LMFDB - Embedded newform 435.4.a.j.1.4

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			1.4
Root			$1.10304$ 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)

$f(q)$	$=$	\(q-1.10304 q^{2} +3.00000 q^{3} -6.78329 q^{4} -5.00000 q^{5} -3.30913 q^{6} +1.72550 q^{7} +16.3066 q^{8} +9.00000 q^{9} +5.51522 q^{10} +30.1148 q^{11} -20.3499 q^{12} -36.1424 q^{13} -1.90330 q^{14} -15.0000 q^{15} +36.2794 q^{16} -107.562 q^{17} -9.92739 q^{18} +131.520 q^{19} +33.9165 q^{20} +5.17649 q^{21} -33.2180 q^{22} +35.9830 q^{23} +48.9199 q^{24} +25.0000 q^{25} +39.8666 q^{26} +27.0000 q^{27} -11.7046 q^{28} -29.0000 q^{29} +16.5457 q^{30} -295.258 q^{31} -170.471 q^{32} +90.3445 q^{33} +118.646 q^{34} -8.62749 q^{35} -61.0496 q^{36} +211.958 q^{37} -145.073 q^{38} -108.427 q^{39} -81.5331 q^{40} -273.607 q^{41} -5.70990 q^{42} -508.456 q^{43} -204.278 q^{44} -45.0000 q^{45} -39.6908 q^{46} -238.686 q^{47} +108.838 q^{48} -340.023 q^{49} -27.5761 q^{50} -322.687 q^{51} +245.164 q^{52} +434.800 q^{53} -29.7822 q^{54} -150.574 q^{55} +28.1370 q^{56} +394.561 q^{57} +31.9883 q^{58} +92.3909 q^{59} +101.749 q^{60} -246.257 q^{61} +325.682 q^{62} +15.5295 q^{63} -102.199 q^{64} +180.712 q^{65} -99.6540 q^{66} -1025.31 q^{67} +729.627 q^{68} +107.949 q^{69} +9.51650 q^{70} -242.943 q^{71} +146.760 q^{72} +331.455 q^{73} -233.799 q^{74} +75.0000 q^{75} -892.140 q^{76} +51.9631 q^{77} +119.600 q^{78} -368.511 q^{79} -181.397 q^{80} +81.0000 q^{81} +301.801 q^{82} -480.424 q^{83} -35.1137 q^{84} +537.812 q^{85} +560.849 q^{86} -87.0000 q^{87} +491.071 q^{88} +680.610 q^{89} +49.6370 q^{90} -62.3636 q^{91} -244.083 q^{92} -885.773 q^{93} +263.281 q^{94} -657.601 q^{95} -511.412 q^{96} -1021.45 q^{97} +375.060 q^{98} +271.034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.10304	−0.389985	−0.194992	−	0.980805i	$-0.562468\pi$
$2$	−1.10304	−0.389985	−0.194992	+	0.980805i	$0.562468\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−6.78329	−0.847912
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−3.30913	−0.225158
$7$	1.72550	0.0931681	0.0465841	−	0.998914i	$-0.485166\pi$
$7$	1.72550	0.0931681	0.0465841	+	0.998914i	$0.485166\pi$
$8$	16.3066	0.720658
$9$	9.00000	0.333333
$10$	5.51522	0.174407
$11$	30.1148	0.825452	0.412726	−	0.910855i	$-0.364577\pi$
$11$	30.1148	0.825452	0.412726	+	0.910855i	$0.364577\pi$
$12$	−20.3499	−0.489542
$13$	−36.1424	−0.771083	−0.385542	−	0.922690i	$-0.625985\pi$
$13$	−36.1424	−0.771083	−0.385542	+	0.922690i	$0.625985\pi$
$14$	−1.90330	−0.0363342
$15$	−15.0000	−0.258199
$16$	36.2794	0.566866
$17$	−107.562	−1.53457	−0.767285	−	0.641306i	$-0.778393\pi$
$17$	−107.562	−1.53457	−0.767285	+	0.641306i	$0.778393\pi$
$18$	−9.92739	−0.129995
$19$	131.520	1.58804	0.794021	−	0.607890i	$-0.207984\pi$
$19$	131.520	1.58804	0.794021	+	0.607890i	$0.207984\pi$
$20$	33.9165	0.379198
$21$	5.17649	0.0537907
$22$	−33.2180	−0.321914
$23$	35.9830	0.326216	0.163108	−	0.986608i	$-0.447848\pi$
$23$	35.9830	0.326216	0.163108	+	0.986608i	$0.447848\pi$
$24$	48.9199	0.416072
$25$	25.0000	0.200000
$26$	39.8666	0.300711
$27$	27.0000	0.192450
$28$	−11.7046	−0.0789984
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	16.5457	0.100694
$31$	−295.258	−1.71064	−0.855320	−	0.518101i	$-0.826639\pi$
$31$	−295.258	−1.71064	−0.855320	+	0.518101i	$0.826639\pi$
$32$	−170.471	−0.941727
$33$	90.3445	0.476575
$34$	118.646	0.598459
$35$	−8.62749	−0.0416661
$36$	−61.0496	−0.282637
$37$	211.958	0.941776	0.470888	−	0.882193i	$-0.343934\pi$
$37$	211.958	0.941776	0.470888	+	0.882193i	$0.343934\pi$
$38$	−145.073	−0.619312
$39$	−108.427	−0.445185
$40$	−81.5331	−0.322288
$41$	−273.607	−1.04220	−0.521101	−	0.853495i	$-0.674479\pi$
$41$	−273.607	−1.04220	−0.521101	+	0.853495i	$0.674479\pi$
$42$	−5.70990	−0.0209775
$43$	−508.456	−1.80323	−0.901614	−	0.432542i	$-0.857617\pi$
$43$	−508.456	−1.80323	−0.901614	+	0.432542i	$0.857617\pi$
$44$	−204.278	−0.699910
$45$	−45.0000	−0.149071
$46$	−39.6908	−0.127219
$47$	−238.686	−0.740764	−0.370382	−	0.928879i	$-0.620773\pi$
$47$	−238.686	−0.740764	−0.370382	+	0.928879i	$0.620773\pi$
$48$	108.838	0.327280
$49$	−340.023	−0.991320
$50$	−27.5761	−0.0779970
$51$	−322.687	−0.885984
$52$	245.164	0.653811
$53$	434.800	1.12688	0.563438	−	0.826158i	$-0.309478\pi$
$53$	434.800	1.12688	0.563438	+	0.826158i	$0.309478\pi$
$54$	−29.7822	−0.0750526
$55$	−150.574	−0.369153
$56$	28.1370	0.0671423
$57$	394.561	0.916857
$58$	31.9883	0.0724184
$59$	92.3909	0.203869	0.101935	−	0.994791i	$-0.467497\pi$
$59$	92.3909	0.203869	0.101935	+	0.994791i	$0.467497\pi$
$60$	101.749	0.218930
$61$	−246.257	−0.516885	−0.258442	−	0.966027i	$-0.583209\pi$
$61$	−246.257	−0.516885	−0.258442	+	0.966027i	$0.583209\pi$
$62$	325.682	0.667123
$63$	15.5295	0.0310560
$64$	−102.199	−0.199607
$65$	180.712	0.344839
$66$	−99.6540	−0.185857
$67$	−1025.31	−1.86957	−0.934783	−	0.355218i	$-0.884407\pi$
$67$	−1025.31	−1.86957	−0.934783	+	0.355218i	$0.884407\pi$
$68$	729.627	1.30118
$69$	107.949	0.188341
$70$	9.51650	0.0162491
$71$	−242.943	−0.406086	−0.203043	−	0.979170i	$-0.565083\pi$
$71$	−242.943	−0.406086	−0.203043	+	0.979170i	$0.565083\pi$
$72$	146.760	0.240219
$73$	331.455	0.531423	0.265711	−	0.964053i	$-0.414393\pi$
$73$	331.455	0.531423	0.265711	+	0.964053i	$0.414393\pi$
$74$	−233.799	−0.367278
$75$	75.0000	0.115470
$76$	−892.140	−1.34652
$77$	51.9631	0.0769058
$78$	119.600	0.173616
$79$	−368.511	−0.524819	−0.262409	−	0.964957i	$-0.584517\pi$
$79$	−368.511	−0.524819	−0.262409	+	0.964957i	$0.584517\pi$
$80$	−181.397	−0.253510
$81$	81.0000	0.111111
$82$	301.801	0.406443
$83$	−480.424	−0.635342	−0.317671	−	0.948201i	$-0.602901\pi$
$83$	−480.424	−0.635342	−0.317671	+	0.948201i	$0.602901\pi$
$84$	−35.1137	−0.0456097
$85$	537.812	0.686281
$86$	560.849	0.703231
$87$	−87.0000	−0.107211
$88$	491.071	0.594868
$89$	680.610	0.810613	0.405306	−	0.914181i	$-0.367165\pi$
$89$	680.610	0.810613	0.405306	+	0.914181i	$0.367165\pi$
$90$	49.6370	0.0581355
$91$	−62.3636	−0.0718404
$92$	−244.083	−0.276602
$93$	−885.773	−0.987638
$94$	263.281	0.288887
$95$	−657.601	−0.710194
$96$	−511.412	−0.543706
$97$	−1021.45	−1.06920	−0.534599	−	0.845106i	$-0.679537\pi$
$97$	−1021.45	−1.06920	−0.534599	+	0.845106i	$0.679537\pi$
$98$	375.060	0.386600
$99$	271.034	0.275151
$100$	−169.582	−0.169582
$101$	−1096.18	−1.07994	−0.539968	−	0.841685i	$-0.681564\pi$
$101$	−1096.18	−1.07994	−0.539968	+	0.841685i	$0.681564\pi$
$102$	355.938	0.345521
$103$	−848.067	−0.811287	−0.405643	−	0.914031i	$-0.632952\pi$
$103$	−848.067	−0.811287	−0.405643	+	0.914031i	$0.632952\pi$
$104$	−589.360	−0.555687
$105$	−25.8825	−0.0240559
$106$	−479.604	−0.439465
$107$	−269.467	−0.243462	−0.121731	−	0.992563i	$-0.538844\pi$
$107$	−269.467	−0.243462	−0.121731	+	0.992563i	$0.538844\pi$
$108$	−183.149	−0.163181
$109$	1922.71	1.68956	0.844782	−	0.535111i	$-0.179730\pi$
$109$	1922.71	1.68956	0.844782	+	0.535111i	$0.179730\pi$
$110$	166.090	0.143964
$111$	635.875	0.543735
$112$	62.6001	0.0528139
$113$	−611.452	−0.509032	−0.254516	−	0.967069i	$-0.581916\pi$
$113$	−611.452	−0.509032	−0.254516	+	0.967069i	$0.581916\pi$
$114$	−435.218	−0.357560
$115$	−179.915	−0.145888
$116$	196.716	0.157453
$117$	−325.281	−0.257028
$118$	−101.911	−0.0795059
$119$	−185.599	−0.142973
$120$	−244.599	−0.186073
$121$	−424.096	−0.318630
$122$	271.632	0.201577
$123$	−820.822	−0.601716
$124$	2002.82	1.45047
$125$	−125.000	−0.0894427
$126$	−17.1297	−0.0121114
$127$	−1388.20	−0.969941	−0.484971	−	0.874530i	$-0.661170\pi$
$127$	−1388.20	−0.969941	−0.484971	+	0.874530i	$0.661170\pi$
$128$	1476.50	1.01957
$129$	−1525.37	−1.04109
$130$	−199.333	−0.134482
$131$	2965.45	1.97781	0.988904	−	0.148555i	$-0.0474622\pi$
$131$	2965.45	1.97781	0.988904	+	0.148555i	$0.0474622\pi$
$132$	−612.834	−0.404093
$133$	226.938	0.147955
$134$	1130.96	0.729103
$135$	−135.000	−0.0860663
$136$	−1753.98	−1.10590
$137$	133.181	0.0830539	0.0415269	−	0.999137i	$-0.486778\pi$
$137$	133.181	0.0830539	0.0415269	+	0.999137i	$0.486778\pi$
$138$	−119.072	−0.0734501
$139$	−857.897	−0.523495	−0.261748	−	0.965136i	$-0.584299\pi$
$139$	−857.897	−0.523495	−0.261748	+	0.965136i	$0.584299\pi$
$140$	58.5228	0.0353291
$141$	−716.058	−0.427680
$142$	267.977	0.158367
$143$	−1088.42	−0.636492
$144$	326.515	0.188955
$145$	145.000	0.0830455
$146$	−365.609	−0.207247
$147$	−1020.07	−0.572339
$148$	−1437.77	−0.798543
$149$	2706.16	1.48790	0.743949	−	0.668236i	$-0.232950\pi$
$149$	2706.16	1.48790	0.743949	+	0.668236i	$0.232950\pi$
$150$	−82.7283	−0.0450316
$151$	−3063.52	−1.65103	−0.825516	−	0.564379i	$-0.809116\pi$
$151$	−3063.52	−1.65103	−0.825516	+	0.564379i	$0.809116\pi$
$152$	2144.65	1.14443
$153$	−968.061	−0.511523
$154$	−57.3176	−0.0299921
$155$	1476.29	0.765021
$156$	735.493	0.377478
$157$	−1256.30	−0.638624	−0.319312	−	0.947650i	$-0.603452\pi$
$157$	−1256.30	−0.638624	−0.319312	+	0.947650i	$0.603452\pi$
$158$	406.483	0.204671
$159$	1304.40	0.650602
$160$	852.354	0.421153
$161$	62.0886	0.0303929
$162$	−89.3466	−0.0433317
$163$	3030.03	1.45601	0.728007	−	0.685570i	$-0.240447\pi$
$163$	3030.03	1.45601	0.728007	+	0.685570i	$0.240447\pi$
$164$	1855.96	0.883696
$165$	−451.723	−0.213131
$166$	529.929	0.247774
$167$	960.024	0.444844	0.222422	−	0.974951i	$-0.428604\pi$
$167$	960.024	0.444844	0.222422	+	0.974951i	$0.428604\pi$
$168$	84.4111	0.0387646
$169$	−890.730	−0.405430
$170$	−593.230	−0.267639
$171$	1183.68	0.529347
$172$	3449.01	1.52898
$173$	−894.411	−0.393068	−0.196534	−	0.980497i	$-0.562969\pi$
$173$	−894.411	−0.393068	−0.196534	+	0.980497i	$0.562969\pi$
$174$	95.9648	0.0418108
$175$	43.1375	0.0186336
$176$	1092.55	0.467921
$177$	277.173	0.117704
$178$	−750.743	−0.316127
$179$	3389.40	1.41529	0.707643	−	0.706571i	$-0.249759\pi$
$179$	3389.40	1.41529	0.707643	+	0.706571i	$0.249759\pi$
$180$	305.248	0.126399
$181$	−2631.46	−1.08063	−0.540317	−	0.841461i	$-0.681696\pi$
$181$	−2631.46	−1.08063	−0.540317	+	0.841461i	$0.681696\pi$
$182$	68.7897	0.0280167
$183$	−738.771	−0.298424
$184$	586.761	0.235090
$185$	−1059.79	−0.421175
$186$	977.046	0.385164
$187$	−3239.22	−1.26671
$188$	1619.08	0.628103
$189$	46.5885	0.0179302
$190$	725.363	0.276965
$191$	−72.3828	−0.0274211	−0.0137106	−	0.999906i	$-0.504364\pi$
$191$	−72.3828	−0.0274211	−0.0137106	+	0.999906i	$0.504364\pi$
$192$	−306.596	−0.115243
$193$	−142.793	−0.0532564	−0.0266282	−	0.999645i	$-0.508477\pi$
$193$	−142.793	−0.0532564	−0.0266282	+	0.999645i	$0.508477\pi$
$194$	1126.70	0.416971
$195$	542.135	0.199093
$196$	2306.47	0.840552
$197$	546.378	0.197603	0.0988016	−	0.995107i	$-0.468499\pi$
$197$	546.378	0.197603	0.0988016	+	0.995107i	$0.468499\pi$
$198$	−298.962	−0.107305
$199$	−67.5285	−0.0240551	−0.0120276	−	0.999928i	$-0.503829\pi$
$199$	−67.5285	−0.0240551	−0.0120276	+	0.999928i	$0.503829\pi$
$200$	407.666	0.144132
$201$	−3075.92	−1.07939
$202$	1209.13	0.421159
$203$	−50.0394	−0.0173009
$204$	2188.88	0.751237
$205$	1368.04	0.466087
$206$	935.455	0.316390
$207$	323.847	0.108739
$208$	−1311.22	−0.437101
$209$	3960.71	1.31085
$210$	28.5495	0.00938144
$211$	5186.13	1.69208	0.846038	−	0.533123i	$-0.178982\pi$
$211$	5186.13	1.69208	0.846038	+	0.533123i	$0.178982\pi$
$212$	−2949.38	−0.955491
$213$	−728.830	−0.234454
$214$	297.234	0.0949464
$215$	2542.28	0.806428
$216$	440.279	0.138691
$217$	−509.466	−0.159377
$218$	−2120.84	−0.658904
$219$	994.365	0.306817
$220$	1021.39	0.313009
$221$	3887.55	1.18328
$222$	−701.398	−0.212048
$223$	2909.82	0.873795	0.436897	−	0.899511i	$-0.356077\pi$
$223$	2909.82	0.873795	0.436897	+	0.899511i	$0.356077\pi$
$224$	−294.147	−0.0877390
$225$	225.000	0.0666667
$226$	674.459	0.198515
$227$	5506.65	1.61009	0.805043	−	0.593217i	$-0.202142\pi$
$227$	5506.65	1.61009	0.805043	+	0.593217i	$0.202142\pi$
$228$	−2676.42	−0.777414
$229$	632.465	0.182509	0.0912543	−	0.995828i	$-0.470912\pi$
$229$	632.465	0.182509	0.0912543	+	0.995828i	$0.470912\pi$
$230$	198.454	0.0568942
$231$	155.889	0.0444016
$232$	−472.892	−0.133823
$233$	5105.62	1.43554	0.717769	−	0.696281i	$-0.245163\pi$
$233$	5105.62	1.43554	0.717769	+	0.696281i	$0.245163\pi$
$234$	358.799	0.100237
$235$	1193.43	0.331280
$236$	−626.715	−0.172863
$237$	−1105.53	−0.303004
$238$	204.723	0.0557573
$239$	−6409.22	−1.73464	−0.867318	−	0.497755i	$-0.834158\pi$
$239$	−6409.22	−1.73464	−0.867318	+	0.497755i	$0.834158\pi$
$240$	−544.192	−0.146364
$241$	1462.61	0.390934	0.195467	−	0.980710i	$-0.437378\pi$
$241$	1462.61	0.390934	0.195467	+	0.980710i	$0.437378\pi$
$242$	467.797	0.124261
$243$	243.000	0.0641500
$244$	1670.43	0.438273
$245$	1700.11	0.443332
$246$	905.403	0.234660
$247$	−4753.45	−1.22451
$248$	−4814.65	−1.23279
$249$	−1441.27	−0.366815
$250$	137.880	0.0348813
$251$	−2363.88	−0.594451	−0.297225	−	0.954807i	$-0.596061\pi$
$251$	−2363.88	−0.594451	−0.297225	+	0.954807i	$0.596061\pi$
$252$	−105.341	−0.0263328
$253$	1083.62	0.269276
$254$	1531.24	0.378262
$255$	1613.43	0.396224
$256$	−811.050	−0.198010
$257$	−3749.02	−0.909950	−0.454975	−	0.890504i	$-0.650352\pi$
$257$	−3749.02	−0.909950	−0.454975	+	0.890504i	$0.650352\pi$
$258$	1682.55	0.406011
$259$	365.733	0.0877435
$260$	−1225.82	−0.292393
$261$	−261.000	−0.0618984
$262$	−3271.03	−0.771315
$263$	742.796	0.174155	0.0870775	−	0.996202i	$-0.472247\pi$
$263$	742.796	0.174155	0.0870775	+	0.996202i	$0.472247\pi$
$264$	1473.21	0.343447
$265$	−2174.00	−0.503954
$266$	−250.322	−0.0577002
$267$	2041.83	0.468007
$268$	6954.95	1.58523
$269$	2588.34	0.586668	0.293334	−	0.956010i	$-0.405235\pi$
$269$	2588.34	0.586668	0.293334	+	0.956010i	$0.405235\pi$
$270$	148.911	0.0335646
$271$	−7715.20	−1.72939	−0.864696	−	0.502296i	$-0.832489\pi$
$271$	−7715.20	−1.72939	−0.864696	+	0.502296i	$0.832489\pi$
$272$	−3902.30	−0.869896
$273$	−187.091	−0.0414771
$274$	−146.904	−0.0323898
$275$	752.871	0.165090
$276$	−732.249	−0.159696
$277$	−6609.81	−1.43374	−0.716868	−	0.697209i	$-0.754425\pi$
$277$	−6609.81	−1.43374	−0.716868	+	0.697209i	$0.754425\pi$
$278$	946.298	0.204155
$279$	−2657.32	−0.570213
$280$	−140.685	−0.0300270
$281$	7909.91	1.67924	0.839618	−	0.543177i	$-0.182779\pi$
$281$	7909.91	1.67924	0.839618	+	0.543177i	$0.182779\pi$
$282$	789.843	0.166789
$283$	−2550.41	−0.535710	−0.267855	−	0.963459i	$-0.586315\pi$
$283$	−2550.41	−0.535710	−0.267855	+	0.963459i	$0.586315\pi$
$284$	1647.96	0.344325
$285$	−1972.80	−0.410031
$286$	1200.58	0.248222
$287$	−472.109	−0.0971001
$288$	−1534.24	−0.313909
$289$	6656.65	1.35491
$290$	−159.941	−0.0323865
$291$	−3064.34	−0.617302
$292$	−2248.36	−0.450600
$293$	−7477.34	−1.49089	−0.745446	−	0.666566i	$-0.767763\pi$
$293$	−7477.34	−1.49089	−0.745446	+	0.666566i	$0.767763\pi$
$294$	1125.18	0.223203
$295$	−461.955	−0.0911730
$296$	3456.32	0.678698
$297$	813.101	0.158858
$298$	−2985.01	−0.580258
$299$	−1300.51	−0.251540
$300$	−508.747	−0.0979084
$301$	−877.340	−0.168003
$302$	3379.20	0.643877
$303$	−3288.53	−0.623502
$304$	4771.48	0.900207
$305$	1231.28	0.231158
$306$	1067.81	0.199486
$307$	6194.09	1.15152	0.575758	−	0.817620i	$-0.304707\pi$
$307$	6194.09	1.15152	0.575758	+	0.817620i	$0.304707\pi$
$308$	−352.481	−0.0652093
$309$	−2544.20	−0.468397
$310$	−1628.41	−0.298347
$311$	−771.827	−0.140728	−0.0703638	−	0.997521i	$-0.522416\pi$
$311$	−771.827	−0.140728	−0.0703638	+	0.997521i	$0.522416\pi$
$312$	−1768.08	−0.320826
$313$	−7320.30	−1.32194	−0.660971	−	0.750411i	$-0.729856\pi$
$313$	−7320.30	−1.32194	−0.660971	+	0.750411i	$0.729856\pi$
$314$	1385.76	0.249054
$315$	−77.6474	−0.0138887
$316$	2499.72	0.445000
$317$	3074.20	0.544682	0.272341	−	0.962201i	$-0.412202\pi$
$317$	3074.20	0.544682	0.272341	+	0.962201i	$0.412202\pi$
$318$	−1438.81	−0.253725
$319$	−873.330	−0.153282
$320$	510.994	0.0892669
$321$	−808.402	−0.140563
$322$	−68.4864	−0.0118528
$323$	−14146.6	−2.43696
$324$	−549.447	−0.0942124
$325$	−903.559	−0.154217
$326$	−3342.26	−0.567824
$327$	5768.14	0.975470
$328$	−4461.61	−0.751071
$329$	−411.852	−0.0690156
$330$	498.270	0.0831177
$331$	−9558.97	−1.58734	−0.793669	−	0.608350i	$-0.791832\pi$
$331$	−9558.97	−1.58734	−0.793669	+	0.608350i	$0.791832\pi$
$332$	3258.86	0.538714
$333$	1907.62	0.313925
$334$	−1058.95	−0.173482
$335$	5126.53	0.836096
$336$	187.800	0.0304921
$337$	5645.65	0.912576	0.456288	−	0.889832i	$-0.349179\pi$
$337$	5645.65	0.912576	0.456288	+	0.889832i	$0.349179\pi$
$338$	982.515	0.158112
$339$	−1834.36	−0.293890
$340$	−3648.13	−0.581905
$341$	−8891.63	−1.41205
$342$	−1305.65	−0.206437
$343$	−1178.55	−0.185528
$344$	−8291.20	−1.29951
$345$	−539.745	−0.0842286
$346$	986.574	0.153291
$347$	−8043.06	−1.24431	−0.622153	−	0.782896i	$-0.713742\pi$
$347$	−8043.06	−1.24431	−0.622153	+	0.782896i	$0.713742\pi$
$348$	590.147	0.0909057
$349$	4166.95	0.639117	0.319559	−	0.947567i	$-0.396465\pi$
$349$	4166.95	0.639117	0.319559	+	0.947567i	$0.396465\pi$
$350$	−47.5825	−0.00726683
$351$	−975.844	−0.148395
$352$	−5133.70	−0.777350
$353$	−9367.10	−1.41235	−0.706176	−	0.708036i	$-0.749581\pi$
$353$	−9367.10	−1.41235	−0.706176	+	0.708036i	$0.749581\pi$
$354$	−305.734	−0.0459027
$355$	1214.72	0.181607
$356$	−4616.78	−0.687328
$357$	−556.796	−0.0825455
$358$	−3738.66	−0.551940
$359$	−7379.61	−1.08491	−0.542453	−	0.840086i	$-0.682504\pi$
$359$	−7379.61	−1.08491	−0.542453	+	0.840086i	$0.682504\pi$
$360$	−733.798	−0.107429
$361$	10438.6	1.52188
$362$	2902.62	0.421431
$363$	−1272.29	−0.183961
$364$	423.030	0.0609143
$365$	−1657.27	−0.237659
$366$	814.897	0.116381
$367$	−1182.86	−0.168242	−0.0841208	−	0.996456i	$-0.526808\pi$
$367$	−1182.86	−0.168242	−0.0841208	+	0.996456i	$0.526808\pi$
$368$	1305.44	0.184921
$369$	−2462.47	−0.347401
$370$	1169.00	0.164252
$371$	750.247	0.104989
$372$	6008.46	0.837430
$373$	−4056.42	−0.563092	−0.281546	−	0.959548i	$-0.590847\pi$
$373$	−4056.42	−0.563092	−0.281546	+	0.959548i	$0.590847\pi$
$374$	3573.00	0.493999
$375$	−375.000	−0.0516398
$376$	−3892.16	−0.533837
$377$	1048.13	0.143187
$378$	−51.3891	−0.00699251
$379$	12203.7	1.65399	0.826995	−	0.562209i	$-0.190048\pi$
$379$	12203.7	1.65399	0.826995	+	0.562209i	$0.190048\pi$
$380$	4460.70	0.602182
$381$	−4164.59	−0.559996
$382$	79.8414	0.0106938
$383$	−11970.1	−1.59698	−0.798488	−	0.602011i	$-0.794366\pi$
$383$	−11970.1	−1.59698	−0.798488	+	0.602011i	$0.794366\pi$
$384$	4429.49	0.588649
$385$	−259.816	−0.0343933
$386$	157.507	0.0207692
$387$	−4576.10	−0.601076
$388$	6928.77	0.906585
$389$	−1476.58	−0.192456	−0.0962280	−	0.995359i	$-0.530678\pi$
$389$	−1476.58	−0.192456	−0.0962280	+	0.995359i	$0.530678\pi$
$390$	−597.999	−0.0776432
$391$	−3870.41	−0.500601
$392$	−5544.62	−0.714402
$393$	8896.36	1.14189
$394$	−602.679	−0.0770622
$395$	1842.55	0.234706
$396$	−1838.50	−0.233303
$397$	−2728.51	−0.344937	−0.172469	−	0.985015i	$-0.555174\pi$
$397$	−2728.51	−0.344937	−0.172469	+	0.985015i	$0.555174\pi$
$398$	74.4869	0.00938113
$399$	680.814	0.0854218
$400$	906.986	0.113373
$401$	810.223	0.100899	0.0504496	−	0.998727i	$-0.483935\pi$
$401$	810.223	0.100899	0.0504496	+	0.998727i	$0.483935\pi$
$402$	3392.87	0.420948
$403$	10671.3	1.31905
$404$	7435.68	0.915691
$405$	−405.000	−0.0496904
$406$	55.1957	0.00674709
$407$	6383.09	0.777390
$408$	−5261.93	−0.638492
$409$	8303.55	1.00387	0.501937	−	0.864904i	$-0.332621\pi$
$409$	8303.55	1.00387	0.501937	+	0.864904i	$0.332621\pi$
$410$	−1509.01	−0.181767
$411$	399.542	0.0479512
$412$	5752.69	0.687900
$413$	159.420	0.0189941
$414$	−357.217	−0.0424064
$415$	2402.12	0.284134
$416$	6161.22	0.726150
$417$	−2573.69	−0.302240
$418$	−4368.84	−0.511212
$419$	12437.2	1.45011	0.725055	−	0.688690i	$-0.241814\pi$
$419$	12437.2	1.45011	0.725055	+	0.688690i	$0.241814\pi$
$420$	175.568	0.0203973
$421$	14668.3	1.69808	0.849038	−	0.528333i	$-0.177183\pi$
$421$	14668.3	1.69808	0.849038	+	0.528333i	$0.177183\pi$
$422$	−5720.53	−0.659884
$423$	−2148.17	−0.246921
$424$	7090.12	0.812092
$425$	−2689.06	−0.306914
$426$	803.932	0.0914334
$427$	−424.916	−0.0481572
$428$	1827.88	0.206434
$429$	−3265.26	−0.367479
$430$	−2804.25	−0.314495
$431$	12377.8	1.38334	0.691669	−	0.722214i	$-0.256876\pi$
$431$	12377.8	1.38334	0.691669	+	0.722214i	$0.256876\pi$
$432$	979.545	0.109093
$433$	−14713.2	−1.63296	−0.816481	−	0.577372i	$-0.804078\pi$
$433$	−14713.2	−1.63296	−0.816481	+	0.577372i	$0.804078\pi$
$434$	561.964	0.0621547
$435$	435.000	0.0479463
$436$	−13042.3	−1.43260
$437$	4732.49	0.518045
$438$	−1096.83	−0.119654
$439$	−15732.7	−1.71044	−0.855219	−	0.518267i	$-0.826577\pi$
$439$	−15732.7	−1.71044	−0.855219	+	0.518267i	$0.826577\pi$
$440$	−2455.36	−0.266033
$441$	−3060.20	−0.330440
$442$	−4288.14	−0.461462
$443$	3429.39	0.367799	0.183900	−	0.982945i	$-0.441128\pi$
$443$	3429.39	0.367799	0.183900	+	0.982945i	$0.441128\pi$
$444$	−4313.32	−0.461039
$445$	−3403.05	−0.362517
$446$	−3209.66	−0.340767
$447$	8118.47	0.859039
$448$	−176.344	−0.0185970
$449$	651.040	0.0684287	0.0342143	−	0.999415i	$-0.489107\pi$
$449$	651.040	0.0684287	0.0342143	+	0.999415i	$0.489107\pi$
$450$	−248.185	−0.0259990
$451$	−8239.64	−0.860288
$452$	4147.66	0.431614
$453$	−9190.56	−0.953224
$454$	−6074.08	−0.627909
$455$	311.818	0.0321280
$456$	6433.95	0.660740
$457$	5567.93	0.569928	0.284964	−	0.958538i	$-0.408018\pi$
$457$	5567.93	0.569928	0.284964	+	0.958538i	$0.408018\pi$
$458$	−697.637	−0.0711756
$459$	−2904.18	−0.295328
$460$	1220.42	0.123700
$461$	−1231.35	−0.124403	−0.0622016	−	0.998064i	$-0.519812\pi$
$461$	−1231.35	−0.124403	−0.0622016	+	0.998064i	$0.519812\pi$
$462$	−171.953	−0.0173159
$463$	2241.38	0.224980	0.112490	−	0.993653i	$-0.464117\pi$
$463$	2241.38	0.224980	0.112490	+	0.993653i	$0.464117\pi$
$464$	−1052.10	−0.105264
$465$	4428.86	0.441685
$466$	−5631.73	−0.559838
$467$	−17434.9	−1.72760	−0.863801	−	0.503834i	$-0.831922\pi$
$467$	−17434.9	−1.72760	−0.863801	+	0.503834i	$0.831922\pi$
$468$	2206.48	0.217937
$469$	−1769.16	−0.174184
$470$	−1316.41	−0.129194
$471$	−3768.91	−0.368710
$472$	1506.58	0.146920
$473$	−15312.1	−1.48848
$474$	1219.45	0.118167
$475$	3288.00	0.317608
$476$	1258.97	0.121229
$477$	3913.20	0.375625
$478$	7069.65	0.676482
$479$	10014.3	0.955248	0.477624	−	0.878564i	$-0.341498\pi$
$479$	10014.3	0.955248	0.477624	+	0.878564i	$0.341498\pi$
$480$	2557.06	0.243153
$481$	−7660.67	−0.726188
$482$	−1613.32	−0.152458
$483$	186.266	0.0175474
$484$	2876.77	0.270170
$485$	5107.23	0.478160
$486$	−268.040	−0.0250175
$487$	869.838	0.0809366	0.0404683	−	0.999181i	$-0.487115\pi$
$487$	869.838	0.0809366	0.0404683	+	0.999181i	$0.487115\pi$
$488$	−4015.62	−0.372497
$489$	9090.09	0.840630
$490$	−1875.30	−0.172893
$491$	−539.113	−0.0495516	−0.0247758	−	0.999693i	$-0.507887\pi$
$491$	−539.113	−0.0495516	−0.0247758	+	0.999693i	$0.507887\pi$
$492$	5567.88	0.510202
$493$	3119.31	0.284963
$494$	5243.26	0.477542
$495$	−1355.17	−0.123051
$496$	−10711.8	−0.969703
$497$	−419.199	−0.0378343
$498$	1589.79	0.143052
$499$	13992.3	1.25527	0.627636	−	0.778507i	$-0.284023\pi$
$499$	13992.3	1.25527	0.627636	+	0.778507i	$0.284023\pi$
$500$	847.912	0.0758395
$501$	2880.07	0.256831
$502$	2607.47	0.231827
$503$	6527.85	0.578653	0.289326	−	0.957231i	$-0.406569\pi$
$503$	6527.85	0.578653	0.289326	+	0.957231i	$0.406569\pi$
$504$	253.233	0.0223808
$505$	5480.88	0.482962
$506$	−1195.28	−0.105013
$507$	−2672.19	−0.234075
$508$	9416.55	0.822425
$509$	7495.40	0.652707	0.326354	−	0.945248i	$-0.394180\pi$
$509$	7495.40	0.652707	0.326354	+	0.945248i	$0.394180\pi$
$510$	−1779.69	−0.154521
$511$	571.925	0.0495117
$512$	−10917.3	−0.942350
$513$	3551.05	0.305619
$514$	4135.33	0.354867
$515$	4240.34	0.362818
$516$	10347.0	0.882756
$517$	−7187.99	−0.611465
$518$	−403.420	−0.0342187
$519$	−2683.23	−0.226938
$520$	2946.80	0.248511
$521$	−17023.1	−1.43147	−0.715733	−	0.698374i	$-0.753907\pi$
$521$	−17023.1	−1.43147	−0.715733	+	0.698374i	$0.753907\pi$
$522$	287.894	0.0241395
$523$	−12295.3	−1.02798	−0.513991	−	0.857796i	$-0.671834\pi$
$523$	−12295.3	−1.02798	−0.513991	+	0.857796i	$0.671834\pi$
$524$	−20115.5	−1.67701
$525$	129.412	0.0107581
$526$	−819.336	−0.0679178
$527$	31758.6	2.62510
$528$	3277.65	0.270154
$529$	−10872.2	−0.893583
$530$	2398.02	0.196535
$531$	831.518	0.0679564
$532$	−1539.39	−0.125453
$533$	9888.82	0.803625
$534$	−2252.23	−0.182516
$535$	1347.34	0.108879
$536$	−16719.3	−1.34732
$537$	10168.2	0.817115
$538$	−2855.05	−0.228792
$539$	−10239.7	−0.818286
$540$	915.745	0.0729766
$541$	−9530.45	−0.757386	−0.378693	−	0.925522i	$-0.623626\pi$
$541$	−9530.45	−0.757386	−0.378693	+	0.925522i	$0.623626\pi$
$542$	8510.21	0.674437
$543$	−7894.38	−0.623905
$544$	18336.2	1.44515
$545$	−9613.56	−0.755596
$546$	206.369	0.0161754
$547$	−8818.09	−0.689277	−0.344638	−	0.938736i	$-0.611998\pi$
$547$	−8818.09	−0.689277	−0.344638	+	0.938736i	$0.611998\pi$
$548$	−903.403	−0.0704224
$549$	−2216.31	−0.172295
$550$	−830.450	−0.0643827
$551$	−3814.09	−0.294892
$552$	1760.28	0.135729
$553$	−635.865	−0.0488964
$554$	7290.91	0.559135
$555$	−3179.37	−0.243166
$556$	5819.37	0.443878
$557$	−21207.0	−1.61323	−0.806615	−	0.591077i	$-0.798703\pi$
$557$	−21207.0	−1.61323	−0.806615	+	0.591077i	$0.798703\pi$
$558$	2931.14	0.222374
$559$	18376.8	1.39044
$560$	−313.000	−0.0236191
$561$	−9717.67	−0.731337
$562$	−8724.97	−0.654877
$563$	23507.2	1.75970	0.879848	−	0.475255i	$-0.157644\pi$
$563$	23507.2	1.75970	0.879848	+	0.475255i	$0.157644\pi$
$564$	4857.23	0.362635
$565$	3057.26	0.227646
$566$	2813.21	0.208919
$567$	139.765	0.0103520
$568$	−3961.59	−0.292649
$569$	−16083.3	−1.18497	−0.592483	−	0.805583i	$-0.701852\pi$
$569$	−16083.3	−1.18497	−0.592483	+	0.805583i	$0.701852\pi$
$570$	2176.09	0.159906
$571$	14.6852	0.00107628	0.000538140	−	1.00000i	$-0.499829\pi$
$571$	14.6852	0.00107628	0.000538140		1.00000i	$0.499829\pi$
$572$	7383.08	0.539689
$573$	−217.148	−0.0158316
$574$	520.757	0.0378676
$575$	899.574	0.0652432
$576$	−919.788	−0.0665356
$577$	4709.43	0.339785	0.169893	−	0.985463i	$-0.445658\pi$
$577$	4709.43	0.339785	0.169893	+	0.985463i	$0.445658\pi$
$578$	−7342.58	−0.528393
$579$	−428.380	−0.0307476
$580$	−983.578	−0.0704152
$581$	−828.971	−0.0591936
$582$	3380.10	0.240738
$583$	13093.9	0.930181
$584$	5404.91	0.382974
$585$	1626.41	0.114946
$586$	8247.84	0.581425
$587$	9373.45	0.659086	0.329543	−	0.944141i	$-0.393105\pi$
$587$	9373.45	0.659086	0.329543	+	0.944141i	$0.393105\pi$
$588$	6919.42	0.485293
$589$	−38832.3	−2.71657
$590$	509.556	0.0355561
$591$	1639.13	0.114086
$592$	7689.72	0.533861
$593$	13373.3	0.926095	0.463047	−	0.886333i	$-0.346756\pi$
$593$	13373.3	0.926095	0.463047	+	0.886333i	$0.346756\pi$
$594$	−896.886	−0.0619523
$595$	927.993	0.0639395
$596$	−18356.6	−1.26161
$597$	−202.585	−0.0138882
$598$	1434.52	0.0980967
$599$	−8704.03	−0.593718	−0.296859	−	0.954921i	$-0.595939\pi$
$599$	−8704.03	−0.593718	−0.296859	+	0.954921i	$0.595939\pi$
$600$	1223.00	0.0832144
$601$	24136.6	1.63819	0.819095	−	0.573658i	$-0.194476\pi$
$601$	24136.6	1.63819	0.819095	+	0.573658i	$0.194476\pi$
$602$	967.744	0.0655188
$603$	−9227.75	−0.623189
$604$	20780.8	1.39993
$605$	2120.48	0.142496
$606$	3627.39	0.243156
$607$	−25507.2	−1.70561	−0.852804	−	0.522231i	$-0.825100\pi$
$607$	−25507.2	−1.70561	−0.852804	+	0.522231i	$0.825100\pi$
$608$	−22420.4	−1.49550
$609$	−150.118	−0.00998867
$610$	−1358.16	−0.0901481
$611$	8626.67	0.571191
$612$	6566.64	0.433727
$613$	14819.5	0.976431	0.488216	−	0.872723i	$-0.337648\pi$
$613$	14819.5	0.976431	0.488216	+	0.872723i	$0.337648\pi$
$614$	−6832.35	−0.449074
$615$	4104.11	0.269096
$616$	847.343	0.0554227
$617$	9092.57	0.593279	0.296639	−	0.954990i	$-0.404134\pi$
$617$	9092.57	0.593279	0.296639	+	0.954990i	$0.404134\pi$
$618$	2806.37	0.182668
$619$	20874.2	1.35542	0.677711	−	0.735328i	$-0.262972\pi$
$619$	20874.2	1.35542	0.677711	+	0.735328i	$0.262972\pi$
$620$	−10014.1	−0.648670
$621$	971.540	0.0627803
$622$	851.359	0.0548817
$623$	1174.39	0.0755233
$624$	−3933.67	−0.252360
$625$	625.000	0.0400000
$626$	8074.62	0.515538
$627$	11882.1	0.756821
$628$	8521.89	0.541497
$629$	−22798.7	−1.44522
$630$	85.6485	0.00541638
$631$	−1658.34	−0.104624	−0.0523118	−	0.998631i	$-0.516659\pi$
$631$	−1658.34	−0.104624	−0.0523118	+	0.998631i	$0.516659\pi$
$632$	−6009.17	−0.378215
$633$	15558.4	0.976921
$634$	−3390.98	−0.212418
$635$	6940.98	0.433771
$636$	−8848.14	−0.551653
$637$	12289.2	0.764390
$638$	963.322	0.0597779
$639$	−2186.49	−0.135362
$640$	−7382.48	−0.455966
$641$	−9114.17	−0.561604	−0.280802	−	0.959766i	$-0.590600\pi$
$641$	−9114.17	−0.561604	−0.280802	+	0.959766i	$0.590600\pi$
$642$	891.703	0.0548173
$643$	−4661.18	−0.285877	−0.142938	−	0.989732i	$-0.545655\pi$
$643$	−4661.18	−0.285877	−0.142938	+	0.989732i	$0.545655\pi$
$644$	−421.165	−0.0257705
$645$	7626.84	0.465591
$646$	15604.3	0.950378
$647$	11020.7	0.669657	0.334828	−	0.942279i	$-0.391322\pi$
$647$	11020.7	0.669657	0.334828	+	0.942279i	$0.391322\pi$
$648$	1320.84	0.0800731
$649$	2782.34	0.168284
$650$	996.665	0.0601422
$651$	−1528.40	−0.0920164
$652$	−20553.6	−1.23457
$653$	28163.5	1.68778	0.843892	−	0.536513i	$-0.180259\pi$
$653$	28163.5	1.68778	0.843892	+	0.536513i	$0.180259\pi$
$654$	−6362.51	−0.380418
$655$	−14827.3	−0.884503
$656$	−9926.32	−0.590789
$657$	2983.09	0.177141
$658$	454.291	0.0269151
$659$	4023.36	0.237827	0.118913	−	0.992905i	$-0.462059\pi$
$659$	4023.36	0.237827	0.118913	+	0.992905i	$0.462059\pi$
$660$	3064.17	0.180716
$661$	12936.4	0.761221	0.380611	−	0.924735i	$-0.375714\pi$
$661$	12936.4	0.761221	0.380611	+	0.924735i	$0.375714\pi$
$662$	10544.0	0.619038
$663$	11662.7	0.683168
$664$	−7834.09	−0.457864
$665$	−1134.69	−0.0661675
$666$	−2104.19	−0.122426
$667$	−1043.51	−0.0605768
$668$	−6512.12	−0.377188
$669$	8729.47	0.504486
$670$	−5654.78	−0.326065
$671$	−7415.99	−0.426663
$672$	−882.441	−0.0506561
$673$	−218.147	−0.0124947	−0.00624735	−	0.999980i	$-0.501989\pi$
$673$	−218.147	−0.0124947	−0.00624735	+	0.999980i	$0.501989\pi$
$674$	−6227.40	−0.355891
$675$	675.000	0.0384900
$676$	6042.09	0.343769
$677$	−21089.3	−1.19724	−0.598618	−	0.801035i	$-0.704283\pi$
$677$	−21089.3	−1.19724	−0.598618	+	0.801035i	$0.704283\pi$
$678$	2023.38	0.114612
$679$	−1762.50	−0.0996152
$680$	8769.89	0.494573
$681$	16520.0	0.929583
$682$	9807.86	0.550678
$683$	−13809.6	−0.773657	−0.386829	−	0.922152i	$-0.626430\pi$
$683$	−13809.6	−0.773657	−0.386829	+	0.922152i	$0.626430\pi$
$684$	−8029.26	−0.448840
$685$	−665.903	−0.0371428
$686$	1300.00	0.0723529
$687$	1897.40	0.105371
$688$	−18446.5	−1.02219
$689$	−15714.7	−0.868915
$690$	595.362	0.0328479
$691$	9701.40	0.534094	0.267047	−	0.963684i	$-0.413952\pi$
$691$	9701.40	0.534094	0.267047	+	0.963684i	$0.413952\pi$
$692$	6067.05	0.333287
$693$	467.668	0.0256353
$694$	8871.85	0.485261
$695$	4289.49	0.234114
$696$	−1418.68	−0.0772626
$697$	29429.8	1.59933
$698$	−4596.33	−0.249246
$699$	15316.9	0.828808
$700$	−292.614	−0.0157997
$701$	15338.9	0.826453	0.413226	−	0.910628i	$-0.364402\pi$
$701$	15338.9	0.826453	0.413226	+	0.910628i	$0.364402\pi$
$702$	1076.40	0.0578718
$703$	27876.8	1.49558
$704$	−3077.70	−0.164766
$705$	3580.29	0.191265
$706$	10332.3	0.550796
$707$	−1891.45	−0.100616
$708$	−1880.14	−0.0998025
$709$	−7479.00	−0.396163	−0.198082	−	0.980186i	$-0.563471\pi$
$709$	−7479.00	−0.396163	−0.198082	+	0.980186i	$0.563471\pi$
$710$	−1339.89	−0.0708240
$711$	−3316.60	−0.174940
$712$	11098.5	0.584174
$713$	−10624.2	−0.558038
$714$	614.170	0.0321915
$715$	5442.11	0.284648
$716$	−22991.3	−1.20004
$717$	−19227.7	−1.00149
$718$	8140.04	0.423097
$719$	8527.03	0.442287	0.221144	−	0.975241i	$-0.429021\pi$
$719$	8527.03	0.442287	0.221144	+	0.975241i	$0.429021\pi$
$720$	−1632.57	−0.0845034
$721$	−1463.34	−0.0755861
$722$	−11514.2	−0.593509
$723$	4387.83	0.225706
$724$	17850.0	0.916283
$725$	−725.000	−0.0371391
$726$	1403.39	0.0717420
$727$	9808.65	0.500389	0.250194	−	0.968196i	$-0.419505\pi$
$727$	9808.65	0.500389	0.250194	+	0.968196i	$0.419505\pi$
$728$	−1016.94	−0.0517724
$729$	729.000	0.0370370
$730$	1828.05	0.0926836
$731$	54690.7	2.76718
$732$	5011.30	0.253037
$733$	−30465.7	−1.53516	−0.767582	−	0.640951i	$-0.778540\pi$
$733$	−30465.7	−1.53516	−0.767582	+	0.640951i	$0.778540\pi$
$734$	1304.74	0.0656117
$735$	5100.34	0.255958
$736$	−6134.05	−0.307206
$737$	−30876.9	−1.54324
$738$	2716.21	0.135481
$739$	7622.76	0.379442	0.189721	−	0.981838i	$-0.439242\pi$
$739$	7622.76	0.379442	0.189721	+	0.981838i	$0.439242\pi$
$740$	7188.87	0.357119
$741$	−14260.3	−0.706973
$742$	−827.556	−0.0409441
$743$	13692.2	0.676070	0.338035	−	0.941134i	$-0.390238\pi$
$743$	13692.2	0.676070	0.338035	+	0.941134i	$0.390238\pi$
$744$	−14444.0	−0.711749
$745$	−13530.8	−0.665409
$746$	4474.40	0.219597
$747$	−4323.82	−0.211781
$748$	21972.6	1.07406
$749$	−464.965	−0.0226829
$750$	413.641	0.0201387
$751$	5741.47	0.278974	0.139487	−	0.990224i	$-0.455455\pi$
$751$	5741.47	0.278974	0.139487	+	0.990224i	$0.455455\pi$
$752$	−8659.39	−0.419914
$753$	−7091.65	−0.343206
$754$	−1156.13	−0.0558406
$755$	15317.6	0.738364
$756$	−316.023	−0.0152032
$757$	−18962.5	−0.910440	−0.455220	−	0.890379i	$-0.650439\pi$
$757$	−18962.5	−0.910440	−0.455220	+	0.890379i	$0.650439\pi$
$758$	−13461.2	−0.645031
$759$	3250.87	0.155466
$760$	−10723.3	−0.511807
$761$	31732.0	1.51154	0.755771	−	0.654836i	$-0.227262\pi$
$761$	31732.0	1.51154	0.755771	+	0.654836i	$0.227262\pi$
$762$	4593.73	0.218390
$763$	3317.64	0.157413
$764$	490.994	0.0232507
$765$	4840.30	0.228760
$766$	13203.5	0.622796
$767$	−3339.23	−0.157200
$768$	−2433.15	−0.114321
$769$	28899.8	1.35521	0.677604	−	0.735427i	$-0.263018\pi$
$769$	28899.8	1.35521	0.677604	+	0.735427i	$0.263018\pi$
$770$	286.588	0.0134129
$771$	−11247.0	−0.525360
$772$	968.609	0.0451567
$773$	21909.5	1.01945	0.509723	−	0.860339i	$-0.329748\pi$
$773$	21909.5	1.01945	0.509723	+	0.860339i	$0.329748\pi$
$774$	5047.64	0.234410
$775$	−7381.44	−0.342128
$776$	−16656.3	−0.770526
$777$	1097.20	0.0506587
$778$	1628.73	0.0750549
$779$	−35984.9	−1.65506
$780$	−3677.46	−0.168813
$781$	−7316.20	−0.335204
$782$	4269.23	0.195227
$783$	−783.000	−0.0357371
$784$	−12335.8	−0.561946
$785$	6281.52	0.285602
$786$	−9813.08	−0.445319
$787$	−16602.7	−0.751998	−0.375999	−	0.926620i	$-0.622700\pi$
$787$	−16602.7	−0.751998	−0.375999	+	0.926620i	$0.622700\pi$
$788$	−3706.24	−0.167550
$789$	2228.39	0.100548
$790$	−2032.42	−0.0915319
$791$	−1055.06	−0.0474255
$792$	4419.64	0.198289
$793$	8900.31	0.398561
$794$	3009.67	0.134520
$795$	−6522.00	−0.290958
$796$	458.066	0.0203966
$797$	−18463.4	−0.820585	−0.410293	−	0.911954i	$-0.634573\pi$
$797$	−18463.4	−0.820585	−0.410293	+	0.911954i	$0.634573\pi$
$798$	−750.967	−0.0333132
$799$	25673.6	1.13675
$800$	−4261.77	−0.188345
$801$	6125.49	0.270204
$802$	−893.712	−0.0393492
$803$	9981.71	0.438664
$804$	20864.8	0.915232
$805$	−310.443	−0.0135921
$806$	−11770.9	−0.514408
$807$	7765.01	0.338713
$808$	−17874.9	−0.778264
$809$	−18567.0	−0.806899	−0.403449	−	0.915002i	$-0.632189\pi$
$809$	−18567.0	−0.806899	−0.403449	+	0.915002i	$0.632189\pi$
$810$	446.733	0.0193785
$811$	16409.2	0.710487	0.355243	−	0.934774i	$-0.384398\pi$
$811$	16409.2	0.710487	0.355243	+	0.934774i	$0.384398\pi$
$812$	339.432	0.0146696
$813$	−23145.6	−0.998465
$814$	−7040.83	−0.303171
$815$	−15150.2	−0.651149
$816$	−11706.9	−0.502235
$817$	−66872.2	−2.86360
$818$	−9159.18	−0.391495
$819$	−561.272	−0.0239468
$820$	−9279.80	−0.395201
$821$	14164.8	0.602137	0.301069	−	0.953602i	$-0.402657\pi$
$821$	14164.8	0.602137	0.301069	+	0.953602i	$0.402657\pi$
$822$	−440.712	−0.0187002
$823$	8404.36	0.355963	0.177981	−	0.984034i	$-0.443043\pi$
$823$	8404.36	0.355963	0.177981	+	0.984034i	$0.443043\pi$
$824$	−13829.1	−0.584660
$825$	2258.61	0.0953149
$826$	−175.848	−0.00740741
$827$	−27459.3	−1.15460	−0.577300	−	0.816532i	$-0.695894\pi$
$827$	−27459.3	−1.15460	−0.577300	+	0.816532i	$0.695894\pi$
$828$	−2196.75	−0.0922008
$829$	−6033.61	−0.252782	−0.126391	−	0.991981i	$-0.540339\pi$
$829$	−6033.61	−0.252782	−0.126391	+	0.991981i	$0.540339\pi$
$830$	−2649.64	−0.110808
$831$	−19829.4	−0.827768
$832$	3693.70	0.153914
$833$	36573.6	1.52125
$834$	2838.89	0.117869
$835$	−4800.12	−0.198940
$836$	−26866.7	−1.11149
$837$	−7971.95	−0.329213
$838$	−13718.8	−0.565521
$839$	−30481.3	−1.25427	−0.627134	−	0.778911i	$-0.715772\pi$
$839$	−30481.3	−1.25427	−0.627134	+	0.778911i	$0.715772\pi$
$840$	−422.056	−0.0173361
$841$	841.000	0.0344828
$842$	−16179.8	−0.662224
$843$	23729.7	0.969508
$844$	−35179.1	−1.43473
$845$	4453.65	0.181314
$846$	2369.53	0.0962956
$847$	−731.777	−0.0296861
$848$	15774.3	0.638788
$849$	−7651.23	−0.309293
$850$	2966.15	0.119692
$851$	7626.89	0.307222
$852$	4943.87	0.198796
$853$	−3077.84	−0.123544	−0.0617720	−	0.998090i	$-0.519675\pi$
$853$	−3077.84	−0.123544	−0.0617720	+	0.998090i	$0.519675\pi$
$854$	468.701	0.0187806
$855$	−5918.41	−0.236731
$856$	−4394.10	−0.175453
$857$	39694.5	1.58219	0.791095	−	0.611693i	$-0.209511\pi$
$857$	39694.5	1.58219	0.791095	+	0.611693i	$0.209511\pi$
$858$	3601.73	0.143311
$859$	2122.38	0.0843011	0.0421506	−	0.999111i	$-0.486579\pi$
$859$	2122.38	0.0843011	0.0421506	+	0.999111i	$0.486579\pi$
$860$	−17245.0	−0.683780
$861$	−1416.33	−0.0560608
$862$	−13653.3	−0.539481
$863$	5192.04	0.204796	0.102398	−	0.994743i	$-0.467348\pi$
$863$	5192.04	0.204796	0.102398	+	0.994743i	$0.467348\pi$
$864$	−4602.71	−0.181235
$865$	4472.05	0.175785
$866$	16229.3	0.636831
$867$	19969.9	0.782255
$868$	3455.86	0.135138
$869$	−11097.6	−0.433213
$870$	−479.824	−0.0186983
$871$	37056.9	1.44159
$872$	31352.9	1.21760
$873$	−9193.02	−0.356399
$874$	−5220.14	−0.202030
$875$	−215.687	−0.00833321
$876$	−6745.07	−0.260154
$877$	7307.13	0.281350	0.140675	−	0.990056i	$-0.455073\pi$
$877$	7307.13	0.281350	0.140675	+	0.990056i	$0.455073\pi$
$878$	17353.9	0.667045
$879$	−22432.0	−0.860766
$880$	−5462.75	−0.209260
$881$	20149.2	0.770539	0.385270	−	0.922804i	$-0.374108\pi$
$881$	20149.2	0.770539	0.385270	+	0.922804i	$0.374108\pi$
$882$	3375.54	0.128867
$883$	40573.7	1.54634	0.773168	−	0.634201i	$-0.218671\pi$
$883$	40573.7	1.54634	0.773168	+	0.634201i	$0.218671\pi$
$884$	−26370.4	−1.00332
$885$	−1385.86	−0.0526388
$886$	−3782.77	−0.143436
$887$	45099.5	1.70721	0.853604	−	0.520923i	$-0.174412\pi$
$887$	45099.5	1.70721	0.853604	+	0.520923i	$0.174412\pi$
$888$	10369.0	0.391847
$889$	−2395.33	−0.0903676
$890$	3753.71	0.141376
$891$	2439.30	0.0917168
$892$	−19738.2	−0.740901
$893$	−31392.0	−1.17636
$894$	−8955.03	−0.335012
$895$	−16947.0	−0.632935
$896$	2547.69	0.0949915
$897$	−3901.53	−0.145227
$898$	−718.126	−0.0266862
$899$	8562.47	0.317658
$900$	−1526.24	−0.0565275
$901$	−46768.1	−1.72927
$902$	9088.69	0.335499
$903$	−2632.02	−0.0969968
$904$	−9970.72	−0.366838
$905$	13157.3	0.483275
$906$	10137.6	0.371743
$907$	12242.7	0.448195	0.224098	−	0.974567i	$-0.428057\pi$
$907$	12242.7	0.448195	0.224098	+	0.974567i	$0.428057\pi$
$908$	−37353.2	−1.36521
$909$	−9865.58	−0.359979
$910$	−343.949	−0.0125294
$911$	−10749.0	−0.390922	−0.195461	−	0.980711i	$-0.562620\pi$
$911$	−10749.0	−0.390922	−0.195461	+	0.980711i	$0.562620\pi$
$912$	14314.4	0.519735
$913$	−14467.9	−0.524444
$914$	−6141.67	−0.222263
$915$	3693.85	0.133459
$916$	−4290.20	−0.154751
$917$	5116.89	0.184269
$918$	3203.44	0.115174
$919$	22093.9	0.793048	0.396524	−	0.918024i	$-0.370216\pi$
$919$	22093.9	0.793048	0.396524	+	0.918024i	$0.370216\pi$
$920$	−2933.80	−0.105135
$921$	18582.3	0.664828
$922$	1358.24	0.0485154
$923$	8780.55	0.313126
$924$	−1057.44	−0.0376486
$925$	5298.95	0.188355
$926$	−2472.34	−0.0877388
$927$	−7632.60	−0.270429
$928$	4943.65	0.174874
$929$	−4098.79	−0.144755	−0.0723773	−	0.997377i	$-0.523059\pi$
$929$	−4098.79	−0.144755	−0.0723773	+	0.997377i	$0.523059\pi$
$930$	−4885.23	−0.172251
$931$	−44719.8	−1.57426
$932$	−34632.9	−1.21721
$933$	−2315.48	−0.0812492
$934$	19231.4	0.673738
$935$	16196.1	0.566491
$936$	−5304.24	−0.185229
$937$	−9876.92	−0.344359	−0.172180	−	0.985066i	$-0.555081\pi$
$937$	−9876.92	−0.344359	−0.172180	+	0.985066i	$0.555081\pi$
$938$	1951.46	0.0679292
$939$	−21960.9	−0.763224
$940$	−8095.38	−0.280896
$941$	−39061.8	−1.35322	−0.676609	−	0.736343i	$-0.736551\pi$
$941$	−39061.8	−1.35322	−0.676609	+	0.736343i	$0.736551\pi$
$942$	4157.28	0.143791
$943$	−9845.21	−0.339983
$944$	3351.89	0.115566
$945$	−232.942	−0.00801864
$946$	16889.9	0.580483
$947$	−14053.5	−0.482236	−0.241118	−	0.970496i	$-0.577514\pi$
$947$	−14053.5	−0.482236	−0.241118	+	0.970496i	$0.577514\pi$
$948$	7499.15	0.256921
$949$	−11979.6	−0.409771
$950$	−3626.81	−0.123862
$951$	9222.60	0.314472
$952$	−3026.49	−0.103035
$953$	−45208.0	−1.53665	−0.768327	−	0.640058i	$-0.778910\pi$
$953$	−45208.0	−1.53665	−0.768327	+	0.640058i	$0.778910\pi$
$954$	−4316.43	−0.146488
$955$	361.914	0.0122631
$956$	43475.6	1.47082
$957$	−2619.99	−0.0884977
$958$	−11046.2	−0.372532
$959$	229.803	0.00773798
$960$	1532.98	0.0515383
$961$	57386.0	1.92629
$962$	8450.05	0.283202
$963$	−2425.21	−0.0811539
$964$	−9921.32	−0.331478
$965$	713.967	0.0238170
$966$	−205.459	−0.00684321
$967$	−46263.2	−1.53849	−0.769247	−	0.638951i	$-0.779368\pi$
$967$	−46263.2	−1.53849	−0.769247	+	0.638951i	$0.779368\pi$
$968$	−6915.58	−0.229623
$969$	−42439.8	−1.40698
$970$	−5633.50	−0.186475
$971$	19893.5	0.657478	0.328739	−	0.944421i	$-0.393376\pi$
$971$	19893.5	0.657478	0.328739	+	0.944421i	$0.393376\pi$
$972$	−1648.34	−0.0543936
$973$	−1480.30	−0.0487731
$974$	−959.469	−0.0315640
$975$	−2710.68	−0.0890371
$976$	−8934.06	−0.293005
$977$	1279.87	0.0419107	0.0209554	−	0.999780i	$-0.493329\pi$
$977$	1279.87	0.0419107	0.0209554	+	0.999780i	$0.493329\pi$
$978$	−10026.8	−0.327833
$979$	20496.5	0.669122
$980$	−11532.4	−0.375906
$981$	17304.4	0.563188
$982$	594.666	0.0193244
$983$	46272.0	1.50137	0.750686	−	0.660659i	$-0.229723\pi$
$983$	46272.0	1.50137	0.750686	+	0.660659i	$0.229723\pi$
$984$	−13384.8	−0.433631
$985$	−2731.89	−0.0883708
$986$	−3440.73	−0.111131
$987$	−1235.56	−0.0398462
$988$	32244.0	1.03828
$989$	−18295.8	−0.588242
$990$	1494.81	0.0479881
$991$	−22567.4	−0.723388	−0.361694	−	0.932297i	$-0.617802\pi$
$991$	−22567.4	−0.723388	−0.361694	+	0.932297i	$0.617802\pi$
$992$	50332.8	1.61095
$993$	−28676.9	−0.916450
$994$	462.394	0.0147548
$995$	337.642	0.0107578
$996$	9776.57	0.311027
$997$	−56510.6	−1.79509	−0.897547	−	0.440919i	$-0.854653\pi$
$997$	−56510.6	−1.79509	−0.897547	+	0.440919i	$0.854653\pi$
$998$	−15434.1	−0.489537
$999$	5722.87	0.181245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.j.1.4	✓	7
3.2	odd	2		1305.4.a.m.1.4		7
5.4	even	2		2175.4.a.m.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.j.1.4	✓	7	1.1	even	1	trivial
1305.4.a.m.1.4		7	3.2	odd	2
2175.4.a.m.1.4		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)

\(f(q)\)	\(=\)	\(q-1.10304 q^{2} +3.00000 q^{3} -6.78329 q^{4} -5.00000 q^{5} -3.30913 q^{6} +1.72550 q^{7} +16.3066 q^{8} +9.00000 q^{9} +5.51522 q^{10} +30.1148 q^{11} -20.3499 q^{12} -36.1424 q^{13} -1.90330 q^{14} -15.0000 q^{15} +36.2794 q^{16} -107.562 q^{17} -9.92739 q^{18} +131.520 q^{19} +33.9165 q^{20} +5.17649 q^{21} -33.2180 q^{22} +35.9830 q^{23} +48.9199 q^{24} +25.0000 q^{25} +39.8666 q^{26} +27.0000 q^{27} -11.7046 q^{28} -29.0000 q^{29} +16.5457 q^{30} -295.258 q^{31} -170.471 q^{32} +90.3445 q^{33} +118.646 q^{34} -8.62749 q^{35} -61.0496 q^{36} +211.958 q^{37} -145.073 q^{38} -108.427 q^{39} -81.5331 q^{40} -273.607 q^{41} -5.70990 q^{42} -508.456 q^{43} -204.278 q^{44} -45.0000 q^{45} -39.6908 q^{46} -238.686 q^{47} +108.838 q^{48} -340.023 q^{49} -27.5761 q^{50} -322.687 q^{51} +245.164 q^{52} +434.800 q^{53} -29.7822 q^{54} -150.574 q^{55} +28.1370 q^{56} +394.561 q^{57} +31.9883 q^{58} +92.3909 q^{59} +101.749 q^{60} -246.257 q^{61} +325.682 q^{62} +15.5295 q^{63} -102.199 q^{64} +180.712 q^{65} -99.6540 q^{66} -1025.31 q^{67} +729.627 q^{68} +107.949 q^{69} +9.51650 q^{70} -242.943 q^{71} +146.760 q^{72} +331.455 q^{73} -233.799 q^{74} +75.0000 q^{75} -892.140 q^{76} +51.9631 q^{77} +119.600 q^{78} -368.511 q^{79} -181.397 q^{80} +81.0000 q^{81} +301.801 q^{82} -480.424 q^{83} -35.1137 q^{84} +537.812 q^{85} +560.849 q^{86} -87.0000 q^{87} +491.071 q^{88} +680.610 q^{89} +49.6370 q^{90} -62.3636 q^{91} -244.083 q^{92} -885.773 q^{93} +263.281 q^{94} -657.601 q^{95} -511.412 q^{96} -1021.45 q^{97} +375.060 q^{98} +271.034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) \) 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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