LMFDB - Embedded newform 4477.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4477,2,Mod(1,4477)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4477, 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("4477.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4477 = 11^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4477.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:	$35.7490249849$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 16 x^{9} + 32 x^{8} + 89 x^{7} - 179 x^{6} - 201 x^{5} + 407 x^{4} + 168 x^{3} + \cdots + 75 $ x^11 - 2x^10 - 16x^9 + 32x^8 + 89x^7 - 179x^6 - 201x^5 + 407x^4 + 168x^3 - 333x^2 - 51x + 75
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 407)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.12601$ of defining polynomial
Character	$\chi$	$=$	4477.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12601 q^{2} +3.05580 q^{3} +2.51992 q^{4} -1.92378 q^{5} -6.49666 q^{6} +2.08676 q^{7} -1.10536 q^{8} +6.33790 q^{9} +O(q^{10})$	\(q-2.12601 q^{2} +3.05580 q^{3} +2.51992 q^{4} -1.92378 q^{5} -6.49666 q^{6} +2.08676 q^{7} -1.10536 q^{8} +6.33790 q^{9} +4.08997 q^{10} +7.70037 q^{12} +3.35798 q^{13} -4.43647 q^{14} -5.87867 q^{15} -2.68984 q^{16} -6.78748 q^{17} -13.4744 q^{18} -0.267136 q^{19} -4.84776 q^{20} +6.37671 q^{21} -4.66206 q^{23} -3.37775 q^{24} -1.29909 q^{25} -7.13911 q^{26} +10.1999 q^{27} +5.25847 q^{28} -9.44474 q^{29} +12.4981 q^{30} -3.22663 q^{31} +7.92934 q^{32} +14.4302 q^{34} -4.01445 q^{35} +15.9710 q^{36} +1.00000 q^{37} +0.567934 q^{38} +10.2613 q^{39} +2.12646 q^{40} -0.209019 q^{41} -13.5570 q^{42} -3.75750 q^{43} -12.1927 q^{45} +9.91159 q^{46} -11.2166 q^{47} -8.21960 q^{48} -2.64544 q^{49} +2.76188 q^{50} -20.7412 q^{51} +8.46185 q^{52} +2.74980 q^{53} -21.6852 q^{54} -2.30662 q^{56} -0.816313 q^{57} +20.0796 q^{58} -0.914017 q^{59} -14.8138 q^{60} -13.1842 q^{61} +6.85985 q^{62} +13.2257 q^{63} -11.4782 q^{64} -6.46000 q^{65} +3.42780 q^{67} -17.1039 q^{68} -14.2463 q^{69} +8.53477 q^{70} -0.854668 q^{71} -7.00566 q^{72} -9.96667 q^{73} -2.12601 q^{74} -3.96976 q^{75} -0.673162 q^{76} -21.8157 q^{78} -13.6528 q^{79} +5.17464 q^{80} +12.1553 q^{81} +0.444376 q^{82} -6.20180 q^{83} +16.0688 q^{84} +13.0576 q^{85} +7.98848 q^{86} -28.8612 q^{87} -9.11340 q^{89} +25.9218 q^{90} +7.00730 q^{91} -11.7480 q^{92} -9.85993 q^{93} +23.8465 q^{94} +0.513909 q^{95} +24.2305 q^{96} +11.7443 q^{97} +5.62423 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} + 14 q^{4} + q^{5} - 4 q^{6} - 9 q^{7} + 15 q^{9}+O(q^{10}) $ 11 * q - 2 * q^2 + 14 * q^4 + q^5 - 4 * q^6 - 9 * q^7 + 15 * q^9	$ 11 q - 2 q^{2} + 14 q^{4} + q^{5} - 4 q^{6} - 9 q^{7} + 15 q^{9} - 5 q^{10} + q^{12} - 22 q^{13} + 3 q^{14} - 10 q^{15} - 19 q^{17} - 18 q^{18} - 14 q^{19} + 6 q^{20} + 13 q^{21} - 14 q^{23} + 11 q^{24} + 38 q^{25} - 10 q^{26} - 9 q^{27} - q^{28} - 13 q^{29} - 19 q^{30} + 12 q^{31} + 3 q^{32} + q^{34} - 12 q^{35} + 18 q^{36} + 11 q^{37} - 31 q^{38} + 8 q^{39} - 22 q^{40} - 8 q^{41} + 15 q^{42} - 21 q^{43} - 8 q^{45} + 45 q^{46} - 14 q^{47} - 37 q^{48} + 20 q^{49} + 41 q^{50} + 2 q^{51} - 51 q^{52} - 2 q^{53} - 6 q^{54} - 22 q^{56} + 3 q^{57} + 15 q^{58} - 30 q^{59} - 107 q^{60} - 20 q^{61} - 22 q^{62} - 31 q^{63} - 14 q^{64} + 7 q^{67} - 24 q^{68} + 9 q^{69} - 86 q^{70} - 15 q^{71} + 7 q^{72} - 47 q^{73} - 2 q^{74} - 40 q^{75} - 6 q^{76} - 42 q^{78} - 2 q^{79} + 3 q^{80} - 17 q^{81} - 54 q^{82} - 24 q^{83} + 33 q^{84} + 25 q^{85} - 13 q^{86} - 21 q^{87} + 4 q^{89} + 107 q^{90} + 21 q^{91} - 46 q^{92} - 37 q^{93} - 3 q^{94} + 36 q^{95} + 49 q^{96} + 25 q^{97} + 52 q^{98}+O(q^{100}) $ 11 * q - 2 * q^2 + 14 * q^4 + q^5 - 4 * q^6 - 9 * q^7 + 15 * q^9 - 5 * q^10 + q^12 - 22 * q^13 + 3 * q^14 - 10 * q^15 - 19 * q^17 - 18 * q^18 - 14 * q^19 + 6 * q^20 + 13 * q^21 - 14 * q^23 + 11 * q^24 + 38 * q^25 - 10 * q^26 - 9 * q^27 - q^28 - 13 * q^29 - 19 * q^30 + 12 * q^31 + 3 * q^32 + q^34 - 12 * q^35 + 18 * q^36 + 11 * q^37 - 31 * q^38 + 8 * q^39 - 22 * q^40 - 8 * q^41 + 15 * q^42 - 21 * q^43 - 8 * q^45 + 45 * q^46 - 14 * q^47 - 37 * q^48 + 20 * q^49 + 41 * q^50 + 2 * q^51 - 51 * q^52 - 2 * q^53 - 6 * q^54 - 22 * q^56 + 3 * q^57 + 15 * q^58 - 30 * q^59 - 107 * q^60 - 20 * q^61 - 22 * q^62 - 31 * q^63 - 14 * q^64 + 7 * q^67 - 24 * q^68 + 9 * q^69 - 86 * q^70 - 15 * q^71 + 7 * q^72 - 47 * q^73 - 2 * q^74 - 40 * q^75 - 6 * q^76 - 42 * q^78 - 2 * q^79 + 3 * q^80 - 17 * q^81 - 54 * q^82 - 24 * q^83 + 33 * q^84 + 25 * q^85 - 13 * q^86 - 21 * q^87 + 4 * q^89 + 107 * q^90 + 21 * q^91 - 46 * q^92 - 37 * q^93 - 3 * q^94 + 36 * q^95 + 49 * q^96 + 25 * q^97 + 52 * 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 $

$2$	−2.12601	−1.50332	−0.751658	−	0.659553i	$-0.770746\pi$
$2$	−2.12601	−1.50332	−0.751658	+	0.659553i	$0.770746\pi$
$3$	3.05580	1.76427	0.882133	−	0.471001i	$-0.156107\pi$
$3$	3.05580	1.76427	0.882133	+	0.471001i	$0.156107\pi$
$4$	2.51992	1.25996
$5$	−1.92378	−0.860338	−0.430169	−	0.902748i	$-0.641546\pi$
$5$	−1.92378	−0.860338	−0.430169	+	0.902748i	$0.641546\pi$
$6$	−6.49666	−2.65225
$7$	2.08676	0.788720	0.394360	−	0.918956i	$-0.370966\pi$
$7$	2.08676	0.788720	0.394360	+	0.918956i	$0.370966\pi$
$8$	−1.10536	−0.390803
$9$	6.33790	2.11263
$10$	4.08997	1.29336
$11$	0	0
$11$	0	0
$12$	7.70037	2.22291
$13$	3.35798	0.931337	0.465668	−	0.884959i	$-0.345814\pi$
$13$	3.35798	0.931337	0.465668	+	0.884959i	$0.345814\pi$
$14$	−4.43647	−1.18570
$15$	−5.87867	−1.51787
$16$	−2.68984	−0.672460
$17$	−6.78748	−1.64620	−0.823102	−	0.567893i	$-0.807759\pi$
$17$	−6.78748	−1.64620	−0.823102	+	0.567893i	$0.807759\pi$
$18$	−13.4744	−3.17596
$19$	−0.267136	−0.0612852	−0.0306426	−	0.999530i	$-0.509755\pi$
$19$	−0.267136	−0.0612852	−0.0306426	+	0.999530i	$0.509755\pi$
$20$	−4.84776	−1.08399
$21$	6.37671	1.39151
$22$	0	0
$23$	−4.66206	−0.972107	−0.486053	−	0.873929i	$-0.661564\pi$
$23$	−4.66206	−0.972107	−0.486053	+	0.873929i	$0.661564\pi$
$24$	−3.37775	−0.689481
$25$	−1.29909	−0.259818
$26$	−7.13911	−1.40009
$27$	10.1999	1.96298
$28$	5.25847	0.993757
$29$	−9.44474	−1.75384	−0.876922	−	0.480633i	$-0.840407\pi$
$29$	−9.44474	−1.75384	−0.876922	+	0.480633i	$0.840407\pi$
$30$	12.4981	2.28183
$31$	−3.22663	−0.579520	−0.289760	−	0.957099i	$-0.593576\pi$
$31$	−3.22663	−0.579520	−0.289760	+	0.957099i	$0.593576\pi$
$32$	7.92934	1.40172
$33$	0	0
$34$	14.4302	2.47477
$35$	−4.01445	−0.678566
$36$	15.9710	2.66184
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0.567934	0.0921310
$39$	10.2613	1.64313
$40$	2.12646	0.336223
$41$	−0.209019	−0.0326432	−0.0163216	−	0.999867i	$-0.505196\pi$
$41$	−0.209019	−0.0326432	−0.0163216	+	0.999867i	$0.505196\pi$
$42$	−13.5570	−2.09188
$43$	−3.75750	−0.573013	−0.286507	−	0.958078i	$-0.592494\pi$
$43$	−3.75750	−0.573013	−0.286507	+	0.958078i	$0.592494\pi$
$44$	0	0
$45$	−12.1927	−1.81758
$46$	9.91159	1.46138
$47$	−11.2166	−1.63610	−0.818052	−	0.575144i	$-0.804946\pi$
$47$	−11.2166	−1.63610	−0.818052	+	0.575144i	$0.804946\pi$
$48$	−8.21960	−1.18640
$49$	−2.64544	−0.377920
$50$	2.76188	0.390589
$51$	−20.7412	−2.90434
$52$	8.46185	1.17345
$53$	2.74980	0.377714	0.188857	−	0.982005i	$-0.439522\pi$
$53$	2.74980	0.377714	0.188857	+	0.982005i	$0.439522\pi$
$54$	−21.6852	−2.95098
$55$	0	0
$56$	−2.30662	−0.308235
$57$	−0.816313	−0.108123
$58$	20.0796	2.63658
$59$	−0.914017	−0.118995	−0.0594974	−	0.998228i	$-0.518950\pi$
$59$	−0.914017	−0.118995	−0.0594974	+	0.998228i	$0.518950\pi$
$60$	−14.8138	−1.91245
$61$	−13.1842	−1.68807	−0.844033	−	0.536291i	$-0.819825\pi$
$61$	−13.1842	−1.68807	−0.844033	+	0.536291i	$0.819825\pi$
$62$	6.85985	0.871202
$63$	13.2257	1.66628
$64$	−11.4782	−1.43477
$65$	−6.46000	−0.801265
$66$	0	0
$67$	3.42780	0.418772	0.209386	−	0.977833i	$-0.432853\pi$
$67$	3.42780	0.418772	0.209386	+	0.977833i	$0.432853\pi$
$68$	−17.1039	−2.07415
$69$	−14.2463	−1.71505
$70$	8.53477	1.02010
$71$	−0.854668	−0.101430	−0.0507152	−	0.998713i	$-0.516150\pi$
$71$	−0.854668	−0.101430	−0.0507152	+	0.998713i	$0.516150\pi$
$72$	−7.00566	−0.825624
$73$	−9.96667	−1.16651	−0.583255	−	0.812289i	$-0.698221\pi$
$73$	−9.96667	−1.16651	−0.583255	+	0.812289i	$0.698221\pi$
$74$	−2.12601	−0.247144
$75$	−3.96976	−0.458388
$76$	−0.673162	−0.0772169
$77$	0	0
$78$	−21.8157	−2.47014
$79$	−13.6528	−1.53606	−0.768032	−	0.640411i	$-0.778764\pi$
$79$	−13.6528	−1.53606	−0.768032	+	0.640411i	$0.778764\pi$
$80$	5.17464	0.578543
$81$	12.1553	1.35059
$82$	0.444376	0.0490731
$83$	−6.20180	−0.680736	−0.340368	−	0.940292i	$-0.610552\pi$
$83$	−6.20180	−0.680736	−0.340368	+	0.940292i	$0.610552\pi$
$84$	16.0688	1.75325
$85$	13.0576	1.41629
$86$	7.98848	0.861420
$87$	−28.8612	−3.09425
$88$	0	0
$89$	−9.11340	−0.966019	−0.483009	−	0.875615i	$-0.660456\pi$
$89$	−9.11340	−0.966019	−0.483009	+	0.875615i	$0.660456\pi$
$90$	25.9218	2.73240
$91$	7.00730	0.734564
$92$	−11.7480	−1.22482
$93$	−9.85993	−1.02243
$94$	23.8465	2.45958
$95$	0.513909	0.0527260
$96$	24.2305	2.47301
$97$	11.7443	1.19245	0.596225	−	0.802817i	$-0.296666\pi$
$97$	11.7443	1.19245	0.596225	+	0.802817i	$0.296666\pi$
$98$	5.62423	0.568133
$99$	0	0
$100$	−3.27360	−0.327360
$101$	6.43172	0.639980	0.319990	−	0.947421i	$-0.396320\pi$
$101$	6.43172	0.639980	0.319990	+	0.947421i	$0.396320\pi$
$102$	44.0959	4.36615
$103$	17.7730	1.75122	0.875612	−	0.483016i	$-0.160459\pi$
$103$	17.7730	1.75122	0.875612	+	0.483016i	$0.160459\pi$
$104$	−3.71178	−0.363970
$105$	−12.2674	−1.19717
$106$	−5.84611	−0.567824
$107$	−0.604301	−0.0584200	−0.0292100	−	0.999573i	$-0.509299\pi$
$107$	−0.604301	−0.0584200	−0.0292100	+	0.999573i	$0.509299\pi$
$108$	25.7031	2.47328
$109$	17.6594	1.69146	0.845732	−	0.533608i	$-0.179164\pi$
$109$	17.6594	1.69146	0.845732	+	0.533608i	$0.179164\pi$
$110$	0	0
$111$	3.05580	0.290043
$112$	−5.61304	−0.530383
$113$	−10.6523	−1.00208	−0.501040	−	0.865424i	$-0.667049\pi$
$113$	−10.6523	−1.00208	−0.501040	+	0.865424i	$0.667049\pi$
$114$	1.73549	0.162544
$115$	8.96875	0.836341
$116$	−23.8000	−2.20977
$117$	21.2826	1.96757
$118$	1.94321	0.178887
$119$	−14.1638	−1.29840
$120$	6.49804	0.593187
$121$	0	0
$122$	28.0298	2.53770
$123$	−0.638719	−0.0575913
$124$	−8.13086	−0.730173
$125$	12.1180	1.08387
$126$	−28.1179	−2.50494
$127$	12.5416	1.11289	0.556443	−	0.830886i	$-0.312166\pi$
$127$	12.5416	1.11289	0.556443	+	0.830886i	$0.312166\pi$
$128$	8.54407	0.755197
$129$	−11.4822	−1.01095
$130$	13.7340	1.20455
$131$	7.04400	0.615437	0.307719	−	0.951477i	$-0.400434\pi$
$131$	7.04400	0.615437	0.307719	+	0.951477i	$0.400434\pi$
$132$	0	0
$133$	−0.557448	−0.0483369
$134$	−7.28753	−0.629547
$135$	−19.6224	−1.68883
$136$	7.50260	0.643342
$137$	−14.5382	−1.24208	−0.621042	−	0.783777i	$-0.713291\pi$
$137$	−14.5382	−1.24208	−0.621042	+	0.783777i	$0.713291\pi$
$138$	30.2878	2.57827
$139$	18.6991	1.58604	0.793019	−	0.609197i	$-0.208508\pi$
$139$	18.6991	1.58604	0.793019	+	0.609197i	$0.208508\pi$
$140$	−10.1161	−0.854967
$141$	−34.2756	−2.88652
$142$	1.81703	0.152482
$143$	0	0
$144$	−17.0479	−1.42066
$145$	18.1696	1.50890
$146$	21.1893	1.75364
$147$	−8.08393	−0.666751
$148$	2.51992	0.207136
$149$	8.76200	0.717811	0.358905	−	0.933374i	$-0.383150\pi$
$149$	8.76200	0.717811	0.358905	+	0.933374i	$0.383150\pi$
$150$	8.43974	0.689102
$151$	−9.03624	−0.735359	−0.367680	−	0.929953i	$-0.619848\pi$
$151$	−9.03624	−0.735359	−0.367680	+	0.929953i	$0.619848\pi$
$152$	0.295281	0.0239505
$153$	−43.0183	−3.47783
$154$	0	0
$155$	6.20731	0.498583
$156$	25.8577	2.07027
$157$	11.7809	0.940220	0.470110	−	0.882608i	$-0.344214\pi$
$157$	11.7809	0.940220	0.470110	+	0.882608i	$0.344214\pi$
$158$	29.0261	2.30919
$159$	8.40284	0.666388
$160$	−15.2543	−1.20596
$161$	−9.72859	−0.766720
$162$	−25.8423	−2.03036
$163$	−0.518576	−0.0406180	−0.0203090	−	0.999794i	$-0.506465\pi$
$163$	−0.518576	−0.0406180	−0.0203090	+	0.999794i	$0.506465\pi$
$164$	−0.526711	−0.0411292
$165$	0	0
$166$	13.1851	1.02336
$167$	4.12508	0.319208	0.159604	−	0.987181i	$-0.448978\pi$
$167$	4.12508	0.319208	0.159604	+	0.987181i	$0.448978\pi$
$168$	−7.04856	−0.543808
$169$	−1.72396	−0.132612
$170$	−27.7605	−2.12914
$171$	−1.69308	−0.129473
$172$	−9.46860	−0.721974
$173$	−0.362357	−0.0275495	−0.0137748	−	0.999905i	$-0.504385\pi$
$173$	−0.362357	−0.0275495	−0.0137748	+	0.999905i	$0.504385\pi$
$174$	61.3593	4.65163
$175$	−2.71089	−0.204924
$176$	0	0
$177$	−2.79305	−0.209938
$178$	19.3752	1.45223
$179$	−5.97272	−0.446422	−0.223211	−	0.974770i	$-0.571654\pi$
$179$	−5.97272	−0.446422	−0.223211	+	0.974770i	$0.571654\pi$
$180$	−30.7246	−2.29008
$181$	4.95609	0.368383	0.184192	−	0.982890i	$-0.441033\pi$
$181$	4.95609	0.368383	0.184192	+	0.982890i	$0.441033\pi$
$182$	−14.8976	−1.10428
$183$	−40.2883	−2.97820
$184$	5.15325	0.379903
$185$	−1.92378	−0.141439
$186$	20.9623	1.53703
$187$	0	0
$188$	−28.2649	−2.06143
$189$	21.2848	1.54824
$190$	−1.09258	−0.0792639
$191$	20.1437	1.45755	0.728774	−	0.684754i	$-0.240090\pi$
$191$	20.1437	1.45755	0.728774	+	0.684754i	$0.240090\pi$
$192$	−35.0750	−2.53132
$193$	−22.4900	−1.61886	−0.809431	−	0.587214i	$-0.800225\pi$
$193$	−22.4900	−1.61886	−0.809431	+	0.587214i	$0.800225\pi$
$194$	−24.9685	−1.79263
$195$	−19.7405	−1.41364
$196$	−6.66630	−0.476164
$197$	19.9181	1.41911	0.709554	−	0.704651i	$-0.248896\pi$
$197$	19.9181	1.41911	0.709554	+	0.704651i	$0.248896\pi$
$198$	0	0
$199$	−27.7838	−1.96954	−0.984772	−	0.173849i	$-0.944379\pi$
$199$	−27.7838	−1.96954	−0.984772	+	0.173849i	$0.944379\pi$
$200$	1.43596	0.101538
$201$	10.4747	0.738825
$202$	−13.6739	−0.962092
$203$	−19.7089	−1.38329
$204$	−52.2661	−3.65936
$205$	0.402105	0.0280842
$206$	−37.7855	−2.63264
$207$	−29.5477	−2.05370
$208$	−9.03243	−0.626286
$209$	0	0
$210$	26.0805	1.79973
$211$	12.9636	0.892450	0.446225	−	0.894921i	$-0.352768\pi$
$211$	12.9636	0.892450	0.446225	+	0.894921i	$0.352768\pi$
$212$	6.92928	0.475905
$213$	−2.61169	−0.178950
$214$	1.28475	0.0878237
$215$	7.22858	0.492985
$216$	−11.2746	−0.767140
$217$	−6.73320	−0.457079
$218$	−37.5441	−2.54281
$219$	−30.4561	−2.05804
$220$	0	0
$221$	−22.7922	−1.53317
$222$	−6.49666	−0.436027
$223$	4.83430	0.323729	0.161864	−	0.986813i	$-0.448249\pi$
$223$	4.83430	0.323729	0.161864	+	0.986813i	$0.448249\pi$
$224$	16.5466	1.10557
$225$	−8.23350	−0.548900
$226$	22.6468	1.50644
$227$	−8.12378	−0.539194	−0.269597	−	0.962973i	$-0.586891\pi$
$227$	−8.12378	−0.539194	−0.269597	+	0.962973i	$0.586891\pi$
$228$	−2.05705	−0.136231
$229$	−2.65582	−0.175502	−0.0877509	−	0.996142i	$-0.527968\pi$
$229$	−2.65582	−0.175502	−0.0877509	+	0.996142i	$0.527968\pi$
$230$	−19.0677	−1.25728
$231$	0	0
$232$	10.4398	0.685408
$233$	−7.79662	−0.510774	−0.255387	−	0.966839i	$-0.582203\pi$
$233$	−7.79662	−0.510774	−0.255387	+	0.966839i	$0.582203\pi$
$234$	−45.2469	−2.95788
$235$	21.5782	1.40760
$236$	−2.30325	−0.149929
$237$	−41.7203	−2.71003
$238$	30.1124	1.95190
$239$	−6.04134	−0.390782	−0.195391	−	0.980725i	$-0.562598\pi$
$239$	−6.04134	−0.390782	−0.195391	+	0.980725i	$0.562598\pi$
$240$	15.8127	1.02070
$241$	15.9812	1.02944	0.514720	−	0.857358i	$-0.327896\pi$
$241$	15.9812	1.02944	0.514720	+	0.857358i	$0.327896\pi$
$242$	0	0
$243$	6.54423	0.419813
$244$	−33.2232	−2.12690
$245$	5.08923	0.325139
$246$	1.35792	0.0865780
$247$	−0.897038	−0.0570771
$248$	3.56659	0.226478
$249$	−18.9514	−1.20100
$250$	−25.7631	−1.62940
$251$	3.10149	0.195764	0.0978822	−	0.995198i	$-0.468793\pi$
$251$	3.10149	0.195764	0.0978822	+	0.995198i	$0.468793\pi$
$252$	33.3276	2.09944
$253$	0	0
$254$	−26.6636	−1.67302
$255$	39.9013	2.49872
$256$	4.79159	0.299474
$257$	23.3276	1.45513	0.727566	−	0.686037i	$-0.240651\pi$
$257$	23.3276	1.45513	0.727566	+	0.686037i	$0.240651\pi$
$258$	24.4112	1.51977
$259$	2.08676	0.129665
$260$	−16.2787	−1.00956
$261$	−59.8598	−3.70523
$262$	−14.9756	−0.925197
$263$	21.4858	1.32487	0.662435	−	0.749120i	$-0.269523\pi$
$263$	21.4858	1.32487	0.662435	+	0.749120i	$0.269523\pi$
$264$	0	0
$265$	−5.29000	−0.324962
$266$	1.18514	0.0726656
$267$	−27.8487	−1.70431
$268$	8.63778	0.527636
$269$	25.8012	1.57313	0.786564	−	0.617509i	$-0.211858\pi$
$269$	25.8012	1.57313	0.786564	+	0.617509i	$0.211858\pi$
$270$	41.7174	2.53884
$271$	−22.7410	−1.38142	−0.690709	−	0.723132i	$-0.742702\pi$
$271$	−22.7410	−1.38142	−0.690709	+	0.723132i	$0.742702\pi$
$272$	18.2572	1.10701
$273$	21.4129	1.29597
$274$	30.9084	1.86725
$275$	0	0
$276$	−35.8996	−2.16090
$277$	2.80145	0.168323	0.0841615	−	0.996452i	$-0.473179\pi$
$277$	2.80145	0.168323	0.0841615	+	0.996452i	$0.473179\pi$
$278$	−39.7545	−2.38432
$279$	−20.4501	−1.22431
$280$	4.43741	0.265186
$281$	14.7748	0.881388	0.440694	−	0.897657i	$-0.354732\pi$
$281$	14.7748	0.881388	0.440694	+	0.897657i	$0.354732\pi$
$282$	72.8702	4.33936
$283$	15.4996	0.921357	0.460679	−	0.887567i	$-0.347606\pi$
$283$	15.4996	0.921357	0.460679	+	0.887567i	$0.347606\pi$
$284$	−2.15370	−0.127798
$285$	1.57040	0.0930227
$286$	0	0
$287$	−0.436171	−0.0257464
$288$	50.2554	2.96133
$289$	29.0698	1.70999
$290$	−38.6287	−2.26835
$291$	35.8881	2.10380
$292$	−25.1152	−1.46976
$293$	0.910769	0.0532077	0.0266038	−	0.999646i	$-0.491531\pi$
$293$	0.910769	0.0532077	0.0266038	+	0.999646i	$0.491531\pi$
$294$	17.1865	1.00234
$295$	1.75836	0.102376
$296$	−1.10536	−0.0642477
$297$	0	0
$298$	−18.6281	−1.07910
$299$	−15.6551	−0.905358
$300$	−10.0035	−0.577551
$301$	−7.84099	−0.451947
$302$	19.2112	1.10548
$303$	19.6540	1.12909
$304$	0.718552	0.0412118
$305$	25.3635	1.45231
$306$	91.4575	5.22827
$307$	−2.62103	−0.149590	−0.0747950	−	0.997199i	$-0.523830\pi$
$307$	−2.62103	−0.149590	−0.0747950	+	0.997199i	$0.523830\pi$
$308$	0	0
$309$	54.3106	3.08962
$310$	−13.1968	−0.749529
$311$	−21.5713	−1.22320	−0.611599	−	0.791168i	$-0.709473\pi$
$311$	−21.5713	−1.22320	−0.611599	+	0.791168i	$0.709473\pi$
$312$	−11.3424	−0.642139
$313$	15.7157	0.888302	0.444151	−	0.895952i	$-0.353505\pi$
$313$	15.7157	0.888302	0.444151	+	0.895952i	$0.353505\pi$
$314$	−25.0464	−1.41345
$315$	−25.4432	−1.43356
$316$	−34.4041	−1.93538
$317$	1.05813	0.0594307	0.0297154	−	0.999558i	$-0.490540\pi$
$317$	1.05813	0.0594307	0.0297154	+	0.999558i	$0.490540\pi$
$318$	−17.8645	−1.00179
$319$	0	0
$320$	22.0815	1.23439
$321$	−1.84662	−0.103068
$322$	20.6831	1.15262
$323$	1.81318	0.100888
$324$	30.6304	1.70169
$325$	−4.36232	−0.241978
$326$	1.10250	0.0610617
$327$	53.9635	2.98419
$328$	0.231041	0.0127571
$329$	−23.4063	−1.29043
$330$	0	0
$331$	24.7129	1.35835	0.679173	−	0.733978i	$-0.262339\pi$
$331$	24.7129	1.35835	0.679173	+	0.733978i	$0.262339\pi$
$332$	−15.6280	−0.857700
$333$	6.33790	0.347315
$334$	−8.76996	−0.479871
$335$	−6.59431	−0.360286
$336$	−17.1523	−0.935736
$337$	16.7192	0.910750	0.455375	−	0.890300i	$-0.349505\pi$
$337$	16.7192	0.910750	0.455375	+	0.890300i	$0.349505\pi$
$338$	3.66516	0.199358
$339$	−32.5512	−1.76794
$340$	32.9041	1.78447
$341$	0	0
$342$	3.59951	0.194639
$343$	−20.1277	−1.08679
$344$	4.15339	0.223936
$345$	27.4067	1.47553
$346$	0.770375	0.0414156
$347$	23.3650	1.25430	0.627150	−	0.778899i	$-0.284221\pi$
$347$	23.3650	1.25430	0.627150	+	0.778899i	$0.284221\pi$
$348$	−72.7280	−3.89863
$349$	−29.6422	−1.58671	−0.793354	−	0.608760i	$-0.791667\pi$
$349$	−29.6422	−1.58671	−0.793354	+	0.608760i	$0.791667\pi$
$350$	5.76337	0.308065
$351$	34.2512	1.82820
$352$	0	0
$353$	−11.2952	−0.601182	−0.300591	−	0.953753i	$-0.597184\pi$
$353$	−11.2952	−0.601182	−0.300591	+	0.953753i	$0.597184\pi$
$354$	5.93805	0.315604
$355$	1.64419	0.0872645
$356$	−22.9651	−1.21715
$357$	−43.2818	−2.29071
$358$	12.6981	0.671113
$359$	14.1843	0.748621	0.374310	−	0.927303i	$-0.377879\pi$
$359$	14.1843	0.748621	0.374310	+	0.927303i	$0.377879\pi$
$360$	13.4773	0.710316
$361$	−18.9286	−0.996244
$362$	−10.5367	−0.553797
$363$	0	0
$364$	17.6578	0.925522
$365$	19.1736	1.00359
$366$	85.6534	4.47717
$367$	−13.9885	−0.730194	−0.365097	−	0.930969i	$-0.618964\pi$
$367$	−13.9885	−0.730194	−0.365097	+	0.930969i	$0.618964\pi$
$368$	12.5402	0.653702
$369$	−1.32474	−0.0689632
$370$	4.08997	0.212627
$371$	5.73817	0.297911
$372$	−24.8463	−1.28822
$373$	−20.9389	−1.08418	−0.542089	−	0.840321i	$-0.682366\pi$
$373$	−20.9389	−1.08418	−0.542089	+	0.840321i	$0.682366\pi$
$374$	0	0
$375$	37.0303	1.91223
$376$	12.3983	0.639395
$377$	−31.7153	−1.63342
$378$	−45.2518	−2.32750
$379$	−29.7250	−1.52687	−0.763436	−	0.645884i	$-0.776489\pi$
$379$	−29.7250	−1.52687	−0.763436	+	0.645884i	$0.776489\pi$
$380$	1.29501	0.0664327
$381$	38.3246	1.96343
$382$	−42.8258	−2.19116
$383$	7.92443	0.404919	0.202460	−	0.979291i	$-0.435106\pi$
$383$	7.92443	0.404919	0.202460	+	0.979291i	$0.435106\pi$
$384$	26.1090	1.33237
$385$	0	0
$386$	47.8139	2.43366
$387$	−23.8147	−1.21057
$388$	29.5947	1.50244
$389$	−27.9035	−1.41476	−0.707382	−	0.706831i	$-0.750124\pi$
$389$	−27.9035	−1.41476	−0.707382	+	0.706831i	$0.750124\pi$
$390$	41.9684	2.12515
$391$	31.6436	1.60029
$392$	2.92416	0.147692
$393$	21.5250	1.08579
$394$	−42.3462	−2.13337
$395$	26.2650	1.32153
$396$	0	0
$397$	−23.4461	−1.17673	−0.588364	−	0.808596i	$-0.700228\pi$
$397$	−23.4461	−1.17673	−0.588364	+	0.808596i	$0.700228\pi$
$398$	59.0688	2.96085
$399$	−1.70345	−0.0852791
$400$	3.49434	0.174717
$401$	−11.6855	−0.583544	−0.291772	−	0.956488i	$-0.594245\pi$
$401$	−11.6855	−0.583544	−0.291772	+	0.956488i	$0.594245\pi$
$402$	−22.2692	−1.11069
$403$	−10.8350	−0.539728
$404$	16.2074	0.806350
$405$	−23.3840	−1.16196
$406$	41.9013	2.07953
$407$	0	0
$408$	22.9264	1.13503
$409$	−31.8911	−1.57691	−0.788457	−	0.615090i	$-0.789120\pi$
$409$	−31.8911	−1.57691	−0.788457	+	0.615090i	$0.789120\pi$
$410$	−0.854879	−0.0422195
$411$	−44.4259	−2.19137
$412$	44.7865	2.20647
$413$	−1.90733	−0.0938536
$414$	62.8187	3.08737
$415$	11.9309	0.585663
$416$	26.6266	1.30548
$417$	57.1407	2.79819
$418$	0	0
$419$	5.60124	0.273638	0.136819	−	0.990596i	$-0.456312\pi$
$419$	5.60124	0.273638	0.136819	+	0.990596i	$0.456312\pi$
$420$	−30.9128	−1.50839
$421$	26.9004	1.31104	0.655522	−	0.755176i	$-0.272449\pi$
$421$	26.9004	1.31104	0.655522	+	0.755176i	$0.272449\pi$
$422$	−27.5607	−1.34163
$423$	−71.0895	−3.45649
$424$	−3.03952	−0.147612
$425$	8.81754	0.427713
$426$	5.55249	0.269019
$427$	−27.5123	−1.33141
$428$	−1.52279	−0.0736069
$429$	0	0
$430$	−15.3680	−0.741113
$431$	−37.6161	−1.81190	−0.905952	−	0.423380i	$-0.860844\pi$
$431$	−37.6161	−1.81190	−0.905952	+	0.423380i	$0.860844\pi$
$432$	−27.4362	−1.32003
$433$	31.0239	1.49091	0.745457	−	0.666554i	$-0.232231\pi$
$433$	31.0239	1.49091	0.745457	+	0.666554i	$0.232231\pi$
$434$	14.3149	0.687135
$435$	55.5225	2.66210
$436$	44.5003	2.13118
$437$	1.24540	0.0595757
$438$	64.7501	3.09388
$439$	4.01368	0.191563	0.0957813	−	0.995402i	$-0.469465\pi$
$439$	4.01368	0.191563	0.0957813	+	0.995402i	$0.469465\pi$
$440$	0	0
$441$	−16.7665	−0.798407
$442$	48.4565	2.30484
$443$	−23.6652	−1.12437	−0.562184	−	0.827012i	$-0.690039\pi$
$443$	−23.6652	−1.12437	−0.562184	+	0.827012i	$0.690039\pi$
$444$	7.70037	0.365443
$445$	17.5321	0.831103
$446$	−10.2778	−0.486667
$447$	26.7749	1.26641
$448$	−23.9522	−1.13164
$449$	−10.1536	−0.479178	−0.239589	−	0.970874i	$-0.577013\pi$
$449$	−10.1536	−0.479178	−0.239589	+	0.970874i	$0.577013\pi$
$450$	17.5045	0.825171
$451$	0	0
$452$	−26.8429	−1.26258
$453$	−27.6129	−1.29737
$454$	17.2712	0.810580
$455$	−13.4805	−0.631974
$456$	0.902320	0.0422550
$457$	−34.8210	−1.62886	−0.814428	−	0.580265i	$-0.802949\pi$
$457$	−34.8210	−1.62886	−0.814428	+	0.580265i	$0.802949\pi$
$458$	5.64631	0.263835
$459$	−69.2319	−3.23147
$460$	22.6006	1.05376
$461$	19.3500	0.901218	0.450609	−	0.892721i	$-0.351207\pi$
$461$	19.3500	0.901218	0.450609	+	0.892721i	$0.351207\pi$
$462$	0	0
$463$	−5.80193	−0.269639	−0.134819	−	0.990870i	$-0.543045\pi$
$463$	−5.80193	−0.269639	−0.134819	+	0.990870i	$0.543045\pi$
$464$	25.4048	1.17939
$465$	18.9683	0.879634
$466$	16.5757	0.767855
$467$	−37.2343	−1.72300	−0.861498	−	0.507760i	$-0.830473\pi$
$467$	−37.2343	−1.72300	−0.861498	+	0.507760i	$0.830473\pi$
$468$	53.6304	2.47906
$469$	7.15298	0.330294
$470$	−45.8754	−2.11607
$471$	36.0001	1.65880
$472$	1.01032	0.0465036
$473$	0	0
$474$	88.6978	4.07403
$475$	0.347034	0.0159230
$476$	−35.6917	−1.63593
$477$	17.4280	0.797972
$478$	12.8440	0.587469
$479$	1.60037	0.0731227	0.0365614	−	0.999331i	$-0.488360\pi$
$479$	1.60037	0.0731227	0.0365614	+	0.999331i	$0.488360\pi$
$480$	−46.6140	−2.12763
$481$	3.35798	0.153111
$482$	−33.9762	−1.54757
$483$	−29.7286	−1.35270
$484$	0	0
$485$	−22.5933	−1.02591
$486$	−13.9131	−0.631111
$487$	25.1312	1.13880	0.569401	−	0.822060i	$-0.307175\pi$
$487$	25.1312	1.13880	0.569401	+	0.822060i	$0.307175\pi$
$488$	14.5733	0.659702
$489$	−1.58466	−0.0716609
$490$	−10.8198	−0.488787
$491$	21.4265	0.966964	0.483482	−	0.875354i	$-0.339372\pi$
$491$	21.4265	0.966964	0.483482	+	0.875354i	$0.339372\pi$
$492$	−1.60952	−0.0725628
$493$	64.1059	2.88719
$494$	1.90711	0.0858050
$495$	0	0
$496$	8.67912	0.389704
$497$	−1.78349	−0.0800003
$498$	40.2910	1.80548
$499$	−38.7484	−1.73462	−0.867308	−	0.497772i	$-0.834152\pi$
$499$	−38.7484	−1.73462	−0.867308	+	0.497772i	$0.834152\pi$
$500$	30.5365	1.36563
$501$	12.6054	0.563168
$502$	−6.59380	−0.294296
$503$	−9.68221	−0.431708	−0.215854	−	0.976426i	$-0.569254\pi$
$503$	−9.68221	−0.431708	−0.215854	+	0.976426i	$0.569254\pi$
$504$	−14.6191	−0.651187
$505$	−12.3732	−0.550599
$506$	0	0
$507$	−5.26807	−0.233963
$508$	31.6038	1.40219
$509$	6.38700	0.283099	0.141549	−	0.989931i	$-0.454792\pi$
$509$	6.38700	0.283099	0.141549	+	0.989931i	$0.454792\pi$
$510$	−84.8306	−3.75636
$511$	−20.7980	−0.920051
$512$	−27.2751	−1.20540
$513$	−2.72477	−0.120302
$514$	−49.5946	−2.18753
$515$	−34.1912	−1.50664
$516$	−28.9341	−1.27375
$517$	0	0
$518$	−4.43647	−0.194927
$519$	−1.10729	−0.0486046
$520$	7.14062	0.313137
$521$	1.72590	0.0756129	0.0378065	−	0.999285i	$-0.487963\pi$
$521$	1.72590	0.0756129	0.0378065	+	0.999285i	$0.487963\pi$
$522$	127.263	5.57013
$523$	−1.96843	−0.0860736	−0.0430368	−	0.999073i	$-0.513703\pi$
$523$	−1.96843	−0.0860736	−0.0430368	+	0.999073i	$0.513703\pi$
$524$	17.7503	0.775427
$525$	−8.28392	−0.361540
$526$	−45.6790	−1.99170
$527$	21.9007	0.954009
$528$	0	0
$529$	−1.26520	−0.0550088
$530$	11.2466	0.488521
$531$	−5.79295	−0.251392
$532$	−1.40473	−0.0609026
$533$	−0.701881	−0.0304018
$534$	59.2067	2.56212
$535$	1.16254	0.0502610
$536$	−3.78895	−0.163658
$537$	−18.2514	−0.787607
$538$	−54.8536	−2.36491
$539$	0	0
$540$	−49.4469	−2.12786
$541$	−6.73387	−0.289512	−0.144756	−	0.989467i	$-0.546240\pi$
$541$	−6.73387	−0.289512	−0.144756	+	0.989467i	$0.546240\pi$
$542$	48.3477	2.07671
$543$	15.1448	0.649926
$544$	−53.8202	−2.30752
$545$	−33.9727	−1.45523
$546$	−45.5240	−1.94825
$547$	19.7548	0.844656	0.422328	−	0.906443i	$-0.361213\pi$
$547$	19.7548	0.844656	0.422328	+	0.906443i	$0.361213\pi$
$548$	−36.6352	−1.56498
$549$	−83.5603	−3.56626
$550$	0	0
$551$	2.52303	0.107485
$552$	15.7473	0.670249
$553$	−28.4902	−1.21153
$554$	−5.95592	−0.253043
$555$	−5.87867	−0.249536
$556$	47.1203	1.99835
$557$	37.2839	1.57977	0.789885	−	0.613255i	$-0.210140\pi$
$557$	37.2839	1.57977	0.789885	+	0.613255i	$0.210140\pi$
$558$	43.4771	1.84053
$559$	−12.6176	−0.533668
$560$	10.7982	0.456308
$561$	0	0
$562$	−31.4113	−1.32501
$563$	−29.9539	−1.26241	−0.631204	−	0.775617i	$-0.717439\pi$
$563$	−29.9539	−1.26241	−0.631204	+	0.775617i	$0.717439\pi$
$564$	−86.3717	−3.63691
$565$	20.4926	0.862128
$566$	−32.9524	−1.38509
$567$	25.3651	1.06524
$568$	0.944715	0.0396394
$569$	−38.5030	−1.61413	−0.807065	−	0.590462i	$-0.798946\pi$
$569$	−38.5030	−1.61413	−0.807065	+	0.590462i	$0.798946\pi$
$570$	−3.33869	−0.139843
$571$	12.3146	0.515352	0.257676	−	0.966231i	$-0.417043\pi$
$571$	12.3146	0.515352	0.257676	+	0.966231i	$0.417043\pi$
$572$	0	0
$573$	61.5551	2.57150
$574$	0.927305	0.0387050
$575$	6.05643	0.252571
$576$	−72.7476	−3.03115
$577$	28.5802	1.18981	0.594905	−	0.803796i	$-0.297190\pi$
$577$	28.5802	1.18981	0.594905	+	0.803796i	$0.297190\pi$
$578$	−61.8028	−2.57066
$579$	−68.7248	−2.85610
$580$	45.7859	1.90115
$581$	−12.9417	−0.536910
$582$	−76.2986	−3.16268
$583$	0	0
$584$	11.0168	0.455876
$585$	−40.9428	−1.69278
$586$	−1.93630	−0.0799880
$587$	33.2549	1.37258	0.686289	−	0.727329i	$-0.259238\pi$
$587$	33.2549	1.37258	0.686289	+	0.727329i	$0.259238\pi$
$588$	−20.3709	−0.840081
$589$	0.861949	0.0355160
$590$	−3.73830	−0.153903
$591$	60.8658	2.50368
$592$	−2.68984	−0.110552
$593$	−23.9716	−0.984396	−0.492198	−	0.870483i	$-0.663806\pi$
$593$	−23.9716	−0.984396	−0.492198	+	0.870483i	$0.663806\pi$
$594$	0	0
$595$	27.2480	1.11706
$596$	22.0796	0.904414
$597$	−84.9018	−3.47480
$598$	33.2829	1.36104
$599$	−12.2965	−0.502419	−0.251210	−	0.967933i	$-0.580828\pi$
$599$	−12.2965	−0.502419	−0.251210	+	0.967933i	$0.580828\pi$
$600$	4.38801	0.179140
$601$	2.67070	0.108940	0.0544701	−	0.998515i	$-0.482653\pi$
$601$	2.67070	0.108940	0.0544701	+	0.998515i	$0.482653\pi$
$602$	16.6700	0.679420
$603$	21.7250	0.884712
$604$	−22.7706	−0.926524
$605$	0	0
$606$	−41.7847	−1.69739
$607$	15.4519	0.627173	0.313586	−	0.949560i	$-0.398469\pi$
$607$	15.4519	0.627173	0.313586	+	0.949560i	$0.398469\pi$
$608$	−2.11821	−0.0859049
$609$	−60.2264	−2.44050
$610$	−53.9230	−2.18328
$611$	−37.6650	−1.52376
$612$	−108.403	−4.38193
$613$	15.9922	0.645921	0.322960	−	0.946412i	$-0.395322\pi$
$613$	15.9922	0.645921	0.322960	+	0.946412i	$0.395322\pi$
$614$	5.57234	0.224881
$615$	1.22875	0.0495480
$616$	0	0
$617$	17.2120	0.692931	0.346466	−	0.938063i	$-0.387382\pi$
$617$	17.2120	0.692931	0.346466	+	0.938063i	$0.387382\pi$
$618$	−115.465	−4.64468
$619$	26.1156	1.04967	0.524836	−	0.851203i	$-0.324126\pi$
$619$	26.1156	1.04967	0.524836	+	0.851203i	$0.324126\pi$
$620$	15.6419	0.628196
$621$	−47.5528	−1.90823
$622$	45.8609	1.83885
$623$	−19.0175	−0.761919
$624$	−27.6013	−1.10494
$625$	−16.8169	−0.672677
$626$	−33.4117	−1.33540
$627$	0	0
$628$	29.6870	1.18464
$629$	−6.78748	−0.270634
$630$	54.0925	2.15510
$631$	41.1080	1.63648	0.818241	−	0.574875i	$-0.194949\pi$
$631$	41.1080	1.63648	0.818241	+	0.574875i	$0.194949\pi$
$632$	15.0913	0.600299
$633$	39.6141	1.57452
$634$	−2.24960	−0.0893432
$635$	−24.1272	−0.957459
$636$	21.1745	0.839623
$637$	−8.88334	−0.351971
$638$	0	0
$639$	−5.41680	−0.214285
$640$	−16.4369	−0.649725
$641$	−34.8883	−1.37801	−0.689003	−	0.724759i	$-0.741951\pi$
$641$	−34.8883	−1.37801	−0.689003	+	0.724759i	$0.741951\pi$
$642$	3.92594	0.154944
$643$	−10.3654	−0.408773	−0.204387	−	0.978890i	$-0.565520\pi$
$643$	−10.3654	−0.408773	−0.204387	+	0.978890i	$0.565520\pi$
$644$	−24.5153	−0.966038
$645$	22.0891	0.869757
$646$	−3.85484	−0.151667
$647$	44.0522	1.73187	0.865936	−	0.500155i	$-0.166724\pi$
$647$	44.0522	1.73187	0.865936	+	0.500155i	$0.166724\pi$
$648$	−13.4359	−0.527814
$649$	0	0
$650$	9.27434	0.363769
$651$	−20.5753	−0.806409
$652$	−1.30677	−0.0511771
$653$	20.0366	0.784093	0.392046	−	0.919945i	$-0.371767\pi$
$653$	20.0366	0.784093	0.392046	+	0.919945i	$0.371767\pi$
$654$	−114.727	−4.48618
$655$	−13.5511	−0.529484
$656$	0.562226	0.0219513
$657$	−63.1678	−2.46441
$658$	49.7620	1.93992
$659$	−25.6086	−0.997570	−0.498785	−	0.866726i	$-0.666220\pi$
$659$	−25.6086	−0.997570	−0.498785	+	0.866726i	$0.666220\pi$
$660$	0	0
$661$	−10.9122	−0.424434	−0.212217	−	0.977223i	$-0.568068\pi$
$661$	−10.9122	−0.424434	−0.212217	+	0.977223i	$0.568068\pi$
$662$	−52.5400	−2.04202
$663$	−69.6484	−2.70492
$664$	6.85521	0.266034
$665$	1.07240	0.0415861
$666$	−13.4744	−0.522124
$667$	44.0319	1.70492
$668$	10.3949	0.402190
$669$	14.7726	0.571144
$670$	14.0196	0.541623
$671$	0	0
$672$	50.5631	1.95052
$673$	9.42551	0.363327	0.181663	−	0.983361i	$-0.441852\pi$
$673$	9.42551	0.363327	0.181663	+	0.983361i	$0.441852\pi$
$674$	−35.5451	−1.36915
$675$	−13.2506	−0.510018
$676$	−4.34424	−0.167086
$677$	−19.9013	−0.764870	−0.382435	−	0.923982i	$-0.624914\pi$
$677$	−19.9013	−0.764870	−0.382435	+	0.923982i	$0.624914\pi$
$678$	69.2041	2.65777
$679$	24.5075	0.940510
$680$	−14.4333	−0.553492
$681$	−24.8246	−0.951282
$682$	0	0
$683$	−42.0283	−1.60817	−0.804084	−	0.594515i	$-0.797344\pi$
$683$	−42.0283	−1.60817	−0.804084	+	0.594515i	$0.797344\pi$
$684$	−4.26643	−0.163131
$685$	27.9683	1.06861
$686$	42.7917	1.63380
$687$	−8.11566	−0.309632
$688$	10.1071	0.385328
$689$	9.23378	0.351779
$690$	−58.2669	−2.21818
$691$	28.7121	1.09226	0.546130	−	0.837700i	$-0.316100\pi$
$691$	28.7121	1.09226	0.546130	+	0.837700i	$0.316100\pi$
$692$	−0.913112	−0.0347113
$693$	0	0
$694$	−49.6743	−1.88561
$695$	−35.9729	−1.36453
$696$	31.9020	1.20924
$697$	1.41871	0.0537374
$698$	63.0196	2.38533
$699$	−23.8249	−0.901141
$700$	−6.83122	−0.258196
$701$	−3.74884	−0.141592	−0.0707959	−	0.997491i	$-0.522554\pi$
$701$	−3.74884	−0.141592	−0.0707959	+	0.997491i	$0.522554\pi$
$702$	−72.8185	−2.74836
$703$	−0.267136	−0.0100752
$704$	0	0
$705$	65.9385	2.48339
$706$	24.0137	0.903767
$707$	13.4214	0.504765
$708$	−7.03827	−0.264514
$709$	−36.0268	−1.35302	−0.676508	−	0.736436i	$-0.736507\pi$
$709$	−36.0268	−1.35302	−0.676508	+	0.736436i	$0.736507\pi$
$710$	−3.49556	−0.131186
$711$	−86.5303	−3.24514
$712$	10.0736	0.377523
$713$	15.0427	0.563355
$714$	92.0175	3.44367
$715$	0	0
$716$	−15.0508	−0.562474
$717$	−18.4611	−0.689443
$718$	−30.1561	−1.12541
$719$	20.3249	0.757992	0.378996	−	0.925398i	$-0.376269\pi$
$719$	20.3249	0.757992	0.378996	+	0.925398i	$0.376269\pi$
$720$	32.7964	1.22225
$721$	37.0879	1.38123
$722$	40.2425	1.49767
$723$	48.8354	1.81621
$724$	12.4890	0.464149
$725$	12.2696	0.455680
$726$	0	0
$727$	−33.0084	−1.22422	−0.612108	−	0.790774i	$-0.709678\pi$
$727$	−33.0084	−1.22422	−0.612108	+	0.790774i	$0.709678\pi$
$728$	−7.74558	−0.287070
$729$	−16.4680	−0.609926
$730$	−40.7634	−1.50872
$731$	25.5039	0.943297
$732$	−101.523	−3.75241
$733$	−20.6847	−0.764008	−0.382004	−	0.924161i	$-0.624766\pi$
$733$	−20.6847	−0.764008	−0.382004	+	0.924161i	$0.624766\pi$
$734$	29.7397	1.09771
$735$	15.5517	0.573632
$736$	−36.9671	−1.36262
$737$	0	0
$738$	2.81641	0.103674
$739$	26.4355	0.972446	0.486223	−	0.873835i	$-0.338374\pi$
$739$	26.4355	0.972446	0.486223	+	0.873835i	$0.338374\pi$
$740$	−4.84776	−0.178207
$741$	−2.74117	−0.100699
$742$	−12.1994	−0.447855
$743$	4.74696	0.174149	0.0870745	−	0.996202i	$-0.472248\pi$
$743$	4.74696	0.174149	0.0870745	+	0.996202i	$0.472248\pi$
$744$	10.8988	0.399568
$745$	−16.8561	−0.617560
$746$	44.5164	1.62986
$747$	−39.3064	−1.43814
$748$	0	0
$749$	−1.26103	−0.0460770
$750$	−78.7267	−2.87469
$751$	7.84002	0.286087	0.143043	−	0.989716i	$-0.454311\pi$
$751$	7.84002	0.286087	0.143043	+	0.989716i	$0.454311\pi$
$752$	30.1708	1.10021
$753$	9.47753	0.345380
$754$	67.4270	2.45555
$755$	17.3837	0.632658
$756$	53.6361	1.95073
$757$	2.28648	0.0831035	0.0415517	−	0.999136i	$-0.486770\pi$
$757$	2.28648	0.0831035	0.0415517	+	0.999136i	$0.486770\pi$
$758$	63.1957	2.29537
$759$	0	0
$760$	−0.568055	−0.0206055
$761$	−36.3530	−1.31779	−0.658897	−	0.752233i	$-0.728977\pi$
$761$	−36.3530	−1.31779	−0.658897	+	0.752233i	$0.728977\pi$
$762$	−81.4784	−2.95165
$763$	36.8509	1.33409
$764$	50.7606	1.83645
$765$	82.7576	2.99211
$766$	−16.8474	−0.608722
$767$	−3.06925	−0.110824
$768$	14.6421	0.528352
$769$	−26.8095	−0.966775	−0.483388	−	0.875406i	$-0.660594\pi$
$769$	−26.8095	−0.966775	−0.483388	+	0.875406i	$0.660594\pi$
$770$	0	0
$771$	71.2843	2.56724
$772$	−56.6729	−2.03970
$773$	−36.4425	−1.31074	−0.655372	−	0.755306i	$-0.727488\pi$
$773$	−36.4425	−1.31074	−0.655372	+	0.755306i	$0.727488\pi$
$774$	50.6302	1.81987
$775$	4.19168	0.150570
$776$	−12.9816	−0.466014
$777$	6.37671	0.228763
$778$	59.3232	2.12684
$779$	0.0558364	0.00200055
$780$	−49.7444	−1.78114
$781$	0	0
$782$	−67.2747	−2.40574
$783$	−96.3359	−3.44276
$784$	7.11581	0.254136
$785$	−22.6638	−0.808907
$786$	−45.7625	−1.63229
$787$	−0.944598	−0.0336713	−0.0168356	−	0.999858i	$-0.505359\pi$
$787$	−0.944598	−0.0336713	−0.0168356	+	0.999858i	$0.505359\pi$
$788$	50.1921	1.78802
$789$	65.6562	2.33742
$790$	−55.8396	−1.98669
$791$	−22.2287	−0.790362
$792$	0	0
$793$	−44.2724	−1.57216
$794$	49.8467	1.76899
$795$	−16.1652	−0.573319
$796$	−70.0131	−2.48155
$797$	−7.04884	−0.249683	−0.124841	−	0.992177i	$-0.539842\pi$
$797$	−7.04884	−0.249683	−0.124841	+	0.992177i	$0.539842\pi$
$798$	3.62155	0.128202
$799$	76.1322	2.69336
$800$	−10.3009	−0.364193
$801$	−57.7598	−2.04084
$802$	24.8434	0.877252
$803$	0	0
$804$	26.3953	0.930890
$805$	18.7156	0.659639
$806$	23.0353	0.811382
$807$	78.8433	2.77541
$808$	−7.10936	−0.250106
$809$	−3.60812	−0.126855	−0.0634274	−	0.997986i	$-0.520203\pi$
$809$	−3.60812	−0.126855	−0.0634274	+	0.997986i	$0.520203\pi$
$810$	49.7147	1.74680
$811$	−27.7320	−0.973802	−0.486901	−	0.873457i	$-0.661873\pi$
$811$	−27.7320	−0.973802	−0.486901	+	0.873457i	$0.661873\pi$
$812$	−49.6649	−1.74289
$813$	−69.4920	−2.43719
$814$	0	0
$815$	0.997623	0.0349452
$816$	55.7903	1.95305
$817$	1.00376	0.0351172
$818$	67.8008	2.37060
$819$	44.4115	1.55186
$820$	1.01327	0.0353850
$821$	6.23573	0.217628	0.108814	−	0.994062i	$-0.465295\pi$
$821$	6.23573	0.217628	0.108814	+	0.994062i	$0.465295\pi$
$822$	94.4499	3.29432
$823$	−51.8846	−1.80858	−0.904292	−	0.426914i	$-0.859601\pi$
$823$	−51.8846	−1.80858	−0.904292	+	0.426914i	$0.859601\pi$
$824$	−19.6455	−0.684384
$825$	0	0
$826$	4.05501	0.141092
$827$	31.1839	1.08437	0.542185	−	0.840259i	$-0.317597\pi$
$827$	31.1839	1.08437	0.542185	+	0.840259i	$0.317597\pi$
$828$	−74.4578	−2.58759
$829$	−11.3360	−0.393715	−0.196858	−	0.980432i	$-0.563074\pi$
$829$	−11.3360	−0.393715	−0.196858	+	0.980432i	$0.563074\pi$
$830$	−25.3651	−0.880437
$831$	8.56068	0.296967
$832$	−38.5436	−1.33626
$833$	17.9559	0.622134
$834$	−121.482	−4.20657
$835$	−7.93572	−0.274627
$836$	0	0
$837$	−32.9115	−1.13759
$838$	−11.9083	−0.411365
$839$	−16.6723	−0.575593	−0.287796	−	0.957692i	$-0.592923\pi$
$839$	−16.6723	−0.575593	−0.287796	+	0.957692i	$0.592923\pi$
$840$	13.5598	0.467859
$841$	60.2031	2.07597
$842$	−57.1904	−1.97091
$843$	45.1487	1.55500
$844$	32.6672	1.12445
$845$	3.31651	0.114091
$846$	151.137	5.19620
$847$	0	0
$848$	−7.39652	−0.253998
$849$	47.3637	1.62552
$850$	−18.7462	−0.642989
$851$	−4.66206	−0.159813
$852$	−6.58126	−0.225470
$853$	18.3944	0.629814	0.314907	−	0.949123i	$-0.398027\pi$
$853$	18.3944	0.629814	0.314907	+	0.949123i	$0.398027\pi$
$854$	58.4914	2.00153
$855$	3.25711	0.111391
$856$	0.667970	0.0228307
$857$	3.58503	0.122462	0.0612312	−	0.998124i	$-0.480497\pi$
$857$	3.58503	0.122462	0.0612312	+	0.998124i	$0.480497\pi$
$858$	0	0
$859$	20.5747	0.702001	0.351001	−	0.936375i	$-0.385842\pi$
$859$	20.5747	0.702001	0.351001	+	0.936375i	$0.385842\pi$
$860$	18.2155	0.621142
$861$	−1.33285	−0.0454235
$862$	79.9723	2.72387
$863$	30.2180	1.02863	0.514316	−	0.857601i	$-0.328046\pi$
$863$	30.2180	1.02863	0.514316	+	0.857601i	$0.328046\pi$
$864$	80.8789	2.75156
$865$	0.697094	0.0237019
$866$	−65.9572	−2.24132
$867$	88.8315	3.01688
$868$	−16.9671	−0.575902
$869$	0	0
$870$	−118.041	−4.00198
$871$	11.5105	0.390018
$872$	−19.5200	−0.661030
$873$	74.4341	2.51921
$874$	−2.64774	−0.0895612
$875$	25.2874	0.854870
$876$	−76.7471	−2.59304
$877$	−11.6760	−0.394271	−0.197136	−	0.980376i	$-0.563164\pi$
$877$	−11.6760	−0.394271	−0.197136	+	0.980376i	$0.563164\pi$
$878$	−8.53313	−0.287979
$879$	2.78313	0.0938725
$880$	0	0
$881$	−15.7736	−0.531427	−0.265714	−	0.964052i	$-0.585608\pi$
$881$	−15.7736	−0.531427	−0.265714	+	0.964052i	$0.585608\pi$
$882$	35.6458	1.20026
$883$	43.8740	1.47648	0.738238	−	0.674540i	$-0.235658\pi$
$883$	43.8740	1.47648	0.738238	+	0.674540i	$0.235658\pi$
$884$	−57.4346	−1.93173
$885$	5.37320	0.180618
$886$	50.3125	1.69028
$887$	−19.4896	−0.654398	−0.327199	−	0.944955i	$-0.606105\pi$
$887$	−19.4896	−0.654398	−0.327199	+	0.944955i	$0.606105\pi$
$888$	−3.37775	−0.113350
$889$	26.1713	0.877756
$890$	−37.2735	−1.24941
$891$	0	0
$892$	12.1821	0.407886
$893$	2.99635	0.100269
$894$	−56.9237	−1.90381
$895$	11.4902	0.384074
$896$	17.8294	0.595639
$897$	−47.8389	−1.59729
$898$	21.5867	0.720357
$899$	30.4747	1.01639
$900$	−20.7478	−0.691593
$901$	−18.6642	−0.621795
$902$	0	0
$903$	−23.9605	−0.797355
$904$	11.7746	0.391617
$905$	−9.53440	−0.316934
$906$	58.7054	1.95036
$907$	−21.6115	−0.717599	−0.358799	−	0.933415i	$-0.616814\pi$
$907$	−21.6115	−0.717599	−0.358799	+	0.933415i	$0.616814\pi$
$908$	−20.4713	−0.679364
$909$	40.7636	1.35204
$910$	28.6596	0.950057
$911$	13.6899	0.453567	0.226784	−	0.973945i	$-0.427179\pi$
$911$	13.6899	0.453567	0.226784	+	0.973945i	$0.427179\pi$
$912$	2.19575	0.0727086
$913$	0	0
$914$	74.0297	2.44869
$915$	77.5056	2.56226
$916$	−6.69247	−0.221125
$917$	14.6991	0.485408
$918$	147.188	4.85792
$919$	21.4138	0.706375	0.353187	−	0.935553i	$-0.385098\pi$
$919$	21.4138	0.706375	0.353187	+	0.935553i	$0.385098\pi$
$920$	−9.91369	−0.326845
$921$	−8.00934	−0.263917
$922$	−41.1383	−1.35482
$923$	−2.86996	−0.0944659
$924$	0	0
$925$	−1.29909	−0.0427138
$926$	12.3350	0.405352
$927$	112.643	3.69969
$928$	−74.8906	−2.45840
$929$	−30.3444	−0.995567	−0.497784	−	0.867301i	$-0.665853\pi$
$929$	−30.3444	−0.995567	−0.497784	+	0.867301i	$0.665853\pi$
$930$	−40.3268	−1.32237
$931$	0.706692	0.0231609
$932$	−19.6469	−0.643555
$933$	−65.9177	−2.15805
$934$	79.1605	2.59021
$935$	0	0
$936$	−23.5249	−0.768934
$937$	−8.51073	−0.278034	−0.139017	−	0.990290i	$-0.544394\pi$
$937$	−8.51073	−0.278034	−0.139017	+	0.990290i	$0.544394\pi$
$938$	−15.2073	−0.496536
$939$	48.0239	1.56720
$940$	54.3753	1.77353
$941$	−28.8295	−0.939816	−0.469908	−	0.882715i	$-0.655713\pi$
$941$	−28.8295	−0.939816	−0.469908	+	0.882715i	$0.655713\pi$
$942$	−76.5366	−2.49370
$943$	0.974458	0.0317327
$944$	2.45856	0.0800192
$945$	−40.9472	−1.33201
$946$	0	0
$947$	13.0404	0.423756	0.211878	−	0.977296i	$-0.432042\pi$
$947$	13.0404	0.423756	0.211878	+	0.977296i	$0.432042\pi$
$948$	−105.132	−3.41453
$949$	−33.4679	−1.08641
$950$	−0.737797	−0.0239373
$951$	3.23344	0.104852
$952$	15.6561	0.507417
$953$	−35.9090	−1.16321	−0.581603	−	0.813473i	$-0.697574\pi$
$953$	−35.9090	−1.16321	−0.581603	+	0.813473i	$0.697574\pi$
$954$	−37.0520	−1.19960
$955$	−38.7520	−1.25399
$956$	−15.2237	−0.492370
$957$	0	0
$958$	−3.40240	−0.109927
$959$	−30.3378	−0.979658
$960$	67.4765	2.17779
$961$	−20.5888	−0.664156
$962$	−7.13911	−0.230174
$963$	−3.83000	−0.123420
$964$	40.2714	1.29705
$965$	43.2656	1.39277
$966$	63.2033	2.03353
$967$	−0.668271	−0.0214902	−0.0107451	−	0.999942i	$-0.503420\pi$
$967$	−0.668271	−0.0214902	−0.0107451	+	0.999942i	$0.503420\pi$
$968$	0	0
$969$	5.54071	0.177993
$970$	48.0337	1.54227
$971$	14.8373	0.476150	0.238075	−	0.971247i	$-0.423484\pi$
$971$	14.8373	0.476150	0.238075	+	0.971247i	$0.423484\pi$
$972$	16.4910	0.528948
$973$	39.0205	1.25094
$974$	−53.4291	−1.71198
$975$	−13.3304	−0.426913
$976$	35.4634	1.13516
$977$	−16.0924	−0.514840	−0.257420	−	0.966300i	$-0.582872\pi$
$977$	−16.0924	−0.514840	−0.257420	+	0.966300i	$0.582872\pi$
$978$	3.36901	0.107729
$979$	0	0
$980$	12.8245	0.409663
$981$	111.924	3.57344
$982$	−45.5530	−1.45365
$983$	−12.6587	−0.403749	−0.201875	−	0.979411i	$-0.564703\pi$
$983$	−12.6587	−0.403749	−0.201875	+	0.979411i	$0.564703\pi$
$984$	0.706014	0.0225069
$985$	−38.3180	−1.22091
$986$	−136.290	−4.34036
$987$	−71.5248	−2.27666
$988$	−2.26046	−0.0719150
$989$	17.5177	0.557030
$990$	0	0
$991$	10.3785	0.329685	0.164843	−	0.986320i	$-0.447288\pi$
$991$	10.3785	0.329685	0.164843	+	0.986320i	$0.447288\pi$
$992$	−25.5851	−0.812327
$993$	75.5177	2.39648
$994$	3.79171	0.120266
$995$	53.4499	1.69447
$996$	−47.7561	−1.51321
$997$	−14.3188	−0.453482	−0.226741	−	0.973955i	$-0.572807\pi$
$997$	−14.3188	−0.453482	−0.226741	+	0.973955i	$0.572807\pi$
$998$	82.3795	2.60768
$999$	10.1999	0.322712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4477.2.a.k.1.2		11
11.10	odd	2		407.2.a.c.1.10	✓	11
33.32	even	2		3663.2.a.u.1.2		11
44.43	even	2		6512.2.a.bb.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
407.2.a.c.1.10	✓	11	11.10	odd	2
3663.2.a.u.1.2		11	33.32	even	2
4477.2.a.k.1.2		11	1.1	even	1	trivial
6512.2.a.bb.1.1		11	44.43	even	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:	\( N \)	\(=\)	\( 4477 = 11^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4477.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12601 q^{2} +3.05580 q^{3} +2.51992 q^{4} -1.92378 q^{5} -6.49666 q^{6} +2.08676 q^{7} -1.10536 q^{8} +6.33790 q^{9} +O(q^{10})\)	\(q-2.12601 q^{2} +3.05580 q^{3} +2.51992 q^{4} -1.92378 q^{5} -6.49666 q^{6} +2.08676 q^{7} -1.10536 q^{8} +6.33790 q^{9} +4.08997 q^{10} +7.70037 q^{12} +3.35798 q^{13} -4.43647 q^{14} -5.87867 q^{15} -2.68984 q^{16} -6.78748 q^{17} -13.4744 q^{18} -0.267136 q^{19} -4.84776 q^{20} +6.37671 q^{21} -4.66206 q^{23} -3.37775 q^{24} -1.29909 q^{25} -7.13911 q^{26} +10.1999 q^{27} +5.25847 q^{28} -9.44474 q^{29} +12.4981 q^{30} -3.22663 q^{31} +7.92934 q^{32} +14.4302 q^{34} -4.01445 q^{35} +15.9710 q^{36} +1.00000 q^{37} +0.567934 q^{38} +10.2613 q^{39} +2.12646 q^{40} -0.209019 q^{41} -13.5570 q^{42} -3.75750 q^{43} -12.1927 q^{45} +9.91159 q^{46} -11.2166 q^{47} -8.21960 q^{48} -2.64544 q^{49} +2.76188 q^{50} -20.7412 q^{51} +8.46185 q^{52} +2.74980 q^{53} -21.6852 q^{54} -2.30662 q^{56} -0.816313 q^{57} +20.0796 q^{58} -0.914017 q^{59} -14.8138 q^{60} -13.1842 q^{61} +6.85985 q^{62} +13.2257 q^{63} -11.4782 q^{64} -6.46000 q^{65} +3.42780 q^{67} -17.1039 q^{68} -14.2463 q^{69} +8.53477 q^{70} -0.854668 q^{71} -7.00566 q^{72} -9.96667 q^{73} -2.12601 q^{74} -3.96976 q^{75} -0.673162 q^{76} -21.8157 q^{78} -13.6528 q^{79} +5.17464 q^{80} +12.1553 q^{81} +0.444376 q^{82} -6.20180 q^{83} +16.0688 q^{84} +13.0576 q^{85} +7.98848 q^{86} -28.8612 q^{87} -9.11340 q^{89} +25.9218 q^{90} +7.00730 q^{91} -11.7480 q^{92} -9.85993 q^{93} +23.8465 q^{94} +0.513909 q^{95} +24.2305 q^{96} +11.7443 q^{97} +5.62423 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} + 14 q^{4} + q^{5} - 4 q^{6} - 9 q^{7} + 15 q^{9}+O(q^{10}) \) 11 * q - 2 * q^2 + 14 * q^4 + q^5 - 4 * q^6 - 9 * q^7 + 15 * q^9	\( 11 q - 2 q^{2} + 14 q^{4} + q^{5} - 4 q^{6} - 9 q^{7} + 15 q^{9} - 5 q^{10} + q^{12} - 22 q^{13} + 3 q^{14} - 10 q^{15} - 19 q^{17} - 18 q^{18} - 14 q^{19} + 6 q^{20} + 13 q^{21} - 14 q^{23} + 11 q^{24} + 38 q^{25} - 10 q^{26} - 9 q^{27} - q^{28} - 13 q^{29} - 19 q^{30} + 12 q^{31} + 3 q^{32} + q^{34} - 12 q^{35} + 18 q^{36} + 11 q^{37} - 31 q^{38} + 8 q^{39} - 22 q^{40} - 8 q^{41} + 15 q^{42} - 21 q^{43} - 8 q^{45} + 45 q^{46} - 14 q^{47} - 37 q^{48} + 20 q^{49} + 41 q^{50} + 2 q^{51} - 51 q^{52} - 2 q^{53} - 6 q^{54} - 22 q^{56} + 3 q^{57} + 15 q^{58} - 30 q^{59} - 107 q^{60} - 20 q^{61} - 22 q^{62} - 31 q^{63} - 14 q^{64} + 7 q^{67} - 24 q^{68} + 9 q^{69} - 86 q^{70} - 15 q^{71} + 7 q^{72} - 47 q^{73} - 2 q^{74} - 40 q^{75} - 6 q^{76} - 42 q^{78} - 2 q^{79} + 3 q^{80} - 17 q^{81} - 54 q^{82} - 24 q^{83} + 33 q^{84} + 25 q^{85} - 13 q^{86} - 21 q^{87} + 4 q^{89} + 107 q^{90} + 21 q^{91} - 46 q^{92} - 37 q^{93} - 3 q^{94} + 36 q^{95} + 49 q^{96} + 25 q^{97} + 52 q^{98}+O(q^{100}) \) 11 * q - 2 * q^2 + 14 * q^4 + q^5 - 4 * q^6 - 9 * q^7 + 15 * q^9 - 5 * q^10 + q^12 - 22 * q^13 + 3 * q^14 - 10 * q^15 - 19 * q^17 - 18 * q^18 - 14 * q^19 + 6 * q^20 + 13 * q^21 - 14 * q^23 + 11 * q^24 + 38 * q^25 - 10 * q^26 - 9 * q^27 - q^28 - 13 * q^29 - 19 * q^30 + 12 * q^31 + 3 * q^32 + q^34 - 12 * q^35 + 18 * q^36 + 11 * q^37 - 31 * q^38 + 8 * q^39 - 22 * q^40 - 8 * q^41 + 15 * q^42 - 21 * q^43 - 8 * q^45 + 45 * q^46 - 14 * q^47 - 37 * q^48 + 20 * q^49 + 41 * q^50 + 2 * q^51 - 51 * q^52 - 2 * q^53 - 6 * q^54 - 22 * q^56 + 3 * q^57 + 15 * q^58 - 30 * q^59 - 107 * q^60 - 20 * q^61 - 22 * q^62 - 31 * q^63 - 14 * q^64 + 7 * q^67 - 24 * q^68 + 9 * q^69 - 86 * q^70 - 15 * q^71 + 7 * q^72 - 47 * q^73 - 2 * q^74 - 40 * q^75 - 6 * q^76 - 42 * q^78 - 2 * q^79 + 3 * q^80 - 17 * q^81 - 54 * q^82 - 24 * q^83 + 33 * q^84 + 25 * q^85 - 13 * q^86 - 21 * q^87 + 4 * q^89 + 107 * q^90 + 21 * q^91 - 46 * q^92 - 37 * q^93 - 3 * q^94 + 36 * q^95 + 49 * q^96 + 25 * q^97 + 52 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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