LMFDB - Embedded newform 1587.4.a.n.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	$-0.829398\pi$
$5$	−19.2252	−1.71955	−0.859777	+	0.510669i	$0.829398\pi$
$6$	−16.4618	−1.12008
$7$	−5.31484	−0.286975	−0.143487	−	0.989652i	$-0.545832\pi$
$7$	−5.31484	−0.286975	−0.143487	+	0.989652i	$0.545832\pi$
$8$	−77.4259	−3.42177
$9$	9.00000	0.333333
$10$	105.494	3.33601
$11$	−51.2932	−1.40595	−0.702976	−	0.711213i	$-0.748146\pi$
$11$	−51.2932	−1.40595	−0.702976	+	0.711213i	$0.748146\pi$
$12$	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	$-0.562417\pi$
$17$	−27.3129	−0.389668	−0.194834	+	0.980836i	$0.562417\pi$
$18$	−49.3854	−0.646681
$19$	−68.8864	−0.831769	−0.415885	−	0.909417i	$-0.636528\pi$
$19$	−68.8864	−0.831769	−0.415885	+	0.909417i	$0.636528\pi$
$20$	−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	$-0.518984\pi$
$37$	−26.8290	−0.119207	−0.0596034	+	0.998222i	$0.518984\pi$
$38$	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	$-0.736326\pi$
$43$	−381.273	−1.35217	−0.676087	+	0.736821i	$0.736326\pi$
$44$	−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	$-0.728915\pi$
$53$	−508.353	−1.31750	−0.658752	+	0.752360i	$0.728915\pi$
$54$	−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	$-0.601690\pi$
$61$	−299.254	−0.628124	−0.314062	+	0.949402i	$0.601690\pi$
$62$	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	$-0.602363\pi$
$67$	−346.675	−0.632136	−0.316068	+	0.948737i	$0.602363\pi$
$68$	−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	$-0.665928\pi$
$79$	−699.342	−0.995976	−0.497988	+	0.867184i	$0.665928\pi$
$80$	−4767.39	−6.66262
$81$	81.0000	0.111111
$82$	2064.65	2.78052
$83$	−113.575	−0.150198	−0.0750990	−	0.997176i	$-0.523927\pi$
$83$	−113.575	−0.150198	−0.0750990	+	0.997176i	$0.523927\pi$
$84$	−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	$-0.292962\pi$
$89$	1016.83	1.21106	0.605529	+	0.795824i	$0.292962\pi$
$90$	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	$-0.703101\pi$
$97$	−1138.08	−1.19128	−0.595640	+	0.803252i	$0.703101\pi$
$98$	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	$-0.461115\pi$
$103$	254.760	0.243712	0.121856	+	0.992548i	$0.461115\pi$
$104$	−513.468	−0.484131
$105$	306.537	0.284904
$106$	2789.47	2.55601
$107$	−1285.51	−1.16144	−0.580722	−	0.814102i	$-0.697230\pi$
$107$	−1285.51	−1.16144	−0.580722	+	0.814102i	$0.697230\pi$
$108$	596.973	0.531886
$109$	−29.1605	−0.0256245	−0.0128122	−	0.999918i	$-0.504078\pi$
$109$	−29.1605	−0.0256245	−0.0128122	+	0.999918i	$0.504078\pi$
$110$	−5411.12	−4.69027
$111$	−80.4869	−0.0688241
$112$	−1317.95	−1.11192
$113$	727.070	0.605283	0.302642	−	0.953104i	$-0.402131\pi$
$113$	727.070	0.605283	0.302642	+	0.953104i	$0.402131\pi$
$114$	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	$-0.386869\pi$
$137$	1115.99	0.695955	0.347977	+	0.937503i	$0.386869\pi$
$138$	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	$-0.262860\pi$
$149$	2466.15	1.35594	0.677969	+	0.735090i	$0.262860\pi$
$150$	−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	$-0.548992\pi$
$157$	−603.164	−0.306610	−0.153305	+	0.988179i	$0.548992\pi$
$158$	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	$-0.490763\pi$
$181$	141.305	0.0580282	0.0290141	+	0.999579i	$0.490763\pi$
$182$	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	$-0.522551\pi$
$191$	−373.701	−0.141571	−0.0707855	+	0.997492i	$0.522551\pi$
$192$	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	$-0.718309\pi$
$199$	−3555.77	−1.26664	−0.633322	+	0.773889i	$0.718309\pi$
$200$	−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	$-0.749967\pi$
$227$	−4836.24	−1.41407	−0.707033	+	0.707181i	$0.749967\pi$
$228$	−4569.25	−1.32722
$229$	1264.66	0.364939	0.182469	−	0.983212i	$-0.441591\pi$
$229$	1264.66	0.364939	0.182469	+	0.983212i	$0.441591\pi$
$230$	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	$-0.567385\pi$
$241$	−1572.24	−0.420236	−0.210118	+	0.977676i	$0.567385\pi$
$242$	−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	$-0.173628\pi$
$251$	6799.05	1.70977	0.854885	+	0.518818i	$0.173628\pi$
$252$	−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	$-0.527059\pi$
$263$	−724.284	−0.169815	−0.0849073	+	0.996389i	$0.527059\pi$
$264$	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	$-0.155194\pi$
$281$	8323.12	1.76696	0.883480	+	0.468469i	$0.155194\pi$
$282$	5969.51	1.26057
$283$	1594.24	0.334869	0.167434	−	0.985883i	$-0.446452\pi$
$283$	1594.24	0.334869	0.167434	+	0.985883i	$0.446452\pi$
$284$	−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	$-0.288993\pi$
$293$	6172.93	1.23081	0.615403	+	0.788212i	$0.288993\pi$
$294$	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	$-0.427926\pi$
$313$	2486.32	0.448995	0.224497	+	0.974475i	$0.427926\pi$
$314$	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	$-0.445916\pi$
$337$	2092.20	0.338188	0.169094	+	0.985600i	$0.445916\pi$
$338$	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	$-0.720113\pi$
$359$	−8675.35	−1.27540	−0.637699	+	0.770286i	$0.720113\pi$
$360$	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	$-0.439926\pi$
$367$	2638.05	0.375218	0.187609	+	0.982244i	$0.439926\pi$
$368$	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	$-0.582494\pi$
$373$	−3692.27	−0.512542	−0.256271	+	0.966605i	$0.582494\pi$
$374$	−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	$-0.330107\pi$
$379$	7507.48	1.01750	0.508751	+	0.860914i	$0.330107\pi$
$380$	29281.6	3.95293
$381$	−1966.94	−0.264487
$382$	2050.60	0.274654
$383$	11075.6	1.47764	0.738822	−	0.673901i	$-0.235383\pi$
$383$	11075.6	1.47764	0.738822	+	0.673901i	$0.235383\pi$
$384$	−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	$-0.484219\pi$
$389$	760.409	0.0991113	0.0495556	+	0.998771i	$0.484219\pi$
$390$	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	$-0.623811\pi$
$401$	−6090.46	−0.758462	−0.379231	+	0.925302i	$0.623811\pi$
$402$	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	$-0.483861\pi$
$419$	869.329	0.101359	0.0506796	+	0.998715i	$0.483861\pi$
$420$	6777.56	0.787407
$421$	−16729.8	−1.93672	−0.968362	−	0.249551i	$-0.919717\pi$
$421$	−16729.8	−1.93672	−0.968362	+	0.249551i	$0.919717\pi$
$422$	−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	$-0.409473\pi$
$431$	5021.18	0.561164	0.280582	+	0.959830i	$0.409473\pi$
$432$	6695.35	0.745671
$433$	7884.30	0.875047	0.437523	−	0.899207i	$-0.355856\pi$
$433$	7884.30	0.875047	0.437523	+	0.899207i	$0.355856\pi$
$434$	−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	$-0.247207\pi$
$457$	13936.9	1.42657	0.713283	+	0.700876i	$0.247207\pi$
$458$	−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	$-0.937200\pi$
$467$	−19792.4	−1.96120	−0.980601	+	0.196014i	$0.937200\pi$
$468$	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	$-0.642886\pi$
$479$	−9098.87	−0.867929	−0.433965	+	0.900930i	$0.642886\pi$
$480$	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	$-0.422168\pi$
$503$	5462.01	0.484173	0.242086	+	0.970255i	$0.422168\pi$
$504$	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	$-0.778955\pi$
$521$	−18276.1	−1.53683	−0.768416	+	0.639951i	$0.778955\pi$
$522$	−7003.75	−0.587252
$523$	−4461.02	−0.372977	−0.186488	−	0.982457i	$-0.559711\pi$
$523$	−4461.02	−0.372977	−0.186488	+	0.982457i	$0.559711\pi$
$524$	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	$-0.218376\pi$
$557$	20343.1	1.54751	0.773756	+	0.633484i	$0.218376\pi$
$558$	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	$-0.361149\pi$
$563$	11288.3	0.845019	0.422510	+	0.906358i	$0.361149\pi$
$564$	−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	$-0.924145\pi$
$569$	−26378.4	−1.94348	−0.971740	+	0.236056i	$0.924145\pi$
$570$	−21801.3	−1.60203
$571$	2913.64	0.213541	0.106770	−	0.994284i	$-0.465949\pi$
$571$	2913.64	0.213541	0.106770	+	0.994284i	$0.465949\pi$
$572$	−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	$-0.427224\pi$
$613$	6879.73	0.453294	0.226647	+	0.973977i	$0.427224\pi$
$614$	11291.7	0.742178
$615$	21701.2	1.42289
$616$	−21107.5	−1.38059
$617$	−6232.26	−0.406647	−0.203324	−	0.979112i	$-0.565174\pi$
$617$	−6232.26	−0.406647	−0.203324	+	0.979112i	$0.565174\pi$
$618$	−4193.82	−0.272977
$619$	4161.10	0.270192	0.135096	−	0.990833i	$-0.456866\pi$
$619$	4161.10	0.270192	0.135096	+	0.990833i	$0.456866\pi$
$620$	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	$-0.373819\pi$
$631$	12240.1	0.772218	0.386109	+	0.922453i	$0.373819\pi$
$632$	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	$-0.0902378\pi$
$641$	31162.1	1.92017	0.960085	+	0.279709i	$0.0902378\pi$
$642$	21161.7	1.30091
$643$	−6621.17	−0.406086	−0.203043	−	0.979170i	$-0.565083\pi$
$643$	−6621.17	−0.406086	−0.203043	+	0.979170i	$0.565083\pi$
$644$	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	$-0.595478\pi$
$659$	−9997.24	−0.590952	−0.295476	+	0.955350i	$0.595478\pi$
$660$	65409.8	3.85769
$661$	−31185.4	−1.83506	−0.917529	−	0.397669i	$-0.869819\pi$
$661$	−31185.4	−1.83506	−0.917529	+	0.397669i	$0.869819\pi$
$662$	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	$-0.384053\pi$
$677$	12550.9	0.712513	0.356257	+	0.934388i	$0.384053\pi$
$678$	−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	$-0.806146\pi$
$701$	−30446.3	−1.64043	−0.820214	+	0.572057i	$0.806146\pi$
$702$	−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	$-0.522399\pi$
$709$	−2654.68	−0.140619	−0.0703093	+	0.997525i	$0.522399\pi$
$710$	−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	$-0.470780\pi$
$727$	3593.76	0.183336	0.0916680	+	0.995790i	$0.470780\pi$
$728$	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	$-0.662463\pi$
$733$	−19389.6	−0.977039	−0.488519	+	0.872553i	$0.662463\pi$
$734$	−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	$-0.536724\pi$
$743$	−4662.85	−0.230234	−0.115117	+	0.993352i	$0.536724\pi$
$744$	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	$-0.723354\pi$
$751$	−26570.0	−1.29102	−0.645508	+	0.763753i	$0.723354\pi$
$752$	−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	$-0.521676\pi$
$757$	−2834.37	−0.136086	−0.0680430	+	0.997682i	$0.521676\pi$
$758$	−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	$-0.623663\pi$
$769$	−16155.8	−0.757599	−0.378799	+	0.925479i	$0.623663\pi$
$770$	28759.2	1.34599
$771$	−16910.9	−0.789924
$772$	38012.2	1.77214
$773$	−22128.2	−1.02962	−0.514810	−	0.857304i	$-0.672138\pi$
$773$	−22128.2	−1.02962	−0.514810	+	0.857304i	$0.672138\pi$
$774$	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	$-0.410366\pi$
$787$	12270.5	0.555775	0.277887	+	0.960614i	$0.410366\pi$
$788$	−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	$-0.516996\pi$
$797$	−2401.69	−0.106741	−0.0533703	+	0.998575i	$0.516996\pi$
$798$	−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	$-0.492591\pi$
$827$	1106.96	0.0465451	0.0232726	+	0.999729i	$0.492591\pi$
$828$	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	$-0.572028\pi$
$839$	−10904.7	−0.448714	−0.224357	+	0.974507i	$0.572028\pi$
$840$	−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	$-0.591813\pi$
$881$	−14876.9	−0.568915	−0.284457	+	0.958689i	$0.591813\pi$
$882$	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	$-0.169364\pi$
$907$	47078.8	1.72351	0.861757	+	0.507322i	$0.169364\pi$
$908$	−106930.	−3.90814
$909$	862.568	0.0314737
$910$	−3718.30	−0.135451
$911$	3032.26	0.110278	0.0551389	−	0.998479i	$-0.482440\pi$
$911$	3032.26	0.110278	0.0551389	+	0.998479i	$0.482440\pi$
$912$	−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	$-0.808058\pi$
$919$	−45892.2	−1.64727	−0.823637	+	0.567118i	$0.808058\pi$
$920$	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	$-0.607285\pi$
$937$	−18970.3	−0.661401	−0.330700	+	0.943736i	$0.607285\pi$
$938$	−10110.4	−0.351937
$939$	7458.97	0.259227
$940$	154143.	5.34849
$941$	−32141.2	−1.11347	−0.556734	−	0.830691i	$-0.687946\pi$
$941$	−32141.2	−1.11347	−0.556734	+	0.830691i	$0.687946\pi$
$942$	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	$-0.661591\pi$
$953$	−28603.5	−0.972256	−0.486128	+	0.873888i	$0.661591\pi$
$954$	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	$-0.492634\pi$
$971$	1400.23	0.0462775	0.0231388	+	0.999732i	$0.492634\pi$
$972$	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	$-0.598311\pi$
$977$	−18565.1	−0.607933	−0.303966	+	0.952683i	$0.598311\pi$
$978$	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	$-0.288821\pi$
$983$	37959.6	1.23166	0.615830	+	0.787879i	$0.288821\pi$
$984$	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.n.1.1	✓	7
23.22	odd	2		1587.4.a.o.1.1	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1587.4.a.n.1.1	✓	7	1.1	even	1	trivial
1587.4.a.o.1.1	yes	7	23.22	odd	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:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
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

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Groups

Database

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