LMFDB - Embedded newform 1210.2.a.p.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1210,2,Mod(1,1210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1210.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1210, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1210 = 2 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1210.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,2,2,-2,-2,-3,-2,6,2,0,2,1,3,-2,2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.66189864457$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1210.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.23607 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.23607 q^{6} -0.381966 q^{7} -1.00000 q^{8} -1.47214 q^{9} +1.00000 q^{10} -1.23607 q^{12} -0.618034 q^{13} +0.381966 q^{14} +1.23607 q^{15} +1.00000 q^{16} +0.763932 q^{17} +1.47214 q^{18} -7.09017 q^{19} -1.00000 q^{20} +0.472136 q^{21} +6.85410 q^{23} +1.23607 q^{24} +1.00000 q^{25} +0.618034 q^{26} +5.52786 q^{27} -0.381966 q^{28} -3.23607 q^{29} -1.23607 q^{30} -2.76393 q^{31} -1.00000 q^{32} -0.763932 q^{34} +0.381966 q^{35} -1.47214 q^{36} +5.85410 q^{37} +7.09017 q^{38} +0.763932 q^{39} +1.00000 q^{40} -4.85410 q^{41} -0.472136 q^{42} +4.76393 q^{43} +1.47214 q^{45} -6.85410 q^{46} -4.32624 q^{47} -1.23607 q^{48} -6.85410 q^{49} -1.00000 q^{50} -0.944272 q^{51} -0.618034 q^{52} +12.0902 q^{53} -5.52786 q^{54} +0.381966 q^{56} +8.76393 q^{57} +3.23607 q^{58} +4.61803 q^{59} +1.23607 q^{60} +8.94427 q^{61} +2.76393 q^{62} +0.562306 q^{63} +1.00000 q^{64} +0.618034 q^{65} +5.23607 q^{67} +0.763932 q^{68} -8.47214 q^{69} -0.381966 q^{70} +8.76393 q^{71} +1.47214 q^{72} -11.7082 q^{73} -5.85410 q^{74} -1.23607 q^{75} -7.09017 q^{76} -0.763932 q^{78} +10.4721 q^{79} -1.00000 q^{80} -2.41641 q^{81} +4.85410 q^{82} -2.29180 q^{83} +0.472136 q^{84} -0.763932 q^{85} -4.76393 q^{86} +4.00000 q^{87} +17.0344 q^{89} -1.47214 q^{90} +0.236068 q^{91} +6.85410 q^{92} +3.41641 q^{93} +4.32624 q^{94} +7.09017 q^{95} +1.23607 q^{96} -12.0000 q^{97} +6.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 2 q^{20} - 8 q^{21}+ \cdots + 7 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 6 * q^9 + 2 * q^10 + 2 * q^12 + q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 2 * q^20 - 8 * q^21 + 7 * q^23 - 2 * q^24 + 2 * q^25 - q^26 + 20 * q^27 - 3 * q^28 - 2 * q^29 + 2 * q^30 - 10 * q^31 - 2 * q^32 - 6 * q^34 + 3 * q^35 + 6 * q^36 + 5 * q^37 + 3 * q^38 + 6 * q^39 + 2 * q^40 - 3 * q^41 + 8 * q^42 + 14 * q^43 - 6 * q^45 - 7 * q^46 + 7 * q^47 + 2 * q^48 - 7 * q^49 - 2 * q^50 + 16 * q^51 + q^52 + 13 * q^53 - 20 * q^54 + 3 * q^56 + 22 * q^57 + 2 * q^58 + 7 * q^59 - 2 * q^60 + 10 * q^62 - 19 * q^63 + 2 * q^64 - q^65 + 6 * q^67 + 6 * q^68 - 8 * q^69 - 3 * q^70 + 22 * q^71 - 6 * q^72 - 10 * q^73 - 5 * q^74 + 2 * q^75 - 3 * q^76 - 6 * q^78 + 12 * q^79 - 2 * q^80 + 22 * q^81 + 3 * q^82 - 18 * q^83 - 8 * q^84 - 6 * q^85 - 14 * q^86 + 8 * q^87 + 5 * q^89 + 6 * q^90 - 4 * q^91 + 7 * q^92 - 20 * q^93 - 7 * q^94 + 3 * q^95 - 2 * q^96 - 24 * q^97 + 7 * q^98

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
$3$	−1.23607	−0.713644	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	−1.23607	−0.713644	−0.356822	+	0.934172i	$0.616140\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.23607	0.504623
$7$	−0.381966	−0.144370	−0.0721848	−	0.997391i	$-0.522997\pi$
$7$	−0.381966	−0.144370	−0.0721848	+	0.997391i	$0.522997\pi$
$8$	−1.00000	−0.353553
$9$	−1.47214	−0.490712
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.23607	−0.356822
$13$	−0.618034	−0.171412	−0.0857059	−	0.996320i	$-0.527315\pi$
$13$	−0.618034	−0.171412	−0.0857059	+	0.996320i	$0.527315\pi$
$14$	0.381966	0.102085
$15$	1.23607	0.319151
$16$	1.00000	0.250000
$17$	0.763932	0.185281	0.0926404	−	0.995700i	$-0.470469\pi$
$17$	0.763932	0.185281	0.0926404	+	0.995700i	$0.470469\pi$
$18$	1.47214	0.346986
$19$	−7.09017	−1.62660	−0.813298	−	0.581847i	$-0.802330\pi$
$19$	−7.09017	−1.62660	−0.813298	+	0.581847i	$0.802330\pi$
$20$	−1.00000	−0.223607
$21$	0.472136	0.103029
$22$	0	0
$23$	6.85410	1.42918	0.714590	−	0.699544i	$-0.246614\pi$
$23$	6.85410	1.42918	0.714590	+	0.699544i	$0.246614\pi$
$24$	1.23607	0.252311
$25$	1.00000	0.200000
$26$	0.618034	0.121206
$27$	5.52786	1.06384
$28$	−0.381966	−0.0721848
$29$	−3.23607	−0.600923	−0.300461	−	0.953794i	$-0.597141\pi$
$29$	−3.23607	−0.600923	−0.300461	+	0.953794i	$0.597141\pi$
$30$	−1.23607	−0.225674
$31$	−2.76393	−0.496417	−0.248208	−	0.968707i	$-0.579842\pi$
$31$	−2.76393	−0.496417	−0.248208	+	0.968707i	$0.579842\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.763932	−0.131013
$35$	0.381966	0.0645640
$36$	−1.47214	−0.245356
$37$	5.85410	0.962408	0.481204	−	0.876609i	$-0.340200\pi$
$37$	5.85410	0.962408	0.481204	+	0.876609i	$0.340200\pi$
$38$	7.09017	1.15018
$39$	0.763932	0.122327
$40$	1.00000	0.158114
$41$	−4.85410	−0.758083	−0.379042	−	0.925380i	$-0.623746\pi$
$41$	−4.85410	−0.758083	−0.379042	+	0.925380i	$0.623746\pi$
$42$	−0.472136	−0.0728522
$43$	4.76393	0.726493	0.363246	−	0.931693i	$-0.381668\pi$
$43$	4.76393	0.726493	0.363246	+	0.931693i	$0.381668\pi$
$44$	0	0
$45$	1.47214	0.219453
$46$	−6.85410	−1.01058
$47$	−4.32624	−0.631047	−0.315523	−	0.948918i	$-0.602180\pi$
$47$	−4.32624	−0.631047	−0.315523	+	0.948918i	$0.602180\pi$
$48$	−1.23607	−0.178411
$49$	−6.85410	−0.979157
$50$	−1.00000	−0.141421
$51$	−0.944272	−0.132225
$52$	−0.618034	−0.0857059
$53$	12.0902	1.66071	0.830356	−	0.557233i	$-0.188137\pi$
$53$	12.0902	1.66071	0.830356	+	0.557233i	$0.188137\pi$
$54$	−5.52786	−0.752247
$55$	0	0
$56$	0.381966	0.0510424
$57$	8.76393	1.16081
$58$	3.23607	0.424917
$59$	4.61803	0.601217	0.300608	−	0.953748i	$-0.402810\pi$
$59$	4.61803	0.601217	0.300608	+	0.953748i	$0.402810\pi$
$60$	1.23607	0.159576
$61$	8.94427	1.14520	0.572598	−	0.819836i	$-0.305935\pi$
$61$	8.94427	1.14520	0.572598	+	0.819836i	$0.305935\pi$
$62$	2.76393	0.351020
$63$	0.562306	0.0708439
$64$	1.00000	0.125000
$65$	0.618034	0.0766577
$66$	0	0
$67$	5.23607	0.639688	0.319844	−	0.947470i	$-0.396370\pi$
$67$	5.23607	0.639688	0.319844	+	0.947470i	$0.396370\pi$
$68$	0.763932	0.0926404
$69$	−8.47214	−1.01993
$70$	−0.381966	−0.0456537
$71$	8.76393	1.04009	0.520044	−	0.854140i	$-0.325916\pi$
$71$	8.76393	1.04009	0.520044	+	0.854140i	$0.325916\pi$
$72$	1.47214	0.173493
$73$	−11.7082	−1.37034	−0.685171	−	0.728382i	$-0.740272\pi$
$73$	−11.7082	−1.37034	−0.685171	+	0.728382i	$0.740272\pi$
$74$	−5.85410	−0.680526
$75$	−1.23607	−0.142729
$76$	−7.09017	−0.813298
$77$	0	0
$78$	−0.763932	−0.0864983
$79$	10.4721	1.17821	0.589104	−	0.808057i	$-0.299481\pi$
$79$	10.4721	1.17821	0.589104	+	0.808057i	$0.299481\pi$
$80$	−1.00000	−0.111803
$81$	−2.41641	−0.268490
$82$	4.85410	0.536046
$83$	−2.29180	−0.251557	−0.125779	−	0.992058i	$-0.540143\pi$
$83$	−2.29180	−0.251557	−0.125779	+	0.992058i	$0.540143\pi$
$84$	0.472136	0.0515143
$85$	−0.763932	−0.0828601
$86$	−4.76393	−0.513708
$87$	4.00000	0.428845
$88$	0	0
$89$	17.0344	1.80565	0.902824	−	0.430011i	$-0.141490\pi$
$89$	17.0344	1.80565	0.902824	+	0.430011i	$0.141490\pi$
$90$	−1.47214	−0.155177
$91$	0.236068	0.0247466
$92$	6.85410	0.714590
$93$	3.41641	0.354265
$94$	4.32624	0.446217
$95$	7.09017	0.727436
$96$	1.23607	0.126156
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	6.85410	0.692369
$99$	0	0
$100$	1.00000	0.100000
$101$	9.70820	0.966002	0.483001	−	0.875620i	$-0.339547\pi$
$101$	9.70820	0.966002	0.483001	+	0.875620i	$0.339547\pi$
$102$	0.944272	0.0934969
$103$	4.32624	0.426277	0.213138	−	0.977022i	$-0.431631\pi$
$103$	4.32624	0.426277	0.213138	+	0.977022i	$0.431631\pi$
$104$	0.618034	0.0606032
$105$	−0.472136	−0.0460758
$106$	−12.0902	−1.17430
$107$	16.4721	1.59242	0.796211	−	0.605019i	$-0.206835\pi$
$107$	16.4721	1.59242	0.796211	+	0.605019i	$0.206835\pi$
$108$	5.52786	0.531919
$109$	−16.4721	−1.57774	−0.788872	−	0.614557i	$-0.789335\pi$
$109$	−16.4721	−1.57774	−0.788872	+	0.614557i	$0.789335\pi$
$110$	0	0
$111$	−7.23607	−0.686817
$112$	−0.381966	−0.0360924
$113$	19.7082	1.85399	0.926996	−	0.375071i	$-0.122382\pi$
$113$	19.7082	1.85399	0.926996	+	0.375071i	$0.122382\pi$
$114$	−8.76393	−0.820817
$115$	−6.85410	−0.639148
$116$	−3.23607	−0.300461
$117$	0.909830	0.0841138
$118$	−4.61803	−0.425124
$119$	−0.291796	−0.0267489
$120$	−1.23607	−0.112837
$121$	0	0
$122$	−8.94427	−0.809776
$123$	6.00000	0.541002
$124$	−2.76393	−0.248208
$125$	−1.00000	−0.0894427
$126$	−0.562306	−0.0500942
$127$	4.61803	0.409784	0.204892	−	0.978785i	$-0.434316\pi$
$127$	4.61803	0.409784	0.204892	+	0.978785i	$0.434316\pi$
$128$	−1.00000	−0.0883883
$129$	−5.88854	−0.518457
$130$	−0.618034	−0.0542052
$131$	15.4164	1.34694	0.673469	−	0.739216i	$-0.264804\pi$
$131$	15.4164	1.34694	0.673469	+	0.739216i	$0.264804\pi$
$132$	0	0
$133$	2.70820	0.234831
$134$	−5.23607	−0.452327
$135$	−5.52786	−0.475763
$136$	−0.763932	−0.0655066
$137$	−0.763932	−0.0652671	−0.0326336	−	0.999467i	$-0.510389\pi$
$137$	−0.763932	−0.0652671	−0.0326336	+	0.999467i	$0.510389\pi$
$138$	8.47214	0.721196
$139$	14.8541	1.25991	0.629954	−	0.776632i	$-0.283074\pi$
$139$	14.8541	1.25991	0.629954	+	0.776632i	$0.283074\pi$
$140$	0.381966	0.0322820
$141$	5.34752	0.450343
$142$	−8.76393	−0.735453
$143$	0	0
$144$	−1.47214	−0.122678
$145$	3.23607	0.268741
$146$	11.7082	0.968978
$147$	8.47214	0.698770
$148$	5.85410	0.481204
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	1.23607	0.100925
$151$	18.6525	1.51792	0.758958	−	0.651139i	$-0.225709\pi$
$151$	18.6525	1.51792	0.758958	+	0.651139i	$0.225709\pi$
$152$	7.09017	0.575089
$153$	−1.12461	−0.0909195
$154$	0	0
$155$	2.76393	0.222004
$156$	0.763932	0.0611635
$157$	6.38197	0.509336	0.254668	−	0.967029i	$-0.418034\pi$
$157$	6.38197	0.509336	0.254668	+	0.967029i	$0.418034\pi$
$158$	−10.4721	−0.833118
$159$	−14.9443	−1.18516
$160$	1.00000	0.0790569
$161$	−2.61803	−0.206330
$162$	2.41641	0.189851
$163$	−2.76393	−0.216488	−0.108244	−	0.994124i	$-0.534523\pi$
$163$	−2.76393	−0.216488	−0.108244	+	0.994124i	$0.534523\pi$
$164$	−4.85410	−0.379042
$165$	0	0
$166$	2.29180	0.177878
$167$	−19.0902	−1.47724	−0.738621	−	0.674121i	$-0.764523\pi$
$167$	−19.0902	−1.47724	−0.738621	+	0.674121i	$0.764523\pi$
$168$	−0.472136	−0.0364261
$169$	−12.6180	−0.970618
$170$	0.763932	0.0585909
$171$	10.4377	0.798190
$172$	4.76393	0.363246
$173$	10.3820	0.789326	0.394663	−	0.918826i	$-0.370861\pi$
$173$	10.3820	0.789326	0.394663	+	0.918826i	$0.370861\pi$
$174$	−4.00000	−0.303239
$175$	−0.381966	−0.0288739
$176$	0	0
$177$	−5.70820	−0.429055
$178$	−17.0344	−1.27679
$179$	−14.0902	−1.05315	−0.526574	−	0.850129i	$-0.676524\pi$
$179$	−14.0902	−1.05315	−0.526574	+	0.850129i	$0.676524\pi$
$180$	1.47214	0.109727
$181$	−11.5279	−0.856859	−0.428430	−	0.903575i	$-0.640933\pi$
$181$	−11.5279	−0.856859	−0.428430	+	0.903575i	$0.640933\pi$
$182$	−0.236068	−0.0174985
$183$	−11.0557	−0.817263
$184$	−6.85410	−0.505291
$185$	−5.85410	−0.430402
$186$	−3.41641	−0.250503
$187$	0	0
$188$	−4.32624	−0.315523
$189$	−2.11146	−0.153586
$190$	−7.09017	−0.514375
$191$	−1.41641	−0.102488	−0.0512438	−	0.998686i	$-0.516319\pi$
$191$	−1.41641	−0.102488	−0.0512438	+	0.998686i	$0.516319\pi$
$192$	−1.23607	−0.0892055
$193$	−21.4164	−1.54159	−0.770793	−	0.637085i	$-0.780140\pi$
$193$	−21.4164	−1.54159	−0.770793	+	0.637085i	$0.780140\pi$
$194$	12.0000	0.861550
$195$	−0.763932	−0.0547063
$196$	−6.85410	−0.489579
$197$	16.0902	1.14638	0.573189	−	0.819423i	$-0.305706\pi$
$197$	16.0902	1.14638	0.573189	+	0.819423i	$0.305706\pi$
$198$	0	0
$199$	−11.7082	−0.829973	−0.414986	−	0.909828i	$-0.636214\pi$
$199$	−11.7082	−0.829973	−0.414986	+	0.909828i	$0.636214\pi$
$200$	−1.00000	−0.0707107
$201$	−6.47214	−0.456509
$202$	−9.70820	−0.683067
$203$	1.23607	0.0867550
$204$	−0.944272	−0.0661123
$205$	4.85410	0.339025
$206$	−4.32624	−0.301423
$207$	−10.0902	−0.701315
$208$	−0.618034	−0.0428529
$209$	0	0
$210$	0.472136	0.0325805
$211$	−3.05573	−0.210365	−0.105182	−	0.994453i	$-0.533543\pi$
$211$	−3.05573	−0.210365	−0.105182	+	0.994453i	$0.533543\pi$
$212$	12.0902	0.830356
$213$	−10.8328	−0.742252
$214$	−16.4721	−1.12601
$215$	−4.76393	−0.324897
$216$	−5.52786	−0.376124
$217$	1.05573	0.0716675
$218$	16.4721	1.11563
$219$	14.4721	0.977936
$220$	0	0
$221$	−0.472136	−0.0317593
$222$	7.23607	0.485653
$223$	25.3262	1.69597	0.847985	−	0.530020i	$-0.177816\pi$
$223$	25.3262	1.69597	0.847985	+	0.530020i	$0.177816\pi$
$224$	0.381966	0.0255212
$225$	−1.47214	−0.0981424
$226$	−19.7082	−1.31097
$227$	7.52786	0.499642	0.249821	−	0.968292i	$-0.419628\pi$
$227$	7.52786	0.499642	0.249821	+	0.968292i	$0.419628\pi$
$228$	8.76393	0.580406
$229$	−5.81966	−0.384574	−0.192287	−	0.981339i	$-0.561590\pi$
$229$	−5.81966	−0.384574	−0.192287	+	0.981339i	$0.561590\pi$
$230$	6.85410	0.451946
$231$	0	0
$232$	3.23607	0.212458
$233$	−10.7639	−0.705169	−0.352584	−	0.935780i	$-0.614697\pi$
$233$	−10.7639	−0.705169	−0.352584	+	0.935780i	$0.614697\pi$
$234$	−0.909830	−0.0594775
$235$	4.32624	0.282213
$236$	4.61803	0.300608
$237$	−12.9443	−0.840821
$238$	0.291796	0.0189143
$239$	−18.4721	−1.19486	−0.597432	−	0.801920i	$-0.703812\pi$
$239$	−18.4721	−1.19486	−0.597432	+	0.801920i	$0.703812\pi$
$240$	1.23607	0.0797878
$241$	−4.85410	−0.312680	−0.156340	−	0.987703i	$-0.549970\pi$
$241$	−4.85410	−0.312680	−0.156340	+	0.987703i	$0.549970\pi$
$242$	0	0
$243$	−13.5967	−0.872232
$244$	8.94427	0.572598
$245$	6.85410	0.437893
$246$	−6.00000	−0.382546
$247$	4.38197	0.278818
$248$	2.76393	0.175510
$249$	2.83282	0.179522
$250$	1.00000	0.0632456
$251$	19.0344	1.20144	0.600722	−	0.799458i	$-0.294880\pi$
$251$	19.0344	1.20144	0.600722	+	0.799458i	$0.294880\pi$
$252$	0.562306	0.0354219
$253$	0	0
$254$	−4.61803	−0.289761
$255$	0.944272	0.0591326
$256$	1.00000	0.0625000
$257$	−12.0000	−0.748539	−0.374270	−	0.927320i	$-0.622107\pi$
$257$	−12.0000	−0.748539	−0.374270	+	0.927320i	$0.622107\pi$
$258$	5.88854	0.366605
$259$	−2.23607	−0.138943
$260$	0.618034	0.0383288
$261$	4.76393	0.294880
$262$	−15.4164	−0.952429
$263$	−1.20163	−0.0740954	−0.0370477	−	0.999313i	$-0.511795\pi$
$263$	−1.20163	−0.0740954	−0.0370477	+	0.999313i	$0.511795\pi$
$264$	0	0
$265$	−12.0902	−0.742693
$266$	−2.70820	−0.166051
$267$	−21.0557	−1.28859
$268$	5.23607	0.319844
$269$	−31.5967	−1.92649	−0.963244	−	0.268629i	$-0.913430\pi$
$269$	−31.5967	−1.92649	−0.963244	+	0.268629i	$0.913430\pi$
$270$	5.52786	0.336415
$271$	13.4164	0.814989	0.407494	−	0.913208i	$-0.366403\pi$
$271$	13.4164	0.814989	0.407494	+	0.913208i	$0.366403\pi$
$272$	0.763932	0.0463202
$273$	−0.291796	−0.0176603
$274$	0.763932	0.0461508
$275$	0	0
$276$	−8.47214	−0.509963
$277$	−1.61803	−0.0972182	−0.0486091	−	0.998818i	$-0.515479\pi$
$277$	−1.61803	−0.0972182	−0.0486091	+	0.998818i	$0.515479\pi$
$278$	−14.8541	−0.890890
$279$	4.06888	0.243598
$280$	−0.381966	−0.0228268
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−5.34752	−0.318440
$283$	28.8328	1.71393	0.856966	−	0.515372i	$-0.172346\pi$
$283$	28.8328	1.71393	0.856966	+	0.515372i	$0.172346\pi$
$284$	8.76393	0.520044
$285$	−8.76393	−0.519131
$286$	0	0
$287$	1.85410	0.109444
$288$	1.47214	0.0867464
$289$	−16.4164	−0.965671
$290$	−3.23607	−0.190028
$291$	14.8328	0.869515
$292$	−11.7082	−0.685171
$293$	−18.7426	−1.09496	−0.547479	−	0.836820i	$-0.684412\pi$
$293$	−18.7426	−1.09496	−0.547479	+	0.836820i	$0.684412\pi$
$294$	−8.47214	−0.494105
$295$	−4.61803	−0.268872
$296$	−5.85410	−0.340263
$297$	0	0
$298$	−4.00000	−0.231714
$299$	−4.23607	−0.244978
$300$	−1.23607	−0.0713644
$301$	−1.81966	−0.104883
$302$	−18.6525	−1.07333
$303$	−12.0000	−0.689382
$304$	−7.09017	−0.406649
$305$	−8.94427	−0.512148
$306$	1.12461	0.0642898
$307$	9.05573	0.516838	0.258419	−	0.966033i	$-0.416799\pi$
$307$	9.05573	0.516838	0.258419	+	0.966033i	$0.416799\pi$
$308$	0	0
$309$	−5.34752	−0.304210
$310$	−2.76393	−0.156981
$311$	6.47214	0.367001	0.183501	−	0.983020i	$-0.441257\pi$
$311$	6.47214	0.367001	0.183501	+	0.983020i	$0.441257\pi$
$312$	−0.763932	−0.0432491
$313$	0.583592	0.0329866	0.0164933	−	0.999864i	$-0.494750\pi$
$313$	0.583592	0.0329866	0.0164933	+	0.999864i	$0.494750\pi$
$314$	−6.38197	−0.360155
$315$	−0.562306	−0.0316823
$316$	10.4721	0.589104
$317$	30.7984	1.72981	0.864905	−	0.501936i	$-0.167379\pi$
$317$	30.7984	1.72981	0.864905	+	0.501936i	$0.167379\pi$
$318$	14.9443	0.838033
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−20.3607	−1.13642
$322$	2.61803	0.145897
$323$	−5.41641	−0.301377
$324$	−2.41641	−0.134245
$325$	−0.618034	−0.0342824
$326$	2.76393	0.153080
$327$	20.3607	1.12595
$328$	4.85410	0.268023
$329$	1.65248	0.0911039
$330$	0	0
$331$	−16.6180	−0.913410	−0.456705	−	0.889618i	$-0.650970\pi$
$331$	−16.6180	−0.913410	−0.456705	+	0.889618i	$0.650970\pi$
$332$	−2.29180	−0.125779
$333$	−8.61803	−0.472265
$334$	19.0902	1.04457
$335$	−5.23607	−0.286077
$336$	0.472136	0.0257571
$337$	−8.58359	−0.467578	−0.233789	−	0.972287i	$-0.575113\pi$
$337$	−8.58359	−0.467578	−0.233789	+	0.972287i	$0.575113\pi$
$338$	12.6180	0.686331
$339$	−24.3607	−1.32309
$340$	−0.763932	−0.0414300
$341$	0	0
$342$	−10.4377	−0.564406
$343$	5.29180	0.285730
$344$	−4.76393	−0.256854
$345$	8.47214	0.456124
$346$	−10.3820	−0.558138
$347$	−13.1246	−0.704566	−0.352283	−	0.935894i	$-0.614595\pi$
$347$	−13.1246	−0.704566	−0.352283	+	0.935894i	$0.614595\pi$
$348$	4.00000	0.214423
$349$	−13.0557	−0.698857	−0.349429	−	0.936963i	$-0.613624\pi$
$349$	−13.0557	−0.698857	−0.349429	+	0.936963i	$0.613624\pi$
$350$	0.381966	0.0204169
$351$	−3.41641	−0.182354
$352$	0	0
$353$	−1.70820	−0.0909185	−0.0454593	−	0.998966i	$-0.514475\pi$
$353$	−1.70820	−0.0909185	−0.0454593	+	0.998966i	$0.514475\pi$
$354$	5.70820	0.303388
$355$	−8.76393	−0.465141
$356$	17.0344	0.902824
$357$	0.360680	0.0190892
$358$	14.0902	0.744689
$359$	21.5279	1.13620	0.568099	−	0.822960i	$-0.307679\pi$
$359$	21.5279	1.13620	0.568099	+	0.822960i	$0.307679\pi$
$360$	−1.47214	−0.0775884
$361$	31.2705	1.64582
$362$	11.5279	0.605891
$363$	0	0
$364$	0.236068	0.0123733
$365$	11.7082	0.612835
$366$	11.0557	0.577892
$367$	1.52786	0.0797539	0.0398769	−	0.999205i	$-0.487303\pi$
$367$	1.52786	0.0797539	0.0398769	+	0.999205i	$0.487303\pi$
$368$	6.85410	0.357295
$369$	7.14590	0.372001
$370$	5.85410	0.304340
$371$	−4.61803	−0.239756
$372$	3.41641	0.177132
$373$	−36.0344	−1.86579	−0.932896	−	0.360145i	$-0.882727\pi$
$373$	−36.0344	−1.86579	−0.932896	+	0.360145i	$0.882727\pi$
$374$	0	0
$375$	1.23607	0.0638303
$376$	4.32624	0.223109
$377$	2.00000	0.103005
$378$	2.11146	0.108602
$379$	5.32624	0.273590	0.136795	−	0.990599i	$-0.456320\pi$
$379$	5.32624	0.273590	0.136795	+	0.990599i	$0.456320\pi$
$380$	7.09017	0.363718
$381$	−5.70820	−0.292440
$382$	1.41641	0.0724697
$383$	−9.14590	−0.467334	−0.233667	−	0.972317i	$-0.575072\pi$
$383$	−9.14590	−0.467334	−0.233667	+	0.972317i	$0.575072\pi$
$384$	1.23607	0.0630778
$385$	0	0
$386$	21.4164	1.09007
$387$	−7.01316	−0.356499
$388$	−12.0000	−0.609208
$389$	−10.1803	−0.516164	−0.258082	−	0.966123i	$-0.583090\pi$
$389$	−10.1803	−0.516164	−0.258082	+	0.966123i	$0.583090\pi$
$390$	0.763932	0.0386832
$391$	5.23607	0.264799
$392$	6.85410	0.346184
$393$	−19.0557	−0.961234
$394$	−16.0902	−0.810611
$395$	−10.4721	−0.526910
$396$	0	0
$397$	−17.7984	−0.893275	−0.446637	−	0.894715i	$-0.647379\pi$
$397$	−17.7984	−0.893275	−0.446637	+	0.894715i	$0.647379\pi$
$398$	11.7082	0.586879
$399$	−3.34752	−0.167586
$400$	1.00000	0.0500000
$401$	31.7426	1.58515	0.792576	−	0.609773i	$-0.208739\pi$
$401$	31.7426	1.58515	0.792576	+	0.609773i	$0.208739\pi$
$402$	6.47214	0.322801
$403$	1.70820	0.0850917
$404$	9.70820	0.483001
$405$	2.41641	0.120072
$406$	−1.23607	−0.0613450
$407$	0	0
$408$	0.944272	0.0467484
$409$	7.67376	0.379443	0.189722	−	0.981838i	$-0.439241\pi$
$409$	7.67376	0.379443	0.189722	+	0.981838i	$0.439241\pi$
$410$	−4.85410	−0.239727
$411$	0.944272	0.0465775
$412$	4.32624	0.213138
$413$	−1.76393	−0.0867974
$414$	10.0902	0.495905
$415$	2.29180	0.112500
$416$	0.618034	0.0303016
$417$	−18.3607	−0.899126
$418$	0	0
$419$	0.618034	0.0301929	0.0150965	−	0.999886i	$-0.495194\pi$
$419$	0.618034	0.0301929	0.0150965	+	0.999886i	$0.495194\pi$
$420$	−0.472136	−0.0230379
$421$	12.6525	0.616644	0.308322	−	0.951282i	$-0.400233\pi$
$421$	12.6525	0.616644	0.308322	+	0.951282i	$0.400233\pi$
$422$	3.05573	0.148751
$423$	6.36881	0.309662
$424$	−12.0902	−0.587151
$425$	0.763932	0.0370561
$426$	10.8328	0.524852
$427$	−3.41641	−0.165332
$428$	16.4721	0.796211
$429$	0	0
$430$	4.76393	0.229737
$431$	3.81966	0.183987	0.0919933	−	0.995760i	$-0.470676\pi$
$431$	3.81966	0.183987	0.0919933	+	0.995760i	$0.470676\pi$
$432$	5.52786	0.265959
$433$	18.4721	0.887714	0.443857	−	0.896098i	$-0.353610\pi$
$433$	18.4721	0.887714	0.443857	+	0.896098i	$0.353610\pi$
$434$	−1.05573	−0.0506766
$435$	−4.00000	−0.191785
$436$	−16.4721	−0.788872
$437$	−48.5967	−2.32470
$438$	−14.4721	−0.691505
$439$	−27.1246	−1.29459	−0.647294	−	0.762241i	$-0.724099\pi$
$439$	−27.1246	−1.29459	−0.647294	+	0.762241i	$0.724099\pi$
$440$	0	0
$441$	10.0902	0.480484
$442$	0.472136	0.0224572
$443$	32.6525	1.55137	0.775683	−	0.631123i	$-0.217406\pi$
$443$	32.6525	1.55137	0.775683	+	0.631123i	$0.217406\pi$
$444$	−7.23607	−0.343409
$445$	−17.0344	−0.807510
$446$	−25.3262	−1.19923
$447$	−4.94427	−0.233856
$448$	−0.381966	−0.0180462
$449$	9.85410	0.465044	0.232522	−	0.972591i	$-0.425302\pi$
$449$	9.85410	0.465044	0.232522	+	0.972591i	$0.425302\pi$
$450$	1.47214	0.0693972
$451$	0	0
$452$	19.7082	0.926996
$453$	−23.0557	−1.08325
$454$	−7.52786	−0.353300
$455$	−0.236068	−0.0110670
$456$	−8.76393	−0.410409
$457$	34.5410	1.61576	0.807880	−	0.589347i	$-0.200615\pi$
$457$	34.5410	1.61576	0.807880	+	0.589347i	$0.200615\pi$
$458$	5.81966	0.271935
$459$	4.22291	0.197109
$460$	−6.85410	−0.319574
$461$	38.5410	1.79503	0.897517	−	0.440980i	$-0.145369\pi$
$461$	38.5410	1.79503	0.897517	+	0.440980i	$0.145369\pi$
$462$	0	0
$463$	−22.5066	−1.04597	−0.522985	−	0.852342i	$-0.675182\pi$
$463$	−22.5066	−1.04597	−0.522985	+	0.852342i	$0.675182\pi$
$464$	−3.23607	−0.150231
$465$	−3.41641	−0.158432
$466$	10.7639	0.498630
$467$	12.7639	0.590644	0.295322	−	0.955398i	$-0.404573\pi$
$467$	12.7639	0.590644	0.295322	+	0.955398i	$0.404573\pi$
$468$	0.909830	0.0420569
$469$	−2.00000	−0.0923514
$470$	−4.32624	−0.199554
$471$	−7.88854	−0.363485
$472$	−4.61803	−0.212562
$473$	0	0
$474$	12.9443	0.594550
$475$	−7.09017	−0.325319
$476$	−0.291796	−0.0133745
$477$	−17.7984	−0.814932
$478$	18.4721	0.844896
$479$	−19.5967	−0.895398	−0.447699	−	0.894184i	$-0.647756\pi$
$479$	−19.5967	−0.895398	−0.447699	+	0.894184i	$0.647756\pi$
$480$	−1.23607	−0.0564185
$481$	−3.61803	−0.164968
$482$	4.85410	0.221098
$483$	3.23607	0.147246
$484$	0	0
$485$	12.0000	0.544892
$486$	13.5967	0.616761
$487$	19.0557	0.863497	0.431749	−	0.901994i	$-0.357897\pi$
$487$	19.0557	0.863497	0.431749	+	0.901994i	$0.357897\pi$
$488$	−8.94427	−0.404888
$489$	3.41641	0.154495
$490$	−6.85410	−0.309637
$491$	19.4508	0.877805	0.438902	−	0.898535i	$-0.355367\pi$
$491$	19.4508	0.877805	0.438902	+	0.898535i	$0.355367\pi$
$492$	6.00000	0.270501
$493$	−2.47214	−0.111339
$494$	−4.38197	−0.197154
$495$	0	0
$496$	−2.76393	−0.124104
$497$	−3.34752	−0.150157
$498$	−2.83282	−0.126942
$499$	11.7984	0.528168	0.264084	−	0.964500i	$-0.414930\pi$
$499$	11.7984	0.528168	0.264084	+	0.964500i	$0.414930\pi$
$500$	−1.00000	−0.0447214
$501$	23.5967	1.05422
$502$	−19.0344	−0.849549
$503$	30.5066	1.36022	0.680111	−	0.733110i	$-0.261932\pi$
$503$	30.5066	1.36022	0.680111	+	0.733110i	$0.261932\pi$
$504$	−0.562306	−0.0250471
$505$	−9.70820	−0.432009
$506$	0	0
$507$	15.5967	0.692676
$508$	4.61803	0.204892
$509$	9.12461	0.404441	0.202221	−	0.979340i	$-0.435184\pi$
$509$	9.12461	0.404441	0.202221	+	0.979340i	$0.435184\pi$
$510$	−0.944272	−0.0418131
$511$	4.47214	0.197836
$512$	−1.00000	−0.0441942
$513$	−39.1935	−1.73044
$514$	12.0000	0.529297
$515$	−4.32624	−0.190637
$516$	−5.88854	−0.259229
$517$	0	0
$518$	2.23607	0.0982472
$519$	−12.8328	−0.563298
$520$	−0.618034	−0.0271026
$521$	−6.38197	−0.279599	−0.139800	−	0.990180i	$-0.544646\pi$
$521$	−6.38197	−0.279599	−0.139800	+	0.990180i	$0.544646\pi$
$522$	−4.76393	−0.208512
$523$	38.6525	1.69015	0.845077	−	0.534644i	$-0.179554\pi$
$523$	38.6525	1.69015	0.845077	+	0.534644i	$0.179554\pi$
$524$	15.4164	0.673469
$525$	0.472136	0.0206057
$526$	1.20163	0.0523934
$527$	−2.11146	−0.0919765
$528$	0	0
$529$	23.9787	1.04255
$530$	12.0902	0.525163
$531$	−6.79837	−0.295024
$532$	2.70820	0.117416
$533$	3.00000	0.129944
$534$	21.0557	0.911170
$535$	−16.4721	−0.712153
$536$	−5.23607	−0.226164
$537$	17.4164	0.751573
$538$	31.5967	1.36223
$539$	0	0
$540$	−5.52786	−0.237881
$541$	8.00000	0.343947	0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000	0.343947	0.171973	+	0.985102i	$0.444986\pi$
$542$	−13.4164	−0.576284
$543$	14.2492	0.611493
$544$	−0.763932	−0.0327533
$545$	16.4721	0.705589
$546$	0.291796	0.0124877
$547$	−33.5967	−1.43649	−0.718247	−	0.695789i	$-0.755055\pi$
$547$	−33.5967	−1.43649	−0.718247	+	0.695789i	$0.755055\pi$
$548$	−0.763932	−0.0326336
$549$	−13.1672	−0.561962
$550$	0	0
$551$	22.9443	0.977459
$552$	8.47214	0.360598
$553$	−4.00000	−0.170097
$554$	1.61803	0.0687437
$555$	7.23607	0.307154
$556$	14.8541	0.629954
$557$	18.2148	0.771785	0.385893	−	0.922544i	$-0.373894\pi$
$557$	18.2148	0.771785	0.385893	+	0.922544i	$0.373894\pi$
$558$	−4.06888	−0.172250
$559$	−2.94427	−0.124529
$560$	0.381966	0.0161410
$561$	0	0
$562$	18.0000	0.759284
$563$	11.8885	0.501042	0.250521	−	0.968111i	$-0.419398\pi$
$563$	11.8885	0.501042	0.250521	+	0.968111i	$0.419398\pi$
$564$	5.34752	0.225171
$565$	−19.7082	−0.829130
$566$	−28.8328	−1.21193
$567$	0.922986	0.0387618
$568$	−8.76393	−0.367726
$569$	7.32624	0.307132	0.153566	−	0.988138i	$-0.450924\pi$
$569$	7.32624	0.307132	0.153566	+	0.988138i	$0.450924\pi$
$570$	8.76393	0.367081
$571$	17.9098	0.749503	0.374752	−	0.927125i	$-0.377728\pi$
$571$	17.9098	0.749503	0.374752	+	0.927125i	$0.377728\pi$
$572$	0	0
$573$	1.75078	0.0731397
$574$	−1.85410	−0.0773887
$575$	6.85410	0.285836
$576$	−1.47214	−0.0613390
$577$	−2.94427	−0.122572	−0.0612858	−	0.998120i	$-0.519520\pi$
$577$	−2.94427	−0.122572	−0.0612858	+	0.998120i	$0.519520\pi$
$578$	16.4164	0.682833
$579$	26.4721	1.10014
$580$	3.23607	0.134370
$581$	0.875388	0.0363172
$582$	−14.8328	−0.614840
$583$	0	0
$584$	11.7082	0.484489
$585$	−0.909830	−0.0376168
$586$	18.7426	0.774252
$587$	−25.2361	−1.04160	−0.520802	−	0.853678i	$-0.674367\pi$
$587$	−25.2361	−1.04160	−0.520802	+	0.853678i	$0.674367\pi$
$588$	8.47214	0.349385
$589$	19.5967	0.807470
$590$	4.61803	0.190121
$591$	−19.8885	−0.818105
$592$	5.85410	0.240602
$593$	6.29180	0.258373	0.129187	−	0.991620i	$-0.458763\pi$
$593$	6.29180	0.258373	0.129187	+	0.991620i	$0.458763\pi$
$594$	0	0
$595$	0.291796	0.0119625
$596$	4.00000	0.163846
$597$	14.4721	0.592305
$598$	4.23607	0.173226
$599$	7.52786	0.307580	0.153790	−	0.988104i	$-0.450852\pi$
$599$	7.52786	0.307580	0.153790	+	0.988104i	$0.450852\pi$
$600$	1.23607	0.0504623
$601$	−2.43769	−0.0994356	−0.0497178	−	0.998763i	$-0.515832\pi$
$601$	−2.43769	−0.0994356	−0.0497178	+	0.998763i	$0.515832\pi$
$602$	1.81966	0.0741638
$603$	−7.70820	−0.313902
$604$	18.6525	0.758958
$605$	0	0
$606$	12.0000	0.487467
$607$	12.3607	0.501705	0.250852	−	0.968025i	$-0.419289\pi$
$607$	12.3607	0.501705	0.250852	+	0.968025i	$0.419289\pi$
$608$	7.09017	0.287544
$609$	−1.52786	−0.0619122
$610$	8.94427	0.362143
$611$	2.67376	0.108169
$612$	−1.12461	−0.0454597
$613$	−20.4721	−0.826862	−0.413431	−	0.910536i	$-0.635670\pi$
$613$	−20.4721	−0.826862	−0.413431	+	0.910536i	$0.635670\pi$
$614$	−9.05573	−0.365459
$615$	−6.00000	−0.241943
$616$	0	0
$617$	15.0557	0.606121	0.303060	−	0.952971i	$-0.401992\pi$
$617$	15.0557	0.606121	0.303060	+	0.952971i	$0.401992\pi$
$618$	5.34752	0.215109
$619$	−19.7426	−0.793524	−0.396762	−	0.917922i	$-0.629866\pi$
$619$	−19.7426	−0.793524	−0.396762	+	0.917922i	$0.629866\pi$
$620$	2.76393	0.111002
$621$	37.8885	1.52041
$622$	−6.47214	−0.259509
$623$	−6.50658	−0.260681
$624$	0.763932	0.0305818
$625$	1.00000	0.0400000
$626$	−0.583592	−0.0233250
$627$	0	0
$628$	6.38197	0.254668
$629$	4.47214	0.178316
$630$	0.562306	0.0224028
$631$	−19.4164	−0.772955	−0.386477	−	0.922299i	$-0.626308\pi$
$631$	−19.4164	−0.772955	−0.386477	+	0.922299i	$0.626308\pi$
$632$	−10.4721	−0.416559
$633$	3.77709	0.150126
$634$	−30.7984	−1.22316
$635$	−4.61803	−0.183261
$636$	−14.9443	−0.592579
$637$	4.23607	0.167839
$638$	0	0
$639$	−12.9017	−0.510383
$640$	1.00000	0.0395285
$641$	−31.1591	−1.23071	−0.615354	−	0.788251i	$-0.710987\pi$
$641$	−31.1591	−1.23071	−0.615354	+	0.788251i	$0.710987\pi$
$642$	20.3607	0.803572
$643$	13.4164	0.529091	0.264546	−	0.964373i	$-0.414778\pi$
$643$	13.4164	0.529091	0.264546	+	0.964373i	$0.414778\pi$
$644$	−2.61803	−0.103165
$645$	5.88854	0.231861
$646$	5.41641	0.213106
$647$	−24.9443	−0.980661	−0.490330	−	0.871537i	$-0.663124\pi$
$647$	−24.9443	−0.980661	−0.490330	+	0.871537i	$0.663124\pi$
$648$	2.41641	0.0949255
$649$	0	0
$650$	0.618034	0.0242413
$651$	−1.30495	−0.0511451
$652$	−2.76393	−0.108244
$653$	1.20163	0.0470233	0.0235116	−	0.999724i	$-0.492515\pi$
$653$	1.20163	0.0470233	0.0235116	+	0.999724i	$0.492515\pi$
$654$	−20.3607	−0.796166
$655$	−15.4164	−0.602369
$656$	−4.85410	−0.189521
$657$	17.2361	0.672443
$658$	−1.65248	−0.0644202
$659$	15.6180	0.608392	0.304196	−	0.952609i	$-0.401612\pi$
$659$	15.6180	0.608392	0.304196	+	0.952609i	$0.401612\pi$
$660$	0	0
$661$	−20.1803	−0.784924	−0.392462	−	0.919768i	$-0.628377\pi$
$661$	−20.1803	−0.784924	−0.392462	+	0.919768i	$0.628377\pi$
$662$	16.6180	0.645878
$663$	0.583592	0.0226648
$664$	2.29180	0.0889389
$665$	−2.70820	−0.105020
$666$	8.61803	0.333942
$667$	−22.1803	−0.858826
$668$	−19.0902	−0.738621
$669$	−31.3050	−1.21032
$670$	5.23607	0.202287
$671$	0	0
$672$	−0.472136	−0.0182130
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	8.58359	0.330628
$675$	5.52786	0.212768
$676$	−12.6180	−0.485309
$677$	10.0000	0.384331	0.192166	−	0.981363i	$-0.438449\pi$
$677$	10.0000	0.384331	0.192166	+	0.981363i	$0.438449\pi$
$678$	24.3607	0.935566
$679$	4.58359	0.175902
$680$	0.763932	0.0292955
$681$	−9.30495	−0.356567
$682$	0	0
$683$	29.0132	1.11016	0.555079	−	0.831798i	$-0.312688\pi$
$683$	29.0132	1.11016	0.555079	+	0.831798i	$0.312688\pi$
$684$	10.4377	0.399095
$685$	0.763932	0.0291883
$686$	−5.29180	−0.202042
$687$	7.19350	0.274449
$688$	4.76393	0.181623
$689$	−7.47214	−0.284666
$690$	−8.47214	−0.322529
$691$	−28.7426	−1.09342	−0.546711	−	0.837321i	$-0.684120\pi$
$691$	−28.7426	−1.09342	−0.546711	+	0.837321i	$0.684120\pi$
$692$	10.3820	0.394663
$693$	0	0
$694$	13.1246	0.498203
$695$	−14.8541	−0.563448
$696$	−4.00000	−0.151620
$697$	−3.70820	−0.140458
$698$	13.0557	0.494167
$699$	13.3050	0.503239
$700$	−0.381966	−0.0144370
$701$	−28.1803	−1.06436	−0.532178	−	0.846632i	$-0.678626\pi$
$701$	−28.1803	−1.06436	−0.532178	+	0.846632i	$0.678626\pi$
$702$	3.41641	0.128944
$703$	−41.5066	−1.56545
$704$	0	0
$705$	−5.34752	−0.201399
$706$	1.70820	0.0642891
$707$	−3.70820	−0.139461
$708$	−5.70820	−0.214527
$709$	51.1246	1.92003	0.960013	−	0.279957i	$-0.0903202\pi$
$709$	51.1246	1.92003	0.960013	+	0.279957i	$0.0903202\pi$
$710$	8.76393	0.328905
$711$	−15.4164	−0.578160
$712$	−17.0344	−0.638393
$713$	−18.9443	−0.709469
$714$	−0.360680	−0.0134981
$715$	0	0
$716$	−14.0902	−0.526574
$717$	22.8328	0.852707
$718$	−21.5279	−0.803413
$719$	46.1803	1.72224	0.861118	−	0.508405i	$-0.169765\pi$
$719$	46.1803	1.72224	0.861118	+	0.508405i	$0.169765\pi$
$720$	1.47214	0.0548633
$721$	−1.65248	−0.0615414
$722$	−31.2705	−1.16377
$723$	6.00000	0.223142
$724$	−11.5279	−0.428430
$725$	−3.23607	−0.120185
$726$	0	0
$727$	15.7984	0.585929	0.292965	−	0.956123i	$-0.405358\pi$
$727$	15.7984	0.585929	0.292965	+	0.956123i	$0.405358\pi$
$728$	−0.236068	−0.00874926
$729$	24.0557	0.890953
$730$	−11.7082	−0.433340
$731$	3.63932	0.134605
$732$	−11.0557	−0.408631
$733$	44.2492	1.63438	0.817191	−	0.576367i	$-0.195530\pi$
$733$	44.2492	1.63438	0.817191	+	0.576367i	$0.195530\pi$
$734$	−1.52786	−0.0563945
$735$	−8.47214	−0.312499
$736$	−6.85410	−0.252646
$737$	0	0
$738$	−7.14590	−0.263044
$739$	25.1459	0.925007	0.462503	−	0.886618i	$-0.346951\pi$
$739$	25.1459	0.925007	0.462503	+	0.886618i	$0.346951\pi$
$740$	−5.85410	−0.215201
$741$	−5.41641	−0.198977
$742$	4.61803	0.169533
$743$	−24.7426	−0.907720	−0.453860	−	0.891073i	$-0.649953\pi$
$743$	−24.7426	−0.907720	−0.453860	+	0.891073i	$0.649953\pi$
$744$	−3.41641	−0.125252
$745$	−4.00000	−0.146549
$746$	36.0344	1.31931
$747$	3.37384	0.123442
$748$	0	0
$749$	−6.29180	−0.229897
$750$	−1.23607	−0.0451348
$751$	6.94427	0.253400	0.126700	−	0.991941i	$-0.459561\pi$
$751$	6.94427	0.253400	0.126700	+	0.991941i	$0.459561\pi$
$752$	−4.32624	−0.157762
$753$	−23.5279	−0.857403
$754$	−2.00000	−0.0728357
$755$	−18.6525	−0.678833
$756$	−2.11146	−0.0767929
$757$	46.7984	1.70092	0.850458	−	0.526043i	$-0.176325\pi$
$757$	46.7984	1.70092	0.850458	+	0.526043i	$0.176325\pi$
$758$	−5.32624	−0.193458
$759$	0	0
$760$	−7.09017	−0.257187
$761$	−33.4164	−1.21134	−0.605672	−	0.795714i	$-0.707096\pi$
$761$	−33.4164	−1.21134	−0.605672	+	0.795714i	$0.707096\pi$
$762$	5.70820	0.206786
$763$	6.29180	0.227778
$764$	−1.41641	−0.0512438
$765$	1.12461	0.0406604
$766$	9.14590	0.330455
$767$	−2.85410	−0.103056
$768$	−1.23607	−0.0446028
$769$	20.9098	0.754028	0.377014	−	0.926208i	$-0.376951\pi$
$769$	20.9098	0.754028	0.377014	+	0.926208i	$0.376951\pi$
$770$	0	0
$771$	14.8328	0.534191
$772$	−21.4164	−0.770793
$773$	−17.4377	−0.627190	−0.313595	−	0.949557i	$-0.601533\pi$
$773$	−17.4377	−0.627190	−0.313595	+	0.949557i	$0.601533\pi$
$774$	7.01316	0.252083
$775$	−2.76393	−0.0992834
$776$	12.0000	0.430775
$777$	2.76393	0.0991555
$778$	10.1803	0.364983
$779$	34.4164	1.23310
$780$	−0.763932	−0.0273532
$781$	0	0
$782$	−5.23607	−0.187241
$783$	−17.8885	−0.639284
$784$	−6.85410	−0.244789
$785$	−6.38197	−0.227782
$786$	19.0557	0.679695
$787$	36.0000	1.28326	0.641631	−	0.767014i	$-0.278258\pi$
$787$	36.0000	1.28326	0.641631	+	0.767014i	$0.278258\pi$
$788$	16.0902	0.573189
$789$	1.48529	0.0528778
$790$	10.4721	0.372582
$791$	−7.52786	−0.267660
$792$	0	0
$793$	−5.52786	−0.196300
$794$	17.7984	0.631641
$795$	14.9443	0.530019
$796$	−11.7082	−0.414986
$797$	7.96556	0.282155	0.141077	−	0.989999i	$-0.454943\pi$
$797$	7.96556	0.282155	0.141077	+	0.989999i	$0.454943\pi$
$798$	3.34752	0.118501
$799$	−3.30495	−0.116921
$800$	−1.00000	−0.0353553
$801$	−25.0770	−0.886053
$802$	−31.7426	−1.12087
$803$	0	0
$804$	−6.47214	−0.228255
$805$	2.61803	0.0922736
$806$	−1.70820	−0.0601689
$807$	39.0557	1.37483
$808$	−9.70820	−0.341533
$809$	−20.0344	−0.704373	−0.352187	−	0.935930i	$-0.614562\pi$
$809$	−20.0344	−0.704373	−0.352187	+	0.935930i	$0.614562\pi$
$810$	−2.41641	−0.0849039
$811$	44.3820	1.55846	0.779231	−	0.626737i	$-0.215610\pi$
$811$	44.3820	1.55846	0.779231	+	0.626737i	$0.215610\pi$
$812$	1.23607	0.0433775
$813$	−16.5836	−0.581612
$814$	0	0
$815$	2.76393	0.0968163
$816$	−0.944272	−0.0330561
$817$	−33.7771	−1.18171
$818$	−7.67376	−0.268307
$819$	−0.347524	−0.0121435
$820$	4.85410	0.169513
$821$	−20.3607	−0.710593	−0.355296	−	0.934754i	$-0.615620\pi$
$821$	−20.3607	−0.710593	−0.355296	+	0.934754i	$0.615620\pi$
$822$	−0.944272	−0.0329353
$823$	12.0344	0.419494	0.209747	−	0.977756i	$-0.432736\pi$
$823$	12.0344	0.419494	0.209747	+	0.977756i	$0.432736\pi$
$824$	−4.32624	−0.150712
$825$	0	0
$826$	1.76393	0.0613750
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	−10.0902	−0.350658
$829$	4.94427	0.171722	0.0858608	−	0.996307i	$-0.472636\pi$
$829$	4.94427	0.171722	0.0858608	+	0.996307i	$0.472636\pi$
$830$	−2.29180	−0.0795494
$831$	2.00000	0.0693792
$832$	−0.618034	−0.0214265
$833$	−5.23607	−0.181419
$834$	18.3607	0.635778
$835$	19.0902	0.660643
$836$	0	0
$837$	−15.2786	−0.528107
$838$	−0.618034	−0.0213496
$839$	14.5410	0.502012	0.251006	−	0.967986i	$-0.419239\pi$
$839$	14.5410	0.502012	0.251006	+	0.967986i	$0.419239\pi$
$840$	0.472136	0.0162902
$841$	−18.5279	−0.638892
$842$	−12.6525	−0.436033
$843$	22.2492	0.766304
$844$	−3.05573	−0.105182
$845$	12.6180	0.434074
$846$	−6.36881	−0.218964
$847$	0	0
$848$	12.0902	0.415178
$849$	−35.6393	−1.22314
$850$	−0.763932	−0.0262027
$851$	40.1246	1.37545
$852$	−10.8328	−0.371126
$853$	−45.0344	−1.54195	−0.770975	−	0.636865i	$-0.780231\pi$
$853$	−45.0344	−1.54195	−0.770975	+	0.636865i	$0.780231\pi$
$854$	3.41641	0.116907
$855$	−10.4377	−0.356962
$856$	−16.4721	−0.563006
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	−42.0902	−1.43610	−0.718049	−	0.695993i	$-0.754965\pi$
$859$	−42.0902	−1.43610	−0.718049	+	0.695993i	$0.754965\pi$
$860$	−4.76393	−0.162449
$861$	−2.29180	−0.0781042
$862$	−3.81966	−0.130098
$863$	−30.7984	−1.04839	−0.524194	−	0.851599i	$-0.675633\pi$
$863$	−30.7984	−1.04839	−0.524194	+	0.851599i	$0.675633\pi$
$864$	−5.52786	−0.188062
$865$	−10.3820	−0.352997
$866$	−18.4721	−0.627709
$867$	20.2918	0.689146
$868$	1.05573	0.0358337
$869$	0	0
$870$	4.00000	0.135613
$871$	−3.23607	−0.109650
$872$	16.4721	0.557817
$873$	17.6656	0.597891
$874$	48.5967	1.64381
$875$	0.381966	0.0129128
$876$	14.4721	0.488968
$877$	−4.61803	−0.155940	−0.0779700	−	0.996956i	$-0.524844\pi$
$877$	−4.61803	−0.155940	−0.0779700	+	0.996956i	$0.524844\pi$
$878$	27.1246	0.915411
$879$	23.1672	0.781410
$880$	0	0
$881$	28.4508	0.958533	0.479267	−	0.877669i	$-0.340903\pi$
$881$	28.4508	0.958533	0.479267	+	0.877669i	$0.340903\pi$
$882$	−10.0902	−0.339754
$883$	−0.652476	−0.0219576	−0.0109788	−	0.999940i	$-0.503495\pi$
$883$	−0.652476	−0.0219576	−0.0109788	+	0.999940i	$0.503495\pi$
$884$	−0.472136	−0.0158797
$885$	5.70820	0.191879
$886$	−32.6525	−1.09698
$887$	−13.7295	−0.460991	−0.230496	−	0.973073i	$-0.574035\pi$
$887$	−13.7295	−0.460991	−0.230496	+	0.973073i	$0.574035\pi$
$888$	7.23607	0.242827
$889$	−1.76393	−0.0591604
$890$	17.0344	0.570996
$891$	0	0
$892$	25.3262	0.847985
$893$	30.6738	1.02646
$894$	4.94427	0.165361
$895$	14.0902	0.470982
$896$	0.381966	0.0127606
$897$	5.23607	0.174827
$898$	−9.85410	−0.328836
$899$	8.94427	0.298308
$900$	−1.47214	−0.0490712
$901$	9.23607	0.307698
$902$	0	0
$903$	2.24922	0.0748495
$904$	−19.7082	−0.655485
$905$	11.5279	0.383199
$906$	23.0557	0.765975
$907$	18.6525	0.619345	0.309673	−	0.950843i	$-0.399781\pi$
$907$	18.6525	0.619345	0.309673	+	0.950843i	$0.399781\pi$
$908$	7.52786	0.249821
$909$	−14.2918	−0.474029
$910$	0.236068	0.00782558
$911$	−3.05573	−0.101241	−0.0506204	−	0.998718i	$-0.516120\pi$
$911$	−3.05573	−0.101241	−0.0506204	+	0.998718i	$0.516120\pi$
$912$	8.76393	0.290203
$913$	0	0
$914$	−34.5410	−1.14252
$915$	11.0557	0.365491
$916$	−5.81966	−0.192287
$917$	−5.88854	−0.194457
$918$	−4.22291	−0.139377
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	6.85410	0.225973
$921$	−11.1935	−0.368838
$922$	−38.5410	−1.26928
$923$	−5.41641	−0.178283
$924$	0	0
$925$	5.85410	0.192482
$926$	22.5066	0.739612
$927$	−6.36881	−0.209179
$928$	3.23607	0.106229
$929$	19.7295	0.647304	0.323652	−	0.946176i	$-0.395089\pi$
$929$	19.7295	0.647304	0.323652	+	0.946176i	$0.395089\pi$
$930$	3.41641	0.112028
$931$	48.5967	1.59269
$932$	−10.7639	−0.352584
$933$	−8.00000	−0.261908
$934$	−12.7639	−0.417649
$935$	0	0
$936$	−0.909830	−0.0297387
$937$	25.8197	0.843492	0.421746	−	0.906714i	$-0.361417\pi$
$937$	25.8197	0.843492	0.421746	+	0.906714i	$0.361417\pi$
$938$	2.00000	0.0653023
$939$	−0.721360	−0.0235407
$940$	4.32624	0.141106
$941$	2.06888	0.0674437	0.0337218	−	0.999431i	$-0.489264\pi$
$941$	2.06888	0.0674437	0.0337218	+	0.999431i	$0.489264\pi$
$942$	7.88854	0.257023
$943$	−33.2705	−1.08344
$944$	4.61803	0.150304
$945$	2.11146	0.0686857
$946$	0	0
$947$	−43.9574	−1.42842	−0.714212	−	0.699929i	$-0.753215\pi$
$947$	−43.9574	−1.42842	−0.714212	+	0.699929i	$0.753215\pi$
$948$	−12.9443	−0.420410
$949$	7.23607	0.234893
$950$	7.09017	0.230035
$951$	−38.0689	−1.23447
$952$	0.291796	0.00945716
$953$	−2.29180	−0.0742386	−0.0371193	−	0.999311i	$-0.511818\pi$
$953$	−2.29180	−0.0742386	−0.0371193	+	0.999311i	$0.511818\pi$
$954$	17.7984	0.576244
$955$	1.41641	0.0458339
$956$	−18.4721	−0.597432
$957$	0	0
$958$	19.5967	0.633142
$959$	0.291796	0.00942259
$960$	1.23607	0.0398939
$961$	−23.3607	−0.753570
$962$	3.61803	0.116650
$963$	−24.2492	−0.781420
$964$	−4.85410	−0.156340
$965$	21.4164	0.689419
$966$	−3.23607	−0.104119
$967$	−15.0902	−0.485267	−0.242634	−	0.970118i	$-0.578011\pi$
$967$	−15.0902	−0.485267	−0.242634	+	0.970118i	$0.578011\pi$
$968$	0	0
$969$	6.69505	0.215076
$970$	−12.0000	−0.385297
$971$	−52.3394	−1.67965	−0.839826	−	0.542856i	$-0.817343\pi$
$971$	−52.3394	−1.67965	−0.839826	+	0.542856i	$0.817343\pi$
$972$	−13.5967	−0.436116
$973$	−5.67376	−0.181892
$974$	−19.0557	−0.610585
$975$	0.763932	0.0244654
$976$	8.94427	0.286299
$977$	18.1803	0.581641	0.290820	−	0.956778i	$-0.406072\pi$
$977$	18.1803	0.581641	0.290820	+	0.956778i	$0.406072\pi$
$978$	−3.41641	−0.109245
$979$	0	0
$980$	6.85410	0.218946
$981$	24.2492	0.774218
$982$	−19.4508	−0.620702
$983$	−19.0344	−0.607104	−0.303552	−	0.952815i	$-0.598173\pi$
$983$	−19.0344	−0.607104	−0.303552	+	0.952815i	$0.598173\pi$
$984$	−6.00000	−0.191273
$985$	−16.0902	−0.512675
$986$	2.47214	0.0787288
$987$	−2.04257	−0.0650158
$988$	4.38197	0.139409
$989$	32.6525	1.03829
$990$	0	0
$991$	−34.7214	−1.10296	−0.551480	−	0.834188i	$-0.685937\pi$
$991$	−34.7214	−1.10296	−0.551480	+	0.834188i	$0.685937\pi$
$992$	2.76393	0.0877549
$993$	20.5410	0.651850
$994$	3.34752	0.106177
$995$	11.7082	0.371175
$996$	2.83282	0.0897612
$997$	43.5279	1.37854	0.689271	−	0.724504i	$-0.257931\pi$
$997$	43.5279	1.37854	0.689271	+	0.724504i	$0.257931\pi$
$998$	−11.7984	−0.373471
$999$	32.3607	1.02385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.2.a.p.1.1		2
4.3	odd	2		9680.2.a.bi.1.2		2
5.4	even	2		6050.2.a.cm.1.2		2
11.7	odd	10		110.2.g.a.71.1	yes	4
11.8	odd	10		110.2.g.a.31.1	✓	4
11.10	odd	2		1210.2.a.t.1.1		2
33.8	even	10		990.2.n.f.361.1		4
33.29	even	10		990.2.n.f.181.1		4
44.7	even	10		880.2.bo.a.401.1		4
44.19	even	10		880.2.bo.a.801.1		4
44.43	even	2		9680.2.a.bh.1.2		2
55.7	even	20		550.2.ba.a.49.1		8
55.8	even	20		550.2.ba.a.449.1		8
55.18	even	20		550.2.ba.a.49.2		8
55.19	odd	10		550.2.h.f.251.1		4
55.29	odd	10		550.2.h.f.401.1		4
55.52	even	20		550.2.ba.a.449.2		8
55.54	odd	2		6050.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.31.1	✓	4	11.8	odd	10
110.2.g.a.71.1	yes	4	11.7	odd	10
550.2.h.f.251.1		4	55.19	odd	10
550.2.h.f.401.1		4	55.29	odd	10
550.2.ba.a.49.1		8	55.7	even	20
550.2.ba.a.49.2		8	55.18	even	20
550.2.ba.a.449.1		8	55.8	even	20
550.2.ba.a.449.2		8	55.52	even	20
880.2.bo.a.401.1		4	44.7	even	10
880.2.bo.a.801.1		4	44.19	even	10
990.2.n.f.181.1		4	33.29	even	10
990.2.n.f.361.1		4	33.8	even	10
1210.2.a.p.1.1		2	1.1	even	1	trivial
1210.2.a.t.1.1		2	11.10	odd	2
6050.2.a.bu.1.2		2	55.54	odd	2
6050.2.a.cm.1.2		2	5.4	even	2
9680.2.a.bh.1.2		2	44.43	even	2
9680.2.a.bi.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.23607 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.23607 q^{6} -0.381966 q^{7} -1.00000 q^{8} -1.47214 q^{9} +1.00000 q^{10} -1.23607 q^{12} -0.618034 q^{13} +0.381966 q^{14} +1.23607 q^{15} +1.00000 q^{16} +0.763932 q^{17} +1.47214 q^{18} -7.09017 q^{19} -1.00000 q^{20} +0.472136 q^{21} +6.85410 q^{23} +1.23607 q^{24} +1.00000 q^{25} +0.618034 q^{26} +5.52786 q^{27} -0.381966 q^{28} -3.23607 q^{29} -1.23607 q^{30} -2.76393 q^{31} -1.00000 q^{32} -0.763932 q^{34} +0.381966 q^{35} -1.47214 q^{36} +5.85410 q^{37} +7.09017 q^{38} +0.763932 q^{39} +1.00000 q^{40} -4.85410 q^{41} -0.472136 q^{42} +4.76393 q^{43} +1.47214 q^{45} -6.85410 q^{46} -4.32624 q^{47} -1.23607 q^{48} -6.85410 q^{49} -1.00000 q^{50} -0.944272 q^{51} -0.618034 q^{52} +12.0902 q^{53} -5.52786 q^{54} +0.381966 q^{56} +8.76393 q^{57} +3.23607 q^{58} +4.61803 q^{59} +1.23607 q^{60} +8.94427 q^{61} +2.76393 q^{62} +0.562306 q^{63} +1.00000 q^{64} +0.618034 q^{65} +5.23607 q^{67} +0.763932 q^{68} -8.47214 q^{69} -0.381966 q^{70} +8.76393 q^{71} +1.47214 q^{72} -11.7082 q^{73} -5.85410 q^{74} -1.23607 q^{75} -7.09017 q^{76} -0.763932 q^{78} +10.4721 q^{79} -1.00000 q^{80} -2.41641 q^{81} +4.85410 q^{82} -2.29180 q^{83} +0.472136 q^{84} -0.763932 q^{85} -4.76393 q^{86} +4.00000 q^{87} +17.0344 q^{89} -1.47214 q^{90} +0.236068 q^{91} +6.85410 q^{92} +3.41641 q^{93} +4.32624 q^{94} +7.09017 q^{95} +1.23607 q^{96} -12.0000 q^{97} +6.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 2 q^{20} - 8 q^{21}+ \cdots + 7 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 6 * q^9 + 2 * q^10 + 2 * q^12 + q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 2 * q^20 - 8 * q^21 + 7 * q^23 - 2 * q^24 + 2 * q^25 - q^26 + 20 * q^27 - 3 * q^28 - 2 * q^29 + 2 * q^30 - 10 * q^31 - 2 * q^32 - 6 * q^34 + 3 * q^35 + 6 * q^36 + 5 * q^37 + 3 * q^38 + 6 * q^39 + 2 * q^40 - 3 * q^41 + 8 * q^42 + 14 * q^43 - 6 * q^45 - 7 * q^46 + 7 * q^47 + 2 * q^48 - 7 * q^49 - 2 * q^50 + 16 * q^51 + q^52 + 13 * q^53 - 20 * q^54 + 3 * q^56 + 22 * q^57 + 2 * q^58 + 7 * q^59 - 2 * q^60 + 10 * q^62 - 19 * q^63 + 2 * q^64 - q^65 + 6 * q^67 + 6 * q^68 - 8 * q^69 - 3 * q^70 + 22 * q^71 - 6 * q^72 - 10 * q^73 - 5 * q^74 + 2 * q^75 - 3 * q^76 - 6 * q^78 + 12 * q^79 - 2 * q^80 + 22 * q^81 + 3 * q^82 - 18 * q^83 - 8 * q^84 - 6 * q^85 - 14 * q^86 + 8 * q^87 + 5 * q^89 + 6 * q^90 - 4 * q^91 + 7 * q^92 - 20 * q^93 - 7 * q^94 + 3 * q^95 - 2 * q^96 - 24 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

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Database

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