$	−21503.5	−1.03244	−0.516221	+	0.856456i	$0.672662\pi$
$758$	17007.6	0.814966
$759$	−22755.2	−1.08823
$760$	8856.68	0.422718
$761$	26870.1	1.27995	0.639974	−	0.768397i	$-0.278945\pi$
$761$	26870.1	1.27995	0.639974	+	0.768397i	$0.278945\pi$
$762$	9895.71	0.470451
$763$	−17816.3	−0.845341
$764$	1761.04	0.0833927
$765$	−3725.78	−0.176086
$766$	−32131.8	−1.51563
$767$	48160.6	2.26725
$768$	6607.12	0.310435
$769$	−12864.4	−0.603254	−0.301627	−	0.953426i	$-0.597530\pi$
$769$	−12864.4	−0.603254	−0.301627	+	0.953426i	$0.597530\pi$
$770$	−15369.6	−0.719329
$771$	3068.89	0.143350
$772$	3342.93	0.155848
$773$	−18534.1	−0.862388	−0.431194	−	0.902259i	$-0.641908\pi$
$773$	−18534.1	−0.862388	−0.431194	+	0.902259i	$0.641908\pi$
$774$	−1795.19	−0.0833681
$775$	353.539	0.0163864
$776$	−18994.5	−0.878689
$777$	−12259.8	−0.566047
$778$	12420.6	0.572364
$779$	12210.0	0.561575
$780$	1658.19	0.0761190
$781$	43742.9	2.00415
$782$	−44849.7	−2.05092
$783$	−783.000	−0.0357371
$784$	−14221.0	−0.647822
$785$	8991.54	0.408818
$786$	20251.8	0.919030
$787$	−26438.7	−1.19751	−0.598754	−	0.800933i	$-0.704337\pi$
$787$	−26438.7	−1.19751	−0.598754	+	0.800933i	$0.704337\pi$
$788$	−1399.36	−0.0632616
$789$	8775.16	0.395949
$790$	10993.4	0.495097
$791$	24704.1	1.11046
$792$	−7788.83	−0.349450
$793$	28854.2	1.29211
$794$	44569.1	1.99206
$795$	−3977.68	−0.177451
$796$	−256.204	−0.0114082
$797$	−33935.7	−1.50823	−0.754117	−	0.656740i	$-0.771935\pi$
$797$	−33935.7	−1.50823	−0.754117	+	0.656740i	$0.771935\pi$
$798$	18875.0	0.837301
$799$	−8390.57	−0.371510
$800$	1655.79	0.0731761
$801$	−4665.27	−0.205792
$802$	11378.7	0.500993
$803$	49967.3	2.19590
$804$	−3276.07	−0.143704
$805$	−20365.6	−0.891668
$806$	3249.19	0.141995
$807$	11807.1	0.515028
$808$	17347.1	0.755281
$809$	2918.27	0.126824	0.0634121	−	0.997987i	$-0.479802\pi$
$809$	2918.27	0.126824	0.0634121	+	0.997987i	$0.479802\pi$
$810$	1247.08	0.0540961
$811$	9351.59	0.404906	0.202453	−	0.979292i	$-0.435109\pi$
$811$	9351.59	0.404906	0.202453	+	0.979292i	$0.435109\pi$
$812$	−994.748	−0.0429911
$813$	21299.6	0.918831
$814$	−23433.4	−1.00902
$815$	−1792.90	−0.0770585
$816$	−18295.4	−0.784885
$817$	−5716.70	−0.244800
$818$	−18106.2	−0.773922
$819$	−15548.7	−0.663387
$820$	1024.88	0.0436468
$821$	−36272.1	−1.54191	−0.770954	−	0.636891i	$-0.780220\pi$
$821$	−36272.1	−1.54191	−0.770954	+	0.636891i	$0.780220\pi$
$822$	−5471.28	−0.232157
$823$	37236.3	1.57713	0.788563	−	0.614954i	$-0.210825\pi$
$823$	37236.3	1.57713	0.788563	+	0.614954i	$0.210825\pi$
$824$	−27814.2	−1.17591
$825$	−3233.74	−0.136466
$826$	46015.2	1.93835
$827$	1886.24	0.0793118	0.0396559	−	0.999213i	$-0.487374\pi$
$827$	1886.24	0.0793118	0.0396559	+	0.999213i	$0.487374\pi$
$828$	2345.65	0.0984504
$829$	7608.68	0.318770	0.159385	−	0.987216i	$-0.449049\pi$
$829$	7608.68	0.318770	0.159385	+	0.987216i	$0.449049\pi$
$830$	11508.9	0.481299
$831$	15301.4	0.638748
$832$	−28751.3	−1.19805
$833$	15985.3	0.664893
$834$	−18292.2	−0.759483
$835$	19968.9	0.827607
$836$	5637.20	0.233214
$837$	381.822	0.0157678
$838$	33254.9	1.37085
$839$	6779.04	0.278949	0.139475	−	0.990226i	$-0.455459\pi$
$839$	6779.04	0.278949	0.139475	+	0.990226i	$0.455459\pi$
$840$	−6970.88	−0.286331
$841$	841.000	0.0344828
$842$	−16998.8	−0.695746
$843$	23505.6	0.960350
$844$	−5897.74	−0.240531
$845$	−16853.7	−0.686137
$846$	2808.46	0.114133
$847$	12225.7	0.495963
$848$	−19532.3	−0.790969
$849$	21445.7	0.866918
$850$	−6373.58	−0.257191
$851$	−31050.5	−1.25076
$852$	−4509.09	−0.181313
$853$	8817.97	0.353953	0.176976	−	0.984215i	$-0.443368\pi$
$853$	8817.97	0.353953	0.176976	+	0.984215i	$0.443368\pi$
$854$	27568.9	1.10467
$855$	3971.25	0.158847
$856$	−6734.00	−0.268882
$857$	5429.28	0.216407	0.108203	−	0.994129i	$-0.465490\pi$
$857$	5429.28	0.216407	0.108203	+	0.994129i	$0.465490\pi$
$858$	−29719.6	−1.18253
$859$	−43734.8	−1.73715	−0.868574	−	0.495559i	$-0.834963\pi$
$859$	−43734.8	−1.73715	−0.868574	+	0.495559i	$0.834963\pi$
$860$	−479.849	−0.0190264
$861$	−9610.16	−0.380387
$862$	10346.3	0.408811
$863$	−20597.8	−0.812464	−0.406232	−	0.913770i	$-0.633158\pi$
$863$	−20597.8	−0.812464	−0.406232	+	0.913770i	$0.633158\pi$
$864$	1788.25	0.0704138
$865$	−4513.64	−0.177420
$866$	16400.9	0.643563
$867$	5826.11	0.228218
$868$	485.078	0.0189685
$869$	−30786.9	−1.20181
$870$	−1339.45	−0.0521974
$871$	55000.7	2.13964
$872$	−15445.2	−0.599817
$873$	−8516.95	−0.330189
$874$	47804.6	1.85013
$875$	−2894.15	−0.111817
$876$	−5150.71	−0.198660
$877$	22182.9	0.854121	0.427061	−	0.904223i	$-0.359549\pi$
$877$	22182.9	0.854121	0.427061	+	0.904223i	$0.359549\pi$
$878$	8738.08	0.335872
$879$	−18161.0	−0.696878
$880$	−15879.2	−0.608282
$881$	−41017.8	−1.56859	−0.784293	−	0.620391i	$-0.786974\pi$
$881$	−41017.8	−1.56859	−0.784293	+	0.620391i	$0.786974\pi$
$882$	−5350.52	−0.204265
$883$	18142.8	0.691452	0.345726	−	0.938335i	$-0.387633\pi$
$883$	18142.8	0.691452	0.345726	+	0.938335i	$0.387633\pi$
$884$	−9152.69	−0.348233
$885$	9681.51	0.367729
$886$	−32954.0	−1.24956
$887$	−14723.4	−0.557341	−0.278671	−	0.960387i	$-0.589894\pi$
$887$	−14723.4	−0.557341	−0.278671	+	0.960387i	$0.589894\pi$
$888$	−10628.2	−0.401643
$889$	−24802.6	−0.935718
$890$	−7980.73	−0.300578
$891$	−3492.44	−0.131314
$892$	2873.27	0.107852
$893$	8943.38	0.335139
$894$	−12623.2	−0.472239
$895$	−2190.03	−0.0817930
$896$	−39738.3	−1.48166
$897$	−39380.1	−1.46585
$898$	−24499.5	−0.910422
$899$	−410.105	−0.0152144
$900$	333.339	0.0123459
$901$	21955.5	0.811813
$902$	−18368.8	−0.678066
$903$	4499.48	0.165818
$904$	21416.3	0.787937
$905$	−21927.3	−0.805400
$906$	20366.6	0.746838
$907$	−19250.3	−0.704738	−0.352369	−	0.935861i	$-0.614624\pi$
$907$	−19250.3	−0.704738	−0.352369	+	0.935861i	$0.614624\pi$
$908$	−9567.34	−0.349673
$909$	7778.26	0.283816
$910$	−26598.6	−0.968940
$911$	46931.6	1.70682	0.853410	−	0.521241i	$-0.174531\pi$
$911$	46931.6	1.70682	0.853410	+	0.521241i	$0.174531\pi$
$912$	19500.8	0.708043
$913$	−32230.5	−1.16832
$914$	−22678.7	−0.820726
$915$	5800.44	0.209570
$916$	−1884.46	−0.0679742
$917$	−50759.2	−1.82793
$918$	−6883.47	−0.247482
$919$	−35021.9	−1.25709	−0.628546	−	0.777773i	$-0.716349\pi$
$919$	−35021.9	−1.25709	−0.628546	+	0.777773i	$0.716349\pi$
$920$	−17655.2	−0.632689
$921$	17091.3	0.611483
$922$	−48933.1	−1.74786
$923$	75701.3	2.69961
$924$	−4436.90	−0.157969
$925$	−4412.57	−0.156848
$926$	−44515.4	−1.57977
$927$	−12471.6	−0.441879
$928$	−1920.71	−0.0679423
$929$	−6090.61	−0.215098	−0.107549	−	0.994200i	$-0.534300\pi$
$929$	−6090.61	−0.215098	−0.107549	+	0.994200i	$0.534300\pi$
$930$	653.171	0.0230305
$931$	−17038.4	−0.599798
$932$	1524.68	0.0535864
$933$	−30726.7	−1.07819
$934$	45905.4	1.60821
$935$	17849.2	0.624312
$936$	−13479.3	−0.470711
$937$	29684.0	1.03494	0.517468	−	0.855703i	$-0.326875\pi$
$937$	29684.0	1.03494	0.517468	+	0.855703i	$0.326875\pi$
$938$	52550.6	1.82925
$939$	9055.15	0.314700
$940$	750.690	0.0260477
$941$	2691.42	0.0932390	0.0466195	−	0.998913i	$-0.485155\pi$
$941$	2691.42	0.0932390	0.0466195	+	0.998913i	$0.485155\pi$
$942$	16612.1	0.574576
$943$	−24339.7	−0.840519
$944$	47540.9	1.63911
$945$	−3125.68	−0.107596
$946$	8600.29	0.295581
$947$	−25412.5	−0.872012	−0.436006	−	0.899944i	$-0.643607\pi$
$947$	−25412.5	−0.872012	−0.436006	+	0.899944i	$0.643607\pi$
$948$	3173.56	0.108726
$949$	86473.2	2.95789
$950$	6793.51	0.232011
$951$	11271.3	0.384329
$952$	38477.0	1.30992
$953$	−46599.6	−1.58395	−0.791977	−	0.610551i	$-0.790948\pi$
$953$	−46599.6	−1.58395	−0.791977	+	0.610551i	$0.790948\pi$
$954$	−7348.85	−0.249400
$955$	−5943.39	−0.201386
$956$	3840.74	0.129935
$957$	3751.14	0.126705
$958$	−36205.4	−1.22103
$959$	13713.2	0.461755
$960$	−5779.76	−0.194313
$961$	−29591.0	−0.993287
$962$	−40553.7	−1.35915
$963$	−3019.46	−0.101039
$964$	−7603.56	−0.254040
$965$	−11282.2	−0.376359
$966$	−37625.9	−1.25320
$967$	−12852.9	−0.427426	−0.213713	−	0.976896i	$-0.568556\pi$
$967$	−12852.9	−0.427426	−0.213713	+	0.976896i	$0.568556\pi$
$968$	10598.6	0.351914
$969$	−21920.0	−0.726701
$970$	−14569.7	−0.482273
$971$	−43098.2	−1.42439	−0.712196	−	0.701980i	$-0.752299\pi$
$971$	−43098.2	−1.42439	−0.712196	+	0.701980i	$0.752299\pi$
$972$	360.007	0.0118799
$973$	45847.7	1.51060
$974$	27084.1	0.890998
$975$	−5596.30	−0.183821
$976$	28483.0	0.934137
$977$	−32446.8	−1.06250	−0.531251	−	0.847215i	$-0.678278\pi$
$977$	−32446.8	−1.06250	−0.531251	+	0.847215i	$0.678278\pi$
$978$	−3312.43	−0.108303
$979$	22350.0	0.729632
$980$	−1430.17	−0.0466176
$981$	−6925.49	−0.225396
$982$	45507.1	1.47881
$983$	−16990.2	−0.551276	−0.275638	−	0.961262i	$-0.588889\pi$
$983$	−16990.2	−0.551276	−0.275638	+	0.961262i	$0.588889\pi$
$984$	−8331.17	−0.269906
$985$	4722.75	0.152771
$986$	7393.36	0.238796
$987$	−7039.12	−0.227009
$988$	9755.71	0.314140
$989$	11395.8	0.366397
$990$	−5974.41	−0.191797
$991$	−28350.3	−0.908757	−0.454379	−	0.890809i	$-0.650139\pi$
$991$	−28350.3	−0.908757	−0.454379	+	0.890809i	$0.650139\pi$
$992$	936.615	0.0299774
$993$	8651.61	0.276486
$994$	72329.1	2.30799
$995$	864.671	0.0275497
$996$	3322.38	0.105696
$997$	−41329.0	−1.31284	−0.656420	−	0.754396i	$-0.727930\pi$
$997$	−41329.0	−1.31284	−0.656420	+	0.754396i	$0.727930\pi$
$998$	−33689.6	−1.06856
$999$	−4765.58	−0.150927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.j.1.2	✓	7
3.2	odd	2		1305.4.a.m.1.6		7
5.4	even	2		2175.4.a.m.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.j.1.2	✓	7	1.1	even	1	trivial
1305.4.a.m.1.6		7	3.2	odd	2
2175.4.a.m.1.6		7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q-3.07921 q^{2} +3.00000 q^{3} +1.48151 q^{4} -5.00000 q^{5} -9.23762 q^{6} +23.1532 q^{7} +20.0718 q^{8} +9.00000 q^{9} +15.3960 q^{10} -43.1165 q^{11} +4.44453 q^{12} -74.6173 q^{13} -71.2934 q^{14} -15.0000 q^{15} -73.6572 q^{16} +82.7951 q^{17} -27.7129 q^{18} -88.2501 q^{19} -7.40754 q^{20} +69.4596 q^{21} +132.765 q^{22} +175.920 q^{23} +60.2153 q^{24} +25.0000 q^{25} +229.762 q^{26} +27.0000 q^{27} +34.3016 q^{28} -29.0000 q^{29} +46.1881 q^{30} +14.1415 q^{31} +66.2315 q^{32} -129.350 q^{33} -254.943 q^{34} -115.766 q^{35} +13.3336 q^{36} -176.503 q^{37} +271.740 q^{38} -223.852 q^{39} -100.359 q^{40} -138.356 q^{41} -213.880 q^{42} +64.7784 q^{43} -63.8775 q^{44} -45.0000 q^{45} -541.695 q^{46} -101.341 q^{47} -220.972 q^{48} +193.070 q^{49} -76.9801 q^{50} +248.385 q^{51} -110.546 q^{52} +265.178 q^{53} -83.1386 q^{54} +215.583 q^{55} +464.726 q^{56} -264.750 q^{57} +89.2970 q^{58} -645.434 q^{59} -22.2226 q^{60} -386.696 q^{61} -43.5447 q^{62} +208.379 q^{63} +385.317 q^{64} +373.087 q^{65} +398.294 q^{66} -737.103 q^{67} +122.662 q^{68} +527.761 q^{69} +356.467 q^{70} -1014.53 q^{71} +180.646 q^{72} -1158.89 q^{73} +543.489 q^{74} +75.0000 q^{75} -130.743 q^{76} -998.285 q^{77} +689.286 q^{78} +714.039 q^{79} +368.286 q^{80} +81.0000 q^{81} +426.027 q^{82} +747.521 q^{83} +102.905 q^{84} -413.976 q^{85} -199.466 q^{86} -87.0000 q^{87} -865.426 q^{88} -518.363 q^{89} +138.564 q^{90} -1727.63 q^{91} +260.628 q^{92} +42.4246 q^{93} +312.051 q^{94} +441.250 q^{95} +198.694 q^{96} -946.328 q^{97} -594.502 q^{98} -388.049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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