LMFDB - Embedded newform 925.2.b.f.149.2

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			149.2
Root			$2.47408i$ of defining polynomial
Character	$\chi$	$=$	925.149
Dual form			925.2.b.f.149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47408i q^{2} -2.38679i q^{3} -4.12105 q^{4} -5.90509 q^{6} +4.78404i q^{7} +5.24765i q^{8} -2.69675 q^{9} +O(q^{10})$	\(q-2.47408i q^{2} -2.38679i q^{3} -4.12105 q^{4} -5.90509 q^{6} +4.78404i q^{7} +5.24765i q^{8} -2.69675 q^{9} -3.12105 q^{11} +9.83607i q^{12} +2.81780i q^{13} +11.8361 q^{14} +4.74097 q^{16} +6.37246i q^{17} +6.67196i q^{18} -0.114347 q^{19} +11.4185 q^{21} +7.72172i q^{22} -5.62219i q^{23} +12.5250 q^{24} +6.97145 q^{26} -0.723803i q^{27} -19.7153i q^{28} -2.77357 q^{29} -6.67866 q^{31} -1.23424i q^{32} +7.44929i q^{33} +15.7660 q^{34} +11.1134 q^{36} +1.00000i q^{37} +0.282904i q^{38} +6.72548 q^{39} -3.12105 q^{41} -28.2502i q^{42} +8.57034i q^{43} +12.8620 q^{44} -13.9097 q^{46} +3.40396i q^{47} -11.3157i q^{48} -15.8870 q^{49} +15.2097 q^{51} -11.6123i q^{52} +10.2438i q^{53} -1.79074 q^{54} -25.1049 q^{56} +0.272922i q^{57} +6.86203i q^{58} +9.11059 q^{59} -5.55466 q^{61} +16.5235i q^{62} -12.9013i q^{63} +6.42836 q^{64} +18.4301 q^{66} -7.84948i q^{67} -26.2612i q^{68} -13.4190 q^{69} -4.33996 q^{71} -14.1516i q^{72} -3.22811i q^{73} +2.47408 q^{74} +0.471231 q^{76} -14.9312i q^{77} -16.6394i q^{78} -15.3847 q^{79} -9.81780 q^{81} +7.72172i q^{82} -5.68074i q^{83} -47.0561 q^{84} +21.2037 q^{86} +6.61992i q^{87} -16.3782i q^{88} +9.95042 q^{89} -13.4805 q^{91} +23.1693i q^{92} +15.9405i q^{93} +8.42165 q^{94} -2.94586 q^{96} -5.62970i q^{97} +39.3057i q^{98} +8.41669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 2.47408i	− 1.74944i	−0.484632	−	0.874718i	$-0.661047\pi$
$2$	− 2.47408i	− 1.74944i	0.484632	−	0.874718i	$-0.338953\pi$
$3$	− 2.38679i	− 1.37801i	−0.724756	−	0.689006i	$-0.758047\pi$
$3$	− 2.38679i	− 1.37801i	0.724756	−	0.689006i	$-0.241953\pi$
$4$	−4.12105	−2.06053
$5$	0	0
$5$	0	0
$6$	−5.90509	−2.41074
$7$	4.78404i	1.80820i	0.427325	+	0.904098i	$0.359456\pi$
$7$	4.78404i	1.80820i	−0.427325	+	0.904098i	$0.640544\pi$
$8$	5.24765i	1.85532i
$9$	−2.69675	−0.898915
$10$	0	0
$11$	−3.12105	−0.941033	−0.470516	−	0.882391i	$-0.655932\pi$
$11$	−3.12105	−0.941033	−0.470516	+	0.882391i	$0.655932\pi$
$12$	9.83607i	2.83943i
$13$	2.81780i	0.781517i	0.920493	+	0.390758i	$0.127787\pi$
$13$	2.81780i	0.781517i	−0.920493	+	0.390758i	$0.872213\pi$
$14$	11.8361	3.16332
$15$	0	0
$16$	4.74097	1.18524
$17$	6.37246i	1.54555i	0.634681	+	0.772774i	$0.281132\pi$
$17$	6.37246i	1.54555i	−0.634681	+	0.772774i	$0.718868\pi$
$18$	6.67196i	1.57259i
$19$	−0.114347	−0.0262330	−0.0131165	−	0.999914i	$-0.504175\pi$
$19$	−0.114347	−0.0262330	−0.0131165	+	0.999914i	$0.504175\pi$
$20$	0	0
$21$	11.4185	2.49171
$22$	7.72172i	1.64628i
$23$	− 5.62219i	− 1.17231i	−0.810200	−	0.586153i	$-0.800642\pi$
$23$	− 5.62219i	− 1.17231i	0.810200	−	0.586153i	$-0.199358\pi$
$24$	12.5250	2.55666
$25$	0	0
$26$	6.97145	1.36721
$27$	− 0.723803i	− 0.139296i
$28$	− 19.7153i	− 3.72584i
$29$	−2.77357	−0.515039	−0.257520	−	0.966273i	$-0.582905\pi$
$29$	−2.77357	−0.515039	−0.257520	+	0.966273i	$0.582905\pi$
$30$	0	0
$31$	−6.67866	−1.19952	−0.599761	−	0.800179i	$-0.704738\pi$
$31$	−6.67866	−1.19952	−0.599761	+	0.800179i	$0.704738\pi$
$32$	− 1.23424i	− 0.218184i
$33$	7.44929i	1.29675i
$34$	15.7660	2.70384
$35$	0	0
$36$	11.1134	1.85224
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	0.282904i	0.0458930i
$39$	6.72548	1.07694
$40$	0	0
$41$	−3.12105	−0.487427	−0.243713	−	0.969847i	$-0.578366\pi$
$41$	−3.12105	−0.487427	−0.243713	+	0.969847i	$0.578366\pi$
$42$	− 28.2502i	− 4.35910i
$43$	8.57034i	1.30696i	0.756942	+	0.653482i	$0.226693\pi$
$43$	8.57034i	1.30696i	−0.756942	+	0.653482i	$0.773307\pi$
$44$	12.8620	1.93902
$45$	0	0
$46$	−13.9097	−2.05088
$47$	3.40396i	0.496518i	0.968694	+	0.248259i	$0.0798584\pi$
$47$	3.40396i	0.496518i	−0.968694	+	0.248259i	$0.920142\pi$
$48$	− 11.3157i	− 1.63328i
$49$	−15.8870	−2.26957
$50$	0	0
$51$	15.2097	2.12978
$52$	− 11.6123i	− 1.61034i
$53$	10.2438i	1.40709i	0.710650	+	0.703546i	$0.248401\pi$
$53$	10.2438i	1.40709i	−0.710650	+	0.703546i	$0.751599\pi$
$54$	−1.79074	−0.243689
$55$	0	0
$56$	−25.1049	−3.35479
$57$	0.272922i	0.0361494i
$58$	6.86203i	0.901028i
$59$	9.11059	1.18610	0.593049	−	0.805167i	$-0.297924\pi$
$59$	9.11059	1.18610	0.593049	+	0.805167i	$0.297924\pi$
$60$	0	0
$61$	−5.55466	−0.711201	−0.355601	−	0.934638i	$-0.615724\pi$
$61$	−5.55466	−0.711201	−0.355601	+	0.934638i	$0.615724\pi$
$62$	16.5235i	2.09849i
$63$	− 12.9013i	− 1.62541i
$64$	6.42836	0.803544
$65$	0	0
$66$	18.4301	2.26859
$67$	− 7.84948i	− 0.958967i	−0.877551	−	0.479484i	$-0.840824\pi$
$67$	− 7.84948i	− 0.958967i	0.877551	−	0.479484i	$-0.159176\pi$
$68$	− 26.2612i	− 3.18464i
$69$	−13.4190	−1.61545
$70$	0	0
$71$	−4.33996	−0.515059	−0.257529	−	0.966270i	$-0.582908\pi$
$71$	−4.33996	−0.515059	−0.257529	+	0.966270i	$0.582908\pi$
$72$	− 14.1516i	− 1.66778i
$73$	− 3.22811i	− 0.377822i	−0.981994	−	0.188911i	$-0.939504\pi$
$73$	− 3.22811i	− 0.377822i	0.981994	−	0.188911i	$-0.0604957\pi$
$74$	2.47408	0.287606
$75$	0	0
$76$	0.471231	0.0540539
$77$	− 14.9312i	− 1.70157i
$78$	− 16.6394i	− 1.88404i
$79$	−15.3847	−1.73091	−0.865457	−	0.500983i	$-0.832972\pi$
$79$	−15.3847	−1.73091	−0.865457	+	0.500983i	$0.832972\pi$
$80$	0	0
$81$	−9.81780	−1.09087
$82$	7.72172i	0.852722i
$83$	− 5.68074i	− 0.623542i	−0.950157	−	0.311771i	$-0.899078\pi$
$83$	− 5.68074i	− 0.623542i	0.950157	−	0.311771i	$-0.100922\pi$
$84$	−47.0561	−5.13424
$85$	0	0
$86$	21.2037	2.28645
$87$	6.61992i	0.709730i
$88$	− 16.3782i	− 1.74592i
$89$	9.95042	1.05474	0.527371	−	0.849635i	$-0.323178\pi$
$89$	9.95042	1.05474	0.527371	+	0.849635i	$0.323178\pi$
$90$	0	0
$91$	−13.4805	−1.41314
$92$	23.1693i	2.41557i
$93$	15.9405i	1.65296i
$94$	8.42165	0.868627
$95$	0	0
$96$	−2.94586	−0.300660
$97$	− 5.62970i	− 0.571610i	−0.958288	−	0.285805i	$-0.907739\pi$
$97$	− 5.62970i	− 0.571610i	0.958288	−	0.285805i	$-0.0922609\pi$
$98$	39.3057i	3.97047i
$99$	8.41669	0.845909
$100$	0	0
$101$	4.09250	0.407219	0.203610	−	0.979052i	$-0.434733\pi$
$101$	4.09250	0.407219	0.203610	+	0.979052i	$0.434733\pi$
$102$	− 37.6299i	− 3.72592i
$103$	4.43010i	0.436511i	0.975892	+	0.218255i	$0.0700366\pi$
$103$	4.43010i	0.436511i	−0.975892	+	0.218255i	$0.929963\pi$
$104$	−14.7868	−1.44997
$105$	0	0
$106$	25.3439	2.46162
$107$	− 5.83005i	− 0.563612i	−0.959471	−	0.281806i	$-0.909067\pi$
$107$	− 5.83005i	− 0.563612i	0.959471	−	0.281806i	$-0.0909334\pi$
$108$	2.98283i	0.287023i
$109$	−10.3958	−0.995733	−0.497866	−	0.867254i	$-0.665883\pi$
$109$	−10.3958	−0.995733	−0.497866	+	0.867254i	$0.665883\pi$
$110$	0	0
$111$	2.38679	0.226544
$112$	22.6810i	2.14315i
$113$	4.57569i	0.430445i	0.976565	+	0.215222i	$0.0690477\pi$
$113$	4.57569i	0.430445i	−0.976565	+	0.215222i	$0.930952\pi$
$114$	0.675230	0.0632411
$115$	0	0
$116$	11.4300	1.06125
$117$	− 7.59889i	− 0.702517i
$118$	− 22.5403i	− 2.07500i
$119$	−30.4861	−2.79465
$120$	0	0
$121$	−1.25903	−0.114457
$122$	13.7427i	1.24420i
$123$	7.44929i	0.671679i
$124$	27.5231	2.47165
$125$	0	0
$126$	−31.9189	−2.84356
$127$	19.2279i	1.70620i	0.521749	+	0.853099i	$0.325280\pi$
$127$	19.2279i	1.70620i	−0.521749	+	0.853099i	$0.674720\pi$
$128$	− 18.3727i	− 1.62393i
$129$	20.4556	1.80101
$130$	0	0
$131$	7.31802	0.639378	0.319689	−	0.947522i	$-0.396422\pi$
$131$	7.31802	0.639378	0.319689	+	0.947522i	$0.396422\pi$
$132$	− 30.6989i	− 2.67200i
$133$	− 0.547041i	− 0.0474345i
$134$	−19.4202	−1.67765
$135$	0	0
$136$	−33.4404	−2.86749
$137$	− 7.40690i	− 0.632815i	−0.948623	−	0.316407i	$-0.897523\pi$
$137$	− 7.40690i	− 0.632815i	0.948623	−	0.316407i	$-0.102477\pi$
$138$	33.1995i	2.82613i
$139$	11.0477	0.937053	0.468526	−	0.883449i	$-0.344785\pi$
$139$	11.0477	0.937053	0.468526	+	0.883449i	$0.344785\pi$
$140$	0	0
$141$	8.12452	0.684208
$142$	10.7374i	0.901063i
$143$	− 8.79450i	− 0.735433i
$144$	−12.7852	−1.06543
$145$	0	0
$146$	−7.98659	−0.660975
$147$	37.9189i	3.12750i
$148$	− 4.12105i	− 0.338748i
$149$	13.5401	1.10925	0.554624	−	0.832101i	$-0.312862\pi$
$149$	13.5401	1.10925	0.554624	+	0.832101i	$0.312862\pi$
$150$	0	0
$151$	−11.6255	−0.946074	−0.473037	−	0.881043i	$-0.656842\pi$
$151$	−11.6255	−0.946074	−0.473037	+	0.881043i	$0.656842\pi$
$152$	− 0.600054i	− 0.0486708i
$153$	− 17.1849i	− 1.38932i
$154$	−36.9410	−2.97679
$155$	0	0
$156$	−27.7161	−2.21906
$157$	7.01400i	0.559778i	0.960032	+	0.279889i	$0.0902977\pi$
$157$	7.01400i	0.559778i	−0.960032	+	0.279889i	$0.909702\pi$
$158$	38.0629i	3.02812i
$159$	24.4497	1.93899
$160$	0	0
$161$	26.8967	2.11976
$162$	24.2900i	1.90840i
$163$	− 13.7892i	− 1.08006i	−0.841647	−	0.540029i	$-0.818413\pi$
$163$	− 13.7892i	− 1.08006i	0.841647	−	0.540029i	$-0.181587\pi$
$164$	12.8620	1.00436
$165$	0	0
$166$	−14.0546	−1.09085
$167$	− 8.49173i	− 0.657110i	−0.944485	−	0.328555i	$-0.893438\pi$
$167$	− 8.49173i	− 0.657110i	0.944485	−	0.328555i	$-0.106562\pi$
$168$	59.9201i	4.62294i
$169$	5.06001	0.389231
$170$	0	0
$171$	0.308365	0.0235813
$172$	− 35.3188i	− 2.69303i
$173$	− 3.55115i	− 0.269989i	−0.990846	−	0.134995i	$-0.956898\pi$
$173$	− 3.55115i	− 0.269989i	0.990846	−	0.134995i	$-0.0431017\pi$
$174$	16.3782	1.24163
$175$	0	0
$176$	−14.7968	−1.11535
$177$	− 21.7450i	− 1.63446i
$178$	− 24.6181i	− 1.84520i
$179$	−1.43280	−0.107092	−0.0535461	−	0.998565i	$-0.517052\pi$
$179$	−1.43280	−0.107092	−0.0535461	+	0.998565i	$0.517052\pi$
$180$	0	0
$181$	2.64490	0.196594	0.0982969	−	0.995157i	$-0.468661\pi$
$181$	2.64490	0.196594	0.0982969	+	0.995157i	$0.468661\pi$
$182$	33.3517i	2.47219i
$183$	13.2578i	0.980044i
$184$	29.5033	2.17501
$185$	0	0
$186$	39.4381	2.89174
$187$	− 19.8888i	− 1.45441i
$188$	− 14.0279i	− 1.02309i
$189$	3.46270	0.251874
$190$	0	0
$191$	19.8899	1.43918	0.719590	−	0.694400i	$-0.244330\pi$
$191$	19.8899	1.43918	0.719590	+	0.694400i	$0.244330\pi$
$192$	− 15.3431i	− 1.10729i
$193$	2.51805i	0.181253i	0.995885	+	0.0906267i	$0.0288870\pi$
$193$	2.51805i	0.181253i	−0.995885	+	0.0906267i	$0.971113\pi$
$194$	−13.9283	−0.999995
$195$	0	0
$196$	65.4712	4.67651
$197$	19.8229i	1.41233i	0.708049	+	0.706163i	$0.249575\pi$
$197$	19.8229i	1.41233i	−0.708049	+	0.706163i	$0.750425\pi$
$198$	− 20.8235i	− 1.47986i
$199$	−2.83381	−0.200883	−0.100442	−	0.994943i	$-0.532026\pi$
$199$	−2.83381	−0.200883	−0.100442	+	0.994943i	$0.532026\pi$
$200$	0	0
$201$	−18.7350	−1.32147
$202$	− 10.1252i	− 0.712404i
$203$	− 13.2689i	− 0.931292i
$204$	−62.6800	−4.38848
$205$	0	0
$206$	10.9604	0.763648
$207$	15.1616i	1.05380i
$208$	13.3591i	0.926288i
$209$	0.356884	0.0246862
$210$	0	0
$211$	10.5932	0.729263	0.364631	−	0.931152i	$-0.381195\pi$
$211$	10.5932	0.729263	0.364631	+	0.931152i	$0.381195\pi$
$212$	− 42.2152i	− 2.89935i
$213$	10.3586i	0.709757i
$214$	−14.4240	−0.986003
$215$	0	0
$216$	3.79826	0.258439
$217$	− 31.9510i	− 2.16897i
$218$	25.7199i	1.74197i
$219$	−7.70480	−0.520642
$220$	0	0
$221$	−17.9563	−1.20787
$222$	− 5.90509i	− 0.396324i
$223$	− 1.07942i	− 0.0722833i	−0.999347	−	0.0361416i	$-0.988493\pi$
$223$	− 1.07942i	− 0.0722833i	0.999347	−	0.0361416i	$-0.0115067\pi$
$224$	5.90463	0.394519
$225$	0	0
$226$	11.3206	0.753036
$227$	24.8788i	1.65126i	0.564209	+	0.825632i	$0.309181\pi$
$227$	24.8788i	1.65126i	−0.564209	+	0.825632i	$0.690819\pi$
$228$	− 1.12473i	− 0.0744869i
$229$	−6.71123	−0.443490	−0.221745	−	0.975105i	$-0.571175\pi$
$229$	−6.71123	−0.443490	−0.221745	+	0.975105i	$0.571175\pi$
$230$	0	0
$231$	−35.6377	−2.34479
$232$	− 14.5547i	− 0.955565i
$233$	20.9929i	1.37529i	0.726046	+	0.687646i	$0.241356\pi$
$233$	20.9929i	1.37529i	−0.726046	+	0.687646i	$0.758644\pi$
$234$	−18.8002	−1.22901
$235$	0	0
$236$	−37.5452	−2.44399
$237$	36.7200i	2.38522i
$238$	75.4249i	4.88907i
$239$	14.1050	0.912377	0.456188	−	0.889883i	$-0.349214\pi$
$239$	14.1050	0.912377	0.456188	+	0.889883i	$0.349214\pi$
$240$	0	0
$241$	−15.0611	−0.970171	−0.485085	−	0.874467i	$-0.661212\pi$
$241$	−15.0611	−0.970171	−0.485085	+	0.874467i	$0.661212\pi$
$242$	3.11493i	0.200235i
$243$	21.2616i	1.36393i
$244$	22.8911	1.46545
$245$	0	0
$246$	18.4301	1.17506
$247$	− 0.322207i	− 0.0205016i
$248$	− 35.0473i	− 2.22550i
$249$	−13.5587	−0.859248
$250$	0	0
$251$	−3.27325	−0.206606	−0.103303	−	0.994650i	$-0.532941\pi$
$251$	−3.27325	−0.206606	−0.103303	+	0.994650i	$0.532941\pi$
$252$	53.1671i	3.34921i
$253$	17.5471i	1.10318i
$254$	47.5712	2.98489
$255$	0	0
$256$	−32.5988	−2.03742
$257$	12.9715i	0.809137i	0.914508	+	0.404568i	$0.132578\pi$
$257$	12.9715i	0.809137i	−0.914508	+	0.404568i	$0.867422\pi$
$258$	− 50.6086i	− 3.15076i
$259$	−4.78404	−0.297266
$260$	0	0
$261$	7.47962	0.462977
$262$	− 18.1053i	− 1.11855i
$263$	− 23.4677i	− 1.44708i	−0.690284	−	0.723539i	$-0.742514\pi$
$263$	− 23.4677i	− 1.44708i	0.690284	−	0.723539i	$-0.257486\pi$
$264$	−39.0912	−2.40590
$265$	0	0
$266$	−1.35342	−0.0829836
$267$	− 23.7495i	− 1.45345i
$268$	32.3481i	1.97598i
$269$	−22.5925	−1.37749	−0.688743	−	0.725005i	$-0.741837\pi$
$269$	−22.5925	−1.37749	−0.688743	+	0.725005i	$0.741837\pi$
$270$	0	0
$271$	11.6989	0.710658	0.355329	−	0.934741i	$-0.384369\pi$
$271$	11.6989	0.710658	0.355329	+	0.934741i	$0.384369\pi$
$272$	30.2117i	1.83185i
$273$	32.1750i	1.94732i
$274$	−18.3252	−1.10707
$275$	0	0
$276$	55.3002	3.32868
$277$	16.2654i	0.977293i	0.872482	+	0.488647i	$0.162509\pi$
$277$	16.2654i	0.977293i	−0.872482	+	0.488647i	$0.837491\pi$
$278$	− 27.3328i	− 1.63931i
$279$	18.0107	1.07827
$280$	0	0
$281$	−0.135707	−0.00809561	−0.00404781	−	0.999992i	$-0.501288\pi$
$281$	−0.135707	−0.00809561	−0.00404781	+	0.999992i	$0.501288\pi$
$282$	− 20.1007i	− 1.19698i
$283$	− 16.4878i	− 0.980097i	−0.871695	−	0.490048i	$-0.836979\pi$
$283$	− 16.4878i	− 0.980097i	0.871695	−	0.490048i	$-0.163021\pi$
$284$	17.8852	1.06129
$285$	0	0
$286$	−21.7583	−1.28659
$287$	− 14.9312i	− 0.881363i
$288$	3.32842i	0.196129i
$289$	−23.6082	−1.38872
$290$	0	0
$291$	−13.4369	−0.787685
$292$	13.3032i	0.778511i
$293$	9.68971i	0.566079i	0.959108	+	0.283039i	$0.0913428\pi$
$293$	9.68971i	0.566079i	−0.959108	+	0.283039i	$0.908657\pi$
$294$	93.8142	5.47135
$295$	0	0
$296$	−5.24765	−0.305013
$297$	2.25903i	0.131082i
$298$	− 33.4993i	− 1.94056i
$299$	15.8422	0.916178
$300$	0	0
$301$	−41.0008	−2.36325
$302$	28.7625i	1.65510i
$303$	− 9.76793i	− 0.561153i
$304$	−0.542117	−0.0310925
$305$	0	0
$306$	−42.5168	−2.43052
$307$	21.4085i	1.22185i	0.791690	+	0.610923i	$0.209202\pi$
$307$	21.4085i	1.22185i	−0.791690	+	0.610923i	$0.790798\pi$
$308$	61.5324i	3.50613i
$309$	10.5737	0.601517
$310$	0	0
$311$	−16.6304	−0.943026	−0.471513	−	0.881859i	$-0.656292\pi$
$311$	−16.6304	−0.943026	−0.471513	+	0.881859i	$0.656292\pi$
$312$	35.2930i	1.99807i
$313$	− 10.7195i	− 0.605900i	−0.953007	−	0.302950i	$-0.902029\pi$
$313$	− 10.7195i	− 0.605900i	0.953007	−	0.302950i	$-0.0979715\pi$
$314$	17.3532	0.979296
$315$	0	0
$316$	63.4012	3.56660
$317$	20.6588i	1.16031i	0.814505	+	0.580157i	$0.197009\pi$
$317$	20.6588i	1.16031i	−0.814505	+	0.580157i	$0.802991\pi$
$318$	− 60.4905i	− 3.39214i
$319$	8.65646	0.484669
$320$	0	0
$321$	−13.9151	−0.776664
$322$	− 66.5446i	− 3.70839i
$323$	− 0.728673i	− 0.0405444i
$324$	40.4597	2.24776
$325$	0	0
$326$	−34.1157	−1.88949
$327$	24.8124i	1.37213i
$328$	− 16.3782i	− 0.904334i
$329$	−16.2847	−0.897802
$330$	0	0
$331$	15.2009	0.835518	0.417759	−	0.908558i	$-0.362816\pi$
$331$	15.2009	0.835518	0.417759	+	0.908558i	$0.362816\pi$
$332$	23.4106i	1.28483i
$333$	− 2.69675i	− 0.147781i
$334$	−21.0092	−1.14957
$335$	0	0
$336$	54.1347	2.95329
$337$	− 13.4672i	− 0.733607i	−0.930298	−	0.366803i	$-0.880452\pi$
$337$	− 13.4672i	− 0.733607i	0.930298	−	0.366803i	$-0.119548\pi$
$338$	− 12.5188i	− 0.680935i
$339$	10.9212	0.593158
$340$	0	0
$341$	20.8445	1.12879
$342$	− 0.762919i	− 0.0412539i
$343$	− 42.5158i	− 2.29564i
$344$	−44.9741	−2.42484
$345$	0	0
$346$	−8.78582	−0.472329
$347$	− 21.7251i	− 1.16626i	−0.812378	−	0.583132i	$-0.801827\pi$
$347$	− 21.7251i	− 1.16626i	0.812378	−	0.583132i	$-0.198173\pi$
$348$	− 27.2810i	− 1.46242i
$349$	10.0908	0.540149	0.270075	−	0.962839i	$-0.412952\pi$
$349$	10.0908	0.540149	0.270075	+	0.962839i	$0.412952\pi$
$350$	0	0
$351$	2.03953	0.108862
$352$	3.85211i	0.205318i
$353$	− 12.0314i	− 0.640364i	−0.947356	−	0.320182i	$-0.896256\pi$
$353$	− 12.0314i	− 0.640364i	0.947356	−	0.320182i	$-0.103744\pi$
$354$	−53.7988	−2.85938
$355$	0	0
$356$	−41.0062	−2.17332
$357$	72.7637i	3.85107i
$358$	3.54485i	0.187351i
$359$	−13.0174	−0.687030	−0.343515	−	0.939147i	$-0.611618\pi$
$359$	−13.0174	−0.687030	−0.343515	+	0.939147i	$0.611618\pi$
$360$	0	0
$361$	−18.9869	−0.999312
$362$	− 6.54368i	− 0.343928i
$363$	3.00503i	0.157723i
$364$	55.5537	2.91180
$365$	0	0
$366$	32.8008	1.71452
$367$	− 15.0870i	− 0.787535i	−0.919210	−	0.393767i	$-0.871172\pi$
$367$	− 15.0870i	− 0.787535i	0.919210	−	0.393767i	$-0.128828\pi$
$368$	− 26.6546i	− 1.38947i
$369$	8.41669	0.438155
$370$	0	0
$371$	−49.0067	−2.54430
$372$	− 65.6918i	− 3.40596i
$373$	− 21.8164i	− 1.12961i	−0.825224	−	0.564805i	$-0.808951\pi$
$373$	− 21.8164i	− 1.12961i	0.825224	−	0.564805i	$-0.191049\pi$
$374$	−49.2064	−2.54440
$375$	0	0
$376$	−17.8628	−0.921202
$377$	− 7.81537i	− 0.402512i
$378$	− 8.56698i	− 0.440638i
$379$	−20.0074	−1.02771	−0.513855	−	0.857877i	$-0.671783\pi$
$379$	−20.0074	−1.02771	−0.513855	+	0.857877i	$0.671783\pi$
$380$	0	0
$381$	45.8928	2.35116
$382$	− 49.2090i	− 2.51775i
$383$	− 22.7769i	− 1.16385i	−0.813244	−	0.581923i	$-0.802300\pi$
$383$	− 22.7769i	− 1.16385i	0.813244	−	0.581923i	$-0.197700\pi$
$384$	−43.8517	−2.23780
$385$	0	0
$386$	6.22985	0.317091
$387$	− 23.1120i	− 1.17485i
$388$	23.2003i	1.17782i
$389$	10.3991	0.527256	0.263628	−	0.964624i	$-0.415081\pi$
$389$	10.3991	0.527256	0.263628	+	0.964624i	$0.415081\pi$
$390$	0	0
$391$	35.8272	1.81186
$392$	− 83.3694i	− 4.21079i
$393$	− 17.4665i	− 0.881070i
$394$	49.0435	2.47077
$395$	0	0
$396$	−34.6856	−1.74302
$397$	25.3769i	1.27363i	0.771016	+	0.636816i	$0.219749\pi$
$397$	25.3769i	1.27363i	−0.771016	+	0.636816i	$0.780251\pi$
$398$	7.01105i	0.351432i
$399$	−1.30567	−0.0653652
$400$	0	0
$401$	−25.7926	−1.28802	−0.644011	−	0.765016i	$-0.722731\pi$
$401$	−25.7926	−1.28802	−0.644011	+	0.765016i	$0.722731\pi$
$402$	46.3519i	2.31182i
$403$	− 18.8191i	− 0.937447i
$404$	−16.8654	−0.839086
$405$	0	0
$406$	−32.8282	−1.62924
$407$	− 3.12105i	− 0.154705i
$408$	79.8151i	3.95144i
$409$	24.6967	1.22117	0.610587	−	0.791949i	$-0.290934\pi$
$409$	24.6967	1.22117	0.610587	+	0.791949i	$0.290934\pi$
$410$	0	0
$411$	−17.6787	−0.872026
$412$	− 18.2567i	− 0.899442i
$413$	43.5854i	2.14470i
$414$	37.5110	1.84356
$415$	0	0
$416$	3.47783	0.170515
$417$	− 26.3685i	− 1.29127i
$418$	− 0.882957i	− 0.0431869i
$419$	−7.25946	−0.354648	−0.177324	−	0.984153i	$-0.556744\pi$
$419$	−7.25946	−0.354648	−0.177324	+	0.984153i	$0.556744\pi$
$420$	0	0
$421$	−20.1805	−0.983536	−0.491768	−	0.870726i	$-0.663649\pi$
$421$	−20.1805	−0.983536	−0.491768	+	0.870726i	$0.663649\pi$
$422$	− 26.2083i	− 1.27580i
$423$	− 9.17961i	− 0.446328i
$424$	−53.7558	−2.61061
$425$	0	0
$426$	25.6279	1.24167
$427$	− 26.5737i	− 1.28599i
$428$	24.0259i	1.16134i
$429$	−20.9906	−1.01344
$430$	0	0
$431$	7.19925	0.346776	0.173388	−	0.984854i	$-0.444529\pi$
$431$	7.19925	0.346776	0.173388	+	0.984854i	$0.444529\pi$
$432$	− 3.43153i	− 0.165100i
$433$	20.2043i	0.970955i	0.874249	+	0.485477i	$0.161354\pi$
$433$	20.2043i	0.970955i	−0.874249	+	0.485477i	$0.838646\pi$
$434$	−79.0491	−3.79448
$435$	0	0
$436$	42.8415	2.05173
$437$	0.642881i	0.0307532i
$438$	19.0623i	0.910831i
$439$	−10.5790	−0.504908	−0.252454	−	0.967609i	$-0.581238\pi$
$439$	−10.5790	−0.504908	−0.252454	+	0.967609i	$0.581238\pi$
$440$	0	0
$441$	42.8432	2.04015
$442$	44.4253i	2.11310i
$443$	− 7.13975i	− 0.339220i	−0.985511	−	0.169610i	$-0.945749\pi$
$443$	− 7.13975i	− 0.339220i	0.985511	−	0.169610i	$-0.0542508\pi$
$444$	−9.83607	−0.466799
$445$	0	0
$446$	−2.67057	−0.126455
$447$	− 32.3173i	− 1.52856i
$448$	30.7535i	1.45297i
$449$	−9.74149	−0.459730	−0.229865	−	0.973223i	$-0.573828\pi$
$449$	−9.74149	−0.459730	−0.229865	+	0.973223i	$0.573828\pi$
$450$	0	0
$451$	9.74097	0.458685
$452$	− 18.8567i	− 0.886943i
$453$	27.7477i	1.30370i
$454$	61.5520	2.88878
$455$	0	0
$456$	−1.43220	−0.0670689
$457$	− 14.2862i	− 0.668279i	−0.942524	−	0.334139i	$-0.891554\pi$
$457$	− 14.2862i	− 0.668279i	0.942524	−	0.334139i	$-0.108446\pi$
$458$	16.6041i	0.775858i
$459$	4.61240	0.215289
$460$	0	0
$461$	−11.1338	−0.518553	−0.259277	−	0.965803i	$-0.583484\pi$
$461$	−11.1338	−0.518553	−0.259277	+	0.965803i	$0.583484\pi$
$462$	88.1703i	4.10205i
$463$	31.5684i	1.46711i	0.679630	+	0.733555i	$0.262140\pi$
$463$	31.5684i	1.46711i	−0.679630	+	0.733555i	$0.737860\pi$
$464$	−13.1494	−0.610447
$465$	0	0
$466$	51.9381	2.40599
$467$	− 2.53380i	− 0.117250i	−0.998280	−	0.0586250i	$-0.981328\pi$
$467$	− 2.53380i	− 0.117250i	0.998280	−	0.0586250i	$-0.0186716\pi$
$468$	31.3154i	1.44756i
$469$	37.5522	1.73400
$470$	0	0
$471$	16.7409	0.771380
$472$	47.8092i	2.20059i
$473$	− 26.7485i	− 1.22990i
$474$	90.8481	4.17279
$475$	0	0
$476$	125.635	5.75846
$477$	− 27.6249i	− 1.26486i
$478$	− 34.8969i	− 1.59614i
$479$	20.1584	0.921061	0.460531	−	0.887644i	$-0.347659\pi$
$479$	20.1584	0.921061	0.460531	+	0.887644i	$0.347659\pi$
$480$	0	0
$481$	−2.81780	−0.128481
$482$	37.2623i	1.69725i
$483$	− 64.1968i	− 2.92105i
$484$	5.18851	0.235842
$485$	0	0
$486$	52.6028	2.38611
$487$	30.1157i	1.36467i	0.731039	+	0.682335i	$0.239036\pi$
$487$	30.1157i	1.36467i	−0.731039	+	0.682335i	$0.760964\pi$
$488$	− 29.1489i	− 1.31951i
$489$	−32.9120	−1.48833
$490$	0	0
$491$	−21.3893	−0.965287	−0.482644	−	0.875817i	$-0.660323\pi$
$491$	−21.3893	−0.965287	−0.482644	+	0.875817i	$0.660323\pi$
$492$	− 30.6989i	− 1.38401i
$493$	− 17.6745i	− 0.796018i
$494$	−0.797166	−0.0358662
$495$	0	0
$496$	−31.6634	−1.42173
$497$	− 20.7625i	− 0.931327i
$498$	33.5453i	1.50320i
$499$	−2.62908	−0.117694	−0.0588469	−	0.998267i	$-0.518742\pi$
$499$	−2.62908	−0.117694	−0.0588469	+	0.998267i	$0.518742\pi$
$500$	0	0
$501$	−20.2679	−0.905505
$502$	8.09827i	0.361444i
$503$	28.9400i	1.29037i	0.764026	+	0.645185i	$0.223220\pi$
$503$	28.9400i	1.29037i	−0.764026	+	0.645185i	$0.776780\pi$
$504$	67.7016	3.01567
$505$	0	0
$506$	43.4130	1.92994
$507$	− 12.0772i	− 0.536365i
$508$	− 79.2391i	− 3.51567i
$509$	−31.4997	−1.39620	−0.698101	−	0.715999i	$-0.745971\pi$
$509$	−31.4997	−1.39620	−0.698101	+	0.715999i	$0.745971\pi$
$510$	0	0
$511$	15.4434	0.683175
$512$	43.9064i	1.94041i
$513$	0.0827648i	0.00365415i
$514$	32.0924	1.41553
$515$	0	0
$516$	−84.2985	−3.71103
$517$	− 10.6239i	− 0.467240i
$518$	11.8361i	0.520047i
$519$	−8.47584	−0.372048
$520$	0	0
$521$	−18.6342	−0.816379	−0.408189	−	0.912897i	$-0.633840\pi$
$521$	−18.6342	−0.816379	−0.408189	+	0.912897i	$0.633840\pi$
$522$	− 18.5051i	− 0.809948i
$523$	26.4935i	1.15848i	0.815158	+	0.579239i	$0.196650\pi$
$523$	26.4935i	1.15848i	−0.815158	+	0.579239i	$0.803350\pi$
$524$	−30.1579	−1.31746
$525$	0	0
$526$	−58.0608	−2.53157
$527$	− 42.5595i	− 1.85392i
$528$	35.3169i	1.53697i
$529$	−8.60898	−0.374303
$530$	0	0
$531$	−24.5689	−1.06620
$532$	2.25439i	0.0977400i
$533$	− 8.79450i	− 0.380932i
$534$	−58.7581	−2.54271
$535$	0	0
$536$	41.1913	1.77919
$537$	3.41978i	0.147574i
$538$	55.8955i	2.40983i
$539$	49.5842	2.13574
$540$	0	0
$541$	33.5066	1.44056	0.720281	−	0.693683i	$-0.244013\pi$
$541$	33.5066	1.44056	0.720281	+	0.693683i	$0.244013\pi$
$542$	− 28.9440i	− 1.24325i
$543$	− 6.31281i	− 0.270908i
$544$	7.86512	0.337214
$545$	0	0
$546$	79.6033	3.40671
$547$	− 15.6535i	− 0.669297i	−0.942343	−	0.334649i	$-0.891382\pi$
$547$	− 15.6535i	− 0.669297i	0.942343	−	0.334649i	$-0.108618\pi$
$548$	30.5242i	1.30393i
$549$	14.9795	0.639310
$550$	0	0
$551$	0.317150	0.0135110
$552$	− 70.4179i	− 2.99719i
$553$	− 73.6010i	− 3.12983i
$554$	40.2419	1.70971
$555$	0	0
$556$	−45.5281	−1.93082
$557$	14.4365i	0.611693i	0.952081	+	0.305847i	$0.0989395\pi$
$557$	14.4365i	0.611693i	−0.952081	+	0.305847i	$0.901060\pi$
$558$	− 44.5597i	− 1.88636i
$559$	−24.1495	−1.02141
$560$	0	0
$561$	−47.4703	−2.00420
$562$	0.335750i	0.0141628i
$563$	− 33.9067i	− 1.42900i	−0.699636	−	0.714499i	$-0.746655\pi$
$563$	− 33.9067i	− 1.42900i	0.699636	−	0.714499i	$-0.253345\pi$
$564$	−33.4816	−1.40983
$565$	0	0
$566$	−40.7920	−1.71462
$567$	− 46.9687i	− 1.97250i
$568$	− 22.7746i	− 0.955601i
$569$	2.51921	0.105611	0.0528054	−	0.998605i	$-0.483184\pi$
$569$	2.51921	0.105611	0.0528054	+	0.998605i	$0.483184\pi$
$570$	0	0
$571$	34.2902	1.43500	0.717500	−	0.696559i	$-0.245286\pi$
$571$	34.2902	1.43500	0.717500	+	0.696559i	$0.245286\pi$
$572$	36.2426i	1.51538i
$573$	− 47.4728i	− 1.98321i
$574$	−36.9410	−1.54189
$575$	0	0
$576$	−17.3356	−0.722318
$577$	35.5322i	1.47923i	0.673032	+	0.739613i	$0.264992\pi$
$577$	35.5322i	1.47923i	−0.673032	+	0.739613i	$0.735008\pi$
$578$	58.4086i	2.42948i
$579$	6.01005	0.249769
$580$	0	0
$581$	27.1769	1.12749
$582$	33.2439i	1.37800i
$583$	− 31.9714i	− 1.32412i
$584$	16.9400	0.700981
$585$	0	0
$586$	23.9731	0.990319
$587$	5.59872i	0.231084i	0.993303	+	0.115542i	$0.0368605\pi$
$587$	5.59872i	0.231084i	−0.993303	+	0.115542i	$0.963140\pi$
$588$	− 156.266i	− 6.44429i
$589$	0.763686	0.0314671
$590$	0	0
$591$	47.3131	1.94620
$592$	4.74097i	0.194853i
$593$	19.1110i	0.784795i	0.919796	+	0.392397i	$0.128354\pi$
$593$	19.1110i	0.784795i	−0.919796	+	0.392397i	$0.871646\pi$
$594$	5.58900	0.229320
$595$	0	0
$596$	−55.7995	−2.28564
$597$	6.76369i	0.276819i
$598$	− 39.1948i	− 1.60279i
$599$	14.8560	0.606999	0.303500	−	0.952832i	$-0.401845\pi$
$599$	14.8560	0.606999	0.303500	+	0.952832i	$0.401845\pi$
$600$	0	0
$601$	45.2240	1.84472	0.922362	−	0.386326i	$-0.126256\pi$
$601$	45.2240	1.84472	0.922362	+	0.386326i	$0.126256\pi$
$602$	101.439i	4.13435i
$603$	21.1681i	0.862030i
$604$	47.9095	1.94941
$605$	0	0
$606$	−24.1666	−0.981701
$607$	− 24.0745i	− 0.977152i	−0.872521	−	0.488576i	$-0.837517\pi$
$607$	− 24.0745i	− 0.977152i	0.872521	−	0.488576i	$-0.162483\pi$
$608$	0.141131i	0.00572363i
$609$	−31.6699	−1.28333
$610$	0	0
$611$	−9.59167	−0.388037
$612$	70.8199i	2.86273i
$613$	36.4363i	1.47165i	0.677172	+	0.735824i	$0.263205\pi$
$613$	36.4363i	1.47165i	−0.677172	+	0.735824i	$0.736795\pi$
$614$	52.9662	2.13754
$615$	0	0
$616$	78.3538	3.15697
$617$	17.3689i	0.699244i	0.936891	+	0.349622i	$0.113690\pi$
$617$	17.3689i	0.699244i	−0.936891	+	0.349622i	$0.886310\pi$
$618$	− 26.1601i	− 1.05232i
$619$	−33.5369	−1.34796	−0.673982	−	0.738748i	$-0.735417\pi$
$619$	−33.5369	−1.34796	−0.673982	+	0.738748i	$0.735417\pi$
$620$	0	0
$621$	−4.06935	−0.163297
$622$	41.1450i	1.64976i
$623$	47.6032i	1.90718i
$624$	31.8853	1.27644
$625$	0	0
$626$	−26.5208	−1.05998
$627$	− 0.851805i	− 0.0340178i
$628$	− 28.9051i	− 1.15344i
$629$	−6.37246	−0.254087
$630$	0	0
$631$	29.4780	1.17350	0.586751	−	0.809768i	$-0.300407\pi$
$631$	29.4780	1.17350	0.586751	+	0.809768i	$0.300407\pi$
$632$	− 80.7335i	− 3.21141i
$633$	− 25.2836i	− 1.00493i
$634$	51.1114	2.02989
$635$	0	0
$636$	−100.759	−3.99534
$637$	− 44.7664i	− 1.77371i
$638$	− 21.4168i	− 0.847897i
$639$	11.7038	0.462994
$640$	0	0
$641$	19.9156	0.786619	0.393309	−	0.919406i	$-0.371330\pi$
$641$	19.9156	0.786619	0.393309	+	0.919406i	$0.371330\pi$
$642$	34.4269i	1.35872i
$643$	33.7051i	1.32920i	0.747199	+	0.664600i	$0.231398\pi$
$643$	33.7051i	1.32920i	−0.747199	+	0.664600i	$0.768602\pi$
$644$	−110.843	−4.36782
$645$	0	0
$646$	−1.80279	−0.0709299
$647$	− 31.1727i	− 1.22552i	−0.790267	−	0.612762i	$-0.790058\pi$
$647$	− 31.1727i	− 1.22552i	0.790267	−	0.612762i	$-0.209942\pi$
$648$	− 51.5204i	− 2.02391i
$649$	−28.4346	−1.11616
$650$	0	0
$651$	−76.2601	−2.98887
$652$	56.8262i	2.22549i
$653$	33.8194i	1.32346i	0.749744	+	0.661728i	$0.230177\pi$
$653$	33.8194i	1.32346i	−0.749744	+	0.661728i	$0.769823\pi$
$654$	61.3879	2.40046
$655$	0	0
$656$	−14.7968	−0.577719
$657$	8.70539i	0.339630i
$658$	40.2895i	1.57065i
$659$	49.2883	1.92000	0.960000	−	0.280002i	$-0.0903350\pi$
$659$	49.2883	1.92000	0.960000	+	0.280002i	$0.0903350\pi$
$660$	0	0
$661$	−8.54371	−0.332312	−0.166156	−	0.986100i	$-0.553135\pi$
$661$	−8.54371	−0.332312	−0.166156	+	0.986100i	$0.553135\pi$
$662$	− 37.6082i	− 1.46168i
$663$	42.8579i	1.66446i
$664$	29.8105	1.15687
$665$	0	0
$666$	−6.67196	−0.258533
$667$	15.5935i	0.603784i
$668$	34.9949i	1.35399i
$669$	−2.57634	−0.0996072
$670$	0	0
$671$	17.3364	0.669264
$672$	− 14.0931i	− 0.543652i
$673$	7.02721i	0.270879i	0.990786	+	0.135439i	$0.0432446\pi$
$673$	7.02721i	0.270879i	−0.990786	+	0.135439i	$0.956755\pi$
$674$	−33.3190	−1.28340
$675$	0	0
$676$	−20.8526	−0.802022
$677$	26.3304i	1.01196i	0.862545	+	0.505980i	$0.168869\pi$
$677$	26.3304i	1.01196i	−0.862545	+	0.505980i	$0.831131\pi$
$678$	− 27.0199i	− 1.03769i
$679$	26.9327	1.03358
$680$	0	0
$681$	59.3804	2.27546
$682$	− 51.5708i	− 1.97475i
$683$	− 21.7961i	− 0.834005i	−0.908905	−	0.417003i	$-0.863081\pi$
$683$	− 21.7961i	− 0.834005i	0.908905	−	0.417003i	$-0.136919\pi$
$684$	−1.27079	−0.0485899
$685$	0	0
$686$	−105.187	−4.01607
$687$	16.0183i	0.611135i
$688$	40.6318i	1.54907i
$689$	−28.8649	−1.09967
$690$	0	0
$691$	14.8160	0.563628	0.281814	−	0.959469i	$-0.409064\pi$
$691$	14.8160	0.563628	0.281814	+	0.959469i	$0.409064\pi$
$692$	14.6345i	0.556320i
$693$	40.2657i	1.52957i
$694$	−53.7495	−2.04030
$695$	0	0
$696$	−34.7390	−1.31678
$697$	− 19.8888i	− 0.753342i
$698$	− 24.9655i	− 0.944957i
$699$	50.1056	1.89517
$700$	0	0
$701$	32.4335	1.22499	0.612497	−	0.790473i	$-0.290165\pi$
$701$	32.4335	1.22499	0.612497	+	0.790473i	$0.290165\pi$
$702$	− 5.04595i	− 0.190447i
$703$	− 0.114347i	− 0.00431269i
$704$	−20.0632	−0.756162
$705$	0	0
$706$	−29.7665	−1.12028
$707$	19.5787i	0.736332i
$708$	89.6124i	3.36784i
$709$	21.4469	0.805457	0.402729	−	0.915319i	$-0.368062\pi$
$709$	21.4469	0.805457	0.402729	+	0.915319i	$0.368062\pi$
$710$	0	0
$711$	41.4886	1.55595
$712$	52.2163i	1.95689i
$713$	37.5487i	1.40621i
$714$	180.023	6.73719
$715$	0	0
$716$	5.90463	0.220666
$717$	− 33.6656i	− 1.25727i
$718$	32.2059i	1.20191i
$719$	−43.8000	−1.63346	−0.816732	−	0.577017i	$-0.804216\pi$
$719$	−43.8000	−1.63346	−0.816732	+	0.577017i	$0.804216\pi$
$720$	0	0
$721$	−21.1938	−0.789297
$722$	46.9751i	1.74823i
$723$	35.9476i	1.33691i
$724$	−10.8998	−0.405087
$725$	0	0
$726$	7.43466	0.275926
$727$	− 9.65770i	− 0.358184i	−0.983832	−	0.179092i	$-0.942684\pi$
$727$	− 9.65770i	− 0.358184i	0.983832	−	0.179092i	$-0.0573160\pi$
$728$	− 70.7407i	− 2.62182i
$729$	21.2934	0.788645
$730$	0	0
$731$	−54.6141	−2.01998
$732$	− 54.6360i	− 2.01941i
$733$	36.9457i	1.36462i	0.731063	+	0.682310i	$0.239024\pi$
$733$	36.9457i	1.36462i	−0.731063	+	0.682310i	$0.760976\pi$
$734$	−37.3264	−1.37774
$735$	0	0
$736$	−6.93910	−0.255779
$737$	24.4987i	0.902420i
$738$	− 20.8235i	− 0.766525i
$739$	−14.9966	−0.551660	−0.275830	−	0.961206i	$-0.588953\pi$
$739$	−14.9966	−0.551660	−0.275830	+	0.961206i	$0.588953\pi$
$740$	0	0
$741$	−0.769040	−0.0282514
$742$	121.246i	4.45109i
$743$	− 33.3328i	− 1.22286i	−0.791298	−	0.611431i	$-0.790594\pi$
$743$	− 33.3328i	− 1.22286i	0.791298	−	0.611431i	$-0.209406\pi$
$744$	−83.6503	−3.06677
$745$	0	0
$746$	−53.9754	−1.97618
$747$	15.3195i	0.560512i
$748$	81.9628i	2.99686i
$749$	27.8912	1.01912
$750$	0	0
$751$	−37.4403	−1.36622	−0.683108	−	0.730317i	$-0.739372\pi$
$751$	−37.4403	−1.36622	−0.683108	+	0.730317i	$0.739372\pi$
$752$	16.1381i	0.588495i
$753$	7.81255i	0.284705i
$754$	−19.3358	−0.704169
$755$	0	0
$756$	−14.2700	−0.518993
$757$	− 42.7798i	− 1.55486i	−0.628970	−	0.777430i	$-0.716523\pi$
$757$	− 42.7798i	− 1.55486i	0.628970	−	0.777430i	$-0.283477\pi$
$758$	49.4998i	1.79791i
$759$	41.8813	1.52019
$760$	0	0
$761$	15.9517	0.578250	0.289125	−	0.957291i	$-0.406636\pi$
$761$	15.9517	0.578250	0.289125	+	0.957291i	$0.406636\pi$
$762$	− 113.542i	− 4.11321i
$763$	− 49.7337i	− 1.80048i
$764$	−81.9671	−2.96547
$765$	0	0
$766$	−56.3519	−2.03608
$767$	25.6718i	0.926955i
$768$	77.8063i	2.80759i
$769$	−26.0272	−0.938565	−0.469282	−	0.883048i	$-0.655487\pi$
$769$	−26.0272	−0.938565	−0.469282	+	0.883048i	$0.655487\pi$
$770$	0	0
$771$	30.9601	1.11500
$772$	− 10.3770i	− 0.373477i
$773$	15.4131i	0.554371i	0.960816	+	0.277186i	$0.0894017\pi$
$773$	15.4131i	0.554371i	−0.960816	+	0.277186i	$0.910598\pi$
$774$	−57.1809	−2.05533
$775$	0	0
$776$	29.5427	1.06052
$777$	11.4185i	0.409635i
$778$	− 25.7282i	− 0.922401i
$779$	0.356884	0.0127867
$780$	0	0
$781$	13.5453	0.484687
$782$	− 88.6391i	− 3.16973i
$783$	2.00752i	0.0717428i
$784$	−75.3199	−2.69000
$785$	0	0
$786$	−43.2136	−1.54138
$787$	− 41.0054i	− 1.46168i	−0.682547	−	0.730842i	$-0.739128\pi$
$787$	− 41.0054i	− 1.46168i	0.682547	−	0.730842i	$-0.260872\pi$
$788$	− 81.6914i	− 2.91014i
$789$	−56.0123	−1.99409
$790$	0	0
$791$	−21.8903	−0.778329
$792$	44.1678i	1.56943i
$793$	− 15.6519i	− 0.555816i
$794$	62.7845	2.22814
$795$	0	0
$796$	11.6783	0.413925
$797$	− 10.4609i	− 0.370545i	−0.982687	−	0.185272i	$-0.940683\pi$
$797$	− 10.4609i	− 0.370545i	0.982687	−	0.185272i	$-0.0593167\pi$
$798$	3.23033i	0.114352i
$799$	−21.6916	−0.767393
$800$	0	0
$801$	−26.8337	−0.948124
$802$	63.8129i	2.25331i
$803$	10.0751i	0.355543i
$804$	77.2081	2.72292
$805$	0	0
$806$	−46.5600	−1.64000
$807$	53.9234i	1.89819i
$808$	21.4760i	0.755524i
$809$	30.5114	1.07272	0.536362	−	0.843988i	$-0.319798\pi$
$809$	30.5114	1.07272	0.536362	+	0.843988i	$0.319798\pi$
$810$	0	0
$811$	−13.7530	−0.482934	−0.241467	−	0.970409i	$-0.577629\pi$
$811$	−13.7530	−0.482934	−0.241467	+	0.970409i	$0.577629\pi$
$812$	54.6817i	1.91895i
$813$	− 27.9228i	− 0.979295i
$814$	−7.72172	−0.270646
$815$	0	0
$816$	72.1088	2.52431
$817$	− 0.979994i	− 0.0342856i
$818$	− 61.1015i	− 2.13636i
$819$	36.3534	1.27029
$820$	0	0
$821$	8.25903	0.288242	0.144121	−	0.989560i	$-0.453965\pi$
$821$	8.25903	0.288242	0.144121	+	0.989560i	$0.453965\pi$
$822$	43.7384i	1.52555i
$823$	− 10.4094i	− 0.362847i	−0.983405	−	0.181424i	$-0.941929\pi$
$823$	− 10.4094i	− 0.362847i	0.983405	−	0.181424i	$-0.0580705\pi$
$824$	−23.2476	−0.809869
$825$	0	0
$826$	107.834	3.75201
$827$	31.6239i	1.09967i	0.835273	+	0.549836i	$0.185310\pi$
$827$	31.6239i	1.09967i	−0.835273	+	0.549836i	$0.814690\pi$
$828$	− 62.4818i	− 2.17139i
$829$	53.4364	1.85592	0.927962	−	0.372675i	$-0.121559\pi$
$829$	53.4364	1.85592	0.927962	+	0.372675i	$0.121559\pi$
$830$	0	0
$831$	38.8220	1.34672
$832$	18.1138i	0.627984i
$833$	− 101.239i	− 3.50773i
$834$	−65.2376	−2.25899
$835$	0	0
$836$	−1.47074	−0.0508665
$837$	4.83403i	0.167089i
$838$	17.9605i	0.620434i
$839$	18.1104	0.625241	0.312621	−	0.949878i	$-0.398793\pi$
$839$	18.1104	0.625241	0.312621	+	0.949878i	$0.398793\pi$
$840$	0	0
$841$	−21.3073	−0.734735
$842$	49.9280i	1.72063i
$843$	0.323904i	0.0111558i
$844$	−43.6549	−1.50267
$845$	0	0
$846$	−22.7110	−0.780822
$847$	− 6.02323i	− 0.206961i
$848$	48.5655i	1.66775i
$849$	−39.3528	−1.35058
$850$	0	0
$851$	5.62219	0.192726
$852$	− 42.6882i	− 1.46247i
$853$	47.7844i	1.63611i	0.575141	+	0.818054i	$0.304947\pi$
$853$	47.7844i	1.63611i	−0.575141	+	0.818054i	$0.695053\pi$
$854$	−65.7454	−2.24976
$855$	0	0
$856$	30.5940	1.04568
$857$	− 45.5305i	− 1.55529i	−0.628701	−	0.777647i	$-0.716413\pi$
$857$	− 45.5305i	− 1.55529i	0.628701	−	0.777647i	$-0.283587\pi$
$858$	51.9323i	1.77294i
$859$	1.38588	0.0472855	0.0236428	−	0.999720i	$-0.492474\pi$
$859$	1.38588	0.0472855	0.0236428	+	0.999720i	$0.492474\pi$
$860$	0	0
$861$	−35.6377	−1.21453
$862$	− 17.8115i	− 0.606662i
$863$	13.2425i	0.450779i	0.974269	+	0.225389i	$0.0723655\pi$
$863$	13.2425i	0.450779i	−0.974269	+	0.225389i	$0.927635\pi$
$864$	−0.893343	−0.0303921
$865$	0	0
$866$	49.9869	1.69862
$867$	56.3478i	1.91367i
$868$	131.672i	4.46923i
$869$	48.0165	1.62885
$870$	0	0
$871$	22.1183	0.749449
$872$	− 54.5533i	− 1.84741i
$873$	15.1819i	0.513829i
$874$	1.59054	0.0538007
$875$	0	0
$876$	31.7519	1.07280
$877$	− 2.17005i	− 0.0732774i	−0.999329	−	0.0366387i	$-0.988335\pi$
$877$	− 2.17005i	− 0.0732774i	0.999329	−	0.0366387i	$-0.0116651\pi$
$878$	26.1732i	0.883304i
$879$	23.1273	0.780063
$880$	0	0
$881$	−15.4067	−0.519066	−0.259533	−	0.965734i	$-0.583569\pi$
$881$	−15.4067	−0.519066	−0.259533	+	0.965734i	$0.583569\pi$
$882$	− 105.997i	− 3.56912i
$883$	− 2.16284i	− 0.0727855i	−0.999338	−	0.0363927i	$-0.988413\pi$
$883$	− 2.16284i	− 0.0727855i	0.999338	−	0.0363927i	$-0.0115867\pi$
$884$	73.9989	2.48885
$885$	0	0
$886$	−17.6643	−0.593443
$887$	− 37.0458i	− 1.24388i	−0.783066	−	0.621939i	$-0.786345\pi$
$887$	− 37.0458i	− 1.24388i	0.783066	−	0.621939i	$-0.213655\pi$
$888$	12.5250i	0.420312i
$889$	−91.9869	−3.08514
$890$	0	0
$891$	30.6419	1.02654
$892$	4.44834i	0.148942i
$893$	− 0.389233i	− 0.0130252i
$894$	−79.9556	−2.67411
$895$	0	0
$896$	87.8957	2.93639
$897$	− 37.8119i	− 1.26250i
$898$	24.1012i	0.804267i
$899$	18.5237	0.617801
$900$	0	0
$901$	−65.2781	−2.17473
$902$	− 24.0999i	− 0.802439i
$903$	97.8602i	3.25658i
$904$	−24.0116	−0.798615
$905$	0	0
$906$	68.6499	2.28074
$907$	36.8420i	1.22332i	0.791122	+	0.611659i	$0.209497\pi$
$907$	36.8420i	1.22332i	−0.791122	+	0.611659i	$0.790503\pi$
$908$	− 102.527i	− 3.40247i
$909$	−11.0364	−0.366056
$910$	0	0
$911$	41.1165	1.36225	0.681125	−	0.732167i	$-0.261491\pi$
$911$	41.1165	1.36225	0.681125	+	0.732167i	$0.261491\pi$
$912$	1.29392i	0.0428459i
$913$	17.7299i	0.586774i
$914$	−35.3451	−1.16911
$915$	0	0
$916$	27.6573	0.913824
$917$	35.0097i	1.15612i
$918$	− 11.4114i	− 0.376633i
$919$	−27.3887	−0.903469	−0.451734	−	0.892153i	$-0.649194\pi$
$919$	−27.3887	−0.903469	−0.451734	+	0.892153i	$0.649194\pi$
$920$	0	0
$921$	51.0975	1.68372
$922$	27.5459i	0.907176i
$923$	− 12.2291i	− 0.402527i
$924$	146.865	4.83149
$925$	0	0
$926$	78.1027	2.56662
$927$	− 11.9469i	− 0.392386i
$928$	3.42324i	0.112373i
$929$	−7.83630	−0.257101	−0.128550	−	0.991703i	$-0.541032\pi$
$929$	−7.83630	−0.257101	−0.128550	+	0.991703i	$0.541032\pi$
$930$	0	0
$931$	1.81663	0.0595378
$932$	− 86.5129i	− 2.83383i
$933$	39.6933i	1.29950i
$934$	−6.26880	−0.205121
$935$	0	0
$936$	39.8763	1.30340
$937$	− 54.0007i	− 1.76413i	−0.471131	−	0.882063i	$-0.656154\pi$
$937$	− 54.0007i	− 1.76413i	0.471131	−	0.882063i	$-0.343846\pi$
$938$	− 92.9070i	− 3.03352i
$939$	−25.5850	−0.834937
$940$	0	0
$941$	−23.1621	−0.755064	−0.377532	−	0.925996i	$-0.623227\pi$
$941$	−23.1621	−0.755064	−0.377532	+	0.925996i	$0.623227\pi$
$942$	− 41.4183i	− 1.34948i
$943$	17.5471i	0.571414i
$944$	43.1931	1.40581
$945$	0	0
$946$	−66.1778	−2.15163
$947$	55.0147i	1.78774i	0.448328	+	0.893869i	$0.352020\pi$
$947$	55.0147i	1.78774i	−0.448328	+	0.893869i	$0.647980\pi$
$948$	− 151.325i	− 4.91481i
$949$	9.09616	0.295274
$950$	0	0
$951$	49.3081	1.59893
$952$	− 159.980i	− 5.18499i
$953$	8.16285i	0.264421i	0.991222	+	0.132210i	$0.0422074\pi$
$953$	8.16285i	0.264421i	−0.991222	+	0.132210i	$0.957793\pi$
$954$	−68.3461	−2.21279
$955$	0	0
$956$	−58.1275	−1.87998
$957$	− 20.6611i	− 0.667879i
$958$	− 49.8734i	− 1.61134i
$959$	35.4349	1.14425
$960$	0	0
$961$	13.6045	0.438855
$962$	6.97145i	0.224769i
$963$	15.7222i	0.506639i
$964$	62.0676	1.99906
$965$	0	0
$966$	−158.828	−5.11020
$967$	53.3125i	1.71441i	0.514973	+	0.857207i	$0.327802\pi$
$967$	53.3125i	1.71441i	−0.514973	+	0.857207i	$0.672198\pi$
$968$	− 6.60693i	− 0.212355i
$969$	−1.73919	−0.0558707
$970$	0	0
$971$	16.3998	0.526295	0.263148	−	0.964756i	$-0.415239\pi$
$971$	16.3998	0.526295	0.263148	+	0.964756i	$0.415239\pi$
$972$	− 87.6201i	− 2.81042i
$973$	52.8526i	1.69438i
$974$	74.5084	2.38740
$975$	0	0
$976$	−26.3345	−0.842947
$977$	− 0.0290257i	0 0.000928615i	−1.00000		0.000464308i	$-0.999852\pi$
$977$	− 0.0290257i	0 0.000928615i	1.00000		0.000464308i	$-0.000147794\pi$
$978$	81.4268i	2.60374i
$979$	−31.0558	−0.992547
$980$	0	0
$981$	28.0347	0.895080
$982$	52.9188i	1.68871i
$983$	− 14.6004i	− 0.465682i	−0.972515	−	0.232841i	$-0.925198\pi$
$983$	− 14.6004i	− 0.465682i	0.972515	−	0.232841i	$-0.0748021\pi$
$984$	−39.0912	−1.24618
$985$	0	0
$986$	−43.7280	−1.39258
$987$	38.8680i	1.23718i
$988$	1.32783i	0.0422440i
$989$	48.1840	1.53216
$990$	0	0
$991$	17.3653	0.551626	0.275813	−	0.961211i	$-0.411053\pi$
$991$	17.3653	0.551626	0.275813	+	0.961211i	$0.411053\pi$
$992$	8.24304i	0.261717i
$993$	− 36.2813i	− 1.15135i
$994$	−51.3681	−1.62930
$995$	0	0
$996$	55.8762	1.77050
$997$	− 17.2896i	− 0.547567i	−0.961791	−	0.273783i	$-0.911725\pi$
$997$	− 17.2896i	− 0.547567i	0.961791	−	0.273783i	$-0.0882752\pi$
$998$	6.50454i	0.205898i
$999$	0.723803	0.0229001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.b.f.149.2		10
5.2	odd	4		925.2.a.f.1.5		5
5.3	odd	4		185.2.a.e.1.1	✓	5
5.4	even	2	inner	925.2.b.f.149.9		10
15.2	even	4		8325.2.a.ch.1.1		5
15.8	even	4		1665.2.a.p.1.5		5
20.3	even	4		2960.2.a.w.1.2		5
35.13	even	4		9065.2.a.k.1.1		5
185.73	odd	4		6845.2.a.f.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.e.1.1	✓	5	5.3	odd	4
925.2.a.f.1.5		5	5.2	odd	4
925.2.b.f.149.2		10	1.1	even	1	trivial
925.2.b.f.149.9		10	5.4	even	2	inner
1665.2.a.p.1.5		5	15.8	even	4
2960.2.a.w.1.2		5	20.3	even	4
6845.2.a.f.1.5		5	185.73	odd	4
8325.2.a.ch.1.1		5	15.2	even	4
9065.2.a.k.1.1		5	35.13	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)

\(f(q)\)	\(=\)	\(q-2.47408i q^{2} -2.38679i q^{3} -4.12105 q^{4} -5.90509 q^{6} +4.78404i q^{7} +5.24765i q^{8} -2.69675 q^{9} +O(q^{10})\)	\(q-2.47408i q^{2} -2.38679i q^{3} -4.12105 q^{4} -5.90509 q^{6} +4.78404i q^{7} +5.24765i q^{8} -2.69675 q^{9} -3.12105 q^{11} +9.83607i q^{12} +2.81780i q^{13} +11.8361 q^{14} +4.74097 q^{16} +6.37246i q^{17} +6.67196i q^{18} -0.114347 q^{19} +11.4185 q^{21} +7.72172i q^{22} -5.62219i q^{23} +12.5250 q^{24} +6.97145 q^{26} -0.723803i q^{27} -19.7153i q^{28} -2.77357 q^{29} -6.67866 q^{31} -1.23424i q^{32} +7.44929i q^{33} +15.7660 q^{34} +11.1134 q^{36} +1.00000i q^{37} +0.282904i q^{38} +6.72548 q^{39} -3.12105 q^{41} -28.2502i q^{42} +8.57034i q^{43} +12.8620 q^{44} -13.9097 q^{46} +3.40396i q^{47} -11.3157i q^{48} -15.8870 q^{49} +15.2097 q^{51} -11.6123i q^{52} +10.2438i q^{53} -1.79074 q^{54} -25.1049 q^{56} +0.272922i q^{57} +6.86203i q^{58} +9.11059 q^{59} -5.55466 q^{61} +16.5235i q^{62} -12.9013i q^{63} +6.42836 q^{64} +18.4301 q^{66} -7.84948i q^{67} -26.2612i q^{68} -13.4190 q^{69} -4.33996 q^{71} -14.1516i q^{72} -3.22811i q^{73} +2.47408 q^{74} +0.471231 q^{76} -14.9312i q^{77} -16.6394i q^{78} -15.3847 q^{79} -9.81780 q^{81} +7.72172i q^{82} -5.68074i q^{83} -47.0561 q^{84} +21.2037 q^{86} +6.61992i q^{87} -16.3782i q^{88} +9.95042 q^{89} -13.4805 q^{91} +23.1693i q^{92} +15.9405i q^{93} +8.42165 q^{94} -2.94586 q^{96} -5.62970i q^{97} +39.3057i q^{98} +8.41669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 20 q^{4} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 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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