LMFDB - Embedded newform 925.2.d.f.924.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(924,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.924"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,18,0,0,0,6,-22,0,2,0,20,0,0,30,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 21x^{10} + 162x^{8} + 574x^{6} + 985x^{4} + 765x^{2} + 196 $ x^12 + 21x^10 + 162x^8 + 574x^6 + 985x^4 + 765*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			924.6
Root			$-0.694469i$ of defining polynomial
Character	$\chi$	$=$	925.924
Dual form			925.2.d.f.924.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.694469 q^{2} +2.37730i q^{3} -1.51771 q^{4} -1.65096i q^{6} +2.16868i q^{7} +2.44294 q^{8} -2.65157 q^{9} +4.35199 q^{11} -3.60806i q^{12} +5.72273 q^{13} -1.50608i q^{14} +1.33888 q^{16} +6.00355 q^{17} +1.84143 q^{18} -4.14041i q^{19} -5.15560 q^{21} -3.02232 q^{22} -0.165727 q^{23} +5.80761i q^{24} -3.97426 q^{26} +0.828325i q^{27} -3.29143i q^{28} +8.05774i q^{29} -0.0682170i q^{31} -5.81569 q^{32} +10.3460i q^{33} -4.16928 q^{34} +4.02432 q^{36} +(4.69802 - 3.86375i) q^{37} +2.87539i q^{38} +13.6047i q^{39} -8.59751 q^{41} +3.58040 q^{42} -0.445335 q^{43} -6.60506 q^{44} +0.115093 q^{46} -6.94655i q^{47} +3.18292i q^{48} +2.29684 q^{49} +14.2723i q^{51} -8.68547 q^{52} -4.63281i q^{53} -0.575246i q^{54} +5.29795i q^{56} +9.84301 q^{57} -5.59585i q^{58} -9.44099i q^{59} -2.38799i q^{61} +0.0473746i q^{62} -5.75039i q^{63} +1.36106 q^{64} -7.18497i q^{66} +11.4214i q^{67} -9.11167 q^{68} -0.393984i q^{69} -2.32872 q^{71} -6.47763 q^{72} +10.6095i q^{73} +(-3.26263 + 2.68326i) q^{74} +6.28395i q^{76} +9.43805i q^{77} -9.44802i q^{78} -8.06222i q^{79} -9.92389 q^{81} +5.97071 q^{82} +6.59438i q^{83} +7.82472 q^{84} +0.309271 q^{86} -19.1557 q^{87} +10.6316 q^{88} +2.34335i q^{89} +12.4108i q^{91} +0.251527 q^{92} +0.162173 q^{93} +4.82416i q^{94} -13.8257i q^{96} +8.58288 q^{97} -1.59509 q^{98} -11.5396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 18 q^{4} + 6 q^{8} - 22 q^{9} + 2 q^{11} + 20 q^{13} + 30 q^{16} + 12 q^{17} - 26 q^{18} - 6 q^{21} - 28 q^{22} - 16 q^{23} - 12 q^{26} + 14 q^{32} - 4 q^{34} - 22 q^{36} - 14 q^{37} - 10 q^{41}+ \cdots + 84 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 18 * q^4 + 6 * q^8 - 22 * q^9 + 2 * q^11 + 20 * q^13 + 30 * q^16 + 12 * q^17 - 26 * q^18 - 6 * q^21 - 28 * q^22 - 16 * q^23 - 12 * q^26 + 14 * q^32 - 4 * q^34 - 22 * q^36 - 14 * q^37 - 10 * q^41 + 72 * q^42 - 12 * q^43 - 44 * q^44 - 24 * q^46 - 30 * q^49 + 80 * q^52 - 32 * q^57 + 126 * q^64 - 40 * q^68 + 42 * q^71 - 178 * q^72 - 50 * q^74 - 12 * q^81 + 96 * q^82 + 84 * q^84 - 64 * q^86 - 56 * q^87 - 72 * q^88 + 16 * q^92 + 76 * q^93 - 28 * q^97 + 118 * q^98 + 84 * q^99

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 $

$2$	−0.694469			−0.491064			−0.245532	−	0.969389i	$-0.578963\pi$
$2$	−0.694469			−0.491064			−0.245532	+	0.969389i	$0.578963\pi$
$3$			2.37730i			1.37254i	0.727349	+	0.686268i	$0.240752\pi$
$3$			2.37730i			1.37254i	−0.727349	+	0.686268i	$0.759248\pi$
$4$	−1.51771			−0.758856
$5$		0			0
$5$		0			0
$6$		−	1.65096i		−	0.674003i
$7$			2.16868i			0.819682i	0.912157	+	0.409841i	$0.134416\pi$
$7$			2.16868i			0.819682i	−0.912157	+	0.409841i	$0.865584\pi$
$8$	2.44294			0.863711
$9$	−2.65157			−0.883856
$10$		0			0
$11$	4.35199			1.31217			0.656087	−	0.754686i	$-0.272211\pi$
$11$	4.35199			1.31217			0.656087	+	0.754686i	$0.272211\pi$
$12$		−	3.60806i		−	1.04156i
$13$	5.72273			1.58720			0.793601	−	0.608439i	$-0.208204\pi$
$13$	5.72273			1.58720			0.793601	+	0.608439i	$0.208204\pi$
$14$		−	1.50608i		−	0.402516i
$15$		0			0
$16$	1.33888			0.334720
$17$	6.00355			1.45608			0.728038	−	0.685537i	$-0.240432\pi$
$17$	6.00355			1.45608			0.728038	+	0.685537i	$0.240432\pi$
$18$	1.84143			0.434030
$19$		−	4.14041i		−	0.949875i	−0.880019	−	0.474938i	$-0.842471\pi$
$19$		−	4.14041i		−	0.949875i	0.880019	−	0.474938i	$-0.157529\pi$
$20$		0			0
$21$	−5.15560			−1.12504
$22$	−3.02232			−0.644361
$23$	−0.165727			−0.0345566			−0.0172783	−	0.999851i	$-0.505500\pi$
$23$	−0.165727			−0.0345566			−0.0172783	+	0.999851i	$0.505500\pi$
$24$			5.80761i			1.18547i
$25$		0			0
$26$	−3.97426			−0.779417
$27$			0.828325i			0.159411i
$28$		−	3.29143i		−	0.622021i
$29$			8.05774i			1.49629i	0.663538	+	0.748143i	$0.269054\pi$
$29$			8.05774i			1.49629i	−0.663538	+	0.748143i	$0.730946\pi$
$30$		0			0
$31$		−	0.0682170i		−	0.0122521i	−0.999981	−	0.00612607i	$-0.998050\pi$
$31$		−	0.0682170i		−	0.0122521i	0.999981	−	0.00612607i	$-0.00195000\pi$
$32$	−5.81569			−1.02808
$33$			10.3460i			1.80101i
$34$	−4.16928			−0.715026
$35$		0			0
$36$	4.02432			0.670720
$37$	4.69802	−	3.86375i	0.772350	−	0.635197i
$37$	4.69802	−	3.86375i	0.772350	−	0.635197i
$38$			2.87539i			0.466449i
$39$			13.6047i			2.17849i
$40$		0			0
$41$	−8.59751			−1.34271			−0.671353	−	0.741138i	$-0.734287\pi$
$41$	−8.59751			−1.34271			−0.671353	+	0.741138i	$0.734287\pi$
$42$	3.58040			0.552468
$43$	−0.445335			−0.0679129			−0.0339565	−	0.999423i	$-0.510811\pi$
$43$	−0.445335			−0.0679129			−0.0339565	+	0.999423i	$0.510811\pi$
$44$	−6.60506			−0.995751
$45$		0			0
$46$	0.115093			0.0169695
$47$		−	6.94655i		−	1.01326i	−0.862164	−	0.506629i	$-0.830891\pi$
$47$		−	6.94655i		−	1.01326i	0.862164	−	0.506629i	$-0.169109\pi$
$48$			3.18292i			0.459415i
$49$	2.29684			0.328121
$50$		0			0
$51$			14.2723i			1.99852i
$52$	−8.68547			−1.20446
$53$		−	4.63281i		−	0.636365i	−0.948030	−	0.318182i	$-0.896928\pi$
$53$		−	4.63281i		−	0.636365i	0.948030	−	0.318182i	$-0.103072\pi$
$54$		−	0.575246i		−	0.0782811i
$55$		0			0
$56$			5.29795i			0.707968i
$57$	9.84301			1.30374
$58$		−	5.59585i		−	0.734772i
$59$		−	9.44099i		−	1.22911i	−0.788873	−	0.614556i	$-0.789335\pi$
$59$		−	9.44099i		−	1.22911i	0.788873	−	0.614556i	$-0.210665\pi$
$60$		0			0
$61$		−	2.38799i		−	0.305750i	−0.988246	−	0.152875i	$-0.951147\pi$
$61$		−	2.38799i		−	0.305750i	0.988246	−	0.152875i	$-0.0488532\pi$
$62$			0.0473746i			0.00601658i
$63$		−	5.75039i		−	0.724482i
$64$	1.36106			0.170133
$65$		0			0
$66$		−	7.18497i		−	0.884408i
$67$			11.4214i			1.39534i	0.716418	+	0.697671i	$0.245780\pi$
$67$			11.4214i			1.39534i	−0.716418	+	0.697671i	$0.754220\pi$
$68$	−9.11167			−1.10495
$69$		−	0.393984i		−	0.0474301i
$70$		0			0
$71$	−2.32872			−0.276368			−0.138184	−	0.990407i	$-0.544126\pi$
$71$	−2.32872			−0.276368			−0.138184	+	0.990407i	$0.544126\pi$
$72$	−6.47763			−0.763396
$73$			10.6095i			1.24175i	0.783909	+	0.620876i	$0.213223\pi$
$73$			10.6095i			1.24175i	−0.783909	+	0.620876i	$0.786777\pi$
$74$	−3.26263	+	2.68326i	−0.379273	+	0.311922i
$75$		0			0
$76$			6.28395i			0.720819i
$77$			9.43805i			1.07557i
$78$		−	9.44802i		−	1.06978i
$79$		−	8.06222i		−	0.907071i	−0.891238	−	0.453535i	$-0.850163\pi$
$79$		−	8.06222i		−	0.907071i	0.891238	−	0.453535i	$-0.149837\pi$
$80$		0			0
$81$	−9.92389			−1.10265
$82$	5.97071			0.659354
$83$			6.59438i			0.723827i	0.932212	+	0.361914i	$0.117876\pi$
$83$			6.59438i			0.723827i	−0.932212	+	0.361914i	$0.882124\pi$
$84$	7.82472			0.853747
$85$		0			0
$86$	0.309271			0.0333496
$87$	−19.1557			−2.05371
$88$	10.6316			1.13334
$89$			2.34335i			0.248395i	0.992258	+	0.124197i	$0.0396356\pi$
$89$			2.34335i			0.248395i	−0.992258	+	0.124197i	$0.960364\pi$
$90$		0			0
$91$			12.4108i			1.30100i
$92$	0.251527			0.0262235
$93$	0.162173			0.0168165
$94$			4.82416i			0.497575i
$95$		0			0
$96$		−	13.8257i		−	1.41108i
$97$	8.58288			0.871460			0.435730	−	0.900078i	$-0.356490\pi$
$97$	8.58288			0.871460			0.435730	+	0.900078i	$0.356490\pi$
$98$	−1.59509			−0.161128
$99$	−11.5396			−1.15977
$100$		0			0
$101$	0.976765			0.0971918			0.0485959	−	0.998819i	$-0.484525\pi$
$101$	0.976765			0.0971918			0.0485959	+	0.998819i	$0.484525\pi$
$102$		−	9.91165i		−	0.981399i
$103$	−19.1838			−1.89023			−0.945117	−	0.326732i	$-0.894053\pi$
$103$	−19.1838			−1.89023			−0.945117	+	0.326732i	$0.894053\pi$
$104$	13.9803			1.37088
$105$		0			0
$106$			3.21734i			0.312496i
$107$		−	4.92481i		−	0.476099i	−0.971253	−	0.238050i	$-0.923492\pi$
$107$		−	4.92481i		−	0.476099i	0.971253	−	0.238050i	$-0.0765081\pi$
$108$		−	1.25716i		−	0.120970i
$109$		−	6.66759i		−	0.638640i	−0.947647	−	0.319320i	$-0.896546\pi$
$109$		−	6.66759i		−	0.638640i	0.947647	−	0.319320i	$-0.103454\pi$
$110$		0			0
$111$	9.18531	+	11.1686i	0.871831	+	1.06008i
$112$			2.90359i			0.274364i
$113$	4.69442			0.441614			0.220807	−	0.975318i	$-0.429131\pi$
$113$	4.69442			0.441614			0.220807	+	0.975318i	$0.429131\pi$
$114$	−6.83566			−0.640219
$115$		0			0
$116$		−	12.2293i		−	1.13547i
$117$	−15.1742			−1.40286
$118$			6.55648i			0.603573i
$119$			13.0198i			1.19352i
$120$		0			0
$121$	7.93978			0.721798
$122$			1.65838i			0.150143i
$123$		−	20.4389i		−	1.84291i
$124$			0.103534i			0.00929762i
$125$		0			0
$126$			3.99347i			0.355767i
$127$			9.18965i			0.815450i	0.913105	+	0.407725i	$0.133678\pi$
$127$			9.18965i			0.815450i	−0.913105	+	0.407725i	$0.866322\pi$
$128$	10.6862			0.944533
$129$		−	1.05870i		−	0.0932130i
$130$		0			0
$131$		−	22.4849i		−	1.96451i	−0.187544	−	0.982256i	$-0.560053\pi$
$131$		−	22.4849i		−	1.96451i	0.187544	−	0.982256i	$-0.439947\pi$
$132$		−	15.7022i		−	1.36670i
$133$	8.97921			0.778596
$134$		−	7.93178i		−	0.685202i
$135$		0			0
$136$	14.6663			1.25763
$137$			8.66881i			0.740626i	0.928907	+	0.370313i	$0.120750\pi$
$137$			8.66881i			0.740626i	−0.928907	+	0.370313i	$0.879250\pi$
$138$			0.273610i			0.0232912i
$139$	−14.0011			−1.18756			−0.593779	−	0.804628i	$-0.702365\pi$
$139$	−14.0011			−1.18756			−0.593779	+	0.804628i	$0.702365\pi$
$140$		0			0
$141$	16.5141			1.39073
$142$	1.61722			0.135714
$143$	24.9053			2.08268
$144$	−3.55013			−0.295844
$145$		0			0
$146$		−	7.36799i		−	0.609779i
$147$			5.46030i			0.450358i
$148$	−7.13025	+	5.86407i	−0.586103	+	0.482023i
$149$	19.5226			1.59935			0.799677	−	0.600430i	$-0.205004\pi$
$149$	19.5226			1.59935			0.799677	+	0.600430i	$0.205004\pi$
$150$		0			0
$151$	−23.2295			−1.89039			−0.945195	−	0.326506i	$-0.894129\pi$
$151$	−23.2295			−1.89039			−0.945195	+	0.326506i	$0.894129\pi$
$152$		−	10.1148i		−	0.820417i
$153$	−15.9188			−1.28696
$154$		−	6.55443i		−	0.528171i
$155$		0			0
$156$		−	20.6480i		−	1.65316i
$157$			14.2147i			1.13446i	0.823560	+	0.567229i	$0.191984\pi$
$157$			14.2147i			1.13446i	−0.823560	+	0.567229i	$0.808016\pi$
$158$			5.59896i			0.445429i
$159$	11.0136			0.873434
$160$		0			0
$161$		−	0.359409i		−	0.0283254i
$162$	6.89183			0.541473
$163$	−10.8566			−0.850354			−0.425177	−	0.905110i	$-0.639788\pi$
$163$	−10.8566			−0.850354			−0.425177	+	0.905110i	$0.639788\pi$
$164$	13.0486			1.01892
$165$		0			0
$166$		−	4.57959i		−	0.355445i
$167$	−7.41823			−0.574040			−0.287020	−	0.957925i	$-0.592665\pi$
$167$	−7.41823			−0.574040			−0.287020	+	0.957925i	$0.592665\pi$
$168$	−12.5948			−0.971712
$169$	19.7497			1.51921
$170$		0			0
$171$			10.9786i			0.839553i
$172$	0.675890			0.0515362
$173$			7.71644i			0.586670i	0.956010	+	0.293335i	$0.0947652\pi$
$173$			7.71644i			0.586670i	−0.956010	+	0.293335i	$0.905235\pi$
$174$	13.3030			1.00850
$175$		0			0
$176$	5.82678			0.439210
$177$	22.4441			1.68700
$178$		−	1.62738i		−	0.121978i
$179$		−	3.95371i		−	0.295514i	−0.989024	−	0.147757i	$-0.952795\pi$
$179$		−	3.95371i		−	0.295514i	0.989024	−	0.147757i	$-0.0472054\pi$
$180$		0			0
$181$	13.4910			1.00278			0.501390	−	0.865221i	$-0.332822\pi$
$181$	13.4910			1.00278			0.501390	+	0.865221i	$0.332822\pi$
$182$		−	8.61889i		−	0.638874i
$183$	5.67697			0.419654
$184$	−0.404862			−0.0298469
$185$		0			0
$186$	−0.112624			−0.00825798
$187$	26.1274			1.91062
$188$			10.5429i			0.768918i
$189$	−1.79637			−0.130667
$190$		0			0
$191$		−	3.91989i		−	0.283633i	−0.989893	−	0.141817i	$-0.954706\pi$
$191$		−	3.91989i		−	0.283633i	0.989893	−	0.141817i	$-0.0452943\pi$
$192$			3.23566i			0.233513i
$193$	−8.40231			−0.604811			−0.302406	−	0.953179i	$-0.597790\pi$
$193$	−8.40231			−0.604811			−0.302406	+	0.953179i	$0.597790\pi$
$194$	−5.96054			−0.427942
$195$		0			0
$196$	−3.48595			−0.248996
$197$		−	7.79756i		−	0.555553i	−0.960646	−	0.277776i	$-0.910403\pi$
$197$		−	7.79756i		−	0.555553i	0.960646	−	0.277776i	$-0.0895974\pi$
$198$	8.01389			0.569522
$199$		−	1.51208i		−	0.107188i	−0.998563	−	0.0535941i	$-0.982932\pi$
$199$		−	1.51208i		−	0.107188i	0.998563	−	0.0535941i	$-0.0170677\pi$
$200$		0			0
$201$	−27.1520			−1.91516
$202$	−0.678333			−0.0477273
$203$	−17.4746			−1.22648
$204$		−	21.6612i		−	1.51659i
$205$		0			0
$206$	13.3225			0.928225
$207$	0.439438			0.0305430
$208$	7.66205			0.531267
$209$		−	18.0190i		−	1.24640i
$210$		0			0
$211$	−11.6259			−0.800357			−0.400178	−	0.916437i	$-0.631052\pi$
$211$	−11.6259			−0.800357			−0.400178	+	0.916437i	$0.631052\pi$
$212$			7.03127i			0.482910i
$213$		−	5.53606i		−	0.379325i
$214$			3.42013i			0.233795i
$215$		0			0
$216$			2.02355i			0.137685i
$217$	0.147941			0.0100429
$218$			4.63044i			0.313613i
$219$	−25.2221			−1.70435
$220$		0			0
$221$	34.3568			2.31109
$222$	−6.37891	−	7.75626i	−0.428124	−	0.520566i
$223$		−	2.59438i		−	0.173733i	−0.996220	−	0.0868663i	$-0.972315\pi$
$223$		−	2.59438i		−	0.173733i	0.996220	−	0.0868663i	$-0.0276853\pi$
$224$		−	12.6124i		−	0.842698i
$225$		0			0
$226$	−3.26013			−0.216860
$227$	−2.99424			−0.198735			−0.0993673	−	0.995051i	$-0.531682\pi$
$227$	−2.99424			−0.198735			−0.0993673	+	0.995051i	$0.531682\pi$
$228$	−14.9389			−0.989350
$229$	−6.89738			−0.455792			−0.227896	−	0.973686i	$-0.573185\pi$
$229$	−6.89738			−0.455792			−0.227896	+	0.973686i	$0.573185\pi$
$230$		0			0
$231$	−22.4371			−1.47625
$232$			19.6846i			1.29236i
$233$		−	23.8710i		−	1.56384i	−0.623376	−	0.781922i	$-0.714239\pi$
$233$		−	23.8710i		−	1.56384i	0.623376	−	0.781922i	$-0.285761\pi$
$234$	10.5380			0.688893
$235$		0			0
$236$			14.3287i			0.932720i
$237$	19.1663			1.24499
$238$		−	9.04182i		−	0.586094i
$239$		−	5.31643i		−	0.343892i	−0.985106	−	0.171946i	$-0.944995\pi$
$239$		−	5.31643i		−	0.343892i	0.985106	−	0.171946i	$-0.0550054\pi$
$240$		0			0
$241$			13.3776i			0.861725i	0.902418	+	0.430862i	$0.141791\pi$
$241$			13.3776i			0.861725i	−0.902418	+	0.430862i	$0.858209\pi$
$242$	−5.51393			−0.354449
$243$		−	21.1071i		−	1.35402i
$244$			3.62428i			0.232021i
$245$		0			0
$246$			14.1942i			0.904988i
$247$		−	23.6945i		−	1.50764i
$248$		−	0.166650i		−	0.0105823i
$249$	−15.6768			−0.993479
$250$		0			0
$251$			12.4789i			0.787660i	0.919183	+	0.393830i	$0.128850\pi$
$251$			12.4789i			0.787660i	−0.919183	+	0.393830i	$0.871150\pi$
$252$			8.72745i			0.549778i
$253$	−0.721243			−0.0453442
$254$		−	6.38193i		−	0.400438i
$255$		0			0
$256$	−10.1433			−0.633959
$257$	−20.8290			−1.29928			−0.649639	−	0.760243i	$-0.725080\pi$
$257$	−20.8290			−1.29928			−0.649639	+	0.760243i	$0.725080\pi$
$258$			0.735231i			0.0457735i
$259$	8.37922	+	10.1885i	0.520660	+	0.633082i
$260$		0			0
$261$		−	21.3657i		−	1.32250i
$262$			15.6150i			0.964701i
$263$			5.45327i			0.336263i	0.985765	+	0.168132i	$0.0537733\pi$
$263$			5.45327i			0.336263i	−0.985765	+	0.168132i	$0.946227\pi$
$264$			25.2747i			1.55555i
$265$		0			0
$266$	−6.23578			−0.382340
$267$	−5.57085			−0.340931
$268$		−	17.3344i		−	1.05886i
$269$	−20.0095			−1.22000			−0.609999	−	0.792402i	$-0.708830\pi$
$269$	−20.0095			−1.22000			−0.609999	+	0.792402i	$0.708830\pi$
$270$		0			0
$271$	10.1158			0.614491			0.307246	−	0.951630i	$-0.400593\pi$
$271$	10.1158			0.614491			0.307246	+	0.951630i	$0.400593\pi$
$272$	8.03803			0.487377
$273$	−29.5041			−1.78567
$274$		−	6.02022i		−	0.363695i
$275$		0			0
$276$			0.597955i			0.0359927i
$277$	−13.8144			−0.830029			−0.415014	−	0.909815i	$-0.636223\pi$
$277$	−13.8144			−0.830029			−0.415014	+	0.909815i	$0.636223\pi$
$278$	9.72334			0.583167
$279$			0.180882i			0.0108291i
$280$		0			0
$281$		−	19.8826i		−	1.18609i	−0.805168	−	0.593047i	$-0.797925\pi$
$281$		−	19.8826i		−	1.18609i	0.805168	−	0.593047i	$-0.202075\pi$
$282$	−11.4685			−0.682939
$283$	24.9559			1.48348			0.741738	−	0.670690i	$-0.234002\pi$
$283$	24.9559			1.48348			0.741738	+	0.670690i	$0.234002\pi$
$284$	3.53432			0.209723
$285$		0			0
$286$	−17.2959			−1.02273
$287$		−	18.6452i		−	1.10059i
$288$	15.4207			0.908674
$289$	19.0427			1.12016
$290$		0			0
$291$			20.4041i			1.19611i
$292$		−	16.1022i		−	0.942312i
$293$		−	5.19503i		−	0.303497i	−0.988419	−	0.151748i	$-0.951510\pi$
$293$		−	5.19503i		−	0.303497i	0.988419	−	0.151748i	$-0.0484904\pi$
$294$		−	3.79201i		−	0.221154i
$295$		0			0
$296$	11.4770	−	9.43892i	0.667087	−	0.548626i
$297$			3.60486i			0.209175i
$298$	−13.5578			−0.785385
$299$	−0.948414			−0.0548482
$300$		0			0
$301$		−	0.965787i		−	0.0556670i
$302$	16.1322			0.928302
$303$			2.32207i			0.133399i
$304$		−	5.54351i		−	0.317942i
$305$		0			0
$306$	11.0551			0.631980
$307$		−	20.7362i		−	1.18348i	−0.806130	−	0.591739i	$-0.798442\pi$
$307$		−	20.7362i		−	1.18348i	0.806130	−	0.591739i	$-0.201558\pi$
$308$		−	14.3242i		−	0.816200i
$309$		−	45.6057i		−	2.59442i
$310$		0			0
$311$		−	23.7997i		−	1.34956i	−0.738020	−	0.674779i	$-0.764239\pi$
$311$		−	23.7997i		−	1.34956i	0.738020	−	0.674779i	$-0.235761\pi$
$312$			33.2354i			1.88159i
$313$	−13.7661			−0.778107			−0.389053	−	0.921215i	$-0.627198\pi$
$313$	−13.7661			−0.778107			−0.389053	+	0.921215i	$0.627198\pi$
$314$		−	9.87167i		−	0.557091i
$315$		0			0
$316$			12.2361i			0.688336i
$317$		−	26.3650i		−	1.48081i	−0.672164	−	0.740403i	$-0.734635\pi$
$317$		−	26.3650i		−	1.48081i	0.672164	−	0.740403i	$-0.265365\pi$
$318$	−7.64859			−0.428912
$319$			35.0672i			1.96339i
$320$		0			0
$321$	11.7078			0.653464
$322$			0.249598i			0.0139096i
$323$		−	24.8572i		−	1.38309i
$324$	15.0616			0.836756
$325$		0			0
$326$	7.53957			0.417578
$327$	15.8509			0.876556
$328$	−21.0032			−1.15971
$329$	15.0648			0.830550
$330$		0			0
$331$			34.9649i			1.92185i	0.276816	+	0.960923i	$0.410721\pi$
$331$			34.9649i			1.92185i	−0.276816	+	0.960923i	$0.589279\pi$
$332$		−	10.0084i		−	0.549281i
$333$	−12.4571	+	10.2450i	−0.682647	+	0.561423i
$334$	5.15173			0.281890
$335$		0			0
$336$	−6.90272			−0.376574
$337$			9.97937i			0.543611i	0.962352	+	0.271805i	$0.0876207\pi$
$337$			9.97937i			0.543611i	−0.962352	+	0.271805i	$0.912379\pi$
$338$	−13.7155			−0.746028
$339$			11.1601i			0.606131i
$340$		0			0
$341$		−	0.296880i		−	0.0160769i
$342$		−	7.62429i		−	0.412274i
$343$			20.1618i			1.08864i
$344$	−1.08793			−0.0586571
$345$		0			0
$346$		−	5.35883i		−	0.288092i
$347$	−14.3875			−0.772361			−0.386180	−	0.922423i	$-0.626206\pi$
$347$	−14.3875			−0.772361			−0.386180	+	0.922423i	$0.626206\pi$
$348$	29.0729			1.55847
$349$	−7.24895			−0.388027			−0.194014	−	0.980999i	$-0.562151\pi$
$349$	−7.24895			−0.388027			−0.194014	+	0.980999i	$0.562151\pi$
$350$		0			0
$351$			4.74029i			0.253018i
$352$	−25.3098			−1.34902
$353$	10.8049			0.575085			0.287543	−	0.957768i	$-0.407162\pi$
$353$	10.8049			0.575085			0.287543	+	0.957768i	$0.407162\pi$
$354$	−15.5867			−0.828426
$355$		0			0
$356$		−	3.55653i		−	0.188496i
$357$	−30.9519			−1.63815
$358$			2.74573i			0.145116i
$359$	−13.1745			−0.695323			−0.347662	−	0.937620i	$-0.613024\pi$
$359$	−13.1745			−0.695323			−0.347662	+	0.937620i	$0.613024\pi$
$360$		0			0
$361$	1.85701			0.0977371
$362$	−9.36910			−0.492429
$363$			18.8753i			0.990694i
$364$		−	18.8360i		−	0.987273i
$365$		0			0
$366$	−3.94248			−0.206077
$367$			24.5181i			1.27983i	0.768444	+	0.639917i	$0.221031\pi$
$367$			24.5181i			1.27983i	−0.768444	+	0.639917i	$0.778969\pi$
$368$	−0.221889			−0.0115668
$369$	22.7969			1.18676
$370$		0			0
$371$	10.0471			0.521617
$372$	−0.246131			−0.0127613
$373$			18.8794i			0.977539i	0.872413	+	0.488770i	$0.162554\pi$
$373$			18.8794i			0.977539i	−0.872413	+	0.488770i	$0.837446\pi$
$374$	−18.1447			−0.938238
$375$		0			0
$376$		−	16.9700i		−	0.875162i
$377$			46.1123i			2.37491i
$378$	1.24752			0.0641656
$379$	4.90409			0.251906			0.125953	−	0.992036i	$-0.459801\pi$
$379$	4.90409			0.251906			0.125953	+	0.992036i	$0.459801\pi$
$380$		0			0
$381$	−21.8466			−1.11923
$382$			2.72224i			0.139282i
$383$	−4.51567			−0.230740			−0.115370	−	0.993323i	$-0.536805\pi$
$383$	−4.51567			−0.230740			−0.115370	+	0.993323i	$0.536805\pi$
$384$			25.4043i			1.29641i
$385$		0			0
$386$	5.83514			0.297001
$387$	1.18084			0.0600253
$388$	−13.0263			−0.661313
$389$			9.09674i			0.461223i	0.973046	+	0.230612i	$0.0740727\pi$
$389$			9.09674i			0.461223i	−0.973046	+	0.230612i	$0.925927\pi$
$390$		0			0
$391$	−0.994954			−0.0503170
$392$	5.61106			0.283401
$393$	53.4534			2.69636
$394$			5.41516i			0.272812i
$395$		0			0
$396$	17.5138			0.880101
$397$		−	23.4743i		−	1.17814i	−0.808081	−	0.589071i	$-0.799494\pi$
$397$		−	23.4743i		−	1.17814i	0.808081	−	0.589071i	$-0.200506\pi$
$398$			1.05009i			0.0526362i
$399$			21.3463i			1.06865i
$400$		0			0
$401$			21.4285i			1.07009i	0.844825	+	0.535043i	$0.179705\pi$
$401$			21.4285i			1.07009i	−0.844825	+	0.535043i	$0.820295\pi$
$402$	18.8563			0.940464
$403$		−	0.390388i		−	0.0194466i
$404$	−1.48245			−0.0737546
$405$		0			0
$406$	12.1356			0.602279
$407$	20.4457	−	16.8150i	1.01346	−	0.833488i
$408$			34.8663i			1.72614i
$409$			22.3741i			1.10633i	0.833072	+	0.553164i	$0.186580\pi$
$409$			22.3741i			1.10633i	−0.833072	+	0.553164i	$0.813420\pi$
$410$		0			0
$411$	−20.6084			−1.01654
$412$	29.1155			1.43442
$413$	20.4745			1.00748
$414$	−0.305176			−0.0149986
$415$		0			0
$416$	−33.2817			−1.63177
$417$		−	33.2849i		−	1.62997i
$418$			12.5136i			0.612062i
$419$	3.38447			0.165342			0.0826710	−	0.996577i	$-0.473655\pi$
$419$	3.38447			0.165342			0.0826710	+	0.996577i	$0.473655\pi$
$420$		0			0
$421$		−	38.7578i		−	1.88894i	−0.328597	−	0.944470i	$-0.606576\pi$
$421$		−	38.7578i		−	1.88894i	0.328597	−	0.944470i	$-0.393424\pi$
$422$	8.07380			0.393026
$423$			18.4193i			0.895575i
$424$		−	11.3177i		−	0.549635i
$425$		0			0
$426$			3.84462i			0.186273i
$427$	5.17877			0.250618
$428$			7.47445i			0.361291i
$429$			59.2073i			2.85856i
$430$		0			0
$431$			4.50684i			0.217087i	0.994092	+	0.108543i	$0.0346186\pi$
$431$			4.50684i			0.217087i	−0.994092	+	0.108543i	$0.965381\pi$
$432$			1.10903i			0.0533581i
$433$			5.62353i			0.270250i	0.990829	+	0.135125i	$0.0431436\pi$
$433$			5.62353i			0.270250i	−0.990829	+	0.135125i	$0.956856\pi$
$434$	−0.102740			−0.00493169
$435$		0			0
$436$			10.1195i			0.484636i
$437$			0.686179i			0.0328244i
$438$	17.5160			0.836945
$439$			31.3943i			1.49837i	0.662362	+	0.749184i	$0.269554\pi$
$439$			31.3943i			1.49837i	−0.662362	+	0.749184i	$0.730446\pi$
$440$		0			0
$441$	−6.09024			−0.290012
$442$	−23.8597			−1.13489
$443$			25.2783i			1.20101i	0.799622	+	0.600504i	$0.205033\pi$
$443$			25.2783i			1.20101i	−0.799622	+	0.600504i	$0.794967\pi$
$444$	−13.9407	−	16.9508i	−0.661594	−	0.804448i
$445$		0			0
$446$			1.80172i			0.0853138i
$447$			46.4112i			2.19517i
$448$			2.95170i			0.139455i
$449$		−	12.0163i		−	0.567086i	−0.958960	−	0.283543i	$-0.908490\pi$
$449$		−	12.0163i		−	0.567086i	0.958960	−	0.283543i	$-0.0915098\pi$
$450$		0			0
$451$	−37.4163			−1.76186
$452$	−7.12478			−0.335121
$453$		−	55.2236i		−	2.59463i
$454$	2.07941			0.0975913
$455$		0			0
$456$	24.0459			1.12605
$457$	38.7961			1.81480			0.907402	−	0.420264i	$-0.138063\pi$
$457$	38.7961			1.81480			0.907402	+	0.420264i	$0.138063\pi$
$458$	4.79001			0.223823
$459$			4.97290i			0.232115i
$460$		0			0
$461$		−	34.7227i		−	1.61720i	−0.588360	−	0.808599i	$-0.700226\pi$
$461$		−	34.7227i		−	1.61720i	0.588360	−	0.808599i	$-0.299774\pi$
$462$	15.5819			0.724934
$463$	6.90276			0.320798			0.160399	−	0.987052i	$-0.448722\pi$
$463$	6.90276			0.320798			0.160399	+	0.987052i	$0.448722\pi$
$464$			10.7883i			0.500836i
$465$		0			0
$466$			16.5777i			0.767947i
$467$	−27.2476			−1.26087			−0.630434	−	0.776243i	$-0.717123\pi$
$467$	−27.2476			−1.26087			−0.630434	+	0.776243i	$0.717123\pi$
$468$	23.0301			1.06457
$469$	−24.7692			−1.14374
$470$		0			0
$471$	−33.7927			−1.55708
$472$		−	23.0638i		−	1.06160i
$473$	−1.93809			−0.0891135
$474$	−13.3104			−0.611368
$475$		0			0
$476$		−	19.7603i		−	0.905710i
$477$			12.2842i			0.562455i
$478$			3.69210i			0.168873i
$479$		−	38.6778i		−	1.76724i	−0.468209	−	0.883618i	$-0.655101\pi$
$479$		−	38.6778i		−	1.76724i	0.468209	−	0.883618i	$-0.344899\pi$
$480$		0			0
$481$	26.8855	−	22.1112i	1.22588	−	1.00819i
$482$		−	9.29030i		−	0.423162i
$483$	0.854424			0.0388776
$484$	−12.0503			−0.547741
$485$		0			0
$486$			14.6582i			0.664911i
$487$	−2.02287			−0.0916651			−0.0458326	−	0.998949i	$-0.514594\pi$
$487$	−2.02287			−0.0916651			−0.0458326	+	0.998949i	$0.514594\pi$
$488$		−	5.83371i		−	0.264080i
$489$		−	25.8094i		−	1.16714i
$490$		0			0
$491$	34.4832			1.55621			0.778103	−	0.628137i	$-0.216182\pi$
$491$	34.4832			1.55621			0.778103	+	0.628137i	$0.216182\pi$
$492$			31.0204i			1.39851i
$493$			48.3751i			2.17871i
$494$			16.4551i			0.740349i
$495$		0			0
$496$		−	0.0913343i		−	0.00410103i
$497$		−	5.05023i		−	0.226534i
$498$	10.8871			0.487862
$499$			8.93562i			0.400013i	0.979795	+	0.200007i	$0.0640964\pi$
$499$			8.93562i			0.400013i	−0.979795	+	0.200007i	$0.935904\pi$
$500$		0			0
$501$		−	17.6354i		−	0.787891i
$502$		−	8.66619i		−	0.386791i
$503$	−2.50197			−0.111557			−0.0557786	−	0.998443i	$-0.517764\pi$
$503$	−2.50197			−0.111557			−0.0557786	+	0.998443i	$0.517764\pi$
$504$		−	14.0479i		−	0.625742i
$505$		0			0
$506$	0.500881			0.0222669
$507$			46.9510i			2.08517i
$508$		−	13.9473i		−	0.618809i
$509$	12.8713			0.570508			0.285254	−	0.958452i	$-0.407922\pi$
$509$	12.8713			0.570508			0.285254	+	0.958452i	$0.407922\pi$
$510$		0			0
$511$	−23.0086			−1.01784
$512$	−14.3281			−0.633219
$513$	3.42961			0.151421
$514$	14.4651			0.638028
$515$		0			0
$516$			1.60680i			0.0707353i
$517$		−	30.2313i		−	1.32957i
$518$	−5.81911	−	7.07559i	−0.255677	−	0.310884i
$519$	−18.3443			−0.805226
$520$		0			0
$521$	21.2718			0.931935			0.465967	−	0.884802i	$-0.345706\pi$
$521$	21.2718			0.931935			0.465967	+	0.884802i	$0.345706\pi$
$522$			14.8378i			0.649433i
$523$	22.9221			1.00231			0.501156	−	0.865357i	$-0.332908\pi$
$523$	22.9221			1.00231			0.501156	+	0.865357i	$0.332908\pi$
$524$			34.1256i			1.49078i
$525$		0			0
$526$		−	3.78713i		−	0.165127i
$527$		−	0.409545i		−	0.0178401i
$528$			13.8520i			0.602832i
$529$	−22.9725			−0.998806
$530$		0			0
$531$			25.0335i			1.08636i
$532$	−13.6279			−0.590843
$533$	−49.2013			−2.13114
$534$	3.86878			0.167419
$535$		0			0
$536$			27.9017i			1.20517i
$537$	9.39917			0.405604
$538$	13.8959			0.599097
$539$	9.99583			0.430551
$540$		0			0
$541$			27.5498i			1.18446i	0.805770	+	0.592228i	$0.201752\pi$
$541$			27.5498i			1.18446i	−0.805770	+	0.592228i	$0.798248\pi$
$542$	−7.02511			−0.301754
$543$			32.0722i			1.37635i
$544$	−34.9148			−1.49696
$545$		0			0
$546$	20.4897			0.876878
$547$	−14.7301			−0.629812			−0.314906	−	0.949123i	$-0.601973\pi$
$547$	−14.7301			−0.629812			−0.314906	+	0.949123i	$0.601973\pi$
$548$		−	13.1568i		−	0.562029i
$549$			6.33191i			0.270239i
$550$		0			0
$551$	33.3624			1.42128
$552$		−	0.962481i		−	0.0409659i
$553$	17.4843			0.743510
$554$	9.59369			0.407597
$555$		0			0
$556$	21.2497			0.901187
$557$	−41.3384			−1.75156			−0.875782	−	0.482707i	$-0.839654\pi$
$557$	−41.3384			−1.75156			−0.875782	+	0.482707i	$0.839654\pi$
$558$		−	0.125617i		−	0.00531780i
$559$	−2.54853			−0.107791
$560$		0			0
$561$			62.1127i			2.62240i
$562$			13.8078i			0.582448i
$563$	12.3396			0.520052			0.260026	−	0.965602i	$-0.416269\pi$
$563$	12.3396			0.520052			0.260026	+	0.965602i	$0.416269\pi$
$564$	−25.0636			−1.05537
$565$		0			0
$566$	−17.3311			−0.728481
$567$		−	21.5217i		−	0.903826i
$568$	−5.68892			−0.238702
$569$			20.3376i			0.852597i	0.904582	+	0.426299i	$0.140183\pi$
$569$			20.3376i			0.852597i	−0.904582	+	0.426299i	$0.859817\pi$
$570$		0			0
$571$	2.20913			0.0924493			0.0462246	−	0.998931i	$-0.485281\pi$
$571$	2.20913			0.0924493			0.0462246	+	0.998931i	$0.485281\pi$
$572$	−37.7990			−1.58046
$573$	9.31876			0.389297
$574$			12.9485i			0.540461i
$575$		0			0
$576$	−3.60895			−0.150373
$577$	27.2952			1.13631			0.568157	−	0.822920i	$-0.307656\pi$
$577$	27.2952			1.13631			0.568157	+	0.822920i	$0.307656\pi$
$578$	−13.2245			−0.550068
$579$		−	19.9748i		−	0.830126i
$580$		0			0
$581$	−14.3011			−0.593309
$582$		−	14.1700i		−	0.587366i
$583$		−	20.1619i		−	0.835021i
$584$			25.9185i			1.07251i
$585$		0			0
$586$			3.60779i			0.149036i
$587$	−0.417280			−0.0172230			−0.00861150	−	0.999963i	$-0.502741\pi$
$587$	−0.417280			−0.0172230			−0.00861150	+	0.999963i	$0.502741\pi$
$588$		−	8.28716i		−	0.341757i
$589$	−0.282447			−0.0116380
$590$		0			0
$591$	18.5372			0.762517
$592$	6.29008	−	5.17309i	0.258521	−	0.212613i
$593$		−	2.54532i		−	0.104524i	−0.998633	−	0.0522619i	$-0.983357\pi$
$593$		−	2.54532i		−	0.104524i	0.998633	−	0.0522619i	$-0.0166431\pi$
$594$		−	2.50346i		−	0.102718i
$595$		0			0
$596$	−29.6297			−1.21368
$597$	3.59466			0.147120
$598$	0.658644			0.0269340
$599$	17.2975			0.706757			0.353379	−	0.935480i	$-0.385033\pi$
$599$	17.2975			0.706757			0.353379	+	0.935480i	$0.385033\pi$
$600$		0			0
$601$	−39.3207			−1.60392			−0.801962	−	0.597375i	$-0.796211\pi$
$601$	−39.3207			−1.60392			−0.801962	+	0.597375i	$0.796211\pi$
$602$			0.670709i			0.0273361i
$603$		−	30.2845i		−	1.23328i
$604$	35.2557			1.43453
$605$		0			0
$606$		−	1.61260i		−	0.0655075i
$607$	−14.0635			−0.570820			−0.285410	−	0.958405i	$-0.592130\pi$
$607$	−14.0635			−0.570820			−0.285410	+	0.958405i	$0.592130\pi$
$608$			24.0794i			0.976547i
$609$		−	41.5425i		−	1.68339i
$610$		0			0
$611$		−	39.7533i		−	1.60825i
$612$	24.1602			0.976619
$613$		−	28.9940i		−	1.17105i	−0.810653	−	0.585527i	$-0.800887\pi$
$613$		−	28.9940i		−	1.17105i	0.810653	−	0.585527i	$-0.199113\pi$
$614$			14.4007i			0.581163i
$615$		0			0
$616$			23.0566i			0.928977i
$617$			13.4011i			0.539510i	0.962929	+	0.269755i	$0.0869427\pi$
$617$			13.4011i			0.539510i	−0.962929	+	0.269755i	$0.913057\pi$
$618$			31.6717i			1.27402i
$619$	−42.6050			−1.71244			−0.856220	−	0.516611i	$-0.827193\pi$
$619$	−42.6050			−1.71244			−0.856220	+	0.516611i	$0.827193\pi$
$620$		0			0
$621$		−	0.137276i		−	0.00550870i
$622$			16.5282i			0.662719i
$623$	−5.08197			−0.203605
$624$			18.2150i			0.729184i
$625$		0			0
$626$	9.56014			0.382100
$627$	42.8366			1.71073
$628$		−	21.5738i		−	0.860890i
$629$	28.2048	−	23.1962i	1.12460	−	0.924895i
$630$		0			0
$631$		−	37.8981i		−	1.50870i	−0.656472	−	0.754350i	$-0.727952\pi$
$631$		−	37.8981i		−	1.50870i	0.656472	−	0.754350i	$-0.272048\pi$
$632$		−	19.6955i		−	0.783446i
$633$		−	27.6382i		−	1.09852i
$634$			18.3097i			0.727170i
$635$		0			0
$636$	−16.7155			−0.662811
$637$	13.1442			0.520793
$638$		−	24.3531i		−	0.964147i
$639$	6.17475			0.244269
$640$		0			0
$641$	−5.17563			−0.204425			−0.102213	−	0.994763i	$-0.532592\pi$
$641$	−5.17563			−0.204425			−0.102213	+	0.994763i	$0.532592\pi$
$642$	−8.13068			−0.320892
$643$	40.7663			1.60767			0.803834	−	0.594854i	$-0.202790\pi$
$643$	40.7663			1.60767			0.803834	+	0.594854i	$0.202790\pi$
$644$			0.545480i			0.0214949i
$645$		0			0
$646$			17.2625i			0.679185i
$647$	0.183619			0.00721883			0.00360941	−	0.999993i	$-0.498851\pi$
$647$	0.183619			0.00721883			0.00360941	+	0.999993i	$0.498851\pi$
$648$	−24.2435			−0.952374
$649$		−	41.0871i		−	1.61281i
$650$		0			0
$651$			0.351700i			0.0137842i
$652$	16.4772			0.645297
$653$	−16.8021			−0.657516			−0.328758	−	0.944414i	$-0.606630\pi$
$653$	−16.8021			−0.657516			−0.328758	+	0.944414i	$0.606630\pi$
$654$	−11.0080			−0.430445
$655$		0			0
$656$	−11.5110			−0.449430
$657$		−	28.1319i		−	1.09753i
$658$	−10.4620			−0.407853
$659$	−21.1834			−0.825190			−0.412595	−	0.910915i	$-0.635377\pi$
$659$	−21.1834			−0.825190			−0.412595	+	0.910915i	$0.635377\pi$
$660$		0			0
$661$			26.3955i			1.02666i	0.858190	+	0.513332i	$0.171589\pi$
$661$			26.3955i			1.02666i	−0.858190	+	0.513332i	$0.828411\pi$
$662$		−	24.2821i		−	0.943749i
$663$			81.6764i			3.17205i
$664$			16.1097i			0.625177i
$665$		0			0
$666$	8.65109	−	7.11484i	0.335223	−	0.275694i
$667$		−	1.33539i		−	0.0517065i
$668$	11.2587			0.435614
$669$	6.16763			0.238454
$670$		0			0
$671$		−	10.3925i		−	0.401197i
$672$	29.9834			1.15663
$673$		−	44.0680i		−	1.69870i	−0.527832	−	0.849349i	$-0.676995\pi$
$673$		−	44.0680i		−	1.69870i	0.527832	−	0.849349i	$-0.323005\pi$
$674$		−	6.93036i		−	0.266948i
$675$		0			0
$676$	−29.9744			−1.15286
$677$			1.37058i			0.0526756i	0.999653	+	0.0263378i	$0.00838456\pi$
$677$			1.37058i			0.0526756i	−0.999653	+	0.0263378i	$0.991615\pi$
$678$		−	7.75031i		−	0.297649i
$679$			18.6135i			0.714320i
$680$		0			0
$681$		−	7.11821i		−	0.272770i
$682$			0.206174i			0.00789480i
$683$	−9.46755			−0.362266			−0.181133	−	0.983459i	$-0.557976\pi$
$683$	−9.46755			−0.362266			−0.181133	+	0.983459i	$0.557976\pi$
$684$		−	16.6623i		−	0.637100i
$685$		0			0
$686$		−	14.0018i		−	0.534590i
$687$		−	16.3972i		−	0.625591i
$688$	−0.596249			−0.0227318
$689$		−	26.5123i		−	1.01004i
$690$		0			0
$691$	28.7211			1.09260			0.546301	−	0.837589i	$-0.316036\pi$
$691$	28.7211			1.09260			0.546301	+	0.837589i	$0.316036\pi$
$692$		−	11.7113i		−	0.445198i
$693$		−	25.0256i		−	0.950645i
$694$	9.99166			0.379278
$695$		0			0
$696$	−46.7963			−1.77381
$697$	−51.6157			−1.95508
$698$	5.03417			0.190546
$699$	56.7487			2.14643
$700$		0			0
$701$			17.9577i			0.678252i	0.940741	+	0.339126i	$0.110131\pi$
$701$			17.9577i			0.678252i	−0.940741	+	0.339126i	$0.889869\pi$
$702$		−	3.29198i		−	0.124248i
$703$	−15.9975	−	19.4517i	−0.603358	−	0.733636i
$704$	5.92332			0.223244
$705$		0			0
$706$	−7.50365			−0.282403
$707$			2.11829i			0.0796664i
$708$	−34.0637			−1.28019
$709$		−	15.3109i		−	0.575012i	−0.957779	−	0.287506i	$-0.907174\pi$
$709$		−	15.3109i		−	0.575012i	0.957779	−	0.287506i	$-0.0928261\pi$
$710$		0			0
$711$			21.3775i			0.801720i
$712$			5.72467i			0.214541i
$713$			0.0113054i			0.000423392i
$714$	21.4952			0.804436
$715$		0			0
$716$			6.00060i			0.224253i
$717$	12.6388			0.472004
$718$	9.14928			0.341448
$719$	−13.6890			−0.510514			−0.255257	−	0.966873i	$-0.582160\pi$
$719$	−13.6890			−0.510514			−0.255257	+	0.966873i	$0.582160\pi$
$720$		0			0
$721$		−	41.6034i		−	1.54939i
$722$	−1.28963			−0.0479951
$723$	−31.8025			−1.18275
$724$	−20.4755			−0.760966
$725$		0			0
$726$		−	13.1083i		−	0.486494i
$727$	11.9352			0.442651			0.221326	−	0.975200i	$-0.428962\pi$
$727$	11.9352			0.442651			0.221326	+	0.975200i	$0.428962\pi$
$728$			30.3188i			1.12369i
$729$	20.4063			0.755790
$730$		0			0
$731$	−2.67359			−0.0988864
$732$	−8.61601			−0.318457
$733$			10.0865i			0.372555i	0.982497	+	0.186277i	$0.0596423\pi$
$733$			10.0865i			0.372555i	−0.982497	+	0.186277i	$0.940358\pi$
$734$		−	17.0271i		−	0.628480i
$735$		0			0
$736$	0.963820			0.0355269
$737$			49.7056i			1.83093i
$738$	−15.8317			−0.582774
$739$	−11.5583			−0.425180			−0.212590	−	0.977142i	$-0.568190\pi$
$739$	−11.5583			−0.425180			−0.212590	+	0.977142i	$0.568190\pi$
$740$		0			0
$741$	56.3289			2.06929
$742$	−6.97737			−0.256147
$743$		−	4.00230i		−	0.146830i	−0.997301	−	0.0734151i	$-0.976610\pi$
$743$		−	4.00230i		−	0.146830i	0.997301	−	0.0734151i	$-0.0233898\pi$
$744$	0.396178			0.0145246
$745$		0			0
$746$		−	13.1112i		−	0.480034i
$747$		−	17.4855i		−	0.639759i
$748$	−39.6539			−1.44989
$749$	10.6803			0.390250
$750$		0			0
$751$	12.6259			0.460724			0.230362	−	0.973105i	$-0.426009\pi$
$751$	12.6259			0.460724			0.230362	+	0.973105i	$0.426009\pi$
$752$		−	9.30059i		−	0.339158i
$753$	−29.6661			−1.08109
$754$		−	32.0236i		−	1.16623i
$755$		0			0
$756$	2.72637			0.0991572
$757$	0.686799			0.0249621			0.0124811	−	0.999922i	$-0.496027\pi$
$757$	0.686799			0.0249621			0.0124811	+	0.999922i	$0.496027\pi$
$758$	−3.40574			−0.123702
$759$		−	1.71461i		−	0.0622365i
$760$		0			0
$761$	45.5758			1.65212			0.826060	−	0.563582i	$-0.190577\pi$
$761$	45.5758			1.65212			0.826060	+	0.563582i	$0.190577\pi$
$762$	15.1718			0.549616
$763$	14.4599			0.523482
$764$			5.94927i			0.215237i
$765$		0			0
$766$	3.13599			0.113308
$767$		−	54.0283i		−	1.95085i
$768$		−	24.1138i		−	0.870131i
$769$		−	40.5462i		−	1.46213i	−0.682306	−	0.731067i	$-0.739023\pi$
$769$		−	40.5462i		−	1.46213i	0.682306	−	0.731067i	$-0.260977\pi$
$770$		0			0
$771$		−	49.5169i		−	1.78331i
$772$	12.7523			0.458965
$773$		−	33.7970i		−	1.21559i	−0.794093	−	0.607797i	$-0.792054\pi$
$773$		−	33.7970i		−	1.21559i	0.794093	−	0.607797i	$-0.207946\pi$
$774$	−0.820054			−0.0294762
$775$		0			0
$776$	20.9675			0.752689
$777$	−24.2211	+	19.9200i	−0.868928	+	0.714624i
$778$		−	6.31741i		−	0.226490i
$779$			35.5972i			1.27540i
$780$		0			0
$781$	−10.1345			−0.362642
$782$	0.690964			0.0247088
$783$	−6.67443			−0.238525
$784$	3.07520			0.109828
$785$		0			0
$786$	−37.1217			−1.32409
$787$			7.98198i			0.284527i	0.989829	+	0.142263i	$0.0454380\pi$
$787$			7.98198i			0.284527i	−0.989829	+	0.142263i	$0.954562\pi$
$788$			11.8345i			0.421585i
$789$	−12.9641			−0.461533
$790$		0			0
$791$			10.1807i			0.361983i
$792$	−28.1906			−1.00171
$793$		−	13.6658i		−	0.485287i
$794$			16.3022i			0.578543i
$795$		0			0
$796$			2.29490i			0.0813405i
$797$	−26.0890			−0.924119			−0.462060	−	0.886849i	$-0.652889\pi$
$797$	−26.0890			−0.924119			−0.462060	+	0.886849i	$0.652889\pi$
$798$		−	14.8243i		−	0.524776i
$799$		−	41.7040i		−	1.47538i
$800$		0			0
$801$		−	6.21355i		−	0.219545i
$802$		−	14.8814i		−	0.525481i
$803$			46.1725i			1.62939i
$804$	41.2090			1.45333
$805$		0			0
$806$			0.271112i			0.00954953i
$807$		−	47.5685i		−	1.67449i
$808$	2.38618			0.0839455
$809$		−	37.3911i		−	1.31460i	−0.753629	−	0.657300i	$-0.771698\pi$
$809$		−	37.3911i		−	1.31460i	0.753629	−	0.657300i	$-0.228302\pi$
$810$		0			0
$811$	40.7822			1.43206			0.716029	−	0.698070i	$-0.245958\pi$
$811$	40.7822			1.43206			0.716029	+	0.698070i	$0.245958\pi$
$812$	26.5215			0.930722
$813$			24.0483i			0.843412i
$814$	−14.1989	+	11.6775i	−0.497672	+	0.409296i
$815$		0			0
$816$			19.1088i			0.668943i
$817$			1.84387i			0.0645088i
$818$		−	15.5381i		−	0.543278i
$819$		−	32.9080i		−	1.14990i
$820$		0			0
$821$	−49.7348			−1.73576			−0.867879	−	0.496776i	$-0.834517\pi$
$821$	−49.7348			−1.73576			−0.867879	+	0.496776i	$0.834517\pi$
$822$	14.3119			0.499184
$823$			6.32881i			0.220608i	0.993898	+	0.110304i	$0.0351825\pi$
$823$			6.32881i			0.220608i	−0.993898	+	0.110304i	$0.964817\pi$
$824$	−46.8649			−1.63262
$825$		0			0
$826$	−14.2189			−0.494738
$827$	−24.9486			−0.867548			−0.433774	−	0.901022i	$-0.642818\pi$
$827$	−24.9486			−0.867548			−0.433774	+	0.901022i	$0.642818\pi$
$828$	−0.666940			−0.0231778
$829$			16.7582i			0.582036i	0.956718	+	0.291018i	$0.0939939\pi$
$829$			16.7582i			0.582036i	−0.956718	+	0.291018i	$0.906006\pi$
$830$		0			0
$831$		−	32.8411i		−	1.13924i
$832$	7.78900			0.270035
$833$	13.7892			0.477769
$834$			23.1153i			0.800418i
$835$		0			0
$836$			27.3477i			0.945839i
$837$	0.0565059			0.00195313
$838$	−2.35041			−0.0811935
$839$	45.1407			1.55843			0.779215	−	0.626756i	$-0.215618\pi$
$839$	45.1407			1.55843			0.779215	+	0.626756i	$0.215618\pi$
$840$		0			0
$841$	−35.9272			−1.23887
$842$			26.9161i			0.927590i
$843$	47.2669			1.62796
$844$	17.6447			0.607356
$845$		0			0
$846$		−	12.7916i		−	0.439784i
$847$			17.2188i			0.591645i
$848$		−	6.20276i		−	0.213004i
$849$			59.3278i			2.03612i
$850$		0			0
$851$	−0.778591	+	0.640329i	−0.0266898	+	0.0219502i
$852$			8.40215i			0.287853i
$853$	−3.04298			−0.104190			−0.0520948	−	0.998642i	$-0.516590\pi$
$853$	−3.04298			−0.104190			−0.0520948	+	0.998642i	$0.516590\pi$
$854$	−3.59649			−0.123070
$855$		0			0
$856$		−	12.0310i		−	0.411212i
$857$	0.397815			0.0135891			0.00679455	−	0.999977i	$-0.497837\pi$
$857$	0.397815			0.0135891			0.00679455	+	0.999977i	$0.497837\pi$
$858$		−	41.1177i		−	1.40373i
$859$			28.4886i			0.972018i	0.873954	+	0.486009i	$0.161548\pi$
$859$			28.4886i			0.972018i	−0.873954	+	0.486009i	$0.838452\pi$
$860$		0			0
$861$	44.3253			1.51060
$862$		−	3.12986i		−	0.106603i
$863$			31.2137i			1.06253i	0.847207	+	0.531263i	$0.178282\pi$
$863$			31.2137i			1.06253i	−0.847207	+	0.531263i	$0.821718\pi$
$864$		−	4.81729i		−	0.163887i
$865$		0			0
$866$		−	3.90537i		−	0.132710i
$867$			45.2702i			1.53746i
$868$	−0.224531			−0.00762109
$869$		−	35.0867i		−	1.19023i
$870$		0			0
$871$			65.3614i			2.21469i
$872$		−	16.2885i		−	0.551600i
$873$	−22.7581			−0.770245
$874$		−	0.476530i		−	0.0161189i
$875$		0			0
$876$	38.2799			1.29336
$877$			31.9398i			1.07853i	0.842136	+	0.539266i	$0.181298\pi$
$877$			31.9398i			1.07853i	−0.842136	+	0.539266i	$0.818702\pi$
$878$		−	21.8024i		−	0.735794i
$879$	12.3502			0.416561
$880$		0			0
$881$	20.6857			0.696920			0.348460	−	0.937324i	$-0.386705\pi$
$881$	20.6857			0.696920			0.348460	+	0.937324i	$0.386705\pi$
$882$	4.22948			0.142414
$883$	30.1761			1.01551			0.507754	−	0.861502i	$-0.330476\pi$
$883$	30.1761			1.01551			0.507754	+	0.861502i	$0.330476\pi$
$884$	−52.1437			−1.75378
$885$		0			0
$886$		−	17.5550i		−	0.589771i
$887$		−	34.4783i		−	1.15767i	−0.815445	−	0.578834i	$-0.803508\pi$
$887$		−	34.4783i		−	1.15767i	0.815445	−	0.578834i	$-0.196492\pi$
$888$	22.4392	+	27.2843i	0.753009	+	0.915601i
$889$	−19.9294			−0.668410
$890$		0			0
$891$	−43.1886			−1.44687
$892$			3.93753i			0.131838i
$893$	−28.7616			−0.962469
$894$		−	32.2311i		−	1.07797i
$895$		0			0
$896$			23.1748i			0.774217i
$897$		−	2.25467i		−	0.0752812i
$898$			8.34497i			0.278475i
$899$	0.549676			0.0183327
$900$		0			0
$901$		−	27.8133i		−	0.926595i
$902$	25.9844			0.865187
$903$	2.29597			0.0764050
$904$	11.4682			0.381426
$905$		0			0
$906$			38.3511i			1.27413i
$907$	1.66867			0.0554073			0.0277037	−	0.999616i	$-0.491181\pi$
$907$	1.66867			0.0554073			0.0277037	+	0.999616i	$0.491181\pi$
$908$	4.54439			0.150811
$909$	−2.58996			−0.0859036
$910$		0			0
$911$		−	53.6779i		−	1.77843i	−0.457492	−	0.889214i	$-0.651252\pi$
$911$		−	53.6779i		−	1.77843i	0.457492	−	0.889214i	$-0.348748\pi$
$912$	13.1786			0.436387
$913$			28.6986i			0.949787i
$914$	−26.9427			−0.891184
$915$		0			0
$916$	10.4682			0.345880
$917$	48.7624			1.61028
$918$		−	3.45352i		−	0.113983i
$919$		−	2.69177i		−	0.0887932i	−0.999014	−	0.0443966i	$-0.985863\pi$
$919$		−	2.69177i		−	0.0887932i	0.999014	−	0.0443966i	$-0.0141365\pi$
$920$		0			0
$921$	49.2963			1.62437
$922$			24.1139i			0.794147i
$923$	−13.3266			−0.438651
$924$	34.0531			1.12026
$925$		0			0
$926$	−4.79375			−0.157532
$927$	50.8671			1.67070
$928$		−	46.8614i		−	1.53830i
$929$	38.5193			1.26378			0.631888	−	0.775060i	$-0.282280\pi$
$929$	38.5193			1.26378			0.631888	+	0.775060i	$0.282280\pi$
$930$		0			0
$931$		−	9.50988i		−	0.311674i
$932$			36.2294i			1.18673i
$933$	56.5791			1.85232
$934$	18.9226			0.619167
$935$		0			0
$936$	−37.0698			−1.21166
$937$			56.0419i			1.83081i	0.402537	+	0.915404i	$0.368129\pi$
$937$			56.0419i			1.83081i	−0.402537	+	0.915404i	$0.631871\pi$
$938$	17.2015			0.561648
$939$		−	32.7262i		−	1.06798i
$940$		0			0
$941$	−36.5917			−1.19286			−0.596428	−	0.802666i	$-0.703414\pi$
$941$	−36.5917			−1.19286			−0.596428	+	0.802666i	$0.703414\pi$
$942$	23.4680			0.764627
$943$	1.42484			0.0463993
$944$		−	12.6403i		−	0.411408i
$945$		0			0
$946$	1.34594			0.0437604
$947$	8.48377			0.275685			0.137843	−	0.990454i	$-0.455983\pi$
$947$	8.48377			0.275685			0.137843	+	0.990454i	$0.455983\pi$
$948$	−29.0890			−0.944767
$949$			60.7156i			1.97091i
$950$		0			0
$951$	62.6776			2.03246
$952$			31.8065i			1.03086i
$953$		−	16.3555i		−	0.529807i	−0.964275	−	0.264904i	$-0.914660\pi$
$953$		−	16.3555i		−	0.529807i	0.964275	−	0.264904i	$-0.0853402\pi$
$954$		−	8.53100i		−	0.276201i
$955$		0			0
$956$			8.06882i			0.260964i
$957$	−83.3653			−2.69482
$958$			26.8606i			0.867825i
$959$	−18.7998			−0.607078
$960$		0			0
$961$	30.9953			0.999850
$962$	−18.6712	+	15.3556i	−0.601983	+	0.495083i
$963$			13.0585i			0.420803i
$964$		−	20.3033i		−	0.653925i
$965$		0			0
$966$	−0.593371			−0.0190914
$967$	−26.0712			−0.838393			−0.419197	−	0.907895i	$-0.637688\pi$
$967$	−26.0712			−0.838393			−0.419197	+	0.907895i	$0.637688\pi$
$968$	19.3964			0.623425
$969$	59.0930			1.89834
$970$		0			0
$971$	12.3808			0.397320			0.198660	−	0.980068i	$-0.436341\pi$
$971$	12.3808			0.397320			0.198660	+	0.980068i	$0.436341\pi$
$972$			32.0345i			1.02751i
$973$		−	30.3639i		−	0.973421i
$974$	1.40482			0.0450134
$975$		0			0
$976$		−	3.19722i		−	0.102341i
$977$	15.7957			0.505348			0.252674	−	0.967552i	$-0.418690\pi$
$977$	15.7957			0.505348			0.252674	+	0.967552i	$0.418690\pi$
$978$			17.9238i			0.573141i
$979$			10.1982i			0.325937i
$980$		0			0
$981$			17.6796i			0.564466i
$982$	−23.9475			−0.764196
$983$		−	26.9238i		−	0.858737i	−0.903129	−	0.429369i	$-0.858736\pi$
$983$		−	26.9238i		−	0.858737i	0.903129	−	0.429369i	$-0.141264\pi$
$984$		−	49.9310i		−	1.59174i
$985$		0			0
$986$		−	33.5950i		−	1.06988i
$987$			35.8136i			1.13996i
$988$			35.9614i			1.14408i
$989$	0.0738042			0.00234684
$990$		0			0
$991$		−	54.2528i		−	1.72340i	−0.507420	−	0.861699i	$-0.669401\pi$
$991$		−	54.2528i		−	1.72340i	0.507420	−	0.861699i	$-0.330599\pi$
$992$			0.396729i			0.0125962i
$993$	−83.1222			−2.63780
$994$			3.50723i			0.111243i
$995$		0			0
$996$	23.7929			0.753908
$997$	13.2613			0.419989			0.209995	−	0.977703i	$-0.432655\pi$
$997$	13.2613			0.419989			0.209995	+	0.977703i	$0.432655\pi$
$998$		−	6.20551i		−	0.196432i
$999$	3.20044	+	3.89149i	0.101258	+	0.123121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.d.f.924.6		12
5.2	odd	4		925.2.c.c.776.6		12
5.3	odd	4		185.2.c.b.36.7	yes	12
5.4	even	2		925.2.d.e.924.7		12
15.8	even	4		1665.2.e.e.406.6		12
20.3	even	4		2960.2.p.h.961.9		12
37.36	even	2		925.2.d.e.924.8		12
185.43	even	4		6845.2.a.h.1.4		6
185.68	even	4		6845.2.a.i.1.3		6
185.73	odd	4		185.2.c.b.36.6	✓	12
185.147	odd	4		925.2.c.c.776.7		12
185.184	even	2	inner	925.2.d.f.924.5		12
555.443	even	4		1665.2.e.e.406.7		12
740.443	even	4		2960.2.p.h.961.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.6	✓	12	185.73	odd	4
185.2.c.b.36.7	yes	12	5.3	odd	4
925.2.c.c.776.6		12	5.2	odd	4
925.2.c.c.776.7		12	185.147	odd	4
925.2.d.e.924.7		12	5.4	even	2
925.2.d.e.924.8		12	37.36	even	2
925.2.d.f.924.5		12	185.184	even	2	inner
925.2.d.f.924.6		12	1.1	even	1	trivial
1665.2.e.e.406.6		12	15.8	even	4
1665.2.e.e.406.7		12	555.443	even	4
2960.2.p.h.961.9		12	20.3	even	4
2960.2.p.h.961.10		12	740.443	even	4
6845.2.a.h.1.4		6	185.43	even	4
6845.2.a.i.1.3		6	185.68	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.694469 q^{2} +2.37730i q^{3} -1.51771 q^{4} -1.65096i q^{6} +2.16868i q^{7} +2.44294 q^{8} -2.65157 q^{9} +4.35199 q^{11} -3.60806i q^{12} +5.72273 q^{13} -1.50608i q^{14} +1.33888 q^{16} +6.00355 q^{17} +1.84143 q^{18} -4.14041i q^{19} -5.15560 q^{21} -3.02232 q^{22} -0.165727 q^{23} +5.80761i q^{24} -3.97426 q^{26} +0.828325i q^{27} -3.29143i q^{28} +8.05774i q^{29} -0.0682170i q^{31} -5.81569 q^{32} +10.3460i q^{33} -4.16928 q^{34} +4.02432 q^{36} +(4.69802 - 3.86375i) q^{37} +2.87539i q^{38} +13.6047i q^{39} -8.59751 q^{41} +3.58040 q^{42} -0.445335 q^{43} -6.60506 q^{44} +0.115093 q^{46} -6.94655i q^{47} +3.18292i q^{48} +2.29684 q^{49} +14.2723i q^{51} -8.68547 q^{52} -4.63281i q^{53} -0.575246i q^{54} +5.29795i q^{56} +9.84301 q^{57} -5.59585i q^{58} -9.44099i q^{59} -2.38799i q^{61} +0.0473746i q^{62} -5.75039i q^{63} +1.36106 q^{64} -7.18497i q^{66} +11.4214i q^{67} -9.11167 q^{68} -0.393984i q^{69} -2.32872 q^{71} -6.47763 q^{72} +10.6095i q^{73} +(-3.26263 + 2.68326i) q^{74} +6.28395i q^{76} +9.43805i q^{77} -9.44802i q^{78} -8.06222i q^{79} -9.92389 q^{81} +5.97071 q^{82} +6.59438i q^{83} +7.82472 q^{84} +0.309271 q^{86} -19.1557 q^{87} +10.6316 q^{88} +2.34335i q^{89} +12.4108i q^{91} +0.251527 q^{92} +0.162173 q^{93} +4.82416i q^{94} -13.8257i q^{96} +8.58288 q^{97} -1.59509 q^{98} -11.5396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 18 q^{4} + 6 q^{8} - 22 q^{9} + 2 q^{11} + 20 q^{13} + 30 q^{16} + 12 q^{17} - 26 q^{18} - 6 q^{21} - 28 q^{22} - 16 q^{23} - 12 q^{26} + 14 q^{32} - 4 q^{34} - 22 q^{36} - 14 q^{37} - 10 q^{41}+ \cdots + 84 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 18 * q^4 + 6 * q^8 - 22 * q^9 + 2 * q^11 + 20 * q^13 + 30 * q^16 + 12 * q^17 - 26 * q^18 - 6 * q^21 - 28 * q^22 - 16 * q^23 - 12 * q^26 + 14 * q^32 - 4 * q^34 - 22 * q^36 - 14 * q^37 - 10 * q^41 + 72 * q^42 - 12 * q^43 - 44 * q^44 - 24 * q^46 - 30 * q^49 + 80 * q^52 - 32 * q^57 + 126 * q^64 - 40 * q^68 + 42 * q^71 - 178 * q^72 - 50 * q^74 - 12 * q^81 + 96 * q^82 + 84 * q^84 - 64 * q^86 - 56 * q^87 - 72 * q^88 + 16 * q^92 + 76 * q^93 - 28 * q^97 + 118 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more