LMFDB - Embedded newform 5239.2.a.v.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, 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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.208462 q^{2} -2.98137 q^{3} -1.95654 q^{4} +2.86174 q^{5} -0.621501 q^{6} -2.98726 q^{7} -0.824787 q^{8} +5.88856 q^{9} +O(q^{10})$	\(q+0.208462 q^{2} -2.98137 q^{3} -1.95654 q^{4} +2.86174 q^{5} -0.621501 q^{6} -2.98726 q^{7} -0.824787 q^{8} +5.88856 q^{9} +0.596563 q^{10} +5.42700 q^{11} +5.83318 q^{12} -0.622728 q^{14} -8.53191 q^{15} +3.74115 q^{16} +6.33159 q^{17} +1.22754 q^{18} -4.69253 q^{19} -5.59913 q^{20} +8.90611 q^{21} +1.13132 q^{22} +5.38636 q^{23} +2.45899 q^{24} +3.18957 q^{25} -8.61185 q^{27} +5.84470 q^{28} +10.3946 q^{29} -1.77858 q^{30} +1.00000 q^{31} +2.42946 q^{32} -16.1799 q^{33} +1.31989 q^{34} -8.54876 q^{35} -11.5212 q^{36} +4.96485 q^{37} -0.978212 q^{38} -2.36033 q^{40} +2.04411 q^{41} +1.85658 q^{42} -7.68071 q^{43} -10.6182 q^{44} +16.8515 q^{45} +1.12285 q^{46} -2.35921 q^{47} -11.1537 q^{48} +1.92370 q^{49} +0.664904 q^{50} -18.8768 q^{51} +13.0516 q^{53} -1.79524 q^{54} +15.5307 q^{55} +2.46385 q^{56} +13.9902 q^{57} +2.16687 q^{58} -6.78783 q^{59} +16.6931 q^{60} +3.33677 q^{61} +0.208462 q^{62} -17.5906 q^{63} -6.97585 q^{64} -3.37288 q^{66} -11.2697 q^{67} -12.3880 q^{68} -16.0587 q^{69} -1.78209 q^{70} +9.13148 q^{71} -4.85681 q^{72} -3.60652 q^{73} +1.03498 q^{74} -9.50929 q^{75} +9.18114 q^{76} -16.2118 q^{77} -0.117477 q^{79} +10.7062 q^{80} +8.00943 q^{81} +0.426118 q^{82} +13.0820 q^{83} -17.4252 q^{84} +18.1194 q^{85} -1.60113 q^{86} -30.9901 q^{87} -4.47612 q^{88} -6.78700 q^{89} +3.51290 q^{90} -10.5387 q^{92} -2.98137 q^{93} -0.491805 q^{94} -13.4288 q^{95} -7.24312 q^{96} -2.93717 q^{97} +0.401017 q^{98} +31.9572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) $ 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9} - 6 q^{10} - 7 q^{11} + 5 q^{12} + 38 q^{14} + 4 q^{15} + 76 q^{16} + 62 q^{17} - 9 q^{18} + 8 q^{19} + 16 q^{20} - 6 q^{21} + 15 q^{22} + 38 q^{23} - 99 q^{24} + 87 q^{25} + 25 q^{27} + 19 q^{28} + 95 q^{29} + 41 q^{30} + 54 q^{31} + 9 q^{32} + 12 q^{33} + 7 q^{34} + 53 q^{35} + 97 q^{36} - 24 q^{37} - 16 q^{38} - 28 q^{40} + 22 q^{41} + 11 q^{42} + 11 q^{43} - 24 q^{44} + 8 q^{45} + 9 q^{46} + 45 q^{47} + 2 q^{48} + 105 q^{49} + 6 q^{50} + 58 q^{51} + 56 q^{53} + 50 q^{54} + q^{55} + 91 q^{56} - 51 q^{57} + 25 q^{58} + 36 q^{59} + 100 q^{60} + 48 q^{61} + 2 q^{62} - 56 q^{63} + 90 q^{64} - 24 q^{66} + 26 q^{67} + 140 q^{68} + 47 q^{69} - 24 q^{70} + 40 q^{71} + 7 q^{72} + 9 q^{73} + 114 q^{74} + 18 q^{75} - 67 q^{76} + 65 q^{77} + 33 q^{79} + 53 q^{80} + 210 q^{81} - 6 q^{82} - 41 q^{83} - 37 q^{84} + 37 q^{85} - 42 q^{86} - 16 q^{87} - 22 q^{88} - 24 q^{89} - 40 q^{90} + 87 q^{92} + 7 q^{93} - 4 q^{94} + 61 q^{95} - 200 q^{96} + 28 q^{97} + 68 q^{98} + 39 q^{99}+O(q^{100}) \) 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9 - 6 * q^10 - 7 * q^11 + 5 * q^12 + 38 * q^14 + 4 * q^15 + 76 * q^16 + 62 * q^17 - 9 * q^18 + 8 * q^19 + 16 * q^20 - 6 * q^21 + 15 * q^22 + 38 * q^23 - 99 * q^24 + 87 * q^25 + 25 * q^27 + 19 * q^28 + 95 * q^29 + 41 * q^30 + 54 * q^31 + 9 * q^32 + 12 * q^33 + 7 * q^34 + 53 * q^35 + 97 * q^36 - 24 * q^37 - 16 * q^38 - 28 * q^40 + 22 * q^41 + 11 * q^42 + 11 * q^43 - 24 * q^44 + 8 * q^45 + 9 * q^46 + 45 * q^47 + 2 * q^48 + 105 * q^49 + 6 * q^50 + 58 * q^51 + 56 * q^53 + 50 * q^54 + q^55 + 91 * q^56 - 51 * q^57 + 25 * q^58 + 36 * q^59 + 100 * q^60 + 48 * q^61 + 2 * q^62 - 56 * q^63 + 90 * q^64 - 24 * q^66 + 26 * q^67 + 140 * q^68 + 47 * q^69 - 24 * q^70 + 40 * q^71 + 7 * q^72 + 9 * q^73 + 114 * q^74 + 18 * q^75 - 67 * q^76 + 65 * q^77 + 33 * q^79 + 53 * q^80 + 210 * q^81 - 6 * q^82 - 41 * q^83 - 37 * q^84 + 37 * q^85 - 42 * q^86 - 16 * q^87 - 22 * q^88 - 24 * q^89 - 40 * q^90 + 87 * q^92 + 7 * q^93 - 4 * q^94 + 61 * q^95 - 200 * q^96 + 28 * q^97 + 68 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.208462	0.147405	0.0737023	−	0.997280i	$-0.476519\pi$
$2$	0.208462	0.147405	0.0737023	+	0.997280i	$0.476519\pi$
$3$	−2.98137	−1.72129	−0.860647	−	0.509202i	$-0.829941\pi$
$3$	−2.98137	−1.72129	−0.860647	+	0.509202i	$0.829941\pi$
$4$	−1.95654	−0.978272
$5$	2.86174	1.27981	0.639905	−	0.768454i	$-0.278974\pi$
$5$	2.86174	1.27981	0.639905	+	0.768454i	$0.278974\pi$
$6$	−0.621501	−0.253727
$7$	−2.98726	−1.12908	−0.564538	−	0.825407i	$-0.690946\pi$
$7$	−2.98726	−1.12908	−0.564538	+	0.825407i	$0.690946\pi$
$8$	−0.824787	−0.291606
$9$	5.88856	1.96285
$10$	0.596563	0.188650
$11$	5.42700	1.63630	0.818151	−	0.575003i	$-0.194999\pi$
$11$	5.42700	1.63630	0.818151	+	0.575003i	$0.194999\pi$
$12$	5.83318	1.68389
$13$	0	0
$13$	0	0
$14$	−0.622728	−0.166431
$15$	−8.53191	−2.20293
$16$	3.74115	0.935288
$17$	6.33159	1.53564	0.767818	−	0.640668i	$-0.221342\pi$
$17$	6.33159	1.53564	0.767818	+	0.640668i	$0.221342\pi$
$18$	1.22754	0.289333
$19$	−4.69253	−1.07654	−0.538270	−	0.842772i	$-0.680922\pi$
$19$	−4.69253	−1.07654	−0.538270	+	0.842772i	$0.680922\pi$
$20$	−5.59913	−1.25200
$21$	8.90611	1.94347
$22$	1.13132	0.241198
$23$	5.38636	1.12313	0.561567	−	0.827431i	$-0.310199\pi$
$23$	5.38636	1.12313	0.561567	+	0.827431i	$0.310199\pi$
$24$	2.45899	0.501940
$25$	3.18957	0.637915
$26$	0	0
$27$	−8.61185	−1.65735
$28$	5.84470	1.10454
$29$	10.3946	1.93022	0.965112	−	0.261837i	$-0.0843282\pi$
$29$	10.3946	1.93022	0.965112	+	0.261837i	$0.0843282\pi$
$30$	−1.77858	−0.324722
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	2.42946	0.429472
$33$	−16.1799	−2.81656
$34$	1.31989	0.226360
$35$	−8.54876	−1.44500
$36$	−11.5212	−1.92020
$37$	4.96485	0.816217	0.408108	−	0.912933i	$-0.366189\pi$
$37$	4.96485	0.816217	0.408108	+	0.912933i	$0.366189\pi$
$38$	−0.978212	−0.158687
$39$	0	0
$40$	−2.36033	−0.373201
$41$	2.04411	0.319236	0.159618	−	0.987179i	$-0.448974\pi$
$41$	2.04411	0.319236	0.159618	+	0.987179i	$0.448974\pi$
$42$	1.85658	0.286477
$43$	−7.68071	−1.17130	−0.585649	−	0.810565i	$-0.699160\pi$
$43$	−7.68071	−1.17130	−0.585649	+	0.810565i	$0.699160\pi$
$44$	−10.6182	−1.60075
$45$	16.8515	2.51208
$46$	1.12285	0.165555
$47$	−2.35921	−0.344127	−0.172063	−	0.985086i	$-0.555043\pi$
$47$	−2.35921	−0.344127	−0.172063	+	0.985086i	$0.555043\pi$
$48$	−11.1537	−1.60991
$49$	1.92370	0.274814
$50$	0.664904	0.0940316
$51$	−18.8768	−2.64328
$52$	0	0
$53$	13.0516	1.79278	0.896389	−	0.443268i	$-0.146181\pi$
$53$	13.0516	1.79278	0.896389	+	0.443268i	$0.146181\pi$
$54$	−1.79524	−0.244301
$55$	15.5307	2.09416
$56$	2.46385	0.329246
$57$	13.9902	1.85304
$58$	2.16687	0.284524
$59$	−6.78783	−0.883701	−0.441850	−	0.897089i	$-0.645678\pi$
$59$	−6.78783	−0.883701	−0.441850	+	0.897089i	$0.645678\pi$
$60$	16.6931	2.15506
$61$	3.33677	0.427229	0.213615	−	0.976918i	$-0.431476\pi$
$61$	3.33677	0.427229	0.213615	+	0.976918i	$0.431476\pi$
$62$	0.208462	0.0264746
$63$	−17.5906	−2.21621
$64$	−6.97585	−0.871982
$65$	0	0
$66$	−3.37288	−0.415173
$67$	−11.2697	−1.37681	−0.688407	−	0.725325i	$-0.741690\pi$
$67$	−11.2697	−1.37681	−0.688407	+	0.725325i	$0.741690\pi$
$68$	−12.3880	−1.50227
$69$	−16.0587	−1.93324
$70$	−1.78209	−0.213000
$71$	9.13148	1.08371	0.541853	−	0.840473i	$-0.317723\pi$
$71$	9.13148	1.08371	0.541853	+	0.840473i	$0.317723\pi$
$72$	−4.85681	−0.572380
$73$	−3.60652	−0.422111	−0.211055	−	0.977474i	$-0.567690\pi$
$73$	−3.60652	−0.422111	−0.211055	+	0.977474i	$0.567690\pi$
$74$	1.03498	0.120314
$75$	−9.50929	−1.09804
$76$	9.18114	1.05315
$77$	−16.2118	−1.84751
$78$	0	0
$79$	−0.117477	−0.0132172	−0.00660858	−	0.999978i	$-0.502104\pi$
$79$	−0.117477	−0.0132172	−0.00660858	+	0.999978i	$0.502104\pi$
$80$	10.7062	1.19699
$81$	8.00943	0.889936
$82$	0.426118	0.0470568
$83$	13.0820	1.43593	0.717966	−	0.696078i	$-0.245073\pi$
$83$	13.0820	1.43593	0.717966	+	0.696078i	$0.245073\pi$
$84$	−17.4252	−1.90124
$85$	18.1194	1.96532
$86$	−1.60113	−0.172655
$87$	−30.9901	−3.32248
$88$	−4.47612	−0.477156
$89$	−6.78700	−0.719420	−0.359710	−	0.933064i	$-0.617124\pi$
$89$	−6.78700	−0.719420	−0.359710	+	0.933064i	$0.617124\pi$
$90$	3.51290	0.370292
$91$	0	0
$92$	−10.5387	−1.09873
$93$	−2.98137	−0.309153
$94$	−0.491805	−0.0507259
$95$	−13.4288	−1.37777
$96$	−7.24312	−0.739247
$97$	−2.93717	−0.298225	−0.149112	−	0.988820i	$-0.547642\pi$
$97$	−2.93717	−0.298225	−0.149112	+	0.988820i	$0.547642\pi$
$98$	0.401017	0.0405088
$99$	31.9572	3.21182
$100$	−6.24054	−0.624054
$101$	−18.5499	−1.84578	−0.922890	−	0.385065i	$-0.874179\pi$
$101$	−18.5499	−1.84578	−0.922890	+	0.385065i	$0.874179\pi$
$102$	−3.93509	−0.389632
$103$	2.46930	0.243308	0.121654	−	0.992573i	$-0.461180\pi$
$103$	2.46930	0.243308	0.121654	+	0.992573i	$0.461180\pi$
$104$	0	0
$105$	25.4870	2.48728
$106$	2.72076	0.264264
$107$	−9.43982	−0.912582	−0.456291	−	0.889831i	$-0.650822\pi$
$107$	−9.43982	−0.912582	−0.456291	+	0.889831i	$0.650822\pi$
$108$	16.8495	1.62134
$109$	2.95894	0.283415	0.141707	−	0.989909i	$-0.454741\pi$
$109$	2.95894	0.283415	0.141707	+	0.989909i	$0.454741\pi$
$110$	3.23755	0.308688
$111$	−14.8021	−1.40495
$112$	−11.1758	−1.05601
$113$	6.74872	0.634866	0.317433	−	0.948281i	$-0.397179\pi$
$113$	6.74872	0.634866	0.317433	+	0.948281i	$0.397179\pi$
$114$	2.91641	0.273147
$115$	15.4144	1.43740
$116$	−20.3374	−1.88828
$117$	0	0
$118$	−1.41500	−0.130261
$119$	−18.9141	−1.73385
$120$	7.03701	0.642388
$121$	18.4523	1.67748
$122$	0.695588	0.0629755
$123$	−6.09424	−0.549499
$124$	−1.95654	−0.175703
$125$	−5.18097	−0.463400
$126$	−3.66697	−0.326679
$127$	8.42428	0.747534	0.373767	−	0.927523i	$-0.378066\pi$
$127$	8.42428	0.747534	0.373767	+	0.927523i	$0.378066\pi$
$128$	−6.31312	−0.558006
$129$	22.8990	2.01615
$130$	0	0
$131$	10.7648	0.940523	0.470261	−	0.882527i	$-0.344160\pi$
$131$	10.7648	0.940523	0.470261	+	0.882527i	$0.344160\pi$
$132$	31.6567	2.75536
$133$	14.0178	1.21550
$134$	−2.34930	−0.202949
$135$	−24.6449	−2.12110
$136$	−5.22222	−0.447801
$137$	−8.64128	−0.738274	−0.369137	−	0.929375i	$-0.620347\pi$
$137$	−8.64128	−0.738274	−0.369137	+	0.929375i	$0.620347\pi$
$138$	−3.34763	−0.284969
$139$	−10.9827	−0.931543	−0.465771	−	0.884905i	$-0.654223\pi$
$139$	−10.9827	−0.931543	−0.465771	+	0.884905i	$0.654223\pi$
$140$	16.7260	1.41361
$141$	7.03369	0.592343
$142$	1.90356	0.159743
$143$	0	0
$144$	22.0300	1.83583
$145$	29.7466	2.47032
$146$	−0.751820	−0.0622211
$147$	−5.73524	−0.473035
$148$	−9.71395	−0.798482
$149$	11.1210	0.911065	0.455533	−	0.890219i	$-0.349449\pi$
$149$	11.1210	0.911065	0.455533	+	0.890219i	$0.349449\pi$
$150$	−1.98232	−0.161856
$151$	17.7639	1.44561	0.722805	−	0.691052i	$-0.242853\pi$
$151$	17.7639	1.44561	0.722805	+	0.691052i	$0.242853\pi$
$152$	3.87034	0.313926
$153$	37.2839	3.01423
$154$	−3.37954	−0.272331
$155$	2.86174	0.229861
$156$	0	0
$157$	−15.3366	−1.22400	−0.611999	−	0.790859i	$-0.709634\pi$
$157$	−15.3366	−1.22400	−0.611999	+	0.790859i	$0.709634\pi$
$158$	−0.0244894	−0.00194827
$159$	−38.9117	−3.08590
$160$	6.95249	0.549643
$161$	−16.0904	−1.26810
$162$	1.66966	0.131181
$163$	2.15308	0.168642	0.0843212	−	0.996439i	$-0.473128\pi$
$163$	2.15308	0.168642	0.0843212	+	0.996439i	$0.473128\pi$
$164$	−3.99938	−0.312299
$165$	−46.3027	−3.60466
$166$	2.72709	0.211663
$167$	0.569352	0.0440578	0.0220289	−	0.999757i	$-0.492987\pi$
$167$	0.569352	0.0440578	0.0220289	+	0.999757i	$0.492987\pi$
$168$	−7.34564	−0.566729
$169$	0	0
$170$	3.77720	0.289698
$171$	−27.6322	−2.11309
$172$	15.0276	1.14585
$173$	4.27346	0.324905	0.162452	−	0.986716i	$-0.448060\pi$
$173$	4.27346	0.324905	0.162452	+	0.986716i	$0.448060\pi$
$174$	−6.46024	−0.489749
$175$	−9.52807	−0.720255
$176$	20.3032	1.53041
$177$	20.2370	1.52111
$178$	−1.41483	−0.106046
$179$	15.5691	1.16369	0.581846	−	0.813299i	$-0.302331\pi$
$179$	15.5691	1.16369	0.581846	+	0.813299i	$0.302331\pi$
$180$	−32.9708	−2.45750
$181$	−2.41581	−0.179566	−0.0897828	−	0.995961i	$-0.528617\pi$
$181$	−2.41581	−0.179566	−0.0897828	+	0.995961i	$0.528617\pi$
$182$	0	0
$183$	−9.94813	−0.735387
$184$	−4.44260	−0.327513
$185$	14.2081	1.04460
$186$	−0.621501	−0.0455706
$187$	34.3615	2.51277
$188$	4.61591	0.336650
$189$	25.7258	1.87128
$190$	−2.79939	−0.203089
$191$	13.8802	1.00434	0.502169	−	0.864770i	$-0.332536\pi$
$191$	13.8802	1.00434	0.502169	+	0.864770i	$0.332536\pi$
$192$	20.7976	1.50094
$193$	−20.4333	−1.47082	−0.735409	−	0.677623i	$-0.763010\pi$
$193$	−20.4333	−1.47082	−0.735409	+	0.677623i	$0.763010\pi$
$194$	−0.612288	−0.0439597
$195$	0	0
$196$	−3.76379	−0.268842
$197$	−4.51496	−0.321678	−0.160839	−	0.986981i	$-0.551420\pi$
$197$	−4.51496	−0.321678	−0.160839	+	0.986981i	$0.551420\pi$
$198$	6.66185	0.473437
$199$	−10.1971	−0.722851	−0.361425	−	0.932401i	$-0.617710\pi$
$199$	−10.1971	−0.722851	−0.361425	+	0.932401i	$0.617710\pi$
$200$	−2.63072	−0.186020
$201$	33.5991	2.36990
$202$	−3.86693	−0.272076
$203$	−31.0513	−2.17937
$204$	36.9333	2.58585
$205$	5.84971	0.408561
$206$	0.514755	0.0358647
$207$	31.7179	2.20455
$208$	0	0
$209$	−25.4664	−1.76155
$210$	5.31306	0.366636
$211$	8.77905	0.604375	0.302188	−	0.953249i	$-0.402283\pi$
$211$	8.77905	0.604375	0.302188	+	0.953249i	$0.402283\pi$
$212$	−25.5361	−1.75383
$213$	−27.2243	−1.86538
$214$	−1.96784	−0.134519
$215$	−21.9802	−1.49904
$216$	7.10294	0.483294
$217$	−2.98726	−0.202788
$218$	0.616825	0.0417766
$219$	10.7524	0.726577
$220$	−30.3865	−2.04865
$221$	0	0
$222$	−3.08566	−0.207096
$223$	−7.06201	−0.472907	−0.236454	−	0.971643i	$-0.575985\pi$
$223$	−7.06201	−0.472907	−0.236454	+	0.971643i	$0.575985\pi$
$224$	−7.25742	−0.484907
$225$	18.7820	1.25213
$226$	1.40685	0.0935822
$227$	−12.2899	−0.815710	−0.407855	−	0.913047i	$-0.633723\pi$
$227$	−12.2899	−0.815710	−0.407855	+	0.913047i	$0.633723\pi$
$228$	−27.3724	−1.81278
$229$	11.0402	0.729559	0.364780	−	0.931094i	$-0.381144\pi$
$229$	11.0402	0.729559	0.364780	+	0.931094i	$0.381144\pi$
$230$	3.21331	0.211879
$231$	48.3335	3.18011
$232$	−8.57331	−0.562866
$233$	5.67541	0.371809	0.185904	−	0.982568i	$-0.440479\pi$
$233$	5.67541	0.371809	0.185904	+	0.982568i	$0.440479\pi$
$234$	0	0
$235$	−6.75146	−0.440417
$236$	13.2807	0.864499
$237$	0.350241	0.0227506
$238$	−3.94286	−0.255578
$239$	8.19099	0.529831	0.264916	−	0.964272i	$-0.414656\pi$
$239$	8.19099	0.529831	0.264916	+	0.964272i	$0.414656\pi$
$240$	−31.9192	−2.06037
$241$	−1.13997	−0.0734320	−0.0367160	−	0.999326i	$-0.511690\pi$
$241$	−1.13997	−0.0734320	−0.0367160	+	0.999326i	$0.511690\pi$
$242$	3.84660	0.247269
$243$	1.95650	0.125510
$244$	−6.52853	−0.417946
$245$	5.50512	0.351709
$246$	−1.27041	−0.0809986
$247$	0	0
$248$	−0.824787	−0.0523740
$249$	−39.0022	−2.47166
$250$	−1.08003	−0.0683073
$251$	12.1790	0.768732	0.384366	−	0.923181i	$-0.374420\pi$
$251$	12.1790	0.768732	0.384366	+	0.923181i	$0.374420\pi$
$252$	34.4168	2.16806
$253$	29.2318	1.83779
$254$	1.75614	0.110190
$255$	−54.0206	−3.38290
$256$	12.6357	0.789729
$257$	−0.399753	−0.0249359	−0.0124680	−	0.999922i	$-0.503969\pi$
$257$	−0.399753	−0.0249359	−0.0124680	+	0.999922i	$0.503969\pi$
$258$	4.77357	0.297189
$259$	−14.8313	−0.921571
$260$	0	0
$261$	61.2090	3.78874
$262$	2.24404	0.138637
$263$	1.01804	0.0627752	0.0313876	−	0.999507i	$-0.490007\pi$
$263$	1.01804	0.0627752	0.0313876	+	0.999507i	$0.490007\pi$
$264$	13.3450	0.821326
$265$	37.3504	2.29442
$266$	2.92217	0.179170
$267$	20.2345	1.23833
$268$	22.0497	1.34690
$269$	26.6036	1.62205	0.811024	−	0.585013i	$-0.198911\pi$
$269$	26.6036	1.62205	0.811024	+	0.585013i	$0.198911\pi$
$270$	−5.13751	−0.312659
$271$	8.26623	0.502138	0.251069	−	0.967969i	$-0.419218\pi$
$271$	8.26623	0.502138	0.251069	+	0.967969i	$0.419218\pi$
$272$	23.6874	1.43626
$273$	0	0
$274$	−1.80137	−0.108825
$275$	17.3098	1.04382
$276$	31.4196	1.89124
$277$	−6.83911	−0.410922	−0.205461	−	0.978665i	$-0.565869\pi$
$277$	−6.83911	−0.410922	−0.205461	+	0.978665i	$0.565869\pi$
$278$	−2.28948	−0.137314
$279$	5.88856	0.352539
$280$	7.05091	0.421372
$281$	7.03057	0.419409	0.209704	−	0.977765i	$-0.432750\pi$
$281$	7.03057	0.419409	0.209704	+	0.977765i	$0.432750\pi$
$282$	1.46625	0.0873141
$283$	−2.54204	−0.151109	−0.0755544	−	0.997142i	$-0.524073\pi$
$283$	−2.54204	−0.151109	−0.0755544	+	0.997142i	$0.524073\pi$
$284$	−17.8661	−1.06016
$285$	40.0362	2.37154
$286$	0	0
$287$	−6.10627	−0.360442
$288$	14.3060	0.842990
$289$	23.0890	1.35818
$290$	6.20102	0.364137
$291$	8.75680	0.513333
$292$	7.05631	0.412939
$293$	2.09392	0.122328	0.0611640	−	0.998128i	$-0.480519\pi$
$293$	2.09392	0.122328	0.0611640	+	0.998128i	$0.480519\pi$
$294$	−1.19558	−0.0697275
$295$	−19.4250	−1.13097
$296$	−4.09495	−0.238014
$297$	−46.7365	−2.71193
$298$	2.31829	0.134295
$299$	0	0
$300$	18.6054	1.07418
$301$	22.9442	1.32248
$302$	3.70310	0.213089
$303$	55.3039	3.17713
$304$	−17.5555	−1.00687
$305$	9.54897	0.546772
$306$	7.77227	0.444311
$307$	5.54670	0.316567	0.158284	−	0.987394i	$-0.449404\pi$
$307$	5.54670	0.316567	0.158284	+	0.987394i	$0.449404\pi$
$308$	31.7192	1.80737
$309$	−7.36190	−0.418804
$310$	0.596563	0.0338825
$311$	10.2545	0.581479	0.290739	−	0.956802i	$-0.406099\pi$
$311$	10.2545	0.581479	0.290739	+	0.956802i	$0.406099\pi$
$312$	0	0
$313$	15.0552	0.850972	0.425486	−	0.904965i	$-0.360103\pi$
$313$	15.0552	0.850972	0.425486	+	0.904965i	$0.360103\pi$
$314$	−3.19710	−0.180423
$315$	−50.3398	−2.83633
$316$	0.229848	0.0129300
$317$	−10.5767	−0.594047	−0.297024	−	0.954870i	$-0.595994\pi$
$317$	−10.5767	−0.594047	−0.297024	+	0.954870i	$0.595994\pi$
$318$	−8.11159	−0.454876
$319$	56.4114	3.15843
$320$	−19.9631	−1.11597
$321$	28.1436	1.57082
$322$	−3.35424	−0.186924
$323$	−29.7112	−1.65317
$324$	−15.6708	−0.870600
$325$	0	0
$326$	0.448835	0.0248587
$327$	−8.82168	−0.487840
$328$	−1.68595	−0.0930912
$329$	7.04758	0.388545
$330$	−9.65233	−0.531343
$331$	27.7270	1.52401	0.762006	−	0.647570i	$-0.224215\pi$
$331$	27.7270	1.52401	0.762006	+	0.647570i	$0.224215\pi$
$332$	−25.5955	−1.40473
$333$	29.2358	1.60211
$334$	0.118688	0.00649432
$335$	−32.2510	−1.76206
$336$	33.3191	1.81771
$337$	−13.0808	−0.712557	−0.356279	−	0.934380i	$-0.615955\pi$
$337$	−13.0808	−0.712557	−0.356279	+	0.934380i	$0.615955\pi$
$338$	0	0
$339$	−20.1204	−1.09279
$340$	−35.4514	−1.92262
$341$	5.42700	0.293889
$342$	−5.76026	−0.311479
$343$	15.1642	0.818791
$344$	6.33495	0.341558
$345$	−45.9559	−2.47418
$346$	0.890851	0.0478925
$347$	4.18028	0.224409	0.112205	−	0.993685i	$-0.464209\pi$
$347$	4.18028	0.224409	0.112205	+	0.993685i	$0.464209\pi$
$348$	60.6334	3.25029
$349$	−0.461986	−0.0247295	−0.0123648	−	0.999924i	$-0.503936\pi$
$349$	−0.461986	−0.0247295	−0.0123648	+	0.999924i	$0.503936\pi$
$350$	−1.98624	−0.106169
$351$	0	0
$352$	13.1847	0.702746
$353$	5.26668	0.280317	0.140158	−	0.990129i	$-0.455239\pi$
$353$	5.26668	0.280317	0.140158	+	0.990129i	$0.455239\pi$
$354$	4.21864	0.224218
$355$	26.1319	1.38694
$356$	13.2791	0.703788
$357$	56.3898	2.98447
$358$	3.24557	0.171534
$359$	−20.9128	−1.10373	−0.551867	−	0.833932i	$-0.686084\pi$
$359$	−20.9128	−1.10373	−0.551867	+	0.833932i	$0.686084\pi$
$360$	−13.8989	−0.732538
$361$	3.01984	0.158939
$362$	−0.503603	−0.0264688
$363$	−55.0132	−2.88744
$364$	0	0
$365$	−10.3209	−0.540222
$366$	−2.07380	−0.108399
$367$	29.0411	1.51593	0.757967	−	0.652293i	$-0.226193\pi$
$367$	29.0411	1.51593	0.757967	+	0.652293i	$0.226193\pi$
$368$	20.1512	1.05045
$369$	12.0368	0.626613
$370$	2.96185	0.153979
$371$	−38.9885	−2.02418
$372$	5.83318	0.302436
$373$	10.6397	0.550903	0.275452	−	0.961315i	$-0.411173\pi$
$373$	10.6397	0.550903	0.275452	+	0.961315i	$0.411173\pi$
$374$	7.16306	0.370393
$375$	15.4464	0.797648
$376$	1.94585	0.100350
$377$	0	0
$378$	5.36284	0.275835
$379$	20.1251	1.03376	0.516880	−	0.856058i	$-0.327093\pi$
$379$	20.1251	1.03376	0.516880	+	0.856058i	$0.327093\pi$
$380$	26.2741	1.34783
$381$	−25.1159	−1.28673
$382$	2.89349	0.148044
$383$	−24.4338	−1.24851	−0.624254	−	0.781222i	$-0.714597\pi$
$383$	−24.4338	−1.24851	−0.624254	+	0.781222i	$0.714597\pi$
$384$	18.8217	0.960492
$385$	−46.3941	−2.36446
$386$	−4.25955	−0.216805
$387$	−45.2283	−2.29908
$388$	5.74671	0.291745
$389$	3.45644	0.175249	0.0876243	−	0.996154i	$-0.472072\pi$
$389$	3.45644	0.175249	0.0876243	+	0.996154i	$0.472072\pi$
$390$	0	0
$391$	34.1042	1.72473
$392$	−1.58664	−0.0801374
$393$	−32.0938	−1.61892
$394$	−0.941196	−0.0474168
$395$	−0.336188	−0.0169155
$396$	−62.5257	−3.14203
$397$	−18.7486	−0.940967	−0.470483	−	0.882409i	$-0.655920\pi$
$397$	−18.7486	−0.940967	−0.470483	+	0.882409i	$0.655920\pi$
$398$	−2.12570	−0.106552
$399$	−41.7922	−2.09223
$400$	11.9327	0.596634
$401$	−15.7870	−0.788366	−0.394183	−	0.919032i	$-0.628972\pi$
$401$	−15.7870	−0.788366	−0.394183	+	0.919032i	$0.628972\pi$
$402$	7.00413	0.349334
$403$	0	0
$404$	36.2936	1.80567
$405$	22.9209	1.13895
$406$	−6.47299	−0.321249
$407$	26.9443	1.33558
$408$	15.5693	0.770798
$409$	−33.8093	−1.67176	−0.835880	−	0.548912i	$-0.815042\pi$
$409$	−33.8093	−1.67176	−0.835880	+	0.548912i	$0.815042\pi$
$410$	1.21944	0.0602238
$411$	25.7628	1.27079
$412$	−4.83130	−0.238021
$413$	20.2770	0.997766
$414$	6.61196	0.324960
$415$	37.4372	1.83772
$416$	0	0
$417$	32.7436	1.60346
$418$	−5.30876	−0.259660
$419$	−26.8346	−1.31096	−0.655478	−	0.755214i	$-0.727533\pi$
$419$	−26.8346	−1.31096	−0.655478	+	0.755214i	$0.727533\pi$
$420$	−49.8664	−2.43323
$421$	0.916981	0.0446909	0.0223455	−	0.999750i	$-0.492887\pi$
$421$	0.916981	0.0446909	0.0223455	+	0.999750i	$0.492887\pi$
$422$	1.83010	0.0890876
$423$	−13.8924	−0.675470
$424$	−10.7648	−0.522786
$425$	20.1951	0.979605
$426$	−5.67522	−0.274965
$427$	−9.96778	−0.482374
$428$	18.4694	0.892753
$429$	0	0
$430$	−4.58203	−0.220965
$431$	30.4128	1.46493	0.732465	−	0.680804i	$-0.238370\pi$
$431$	30.4128	1.46493	0.732465	+	0.680804i	$0.238370\pi$
$432$	−32.2182	−1.55010
$433$	−4.77721	−0.229578	−0.114789	−	0.993390i	$-0.536619\pi$
$433$	−4.77721	−0.229578	−0.114789	+	0.993390i	$0.536619\pi$
$434$	−0.622728	−0.0298919
$435$	−88.6856	−4.25215
$436$	−5.78929	−0.277257
$437$	−25.2757	−1.20910
$438$	2.24145	0.107101
$439$	0.337221	0.0160947	0.00804734	−	0.999968i	$-0.497438\pi$
$439$	0.337221	0.0160947	0.00804734	+	0.999968i	$0.497438\pi$
$440$	−12.8095	−0.610669
$441$	11.3278	0.539419
$442$	0	0
$443$	−32.4167	−1.54016	−0.770082	−	0.637944i	$-0.779785\pi$
$443$	−32.4167	−1.54016	−0.770082	+	0.637944i	$0.779785\pi$
$444$	28.9609	1.37442
$445$	−19.4226	−0.920721
$446$	−1.47216	−0.0697087
$447$	−33.1557	−1.56821
$448$	20.8387	0.984534
$449$	−34.8480	−1.64458	−0.822289	−	0.569070i	$-0.807303\pi$
$449$	−34.8480	−1.64458	−0.822289	+	0.569070i	$0.807303\pi$
$450$	3.91532	0.184570
$451$	11.0934	0.522366
$452$	−13.2042	−0.621072
$453$	−52.9609	−2.48832
$454$	−2.56197	−0.120239
$455$	0	0
$456$	−11.5389	−0.540359
$457$	32.9828	1.54287	0.771436	−	0.636307i	$-0.219539\pi$
$457$	32.9828	1.54287	0.771436	+	0.636307i	$0.219539\pi$
$458$	2.30146	0.107540
$459$	−54.5267	−2.54509
$460$	−30.1589	−1.40617
$461$	29.9916	1.39685	0.698423	−	0.715685i	$-0.253885\pi$
$461$	29.9916	1.39685	0.698423	+	0.715685i	$0.253885\pi$
$462$	10.0757	0.468762
$463$	27.7355	1.28898	0.644489	−	0.764614i	$-0.277070\pi$
$463$	27.7355	1.28898	0.644489	+	0.764614i	$0.277070\pi$
$464$	38.8877	1.80532
$465$	−8.53191	−0.395658
$466$	1.18311	0.0548063
$467$	−1.58687	−0.0734315	−0.0367157	−	0.999326i	$-0.511690\pi$
$467$	−1.58687	−0.0734315	−0.0367157	+	0.999326i	$0.511690\pi$
$468$	0	0
$469$	33.6655	1.55453
$470$	−1.40742	−0.0649195
$471$	45.7242	2.10686
$472$	5.59852	0.257693
$473$	−41.6832	−1.91660
$474$	0.0730119	0.00335355
$475$	−14.9672	−0.686741
$476$	37.0062	1.69618
$477$	76.8552	3.51896
$478$	1.70751	0.0780995
$479$	0.345330	0.0157785	0.00788926	−	0.999969i	$-0.497489\pi$
$479$	0.345330	0.0157785	0.00788926	+	0.999969i	$0.497489\pi$
$480$	−20.7279	−0.946097
$481$	0	0
$482$	−0.237640	−0.0108242
$483$	47.9715	2.18278
$484$	−36.1028	−1.64104
$485$	−8.40544	−0.381671
$486$	0.407855	0.0185007
$487$	−24.7122	−1.11982	−0.559909	−	0.828554i	$-0.689164\pi$
$487$	−24.7122	−1.11982	−0.559909	+	0.828554i	$0.689164\pi$
$488$	−2.75212	−0.124583
$489$	−6.41913	−0.290283
$490$	1.14761	0.0518436
$491$	−22.7899	−1.02849	−0.514247	−	0.857642i	$-0.671929\pi$
$491$	−22.7899	−1.02849	−0.514247	+	0.857642i	$0.671929\pi$
$492$	11.9236	0.537559
$493$	65.8142	2.96412
$494$	0	0
$495$	91.4533	4.11052
$496$	3.74115	0.167983
$497$	−27.2780	−1.22359
$498$	−8.13045	−0.364334
$499$	5.46697	0.244735	0.122368	−	0.992485i	$-0.460951\pi$
$499$	5.46697	0.244735	0.122368	+	0.992485i	$0.460951\pi$
$500$	10.1368	0.453332
$501$	−1.69745	−0.0758364
$502$	2.53885	0.113315
$503$	10.7081	0.477452	0.238726	−	0.971087i	$-0.423270\pi$
$503$	10.7081	0.477452	0.238726	+	0.971087i	$0.423270\pi$
$504$	14.5085	0.646261
$505$	−53.0849	−2.36225
$506$	6.09370	0.270898
$507$	0	0
$508$	−16.4825	−0.731292
$509$	11.8705	0.526151	0.263075	−	0.964775i	$-0.415263\pi$
$509$	11.8705	0.526151	0.263075	+	0.964775i	$0.415263\pi$
$510$	−11.2612	−0.498655
$511$	10.7736	0.476595
$512$	15.2603	0.674416
$513$	40.4114	1.78421
$514$	−0.0833332	−0.00367567
$515$	7.06651	0.311388
$516$	−44.8030	−1.97234
$517$	−12.8035	−0.563095
$518$	−3.09175	−0.135844
$519$	−12.7407	−0.559257
$520$	0	0
$521$	−26.5822	−1.16459	−0.582294	−	0.812978i	$-0.697845\pi$
$521$	−26.5822	−1.16459	−0.582294	+	0.812978i	$0.697845\pi$
$522$	12.7597	0.558478
$523$	−3.41300	−0.149240	−0.0746200	−	0.997212i	$-0.523774\pi$
$523$	−3.41300	−0.149240	−0.0746200	+	0.997212i	$0.523774\pi$
$524$	−21.0618	−0.920087
$525$	28.4067	1.23977
$526$	0.212223	0.00925336
$527$	6.33159	0.275808
$528$	−60.5314	−2.63429
$529$	6.01288	0.261430
$530$	7.78612	0.338208
$531$	−39.9705	−1.73457
$532$	−27.4264	−1.18909
$533$	0	0
$534$	4.21812	0.182536
$535$	−27.0143	−1.16793
$536$	9.29511	0.401488
$537$	−46.4173	−2.00306
$538$	5.54582	0.239097
$539$	10.4399	0.449678
$540$	48.2188	2.07501
$541$	18.7415	0.805760	0.402880	−	0.915253i	$-0.368009\pi$
$541$	18.7415	0.805760	0.402880	+	0.915253i	$0.368009\pi$
$542$	1.72319	0.0740174
$543$	7.20241	0.309085
$544$	15.3824	0.659513
$545$	8.46772	0.362717
$546$	0	0
$547$	−6.23925	−0.266771	−0.133385	−	0.991064i	$-0.542585\pi$
$547$	−6.23925	−0.266771	−0.133385	+	0.991064i	$0.542585\pi$
$548$	16.9070	0.722233
$549$	19.6487	0.838588
$550$	3.60843	0.153864
$551$	−48.7769	−2.07796
$552$	13.2450	0.563746
$553$	0.350933	0.0149232
$554$	−1.42569	−0.0605718
$555$	−42.3597	−1.79807
$556$	21.4882	0.911302
$557$	14.8576	0.629537	0.314768	−	0.949169i	$-0.398073\pi$
$557$	14.8576	0.629537	0.314768	+	0.949169i	$0.398073\pi$
$558$	1.22754	0.0519658
$559$	0	0
$560$	−31.9822	−1.35149
$561$	−102.444	−4.32521
$562$	1.46560	0.0618227
$563$	−28.4012	−1.19697	−0.598484	−	0.801135i	$-0.704230\pi$
$563$	−28.4012	−1.19697	−0.598484	+	0.801135i	$0.704230\pi$
$564$	−13.7617	−0.579473
$565$	19.3131	0.812508
$566$	−0.529918	−0.0222741
$567$	−23.9262	−1.00481
$568$	−7.53152	−0.316016
$569$	1.59766	0.0669774	0.0334887	−	0.999439i	$-0.489338\pi$
$569$	1.59766	0.0669774	0.0334887	+	0.999439i	$0.489338\pi$
$570$	8.34602	0.349576
$571$	31.2448	1.30756	0.653778	−	0.756687i	$-0.273183\pi$
$571$	31.2448	1.30756	0.653778	+	0.756687i	$0.273183\pi$
$572$	0	0
$573$	−41.3821	−1.72876
$574$	−1.27292	−0.0531308
$575$	17.1802	0.716464
$576$	−41.0777	−1.71157
$577$	19.8952	0.828248	0.414124	−	0.910221i	$-0.364088\pi$
$577$	19.8952	0.828248	0.414124	+	0.910221i	$0.364088\pi$
$578$	4.81318	0.200202
$579$	60.9191	2.53171
$580$	−58.2005	−2.41665
$581$	−39.0792	−1.62128
$582$	1.82546	0.0756676
$583$	70.8312	2.93353
$584$	2.97461	0.123090
$585$	0	0
$586$	0.436502	0.0180317
$587$	−31.9215	−1.31754	−0.658771	−	0.752343i	$-0.728923\pi$
$587$	−31.9215	−1.31754	−0.658771	+	0.752343i	$0.728923\pi$
$588$	11.2213	0.462757
$589$	−4.69253	−0.193352
$590$	−4.04937	−0.166710
$591$	13.4608	0.553702
$592$	18.5743	0.763398
$593$	8.16822	0.335429	0.167714	−	0.985836i	$-0.446361\pi$
$593$	8.16822	0.335429	0.167714	+	0.985836i	$0.446361\pi$
$594$	−9.74276	−0.399750
$595$	−54.1272	−2.21900
$596$	−21.7587	−0.891270
$597$	30.4012	1.24424
$598$	0	0
$599$	39.9330	1.63162	0.815809	−	0.578321i	$-0.196292\pi$
$599$	39.9330	1.63162	0.815809	+	0.578321i	$0.196292\pi$
$600$	7.84314	0.320195
$601$	−18.7306	−0.764036	−0.382018	−	0.924155i	$-0.624771\pi$
$601$	−18.7306	−0.764036	−0.382018	+	0.924155i	$0.624771\pi$
$602$	4.78299	0.194940
$603$	−66.3623	−2.70248
$604$	−34.7559	−1.41420
$605$	52.8058	2.14686
$606$	11.5287	0.468323
$607$	−30.7481	−1.24803	−0.624014	−	0.781413i	$-0.714499\pi$
$607$	−30.7481	−1.24803	−0.624014	+	0.781413i	$0.714499\pi$
$608$	−11.4003	−0.462344
$609$	92.5752	3.75134
$610$	1.99059	0.0805968
$611$	0	0
$612$	−72.9476	−2.94873
$613$	−41.5455	−1.67801	−0.839004	−	0.544125i	$-0.816862\pi$
$613$	−41.5455	−1.67801	−0.839004	+	0.544125i	$0.816862\pi$
$614$	1.15627	0.0466634
$615$	−17.4401	−0.703254
$616$	13.3713	0.538746
$617$	14.8705	0.598663	0.299332	−	0.954149i	$-0.403236\pi$
$617$	14.8705	0.598663	0.299332	+	0.954149i	$0.403236\pi$
$618$	−1.53467	−0.0617336
$619$	10.9639	0.440677	0.220339	−	0.975423i	$-0.429284\pi$
$619$	10.9639	0.440677	0.220339	+	0.975423i	$0.429284\pi$
$620$	−5.59913	−0.224866
$621$	−46.3865	−1.86143
$622$	2.13767	0.0857126
$623$	20.2745	0.812280
$624$	0	0
$625$	−30.7745	−1.23098
$626$	3.13844	0.125437
$627$	75.9246	3.03214
$628$	30.0068	1.19740
$629$	31.4354	1.25341
$630$	−10.4939	−0.418088
$631$	−28.3211	−1.12745	−0.563723	−	0.825964i	$-0.690631\pi$
$631$	−28.3211	−1.12745	−0.563723	+	0.825964i	$0.690631\pi$
$632$	0.0968933	0.00385421
$633$	−26.1736	−1.04031
$634$	−2.20484	−0.0875653
$635$	24.1081	0.956702
$636$	76.1325	3.01885
$637$	0	0
$638$	11.7596	0.465567
$639$	53.7712	2.12716
$640$	−18.0665	−0.714142
$641$	35.4775	1.40128	0.700639	−	0.713516i	$-0.252898\pi$
$641$	35.4775	1.40128	0.700639	+	0.713516i	$0.252898\pi$
$642$	5.86685	0.231546
$643$	33.9769	1.33992	0.669960	−	0.742397i	$-0.266311\pi$
$643$	33.9769	1.33992	0.669960	+	0.742397i	$0.266311\pi$
$644$	31.4816	1.24055
$645$	65.5311	2.58029
$646$	−6.19364	−0.243685
$647$	−24.0221	−0.944407	−0.472203	−	0.881490i	$-0.656541\pi$
$647$	−24.0221	−0.944407	−0.472203	+	0.881490i	$0.656541\pi$
$648$	−6.60607	−0.259511
$649$	−36.8376	−1.44600
$650$	0	0
$651$	8.90611	0.349058
$652$	−4.21260	−0.164978
$653$	−13.1685	−0.515322	−0.257661	−	0.966235i	$-0.582952\pi$
$653$	−13.1685	−0.515322	−0.257661	+	0.966235i	$0.582952\pi$
$654$	−1.83898	−0.0719099
$655$	30.8060	1.20369
$656$	7.64731	0.298577
$657$	−21.2372	−0.828541
$658$	1.46915	0.0572734
$659$	14.0783	0.548411	0.274205	−	0.961671i	$-0.411585\pi$
$659$	14.0783	0.548411	0.274205	+	0.961671i	$0.411585\pi$
$660$	90.5932	3.52634
$661$	−9.69620	−0.377139	−0.188569	−	0.982060i	$-0.560385\pi$
$661$	−9.69620	−0.377139	−0.188569	+	0.982060i	$0.560385\pi$
$662$	5.78001	0.224646
$663$	0	0
$664$	−10.7898	−0.418727
$665$	40.1153	1.55560
$666$	6.09454	0.236159
$667$	55.9889	2.16790
$668$	−1.11396	−0.0431005
$669$	21.0545	0.814013
$670$	−6.72309	−0.259736
$671$	18.1086	0.699076
$672$	21.6370	0.834667
$673$	−23.5939	−0.909477	−0.454739	−	0.890625i	$-0.650267\pi$
$673$	−23.5939	−0.909477	−0.454739	+	0.890625i	$0.650267\pi$
$674$	−2.72685	−0.105034
$675$	−27.4681	−1.05725
$676$	0	0
$677$	19.0460	0.731999	0.366000	−	0.930615i	$-0.380727\pi$
$677$	19.0460	0.731999	0.366000	+	0.930615i	$0.380727\pi$
$678$	−4.19433	−0.161082
$679$	8.77409	0.336719
$680$	−14.9446	−0.573101
$681$	36.6407	1.40408
$682$	1.13132	0.0433205
$683$	−19.2915	−0.738170	−0.369085	−	0.929396i	$-0.620329\pi$
$683$	−19.2915	−0.738170	−0.369085	+	0.929396i	$0.620329\pi$
$684$	54.0637	2.06718
$685$	−24.7291	−0.944851
$686$	3.16116	0.120694
$687$	−32.9150	−1.25579
$688$	−28.7347	−1.09550
$689$	0	0
$690$	−9.58005	−0.364706
$691$	−11.9789	−0.455700	−0.227850	−	0.973696i	$-0.573170\pi$
$691$	−11.9789	−0.455700	−0.227850	+	0.973696i	$0.573170\pi$
$692$	−8.36120	−0.317845
$693$	−95.4643	−3.62639
$694$	0.871429	0.0330790
$695$	−31.4298	−1.19220
$696$	25.5602	0.968857
$697$	12.9424	0.490230
$698$	−0.0963063	−0.00364525
$699$	−16.9205	−0.639992
$700$	18.6421	0.704605
$701$	44.5233	1.68162	0.840811	−	0.541329i	$-0.182078\pi$
$701$	44.5233	1.68162	0.840811	+	0.541329i	$0.182078\pi$
$702$	0	0
$703$	−23.2977	−0.878690
$704$	−37.8580	−1.42683
$705$	20.1286	0.758087
$706$	1.09790	0.0413200
$707$	55.4131	2.08403
$708$	−39.5946	−1.48806
$709$	−34.9481	−1.31250	−0.656252	−	0.754542i	$-0.727859\pi$
$709$	−34.9481	−1.31250	−0.656252	+	0.754542i	$0.727859\pi$
$710$	5.44750	0.204441
$711$	−0.691768	−0.0259433
$712$	5.59783	0.209787
$713$	5.38636	0.201721
$714$	11.7551	0.439924
$715$	0	0
$716$	−30.4617	−1.13841
$717$	−24.4204	−0.911995
$718$	−4.35951	−0.162695
$719$	47.7629	1.78126	0.890628	−	0.454733i	$-0.150265\pi$
$719$	47.7629	1.78126	0.890628	+	0.454733i	$0.150265\pi$
$720$	63.0441	2.34952
$721$	−7.37644	−0.274713
$722$	0.629520	0.0234283
$723$	3.39867	0.126398
$724$	4.72663	0.175664
$725$	33.1543	1.23132
$726$	−11.4681	−0.425622
$727$	−33.6415	−1.24770	−0.623848	−	0.781546i	$-0.714431\pi$
$727$	−33.6415	−1.24770	−0.623848	+	0.781546i	$0.714431\pi$
$728$	0	0
$729$	−29.8613	−1.10598
$730$	−2.15152	−0.0796312
$731$	−48.6311	−1.79869
$732$	19.4640	0.719408
$733$	30.0960	1.11162	0.555811	−	0.831308i	$-0.312408\pi$
$733$	30.0960	1.11162	0.555811	+	0.831308i	$0.312408\pi$
$734$	6.05395	0.223456
$735$	−16.4128	−0.605395
$736$	13.0860	0.482355
$737$	−61.1607	−2.25288
$738$	2.50922	0.0923656
$739$	49.0550	1.80452	0.902258	−	0.431196i	$-0.141908\pi$
$739$	49.0550	1.80452	0.902258	+	0.431196i	$0.141908\pi$
$740$	−27.7988	−1.02191
$741$	0	0
$742$	−8.12761	−0.298374
$743$	35.7509	1.31157	0.655787	−	0.754946i	$-0.272337\pi$
$743$	35.7509	1.31157	0.655787	+	0.754946i	$0.272337\pi$
$744$	2.45899	0.0901511
$745$	31.8254	1.16599
$746$	2.21797	0.0812057
$747$	77.0339	2.81852
$748$	−67.2299	−2.45817
$749$	28.1991	1.03037
$750$	3.21998	0.117577
$751$	−46.8848	−1.71085	−0.855425	−	0.517926i	$-0.826704\pi$
$751$	−46.8848	−1.71085	−0.855425	+	0.517926i	$0.826704\pi$
$752$	−8.82618	−0.321858
$753$	−36.3101	−1.32321
$754$	0	0
$755$	50.8359	1.85011
$756$	−50.3336	−1.83062
$757$	49.8138	1.81051	0.905257	−	0.424865i	$-0.139679\pi$
$757$	49.8138	1.81051	0.905257	+	0.424865i	$0.139679\pi$
$758$	4.19532	0.152381
$759$	−87.1507	−3.16337
$760$	11.0759	0.401766
$761$	18.7507	0.679714	0.339857	−	0.940477i	$-0.389621\pi$
$761$	18.7507	0.679714	0.339857	+	0.940477i	$0.389621\pi$
$762$	−5.23570	−0.189669
$763$	−8.83910	−0.319997
$764$	−27.1573	−0.982516
$765$	106.697	3.85764
$766$	−5.09350	−0.184036
$767$	0	0
$768$	−37.6716	−1.35936
$769$	51.4493	1.85531	0.927654	−	0.373441i	$-0.121822\pi$
$769$	51.4493	1.85531	0.927654	+	0.373441i	$0.121822\pi$
$770$	−9.67139	−0.348533
$771$	1.19181	0.0429221
$772$	39.9786	1.43886
$773$	−21.4552	−0.771690	−0.385845	−	0.922564i	$-0.626090\pi$
$773$	−21.4552	−0.771690	−0.385845	+	0.922564i	$0.626090\pi$
$774$	−9.42836	−0.338895
$775$	3.18957	0.114573
$776$	2.42254	0.0869643
$777$	44.2175	1.58629
$778$	0.720536	0.0258325
$779$	−9.59203	−0.343670
$780$	0	0
$781$	49.5565	1.77327
$782$	7.10942	0.254232
$783$	−89.5165	−3.19906
$784$	7.19684	0.257030
$785$	−43.8896	−1.56649
$786$	−6.69031	−0.238636
$787$	−44.4746	−1.58535	−0.792673	−	0.609647i	$-0.791311\pi$
$787$	−44.4746	−1.58535	−0.792673	+	0.609647i	$0.791311\pi$
$788$	8.83373	0.314688
$789$	−3.03516	−0.108055
$790$	−0.0700823	−0.00249342
$791$	−20.1602	−0.716813
$792$	−26.3579	−0.936587
$793$	0	0
$794$	−3.90837	−0.138703
$795$	−111.355	−3.94937
$796$	19.9510	0.707145
$797$	−50.6384	−1.79370	−0.896852	−	0.442331i	$-0.854152\pi$
$797$	−50.6384	−1.79370	−0.896852	+	0.442331i	$0.854152\pi$
$798$	−8.71206	−0.308404
$799$	−14.9376	−0.528454
$800$	7.74894	0.273967
$801$	−39.9656	−1.41212
$802$	−3.29098	−0.116209
$803$	−19.5726	−0.690701
$804$	−65.7382	−2.31841
$805$	−46.0467	−1.62293
$806$	0	0
$807$	−79.3150	−2.79202
$808$	15.2997	0.538241
$809$	−24.6655	−0.867194	−0.433597	−	0.901107i	$-0.642756\pi$
$809$	−24.6655	−0.867194	−0.433597	+	0.901107i	$0.642756\pi$
$810$	4.77813	0.167886
$811$	−11.4176	−0.400927	−0.200463	−	0.979701i	$-0.564245\pi$
$811$	−11.4176	−0.400927	−0.200463	+	0.979701i	$0.564245\pi$
$812$	60.7531	2.13202
$813$	−24.6447	−0.864327
$814$	5.61684	0.196870
$815$	6.16157	0.215830
$816$	−70.6210	−2.47223
$817$	36.0420	1.26095
$818$	−7.04793	−0.246425
$819$	0	0
$820$	−11.4452	−0.399684
$821$	−34.9126	−1.21846	−0.609228	−	0.792995i	$-0.708521\pi$
$821$	−34.9126	−1.21846	−0.609228	+	0.792995i	$0.708521\pi$
$822$	5.37056	0.187320
$823$	−16.8934	−0.588867	−0.294433	−	0.955672i	$-0.595131\pi$
$823$	−16.8934	−0.588867	−0.294433	+	0.955672i	$0.595131\pi$
$824$	−2.03665	−0.0709501
$825$	−51.6069	−1.79672
$826$	4.22697	0.147075
$827$	−51.4830	−1.79024	−0.895120	−	0.445825i	$-0.852910\pi$
$827$	−51.4830	−1.79024	−0.895120	+	0.445825i	$0.852910\pi$
$828$	−62.0574	−2.15665
$829$	55.8445	1.93956	0.969781	−	0.243979i	$-0.0784527\pi$
$829$	55.8445	1.93956	0.969781	+	0.243979i	$0.0784527\pi$
$830$	7.80423	0.270889
$831$	20.3899	0.707318
$832$	0	0
$833$	12.1801	0.422014
$834$	6.82577	0.236357
$835$	1.62934	0.0563856
$836$	49.8261	1.72327
$837$	−8.61185	−0.297669
$838$	−5.59399	−0.193241
$839$	16.8385	0.581331	0.290665	−	0.956825i	$-0.406123\pi$
$839$	16.8385	0.581331	0.290665	+	0.956825i	$0.406123\pi$
$840$	−21.0213	−0.725305
$841$	79.0472	2.72577
$842$	0.191155	0.00658765
$843$	−20.9607	−0.721925
$844$	−17.1766	−0.591243
$845$	0	0
$846$	−2.89602	−0.0995673
$847$	−55.1218	−1.89401
$848$	48.8281	1.67676
$849$	7.57877	0.260103
$850$	4.20990	0.144398
$851$	26.7425	0.916721
$852$	53.2655	1.82485
$853$	2.19711	0.0752278	0.0376139	−	0.999292i	$-0.488024\pi$
$853$	2.19711	0.0752278	0.0376139	+	0.999292i	$0.488024\pi$
$854$	−2.07790	−0.0711042
$855$	−79.0763	−2.70435
$856$	7.78584	0.266115
$857$	−29.1066	−0.994261	−0.497131	−	0.867676i	$-0.665613\pi$
$857$	−29.1066	−0.994261	−0.497131	+	0.867676i	$0.665613\pi$
$858$	0	0
$859$	−18.6415	−0.636040	−0.318020	−	0.948084i	$-0.603018\pi$
$859$	−18.6415	−0.636040	−0.318020	+	0.948084i	$0.603018\pi$
$860$	43.0053	1.46647
$861$	18.2050	0.620426
$862$	6.33989	0.215938
$863$	−0.0299250	−0.00101866	−0.000509330	−	1.00000i	$-0.500162\pi$
$863$	−0.0299250	−0.00101866	−0.000509330		1.00000i	$0.500162\pi$
$864$	−20.9221	−0.711786
$865$	12.2295	0.415817
$866$	−0.995864	−0.0338408
$867$	−68.8369	−2.33783
$868$	5.84470	0.198382
$869$	−0.637546	−0.0216273
$870$	−18.4875	−0.626786
$871$	0	0
$872$	−2.44049	−0.0826456
$873$	−17.2957	−0.585371
$874$	−5.26900	−0.178227
$875$	15.4769	0.523214
$876$	−21.0375	−0.710790
$877$	−9.35982	−0.316059	−0.158029	−	0.987434i	$-0.550514\pi$
$877$	−9.35982	−0.316059	−0.158029	+	0.987434i	$0.550514\pi$
$878$	0.0702976	0.00237243
$879$	−6.24274	−0.210562
$880$	58.1026	1.95864
$881$	33.7354	1.13657	0.568287	−	0.822831i	$-0.307607\pi$
$881$	33.7354	1.13657	0.568287	+	0.822831i	$0.307607\pi$
$882$	2.36141	0.0795128
$883$	−16.1187	−0.542436	−0.271218	−	0.962518i	$-0.587426\pi$
$883$	−16.1187	−0.542436	−0.271218	+	0.962518i	$0.587426\pi$
$884$	0	0
$885$	57.9132	1.94673
$886$	−6.75764	−0.227027
$887$	56.9438	1.91199	0.955993	−	0.293391i	$-0.0947838\pi$
$887$	56.9438	1.91199	0.955993	+	0.293391i	$0.0947838\pi$
$888$	12.2085	0.409692
$889$	−25.1655	−0.844023
$890$	−4.04887	−0.135719
$891$	43.4672	1.45620
$892$	13.8171	0.462632
$893$	11.0707	0.370466
$894$	−6.91169	−0.231161
$895$	44.5549	1.48931
$896$	18.8589	0.630032
$897$	0	0
$898$	−7.26446	−0.242418
$899$	10.3946	0.346679
$900$	−36.7478	−1.22493
$901$	82.6376	2.75306
$902$	2.31254	0.0769992
$903$	−68.4053	−2.27638
$904$	−5.56626	−0.185131
$905$	−6.91342	−0.229810
$906$	−11.0403	−0.366790
$907$	−12.9793	−0.430972	−0.215486	−	0.976507i	$-0.569134\pi$
$907$	−12.9793	−0.430972	−0.215486	+	0.976507i	$0.569134\pi$
$908$	24.0457	0.797986
$909$	−109.232	−3.62299
$910$	0	0
$911$	25.8415	0.856167	0.428083	−	0.903739i	$-0.359189\pi$
$911$	25.8415	0.856167	0.428083	+	0.903739i	$0.359189\pi$
$912$	52.3393	1.73313
$913$	70.9959	2.34962
$914$	6.87565	0.227426
$915$	−28.4690	−0.941156
$916$	−21.6007	−0.713707
$917$	−32.1571	−1.06192
$918$	−11.3667	−0.375158
$919$	31.1176	1.02648	0.513238	−	0.858246i	$-0.328446\pi$
$919$	31.1176	1.02648	0.513238	+	0.858246i	$0.328446\pi$
$920$	−12.7136	−0.419154
$921$	−16.5368	−0.544905
$922$	6.25209	0.205902
$923$	0	0
$924$	−94.5665	−3.11101
$925$	15.8358	0.520677
$926$	5.78179	0.190001
$927$	14.5406	0.477577
$928$	25.2532	0.828977
$929$	29.2061	0.958222	0.479111	−	0.877754i	$-0.340959\pi$
$929$	29.2061	0.958222	0.479111	+	0.877754i	$0.340959\pi$
$930$	−1.77858	−0.0583218
$931$	−9.02700	−0.295848
$932$	−11.1042	−0.363730
$933$	−30.5724	−1.00090
$934$	−0.330801	−0.0108241
$935$	98.3339	3.21586
$936$	0	0
$937$	2.24449	0.0733242	0.0366621	−	0.999328i	$-0.488327\pi$
$937$	2.24449	0.0733242	0.0366621	+	0.999328i	$0.488327\pi$
$938$	7.01796	0.229145
$939$	−44.8852	−1.46477
$940$	13.2095	0.430848
$941$	48.3550	1.57633	0.788163	−	0.615466i	$-0.211032\pi$
$941$	48.3550	1.57633	0.788163	+	0.615466i	$0.211032\pi$
$942$	9.53174	0.310561
$943$	11.0103	0.358545
$944$	−25.3943	−0.826514
$945$	73.6206	2.39488
$946$	−8.68935	−0.282515
$947$	−2.68176	−0.0871455	−0.0435727	−	0.999050i	$-0.513874\pi$
$947$	−2.68176	−0.0871455	−0.0435727	+	0.999050i	$0.513874\pi$
$948$	−0.685263	−0.0222563
$949$	0	0
$950$	−3.12008	−0.101229
$951$	31.5331	1.02253
$952$	15.6001	0.505602
$953$	−8.38473	−0.271608	−0.135804	−	0.990736i	$-0.543362\pi$
$953$	−8.38473	−0.271608	−0.135804	+	0.990736i	$0.543362\pi$
$954$	16.0214	0.518711
$955$	39.7216	1.28536
$956$	−16.0260	−0.518319
$957$	−168.183	−5.43659
$958$	0.0719880	0.00232583
$959$	25.8137	0.833568
$960$	59.5174	1.92091
$961$	1.00000	0.0322581
$962$	0	0
$963$	−55.5869	−1.79126
$964$	2.23040	0.0718365
$965$	−58.4748	−1.88237
$966$	10.0002	0.321752
$967$	−8.05805	−0.259129	−0.129565	−	0.991571i	$-0.541358\pi$
$967$	−8.05805	−0.259129	−0.129565	+	0.991571i	$0.541358\pi$
$968$	−15.2192	−0.489165
$969$	88.5800	2.84560
$970$	−1.75221	−0.0562601
$971$	0.534258	0.0171452	0.00857258	−	0.999963i	$-0.497271\pi$
$971$	0.534258	0.0171452	0.00857258	+	0.999963i	$0.497271\pi$
$972$	−3.82798	−0.122783
$973$	32.8082	1.05178
$974$	−5.15155	−0.165066
$975$	0	0
$976$	12.4833	0.399582
$977$	−42.7815	−1.36870	−0.684351	−	0.729153i	$-0.739914\pi$
$977$	−42.7815	−1.36870	−0.684351	+	0.729153i	$0.739914\pi$
$978$	−1.33814	−0.0427891
$979$	−36.8330	−1.17719
$980$	−10.7710	−0.344067
$981$	17.4239	0.556301
$982$	−4.75082	−0.151605
$983$	−41.2094	−1.31438	−0.657188	−	0.753727i	$-0.728254\pi$
$983$	−41.2094	−1.31438	−0.657188	+	0.753727i	$0.728254\pi$
$984$	5.02645	0.160237
$985$	−12.9207	−0.411687
$986$	13.7197	0.436925
$987$	−21.0114	−0.668801
$988$	0	0
$989$	−41.3711	−1.31552
$990$	19.0645	0.605909
$991$	−0.506777	−0.0160983	−0.00804915	−	0.999968i	$-0.502562\pi$
$991$	−0.506777	−0.0160983	−0.00804915	+	0.999968i	$0.502562\pi$
$992$	2.42946	0.0771354
$993$	−82.6643	−2.62327
$994$	−5.68642	−0.180362
$995$	−29.1814	−0.925112
$996$	76.3095	2.41796
$997$	12.3475	0.391050	0.195525	−	0.980699i	$-0.437359\pi$
$997$	12.3475	0.391050	0.195525	+	0.980699i	$0.437359\pi$
$998$	1.13965	0.0360751
$999$	−42.7566	−1.35276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.v.1.28	yes	54
13.12	even	2		5239.2.a.u.1.27	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.27	✓	54	13.12	even	2
5239.2.a.v.1.28	yes	54	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+0.208462 q^{2} -2.98137 q^{3} -1.95654 q^{4} +2.86174 q^{5} -0.621501 q^{6} -2.98726 q^{7} -0.824787 q^{8} +5.88856 q^{9} +O(q^{10})\)	\(q+0.208462 q^{2} -2.98137 q^{3} -1.95654 q^{4} +2.86174 q^{5} -0.621501 q^{6} -2.98726 q^{7} -0.824787 q^{8} +5.88856 q^{9} +0.596563 q^{10} +5.42700 q^{11} +5.83318 q^{12} -0.622728 q^{14} -8.53191 q^{15} +3.74115 q^{16} +6.33159 q^{17} +1.22754 q^{18} -4.69253 q^{19} -5.59913 q^{20} +8.90611 q^{21} +1.13132 q^{22} +5.38636 q^{23} +2.45899 q^{24} +3.18957 q^{25} -8.61185 q^{27} +5.84470 q^{28} +10.3946 q^{29} -1.77858 q^{30} +1.00000 q^{31} +2.42946 q^{32} -16.1799 q^{33} +1.31989 q^{34} -8.54876 q^{35} -11.5212 q^{36} +4.96485 q^{37} -0.978212 q^{38} -2.36033 q^{40} +2.04411 q^{41} +1.85658 q^{42} -7.68071 q^{43} -10.6182 q^{44} +16.8515 q^{45} +1.12285 q^{46} -2.35921 q^{47} -11.1537 q^{48} +1.92370 q^{49} +0.664904 q^{50} -18.8768 q^{51} +13.0516 q^{53} -1.79524 q^{54} +15.5307 q^{55} +2.46385 q^{56} +13.9902 q^{57} +2.16687 q^{58} -6.78783 q^{59} +16.6931 q^{60} +3.33677 q^{61} +0.208462 q^{62} -17.5906 q^{63} -6.97585 q^{64} -3.37288 q^{66} -11.2697 q^{67} -12.3880 q^{68} -16.0587 q^{69} -1.78209 q^{70} +9.13148 q^{71} -4.85681 q^{72} -3.60652 q^{73} +1.03498 q^{74} -9.50929 q^{75} +9.18114 q^{76} -16.2118 q^{77} -0.117477 q^{79} +10.7062 q^{80} +8.00943 q^{81} +0.426118 q^{82} +13.0820 q^{83} -17.4252 q^{84} +18.1194 q^{85} -1.60113 q^{86} -30.9901 q^{87} -4.47612 q^{88} -6.78700 q^{89} +3.51290 q^{90} -10.5387 q^{92} -2.98137 q^{93} -0.491805 q^{94} -13.4288 q^{95} -7.24312 q^{96} -2.93717 q^{97} +0.401017 q^{98} +31.9572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) \) 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9} - 6 q^{10} - 7 q^{11} + 5 q^{12} + 38 q^{14} + 4 q^{15} + 76 q^{16} + 62 q^{17} - 9 q^{18} + 8 q^{19} + 16 q^{20} - 6 q^{21} + 15 q^{22} + 38 q^{23} - 99 q^{24} + 87 q^{25} + 25 q^{27} + 19 q^{28} + 95 q^{29} + 41 q^{30} + 54 q^{31} + 9 q^{32} + 12 q^{33} + 7 q^{34} + 53 q^{35} + 97 q^{36} - 24 q^{37} - 16 q^{38} - 28 q^{40} + 22 q^{41} + 11 q^{42} + 11 q^{43} - 24 q^{44} + 8 q^{45} + 9 q^{46} + 45 q^{47} + 2 q^{48} + 105 q^{49} + 6 q^{50} + 58 q^{51} + 56 q^{53} + 50 q^{54} + q^{55} + 91 q^{56} - 51 q^{57} + 25 q^{58} + 36 q^{59} + 100 q^{60} + 48 q^{61} + 2 q^{62} - 56 q^{63} + 90 q^{64} - 24 q^{66} + 26 q^{67} + 140 q^{68} + 47 q^{69} - 24 q^{70} + 40 q^{71} + 7 q^{72} + 9 q^{73} + 114 q^{74} + 18 q^{75} - 67 q^{76} + 65 q^{77} + 33 q^{79} + 53 q^{80} + 210 q^{81} - 6 q^{82} - 41 q^{83} - 37 q^{84} + 37 q^{85} - 42 q^{86} - 16 q^{87} - 22 q^{88} - 24 q^{89} - 40 q^{90} + 87 q^{92} + 7 q^{93} - 4 q^{94} + 61 q^{95} - 200 q^{96} + 28 q^{97} + 68 q^{98} + 39 q^{99}+O(q^{100}) \) 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9 - 6 * q^10 - 7 * q^11 + 5 * q^12 + 38 * q^14 + 4 * q^15 + 76 * q^16 + 62 * q^17 - 9 * q^18 + 8 * q^19 + 16 * q^20 - 6 * q^21 + 15 * q^22 + 38 * q^23 - 99 * q^24 + 87 * q^25 + 25 * q^27 + 19 * q^28 + 95 * q^29 + 41 * q^30 + 54 * q^31 + 9 * q^32 + 12 * q^33 + 7 * q^34 + 53 * q^35 + 97 * q^36 - 24 * q^37 - 16 * q^38 - 28 * q^40 + 22 * q^41 + 11 * q^42 + 11 * q^43 - 24 * q^44 + 8 * q^45 + 9 * q^46 + 45 * q^47 + 2 * q^48 + 105 * q^49 + 6 * q^50 + 58 * q^51 + 56 * q^53 + 50 * q^54 + q^55 + 91 * q^56 - 51 * q^57 + 25 * q^58 + 36 * q^59 + 100 * q^60 + 48 * q^61 + 2 * q^62 - 56 * q^63 + 90 * q^64 - 24 * q^66 + 26 * q^67 + 140 * q^68 + 47 * q^69 - 24 * q^70 + 40 * q^71 + 7 * q^72 + 9 * q^73 + 114 * q^74 + 18 * q^75 - 67 * q^76 + 65 * q^77 + 33 * q^79 + 53 * q^80 + 210 * q^81 - 6 * q^82 - 41 * q^83 - 37 * q^84 + 37 * q^85 - 42 * q^86 - 16 * q^87 - 22 * q^88 - 24 * q^89 - 40 * q^90 + 87 * q^92 + 7 * q^93 - 4 * q^94 + 61 * q^95 - 200 * q^96 + 28 * q^97 + 68 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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