LMFDB - Embedded newform 925.2.b.f.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(149,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, 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("925.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 20x^{8} + 142x^{6} + 420x^{4} + 457x^{2} + 144 $ x^10 + 20x^8 + 142x^6 + 420x^4 + 457x^2 + 144
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.3
Root			$2.15510i$ of defining polynomial
Character	$\chi$	$=$	925.149
Dual form			925.2.b.f.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15510i q^{2} +1.38311i q^{3} -2.64446 q^{4} +2.98075 q^{6} +2.62521i q^{7} +1.38887i q^{8} +1.08699 q^{9} +O(q^{10})$	\(q-2.15510i q^{2} +1.38311i q^{3} -2.64446 q^{4} +2.98075 q^{6} +2.62521i q^{7} +1.38887i q^{8} +1.08699 q^{9} -1.64446 q^{11} -3.65759i q^{12} +2.44254i q^{13} +5.65759 q^{14} -2.29576 q^{16} +0.578749i q^{17} -2.34258i q^{18} -5.20156 q^{19} -3.63096 q^{21} +3.54397i q^{22} +8.22913i q^{23} -1.92097 q^{24} +5.26391 q^{26} +5.65278i q^{27} -6.94225i q^{28} -0.766229 q^{29} +4.21452 q^{31} +7.72533i q^{32} -2.27447i q^{33} +1.24726 q^{34} -2.87451 q^{36} -1.00000i q^{37} +11.2099i q^{38} -3.37831 q^{39} -1.64446 q^{41} +7.82509i q^{42} -1.91893i q^{43} +4.34870 q^{44} +17.7346 q^{46} +9.56543i q^{47} -3.17530i q^{48} +0.108279 q^{49} -0.800477 q^{51} -6.45918i q^{52} +7.74217i q^{53} +12.1823 q^{54} -3.64608 q^{56} -7.19435i q^{57} +1.65130i q^{58} +13.0359 q^{59} -3.86379 q^{61} -9.08272i q^{62} +2.85359i q^{63} +12.0574 q^{64} -4.90172 q^{66} -11.4566i q^{67} -1.53048i q^{68} -11.3818 q^{69} -2.54690 q^{71} +1.50969i q^{72} -9.79732i q^{73} -2.15510 q^{74} +13.7553 q^{76} -4.31704i q^{77} +7.28059i q^{78} +1.81364 q^{79} -4.55746 q^{81} +3.54397i q^{82} +10.9822i q^{83} +9.60193 q^{84} -4.13549 q^{86} -1.05978i q^{87} -2.28394i q^{88} +8.85915 q^{89} -6.41217 q^{91} -21.7616i q^{92} +5.82917i q^{93} +20.6145 q^{94} -10.6850 q^{96} +10.5605i q^{97} -0.233352i q^{98} -1.78751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 20 q^{4} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 10 * q - 20 * q^4 - 12 * q^6 - 12 * q^9	$ 10 q - 20 q^{4} - 12 q^{6} - 12 q^{9} - 10 q^{11} + 16 q^{14} + 32 q^{16} + 8 q^{19} + 6 q^{21} + 84 q^{24} - 8 q^{26} + 8 q^{29} + 16 q^{31} + 64 q^{34} + 32 q^{36} - 4 q^{39} - 10 q^{41} + 92 q^{44} - 44 q^{49} - 4 q^{51} + 20 q^{54} + 16 q^{56} + 60 q^{59} - 28 q^{61} - 40 q^{64} + 96 q^{66} - 16 q^{69} - 14 q^{71} - 4 q^{74} + 24 q^{76} - 56 q^{79} - 62 q^{81} + 36 q^{84} + 88 q^{86} - 12 q^{89} - 28 q^{91} - 8 q^{94} - 84 q^{96} + 20 q^{99}+O(q^{100}) $ 10 * q - 20 * q^4 - 12 * q^6 - 12 * q^9 - 10 * q^11 + 16 * q^14 + 32 * q^16 + 8 * q^19 + 6 * q^21 + 84 * q^24 - 8 * q^26 + 8 * q^29 + 16 * q^31 + 64 * q^34 + 32 * q^36 - 4 * q^39 - 10 * q^41 + 92 * q^44 - 44 * q^49 - 4 * q^51 + 20 * q^54 + 16 * q^56 + 60 * q^59 - 28 * q^61 - 40 * q^64 + 96 * q^66 - 16 * q^69 - 14 * q^71 - 4 * q^74 + 24 * q^76 - 56 * q^79 - 62 * q^81 + 36 * q^84 + 88 * q^86 - 12 * q^89 - 28 * q^91 - 8 * q^94 - 84 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.15510i	− 1.52389i	−0.647644	−	0.761943i	$-0.724246\pi$
$2$	− 2.15510i	− 1.52389i	0.647644	−	0.761943i	$-0.275754\pi$
$3$	1.38311i	0.798542i	0.916833	+	0.399271i	$0.130737\pi$
$3$	1.38311i	0.798542i	−0.916833	+	0.399271i	$0.869263\pi$
$4$	−2.64446	−1.32223
$5$	0	0
$5$	0	0
$6$	2.98075	1.21689
$7$	2.62521i	0.992236i	0.868255	+	0.496118i	$0.165242\pi$
$7$	2.62521i	0.992236i	−0.868255	+	0.496118i	$0.834758\pi$
$8$	1.38887i	0.491040i
$9$	1.08699	0.362331
$10$	0	0
$11$	−1.64446	−0.495823	−0.247911	−	0.968783i	$-0.579744\pi$
$11$	−1.64446	−0.495823	−0.247911	+	0.968783i	$0.579744\pi$
$12$	− 3.65759i	− 1.05585i
$13$	2.44254i	0.677438i	0.940888	+	0.338719i	$0.109994\pi$
$13$	2.44254i	0.677438i	−0.940888	+	0.338719i	$0.890006\pi$
$14$	5.65759	1.51205
$15$	0	0
$16$	−2.29576	−0.573940
$17$	0.578749i	0.140367i	0.997534	+	0.0701837i	$0.0223585\pi$
$17$	0.578749i	0.140367i	−0.997534	+	0.0701837i	$0.977641\pi$
$18$	− 2.34258i	− 0.552151i
$19$	−5.20156	−1.19332	−0.596660	−	0.802494i	$-0.703506\pi$
$19$	−5.20156	−1.19332	−0.596660	+	0.802494i	$0.703506\pi$
$20$	0	0
$21$	−3.63096	−0.792341
$22$	3.54397i	0.755577i
$23$	8.22913i	1.71589i	0.513739	+	0.857946i	$0.328260\pi$
$23$	8.22913i	1.71589i	−0.513739	+	0.857946i	$0.671740\pi$
$24$	−1.92097	−0.392116
$25$	0	0
$26$	5.26391	1.03234
$27$	5.65278i	1.08788i
$28$	− 6.94225i	− 1.31196i
$29$	−0.766229	−0.142285	−0.0711426	−	0.997466i	$-0.522665\pi$
$29$	−0.766229	−0.142285	−0.0711426	+	0.997466i	$0.522665\pi$
$30$	0	0
$31$	4.21452	0.756950	0.378475	−	0.925611i	$-0.376449\pi$
$31$	4.21452	0.756950	0.378475	+	0.925611i	$0.376449\pi$
$32$	7.72533i	1.36566i
$33$	− 2.27447i	− 0.395935i
$34$	1.24726	0.213904
$35$	0	0
$36$	−2.87451	−0.479085
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	11.2099i	1.81848i
$39$	−3.37831	−0.540962
$40$	0	0
$41$	−1.64446	−0.256821	−0.128411	−	0.991721i	$-0.540988\pi$
$41$	−1.64446	−0.256821	−0.128411	+	0.991721i	$0.540988\pi$
$42$	7.82509i	1.20744i
$43$	− 1.91893i	− 0.292634i	−0.989238	−	0.146317i	$-0.953258\pi$
$43$	− 1.91893i	− 0.292634i	0.989238	−	0.146317i	$-0.0467420\pi$
$44$	4.34870	0.655591
$45$	0	0
$46$	17.7346	2.61482
$47$	9.56543i	1.39526i	0.716458	+	0.697630i	$0.245762\pi$
$47$	9.56543i	1.39526i	−0.716458	+	0.697630i	$0.754238\pi$
$48$	− 3.17530i	− 0.458315i
$49$	0.108279	0.0154684
$50$	0	0
$51$	−0.800477	−0.112089
$52$	− 6.45918i	− 0.895728i
$53$	7.74217i	1.06347i	0.846911	+	0.531735i	$0.178460\pi$
$53$	7.74217i	1.06347i	−0.846911	+	0.531735i	$0.821540\pi$
$54$	12.1823	1.65780
$55$	0	0
$56$	−3.64608	−0.487227
$57$	− 7.19435i	− 0.952915i
$58$	1.65130i	0.216827i
$59$	13.0359	1.69713	0.848565	−	0.529092i	$-0.177467\pi$
$59$	13.0359	1.69713	0.848565	+	0.529092i	$0.177467\pi$
$60$	0	0
$61$	−3.86379	−0.494707	−0.247354	−	0.968925i	$-0.579561\pi$
$61$	−3.86379	−0.494707	−0.247354	+	0.968925i	$0.579561\pi$
$62$	− 9.08272i	− 1.15351i
$63$	2.85359i	0.359518i
$64$	12.0574	1.50717
$65$	0	0
$66$	−4.90172	−0.603360
$67$	− 11.4566i	− 1.39965i	−0.714315	−	0.699824i	$-0.753262\pi$
$67$	− 11.4566i	− 1.39965i	0.714315	−	0.699824i	$-0.246738\pi$
$68$	− 1.53048i	− 0.185598i
$69$	−11.3818	−1.37021
$70$	0	0
$71$	−2.54690	−0.302261	−0.151131	−	0.988514i	$-0.548291\pi$
$71$	−2.54690	−0.302261	−0.151131	+	0.988514i	$0.548291\pi$
$72$	1.50969i	0.177919i
$73$	− 9.79732i	− 1.14669i	−0.819314	−	0.573345i	$-0.805646\pi$
$73$	− 9.79732i	− 1.14669i	0.819314	−	0.573345i	$-0.194354\pi$
$74$	−2.15510	−0.250525
$75$	0	0
$76$	13.7553	1.57784
$77$	− 4.31704i	− 0.491973i
$78$	7.28059i	0.824365i
$79$	1.81364	0.204050	0.102025	−	0.994782i	$-0.467468\pi$
$79$	1.81364	0.204050	0.102025	+	0.994782i	$0.467468\pi$
$80$	0	0
$81$	−4.55746	−0.506385
$82$	3.54397i	0.391366i
$83$	10.9822i	1.20546i	0.797947	+	0.602728i	$0.205920\pi$
$83$	10.9822i	1.20546i	−0.797947	+	0.602728i	$0.794080\pi$
$84$	9.60193	1.04766
$85$	0	0
$86$	−4.13549	−0.445941
$87$	− 1.05978i	− 0.113621i
$88$	− 2.28394i	− 0.243469i
$89$	8.85915	0.939068	0.469534	−	0.882914i	$-0.344422\pi$
$89$	8.85915	0.939068	0.469534	+	0.882914i	$0.344422\pi$
$90$	0	0
$91$	−6.41217	−0.672178
$92$	− 21.7616i	− 2.26880i
$93$	5.82917i	0.604456i
$94$	20.6145	2.12622
$95$	0	0
$96$	−10.6850	−1.09054
$97$	10.5605i	1.07225i	0.844138	+	0.536126i	$0.180113\pi$
$97$	10.5605i	1.07225i	−0.844138	+	0.536126i	$0.819887\pi$
$98$	− 0.233352i	− 0.0235721i
$99$	−1.78751	−0.179652
$100$	0	0
$101$	0.908368	0.0903860	0.0451930	−	0.998978i	$-0.485610\pi$
$101$	0.908368	0.0903860	0.0451930	+	0.998978i	$0.485610\pi$
$102$	1.72511i	0.170811i
$103$	18.9017i	1.86244i	0.364455	+	0.931221i	$0.381255\pi$
$103$	18.9017i	1.86244i	−0.364455	+	0.931221i	$0.618745\pi$
$104$	−3.39237	−0.332649
$105$	0	0
$106$	16.6852	1.62061
$107$	− 9.67742i	− 0.935552i	−0.883847	−	0.467776i	$-0.845055\pi$
$107$	− 9.67742i	− 0.935552i	0.883847	−	0.467776i	$-0.154945\pi$
$108$	− 14.9485i	− 1.43842i
$109$	−10.9954	−1.05316	−0.526582	−	0.850124i	$-0.676527\pi$
$109$	−10.9954	−1.05316	−0.526582	+	0.850124i	$0.676527\pi$
$110$	0	0
$111$	1.38311	0.131279
$112$	− 6.02685i	− 0.569483i
$113$	− 2.26855i	− 0.213407i	−0.994291	−	0.106704i	$-0.965970\pi$
$113$	− 2.26855i	− 0.213407i	0.994291	−	0.106704i	$-0.0340296\pi$
$114$	−15.5046	−1.45213
$115$	0	0
$116$	2.02626	0.188134
$117$	2.65502i	0.245457i
$118$	− 28.0937i	− 2.58623i
$119$	−1.51934	−0.139278
$120$	0	0
$121$	−8.29576	−0.754160
$122$	8.32685i	0.753877i
$123$	− 2.27447i	− 0.205082i
$124$	−11.1451	−1.00086
$125$	0	0
$126$	6.14976	0.547864
$127$	− 20.5147i	− 1.82038i	−0.414186	−	0.910192i	$-0.635934\pi$
$127$	− 20.5147i	− 1.82038i	0.414186	−	0.910192i	$-0.364066\pi$
$128$	− 10.5341i	− 0.931095i
$129$	2.65410	0.233681
$130$	0	0
$131$	−12.9339	−1.13004	−0.565021	−	0.825076i	$-0.691132\pi$
$131$	−12.9339	−1.13004	−0.565021	+	0.825076i	$0.691132\pi$
$132$	6.01475i	0.523517i
$133$	− 13.6552i	− 1.18405i
$134$	−24.6902	−2.13290
$135$	0	0
$136$	−0.803808	−0.0689260
$137$	− 13.2882i	− 1.13529i	−0.823275	−	0.567643i	$-0.807855\pi$
$137$	− 13.2882i	− 1.13529i	0.823275	−	0.567643i	$-0.192145\pi$
$138$	24.5290i	2.08805i
$139$	−12.0833	−1.02489	−0.512446	−	0.858719i	$-0.671261\pi$
$139$	−12.0833	−1.02489	−0.512446	+	0.858719i	$0.671261\pi$
$140$	0	0
$141$	−13.2301	−1.11417
$142$	5.48883i	0.460612i
$143$	− 4.01665i	− 0.335889i
$144$	−2.49548	−0.207956
$145$	0	0
$146$	−21.1142	−1.74742
$147$	0.149762i	0.0123522i
$148$	2.64446i	0.217373i
$149$	20.2139	1.65599	0.827995	−	0.560736i	$-0.189482\pi$
$149$	20.2139	1.65599	0.827995	+	0.560736i	$0.189482\pi$
$150$	0	0
$151$	15.8330	1.28847	0.644237	−	0.764826i	$-0.277175\pi$
$151$	15.8330	1.28847	0.644237	+	0.764826i	$0.277175\pi$
$152$	− 7.22429i	− 0.585968i
$153$	0.629097i	0.0508595i
$154$	−9.30366	−0.749711
$155$	0	0
$156$	8.93379	0.715276
$157$	− 17.0862i	− 1.36363i	−0.731525	−	0.681815i	$-0.761191\pi$
$157$	− 17.0862i	− 1.36363i	0.731525	−	0.681815i	$-0.238809\pi$
$158$	− 3.90857i	− 0.310949i
$159$	−10.7083	−0.849225
$160$	0	0
$161$	−21.6032	−1.70257
$162$	9.82179i	0.771673i
$163$	6.82137i	0.534291i	0.963656	+	0.267146i	$0.0860805\pi$
$163$	6.82137i	0.534291i	−0.963656	+	0.267146i	$0.913920\pi$
$164$	4.34870	0.339576
$165$	0	0
$166$	23.6678	1.83698
$167$	4.90916i	0.379882i	0.981796	+	0.189941i	$0.0608297\pi$
$167$	4.90916i	0.379882i	−0.981796	+	0.189941i	$0.939170\pi$
$168$	− 5.04294i	− 0.389071i
$169$	7.03402	0.541078
$170$	0	0
$171$	−5.65406	−0.432377
$172$	5.07453i	0.386929i
$173$	− 21.2573i	− 1.61616i	−0.589073	−	0.808080i	$-0.700507\pi$
$173$	− 21.2573i	− 1.61616i	0.589073	−	0.808080i	$-0.299493\pi$
$174$	−2.28394	−0.173145
$175$	0	0
$176$	3.77528	0.284572
$177$	18.0301i	1.35523i
$178$	− 19.0924i	− 1.43103i
$179$	7.66910	0.573215	0.286608	−	0.958048i	$-0.407472\pi$
$179$	7.66910	0.573215	0.286608	+	0.958048i	$0.407472\pi$
$180$	0	0
$181$	−10.3972	−0.772817	−0.386409	−	0.922328i	$-0.626285\pi$
$181$	−10.3972	−0.772817	−0.386409	+	0.922328i	$0.626285\pi$
$182$	13.8189i	1.02432i
$183$	− 5.34406i	− 0.395044i
$184$	−11.4292	−0.842572
$185$	0	0
$186$	12.5624	0.921123
$187$	− 0.951729i	− 0.0695973i
$188$	− 25.2954i	− 1.84485i
$189$	−14.8397	−1.07943
$190$	0	0
$191$	−14.0187	−1.01436	−0.507178	−	0.861841i	$-0.669311\pi$
$191$	−14.0187	−1.01436	−0.507178	+	0.861841i	$0.669311\pi$
$192$	16.6767i	1.20354i
$193$	− 16.5915i	− 1.19428i	−0.802136	−	0.597142i	$-0.796303\pi$
$193$	− 16.5915i	− 1.19428i	0.802136	−	0.597142i	$-0.203697\pi$
$194$	22.7589	1.63399
$195$	0	0
$196$	−0.286339	−0.0204528
$197$	20.3482i	1.44975i	0.688882	+	0.724873i	$0.258102\pi$
$197$	20.3482i	1.44975i	−0.688882	+	0.724873i	$0.741898\pi$
$198$	3.85227i	0.273769i
$199$	11.5118	0.816047	0.408024	−	0.912971i	$-0.366218\pi$
$199$	11.5118	0.816047	0.408024	+	0.912971i	$0.366218\pi$
$200$	0	0
$201$	15.8458	1.11768
$202$	− 1.95762i	− 0.137738i
$203$	− 2.01151i	− 0.141180i
$204$	2.11683	0.148208
$205$	0	0
$206$	40.7351	2.83815
$207$	8.94501i	0.621721i
$208$	− 5.60747i	− 0.388808i
$209$	8.55374	0.591675
$210$	0	0
$211$	−1.51976	−0.104624	−0.0523122	−	0.998631i	$-0.516659\pi$
$211$	−1.51976	−0.104624	−0.0523122	+	0.998631i	$0.516659\pi$
$212$	− 20.4738i	− 1.40615i
$213$	− 3.52266i	− 0.241368i
$214$	−20.8558	−1.42567
$215$	0	0
$216$	−7.85098	−0.534192
$217$	11.0640i	0.751073i
$218$	23.6961i	1.60490i
$219$	13.5508	0.915679
$220$	0	0
$221$	−1.41362	−0.0950901
$222$	− 2.98075i	− 0.200055i
$223$	6.89820i	0.461938i	0.972961	+	0.230969i	$0.0741896\pi$
$223$	6.89820i	0.461938i	−0.972961	+	0.230969i	$0.925810\pi$
$224$	−20.2806	−1.35506
$225$	0	0
$226$	−4.88895	−0.325208
$227$	26.8277i	1.78062i	0.455359	+	0.890308i	$0.349511\pi$
$227$	26.8277i	1.78062i	−0.455359	+	0.890308i	$0.650489\pi$
$228$	19.0252i	1.25997i
$229$	−26.0120	−1.71892	−0.859462	−	0.511200i	$-0.829201\pi$
$229$	−26.0120	−1.71892	−0.859462	+	0.511200i	$0.829201\pi$
$230$	0	0
$231$	5.97097	0.392861
$232$	− 1.06419i	− 0.0698677i
$233$	11.3141i	0.741212i	0.928790	+	0.370606i	$0.120850\pi$
$233$	11.3141i	0.741212i	−0.928790	+	0.370606i	$0.879150\pi$
$234$	5.72184	0.374048
$235$	0	0
$236$	−34.4729	−2.24399
$237$	2.50847i	0.162943i
$238$	3.27433i	0.212243i
$239$	−21.2819	−1.37661	−0.688306	−	0.725420i	$-0.741645\pi$
$239$	−21.2819	−1.37661	−0.688306	+	0.725420i	$0.741645\pi$
$240$	0	0
$241$	21.1975	1.36545	0.682726	−	0.730675i	$-0.260794\pi$
$241$	21.1975	1.36545	0.682726	+	0.730675i	$0.260794\pi$
$242$	17.8782i	1.14925i
$243$	10.6548i	0.683509i
$244$	10.2176	0.654116
$245$	0	0
$246$	−4.90172	−0.312522
$247$	− 12.7050i	− 0.808400i
$248$	5.85343i	0.371693i
$249$	−15.1897	−0.962607
$250$	0	0
$251$	−6.06998	−0.383134	−0.191567	−	0.981480i	$-0.561357\pi$
$251$	−6.06998	−0.383134	−0.191567	+	0.981480i	$0.561357\pi$
$252$	− 7.54619i	− 0.475365i
$253$	− 13.5325i	− 0.850778i
$254$	−44.2112	−2.77406
$255$	0	0
$256$	1.41258	0.0882866
$257$	− 11.2639i	− 0.702623i	−0.936259	−	0.351312i	$-0.885736\pi$
$257$	− 11.2639i	− 0.702623i	0.936259	−	0.351312i	$-0.114264\pi$
$258$	− 5.71986i	− 0.356103i
$259$	2.62521	0.163123
$260$	0	0
$261$	−0.832887	−0.0515544
$262$	27.8739i	1.72206i
$263$	27.5622i	1.69956i	0.527137	+	0.849780i	$0.323265\pi$
$263$	27.5622i	1.69956i	−0.527137	+	0.849780i	$0.676735\pi$
$264$	3.15895	0.194420
$265$	0	0
$266$	−29.4283	−1.80436
$267$	12.2532i	0.749885i
$268$	30.2965i	1.85066i
$269$	22.9078	1.39672	0.698358	−	0.715749i	$-0.253915\pi$
$269$	22.9078	1.39672	0.698358	+	0.715749i	$0.253915\pi$
$270$	0	0
$271$	5.89472	0.358079	0.179039	−	0.983842i	$-0.442701\pi$
$271$	5.89472	0.358079	0.179039	+	0.983842i	$0.442701\pi$
$272$	− 1.32867i	− 0.0805624i
$273$	− 8.86876i	− 0.536762i
$274$	−28.6374	−1.73005
$275$	0	0
$276$	30.0988	1.81173
$277$	− 20.8630i	− 1.25354i	−0.779205	−	0.626769i	$-0.784377\pi$
$277$	− 20.8630i	− 1.25354i	0.779205	−	0.626769i	$-0.215623\pi$
$278$	26.0407i	1.56182i
$279$	4.58116	0.274267
$280$	0	0
$281$	−0.481953	−0.0287509	−0.0143754	−	0.999897i	$-0.504576\pi$
$281$	−0.481953	−0.0287509	−0.0143754	+	0.999897i	$0.504576\pi$
$282$	28.5122i	1.69787i
$283$	0.890931i	0.0529603i	0.999649	+	0.0264802i	$0.00842988\pi$
$283$	0.890931i	0.0529603i	−0.999649	+	0.0264802i	$0.991570\pi$
$284$	6.73517	0.399659
$285$	0	0
$286$	−8.65628	−0.511856
$287$	− 4.31704i	− 0.254827i
$288$	8.39739i	0.494821i
$289$	16.6650	0.980297
$290$	0	0
$291$	−14.6063	−0.856238
$292$	25.9086i	1.51619i
$293$	− 16.5945i	− 0.969460i	−0.874664	−	0.484730i	$-0.838918\pi$
$293$	− 16.5945i	− 0.969460i	0.874664	−	0.484730i	$-0.161082\pi$
$294$	0.322753	0.0188233
$295$	0	0
$296$	1.38887	0.0807265
$297$	− 9.29576i	− 0.539395i
$298$	− 43.5630i	− 2.52354i
$299$	−20.1000	−1.16241
$300$	0	0
$301$	5.03760	0.290362
$302$	− 34.1218i	− 1.96349i
$303$	1.25638i	0.0721770i
$304$	11.9415	0.684894
$305$	0	0
$306$	1.35577	0.0775041
$307$	− 24.7733i	− 1.41389i	−0.707271	−	0.706943i	$-0.750074\pi$
$307$	− 24.7733i	− 1.41389i	0.707271	−	0.706943i	$-0.249926\pi$
$308$	11.4162i	0.650501i
$309$	−26.1432	−1.48724
$310$	0	0
$311$	27.1396	1.53895	0.769473	−	0.638680i	$-0.220519\pi$
$311$	27.1396	1.53895	0.769473	+	0.638680i	$0.220519\pi$
$312$	− 4.69203i	− 0.265634i
$313$	− 8.71332i	− 0.492506i	−0.969206	−	0.246253i	$-0.920801\pi$
$313$	− 8.71332i	− 0.492506i	0.969206	−	0.246253i	$-0.0791994\pi$
$314$	−36.8225	−2.07802
$315$	0	0
$316$	−4.79609	−0.269801
$317$	− 7.50140i	− 0.421321i	−0.977559	−	0.210660i	$-0.932439\pi$
$317$	− 7.50140i	− 0.421321i	0.977559	−	0.210660i	$-0.0675614\pi$
$318$	23.0775i	1.29412i
$319$	1.26003	0.0705482
$320$	0	0
$321$	13.3850	0.747077
$322$	46.5570i	2.59452i
$323$	− 3.01040i	− 0.167503i
$324$	12.0520	0.669557
$325$	0	0
$326$	14.7007	0.814199
$327$	− 15.2078i	− 0.840996i
$328$	− 2.28394i	− 0.126109i
$329$	−25.1112	−1.38443
$330$	0	0
$331$	−10.4401	−0.573841	−0.286921	−	0.957954i	$-0.592632\pi$
$331$	−10.4401	−0.573841	−0.286921	+	0.957954i	$0.592632\pi$
$332$	− 29.0420i	− 1.59389i
$333$	− 1.08699i	− 0.0595669i
$334$	10.5797	0.578897
$335$	0	0
$336$	8.33582	0.454756
$337$	11.4990i	0.626389i	0.949689	+	0.313194i	$0.101399\pi$
$337$	11.4990i	0.626389i	−0.949689	+	0.313194i	$0.898601\pi$
$338$	− 15.1590i	− 0.824542i
$339$	3.13766	0.170414
$340$	0	0
$341$	−6.93060	−0.375313
$342$	12.1851i	0.658893i
$343$	18.6607i	1.00758i
$344$	2.66515	0.143695
$345$	0	0
$346$	−45.8115	−2.46284
$347$	− 19.6061i	− 1.05251i	−0.850326	−	0.526257i	$-0.823595\pi$
$347$	− 19.6061i	− 1.05251i	0.850326	−	0.526257i	$-0.176405\pi$
$348$	2.80255i	0.150233i
$349$	21.9395	1.17439	0.587196	−	0.809445i	$-0.300232\pi$
$349$	21.9395	1.17439	0.587196	+	0.809445i	$0.300232\pi$
$350$	0	0
$351$	−13.8071	−0.736970
$352$	− 12.7040i	− 0.677125i
$353$	2.11029i	0.112319i	0.998422	+	0.0561597i	$0.0178856\pi$
$353$	2.11029i	0.112319i	−0.998422	+	0.0561597i	$0.982114\pi$
$354$	38.8568	2.06521
$355$	0	0
$356$	−23.4276	−1.24166
$357$	− 2.10142i	− 0.111219i
$358$	− 16.5277i	− 0.873515i
$359$	6.97594	0.368176	0.184088	−	0.982910i	$-0.441067\pi$
$359$	6.97594	0.368176	0.184088	+	0.982910i	$0.441067\pi$
$360$	0	0
$361$	8.05622	0.424012
$362$	22.4070i	1.17769i
$363$	− 11.4740i	− 0.602228i
$364$	16.9567	0.888773
$365$	0	0
$366$	−11.5170	−0.602002
$367$	− 9.57842i	− 0.499989i	−0.968247	−	0.249995i	$-0.919571\pi$
$367$	− 9.57842i	− 0.499989i	0.968247	−	0.249995i	$-0.0804289\pi$
$368$	− 18.8921i	− 0.984819i
$369$	−1.78751	−0.0930543
$370$	0	0
$371$	−20.3248	−1.05521
$372$	− 15.4150i	− 0.799230i
$373$	5.34611i	0.276811i	0.990376	+	0.138405i	$0.0441977\pi$
$373$	5.34611i	0.276811i	−0.990376	+	0.138405i	$0.955802\pi$
$374$	−2.05107	−0.106058
$375$	0	0
$376$	−13.2851	−0.685129
$377$	− 1.87154i	− 0.0963894i
$378$	31.9811i	1.64493i
$379$	30.8519	1.58476	0.792378	−	0.610031i	$-0.208843\pi$
$379$	30.8519	1.58476	0.792378	+	0.610031i	$0.208843\pi$
$380$	0	0
$381$	28.3742	1.45365
$382$	30.2117i	1.54576i
$383$	− 9.29595i	− 0.475001i	−0.971387	−	0.237500i	$-0.923672\pi$
$383$	− 9.29595i	− 0.475001i	0.971387	−	0.237500i	$-0.0763281\pi$
$384$	14.5699	0.743518
$385$	0	0
$386$	−35.7564	−1.81995
$387$	− 2.08587i	− 0.106031i
$388$	− 27.9267i	− 1.41776i
$389$	−19.0668	−0.966726	−0.483363	−	0.875420i	$-0.660585\pi$
$389$	−19.0668	−0.966726	−0.483363	+	0.875420i	$0.660585\pi$
$390$	0	0
$391$	−4.76261	−0.240855
$392$	0.150386i	0.00759562i
$393$	− 17.8891i	− 0.902386i
$394$	43.8523	2.20925
$395$	0	0
$396$	4.72701	0.237541
$397$	8.23564i	0.413335i	0.978411	+	0.206667i	$0.0662618\pi$
$397$	8.23564i	0.413335i	−0.978411	+	0.206667i	$0.933738\pi$
$398$	− 24.8090i	− 1.24356i
$399$	18.8867	0.945517
$400$	0	0
$401$	11.2408	0.561339	0.280669	−	0.959804i	$-0.409444\pi$
$401$	11.2408	0.561339	0.280669	+	0.959804i	$0.409444\pi$
$402$	− 34.1493i	− 1.70321i
$403$	10.2941i	0.512787i
$404$	−2.40214	−0.119511
$405$	0	0
$406$	−4.33501	−0.215143
$407$	1.64446i	0.0815127i
$408$	− 1.11176i	− 0.0550403i
$409$	−22.0826	−1.09191	−0.545957	−	0.837813i	$-0.683834\pi$
$409$	−22.0826	−1.09191	−0.545957	+	0.837813i	$0.683834\pi$
$410$	0	0
$411$	18.3791	0.906574
$412$	− 49.9848i	− 2.46257i
$413$	34.2219i	1.68395i
$414$	19.2774	0.947433
$415$	0	0
$416$	−18.8694	−0.925149
$417$	− 16.7126i	− 0.818419i
$418$	− 18.4342i	− 0.901645i
$419$	15.6870	0.766361	0.383181	−	0.923673i	$-0.374829\pi$
$419$	15.6870	0.766361	0.383181	+	0.923673i	$0.374829\pi$
$420$	0	0
$421$	2.52196	0.122913	0.0614564	−	0.998110i	$-0.480425\pi$
$421$	2.52196	0.122913	0.0614564	+	0.998110i	$0.480425\pi$
$422$	3.27523i	0.159436i
$423$	10.3976i	0.505546i
$424$	−10.7529	−0.522206
$425$	0	0
$426$	−7.59168	−0.367818
$427$	− 10.1432i	− 0.490866i
$428$	25.5915i	1.23701i
$429$	5.55548	0.268221
$430$	0	0
$431$	24.9936	1.20390	0.601951	−	0.798533i	$-0.294390\pi$
$431$	24.9936	1.20390	0.601951	+	0.798533i	$0.294390\pi$
$432$	− 12.9774i	− 0.624377i
$433$	− 18.0649i	− 0.868146i	−0.900878	−	0.434073i	$-0.857076\pi$
$433$	− 18.0649i	− 0.868146i	0.900878	−	0.434073i	$-0.142924\pi$
$434$	23.8440	1.14455
$435$	0	0
$436$	29.0768	1.39252
$437$	− 42.8043i	− 2.04761i
$438$	− 29.2034i	− 1.39539i
$439$	11.2220	0.535595	0.267798	−	0.963475i	$-0.413704\pi$
$439$	11.2220	0.535595	0.267798	+	0.963475i	$0.413704\pi$
$440$	0	0
$441$	0.117699	0.00560470
$442$	3.04649i	0.144907i
$443$	− 38.4723i	− 1.82788i	−0.405854	−	0.913938i	$-0.633026\pi$
$443$	− 38.4723i	− 1.82788i	0.405854	−	0.913938i	$-0.366974\pi$
$444$	−3.65759	−0.173581
$445$	0	0
$446$	14.8663	0.703941
$447$	27.9582i	1.32238i
$448$	31.6531i	1.49547i
$449$	−39.8327	−1.87982	−0.939910	−	0.341423i	$-0.889091\pi$
$449$	−39.8327	−1.87982	−0.939910	+	0.341423i	$0.889091\pi$
$450$	0	0
$451$	2.70424	0.127338
$452$	5.99908i	0.282173i
$453$	21.8989i	1.02890i
$454$	57.8163	2.71346
$455$	0	0
$456$	9.99203	0.467920
$457$	11.8205i	0.552939i	0.961023	+	0.276470i	$0.0891645\pi$
$457$	11.8205i	0.552939i	−0.961023	+	0.276470i	$0.910835\pi$
$458$	56.0586i	2.61944i
$459$	−3.27154	−0.152703
$460$	0	0
$461$	12.7422	0.593464	0.296732	−	0.954961i	$-0.404103\pi$
$461$	12.7422	0.593464	0.296732	+	0.954961i	$0.404103\pi$
$462$	− 12.8680i	− 0.598675i
$463$	− 0.694775i	− 0.0322889i	−0.999870	−	0.0161445i	$-0.994861\pi$
$463$	− 0.694775i	− 0.0322889i	0.999870	−	0.0161445i	$-0.00513917\pi$
$464$	1.75908	0.0816632
$465$	0	0
$466$	24.3831	1.12952
$467$	− 2.28132i	− 0.105567i	−0.998606	−	0.0527834i	$-0.983191\pi$
$467$	− 2.28132i	− 0.105567i	0.998606	−	0.0527834i	$-0.0168093\pi$
$468$	− 7.02109i	− 0.324550i
$469$	30.0760	1.38878
$470$	0	0
$471$	23.6322	1.08892
$472$	18.1052i	0.833358i
$473$	3.15560i	0.145095i
$474$	5.40600	0.248306
$475$	0	0
$476$	4.01783	0.184157
$477$	8.41569i	0.385328i
$478$	45.8646i	2.09780i
$479$	25.7331	1.17578	0.587888	−	0.808942i	$-0.299959\pi$
$479$	25.7331	1.17578	0.587888	+	0.808942i	$0.299959\pi$
$480$	0	0
$481$	2.44254	0.111370
$482$	− 45.6828i	− 2.08079i
$483$	− 29.8797i	− 1.35957i
$484$	21.9378	0.997172
$485$	0	0
$486$	22.9623	1.04159
$487$	18.7007i	0.847412i	0.905800	+	0.423706i	$0.139271\pi$
$487$	18.7007i	0.847412i	−0.905800	+	0.423706i	$0.860729\pi$
$488$	− 5.36630i	− 0.242921i
$489$	−9.43474	−0.426654
$490$	0	0
$491$	18.5675	0.837939	0.418970	−	0.908000i	$-0.362391\pi$
$491$	18.5675	0.837939	0.418970	+	0.908000i	$0.362391\pi$
$492$	6.01475i	0.271166i
$493$	− 0.443455i	− 0.0199722i
$494$	−27.3805	−1.23191
$495$	0	0
$496$	−9.67553	−0.434444
$497$	− 6.68615i	− 0.299915i
$498$	32.7353i	1.46690i
$499$	9.35537	0.418804	0.209402	−	0.977830i	$-0.432848\pi$
$499$	9.35537	0.418804	0.209402	+	0.977830i	$0.432848\pi$
$500$	0	0
$501$	−6.78993	−0.303352
$502$	13.0814i	0.583853i
$503$	− 25.6072i	− 1.14177i	−0.821030	−	0.570885i	$-0.806600\pi$
$503$	− 25.6072i	− 1.14177i	0.821030	−	0.570885i	$-0.193400\pi$
$504$	−3.96326	−0.176538
$505$	0	0
$506$	−29.1638	−1.29649
$507$	9.72885i	0.432074i
$508$	54.2502i	2.40696i
$509$	32.5502	1.44276	0.721382	−	0.692537i	$-0.243507\pi$
$509$	32.5502	1.44276	0.721382	+	0.692537i	$0.243507\pi$
$510$	0	0
$511$	25.7200	1.13779
$512$	− 24.1125i	− 1.06563i
$513$	− 29.4033i	− 1.29819i
$514$	−24.2749	−1.07072
$515$	0	0
$516$	−7.01866	−0.308979
$517$	− 15.7299i	− 0.691802i
$518$	− 5.65759i	− 0.248580i
$519$	29.4012	1.29057
$520$	0	0
$521$	3.09643	0.135657	0.0678285	−	0.997697i	$-0.478393\pi$
$521$	3.09643	0.135657	0.0678285	+	0.997697i	$0.478393\pi$
$522$	1.79495i	0.0785630i
$523$	24.9299i	1.09011i	0.838401	+	0.545054i	$0.183491\pi$
$523$	24.9299i	1.09011i	−0.838401	+	0.545054i	$0.816509\pi$
$524$	34.2032	1.49418
$525$	0	0
$526$	59.3994	2.58994
$527$	2.43915i	0.106251i
$528$	5.22164i	0.227243i
$529$	−44.7186	−1.94429
$530$	0	0
$531$	14.1699	0.614923
$532$	36.1105i	1.56559i
$533$	− 4.01665i	− 0.173980i
$534$	26.4069	1.14274
$535$	0	0
$536$	15.9118	0.687283
$537$	10.6072i	0.457736i
$538$	− 49.3687i	− 2.12843i
$539$	−0.178060	−0.00766960
$540$	0	0
$541$	−37.4914	−1.61188	−0.805940	−	0.591997i	$-0.798340\pi$
$541$	−37.4914	−1.61188	−0.805940	+	0.591997i	$0.798340\pi$
$542$	− 12.7037i	− 0.545671i
$543$	− 14.3805i	− 0.617127i
$544$	−4.47103	−0.191694
$545$	0	0
$546$	−19.1131	−0.817964
$547$	8.33942i	0.356568i	0.983979	+	0.178284i	$0.0570546\pi$
$547$	8.33942i	0.356568i	−0.983979	+	0.178284i	$0.942945\pi$
$548$	35.1401i	1.50111i
$549$	−4.19991	−0.179248
$550$	0	0
$551$	3.98559	0.169792
$552$	− 15.8079i	− 0.672829i
$553$	4.76118i	0.202466i
$554$	−44.9619	−1.91025
$555$	0	0
$556$	31.9538	1.35514
$557$	28.8556i	1.22265i	0.791378	+	0.611327i	$0.209364\pi$
$557$	28.8556i	1.22265i	−0.791378	+	0.611327i	$0.790636\pi$
$558$	− 9.87286i	− 0.417951i
$559$	4.68706	0.198241
$560$	0	0
$561$	1.31635	0.0555764
$562$	1.03866i	0.0438131i
$563$	16.2728i	0.685815i	0.939369	+	0.342908i	$0.111412\pi$
$563$	16.2728i	0.685815i	−0.939369	+	0.342908i	$0.888588\pi$
$564$	34.9864	1.47319
$565$	0	0
$566$	1.92005	0.0807055
$567$	− 11.9643i	− 0.502453i
$568$	− 3.53732i	− 0.148422i
$569$	−35.5680	−1.49109	−0.745544	−	0.666457i	$-0.767810\pi$
$569$	−35.5680	−1.49109	−0.745544	+	0.666457i	$0.767810\pi$
$570$	0	0
$571$	11.0308	0.461623	0.230812	−	0.972998i	$-0.425862\pi$
$571$	11.0308	0.461623	0.230812	+	0.972998i	$0.425862\pi$
$572$	10.6219i	0.444122i
$573$	− 19.3894i	− 0.810006i
$574$	−9.30366	−0.388327
$575$	0	0
$576$	13.1063	0.546094
$577$	33.6759i	1.40195i	0.713188	+	0.700973i	$0.247251\pi$
$577$	33.6759i	1.40195i	−0.713188	+	0.700973i	$0.752749\pi$
$578$	− 35.9149i	− 1.49386i
$579$	22.9480	0.953685
$580$	0	0
$581$	−28.8306	−1.19610
$582$	31.4781i	1.30481i
$583$	− 12.7317i	− 0.527292i
$584$	13.6072	0.563070
$585$	0	0
$586$	−35.7628	−1.47735
$587$	− 4.39536i	− 0.181416i	−0.995878	−	0.0907080i	$-0.971087\pi$
$587$	− 4.39536i	− 0.181416i	0.995878	−	0.0907080i	$-0.0289130\pi$
$588$	− 0.396040i	− 0.0163324i
$589$	−21.9221	−0.903284
$590$	0	0
$591$	−28.1438	−1.15768
$592$	2.29576i	0.0943551i
$593$	− 0.696484i	− 0.0286012i	−0.999898	−	0.0143006i	$-0.995448\pi$
$593$	− 0.696484i	− 0.0286012i	0.999898	−	0.0143006i	$-0.00455217\pi$
$594$	−20.0333	−0.821976
$595$	0	0
$596$	−53.4549	−2.18960
$597$	15.9221i	0.651648i
$598$	43.3174i	1.77138i
$599$	−31.3890	−1.28252	−0.641260	−	0.767324i	$-0.721588\pi$
$599$	−31.3890	−1.28252	−0.641260	+	0.767324i	$0.721588\pi$
$600$	0	0
$601$	41.4460	1.69062	0.845309	−	0.534278i	$-0.179417\pi$
$601$	41.4460	1.69062	0.845309	+	0.534278i	$0.179417\pi$
$602$	− 10.8565i	− 0.442479i
$603$	− 12.4533i	− 0.507136i
$604$	−41.8698	−1.70366
$605$	0	0
$606$	2.70762	0.109989
$607$	− 11.3837i	− 0.462051i	−0.972948	−	0.231026i	$-0.925792\pi$
$607$	− 11.3837i	− 0.462051i	0.972948	−	0.231026i	$-0.0742081\pi$
$608$	− 40.1838i	− 1.62967i
$609$	2.78215	0.112739
$610$	0	0
$611$	−23.3639	−0.945202
$612$	− 1.66362i	− 0.0672479i
$613$	− 14.4059i	− 0.581848i	−0.956746	−	0.290924i	$-0.906037\pi$
$613$	− 14.4059i	− 0.581848i	0.956746	−	0.290924i	$-0.0939627\pi$
$614$	−53.3889	−2.15460
$615$	0	0
$616$	5.99582	0.241578
$617$	22.8874i	0.921413i	0.887552	+	0.460707i	$0.152404\pi$
$617$	22.8874i	0.921413i	−0.887552	+	0.460707i	$0.847596\pi$
$618$	56.3413i	2.26638i
$619$	40.5987	1.63180	0.815901	−	0.578192i	$-0.196242\pi$
$619$	40.5987	1.63180	0.815901	+	0.578192i	$0.196242\pi$
$620$	0	0
$621$	−46.5175	−1.86668
$622$	− 58.4886i	− 2.34518i
$623$	23.2571i	0.931777i
$624$	7.75578	0.310480
$625$	0	0
$626$	−18.7781	−0.750523
$627$	11.8308i	0.472477i
$628$	45.1838i	1.80303i
$629$	0.578749	0.0230763
$630$	0	0
$631$	−31.2970	−1.24592	−0.622958	−	0.782256i	$-0.714069\pi$
$631$	−31.2970	−1.24592	−0.622958	+	0.782256i	$0.714069\pi$
$632$	2.51891i	0.100197i
$633$	− 2.10200i	− 0.0835469i
$634$	−16.1663	−0.642045
$635$	0	0
$636$	28.3177	1.12287
$637$	0.264476i	0.0104789i
$638$	− 2.71550i	− 0.107507i
$639$	−2.76846	−0.109519
$640$	0	0
$641$	29.7434	1.17479	0.587397	−	0.809299i	$-0.300153\pi$
$641$	29.7434	1.17479	0.587397	+	0.809299i	$0.300153\pi$
$642$	− 28.8460i	− 1.13846i
$643$	− 29.2023i	− 1.15163i	−0.817581	−	0.575814i	$-0.804685\pi$
$643$	− 29.2023i	− 1.15163i	0.817581	−	0.575814i	$-0.195315\pi$
$644$	57.1287	2.25119
$645$	0	0
$646$	−6.48771	−0.255256
$647$	− 0.300586i	− 0.0118173i	−0.999983	−	0.00590863i	$-0.998119\pi$
$647$	− 0.300586i	− 0.0118173i	0.999983	−	0.00590863i	$-0.00188079\pi$
$648$	− 6.32973i	− 0.248655i
$649$	−21.4370	−0.841475
$650$	0	0
$651$	−15.3028	−0.599763
$652$	− 18.0388i	− 0.706455i
$653$	29.4692i	1.15322i	0.817020	+	0.576610i	$0.195625\pi$
$653$	29.4692i	1.15322i	−0.817020	+	0.576610i	$0.804375\pi$
$654$	−32.7744	−1.28158
$655$	0	0
$656$	3.77528	0.147400
$657$	− 10.6496i	− 0.415481i
$658$	54.1172i	2.10971i
$659$	1.80662	0.0703757	0.0351879	−	0.999381i	$-0.488797\pi$
$659$	1.80662	0.0703757	0.0351879	+	0.999381i	$0.488797\pi$
$660$	0	0
$661$	50.0378	1.94624	0.973122	−	0.230291i	$-0.0739679\pi$
$661$	50.0378	1.94624	0.973122	+	0.230291i	$0.0739679\pi$
$662$	22.4995i	0.874469i
$663$	− 1.95519i	− 0.0759334i
$664$	−15.2529	−0.591927
$665$	0	0
$666$	−2.34258	−0.0907731
$667$	− 6.30540i	− 0.244146i
$668$	− 12.9821i	− 0.502291i
$669$	−9.54101	−0.368877
$670$	0	0
$671$	6.35383	0.245287
$672$	− 28.0504i	− 1.08207i
$673$	16.4032i	0.632299i	0.948709	+	0.316149i	$0.102390\pi$
$673$	16.4032i	0.632299i	−0.948709	+	0.316149i	$0.897610\pi$
$674$	24.7814	0.954545
$675$	0	0
$676$	−18.6012	−0.715429
$677$	36.3118i	1.39558i	0.716304	+	0.697789i	$0.245833\pi$
$677$	36.3118i	1.39558i	−0.716304	+	0.697789i	$0.754167\pi$
$678$	− 6.76198i	− 0.259692i
$679$	−27.7234	−1.06393
$680$	0	0
$681$	−37.1058	−1.42190
$682$	14.9361i	0.571934i
$683$	25.4014i	0.971959i	0.873970	+	0.485980i	$0.161537\pi$
$683$	25.4014i	0.971959i	−0.873970	+	0.485980i	$0.838463\pi$
$684$	14.9519	0.571701
$685$	0	0
$686$	40.2157	1.53544
$687$	− 35.9776i	− 1.37263i
$688$	4.40540i	0.167954i
$689$	−18.9105	−0.720434
$690$	0	0
$691$	−4.47905	−0.170391	−0.0851956	−	0.996364i	$-0.527152\pi$
$691$	−4.47905	−0.170391	−0.0851956	+	0.996364i	$0.527152\pi$
$692$	56.2139i	2.13693i
$693$	− 4.69260i	− 0.178257i
$694$	−42.2532	−1.60391
$695$	0	0
$696$	1.47190	0.0557923
$697$	− 0.951729i	− 0.0360493i
$698$	− 47.2817i	− 1.78964i
$699$	−15.6487	−0.591889
$700$	0	0
$701$	−20.9639	−0.791795	−0.395898	−	0.918295i	$-0.629567\pi$
$701$	−20.9639	−0.791795	−0.395898	+	0.918295i	$0.629567\pi$
$702$	29.7557i	1.12306i
$703$	5.20156i	0.196181i
$704$	−19.8278	−0.747288
$705$	0	0
$706$	4.54789	0.171162
$707$	2.38466i	0.0896842i
$708$	− 47.6799i	− 1.79192i
$709$	39.5543	1.48549	0.742746	−	0.669573i	$-0.233523\pi$
$709$	39.5543	1.48549	0.742746	+	0.669573i	$0.233523\pi$
$710$	0	0
$711$	1.97141	0.0739337
$712$	12.3042i	0.461120i
$713$	34.6819i	1.29885i
$714$	−4.52877	−0.169485
$715$	0	0
$716$	−20.2806	−0.757922
$717$	− 29.4353i	− 1.09928i
$718$	− 15.0339i	− 0.561059i
$719$	44.0927	1.64438	0.822190	−	0.569213i	$-0.192752\pi$
$719$	44.0927	1.64438	0.822190	+	0.569213i	$0.192752\pi$
$720$	0	0
$721$	−49.6210	−1.84798
$722$	− 17.3620i	− 0.646146i
$723$	29.3186i	1.09037i
$724$	27.4949	1.02184
$725$	0	0
$726$	−24.7276	−0.917727
$727$	34.7329i	1.28817i	0.764953	+	0.644086i	$0.222762\pi$
$727$	34.7329i	1.28817i	−0.764953	+	0.644086i	$0.777238\pi$
$728$	− 8.90567i	− 0.330066i
$729$	−28.4093	−1.05220
$730$	0	0
$731$	1.11058	0.0410763
$732$	14.1321i	0.522339i
$733$	19.7348i	0.728921i	0.931219	+	0.364461i	$0.118747\pi$
$733$	19.7348i	0.728921i	−0.931219	+	0.364461i	$0.881253\pi$
$734$	−20.6425	−0.761927
$735$	0	0
$736$	−63.5728	−2.34332
$737$	18.8399i	0.693977i
$738$	3.85227i	0.141804i
$739$	−26.1822	−0.963128	−0.481564	−	0.876411i	$-0.659931\pi$
$739$	−26.1822	−0.963128	−0.481564	+	0.876411i	$0.659931\pi$
$740$	0	0
$741$	17.5725	0.645541
$742$	43.8020i	1.60802i
$743$	38.3253i	1.40602i	0.711180	+	0.703010i	$0.248161\pi$
$743$	38.3253i	1.40602i	−0.711180	+	0.703010i	$0.751839\pi$
$744$	−8.09596	−0.296812
$745$	0	0
$746$	11.5214	0.421828
$747$	11.9376i	0.436774i
$748$	2.51681i	0.0920236i
$749$	25.4053	0.928288
$750$	0	0
$751$	24.2638	0.885399	0.442699	−	0.896670i	$-0.354021\pi$
$751$	24.2638	0.885399	0.442699	+	0.896670i	$0.354021\pi$
$752$	− 21.9599i	− 0.800796i
$753$	− 8.39549i	− 0.305948i
$754$	−4.03336	−0.146886
$755$	0	0
$756$	39.2430	1.42726
$757$	9.26589i	0.336775i	0.985721	+	0.168387i	$0.0538559\pi$
$757$	9.26589i	0.336775i	−0.985721	+	0.168387i	$0.946144\pi$
$758$	− 66.4889i	− 2.41499i
$759$	18.7169	0.679382
$760$	0	0
$761$	15.8829	0.575753	0.287877	−	0.957667i	$-0.407051\pi$
$761$	15.8829	0.575753	0.287877	+	0.957667i	$0.407051\pi$
$762$	− 61.1492i	− 2.21520i
$763$	− 28.8651i	− 1.04499i
$764$	37.0718	1.34121
$765$	0	0
$766$	−20.0337	−0.723847
$767$	31.8406i	1.14970i
$768$	1.95377i	0.0705005i
$769$	16.2832	0.587188	0.293594	−	0.955930i	$-0.405149\pi$
$769$	16.2832	0.587188	0.293594	+	0.955930i	$0.405149\pi$
$770$	0	0
$771$	15.5793	0.561074
$772$	43.8756i	1.57912i
$773$	3.98058i	0.143172i	0.997434	+	0.0715858i	$0.0228060\pi$
$773$	3.98058i	0.143172i	−0.997434	+	0.0715858i	$0.977194\pi$
$774$	−4.49525	−0.161578
$775$	0	0
$776$	−14.6671	−0.526519
$777$	3.63096i	0.130260i
$778$	41.0909i	1.47318i
$779$	8.55374	0.306470
$780$	0	0
$781$	4.18827	0.149868
$782$	10.2639i	0.367036i
$783$	− 4.33133i	− 0.154789i
$784$	−0.248583	−0.00887795
$785$	0	0
$786$	−38.5528	−1.37513
$787$	5.01650i	0.178819i	0.995995	+	0.0894094i	$0.0284980\pi$
$787$	5.01650i	0.178819i	−0.995995	+	0.0894094i	$0.971502\pi$
$788$	− 53.8099i	− 1.91690i
$789$	−38.1217	−1.35717
$790$	0	0
$791$	5.95541	0.211750
$792$	− 2.48263i	− 0.0882163i
$793$	− 9.43744i	− 0.335133i
$794$	17.7486	0.629875
$795$	0	0
$796$	−30.4424	−1.07900
$797$	− 2.99628i	− 0.106134i	−0.998591	−	0.0530668i	$-0.983100\pi$
$797$	− 2.99628i	− 0.106134i	0.998591	−	0.0530668i	$-0.0168996\pi$
$798$	− 40.7027i	− 1.44086i
$799$	−5.53599	−0.195849
$800$	0	0
$801$	9.62984	0.340254
$802$	− 24.2251i	− 0.855417i
$803$	16.1113i	0.568555i
$804$	−41.9036	−1.47783
$805$	0	0
$806$	22.1849	0.781428
$807$	31.6842i	1.11534i
$808$	1.26161i	0.0443831i
$809$	−17.7054	−0.622488	−0.311244	−	0.950330i	$-0.600746\pi$
$809$	−17.7054	−0.622488	−0.311244	+	0.950330i	$0.600746\pi$
$810$	0	0
$811$	−25.3743	−0.891011	−0.445505	−	0.895279i	$-0.646976\pi$
$811$	−25.3743	−0.891011	−0.445505	+	0.895279i	$0.646976\pi$
$812$	5.31936i	0.186673i
$813$	8.15307i	0.285941i
$814$	3.54397	0.124216
$815$	0	0
$816$	1.83770	0.0643324
$817$	9.98144i	0.349206i
$818$	47.5902i	1.66395i
$819$	−6.96998	−0.243551
$820$	0	0
$821$	15.2958	0.533826	0.266913	−	0.963721i	$-0.413996\pi$
$821$	15.2958	0.533826	0.266913	+	0.963721i	$0.413996\pi$
$822$	− 39.6088i	− 1.38152i
$823$	44.7798i	1.56092i	0.625203	+	0.780462i	$0.285016\pi$
$823$	44.7798i	1.56092i	−0.625203	+	0.780462i	$0.714984\pi$
$824$	−26.2520	−0.914533
$825$	0	0
$826$	73.7517	2.56615
$827$	13.6099i	0.473263i	0.971600	+	0.236631i	$0.0760434\pi$
$827$	13.6099i	0.473263i	−0.971600	+	0.236631i	$0.923957\pi$
$828$	− 23.6547i	− 0.822058i
$829$	−15.3300	−0.532434	−0.266217	−	0.963913i	$-0.585774\pi$
$829$	−15.3300	−0.532434	−0.266217	+	0.963913i	$0.585774\pi$
$830$	0	0
$831$	28.8560	1.00100
$832$	29.4505i	1.02101i
$833$	0.0626665i	0.00217126i
$834$	−36.0173	−1.24718
$835$	0	0
$836$	−22.6200	−0.782330
$837$	23.8238i	0.823470i
$838$	− 33.8071i	− 1.16785i
$839$	−23.5040	−0.811447	−0.405723	−	0.913996i	$-0.632980\pi$
$839$	−23.5040	−0.811447	−0.405723	+	0.913996i	$0.632980\pi$
$840$	0	0
$841$	−28.4129	−0.979755
$842$	− 5.43508i	− 0.187305i
$843$	− 0.666596i	− 0.0229588i
$844$	4.01893	0.138337
$845$	0	0
$846$	22.4078	0.770395
$847$	− 21.7781i	− 0.748304i
$848$	− 17.7742i	− 0.610367i
$849$	−1.23226	−0.0422910
$850$	0	0
$851$	8.22913	0.282091
$852$	9.31551i	0.319144i
$853$	− 16.6766i	− 0.570996i	−0.958379	−	0.285498i	$-0.907841\pi$
$853$	− 16.6766i	− 0.570996i	0.958379	−	0.285498i	$-0.0921590\pi$
$854$	−21.8597	−0.748024
$855$	0	0
$856$	13.4407	0.459393
$857$	48.2788i	1.64917i	0.565737	+	0.824585i	$0.308592\pi$
$857$	48.2788i	1.64917i	−0.565737	+	0.824585i	$0.691408\pi$
$858$	− 11.9726i	− 0.408739i
$859$	30.5872	1.04362	0.521812	−	0.853061i	$-0.325256\pi$
$859$	30.5872	1.04362	0.521812	+	0.853061i	$0.325256\pi$
$860$	0	0
$861$	5.97097	0.203490
$862$	− 53.8638i	− 1.83461i
$863$	− 30.2802i	− 1.03075i	−0.856965	−	0.515374i	$-0.827653\pi$
$863$	− 30.2802i	− 1.03075i	0.856965	−	0.515374i	$-0.172347\pi$
$864$	−43.6696	−1.48567
$865$	0	0
$866$	−38.9318	−1.32296
$867$	23.0497i	0.782808i
$868$	− 29.2583i	− 0.993091i
$869$	−2.98245	−0.101173
$870$	0	0
$871$	27.9832	0.948174
$872$	− 15.2711i	− 0.517146i
$873$	11.4792i	0.388510i
$874$	−92.2476	−3.12032
$875$	0	0
$876$	−35.8346	−1.21074
$877$	− 21.4151i	− 0.723137i	−0.932345	−	0.361569i	$-0.882241\pi$
$877$	− 21.4151i	− 0.723137i	0.932345	−	0.361569i	$-0.117759\pi$
$878$	− 24.1845i	− 0.816186i
$879$	22.9521	0.774154
$880$	0	0
$881$	1.54785	0.0521484	0.0260742	−	0.999660i	$-0.491699\pi$
$881$	1.54785	0.0521484	0.0260742	+	0.999660i	$0.491699\pi$
$882$	− 0.253652i	− 0.00854092i
$883$	10.5279i	0.354291i	0.984185	+	0.177146i	$0.0566864\pi$
$883$	10.5279i	0.354291i	−0.984185	+	0.177146i	$0.943314\pi$
$884$	3.73825	0.125731
$885$	0	0
$886$	−82.9118	−2.78547
$887$	− 17.9508i	− 0.602730i	−0.953509	−	0.301365i	$-0.902558\pi$
$887$	− 17.9508i	− 0.602730i	0.953509	−	0.301365i	$-0.0974423\pi$
$888$	1.92097i	0.0644635i
$889$	53.8553	1.80625
$890$	0	0
$891$	7.49456	0.251077
$892$	− 18.2420i	− 0.610787i
$893$	− 49.7551i	− 1.66499i
$894$	60.2527	2.01515
$895$	0	0
$896$	27.6543	0.923865
$897$	− 27.8005i	− 0.928233i
$898$	85.8434i	2.86463i
$899$	−3.22929	−0.107703
$900$	0	0
$901$	−4.48078	−0.149276
$902$	− 5.82791i	− 0.194048i
$903$	6.96757i	0.231866i
$904$	3.15072	0.104791
$905$	0	0
$906$	47.1944	1.56793
$907$	20.8340i	0.691782i	0.938275	+	0.345891i	$0.112423\pi$
$907$	20.8340i	0.691782i	−0.938275	+	0.345891i	$0.887577\pi$
$908$	− 70.9447i	− 2.35438i
$909$	0.987390	0.0327497
$910$	0	0
$911$	29.5904	0.980373	0.490186	−	0.871618i	$-0.336929\pi$
$911$	29.5904	0.980373	0.490186	+	0.871618i	$0.336929\pi$
$912$	16.5165i	0.546916i
$913$	− 18.0598i	− 0.597693i
$914$	25.4743	0.842616
$915$	0	0
$916$	68.7877	2.27281
$917$	− 33.9543i	− 1.12127i
$918$	7.05051i	0.232701i
$919$	−22.2046	−0.732462	−0.366231	−	0.930524i	$-0.619352\pi$
$919$	−22.2046	−0.732462	−0.366231	+	0.930524i	$0.619352\pi$
$920$	0	0
$921$	34.2643	1.12905
$922$	− 27.4607i	− 0.904371i
$923$	− 6.22090i	− 0.204763i
$924$	−15.7900	−0.519452
$925$	0	0
$926$	−1.49731	−0.0492047
$927$	20.5460i	0.674821i
$928$	− 5.91938i	− 0.194313i
$929$	12.6544	0.415178	0.207589	−	0.978216i	$-0.433438\pi$
$929$	12.6544	0.415178	0.207589	+	0.978216i	$0.433438\pi$
$930$	0	0
$931$	−0.563220	−0.0184588
$932$	− 29.9197i	− 0.980052i
$933$	37.5372i	1.22891i
$934$	−4.91647	−0.160872
$935$	0	0
$936$	−3.68748	−0.120529
$937$	− 59.1488i	− 1.93231i	−0.257968	−	0.966154i	$-0.583053\pi$
$937$	− 59.1488i	− 1.93231i	0.257968	−	0.966154i	$-0.416947\pi$
$938$	− 64.8168i	− 2.11634i
$939$	12.0515	0.393287
$940$	0	0
$941$	20.7402	0.676110	0.338055	−	0.941126i	$-0.390231\pi$
$941$	20.7402	0.676110	0.338055	+	0.941126i	$0.390231\pi$
$942$	− 50.9298i	− 1.65938i
$943$	− 13.5325i	− 0.440677i
$944$	−29.9273	−0.974050
$945$	0	0
$946$	6.80064	0.221108
$947$	48.0626i	1.56182i	0.624641	+	0.780912i	$0.285245\pi$
$947$	48.0626i	1.56182i	−0.624641	+	0.780912i	$0.714755\pi$
$948$	− 6.63354i	− 0.215447i
$949$	23.9303	0.776810
$950$	0	0
$951$	10.3753	0.336442
$952$	− 2.11016i	− 0.0683908i
$953$	0.993315i	0.0321766i	0.999871	+	0.0160883i	$0.00512129\pi$
$953$	0.993315i	0.0321766i	−0.999871	+	0.0160883i	$0.994879\pi$
$954$	18.1367	0.587196
$955$	0	0
$956$	56.2791	1.82020
$957$	1.74277i	0.0563357i
$958$	− 55.4575i	− 1.79175i
$959$	34.8843	1.12647
$960$	0	0
$961$	−13.2378	−0.427026
$962$	− 5.26391i	− 0.169715i
$963$	− 10.5193i	− 0.338980i
$964$	−56.0559	−1.80544
$965$	0	0
$966$	−64.3937	−2.07183
$967$	31.4163i	1.01028i	0.863037	+	0.505140i	$0.168559\pi$
$967$	31.4163i	1.01028i	−0.863037	+	0.505140i	$0.831441\pi$
$968$	− 11.5217i	− 0.370323i
$969$	4.16373	0.133758
$970$	0	0
$971$	−36.6023	−1.17462	−0.587312	−	0.809361i	$-0.699814\pi$
$971$	−36.6023	−1.17462	−0.587312	+	0.809361i	$0.699814\pi$
$972$	− 28.1763i	− 0.903755i
$973$	− 31.7212i	− 1.01693i
$974$	40.3020	1.29136
$975$	0	0
$976$	8.87032	0.283932
$977$	− 4.13108i	− 0.132165i	−0.997814	−	0.0660825i	$-0.978950\pi$
$977$	− 4.13108i	− 0.132165i	0.997814	−	0.0660825i	$-0.0210500\pi$
$978$	20.3328i	0.650172i
$979$	−14.5685	−0.465611
$980$	0	0
$981$	−11.9519	−0.381594
$982$	− 40.0148i	− 1.27692i
$983$	19.1236i	0.609947i	0.952361	+	0.304974i	$0.0986477\pi$
$983$	19.1236i	0.609947i	−0.952361	+	0.304974i	$0.901352\pi$
$984$	3.15895	0.100704
$985$	0	0
$986$	−0.955690	−0.0304354
$987$	− 34.7317i	− 1.10552i
$988$	33.5978i	1.06889i
$989$	15.7911	0.502129
$990$	0	0
$991$	3.96555	0.125970	0.0629850	−	0.998014i	$-0.479938\pi$
$991$	3.96555	0.125970	0.0629850	+	0.998014i	$0.479938\pi$
$992$	32.5586i	1.03374i
$993$	− 14.4399i	− 0.458236i
$994$	−14.4093	−0.457036
$995$	0	0
$996$	40.1685	1.27279
$997$	− 29.1697i	− 0.923813i	−0.886929	−	0.461906i	$-0.847166\pi$
$997$	− 29.1697i	− 0.923813i	0.886929	−	0.461906i	$-0.152834\pi$
$998$	− 20.1618i	− 0.638210i
$999$	5.65278	0.178846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.b.f.149.3		10
5.2	odd	4		185.2.a.e.1.4	✓	5
5.3	odd	4		925.2.a.f.1.2		5
5.4	even	2	inner	925.2.b.f.149.8		10
15.2	even	4		1665.2.a.p.1.2		5
15.8	even	4		8325.2.a.ch.1.4		5
20.7	even	4		2960.2.a.w.1.3		5
35.27	even	4		9065.2.a.k.1.4		5
185.147	odd	4		6845.2.a.f.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.e.1.4	✓	5	5.2	odd	4
925.2.a.f.1.2		5	5.3	odd	4
925.2.b.f.149.3		10	1.1	even	1	trivial
925.2.b.f.149.8		10	5.4	even	2	inner
1665.2.a.p.1.2		5	15.2	even	4
2960.2.a.w.1.3		5	20.7	even	4
6845.2.a.f.1.2		5	185.147	odd	4
8325.2.a.ch.1.4		5	15.8	even	4
9065.2.a.k.1.4		5	35.27	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.15510i q^{2} +1.38311i q^{3} -2.64446 q^{4} +2.98075 q^{6} +2.62521i q^{7} +1.38887i q^{8} +1.08699 q^{9} +O(q^{10})\)	\(q-2.15510i q^{2} +1.38311i q^{3} -2.64446 q^{4} +2.98075 q^{6} +2.62521i q^{7} +1.38887i q^{8} +1.08699 q^{9} -1.64446 q^{11} -3.65759i q^{12} +2.44254i q^{13} +5.65759 q^{14} -2.29576 q^{16} +0.578749i q^{17} -2.34258i q^{18} -5.20156 q^{19} -3.63096 q^{21} +3.54397i q^{22} +8.22913i q^{23} -1.92097 q^{24} +5.26391 q^{26} +5.65278i q^{27} -6.94225i q^{28} -0.766229 q^{29} +4.21452 q^{31} +7.72533i q^{32} -2.27447i q^{33} +1.24726 q^{34} -2.87451 q^{36} -1.00000i q^{37} +11.2099i q^{38} -3.37831 q^{39} -1.64446 q^{41} +7.82509i q^{42} -1.91893i q^{43} +4.34870 q^{44} +17.7346 q^{46} +9.56543i q^{47} -3.17530i q^{48} +0.108279 q^{49} -0.800477 q^{51} -6.45918i q^{52} +7.74217i q^{53} +12.1823 q^{54} -3.64608 q^{56} -7.19435i q^{57} +1.65130i q^{58} +13.0359 q^{59} -3.86379 q^{61} -9.08272i q^{62} +2.85359i q^{63} +12.0574 q^{64} -4.90172 q^{66} -11.4566i q^{67} -1.53048i q^{68} -11.3818 q^{69} -2.54690 q^{71} +1.50969i q^{72} -9.79732i q^{73} -2.15510 q^{74} +13.7553 q^{76} -4.31704i q^{77} +7.28059i q^{78} +1.81364 q^{79} -4.55746 q^{81} +3.54397i q^{82} +10.9822i q^{83} +9.60193 q^{84} -4.13549 q^{86} -1.05978i q^{87} -2.28394i q^{88} +8.85915 q^{89} -6.41217 q^{91} -21.7616i q^{92} +5.82917i q^{93} +20.6145 q^{94} -10.6850 q^{96} +10.5605i q^{97} -0.233352i q^{98} -1.78751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 20 q^{4} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 10 * q - 20 * q^4 - 12 * q^6 - 12 * q^9	\( 10 q - 20 q^{4} - 12 q^{6} - 12 q^{9} - 10 q^{11} + 16 q^{14} + 32 q^{16} + 8 q^{19} + 6 q^{21} + 84 q^{24} - 8 q^{26} + 8 q^{29} + 16 q^{31} + 64 q^{34} + 32 q^{36} - 4 q^{39} - 10 q^{41} + 92 q^{44} - 44 q^{49} - 4 q^{51} + 20 q^{54} + 16 q^{56} + 60 q^{59} - 28 q^{61} - 40 q^{64} + 96 q^{66} - 16 q^{69} - 14 q^{71} - 4 q^{74} + 24 q^{76} - 56 q^{79} - 62 q^{81} + 36 q^{84} + 88 q^{86} - 12 q^{89} - 28 q^{91} - 8 q^{94} - 84 q^{96} + 20 q^{99}+O(q^{100}) \) 10 * q - 20 * q^4 - 12 * q^6 - 12 * q^9 - 10 * q^11 + 16 * q^14 + 32 * q^16 + 8 * q^19 + 6 * q^21 + 84 * q^24 - 8 * q^26 + 8 * q^29 + 16 * q^31 + 64 * q^34 + 32 * q^36 - 4 * q^39 - 10 * q^41 + 92 * q^44 - 44 * q^49 - 4 * q^51 + 20 * q^54 + 16 * q^56 + 60 * q^59 - 28 * q^61 - 40 * q^64 + 96 * q^66 - 16 * q^69 - 14 * q^71 - 4 * q^74 + 24 * q^76 - 56 * q^79 - 62 * q^81 + 36 * q^84 + 88 * q^86 - 12 * q^89 - 28 * q^91 - 8 * q^94 - 84 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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