LMFDB - Embedded newform 637.4.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,4,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	637.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$37.5842166737$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5364412.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 27x^{2} - 24x + 76 $ x^4 - 27x^2 - 24x + 76
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.32361$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.323612 q^{2} -1.75980 q^{3} -7.89528 q^{4} +5.91876 q^{5} -0.569491 q^{6} -5.14391 q^{8} -23.9031 q^{9} +O(q^{10})$	\(q+0.323612 q^{2} -1.75980 q^{3} -7.89528 q^{4} +5.91876 q^{5} -0.569491 q^{6} -5.14391 q^{8} -23.9031 q^{9} +1.91538 q^{10} -60.8448 q^{11} +13.8941 q^{12} +13.0000 q^{13} -10.4158 q^{15} +61.4976 q^{16} +1.36094 q^{17} -7.73534 q^{18} +4.20658 q^{19} -46.7303 q^{20} -19.6901 q^{22} -10.6695 q^{23} +9.05222 q^{24} -89.9682 q^{25} +4.20696 q^{26} +89.5791 q^{27} +124.031 q^{29} -3.37068 q^{30} -90.9367 q^{31} +61.0526 q^{32} +107.074 q^{33} +0.440417 q^{34} +188.722 q^{36} +101.085 q^{37} +1.36130 q^{38} -22.8773 q^{39} -30.4456 q^{40} -235.305 q^{41} +6.98363 q^{43} +480.386 q^{44} -141.477 q^{45} -3.45278 q^{46} +243.878 q^{47} -108.223 q^{48} -29.1148 q^{50} -2.39498 q^{51} -102.639 q^{52} -282.024 q^{53} +28.9889 q^{54} -360.126 q^{55} -7.40271 q^{57} +40.1380 q^{58} +675.683 q^{59} +82.2357 q^{60} -87.6018 q^{61} -29.4282 q^{62} -472.223 q^{64} +76.9439 q^{65} +34.6506 q^{66} +122.719 q^{67} -10.7450 q^{68} +18.7761 q^{69} +35.3966 q^{71} +122.955 q^{72} +1073.70 q^{73} +32.7124 q^{74} +158.326 q^{75} -33.2121 q^{76} -7.40339 q^{78} +811.612 q^{79} +363.990 q^{80} +487.743 q^{81} -76.1477 q^{82} +1102.66 q^{83} +8.05509 q^{85} +2.25999 q^{86} -218.269 q^{87} +312.980 q^{88} +1093.27 q^{89} -45.7837 q^{90} +84.2387 q^{92} +160.030 q^{93} +78.9220 q^{94} +24.8977 q^{95} -107.440 q^{96} -911.865 q^{97} +1454.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9 + 44 * q^10 - 95 * q^11 + 17 * q^12 + 52 * q^13 - 16 * q^15 + 58 * q^16 + 146 * q^17 + 65 * q^18 + 48 * q^19 + 474 * q^20 - 143 * q^22 - 121 * q^23 + 469 * q^24 + 506 * q^25 - 52 * q^26 + 83 * q^27 - 440 * q^29 + 1548 * q^30 + 283 * q^31 - 114 * q^32 - 227 * q^33 - 1234 * q^34 + 755 * q^36 - 209 * q^37 - 440 * q^38 + 65 * q^39 - 754 * q^40 + 93 * q^41 + 526 * q^43 + 217 * q^44 + 768 * q^45 - 841 * q^46 + 783 * q^47 - 1407 * q^48 + 446 * q^50 - 672 * q^51 + 338 * q^52 - 340 * q^53 + 199 * q^54 - 756 * q^55 - 1014 * q^57 + 1916 * q^58 + 922 * q^59 - 396 * q^60 + 141 * q^61 - 1745 * q^62 - 1510 * q^64 + 468 * q^65 - 503 * q^66 - 523 * q^67 + 1710 * q^68 - 1595 * q^69 + 1468 * q^71 - 9 * q^72 + 47 * q^73 - 2249 * q^74 + 1547 * q^75 + 1382 * q^76 + 585 * q^78 + 1025 * q^79 + 2538 * q^80 - 1772 * q^81 + 1561 * q^82 + 1190 * q^83 - 568 * q^85 + 738 * q^86 - 720 * q^87 - 555 * q^88 + 2962 * q^89 + 1960 * q^90 - 599 * q^92 - 763 * q^93 - 317 * q^94 + 2082 * q^95 + 45 * q^96 - 2715 * q^97 + 586 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.323612	0.114414	0.0572071	−	0.998362i	$-0.481780\pi$
$2$	0.323612	0.114414	0.0572071	+	0.998362i	$0.481780\pi$
$3$	−1.75980	−0.338673	−0.169336	−	0.985558i	$-0.554162\pi$
$3$	−1.75980	−0.338673	−0.169336	+	0.985558i	$0.554162\pi$
$4$	−7.89528	−0.986909
$5$	5.91876	0.529390	0.264695	−	0.964332i	$-0.414729\pi$
$5$	5.91876	0.529390	0.264695	+	0.964332i	$0.414729\pi$
$6$	−0.569491	−0.0387490
$7$	0	0
$7$	0	0
$8$	−5.14391	−0.227331
$9$	−23.9031	−0.885301
$10$	1.91538	0.0605698
$11$	−60.8448	−1.66776	−0.833882	−	0.551943i	$-0.813886\pi$
$11$	−60.8448	−1.66776	−0.833882	+	0.551943i	$0.813886\pi$
$12$	13.8941	0.334239
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	−10.4158	−0.179290
$16$	61.4976	0.960900
$17$	1.36094	0.0194163	0.00970813	−	0.999953i	$-0.496910\pi$
$17$	1.36094	0.0194163	0.00970813	+	0.999953i	$0.496910\pi$
$18$	−7.73534	−0.101291
$19$	4.20658	0.0507923	0.0253962	−	0.999677i	$-0.491915\pi$
$19$	4.20658	0.0507923	0.0253962	+	0.999677i	$0.491915\pi$
$20$	−46.7303	−0.522460
$21$	0	0
$22$	−19.6901	−0.190816
$23$	−10.6695	−0.0967281	−0.0483640	−	0.998830i	$-0.515401\pi$
$23$	−10.6695	−0.0967281	−0.0483640	+	0.998830i	$0.515401\pi$
$24$	9.05222	0.0769907
$25$	−89.9682	−0.719746
$26$	4.20696	0.0317328
$27$	89.5791	0.638500
$28$	0	0
$29$	124.031	0.794207	0.397103	−	0.917774i	$-0.370015\pi$
$29$	124.031	0.794207	0.397103	+	0.917774i	$0.370015\pi$
$30$	−3.37068	−0.0205133
$31$	−90.9367	−0.526862	−0.263431	−	0.964678i	$-0.584854\pi$
$31$	−90.9367	−0.526862	−0.263431	+	0.964678i	$0.584854\pi$
$32$	61.0526	0.337271
$33$	107.074	0.564826
$34$	0.440417	0.00222150
$35$	0	0
$36$	188.722	0.873712
$37$	101.085	0.449143	0.224572	−	0.974458i	$-0.427902\pi$
$37$	101.085	0.449143	0.224572	+	0.974458i	$0.427902\pi$
$38$	1.36130	0.00581137
$39$	−22.8773	−0.0939309
$40$	−30.4456	−0.120347
$41$	−235.305	−0.896306	−0.448153	−	0.893957i	$-0.647918\pi$
$41$	−235.305	−0.896306	−0.448153	+	0.893957i	$0.647918\pi$
$42$	0	0
$43$	6.98363	0.0247673	0.0123836	−	0.999923i	$-0.496058\pi$
$43$	6.98363	0.0247673	0.0123836	+	0.999923i	$0.496058\pi$
$44$	480.386	1.64593
$45$	−141.477	−0.468670
$46$	−3.45278	−0.0110671
$47$	243.878	0.756879	0.378440	−	0.925626i	$-0.376461\pi$
$47$	243.878	0.756879	0.378440	+	0.925626i	$0.376461\pi$
$48$	−108.223	−0.325430
$49$	0	0
$50$	−29.1148	−0.0823491
$51$	−2.39498	−0.00657576
$52$	−102.639	−0.273719
$53$	−282.024	−0.730924	−0.365462	−	0.930826i	$-0.619089\pi$
$53$	−282.024	−0.730924	−0.365462	+	0.930826i	$0.619089\pi$
$54$	28.9889	0.0730535
$55$	−360.126	−0.882898
$56$	0	0
$57$	−7.40271	−0.0172020
$58$	40.1380	0.0908685
$59$	675.683	1.49096	0.745479	−	0.666529i	$-0.232221\pi$
$59$	675.683	1.49096	0.745479	+	0.666529i	$0.232221\pi$
$60$	82.2357	0.176943
$61$	−87.6018	−0.183873	−0.0919365	−	0.995765i	$-0.529306\pi$
$61$	−87.6018	−0.183873	−0.0919365	+	0.995765i	$0.529306\pi$
$62$	−29.4282	−0.0602805
$63$	0	0
$64$	−472.223	−0.922311
$65$	76.9439	0.146826
$66$	34.6506	0.0646241
$67$	122.719	0.223768	0.111884	−	0.993721i	$-0.464311\pi$
$67$	122.719	0.223768	0.111884	+	0.993721i	$0.464311\pi$
$68$	−10.7450	−0.0191621
$69$	18.7761	0.0327592
$70$	0	0
$71$	35.3966	0.0591663	0.0295831	−	0.999562i	$-0.490582\pi$
$71$	35.3966	0.0591663	0.0295831	+	0.999562i	$0.490582\pi$
$72$	122.955	0.201256
$73$	1073.70	1.72147	0.860733	−	0.509057i	$-0.170006\pi$
$73$	1073.70	1.72147	0.860733	+	0.509057i	$0.170006\pi$
$74$	32.7124	0.0513884
$75$	158.326	0.243758
$76$	−33.2121	−0.0501274
$77$	0	0
$78$	−7.40339	−0.0107470
$79$	811.612	1.15587	0.577934	−	0.816084i	$-0.303859\pi$
$79$	811.612	1.15587	0.577934	+	0.816084i	$0.303859\pi$
$80$	363.990	0.508691
$81$	487.743	0.669058
$82$	−76.1477	−0.102550
$83$	1102.66	1.45823	0.729116	−	0.684391i	$-0.239932\pi$
$83$	1102.66	1.45823	0.729116	+	0.684391i	$0.239932\pi$
$84$	0	0
$85$	8.05509	0.0102788
$86$	2.25999	0.00283373
$87$	−218.269	−0.268976
$88$	312.980	0.379134
$89$	1093.27	1.30209	0.651044	−	0.759040i	$-0.274331\pi$
$89$	1093.27	1.30209	0.651044	+	0.759040i	$0.274331\pi$
$90$	−45.7837	−0.0536225
$91$	0	0
$92$	84.2387	0.0954618
$93$	160.030	0.178434
$94$	78.9220	0.0865977
$95$	24.8977	0.0268890
$96$	−107.440	−0.114225
$97$	−911.865	−0.954494	−0.477247	−	0.878769i	$-0.658365\pi$
$97$	−911.865	−0.954494	−0.477247	+	0.878769i	$0.658365\pi$
$98$	0	0
$99$	1454.38	1.47647
$100$	710.324	0.710324
$101$	1708.38	1.68307	0.841535	−	0.540202i	$-0.181652\pi$
$101$	1708.38	1.68307	0.841535	+	0.540202i	$0.181652\pi$
$102$	−0.775044	−0.000752360 0
$103$	833.431	0.797285	0.398643	−	0.917106i	$-0.369481\pi$
$103$	833.431	0.797285	0.398643	+	0.917106i	$0.369481\pi$
$104$	−66.8708	−0.0630502
$105$	0	0
$106$	−91.2664	−0.0836281
$107$	296.677	0.268045	0.134022	−	0.990978i	$-0.457211\pi$
$107$	296.677	0.268045	0.134022	+	0.990978i	$0.457211\pi$
$108$	−707.251	−0.630142
$109$	−2012.35	−1.76833	−0.884166	−	0.467173i	$-0.845272\pi$
$109$	−2012.35	−1.76833	−0.884166	+	0.467173i	$0.845272\pi$
$110$	−116.541	−0.101016
$111$	−177.889	−0.152113
$112$	0	0
$113$	−459.400	−0.382448	−0.191224	−	0.981546i	$-0.561246\pi$
$113$	−459.400	−0.382448	−0.191224	+	0.981546i	$0.561246\pi$
$114$	−2.39561	−0.00196815
$115$	−63.1503	−0.0512069
$116$	−979.259	−0.783810
$117$	−310.741	−0.245538
$118$	218.659	0.170587
$119$	0	0
$120$	53.5780	0.0407581
$121$	2371.09	1.78143
$122$	−28.3490	−0.0210377
$123$	414.089	0.303554
$124$	717.971	0.519965
$125$	−1272.35	−0.910417
$126$	0	0
$127$	2573.78	1.79832	0.899158	−	0.437624i	$-0.144180\pi$
$127$	2573.78	1.79832	0.899158	+	0.437624i	$0.144180\pi$
$128$	−641.238	−0.442797
$129$	−12.2898	−0.00838801
$130$	24.9000	0.0167990
$131$	−599.610	−0.399910	−0.199955	−	0.979805i	$-0.564080\pi$
$131$	−599.610	−0.399910	−0.199955	+	0.979805i	$0.564080\pi$
$132$	−845.382	−0.557432
$133$	0	0
$134$	39.7133	0.0256023
$135$	530.197	0.338016
$136$	−7.00055	−0.00441391
$137$	−1501.25	−0.936207	−0.468104	−	0.883674i	$-0.655063\pi$
$137$	−1501.25	−0.936207	−0.468104	+	0.883674i	$0.655063\pi$
$138$	6.07619	0.00374811
$139$	−2652.59	−1.61863	−0.809316	−	0.587374i	$-0.800162\pi$
$139$	−2652.59	−1.61863	−0.809316	+	0.587374i	$0.800162\pi$
$140$	0	0
$141$	−429.176	−0.256334
$142$	11.4548	0.00676946
$143$	−790.982	−0.462554
$144$	−1469.98	−0.850685
$145$	734.111	0.420445
$146$	347.462	0.196960
$147$	0	0
$148$	−798.095	−0.443264
$149$	1316.52	0.723852	0.361926	−	0.932207i	$-0.382119\pi$
$149$	1316.52	0.723852	0.361926	+	0.932207i	$0.382119\pi$
$150$	51.2361	0.0278894
$151$	2051.26	1.10549	0.552744	−	0.833351i	$-0.313581\pi$
$151$	2051.26	1.10549	0.552744	+	0.833351i	$0.313581\pi$
$152$	−21.6382	−0.0115467
$153$	−32.5307	−0.0171892
$154$	0	0
$155$	−538.233	−0.278916
$156$	180.623	0.0927013
$157$	−1313.72	−0.667809	−0.333904	−	0.942607i	$-0.608366\pi$
$157$	−1313.72	−0.667809	−0.333904	+	0.942607i	$0.608366\pi$
$158$	262.648	0.132248
$159$	496.305	0.247544
$160$	361.356	0.178548
$161$	0	0
$162$	157.840	0.0765498
$163$	−1850.44	−0.889190	−0.444595	−	0.895732i	$-0.646652\pi$
$163$	−1850.44	−0.889190	−0.444595	+	0.895732i	$0.646652\pi$
$164$	1857.80	0.884572
$165$	633.748	0.299013
$166$	356.836	0.166842
$167$	1090.13	0.505130	0.252565	−	0.967580i	$-0.418726\pi$
$167$	1090.13	0.505130	0.252565	+	0.967580i	$0.418726\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	2.60672	0.00117604
$171$	−100.550	−0.0449665
$172$	−55.1377	−0.0244431
$173$	−2306.38	−1.01359	−0.506795	−	0.862066i	$-0.669170\pi$
$173$	−2306.38	−1.01359	−0.506795	+	0.862066i	$0.669170\pi$
$174$	−70.6346	−0.0307747
$175$	0	0
$176$	−3741.81	−1.60255
$177$	−1189.06	−0.504947
$178$	353.794	0.148977
$179$	−363.408	−0.151745	−0.0758726	−	0.997118i	$-0.524174\pi$
$179$	−363.408	−0.151745	−0.0758726	+	0.997118i	$0.524174\pi$
$180$	1117.00	0.462535
$181$	3863.47	1.58657	0.793287	−	0.608848i	$-0.208368\pi$
$181$	3863.47	1.58657	0.793287	+	0.608848i	$0.208368\pi$
$182$	0	0
$183$	154.161	0.0622728
$184$	54.8829	0.0219893
$185$	598.299	0.237772
$186$	51.7877	0.0204154
$187$	−82.8061	−0.0323817
$188$	−1925.49	−0.746971
$189$	0	0
$190$	8.05721	0.00307648
$191$	−1304.09	−0.494035	−0.247017	−	0.969011i	$-0.579450\pi$
$191$	−1304.09	−0.494035	−0.247017	+	0.969011i	$0.579450\pi$
$192$	831.016	0.312362
$193$	−96.9311	−0.0361516	−0.0180758	−	0.999837i	$-0.505754\pi$
$193$	−96.9311	−0.0361516	−0.0180758	+	0.999837i	$0.505754\pi$
$194$	−295.091	−0.109208
$195$	−135.406	−0.0497261
$196$	0	0
$197$	−3135.09	−1.13384	−0.566919	−	0.823774i	$-0.691865\pi$
$197$	−3135.09	−1.13384	−0.566919	+	0.823774i	$0.691865\pi$
$198$	470.655	0.168929
$199$	−3431.34	−1.22232	−0.611159	−	0.791508i	$-0.709296\pi$
$199$	−3431.34	−1.22232	−0.611159	+	0.791508i	$0.709296\pi$
$200$	462.788	0.163620
$201$	−215.960	−0.0757842
$202$	552.853	0.192567
$203$	0	0
$204$	18.9090	0.00648968
$205$	−1392.72	−0.474496
$206$	269.708	0.0912207
$207$	255.034	0.0856334
$208$	799.468	0.266506
$209$	−255.948	−0.0847096
$210$	0	0
$211$	4599.00	1.50051	0.750256	−	0.661147i	$-0.229930\pi$
$211$	4599.00	1.50051	0.750256	+	0.661147i	$0.229930\pi$
$212$	2226.66	0.721356
$213$	−62.2908	−0.0200380
$214$	96.0082	0.0306681
$215$	41.3345	0.0131116
$216$	−460.786	−0.145151
$217$	0	0
$218$	−651.221	−0.202322
$219$	−1889.49	−0.583014
$220$	2843.29	0.871340
$221$	17.6922	0.00538510
$222$	−57.5671	−0.0174038
$223$	4769.56	1.43226	0.716129	−	0.697968i	$-0.245912\pi$
$223$	4769.56	1.43226	0.716129	+	0.697968i	$0.245912\pi$
$224$	0	0
$225$	2150.52	0.637192
$226$	−148.667	−0.0437575
$227$	−5426.06	−1.58652	−0.793260	−	0.608883i	$-0.791618\pi$
$227$	−5426.06	−1.58652	−0.793260	+	0.608883i	$0.791618\pi$
$228$	58.4464	0.0169768
$229$	3946.45	1.13881	0.569407	−	0.822056i	$-0.307173\pi$
$229$	3946.45	1.13881	0.569407	+	0.822056i	$0.307173\pi$
$230$	−20.4362	−0.00585880
$231$	0	0
$232$	−638.004	−0.180547
$233$	−4611.04	−1.29648	−0.648238	−	0.761437i	$-0.724494\pi$
$233$	−4611.04	−1.29648	−0.648238	+	0.761437i	$0.724494\pi$
$234$	−100.559	−0.0280931
$235$	1443.46	0.400685
$236$	−5334.71	−1.47144
$237$	−1428.27	−0.391461
$238$	0	0
$239$	−1663.03	−0.450094	−0.225047	−	0.974348i	$-0.572253\pi$
$239$	−1663.03	−0.450094	−0.225047	+	0.974348i	$0.572253\pi$
$240$	−640.547	−0.172280
$241$	−2964.29	−0.792311	−0.396156	−	0.918183i	$-0.629656\pi$
$241$	−2964.29	−0.792311	−0.396156	+	0.918183i	$0.629656\pi$
$242$	767.313	0.203821
$243$	−3276.96	−0.865092
$244$	691.640	0.181466
$245$	0	0
$246$	134.004	0.0347309
$247$	54.6855	0.0140873
$248$	467.770	0.119772
$249$	−1940.46	−0.493863
$250$	−411.747	−0.104165
$251$	3483.07	0.875893	0.437947	−	0.899001i	$-0.355706\pi$
$251$	3483.07	0.875893	0.437947	+	0.899001i	$0.355706\pi$
$252$	0	0
$253$	649.184	0.161320
$254$	832.907	0.205753
$255$	−14.1753	−0.00348114
$256$	3570.27	0.871649
$257$	−4983.36	−1.20955	−0.604774	−	0.796397i	$-0.706736\pi$
$257$	−4983.36	−1.20955	−0.604774	+	0.796397i	$0.706736\pi$
$258$	−3.97712	−0.000959707 0
$259$	0	0
$260$	−607.494	−0.144904
$261$	−2964.73	−0.703112
$262$	−194.041	−0.0457553
$263$	7413.00	1.73804	0.869021	−	0.494776i	$-0.164750\pi$
$263$	7413.00	1.73804	0.869021	+	0.494776i	$0.164750\pi$
$264$	−550.780	−0.128402
$265$	−1669.23	−0.386944
$266$	0	0
$267$	−1923.92	−0.440982
$268$	−968.898	−0.220839
$269$	7815.61	1.77147	0.885736	−	0.464189i	$-0.153654\pi$
$269$	7815.61	1.77147	0.885736	+	0.464189i	$0.153654\pi$
$270$	171.578	0.0386738
$271$	940.210	0.210752	0.105376	−	0.994432i	$-0.466395\pi$
$271$	940.210	0.210752	0.105376	+	0.994432i	$0.466395\pi$
$272$	83.6945	0.0186571
$273$	0	0
$274$	−485.823	−0.107115
$275$	5474.10	1.20037
$276$	−148.243	−0.0323303
$277$	1086.00	0.235565	0.117783	−	0.993039i	$-0.462421\pi$
$277$	1086.00	0.235565	0.117783	+	0.993039i	$0.462421\pi$
$278$	−858.411	−0.185194
$279$	2173.67	0.466431
$280$	0	0
$281$	81.9702	0.0174019	0.00870095	−	0.999962i	$-0.497230\pi$
$281$	81.9702	0.0174019	0.00870095	+	0.999962i	$0.497230\pi$
$282$	−138.887	−0.0293283
$283$	−8459.84	−1.77698	−0.888490	−	0.458896i	$-0.848245\pi$
$283$	−8459.84	−1.77698	−0.888490	+	0.458896i	$0.848245\pi$
$284$	−279.466	−0.0583918
$285$	−43.8149	−0.00910656
$286$	−255.972	−0.0529228
$287$	0	0
$288$	−1459.35	−0.298586
$289$	−4911.15	−0.999623
$290$	237.567	0.0481049
$291$	1604.70	0.323261
$292$	−8477.15	−1.69893
$293$	3439.10	0.685714	0.342857	−	0.939388i	$-0.388605\pi$
$293$	3439.10	0.685714	0.342857	+	0.939388i	$0.388605\pi$
$294$	0	0
$295$	3999.21	0.789298
$296$	−519.973	−0.102104
$297$	−5450.42	−1.06487
$298$	426.043	0.0828189
$299$	−138.704	−0.0268275
$300$	−1250.02	−0.240567
$301$	0	0
$302$	663.811	0.126484
$303$	−3006.40	−0.570010
$304$	258.694	0.0488063
$305$	−518.494	−0.0973406
$306$	−10.5273	−0.00196669
$307$	1076.49	0.200126	0.100063	−	0.994981i	$-0.468096\pi$
$307$	1076.49	0.200126	0.100063	+	0.994981i	$0.468096\pi$
$308$	0	0
$309$	−1466.67	−0.270019
$310$	−174.179	−0.0319119
$311$	7001.34	1.27656	0.638279	−	0.769805i	$-0.279647\pi$
$311$	7001.34	1.27656	0.638279	+	0.769805i	$0.279647\pi$
$312$	117.679	0.0213534
$313$	7431.60	1.34204	0.671020	−	0.741439i	$-0.265856\pi$
$313$	7431.60	1.34204	0.671020	+	0.741439i	$0.265856\pi$
$314$	−425.135	−0.0764068
$315$	0	0
$316$	−6407.90	−1.14074
$317$	−7181.40	−1.27239	−0.636195	−	0.771528i	$-0.719493\pi$
$317$	−7181.40	−1.27239	−0.636195	+	0.771528i	$0.719493\pi$
$318$	160.610	0.0283226
$319$	−7546.64	−1.32455
$320$	−2794.98	−0.488263
$321$	−522.090	−0.0907795
$322$	0	0
$323$	5.72490	0.000986198 0
$324$	−3850.87	−0.660300
$325$	−1169.59	−0.199622
$326$	−598.826	−0.101736
$327$	3541.32	0.598886
$328$	1210.39	0.203758
$329$	0	0
$330$	205.089	0.0342114
$331$	−3742.93	−0.621540	−0.310770	−	0.950485i	$-0.600587\pi$
$331$	−3742.93	−0.621540	−0.310770	+	0.950485i	$0.600587\pi$
$332$	−8705.84	−1.43914
$333$	−2416.25	−0.397627
$334$	352.779	0.0577940
$335$	726.343	0.118461
$336$	0	0
$337$	10859.5	1.75535	0.877674	−	0.479258i	$-0.159094\pi$
$337$	10859.5	1.75535	0.877674	+	0.479258i	$0.159094\pi$
$338$	54.6905	0.00880109
$339$	808.449	0.129525
$340$	−63.5971	−0.0101442
$341$	5533.03	0.878681
$342$	−32.5393	−0.00514481
$343$	0	0
$344$	−35.9231	−0.00563037
$345$	111.132	0.0173424
$346$	−746.374	−0.115969
$347$	267.989	0.0414594	0.0207297	−	0.999785i	$-0.493401\pi$
$347$	267.989	0.0414594	0.0207297	+	0.999785i	$0.493401\pi$
$348$	1723.30	0.265455
$349$	5082.15	0.779488	0.389744	−	0.920923i	$-0.372563\pi$
$349$	5082.15	0.779488	0.389744	+	0.920923i	$0.372563\pi$
$350$	0	0
$351$	1164.53	0.177088
$352$	−3714.73	−0.562489
$353$	−9356.72	−1.41079	−0.705394	−	0.708815i	$-0.749230\pi$
$353$	−9356.72	−1.41079	−0.705394	+	0.708815i	$0.749230\pi$
$354$	−384.796	−0.0577731
$355$	209.504	0.0313221
$356$	−8631.63	−1.28504
$357$	0	0
$358$	−117.603	−0.0173618
$359$	−499.977	−0.0735036	−0.0367518	−	0.999324i	$-0.511701\pi$
$359$	−499.977	−0.0735036	−0.0367518	+	0.999324i	$0.511701\pi$
$360$	727.744	0.106543
$361$	−6841.30	−0.997420
$362$	1250.27	0.181527
$363$	−4172.63	−0.603323
$364$	0	0
$365$	6354.97	0.911327
$366$	49.8884	0.00712489
$367$	2754.73	0.391814	0.195907	−	0.980622i	$-0.437235\pi$
$367$	2754.73	0.391814	0.195907	+	0.980622i	$0.437235\pi$
$368$	−656.149	−0.0929460
$369$	5624.53	0.793500
$370$	193.617	0.0272045
$371$	0	0
$372$	−1263.48	−0.176098
$373$	−9414.45	−1.30687	−0.653434	−	0.756984i	$-0.726672\pi$
$373$	−9414.45	−1.30687	−0.653434	+	0.756984i	$0.726672\pi$
$374$	−26.7971	−0.00370493
$375$	2239.07	0.308333
$376$	−1254.49	−0.172062
$377$	1612.40	0.220273
$378$	0	0
$379$	−11295.5	−1.53090	−0.765451	−	0.643494i	$-0.777484\pi$
$379$	−11295.5	−1.53090	−0.765451	+	0.643494i	$0.777484\pi$
$380$	−196.574	−0.0265370
$381$	−4529.33	−0.609041
$382$	−422.019	−0.0565246
$383$	−265.629	−0.0354386	−0.0177193	−	0.999843i	$-0.505641\pi$
$383$	−265.629	−0.0354386	−0.0177193	+	0.999843i	$0.505641\pi$
$384$	1128.45	0.149963
$385$	0	0
$386$	−31.3681	−0.00413625
$387$	−166.931	−0.0219265
$388$	7199.43	0.941999
$389$	11601.0	1.51207	0.756037	−	0.654529i	$-0.227133\pi$
$389$	11601.0	1.51207	0.756037	+	0.654529i	$0.227133\pi$
$390$	−43.8189	−0.00568937
$391$	−14.5206	−0.00187810
$392$	0	0
$393$	1055.19	0.135438
$394$	−1014.55	−0.129727
$395$	4803.74	0.611905
$396$	−11482.7	−1.45714
$397$	−6664.32	−0.842501	−0.421250	−	0.906944i	$-0.638409\pi$
$397$	−6664.32	−0.842501	−0.421250	+	0.906944i	$0.638409\pi$
$398$	−1110.42	−0.139851
$399$	0	0
$400$	−5532.83	−0.691603
$401$	7874.09	0.980582	0.490291	−	0.871559i	$-0.336891\pi$
$401$	7874.09	0.980582	0.490291	+	0.871559i	$0.336891\pi$
$402$	−69.8872	−0.00867079
$403$	−1182.18	−0.146125
$404$	−13488.1	−1.66104
$405$	2886.84	0.354193
$406$	0	0
$407$	−6150.51	−0.749065
$408$	12.3195	0.00149487
$409$	2311.74	0.279483	0.139741	−	0.990188i	$-0.455373\pi$
$409$	2311.74	0.279483	0.139741	+	0.990188i	$0.455373\pi$
$410$	−450.700	−0.0542890
$411$	2641.89	0.317068
$412$	−6580.16	−0.786848
$413$	0	0
$414$	82.5323	0.00979768
$415$	6526.41	0.771973
$416$	793.684	0.0935422
$417$	4668.02	0.548186
$418$	−82.8280	−0.00969198
$419$	3945.48	0.460023	0.230011	−	0.973188i	$-0.426124\pi$
$419$	3945.48	0.460023	0.230011	+	0.973188i	$0.426124\pi$
$420$	0	0
$421$	−699.284	−0.0809526	−0.0404763	−	0.999180i	$-0.512888\pi$
$421$	−699.284	−0.0809526	−0.0404763	+	0.999180i	$0.512888\pi$
$422$	1488.29	0.171680
$423$	−5829.46	−0.670066
$424$	1450.70	0.166161
$425$	−122.441	−0.0139748
$426$	−20.1581	−0.00229263
$427$	0	0
$428$	−2342.34	−0.264536
$429$	1391.97	0.156655
$430$	13.3763	0.00150015
$431$	14778.0	1.65158	0.825789	−	0.563980i	$-0.190730\pi$
$431$	14778.0	1.65158	0.825789	+	0.563980i	$0.190730\pi$
$432$	5508.89	0.613534
$433$	−4217.17	−0.468046	−0.234023	−	0.972231i	$-0.575189\pi$
$433$	−4217.17	−0.468046	−0.234023	+	0.972231i	$0.575189\pi$
$434$	0	0
$435$	−1291.88	−0.142393
$436$	15888.1	1.74518
$437$	−44.8821	−0.00491305
$438$	−611.462	−0.0667050
$439$	−6372.34	−0.692791	−0.346395	−	0.938089i	$-0.612594\pi$
$439$	−6372.34	−0.692791	−0.346395	+	0.938089i	$0.612594\pi$
$440$	1852.45	0.200710
$441$	0	0
$442$	5.72542	0.000616132 0
$443$	7824.17	0.839137	0.419568	−	0.907724i	$-0.362181\pi$
$443$	7824.17	0.839137	0.419568	+	0.907724i	$0.362181\pi$
$444$	1404.48	0.150121
$445$	6470.78	0.689313
$446$	1543.49	0.163871
$447$	−2316.81	−0.245149
$448$	0	0
$449$	3132.31	0.329226	0.164613	−	0.986358i	$-0.447362\pi$
$449$	3132.31	0.329226	0.164613	+	0.986358i	$0.447362\pi$
$450$	695.935	0.0729038
$451$	14317.1	1.49483
$452$	3627.09	0.377442
$453$	−3609.79	−0.374399
$454$	−1755.94	−0.181520
$455$	0	0
$456$	38.0788	0.00391054
$457$	2253.14	0.230629	0.115314	−	0.993329i	$-0.463212\pi$
$457$	2253.14	0.230629	0.115314	+	0.993329i	$0.463212\pi$
$458$	1277.12	0.130297
$459$	121.912	0.0123973
$460$	498.589	0.0505366
$461$	9164.98	0.925934	0.462967	−	0.886375i	$-0.346785\pi$
$461$	9164.98	0.925934	0.462967	+	0.886375i	$0.346785\pi$
$462$	0	0
$463$	7086.00	0.711263	0.355631	−	0.934626i	$-0.384266\pi$
$463$	7086.00	0.711263	0.355631	+	0.934626i	$0.384266\pi$
$464$	7627.61	0.763153
$465$	947.180	0.0944611
$466$	−1492.19	−0.148335
$467$	−11174.0	−1.10721	−0.553607	−	0.832778i	$-0.686749\pi$
$467$	−11174.0	−1.10721	−0.553607	+	0.832778i	$0.686749\pi$
$468$	2453.38	0.242324
$469$	0	0
$470$	467.121	0.0458440
$471$	2311.87	0.226169
$472$	−3475.65	−0.338940
$473$	−424.918	−0.0413060
$474$	−462.206	−0.0447887
$475$	−378.458	−0.0365576
$476$	0	0
$477$	6741.25	0.647088
$478$	−538.176	−0.0514971
$479$	−8240.34	−0.786035	−0.393018	−	0.919531i	$-0.628569\pi$
$479$	−8240.34	−0.786035	−0.393018	+	0.919531i	$0.628569\pi$
$480$	−635.913	−0.0604694
$481$	1314.11	0.124570
$482$	−959.282	−0.0906517
$483$	0	0
$484$	−18720.4	−1.75811
$485$	−5397.12	−0.505300
$486$	−1060.47	−0.0989788
$487$	−9967.60	−0.927464	−0.463732	−	0.885975i	$-0.653490\pi$
$487$	−9967.60	−0.927464	−0.463732	+	0.885975i	$0.653490\pi$
$488$	450.615	0.0418000
$489$	3256.40	0.301144
$490$	0	0
$491$	11339.8	1.04228	0.521138	−	0.853473i	$-0.325508\pi$
$491$	11339.8	1.04228	0.521138	+	0.853473i	$0.325508\pi$
$492$	−3269.35	−0.299581
$493$	168.799	0.0154205
$494$	17.6969	0.00161178
$495$	8608.14	0.781630
$496$	−5592.39	−0.506261
$497$	0	0
$498$	−627.958	−0.0565050
$499$	8011.01	0.718682	0.359341	−	0.933206i	$-0.383002\pi$
$499$	8011.01	0.718682	0.359341	+	0.933206i	$0.383002\pi$
$500$	10045.5	0.898499
$501$	−1918.40	−0.171074
$502$	1127.16	0.100215
$503$	17925.8	1.58901	0.794503	−	0.607260i	$-0.207731\pi$
$503$	17925.8	1.58901	0.794503	+	0.607260i	$0.207731\pi$
$504$	0	0
$505$	10111.5	0.891001
$506$	210.084	0.0184572
$507$	−297.405	−0.0260517
$508$	−20320.7	−1.77477
$509$	13744.2	1.19686	0.598429	−	0.801176i	$-0.295792\pi$
$509$	13744.2	1.19686	0.598429	+	0.801176i	$0.295792\pi$
$510$	−4.58730	−0.000398292 0
$511$	0	0
$512$	6285.29	0.542526
$513$	376.821	0.0324309
$514$	−1612.68	−0.138389
$515$	4932.88	0.422075
$516$	97.0310	0.00827820
$517$	−14838.7	−1.26230
$518$	0	0
$519$	4058.77	0.343276
$520$	−395.792	−0.0333782
$521$	−2637.79	−0.221811	−0.110906	−	0.993831i	$-0.535375\pi$
$521$	−2637.79	−0.221811	−0.110906	+	0.993831i	$0.535375\pi$
$522$	−959.423	−0.0804460
$523$	16059.6	1.34271	0.671353	−	0.741138i	$-0.265713\pi$
$523$	16059.6	1.34271	0.671353	+	0.741138i	$0.265713\pi$
$524$	4734.08	0.394674
$525$	0	0
$526$	2398.94	0.198857
$527$	−123.759	−0.0102297
$528$	6584.81	0.542741
$529$	−12053.2	−0.990644
$530$	−540.184	−0.0442719
$531$	−16150.9	−1.31995
$532$	0	0
$533$	−3058.97	−0.248590
$534$	−622.605	−0.0504546
$535$	1755.96	0.141900
$536$	−631.253	−0.0508694
$537$	639.524	0.0513920
$538$	2529.23	0.202682
$539$	0	0
$540$	−4186.05	−0.333591
$541$	10315.9	0.819804	0.409902	−	0.912130i	$-0.365563\pi$
$541$	10315.9	0.819804	0.409902	+	0.912130i	$0.365563\pi$
$542$	304.263	0.0241130
$543$	−6798.92	−0.537329
$544$	83.0890	0.00654855
$545$	−11910.6	−0.936138
$546$	0	0
$547$	−5327.06	−0.416396	−0.208198	−	0.978087i	$-0.566760\pi$
$547$	−5327.06	−0.416396	−0.208198	+	0.978087i	$0.566760\pi$
$548$	11852.8	0.923952
$549$	2093.96	0.162783
$550$	1771.49	0.137339
$551$	521.746	0.0403396
$552$	−96.5827	−0.00744716
$553$	0	0
$554$	351.444	0.0269520
$555$	−1052.88	−0.0805270
$556$	20942.9	1.59744
$557$	11816.4	0.898884	0.449442	−	0.893310i	$-0.351623\pi$
$557$	11816.4	0.898884	0.449442	+	0.893310i	$0.351623\pi$
$558$	703.427	0.0533664
$559$	90.7872	0.00686921
$560$	0	0
$561$	145.722	0.0109668
$562$	26.5266	0.00199102
$563$	20627.2	1.54411	0.772054	−	0.635557i	$-0.219230\pi$
$563$	20627.2	1.54411	0.772054	+	0.635557i	$0.219230\pi$
$564$	3388.46	0.252979
$565$	−2719.08	−0.202465
$566$	−2737.71	−0.203312
$567$	0	0
$568$	−182.077	−0.0134503
$569$	−13529.3	−0.996798	−0.498399	−	0.866948i	$-0.666078\pi$
$569$	−13529.3	−0.996798	−0.498399	+	0.866948i	$0.666078\pi$
$570$	−14.1790	−0.00104192
$571$	−13230.8	−0.969690	−0.484845	−	0.874600i	$-0.661124\pi$
$571$	−13230.8	−0.969690	−0.484845	+	0.874600i	$0.661124\pi$
$572$	6245.02	0.456499
$573$	2294.93	0.167316
$574$	0	0
$575$	959.917	0.0696196
$576$	11287.6	0.816523
$577$	−21279.3	−1.53530	−0.767650	−	0.640870i	$-0.778574\pi$
$577$	−21279.3	−1.53530	−0.767650	+	0.640870i	$0.778574\pi$
$578$	−1589.31	−0.114371
$579$	170.579	0.0122435
$580$	−5796.00	−0.414941
$581$	0	0
$582$	519.299	0.0369857
$583$	17159.7	1.21901
$584$	−5523.01	−0.391342
$585$	−1839.20	−0.129986
$586$	1112.93	0.0784555
$587$	13737.6	0.965945	0.482972	−	0.875636i	$-0.339557\pi$
$587$	13737.6	0.965945	0.482972	+	0.875636i	$0.339557\pi$
$588$	0	0
$589$	−382.532	−0.0267606
$590$	1294.19	0.0903070
$591$	5517.12	0.384000
$592$	6216.49	0.431582
$593$	22012.2	1.52434	0.762169	−	0.647379i	$-0.224135\pi$
$593$	22012.2	1.52434	0.762169	+	0.647379i	$0.224135\pi$
$594$	−1763.82	−0.121836
$595$	0	0
$596$	−10394.3	−0.714376
$597$	6038.46	0.413966
$598$	−44.8862	−0.00306945
$599$	3333.73	0.227400	0.113700	−	0.993515i	$-0.463730\pi$
$599$	3333.73	0.227400	0.113700	+	0.993515i	$0.463730\pi$
$600$	−814.412	−0.0554137
$601$	−17140.5	−1.16336	−0.581678	−	0.813419i	$-0.697604\pi$
$601$	−17140.5	−1.16336	−0.581678	+	0.813419i	$0.697604\pi$
$602$	0	0
$603$	−2933.36	−0.198102
$604$	−16195.2	−1.09102
$605$	14033.9	0.943074
$606$	−972.907	−0.0652173
$607$	2365.32	0.158164	0.0790818	−	0.996868i	$-0.474801\pi$
$607$	2365.32	0.158164	0.0790818	+	0.996868i	$0.474801\pi$
$608$	256.822	0.0171308
$609$	0	0
$610$	−167.791	−0.0111372
$611$	3170.42	0.209921
$612$	256.839	0.0169642
$613$	−165.695	−0.0109174	−0.00545869	−	0.999985i	$-0.501738\pi$
$613$	−165.695	−0.0109174	−0.00545869	+	0.999985i	$0.501738\pi$
$614$	348.367	0.0228973
$615$	2450.90	0.160699
$616$	0	0
$617$	5993.71	0.391082	0.195541	−	0.980696i	$-0.437354\pi$
$617$	5993.71	0.391082	0.195541	+	0.980696i	$0.437354\pi$
$618$	−474.632	−0.0308940
$619$	7157.52	0.464758	0.232379	−	0.972625i	$-0.425349\pi$
$619$	7157.52	0.464758	0.232379	+	0.972625i	$0.425349\pi$
$620$	4249.50	0.275264
$621$	−955.764	−0.0617609
$622$	2265.72	0.146056
$623$	0	0
$624$	−1406.90	−0.0902582
$625$	3715.31	0.237780
$626$	2404.96	0.153549
$627$	450.416	0.0286888
$628$	10372.2	0.659067
$629$	137.571	0.00872069
$630$	0	0
$631$	25765.6	1.62554	0.812769	−	0.582586i	$-0.197959\pi$
$631$	25765.6	1.62554	0.812769	+	0.582586i	$0.197959\pi$
$632$	−4174.86	−0.262764
$633$	−8093.30	−0.508183
$634$	−2323.99	−0.145580
$635$	15233.6	0.952011
$636$	−3918.46	−0.244304
$637$	0	0
$638$	−2442.19	−0.151547
$639$	−846.090	−0.0523800
$640$	−3795.34	−0.234412
$641$	−20628.0	−1.27107	−0.635536	−	0.772072i	$-0.719221\pi$
$641$	−20628.0	−1.27107	−0.635536	+	0.772072i	$0.719221\pi$
$642$	−168.955	−0.0103865
$643$	−25301.9	−1.55180	−0.775901	−	0.630854i	$-0.782704\pi$
$643$	−25301.9	−1.55180	−0.775901	+	0.630854i	$0.782704\pi$
$644$	0	0
$645$	−72.7402	−0.00444053
$646$	1.85265	0.000112835 0
$647$	14852.8	0.902508	0.451254	−	0.892396i	$-0.350977\pi$
$647$	14852.8	0.902508	0.451254	+	0.892396i	$0.350977\pi$
$648$	−2508.91	−0.152097
$649$	−41111.8	−2.48656
$650$	−378.493	−0.0228395
$651$	0	0
$652$	14609.8	0.877550
$653$	25682.0	1.53907	0.769537	−	0.638602i	$-0.220487\pi$
$653$	25682.0	1.53907	0.769537	+	0.638602i	$0.220487\pi$
$654$	1146.02	0.0685210
$655$	−3548.95	−0.211708
$656$	−14470.7	−0.861260
$657$	−25664.8	−1.52402
$658$	0	0
$659$	−7290.57	−0.430956	−0.215478	−	0.976509i	$-0.569131\pi$
$659$	−7290.57	−0.430956	−0.215478	+	0.976509i	$0.569131\pi$
$660$	−5003.61	−0.295099
$661$	−16930.0	−0.996222	−0.498111	−	0.867113i	$-0.665973\pi$
$661$	−16930.0	−0.996222	−0.498111	+	0.867113i	$0.665973\pi$
$662$	−1211.26	−0.0711131
$663$	−31.1347	−0.00182379
$664$	−5672.00	−0.331501
$665$	0	0
$666$	−781.929	−0.0454942
$667$	−1323.35	−0.0768221
$668$	−8606.87	−0.498517
$669$	−8393.45	−0.485067
$670$	235.053	0.0135536
$671$	5330.11	0.306657
$672$	0	0
$673$	16730.2	0.958249	0.479125	−	0.877747i	$-0.340954\pi$
$673$	16730.2	0.958249	0.479125	+	0.877747i	$0.340954\pi$
$674$	3514.25	0.200837
$675$	−8059.27	−0.459558
$676$	−1334.30	−0.0759161
$677$	5093.48	0.289156	0.144578	−	0.989493i	$-0.453818\pi$
$677$	5093.48	0.289156	0.144578	+	0.989493i	$0.453818\pi$
$678$	261.624	0.0148195
$679$	0	0
$680$	−41.4346	−0.00233668
$681$	9548.75	0.537311
$682$	1790.56	0.100534
$683$	25619.5	1.43529	0.717645	−	0.696409i	$-0.245220\pi$
$683$	25619.5	1.43529	0.717645	+	0.696409i	$0.245220\pi$
$684$	793.872	0.0443779
$685$	−8885.54	−0.495619
$686$	0	0
$687$	−6944.94	−0.385685
$688$	429.476	0.0237989
$689$	−3666.31	−0.202722
$690$	35.9635	0.00198422
$691$	31693.2	1.74482	0.872408	−	0.488778i	$-0.162557\pi$
$691$	31693.2	1.74482	0.872408	+	0.488778i	$0.162557\pi$
$692$	18209.5	1.00032
$693$	0	0
$694$	86.7245	0.00474354
$695$	−15700.1	−0.856888
$696$	1122.76	0.0611465
$697$	−320.237	−0.0174029
$698$	1644.65	0.0891845
$699$	8114.48	0.439081
$700$	0	0
$701$	2661.14	0.143381	0.0716905	−	0.997427i	$-0.477161\pi$
$701$	2661.14	0.143381	0.0716905	+	0.997427i	$0.477161\pi$
$702$	376.855	0.0202614
$703$	425.223	0.0228130
$704$	28732.3	1.53820
$705$	−2540.19	−0.135701
$706$	−3027.95	−0.161414
$707$	0	0
$708$	9387.99	0.498337
$709$	−16745.3	−0.887000	−0.443500	−	0.896274i	$-0.646263\pi$
$709$	−16745.3	−0.887000	−0.443500	+	0.896274i	$0.646263\pi$
$710$	67.7981	0.00358369
$711$	−19400.1	−1.02329
$712$	−5623.65	−0.296005
$713$	970.250	0.0509623
$714$	0	0
$715$	−4681.64	−0.244872
$716$	2869.21	0.149759
$717$	2926.59	0.152434
$718$	−161.799	−0.00840986
$719$	−7621.40	−0.395313	−0.197657	−	0.980271i	$-0.563333\pi$
$719$	−7621.40	−0.395313	−0.197657	+	0.980271i	$0.563333\pi$
$720$	−8700.49	−0.450344
$721$	0	0
$722$	−2213.93	−0.114119
$723$	5216.55	0.268334
$724$	−30503.2	−1.56580
$725$	−11158.9	−0.571627
$726$	−1350.31	−0.0690287
$727$	33363.8	1.70206	0.851028	−	0.525120i	$-0.175979\pi$
$727$	33363.8	1.70206	0.851028	+	0.525120i	$0.175979\pi$
$728$	0	0
$729$	−7402.29	−0.376075
$730$	2056.55	0.104269
$731$	9.50431	0.000480888 0
$732$	−1217.14	−0.0614576
$733$	10628.8	0.535583	0.267791	−	0.963477i	$-0.413706\pi$
$733$	10628.8	0.535583	0.267791	+	0.963477i	$0.413706\pi$
$734$	891.465	0.0448291
$735$	0	0
$736$	−651.401	−0.0326236
$737$	−7466.79	−0.373192
$738$	1820.17	0.0907877
$739$	13321.7	0.663120	0.331560	−	0.943434i	$-0.392425\pi$
$739$	13321.7	0.663120	0.331560	+	0.943434i	$0.392425\pi$
$740$	−4723.74	−0.234660
$741$	−96.2352	−0.00477097
$742$	0	0
$743$	−1456.36	−0.0719092	−0.0359546	−	0.999353i	$-0.511447\pi$
$743$	−1456.36	−0.0719092	−0.0359546	+	0.999353i	$0.511447\pi$
$744$	−823.179	−0.0405635
$745$	7792.20	0.383200
$746$	−3046.63	−0.149524
$747$	−26357.1	−1.29097
$748$	653.777	0.0319578
$749$	0	0
$750$	724.590	0.0352777
$751$	−3929.23	−0.190918	−0.0954591	−	0.995433i	$-0.530432\pi$
$751$	−3929.23	−0.190918	−0.0954591	+	0.995433i	$0.530432\pi$
$752$	14997.9	0.727285
$753$	−6129.48	−0.296641
$754$	521.794	0.0252024
$755$	12140.9	0.585235
$756$	0	0
$757$	−27434.8	−1.31722	−0.658610	−	0.752484i	$-0.728855\pi$
$757$	−27434.8	−1.31722	−0.658610	+	0.752484i	$0.728855\pi$
$758$	−3655.37	−0.175157
$759$	−1142.43	−0.0546345
$760$	−128.072	−0.00611269
$761$	19994.8	0.952445	0.476222	−	0.879325i	$-0.342006\pi$
$761$	19994.8	0.952445	0.476222	+	0.879325i	$0.342006\pi$
$762$	−1465.75	−0.0696829
$763$	0	0
$764$	10296.1	0.487567
$765$	−192.542	−0.00909982
$766$	−85.9607	−0.00405468
$767$	8783.88	0.413517
$768$	−6282.95	−0.295204
$769$	7948.30	0.372722	0.186361	−	0.982481i	$-0.440331\pi$
$769$	7948.30	0.372722	0.186361	+	0.982481i	$0.440331\pi$
$770$	0	0
$771$	8769.70	0.409641
$772$	765.297	0.0356783
$773$	21350.2	0.993418	0.496709	−	0.867917i	$-0.334542\pi$
$773$	21350.2	0.993418	0.496709	+	0.867917i	$0.334542\pi$
$774$	−54.0208	−0.00250870
$775$	8181.42	0.379207
$776$	4690.55	0.216986
$777$	0	0
$778$	3754.24	0.173003
$779$	−989.830	−0.0455255
$780$	1069.06	0.0490752
$781$	−2153.70	−0.0986754
$782$	−4.69903	−0.000214881 0
$783$	11110.6	0.507101
$784$	0	0
$785$	−7775.58	−0.353532
$786$	341.473	0.0154961
$787$	20880.3	0.945744	0.472872	−	0.881131i	$-0.343217\pi$
$787$	20880.3	0.945744	0.472872	+	0.881131i	$0.343217\pi$
$788$	24752.4	1.11900
$789$	−13045.4	−0.588627
$790$	1554.55	0.0700106
$791$	0	0
$792$	−7481.20	−0.335647
$793$	−1138.82	−0.0509972
$794$	−2156.66	−0.0963941
$795$	2937.51	0.131047
$796$	27091.4	1.20632
$797$	40432.4	1.79697	0.898487	−	0.439001i	$-0.144668\pi$
$797$	40432.4	1.79697	0.898487	+	0.439001i	$0.144668\pi$
$798$	0	0
$799$	331.904	0.0146958
$800$	−5492.80	−0.242750
$801$	−26132.4	−1.15274
$802$	2548.15	0.112192
$803$	−65329.0	−2.87100
$804$	1705.06	0.0747921
$805$	0	0
$806$	−382.567	−0.0167188
$807$	−13753.9	−0.599950
$808$	−8787.74	−0.382614
$809$	19268.3	0.837376	0.418688	−	0.908130i	$-0.362490\pi$
$809$	19268.3	0.837376	0.418688	+	0.908130i	$0.362490\pi$
$810$	934.216	0.0405247
$811$	37223.2	1.61169	0.805846	−	0.592125i	$-0.201711\pi$
$811$	37223.2	1.61169	0.805846	+	0.592125i	$0.201711\pi$
$812$	0	0
$813$	−1654.58	−0.0713758
$814$	−1990.38	−0.0857037
$815$	−10952.3	−0.470729
$816$	−147.285	−0.00631864
$817$	29.3772	0.00125799
$818$	748.109	0.0319768
$819$	0	0
$820$	10995.9	0.468284
$821$	−883.967	−0.0375769	−0.0187885	−	0.999823i	$-0.505981\pi$
$821$	−883.967	−0.0375769	−0.0187885	+	0.999823i	$0.505981\pi$
$822$	854.949	0.0362771
$823$	41410.5	1.75392	0.876961	−	0.480561i	$-0.159567\pi$
$823$	41410.5	1.75392	0.876961	+	0.480561i	$0.159567\pi$
$824$	−4287.09	−0.181247
$825$	−9633.29	−0.406531
$826$	0	0
$827$	−37881.9	−1.59285	−0.796423	−	0.604739i	$-0.793277\pi$
$827$	−37881.9	−1.59285	−0.796423	+	0.604739i	$0.793277\pi$
$828$	−2013.57	−0.0845124
$829$	4896.97	0.205161	0.102581	−	0.994725i	$-0.467290\pi$
$829$	4896.97	0.205161	0.102581	+	0.994725i	$0.467290\pi$
$830$	2112.03	0.0883247
$831$	−1911.14	−0.0797795
$832$	−6138.90	−0.255803
$833$	0	0
$834$	1510.63	0.0627203
$835$	6452.21	0.267411
$836$	2020.78	0.0836007
$837$	−8146.03	−0.336401
$838$	1276.81	0.0526331
$839$	−93.0019	−0.00382692	−0.00191346	−	0.999998i	$-0.500609\pi$
$839$	−93.0019	−0.00382692	−0.00191346	+	0.999998i	$0.500609\pi$
$840$	0	0
$841$	−9005.30	−0.369236
$842$	−226.297	−0.00926212
$843$	−144.251	−0.00589355
$844$	−36310.4	−1.48087
$845$	1000.27	0.0407223
$846$	−1886.48	−0.0766650
$847$	0	0
$848$	−17343.8	−0.702345
$849$	14887.6	0.601815
$850$	−39.6235	−0.00159891
$851$	−1078.53	−0.0434448
$852$	491.803	0.0197757
$853$	8325.23	0.334174	0.167087	−	0.985942i	$-0.446564\pi$
$853$	8325.23	0.334174	0.167087	+	0.985942i	$0.446564\pi$
$854$	0	0
$855$	−595.133	−0.0238048
$856$	−1526.08	−0.0609348
$857$	3891.72	0.155121	0.0775606	−	0.996988i	$-0.475287\pi$
$857$	3891.72	0.155121	0.0775606	+	0.996988i	$0.475287\pi$
$858$	450.458	0.0179235
$859$	−35346.9	−1.40398	−0.701991	−	0.712186i	$-0.747705\pi$
$859$	−35346.9	−1.40398	−0.701991	+	0.712186i	$0.747705\pi$
$860$	−326.347	−0.0129399
$861$	0	0
$862$	4782.33	0.188964
$863$	−21075.1	−0.831290	−0.415645	−	0.909527i	$-0.636444\pi$
$863$	−21075.1	−0.831290	−0.415645	+	0.909527i	$0.636444\pi$
$864$	5469.04	0.215348
$865$	−13650.9	−0.536585
$866$	−1364.73	−0.0535512
$867$	8642.61	0.338545
$868$	0	0
$869$	−49382.4	−1.92771
$870$	−418.070	−0.0162918
$871$	1595.34	0.0620621
$872$	10351.3	0.401996
$873$	21796.4	0.845014
$874$	−14.5244	−0.000562122 0
$875$	0	0
$876$	14918.1	0.575382
$877$	−47944.7	−1.84604	−0.923021	−	0.384751i	$-0.874287\pi$
$877$	−47944.7	−1.84604	−0.923021	+	0.384751i	$0.874287\pi$
$878$	−2062.17	−0.0792651
$879$	−6052.11	−0.232233
$880$	−22146.9	−0.848376
$881$	−37133.6	−1.42005	−0.710024	−	0.704178i	$-0.751316\pi$
$881$	−37133.6	−1.42005	−0.710024	+	0.704178i	$0.751316\pi$
$882$	0	0
$883$	1686.40	0.0642715	0.0321358	−	0.999484i	$-0.489769\pi$
$883$	1686.40	0.0642715	0.0321358	+	0.999484i	$0.489769\pi$
$884$	−139.685	−0.00531461
$885$	−7037.79	−0.267314
$886$	2532.00	0.0960092
$887$	−11389.6	−0.431146	−0.215573	−	0.976488i	$-0.569162\pi$
$887$	−11389.6	−0.431146	−0.215573	+	0.976488i	$0.569162\pi$
$888$	915.046	0.0345799
$889$	0	0
$890$	2094.02	0.0788672
$891$	−29676.7	−1.11583
$892$	−37657.0	−1.41351
$893$	1025.89	0.0384437
$894$	−749.749	−0.0280485
$895$	−2150.93	−0.0803325
$896$	0	0
$897$	244.090	0.00908576
$898$	1013.65	0.0376682
$899$	−11279.0	−0.418437
$900$	−16979.0	−0.628850
$901$	−383.818	−0.0141918
$902$	4633.19	0.171029
$903$	0	0
$904$	2363.11	0.0869423
$905$	22867.0	0.839917
$906$	−1168.17	−0.0428366
$907$	−29663.9	−1.08597	−0.542985	−	0.839743i	$-0.682706\pi$
$907$	−29663.9	−1.08597	−0.542985	+	0.839743i	$0.682706\pi$
$908$	42840.2	1.56575
$909$	−40835.6	−1.49002
$910$	0	0
$911$	16210.3	0.589541	0.294770	−	0.955568i	$-0.404757\pi$
$911$	16210.3	0.589541	0.294770	+	0.955568i	$0.404757\pi$
$912$	−455.249	−0.0165294
$913$	−67091.4	−2.43198
$914$	729.143	0.0263872
$915$	912.444	0.0329666
$916$	−31158.3	−1.12391
$917$	0	0
$918$	39.4521	0.00141843
$919$	−13025.5	−0.467542	−0.233771	−	0.972292i	$-0.575107\pi$
$919$	−13025.5	−0.467542	−0.233771	+	0.972292i	$0.575107\pi$
$920$	324.839	0.0116409
$921$	−1894.41	−0.0677773
$922$	2965.90	0.105940
$923$	460.156	0.0164098
$924$	0	0
$925$	−9094.46	−0.323269
$926$	2293.12	0.0813785
$927$	−19921.6	−0.705837
$928$	7572.42	0.267863
$929$	−46834.2	−1.65401	−0.827007	−	0.562192i	$-0.809958\pi$
$929$	−46834.2	−1.65401	−0.827007	+	0.562192i	$0.809958\pi$
$930$	306.519	0.0108077
$931$	0	0
$932$	36405.4	1.27951
$933$	−12320.9	−0.432335
$934$	−3616.03	−0.126681
$935$	−490.110	−0.0171426
$936$	1598.42	0.0558184
$937$	−24171.1	−0.842727	−0.421363	−	0.906892i	$-0.638448\pi$
$937$	−24171.1	−0.842727	−0.421363	+	0.906892i	$0.638448\pi$
$938$	0	0
$939$	−13078.1	−0.454513
$940$	−11396.5	−0.395439
$941$	32410.4	1.12279	0.561397	−	0.827547i	$-0.310264\pi$
$941$	32410.4	1.12279	0.561397	+	0.827547i	$0.310264\pi$
$942$	748.150	0.0258769
$943$	2510.59	0.0866979
$944$	41552.9	1.43266
$945$	0	0
$946$	−137.509	−0.00472599
$947$	−36285.0	−1.24509	−0.622547	−	0.782582i	$-0.713902\pi$
$947$	−36285.0	−1.24509	−0.622547	+	0.782582i	$0.713902\pi$
$948$	11276.6	0.386336
$949$	13958.1	0.477449
$950$	−122.474	−0.00418271
$951$	12637.8	0.430924
$952$	0	0
$953$	31851.1	1.08264	0.541321	−	0.840816i	$-0.317924\pi$
$953$	31851.1	1.08264	0.541321	+	0.840816i	$0.317924\pi$
$954$	2181.55	0.0740360
$955$	−7718.60	−0.261537
$956$	13130.1	0.444202
$957$	13280.5	0.448588
$958$	−2666.68	−0.0899336
$959$	0	0
$960$	4918.59	0.165361
$961$	−21521.5	−0.722416
$962$	425.261	0.0142526
$963$	−7091.50	−0.237300
$964$	23403.9	0.781939
$965$	−573.712	−0.0191383
$966$	0	0
$967$	455.696	0.0151543	0.00757714	−	0.999971i	$-0.497588\pi$
$967$	455.696	0.0151543	0.00757714	+	0.999971i	$0.497588\pi$
$968$	−12196.7	−0.404975
$969$	−10.0746	−0.000333998 0
$970$	−1746.57	−0.0578135
$971$	−10641.2	−0.351690	−0.175845	−	0.984418i	$-0.556266\pi$
$971$	−10641.2	−0.351690	−0.175845	+	0.984418i	$0.556266\pi$
$972$	25872.5	0.853767
$973$	0	0
$974$	−3225.64	−0.106115
$975$	2058.23	0.0676064
$976$	−5387.30	−0.176684
$977$	19412.9	0.635694	0.317847	−	0.948142i	$-0.397040\pi$
$977$	19412.9	0.635694	0.317847	+	0.948142i	$0.397040\pi$
$978$	1053.81	0.0344552
$979$	−66519.5	−2.17158
$980$	0	0
$981$	48101.4	1.56551
$982$	3669.69	0.119251
$983$	−44913.0	−1.45728	−0.728639	−	0.684898i	$-0.759847\pi$
$983$	−44913.0	−1.45728	−0.728639	+	0.684898i	$0.759847\pi$
$984$	−2130.04	−0.0690072
$985$	−18555.9	−0.600243
$986$	54.6254	0.00176433
$987$	0	0
$988$	−431.757	−0.0139029
$989$	−74.5119	−0.00239569
$990$	2785.70	0.0894296
$991$	36377.2	1.16605	0.583027	−	0.812453i	$-0.301868\pi$
$991$	36377.2	1.16605	0.583027	+	0.812453i	$0.301868\pi$
$992$	−5551.93	−0.177695
$993$	6586.79	0.210499
$994$	0	0
$995$	−20309.3	−0.647083
$996$	15320.5	0.487398
$997$	−6366.39	−0.202232	−0.101116	−	0.994875i	$-0.532241\pi$
$997$	−6366.39	−0.202232	−0.101116	+	0.994875i	$0.532241\pi$
$998$	2592.46	0.0822274
$999$	9055.12	0.286778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.4.a.d.1.3		4
7.6	odd	2		91.4.a.b.1.3	✓	4
21.20	even	2		819.4.a.h.1.2		4
28.27	even	2		1456.4.a.s.1.2		4
35.34	odd	2		2275.4.a.h.1.2		4
91.90	odd	2		1183.4.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.4.a.b.1.3	✓	4	7.6	odd	2
637.4.a.d.1.3		4	1.1	even	1	trivial
819.4.a.h.1.2		4	21.20	even	2
1183.4.a.e.1.2		4	91.90	odd	2
1456.4.a.s.1.2		4	28.27	even	2
2275.4.a.h.1.2		4	35.34	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+0.323612 q^{2} -1.75980 q^{3} -7.89528 q^{4} +5.91876 q^{5} -0.569491 q^{6} -5.14391 q^{8} -23.9031 q^{9} +O(q^{10})\)	\(q+0.323612 q^{2} -1.75980 q^{3} -7.89528 q^{4} +5.91876 q^{5} -0.569491 q^{6} -5.14391 q^{8} -23.9031 q^{9} +1.91538 q^{10} -60.8448 q^{11} +13.8941 q^{12} +13.0000 q^{13} -10.4158 q^{15} +61.4976 q^{16} +1.36094 q^{17} -7.73534 q^{18} +4.20658 q^{19} -46.7303 q^{20} -19.6901 q^{22} -10.6695 q^{23} +9.05222 q^{24} -89.9682 q^{25} +4.20696 q^{26} +89.5791 q^{27} +124.031 q^{29} -3.37068 q^{30} -90.9367 q^{31} +61.0526 q^{32} +107.074 q^{33} +0.440417 q^{34} +188.722 q^{36} +101.085 q^{37} +1.36130 q^{38} -22.8773 q^{39} -30.4456 q^{40} -235.305 q^{41} +6.98363 q^{43} +480.386 q^{44} -141.477 q^{45} -3.45278 q^{46} +243.878 q^{47} -108.223 q^{48} -29.1148 q^{50} -2.39498 q^{51} -102.639 q^{52} -282.024 q^{53} +28.9889 q^{54} -360.126 q^{55} -7.40271 q^{57} +40.1380 q^{58} +675.683 q^{59} +82.2357 q^{60} -87.6018 q^{61} -29.4282 q^{62} -472.223 q^{64} +76.9439 q^{65} +34.6506 q^{66} +122.719 q^{67} -10.7450 q^{68} +18.7761 q^{69} +35.3966 q^{71} +122.955 q^{72} +1073.70 q^{73} +32.7124 q^{74} +158.326 q^{75} -33.2121 q^{76} -7.40339 q^{78} +811.612 q^{79} +363.990 q^{80} +487.743 q^{81} -76.1477 q^{82} +1102.66 q^{83} +8.05509 q^{85} +2.25999 q^{86} -218.269 q^{87} +312.980 q^{88} +1093.27 q^{89} -45.7837 q^{90} +84.2387 q^{92} +160.030 q^{93} +78.9220 q^{94} +24.8977 q^{95} -107.440 q^{96} -911.865 q^{97} +1454.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9 + 44 * q^10 - 95 * q^11 + 17 * q^12 + 52 * q^13 - 16 * q^15 + 58 * q^16 + 146 * q^17 + 65 * q^18 + 48 * q^19 + 474 * q^20 - 143 * q^22 - 121 * q^23 + 469 * q^24 + 506 * q^25 - 52 * q^26 + 83 * q^27 - 440 * q^29 + 1548 * q^30 + 283 * q^31 - 114 * q^32 - 227 * q^33 - 1234 * q^34 + 755 * q^36 - 209 * q^37 - 440 * q^38 + 65 * q^39 - 754 * q^40 + 93 * q^41 + 526 * q^43 + 217 * q^44 + 768 * q^45 - 841 * q^46 + 783 * q^47 - 1407 * q^48 + 446 * q^50 - 672 * q^51 + 338 * q^52 - 340 * q^53 + 199 * q^54 - 756 * q^55 - 1014 * q^57 + 1916 * q^58 + 922 * q^59 - 396 * q^60 + 141 * q^61 - 1745 * q^62 - 1510 * q^64 + 468 * q^65 - 503 * q^66 - 523 * q^67 + 1710 * q^68 - 1595 * q^69 + 1468 * q^71 - 9 * q^72 + 47 * q^73 - 2249 * q^74 + 1547 * q^75 + 1382 * q^76 + 585 * q^78 + 1025 * q^79 + 2538 * q^80 - 1772 * q^81 + 1561 * q^82 + 1190 * q^83 - 568 * q^85 + 738 * q^86 - 720 * q^87 - 555 * q^88 + 2962 * q^89 + 1960 * q^90 - 599 * q^92 - 763 * q^93 - 317 * q^94 + 2082 * q^95 + 45 * q^96 - 2715 * q^97 + 586 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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