LMFDB - Embedded newform 1925.2.b.n.1849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1849,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1925.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 385)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.2
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1925.1849
Dual form			1925.2.b.n.1849.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53919i q^{2} -1.17009i q^{3} -0.369102 q^{4} -1.80098 q^{6} -1.00000i q^{7} -2.51026i q^{8} +1.63090 q^{9} +O(q^{10})$	\(q-1.53919i q^{2} -1.17009i q^{3} -0.369102 q^{4} -1.80098 q^{6} -1.00000i q^{7} -2.51026i q^{8} +1.63090 q^{9} -1.00000 q^{11} +0.431882i q^{12} +0.0917087i q^{13} -1.53919 q^{14} -4.60197 q^{16} -5.51026i q^{17} -2.51026i q^{18} -0.921622 q^{19} -1.17009 q^{21} +1.53919i q^{22} +5.70928i q^{23} -2.93722 q^{24} +0.141157 q^{26} -5.41855i q^{27} +0.369102i q^{28} -1.41855 q^{29} +0.879362 q^{31} +2.06278i q^{32} +1.17009i q^{33} -8.48133 q^{34} -0.601968 q^{36} -8.78765i q^{37} +1.41855i q^{38} +0.107307 q^{39} -1.61757 q^{41} +1.80098i q^{42} -3.86603i q^{43} +0.369102 q^{44} +8.78765 q^{46} -5.90829i q^{47} +5.38470i q^{48} -1.00000 q^{49} -6.44748 q^{51} -0.0338499i q^{52} +10.0494i q^{53} -8.34017 q^{54} -2.51026 q^{56} +1.07838i q^{57} +2.18342i q^{58} +2.14116 q^{59} -3.03612 q^{61} -1.35350i q^{62} -1.63090i q^{63} -6.02893 q^{64} +1.80098 q^{66} -1.52586i q^{67} +2.03385i q^{68} +6.68035 q^{69} +4.09890 q^{71} -4.09398i q^{72} -14.1906i q^{73} -13.5259 q^{74} +0.340173 q^{76} +1.00000i q^{77} -0.165166i q^{78} -14.5464 q^{79} -1.44748 q^{81} +2.48974i q^{82} +8.52359i q^{83} +0.431882 q^{84} -5.95055 q^{86} +1.65983i q^{87} +2.51026i q^{88} +2.83710 q^{89} +0.0917087 q^{91} -2.10731i q^{92} -1.02893i q^{93} -9.09398 q^{94} +2.41363 q^{96} +14.2557i q^{97} +1.53919i q^{98} -1.63090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9	$ 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9} - 6 q^{11} - 6 q^{14} + 10 q^{16} - 12 q^{19} + 4 q^{21} - 52 q^{24} - 40 q^{26} + 20 q^{29} - 20 q^{31} + 12 q^{34} + 34 q^{36} + 24 q^{39} + 10 q^{44} + 32 q^{46} - 6 q^{49} - 40 q^{51} - 28 q^{54} + 18 q^{56} - 28 q^{59} + 20 q^{61} - 66 q^{64} - 8 q^{66} - 4 q^{69} - 48 q^{71} - 76 q^{74} - 20 q^{76} - 16 q^{79} - 10 q^{81} - 24 q^{84} - 72 q^{86} - 40 q^{89} - 4 q^{91} - 76 q^{94} + 80 q^{96} - 2 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9 - 6 * q^11 - 6 * q^14 + 10 * q^16 - 12 * q^19 + 4 * q^21 - 52 * q^24 - 40 * q^26 + 20 * q^29 - 20 * q^31 + 12 * q^34 + 34 * q^36 + 24 * q^39 + 10 * q^44 + 32 * q^46 - 6 * q^49 - 40 * q^51 - 28 * q^54 + 18 * q^56 - 28 * q^59 + 20 * q^61 - 66 * q^64 - 8 * q^66 - 4 * q^69 - 48 * q^71 - 76 * q^74 - 20 * q^76 - 16 * q^79 - 10 * q^81 - 24 * q^84 - 72 * q^86 - 40 * q^89 - 4 * q^91 - 76 * q^94 + 80 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1925\mathbb{Z}\right)^\times$.

$n$	$276$	$1002$	$1751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	− 1.53919i	− 1.08837i	−0.838965	−	0.544185i	$-0.816839\pi$
$2$	− 1.53919i	− 1.08837i	0.838965	−	0.544185i	$-0.183161\pi$
$3$	− 1.17009i	− 0.675550i	−0.941227	−	0.337775i	$-0.890326\pi$
$3$	− 1.17009i	− 0.675550i	0.941227	−	0.337775i	$-0.109674\pi$
$4$	−0.369102	−0.184551
$5$	0	0
$5$	0	0
$6$	−1.80098	−0.735249
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 2.51026i	− 0.887511i
$9$	1.63090	0.543633
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.431882i	0.124674i
$13$	0.0917087i	0.0254354i	0.999919	+	0.0127177i	$0.00404828\pi$
$13$	0.0917087i	0.0254354i	−0.999919	+	0.0127177i	$0.995952\pi$
$14$	−1.53919	−0.411366
$15$	0	0
$16$	−4.60197	−1.15049
$17$	− 5.51026i	− 1.33643i	−0.743966	−	0.668217i	$-0.767058\pi$
$17$	− 5.51026i	− 1.33643i	0.743966	−	0.668217i	$-0.232942\pi$
$18$	− 2.51026i	− 0.591674i
$19$	−0.921622	−0.211435	−0.105717	−	0.994396i	$-0.533714\pi$
$19$	−0.921622	−0.211435	−0.105717	+	0.994396i	$0.533714\pi$
$20$	0	0
$21$	−1.17009	−0.255334
$22$	1.53919i	0.328156i
$23$	5.70928i	1.19047i	0.803553	+	0.595233i	$0.202940\pi$
$23$	5.70928i	1.19047i	−0.803553	+	0.595233i	$0.797060\pi$
$24$	−2.93722	−0.599558
$25$	0	0
$26$	0.141157	0.0276832
$27$	− 5.41855i	− 1.04280i
$28$	0.369102i	0.0697538i
$29$	−1.41855	−0.263418	−0.131709	−	0.991288i	$-0.542046\pi$
$29$	−1.41855	−0.263418	−0.131709	+	0.991288i	$0.542046\pi$
$30$	0	0
$31$	0.879362	0.157938	0.0789690	−	0.996877i	$-0.474837\pi$
$31$	0.879362	0.157938	0.0789690	+	0.996877i	$0.474837\pi$
$32$	2.06278i	0.364651i
$33$	1.17009i	0.203686i
$34$	−8.48133	−1.45454
$35$	0	0
$36$	−0.601968	−0.100328
$37$	− 8.78765i	− 1.44468i	−0.691537	−	0.722341i	$-0.743066\pi$
$37$	− 8.78765i	− 1.44468i	0.691537	−	0.722341i	$-0.256934\pi$
$38$	1.41855i	0.230119i
$39$	0.107307	0.0171829
$40$	0	0
$41$	−1.61757	−0.252621	−0.126311	−	0.991991i	$-0.540314\pi$
$41$	−1.61757	−0.252621	−0.126311	+	0.991991i	$0.540314\pi$
$42$	1.80098i	0.277898i
$43$	− 3.86603i	− 0.589564i	−0.955565	−	0.294782i	$-0.904753\pi$
$43$	− 3.86603i	− 0.589564i	0.955565	−	0.294782i	$-0.0952471\pi$
$44$	0.369102	0.0556443
$45$	0	0
$46$	8.78765	1.29567
$47$	− 5.90829i	− 0.861813i	−0.902397	−	0.430906i	$-0.858194\pi$
$47$	− 5.90829i	− 0.861813i	0.902397	−	0.430906i	$-0.141806\pi$
$48$	5.38470i	0.777215i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−6.44748	−0.902828
$52$	− 0.0338499i	− 0.00469414i
$53$	10.0494i	1.38040i	0.723620	+	0.690199i	$0.242477\pi$
$53$	10.0494i	1.38040i	−0.723620	+	0.690199i	$0.757523\pi$
$54$	−8.34017	−1.13495
$55$	0	0
$56$	−2.51026	−0.335448
$57$	1.07838i	0.142835i
$58$	2.18342i	0.286697i
$59$	2.14116	0.278755	0.139377	−	0.990239i	$-0.455490\pi$
$59$	2.14116	0.278755	0.139377	+	0.990239i	$0.455490\pi$
$60$	0	0
$61$	−3.03612	−0.388735	−0.194367	−	0.980929i	$-0.562265\pi$
$61$	−3.03612	−0.388735	−0.194367	+	0.980929i	$0.562265\pi$
$62$	− 1.35350i	− 0.171895i
$63$	− 1.63090i	− 0.205474i
$64$	−6.02893	−0.753616
$65$	0	0
$66$	1.80098	0.221686
$67$	− 1.52586i	− 0.186413i	−0.995647	−	0.0932066i	$-0.970288\pi$
$67$	− 1.52586i	− 0.186413i	0.995647	−	0.0932066i	$-0.0297117\pi$
$68$	2.03385i	0.246641i
$69$	6.68035	0.804219
$70$	0	0
$71$	4.09890	0.486450	0.243225	−	0.969970i	$-0.421795\pi$
$71$	4.09890	0.486450	0.243225	+	0.969970i	$0.421795\pi$
$72$	− 4.09398i	− 0.482480i
$73$	− 14.1906i	− 1.66088i	−0.557105	−	0.830442i	$-0.688088\pi$
$73$	− 14.1906i	− 1.66088i	0.557105	−	0.830442i	$-0.311912\pi$
$74$	−13.5259	−1.57235
$75$	0	0
$76$	0.340173	0.0390205
$77$	1.00000i	0.113961i
$78$	− 0.165166i	− 0.0187014i
$79$	−14.5464	−1.63660	−0.818298	−	0.574795i	$-0.805082\pi$
$79$	−14.5464	−1.63660	−0.818298	+	0.574795i	$0.805082\pi$
$80$	0	0
$81$	−1.44748	−0.160831
$82$	2.48974i	0.274946i
$83$	8.52359i	0.935586i	0.883838	+	0.467793i	$0.154951\pi$
$83$	8.52359i	0.935586i	−0.883838	+	0.467793i	$0.845049\pi$
$84$	0.431882	0.0471222
$85$	0	0
$86$	−5.95055	−0.641664
$87$	1.65983i	0.177952i
$88$	2.51026i	0.267595i
$89$	2.83710	0.300732	0.150366	−	0.988630i	$-0.451955\pi$
$89$	2.83710	0.300732	0.150366	+	0.988630i	$0.451955\pi$
$90$	0	0
$91$	0.0917087	0.00961369
$92$	− 2.10731i	− 0.219702i
$93$	− 1.02893i	− 0.106695i
$94$	−9.09398	−0.937972
$95$	0	0
$96$	2.41363	0.246340
$97$	14.2557i	1.44744i	0.690093	+	0.723721i	$0.257570\pi$
$97$	14.2557i	1.44744i	−0.690093	+	0.723721i	$0.742430\pi$
$98$	1.53919i	0.155482i
$99$	−1.63090	−0.163911
$100$	0	0
$101$	9.03612	0.899127	0.449564	−	0.893248i	$-0.351579\pi$
$101$	9.03612	0.899127	0.449564	+	0.893248i	$0.351579\pi$
$102$	9.92389i	0.982611i
$103$	− 3.32684i	− 0.327803i	−0.986477	−	0.163902i	$-0.947592\pi$
$103$	− 3.32684i	− 0.327803i	0.986477	−	0.163902i	$-0.0524080\pi$
$104$	0.230213	0.0225742
$105$	0	0
$106$	15.4680	1.50238
$107$	8.09890i	0.782950i	0.920189	+	0.391475i	$0.128035\pi$
$107$	8.09890i	0.782950i	−0.920189	+	0.391475i	$0.871965\pi$
$108$	2.00000i	0.192450i
$109$	−15.1773	−1.45372	−0.726860	−	0.686786i	$-0.759021\pi$
$109$	−15.1773	−1.45372	−0.726860	+	0.686786i	$0.759021\pi$
$110$	0	0
$111$	−10.2823	−0.975954
$112$	4.60197i	0.434845i
$113$	7.07838i	0.665878i	0.942948	+	0.332939i	$0.108040\pi$
$113$	7.07838i	0.665878i	−0.942948	+	0.332939i	$0.891960\pi$
$114$	1.65983	0.155457
$115$	0	0
$116$	0.523590	0.0486142
$117$	0.149568i	0.0138275i
$118$	− 3.29565i	− 0.303389i
$119$	−5.51026	−0.505125
$120$	0	0
$121$	1.00000	0.0909091
$122$	4.67316i	0.423088i
$123$	1.89269i	0.170658i
$124$	−0.324575	−0.0291477
$125$	0	0
$126$	−2.51026	−0.223632
$127$	− 9.65983i	− 0.857171i	−0.903501	−	0.428586i	$-0.859012\pi$
$127$	− 9.65983i	− 0.857171i	0.903501	−	0.428586i	$-0.140988\pi$
$128$	13.4052i	1.18487i
$129$	−4.52359	−0.398280
$130$	0	0
$131$	4.68035	0.408924	0.204462	−	0.978875i	$-0.434456\pi$
$131$	4.68035	0.408924	0.204462	+	0.978875i	$0.434456\pi$
$132$	− 0.431882i	− 0.0375905i
$133$	0.921622i	0.0799148i
$134$	−2.34858	−0.202887
$135$	0	0
$136$	−13.8322	−1.18610
$137$	8.88655i	0.759229i	0.925145	+	0.379615i	$0.123943\pi$
$137$	8.88655i	0.759229i	−0.925145	+	0.379615i	$0.876057\pi$
$138$	− 10.2823i	− 0.875289i
$139$	15.0205	1.27402	0.637012	−	0.770854i	$-0.280170\pi$
$139$	15.0205	1.27402	0.637012	+	0.770854i	$0.280170\pi$
$140$	0	0
$141$	−6.91321	−0.582197
$142$	− 6.30898i	− 0.529438i
$143$	− 0.0917087i	− 0.00766907i
$144$	−7.50534	−0.625445
$145$	0	0
$146$	−21.8420	−1.80766
$147$	1.17009i	0.0965071i
$148$	3.24354i	0.266618i
$149$	13.7009	1.12242	0.561209	−	0.827674i	$-0.310336\pi$
$149$	13.7009	1.12242	0.561209	+	0.827674i	$0.310336\pi$
$150$	0	0
$151$	1.05559	0.0859028	0.0429514	−	0.999077i	$-0.486324\pi$
$151$	1.05559	0.0859028	0.0429514	+	0.999077i	$0.486324\pi$
$152$	2.31351i	0.187651i
$153$	− 8.98667i	− 0.726529i
$154$	1.53919	0.124031
$155$	0	0
$156$	−0.0396073	−0.00317112
$157$	− 17.7587i	− 1.41730i	−0.705560	−	0.708650i	$-0.749304\pi$
$157$	− 17.7587i	− 1.41730i	0.705560	−	0.708650i	$-0.250696\pi$
$158$	22.3896i	1.78122i
$159$	11.7587	0.932527
$160$	0	0
$161$	5.70928	0.449954
$162$	2.22795i	0.175044i
$163$	11.4680i	0.898243i	0.893471	+	0.449122i	$0.148263\pi$
$163$	11.4680i	0.898243i	−0.893471	+	0.449122i	$0.851737\pi$
$164$	0.597048	0.0466216
$165$	0	0
$166$	13.1194	1.01826
$167$	− 5.60197i	− 0.433493i	−0.976228	−	0.216747i	$-0.930455\pi$
$167$	− 5.60197i	− 0.433493i	0.976228	−	0.216747i	$-0.0695446\pi$
$168$	2.93722i	0.226611i
$169$	12.9916	0.999353
$170$	0	0
$171$	−1.50307	−0.114943
$172$	1.42696i	0.108805i
$173$	− 21.6092i	− 1.64291i	−0.570271	−	0.821457i	$-0.693162\pi$
$173$	− 21.6092i	− 1.64291i	0.570271	−	0.821457i	$-0.306838\pi$
$174$	2.55479	0.193678
$175$	0	0
$176$	4.60197	0.346886
$177$	− 2.50534i	− 0.188313i
$178$	− 4.36683i	− 0.327308i
$179$	2.05786	0.153812	0.0769058	−	0.997038i	$-0.475496\pi$
$179$	2.05786	0.153812	0.0769058	+	0.997038i	$0.475496\pi$
$180$	0	0
$181$	20.2823	1.50757	0.753786	−	0.657120i	$-0.228225\pi$
$181$	20.2823	1.50757	0.753786	+	0.657120i	$0.228225\pi$
$182$	− 0.141157i	− 0.0104633i
$183$	3.55252i	0.262610i
$184$	14.3318	1.05655
$185$	0	0
$186$	−1.58372	−0.116124
$187$	5.51026i	0.402950i
$188$	2.18076i	0.159049i
$189$	−5.41855	−0.394142
$190$	0	0
$191$	−20.2823	−1.46758	−0.733788	−	0.679378i	$-0.762250\pi$
$191$	−20.2823	−1.46758	−0.733788	+	0.679378i	$0.762250\pi$
$192$	7.05437i	0.509105i
$193$	24.3051i	1.74952i	0.484557	+	0.874760i	$0.338981\pi$
$193$	24.3051i	1.74952i	−0.484557	+	0.874760i	$0.661019\pi$
$194$	21.9421	1.57535
$195$	0	0
$196$	0.369102	0.0263645
$197$	− 14.1483i	− 1.00803i	−0.863696	−	0.504014i	$-0.831856\pi$
$197$	− 14.1483i	− 1.00803i	0.863696	−	0.504014i	$-0.168144\pi$
$198$	2.51026i	0.178396i
$199$	−10.4813	−0.743002	−0.371501	−	0.928433i	$-0.621157\pi$
$199$	−10.4813	−0.743002	−0.371501	+	0.928433i	$0.621157\pi$
$200$	0	0
$201$	−1.78539	−0.125931
$202$	− 13.9083i	− 0.978584i
$203$	1.41855i	0.0995627i
$204$	2.37978	0.166618
$205$	0	0
$206$	−5.12064	−0.356772
$207$	9.31124i	0.647176i
$208$	− 0.422041i	− 0.0292633i
$209$	0.921622	0.0637499
$210$	0	0
$211$	−2.65368	−0.182687	−0.0913436	−	0.995819i	$-0.529116\pi$
$211$	−2.65368	−0.182687	−0.0913436	+	0.995819i	$0.529116\pi$
$212$	− 3.70928i	− 0.254754i
$213$	− 4.79606i	− 0.328621i
$214$	12.4657	0.852140
$215$	0	0
$216$	−13.6020	−0.925497
$217$	− 0.879362i	− 0.0596950i
$218$	23.3607i	1.58219i
$219$	−16.6042	−1.12201
$220$	0	0
$221$	0.505339	0.0339928
$222$	15.8264i	1.06220i
$223$	8.67316i	0.580798i	0.956906	+	0.290399i	$0.0937880\pi$
$223$	8.67316i	0.580798i	−0.956906	+	0.290399i	$0.906212\pi$
$224$	2.06278	0.137825
$225$	0	0
$226$	10.8950	0.724722
$227$	9.67420i	0.642099i	0.947062	+	0.321050i	$0.104036\pi$
$227$	9.67420i	0.642099i	−0.947062	+	0.321050i	$0.895964\pi$
$228$	− 0.398032i	− 0.0263603i
$229$	13.5486	0.895320	0.447660	−	0.894204i	$-0.352258\pi$
$229$	13.5486	0.895320	0.447660	+	0.894204i	$0.352258\pi$
$230$	0	0
$231$	1.17009	0.0769860
$232$	3.56093i	0.233787i
$233$	− 8.38962i	− 0.549622i	−0.961498	−	0.274811i	$-0.911385\pi$
$233$	− 8.38962i	− 0.549622i	0.961498	−	0.274811i	$-0.0886153\pi$
$234$	0.230213	0.0150495
$235$	0	0
$236$	−0.790306	−0.0514446
$237$	17.0205i	1.10560i
$238$	8.48133i	0.549763i
$239$	29.4908	1.90760	0.953800	−	0.300442i	$-0.0971341\pi$
$239$	29.4908	1.90760	0.953800	+	0.300442i	$0.0971341\pi$
$240$	0	0
$241$	3.64423	0.234745	0.117373	−	0.993088i	$-0.462553\pi$
$241$	3.64423	0.234745	0.117373	+	0.993088i	$0.462553\pi$
$242$	− 1.53919i	− 0.0989428i
$243$	− 14.5620i	− 0.934151i
$244$	1.12064	0.0717415
$245$	0	0
$246$	2.91321	0.185740
$247$	− 0.0845208i	− 0.00537793i
$248$	− 2.20743i	− 0.140172i
$249$	9.97334	0.632035
$250$	0	0
$251$	23.1350	1.46027	0.730135	−	0.683303i	$-0.239457\pi$
$251$	23.1350	1.46027	0.730135	+	0.683303i	$0.239457\pi$
$252$	0.601968i	0.0379204i
$253$	− 5.70928i	− 0.358939i
$254$	−14.8683	−0.932920
$255$	0	0
$256$	8.57531	0.535957
$257$	20.8104i	1.29812i	0.760737	+	0.649060i	$0.224838\pi$
$257$	20.8104i	1.29812i	−0.760737	+	0.649060i	$0.775162\pi$
$258$	6.96266i	0.433476i
$259$	−8.78765	−0.546038
$260$	0	0
$261$	−2.31351	−0.143203
$262$	− 7.20394i	− 0.445061i
$263$	23.7009i	1.46146i	0.682668	+	0.730729i	$0.260820\pi$
$263$	23.7009i	1.46146i	−0.682668	+	0.730729i	$0.739180\pi$
$264$	2.93722	0.180773
$265$	0	0
$266$	1.41855	0.0869769
$267$	− 3.31965i	− 0.203160i
$268$	0.563198i	0.0344028i
$269$	3.50307	0.213586	0.106793	−	0.994281i	$-0.465942\pi$
$269$	3.50307	0.213586	0.106793	+	0.994281i	$0.465942\pi$
$270$	0	0
$271$	−8.49693	−0.516152	−0.258076	−	0.966125i	$-0.583088\pi$
$271$	−8.49693	−0.516152	−0.258076	+	0.966125i	$0.583088\pi$
$272$	25.3580i	1.53756i
$273$	− 0.107307i	− 0.00649452i
$274$	13.6781	0.826323
$275$	0	0
$276$	−2.46573	−0.148420
$277$	− 25.9649i	− 1.56008i	−0.625729	−	0.780041i	$-0.715198\pi$
$277$	− 25.9649i	− 1.56008i	0.625729	−	0.780041i	$-0.284802\pi$
$278$	− 23.1194i	− 1.38661i
$279$	1.43415	0.0858603
$280$	0	0
$281$	11.6742	0.696425	0.348212	−	0.937416i	$-0.386789\pi$
$281$	11.6742	0.696425	0.348212	+	0.937416i	$0.386789\pi$
$282$	10.6407i	0.633647i
$283$	14.2557i	0.847411i	0.905800	+	0.423705i	$0.139271\pi$
$283$	14.2557i	0.847411i	−0.905800	+	0.423705i	$0.860729\pi$
$284$	−1.51291	−0.0897748
$285$	0	0
$286$	−0.141157	−0.00834679
$287$	1.61757i	0.0954819i
$288$	3.36418i	0.198236i
$289$	−13.3630	−0.786056
$290$	0	0
$291$	16.6803	0.977819
$292$	5.23779i	0.306518i
$293$	− 25.1122i	− 1.46707i	−0.679651	−	0.733536i	$-0.737869\pi$
$293$	− 25.1122i	− 1.46707i	0.679651	−	0.733536i	$-0.262131\pi$
$294$	1.80098	0.105036
$295$	0	0
$296$	−22.0593	−1.28217
$297$	5.41855i	0.314416i
$298$	− 21.0882i	− 1.22161i
$299$	−0.523590	−0.0302800
$300$	0	0
$301$	−3.86603	−0.222834
$302$	− 1.62475i	− 0.0934941i
$303$	− 10.5730i	− 0.607405i
$304$	4.24128	0.243254
$305$	0	0
$306$	−13.8322	−0.790733
$307$	8.02666i	0.458106i	0.973414	+	0.229053i	$0.0735629\pi$
$307$	8.02666i	0.458106i	−0.973414	+	0.229053i	$0.926437\pi$
$308$	− 0.369102i	− 0.0210316i
$309$	−3.89269	−0.221448
$310$	0	0
$311$	−26.3968	−1.49683	−0.748413	−	0.663233i	$-0.769184\pi$
$311$	−26.3968	−1.49683	−0.748413	+	0.663233i	$0.769184\pi$
$312$	− 0.269369i	− 0.0152500i
$313$	− 25.7321i	− 1.45446i	−0.686393	−	0.727231i	$-0.740807\pi$
$313$	− 25.7321i	− 1.45446i	0.686393	−	0.727231i	$-0.259193\pi$
$314$	−27.3340	−1.54255
$315$	0	0
$316$	5.36910	0.302036
$317$	6.31351i	0.354602i	0.984157	+	0.177301i	$0.0567366\pi$
$317$	6.31351i	0.354602i	−0.984157	+	0.177301i	$0.943263\pi$
$318$	− 18.0989i	− 1.01494i
$319$	1.41855	0.0794236
$320$	0	0
$321$	9.47641	0.528922
$322$	− 8.78765i	− 0.489717i
$323$	5.07838i	0.282568i
$324$	0.534268	0.0296816
$325$	0	0
$326$	17.6514	0.977622
$327$	17.7587i	0.982060i
$328$	4.06051i	0.224204i
$329$	−5.90829	−0.325735
$330$	0	0
$331$	3.50307	0.192546	0.0962731	−	0.995355i	$-0.469308\pi$
$331$	3.50307	0.192546	0.0962731	+	0.995355i	$0.469308\pi$
$332$	− 3.14608i	− 0.172663i
$333$	− 14.3318i	− 0.785376i
$334$	−8.62249	−0.471802
$335$	0	0
$336$	5.38470	0.293760
$337$	7.57918i	0.412864i	0.978461	+	0.206432i	$0.0661853\pi$
$337$	7.57918i	0.412864i	−0.978461	+	0.206432i	$0.933815\pi$
$338$	− 19.9965i	− 1.08767i
$339$	8.28231	0.449834
$340$	0	0
$341$	−0.879362	−0.0476201
$342$	2.31351i	0.125100i
$343$	1.00000i	0.0539949i
$344$	−9.70474	−0.523245
$345$	0	0
$346$	−33.2606	−1.78810
$347$	− 35.4824i	− 1.90479i	−0.304861	−	0.952397i	$-0.598610\pi$
$347$	− 35.4824i	− 1.90479i	0.304861	−	0.952397i	$-0.401390\pi$
$348$	− 0.612646i	− 0.0328413i
$349$	13.6586	0.731128	0.365564	−	0.930786i	$-0.380876\pi$
$349$	13.6586	0.731128	0.365564	+	0.930786i	$0.380876\pi$
$350$	0	0
$351$	0.496928	0.0265241
$352$	− 2.06278i	− 0.109947i
$353$	− 26.4657i	− 1.40863i	−0.709888	−	0.704314i	$-0.751255\pi$
$353$	− 26.4657i	− 1.40863i	0.709888	−	0.704314i	$-0.248745\pi$
$354$	−3.85619	−0.204954
$355$	0	0
$356$	−1.04718	−0.0555005
$357$	6.44748i	0.341237i
$358$	− 3.16743i	− 0.167404i
$359$	15.3958	0.812557	0.406279	−	0.913749i	$-0.366826\pi$
$359$	15.3958	0.812557	0.406279	+	0.913749i	$0.366826\pi$
$360$	0	0
$361$	−18.1506	−0.955295
$362$	− 31.2183i	− 1.64080i
$363$	− 1.17009i	− 0.0614136i
$364$	−0.0338499	−0.00177422
$365$	0	0
$366$	5.46800	0.285817
$367$	− 34.6875i	− 1.81067i	−0.424693	−	0.905337i	$-0.639618\pi$
$367$	− 34.6875i	− 1.81067i	0.424693	−	0.905337i	$-0.360382\pi$
$368$	− 26.2739i	− 1.36962i
$369$	−2.63809	−0.137333
$370$	0	0
$371$	10.0494	0.521741
$372$	0.379780i	0.0196907i
$373$	− 36.3584i	− 1.88257i	−0.337616	−	0.941284i	$-0.609621\pi$
$373$	− 36.3584i	− 1.88257i	0.337616	−	0.941284i	$-0.390379\pi$
$374$	8.48133	0.438559
$375$	0	0
$376$	−14.8313	−0.764868
$377$	− 0.130094i	− 0.00670016i
$378$	8.34017i	0.428972i
$379$	33.1461	1.70260	0.851300	−	0.524680i	$-0.175815\pi$
$379$	33.1461	1.70260	0.851300	+	0.524680i	$0.175815\pi$
$380$	0	0
$381$	−11.3028	−0.579062
$382$	31.2183i	1.59727i
$383$	34.2628i	1.75075i	0.483445	+	0.875375i	$0.339385\pi$
$383$	34.2628i	1.75075i	−0.483445	+	0.875375i	$0.660615\pi$
$384$	15.6853	0.800435
$385$	0	0
$386$	37.4101	1.90413
$387$	− 6.30510i	− 0.320506i
$388$	− 5.26180i	− 0.267127i
$389$	−23.2762	−1.18015	−0.590074	−	0.807349i	$-0.700902\pi$
$389$	−23.2762	−1.18015	−0.590074	+	0.807349i	$0.700902\pi$
$390$	0	0
$391$	31.4596	1.59098
$392$	2.51026i	0.126787i
$393$	− 5.47641i	− 0.276248i
$394$	−21.7770	−1.09711
$395$	0	0
$396$	0.601968	0.0302500
$397$	− 29.8576i	− 1.49851i	−0.662281	−	0.749256i	$-0.730412\pi$
$397$	− 29.8576i	− 1.49851i	0.662281	−	0.749256i	$-0.269588\pi$
$398$	16.1327i	0.808662i
$399$	1.07838	0.0539864
$400$	0	0
$401$	−5.51745	−0.275528	−0.137764	−	0.990465i	$-0.543992\pi$
$401$	−5.51745	−0.275528	−0.137764	+	0.990465i	$0.543992\pi$
$402$	2.74805i	0.137060i
$403$	0.0806452i	0.00401722i
$404$	−3.33525	−0.165935
$405$	0	0
$406$	2.18342	0.108361
$407$	8.78765i	0.435588i
$408$	16.1848i	0.801269i
$409$	3.43415	0.169808	0.0849039	−	0.996389i	$-0.472942\pi$
$409$	3.43415	0.169808	0.0849039	+	0.996389i	$0.472942\pi$
$410$	0	0
$411$	10.3980	0.512897
$412$	1.22795i	0.0604965i
$413$	− 2.14116i	− 0.105359i
$414$	14.3318	0.704368
$415$	0	0
$416$	−0.189175	−0.00927506
$417$	− 17.5753i	− 0.860666i
$418$	− 1.41855i	− 0.0693836i
$419$	−18.2134	−0.889782	−0.444891	−	0.895585i	$-0.646758\pi$
$419$	−18.2134	−0.889782	−0.444891	+	0.895585i	$0.646758\pi$
$420$	0	0
$421$	10.6576	0.519418	0.259709	−	0.965687i	$-0.416373\pi$
$421$	10.6576	0.519418	0.259709	+	0.965687i	$0.416373\pi$
$422$	4.08452i	0.198831i
$423$	− 9.63582i	− 0.468510i
$424$	25.2267	1.22512
$425$	0	0
$426$	−7.38205	−0.357661
$427$	3.03612i	0.146928i
$428$	− 2.98932i	− 0.144494i
$429$	−0.107307	−0.00518084
$430$	0	0
$431$	−7.61038	−0.366579	−0.183290	−	0.983059i	$-0.558675\pi$
$431$	−7.61038	−0.366579	−0.183290	+	0.983059i	$0.558675\pi$
$432$	24.9360i	1.19973i
$433$	− 33.5318i	− 1.61144i	−0.592299	−	0.805718i	$-0.701780\pi$
$433$	− 33.5318i	− 1.61144i	0.592299	−	0.805718i	$-0.298220\pi$
$434$	−1.35350	−0.0649703
$435$	0	0
$436$	5.60197	0.268286
$437$	− 5.26180i	− 0.251706i
$438$	25.5571i	1.22116i
$439$	13.7587	0.656668	0.328334	−	0.944562i	$-0.393513\pi$
$439$	13.7587	0.656668	0.328334	+	0.944562i	$0.393513\pi$
$440$	0	0
$441$	−1.63090	−0.0776618
$442$	− 0.777812i	− 0.0369967i
$443$	11.1689i	0.530649i	0.964159	+	0.265324i	$0.0854790\pi$
$443$	11.1689i	0.530649i	−0.964159	+	0.265324i	$0.914521\pi$
$444$	3.79523	0.180113
$445$	0	0
$446$	13.3496	0.632123
$447$	− 16.0312i	− 0.758250i
$448$	6.02893i	0.284840i
$449$	19.0700	0.899967	0.449984	−	0.893037i	$-0.351430\pi$
$449$	19.0700	0.899967	0.449984	+	0.893037i	$0.351430\pi$
$450$	0	0
$451$	1.61757	0.0761682
$452$	− 2.61265i	− 0.122889i
$453$	− 1.23513i	− 0.0580316i
$454$	14.8904	0.698842
$455$	0	0
$456$	2.70701	0.126767
$457$	− 0.787653i	− 0.0368449i	−0.999830	−	0.0184224i	$-0.994136\pi$
$457$	− 0.787653i	− 0.0368449i	0.999830	−	0.0184224i	$-0.00586437\pi$
$458$	− 20.8539i	− 0.974440i
$459$	−29.8576	−1.39363
$460$	0	0
$461$	25.5864	1.19168	0.595838	−	0.803105i	$-0.296820\pi$
$461$	25.5864	1.19168	0.595838	+	0.803105i	$0.296820\pi$
$462$	− 1.80098i	− 0.0837894i
$463$	14.2595i	0.662696i	0.943509	+	0.331348i	$0.107503\pi$
$463$	14.2595i	0.662696i	−0.943509	+	0.331348i	$0.892497\pi$
$464$	6.52813	0.303061
$465$	0	0
$466$	−12.9132	−0.598193
$467$	18.3474i	0.849015i	0.905425	+	0.424507i	$0.139553\pi$
$467$	18.3474i	0.849015i	−0.905425	+	0.424507i	$0.860447\pi$
$468$	− 0.0552057i	− 0.00255189i
$469$	−1.52586	−0.0704576
$470$	0	0
$471$	−20.7792	−0.957457
$472$	− 5.37486i	− 0.247398i
$473$	3.86603i	0.177760i
$474$	26.1978	1.20330
$475$	0	0
$476$	2.03385	0.0932214
$477$	16.3896i	0.750429i
$478$	− 45.3919i	− 2.07618i
$479$	−12.1711	−0.556113	−0.278057	−	0.960565i	$-0.589690\pi$
$479$	−12.1711	−0.556113	−0.278057	+	0.960565i	$0.589690\pi$
$480$	0	0
$481$	0.805905	0.0367461
$482$	− 5.60916i	− 0.255490i
$483$	− 6.68035i	− 0.303966i
$484$	−0.369102	−0.0167774
$485$	0	0
$486$	−22.4136	−1.01670
$487$	− 4.23287i	− 0.191809i	−0.995391	−	0.0959047i	$-0.969426\pi$
$487$	− 4.23287i	− 0.191809i	0.995391	−	0.0959047i	$-0.0305744\pi$
$488$	7.62144i	0.345006i
$489$	13.4186	0.606808
$490$	0	0
$491$	22.0183	0.993670	0.496835	−	0.867845i	$-0.334495\pi$
$491$	22.0183	0.993670	0.496835	+	0.867845i	$0.334495\pi$
$492$	− 0.698597i	− 0.0314952i
$493$	7.81658i	0.352041i
$494$	−0.130094	−0.00585318
$495$	0	0
$496$	−4.04680	−0.181706
$497$	− 4.09890i	− 0.183861i
$498$	− 15.3509i	− 0.687888i
$499$	−32.9939	−1.47701	−0.738504	−	0.674249i	$-0.764467\pi$
$499$	−32.9939	−1.47701	−0.738504	+	0.674249i	$0.764467\pi$
$500$	0	0
$501$	−6.55479	−0.292846
$502$	− 35.6092i	− 1.58931i
$503$	29.0349i	1.29460i	0.762235	+	0.647301i	$0.224102\pi$
$503$	29.0349i	1.29460i	−0.762235	+	0.647301i	$0.775898\pi$
$504$	−4.09398	−0.182360
$505$	0	0
$506$	−8.78765	−0.390659
$507$	− 15.2013i	− 0.675113i
$508$	3.56547i	0.158192i
$509$	21.5031	0.953107	0.476553	−	0.879146i	$-0.341886\pi$
$509$	21.5031	0.953107	0.476553	+	0.879146i	$0.341886\pi$
$510$	0	0
$511$	−14.1906	−0.627755
$512$	13.6114i	0.601546i
$513$	4.99386i	0.220484i
$514$	32.0312	1.41284
$515$	0	0
$516$	1.66967	0.0735030
$517$	5.90829i	0.259846i
$518$	13.5259i	0.594292i
$519$	−25.2846	−1.10987
$520$	0	0
$521$	24.5958	1.07756	0.538781	−	0.842446i	$-0.318885\pi$
$521$	24.5958	1.07756	0.538781	+	0.842446i	$0.318885\pi$
$522$	3.56093i	0.155858i
$523$	− 38.0677i	− 1.66458i	−0.554337	−	0.832292i	$-0.687028\pi$
$523$	− 38.0677i	− 1.66458i	0.554337	−	0.832292i	$-0.312972\pi$
$524$	−1.72753	−0.0754674
$525$	0	0
$526$	36.4801	1.59061
$527$	− 4.84551i	− 0.211074i
$528$	− 5.38470i	− 0.234339i
$529$	−9.59583	−0.417210
$530$	0	0
$531$	3.49201	0.151540
$532$	− 0.340173i	− 0.0147484i
$533$	− 0.148345i	− 0.00642554i
$534$	−5.10957	−0.221113
$535$	0	0
$536$	−3.83030	−0.165444
$537$	− 2.40787i	− 0.103907i
$538$	− 5.39189i	− 0.232461i
$539$	1.00000	0.0430730
$540$	0	0
$541$	2.13009	0.0915799	0.0457899	−	0.998951i	$-0.485420\pi$
$541$	2.13009	0.0915799	0.0457899	+	0.998951i	$0.485420\pi$
$542$	13.0784i	0.561764i
$543$	− 23.7321i	− 1.01844i
$544$	11.3664	0.487332
$545$	0	0
$546$	−0.165166	−0.00706845
$547$	− 9.13170i	− 0.390443i	−0.980759	−	0.195222i	$-0.937457\pi$
$547$	− 9.13170i	− 0.390443i	0.980759	−	0.195222i	$-0.0625426\pi$
$548$	− 3.28005i	− 0.140117i
$549$	−4.95160	−0.211329
$550$	0	0
$551$	1.30737	0.0556957
$552$	− 16.7694i	− 0.713753i
$553$	14.5464i	0.618575i
$554$	−39.9649	−1.69795
$555$	0	0
$556$	−5.54411	−0.235123
$557$	− 11.7093i	− 0.496138i	−0.968742	−	0.248069i	$-0.920204\pi$
$557$	− 11.7093i	− 0.496138i	0.968742	−	0.248069i	$-0.0797960\pi$
$558$	− 2.20743i	− 0.0934478i
$559$	0.354549	0.0149958
$560$	0	0
$561$	6.44748	0.272213
$562$	− 17.9688i	− 0.757968i
$563$	− 12.5958i	− 0.530851i	−0.964131	−	0.265425i	$-0.914488\pi$
$563$	− 12.5958i	− 0.530851i	0.964131	−	0.265425i	$-0.0855124\pi$
$564$	2.55168	0.107445
$565$	0	0
$566$	21.9421	0.922297
$567$	1.44748i	0.0607885i
$568$	− 10.2893i	− 0.431729i
$569$	−7.54411	−0.316266	−0.158133	−	0.987418i	$-0.550547\pi$
$569$	−7.54411	−0.316266	−0.158133	+	0.987418i	$0.550547\pi$
$570$	0	0
$571$	36.8104	1.54047	0.770234	−	0.637761i	$-0.220139\pi$
$571$	36.8104	1.54047	0.770234	+	0.637761i	$0.220139\pi$
$572$	0.0338499i	0.00141534i
$573$	23.7321i	0.991421i
$574$	2.48974	0.103920
$575$	0	0
$576$	−9.83257	−0.409690
$577$	− 39.5174i	− 1.64513i	−0.568669	−	0.822566i	$-0.692541\pi$
$577$	− 39.5174i	− 1.64513i	0.568669	−	0.822566i	$-0.307459\pi$
$578$	20.5681i	0.855521i
$579$	28.4391	1.18189
$580$	0	0
$581$	8.52359	0.353618
$582$	− 25.6742i	− 1.06423i
$583$	− 10.0494i	− 0.416206i
$584$	−35.6221	−1.47405
$585$	0	0
$586$	−38.6525	−1.59672
$587$	1.56812i	0.0647232i	0.999476	+	0.0323616i	$0.0103028\pi$
$587$	1.56812i	0.0647232i	−0.999476	+	0.0323616i	$0.989697\pi$
$588$	− 0.431882i	− 0.0178105i
$589$	−0.810439	−0.0333936
$590$	0	0
$591$	−16.5548	−0.680973
$592$	40.4405i	1.66209i
$593$	− 4.95547i	− 0.203497i	−0.994810	−	0.101748i	$-0.967556\pi$
$593$	− 4.95547i	− 0.203497i	0.994810	−	0.101748i	$-0.0324437\pi$
$594$	8.34017	0.342201
$595$	0	0
$596$	−5.05702	−0.207144
$597$	12.2641i	0.501935i
$598$	0.805905i	0.0329559i
$599$	12.3668	0.505295	0.252648	−	0.967558i	$-0.418699\pi$
$599$	12.3668	0.505295	0.252648	+	0.967558i	$0.418699\pi$
$600$	0	0
$601$	24.9516	1.01780	0.508898	−	0.860827i	$-0.330053\pi$
$601$	24.9516	1.01780	0.508898	+	0.860827i	$0.330053\pi$
$602$	5.95055i	0.242526i
$603$	− 2.48852i	− 0.101340i
$604$	−0.389621	−0.0158535
$605$	0	0
$606$	−16.2739	−0.661082
$607$	− 19.2762i	− 0.782396i	−0.920307	−	0.391198i	$-0.872061\pi$
$607$	− 19.2762i	− 0.782396i	0.920307	−	0.391198i	$-0.127939\pi$
$608$	− 1.90110i	− 0.0770999i
$609$	1.65983	0.0672596
$610$	0	0
$611$	0.541842	0.0219206
$612$	3.31700i	0.134082i
$613$	42.6986i	1.72458i	0.506415	+	0.862290i	$0.330971\pi$
$613$	42.6986i	1.72458i	−0.506415	+	0.862290i	$0.669029\pi$
$614$	12.3545	0.498589
$615$	0	0
$616$	2.51026	0.101141
$617$	31.7770i	1.27929i	0.768669	+	0.639646i	$0.220919\pi$
$617$	31.7770i	1.27929i	−0.768669	+	0.639646i	$0.779081\pi$
$618$	5.99159i	0.241017i
$619$	19.8420	0.797518	0.398759	−	0.917056i	$-0.369441\pi$
$619$	19.8420	0.797518	0.398759	+	0.917056i	$0.369441\pi$
$620$	0	0
$621$	30.9360	1.24142
$622$	40.6297i	1.62910i
$623$	− 2.83710i	− 0.113666i
$624$	−0.493824	−0.0197688
$625$	0	0
$626$	−39.6065	−1.58299
$627$	− 1.07838i	− 0.0430663i
$628$	6.55479i	0.261564i
$629$	−48.4222	−1.93072
$630$	0	0
$631$	−3.63317	−0.144634	−0.0723170	−	0.997382i	$-0.523039\pi$
$631$	−3.63317	−0.144634	−0.0723170	+	0.997382i	$0.523039\pi$
$632$	36.5152i	1.45250i
$633$	3.10504i	0.123414i
$634$	9.71769	0.385939
$635$	0	0
$636$	−4.34017	−0.172099
$637$	− 0.0917087i	− 0.00363363i
$638$	− 2.18342i	− 0.0864423i
$639$	6.68488	0.264450
$640$	0	0
$641$	37.5402	1.48275	0.741375	−	0.671091i	$-0.234174\pi$
$641$	37.5402	1.48275	0.741375	+	0.671091i	$0.234174\pi$
$642$	− 14.5860i	− 0.575663i
$643$	34.8710i	1.37518i	0.726101	+	0.687588i	$0.241330\pi$
$643$	34.8710i	1.37518i	−0.726101	+	0.687588i	$0.758670\pi$
$644$	−2.10731	−0.0830395
$645$	0	0
$646$	7.81658	0.307539
$647$	30.6342i	1.20436i	0.798362	+	0.602178i	$0.205700\pi$
$647$	30.6342i	1.20436i	−0.798362	+	0.602178i	$0.794300\pi$
$648$	3.63355i	0.142739i
$649$	−2.14116	−0.0840478
$650$	0	0
$651$	−1.02893	−0.0403269
$652$	− 4.23287i	− 0.165772i
$653$	− 5.40417i	− 0.211482i	−0.994394	−	0.105741i	$-0.966279\pi$
$653$	− 5.40417i	− 0.211482i	0.994394	−	0.105741i	$-0.0337214\pi$
$654$	27.3340	1.06885
$655$	0	0
$656$	7.44399	0.290639
$657$	− 23.1434i	− 0.902911i
$658$	9.09398i	0.354520i
$659$	19.4101	0.756112	0.378056	−	0.925783i	$-0.376593\pi$
$659$	19.4101	0.756112	0.378056	+	0.925783i	$0.376593\pi$
$660$	0	0
$661$	−26.3090	−1.02330	−0.511650	−	0.859194i	$-0.670966\pi$
$661$	−26.3090	−1.02330	−0.511650	+	0.859194i	$0.670966\pi$
$662$	− 5.39189i	− 0.209562i
$663$	− 0.591290i	− 0.0229638i
$664$	21.3964	0.830342
$665$	0	0
$666$	−22.0593	−0.854780
$667$	− 8.09890i	− 0.313591i
$668$	2.06770i	0.0800017i
$669$	10.1483	0.392358
$670$	0	0
$671$	3.03612	0.117208
$672$	− 2.41363i	− 0.0931078i
$673$	15.7938i	0.608806i	0.952543	+	0.304403i	$0.0984570\pi$
$673$	15.7938i	0.608806i	−0.952543	+	0.304403i	$0.901543\pi$
$674$	11.6658	0.449350
$675$	0	0
$676$	−4.79523	−0.184432
$677$	− 15.7081i	− 0.603710i	−0.953354	−	0.301855i	$-0.902394\pi$
$677$	− 15.7081i	− 0.603710i	0.953354	−	0.301855i	$-0.0976058\pi$
$678$	− 12.7480i	− 0.489586i
$679$	14.2557	0.547082
$680$	0	0
$681$	11.3197	0.433770
$682$	1.35350i	0.0518283i
$683$	44.0326i	1.68486i	0.538805	+	0.842431i	$0.318876\pi$
$683$	44.0326i	1.68486i	−0.538805	+	0.842431i	$0.681124\pi$
$684$	0.554787	0.0212128
$685$	0	0
$686$	1.53919	0.0587665
$687$	− 15.8531i	− 0.604833i
$688$	17.7914i	0.678289i
$689$	−0.921622	−0.0351110
$690$	0	0
$691$	4.63809	0.176441	0.0882205	−	0.996101i	$-0.471882\pi$
$691$	4.63809	0.176441	0.0882205	+	0.996101i	$0.471882\pi$
$692$	7.97599i	0.303202i
$693$	1.63090i	0.0619527i
$694$	−54.6141	−2.07312
$695$	0	0
$696$	4.16660	0.157934
$697$	8.91321i	0.337612i
$698$	− 21.0232i	− 0.795739i
$699$	−9.81658	−0.371297
$700$	0	0
$701$	−14.6491	−0.553291	−0.276645	−	0.960972i	$-0.589223\pi$
$701$	−14.6491	−0.553291	−0.276645	+	0.960972i	$0.589223\pi$
$702$	− 0.764867i	− 0.0288680i
$703$	8.09890i	0.305456i
$704$	6.02893	0.227224
$705$	0	0
$706$	−40.7358	−1.53311
$707$	− 9.03612i	− 0.339838i
$708$	0.924727i	0.0347534i
$709$	25.5174	0.958328	0.479164	−	0.877725i	$-0.340940\pi$
$709$	25.5174	0.958328	0.479164	+	0.877725i	$0.340940\pi$
$710$	0	0
$711$	−23.7237	−0.889706
$712$	− 7.12186i	− 0.266903i
$713$	5.02052i	0.188020i
$714$	9.92389	0.371392
$715$	0	0
$716$	−0.759561	−0.0283861
$717$	− 34.5068i	− 1.28868i
$718$	− 23.6970i	− 0.884364i
$719$	−39.2918	−1.46534	−0.732668	−	0.680586i	$-0.761725\pi$
$719$	−39.2918	−1.46534	−0.732668	+	0.680586i	$0.761725\pi$
$720$	0	0
$721$	−3.32684	−0.123898
$722$	27.9372i	1.03972i
$723$	− 4.26406i	− 0.158582i
$724$	−7.48625	−0.278224
$725$	0	0
$726$	−1.80098	−0.0668408
$727$	− 37.7081i	− 1.39851i	−0.714870	−	0.699257i	$-0.753514\pi$
$727$	− 37.7081i	− 1.39851i	0.714870	−	0.699257i	$-0.246486\pi$
$728$	− 0.230213i	− 0.00853225i
$729$	−21.3812	−0.791897
$730$	0	0
$731$	−21.3028	−0.787914
$732$	− 1.31124i	− 0.0484650i
$733$	4.34736i	0.160573i	0.996772	+	0.0802867i	$0.0255836\pi$
$733$	4.34736i	0.160573i	−0.996772	+	0.0802867i	$0.974416\pi$
$734$	−53.3907	−1.97069
$735$	0	0
$736$	−11.7770	−0.434105
$737$	1.52586i	0.0562057i
$738$	4.06051i	0.149470i
$739$	−38.1568	−1.40362	−0.701809	−	0.712365i	$-0.747624\pi$
$739$	−38.1568	−1.40362	−0.701809	+	0.712365i	$0.747624\pi$
$740$	0	0
$741$	−0.0988967	−0.00363306
$742$	− 15.4680i	− 0.567848i
$743$	29.2618i	1.07351i	0.843738	+	0.536756i	$0.180350\pi$
$743$	29.2618i	1.07351i	−0.843738	+	0.536756i	$0.819650\pi$
$744$	−2.58288	−0.0946930
$745$	0	0
$746$	−55.9625	−2.04893
$747$	13.9011i	0.508615i
$748$	− 2.03385i	− 0.0743649i
$749$	8.09890	0.295927
$750$	0	0
$751$	41.6886	1.52124	0.760619	−	0.649199i	$-0.224896\pi$
$751$	41.6886	1.52124	0.760619	+	0.649199i	$0.224896\pi$
$752$	27.1898i	0.991509i
$753$	− 27.0700i	− 0.986484i
$754$	−0.200238	−0.00729225
$755$	0	0
$756$	2.00000	0.0727393
$757$	39.7419i	1.44444i	0.691661	+	0.722222i	$0.256879\pi$
$757$	39.7419i	1.44444i	−0.691661	+	0.722222i	$0.743121\pi$
$758$	− 51.0181i	− 1.85306i
$759$	−6.68035	−0.242481
$760$	0	0
$761$	−36.4112	−1.31990	−0.659952	−	0.751308i	$-0.729423\pi$
$761$	−36.4112	−1.31990	−0.659952	+	0.751308i	$0.729423\pi$
$762$	17.3972i	0.630234i
$763$	15.1773i	0.549454i
$764$	7.48625	0.270843
$765$	0	0
$766$	52.7370	1.90546
$767$	0.196363i	0.00709025i
$768$	− 10.0338i	− 0.362065i
$769$	10.5347	0.379889	0.189945	−	0.981795i	$-0.439169\pi$
$769$	10.5347	0.379889	0.189945	+	0.981795i	$0.439169\pi$
$770$	0	0
$771$	24.3500	0.876944
$772$	− 8.97107i	− 0.322876i
$773$	1.52198i	0.0547419i	0.999625	+	0.0273709i	$0.00871353\pi$
$773$	1.52198i	0.0547419i	−0.999625	+	0.0273709i	$0.991286\pi$
$774$	−9.70474	−0.348830
$775$	0	0
$776$	35.7854	1.28462
$777$	10.2823i	0.368876i
$778$	35.8264i	1.28444i
$779$	1.49079	0.0534129
$780$	0	0
$781$	−4.09890	−0.146670
$782$	− 48.4222i	− 1.73158i
$783$	7.68649i	0.274693i
$784$	4.60197	0.164356
$785$	0	0
$786$	−8.42923	−0.300661
$787$	− 15.6020i	− 0.556150i	−0.960559	−	0.278075i	$-0.910304\pi$
$787$	− 15.6020i	− 0.556150i	0.960559	−	0.278075i	$-0.0896964\pi$
$788$	5.22219i	0.186033i
$789$	27.7321	0.987288
$790$	0	0
$791$	7.07838	0.251678
$792$	4.09398i	0.145473i
$793$	− 0.278438i	− 0.00988764i
$794$	−45.9565	−1.63094
$795$	0	0
$796$	3.86868	0.137122
$797$	12.6491i	0.448056i	0.974583	+	0.224028i	$0.0719207\pi$
$797$	12.6491i	0.448056i	−0.974583	+	0.224028i	$0.928079\pi$
$798$	− 1.65983i	− 0.0587572i
$799$	−32.5562	−1.15176
$800$	0	0
$801$	4.62702	0.163488
$802$	8.49239i	0.299877i
$803$	14.1906i	0.500776i
$804$	0.658990	0.0232408
$805$	0	0
$806$	0.124128	0.00437223
$807$	− 4.09890i	− 0.144288i
$808$	− 22.6830i	− 0.797985i
$809$	49.9299	1.75544	0.877720	−	0.479174i	$-0.159064\pi$
$809$	49.9299	1.75544	0.877720	+	0.479174i	$0.159064\pi$
$810$	0	0
$811$	7.95896	0.279477	0.139738	−	0.990188i	$-0.455374\pi$
$811$	7.95896	0.279477	0.139738	+	0.990188i	$0.455374\pi$
$812$	− 0.523590i	− 0.0183744i
$813$	9.94214i	0.348686i
$814$	13.5259	0.474081
$815$	0	0
$816$	29.6711	1.03870
$817$	3.56302i	0.124654i
$818$	− 5.28580i	− 0.184814i
$819$	0.149568	0.00522631
$820$	0	0
$821$	4.92162	0.171766	0.0858829	−	0.996305i	$-0.472629\pi$
$821$	4.92162	0.171766	0.0858829	+	0.996305i	$0.472629\pi$
$822$	− 16.0045i	− 0.558222i
$823$	4.04945i	0.141155i	0.997506	+	0.0705774i	$0.0224842\pi$
$823$	4.04945i	0.141155i	−0.997506	+	0.0705774i	$0.977516\pi$
$824$	−8.35124	−0.290929
$825$	0	0
$826$	−3.29565	−0.114670
$827$	33.3256i	1.15885i	0.815027	+	0.579423i	$0.196722\pi$
$827$	33.3256i	1.15885i	−0.815027	+	0.579423i	$0.803278\pi$
$828$	− 3.43680i	− 0.119437i
$829$	0.156755	0.00544434	0.00272217	−	0.999996i	$-0.499134\pi$
$829$	0.156755	0.00544434	0.00272217	+	0.999996i	$0.499134\pi$
$830$	0	0
$831$	−30.3812	−1.05391
$832$	− 0.552906i	− 0.0191686i
$833$	5.51026i	0.190919i
$834$	−27.0517	−0.936724
$835$	0	0
$836$	−0.340173	−0.0117651
$837$	− 4.76487i	− 0.164698i
$838$	28.0338i	0.968413i
$839$	49.6775	1.71506	0.857529	−	0.514435i	$-0.171998\pi$
$839$	49.6775	1.71506	0.857529	+	0.514435i	$0.171998\pi$
$840$	0	0
$841$	−26.9877	−0.930611
$842$	− 16.4040i	− 0.565319i
$843$	− 13.6598i	− 0.470469i
$844$	0.979481	0.0337151
$845$	0	0
$846$	−14.8313	−0.509912
$847$	− 1.00000i	− 0.0343604i
$848$	− 46.2472i	− 1.58814i
$849$	16.6803	0.572468
$850$	0	0
$851$	50.1711	1.71984
$852$	1.77024i	0.0606474i
$853$	− 39.4257i	− 1.34991i	−0.737858	−	0.674956i	$-0.764163\pi$
$853$	− 39.4257i	− 1.34991i	0.737858	−	0.674956i	$-0.235837\pi$
$854$	4.67316	0.159912
$855$	0	0
$856$	20.3303	0.694876
$857$	33.2423i	1.13554i	0.823189	+	0.567768i	$0.192193\pi$
$857$	33.2423i	1.13554i	−0.823189	+	0.567768i	$0.807807\pi$
$858$	0.165166i	0.00563867i
$859$	−7.71646	−0.263282	−0.131641	−	0.991297i	$-0.542025\pi$
$859$	−7.71646	−0.263282	−0.131641	+	0.991297i	$0.542025\pi$
$860$	0	0
$861$	1.89269	0.0645028
$862$	11.7138i	0.398974i
$863$	24.6453i	0.838935i	0.907770	+	0.419467i	$0.137783\pi$
$863$	24.6453i	0.838935i	−0.907770	+	0.419467i	$0.862217\pi$
$864$	11.1773	0.380259
$865$	0	0
$866$	−51.6118	−1.75384
$867$	15.6358i	0.531020i
$868$	0.324575i	0.0110168i
$869$	14.5464	0.493452
$870$	0	0
$871$	0.139935	0.00474150
$872$	38.0989i	1.29019i
$873$	23.2495i	0.786877i
$874$	−8.09890	−0.273949
$875$	0	0
$876$	6.12866	0.207068
$877$	6.17954i	0.208668i	0.994542	+	0.104334i	$0.0332711\pi$
$877$	6.17954i	0.208668i	−0.994542	+	0.104334i	$0.966729\pi$
$878$	− 21.1773i	− 0.714698i
$879$	−29.3835	−0.991080
$880$	0	0
$881$	−49.3295	−1.66195	−0.830976	−	0.556308i	$-0.812218\pi$
$881$	−49.3295	−1.66195	−0.830976	+	0.556308i	$0.812218\pi$
$882$	2.51026i	0.0845248i
$883$	22.1529i	0.745504i	0.927931	+	0.372752i	$0.121586\pi$
$883$	22.1529i	0.745504i	−0.927931	+	0.372752i	$0.878414\pi$
$884$	−0.186522	−0.00627341
$885$	0	0
$886$	17.1910	0.577543
$887$	38.7358i	1.30062i	0.759669	+	0.650310i	$0.225361\pi$
$887$	38.7358i	1.30062i	−0.759669	+	0.650310i	$0.774639\pi$
$888$	25.8113i	0.866170i
$889$	−9.65983	−0.323980
$890$	0	0
$891$	1.44748	0.0484924
$892$	− 3.20128i	− 0.107187i
$893$	5.44521i	0.182217i
$894$	−24.6750	−0.825257
$895$	0	0
$896$	13.4052	0.447837
$897$	0.612646i	0.0204557i
$898$	− 29.3523i	− 0.979498i
$899$	−1.24742	−0.0416038
$900$	0	0
$901$	55.3751	1.84481
$902$	− 2.48974i	− 0.0828993i
$903$	4.52359i	0.150536i
$904$	17.7686	0.590974
$905$	0	0
$906$	−1.90110	−0.0631599
$907$	18.4352i	0.612131i	0.952011	+	0.306065i	$0.0990126\pi$
$907$	18.4352i	0.612131i	−0.952011	+	0.306065i	$0.900987\pi$
$908$	− 3.57077i	− 0.118500i
$909$	14.7370	0.488795
$910$	0	0
$911$	−11.9011	−0.394301	−0.197151	−	0.980373i	$-0.563169\pi$
$911$	−11.9011	−0.394301	−0.197151	+	0.980373i	$0.563169\pi$
$912$	− 4.96266i	− 0.164330i
$913$	− 8.52359i	− 0.282090i
$914$	−1.21235	−0.0401009
$915$	0	0
$916$	−5.00084	−0.165232
$917$	− 4.68035i	− 0.154559i
$918$	45.9565i	1.51679i
$919$	−56.3812	−1.85984	−0.929922	−	0.367756i	$-0.880126\pi$
$919$	−56.3812	−1.85984	−0.929922	+	0.367756i	$0.880126\pi$
$920$	0	0
$921$	9.39189	0.309473
$922$	− 39.3823i	− 1.29699i
$923$	0.375905i	0.0123731i
$924$	−0.431882	−0.0142079
$925$	0	0
$926$	21.9481	0.721260
$927$	− 5.42574i	− 0.178205i
$928$	− 2.92616i	− 0.0960558i
$929$	−19.2351	−0.631084	−0.315542	−	0.948912i	$-0.602186\pi$
$929$	−19.2351	−0.631084	−0.315542	+	0.948912i	$0.602186\pi$
$930$	0	0
$931$	0.921622	0.0302049
$932$	3.09663i	0.101433i
$933$	30.8865i	1.01118i
$934$	28.2401	0.924043
$935$	0	0
$936$	0.375453	0.0122721
$937$	17.6358i	0.576137i	0.957610	+	0.288069i	$0.0930131\pi$
$937$	17.6358i	0.576137i	−0.957610	+	0.288069i	$0.906987\pi$
$938$	2.34858i	0.0766840i
$939$	−30.1087	−0.982562
$940$	0	0
$941$	−20.1990	−0.658469	−0.329235	−	0.944248i	$-0.606791\pi$
$941$	−20.1990	−0.658469	−0.329235	+	0.944248i	$0.606791\pi$
$942$	31.9832i	1.04207i
$943$	− 9.23513i	− 0.300737i
$944$	−9.85354	−0.320705
$945$	0	0
$946$	5.95055	0.193469
$947$	17.6925i	0.574928i	0.957792	+	0.287464i	$0.0928121\pi$
$947$	17.6925i	0.574928i	−0.957792	+	0.287464i	$0.907188\pi$
$948$	− 6.28231i	− 0.204040i
$949$	1.30140	0.0422453
$950$	0	0
$951$	7.38735	0.239551
$952$	13.8322i	0.448304i
$953$	− 39.7093i	− 1.28631i	−0.765736	−	0.643155i	$-0.777625\pi$
$953$	− 39.7093i	− 1.28631i	0.765736	−	0.643155i	$-0.222375\pi$
$954$	25.2267	0.816745
$955$	0	0
$956$	−10.8851	−0.352050
$957$	− 1.65983i	− 0.0536546i
$958$	18.7337i	0.605257i
$959$	8.88655	0.286962
$960$	0	0
$961$	−30.2267	−0.975056
$962$	− 1.24044i	− 0.0399934i
$963$	13.2085i	0.425637i
$964$	−1.34509	−0.0433225
$965$	0	0
$966$	−10.2823	−0.330828
$967$	3.01664i	0.0970087i	0.998823	+	0.0485044i	$0.0154455\pi$
$967$	3.01664i	0.0970087i	−0.998823	+	0.0485044i	$0.984555\pi$
$968$	− 2.51026i	− 0.0806828i
$969$	5.94214	0.190889
$970$	0	0
$971$	−18.2134	−0.584496	−0.292248	−	0.956343i	$-0.594403\pi$
$971$	−18.2134	−0.584496	−0.292248	+	0.956343i	$0.594403\pi$
$972$	5.37486i	0.172399i
$973$	− 15.0205i	− 0.481536i
$974$	−6.51518	−0.208760
$975$	0	0
$976$	13.9721	0.447237
$977$	− 30.0845i	− 0.962489i	−0.876586	−	0.481245i	$-0.840185\pi$
$977$	− 30.0845i	− 0.962489i	0.876586	−	0.481245i	$-0.159815\pi$
$978$	− 20.6537i	− 0.660432i
$979$	−2.83710	−0.0906742
$980$	0	0
$981$	−24.7526	−0.790289
$982$	− 33.8902i	− 1.08148i
$983$	− 5.92267i	− 0.188904i	−0.995529	−	0.0944519i	$-0.969890\pi$
$983$	− 5.92267i	− 0.188904i	0.995529	−	0.0944519i	$-0.0301098\pi$
$984$	4.75115	0.151461
$985$	0	0
$986$	12.0312	0.383151
$987$	6.91321i	0.220050i
$988$	0.0311968i	0 0.000992504i
$989$	22.0722	0.701856
$990$	0	0
$991$	9.24742	0.293754	0.146877	−	0.989155i	$-0.453078\pi$
$991$	9.24742	0.293754	0.146877	+	0.989155i	$0.453078\pi$
$992$	1.81393i	0.0575923i
$993$	− 4.09890i	− 0.130075i
$994$	−6.30898	−0.200109
$995$	0	0
$996$	−3.68118	−0.116643
$997$	32.1496i	1.01819i	0.860711	+	0.509094i	$0.170019\pi$
$997$	32.1496i	1.01819i	−0.860711	+	0.509094i	$0.829981\pi$
$998$	50.7838i	1.60753i
$999$	−47.6163	−1.50651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.b.n.1849.2		6
5.2	odd	4		1925.2.a.v.1.2		3
5.3	odd	4		385.2.a.f.1.2	✓	3
5.4	even	2	inner	1925.2.b.n.1849.5		6
15.8	even	4		3465.2.a.bh.1.2		3
20.3	even	4		6160.2.a.bn.1.1		3
35.13	even	4		2695.2.a.g.1.2		3
55.43	even	4		4235.2.a.q.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.2	✓	3	5.3	odd	4
1925.2.a.v.1.2		3	5.2	odd	4
1925.2.b.n.1849.2		6	1.1	even	1	trivial
1925.2.b.n.1849.5		6	5.4	even	2	inner
2695.2.a.g.1.2		3	35.13	even	4
3465.2.a.bh.1.2		3	15.8	even	4
4235.2.a.q.1.2		3	55.43	even	4
6160.2.a.bn.1.1		3	20.3	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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.53919i q^{2} -1.17009i q^{3} -0.369102 q^{4} -1.80098 q^{6} -1.00000i q^{7} -2.51026i q^{8} +1.63090 q^{9} +O(q^{10})\)	\(q-1.53919i q^{2} -1.17009i q^{3} -0.369102 q^{4} -1.80098 q^{6} -1.00000i q^{7} -2.51026i q^{8} +1.63090 q^{9} -1.00000 q^{11} +0.431882i q^{12} +0.0917087i q^{13} -1.53919 q^{14} -4.60197 q^{16} -5.51026i q^{17} -2.51026i q^{18} -0.921622 q^{19} -1.17009 q^{21} +1.53919i q^{22} +5.70928i q^{23} -2.93722 q^{24} +0.141157 q^{26} -5.41855i q^{27} +0.369102i q^{28} -1.41855 q^{29} +0.879362 q^{31} +2.06278i q^{32} +1.17009i q^{33} -8.48133 q^{34} -0.601968 q^{36} -8.78765i q^{37} +1.41855i q^{38} +0.107307 q^{39} -1.61757 q^{41} +1.80098i q^{42} -3.86603i q^{43} +0.369102 q^{44} +8.78765 q^{46} -5.90829i q^{47} +5.38470i q^{48} -1.00000 q^{49} -6.44748 q^{51} -0.0338499i q^{52} +10.0494i q^{53} -8.34017 q^{54} -2.51026 q^{56} +1.07838i q^{57} +2.18342i q^{58} +2.14116 q^{59} -3.03612 q^{61} -1.35350i q^{62} -1.63090i q^{63} -6.02893 q^{64} +1.80098 q^{66} -1.52586i q^{67} +2.03385i q^{68} +6.68035 q^{69} +4.09890 q^{71} -4.09398i q^{72} -14.1906i q^{73} -13.5259 q^{74} +0.340173 q^{76} +1.00000i q^{77} -0.165166i q^{78} -14.5464 q^{79} -1.44748 q^{81} +2.48974i q^{82} +8.52359i q^{83} +0.431882 q^{84} -5.95055 q^{86} +1.65983i q^{87} +2.51026i q^{88} +2.83710 q^{89} +0.0917087 q^{91} -2.10731i q^{92} -1.02893i q^{93} -9.09398 q^{94} +2.41363 q^{96} +14.2557i q^{97} +1.53919i q^{98} -1.63090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9	\( 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9} - 6 q^{11} - 6 q^{14} + 10 q^{16} - 12 q^{19} + 4 q^{21} - 52 q^{24} - 40 q^{26} + 20 q^{29} - 20 q^{31} + 12 q^{34} + 34 q^{36} + 24 q^{39} + 10 q^{44} + 32 q^{46} - 6 q^{49} - 40 q^{51} - 28 q^{54} + 18 q^{56} - 28 q^{59} + 20 q^{61} - 66 q^{64} - 8 q^{66} - 4 q^{69} - 48 q^{71} - 76 q^{74} - 20 q^{76} - 16 q^{79} - 10 q^{81} - 24 q^{84} - 72 q^{86} - 40 q^{89} - 4 q^{91} - 76 q^{94} + 80 q^{96} - 2 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9 - 6 * q^11 - 6 * q^14 + 10 * q^16 - 12 * q^19 + 4 * q^21 - 52 * q^24 - 40 * q^26 + 20 * q^29 - 20 * q^31 + 12 * q^34 + 34 * q^36 + 24 * q^39 + 10 * q^44 + 32 * q^46 - 6 * q^49 - 40 * q^51 - 28 * q^54 + 18 * q^56 - 28 * q^59 + 20 * q^61 - 66 * q^64 - 8 * q^66 - 4 * q^69 - 48 * q^71 - 76 * q^74 - 20 * q^76 - 16 * q^79 - 10 * q^81 - 24 * q^84 - 72 * q^86 - 40 * q^89 - 4 * q^91 - 76 * q^94 + 80 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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