LMFDB - Embedded newform 4205.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4205,2,Mod(1,4205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4205 = 5 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4205.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$33.5770940499$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.942577.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 7x^{3} + 8x^{2} + 5x - 3 $ x^5 - x^4 - 7x^3 + 8x^2 + 5*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.423235$ of defining polynomial
Character	$\chi$	$=$	4205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.423235 q^{2} +2.22702 q^{3} -1.82087 q^{4} -1.00000 q^{5} +0.942555 q^{6} +3.43800 q^{7} -1.61713 q^{8} +1.95964 q^{9} -0.423235 q^{10} +3.47836 q^{11} -4.05513 q^{12} -7.04790 q^{13} +1.45508 q^{14} -2.22702 q^{15} +2.95732 q^{16} -0.423235 q^{17} +0.829387 q^{18} -6.35496 q^{19} +1.82087 q^{20} +7.65651 q^{21} +1.47216 q^{22} -8.44553 q^{23} -3.60138 q^{24} +1.00000 q^{25} -2.98292 q^{26} -2.31691 q^{27} -6.26016 q^{28} -0.942555 q^{30} +3.41472 q^{31} +4.48590 q^{32} +7.74640 q^{33} -0.179128 q^{34} -3.43800 q^{35} -3.56825 q^{36} -2.69166 q^{37} -2.68964 q^{38} -15.6958 q^{39} +1.61713 q^{40} -0.715531 q^{41} +3.24050 q^{42} -8.55013 q^{43} -6.33365 q^{44} -1.95964 q^{45} -3.57445 q^{46} +8.52454 q^{47} +6.58602 q^{48} +4.81984 q^{49} +0.423235 q^{50} -0.942555 q^{51} +12.8333 q^{52} -0.0380437 q^{53} -0.980599 q^{54} -3.47836 q^{55} -5.55968 q^{56} -14.1526 q^{57} -13.6168 q^{59} +4.05513 q^{60} +2.64071 q^{61} +1.44523 q^{62} +6.73723 q^{63} -4.01605 q^{64} +7.04790 q^{65} +3.27855 q^{66} +0.311101 q^{67} +0.770657 q^{68} -18.8084 q^{69} -1.45508 q^{70} -12.1690 q^{71} -3.16898 q^{72} +10.5672 q^{73} -1.13920 q^{74} +2.22702 q^{75} +11.5716 q^{76} +11.9586 q^{77} -6.64303 q^{78} +4.35392 q^{79} -2.95732 q^{80} -11.0387 q^{81} -0.302838 q^{82} -0.361153 q^{83} -13.9415 q^{84} +0.423235 q^{85} -3.61872 q^{86} -5.62495 q^{88} -5.02230 q^{89} -0.829387 q^{90} -24.2307 q^{91} +15.3782 q^{92} +7.60466 q^{93} +3.60788 q^{94} +6.35496 q^{95} +9.99020 q^{96} -4.77367 q^{97} +2.03993 q^{98} +6.81633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 2 q^{3} + 5 q^{4} - 5 q^{5} + 10 q^{6} + q^{7} - 6 q^{8} + 13 q^{9} - q^{10} - 2 q^{11} - 2 q^{12} - 8 q^{13} - 11 q^{14} + 2 q^{15} + 5 q^{16} - q^{17} + 4 q^{18} - 9 q^{19} - 5 q^{20}+ \cdots - 59 q^{99}+O(q^{100}) $ 5 * q + q^2 - 2 * q^3 + 5 * q^4 - 5 * q^5 + 10 * q^6 + q^7 - 6 * q^8 + 13 * q^9 - q^10 - 2 * q^11 - 2 * q^12 - 8 * q^13 - 11 * q^14 + 2 * q^15 + 5 * q^16 - q^17 + 4 * q^18 - 9 * q^19 - 5 * q^20 - 5 * q^21 - 13 * q^22 - 2 * q^23 + 7 * q^24 + 5 * q^25 - 17 * q^26 - 5 * q^27 - 6 * q^28 - 10 * q^30 + 2 * q^31 - 21 * q^32 + 2 * q^33 - 15 * q^34 - q^35 - 5 * q^36 - 4 * q^37 + 42 * q^38 - 24 * q^39 + 6 * q^40 - 22 * q^41 - 17 * q^42 - 24 * q^43 + 9 * q^44 - 13 * q^45 - 6 * q^46 + 12 * q^47 - 6 * q^48 + 2 * q^49 + q^50 - 10 * q^51 + 22 * q^52 + 16 * q^53 + 6 * q^54 + 2 * q^55 - 31 * q^56 + 18 * q^57 - 4 * q^59 + 2 * q^60 - 23 * q^61 - 16 * q^63 - 10 * q^64 + 8 * q^65 - 33 * q^66 + 3 * q^67 + 4 * q^68 - 16 * q^69 + 11 * q^70 - 24 * q^71 + 21 * q^72 + 32 * q^73 - 2 * q^74 - 2 * q^75 + q^76 + 55 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 + 14 * q^82 + 20 * q^83 - 67 * q^84 + q^85 + 12 * q^86 - 64 * q^88 + 14 * q^89 - 4 * q^90 - 4 * q^91 + 53 * q^92 - 28 * q^93 - 39 * q^94 + 9 * q^95 + 31 * q^96 - 13 * q^97 + 28 * q^98 - 59 * q^99

Coefficient data

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

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

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

$2$	0.423235	0.299272	0.149636	−	0.988741i	$-0.452190\pi$
$2$	0.423235	0.299272	0.149636	+	0.988741i	$0.452190\pi$
$3$	2.22702	1.28577	0.642887	−	0.765961i	$-0.277737\pi$
$3$	2.22702	1.28577	0.642887	+	0.765961i	$0.277737\pi$
$4$	−1.82087	−0.910436
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.942555	0.384796
$7$	3.43800	1.29944	0.649721	−	0.760173i	$-0.274886\pi$
$7$	3.43800	1.29944	0.649721	+	0.760173i	$0.274886\pi$
$8$	−1.61713	−0.571741
$9$	1.95964	0.653213
$10$	−0.423235	−0.133839
$11$	3.47836	1.04877	0.524383	−	0.851483i	$-0.324296\pi$
$11$	3.47836	1.04877	0.524383	+	0.851483i	$0.324296\pi$
$12$	−4.05513	−1.17061
$13$	−7.04790	−1.95473	−0.977367	−	0.211549i	$-0.932149\pi$
$13$	−7.04790	−1.95473	−0.977367	+	0.211549i	$0.932149\pi$
$14$	1.45508	0.388887
$15$	−2.22702	−0.575015
$16$	2.95732	0.739330
$17$	−0.423235	−0.102650	−0.0513248	−	0.998682i	$-0.516344\pi$
$17$	−0.423235	−0.102650	−0.0513248	+	0.998682i	$0.516344\pi$
$18$	0.829387	0.195489
$19$	−6.35496	−1.45793	−0.728963	−	0.684553i	$-0.759998\pi$
$19$	−6.35496	−1.45793	−0.728963	+	0.684553i	$0.759998\pi$
$20$	1.82087	0.407159
$21$	7.65651	1.67079
$22$	1.47216	0.313867
$23$	−8.44553	−1.76102	−0.880508	−	0.474032i	$-0.842798\pi$
$23$	−8.44553	−1.76102	−0.880508	+	0.474032i	$0.842798\pi$
$24$	−3.60138	−0.735129
$25$	1.00000	0.200000
$26$	−2.98292	−0.584998
$27$	−2.31691	−0.445890
$28$	−6.26016	−1.18306
$29$	0	0
$29$	0	0
$30$	−0.942555	−0.172086
$31$	3.41472	0.613302	0.306651	−	0.951822i	$-0.400792\pi$
$31$	3.41472	0.613302	0.306651	+	0.951822i	$0.400792\pi$
$32$	4.48590	0.793002
$33$	7.74640	1.34847
$34$	−0.179128	−0.0307202
$35$	−3.43800	−0.581128
$36$	−3.56825	−0.594708
$37$	−2.69166	−0.442505	−0.221253	−	0.975217i	$-0.571015\pi$
$37$	−2.69166	−0.442505	−0.221253	+	0.975217i	$0.571015\pi$
$38$	−2.68964	−0.436317
$39$	−15.6958	−2.51335
$40$	1.61713	0.255690
$41$	−0.715531	−0.111747	−0.0558735	−	0.998438i	$-0.517794\pi$
$41$	−0.715531	−0.111747	−0.0558735	+	0.998438i	$0.517794\pi$
$42$	3.24050	0.500020
$43$	−8.55013	−1.30388	−0.651942	−	0.758269i	$-0.726045\pi$
$43$	−8.55013	−1.30388	−0.651942	+	0.758269i	$0.726045\pi$
$44$	−6.33365	−0.954834
$45$	−1.95964	−0.292126
$46$	−3.57445	−0.527023
$47$	8.52454	1.24343	0.621716	−	0.783243i	$-0.286436\pi$
$47$	8.52454	1.24343	0.621716	+	0.783243i	$0.286436\pi$
$48$	6.58602	0.950610
$49$	4.81984	0.688548
$50$	0.423235	0.0598545
$51$	−0.942555	−0.131984
$52$	12.8333	1.77966
$53$	−0.0380437	−0.00522571	−0.00261285	−	0.999997i	$-0.500832\pi$
$53$	−0.0380437	−0.00522571	−0.00261285	+	0.999997i	$0.500832\pi$
$54$	−0.980599	−0.133443
$55$	−3.47836	−0.469022
$56$	−5.55968	−0.742944
$57$	−14.1526	−1.87456
$58$	0	0
$59$	−13.6168	−1.77276	−0.886380	−	0.462957i	$-0.846788\pi$
$59$	−13.6168	−1.77276	−0.886380	+	0.462957i	$0.846788\pi$
$60$	4.05513	0.523515
$61$	2.64071	0.338108	0.169054	−	0.985607i	$-0.445929\pi$
$61$	2.64071	0.338108	0.169054	+	0.985607i	$0.445929\pi$
$62$	1.44523	0.183544
$63$	6.73723	0.848812
$64$	−4.01605	−0.502006
$65$	7.04790	0.874184
$66$	3.27855	0.403561
$67$	0.311101	0.0380070	0.0190035	−	0.999819i	$-0.493951\pi$
$67$	0.311101	0.0380070	0.0190035	+	0.999819i	$0.493951\pi$
$68$	0.770657	0.0934559
$69$	−18.8084	−2.26427
$70$	−1.45508	−0.173916
$71$	−12.1690	−1.44419	−0.722096	−	0.691793i	$-0.756821\pi$
$71$	−12.1690	−1.44419	−0.722096	+	0.691793i	$0.756821\pi$
$72$	−3.16898	−0.373468
$73$	10.5672	1.23680	0.618400	−	0.785864i	$-0.287781\pi$
$73$	10.5672	1.23680	0.618400	+	0.785864i	$0.287781\pi$
$74$	−1.13920	−0.132430
$75$	2.22702	0.257155
$76$	11.5716	1.32735
$77$	11.9586	1.36281
$78$	−6.64303	−0.752175
$79$	4.35392	0.489855	0.244927	−	0.969541i	$-0.421236\pi$
$79$	4.35392	0.489855	0.244927	+	0.969541i	$0.421236\pi$
$80$	−2.95732	−0.330638
$81$	−11.0387	−1.22653
$82$	−0.302838	−0.0334428
$83$	−0.361153	−0.0396417	−0.0198208	−	0.999804i	$-0.506310\pi$
$83$	−0.361153	−0.0396417	−0.0198208	+	0.999804i	$0.506310\pi$
$84$	−13.9415	−1.52114
$85$	0.423235	0.0459063
$86$	−3.61872	−0.390216
$87$	0	0
$88$	−5.62495	−0.599622
$89$	−5.02230	−0.532363	−0.266181	−	0.963923i	$-0.585762\pi$
$89$	−5.02230	−0.532363	−0.266181	+	0.963923i	$0.585762\pi$
$90$	−0.829387	−0.0874251
$91$	−24.2307	−2.54006
$92$	15.3782	1.60329
$93$	7.60466	0.788567
$94$	3.60788	0.372125
$95$	6.35496	0.652005
$96$	9.99020	1.01962
$97$	−4.77367	−0.484692	−0.242346	−	0.970190i	$-0.577917\pi$
$97$	−4.77367	−0.484692	−0.242346	+	0.970190i	$0.577917\pi$
$98$	2.03993	0.206064
$99$	6.81633	0.685067
$100$	−1.82087	−0.182087
$101$	2.10465	0.209421	0.104710	−	0.994503i	$-0.466608\pi$
$101$	2.10465	0.209421	0.104710	+	0.994503i	$0.466608\pi$
$102$	−0.398922	−0.0394992
$103$	−5.03933	−0.496540	−0.248270	−	0.968691i	$-0.579862\pi$
$103$	−5.03933	−0.496540	−0.248270	+	0.968691i	$0.579862\pi$
$104$	11.3973	1.11760
$105$	−7.65651	−0.747199
$106$	−0.0161014	−0.00156391
$107$	−5.64273	−0.545503	−0.272751	−	0.962085i	$-0.587934\pi$
$107$	−5.64273	−0.545503	−0.272751	+	0.962085i	$0.587934\pi$
$108$	4.21880	0.405954
$109$	−2.77238	−0.265546	−0.132773	−	0.991146i	$-0.542388\pi$
$109$	−2.77238	−0.265546	−0.132773	+	0.991146i	$0.542388\pi$
$110$	−1.47216	−0.140365
$111$	−5.99438	−0.568962
$112$	10.1673	0.960716
$113$	10.8920	1.02464	0.512319	−	0.858795i	$-0.328787\pi$
$113$	10.8920	1.02464	0.512319	+	0.858795i	$0.328787\pi$
$114$	−5.98990	−0.561005
$115$	8.44553	0.787550
$116$	0	0
$117$	−13.8113	−1.27686
$118$	−5.76312	−0.530538
$119$	−1.45508	−0.133387
$120$	3.60138	0.328760
$121$	1.09900	0.0999090
$122$	1.11764	0.101187
$123$	−1.59350	−0.143681
$124$	−6.21777	−0.558372
$125$	−1.00000	−0.0894427
$126$	2.85143	0.254026
$127$	−4.88683	−0.433636	−0.216818	−	0.976212i	$-0.569568\pi$
$127$	−4.88683	−0.433636	−0.216818	+	0.976212i	$0.569568\pi$
$128$	−10.6715	−0.943238
$129$	−19.0414	−1.67650
$130$	2.98292	0.261619
$131$	−6.69166	−0.584653	−0.292326	−	0.956319i	$-0.594429\pi$
$131$	−6.69166	−0.584653	−0.292326	+	0.956319i	$0.594429\pi$
$132$	−14.1052	−1.22770
$133$	−21.8483	−1.89449
$134$	0.131669	0.0113745
$135$	2.31691	0.199408
$136$	0.684425	0.0586890
$137$	0.422546	0.0361005	0.0180503	−	0.999837i	$-0.494254\pi$
$137$	0.422546	0.0361005	0.0180503	+	0.999837i	$0.494254\pi$
$138$	−7.96038	−0.677632
$139$	15.4758	1.31264	0.656318	−	0.754484i	$-0.272113\pi$
$139$	15.4758	1.31264	0.656318	+	0.754484i	$0.272113\pi$
$140$	6.26016	0.529080
$141$	18.9843	1.59877
$142$	−5.15034	−0.432207
$143$	−24.5151	−2.05006
$144$	5.79527	0.482939
$145$	0	0
$146$	4.47242	0.370140
$147$	10.7339	0.885317
$148$	4.90116	0.402873
$149$	12.8077	1.04925	0.524625	−	0.851334i	$-0.324206\pi$
$149$	12.8077	1.04925	0.524625	+	0.851334i	$0.324206\pi$
$150$	0.942555	0.0769593
$151$	7.82781	0.637018	0.318509	−	0.947920i	$-0.396818\pi$
$151$	7.82781	0.637018	0.318509	+	0.947920i	$0.396818\pi$
$152$	10.2768	0.833556
$153$	−0.829387	−0.0670520
$154$	5.06130	0.407851
$155$	−3.41472	−0.274277
$156$	28.5801	2.28824
$157$	3.62422	0.289245	0.144622	−	0.989487i	$-0.453803\pi$
$157$	3.62422	0.289245	0.144622	+	0.989487i	$0.453803\pi$
$158$	1.84273	0.146600
$159$	−0.0847243	−0.00671907
$160$	−4.48590	−0.354641
$161$	−29.0357	−2.28834
$162$	−4.67198	−0.367065
$163$	8.13585	0.637249	0.318625	−	0.947881i	$-0.396779\pi$
$163$	8.13585	0.637249	0.318625	+	0.947881i	$0.396779\pi$
$164$	1.30289	0.101739
$165$	−7.74640	−0.603056
$166$	−0.152853	−0.0118637
$167$	−5.84377	−0.452204	−0.226102	−	0.974104i	$-0.572598\pi$
$167$	−5.84377	−0.452204	−0.226102	+	0.974104i	$0.572598\pi$
$168$	−12.3815	−0.955257
$169$	36.6728	2.82099
$170$	0.179128	0.0137385
$171$	−12.4534	−0.952336
$172$	15.5687	1.18710
$173$	14.8170	1.12651	0.563257	−	0.826282i	$-0.309548\pi$
$173$	14.8170	1.12651	0.563257	+	0.826282i	$0.309548\pi$
$174$	0	0
$175$	3.43800	0.259888
$176$	10.2866	0.775384
$177$	−30.3250	−2.27937
$178$	−2.12561	−0.159321
$179$	−7.12114	−0.532259	−0.266129	−	0.963937i	$-0.585745\pi$
$179$	−7.12114	−0.532259	−0.266129	+	0.963937i	$0.585745\pi$
$180$	3.56825	0.265962
$181$	−0.930688	−0.0691775	−0.0345887	−	0.999402i	$-0.511012\pi$
$181$	−0.930688	−0.0691775	−0.0345887	+	0.999402i	$0.511012\pi$
$182$	−10.2553	−0.760171
$183$	5.88093	0.434731
$184$	13.6575	1.00684
$185$	2.69166	0.197894
$186$	3.21856	0.235996
$187$	−1.47216	−0.107655
$188$	−15.5221	−1.13206
$189$	−7.96554	−0.579408
$190$	2.68964	0.195127
$191$	−23.6437	−1.71080	−0.855398	−	0.517972i	$-0.826687\pi$
$191$	−23.6437	−1.71080	−0.855398	+	0.517972i	$0.826687\pi$
$192$	−8.94384	−0.645466
$193$	9.31430	0.670458	0.335229	−	0.942137i	$-0.391186\pi$
$193$	9.31430	0.670458	0.335229	+	0.942137i	$0.391186\pi$
$194$	−2.02038	−0.145055
$195$	15.6958	1.12400
$196$	−8.77631	−0.626879
$197$	8.27724	0.589729	0.294864	−	0.955539i	$-0.404726\pi$
$197$	8.27724	0.589729	0.294864	+	0.955539i	$0.404726\pi$
$198$	2.88491	0.205022
$199$	−7.80074	−0.552980	−0.276490	−	0.961017i	$-0.589171\pi$
$199$	−7.80074	−0.552980	−0.276490	+	0.961017i	$0.589171\pi$
$200$	−1.61713	−0.114348
$201$	0.692829	0.0488684
$202$	0.890763	0.0626738
$203$	0	0
$204$	1.71627	0.120163
$205$	0.715531	0.0499748
$206$	−2.13282	−0.148601
$207$	−16.5502	−1.15032
$208$	−20.8429	−1.44519
$209$	−22.1048	−1.52902
$210$	−3.24050	−0.223616
$211$	−27.0322	−1.86098	−0.930488	−	0.366322i	$-0.880617\pi$
$211$	−27.0322	−1.86098	−0.930488	+	0.366322i	$0.880617\pi$
$212$	0.0692727	0.00475767
$213$	−27.1006	−1.85690
$214$	−2.38820	−0.163254
$215$	8.55013	0.583114
$216$	3.74674	0.254933
$217$	11.7398	0.796950
$218$	−1.17337	−0.0794705
$219$	23.5334	1.59024
$220$	6.33365	0.427015
$221$	2.98292	0.200653
$222$	−2.53703	−0.170274
$223$	−17.4088	−1.16578	−0.582890	−	0.812551i	$-0.698078\pi$
$223$	−17.4088	−1.16578	−0.582890	+	0.812551i	$0.698078\pi$
$224$	15.4225	1.03046
$225$	1.95964	0.130643
$226$	4.60990	0.306646
$227$	−15.0614	−0.999659	−0.499829	−	0.866124i	$-0.666604\pi$
$227$	−15.0614	−0.999659	−0.499829	+	0.866124i	$0.666604\pi$
$228$	25.7702	1.70667
$229$	−8.67359	−0.573167	−0.286584	−	0.958055i	$-0.592520\pi$
$229$	−8.67359	−0.573167	−0.286584	+	0.958055i	$0.592520\pi$
$230$	3.57445	0.235692
$231$	26.6321	1.75226
$232$	0	0
$233$	14.1622	0.927799	0.463900	−	0.885888i	$-0.346450\pi$
$233$	14.1622	0.927799	0.463900	+	0.885888i	$0.346450\pi$
$234$	−5.84544	−0.382128
$235$	−8.52454	−0.556079
$236$	24.7945	1.61399
$237$	9.69629	0.629842
$238$	−0.615842	−0.0399191
$239$	−8.49634	−0.549583	−0.274791	−	0.961504i	$-0.588609\pi$
$239$	−8.49634	−0.549583	−0.274791	+	0.961504i	$0.588609\pi$
$240$	−6.58602	−0.425126
$241$	18.0167	1.16056	0.580278	−	0.814418i	$-0.302944\pi$
$241$	18.0167	1.16056	0.580278	+	0.814418i	$0.302944\pi$
$242$	0.465135	0.0299000
$243$	−17.6328	−1.13114
$244$	−4.80840	−0.307826
$245$	−4.81984	−0.307928
$246$	−0.674427	−0.0429999
$247$	44.7891	2.84986
$248$	−5.52204	−0.350650
$249$	−0.804296	−0.0509702
$250$	−0.423235	−0.0267677
$251$	−25.3036	−1.59715	−0.798574	−	0.601897i	$-0.794412\pi$
$251$	−25.3036	−1.59715	−0.798574	+	0.601897i	$0.794412\pi$
$252$	−12.2676	−0.772789
$253$	−29.3766	−1.84689
$254$	−2.06828	−0.129775
$255$	0.942555	0.0590251
$256$	3.51554	0.219721
$257$	−11.9109	−0.742979	−0.371489	−	0.928437i	$-0.621153\pi$
$257$	−11.9109	−0.742979	−0.371489	+	0.928437i	$0.621153\pi$
$258$	−8.05897	−0.501730
$259$	−9.25391	−0.575010
$260$	−12.8333	−0.795889
$261$	0	0
$262$	−2.83214	−0.174970
$263$	9.01777	0.556060	0.278030	−	0.960572i	$-0.410319\pi$
$263$	9.01777	0.556060	0.278030	+	0.960572i	$0.410319\pi$
$264$	−12.5269	−0.770978
$265$	0.0380437	0.00233701
$266$	−9.24698	−0.566969
$267$	−11.1848	−0.684497
$268$	−0.566475	−0.0346030
$269$	−6.88934	−0.420051	−0.210025	−	0.977696i	$-0.567355\pi$
$269$	−6.88934	−0.420051	−0.210025	+	0.977696i	$0.567355\pi$
$270$	0.980599	0.0596773
$271$	15.6511	0.950739	0.475370	−	0.879786i	$-0.342314\pi$
$271$	15.6511	0.950739	0.475370	+	0.879786i	$0.342314\pi$
$272$	−1.25164	−0.0758919
$273$	−53.9623	−3.26595
$274$	0.178836	0.0108039
$275$	3.47836	0.209753
$276$	34.2477	2.06147
$277$	−17.6949	−1.06318	−0.531590	−	0.847002i	$-0.678405\pi$
$277$	−17.6949	−1.06318	−0.531590	+	0.847002i	$0.678405\pi$
$278$	6.54988	0.392836
$279$	6.69161	0.400616
$280$	5.55968	0.332255
$281$	8.34222	0.497655	0.248828	−	0.968548i	$-0.419955\pi$
$281$	8.34222	0.497655	0.248828	+	0.968548i	$0.419955\pi$
$282$	8.03484	0.478468
$283$	16.8894	1.00397	0.501986	−	0.864875i	$-0.332603\pi$
$283$	16.8894	1.00397	0.501986	+	0.864875i	$0.332603\pi$
$284$	22.1582	1.31484
$285$	14.1526	0.838330
$286$	−10.3757	−0.613526
$287$	−2.45999	−0.145209
$288$	8.79073	0.517999
$289$	−16.8209	−0.989463
$290$	0	0
$291$	−10.6311	−0.623204
$292$	−19.2415	−1.12603
$293$	−5.11549	−0.298850	−0.149425	−	0.988773i	$-0.547742\pi$
$293$	−5.11549	−0.298850	−0.149425	+	0.988773i	$0.547742\pi$
$294$	4.54296	0.264951
$295$	13.6168	0.792803
$296$	4.35275	0.252998
$297$	−8.05906	−0.467634
$298$	5.42068	0.314011
$299$	59.5232	3.44232
$300$	−4.05513	−0.234123
$301$	−29.3954	−1.69432
$302$	3.31300	0.190642
$303$	4.68711	0.269268
$304$	−18.7936	−1.07789
$305$	−2.64071	−0.151207
$306$	−0.351026	−0.0200668
$307$	−18.1953	−1.03846	−0.519229	−	0.854635i	$-0.673781\pi$
$307$	−18.1953	−1.03846	−0.519229	+	0.854635i	$0.673781\pi$
$308$	−21.7751	−1.24075
$309$	−11.2227	−0.638438
$310$	−1.44523	−0.0820835
$311$	−16.3179	−0.925302	−0.462651	−	0.886541i	$-0.653102\pi$
$311$	−16.3179	−0.925302	−0.462651	+	0.886541i	$0.653102\pi$
$312$	25.3822	1.43698
$313$	0.735317	0.0415626	0.0207813	−	0.999784i	$-0.493385\pi$
$313$	0.735317	0.0415626	0.0207813	+	0.999784i	$0.493385\pi$
$314$	1.53390	0.0865629
$315$	−6.73723	−0.379600
$316$	−7.92794	−0.445981
$317$	−21.2027	−1.19086	−0.595431	−	0.803406i	$-0.703019\pi$
$317$	−21.2027	−1.19086	−0.595431	+	0.803406i	$0.703019\pi$
$318$	−0.0358583	−0.00201083
$319$	0	0
$320$	4.01605	0.224504
$321$	−12.5665	−0.701393
$322$	−12.2889	−0.684836
$323$	2.68964	0.149656
$324$	20.1001	1.11667
$325$	−7.04790	−0.390947
$326$	3.44338	0.190711
$327$	−6.17416	−0.341432
$328$	1.15710	0.0638904
$329$	29.3073	1.61577
$330$	−3.27855	−0.180478
$331$	−20.4678	−1.12501	−0.562505	−	0.826794i	$-0.690162\pi$
$331$	−20.4678	−1.12501	−0.562505	+	0.826794i	$0.690162\pi$
$332$	0.657613	0.0360912
$333$	−5.27467	−0.289050
$334$	−2.47329	−0.135332
$335$	−0.311101	−0.0169973
$336$	22.6427	1.23526
$337$	−28.3715	−1.54550	−0.772748	−	0.634713i	$-0.781118\pi$
$337$	−28.3715	−1.54550	−0.772748	+	0.634713i	$0.781118\pi$
$338$	15.5212	0.844244
$339$	24.2569	1.31745
$340$	−0.770657	−0.0417947
$341$	11.8776	0.643210
$342$	−5.27072	−0.285008
$343$	−7.49539	−0.404713
$344$	13.8267	0.745483
$345$	18.8084	1.01261
$346$	6.27106	0.337135
$347$	20.5902	1.10534	0.552670	−	0.833400i	$-0.313609\pi$
$347$	20.5902	1.10534	0.552670	+	0.833400i	$0.313609\pi$
$348$	0	0
$349$	−17.6161	−0.942971	−0.471485	−	0.881874i	$-0.656282\pi$
$349$	−17.6161	−0.942971	−0.471485	+	0.881874i	$0.656282\pi$
$350$	1.45508	0.0777774
$351$	16.3294	0.871597
$352$	15.6036	0.831673
$353$	−10.3899	−0.552999	−0.276499	−	0.961014i	$-0.589174\pi$
$353$	−10.3899	−0.552999	−0.276499	+	0.961014i	$0.589174\pi$
$354$	−12.8346	−0.682152
$355$	12.1690	0.645863
$356$	9.14496	0.484682
$357$	−3.24050	−0.171506
$358$	−3.01392	−0.159290
$359$	15.7219	0.829771	0.414886	−	0.909874i	$-0.363822\pi$
$359$	15.7219	0.829771	0.414886	+	0.909874i	$0.363822\pi$
$360$	3.16898	0.167020
$361$	21.3855	1.12555
$362$	−0.393900	−0.0207029
$363$	2.44750	0.128460
$364$	44.1209	2.31257
$365$	−10.5672	−0.553113
$366$	2.48902	0.130103
$367$	24.8925	1.29938	0.649690	−	0.760199i	$-0.274899\pi$
$367$	24.8925	1.29938	0.649690	+	0.760199i	$0.274899\pi$
$368$	−24.9761	−1.30197
$369$	−1.40218	−0.0729946
$370$	1.13920	0.0592243
$371$	−0.130794	−0.00679050
$372$	−13.8471	−0.717940
$373$	−11.7536	−0.608580	−0.304290	−	0.952579i	$-0.598419\pi$
$373$	−11.7536	−0.608580	−0.304290	+	0.952579i	$0.598419\pi$
$374$	−0.623072	−0.0322183
$375$	−2.22702	−0.115003
$376$	−13.7853	−0.710920
$377$	0	0
$378$	−3.37130	−0.173401
$379$	−12.5028	−0.642227	−0.321114	−	0.947041i	$-0.604057\pi$
$379$	−12.5028	−0.642227	−0.321114	+	0.947041i	$0.604057\pi$
$380$	−11.5716	−0.593609
$381$	−10.8831	−0.557558
$382$	−10.0068	−0.511994
$383$	22.6951	1.15967	0.579833	−	0.814735i	$-0.303118\pi$
$383$	22.6951	1.15967	0.579833	+	0.814735i	$0.303118\pi$
$384$	−23.7657	−1.21279
$385$	−11.9586	−0.609467
$386$	3.94214	0.200650
$387$	−16.7552	−0.851713
$388$	8.69223	0.441281
$389$	20.8880	1.05906	0.529532	−	0.848290i	$-0.322367\pi$
$389$	20.8880	1.05906	0.529532	+	0.848290i	$0.322367\pi$
$390$	6.64303	0.336383
$391$	3.57445	0.180768
$392$	−7.79429	−0.393671
$393$	−14.9025	−0.751731
$394$	3.50322	0.176490
$395$	−4.35392	−0.219070
$396$	−12.4117	−0.623709
$397$	9.65226	0.484433	0.242216	−	0.970222i	$-0.422126\pi$
$397$	9.65226	0.484433	0.242216	+	0.970222i	$0.422126\pi$
$398$	−3.30155	−0.165492
$399$	−48.6568	−2.43589
$400$	2.95732	0.147866
$401$	8.66079	0.432499	0.216250	−	0.976338i	$-0.430618\pi$
$401$	8.66079	0.432499	0.216250	+	0.976338i	$0.430618\pi$
$402$	0.293230	0.0146250
$403$	−24.0666	−1.19884
$404$	−3.83230	−0.190664
$405$	11.0387	0.548519
$406$	0	0
$407$	−9.36255	−0.464084
$408$	1.52423	0.0754607
$409$	−19.8447	−0.981259	−0.490629	−	0.871368i	$-0.663233\pi$
$409$	−19.8447	−0.981259	−0.490629	+	0.871368i	$0.663233\pi$
$410$	0.302838	0.0149561
$411$	0.941019	0.0464171
$412$	9.17597	0.452068
$413$	−46.8147	−2.30360
$414$	−7.00462	−0.344258
$415$	0.361153	0.0177283
$416$	−31.6161	−1.55011
$417$	34.4649	1.68775
$418$	−9.35554	−0.457595
$419$	13.4996	0.659500	0.329750	−	0.944068i	$-0.393036\pi$
$419$	13.4996	0.659500	0.329750	+	0.944068i	$0.393036\pi$
$420$	13.9415	0.680277
$421$	1.53657	0.0748876	0.0374438	−	0.999299i	$-0.488078\pi$
$421$	1.53657	0.0748876	0.0374438	+	0.999299i	$0.488078\pi$
$422$	−11.4410	−0.556939
$423$	16.7050	0.812225
$424$	0.0615215	0.00298775
$425$	−0.423235	−0.0205299
$426$	−11.4699	−0.555720
$427$	9.07876	0.439352
$428$	10.2747	0.496645
$429$	−54.5958	−2.63591
$430$	3.61872	0.174510
$431$	37.2536	1.79444	0.897220	−	0.441583i	$-0.145583\pi$
$431$	37.2536	1.79444	0.897220	+	0.441583i	$0.145583\pi$
$432$	−6.85185	−0.329660
$433$	−28.2772	−1.35892	−0.679458	−	0.733714i	$-0.737785\pi$
$433$	−28.2772	−1.35892	−0.679458	+	0.733714i	$0.737785\pi$
$434$	4.96870	0.238505
$435$	0	0
$436$	5.04815	0.241762
$437$	53.6710	2.56743
$438$	9.96018	0.475916
$439$	26.0676	1.24414	0.622069	−	0.782962i	$-0.286292\pi$
$439$	26.0676	1.24414	0.622069	+	0.782962i	$0.286292\pi$
$440$	5.62495	0.268159
$441$	9.44514	0.449768
$442$	1.26248	0.0600498
$443$	24.4309	1.16075	0.580373	−	0.814351i	$-0.302907\pi$
$443$	24.4309	1.16075	0.580373	+	0.814351i	$0.302907\pi$
$444$	10.9150	0.518003
$445$	5.02230	0.238080
$446$	−7.36802	−0.348886
$447$	28.5231	1.34910
$448$	−13.8072	−0.652328
$449$	9.17312	0.432906	0.216453	−	0.976293i	$-0.430551\pi$
$449$	9.17312	0.432906	0.216453	+	0.976293i	$0.430551\pi$
$450$	0.829387	0.0390977
$451$	−2.48887	−0.117196
$452$	−19.8330	−0.932867
$453$	17.4327	0.819061
$454$	−6.37450	−0.299170
$455$	24.2307	1.13595
$456$	22.8866	1.07176
$457$	23.4235	1.09570	0.547852	−	0.836575i	$-0.315446\pi$
$457$	23.4235	1.09570	0.547852	+	0.836575i	$0.315446\pi$
$458$	−3.67097	−0.171533
$459$	0.980599	0.0457704
$460$	−15.3782	−0.717014
$461$	27.7980	1.29468	0.647341	−	0.762201i	$-0.275881\pi$
$461$	27.7980	1.29468	0.647341	+	0.762201i	$0.275881\pi$
$462$	11.2716	0.524404
$463$	30.3570	1.41081	0.705405	−	0.708804i	$-0.250765\pi$
$463$	30.3570	1.41081	0.705405	+	0.708804i	$0.250765\pi$
$464$	0	0
$465$	−7.60466	−0.352658
$466$	5.99396	0.277665
$467$	42.6987	1.97586	0.987929	−	0.154907i	$-0.0495079\pi$
$467$	42.6987	1.97586	0.987929	+	0.154907i	$0.0495079\pi$
$468$	25.1487	1.16250
$469$	1.06956	0.0493879
$470$	−3.60788	−0.166419
$471$	8.07124	0.371903
$472$	22.0202	1.01356
$473$	−29.7405	−1.36747
$474$	4.10381	0.188494
$475$	−6.35496	−0.291585
$476$	2.64952	0.121440
$477$	−0.0745519	−0.00341350
$478$	−3.59595	−0.164475
$479$	−17.8461	−0.815410	−0.407705	−	0.913114i	$-0.633671\pi$
$479$	−17.8461	−0.815410	−0.407705	+	0.913114i	$0.633671\pi$
$480$	−9.99020	−0.455988
$481$	18.9705	0.864981
$482$	7.62529	0.347323
$483$	−64.6633	−2.94228
$484$	−2.00114	−0.0909608
$485$	4.77367	0.216761
$486$	−7.46282	−0.338520
$487$	3.64836	0.165323	0.0826614	−	0.996578i	$-0.473658\pi$
$487$	3.64836	0.165323	0.0826614	+	0.996578i	$0.473658\pi$
$488$	−4.27037	−0.193310
$489$	18.1187	0.819358
$490$	−2.03993	−0.0921544
$491$	−4.08821	−0.184498	−0.0922491	−	0.995736i	$-0.529406\pi$
$491$	−4.08821	−0.184498	−0.0922491	+	0.995736i	$0.529406\pi$
$492$	2.90157	0.130813
$493$	0	0
$494$	18.9563	0.852885
$495$	−6.81633	−0.306371
$496$	10.0984	0.453432
$497$	−41.8370	−1.87664
$498$	−0.340406	−0.0152540
$499$	−8.15097	−0.364888	−0.182444	−	0.983216i	$-0.558401\pi$
$499$	−8.15097	−0.364888	−0.182444	+	0.983216i	$0.558401\pi$
$500$	1.82087	0.0814319
$501$	−13.0142	−0.581432
$502$	−10.7094	−0.477982
$503$	31.9551	1.42481	0.712403	−	0.701771i	$-0.247607\pi$
$503$	31.9551	1.42481	0.712403	+	0.701771i	$0.247607\pi$
$504$	−10.8950	−0.485300
$505$	−2.10465	−0.0936558
$506$	−12.4332	−0.552724
$507$	81.6713	3.62715
$508$	8.89830	0.394798
$509$	43.7200	1.93786	0.968928	−	0.247345i	$-0.0795580\pi$
$509$	43.7200	1.93786	0.968928	+	0.247345i	$0.0795580\pi$
$510$	0.398922	0.0176646
$511$	36.3301	1.60715
$512$	22.8309	1.00899
$513$	14.7239	0.650075
$514$	−5.04109	−0.222353
$515$	5.03933	0.222059
$516$	34.6719	1.52634
$517$	29.6514	1.30407
$518$	−3.91658	−0.172085
$519$	32.9978	1.44844
$520$	−11.3973	−0.499807
$521$	−22.4604	−0.984010	−0.492005	−	0.870592i	$-0.663736\pi$
$521$	−22.4604	−0.984010	−0.492005	+	0.870592i	$0.663736\pi$
$522$	0	0
$523$	−6.08703	−0.266167	−0.133084	−	0.991105i	$-0.542488\pi$
$523$	−6.08703	−0.266167	−0.133084	+	0.991105i	$0.542488\pi$
$524$	12.1846	0.532289
$525$	7.65651	0.334157
$526$	3.81664	0.166413
$527$	−1.44523	−0.0629552
$528$	22.9086	0.996967
$529$	48.3270	2.10118
$530$	0.0161014	0.000699402 0
$531$	−26.6841	−1.15799
$532$	39.7830	1.72481
$533$	5.04299	0.218436
$534$	−4.73379	−0.204851
$535$	5.64273	0.243956
$536$	−0.503090	−0.0217302
$537$	−15.8589	−0.684364
$538$	−2.91581	−0.125710
$539$	16.7651	0.722126
$540$	−4.21880	−0.181548
$541$	37.1228	1.59603	0.798017	−	0.602635i	$-0.205883\pi$
$541$	37.1228	1.59603	0.798017	+	0.602635i	$0.205883\pi$
$542$	6.62411	0.284530
$543$	−2.07266	−0.0889465
$544$	−1.89859	−0.0814013
$545$	2.77238	0.118756
$546$	−22.8387	−0.977407
$547$	−28.2162	−1.20644	−0.603218	−	0.797577i	$-0.706115\pi$
$547$	−28.2162	−1.20644	−0.603218	+	0.797577i	$0.706115\pi$
$548$	−0.769401	−0.0328672
$549$	5.17484	0.220857
$550$	1.47216	0.0627733
$551$	0	0
$552$	30.4156	1.29457
$553$	14.9688	0.636537
$554$	−7.48908	−0.318181
$555$	5.99438	0.254447
$556$	−28.1794	−1.19507
$557$	−23.0897	−0.978344	−0.489172	−	0.872187i	$-0.662701\pi$
$557$	−23.0897	−0.978344	−0.489172	+	0.872187i	$0.662701\pi$
$558$	2.83213	0.119893
$559$	60.2605	2.54875
$560$	−10.1673	−0.429645
$561$	−3.27855	−0.138420
$562$	3.53072	0.148934
$563$	8.98400	0.378630	0.189315	−	0.981916i	$-0.439373\pi$
$563$	8.98400	0.378630	0.189315	+	0.981916i	$0.439373\pi$
$564$	−34.5681	−1.45558
$565$	−10.8920	−0.458232
$566$	7.14820	0.300461
$567$	−37.9512	−1.59380
$568$	19.6788	0.825704
$569$	21.4554	0.899458	0.449729	−	0.893165i	$-0.351521\pi$
$569$	21.4554	0.899458	0.449729	+	0.893165i	$0.351521\pi$
$570$	5.98990	0.250889
$571$	−0.850307	−0.0355842	−0.0177921	−	0.999842i	$-0.505664\pi$
$571$	−0.850307	−0.0355842	−0.0177921	+	0.999842i	$0.505664\pi$
$572$	44.6389	1.86645
$573$	−52.6550	−2.19969
$574$	−1.04116	−0.0434570
$575$	−8.44553	−0.352203
$576$	−7.87000	−0.327917
$577$	21.5697	0.897959	0.448980	−	0.893542i	$-0.351788\pi$
$577$	21.5697	0.897959	0.448980	+	0.893542i	$0.351788\pi$
$578$	−7.11918	−0.296119
$579$	20.7432	0.862057
$580$	0	0
$581$	−1.24164	−0.0515120
$582$	−4.49944	−0.186508
$583$	−0.132330	−0.00548054
$584$	−17.0885	−0.707129
$585$	13.8113	0.571028
$586$	−2.16505	−0.0894375
$587$	39.6266	1.63557	0.817783	−	0.575527i	$-0.195203\pi$
$587$	39.6266	1.63557	0.817783	+	0.575527i	$0.195203\pi$
$588$	−19.5451	−0.806025
$589$	−21.7004	−0.894149
$590$	5.76312	0.237264
$591$	18.4336	0.758258
$592$	−7.96008	−0.327157
$593$	6.91287	0.283877	0.141939	−	0.989875i	$-0.454666\pi$
$593$	6.91287	0.283877	0.141939	+	0.989875i	$0.454666\pi$
$594$	−3.41088	−0.139950
$595$	1.45508	0.0596525
$596$	−23.3212	−0.955274
$597$	−17.3724	−0.711007
$598$	25.1923	1.03019
$599$	−36.0897	−1.47458	−0.737292	−	0.675574i	$-0.763896\pi$
$599$	−36.0897	−1.47458	−0.737292	+	0.675574i	$0.763896\pi$
$600$	−3.60138	−0.147026
$601$	−20.4150	−0.832746	−0.416373	−	0.909194i	$-0.636699\pi$
$601$	−20.4150	−0.832746	−0.416373	+	0.909194i	$0.636699\pi$
$602$	−12.4411	−0.507063
$603$	0.609645	0.0248267
$604$	−14.2534	−0.579964
$605$	−1.09900	−0.0446807
$606$	1.98375	0.0805843
$607$	13.6972	0.555953	0.277976	−	0.960588i	$-0.410336\pi$
$607$	13.6972	0.555953	0.277976	+	0.960588i	$0.410336\pi$
$608$	−28.5077	−1.15614
$609$	0	0
$610$	−1.11764	−0.0452520
$611$	−60.0800	−2.43058
$612$	1.51021	0.0610466
$613$	−8.86537	−0.358069	−0.179035	−	0.983843i	$-0.557297\pi$
$613$	−8.86537	−0.358069	−0.179035	+	0.983843i	$0.557297\pi$
$614$	−7.70088	−0.310782
$615$	1.59350	0.0642563
$616$	−19.3386	−0.779174
$617$	30.5406	1.22952	0.614759	−	0.788715i	$-0.289253\pi$
$617$	30.5406	1.22952	0.614759	+	0.788715i	$0.289253\pi$
$618$	−4.74984	−0.191067
$619$	−35.3049	−1.41902	−0.709512	−	0.704694i	$-0.751085\pi$
$619$	−35.3049	−1.41902	−0.709512	+	0.704694i	$0.751085\pi$
$620$	6.21777	0.249712
$621$	19.5676	0.785219
$622$	−6.90630	−0.276917
$623$	−17.2667	−0.691774
$624$	−46.4176	−1.85819
$625$	1.00000	0.0400000
$626$	0.311212	0.0124385
$627$	−49.2280	−1.96598
$628$	−6.59925	−0.263339
$629$	1.13920	0.0454230
$630$	−2.85143	−0.113604
$631$	31.5705	1.25680	0.628400	−	0.777890i	$-0.283710\pi$
$631$	31.5705	1.25680	0.628400	+	0.777890i	$0.283710\pi$
$632$	−7.04085	−0.280070
$633$	−60.2015	−2.39279
$634$	−8.97372	−0.356392
$635$	4.88683	0.193928
$636$	0.154272	0.00611728
$637$	−33.9697	−1.34593
$638$	0	0
$639$	−23.8468	−0.943365
$640$	10.6715	0.421829
$641$	−15.5707	−0.615006	−0.307503	−	0.951547i	$-0.599493\pi$
$641$	−15.5707	−0.615006	−0.307503	+	0.951547i	$0.599493\pi$
$642$	−5.31858	−0.209908
$643$	20.9016	0.824278	0.412139	−	0.911121i	$-0.364782\pi$
$643$	20.9016	0.824278	0.412139	+	0.911121i	$0.364782\pi$
$644$	52.8704	2.08338
$645$	19.0414	0.749753
$646$	1.13835	0.0447878
$647$	−8.18361	−0.321731	−0.160866	−	0.986976i	$-0.551429\pi$
$647$	−8.18361	−0.321731	−0.160866	+	0.986976i	$0.551429\pi$
$648$	17.8510	0.701255
$649$	−47.3643	−1.85921
$650$	−2.98292	−0.117000
$651$	26.1448	1.02470
$652$	−14.8143	−0.580174
$653$	−10.9265	−0.427586	−0.213793	−	0.976879i	$-0.568582\pi$
$653$	−10.9265	−0.427586	−0.213793	+	0.976879i	$0.568582\pi$
$654$	−2.61312	−0.102181
$655$	6.69166	0.261465
$656$	−2.11605	−0.0826180
$657$	20.7079	0.807893
$658$	12.4039	0.483554
$659$	2.14934	0.0837265	0.0418632	−	0.999123i	$-0.486671\pi$
$659$	2.14934	0.0837265	0.0418632	+	0.999123i	$0.486671\pi$
$660$	14.1052	0.549044
$661$	−8.58990	−0.334108	−0.167054	−	0.985948i	$-0.553425\pi$
$661$	−8.58990	−0.334108	−0.167054	+	0.985948i	$0.553425\pi$
$662$	−8.66268	−0.336685
$663$	6.64303	0.257994
$664$	0.584030	0.0226648
$665$	21.8483	0.847242
$666$	−2.23242	−0.0865047
$667$	0	0
$668$	10.6408	0.411703
$669$	−38.7698	−1.49893
$670$	−0.131669	−0.00508681
$671$	9.18535	0.354596
$672$	34.3463	1.32494
$673$	−29.9690	−1.15522	−0.577610	−	0.816313i	$-0.696014\pi$
$673$	−29.9690	−1.15522	−0.577610	+	0.816313i	$0.696014\pi$
$674$	−12.0078	−0.462524
$675$	−2.31691	−0.0891780
$676$	−66.7766	−2.56833
$677$	−46.4832	−1.78649	−0.893247	−	0.449566i	$-0.851579\pi$
$677$	−46.4832	−1.78649	−0.893247	+	0.449566i	$0.851579\pi$
$678$	10.2664	0.394277
$679$	−16.4119	−0.629829
$680$	−0.684425	−0.0262465
$681$	−33.5420	−1.28533
$682$	5.02703	0.192495
$683$	24.2294	0.927111	0.463556	−	0.886068i	$-0.346573\pi$
$683$	24.2294	0.927111	0.463556	+	0.886068i	$0.346573\pi$
$684$	22.6761	0.867041
$685$	−0.422546	−0.0161446
$686$	−3.17231	−0.121119
$687$	−19.3163	−0.736963
$688$	−25.2855	−0.964000
$689$	0.268128	0.0102149
$690$	7.96038	0.303046
$691$	−7.32074	−0.278494	−0.139247	−	0.990258i	$-0.544468\pi$
$691$	−7.32074	−0.278494	−0.139247	+	0.990258i	$0.544468\pi$
$692$	−26.9798	−1.02562
$693$	23.4345	0.890204
$694$	8.71450	0.330798
$695$	−15.4758	−0.587029
$696$	0	0
$697$	0.302838	0.0114708
$698$	−7.45577	−0.282205
$699$	31.5396	1.19294
$700$	−6.26016	−0.236612
$701$	20.7603	0.784105	0.392052	−	0.919943i	$-0.371765\pi$
$701$	20.7603	0.784105	0.392052	+	0.919943i	$0.371765\pi$
$702$	6.91116	0.260845
$703$	17.1053	0.645140
$704$	−13.9693	−0.526487
$705$	−18.9843	−0.714992
$706$	−4.39737	−0.165497
$707$	7.23579	0.272130
$708$	55.2180	2.07522
$709$	−23.9455	−0.899291	−0.449645	−	0.893207i	$-0.648450\pi$
$709$	−23.9455	−0.899291	−0.449645	+	0.893207i	$0.648450\pi$
$710$	5.15034	0.193289
$711$	8.53211	0.319979
$712$	8.12170	0.304373
$713$	−28.8391	−1.08003
$714$	−1.37149	−0.0513269
$715$	24.5151	0.916814
$716$	12.9667	0.484588
$717$	−18.9216	−0.706639
$718$	6.65407	0.248328
$719$	44.3444	1.65377	0.826883	−	0.562374i	$-0.190112\pi$
$719$	44.3444	1.65377	0.826883	+	0.562374i	$0.190112\pi$
$720$	−5.79527	−0.215977
$721$	−17.3252	−0.645225
$722$	9.05108	0.336846
$723$	40.1236	1.49221
$724$	1.69466	0.0629817
$725$	0	0
$726$	1.03587	0.0384446
$727$	25.2973	0.938223	0.469112	−	0.883139i	$-0.344574\pi$
$727$	25.2973	0.938223	0.469112	+	0.883139i	$0.344574\pi$
$728$	39.1841	1.45226
$729$	−6.15246	−0.227869
$730$	−4.47242	−0.165532
$731$	3.61872	0.133843
$732$	−10.7084	−0.395794
$733$	−18.1893	−0.671837	−0.335918	−	0.941891i	$-0.609047\pi$
$733$	−18.1893	−0.671837	−0.335918	+	0.941891i	$0.609047\pi$
$734$	10.5354	0.388869
$735$	−10.7339	−0.395926
$736$	−37.8858	−1.39649
$737$	1.08212	0.0398605
$738$	−0.593452	−0.0218453
$739$	−41.9470	−1.54304	−0.771522	−	0.636202i	$-0.780504\pi$
$739$	−41.9470	−1.54304	−0.771522	+	0.636202i	$0.780504\pi$
$740$	−4.90116	−0.180170
$741$	99.7464	3.66427
$742$	−0.0553567	−0.00203221
$743$	6.84909	0.251269	0.125634	−	0.992077i	$-0.459903\pi$
$743$	6.84909	0.251269	0.125634	+	0.992077i	$0.459903\pi$
$744$	−12.2977	−0.450856
$745$	−12.8077	−0.469239
$746$	−4.97455	−0.182131
$747$	−0.707729	−0.0258944
$748$	2.68062	0.0980133
$749$	−19.3997	−0.708849
$750$	−0.942555	−0.0344172
$751$	30.3234	1.10652	0.553259	−	0.833009i	$-0.313384\pi$
$751$	30.3234	1.10652	0.553259	+	0.833009i	$0.313384\pi$
$752$	25.2098	0.919306
$753$	−56.3517	−2.05357
$754$	0	0
$755$	−7.82781	−0.284883
$756$	14.5042	0.527514
$757$	18.1401	0.659314	0.329657	−	0.944101i	$-0.393067\pi$
$757$	18.1401	0.659314	0.329657	+	0.944101i	$0.393067\pi$
$758$	−5.29164	−0.192201
$759$	−65.4224	−2.37468
$760$	−10.2768	−0.372778
$761$	22.8124	0.826951	0.413475	−	0.910515i	$-0.364315\pi$
$761$	22.8124	0.826951	0.413475	+	0.910515i	$0.364315\pi$
$762$	−4.60611	−0.166862
$763$	−9.53144	−0.345061
$764$	43.0521	1.55757
$765$	0.829387	0.0299866
$766$	9.60537	0.347056
$767$	95.9700	3.46528
$768$	7.82918	0.282511
$769$	−23.4081	−0.844117	−0.422058	−	0.906569i	$-0.638692\pi$
$769$	−23.4081	−0.844117	−0.422058	+	0.906569i	$0.638692\pi$
$770$	−5.06130	−0.182397
$771$	−26.5258	−0.955302
$772$	−16.9602	−0.610409
$773$	31.3406	1.12724	0.563622	−	0.826033i	$-0.309407\pi$
$773$	31.3406	1.12724	0.563622	+	0.826033i	$0.309407\pi$
$774$	−7.09137	−0.254894
$775$	3.41472	0.122660
$776$	7.71962	0.277118
$777$	−20.6087	−0.739332
$778$	8.84054	0.316949
$779$	4.54716	0.162919
$780$	−28.5801	−1.02333
$781$	−42.3281	−1.51462
$782$	1.51283	0.0540987
$783$	0	0
$784$	14.2538	0.509064
$785$	−3.62422	−0.129354
$786$	−6.30725	−0.224972
$787$	22.1597	0.789909	0.394954	−	0.918701i	$-0.370760\pi$
$787$	22.1597	0.789909	0.394954	+	0.918701i	$0.370760\pi$
$788$	−15.0718	−0.536910
$789$	20.0828	0.714967
$790$	−1.84273	−0.0655615
$791$	37.4469	1.33146
$792$	−11.0229	−0.391681
$793$	−18.6115	−0.660912
$794$	4.08517	0.144977
$795$	0.0847243	0.00300486
$796$	14.2042	0.503453
$797$	3.86966	0.137070	0.0685351	−	0.997649i	$-0.478167\pi$
$797$	3.86966	0.137070	0.0685351	+	0.997649i	$0.478167\pi$
$798$	−20.5933	−0.728993
$799$	−3.60788	−0.127638
$800$	4.48590	0.158600
$801$	−9.84188	−0.347746
$802$	3.66555	0.129435
$803$	36.7566	1.29711
$804$	−1.26155	−0.0444916
$805$	29.0357	1.02338
$806$	−10.1858	−0.358780
$807$	−15.3427	−0.540090
$808$	−3.40349	−0.119734
$809$	−44.8201	−1.57579	−0.787895	−	0.615810i	$-0.788829\pi$
$809$	−44.8201	−1.57579	−0.787895	+	0.615810i	$0.788829\pi$
$810$	4.67198	0.164157
$811$	−26.8646	−0.943343	−0.471671	−	0.881774i	$-0.656349\pi$
$811$	−26.8646	−0.943343	−0.471671	+	0.881774i	$0.656349\pi$
$812$	0	0
$813$	34.8555	1.22243
$814$	−3.96256	−0.138888
$815$	−8.13585	−0.284986
$816$	−2.78744	−0.0975798
$817$	54.3357	1.90097
$818$	−8.39899	−0.293664
$819$	−47.4833	−1.65920
$820$	−1.30289	−0.0454989
$821$	2.53533	0.0884836	0.0442418	−	0.999021i	$-0.485913\pi$
$821$	2.53533	0.0884836	0.0442418	+	0.999021i	$0.485913\pi$
$822$	0.398272	0.0138913
$823$	−23.8799	−0.832403	−0.416201	−	0.909272i	$-0.636639\pi$
$823$	−23.8799	−0.832403	−0.416201	+	0.909272i	$0.636639\pi$
$824$	8.14924	0.283892
$825$	7.74640	0.269695
$826$	−19.8136	−0.689404
$827$	−28.1645	−0.979374	−0.489687	−	0.871898i	$-0.662889\pi$
$827$	−28.1645	−0.979374	−0.489687	+	0.871898i	$0.662889\pi$
$828$	30.1358	1.04729
$829$	17.6553	0.613194	0.306597	−	0.951839i	$-0.400810\pi$
$829$	17.6553	0.613194	0.306597	+	0.951839i	$0.400810\pi$
$830$	0.152853	0.00530559
$831$	−39.4069	−1.36701
$832$	28.3047	0.981289
$833$	−2.03993	−0.0706792
$834$	14.5867	0.505098
$835$	5.84377	0.202232
$836$	40.2501	1.39208
$837$	−7.91161	−0.273465
$838$	5.71352	0.197370
$839$	12.6232	0.435802	0.217901	−	0.975971i	$-0.430079\pi$
$839$	12.6232	0.435802	0.217901	+	0.975971i	$0.430079\pi$
$840$	12.3815	0.427204
$841$	0	0
$842$	0.650329	0.0224118
$843$	18.5783	0.639871
$844$	49.2223	1.69430
$845$	−36.6728	−1.26158
$846$	7.07014	0.243077
$847$	3.77836	0.129826
$848$	−0.112507	−0.00386352
$849$	37.6132	1.29088
$850$	−0.179128	−0.00614404
$851$	22.7325	0.779259
$852$	49.3468	1.69059
$853$	37.3362	1.27837	0.639184	−	0.769054i	$-0.279272\pi$
$853$	37.3362	1.27837	0.639184	+	0.769054i	$0.279272\pi$
$854$	3.84245	0.131486
$855$	12.4534	0.425898
$856$	9.12500	0.311886
$857$	−14.8210	−0.506276	−0.253138	−	0.967430i	$-0.581463\pi$
$857$	−14.8210	−0.506276	−0.253138	+	0.967430i	$0.581463\pi$
$858$	−23.1069	−0.788855
$859$	−26.6683	−0.909911	−0.454955	−	0.890514i	$-0.650345\pi$
$859$	−26.6683	−0.909911	−0.454955	+	0.890514i	$0.650345\pi$
$860$	−15.5687	−0.530888
$861$	−5.47847	−0.186706
$862$	15.7670	0.537027
$863$	−40.6824	−1.38484	−0.692422	−	0.721493i	$-0.743456\pi$
$863$	−40.6824	−1.38484	−0.692422	+	0.721493i	$0.743456\pi$
$864$	−10.3934	−0.353592
$865$	−14.8170	−0.503792
$866$	−11.9679	−0.406686
$867$	−37.4605	−1.27223
$868$	−21.3767	−0.725572
$869$	15.1445	0.513743
$870$	0	0
$871$	−2.19261	−0.0742936
$872$	4.48329	0.151823
$873$	−9.35465	−0.316607
$874$	22.7154	0.768362
$875$	−3.43800	−0.116226
$876$	−42.8514	−1.44781
$877$	17.7793	0.600363	0.300182	−	0.953882i	$-0.402953\pi$
$877$	17.7793	0.600363	0.300182	+	0.953882i	$0.402953\pi$
$878$	11.0327	0.372336
$879$	−11.3923	−0.384253
$880$	−10.2866	−0.346762
$881$	40.9598	1.37997	0.689986	−	0.723823i	$-0.257617\pi$
$881$	40.9598	1.37997	0.689986	+	0.723823i	$0.257617\pi$
$882$	3.99751	0.134603
$883$	2.78146	0.0936036	0.0468018	−	0.998904i	$-0.485097\pi$
$883$	2.78146	0.0936036	0.0468018	+	0.998904i	$0.485097\pi$
$884$	−5.43151	−0.182681
$885$	30.3250	1.01936
$886$	10.3400	0.347379
$887$	3.65945	0.122872	0.0614362	−	0.998111i	$-0.480432\pi$
$887$	3.65945	0.122872	0.0614362	+	0.998111i	$0.480432\pi$
$888$	9.69368	0.325299
$889$	−16.8009	−0.563485
$890$	2.12561	0.0712507
$891$	−38.3967	−1.28634
$892$	31.6992	1.06137
$893$	−54.1730	−1.81283
$894$	12.0720	0.403747
$895$	7.12114	0.238033
$896$	−36.6887	−1.22568
$897$	132.560	4.42604
$898$	3.88239	0.129557
$899$	0	0
$900$	−3.56825	−0.118942
$901$	0.0161014	0.000536416 0
$902$	−1.05338	−0.0350737
$903$	−65.4642	−2.17851
$904$	−17.6138	−0.585827
$905$	0.930688	0.0309371
$906$	7.37814	0.245122
$907$	−24.5644	−0.815647	−0.407824	−	0.913061i	$-0.633712\pi$
$907$	−24.5644	−0.815647	−0.407824	+	0.913061i	$0.633712\pi$
$908$	27.4248	0.910125
$909$	4.12436	0.136796
$910$	10.2553	0.339959
$911$	−47.0200	−1.55784	−0.778921	−	0.627122i	$-0.784233\pi$
$911$	−47.0200	−1.55784	−0.778921	+	0.627122i	$0.784233\pi$
$912$	−41.8539	−1.38592
$913$	−1.25622	−0.0415748
$914$	9.91364	0.327914
$915$	−5.88093	−0.194417
$916$	15.7935	0.521832
$917$	−23.0059	−0.759722
$918$	0.415024	0.0136978
$919$	23.4152	0.772396	0.386198	−	0.922416i	$-0.373788\pi$
$919$	23.4152	0.772396	0.386198	+	0.922416i	$0.373788\pi$
$920$	−13.6575	−0.450275
$921$	−40.5213	−1.33522
$922$	11.7651	0.387462
$923$	85.7657	2.82301
$924$	−48.4937	−1.59532
$925$	−2.69166	−0.0885011
$926$	12.8482	0.422217
$927$	−9.87526	−0.324346
$928$	0	0
$929$	35.4231	1.16219	0.581097	−	0.813834i	$-0.302624\pi$
$929$	35.4231	1.16219	0.581097	+	0.813834i	$0.302624\pi$
$930$	−3.21856	−0.105541
$931$	−30.6299	−1.00385
$932$	−25.7876	−0.844702
$933$	−36.3403	−1.18973
$934$	18.0716	0.591320
$935$	1.47216	0.0481449
$936$	22.3347	0.730031
$937$	−57.9633	−1.89358	−0.946789	−	0.321855i	$-0.895694\pi$
$937$	−57.9633	−1.89358	−0.946789	+	0.321855i	$0.895694\pi$
$938$	0.452677	0.0147804
$939$	1.63757	0.0534401
$940$	15.5221	0.506275
$941$	−38.1343	−1.24314	−0.621571	−	0.783358i	$-0.713505\pi$
$941$	−38.1343	−1.24314	−0.621571	+	0.783358i	$0.713505\pi$
$942$	3.41603	0.111300
$943$	6.04304	0.196788
$944$	−40.2693	−1.31065
$945$	7.96554	0.259119
$946$	−12.5872	−0.409245
$947$	−50.8389	−1.65204	−0.826022	−	0.563638i	$-0.809401\pi$
$947$	−50.8389	−1.65204	−0.826022	+	0.563638i	$0.809401\pi$
$948$	−17.6557	−0.573431
$949$	−74.4766	−2.41761
$950$	−2.68964	−0.0872635
$951$	−47.2189	−1.53118
$952$	2.35305	0.0762629
$953$	−15.8383	−0.513052	−0.256526	−	0.966537i	$-0.582578\pi$
$953$	−15.8383	−0.513052	−0.256526	+	0.966537i	$0.582578\pi$
$954$	−0.0315530	−0.00102157
$955$	23.6437	0.765091
$956$	15.4708	0.500360
$957$	0	0
$958$	−7.55311	−0.244030
$959$	1.45271	0.0469105
$960$	8.94384	0.288661
$961$	−19.3397	−0.623861
$962$	8.02898	0.258865
$963$	−11.0577	−0.356329
$964$	−32.8061	−1.05661
$965$	−9.31430	−0.299838
$966$	−27.3678	−0.880544
$967$	−2.86192	−0.0920332	−0.0460166	−	0.998941i	$-0.514653\pi$
$967$	−2.86192	−0.0920332	−0.0460166	+	0.998941i	$0.514653\pi$
$968$	−1.77722	−0.0571221
$969$	5.98990	0.192423
$970$	2.02038	0.0648706
$971$	−0.472066	−0.0151493	−0.00757466	−	0.999971i	$-0.502411\pi$
$971$	−0.472066	−0.0151493	−0.00757466	+	0.999971i	$0.502411\pi$
$972$	32.1071	1.02983
$973$	53.2056	1.70569
$974$	1.54411	0.0494766
$975$	−15.6958	−0.502669
$976$	7.80942	0.249974
$977$	−57.8393	−1.85044	−0.925222	−	0.379426i	$-0.876121\pi$
$977$	−57.8393	−1.85044	−0.925222	+	0.379426i	$0.876121\pi$
$978$	7.66849	0.245211
$979$	−17.4694	−0.558323
$980$	8.77631	0.280349
$981$	−5.43286	−0.173458
$982$	−1.73027	−0.0552152
$983$	48.0654	1.53305	0.766524	−	0.642215i	$-0.221984\pi$
$983$	48.0654	1.53305	0.766524	+	0.642215i	$0.221984\pi$
$984$	2.57690	0.0821485
$985$	−8.27724	−0.263735
$986$	0	0
$987$	65.2682	2.07751
$988$	−81.5552	−2.59462
$989$	72.2104	2.29616
$990$	−2.88491	−0.0916884
$991$	−4.39885	−0.139734	−0.0698670	−	0.997556i	$-0.522257\pi$
$991$	−4.39885	−0.139734	−0.0698670	+	0.997556i	$0.522257\pi$
$992$	15.3181	0.486349
$993$	−45.5822	−1.44651
$994$	−17.7069	−0.561628
$995$	7.80074	0.247300
$996$	1.46452	0.0464051
$997$	7.53626	0.238676	0.119338	−	0.992854i	$-0.461923\pi$
$997$	7.53626	0.238676	0.119338	+	0.992854i	$0.461923\pi$
$998$	−3.44978	−0.109201
$999$	6.23633	0.197309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4205.2.a.j.1.3	yes	5
29.28	even	2		4205.2.a.i.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4205.2.a.i.1.3	✓	5	29.28	even	2
4205.2.a.j.1.3	yes	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4205 = 5 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4205.a (trivial)

\(f(q)\)	\(=\)	\(q+0.423235 q^{2} +2.22702 q^{3} -1.82087 q^{4} -1.00000 q^{5} +0.942555 q^{6} +3.43800 q^{7} -1.61713 q^{8} +1.95964 q^{9} -0.423235 q^{10} +3.47836 q^{11} -4.05513 q^{12} -7.04790 q^{13} +1.45508 q^{14} -2.22702 q^{15} +2.95732 q^{16} -0.423235 q^{17} +0.829387 q^{18} -6.35496 q^{19} +1.82087 q^{20} +7.65651 q^{21} +1.47216 q^{22} -8.44553 q^{23} -3.60138 q^{24} +1.00000 q^{25} -2.98292 q^{26} -2.31691 q^{27} -6.26016 q^{28} -0.942555 q^{30} +3.41472 q^{31} +4.48590 q^{32} +7.74640 q^{33} -0.179128 q^{34} -3.43800 q^{35} -3.56825 q^{36} -2.69166 q^{37} -2.68964 q^{38} -15.6958 q^{39} +1.61713 q^{40} -0.715531 q^{41} +3.24050 q^{42} -8.55013 q^{43} -6.33365 q^{44} -1.95964 q^{45} -3.57445 q^{46} +8.52454 q^{47} +6.58602 q^{48} +4.81984 q^{49} +0.423235 q^{50} -0.942555 q^{51} +12.8333 q^{52} -0.0380437 q^{53} -0.980599 q^{54} -3.47836 q^{55} -5.55968 q^{56} -14.1526 q^{57} -13.6168 q^{59} +4.05513 q^{60} +2.64071 q^{61} +1.44523 q^{62} +6.73723 q^{63} -4.01605 q^{64} +7.04790 q^{65} +3.27855 q^{66} +0.311101 q^{67} +0.770657 q^{68} -18.8084 q^{69} -1.45508 q^{70} -12.1690 q^{71} -3.16898 q^{72} +10.5672 q^{73} -1.13920 q^{74} +2.22702 q^{75} +11.5716 q^{76} +11.9586 q^{77} -6.64303 q^{78} +4.35392 q^{79} -2.95732 q^{80} -11.0387 q^{81} -0.302838 q^{82} -0.361153 q^{83} -13.9415 q^{84} +0.423235 q^{85} -3.61872 q^{86} -5.62495 q^{88} -5.02230 q^{89} -0.829387 q^{90} -24.2307 q^{91} +15.3782 q^{92} +7.60466 q^{93} +3.60788 q^{94} +6.35496 q^{95} +9.99020 q^{96} -4.77367 q^{97} +2.03993 q^{98} +6.81633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 2 q^{3} + 5 q^{4} - 5 q^{5} + 10 q^{6} + q^{7} - 6 q^{8} + 13 q^{9} - q^{10} - 2 q^{11} - 2 q^{12} - 8 q^{13} - 11 q^{14} + 2 q^{15} + 5 q^{16} - q^{17} + 4 q^{18} - 9 q^{19} - 5 q^{20}+ \cdots - 59 q^{99}+O(q^{100}) \) 5 * q + q^2 - 2 * q^3 + 5 * q^4 - 5 * q^5 + 10 * q^6 + q^7 - 6 * q^8 + 13 * q^9 - q^10 - 2 * q^11 - 2 * q^12 - 8 * q^13 - 11 * q^14 + 2 * q^15 + 5 * q^16 - q^17 + 4 * q^18 - 9 * q^19 - 5 * q^20 - 5 * q^21 - 13 * q^22 - 2 * q^23 + 7 * q^24 + 5 * q^25 - 17 * q^26 - 5 * q^27 - 6 * q^28 - 10 * q^30 + 2 * q^31 - 21 * q^32 + 2 * q^33 - 15 * q^34 - q^35 - 5 * q^36 - 4 * q^37 + 42 * q^38 - 24 * q^39 + 6 * q^40 - 22 * q^41 - 17 * q^42 - 24 * q^43 + 9 * q^44 - 13 * q^45 - 6 * q^46 + 12 * q^47 - 6 * q^48 + 2 * q^49 + q^50 - 10 * q^51 + 22 * q^52 + 16 * q^53 + 6 * q^54 + 2 * q^55 - 31 * q^56 + 18 * q^57 - 4 * q^59 + 2 * q^60 - 23 * q^61 - 16 * q^63 - 10 * q^64 + 8 * q^65 - 33 * q^66 + 3 * q^67 + 4 * q^68 - 16 * q^69 + 11 * q^70 - 24 * q^71 + 21 * q^72 + 32 * q^73 - 2 * q^74 - 2 * q^75 + q^76 + 55 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 + 14 * q^82 + 20 * q^83 - 67 * q^84 + q^85 + 12 * q^86 - 64 * q^88 + 14 * q^89 - 4 * q^90 - 4 * q^91 + 53 * q^92 - 28 * q^93 - 39 * q^94 + 9 * q^95 + 31 * q^96 - 13 * q^97 + 28 * q^98 - 59 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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