LMFDB - Embedded newform 4598.2.a.ca.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.07616$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.05958 q^{3} +1.00000 q^{4} +1.96511 q^{5} +2.05958 q^{6} +4.12502 q^{7} +1.00000 q^{8} +1.24187 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.05958 q^{3} +1.00000 q^{4} +1.96511 q^{5} +2.05958 q^{6} +4.12502 q^{7} +1.00000 q^{8} +1.24187 q^{9} +1.96511 q^{10} +2.05958 q^{12} -4.76986 q^{13} +4.12502 q^{14} +4.04730 q^{15} +1.00000 q^{16} +7.01028 q^{17} +1.24187 q^{18} -1.00000 q^{19} +1.96511 q^{20} +8.49580 q^{21} +3.10979 q^{23} +2.05958 q^{24} -1.13834 q^{25} -4.76986 q^{26} -3.62101 q^{27} +4.12502 q^{28} -0.675883 q^{29} +4.04730 q^{30} -0.811231 q^{31} +1.00000 q^{32} +7.01028 q^{34} +8.10611 q^{35} +1.24187 q^{36} -11.7536 q^{37} -1.00000 q^{38} -9.82390 q^{39} +1.96511 q^{40} +8.27614 q^{41} +8.49580 q^{42} +7.01961 q^{43} +2.44041 q^{45} +3.10979 q^{46} -6.04189 q^{47} +2.05958 q^{48} +10.0158 q^{49} -1.13834 q^{50} +14.4382 q^{51} -4.76986 q^{52} -4.92993 q^{53} -3.62101 q^{54} +4.12502 q^{56} -2.05958 q^{57} -0.675883 q^{58} +6.10492 q^{59} +4.04730 q^{60} -3.70791 q^{61} -0.811231 q^{62} +5.12273 q^{63} +1.00000 q^{64} -9.37329 q^{65} -12.3789 q^{67} +7.01028 q^{68} +6.40485 q^{69} +8.10611 q^{70} +8.67449 q^{71} +1.24187 q^{72} +9.96615 q^{73} -11.7536 q^{74} -2.34451 q^{75} -1.00000 q^{76} -9.82390 q^{78} -14.3691 q^{79} +1.96511 q^{80} -11.1834 q^{81} +8.27614 q^{82} -2.49600 q^{83} +8.49580 q^{84} +13.7760 q^{85} +7.01961 q^{86} -1.39203 q^{87} +8.51163 q^{89} +2.44041 q^{90} -19.6757 q^{91} +3.10979 q^{92} -1.67080 q^{93} -6.04189 q^{94} -1.96511 q^{95} +2.05958 q^{96} +14.2558 q^{97} +10.0158 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.05958	1.18910	0.594549	−	0.804059i	$-0.297330\pi$
$3$	2.05958	1.18910	0.594549	+	0.804059i	$0.297330\pi$
$4$	1.00000	0.500000
$5$	1.96511	0.878824	0.439412	−	0.898286i	$-0.355187\pi$
$5$	1.96511	0.878824	0.439412	+	0.898286i	$0.355187\pi$
$6$	2.05958	0.840820
$7$	4.12502	1.55911	0.779555	−	0.626334i	$-0.215445\pi$
$7$	4.12502	1.55911	0.779555	+	0.626334i	$0.215445\pi$
$8$	1.00000	0.353553
$9$	1.24187	0.413956
$10$	1.96511	0.621422
$11$	0	0
$11$	0	0
$12$	2.05958	0.594549
$13$	−4.76986	−1.32292	−0.661460	−	0.749980i	$-0.730063\pi$
$13$	−4.76986	−1.32292	−0.661460	+	0.749980i	$0.730063\pi$
$14$	4.12502	1.10246
$15$	4.04730	1.04501
$16$	1.00000	0.250000
$17$	7.01028	1.70024	0.850122	−	0.526586i	$-0.176528\pi$
$17$	7.01028	1.70024	0.850122	+	0.526586i	$0.176528\pi$
$18$	1.24187	0.292711
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.96511	0.439412
$21$	8.49580	1.85394
$22$	0	0
$23$	3.10979	0.648435	0.324218	−	0.945982i	$-0.394899\pi$
$23$	3.10979	0.648435	0.324218	+	0.945982i	$0.394899\pi$
$24$	2.05958	0.420410
$25$	−1.13834	−0.227669
$26$	−4.76986	−0.935446
$27$	−3.62101	−0.696864
$28$	4.12502	0.779555
$29$	−0.675883	−0.125508	−0.0627541	−	0.998029i	$-0.519988\pi$
$29$	−0.675883	−0.125508	−0.0627541	+	0.998029i	$0.519988\pi$
$30$	4.04730	0.738932
$31$	−0.811231	−0.145701	−0.0728507	−	0.997343i	$-0.523210\pi$
$31$	−0.811231	−0.145701	−0.0728507	+	0.997343i	$0.523210\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	7.01028	1.20225
$35$	8.10611	1.37018
$36$	1.24187	0.206978
$37$	−11.7536	−1.93228	−0.966139	−	0.258023i	$-0.916929\pi$
$37$	−11.7536	−1.93228	−0.966139	+	0.258023i	$0.916929\pi$
$38$	−1.00000	−0.162221
$39$	−9.82390	−1.57308
$40$	1.96511	0.310711
$41$	8.27614	1.29252	0.646258	−	0.763119i	$-0.276333\pi$
$41$	8.27614	1.29252	0.646258	+	0.763119i	$0.276333\pi$
$42$	8.49580	1.31093
$43$	7.01961	1.07048	0.535240	−	0.844700i	$-0.320221\pi$
$43$	7.01961	1.07048	0.535240	+	0.844700i	$0.320221\pi$
$44$	0	0
$45$	2.44041	0.363794
$46$	3.10979	0.458513
$47$	−6.04189	−0.881301	−0.440650	−	0.897679i	$-0.645252\pi$
$47$	−6.04189	−0.881301	−0.440650	+	0.897679i	$0.645252\pi$
$48$	2.05958	0.297275
$49$	10.0158	1.43082
$50$	−1.13834	−0.160986
$51$	14.4382	2.02176
$52$	−4.76986	−0.661460
$53$	−4.92993	−0.677178	−0.338589	−	0.940934i	$-0.609950\pi$
$53$	−4.92993	−0.677178	−0.338589	+	0.940934i	$0.609950\pi$
$54$	−3.62101	−0.492757
$55$	0	0
$56$	4.12502	0.551229
$57$	−2.05958	−0.272798
$58$	−0.675883	−0.0887477
$59$	6.10492	0.794793	0.397396	−	0.917647i	$-0.369914\pi$
$59$	6.10492	0.794793	0.397396	+	0.917647i	$0.369914\pi$
$60$	4.04730	0.522504
$61$	−3.70791	−0.474749	−0.237374	−	0.971418i	$-0.576287\pi$
$61$	−3.70791	−0.474749	−0.237374	+	0.971418i	$0.576287\pi$
$62$	−0.811231	−0.103026
$63$	5.12273	0.645403
$64$	1.00000	0.125000
$65$	−9.37329	−1.16261
$66$	0	0
$67$	−12.3789	−1.51233	−0.756164	−	0.654383i	$-0.772929\pi$
$67$	−12.3789	−1.51233	−0.756164	+	0.654383i	$0.772929\pi$
$68$	7.01028	0.850122
$69$	6.40485	0.771054
$70$	8.10611	0.968866
$71$	8.67449	1.02947	0.514736	−	0.857349i	$-0.327890\pi$
$71$	8.67449	1.02947	0.514736	+	0.857349i	$0.327890\pi$
$72$	1.24187	0.146356
$73$	9.96615	1.16645	0.583225	−	0.812311i	$-0.301791\pi$
$73$	9.96615	1.16645	0.583225	+	0.812311i	$0.301791\pi$
$74$	−11.7536	−1.36633
$75$	−2.34451	−0.270721
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−9.82390	−1.11234
$79$	−14.3691	−1.61665	−0.808324	−	0.588738i	$-0.799625\pi$
$79$	−14.3691	−1.61665	−0.808324	+	0.588738i	$0.799625\pi$
$80$	1.96511	0.219706
$81$	−11.1834	−1.24260
$82$	8.27614	0.913947
$83$	−2.49600	−0.273972	−0.136986	−	0.990573i	$-0.543741\pi$
$83$	−2.49600	−0.273972	−0.136986	+	0.990573i	$0.543741\pi$
$84$	8.49580	0.926968
$85$	13.7760	1.49421
$86$	7.01961	0.756944
$87$	−1.39203	−0.149242
$88$	0	0
$89$	8.51163	0.902231	0.451116	−	0.892466i	$-0.351026\pi$
$89$	8.51163	0.902231	0.451116	+	0.892466i	$0.351026\pi$
$90$	2.44041	0.257241
$91$	−19.6757	−2.06258
$92$	3.10979	0.324218
$93$	−1.67080	−0.173253
$94$	−6.04189	−0.623174
$95$	−1.96511	−0.201616
$96$	2.05958	0.210205
$97$	14.2558	1.44746	0.723728	−	0.690086i	$-0.242427\pi$
$97$	14.2558	1.44746	0.723728	+	0.690086i	$0.242427\pi$
$98$	10.0158	1.01175
$99$	0	0
$100$	−1.13834	−0.113834
$101$	−12.0190	−1.19593	−0.597967	−	0.801521i	$-0.704025\pi$
$101$	−12.0190	−1.19593	−0.597967	+	0.801521i	$0.704025\pi$
$102$	14.4382	1.42960
$103$	−7.10389	−0.699967	−0.349984	−	0.936756i	$-0.613813\pi$
$103$	−7.10389	−0.699967	−0.349984	+	0.936756i	$0.613813\pi$
$104$	−4.76986	−0.467723
$105$	16.6952	1.62928
$106$	−4.92993	−0.478837
$107$	8.59343	0.830759	0.415379	−	0.909648i	$-0.363649\pi$
$107$	8.59343	0.830759	0.415379	+	0.909648i	$0.363649\pi$
$108$	−3.62101	−0.348432
$109$	−10.3108	−0.987591	−0.493795	−	0.869578i	$-0.664391\pi$
$109$	−10.3108	−0.987591	−0.493795	+	0.869578i	$0.664391\pi$
$110$	0	0
$111$	−24.2074	−2.29767
$112$	4.12502	0.389778
$113$	−2.89424	−0.272267	−0.136133	−	0.990691i	$-0.543468\pi$
$113$	−2.89424	−0.272267	−0.136133	+	0.990691i	$0.543468\pi$
$114$	−2.05958	−0.192897
$115$	6.11107	0.569860
$116$	−0.675883	−0.0627541
$117$	−5.92353	−0.547631
$118$	6.10492	0.562003
$119$	28.9175	2.65087
$120$	4.04730	0.369466
$121$	0	0
$122$	−3.70791	−0.335698
$123$	17.0454	1.53693
$124$	−0.811231	−0.0728507
$125$	−12.0625	−1.07890
$126$	5.12273	0.456369
$127$	−2.48900	−0.220863	−0.110431	−	0.993884i	$-0.535223\pi$
$127$	−2.48900	−0.220863	−0.110431	+	0.993884i	$0.535223\pi$
$128$	1.00000	0.0883883
$129$	14.4574	1.27291
$130$	−9.37329	−0.822092
$131$	3.29365	0.287767	0.143884	−	0.989595i	$-0.454041\pi$
$131$	3.29365	0.287767	0.143884	+	0.989595i	$0.454041\pi$
$132$	0	0
$133$	−4.12502	−0.357684
$134$	−12.3789	−1.06938
$135$	−7.11569	−0.612421
$136$	7.01028	0.601127
$137$	−5.10805	−0.436410	−0.218205	−	0.975903i	$-0.570020\pi$
$137$	−5.10805	−0.436410	−0.218205	+	0.975903i	$0.570020\pi$
$138$	6.40485	0.545217
$139$	18.4361	1.56373	0.781866	−	0.623447i	$-0.214268\pi$
$139$	18.4361	1.56373	0.781866	+	0.623447i	$0.214268\pi$
$140$	8.10611	0.685091
$141$	−12.4438	−1.04795
$142$	8.67449	0.727947
$143$	0	0
$144$	1.24187	0.103489
$145$	−1.32818	−0.110300
$146$	9.96615	0.824805
$147$	20.6283	1.70139
$148$	−11.7536	−0.966139
$149$	−3.22972	−0.264589	−0.132295	−	0.991210i	$-0.542234\pi$
$149$	−3.22972	−0.264589	−0.132295	+	0.991210i	$0.542234\pi$
$150$	−2.34451	−0.191429
$151$	−6.78491	−0.552148	−0.276074	−	0.961136i	$-0.589034\pi$
$151$	−6.78491	−0.552148	−0.276074	+	0.961136i	$0.589034\pi$
$152$	−1.00000	−0.0811107
$153$	8.70585	0.703826
$154$	0	0
$155$	−1.59416	−0.128046
$156$	−9.82390	−0.786542
$157$	6.83869	0.545787	0.272894	−	0.962044i	$-0.412019\pi$
$157$	6.83869	0.545787	0.272894	+	0.962044i	$0.412019\pi$
$158$	−14.3691	−1.14314
$159$	−10.1536	−0.805231
$160$	1.96511	0.155356
$161$	12.8279	1.01098
$162$	−11.1834	−0.878648
$163$	−18.5559	−1.45341	−0.726704	−	0.686951i	$-0.758949\pi$
$163$	−18.5559	−1.45341	−0.726704	+	0.686951i	$0.758949\pi$
$164$	8.27614	0.646258
$165$	0	0
$166$	−2.49600	−0.193727
$167$	7.85416	0.607773	0.303887	−	0.952708i	$-0.401716\pi$
$167$	7.85416	0.607773	0.303887	+	0.952708i	$0.401716\pi$
$168$	8.49580	0.655465
$169$	9.75154	0.750118
$170$	13.7760	1.05657
$171$	−1.24187	−0.0949680
$172$	7.01961	0.535240
$173$	22.4632	1.70785	0.853923	−	0.520399i	$-0.174217\pi$
$173$	22.4632	1.70785	0.853923	+	0.520399i	$0.174217\pi$
$174$	−1.39203	−0.105530
$175$	−4.69569	−0.354961
$176$	0	0
$177$	12.5736	0.945087
$178$	8.51163	0.637974
$179$	−8.60585	−0.643232	−0.321616	−	0.946870i	$-0.604226\pi$
$179$	−8.60585	−0.643232	−0.321616	+	0.946870i	$0.604226\pi$
$180$	2.44041	0.181897
$181$	−9.93724	−0.738629	−0.369315	−	0.929304i	$-0.620408\pi$
$181$	−9.93724	−0.738629	−0.369315	+	0.929304i	$0.620408\pi$
$182$	−19.6757	−1.45846
$183$	−7.63673	−0.564523
$184$	3.10979	0.229257
$185$	−23.0971	−1.69813
$186$	−1.67080	−0.122509
$187$	0	0
$188$	−6.04189	−0.440650
$189$	−14.9367	−1.08649
$190$	−1.96511	−0.142564
$191$	−8.11362	−0.587081	−0.293541	−	0.955947i	$-0.594834\pi$
$191$	−8.11362	−0.587081	−0.293541	+	0.955947i	$0.594834\pi$
$192$	2.05958	0.148637
$193$	−17.2125	−1.23898	−0.619492	−	0.785003i	$-0.712661\pi$
$193$	−17.2125	−1.23898	−0.619492	+	0.785003i	$0.712661\pi$
$194$	14.2558	1.02351
$195$	−19.3050	−1.38246
$196$	10.0158	0.715412
$197$	18.5503	1.32165	0.660826	−	0.750539i	$-0.270206\pi$
$197$	18.5503	1.32165	0.660826	+	0.750539i	$0.270206\pi$
$198$	0	0
$199$	−13.4114	−0.950710	−0.475355	−	0.879794i	$-0.657680\pi$
$199$	−13.4114	−0.950710	−0.475355	+	0.879794i	$0.657680\pi$
$200$	−1.13834	−0.0804931
$201$	−25.4954	−1.79831
$202$	−12.0190	−0.845653
$203$	−2.78803	−0.195681
$204$	14.4382	1.01088
$205$	16.2635	1.13589
$206$	−7.10389	−0.494952
$207$	3.86195	0.268424
$208$	−4.76986	−0.330730
$209$	0	0
$210$	16.6952	1.15208
$211$	−10.6127	−0.730607	−0.365304	−	0.930888i	$-0.619035\pi$
$211$	−10.6127	−0.730607	−0.365304	+	0.930888i	$0.619035\pi$
$212$	−4.92993	−0.338589
$213$	17.8658	1.22414
$214$	8.59343	0.587435
$215$	13.7943	0.940764
$216$	−3.62101	−0.246379
$217$	−3.34634	−0.227165
$218$	−10.3108	−0.698332
$219$	20.5261	1.38702
$220$	0	0
$221$	−33.4381	−2.24929
$222$	−24.2074	−1.62470
$223$	21.4887	1.43899	0.719496	−	0.694497i	$-0.244373\pi$
$223$	21.4887	1.43899	0.719496	+	0.694497i	$0.244373\pi$
$224$	4.12502	0.275614
$225$	−1.41367	−0.0942450
$226$	−2.89424	−0.192522
$227$	−12.6367	−0.838730	−0.419365	−	0.907818i	$-0.637747\pi$
$227$	−12.6367	−0.838730	−0.419365	+	0.907818i	$0.637747\pi$
$228$	−2.05958	−0.136399
$229$	−14.1933	−0.937919	−0.468959	−	0.883220i	$-0.655371\pi$
$229$	−14.1933	−0.937919	−0.468959	+	0.883220i	$0.655371\pi$
$230$	6.11107	0.402952
$231$	0	0
$232$	−0.675883	−0.0443739
$233$	7.42529	0.486447	0.243223	−	0.969970i	$-0.421795\pi$
$233$	7.42529	0.486447	0.243223	+	0.969970i	$0.421795\pi$
$234$	−5.92353	−0.387234
$235$	−11.8730	−0.774508
$236$	6.10492	0.397396
$237$	−29.5943	−1.92235
$238$	28.9175	1.87445
$239$	−5.48322	−0.354680	−0.177340	−	0.984150i	$-0.556749\pi$
$239$	−5.48322	−0.354680	−0.177340	+	0.984150i	$0.556749\pi$
$240$	4.04730	0.261252
$241$	−13.6790	−0.881139	−0.440570	−	0.897718i	$-0.645224\pi$
$241$	−13.6790	−0.881139	−0.440570	+	0.897718i	$0.645224\pi$
$242$	0	0
$243$	−12.1700	−0.780706
$244$	−3.70791	−0.237374
$245$	19.6821	1.25744
$246$	17.0454	1.08677
$247$	4.76986	0.303499
$248$	−0.811231	−0.0515132
$249$	−5.14071	−0.325779
$250$	−12.0625	−0.762901
$251$	−8.28409	−0.522887	−0.261444	−	0.965219i	$-0.584199\pi$
$251$	−8.28409	−0.522887	−0.261444	+	0.965219i	$0.584199\pi$
$252$	5.12273	0.322702
$253$	0	0
$254$	−2.48900	−0.156173
$255$	28.3727	1.77677
$256$	1.00000	0.0625000
$257$	19.0887	1.19072	0.595360	−	0.803459i	$-0.297010\pi$
$257$	19.0887	1.19072	0.595360	+	0.803459i	$0.297010\pi$
$258$	14.4574	0.900081
$259$	−48.4838	−3.01263
$260$	−9.37329	−0.581307
$261$	−0.839357	−0.0519549
$262$	3.29365	0.203482
$263$	−20.9903	−1.29431	−0.647157	−	0.762357i	$-0.724042\pi$
$263$	−20.9903	−1.29431	−0.647157	+	0.762357i	$0.724042\pi$
$264$	0	0
$265$	−9.68785	−0.595120
$266$	−4.12502	−0.252921
$267$	17.5304	1.07284
$268$	−12.3789	−0.756164
$269$	−25.9056	−1.57949	−0.789747	−	0.613433i	$-0.789788\pi$
$269$	−25.9056	−1.57949	−0.789747	+	0.613433i	$0.789788\pi$
$270$	−7.11569	−0.433047
$271$	10.6882	0.649263	0.324632	−	0.945841i	$-0.394760\pi$
$271$	10.6882	0.649263	0.324632	+	0.945841i	$0.394760\pi$
$272$	7.01028	0.425061
$273$	−40.5238	−2.45261
$274$	−5.10805	−0.308589
$275$	0	0
$276$	6.40485	0.385527
$277$	23.4491	1.40892	0.704460	−	0.709744i	$-0.251189\pi$
$277$	23.4491	1.40892	0.704460	+	0.709744i	$0.251189\pi$
$278$	18.4361	1.10573
$279$	−1.00744	−0.0603140
$280$	8.10611	0.484433
$281$	16.5620	0.988008	0.494004	−	0.869460i	$-0.335533\pi$
$281$	16.5620	0.988008	0.494004	+	0.869460i	$0.335533\pi$
$282$	−12.4438	−0.741015
$283$	−1.56041	−0.0927567	−0.0463783	−	0.998924i	$-0.514768\pi$
$283$	−1.56041	−0.0927567	−0.0463783	+	0.998924i	$0.514768\pi$
$284$	8.67449	0.514736
$285$	−4.04730	−0.239741
$286$	0	0
$287$	34.1392	2.01517
$288$	1.24187	0.0731778
$289$	32.1441	1.89083
$290$	−1.32818	−0.0779936
$291$	29.3609	1.72117
$292$	9.96615	0.583225
$293$	2.27229	0.132749	0.0663743	−	0.997795i	$-0.478857\pi$
$293$	2.27229	0.132749	0.0663743	+	0.997795i	$0.478857\pi$
$294$	20.6283	1.20307
$295$	11.9968	0.698483
$296$	−11.7536	−0.683163
$297$	0	0
$298$	−3.22972	−0.187093
$299$	−14.8332	−0.857829
$300$	−2.34451	−0.135360
$301$	28.9560	1.66900
$302$	−6.78491	−0.390428
$303$	−24.7541	−1.42208
$304$	−1.00000	−0.0573539
$305$	−7.28645	−0.417221
$306$	8.70585	0.497680
$307$	−15.9893	−0.912556	−0.456278	−	0.889837i	$-0.650818\pi$
$307$	−15.9893	−0.912556	−0.456278	+	0.889837i	$0.650818\pi$
$308$	0	0
$309$	−14.6310	−0.832330
$310$	−1.59416	−0.0905421
$311$	12.2309	0.693553	0.346777	−	0.937948i	$-0.387276\pi$
$311$	12.2309	0.693553	0.346777	+	0.937948i	$0.387276\pi$
$312$	−9.82390	−0.556169
$313$	−28.7920	−1.62742	−0.813711	−	0.581270i	$-0.802556\pi$
$313$	−28.7920	−1.62742	−0.813711	+	0.581270i	$0.802556\pi$
$314$	6.83869	0.385930
$315$	10.0667	0.567196
$316$	−14.3691	−0.808324
$317$	10.3072	0.578910	0.289455	−	0.957192i	$-0.406526\pi$
$317$	10.3072	0.578910	0.289455	+	0.957192i	$0.406526\pi$
$318$	−10.1536	−0.569385
$319$	0	0
$320$	1.96511	0.109853
$321$	17.6989	0.987854
$322$	12.8279	0.714873
$323$	−7.01028	−0.390063
$324$	−11.1834	−0.621298
$325$	5.42974	0.301188
$326$	−18.5559	−1.02771
$327$	−21.2358	−1.17434
$328$	8.27614	0.456973
$329$	−24.9229	−1.37405
$330$	0	0
$331$	−1.18204	−0.0649706	−0.0324853	−	0.999472i	$-0.510342\pi$
$331$	−1.18204	−0.0649706	−0.0324853	+	0.999472i	$0.510342\pi$
$332$	−2.49600	−0.136986
$333$	−14.5964	−0.799878
$334$	7.85416	0.429760
$335$	−24.3260	−1.32907
$336$	8.49580	0.463484
$337$	−3.82507	−0.208365	−0.104182	−	0.994558i	$-0.533223\pi$
$337$	−3.82507	−0.208365	−0.104182	+	0.994558i	$0.533223\pi$
$338$	9.75154	0.530414
$339$	−5.96091	−0.323752
$340$	13.7760	0.747107
$341$	0	0
$342$	−1.24187	−0.0671525
$343$	12.4401	0.671703
$344$	7.01961	0.378472
$345$	12.5862	0.677620
$346$	22.4632	1.20763
$347$	−15.7136	−0.843551	−0.421776	−	0.906700i	$-0.638593\pi$
$347$	−15.7136	−0.843551	−0.421776	+	0.906700i	$0.638593\pi$
$348$	−1.39203	−0.0746209
$349$	28.8965	1.54679	0.773396	−	0.633923i	$-0.218556\pi$
$349$	28.8965	1.54679	0.773396	+	0.633923i	$0.218556\pi$
$350$	−4.69569	−0.250995
$351$	17.2717	0.921896
$352$	0	0
$353$	22.1628	1.17960	0.589802	−	0.807548i	$-0.299206\pi$
$353$	22.1628	1.17960	0.589802	+	0.807548i	$0.299206\pi$
$354$	12.5736	0.668277
$355$	17.0463	0.904725
$356$	8.51163	0.451116
$357$	59.5580	3.15214
$358$	−8.60585	−0.454834
$359$	23.7708	1.25458	0.627288	−	0.778788i	$-0.284165\pi$
$359$	23.7708	1.25458	0.627288	+	0.778788i	$0.284165\pi$
$360$	2.44041	0.128621
$361$	1.00000	0.0526316
$362$	−9.93724	−0.522290
$363$	0	0
$364$	−19.6757	−1.03129
$365$	19.5846	1.02510
$366$	−7.63673	−0.399178
$367$	22.8787	1.19426	0.597129	−	0.802145i	$-0.296308\pi$
$367$	22.8787	1.19426	0.597129	+	0.802145i	$0.296308\pi$
$368$	3.10979	0.162109
$369$	10.2779	0.535045
$370$	−23.0971	−1.20076
$371$	−20.3360	−1.05579
$372$	−1.67080	−0.0866267
$373$	−0.861889	−0.0446269	−0.0223135	−	0.999751i	$-0.507103\pi$
$373$	−0.861889	−0.0446269	−0.0223135	+	0.999751i	$0.507103\pi$
$374$	0	0
$375$	−24.8437	−1.28292
$376$	−6.04189	−0.311587
$377$	3.22386	0.166037
$378$	−14.9367	−0.768263
$379$	27.3522	1.40499	0.702493	−	0.711691i	$-0.252070\pi$
$379$	27.3522	1.40499	0.702493	+	0.711691i	$0.252070\pi$
$380$	−1.96511	−0.100808
$381$	−5.12628	−0.262627
$382$	−8.11362	−0.415129
$383$	11.3104	0.577937	0.288968	−	0.957339i	$-0.406688\pi$
$383$	11.3104	0.577937	0.288968	+	0.957339i	$0.406688\pi$
$384$	2.05958	0.105102
$385$	0	0
$386$	−17.2125	−0.876093
$387$	8.71743	0.443132
$388$	14.2558	0.723728
$389$	−15.3376	−0.777648	−0.388824	−	0.921312i	$-0.627119\pi$
$389$	−15.3376	−0.777648	−0.388824	+	0.921312i	$0.627119\pi$
$390$	−19.3050	−0.977549
$391$	21.8005	1.10250
$392$	10.0158	0.505873
$393$	6.78353	0.342184
$394$	18.5503	0.934550
$395$	−28.2368	−1.42075
$396$	0	0
$397$	−14.1783	−0.711591	−0.355795	−	0.934564i	$-0.615790\pi$
$397$	−14.1783	−0.711591	−0.355795	+	0.934564i	$0.615790\pi$
$398$	−13.4114	−0.672253
$399$	−8.49580	−0.425322
$400$	−1.13834	−0.0569172
$401$	18.6618	0.931924	0.465962	−	0.884805i	$-0.345708\pi$
$401$	18.6618	0.931924	0.465962	+	0.884805i	$0.345708\pi$
$402$	−25.4954	−1.27159
$403$	3.86946	0.192751
$404$	−12.0190	−0.597967
$405$	−21.9765	−1.09202
$406$	−2.78803	−0.138368
$407$	0	0
$408$	14.4382	0.714799
$409$	25.9246	1.28189	0.640944	−	0.767588i	$-0.278543\pi$
$409$	25.9246	1.28189	0.640944	+	0.767588i	$0.278543\pi$
$410$	16.2635	0.803198
$411$	−10.5204	−0.518935
$412$	−7.10389	−0.349984
$413$	25.1829	1.23917
$414$	3.86195	0.189804
$415$	−4.90491	−0.240773
$416$	−4.76986	−0.233862
$417$	37.9707	1.85943
$418$	0	0
$419$	6.07570	0.296818	0.148409	−	0.988926i	$-0.452585\pi$
$419$	6.07570	0.296818	0.148409	+	0.988926i	$0.452585\pi$
$420$	16.6952	0.814641
$421$	3.55276	0.173151	0.0865754	−	0.996245i	$-0.472408\pi$
$421$	3.55276	0.173151	0.0865754	+	0.996245i	$0.472408\pi$
$422$	−10.6127	−0.516617
$423$	−7.50324	−0.364820
$424$	−4.92993	−0.239419
$425$	−7.98012	−0.387093
$426$	17.8658	0.865601
$427$	−15.2952	−0.740186
$428$	8.59343	0.415379
$429$	0	0
$430$	13.7943	0.665220
$431$	−29.6777	−1.42952	−0.714762	−	0.699368i	$-0.753465\pi$
$431$	−29.6777	−1.42952	−0.714762	+	0.699368i	$0.753465\pi$
$432$	−3.62101	−0.174216
$433$	−21.8264	−1.04891	−0.524454	−	0.851438i	$-0.675731\pi$
$433$	−21.8264	−1.04891	−0.524454	+	0.851438i	$0.675731\pi$
$434$	−3.34634	−0.160630
$435$	−2.73550	−0.131157
$436$	−10.3108	−0.493795
$437$	−3.10979	−0.148761
$438$	20.5261	0.980774
$439$	21.6449	1.03305	0.516527	−	0.856271i	$-0.327224\pi$
$439$	21.6449	1.03305	0.516527	+	0.856271i	$0.327224\pi$
$440$	0	0
$441$	12.4383	0.592299
$442$	−33.4381	−1.59049
$443$	−8.31451	−0.395034	−0.197517	−	0.980299i	$-0.563288\pi$
$443$	−8.31451	−0.395034	−0.197517	+	0.980299i	$0.563288\pi$
$444$	−24.2074	−1.14883
$445$	16.7263	0.792902
$446$	21.4887	1.01752
$447$	−6.65187	−0.314623
$448$	4.12502	0.194889
$449$	−3.44980	−0.162806	−0.0814031	−	0.996681i	$-0.525940\pi$
$449$	−3.44980	−0.162806	−0.0814031	+	0.996681i	$0.525940\pi$
$450$	−1.41367	−0.0666413
$451$	0	0
$452$	−2.89424	−0.136133
$453$	−13.9741	−0.656559
$454$	−12.6367	−0.593071
$455$	−38.6650	−1.81264
$456$	−2.05958	−0.0964487
$457$	40.7759	1.90742	0.953709	−	0.300731i	$-0.0972307\pi$
$457$	40.7759	1.90742	0.953709	+	0.300731i	$0.0972307\pi$
$458$	−14.1933	−0.663209
$459$	−25.3843	−1.18484
$460$	6.11107	0.284930
$461$	39.4014	1.83510	0.917552	−	0.397616i	$-0.130162\pi$
$461$	39.4014	1.83510	0.917552	+	0.397616i	$0.130162\pi$
$462$	0	0
$463$	4.81281	0.223670	0.111835	−	0.993727i	$-0.464327\pi$
$463$	4.81281	0.223670	0.111835	+	0.993727i	$0.464327\pi$
$464$	−0.675883	−0.0313771
$465$	−3.28330	−0.152259
$466$	7.42529	0.343970
$467$	4.64479	0.214935	0.107468	−	0.994209i	$-0.465726\pi$
$467$	4.64479	0.214935	0.107468	+	0.994209i	$0.465726\pi$
$468$	−5.92353	−0.273815
$469$	−51.0633	−2.35789
$470$	−11.8730	−0.547660
$471$	14.0848	0.648995
$472$	6.10492	0.281002
$473$	0	0
$474$	−29.5943	−1.35931
$475$	1.13834	0.0522308
$476$	28.9175	1.32543
$477$	−6.12232	−0.280322
$478$	−5.48322	−0.250797
$479$	−28.6880	−1.31079	−0.655394	−	0.755287i	$-0.727497\pi$
$479$	−28.6880	−1.31079	−0.655394	+	0.755287i	$0.727497\pi$
$480$	4.04730	0.184733
$481$	56.0629	2.55625
$482$	−13.6790	−0.623060
$483$	26.4201	1.20216
$484$	0	0
$485$	28.0142	1.27206
$486$	−12.1700	−0.552042
$487$	−20.1244	−0.911921	−0.455961	−	0.890000i	$-0.650704\pi$
$487$	−20.1244	−0.911921	−0.455961	+	0.890000i	$0.650704\pi$
$488$	−3.70791	−0.167849
$489$	−38.2173	−1.72825
$490$	19.6821	0.889146
$491$	11.5207	0.519923	0.259961	−	0.965619i	$-0.416290\pi$
$491$	11.5207	0.519923	0.259961	+	0.965619i	$0.416290\pi$
$492$	17.0454	0.768465
$493$	−4.73813	−0.213395
$494$	4.76986	0.214606
$495$	0	0
$496$	−0.811231	−0.0364254
$497$	35.7824	1.60506
$498$	−5.14071	−0.230361
$499$	−1.71047	−0.0765713	−0.0382856	−	0.999267i	$-0.512190\pi$
$499$	−1.71047	−0.0765713	−0.0382856	+	0.999267i	$0.512190\pi$
$500$	−12.0625	−0.539452
$501$	16.1763	0.722702
$502$	−8.28409	−0.369737
$503$	−22.3243	−0.995390	−0.497695	−	0.867352i	$-0.665820\pi$
$503$	−22.3243	−0.995390	−0.497695	+	0.867352i	$0.665820\pi$
$504$	5.12273	0.228184
$505$	−23.6186	−1.05102
$506$	0	0
$507$	20.0841	0.891965
$508$	−2.48900	−0.110431
$509$	−9.00091	−0.398958	−0.199479	−	0.979902i	$-0.563925\pi$
$509$	−9.00091	−0.398958	−0.199479	+	0.979902i	$0.563925\pi$
$510$	28.3727	1.25637
$511$	41.1106	1.81862
$512$	1.00000	0.0441942
$513$	3.62101	0.159872
$514$	19.0887	0.841966
$515$	−13.9599	−0.615148
$516$	14.4574	0.636454
$517$	0	0
$518$	−48.4838	−2.13025
$519$	46.2648	2.03080
$520$	−9.37329	−0.411046
$521$	24.4698	1.07204	0.536020	−	0.844205i	$-0.319927\pi$
$521$	24.4698	1.07204	0.536020	+	0.844205i	$0.319927\pi$
$522$	−0.839357	−0.0367377
$523$	3.07224	0.134340	0.0671699	−	0.997742i	$-0.478603\pi$
$523$	3.07224	0.134340	0.0671699	+	0.997742i	$0.478603\pi$
$524$	3.29365	0.143884
$525$	−9.67115	−0.422084
$526$	−20.9903	−0.915219
$527$	−5.68696	−0.247728
$528$	0	0
$529$	−13.3292	−0.579531
$530$	−9.68785	−0.420813
$531$	7.58150	0.329009
$532$	−4.12502	−0.178842
$533$	−39.4760	−1.70990
$534$	17.5304	0.758614
$535$	16.8870	0.730090
$536$	−12.3789	−0.534688
$537$	−17.7244	−0.764866
$538$	−25.9056	−1.11687
$539$	0	0
$540$	−7.11569	−0.306210
$541$	−14.1995	−0.610486	−0.305243	−	0.952274i	$-0.598738\pi$
$541$	−14.1995	−0.610486	−0.305243	+	0.952274i	$0.598738\pi$
$542$	10.6882	0.459098
$543$	−20.4665	−0.878303
$544$	7.01028	0.300563
$545$	−20.2618	−0.867918
$546$	−40.5238	−1.73426
$547$	14.9111	0.637553	0.318776	−	0.947830i	$-0.396728\pi$
$547$	14.9111	0.637553	0.318776	+	0.947830i	$0.396728\pi$
$548$	−5.10805	−0.218205
$549$	−4.60473	−0.196525
$550$	0	0
$551$	0.675883	0.0287936
$552$	6.40485	0.272609
$553$	−59.2727	−2.52053
$554$	23.4491	0.996257
$555$	−47.5703	−2.01925
$556$	18.4361	0.781866
$557$	−6.67298	−0.282743	−0.141372	−	0.989957i	$-0.545151\pi$
$557$	−6.67298	−0.282743	−0.141372	+	0.989957i	$0.545151\pi$
$558$	−1.00744	−0.0426484
$559$	−33.4825	−1.41616
$560$	8.10611	0.342546
$561$	0	0
$562$	16.5620	0.698627
$563$	−40.9621	−1.72635	−0.863174	−	0.504906i	$-0.831527\pi$
$563$	−40.9621	−1.72635	−0.863174	+	0.504906i	$0.831527\pi$
$564$	−12.4438	−0.523977
$565$	−5.68749	−0.239275
$566$	−1.56041	−0.0655889
$567$	−46.1316	−1.93734
$568$	8.67449	0.363973
$569$	−24.0821	−1.00957	−0.504787	−	0.863244i	$-0.668429\pi$
$569$	−24.0821	−1.00957	−0.504787	+	0.863244i	$0.668429\pi$
$570$	−4.04730	−0.169523
$571$	32.6098	1.36468	0.682339	−	0.731036i	$-0.260963\pi$
$571$	32.6098	1.36468	0.682339	+	0.731036i	$0.260963\pi$
$572$	0	0
$573$	−16.7107	−0.698097
$574$	34.1392	1.42494
$575$	−3.54001	−0.147629
$576$	1.24187	0.0517445
$577$	2.80491	0.116770	0.0583850	−	0.998294i	$-0.481405\pi$
$577$	2.80491	0.116770	0.0583850	+	0.998294i	$0.481405\pi$
$578$	32.1441	1.33702
$579$	−35.4505	−1.47327
$580$	−1.32818	−0.0551498
$581$	−10.2960	−0.427152
$582$	29.3609	1.21705
$583$	0	0
$584$	9.96615	0.412402
$585$	−11.6404	−0.481271
$586$	2.27229	0.0938674
$587$	−5.12202	−0.211408	−0.105704	−	0.994398i	$-0.533710\pi$
$587$	−5.12202	−0.211408	−0.105704	+	0.994398i	$0.533710\pi$
$588$	20.6283	0.850696
$589$	0.811231	0.0334262
$590$	11.9968	0.493902
$591$	38.2058	1.57158
$592$	−11.7536	−0.483069
$593$	−40.3565	−1.65724	−0.828621	−	0.559810i	$-0.810874\pi$
$593$	−40.3565	−1.65724	−0.828621	+	0.559810i	$0.810874\pi$
$594$	0	0
$595$	56.8261	2.32964
$596$	−3.22972	−0.132295
$597$	−27.6219	−1.13049
$598$	−14.8332	−0.606576
$599$	−14.3396	−0.585899	−0.292949	−	0.956128i	$-0.594637\pi$
$599$	−14.3396	−0.585899	−0.292949	+	0.956128i	$0.594637\pi$
$600$	−2.34451	−0.0957143
$601$	4.41103	0.179930	0.0899649	−	0.995945i	$-0.471325\pi$
$601$	4.41103	0.179930	0.0899649	+	0.995945i	$0.471325\pi$
$602$	28.9560	1.18016
$603$	−15.3730	−0.626037
$604$	−6.78491	−0.276074
$605$	0	0
$606$	−24.7541	−1.00557
$607$	19.9815	0.811024	0.405512	−	0.914090i	$-0.367093\pi$
$607$	19.9815	0.811024	0.405512	+	0.914090i	$0.367093\pi$
$608$	−1.00000	−0.0405554
$609$	−5.74217	−0.232684
$610$	−7.28645	−0.295020
$611$	28.8190	1.16589
$612$	8.70585	0.351913
$613$	−31.7927	−1.28409	−0.642047	−	0.766665i	$-0.721915\pi$
$613$	−31.7927	−1.28409	−0.642047	+	0.766665i	$0.721915\pi$
$614$	−15.9893	−0.645274
$615$	33.4960	1.35069
$616$	0	0
$617$	11.2190	0.451658	0.225829	−	0.974167i	$-0.427491\pi$
$617$	11.2190	0.451658	0.225829	+	0.974167i	$0.427491\pi$
$618$	−14.6310	−0.588546
$619$	42.7367	1.71773	0.858866	−	0.512200i	$-0.171169\pi$
$619$	42.7367	1.71773	0.858866	+	0.512200i	$0.171169\pi$
$620$	−1.59416	−0.0640229
$621$	−11.2606	−0.451871
$622$	12.2309	0.490416
$623$	35.1106	1.40668
$624$	−9.82390	−0.393271
$625$	−18.0124	−0.720498
$626$	−28.7920	−1.15076
$627$	0	0
$628$	6.83869	0.272894
$629$	−82.3960	−3.28534
$630$	10.0667	0.401068
$631$	−29.4770	−1.17346	−0.586730	−	0.809782i	$-0.699585\pi$
$631$	−29.4770	−1.17346	−0.586730	+	0.809782i	$0.699585\pi$
$632$	−14.3691	−0.571571
$633$	−21.8577	−0.868764
$634$	10.3072	0.409351
$635$	−4.89115	−0.194099
$636$	−10.1536	−0.402616
$637$	−47.7738	−1.89287
$638$	0	0
$639$	10.7726	0.426156
$640$	1.96511	0.0776778
$641$	9.64607	0.380997	0.190498	−	0.981688i	$-0.438990\pi$
$641$	9.64607	0.380997	0.190498	+	0.981688i	$0.438990\pi$
$642$	17.6989	0.698518
$643$	−6.07583	−0.239607	−0.119804	−	0.992798i	$-0.538227\pi$
$643$	−6.07583	−0.239607	−0.119804	+	0.992798i	$0.538227\pi$
$644$	12.8279	0.505491
$645$	28.4105	1.11866
$646$	−7.01028	−0.275816
$647$	40.0282	1.57367	0.786835	−	0.617164i	$-0.211718\pi$
$647$	40.0282	1.57367	0.786835	+	0.617164i	$0.211718\pi$
$648$	−11.1834	−0.439324
$649$	0	0
$650$	5.42974	0.212972
$651$	−6.89206	−0.270121
$652$	−18.5559	−0.726704
$653$	−4.62411	−0.180956	−0.0904778	−	0.995898i	$-0.528839\pi$
$653$	−4.62411	−0.180956	−0.0904778	+	0.995898i	$0.528839\pi$
$654$	−21.2358	−0.830386
$655$	6.47238	0.252897
$656$	8.27614	0.323129
$657$	12.3766	0.482859
$658$	−24.9229	−0.971597
$659$	−37.9621	−1.47879	−0.739397	−	0.673270i	$-0.764889\pi$
$659$	−37.9621	−1.47879	−0.739397	+	0.673270i	$0.764889\pi$
$660$	0	0
$661$	−18.2744	−0.710791	−0.355396	−	0.934716i	$-0.615654\pi$
$661$	−18.2744	−0.710791	−0.355396	+	0.934716i	$0.615654\pi$
$662$	−1.18204	−0.0459412
$663$	−68.8683	−2.67462
$664$	−2.49600	−0.0968636
$665$	−8.10611	−0.314342
$666$	−14.5964	−0.565599
$667$	−2.10185	−0.0813840
$668$	7.85416	0.303887
$669$	44.2577	1.71110
$670$	−24.3260	−0.939794
$671$	0	0
$672$	8.49580	0.327733
$673$	24.7391	0.953621	0.476811	−	0.879006i	$-0.341793\pi$
$673$	24.7391	0.953621	0.476811	+	0.879006i	$0.341793\pi$
$674$	−3.82507	−0.147336
$675$	4.12196	0.158654
$676$	9.75154	0.375059
$677$	14.1154	0.542498	0.271249	−	0.962509i	$-0.412563\pi$
$677$	14.1154	0.542498	0.271249	+	0.962509i	$0.412563\pi$
$678$	−5.96091	−0.228927
$679$	58.8054	2.25674
$680$	13.7760	0.528285
$681$	−26.0264	−0.997332
$682$	0	0
$683$	7.29411	0.279101	0.139551	−	0.990215i	$-0.455434\pi$
$683$	7.29411	0.279101	0.139551	+	0.990215i	$0.455434\pi$
$684$	−1.24187	−0.0474840
$685$	−10.0379	−0.383528
$686$	12.4401	0.474966
$687$	−29.2322	−1.11528
$688$	7.01961	0.267620
$689$	23.5151	0.895852
$690$	12.5862	0.479150
$691$	−0.0872720	−0.00331998	−0.00165999	−	0.999999i	$-0.500528\pi$
$691$	−0.0872720	−0.00331998	−0.00165999	+	0.999999i	$0.500528\pi$
$692$	22.4632	0.853923
$693$	0	0
$694$	−15.7136	−0.596481
$695$	36.2290	1.37424
$696$	−1.39203	−0.0527649
$697$	58.0181	2.19759
$698$	28.8965	1.09375
$699$	15.2930	0.578433
$700$	−4.69569	−0.177481
$701$	−32.1823	−1.21551	−0.607754	−	0.794125i	$-0.707929\pi$
$701$	−32.1823	−1.21551	−0.607754	+	0.794125i	$0.707929\pi$
$702$	17.2717	0.651879
$703$	11.7536	0.443295
$704$	0	0
$705$	−24.4534	−0.920967
$706$	22.1628	0.834107
$707$	−49.5786	−1.86459
$708$	12.5736	0.472543
$709$	11.3450	0.426070	0.213035	−	0.977045i	$-0.431665\pi$
$709$	11.3450	0.426070	0.213035	+	0.977045i	$0.431665\pi$
$710$	17.0463	0.639737
$711$	−17.8445	−0.669221
$712$	8.51163	0.318987
$713$	−2.52276	−0.0944780
$714$	59.5580	2.22890
$715$	0	0
$716$	−8.60585	−0.321616
$717$	−11.2931	−0.421750
$718$	23.7708	0.887119
$719$	41.3224	1.54106	0.770532	−	0.637401i	$-0.219991\pi$
$719$	41.3224	1.54106	0.770532	+	0.637401i	$0.219991\pi$
$720$	2.44041	0.0909486
$721$	−29.3037	−1.09133
$722$	1.00000	0.0372161
$723$	−28.1729	−1.04776
$724$	−9.93724	−0.369315
$725$	0.769388	0.0285743
$726$	0	0
$727$	37.0528	1.37421	0.687107	−	0.726556i	$-0.258880\pi$
$727$	37.0528	1.37421	0.687107	+	0.726556i	$0.258880\pi$
$728$	−19.6757	−0.729232
$729$	8.48502	0.314260
$730$	19.5846	0.724858
$731$	49.2095	1.82008
$732$	−7.63673	−0.282262
$733$	−14.9259	−0.551302	−0.275651	−	0.961258i	$-0.588893\pi$
$733$	−14.9259	−0.551302	−0.275651	+	0.961258i	$0.588893\pi$
$734$	22.8787	0.844468
$735$	40.5368	1.49522
$736$	3.10979	0.114628
$737$	0	0
$738$	10.2779	0.378334
$739$	5.79969	0.213345	0.106673	−	0.994294i	$-0.465980\pi$
$739$	5.79969	0.213345	0.106673	+	0.994294i	$0.465980\pi$
$740$	−23.0971	−0.849066
$741$	9.82390	0.360890
$742$	−20.3360	−0.746560
$743$	−4.09972	−0.150404	−0.0752021	−	0.997168i	$-0.523960\pi$
$743$	−4.09972	−0.150404	−0.0752021	+	0.997168i	$0.523960\pi$
$744$	−1.67080	−0.0612543
$745$	−6.34675	−0.232527
$746$	−0.861889	−0.0315560
$747$	−3.09970	−0.113412
$748$	0	0
$749$	35.4481	1.29524
$750$	−24.8437	−0.907164
$751$	28.5717	1.04260	0.521299	−	0.853374i	$-0.325448\pi$
$751$	28.5717	1.04260	0.521299	+	0.853374i	$0.325448\pi$
$752$	−6.04189	−0.220325
$753$	−17.0617	−0.621765
$754$	3.22386	0.117406
$755$	−13.3331	−0.485241
$756$	−14.9367	−0.543244
$757$	24.4066	0.887074	0.443537	−	0.896256i	$-0.353723\pi$
$757$	24.4066	0.887074	0.443537	+	0.896256i	$0.353723\pi$
$758$	27.3522	0.993475
$759$	0	0
$760$	−1.96511	−0.0712820
$761$	−12.5623	−0.455384	−0.227692	−	0.973733i	$-0.573118\pi$
$761$	−12.5623	−0.455384	−0.227692	+	0.973733i	$0.573118\pi$
$762$	−5.12628	−0.185706
$763$	−42.5320	−1.53976
$764$	−8.11362	−0.293541
$765$	17.1079	0.618539
$766$	11.3104	0.408663
$767$	−29.1196	−1.05145
$768$	2.05958	0.0743187
$769$	−4.12912	−0.148900	−0.0744500	−	0.997225i	$-0.523720\pi$
$769$	−4.12912	−0.148900	−0.0744500	+	0.997225i	$0.523720\pi$
$770$	0	0
$771$	39.3147	1.41588
$772$	−17.2125	−0.619492
$773$	1.46863	0.0528228	0.0264114	−	0.999651i	$-0.491592\pi$
$773$	1.46863	0.0528228	0.0264114	+	0.999651i	$0.491592\pi$
$774$	8.71743	0.313342
$775$	0.923461	0.0331717
$776$	14.2558	0.511753
$777$	−99.8562	−3.58232
$778$	−15.3376	−0.549880
$779$	−8.27614	−0.296523
$780$	−19.3050	−0.691231
$781$	0	0
$782$	21.8005	0.779584
$783$	2.44738	0.0874622
$784$	10.0158	0.357706
$785$	13.4388	0.479651
$786$	6.78353	0.241960
$787$	−6.88782	−0.245524	−0.122762	−	0.992436i	$-0.539175\pi$
$787$	−6.88782	−0.245524	−0.122762	+	0.992436i	$0.539175\pi$
$788$	18.5503	0.660826
$789$	−43.2311	−1.53907
$790$	−28.2368	−1.00462
$791$	−11.9388	−0.424494
$792$	0	0
$793$	17.6862	0.628055
$794$	−14.1783	−0.503170
$795$	−19.9529	−0.707656
$796$	−13.4114	−0.475355
$797$	−37.7416	−1.33688	−0.668438	−	0.743768i	$-0.733037\pi$
$797$	−37.7416	−1.33688	−0.668438	+	0.743768i	$0.733037\pi$
$798$	−8.49580	−0.300748
$799$	−42.3554	−1.49843
$800$	−1.13834	−0.0402466
$801$	10.5703	0.373484
$802$	18.6618	0.658970
$803$	0	0
$804$	−25.4954	−0.899153
$805$	25.2083	0.888475
$806$	3.86946	0.136296
$807$	−53.3547	−1.87817
$808$	−12.0190	−0.422827
$809$	49.2825	1.73268	0.866340	−	0.499456i	$-0.166467\pi$
$809$	49.2825	1.73268	0.866340	+	0.499456i	$0.166467\pi$
$810$	−21.9765	−0.772177
$811$	−22.0589	−0.774593	−0.387297	−	0.921955i	$-0.626591\pi$
$811$	−22.0589	−0.774593	−0.387297	+	0.921955i	$0.626591\pi$
$812$	−2.78803	−0.0978406
$813$	22.0132	0.772038
$814$	0	0
$815$	−36.4643	−1.27729
$816$	14.4382	0.505439
$817$	−7.01961	−0.245585
$818$	25.9246	0.906431
$819$	−24.4347	−0.853817
$820$	16.2635	0.567947
$821$	−5.90407	−0.206054	−0.103027	−	0.994679i	$-0.532853\pi$
$821$	−5.90407	−0.206054	−0.103027	+	0.994679i	$0.532853\pi$
$822$	−10.5204	−0.366942
$823$	28.1708	0.981974	0.490987	−	0.871167i	$-0.336636\pi$
$823$	28.1708	0.981974	0.490987	+	0.871167i	$0.336636\pi$
$824$	−7.10389	−0.247476
$825$	0	0
$826$	25.1829	0.876225
$827$	−35.8445	−1.24643	−0.623217	−	0.782049i	$-0.714175\pi$
$827$	−35.8445	−1.24643	−0.623217	+	0.782049i	$0.714175\pi$
$828$	3.86195	0.134212
$829$	−1.08065	−0.0375325	−0.0187662	−	0.999824i	$-0.505974\pi$
$829$	−1.08065	−0.0375325	−0.0187662	+	0.999824i	$0.505974\pi$
$830$	−4.90491	−0.170252
$831$	48.2953	1.67535
$832$	−4.76986	−0.165365
$833$	70.2134	2.43275
$834$	37.9707	1.31482
$835$	15.4343	0.534125
$836$	0	0
$837$	2.93748	0.101534
$838$	6.07570	0.209882
$839$	−10.6310	−0.367024	−0.183512	−	0.983018i	$-0.558747\pi$
$839$	−10.6310	−0.367024	−0.183512	+	0.983018i	$0.558747\pi$
$840$	16.6952	0.576039
$841$	−28.5432	−0.984248
$842$	3.55276	0.122436
$843$	34.1108	1.17484
$844$	−10.6127	−0.365304
$845$	19.1628	0.659222
$846$	−7.50324	−0.257967
$847$	0	0
$848$	−4.92993	−0.169294
$849$	−3.21379	−0.110297
$850$	−7.98012	−0.273716
$851$	−36.5512	−1.25296
$852$	17.8658	0.612072
$853$	−50.8181	−1.73998	−0.869990	−	0.493070i	$-0.835875\pi$
$853$	−50.8181	−1.73998	−0.869990	+	0.493070i	$0.835875\pi$
$854$	−15.2952	−0.523391
$855$	−2.44041	−0.0834602
$856$	8.59343	0.293718
$857$	−15.0596	−0.514427	−0.257214	−	0.966355i	$-0.582804\pi$
$857$	−15.0596	−0.514427	−0.257214	+	0.966355i	$0.582804\pi$
$858$	0	0
$859$	3.74888	0.127910	0.0639551	−	0.997953i	$-0.479629\pi$
$859$	3.74888	0.127910	0.0639551	+	0.997953i	$0.479629\pi$
$860$	13.7943	0.470382
$861$	70.3125	2.39624
$862$	−29.6777	−1.01083
$863$	−22.5942	−0.769116	−0.384558	−	0.923101i	$-0.625646\pi$
$863$	−22.5942	−0.769116	−0.384558	+	0.923101i	$0.625646\pi$
$864$	−3.62101	−0.123189
$865$	44.1427	1.50090
$866$	−21.8264	−0.741691
$867$	66.2033	2.24838
$868$	−3.34634	−0.113582
$869$	0	0
$870$	−2.73550	−0.0927421
$871$	59.0457	2.00069
$872$	−10.3108	−0.349166
$873$	17.7038	0.599183
$874$	−3.10979	−0.105190
$875$	−49.7581	−1.68213
$876$	20.5261	0.693512
$877$	−19.9431	−0.673429	−0.336715	−	0.941607i	$-0.609316\pi$
$877$	−19.9431	−0.673429	−0.336715	+	0.941607i	$0.609316\pi$
$878$	21.6449	0.730480
$879$	4.67996	0.157851
$880$	0	0
$881$	−11.0913	−0.373676	−0.186838	−	0.982391i	$-0.559824\pi$
$881$	−11.0913	−0.373676	−0.186838	+	0.982391i	$0.559824\pi$
$882$	12.4383	0.418818
$883$	−9.54160	−0.321101	−0.160550	−	0.987028i	$-0.551327\pi$
$883$	−9.54160	−0.321101	−0.160550	+	0.987028i	$0.551327\pi$
$884$	−33.4381	−1.12464
$885$	24.7084	0.830565
$886$	−8.31451	−0.279331
$887$	−28.9170	−0.970939	−0.485470	−	0.874253i	$-0.661351\pi$
$887$	−28.9170	−0.970939	−0.485470	+	0.874253i	$0.661351\pi$
$888$	−24.2074	−0.812349
$889$	−10.2672	−0.344349
$890$	16.7263	0.560666
$891$	0	0
$892$	21.4887	0.719496
$893$	6.04189	0.202184
$894$	−6.65187	−0.222472
$895$	−16.9114	−0.565287
$896$	4.12502	0.137807
$897$	−30.5502	−1.02004
$898$	−3.44980	−0.115121
$899$	0.548297	0.0182867
$900$	−1.41367	−0.0471225
$901$	−34.5602	−1.15137
$902$	0	0
$903$	59.6372	1.98460
$904$	−2.89424	−0.0962609
$905$	−19.5278	−0.649125
$906$	−13.9741	−0.464257
$907$	−24.3652	−0.809034	−0.404517	−	0.914531i	$-0.632560\pi$
$907$	−24.3652	−0.809034	−0.404517	+	0.914531i	$0.632560\pi$
$908$	−12.6367	−0.419365
$909$	−14.9260	−0.495064
$910$	−38.6650	−1.28173
$911$	0.925900	0.0306765	0.0153382	−	0.999882i	$-0.495117\pi$
$911$	0.925900	0.0306765	0.0153382	+	0.999882i	$0.495117\pi$
$912$	−2.05958	−0.0681995
$913$	0	0
$914$	40.7759	1.34875
$915$	−15.0070	−0.496117
$916$	−14.1933	−0.468959
$917$	13.5864	0.448661
$918$	−25.3843	−0.837808
$919$	11.2408	0.370800	0.185400	−	0.982663i	$-0.440642\pi$
$919$	11.2408	0.370800	0.185400	+	0.982663i	$0.440642\pi$
$920$	6.11107	0.201476
$921$	−32.9312	−1.08512
$922$	39.4014	1.29761
$923$	−41.3761	−1.36191
$924$	0	0
$925$	13.3796	0.439920
$926$	4.81281	0.158159
$927$	−8.82210	−0.289756
$928$	−0.675883	−0.0221869
$929$	51.8934	1.70257	0.851283	−	0.524707i	$-0.175825\pi$
$929$	51.8934	1.70257	0.851283	+	0.524707i	$0.175825\pi$
$930$	−3.28330	−0.107664
$931$	−10.0158	−0.328254
$932$	7.42529	0.243223
$933$	25.1906	0.824704
$934$	4.64479	0.151982
$935$	0	0
$936$	−5.92353	−0.193617
$937$	−4.41447	−0.144214	−0.0721072	−	0.997397i	$-0.522972\pi$
$937$	−4.41447	−0.144214	−0.0721072	+	0.997397i	$0.522972\pi$
$938$	−51.0633	−1.66728
$939$	−59.2995	−1.93516
$940$	−11.8730	−0.387254
$941$	7.10670	0.231672	0.115836	−	0.993268i	$-0.463045\pi$
$941$	7.10670	0.231672	0.115836	+	0.993268i	$0.463045\pi$
$942$	14.0848	0.458909
$943$	25.7370	0.838113
$944$	6.10492	0.198698
$945$	−29.3523	−0.954831
$946$	0	0
$947$	−22.6251	−0.735218	−0.367609	−	0.929980i	$-0.619824\pi$
$947$	−22.6251	−0.735218	−0.367609	+	0.929980i	$0.619824\pi$
$948$	−29.5943	−0.961177
$949$	−47.5371	−1.54312
$950$	1.13834	0.0369328
$951$	21.2285	0.688381
$952$	28.9175	0.937223
$953$	23.2486	0.753097	0.376548	−	0.926397i	$-0.377111\pi$
$953$	23.2486	0.753097	0.376548	+	0.926397i	$0.377111\pi$
$954$	−6.12232	−0.198218
$955$	−15.9442	−0.515941
$956$	−5.48322	−0.177340
$957$	0	0
$958$	−28.6880	−0.926867
$959$	−21.0708	−0.680412
$960$	4.04730	0.130626
$961$	−30.3419	−0.978771
$962$	56.0629	1.80754
$963$	10.6719	0.343898
$964$	−13.6790	−0.440570
$965$	−33.8245	−1.08885
$966$	26.4201	0.850054
$967$	31.0356	0.998036	0.499018	−	0.866592i	$-0.333694\pi$
$967$	31.0356	0.998036	0.499018	+	0.866592i	$0.333694\pi$
$968$	0	0
$969$	−14.4382	−0.463823
$970$	28.0142	0.899481
$971$	39.5454	1.26907	0.634536	−	0.772893i	$-0.281191\pi$
$971$	39.5454	1.26907	0.634536	+	0.772893i	$0.281191\pi$
$972$	−12.1700	−0.390353
$973$	76.0494	2.43803
$974$	−20.1244	−0.644826
$975$	11.1830	0.358142
$976$	−3.70791	−0.118687
$977$	0.839139	0.0268464	0.0134232	−	0.999910i	$-0.495727\pi$
$977$	0.839139	0.0268464	0.0134232	+	0.999910i	$0.495727\pi$
$978$	−38.2173	−1.22205
$979$	0	0
$980$	19.6821	0.628721
$981$	−12.8046	−0.408819
$982$	11.5207	0.367641
$983$	−24.1530	−0.770361	−0.385181	−	0.922841i	$-0.625861\pi$
$983$	−24.1530	−0.770361	−0.385181	+	0.922841i	$0.625861\pi$
$984$	17.0454	0.543387
$985$	36.4533	1.16150
$986$	−4.73813	−0.150893
$987$	−51.3307	−1.63388
$988$	4.76986	0.151749
$989$	21.8295	0.694138
$990$	0	0
$991$	25.2153	0.800992	0.400496	−	0.916299i	$-0.368838\pi$
$991$	25.2153	0.800992	0.400496	+	0.916299i	$0.368838\pi$
$992$	−0.811231	−0.0257566
$993$	−2.43450	−0.0772565
$994$	35.7824	1.13495
$995$	−26.3549	−0.835506
$996$	−5.14071	−0.162890
$997$	31.9863	1.01302	0.506508	−	0.862236i	$-0.330936\pi$
$997$	31.9863	1.01302	0.506508	+	0.862236i	$0.330936\pi$
$998$	−1.71047	−0.0541441
$999$	42.5599	1.34654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.ca.1.6		8
11.5	even	5		418.2.f.f.267.3	yes	16
11.9	even	5		418.2.f.f.191.3	✓	16
11.10	odd	2		4598.2.a.bx.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.3	✓	16	11.9	even	5
418.2.f.f.267.3	yes	16	11.5	even	5
4598.2.a.bx.1.6		8	11.10	odd	2
4598.2.a.ca.1.6		8	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.05958 q^{3} +1.00000 q^{4} +1.96511 q^{5} +2.05958 q^{6} +4.12502 q^{7} +1.00000 q^{8} +1.24187 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.05958 q^{3} +1.00000 q^{4} +1.96511 q^{5} +2.05958 q^{6} +4.12502 q^{7} +1.00000 q^{8} +1.24187 q^{9} +1.96511 q^{10} +2.05958 q^{12} -4.76986 q^{13} +4.12502 q^{14} +4.04730 q^{15} +1.00000 q^{16} +7.01028 q^{17} +1.24187 q^{18} -1.00000 q^{19} +1.96511 q^{20} +8.49580 q^{21} +3.10979 q^{23} +2.05958 q^{24} -1.13834 q^{25} -4.76986 q^{26} -3.62101 q^{27} +4.12502 q^{28} -0.675883 q^{29} +4.04730 q^{30} -0.811231 q^{31} +1.00000 q^{32} +7.01028 q^{34} +8.10611 q^{35} +1.24187 q^{36} -11.7536 q^{37} -1.00000 q^{38} -9.82390 q^{39} +1.96511 q^{40} +8.27614 q^{41} +8.49580 q^{42} +7.01961 q^{43} +2.44041 q^{45} +3.10979 q^{46} -6.04189 q^{47} +2.05958 q^{48} +10.0158 q^{49} -1.13834 q^{50} +14.4382 q^{51} -4.76986 q^{52} -4.92993 q^{53} -3.62101 q^{54} +4.12502 q^{56} -2.05958 q^{57} -0.675883 q^{58} +6.10492 q^{59} +4.04730 q^{60} -3.70791 q^{61} -0.811231 q^{62} +5.12273 q^{63} +1.00000 q^{64} -9.37329 q^{65} -12.3789 q^{67} +7.01028 q^{68} +6.40485 q^{69} +8.10611 q^{70} +8.67449 q^{71} +1.24187 q^{72} +9.96615 q^{73} -11.7536 q^{74} -2.34451 q^{75} -1.00000 q^{76} -9.82390 q^{78} -14.3691 q^{79} +1.96511 q^{80} -11.1834 q^{81} +8.27614 q^{82} -2.49600 q^{83} +8.49580 q^{84} +13.7760 q^{85} +7.01961 q^{86} -1.39203 q^{87} +8.51163 q^{89} +2.44041 q^{90} -19.6757 q^{91} +3.10979 q^{92} -1.67080 q^{93} -6.04189 q^{94} -1.96511 q^{95} +2.05958 q^{96} +14.2558 q^{97} +10.0158 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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