LMFDB - Embedded newform 7581.2.a.be.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7581,2,Mod(1,7581)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7581, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7581.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7581 = 3 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7581.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:	$60.5345897723$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.8512625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 17x^{3} + 11x^{2} - 31x + 11 $ x^6 - 2x^5 - 8x^4 + 17x^3 + 11x^2 - 31*x + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.14337$ of defining polynomial
Character	$\chi$	$=$	7581.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.14337 q^{2} +1.00000 q^{3} -0.692703 q^{4} +2.31074 q^{5} +1.14337 q^{6} -1.00000 q^{7} -3.07876 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.14337 q^{2} +1.00000 q^{3} -0.692703 q^{4} +2.31074 q^{5} +1.14337 q^{6} -1.00000 q^{7} -3.07876 q^{8} +1.00000 q^{9} +2.64203 q^{10} -3.82746 q^{11} -0.692703 q^{12} +4.12491 q^{13} -1.14337 q^{14} +2.31074 q^{15} -2.13476 q^{16} -3.31074 q^{17} +1.14337 q^{18} -1.60065 q^{20} -1.00000 q^{21} -4.37621 q^{22} -7.29960 q^{23} -3.07876 q^{24} +0.339506 q^{25} +4.71630 q^{26} +1.00000 q^{27} +0.692703 q^{28} -4.25822 q^{29} +2.64203 q^{30} +8.41762 q^{31} +3.71670 q^{32} -3.82746 q^{33} -3.78540 q^{34} -2.31074 q^{35} -0.692703 q^{36} +3.32338 q^{37} +4.12491 q^{39} -7.11420 q^{40} +7.10106 q^{41} -1.14337 q^{42} -5.75888 q^{43} +2.65129 q^{44} +2.31074 q^{45} -8.34614 q^{46} -0.140137 q^{47} -2.13476 q^{48} +1.00000 q^{49} +0.388181 q^{50} -3.31074 q^{51} -2.85734 q^{52} +13.9466 q^{53} +1.14337 q^{54} -8.84425 q^{55} +3.07876 q^{56} -4.86873 q^{58} -13.9651 q^{59} -1.60065 q^{60} -5.75901 q^{61} +9.62446 q^{62} -1.00000 q^{63} +8.51908 q^{64} +9.53157 q^{65} -4.37621 q^{66} -12.2720 q^{67} +2.29336 q^{68} -7.29960 q^{69} -2.64203 q^{70} -6.29536 q^{71} -3.07876 q^{72} -11.6138 q^{73} +3.79986 q^{74} +0.339506 q^{75} +3.82746 q^{77} +4.71630 q^{78} -13.3734 q^{79} -4.93286 q^{80} +1.00000 q^{81} +8.11915 q^{82} -13.1411 q^{83} +0.692703 q^{84} -7.65024 q^{85} -6.58453 q^{86} -4.25822 q^{87} +11.7838 q^{88} -5.44718 q^{89} +2.64203 q^{90} -4.12491 q^{91} +5.05645 q^{92} +8.41762 q^{93} -0.160229 q^{94} +3.71670 q^{96} -2.60598 q^{97} +1.14337 q^{98} -3.82746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 6 q^{3} + 8 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 6 * q^3 + 8 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9	$ 6 q + 2 q^{2} + 6 q^{3} + 8 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9} - 2 q^{11} + 8 q^{12} - q^{13} - 2 q^{14} - 5 q^{15} - 4 q^{16} - q^{17} + 2 q^{18} - 27 q^{20} - 6 q^{21} - 6 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - 5 q^{26} + 6 q^{27} - 8 q^{28} - 11 q^{29} + 9 q^{31} + q^{32} - 2 q^{33} - 2 q^{34} + 5 q^{35} + 8 q^{36} - 4 q^{37} - q^{39} - 12 q^{40} - 6 q^{41} - 2 q^{42} + 2 q^{43} + 25 q^{44} - 5 q^{45} - 4 q^{46} + 6 q^{47} - 4 q^{48} + 6 q^{49} + 12 q^{50} - q^{51} + q^{52} + 10 q^{53} + 2 q^{54} - 16 q^{55} + 3 q^{56} - 49 q^{58} - 31 q^{59} - 27 q^{60} - 22 q^{61} + 21 q^{62} - 6 q^{63} - 27 q^{64} + 6 q^{65} - 6 q^{66} - 21 q^{67} + 19 q^{68} + 4 q^{69} - 32 q^{71} - 3 q^{72} - 28 q^{73} + 6 q^{74} - 3 q^{75} + 2 q^{77} - 5 q^{78} - 26 q^{79} + 6 q^{80} + 6 q^{81} - 4 q^{82} - 16 q^{83} - 8 q^{84} - 22 q^{85} - 38 q^{86} - 11 q^{87} - 19 q^{88} + 6 q^{89} + q^{91} + 13 q^{92} + 9 q^{93} + 25 q^{94} + q^{96} - 36 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 6 * q^3 + 8 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9 - 2 * q^11 + 8 * q^12 - q^13 - 2 * q^14 - 5 * q^15 - 4 * q^16 - q^17 + 2 * q^18 - 27 * q^20 - 6 * q^21 - 6 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - 5 * q^26 + 6 * q^27 - 8 * q^28 - 11 * q^29 + 9 * q^31 + q^32 - 2 * q^33 - 2 * q^34 + 5 * q^35 + 8 * q^36 - 4 * q^37 - q^39 - 12 * q^40 - 6 * q^41 - 2 * q^42 + 2 * q^43 + 25 * q^44 - 5 * q^45 - 4 * q^46 + 6 * q^47 - 4 * q^48 + 6 * q^49 + 12 * q^50 - q^51 + q^52 + 10 * q^53 + 2 * q^54 - 16 * q^55 + 3 * q^56 - 49 * q^58 - 31 * q^59 - 27 * q^60 - 22 * q^61 + 21 * q^62 - 6 * q^63 - 27 * q^64 + 6 * q^65 - 6 * q^66 - 21 * q^67 + 19 * q^68 + 4 * q^69 - 32 * q^71 - 3 * q^72 - 28 * q^73 + 6 * q^74 - 3 * q^75 + 2 * q^77 - 5 * q^78 - 26 * q^79 + 6 * q^80 + 6 * q^81 - 4 * q^82 - 16 * q^83 - 8 * q^84 - 22 * q^85 - 38 * q^86 - 11 * q^87 - 19 * q^88 + 6 * q^89 + q^91 + 13 * q^92 + 9 * q^93 + 25 * q^94 + q^96 - 36 * q^97 + 2 * q^98 - 2 * 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 $

$2$	1.14337	0.808485	0.404243	−	0.914652i	$-0.367535\pi$
$2$	1.14337	0.808485	0.404243	+	0.914652i	$0.367535\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.692703	−0.346352
$5$	2.31074	1.03339	0.516697	−	0.856169i	$-0.327162\pi$
$5$	2.31074	1.03339	0.516697	+	0.856169i	$0.327162\pi$
$6$	1.14337	0.466779
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.07876	−1.08851
$9$	1.00000	0.333333
$10$	2.64203	0.835483
$11$	−3.82746	−1.15402	−0.577011	−	0.816736i	$-0.695781\pi$
$11$	−3.82746	−1.15402	−0.577011	+	0.816736i	$0.695781\pi$
$12$	−0.692703	−0.199966
$13$	4.12491	1.14404	0.572022	−	0.820239i	$-0.306159\pi$
$13$	4.12491	1.14404	0.572022	+	0.820239i	$0.306159\pi$
$14$	−1.14337	−0.305579
$15$	2.31074	0.596630
$16$	−2.13476	−0.533689
$17$	−3.31074	−0.802972	−0.401486	−	0.915865i	$-0.631506\pi$
$17$	−3.31074	−0.802972	−0.401486	+	0.915865i	$0.631506\pi$
$18$	1.14337	0.269495
$19$	0	0
$19$	0	0
$20$	−1.60065	−0.357917
$21$	−1.00000	−0.218218
$22$	−4.37621	−0.933010
$23$	−7.29960	−1.52207	−0.761035	−	0.648710i	$-0.775309\pi$
$23$	−7.29960	−1.52207	−0.761035	+	0.648710i	$0.775309\pi$
$24$	−3.07876	−0.628449
$25$	0.339506	0.0679012
$26$	4.71630	0.924942
$27$	1.00000	0.192450
$28$	0.692703	0.130909
$29$	−4.25822	−0.790732	−0.395366	−	0.918524i	$-0.629382\pi$
$29$	−4.25822	−0.790732	−0.395366	+	0.918524i	$0.629382\pi$
$30$	2.64203	0.482366
$31$	8.41762	1.51185	0.755924	−	0.654659i	$-0.227188\pi$
$31$	8.41762	1.51185	0.755924	+	0.654659i	$0.227188\pi$
$32$	3.71670	0.657026
$33$	−3.82746	−0.666275
$34$	−3.78540	−0.649191
$35$	−2.31074	−0.390586
$36$	−0.692703	−0.115451
$37$	3.32338	0.546361	0.273180	−	0.961963i	$-0.411924\pi$
$37$	3.32338	0.546361	0.273180	+	0.961963i	$0.411924\pi$
$38$	0	0
$39$	4.12491	0.660514
$40$	−7.11420	−1.12485
$41$	7.10106	1.10900	0.554500	−	0.832184i	$-0.312910\pi$
$41$	7.10106	1.10900	0.554500	+	0.832184i	$0.312910\pi$
$42$	−1.14337	−0.176426
$43$	−5.75888	−0.878221	−0.439110	−	0.898433i	$-0.644706\pi$
$43$	−5.75888	−0.878221	−0.439110	+	0.898433i	$0.644706\pi$
$44$	2.65129	0.399697
$45$	2.31074	0.344464
$46$	−8.34614	−1.23057
$47$	−0.140137	−0.0204411	−0.0102206	−	0.999948i	$-0.503253\pi$
$47$	−0.140137	−0.0204411	−0.0102206	+	0.999948i	$0.503253\pi$
$48$	−2.13476	−0.308126
$49$	1.00000	0.142857
$50$	0.388181	0.0548971
$51$	−3.31074	−0.463596
$52$	−2.85734	−0.396241
$53$	13.9466	1.91571	0.957857	−	0.287246i	$-0.0927398\pi$
$53$	13.9466	1.91571	0.957857	+	0.287246i	$0.0927398\pi$
$54$	1.14337	0.155593
$55$	−8.84425	−1.19256
$56$	3.07876	0.411416
$57$	0	0
$58$	−4.86873	−0.639295
$59$	−13.9651	−1.81810	−0.909049	−	0.416690i	$-0.863190\pi$
$59$	−13.9651	−1.81810	−0.909049	+	0.416690i	$0.863190\pi$
$60$	−1.60065	−0.206644
$61$	−5.75901	−0.737365	−0.368683	−	0.929555i	$-0.620191\pi$
$61$	−5.75901	−0.737365	−0.368683	+	0.929555i	$0.620191\pi$
$62$	9.62446	1.22231
$63$	−1.00000	−0.125988
$64$	8.51908	1.06488
$65$	9.53157	1.18225
$66$	−4.37621	−0.538674
$67$	−12.2720	−1.49926	−0.749630	−	0.661858i	$-0.769768\pi$
$67$	−12.2720	−1.49926	−0.749630	+	0.661858i	$0.769768\pi$
$68$	2.29336	0.278111
$69$	−7.29960	−0.878768
$70$	−2.64203	−0.315783
$71$	−6.29536	−0.747121	−0.373561	−	0.927606i	$-0.621863\pi$
$71$	−6.29536	−0.747121	−0.373561	+	0.927606i	$0.621863\pi$
$72$	−3.07876	−0.362835
$73$	−11.6138	−1.35929	−0.679643	−	0.733543i	$-0.737865\pi$
$73$	−11.6138	−1.35929	−0.679643	+	0.733543i	$0.737865\pi$
$74$	3.79986	0.441725
$75$	0.339506	0.0392028
$76$	0	0
$77$	3.82746	0.436179
$78$	4.71630	0.534016
$79$	−13.3734	−1.50463	−0.752314	−	0.658804i	$-0.771062\pi$
$79$	−13.3734	−1.50463	−0.752314	+	0.658804i	$0.771062\pi$
$80$	−4.93286	−0.551511
$81$	1.00000	0.111111
$82$	8.11915	0.896610
$83$	−13.1411	−1.44242	−0.721209	−	0.692718i	$-0.756413\pi$
$83$	−13.1411	−1.44242	−0.721209	+	0.692718i	$0.756413\pi$
$84$	0.692703	0.0755801
$85$	−7.65024	−0.829785
$86$	−6.58453	−0.710028
$87$	−4.25822	−0.456529
$88$	11.7838	1.25616
$89$	−5.44718	−0.577400	−0.288700	−	0.957420i	$-0.593223\pi$
$89$	−5.44718	−0.577400	−0.288700	+	0.957420i	$0.593223\pi$
$90$	2.64203	0.278494
$91$	−4.12491	−0.432408
$92$	5.05645	0.527172
$93$	8.41762	0.872866
$94$	−0.160229	−0.0165263
$95$	0	0
$96$	3.71670	0.379334
$97$	−2.60598	−0.264597	−0.132299	−	0.991210i	$-0.542236\pi$
$97$	−2.60598	−0.264597	−0.132299	+	0.991210i	$0.542236\pi$
$98$	1.14337	0.115498
$99$	−3.82746	−0.384674
$100$	−0.235177	−0.0235177
$101$	1.52918	0.152159	0.0760797	−	0.997102i	$-0.475760\pi$
$101$	1.52918	0.152159	0.0760797	+	0.997102i	$0.475760\pi$
$102$	−3.78540	−0.374810
$103$	−18.1334	−1.78674	−0.893368	−	0.449326i	$-0.851664\pi$
$103$	−18.1334	−1.78674	−0.893368	+	0.449326i	$0.851664\pi$
$104$	−12.6996	−1.24530
$105$	−2.31074	−0.225505
$106$	15.9461	1.54883
$107$	1.96763	0.190218	0.0951091	−	0.995467i	$-0.469680\pi$
$107$	1.96763	0.190218	0.0951091	+	0.995467i	$0.469680\pi$
$108$	−0.692703	−0.0666554
$109$	−16.2152	−1.55313	−0.776567	−	0.630034i	$-0.783041\pi$
$109$	−16.2152	−1.55313	−0.776567	+	0.630034i	$0.783041\pi$
$110$	−10.1123	−0.964166
$111$	3.32338	0.315442
$112$	2.13476	0.201715
$113$	14.1452	1.33067	0.665334	−	0.746546i	$-0.268289\pi$
$113$	14.1452	1.33067	0.665334	+	0.746546i	$0.268289\pi$
$114$	0	0
$115$	−16.8674	−1.57290
$116$	2.94968	0.273871
$117$	4.12491	0.381348
$118$	−15.9673	−1.46990
$119$	3.31074	0.303495
$120$	−7.11420	−0.649435
$121$	3.64944	0.331768
$122$	−6.58468	−0.596149
$123$	7.10106	0.640281
$124$	−5.83091	−0.523631
$125$	−10.7692	−0.963224
$126$	−1.14337	−0.101860
$127$	−8.64735	−0.767329	−0.383664	−	0.923473i	$-0.625338\pi$
$127$	−8.64735	−0.767329	−0.383664	+	0.923473i	$0.625338\pi$
$128$	2.30707	0.203918
$129$	−5.75888	−0.507041
$130$	10.8981	0.955829
$131$	13.3604	1.16731	0.583653	−	0.812004i	$-0.301623\pi$
$131$	13.3604	1.16731	0.583653	+	0.812004i	$0.301623\pi$
$132$	2.65129	0.230765
$133$	0	0
$134$	−14.0314	−1.21213
$135$	2.31074	0.198877
$136$	10.1930	0.874039
$137$	4.20944	0.359637	0.179819	−	0.983700i	$-0.442449\pi$
$137$	4.20944	0.359637	0.179819	+	0.983700i	$0.442449\pi$
$138$	−8.34614	−0.710471
$139$	−5.35031	−0.453807	−0.226904	−	0.973917i	$-0.572860\pi$
$139$	−5.35031	−0.453807	−0.226904	+	0.973917i	$0.572860\pi$
$140$	1.60065	0.135280
$141$	−0.140137	−0.0118017
$142$	−7.19793	−0.604037
$143$	−15.7879	−1.32025
$144$	−2.13476	−0.177896
$145$	−9.83963	−0.817137
$146$	−13.2788	−1.09896
$147$	1.00000	0.0824786
$148$	−2.30212	−0.189233
$149$	12.2291	1.00185	0.500925	−	0.865491i	$-0.332993\pi$
$149$	12.2291	1.00185	0.500925	+	0.865491i	$0.332993\pi$
$150$	0.388181	0.0316949
$151$	0.237459	0.0193241	0.00966206	−	0.999953i	$-0.496924\pi$
$151$	0.237459	0.0193241	0.00966206	+	0.999953i	$0.496924\pi$
$152$	0	0
$153$	−3.31074	−0.267657
$154$	4.37621	0.352645
$155$	19.4509	1.56233
$156$	−2.85734	−0.228770
$157$	14.8067	1.18170	0.590851	−	0.806781i	$-0.298792\pi$
$157$	14.8067	1.18170	0.590851	+	0.806781i	$0.298792\pi$
$158$	−15.2908	−1.21647
$159$	13.9466	1.10604
$160$	8.58831	0.678966
$161$	7.29960	0.575289
$162$	1.14337	0.0898317
$163$	−6.61997	−0.518516	−0.259258	−	0.965808i	$-0.583478\pi$
$163$	−6.61997	−0.518516	−0.259258	+	0.965808i	$0.583478\pi$
$164$	−4.91893	−0.384104
$165$	−8.84425	−0.688524
$166$	−15.0251	−1.16617
$167$	−2.27563	−0.176094	−0.0880469	−	0.996116i	$-0.528063\pi$
$167$	−2.27563	−0.176094	−0.0880469	+	0.996116i	$0.528063\pi$
$168$	3.07876	0.237531
$169$	4.01485	0.308835
$170$	−8.74706	−0.670869
$171$	0	0
$172$	3.98919	0.304173
$173$	1.61272	0.122612	0.0613062	−	0.998119i	$-0.480473\pi$
$173$	1.61272	0.122612	0.0613062	+	0.998119i	$0.480473\pi$
$174$	−4.86873	−0.369097
$175$	−0.339506	−0.0256642
$176$	8.17069	0.615889
$177$	−13.9651	−1.04968
$178$	−6.22815	−0.466820
$179$	15.6750	1.17160	0.585802	−	0.810454i	$-0.300780\pi$
$179$	15.6750	1.17160	0.585802	+	0.810454i	$0.300780\pi$
$180$	−1.60065	−0.119306
$181$	0.292251	0.0217228	0.0108614	−	0.999941i	$-0.496543\pi$
$181$	0.292251	0.0217228	0.0108614	+	0.999941i	$0.496543\pi$
$182$	−4.71630	−0.349595
$183$	−5.75901	−0.425718
$184$	22.4737	1.65678
$185$	7.67947	0.564606
$186$	9.62446	0.705699
$187$	12.6717	0.926647
$188$	0.0970735	0.00707982
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−6.76336	−0.489380	−0.244690	−	0.969601i	$-0.578686\pi$
$191$	−6.76336	−0.489380	−0.244690	+	0.969601i	$0.578686\pi$
$192$	8.51908	0.614811
$193$	10.4078	0.749172	0.374586	−	0.927192i	$-0.377785\pi$
$193$	10.4078	0.749172	0.374586	+	0.927192i	$0.377785\pi$
$194$	−2.97960	−0.213923
$195$	9.53157	0.682570
$196$	−0.692703	−0.0494788
$197$	−3.81353	−0.271702	−0.135851	−	0.990729i	$-0.543377\pi$
$197$	−3.81353	−0.271702	−0.135851	+	0.990729i	$0.543377\pi$
$198$	−4.37621	−0.311003
$199$	3.43449	0.243464	0.121732	−	0.992563i	$-0.461155\pi$
$199$	3.43449	0.243464	0.121732	+	0.992563i	$0.461155\pi$
$200$	−1.04526	−0.0739108
$201$	−12.2720	−0.865598
$202$	1.74842	0.123019
$203$	4.25822	0.298868
$204$	2.29336	0.160567
$205$	16.4087	1.14603
$206$	−20.7332	−1.44455
$207$	−7.29960	−0.507357
$208$	−8.80567	−0.610563
$209$	0	0
$210$	−2.64203	−0.182317
$211$	2.67876	0.184413	0.0922067	−	0.995740i	$-0.470608\pi$
$211$	2.67876	0.184413	0.0922067	+	0.995740i	$0.470608\pi$
$212$	−9.66086	−0.663510
$213$	−6.29536	−0.431351
$214$	2.24973	0.153789
$215$	−13.3073	−0.907547
$216$	−3.07876	−0.209483
$217$	−8.41762	−0.571425
$218$	−18.5400	−1.25569
$219$	−11.6138	−0.784785
$220$	6.12644	0.413045
$221$	−13.6565	−0.918634
$222$	3.79986	0.255030
$223$	−17.2704	−1.15651	−0.578256	−	0.815855i	$-0.696267\pi$
$223$	−17.2704	−1.15651	−0.578256	+	0.815855i	$0.696267\pi$
$224$	−3.71670	−0.248332
$225$	0.339506	0.0226337
$226$	16.1732	1.07583
$227$	7.62974	0.506404	0.253202	−	0.967413i	$-0.418516\pi$
$227$	7.62974	0.506404	0.253202	+	0.967413i	$0.418516\pi$
$228$	0	0
$229$	2.31366	0.152891	0.0764455	−	0.997074i	$-0.475643\pi$
$229$	2.31366	0.152891	0.0764455	+	0.997074i	$0.475643\pi$
$230$	−19.2857	−1.27166
$231$	3.82746	0.251828
$232$	13.1100	0.860716
$233$	−5.70396	−0.373679	−0.186839	−	0.982390i	$-0.559824\pi$
$233$	−5.70396	−0.373679	−0.186839	+	0.982390i	$0.559824\pi$
$234$	4.71630	0.308314
$235$	−0.323820	−0.0211237
$236$	9.67365	0.629701
$237$	−13.3734	−0.868698
$238$	3.78540	0.245371
$239$	8.82770	0.571017	0.285508	−	0.958376i	$-0.407838\pi$
$239$	8.82770	0.571017	0.285508	+	0.958376i	$0.407838\pi$
$240$	−4.93286	−0.318415
$241$	29.2185	1.88213	0.941063	−	0.338231i	$-0.109829\pi$
$241$	29.2185	1.88213	0.941063	+	0.338231i	$0.109829\pi$
$242$	4.17267	0.268229
$243$	1.00000	0.0641500
$244$	3.98928	0.255388
$245$	2.31074	0.147628
$246$	8.11915	0.517658
$247$	0	0
$248$	−25.9158	−1.64566
$249$	−13.1411	−0.832780
$250$	−12.3132	−0.778753
$251$	−6.86118	−0.433074	−0.216537	−	0.976274i	$-0.569476\pi$
$251$	−6.86118	−0.433074	−0.216537	+	0.976274i	$0.569476\pi$
$252$	0.692703	0.0436362
$253$	27.9389	1.75650
$254$	−9.88713	−0.620374
$255$	−7.65024	−0.479077
$256$	−14.4003	−0.900020
$257$	−1.60871	−0.100348	−0.0501741	−	0.998740i	$-0.515978\pi$
$257$	−1.60871	−0.100348	−0.0501741	+	0.998740i	$0.515978\pi$
$258$	−6.58453	−0.409935
$259$	−3.32338	−0.206505
$260$	−6.60255	−0.409473
$261$	−4.25822	−0.263577
$262$	15.2759	0.943749
$263$	18.4455	1.13740	0.568699	−	0.822545i	$-0.307447\pi$
$263$	18.4455	1.13740	0.568699	+	0.822545i	$0.307447\pi$
$264$	11.7838	0.725244
$265$	32.2269	1.97969
$266$	0	0
$267$	−5.44718	−0.333362
$268$	8.50083	0.519271
$269$	5.16887	0.315152	0.157576	−	0.987507i	$-0.449632\pi$
$269$	5.16887	0.315152	0.157576	+	0.987507i	$0.449632\pi$
$270$	2.64203	0.160789
$271$	−17.5641	−1.06694	−0.533472	−	0.845818i	$-0.679113\pi$
$271$	−17.5641	−1.06694	−0.533472	+	0.845818i	$0.679113\pi$
$272$	7.06762	0.428537
$273$	−4.12491	−0.249651
$274$	4.81295	0.290761
$275$	−1.29945	−0.0783595
$276$	5.05645	0.304363
$277$	−12.4135	−0.745852	−0.372926	−	0.927861i	$-0.621645\pi$
$277$	−12.4135	−0.745852	−0.372926	+	0.927861i	$0.621645\pi$
$278$	−6.11739	−0.366896
$279$	8.41762	0.503949
$280$	7.11420	0.425155
$281$	−15.9626	−0.952250	−0.476125	−	0.879378i	$-0.657959\pi$
$281$	−15.9626	−0.952250	−0.476125	+	0.879378i	$0.657959\pi$
$282$	−0.160229	−0.00954149
$283$	−19.4069	−1.15362	−0.576810	−	0.816878i	$-0.695703\pi$
$283$	−19.4069	−1.15362	−0.576810	+	0.816878i	$0.695703\pi$
$284$	4.36081	0.258767
$285$	0	0
$286$	−18.0514	−1.06740
$287$	−7.10106	−0.419162
$288$	3.71670	0.219009
$289$	−6.03902	−0.355236
$290$	−11.2503	−0.660643
$291$	−2.60598	−0.152765
$292$	8.04488	0.470791
$293$	12.3471	0.721323	0.360661	−	0.932697i	$-0.382551\pi$
$293$	12.3471	0.721323	0.360661	+	0.932697i	$0.382551\pi$
$294$	1.14337	0.0666827
$295$	−32.2696	−1.87881
$296$	−10.2319	−0.594717
$297$	−3.82746	−0.222092
$298$	13.9824	0.809981
$299$	−30.1101	−1.74131
$300$	−0.235177	−0.0135779
$301$	5.75888	0.331936
$302$	0.271503	0.0156233
$303$	1.52918	0.0878493
$304$	0	0
$305$	−13.3075	−0.761988
$306$	−3.78540	−0.216397
$307$	−8.92723	−0.509504	−0.254752	−	0.967006i	$-0.581994\pi$
$307$	−8.92723	−0.509504	−0.254752	+	0.967006i	$0.581994\pi$
$308$	−2.65129	−0.151071
$309$	−18.1334	−1.03157
$310$	22.2396	1.26312
$311$	25.1416	1.42565	0.712825	−	0.701342i	$-0.247415\pi$
$311$	25.1416	1.42565	0.712825	+	0.701342i	$0.247415\pi$
$312$	−12.6996	−0.718973
$313$	−13.1928	−0.745702	−0.372851	−	0.927891i	$-0.621620\pi$
$313$	−13.1928	−0.745702	−0.372851	+	0.927891i	$0.621620\pi$
$314$	16.9295	0.955388
$315$	−2.31074	−0.130195
$316$	9.26382	0.521130
$317$	−5.70141	−0.320223	−0.160112	−	0.987099i	$-0.551185\pi$
$317$	−5.70141	−0.320223	−0.160112	+	0.987099i	$0.551185\pi$
$318$	15.9461	0.894215
$319$	16.2982	0.912522
$320$	19.6853	1.10044
$321$	1.96763	0.109823
$322$	8.34614	0.465112
$323$	0	0
$324$	−0.692703	−0.0384835
$325$	1.40043	0.0776819
$326$	−7.56908	−0.419212
$327$	−16.2152	−0.896703
$328$	−21.8624	−1.20715
$329$	0.140137	0.00772602
$330$	−10.1123	−0.556662
$331$	−32.1319	−1.76613	−0.883064	−	0.469253i	$-0.844523\pi$
$331$	−32.1319	−1.76613	−0.883064	+	0.469253i	$0.844523\pi$
$332$	9.10285	0.499584
$333$	3.32338	0.182120
$334$	−2.60189	−0.142369
$335$	−28.3573	−1.54932
$336$	2.13476	0.116460
$337$	20.1482	1.09754	0.548771	−	0.835972i	$-0.315096\pi$
$337$	20.1482	1.09754	0.548771	+	0.835972i	$0.315096\pi$
$338$	4.59046	0.249688
$339$	14.1452	0.768262
$340$	5.29935	0.287397
$341$	−32.2181	−1.74471
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	17.7302	0.955948
$345$	−16.8674	−0.908113
$346$	1.84393	0.0991304
$347$	30.9762	1.66289	0.831444	−	0.555609i	$-0.187515\pi$
$347$	30.9762	1.66289	0.831444	+	0.555609i	$0.187515\pi$
$348$	2.94968	0.158120
$349$	−13.1310	−0.702889	−0.351444	−	0.936209i	$-0.614309\pi$
$349$	−13.1310	−0.702889	−0.351444	+	0.936209i	$0.614309\pi$
$350$	−0.388181	−0.0207492
$351$	4.12491	0.220171
$352$	−14.2255	−0.758222
$353$	−2.37288	−0.126296	−0.0631479	−	0.998004i	$-0.520114\pi$
$353$	−2.37288	−0.126296	−0.0631479	+	0.998004i	$0.520114\pi$
$354$	−15.9673	−0.848650
$355$	−14.5469	−0.772070
$356$	3.77328	0.199983
$357$	3.31074	0.175223
$358$	17.9223	0.947225
$359$	21.3112	1.12476	0.562380	−	0.826879i	$-0.309886\pi$
$359$	21.3112	1.12476	0.562380	+	0.826879i	$0.309886\pi$
$360$	−7.11420	−0.374951
$361$	0	0
$362$	0.334151	0.0175626
$363$	3.64944	0.191546
$364$	2.85734	0.149765
$365$	−26.8363	−1.40468
$366$	−6.58468	−0.344187
$367$	−0.568943	−0.0296986	−0.0148493	−	0.999890i	$-0.504727\pi$
$367$	−0.568943	−0.0296986	−0.0148493	+	0.999890i	$0.504727\pi$
$368$	15.5829	0.812312
$369$	7.10106	0.369666
$370$	8.78048	0.456475
$371$	−13.9466	−0.724072
$372$	−5.83091	−0.302319
$373$	−7.29725	−0.377837	−0.188919	−	0.981993i	$-0.560498\pi$
$373$	−7.29725	−0.377837	−0.188919	+	0.981993i	$0.560498\pi$
$374$	14.4885	0.749181
$375$	−10.7692	−0.556118
$376$	0.431449	0.0222503
$377$	−17.5648	−0.904631
$378$	−1.14337	−0.0588087
$379$	36.0003	1.84921	0.924606	−	0.380925i	$-0.124394\pi$
$379$	36.0003	1.84921	0.924606	+	0.380925i	$0.124394\pi$
$380$	0	0
$381$	−8.64735	−0.443017
$382$	−7.73303	−0.395656
$383$	4.26136	0.217745	0.108873	−	0.994056i	$-0.465276\pi$
$383$	4.26136	0.217745	0.108873	+	0.994056i	$0.465276\pi$
$384$	2.30707	0.117732
$385$	8.84425	0.450745
$386$	11.9000	0.605694
$387$	−5.75888	−0.292740
$388$	1.80517	0.0916436
$389$	−36.7023	−1.86088	−0.930440	−	0.366445i	$-0.880575\pi$
$389$	−36.7023	−1.86088	−0.930440	+	0.366445i	$0.880575\pi$
$390$	10.8981	0.551848
$391$	24.1670	1.22218
$392$	−3.07876	−0.155501
$393$	13.3604	0.673944
$394$	−4.36027	−0.219667
$395$	−30.9025	−1.55487
$396$	2.65129	0.133232
$397$	−34.6530	−1.73919	−0.869593	−	0.493770i	$-0.835619\pi$
$397$	−34.6530	−1.73919	−0.869593	+	0.493770i	$0.835619\pi$
$398$	3.92689	0.196837
$399$	0	0
$400$	−0.724763	−0.0362381
$401$	−29.9894	−1.49760	−0.748798	−	0.662798i	$-0.769369\pi$
$401$	−29.9894	−1.49760	−0.748798	+	0.662798i	$0.769369\pi$
$402$	−14.0314	−0.699823
$403$	34.7219	1.72962
$404$	−1.05927	−0.0527007
$405$	2.31074	0.114821
$406$	4.86873	0.241631
$407$	−12.7201	−0.630513
$408$	10.1930	0.504627
$409$	19.0836	0.943621	0.471811	−	0.881700i	$-0.343601\pi$
$409$	19.0836	0.943621	0.471811	+	0.881700i	$0.343601\pi$
$410$	18.7612	0.926550
$411$	4.20944	0.207637
$412$	12.5611	0.618839
$413$	13.9651	0.687176
$414$	−8.34614	−0.410191
$415$	−30.3655	−1.49058
$416$	15.3310	0.751666
$417$	−5.35031	−0.262006
$418$	0	0
$419$	−4.57241	−0.223377	−0.111688	−	0.993743i	$-0.535626\pi$
$419$	−4.57241	−0.223377	−0.111688	+	0.993743i	$0.535626\pi$
$420$	1.60065	0.0781040
$421$	2.43380	0.118616	0.0593082	−	0.998240i	$-0.481111\pi$
$421$	2.43380	0.118616	0.0593082	+	0.998240i	$0.481111\pi$
$422$	3.06282	0.149096
$423$	−0.140137	−0.00681371
$424$	−42.9382	−2.08526
$425$	−1.12402	−0.0545227
$426$	−7.19793	−0.348741
$427$	5.75901	0.278698
$428$	−1.36298	−0.0658824
$429$	−15.7879	−0.762248
$430$	−15.2151	−0.733738
$431$	31.8687	1.53506	0.767530	−	0.641013i	$-0.221486\pi$
$431$	31.8687	1.53506	0.767530	+	0.641013i	$0.221486\pi$
$432$	−2.13476	−0.102709
$433$	−38.8760	−1.86826	−0.934131	−	0.356931i	$-0.883823\pi$
$433$	−38.8760	−1.86826	−0.934131	+	0.356931i	$0.883823\pi$
$434$	−9.62446	−0.461989
$435$	−9.83963	−0.471774
$436$	11.2323	0.537931
$437$	0	0
$438$	−13.2788	−0.634487
$439$	−13.6766	−0.652747	−0.326374	−	0.945241i	$-0.605827\pi$
$439$	−13.6766	−0.652747	−0.326374	+	0.945241i	$0.605827\pi$
$440$	27.2293	1.29811
$441$	1.00000	0.0476190
$442$	−15.6144	−0.742702
$443$	41.2201	1.95843	0.979214	−	0.202831i	$-0.0650142\pi$
$443$	41.2201	1.95843	0.979214	+	0.202831i	$0.0650142\pi$
$444$	−2.30212	−0.109254
$445$	−12.5870	−0.596681
$446$	−19.7465	−0.935024
$447$	12.2291	0.578419
$448$	−8.51908	−0.402489
$449$	−4.35463	−0.205508	−0.102754	−	0.994707i	$-0.532765\pi$
$449$	−4.35463	−0.205508	−0.102754	+	0.994707i	$0.532765\pi$
$450$	0.388181	0.0182990
$451$	−27.1790	−1.27981
$452$	−9.79842	−0.460879
$453$	0.237459	0.0111568
$454$	8.72363	0.409420
$455$	−9.53157	−0.446847
$456$	0	0
$457$	5.12125	0.239562	0.119781	−	0.992800i	$-0.461781\pi$
$457$	5.12125	0.239562	0.119781	+	0.992800i	$0.461781\pi$
$458$	2.64537	0.123610
$459$	−3.31074	−0.154532
$460$	11.6841	0.544775
$461$	14.7013	0.684708	0.342354	−	0.939571i	$-0.388776\pi$
$461$	14.7013	0.684708	0.342354	+	0.939571i	$0.388776\pi$
$462$	4.37621	0.203599
$463$	24.5665	1.14170	0.570851	−	0.821053i	$-0.306613\pi$
$463$	24.5665	1.14170	0.570851	+	0.821053i	$0.306613\pi$
$464$	9.09026	0.422005
$465$	19.4509	0.902014
$466$	−6.52174	−0.302114
$467$	30.8040	1.42544	0.712719	−	0.701449i	$-0.247463\pi$
$467$	30.8040	1.42544	0.712719	+	0.701449i	$0.247463\pi$
$468$	−2.85734	−0.132080
$469$	12.2720	0.566667
$470$	−0.370247	−0.0170782
$471$	14.8067	0.682256
$472$	42.9951	1.97901
$473$	22.0419	1.01349
$474$	−15.2908	−0.702329
$475$	0	0
$476$	−2.29336	−0.105116
$477$	13.9466	0.638571
$478$	10.0933	0.461658
$479$	8.08205	0.369279	0.184639	−	0.982806i	$-0.440888\pi$
$479$	8.08205	0.369279	0.184639	+	0.982806i	$0.440888\pi$
$480$	8.58831	0.392001
$481$	13.7086	0.625061
$482$	33.4075	1.52167
$483$	7.29960	0.332143
$484$	−2.52798	−0.114908
$485$	−6.02173	−0.273433
$486$	1.14337	0.0518644
$487$	33.0673	1.49842	0.749211	−	0.662332i	$-0.230433\pi$
$487$	33.0673	1.49842	0.749211	+	0.662332i	$0.230433\pi$
$488$	17.7306	0.802626
$489$	−6.61997	−0.299365
$490$	2.64203	0.119355
$491$	−3.82131	−0.172453	−0.0862266	−	0.996276i	$-0.527481\pi$
$491$	−3.82131	−0.172453	−0.0862266	+	0.996276i	$0.527481\pi$
$492$	−4.91893	−0.221762
$493$	14.0978	0.634935
$494$	0	0
$495$	−8.84425	−0.397520
$496$	−17.9696	−0.806857
$497$	6.29536	0.282385
$498$	−15.0251	−0.673291
$499$	32.3677	1.44898	0.724489	−	0.689286i	$-0.242076\pi$
$499$	32.3677	1.44898	0.724489	+	0.689286i	$0.242076\pi$
$500$	7.45984	0.333614
$501$	−2.27563	−0.101668
$502$	−7.84488	−0.350134
$503$	−7.13720	−0.318232	−0.159116	−	0.987260i	$-0.550864\pi$
$503$	−7.13720	−0.318232	−0.159116	+	0.987260i	$0.550864\pi$
$504$	3.07876	0.137139
$505$	3.53354	0.157241
$506$	31.9445	1.42011
$507$	4.01485	0.178306
$508$	5.99005	0.265765
$509$	−33.8240	−1.49922	−0.749612	−	0.661877i	$-0.769760\pi$
$509$	−33.8240	−1.49922	−0.749612	+	0.661877i	$0.769760\pi$
$510$	−8.74706	−0.387327
$511$	11.6138	0.513762
$512$	−21.0790	−0.931571
$513$	0	0
$514$	−1.83935	−0.0811301
$515$	−41.9015	−1.84640
$516$	3.98919	0.175614
$517$	0.536370	0.0235895
$518$	−3.79986	−0.166956
$519$	1.61272	0.0707903
$520$	−29.3454	−1.28688
$521$	−13.3647	−0.585518	−0.292759	−	0.956186i	$-0.594573\pi$
$521$	−13.3647	−0.585518	−0.292759	+	0.956186i	$0.594573\pi$
$522$	−4.86873	−0.213098
$523$	10.9315	0.478002	0.239001	−	0.971019i	$-0.423180\pi$
$523$	10.9315	0.478002	0.239001	+	0.971019i	$0.423180\pi$
$524$	−9.25480	−0.404298
$525$	−0.339506	−0.0148173
$526$	21.0901	0.919570
$527$	−27.8685	−1.21397
$528$	8.17069	0.355584
$529$	30.2841	1.31670
$530$	36.8473	1.60055
$531$	−13.9651	−0.606032
$532$	0	0
$533$	29.2912	1.26874
$534$	−6.22815	−0.269518
$535$	4.54668	0.196570
$536$	37.7824	1.63195
$537$	15.6750	0.676426
$538$	5.90994	0.254795
$539$	−3.82746	−0.164860
$540$	−1.60065	−0.0688812
$541$	−32.4127	−1.39353	−0.696766	−	0.717299i	$-0.745378\pi$
$541$	−32.4127	−1.39353	−0.696766	+	0.717299i	$0.745378\pi$
$542$	−20.0823	−0.862608
$543$	0.292251	0.0125417
$544$	−12.3050	−0.527573
$545$	−37.4691	−1.60500
$546$	−4.71630	−0.201839
$547$	35.2365	1.50660	0.753301	−	0.657676i	$-0.228460\pi$
$547$	35.2365	1.50660	0.753301	+	0.657676i	$0.228460\pi$
$548$	−2.91589	−0.124561
$549$	−5.75901	−0.245788
$550$	−1.48575	−0.0633525
$551$	0	0
$552$	22.4737	0.956544
$553$	13.3734	0.568696
$554$	−14.1932	−0.603010
$555$	7.67947	0.325975
$556$	3.70617	0.157177
$557$	0.695473	0.0294681	0.0147341	−	0.999891i	$-0.495310\pi$
$557$	0.695473	0.0294681	0.0147341	+	0.999891i	$0.495310\pi$
$558$	9.62446	0.407436
$559$	−23.7548	−1.00472
$560$	4.93286	0.208451
$561$	12.6717	0.535000
$562$	−18.2512	−0.769880
$563$	−4.08062	−0.171977	−0.0859887	−	0.996296i	$-0.527405\pi$
$563$	−4.08062	−0.171977	−0.0859887	+	0.996296i	$0.527405\pi$
$564$	0.0970735	0.00408753
$565$	32.6858	1.37510
$566$	−22.1893	−0.932685
$567$	−1.00000	−0.0419961
$568$	19.3819	0.813246
$569$	21.4625	0.899755	0.449878	−	0.893090i	$-0.351468\pi$
$569$	21.4625	0.899755	0.449878	+	0.893090i	$0.351468\pi$
$570$	0	0
$571$	17.5520	0.734530	0.367265	−	0.930116i	$-0.380294\pi$
$571$	17.5520	0.734530	0.367265	+	0.930116i	$0.380294\pi$
$572$	10.9363	0.457271
$573$	−6.76336	−0.282544
$574$	−8.11915	−0.338887
$575$	−2.47826	−0.103350
$576$	8.51908	0.354962
$577$	35.3442	1.47140	0.735699	−	0.677308i	$-0.236854\pi$
$577$	35.3442	1.47140	0.735699	+	0.677308i	$0.236854\pi$
$578$	−6.90484	−0.287203
$579$	10.4078	0.432535
$580$	6.81594	0.283017
$581$	13.1411	0.545183
$582$	−2.97960	−0.123508
$583$	−53.3801	−2.21078
$584$	35.7559	1.47959
$585$	9.53157	0.394082
$586$	14.1173	0.583179
$587$	−25.3110	−1.04470	−0.522348	−	0.852732i	$-0.674944\pi$
$587$	−25.3110	−1.04470	−0.522348	+	0.852732i	$0.674944\pi$
$588$	−0.692703	−0.0285666
$589$	0	0
$590$	−36.8961	−1.51899
$591$	−3.81353	−0.156867
$592$	−7.09461	−0.291587
$593$	37.7609	1.55065	0.775327	−	0.631559i	$-0.217585\pi$
$593$	37.7609	1.55065	0.775327	+	0.631559i	$0.217585\pi$
$594$	−4.37621	−0.179558
$595$	7.65024	0.313629
$596$	−8.47117	−0.346992
$597$	3.43449	0.140564
$598$	−34.4271	−1.40783
$599$	−8.70691	−0.355755	−0.177877	−	0.984053i	$-0.556923\pi$
$599$	−8.70691	−0.355755	−0.177877	+	0.984053i	$0.556923\pi$
$600$	−1.04526	−0.0426724
$601$	1.02636	0.0418661	0.0209330	−	0.999781i	$-0.493336\pi$
$601$	1.02636	0.0418661	0.0209330	+	0.999781i	$0.493336\pi$
$602$	6.58453	0.268366
$603$	−12.2720	−0.499753
$604$	−0.164488	−0.00669294
$605$	8.43291	0.342846
$606$	1.74842	0.0710249
$607$	−7.38240	−0.299642	−0.149821	−	0.988713i	$-0.547870\pi$
$607$	−7.38240	−0.299642	−0.149821	+	0.988713i	$0.547870\pi$
$608$	0	0
$609$	4.25822	0.172552
$610$	−15.2155	−0.616056
$611$	−0.578053	−0.0233855
$612$	2.29336	0.0927035
$613$	27.8123	1.12333	0.561663	−	0.827366i	$-0.310162\pi$
$613$	27.8123	1.12333	0.561663	+	0.827366i	$0.310162\pi$
$614$	−10.2071	−0.411926
$615$	16.4087	0.661662
$616$	−11.7838	−0.474784
$617$	17.6673	0.711260	0.355630	−	0.934627i	$-0.384266\pi$
$617$	17.6673	0.711260	0.355630	+	0.934627i	$0.384266\pi$
$618$	−20.7332	−0.834011
$619$	9.05361	0.363895	0.181948	−	0.983308i	$-0.441760\pi$
$619$	9.05361	0.363895	0.181948	+	0.983308i	$0.441760\pi$
$620$	−13.4737	−0.541117
$621$	−7.29960	−0.292923
$622$	28.7462	1.15262
$623$	5.44718	0.218237
$624$	−8.80567	−0.352509
$625$	−26.5823	−1.06329
$626$	−15.0843	−0.602889
$627$	0	0
$628$	−10.2566	−0.409284
$629$	−11.0029	−0.438712
$630$	−2.64203	−0.105261
$631$	−1.10545	−0.0440071	−0.0220036	−	0.999758i	$-0.507005\pi$
$631$	−1.10545	−0.0440071	−0.0220036	+	0.999758i	$0.507005\pi$
$632$	41.1736	1.63780
$633$	2.67876	0.106471
$634$	−6.51883	−0.258896
$635$	−19.9818	−0.792952
$636$	−9.66086	−0.383078
$637$	4.12491	0.163435
$638$	18.6348	0.737761
$639$	−6.29536	−0.249040
$640$	5.33103	0.210727
$641$	21.5483	0.851106	0.425553	−	0.904934i	$-0.360080\pi$
$641$	21.5483	0.851106	0.425553	+	0.904934i	$0.360080\pi$
$642$	2.24973	0.0887899
$643$	−41.9439	−1.65411	−0.827053	−	0.562124i	$-0.809984\pi$
$643$	−41.9439	−1.65411	−0.827053	+	0.562124i	$0.809984\pi$
$644$	−5.05645	−0.199252
$645$	−13.3073	−0.523973
$646$	0	0
$647$	8.78996	0.345569	0.172784	−	0.984960i	$-0.444724\pi$
$647$	8.78996	0.345569	0.172784	+	0.984960i	$0.444724\pi$
$648$	−3.07876	−0.120945
$649$	53.4507	2.09812
$650$	1.60121	0.0628047
$651$	−8.41762	−0.329912
$652$	4.58567	0.179589
$653$	−15.4159	−0.603270	−0.301635	−	0.953424i	$-0.597532\pi$
$653$	−15.4159	−0.603270	−0.301635	+	0.953424i	$0.597532\pi$
$654$	−18.5400	−0.724971
$655$	30.8724	1.20628
$656$	−15.1590	−0.591861
$657$	−11.6138	−0.453096
$658$	0.160229	0.00624637
$659$	−27.6618	−1.07755	−0.538775	−	0.842449i	$-0.681113\pi$
$659$	−27.6618	−1.07755	−0.538775	+	0.842449i	$0.681113\pi$
$660$	6.12644	0.238471
$661$	14.4566	0.562296	0.281148	−	0.959664i	$-0.409285\pi$
$661$	14.4566	0.562296	0.281148	+	0.959664i	$0.409285\pi$
$662$	−36.7386	−1.42789
$663$	−13.6565	−0.530374
$664$	40.4581	1.57008
$665$	0	0
$666$	3.79986	0.147242
$667$	31.0833	1.20355
$668$	1.57634	0.0609903
$669$	−17.2704	−0.667713
$670$	−32.4229	−1.25261
$671$	22.0424	0.850936
$672$	−3.71670	−0.143375
$673$	−18.6438	−0.718664	−0.359332	−	0.933210i	$-0.616995\pi$
$673$	−18.6438	−0.718664	−0.359332	+	0.933210i	$0.616995\pi$
$674$	23.0369	0.887347
$675$	0.339506	0.0130676
$676$	−2.78110	−0.106965
$677$	15.8037	0.607386	0.303693	−	0.952770i	$-0.401780\pi$
$677$	15.8037	0.607386	0.303693	+	0.952770i	$0.401780\pi$
$678$	16.1732	0.621128
$679$	2.60598	0.100008
$680$	23.5532	0.903226
$681$	7.62974	0.292372
$682$	−36.8372	−1.41057
$683$	−39.7638	−1.52152	−0.760760	−	0.649033i	$-0.775174\pi$
$683$	−39.7638	−1.52152	−0.760760	+	0.649033i	$0.775174\pi$
$684$	0	0
$685$	9.72692	0.371646
$686$	−1.14337	−0.0436541
$687$	2.31366	0.0882717
$688$	12.2938	0.468697
$689$	57.5284	2.19166
$690$	−19.2857	−0.734196
$691$	−35.6119	−1.35474	−0.677371	−	0.735642i	$-0.736881\pi$
$691$	−35.6119	−1.35474	−0.677371	+	0.735642i	$0.736881\pi$
$692$	−1.11713	−0.0424670
$693$	3.82746	0.145393
$694$	35.4173	1.34442
$695$	−12.3632	−0.468961
$696$	13.1100	0.496934
$697$	−23.5097	−0.890495
$698$	−15.0137	−0.568275
$699$	−5.70396	−0.215743
$700$	0.235177	0.00888885
$701$	−19.1094	−0.721751	−0.360876	−	0.932614i	$-0.617522\pi$
$701$	−19.1094	−0.721751	−0.360876	+	0.932614i	$0.617522\pi$
$702$	4.71630	0.178005
$703$	0	0
$704$	−32.6064	−1.22890
$705$	−0.323820	−0.0121958
$706$	−2.71309	−0.102108
$707$	−1.52918	−0.0575109
$708$	9.67365	0.363558
$709$	−46.0824	−1.73066	−0.865330	−	0.501202i	$-0.832891\pi$
$709$	−46.0824	−1.73066	−0.865330	+	0.501202i	$0.832891\pi$
$710$	−16.6325	−0.624207
$711$	−13.3734	−0.501543
$712$	16.7706	0.628503
$713$	−61.4452	−2.30114
$714$	3.78540	0.141665
$715$	−36.4817	−1.36434
$716$	−10.8581	−0.405787
$717$	8.82770	0.329677
$718$	24.3666	0.909353
$719$	30.4417	1.13528	0.567642	−	0.823275i	$-0.307856\pi$
$719$	30.4417	1.13528	0.567642	+	0.823275i	$0.307856\pi$
$720$	−4.93286	−0.183837
$721$	18.1334	0.675323
$722$	0	0
$723$	29.2185	1.08665
$724$	−0.202443	−0.00752373
$725$	−1.44569	−0.0536916
$726$	4.17267	0.154862
$727$	−43.2668	−1.60468	−0.802339	−	0.596869i	$-0.796411\pi$
$727$	−43.2668	−1.60468	−0.802339	+	0.596869i	$0.796411\pi$
$728$	12.6996	0.470678
$729$	1.00000	0.0370370
$730$	−30.6839	−1.13566
$731$	19.0661	0.705186
$732$	3.98928	0.147448
$733$	51.6443	1.90753	0.953763	−	0.300559i	$-0.0971733\pi$
$733$	51.6443	1.90753	0.953763	+	0.300559i	$0.0971733\pi$
$734$	−0.650513	−0.0240109
$735$	2.31074	0.0852328
$736$	−27.1304	−1.00004
$737$	46.9704	1.73018
$738$	8.11915	0.298870
$739$	−0.861365	−0.0316858	−0.0158429	−	0.999874i	$-0.505043\pi$
$739$	−0.861365	−0.0316858	−0.0158429	+	0.999874i	$0.505043\pi$
$740$	−5.31959	−0.195552
$741$	0	0
$742$	−15.9461	−0.585401
$743$	−21.4297	−0.786180	−0.393090	−	0.919500i	$-0.628594\pi$
$743$	−21.4297	−0.786180	−0.393090	+	0.919500i	$0.628594\pi$
$744$	−25.9158	−0.950119
$745$	28.2583	1.03531
$746$	−8.34347	−0.305476
$747$	−13.1411	−0.480806
$748$	−8.77773	−0.320946
$749$	−1.96763	−0.0718957
$750$	−12.3132	−0.449613
$751$	1.42871	0.0521345	0.0260672	−	0.999660i	$-0.491702\pi$
$751$	1.42871	0.0521345	0.0260672	+	0.999660i	$0.491702\pi$
$752$	0.299159	0.0109092
$753$	−6.86118	−0.250035
$754$	−20.0830	−0.731381
$755$	0.548705	0.0199694
$756$	0.692703	0.0251934
$757$	18.0813	0.657176	0.328588	−	0.944473i	$-0.393427\pi$
$757$	18.0813	0.657176	0.328588	+	0.944473i	$0.393427\pi$
$758$	41.1617	1.49506
$759$	27.9389	1.01412
$760$	0	0
$761$	28.0824	1.01799	0.508993	−	0.860771i	$-0.330018\pi$
$761$	28.0824	1.01799	0.508993	+	0.860771i	$0.330018\pi$
$762$	−9.88713	−0.358173
$763$	16.2152	0.587030
$764$	4.68500	0.169497
$765$	−7.65024	−0.276595
$766$	4.87232	0.176044
$767$	−57.6046	−2.07998
$768$	−14.4003	−0.519627
$769$	−24.9615	−0.900135	−0.450068	−	0.892994i	$-0.648600\pi$
$769$	−24.9615	−0.900135	−0.450068	+	0.892994i	$0.648600\pi$
$770$	10.1123	0.364421
$771$	−1.60871	−0.0579361
$772$	−7.20954	−0.259477
$773$	18.6401	0.670438	0.335219	−	0.942140i	$-0.391190\pi$
$773$	18.6401	0.670438	0.335219	+	0.942140i	$0.391190\pi$
$774$	−6.58453	−0.236676
$775$	2.85783	0.102656
$776$	8.02318	0.288015
$777$	−3.32338	−0.119226
$778$	−41.9643	−1.50449
$779$	0	0
$780$	−6.60255	−0.236409
$781$	24.0952	0.862195
$782$	27.6319	0.988114
$783$	−4.25822	−0.152176
$784$	−2.13476	−0.0762413
$785$	34.2143	1.22116
$786$	15.2759	0.544874
$787$	13.4619	0.479866	0.239933	−	0.970790i	$-0.422875\pi$
$787$	13.4619	0.479866	0.239933	+	0.970790i	$0.422875\pi$
$788$	2.64164	0.0941046
$789$	18.4455	0.656678
$790$	−35.3330	−1.25709
$791$	−14.1452	−0.502945
$792$	11.7838	0.418720
$793$	−23.7554	−0.843577
$794$	−39.6213	−1.40611
$795$	32.2269	1.14297
$796$	−2.37908	−0.0843243
$797$	13.2754	0.470238	0.235119	−	0.971967i	$-0.424452\pi$
$797$	13.2754	0.470238	0.235119	+	0.971967i	$0.424452\pi$
$798$	0	0
$799$	0.463958	0.0164136
$800$	1.26184	0.0446128
$801$	−5.44718	−0.192467
$802$	−34.2890	−1.21079
$803$	44.4512	1.56865
$804$	8.50083	0.299801
$805$	16.8674	0.594499
$806$	39.7000	1.39837
$807$	5.16887	0.181953
$808$	−4.70799	−0.165626
$809$	11.7919	0.414581	0.207290	−	0.978279i	$-0.433536\pi$
$809$	11.7919	0.414581	0.207290	+	0.978279i	$0.433536\pi$
$810$	2.64203	0.0928315
$811$	−47.0891	−1.65352	−0.826761	−	0.562553i	$-0.809819\pi$
$811$	−47.0891	−1.65352	−0.826761	+	0.562553i	$0.809819\pi$
$812$	−2.94968	−0.103514
$813$	−17.5641	−0.616000
$814$	−14.5438	−0.509760
$815$	−15.2970	−0.535831
$816$	7.06762	0.247416
$817$	0	0
$818$	21.8196	0.762904
$819$	−4.12491	−0.144136
$820$	−11.3663	−0.396930
$821$	−47.1480	−1.64548	−0.822739	−	0.568419i	$-0.807555\pi$
$821$	−47.1480	−1.64548	−0.822739	+	0.568419i	$0.807555\pi$
$822$	4.81295	0.167871
$823$	−37.5960	−1.31052	−0.655258	−	0.755406i	$-0.727440\pi$
$823$	−37.5960	−1.31052	−0.655258	+	0.755406i	$0.727440\pi$
$824$	55.8283	1.94487
$825$	−1.29945	−0.0452409
$826$	15.9673	0.555572
$827$	18.0488	0.627620	0.313810	−	0.949486i	$-0.398395\pi$
$827$	18.0488	0.627620	0.313810	+	0.949486i	$0.398395\pi$
$828$	5.05645	0.175724
$829$	−53.5059	−1.85834	−0.929168	−	0.369658i	$-0.879475\pi$
$829$	−53.5059	−1.85834	−0.929168	+	0.369658i	$0.879475\pi$
$830$	−34.7190	−1.20512
$831$	−12.4135	−0.430618
$832$	35.1404	1.21827
$833$	−3.31074	−0.114710
$834$	−6.11739	−0.211828
$835$	−5.25839	−0.181974
$836$	0	0
$837$	8.41762	0.290955
$838$	−5.22796	−0.180597
$839$	−37.7365	−1.30281	−0.651404	−	0.758731i	$-0.725819\pi$
$839$	−37.7365	−1.30281	−0.651404	+	0.758731i	$0.725819\pi$
$840$	7.11420	0.245463
$841$	−10.8676	−0.374743
$842$	2.78274	0.0958996
$843$	−15.9626	−0.549782
$844$	−1.85559	−0.0638719
$845$	9.27727	0.319148
$846$	−0.160229	−0.00550878
$847$	−3.64944	−0.125396
$848$	−29.7726	−1.02240
$849$	−19.4069	−0.666043
$850$	−1.28517	−0.0440808
$851$	−24.2594	−0.831600
$852$	4.36081	0.149399
$853$	−37.6641	−1.28959	−0.644797	−	0.764354i	$-0.723058\pi$
$853$	−37.6641	−1.28959	−0.644797	+	0.764354i	$0.723058\pi$
$854$	6.58468	0.225323
$855$	0	0
$856$	−6.05786	−0.207054
$857$	16.7648	0.572676	0.286338	−	0.958129i	$-0.407562\pi$
$857$	16.7648	0.572676	0.286338	+	0.958129i	$0.407562\pi$
$858$	−18.0514	−0.616266
$859$	37.3684	1.27499	0.637496	−	0.770454i	$-0.279970\pi$
$859$	37.3684	1.27499	0.637496	+	0.770454i	$0.279970\pi$
$860$	9.21798	0.314330
$861$	−7.10106	−0.242003
$862$	36.4377	1.24107
$863$	37.6588	1.28192	0.640960	−	0.767574i	$-0.278536\pi$
$863$	37.6588	1.28192	0.640960	+	0.767574i	$0.278536\pi$
$864$	3.71670	0.126445
$865$	3.72656	0.126707
$866$	−44.4497	−1.51046
$867$	−6.03902	−0.205096
$868$	5.83091	0.197914
$869$	51.1863	1.73637
$870$	−11.2503	−0.381422
$871$	−50.6207	−1.71522
$872$	49.9227	1.69060
$873$	−2.60598	−0.0881990
$874$	0	0
$875$	10.7692	0.364065
$876$	8.04488	0.271811
$877$	−13.3402	−0.450467	−0.225234	−	0.974305i	$-0.572315\pi$
$877$	−13.3402	−0.450467	−0.225234	+	0.974305i	$0.572315\pi$
$878$	−15.6374	−0.527736
$879$	12.3471	0.416456
$880$	18.8803	0.636456
$881$	38.9372	1.31183	0.655913	−	0.754836i	$-0.272284\pi$
$881$	38.9372	1.31183	0.655913	+	0.754836i	$0.272284\pi$
$882$	1.14337	0.0384993
$883$	−40.1789	−1.35213	−0.676064	−	0.736843i	$-0.736316\pi$
$883$	−40.1789	−1.35213	−0.676064	+	0.736843i	$0.736316\pi$
$884$	9.45989	0.318170
$885$	−32.2696	−1.08473
$886$	47.1299	1.58336
$887$	−31.7850	−1.06724	−0.533619	−	0.845725i	$-0.679168\pi$
$887$	−31.7850	−1.06724	−0.533619	+	0.845725i	$0.679168\pi$
$888$	−10.2319	−0.343360
$889$	8.64735	0.290023
$890$	−14.3916	−0.482408
$891$	−3.82746	−0.128225
$892$	11.9633	0.400560
$893$	0	0
$894$	13.9824	0.467643
$895$	36.2208	1.21073
$896$	−2.30707	−0.0770737
$897$	−30.1101	−1.00535
$898$	−4.97895	−0.166150
$899$	−35.8441	−1.19547
$900$	−0.235177	−0.00783923
$901$	−46.1735	−1.53826
$902$	−31.0757	−1.03471
$903$	5.75888	0.191643
$904$	−43.5496	−1.44844
$905$	0.675314	0.0224482
$906$	0.271503	0.00902009
$907$	44.5936	1.48071	0.740354	−	0.672217i	$-0.234658\pi$
$907$	44.5936	1.48071	0.740354	+	0.672217i	$0.234658\pi$
$908$	−5.28515	−0.175394
$909$	1.52918	0.0507198
$910$	−10.8981	−0.361269
$911$	−22.5134	−0.745903	−0.372951	−	0.927851i	$-0.621654\pi$
$911$	−22.5134	−0.745903	−0.372951	+	0.927851i	$0.621654\pi$
$912$	0	0
$913$	50.2968	1.66458
$914$	5.85549	0.193682
$915$	−13.3075	−0.439934
$916$	−1.60268	−0.0529541
$917$	−13.3604	−0.441200
$918$	−3.78540	−0.124937
$919$	21.6807	0.715181	0.357591	−	0.933878i	$-0.383598\pi$
$919$	21.6807	0.715181	0.357591	+	0.933878i	$0.383598\pi$
$920$	51.9308	1.71211
$921$	−8.92723	−0.294162
$922$	16.8090	0.553577
$923$	−25.9678	−0.854739
$924$	−2.65129	−0.0872211
$925$	1.12831	0.0370986
$926$	28.0886	0.923050
$927$	−18.1334	−0.595578
$928$	−15.8265	−0.519531
$929$	−18.0298	−0.591537	−0.295768	−	0.955260i	$-0.595576\pi$
$929$	−18.0298	−0.591537	−0.295768	+	0.955260i	$0.595576\pi$
$930$	22.2396	0.729265
$931$	0	0
$932$	3.95115	0.129424
$933$	25.1416	0.823099
$934$	35.2204	1.15245
$935$	29.2810	0.957591
$936$	−12.6996	−0.415099
$937$	−5.32482	−0.173954	−0.0869771	−	0.996210i	$-0.527721\pi$
$937$	−5.32482	−0.173954	−0.0869771	+	0.996210i	$0.527721\pi$
$938$	14.0314	0.458142
$939$	−13.1928	−0.430531
$940$	0.224311	0.00731623
$941$	−18.8787	−0.615429	−0.307715	−	0.951479i	$-0.599564\pi$
$941$	−18.8787	−0.615429	−0.307715	+	0.951479i	$0.599564\pi$
$942$	16.9295	0.551594
$943$	−51.8349	−1.68798
$944$	29.8120	0.970299
$945$	−2.31074	−0.0751683
$946$	25.2020	0.819389
$947$	−31.3180	−1.01770	−0.508849	−	0.860856i	$-0.669929\pi$
$947$	−31.3180	−1.01770	−0.508849	+	0.860856i	$0.669929\pi$
$948$	9.26382	0.300875
$949$	−47.9056	−1.55508
$950$	0	0
$951$	−5.70141	−0.184881
$952$	−10.1930	−0.330356
$953$	33.2382	1.07669	0.538346	−	0.842724i	$-0.319050\pi$
$953$	33.2382	1.07669	0.538346	+	0.842724i	$0.319050\pi$
$954$	15.9461	0.516275
$955$	−15.6284	−0.505722
$956$	−6.11498	−0.197772
$957$	16.2982	0.526845
$958$	9.24079	0.298556
$959$	−4.20944	−0.135930
$960$	19.6853	0.635342
$961$	39.8562	1.28569
$962$	15.6741	0.505352
$963$	1.96763	0.0634061
$964$	−20.2397	−0.651877
$965$	24.0498	0.774189
$966$	8.34614	0.268533
$967$	24.1065	0.775211	0.387606	−	0.921825i	$-0.373302\pi$
$967$	24.1065	0.775211	0.387606	+	0.921825i	$0.373302\pi$
$968$	−11.2358	−0.361131
$969$	0	0
$970$	−6.88507	−0.221066
$971$	16.6715	0.535012	0.267506	−	0.963556i	$-0.413800\pi$
$971$	16.6715	0.535012	0.267506	+	0.963556i	$0.413800\pi$
$972$	−0.692703	−0.0222185
$973$	5.35031	0.171523
$974$	37.8082	1.21145
$975$	1.40043	0.0448497
$976$	12.2941	0.393524
$977$	−48.9492	−1.56602	−0.783011	−	0.622008i	$-0.786317\pi$
$977$	−48.9492	−1.56602	−0.783011	+	0.622008i	$0.786317\pi$
$978$	−7.56908	−0.242032
$979$	20.8489	0.666333
$980$	−1.60065	−0.0511310
$981$	−16.2152	−0.517712
$982$	−4.36917	−0.139426
$983$	26.3637	0.840871	0.420436	−	0.907322i	$-0.361877\pi$
$983$	26.3637	0.840871	0.420436	+	0.907322i	$0.361877\pi$
$984$	−21.8624	−0.696949
$985$	−8.81206	−0.280775
$986$	16.1191	0.513336
$987$	0.140137	0.00446062
$988$	0	0
$989$	42.0375	1.33671
$990$	−10.1123	−0.321389
$991$	11.6852	0.371194	0.185597	−	0.982626i	$-0.440578\pi$
$991$	11.6852	0.371194	0.185597	+	0.982626i	$0.440578\pi$
$992$	31.2857	0.993323
$993$	−32.1319	−1.01967
$994$	7.19793	0.228304
$995$	7.93620	0.251594
$996$	9.10285	0.288435
$997$	50.8039	1.60898	0.804488	−	0.593969i	$-0.202440\pi$
$997$	50.8039	1.60898	0.804488	+	0.593969i	$0.202440\pi$
$998$	37.0083	1.17148
$999$	3.32338	0.105147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7581.2.a.be.1.4	yes	6
19.18	odd	2		7581.2.a.z.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7581.2.a.z.1.3	✓	6	19.18	odd	2
7581.2.a.be.1.4	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7581 = 3 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7581.a (trivial)

\(f(q)\)	\(=\)	\(q+1.14337 q^{2} +1.00000 q^{3} -0.692703 q^{4} +2.31074 q^{5} +1.14337 q^{6} -1.00000 q^{7} -3.07876 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.14337 q^{2} +1.00000 q^{3} -0.692703 q^{4} +2.31074 q^{5} +1.14337 q^{6} -1.00000 q^{7} -3.07876 q^{8} +1.00000 q^{9} +2.64203 q^{10} -3.82746 q^{11} -0.692703 q^{12} +4.12491 q^{13} -1.14337 q^{14} +2.31074 q^{15} -2.13476 q^{16} -3.31074 q^{17} +1.14337 q^{18} -1.60065 q^{20} -1.00000 q^{21} -4.37621 q^{22} -7.29960 q^{23} -3.07876 q^{24} +0.339506 q^{25} +4.71630 q^{26} +1.00000 q^{27} +0.692703 q^{28} -4.25822 q^{29} +2.64203 q^{30} +8.41762 q^{31} +3.71670 q^{32} -3.82746 q^{33} -3.78540 q^{34} -2.31074 q^{35} -0.692703 q^{36} +3.32338 q^{37} +4.12491 q^{39} -7.11420 q^{40} +7.10106 q^{41} -1.14337 q^{42} -5.75888 q^{43} +2.65129 q^{44} +2.31074 q^{45} -8.34614 q^{46} -0.140137 q^{47} -2.13476 q^{48} +1.00000 q^{49} +0.388181 q^{50} -3.31074 q^{51} -2.85734 q^{52} +13.9466 q^{53} +1.14337 q^{54} -8.84425 q^{55} +3.07876 q^{56} -4.86873 q^{58} -13.9651 q^{59} -1.60065 q^{60} -5.75901 q^{61} +9.62446 q^{62} -1.00000 q^{63} +8.51908 q^{64} +9.53157 q^{65} -4.37621 q^{66} -12.2720 q^{67} +2.29336 q^{68} -7.29960 q^{69} -2.64203 q^{70} -6.29536 q^{71} -3.07876 q^{72} -11.6138 q^{73} +3.79986 q^{74} +0.339506 q^{75} +3.82746 q^{77} +4.71630 q^{78} -13.3734 q^{79} -4.93286 q^{80} +1.00000 q^{81} +8.11915 q^{82} -13.1411 q^{83} +0.692703 q^{84} -7.65024 q^{85} -6.58453 q^{86} -4.25822 q^{87} +11.7838 q^{88} -5.44718 q^{89} +2.64203 q^{90} -4.12491 q^{91} +5.05645 q^{92} +8.41762 q^{93} -0.160229 q^{94} +3.71670 q^{96} -2.60598 q^{97} +1.14337 q^{98} -3.82746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 6 q^{3} + 8 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 6 * q^3 + 8 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q + 2 q^{2} + 6 q^{3} + 8 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9} - 2 q^{11} + 8 q^{12} - q^{13} - 2 q^{14} - 5 q^{15} - 4 q^{16} - q^{17} + 2 q^{18} - 27 q^{20} - 6 q^{21} - 6 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - 5 q^{26} + 6 q^{27} - 8 q^{28} - 11 q^{29} + 9 q^{31} + q^{32} - 2 q^{33} - 2 q^{34} + 5 q^{35} + 8 q^{36} - 4 q^{37} - q^{39} - 12 q^{40} - 6 q^{41} - 2 q^{42} + 2 q^{43} + 25 q^{44} - 5 q^{45} - 4 q^{46} + 6 q^{47} - 4 q^{48} + 6 q^{49} + 12 q^{50} - q^{51} + q^{52} + 10 q^{53} + 2 q^{54} - 16 q^{55} + 3 q^{56} - 49 q^{58} - 31 q^{59} - 27 q^{60} - 22 q^{61} + 21 q^{62} - 6 q^{63} - 27 q^{64} + 6 q^{65} - 6 q^{66} - 21 q^{67} + 19 q^{68} + 4 q^{69} - 32 q^{71} - 3 q^{72} - 28 q^{73} + 6 q^{74} - 3 q^{75} + 2 q^{77} - 5 q^{78} - 26 q^{79} + 6 q^{80} + 6 q^{81} - 4 q^{82} - 16 q^{83} - 8 q^{84} - 22 q^{85} - 38 q^{86} - 11 q^{87} - 19 q^{88} + 6 q^{89} + q^{91} + 13 q^{92} + 9 q^{93} + 25 q^{94} + q^{96} - 36 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 6 * q^3 + 8 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9 - 2 * q^11 + 8 * q^12 - q^13 - 2 * q^14 - 5 * q^15 - 4 * q^16 - q^17 + 2 * q^18 - 27 * q^20 - 6 * q^21 - 6 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - 5 * q^26 + 6 * q^27 - 8 * q^28 - 11 * q^29 + 9 * q^31 + q^32 - 2 * q^33 - 2 * q^34 + 5 * q^35 + 8 * q^36 - 4 * q^37 - q^39 - 12 * q^40 - 6 * q^41 - 2 * q^42 + 2 * q^43 + 25 * q^44 - 5 * q^45 - 4 * q^46 + 6 * q^47 - 4 * q^48 + 6 * q^49 + 12 * q^50 - q^51 + q^52 + 10 * q^53 + 2 * q^54 - 16 * q^55 + 3 * q^56 - 49 * q^58 - 31 * q^59 - 27 * q^60 - 22 * q^61 + 21 * q^62 - 6 * q^63 - 27 * q^64 + 6 * q^65 - 6 * q^66 - 21 * q^67 + 19 * q^68 + 4 * q^69 - 32 * q^71 - 3 * q^72 - 28 * q^73 + 6 * q^74 - 3 * q^75 + 2 * q^77 - 5 * q^78 - 26 * q^79 + 6 * q^80 + 6 * q^81 - 4 * q^82 - 16 * q^83 - 8 * q^84 - 22 * q^85 - 38 * q^86 - 11 * q^87 - 19 * q^88 + 6 * q^89 + q^91 + 13 * q^92 + 9 * q^93 + 25 * q^94 + q^96 - 36 * q^97 + 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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