LMFDB - Embedded newform 1587.4.a.o.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1587,4,Mod(1,1587)] 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("1587.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1587, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1587 = 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1587.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,0,21,38,10,0,-17,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	yes
Analytic conductor:	$93.6360311791$
Analytic rank:	$0$
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} - 47x^{5} - 12x^{4} + 574x^{3} + 240x^{2} - 1436x + 720 $ x^7 - 47x^5 - 12x^4 + 574x^3 + 240x^2 - 1436*x + 720
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.48727$ of defining polynomial
Character	$\chi$	$=$	1587.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.48727 q^{2} +3.00000 q^{3} +22.1101 q^{4} +19.2252 q^{5} -16.4618 q^{6} +5.31484 q^{7} -77.4259 q^{8} +9.00000 q^{9} -105.494 q^{10} +51.2932 q^{11} +66.3303 q^{12} +6.63173 q^{13} -29.1640 q^{14} +57.6756 q^{15} +247.976 q^{16} +27.3129 q^{17} -49.3854 q^{18} +68.8864 q^{19} +425.071 q^{20} +15.9445 q^{21} -281.459 q^{22} -232.278 q^{24} +244.609 q^{25} -36.3901 q^{26} +27.0000 q^{27} +117.512 q^{28} +141.818 q^{29} -316.482 q^{30} -178.803 q^{31} -741.302 q^{32} +153.880 q^{33} -149.873 q^{34} +102.179 q^{35} +198.991 q^{36} +26.8290 q^{37} -377.998 q^{38} +19.8952 q^{39} -1488.53 q^{40} -376.262 q^{41} -87.4919 q^{42} +381.273 q^{43} +1134.10 q^{44} +173.027 q^{45} -362.628 q^{47} +743.927 q^{48} -314.752 q^{49} -1342.23 q^{50} +81.9388 q^{51} +146.628 q^{52} +508.353 q^{53} -148.156 q^{54} +986.122 q^{55} -411.507 q^{56} +206.659 q^{57} -778.194 q^{58} +97.9012 q^{59} +1275.21 q^{60} +299.254 q^{61} +981.141 q^{62} +47.8336 q^{63} +2083.92 q^{64} +127.496 q^{65} -844.378 q^{66} +346.675 q^{67} +603.891 q^{68} -560.683 q^{70} -827.048 q^{71} -696.833 q^{72} +630.506 q^{73} -147.218 q^{74} +733.826 q^{75} +1523.08 q^{76} +272.615 q^{77} -109.170 q^{78} +699.342 q^{79} +4767.39 q^{80} +81.0000 q^{81} +2064.65 q^{82} +113.575 q^{83} +352.535 q^{84} +525.096 q^{85} -2092.14 q^{86} +425.454 q^{87} -3971.42 q^{88} -1016.83 q^{89} -949.445 q^{90} +35.2466 q^{91} -536.409 q^{93} +1989.84 q^{94} +1324.35 q^{95} -2223.91 q^{96} +1138.08 q^{97} +1727.13 q^{98} +461.639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 21 q^{3} + 38 q^{4} + 10 q^{5} - 17 q^{7} - 36 q^{8} + 63 q^{9} - 65 q^{10} + 5 q^{11} + 114 q^{12} + 152 q^{13} + 23 q^{14} + 30 q^{15} + 314 q^{16} - 22 q^{17} + 38 q^{19} + 171 q^{20} - 51 q^{21}+ \cdots + 45 q^{99}+O(q^{100}) $ 7 * q + 21 * q^3 + 38 * q^4 + 10 * q^5 - 17 * q^7 - 36 * q^8 + 63 * q^9 - 65 * q^10 + 5 * q^11 + 114 * q^12 + 152 * q^13 + 23 * q^14 + 30 * q^15 + 314 * q^16 - 22 * q^17 + 38 * q^19 + 171 * q^20 - 51 * q^21 - 233 * q^22 - 108 * q^24 + 643 * q^25 - 221 * q^26 + 189 * q^27 + 145 * q^28 + 567 * q^29 - 195 * q^30 + 121 * q^31 - 468 * q^32 + 15 * q^33 + 260 * q^34 + 256 * q^35 + 342 * q^36 + 108 * q^37 - 964 * q^38 + 456 * q^39 - 1089 * q^40 + 442 * q^41 + 69 * q^42 + 68 * q^43 + 2121 * q^44 + 90 * q^45 + 464 * q^47 + 942 * q^48 + 48 * q^49 - 2111 * q^50 - 66 * q^51 + 1979 * q^52 + 189 * q^53 + 314 * q^55 - 1561 * q^56 + 114 * q^57 + 1384 * q^58 + 241 * q^59 + 513 * q^60 - 1084 * q^61 - 143 * q^62 - 153 * q^63 + 2458 * q^64 + 1126 * q^65 - 699 * q^66 + 1368 * q^67 - 1284 * q^68 + 1618 * q^70 + 232 * q^71 - 324 * q^72 - 657 * q^73 + 3190 * q^74 + 1929 * q^75 - 132 * q^76 + 2089 * q^77 - 663 * q^78 + 447 * q^79 + 6707 * q^80 + 567 * q^81 + 2823 * q^82 - 1675 * q^83 + 435 * q^84 + 1320 * q^85 - 4566 * q^86 + 1701 * q^87 + 715 * q^88 - 1552 * q^89 - 585 * q^90 - 2498 * q^91 + 363 * q^93 + 5240 * q^94 + 1722 * q^95 - 1404 * q^96 + 1599 * q^97 + 3491 * q^98 + 45 * 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 $

$2$	−5.48727	−1.94004	−0.970021	−	0.243021i	$-0.921862\pi$
$2$	−5.48727	−1.94004	−0.970021	+	0.243021i	$0.921862\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	22.1101	2.76376
$5$	19.2252	1.71955	0.859777	−	0.510669i	$-0.170602\pi$
$5$	19.2252	1.71955	0.859777	+	0.510669i	$0.170602\pi$
$6$	−16.4618	−1.12008
$7$	5.31484	0.286975	0.143487	−	0.989652i	$-0.454168\pi$
$7$	5.31484	0.286975	0.143487	+	0.989652i	$0.454168\pi$
$8$	−77.4259	−3.42177
$9$	9.00000	0.333333
$10$	−105.494	−3.33601
$11$	51.2932	1.40595	0.702976	−	0.711213i	$-0.251854\pi$
$11$	51.2932	1.40595	0.702976	+	0.711213i	$0.251854\pi$
$12$	66.3303	1.59566
$13$	6.63173	0.141485	0.0707427	−	0.997495i	$-0.477463\pi$
$13$	6.63173	0.141485	0.0707427	+	0.997495i	$0.477463\pi$
$14$	−29.1640	−0.556743
$15$	57.6756	0.992785
$16$	247.976	3.87462
$17$	27.3129	0.389668	0.194834	−	0.980836i	$-0.437583\pi$
$17$	27.3129	0.389668	0.194834	+	0.980836i	$0.437583\pi$
$18$	−49.3854	−0.646681
$19$	68.8864	0.831769	0.415885	−	0.909417i	$-0.363472\pi$
$19$	68.8864	0.831769	0.415885	+	0.909417i	$0.363472\pi$
$20$	425.071	4.75244
$21$	15.9445	0.165685
$22$	−281.459	−2.72761
$23$	0	0
$23$	0	0
$24$	−232.278	−1.97556
$25$	244.609	1.95687
$26$	−36.3901	−0.274488
$27$	27.0000	0.192450
$28$	117.512	0.793130
$29$	141.818	0.908102	0.454051	−	0.890976i	$-0.349978\pi$
$29$	141.818	0.908102	0.454051	+	0.890976i	$0.349978\pi$
$30$	−316.482	−1.92605
$31$	−178.803	−1.03594	−0.517968	−	0.855400i	$-0.673311\pi$
$31$	−178.803	−1.03594	−0.517968	+	0.855400i	$0.673311\pi$
$32$	−741.302	−4.09516
$33$	153.880	0.811727
$34$	−149.873	−0.755972
$35$	102.179	0.493468
$36$	198.991	0.921254
$37$	26.8290	0.119207	0.0596034	−	0.998222i	$-0.481016\pi$
$37$	26.8290	0.119207	0.0596034	+	0.998222i	$0.481016\pi$
$38$	−377.998	−1.61367
$39$	19.8952	0.0816866
$40$	−1488.53	−5.88393
$41$	−376.262	−1.43323	−0.716613	−	0.697471i	$-0.754309\pi$
$41$	−376.262	−1.43323	−0.716613	+	0.697471i	$0.754309\pi$
$42$	−87.4919	−0.321436
$43$	381.273	1.35217	0.676087	−	0.736821i	$-0.263674\pi$
$43$	381.273	1.35217	0.676087	+	0.736821i	$0.263674\pi$
$44$	1134.10	3.88572
$45$	173.027	0.573185
$46$	0	0
$47$	−362.628	−1.12542	−0.562710	−	0.826654i	$-0.690241\pi$
$47$	−362.628	−1.12542	−0.562710	+	0.826654i	$0.690241\pi$
$48$	743.927	2.23701
$49$	−314.752	−0.917646
$50$	−1342.23	−3.79641
$51$	81.9388	0.224975
$52$	146.628	0.391032
$53$	508.353	1.31750	0.658752	−	0.752360i	$-0.271085\pi$
$53$	508.353	1.31750	0.658752	+	0.752360i	$0.271085\pi$
$54$	−148.156	−0.373361
$55$	986.122	2.41761
$56$	−411.507	−0.981962
$57$	206.659	0.480222
$58$	−778.194	−1.76176
$59$	97.9012	0.216028	0.108014	−	0.994149i	$-0.465551\pi$
$59$	97.9012	0.216028	0.108014	+	0.994149i	$0.465551\pi$
$60$	1275.21	2.74382
$61$	299.254	0.628124	0.314062	−	0.949402i	$-0.398310\pi$
$61$	299.254	0.628124	0.314062	+	0.949402i	$0.398310\pi$
$62$	981.141	2.00976
$63$	47.8336	0.0956582
$64$	2083.92	4.07015
$65$	127.496	0.243292
$66$	−844.378	−1.57478
$67$	346.675	0.632136	0.316068	−	0.948737i	$-0.397637\pi$
$67$	346.675	0.632136	0.316068	+	0.948737i	$0.397637\pi$
$68$	603.891	1.07695
$69$	0	0
$70$	−560.683	−0.957349
$71$	−827.048	−1.38243	−0.691215	−	0.722649i	$-0.742924\pi$
$71$	−827.048	−1.38243	−0.691215	+	0.722649i	$0.742924\pi$
$72$	−696.833	−1.14059
$73$	630.506	1.01089	0.505446	−	0.862858i	$-0.331328\pi$
$73$	630.506	1.01089	0.505446	+	0.862858i	$0.331328\pi$
$74$	−147.218	−0.231266
$75$	733.826	1.12980
$76$	1523.08	2.29881
$77$	272.615	0.403473
$78$	−109.170	−0.158476
$79$	699.342	0.995976	0.497988	−	0.867184i	$-0.334072\pi$
$79$	699.342	0.995976	0.497988	+	0.867184i	$0.334072\pi$
$80$	4767.39	6.66262
$81$	81.0000	0.111111
$82$	2064.65	2.78052
$83$	113.575	0.150198	0.0750990	−	0.997176i	$-0.476073\pi$
$83$	113.575	0.150198	0.0750990	+	0.997176i	$0.476073\pi$
$84$	352.535	0.457914
$85$	525.096	0.670055
$86$	−2092.14	−2.62328
$87$	425.454	0.524293
$88$	−3971.42	−4.81085
$89$	−1016.83	−1.21106	−0.605529	−	0.795824i	$-0.707038\pi$
$89$	−1016.83	−1.21106	−0.605529	+	0.795824i	$0.707038\pi$
$90$	−949.445	−1.11200
$91$	35.2466	0.0406027
$92$	0	0
$93$	−536.409	−0.598097
$94$	1989.84	2.18336
$95$	1324.35	1.43027
$96$	−2223.91	−2.36434
$97$	1138.08	1.19128	0.595640	−	0.803252i	$-0.296899\pi$
$97$	1138.08	1.19128	0.595640	+	0.803252i	$0.296899\pi$
$98$	1727.13	1.78027
$99$	461.639	0.468651
$100$	5408.32	5.40832
$101$	95.8409	0.0944211	0.0472105	−	0.998885i	$-0.484967\pi$
$101$	95.8409	0.0944211	0.0472105	+	0.998885i	$0.484967\pi$
$102$	−449.620	−0.436461
$103$	−254.760	−0.243712	−0.121856	−	0.992548i	$-0.538885\pi$
$103$	−254.760	−0.243712	−0.121856	+	0.992548i	$0.538885\pi$
$104$	−513.468	−0.484131
$105$	306.537	0.284904
$106$	−2789.47	−2.55601
$107$	1285.51	1.16144	0.580722	−	0.814102i	$-0.302770\pi$
$107$	1285.51	1.16144	0.580722	+	0.814102i	$0.302770\pi$
$108$	596.973	0.531886
$109$	29.1605	0.0256245	0.0128122	−	0.999918i	$-0.495922\pi$
$109$	29.1605	0.0256245	0.0128122	+	0.999918i	$0.495922\pi$
$110$	−5411.12	−4.69027
$111$	80.4869	0.0688241
$112$	1317.95	1.11192
$113$	−727.070	−0.605283	−0.302642	−	0.953104i	$-0.597869\pi$
$113$	−727.070	−0.605283	−0.302642	+	0.953104i	$0.597869\pi$
$114$	−1133.99	−0.931651
$115$	0	0
$116$	3135.61	2.50978
$117$	59.6856	0.0471618
$118$	−537.210	−0.419104
$119$	145.164	0.111825
$120$	−4465.59	−3.39709
$121$	1299.99	0.976703
$122$	−1642.09	−1.21859
$123$	−1128.79	−0.827474
$124$	−3953.36	−2.86308
$125$	2299.50	1.64539
$126$	−262.476	−0.185581
$127$	−655.648	−0.458105	−0.229053	−	0.973414i	$-0.573563\pi$
$127$	−655.648	−0.458105	−0.229053	+	0.973414i	$0.573563\pi$
$128$	−5504.59	−3.80111
$129$	1143.82	0.780679
$130$	−699.606	−0.471996
$131$	65.6615	0.0437929	0.0218965	−	0.999760i	$-0.493030\pi$
$131$	65.6615	0.0437929	0.0218965	+	0.999760i	$0.493030\pi$
$132$	3402.29	2.24342
$133$	366.120	0.238697
$134$	−1902.30	−1.22637
$135$	519.081	0.330928
$136$	−2114.73	−1.33336
$137$	−1115.99	−0.695955	−0.347977	−	0.937503i	$-0.613131\pi$
$137$	−1115.99	−0.695955	−0.347977	+	0.937503i	$0.613131\pi$
$138$	0	0
$139$	−698.532	−0.426250	−0.213125	−	0.977025i	$-0.568364\pi$
$139$	−698.532	−0.426250	−0.213125	+	0.977025i	$0.568364\pi$
$140$	2259.19	1.36383
$141$	−1087.88	−0.649762
$142$	4538.23	2.68197
$143$	340.163	0.198922
$144$	2231.78	1.29154
$145$	2726.48	1.56153
$146$	−3459.75	−1.96117
$147$	−944.257	−0.529803
$148$	593.191	0.329459
$149$	−2466.15	−1.35594	−0.677969	−	0.735090i	$-0.737140\pi$
$149$	−2466.15	−1.35594	−0.677969	+	0.735090i	$0.737140\pi$
$150$	−4026.70	−2.19186
$151$	−2782.49	−1.49958	−0.749788	−	0.661678i	$-0.769845\pi$
$151$	−2782.49	−1.49958	−0.749788	+	0.661678i	$0.769845\pi$
$152$	−5333.59	−2.84613
$153$	245.816	0.129889
$154$	−1495.91	−0.782754
$155$	−3437.53	−1.78135
$156$	439.885	0.225763
$157$	603.164	0.306610	0.153305	−	0.988179i	$-0.451008\pi$
$157$	603.164	0.306610	0.153305	+	0.988179i	$0.451008\pi$
$158$	−3837.48	−1.93224
$159$	1525.06	0.760661
$160$	−14251.7	−7.04184
$161$	0	0
$162$	−444.469	−0.215560
$163$	−206.664	−0.0993076	−0.0496538	−	0.998766i	$-0.515812\pi$
$163$	−206.664	−0.0993076	−0.0496538	+	0.998766i	$0.515812\pi$
$164$	−8319.20	−3.96110
$165$	2958.37	1.39581
$166$	−623.214	−0.291390
$167$	−3335.19	−1.54542	−0.772709	−	0.634761i	$-0.781099\pi$
$167$	−3335.19	−1.54542	−0.772709	+	0.634761i	$0.781099\pi$
$168$	−1234.52	−0.566936
$169$	−2153.02	−0.979982
$170$	−2881.34	−1.29994
$171$	619.977	0.277256
$172$	8429.98	3.73709
$173$	3784.96	1.66338	0.831692	−	0.555237i	$-0.187372\pi$
$173$	3784.96	1.66338	0.831692	+	0.555237i	$0.187372\pi$
$174$	−2334.58	−1.01715
$175$	1300.06	0.561571
$176$	12719.5	5.44754
$177$	293.704	0.124724
$178$	5579.63	2.34950
$179$	−4343.39	−1.81363	−0.906817	−	0.421525i	$-0.861495\pi$
$179$	−4343.39	−1.81363	−0.906817	+	0.421525i	$0.861495\pi$
$180$	3825.64	1.58415
$181$	−141.305	−0.0580282	−0.0290141	−	0.999579i	$-0.509237\pi$
$181$	−141.305	−0.0580282	−0.0290141	+	0.999579i	$0.509237\pi$
$182$	−193.407	−0.0787710
$183$	897.763	0.362648
$184$	0	0
$185$	515.792	0.204983
$186$	2943.42	1.16033
$187$	1400.97	0.547855
$188$	−8017.75	−3.11040
$189$	143.501	0.0552283
$190$	−7267.09	−2.77479
$191$	373.701	0.141571	0.0707855	−	0.997492i	$-0.477449\pi$
$191$	373.701	0.141571	0.0707855	+	0.997492i	$0.477449\pi$
$192$	6251.75	2.34990
$193$	1719.22	0.641204	0.320602	−	0.947214i	$-0.396115\pi$
$193$	1719.22	0.641204	0.320602	+	0.947214i	$0.396115\pi$
$194$	−6244.93	−2.31113
$195$	382.489	0.140465
$196$	−6959.21	−2.53615
$197$	−1538.98	−0.556587	−0.278294	−	0.960496i	$-0.589769\pi$
$197$	−1538.98	−0.556587	−0.278294	+	0.960496i	$0.589769\pi$
$198$	−2533.14	−0.909202
$199$	3555.77	1.26664	0.633322	−	0.773889i	$-0.281691\pi$
$199$	3555.77	1.26664	0.633322	+	0.773889i	$0.281691\pi$
$200$	−18939.0	−6.69596
$201$	1040.03	0.364964
$202$	−525.905	−0.183181
$203$	753.741	0.260602
$204$	1811.67	0.621777
$205$	−7233.72	−2.46451
$206$	1397.94	0.472811
$207$	0	0
$208$	1644.51	0.548203
$209$	3533.40	1.16943
$210$	−1682.05	−0.552726
$211$	2758.93	0.900155	0.450077	−	0.892990i	$-0.351396\pi$
$211$	2758.93	0.900155	0.450077	+	0.892990i	$0.351396\pi$
$212$	11239.7	3.64127
$213$	−2481.14	−0.798146
$214$	−7053.91	−2.25325
$215$	7330.04	2.32514
$216$	−2090.50	−0.658521
$217$	−950.311	−0.297287
$218$	−160.011	−0.0497125
$219$	1891.52	0.583639
$220$	21803.3	6.68171
$221$	181.132	0.0551323
$222$	−441.653	−0.133522
$223$	4373.87	1.31344	0.656718	−	0.754137i	$-0.271944\pi$
$223$	4373.87	1.31344	0.656718	+	0.754137i	$0.271944\pi$
$224$	−3939.91	−1.17521
$225$	2201.48	0.652289
$226$	3989.63	1.17427
$227$	4836.24	1.41407	0.707033	−	0.707181i	$-0.250033\pi$
$227$	4836.24	1.41407	0.707033	+	0.707181i	$0.250033\pi$
$228$	4569.25	1.32722
$229$	−1264.66	−0.364939	−0.182469	−	0.983212i	$-0.558409\pi$
$229$	−1264.66	−0.364939	−0.182469	+	0.983212i	$0.558409\pi$
$230$	0	0
$231$	817.846	0.232945
$232$	−10980.4	−3.10732
$233$	5574.72	1.56743	0.783716	−	0.621119i	$-0.213322\pi$
$233$	5574.72	1.56743	0.783716	+	0.621119i	$0.213322\pi$
$234$	−327.511	−0.0914959
$235$	−6971.60	−1.93522
$236$	2164.61	0.597050
$237$	2098.03	0.575027
$238$	−796.553	−0.216945
$239$	−3145.32	−0.851272	−0.425636	−	0.904894i	$-0.639950\pi$
$239$	−3145.32	−0.851272	−0.425636	+	0.904894i	$0.639950\pi$
$240$	14302.2	3.84667
$241$	1572.24	0.420236	0.210118	−	0.977676i	$-0.432615\pi$
$241$	1572.24	0.420236	0.210118	+	0.977676i	$0.432615\pi$
$242$	−7133.40	−1.89485
$243$	243.000	0.0641500
$244$	6616.54	1.73599
$245$	−6051.18	−1.57794
$246$	6193.95	1.60533
$247$	456.836	0.117683
$248$	13844.0	3.54474
$249$	340.724	0.0867169
$250$	−12618.0	−3.19212
$251$	−6799.05	−1.70977	−0.854885	−	0.518818i	$-0.826372\pi$
$251$	−6799.05	−1.70977	−0.854885	+	0.518818i	$0.826372\pi$
$252$	1057.61	0.264377
$253$	0	0
$254$	3597.72	0.888744
$255$	1575.29	0.386857
$256$	13533.8	3.30416
$257$	−5636.97	−1.36819	−0.684094	−	0.729394i	$-0.739802\pi$
$257$	−5636.97	−1.36819	−0.684094	+	0.729394i	$0.739802\pi$
$258$	−6276.43	−1.51455
$259$	142.592	0.0342093
$260$	2818.96	0.672401
$261$	1276.36	0.302701
$262$	−360.302	−0.0849601
$263$	724.284	0.169815	0.0849073	−	0.996389i	$-0.472941\pi$
$263$	724.284	0.169815	0.0849073	+	0.996389i	$0.472941\pi$
$264$	−11914.3	−2.77755
$265$	9773.20	2.26552
$266$	−2009.00	−0.463081
$267$	−3050.50	−0.699204
$268$	7665.02	1.74707
$269$	−5092.24	−1.15420	−0.577099	−	0.816674i	$-0.695815\pi$
$269$	−5092.24	−1.15420	−0.577099	+	0.816674i	$0.695815\pi$
$270$	−2848.33	−0.642015
$271$	2487.64	0.557613	0.278807	−	0.960347i	$-0.410061\pi$
$271$	2487.64	0.557613	0.278807	+	0.960347i	$0.410061\pi$
$272$	6772.94	1.50982
$273$	105.740	0.0234420
$274$	6123.76	1.35018
$275$	12546.8	2.75126
$276$	0	0
$277$	2847.48	0.617648	0.308824	−	0.951119i	$-0.400065\pi$
$277$	2847.48	0.617648	0.308824	+	0.951119i	$0.400065\pi$
$278$	3833.03	0.826943
$279$	−1609.23	−0.345312
$280$	−7911.30	−1.68854
$281$	−8323.12	−1.76696	−0.883480	−	0.468469i	$-0.844806\pi$
$281$	−8323.12	−1.76696	−0.883480	+	0.468469i	$0.844806\pi$
$282$	5969.51	1.26057
$283$	−1594.24	−0.334869	−0.167434	−	0.985883i	$-0.553548\pi$
$283$	−1594.24	−0.334869	−0.167434	+	0.985883i	$0.553548\pi$
$284$	−18286.1	−3.82071
$285$	3973.06	0.825768
$286$	−1866.56	−0.385917
$287$	−1999.77	−0.411299
$288$	−6671.72	−1.36505
$289$	−4167.00	−0.848159
$290$	−14960.9	−3.02944
$291$	3414.23	0.687786
$292$	13940.5	2.79387
$293$	−6172.93	−1.23081	−0.615403	−	0.788212i	$-0.711007\pi$
$293$	−6172.93	−1.23081	−0.615403	+	0.788212i	$0.711007\pi$
$294$	5181.39	1.02784
$295$	1882.17	0.371472
$296$	−2077.26	−0.407899
$297$	1384.92	0.270576
$298$	13532.4	2.63058
$299$	0	0
$300$	16225.0	3.12249
$301$	2026.40	0.388040
$302$	15268.3	2.90924
$303$	287.523	0.0545140
$304$	17082.2	3.22279
$305$	5753.23	1.08009
$306$	−1348.86	−0.251991
$307$	−2057.81	−0.382558	−0.191279	−	0.981536i	$-0.561264\pi$
$307$	−2057.81	−0.382558	−0.191279	+	0.981536i	$0.561264\pi$
$308$	6027.55	1.11510
$309$	−764.281	−0.140707
$310$	18862.6	3.45589
$311$	646.726	0.117918	0.0589589	−	0.998260i	$-0.481222\pi$
$311$	646.726	0.117918	0.0589589	+	0.998260i	$0.481222\pi$
$312$	−1540.40	−0.279513
$313$	−2486.32	−0.448995	−0.224497	−	0.974475i	$-0.572074\pi$
$313$	−2486.32	−0.448995	−0.224497	+	0.974475i	$0.572074\pi$
$314$	−3309.72	−0.594836
$315$	919.610	0.164489
$316$	15462.5	2.75264
$317$	774.946	0.137304	0.0686519	−	0.997641i	$-0.478130\pi$
$317$	774.946	0.137304	0.0686519	+	0.997641i	$0.478130\pi$
$318$	−8368.41	−1.47572
$319$	7274.31	1.27675
$320$	40063.7	6.99885
$321$	3856.52	0.670560
$322$	0	0
$323$	1881.49	0.324114
$324$	1790.92	0.307085
$325$	1622.18	0.276868
$326$	1134.02	0.192661
$327$	87.4814	0.0147943
$328$	29132.4	4.90418
$329$	−1927.31	−0.322967
$330$	−16233.3	−2.70793
$331$	−8490.89	−1.40998	−0.704988	−	0.709220i	$-0.749047\pi$
$331$	−8490.89	−1.40998	−0.704988	+	0.709220i	$0.749047\pi$
$332$	2511.15	0.415112
$333$	241.461	0.0397356
$334$	18301.1	2.99817
$335$	6664.90	1.08699
$336$	3953.86	0.641966
$337$	−2092.20	−0.338188	−0.169094	−	0.985600i	$-0.554084\pi$
$337$	−2092.20	−0.338188	−0.169094	+	0.985600i	$0.554084\pi$
$338$	11814.2	1.90121
$339$	−2181.21	−0.349460
$340$	11609.9	1.85187
$341$	−9171.38	−1.45648
$342$	−3401.98	−0.537889
$343$	−3495.85	−0.550315
$344$	−29520.4	−4.62684
$345$	0	0
$346$	−20769.1	−3.22704
$347$	−1206.65	−0.186675	−0.0933374	−	0.995635i	$-0.529754\pi$
$347$	−1206.65	−0.186675	−0.0933374	+	0.995635i	$0.529754\pi$
$348$	9406.84	1.44902
$349$	11947.6	1.83249	0.916246	−	0.400616i	$-0.131204\pi$
$349$	11947.6	1.83249	0.916246	+	0.400616i	$0.131204\pi$
$350$	−7133.75	−1.08947
$351$	179.057	0.0272289
$352$	−38023.8	−5.75760
$353$	1261.25	0.190169	0.0950844	−	0.995469i	$-0.469688\pi$
$353$	1261.25	0.190169	0.0950844	+	0.995469i	$0.469688\pi$
$354$	−1611.63	−0.241970
$355$	−15900.2	−2.37716
$356$	−22482.3	−3.34707
$357$	435.492	0.0645621
$358$	23833.4	3.51852
$359$	8675.35	1.27540	0.637699	−	0.770286i	$-0.279887\pi$
$359$	8675.35	1.27540	0.637699	+	0.770286i	$0.279887\pi$
$360$	−13396.8	−1.96131
$361$	−2113.67	−0.308160
$362$	775.377	0.112577
$363$	3899.98	0.563900
$364$	779.306	0.112216
$365$	12121.6	1.73828
$366$	−4926.26	−0.703552
$367$	−2638.05	−0.375218	−0.187609	−	0.982244i	$-0.560074\pi$
$367$	−2638.05	−0.375218	−0.187609	+	0.982244i	$0.560074\pi$
$368$	0	0
$369$	−3386.36	−0.477742
$370$	−2830.29	−0.397675
$371$	2701.82	0.378090
$372$	−11860.1	−1.65300
$373$	3692.27	0.512542	0.256271	−	0.966605i	$-0.417506\pi$
$373$	3692.27	0.512542	0.256271	+	0.966605i	$0.417506\pi$
$374$	−7687.48	−1.06286
$375$	6898.49	0.949965
$376$	28076.8	3.85093
$377$	940.499	0.128483
$378$	−787.427	−0.107145
$379$	−7507.48	−1.01750	−0.508751	−	0.860914i	$-0.669893\pi$
$379$	−7507.48	−1.01750	−0.508751	+	0.860914i	$0.669893\pi$
$380$	29281.6	3.95293
$381$	−1966.94	−0.264487
$382$	−2050.60	−0.274654
$383$	−11075.6	−1.47764	−0.738822	−	0.673901i	$-0.764617\pi$
$383$	−11075.6	−1.47764	−0.738822	+	0.673901i	$0.764617\pi$
$384$	−16513.8	−2.19457
$385$	5241.08	0.693793
$386$	−9433.84	−1.24396
$387$	3431.45	0.450725
$388$	25163.0	3.29241
$389$	−760.409	−0.0991113	−0.0495556	−	0.998771i	$-0.515781\pi$
$389$	−760.409	−0.0991113	−0.0495556	+	0.998771i	$0.515781\pi$
$390$	−2098.82	−0.272507
$391$	0	0
$392$	24370.0	3.13998
$393$	196.984	0.0252838
$394$	8444.79	1.07980
$395$	13445.0	1.71264
$396$	10206.9	1.29524
$397$	−8412.57	−1.06351	−0.531757	−	0.846897i	$-0.678468\pi$
$397$	−8412.57	−1.06351	−0.531757	+	0.846897i	$0.678468\pi$
$398$	−19511.5	−2.45734
$399$	1098.36	0.137812
$400$	60657.0	7.58212
$401$	6090.46	0.758462	0.379231	−	0.925302i	$-0.376189\pi$
$401$	6090.46	0.758462	0.379231	+	0.925302i	$0.376189\pi$
$402$	−5706.90	−0.708045
$403$	−1185.77	−0.146570
$404$	2119.05	0.260957
$405$	1557.24	0.191062
$406$	−4135.98	−0.505579
$407$	1376.14	0.167599
$408$	−6344.18	−0.769813
$409$	−10320.5	−1.24772	−0.623859	−	0.781537i	$-0.714436\pi$
$409$	−10320.5	−1.24772	−0.623859	+	0.781537i	$0.714436\pi$
$410$	39693.3	4.78125
$411$	−3347.98	−0.401810
$412$	−5632.78	−0.673561
$413$	520.330	0.0619946
$414$	0	0
$415$	2183.50	0.258274
$416$	−4916.12	−0.579405
$417$	−2095.60	−0.246095
$418$	−19388.7	−2.26874
$419$	−869.329	−0.101359	−0.0506796	−	0.998715i	$-0.516139\pi$
$419$	−869.329	−0.101359	−0.0506796	+	0.998715i	$0.516139\pi$
$420$	6777.56	0.787407
$421$	16729.8	1.93672	0.968362	−	0.249551i	$-0.0802829\pi$
$421$	16729.8	1.93672	0.968362	+	0.249551i	$0.0802829\pi$
$422$	−15139.0	−1.74634
$423$	−3263.65	−0.375140
$424$	−39359.7	−4.50820
$425$	6680.97	0.762529
$426$	13614.7	1.54844
$427$	1590.49	0.180256
$428$	28422.7	3.20995
$429$	1020.49	0.114848
$430$	−40221.9	−4.51087
$431$	−5021.18	−0.561164	−0.280582	−	0.959830i	$-0.590527\pi$
$431$	−5021.18	−0.561164	−0.280582	+	0.959830i	$0.590527\pi$
$432$	6695.35	0.745671
$433$	−7884.30	−0.875047	−0.437523	−	0.899207i	$-0.644144\pi$
$433$	−7884.30	−0.875047	−0.437523	+	0.899207i	$0.644144\pi$
$434$	5214.61	0.576749
$435$	8179.45	0.901551
$436$	644.741	0.0708199
$437$	0	0
$438$	−10379.3	−1.13228
$439$	6487.86	0.705350	0.352675	−	0.935746i	$-0.385272\pi$
$439$	6487.86	0.705350	0.352675	+	0.935746i	$0.385272\pi$
$440$	−76351.4	−8.27252
$441$	−2832.77	−0.305882
$442$	−993.919	−0.106959
$443$	15403.3	1.65200	0.825998	−	0.563673i	$-0.190612\pi$
$443$	15403.3	1.65200	0.825998	+	0.563673i	$0.190612\pi$
$444$	1779.57	0.190213
$445$	−19548.8	−2.08248
$446$	−24000.6	−2.54812
$447$	−7398.45	−0.782852
$448$	11075.7	1.16803
$449$	308.829	0.0324600	0.0162300	−	0.999868i	$-0.494834\pi$
$449$	308.829	0.0324600	0.0162300	+	0.999868i	$0.494834\pi$
$450$	−12080.1	−1.26547
$451$	−19299.7	−2.01505
$452$	−16075.6	−1.67286
$453$	−8347.47	−0.865781
$454$	−26537.8	−2.74335
$455$	677.623	0.0698186
$456$	−16000.8	−1.64321
$457$	−13936.9	−1.42657	−0.713283	−	0.700876i	$-0.752793\pi$
$457$	−13936.9	−1.42657	−0.713283	+	0.700876i	$0.752793\pi$
$458$	6939.52	0.707997
$459$	737.449	0.0749916
$460$	0	0
$461$	12200.6	1.23262	0.616309	−	0.787504i	$-0.288627\pi$
$461$	12200.6	1.23262	0.616309	+	0.787504i	$0.288627\pi$
$462$	−4487.74	−0.451923
$463$	14019.6	1.40723	0.703615	−	0.710581i	$-0.251568\pi$
$463$	14019.6	1.40723	0.703615	+	0.710581i	$0.251568\pi$
$464$	35167.5	3.51855
$465$	−10312.6	−1.02846
$466$	−30590.0	−3.04088
$467$	19792.4	1.96120	0.980601	−	0.196014i	$-0.0627997\pi$
$467$	19792.4	1.96120	0.980601	+	0.196014i	$0.0627997\pi$
$468$	1319.65	0.130344
$469$	1842.52	0.181407
$470$	38255.0	3.75441
$471$	1809.49	0.177021
$472$	−7580.09	−0.739199
$473$	19556.7	1.90109
$474$	−11512.4	−1.11558
$475$	16850.2	1.62766
$476$	3209.59	0.309057
$477$	4575.18	0.439168
$478$	17259.2	1.65150
$479$	9098.87	0.867929	0.433965	−	0.900930i	$-0.357114\pi$
$479$	9098.87	0.867929	0.433965	+	0.900930i	$0.357114\pi$
$480$	−42755.1	−4.06561
$481$	177.922	0.0168660
$482$	−8627.31	−0.815276
$483$	0	0
$484$	28743.0	2.69938
$485$	21879.7	2.04847
$486$	−1333.41	−0.124454
$487$	10332.6	0.961423	0.480711	−	0.876879i	$-0.340378\pi$
$487$	10332.6	0.961423	0.480711	+	0.876879i	$0.340378\pi$
$488$	−23170.0	−2.14930
$489$	−619.991	−0.0573353
$490$	33204.4	3.06127
$491$	184.177	0.0169283	0.00846416	−	0.999964i	$-0.497306\pi$
$491$	184.177	0.0169283	0.00846416	+	0.999964i	$0.497306\pi$
$492$	−24957.6	−2.28694
$493$	3873.47	0.353858
$494$	−2506.78	−0.228310
$495$	8875.10	0.805871
$496$	−44338.9	−4.01386
$497$	−4395.63	−0.396722
$498$	−1869.64	−0.168234
$499$	9165.68	0.822269	0.411135	−	0.911575i	$-0.365133\pi$
$499$	9165.68	0.822269	0.411135	+	0.911575i	$0.365133\pi$
$500$	50842.1	4.54746
$501$	−10005.6	−0.892247
$502$	37308.2	3.31702
$503$	−5462.01	−0.484173	−0.242086	−	0.970255i	$-0.577832\pi$
$503$	−5462.01	−0.484173	−0.242086	+	0.970255i	$0.577832\pi$
$504$	−3703.56	−0.327321
$505$	1842.56	0.162362
$506$	0	0
$507$	−6459.06	−0.565793
$508$	−14496.5	−1.26609
$509$	9415.87	0.819944	0.409972	−	0.912098i	$-0.365539\pi$
$509$	9415.87	0.819944	0.409972	+	0.912098i	$0.365539\pi$
$510$	−8644.03	−0.750518
$511$	3351.04	0.290100
$512$	−30227.0	−2.60910
$513$	1859.93	0.160074
$514$	30931.6	2.65434
$515$	−4897.82	−0.419075
$516$	25289.9	2.15761
$517$	−18600.4	−1.58229
$518$	−782.439	−0.0663675
$519$	11354.9	0.960355
$520$	−9871.52	−0.832490
$521$	18276.1	1.53683	0.768416	−	0.639951i	$-0.221045\pi$
$521$	18276.1	1.53683	0.768416	+	0.639951i	$0.221045\pi$
$522$	−7003.75	−0.587252
$523$	4461.02	0.372977	0.186488	−	0.982457i	$-0.440289\pi$
$523$	4461.02	0.372977	0.186488	+	0.982457i	$0.440289\pi$
$524$	1451.78	0.121033
$525$	3900.17	0.324223
$526$	−3974.34	−0.329447
$527$	−4883.64	−0.403671
$528$	38158.4	3.14514
$529$	0	0
$530$	−53628.2	−4.39520
$531$	881.111	0.0720094
$532$	8094.96	0.659701
$533$	−2495.27	−0.202781
$534$	16738.9	1.35649
$535$	24714.1	1.99717
$536$	−26841.6	−2.16303
$537$	−13030.2	−1.04710
$538$	27942.5	2.23919
$539$	−16144.7	−1.29017
$540$	11476.9	0.914608
$541$	−15313.0	−1.21692	−0.608462	−	0.793583i	$-0.708213\pi$
$541$	−15313.0	−1.21692	−0.608462	+	0.793583i	$0.708213\pi$
$542$	−13650.3	−1.08179
$543$	−423.914	−0.0335026
$544$	−20247.1	−1.59575
$545$	560.616	0.0440627
$546$	−580.222	−0.0454784
$547$	−13018.3	−1.01759	−0.508795	−	0.860888i	$-0.669909\pi$
$547$	−13018.3	−1.01759	−0.508795	+	0.860888i	$0.669909\pi$
$548$	−24674.7	−1.92345
$549$	2693.29	0.209375
$550$	−68847.4	−5.33757
$551$	9769.34	0.755332
$552$	0	0
$553$	3716.89	0.285820
$554$	−15624.9	−1.19826
$555$	1547.38	0.118347
$556$	−15444.6	−1.17805
$557$	−20343.1	−1.54751	−0.773756	−	0.633484i	$-0.781624\pi$
$557$	−20343.1	−1.54751	−0.773756	+	0.633484i	$0.781624\pi$
$558$	8830.26	0.669919
$559$	2528.50	0.191313
$560$	25337.9	1.91200
$561$	4202.90	0.316304
$562$	45671.2	3.42798
$563$	−11288.3	−0.845019	−0.422510	−	0.906358i	$-0.638851\pi$
$563$	−11288.3	−0.845019	−0.422510	+	0.906358i	$0.638851\pi$
$564$	−24053.2	−1.79579
$565$	−13978.1	−1.04082
$566$	8748.04	0.649660
$567$	430.502	0.0318861
$568$	64034.9	4.73036
$569$	26378.4	1.94348	0.971740	−	0.236056i	$-0.0758548\pi$
$569$	26378.4	1.94348	0.971740	+	0.236056i	$0.0758548\pi$
$570$	−21801.3	−1.60203
$571$	−2913.64	−0.213541	−0.106770	−	0.994284i	$-0.534051\pi$
$571$	−2913.64	−0.213541	−0.106770	+	0.994284i	$0.534051\pi$
$572$	7521.03	0.549773
$573$	1121.10	0.0817360
$574$	10973.3	0.797938
$575$	0	0
$576$	18755.3	1.35672
$577$	9221.13	0.665305	0.332652	−	0.943050i	$-0.392056\pi$
$577$	9221.13	0.665305	0.332652	+	0.943050i	$0.392056\pi$
$578$	22865.5	1.64546
$579$	5157.67	0.370200
$580$	60282.8	4.31570
$581$	603.631	0.0431030
$582$	−18734.8	−1.33433
$583$	26075.1	1.85235
$584$	−48817.5	−3.45904
$585$	1147.47	0.0810973
$586$	33872.5	2.38782
$587$	−19467.8	−1.36886	−0.684432	−	0.729077i	$-0.739950\pi$
$587$	−19467.8	−1.36886	−0.684432	+	0.729077i	$0.739950\pi$
$588$	−20877.6	−1.46425
$589$	−12317.1	−0.861659
$590$	−10328.0	−0.720671
$591$	−4616.94	−0.321346
$592$	6652.93	0.461881
$593$	−15038.6	−1.04142	−0.520708	−	0.853735i	$-0.674332\pi$
$593$	−15038.6	−1.04142	−0.520708	+	0.853735i	$0.674332\pi$
$594$	−7599.41	−0.524928
$595$	2790.81	0.192289
$596$	−54526.8	−3.74749
$597$	10667.3	0.731297
$598$	0	0
$599$	−19320.4	−1.31788	−0.658942	−	0.752194i	$-0.728996\pi$
$599$	−19320.4	−1.31788	−0.658942	+	0.752194i	$0.728996\pi$
$600$	−56817.1	−3.86591
$601$	23266.2	1.57912	0.789558	−	0.613676i	$-0.210310\pi$
$601$	23266.2	1.57912	0.789558	+	0.613676i	$0.210310\pi$
$602$	−11119.4	−0.752813
$603$	3120.08	0.210712
$604$	−61521.2	−4.14447
$605$	24992.6	1.67949
$606$	−1577.71	−0.105760
$607$	−8433.69	−0.563942	−0.281971	−	0.959423i	$-0.590988\pi$
$607$	−8433.69	−0.563942	−0.281971	+	0.959423i	$0.590988\pi$
$608$	−51065.6	−3.40622
$609$	2261.22	0.150459
$610$	−31569.5	−2.09543
$611$	−2404.85	−0.159231
$612$	5435.02	0.358983
$613$	−6879.73	−0.453294	−0.226647	−	0.973977i	$-0.572776\pi$
$613$	−6879.73	−0.453294	−0.226647	+	0.973977i	$0.572776\pi$
$614$	11291.7	0.742178
$615$	−21701.2	−1.42289
$616$	−21107.5	−1.38059
$617$	6232.26	0.406647	0.203324	−	0.979112i	$-0.434826\pi$
$617$	6232.26	0.406647	0.203324	+	0.979112i	$0.434826\pi$
$618$	4193.82	0.272977
$619$	−4161.10	−0.270192	−0.135096	−	0.990833i	$-0.543134\pi$
$619$	−4161.10	−0.270192	−0.135096	+	0.990833i	$0.543134\pi$
$620$	−76004.1	−4.92322
$621$	0	0
$622$	−3548.76	−0.228766
$623$	−5404.31	−0.347543
$624$	4933.52	0.316505
$625$	13632.3	0.872464
$626$	13643.1	0.871069
$627$	10600.2	0.675170
$628$	13336.0	0.847397
$629$	732.777	0.0464511
$630$	−5046.15	−0.319116
$631$	−12240.1	−0.772218	−0.386109	−	0.922453i	$-0.626181\pi$
$631$	−12240.1	−0.772218	−0.386109	+	0.922453i	$0.626181\pi$
$632$	−54147.2	−3.40801
$633$	8276.80	0.519705
$634$	−4252.34	−0.266375
$635$	−12605.0	−0.787737
$636$	33719.2	2.10229
$637$	−2087.35	−0.129833
$638$	−39916.1	−2.47695
$639$	−7443.43	−0.460810
$640$	−105827.	−6.53621
$641$	−31162.1	−1.92017	−0.960085	−	0.279709i	$-0.909762\pi$
$641$	−31162.1	−1.92017	−0.960085	+	0.279709i	$0.909762\pi$
$642$	−21161.7	−1.30091
$643$	6621.17	0.406086	0.203043	−	0.979170i	$-0.434917\pi$
$643$	6621.17	0.406086	0.203043	+	0.979170i	$0.434917\pi$
$644$	0	0
$645$	21990.1	1.34242
$646$	−10324.2	−0.628795
$647$	−12312.1	−0.748126	−0.374063	−	0.927403i	$-0.622036\pi$
$647$	−12312.1	−0.748126	−0.374063	+	0.927403i	$0.622036\pi$
$648$	−6271.50	−0.380197
$649$	5021.67	0.303725
$650$	−8901.32	−0.537136
$651$	−2850.93	−0.171639
$652$	−4569.35	−0.274463
$653$	23980.9	1.43713	0.718565	−	0.695460i	$-0.244799\pi$
$653$	23980.9	1.43713	0.718565	+	0.695460i	$0.244799\pi$
$654$	−480.034	−0.0287015
$655$	1262.36	0.0753043
$656$	−93303.9	−5.55321
$657$	5674.55	0.336964
$658$	10575.7	0.626570
$659$	9997.24	0.590952	0.295476	−	0.955350i	$-0.404522\pi$
$659$	9997.24	0.590952	0.295476	+	0.955350i	$0.404522\pi$
$660$	65409.8	3.85769
$661$	31185.4	1.83506	0.917529	−	0.397669i	$-0.130181\pi$
$661$	31185.4	1.83506	0.917529	+	0.397669i	$0.130181\pi$
$662$	46591.8	2.73541
$663$	543.396	0.0318307
$664$	−8793.62	−0.513944
$665$	7038.74	0.410452
$666$	−1324.96	−0.0770888
$667$	0	0
$668$	−73741.4	−4.27117
$669$	13121.6	0.758312
$670$	−36572.1	−2.10881
$671$	15349.7	0.883113
$672$	−11819.7	−0.678505
$673$	8399.39	0.481089	0.240544	−	0.970638i	$-0.422674\pi$
$673$	8399.39	0.481089	0.240544	+	0.970638i	$0.422674\pi$
$674$	11480.5	0.656100
$675$	6604.43	0.376599
$676$	−47603.5	−2.70844
$677$	−12550.9	−0.712513	−0.356257	−	0.934388i	$-0.615947\pi$
$677$	−12550.9	−0.712513	−0.356257	+	0.934388i	$0.615947\pi$
$678$	11968.9	0.677968
$679$	6048.70	0.341867
$680$	−40656.1	−2.29278
$681$	14508.7	0.816411
$682$	50325.8	2.82562
$683$	535.762	0.0300152	0.0150076	−	0.999887i	$-0.495223\pi$
$683$	535.762	0.0300152	0.0150076	+	0.999887i	$0.495223\pi$
$684$	13707.8	0.766271
$685$	−21455.2	−1.19673
$686$	19182.7	1.06764
$687$	−3793.98	−0.210698
$688$	94546.4	5.23917
$689$	3371.26	0.186408
$690$	0	0
$691$	−1756.89	−0.0967227	−0.0483614	−	0.998830i	$-0.515400\pi$
$691$	−1756.89	−0.0967227	−0.0483614	+	0.998830i	$0.515400\pi$
$692$	83685.9	4.59720
$693$	2453.54	0.134491
$694$	6621.19	0.362157
$695$	−13429.4	−0.732960
$696$	−32941.2	−1.79401
$697$	−10276.8	−0.558482
$698$	−65559.6	−3.55511
$699$	16724.1	0.904958
$700$	28744.4	1.55205
$701$	30446.3	1.64043	0.820214	−	0.572057i	$-0.193854\pi$
$701$	30446.3	1.64043	0.820214	+	0.572057i	$0.193854\pi$
$702$	−982.532	−0.0528252
$703$	1848.15	0.0991526
$704$	106891.	5.72244
$705$	−20914.8	−1.11730
$706$	−6920.82	−0.368935
$707$	509.379	0.0270964
$708$	6493.82	0.344707
$709$	2654.68	0.140619	0.0703093	−	0.997525i	$-0.477601\pi$
$709$	2654.68	0.140619	0.0703093	+	0.997525i	$0.477601\pi$
$710$	87248.5	4.61180
$711$	6294.08	0.331992
$712$	78729.2	4.14396
$713$	0	0
$714$	−2389.66	−0.125253
$715$	6539.69	0.342057
$716$	−96032.8	−5.01245
$717$	−9435.97	−0.491482
$718$	−47604.0	−2.47432
$719$	18176.8	0.942812	0.471406	−	0.881916i	$-0.343747\pi$
$719$	18176.8	0.942812	0.471406	+	0.881916i	$0.343747\pi$
$720$	42906.5	2.22087
$721$	−1354.01	−0.0699390
$722$	11598.3	0.597843
$723$	4716.72	0.242624
$724$	−3124.26	−0.160376
$725$	34689.9	1.77704
$726$	−21400.2	−1.09399
$727$	−3593.76	−0.183336	−0.0916680	−	0.995790i	$-0.529220\pi$
$727$	−3593.76	−0.183336	−0.0916680	+	0.995790i	$0.529220\pi$
$728$	−2729.00	−0.138933
$729$	729.000	0.0370370
$730$	−66514.5	−3.37234
$731$	10413.7	0.526899
$732$	19849.6	1.00227
$733$	19389.6	0.977039	0.488519	−	0.872553i	$-0.337537\pi$
$733$	19389.6	0.977039	0.488519	+	0.872553i	$0.337537\pi$
$734$	14475.7	0.727940
$735$	−18153.5	−0.911025
$736$	0	0
$737$	17782.1	0.888753
$738$	18581.9	0.926840
$739$	−10088.3	−0.502171	−0.251085	−	0.967965i	$-0.580787\pi$
$739$	−10088.3	−0.502171	−0.251085	+	0.967965i	$0.580787\pi$
$740$	11404.2	0.566523
$741$	1370.51	0.0679444
$742$	−14825.6	−0.733511
$743$	4662.85	0.230234	0.115117	−	0.993352i	$-0.463276\pi$
$743$	4662.85	0.230234	0.115117	+	0.993352i	$0.463276\pi$
$744$	41532.0	2.04655
$745$	−47412.2	−2.33161
$746$	−20260.4	−0.994353
$747$	1022.17	0.0500660
$748$	30975.5	1.51414
$749$	6832.26	0.333305
$750$	−37853.9	−1.84297
$751$	26570.0	1.29102	0.645508	−	0.763753i	$-0.276646\pi$
$751$	26570.0	1.29102	0.645508	+	0.763753i	$0.276646\pi$
$752$	−89923.0	−4.36058
$753$	−20397.1	−0.987136
$754$	−5160.77	−0.249263
$755$	−53494.0	−2.57860
$756$	3172.82	0.152638
$757$	2834.37	0.136086	0.0680430	−	0.997682i	$-0.478324\pi$
$757$	2834.37	0.136086	0.0680430	+	0.997682i	$0.478324\pi$
$758$	41195.5	1.97400
$759$	0	0
$760$	−102539.	−4.89407
$761$	15080.2	0.718339	0.359169	−	0.933272i	$-0.383060\pi$
$761$	15080.2	0.718339	0.359169	+	0.933272i	$0.383060\pi$
$762$	10793.2	0.513116
$763$	154.983	0.00735357
$764$	8262.56	0.391268
$765$	4725.87	0.223352
$766$	60774.9	2.86669
$767$	649.254	0.0305648
$768$	40601.5	1.90766
$769$	16155.8	0.757599	0.378799	−	0.925479i	$-0.376337\pi$
$769$	16155.8	0.757599	0.378799	+	0.925479i	$0.376337\pi$
$770$	−28759.2	−1.34599
$771$	−16910.9	−0.789924
$772$	38012.2	1.77214
$773$	22128.2	1.02962	0.514810	−	0.857304i	$-0.327862\pi$
$773$	22128.2	1.02962	0.514810	+	0.857304i	$0.327862\pi$
$774$	−18829.3	−0.874425
$775$	−43736.8	−2.02719
$776$	−88116.6	−4.07629
$777$	427.775	0.0197508
$778$	4172.57	0.192280
$779$	−25919.3	−1.19211
$780$	8456.87	0.388211
$781$	−42421.9	−1.94363
$782$	0	0
$783$	3829.09	0.174764
$784$	−78051.0	−3.55553
$785$	11596.0	0.527232
$786$	−1080.91	−0.0490517
$787$	−12270.5	−0.555775	−0.277887	−	0.960614i	$-0.589634\pi$
$787$	−12270.5	−0.555775	−0.277887	+	0.960614i	$0.589634\pi$
$788$	−34027.0	−1.53827
$789$	2172.85	0.0980425
$790$	−73776.3	−3.32258
$791$	−3864.26	−0.173701
$792$	−35742.8	−1.60362
$793$	1984.57	0.0888704
$794$	46162.0	2.06326
$795$	29319.6	1.30800
$796$	78618.5	3.50070
$797$	2401.69	0.106741	0.0533703	−	0.998575i	$-0.483004\pi$
$797$	2401.69	0.106741	0.0533703	+	0.998575i	$0.483004\pi$
$798$	−6027.00	−0.267360
$799$	−9904.44	−0.438540
$800$	−181329.	−8.01368
$801$	−9151.50	−0.403686
$802$	−33420.0	−1.47145
$803$	32340.7	1.42127
$804$	22995.1	1.00867
$805$	0	0
$806$	6506.66	0.284351
$807$	−15276.7	−0.666376
$808$	−7420.57	−0.323088
$809$	−4011.22	−0.174323	−0.0871613	−	0.996194i	$-0.527780\pi$
$809$	−4011.22	−0.174323	−0.0871613	+	0.996194i	$0.527780\pi$
$810$	−8545.00	−0.370668
$811$	−29258.1	−1.26682	−0.633410	−	0.773816i	$-0.718346\pi$
$811$	−29258.1	−1.26682	−0.633410	+	0.773816i	$0.718346\pi$
$812$	16665.3	0.720243
$813$	7462.91	0.321938
$814$	−7551.26	−0.325149
$815$	−3973.15	−0.170765
$816$	20318.8	0.871693
$817$	26264.5	1.12470
$818$	56631.4	2.42063
$819$	317.219	0.0135342
$820$	−159938.	−6.81132
$821$	43963.1	1.86885	0.934423	−	0.356166i	$-0.115916\pi$
$821$	43963.1	1.86885	0.934423	+	0.356166i	$0.115916\pi$
$822$	18371.3	0.779527
$823$	−28001.7	−1.18600	−0.592999	−	0.805203i	$-0.702056\pi$
$823$	−28001.7	−1.18600	−0.592999	+	0.805203i	$0.702056\pi$
$824$	19725.1	0.833926
$825$	37640.3	1.58844
$826$	−2855.19	−0.120272
$827$	−1106.96	−0.0465451	−0.0232726	−	0.999729i	$-0.507409\pi$
$827$	−1106.96	−0.0465451	−0.0232726	+	0.999729i	$0.507409\pi$
$828$	0	0
$829$	24536.1	1.02795	0.513977	−	0.857804i	$-0.328172\pi$
$829$	24536.1	1.02795	0.513977	+	0.857804i	$0.328172\pi$
$830$	−11981.4	−0.501062
$831$	8542.44	0.356599
$832$	13820.0	0.575867
$833$	−8596.81	−0.357577
$834$	11499.1	0.477436
$835$	−64119.7	−2.65743
$836$	78123.9	3.23202
$837$	−4827.68	−0.199366
$838$	4770.24	0.196641
$839$	10904.7	0.448714	0.224357	−	0.974507i	$-0.427972\pi$
$839$	10904.7	0.448714	0.224357	+	0.974507i	$0.427972\pi$
$840$	−23733.9	−0.974877
$841$	−4276.62	−0.175350
$842$	−91800.9	−3.75732
$843$	−24969.4	−1.02015
$844$	61000.3	2.48781
$845$	−41392.3	−1.68513
$846$	17908.5	0.727788
$847$	6909.25	0.280289
$848$	126059.	5.10483
$849$	−4782.73	−0.193337
$850$	−36660.3	−1.47934
$851$	0	0
$852$	−54858.3	−2.20589
$853$	34387.1	1.38030	0.690148	−	0.723668i	$-0.257545\pi$
$853$	34387.1	1.38030	0.690148	+	0.723668i	$0.257545\pi$
$854$	−8727.44	−0.349704
$855$	11919.2	0.476758
$856$	−99531.4	−3.97420
$857$	−37567.6	−1.49742	−0.748708	−	0.662899i	$-0.769326\pi$
$857$	−37567.6	−1.49742	−0.748708	+	0.662899i	$0.769326\pi$
$858$	−5599.69	−0.222809
$859$	13616.2	0.540835	0.270417	−	0.962743i	$-0.412838\pi$
$859$	13616.2	0.540835	0.270417	+	0.962743i	$0.412838\pi$
$860$	162068.	6.42613
$861$	−5999.32	−0.237464
$862$	27552.5	1.08868
$863$	21103.0	0.832394	0.416197	−	0.909275i	$-0.363363\pi$
$863$	21103.0	0.832394	0.416197	+	0.909275i	$0.363363\pi$
$864$	−20015.2	−0.788113
$865$	72766.7	2.86028
$866$	43263.3	1.69763
$867$	−12501.0	−0.489685
$868$	−21011.5	−0.821631
$869$	35871.5	1.40030
$870$	−44882.8	−1.74905
$871$	2299.05	0.0894380
$872$	−2257.78	−0.0876811
$873$	10242.7	0.397093
$874$	0	0
$875$	12221.5	0.472184
$876$	41821.6	1.61304
$877$	14346.1	0.552377	0.276188	−	0.961104i	$-0.410929\pi$
$877$	14346.1	0.552377	0.276188	+	0.961104i	$0.410929\pi$
$878$	−35600.6	−1.36841
$879$	−18518.8	−0.710607
$880$	244534.	9.36734
$881$	14876.9	0.568915	0.284457	−	0.958689i	$-0.408187\pi$
$881$	14876.9	0.568915	0.284457	+	0.958689i	$0.408187\pi$
$882$	15544.2	0.593424
$883$	−5526.75	−0.210634	−0.105317	−	0.994439i	$-0.533586\pi$
$883$	−5526.75	−0.210634	−0.105317	+	0.994439i	$0.533586\pi$
$884$	4004.84	0.152373
$885$	5646.51	0.214470
$886$	−84522.2	−3.20494
$887$	6294.73	0.238282	0.119141	−	0.992877i	$-0.461986\pi$
$887$	6294.73	0.238282	0.119141	+	0.992877i	$0.461986\pi$
$888$	−6231.77	−0.235501
$889$	−3484.67	−0.131465
$890$	107270.	4.04010
$891$	4154.75	0.156217
$892$	96706.7	3.63002
$893$	−24980.1	−0.936090
$894$	40597.3	1.51876
$895$	−83502.6	−3.11864
$896$	−29256.1	−1.09082
$897$	0	0
$898$	−1694.63	−0.0629738
$899$	−25357.5	−0.940735
$900$	48674.9	1.80277
$901$	13884.6	0.513389
$902$	105903.	3.90928
$903$	6079.21	0.224035
$904$	56294.1	2.07114
$905$	−2716.61	−0.0997826
$906$	45804.8	1.67965
$907$	−47078.8	−1.72351	−0.861757	−	0.507322i	$-0.830636\pi$
$907$	−47078.8	−1.72351	−0.861757	+	0.507322i	$0.830636\pi$
$908$	106930.	3.90814
$909$	862.568	0.0314737
$910$	−3718.30	−0.135451
$911$	−3032.26	−0.110278	−0.0551389	−	0.998479i	$-0.517560\pi$
$911$	−3032.26	−0.110278	−0.0551389	+	0.998479i	$0.517560\pi$
$912$	51246.5	1.86068
$913$	5825.61	0.211171
$914$	76475.5	2.76760
$915$	17259.7	0.623593
$916$	−27961.7	−1.00860
$917$	348.980	0.0125674
$918$	−4046.58	−0.145487
$919$	45892.2	1.64727	0.823637	−	0.567118i	$-0.191942\pi$
$919$	45892.2	1.64727	0.823637	+	0.567118i	$0.191942\pi$
$920$	0	0
$921$	−6173.42	−0.220870
$922$	−66947.8	−2.39133
$923$	−5484.76	−0.195594
$924$	18082.7	0.643805
$925$	6562.59	0.233272
$926$	−76929.5	−2.73009
$927$	−2292.84	−0.0812372
$928$	−105130.	−3.71882
$929$	−25198.6	−0.889922	−0.444961	−	0.895550i	$-0.646783\pi$
$929$	−25198.6	−0.889922	−0.444961	+	0.895550i	$0.646783\pi$
$930$	56587.9	1.99526
$931$	−21682.2	−0.763270
$932$	123258.	4.33201
$933$	1940.18	0.0680799
$934$	−108606.	−3.80481
$935$	26933.9	0.942066
$936$	−4621.21	−0.161377
$937$	18970.3	0.661401	0.330700	−	0.943736i	$-0.392715\pi$
$937$	18970.3	0.661401	0.330700	+	0.943736i	$0.392715\pi$
$938$	−10110.4	−0.351937
$939$	−7458.97	−0.259227
$940$	−154143.	−5.34849
$941$	32141.2	1.11347	0.556734	−	0.830691i	$-0.312054\pi$
$941$	32141.2	1.11347	0.556734	+	0.830691i	$0.312054\pi$
$942$	−9929.17	−0.343429
$943$	0	0
$944$	24277.1	0.837027
$945$	2758.83	0.0949680
$946$	−107313.	−3.68820
$947$	30613.9	1.05049	0.525247	−	0.850950i	$-0.323973\pi$
$947$	30613.9	1.05049	0.525247	+	0.850950i	$0.323973\pi$
$948$	46387.6	1.58924
$949$	4181.34	0.143026
$950$	−92461.5	−3.15773
$951$	2324.84	0.0792724
$952$	−11239.4	−0.382639
$953$	28603.5	0.972256	0.486128	−	0.873888i	$-0.338409\pi$
$953$	28603.5	0.972256	0.486128	+	0.873888i	$0.338409\pi$
$954$	−25105.2	−0.852004
$955$	7184.48	0.243439
$956$	−69543.4	−2.35271
$957$	21822.9	0.737131
$958$	−49927.9	−1.68382
$959$	−5931.33	−0.199721
$960$	120191.	4.04079
$961$	2179.56	0.0731616
$962$	−976.307	−0.0327208
$963$	11569.5	0.387148
$964$	34762.4	1.16143
$965$	33052.4	1.10259
$966$	0	0
$967$	46216.2	1.53693	0.768466	−	0.639891i	$-0.221021\pi$
$967$	46216.2	1.53693	0.768466	+	0.639891i	$0.221021\pi$
$968$	−100653.	−3.34206
$969$	5644.46	0.187127
$970$	−120060.	−3.97412
$971$	−1400.23	−0.0462775	−0.0231388	−	0.999732i	$-0.507366\pi$
$971$	−1400.23	−0.0462775	−0.0231388	+	0.999732i	$0.507366\pi$
$972$	5372.75	0.177295
$973$	−3712.59	−0.122323
$974$	−56697.5	−1.86520
$975$	4866.53	0.159850
$976$	74207.8	2.43374
$977$	18565.1	0.607933	0.303966	−	0.952683i	$-0.401689\pi$
$977$	18565.1	0.607933	0.303966	+	0.952683i	$0.401689\pi$
$978$	3402.06	0.111233
$979$	−52156.6	−1.70269
$980$	−133792.	−4.36106
$981$	262.444	0.00854149
$982$	−1010.63	−0.0328417
$983$	−37959.6	−1.23166	−0.615830	−	0.787879i	$-0.711179\pi$
$983$	−37959.6	−1.23166	−0.615830	+	0.787879i	$0.711179\pi$
$984$	87397.3	2.83143
$985$	−29587.2	−0.957082
$986$	−21254.7	−0.686500
$987$	−5781.94	−0.186465
$988$	10100.7	0.325249
$989$	0	0
$990$	−48700.0	−1.56342
$991$	−45809.5	−1.46840	−0.734201	−	0.678932i	$-0.762443\pi$
$991$	−45809.5	−1.46840	−0.734201	+	0.678932i	$0.762443\pi$
$992$	132547.	4.24232
$993$	−25472.7	−0.814050
$994$	24120.0	0.769658
$995$	68360.5	2.17806
$996$	7533.44	0.239665
$997$	−334.176	−0.0106153	−0.00530765	−	0.999986i	$-0.501689\pi$
$997$	−334.176	−0.0106153	−0.00530765	+	0.999986i	$0.501689\pi$
$998$	−50294.6	−1.59524
$999$	724.382	0.0229414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.4.a.o.1.1	yes	7
23.22	odd	2		1587.4.a.n.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1587.4.a.n.1.1	✓	7	23.22	odd	2
1587.4.a.o.1.1	yes	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)

\(f(q)\)	\(=\)	\(q-5.48727 q^{2} +3.00000 q^{3} +22.1101 q^{4} +19.2252 q^{5} -16.4618 q^{6} +5.31484 q^{7} -77.4259 q^{8} +9.00000 q^{9} -105.494 q^{10} +51.2932 q^{11} +66.3303 q^{12} +6.63173 q^{13} -29.1640 q^{14} +57.6756 q^{15} +247.976 q^{16} +27.3129 q^{17} -49.3854 q^{18} +68.8864 q^{19} +425.071 q^{20} +15.9445 q^{21} -281.459 q^{22} -232.278 q^{24} +244.609 q^{25} -36.3901 q^{26} +27.0000 q^{27} +117.512 q^{28} +141.818 q^{29} -316.482 q^{30} -178.803 q^{31} -741.302 q^{32} +153.880 q^{33} -149.873 q^{34} +102.179 q^{35} +198.991 q^{36} +26.8290 q^{37} -377.998 q^{38} +19.8952 q^{39} -1488.53 q^{40} -376.262 q^{41} -87.4919 q^{42} +381.273 q^{43} +1134.10 q^{44} +173.027 q^{45} -362.628 q^{47} +743.927 q^{48} -314.752 q^{49} -1342.23 q^{50} +81.9388 q^{51} +146.628 q^{52} +508.353 q^{53} -148.156 q^{54} +986.122 q^{55} -411.507 q^{56} +206.659 q^{57} -778.194 q^{58} +97.9012 q^{59} +1275.21 q^{60} +299.254 q^{61} +981.141 q^{62} +47.8336 q^{63} +2083.92 q^{64} +127.496 q^{65} -844.378 q^{66} +346.675 q^{67} +603.891 q^{68} -560.683 q^{70} -827.048 q^{71} -696.833 q^{72} +630.506 q^{73} -147.218 q^{74} +733.826 q^{75} +1523.08 q^{76} +272.615 q^{77} -109.170 q^{78} +699.342 q^{79} +4767.39 q^{80} +81.0000 q^{81} +2064.65 q^{82} +113.575 q^{83} +352.535 q^{84} +525.096 q^{85} -2092.14 q^{86} +425.454 q^{87} -3971.42 q^{88} -1016.83 q^{89} -949.445 q^{90} +35.2466 q^{91} -536.409 q^{93} +1989.84 q^{94} +1324.35 q^{95} -2223.91 q^{96} +1138.08 q^{97} +1727.13 q^{98} +461.639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 21 q^{3} + 38 q^{4} + 10 q^{5} - 17 q^{7} - 36 q^{8} + 63 q^{9} - 65 q^{10} + 5 q^{11} + 114 q^{12} + 152 q^{13} + 23 q^{14} + 30 q^{15} + 314 q^{16} - 22 q^{17} + 38 q^{19} + 171 q^{20} - 51 q^{21}+ \cdots + 45 q^{99}+O(q^{100}) \) 7 * q + 21 * q^3 + 38 * q^4 + 10 * q^5 - 17 * q^7 - 36 * q^8 + 63 * q^9 - 65 * q^10 + 5 * q^11 + 114 * q^12 + 152 * q^13 + 23 * q^14 + 30 * q^15 + 314 * q^16 - 22 * q^17 + 38 * q^19 + 171 * q^20 - 51 * q^21 - 233 * q^22 - 108 * q^24 + 643 * q^25 - 221 * q^26 + 189 * q^27 + 145 * q^28 + 567 * q^29 - 195 * q^30 + 121 * q^31 - 468 * q^32 + 15 * q^33 + 260 * q^34 + 256 * q^35 + 342 * q^36 + 108 * q^37 - 964 * q^38 + 456 * q^39 - 1089 * q^40 + 442 * q^41 + 69 * q^42 + 68 * q^43 + 2121 * q^44 + 90 * q^45 + 464 * q^47 + 942 * q^48 + 48 * q^49 - 2111 * q^50 - 66 * q^51 + 1979 * q^52 + 189 * q^53 + 314 * q^55 - 1561 * q^56 + 114 * q^57 + 1384 * q^58 + 241 * q^59 + 513 * q^60 - 1084 * q^61 - 143 * q^62 - 153 * q^63 + 2458 * q^64 + 1126 * q^65 - 699 * q^66 + 1368 * q^67 - 1284 * q^68 + 1618 * q^70 + 232 * q^71 - 324 * q^72 - 657 * q^73 + 3190 * q^74 + 1929 * q^75 - 132 * q^76 + 2089 * q^77 - 663 * q^78 + 447 * q^79 + 6707 * q^80 + 567 * q^81 + 2823 * q^82 - 1675 * q^83 + 435 * q^84 + 1320 * q^85 - 4566 * q^86 + 1701 * q^87 + 715 * q^88 - 1552 * q^89 - 585 * q^90 - 2498 * q^91 + 363 * q^93 + 5240 * q^94 + 1722 * q^95 - 1404 * q^96 + 1599 * q^97 + 3491 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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