LMFDB - Embedded newform 1210.2.a.p.1.2

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			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	\(q-1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.23607 q^{6} -2.61803 q^{7} -1.00000 q^{8} +7.47214 q^{9} +1.00000 q^{10} +3.23607 q^{12} +1.61803 q^{13} +2.61803 q^{14} -3.23607 q^{15} +1.00000 q^{16} +5.23607 q^{17} -7.47214 q^{18} +4.09017 q^{19} -1.00000 q^{20} -8.47214 q^{21} +0.145898 q^{23} -3.23607 q^{24} +1.00000 q^{25} -1.61803 q^{26} +14.4721 q^{27} -2.61803 q^{28} +1.23607 q^{29} +3.23607 q^{30} -7.23607 q^{31} -1.00000 q^{32} -5.23607 q^{34} +2.61803 q^{35} +7.47214 q^{36} -0.854102 q^{37} -4.09017 q^{38} +5.23607 q^{39} +1.00000 q^{40} +1.85410 q^{41} +8.47214 q^{42} +9.23607 q^{43} -7.47214 q^{45} -0.145898 q^{46} +11.3262 q^{47} +3.23607 q^{48} -0.145898 q^{49} -1.00000 q^{50} +16.9443 q^{51} +1.61803 q^{52} +0.909830 q^{53} -14.4721 q^{54} +2.61803 q^{56} +13.2361 q^{57} -1.23607 q^{58} +2.38197 q^{59} -3.23607 q^{60} -8.94427 q^{61} +7.23607 q^{62} -19.5623 q^{63} +1.00000 q^{64} -1.61803 q^{65} +0.763932 q^{67} +5.23607 q^{68} +0.472136 q^{69} -2.61803 q^{70} +13.2361 q^{71} -7.47214 q^{72} +1.70820 q^{73} +0.854102 q^{74} +3.23607 q^{75} +4.09017 q^{76} -5.23607 q^{78} +1.52786 q^{79} -1.00000 q^{80} +24.4164 q^{81} -1.85410 q^{82} -15.7082 q^{83} -8.47214 q^{84} -5.23607 q^{85} -9.23607 q^{86} +4.00000 q^{87} -12.0344 q^{89} +7.47214 q^{90} -4.23607 q^{91} +0.145898 q^{92} -23.4164 q^{93} -11.3262 q^{94} -4.09017 q^{95} -3.23607 q^{96} -12.0000 q^{97} +0.145898 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.23607	1.86834	0.934172	−	0.356822i	$-0.116140\pi$
$3$	3.23607	1.86834	0.934172	+	0.356822i	$0.116140\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.23607	−1.32112
$7$	−2.61803	−0.989524	−0.494762	−	0.869029i	$-0.664745\pi$
$7$	−2.61803	−0.989524	−0.494762	+	0.869029i	$0.664745\pi$
$8$	−1.00000	−0.353553
$9$	7.47214	2.49071
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	3.23607	0.934172
$13$	1.61803	0.448762	0.224381	−	0.974502i	$-0.427964\pi$
$13$	1.61803	0.448762	0.224381	+	0.974502i	$0.427964\pi$
$14$	2.61803	0.699699
$15$	−3.23607	−0.835549
$16$	1.00000	0.250000
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	−7.47214	−1.76120
$19$	4.09017	0.938349	0.469175	−	0.883105i	$-0.344551\pi$
$19$	4.09017	0.938349	0.469175	+	0.883105i	$0.344551\pi$
$20$	−1.00000	−0.223607
$21$	−8.47214	−1.84877
$22$	0	0
$23$	0.145898	0.0304218	0.0152109	−	0.999884i	$-0.495158\pi$
$23$	0.145898	0.0304218	0.0152109	+	0.999884i	$0.495158\pi$
$24$	−3.23607	−0.660560
$25$	1.00000	0.200000
$26$	−1.61803	−0.317323
$27$	14.4721	2.78516
$28$	−2.61803	−0.494762
$29$	1.23607	0.229532	0.114766	−	0.993393i	$-0.463388\pi$
$29$	1.23607	0.229532	0.114766	+	0.993393i	$0.463388\pi$
$30$	3.23607	0.590822
$31$	−7.23607	−1.29964	−0.649818	−	0.760090i	$-0.725155\pi$
$31$	−7.23607	−1.29964	−0.649818	+	0.760090i	$0.725155\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−5.23607	−0.897978
$35$	2.61803	0.442529
$36$	7.47214	1.24536
$37$	−0.854102	−0.140413	−0.0702067	−	0.997532i	$-0.522366\pi$
$37$	−0.854102	−0.140413	−0.0702067	+	0.997532i	$0.522366\pi$
$38$	−4.09017	−0.663513
$39$	5.23607	0.838442
$40$	1.00000	0.158114
$41$	1.85410	0.289562	0.144781	−	0.989464i	$-0.453752\pi$
$41$	1.85410	0.289562	0.144781	+	0.989464i	$0.453752\pi$
$42$	8.47214	1.30728
$43$	9.23607	1.40849	0.704244	−	0.709958i	$-0.251286\pi$
$43$	9.23607	1.40849	0.704244	+	0.709958i	$0.251286\pi$
$44$	0	0
$45$	−7.47214	−1.11388
$46$	−0.145898	−0.0215115
$47$	11.3262	1.65210	0.826051	−	0.563596i	$-0.190582\pi$
$47$	11.3262	1.65210	0.826051	+	0.563596i	$0.190582\pi$
$48$	3.23607	0.467086
$49$	−0.145898	−0.0208426
$50$	−1.00000	−0.141421
$51$	16.9443	2.37267
$52$	1.61803	0.224381
$53$	0.909830	0.124975	0.0624874	−	0.998046i	$-0.480097\pi$
$53$	0.909830	0.124975	0.0624874	+	0.998046i	$0.480097\pi$
$54$	−14.4721	−1.96941
$55$	0	0
$56$	2.61803	0.349850
$57$	13.2361	1.75316
$58$	−1.23607	−0.162304
$59$	2.38197	0.310106	0.155053	−	0.987906i	$-0.450445\pi$
$59$	2.38197	0.310106	0.155053	+	0.987906i	$0.450445\pi$
$60$	−3.23607	−0.417775
$61$	−8.94427	−1.14520	−0.572598	−	0.819836i	$-0.694065\pi$
$61$	−8.94427	−1.14520	−0.572598	+	0.819836i	$0.694065\pi$
$62$	7.23607	0.918982
$63$	−19.5623	−2.46462
$64$	1.00000	0.125000
$65$	−1.61803	−0.200692
$66$	0	0
$67$	0.763932	0.0933292	0.0466646	−	0.998911i	$-0.485141\pi$
$67$	0.763932	0.0933292	0.0466646	+	0.998911i	$0.485141\pi$
$68$	5.23607	0.634967
$69$	0.472136	0.0568385
$70$	−2.61803	−0.312915
$71$	13.2361	1.57083	0.785416	−	0.618968i	$-0.212449\pi$
$71$	13.2361	1.57083	0.785416	+	0.618968i	$0.212449\pi$
$72$	−7.47214	−0.880600
$73$	1.70820	0.199930	0.0999651	−	0.994991i	$-0.468127\pi$
$73$	1.70820	0.199930	0.0999651	+	0.994991i	$0.468127\pi$
$74$	0.854102	0.0992873
$75$	3.23607	0.373669
$76$	4.09017	0.469175
$77$	0	0
$78$	−5.23607	−0.592868
$79$	1.52786	0.171898	0.0859491	−	0.996300i	$-0.472608\pi$
$79$	1.52786	0.171898	0.0859491	+	0.996300i	$0.472608\pi$
$80$	−1.00000	−0.111803
$81$	24.4164	2.71293
$82$	−1.85410	−0.204751
$83$	−15.7082	−1.72420	−0.862100	−	0.506739i	$-0.830851\pi$
$83$	−15.7082	−1.72420	−0.862100	+	0.506739i	$0.830851\pi$
$84$	−8.47214	−0.924386
$85$	−5.23607	−0.567931
$86$	−9.23607	−0.995951
$87$	4.00000	0.428845
$88$	0	0
$89$	−12.0344	−1.27565	−0.637824	−	0.770182i	$-0.720165\pi$
$89$	−12.0344	−1.27565	−0.637824	+	0.770182i	$0.720165\pi$
$90$	7.47214	0.787632
$91$	−4.23607	−0.444061
$92$	0.145898	0.0152109
$93$	−23.4164	−2.42817
$94$	−11.3262	−1.16821
$95$	−4.09017	−0.419643
$96$	−3.23607	−0.330280
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	0.145898	0.0147379
$99$	0	0
$100$	1.00000	0.100000
$101$	−3.70820	−0.368980	−0.184490	−	0.982834i	$-0.559063\pi$
$101$	−3.70820	−0.368980	−0.184490	+	0.982834i	$0.559063\pi$
$102$	−16.9443	−1.67773
$103$	−11.3262	−1.11601	−0.558004	−	0.829838i	$-0.688433\pi$
$103$	−11.3262	−1.11601	−0.558004	+	0.829838i	$0.688433\pi$
$104$	−1.61803	−0.158661
$105$	8.47214	0.826796
$106$	−0.909830	−0.0883705
$107$	7.52786	0.727746	0.363873	−	0.931449i	$-0.381454\pi$
$107$	7.52786	0.727746	0.363873	+	0.931449i	$0.381454\pi$
$108$	14.4721	1.39258
$109$	−7.52786	−0.721039	−0.360519	−	0.932752i	$-0.617401\pi$
$109$	−7.52786	−0.721039	−0.360519	+	0.932752i	$0.617401\pi$
$110$	0	0
$111$	−2.76393	−0.262341
$112$	−2.61803	−0.247381
$113$	6.29180	0.591882	0.295941	−	0.955206i	$-0.404367\pi$
$113$	6.29180	0.591882	0.295941	+	0.955206i	$0.404367\pi$
$114$	−13.2361	−1.23967
$115$	−0.145898	−0.0136051
$116$	1.23607	0.114766
$117$	12.0902	1.11774
$118$	−2.38197	−0.219278
$119$	−13.7082	−1.25663
$120$	3.23607	0.295411
$121$	0	0
$122$	8.94427	0.809776
$123$	6.00000	0.541002
$124$	−7.23607	−0.649818
$125$	−1.00000	−0.0894427
$126$	19.5623	1.74275
$127$	2.38197	0.211365	0.105683	−	0.994400i	$-0.466297\pi$
$127$	2.38197	0.211365	0.105683	+	0.994400i	$0.466297\pi$
$128$	−1.00000	−0.0883883
$129$	29.8885	2.63154
$130$	1.61803	0.141911
$131$	−11.4164	−0.997456	−0.498728	−	0.866758i	$-0.666199\pi$
$131$	−11.4164	−0.997456	−0.498728	+	0.866758i	$0.666199\pi$
$132$	0	0
$133$	−10.7082	−0.928519
$134$	−0.763932	−0.0659937
$135$	−14.4721	−1.24556
$136$	−5.23607	−0.448989
$137$	−5.23607	−0.447347	−0.223674	−	0.974664i	$-0.571805\pi$
$137$	−5.23607	−0.447347	−0.223674	+	0.974664i	$0.571805\pi$
$138$	−0.472136	−0.0401909
$139$	8.14590	0.690926	0.345463	−	0.938432i	$-0.387722\pi$
$139$	8.14590	0.690926	0.345463	+	0.938432i	$0.387722\pi$
$140$	2.61803	0.221264
$141$	36.6525	3.08670
$142$	−13.2361	−1.11075
$143$	0	0
$144$	7.47214	0.622678
$145$	−1.23607	−0.102650
$146$	−1.70820	−0.141372
$147$	−0.472136	−0.0389411
$148$	−0.854102	−0.0702067
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	−3.23607	−0.264224
$151$	−12.6525	−1.02964	−0.514822	−	0.857297i	$-0.672142\pi$
$151$	−12.6525	−1.02964	−0.514822	+	0.857297i	$0.672142\pi$
$152$	−4.09017	−0.331757
$153$	39.1246	3.16304
$154$	0	0
$155$	7.23607	0.581215
$156$	5.23607	0.419221
$157$	8.61803	0.687794	0.343897	−	0.939007i	$-0.388253\pi$
$157$	8.61803	0.687794	0.343897	+	0.939007i	$0.388253\pi$
$158$	−1.52786	−0.121550
$159$	2.94427	0.233496
$160$	1.00000	0.0790569
$161$	−0.381966	−0.0301031
$162$	−24.4164	−1.91833
$163$	−7.23607	−0.566773	−0.283386	−	0.959006i	$-0.591458\pi$
$163$	−7.23607	−0.566773	−0.283386	+	0.959006i	$0.591458\pi$
$164$	1.85410	0.144781
$165$	0	0
$166$	15.7082	1.21919
$167$	−7.90983	−0.612081	−0.306041	−	0.952018i	$-0.599004\pi$
$167$	−7.90983	−0.612081	−0.306041	+	0.952018i	$0.599004\pi$
$168$	8.47214	0.653639
$169$	−10.3820	−0.798613
$170$	5.23607	0.401588
$171$	30.5623	2.33716
$172$	9.23607	0.704244
$173$	12.6180	0.959331	0.479666	−	0.877451i	$-0.340758\pi$
$173$	12.6180	0.959331	0.479666	+	0.877451i	$0.340758\pi$
$174$	−4.00000	−0.303239
$175$	−2.61803	−0.197905
$176$	0	0
$177$	7.70820	0.579384
$178$	12.0344	0.902020
$179$	−2.90983	−0.217491	−0.108745	−	0.994070i	$-0.534683\pi$
$179$	−2.90983	−0.217491	−0.108745	+	0.994070i	$0.534683\pi$
$180$	−7.47214	−0.556940
$181$	−20.4721	−1.52168	−0.760841	−	0.648938i	$-0.775213\pi$
$181$	−20.4721	−1.52168	−0.760841	+	0.648938i	$0.775213\pi$
$182$	4.23607	0.313998
$183$	−28.9443	−2.13962
$184$	−0.145898	−0.0107557
$185$	0.854102	0.0627948
$186$	23.4164	1.71697
$187$	0	0
$188$	11.3262	0.826051
$189$	−37.8885	−2.75599
$190$	4.09017	0.296732
$191$	25.4164	1.83907	0.919533	−	0.393012i	$-0.128567\pi$
$191$	25.4164	1.83907	0.919533	+	0.393012i	$0.128567\pi$
$192$	3.23607	0.233543
$193$	5.41641	0.389882	0.194941	−	0.980815i	$-0.437549\pi$
$193$	5.41641	0.389882	0.194941	+	0.980815i	$0.437549\pi$
$194$	12.0000	0.861550
$195$	−5.23607	−0.374963
$196$	−0.145898	−0.0104213
$197$	4.90983	0.349811	0.174905	−	0.984585i	$-0.444038\pi$
$197$	4.90983	0.349811	0.174905	+	0.984585i	$0.444038\pi$
$198$	0	0
$199$	1.70820	0.121091	0.0605457	−	0.998165i	$-0.480716\pi$
$199$	1.70820	0.121091	0.0605457	+	0.998165i	$0.480716\pi$
$200$	−1.00000	−0.0707107
$201$	2.47214	0.174371
$202$	3.70820	0.260908
$203$	−3.23607	−0.227127
$204$	16.9443	1.18634
$205$	−1.85410	−0.129496
$206$	11.3262	0.789136
$207$	1.09017	0.0757720
$208$	1.61803	0.112190
$209$	0	0
$210$	−8.47214	−0.584633
$211$	−20.9443	−1.44186	−0.720932	−	0.693006i	$-0.756286\pi$
$211$	−20.9443	−1.44186	−0.720932	+	0.693006i	$0.756286\pi$
$212$	0.909830	0.0624874
$213$	42.8328	2.93486
$214$	−7.52786	−0.514594
$215$	−9.23607	−0.629895
$216$	−14.4721	−0.984704
$217$	18.9443	1.28602
$218$	7.52786	0.509851
$219$	5.52786	0.373538
$220$	0	0
$221$	8.47214	0.569898
$222$	2.76393	0.185503
$223$	9.67376	0.647803	0.323902	−	0.946091i	$-0.395005\pi$
$223$	9.67376	0.647803	0.323902	+	0.946091i	$0.395005\pi$
$224$	2.61803	0.174925
$225$	7.47214	0.498142
$226$	−6.29180	−0.418524
$227$	16.4721	1.09329	0.546647	−	0.837363i	$-0.315904\pi$
$227$	16.4721	1.09329	0.546647	+	0.837363i	$0.315904\pi$
$228$	13.2361	0.876580
$229$	−28.1803	−1.86221	−0.931105	−	0.364752i	$-0.881154\pi$
$229$	−28.1803	−1.86221	−0.931105	+	0.364752i	$0.881154\pi$
$230$	0.145898	0.00962023
$231$	0	0
$232$	−1.23607	−0.0811518
$233$	−15.2361	−0.998148	−0.499074	−	0.866559i	$-0.666326\pi$
$233$	−15.2361	−0.998148	−0.499074	+	0.866559i	$0.666326\pi$
$234$	−12.0902	−0.790359
$235$	−11.3262	−0.738842
$236$	2.38197	0.155053
$237$	4.94427	0.321165
$238$	13.7082	0.888571
$239$	−9.52786	−0.616306	−0.308153	−	0.951337i	$-0.599711\pi$
$239$	−9.52786	−0.616306	−0.308153	+	0.951337i	$0.599711\pi$
$240$	−3.23607	−0.208887
$241$	1.85410	0.119433	0.0597166	−	0.998215i	$-0.480980\pi$
$241$	1.85410	0.119433	0.0597166	+	0.998215i	$0.480980\pi$
$242$	0	0
$243$	35.5967	2.28353
$244$	−8.94427	−0.572598
$245$	0.145898	0.00932108
$246$	−6.00000	−0.382546
$247$	6.61803	0.421095
$248$	7.23607	0.459491
$249$	−50.8328	−3.22140
$250$	1.00000	0.0632456
$251$	−10.0344	−0.633368	−0.316684	−	0.948531i	$-0.602570\pi$
$251$	−10.0344	−0.633368	−0.316684	+	0.948531i	$0.602570\pi$
$252$	−19.5623	−1.23231
$253$	0	0
$254$	−2.38197	−0.149458
$255$	−16.9443	−1.06109
$256$	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	$0.622107\pi$
$258$	−29.8885	−1.86078
$259$	2.23607	0.138943
$260$	−1.61803	−0.100346
$261$	9.23607	0.571698
$262$	11.4164	0.705308
$263$	−25.7984	−1.59080	−0.795398	−	0.606088i	$-0.792738\pi$
$263$	−25.7984	−1.59080	−0.795398	+	0.606088i	$0.792738\pi$
$264$	0	0
$265$	−0.909830	−0.0558904
$266$	10.7082	0.656562
$267$	−38.9443	−2.38335
$268$	0.763932	0.0466646
$269$	17.5967	1.07289	0.536446	−	0.843934i	$-0.319766\pi$
$269$	17.5967	1.07289	0.536446	+	0.843934i	$0.319766\pi$
$270$	14.4721	0.880746
$271$	−13.4164	−0.814989	−0.407494	−	0.913208i	$-0.633597\pi$
$271$	−13.4164	−0.814989	−0.407494	+	0.913208i	$0.633597\pi$
$272$	5.23607	0.317483
$273$	−13.7082	−0.829658
$274$	5.23607	0.316322
$275$	0	0
$276$	0.472136	0.0284192
$277$	0.618034	0.0371341	0.0185670	−	0.999828i	$-0.494090\pi$
$277$	0.618034	0.0371341	0.0185670	+	0.999828i	$0.494090\pi$
$278$	−8.14590	−0.488558
$279$	−54.0689	−3.23702
$280$	−2.61803	−0.156457
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−36.6525	−2.18262
$283$	−24.8328	−1.47616	−0.738079	−	0.674714i	$-0.764267\pi$
$283$	−24.8328	−1.47616	−0.738079	+	0.674714i	$0.764267\pi$
$284$	13.2361	0.785416
$285$	−13.2361	−0.784037
$286$	0	0
$287$	−4.85410	−0.286529
$288$	−7.47214	−0.440300
$289$	10.4164	0.612730
$290$	1.23607	0.0725844
$291$	−38.8328	−2.27642
$292$	1.70820	0.0999651
$293$	23.7426	1.38706	0.693530	−	0.720428i	$-0.256054\pi$
$293$	23.7426	1.38706	0.693530	+	0.720428i	$0.256054\pi$
$294$	0.472136	0.0275355
$295$	−2.38197	−0.138683
$296$	0.854102	0.0496437
$297$	0	0
$298$	−4.00000	−0.231714
$299$	0.236068	0.0136522
$300$	3.23607	0.186834
$301$	−24.1803	−1.39373
$302$	12.6525	0.728068
$303$	−12.0000	−0.689382
$304$	4.09017	0.234587
$305$	8.94427	0.512148
$306$	−39.1246	−2.23661
$307$	26.9443	1.53779	0.768895	−	0.639375i	$-0.220807\pi$
$307$	26.9443	1.53779	0.768895	+	0.639375i	$0.220807\pi$
$308$	0	0
$309$	−36.6525	−2.08509
$310$	−7.23607	−0.410981
$311$	−2.47214	−0.140182	−0.0700910	−	0.997541i	$-0.522329\pi$
$311$	−2.47214	−0.140182	−0.0700910	+	0.997541i	$0.522329\pi$
$312$	−5.23607	−0.296434
$313$	27.4164	1.54967	0.774833	−	0.632165i	$-0.217834\pi$
$313$	27.4164	1.54967	0.774833	+	0.632165i	$0.217834\pi$
$314$	−8.61803	−0.486344
$315$	19.5623	1.10221
$316$	1.52786	0.0859491
$317$	6.20163	0.348318	0.174159	−	0.984718i	$-0.444279\pi$
$317$	6.20163	0.348318	0.174159	+	0.984718i	$0.444279\pi$
$318$	−2.94427	−0.165107
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	24.3607	1.35968
$322$	0.381966	0.0212861
$323$	21.4164	1.19164
$324$	24.4164	1.35647
$325$	1.61803	0.0897524
$326$	7.23607	0.400769
$327$	−24.3607	−1.34715
$328$	−1.85410	−0.102376
$329$	−29.6525	−1.63479
$330$	0	0
$331$	−14.3820	−0.790504	−0.395252	−	0.918573i	$-0.629343\pi$
$331$	−14.3820	−0.790504	−0.395252	+	0.918573i	$0.629343\pi$
$332$	−15.7082	−0.862100
$333$	−6.38197	−0.349730
$334$	7.90983	0.432807
$335$	−0.763932	−0.0417381
$336$	−8.47214	−0.462193
$337$	−35.4164	−1.92925	−0.964627	−	0.263617i	$-0.915084\pi$
$337$	−35.4164	−1.92925	−0.964627	+	0.263617i	$0.915084\pi$
$338$	10.3820	0.564705
$339$	20.3607	1.10584
$340$	−5.23607	−0.283966
$341$	0	0
$342$	−30.5623	−1.65262
$343$	18.7082	1.01015
$344$	−9.23607	−0.497975
$345$	−0.472136	−0.0254189
$346$	−12.6180	−0.678350
$347$	27.1246	1.45613	0.728063	−	0.685511i	$-0.240421\pi$
$347$	27.1246	1.45613	0.728063	+	0.685511i	$0.240421\pi$
$348$	4.00000	0.214423
$349$	−30.9443	−1.65641	−0.828204	−	0.560426i	$-0.810637\pi$
$349$	−30.9443	−1.65641	−0.828204	+	0.560426i	$0.810637\pi$
$350$	2.61803	0.139940
$351$	23.4164	1.24988
$352$	0	0
$353$	11.7082	0.623165	0.311582	−	0.950219i	$-0.399141\pi$
$353$	11.7082	0.623165	0.311582	+	0.950219i	$0.399141\pi$
$354$	−7.70820	−0.409686
$355$	−13.2361	−0.702498
$356$	−12.0344	−0.637824
$357$	−44.3607	−2.34782
$358$	2.90983	0.153789
$359$	30.4721	1.60826	0.804129	−	0.594455i	$-0.202632\pi$
$359$	30.4721	1.60826	0.804129	+	0.594455i	$0.202632\pi$
$360$	7.47214	0.393816
$361$	−2.27051	−0.119501
$362$	20.4721	1.07599
$363$	0	0
$364$	−4.23607	−0.222030
$365$	−1.70820	−0.0894115
$366$	28.9443	1.51294
$367$	10.4721	0.546641	0.273321	−	0.961923i	$-0.411878\pi$
$367$	10.4721	0.546641	0.273321	+	0.961923i	$0.411878\pi$
$368$	0.145898	0.00760546
$369$	13.8541	0.721216
$370$	−0.854102	−0.0444026
$371$	−2.38197	−0.123666
$372$	−23.4164	−1.21408
$373$	−6.96556	−0.360663	−0.180331	−	0.983606i	$-0.557717\pi$
$373$	−6.96556	−0.360663	−0.180331	+	0.983606i	$0.557717\pi$
$374$	0	0
$375$	−3.23607	−0.167110
$376$	−11.3262	−0.584106
$377$	2.00000	0.103005
$378$	37.8885	1.94878
$379$	−10.3262	−0.530423	−0.265212	−	0.964190i	$-0.585442\pi$
$379$	−10.3262	−0.530423	−0.265212	+	0.964190i	$0.585442\pi$
$380$	−4.09017	−0.209821
$381$	7.70820	0.394903
$382$	−25.4164	−1.30042
$383$	−15.8541	−0.810107	−0.405053	−	0.914293i	$-0.632747\pi$
$383$	−15.8541	−0.810107	−0.405053	+	0.914293i	$0.632747\pi$
$384$	−3.23607	−0.165140
$385$	0	0
$386$	−5.41641	−0.275688
$387$	69.0132	3.50814
$388$	−12.0000	−0.609208
$389$	12.1803	0.617568	0.308784	−	0.951132i	$-0.400078\pi$
$389$	12.1803	0.617568	0.308784	+	0.951132i	$0.400078\pi$
$390$	5.23607	0.265139
$391$	0.763932	0.0386337
$392$	0.145898	0.00736896
$393$	−36.9443	−1.86359
$394$	−4.90983	−0.247354
$395$	−1.52786	−0.0768752
$396$	0	0
$397$	6.79837	0.341201	0.170600	−	0.985340i	$-0.445429\pi$
$397$	6.79837	0.341201	0.170600	+	0.985340i	$0.445429\pi$
$398$	−1.70820	−0.0856245
$399$	−34.6525	−1.73479
$400$	1.00000	0.0500000
$401$	−10.7426	−0.536462	−0.268231	−	0.963355i	$-0.586439\pi$
$401$	−10.7426	−0.536462	−0.268231	+	0.963355i	$0.586439\pi$
$402$	−2.47214	−0.123299
$403$	−11.7082	−0.583227
$404$	−3.70820	−0.184490
$405$	−24.4164	−1.21326
$406$	3.23607	0.160603
$407$	0	0
$408$	−16.9443	−0.838866
$409$	23.3262	1.15341	0.576704	−	0.816953i	$-0.304339\pi$
$409$	23.3262	1.15341	0.576704	+	0.816953i	$0.304339\pi$
$410$	1.85410	0.0915676
$411$	−16.9443	−0.835799
$412$	−11.3262	−0.558004
$413$	−6.23607	−0.306857
$414$	−1.09017	−0.0535789
$415$	15.7082	0.771085
$416$	−1.61803	−0.0793306
$417$	26.3607	1.29089
$418$	0	0
$419$	−1.61803	−0.0790461	−0.0395231	−	0.999219i	$-0.512584\pi$
$419$	−1.61803	−0.0790461	−0.0395231	+	0.999219i	$0.512584\pi$
$420$	8.47214	0.413398
$421$	−18.6525	−0.909066	−0.454533	−	0.890730i	$-0.650194\pi$
$421$	−18.6525	−0.909066	−0.454533	+	0.890730i	$0.650194\pi$
$422$	20.9443	1.01955
$423$	84.6312	4.11491
$424$	−0.909830	−0.0441853
$425$	5.23607	0.253987
$426$	−42.8328	−2.07526
$427$	23.4164	1.13320
$428$	7.52786	0.363873
$429$	0	0
$430$	9.23607	0.445403
$431$	26.1803	1.26106	0.630531	−	0.776164i	$-0.282837\pi$
$431$	26.1803	1.26106	0.630531	+	0.776164i	$0.282837\pi$
$432$	14.4721	0.696291
$433$	9.52786	0.457880	0.228940	−	0.973441i	$-0.426474\pi$
$433$	9.52786	0.457880	0.228940	+	0.973441i	$0.426474\pi$
$434$	−18.9443	−0.909354
$435$	−4.00000	−0.191785
$436$	−7.52786	−0.360519
$437$	0.596748	0.0285463
$438$	−5.52786	−0.264132
$439$	13.1246	0.626404	0.313202	−	0.949687i	$-0.398598\pi$
$439$	13.1246	0.626404	0.313202	+	0.949687i	$0.398598\pi$
$440$	0	0
$441$	−1.09017	−0.0519129
$442$	−8.47214	−0.402978
$443$	1.34752	0.0640228	0.0320114	−	0.999488i	$-0.489809\pi$
$443$	1.34752	0.0640228	0.0320114	+	0.999488i	$0.489809\pi$
$444$	−2.76393	−0.131170
$445$	12.0344	0.570487
$446$	−9.67376	−0.458066
$447$	12.9443	0.612243
$448$	−2.61803	−0.123690
$449$	3.14590	0.148464	0.0742321	−	0.997241i	$-0.476349\pi$
$449$	3.14590	0.148464	0.0742321	+	0.997241i	$0.476349\pi$
$450$	−7.47214	−0.352240
$451$	0	0
$452$	6.29180	0.295941
$453$	−40.9443	−1.92373
$454$	−16.4721	−0.773076
$455$	4.23607	0.198590
$456$	−13.2361	−0.619836
$457$	−32.5410	−1.52220	−0.761102	−	0.648632i	$-0.775342\pi$
$457$	−32.5410	−1.52220	−0.761102	+	0.648632i	$0.775342\pi$
$458$	28.1803	1.31678
$459$	75.7771	3.53697
$460$	−0.145898	−0.00680253
$461$	−28.5410	−1.32929	−0.664644	−	0.747160i	$-0.731417\pi$
$461$	−28.5410	−1.32929	−0.664644	+	0.747160i	$0.731417\pi$
$462$	0	0
$463$	15.5066	0.720652	0.360326	−	0.932826i	$-0.382665\pi$
$463$	15.5066	0.720652	0.360326	+	0.932826i	$0.382665\pi$
$464$	1.23607	0.0573830
$465$	23.4164	1.08591
$466$	15.2361	0.705797
$467$	17.2361	0.797590	0.398795	−	0.917040i	$-0.369428\pi$
$467$	17.2361	0.797590	0.398795	+	0.917040i	$0.369428\pi$
$468$	12.0902	0.558868
$469$	−2.00000	−0.0923514
$470$	11.3262	0.522440
$471$	27.8885	1.28504
$472$	−2.38197	−0.109639
$473$	0	0
$474$	−4.94427	−0.227098
$475$	4.09017	0.187670
$476$	−13.7082	−0.628314
$477$	6.79837	0.311276
$478$	9.52786	0.435794
$479$	29.5967	1.35231	0.676155	−	0.736759i	$-0.263645\pi$
$479$	29.5967	1.35231	0.676155	+	0.736759i	$0.263645\pi$
$480$	3.23607	0.147706
$481$	−1.38197	−0.0630122
$482$	−1.85410	−0.0844520
$483$	−1.23607	−0.0562430
$484$	0	0
$485$	12.0000	0.544892
$486$	−35.5967	−1.61470
$487$	36.9443	1.67410	0.837052	−	0.547123i	$-0.184277\pi$
$487$	36.9443	1.67410	0.837052	+	0.547123i	$0.184277\pi$
$488$	8.94427	0.404888
$489$	−23.4164	−1.05893
$490$	−0.145898	−0.00659100
$491$	−36.4508	−1.64500	−0.822502	−	0.568762i	$-0.807422\pi$
$491$	−36.4508	−1.64500	−0.822502	+	0.568762i	$0.807422\pi$
$492$	6.00000	0.270501
$493$	6.47214	0.291490
$494$	−6.61803	−0.297759
$495$	0	0
$496$	−7.23607	−0.324909
$497$	−34.6525	−1.55438
$498$	50.8328	2.27787
$499$	−12.7984	−0.572934	−0.286467	−	0.958090i	$-0.592481\pi$
$499$	−12.7984	−0.572934	−0.286467	+	0.958090i	$0.592481\pi$
$500$	−1.00000	−0.0447214
$501$	−25.5967	−1.14358
$502$	10.0344	0.447859
$503$	−7.50658	−0.334702	−0.167351	−	0.985897i	$-0.553521\pi$
$503$	−7.50658	−0.334702	−0.167351	+	0.985897i	$0.553521\pi$
$504$	19.5623	0.871374
$505$	3.70820	0.165013
$506$	0	0
$507$	−33.5967	−1.49208
$508$	2.38197	0.105683
$509$	−31.1246	−1.37957	−0.689787	−	0.724012i	$-0.742296\pi$
$509$	−31.1246	−1.37957	−0.689787	+	0.724012i	$0.742296\pi$
$510$	16.9443	0.750305
$511$	−4.47214	−0.197836
$512$	−1.00000	−0.0441942
$513$	59.1935	2.61346
$514$	12.0000	0.529297
$515$	11.3262	0.499094
$516$	29.8885	1.31577
$517$	0	0
$518$	−2.23607	−0.0982472
$519$	40.8328	1.79236
$520$	1.61803	0.0709555
$521$	−8.61803	−0.377563	−0.188781	−	0.982019i	$-0.560454\pi$
$521$	−8.61803	−0.377563	−0.188781	+	0.982019i	$0.560454\pi$
$522$	−9.23607	−0.404252
$523$	7.34752	0.321285	0.160642	−	0.987013i	$-0.448643\pi$
$523$	7.34752	0.321285	0.160642	+	0.987013i	$0.448643\pi$
$524$	−11.4164	−0.498728
$525$	−8.47214	−0.369754
$526$	25.7984	1.12486
$527$	−37.8885	−1.65045
$528$	0	0
$529$	−22.9787	−0.999075
$530$	0.909830	0.0395205
$531$	17.7984	0.772384
$532$	−10.7082	−0.464260
$533$	3.00000	0.129944
$534$	38.9443	1.68528
$535$	−7.52786	−0.325458
$536$	−0.763932	−0.0329968
$537$	−9.41641	−0.406348
$538$	−17.5967	−0.758650
$539$	0	0
$540$	−14.4721	−0.622782
$541$	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
$543$	−66.2492	−2.84303
$544$	−5.23607	−0.224495
$545$	7.52786	0.322458
$546$	13.7082	0.586657
$547$	15.5967	0.666869	0.333434	−	0.942773i	$-0.391792\pi$
$547$	15.5967	0.666869	0.333434	+	0.942773i	$0.391792\pi$
$548$	−5.23607	−0.223674
$549$	−66.8328	−2.85236
$550$	0	0
$551$	5.05573	0.215381
$552$	−0.472136	−0.0200954
$553$	−4.00000	−0.170097
$554$	−0.618034	−0.0262577
$555$	2.76393	0.117322
$556$	8.14590	0.345463
$557$	−33.2148	−1.40736	−0.703678	−	0.710519i	$-0.748460\pi$
$557$	−33.2148	−1.40736	−0.703678	+	0.710519i	$0.748460\pi$
$558$	54.0689	2.28892
$559$	14.9443	0.632075
$560$	2.61803	0.110632
$561$	0	0
$562$	18.0000	0.759284
$563$	−23.8885	−1.00678	−0.503391	−	0.864059i	$-0.667914\pi$
$563$	−23.8885	−1.00678	−0.503391	+	0.864059i	$0.667914\pi$
$564$	36.6525	1.54335
$565$	−6.29180	−0.264698
$566$	24.8328	1.04380
$567$	−63.9230	−2.68451
$568$	−13.2361	−0.555373
$569$	−8.32624	−0.349054	−0.174527	−	0.984652i	$-0.555840\pi$
$569$	−8.32624	−0.349054	−0.174527	+	0.984652i	$0.555840\pi$
$570$	13.2361	0.554398
$571$	29.0902	1.21739	0.608693	−	0.793406i	$-0.291694\pi$
$571$	29.0902	1.21739	0.608693	+	0.793406i	$0.291694\pi$
$572$	0	0
$573$	82.2492	3.43601
$574$	4.85410	0.202606
$575$	0.145898	0.00608437
$576$	7.47214	0.311339
$577$	14.9443	0.622138	0.311069	−	0.950387i	$-0.399313\pi$
$577$	14.9443	0.622138	0.311069	+	0.950387i	$0.399313\pi$
$578$	−10.4164	−0.433265
$579$	17.5279	0.728433
$580$	−1.23607	−0.0513249
$581$	41.1246	1.70614
$582$	38.8328	1.60967
$583$	0	0
$584$	−1.70820	−0.0706860
$585$	−12.0902	−0.499867
$586$	−23.7426	−0.980800
$587$	−20.7639	−0.857019	−0.428510	−	0.903537i	$-0.640961\pi$
$587$	−20.7639	−0.857019	−0.428510	+	0.903537i	$0.640961\pi$
$588$	−0.472136	−0.0194706
$589$	−29.5967	−1.21951
$590$	2.38197	0.0980640
$591$	15.8885	0.653567
$592$	−0.854102	−0.0351034
$593$	19.7082	0.809319	0.404659	−	0.914467i	$-0.367390\pi$
$593$	19.7082	0.809319	0.404659	+	0.914467i	$0.367390\pi$
$594$	0	0
$595$	13.7082	0.561982
$596$	4.00000	0.163846
$597$	5.52786	0.226240
$598$	−0.236068	−0.00965354
$599$	16.4721	0.673033	0.336517	−	0.941678i	$-0.390751\pi$
$599$	16.4721	0.673033	0.336517	+	0.941678i	$0.390751\pi$
$600$	−3.23607	−0.132112
$601$	−22.5623	−0.920336	−0.460168	−	0.887832i	$-0.652211\pi$
$601$	−22.5623	−0.920336	−0.460168	+	0.887832i	$0.652211\pi$
$602$	24.1803	0.985517
$603$	5.70820	0.232456
$604$	−12.6525	−0.514822
$605$	0	0
$606$	12.0000	0.487467
$607$	−32.3607	−1.31348	−0.656740	−	0.754117i	$-0.728065\pi$
$607$	−32.3607	−1.31348	−0.656740	+	0.754117i	$0.728065\pi$
$608$	−4.09017	−0.165878
$609$	−10.4721	−0.424352
$610$	−8.94427	−0.362143
$611$	18.3262	0.741400
$612$	39.1246	1.58152
$613$	−11.5279	−0.465606	−0.232803	−	0.972524i	$-0.574790\pi$
$613$	−11.5279	−0.465606	−0.232803	+	0.972524i	$0.574790\pi$
$614$	−26.9443	−1.08738
$615$	−6.00000	−0.241943
$616$	0	0
$617$	32.9443	1.32629	0.663143	−	0.748493i	$-0.269222\pi$
$617$	32.9443	1.32629	0.663143	+	0.748493i	$0.269222\pi$
$618$	36.6525	1.47438
$619$	22.7426	0.914104	0.457052	−	0.889440i	$-0.348905\pi$
$619$	22.7426	0.914104	0.457052	+	0.889440i	$0.348905\pi$
$620$	7.23607	0.290607
$621$	2.11146	0.0847298
$622$	2.47214	0.0991236
$623$	31.5066	1.26228
$624$	5.23607	0.209610
$625$	1.00000	0.0400000
$626$	−27.4164	−1.09578
$627$	0	0
$628$	8.61803	0.343897
$629$	−4.47214	−0.178316
$630$	−19.5623	−0.779381
$631$	7.41641	0.295243	0.147621	−	0.989044i	$-0.452838\pi$
$631$	7.41641	0.295243	0.147621	+	0.989044i	$0.452838\pi$
$632$	−1.52786	−0.0607752
$633$	−67.7771	−2.69390
$634$	−6.20163	−0.246298
$635$	−2.38197	−0.0945254
$636$	2.94427	0.116748
$637$	−0.236068	−0.00935335
$638$	0	0
$639$	98.9017	3.91249
$640$	1.00000	0.0395285
$641$	38.1591	1.50719	0.753596	−	0.657338i	$-0.228318\pi$
$641$	38.1591	1.50719	0.753596	+	0.657338i	$0.228318\pi$
$642$	−24.3607	−0.961439
$643$	−13.4164	−0.529091	−0.264546	−	0.964373i	$-0.585222\pi$
$643$	−13.4164	−0.529091	−0.264546	+	0.964373i	$0.585222\pi$
$644$	−0.381966	−0.0150516
$645$	−29.8885	−1.17686
$646$	−21.4164	−0.842617
$647$	−7.05573	−0.277389	−0.138695	−	0.990335i	$-0.544291\pi$
$647$	−7.05573	−0.277389	−0.138695	+	0.990335i	$0.544291\pi$
$648$	−24.4164	−0.959167
$649$	0	0
$650$	−1.61803	−0.0634645
$651$	61.3050	2.40273
$652$	−7.23607	−0.283386
$653$	25.7984	1.00957	0.504784	−	0.863246i	$-0.331572\pi$
$653$	25.7984	1.00957	0.504784	+	0.863246i	$0.331572\pi$
$654$	24.3607	0.952578
$655$	11.4164	0.446076
$656$	1.85410	0.0723905
$657$	12.7639	0.497968
$658$	29.6525	1.15597
$659$	13.3820	0.521287	0.260644	−	0.965435i	$-0.416065\pi$
$659$	13.3820	0.521287	0.260644	+	0.965435i	$0.416065\pi$
$660$	0	0
$661$	2.18034	0.0848054	0.0424027	−	0.999101i	$-0.486499\pi$
$661$	2.18034	0.0848054	0.0424027	+	0.999101i	$0.486499\pi$
$662$	14.3820	0.558971
$663$	27.4164	1.06477
$664$	15.7082	0.609597
$665$	10.7082	0.415246
$666$	6.38197	0.247296
$667$	0.180340	0.00698279
$668$	−7.90983	−0.306041
$669$	31.3050	1.21032
$670$	0.763932	0.0295133
$671$	0	0
$672$	8.47214	0.326820
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	35.4164	1.36419
$675$	14.4721	0.557033
$676$	−10.3820	−0.399306
$677$	10.0000	0.384331	0.192166	−	0.981363i	$-0.438449\pi$
$677$	10.0000	0.384331	0.192166	+	0.981363i	$0.438449\pi$
$678$	−20.3607	−0.781947
$679$	31.4164	1.20565
$680$	5.23607	0.200794
$681$	53.3050	2.04265
$682$	0	0
$683$	−47.0132	−1.79891	−0.899454	−	0.437015i	$-0.856036\pi$
$683$	−47.0132	−1.79891	−0.899454	+	0.437015i	$0.856036\pi$
$684$	30.5623	1.16858
$685$	5.23607	0.200060
$686$	−18.7082	−0.714283
$687$	−91.1935	−3.47925
$688$	9.23607	0.352122
$689$	1.47214	0.0560839
$690$	0.472136	0.0179739
$691$	13.7426	0.522795	0.261397	−	0.965231i	$-0.415817\pi$
$691$	13.7426	0.522795	0.261397	+	0.965231i	$0.415817\pi$
$692$	12.6180	0.479666
$693$	0	0
$694$	−27.1246	−1.02964
$695$	−8.14590	−0.308992
$696$	−4.00000	−0.151620
$697$	9.70820	0.367724
$698$	30.9443	1.17126
$699$	−49.3050	−1.86488
$700$	−2.61803	−0.0989524
$701$	−5.81966	−0.219806	−0.109903	−	0.993942i	$-0.535054\pi$
$701$	−5.81966	−0.219806	−0.109903	+	0.993942i	$0.535054\pi$
$702$	−23.4164	−0.883795
$703$	−3.49342	−0.131757
$704$	0	0
$705$	−36.6525	−1.38041
$706$	−11.7082	−0.440644
$707$	9.70820	0.365115
$708$	7.70820	0.289692
$709$	10.8754	0.408434	0.204217	−	0.978926i	$-0.434535\pi$
$709$	10.8754	0.408434	0.204217	+	0.978926i	$0.434535\pi$
$710$	13.2361	0.496741
$711$	11.4164	0.428149
$712$	12.0344	0.451010
$713$	−1.05573	−0.0395373
$714$	44.3607	1.66016
$715$	0	0
$716$	−2.90983	−0.108745
$717$	−30.8328	−1.15147
$718$	−30.4721	−1.13721
$719$	23.8197	0.888323	0.444162	−	0.895947i	$-0.353502\pi$
$719$	23.8197	0.888323	0.444162	+	0.895947i	$0.353502\pi$
$720$	−7.47214	−0.278470
$721$	29.6525	1.10432
$722$	2.27051	0.0844996
$723$	6.00000	0.223142
$724$	−20.4721	−0.760841
$725$	1.23607	0.0459064
$726$	0	0
$727$	−8.79837	−0.326314	−0.163157	−	0.986600i	$-0.552168\pi$
$727$	−8.79837	−0.326314	−0.163157	+	0.986600i	$0.552168\pi$
$728$	4.23607	0.156999
$729$	41.9443	1.55349
$730$	1.70820	0.0632235
$731$	48.3607	1.78868
$732$	−28.9443	−1.06981
$733$	−36.2492	−1.33890	−0.669448	−	0.742859i	$-0.733469\pi$
$733$	−36.2492	−1.33890	−0.669448	+	0.742859i	$0.733469\pi$
$734$	−10.4721	−0.386534
$735$	0.472136	0.0174150
$736$	−0.145898	−0.00537787
$737$	0	0
$738$	−13.8541	−0.509977
$739$	31.8541	1.17177	0.585886	−	0.810393i	$-0.300747\pi$
$739$	31.8541	1.17177	0.585886	+	0.810393i	$0.300747\pi$
$740$	0.854102	0.0313974
$741$	21.4164	0.786751
$742$	2.38197	0.0874447
$743$	17.7426	0.650915	0.325457	−	0.945557i	$-0.394482\pi$
$743$	17.7426	0.650915	0.325457	+	0.945557i	$0.394482\pi$
$744$	23.4164	0.858487
$745$	−4.00000	−0.146549
$746$	6.96556	0.255027
$747$	−117.374	−4.29448
$748$	0	0
$749$	−19.7082	−0.720122
$750$	3.23607	0.118164
$751$	−10.9443	−0.399362	−0.199681	−	0.979861i	$-0.563991\pi$
$751$	−10.9443	−0.399362	−0.199681	+	0.979861i	$0.563991\pi$
$752$	11.3262	0.413025
$753$	−32.4721	−1.18335
$754$	−2.00000	−0.0728357
$755$	12.6525	0.460471
$756$	−37.8885	−1.37799
$757$	22.2016	0.806932	0.403466	−	0.914995i	$-0.367805\pi$
$757$	22.2016	0.806932	0.403466	+	0.914995i	$0.367805\pi$
$758$	10.3262	0.375066
$759$	0	0
$760$	4.09017	0.148366
$761$	−6.58359	−0.238655	−0.119328	−	0.992855i	$-0.538074\pi$
$761$	−6.58359	−0.238655	−0.119328	+	0.992855i	$0.538074\pi$
$762$	−7.70820	−0.279239
$763$	19.7082	0.713485
$764$	25.4164	0.919533
$765$	−39.1246	−1.41455
$766$	15.8541	0.572832
$767$	3.85410	0.139164
$768$	3.23607	0.116772
$769$	32.0902	1.15720	0.578601	−	0.815611i	$-0.303599\pi$
$769$	32.0902	1.15720	0.578601	+	0.815611i	$0.303599\pi$
$770$	0	0
$771$	−38.8328	−1.39853
$772$	5.41641	0.194941
$773$	−37.5623	−1.35102	−0.675511	−	0.737350i	$-0.736077\pi$
$773$	−37.5623	−1.35102	−0.675511	+	0.737350i	$0.736077\pi$
$774$	−69.0132	−2.48063
$775$	−7.23607	−0.259927
$776$	12.0000	0.430775
$777$	7.23607	0.259592
$778$	−12.1803	−0.436686
$779$	7.58359	0.271710
$780$	−5.23607	−0.187481
$781$	0	0
$782$	−0.763932	−0.0273182
$783$	17.8885	0.639284
$784$	−0.145898	−0.00521064
$785$	−8.61803	−0.307591
$786$	36.9443	1.31776
$787$	36.0000	1.28326	0.641631	−	0.767014i	$-0.278258\pi$
$787$	36.0000	1.28326	0.641631	+	0.767014i	$0.278258\pi$
$788$	4.90983	0.174905
$789$	−83.4853	−2.97216
$790$	1.52786	0.0543590
$791$	−16.4721	−0.585682
$792$	0	0
$793$	−14.4721	−0.513921
$794$	−6.79837	−0.241265
$795$	−2.94427	−0.104423
$796$	1.70820	0.0605457
$797$	37.0344	1.31183	0.655914	−	0.754836i	$-0.272284\pi$
$797$	37.0344	1.31183	0.655914	+	0.754836i	$0.272284\pi$
$798$	34.6525	1.22668
$799$	59.3050	2.09806
$800$	−1.00000	−0.0353553
$801$	−89.9230	−3.17727
$802$	10.7426	0.379336
$803$	0	0
$804$	2.47214	0.0871855
$805$	0.381966	0.0134625
$806$	11.7082	0.412404
$807$	56.9443	2.00453
$808$	3.70820	0.130454
$809$	9.03444	0.317634	0.158817	−	0.987308i	$-0.449232\pi$
$809$	9.03444	0.317634	0.158817	+	0.987308i	$0.449232\pi$
$810$	24.4164	0.857905
$811$	46.6180	1.63698	0.818490	−	0.574520i	$-0.194811\pi$
$811$	46.6180	1.63698	0.818490	+	0.574520i	$0.194811\pi$
$812$	−3.23607	−0.113564
$813$	−43.4164	−1.52268
$814$	0	0
$815$	7.23607	0.253468
$816$	16.9443	0.593168
$817$	37.7771	1.32165
$818$	−23.3262	−0.815583
$819$	−31.6525	−1.10603
$820$	−1.85410	−0.0647480
$821$	24.3607	0.850194	0.425097	−	0.905148i	$-0.360240\pi$
$821$	24.3607	0.850194	0.425097	+	0.905148i	$0.360240\pi$
$822$	16.9443	0.590999
$823$	−17.0344	−0.593783	−0.296892	−	0.954911i	$-0.595950\pi$
$823$	−17.0344	−0.593783	−0.296892	+	0.954911i	$0.595950\pi$
$824$	11.3262	0.394568
$825$	0	0
$826$	6.23607	0.216981
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	1.09017	0.0378860
$829$	−12.9443	−0.449573	−0.224787	−	0.974408i	$-0.572168\pi$
$829$	−12.9443	−0.449573	−0.224787	+	0.974408i	$0.572168\pi$
$830$	−15.7082	−0.545240
$831$	2.00000	0.0693792
$832$	1.61803	0.0560952
$833$	−0.763932	−0.0264687
$834$	−26.3607	−0.912796
$835$	7.90983	0.273731
$836$	0	0
$837$	−104.721	−3.61970
$838$	1.61803	0.0558941
$839$	−52.5410	−1.81392	−0.906959	−	0.421220i	$-0.861602\pi$
$839$	−52.5410	−1.81392	−0.906959	+	0.421220i	$0.861602\pi$
$840$	−8.47214	−0.292316
$841$	−27.4721	−0.947315
$842$	18.6525	0.642807
$843$	−58.2492	−2.00621
$844$	−20.9443	−0.720932
$845$	10.3820	0.357150
$846$	−84.6312	−2.90968
$847$	0	0
$848$	0.909830	0.0312437
$849$	−80.3607	−2.75797
$850$	−5.23607	−0.179596
$851$	−0.124612	−0.00427164
$852$	42.8328	1.46743
$853$	−15.9656	−0.546650	−0.273325	−	0.961922i	$-0.588123\pi$
$853$	−15.9656	−0.546650	−0.273325	+	0.961922i	$0.588123\pi$
$854$	−23.4164	−0.801293
$855$	−30.5623	−1.04521
$856$	−7.52786	−0.257297
$857$	−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
$859$	−30.9098	−1.05463	−0.527315	−	0.849670i	$-0.676801\pi$
$859$	−30.9098	−1.05463	−0.527315	+	0.849670i	$0.676801\pi$
$860$	−9.23607	−0.314947
$861$	−15.7082	−0.535334
$862$	−26.1803	−0.891706
$863$	−6.20163	−0.211106	−0.105553	−	0.994414i	$-0.533661\pi$
$863$	−6.20163	−0.211106	−0.105553	+	0.994414i	$0.533661\pi$
$864$	−14.4721	−0.492352
$865$	−12.6180	−0.429026
$866$	−9.52786	−0.323770
$867$	33.7082	1.14479
$868$	18.9443	0.643010
$869$	0	0
$870$	4.00000	0.135613
$871$	1.23607	0.0418826
$872$	7.52786	0.254926
$873$	−89.6656	−3.03472
$874$	−0.596748	−0.0201853
$875$	2.61803	0.0885057
$876$	5.52786	0.186769
$877$	−2.38197	−0.0804333	−0.0402166	−	0.999191i	$-0.512805\pi$
$877$	−2.38197	−0.0804333	−0.0402166	+	0.999191i	$0.512805\pi$
$878$	−13.1246	−0.442934
$879$	76.8328	2.59151
$880$	0	0
$881$	−27.4508	−0.924843	−0.462421	−	0.886660i	$-0.653019\pi$
$881$	−27.4508	−0.924843	−0.462421	+	0.886660i	$0.653019\pi$
$882$	1.09017	0.0367079
$883$	30.6525	1.03154	0.515769	−	0.856728i	$-0.327506\pi$
$883$	30.6525	1.03154	0.515769	+	0.856728i	$0.327506\pi$
$884$	8.47214	0.284949
$885$	−7.70820	−0.259108
$886$	−1.34752	−0.0452710
$887$	−47.2705	−1.58719	−0.793594	−	0.608447i	$-0.791793\pi$
$887$	−47.2705	−1.58719	−0.793594	+	0.608447i	$0.791793\pi$
$888$	2.76393	0.0927515
$889$	−6.23607	−0.209151
$890$	−12.0344	−0.403395
$891$	0	0
$892$	9.67376	0.323902
$893$	46.3262	1.55025
$894$	−12.9443	−0.432921
$895$	2.90983	0.0972649
$896$	2.61803	0.0874624
$897$	0.763932	0.0255069
$898$	−3.14590	−0.104980
$899$	−8.94427	−0.298308
$900$	7.47214	0.249071
$901$	4.76393	0.158710
$902$	0	0
$903$	−78.2492	−2.60397
$904$	−6.29180	−0.209262
$905$	20.4721	0.680517
$906$	40.9443	1.36028
$907$	−12.6525	−0.420119	−0.210059	−	0.977689i	$-0.567366\pi$
$907$	−12.6525	−0.420119	−0.210059	+	0.977689i	$0.567366\pi$
$908$	16.4721	0.546647
$909$	−27.7082	−0.919023
$910$	−4.23607	−0.140424
$911$	−20.9443	−0.693915	−0.346957	−	0.937881i	$-0.612785\pi$
$911$	−20.9443	−0.693915	−0.346957	+	0.937881i	$0.612785\pi$
$912$	13.2361	0.438290
$913$	0	0
$914$	32.5410	1.07636
$915$	28.9443	0.956868
$916$	−28.1803	−0.931105
$917$	29.8885	0.987007
$918$	−75.7771	−2.50102
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	0.145898	0.00481012
$921$	87.1935	2.87312
$922$	28.5410	0.939948
$923$	21.4164	0.704930
$924$	0	0
$925$	−0.854102	−0.0280827
$926$	−15.5066	−0.509578
$927$	−84.6312	−2.77965
$928$	−1.23607	−0.0405759
$929$	53.2705	1.74775	0.873874	−	0.486152i	$-0.161600\pi$
$929$	53.2705	1.74775	0.873874	+	0.486152i	$0.161600\pi$
$930$	−23.4164	−0.767854
$931$	−0.596748	−0.0195576
$932$	−15.2361	−0.499074
$933$	−8.00000	−0.261908
$934$	−17.2361	−0.563981
$935$	0	0
$936$	−12.0902	−0.395180
$937$	48.1803	1.57398	0.786992	−	0.616964i	$-0.211638\pi$
$937$	48.1803	1.57398	0.786992	+	0.616964i	$0.211638\pi$
$938$	2.00000	0.0653023
$939$	88.7214	2.89531
$940$	−11.3262	−0.369421
$941$	−56.0689	−1.82779	−0.913897	−	0.405947i	$-0.866942\pi$
$941$	−56.0689	−1.82779	−0.913897	+	0.405947i	$0.866942\pi$
$942$	−27.8885	−0.908658
$943$	0.270510	0.00880901
$944$	2.38197	0.0775264
$945$	37.8885	1.23251
$946$	0	0
$947$	49.9574	1.62340	0.811699	−	0.584076i	$-0.198543\pi$
$947$	49.9574	1.62340	0.811699	+	0.584076i	$0.198543\pi$
$948$	4.94427	0.160582
$949$	2.76393	0.0897210
$950$	−4.09017	−0.132703
$951$	20.0689	0.650778
$952$	13.7082	0.444285
$953$	−15.7082	−0.508839	−0.254419	−	0.967094i	$-0.581884\pi$
$953$	−15.7082	−0.508839	−0.254419	+	0.967094i	$0.581884\pi$
$954$	−6.79837	−0.220105
$955$	−25.4164	−0.822456
$956$	−9.52786	−0.308153
$957$	0	0
$958$	−29.5967	−0.956228
$959$	13.7082	0.442661
$960$	−3.23607	−0.104444
$961$	21.3607	0.689054
$962$	1.38197	0.0445564
$963$	56.2492	1.81261
$964$	1.85410	0.0597166
$965$	−5.41641	−0.174360
$966$	1.23607	0.0397698
$967$	−3.90983	−0.125732	−0.0628658	−	0.998022i	$-0.520024\pi$
$967$	−3.90983	−0.125732	−0.0628658	+	0.998022i	$0.520024\pi$
$968$	0	0
$969$	69.3050	2.22640
$970$	−12.0000	−0.385297
$971$	39.3394	1.26246	0.631231	−	0.775595i	$-0.282550\pi$
$971$	39.3394	1.26246	0.631231	+	0.775595i	$0.282550\pi$
$972$	35.5967	1.14177
$973$	−21.3262	−0.683688
$974$	−36.9443	−1.18377
$975$	5.23607	0.167688
$976$	−8.94427	−0.286299
$977$	−4.18034	−0.133741	−0.0668705	−	0.997762i	$-0.521301\pi$
$977$	−4.18034	−0.133741	−0.0668705	+	0.997762i	$0.521301\pi$
$978$	23.4164	0.748774
$979$	0	0
$980$	0.145898	0.00466054
$981$	−56.2492	−1.79590
$982$	36.4508	1.16319
$983$	10.0344	0.320049	0.160024	−	0.987113i	$-0.448843\pi$
$983$	10.0344	0.320049	0.160024	+	0.987113i	$0.448843\pi$
$984$	−6.00000	−0.191273
$985$	−4.90983	−0.156440
$986$	−6.47214	−0.206115
$987$	−95.9574	−3.05436
$988$	6.61803	0.210548
$989$	1.34752	0.0428488
$990$	0	0
$991$	54.7214	1.73828	0.869141	−	0.494565i	$-0.164673\pi$
$991$	54.7214	1.73828	0.869141	+	0.494565i	$0.164673\pi$
$992$	7.23607	0.229745
$993$	−46.5410	−1.47693
$994$	34.6525	1.09911
$995$	−1.70820	−0.0541537
$996$	−50.8328	−1.61070
$997$	52.4721	1.66181	0.830905	−	0.556415i	$-0.187823\pi$
$997$	52.4721	1.66181	0.830905	+	0.556415i	$0.187823\pi$
$998$	12.7984	0.405125
$999$	−12.3607	−0.391075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.2.a.p.1.2		2
4.3	odd	2		9680.2.a.bi.1.1		2
5.4	even	2		6050.2.a.cm.1.1		2
11.2	odd	10		110.2.g.a.81.1	✓	4
11.6	odd	10		110.2.g.a.91.1	yes	4
11.10	odd	2		1210.2.a.t.1.2		2
33.2	even	10		990.2.n.f.631.1		4
33.17	even	10		990.2.n.f.91.1		4
44.35	even	10		880.2.bo.a.81.1		4
44.39	even	10		880.2.bo.a.641.1		4
44.43	even	2		9680.2.a.bh.1.1		2
55.2	even	20		550.2.ba.a.499.2		8
55.13	even	20		550.2.ba.a.499.1		8
55.17	even	20		550.2.ba.a.399.1		8
55.24	odd	10		550.2.h.f.301.1		4
55.28	even	20		550.2.ba.a.399.2		8
55.39	odd	10		550.2.h.f.201.1		4
55.54	odd	2		6050.2.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.81.1	✓	4	11.2	odd	10
110.2.g.a.91.1	yes	4	11.6	odd	10
550.2.h.f.201.1		4	55.39	odd	10
550.2.h.f.301.1		4	55.24	odd	10
550.2.ba.a.399.1		8	55.17	even	20
550.2.ba.a.399.2		8	55.28	even	20
550.2.ba.a.499.1		8	55.13	even	20
550.2.ba.a.499.2		8	55.2	even	20
880.2.bo.a.81.1		4	44.35	even	10
880.2.bo.a.641.1		4	44.39	even	10
990.2.n.f.91.1		4	33.17	even	10
990.2.n.f.631.1		4	33.2	even	10
1210.2.a.p.1.2		2	1.1	even	1	trivial
1210.2.a.t.1.2		2	11.10	odd	2
6050.2.a.bu.1.1		2	55.54	odd	2
6050.2.a.cm.1.1		2	5.4	even	2
9680.2.a.bh.1.1		2	44.43	even	2
9680.2.a.bi.1.1		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.23607 q^{6} -2.61803 q^{7} -1.00000 q^{8} +7.47214 q^{9} +1.00000 q^{10} +3.23607 q^{12} +1.61803 q^{13} +2.61803 q^{14} -3.23607 q^{15} +1.00000 q^{16} +5.23607 q^{17} -7.47214 q^{18} +4.09017 q^{19} -1.00000 q^{20} -8.47214 q^{21} +0.145898 q^{23} -3.23607 q^{24} +1.00000 q^{25} -1.61803 q^{26} +14.4721 q^{27} -2.61803 q^{28} +1.23607 q^{29} +3.23607 q^{30} -7.23607 q^{31} -1.00000 q^{32} -5.23607 q^{34} +2.61803 q^{35} +7.47214 q^{36} -0.854102 q^{37} -4.09017 q^{38} +5.23607 q^{39} +1.00000 q^{40} +1.85410 q^{41} +8.47214 q^{42} +9.23607 q^{43} -7.47214 q^{45} -0.145898 q^{46} +11.3262 q^{47} +3.23607 q^{48} -0.145898 q^{49} -1.00000 q^{50} +16.9443 q^{51} +1.61803 q^{52} +0.909830 q^{53} -14.4721 q^{54} +2.61803 q^{56} +13.2361 q^{57} -1.23607 q^{58} +2.38197 q^{59} -3.23607 q^{60} -8.94427 q^{61} +7.23607 q^{62} -19.5623 q^{63} +1.00000 q^{64} -1.61803 q^{65} +0.763932 q^{67} +5.23607 q^{68} +0.472136 q^{69} -2.61803 q^{70} +13.2361 q^{71} -7.47214 q^{72} +1.70820 q^{73} +0.854102 q^{74} +3.23607 q^{75} +4.09017 q^{76} -5.23607 q^{78} +1.52786 q^{79} -1.00000 q^{80} +24.4164 q^{81} -1.85410 q^{82} -15.7082 q^{83} -8.47214 q^{84} -5.23607 q^{85} -9.23607 q^{86} +4.00000 q^{87} -12.0344 q^{89} +7.47214 q^{90} -4.23607 q^{91} +0.145898 q^{92} -23.4164 q^{93} -11.3262 q^{94} -4.09017 q^{95} -3.23607 q^{96} -12.0000 q^{97} +0.145898 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 2 q^{20} - 8 q^{21}+ \cdots + 7 q^{98}+O(q^{100}) \) 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

Varieties

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Database

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