LMFDB - Embedded newform 5915.2.a.bp.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5915,2,Mod(1,5915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5915, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5915.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5915 = 5 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5915.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:	$47.2315127956$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	5915.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.37365 q^{2} +1.75471 q^{3} -0.113079 q^{4} +1.00000 q^{5} +2.41036 q^{6} +1.00000 q^{7} -2.90264 q^{8} +0.0789971 q^{9} +O(q^{10})$	\(q+1.37365 q^{2} +1.75471 q^{3} -0.113079 q^{4} +1.00000 q^{5} +2.41036 q^{6} +1.00000 q^{7} -2.90264 q^{8} +0.0789971 q^{9} +1.37365 q^{10} +2.75740 q^{11} -0.198421 q^{12} +1.37365 q^{14} +1.75471 q^{15} -3.76106 q^{16} +2.28419 q^{17} +0.108514 q^{18} +1.32904 q^{19} -0.113079 q^{20} +1.75471 q^{21} +3.78771 q^{22} +5.27011 q^{23} -5.09328 q^{24} +1.00000 q^{25} -5.12550 q^{27} -0.113079 q^{28} +7.06407 q^{29} +2.41036 q^{30} +5.25679 q^{31} +0.638890 q^{32} +4.83843 q^{33} +3.13769 q^{34} +1.00000 q^{35} -0.00893291 q^{36} -8.65483 q^{37} +1.82563 q^{38} -2.90264 q^{40} +7.90714 q^{41} +2.41036 q^{42} -0.261578 q^{43} -0.311804 q^{44} +0.0789971 q^{45} +7.23930 q^{46} -6.58603 q^{47} -6.59955 q^{48} +1.00000 q^{49} +1.37365 q^{50} +4.00809 q^{51} -4.00433 q^{53} -7.04066 q^{54} +2.75740 q^{55} -2.90264 q^{56} +2.33207 q^{57} +9.70358 q^{58} +0.940809 q^{59} -0.198421 q^{60} +2.81745 q^{61} +7.22100 q^{62} +0.0789971 q^{63} +8.39972 q^{64} +6.64632 q^{66} -8.74905 q^{67} -0.258294 q^{68} +9.24750 q^{69} +1.37365 q^{70} +13.1114 q^{71} -0.229300 q^{72} -11.4914 q^{73} -11.8887 q^{74} +1.75471 q^{75} -0.150286 q^{76} +2.75740 q^{77} -4.11077 q^{79} -3.76106 q^{80} -9.23075 q^{81} +10.8617 q^{82} +12.2159 q^{83} -0.198421 q^{84} +2.28419 q^{85} -0.359317 q^{86} +12.3954 q^{87} -8.00373 q^{88} +11.3673 q^{89} +0.108514 q^{90} -0.595939 q^{92} +9.22412 q^{93} -9.04692 q^{94} +1.32904 q^{95} +1.12106 q^{96} -0.589588 q^{97} +1.37365 q^{98} +0.217827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9}+O(q^{10}) $ 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9	\( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9} + 4 q^{10} + 2 q^{11} + 23 q^{12} + 4 q^{14} + 5 q^{15} + 18 q^{16} - 6 q^{17} + 32 q^{18} + 8 q^{19} + 20 q^{20} + 5 q^{21} - 17 q^{22} - 14 q^{23} + 27 q^{24} + 21 q^{25} + 11 q^{27} + 20 q^{28} + 20 q^{29} + 4 q^{30} + 22 q^{31} + 22 q^{32} + 33 q^{33} + 22 q^{34} + 21 q^{35} - 8 q^{36} + 48 q^{37} + 42 q^{38} + 9 q^{40} - 5 q^{41} + 4 q^{42} - 27 q^{43} - 4 q^{44} + 28 q^{45} + 9 q^{46} + 27 q^{48} + 21 q^{49} + 4 q^{50} - 4 q^{51} - 28 q^{53} + 27 q^{54} + 2 q^{55} + 9 q^{56} + 56 q^{57} + 44 q^{58} + 7 q^{59} + 23 q^{60} + 25 q^{61} - 17 q^{62} + 28 q^{63} + 47 q^{64} - 30 q^{66} + 40 q^{67} - 19 q^{68} + 13 q^{69} + 4 q^{70} + 15 q^{71} + 42 q^{72} + 16 q^{73} + 37 q^{74} + 5 q^{75} + 58 q^{76} + 2 q^{77} - 10 q^{79} + 18 q^{80} + 25 q^{81} + 14 q^{82} - 11 q^{83} + 23 q^{84} - 6 q^{85} + 35 q^{86} + 65 q^{87} - 74 q^{88} + 24 q^{89} + 32 q^{90} - 89 q^{92} + 82 q^{93} + 21 q^{94} + 8 q^{95} - 22 q^{96} + 57 q^{97} + 4 q^{98} + 6 q^{99}+O(q^{100}) \) 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9 + 4 * q^10 + 2 * q^11 + 23 * q^12 + 4 * q^14 + 5 * q^15 + 18 * q^16 - 6 * q^17 + 32 * q^18 + 8 * q^19 + 20 * q^20 + 5 * q^21 - 17 * q^22 - 14 * q^23 + 27 * q^24 + 21 * q^25 + 11 * q^27 + 20 * q^28 + 20 * q^29 + 4 * q^30 + 22 * q^31 + 22 * q^32 + 33 * q^33 + 22 * q^34 + 21 * q^35 - 8 * q^36 + 48 * q^37 + 42 * q^38 + 9 * q^40 - 5 * q^41 + 4 * q^42 - 27 * q^43 - 4 * q^44 + 28 * q^45 + 9 * q^46 + 27 * q^48 + 21 * q^49 + 4 * q^50 - 4 * q^51 - 28 * q^53 + 27 * q^54 + 2 * q^55 + 9 * q^56 + 56 * q^57 + 44 * q^58 + 7 * q^59 + 23 * q^60 + 25 * q^61 - 17 * q^62 + 28 * q^63 + 47 * q^64 - 30 * q^66 + 40 * q^67 - 19 * q^68 + 13 * q^69 + 4 * q^70 + 15 * q^71 + 42 * q^72 + 16 * q^73 + 37 * q^74 + 5 * q^75 + 58 * q^76 + 2 * q^77 - 10 * q^79 + 18 * q^80 + 25 * q^81 + 14 * q^82 - 11 * q^83 + 23 * q^84 - 6 * q^85 + 35 * q^86 + 65 * q^87 - 74 * q^88 + 24 * q^89 + 32 * q^90 - 89 * q^92 + 82 * q^93 + 21 * q^94 + 8 * q^95 - 22 * q^96 + 57 * q^97 + 4 * q^98 + 6 * q^99

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 $

$2$	1.37365	0.971319	0.485659	−	0.874148i	$-0.338580\pi$
$2$	1.37365	0.971319	0.485659	+	0.874148i	$0.338580\pi$
$3$	1.75471	1.01308	0.506540	−	0.862216i	$-0.330924\pi$
$3$	1.75471	1.01308	0.506540	+	0.862216i	$0.330924\pi$
$4$	−0.113079	−0.0565395
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.41036	0.984024
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.90264	−1.02624
$9$	0.0789971	0.0263324
$10$	1.37365	0.434387
$11$	2.75740	0.831388	0.415694	−	0.909505i	$-0.363539\pi$
$11$	2.75740	0.831388	0.415694	+	0.909505i	$0.363539\pi$
$12$	−0.198421	−0.0572791
$13$	0	0
$13$	0	0
$14$	1.37365	0.367124
$15$	1.75471	0.453063
$16$	−3.76106	−0.940264
$17$	2.28419	0.553998	0.276999	−	0.960870i	$-0.410660\pi$
$17$	2.28419	0.553998	0.276999	+	0.960870i	$0.410660\pi$
$18$	0.108514	0.0255771
$19$	1.32904	0.304902	0.152451	−	0.988311i	$-0.451283\pi$
$19$	1.32904	0.304902	0.152451	+	0.988311i	$0.451283\pi$
$20$	−0.113079	−0.0252852
$21$	1.75471	0.382908
$22$	3.78771	0.807543
$23$	5.27011	1.09889	0.549447	−	0.835529i	$-0.314839\pi$
$23$	5.27011	1.09889	0.549447	+	0.835529i	$0.314839\pi$
$24$	−5.09328	−1.03966
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.12550	−0.986404
$28$	−0.113079	−0.0213699
$29$	7.06407	1.31177	0.655883	−	0.754863i	$-0.272297\pi$
$29$	7.06407	1.31177	0.655883	+	0.754863i	$0.272297\pi$
$30$	2.41036	0.440069
$31$	5.25679	0.944146	0.472073	−	0.881559i	$-0.343506\pi$
$31$	5.25679	0.944146	0.472073	+	0.881559i	$0.343506\pi$
$32$	0.638890	0.112941
$33$	4.83843	0.842263
$34$	3.13769	0.538109
$35$	1.00000	0.169031
$36$	−0.00893291	−0.00148882
$37$	−8.65483	−1.42285	−0.711423	−	0.702765i	$-0.751949\pi$
$37$	−8.65483	−1.42285	−0.711423	+	0.702765i	$0.751949\pi$
$38$	1.82563	0.296157
$39$	0	0
$40$	−2.90264	−0.458947
$41$	7.90714	1.23489	0.617444	−	0.786615i	$-0.288168\pi$
$41$	7.90714	1.23489	0.617444	+	0.786615i	$0.288168\pi$
$42$	2.41036	0.371926
$43$	−0.261578	−0.0398903	−0.0199451	−	0.999801i	$-0.506349\pi$
$43$	−0.261578	−0.0398903	−0.0199451	+	0.999801i	$0.506349\pi$
$44$	−0.311804	−0.0470063
$45$	0.0789971	0.0117762
$46$	7.23930	1.06738
$47$	−6.58603	−0.960672	−0.480336	−	0.877085i	$-0.659485\pi$
$47$	−6.58603	−0.960672	−0.480336	+	0.877085i	$0.659485\pi$
$48$	−6.59955	−0.952563
$49$	1.00000	0.142857
$50$	1.37365	0.194264
$51$	4.00809	0.561245
$52$	0	0
$53$	−4.00433	−0.550038	−0.275019	−	0.961439i	$-0.588684\pi$
$53$	−4.00433	−0.550038	−0.275019	+	0.961439i	$0.588684\pi$
$54$	−7.04066	−0.958113
$55$	2.75740	0.371808
$56$	−2.90264	−0.387881
$57$	2.33207	0.308890
$58$	9.70358	1.27414
$59$	0.940809	0.122483	0.0612415	−	0.998123i	$-0.480494\pi$
$59$	0.940809	0.122483	0.0612415	+	0.998123i	$0.480494\pi$
$60$	−0.198421	−0.0256160
$61$	2.81745	0.360738	0.180369	−	0.983599i	$-0.442271\pi$
$61$	2.81745	0.360738	0.180369	+	0.983599i	$0.442271\pi$
$62$	7.22100	0.917067
$63$	0.0789971	0.00995269
$64$	8.39972	1.04997
$65$	0	0
$66$	6.64632	0.818106
$67$	−8.74905	−1.06887	−0.534433	−	0.845211i	$-0.679475\pi$
$67$	−8.74905	−1.06887	−0.534433	+	0.845211i	$0.679475\pi$
$68$	−0.258294	−0.0313228
$69$	9.24750	1.11327
$70$	1.37365	0.164183
$71$	13.1114	1.55603	0.778017	−	0.628243i	$-0.216226\pi$
$71$	13.1114	1.55603	0.778017	+	0.628243i	$0.216226\pi$
$72$	−0.229300	−0.0270232
$73$	−11.4914	−1.34497	−0.672484	−	0.740112i	$-0.734773\pi$
$73$	−11.4914	−1.34497	−0.672484	+	0.740112i	$0.734773\pi$
$74$	−11.8887	−1.38204
$75$	1.75471	0.202616
$76$	−0.150286	−0.0172390
$77$	2.75740	0.314235
$78$	0	0
$79$	−4.11077	−0.462498	−0.231249	−	0.972895i	$-0.574281\pi$
$79$	−4.11077	−0.462498	−0.231249	+	0.972895i	$0.574281\pi$
$80$	−3.76106	−0.420499
$81$	−9.23075	−1.02564
$82$	10.8617	1.19947
$83$	12.2159	1.34087	0.670434	−	0.741969i	$-0.266108\pi$
$83$	12.2159	1.34087	0.670434	+	0.741969i	$0.266108\pi$
$84$	−0.198421	−0.0216495
$85$	2.28419	0.247756
$86$	−0.359317	−0.0387462
$87$	12.3954	1.32892
$88$	−8.00373	−0.853201
$89$	11.3673	1.20494	0.602468	−	0.798143i	$-0.294184\pi$
$89$	11.3673	1.20494	0.602468	+	0.798143i	$0.294184\pi$
$90$	0.108514	0.0114384
$91$	0	0
$92$	−0.595939	−0.0621309
$93$	9.22412	0.956496
$94$	−9.04692	−0.933118
$95$	1.32904	0.136356
$96$	1.12106	0.114418
$97$	−0.589588	−0.0598636	−0.0299318	−	0.999552i	$-0.509529\pi$
$97$	−0.589588	−0.0598636	−0.0299318	+	0.999552i	$0.509529\pi$
$98$	1.37365	0.138760
$99$	0.217827	0.0218924
$100$	−0.113079	−0.0113079
$101$	9.94889	0.989952	0.494976	−	0.868907i	$-0.335177\pi$
$101$	9.94889	0.989952	0.494976	+	0.868907i	$0.335177\pi$
$102$	5.50572	0.545148
$103$	11.1878	1.10236	0.551182	−	0.834385i	$-0.314177\pi$
$103$	11.1878	1.10236	0.551182	+	0.834385i	$0.314177\pi$
$104$	0	0
$105$	1.75471	0.171242
$106$	−5.50056	−0.534262
$107$	1.88609	0.182336	0.0911678	−	0.995836i	$-0.470940\pi$
$107$	1.88609	0.182336	0.0911678	+	0.995836i	$0.470940\pi$
$108$	0.579587	0.0557708
$109$	14.3067	1.37033	0.685167	−	0.728386i	$-0.259729\pi$
$109$	14.3067	1.37033	0.685167	+	0.728386i	$0.259729\pi$
$110$	3.78771	0.361144
$111$	−15.1867	−1.44146
$112$	−3.76106	−0.355386
$113$	−1.40148	−0.131840	−0.0659201	−	0.997825i	$-0.520998\pi$
$113$	−1.40148	−0.131840	−0.0659201	+	0.997825i	$0.520998\pi$
$114$	3.20345	0.300031
$115$	5.27011	0.491440
$116$	−0.798799	−0.0741666
$117$	0	0
$118$	1.29235	0.118970
$119$	2.28419	0.209392
$120$	−5.09328	−0.464950
$121$	−3.39674	−0.308794
$122$	3.87020	0.350392
$123$	13.8747	1.25104
$124$	−0.594432	−0.0533816
$125$	1.00000	0.0894427
$126$	0.108514	0.00966724
$127$	−3.21199	−0.285018	−0.142509	−	0.989793i	$-0.545517\pi$
$127$	−3.21199	−0.285018	−0.142509	+	0.989793i	$0.545517\pi$
$128$	10.2605	0.906910
$129$	−0.458993	−0.0404121
$130$	0	0
$131$	2.30252	0.201172	0.100586	−	0.994928i	$-0.467928\pi$
$131$	2.30252	0.201172	0.100586	+	0.994928i	$0.467928\pi$
$132$	−0.547125	−0.0476211
$133$	1.32904	0.115242
$134$	−12.0181	−1.03821
$135$	−5.12550	−0.441133
$136$	−6.63018	−0.568533
$137$	14.9323	1.27575	0.637877	−	0.770139i	$-0.279813\pi$
$137$	14.9323	1.27575	0.637877	+	0.770139i	$0.279813\pi$
$138$	12.7028	1.08134
$139$	7.79719	0.661349	0.330675	−	0.943745i	$-0.392724\pi$
$139$	7.79719	0.661349	0.330675	+	0.943745i	$0.392724\pi$
$140$	−0.113079	−0.00955692
$141$	−11.5566	−0.973238
$142$	18.0105	1.51141
$143$	0	0
$144$	−0.297112	−0.0247594
$145$	7.06407	0.586639
$146$	−15.7852	−1.30639
$147$	1.75471	0.144726
$148$	0.978680	0.0804470
$149$	18.7006	1.53201	0.766006	−	0.642833i	$-0.222241\pi$
$149$	18.7006	1.53201	0.766006	+	0.642833i	$0.222241\pi$
$150$	2.41036	0.196805
$151$	15.5901	1.26871	0.634353	−	0.773043i	$-0.281267\pi$
$151$	15.5901	1.26871	0.634353	+	0.773043i	$0.281267\pi$
$152$	−3.85771	−0.312901
$153$	0.180445	0.0145881
$154$	3.78771	0.305222
$155$	5.25679	0.422235
$156$	0	0
$157$	−20.6013	−1.64416	−0.822080	−	0.569372i	$-0.807187\pi$
$157$	−20.6013	−1.64416	−0.822080	+	0.569372i	$0.807187\pi$
$158$	−5.64677	−0.449233
$159$	−7.02643	−0.557232
$160$	0.638890	0.0505087
$161$	5.27011	0.415343
$162$	−12.6798	−0.996223
$163$	7.54547	0.591007	0.295503	−	0.955342i	$-0.404513\pi$
$163$	7.54547	0.591007	0.295503	+	0.955342i	$0.404513\pi$
$164$	−0.894132	−0.0698199
$165$	4.83843	0.376671
$166$	16.7804	1.30241
$167$	−19.8017	−1.53230	−0.766152	−	0.642659i	$-0.777831\pi$
$167$	−19.8017	−1.53230	−0.766152	+	0.642659i	$0.777831\pi$
$168$	−5.09328	−0.392955
$169$	0	0
$170$	3.13769	0.240650
$171$	0.104990	0.00802878
$172$	0.0295790	0.00225538
$173$	−3.02577	−0.230045	−0.115023	−	0.993363i	$-0.536694\pi$
$173$	−3.02577	−0.230045	−0.115023	+	0.993363i	$0.536694\pi$
$174$	17.0269	1.29081
$175$	1.00000	0.0755929
$176$	−10.3707	−0.781724
$177$	1.65084	0.124085
$178$	15.6148	1.17038
$179$	−5.16697	−0.386198	−0.193099	−	0.981179i	$-0.561854\pi$
$179$	−5.16697	−0.386198	−0.193099	+	0.981179i	$0.561854\pi$
$180$	−0.00893291	−0.000665820 0
$181$	−19.9289	−1.48130	−0.740652	−	0.671888i	$-0.765483\pi$
$181$	−19.9289	−1.48130	−0.740652	+	0.671888i	$0.765483\pi$
$182$	0	0
$183$	4.94380	0.365457
$184$	−15.2972	−1.12772
$185$	−8.65483	−0.636316
$186$	12.6707	0.929063
$187$	6.29844	0.460587
$188$	0.744742	0.0543159
$189$	−5.12550	−0.372826
$190$	1.82563	0.132445
$191$	8.39109	0.607158	0.303579	−	0.952806i	$-0.401818\pi$
$191$	8.39109	0.607158	0.303579	+	0.952806i	$0.401818\pi$
$192$	14.7391	1.06370
$193$	5.63512	0.405625	0.202812	−	0.979218i	$-0.434992\pi$
$193$	5.63512	0.405625	0.202812	+	0.979218i	$0.434992\pi$
$194$	−0.809889	−0.0581467
$195$	0	0
$196$	−0.113079	−0.00807707
$197$	−22.8608	−1.62877	−0.814384	−	0.580326i	$-0.802925\pi$
$197$	−22.8608	−1.62877	−0.814384	+	0.580326i	$0.802925\pi$
$198$	0.299218	0.0212645
$199$	−17.2140	−1.22026	−0.610132	−	0.792299i	$-0.708884\pi$
$199$	−17.2140	−1.22026	−0.610132	+	0.792299i	$0.708884\pi$
$200$	−2.90264	−0.205247
$201$	−15.3520	−1.08285
$202$	13.6663	0.961559
$203$	7.06407	0.495801
$204$	−0.453231	−0.0317325
$205$	7.90714	0.552258
$206$	15.3681	1.07075
$207$	0.416323	0.0289365
$208$	0	0
$209$	3.66468	0.253492
$210$	2.41036	0.166330
$211$	3.38109	0.232764	0.116382	−	0.993205i	$-0.462870\pi$
$211$	3.38109	0.232764	0.116382	+	0.993205i	$0.462870\pi$
$212$	0.452806	0.0310989
$213$	23.0066	1.57639
$214$	2.59084	0.177106
$215$	−0.261578	−0.0178395
$216$	14.8775	1.01228
$217$	5.25679	0.356854
$218$	19.6525	1.33103
$219$	−20.1641	−1.36256
$220$	−0.311804	−0.0210218
$221$	0	0
$222$	−20.8612	−1.40011
$223$	−24.8993	−1.66738	−0.833690	−	0.552233i	$-0.813776\pi$
$223$	−24.8993	−1.66738	−0.833690	+	0.552233i	$0.813776\pi$
$224$	0.638890	0.0426876
$225$	0.0789971	0.00526647
$226$	−1.92515	−0.128059
$227$	−15.6881	−1.04125	−0.520627	−	0.853785i	$-0.674302\pi$
$227$	−15.6881	−1.04125	−0.520627	+	0.853785i	$0.674302\pi$
$228$	−0.263708	−0.0174645
$229$	−10.7577	−0.710888	−0.355444	−	0.934698i	$-0.615670\pi$
$229$	−10.7577	−0.710888	−0.355444	+	0.934698i	$0.615670\pi$
$230$	7.23930	0.477345
$231$	4.83843	0.318345
$232$	−20.5044	−1.34618
$233$	5.22064	0.342016	0.171008	−	0.985270i	$-0.445298\pi$
$233$	5.22064	0.342016	0.171008	+	0.985270i	$0.445298\pi$
$234$	0	0
$235$	−6.58603	−0.429625
$236$	−0.106386	−0.00692513
$237$	−7.21320	−0.468548
$238$	3.13769	0.203386
$239$	24.6347	1.59348	0.796742	−	0.604319i	$-0.206555\pi$
$239$	24.6347	1.59348	0.796742	+	0.604319i	$0.206555\pi$
$240$	−6.59955	−0.425999
$241$	12.8276	0.826300	0.413150	−	0.910663i	$-0.364428\pi$
$241$	12.8276	0.826300	0.413150	+	0.910663i	$0.364428\pi$
$242$	−4.66594	−0.299938
$243$	−0.820750	−0.0526511
$244$	−0.318595	−0.0203959
$245$	1.00000	0.0638877
$246$	19.0590	1.21516
$247$	0	0
$248$	−15.2585	−0.968918
$249$	21.4353	1.35841
$250$	1.37365	0.0868774
$251$	−4.59580	−0.290084	−0.145042	−	0.989425i	$-0.546332\pi$
$251$	−4.59580	−0.290084	−0.145042	+	0.989425i	$0.546332\pi$
$252$	−0.00893291	−0.000562721 0
$253$	14.5318	0.913607
$254$	−4.41216	−0.276844
$255$	4.00809	0.250996
$256$	−2.70506	−0.169066
$257$	−4.19360	−0.261590	−0.130795	−	0.991409i	$-0.541753\pi$
$257$	−4.19360	−0.261590	−0.130795	+	0.991409i	$0.541753\pi$
$258$	−0.630497	−0.0392530
$259$	−8.65483	−0.537785
$260$	0	0
$261$	0.558041	0.0345419
$262$	3.16286	0.195402
$263$	−7.60999	−0.469252	−0.234626	−	0.972086i	$-0.575387\pi$
$263$	−7.60999	−0.469252	−0.234626	+	0.972086i	$0.575387\pi$
$264$	−14.0442	−0.864361
$265$	−4.00433	−0.245984
$266$	1.82563	0.111937
$267$	19.9464	1.22070
$268$	0.989334	0.0604332
$269$	8.48291	0.517212	0.258606	−	0.965983i	$-0.416737\pi$
$269$	8.48291	0.517212	0.258606	+	0.965983i	$0.416737\pi$
$270$	−7.04066	−0.428481
$271$	9.22606	0.560443	0.280222	−	0.959935i	$-0.409592\pi$
$271$	9.22606	0.560443	0.280222	+	0.959935i	$0.409592\pi$
$272$	−8.59098	−0.520904
$273$	0	0
$274$	20.5118	1.23916
$275$	2.75740	0.166278
$276$	−1.04570	−0.0629436
$277$	−11.5967	−0.696781	−0.348390	−	0.937350i	$-0.613272\pi$
$277$	−11.5967	−0.696781	−0.348390	+	0.937350i	$0.613272\pi$
$278$	10.7106	0.642381
$279$	0.415271	0.0248616
$280$	−2.90264	−0.173466
$281$	16.4415	0.980816	0.490408	−	0.871493i	$-0.336848\pi$
$281$	16.4415	0.980816	0.490408	+	0.871493i	$0.336848\pi$
$282$	−15.8747	−0.945324
$283$	−28.3539	−1.68546	−0.842731	−	0.538335i	$-0.819054\pi$
$283$	−28.3539	−1.68546	−0.842731	+	0.538335i	$0.819054\pi$
$284$	−1.48262	−0.0879774
$285$	2.33207	0.138140
$286$	0	0
$287$	7.90714	0.466744
$288$	0.0504704	0.00297400
$289$	−11.7825	−0.693086
$290$	9.70358	0.569814
$291$	−1.03455	−0.0606467
$292$	1.29944	0.0760438
$293$	14.0354	0.819959	0.409980	−	0.912095i	$-0.365536\pi$
$293$	14.0354	0.819959	0.409980	+	0.912095i	$0.365536\pi$
$294$	2.41036	0.140575
$295$	0.940809	0.0547760
$296$	25.1218	1.46018
$297$	−14.1331	−0.820084
$298$	25.6881	1.48807
$299$	0	0
$300$	−0.198421	−0.0114558
$301$	−0.261578	−0.0150771
$302$	21.4154	1.23232
$303$	17.4574	1.00290
$304$	−4.99858	−0.286688
$305$	2.81745	0.161327
$306$	0.247868	0.0141697
$307$	15.9059	0.907798	0.453899	−	0.891053i	$-0.350033\pi$
$307$	15.9059	0.907798	0.453899	+	0.891053i	$0.350033\pi$
$308$	−0.311804	−0.0177667
$309$	19.6313	1.11678
$310$	7.22100	0.410125
$311$	−10.6132	−0.601817	−0.300909	−	0.953653i	$-0.597290\pi$
$311$	−10.6132	−0.601817	−0.300909	+	0.953653i	$0.597290\pi$
$312$	0	0
$313$	−22.6491	−1.28020	−0.640101	−	0.768291i	$-0.721108\pi$
$313$	−22.6491	−1.28020	−0.640101	+	0.768291i	$0.721108\pi$
$314$	−28.2990	−1.59700
$315$	0.0789971	0.00445098
$316$	0.464842	0.0261494
$317$	−25.8114	−1.44971	−0.724857	−	0.688900i	$-0.758094\pi$
$317$	−25.8114	−1.44971	−0.724857	+	0.688900i	$0.758094\pi$
$318$	−9.65188	−0.541250
$319$	19.4785	1.09059
$320$	8.39972	0.469559
$321$	3.30954	0.184721
$322$	7.23930	0.403430
$323$	3.03577	0.168915
$324$	1.04380	0.0579891
$325$	0	0
$326$	10.3649	0.574056
$327$	25.1041	1.38826
$328$	−22.9515	−1.26729
$329$	−6.58603	−0.363100
$330$	6.64632	0.365868
$331$	−16.7755	−0.922064	−0.461032	−	0.887384i	$-0.652521\pi$
$331$	−16.7755	−0.922064	−0.461032	+	0.887384i	$0.652521\pi$
$332$	−1.38136	−0.0758120
$333$	−0.683706	−0.0374669
$334$	−27.2007	−1.48836
$335$	−8.74905	−0.478011
$336$	−6.59955	−0.360035
$337$	−28.6594	−1.56118	−0.780589	−	0.625045i	$-0.785081\pi$
$337$	−28.6594	−1.56118	−0.780589	+	0.625045i	$0.785081\pi$
$338$	0	0
$339$	−2.45919	−0.133565
$340$	−0.258294	−0.0140080
$341$	14.4951	0.784952
$342$	0.144220	0.00779850
$343$	1.00000	0.0539949
$344$	0.759266	0.0409369
$345$	9.24750	0.497868
$346$	−4.15636	−0.223447
$347$	2.32686	0.124912	0.0624562	−	0.998048i	$-0.480107\pi$
$347$	2.32686	0.124912	0.0624562	+	0.998048i	$0.480107\pi$
$348$	−1.40166	−0.0751367
$349$	4.67439	0.250214	0.125107	−	0.992143i	$-0.460073\pi$
$349$	4.67439	0.250214	0.125107	+	0.992143i	$0.460073\pi$
$350$	1.37365	0.0734248
$351$	0	0
$352$	1.76168	0.0938977
$353$	17.0594	0.907978	0.453989	−	0.891007i	$-0.350001\pi$
$353$	17.0594	0.907978	0.453989	+	0.891007i	$0.350001\pi$
$354$	2.26769	0.120526
$355$	13.1114	0.695880
$356$	−1.28541	−0.0681265
$357$	4.00809	0.212131
$358$	−7.09763	−0.375121
$359$	−29.4789	−1.55584	−0.777918	−	0.628366i	$-0.783724\pi$
$359$	−29.4789	−1.55584	−0.777918	+	0.628366i	$0.783724\pi$
$360$	−0.229300	−0.0120852
$361$	−17.2337	−0.907035
$362$	−27.3754	−1.43882
$363$	−5.96028	−0.312834
$364$	0	0
$365$	−11.4914	−0.601488
$366$	6.79107	0.354975
$367$	−1.03410	−0.0539797	−0.0269898	−	0.999636i	$-0.508592\pi$
$367$	−1.03410	−0.0539797	−0.0269898	+	0.999636i	$0.508592\pi$
$368$	−19.8212	−1.03325
$369$	0.624641	0.0325175
$370$	−11.8887	−0.618065
$371$	−4.00433	−0.207895
$372$	−1.04305	−0.0540799
$373$	−16.6039	−0.859718	−0.429859	−	0.902896i	$-0.641437\pi$
$373$	−16.6039	−0.859718	−0.429859	+	0.902896i	$0.641437\pi$
$374$	8.65186	0.447377
$375$	1.75471	0.0906127
$376$	19.1169	0.985877
$377$	0	0
$378$	−7.04066	−0.362133
$379$	10.8186	0.555712	0.277856	−	0.960623i	$-0.410376\pi$
$379$	10.8186	0.555712	0.277856	+	0.960623i	$0.410376\pi$
$380$	−0.150286	−0.00770951
$381$	−5.63611	−0.288747
$382$	11.5264	0.589744
$383$	6.38778	0.326400	0.163200	−	0.986593i	$-0.447818\pi$
$383$	6.38778	0.326400	0.163200	+	0.986593i	$0.447818\pi$
$384$	18.0042	0.918773
$385$	2.75740	0.140530
$386$	7.74070	0.393991
$387$	−0.0206639	−0.00105041
$388$	0.0666701	0.00338466
$389$	−13.6579	−0.692482	−0.346241	−	0.938146i	$-0.612542\pi$
$389$	−13.6579	−0.692482	−0.346241	+	0.938146i	$0.612542\pi$
$390$	0	0
$391$	12.0379	0.608785
$392$	−2.90264	−0.146605
$393$	4.04025	0.203803
$394$	−31.4029	−1.58205
$395$	−4.11077	−0.206835
$396$	−0.0246316	−0.00123779
$397$	−3.09178	−0.155172	−0.0775859	−	0.996986i	$-0.524721\pi$
$397$	−3.09178	−0.155172	−0.0775859	+	0.996986i	$0.524721\pi$
$398$	−23.6460	−1.18527
$399$	2.33207	0.116749
$400$	−3.76106	−0.188053
$401$	−29.5053	−1.47342	−0.736712	−	0.676207i	$-0.763623\pi$
$401$	−29.5053	−1.47342	−0.736712	+	0.676207i	$0.763623\pi$
$402$	−21.0883	−1.05179
$403$	0	0
$404$	−1.12501	−0.0559714
$405$	−9.23075	−0.458680
$406$	9.70358	0.481581
$407$	−23.8648	−1.18294
$408$	−11.6340	−0.575970
$409$	0.374083	0.0184972	0.00924861	−	0.999957i	$-0.497056\pi$
$409$	0.374083	0.0184972	0.00924861	+	0.999957i	$0.497056\pi$
$410$	10.8617	0.536419
$411$	26.2018	1.29244
$412$	−1.26510	−0.0623271
$413$	0.940809	0.0462942
$414$	0.571883	0.0281065
$415$	12.2159	0.599654
$416$	0	0
$417$	13.6818	0.670000
$418$	5.03400	0.246221
$419$	−12.7051	−0.620687	−0.310343	−	0.950625i	$-0.600444\pi$
$419$	−12.7051	−0.620687	−0.310343	+	0.950625i	$0.600444\pi$
$420$	−0.198421	−0.00968193
$421$	−7.95449	−0.387678	−0.193839	−	0.981033i	$-0.562094\pi$
$421$	−7.95449	−0.387678	−0.193839	+	0.981033i	$0.562094\pi$
$422$	4.64444	0.226088
$423$	−0.520277	−0.0252967
$424$	11.6231	0.564469
$425$	2.28419	0.110800
$426$	31.6031	1.53118
$427$	2.81745	0.136346
$428$	−0.213278	−0.0103092
$429$	0	0
$430$	−0.359317	−0.0173278
$431$	13.4633	0.648507	0.324253	−	0.945970i	$-0.394887\pi$
$431$	13.4633	0.648507	0.324253	+	0.945970i	$0.394887\pi$
$432$	19.2773	0.927480
$433$	−5.66326	−0.272159	−0.136079	−	0.990698i	$-0.543450\pi$
$433$	−5.66326	−0.272159	−0.136079	+	0.990698i	$0.543450\pi$
$434$	7.22100	0.346619
$435$	12.3954	0.594313
$436$	−1.61779	−0.0774781
$437$	7.00416	0.335054
$438$	−27.6984	−1.32348
$439$	6.34757	0.302953	0.151477	−	0.988461i	$-0.451597\pi$
$439$	6.34757	0.302953	0.151477	+	0.988461i	$0.451597\pi$
$440$	−8.00373	−0.381563
$441$	0.0789971	0.00376176
$442$	0	0
$443$	6.79586	0.322881	0.161440	−	0.986882i	$-0.448386\pi$
$443$	6.79586	0.322881	0.161440	+	0.986882i	$0.448386\pi$
$444$	1.71730	0.0814993
$445$	11.3673	0.538864
$446$	−34.2030	−1.61956
$447$	32.8141	1.55205
$448$	8.39972	0.396850
$449$	−33.0514	−1.55979	−0.779897	−	0.625908i	$-0.784729\pi$
$449$	−33.0514	−1.55979	−0.779897	+	0.625908i	$0.784729\pi$
$450$	0.108514	0.00511542
$451$	21.8032	1.02667
$452$	0.158478	0.00745419
$453$	27.3561	1.28530
$454$	−21.5499	−1.01139
$455$	0	0
$456$	−6.76914	−0.316994
$457$	27.1460	1.26984	0.634918	−	0.772580i	$-0.281034\pi$
$457$	27.1460	1.26984	0.634918	+	0.772580i	$0.281034\pi$
$458$	−14.7773	−0.690499
$459$	−11.7076	−0.546466
$460$	−0.595939	−0.0277858
$461$	−17.0536	−0.794266	−0.397133	−	0.917761i	$-0.629995\pi$
$461$	−17.0536	−0.794266	−0.397133	+	0.917761i	$0.629995\pi$
$462$	6.64632	0.309215
$463$	15.4787	0.719357	0.359679	−	0.933076i	$-0.382886\pi$
$463$	15.4787	0.719357	0.359679	+	0.933076i	$0.382886\pi$
$464$	−26.5684	−1.23341
$465$	9.22412	0.427758
$466$	7.17135	0.332206
$467$	28.3105	1.31005	0.655027	−	0.755605i	$-0.272657\pi$
$467$	28.3105	1.31005	0.655027	+	0.755605i	$0.272657\pi$
$468$	0	0
$469$	−8.74905	−0.403993
$470$	−9.04692	−0.417303
$471$	−36.1492	−1.66567
$472$	−2.73083	−0.125697
$473$	−0.721276	−0.0331643
$474$	−9.90843	−0.455109
$475$	1.32904	0.0609803
$476$	−0.258294	−0.0118389
$477$	−0.316331	−0.0144838
$478$	33.8395	1.54778
$479$	−31.0248	−1.41756	−0.708779	−	0.705431i	$-0.750753\pi$
$479$	−31.0248	−1.41756	−0.708779	+	0.705431i	$0.750753\pi$
$480$	1.12106	0.0511694
$481$	0	0
$482$	17.6207	0.802601
$483$	9.24750	0.420776
$484$	0.384100	0.0174591
$485$	−0.589588	−0.0267718
$486$	−1.12743	−0.0511410
$487$	−41.1237	−1.86349	−0.931747	−	0.363109i	$-0.881715\pi$
$487$	−41.1237	−1.86349	−0.931747	+	0.363109i	$0.881715\pi$
$488$	−8.17804	−0.370203
$489$	13.2401	0.598738
$490$	1.37365	0.0620553
$491$	26.4414	1.19328	0.596641	−	0.802508i	$-0.296502\pi$
$491$	26.4414	1.19328	0.596641	+	0.802508i	$0.296502\pi$
$492$	−1.56894	−0.0707332
$493$	16.1357	0.726716
$494$	0	0
$495$	0.217827	0.00979058
$496$	−19.7711	−0.887747
$497$	13.1114	0.588126
$498$	29.4447	1.31945
$499$	−13.1163	−0.587168	−0.293584	−	0.955933i	$-0.594848\pi$
$499$	−13.1163	−0.587168	−0.293584	+	0.955933i	$0.594848\pi$
$500$	−0.113079	−0.00505705
$501$	−34.7462	−1.55235
$502$	−6.31303	−0.281764
$503$	−4.04940	−0.180554	−0.0902768	−	0.995917i	$-0.528775\pi$
$503$	−4.04940	−0.180554	−0.0902768	+	0.995917i	$0.528775\pi$
$504$	−0.229300	−0.0102138
$505$	9.94889	0.442720
$506$	19.9616	0.887403
$507$	0	0
$508$	0.363209	0.0161148
$509$	34.9168	1.54766	0.773831	−	0.633393i	$-0.218338\pi$
$509$	34.9168	1.54766	0.773831	+	0.633393i	$0.218338\pi$
$510$	5.50572	0.243797
$511$	−11.4914	−0.508350
$512$	−24.2368	−1.07113
$513$	−6.81198	−0.300756
$514$	−5.76055	−0.254087
$515$	11.1878	0.492992
$516$	0.0519025	0.00228488
$517$	−18.1603	−0.798691
$518$	−11.8887	−0.522361
$519$	−5.30935	−0.233054
$520$	0	0
$521$	6.45884	0.282967	0.141484	−	0.989941i	$-0.454813\pi$
$521$	6.45884	0.282967	0.141484	+	0.989941i	$0.454813\pi$
$522$	0.766554	0.0335512
$523$	22.9246	1.00242	0.501212	−	0.865325i	$-0.332888\pi$
$523$	22.9246	1.00242	0.501212	+	0.865325i	$0.332888\pi$
$524$	−0.260367	−0.0113742
$525$	1.75471	0.0765817
$526$	−10.4535	−0.455793
$527$	12.0075	0.523055
$528$	−18.1976	−0.791949
$529$	4.77404	0.207567
$530$	−5.50056	−0.238929
$531$	0.0743212	0.00322526
$532$	−0.150286	−0.00651573
$533$	0	0
$534$	27.3994	1.18569
$535$	1.88609	0.0815429
$536$	25.3953	1.09691
$537$	−9.06653	−0.391249
$538$	11.6526	0.502378
$539$	2.75740	0.118770
$540$	0.579587	0.0249415
$541$	35.9577	1.54594	0.772972	−	0.634440i	$-0.218769\pi$
$541$	35.9577	1.54594	0.772972	+	0.634440i	$0.218769\pi$
$542$	12.6734	0.544369
$543$	−34.9694	−1.50068
$544$	1.45935	0.0625690
$545$	14.3067	0.612832
$546$	0	0
$547$	−23.4363	−1.00206	−0.501032	−	0.865429i	$-0.667046\pi$
$547$	−23.4363	−1.00206	−0.501032	+	0.865429i	$0.667046\pi$
$548$	−1.68853	−0.0721305
$549$	0.222570	0.00949908
$550$	3.78771	0.161509
$551$	9.38840	0.399959
$552$	−26.8421	−1.14248
$553$	−4.11077	−0.174808
$554$	−15.9299	−0.676796
$555$	−15.1867	−0.644639
$556$	−0.881699	−0.0373924
$557$	−15.6410	−0.662729	−0.331364	−	0.943503i	$-0.607509\pi$
$557$	−15.6410	−0.662729	−0.331364	+	0.943503i	$0.607509\pi$
$558$	0.570437	0.0241485
$559$	0	0
$560$	−3.76106	−0.158934
$561$	11.0519	0.466612
$562$	22.5849	0.952685
$563$	−43.9929	−1.85408	−0.927040	−	0.374962i	$-0.877656\pi$
$563$	−43.9929	−1.85408	−0.927040	+	0.374962i	$0.877656\pi$
$564$	1.30680	0.0550264
$565$	−1.40148	−0.0589608
$566$	−38.9484	−1.63712
$567$	−9.23075	−0.387655
$568$	−38.0576	−1.59686
$569$	−17.2393	−0.722708	−0.361354	−	0.932429i	$-0.617685\pi$
$569$	−17.2393	−0.722708	−0.361354	+	0.932429i	$0.617685\pi$
$570$	3.20345	0.134178
$571$	27.3411	1.14419	0.572094	−	0.820188i	$-0.306131\pi$
$571$	27.3411	1.14419	0.572094	+	0.820188i	$0.306131\pi$
$572$	0	0
$573$	14.7239	0.615100
$574$	10.8617	0.453357
$575$	5.27011	0.219779
$576$	0.663553	0.0276481
$577$	−4.17337	−0.173740	−0.0868699	−	0.996220i	$-0.527686\pi$
$577$	−4.17337	−0.173740	−0.0868699	+	0.996220i	$0.527686\pi$
$578$	−16.1850	−0.673208
$579$	9.88799	0.410931
$580$	−0.798799	−0.0331683
$581$	12.2159	0.506800
$582$	−1.42112	−0.0589072
$583$	−11.0416	−0.457295
$584$	33.3554	1.38026
$585$	0	0
$586$	19.2798	0.796442
$587$	−20.5568	−0.848470	−0.424235	−	0.905552i	$-0.639457\pi$
$587$	−20.5568	−0.848470	−0.424235	+	0.905552i	$0.639457\pi$
$588$	−0.198421	−0.00818273
$589$	6.98645	0.287872
$590$	1.29235	0.0532050
$591$	−40.1141	−1.65007
$592$	32.5513	1.33785
$593$	−32.2130	−1.32283	−0.661416	−	0.750020i	$-0.730044\pi$
$593$	−32.2130	−1.32283	−0.661416	+	0.750020i	$0.730044\pi$
$594$	−19.4139	−0.796563
$595$	2.28419	0.0936428
$596$	−2.11465	−0.0866192
$597$	−30.2054	−1.23623
$598$	0	0
$599$	−39.0364	−1.59499	−0.797493	−	0.603328i	$-0.793841\pi$
$599$	−39.0364	−1.59499	−0.797493	+	0.603328i	$0.793841\pi$
$600$	−5.09328	−0.207932
$601$	−29.3483	−1.19714	−0.598572	−	0.801069i	$-0.704265\pi$
$601$	−29.3483	−1.19714	−0.598572	+	0.801069i	$0.704265\pi$
$602$	−0.359317	−0.0146447
$603$	−0.691149	−0.0281458
$604$	−1.76292	−0.0717320
$605$	−3.39674	−0.138097
$606$	23.9804	0.974137
$607$	15.6861	0.636679	0.318340	−	0.947977i	$-0.396875\pi$
$607$	15.6861	0.636679	0.318340	+	0.947977i	$0.396875\pi$
$608$	0.849107	0.0344359
$609$	12.3954	0.502286
$610$	3.87020	0.156700
$611$	0	0
$612$	−0.0204045	−0.000824803 0
$613$	12.7162	0.513600	0.256800	−	0.966465i	$-0.417332\pi$
$613$	12.7162	0.513600	0.256800	+	0.966465i	$0.417332\pi$
$614$	21.8492	0.881761
$615$	13.8747	0.559482
$616$	−8.00373	−0.322480
$617$	43.0904	1.73475	0.867377	−	0.497652i	$-0.165804\pi$
$617$	43.0904	1.73475	0.867377	+	0.497652i	$0.165804\pi$
$618$	26.9665	1.08475
$619$	−18.8203	−0.756452	−0.378226	−	0.925713i	$-0.623466\pi$
$619$	−18.8203	−0.756452	−0.378226	+	0.925713i	$0.623466\pi$
$620$	−0.594432	−0.0238730
$621$	−27.0120	−1.08395
$622$	−14.5788	−0.584557
$623$	11.3673	0.455423
$624$	0	0
$625$	1.00000	0.0400000
$626$	−31.1120	−1.24348
$627$	6.43045	0.256807
$628$	2.32957	0.0929601
$629$	−19.7693	−0.788254
$630$	0.108514	0.00432332
$631$	13.3159	0.530100	0.265050	−	0.964235i	$-0.414612\pi$
$631$	13.3159	0.530100	0.265050	+	0.964235i	$0.414612\pi$
$632$	11.9321	0.474632
$633$	5.93282	0.235808
$634$	−35.4559	−1.40813
$635$	−3.21199	−0.127464
$636$	0.794542	0.0315057
$637$	0	0
$638$	26.7567	1.05931
$639$	1.03576	0.0409740
$640$	10.2605	0.405583
$641$	−48.1794	−1.90297	−0.951486	−	0.307691i	$-0.900444\pi$
$641$	−48.1794	−1.90297	−0.951486	+	0.307691i	$0.900444\pi$
$642$	4.54616	0.179423
$643$	44.1624	1.74159	0.870797	−	0.491642i	$-0.163603\pi$
$643$	44.1624	1.74159	0.870797	+	0.491642i	$0.163603\pi$
$644$	−0.595939	−0.0234833
$645$	−0.458993	−0.0180728
$646$	4.17010	0.164070
$647$	49.7365	1.95534	0.977672	−	0.210138i	$-0.0673913\pi$
$647$	49.7365	1.95534	0.977672	+	0.210138i	$0.0673913\pi$
$648$	26.7935	1.05255
$649$	2.59419	0.101831
$650$	0	0
$651$	9.22412	0.361522
$652$	−0.853235	−0.0334152
$653$	−2.44073	−0.0955130	−0.0477565	−	0.998859i	$-0.515207\pi$
$653$	−2.44073	−0.0955130	−0.0477565	+	0.998859i	$0.515207\pi$
$654$	34.4843	1.34844
$655$	2.30252	0.0899669
$656$	−29.7392	−1.16112
$657$	−0.907788	−0.0354162
$658$	−9.04692	−0.352686
$659$	−11.5892	−0.451451	−0.225726	−	0.974191i	$-0.572475\pi$
$659$	−11.5892	−0.451451	−0.225726	+	0.974191i	$0.572475\pi$
$660$	−0.547125	−0.0212968
$661$	34.6636	1.34826	0.674129	−	0.738613i	$-0.264519\pi$
$661$	34.6636	1.34826	0.674129	+	0.738613i	$0.264519\pi$
$662$	−23.0437	−0.895618
$663$	0	0
$664$	−35.4583	−1.37605
$665$	1.32904	0.0515378
$666$	−0.939174	−0.0363923
$667$	37.2284	1.44149
$668$	2.23916	0.0866357
$669$	−43.6910	−1.68919
$670$	−12.0181	−0.464302
$671$	7.76885	0.299913
$672$	1.12106	0.0432460
$673$	−16.3189	−0.629049	−0.314524	−	0.949249i	$-0.601845\pi$
$673$	−16.3189	−0.629049	−0.314524	+	0.949249i	$0.601845\pi$
$674$	−39.3681	−1.51640
$675$	−5.12550	−0.197281
$676$	0	0
$677$	−5.65518	−0.217346	−0.108673	−	0.994078i	$-0.534660\pi$
$677$	−5.65518	−0.217346	−0.108673	+	0.994078i	$0.534660\pi$
$678$	−3.37807	−0.129734
$679$	−0.589588	−0.0226263
$680$	−6.63018	−0.254256
$681$	−27.5280	−1.05487
$682$	19.9112	0.762439
$683$	34.4920	1.31980	0.659899	−	0.751354i	$-0.270599\pi$
$683$	34.4920	1.31980	0.659899	+	0.751354i	$0.270599\pi$
$684$	−0.0118722	−0.000453943 0
$685$	14.9323	0.570534
$686$	1.37365	0.0524463
$687$	−18.8766	−0.720187
$688$	0.983810	0.0375074
$689$	0	0
$690$	12.7028	0.483589
$691$	−24.6792	−0.938840	−0.469420	−	0.882975i	$-0.655537\pi$
$691$	−24.6792	−0.938840	−0.469420	+	0.882975i	$0.655537\pi$
$692$	0.342152	0.0130067
$693$	0.217827	0.00827455
$694$	3.19630	0.121330
$695$	7.79719	0.295764
$696$	−35.9793	−1.36379
$697$	18.0614	0.684125
$698$	6.42099	0.243038
$699$	9.16070	0.346490
$700$	−0.113079	−0.00427399
$701$	26.3117	0.993778	0.496889	−	0.867814i	$-0.334476\pi$
$701$	26.3117	0.993778	0.496889	+	0.867814i	$0.334476\pi$
$702$	0	0
$703$	−11.5026	−0.433828
$704$	23.1614	0.872928
$705$	−11.5566	−0.435245
$706$	23.4336	0.881936
$707$	9.94889	0.374167
$708$	−0.186676	−0.00701571
$709$	−29.5828	−1.11101	−0.555503	−	0.831514i	$-0.687474\pi$
$709$	−29.5828	−1.11101	−0.555503	+	0.831514i	$0.687474\pi$
$710$	18.0105	0.675921
$711$	−0.324739	−0.0121787
$712$	−32.9953	−1.23655
$713$	27.7038	1.03752
$714$	5.50572	0.206046
$715$	0	0
$716$	0.584277	0.0218354
$717$	43.2266	1.61433
$718$	−40.4937	−1.51121
$719$	−25.5313	−0.952158	−0.476079	−	0.879403i	$-0.657942\pi$
$719$	−25.5313	−0.952158	−0.476079	+	0.879403i	$0.657942\pi$
$720$	−0.297112	−0.0110727
$721$	11.1878	0.416654
$722$	−23.6731	−0.881020
$723$	22.5087	0.837109
$724$	2.25354	0.0837523
$725$	7.06407	0.262353
$726$	−8.18735	−0.303861
$727$	−20.3527	−0.754840	−0.377420	−	0.926042i	$-0.623189\pi$
$727$	−20.3527	−0.754840	−0.377420	+	0.926042i	$0.623189\pi$
$728$	0	0
$729$	26.2521	0.972299
$730$	−15.7852	−0.584237
$731$	−0.597495	−0.0220992
$732$	−0.559041	−0.0206627
$733$	−38.2744	−1.41370	−0.706849	−	0.707365i	$-0.749884\pi$
$733$	−38.2744	−1.41370	−0.706849	+	0.707365i	$0.749884\pi$
$734$	−1.42050	−0.0524315
$735$	1.75471	0.0647233
$736$	3.36702	0.124110
$737$	−24.1246	−0.888642
$738$	0.858039	0.0315849
$739$	48.1553	1.77142	0.885711	−	0.464236i	$-0.153671\pi$
$739$	48.1553	1.77142	0.885711	+	0.464236i	$0.153671\pi$
$740$	0.978680	0.0359770
$741$	0	0
$742$	−5.50056	−0.201932
$743$	43.1028	1.58129	0.790643	−	0.612277i	$-0.209746\pi$
$743$	43.1028	1.58129	0.790643	+	0.612277i	$0.209746\pi$
$744$	−26.7743	−0.981592
$745$	18.7006	0.685137
$746$	−22.8080	−0.835060
$747$	0.965019	0.0353082
$748$	−0.712221	−0.0260414
$749$	1.88609	0.0689163
$750$	2.41036	0.0880138
$751$	−25.7260	−0.938756	−0.469378	−	0.882997i	$-0.655522\pi$
$751$	−25.7260	−0.938756	−0.469378	+	0.882997i	$0.655522\pi$
$752$	24.7704	0.903285
$753$	−8.06428	−0.293879
$754$	0	0
$755$	15.5901	0.567383
$756$	0.579587	0.0210794
$757$	−18.7598	−0.681835	−0.340918	−	0.940093i	$-0.610738\pi$
$757$	−18.7598	−0.681835	−0.340918	+	0.940093i	$0.610738\pi$
$758$	14.8609	0.539773
$759$	25.4991	0.925557
$760$	−3.85771	−0.139934
$761$	−9.64441	−0.349609	−0.174805	−	0.984603i	$-0.555929\pi$
$761$	−9.64441	−0.349609	−0.174805	+	0.984603i	$0.555929\pi$
$762$	−7.74205	−0.280465
$763$	14.3067	0.517938
$764$	−0.948856	−0.0343284
$765$	0.180445	0.00652399
$766$	8.77458	0.317039
$767$	0	0
$768$	−4.74658	−0.171278
$769$	−26.9500	−0.971842	−0.485921	−	0.874003i	$-0.661516\pi$
$769$	−26.9500	−0.971842	−0.485921	+	0.874003i	$0.661516\pi$
$770$	3.78771	0.136500
$771$	−7.35854	−0.265012
$772$	−0.637214	−0.0229338
$773$	49.9848	1.79783	0.898915	−	0.438123i	$-0.144357\pi$
$773$	49.9848	1.79783	0.898915	+	0.438123i	$0.144357\pi$
$774$	−0.0283850	−0.00102028
$775$	5.25679	0.188829
$776$	1.71136	0.0614342
$777$	−15.1867	−0.544819
$778$	−18.7612	−0.672621
$779$	10.5089	0.376519
$780$	0	0
$781$	36.1533	1.29367
$782$	16.5360	0.591324
$783$	−36.2069	−1.29393
$784$	−3.76106	−0.134323
$785$	−20.6013	−0.735291
$786$	5.54989	0.197958
$787$	22.0576	0.786269	0.393135	−	0.919481i	$-0.371391\pi$
$787$	22.0576	0.786269	0.393135	+	0.919481i	$0.371391\pi$
$788$	2.58508	0.0920898
$789$	−13.3533	−0.475390
$790$	−5.64677	−0.200903
$791$	−1.40148	−0.0498309
$792$	−0.632271	−0.0224668
$793$	0	0
$794$	−4.24703	−0.150721
$795$	−7.02643	−0.249202
$796$	1.94654	0.0689932
$797$	34.3194	1.21566	0.607828	−	0.794069i	$-0.292041\pi$
$797$	34.3194	1.21566	0.607828	+	0.794069i	$0.292041\pi$
$798$	3.20345	0.113401
$799$	−15.0438	−0.532210
$800$	0.638890	0.0225882
$801$	0.897986	0.0317288
$802$	−40.5300	−1.43116
$803$	−31.6864	−1.11819
$804$	1.73599	0.0612237
$805$	5.27011	0.185747
$806$	0	0
$807$	14.8850	0.523978
$808$	−28.8780	−1.01593
$809$	−22.2577	−0.782541	−0.391270	−	0.920276i	$-0.627964\pi$
$809$	−22.2577	−0.782541	−0.391270	+	0.920276i	$0.627964\pi$
$810$	−12.6798	−0.445524
$811$	−12.6010	−0.442480	−0.221240	−	0.975219i	$-0.571010\pi$
$811$	−12.6010	−0.442480	−0.221240	+	0.975219i	$0.571010\pi$
$812$	−0.798799	−0.0280323
$813$	16.1890	0.567774
$814$	−32.7820	−1.14901
$815$	7.54547	0.264306
$816$	−15.0746	−0.527718
$817$	−0.347647	−0.0121626
$818$	0.513860	0.0179667
$819$	0	0
$820$	−0.894132	−0.0312244
$821$	−18.0731	−0.630756	−0.315378	−	0.948966i	$-0.602131\pi$
$821$	−18.0731	−0.630756	−0.315378	+	0.948966i	$0.602131\pi$
$822$	35.9922	1.25537
$823$	−3.89496	−0.135770	−0.0678848	−	0.997693i	$-0.521625\pi$
$823$	−3.89496	−0.135770	−0.0678848	+	0.997693i	$0.521625\pi$
$824$	−32.4740	−1.13129
$825$	4.83843	0.168453
$826$	1.29235	0.0449664
$827$	37.2831	1.29646	0.648230	−	0.761444i	$-0.275509\pi$
$827$	37.2831	1.29646	0.648230	+	0.761444i	$0.275509\pi$
$828$	−0.0470774	−0.00163605
$829$	−11.4245	−0.396791	−0.198395	−	0.980122i	$-0.563573\pi$
$829$	−11.4245	−0.396791	−0.198395	+	0.980122i	$0.563573\pi$
$830$	16.7804	0.582456
$831$	−20.3489	−0.705895
$832$	0	0
$833$	2.28419	0.0791426
$834$	18.7940	0.650784
$835$	−19.8017	−0.685267
$836$	−0.414399	−0.0143323
$837$	−26.9437	−0.931310
$838$	−17.4524	−0.602885
$839$	35.4562	1.22408	0.612042	−	0.790825i	$-0.290348\pi$
$839$	35.4562	1.22408	0.612042	+	0.790825i	$0.290348\pi$
$840$	−5.09328	−0.175735
$841$	20.9011	0.720728
$842$	−10.9267	−0.376559
$843$	28.8500	0.993646
$844$	−0.382330	−0.0131603
$845$	0	0
$846$	−0.714680	−0.0245712
$847$	−3.39674	−0.116713
$848$	15.0605	0.517180
$849$	−49.7527	−1.70751
$850$	3.13769	0.107622
$851$	−45.6119	−1.56356
$852$	−2.60157	−0.0891282
$853$	−17.7762	−0.608644	−0.304322	−	0.952569i	$-0.598430\pi$
$853$	−17.7762	−0.608644	−0.304322	+	0.952569i	$0.598430\pi$
$854$	3.87020	0.132436
$855$	0.104990	0.00359058
$856$	−5.47464	−0.187119
$857$	−38.1540	−1.30332	−0.651658	−	0.758513i	$-0.725926\pi$
$857$	−38.1540	−1.30332	−0.651658	+	0.758513i	$0.725926\pi$
$858$	0	0
$859$	−15.5331	−0.529983	−0.264991	−	0.964251i	$-0.585369\pi$
$859$	−15.5331	−0.529983	−0.264991	+	0.964251i	$0.585369\pi$
$860$	0.0295790	0.00100864
$861$	13.8747	0.472849
$862$	18.4940	0.629907
$863$	−50.7432	−1.72732	−0.863659	−	0.504077i	$-0.831833\pi$
$863$	−50.7432	−1.72732	−0.863659	+	0.504077i	$0.831833\pi$
$864$	−3.27463	−0.111405
$865$	−3.02577	−0.102879
$866$	−7.77935	−0.264353
$867$	−20.6748	−0.702152
$868$	−0.594432	−0.0201763
$869$	−11.3350	−0.384515
$870$	17.0269	0.577267
$871$	0	0
$872$	−41.5272	−1.40629
$873$	−0.0465757	−0.00157635
$874$	9.62128	0.325445
$875$	1.00000	0.0338062
$876$	2.28013	0.0770386
$877$	38.6600	1.30546	0.652728	−	0.757592i	$-0.273624\pi$
$877$	38.6600	1.30546	0.652728	+	0.757592i	$0.273624\pi$
$878$	8.71936	0.294264
$879$	24.6281	0.830685
$880$	−10.3707	−0.349598
$881$	−40.6130	−1.36829	−0.684144	−	0.729347i	$-0.739824\pi$
$881$	−40.6130	−1.36829	−0.684144	+	0.729347i	$0.739824\pi$
$882$	0.108514	0.00365387
$883$	47.2511	1.59013	0.795063	−	0.606527i	$-0.207438\pi$
$883$	47.2511	1.59013	0.795063	+	0.606527i	$0.207438\pi$
$884$	0	0
$885$	1.65084	0.0554925
$886$	9.33514	0.313620
$887$	12.6048	0.423229	0.211614	−	0.977353i	$-0.432128\pi$
$887$	12.6048	0.423229	0.211614	+	0.977353i	$0.432128\pi$
$888$	44.0814	1.47928
$889$	−3.21199	−0.107727
$890$	15.6148	0.523408
$891$	−25.4529	−0.852704
$892$	2.81559	0.0942729
$893$	−8.75307	−0.292910
$894$	45.0751	1.50754
$895$	−5.16697	−0.172713
$896$	10.2605	0.342780
$897$	0	0
$898$	−45.4012	−1.51506
$899$	37.1343	1.23850
$900$	−0.00893291	−0.000297764 0
$901$	−9.14667	−0.304720
$902$	29.9500	0.997224
$903$	−0.458993	−0.0152743
$904$	4.06799	0.135299
$905$	−19.9289	−0.662460
$906$	37.5778	1.24844
$907$	−14.4045	−0.478294	−0.239147	−	0.970983i	$-0.576868\pi$
$907$	−14.4045	−0.478294	−0.239147	+	0.970983i	$0.576868\pi$
$908$	1.77399	0.0588720
$909$	0.785933	0.0260678
$910$	0	0
$911$	18.5299	0.613923	0.306962	−	0.951722i	$-0.400688\pi$
$911$	18.5299	0.613923	0.306962	+	0.951722i	$0.400688\pi$
$912$	−8.77104	−0.290438
$913$	33.6841	1.11478
$914$	37.2892	1.23342
$915$	4.94380	0.163437
$916$	1.21647	0.0401933
$917$	2.30252	0.0760359
$918$	−16.0822	−0.530793
$919$	17.1818	0.566776	0.283388	−	0.959005i	$-0.408542\pi$
$919$	17.1818	0.566776	0.283388	+	0.959005i	$0.408542\pi$
$920$	−15.2972	−0.504334
$921$	27.9102	0.919673
$922$	−23.4257	−0.771486
$923$	0	0
$924$	−0.547125	−0.0179991
$925$	−8.65483	−0.284569
$926$	21.2624	0.698725
$927$	0.883801	0.0290278
$928$	4.51317	0.148152
$929$	−16.4328	−0.539143	−0.269571	−	0.962980i	$-0.586882\pi$
$929$	−16.4328	−0.539143	−0.269571	+	0.962980i	$0.586882\pi$
$930$	12.6707	0.415490
$931$	1.32904	0.0435574
$932$	−0.590346	−0.0193374
$933$	−18.6230	−0.609690
$934$	38.8888	1.27248
$935$	6.29844	0.205981
$936$	0	0
$937$	31.9685	1.04437	0.522183	−	0.852834i	$-0.325118\pi$
$937$	31.9685	1.04437	0.522183	+	0.852834i	$0.325118\pi$
$938$	−12.0181	−0.392406
$939$	−39.7425	−1.29695
$940$	0.744742	0.0242908
$941$	59.2571	1.93173	0.965864	−	0.259051i	$-0.0834099\pi$
$941$	59.2571	1.93173	0.965864	+	0.259051i	$0.0834099\pi$
$942$	−49.6564	−1.61789
$943$	41.6715	1.35701
$944$	−3.53844	−0.115166
$945$	−5.12550	−0.166733
$946$	−0.990783	−0.0322131
$947$	−49.7008	−1.61506	−0.807529	−	0.589828i	$-0.799195\pi$
$947$	−49.7008	−1.61506	−0.807529	+	0.589828i	$0.799195\pi$
$948$	0.815662	0.0264915
$949$	0	0
$950$	1.82563	0.0592313
$951$	−45.2915	−1.46868
$952$	−6.63018	−0.214885
$953$	48.8738	1.58318	0.791589	−	0.611054i	$-0.209254\pi$
$953$	48.8738	1.58318	0.791589	+	0.611054i	$0.209254\pi$
$954$	−0.434528	−0.0140684
$955$	8.39109	0.271529
$956$	−2.78567	−0.0900949
$957$	34.1790	1.10485
$958$	−42.6172	−1.37690
$959$	14.9323	0.482189
$960$	14.7391	0.475701
$961$	−3.36621	−0.108587
$962$	0	0
$963$	0.148996	0.00480132
$964$	−1.45054	−0.0467186
$965$	5.63512	0.181401
$966$	12.7028	0.408707
$967$	−13.5121	−0.434520	−0.217260	−	0.976114i	$-0.569712\pi$
$967$	−13.5121	−0.434520	−0.217260	+	0.976114i	$0.569712\pi$
$968$	9.85949	0.316896
$969$	5.32689	0.171124
$970$	−0.809889	−0.0260040
$971$	24.5418	0.787585	0.393792	−	0.919199i	$-0.371163\pi$
$971$	24.5418	0.787585	0.393792	+	0.919199i	$0.371163\pi$
$972$	0.0928096	0.00297687
$973$	7.79719	0.249966
$974$	−56.4897	−1.81005
$975$	0	0
$976$	−10.5966	−0.339189
$977$	9.67546	0.309545	0.154773	−	0.987950i	$-0.450536\pi$
$977$	9.67546	0.309545	0.154773	+	0.987950i	$0.450536\pi$
$978$	18.1873	0.581565
$979$	31.3443	1.00177
$980$	−0.113079	−0.00361218
$981$	1.13019	0.0360841
$982$	36.3213	1.15906
$983$	−19.8616	−0.633488	−0.316744	−	0.948511i	$-0.602590\pi$
$983$	−19.8616	−0.633488	−0.316744	+	0.948511i	$0.602590\pi$
$984$	−40.2732	−1.28386
$985$	−22.8608	−0.728407
$986$	22.1649	0.705873
$987$	−11.5566	−0.367849
$988$	0	0
$989$	−1.37855	−0.0438352
$990$	0.299218	0.00950977
$991$	−16.7605	−0.532416	−0.266208	−	0.963916i	$-0.585771\pi$
$991$	−16.7605	−0.532416	−0.266208	+	0.963916i	$0.585771\pi$
$992$	3.35851	0.106633
$993$	−29.4360	−0.934125
$994$	18.0105	0.571258
$995$	−17.2140	−0.545719
$996$	−2.42388	−0.0768037
$997$	−34.5407	−1.09392	−0.546958	−	0.837160i	$-0.684214\pi$
$997$	−34.5407	−1.09392	−0.546958	+	0.837160i	$0.684214\pi$
$998$	−18.0173	−0.570328
$999$	44.3604	1.40350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5915.2.a.bp.1.15	yes	21
13.12	even	2		5915.2.a.bo.1.7	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5915.2.a.bo.1.7	✓	21	13.12	even	2
5915.2.a.bp.1.15	yes	21	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5915.a (trivial)

\(f(q)\)	\(=\)	\(q+1.37365 q^{2} +1.75471 q^{3} -0.113079 q^{4} +1.00000 q^{5} +2.41036 q^{6} +1.00000 q^{7} -2.90264 q^{8} +0.0789971 q^{9} +O(q^{10})\)	\(q+1.37365 q^{2} +1.75471 q^{3} -0.113079 q^{4} +1.00000 q^{5} +2.41036 q^{6} +1.00000 q^{7} -2.90264 q^{8} +0.0789971 q^{9} +1.37365 q^{10} +2.75740 q^{11} -0.198421 q^{12} +1.37365 q^{14} +1.75471 q^{15} -3.76106 q^{16} +2.28419 q^{17} +0.108514 q^{18} +1.32904 q^{19} -0.113079 q^{20} +1.75471 q^{21} +3.78771 q^{22} +5.27011 q^{23} -5.09328 q^{24} +1.00000 q^{25} -5.12550 q^{27} -0.113079 q^{28} +7.06407 q^{29} +2.41036 q^{30} +5.25679 q^{31} +0.638890 q^{32} +4.83843 q^{33} +3.13769 q^{34} +1.00000 q^{35} -0.00893291 q^{36} -8.65483 q^{37} +1.82563 q^{38} -2.90264 q^{40} +7.90714 q^{41} +2.41036 q^{42} -0.261578 q^{43} -0.311804 q^{44} +0.0789971 q^{45} +7.23930 q^{46} -6.58603 q^{47} -6.59955 q^{48} +1.00000 q^{49} +1.37365 q^{50} +4.00809 q^{51} -4.00433 q^{53} -7.04066 q^{54} +2.75740 q^{55} -2.90264 q^{56} +2.33207 q^{57} +9.70358 q^{58} +0.940809 q^{59} -0.198421 q^{60} +2.81745 q^{61} +7.22100 q^{62} +0.0789971 q^{63} +8.39972 q^{64} +6.64632 q^{66} -8.74905 q^{67} -0.258294 q^{68} +9.24750 q^{69} +1.37365 q^{70} +13.1114 q^{71} -0.229300 q^{72} -11.4914 q^{73} -11.8887 q^{74} +1.75471 q^{75} -0.150286 q^{76} +2.75740 q^{77} -4.11077 q^{79} -3.76106 q^{80} -9.23075 q^{81} +10.8617 q^{82} +12.2159 q^{83} -0.198421 q^{84} +2.28419 q^{85} -0.359317 q^{86} +12.3954 q^{87} -8.00373 q^{88} +11.3673 q^{89} +0.108514 q^{90} -0.595939 q^{92} +9.22412 q^{93} -9.04692 q^{94} +1.32904 q^{95} +1.12106 q^{96} -0.589588 q^{97} +1.37365 q^{98} +0.217827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9}+O(q^{10}) \) 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9	\( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9} + 4 q^{10} + 2 q^{11} + 23 q^{12} + 4 q^{14} + 5 q^{15} + 18 q^{16} - 6 q^{17} + 32 q^{18} + 8 q^{19} + 20 q^{20} + 5 q^{21} - 17 q^{22} - 14 q^{23} + 27 q^{24} + 21 q^{25} + 11 q^{27} + 20 q^{28} + 20 q^{29} + 4 q^{30} + 22 q^{31} + 22 q^{32} + 33 q^{33} + 22 q^{34} + 21 q^{35} - 8 q^{36} + 48 q^{37} + 42 q^{38} + 9 q^{40} - 5 q^{41} + 4 q^{42} - 27 q^{43} - 4 q^{44} + 28 q^{45} + 9 q^{46} + 27 q^{48} + 21 q^{49} + 4 q^{50} - 4 q^{51} - 28 q^{53} + 27 q^{54} + 2 q^{55} + 9 q^{56} + 56 q^{57} + 44 q^{58} + 7 q^{59} + 23 q^{60} + 25 q^{61} - 17 q^{62} + 28 q^{63} + 47 q^{64} - 30 q^{66} + 40 q^{67} - 19 q^{68} + 13 q^{69} + 4 q^{70} + 15 q^{71} + 42 q^{72} + 16 q^{73} + 37 q^{74} + 5 q^{75} + 58 q^{76} + 2 q^{77} - 10 q^{79} + 18 q^{80} + 25 q^{81} + 14 q^{82} - 11 q^{83} + 23 q^{84} - 6 q^{85} + 35 q^{86} + 65 q^{87} - 74 q^{88} + 24 q^{89} + 32 q^{90} - 89 q^{92} + 82 q^{93} + 21 q^{94} + 8 q^{95} - 22 q^{96} + 57 q^{97} + 4 q^{98} + 6 q^{99}+O(q^{100}) \) 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9 + 4 * q^10 + 2 * q^11 + 23 * q^12 + 4 * q^14 + 5 * q^15 + 18 * q^16 - 6 * q^17 + 32 * q^18 + 8 * q^19 + 20 * q^20 + 5 * q^21 - 17 * q^22 - 14 * q^23 + 27 * q^24 + 21 * q^25 + 11 * q^27 + 20 * q^28 + 20 * q^29 + 4 * q^30 + 22 * q^31 + 22 * q^32 + 33 * q^33 + 22 * q^34 + 21 * q^35 - 8 * q^36 + 48 * q^37 + 42 * q^38 + 9 * q^40 - 5 * q^41 + 4 * q^42 - 27 * q^43 - 4 * q^44 + 28 * q^45 + 9 * q^46 + 27 * q^48 + 21 * q^49 + 4 * q^50 - 4 * q^51 - 28 * q^53 + 27 * q^54 + 2 * q^55 + 9 * q^56 + 56 * q^57 + 44 * q^58 + 7 * q^59 + 23 * q^60 + 25 * q^61 - 17 * q^62 + 28 * q^63 + 47 * q^64 - 30 * q^66 + 40 * q^67 - 19 * q^68 + 13 * q^69 + 4 * q^70 + 15 * q^71 + 42 * q^72 + 16 * q^73 + 37 * q^74 + 5 * q^75 + 58 * q^76 + 2 * q^77 - 10 * q^79 + 18 * q^80 + 25 * q^81 + 14 * q^82 - 11 * q^83 + 23 * q^84 - 6 * q^85 + 35 * q^86 + 65 * q^87 - 74 * q^88 + 24 * q^89 + 32 * q^90 - 89 * q^92 + 82 * q^93 + 21 * q^94 + 8 * q^95 - 22 * q^96 + 57 * q^97 + 4 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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