LMFDB - Embedded newform 1525.2.b.b.1099.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1525,2,Mod(1099,1525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1525, 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("1525.1099");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1525 = 5^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1525.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:	$12.1771863082$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1099.6
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1525.1099
Dual form			1525.2.b.b.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17009i q^{2} +1.70928i q^{3} -2.70928 q^{4} -3.70928 q^{6} -0.460811i q^{7} -1.53919i q^{8} +0.0783777 q^{9} +O(q^{10})$	\(q+2.17009i q^{2} +1.70928i q^{3} -2.70928 q^{4} -3.70928 q^{6} -0.460811i q^{7} -1.53919i q^{8} +0.0783777 q^{9} +6.17009 q^{11} -4.63090i q^{12} +4.07838i q^{13} +1.00000 q^{14} -2.07838 q^{16} +0.630898i q^{17} +0.170086i q^{18} -7.12783 q^{19} +0.787653 q^{21} +13.3896i q^{22} +0.170086i q^{23} +2.63090 q^{24} -8.85043 q^{26} +5.26180i q^{27} +1.24846i q^{28} -2.63090 q^{29} -10.3896 q^{31} -7.58864i q^{32} +10.5464i q^{33} -1.36910 q^{34} -0.212347 q^{36} +5.12783i q^{37} -15.4680i q^{38} -6.97107 q^{39} +3.15676 q^{41} +1.70928i q^{42} +3.36910i q^{43} -16.7165 q^{44} -0.369102 q^{46} +0.183417i q^{47} -3.55252i q^{48} +6.78765 q^{49} -1.07838 q^{51} -11.0494i q^{52} +4.34017i q^{53} -11.4186 q^{54} -0.709275 q^{56} -12.1834i q^{57} -5.70928i q^{58} -1.78047 q^{59} +1.00000 q^{61} -22.5464i q^{62} -0.0361173i q^{63} +12.3112 q^{64} -22.8865 q^{66} -8.55971i q^{67} -1.70928i q^{68} -0.290725 q^{69} +14.3896 q^{71} -0.120638i q^{72} +0.552520i q^{73} -11.1278 q^{74} +19.3112 q^{76} -2.84324i q^{77} -15.1278i q^{78} +7.00719 q^{79} -8.75872 q^{81} +6.85043i q^{82} -6.83710i q^{83} -2.13397 q^{84} -7.31124 q^{86} -4.49693i q^{87} -9.49693i q^{88} -4.49693 q^{89} +1.87936 q^{91} -0.460811i q^{92} -17.7587i q^{93} -0.398032 q^{94} +12.9711 q^{96} +8.52359i q^{97} +14.7298i q^{98} +0.483597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} - 8 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^4 - 8 * q^6 - 6 * q^9	$ 6 q - 2 q^{4} - 8 q^{6} - 6 q^{9} + 26 q^{11} + 6 q^{14} - 6 q^{16} - 16 q^{21} + 8 q^{24} + 2 q^{26} - 8 q^{29} - 4 q^{31} - 16 q^{34} - 22 q^{36} - 12 q^{39} + 6 q^{41} - 18 q^{44} - 10 q^{46} + 20 q^{49} - 40 q^{54} + 10 q^{56} - 58 q^{59} + 6 q^{61} + 22 q^{64} - 44 q^{66} - 16 q^{69} + 28 q^{71} - 24 q^{74} + 64 q^{76} - 26 q^{79} - 2 q^{81} - 40 q^{84} + 8 q^{86} + 8 q^{89} - 14 q^{91} - 40 q^{94} + 48 q^{96} - 34 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 - 8 * q^6 - 6 * q^9 + 26 * q^11 + 6 * q^14 - 6 * q^16 - 16 * q^21 + 8 * q^24 + 2 * q^26 - 8 * q^29 - 4 * q^31 - 16 * q^34 - 22 * q^36 - 12 * q^39 + 6 * q^41 - 18 * q^44 - 10 * q^46 + 20 * q^49 - 40 * q^54 + 10 * q^56 - 58 * q^59 + 6 * q^61 + 22 * q^64 - 44 * q^66 - 16 * q^69 + 28 * q^71 - 24 * q^74 + 64 * q^76 - 26 * q^79 - 2 * q^81 - 40 * q^84 + 8 * q^86 + 8 * q^89 - 14 * q^91 - 40 * q^94 + 48 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1525\mathbb{Z}\right)^\times$.

$n$	$551$	$977$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.17009i	1.53448i	0.641358	+	0.767241i	$0.278371\pi$
$2$	2.17009i	1.53448i	−0.641358	+	0.767241i	$0.721629\pi$
$3$	1.70928i	0.986851i	0.869788	+	0.493425i	$0.164255\pi$
$3$	1.70928i	0.986851i	−0.869788	+	0.493425i	$0.835745\pi$
$4$	−2.70928	−1.35464
$5$	0	0
$5$	0	0
$6$	−3.70928	−1.51431
$7$	− 0.460811i	− 0.174170i	−0.996201	−	0.0870851i	$-0.972245\pi$
$7$	− 0.460811i	− 0.174170i	0.996201	−	0.0870851i	$-0.0277552\pi$
$8$	− 1.53919i	− 0.544185i
$9$	0.0783777	0.0261259
$10$	0	0
$11$	6.17009	1.86035	0.930176	−	0.367115i	$-0.119654\pi$
$11$	6.17009	1.86035	0.930176	+	0.367115i	$0.119654\pi$
$12$	− 4.63090i	− 1.33682i
$13$	4.07838i	1.13114i	0.824701	+	0.565569i	$0.191343\pi$
$13$	4.07838i	1.13114i	−0.824701	+	0.565569i	$0.808657\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−2.07838	−0.519594
$17$	0.630898i	0.153015i	0.997069	+	0.0765076i	$0.0243769\pi$
$17$	0.630898i	0.153015i	−0.997069	+	0.0765076i	$0.975623\pi$
$18$	0.170086i	0.0400898i
$19$	−7.12783	−1.63524	−0.817618	−	0.575761i	$-0.804706\pi$
$19$	−7.12783	−1.63524	−0.817618	+	0.575761i	$0.804706\pi$
$20$	0	0
$21$	0.787653	0.171880
$22$	13.3896i	2.85468i
$23$	0.170086i	0.0354655i	0.999843	+	0.0177327i	$0.00564480\pi$
$23$	0.170086i	0.0354655i	−0.999843	+	0.0177327i	$0.994355\pi$
$24$	2.63090	0.537030
$25$	0	0
$26$	−8.85043	−1.73571
$27$	5.26180i	1.01263i
$28$	1.24846i	0.235938i
$29$	−2.63090	−0.488545	−0.244273	−	0.969707i	$-0.578549\pi$
$29$	−2.63090	−0.488545	−0.244273	+	0.969707i	$0.578549\pi$
$30$	0	0
$31$	−10.3896	−1.86603	−0.933016	−	0.359836i	$-0.882833\pi$
$31$	−10.3896	−1.86603	−0.933016	+	0.359836i	$0.882833\pi$
$32$	− 7.58864i	− 1.34149i
$33$	10.5464i	1.83589i
$34$	−1.36910	−0.234799
$35$	0	0
$36$	−0.212347	−0.0353911
$37$	5.12783i	0.843009i	0.906826	+	0.421505i	$0.138498\pi$
$37$	5.12783i	0.843009i	−0.906826	+	0.421505i	$0.861502\pi$
$38$	− 15.4680i	− 2.50924i
$39$	−6.97107	−1.11626
$40$	0	0
$41$	3.15676	0.493002	0.246501	−	0.969142i	$-0.420719\pi$
$41$	3.15676	0.493002	0.246501	+	0.969142i	$0.420719\pi$
$42$	1.70928i	0.263747i
$43$	3.36910i	0.513783i	0.966440	+	0.256892i	$0.0826984\pi$
$43$	3.36910i	0.513783i	−0.966440	+	0.256892i	$0.917302\pi$
$44$	−16.7165	−2.52010
$45$	0	0
$46$	−0.369102	−0.0544212
$47$	0.183417i	0.0267542i	0.999911	+	0.0133771i	$0.00425819\pi$
$47$	0.183417i	0.0267542i	−0.999911	+	0.0133771i	$0.995742\pi$
$48$	− 3.55252i	− 0.512762i
$49$	6.78765	0.969665
$50$	0	0
$51$	−1.07838	−0.151003
$52$	− 11.0494i	− 1.53228i
$53$	4.34017i	0.596169i	0.954540	+	0.298084i	$0.0963477\pi$
$53$	4.34017i	0.596169i	−0.954540	+	0.298084i	$0.903652\pi$
$54$	−11.4186	−1.55387
$55$	0	0
$56$	−0.709275	−0.0947809
$57$	− 12.1834i	− 1.61373i
$58$	− 5.70928i	− 0.749665i
$59$	−1.78047	−0.231797	−0.115898	−	0.993261i	$-0.536975\pi$
$59$	−1.78047	−0.231797	−0.115898	+	0.993261i	$0.536975\pi$
$60$	0	0
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	− 22.5464i	− 2.86339i
$63$	− 0.0361173i	− 0.00455036i
$64$	12.3112	1.53891
$65$	0	0
$66$	−22.8865	−2.81714
$67$	− 8.55971i	− 1.04573i	−0.852414	−	0.522867i	$-0.824862\pi$
$67$	− 8.55971i	− 1.04573i	0.852414	−	0.522867i	$-0.175138\pi$
$68$	− 1.70928i	− 0.207280i
$69$	−0.290725	−0.0349991
$70$	0	0
$71$	14.3896	1.70773	0.853867	−	0.520491i	$-0.174251\pi$
$71$	14.3896	1.70773	0.853867	+	0.520491i	$0.174251\pi$
$72$	− 0.120638i	− 0.0142173i
$73$	0.552520i	0.0646676i	0.999477	+	0.0323338i	$0.0102940\pi$
$73$	0.552520i	0.0646676i	−0.999477	+	0.0323338i	$0.989706\pi$
$74$	−11.1278	−1.29358
$75$	0	0
$76$	19.3112	2.21515
$77$	− 2.84324i	− 0.324018i
$78$	− 15.1278i	− 1.71289i
$79$	7.00719	0.788370	0.394185	−	0.919031i	$-0.371027\pi$
$79$	7.00719	0.788370	0.394185	+	0.919031i	$0.371027\pi$
$80$	0	0
$81$	−8.75872	−0.973192
$82$	6.85043i	0.756504i
$83$	− 6.83710i	− 0.750469i	−0.926930	−	0.375235i	$-0.877562\pi$
$83$	− 6.83710i	− 0.750469i	0.926930	−	0.375235i	$-0.122438\pi$
$84$	−2.13397	−0.232835
$85$	0	0
$86$	−7.31124	−0.788392
$87$	− 4.49693i	− 0.482121i
$88$	− 9.49693i	− 1.01238i
$89$	−4.49693	−0.476673	−0.238337	−	0.971183i	$-0.576602\pi$
$89$	−4.49693	−0.476673	−0.238337	+	0.971183i	$0.576602\pi$
$90$	0	0
$91$	1.87936	0.197011
$92$	− 0.460811i	− 0.0480429i
$93$	− 17.7587i	− 1.84149i
$94$	−0.398032	−0.0410538
$95$	0	0
$96$	12.9711	1.32385
$97$	8.52359i	0.865439i	0.901528	+	0.432720i	$0.142446\pi$
$97$	8.52359i	0.865439i	−0.901528	+	0.432720i	$0.857554\pi$
$98$	14.7298i	1.48793i
$99$	0.483597	0.0486034
$100$	0	0
$101$	−6.78765	−0.675397	−0.337698	−	0.941254i	$-0.609648\pi$
$101$	−6.78765	−0.675397	−0.337698	+	0.941254i	$0.609648\pi$
$102$	− 2.34017i	− 0.231712i
$103$	− 11.1278i	− 1.09646i	−0.836328	−	0.548229i	$-0.815302\pi$
$103$	− 11.1278i	− 1.09646i	0.836328	−	0.548229i	$-0.184698\pi$
$104$	6.27739	0.615549
$105$	0	0
$106$	−9.41855	−0.914811
$107$	15.5753i	1.50572i	0.658180	+	0.752861i	$0.271327\pi$
$107$	15.5753i	1.50572i	−0.658180	+	0.752861i	$0.728673\pi$
$108$	− 14.2557i	− 1.37175i
$109$	−11.6803	−1.11877	−0.559387	−	0.828907i	$-0.688963\pi$
$109$	−11.6803	−1.11877	−0.559387	+	0.828907i	$0.688963\pi$
$110$	0	0
$111$	−8.76487	−0.831924
$112$	0.957740i	0.0904979i
$113$	12.9421i	1.21749i	0.793364	+	0.608747i	$0.208328\pi$
$113$	12.9421i	1.21749i	−0.793364	+	0.608747i	$0.791672\pi$
$114$	26.4391	2.47625
$115$	0	0
$116$	7.12783	0.661802
$117$	0.319654i	0.0295520i
$118$	− 3.86376i	− 0.355688i
$119$	0.290725	0.0266507
$120$	0	0
$121$	27.0700	2.46091
$122$	2.17009i	0.196470i
$123$	5.39576i	0.486520i
$124$	28.1483	2.52780
$125$	0	0
$126$	0.0783777	0.00698244
$127$	− 1.02893i	− 0.0913027i	−0.998957	−	0.0456514i	$-0.985464\pi$
$127$	− 1.02893i	− 0.0913027i	0.998957	−	0.0456514i	$-0.0145363\pi$
$128$	11.5392i	1.01993i
$129$	−5.75872	−0.507027
$130$	0	0
$131$	2.44748	0.213837	0.106919	−	0.994268i	$-0.465902\pi$
$131$	2.44748	0.213837	0.106919	+	0.994268i	$0.465902\pi$
$132$	− 28.5730i	− 2.48696i
$133$	3.28458i	0.284809i
$134$	18.5753	1.60466
$135$	0	0
$136$	0.971071	0.0832686
$137$	− 16.0700i	− 1.37295i	−0.727153	−	0.686475i	$-0.759157\pi$
$137$	− 16.0700i	− 1.37295i	0.727153	−	0.686475i	$-0.240843\pi$
$138$	− 0.630898i	− 0.0537056i
$139$	1.53919	0.130552	0.0652761	−	0.997867i	$-0.479207\pi$
$139$	1.53919	0.130552	0.0652761	+	0.997867i	$0.479207\pi$
$140$	0	0
$141$	−0.313511	−0.0264024
$142$	31.2267i	2.62049i
$143$	25.1639i	2.10431i
$144$	−0.162899	−0.0135749
$145$	0	0
$146$	−1.19902	−0.0992313
$147$	11.6020i	0.956914i
$148$	− 13.8927i	− 1.14197i
$149$	−1.92162	−0.157425	−0.0787127	−	0.996897i	$-0.525081\pi$
$149$	−1.92162	−0.157425	−0.0787127	+	0.996897i	$0.525081\pi$
$150$	0	0
$151$	9.32457	0.758823	0.379412	−	0.925228i	$-0.376126\pi$
$151$	9.32457	0.758823	0.379412	+	0.925228i	$0.376126\pi$
$152$	10.9711i	0.889871i
$153$	0.0494483i	0.00399766i
$154$	6.17009	0.497200
$155$	0	0
$156$	18.8865	1.51213
$157$	− 13.4947i	− 1.07699i	−0.842628	−	0.538496i	$-0.818993\pi$
$157$	− 13.4947i	− 1.07699i	0.842628	−	0.538496i	$-0.181007\pi$
$158$	15.2062i	1.20974i
$159$	−7.41855	−0.588329
$160$	0	0
$161$	0.0783777	0.00617703
$162$	− 19.0072i	− 1.49335i
$163$	10.7031i	0.838334i	0.907909	+	0.419167i	$0.137678\pi$
$163$	10.7031i	0.838334i	−0.907909	+	0.419167i	$0.862322\pi$
$164$	−8.55252	−0.667840
$165$	0	0
$166$	14.8371	1.15158
$167$	4.88655i	0.378133i	0.981964	+	0.189066i	$0.0605461\pi$
$167$	4.88655i	0.378133i	−0.981964	+	0.189066i	$0.939454\pi$
$168$	− 1.21235i	− 0.0935346i
$169$	−3.63317	−0.279474
$170$	0	0
$171$	−0.558663	−0.0427220
$172$	− 9.12783i	− 0.695990i
$173$	0.738205i	0.0561247i	0.999606	+	0.0280623i	$0.00893369\pi$
$173$	0.738205i	0.0561247i	−0.999606	+	0.0280623i	$0.991066\pi$
$174$	9.75872	0.739807
$175$	0	0
$176$	−12.8238	−0.966628
$177$	− 3.04331i	− 0.228749i
$178$	− 9.75872i	− 0.731447i
$179$	−1.90110	−0.142095	−0.0710476	−	0.997473i	$-0.522634\pi$
$179$	−1.90110	−0.142095	−0.0710476	+	0.997473i	$0.522634\pi$
$180$	0	0
$181$	−21.3607	−1.58773	−0.793864	−	0.608096i	$-0.791934\pi$
$181$	−21.3607	−1.58773	−0.793864	+	0.608096i	$0.791934\pi$
$182$	4.07838i	0.302309i
$183$	1.70928i	0.126353i
$184$	0.261795	0.0192998
$185$	0	0
$186$	38.5380	2.82574
$187$	3.89269i	0.284662i
$188$	− 0.496928i	− 0.0362422i
$189$	2.42469	0.176371
$190$	0	0
$191$	2.88550	0.208788	0.104394	−	0.994536i	$-0.466710\pi$
$191$	2.88550	0.208788	0.104394	+	0.994536i	$0.466710\pi$
$192$	21.0433i	1.51867i
$193$	− 0.680346i	− 0.0489724i	−0.999700	−	0.0244862i	$-0.992205\pi$
$193$	− 0.680346i	− 0.0489724i	0.999700	−	0.0244862i	$-0.00779497\pi$
$194$	−18.4969	−1.32800
$195$	0	0
$196$	−18.3896	−1.31354
$197$	− 19.3896i	− 1.38145i	−0.723116	−	0.690727i	$-0.757291\pi$
$197$	− 19.3896i	− 1.38145i	0.723116	−	0.690727i	$-0.242709\pi$
$198$	1.04945i	0.0745810i
$199$	21.4186	1.51832	0.759160	−	0.650904i	$-0.225610\pi$
$199$	21.4186	1.51832	0.759160	+	0.650904i	$0.225610\pi$
$200$	0	0
$201$	14.6309	1.03198
$202$	− 14.7298i	− 1.03638i
$203$	1.21235i	0.0850901i
$204$	2.92162	0.204554
$205$	0	0
$206$	24.1483	1.68249
$207$	0.0133310i	0 0.000926568i
$208$	− 8.47641i	− 0.587733i
$209$	−43.9793	−3.04211
$210$	0	0
$211$	5.39576	0.371460	0.185730	−	0.982601i	$-0.440535\pi$
$211$	5.39576	0.371460	0.185730	+	0.982601i	$0.440535\pi$
$212$	− 11.7587i	− 0.807592i
$213$	24.5958i	1.68528i
$214$	−33.7998	−2.31050
$215$	0	0
$216$	8.09890	0.551060
$217$	4.78765i	0.325007i
$218$	− 25.3474i	− 1.71674i
$219$	−0.944409	−0.0638172
$220$	0	0
$221$	−2.57304	−0.173081
$222$	− 19.0205i	− 1.27657i
$223$	− 12.4257i	− 0.832089i	−0.909344	−	0.416045i	$-0.863416\pi$
$223$	− 12.4257i	− 0.832089i	0.909344	−	0.416045i	$-0.136584\pi$
$224$	−3.49693	−0.233648
$225$	0	0
$226$	−28.0856	−1.86822
$227$	− 22.3679i	− 1.48461i	−0.670063	−	0.742304i	$-0.733733\pi$
$227$	− 22.3679i	− 1.48461i	0.670063	−	0.742304i	$-0.266267\pi$
$228$	33.0082i	2.18602i
$229$	0.185685	0.0122704	0.00613520	−	0.999981i	$-0.498047\pi$
$229$	0.185685	0.0122704	0.00613520	+	0.999981i	$0.498047\pi$
$230$	0	0
$231$	4.85989	0.319757
$232$	4.04945i	0.265859i
$233$	17.8660i	1.17044i	0.810874	+	0.585221i	$0.198992\pi$
$233$	17.8660i	1.17044i	−0.810874	+	0.585221i	$0.801008\pi$
$234$	−0.693677	−0.0453471
$235$	0	0
$236$	4.82377	0.314001
$237$	11.9772i	0.778004i
$238$	0.630898i	0.0408950i
$239$	22.3896	1.44826	0.724132	−	0.689661i	$-0.242241\pi$
$239$	22.3896	1.44826	0.724132	+	0.689661i	$0.242241\pi$
$240$	0	0
$241$	20.0433	1.29110	0.645551	−	0.763717i	$-0.276628\pi$
$241$	20.0433	1.29110	0.645551	+	0.763717i	$0.276628\pi$
$242$	58.7442i	3.77622i
$243$	0.814315i	0.0522383i
$244$	−2.70928	−0.173444
$245$	0	0
$246$	−11.7093	−0.746556
$247$	− 29.0700i	− 1.84968i
$248$	15.9916i	1.01547i
$249$	11.6865	0.740601
$250$	0	0
$251$	7.05559	0.445345	0.222672	−	0.974893i	$-0.428522\pi$
$251$	7.05559	0.445345	0.222672	+	0.974893i	$0.428522\pi$
$252$	0.0978518i	0.00616408i
$253$	1.04945i	0.0659783i
$254$	2.23287	0.140102
$255$	0	0
$256$	−0.418551	−0.0261594
$257$	3.26180i	0.203465i	0.994812	+	0.101733i	$0.0324386\pi$
$257$	3.26180i	0.203465i	−0.994812	+	0.101733i	$0.967561\pi$
$258$	− 12.4969i	− 0.778025i
$259$	2.36296	0.146827
$260$	0	0
$261$	−0.206204	−0.0127637
$262$	5.31124i	0.328130i
$263$	20.5730i	1.26859i	0.773092	+	0.634294i	$0.218709\pi$
$263$	20.5730i	1.26859i	−0.773092	+	0.634294i	$0.781291\pi$
$264$	16.2329	0.999064
$265$	0	0
$266$	−7.12783	−0.437035
$267$	− 7.68649i	− 0.470405i
$268$	23.1906i	1.41659i
$269$	3.97334	0.242259	0.121129	−	0.992637i	$-0.461348\pi$
$269$	3.97334	0.242259	0.121129	+	0.992637i	$0.461348\pi$
$270$	0	0
$271$	−4.99773	−0.303591	−0.151795	−	0.988412i	$-0.548505\pi$
$271$	−4.99773	−0.303591	−0.151795	+	0.988412i	$0.548505\pi$
$272$	− 1.31124i	− 0.0795058i
$273$	3.21235i	0.194420i
$274$	34.8732	2.10677
$275$	0	0
$276$	0.787653	0.0474111
$277$	17.9649i	1.07941i	0.841855	+	0.539704i	$0.181464\pi$
$277$	17.9649i	1.07941i	−0.841855	+	0.539704i	$0.818536\pi$
$278$	3.34017i	0.200330i
$279$	−0.814315	−0.0487518
$280$	0	0
$281$	15.6020	0.930735	0.465368	−	0.885117i	$-0.345922\pi$
$281$	15.6020	0.930735	0.465368	+	0.885117i	$0.345922\pi$
$282$	− 0.680346i	− 0.0405140i
$283$	− 24.7298i	− 1.47003i	−0.678049	−	0.735017i	$-0.737174\pi$
$283$	− 24.7298i	− 1.47003i	0.678049	−	0.735017i	$-0.262826\pi$
$284$	−38.9854	−2.31336
$285$	0	0
$286$	−54.6079	−3.22903
$287$	− 1.45467i	− 0.0858663i
$288$	− 0.594780i	− 0.0350478i
$289$	16.6020	0.976586
$290$	0	0
$291$	−14.5692	−0.854059
$292$	− 1.49693i	− 0.0876011i
$293$	− 24.1711i	− 1.41209i	−0.708166	−	0.706046i	$-0.750477\pi$
$293$	− 24.1711i	− 1.41209i	0.708166	−	0.706046i	$-0.249523\pi$
$294$	−25.1773	−1.46837
$295$	0	0
$296$	7.89269	0.458753
$297$	32.4657i	1.88385i
$298$	− 4.17009i	− 0.241567i
$299$	−0.693677	−0.0401164
$300$	0	0
$301$	1.55252	0.0894858
$302$	20.2351i	1.16440i
$303$	− 11.6020i	− 0.666516i
$304$	14.8143	0.849659
$305$	0	0
$306$	−0.107307	−0.00613434
$307$	19.5041i	1.11316i	0.830794	+	0.556579i	$0.187886\pi$
$307$	19.5041i	1.11316i	−0.830794	+	0.556579i	$0.812114\pi$
$308$	7.70313i	0.438927i
$309$	19.0205	1.08204
$310$	0	0
$311$	8.35350	0.473684	0.236842	−	0.971548i	$-0.423888\pi$
$311$	8.35350	0.473684	0.236842	+	0.971548i	$0.423888\pi$
$312$	10.7298i	0.607455i
$313$	− 2.09890i	− 0.118637i	−0.998239	−	0.0593183i	$-0.981107\pi$
$313$	− 2.09890i	− 0.118637i	0.998239	−	0.0593183i	$-0.0188927\pi$
$314$	29.2846	1.65262
$315$	0	0
$316$	−18.9844	−1.06796
$317$	27.7587i	1.55909i	0.626349	+	0.779543i	$0.284548\pi$
$317$	27.7587i	1.55909i	−0.626349	+	0.779543i	$0.715452\pi$
$318$	− 16.0989i	− 0.902781i
$319$	−16.2329	−0.908866
$320$	0	0
$321$	−26.6225	−1.48592
$322$	0.170086i	0.00947855i
$323$	− 4.49693i	− 0.250216i
$324$	23.7298	1.31832
$325$	0	0
$326$	−23.2267	−1.28641
$327$	− 19.9649i	− 1.10406i
$328$	− 4.85884i	− 0.268285i
$329$	0.0845208	0.00465978
$330$	0	0
$331$	−1.19902	−0.0659039	−0.0329519	−	0.999457i	$-0.510491\pi$
$331$	−1.19902	−0.0659039	−0.0329519	+	0.999457i	$0.510491\pi$
$332$	18.5236i	1.01661i
$333$	0.401907i	0.0220244i
$334$	−10.6042	−0.580238
$335$	0	0
$336$	−1.63704	−0.0893079
$337$	20.9672i	1.14216i	0.820896	+	0.571078i	$0.193475\pi$
$337$	20.9672i	1.14216i	−0.820896	+	0.571078i	$0.806525\pi$
$338$	− 7.88428i	− 0.428848i
$339$	−22.1217	−1.20148
$340$	0	0
$341$	−64.1049	−3.47147
$342$	− 1.21235i	− 0.0655562i
$343$	− 6.35350i	− 0.343057i
$344$	5.18568	0.279593
$345$	0	0
$346$	−1.60197	−0.0861223
$347$	20.3896i	1.09457i	0.836946	+	0.547286i	$0.184339\pi$
$347$	20.3896i	1.09457i	−0.836946	+	0.547286i	$0.815661\pi$
$348$	12.1834i	0.653100i
$349$	7.65142	0.409571	0.204785	−	0.978807i	$-0.434350\pi$
$349$	7.65142	0.409571	0.204785	+	0.978807i	$0.434350\pi$
$350$	0	0
$351$	−21.4596	−1.14543
$352$	− 46.8225i	− 2.49565i
$353$	19.6765i	1.04727i	0.851942	+	0.523636i	$0.175425\pi$
$353$	19.6765i	1.04727i	−0.851942	+	0.523636i	$0.824575\pi$
$354$	6.60424	0.351011
$355$	0	0
$356$	12.1834	0.645720
$357$	0.496928i	0.0263002i
$358$	− 4.12556i	− 0.218043i
$359$	−20.8599	−1.10094	−0.550471	−	0.834854i	$-0.685552\pi$
$359$	−20.8599	−1.10094	−0.550471	+	0.834854i	$0.685552\pi$
$360$	0	0
$361$	31.8059	1.67399
$362$	− 46.3545i	− 2.43634i
$363$	46.2700i	2.42855i
$364$	−5.09171	−0.266878
$365$	0	0
$366$	−3.70928	−0.193887
$367$	− 5.31965i	− 0.277684i	−0.990315	−	0.138842i	$-0.955662\pi$
$367$	− 5.31965i	− 0.277684i	0.990315	−	0.138842i	$-0.0443380\pi$
$368$	− 0.353504i	− 0.0184277i
$369$	0.247419	0.0128801
$370$	0	0
$371$	2.00000	0.103835
$372$	48.1133i	2.49456i
$373$	20.0905i	1.04025i	0.854091	+	0.520123i	$0.174114\pi$
$373$	20.0905i	1.04025i	−0.854091	+	0.520123i	$0.825886\pi$
$374$	−8.44748	−0.436809
$375$	0	0
$376$	0.282314	0.0145592
$377$	− 10.7298i	− 0.552613i
$378$	5.26180i	0.270638i
$379$	26.4040	1.35628	0.678141	−	0.734932i	$-0.262786\pi$
$379$	26.4040	1.35628	0.678141	+	0.734932i	$0.262786\pi$
$380$	0	0
$381$	1.75872	0.0901021
$382$	6.26180i	0.320381i
$383$	10.9350i	0.558750i	0.960182	+	0.279375i	$0.0901273\pi$
$383$	10.9350i	0.558750i	−0.960182	+	0.279375i	$0.909873\pi$
$384$	−19.7237	−1.00652
$385$	0	0
$386$	1.47641	0.0751473
$387$	0.264063i	0.0134231i
$388$	− 23.0928i	− 1.17236i
$389$	5.50307	0.279017	0.139508	−	0.990221i	$-0.455448\pi$
$389$	5.50307	0.279017	0.139508	+	0.990221i	$0.455448\pi$
$390$	0	0
$391$	−0.107307	−0.00542676
$392$	− 10.4475i	− 0.527677i
$393$	4.18342i	0.211025i
$394$	42.0772	2.11982
$395$	0	0
$396$	−1.31020	−0.0658400
$397$	14.7565i	0.740605i	0.928911	+	0.370303i	$0.120746\pi$
$397$	14.7565i	0.740605i	−0.928911	+	0.370303i	$0.879254\pi$
$398$	46.4801i	2.32984i
$399$	−5.61425	−0.281064
$400$	0	0
$401$	−17.7587	−0.886828	−0.443414	−	0.896317i	$-0.646233\pi$
$401$	−17.7587	−0.886828	−0.443414	+	0.896317i	$0.646233\pi$
$402$	31.7503i	1.58356i
$403$	− 42.3728i	− 2.11074i
$404$	18.3896	0.914918
$405$	0	0
$406$	−2.63090	−0.130569
$407$	31.6391i	1.56829i
$408$	1.65983i	0.0821737i
$409$	16.4391	0.812860	0.406430	−	0.913682i	$-0.366774\pi$
$409$	16.4391	0.812860	0.406430	+	0.913682i	$0.366774\pi$
$410$	0	0
$411$	27.4680	1.35490
$412$	30.1483i	1.48530i
$413$	0.820458i	0.0403721i
$414$	−0.0289294	−0.00142180
$415$	0	0
$416$	30.9493	1.51742
$417$	2.63090i	0.128836i
$418$	− 95.4389i	− 4.66807i
$419$	−32.0183	−1.56419	−0.782097	−	0.623157i	$-0.785850\pi$
$419$	−32.0183	−1.56419	−0.782097	+	0.623157i	$0.785850\pi$
$420$	0	0
$421$	−0.630898	−0.0307481	−0.0153740	−	0.999882i	$-0.504894\pi$
$421$	−0.630898	−0.0307481	−0.0153740	+	0.999882i	$0.504894\pi$
$422$	11.7093i	0.569999i
$423$	0.0143758i	0 0.000698978i
$424$	6.68035	0.324426
$425$	0	0
$426$	−53.3751	−2.58603
$427$	− 0.460811i	− 0.0223002i
$428$	− 42.1978i	− 2.03971i
$429$	−43.0121	−2.07664
$430$	0	0
$431$	−16.6225	−0.800677	−0.400339	−	0.916367i	$-0.631107\pi$
$431$	−16.6225	−0.800677	−0.400339	+	0.916367i	$0.631107\pi$
$432$	− 10.9360i	− 0.526158i
$433$	20.4969i	0.985020i	0.870307	+	0.492510i	$0.163920\pi$
$433$	20.4969i	0.985020i	−0.870307	+	0.492510i	$0.836080\pi$
$434$	−10.3896	−0.498718
$435$	0	0
$436$	31.6453	1.51553
$437$	− 1.21235i	− 0.0579944i
$438$	− 2.04945i	− 0.0979264i
$439$	2.34858	0.112092	0.0560459	−	0.998428i	$-0.482151\pi$
$439$	2.34858	0.112092	0.0560459	+	0.998428i	$0.482151\pi$
$440$	0	0
$441$	0.532001	0.0253334
$442$	− 5.58372i	− 0.265590i
$443$	− 16.5958i	− 0.788491i	−0.919005	−	0.394246i	$-0.871006\pi$
$443$	− 16.5958i	− 0.788491i	0.919005	−	0.394246i	$-0.128994\pi$
$444$	23.7464	1.12696
$445$	0	0
$446$	26.9649	1.27683
$447$	− 3.28458i	− 0.155355i
$448$	− 5.67316i	− 0.268032i
$449$	20.4680	0.965945	0.482972	−	0.875636i	$-0.339557\pi$
$449$	20.4680	0.965945	0.482972	+	0.875636i	$0.339557\pi$
$450$	0	0
$451$	19.4775	0.917158
$452$	− 35.0638i	− 1.64926i
$453$	15.9383i	0.748845i
$454$	48.5402	2.27811
$455$	0	0
$456$	−18.7526	−0.878170
$457$	23.9506i	1.12036i	0.828371	+	0.560180i	$0.189268\pi$
$457$	23.9506i	1.12036i	−0.828371	+	0.560180i	$0.810732\pi$
$458$	0.402952i	0.0188287i
$459$	−3.31965	−0.154948
$460$	0	0
$461$	−26.5113	−1.23475	−0.617377	−	0.786667i	$-0.711805\pi$
$461$	−26.5113	−1.23475	−0.617377	+	0.786667i	$0.711805\pi$
$462$	10.5464i	0.490662i
$463$	− 34.0410i	− 1.58202i	−0.611802	−	0.791011i	$-0.709555\pi$
$463$	− 34.0410i	− 1.58202i	0.611802	−	0.791011i	$-0.290445\pi$
$464$	5.46800	0.253845
$465$	0	0
$466$	−38.7708	−1.79602
$467$	4.55971i	0.210998i	0.994419	+	0.105499i	$0.0336440\pi$
$467$	4.55971i	0.210998i	−0.994419	+	0.105499i	$0.966356\pi$
$468$	− 0.866031i	− 0.0400323i
$469$	−3.94441	−0.182136
$470$	0	0
$471$	23.0661	1.06283
$472$	2.74047i	0.126140i
$473$	20.7877i	0.955817i
$474$	−25.9916	−1.19383
$475$	0	0
$476$	−0.787653	−0.0361020
$477$	0.340173i	0.0155755i
$478$	48.5874i	2.22234i
$479$	0.653684	0.0298676	0.0149338	−	0.999888i	$-0.495246\pi$
$479$	0.653684	0.0298676	0.0149338	+	0.999888i	$0.495246\pi$
$480$	0	0
$481$	−20.9132	−0.953560
$482$	43.4957i	1.98118i
$483$	0.133969i	0.00609581i
$484$	−73.3400	−3.33364
$485$	0	0
$486$	−1.76713	−0.0801588
$487$	− 0.0227863i	− 0.00103255i	−1.00000		0.000516274i	$-0.999836\pi$
$487$	− 0.0227863i	− 0.00103255i	1.00000		0.000516274i	$-0.000164335\pi$
$488$	− 1.53919i	− 0.0696758i
$489$	−18.2946	−0.827310
$490$	0	0
$491$	−2.94441	−0.132879	−0.0664396	−	0.997790i	$-0.521164\pi$
$491$	−2.94441	−0.132879	−0.0664396	+	0.997790i	$0.521164\pi$
$492$	− 14.6186i	− 0.659058i
$493$	− 1.65983i	− 0.0747548i
$494$	63.0843	2.83830
$495$	0	0
$496$	21.5936	0.969579
$497$	− 6.63090i	− 0.297436i
$498$	25.3607i	1.13644i
$499$	−23.0878	−1.03355	−0.516777	−	0.856120i	$-0.672868\pi$
$499$	−23.0878	−1.03355	−0.516777	+	0.856120i	$0.672868\pi$
$500$	0	0
$501$	−8.35246	−0.373160
$502$	15.3112i	0.683374i
$503$	− 5.62475i	− 0.250795i	−0.992107	−	0.125398i	$-0.959979\pi$
$503$	− 5.62475i	− 0.250795i	0.992107	−	0.125398i	$-0.0400207\pi$
$504$	−0.0555914	−0.00247624
$505$	0	0
$506$	−2.27739	−0.101242
$507$	− 6.21008i	− 0.275799i
$508$	2.78765i	0.123682i
$509$	19.5525	0.866650	0.433325	−	0.901238i	$-0.357340\pi$
$509$	19.5525	0.866650	0.433325	+	0.901238i	$0.357340\pi$
$510$	0	0
$511$	0.254607	0.0112632
$512$	22.1701i	0.979789i
$513$	− 37.5052i	− 1.65589i
$514$	−7.07838	−0.312214
$515$	0	0
$516$	15.6020	0.686838
$517$	1.13170i	0.0497722i
$518$	5.12783i	0.225304i
$519$	−1.26180	−0.0553867
$520$	0	0
$521$	16.7442	0.733575	0.366788	−	0.930305i	$-0.380458\pi$
$521$	16.7442	0.733575	0.366788	+	0.930305i	$0.380458\pi$
$522$	− 0.447480i	− 0.0195857i
$523$	1.69982i	0.0743279i	0.999309	+	0.0371640i	$0.0118324\pi$
$523$	1.69982i	0.0743279i	−0.999309	+	0.0371640i	$0.988168\pi$
$524$	−6.63090	−0.289672
$525$	0	0
$526$	−44.6453	−1.94663
$527$	− 6.55479i	− 0.285531i
$528$	− 21.9194i	− 0.953917i
$529$	22.9711	0.998742
$530$	0	0
$531$	−0.139549	−0.00605590
$532$	− 8.89884i	− 0.385813i
$533$	12.8744i	0.557654i
$534$	16.6803	0.721829
$535$	0	0
$536$	−13.1750	−0.569074
$537$	− 3.24951i	− 0.140227i
$538$	8.62249i	0.371742i
$539$	41.8804	1.80392
$540$	0	0
$541$	13.3074	0.572128	0.286064	−	0.958210i	$-0.407653\pi$
$541$	13.3074	0.572128	0.286064	+	0.958210i	$0.407653\pi$
$542$	− 10.8455i	− 0.465855i
$543$	− 36.5113i	− 1.56685i
$544$	4.78765	0.205269
$545$	0	0
$546$	−6.97107	−0.298334
$547$	− 24.2690i	− 1.03767i	−0.854875	−	0.518833i	$-0.826366\pi$
$547$	− 24.2690i	− 1.03767i	0.854875	−	0.518833i	$-0.173634\pi$
$548$	43.5380i	1.85985i
$549$	0.0783777	0.00334508
$550$	0	0
$551$	18.7526	0.798887
$552$	0.447480i	0.0190460i
$553$	− 3.22899i	− 0.137311i
$554$	−38.9854	−1.65633
$555$	0	0
$556$	−4.17009	−0.176851
$557$	1.36069i	0.0576544i	0.999584	+	0.0288272i	$0.00917725\pi$
$557$	1.36069i	0.0576544i	−0.999584	+	0.0288272i	$0.990823\pi$
$558$	− 1.76713i	− 0.0748088i
$559$	−13.7405	−0.581160
$560$	0	0
$561$	−6.65368	−0.280919
$562$	33.8576i	1.42820i
$563$	− 14.4885i	− 0.610618i	−0.952253	−	0.305309i	$-0.901240\pi$
$563$	− 14.4885i	− 0.610618i	0.952253	−	0.305309i	$-0.0987598\pi$
$564$	0.849388	0.0357657
$565$	0	0
$566$	53.6658	2.25574
$567$	4.03612i	0.169501i
$568$	− 22.1483i	− 0.929324i
$569$	3.78765	0.158787	0.0793933	−	0.996843i	$-0.474702\pi$
$569$	3.78765	0.158787	0.0793933	+	0.996843i	$0.474702\pi$
$570$	0	0
$571$	−3.87444	−0.162140	−0.0810702	−	0.996708i	$-0.525834\pi$
$571$	−3.87444	−0.162140	−0.0810702	+	0.996708i	$0.525834\pi$
$572$	− 68.1761i	− 2.85058i
$573$	4.93212i	0.206042i
$574$	3.15676	0.131760
$575$	0	0
$576$	0.964928	0.0402053
$577$	− 23.9071i	− 0.995264i	−0.867388	−	0.497632i	$-0.834203\pi$
$577$	− 23.9071i	− 0.995264i	0.867388	−	0.497632i	$-0.165797\pi$
$578$	36.0277i	1.49856i
$579$	1.16290	0.0483284
$580$	0	0
$581$	−3.15061	−0.130709
$582$	− 31.6163i	− 1.31054i
$583$	26.7792i	1.10908i
$584$	0.850432	0.0351911
$585$	0	0
$586$	52.4534	2.16683
$587$	12.3318i	0.508986i	0.967075	+	0.254493i	$0.0819086\pi$
$587$	12.3318i	0.508986i	−0.967075	+	0.254493i	$0.918091\pi$
$588$	− 31.4329i	− 1.29627i
$589$	74.0554	3.05140
$590$	0	0
$591$	33.1422	1.36329
$592$	− 10.6576i	− 0.438023i
$593$	− 11.1278i	− 0.456965i	−0.973548	−	0.228483i	$-0.926624\pi$
$593$	− 11.1278i	− 0.456965i	0.973548	−	0.228483i	$-0.0733764\pi$
$594$	−70.4534	−2.89074
$595$	0	0
$596$	5.20620	0.213254
$597$	36.6102i	1.49836i
$598$	− 1.50534i	− 0.0615579i
$599$	−23.0878	−0.943343	−0.471672	−	0.881774i	$-0.656349\pi$
$599$	−23.0878	−0.943343	−0.471672	+	0.881774i	$0.656349\pi$
$600$	0	0
$601$	−10.3340	−0.421534	−0.210767	−	0.977536i	$-0.567596\pi$
$601$	−10.3340	−0.421534	−0.210767	+	0.977536i	$0.567596\pi$
$602$	3.36910i	0.137314i
$603$	− 0.670891i	− 0.0273208i
$604$	−25.2628	−1.02793
$605$	0	0
$606$	25.1773	1.02276
$607$	− 24.8371i	− 1.00811i	−0.863672	−	0.504053i	$-0.831841\pi$
$607$	− 24.8371i	− 1.00811i	0.863672	−	0.504053i	$-0.168159\pi$
$608$	54.0905i	2.19366i
$609$	−2.07223	−0.0839712
$610$	0	0
$611$	−0.748046	−0.0302627
$612$	− 0.133969i	− 0.00541538i
$613$	23.9877i	0.968855i	0.874832	+	0.484427i	$0.160972\pi$
$613$	23.9877i	0.968855i	−0.874832	+	0.484427i	$0.839028\pi$
$614$	−42.3256	−1.70812
$615$	0	0
$616$	−4.37629	−0.176326
$617$	21.6020i	0.869662i	0.900512	+	0.434831i	$0.143192\pi$
$617$	21.6020i	0.869662i	−0.900512	+	0.434831i	$0.856808\pi$
$618$	41.2762i	1.66037i
$619$	46.2388	1.85850	0.929248	−	0.369457i	$-0.120456\pi$
$619$	46.2388	1.85850	0.929248	+	0.369457i	$0.120456\pi$
$620$	0	0
$621$	−0.894960	−0.0359135
$622$	18.1278i	0.726860i
$623$	2.07223i	0.0830223i
$624$	14.4885	0.580005
$625$	0	0
$626$	4.55479	0.182046
$627$	− 75.1727i	− 3.00211i
$628$	36.5608i	1.45893i
$629$	−3.23513	−0.128993
$630$	0	0
$631$	33.2628	1.32417	0.662086	−	0.749428i	$-0.269671\pi$
$631$	33.2628	1.32417	0.662086	+	0.749428i	$0.269671\pi$
$632$	− 10.7854i	− 0.429020i
$633$	9.22285i	0.366575i
$634$	−60.2388	−2.39239
$635$	0	0
$636$	20.0989	0.796973
$637$	27.6826i	1.09683i
$638$	− 35.2267i	− 1.39464i
$639$	1.12783	0.0446161
$640$	0	0
$641$	33.7009	1.33110	0.665552	−	0.746351i	$-0.268196\pi$
$641$	33.7009	1.33110	0.665552	+	0.746351i	$0.268196\pi$
$642$	− 57.7731i	− 2.28012i
$643$	6.97107i	0.274912i	0.990508	+	0.137456i	$0.0438926\pi$
$643$	6.97107i	0.274912i	−0.990508	+	0.137456i	$0.956107\pi$
$644$	−0.212347	−0.00836764
$645$	0	0
$646$	9.75872	0.383952
$647$	− 16.0049i	− 0.629218i	−0.949221	−	0.314609i	$-0.898127\pi$
$647$	− 16.0049i	− 0.629218i	0.949221	−	0.314609i	$-0.101873\pi$
$648$	13.4813i	0.529597i
$649$	−10.9856	−0.431223
$650$	0	0
$651$	−8.18342	−0.320733
$652$	− 28.9977i	− 1.13564i
$653$	− 43.2762i	− 1.69353i	−0.531969	−	0.846764i	$-0.678548\pi$
$653$	− 43.2762i	− 1.69353i	0.531969	−	0.846764i	$-0.321452\pi$
$654$	43.3256	1.69417
$655$	0	0
$656$	−6.56093	−0.256161
$657$	0.0433053i	0.00168950i
$658$	0.183417i	0.00715036i
$659$	16.9276	0.659405	0.329703	−	0.944085i	$-0.393052\pi$
$659$	16.9276	0.659405	0.329703	+	0.944085i	$0.393052\pi$
$660$	0	0
$661$	15.6781	0.609807	0.304903	−	0.952383i	$-0.401376\pi$
$661$	15.6781	0.609807	0.304903	+	0.952383i	$0.401376\pi$
$662$	− 2.60197i	− 0.101128i
$663$	− 4.39803i	− 0.170805i
$664$	−10.5236	−0.408395
$665$	0	0
$666$	−0.872174	−0.0337961
$667$	− 0.447480i	− 0.0173265i
$668$	− 13.2390i	− 0.512233i
$669$	21.2390	0.821148
$670$	0	0
$671$	6.17009	0.238194
$672$	− 5.97721i	− 0.230576i
$673$	50.6330i	1.95176i	0.218312	+	0.975879i	$0.429945\pi$
$673$	50.6330i	1.95176i	−0.218312	+	0.975879i	$0.570055\pi$
$674$	−45.5006	−1.75262
$675$	0	0
$676$	9.84324	0.378586
$677$	38.1711i	1.46704i	0.679670	+	0.733518i	$0.262123\pi$
$677$	38.1711i	1.46704i	−0.679670	+	0.733518i	$0.737877\pi$
$678$	− 48.0060i	− 1.84366i
$679$	3.92777	0.150734
$680$	0	0
$681$	38.2329	1.46509
$682$	− 139.113i	− 5.32692i
$683$	− 36.6309i	− 1.40164i	−0.713337	−	0.700821i	$-0.752817\pi$
$683$	− 36.6309i	− 1.40164i	0.713337	−	0.700821i	$-0.247183\pi$
$684$	1.51357	0.0578729
$685$	0	0
$686$	13.7877	0.526415
$687$	0.317387i	0.0121091i
$688$	− 7.00227i	− 0.266959i
$689$	−17.7009	−0.674349
$690$	0	0
$691$	−17.4764	−0.664834	−0.332417	−	0.943133i	$-0.607864\pi$
$691$	−17.4764	−0.664834	−0.332417	+	0.943133i	$0.607864\pi$
$692$	− 2.00000i	− 0.0760286i
$693$	− 0.222847i	− 0.00846526i
$694$	−44.2472	−1.67960
$695$	0	0
$696$	−6.92162	−0.262363
$697$	1.99159i	0.0754368i
$698$	16.6042i	0.628480i
$699$	−30.5380	−1.15505
$700$	0	0
$701$	−9.83096	−0.371310	−0.185655	−	0.982615i	$-0.559441\pi$
$701$	−9.83096	−0.371310	−0.185655	+	0.982615i	$0.559441\pi$
$702$	− 46.5692i	− 1.75764i
$703$	− 36.5503i	− 1.37852i
$704$	75.9614	2.86290
$705$	0	0
$706$	−42.6996	−1.60702
$707$	3.12783i	0.117634i
$708$	8.24515i	0.309872i
$709$	−35.9214	−1.34906	−0.674529	−	0.738248i	$-0.735653\pi$
$709$	−35.9214	−1.34906	−0.674529	+	0.738248i	$0.735653\pi$
$710$	0	0
$711$	0.549208	0.0205969
$712$	6.92162i	0.259399i
$713$	− 1.76713i	− 0.0661797i
$714$	−1.07838	−0.0403573
$715$	0	0
$716$	5.15061	0.192487
$717$	38.2700i	1.42922i
$718$	− 45.2678i	− 1.68938i
$719$	20.3773	0.759946	0.379973	−	0.924998i	$-0.375933\pi$
$719$	20.3773	0.759946	0.379973	+	0.924998i	$0.375933\pi$
$720$	0	0
$721$	−5.12783	−0.190970
$722$	69.0216i	2.56872i
$723$	34.2595i	1.27413i
$724$	57.8720	2.15080
$725$	0	0
$726$	−100.410	−3.72656
$727$	30.0722i	1.11532i	0.830070	+	0.557659i	$0.188300\pi$
$727$	30.0722i	1.11532i	−0.830070	+	0.557659i	$0.811700\pi$
$728$	− 2.89269i	− 0.107210i
$729$	−27.6681	−1.02474
$730$	0	0
$731$	−2.12556	−0.0786166
$732$	− 4.63090i	− 0.171163i
$733$	− 1.44360i	− 0.0533207i	−0.999645	−	0.0266604i	$-0.991513\pi$
$733$	− 1.44360i	− 0.0533207i	0.999645	−	0.0266604i	$-0.00848727\pi$
$734$	11.5441	0.426101
$735$	0	0
$736$	1.29072	0.0475767
$737$	− 52.8141i	− 1.94543i
$738$	0.536921i	0.0197644i
$739$	16.1122	0.592698	0.296349	−	0.955080i	$-0.404231\pi$
$739$	16.1122	0.592698	0.296349	+	0.955080i	$0.404231\pi$
$740$	0	0
$741$	49.6886	1.82536
$742$	4.34017i	0.159333i
$743$	− 37.1100i	− 1.36143i	−0.732547	−	0.680716i	$-0.761669\pi$
$743$	− 37.1100i	− 1.36143i	0.732547	−	0.680716i	$-0.238331\pi$
$744$	−27.3340	−1.00211
$745$	0	0
$746$	−43.5981	−1.59624
$747$	− 0.535877i	− 0.0196067i
$748$	− 10.5464i	− 0.385614i
$749$	7.17727	0.262252
$750$	0	0
$751$	15.6430	0.570821	0.285411	−	0.958405i	$-0.407870\pi$
$751$	15.6430	0.570821	0.285411	+	0.958405i	$0.407870\pi$
$752$	− 0.381211i	− 0.0139013i
$753$	12.0599i	0.439489i
$754$	23.2846	0.847974
$755$	0	0
$756$	−6.56916	−0.238918
$757$	− 41.3728i	− 1.50372i	−0.659323	−	0.751860i	$-0.729157\pi$
$757$	− 41.3728i	− 1.50372i	0.659323	−	0.751860i	$-0.270843\pi$
$758$	57.2990i	2.08119i
$759$	−1.79380	−0.0651107
$760$	0	0
$761$	−39.4947	−1.43168	−0.715840	−	0.698264i	$-0.753956\pi$
$761$	−39.4947	−1.43168	−0.715840	+	0.698264i	$0.753956\pi$
$762$	3.81658i	0.138260i
$763$	5.38243i	0.194857i
$764$	−7.81763	−0.282832
$765$	0	0
$766$	−23.7298	−0.857392
$767$	− 7.26141i	− 0.262194i
$768$	− 0.715418i	− 0.0258154i
$769$	34.7031	1.25143	0.625713	−	0.780053i	$-0.284808\pi$
$769$	34.7031	1.25143	0.625713	+	0.780053i	$0.284808\pi$
$770$	0	0
$771$	−5.57531	−0.200790
$772$	1.84324i	0.0663398i
$773$	− 3.34632i	− 0.120359i	−0.998188	−	0.0601793i	$-0.980833\pi$
$773$	− 3.34632i	− 0.120359i	0.998188	−	0.0601793i	$-0.0191673\pi$
$774$	−0.573039	−0.0205975
$775$	0	0
$776$	13.1194	0.470960
$777$	4.03895i	0.144896i
$778$	11.9421i	0.428147i
$779$	−22.5008	−0.806175
$780$	0	0
$781$	88.7852	3.17698
$782$	− 0.232866i	− 0.00832726i
$783$	− 13.8432i	− 0.494717i
$784$	−14.1073	−0.503832
$785$	0	0
$786$	−9.07838	−0.323815
$787$	− 32.0950i	− 1.14406i	−0.820231	−	0.572032i	$-0.806155\pi$
$787$	− 32.0950i	− 1.14406i	0.820231	−	0.572032i	$-0.193845\pi$
$788$	52.5318i	1.87137i
$789$	−35.1650	−1.25191
$790$	0	0
$791$	5.96388	0.212051
$792$	− 0.744348i	− 0.0264492i
$793$	4.07838i	0.144827i
$794$	−32.0228	−1.13645
$795$	0	0
$796$	−58.0288	−2.05677
$797$	38.3979i	1.36012i	0.733156	+	0.680061i	$0.238047\pi$
$797$	38.3979i	1.36012i	−0.733156	+	0.680061i	$0.761953\pi$
$798$	− 12.1834i	− 0.431288i
$799$	−0.115718	−0.00409380
$800$	0	0
$801$	−0.352459	−0.0124535
$802$	− 38.5380i	− 1.36082i
$803$	3.40910i	0.120304i
$804$	−39.6391	−1.39796
$805$	0	0
$806$	91.9526	3.23889
$807$	6.79153i	0.239073i
$808$	10.4475i	0.367541i
$809$	22.0577	0.775507	0.387753	−	0.921763i	$-0.373251\pi$
$809$	22.0577	0.775507	0.387753	+	0.921763i	$0.373251\pi$
$810$	0	0
$811$	−31.1100	−1.09242	−0.546209	−	0.837649i	$-0.683930\pi$
$811$	−31.1100	−1.09242	−0.546209	+	0.837649i	$0.683930\pi$
$812$	− 3.28458i	− 0.115266i
$813$	− 8.54250i	− 0.299599i
$814$	−68.6596	−2.40652
$815$	0	0
$816$	2.24128	0.0784604
$817$	− 24.0144i	− 0.840157i
$818$	35.6742i	1.24732i
$819$	0.147300	0.00514708
$820$	0	0
$821$	−35.4641	−1.23771	−0.618853	−	0.785507i	$-0.712402\pi$
$821$	−35.4641	−1.23771	−0.618853	+	0.785507i	$0.712402\pi$
$822$	59.6079i	2.07907i
$823$	4.89884i	0.170763i	0.996348	+	0.0853813i	$0.0272109\pi$
$823$	4.89884i	0.170763i	−0.996348	+	0.0853813i	$0.972789\pi$
$824$	−17.1278	−0.596676
$825$	0	0
$826$	−1.78047	−0.0619503
$827$	13.9506i	0.485108i	0.970138	+	0.242554i	$0.0779852\pi$
$827$	13.9506i	0.485108i	−0.970138	+	0.242554i	$0.922015\pi$
$828$	− 0.0361173i	− 0.00125516i
$829$	−42.4863	−1.47561	−0.737804	−	0.675015i	$-0.764137\pi$
$829$	−42.4863	−1.47561	−0.737804	+	0.675015i	$0.764137\pi$
$830$	0	0
$831$	−30.7070	−1.06521
$832$	50.2099i	1.74072i
$833$	4.28231i	0.148373i
$834$	−5.70928	−0.197696
$835$	0	0
$836$	119.152	4.12096
$837$	− 54.6681i	− 1.88960i
$838$	− 69.4824i	− 2.40023i
$839$	11.9421	0.412288	0.206144	−	0.978522i	$-0.433908\pi$
$839$	11.9421	0.412288	0.206144	+	0.978522i	$0.433908\pi$
$840$	0	0
$841$	−22.0784	−0.761323
$842$	− 1.36910i	− 0.0471824i
$843$	26.6681i	0.918497i
$844$	−14.6186	−0.503193
$845$	0	0
$846$	−0.0311968	−0.00107257
$847$	− 12.4741i	− 0.428617i
$848$	− 9.02052i	− 0.309766i
$849$	42.2700	1.45070
$850$	0	0
$851$	−0.872174	−0.0298977
$852$	− 66.6369i	− 2.28294i
$853$	− 16.2800i	− 0.557418i	−0.960376	−	0.278709i	$-0.910093\pi$
$853$	− 16.2800i	− 0.557418i	0.960376	−	0.278709i	$-0.0899065\pi$
$854$	1.00000	0.0342193
$855$	0	0
$856$	23.9733	0.819392
$857$	26.2085i	0.895264i	0.894218	+	0.447632i	$0.147733\pi$
$857$	26.2085i	0.895264i	−0.894218	+	0.447632i	$0.852267\pi$
$858$	− 93.3400i	− 3.18657i
$859$	0.0350725	0.00119666	0.000598329	−	1.00000i	$-0.499810\pi$
$859$	0.0350725	0.00119666	0.000598329		1.00000i	$0.499810\pi$
$860$	0	0
$861$	2.48643	0.0847372
$862$	− 36.0722i	− 1.22863i
$863$	− 10.8515i	− 0.369389i	−0.982796	−	0.184694i	$-0.940871\pi$
$863$	− 10.8515i	− 0.369389i	0.982796	−	0.184694i	$-0.0591295\pi$
$864$	39.9299	1.35844
$865$	0	0
$866$	−44.4801	−1.51150
$867$	28.3773i	0.963745i
$868$	− 12.9711i	− 0.440267i
$869$	43.2350	1.46665
$870$	0	0
$871$	34.9097	1.18287
$872$	17.9783i	0.608821i
$873$	0.668060i	0.0226104i
$874$	2.63090	0.0889914
$875$	0	0
$876$	2.55866	0.0864492
$877$	0.665970i	0.0224882i	0.999937	+	0.0112441i	$0.00357919\pi$
$877$	0.665970i	0.0224882i	−0.999937	+	0.0112441i	$0.996421\pi$
$878$	5.09663i	0.172003i
$879$	41.3151	1.39352
$880$	0	0
$881$	14.4101	0.485490	0.242745	−	0.970090i	$-0.421952\pi$
$881$	14.4101	0.485490	0.242745	+	0.970090i	$0.421952\pi$
$882$	1.15449i	0.0388736i
$883$	− 57.8937i	− 1.94828i	−0.225947	−	0.974140i	$-0.572547\pi$
$883$	− 57.8937i	− 1.94828i	0.225947	−	0.974140i	$-0.427453\pi$
$884$	6.97107	0.234462
$885$	0	0
$886$	36.0144	1.20993
$887$	− 38.4040i	− 1.28948i	−0.764402	−	0.644740i	$-0.776966\pi$
$887$	− 38.4040i	− 1.28948i	0.764402	−	0.644740i	$-0.223034\pi$
$888$	13.4908i	0.452721i
$889$	−0.474142	−0.0159022
$890$	0	0
$891$	−54.0421	−1.81048
$892$	33.6647i	1.12718i
$893$	− 1.30737i	− 0.0437494i
$894$	7.12783	0.238390
$895$	0	0
$896$	5.31739	0.177641
$897$	− 1.18568i	− 0.0395889i
$898$	44.4173i	1.48223i
$899$	27.3340	0.911641
$900$	0	0
$901$	−2.73820	−0.0912228
$902$	42.2678i	1.40736i
$903$	2.65368i	0.0883091i
$904$	19.9204	0.662543
$905$	0	0
$906$	−34.5874	−1.14909
$907$	− 42.6407i	− 1.41586i	−0.706281	−	0.707931i	$-0.749629\pi$
$907$	− 42.6407i	− 1.41586i	0.706281	−	0.707931i	$-0.250371\pi$
$908$	60.6007i	2.01111i
$909$	−0.532001	−0.0176454
$910$	0	0
$911$	18.6042	0.616386	0.308193	−	0.951324i	$-0.400276\pi$
$911$	18.6042	0.616386	0.308193	+	0.951324i	$0.400276\pi$
$912$	25.3217i	0.838487i
$913$	− 42.1855i	− 1.39614i
$914$	−51.9748	−1.71917
$915$	0	0
$916$	−0.503072	−0.0166220
$917$	− 1.12783i	− 0.0372441i
$918$	− 7.20394i	− 0.237765i
$919$	−33.2306	−1.09618	−0.548088	−	0.836421i	$-0.684644\pi$
$919$	−33.2306	−1.09618	−0.548088	+	0.836421i	$0.684644\pi$
$920$	0	0
$921$	−33.3379	−1.09852
$922$	− 57.5318i	− 1.89471i
$923$	58.6863i	1.93168i
$924$	−13.1668	−0.433155
$925$	0	0
$926$	73.8720	2.42758
$927$	− 0.872174i	− 0.0286460i
$928$	19.9649i	0.655381i
$929$	−13.0989	−0.429761	−0.214880	−	0.976640i	$-0.568936\pi$
$929$	−13.0989	−0.429761	−0.214880	+	0.976640i	$0.568936\pi$
$930$	0	0
$931$	−48.3812	−1.58563
$932$	− 48.4040i	− 1.58553i
$933$	14.2784i	0.467455i
$934$	−9.89496	−0.323773
$935$	0	0
$936$	0.492008	0.0160818
$937$	− 21.0144i	− 0.686510i	−0.939242	−	0.343255i	$-0.888471\pi$
$937$	− 21.0144i	− 0.686510i	0.939242	−	0.343255i	$-0.111529\pi$
$938$	− 8.55971i	− 0.279484i
$939$	3.58759	0.117077
$940$	0	0
$941$	−37.3523	−1.21765	−0.608825	−	0.793305i	$-0.708359\pi$
$941$	−37.3523	−1.21765	−0.608825	+	0.793305i	$0.708359\pi$
$942$	50.0554i	1.63089i
$943$	0.536921i	0.0174846i
$944$	3.70048	0.120440
$945$	0	0
$946$	−45.1110	−1.46669
$947$	− 32.2729i	− 1.04873i	−0.851495	−	0.524363i	$-0.824303\pi$
$947$	− 32.2729i	− 1.04873i	0.851495	−	0.524363i	$-0.175697\pi$
$948$	− 32.4496i	− 1.05391i
$949$	−2.25338	−0.0731480
$950$	0	0
$951$	−47.4473	−1.53858
$952$	− 0.447480i	− 0.0145029i
$953$	− 51.3400i	− 1.66307i	−0.555476	−	0.831533i	$-0.687464\pi$
$953$	− 51.3400i	− 1.66307i	0.555476	−	0.831533i	$-0.312536\pi$
$954$	−0.738205	−0.0239003
$955$	0	0
$956$	−60.6596	−1.96187
$957$	− 27.7464i	− 0.896915i
$958$	1.41855i	0.0458313i
$959$	−7.40522	−0.239127
$960$	0	0
$961$	76.9442	2.48207
$962$	− 45.3835i	− 1.46322i
$963$	1.22076i	0.0393384i
$964$	−54.3028	−1.74898
$965$	0	0
$966$	−0.290725	−0.00935391
$967$	− 0.746615i	− 0.0240095i	−0.999928	−	0.0120048i	$-0.996179\pi$
$967$	− 0.746615i	− 0.0240095i	0.999928	−	0.0120048i	$-0.00382133\pi$
$968$	− 41.6658i	− 1.33919i
$969$	7.68649	0.246926
$970$	0	0
$971$	58.1276	1.86541	0.932703	−	0.360647i	$-0.117444\pi$
$971$	58.1276	1.86541	0.932703	+	0.360647i	$0.117444\pi$
$972$	− 2.20620i	− 0.0707640i
$973$	− 0.709275i	− 0.0227383i
$974$	0.0494483	0.00158443
$975$	0	0
$976$	−2.07838	−0.0665273
$977$	6.86376i	0.219591i	0.993954	+	0.109796i	$0.0350196\pi$
$977$	6.86376i	0.219591i	−0.993954	+	0.109796i	$0.964980\pi$
$978$	− 39.7009i	− 1.26949i
$979$	−27.7464	−0.886780
$980$	0	0
$981$	−0.915479	−0.0292290
$982$	− 6.38962i	− 0.203901i
$983$	27.8660i	0.888788i	0.895831	+	0.444394i	$0.146581\pi$
$983$	27.8660i	0.888788i	−0.895831	+	0.444394i	$0.853419\pi$
$984$	8.30510	0.264757
$985$	0	0
$986$	3.60197	0.114710
$987$	0.144469i	0.00459851i
$988$	78.7585i	2.50564i
$989$	−0.573039	−0.0182216
$990$	0	0
$991$	−20.0312	−0.636312	−0.318156	−	0.948038i	$-0.603064\pi$
$991$	−20.0312	−0.636312	−0.318156	+	0.948038i	$0.603064\pi$
$992$	78.8431i	2.50327i
$993$	− 2.04945i	− 0.0650373i
$994$	14.3896	0.456411
$995$	0	0
$996$	−31.6619	−1.00325
$997$	0.500804i	0.0158606i	0.999969	+	0.00793031i	$0.00252432\pi$
$997$	0.500804i	0.0158606i	−0.999969	+	0.00793031i	$0.997476\pi$
$998$	− 50.1026i	− 1.58597i
$999$	−26.9816	−0.853659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1525.2.b.b.1099.6		6
5.2	odd	4		1525.2.a.d.1.1		3
5.3	odd	4		61.2.a.b.1.3	✓	3
5.4	even	2	inner	1525.2.b.b.1099.1		6
15.8	even	4		549.2.a.g.1.1		3
20.3	even	4		976.2.a.f.1.3		3
35.13	even	4		2989.2.a.i.1.3		3
40.3	even	4		3904.2.a.w.1.1		3
40.13	odd	4		3904.2.a.r.1.3		3
55.43	even	4		7381.2.a.f.1.1		3
60.23	odd	4		8784.2.a.bn.1.2		3
305.243	odd	4		3721.2.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.a.b.1.3	✓	3	5.3	odd	4
549.2.a.g.1.1		3	15.8	even	4
976.2.a.f.1.3		3	20.3	even	4
1525.2.a.d.1.1		3	5.2	odd	4
1525.2.b.b.1099.1		6	5.4	even	2	inner
1525.2.b.b.1099.6		6	1.1	even	1	trivial
2989.2.a.i.1.3		3	35.13	even	4
3721.2.a.c.1.1		3	305.243	odd	4
3904.2.a.r.1.3		3	40.13	odd	4
3904.2.a.w.1.1		3	40.3	even	4
7381.2.a.f.1.1		3	55.43	even	4
8784.2.a.bn.1.2		3	60.23	odd	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:	\( N \)	\(=\)	\( 1525 = 5^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1525.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.17009i q^{2} +1.70928i q^{3} -2.70928 q^{4} -3.70928 q^{6} -0.460811i q^{7} -1.53919i q^{8} +0.0783777 q^{9} +O(q^{10})\)	\(q+2.17009i q^{2} +1.70928i q^{3} -2.70928 q^{4} -3.70928 q^{6} -0.460811i q^{7} -1.53919i q^{8} +0.0783777 q^{9} +6.17009 q^{11} -4.63090i q^{12} +4.07838i q^{13} +1.00000 q^{14} -2.07838 q^{16} +0.630898i q^{17} +0.170086i q^{18} -7.12783 q^{19} +0.787653 q^{21} +13.3896i q^{22} +0.170086i q^{23} +2.63090 q^{24} -8.85043 q^{26} +5.26180i q^{27} +1.24846i q^{28} -2.63090 q^{29} -10.3896 q^{31} -7.58864i q^{32} +10.5464i q^{33} -1.36910 q^{34} -0.212347 q^{36} +5.12783i q^{37} -15.4680i q^{38} -6.97107 q^{39} +3.15676 q^{41} +1.70928i q^{42} +3.36910i q^{43} -16.7165 q^{44} -0.369102 q^{46} +0.183417i q^{47} -3.55252i q^{48} +6.78765 q^{49} -1.07838 q^{51} -11.0494i q^{52} +4.34017i q^{53} -11.4186 q^{54} -0.709275 q^{56} -12.1834i q^{57} -5.70928i q^{58} -1.78047 q^{59} +1.00000 q^{61} -22.5464i q^{62} -0.0361173i q^{63} +12.3112 q^{64} -22.8865 q^{66} -8.55971i q^{67} -1.70928i q^{68} -0.290725 q^{69} +14.3896 q^{71} -0.120638i q^{72} +0.552520i q^{73} -11.1278 q^{74} +19.3112 q^{76} -2.84324i q^{77} -15.1278i q^{78} +7.00719 q^{79} -8.75872 q^{81} +6.85043i q^{82} -6.83710i q^{83} -2.13397 q^{84} -7.31124 q^{86} -4.49693i q^{87} -9.49693i q^{88} -4.49693 q^{89} +1.87936 q^{91} -0.460811i q^{92} -17.7587i q^{93} -0.398032 q^{94} +12.9711 q^{96} +8.52359i q^{97} +14.7298i q^{98} +0.483597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} - 8 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^4 - 8 * q^6 - 6 * q^9	\( 6 q - 2 q^{4} - 8 q^{6} - 6 q^{9} + 26 q^{11} + 6 q^{14} - 6 q^{16} - 16 q^{21} + 8 q^{24} + 2 q^{26} - 8 q^{29} - 4 q^{31} - 16 q^{34} - 22 q^{36} - 12 q^{39} + 6 q^{41} - 18 q^{44} - 10 q^{46} + 20 q^{49} - 40 q^{54} + 10 q^{56} - 58 q^{59} + 6 q^{61} + 22 q^{64} - 44 q^{66} - 16 q^{69} + 28 q^{71} - 24 q^{74} + 64 q^{76} - 26 q^{79} - 2 q^{81} - 40 q^{84} + 8 q^{86} + 8 q^{89} - 14 q^{91} - 40 q^{94} + 48 q^{96} - 34 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 - 8 * q^6 - 6 * q^9 + 26 * q^11 + 6 * q^14 - 6 * q^16 - 16 * q^21 + 8 * q^24 + 2 * q^26 - 8 * q^29 - 4 * q^31 - 16 * q^34 - 22 * q^36 - 12 * q^39 + 6 * q^41 - 18 * q^44 - 10 * q^46 + 20 * q^49 - 40 * q^54 + 10 * q^56 - 58 * q^59 + 6 * q^61 + 22 * q^64 - 44 * q^66 - 16 * q^69 + 28 * q^71 - 24 * q^74 + 64 * q^76 - 26 * q^79 - 2 * q^81 - 40 * q^84 + 8 * q^86 + 8 * q^89 - 14 * q^91 - 40 * q^94 + 48 * q^96 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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