LMFDB - Embedded newform 1850.2.b.j.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.j.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} +0.618034 q^{6} -1.23607i q^{7} +1.00000i q^{8} +2.61803 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} +0.618034 q^{6} -1.23607i q^{7} +1.00000i q^{8} +2.61803 q^{9} -3.61803 q^{11} -0.618034i q^{12} +3.85410i q^{13} -1.23607 q^{14} +1.00000 q^{16} -4.47214i q^{17} -2.61803i q^{18} +4.47214 q^{19} +0.763932 q^{21} +3.61803i q^{22} -3.85410i q^{23} -0.618034 q^{24} +3.85410 q^{26} +3.47214i q^{27} +1.23607i q^{28} -6.32624 q^{29} +9.61803 q^{31} -1.00000i q^{32} -2.23607i q^{33} -4.47214 q^{34} -2.61803 q^{36} +1.00000i q^{37} -4.47214i q^{38} -2.38197 q^{39} +7.38197 q^{41} -0.763932i q^{42} -0.763932i q^{43} +3.61803 q^{44} -3.85410 q^{46} -3.23607i q^{47} +0.618034i q^{48} +5.47214 q^{49} +2.76393 q^{51} -3.85410i q^{52} -8.47214i q^{53} +3.47214 q^{54} +1.23607 q^{56} +2.76393i q^{57} +6.32624i q^{58} +9.23607 q^{59} +8.38197 q^{61} -9.61803i q^{62} -3.23607i q^{63} -1.00000 q^{64} -2.23607 q^{66} +10.0902i q^{67} +4.47214i q^{68} +2.38197 q^{69} -14.9443 q^{71} +2.61803i q^{72} -4.09017i q^{73} +1.00000 q^{74} -4.47214 q^{76} +4.47214i q^{77} +2.38197i q^{78} -11.5623 q^{79} +5.70820 q^{81} -7.38197i q^{82} -5.52786i q^{83} -0.763932 q^{84} -0.763932 q^{86} -3.90983i q^{87} -3.61803i q^{88} +10.4721 q^{89} +4.76393 q^{91} +3.85410i q^{92} +5.94427i q^{93} -3.23607 q^{94} +0.618034 q^{96} -8.47214i q^{97} -5.47214i q^{98} -9.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9} - 10 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{21} + 2 q^{24} + 2 q^{26} + 6 q^{29} + 34 q^{31} - 6 q^{36} - 14 q^{39} + 34 q^{41} + 10 q^{44} - 2 q^{46} + 4 q^{49} + 20 q^{51} - 4 q^{54} - 4 q^{56} + 28 q^{59} + 38 q^{61} - 4 q^{64} + 14 q^{69} - 24 q^{71} + 4 q^{74} - 6 q^{79} - 4 q^{81} - 12 q^{84} - 12 q^{86} + 24 q^{89} + 28 q^{91} - 4 q^{94} - 2 q^{96} - 20 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9 - 10 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^21 + 2 * q^24 + 2 * q^26 + 6 * q^29 + 34 * q^31 - 6 * q^36 - 14 * q^39 + 34 * q^41 + 10 * q^44 - 2 * q^46 + 4 * q^49 + 20 * q^51 - 4 * q^54 - 4 * q^56 + 28 * q^59 + 38 * q^61 - 4 * q^64 + 14 * q^69 - 24 * q^71 + 4 * q^74 - 6 * q^79 - 4 * q^81 - 12 * q^84 - 12 * q^86 + 24 * q^89 + 28 * q^91 - 4 * q^94 - 2 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	0.618034i	0.356822i	0.983956	+	0.178411i	$0.0570957\pi$
$3$	0.618034i	0.356822i	−0.983956	+	0.178411i	$0.942904\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.618034	0.252311
$7$	− 1.23607i	− 0.467190i	−0.972334	−	0.233595i	$-0.924951\pi$
$7$	− 1.23607i	− 0.467190i	0.972334	−	0.233595i	$-0.0750489\pi$
$8$	1.00000i	0.353553i
$9$	2.61803	0.872678
$10$	0	0
$11$	−3.61803	−1.09088	−0.545439	−	0.838150i	$-0.683637\pi$
$11$	−3.61803	−1.09088	−0.545439	+	0.838150i	$0.683637\pi$
$12$	− 0.618034i	− 0.178411i
$13$	3.85410i	1.06894i	0.845189	+	0.534468i	$0.179488\pi$
$13$	3.85410i	1.06894i	−0.845189	+	0.534468i	$0.820512\pi$
$14$	−1.23607	−0.330353
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.47214i	− 1.08465i	−0.840168	−	0.542326i	$-0.817544\pi$
$17$	− 4.47214i	− 1.08465i	0.840168	−	0.542326i	$-0.182456\pi$
$18$	− 2.61803i	− 0.617077i
$19$	4.47214	1.02598	0.512989	−	0.858395i	$-0.328538\pi$
$19$	4.47214	1.02598	0.512989	+	0.858395i	$0.328538\pi$
$20$	0	0
$21$	0.763932	0.166704
$22$	3.61803i	0.771367i
$23$	− 3.85410i	− 0.803636i	−0.915720	−	0.401818i	$-0.868378\pi$
$23$	− 3.85410i	− 0.803636i	0.915720	−	0.401818i	$-0.131622\pi$
$24$	−0.618034	−0.126156
$25$	0	0
$26$	3.85410	0.755852
$27$	3.47214i	0.668213i
$28$	1.23607i	0.233595i
$29$	−6.32624	−1.17475	−0.587376	−	0.809314i	$-0.699839\pi$
$29$	−6.32624	−1.17475	−0.587376	+	0.809314i	$0.699839\pi$
$30$	0	0
$31$	9.61803	1.72745	0.863725	−	0.503964i	$-0.168125\pi$
$31$	9.61803	1.72745	0.863725	+	0.503964i	$0.168125\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 2.23607i	− 0.389249i
$34$	−4.47214	−0.766965
$35$	0	0
$36$	−2.61803	−0.436339
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	− 4.47214i	− 0.725476i
$39$	−2.38197	−0.381420
$40$	0	0
$41$	7.38197	1.15287	0.576435	−	0.817143i	$-0.304444\pi$
$41$	7.38197	1.15287	0.576435	+	0.817143i	$0.304444\pi$
$42$	− 0.763932i	− 0.117877i
$43$	− 0.763932i	− 0.116499i	−0.998302	−	0.0582493i	$-0.981448\pi$
$43$	− 0.763932i	− 0.116499i	0.998302	−	0.0582493i	$-0.0185518\pi$
$44$	3.61803	0.545439
$45$	0	0
$46$	−3.85410	−0.568256
$47$	− 3.23607i	− 0.472029i	−0.971750	−	0.236015i	$-0.924159\pi$
$47$	− 3.23607i	− 0.472029i	0.971750	−	0.236015i	$-0.0758413\pi$
$48$	0.618034i	0.0892055i
$49$	5.47214	0.781734
$50$	0	0
$51$	2.76393	0.387028
$52$	− 3.85410i	− 0.534468i
$53$	− 8.47214i	− 1.16374i	−0.813283	−	0.581869i	$-0.802322\pi$
$53$	− 8.47214i	− 1.16374i	0.813283	−	0.581869i	$-0.197678\pi$
$54$	3.47214	0.472498
$55$	0	0
$56$	1.23607	0.165177
$57$	2.76393i	0.366092i
$58$	6.32624i	0.830676i
$59$	9.23607	1.20243	0.601217	−	0.799086i	$-0.294683\pi$
$59$	9.23607	1.20243	0.601217	+	0.799086i	$0.294683\pi$
$60$	0	0
$61$	8.38197	1.07320	0.536600	−	0.843836i	$-0.319708\pi$
$61$	8.38197	1.07320	0.536600	+	0.843836i	$0.319708\pi$
$62$	− 9.61803i	− 1.22149i
$63$	− 3.23607i	− 0.407706i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.23607	−0.275241
$67$	10.0902i	1.23271i	0.787468	+	0.616355i	$0.211391\pi$
$67$	10.0902i	1.23271i	−0.787468	+	0.616355i	$0.788609\pi$
$68$	4.47214i	0.542326i
$69$	2.38197	0.286755
$70$	0	0
$71$	−14.9443	−1.77356	−0.886779	−	0.462193i	$-0.847063\pi$
$71$	−14.9443	−1.77356	−0.886779	+	0.462193i	$0.847063\pi$
$72$	2.61803i	0.308538i
$73$	− 4.09017i	− 0.478718i	−0.970931	−	0.239359i	$-0.923063\pi$
$73$	− 4.09017i	− 0.478718i	0.970931	−	0.239359i	$-0.0769373\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−4.47214	−0.512989
$77$	4.47214i	0.509647i
$78$	2.38197i	0.269705i
$79$	−11.5623	−1.30086	−0.650431	−	0.759566i	$-0.725411\pi$
$79$	−11.5623	−1.30086	−0.650431	+	0.759566i	$0.725411\pi$
$80$	0	0
$81$	5.70820	0.634245
$82$	− 7.38197i	− 0.815202i
$83$	− 5.52786i	− 0.606762i	−0.952869	−	0.303381i	$-0.901885\pi$
$83$	− 5.52786i	− 0.606762i	0.952869	−	0.303381i	$-0.0981155\pi$
$84$	−0.763932	−0.0833518
$85$	0	0
$86$	−0.763932	−0.0823769
$87$	− 3.90983i	− 0.419178i
$88$	− 3.61803i	− 0.385684i
$89$	10.4721	1.11004	0.555022	−	0.831836i	$-0.312710\pi$
$89$	10.4721	1.11004	0.555022	+	0.831836i	$0.312710\pi$
$90$	0	0
$91$	4.76393	0.499396
$92$	3.85410i	0.401818i
$93$	5.94427i	0.616392i
$94$	−3.23607	−0.333775
$95$	0	0
$96$	0.618034	0.0630778
$97$	− 8.47214i	− 0.860215i	−0.902778	−	0.430108i	$-0.858476\pi$
$97$	− 8.47214i	− 0.860215i	0.902778	−	0.430108i	$-0.141524\pi$
$98$	− 5.47214i	− 0.552769i
$99$	−9.47214	−0.951985
$100$	0	0
$101$	12.4721	1.24102	0.620512	−	0.784197i	$-0.286925\pi$
$101$	12.4721	1.24102	0.620512	+	0.784197i	$0.286925\pi$
$102$	− 2.76393i	− 0.273670i
$103$	− 16.2705i	− 1.60318i	−0.597873	−	0.801590i	$-0.703987\pi$
$103$	− 16.2705i	− 1.60318i	0.597873	−	0.801590i	$-0.296013\pi$
$104$	−3.85410	−0.377926
$105$	0	0
$106$	−8.47214	−0.822887
$107$	− 8.32624i	− 0.804928i	−0.915436	−	0.402464i	$-0.868154\pi$
$107$	− 8.32624i	− 0.804928i	0.915436	−	0.402464i	$-0.131846\pi$
$108$	− 3.47214i	− 0.334106i
$109$	14.9443	1.43140	0.715701	−	0.698407i	$-0.246107\pi$
$109$	14.9443	1.43140	0.715701	+	0.698407i	$0.246107\pi$
$110$	0	0
$111$	−0.618034	−0.0586612
$112$	− 1.23607i	− 0.116797i
$113$	10.9443i	1.02955i	0.857325	+	0.514775i	$0.172125\pi$
$113$	10.9443i	1.02955i	−0.857325	+	0.514775i	$0.827875\pi$
$114$	2.76393	0.258866
$115$	0	0
$116$	6.32624	0.587376
$117$	10.0902i	0.932837i
$118$	− 9.23607i	− 0.850249i
$119$	−5.52786	−0.506738
$120$	0	0
$121$	2.09017	0.190015
$122$	− 8.38197i	− 0.758868i
$123$	4.56231i	0.411369i
$124$	−9.61803	−0.863725
$125$	0	0
$126$	−3.23607	−0.288292
$127$	− 0.472136i	− 0.0418953i	−0.999781	−	0.0209476i	$-0.993332\pi$
$127$	− 0.472136i	− 0.0418953i	0.999781	−	0.0209476i	$-0.00666833\pi$
$128$	1.00000i	0.0883883i
$129$	0.472136	0.0415693
$130$	0	0
$131$	8.65248	0.755970	0.377985	−	0.925812i	$-0.376617\pi$
$131$	8.65248	0.755970	0.377985	+	0.925812i	$0.376617\pi$
$132$	2.23607i	0.194625i
$133$	− 5.52786i	− 0.479327i
$134$	10.0902	0.871658
$135$	0	0
$136$	4.47214	0.383482
$137$	− 19.3262i	− 1.65115i	−0.564291	−	0.825576i	$-0.690850\pi$
$137$	− 19.3262i	− 1.65115i	0.564291	−	0.825576i	$-0.309150\pi$
$138$	− 2.38197i	− 0.202766i
$139$	1.85410	0.157263	0.0786314	−	0.996904i	$-0.474945\pi$
$139$	1.85410	0.157263	0.0786314	+	0.996904i	$0.474945\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	14.9443i	1.25410i
$143$	− 13.9443i	− 1.16608i
$144$	2.61803	0.218169
$145$	0	0
$146$	−4.09017	−0.338505
$147$	3.38197i	0.278940i
$148$	− 1.00000i	− 0.0821995i
$149$	6.18034	0.506313	0.253157	−	0.967425i	$-0.418531\pi$
$149$	6.18034	0.506313	0.253157	+	0.967425i	$0.418531\pi$
$150$	0	0
$151$	17.7082	1.44107	0.720537	−	0.693417i	$-0.243896\pi$
$151$	17.7082	1.44107	0.720537	+	0.693417i	$0.243896\pi$
$152$	4.47214i	0.362738i
$153$	− 11.7082i	− 0.946552i
$154$	4.47214	0.360375
$155$	0	0
$156$	2.38197	0.190710
$157$	7.52786i	0.600789i	0.953815	+	0.300394i	$0.0971183\pi$
$157$	7.52786i	0.600789i	−0.953815	+	0.300394i	$0.902882\pi$
$158$	11.5623i	0.919848i
$159$	5.23607	0.415247
$160$	0	0
$161$	−4.76393	−0.375450
$162$	− 5.70820i	− 0.448479i
$163$	− 12.4721i	− 0.976893i	−0.872594	−	0.488447i	$-0.837564\pi$
$163$	− 12.4721i	− 0.976893i	0.872594	−	0.488447i	$-0.162436\pi$
$164$	−7.38197	−0.576435
$165$	0	0
$166$	−5.52786	−0.429045
$167$	− 7.14590i	− 0.552966i	−0.961019	−	0.276483i	$-0.910831\pi$
$167$	− 7.14590i	− 0.552966i	0.961019	−	0.276483i	$-0.0891690\pi$
$168$	0.763932i	0.0589386i
$169$	−1.85410	−0.142623
$170$	0	0
$171$	11.7082	0.895349
$172$	0.763932i	0.0582493i
$173$	8.47214i	0.644125i	0.946718	+	0.322062i	$0.104376\pi$
$173$	8.47214i	0.644125i	−0.946718	+	0.322062i	$0.895624\pi$
$174$	−3.90983	−0.296403
$175$	0	0
$176$	−3.61803	−0.272720
$177$	5.70820i	0.429055i
$178$	− 10.4721i	− 0.784920i
$179$	−18.6525	−1.39415	−0.697076	−	0.716997i	$-0.745516\pi$
$179$	−18.6525	−1.39415	−0.697076	+	0.716997i	$0.745516\pi$
$180$	0	0
$181$	5.52786	0.410883	0.205441	−	0.978669i	$-0.434137\pi$
$181$	5.52786	0.410883	0.205441	+	0.978669i	$0.434137\pi$
$182$	− 4.76393i	− 0.353126i
$183$	5.18034i	0.382942i
$184$	3.85410	0.284128
$185$	0	0
$186$	5.94427	0.435855
$187$	16.1803i	1.18322i
$188$	3.23607i	0.236015i
$189$	4.29180	0.312182
$190$	0	0
$191$	4.09017	0.295954	0.147977	−	0.988991i	$-0.452724\pi$
$191$	4.09017	0.295954	0.147977	+	0.988991i	$0.452724\pi$
$192$	− 0.618034i	− 0.0446028i
$193$	4.00000i	0.287926i	0.989583	+	0.143963i	$0.0459847\pi$
$193$	4.00000i	0.287926i	−0.989583	+	0.143963i	$0.954015\pi$
$194$	−8.47214	−0.608264
$195$	0	0
$196$	−5.47214	−0.390867
$197$	16.4721i	1.17359i	0.809735	+	0.586796i	$0.199611\pi$
$197$	16.4721i	1.17359i	−0.809735	+	0.586796i	$0.800389\pi$
$198$	9.47214i	0.673155i
$199$	−20.9443	−1.48470	−0.742350	−	0.670012i	$-0.766289\pi$
$199$	−20.9443	−1.48470	−0.742350	+	0.670012i	$0.766289\pi$
$200$	0	0
$201$	−6.23607	−0.439858
$202$	− 12.4721i	− 0.877536i
$203$	7.81966i	0.548833i
$204$	−2.76393	−0.193514
$205$	0	0
$206$	−16.2705	−1.13362
$207$	− 10.0902i	− 0.701315i
$208$	3.85410i	0.267234i
$209$	−16.1803	−1.11922
$210$	0	0
$211$	−22.2705	−1.53317	−0.766583	−	0.642146i	$-0.778044\pi$
$211$	−22.2705	−1.53317	−0.766583	+	0.642146i	$0.778044\pi$
$212$	8.47214i	0.581869i
$213$	− 9.23607i	− 0.632845i
$214$	−8.32624	−0.569170
$215$	0	0
$216$	−3.47214	−0.236249
$217$	− 11.8885i	− 0.807047i
$218$	− 14.9443i	− 1.01215i
$219$	2.52786	0.170817
$220$	0	0
$221$	17.2361	1.15942
$222$	0.618034i	0.0414797i
$223$	− 8.18034i	− 0.547796i	−0.961759	−	0.273898i	$-0.911687\pi$
$223$	− 8.18034i	− 0.547796i	0.961759	−	0.273898i	$-0.0883131\pi$
$224$	−1.23607	−0.0825883
$225$	0	0
$226$	10.9443	0.728002
$227$	17.7082i	1.17533i	0.809103	+	0.587667i	$0.199954\pi$
$227$	17.7082i	1.17533i	−0.809103	+	0.587667i	$0.800046\pi$
$228$	− 2.76393i	− 0.183046i
$229$	−17.1246	−1.13163	−0.565813	−	0.824534i	$-0.691438\pi$
$229$	−17.1246	−1.13163	−0.565813	+	0.824534i	$0.691438\pi$
$230$	0	0
$231$	−2.76393	−0.181853
$232$	− 6.32624i	− 0.415338i
$233$	13.5623i	0.888496i	0.895904	+	0.444248i	$0.146529\pi$
$233$	13.5623i	0.888496i	−0.895904	+	0.444248i	$0.853471\pi$
$234$	10.0902	0.659615
$235$	0	0
$236$	−9.23607	−0.601217
$237$	− 7.14590i	− 0.464176i
$238$	5.52786i	0.358318i
$239$	−3.14590	−0.203491	−0.101746	−	0.994810i	$-0.532443\pi$
$239$	−3.14590	−0.203491	−0.101746	+	0.994810i	$0.532443\pi$
$240$	0	0
$241$	−10.4721	−0.674570	−0.337285	−	0.941403i	$-0.609509\pi$
$241$	−10.4721	−0.674570	−0.337285	+	0.941403i	$0.609509\pi$
$242$	− 2.09017i	− 0.134361i
$243$	13.9443i	0.894525i
$244$	−8.38197	−0.536600
$245$	0	0
$246$	4.56231	0.290882
$247$	17.2361i	1.09670i
$248$	9.61803i	0.610746i
$249$	3.41641	0.216506
$250$	0	0
$251$	−3.05573	−0.192876	−0.0964379	−	0.995339i	$-0.530745\pi$
$251$	−3.05573	−0.192876	−0.0964379	+	0.995339i	$0.530745\pi$
$252$	3.23607i	0.203853i
$253$	13.9443i	0.876669i
$254$	−0.472136	−0.0296244
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.9443i	1.18171i	0.806777	+	0.590856i	$0.201210\pi$
$257$	18.9443i	1.18171i	−0.806777	+	0.590856i	$0.798790\pi$
$258$	− 0.472136i	− 0.0293939i
$259$	1.23607	0.0768055
$260$	0	0
$261$	−16.5623	−1.02518
$262$	− 8.65248i	− 0.534552i
$263$	− 8.76393i	− 0.540407i	−0.962803	−	0.270204i	$-0.912909\pi$
$263$	− 8.76393i	− 0.540407i	0.962803	−	0.270204i	$-0.0870910\pi$
$264$	2.23607	0.137620
$265$	0	0
$266$	−5.52786	−0.338935
$267$	6.47214i	0.396088i
$268$	− 10.0902i	− 0.616355i
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	−4.94427	−0.300343	−0.150172	−	0.988660i	$-0.547983\pi$
$271$	−4.94427	−0.300343	−0.150172	+	0.988660i	$0.547983\pi$
$272$	− 4.47214i	− 0.271163i
$273$	2.94427i	0.178195i
$274$	−19.3262	−1.16754
$275$	0	0
$276$	−2.38197	−0.143378
$277$	7.79837i	0.468559i	0.972169	+	0.234279i	$0.0752731\pi$
$277$	7.79837i	0.468559i	−0.972169	+	0.234279i	$0.924727\pi$
$278$	− 1.85410i	− 0.111202i
$279$	25.1803	1.50751
$280$	0	0
$281$	−5.88854	−0.351281	−0.175641	−	0.984454i	$-0.556200\pi$
$281$	−5.88854	−0.351281	−0.175641	+	0.984454i	$0.556200\pi$
$282$	− 2.00000i	− 0.119098i
$283$	11.2361i	0.667915i	0.942588	+	0.333957i	$0.108384\pi$
$283$	11.2361i	0.667915i	−0.942588	+	0.333957i	$0.891616\pi$
$284$	14.9443	0.886779
$285$	0	0
$286$	−13.9443	−0.824542
$287$	− 9.12461i	− 0.538609i
$288$	− 2.61803i	− 0.154269i
$289$	−3.00000	−0.176471
$290$	0	0
$291$	5.23607	0.306944
$292$	4.09017i	0.239359i
$293$	18.6525i	1.08969i	0.838537	+	0.544845i	$0.183411\pi$
$293$	18.6525i	1.08969i	−0.838537	+	0.544845i	$0.816589\pi$
$294$	3.38197	0.197240
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	− 12.5623i	− 0.728939i
$298$	− 6.18034i	− 0.358017i
$299$	14.8541	0.859035
$300$	0	0
$301$	−0.944272	−0.0544269
$302$	− 17.7082i	− 1.01899i
$303$	7.70820i	0.442825i
$304$	4.47214	0.256495
$305$	0	0
$306$	−11.7082	−0.669313
$307$	6.14590i	0.350765i	0.984500	+	0.175382i	$0.0561162\pi$
$307$	6.14590i	0.350765i	−0.984500	+	0.175382i	$0.943884\pi$
$308$	− 4.47214i	− 0.254824i
$309$	10.0557	0.572050
$310$	0	0
$311$	2.03444	0.115363	0.0576813	−	0.998335i	$-0.481629\pi$
$311$	2.03444	0.115363	0.0576813	+	0.998335i	$0.481629\pi$
$312$	− 2.38197i	− 0.134852i
$313$	5.81966i	0.328947i	0.986382	+	0.164473i	$0.0525924\pi$
$313$	5.81966i	0.328947i	−0.986382	+	0.164473i	$0.947408\pi$
$314$	7.52786	0.424822
$315$	0	0
$316$	11.5623	0.650431
$317$	− 3.05573i	− 0.171627i	−0.996311	−	0.0858134i	$-0.972651\pi$
$317$	− 3.05573i	− 0.171627i	0.996311	−	0.0858134i	$-0.0273489\pi$
$318$	− 5.23607i	− 0.293624i
$319$	22.8885	1.28151
$320$	0	0
$321$	5.14590	0.287216
$322$	4.76393i	0.265484i
$323$	− 20.0000i	− 1.11283i
$324$	−5.70820	−0.317122
$325$	0	0
$326$	−12.4721	−0.690768
$327$	9.23607i	0.510756i
$328$	7.38197i	0.407601i
$329$	−4.00000	−0.220527
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	5.52786i	0.303381i
$333$	2.61803i	0.143467i
$334$	−7.14590	−0.391006
$335$	0	0
$336$	0.763932	0.0416759
$337$	17.0344i	0.927925i	0.885855	+	0.463963i	$0.153573\pi$
$337$	17.0344i	0.927925i	−0.885855	+	0.463963i	$0.846427\pi$
$338$	1.85410i	0.100850i
$339$	−6.76393	−0.367366
$340$	0	0
$341$	−34.7984	−1.88444
$342$	− 11.7082i	− 0.633107i
$343$	− 15.4164i	− 0.832408i
$344$	0.763932	0.0411885
$345$	0	0
$346$	8.47214	0.455465
$347$	− 12.7639i	− 0.685204i	−0.939481	−	0.342602i	$-0.888692\pi$
$347$	− 12.7639i	− 0.685204i	0.939481	−	0.342602i	$-0.111308\pi$
$348$	3.90983i	0.209589i
$349$	−12.1803	−0.651999	−0.325999	−	0.945370i	$-0.605701\pi$
$349$	−12.1803	−0.651999	−0.325999	+	0.945370i	$0.605701\pi$
$350$	0	0
$351$	−13.3820	−0.714277
$352$	3.61803i	0.192842i
$353$	29.7082i	1.58121i	0.612328	+	0.790604i	$0.290233\pi$
$353$	29.7082i	1.58121i	−0.612328	+	0.790604i	$0.709767\pi$
$354$	5.70820	0.303388
$355$	0	0
$356$	−10.4721	−0.555022
$357$	− 3.41641i	− 0.180815i
$358$	18.6525i	0.985814i
$359$	−4.47214	−0.236030	−0.118015	−	0.993012i	$-0.537653\pi$
$359$	−4.47214	−0.236030	−0.118015	+	0.993012i	$0.537653\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 5.52786i	− 0.290538i
$363$	1.29180i	0.0678017i
$364$	−4.76393	−0.249698
$365$	0	0
$366$	5.18034	0.270781
$367$	27.1246i	1.41589i	0.706266	+	0.707947i	$0.250378\pi$
$367$	27.1246i	1.41589i	−0.706266	+	0.707947i	$0.749622\pi$
$368$	− 3.85410i	− 0.200909i
$369$	19.3262	1.00608
$370$	0	0
$371$	−10.4721	−0.543686
$372$	− 5.94427i	− 0.308196i
$373$	14.2918i	0.740001i	0.929032	+	0.370001i	$0.120643\pi$
$373$	14.2918i	0.740001i	−0.929032	+	0.370001i	$0.879357\pi$
$374$	16.1803	0.836665
$375$	0	0
$376$	3.23607	0.166887
$377$	− 24.3820i	− 1.25574i
$378$	− 4.29180i	− 0.220746i
$379$	−16.9098	−0.868600	−0.434300	−	0.900768i	$-0.643004\pi$
$379$	−16.9098	−0.868600	−0.434300	+	0.900768i	$0.643004\pi$
$380$	0	0
$381$	0.291796	0.0149492
$382$	− 4.09017i	− 0.209271i
$383$	− 17.8885i	− 0.914062i	−0.889451	−	0.457031i	$-0.848913\pi$
$383$	− 17.8885i	− 0.914062i	0.889451	−	0.457031i	$-0.151087\pi$
$384$	−0.618034	−0.0315389
$385$	0	0
$386$	4.00000	0.203595
$387$	− 2.00000i	− 0.101666i
$388$	8.47214i	0.430108i
$389$	0.145898	0.00739732	0.00369866	−	0.999993i	$-0.498823\pi$
$389$	0.145898	0.00739732	0.00369866	+	0.999993i	$0.498823\pi$
$390$	0	0
$391$	−17.2361	−0.871665
$392$	5.47214i	0.276385i
$393$	5.34752i	0.269747i
$394$	16.4721	0.829854
$395$	0	0
$396$	9.47214	0.475993
$397$	10.6525i	0.534632i	0.963609	+	0.267316i	$0.0861368\pi$
$397$	10.6525i	0.534632i	−0.963609	+	0.267316i	$0.913863\pi$
$398$	20.9443i	1.04984i
$399$	3.41641	0.171034
$400$	0	0
$401$	−9.23607	−0.461227	−0.230614	−	0.973045i	$-0.574073\pi$
$401$	−9.23607	−0.461227	−0.230614	+	0.973045i	$0.574073\pi$
$402$	6.23607i	0.311027i
$403$	37.0689i	1.84653i
$404$	−12.4721	−0.620512
$405$	0	0
$406$	7.81966	0.388083
$407$	− 3.61803i	− 0.179339i
$408$	2.76393i	0.136835i
$409$	3.81966	0.188870	0.0944350	−	0.995531i	$-0.469896\pi$
$409$	3.81966	0.188870	0.0944350	+	0.995531i	$0.469896\pi$
$410$	0	0
$411$	11.9443	0.589167
$412$	16.2705i	0.801590i
$413$	− 11.4164i	− 0.561765i
$414$	−10.0902	−0.495905
$415$	0	0
$416$	3.85410	0.188963
$417$	1.14590i	0.0561149i
$418$	16.1803i	0.791406i
$419$	−9.56231	−0.467149	−0.233575	−	0.972339i	$-0.575042\pi$
$419$	−9.56231	−0.467149	−0.233575	+	0.972339i	$0.575042\pi$
$420$	0	0
$421$	−1.96556	−0.0957954	−0.0478977	−	0.998852i	$-0.515252\pi$
$421$	−1.96556	−0.0957954	−0.0478977	+	0.998852i	$0.515252\pi$
$422$	22.2705i	1.08411i
$423$	− 8.47214i	− 0.411929i
$424$	8.47214	0.411443
$425$	0	0
$426$	−9.23607	−0.447489
$427$	− 10.3607i	− 0.501388i
$428$	8.32624i	0.402464i
$429$	8.61803	0.416083
$430$	0	0
$431$	−32.3607	−1.55876	−0.779380	−	0.626552i	$-0.784466\pi$
$431$	−32.3607	−1.55876	−0.779380	+	0.626552i	$0.784466\pi$
$432$	3.47214i	0.167053i
$433$	− 36.3262i	− 1.74573i	−0.487964	−	0.872864i	$-0.662260\pi$
$433$	− 36.3262i	− 1.74573i	0.487964	−	0.872864i	$-0.337740\pi$
$434$	−11.8885	−0.570668
$435$	0	0
$436$	−14.9443	−0.715701
$437$	− 17.2361i	− 0.824513i
$438$	− 2.52786i	− 0.120786i
$439$	16.7984	0.801743	0.400871	−	0.916134i	$-0.368707\pi$
$439$	16.7984	0.801743	0.400871	+	0.916134i	$0.368707\pi$
$440$	0	0
$441$	14.3262	0.682202
$442$	− 17.2361i	− 0.819836i
$443$	− 18.2705i	− 0.868058i	−0.900899	−	0.434029i	$-0.857092\pi$
$443$	− 18.2705i	− 0.868058i	0.900899	−	0.434029i	$-0.142908\pi$
$444$	0.618034	0.0293306
$445$	0	0
$446$	−8.18034	−0.387350
$447$	3.81966i	0.180664i
$448$	1.23607i	0.0583987i
$449$	19.5279	0.921577	0.460788	−	0.887510i	$-0.347567\pi$
$449$	19.5279	0.921577	0.460788	+	0.887510i	$0.347567\pi$
$450$	0	0
$451$	−26.7082	−1.25764
$452$	− 10.9443i	− 0.514775i
$453$	10.9443i	0.514207i
$454$	17.7082	0.831087
$455$	0	0
$456$	−2.76393	−0.129433
$457$	29.2361i	1.36761i	0.729667	+	0.683803i	$0.239675\pi$
$457$	29.2361i	1.36761i	−0.729667	+	0.683803i	$0.760325\pi$
$458$	17.1246i	0.800181i
$459$	15.5279	0.724779
$460$	0	0
$461$	−21.0557	−0.980663	−0.490332	−	0.871536i	$-0.663124\pi$
$461$	−21.0557	−0.980663	−0.490332	+	0.871536i	$0.663124\pi$
$462$	2.76393i	0.128590i
$463$	15.5623i	0.723242i	0.932325	+	0.361621i	$0.117777\pi$
$463$	15.5623i	0.723242i	−0.932325	+	0.361621i	$0.882223\pi$
$464$	−6.32624	−0.293688
$465$	0	0
$466$	13.5623	0.628262
$467$	− 20.3607i	− 0.942180i	−0.882085	−	0.471090i	$-0.843861\pi$
$467$	− 20.3607i	− 0.942180i	0.882085	−	0.471090i	$-0.156139\pi$
$468$	− 10.0902i	− 0.466418i
$469$	12.4721	0.575910
$470$	0	0
$471$	−4.65248	−0.214375
$472$	9.23607i	0.425124i
$473$	2.76393i	0.127086i
$474$	−7.14590	−0.328222
$475$	0	0
$476$	5.52786	0.253369
$477$	− 22.1803i	− 1.01557i
$478$	3.14590i	0.143890i
$479$	−16.4377	−0.751057	−0.375529	−	0.926811i	$-0.622539\pi$
$479$	−16.4377	−0.751057	−0.375529	+	0.926811i	$0.622539\pi$
$480$	0	0
$481$	−3.85410	−0.175732
$482$	10.4721i	0.476993i
$483$	− 2.94427i	− 0.133969i
$484$	−2.09017	−0.0950077
$485$	0	0
$486$	13.9443	0.632525
$487$	25.3050i	1.14668i	0.819319	+	0.573338i	$0.194352\pi$
$487$	25.3050i	1.14668i	−0.819319	+	0.573338i	$0.805648\pi$
$488$	8.38197i	0.379434i
$489$	7.70820	0.348577
$490$	0	0
$491$	27.4508	1.23884	0.619420	−	0.785060i	$-0.287368\pi$
$491$	27.4508	1.23884	0.619420	+	0.785060i	$0.287368\pi$
$492$	− 4.56231i	− 0.205685i
$493$	28.2918i	1.27420i
$494$	17.2361	0.775487
$495$	0	0
$496$	9.61803	0.431862
$497$	18.4721i	0.828589i
$498$	− 3.41641i	− 0.153093i
$499$	−23.7082	−1.06132	−0.530662	−	0.847583i	$-0.678057\pi$
$499$	−23.7082	−1.06132	−0.530662	+	0.847583i	$0.678057\pi$
$500$	0	0
$501$	4.41641	0.197311
$502$	3.05573i	0.136384i
$503$	7.90983i	0.352682i	0.984329	+	0.176341i	$0.0564261\pi$
$503$	7.90983i	0.352682i	−0.984329	+	0.176341i	$0.943574\pi$
$504$	3.23607	0.144146
$505$	0	0
$506$	13.9443	0.619898
$507$	− 1.14590i	− 0.0508911i
$508$	0.472136i	0.0209476i
$509$	4.29180	0.190231	0.0951153	−	0.995466i	$-0.469678\pi$
$509$	4.29180	0.190231	0.0951153	+	0.995466i	$0.469678\pi$
$510$	0	0
$511$	−5.05573	−0.223652
$512$	− 1.00000i	− 0.0441942i
$513$	15.5279i	0.685572i
$514$	18.9443	0.835596
$515$	0	0
$516$	−0.472136	−0.0207846
$517$	11.7082i	0.514926i
$518$	− 1.23607i	− 0.0543097i
$519$	−5.23607	−0.229838
$520$	0	0
$521$	25.4164	1.11351	0.556757	−	0.830676i	$-0.312046\pi$
$521$	25.4164	1.11351	0.556757	+	0.830676i	$0.312046\pi$
$522$	16.5623i	0.724912i
$523$	34.1803i	1.49460i	0.664486	+	0.747301i	$0.268651\pi$
$523$	34.1803i	1.49460i	−0.664486	+	0.747301i	$0.731349\pi$
$524$	−8.65248	−0.377985
$525$	0	0
$526$	−8.76393	−0.382126
$527$	− 43.0132i	− 1.87368i
$528$	− 2.23607i	− 0.0973124i
$529$	8.14590	0.354169
$530$	0	0
$531$	24.1803	1.04934
$532$	5.52786i	0.239663i
$533$	28.4508i	1.23234i
$534$	6.47214	0.280077
$535$	0	0
$536$	−10.0902	−0.435829
$537$	− 11.5279i	− 0.497464i
$538$	4.00000i	0.172452i
$539$	−19.7984	−0.852776
$540$	0	0
$541$	5.32624	0.228993	0.114496	−	0.993424i	$-0.463475\pi$
$541$	5.32624	0.228993	0.114496	+	0.993424i	$0.463475\pi$
$542$	4.94427i	0.212375i
$543$	3.41641i	0.146612i
$544$	−4.47214	−0.191741
$545$	0	0
$546$	2.94427	0.126003
$547$	− 42.0689i	− 1.79874i	−0.437193	−	0.899368i	$-0.644027\pi$
$547$	− 42.0689i	− 1.79874i	0.437193	−	0.899368i	$-0.355973\pi$
$548$	19.3262i	0.825576i
$549$	21.9443	0.936559
$550$	0	0
$551$	−28.2918	−1.20527
$552$	2.38197i	0.101383i
$553$	14.2918i	0.607749i
$554$	7.79837	0.331321
$555$	0	0
$556$	−1.85410	−0.0786314
$557$	0.562306i	0.0238257i	0.999929	+	0.0119128i	$0.00379206\pi$
$557$	0.562306i	0.0238257i	−0.999929	+	0.0119128i	$0.996208\pi$
$558$	− 25.1803i	− 1.06597i
$559$	2.94427	0.124529
$560$	0	0
$561$	−10.0000	−0.422200
$562$	5.88854i	0.248393i
$563$	− 27.8885i	− 1.17536i	−0.809093	−	0.587681i	$-0.800041\pi$
$563$	− 27.8885i	− 1.17536i	0.809093	−	0.587681i	$-0.199959\pi$
$564$	−2.00000	−0.0842152
$565$	0	0
$566$	11.2361	0.472287
$567$	− 7.05573i	− 0.296313i
$568$	− 14.9443i	− 0.627048i
$569$	21.8885	0.917615	0.458808	−	0.888536i	$-0.348277\pi$
$569$	21.8885	0.917615	0.458808	+	0.888536i	$0.348277\pi$
$570$	0	0
$571$	9.56231	0.400170	0.200085	−	0.979779i	$-0.435878\pi$
$571$	9.56231	0.400170	0.200085	+	0.979779i	$0.435878\pi$
$572$	13.9443i	0.583039i
$573$	2.52786i	0.105603i
$574$	−9.12461	−0.380854
$575$	0	0
$576$	−2.61803	−0.109085
$577$	20.6525i	0.859774i	0.902883	+	0.429887i	$0.141447\pi$
$577$	20.6525i	0.859774i	−0.902883	+	0.429887i	$0.858553\pi$
$578$	3.00000i	0.124784i
$579$	−2.47214	−0.102738
$580$	0	0
$581$	−6.83282	−0.283473
$582$	− 5.23607i	− 0.217042i
$583$	30.6525i	1.26950i
$584$	4.09017	0.169252
$585$	0	0
$586$	18.6525	0.770527
$587$	30.9443i	1.27721i	0.769536	+	0.638603i	$0.220488\pi$
$587$	30.9443i	1.27721i	−0.769536	+	0.638603i	$0.779512\pi$
$588$	− 3.38197i	− 0.139470i
$589$	43.0132	1.77233
$590$	0	0
$591$	−10.1803	−0.418763
$592$	1.00000i	0.0410997i
$593$	− 2.56231i	− 0.105221i	−0.998615	−	0.0526106i	$-0.983246\pi$
$593$	− 2.56231i	− 0.105221i	0.998615	−	0.0526106i	$-0.0167542\pi$
$594$	−12.5623	−0.515438
$595$	0	0
$596$	−6.18034	−0.253157
$597$	− 12.9443i	− 0.529774i
$598$	− 14.8541i	− 0.607429i
$599$	−38.3607	−1.56737	−0.783687	−	0.621155i	$-0.786664\pi$
$599$	−38.3607	−1.56737	−0.783687	+	0.621155i	$0.786664\pi$
$600$	0	0
$601$	35.6869	1.45570	0.727850	−	0.685737i	$-0.240520\pi$
$601$	35.6869	1.45570	0.727850	+	0.685737i	$0.240520\pi$
$602$	0.944272i	0.0384856i
$603$	26.4164i	1.07576i
$604$	−17.7082	−0.720537
$605$	0	0
$606$	7.70820	0.313124
$607$	− 5.96556i	− 0.242135i	−0.992644	−	0.121067i	$-0.961368\pi$
$607$	− 5.96556i	− 0.242135i	0.992644	−	0.121067i	$-0.0386317\pi$
$608$	− 4.47214i	− 0.181369i
$609$	−4.83282	−0.195836
$610$	0	0
$611$	12.4721	0.504569
$612$	11.7082i	0.473276i
$613$	− 36.1803i	− 1.46131i	−0.682747	−	0.730655i	$-0.739215\pi$
$613$	− 36.1803i	− 1.46131i	0.682747	−	0.730655i	$-0.260785\pi$
$614$	6.14590	0.248028
$615$	0	0
$616$	−4.47214	−0.180187
$617$	11.0902i	0.446473i	0.974764	+	0.223237i	$0.0716623\pi$
$617$	11.0902i	0.446473i	−0.974764	+	0.223237i	$0.928338\pi$
$618$	− 10.0557i	− 0.404501i
$619$	−18.2705	−0.734354	−0.367177	−	0.930151i	$-0.619676\pi$
$619$	−18.2705	−0.734354	−0.367177	+	0.930151i	$0.619676\pi$
$620$	0	0
$621$	13.3820	0.537000
$622$	− 2.03444i	− 0.0815737i
$623$	− 12.9443i	− 0.518601i
$624$	−2.38197	−0.0953550
$625$	0	0
$626$	5.81966	0.232600
$627$	− 10.0000i	− 0.399362i
$628$	− 7.52786i	− 0.300394i
$629$	4.47214	0.178316
$630$	0	0
$631$	26.3951	1.05077	0.525387	−	0.850864i	$-0.323921\pi$
$631$	26.3951	1.05077	0.525387	+	0.850864i	$0.323921\pi$
$632$	− 11.5623i	− 0.459924i
$633$	− 13.7639i	− 0.547067i
$634$	−3.05573	−0.121358
$635$	0	0
$636$	−5.23607	−0.207624
$637$	21.0902i	0.835623i
$638$	− 22.8885i	− 0.906166i
$639$	−39.1246	−1.54775
$640$	0	0
$641$	−22.5066	−0.888956	−0.444478	−	0.895790i	$-0.646611\pi$
$641$	−22.5066	−0.888956	−0.444478	+	0.895790i	$0.646611\pi$
$642$	− 5.14590i	− 0.203092i
$643$	− 33.2361i	− 1.31070i	−0.755324	−	0.655351i	$-0.772521\pi$
$643$	− 33.2361i	− 1.31070i	0.755324	−	0.655351i	$-0.227479\pi$
$644$	4.76393	0.187725
$645$	0	0
$646$	−20.0000	−0.786889
$647$	− 18.9098i	− 0.743422i	−0.928348	−	0.371711i	$-0.878771\pi$
$647$	− 18.9098i	− 0.743422i	0.928348	−	0.371711i	$-0.121229\pi$
$648$	5.70820i	0.224239i
$649$	−33.4164	−1.31171
$650$	0	0
$651$	7.34752	0.287972
$652$	12.4721i	0.488447i
$653$	− 4.72949i	− 0.185079i	−0.995709	−	0.0925396i	$-0.970502\pi$
$653$	− 4.72949i	− 0.185079i	0.995709	−	0.0925396i	$-0.0294985\pi$
$654$	9.23607	0.361159
$655$	0	0
$656$	7.38197	0.288217
$657$	− 10.7082i	− 0.417767i
$658$	4.00000i	0.155936i
$659$	15.4508	0.601880	0.300940	−	0.953643i	$-0.402700\pi$
$659$	15.4508	0.601880	0.300940	+	0.953643i	$0.402700\pi$
$660$	0	0
$661$	1.67376	0.0651018	0.0325509	−	0.999470i	$-0.489637\pi$
$661$	1.67376	0.0651018	0.0325509	+	0.999470i	$0.489637\pi$
$662$	− 28.0000i	− 1.08825i
$663$	10.6525i	0.413708i
$664$	5.52786	0.214523
$665$	0	0
$666$	2.61803	0.101447
$667$	24.3820i	0.944073i
$668$	7.14590i	0.276483i
$669$	5.05573	0.195466
$670$	0	0
$671$	−30.3262	−1.17073
$672$	− 0.763932i	− 0.0294693i
$673$	17.8541i	0.688225i	0.938928	+	0.344113i	$0.111820\pi$
$673$	17.8541i	0.688225i	−0.938928	+	0.344113i	$0.888180\pi$
$674$	17.0344	0.656142
$675$	0	0
$676$	1.85410	0.0713116
$677$	− 3.34752i	− 0.128656i	−0.997929	−	0.0643279i	$-0.979510\pi$
$677$	− 3.34752i	− 0.128656i	0.997929	−	0.0643279i	$-0.0204904\pi$
$678$	6.76393i	0.259767i
$679$	−10.4721	−0.401884
$680$	0	0
$681$	−10.9443	−0.419385
$682$	34.7984i	1.33250i
$683$	− 35.4164i	− 1.35517i	−0.735444	−	0.677586i	$-0.763026\pi$
$683$	− 35.4164i	− 1.35517i	0.735444	−	0.677586i	$-0.236974\pi$
$684$	−11.7082	−0.447674
$685$	0	0
$686$	−15.4164	−0.588601
$687$	− 10.5836i	− 0.403789i
$688$	− 0.763932i	− 0.0291246i
$689$	32.6525	1.24396
$690$	0	0
$691$	−35.7771	−1.36102	−0.680512	−	0.732737i	$-0.738243\pi$
$691$	−35.7771	−1.36102	−0.680512	+	0.732737i	$0.738243\pi$
$692$	− 8.47214i	− 0.322062i
$693$	11.7082i	0.444758i
$694$	−12.7639	−0.484512
$695$	0	0
$696$	3.90983	0.148202
$697$	− 33.0132i	− 1.25046i
$698$	12.1803i	0.461033i
$699$	−8.38197	−0.317035
$700$	0	0
$701$	3.97871	0.150274	0.0751370	−	0.997173i	$-0.476061\pi$
$701$	3.97871	0.150274	0.0751370	+	0.997173i	$0.476061\pi$
$702$	13.3820i	0.505070i
$703$	4.47214i	0.168670i
$704$	3.61803	0.136360
$705$	0	0
$706$	29.7082	1.11808
$707$	− 15.4164i	− 0.579794i
$708$	− 5.70820i	− 0.214527i
$709$	−43.2148	−1.62297	−0.811483	−	0.584377i	$-0.801339\pi$
$709$	−43.2148	−1.62297	−0.811483	+	0.584377i	$0.801339\pi$
$710$	0	0
$711$	−30.2705	−1.13523
$712$	10.4721i	0.392460i
$713$	− 37.0689i	− 1.38824i
$714$	−3.41641	−0.127856
$715$	0	0
$716$	18.6525	0.697076
$717$	− 1.94427i	− 0.0726102i
$718$	4.47214i	0.166899i
$719$	−0.583592	−0.0217643	−0.0108822	−	0.999941i	$-0.503464\pi$
$719$	−0.583592	−0.0217643	−0.0108822	+	0.999941i	$0.503464\pi$
$720$	0	0
$721$	−20.1115	−0.748990
$722$	− 1.00000i	− 0.0372161i
$723$	− 6.47214i	− 0.240701i
$724$	−5.52786	−0.205441
$725$	0	0
$726$	1.29180	0.0479430
$727$	23.1459i	0.858434i	0.903201	+	0.429217i	$0.141210\pi$
$727$	23.1459i	0.858434i	−0.903201	+	0.429217i	$0.858790\pi$
$728$	4.76393i	0.176563i
$729$	8.50658	0.315058
$730$	0	0
$731$	−3.41641	−0.126360
$732$	− 5.18034i	− 0.191471i
$733$	36.4721i	1.34713i	0.739128	+	0.673565i	$0.235238\pi$
$733$	36.4721i	1.34713i	−0.739128	+	0.673565i	$0.764762\pi$
$734$	27.1246	1.00119
$735$	0	0
$736$	−3.85410	−0.142064
$737$	− 36.5066i	− 1.34474i
$738$	− 19.3262i	− 0.711409i
$739$	22.0902	0.812600	0.406300	−	0.913740i	$-0.366819\pi$
$739$	22.0902	0.812600	0.406300	+	0.913740i	$0.366819\pi$
$740$	0	0
$741$	−10.6525	−0.391328
$742$	10.4721i	0.384444i
$743$	10.0689i	0.369392i	0.982796	+	0.184696i	$0.0591300\pi$
$743$	10.0689i	0.369392i	−0.982796	+	0.184696i	$0.940870\pi$
$744$	−5.94427	−0.217928
$745$	0	0
$746$	14.2918	0.523260
$747$	− 14.4721i	− 0.529508i
$748$	− 16.1803i	− 0.591612i
$749$	−10.2918	−0.376054
$750$	0	0
$751$	−18.9443	−0.691286	−0.345643	−	0.938366i	$-0.612339\pi$
$751$	−18.9443	−0.691286	−0.345643	+	0.938366i	$0.612339\pi$
$752$	− 3.23607i	− 0.118007i
$753$	− 1.88854i	− 0.0688224i
$754$	−24.3820	−0.887939
$755$	0	0
$756$	−4.29180	−0.156091
$757$	10.8541i	0.394499i	0.980353	+	0.197250i	$0.0632009\pi$
$757$	10.8541i	0.394499i	−0.980353	+	0.197250i	$0.936799\pi$
$758$	16.9098i	0.614193i
$759$	−8.61803	−0.312815
$760$	0	0
$761$	−25.8541	−0.937210	−0.468605	−	0.883408i	$-0.655243\pi$
$761$	−25.8541	−0.937210	−0.468605	+	0.883408i	$0.655243\pi$
$762$	− 0.291796i	− 0.0105707i
$763$	− 18.4721i	− 0.668736i
$764$	−4.09017	−0.147977
$765$	0	0
$766$	−17.8885	−0.646339
$767$	35.5967i	1.28532i
$768$	0.618034i	0.0223014i
$769$	11.8885	0.428712	0.214356	−	0.976756i	$-0.431235\pi$
$769$	11.8885	0.428712	0.214356	+	0.976756i	$0.431235\pi$
$770$	0	0
$771$	−11.7082	−0.421661
$772$	− 4.00000i	− 0.143963i
$773$	− 24.0000i	− 0.863220i	−0.902060	−	0.431610i	$-0.857946\pi$
$773$	− 24.0000i	− 0.863220i	0.902060	−	0.431610i	$-0.142054\pi$
$774$	−2.00000	−0.0718885
$775$	0	0
$776$	8.47214	0.304132
$777$	0.763932i	0.0274059i
$778$	− 0.145898i	− 0.00523070i
$779$	33.0132	1.18282
$780$	0	0
$781$	54.0689	1.93474
$782$	17.2361i	0.616361i
$783$	− 21.9656i	− 0.784985i
$784$	5.47214	0.195433
$785$	0	0
$786$	5.34752	0.190740
$787$	34.4721i	1.22880i	0.788995	+	0.614399i	$0.210602\pi$
$787$	34.4721i	1.22880i	−0.788995	+	0.614399i	$0.789398\pi$
$788$	− 16.4721i	− 0.586796i
$789$	5.41641	0.192829
$790$	0	0
$791$	13.5279	0.480995
$792$	− 9.47214i	− 0.336578i
$793$	32.3050i	1.14718i
$794$	10.6525	0.378042
$795$	0	0
$796$	20.9443	0.742350
$797$	− 12.7295i	− 0.450902i	−0.974255	−	0.225451i	$-0.927614\pi$
$797$	− 12.7295i	− 0.450902i	0.974255	−	0.225451i	$-0.0723855\pi$
$798$	− 3.41641i	− 0.120940i
$799$	−14.4721	−0.511987
$800$	0	0
$801$	27.4164	0.968711
$802$	9.23607i	0.326137i
$803$	14.7984i	0.522223i
$804$	6.23607	0.219929
$805$	0	0
$806$	37.0689	1.30570
$807$	− 2.47214i	− 0.0870233i
$808$	12.4721i	0.438768i
$809$	−27.1246	−0.953651	−0.476825	−	0.878998i	$-0.658213\pi$
$809$	−27.1246	−0.953651	−0.476825	+	0.878998i	$0.658213\pi$
$810$	0	0
$811$	53.1033	1.86471	0.932355	−	0.361544i	$-0.117750\pi$
$811$	53.1033	1.86471	0.932355	+	0.361544i	$0.117750\pi$
$812$	− 7.81966i	− 0.274416i
$813$	− 3.05573i	− 0.107169i
$814$	−3.61803	−0.126812
$815$	0	0
$816$	2.76393	0.0967570
$817$	− 3.41641i	− 0.119525i
$818$	− 3.81966i	− 0.133551i
$819$	12.4721	0.435812
$820$	0	0
$821$	21.4164	0.747438	0.373719	−	0.927542i	$-0.378082\pi$
$821$	21.4164	0.747438	0.373719	+	0.927542i	$0.378082\pi$
$822$	− 11.9443i	− 0.416604i
$823$	− 33.8885i	− 1.18128i	−0.806935	−	0.590640i	$-0.798875\pi$
$823$	− 33.8885i	− 1.18128i	0.806935	−	0.590640i	$-0.201125\pi$
$824$	16.2705	0.566810
$825$	0	0
$826$	−11.4164	−0.397228
$827$	− 56.0689i	− 1.94971i	−0.222849	−	0.974853i	$-0.571536\pi$
$827$	− 56.0689i	− 1.94971i	0.222849	−	0.974853i	$-0.428464\pi$
$828$	10.0902i	0.350658i
$829$	−31.2016	−1.08368	−0.541839	−	0.840483i	$-0.682272\pi$
$829$	−31.2016	−1.08368	−0.541839	+	0.840483i	$0.682272\pi$
$830$	0	0
$831$	−4.81966	−0.167192
$832$	− 3.85410i	− 0.133617i
$833$	− 24.4721i	− 0.847909i
$834$	1.14590	0.0396792
$835$	0	0
$836$	16.1803	0.559609
$837$	33.3951i	1.15430i
$838$	9.56231i	0.330324i
$839$	5.34752	0.184617	0.0923085	−	0.995730i	$-0.470575\pi$
$839$	5.34752	0.184617	0.0923085	+	0.995730i	$0.470575\pi$
$840$	0	0
$841$	11.0213	0.380044
$842$	1.96556i	0.0677376i
$843$	− 3.63932i	− 0.125345i
$844$	22.2705	0.766583
$845$	0	0
$846$	−8.47214	−0.291278
$847$	− 2.58359i	− 0.0887733i
$848$	− 8.47214i	− 0.290934i
$849$	−6.94427	−0.238327
$850$	0	0
$851$	3.85410	0.132117
$852$	9.23607i	0.316422i
$853$	− 12.7426i	− 0.436300i	−0.975915	−	0.218150i	$-0.929998\pi$
$853$	− 12.7426i	− 0.436300i	0.975915	−	0.218150i	$-0.0700022\pi$
$854$	−10.3607	−0.354535
$855$	0	0
$856$	8.32624	0.284585
$857$	26.9443i	0.920399i	0.887816	+	0.460199i	$0.152222\pi$
$857$	26.9443i	0.920399i	−0.887816	+	0.460199i	$0.847778\pi$
$858$	− 8.61803i	− 0.294215i
$859$	−26.5836	−0.907020	−0.453510	−	0.891251i	$-0.649828\pi$
$859$	−26.5836	−0.907020	−0.453510	+	0.891251i	$0.649828\pi$
$860$	0	0
$861$	5.63932	0.192188
$862$	32.3607i	1.10221i
$863$	− 7.41641i	− 0.252457i	−0.992001	−	0.126229i	$-0.959713\pi$
$863$	− 7.41641i	− 0.252457i	0.992001	−	0.126229i	$-0.0402873\pi$
$864$	3.47214	0.118124
$865$	0	0
$866$	−36.3262	−1.23442
$867$	− 1.85410i	− 0.0629686i
$868$	11.8885i	0.403523i
$869$	41.8328	1.41908
$870$	0	0
$871$	−38.8885	−1.31769
$872$	14.9443i	0.506077i
$873$	− 22.1803i	− 0.750691i
$874$	−17.2361	−0.583019
$875$	0	0
$876$	−2.52786	−0.0854086
$877$	− 36.8328i	− 1.24376i	−0.783114	−	0.621878i	$-0.786370\pi$
$877$	− 36.8328i	− 1.24376i	0.783114	−	0.621878i	$-0.213630\pi$
$878$	− 16.7984i	− 0.566918i
$879$	−11.5279	−0.388825
$880$	0	0
$881$	−22.7426	−0.766219	−0.383110	−	0.923703i	$-0.625147\pi$
$881$	−22.7426	−0.766219	−0.383110	+	0.923703i	$0.625147\pi$
$882$	− 14.3262i	− 0.482390i
$883$	29.3050i	0.986190i	0.869975	+	0.493095i	$0.164135\pi$
$883$	29.3050i	0.986190i	−0.869975	+	0.493095i	$0.835865\pi$
$884$	−17.2361	−0.579712
$885$	0	0
$886$	−18.2705	−0.613810
$887$	7.88854i	0.264871i	0.991192	+	0.132436i	$0.0422798\pi$
$887$	7.88854i	0.264871i	−0.991192	+	0.132436i	$0.957720\pi$
$888$	− 0.618034i	− 0.0207399i
$889$	−0.583592	−0.0195731
$890$	0	0
$891$	−20.6525	−0.691884
$892$	8.18034i	0.273898i
$893$	− 14.4721i	− 0.484292i
$894$	3.81966	0.127749
$895$	0	0
$896$	1.23607	0.0412941
$897$	9.18034i	0.306523i
$898$	− 19.5279i	− 0.651653i
$899$	−60.8460	−2.02933
$900$	0	0
$901$	−37.8885	−1.26225
$902$	26.7082i	0.889286i
$903$	− 0.583592i	− 0.0194207i
$904$	−10.9443	−0.364001
$905$	0	0
$906$	10.9443	0.363599
$907$	20.1115i	0.667790i	0.942610	+	0.333895i	$0.108363\pi$
$907$	20.1115i	0.667790i	−0.942610	+	0.333895i	$0.891637\pi$
$908$	− 17.7082i	− 0.587667i
$909$	32.6525	1.08301
$910$	0	0
$911$	−21.8885	−0.725200	−0.362600	−	0.931945i	$-0.618111\pi$
$911$	−21.8885	−0.725200	−0.362600	+	0.931945i	$0.618111\pi$
$912$	2.76393i	0.0915229i
$913$	20.0000i	0.661903i
$914$	29.2361	0.967043
$915$	0	0
$916$	17.1246	0.565813
$917$	− 10.6950i	− 0.353182i
$918$	− 15.5279i	− 0.512496i
$919$	−29.8885	−0.985932	−0.492966	−	0.870049i	$-0.664087\pi$
$919$	−29.8885	−0.985932	−0.492966	+	0.870049i	$0.664087\pi$
$920$	0	0
$921$	−3.79837	−0.125161
$922$	21.0557i	0.693433i
$923$	− 57.5967i	− 1.89582i
$924$	2.76393	0.0909267
$925$	0	0
$926$	15.5623	0.511409
$927$	− 42.5967i	− 1.39906i
$928$	6.32624i	0.207669i
$929$	−28.4508	−0.933442	−0.466721	−	0.884405i	$-0.654565\pi$
$929$	−28.4508	−0.933442	−0.466721	+	0.884405i	$0.654565\pi$
$930$	0	0
$931$	24.4721	0.802042
$932$	− 13.5623i	− 0.444248i
$933$	1.25735i	0.0411639i
$934$	−20.3607	−0.666222
$935$	0	0
$936$	−10.0902	−0.329808
$937$	− 57.0476i	− 1.86366i	−0.362890	−	0.931832i	$-0.618210\pi$
$937$	− 57.0476i	− 1.86366i	0.362890	−	0.931832i	$-0.381790\pi$
$938$	− 12.4721i	− 0.407230i
$939$	−3.59675	−0.117375
$940$	0	0
$941$	−3.81966	−0.124517	−0.0622587	−	0.998060i	$-0.519830\pi$
$941$	−3.81966	−0.124517	−0.0622587	+	0.998060i	$0.519830\pi$
$942$	4.65248i	0.151586i
$943$	− 28.4508i	− 0.926487i
$944$	9.23607	0.300608
$945$	0	0
$946$	2.76393	0.0898632
$947$	34.8328i	1.13191i	0.824435	+	0.565957i	$0.191493\pi$
$947$	34.8328i	1.13191i	−0.824435	+	0.565957i	$0.808507\pi$
$948$	7.14590i	0.232088i
$949$	15.7639	0.511719
$950$	0	0
$951$	1.88854	0.0612402
$952$	− 5.52786i	− 0.179159i
$953$	− 44.4508i	− 1.43990i	−0.694024	−	0.719952i	$-0.744164\pi$
$953$	− 44.4508i	− 1.43990i	0.694024	−	0.719952i	$-0.255836\pi$
$954$	−22.1803	−0.718115
$955$	0	0
$956$	3.14590	0.101746
$957$	14.1459i	0.457272i
$958$	16.4377i	0.531078i
$959$	−23.8885	−0.771401
$960$	0	0
$961$	61.5066	1.98408
$962$	3.85410i	0.124261i
$963$	− 21.7984i	− 0.702443i
$964$	10.4721	0.337285
$965$	0	0
$966$	−2.94427	−0.0947304
$967$	− 11.7295i	− 0.377195i	−0.982054	−	0.188597i	$-0.939606\pi$
$967$	− 11.7295i	− 0.377195i	0.982054	−	0.188597i	$-0.0603941\pi$
$968$	2.09017i	0.0671806i
$969$	12.3607	0.397082
$970$	0	0
$971$	26.6738	0.856002	0.428001	−	0.903778i	$-0.359218\pi$
$971$	26.6738	0.856002	0.428001	+	0.903778i	$0.359218\pi$
$972$	− 13.9443i	− 0.447263i
$973$	− 2.29180i	− 0.0734716i
$974$	25.3050	0.810823
$975$	0	0
$976$	8.38197	0.268300
$977$	− 52.4721i	− 1.67873i	−0.543566	−	0.839366i	$-0.682926\pi$
$977$	− 52.4721i	− 1.67873i	0.543566	−	0.839366i	$-0.317074\pi$
$978$	− 7.70820i	− 0.246481i
$979$	−37.8885	−1.21092
$980$	0	0
$981$	39.1246	1.24915
$982$	− 27.4508i	− 0.875992i
$983$	39.7771i	1.26869i	0.773049	+	0.634346i	$0.218731\pi$
$983$	39.7771i	1.26869i	−0.773049	+	0.634346i	$0.781269\pi$
$984$	−4.56231	−0.145441
$985$	0	0
$986$	28.2918	0.900994
$987$	− 2.47214i	− 0.0786890i
$988$	− 17.2361i	− 0.548352i
$989$	−2.94427	−0.0936224
$990$	0	0
$991$	−54.1033	−1.71865	−0.859324	−	0.511431i	$-0.829116\pi$
$991$	−54.1033	−1.71865	−0.859324	+	0.511431i	$0.829116\pi$
$992$	− 9.61803i	− 0.305373i
$993$	17.3050i	0.549156i
$994$	18.4721	0.585901
$995$	0	0
$996$	−3.41641	−0.108253
$997$	− 53.7771i	− 1.70314i	−0.524243	−	0.851569i	$-0.675652\pi$
$997$	− 53.7771i	− 1.70314i	0.524243	−	0.851569i	$-0.324348\pi$
$998$	23.7082i	0.750470i
$999$	−3.47214	−0.109854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.j.149.2		4
5.2	odd	4		74.2.a.b.1.2	✓	2
5.3	odd	4		1850.2.a.t.1.1		2
5.4	even	2	inner	1850.2.b.j.149.3		4
15.2	even	4		666.2.a.i.1.2		2
20.7	even	4		592.2.a.g.1.1		2
35.27	even	4		3626.2.a.s.1.1		2
40.27	even	4		2368.2.a.u.1.2		2
40.37	odd	4		2368.2.a.y.1.1		2
55.32	even	4		8954.2.a.j.1.2		2
60.47	odd	4		5328.2.a.bc.1.2		2
185.147	odd	4		2738.2.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.a.b.1.2	✓	2	5.2	odd	4
592.2.a.g.1.1		2	20.7	even	4
666.2.a.i.1.2		2	15.2	even	4
1850.2.a.t.1.1		2	5.3	odd	4
1850.2.b.j.149.2		4	1.1	even	1	trivial
1850.2.b.j.149.3		4	5.4	even	2	inner
2368.2.a.u.1.2		2	40.27	even	4
2368.2.a.y.1.1		2	40.37	odd	4
2738.2.a.g.1.2		2	185.147	odd	4
3626.2.a.s.1.1		2	35.27	even	4
5328.2.a.bc.1.2		2	60.47	odd	4
8954.2.a.j.1.2		2	55.32	even	4

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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} +0.618034 q^{6} -1.23607i q^{7} +1.00000i q^{8} +2.61803 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} +0.618034 q^{6} -1.23607i q^{7} +1.00000i q^{8} +2.61803 q^{9} -3.61803 q^{11} -0.618034i q^{12} +3.85410i q^{13} -1.23607 q^{14} +1.00000 q^{16} -4.47214i q^{17} -2.61803i q^{18} +4.47214 q^{19} +0.763932 q^{21} +3.61803i q^{22} -3.85410i q^{23} -0.618034 q^{24} +3.85410 q^{26} +3.47214i q^{27} +1.23607i q^{28} -6.32624 q^{29} +9.61803 q^{31} -1.00000i q^{32} -2.23607i q^{33} -4.47214 q^{34} -2.61803 q^{36} +1.00000i q^{37} -4.47214i q^{38} -2.38197 q^{39} +7.38197 q^{41} -0.763932i q^{42} -0.763932i q^{43} +3.61803 q^{44} -3.85410 q^{46} -3.23607i q^{47} +0.618034i q^{48} +5.47214 q^{49} +2.76393 q^{51} -3.85410i q^{52} -8.47214i q^{53} +3.47214 q^{54} +1.23607 q^{56} +2.76393i q^{57} +6.32624i q^{58} +9.23607 q^{59} +8.38197 q^{61} -9.61803i q^{62} -3.23607i q^{63} -1.00000 q^{64} -2.23607 q^{66} +10.0902i q^{67} +4.47214i q^{68} +2.38197 q^{69} -14.9443 q^{71} +2.61803i q^{72} -4.09017i q^{73} +1.00000 q^{74} -4.47214 q^{76} +4.47214i q^{77} +2.38197i q^{78} -11.5623 q^{79} +5.70820 q^{81} -7.38197i q^{82} -5.52786i q^{83} -0.763932 q^{84} -0.763932 q^{86} -3.90983i q^{87} -3.61803i q^{88} +10.4721 q^{89} +4.76393 q^{91} +3.85410i q^{92} +5.94427i q^{93} -3.23607 q^{94} +0.618034 q^{96} -8.47214i q^{97} -5.47214i q^{98} -9.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9} - 10 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{21} + 2 q^{24} + 2 q^{26} + 6 q^{29} + 34 q^{31} - 6 q^{36} - 14 q^{39} + 34 q^{41} + 10 q^{44} - 2 q^{46} + 4 q^{49} + 20 q^{51} - 4 q^{54} - 4 q^{56} + 28 q^{59} + 38 q^{61} - 4 q^{64} + 14 q^{69} - 24 q^{71} + 4 q^{74} - 6 q^{79} - 4 q^{81} - 12 q^{84} - 12 q^{86} + 24 q^{89} + 28 q^{91} - 4 q^{94} - 2 q^{96} - 20 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9 - 10 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^21 + 2 * q^24 + 2 * q^26 + 6 * q^29 + 34 * q^31 - 6 * q^36 - 14 * q^39 + 34 * q^41 + 10 * q^44 - 2 * q^46 + 4 * q^49 + 20 * q^51 - 4 * q^54 - 4 * q^56 + 28 * q^59 + 38 * q^61 - 4 * q^64 + 14 * q^69 - 24 * q^71 + 4 * q^74 - 6 * q^79 - 4 * q^81 - 12 * q^84 - 12 * q^86 + 24 * q^89 + 28 * q^91 - 4 * q^94 - 2 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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