LMFDB - Embedded newform 4598.2.a.bp.1.3

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:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.86620$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.34889 q^{3} +1.00000 q^{4} +4.38350 q^{5} +2.34889 q^{6} -0.482696 q^{7} +1.00000 q^{8} +2.51730 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.34889 q^{3} +1.00000 q^{4} +4.38350 q^{5} +2.34889 q^{6} -0.482696 q^{7} +1.00000 q^{8} +2.51730 q^{9} +4.38350 q^{10} +2.34889 q^{12} -5.73240 q^{13} -0.482696 q^{14} +10.2964 q^{15} +1.00000 q^{16} +4.18048 q^{17} +2.51730 q^{18} +1.00000 q^{19} +4.38350 q^{20} -1.13380 q^{21} -1.96539 q^{23} +2.34889 q^{24} +14.2151 q^{25} -5.73240 q^{26} -1.13380 q^{27} -0.482696 q^{28} +0.168410 q^{29} +10.2964 q^{30} +2.00000 q^{31} +1.00000 q^{32} +4.18048 q^{34} -2.11590 q^{35} +2.51730 q^{36} +8.34889 q^{37} +1.00000 q^{38} -13.4648 q^{39} +4.38350 q^{40} +3.59859 q^{41} -1.13380 q^{42} -6.43018 q^{43} +11.0346 q^{45} -1.96539 q^{46} -4.21509 q^{47} +2.34889 q^{48} -6.76700 q^{49} +14.2151 q^{50} +9.81952 q^{51} -5.73240 q^{52} -10.3310 q^{53} -1.13380 q^{54} -0.482696 q^{56} +2.34889 q^{57} +0.168410 q^{58} -5.81369 q^{59} +10.2964 q^{60} +0.314286 q^{61} +2.00000 q^{62} -1.21509 q^{63} +1.00000 q^{64} -25.1280 q^{65} +12.0000 q^{67} +4.18048 q^{68} -4.61650 q^{69} -2.11590 q^{70} +13.2618 q^{71} +2.51730 q^{72} -13.2151 q^{73} +8.34889 q^{74} +33.3897 q^{75} +1.00000 q^{76} -13.4648 q^{78} +15.5986 q^{79} +4.38350 q^{80} -10.2151 q^{81} +3.59859 q^{82} +9.08129 q^{83} -1.13380 q^{84} +18.3252 q^{85} -6.43018 q^{86} +0.395577 q^{87} +2.20302 q^{89} +11.0346 q^{90} +2.76700 q^{91} -1.96539 q^{92} +4.69779 q^{93} -4.21509 q^{94} +4.38350 q^{95} +2.34889 q^{96} +2.62857 q^{97} -6.76700 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} + 4 q^{10} + q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{15} + 3 q^{16} + 2 q^{17} + 6 q^{18} + 3 q^{19} + 4 q^{20} - 11 q^{21} - 9 q^{23} + q^{24} + 29 q^{25} - 2 q^{26} - 11 q^{27} - 3 q^{28} + 5 q^{29} - 4 q^{30} + 6 q^{31} + 3 q^{32} + 2 q^{34} + 18 q^{35} + 6 q^{36} + 19 q^{37} + 3 q^{38} - 10 q^{39} + 4 q^{40} - 12 q^{41} - 11 q^{42} + 8 q^{43} + 30 q^{45} - 9 q^{46} + q^{47} + q^{48} - 2 q^{49} + 29 q^{50} + 40 q^{51} - 2 q^{52} + 7 q^{53} - 11 q^{54} - 3 q^{56} + q^{57} + 5 q^{58} + 19 q^{59} - 4 q^{60} - 2 q^{61} + 6 q^{62} + 10 q^{63} + 3 q^{64} - 36 q^{65} + 36 q^{67} + 2 q^{68} - 23 q^{69} + 18 q^{70} + 8 q^{71} + 6 q^{72} - 26 q^{73} + 19 q^{74} + 29 q^{75} + 3 q^{76} - 10 q^{78} + 24 q^{79} + 4 q^{80} - 17 q^{81} - 12 q^{82} + 6 q^{83} - 11 q^{84} - 30 q^{85} + 8 q^{86} - 23 q^{87} + 8 q^{89} + 30 q^{90} - 10 q^{91} - 9 q^{92} + 2 q^{93} + q^{94} + 4 q^{95} + q^{96} + 2 q^{97} - 2 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 + 4 * q^10 + q^12 - 2 * q^13 - 3 * q^14 - 4 * q^15 + 3 * q^16 + 2 * q^17 + 6 * q^18 + 3 * q^19 + 4 * q^20 - 11 * q^21 - 9 * q^23 + q^24 + 29 * q^25 - 2 * q^26 - 11 * q^27 - 3 * q^28 + 5 * q^29 - 4 * q^30 + 6 * q^31 + 3 * q^32 + 2 * q^34 + 18 * q^35 + 6 * q^36 + 19 * q^37 + 3 * q^38 - 10 * q^39 + 4 * q^40 - 12 * q^41 - 11 * q^42 + 8 * q^43 + 30 * q^45 - 9 * q^46 + q^47 + q^48 - 2 * q^49 + 29 * q^50 + 40 * q^51 - 2 * q^52 + 7 * q^53 - 11 * q^54 - 3 * q^56 + q^57 + 5 * q^58 + 19 * q^59 - 4 * q^60 - 2 * q^61 + 6 * q^62 + 10 * q^63 + 3 * q^64 - 36 * q^65 + 36 * q^67 + 2 * q^68 - 23 * q^69 + 18 * q^70 + 8 * q^71 + 6 * q^72 - 26 * q^73 + 19 * q^74 + 29 * q^75 + 3 * q^76 - 10 * q^78 + 24 * q^79 + 4 * q^80 - 17 * q^81 - 12 * q^82 + 6 * q^83 - 11 * q^84 - 30 * q^85 + 8 * q^86 - 23 * q^87 + 8 * q^89 + 30 * q^90 - 10 * q^91 - 9 * q^92 + 2 * q^93 + q^94 + 4 * q^95 + q^96 + 2 * q^97 - 2 * 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
$3$	2.34889	1.35613	0.678067	−	0.735000i	$-0.262818\pi$
$3$	2.34889	1.35613	0.678067	+	0.735000i	$0.262818\pi$
$4$	1.00000	0.500000
$5$	4.38350	1.96036	0.980181	−	0.198104i	$-0.0634785\pi$
$5$	4.38350	1.96036	0.980181	+	0.198104i	$0.0634785\pi$
$6$	2.34889	0.958932
$7$	−0.482696	−0.182442	−0.0912210	−	0.995831i	$-0.529077\pi$
$7$	−0.482696	−0.182442	−0.0912210	+	0.995831i	$0.529077\pi$
$8$	1.00000	0.353553
$9$	2.51730	0.839101
$10$	4.38350	1.38619
$11$	0	0
$11$	0	0
$12$	2.34889	0.678067
$13$	−5.73240	−1.58988	−0.794940	−	0.606688i	$-0.792498\pi$
$13$	−5.73240	−1.58988	−0.794940	+	0.606688i	$0.792498\pi$
$14$	−0.482696	−0.129006
$15$	10.2964	2.65851
$16$	1.00000	0.250000
$17$	4.18048	1.01392	0.506958	−	0.861971i	$-0.330770\pi$
$17$	4.18048	1.01392	0.506958	+	0.861971i	$0.330770\pi$
$18$	2.51730	0.593334
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	4.38350	0.980181
$21$	−1.13380	−0.247416
$22$	0	0
$23$	−1.96539	−0.409813	−0.204906	−	0.978782i	$-0.565689\pi$
$23$	−1.96539	−0.409813	−0.204906	+	0.978782i	$0.565689\pi$
$24$	2.34889	0.479466
$25$	14.2151	2.84302
$26$	−5.73240	−1.12422
$27$	−1.13380	−0.218200
$28$	−0.482696	−0.0912210
$29$	0.168410	0.0312729	0.0156365	−	0.999878i	$-0.495023\pi$
$29$	0.168410	0.0312729	0.0156365	+	0.999878i	$0.495023\pi$
$30$	10.2964	1.87985
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.18048	0.716947
$35$	−2.11590	−0.357652
$36$	2.51730	0.419551
$37$	8.34889	1.37255	0.686275	−	0.727342i	$-0.259245\pi$
$37$	8.34889	1.37255	0.686275	+	0.727342i	$0.259245\pi$
$38$	1.00000	0.162221
$39$	−13.4648	−2.15609
$40$	4.38350	0.693093
$41$	3.59859	0.562006	0.281003	−	0.959707i	$-0.409333\pi$
$41$	3.59859	0.562006	0.281003	+	0.959707i	$0.409333\pi$
$42$	−1.13380	−0.174949
$43$	−6.43018	−0.980594	−0.490297	−	0.871555i	$-0.663112\pi$
$43$	−6.43018	−0.980594	−0.490297	+	0.871555i	$0.663112\pi$
$44$	0	0
$45$	11.0346	1.64494
$46$	−1.96539	−0.289781
$47$	−4.21509	−0.614834	−0.307417	−	0.951575i	$-0.599465\pi$
$47$	−4.21509	−0.614834	−0.307417	+	0.951575i	$0.599465\pi$
$48$	2.34889	0.339034
$49$	−6.76700	−0.966715
$50$	14.2151	2.01032
$51$	9.81952	1.37501
$52$	−5.73240	−0.794940
$53$	−10.3310	−1.41907	−0.709535	−	0.704670i	$-0.751095\pi$
$53$	−10.3310	−1.41907	−0.709535	+	0.704670i	$0.751095\pi$
$54$	−1.13380	−0.154291
$55$	0	0
$56$	−0.482696	−0.0645030
$57$	2.34889	0.311119
$58$	0.168410	0.0221133
$59$	−5.81369	−0.756878	−0.378439	−	0.925626i	$-0.623539\pi$
$59$	−5.81369	−0.756878	−0.378439	+	0.925626i	$0.623539\pi$
$60$	10.2964	1.32926
$61$	0.314286	0.0402402	0.0201201	−	0.999798i	$-0.493595\pi$
$61$	0.314286	0.0402402	0.0201201	+	0.999798i	$0.493595\pi$
$62$	2.00000	0.254000
$63$	−1.21509	−0.153087
$64$	1.00000	0.125000
$65$	−25.1280	−3.11674
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	4.18048	0.506958
$69$	−4.61650	−0.555761
$70$	−2.11590	−0.252898
$71$	13.2618	1.57388	0.786942	−	0.617028i	$-0.211663\pi$
$71$	13.2618	1.57388	0.786942	+	0.617028i	$0.211663\pi$
$72$	2.51730	0.296667
$73$	−13.2151	−1.54671	−0.773355	−	0.633973i	$-0.781423\pi$
$73$	−13.2151	−1.54671	−0.773355	+	0.633973i	$0.781423\pi$
$74$	8.34889	0.970539
$75$	33.3897	3.85552
$76$	1.00000	0.114708
$77$	0	0
$78$	−13.4648	−1.52459
$79$	15.5986	1.75498	0.877490	−	0.479596i	$-0.159217\pi$
$79$	15.5986	1.75498	0.877490	+	0.479596i	$0.159217\pi$
$80$	4.38350	0.490090
$81$	−10.2151	−1.13501
$82$	3.59859	0.397398
$83$	9.08129	0.996801	0.498401	−	0.866947i	$-0.333921\pi$
$83$	9.08129	0.996801	0.498401	+	0.866947i	$0.333921\pi$
$84$	−1.13380	−0.123708
$85$	18.3252	1.98764
$86$	−6.43018	−0.693385
$87$	0.395577	0.0424103
$88$	0	0
$89$	2.20302	0.233519	0.116760	−	0.993160i	$-0.462749\pi$
$89$	2.20302	0.233519	0.116760	+	0.993160i	$0.462749\pi$
$90$	11.0346	1.16315
$91$	2.76700	0.290061
$92$	−1.96539	−0.204906
$93$	4.69779	0.487138
$94$	−4.21509	−0.434754
$95$	4.38350	0.449738
$96$	2.34889	0.239733
$97$	2.62857	0.266891	0.133446	−	0.991056i	$-0.457396\pi$
$97$	2.62857	0.266891	0.133446	+	0.991056i	$0.457396\pi$
$98$	−6.76700	−0.683571
$99$	0	0
$100$	14.2151	1.42151
$101$	−5.41811	−0.539122	−0.269561	−	0.962983i	$-0.586879\pi$
$101$	−5.41811	−0.539122	−0.269561	+	0.962983i	$0.586879\pi$
$102$	9.81952	0.972277
$103$	−9.59859	−0.945778	−0.472889	−	0.881122i	$-0.656789\pi$
$103$	−9.59859	−0.945778	−0.472889	+	0.881122i	$0.656789\pi$
$104$	−5.73240	−0.562108
$105$	−4.97002	−0.485025
$106$	−10.3310	−1.00343
$107$	9.56399	0.924585	0.462293	−	0.886727i	$-0.347027\pi$
$107$	9.56399	0.924585	0.462293	+	0.886727i	$0.347027\pi$
$108$	−1.13380	−0.109100
$109$	−17.4769	−1.67398	−0.836990	−	0.547218i	$-0.815687\pi$
$109$	−17.4769	−1.67398	−0.836990	+	0.547218i	$0.815687\pi$
$110$	0	0
$111$	19.6107	1.86136
$112$	−0.482696	−0.0456105
$113$	−18.6332	−1.75286	−0.876432	−	0.481525i	$-0.840083\pi$
$113$	−18.6332	−1.75286	−0.876432	+	0.481525i	$0.840083\pi$
$114$	2.34889	0.219994
$115$	−8.61530	−0.803381
$116$	0.168410	0.0156365
$117$	−14.4302	−1.33407
$118$	−5.81369	−0.535193
$119$	−2.01790	−0.184981
$120$	10.2964	0.939927
$121$	0	0
$122$	0.314286	0.0284541
$123$	8.45272	0.762156
$124$	2.00000	0.179605
$125$	40.3944	3.61298
$126$	−1.21509	−0.108249
$127$	9.80161	0.869752	0.434876	−	0.900490i	$-0.356792\pi$
$127$	9.80161	0.869752	0.434876	+	0.900490i	$0.356792\pi$
$128$	1.00000	0.0883883
$129$	−15.1038	−1.32982
$130$	−25.1280	−2.20387
$131$	−16.2318	−1.41818	−0.709089	−	0.705119i	$-0.750894\pi$
$131$	−16.2318	−1.41818	−0.709089	+	0.705119i	$0.750894\pi$
$132$	0	0
$133$	−0.482696	−0.0418550
$134$	12.0000	1.03664
$135$	−4.97002	−0.427751
$136$	4.18048	0.358474
$137$	5.62113	0.480245	0.240123	−	0.970743i	$-0.422812\pi$
$137$	5.62113	0.480245	0.240123	+	0.970743i	$0.422812\pi$
$138$	−4.61650	−0.392982
$139$	1.56982	0.133150	0.0665750	−	0.997781i	$-0.478793\pi$
$139$	1.56982	0.133150	0.0665750	+	0.997781i	$0.478793\pi$
$140$	−2.11590	−0.178826
$141$	−9.90081	−0.833798
$142$	13.2618	1.11290
$143$	0	0
$144$	2.51730	0.209775
$145$	0.738225	0.0613062
$146$	−13.2151	−1.09369
$147$	−15.8950	−1.31100
$148$	8.34889	0.686275
$149$	2.16258	0.177166	0.0885828	−	0.996069i	$-0.471766\pi$
$149$	2.16258	0.177166	0.0885828	+	0.996069i	$0.471766\pi$
$150$	33.3897	2.72626
$151$	−22.4590	−1.82768	−0.913842	−	0.406069i	$-0.866899\pi$
$151$	−22.4590	−1.82768	−0.913842	+	0.406069i	$0.866899\pi$
$152$	1.00000	0.0811107
$153$	10.5236	0.850779
$154$	0	0
$155$	8.76700	0.704183
$156$	−13.4648	−1.07805
$157$	−8.74447	−0.697885	−0.348942	−	0.937144i	$-0.613459\pi$
$157$	−8.74447	−0.697885	−0.348942	+	0.937144i	$0.613459\pi$
$158$	15.5986	1.24096
$159$	−24.2664	−1.92445
$160$	4.38350	0.346546
$161$	0.948687	0.0747670
$162$	−10.2151	−0.802573
$163$	1.56982	0.122957	0.0614787	−	0.998108i	$-0.480418\pi$
$163$	1.56982	0.122957	0.0614787	+	0.998108i	$0.480418\pi$
$164$	3.59859	0.281003
$165$	0	0
$166$	9.08129	0.704845
$167$	10.4302	0.807112	0.403556	−	0.914955i	$-0.367774\pi$
$167$	10.4302	0.807112	0.403556	+	0.914955i	$0.367774\pi$
$168$	−1.13380	−0.0874747
$169$	19.8604	1.52772
$170$	18.3252	1.40548
$171$	2.51730	0.192503
$172$	−6.43018	−0.490297
$173$	−16.6920	−1.26907	−0.634533	−	0.772896i	$-0.718808\pi$
$173$	−16.6920	−1.26907	−0.634533	+	0.772896i	$0.718808\pi$
$174$	0.395577	0.0299886
$175$	−6.86157	−0.518686
$176$	0	0
$177$	−13.6557	−1.02643
$178$	2.20302	0.165123
$179$	7.76237	0.580187	0.290094	−	0.956998i	$-0.406314\pi$
$179$	7.76237	0.580187	0.290094	+	0.956998i	$0.406314\pi$
$180$	11.0346	0.822471
$181$	−17.7324	−1.31804	−0.659019	−	0.752126i	$-0.729028\pi$
$181$	−17.7324	−1.31804	−0.659019	+	0.752126i	$0.729028\pi$
$182$	2.76700	0.205104
$183$	0.738225	0.0545712
$184$	−1.96539	−0.144891
$185$	36.5974	2.69069
$186$	4.69779	0.344459
$187$	0	0
$188$	−4.21509	−0.307417
$189$	0.547282	0.0398089
$190$	4.38350	0.318013
$191$	−10.2151	−0.739138	−0.369569	−	0.929203i	$-0.620495\pi$
$191$	−10.2151	−0.739138	−0.369569	+	0.929203i	$0.620495\pi$
$192$	2.34889	0.169517
$193$	−6.69779	−0.482117	−0.241059	−	0.970511i	$-0.577495\pi$
$193$	−6.69779	−0.482117	−0.241059	+	0.970511i	$0.577495\pi$
$194$	2.62857	0.188720
$195$	−59.0230	−4.22672
$196$	−6.76700	−0.483357
$197$	−0.198387	−0.0141345	−0.00706725	−	0.999975i	$-0.502250\pi$
$197$	−0.198387	−0.0141345	−0.00706725	+	0.999975i	$0.502250\pi$
$198$	0	0
$199$	−9.55191	−0.677117	−0.338559	−	0.940945i	$-0.609939\pi$
$199$	−9.55191	−0.677117	−0.338559	+	0.940945i	$0.609939\pi$
$200$	14.2151	1.00516
$201$	28.1867	1.98814
$202$	−5.41811	−0.381217
$203$	−0.0812907	−0.00570549
$204$	9.81952	0.687504
$205$	15.7744	1.10174
$206$	−9.59859	−0.668766
$207$	−4.94749	−0.343874
$208$	−5.73240	−0.397470
$209$	0	0
$210$	−4.97002	−0.342964
$211$	−3.38350	−0.232930	−0.116465	−	0.993195i	$-0.537156\pi$
$211$	−3.38350	−0.232930	−0.116465	+	0.993195i	$0.537156\pi$
$212$	−10.3310	−0.709535
$213$	31.1505	2.13440
$214$	9.56399	0.653781
$215$	−28.1867	−1.92232
$216$	−1.13380	−0.0771454
$217$	−0.965392	−0.0655351
$218$	−17.4769	−1.18368
$219$	−31.0409	−2.09755
$220$	0	0
$221$	−23.9642	−1.61201
$222$	19.6107	1.31618
$223$	−18.4590	−1.23610	−0.618052	−	0.786137i	$-0.712078\pi$
$223$	−18.4590	−1.23610	−0.618052	+	0.786137i	$0.712078\pi$
$224$	−0.482696	−0.0322515
$225$	35.7837	2.38558
$226$	−18.6332	−1.23946
$227$	15.8258	1.05039	0.525196	−	0.850981i	$-0.323992\pi$
$227$	15.8258	1.05039	0.525196	+	0.850981i	$0.323992\pi$
$228$	2.34889	0.155559
$229$	−20.6620	−1.36538	−0.682691	−	0.730707i	$-0.739191\pi$
$229$	−20.6620	−1.36538	−0.682691	+	0.730707i	$0.739191\pi$
$230$	−8.61530	−0.568076
$231$	0	0
$232$	0.168410	0.0110566
$233$	−13.4123	−0.878668	−0.439334	−	0.898324i	$-0.644785\pi$
$233$	−13.4123	−0.878668	−0.439334	+	0.898324i	$0.644785\pi$
$234$	−14.4302	−0.943331
$235$	−18.4769	−1.20530
$236$	−5.81369	−0.378439
$237$	36.6394	2.37999
$238$	−2.01790	−0.130801
$239$	18.8950	1.22221	0.611107	−	0.791548i	$-0.290724\pi$
$239$	18.8950	1.22221	0.611107	+	0.791548i	$0.290724\pi$
$240$	10.2964	0.664629
$241$	2.56399	0.165161	0.0825805	−	0.996584i	$-0.473684\pi$
$241$	2.56399	0.165161	0.0825805	+	0.996584i	$0.473684\pi$
$242$	0	0
$243$	−20.5928	−1.32103
$244$	0.314286	0.0201201
$245$	−29.6632	−1.89511
$246$	8.45272	0.538926
$247$	−5.73240	−0.364744
$248$	2.00000	0.127000
$249$	21.3310	1.35180
$250$	40.3944	2.55476
$251$	4.69779	0.296522	0.148261	−	0.988948i	$-0.452632\pi$
$251$	4.69779	0.296522	0.148261	+	0.988948i	$0.452632\pi$
$252$	−1.21509	−0.0765436
$253$	0	0
$254$	9.80161	0.615008
$255$	43.0439	2.69551
$256$	1.00000	0.0625000
$257$	−12.0934	−0.754363	−0.377182	−	0.926139i	$-0.623107\pi$
$257$	−12.0934	−0.754363	−0.377182	+	0.926139i	$0.623107\pi$
$258$	−15.1038	−0.940323
$259$	−4.02998	−0.250411
$260$	−25.1280	−1.55837
$261$	0.423939	0.0262411
$262$	−16.2318	−1.00280
$263$	−9.41348	−0.580460	−0.290230	−	0.956957i	$-0.593732\pi$
$263$	−9.41348	−0.580460	−0.290230	+	0.956957i	$0.593732\pi$
$264$	0	0
$265$	−45.2859	−2.78189
$266$	−0.482696	−0.0295960
$267$	5.17466	0.316684
$268$	12.0000	0.733017
$269$	−12.9596	−0.790159	−0.395079	−	0.918647i	$-0.629283\pi$
$269$	−12.9596	−0.790159	−0.395079	+	0.918647i	$0.629283\pi$
$270$	−4.97002	−0.302466
$271$	14.4123	0.875484	0.437742	−	0.899101i	$-0.355778\pi$
$271$	14.4123	0.875484	0.437742	+	0.899101i	$0.355778\pi$
$272$	4.18048	0.253479
$273$	6.49940	0.393362
$274$	5.62113	0.339585
$275$	0	0
$276$	−4.61650	−0.277881
$277$	10.9763	0.659500	0.329750	−	0.944068i	$-0.393036\pi$
$277$	10.9763	0.659500	0.329750	+	0.944068i	$0.393036\pi$
$278$	1.56982	0.0941512
$279$	5.03461	0.301414
$280$	−2.11590	−0.126449
$281$	26.3656	1.57284	0.786420	−	0.617692i	$-0.211932\pi$
$281$	26.3656	1.57284	0.786420	+	0.617692i	$0.211932\pi$
$282$	−9.90081	−0.589584
$283$	15.1972	0.903379	0.451690	−	0.892175i	$-0.350821\pi$
$283$	15.1972	0.903379	0.451690	+	0.892175i	$0.350821\pi$
$284$	13.2618	0.786942
$285$	10.2964	0.609905
$286$	0	0
$287$	−1.73703	−0.102533
$288$	2.51730	0.148334
$289$	0.476450	0.0280265
$290$	0.738225	0.0433501
$291$	6.17424	0.361940
$292$	−13.2151	−0.773355
$293$	6.08129	0.355273	0.177636	−	0.984096i	$-0.443155\pi$
$293$	6.08129	0.355273	0.177636	+	0.984096i	$0.443155\pi$
$294$	−15.8950	−0.927014
$295$	−25.4843	−1.48375
$296$	8.34889	0.485270
$297$	0	0
$298$	2.16258	0.125275
$299$	11.2664	0.651553
$300$	33.3897	1.92776
$301$	3.10382	0.178901
$302$	−22.4590	−1.29237
$303$	−12.7266	−0.731122
$304$	1.00000	0.0573539
$305$	1.37767	0.0788854
$306$	10.5236	0.601591
$307$	−15.9700	−0.911457	−0.455729	−	0.890119i	$-0.650621\pi$
$307$	−15.9700	−0.911457	−0.455729	+	0.890119i	$0.650621\pi$
$308$	0	0
$309$	−22.5461	−1.28260
$310$	8.76700	0.497932
$311$	−22.6799	−1.28606	−0.643029	−	0.765842i	$-0.722323\pi$
$311$	−22.6799	−1.28606	−0.643029	+	0.765842i	$0.722323\pi$
$312$	−13.4648	−0.762294
$313$	6.91288	0.390739	0.195370	−	0.980730i	$-0.437409\pi$
$313$	6.91288	0.390739	0.195370	+	0.980730i	$0.437409\pi$
$314$	−8.74447	−0.493479
$315$	−5.32636	−0.300106
$316$	15.5986	0.877490
$317$	30.0934	1.69021	0.845106	−	0.534599i	$-0.179537\pi$
$317$	30.0934	1.69021	0.845106	+	0.534599i	$0.179537\pi$
$318$	−24.2664	−1.36079
$319$	0	0
$320$	4.38350	0.245045
$321$	22.4648	1.25386
$322$	0.948687	0.0528682
$323$	4.18048	0.232608
$324$	−10.2151	−0.567505
$325$	−81.4865	−4.52006
$326$	1.56982	0.0869440
$327$	−41.0513	−2.27014
$328$	3.59859	0.198699
$329$	2.03461	0.112172
$330$	0	0
$331$	−5.56399	−0.305824	−0.152912	−	0.988240i	$-0.548865\pi$
$331$	−5.56399	−0.305824	−0.152912	+	0.988240i	$0.548865\pi$
$332$	9.08129	0.498401
$333$	21.0167	1.15171
$334$	10.4302	0.570714
$335$	52.6020	2.87396
$336$	−1.13380	−0.0618540
$337$	12.4706	0.679318	0.339659	−	0.940549i	$-0.389688\pi$
$337$	12.4706	0.679318	0.339659	+	0.940549i	$0.389688\pi$
$338$	19.8604	1.08026
$339$	−43.7674	−2.37712
$340$	18.3252	0.993821
$341$	0	0
$342$	2.51730	0.136120
$343$	6.64528	0.358811
$344$	−6.43018	−0.346692
$345$	−20.2364	−1.08949
$346$	−16.6920	−0.897365
$347$	−0.115899	−0.00622178	−0.00311089	−	0.999995i	$-0.500990\pi$
$347$	−0.115899	−0.00622178	−0.00311089	+	0.999995i	$0.500990\pi$
$348$	0.395577	0.0212051
$349$	−25.2664	−1.35248	−0.676240	−	0.736682i	$-0.736392\pi$
$349$	−25.2664	−1.35248	−0.676240	+	0.736682i	$0.736392\pi$
$350$	−6.86157	−0.366766
$351$	6.49940	0.346912
$352$	0	0
$353$	24.3535	1.29621	0.648104	−	0.761552i	$-0.275562\pi$
$353$	24.3535	1.29621	0.648104	+	0.761552i	$0.275562\pi$
$354$	−13.6557	−0.725794
$355$	58.1330	3.08538
$356$	2.20302	0.116760
$357$	−4.73984	−0.250859
$358$	7.76237	0.410254
$359$	−13.0167	−0.686995	−0.343498	−	0.939154i	$-0.611612\pi$
$359$	−13.0167	−0.686995	−0.343498	+	0.939154i	$0.611612\pi$
$360$	11.0346	0.581575
$361$	1.00000	0.0526316
$362$	−17.7324	−0.931994
$363$	0	0
$364$	2.76700	0.145030
$365$	−57.9284	−3.03211
$366$	0.738225	0.0385876
$367$	−34.5761	−1.80486	−0.902428	−	0.430841i	$-0.858217\pi$
$367$	−34.5761	−1.80486	−0.902428	+	0.430841i	$0.858217\pi$
$368$	−1.96539	−0.102453
$369$	9.05876	0.471580
$370$	36.5974	1.90261
$371$	4.98673	0.258898
$372$	4.69779	0.243569
$373$	0.366797	0.0189920	0.00949602	−	0.999955i	$-0.496977\pi$
$373$	0.366797	0.0189920	0.00949602	+	0.999955i	$0.496977\pi$
$374$	0	0
$375$	94.8821	4.89969
$376$	−4.21509	−0.217377
$377$	−0.965392	−0.0497202
$378$	0.547282	0.0281491
$379$	−18.4002	−0.945155	−0.472578	−	0.881289i	$-0.656676\pi$
$379$	−18.4002	−0.945155	−0.472578	+	0.881289i	$0.656676\pi$
$380$	4.38350	0.224869
$381$	23.0230	1.17950
$382$	−10.2151	−0.522650
$383$	0.673639	0.0344214	0.0172107	−	0.999852i	$-0.494521\pi$
$383$	0.673639	0.0344214	0.0172107	+	0.999852i	$0.494521\pi$
$384$	2.34889	0.119867
$385$	0	0
$386$	−6.69779	−0.340908
$387$	−16.1867	−0.822818
$388$	2.62857	0.133446
$389$	13.3730	0.678040	0.339020	−	0.940779i	$-0.389905\pi$
$389$	13.3730	0.678040	0.339020	+	0.940779i	$0.389905\pi$
$390$	−59.0230	−2.98874
$391$	−8.21629	−0.415516
$392$	−6.76700	−0.341785
$393$	−38.1268	−1.92324
$394$	−0.198387	−0.00999461
$395$	68.3765	3.44039
$396$	0	0
$397$	−27.2213	−1.36620	−0.683100	−	0.730325i	$-0.739369\pi$
$397$	−27.2213	−1.36620	−0.683100	+	0.730325i	$0.739369\pi$
$398$	−9.55191	−0.478794
$399$	−1.13380	−0.0567611
$400$	14.2151	0.710755
$401$	35.2952	1.76256	0.881279	−	0.472597i	$-0.156683\pi$
$401$	35.2952	1.76256	0.881279	+	0.472597i	$0.156683\pi$
$402$	28.1867	1.40583
$403$	−11.4648	−0.571102
$404$	−5.41811	−0.269561
$405$	−44.7779	−2.22503
$406$	−0.0812907	−0.00403439
$407$	0	0
$408$	9.81952	0.486138
$409$	3.46479	0.171323	0.0856615	−	0.996324i	$-0.472700\pi$
$409$	3.46479	0.171323	0.0856615	+	0.996324i	$0.472700\pi$
$410$	15.7744	0.779044
$411$	13.2034	0.651277
$412$	−9.59859	−0.472889
$413$	2.80624	0.138086
$414$	−4.94749	−0.243156
$415$	39.8079	1.95409
$416$	−5.73240	−0.281054
$417$	3.68733	0.180569
$418$	0	0
$419$	−12.9187	−0.631120	−0.315560	−	0.948906i	$-0.602192\pi$
$419$	−12.9187	−0.631120	−0.315560	+	0.948906i	$0.602192\pi$
$420$	−4.97002	−0.242512
$421$	19.0738	0.929602	0.464801	−	0.885415i	$-0.346126\pi$
$421$	19.0738	0.929602	0.464801	+	0.885415i	$0.346126\pi$
$422$	−3.38350	−0.164706
$423$	−10.6107	−0.515908
$424$	−10.3310	−0.501717
$425$	59.4260	2.88258
$426$	31.1505	1.50925
$427$	−0.151705	−0.00734150
$428$	9.56399	0.462293
$429$	0	0
$430$	−28.1867	−1.35928
$431$	26.6574	1.28404	0.642020	−	0.766688i	$-0.278097\pi$
$431$	26.6574	1.28404	0.642020	+	0.766688i	$0.278097\pi$
$432$	−1.13380	−0.0545501
$433$	7.32636	0.352082	0.176041	−	0.984383i	$-0.443671\pi$
$433$	7.32636	0.352082	0.176041	+	0.984383i	$0.443671\pi$
$434$	−0.965392	−0.0463403
$435$	1.73401	0.0831395
$436$	−17.4769	−0.836990
$437$	−1.96539	−0.0940174
$438$	−31.0409	−1.48319
$439$	17.3956	0.830246	0.415123	−	0.909765i	$-0.363739\pi$
$439$	17.3956	0.830246	0.415123	+	0.909765i	$0.363739\pi$
$440$	0	0
$441$	−17.0346	−0.811172
$442$	−23.9642	−1.13986
$443$	30.8845	1.46737	0.733684	−	0.679491i	$-0.237799\pi$
$443$	30.8845	1.46737	0.733684	+	0.679491i	$0.237799\pi$
$444$	19.6107	0.930681
$445$	9.65693	0.457783
$446$	−18.4590	−0.874057
$447$	5.07968	0.240260
$448$	−0.482696	−0.0228052
$449$	14.6286	0.690365	0.345183	−	0.938536i	$-0.387817\pi$
$449$	14.6286	0.690365	0.345183	+	0.938536i	$0.387817\pi$
$450$	35.7837	1.68686
$451$	0	0
$452$	−18.6332	−0.876432
$453$	−52.7537	−2.47859
$454$	15.8258	0.742740
$455$	12.1292	0.568624
$456$	2.34889	0.109997
$457$	9.69779	0.453643	0.226822	−	0.973936i	$-0.427167\pi$
$457$	9.69779	0.453643	0.226822	+	0.973936i	$0.427167\pi$
$458$	−20.6620	−0.965471
$459$	−4.73984	−0.221237
$460$	−8.61530	−0.401690
$461$	−28.3835	−1.32195	−0.660976	−	0.750407i	$-0.729857\pi$
$461$	−28.3835	−1.32195	−0.660976	+	0.750407i	$0.729857\pi$
$462$	0	0
$463$	30.8183	1.43225	0.716124	−	0.697973i	$-0.245914\pi$
$463$	30.8183	1.43225	0.716124	+	0.697973i	$0.245914\pi$
$464$	0.168410	0.00781823
$465$	20.5928	0.954967
$466$	−13.4123	−0.621312
$467$	−19.0230	−0.880277	−0.440139	−	0.897930i	$-0.645071\pi$
$467$	−19.0230	−0.880277	−0.440139	+	0.897930i	$0.645071\pi$
$468$	−14.4302	−0.667036
$469$	−5.79235	−0.267466
$470$	−18.4769	−0.852274
$471$	−20.5398	−0.946426
$472$	−5.81369	−0.267597
$473$	0	0
$474$	36.6394	1.68291
$475$	14.2151	0.652233
$476$	−2.01790	−0.0924904
$477$	−26.0062	−1.19074
$478$	18.8950	0.864236
$479$	40.5340	1.85205	0.926023	−	0.377467i	$-0.123205\pi$
$479$	40.5340	1.85205	0.926023	+	0.377467i	$0.123205\pi$
$480$	10.2964	0.469963
$481$	−47.8592	−2.18219
$482$	2.56399	0.116786
$483$	2.22836	0.101394
$484$	0	0
$485$	11.5224	0.523203
$486$	−20.5928	−0.934107
$487$	39.4290	1.78670	0.893349	−	0.449364i	$-0.148349\pi$
$487$	39.4290	1.78670	0.893349	+	0.449364i	$0.148349\pi$
$488$	0.314286	0.0142271
$489$	3.68733	0.166747
$490$	−29.6632	−1.34005
$491$	−33.1614	−1.49655	−0.748276	−	0.663387i	$-0.769118\pi$
$491$	−33.1614	−1.49655	−0.748276	+	0.663387i	$0.769118\pi$
$492$	8.45272	0.381078
$493$	0.704035	0.0317081
$494$	−5.73240	−0.257913
$495$	0	0
$496$	2.00000	0.0898027
$497$	−6.40141	−0.287142
$498$	21.3310	0.955865
$499$	16.7445	0.749585	0.374793	−	0.927109i	$-0.377714\pi$
$499$	16.7445	0.749585	0.374793	+	0.927109i	$0.377714\pi$
$500$	40.3944	1.80649
$501$	24.4994	1.09455
$502$	4.69779	0.209673
$503$	41.5056	1.85065	0.925323	−	0.379181i	$-0.123794\pi$
$503$	41.5056	1.85065	0.925323	+	0.379181i	$0.123794\pi$
$504$	−1.21509	−0.0541245
$505$	−23.7503	−1.05687
$506$	0	0
$507$	46.6499	2.07180
$508$	9.80161	0.434876
$509$	−31.5702	−1.39933	−0.699663	−	0.714473i	$-0.746667\pi$
$509$	−31.5702	−1.39933	−0.699663	+	0.714473i	$0.746667\pi$
$510$	43.0439	1.90601
$511$	6.37887	0.282185
$512$	1.00000	0.0441942
$513$	−1.13380	−0.0500586
$514$	−12.0934	−0.533415
$515$	−42.0755	−1.85407
$516$	−15.1038	−0.664909
$517$	0	0
$518$	−4.02998	−0.177067
$519$	−39.2076	−1.72102
$520$	−25.1280	−1.10193
$521$	27.0588	1.18547	0.592733	−	0.805399i	$-0.298049\pi$
$521$	27.0588	1.18547	0.592733	+	0.805399i	$0.298049\pi$
$522$	0.423939	0.0185553
$523$	19.4590	0.850881	0.425441	−	0.904986i	$-0.360119\pi$
$523$	19.4590	0.850881	0.425441	+	0.904986i	$0.360119\pi$
$524$	−16.2318	−0.709089
$525$	−16.1171	−0.703408
$526$	−9.41348	−0.410447
$527$	8.36097	0.364210
$528$	0	0
$529$	−19.1372	−0.832054
$530$	−45.2859	−1.96709
$531$	−14.6348	−0.635097
$532$	−0.482696	−0.0209275
$533$	−20.6286	−0.893523
$534$	5.17466	0.223929
$535$	41.9238	1.81252
$536$	12.0000	0.518321
$537$	18.2330	0.786812
$538$	−12.9596	−0.558726
$539$	0	0
$540$	−4.97002	−0.213876
$541$	−13.7324	−0.590402	−0.295201	−	0.955435i	$-0.595387\pi$
$541$	−13.7324	−0.590402	−0.295201	+	0.955435i	$0.595387\pi$
$542$	14.4123	0.619061
$543$	−41.6515	−1.78744
$544$	4.18048	0.179237
$545$	−76.6099	−3.28161
$546$	6.49940	0.278149
$547$	−18.8241	−0.804862	−0.402431	−	0.915450i	$-0.631835\pi$
$547$	−18.8241	−0.804862	−0.402431	+	0.915450i	$0.631835\pi$
$548$	5.62113	0.240123
$549$	0.791154	0.0337656
$550$	0	0
$551$	0.168410	0.00717450
$552$	−4.61650	−0.196491
$553$	−7.52938	−0.320182
$554$	10.9763	0.466337
$555$	85.9634	3.64894
$556$	1.56982	0.0665750
$557$	−25.5940	−1.08445	−0.542226	−	0.840233i	$-0.682418\pi$
$557$	−25.5940	−1.08445	−0.542226	+	0.840233i	$0.682418\pi$
$558$	5.03461	0.213132
$559$	36.8604	1.55903
$560$	−2.11590	−0.0894130
$561$	0	0
$562$	26.3656	1.11217
$563$	35.8712	1.51179	0.755896	−	0.654691i	$-0.227201\pi$
$563$	35.8712	1.51179	0.755896	+	0.654691i	$0.227201\pi$
$564$	−9.90081	−0.416899
$565$	−81.6787	−3.43625
$566$	15.1972	0.638786
$567$	4.93078	0.207073
$568$	13.2618	0.556452
$569$	12.8604	0.539135	0.269567	−	0.962982i	$-0.413119\pi$
$569$	12.8604	0.539135	0.269567	+	0.962982i	$0.413119\pi$
$570$	10.2964	0.431268
$571$	−41.6048	−1.74111	−0.870554	−	0.492073i	$-0.836239\pi$
$571$	−41.6048	−1.74111	−0.870554	+	0.492073i	$0.836239\pi$
$572$	0	0
$573$	−23.9942	−1.00237
$574$	−1.73703	−0.0725021
$575$	−27.9382	−1.16510
$576$	2.51730	0.104888
$577$	3.00744	0.125202	0.0626008	−	0.998039i	$-0.480061\pi$
$577$	3.00744	0.125202	0.0626008	+	0.998039i	$0.480061\pi$
$578$	0.476450	0.0198177
$579$	−15.7324	−0.653816
$580$	0.738225	0.0306531
$581$	−4.38350	−0.181858
$582$	6.17424	0.255930
$583$	0	0
$584$	−13.2151	−0.546844
$585$	−63.2547	−2.61526
$586$	6.08129	0.251216
$587$	−33.1389	−1.36779	−0.683893	−	0.729582i	$-0.739715\pi$
$587$	−33.1389	−1.36779	−0.683893	+	0.729582i	$0.739715\pi$
$588$	−15.8950	−0.655498
$589$	2.00000	0.0824086
$590$	−25.4843	−1.04917
$591$	−0.465991	−0.0191683
$592$	8.34889	0.343137
$593$	−23.0755	−0.947596	−0.473798	−	0.880634i	$-0.657117\pi$
$593$	−23.0755	−0.947596	−0.473798	+	0.880634i	$0.657117\pi$
$594$	0	0
$595$	−8.84548	−0.362629
$596$	2.16258	0.0885828
$597$	−22.4364	−0.918262
$598$	11.2664	0.460718
$599$	−2.60442	−0.106414	−0.0532069	−	0.998584i	$-0.516944\pi$
$599$	−2.60442	−0.106414	−0.0532069	+	0.998584i	$0.516944\pi$
$600$	33.3897	1.36313
$601$	−6.80281	−0.277492	−0.138746	−	0.990328i	$-0.544307\pi$
$601$	−6.80281	−0.277492	−0.138746	+	0.990328i	$0.544307\pi$
$602$	3.10382	0.126502
$603$	30.2076	1.23015
$604$	−22.4590	−0.913842
$605$	0	0
$606$	−12.7266	−0.516981
$607$	−29.7370	−1.20699	−0.603494	−	0.797367i	$-0.706225\pi$
$607$	−29.7370	−1.20699	−0.603494	+	0.797367i	$0.706225\pi$
$608$	1.00000	0.0405554
$609$	−0.190943	−0.00773742
$610$	1.37767	0.0557804
$611$	24.1626	0.977513
$612$	10.5236	0.425389
$613$	37.1747	1.50147	0.750735	−	0.660603i	$-0.229699\pi$
$613$	37.1747	1.50147	0.750735	+	0.660603i	$0.229699\pi$
$614$	−15.9700	−0.644498
$615$	37.0525	1.49410
$616$	0	0
$617$	21.8783	0.880786	0.440393	−	0.897805i	$-0.354839\pi$
$617$	21.8783	0.880786	0.440393	+	0.897805i	$0.354839\pi$
$618$	−22.5461	−0.906936
$619$	−20.5686	−0.826723	−0.413361	−	0.910567i	$-0.635645\pi$
$619$	−20.5686	−0.826723	−0.413361	+	0.910567i	$0.635645\pi$
$620$	8.76700	0.352091
$621$	2.22836	0.0894212
$622$	−22.6799	−0.909381
$623$	−1.06339	−0.0426037
$624$	−13.4648	−0.539023
$625$	105.993	4.23974
$626$	6.91288	0.276294
$627$	0	0
$628$	−8.74447	−0.348942
$629$	34.9024	1.39165
$630$	−5.32636	−0.212207
$631$	37.4636	1.49140	0.745701	−	0.666281i	$-0.232115\pi$
$631$	37.4636	1.49140	0.745701	+	0.666281i	$0.232115\pi$
$632$	15.5986	0.620479
$633$	−7.94749	−0.315884
$634$	30.0934	1.19516
$635$	42.9654	1.70503
$636$	−24.2664	−0.962226
$637$	38.7912	1.53696
$638$	0	0
$639$	33.3839	1.32065
$640$	4.38350	0.173273
$641$	−20.6332	−0.814963	−0.407481	−	0.913214i	$-0.633593\pi$
$641$	−20.6332	−0.814963	−0.407481	+	0.913214i	$0.633593\pi$
$642$	22.4648	0.886615
$643$	29.9642	1.18167	0.590836	−	0.806792i	$-0.298798\pi$
$643$	29.9642	1.18167	0.590836	+	0.806792i	$0.298798\pi$
$644$	0.948687	0.0373835
$645$	−66.2076	−2.60692
$646$	4.18048	0.164479
$647$	19.5352	0.768008	0.384004	−	0.923331i	$-0.374545\pi$
$647$	19.5352	0.768008	0.384004	+	0.923331i	$0.374545\pi$
$648$	−10.2151	−0.401287
$649$	0	0
$650$	−81.4865	−3.19617
$651$	−2.26760	−0.0888744
$652$	1.56982	0.0614787
$653$	12.2318	0.478667	0.239334	−	0.970937i	$-0.423071\pi$
$653$	12.2318	0.478667	0.239334	+	0.970937i	$0.423071\pi$
$654$	−41.0513	−1.60523
$655$	−71.1521	−2.78014
$656$	3.59859	0.140502
$657$	−33.2664	−1.29785
$658$	2.03461	0.0793173
$659$	−19.6095	−0.763877	−0.381938	−	0.924188i	$-0.624743\pi$
$659$	−19.6095	−0.763877	−0.381938	+	0.924188i	$0.624743\pi$
$660$	0	0
$661$	−4.01207	−0.156052	−0.0780258	−	0.996951i	$-0.524862\pi$
$661$	−4.01207	−0.156052	−0.0780258	+	0.996951i	$0.524862\pi$
$662$	−5.56399	−0.216250
$663$	−56.2894	−2.18610
$664$	9.08129	0.352422
$665$	−2.11590	−0.0820510
$666$	21.0167	0.814381
$667$	−0.330991	−0.0128160
$668$	10.4302	0.403556
$669$	−43.3582	−1.67632
$670$	52.6020	2.03219
$671$	0	0
$672$	−1.13380	−0.0437374
$673$	−1.02998	−0.0397027	−0.0198514	−	0.999803i	$-0.506319\pi$
$673$	−1.02998	−0.0397027	−0.0198514	+	0.999803i	$0.506319\pi$
$674$	12.4706	0.480350
$675$	−16.1171	−0.620347
$676$	19.8604	0.763860
$677$	37.0980	1.42579	0.712896	−	0.701270i	$-0.247383\pi$
$677$	37.0980	1.42579	0.712896	+	0.701270i	$0.247383\pi$
$678$	−43.7674	−1.68088
$679$	−1.26880	−0.0486921
$680$	18.3252	0.702738
$681$	37.1730	1.42447
$682$	0	0
$683$	17.8374	0.682530	0.341265	−	0.939967i	$-0.389145\pi$
$683$	17.8374	0.682530	0.341265	+	0.939967i	$0.389145\pi$
$684$	2.51730	0.0962515
$685$	24.6402	0.941455
$686$	6.64528	0.253718
$687$	−48.5328	−1.85164
$688$	−6.43018	−0.245149
$689$	59.2213	2.25615
$690$	−20.2364	−0.770388
$691$	42.7537	1.62643	0.813214	−	0.581964i	$-0.197716\pi$
$691$	42.7537	1.62643	0.813214	+	0.581964i	$0.197716\pi$
$692$	−16.6920	−0.634533
$693$	0	0
$694$	−0.115899	−0.00439946
$695$	6.88129	0.261022
$696$	0.395577	0.0149943
$697$	15.0439	0.569827
$698$	−25.2664	−0.956348
$699$	−31.5040	−1.19159
$700$	−6.86157	−0.259343
$701$	11.6966	0.441774	0.220887	−	0.975299i	$-0.429105\pi$
$701$	11.6966	0.441774	0.220887	+	0.975299i	$0.429105\pi$
$702$	6.49940	0.245304
$703$	8.34889	0.314885
$704$	0	0
$705$	−43.4002	−1.63455
$706$	24.3535	0.916557
$707$	2.61530	0.0983585
$708$	−13.6557	−0.513214
$709$	39.1521	1.47039	0.735194	−	0.677856i	$-0.237091\pi$
$709$	39.1521	1.47039	0.735194	+	0.677856i	$0.237091\pi$
$710$	58.1330	2.18169
$711$	39.2664	1.47261
$712$	2.20302	0.0825616
$713$	−3.93078	−0.147209
$714$	−4.73984	−0.177384
$715$	0	0
$716$	7.76237	0.290094
$717$	44.3823	1.65749
$718$	−13.0167	−0.485779
$719$	26.6978	0.995660	0.497830	−	0.867275i	$-0.334130\pi$
$719$	26.6978	0.995660	0.497830	+	0.867275i	$0.334130\pi$
$720$	11.0346	0.411236
$721$	4.63320	0.172549
$722$	1.00000	0.0372161
$723$	6.02253	0.223980
$724$	−17.7324	−0.659019
$725$	2.39396	0.0889095
$726$	0	0
$727$	−20.9821	−0.778183	−0.389091	−	0.921199i	$-0.627211\pi$
$727$	−20.9821	−0.778183	−0.389091	+	0.921199i	$0.627211\pi$
$728$	2.76700	0.102552
$729$	−17.7250	−0.656480
$730$	−57.9284	−2.14403
$731$	−26.8813	−0.994240
$732$	0.738225	0.0272856
$733$	17.3264	0.639964	0.319982	−	0.947424i	$-0.396323\pi$
$733$	17.3264	0.639964	0.319982	+	0.947424i	$0.396323\pi$
$734$	−34.5761	−1.27623
$735$	−69.6757	−2.57003
$736$	−1.96539	−0.0724453
$737$	0	0
$738$	9.05876	0.333457
$739$	0.675255	0.0248397	0.0124198	−	0.999923i	$-0.496047\pi$
$739$	0.675255	0.0248397	0.0124198	+	0.999923i	$0.496047\pi$
$740$	36.5974	1.34535
$741$	−13.4648	−0.494642
$742$	4.98673	0.183069
$743$	−30.6044	−1.12277	−0.561384	−	0.827556i	$-0.689731\pi$
$743$	−30.6044	−1.12277	−0.561384	+	0.827556i	$0.689731\pi$
$744$	4.69779	0.172229
$745$	9.47968	0.347309
$746$	0.366797	0.0134294
$747$	22.8604	0.836417
$748$	0	0
$749$	−4.61650	−0.168683
$750$	94.8821	3.46461
$751$	4.60442	0.168018	0.0840089	−	0.996465i	$-0.473228\pi$
$751$	4.60442	0.168018	0.0840089	+	0.996465i	$0.473228\pi$
$752$	−4.21509	−0.153709
$753$	11.0346	0.402123
$754$	−0.965392	−0.0351575
$755$	−98.4489	−3.58292
$756$	0.547282	0.0199044
$757$	−7.75493	−0.281858	−0.140929	−	0.990020i	$-0.545009\pi$
$757$	−7.75493	−0.281858	−0.140929	+	0.990020i	$0.545009\pi$
$758$	−18.4002	−0.668326
$759$	0	0
$760$	4.38350	0.159006
$761$	−18.8258	−0.682433	−0.341217	−	0.939985i	$-0.610839\pi$
$761$	−18.8258	−0.682433	−0.341217	+	0.939985i	$0.610839\pi$
$762$	23.0230	0.834034
$763$	8.43601	0.305404
$764$	−10.2151	−0.369569
$765$	46.1300	1.66783
$766$	0.673639	0.0243396
$767$	33.3264	1.20335
$768$	2.34889	0.0847584
$769$	7.12917	0.257084	0.128542	−	0.991704i	$-0.458970\pi$
$769$	7.12917	0.257084	0.128542	+	0.991704i	$0.458970\pi$
$770$	0	0
$771$	−28.4060	−1.02302
$772$	−6.69779	−0.241059
$773$	2.42436	0.0871980	0.0435990	−	0.999049i	$-0.486118\pi$
$773$	2.42436	0.0871980	0.0435990	+	0.999049i	$0.486118\pi$
$774$	−16.1867	−0.581820
$775$	28.4302	1.02124
$776$	2.62857	0.0943602
$777$	−9.46599	−0.339591
$778$	13.3730	0.479447
$779$	3.59859	0.128933
$780$	−59.0230	−2.11336
$781$	0	0
$782$	−8.21629	−0.293814
$783$	−0.190943	−0.00682376
$784$	−6.76700	−0.241679
$785$	−38.3314	−1.36811
$786$	−38.1268	−1.35994
$787$	40.1326	1.43057	0.715286	−	0.698831i	$-0.246296\pi$
$787$	40.1326	1.43057	0.715286	+	0.698831i	$0.246296\pi$
$788$	−0.198387	−0.00706725
$789$	−22.1113	−0.787182
$790$	68.3765	2.43273
$791$	8.99417	0.319796
$792$	0	0
$793$	−1.80161	−0.0639771
$794$	−27.2213	−0.966049
$795$	−106.372	−3.77262
$796$	−9.55191	−0.338559
$797$	16.6620	0.590198	0.295099	−	0.955467i	$-0.404647\pi$
$797$	16.6620	0.590198	0.295099	+	0.955467i	$0.404647\pi$
$798$	−1.13380	−0.0401361
$799$	−17.6211	−0.623391
$800$	14.2151	0.502579
$801$	5.54567	0.195946
$802$	35.2952	1.24632
$803$	0	0
$804$	28.1867	0.994069
$805$	4.15857	0.146570
$806$	−11.4648	−0.403830
$807$	−30.4406	−1.07156
$808$	−5.41811	−0.190608
$809$	−22.0743	−0.776090	−0.388045	−	0.921640i	$-0.626849\pi$
$809$	−22.0743	−0.776090	−0.388045	+	0.921640i	$0.626849\pi$
$810$	−44.7779	−1.57333
$811$	8.50523	0.298659	0.149330	−	0.988787i	$-0.452288\pi$
$811$	8.50523	0.298659	0.149330	+	0.988787i	$0.452288\pi$
$812$	−0.0812907	−0.00285275
$813$	33.8529	1.18727
$814$	0	0
$815$	6.88129	0.241041
$816$	9.81952	0.343752
$817$	−6.43018	−0.224964
$818$	3.46479	0.121144
$819$	6.96539	0.243390
$820$	15.7744	0.550868
$821$	−35.3823	−1.23485	−0.617425	−	0.786629i	$-0.711824\pi$
$821$	−35.3823	−1.23485	−0.617425	+	0.786629i	$0.711824\pi$
$822$	13.2034	0.460523
$823$	46.0346	1.60467	0.802333	−	0.596877i	$-0.203592\pi$
$823$	46.0346	1.60467	0.802333	+	0.596877i	$0.203592\pi$
$824$	−9.59859	−0.334383
$825$	0	0
$826$	2.80624	0.0976417
$827$	28.9024	1.00504	0.502518	−	0.864567i	$-0.332407\pi$
$827$	28.9024	1.00504	0.502518	+	0.864567i	$0.332407\pi$
$828$	−4.94749	−0.171937
$829$	−8.83622	−0.306895	−0.153447	−	0.988157i	$-0.549038\pi$
$829$	−8.83622	−0.306895	−0.153447	+	0.988157i	$0.549038\pi$
$830$	39.8079	1.38175
$831$	25.7821	0.894371
$832$	−5.73240	−0.198735
$833$	−28.2894	−0.980168
$834$	3.68733	0.127682
$835$	45.7207	1.58223
$836$	0	0
$837$	−2.26760	−0.0783798
$838$	−12.9187	−0.446269
$839$	−46.6332	−1.60996	−0.804978	−	0.593304i	$-0.797823\pi$
$839$	−46.6332	−1.60996	−0.804978	+	0.593304i	$0.797823\pi$
$840$	−4.97002	−0.171482
$841$	−28.9716	−0.999022
$842$	19.0738	0.657328
$843$	61.9300	2.13298
$844$	−3.38350	−0.116465
$845$	87.0580	2.99489
$846$	−10.6107	−0.364802
$847$	0	0
$848$	−10.3310	−0.354768
$849$	35.6966	1.22510
$850$	59.4260	2.03829
$851$	−16.4088	−0.562488
$852$	31.1505	1.06720
$853$	15.7324	0.538667	0.269333	−	0.963047i	$-0.413197\pi$
$853$	15.7324	0.538667	0.269333	+	0.963047i	$0.413197\pi$
$854$	−0.151705	−0.00519123
$855$	11.0346	0.377376
$856$	9.56399	0.326890
$857$	28.8604	0.985851	0.492926	−	0.870071i	$-0.335927\pi$
$857$	28.8604	0.985851	0.492926	+	0.870071i	$0.335927\pi$
$858$	0	0
$859$	0.314286	0.0107233	0.00536165	−	0.999986i	$-0.498293\pi$
$859$	0.314286	0.0107233	0.00536165	+	0.999986i	$0.498293\pi$
$860$	−28.1867	−0.961160
$861$	−4.08009	−0.139049
$862$	26.6574	0.907953
$863$	5.18793	0.176599	0.0882996	−	0.996094i	$-0.471857\pi$
$863$	5.18793	0.176599	0.0882996	+	0.996094i	$0.471857\pi$
$864$	−1.13380	−0.0385727
$865$	−73.1692	−2.48783
$866$	7.32636	0.248960
$867$	1.11913	0.0380076
$868$	−0.965392	−0.0327675
$869$	0	0
$870$	1.73401	0.0587885
$871$	−68.7888	−2.33082
$872$	−17.4769	−0.591841
$873$	6.61692	0.223949
$874$	−1.96539	−0.0664804
$875$	−19.4982	−0.659160
$876$	−31.0409	−1.04877
$877$	42.2380	1.42628	0.713139	−	0.701023i	$-0.247273\pi$
$877$	42.2380	1.42628	0.713139	+	0.701023i	$0.247273\pi$
$878$	17.3956	0.587072
$879$	14.2843	0.481798
$880$	0	0
$881$	3.39438	0.114360	0.0571798	−	0.998364i	$-0.481789\pi$
$881$	3.39438	0.114360	0.0571798	+	0.998364i	$0.481789\pi$
$882$	−17.0346	−0.573585
$883$	−31.7883	−1.06976	−0.534881	−	0.844927i	$-0.679644\pi$
$883$	−31.7883	−1.06976	−0.534881	+	0.844927i	$0.679644\pi$
$884$	−23.9642	−0.806003
$885$	−59.8600	−2.01217
$886$	30.8845	1.03759
$887$	−31.3551	−1.05280	−0.526401	−	0.850236i	$-0.676459\pi$
$887$	−31.3551	−1.05280	−0.526401	+	0.850236i	$0.676459\pi$
$888$	19.6107	0.658091
$889$	−4.73120	−0.158679
$890$	9.65693	0.323701
$891$	0	0
$892$	−18.4590	−0.618052
$893$	−4.21509	−0.141053
$894$	5.07968	0.169890
$895$	34.0264	1.13738
$896$	−0.482696	−0.0161257
$897$	26.4636	0.883594
$898$	14.6286	0.488162
$899$	0.336820	0.0112336
$900$	35.7837	1.19279
$901$	−43.1885	−1.43882
$902$	0	0
$903$	7.29055	0.242614
$904$	−18.6332	−0.619731
$905$	−77.7300	−2.58383
$906$	−52.7537	−1.75263
$907$	−31.9071	−1.05946	−0.529728	−	0.848167i	$-0.677706\pi$
$907$	−31.9071	−1.05946	−0.529728	+	0.848167i	$0.677706\pi$
$908$	15.8258	0.525196
$909$	−13.6390	−0.452378
$910$	12.1292	0.402078
$911$	−21.3644	−0.707834	−0.353917	−	0.935277i	$-0.615151\pi$
$911$	−21.3644	−0.707834	−0.353917	+	0.935277i	$0.615151\pi$
$912$	2.34889	0.0777797
$913$	0	0
$914$	9.69779	0.320774
$915$	3.23601	0.106979
$916$	−20.6620	−0.682691
$917$	7.83502	0.258735
$918$	−4.73984	−0.156438
$919$	18.7912	0.619863	0.309931	−	0.950759i	$-0.399694\pi$
$919$	18.7912	0.619863	0.309931	+	0.950759i	$0.399694\pi$
$920$	−8.61530	−0.284038
$921$	−37.5119	−1.23606
$922$	−28.3835	−0.934761
$923$	−76.0218	−2.50229
$924$	0	0
$925$	118.680	3.90218
$926$	30.8183	1.01275
$927$	−24.1626	−0.793603
$928$	0.168410	0.00552832
$929$	−8.93078	−0.293010	−0.146505	−	0.989210i	$-0.546802\pi$
$929$	−8.93078	−0.293010	−0.146505	+	0.989210i	$0.546802\pi$
$930$	20.5928	0.675263
$931$	−6.76700	−0.221780
$932$	−13.4123	−0.439334
$933$	−53.2727	−1.74407
$934$	−19.0230	−0.622450
$935$	0	0
$936$	−14.4302	−0.471665
$937$	−38.3419	−1.25257	−0.626287	−	0.779592i	$-0.715426\pi$
$937$	−38.3419	−1.25257	−0.626287	+	0.779592i	$0.715426\pi$
$938$	−5.79235	−0.189127
$939$	16.2376	0.529895
$940$	−18.4769	−0.602649
$941$	−12.9654	−0.422660	−0.211330	−	0.977415i	$-0.567779\pi$
$941$	−12.9654	−0.422660	−0.211330	+	0.977415i	$0.567779\pi$
$942$	−20.5398	−0.669224
$943$	−7.07265	−0.230317
$944$	−5.81369	−0.189219
$945$	2.39901	0.0780398
$946$	0	0
$947$	4.79115	0.155692	0.0778458	−	0.996965i	$-0.475196\pi$
$947$	4.79115	0.155692	0.0778458	+	0.996965i	$0.475196\pi$
$948$	36.6394	1.18999
$949$	75.7542	2.45908
$950$	14.2151	0.461199
$951$	70.6861	2.29215
$952$	−2.01790	−0.0654006
$953$	39.0517	1.26501	0.632505	−	0.774556i	$-0.282027\pi$
$953$	39.0517	1.26501	0.632505	+	0.774556i	$0.282027\pi$
$954$	−26.0062	−0.841983
$955$	−44.7779	−1.44898
$956$	18.8950	0.611107
$957$	0	0
$958$	40.5340	1.30959
$959$	−2.71330	−0.0876169
$960$	10.2964	0.332314
$961$	−27.0000	−0.870968
$962$	−47.8592	−1.54304
$963$	24.0755	0.775821
$964$	2.56399	0.0825805
$965$	−29.3598	−0.945124
$966$	2.22836	0.0716965
$967$	28.1909	0.906560	0.453280	−	0.891368i	$-0.350254\pi$
$967$	28.1909	0.906560	0.453280	+	0.891368i	$0.350254\pi$
$968$	0	0
$969$	9.81952	0.315448
$970$	11.5224	0.369960
$971$	−8.64366	−0.277388	−0.138694	−	0.990335i	$-0.544290\pi$
$971$	−8.64366	−0.277388	−0.138694	+	0.990335i	$0.544290\pi$
$972$	−20.5928	−0.660513
$973$	−0.757743	−0.0242921
$974$	39.4290	1.26339
$975$	−191.403	−6.12981
$976$	0.314286	0.0100601
$977$	−2.22254	−0.0711052	−0.0355526	−	0.999368i	$-0.511319\pi$
$977$	−2.22254	−0.0711052	−0.0355526	+	0.999368i	$0.511319\pi$
$978$	3.68733	0.117908
$979$	0	0
$980$	−29.6632	−0.947556
$981$	−43.9946	−1.40464
$982$	−33.1614	−1.05822
$983$	15.7970	0.503845	0.251923	−	0.967747i	$-0.418937\pi$
$983$	15.7970	0.503845	0.251923	+	0.967747i	$0.418937\pi$
$984$	8.45272	0.269463
$985$	−0.869631	−0.0277088
$986$	0.704035	0.0224210
$987$	4.77908	0.152120
$988$	−5.73240	−0.182372
$989$	12.6378	0.401860
$990$	0	0
$991$	−19.8304	−0.629933	−0.314967	−	0.949103i	$-0.601993\pi$
$991$	−19.8304	−0.629933	−0.314967	+	0.949103i	$0.601993\pi$
$992$	2.00000	0.0635001
$993$	−13.0692	−0.414739
$994$	−6.40141	−0.203040
$995$	−41.8708	−1.32739
$996$	21.3310	0.675898
$997$	−13.4515	−0.426014	−0.213007	−	0.977051i	$-0.568326\pi$
$997$	−13.4515	−0.426014	−0.213007	+	0.977051i	$0.568326\pi$
$998$	16.7445	0.530037
$999$	−9.46599	−0.299491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bp.1.3	yes	3
11.10	odd	2		4598.2.a.bl.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bl.1.3	✓	3	11.10	odd	2
4598.2.a.bp.1.3	yes	3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.34889 q^{3} +1.00000 q^{4} +4.38350 q^{5} +2.34889 q^{6} -0.482696 q^{7} +1.00000 q^{8} +2.51730 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.34889 q^{3} +1.00000 q^{4} +4.38350 q^{5} +2.34889 q^{6} -0.482696 q^{7} +1.00000 q^{8} +2.51730 q^{9} +4.38350 q^{10} +2.34889 q^{12} -5.73240 q^{13} -0.482696 q^{14} +10.2964 q^{15} +1.00000 q^{16} +4.18048 q^{17} +2.51730 q^{18} +1.00000 q^{19} +4.38350 q^{20} -1.13380 q^{21} -1.96539 q^{23} +2.34889 q^{24} +14.2151 q^{25} -5.73240 q^{26} -1.13380 q^{27} -0.482696 q^{28} +0.168410 q^{29} +10.2964 q^{30} +2.00000 q^{31} +1.00000 q^{32} +4.18048 q^{34} -2.11590 q^{35} +2.51730 q^{36} +8.34889 q^{37} +1.00000 q^{38} -13.4648 q^{39} +4.38350 q^{40} +3.59859 q^{41} -1.13380 q^{42} -6.43018 q^{43} +11.0346 q^{45} -1.96539 q^{46} -4.21509 q^{47} +2.34889 q^{48} -6.76700 q^{49} +14.2151 q^{50} +9.81952 q^{51} -5.73240 q^{52} -10.3310 q^{53} -1.13380 q^{54} -0.482696 q^{56} +2.34889 q^{57} +0.168410 q^{58} -5.81369 q^{59} +10.2964 q^{60} +0.314286 q^{61} +2.00000 q^{62} -1.21509 q^{63} +1.00000 q^{64} -25.1280 q^{65} +12.0000 q^{67} +4.18048 q^{68} -4.61650 q^{69} -2.11590 q^{70} +13.2618 q^{71} +2.51730 q^{72} -13.2151 q^{73} +8.34889 q^{74} +33.3897 q^{75} +1.00000 q^{76} -13.4648 q^{78} +15.5986 q^{79} +4.38350 q^{80} -10.2151 q^{81} +3.59859 q^{82} +9.08129 q^{83} -1.13380 q^{84} +18.3252 q^{85} -6.43018 q^{86} +0.395577 q^{87} +2.20302 q^{89} +11.0346 q^{90} +2.76700 q^{91} -1.96539 q^{92} +4.69779 q^{93} -4.21509 q^{94} +4.38350 q^{95} +2.34889 q^{96} +2.62857 q^{97} -6.76700 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} + 4 q^{10} + q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{15} + 3 q^{16} + 2 q^{17} + 6 q^{18} + 3 q^{19} + 4 q^{20} - 11 q^{21} - 9 q^{23} + q^{24} + 29 q^{25} - 2 q^{26} - 11 q^{27} - 3 q^{28} + 5 q^{29} - 4 q^{30} + 6 q^{31} + 3 q^{32} + 2 q^{34} + 18 q^{35} + 6 q^{36} + 19 q^{37} + 3 q^{38} - 10 q^{39} + 4 q^{40} - 12 q^{41} - 11 q^{42} + 8 q^{43} + 30 q^{45} - 9 q^{46} + q^{47} + q^{48} - 2 q^{49} + 29 q^{50} + 40 q^{51} - 2 q^{52} + 7 q^{53} - 11 q^{54} - 3 q^{56} + q^{57} + 5 q^{58} + 19 q^{59} - 4 q^{60} - 2 q^{61} + 6 q^{62} + 10 q^{63} + 3 q^{64} - 36 q^{65} + 36 q^{67} + 2 q^{68} - 23 q^{69} + 18 q^{70} + 8 q^{71} + 6 q^{72} - 26 q^{73} + 19 q^{74} + 29 q^{75} + 3 q^{76} - 10 q^{78} + 24 q^{79} + 4 q^{80} - 17 q^{81} - 12 q^{82} + 6 q^{83} - 11 q^{84} - 30 q^{85} + 8 q^{86} - 23 q^{87} + 8 q^{89} + 30 q^{90} - 10 q^{91} - 9 q^{92} + 2 q^{93} + q^{94} + 4 q^{95} + q^{96} + 2 q^{97} - 2 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 + 4 * q^10 + q^12 - 2 * q^13 - 3 * q^14 - 4 * q^15 + 3 * q^16 + 2 * q^17 + 6 * q^18 + 3 * q^19 + 4 * q^20 - 11 * q^21 - 9 * q^23 + q^24 + 29 * q^25 - 2 * q^26 - 11 * q^27 - 3 * q^28 + 5 * q^29 - 4 * q^30 + 6 * q^31 + 3 * q^32 + 2 * q^34 + 18 * q^35 + 6 * q^36 + 19 * q^37 + 3 * q^38 - 10 * q^39 + 4 * q^40 - 12 * q^41 - 11 * q^42 + 8 * q^43 + 30 * q^45 - 9 * q^46 + q^47 + q^48 - 2 * q^49 + 29 * q^50 + 40 * q^51 - 2 * q^52 + 7 * q^53 - 11 * q^54 - 3 * q^56 + q^57 + 5 * q^58 + 19 * q^59 - 4 * q^60 - 2 * q^61 + 6 * q^62 + 10 * q^63 + 3 * q^64 - 36 * q^65 + 36 * q^67 + 2 * q^68 - 23 * q^69 + 18 * q^70 + 8 * q^71 + 6 * q^72 - 26 * q^73 + 19 * q^74 + 29 * q^75 + 3 * q^76 - 10 * q^78 + 24 * q^79 + 4 * q^80 - 17 * q^81 - 12 * q^82 + 6 * q^83 - 11 * q^84 - 30 * q^85 + 8 * q^86 - 23 * q^87 + 8 * q^89 + 30 * q^90 - 10 * q^91 - 9 * q^92 + 2 * q^93 + q^94 + 4 * q^95 + q^96 + 2 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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