LMFDB - Embedded newform 625.8.a.c.1.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [625,8,Mod(1,625)] 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("625.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(625, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	625.a (trivial)

Newform invariants

comment:select newform

sage:traces = [34,-17] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$195.240640928$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 25)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	625.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+7.51166 q^{2} -8.67312 q^{3} -71.5749 q^{4} -65.1495 q^{6} +1153.54 q^{7} -1499.14 q^{8} -2111.78 q^{9} -431.045 q^{11} +620.778 q^{12} +280.582 q^{13} +8664.99 q^{14} -2099.44 q^{16} -32775.7 q^{17} -15863.0 q^{18} -30708.4 q^{19} -10004.8 q^{21} -3237.87 q^{22} +4439.92 q^{23} +13002.2 q^{24} +2107.64 q^{26} +37283.8 q^{27} -82564.5 q^{28} +111225. q^{29} -145021. q^{31} +176120. q^{32} +3738.50 q^{33} -246200. q^{34} +151150. q^{36} +484149. q^{37} -230671. q^{38} -2433.52 q^{39} -519048. q^{41} -75152.5 q^{42} -146858. q^{43} +30852.0 q^{44} +33351.2 q^{46} +1.16866e6 q^{47} +18208.7 q^{48} +507109. q^{49} +284267. q^{51} -20082.6 q^{52} -894659. q^{53} +280063. q^{54} -1.72932e6 q^{56} +266337. q^{57} +835484. q^{58} -2.59298e6 q^{59} -2.90419e6 q^{61} -1.08935e6 q^{62} -2.43602e6 q^{63} +1.59168e6 q^{64} +28082.4 q^{66} -631516. q^{67} +2.34592e6 q^{68} -38508.0 q^{69} +3.96661e6 q^{71} +3.16585e6 q^{72} -161087. q^{73} +3.63676e6 q^{74} +2.19795e6 q^{76} -497227. q^{77} -18279.8 q^{78} -3.68737e6 q^{79} +4.29509e6 q^{81} -3.89892e6 q^{82} +3.18889e6 q^{83} +716091. q^{84} -1.10315e6 q^{86} -964667. q^{87} +646197. q^{88} -6.63496e6 q^{89} +323662. q^{91} -317787. q^{92} +1.25778e6 q^{93} +8.77861e6 q^{94} -1.52751e6 q^{96} +7.70700e6 q^{97} +3.80923e6 q^{98} +910271. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} - 14 q^{3} + 2177 q^{4} + 993 q^{6} - 867 q^{7} - 2700 q^{8} + 23708 q^{9} + 8718 q^{11} - 2377 q^{12} - 8769 q^{13} + 17674 q^{14} + 139109 q^{16} + 48258 q^{17} - 58104 q^{18} + 61955 q^{19}+ \cdots + 35633116 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 - 14 * q^3 + 2177 * q^4 + 993 * q^6 - 867 * q^7 - 2700 * q^8 + 23708 * q^9 + 8718 * q^11 - 2377 * q^12 - 8769 * q^13 + 17674 * q^14 + 139109 * q^16 + 48258 * q^17 - 58104 * q^18 + 61955 * q^19 + 96943 * q^21 + 52556 * q^22 - 55584 * q^23 + 276990 * q^24 + 337623 * q^26 + 24370 * q^27 - 392941 * q^28 + 449815 * q^29 + 450438 * q^31 - 522987 * q^32 + 689282 * q^33 + 639889 * q^34 + 2024094 * q^36 + 373008 * q^37 - 1272835 * q^38 + 877321 * q^39 + 926418 * q^41 - 580554 * q^42 + 1719911 * q^43 + 1809244 * q^44 + 1186623 * q^46 - 640247 * q^47 - 3924149 * q^48 + 3292177 * q^49 + 1961038 * q^51 - 3900212 * q^52 - 1609214 * q^53 + 3802395 * q^54 + 5709425 * q^56 + 7299205 * q^57 + 4001010 * q^58 + 6056265 * q^59 + 2885628 * q^61 + 14351151 * q^62 - 8834194 * q^63 + 12281872 * q^64 + 8819186 * q^66 + 164318 * q^67 + 14549609 * q^68 + 5884976 * q^69 + 10286173 * q^71 - 41997930 * q^72 - 20595894 * q^73 + 7025034 * q^74 + 11251000 * q^76 - 14569234 * q^77 + 32702012 * q^78 + 11772835 * q^79 + 24408674 * q^81 + 38307271 * q^82 - 2455444 * q^83 + 17190739 * q^84 + 7636893 * q^86 + 39372965 * q^87 - 45397760 * q^88 + 17788560 * q^89 + 15865973 * q^91 - 37183957 * q^92 + 59352382 * q^93 + 29349634 * q^94 + 38027693 * q^96 - 3708847 * q^97 - 6000776 * q^98 + 35633116 * 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 $

$2$	7.51166	0.663943	0.331972	−	0.943289i	$-0.392286\pi$
$2$	7.51166	0.663943	0.331972	+	0.943289i	$0.392286\pi$
$3$	−8.67312	−0.185460	−0.0927301	−	0.995691i	$-0.529559\pi$
$3$	−8.67312	−0.185460	−0.0927301	+	0.995691i	$0.529559\pi$
$4$	−71.5749	−0.559179
$5$	0	0
$5$	0	0
$6$	−65.1495	−0.123135
$7$	1153.54	1.27113	0.635564	−	0.772048i	$-0.280768\pi$
$7$	1153.54	1.27113	0.635564	+	0.772048i	$0.280768\pi$
$8$	−1499.14	−1.03521
$9$	−2111.78	−0.965604
$10$	0	0
$11$	−431.045	−0.0976446	−0.0488223	−	0.998807i	$-0.515547\pi$
$11$	−431.045	−0.0976446	−0.0488223	+	0.998807i	$0.515547\pi$
$12$	620.778	0.103705
$13$	280.582	0.0354208	0.0177104	−	0.999843i	$-0.494362\pi$
$13$	280.582	0.0354208	0.0177104	+	0.999843i	$0.494362\pi$
$14$	8664.99	0.843957
$15$	0	0
$16$	−2099.44	−0.128140
$17$	−32775.7	−1.61801	−0.809004	−	0.587803i	$-0.799993\pi$
$17$	−32775.7	−1.61801	−0.809004	+	0.587803i	$0.799993\pi$
$18$	−15863.0	−0.641107
$19$	−30708.4	−1.02712	−0.513558	−	0.858055i	$-0.671673\pi$
$19$	−30708.4	−1.02712	−0.513558	+	0.858055i	$0.671673\pi$
$20$	0	0
$21$	−10004.8	−0.235744
$22$	−3237.87	−0.0648305
$23$	4439.92	0.0760901	0.0380450	−	0.999276i	$-0.487887\pi$
$23$	4439.92	0.0760901	0.0380450	+	0.999276i	$0.487887\pi$
$24$	13002.2	0.191990
$25$	0	0
$26$	2107.64	0.0235174
$27$	37283.8	0.364541
$28$	−82564.5	−0.710788
$29$	111225.	0.846855	0.423428	−	0.905930i	$-0.360827\pi$
$29$	111225.	0.846855	0.423428	+	0.905930i	$0.360827\pi$
$30$	0	0
$31$	−145021.	−0.874309	−0.437154	−	0.899386i	$-0.644014\pi$
$31$	−145021.	−0.874309	−0.437154	+	0.899386i	$0.644014\pi$
$32$	176120.	0.950129
$33$	3738.50	0.0181092
$34$	−246200.	−1.07427
$35$	0	0
$36$	151150.	0.539946
$37$	484149.	1.57135	0.785675	−	0.618639i	$-0.212316\pi$
$37$	484149.	1.57135	0.785675	+	0.618639i	$0.212316\pi$
$38$	−230671.	−0.681946
$39$	−2433.52	−0.00656915
$40$	0	0
$41$	−519048.	−1.17615	−0.588077	−	0.808805i	$-0.700115\pi$
$41$	−519048.	−1.17615	−0.588077	+	0.808805i	$0.700115\pi$
$42$	−75152.5	−0.156520
$43$	−146858.	−0.281681	−0.140841	−	0.990032i	$-0.544980\pi$
$43$	−146858.	−0.281681	−0.140841	+	0.990032i	$0.544980\pi$
$44$	30852.0	0.0546008
$45$	0	0
$46$	33351.2	0.0505195
$47$	1.16866e6	1.64190	0.820951	−	0.570999i	$-0.193444\pi$
$47$	1.16866e6	1.64190	0.820951	+	0.570999i	$0.193444\pi$
$48$	18208.7	0.0237648
$49$	507109.	0.615765
$50$	0	0
$51$	284267.	0.300076
$52$	−20082.6	−0.0198066
$53$	−894659.	−0.825452	−0.412726	−	0.910855i	$-0.635423\pi$
$53$	−894659.	−0.825452	−0.412726	+	0.910855i	$0.635423\pi$
$54$	280063.	0.242035
$55$	0	0
$56$	−1.72932e6	−1.31588
$57$	266337.	0.190489
$58$	835484.	0.562264
$59$	−2.59298e6	−1.64368	−0.821840	−	0.569719i	$-0.807052\pi$
$59$	−2.59298e6	−1.64368	−0.821840	+	0.569719i	$0.807052\pi$
$60$	0	0
$61$	−2.90419e6	−1.63822	−0.819108	−	0.573640i	$-0.805531\pi$
$61$	−2.90419e6	−1.63822	−0.819108	+	0.573640i	$0.805531\pi$
$62$	−1.08935e6	−0.580492
$63$	−2.43602e6	−1.22741
$64$	1.59168e6	0.758972
$65$	0	0
$66$	28082.4	0.0120235
$67$	−631516.	−0.256521	−0.128260	−	0.991741i	$-0.540939\pi$
$67$	−631516.	−0.256521	−0.128260	+	0.991741i	$0.540939\pi$
$68$	2.34592e6	0.904756
$69$	−38508.0	−0.0141117
$70$	0	0
$71$	3.96661e6	1.31527	0.657635	−	0.753336i	$-0.271557\pi$
$71$	3.96661e6	1.31527	0.657635	+	0.753336i	$0.271557\pi$
$72$	3.16585e6	0.999600
$73$	−161087.	−0.0484651	−0.0242326	−	0.999706i	$-0.507714\pi$
$73$	−161087.	−0.0484651	−0.0242326	+	0.999706i	$0.507714\pi$
$74$	3.63676e6	1.04329
$75$	0	0
$76$	2.19795e6	0.574341
$77$	−497227.	−0.124119
$78$	−18279.8	−0.00436154
$79$	−3.68737e6	−0.841439	−0.420719	−	0.907191i	$-0.638222\pi$
$79$	−3.68737e6	−0.841439	−0.420719	+	0.907191i	$0.638222\pi$
$80$	0	0
$81$	4.29509e6	0.897997
$82$	−3.89892e6	−0.780900
$83$	3.18889e6	0.612161	0.306081	−	0.952006i	$-0.400982\pi$
$83$	3.18889e6	0.612161	0.306081	+	0.952006i	$0.400982\pi$
$84$	716091.	0.131823
$85$	0	0
$86$	−1.10315e6	−0.187020
$87$	−964667.	−0.157058
$88$	646197.	0.101082
$89$	−6.63496e6	−0.997638	−0.498819	−	0.866706i	$-0.666233\pi$
$89$	−6.63496e6	−0.997638	−0.498819	+	0.866706i	$0.666233\pi$
$90$	0	0
$91$	323662.	0.0450243
$92$	−317787.	−0.0425480
$93$	1.25778e6	0.162150
$94$	8.77861e6	1.09013
$95$	0	0
$96$	−1.52751e6	−0.176211
$97$	7.70700e6	0.857401	0.428701	−	0.903447i	$-0.358971\pi$
$97$	7.70700e6	0.857401	0.428701	+	0.903447i	$0.358971\pi$
$98$	3.80923e6	0.408833
$99$	910271.	0.0942861
$100$	0	0
$101$	−8.72630e6	−0.842762	−0.421381	−	0.906884i	$-0.638455\pi$
$101$	−8.72630e6	−0.842762	−0.421381	+	0.906884i	$0.638455\pi$
$102$	2.13532e6	0.199234
$103$	3.70713e6	0.334278	0.167139	−	0.985933i	$-0.446547\pi$
$103$	3.70713e6	0.334278	0.167139	+	0.985933i	$0.446547\pi$
$104$	−420632.	−0.0366678
$105$	0	0
$106$	−6.72038e6	−0.548054
$107$	3.47058e6	0.273879	0.136940	−	0.990579i	$-0.456273\pi$
$107$	3.47058e6	0.273879	0.136940	+	0.990579i	$0.456273\pi$
$108$	−2.66859e6	−0.203844
$109$	1.88426e7	1.39364	0.696818	−	0.717248i	$-0.254599\pi$
$109$	1.88426e7	1.39364	0.696818	+	0.717248i	$0.254599\pi$
$110$	0	0
$111$	−4.19908e6	−0.291423
$112$	−2.42178e6	−0.162882
$113$	1.30688e6	0.0852040	0.0426020	−	0.999092i	$-0.486435\pi$
$113$	1.30688e6	0.0852040	0.0426020	+	0.999092i	$0.486435\pi$
$114$	2.00064e6	0.126474
$115$	0	0
$116$	−7.96092e6	−0.473544
$117$	−592527.	−0.0342025
$118$	−1.94776e7	−1.09131
$119$	−3.78080e7	−2.05669
$120$	0	0
$121$	−1.93014e7	−0.990466
$122$	−2.18153e7	−1.08768
$123$	4.50177e6	0.218130
$124$	1.03799e7	0.488895
$125$	0	0
$126$	−1.82985e7	−0.814928
$127$	7.46597e6	0.323425	0.161712	−	0.986838i	$-0.448298\pi$
$127$	7.46597e6	0.323425	0.161712	+	0.986838i	$0.448298\pi$
$128$	−1.05872e7	−0.446215
$129$	1.27372e6	0.0522406
$130$	0	0
$131$	3.49463e6	0.135816	0.0679081	−	0.997692i	$-0.478368\pi$
$131$	3.49463e6	0.135816	0.0679081	+	0.997692i	$0.478368\pi$
$132$	−267583.	−0.0101263
$133$	−3.54233e7	−1.30559
$134$	−4.74374e6	−0.170315
$135$	0	0
$136$	4.91353e7	1.67497
$137$	1.58891e7	0.527931	0.263965	−	0.964532i	$-0.414970\pi$
$137$	1.58891e7	0.527931	0.263965	+	0.964532i	$0.414970\pi$
$138$	−289259.	−0.00936936
$139$	5.89020e7	1.86028	0.930140	−	0.367204i	$-0.119685\pi$
$139$	5.89020e7	1.86028	0.930140	+	0.367204i	$0.119685\pi$
$140$	0	0
$141$	−1.01360e7	−0.304508
$142$	2.97958e7	0.873265
$143$	−120944.	−0.00345865
$144$	4.43355e6	0.123732
$145$	0	0
$146$	−1.21003e6	−0.0321781
$147$	−4.39821e6	−0.114200
$148$	−3.46529e7	−0.878666
$149$	1.42458e7	0.352804	0.176402	−	0.984318i	$-0.443554\pi$
$149$	1.42458e7	0.352804	0.176402	+	0.984318i	$0.443554\pi$
$150$	0	0
$151$	3.54311e7	0.837463	0.418731	−	0.908110i	$-0.362475\pi$
$151$	3.54311e7	0.837463	0.418731	+	0.908110i	$0.362475\pi$
$152$	4.60361e7	1.06328
$153$	6.92149e7	1.56236
$154$	−3.73500e6	−0.0824078
$155$	0	0
$156$	174179.	0.00367333
$157$	6.89639e7	1.42224	0.711120	−	0.703071i	$-0.248188\pi$
$157$	6.89639e7	1.42224	0.711120	+	0.703071i	$0.248188\pi$
$158$	−2.76983e7	−0.558668
$159$	7.75948e6	0.153089
$160$	0	0
$161$	5.12162e6	0.0967202
$162$	3.22633e7	0.596219
$163$	−1.90470e7	−0.344485	−0.172243	−	0.985055i	$-0.555101\pi$
$163$	−1.90470e7	−0.344485	−0.172243	+	0.985055i	$0.555101\pi$
$164$	3.71508e7	0.657681
$165$	0	0
$166$	2.39539e7	0.406441
$167$	8.40000e7	1.39563	0.697817	−	0.716276i	$-0.254155\pi$
$167$	8.40000e7	1.39563	0.697817	+	0.716276i	$0.254155\pi$
$168$	1.49986e7	0.244043
$169$	−6.26698e7	−0.998745
$170$	0	0
$171$	6.48492e7	0.991787
$172$	1.05113e7	0.157510
$173$	1.06207e8	1.55952	0.779760	−	0.626079i	$-0.215341\pi$
$173$	1.06207e8	1.55952	0.779760	+	0.626079i	$0.215341\pi$
$174$	−7.24625e6	−0.104278
$175$	0	0
$176$	904953.	0.0125121
$177$	2.24892e7	0.304837
$178$	−4.98396e7	−0.662375
$179$	2.63771e7	0.343750	0.171875	−	0.985119i	$-0.445018\pi$
$179$	2.63771e7	0.343750	0.171875	+	0.985119i	$0.445018\pi$
$180$	0	0
$181$	3.85068e7	0.482683	0.241342	−	0.970440i	$-0.422413\pi$
$181$	3.85068e7	0.482683	0.241342	+	0.970440i	$0.422413\pi$
$182$	2.43124e6	0.0298936
$183$	2.51884e7	0.303824
$184$	−6.65607e6	−0.0787690
$185$	0	0
$186$	9.44805e6	0.107658
$187$	1.41278e7	0.157990
$188$	−8.36470e7	−0.918117
$189$	4.30083e7	0.463379
$190$	0	0
$191$	7.29101e7	0.757131	0.378565	−	0.925575i	$-0.376418\pi$
$191$	7.29101e7	0.757131	0.378565	+	0.925575i	$0.376418\pi$
$192$	−1.38048e7	−0.140759
$193$	−2.71019e7	−0.271362	−0.135681	−	0.990753i	$-0.543322\pi$
$193$	−2.71019e7	−0.271362	−0.135681	+	0.990753i	$0.543322\pi$
$194$	5.78924e7	0.569266
$195$	0	0
$196$	−3.62963e7	−0.344323
$197$	1.10128e8	1.02628	0.513140	−	0.858305i	$-0.328482\pi$
$197$	1.10128e8	1.02628	0.513140	+	0.858305i	$0.328482\pi$
$198$	6.83765e6	0.0626006
$199$	1.86918e8	1.68138	0.840689	−	0.541518i	$-0.182150\pi$
$199$	1.86918e8	1.68138	0.840689	+	0.541518i	$0.182150\pi$
$200$	0	0
$201$	5.47721e6	0.0475744
$202$	−6.55490e7	−0.559547
$203$	1.28302e8	1.07646
$204$	−2.03464e7	−0.167796
$205$	0	0
$206$	2.78467e7	0.221942
$207$	−9.37613e6	−0.0734729
$208$	−589065.	−0.00453881
$209$	1.32367e7	0.100292
$210$	0	0
$211$	−2.46634e8	−1.80744	−0.903719	−	0.428125i	$-0.859174\pi$
$211$	−2.46634e8	−1.80744	−0.903719	+	0.428125i	$0.859174\pi$
$212$	6.40352e7	0.461576
$213$	−3.44029e7	−0.243930
$214$	2.60698e7	0.181840
$215$	0	0
$216$	−5.58936e7	−0.377376
$217$	−1.67287e8	−1.11136
$218$	1.41540e8	0.925295
$219$	1.39712e6	0.00898836
$220$	0	0
$221$	−9.19627e6	−0.0573111
$222$	−3.15421e7	−0.193488
$223$	2.42861e8	1.46653	0.733265	−	0.679943i	$-0.237995\pi$
$223$	2.42861e8	1.46653	0.733265	+	0.679943i	$0.237995\pi$
$224$	2.03161e8	1.20774
$225$	0	0
$226$	9.81682e6	0.0565706
$227$	−1.84785e8	−1.04852	−0.524259	−	0.851559i	$-0.675658\pi$
$227$	−1.84785e8	−1.04852	−0.524259	+	0.851559i	$0.675658\pi$
$228$	−1.90631e7	−0.106517
$229$	1.66838e7	0.0918062	0.0459031	−	0.998946i	$-0.485383\pi$
$229$	1.66838e7	0.0918062	0.0459031	+	0.998946i	$0.485383\pi$
$230$	0	0
$231$	4.31251e6	0.0230191
$232$	−1.66742e8	−0.876670
$233$	2.65848e7	0.137685	0.0688426	−	0.997628i	$-0.478069\pi$
$233$	2.65848e7	0.137685	0.0688426	+	0.997628i	$0.478069\pi$
$234$	−4.45086e6	−0.0227085
$235$	0	0
$236$	1.85592e8	0.919111
$237$	3.19810e7	0.156053
$238$	−2.84001e8	−1.36553
$239$	−1.48396e8	−0.703119	−0.351559	−	0.936166i	$-0.614348\pi$
$239$	−1.48396e8	−0.703119	−0.351559	+	0.936166i	$0.614348\pi$
$240$	0	0
$241$	7.70326e7	0.354499	0.177250	−	0.984166i	$-0.443280\pi$
$241$	7.70326e7	0.354499	0.177250	+	0.984166i	$0.443280\pi$
$242$	−1.44985e8	−0.657613
$243$	−1.18791e8	−0.531084
$244$	2.07867e8	0.916056
$245$	0	0
$246$	3.38158e7	0.144826
$247$	−8.61622e6	−0.0363812
$248$	2.17407e8	0.905090
$249$	−2.76576e7	−0.113532
$250$	0	0
$251$	9.68092e7	0.386419	0.193210	−	0.981157i	$-0.438110\pi$
$251$	9.68092e7	0.386419	0.193210	+	0.981157i	$0.438110\pi$
$252$	1.74358e8	0.686340
$253$	−1.91381e6	−0.00742979
$254$	5.60819e7	0.214736
$255$	0	0
$256$	−2.83262e8	−1.05523
$257$	3.81802e8	1.40305	0.701524	−	0.712646i	$-0.252503\pi$
$257$	3.81802e8	1.40305	0.701524	+	0.712646i	$0.252503\pi$
$258$	9.56772e6	0.0346848
$259$	5.58485e8	1.99739
$260$	0	0
$261$	−2.34882e8	−0.817727
$262$	2.62505e7	0.0901742
$263$	−2.62839e8	−0.890933	−0.445467	−	0.895299i	$-0.646962\pi$
$263$	−2.62839e8	−0.890933	−0.445467	+	0.895299i	$0.646962\pi$
$264$	−5.60454e6	−0.0187468
$265$	0	0
$266$	−2.66088e8	−0.866841
$267$	5.75458e7	0.185022
$268$	4.52007e7	0.143441
$269$	4.53771e8	1.42136	0.710679	−	0.703516i	$-0.248388\pi$
$269$	4.53771e8	1.42136	0.710679	+	0.703516i	$0.248388\pi$
$270$	0	0
$271$	2.37184e8	0.723924	0.361962	−	0.932193i	$-0.382107\pi$
$271$	2.37184e8	0.723924	0.361962	+	0.932193i	$0.382107\pi$
$272$	6.88106e7	0.207331
$273$	−2.80716e6	−0.00835022
$274$	1.19353e8	0.350516
$275$	0	0
$276$	2.75621e6	0.00789096
$277$	2.37577e7	0.0671621	0.0335811	−	0.999436i	$-0.489309\pi$
$277$	2.37577e7	0.0671621	0.0335811	+	0.999436i	$0.489309\pi$
$278$	4.42452e8	1.23512
$279$	3.06252e8	0.844237
$280$	0	0
$281$	−2.58925e8	−0.696149	−0.348075	−	0.937467i	$-0.613164\pi$
$281$	−2.58925e8	−0.696149	−0.348075	+	0.937467i	$0.613164\pi$
$282$	−7.61379e7	−0.202176
$283$	−6.58845e8	−1.72795	−0.863975	−	0.503535i	$-0.832032\pi$
$283$	−6.58845e8	−1.72795	−0.863975	+	0.503535i	$0.832032\pi$
$284$	−2.83910e8	−0.735472
$285$	0	0
$286$	−908487.	−0.00229635
$287$	−5.98742e8	−1.49504
$288$	−3.71925e8	−0.917449
$289$	6.63907e8	1.61795
$290$	0	0
$291$	−6.68437e7	−0.159014
$292$	1.15298e7	0.0271007
$293$	−1.72715e8	−0.401138	−0.200569	−	0.979680i	$-0.564279\pi$
$293$	−1.72715e8	−0.401138	−0.200569	+	0.979680i	$0.564279\pi$
$294$	−3.30379e7	−0.0758222
$295$	0	0
$296$	−7.25807e8	−1.62667
$297$	−1.60710e7	−0.0355955
$298$	1.07009e8	0.234242
$299$	1.24576e6	0.00269517
$300$	0	0
$301$	−1.69406e8	−0.358053
$302$	2.66147e8	0.556028
$303$	7.56842e7	0.156299
$304$	6.44703e7	0.131614
$305$	0	0
$306$	5.19919e8	1.03732
$307$	−7.32875e8	−1.44559	−0.722796	−	0.691062i	$-0.757143\pi$
$307$	−7.32875e8	−1.44559	−0.722796	+	0.691062i	$0.757143\pi$
$308$	3.55890e7	0.0694046
$309$	−3.21524e7	−0.0619952
$310$	0	0
$311$	6.16425e8	1.16203	0.581017	−	0.813892i	$-0.302655\pi$
$311$	6.16425e8	1.16203	0.581017	+	0.813892i	$0.302655\pi$
$312$	3.64819e6	0.00680043
$313$	−1.27350e8	−0.234743	−0.117372	−	0.993088i	$-0.537447\pi$
$313$	−1.27350e8	−0.234743	−0.117372	+	0.993088i	$0.537447\pi$
$314$	5.18033e8	0.944287
$315$	0	0
$316$	2.63924e8	0.470515
$317$	8.27570e8	1.45914	0.729571	−	0.683905i	$-0.239720\pi$
$317$	8.27570e8	1.45914	0.729571	+	0.683905i	$0.239720\pi$
$318$	5.82866e7	0.101642
$319$	−4.79430e7	−0.0826909
$320$	0	0
$321$	−3.01007e7	−0.0507937
$322$	3.84719e7	0.0642167
$323$	1.00649e9	1.66188
$324$	−3.07421e8	−0.502141
$325$	0	0
$326$	−1.43075e8	−0.228719
$327$	−1.63424e8	−0.258464
$328$	7.78126e8	1.21756
$329$	1.34810e9	2.08707
$330$	0	0
$331$	6.57727e7	0.0996891	0.0498446	−	0.998757i	$-0.484127\pi$
$331$	6.57727e7	0.0996891	0.0498446	+	0.998757i	$0.484127\pi$
$332$	−2.28244e8	−0.342308
$333$	−1.02241e9	−1.51730
$334$	6.30980e8	0.926622
$335$	0	0
$336$	2.10044e7	0.0302081
$337$	−2.09900e8	−0.298751	−0.149375	−	0.988781i	$-0.547726\pi$
$337$	−2.09900e8	−0.298751	−0.149375	+	0.988781i	$0.547726\pi$
$338$	−4.70754e8	−0.663110
$339$	−1.13347e7	−0.0158020
$340$	0	0
$341$	6.25106e7	0.0853716
$342$	4.87125e8	0.658490
$343$	−3.65019e8	−0.488412
$344$	2.20160e8	0.291598
$345$	0	0
$346$	7.97790e8	1.03543
$347$	−6.20434e8	−0.797154	−0.398577	−	0.917135i	$-0.630496\pi$
$347$	−6.20434e8	−0.797154	−0.398577	+	0.917135i	$0.630496\pi$
$348$	6.90460e7	0.0878235
$349$	−3.39227e8	−0.427171	−0.213585	−	0.976924i	$-0.568514\pi$
$349$	−3.39227e8	−0.427171	−0.213585	+	0.976924i	$0.568514\pi$
$350$	0	0
$351$	1.04612e7	0.0129123
$352$	−7.59155e7	−0.0927750
$353$	5.78449e8	0.699928	0.349964	−	0.936763i	$-0.386194\pi$
$353$	5.78449e8	0.699928	0.349964	+	0.936763i	$0.386194\pi$
$354$	1.68931e8	0.202395
$355$	0	0
$356$	4.74897e8	0.557858
$357$	3.27913e8	0.381435
$358$	1.98136e8	0.228230
$359$	1.13435e9	1.29394	0.646971	−	0.762514i	$-0.276035\pi$
$359$	1.13435e9	1.29394	0.646971	+	0.762514i	$0.276035\pi$
$360$	0	0
$361$	4.91321e7	0.0549655
$362$	2.89250e8	0.320474
$363$	1.67403e8	0.183692
$364$	−2.31661e7	−0.0251767
$365$	0	0
$366$	1.89207e8	0.201722
$367$	−1.78022e9	−1.87993	−0.939965	−	0.341271i	$-0.889143\pi$
$367$	−1.78022e9	−1.87993	−0.939965	+	0.341271i	$0.889143\pi$
$368$	−9.32135e6	−0.00975015
$369$	1.09611e9	1.13570
$370$	0	0
$371$	−1.03202e9	−1.04925
$372$	−9.00258e7	−0.0906706
$373$	1.43035e9	1.42712	0.713561	−	0.700593i	$-0.247081\pi$
$373$	1.43035e9	1.42712	0.713561	+	0.700593i	$0.247081\pi$
$374$	1.06123e8	0.104896
$375$	0	0
$376$	−1.75199e9	−1.69971
$377$	3.12077e7	0.0299963
$378$	3.23064e8	0.307657
$379$	−1.48628e8	−0.140237	−0.0701187	−	0.997539i	$-0.522338\pi$
$379$	−1.48628e8	−0.140237	−0.0701187	+	0.997539i	$0.522338\pi$
$380$	0	0
$381$	−6.47532e7	−0.0599824
$382$	5.47676e8	0.502692
$383$	−6.98654e8	−0.635428	−0.317714	−	0.948187i	$-0.602915\pi$
$383$	−6.98654e8	−0.635428	−0.317714	+	0.948187i	$0.602915\pi$
$384$	9.18236e7	0.0827551
$385$	0	0
$386$	−2.03580e8	−0.180169
$387$	3.10131e8	0.271993
$388$	−5.51628e8	−0.479441
$389$	−9.98228e8	−0.859817	−0.429909	−	0.902872i	$-0.641454\pi$
$389$	−9.98228e8	−0.859817	−0.429909	+	0.902872i	$0.641454\pi$
$390$	0	0
$391$	−1.45522e8	−0.123114
$392$	−7.60227e8	−0.637444
$393$	−3.03093e7	−0.0251885
$394$	8.27245e8	0.681392
$395$	0	0
$396$	−6.51526e7	−0.0527228
$397$	−3.94543e8	−0.316467	−0.158233	−	0.987402i	$-0.550580\pi$
$397$	−3.94543e8	−0.316467	−0.158233	+	0.987402i	$0.550580\pi$
$398$	1.40407e9	1.11634
$399$	3.07230e8	0.242136
$400$	0	0
$401$	2.55787e9	1.98095	0.990475	−	0.137695i	$-0.0439694\pi$
$401$	2.55787e9	1.98095	0.990475	+	0.137695i	$0.0439694\pi$
$402$	4.11430e7	0.0315867
$403$	−4.06903e7	−0.0309687
$404$	6.24584e8	0.471255
$405$	0	0
$406$	9.63763e8	0.714709
$407$	−2.08690e8	−0.153434
$408$	−4.26156e8	−0.310641
$409$	9.25958e8	0.669206	0.334603	−	0.942359i	$-0.391398\pi$
$409$	9.25958e8	0.669206	0.334603	+	0.942359i	$0.391398\pi$
$410$	0	0
$411$	−1.37808e8	−0.0979101
$412$	−2.65338e8	−0.186921
$413$	−2.99110e9	−2.08933
$414$	−7.04303e7	−0.0487819
$415$	0	0
$416$	4.94160e7	0.0336543
$417$	−5.10864e8	−0.345008
$418$	9.94296e7	0.0665884
$419$	1.71958e9	1.14202	0.571009	−	0.820944i	$-0.306552\pi$
$419$	1.71958e9	1.14202	0.571009	+	0.820944i	$0.306552\pi$
$420$	0	0
$421$	1.67565e9	1.09445	0.547226	−	0.836985i	$-0.315684\pi$
$421$	1.67565e9	1.09445	0.547226	+	0.836985i	$0.315684\pi$
$422$	−1.85263e9	−1.20004
$423$	−2.46796e9	−1.58543
$424$	1.34122e9	0.854514
$425$	0	0
$426$	−2.58423e8	−0.161956
$427$	−3.35010e9	−2.08238
$428$	−2.48407e8	−0.153147
$429$	1.04896e6	0.000641442 0
$430$	0	0
$431$	−2.76059e9	−1.66086	−0.830428	−	0.557127i	$-0.811904\pi$
$431$	−2.76059e9	−1.66086	−0.830428	+	0.557127i	$0.811904\pi$
$432$	−7.82751e7	−0.0467122
$433$	1.19084e9	0.704932	0.352466	−	0.935825i	$-0.385343\pi$
$433$	1.19084e9	0.704932	0.352466	+	0.935825i	$0.385343\pi$
$434$	−1.25661e9	−0.737879
$435$	0	0
$436$	−1.34866e9	−0.779292
$437$	−1.36343e8	−0.0781533
$438$	1.04947e7	0.00596776
$439$	1.01975e9	0.575263	0.287632	−	0.957741i	$-0.407132\pi$
$439$	1.01975e9	0.575263	0.287632	+	0.957741i	$0.407132\pi$
$440$	0	0
$441$	−1.07090e9	−0.594585
$442$	−6.90793e7	−0.0380513
$443$	1.28840e9	0.704107	0.352054	−	0.935980i	$-0.385483\pi$
$443$	1.28840e9	0.704107	0.352054	+	0.935980i	$0.385483\pi$
$444$	3.00549e8	0.162958
$445$	0	0
$446$	1.82429e9	0.973693
$447$	−1.23555e8	−0.0654312
$448$	1.83606e9	0.964750
$449$	1.62106e9	0.845158	0.422579	−	0.906326i	$-0.361125\pi$
$449$	1.62106e9	0.845158	0.422579	+	0.906326i	$0.361125\pi$
$450$	0	0
$451$	2.23733e8	0.114845
$452$	−9.35396e7	−0.0476443
$453$	−3.07298e8	−0.155316
$454$	−1.38804e9	−0.696157
$455$	0	0
$456$	−3.99277e8	−0.197196
$457$	−7.13086e8	−0.349490	−0.174745	−	0.984614i	$-0.555910\pi$
$457$	−7.13086e8	−0.349490	−0.174745	+	0.984614i	$0.555910\pi$
$458$	1.25323e8	0.0609541
$459$	−1.22200e9	−0.589831
$460$	0	0
$461$	1.68400e9	0.800552	0.400276	−	0.916395i	$-0.368914\pi$
$461$	1.68400e9	0.800552	0.400276	+	0.916395i	$0.368914\pi$
$462$	3.23941e7	0.0152834
$463$	−3.57567e9	−1.67426	−0.837131	−	0.547002i	$-0.815769\pi$
$463$	−3.57567e9	−1.67426	−0.837131	+	0.547002i	$0.815769\pi$
$464$	−2.33510e8	−0.108516
$465$	0	0
$466$	1.99696e8	0.0914152
$467$	1.91003e9	0.867821	0.433910	−	0.900956i	$-0.357133\pi$
$467$	1.91003e9	0.867821	0.433910	+	0.900956i	$0.357133\pi$
$468$	4.24101e7	0.0191253
$469$	−7.28478e8	−0.326071
$470$	0	0
$471$	−5.98132e8	−0.263769
$472$	3.88724e9	1.70155
$473$	6.33024e7	0.0275046
$474$	2.40231e8	0.103611
$475$	0	0
$476$	2.70611e9	1.15006
$477$	1.88932e9	0.797060
$478$	−1.11470e9	−0.466831
$479$	1.40567e8	0.0584398	0.0292199	−	0.999573i	$-0.490698\pi$
$479$	1.40567e8	0.0584398	0.0292199	+	0.999573i	$0.490698\pi$
$480$	0	0
$481$	1.35844e8	0.0556585
$482$	5.78643e8	0.235367
$483$	−4.44205e7	−0.0179378
$484$	1.38149e9	0.553848
$485$	0	0
$486$	−8.92322e8	−0.352610
$487$	2.40398e9	0.943147	0.471574	−	0.881827i	$-0.343686\pi$
$487$	2.40398e9	0.943147	0.471574	+	0.881827i	$0.343686\pi$
$488$	4.35379e9	1.69589
$489$	1.65197e8	0.0638883
$490$	0	0
$491$	−7.92000e7	−0.0301953	−0.0150977	−	0.999886i	$-0.504806\pi$
$491$	−7.92000e7	−0.0301953	−0.0150977	+	0.999886i	$0.504806\pi$
$492$	−3.22214e8	−0.121974
$493$	−3.64547e9	−1.37022
$494$	−6.47221e7	−0.0241551
$495$	0	0
$496$	3.04463e8	0.112034
$497$	4.57564e9	1.67188
$498$	−2.07755e8	−0.0753786
$499$	−1.86707e9	−0.672681	−0.336341	−	0.941740i	$-0.609189\pi$
$499$	−1.86707e9	−0.672681	−0.336341	+	0.941740i	$0.609189\pi$
$500$	0	0
$501$	−7.28542e8	−0.258835
$502$	7.27198e8	0.256561
$503$	2.66640e9	0.934196	0.467098	−	0.884206i	$-0.345300\pi$
$503$	2.66640e9	0.934196	0.467098	+	0.884206i	$0.345300\pi$
$504$	3.65193e9	1.27062
$505$	0	0
$506$	−1.43759e7	−0.00493296
$507$	5.43542e8	0.185228
$508$	−5.34376e8	−0.180852
$509$	−2.08545e9	−0.700952	−0.350476	−	0.936572i	$-0.613980\pi$
$509$	−2.08545e9	−0.700952	−0.350476	+	0.936572i	$0.613980\pi$
$510$	0	0
$511$	−1.85820e8	−0.0616054
$512$	−7.72613e8	−0.254400
$513$	−1.14492e9	−0.374426
$514$	2.86797e9	0.931544
$515$	0	0
$516$	−9.11661e7	−0.0292119
$517$	−5.03747e8	−0.160323
$518$	4.19515e9	1.32615
$519$	−9.21144e8	−0.289229
$520$	0	0
$521$	−2.87115e9	−0.889456	−0.444728	−	0.895666i	$-0.646700\pi$
$521$	−2.87115e9	−0.889456	−0.444728	+	0.895666i	$0.646700\pi$
$522$	−1.76436e9	−0.542925
$523$	3.01636e8	0.0921992	0.0460996	−	0.998937i	$-0.485321\pi$
$523$	3.01636e8	0.0921992	0.0460996	+	0.998937i	$0.485321\pi$
$524$	−2.50128e8	−0.0759455
$525$	0	0
$526$	−1.97436e9	−0.591529
$527$	4.75316e9	1.41464
$528$	−7.84876e6	−0.00232050
$529$	−3.38511e9	−0.994210
$530$	0	0
$531$	5.47579e9	1.58714
$532$	2.53542e9	0.730061
$533$	−1.45636e8	−0.0416603
$534$	4.32264e8	0.122844
$535$	0	0
$536$	9.46731e8	0.265552
$537$	−2.28772e8	−0.0637519
$538$	3.40857e9	0.943702
$539$	−2.18587e8	−0.0601261
$540$	0	0
$541$	6.16761e9	1.67466	0.837330	−	0.546698i	$-0.184116\pi$
$541$	6.16761e9	1.67466	0.837330	+	0.546698i	$0.184116\pi$
$542$	1.78165e9	0.480644
$543$	−3.33974e8	−0.0895186
$544$	−5.77244e9	−1.53732
$545$	0	0
$546$	−2.10864e7	−0.00554408
$547$	−2.77375e9	−0.724623	−0.362311	−	0.932057i	$-0.618012\pi$
$547$	−2.77375e9	−0.724623	−0.362311	+	0.932057i	$0.618012\pi$
$548$	−1.13726e9	−0.295208
$549$	6.13301e9	1.58187
$550$	0	0
$551$	−3.41554e9	−0.869818
$552$	5.77288e7	0.0146085
$553$	−4.25353e9	−1.06958
$554$	1.78459e8	0.0445918
$555$	0	0
$556$	−4.21591e9	−1.04023
$557$	−2.17301e9	−0.532805	−0.266402	−	0.963862i	$-0.585835\pi$
$557$	−2.17301e9	−0.532805	−0.266402	+	0.963862i	$0.585835\pi$
$558$	2.30046e9	0.560525
$559$	−4.12057e7	−0.00997737
$560$	0	0
$561$	−1.22532e8	−0.0293008
$562$	−1.94496e9	−0.462204
$563$	4.72838e9	1.11669	0.558346	−	0.829609i	$-0.311436\pi$
$563$	4.72838e9	1.11669	0.558346	+	0.829609i	$0.311436\pi$
$564$	7.25481e8	0.170274
$565$	0	0
$566$	−4.94902e9	−1.14726
$567$	4.95455e9	1.14147
$568$	−5.94650e9	−1.36158
$569$	−8.32629e9	−1.89478	−0.947389	−	0.320084i	$-0.896289\pi$
$569$	−8.32629e9	−1.89478	−0.947389	+	0.320084i	$0.896289\pi$
$570$	0	0
$571$	−6.21167e9	−1.39631	−0.698156	−	0.715946i	$-0.745996\pi$
$571$	−6.21167e9	−1.39631	−0.698156	+	0.715946i	$0.745996\pi$
$572$	8.65652e6	0.00193400
$573$	−6.32358e8	−0.140418
$574$	−4.49755e9	−0.992623
$575$	0	0
$576$	−3.36127e9	−0.732866
$577$	1.03081e9	0.223389	0.111695	−	0.993743i	$-0.464372\pi$
$577$	1.03081e9	0.223389	0.111695	+	0.993743i	$0.464372\pi$
$578$	4.98705e9	1.07423
$579$	2.35058e8	0.0503268
$580$	0	0
$581$	3.67851e9	0.778135
$582$	−5.02107e8	−0.105576
$583$	3.85638e8	0.0806010
$584$	2.41491e8	0.0501714
$585$	0	0
$586$	−1.29738e9	−0.266333
$587$	3.52247e9	0.718810	0.359405	−	0.933182i	$-0.382980\pi$
$587$	3.52247e9	0.718810	0.359405	+	0.933182i	$0.382980\pi$
$588$	3.14802e8	0.0638582
$589$	4.45336e9	0.898016
$590$	0	0
$591$	−9.55153e8	−0.190334
$592$	−1.01644e9	−0.201352
$593$	6.88056e9	1.35498	0.677490	−	0.735532i	$-0.263068\pi$
$593$	6.88056e9	1.35498	0.677490	+	0.735532i	$0.263068\pi$
$594$	−1.20720e8	−0.0236334
$595$	0	0
$596$	−1.01964e9	−0.197281
$597$	−1.62116e9	−0.311829
$598$	9.35775e6	0.00178944
$599$	−5.51933e9	−1.04928	−0.524641	−	0.851324i	$-0.675800\pi$
$599$	−5.51933e9	−1.04928	−0.524641	+	0.851324i	$0.675800\pi$
$600$	0	0
$601$	3.02510e9	0.568433	0.284217	−	0.958760i	$-0.408267\pi$
$601$	3.02510e9	0.568433	0.284217	+	0.958760i	$0.408267\pi$
$602$	−1.27252e9	−0.237727
$603$	1.33362e9	0.247698
$604$	−2.53598e9	−0.468292
$605$	0	0
$606$	5.68514e8	0.103774
$607$	−1.47941e9	−0.268489	−0.134245	−	0.990948i	$-0.542861\pi$
$607$	−1.47941e9	−0.268489	−0.134245	+	0.990948i	$0.542861\pi$
$608$	−5.40834e9	−0.975892
$609$	−1.11278e9	−0.199641
$610$	0	0
$611$	3.27906e8	0.0581575
$612$	−4.95405e9	−0.873637
$613$	8.25601e9	1.44763	0.723816	−	0.689993i	$-0.242386\pi$
$613$	8.25601e9	1.44763	0.723816	+	0.689993i	$0.242386\pi$
$614$	−5.50511e9	−0.959791
$615$	0	0
$616$	7.45413e8	0.128489
$617$	3.21145e8	0.0550432	0.0275216	−	0.999621i	$-0.491238\pi$
$617$	3.21145e8	0.0550432	0.0275216	+	0.999621i	$0.491238\pi$
$618$	−2.41518e8	−0.0411613
$619$	5.79681e9	0.982362	0.491181	−	0.871057i	$-0.336565\pi$
$619$	5.79681e9	0.982362	0.491181	+	0.871057i	$0.336565\pi$
$620$	0	0
$621$	1.65537e8	0.0277380
$622$	4.63037e9	0.771524
$623$	−7.65368e9	−1.26813
$624$	5.10903e6	0.000841768 0
$625$	0	0
$626$	−9.56609e8	−0.155856
$627$	−1.14803e8	−0.0186002
$628$	−4.93608e9	−0.795287
$629$	−1.58683e10	−2.54246
$630$	0	0
$631$	−1.00789e10	−1.59703	−0.798513	−	0.601977i	$-0.794380\pi$
$631$	−1.00789e10	−1.59703	−0.798513	+	0.601977i	$0.794380\pi$
$632$	5.52789e9	0.871063
$633$	2.13908e9	0.335208
$634$	6.21643e9	0.968787
$635$	0	0
$636$	−5.55384e8	−0.0856039
$637$	1.42286e8	0.0218109
$638$	−3.60131e8	−0.0549021
$639$	−8.37659e9	−1.27003
$640$	0	0
$641$	−1.27860e9	−0.191749	−0.0958745	−	0.995393i	$-0.530565\pi$
$641$	−1.27860e9	−0.191749	−0.0958745	+	0.995393i	$0.530565\pi$
$642$	−2.26107e8	−0.0337241
$643$	6.82194e8	0.101197	0.0505987	−	0.998719i	$-0.483887\pi$
$643$	6.82194e8	0.101197	0.0505987	+	0.998719i	$0.483887\pi$
$644$	−3.66580e8	−0.0540839
$645$	0	0
$646$	7.56040e9	1.10339
$647$	−9.79624e9	−1.42198	−0.710992	−	0.703200i	$-0.751754\pi$
$647$	−9.79624e9	−1.42198	−0.710992	+	0.703200i	$0.751754\pi$
$648$	−6.43894e9	−0.929612
$649$	1.11769e9	0.160496
$650$	0	0
$651$	1.45090e9	0.206113
$652$	1.36329e9	0.192629
$653$	−8.15971e9	−1.14678	−0.573388	−	0.819284i	$-0.694371\pi$
$653$	−8.15971e9	−1.14678	−0.573388	+	0.819284i	$0.694371\pi$
$654$	−1.22759e9	−0.171605
$655$	0	0
$656$	1.08971e9	0.150712
$657$	3.40179e8	0.0467981
$658$	1.01265e10	1.38569
$659$	−2.52315e9	−0.343435	−0.171717	−	0.985146i	$-0.554932\pi$
$659$	−2.52315e9	−0.343435	−0.171717	+	0.985146i	$0.554932\pi$
$660$	0	0
$661$	4.13332e9	0.556665	0.278332	−	0.960485i	$-0.410218\pi$
$661$	4.13332e9	0.556665	0.278332	+	0.960485i	$0.410218\pi$
$662$	4.94062e8	0.0661879
$663$	7.97603e7	0.0106289
$664$	−4.78059e9	−0.633714
$665$	0	0
$666$	−7.68004e9	−1.00740
$667$	4.93830e8	0.0644373
$668$	−6.01230e9	−0.780410
$669$	−2.10636e9	−0.271983
$670$	0	0
$671$	1.25184e9	0.159963
$672$	−1.76204e9	−0.223987
$673$	−7.54972e9	−0.954725	−0.477363	−	0.878706i	$-0.658407\pi$
$673$	−7.54972e9	−0.954725	−0.477363	+	0.878706i	$0.658407\pi$
$674$	−1.57670e9	−0.198353
$675$	0	0
$676$	4.48559e9	0.558478
$677$	−1.88440e8	−0.0233407	−0.0116703	−	0.999932i	$-0.503715\pi$
$677$	−1.88440e8	−0.0233407	−0.0116703	+	0.999932i	$0.503715\pi$
$678$	−8.51424e7	−0.0104916
$679$	8.89032e9	1.08987
$680$	0	0
$681$	1.60266e9	0.194458
$682$	4.69558e8	0.0566819
$683$	1.37954e9	0.165677	0.0828385	−	0.996563i	$-0.473601\pi$
$683$	1.37954e9	0.165677	0.0828385	+	0.996563i	$0.473601\pi$
$684$	−4.64158e9	−0.554587
$685$	0	0
$686$	−2.74190e9	−0.324278
$687$	−1.44701e8	−0.0170264
$688$	3.08319e8	0.0360945
$689$	−2.51025e8	−0.0292382
$690$	0	0
$691$	1.40583e10	1.62091	0.810457	−	0.585799i	$-0.199219\pi$
$691$	1.40583e10	1.62091	0.810457	+	0.585799i	$0.199219\pi$
$692$	−7.60174e9	−0.872051
$693$	1.05003e9	0.119850
$694$	−4.66049e9	−0.529265
$695$	0	0
$696$	1.44617e9	0.162587
$697$	1.70122e10	1.90303
$698$	−2.54816e9	−0.283617
$699$	−2.30573e8	−0.0255351
$700$	0	0
$701$	9.62820e9	1.05568	0.527840	−	0.849344i	$-0.323002\pi$
$701$	9.62820e9	1.05568	0.527840	+	0.849344i	$0.323002\pi$
$702$	7.85807e7	0.00857307
$703$	−1.48674e10	−1.61396
$704$	−6.86085e8	−0.0741095
$705$	0	0
$706$	4.34511e9	0.464713
$707$	−1.00661e10	−1.07126
$708$	−1.60966e9	−0.170459
$709$	−1.53677e10	−1.61937	−0.809686	−	0.586864i	$-0.800362\pi$
$709$	−1.53677e10	−1.61937	−0.809686	+	0.586864i	$0.800362\pi$
$710$	0	0
$711$	7.78691e9	0.812497
$712$	9.94673e9	1.03276
$713$	−6.43882e8	−0.0665262
$714$	2.46318e9	0.253251
$715$	0	0
$716$	−1.88794e9	−0.192218
$717$	1.28705e9	0.130401
$718$	8.52083e9	0.859105
$719$	−2.94378e9	−0.295362	−0.147681	−	0.989035i	$-0.547181\pi$
$719$	−2.94378e9	−0.295362	−0.147681	+	0.989035i	$0.547181\pi$
$720$	0	0
$721$	4.27632e9	0.424910
$722$	3.69064e8	0.0364940
$723$	−6.68113e8	−0.0657455
$724$	−2.75612e9	−0.269906
$725$	0	0
$726$	1.25748e9	0.121961
$727$	−1.75087e10	−1.68999	−0.844993	−	0.534778i	$-0.820395\pi$
$727$	−1.75087e10	−1.68999	−0.844993	+	0.534778i	$0.820395\pi$
$728$	−4.85215e8	−0.0466095
$729$	−8.36307e9	−0.799502
$730$	0	0
$731$	4.81337e9	0.455762
$732$	−1.80286e9	−0.169892
$733$	1.74257e10	1.63428	0.817141	−	0.576438i	$-0.195558\pi$
$733$	1.74257e10	1.63428	0.817141	+	0.576438i	$0.195558\pi$
$734$	−1.33724e10	−1.24817
$735$	0	0
$736$	7.81958e8	0.0722954
$737$	2.72212e8	0.0250479
$738$	8.23364e9	0.754041
$739$	−6.63370e9	−0.604645	−0.302322	−	0.953206i	$-0.597762\pi$
$739$	−6.63370e9	−0.604645	−0.302322	+	0.953206i	$0.597762\pi$
$740$	0	0
$741$	7.47295e7	0.00674727
$742$	−7.75221e9	−0.696646
$743$	−6.11265e9	−0.546725	−0.273362	−	0.961911i	$-0.588136\pi$
$743$	−6.11265e9	−0.546725	−0.273362	+	0.961911i	$0.588136\pi$
$744$	−1.88559e9	−0.167858
$745$	0	0
$746$	1.07443e10	0.947528
$747$	−6.73422e9	−0.591106
$748$	−1.01120e9	−0.0883446
$749$	4.00345e9	0.348135
$750$	0	0
$751$	−6.47738e9	−0.558033	−0.279016	−	0.960286i	$-0.590008\pi$
$751$	−6.47738e9	−0.558033	−0.279016	+	0.960286i	$0.590008\pi$
$752$	−2.45354e9	−0.210393
$753$	−8.39638e8	−0.0716654
$754$	2.34422e8	0.0199158
$755$	0	0
$756$	−3.07832e9	−0.259112
$757$	1.56639e10	1.31239	0.656195	−	0.754591i	$-0.272165\pi$
$757$	1.56639e10	1.31239	0.656195	+	0.754591i	$0.272165\pi$
$758$	−1.11645e9	−0.0931098
$759$	1.65987e7	0.00137793
$760$	0	0
$761$	−1.34424e10	−1.10568	−0.552840	−	0.833287i	$-0.686456\pi$
$761$	−1.34424e10	−1.10568	−0.552840	+	0.833287i	$0.686456\pi$
$762$	−4.86405e8	−0.0398249
$763$	2.17357e10	1.77149
$764$	−5.21853e9	−0.423372
$765$	0	0
$766$	−5.24805e9	−0.421888
$767$	−7.27544e8	−0.0582204
$768$	2.45676e9	0.195704
$769$	7.15384e9	0.567279	0.283640	−	0.958931i	$-0.408458\pi$
$769$	7.15384e9	0.567279	0.283640	+	0.958931i	$0.408458\pi$
$770$	0	0
$771$	−3.31141e9	−0.260210
$772$	1.93981e9	0.151740
$773$	−7.45322e9	−0.580385	−0.290192	−	0.956968i	$-0.593719\pi$
$773$	−7.45322e9	−0.580385	−0.290192	+	0.956968i	$0.593719\pi$
$774$	2.32960e9	0.180588
$775$	0	0
$776$	−1.15539e10	−0.887588
$777$	−4.84380e9	−0.370436
$778$	−7.49835e9	−0.570870
$779$	1.59391e10	1.20805
$780$	0	0
$781$	−1.70979e9	−0.128429
$782$	−1.09311e9	−0.0817410
$783$	4.14689e9	0.308714
$784$	−1.06464e9	−0.0789038
$785$	0	0
$786$	−2.27673e8	−0.0167237
$787$	1.18197e10	0.864363	0.432182	−	0.901787i	$-0.357744\pi$
$787$	1.18197e10	0.864363	0.432182	+	0.901787i	$0.357744\pi$
$788$	−7.88241e9	−0.573875
$789$	2.27964e9	0.165233
$790$	0	0
$791$	1.50753e9	0.108305
$792$	−1.36462e9	−0.0976056
$793$	−8.14864e8	−0.0580269
$794$	−2.96368e9	−0.210116
$795$	0	0
$796$	−1.33786e10	−0.940192
$797$	2.59127e9	0.181304	0.0906522	−	0.995883i	$-0.471105\pi$
$797$	2.59127e9	0.181304	0.0906522	+	0.995883i	$0.471105\pi$
$798$	2.30781e9	0.160764
$799$	−3.83038e10	−2.65661
$800$	0	0
$801$	1.40115e10	0.963324
$802$	1.92139e10	1.31524
$803$	6.94356e7	0.00473236
$804$	−3.92031e8	−0.0266026
$805$	0	0
$806$	−3.05652e8	−0.0205615
$807$	−3.93561e9	−0.263605
$808$	1.30819e10	0.872433
$809$	4.63994e9	0.308100	0.154050	−	0.988063i	$-0.450768\pi$
$809$	4.63994e9	0.308100	0.154050	+	0.988063i	$0.450768\pi$
$810$	0	0
$811$	−1.12663e10	−0.741665	−0.370833	−	0.928700i	$-0.620928\pi$
$811$	−1.12663e10	−0.741665	−0.370833	+	0.928700i	$0.620928\pi$
$812$	−9.18323e9	−0.601934
$813$	−2.05712e9	−0.134259
$814$	−1.56761e9	−0.101871
$815$	0	0
$816$	−5.96802e8	−0.0384516
$817$	4.50977e9	0.289319
$818$	6.95548e9	0.444315
$819$	−6.83503e8	−0.0434757
$820$	0	0
$821$	1.14770e10	0.723817	0.361909	−	0.932214i	$-0.382125\pi$
$821$	1.14770e10	0.723817	0.361909	+	0.932214i	$0.382125\pi$
$822$	−1.03517e9	−0.0650068
$823$	−1.28816e10	−0.805510	−0.402755	−	0.915308i	$-0.631947\pi$
$823$	−1.28816e10	−0.805510	−0.402755	+	0.915308i	$0.631947\pi$
$824$	−5.55750e9	−0.346047
$825$	0	0
$826$	−2.24682e10	−1.38719
$827$	9.86924e9	0.606757	0.303378	−	0.952870i	$-0.401885\pi$
$827$	9.86924e9	0.606757	0.303378	+	0.952870i	$0.401885\pi$
$828$	6.71096e8	0.0410845
$829$	4.83851e8	0.0294965	0.0147483	−	0.999891i	$-0.495305\pi$
$829$	4.83851e8	0.0294965	0.0147483	+	0.999891i	$0.495305\pi$
$830$	0	0
$831$	−2.06053e8	−0.0124559
$832$	4.46597e8	0.0268834
$833$	−1.66208e10	−0.996312
$834$	−3.83744e9	−0.229066
$835$	0	0
$836$	−9.47415e8	−0.0560813
$837$	−5.40693e9	−0.318722
$838$	1.29169e10	0.758235
$839$	−2.18839e10	−1.27926	−0.639628	−	0.768685i	$-0.720912\pi$
$839$	−2.18839e10	−1.27926	−0.639628	+	0.768685i	$0.720912\pi$
$840$	0	0
$841$	−4.87889e9	−0.282836
$842$	1.25869e10	0.726654
$843$	2.24569e9	0.129108
$844$	1.76528e10	1.01068
$845$	0	0
$846$	−1.85385e10	−1.05263
$847$	−2.22649e10	−1.25901
$848$	1.87828e9	0.105773
$849$	5.71424e9	0.320466
$850$	0	0
$851$	2.14959e9	0.119564
$852$	2.46238e9	0.136401
$853$	9.77094e9	0.539032	0.269516	−	0.962996i	$-0.413136\pi$
$853$	9.77094e9	0.539032	0.269516	+	0.962996i	$0.413136\pi$
$854$	−2.51648e10	−1.38258
$855$	0	0
$856$	−5.20288e9	−0.283521
$857$	1.82327e9	0.0989505	0.0494752	−	0.998775i	$-0.484245\pi$
$857$	1.82327e9	0.0989505	0.0494752	+	0.998775i	$0.484245\pi$
$858$	7.87941e6	0.000425881 0
$859$	1.55684e10	0.838048	0.419024	−	0.907975i	$-0.362372\pi$
$859$	1.55684e10	0.838048	0.419024	+	0.907975i	$0.362372\pi$
$860$	0	0
$861$	5.19296e9	0.277271
$862$	−2.07366e10	−1.10271
$863$	−8.40410e8	−0.0445096	−0.0222548	−	0.999752i	$-0.507085\pi$
$863$	−8.40410e8	−0.0445096	−0.0222548	+	0.999752i	$0.507085\pi$
$864$	6.56641e9	0.346362
$865$	0	0
$866$	8.94522e9	0.468035
$867$	−5.75814e9	−0.300065
$868$	1.19736e10	0.621448
$869$	1.58942e9	0.0821619
$870$	0	0
$871$	−1.77192e8	−0.00908617
$872$	−2.82478e10	−1.44270
$873$	−1.62755e10	−0.827911
$874$	−1.02416e9	−0.0518894
$875$	0	0
$876$	−9.99990e7	−0.00502610
$877$	−2.99816e10	−1.50091	−0.750457	−	0.660919i	$-0.770167\pi$
$877$	−2.99816e10	−1.50091	−0.750457	+	0.660919i	$0.770167\pi$
$878$	7.66000e9	0.381942
$879$	1.49798e9	0.0743952
$880$	0	0
$881$	1.49601e10	0.737087	0.368544	−	0.929610i	$-0.379856\pi$
$881$	1.49601e10	0.737087	0.368544	+	0.929610i	$0.379856\pi$
$882$	−8.04424e9	−0.394771
$883$	−3.11793e10	−1.52407	−0.762033	−	0.647539i	$-0.775798\pi$
$883$	−3.11793e10	−1.52407	−0.762033	+	0.647539i	$0.775798\pi$
$884$	6.58222e8	0.0320472
$885$	0	0
$886$	9.67805e9	0.467487
$887$	−2.56200e10	−1.23267	−0.616335	−	0.787484i	$-0.711383\pi$
$887$	−2.56200e10	−1.23267	−0.616335	+	0.787484i	$0.711383\pi$
$888$	6.29501e9	0.301683
$889$	8.61229e9	0.411114
$890$	0	0
$891$	−1.85138e9	−0.0876845
$892$	−1.73828e10	−0.820053
$893$	−3.58878e10	−1.68642
$894$	−9.28105e8	−0.0434426
$895$	0	0
$896$	−1.22127e10	−0.567196
$897$	−1.08046e7	−0.000499847 0
$898$	1.21769e10	0.561137
$899$	−1.61299e10	−0.740413
$900$	0	0
$901$	2.93231e10	1.33559
$902$	1.68061e9	0.0762507
$903$	1.46928e9	0.0664045
$904$	−1.95919e9	−0.0882038
$905$	0	0
$906$	−2.30832e9	−0.103121
$907$	−3.72736e10	−1.65873	−0.829364	−	0.558708i	$-0.811297\pi$
$907$	−3.72736e10	−1.65873	−0.829364	+	0.558708i	$0.811297\pi$
$908$	1.32260e10	0.586310
$909$	1.84280e10	0.813775
$910$	0	0
$911$	4.21284e10	1.84612	0.923062	−	0.384652i	$-0.125678\pi$
$911$	4.21284e10	1.84612	0.923062	+	0.384652i	$0.125678\pi$
$912$	−5.59159e8	−0.0244092
$913$	−1.37455e9	−0.0597743
$914$	−5.35646e9	−0.232042
$915$	0	0
$916$	−1.19415e9	−0.0513361
$917$	4.03119e9	0.172640
$918$	−9.17927e9	−0.391614
$919$	−2.04320e10	−0.868372	−0.434186	−	0.900823i	$-0.642964\pi$
$919$	−2.04320e10	−0.868372	−0.434186	+	0.900823i	$0.642964\pi$
$920$	0	0
$921$	6.35631e9	0.268100
$922$	1.26497e10	0.531521
$923$	1.11296e9	0.0465879
$924$	−3.08668e8	−0.0128718
$925$	0	0
$926$	−2.68592e10	−1.11162
$927$	−7.82863e9	−0.322780
$928$	1.95889e10	0.804622
$929$	1.78330e10	0.729743	0.364872	−	0.931058i	$-0.381113\pi$
$929$	1.78330e10	0.729743	0.364872	+	0.931058i	$0.381113\pi$
$930$	0	0
$931$	−1.55725e10	−0.632461
$932$	−1.90280e9	−0.0769907
$933$	−5.34632e9	−0.215511
$934$	1.43475e10	0.576184
$935$	0	0
$936$	8.88280e8	0.0354066
$937$	5.78607e9	0.229771	0.114886	−	0.993379i	$-0.463350\pi$
$937$	5.78607e9	0.229771	0.114886	+	0.993379i	$0.463350\pi$
$938$	−5.47208e9	−0.216492
$939$	1.10452e9	0.0435356
$940$	0	0
$941$	−1.39764e10	−0.546803	−0.273402	−	0.961900i	$-0.588149\pi$
$941$	−1.39764e10	−0.546803	−0.273402	+	0.961900i	$0.588149\pi$
$942$	−4.49296e9	−0.175128
$943$	−2.30454e9	−0.0894937
$944$	5.44380e9	0.210620
$945$	0	0
$946$	4.75506e8	0.0182615
$947$	3.10794e10	1.18918	0.594590	−	0.804029i	$-0.297314\pi$
$947$	3.10794e10	1.18918	0.594590	+	0.804029i	$0.297314\pi$
$948$	−2.28904e9	−0.0872618
$949$	−4.51980e7	−0.00171667
$950$	0	0
$951$	−7.17761e9	−0.270613
$952$	5.66795e10	2.12910
$953$	−5.05440e10	−1.89167	−0.945834	−	0.324651i	$-0.894753\pi$
$953$	−5.05440e10	−1.89167	−0.945834	+	0.324651i	$0.894753\pi$
$954$	1.41919e10	0.529203
$955$	0	0
$956$	1.06214e10	0.393169
$957$	4.15815e8	0.0153359
$958$	1.05589e9	0.0388007
$959$	1.83287e10	0.671067
$960$	0	0
$961$	−6.48153e9	−0.235584
$962$	1.02041e9	0.0369541
$963$	−7.32909e9	−0.264459
$964$	−5.51360e9	−0.198228
$965$	0	0
$966$	−3.33671e8	−0.0119097
$967$	5.23575e10	1.86203	0.931014	−	0.364985i	$-0.118926\pi$
$967$	5.23575e10	1.86203	0.931014	+	0.364985i	$0.118926\pi$
$968$	2.89354e10	1.02534
$969$	−8.72939e9	−0.308213
$970$	0	0
$971$	−9.90771e9	−0.347301	−0.173650	−	0.984807i	$-0.555556\pi$
$971$	−9.90771e9	−0.347301	−0.173650	+	0.984807i	$0.555556\pi$
$972$	8.50249e9	0.296971
$973$	6.79458e10	2.36465
$974$	1.80579e10	0.626196
$975$	0	0
$976$	6.09718e9	0.209920
$977$	−2.78051e10	−0.953881	−0.476940	−	0.878936i	$-0.658254\pi$
$977$	−2.78051e10	−0.953881	−0.476940	+	0.878936i	$0.658254\pi$
$978$	1.24091e9	0.0424182
$979$	2.85997e9	0.0974140
$980$	0	0
$981$	−3.97915e10	−1.34570
$982$	−5.94923e8	−0.0200480
$983$	−2.76912e10	−0.929832	−0.464916	−	0.885355i	$-0.653916\pi$
$983$	−2.76912e10	−0.929832	−0.464916	+	0.885355i	$0.653916\pi$
$984$	−6.74878e9	−0.225810
$985$	0	0
$986$	−2.73836e10	−0.909747
$987$	−1.16922e10	−0.387068
$988$	6.16705e8	0.0203436
$989$	−6.52038e8	−0.0214331
$990$	0	0
$991$	2.47025e10	0.806275	0.403137	−	0.915139i	$-0.367920\pi$
$991$	2.47025e10	0.806275	0.403137	+	0.915139i	$0.367920\pi$
$992$	−2.55410e10	−0.830706
$993$	−5.70455e8	−0.0184884
$994$	3.43706e10	1.11003
$995$	0	0
$996$	1.97959e9	0.0634845
$997$	1.48873e10	0.475754	0.237877	−	0.971295i	$-0.423548\pi$
$997$	1.48873e10	0.475754	0.237877	+	0.971295i	$0.423548\pi$
$998$	−1.40248e10	−0.446622
$999$	1.80509e10	0.572822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.8.a.c.1.22		34
5.4	even	2		625.8.a.d.1.13		34
25.4	even	10		25.8.d.a.16.11	yes	68
25.19	even	10		25.8.d.a.11.11	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.11.11	✓	68	25.19	even	10
25.8.d.a.16.11	yes	68	25.4	even	10
625.8.a.c.1.22		34	1.1	even	1	trivial
625.8.a.d.1.13		34	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	625.a (trivial)

\(f(q)\)	\(=\)	\(q+7.51166 q^{2} -8.67312 q^{3} -71.5749 q^{4} -65.1495 q^{6} +1153.54 q^{7} -1499.14 q^{8} -2111.78 q^{9} -431.045 q^{11} +620.778 q^{12} +280.582 q^{13} +8664.99 q^{14} -2099.44 q^{16} -32775.7 q^{17} -15863.0 q^{18} -30708.4 q^{19} -10004.8 q^{21} -3237.87 q^{22} +4439.92 q^{23} +13002.2 q^{24} +2107.64 q^{26} +37283.8 q^{27} -82564.5 q^{28} +111225. q^{29} -145021. q^{31} +176120. q^{32} +3738.50 q^{33} -246200. q^{34} +151150. q^{36} +484149. q^{37} -230671. q^{38} -2433.52 q^{39} -519048. q^{41} -75152.5 q^{42} -146858. q^{43} +30852.0 q^{44} +33351.2 q^{46} +1.16866e6 q^{47} +18208.7 q^{48} +507109. q^{49} +284267. q^{51} -20082.6 q^{52} -894659. q^{53} +280063. q^{54} -1.72932e6 q^{56} +266337. q^{57} +835484. q^{58} -2.59298e6 q^{59} -2.90419e6 q^{61} -1.08935e6 q^{62} -2.43602e6 q^{63} +1.59168e6 q^{64} +28082.4 q^{66} -631516. q^{67} +2.34592e6 q^{68} -38508.0 q^{69} +3.96661e6 q^{71} +3.16585e6 q^{72} -161087. q^{73} +3.63676e6 q^{74} +2.19795e6 q^{76} -497227. q^{77} -18279.8 q^{78} -3.68737e6 q^{79} +4.29509e6 q^{81} -3.89892e6 q^{82} +3.18889e6 q^{83} +716091. q^{84} -1.10315e6 q^{86} -964667. q^{87} +646197. q^{88} -6.63496e6 q^{89} +323662. q^{91} -317787. q^{92} +1.25778e6 q^{93} +8.77861e6 q^{94} -1.52751e6 q^{96} +7.70700e6 q^{97} +3.80923e6 q^{98} +910271. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} - 14 q^{3} + 2177 q^{4} + 993 q^{6} - 867 q^{7} - 2700 q^{8} + 23708 q^{9} + 8718 q^{11} - 2377 q^{12} - 8769 q^{13} + 17674 q^{14} + 139109 q^{16} + 48258 q^{17} - 58104 q^{18} + 61955 q^{19}+ \cdots + 35633116 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 - 14 * q^3 + 2177 * q^4 + 993 * q^6 - 867 * q^7 - 2700 * q^8 + 23708 * q^9 + 8718 * q^11 - 2377 * q^12 - 8769 * q^13 + 17674 * q^14 + 139109 * q^16 + 48258 * q^17 - 58104 * q^18 + 61955 * q^19 + 96943 * q^21 + 52556 * q^22 - 55584 * q^23 + 276990 * q^24 + 337623 * q^26 + 24370 * q^27 - 392941 * q^28 + 449815 * q^29 + 450438 * q^31 - 522987 * q^32 + 689282 * q^33 + 639889 * q^34 + 2024094 * q^36 + 373008 * q^37 - 1272835 * q^38 + 877321 * q^39 + 926418 * q^41 - 580554 * q^42 + 1719911 * q^43 + 1809244 * q^44 + 1186623 * q^46 - 640247 * q^47 - 3924149 * q^48 + 3292177 * q^49 + 1961038 * q^51 - 3900212 * q^52 - 1609214 * q^53 + 3802395 * q^54 + 5709425 * q^56 + 7299205 * q^57 + 4001010 * q^58 + 6056265 * q^59 + 2885628 * q^61 + 14351151 * q^62 - 8834194 * q^63 + 12281872 * q^64 + 8819186 * q^66 + 164318 * q^67 + 14549609 * q^68 + 5884976 * q^69 + 10286173 * q^71 - 41997930 * q^72 - 20595894 * q^73 + 7025034 * q^74 + 11251000 * q^76 - 14569234 * q^77 + 32702012 * q^78 + 11772835 * q^79 + 24408674 * q^81 + 38307271 * q^82 - 2455444 * q^83 + 17190739 * q^84 + 7636893 * q^86 + 39372965 * q^87 - 45397760 * q^88 + 17788560 * q^89 + 15865973 * q^91 - 37183957 * q^92 + 59352382 * q^93 + 29349634 * q^94 + 38027693 * q^96 - 3708847 * q^97 - 6000776 * q^98 + 35633116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more