LMFDB - Embedded newform 5566.2.a.bt.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5566,2,Mod(1,5566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5566, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5566 = 2 \cdot 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5566.a (trivial)

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:	yes
Analytic conductor:	$44.4447337650$
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} - 4x^{9} - 14x^{8} + 50x^{7} + 85x^{6} - 188x^{5} - 248x^{4} + 186x^{3} + 260x^{2} + 52x - 4 $ x^10 - 4x^9 - 14x^8 + 50x^7 + 85x^6 - 188x^5 - 248x^4 + 186x^3 + 260x^2 + 52*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 506)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-2.10337$ of defining polynomial
Character	$\chi$	$=$	5566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.10337 q^{3} +1.00000 q^{4} +2.70739 q^{5} -3.10337 q^{6} +1.47043 q^{7} -1.00000 q^{8} +6.63091 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.10337 q^{3} +1.00000 q^{4} +2.70739 q^{5} -3.10337 q^{6} +1.47043 q^{7} -1.00000 q^{8} +6.63091 q^{9} -2.70739 q^{10} +3.10337 q^{12} -0.908777 q^{13} -1.47043 q^{14} +8.40205 q^{15} +1.00000 q^{16} -3.03254 q^{17} -6.63091 q^{18} +1.45785 q^{19} +2.70739 q^{20} +4.56329 q^{21} -1.00000 q^{23} -3.10337 q^{24} +2.32998 q^{25} +0.908777 q^{26} +11.2681 q^{27} +1.47043 q^{28} +8.39578 q^{29} -8.40205 q^{30} +5.01397 q^{31} -1.00000 q^{32} +3.03254 q^{34} +3.98104 q^{35} +6.63091 q^{36} +1.79423 q^{37} -1.45785 q^{38} -2.82027 q^{39} -2.70739 q^{40} +0.0162536 q^{41} -4.56329 q^{42} -6.50282 q^{43} +17.9525 q^{45} +1.00000 q^{46} -10.3948 q^{47} +3.10337 q^{48} -4.83783 q^{49} -2.32998 q^{50} -9.41108 q^{51} -0.908777 q^{52} +7.30311 q^{53} -11.2681 q^{54} -1.47043 q^{56} +4.52426 q^{57} -8.39578 q^{58} -0.224825 q^{59} +8.40205 q^{60} +12.3494 q^{61} -5.01397 q^{62} +9.75030 q^{63} +1.00000 q^{64} -2.46042 q^{65} -10.5937 q^{67} -3.03254 q^{68} -3.10337 q^{69} -3.98104 q^{70} +8.06760 q^{71} -6.63091 q^{72} +8.36256 q^{73} -1.79423 q^{74} +7.23080 q^{75} +1.45785 q^{76} +2.82027 q^{78} -14.8727 q^{79} +2.70739 q^{80} +15.0762 q^{81} -0.0162536 q^{82} +5.48836 q^{83} +4.56329 q^{84} -8.21027 q^{85} +6.50282 q^{86} +26.0552 q^{87} +15.8454 q^{89} -17.9525 q^{90} -1.33629 q^{91} -1.00000 q^{92} +15.5602 q^{93} +10.3948 q^{94} +3.94699 q^{95} -3.10337 q^{96} +2.29270 q^{97} +4.83783 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.10337	1.79173	0.895866	−	0.444325i	$-0.146556\pi$
$3$	3.10337	1.79173	0.895866	+	0.444325i	$0.146556\pi$
$4$	1.00000	0.500000
$5$	2.70739	1.21078	0.605392	−	0.795928i	$-0.293016\pi$
$5$	2.70739	1.21078	0.605392	+	0.795928i	$0.293016\pi$
$6$	−3.10337	−1.26695
$7$	1.47043	0.555771	0.277885	−	0.960614i	$-0.410366\pi$
$7$	1.47043	0.555771	0.277885	+	0.960614i	$0.410366\pi$
$8$	−1.00000	−0.353553
$9$	6.63091	2.21030
$10$	−2.70739	−0.856153
$11$	0	0
$11$	0	0
$12$	3.10337	0.895866
$13$	−0.908777	−0.252049	−0.126025	−	0.992027i	$-0.540222\pi$
$13$	−0.908777	−0.252049	−0.126025	+	0.992027i	$0.540222\pi$
$14$	−1.47043	−0.392989
$15$	8.40205	2.16940
$16$	1.00000	0.250000
$17$	−3.03254	−0.735498	−0.367749	−	0.929925i	$-0.619871\pi$
$17$	−3.03254	−0.735498	−0.367749	+	0.929925i	$0.619871\pi$
$18$	−6.63091	−1.56292
$19$	1.45785	0.334455	0.167227	−	0.985918i	$-0.446519\pi$
$19$	1.45785	0.334455	0.167227	+	0.985918i	$0.446519\pi$
$20$	2.70739	0.605392
$21$	4.56329	0.995792
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.10337	−0.633473
$25$	2.32998	0.465997
$26$	0.908777	0.178226
$27$	11.2681	2.16854
$28$	1.47043	0.277885
$29$	8.39578	1.55906	0.779528	−	0.626367i	$-0.215459\pi$
$29$	8.39578	1.55906	0.779528	+	0.626367i	$0.215459\pi$
$30$	−8.40205	−1.53400
$31$	5.01397	0.900536	0.450268	−	0.892894i	$-0.351329\pi$
$31$	5.01397	0.900536	0.450268	+	0.892894i	$0.351329\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	3.03254	0.520076
$35$	3.98104	0.672918
$36$	6.63091	1.10515
$37$	1.79423	0.294969	0.147485	−	0.989064i	$-0.452882\pi$
$37$	1.79423	0.294969	0.147485	+	0.989064i	$0.452882\pi$
$38$	−1.45785	−0.236495
$39$	−2.82027	−0.451605
$40$	−2.70739	−0.428077
$41$	0.0162536	0.00253839	0.00126919	−	0.999999i	$-0.499596\pi$
$41$	0.0162536	0.00253839	0.00126919	+	0.999999i	$0.499596\pi$
$42$	−4.56329	−0.704131
$43$	−6.50282	−0.991671	−0.495836	−	0.868416i	$-0.665138\pi$
$43$	−6.50282	−0.991671	−0.495836	+	0.868416i	$0.665138\pi$
$44$	0	0
$45$	17.9525	2.67620
$46$	1.00000	0.147442
$47$	−10.3948	−1.51623	−0.758117	−	0.652119i	$-0.773880\pi$
$47$	−10.3948	−1.51623	−0.758117	+	0.652119i	$0.773880\pi$
$48$	3.10337	0.447933
$49$	−4.83783	−0.691119
$50$	−2.32998	−0.329509
$51$	−9.41108	−1.31781
$52$	−0.908777	−0.126025
$53$	7.30311	1.00316	0.501579	−	0.865112i	$-0.332753\pi$
$53$	7.30311	1.00316	0.501579	+	0.865112i	$0.332753\pi$
$54$	−11.2681	−1.53339
$55$	0	0
$56$	−1.47043	−0.196495
$57$	4.52426	0.599253
$58$	−8.39578	−1.10242
$59$	−0.224825	−0.0292698	−0.0146349	−	0.999893i	$-0.504659\pi$
$59$	−0.224825	−0.0292698	−0.0146349	+	0.999893i	$0.504659\pi$
$60$	8.40205	1.08470
$61$	12.3494	1.58118	0.790588	−	0.612349i	$-0.209775\pi$
$61$	12.3494	1.58118	0.790588	+	0.612349i	$0.209775\pi$
$62$	−5.01397	−0.636775
$63$	9.75030	1.22842
$64$	1.00000	0.125000
$65$	−2.46042	−0.305177
$66$	0	0
$67$	−10.5937	−1.29422	−0.647111	−	0.762396i	$-0.724023\pi$
$67$	−10.5937	−1.29422	−0.647111	+	0.762396i	$0.724023\pi$
$68$	−3.03254	−0.367749
$69$	−3.10337	−0.373602
$70$	−3.98104	−0.475825
$71$	8.06760	0.957448	0.478724	−	0.877965i	$-0.341099\pi$
$71$	8.06760	0.957448	0.478724	+	0.877965i	$0.341099\pi$
$72$	−6.63091	−0.781460
$73$	8.36256	0.978764	0.489382	−	0.872070i	$-0.337222\pi$
$73$	8.36256	0.978764	0.489382	+	0.872070i	$0.337222\pi$
$74$	−1.79423	−0.208575
$75$	7.23080	0.834941
$76$	1.45785	0.167227
$77$	0	0
$78$	2.82027	0.319333
$79$	−14.8727	−1.67331	−0.836655	−	0.547730i	$-0.815492\pi$
$79$	−14.8727	−1.67331	−0.836655	+	0.547730i	$0.815492\pi$
$80$	2.70739	0.302696
$81$	15.0762	1.67514
$82$	−0.0162536	−0.00179491
$83$	5.48836	0.602426	0.301213	−	0.953557i	$-0.402609\pi$
$83$	5.48836	0.602426	0.301213	+	0.953557i	$0.402609\pi$
$84$	4.56329	0.497896
$85$	−8.21027	−0.890529
$86$	6.50282	0.701217
$87$	26.0552	2.79341
$88$	0	0
$89$	15.8454	1.67961	0.839804	−	0.542889i	$-0.182670\pi$
$89$	15.8454	1.67961	0.839804	+	0.542889i	$0.182670\pi$
$90$	−17.9525	−1.89236
$91$	−1.33629	−0.140082
$92$	−1.00000	−0.104257
$93$	15.5602	1.61352
$94$	10.3948	1.07214
$95$	3.94699	0.404952
$96$	−3.10337	−0.316736
$97$	2.29270	0.232788	0.116394	−	0.993203i	$-0.462866\pi$
$97$	2.29270	0.232788	0.116394	+	0.993203i	$0.462866\pi$
$98$	4.83783	0.488695
$99$	0	0
$100$	2.32998	0.232998
$101$	−17.3294	−1.72434	−0.862171	−	0.506617i	$-0.830896\pi$
$101$	−17.3294	−1.72434	−0.862171	+	0.506617i	$0.830896\pi$
$102$	9.41108	0.931836
$103$	0.391799	0.0386051	0.0193026	−	0.999814i	$-0.493855\pi$
$103$	0.391799	0.0386051	0.0193026	+	0.999814i	$0.493855\pi$
$104$	0.908777	0.0891129
$105$	12.3546	1.20569
$106$	−7.30311	−0.709340
$107$	2.49588	0.241286	0.120643	−	0.992696i	$-0.461504\pi$
$107$	2.49588	0.241286	0.120643	+	0.992696i	$0.461504\pi$
$108$	11.2681	1.08427
$109$	11.2694	1.07941	0.539705	−	0.841854i	$-0.318536\pi$
$109$	11.2694	1.07941	0.539705	+	0.841854i	$0.318536\pi$
$110$	0	0
$111$	5.56816	0.528506
$112$	1.47043	0.138943
$113$	−20.2177	−1.90192	−0.950962	−	0.309307i	$-0.899903\pi$
$113$	−20.2177	−1.90192	−0.950962	+	0.309307i	$0.899903\pi$
$114$	−4.52426	−0.423736
$115$	−2.70739	−0.252466
$116$	8.39578	0.779528
$117$	−6.02601	−0.557105
$118$	0.224825	0.0206968
$119$	−4.45914	−0.408768
$120$	−8.40205	−0.766998
$121$	0	0
$122$	−12.3494	−1.11806
$123$	0.0504409	0.00454811
$124$	5.01397	0.450268
$125$	−7.22879	−0.646562
$126$	−9.75030	−0.868625
$127$	16.4481	1.45953	0.729767	−	0.683696i	$-0.239629\pi$
$127$	16.4481	1.45953	0.729767	+	0.683696i	$0.239629\pi$
$128$	−1.00000	−0.0883883
$129$	−20.1807	−1.77681
$130$	2.46042	0.215793
$131$	11.7697	1.02833	0.514163	−	0.857692i	$-0.328103\pi$
$131$	11.7697	1.02833	0.514163	+	0.857692i	$0.328103\pi$
$132$	0	0
$133$	2.14367	0.185880
$134$	10.5937	0.915153
$135$	30.5071	2.62563
$136$	3.03254	0.260038
$137$	−3.53243	−0.301796	−0.150898	−	0.988549i	$-0.548217\pi$
$137$	−3.53243	−0.301796	−0.150898	+	0.988549i	$0.548217\pi$
$138$	3.10337	0.264176
$139$	1.78871	0.151716	0.0758582	−	0.997119i	$-0.475830\pi$
$139$	1.78871	0.151716	0.0758582	+	0.997119i	$0.475830\pi$
$140$	3.98104	0.336459
$141$	−32.2588	−2.71668
$142$	−8.06760	−0.677018
$143$	0	0
$144$	6.63091	0.552576
$145$	22.7307	1.88768
$146$	−8.36256	−0.692091
$147$	−15.0136	−1.23830
$148$	1.79423	0.147485
$149$	4.68542	0.383845	0.191922	−	0.981410i	$-0.438528\pi$
$149$	4.68542	0.383845	0.191922	+	0.981410i	$0.438528\pi$
$150$	−7.23080	−0.590392
$151$	−13.9850	−1.13808	−0.569040	−	0.822310i	$-0.692685\pi$
$151$	−13.9850	−1.13808	−0.569040	+	0.822310i	$0.692685\pi$
$152$	−1.45785	−0.118248
$153$	−20.1085	−1.62567
$154$	0	0
$155$	13.5748	1.09035
$156$	−2.82027	−0.225802
$157$	−1.29303	−0.103195	−0.0515977	−	0.998668i	$-0.516431\pi$
$157$	−1.29303	−0.103195	−0.0515977	+	0.998668i	$0.516431\pi$
$158$	14.8727	1.18321
$159$	22.6642	1.79739
$160$	−2.70739	−0.214038
$161$	−1.47043	−0.115886
$162$	−15.0762	−1.18450
$163$	−22.2730	−1.74455	−0.872277	−	0.489013i	$-0.837357\pi$
$163$	−22.2730	−1.74455	−0.872277	+	0.489013i	$0.837357\pi$
$164$	0.0162536	0.00126919
$165$	0	0
$166$	−5.48836	−0.425979
$167$	−16.4278	−1.27122	−0.635609	−	0.772011i	$-0.719251\pi$
$167$	−16.4278	−1.27122	−0.635609	+	0.772011i	$0.719251\pi$
$168$	−4.56329	−0.352066
$169$	−12.1741	−0.936471
$170$	8.21027	0.629699
$171$	9.66690	0.739246
$172$	−6.50282	−0.495836
$173$	−0.104757	−0.00796455	−0.00398228	−	0.999992i	$-0.501268\pi$
$173$	−0.104757	−0.00796455	−0.00398228	+	0.999992i	$0.501268\pi$
$174$	−26.0552	−1.97524
$175$	3.42608	0.258987
$176$	0	0
$177$	−0.697716	−0.0524435
$178$	−15.8454	−1.18766
$179$	19.9207	1.48894	0.744471	−	0.667655i	$-0.232702\pi$
$179$	19.9207	1.48894	0.744471	+	0.667655i	$0.232702\pi$
$180$	17.9525	1.33810
$181$	19.7952	1.47137	0.735684	−	0.677325i	$-0.236861\pi$
$181$	19.7952	1.47137	0.735684	+	0.677325i	$0.236861\pi$
$182$	1.33629	0.0990527
$183$	38.3247	2.83304
$184$	1.00000	0.0737210
$185$	4.85769	0.357144
$186$	−15.5602	−1.14093
$187$	0	0
$188$	−10.3948	−0.758117
$189$	16.5689	1.20521
$190$	−3.94699	−0.286344
$191$	23.1456	1.67476	0.837379	−	0.546622i	$-0.184087\pi$
$191$	23.1456	1.67476	0.837379	+	0.546622i	$0.184087\pi$
$192$	3.10337	0.223966
$193$	−20.4611	−1.47282	−0.736411	−	0.676534i	$-0.763481\pi$
$193$	−20.4611	−1.47282	−0.736411	+	0.676534i	$0.763481\pi$
$194$	−2.29270	−0.164606
$195$	−7.63558	−0.546796
$196$	−4.83783	−0.345559
$197$	−3.30631	−0.235565	−0.117782	−	0.993039i	$-0.537579\pi$
$197$	−3.30631	−0.235565	−0.117782	+	0.993039i	$0.537579\pi$
$198$	0	0
$199$	6.46438	0.458248	0.229124	−	0.973397i	$-0.426414\pi$
$199$	6.46438	0.458248	0.229124	+	0.973397i	$0.426414\pi$
$200$	−2.32998	−0.164755
$201$	−32.8761	−2.31890
$202$	17.3294	1.21929
$203$	12.3454	0.866478
$204$	−9.41108	−0.658907
$205$	0.0440049	0.00307344
$206$	−0.391799	−0.0272979
$207$	−6.63091	−0.460880
$208$	−0.908777	−0.0630123
$209$	0	0
$210$	−12.3546	−0.852551
$211$	0.187898	0.0129354	0.00646772	−	0.999979i	$-0.497941\pi$
$211$	0.187898	0.0129354	0.00646772	+	0.999979i	$0.497941\pi$
$212$	7.30311	0.501579
$213$	25.0368	1.71549
$214$	−2.49588	−0.170615
$215$	−17.6057	−1.20070
$216$	−11.2681	−0.766694
$217$	7.37270	0.500491
$218$	−11.2694	−0.763258
$219$	25.9521	1.75368
$220$	0	0
$221$	2.75590	0.185382
$222$	−5.56816	−0.373710
$223$	−23.5475	−1.57686	−0.788428	−	0.615128i	$-0.789105\pi$
$223$	−23.5475	−1.57686	−0.788428	+	0.615128i	$0.789105\pi$
$224$	−1.47043	−0.0982473
$225$	15.4499	1.02999
$226$	20.2177	1.34486
$227$	7.89998	0.524340	0.262170	−	0.965022i	$-0.415562\pi$
$227$	7.89998	0.524340	0.262170	+	0.965022i	$0.415562\pi$
$228$	4.52426	0.299627
$229$	14.5945	0.964433	0.482216	−	0.876052i	$-0.339832\pi$
$229$	14.5945	0.964433	0.482216	+	0.876052i	$0.339832\pi$
$230$	2.70739	0.178520
$231$	0	0
$232$	−8.39578	−0.551210
$233$	26.6192	1.74388	0.871940	−	0.489614i	$-0.162862\pi$
$233$	26.6192	1.74388	0.871940	+	0.489614i	$0.162862\pi$
$234$	6.02601	0.393933
$235$	−28.1427	−1.83583
$236$	−0.224825	−0.0146349
$237$	−46.1555	−2.99812
$238$	4.45914	0.289043
$239$	7.19545	0.465435	0.232718	−	0.972544i	$-0.425238\pi$
$239$	7.19545	0.465435	0.232718	+	0.972544i	$0.425238\pi$
$240$	8.40205	0.542350
$241$	−21.1969	−1.36541	−0.682705	−	0.730694i	$-0.739196\pi$
$241$	−21.1969	−1.36541	−0.682705	+	0.730694i	$0.739196\pi$
$242$	0	0
$243$	12.9829	0.832855
$244$	12.3494	0.790588
$245$	−13.0979	−0.836795
$246$	−0.0504409	−0.00321600
$247$	−1.32486	−0.0842991
$248$	−5.01397	−0.318387
$249$	17.0324	1.07939
$250$	7.22879	0.457189
$251$	−3.35220	−0.211589	−0.105794	−	0.994388i	$-0.533739\pi$
$251$	−3.35220	−0.211589	−0.105794	+	0.994388i	$0.533739\pi$
$252$	9.75030	0.614211
$253$	0	0
$254$	−16.4481	−1.03205
$255$	−25.4795	−1.59559
$256$	1.00000	0.0625000
$257$	−29.4494	−1.83700	−0.918502	−	0.395417i	$-0.870600\pi$
$257$	−29.4494	−1.83700	−0.918502	+	0.395417i	$0.870600\pi$
$258$	20.1807	1.25639
$259$	2.63829	0.163935
$260$	−2.46042	−0.152589
$261$	55.6716	3.44599
$262$	−11.7697	−0.727137
$263$	−20.9085	−1.28927	−0.644635	−	0.764490i	$-0.722991\pi$
$263$	−20.9085	−1.28927	−0.644635	+	0.764490i	$0.722991\pi$
$264$	0	0
$265$	19.7724	1.21461
$266$	−2.14367	−0.131437
$267$	49.1741	3.00941
$268$	−10.5937	−0.647111
$269$	−15.6660	−0.955175	−0.477587	−	0.878584i	$-0.658489\pi$
$269$	−15.6660	−0.955175	−0.477587	+	0.878584i	$0.658489\pi$
$270$	−30.5071	−1.85660
$271$	−22.5270	−1.36842	−0.684210	−	0.729285i	$-0.739853\pi$
$271$	−22.5270	−1.36842	−0.684210	+	0.729285i	$0.739853\pi$
$272$	−3.03254	−0.183874
$273$	−4.14701	−0.250989
$274$	3.53243	0.213402
$275$	0	0
$276$	−3.10337	−0.186801
$277$	14.3161	0.860172	0.430086	−	0.902788i	$-0.358483\pi$
$277$	14.3161	0.860172	0.430086	+	0.902788i	$0.358483\pi$
$278$	−1.78871	−0.107280
$279$	33.2472	1.99046
$280$	−3.98104	−0.237912
$281$	16.8978	1.00804	0.504019	−	0.863693i	$-0.331854\pi$
$281$	16.8978	1.00804	0.504019	+	0.863693i	$0.331854\pi$
$282$	32.2588	1.92099
$283$	−11.6611	−0.693179	−0.346589	−	0.938017i	$-0.612660\pi$
$283$	−11.6611	−0.693179	−0.346589	+	0.938017i	$0.612660\pi$
$284$	8.06760	0.478724
$285$	12.2490	0.725566
$286$	0	0
$287$	0.0238998	0.00141076
$288$	−6.63091	−0.390730
$289$	−7.80373	−0.459043
$290$	−22.7307	−1.33479
$291$	7.11509	0.417094
$292$	8.36256	0.489382
$293$	7.17095	0.418931	0.209466	−	0.977816i	$-0.432828\pi$
$293$	7.17095	0.418931	0.209466	+	0.977816i	$0.432828\pi$
$294$	15.0136	0.875610
$295$	−0.608691	−0.0354393
$296$	−1.79423	−0.104287
$297$	0	0
$298$	−4.68542	−0.271419
$299$	0.908777	0.0525559
$300$	7.23080	0.417471
$301$	−9.56195	−0.551142
$302$	13.9850	0.804744
$303$	−53.7796	−3.08956
$304$	1.45785	0.0836137
$305$	33.4346	1.91446
$306$	20.1085	1.14952
$307$	−1.28208	−0.0731721	−0.0365860	−	0.999331i	$-0.511648\pi$
$307$	−1.28208	−0.0731721	−0.0365860	+	0.999331i	$0.511648\pi$
$308$	0	0
$309$	1.21590	0.0691700
$310$	−13.5748	−0.770996
$311$	−5.92251	−0.335835	−0.167917	−	0.985801i	$-0.553704\pi$
$311$	−5.92251	−0.335835	−0.167917	+	0.985801i	$0.553704\pi$
$312$	2.82027	0.159666
$313$	2.95087	0.166793	0.0833965	−	0.996516i	$-0.473423\pi$
$313$	2.95087	0.166793	0.0833965	+	0.996516i	$0.473423\pi$
$314$	1.29303	0.0729702
$315$	26.3979	1.48735
$316$	−14.8727	−0.836655
$317$	1.60898	0.0903691	0.0451845	−	0.998979i	$-0.485612\pi$
$317$	1.60898	0.0903691	0.0451845	+	0.998979i	$0.485612\pi$
$318$	−22.6642	−1.27095
$319$	0	0
$320$	2.70739	0.151348
$321$	7.74564	0.432319
$322$	1.47043	0.0819439
$323$	−4.42100	−0.245991
$324$	15.0762	0.837568
$325$	−2.11743	−0.117454
$326$	22.2730	1.23359
$327$	34.9730	1.93401
$328$	−0.0162536	−0.000897455 0
$329$	−15.2848	−0.842678
$330$	0	0
$331$	19.0225	1.04557	0.522784	−	0.852465i	$-0.324893\pi$
$331$	19.0225	1.04557	0.522784	+	0.852465i	$0.324893\pi$
$332$	5.48836	0.301213
$333$	11.8974	0.651972
$334$	16.4278	0.898887
$335$	−28.6812	−1.56702
$336$	4.56329	0.248948
$337$	−21.4731	−1.16971	−0.584857	−	0.811137i	$-0.698849\pi$
$337$	−21.4731	−1.16971	−0.584857	+	0.811137i	$0.698849\pi$
$338$	12.1741	0.662185
$339$	−62.7431	−3.40774
$340$	−8.21027	−0.445264
$341$	0	0
$342$	−9.66690	−0.522726
$343$	−17.4067	−0.939874
$344$	6.50282	0.350609
$345$	−8.40205	−0.452351
$346$	0.104757	0.00563179
$347$	−5.29182	−0.284080	−0.142040	−	0.989861i	$-0.545366\pi$
$347$	−5.29182	−0.284080	−0.142040	+	0.989861i	$0.545366\pi$
$348$	26.0552	1.39671
$349$	−13.7479	−0.735906	−0.367953	−	0.929844i	$-0.619941\pi$
$349$	−13.7479	−0.735906	−0.367953	+	0.929844i	$0.619941\pi$
$350$	−3.42608	−0.183132
$351$	−10.2401	−0.546578
$352$	0	0
$353$	−14.8133	−0.788430	−0.394215	−	0.919018i	$-0.628984\pi$
$353$	−14.8133	−0.788430	−0.394215	+	0.919018i	$0.628984\pi$
$354$	0.697716	0.0370832
$355$	21.8422	1.15926
$356$	15.8454	0.839804
$357$	−13.8383	−0.732403
$358$	−19.9207	−1.05284
$359$	−15.9929	−0.844071	−0.422035	−	0.906579i	$-0.638684\pi$
$359$	−15.9929	−0.844071	−0.422035	+	0.906579i	$0.638684\pi$
$360$	−17.9525	−0.946179
$361$	−16.8747	−0.888140
$362$	−19.7952	−1.04041
$363$	0	0
$364$	−1.33629	−0.0700408
$365$	22.6408	1.18507
$366$	−38.3247	−2.00326
$367$	1.39485	0.0728106	0.0364053	−	0.999337i	$-0.488409\pi$
$367$	1.39485	0.0728106	0.0364053	+	0.999337i	$0.488409\pi$
$368$	−1.00000	−0.0521286
$369$	0.107776	0.00561060
$370$	−4.85769	−0.252539
$371$	10.7387	0.557526
$372$	15.5602	0.806759
$373$	−27.1179	−1.40411	−0.702055	−	0.712123i	$-0.747734\pi$
$373$	−27.1179	−1.40411	−0.702055	+	0.712123i	$0.747734\pi$
$374$	0	0
$375$	−22.4336	−1.15847
$376$	10.3948	0.536069
$377$	−7.62989	−0.392959
$378$	−16.5689	−0.852212
$379$	22.4156	1.15141	0.575707	−	0.817656i	$-0.304727\pi$
$379$	22.4156	1.15141	0.575707	+	0.817656i	$0.304727\pi$
$380$	3.94699	0.202476
$381$	51.0446	2.61509
$382$	−23.1456	−1.18423
$383$	−18.5297	−0.946824	−0.473412	−	0.880841i	$-0.656978\pi$
$383$	−18.5297	−0.946824	−0.473412	+	0.880841i	$0.656978\pi$
$384$	−3.10337	−0.158368
$385$	0	0
$386$	20.4611	1.04144
$387$	−43.1196	−2.19189
$388$	2.29270	0.116394
$389$	−35.8570	−1.81802	−0.909011	−	0.416772i	$-0.863161\pi$
$389$	−35.8570	−1.81802	−0.909011	+	0.416772i	$0.863161\pi$
$390$	7.63558	0.386643
$391$	3.03254	0.153362
$392$	4.83783	0.244347
$393$	36.5259	1.84249
$394$	3.30631	0.166570
$395$	−40.2663	−2.02602
$396$	0	0
$397$	9.33864	0.468693	0.234346	−	0.972153i	$-0.424705\pi$
$397$	9.33864	0.468693	0.234346	+	0.972153i	$0.424705\pi$
$398$	−6.46438	−0.324030
$399$	6.65262	0.333047
$400$	2.32998	0.116499
$401$	−16.3686	−0.817408	−0.408704	−	0.912667i	$-0.634019\pi$
$401$	−16.3686	−0.817408	−0.408704	+	0.912667i	$0.634019\pi$
$402$	32.8761	1.63971
$403$	−4.55658	−0.226979
$404$	−17.3294	−0.862171
$405$	40.8173	2.02823
$406$	−12.3454	−0.612693
$407$	0	0
$408$	9.41108	0.465918
$409$	30.9879	1.53225	0.766127	−	0.642689i	$-0.222181\pi$
$409$	30.9879	1.53225	0.766127	+	0.642689i	$0.222181\pi$
$410$	−0.0440049	−0.00217325
$411$	−10.9624	−0.540738
$412$	0.391799	0.0193026
$413$	−0.330590	−0.0162673
$414$	6.63091	0.325891
$415$	14.8592	0.729407
$416$	0.908777	0.0445564
$417$	5.55103	0.271835
$418$	0	0
$419$	−38.9707	−1.90384	−0.951921	−	0.306343i	$-0.900895\pi$
$419$	−38.9707	−1.90384	−0.951921	+	0.306343i	$0.900895\pi$
$420$	12.3546	0.602844
$421$	−16.4780	−0.803088	−0.401544	−	0.915840i	$-0.631526\pi$
$421$	−16.4780	−0.803088	−0.401544	+	0.915840i	$0.631526\pi$
$422$	−0.187898	−0.00914674
$423$	−68.9268	−3.35133
$424$	−7.30311	−0.354670
$425$	−7.06576	−0.342740
$426$	−25.0368	−1.21304
$427$	18.1589	0.878771
$428$	2.49588	0.120643
$429$	0	0
$430$	17.6057	0.849022
$431$	−1.74404	−0.0840074	−0.0420037	−	0.999117i	$-0.513374\pi$
$431$	−1.74404	−0.0840074	−0.0420037	+	0.999117i	$0.513374\pi$
$432$	11.2681	0.542134
$433$	8.21653	0.394861	0.197431	−	0.980317i	$-0.436740\pi$
$433$	8.21653	0.394861	0.197431	+	0.980317i	$0.436740\pi$
$434$	−7.37270	−0.353901
$435$	70.5417	3.38222
$436$	11.2694	0.539705
$437$	−1.45785	−0.0697386
$438$	−25.9521	−1.24004
$439$	41.6557	1.98812	0.994060	−	0.108833i	$-0.0347115\pi$
$439$	41.6557	1.98812	0.994060	+	0.108833i	$0.0347115\pi$
$440$	0	0
$441$	−32.0792	−1.52758
$442$	−2.75590	−0.131085
$443$	14.0098	0.665624	0.332812	−	0.942993i	$-0.392003\pi$
$443$	14.0098	0.665624	0.332812	+	0.942993i	$0.392003\pi$
$444$	5.56816	0.264253
$445$	42.8997	2.03364
$446$	23.5475	1.11501
$447$	14.5406	0.687747
$448$	1.47043	0.0694714
$449$	−0.964174	−0.0455022	−0.0227511	−	0.999741i	$-0.507243\pi$
$449$	−0.964174	−0.0455022	−0.0227511	+	0.999741i	$0.507243\pi$
$450$	−15.4499	−0.728316
$451$	0	0
$452$	−20.2177	−0.950962
$453$	−43.4005	−2.03913
$454$	−7.89998	−0.370764
$455$	−3.61787	−0.169609
$456$	−4.52426	−0.211868
$457$	−6.70128	−0.313473	−0.156736	−	0.987640i	$-0.550097\pi$
$457$	−6.70128	−0.313473	−0.156736	+	0.987640i	$0.550097\pi$
$458$	−14.5945	−0.681957
$459$	−34.1708	−1.59496
$460$	−2.70739	−0.126233
$461$	15.2448	0.710019	0.355009	−	0.934863i	$-0.384478\pi$
$461$	15.2448	0.710019	0.355009	+	0.934863i	$0.384478\pi$
$462$	0	0
$463$	−17.7967	−0.827083	−0.413542	−	0.910485i	$-0.635708\pi$
$463$	−17.7967	−0.827083	−0.413542	+	0.910485i	$0.635708\pi$
$464$	8.39578	0.389764
$465$	42.1276	1.95362
$466$	−26.6192	−1.23311
$467$	17.3506	0.802890	0.401445	−	0.915883i	$-0.368508\pi$
$467$	17.3506	0.802890	0.401445	+	0.915883i	$0.368508\pi$
$468$	−6.02601	−0.278553
$469$	−15.5773	−0.719291
$470$	28.1427	1.29813
$471$	−4.01277	−0.184898
$472$	0.224825	0.0103484
$473$	0	0
$474$	46.1555	2.11999
$475$	3.39678	0.155855
$476$	−4.45914	−0.204384
$477$	48.4262	2.21728
$478$	−7.19545	−0.329112
$479$	−24.4556	−1.11740	−0.558701	−	0.829369i	$-0.688700\pi$
$479$	−24.4556	−1.11740	−0.558701	+	0.829369i	$0.688700\pi$
$480$	−8.40205	−0.383499
$481$	−1.63055	−0.0743468
$482$	21.1969	0.965490
$483$	−4.56329	−0.207637
$484$	0	0
$485$	6.20724	0.281856
$486$	−12.9829	−0.588918
$487$	−7.14632	−0.323831	−0.161915	−	0.986805i	$-0.551767\pi$
$487$	−7.14632	−0.323831	−0.161915	+	0.986805i	$0.551767\pi$
$488$	−12.3494	−0.559030
$489$	−69.1213	−3.12577
$490$	13.0979	0.591704
$491$	12.0388	0.543305	0.271652	−	0.962395i	$-0.412430\pi$
$491$	12.0388	0.543305	0.271652	+	0.962395i	$0.412430\pi$
$492$	0.0504409	0.00227405
$493$	−25.4605	−1.14668
$494$	1.32486	0.0596084
$495$	0	0
$496$	5.01397	0.225134
$497$	11.8629	0.532122
$498$	−17.0324	−0.763241
$499$	6.03531	0.270177	0.135089	−	0.990834i	$-0.456868\pi$
$499$	6.03531	0.270177	0.135089	+	0.990834i	$0.456868\pi$
$500$	−7.22879	−0.323281
$501$	−50.9814	−2.27768
$502$	3.35220	0.149616
$503$	−1.06760	−0.0476018	−0.0238009	−	0.999717i	$-0.507577\pi$
$503$	−1.06760	−0.0476018	−0.0238009	+	0.999717i	$0.507577\pi$
$504$	−9.75030	−0.434313
$505$	−46.9176	−2.08781
$506$	0	0
$507$	−37.7808	−1.67791
$508$	16.4481	0.729767
$509$	26.3255	1.16686	0.583428	−	0.812165i	$-0.301711\pi$
$509$	26.3255	1.16686	0.583428	+	0.812165i	$0.301711\pi$
$510$	25.4795	1.12825
$511$	12.2966	0.543968
$512$	−1.00000	−0.0441942
$513$	16.4272	0.725278
$514$	29.4494	1.29896
$515$	1.06076	0.0467425
$516$	−20.1807	−0.888404
$517$	0	0
$518$	−2.63829	−0.115920
$519$	−0.325101	−0.0142703
$520$	2.46042	0.107896
$521$	−3.38428	−0.148268	−0.0741339	−	0.997248i	$-0.523619\pi$
$521$	−3.38428	−0.148268	−0.0741339	+	0.997248i	$0.523619\pi$
$522$	−55.6716	−2.43668
$523$	0.991805	0.0433686	0.0216843	−	0.999765i	$-0.493097\pi$
$523$	0.991805	0.0433686	0.0216843	+	0.999765i	$0.493097\pi$
$524$	11.7697	0.514163
$525$	10.6324	0.464036
$526$	20.9085	0.911652
$527$	−15.2050	−0.662342
$528$	0	0
$529$	1.00000	0.0434783
$530$	−19.7724	−0.858858
$531$	−1.49080	−0.0646950
$532$	2.14367	0.0929401
$533$	−0.0147709	−0.000639798 0
$534$	−49.1741	−2.12797
$535$	6.75733	0.292145
$536$	10.5937	0.457576
$537$	61.8213	2.66778
$538$	15.6660	0.675411
$539$	0	0
$540$	30.5071	1.31281
$541$	−21.2590	−0.913995	−0.456997	−	0.889468i	$-0.651075\pi$
$541$	−21.2590	−0.913995	−0.456997	+	0.889468i	$0.651075\pi$
$542$	22.5270	0.967619
$543$	61.4319	2.63630
$544$	3.03254	0.130019
$545$	30.5106	1.30693
$546$	4.14701	0.177476
$547$	−14.8147	−0.633433	−0.316716	−	0.948520i	$-0.602580\pi$
$547$	−14.8147	−0.633433	−0.316716	+	0.948520i	$0.602580\pi$
$548$	−3.53243	−0.150898
$549$	81.8876	3.49488
$550$	0	0
$551$	12.2398	0.521434
$552$	3.10337	0.132088
$553$	−21.8693	−0.929977
$554$	−14.3161	−0.608234
$555$	15.0752	0.639907
$556$	1.78871	0.0758582
$557$	38.8943	1.64800	0.824002	−	0.566587i	$-0.191737\pi$
$557$	38.8943	1.64800	0.824002	+	0.566587i	$0.191737\pi$
$558$	−33.2472	−1.40747
$559$	5.90961	0.249950
$560$	3.98104	0.168230
$561$	0	0
$562$	−16.8978	−0.712791
$563$	−44.7015	−1.88394	−0.941972	−	0.335691i	$-0.891030\pi$
$563$	−44.7015	−1.88394	−0.941972	+	0.335691i	$0.891030\pi$
$564$	−32.2588	−1.35834
$565$	−54.7374	−2.30282
$566$	11.6611	0.490151
$567$	22.1685	0.930991
$568$	−8.06760	−0.338509
$569$	18.7903	0.787731	0.393865	−	0.919168i	$-0.371138\pi$
$569$	18.7903	0.787731	0.393865	+	0.919168i	$0.371138\pi$
$570$	−12.2490	−0.513053
$571$	9.85668	0.412489	0.206245	−	0.978500i	$-0.433876\pi$
$571$	9.85668	0.412489	0.206245	+	0.978500i	$0.433876\pi$
$572$	0	0
$573$	71.8295	3.00072
$574$	−0.0238998	−0.000997558 0
$575$	−2.32998	−0.0971670
$576$	6.63091	0.276288
$577$	−14.7878	−0.615626	−0.307813	−	0.951447i	$-0.599597\pi$
$577$	−14.7878	−0.615626	−0.307813	+	0.951447i	$0.599597\pi$
$578$	7.80373	0.324592
$579$	−63.4984	−2.63890
$580$	22.7307	0.943840
$581$	8.07026	0.334811
$582$	−7.11509	−0.294930
$583$	0	0
$584$	−8.36256	−0.346045
$585$	−16.3148	−0.674534
$586$	−7.17095	−0.296229
$587$	22.3284	0.921594	0.460797	−	0.887506i	$-0.347564\pi$
$587$	22.3284	0.921594	0.460797	+	0.887506i	$0.347564\pi$
$588$	−15.0136	−0.619150
$589$	7.30964	0.301188
$590$	0.608691	0.0250594
$591$	−10.2607	−0.422069
$592$	1.79423	0.0737424
$593$	−3.98852	−0.163789	−0.0818945	−	0.996641i	$-0.526097\pi$
$593$	−3.98852	−0.163789	−0.0818945	+	0.996641i	$0.526097\pi$
$594$	0	0
$595$	−12.0726	−0.494930
$596$	4.68542	0.191922
$597$	20.0614	0.821058
$598$	−0.908777	−0.0371626
$599$	−1.65935	−0.0677993	−0.0338996	−	0.999425i	$-0.510793\pi$
$599$	−1.65935	−0.0677993	−0.0338996	+	0.999425i	$0.510793\pi$
$600$	−7.23080	−0.295196
$601$	8.20779	0.334803	0.167401	−	0.985889i	$-0.446462\pi$
$601$	8.20779	0.334803	0.167401	+	0.985889i	$0.446462\pi$
$602$	9.56195	0.389716
$603$	−70.2456	−2.86062
$604$	−13.9850	−0.569040
$605$	0	0
$606$	53.7796	2.18465
$607$	−12.8212	−0.520398	−0.260199	−	0.965555i	$-0.583788\pi$
$607$	−12.8212	−0.520398	−0.260199	+	0.965555i	$0.583788\pi$
$608$	−1.45785	−0.0591238
$609$	38.3124	1.55250
$610$	−33.4346	−1.35373
$611$	9.44653	0.382166
$612$	−20.1085	−0.812837
$613$	−4.45233	−0.179828	−0.0899139	−	0.995950i	$-0.528659\pi$
$613$	−4.45233	−0.179828	−0.0899139	+	0.995950i	$0.528659\pi$
$614$	1.28208	0.0517405
$615$	0.136563	0.00550677
$616$	0	0
$617$	39.6576	1.59655	0.798277	−	0.602291i	$-0.205745\pi$
$617$	39.6576	1.59655	0.798277	+	0.602291i	$0.205745\pi$
$618$	−1.21590	−0.0489106
$619$	−14.8921	−0.598564	−0.299282	−	0.954165i	$-0.596747\pi$
$619$	−14.8921	−0.598564	−0.299282	+	0.954165i	$0.596747\pi$
$620$	13.5748	0.545177
$621$	−11.2681	−0.452171
$622$	5.92251	0.237471
$623$	23.2996	0.933477
$624$	−2.82027	−0.112901
$625$	−31.2211	−1.24884
$626$	−2.95087	−0.117941
$627$	0	0
$628$	−1.29303	−0.0515977
$629$	−5.44106	−0.216949
$630$	−26.3979	−1.05172
$631$	−18.6193	−0.741224	−0.370612	−	0.928788i	$-0.620852\pi$
$631$	−18.6193	−0.741224	−0.370612	+	0.928788i	$0.620852\pi$
$632$	14.8727	0.591604
$633$	0.583118	0.0231769
$634$	−1.60898	−0.0639006
$635$	44.5315	1.76718
$636$	22.6642	0.898696
$637$	4.39651	0.174196
$638$	0	0
$639$	53.4955	2.11625
$640$	−2.70739	−0.107019
$641$	32.6528	1.28971	0.644854	−	0.764306i	$-0.276918\pi$
$641$	32.6528	1.28971	0.644854	+	0.764306i	$0.276918\pi$
$642$	−7.74564	−0.305696
$643$	11.0978	0.437655	0.218827	−	0.975764i	$-0.429777\pi$
$643$	11.0978	0.437655	0.218827	+	0.975764i	$0.429777\pi$
$644$	−1.47043	−0.0579431
$645$	−54.6370	−2.15133
$646$	4.42100	0.173942
$647$	5.51815	0.216941	0.108470	−	0.994100i	$-0.465405\pi$
$647$	5.51815	0.216941	0.108470	+	0.994100i	$0.465405\pi$
$648$	−15.0762	−0.592250
$649$	0	0
$650$	2.11743	0.0830526
$651$	22.8802	0.896746
$652$	−22.2730	−0.872277
$653$	−37.4396	−1.46513	−0.732563	−	0.680699i	$-0.761676\pi$
$653$	−37.4396	−1.46513	−0.732563	+	0.680699i	$0.761676\pi$
$654$	−34.9730	−1.36755
$655$	31.8653	1.24508
$656$	0.0162536	0.000634596 0
$657$	55.4514	2.16336
$658$	15.2848	0.595864
$659$	22.2083	0.865114	0.432557	−	0.901607i	$-0.357611\pi$
$659$	22.2083	0.865114	0.432557	+	0.901607i	$0.357611\pi$
$660$	0	0
$661$	−18.3552	−0.713934	−0.356967	−	0.934117i	$-0.616189\pi$
$661$	−18.3552	−0.713934	−0.356967	+	0.934117i	$0.616189\pi$
$662$	−19.0225	−0.739329
$663$	8.55257	0.332154
$664$	−5.48836	−0.212990
$665$	5.80377	0.225061
$666$	−11.8974	−0.461014
$667$	−8.39578	−0.325086
$668$	−16.4278	−0.635609
$669$	−73.0765	−2.82530
$670$	28.6812	1.10805
$671$	0	0
$672$	−4.56329	−0.176033
$673$	31.1969	1.20255	0.601275	−	0.799042i	$-0.294660\pi$
$673$	31.1969	1.20255	0.601275	+	0.799042i	$0.294660\pi$
$674$	21.4731	0.827112
$675$	26.2544	1.01053
$676$	−12.1741	−0.468236
$677$	13.7016	0.526594	0.263297	−	0.964715i	$-0.415190\pi$
$677$	13.7016	0.526594	0.263297	+	0.964715i	$0.415190\pi$
$678$	62.7431	2.40963
$679$	3.37126	0.129377
$680$	8.21027	0.314849
$681$	24.5166	0.939477
$682$	0	0
$683$	43.0074	1.64563	0.822817	−	0.568307i	$-0.192401\pi$
$683$	43.0074	1.64563	0.822817	+	0.568307i	$0.192401\pi$
$684$	9.66690	0.369623
$685$	−9.56369	−0.365410
$686$	17.4067	0.664592
$687$	45.2922	1.72800
$688$	−6.50282	−0.247918
$689$	−6.63689	−0.252845
$690$	8.40205	0.319860
$691$	44.5403	1.69439	0.847196	−	0.531281i	$-0.178289\pi$
$691$	44.5403	1.69439	0.847196	+	0.531281i	$0.178289\pi$
$692$	−0.104757	−0.00398228
$693$	0	0
$694$	5.29182	0.200875
$695$	4.84274	0.183696
$696$	−26.0552	−0.987620
$697$	−0.0492896	−0.00186698
$698$	13.7479	0.520364
$699$	82.6091	3.12456
$700$	3.42608	0.129494
$701$	−11.0057	−0.415680	−0.207840	−	0.978163i	$-0.566643\pi$
$701$	−11.0057	−0.415680	−0.207840	+	0.978163i	$0.566643\pi$
$702$	10.2401	0.386489
$703$	2.61573	0.0986539
$704$	0	0
$705$	−87.3374	−3.28932
$706$	14.8133	0.557504
$707$	−25.4817	−0.958339
$708$	−0.697716	−0.0262218
$709$	27.8023	1.04414	0.522069	−	0.852904i	$-0.325161\pi$
$709$	27.8023	1.04414	0.522069	+	0.852904i	$0.325161\pi$
$710$	−21.8422	−0.819723
$711$	−98.6195	−3.69852
$712$	−15.8454	−0.593831
$713$	−5.01397	−0.187775
$714$	13.8383	0.517887
$715$	0	0
$716$	19.9207	0.744471
$717$	22.3302	0.833935
$718$	15.9929	0.596848
$719$	−7.85001	−0.292756	−0.146378	−	0.989229i	$-0.546762\pi$
$719$	−7.85001	−0.292756	−0.146378	+	0.989229i	$0.546762\pi$
$720$	17.9525	0.669050
$721$	0.576114	0.0214556
$722$	16.8747	0.628010
$723$	−65.7817	−2.44645
$724$	19.7952	0.735684
$725$	19.5620	0.726515
$726$	0	0
$727$	−20.1940	−0.748952	−0.374476	−	0.927237i	$-0.622177\pi$
$727$	−20.1940	−0.748952	−0.374476	+	0.927237i	$0.622177\pi$
$728$	1.33629	0.0495263
$729$	−4.93781	−0.182882
$730$	−22.6408	−0.837972
$731$	19.7200	0.729372
$732$	38.3247	1.41652
$733$	−16.3086	−0.602371	−0.301186	−	0.953566i	$-0.597382\pi$
$733$	−16.3086	−0.602371	−0.301186	+	0.953566i	$0.597382\pi$
$734$	−1.39485	−0.0514848
$735$	−40.6477	−1.49931
$736$	1.00000	0.0368605
$737$	0	0
$738$	−0.107776	−0.00396729
$739$	−0.713100	−0.0262318	−0.0131159	−	0.999914i	$-0.504175\pi$
$739$	−0.713100	−0.0262318	−0.0131159	+	0.999914i	$0.504175\pi$
$740$	4.85769	0.178572
$741$	−4.11154	−0.151041
$742$	−10.7387	−0.394231
$743$	−8.07620	−0.296287	−0.148144	−	0.988966i	$-0.547330\pi$
$743$	−8.07620	−0.296287	−0.148144	+	0.988966i	$0.547330\pi$
$744$	−15.5602	−0.570465
$745$	12.6853	0.464753
$746$	27.1179	0.992856
$747$	36.3928	1.33154
$748$	0	0
$749$	3.67002	0.134100
$750$	22.4336	0.819159
$751$	0.882852	0.0322157	0.0161079	−	0.999870i	$-0.494872\pi$
$751$	0.882852	0.0322157	0.0161079	+	0.999870i	$0.494872\pi$
$752$	−10.3948	−0.379058
$753$	−10.4031	−0.379110
$754$	7.62989	0.277864
$755$	−37.8628	−1.37797
$756$	16.5689	0.602605
$757$	40.0776	1.45664	0.728322	−	0.685235i	$-0.240301\pi$
$757$	40.0776	1.45664	0.728322	+	0.685235i	$0.240301\pi$
$758$	−22.4156	−0.814172
$759$	0	0
$760$	−3.94699	−0.143172
$761$	−23.7629	−0.861404	−0.430702	−	0.902494i	$-0.641734\pi$
$761$	−23.7629	−0.861404	−0.430702	+	0.902494i	$0.641734\pi$
$762$	−51.0446	−1.84915
$763$	16.5708	0.599904
$764$	23.1456	0.837379
$765$	−54.4415	−1.96834
$766$	18.5297	0.669506
$767$	0.204316	0.00737742
$768$	3.10337	0.111983
$769$	24.3898	0.879519	0.439759	−	0.898116i	$-0.355064\pi$
$769$	24.3898	0.879519	0.439759	+	0.898116i	$0.355064\pi$
$770$	0	0
$771$	−91.3924	−3.29142
$772$	−20.4611	−0.736411
$773$	51.8395	1.86454	0.932269	−	0.361766i	$-0.117826\pi$
$773$	51.8395	1.86454	0.932269	+	0.361766i	$0.117826\pi$
$774$	43.1196	1.54990
$775$	11.6825	0.419647
$776$	−2.29270	−0.0823031
$777$	8.18760	0.293728
$778$	35.8570	1.28554
$779$	0.0236954	0.000848975 0
$780$	−7.63558	−0.273398
$781$	0	0
$782$	−3.03254	−0.108443
$783$	94.6041	3.38087
$784$	−4.83783	−0.172780
$785$	−3.50075	−0.124947
$786$	−36.5259	−1.30283
$787$	−33.5124	−1.19459	−0.597294	−	0.802023i	$-0.703757\pi$
$787$	−33.5124	−1.19459	−0.597294	+	0.802023i	$0.703757\pi$
$788$	−3.30631	−0.117782
$789$	−64.8867	−2.31003
$790$	40.2663	1.43261
$791$	−29.7288	−1.05703
$792$	0	0
$793$	−11.2228	−0.398534
$794$	−9.33864	−0.331416
$795$	61.3610	2.17625
$796$	6.46438	0.229124
$797$	18.6614	0.661021	0.330510	−	0.943802i	$-0.392779\pi$
$797$	18.6614	0.661021	0.330510	+	0.943802i	$0.392779\pi$
$798$	−6.65262	−0.235500
$799$	31.5225	1.11519
$800$	−2.32998	−0.0823774
$801$	105.069	3.71244
$802$	16.3686	0.577995
$803$	0	0
$804$	−32.8761	−1.15945
$805$	−3.98104	−0.140313
$806$	4.55658	0.160499
$807$	−48.6175	−1.71142
$808$	17.3294	0.609647
$809$	0.844061	0.0296756	0.0148378	−	0.999890i	$-0.495277\pi$
$809$	0.844061	0.0296756	0.0148378	+	0.999890i	$0.495277\pi$
$810$	−40.8173	−1.43417
$811$	−48.0194	−1.68619	−0.843094	−	0.537766i	$-0.819268\pi$
$811$	−48.0194	−1.68619	−0.843094	+	0.537766i	$0.819268\pi$
$812$	12.3454	0.433239
$813$	−69.9097	−2.45184
$814$	0	0
$815$	−60.3017	−2.11228
$816$	−9.41108	−0.329454
$817$	−9.48017	−0.331669
$818$	−30.9879	−1.08347
$819$	−8.86084	−0.309623
$820$	0.0440049	0.00153672
$821$	−42.2905	−1.47595	−0.737974	−	0.674829i	$-0.764217\pi$
$821$	−42.2905	−1.47595	−0.737974	+	0.674829i	$0.764217\pi$
$822$	10.9624	0.382359
$823$	8.18861	0.285437	0.142718	−	0.989763i	$-0.454416\pi$
$823$	8.18861	0.285437	0.142718	+	0.989763i	$0.454416\pi$
$824$	−0.391799	−0.0136490
$825$	0	0
$826$	0.330590	0.0115027
$827$	32.1253	1.11711	0.558553	−	0.829469i	$-0.311357\pi$
$827$	32.1253	1.11711	0.558553	+	0.829469i	$0.311357\pi$
$828$	−6.63091	−0.230440
$829$	−42.3282	−1.47012	−0.735059	−	0.678003i	$-0.762846\pi$
$829$	−42.3282	−1.47012	−0.735059	+	0.678003i	$0.762846\pi$
$830$	−14.8592	−0.515769
$831$	44.4282	1.54120
$832$	−0.908777	−0.0315062
$833$	14.6709	0.508316
$834$	−5.55103	−0.192216
$835$	−44.4764	−1.53917
$836$	0	0
$837$	56.4977	1.95285
$838$	38.9707	1.34622
$839$	0.983696	0.0339610	0.0169805	−	0.999856i	$-0.494595\pi$
$839$	0.983696	0.0339610	0.0169805	+	0.999856i	$0.494595\pi$
$840$	−12.3546	−0.426275
$841$	41.4891	1.43066
$842$	16.4780	0.567869
$843$	52.4401	1.80613
$844$	0.187898	0.00646772
$845$	−32.9602	−1.13386
$846$	68.9268	2.36975
$847$	0	0
$848$	7.30311	0.250790
$849$	−36.1886	−1.24199
$850$	7.06576	0.242353
$851$	−1.79423	−0.0615054
$852$	25.0368	0.857745
$853$	−17.5489	−0.600862	−0.300431	−	0.953803i	$-0.597131\pi$
$853$	−17.5489	−0.600862	−0.300431	+	0.953803i	$0.597131\pi$
$854$	−18.1589	−0.621385
$855$	26.1721	0.895067
$856$	−2.49588	−0.0853074
$857$	49.1996	1.68063	0.840313	−	0.542101i	$-0.182371\pi$
$857$	49.1996	1.68063	0.840313	+	0.542101i	$0.182371\pi$
$858$	0	0
$859$	−32.3099	−1.10240	−0.551199	−	0.834374i	$-0.685830\pi$
$859$	−32.3099	−1.10240	−0.551199	+	0.834374i	$0.685830\pi$
$860$	−17.6057	−0.600349
$861$	0.0741699	0.00252770
$862$	1.74404	0.0594022
$863$	−1.32831	−0.0452161	−0.0226080	−	0.999744i	$-0.507197\pi$
$863$	−1.32831	−0.0452161	−0.0226080	+	0.999744i	$0.507197\pi$
$864$	−11.2681	−0.383347
$865$	−0.283619	−0.00964335
$866$	−8.21653	−0.279209
$867$	−24.2179	−0.822482
$868$	7.37270	0.250246
$869$	0	0
$870$	−70.5417	−2.39159
$871$	9.62727	0.326208
$872$	−11.2694	−0.381629
$873$	15.2027	0.514533
$874$	1.45785	0.0493127
$875$	−10.6294	−0.359341
$876$	25.9521	0.876841
$877$	25.4059	0.857897	0.428949	−	0.903329i	$-0.358884\pi$
$877$	25.4059	0.857897	0.428949	+	0.903329i	$0.358884\pi$
$878$	−41.6557	−1.40581
$879$	22.2541	0.750612
$880$	0	0
$881$	−6.68927	−0.225367	−0.112684	−	0.993631i	$-0.535945\pi$
$881$	−6.68927	−0.225367	−0.112684	+	0.993631i	$0.535945\pi$
$882$	32.0792	1.08016
$883$	−31.6965	−1.06667	−0.533337	−	0.845903i	$-0.679062\pi$
$883$	−31.6965	−1.06667	−0.533337	+	0.845903i	$0.679062\pi$
$884$	2.75590	0.0926909
$885$	−1.88899	−0.0634978
$886$	−14.0098	−0.470667
$887$	18.4937	0.620958	0.310479	−	0.950580i	$-0.399511\pi$
$887$	18.4937	0.620958	0.310479	+	0.950580i	$0.399511\pi$
$888$	−5.56816	−0.186855
$889$	24.1858	0.811166
$890$	−42.8997	−1.43800
$891$	0	0
$892$	−23.5475	−0.788428
$893$	−15.1541	−0.507111
$894$	−14.5406	−0.486311
$895$	53.9331	1.80279
$896$	−1.47043	−0.0491237
$897$	2.82027	0.0941661
$898$	0.964174	0.0321749
$899$	42.0962	1.40399
$900$	15.4499	0.514997
$901$	−22.1469	−0.737821
$902$	0	0
$903$	−29.6743	−0.987498
$904$	20.2177	0.672432
$905$	53.5935	1.78151
$906$	43.4005	1.44189
$907$	27.3492	0.908116	0.454058	−	0.890972i	$-0.349976\pi$
$907$	27.3492	0.908116	0.454058	+	0.890972i	$0.349976\pi$
$908$	7.89998	0.262170
$909$	−114.910	−3.81132
$910$	3.61787	0.119931
$911$	19.3527	0.641183	0.320592	−	0.947218i	$-0.396118\pi$
$911$	19.3527	0.641183	0.320592	+	0.947218i	$0.396118\pi$
$912$	4.52426	0.149813
$913$	0	0
$914$	6.70128	0.221659
$915$	103.760	3.43020
$916$	14.5945	0.482216
$917$	17.3066	0.571514
$918$	34.1708	1.12780
$919$	−37.4379	−1.23496	−0.617481	−	0.786586i	$-0.711847\pi$
$919$	−37.4379	−1.23496	−0.617481	+	0.786586i	$0.711847\pi$
$920$	2.70739	0.0892601
$921$	−3.97876	−0.131105
$922$	−15.2448	−0.502059
$923$	−7.33165	−0.241324
$924$	0	0
$925$	4.18052	0.137455
$926$	17.7967	0.584836
$927$	2.59799	0.0853290
$928$	−8.39578	−0.275605
$929$	−12.3202	−0.404214	−0.202107	−	0.979363i	$-0.564779\pi$
$929$	−12.3202	−0.404214	−0.202107	+	0.979363i	$0.564779\pi$
$930$	−42.1276	−1.38142
$931$	−7.05285	−0.231148
$932$	26.6192	0.871940
$933$	−18.3797	−0.601726
$934$	−17.3506	−0.567729
$935$	0	0
$936$	6.02601	0.196966
$937$	−23.4701	−0.766736	−0.383368	−	0.923596i	$-0.625236\pi$
$937$	−23.4701	−0.766736	−0.383368	+	0.923596i	$0.625236\pi$
$938$	15.5773	0.508615
$939$	9.15764	0.298848
$940$	−28.1427	−0.917915
$941$	33.7597	1.10054	0.550268	−	0.834988i	$-0.314526\pi$
$941$	33.7597	1.10054	0.550268	+	0.834988i	$0.314526\pi$
$942$	4.01277	0.130743
$943$	−0.0162536	−0.000529290 0
$944$	−0.224825	−0.00731744
$945$	44.8585	1.45925
$946$	0	0
$947$	41.9135	1.36200	0.681002	−	0.732281i	$-0.261544\pi$
$947$	41.9135	1.36200	0.681002	+	0.732281i	$0.261544\pi$
$948$	−46.1555	−1.49906
$949$	−7.59970	−0.246697
$950$	−3.39678	−0.110206
$951$	4.99325	0.161917
$952$	4.45914	0.144521
$953$	−18.9316	−0.613256	−0.306628	−	0.951829i	$-0.599201\pi$
$953$	−18.9316	−0.613256	−0.306628	+	0.951829i	$0.599201\pi$
$954$	−48.4262	−1.56786
$955$	62.6643	2.02777
$956$	7.19545	0.232718
$957$	0	0
$958$	24.4556	0.790123
$959$	−5.19420	−0.167729
$960$	8.40205	0.271175
$961$	−5.86010	−0.189036
$962$	1.63055	0.0525712
$963$	16.5499	0.533315
$964$	−21.1969	−0.682705
$965$	−55.3963	−1.78327
$966$	4.56329	0.146822
$967$	22.8145	0.733666	0.366833	−	0.930287i	$-0.380442\pi$
$967$	22.8145	0.733666	0.366833	+	0.930287i	$0.380442\pi$
$968$	0	0
$969$	−13.7200	−0.440749
$970$	−6.20724	−0.199302
$971$	20.4112	0.655026	0.327513	−	0.944847i	$-0.393789\pi$
$971$	20.4112	0.655026	0.327513	+	0.944847i	$0.393789\pi$
$972$	12.9829	0.416428
$973$	2.63017	0.0843195
$974$	7.14632	0.228983
$975$	−6.57118	−0.210446
$976$	12.3494	0.395294
$977$	0.859598	0.0275010	0.0137505	−	0.999905i	$-0.495623\pi$
$977$	0.859598	0.0275010	0.0137505	+	0.999905i	$0.495623\pi$
$978$	69.1213	2.21025
$979$	0	0
$980$	−13.0979	−0.418398
$981$	74.7261	2.38582
$982$	−12.0388	−0.384175
$983$	0.400867	0.0127857	0.00639284	−	0.999980i	$-0.497965\pi$
$983$	0.400867	0.0127857	0.00639284	+	0.999980i	$0.497965\pi$
$984$	−0.0504409	−0.00160800
$985$	−8.95149	−0.285218
$986$	25.4605	0.810827
$987$	−47.4344	−1.50985
$988$	−1.32486	−0.0421495
$989$	6.50282	0.206778
$990$	0	0
$991$	40.3665	1.28228	0.641142	−	0.767422i	$-0.278461\pi$
$991$	40.3665	1.28228	0.641142	+	0.767422i	$0.278461\pi$
$992$	−5.01397	−0.159194
$993$	59.0337	1.87338
$994$	−11.8629	−0.376267
$995$	17.5016	0.554839
$996$	17.0324	0.539693
$997$	−37.7059	−1.19416	−0.597079	−	0.802183i	$-0.703672\pi$
$997$	−37.7059	−1.19416	−0.597079	+	0.802183i	$0.703672\pi$
$998$	−6.03531	−0.191044
$999$	20.2175	0.639653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5566.2.a.bt.1.9		10
11.2	odd	10		506.2.e.h.323.5	yes	20
11.6	odd	10		506.2.e.h.47.5	✓	20
11.10	odd	2		5566.2.a.bu.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.47.5	✓	20	11.6	odd	10
506.2.e.h.323.5	yes	20	11.2	odd	10
5566.2.a.bt.1.9		10	1.1	even	1	trivial
5566.2.a.bu.1.9		10	11.10	odd	2

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:	\( N \)	\(=\)	\( 5566 = 2 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5566.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.10337 q^{3} +1.00000 q^{4} +2.70739 q^{5} -3.10337 q^{6} +1.47043 q^{7} -1.00000 q^{8} +6.63091 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.10337 q^{3} +1.00000 q^{4} +2.70739 q^{5} -3.10337 q^{6} +1.47043 q^{7} -1.00000 q^{8} +6.63091 q^{9} -2.70739 q^{10} +3.10337 q^{12} -0.908777 q^{13} -1.47043 q^{14} +8.40205 q^{15} +1.00000 q^{16} -3.03254 q^{17} -6.63091 q^{18} +1.45785 q^{19} +2.70739 q^{20} +4.56329 q^{21} -1.00000 q^{23} -3.10337 q^{24} +2.32998 q^{25} +0.908777 q^{26} +11.2681 q^{27} +1.47043 q^{28} +8.39578 q^{29} -8.40205 q^{30} +5.01397 q^{31} -1.00000 q^{32} +3.03254 q^{34} +3.98104 q^{35} +6.63091 q^{36} +1.79423 q^{37} -1.45785 q^{38} -2.82027 q^{39} -2.70739 q^{40} +0.0162536 q^{41} -4.56329 q^{42} -6.50282 q^{43} +17.9525 q^{45} +1.00000 q^{46} -10.3948 q^{47} +3.10337 q^{48} -4.83783 q^{49} -2.32998 q^{50} -9.41108 q^{51} -0.908777 q^{52} +7.30311 q^{53} -11.2681 q^{54} -1.47043 q^{56} +4.52426 q^{57} -8.39578 q^{58} -0.224825 q^{59} +8.40205 q^{60} +12.3494 q^{61} -5.01397 q^{62} +9.75030 q^{63} +1.00000 q^{64} -2.46042 q^{65} -10.5937 q^{67} -3.03254 q^{68} -3.10337 q^{69} -3.98104 q^{70} +8.06760 q^{71} -6.63091 q^{72} +8.36256 q^{73} -1.79423 q^{74} +7.23080 q^{75} +1.45785 q^{76} +2.82027 q^{78} -14.8727 q^{79} +2.70739 q^{80} +15.0762 q^{81} -0.0162536 q^{82} +5.48836 q^{83} +4.56329 q^{84} -8.21027 q^{85} +6.50282 q^{86} +26.0552 q^{87} +15.8454 q^{89} -17.9525 q^{90} -1.33629 q^{91} -1.00000 q^{92} +15.5602 q^{93} +10.3948 q^{94} +3.94699 q^{95} -3.10337 q^{96} +2.29270 q^{97} +4.83783 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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