LMFDB - Embedded newform 1859.2.a.t.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.930026 q^{2} +2.53271 q^{3} -1.13505 q^{4} -3.38691 q^{5} -2.35548 q^{6} -3.38196 q^{7} +2.91568 q^{8} +3.41460 q^{9} +O(q^{10})$	\(q-0.930026 q^{2} +2.53271 q^{3} -1.13505 q^{4} -3.38691 q^{5} -2.35548 q^{6} -3.38196 q^{7} +2.91568 q^{8} +3.41460 q^{9} +3.14991 q^{10} +1.00000 q^{11} -2.87475 q^{12} +3.14532 q^{14} -8.57804 q^{15} -0.441558 q^{16} -7.19830 q^{17} -3.17567 q^{18} -3.06566 q^{19} +3.84431 q^{20} -8.56552 q^{21} -0.930026 q^{22} +5.94916 q^{23} +7.38456 q^{24} +6.47113 q^{25} +1.05006 q^{27} +3.83870 q^{28} +5.43442 q^{29} +7.97780 q^{30} +9.06534 q^{31} -5.42070 q^{32} +2.53271 q^{33} +6.69461 q^{34} +11.4544 q^{35} -3.87574 q^{36} -4.87541 q^{37} +2.85114 q^{38} -9.87513 q^{40} +0.859934 q^{41} +7.96616 q^{42} +5.81891 q^{43} -1.13505 q^{44} -11.5649 q^{45} -5.53287 q^{46} +8.69187 q^{47} -1.11834 q^{48} +4.43768 q^{49} -6.01832 q^{50} -18.2312 q^{51} -9.91682 q^{53} -0.976585 q^{54} -3.38691 q^{55} -9.86073 q^{56} -7.76441 q^{57} -5.05416 q^{58} +7.38488 q^{59} +9.73651 q^{60} +5.88757 q^{61} -8.43101 q^{62} -11.5481 q^{63} +5.92451 q^{64} -2.35548 q^{66} -1.27537 q^{67} +8.17043 q^{68} +15.0675 q^{69} -10.6529 q^{70} +13.2250 q^{71} +9.95588 q^{72} +1.40595 q^{73} +4.53426 q^{74} +16.3895 q^{75} +3.47968 q^{76} -3.38196 q^{77} +4.47756 q^{79} +1.49552 q^{80} -7.58430 q^{81} -0.799761 q^{82} -2.06037 q^{83} +9.72230 q^{84} +24.3800 q^{85} -5.41174 q^{86} +13.7638 q^{87} +2.91568 q^{88} -0.472173 q^{89} +10.7557 q^{90} -6.75259 q^{92} +22.9599 q^{93} -8.08367 q^{94} +10.3831 q^{95} -13.7290 q^{96} +6.51513 q^{97} -4.12716 q^{98} +3.41460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.930026	−0.657628	−0.328814	−	0.944395i	$-0.606649\pi$
$2$	−0.930026	−0.657628	−0.328814	+	0.944395i	$0.606649\pi$
$3$	2.53271	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$3$	2.53271	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$4$	−1.13505	−0.567525
$5$	−3.38691	−1.51467	−0.757335	−	0.653026i	$-0.773499\pi$
$5$	−3.38691	−1.51467	−0.757335	+	0.653026i	$0.773499\pi$
$6$	−2.35548	−0.961622
$7$	−3.38196	−1.27826	−0.639131	−	0.769098i	$-0.720706\pi$
$7$	−3.38196	−1.27826	−0.639131	+	0.769098i	$0.720706\pi$
$8$	2.91568	1.03085
$9$	3.41460	1.13820
$10$	3.14991	0.996090
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.87475	−0.829869
$13$	0	0
$13$	0	0
$14$	3.14532	0.840621
$15$	−8.57804	−2.21484
$16$	−0.441558	−0.110390
$17$	−7.19830	−1.74584	−0.872922	−	0.487860i	$-0.837778\pi$
$17$	−7.19830	−1.74584	−0.872922	+	0.487860i	$0.837778\pi$
$18$	−3.17567	−0.748512
$19$	−3.06566	−0.703310	−0.351655	−	0.936130i	$-0.614381\pi$
$19$	−3.06566	−0.703310	−0.351655	+	0.936130i	$0.614381\pi$
$20$	3.84431	0.859614
$21$	−8.56552	−1.86915
$22$	−0.930026	−0.198282
$23$	5.94916	1.24048	0.620242	−	0.784410i	$-0.287034\pi$
$23$	5.94916	1.24048	0.620242	+	0.784410i	$0.287034\pi$
$24$	7.38456	1.50737
$25$	6.47113	1.29423
$26$	0	0
$27$	1.05006	0.202084
$28$	3.83870	0.725446
$29$	5.43442	1.00915	0.504573	−	0.863369i	$-0.331650\pi$
$29$	5.43442	1.00915	0.504573	+	0.863369i	$0.331650\pi$
$30$	7.97780	1.45654
$31$	9.06534	1.62818	0.814092	−	0.580736i	$-0.197235\pi$
$31$	9.06534	1.62818	0.814092	+	0.580736i	$0.197235\pi$
$32$	−5.42070	−0.958253
$33$	2.53271	0.440888
$34$	6.69461	1.14812
$35$	11.4544	1.93615
$36$	−3.87574	−0.645957
$37$	−4.87541	−0.801512	−0.400756	−	0.916185i	$-0.631253\pi$
$37$	−4.87541	−0.801512	−0.400756	+	0.916185i	$0.631253\pi$
$38$	2.85114	0.462517
$39$	0	0
$40$	−9.87513	−1.56140
$41$	0.859934	0.134299	0.0671495	−	0.997743i	$-0.478610\pi$
$41$	0.859934	0.134299	0.0671495	+	0.997743i	$0.478610\pi$
$42$	7.96616	1.22921
$43$	5.81891	0.887376	0.443688	−	0.896181i	$-0.353670\pi$
$43$	5.81891	0.887376	0.443688	+	0.896181i	$0.353670\pi$
$44$	−1.13505	−0.171115
$45$	−11.5649	−1.72400
$46$	−5.53287	−0.815777
$47$	8.69187	1.26784	0.633920	−	0.773399i	$-0.281445\pi$
$47$	8.69187	1.26784	0.633920	+	0.773399i	$0.281445\pi$
$48$	−1.11834	−0.161418
$49$	4.43768	0.633954
$50$	−6.01832	−0.851119
$51$	−18.2312	−2.55287
$52$	0	0
$53$	−9.91682	−1.36218	−0.681090	−	0.732200i	$-0.738494\pi$
$53$	−9.91682	−1.36218	−0.681090	+	0.732200i	$0.738494\pi$
$54$	−0.976585	−0.132896
$55$	−3.38691	−0.456690
$56$	−9.86073	−1.31769
$57$	−7.76441	−1.02842
$58$	−5.05416	−0.663643
$59$	7.38488	0.961429	0.480715	−	0.876877i	$-0.340377\pi$
$59$	7.38488	0.961429	0.480715	+	0.876877i	$0.340377\pi$
$60$	9.73651	1.25698
$61$	5.88757	0.753827	0.376913	−	0.926249i	$-0.376985\pi$
$61$	5.88757	0.753827	0.376913	+	0.926249i	$0.376985\pi$
$62$	−8.43101	−1.07074
$63$	−11.5481	−1.45492
$64$	5.92451	0.740564
$65$	0	0
$66$	−2.35548	−0.289940
$67$	−1.27537	−0.155812	−0.0779058	−	0.996961i	$-0.524823\pi$
$67$	−1.27537	−0.155812	−0.0779058	+	0.996961i	$0.524823\pi$
$68$	8.17043	0.990810
$69$	15.0675	1.81391
$70$	−10.6529	−1.27326
$71$	13.2250	1.56952	0.784758	−	0.619803i	$-0.212787\pi$
$71$	13.2250	1.56952	0.784758	+	0.619803i	$0.212787\pi$
$72$	9.95588	1.17331
$73$	1.40595	0.164554	0.0822771	−	0.996609i	$-0.473781\pi$
$73$	1.40595	0.164554	0.0822771	+	0.996609i	$0.473781\pi$
$74$	4.53426	0.527097
$75$	16.3895	1.89249
$76$	3.47968	0.399147
$77$	−3.38196	−0.385411
$78$	0	0
$79$	4.47756	0.503765	0.251883	−	0.967758i	$-0.418950\pi$
$79$	4.47756	0.503765	0.251883	+	0.967758i	$0.418950\pi$
$80$	1.49552	0.167204
$81$	−7.58430	−0.842701
$82$	−0.799761	−0.0883188
$83$	−2.06037	−0.226155	−0.113078	−	0.993586i	$-0.536071\pi$
$83$	−2.06037	−0.226155	−0.113078	+	0.993586i	$0.536071\pi$
$84$	9.72230	1.06079
$85$	24.3800	2.64438
$86$	−5.41174	−0.583563
$87$	13.7638	1.47563
$88$	2.91568	0.310813
$89$	−0.472173	−0.0500503	−0.0250251	−	0.999687i	$-0.507967\pi$
$89$	−0.472173	−0.0500503	−0.0250251	+	0.999687i	$0.507967\pi$
$90$	10.7557	1.13375
$91$	0	0
$92$	−6.75259	−0.704007
$93$	22.9599	2.38083
$94$	−8.08367	−0.833767
$95$	10.3831	1.06528
$96$	−13.7290	−1.40121
$97$	6.51513	0.661511	0.330756	−	0.943716i	$-0.392696\pi$
$97$	6.51513	0.661511	0.330756	+	0.943716i	$0.392696\pi$
$98$	−4.12716	−0.416906
$99$	3.41460	0.343180
$100$	−7.34506	−0.734506
$101$	2.64800	0.263486	0.131743	−	0.991284i	$-0.457943\pi$
$101$	2.64800	0.263486	0.131743	+	0.991284i	$0.457943\pi$
$102$	16.9555	1.67884
$103$	1.41401	0.139327	0.0696634	−	0.997571i	$-0.477807\pi$
$103$	1.41401	0.139327	0.0696634	+	0.997571i	$0.477807\pi$
$104$	0	0
$105$	29.0106	2.83115
$106$	9.22290	0.895808
$107$	3.62837	0.350768	0.175384	−	0.984500i	$-0.443883\pi$
$107$	3.62837	0.350768	0.175384	+	0.984500i	$0.443883\pi$
$108$	−1.19187	−0.114688
$109$	9.42565	0.902813	0.451407	−	0.892318i	$-0.350922\pi$
$109$	9.42565	0.902813	0.451407	+	0.892318i	$0.350922\pi$
$110$	3.14991	0.300332
$111$	−12.3480	−1.17202
$112$	1.49333	0.141107
$113$	−11.8576	−1.11547	−0.557734	−	0.830020i	$-0.688329\pi$
$113$	−11.8576	−1.11547	−0.557734	+	0.830020i	$0.688329\pi$
$114$	7.22111	0.676319
$115$	−20.1492	−1.87893
$116$	−6.16834	−0.572716
$117$	0	0
$118$	−6.86813	−0.632263
$119$	24.3444	2.23165
$120$	−25.0108	−2.28316
$121$	1.00000	0.0909091
$122$	−5.47560	−0.495737
$123$	2.17796	0.196380
$124$	−10.2896	−0.924036
$125$	−4.98257	−0.445655
$126$	10.7400	0.956795
$127$	8.65803	0.768276	0.384138	−	0.923276i	$-0.374499\pi$
$127$	8.65803	0.768276	0.384138	+	0.923276i	$0.374499\pi$
$128$	5.33145	0.471238
$129$	14.7376	1.29757
$130$	0	0
$131$	8.57478	0.749182	0.374591	−	0.927190i	$-0.377783\pi$
$131$	8.57478	0.749182	0.374591	+	0.927190i	$0.377783\pi$
$132$	−2.87475	−0.250215
$133$	10.3679	0.899015
$134$	1.18613	0.102466
$135$	−3.55646	−0.306091
$136$	−20.9879	−1.79970
$137$	−12.7244	−1.08712	−0.543559	−	0.839371i	$-0.682924\pi$
$137$	−12.7244	−1.08712	−0.543559	+	0.839371i	$0.682924\pi$
$138$	−14.0131	−1.19288
$139$	7.49251	0.635506	0.317753	−	0.948173i	$-0.397072\pi$
$139$	7.49251	0.635506	0.317753	+	0.948173i	$0.397072\pi$
$140$	−13.0013	−1.09881
$141$	22.0140	1.85391
$142$	−12.2996	−1.03216
$143$	0	0
$144$	−1.50775	−0.125645
$145$	−18.4059	−1.52852
$146$	−1.30757	−0.108215
$147$	11.2393	0.927005
$148$	5.53384	0.454879
$149$	7.25497	0.594350	0.297175	−	0.954823i	$-0.403955\pi$
$149$	7.25497	0.594350	0.297175	+	0.954823i	$0.403955\pi$
$150$	−15.2426	−1.24456
$151$	−14.1259	−1.14955	−0.574775	−	0.818312i	$-0.694910\pi$
$151$	−14.1259	−1.14955	−0.574775	+	0.818312i	$0.694910\pi$
$152$	−8.93848	−0.725007
$153$	−24.5793	−1.98712
$154$	3.14532	0.253457
$155$	−30.7035	−2.46616
$156$	0	0
$157$	8.79175	0.701658	0.350829	−	0.936440i	$-0.385900\pi$
$157$	8.79175	0.701658	0.350829	+	0.936440i	$0.385900\pi$
$158$	−4.16425	−0.331290
$159$	−25.1164	−1.99186
$160$	18.3594	1.45144
$161$	−20.1198	−1.58566
$162$	7.05360	0.554184
$163$	19.3644	1.51674	0.758368	−	0.651826i	$-0.225997\pi$
$163$	19.3644	1.51674	0.758368	+	0.651826i	$0.225997\pi$
$164$	−0.976068	−0.0762181
$165$	−8.57804	−0.667799
$166$	1.91620	0.148726
$167$	−14.5289	−1.12428	−0.562140	−	0.827042i	$-0.690022\pi$
$167$	−14.5289	−1.12428	−0.562140	+	0.827042i	$0.690022\pi$
$168$	−24.9743	−1.92681
$169$	0	0
$170$	−22.6740	−1.73902
$171$	−10.4680	−0.800508
$172$	−6.60476	−0.503608
$173$	−23.5645	−1.79158	−0.895789	−	0.444480i	$-0.853389\pi$
$173$	−23.5645	−1.79158	−0.895789	+	0.444480i	$0.853389\pi$
$174$	−12.8007	−0.970418
$175$	−21.8851	−1.65436
$176$	−0.441558	−0.0332837
$177$	18.7037	1.40586
$178$	0.439134	0.0329144
$179$	9.01232	0.673612	0.336806	−	0.941574i	$-0.390653\pi$
$179$	9.01232	0.673612	0.336806	+	0.941574i	$0.390653\pi$
$180$	13.1268	0.978413
$181$	10.6542	0.791917	0.395958	−	0.918268i	$-0.370412\pi$
$181$	10.6542	0.791917	0.395958	+	0.918268i	$0.370412\pi$
$182$	0	0
$183$	14.9115	1.10229
$184$	17.3458	1.27875
$185$	16.5126	1.21403
$186$	−21.3533	−1.56570
$187$	−7.19830	−0.526392
$188$	−9.86572	−0.719531
$189$	−3.55127	−0.258317
$190$	−9.65656	−0.700560
$191$	20.5050	1.48369	0.741846	−	0.670570i	$-0.233951\pi$
$191$	20.5050	1.48369	0.741846	+	0.670570i	$0.233951\pi$
$192$	15.0050	1.08290
$193$	−11.1839	−0.805035	−0.402518	−	0.915412i	$-0.631865\pi$
$193$	−11.1839	−0.805035	−0.402518	+	0.915412i	$0.631865\pi$
$194$	−6.05925	−0.435028
$195$	0	0
$196$	−5.03699	−0.359785
$197$	14.8983	1.06146	0.530729	−	0.847542i	$-0.321918\pi$
$197$	14.8983	1.06146	0.530729	+	0.847542i	$0.321918\pi$
$198$	−3.17567	−0.225685
$199$	−6.74457	−0.478110	−0.239055	−	0.971006i	$-0.576838\pi$
$199$	−6.74457	−0.478110	−0.239055	+	0.971006i	$0.576838\pi$
$200$	18.8677	1.33415
$201$	−3.23015	−0.227837
$202$	−2.46271	−0.173276
$203$	−18.3790	−1.28995
$204$	20.6933	1.44882
$205$	−2.91251	−0.203419
$206$	−1.31507	−0.0916253
$207$	20.3140	1.41192
$208$	0	0
$209$	−3.06566	−0.212056
$210$	−26.9806	−1.86184
$211$	−24.1718	−1.66406	−0.832029	−	0.554732i	$-0.812821\pi$
$211$	−24.1718	−1.66406	−0.832029	+	0.554732i	$0.812821\pi$
$212$	11.2561	0.773072
$213$	33.4950	2.29504
$214$	−3.37448	−0.230675
$215$	−19.7081	−1.34408
$216$	3.06164	0.208318
$217$	−30.6587	−2.08125
$218$	−8.76610	−0.593715
$219$	3.56086	0.240621
$220$	3.84431	0.259183
$221$	0	0
$222$	11.4839	0.770752
$223$	17.3564	1.16227	0.581134	−	0.813808i	$-0.302609\pi$
$223$	17.3564	1.16227	0.581134	+	0.813808i	$0.302609\pi$
$224$	18.3326	1.22490
$225$	22.0963	1.47309
$226$	11.0279	0.733563
$227$	−10.7311	−0.712247	−0.356123	−	0.934439i	$-0.615902\pi$
$227$	−10.7311	−0.712247	−0.356123	+	0.934439i	$0.615902\pi$
$228$	8.81300	0.583655
$229$	22.4942	1.48646	0.743229	−	0.669037i	$-0.233293\pi$
$229$	22.4942	1.48646	0.743229	+	0.669037i	$0.233293\pi$
$230$	18.7393	1.23563
$231$	−8.56552	−0.563570
$232$	15.8450	1.04028
$233$	−7.41928	−0.486053	−0.243027	−	0.970020i	$-0.578140\pi$
$233$	−7.41928	−0.486053	−0.243027	+	0.970020i	$0.578140\pi$
$234$	0	0
$235$	−29.4386	−1.92036
$236$	−8.38221	−0.545635
$237$	11.3404	0.736635
$238$	−22.6409	−1.46759
$239$	−1.77240	−0.114647	−0.0573235	−	0.998356i	$-0.518257\pi$
$239$	−1.77240	−0.114647	−0.0573235	+	0.998356i	$0.518257\pi$
$240$	3.78770	0.244495
$241$	−11.4199	−0.735622	−0.367811	−	0.929901i	$-0.619893\pi$
$241$	−11.4199	−0.735622	−0.367811	+	0.929901i	$0.619893\pi$
$242$	−0.930026	−0.0597844
$243$	−22.3590	−1.43433
$244$	−6.68269	−0.427816
$245$	−15.0300	−0.960232
$246$	−2.02556	−0.129145
$247$	0	0
$248$	26.4316	1.67841
$249$	−5.21832	−0.330697
$250$	4.63393	0.293075
$251$	18.1455	1.14533	0.572667	−	0.819788i	$-0.305909\pi$
$251$	18.1455	1.14533	0.572667	+	0.819788i	$0.305909\pi$
$252$	13.1076	0.825703
$253$	5.94916	0.374020
$254$	−8.05220	−0.505240
$255$	61.7473	3.86676
$256$	−16.8074	−1.05046
$257$	−7.34137	−0.457942	−0.228971	−	0.973433i	$-0.573536\pi$
$257$	−7.34137	−0.457942	−0.228971	+	0.973433i	$0.573536\pi$
$258$	−13.7064	−0.853320
$259$	16.4885	1.02454
$260$	0	0
$261$	18.5564	1.14861
$262$	−7.97477	−0.492683
$263$	−23.5615	−1.45286	−0.726431	−	0.687239i	$-0.758822\pi$
$263$	−23.5615	−1.45286	−0.726431	+	0.687239i	$0.758822\pi$
$264$	7.38456	0.454488
$265$	33.5873	2.06325
$266$	−9.64247	−0.591218
$267$	−1.19588	−0.0731864
$268$	1.44761	0.0884271
$269$	−12.3713	−0.754291	−0.377146	−	0.926154i	$-0.623094\pi$
$269$	−12.3713	−0.754291	−0.377146	+	0.926154i	$0.623094\pi$
$270$	3.30760	0.201294
$271$	21.6867	1.31737	0.658686	−	0.752418i	$-0.271113\pi$
$271$	21.6867	1.31737	0.658686	+	0.752418i	$0.271113\pi$
$272$	3.17847	0.192723
$273$	0	0
$274$	11.8340	0.714920
$275$	6.47113	0.390224
$276$	−17.1023	−1.02944
$277$	−24.6590	−1.48162	−0.740809	−	0.671716i	$-0.765558\pi$
$277$	−24.6590	−1.48162	−0.740809	+	0.671716i	$0.765558\pi$
$278$	−6.96823	−0.417927
$279$	30.9545	1.85320
$280$	33.3973	1.99587
$281$	−31.3448	−1.86988	−0.934938	−	0.354810i	$-0.884545\pi$
$281$	−31.3448	−1.86988	−0.934938	+	0.354810i	$0.884545\pi$
$282$	−20.4736	−1.21918
$283$	20.4209	1.21390	0.606949	−	0.794741i	$-0.292393\pi$
$283$	20.4209	1.21390	0.606949	+	0.794741i	$0.292393\pi$
$284$	−15.0110	−0.890740
$285$	26.2973	1.55772
$286$	0	0
$287$	−2.90826	−0.171669
$288$	−18.5095	−1.09068
$289$	34.8155	2.04797
$290$	17.1179	1.00520
$291$	16.5009	0.967301
$292$	−1.59583	−0.0933887
$293$	10.9817	0.641555	0.320778	−	0.947155i	$-0.396056\pi$
$293$	10.9817	0.641555	0.320778	+	0.947155i	$0.396056\pi$
$294$	−10.4529	−0.609625
$295$	−25.0119	−1.45625
$296$	−14.2151	−0.826238
$297$	1.05006	0.0609307
$298$	−6.74732	−0.390861
$299$	0	0
$300$	−18.6029	−1.07404
$301$	−19.6793	−1.13430
$302$	13.1375	0.755976
$303$	6.70661	0.385285
$304$	1.35367	0.0776381
$305$	−19.9407	−1.14180
$306$	22.8594	1.30679
$307$	15.5836	0.889402	0.444701	−	0.895679i	$-0.353310\pi$
$307$	15.5836	0.889402	0.444701	+	0.895679i	$0.353310\pi$
$308$	3.83870	0.218730
$309$	3.58128	0.203732
$310$	28.5550	1.62182
$311$	8.37476	0.474889	0.237444	−	0.971401i	$-0.423690\pi$
$311$	8.37476	0.474889	0.237444	+	0.971401i	$0.423690\pi$
$312$	0	0
$313$	15.9360	0.900757	0.450378	−	0.892838i	$-0.351289\pi$
$313$	15.9360	0.900757	0.450378	+	0.892838i	$0.351289\pi$
$314$	−8.17656	−0.461430
$315$	39.1122	2.20372
$316$	−5.08226	−0.285900
$317$	−15.0857	−0.847295	−0.423647	−	0.905827i	$-0.639250\pi$
$317$	−15.0857	−0.847295	−0.423647	+	0.905827i	$0.639250\pi$
$318$	23.3589	1.30990
$319$	5.43442	0.304269
$320$	−20.0658	−1.12171
$321$	9.18959	0.512913
$322$	18.7120	1.04278
$323$	22.0675	1.22787
$324$	8.60857	0.478254
$325$	0	0
$326$	−18.0094	−0.997449
$327$	23.8724	1.32015
$328$	2.50729	0.138442
$329$	−29.3956	−1.62063
$330$	7.97780	0.439163
$331$	1.05736	0.0581180	0.0290590	−	0.999578i	$-0.490749\pi$
$331$	1.05736	0.0581180	0.0290590	+	0.999578i	$0.490749\pi$
$332$	2.33863	0.128349
$333$	−16.6476	−0.912282
$334$	13.5123	0.739358
$335$	4.31957	0.236003
$336$	3.78218	0.206335
$337$	−5.81233	−0.316618	−0.158309	−	0.987390i	$-0.550604\pi$
$337$	−5.81233	−0.316618	−0.158309	+	0.987390i	$0.550604\pi$
$338$	0	0
$339$	−30.0318	−1.63110
$340$	−27.6725	−1.50075
$341$	9.06534	0.490916
$342$	9.73552	0.526437
$343$	8.66567	0.467902
$344$	16.9661	0.914750
$345$	−51.0321	−2.74747
$346$	21.9156	1.17819
$347$	−16.8264	−0.903289	−0.451644	−	0.892198i	$-0.649162\pi$
$347$	−16.8264	−0.903289	−0.451644	+	0.892198i	$0.649162\pi$
$348$	−15.6226	−0.837459
$349$	5.50086	0.294454	0.147227	−	0.989103i	$-0.452965\pi$
$349$	5.50086	0.294454	0.147227	+	0.989103i	$0.452965\pi$
$350$	20.3537	1.08795
$351$	0	0
$352$	−5.42070	−0.288924
$353$	−25.6484	−1.36513	−0.682563	−	0.730826i	$-0.739135\pi$
$353$	−25.6484	−1.36513	−0.682563	+	0.730826i	$0.739135\pi$
$354$	−17.3950	−0.924532
$355$	−44.7917	−2.37730
$356$	0.535940	0.0284048
$357$	61.6572	3.26324
$358$	−8.38170	−0.442986
$359$	−5.58116	−0.294562	−0.147281	−	0.989095i	$-0.547052\pi$
$359$	−5.58116	−0.294562	−0.147281	+	0.989095i	$0.547052\pi$
$360$	−33.7196	−1.77718
$361$	−9.60173	−0.505354
$362$	−9.90864	−0.520787
$363$	2.53271	0.132933
$364$	0	0
$365$	−4.76183	−0.249245
$366$	−13.8681	−0.724896
$367$	26.0854	1.36165	0.680823	−	0.732448i	$-0.261622\pi$
$367$	26.0854	1.36165	0.680823	+	0.732448i	$0.261622\pi$
$368$	−2.62690	−0.136937
$369$	2.93633	0.152859
$370$	−15.3571	−0.798378
$371$	33.5383	1.74122
$372$	−26.0606	−1.35118
$373$	30.8984	1.59986	0.799930	−	0.600094i	$-0.204870\pi$
$373$	30.8984	1.59986	0.799930	+	0.600094i	$0.204870\pi$
$374$	6.69461	0.346170
$375$	−12.6194	−0.651663
$376$	25.3427	1.30695
$377$	0	0
$378$	3.30277	0.169876
$379$	−11.8349	−0.607920	−0.303960	−	0.952685i	$-0.598309\pi$
$379$	−11.8349	−0.607920	−0.303960	+	0.952685i	$0.598309\pi$
$380$	−11.7853	−0.604575
$381$	21.9282	1.12342
$382$	−19.0702	−0.975717
$383$	13.0913	0.668935	0.334468	−	0.942407i	$-0.391443\pi$
$383$	13.0913	0.668935	0.334468	+	0.942407i	$0.391443\pi$
$384$	13.5030	0.689072
$385$	11.4544	0.583770
$386$	10.4013	0.529414
$387$	19.8693	1.01001
$388$	−7.39501	−0.375425
$389$	−1.62816	−0.0825508	−0.0412754	−	0.999148i	$-0.513142\pi$
$389$	−1.62816	−0.0825508	−0.0412754	+	0.999148i	$0.513142\pi$
$390$	0	0
$391$	−42.8238	−2.16569
$392$	12.9389	0.653511
$393$	21.7174	1.09550
$394$	−13.8558	−0.698045
$395$	−15.1651	−0.763038
$396$	−3.87574	−0.194764
$397$	−9.43035	−0.473296	−0.236648	−	0.971596i	$-0.576049\pi$
$397$	−9.43035	−0.473296	−0.236648	+	0.971596i	$0.576049\pi$
$398$	6.27263	0.314419
$399$	26.2590	1.31459
$400$	−2.85738	−0.142869
$401$	9.65745	0.482270	0.241135	−	0.970492i	$-0.422480\pi$
$401$	9.65745	0.482270	0.241135	+	0.970492i	$0.422480\pi$
$402$	3.00412	0.149832
$403$	0	0
$404$	−3.00561	−0.149535
$405$	25.6873	1.27641
$406$	17.0930	0.848310
$407$	−4.87541	−0.241665
$408$	−53.1563	−2.63163
$409$	6.56175	0.324458	0.162229	−	0.986753i	$-0.448132\pi$
$409$	6.56175	0.324458	0.162229	+	0.986753i	$0.448132\pi$
$410$	2.70871	0.133774
$411$	−32.2272	−1.58965
$412$	−1.60498	−0.0790715
$413$	−24.9754	−1.22896
$414$	−18.8925	−0.928518
$415$	6.97829	0.342551
$416$	0	0
$417$	18.9763	0.929274
$418$	2.85114	0.139454
$419$	−25.7883	−1.25984	−0.629921	−	0.776659i	$-0.716913\pi$
$419$	−25.7883	−1.25984	−0.629921	+	0.776659i	$0.716913\pi$
$420$	−32.9285	−1.60675
$421$	2.65368	0.129332	0.0646661	−	0.997907i	$-0.479402\pi$
$421$	2.65368	0.129332	0.0646661	+	0.997907i	$0.479402\pi$
$422$	22.4805	1.09433
$423$	29.6793	1.44306
$424$	−28.9143	−1.40420
$425$	−46.5811	−2.25952
$426$	−31.1512	−1.50928
$427$	−19.9116	−0.963588
$428$	−4.11838	−0.199070
$429$	0	0
$430$	18.3291	0.883906
$431$	21.4843	1.03486	0.517430	−	0.855725i	$-0.326889\pi$
$431$	21.4843	1.03486	0.517430	+	0.855725i	$0.326889\pi$
$432$	−0.463663	−0.0223080
$433$	8.87391	0.426453	0.213226	−	0.977003i	$-0.431603\pi$
$433$	8.87391	0.426453	0.213226	+	0.977003i	$0.431603\pi$
$434$	28.5134	1.36869
$435$	−46.6167	−2.23510
$436$	−10.6986	−0.512370
$437$	−18.2381	−0.872446
$438$	−3.31170	−0.158239
$439$	32.2696	1.54014	0.770072	−	0.637957i	$-0.220220\pi$
$439$	32.2696	1.54014	0.770072	+	0.637957i	$0.220220\pi$
$440$	−9.87513	−0.470779
$441$	15.1529	0.721567
$442$	0	0
$443$	21.3864	1.01610	0.508050	−	0.861327i	$-0.330366\pi$
$443$	21.3864	1.01610	0.508050	+	0.861327i	$0.330366\pi$
$444$	14.0156	0.665150
$445$	1.59921	0.0758096
$446$	−16.1419	−0.764340
$447$	18.3747	0.869094
$448$	−20.0365	−0.946635
$449$	−16.7306	−0.789564	−0.394782	−	0.918775i	$-0.629180\pi$
$449$	−16.7306	−0.789564	−0.394782	+	0.918775i	$0.629180\pi$
$450$	−20.5502	−0.968744
$451$	0.859934	0.0404927
$452$	13.4590	0.633057
$453$	−35.7768	−1.68094
$454$	9.98019	0.468393
$455$	0	0
$456$	−22.6385	−1.06015
$457$	−9.78889	−0.457905	−0.228953	−	0.973438i	$-0.573530\pi$
$457$	−9.78889	−0.457905	−0.228953	+	0.973438i	$0.573530\pi$
$458$	−20.9202	−0.977537
$459$	−7.55865	−0.352808
$460$	22.8704	1.06634
$461$	−18.7517	−0.873352	−0.436676	−	0.899619i	$-0.643844\pi$
$461$	−18.7517	−0.873352	−0.436676	+	0.899619i	$0.643844\pi$
$462$	7.96616	0.370619
$463$	23.2559	1.08079	0.540396	−	0.841411i	$-0.318274\pi$
$463$	23.2559	1.08079	0.540396	+	0.841411i	$0.318274\pi$
$464$	−2.39961	−0.111399
$465$	−77.7628	−3.60617
$466$	6.90013	0.319642
$467$	0.0987954	0.00457171	0.00228585	−	0.999997i	$-0.499272\pi$
$467$	0.0987954	0.00457171	0.00228585	+	0.999997i	$0.499272\pi$
$468$	0	0
$469$	4.31327	0.199168
$470$	27.3786	1.26288
$471$	22.2669	1.02601
$472$	21.5319	0.991088
$473$	5.81891	0.267554
$474$	−10.5468	−0.484432
$475$	−19.8383	−0.910242
$476$	−27.6321	−1.26652
$477$	−33.8620	−1.55043
$478$	1.64838	0.0753951
$479$	−23.4409	−1.07104	−0.535520	−	0.844523i	$-0.679884\pi$
$479$	−23.4409	−1.07104	−0.535520	+	0.844523i	$0.679884\pi$
$480$	46.4990	2.12238
$481$	0	0
$482$	10.6208	0.483766
$483$	−50.9576	−2.31865
$484$	−1.13505	−0.0515932
$485$	−22.0661	−1.00197
$486$	20.7945	0.943256
$487$	1.58984	0.0720424	0.0360212	−	0.999351i	$-0.488532\pi$
$487$	1.58984	0.0720424	0.0360212	+	0.999351i	$0.488532\pi$
$488$	17.1663	0.777081
$489$	49.0443	2.21786
$490$	13.9783	0.631475
$491$	3.34966	0.151168	0.0755841	−	0.997139i	$-0.475918\pi$
$491$	3.34966	0.151168	0.0755841	+	0.997139i	$0.475918\pi$
$492$	−2.47209	−0.111451
$493$	−39.1186	−1.76181
$494$	0	0
$495$	−11.5649	−0.519805
$496$	−4.00288	−0.179734
$497$	−44.7264	−2.00625
$498$	4.85317	0.217476
$499$	33.5789	1.50320	0.751600	−	0.659619i	$-0.229282\pi$
$499$	33.5789	1.50320	0.751600	+	0.659619i	$0.229282\pi$
$500$	5.65547	0.252921
$501$	−36.7974	−1.64399
$502$	−16.8758	−0.753204
$503$	−9.93290	−0.442886	−0.221443	−	0.975173i	$-0.571077\pi$
$503$	−9.93290	−0.442886	−0.221443	+	0.975173i	$0.571077\pi$
$504$	−33.6704	−1.49980
$505$	−8.96853	−0.399094
$506$	−5.53287	−0.245966
$507$	0	0
$508$	−9.82730	−0.436016
$509$	−0.669939	−0.0296945	−0.0148473	−	0.999890i	$-0.504726\pi$
$509$	−0.669939	−0.0296945	−0.0148473	+	0.999890i	$0.504726\pi$
$510$	−57.4266	−2.54289
$511$	−4.75488	−0.210343
$512$	4.96844	0.219576
$513$	−3.21913	−0.142128
$514$	6.82767	0.301155
$515$	−4.78913	−0.211034
$516$	−16.7279	−0.736405
$517$	8.69187	0.382268
$518$	−15.3347	−0.673768
$519$	−59.6820	−2.61975
$520$	0	0
$521$	35.5156	1.55597	0.777983	−	0.628286i	$-0.216243\pi$
$521$	35.5156	1.55597	0.777983	+	0.628286i	$0.216243\pi$
$522$	−17.2579	−0.755359
$523$	12.2650	0.536310	0.268155	−	0.963376i	$-0.413586\pi$
$523$	12.2650	0.536310	0.268155	+	0.963376i	$0.413586\pi$
$524$	−9.73281	−0.425180
$525$	−55.4286	−2.41910
$526$	21.9128	0.955443
$527$	−65.2550	−2.84255
$528$	−1.11834	−0.0486694
$529$	12.3925	0.538802
$530$	−31.2371	−1.35685
$531$	25.2164	1.09430
$532$	−11.7681	−0.510214
$533$	0	0
$534$	1.11220	0.0481294
$535$	−12.2889	−0.531297
$536$	−3.71858	−0.160618
$537$	22.8256	0.984995
$538$	11.5056	0.496043
$539$	4.43768	0.191144
$540$	4.03676	0.173715
$541$	−34.5002	−1.48328	−0.741639	−	0.670799i	$-0.765951\pi$
$541$	−34.5002	−1.48328	−0.741639	+	0.670799i	$0.765951\pi$
$542$	−20.1692	−0.866341
$543$	26.9838	1.15799
$544$	39.0198	1.67296
$545$	−31.9238	−1.36746
$546$	0	0
$547$	23.6264	1.01019	0.505096	−	0.863063i	$-0.331457\pi$
$547$	23.6264	1.01019	0.505096	+	0.863063i	$0.331457\pi$
$548$	14.4428	0.616967
$549$	20.1037	0.858006
$550$	−6.01832	−0.256622
$551$	−16.6601	−0.709743
$552$	43.9319	1.86987
$553$	−15.1430	−0.643944
$554$	22.9336	0.974354
$555$	41.8214	1.77522
$556$	−8.50438	−0.360666
$557$	24.7328	1.04796	0.523981	−	0.851730i	$-0.324446\pi$
$557$	24.7328	1.04796	0.523981	+	0.851730i	$0.324446\pi$
$558$	−28.7885	−1.21872
$559$	0	0
$560$	−5.05778	−0.213730
$561$	−18.2312	−0.769721
$562$	29.1515	1.22968
$563$	25.1410	1.05957	0.529784	−	0.848133i	$-0.322273\pi$
$563$	25.1410	1.05957	0.529784	+	0.848133i	$0.322273\pi$
$564$	−24.9870	−1.05214
$565$	40.1605	1.68957
$566$	−18.9920	−0.798293
$567$	25.6498	1.07719
$568$	38.5598	1.61793
$569$	3.84060	0.161006	0.0805031	−	0.996754i	$-0.474347\pi$
$569$	3.84060	0.161006	0.0805031	+	0.996754i	$0.474347\pi$
$570$	−24.4572	−1.02440
$571$	−11.0865	−0.463954	−0.231977	−	0.972721i	$-0.574519\pi$
$571$	−11.0865	−0.463954	−0.231977	+	0.972721i	$0.574519\pi$
$572$	0	0
$573$	51.9332	2.16954
$574$	2.70476	0.112895
$575$	38.4978	1.60547
$576$	20.2298	0.842910
$577$	−15.9929	−0.665794	−0.332897	−	0.942963i	$-0.608026\pi$
$577$	−15.9929	−0.665794	−0.332897	+	0.942963i	$0.608026\pi$
$578$	−32.3793	−1.34680
$579$	−28.3255	−1.17717
$580$	20.8916	0.867476
$581$	6.96810	0.289086
$582$	−15.3463	−0.636124
$583$	−9.91682	−0.410713
$584$	4.09931	0.169630
$585$	0	0
$586$	−10.2132	−0.421905
$587$	3.37192	0.139174	0.0695869	−	0.997576i	$-0.477832\pi$
$587$	3.37192	0.139174	0.0695869	+	0.997576i	$0.477832\pi$
$588$	−12.7572	−0.526099
$589$	−27.7913	−1.14512
$590$	23.2617	0.957670
$591$	37.7330	1.55213
$592$	2.15278	0.0884786
$593$	46.2935	1.90105	0.950523	−	0.310654i	$-0.100548\pi$
$593$	46.2935	1.90105	0.950523	+	0.310654i	$0.100548\pi$
$594$	−0.976585	−0.0400698
$595$	−82.4521	−3.38021
$596$	−8.23476	−0.337309
$597$	−17.0820	−0.699120
$598$	0	0
$599$	−33.4089	−1.36505	−0.682524	−	0.730863i	$-0.739118\pi$
$599$	−33.4089	−1.36505	−0.682524	+	0.730863i	$0.739118\pi$
$600$	47.7864	1.95087
$601$	8.82058	0.359799	0.179900	−	0.983685i	$-0.442423\pi$
$601$	8.82058	0.359799	0.179900	+	0.983685i	$0.442423\pi$
$602$	18.3023	0.745947
$603$	−4.35489	−0.177345
$604$	16.0336	0.652399
$605$	−3.38691	−0.137697
$606$	−6.23732	−0.253374
$607$	40.4703	1.64264	0.821319	−	0.570469i	$-0.193239\pi$
$607$	40.4703	1.64264	0.821319	+	0.570469i	$0.193239\pi$
$608$	16.6180	0.673950
$609$	−46.5486	−1.88625
$610$	18.5453	0.750879
$611$	0	0
$612$	27.8988	1.12774
$613$	−37.4564	−1.51285	−0.756425	−	0.654081i	$-0.773056\pi$
$613$	−37.4564	−1.51285	−0.756425	+	0.654081i	$0.773056\pi$
$614$	−14.4931	−0.584896
$615$	−7.37654	−0.297451
$616$	−9.86073	−0.397300
$617$	10.7790	0.433946	0.216973	−	0.976178i	$-0.430382\pi$
$617$	10.7790	0.433946	0.216973	+	0.976178i	$0.430382\pi$
$618$	−3.33069	−0.133980
$619$	−18.0458	−0.725321	−0.362660	−	0.931921i	$-0.618131\pi$
$619$	−18.0458	−0.725321	−0.362660	+	0.931921i	$0.618131\pi$
$620$	34.8500	1.39961
$621$	6.24698	0.250683
$622$	−7.78875	−0.312300
$623$	1.59687	0.0639773
$624$	0	0
$625$	−15.4801	−0.619205
$626$	−14.8209	−0.592363
$627$	−7.76441	−0.310081
$628$	−9.97908	−0.398209
$629$	35.0946	1.39932
$630$	−36.3754	−1.44923
$631$	27.7527	1.10482	0.552409	−	0.833573i	$-0.313709\pi$
$631$	27.7527	1.10482	0.552409	+	0.833573i	$0.313709\pi$
$632$	13.0551	0.519306
$633$	−61.2202	−2.43328
$634$	14.0301	0.557205
$635$	−29.3239	−1.16368
$636$	28.5084	1.13043
$637$	0	0
$638$	−5.05416	−0.200096
$639$	45.1580	1.78642
$640$	−18.0571	−0.713770
$641$	12.4477	0.491653	0.245827	−	0.969314i	$-0.420941\pi$
$641$	12.4477	0.491653	0.245827	+	0.969314i	$0.420941\pi$
$642$	−8.54657	−0.337306
$643$	8.59509	0.338957	0.169479	−	0.985534i	$-0.445792\pi$
$643$	8.59509	0.338957	0.169479	+	0.985534i	$0.445792\pi$
$644$	22.8370	0.899905
$645$	−49.9148	−1.96539
$646$	−20.5234	−0.807482
$647$	28.0626	1.10325	0.551627	−	0.834091i	$-0.314007\pi$
$647$	28.0626	1.10325	0.551627	+	0.834091i	$0.314007\pi$
$648$	−22.1134	−0.868697
$649$	7.38488	0.289882
$650$	0	0
$651$	−77.6494	−3.04332
$652$	−21.9796	−0.860787
$653$	−40.9904	−1.60408	−0.802040	−	0.597270i	$-0.796252\pi$
$653$	−40.9904	−1.60408	−0.802040	+	0.597270i	$0.796252\pi$
$654$	−22.2020	−0.868165
$655$	−29.0420	−1.13476
$656$	−0.379711	−0.0148252
$657$	4.80076	0.187296
$658$	27.3387	1.06577
$659$	−41.7306	−1.62559	−0.812797	−	0.582547i	$-0.802056\pi$
$659$	−41.7306	−1.62559	−0.812797	+	0.582547i	$0.802056\pi$
$660$	9.73651	0.378993
$661$	−16.5881	−0.645201	−0.322601	−	0.946535i	$-0.604557\pi$
$661$	−16.5881	−0.645201	−0.322601	+	0.946535i	$0.604557\pi$
$662$	−0.983377	−0.0382200
$663$	0	0
$664$	−6.00739	−0.233132
$665$	−35.1153	−1.36171
$666$	15.4827	0.599942
$667$	32.3302	1.25183
$668$	16.4910	0.638057
$669$	43.9586	1.69954
$670$	−4.01731	−0.155202
$671$	5.88757	0.227287
$672$	46.4311	1.79112
$673$	29.8674	1.15130	0.575652	−	0.817695i	$-0.304748\pi$
$673$	29.8674	1.15130	0.575652	+	0.817695i	$0.304748\pi$
$674$	5.40562	0.208217
$675$	6.79508	0.261543
$676$	0	0
$677$	20.8295	0.800542	0.400271	−	0.916397i	$-0.368916\pi$
$677$	20.8295	0.800542	0.400271	+	0.916397i	$0.368916\pi$
$678$	27.9304	1.07266
$679$	−22.0339	−0.845585
$680$	71.0841	2.72595
$681$	−27.1787	−1.04149
$682$	−8.43101	−0.322840
$683$	34.2842	1.31185	0.655924	−	0.754827i	$-0.272279\pi$
$683$	34.2842	1.31185	0.655924	+	0.754827i	$0.272279\pi$
$684$	11.8817	0.454309
$685$	43.0963	1.64663
$686$	−8.05930	−0.307706
$687$	56.9712	2.17359
$688$	−2.56939	−0.0979570
$689$	0	0
$690$	47.4612	1.80682
$691$	8.39056	0.319192	0.159596	−	0.987182i	$-0.448981\pi$
$691$	8.39056	0.319192	0.159596	+	0.987182i	$0.448981\pi$
$692$	26.7469	1.01677
$693$	−11.5481	−0.438674
$694$	15.6490	0.594028
$695$	−25.3764	−0.962582
$696$	40.1308	1.52115
$697$	−6.19006	−0.234465
$698$	−5.11594	−0.193641
$699$	−18.7909	−0.710735
$700$	24.8407	0.938891
$701$	−33.0702	−1.24904	−0.624522	−	0.781007i	$-0.714706\pi$
$701$	−33.0702	−1.24904	−0.624522	+	0.781007i	$0.714706\pi$
$702$	0	0
$703$	14.9463	0.563712
$704$	5.92451	0.223288
$705$	−74.5592	−2.80806
$706$	23.8537	0.897746
$707$	−8.95544	−0.336804
$708$	−21.2297	−0.797860
$709$	−0.364882	−0.0137034	−0.00685171	−	0.999977i	$-0.502181\pi$
$709$	−0.364882	−0.0137034	−0.00685171	+	0.999977i	$0.502181\pi$
$710$	41.6575	1.56338
$711$	15.2891	0.573386
$712$	−1.37671	−0.0515942
$713$	53.9311	2.01974
$714$	−57.3428	−2.14600
$715$	0	0
$716$	−10.2294	−0.382292
$717$	−4.48897	−0.167644
$718$	5.19063	0.193713
$719$	−18.6303	−0.694794	−0.347397	−	0.937718i	$-0.612934\pi$
$719$	−18.6303	−0.694794	−0.347397	+	0.937718i	$0.612934\pi$
$720$	5.10659	0.190311
$721$	−4.78214	−0.178096
$722$	8.92987	0.332335
$723$	−28.9233	−1.07567
$724$	−12.0930	−0.449433
$725$	35.1668	1.30606
$726$	−2.35548	−0.0874202
$727$	15.2502	0.565599	0.282800	−	0.959179i	$-0.408737\pi$
$727$	15.2502	0.565599	0.282800	+	0.959179i	$0.408737\pi$
$728$	0	0
$729$	−33.8759	−1.25466
$730$	4.42862	0.163911
$731$	−41.8863	−1.54922
$732$	−16.9253	−0.625577
$733$	1.47710	0.0545581	0.0272791	−	0.999628i	$-0.491316\pi$
$733$	1.47710	0.0545581	0.0272791	+	0.999628i	$0.491316\pi$
$734$	−24.2601	−0.895456
$735$	−38.0666	−1.40411
$736$	−32.2486	−1.18870
$737$	−1.27537	−0.0469790
$738$	−2.73086	−0.100524
$739$	31.5462	1.16045	0.580223	−	0.814457i	$-0.302965\pi$
$739$	31.5462	1.16045	0.580223	+	0.814457i	$0.302965\pi$
$740$	−18.7426	−0.688991
$741$	0	0
$742$	−31.1915	−1.14508
$743$	−22.0189	−0.807796	−0.403898	−	0.914804i	$-0.632345\pi$
$743$	−22.0189	−0.807796	−0.403898	+	0.914804i	$0.632345\pi$
$744$	66.9436	2.45427
$745$	−24.5719	−0.900245
$746$	−28.7363	−1.05211
$747$	−7.03535	−0.257410
$748$	8.17043	0.298741
$749$	−12.2710	−0.448373
$750$	11.7364	0.428552
$751$	31.5506	1.15130	0.575649	−	0.817697i	$-0.304749\pi$
$751$	31.5506	1.15130	0.575649	+	0.817697i	$0.304749\pi$
$752$	−3.83797	−0.139956
$753$	45.9572	1.67477
$754$	0	0
$755$	47.8431	1.74119
$756$	4.03087	0.146601
$757$	−15.4522	−0.561618	−0.280809	−	0.959764i	$-0.590603\pi$
$757$	−15.4522	−0.561618	−0.280809	+	0.959764i	$0.590603\pi$
$758$	11.0068	0.399785
$759$	15.0675	0.546914
$760$	30.2738	1.09815
$761$	15.1957	0.550842	0.275421	−	0.961324i	$-0.411183\pi$
$761$	15.1957	0.550842	0.275421	+	0.961324i	$0.411183\pi$
$762$	−20.3938	−0.738791
$763$	−31.8772	−1.15403
$764$	−23.2742	−0.842033
$765$	83.2478	3.00983
$766$	−12.1753	−0.439911
$767$	0	0
$768$	−42.5682	−1.53605
$769$	19.6669	0.709207	0.354603	−	0.935017i	$-0.384616\pi$
$769$	19.6669	0.709207	0.354603	+	0.935017i	$0.384616\pi$
$770$	−10.6529	−0.383903
$771$	−18.5935	−0.669630
$772$	12.6943	0.456878
$773$	4.04584	0.145519	0.0727594	−	0.997350i	$-0.476819\pi$
$773$	4.04584	0.145519	0.0727594	+	0.997350i	$0.476819\pi$
$774$	−18.4789	−0.664212
$775$	58.6630	2.10724
$776$	18.9960	0.681918
$777$	41.7604	1.49815
$778$	1.51423	0.0542877
$779$	−2.63626	−0.0944539
$780$	0	0
$781$	13.2250	0.473227
$782$	39.8273	1.42422
$783$	5.70647	0.203933
$784$	−1.95949	−0.0699819
$785$	−29.7768	−1.06278
$786$	−20.1977	−0.720430
$787$	9.62403	0.343060	0.171530	−	0.985179i	$-0.445129\pi$
$787$	9.62403	0.343060	0.171530	+	0.985179i	$0.445129\pi$
$788$	−16.9103	−0.602404
$789$	−59.6743	−2.12446
$790$	14.1039	0.501795
$791$	40.1020	1.42586
$792$	9.95588	0.353767
$793$	0	0
$794$	8.77047	0.311252
$795$	85.0668	3.01701
$796$	7.65543	0.271340
$797$	12.4277	0.440213	0.220106	−	0.975476i	$-0.429360\pi$
$797$	12.4277	0.440213	0.220106	+	0.975476i	$0.429360\pi$
$798$	−24.4215	−0.864513
$799$	−62.5667	−2.21345
$800$	−35.0780	−1.24020
$801$	−1.61228	−0.0569672
$802$	−8.98169	−0.317154
$803$	1.40595	0.0496150
$804$	3.66638	0.129303
$805$	68.1440	2.40176
$806$	0	0
$807$	−31.3329	−1.10297
$808$	7.72072	0.271614
$809$	−0.111775	−0.00392978	−0.00196489	−	0.999998i	$-0.500625\pi$
$809$	−0.111775	−0.00392978	−0.00196489	+	0.999998i	$0.500625\pi$
$810$	−23.8899	−0.839405
$811$	−3.40641	−0.119615	−0.0598076	−	0.998210i	$-0.519049\pi$
$811$	−3.40641	−0.119615	−0.0598076	+	0.998210i	$0.519049\pi$
$812$	20.8611	0.732082
$813$	54.9260	1.92634
$814$	4.53426	0.158926
$815$	−65.5854	−2.29736
$816$	8.05012	0.281811
$817$	−17.8388	−0.624101
$818$	−6.10260	−0.213372
$819$	0	0
$820$	3.30585	0.115445
$821$	−26.9560	−0.940770	−0.470385	−	0.882461i	$-0.655885\pi$
$821$	−26.9560	−0.940770	−0.470385	+	0.882461i	$0.655885\pi$
$822$	29.9721	1.04540
$823$	−47.1110	−1.64219	−0.821093	−	0.570795i	$-0.806635\pi$
$823$	−47.1110	−1.64219	−0.821093	+	0.570795i	$0.806635\pi$
$824$	4.12281	0.143625
$825$	16.3895	0.570608
$826$	23.2278	0.808198
$827$	2.81708	0.0979595	0.0489798	−	0.998800i	$-0.484403\pi$
$827$	2.81708	0.0979595	0.0489798	+	0.998800i	$0.484403\pi$
$828$	−23.0574	−0.801300
$829$	39.1854	1.36097	0.680483	−	0.732764i	$-0.261770\pi$
$829$	39.1854	1.36097	0.680483	+	0.732764i	$0.261770\pi$
$830$	−6.48999	−0.225271
$831$	−62.4541	−2.16651
$832$	0	0
$833$	−31.9437	−1.10679
$834$	−17.6485	−0.611117
$835$	49.2080	1.70291
$836$	3.47968	0.120347
$837$	9.51917	0.329030
$838$	23.9838	0.828507
$839$	−6.19239	−0.213785	−0.106893	−	0.994271i	$-0.534090\pi$
$839$	−6.19239	−0.213785	−0.106893	+	0.994271i	$0.534090\pi$
$840$	84.5857	2.91848
$841$	0.532928	0.0183768
$842$	−2.46799	−0.0850525
$843$	−79.3873	−2.73424
$844$	27.4363	0.944395
$845$	0	0
$846$	−27.6025	−0.948994
$847$	−3.38196	−0.116206
$848$	4.37885	0.150370
$849$	51.7202	1.77503
$850$	43.3217	1.48592
$851$	−29.0046	−0.994264
$852$	−38.0185	−1.30249
$853$	−34.7550	−1.18999	−0.594995	−	0.803729i	$-0.702846\pi$
$853$	−34.7550	−1.18999	−0.594995	+	0.803729i	$0.702846\pi$
$854$	18.5183	0.633682
$855$	35.4541	1.21251
$856$	10.5792	0.361588
$857$	37.6326	1.28551	0.642753	−	0.766073i	$-0.277792\pi$
$857$	37.6326	1.28551	0.642753	+	0.766073i	$0.277792\pi$
$858$	0	0
$859$	19.8890	0.678606	0.339303	−	0.940677i	$-0.389809\pi$
$859$	19.8890	0.678606	0.339303	+	0.940677i	$0.389809\pi$
$860$	22.3697	0.762800
$861$	−7.36578	−0.251025
$862$	−19.9809	−0.680553
$863$	14.1149	0.480478	0.240239	−	0.970714i	$-0.422774\pi$
$863$	14.1149	0.480478	0.240239	+	0.970714i	$0.422774\pi$
$864$	−5.69207	−0.193648
$865$	79.8108	2.71365
$866$	−8.25297	−0.280447
$867$	88.1774	2.99466
$868$	34.7991	1.18116
$869$	4.47756	0.151891
$870$	43.3547	1.46986
$871$	0	0
$872$	27.4822	0.930664
$873$	22.2466	0.752932
$874$	16.9619	0.573745
$875$	16.8509	0.569664
$876$	−4.04176	−0.136558
$877$	−54.6173	−1.84429	−0.922147	−	0.386839i	$-0.873567\pi$
$877$	−54.6173	−1.84429	−0.922147	+	0.386839i	$0.873567\pi$
$878$	−30.0116	−1.01284
$879$	27.8133	0.938120
$880$	1.49552	0.0504138
$881$	16.5871	0.558835	0.279417	−	0.960170i	$-0.409859\pi$
$881$	16.5871	0.558835	0.279417	+	0.960170i	$0.409859\pi$
$882$	−14.0926	−0.474523
$883$	8.16157	0.274659	0.137329	−	0.990525i	$-0.456148\pi$
$883$	8.16157	0.274659	0.137329	+	0.990525i	$0.456148\pi$
$884$	0	0
$885$	−63.3478	−2.12941
$886$	−19.8900	−0.668216
$887$	28.9794	0.973033	0.486516	−	0.873672i	$-0.338267\pi$
$887$	28.9794	0.973033	0.486516	+	0.873672i	$0.338267\pi$
$888$	−36.0028	−1.20817
$889$	−29.2811	−0.982058
$890$	−1.48730	−0.0498545
$891$	−7.58430	−0.254084
$892$	−19.7004	−0.659617
$893$	−26.6463	−0.891685
$894$	−17.0890	−0.571541
$895$	−30.5239	−1.02030
$896$	−18.0308	−0.602366
$897$	0	0
$898$	15.5599	0.519239
$899$	49.2649	1.64308
$900$	−25.0804	−0.836015
$901$	71.3842	2.37815
$902$	−0.799761	−0.0266291
$903$	−49.8420	−1.65864
$904$	−34.5729	−1.14988
$905$	−36.0846	−1.19949
$906$	33.2733	1.10543
$907$	40.7378	1.35268	0.676339	−	0.736591i	$-0.263566\pi$
$907$	40.7378	1.35268	0.676339	+	0.736591i	$0.263566\pi$
$908$	12.1803	0.404218
$909$	9.04186	0.299900
$910$	0	0
$911$	31.8194	1.05422	0.527111	−	0.849796i	$-0.323275\pi$
$911$	31.8194	1.05422	0.527111	+	0.849796i	$0.323275\pi$
$912$	3.42844	0.113527
$913$	−2.06037	−0.0681884
$914$	9.10393	0.301131
$915$	−50.5038	−1.66960
$916$	−25.5321	−0.843603
$917$	−28.9996	−0.957651
$918$	7.02975	0.232016
$919$	−31.5844	−1.04187	−0.520937	−	0.853595i	$-0.674417\pi$
$919$	−31.5844	−1.04187	−0.520937	+	0.853595i	$0.674417\pi$
$920$	−58.7487	−1.93689
$921$	39.4686	1.30054
$922$	17.4396	0.574341
$923$	0	0
$924$	9.72230	0.319840
$925$	−31.5494	−1.03734
$926$	−21.6286	−0.710759
$927$	4.82829	0.158582
$928$	−29.4584	−0.967018
$929$	−28.6916	−0.941340	−0.470670	−	0.882309i	$-0.655988\pi$
$929$	−28.6916	−0.941340	−0.470670	+	0.882309i	$0.655988\pi$
$930$	72.3215	2.37152
$931$	−13.6044	−0.445867
$932$	8.42126	0.275848
$933$	21.2108	0.694410
$934$	−0.0918824	−0.00300648
$935$	24.3800	0.797310
$936$	0	0
$937$	13.3518	0.436184	0.218092	−	0.975928i	$-0.430017\pi$
$937$	13.3518	0.436184	0.218092	+	0.975928i	$0.430017\pi$
$938$	−4.01145	−0.130979
$939$	40.3612	1.31714
$940$	33.4143	1.08985
$941$	−26.2375	−0.855320	−0.427660	−	0.903940i	$-0.640662\pi$
$941$	−26.2375	−0.855320	−0.427660	+	0.903940i	$0.640662\pi$
$942$	−20.7088	−0.674730
$943$	5.11588	0.166596
$944$	−3.26085	−0.106132
$945$	12.0278	0.391265
$946$	−5.41174	−0.175951
$947$	−18.0926	−0.587929	−0.293965	−	0.955816i	$-0.594975\pi$
$947$	−18.0926	−0.587929	−0.293965	+	0.955816i	$0.594975\pi$
$948$	−12.8719	−0.418059
$949$	0	0
$950$	18.4501	0.598601
$951$	−38.2075	−1.23896
$952$	70.9804	2.30049
$953$	52.7655	1.70924	0.854622	−	0.519251i	$-0.173789\pi$
$953$	52.7655	1.70924	0.854622	+	0.519251i	$0.173789\pi$
$954$	31.4925	1.01961
$955$	−69.4486	−2.24730
$956$	2.01176	0.0650651
$957$	13.7638	0.444920
$958$	21.8006	0.704346
$959$	43.0335	1.38962
$960$	−50.8207	−1.64023
$961$	51.1804	1.65098
$962$	0	0
$963$	12.3894	0.399244
$964$	12.9622	0.417484
$965$	37.8788	1.21936
$966$	47.3919	1.52481
$967$	40.4348	1.30030	0.650148	−	0.759808i	$-0.274707\pi$
$967$	40.4348	1.30030	0.650148	+	0.759808i	$0.274707\pi$
$968$	2.91568	0.0937135
$969$	55.8906	1.79546
$970$	20.5221	0.658925
$971$	46.5419	1.49360	0.746801	−	0.665048i	$-0.231589\pi$
$971$	46.5419	1.49360	0.746801	+	0.665048i	$0.231589\pi$
$972$	25.3786	0.814019
$973$	−25.3394	−0.812344
$974$	−1.47859	−0.0473771
$975$	0	0
$976$	−2.59971	−0.0832146
$977$	−42.0365	−1.34487	−0.672433	−	0.740158i	$-0.734751\pi$
$977$	−42.0365	−1.34487	−0.672433	+	0.740158i	$0.734751\pi$
$978$	−45.6125	−1.45853
$979$	−0.472173	−0.0150907
$980$	17.0598	0.544956
$981$	32.1848	1.02758
$982$	−3.11528	−0.0994124
$983$	15.2856	0.487534	0.243767	−	0.969834i	$-0.421617\pi$
$983$	15.2856	0.487534	0.243767	+	0.969834i	$0.421617\pi$
$984$	6.35023	0.202438
$985$	−50.4591	−1.60776
$986$	36.3813	1.15862
$987$	−74.4504	−2.36978
$988$	0	0
$989$	34.6176	1.10078
$990$	10.7557	0.341838
$991$	23.5932	0.749463	0.374732	−	0.927133i	$-0.377735\pi$
$991$	23.5932	0.749463	0.374732	+	0.927133i	$0.377735\pi$
$992$	−49.1405	−1.56021
$993$	2.67799	0.0849835
$994$	41.5967	1.31937
$995$	22.8432	0.724179
$996$	5.92305	0.187679
$997$	52.3098	1.65667	0.828334	−	0.560235i	$-0.189289\pi$
$997$	52.3098	1.65667	0.828334	+	0.560235i	$0.189289\pi$
$998$	−31.2293	−0.988546
$999$	−5.11948	−0.161973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.8	yes	21
13.12	even	2		1859.2.a.s.1.14	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.14	✓	21	13.12	even	2
1859.2.a.t.1.8	yes	21	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-0.930026 q^{2} +2.53271 q^{3} -1.13505 q^{4} -3.38691 q^{5} -2.35548 q^{6} -3.38196 q^{7} +2.91568 q^{8} +3.41460 q^{9} +O(q^{10})\)	\(q-0.930026 q^{2} +2.53271 q^{3} -1.13505 q^{4} -3.38691 q^{5} -2.35548 q^{6} -3.38196 q^{7} +2.91568 q^{8} +3.41460 q^{9} +3.14991 q^{10} +1.00000 q^{11} -2.87475 q^{12} +3.14532 q^{14} -8.57804 q^{15} -0.441558 q^{16} -7.19830 q^{17} -3.17567 q^{18} -3.06566 q^{19} +3.84431 q^{20} -8.56552 q^{21} -0.930026 q^{22} +5.94916 q^{23} +7.38456 q^{24} +6.47113 q^{25} +1.05006 q^{27} +3.83870 q^{28} +5.43442 q^{29} +7.97780 q^{30} +9.06534 q^{31} -5.42070 q^{32} +2.53271 q^{33} +6.69461 q^{34} +11.4544 q^{35} -3.87574 q^{36} -4.87541 q^{37} +2.85114 q^{38} -9.87513 q^{40} +0.859934 q^{41} +7.96616 q^{42} +5.81891 q^{43} -1.13505 q^{44} -11.5649 q^{45} -5.53287 q^{46} +8.69187 q^{47} -1.11834 q^{48} +4.43768 q^{49} -6.01832 q^{50} -18.2312 q^{51} -9.91682 q^{53} -0.976585 q^{54} -3.38691 q^{55} -9.86073 q^{56} -7.76441 q^{57} -5.05416 q^{58} +7.38488 q^{59} +9.73651 q^{60} +5.88757 q^{61} -8.43101 q^{62} -11.5481 q^{63} +5.92451 q^{64} -2.35548 q^{66} -1.27537 q^{67} +8.17043 q^{68} +15.0675 q^{69} -10.6529 q^{70} +13.2250 q^{71} +9.95588 q^{72} +1.40595 q^{73} +4.53426 q^{74} +16.3895 q^{75} +3.47968 q^{76} -3.38196 q^{77} +4.47756 q^{79} +1.49552 q^{80} -7.58430 q^{81} -0.799761 q^{82} -2.06037 q^{83} +9.72230 q^{84} +24.3800 q^{85} -5.41174 q^{86} +13.7638 q^{87} +2.91568 q^{88} -0.472173 q^{89} +10.7557 q^{90} -6.75259 q^{92} +22.9599 q^{93} -8.08367 q^{94} +10.3831 q^{95} -13.7290 q^{96} +6.51513 q^{97} -4.12716 q^{98} +3.41460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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