LMFDB - Embedded newform 8018.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.34431 q^{3} +1.00000 q^{4} -3.91124 q^{5} +3.34431 q^{6} +0.821669 q^{7} -1.00000 q^{8} +8.18441 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.34431 q^{3} +1.00000 q^{4} -3.91124 q^{5} +3.34431 q^{6} +0.821669 q^{7} -1.00000 q^{8} +8.18441 q^{9} +3.91124 q^{10} -3.67470 q^{11} -3.34431 q^{12} -6.21730 q^{13} -0.821669 q^{14} +13.0804 q^{15} +1.00000 q^{16} +4.49045 q^{17} -8.18441 q^{18} +1.00000 q^{19} -3.91124 q^{20} -2.74792 q^{21} +3.67470 q^{22} +3.64795 q^{23} +3.34431 q^{24} +10.2978 q^{25} +6.21730 q^{26} -17.3383 q^{27} +0.821669 q^{28} +1.42317 q^{29} -13.0804 q^{30} -5.31868 q^{31} -1.00000 q^{32} +12.2893 q^{33} -4.49045 q^{34} -3.21374 q^{35} +8.18441 q^{36} +2.04897 q^{37} -1.00000 q^{38} +20.7926 q^{39} +3.91124 q^{40} -9.69326 q^{41} +2.74792 q^{42} +11.2289 q^{43} -3.67470 q^{44} -32.0112 q^{45} -3.64795 q^{46} +1.00229 q^{47} -3.34431 q^{48} -6.32486 q^{49} -10.2978 q^{50} -15.0174 q^{51} -6.21730 q^{52} +0.0200596 q^{53} +17.3383 q^{54} +14.3726 q^{55} -0.821669 q^{56} -3.34431 q^{57} -1.42317 q^{58} +1.47502 q^{59} +13.0804 q^{60} +13.9089 q^{61} +5.31868 q^{62} +6.72488 q^{63} +1.00000 q^{64} +24.3173 q^{65} -12.2893 q^{66} -5.54658 q^{67} +4.49045 q^{68} -12.1999 q^{69} +3.21374 q^{70} +13.3569 q^{71} -8.18441 q^{72} +15.2017 q^{73} -2.04897 q^{74} -34.4390 q^{75} +1.00000 q^{76} -3.01939 q^{77} -20.7926 q^{78} -4.93964 q^{79} -3.91124 q^{80} +33.4314 q^{81} +9.69326 q^{82} -9.16012 q^{83} -2.74792 q^{84} -17.5632 q^{85} -11.2289 q^{86} -4.75951 q^{87} +3.67470 q^{88} -12.1644 q^{89} +32.0112 q^{90} -5.10856 q^{91} +3.64795 q^{92} +17.7873 q^{93} -1.00229 q^{94} -3.91124 q^{95} +3.34431 q^{96} -16.3177 q^{97} +6.32486 q^{98} -30.0753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.34431	−1.93084	−0.965419	−	0.260702i	$-0.916046\pi$
$3$	−3.34431	−1.93084	−0.965419	+	0.260702i	$0.916046\pi$
$4$	1.00000	0.500000
$5$	−3.91124	−1.74916	−0.874579	−	0.484883i	$-0.838862\pi$
$5$	−3.91124	−1.74916	−0.874579	+	0.484883i	$0.838862\pi$
$6$	3.34431	1.36531
$7$	0.821669	0.310562	0.155281	−	0.987870i	$-0.450372\pi$
$7$	0.821669	0.310562	0.155281	+	0.987870i	$0.450372\pi$
$8$	−1.00000	−0.353553
$9$	8.18441	2.72814
$10$	3.91124	1.23684
$11$	−3.67470	−1.10796	−0.553982	−	0.832529i	$-0.686892\pi$
$11$	−3.67470	−1.10796	−0.553982	+	0.832529i	$0.686892\pi$
$12$	−3.34431	−0.965419
$13$	−6.21730	−1.72437	−0.862184	−	0.506595i	$-0.830904\pi$
$13$	−6.21730	−1.72437	−0.862184	+	0.506595i	$0.830904\pi$
$14$	−0.821669	−0.219600
$15$	13.0804	3.37734
$16$	1.00000	0.250000
$17$	4.49045	1.08909	0.544546	−	0.838731i	$-0.316702\pi$
$17$	4.49045	1.08909	0.544546	+	0.838731i	$0.316702\pi$
$18$	−8.18441	−1.92909
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.91124	−0.874579
$21$	−2.74792	−0.599645
$22$	3.67470	0.783448
$23$	3.64795	0.760651	0.380325	−	0.924853i	$-0.375812\pi$
$23$	3.64795	0.760651	0.380325	+	0.924853i	$0.375812\pi$
$24$	3.34431	0.682655
$25$	10.2978	2.05956
$26$	6.21730	1.21931
$27$	−17.3383	−3.33676
$28$	0.821669	0.155281
$29$	1.42317	0.264276	0.132138	−	0.991231i	$-0.457816\pi$
$29$	1.42317	0.264276	0.132138	+	0.991231i	$0.457816\pi$
$30$	−13.0804	−2.38814
$31$	−5.31868	−0.955262	−0.477631	−	0.878560i	$-0.658504\pi$
$31$	−5.31868	−0.955262	−0.477631	+	0.878560i	$0.658504\pi$
$32$	−1.00000	−0.176777
$33$	12.2893	2.13930
$34$	−4.49045	−0.770105
$35$	−3.21374	−0.543222
$36$	8.18441	1.36407
$37$	2.04897	0.336849	0.168424	−	0.985715i	$-0.446132\pi$
$37$	2.04897	0.336849	0.168424	+	0.985715i	$0.446132\pi$
$38$	−1.00000	−0.162221
$39$	20.7926	3.32948
$40$	3.91124	0.618421
$41$	−9.69326	−1.51383	−0.756916	−	0.653512i	$-0.773295\pi$
$41$	−9.69326	−1.51383	−0.756916	+	0.653512i	$0.773295\pi$
$42$	2.74792	0.424013
$43$	11.2289	1.71239	0.856196	−	0.516652i	$-0.172822\pi$
$43$	11.2289	1.71239	0.856196	+	0.516652i	$0.172822\pi$
$44$	−3.67470	−0.553982
$45$	−32.0112	−4.77195
$46$	−3.64795	−0.537861
$47$	1.00229	0.146200	0.0730998	−	0.997325i	$-0.476711\pi$
$47$	1.00229	0.146200	0.0730998	+	0.997325i	$0.476711\pi$
$48$	−3.34431	−0.482710
$49$	−6.32486	−0.903551
$50$	−10.2978	−1.45633
$51$	−15.0174	−2.10286
$52$	−6.21730	−0.862184
$53$	0.0200596	0.00275540	0.00137770	−	0.999999i	$-0.499561\pi$
$53$	0.0200596	0.00275540	0.00137770	+	0.999999i	$0.499561\pi$
$54$	17.3383	2.35944
$55$	14.3726	1.93800
$56$	−0.821669	−0.109800
$57$	−3.34431	−0.442965
$58$	−1.42317	−0.186871
$59$	1.47502	0.192032	0.0960158	−	0.995380i	$-0.469390\pi$
$59$	1.47502	0.192032	0.0960158	+	0.995380i	$0.469390\pi$
$60$	13.0804	1.68867
$61$	13.9089	1.78086	0.890428	−	0.455124i	$-0.150405\pi$
$61$	13.9089	1.78086	0.890428	+	0.455124i	$0.150405\pi$
$62$	5.31868	0.675473
$63$	6.72488	0.847256
$64$	1.00000	0.125000
$65$	24.3173	3.01619
$66$	−12.2893	−1.51271
$67$	−5.54658	−0.677622	−0.338811	−	0.940854i	$-0.610025\pi$
$67$	−5.54658	−0.677622	−0.338811	+	0.940854i	$0.610025\pi$
$68$	4.49045	0.544546
$69$	−12.1999	−1.46869
$70$	3.21374	0.384116
$71$	13.3569	1.58517	0.792586	−	0.609760i	$-0.208734\pi$
$71$	13.3569	1.58517	0.792586	+	0.609760i	$0.208734\pi$
$72$	−8.18441	−0.964543
$73$	15.2017	1.77922	0.889612	−	0.456718i	$-0.150975\pi$
$73$	15.2017	1.77922	0.889612	+	0.456718i	$0.150975\pi$
$74$	−2.04897	−0.238188
$75$	−34.4390	−3.97667
$76$	1.00000	0.114708
$77$	−3.01939	−0.344091
$78$	−20.7926	−2.35430
$79$	−4.93964	−0.555752	−0.277876	−	0.960617i	$-0.589631\pi$
$79$	−4.93964	−0.555752	−0.277876	+	0.960617i	$0.589631\pi$
$80$	−3.91124	−0.437290
$81$	33.4314	3.71460
$82$	9.69326	1.07044
$83$	−9.16012	−1.00545	−0.502727	−	0.864445i	$-0.667670\pi$
$83$	−9.16012	−1.00545	−0.502727	+	0.864445i	$0.667670\pi$
$84$	−2.74792	−0.299822
$85$	−17.5632	−1.90500
$86$	−11.2289	−1.21084
$87$	−4.75951	−0.510273
$88$	3.67470	0.391724
$89$	−12.1644	−1.28943	−0.644713	−	0.764424i	$-0.723023\pi$
$89$	−12.1644	−1.28943	−0.644713	+	0.764424i	$0.723023\pi$
$90$	32.0112	3.37428
$91$	−5.10856	−0.535523
$92$	3.64795	0.380325
$93$	17.7873	1.84446
$94$	−1.00229	−0.103379
$95$	−3.91124	−0.401285
$96$	3.34431	0.341327
$97$	−16.3177	−1.65682	−0.828408	−	0.560126i	$-0.810753\pi$
$97$	−16.3177	−1.65682	−0.828408	+	0.560126i	$0.810753\pi$
$98$	6.32486	0.638907
$99$	−30.0753	−3.02268
$100$	10.2978	1.02978
$101$	−16.9663	−1.68821	−0.844105	−	0.536177i	$-0.819868\pi$
$101$	−16.9663	−1.68821	−0.844105	+	0.536177i	$0.819868\pi$
$102$	15.0174	1.48695
$103$	18.8518	1.85752	0.928760	−	0.370681i	$-0.120876\pi$
$103$	18.8518	1.85752	0.928760	+	0.370681i	$0.120876\pi$
$104$	6.21730	0.609656
$105$	10.7478	1.04887
$106$	−0.0200596	−0.00194836
$107$	−12.1783	−1.17732	−0.588661	−	0.808380i	$-0.700345\pi$
$107$	−12.1783	−1.17732	−0.588661	+	0.808380i	$0.700345\pi$
$108$	−17.3383	−1.66838
$109$	−1.04711	−0.100295	−0.0501474	−	0.998742i	$-0.515969\pi$
$109$	−1.04711	−0.100295	−0.0501474	+	0.998742i	$0.515969\pi$
$110$	−14.3726	−1.37038
$111$	−6.85240	−0.650401
$112$	0.821669	0.0776404
$113$	−4.88870	−0.459890	−0.229945	−	0.973204i	$-0.573855\pi$
$113$	−4.88870	−0.459890	−0.229945	+	0.973204i	$0.573855\pi$
$114$	3.34431	0.313223
$115$	−14.2680	−1.33050
$116$	1.42317	0.132138
$117$	−50.8849	−4.70431
$118$	−1.47502	−0.135787
$119$	3.68966	0.338231
$120$	−13.0804	−1.19407
$121$	2.50341	0.227582
$122$	−13.9089	−1.25926
$123$	32.4173	2.92297
$124$	−5.31868	−0.477631
$125$	−20.7209	−1.85333
$126$	−6.72488	−0.599100
$127$	−9.54343	−0.846842	−0.423421	−	0.905933i	$-0.639171\pi$
$127$	−9.54343	−0.846842	−0.423421	+	0.905933i	$0.639171\pi$
$128$	−1.00000	−0.0883883
$129$	−37.5529	−3.30635
$130$	−24.3173	−2.13277
$131$	−21.6743	−1.89369	−0.946847	−	0.321685i	$-0.895751\pi$
$131$	−21.6743	−1.89369	−0.946847	+	0.321685i	$0.895751\pi$
$132$	12.2893	1.06965
$133$	0.821669	0.0712478
$134$	5.54658	0.479151
$135$	67.8142	5.83652
$136$	−4.49045	−0.385052
$137$	1.28733	0.109984	0.0549919	−	0.998487i	$-0.482487\pi$
$137$	1.28733	0.109984	0.0549919	+	0.998487i	$0.482487\pi$
$138$	12.1999	1.03852
$139$	2.37875	0.201763	0.100882	−	0.994898i	$-0.467834\pi$
$139$	2.37875	0.201763	0.100882	+	0.994898i	$0.467834\pi$
$140$	−3.21374	−0.271611
$141$	−3.35198	−0.282288
$142$	−13.3569	−1.12089
$143$	22.8467	1.91054
$144$	8.18441	0.682035
$145$	−5.56635	−0.462260
$146$	−15.2017	−1.25810
$147$	21.1523	1.74461
$148$	2.04897	0.168424
$149$	−9.59171	−0.785784	−0.392892	−	0.919585i	$-0.628525\pi$
$149$	−9.59171	−0.785784	−0.392892	+	0.919585i	$0.628525\pi$
$150$	34.4390	2.81193
$151$	−12.2701	−0.998523	−0.499261	−	0.866451i	$-0.666395\pi$
$151$	−12.2701	−0.998523	−0.499261	+	0.866451i	$0.666395\pi$
$152$	−1.00000	−0.0811107
$153$	36.7517	2.97120
$154$	3.01939	0.243309
$155$	20.8026	1.67091
$156$	20.7926	1.66474
$157$	−2.99872	−0.239324	−0.119662	−	0.992815i	$-0.538181\pi$
$157$	−2.99872	−0.239324	−0.119662	+	0.992815i	$0.538181\pi$
$158$	4.93964	0.392976
$159$	−0.0670855	−0.00532022
$160$	3.91124	0.309210
$161$	2.99741	0.236229
$162$	−33.4314	−2.62662
$163$	18.1065	1.41821	0.709104	−	0.705103i	$-0.249099\pi$
$163$	18.1065	1.41821	0.709104	+	0.705103i	$0.249099\pi$
$164$	−9.69326	−0.756916
$165$	−48.0665	−3.74197
$166$	9.16012	0.710963
$167$	5.39236	0.417273	0.208637	−	0.977993i	$-0.433097\pi$
$167$	5.39236	0.417273	0.208637	+	0.977993i	$0.433097\pi$
$168$	2.74792	0.212006
$169$	25.6548	1.97345
$170$	17.5632	1.34704
$171$	8.18441	0.625878
$172$	11.2289	0.856196
$173$	8.08670	0.614821	0.307410	−	0.951577i	$-0.400538\pi$
$173$	8.08670	0.614821	0.307410	+	0.951577i	$0.400538\pi$
$174$	4.75951	0.360818
$175$	8.46137	0.639619
$176$	−3.67470	−0.276991
$177$	−4.93293	−0.370782
$178$	12.1644	0.911762
$179$	11.4160	0.853270	0.426635	−	0.904424i	$-0.359699\pi$
$179$	11.4160	0.853270	0.426635	+	0.904424i	$0.359699\pi$
$180$	−32.0112	−2.38597
$181$	8.09459	0.601666	0.300833	−	0.953677i	$-0.402735\pi$
$181$	8.09459	0.601666	0.300833	+	0.953677i	$0.402735\pi$
$182$	5.10856	0.378672
$183$	−46.5158	−3.43855
$184$	−3.64795	−0.268931
$185$	−8.01401	−0.589202
$186$	−17.7873	−1.30423
$187$	−16.5010	−1.20667
$188$	1.00229	0.0730998
$189$	−14.2463	−1.03627
$190$	3.91124	0.283751
$191$	−0.00978378	−0.000707929 0	−0.000353965	−	1.00000i	$-0.500113\pi$
$191$	−0.00978378	−0.000707929 0	−0.000353965		1.00000i	$0.500113\pi$
$192$	−3.34431	−0.241355
$193$	−11.0591	−0.796053	−0.398027	−	0.917374i	$-0.630305\pi$
$193$	−11.0591	−0.796053	−0.398027	+	0.917374i	$0.630305\pi$
$194$	16.3177	1.17155
$195$	−81.3247	−5.82378
$196$	−6.32486	−0.451776
$197$	−11.7258	−0.835431	−0.417716	−	0.908578i	$-0.637169\pi$
$197$	−11.7258	−0.835431	−0.417716	+	0.908578i	$0.637169\pi$
$198$	30.0753	2.13736
$199$	−5.79075	−0.410496	−0.205248	−	0.978710i	$-0.565800\pi$
$199$	−5.79075	−0.410496	−0.205248	+	0.978710i	$0.565800\pi$
$200$	−10.2978	−0.728163
$201$	18.5495	1.30838
$202$	16.9663	1.19375
$203$	1.16937	0.0820739
$204$	−15.0174	−1.05143
$205$	37.9126	2.64793
$206$	−18.8518	−1.31347
$207$	29.8564	2.07516
$208$	−6.21730	−0.431092
$209$	−3.67470	−0.254184
$210$	−10.7478	−0.741666
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	0.0200596	0.00137770
$213$	−44.6696	−3.06071
$214$	12.1783	0.832492
$215$	−43.9189	−2.99524
$216$	17.3383	1.17972
$217$	−4.37019	−0.296668
$218$	1.04711	0.0709192
$219$	−50.8392	−3.43539
$220$	14.3726	0.969002
$221$	−27.9184	−1.87800
$222$	6.85240	0.459903
$223$	−17.9138	−1.19959	−0.599797	−	0.800152i	$-0.704752\pi$
$223$	−17.9138	−1.19959	−0.599797	+	0.800152i	$0.704752\pi$
$224$	−0.821669	−0.0549001
$225$	84.2813	5.61875
$226$	4.88870	0.325191
$227$	4.94577	0.328262	0.164131	−	0.986439i	$-0.447518\pi$
$227$	4.94577	0.328262	0.164131	+	0.986439i	$0.447518\pi$
$228$	−3.34431	−0.221482
$229$	−15.1413	−1.00056	−0.500282	−	0.865862i	$-0.666770\pi$
$229$	−15.1413	−1.00056	−0.500282	+	0.865862i	$0.666770\pi$
$230$	14.2680	0.940805
$231$	10.0978	0.664384
$232$	−1.42317	−0.0934355
$233$	−12.9989	−0.851586	−0.425793	−	0.904821i	$-0.640005\pi$
$233$	−12.9989	−0.851586	−0.425793	+	0.904821i	$0.640005\pi$
$234$	50.8849	3.32645
$235$	−3.92021	−0.255726
$236$	1.47502	0.0960158
$237$	16.5197	1.07307
$238$	−3.68966	−0.239165
$239$	−14.8289	−0.959204	−0.479602	−	0.877486i	$-0.659219\pi$
$239$	−14.8289	−0.959204	−0.479602	+	0.877486i	$0.659219\pi$
$240$	13.0804	0.844336
$241$	−3.99153	−0.257117	−0.128559	−	0.991702i	$-0.541035\pi$
$241$	−3.99153	−0.257117	−0.128559	+	0.991702i	$0.541035\pi$
$242$	−2.50341	−0.160925
$243$	−59.7901	−3.83554
$244$	13.9089	0.890428
$245$	24.7380	1.58045
$246$	−32.4173	−2.06685
$247$	−6.21730	−0.395597
$248$	5.31868	0.337736
$249$	30.6343	1.94137
$250$	20.7209	1.31050
$251$	−15.1663	−0.957290	−0.478645	−	0.878009i	$-0.658872\pi$
$251$	−15.1663	−0.957290	−0.478645	+	0.878009i	$0.658872\pi$
$252$	6.72488	0.423628
$253$	−13.4051	−0.842773
$254$	9.54343	0.598808
$255$	58.7368	3.67824
$256$	1.00000	0.0625000
$257$	−4.30156	−0.268324	−0.134162	−	0.990959i	$-0.542834\pi$
$257$	−4.30156	−0.268324	−0.134162	+	0.990959i	$0.542834\pi$
$258$	37.5529	2.33794
$259$	1.68358	0.104612
$260$	24.3173	1.50810
$261$	11.6478	0.720980
$262$	21.6743	1.33904
$263$	−21.8207	−1.34552	−0.672759	−	0.739861i	$-0.734891\pi$
$263$	−21.8207	−1.34552	−0.672759	+	0.739861i	$0.734891\pi$
$264$	−12.2893	−0.756356
$265$	−0.0784578	−0.00481962
$266$	−0.821669	−0.0503798
$267$	40.6816	2.48968
$268$	−5.54658	−0.338811
$269$	21.8252	1.33071	0.665353	−	0.746528i	$-0.268281\pi$
$269$	21.8252	1.33071	0.665353	+	0.746528i	$0.268281\pi$
$270$	−67.8142	−4.12704
$271$	−15.3153	−0.930341	−0.465170	−	0.885221i	$-0.654007\pi$
$271$	−15.3153	−0.930341	−0.465170	+	0.885221i	$0.654007\pi$
$272$	4.49045	0.272273
$273$	17.0846	1.03401
$274$	−1.28733	−0.0777702
$275$	−37.8412	−2.28191
$276$	−12.1999	−0.734347
$277$	−26.0986	−1.56811	−0.784056	−	0.620691i	$-0.786852\pi$
$277$	−26.0986	−1.56811	−0.784056	+	0.620691i	$0.786852\pi$
$278$	−2.37875	−0.142668
$279$	−43.5303	−2.60609
$280$	3.21374	0.192058
$281$	−22.3378	−1.33256	−0.666280	−	0.745702i	$-0.732114\pi$
$281$	−22.3378	−1.33256	−0.666280	+	0.745702i	$0.732114\pi$
$282$	3.35198	0.199608
$283$	−1.51340	−0.0899626	−0.0449813	−	0.998988i	$-0.514323\pi$
$283$	−1.51340	−0.0899626	−0.0449813	+	0.998988i	$0.514323\pi$
$284$	13.3569	0.792586
$285$	13.0804	0.774816
$286$	−22.8467	−1.35095
$287$	−7.96465	−0.470139
$288$	−8.18441	−0.482271
$289$	3.16410	0.186123
$290$	5.56635	0.326867
$291$	54.5716	3.19904
$292$	15.2017	0.889612
$293$	−15.1027	−0.882307	−0.441154	−	0.897432i	$-0.645431\pi$
$293$	−15.1027	−0.882307	−0.441154	+	0.897432i	$0.645431\pi$
$294$	−21.1523	−1.23363
$295$	−5.76916	−0.335894
$296$	−2.04897	−0.119094
$297$	63.7130	3.69700
$298$	9.59171	0.555633
$299$	−22.6804	−1.31164
$300$	−34.4390	−1.98834
$301$	9.22644	0.531803
$302$	12.2701	0.706062
$303$	56.7406	3.25966
$304$	1.00000	0.0573539
$305$	−54.4011	−3.11500
$306$	−36.7517	−2.10095
$307$	11.7946	0.673151	0.336576	−	0.941656i	$-0.390731\pi$
$307$	11.7946	0.673151	0.336576	+	0.941656i	$0.390731\pi$
$308$	−3.01939	−0.172046
$309$	−63.0462	−3.58657
$310$	−20.8026	−1.18151
$311$	−0.884177	−0.0501371	−0.0250685	−	0.999686i	$-0.507980\pi$
$311$	−0.884177	−0.0501371	−0.0250685	+	0.999686i	$0.507980\pi$
$312$	−20.7926	−1.17715
$313$	7.00591	0.395997	0.197999	−	0.980202i	$-0.436556\pi$
$313$	7.00591	0.395997	0.197999	+	0.980202i	$0.436556\pi$
$314$	2.99872	0.169227
$315$	−26.3026	−1.48198
$316$	−4.93964	−0.277876
$317$	33.4825	1.88056	0.940281	−	0.340398i	$-0.110562\pi$
$317$	33.4825	1.88056	0.940281	+	0.340398i	$0.110562\pi$
$318$	0.0670855	0.00376197
$319$	−5.22971	−0.292808
$320$	−3.91124	−0.218645
$321$	40.7281	2.27322
$322$	−2.99741	−0.167039
$323$	4.49045	0.249855
$324$	33.4314	1.85730
$325$	−64.0244	−3.55143
$326$	−18.1065	−1.00283
$327$	3.50186	0.193653
$328$	9.69326	0.535221
$329$	0.823554	0.0454040
$330$	48.0665	2.64597
$331$	16.7888	0.922795	0.461398	−	0.887194i	$-0.347348\pi$
$331$	16.7888	0.922795	0.461398	+	0.887194i	$0.347348\pi$
$332$	−9.16012	−0.502727
$333$	16.7696	0.918970
$334$	−5.39236	−0.295057
$335$	21.6940	1.18527
$336$	−2.74792	−0.149911
$337$	−13.2611	−0.722378	−0.361189	−	0.932493i	$-0.617629\pi$
$337$	−13.2611	−0.722378	−0.361189	+	0.932493i	$0.617629\pi$
$338$	−25.6548	−1.39544
$339$	16.3493	0.887973
$340$	−17.5632	−0.952498
$341$	19.5445	1.05840
$342$	−8.18441	−0.442562
$343$	−10.9486	−0.591170
$344$	−11.2289	−0.605422
$345$	47.7167	2.56898
$346$	−8.08670	−0.434744
$347$	21.6482	1.16214	0.581069	−	0.813854i	$-0.302635\pi$
$347$	21.6482	1.16214	0.581069	+	0.813854i	$0.302635\pi$
$348$	−4.75951	−0.255137
$349$	−23.3722	−1.25109	−0.625543	−	0.780190i	$-0.715123\pi$
$349$	−23.3722	−1.25109	−0.625543	+	0.780190i	$0.715123\pi$
$350$	−8.46137	−0.452279
$351$	107.797	5.75380
$352$	3.67470	0.195862
$353$	5.28848	0.281477	0.140739	−	0.990047i	$-0.455052\pi$
$353$	5.28848	0.281477	0.140739	+	0.990047i	$0.455052\pi$
$354$	4.93293	0.262182
$355$	−52.2420	−2.77272
$356$	−12.1644	−0.644713
$357$	−12.3394	−0.653069
$358$	−11.4160	−0.603353
$359$	35.0717	1.85102	0.925508	−	0.378729i	$-0.123639\pi$
$359$	35.0717	1.85102	0.925508	+	0.378729i	$0.123639\pi$
$360$	32.0112	1.68714
$361$	1.00000	0.0526316
$362$	−8.09459	−0.425442
$363$	−8.37217	−0.439425
$364$	−5.10856	−0.267761
$365$	−59.4574	−3.11214
$366$	46.5158	2.43142
$367$	21.5823	1.12659	0.563294	−	0.826257i	$-0.309534\pi$
$367$	21.5823	1.12659	0.563294	+	0.826257i	$0.309534\pi$
$368$	3.64795	0.190163
$369$	−79.3336	−4.12994
$370$	8.01401	0.416629
$371$	0.0164823	0.000855721 0
$372$	17.7873	0.922229
$373$	27.2425	1.41056	0.705281	−	0.708928i	$-0.250821\pi$
$373$	27.2425	1.41056	0.705281	+	0.708928i	$0.250821\pi$
$374$	16.5010	0.853248
$375$	69.2970	3.57848
$376$	−1.00229	−0.0516894
$377$	−8.84826	−0.455708
$378$	14.2463	0.732753
$379$	15.4569	0.793969	0.396985	−	0.917825i	$-0.370057\pi$
$379$	15.4569	0.793969	0.396985	+	0.917825i	$0.370057\pi$
$380$	−3.91124	−0.200642
$381$	31.9162	1.63512
$382$	0.00978378	0.000500582 0
$383$	−11.4850	−0.586858	−0.293429	−	0.955981i	$-0.594796\pi$
$383$	−11.4850	−0.586858	−0.293429	+	0.955981i	$0.594796\pi$
$384$	3.34431	0.170664
$385$	11.8095	0.601870
$386$	11.0591	0.562895
$387$	91.9020	4.67164
$388$	−16.3177	−0.828408
$389$	−18.8053	−0.953467	−0.476733	−	0.879048i	$-0.658179\pi$
$389$	−18.8053	−0.953467	−0.476733	+	0.879048i	$0.658179\pi$
$390$	81.3247	4.11804
$391$	16.3809	0.828419
$392$	6.32486	0.319454
$393$	72.4856	3.65642
$394$	11.7258	0.590739
$395$	19.3201	0.972099
$396$	−30.0753	−1.51134
$397$	31.1760	1.56468	0.782339	−	0.622853i	$-0.214027\pi$
$397$	31.1760	1.56468	0.782339	+	0.622853i	$0.214027\pi$
$398$	5.79075	0.290264
$399$	−2.74792	−0.137568
$400$	10.2978	0.514889
$401$	9.43393	0.471108	0.235554	−	0.971861i	$-0.424310\pi$
$401$	9.43393	0.471108	0.235554	+	0.971861i	$0.424310\pi$
$402$	−18.5495	−0.925164
$403$	33.0678	1.64722
$404$	−16.9663	−0.844105
$405$	−130.758	−6.49742
$406$	−1.16937	−0.0580350
$407$	−7.52935	−0.373216
$408$	15.0174	0.743474
$409$	−12.2531	−0.605878	−0.302939	−	0.953010i	$-0.597968\pi$
$409$	−12.2531	−0.605878	−0.302939	+	0.953010i	$0.597968\pi$
$410$	−37.9126	−1.87237
$411$	−4.30522	−0.212361
$412$	18.8518	0.928760
$413$	1.21198	0.0596377
$414$	−29.8564	−1.46736
$415$	35.8274	1.75870
$416$	6.21730	0.304828
$417$	−7.95529	−0.389572
$418$	3.67470	0.179735
$419$	10.2801	0.502218	0.251109	−	0.967959i	$-0.419205\pi$
$419$	10.2801	0.502218	0.251109	+	0.967959i	$0.419205\pi$
$420$	10.7478	0.524437
$421$	−5.29221	−0.257927	−0.128963	−	0.991649i	$-0.541165\pi$
$421$	−5.29221	−0.257927	−0.128963	+	0.991649i	$0.541165\pi$
$422$	1.00000	0.0486792
$423$	8.20319	0.398853
$424$	−0.0200596	−0.000974179 0
$425$	46.2416	2.24305
$426$	44.6696	2.16425
$427$	11.4285	0.553066
$428$	−12.1783	−0.588661
$429$	−76.4064	−3.68894
$430$	43.9189	2.11796
$431$	3.96165	0.190826	0.0954131	−	0.995438i	$-0.469583\pi$
$431$	3.96165	0.190826	0.0954131	+	0.995438i	$0.469583\pi$
$432$	−17.3383	−0.834189
$433$	14.3642	0.690297	0.345149	−	0.938548i	$-0.387829\pi$
$433$	14.3642	0.690297	0.345149	+	0.938548i	$0.387829\pi$
$434$	4.37019	0.209776
$435$	18.6156	0.892549
$436$	−1.04711	−0.0501474
$437$	3.64795	0.174505
$438$	50.8392	2.42919
$439$	−29.2542	−1.39623	−0.698114	−	0.715987i	$-0.745977\pi$
$439$	−29.2542	−1.39623	−0.698114	+	0.715987i	$0.745977\pi$
$440$	−14.3726	−0.685188
$441$	−51.7653	−2.46501
$442$	27.9184	1.32794
$443$	−17.4801	−0.830506	−0.415253	−	0.909706i	$-0.636307\pi$
$443$	−17.4801	−0.830506	−0.415253	+	0.909706i	$0.636307\pi$
$444$	−6.85240	−0.325200
$445$	47.5780	2.25541
$446$	17.9138	0.848241
$447$	32.0777	1.51722
$448$	0.821669	0.0388202
$449$	23.3336	1.10118	0.550590	−	0.834776i	$-0.314403\pi$
$449$	23.3336	1.10118	0.550590	+	0.834776i	$0.314403\pi$
$450$	−84.2813	−3.97306
$451$	35.6198	1.67727
$452$	−4.88870	−0.229945
$453$	41.0349	1.92799
$454$	−4.94577	−0.232116
$455$	19.9808	0.936714
$456$	3.34431	0.156612
$457$	9.09774	0.425575	0.212787	−	0.977099i	$-0.431746\pi$
$457$	9.09774	0.425575	0.212787	+	0.977099i	$0.431746\pi$
$458$	15.1413	0.707506
$459$	−77.8567	−3.63404
$460$	−14.2680	−0.665249
$461$	−29.6414	−1.38054	−0.690269	−	0.723552i	$-0.742508\pi$
$461$	−29.6414	−1.38054	−0.690269	+	0.723552i	$0.742508\pi$
$462$	−10.0978	−0.469791
$463$	−10.9862	−0.510572	−0.255286	−	0.966866i	$-0.582170\pi$
$463$	−10.9862	−0.510572	−0.255286	+	0.966866i	$0.582170\pi$
$464$	1.42317	0.0660689
$465$	−69.5704	−3.22625
$466$	12.9989	0.602162
$467$	16.0958	0.744826	0.372413	−	0.928067i	$-0.378531\pi$
$467$	16.0958	0.744826	0.372413	+	0.928067i	$0.378531\pi$
$468$	−50.8849	−2.35216
$469$	−4.55745	−0.210444
$470$	3.92021	0.180826
$471$	10.0286	0.462095
$472$	−1.47502	−0.0678934
$473$	−41.2628	−1.89727
$474$	−16.5197	−0.758774
$475$	10.2978	0.472495
$476$	3.68966	0.169115
$477$	0.164176	0.00751710
$478$	14.8289	0.678260
$479$	−5.67862	−0.259463	−0.129731	−	0.991549i	$-0.541412\pi$
$479$	−5.67862	−0.259463	−0.129731	+	0.991549i	$0.541412\pi$
$480$	−13.0804	−0.597036
$481$	−12.7391	−0.580851
$482$	3.99153	0.181809
$483$	−10.0243	−0.456120
$484$	2.50341	0.113791
$485$	63.8226	2.89803
$486$	59.7901	2.71213
$487$	25.9253	1.17479	0.587393	−	0.809302i	$-0.300154\pi$
$487$	25.9253	1.17479	0.587393	+	0.809302i	$0.300154\pi$
$488$	−13.9089	−0.629628
$489$	−60.5537	−2.73833
$490$	−24.7380	−1.11755
$491$	−18.1650	−0.819774	−0.409887	−	0.912136i	$-0.634432\pi$
$491$	−18.1650	−0.819774	−0.409887	+	0.912136i	$0.634432\pi$
$492$	32.4173	1.46148
$493$	6.39066	0.287821
$494$	6.21730	0.279729
$495$	117.631	5.28714
$496$	−5.31868	−0.238816
$497$	10.9750	0.492294
$498$	−30.6343	−1.37276
$499$	−6.06335	−0.271433	−0.135716	−	0.990748i	$-0.543334\pi$
$499$	−6.06335	−0.271433	−0.135716	+	0.990748i	$0.543334\pi$
$500$	−20.7209	−0.926666
$501$	−18.0337	−0.805688
$502$	15.1663	0.676906
$503$	6.58083	0.293425	0.146712	−	0.989179i	$-0.453131\pi$
$503$	6.58083	0.293425	0.146712	+	0.989179i	$0.453131\pi$
$504$	−6.72488	−0.299550
$505$	66.3593	2.95295
$506$	13.4051	0.595930
$507$	−85.7976	−3.81040
$508$	−9.54343	−0.423421
$509$	−43.2525	−1.91714	−0.958568	−	0.284865i	$-0.908051\pi$
$509$	−43.2525	−1.91714	−0.958568	+	0.284865i	$0.908051\pi$
$510$	−58.7368	−2.60091
$511$	12.4908	0.552559
$512$	−1.00000	−0.0441942
$513$	−17.3383	−0.765504
$514$	4.30156	0.189734
$515$	−73.7338	−3.24910
$516$	−37.5529	−1.65318
$517$	−3.68313	−0.161984
$518$	−1.68358	−0.0739721
$519$	−27.0444	−1.18712
$520$	−24.3173	−1.06639
$521$	−0.767485	−0.0336241	−0.0168121	−	0.999859i	$-0.505352\pi$
$521$	−0.767485	−0.0336241	−0.0168121	+	0.999859i	$0.505352\pi$
$522$	−11.6478	−0.509810
$523$	−0.773124	−0.0338064	−0.0169032	−	0.999857i	$-0.505381\pi$
$523$	−0.773124	−0.0338064	−0.0169032	+	0.999857i	$0.505381\pi$
$524$	−21.6743	−0.946847
$525$	−28.2974	−1.23500
$526$	21.8207	0.951426
$527$	−23.8832	−1.04037
$528$	12.2893	0.534825
$529$	−9.69245	−0.421411
$530$	0.0784578	0.00340799
$531$	12.0722	0.523889
$532$	0.821669	0.0356239
$533$	60.2659	2.61040
$534$	−40.6816	−1.76047
$535$	47.6323	2.05932
$536$	5.54658	0.239576
$537$	−38.1786	−1.64753
$538$	−21.8252	−0.940952
$539$	23.2419	1.00110
$540$	67.8142	2.91826
$541$	7.54448	0.324362	0.162181	−	0.986761i	$-0.448147\pi$
$541$	7.54448	0.324362	0.162181	+	0.986761i	$0.448147\pi$
$542$	15.3153	0.657850
$543$	−27.0708	−1.16172
$544$	−4.49045	−0.192526
$545$	4.09549	0.175432
$546$	−17.0846	−0.731154
$547$	32.4349	1.38682	0.693409	−	0.720544i	$-0.256108\pi$
$547$	32.4349	1.38682	0.693409	+	0.720544i	$0.256108\pi$
$548$	1.28733	0.0549919
$549$	113.836	4.85842
$550$	37.8412	1.61356
$551$	1.42317	0.0606290
$552$	12.1999	0.519262
$553$	−4.05875	−0.172595
$554$	26.0986	1.10882
$555$	26.8013	1.13765
$556$	2.37875	0.100882
$557$	11.6926	0.495432	0.247716	−	0.968833i	$-0.420320\pi$
$557$	11.6926	0.495432	0.247716	+	0.968833i	$0.420320\pi$
$558$	43.5303	1.84278
$559$	−69.8134	−2.95279
$560$	−3.21374	−0.135805
$561$	55.1846	2.32989
$562$	22.3378	0.942262
$563$	33.9362	1.43024	0.715121	−	0.699001i	$-0.246372\pi$
$563$	33.9362	1.43024	0.715121	+	0.699001i	$0.246372\pi$
$564$	−3.35198	−0.141144
$565$	19.1209	0.804421
$566$	1.51340	0.0636131
$567$	27.4696	1.15361
$568$	−13.3569	−0.560443
$569$	−7.74708	−0.324775	−0.162387	−	0.986727i	$-0.551919\pi$
$569$	−7.74708	−0.324775	−0.162387	+	0.986727i	$0.551919\pi$
$570$	−13.0804	−0.547877
$571$	−27.5176	−1.15158	−0.575788	−	0.817599i	$-0.695305\pi$
$571$	−27.5176	−1.15158	−0.575788	+	0.817599i	$0.695305\pi$
$572$	22.8467	0.955268
$573$	0.0327200	0.00136690
$574$	7.96465	0.332438
$575$	37.5658	1.56660
$576$	8.18441	0.341017
$577$	14.4157	0.600134	0.300067	−	0.953918i	$-0.402991\pi$
$577$	14.4157	0.600134	0.300067	+	0.953918i	$0.402991\pi$
$578$	−3.16410	−0.131609
$579$	36.9851	1.53705
$580$	−5.56635	−0.231130
$581$	−7.52659	−0.312256
$582$	−54.5716	−2.26207
$583$	−0.0737129	−0.00305288
$584$	−15.2017	−0.629050
$585$	199.023	8.22859
$586$	15.1027	0.623885
$587$	26.5366	1.09528	0.547641	−	0.836713i	$-0.315526\pi$
$587$	26.5366	1.09528	0.547641	+	0.836713i	$0.315526\pi$
$588$	21.1523	0.872306
$589$	−5.31868	−0.219152
$590$	5.76916	0.237513
$591$	39.2148	1.61308
$592$	2.04897	0.0842122
$593$	−17.5137	−0.719200	−0.359600	−	0.933107i	$-0.617087\pi$
$593$	−17.5137	−0.719200	−0.359600	+	0.933107i	$0.617087\pi$
$594$	−63.7130	−2.61418
$595$	−14.4311	−0.591619
$596$	−9.59171	−0.392892
$597$	19.3661	0.792601
$598$	22.6804	0.927471
$599$	1.02321	0.0418073	0.0209036	−	0.999781i	$-0.493346\pi$
$599$	1.02321	0.0418073	0.0209036	+	0.999781i	$0.493346\pi$
$600$	34.4390	1.40597
$601$	14.4436	0.589168	0.294584	−	0.955626i	$-0.404819\pi$
$601$	14.4436	0.589168	0.294584	+	0.955626i	$0.404819\pi$
$602$	−9.22644	−0.376042
$603$	−45.3955	−1.84865
$604$	−12.2701	−0.499261
$605$	−9.79141	−0.398078
$606$	−56.7406	−2.30493
$607$	46.6805	1.89470	0.947352	−	0.320195i	$-0.103748\pi$
$607$	46.6805	1.89470	0.947352	+	0.320195i	$0.103748\pi$
$608$	−1.00000	−0.0405554
$609$	−3.91075	−0.158471
$610$	54.4011	2.20264
$611$	−6.23156	−0.252102
$612$	36.7517	1.48560
$613$	1.36257	0.0550337	0.0275169	−	0.999621i	$-0.491240\pi$
$613$	1.36257	0.0550337	0.0275169	+	0.999621i	$0.491240\pi$
$614$	−11.7946	−0.475990
$615$	−126.792	−5.11273
$616$	3.01939	0.121655
$617$	−12.7131	−0.511809	−0.255904	−	0.966702i	$-0.582373\pi$
$617$	−12.7131	−0.511809	−0.255904	+	0.966702i	$0.582373\pi$
$618$	63.0462	2.53609
$619$	35.0498	1.40877	0.704384	−	0.709819i	$-0.251223\pi$
$619$	35.0498	1.40877	0.704384	+	0.709819i	$0.251223\pi$
$620$	20.8026	0.835453
$621$	−63.2493	−2.53811
$622$	0.884177	0.0354523
$623$	−9.99514	−0.400447
$624$	20.7926	0.832369
$625$	29.5554	1.18221
$626$	−7.00591	−0.280012
$627$	12.2893	0.490789
$628$	−2.99872	−0.119662
$629$	9.20079	0.366860
$630$	26.3026	1.04792
$631$	6.86231	0.273184	0.136592	−	0.990627i	$-0.456385\pi$
$631$	6.86231	0.273184	0.136592	+	0.990627i	$0.456385\pi$
$632$	4.93964	0.196488
$633$	3.34431	0.132924
$634$	−33.4825	−1.32976
$635$	37.3266	1.48126
$636$	−0.0670855	−0.00266011
$637$	39.3235	1.55806
$638$	5.22971	0.207046
$639$	109.318	4.32457
$640$	3.91124	0.154605
$641$	21.8822	0.864294	0.432147	−	0.901803i	$-0.357756\pi$
$641$	21.8822	0.864294	0.432147	+	0.901803i	$0.357756\pi$
$642$	−40.7281	−1.60741
$643$	−0.829979	−0.0327312	−0.0163656	−	0.999866i	$-0.505210\pi$
$643$	−0.829979	−0.0327312	−0.0163656	+	0.999866i	$0.505210\pi$
$644$	2.99741	0.118115
$645$	146.878	5.78333
$646$	−4.49045	−0.176674
$647$	−36.3428	−1.42878	−0.714391	−	0.699747i	$-0.753296\pi$
$647$	−36.3428	−1.42878	−0.714391	+	0.699747i	$0.753296\pi$
$648$	−33.4314	−1.31331
$649$	−5.42026	−0.212764
$650$	64.0244	2.51124
$651$	14.6153	0.572818
$652$	18.1065	0.709104
$653$	20.2323	0.791750	0.395875	−	0.918304i	$-0.370441\pi$
$653$	20.2323	0.791750	0.395875	+	0.918304i	$0.370441\pi$
$654$	−3.50186	−0.136933
$655$	84.7734	3.31237
$656$	−9.69326	−0.378458
$657$	124.417	4.85397
$658$	−0.823554	−0.0321055
$659$	−6.99755	−0.272586	−0.136293	−	0.990669i	$-0.543519\pi$
$659$	−6.99755	−0.272586	−0.136293	+	0.990669i	$0.543519\pi$
$660$	−48.0665	−1.87099
$661$	−11.9029	−0.462969	−0.231484	−	0.972839i	$-0.574358\pi$
$661$	−11.9029	−0.462969	−0.231484	+	0.972839i	$0.574358\pi$
$662$	−16.7888	−0.652515
$663$	93.3679	3.62611
$664$	9.16012	0.355482
$665$	−3.21374	−0.124624
$666$	−16.7696	−0.649810
$667$	5.19165	0.201021
$668$	5.39236	0.208637
$669$	59.9092	2.31622
$670$	−21.6940	−0.838111
$671$	−51.1111	−1.97312
$672$	2.74792	0.106003
$673$	17.4145	0.671278	0.335639	−	0.941991i	$-0.391048\pi$
$673$	17.4145	0.671278	0.335639	+	0.941991i	$0.391048\pi$
$674$	13.2611	0.510799
$675$	−178.546	−6.87224
$676$	25.6548	0.986723
$677$	−18.7626	−0.721105	−0.360553	−	0.932739i	$-0.617412\pi$
$677$	−18.7626	−0.721105	−0.360553	+	0.932739i	$0.617412\pi$
$678$	−16.3493	−0.627892
$679$	−13.4078	−0.514544
$680$	17.5632	0.673518
$681$	−16.5402	−0.633822
$682$	−19.5445	−0.748399
$683$	2.89044	0.110600	0.0552998	−	0.998470i	$-0.482389\pi$
$683$	2.89044	0.110600	0.0552998	+	0.998470i	$0.482389\pi$
$684$	8.18441	0.312939
$685$	−5.03504	−0.192379
$686$	10.9486	0.418021
$687$	50.6372	1.93193
$688$	11.2289	0.428098
$689$	−0.124716	−0.00475132
$690$	−47.7167	−1.81654
$691$	−4.26574	−0.162277	−0.0811383	−	0.996703i	$-0.525856\pi$
$691$	−4.26574	−0.162277	−0.0811383	+	0.996703i	$0.525856\pi$
$692$	8.08670	0.307410
$693$	−24.7119	−0.938728
$694$	−21.6482	−0.821755
$695$	−9.30387	−0.352916
$696$	4.75951	0.180409
$697$	−43.5270	−1.64870
$698$	23.3722	0.884651
$699$	43.4723	1.64427
$700$	8.46137	0.319810
$701$	42.8256	1.61750	0.808750	−	0.588153i	$-0.200145\pi$
$701$	42.8256	1.61750	0.808750	+	0.588153i	$0.200145\pi$
$702$	−107.797	−4.06855
$703$	2.04897	0.0772784
$704$	−3.67470	−0.138495
$705$	13.1104	0.493766
$706$	−5.28848	−0.199035
$707$	−13.9407	−0.524294
$708$	−4.93293	−0.185391
$709$	−50.8642	−1.91025	−0.955123	−	0.296210i	$-0.904277\pi$
$709$	−50.8642	−1.91025	−0.955123	+	0.296210i	$0.904277\pi$
$710$	52.2420	1.96061
$711$	−40.4280	−1.51617
$712$	12.1644	0.455881
$713$	−19.4023	−0.726621
$714$	12.3394	0.461789
$715$	−89.3588	−3.34183
$716$	11.4160	0.426635
$717$	49.5926	1.85207
$718$	−35.0717	−1.30887
$719$	9.91886	0.369911	0.184955	−	0.982747i	$-0.440786\pi$
$719$	9.91886	0.369911	0.184955	+	0.982747i	$0.440786\pi$
$720$	−32.0112	−1.19299
$721$	15.4899	0.576875
$722$	−1.00000	−0.0372161
$723$	13.3489	0.496452
$724$	8.09459	0.300833
$725$	14.6555	0.544290
$726$	8.37217	0.310720
$727$	46.4879	1.72414	0.862070	−	0.506789i	$-0.169168\pi$
$727$	46.4879	1.72414	0.862070	+	0.506789i	$0.169168\pi$
$728$	5.10856	0.189336
$729$	99.6625	3.69120
$730$	59.4574	2.20062
$731$	50.4228	1.86495
$732$	−46.5158	−1.71927
$733$	−12.1557	−0.448981	−0.224491	−	0.974476i	$-0.572072\pi$
$733$	−12.1557	−0.448981	−0.224491	+	0.974476i	$0.572072\pi$
$734$	−21.5823	−0.796617
$735$	−82.7317	−3.05160
$736$	−3.64795	−0.134465
$737$	20.3820	0.750780
$738$	79.3336	2.92031
$739$	37.6875	1.38636	0.693178	−	0.720766i	$-0.256210\pi$
$739$	37.6875	1.38636	0.693178	+	0.720766i	$0.256210\pi$
$740$	−8.01401	−0.294601
$741$	20.7926	0.763834
$742$	−0.0164823	−0.000605086 0
$743$	−44.9280	−1.64825	−0.824125	−	0.566408i	$-0.808333\pi$
$743$	−44.9280	−1.64825	−0.824125	+	0.566408i	$0.808333\pi$
$744$	−17.7873	−0.652114
$745$	37.5155	1.37446
$746$	−27.2425	−0.997418
$747$	−74.9702	−2.74302
$748$	−16.5010	−0.603337
$749$	−10.0065	−0.365631
$750$	−69.2970	−2.53037
$751$	−22.8306	−0.833101	−0.416551	−	0.909113i	$-0.636761\pi$
$751$	−22.8306	−0.833101	−0.416551	+	0.909113i	$0.636761\pi$
$752$	1.00229	0.0365499
$753$	50.7209	1.84837
$754$	8.84826	0.322234
$755$	47.9911	1.74658
$756$	−14.2463	−0.518135
$757$	−12.3037	−0.447185	−0.223592	−	0.974683i	$-0.571778\pi$
$757$	−12.3037	−0.447185	−0.223592	+	0.974683i	$0.571778\pi$
$758$	−15.4569	−0.561421
$759$	44.8309	1.62726
$760$	3.91124	0.141875
$761$	24.0720	0.872610	0.436305	−	0.899799i	$-0.356287\pi$
$761$	24.0720	0.872610	0.436305	+	0.899799i	$0.356287\pi$
$762$	−31.9162	−1.15620
$763$	−0.860377	−0.0311478
$764$	−0.00978378	−0.000353965 0
$765$	−143.744	−5.19709
$766$	11.4850	0.414971
$767$	−9.17065	−0.331133
$768$	−3.34431	−0.120677
$769$	26.2259	0.945730	0.472865	−	0.881135i	$-0.343220\pi$
$769$	26.2259	0.945730	0.472865	+	0.881135i	$0.343220\pi$
$770$	−11.8095	−0.425586
$771$	14.3858	0.518091
$772$	−11.0591	−0.398027
$773$	29.1428	1.04819	0.524096	−	0.851659i	$-0.324403\pi$
$773$	29.1428	1.04819	0.524096	+	0.851659i	$0.324403\pi$
$774$	−91.9020	−3.30335
$775$	−54.7705	−1.96742
$776$	16.3177	0.585773
$777$	−5.63040	−0.201990
$778$	18.8053	0.674203
$779$	−9.69326	−0.347297
$780$	−81.3247	−2.91189
$781$	−49.0826	−1.75631
$782$	−16.3809	−0.585781
$783$	−24.6753	−0.881823
$784$	−6.32486	−0.225888
$785$	11.7287	0.418615
$786$	−72.4856	−2.58548
$787$	−5.63533	−0.200878	−0.100439	−	0.994943i	$-0.532025\pi$
$787$	−5.63533	−0.200878	−0.100439	+	0.994943i	$0.532025\pi$
$788$	−11.7258	−0.417716
$789$	72.9750	2.59798
$790$	−19.3201	−0.687378
$791$	−4.01689	−0.142824
$792$	30.0753	1.06868
$793$	−86.4760	−3.07085
$794$	−31.1760	−1.10639
$795$	0.262387	0.00930592
$796$	−5.79075	−0.205248
$797$	−10.4675	−0.370776	−0.185388	−	0.982665i	$-0.559354\pi$
$797$	−10.4675	−0.370776	−0.185388	+	0.982665i	$0.559354\pi$
$798$	2.74792	0.0972752
$799$	4.50075	0.159225
$800$	−10.2978	−0.364081
$801$	−99.5587	−3.51773
$802$	−9.43393	−0.333124
$803$	−55.8616	−1.97131
$804$	18.5495	0.654189
$805$	−11.7236	−0.413202
$806$	−33.0678	−1.16476
$807$	−72.9903	−2.56938
$808$	16.9663	0.596873
$809$	−51.6353	−1.81540	−0.907701	−	0.419618i	$-0.862164\pi$
$809$	−51.6353	−1.81540	−0.907701	+	0.419618i	$0.862164\pi$
$810$	130.758	4.59437
$811$	53.7296	1.88670	0.943350	−	0.331799i	$-0.107656\pi$
$811$	53.7296	1.88670	0.943350	+	0.331799i	$0.107656\pi$
$812$	1.16937	0.0410369
$813$	51.2193	1.79634
$814$	7.52935	0.263904
$815$	−70.8187	−2.48067
$816$	−15.0174	−0.525716
$817$	11.2289	0.392850
$818$	12.2531	0.428421
$819$	−41.8106	−1.46098
$820$	37.9126	1.32397
$821$	−39.4648	−1.37733	−0.688666	−	0.725079i	$-0.741803\pi$
$821$	−39.4648	−1.37733	−0.688666	+	0.725079i	$0.741803\pi$
$822$	4.30522	0.150162
$823$	40.7343	1.41991	0.709955	−	0.704248i	$-0.248715\pi$
$823$	40.7343	1.41991	0.709955	+	0.704248i	$0.248715\pi$
$824$	−18.8518	−0.656733
$825$	126.553	4.40600
$826$	−1.21198	−0.0421702
$827$	−24.1299	−0.839078	−0.419539	−	0.907737i	$-0.637808\pi$
$827$	−24.1299	−0.839078	−0.419539	+	0.907737i	$0.637808\pi$
$828$	29.8564	1.03758
$829$	18.2451	0.633678	0.316839	−	0.948479i	$-0.397378\pi$
$829$	18.2451	0.633678	0.316839	+	0.948479i	$0.397378\pi$
$830$	−35.8274	−1.24359
$831$	87.2817	3.02777
$832$	−6.21730	−0.215546
$833$	−28.4014	−0.984051
$834$	7.95529	0.275469
$835$	−21.0908	−0.729877
$836$	−3.67470	−0.127092
$837$	92.2168	3.18748
$838$	−10.2801	−0.355122
$839$	14.7639	0.509707	0.254854	−	0.966980i	$-0.417973\pi$
$839$	14.7639	0.509707	0.254854	+	0.966980i	$0.417973\pi$
$840$	−10.7478	−0.370833
$841$	−26.9746	−0.930158
$842$	5.29221	0.182382
$843$	74.7044	2.57296
$844$	−1.00000	−0.0344214
$845$	−100.342	−3.45187
$846$	−8.20319	−0.282032
$847$	2.05697	0.0706784
$848$	0.0200596	0.000688849 0
$849$	5.06129	0.173703
$850$	−46.2416	−1.58607
$851$	7.47455	0.256224
$852$	−44.6696	−1.53036
$853$	36.3374	1.24417	0.622085	−	0.782950i	$-0.286286\pi$
$853$	36.3374	1.24417	0.622085	+	0.782950i	$0.286286\pi$
$854$	−11.4285	−0.391077
$855$	−32.0112	−1.09476
$856$	12.1783	0.416246
$857$	−34.8602	−1.19080	−0.595402	−	0.803428i	$-0.703007\pi$
$857$	−34.8602	−1.19080	−0.595402	+	0.803428i	$0.703007\pi$
$858$	76.4064	2.60847
$859$	−49.7543	−1.69759	−0.848797	−	0.528718i	$-0.822673\pi$
$859$	−49.7543	−1.69759	−0.848797	+	0.528718i	$0.822673\pi$
$860$	−43.9189	−1.49762
$861$	26.6363	0.907762
$862$	−3.96165	−0.134934
$863$	8.96682	0.305234	0.152617	−	0.988285i	$-0.451230\pi$
$863$	8.96682	0.305234	0.152617	+	0.988285i	$0.451230\pi$
$864$	17.3383	0.589861
$865$	−31.6290	−1.07542
$866$	−14.3642	−0.488114
$867$	−10.5817	−0.359374
$868$	−4.37019	−0.148334
$869$	18.1517	0.615753
$870$	−18.6156	−0.631128
$871$	34.4847	1.16847
$872$	1.04711	0.0354596
$873$	−133.551	−4.52002
$874$	−3.64795	−0.123394
$875$	−17.0257	−0.575574
$876$	−50.8392	−1.71770
$877$	−0.610876	−0.0206278	−0.0103139	−	0.999947i	$-0.503283\pi$
$877$	−0.610876	−0.0206278	−0.0103139	+	0.999947i	$0.503283\pi$
$878$	29.2542	0.987282
$879$	50.5080	1.70359
$880$	14.3726	0.484501
$881$	−35.7553	−1.20463	−0.602313	−	0.798260i	$-0.705754\pi$
$881$	−35.7553	−1.20463	−0.602313	+	0.798260i	$0.705754\pi$
$882$	51.7653	1.74303
$883$	5.31090	0.178726	0.0893630	−	0.995999i	$-0.471517\pi$
$883$	5.31090	0.178726	0.0893630	+	0.995999i	$0.471517\pi$
$884$	−27.9184	−0.938999
$885$	19.2939	0.648556
$886$	17.4801	0.587256
$887$	−23.2065	−0.779197	−0.389599	−	0.920985i	$-0.627386\pi$
$887$	−23.2065	−0.779197	−0.389599	+	0.920985i	$0.627386\pi$
$888$	6.85240	0.229951
$889$	−7.84154	−0.262997
$890$	−47.5780	−1.59482
$891$	−122.850	−4.11564
$892$	−17.9138	−0.599797
$893$	1.00229	0.0335405
$894$	−32.0777	−1.07284
$895$	−44.6506	−1.49250
$896$	−0.821669	−0.0274500
$897$	75.8503	2.53257
$898$	−23.3336	−0.778651
$899$	−7.56937	−0.252452
$900$	84.2813	2.80938
$901$	0.0900765	0.00300088
$902$	−35.6198	−1.18601
$903$	−30.8561	−1.02683
$904$	4.88870	0.162596
$905$	−31.6598	−1.05241
$906$	−41.0349	−1.36329
$907$	21.6784	0.719821	0.359910	−	0.932987i	$-0.382807\pi$
$907$	21.6784	0.719821	0.359910	+	0.932987i	$0.382807\pi$
$908$	4.94577	0.164131
$909$	−138.859	−4.60567
$910$	−19.9808	−0.662357
$911$	−17.9148	−0.593544	−0.296772	−	0.954948i	$-0.595910\pi$
$911$	−17.9148	−0.593544	−0.296772	+	0.954948i	$0.595910\pi$
$912$	−3.34431	−0.110741
$913$	33.6607	1.11401
$914$	−9.09774	−0.300927
$915$	181.934	6.01456
$916$	−15.1413	−0.500282
$917$	−17.8091	−0.588109
$918$	77.8567	2.56965
$919$	26.8061	0.884250	0.442125	−	0.896953i	$-0.354225\pi$
$919$	26.8061	0.884250	0.442125	+	0.896953i	$0.354225\pi$
$920$	14.2680	0.470402
$921$	−39.4447	−1.29975
$922$	29.6414	0.976188
$923$	−83.0438	−2.73342
$924$	10.0978	0.332192
$925$	21.0999	0.693759
$926$	10.9862	0.361029
$927$	154.291	5.06757
$928$	−1.42317	−0.0467178
$929$	−3.75571	−0.123221	−0.0616104	−	0.998100i	$-0.519624\pi$
$929$	−3.75571	−0.123221	−0.0616104	+	0.998100i	$0.519624\pi$
$930$	69.5704	2.28130
$931$	−6.32486	−0.207289
$932$	−12.9989	−0.425793
$933$	2.95696	0.0968067
$934$	−16.0958	−0.526671
$935$	64.5394	2.11067
$936$	50.8849	1.66323
$937$	−10.0030	−0.326782	−0.163391	−	0.986561i	$-0.552243\pi$
$937$	−10.0030	−0.326782	−0.163391	+	0.986561i	$0.552243\pi$
$938$	4.55745	0.148806
$939$	−23.4299	−0.764607
$940$	−3.92021	−0.127863
$941$	−14.7703	−0.481497	−0.240749	−	0.970587i	$-0.577393\pi$
$941$	−14.7703	−0.481497	−0.240749	+	0.970587i	$0.577393\pi$
$942$	−10.0286	−0.326751
$943$	−35.3605	−1.15150
$944$	1.47502	0.0480079
$945$	55.7208	1.81260
$946$	41.2628	1.34157
$947$	29.5370	0.959823	0.479912	−	0.877317i	$-0.340669\pi$
$947$	29.5370	0.959823	0.479912	+	0.877317i	$0.340669\pi$
$948$	16.5197	0.536534
$949$	−94.5134	−3.06804
$950$	−10.2978	−0.334104
$951$	−111.976	−3.63106
$952$	−3.68966	−0.119583
$953$	−33.8306	−1.09588	−0.547940	−	0.836517i	$-0.684588\pi$
$953$	−33.8306	−1.09588	−0.547940	+	0.836517i	$0.684588\pi$
$954$	−0.164176	−0.00531539
$955$	0.0382667	0.00123828
$956$	−14.8289	−0.479602
$957$	17.4898	0.565364
$958$	5.67862	0.183468
$959$	1.05776	0.0341567
$960$	13.0804	0.422168
$961$	−2.71169	−0.0874737
$962$	12.7391	0.410724
$963$	−99.6723	−3.21190
$964$	−3.99153	−0.128559
$965$	43.2549	1.39242
$966$	10.0243	0.322526
$967$	45.8986	1.47600	0.738000	−	0.674801i	$-0.235771\pi$
$967$	45.8986	1.47600	0.738000	+	0.674801i	$0.235771\pi$
$968$	−2.50341	−0.0804625
$969$	−15.0174	−0.482430
$970$	−63.8226	−2.04922
$971$	51.1565	1.64169	0.820846	−	0.571150i	$-0.193503\pi$
$971$	51.1565	1.64169	0.820846	+	0.571150i	$0.193503\pi$
$972$	−59.7901	−1.91777
$973$	1.95455	0.0626599
$974$	−25.9253	−0.830700
$975$	214.117	6.85724
$976$	13.9089	0.445214
$977$	−11.1396	−0.356386	−0.178193	−	0.983996i	$-0.557025\pi$
$977$	−11.1396	−0.356386	−0.178193	+	0.983996i	$0.557025\pi$
$978$	60.5537	1.93629
$979$	44.7006	1.42864
$980$	24.7380	0.790227
$981$	−8.56997	−0.273618
$982$	18.1650	0.579668
$983$	15.0040	0.478553	0.239277	−	0.970951i	$-0.423090\pi$
$983$	15.0040	0.478553	0.239277	+	0.970951i	$0.423090\pi$
$984$	−32.4173	−1.03342
$985$	45.8625	1.46130
$986$	−6.39066	−0.203520
$987$	−2.75422	−0.0876679
$988$	−6.21730	−0.197799
$989$	40.9625	1.30253
$990$	−117.631	−3.73857
$991$	52.6986	1.67403	0.837013	−	0.547183i	$-0.184300\pi$
$991$	52.6986	1.67403	0.837013	+	0.547183i	$0.184300\pi$
$992$	5.31868	0.168868
$993$	−56.1469	−1.78177
$994$	−10.9750	−0.348104
$995$	22.6490	0.718022
$996$	30.6343	0.970685
$997$	−35.2568	−1.11660	−0.558298	−	0.829641i	$-0.688545\pi$
$997$	−35.2568	−1.11660	−0.558298	+	0.829641i	$0.688545\pi$
$998$	6.06335	0.191932
$999$	−35.5257	−1.12398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.1	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.1	✓	43	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.34431 q^{3} +1.00000 q^{4} -3.91124 q^{5} +3.34431 q^{6} +0.821669 q^{7} -1.00000 q^{8} +8.18441 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.34431 q^{3} +1.00000 q^{4} -3.91124 q^{5} +3.34431 q^{6} +0.821669 q^{7} -1.00000 q^{8} +8.18441 q^{9} +3.91124 q^{10} -3.67470 q^{11} -3.34431 q^{12} -6.21730 q^{13} -0.821669 q^{14} +13.0804 q^{15} +1.00000 q^{16} +4.49045 q^{17} -8.18441 q^{18} +1.00000 q^{19} -3.91124 q^{20} -2.74792 q^{21} +3.67470 q^{22} +3.64795 q^{23} +3.34431 q^{24} +10.2978 q^{25} +6.21730 q^{26} -17.3383 q^{27} +0.821669 q^{28} +1.42317 q^{29} -13.0804 q^{30} -5.31868 q^{31} -1.00000 q^{32} +12.2893 q^{33} -4.49045 q^{34} -3.21374 q^{35} +8.18441 q^{36} +2.04897 q^{37} -1.00000 q^{38} +20.7926 q^{39} +3.91124 q^{40} -9.69326 q^{41} +2.74792 q^{42} +11.2289 q^{43} -3.67470 q^{44} -32.0112 q^{45} -3.64795 q^{46} +1.00229 q^{47} -3.34431 q^{48} -6.32486 q^{49} -10.2978 q^{50} -15.0174 q^{51} -6.21730 q^{52} +0.0200596 q^{53} +17.3383 q^{54} +14.3726 q^{55} -0.821669 q^{56} -3.34431 q^{57} -1.42317 q^{58} +1.47502 q^{59} +13.0804 q^{60} +13.9089 q^{61} +5.31868 q^{62} +6.72488 q^{63} +1.00000 q^{64} +24.3173 q^{65} -12.2893 q^{66} -5.54658 q^{67} +4.49045 q^{68} -12.1999 q^{69} +3.21374 q^{70} +13.3569 q^{71} -8.18441 q^{72} +15.2017 q^{73} -2.04897 q^{74} -34.4390 q^{75} +1.00000 q^{76} -3.01939 q^{77} -20.7926 q^{78} -4.93964 q^{79} -3.91124 q^{80} +33.4314 q^{81} +9.69326 q^{82} -9.16012 q^{83} -2.74792 q^{84} -17.5632 q^{85} -11.2289 q^{86} -4.75951 q^{87} +3.67470 q^{88} -12.1644 q^{89} +32.0112 q^{90} -5.10856 q^{91} +3.64795 q^{92} +17.7873 q^{93} -1.00229 q^{94} -3.91124 q^{95} +3.34431 q^{96} -16.3177 q^{97} +6.32486 q^{98} -30.0753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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