LMFDB - Embedded newform 2366.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*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			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.35690 q^{3} +1.00000 q^{4} -1.19806 q^{5} +1.35690 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.15883 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.35690 q^{3} +1.00000 q^{4} -1.19806 q^{5} +1.35690 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.15883 q^{9} -1.19806 q^{10} -6.04892 q^{11} +1.35690 q^{12} -1.00000 q^{14} -1.62565 q^{15} +1.00000 q^{16} +6.82908 q^{17} -1.15883 q^{18} -6.85086 q^{19} -1.19806 q^{20} -1.35690 q^{21} -6.04892 q^{22} +2.69202 q^{23} +1.35690 q^{24} -3.56465 q^{25} -5.64310 q^{27} -1.00000 q^{28} -9.28382 q^{29} -1.62565 q^{30} -6.30798 q^{31} +1.00000 q^{32} -8.20775 q^{33} +6.82908 q^{34} +1.19806 q^{35} -1.15883 q^{36} +8.89977 q^{37} -6.85086 q^{38} -1.19806 q^{40} +8.78986 q^{41} -1.35690 q^{42} -1.64310 q^{43} -6.04892 q^{44} +1.38835 q^{45} +2.69202 q^{46} -5.55496 q^{47} +1.35690 q^{48} +1.00000 q^{49} -3.56465 q^{50} +9.26636 q^{51} -5.13706 q^{53} -5.64310 q^{54} +7.24698 q^{55} -1.00000 q^{56} -9.29590 q^{57} -9.28382 q^{58} -5.43296 q^{59} -1.62565 q^{60} +3.87263 q^{61} -6.30798 q^{62} +1.15883 q^{63} +1.00000 q^{64} -8.20775 q^{66} -2.18060 q^{67} +6.82908 q^{68} +3.65279 q^{69} +1.19806 q^{70} -1.56704 q^{71} -1.15883 q^{72} -1.46681 q^{73} +8.89977 q^{74} -4.83685 q^{75} -6.85086 q^{76} +6.04892 q^{77} -10.4426 q^{79} -1.19806 q^{80} -4.18060 q^{81} +8.78986 q^{82} -11.7778 q^{83} -1.35690 q^{84} -8.18167 q^{85} -1.64310 q^{86} -12.5972 q^{87} -6.04892 q^{88} -1.91185 q^{89} +1.38835 q^{90} +2.69202 q^{92} -8.55927 q^{93} -5.55496 q^{94} +8.20775 q^{95} +1.35690 q^{96} +7.30798 q^{97} +1.00000 q^{98} +7.00969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 8 q^{5} - 3 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 8 * q^5 - 3 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 8 q^{5} - 3 q^{7} + 3 q^{8} + 5 q^{9} - 8 q^{10} - 9 q^{11} - 3 q^{14} + 7 q^{15} + 3 q^{16} + 10 q^{17} + 5 q^{18} - 7 q^{19} - 8 q^{20} - 9 q^{22} + 3 q^{23} + 11 q^{25} - 21 q^{27} - 3 q^{28} + 5 q^{29} + 7 q^{30} - 24 q^{31} + 3 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{35} + 5 q^{36} + 4 q^{37} - 7 q^{38} - 8 q^{40} + 3 q^{41} - 9 q^{43} - 9 q^{44} - 25 q^{45} + 3 q^{46} - 17 q^{47} + 3 q^{49} + 11 q^{50} - 21 q^{51} - 10 q^{53} - 21 q^{54} + 17 q^{55} - 3 q^{56} - 14 q^{57} + 5 q^{58} + 3 q^{59} + 7 q^{60} - 5 q^{61} - 24 q^{62} - 5 q^{63} + 3 q^{64} - 7 q^{66} + 5 q^{67} + 10 q^{68} - 7 q^{69} + 8 q^{70} - 24 q^{71} + 5 q^{72} - q^{73} + 4 q^{74} - 42 q^{75} - 7 q^{76} + 9 q^{77} + 10 q^{79} - 8 q^{80} - q^{81} + 3 q^{82} + 7 q^{83} - 29 q^{85} - 9 q^{86} - 7 q^{87} - 9 q^{88} - 2 q^{89} - 25 q^{90} + 3 q^{92} - 7 q^{93} - 17 q^{94} + 7 q^{95} + 27 q^{97} + 3 q^{98} - q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 8 * q^5 - 3 * q^7 + 3 * q^8 + 5 * q^9 - 8 * q^10 - 9 * q^11 - 3 * q^14 + 7 * q^15 + 3 * q^16 + 10 * q^17 + 5 * q^18 - 7 * q^19 - 8 * q^20 - 9 * q^22 + 3 * q^23 + 11 * q^25 - 21 * q^27 - 3 * q^28 + 5 * q^29 + 7 * q^30 - 24 * q^31 + 3 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^35 + 5 * q^36 + 4 * q^37 - 7 * q^38 - 8 * q^40 + 3 * q^41 - 9 * q^43 - 9 * q^44 - 25 * q^45 + 3 * q^46 - 17 * q^47 + 3 * q^49 + 11 * q^50 - 21 * q^51 - 10 * q^53 - 21 * q^54 + 17 * q^55 - 3 * q^56 - 14 * q^57 + 5 * q^58 + 3 * q^59 + 7 * q^60 - 5 * q^61 - 24 * q^62 - 5 * q^63 + 3 * q^64 - 7 * q^66 + 5 * q^67 + 10 * q^68 - 7 * q^69 + 8 * q^70 - 24 * q^71 + 5 * q^72 - q^73 + 4 * q^74 - 42 * q^75 - 7 * q^76 + 9 * q^77 + 10 * q^79 - 8 * q^80 - q^81 + 3 * q^82 + 7 * q^83 - 29 * q^85 - 9 * q^86 - 7 * q^87 - 9 * q^88 - 2 * q^89 - 25 * q^90 + 3 * q^92 - 7 * q^93 - 17 * q^94 + 7 * q^95 + 27 * q^97 + 3 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.35690	0.783404	0.391702	−	0.920092i	$-0.371886\pi$
$3$	1.35690	0.783404	0.391702	+	0.920092i	$0.371886\pi$
$4$	1.00000	0.500000
$5$	−1.19806	−0.535790	−0.267895	−	0.963448i	$-0.586328\pi$
$5$	−1.19806	−0.535790	−0.267895	+	0.963448i	$0.586328\pi$
$6$	1.35690	0.553950
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.15883	−0.386278
$10$	−1.19806	−0.378861
$11$	−6.04892	−1.82382	−0.911909	−	0.410393i	$-0.865391\pi$
$11$	−6.04892	−1.82382	−0.911909	+	0.410393i	$0.865391\pi$
$12$	1.35690	0.391702
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−1.62565	−0.419740
$16$	1.00000	0.250000
$17$	6.82908	1.65630	0.828148	−	0.560509i	$-0.189395\pi$
$17$	6.82908	1.65630	0.828148	+	0.560509i	$0.189395\pi$
$18$	−1.15883	−0.273140
$19$	−6.85086	−1.57169	−0.785847	−	0.618421i	$-0.787773\pi$
$19$	−6.85086	−1.57169	−0.785847	+	0.618421i	$0.787773\pi$
$20$	−1.19806	−0.267895
$21$	−1.35690	−0.296099
$22$	−6.04892	−1.28963
$23$	2.69202	0.561325	0.280663	−	0.959806i	$-0.409446\pi$
$23$	2.69202	0.561325	0.280663	+	0.959806i	$0.409446\pi$
$24$	1.35690	0.276975
$25$	−3.56465	−0.712929
$26$	0	0
$27$	−5.64310	−1.08602
$28$	−1.00000	−0.188982
$29$	−9.28382	−1.72396	−0.861981	−	0.506941i	$-0.830776\pi$
$29$	−9.28382	−1.72396	−0.861981	+	0.506941i	$0.830776\pi$
$30$	−1.62565	−0.296801
$31$	−6.30798	−1.13295	−0.566473	−	0.824080i	$-0.691693\pi$
$31$	−6.30798	−1.13295	−0.566473	+	0.824080i	$0.691693\pi$
$32$	1.00000	0.176777
$33$	−8.20775	−1.42879
$34$	6.82908	1.17118
$35$	1.19806	0.202509
$36$	−1.15883	−0.193139
$37$	8.89977	1.46311	0.731557	−	0.681781i	$-0.238794\pi$
$37$	8.89977	1.46311	0.731557	+	0.681781i	$0.238794\pi$
$38$	−6.85086	−1.11136
$39$	0	0
$40$	−1.19806	−0.189430
$41$	8.78986	1.37274	0.686372	−	0.727250i	$-0.259202\pi$
$41$	8.78986	1.37274	0.686372	+	0.727250i	$0.259202\pi$
$42$	−1.35690	−0.209374
$43$	−1.64310	−0.250571	−0.125286	−	0.992121i	$-0.539985\pi$
$43$	−1.64310	−0.250571	−0.125286	+	0.992121i	$0.539985\pi$
$44$	−6.04892	−0.911909
$45$	1.38835	0.206964
$46$	2.69202	0.396917
$47$	−5.55496	−0.810274	−0.405137	−	0.914256i	$-0.632776\pi$
$47$	−5.55496	−0.810274	−0.405137	+	0.914256i	$0.632776\pi$
$48$	1.35690	0.195851
$49$	1.00000	0.142857
$50$	−3.56465	−0.504117
$51$	9.26636	1.29755
$52$	0	0
$53$	−5.13706	−0.705630	−0.352815	−	0.935693i	$-0.614775\pi$
$53$	−5.13706	−0.705630	−0.352815	+	0.935693i	$0.614775\pi$
$54$	−5.64310	−0.767929
$55$	7.24698	0.977183
$56$	−1.00000	−0.133631
$57$	−9.29590	−1.23127
$58$	−9.28382	−1.21902
$59$	−5.43296	−0.707311	−0.353656	−	0.935376i	$-0.615062\pi$
$59$	−5.43296	−0.707311	−0.353656	+	0.935376i	$0.615062\pi$
$60$	−1.62565	−0.209870
$61$	3.87263	0.495839	0.247919	−	0.968781i	$-0.420253\pi$
$61$	3.87263	0.495839	0.247919	+	0.968781i	$0.420253\pi$
$62$	−6.30798	−0.801114
$63$	1.15883	0.145999
$64$	1.00000	0.125000
$65$	0	0
$66$	−8.20775	−1.01030
$67$	−2.18060	−0.266403	−0.133202	−	0.991089i	$-0.542526\pi$
$67$	−2.18060	−0.266403	−0.133202	+	0.991089i	$0.542526\pi$
$68$	6.82908	0.828148
$69$	3.65279	0.439745
$70$	1.19806	0.143196
$71$	−1.56704	−0.185973	−0.0929867	−	0.995667i	$-0.529641\pi$
$71$	−1.56704	−0.185973	−0.0929867	+	0.995667i	$0.529641\pi$
$72$	−1.15883	−0.136570
$73$	−1.46681	−0.171677	−0.0858387	−	0.996309i	$-0.527357\pi$
$73$	−1.46681	−0.171677	−0.0858387	+	0.996309i	$0.527357\pi$
$74$	8.89977	1.03458
$75$	−4.83685	−0.558512
$76$	−6.85086	−0.785847
$77$	6.04892	0.689338
$78$	0	0
$79$	−10.4426	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$79$	−10.4426	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$80$	−1.19806	−0.133947
$81$	−4.18060	−0.464512
$82$	8.78986	0.970677
$83$	−11.7778	−1.29278	−0.646389	−	0.763008i	$-0.723722\pi$
$83$	−11.7778	−1.29278	−0.646389	+	0.763008i	$0.723722\pi$
$84$	−1.35690	−0.148049
$85$	−8.18167	−0.887427
$86$	−1.64310	−0.177180
$87$	−12.5972	−1.35056
$88$	−6.04892	−0.644817
$89$	−1.91185	−0.202656	−0.101328	−	0.994853i	$-0.532309\pi$
$89$	−1.91185	−0.202656	−0.101328	+	0.994853i	$0.532309\pi$
$90$	1.38835	0.146345
$91$	0	0
$92$	2.69202	0.280663
$93$	−8.55927	−0.887555
$94$	−5.55496	−0.572950
$95$	8.20775	0.842097
$96$	1.35690	0.138488
$97$	7.30798	0.742013	0.371006	−	0.928630i	$-0.379013\pi$
$97$	7.30798	0.742013	0.371006	+	0.928630i	$0.379013\pi$
$98$	1.00000	0.101015
$99$	7.00969	0.704500
$100$	−3.56465	−0.356465
$101$	6.58211	0.654944	0.327472	−	0.944861i	$-0.393803\pi$
$101$	6.58211	0.654944	0.327472	+	0.944861i	$0.393803\pi$
$102$	9.26636	0.917506
$103$	5.16852	0.509270	0.254635	−	0.967037i	$-0.418045\pi$
$103$	5.16852	0.509270	0.254635	+	0.967037i	$0.418045\pi$
$104$	0	0
$105$	1.62565	0.158647
$106$	−5.13706	−0.498956
$107$	−19.3110	−1.86686	−0.933431	−	0.358758i	$-0.883200\pi$
$107$	−19.3110	−1.86686	−0.933431	+	0.358758i	$0.883200\pi$
$108$	−5.64310	−0.543008
$109$	3.67994	0.352474	0.176237	−	0.984348i	$-0.443607\pi$
$109$	3.67994	0.352474	0.176237	+	0.984348i	$0.443607\pi$
$110$	7.24698	0.690972
$111$	12.0761	1.14621
$112$	−1.00000	−0.0944911
$113$	13.1739	1.23930	0.619648	−	0.784880i	$-0.287275\pi$
$113$	13.1739	1.23930	0.619648	+	0.784880i	$0.287275\pi$
$114$	−9.29590	−0.870641
$115$	−3.22521	−0.300752
$116$	−9.28382	−0.861981
$117$	0	0
$118$	−5.43296	−0.500145
$119$	−6.82908	−0.626021
$120$	−1.62565	−0.148400
$121$	25.5894	2.32631
$122$	3.87263	0.350611
$123$	11.9269	1.07541
$124$	−6.30798	−0.566473
$125$	10.2610	0.917770
$126$	1.15883	0.103237
$127$	14.1129	1.25232	0.626159	−	0.779696i	$-0.284626\pi$
$127$	14.1129	1.25232	0.626159	+	0.779696i	$0.284626\pi$
$128$	1.00000	0.0883883
$129$	−2.22952	−0.196298
$130$	0	0
$131$	1.93900	0.169411	0.0847057	−	0.996406i	$-0.473005\pi$
$131$	1.93900	0.169411	0.0847057	+	0.996406i	$0.473005\pi$
$132$	−8.20775	−0.714393
$133$	6.85086	0.594044
$134$	−2.18060	−0.188375
$135$	6.76079	0.581876
$136$	6.82908	0.585589
$137$	−4.26205	−0.364131	−0.182066	−	0.983286i	$-0.558278\pi$
$137$	−4.26205	−0.364131	−0.182066	+	0.983286i	$0.558278\pi$
$138$	3.65279	0.310946
$139$	16.9879	1.44090	0.720448	−	0.693509i	$-0.243936\pi$
$139$	16.9879	1.44090	0.720448	+	0.693509i	$0.243936\pi$
$140$	1.19806	0.101255
$141$	−7.53750	−0.634772
$142$	−1.56704	−0.131503
$143$	0	0
$144$	−1.15883	−0.0965695
$145$	11.1226	0.923681
$146$	−1.46681	−0.121394
$147$	1.35690	0.111915
$148$	8.89977	0.731557
$149$	4.17092	0.341695	0.170847	−	0.985298i	$-0.445350\pi$
$149$	4.17092	0.341695	0.170847	+	0.985298i	$0.445350\pi$
$150$	−4.83685	−0.394928
$151$	0.872625	0.0710132	0.0355066	−	0.999369i	$-0.488696\pi$
$151$	0.872625	0.0710132	0.0355066	+	0.999369i	$0.488696\pi$
$152$	−6.85086	−0.555678
$153$	−7.91377	−0.639791
$154$	6.04892	0.487436
$155$	7.55735	0.607021
$156$	0	0
$157$	−19.0532	−1.52061	−0.760307	−	0.649564i	$-0.774951\pi$
$157$	−19.0532	−1.52061	−0.760307	+	0.649564i	$0.774951\pi$
$158$	−10.4426	−0.830773
$159$	−6.97046	−0.552793
$160$	−1.19806	−0.0947151
$161$	−2.69202	−0.212161
$162$	−4.18060	−0.328459
$163$	0.571352	0.0447517	0.0223759	−	0.999750i	$-0.492877\pi$
$163$	0.571352	0.0447517	0.0223759	+	0.999750i	$0.492877\pi$
$164$	8.78986	0.686372
$165$	9.83340	0.765529
$166$	−11.7778	−0.914133
$167$	11.9269	0.922933	0.461466	−	0.887158i	$-0.347323\pi$
$167$	11.9269	0.922933	0.461466	+	0.887158i	$0.347323\pi$
$168$	−1.35690	−0.104687
$169$	0	0
$170$	−8.18167	−0.627505
$171$	7.93900	0.607111
$172$	−1.64310	−0.125286
$173$	−11.4993	−0.874278	−0.437139	−	0.899394i	$-0.644008\pi$
$173$	−11.4993	−0.874278	−0.437139	+	0.899394i	$0.644008\pi$
$174$	−12.5972	−0.954989
$175$	3.56465	0.269462
$176$	−6.04892	−0.455954
$177$	−7.37196	−0.554111
$178$	−1.91185	−0.143300
$179$	16.6775	1.24654	0.623269	−	0.782007i	$-0.285804\pi$
$179$	16.6775	1.24654	0.623269	+	0.782007i	$0.285804\pi$
$180$	1.38835	0.103482
$181$	−10.0543	−0.747330	−0.373665	−	0.927564i	$-0.621899\pi$
$181$	−10.0543	−0.747330	−0.373665	+	0.927564i	$0.621899\pi$
$182$	0	0
$183$	5.25475	0.388442
$184$	2.69202	0.198458
$185$	−10.6625	−0.783921
$186$	−8.55927	−0.627596
$187$	−41.3086	−3.02078
$188$	−5.55496	−0.405137
$189$	5.64310	0.410475
$190$	8.20775	0.595453
$191$	17.1075	1.23786	0.618928	−	0.785447i	$-0.287567\pi$
$191$	17.1075	1.23786	0.618928	+	0.785447i	$0.287567\pi$
$192$	1.35690	0.0979255
$193$	−12.2687	−0.883124	−0.441562	−	0.897231i	$-0.645575\pi$
$193$	−12.2687	−0.883124	−0.441562	+	0.897231i	$0.645575\pi$
$194$	7.30798	0.524682
$195$	0	0
$196$	1.00000	0.0714286
$197$	14.0043	0.997766	0.498883	−	0.866669i	$-0.333744\pi$
$197$	14.0043	0.997766	0.498883	+	0.866669i	$0.333744\pi$
$198$	7.00969	0.498157
$199$	−0.188374	−0.0133534	−0.00667672	−	0.999978i	$-0.502125\pi$
$199$	−0.188374	−0.0133534	−0.00667672	+	0.999978i	$0.502125\pi$
$200$	−3.56465	−0.252059
$201$	−2.95885	−0.208701
$202$	6.58211	0.463115
$203$	9.28382	0.651596
$204$	9.26636	0.648775
$205$	−10.5308	−0.735503
$206$	5.16852	0.360108
$207$	−3.11960	−0.216828
$208$	0	0
$209$	41.4403	2.86648
$210$	1.62565	0.112180
$211$	−10.2131	−0.703101	−0.351550	−	0.936169i	$-0.614345\pi$
$211$	−10.2131	−0.703101	−0.351550	+	0.936169i	$0.614345\pi$
$212$	−5.13706	−0.352815
$213$	−2.12631	−0.145692
$214$	−19.3110	−1.32007
$215$	1.96854	0.134253
$216$	−5.64310	−0.383965
$217$	6.30798	0.428213
$218$	3.67994	0.249237
$219$	−1.99031	−0.134493
$220$	7.24698	0.488591
$221$	0	0
$222$	12.0761	0.810492
$223$	−20.3207	−1.36077	−0.680386	−	0.732854i	$-0.738188\pi$
$223$	−20.3207	−1.36077	−0.680386	+	0.732854i	$0.738188\pi$
$224$	−1.00000	−0.0668153
$225$	4.13083	0.275389
$226$	13.1739	0.876315
$227$	9.36227	0.621396	0.310698	−	0.950509i	$-0.399437\pi$
$227$	9.36227	0.621396	0.310698	+	0.950509i	$0.399437\pi$
$228$	−9.29590	−0.615636
$229$	−13.6866	−0.904439	−0.452219	−	0.891907i	$-0.649368\pi$
$229$	−13.6866	−0.904439	−0.452219	+	0.891907i	$0.649368\pi$
$230$	−3.22521	−0.212664
$231$	8.20775	0.540030
$232$	−9.28382	−0.609512
$233$	−12.3773	−0.810866	−0.405433	−	0.914125i	$-0.632879\pi$
$233$	−12.3773	−0.810866	−0.405433	+	0.914125i	$0.632879\pi$
$234$	0	0
$235$	6.65519	0.434136
$236$	−5.43296	−0.353656
$237$	−14.1696	−0.920414
$238$	−6.82908	−0.442664
$239$	29.9801	1.93925	0.969627	−	0.244587i	$-0.0786524\pi$
$239$	29.9801	1.93925	0.969627	+	0.244587i	$0.0786524\pi$
$240$	−1.62565	−0.104935
$241$	−22.3448	−1.43936	−0.719678	−	0.694308i	$-0.755711\pi$
$241$	−22.3448	−1.43936	−0.719678	+	0.694308i	$0.755711\pi$
$242$	25.5894	1.64495
$243$	11.2567	0.722116
$244$	3.87263	0.247919
$245$	−1.19806	−0.0765414
$246$	11.9269	0.760433
$247$	0	0
$248$	−6.30798	−0.400557
$249$	−15.9812	−1.01277
$250$	10.2610	0.648961
$251$	−12.7657	−0.805763	−0.402882	−	0.915252i	$-0.631991\pi$
$251$	−12.7657	−0.805763	−0.402882	+	0.915252i	$0.631991\pi$
$252$	1.15883	0.0729997
$253$	−16.2838	−1.02375
$254$	14.1129	0.885522
$255$	−11.1017	−0.695214
$256$	1.00000	0.0625000
$257$	−4.99761	−0.311742	−0.155871	−	0.987777i	$-0.549818\pi$
$257$	−4.99761	−0.311742	−0.155871	+	0.987777i	$0.549818\pi$
$258$	−2.22952	−0.138804
$259$	−8.89977	−0.553005
$260$	0	0
$261$	10.7584	0.665928
$262$	1.93900	0.119792
$263$	−5.77910	−0.356355	−0.178177	−	0.983998i	$-0.557020\pi$
$263$	−5.77910	−0.356355	−0.178177	+	0.983998i	$0.557020\pi$
$264$	−8.20775	−0.505152
$265$	6.15452	0.378069
$266$	6.85086	0.420053
$267$	−2.59419	−0.158762
$268$	−2.18060	−0.133202
$269$	−21.9651	−1.33923	−0.669617	−	0.742706i	$-0.733542\pi$
$269$	−21.9651	−1.33923	−0.669617	+	0.742706i	$0.733542\pi$
$270$	6.76079	0.411449
$271$	−14.7192	−0.894126	−0.447063	−	0.894503i	$-0.647530\pi$
$271$	−14.7192	−0.894126	−0.447063	+	0.894503i	$0.647530\pi$
$272$	6.82908	0.414074
$273$	0	0
$274$	−4.26205	−0.257480
$275$	21.5623	1.30025
$276$	3.65279	0.219872
$277$	−2.31096	−0.138852	−0.0694261	−	0.997587i	$-0.522117\pi$
$277$	−2.31096	−0.138852	−0.0694261	+	0.997587i	$0.522117\pi$
$278$	16.9879	1.01887
$279$	7.30990	0.437632
$280$	1.19806	0.0715979
$281$	32.7821	1.95562	0.977808	−	0.209505i	$-0.0671851\pi$
$281$	32.7821	1.95562	0.977808	+	0.209505i	$0.0671851\pi$
$282$	−7.53750	−0.448852
$283$	−1.88471	−0.112034	−0.0560171	−	0.998430i	$-0.517840\pi$
$283$	−1.88471	−0.112034	−0.0560171	+	0.998430i	$0.517840\pi$
$284$	−1.56704	−0.0929867
$285$	11.1371	0.659703
$286$	0	0
$287$	−8.78986	−0.518849
$288$	−1.15883	−0.0682849
$289$	29.6364	1.74332
$290$	11.1226	0.653141
$291$	9.91617	0.581296
$292$	−1.46681	−0.0858387
$293$	1.07175	0.0626125	0.0313062	−	0.999510i	$-0.490033\pi$
$293$	1.07175	0.0626125	0.0313062	+	0.999510i	$0.490033\pi$
$294$	1.35690	0.0791358
$295$	6.50902	0.378970
$296$	8.89977	0.517289
$297$	34.1347	1.98069
$298$	4.17092	0.241615
$299$	0	0
$300$	−4.83685	−0.279256
$301$	1.64310	0.0947069
$302$	0.872625	0.0502139
$303$	8.93123	0.513086
$304$	−6.85086	−0.392923
$305$	−4.63965	−0.265665
$306$	−7.91377	−0.452400
$307$	−22.4112	−1.27907	−0.639537	−	0.768760i	$-0.720874\pi$
$307$	−22.4112	−1.27907	−0.639537	+	0.768760i	$0.720874\pi$
$308$	6.04892	0.344669
$309$	7.01315	0.398964
$310$	7.55735	0.429229
$311$	−11.0000	−0.623753	−0.311876	−	0.950123i	$-0.600957\pi$
$311$	−11.0000	−0.623753	−0.311876	+	0.950123i	$0.600957\pi$
$312$	0	0
$313$	−6.95348	−0.393034	−0.196517	−	0.980500i	$-0.562963\pi$
$313$	−6.95348	−0.393034	−0.196517	+	0.980500i	$0.562963\pi$
$314$	−19.0532	−1.07524
$315$	−1.38835	−0.0782249
$316$	−10.4426	−0.587445
$317$	−18.2881	−1.02716	−0.513582	−	0.858041i	$-0.671682\pi$
$317$	−18.2881	−1.02716	−0.513582	+	0.858041i	$0.671682\pi$
$318$	−6.97046	−0.390884
$319$	56.1570	3.14419
$320$	−1.19806	−0.0669737
$321$	−26.2030	−1.46251
$322$	−2.69202	−0.150020
$323$	−46.7851	−2.60319
$324$	−4.18060	−0.232256
$325$	0	0
$326$	0.571352	0.0316442
$327$	4.99330	0.276130
$328$	8.78986	0.485339
$329$	5.55496	0.306255
$330$	9.83340	0.541311
$331$	16.5646	0.910475	0.455238	−	0.890370i	$-0.349554\pi$
$331$	16.5646	0.910475	0.455238	+	0.890370i	$0.349554\pi$
$332$	−11.7778	−0.646389
$333$	−10.3134	−0.565168
$334$	11.9269	0.652612
$335$	2.61250	0.142736
$336$	−1.35690	−0.0740247
$337$	−6.54288	−0.356413	−0.178207	−	0.983993i	$-0.557030\pi$
$337$	−6.54288	−0.356413	−0.178207	+	0.983993i	$0.557030\pi$
$338$	0	0
$339$	17.8756	0.970870
$340$	−8.18167	−0.443713
$341$	38.1564	2.06629
$342$	7.93900	0.429292
$343$	−1.00000	−0.0539949
$344$	−1.64310	−0.0885902
$345$	−4.37627	−0.235611
$346$	−11.4993	−0.618208
$347$	6.55496	0.351889	0.175944	−	0.984400i	$-0.443702\pi$
$347$	6.55496	0.351889	0.175944	+	0.984400i	$0.443702\pi$
$348$	−12.5972	−0.675279
$349$	−19.9782	−1.06941	−0.534705	−	0.845039i	$-0.679577\pi$
$349$	−19.9782	−1.06941	−0.534705	+	0.845039i	$0.679577\pi$
$350$	3.56465	0.190538
$351$	0	0
$352$	−6.04892	−0.322408
$353$	8.10560	0.431418	0.215709	−	0.976458i	$-0.430794\pi$
$353$	8.10560	0.431418	0.215709	+	0.976458i	$0.430794\pi$
$354$	−7.37196	−0.391815
$355$	1.87741	0.0996426
$356$	−1.91185	−0.101328
$357$	−9.26636	−0.490428
$358$	16.6775	0.881436
$359$	9.16315	0.483612	0.241806	−	0.970325i	$-0.422260\pi$
$359$	9.16315	0.483612	0.241806	+	0.970325i	$0.422260\pi$
$360$	1.38835	0.0731727
$361$	27.9342	1.47022
$362$	−10.0543	−0.528442
$363$	34.7222	1.82244
$364$	0	0
$365$	1.75733	0.0919830
$366$	5.25475	0.274670
$367$	2.67456	0.139611	0.0698055	−	0.997561i	$-0.477762\pi$
$367$	2.67456	0.139611	0.0698055	+	0.997561i	$0.477762\pi$
$368$	2.69202	0.140331
$369$	−10.1860	−0.530261
$370$	−10.6625	−0.554316
$371$	5.13706	0.266703
$372$	−8.55927	−0.443777
$373$	−11.6165	−0.601482	−0.300741	−	0.953706i	$-0.597234\pi$
$373$	−11.6165	−0.601482	−0.300741	+	0.953706i	$0.597234\pi$
$374$	−41.3086	−2.13602
$375$	13.9231	0.718985
$376$	−5.55496	−0.286475
$377$	0	0
$378$	5.64310	0.290250
$379$	2.76271	0.141911	0.0709554	−	0.997479i	$-0.477395\pi$
$379$	2.76271	0.141911	0.0709554	+	0.997479i	$0.477395\pi$
$380$	8.20775	0.421049
$381$	19.1497	0.981071
$382$	17.1075	0.875297
$383$	16.8877	0.862921	0.431460	−	0.902132i	$-0.357998\pi$
$383$	16.8877	0.862921	0.431460	+	0.902132i	$0.357998\pi$
$384$	1.35690	0.0692438
$385$	−7.24698	−0.369340
$386$	−12.2687	−0.624463
$387$	1.90408	0.0967900
$388$	7.30798	0.371006
$389$	−4.07739	−0.206732	−0.103366	−	0.994643i	$-0.532961\pi$
$389$	−4.07739	−0.206732	−0.103366	+	0.994643i	$0.532961\pi$
$390$	0	0
$391$	18.3840	0.929721
$392$	1.00000	0.0505076
$393$	2.63102	0.132718
$394$	14.0043	0.705527
$395$	12.5109	0.629494
$396$	7.00969	0.352250
$397$	4.46548	0.224116	0.112058	−	0.993702i	$-0.464256\pi$
$397$	4.46548	0.224116	0.112058	+	0.993702i	$0.464256\pi$
$398$	−0.188374	−0.00944231
$399$	9.29590	0.465377
$400$	−3.56465	−0.178232
$401$	28.2349	1.40998	0.704992	−	0.709215i	$-0.250951\pi$
$401$	28.2349	1.40998	0.704992	+	0.709215i	$0.250951\pi$
$402$	−2.95885	−0.147574
$403$	0	0
$404$	6.58211	0.327472
$405$	5.00862	0.248881
$406$	9.28382	0.460748
$407$	−53.8340	−2.66845
$408$	9.26636	0.458753
$409$	−22.7004	−1.12246	−0.561231	−	0.827659i	$-0.689672\pi$
$409$	−22.7004	−1.12246	−0.561231	+	0.827659i	$0.689672\pi$
$410$	−10.5308	−0.520079
$411$	−5.78315	−0.285262
$412$	5.16852	0.254635
$413$	5.43296	0.267338
$414$	−3.11960	−0.153320
$415$	14.1105	0.692658
$416$	0	0
$417$	23.0508	1.12880
$418$	41.4403	2.02691
$419$	14.1933	0.693387	0.346693	−	0.937978i	$-0.387304\pi$
$419$	14.1933	0.693387	0.346693	+	0.937978i	$0.387304\pi$
$420$	1.62565	0.0793234
$421$	−30.7899	−1.50061	−0.750303	−	0.661094i	$-0.770092\pi$
$421$	−30.7899	−1.50061	−0.750303	+	0.661094i	$0.770092\pi$
$422$	−10.2131	−0.497167
$423$	6.43727	0.312991
$424$	−5.13706	−0.249478
$425$	−24.3433	−1.18082
$426$	−2.12631	−0.103020
$427$	−3.87263	−0.187409
$428$	−19.3110	−0.933431
$429$	0	0
$430$	1.96854	0.0949315
$431$	−24.4456	−1.17750	−0.588752	−	0.808313i	$-0.700381\pi$
$431$	−24.4456	−1.17750	−0.588752	+	0.808313i	$0.700381\pi$
$432$	−5.64310	−0.271504
$433$	−18.5633	−0.892096	−0.446048	−	0.895009i	$-0.647169\pi$
$433$	−18.5633	−0.892096	−0.446048	+	0.895009i	$0.647169\pi$
$434$	6.30798	0.302793
$435$	15.0922	0.723615
$436$	3.67994	0.176237
$437$	−18.4426	−0.882232
$438$	−1.99031	−0.0951008
$439$	−14.7748	−0.705162	−0.352581	−	0.935781i	$-0.614696\pi$
$439$	−14.7748	−0.705162	−0.352581	+	0.935781i	$0.614696\pi$
$440$	7.24698	0.345486
$441$	−1.15883	−0.0551826
$442$	0	0
$443$	−27.1588	−1.29036	−0.645178	−	0.764033i	$-0.723217\pi$
$443$	−27.1588	−1.29036	−0.645178	+	0.764033i	$0.723217\pi$
$444$	12.0761	0.573105
$445$	2.29052	0.108581
$446$	−20.3207	−0.962211
$447$	5.65950	0.267685
$448$	−1.00000	−0.0472456
$449$	24.1521	1.13981	0.569905	−	0.821711i	$-0.306980\pi$
$449$	24.1521	1.13981	0.569905	+	0.821711i	$0.306980\pi$
$450$	4.13083	0.194729
$451$	−53.1691	−2.50364
$452$	13.1739	0.619648
$453$	1.18406	0.0556321
$454$	9.36227	0.439393
$455$	0	0
$456$	−9.29590	−0.435320
$457$	11.4470	0.535466	0.267733	−	0.963493i	$-0.413725\pi$
$457$	11.4470	0.535466	0.267733	+	0.963493i	$0.413725\pi$
$458$	−13.6866	−0.639535
$459$	−38.5372	−1.79876
$460$	−3.22521	−0.150376
$461$	−17.1728	−0.799819	−0.399909	−	0.916555i	$-0.630958\pi$
$461$	−17.1728	−0.799819	−0.399909	+	0.916555i	$0.630958\pi$
$462$	8.20775	0.381859
$463$	−8.36360	−0.388689	−0.194345	−	0.980933i	$-0.562258\pi$
$463$	−8.36360	−0.388689	−0.194345	+	0.980933i	$0.562258\pi$
$464$	−9.28382	−0.430990
$465$	10.2545	0.475543
$466$	−12.3773	−0.573369
$467$	4.05621	0.187699	0.0938496	−	0.995586i	$-0.470083\pi$
$467$	4.05621	0.187699	0.0938496	+	0.995586i	$0.470083\pi$
$468$	0	0
$469$	2.18060	0.100691
$470$	6.65519	0.306981
$471$	−25.8532	−1.19125
$472$	−5.43296	−0.250072
$473$	9.93900	0.456996
$474$	−14.1696	−0.650831
$475$	24.4209	1.12051
$476$	−6.82908	−0.313011
$477$	5.95300	0.272569
$478$	29.9801	1.37126
$479$	1.79225	0.0818899	0.0409450	−	0.999161i	$-0.486963\pi$
$479$	1.79225	0.0818899	0.0409450	+	0.999161i	$0.486963\pi$
$480$	−1.62565	−0.0742002
$481$	0	0
$482$	−22.3448	−1.01778
$483$	−3.65279	−0.166208
$484$	25.5894	1.16315
$485$	−8.75541	−0.397563
$486$	11.2567	0.510613
$487$	−9.83579	−0.445702	−0.222851	−	0.974852i	$-0.571536\pi$
$487$	−9.83579	−0.445702	−0.222851	+	0.974852i	$0.571536\pi$
$488$	3.87263	0.175306
$489$	0.775265	0.0350587
$490$	−1.19806	−0.0541229
$491$	−4.21983	−0.190438	−0.0952192	−	0.995456i	$-0.530355\pi$
$491$	−4.21983	−0.190438	−0.0952192	+	0.995456i	$0.530355\pi$
$492$	11.9269	0.537707
$493$	−63.4000	−2.85539
$494$	0	0
$495$	−8.39804	−0.377464
$496$	−6.30798	−0.283237
$497$	1.56704	0.0702913
$498$	−15.9812	−0.716135
$499$	5.44696	0.243839	0.121920	−	0.992540i	$-0.461095\pi$
$499$	5.44696	0.243839	0.121920	+	0.992540i	$0.461095\pi$
$500$	10.2610	0.458885
$501$	16.1836	0.723029
$502$	−12.7657	−0.569761
$503$	15.2500	0.679962	0.339981	−	0.940432i	$-0.389579\pi$
$503$	15.2500	0.679962	0.339981	+	0.940432i	$0.389579\pi$
$504$	1.15883	0.0516186
$505$	−7.88577	−0.350912
$506$	−16.2838	−0.723904
$507$	0	0
$508$	14.1129	0.626159
$509$	30.9071	1.36993	0.684966	−	0.728575i	$-0.259817\pi$
$509$	30.9071	1.36993	0.684966	+	0.728575i	$0.259817\pi$
$510$	−11.1017	−0.491590
$511$	1.46681	0.0648879
$512$	1.00000	0.0441942
$513$	38.6601	1.70688
$514$	−4.99761	−0.220435
$515$	−6.19221	−0.272861
$516$	−2.22952	−0.0981492
$517$	33.6015	1.47779
$518$	−8.89977	−0.391034
$519$	−15.6034	−0.684913
$520$	0	0
$521$	−19.2881	−0.845028	−0.422514	−	0.906356i	$-0.638852\pi$
$521$	−19.2881	−0.845028	−0.422514	+	0.906356i	$0.638852\pi$
$522$	10.7584	0.470882
$523$	−17.4504	−0.763054	−0.381527	−	0.924358i	$-0.624602\pi$
$523$	−17.4504	−0.763054	−0.381527	+	0.924358i	$0.624602\pi$
$524$	1.93900	0.0847057
$525$	4.83685	0.211098
$526$	−5.77910	−0.251981
$527$	−43.0777	−1.87649
$528$	−8.20775	−0.357197
$529$	−15.7530	−0.684914
$530$	6.15452	0.267335
$531$	6.29590	0.273219
$532$	6.85086	0.297022
$533$	0	0
$534$	−2.59419	−0.112261
$535$	23.1357	1.00025
$536$	−2.18060	−0.0941877
$537$	22.6297	0.976543
$538$	−21.9651	−0.946982
$539$	−6.04892	−0.260545
$540$	6.76079	0.290938
$541$	−13.1981	−0.567429	−0.283715	−	0.958909i	$-0.591567\pi$
$541$	−13.1981	−0.567429	−0.283715	+	0.958909i	$0.591567\pi$
$542$	−14.7192	−0.632242
$543$	−13.6426	−0.585461
$544$	6.82908	0.292795
$545$	−4.40880	−0.188852
$546$	0	0
$547$	29.4306	1.25836	0.629180	−	0.777260i	$-0.283391\pi$
$547$	29.4306	1.25836	0.629180	+	0.777260i	$0.283391\pi$
$548$	−4.26205	−0.182066
$549$	−4.48773	−0.191532
$550$	21.5623	0.919418
$551$	63.6021	2.70954
$552$	3.65279	0.155473
$553$	10.4426	0.444067
$554$	−2.31096	−0.0981834
$555$	−14.4679	−0.614127
$556$	16.9879	0.720448
$557$	29.5961	1.25403	0.627014	−	0.779008i	$-0.284277\pi$
$557$	29.5961	1.25403	0.627014	+	0.779008i	$0.284277\pi$
$558$	7.30990	0.309453
$559$	0	0
$560$	1.19806	0.0506274
$561$	−56.0514	−2.36649
$562$	32.7821	1.38283
$563$	37.5754	1.58361	0.791807	−	0.610771i	$-0.209140\pi$
$563$	37.5754	1.58361	0.791807	+	0.610771i	$0.209140\pi$
$564$	−7.53750	−0.317386
$565$	−15.7832	−0.664002
$566$	−1.88471	−0.0792201
$567$	4.18060	0.175569
$568$	−1.56704	−0.0657515
$569$	−23.5066	−0.985449	−0.492725	−	0.870185i	$-0.663999\pi$
$569$	−23.5066	−0.985449	−0.492725	+	0.870185i	$0.663999\pi$
$570$	11.1371	0.466480
$571$	8.21744	0.343889	0.171945	−	0.985107i	$-0.444995\pi$
$571$	8.21744	0.343889	0.171945	+	0.985107i	$0.444995\pi$
$572$	0	0
$573$	23.2131	0.969742
$574$	−8.78986	−0.366882
$575$	−9.59611	−0.400185
$576$	−1.15883	−0.0482847
$577$	28.6316	1.19195	0.595975	−	0.803003i	$-0.296766\pi$
$577$	28.6316	1.19195	0.595975	+	0.803003i	$0.296766\pi$
$578$	29.6364	1.23271
$579$	−16.6474	−0.691843
$580$	11.1226	0.461840
$581$	11.7778	0.488624
$582$	9.91617	0.411038
$583$	31.0737	1.28694
$584$	−1.46681	−0.0606971
$585$	0	0
$586$	1.07175	0.0442737
$587$	29.8552	1.23225	0.616127	−	0.787647i	$-0.288701\pi$
$587$	29.8552	1.23225	0.616127	+	0.787647i	$0.288701\pi$
$588$	1.35690	0.0559574
$589$	43.2150	1.78064
$590$	6.50902	0.267972
$591$	19.0024	0.781654
$592$	8.89977	0.365778
$593$	−16.8189	−0.690670	−0.345335	−	0.938479i	$-0.612235\pi$
$593$	−16.8189	−0.690670	−0.345335	+	0.938479i	$0.612235\pi$
$594$	34.1347	1.40056
$595$	8.18167	0.335416
$596$	4.17092	0.170847
$597$	−0.255603	−0.0104611
$598$	0	0
$599$	−27.0790	−1.10642	−0.553210	−	0.833042i	$-0.686597\pi$
$599$	−27.0790	−1.10642	−0.553210	+	0.833042i	$0.686597\pi$
$600$	−4.83685	−0.197464
$601$	21.2403	0.866409	0.433204	−	0.901296i	$-0.357383\pi$
$601$	21.2403	0.866409	0.433204	+	0.901296i	$0.357383\pi$
$602$	1.64310	0.0669679
$603$	2.52696	0.102906
$604$	0.872625	0.0355066
$605$	−30.6577	−1.24641
$606$	8.93123	0.362806
$607$	−41.5948	−1.68828	−0.844140	−	0.536123i	$-0.819888\pi$
$607$	−41.5948	−1.68828	−0.844140	+	0.536123i	$0.819888\pi$
$608$	−6.85086	−0.277839
$609$	12.5972	0.510463
$610$	−4.63965	−0.187854
$611$	0	0
$612$	−7.91377	−0.319895
$613$	39.5133	1.59593	0.797964	−	0.602705i	$-0.205910\pi$
$613$	39.5133	1.59593	0.797964	+	0.602705i	$0.205910\pi$
$614$	−22.4112	−0.904442
$615$	−14.2892	−0.576196
$616$	6.04892	0.243718
$617$	17.4252	0.701512	0.350756	−	0.936467i	$-0.385925\pi$
$617$	17.4252	0.701512	0.350756	+	0.936467i	$0.385925\pi$
$618$	7.01315	0.282110
$619$	−24.4510	−0.982769	−0.491385	−	0.870943i	$-0.663509\pi$
$619$	−24.4510	−0.982769	−0.491385	+	0.870943i	$0.663509\pi$
$620$	7.55735	0.303511
$621$	−15.1914	−0.609608
$622$	−11.0000	−0.441060
$623$	1.91185	0.0765968
$624$	0	0
$625$	5.52994	0.221198
$626$	−6.95348	−0.277917
$627$	56.2301	2.24561
$628$	−19.0532	−0.760307
$629$	60.7773	2.42335
$630$	−1.38835	−0.0553134
$631$	−9.17092	−0.365088	−0.182544	−	0.983198i	$-0.558433\pi$
$631$	−9.17092	−0.365088	−0.182544	+	0.983198i	$0.558433\pi$
$632$	−10.4426	−0.415386
$633$	−13.8582	−0.550812
$634$	−18.2881	−0.726314
$635$	−16.9081	−0.670979
$636$	−6.97046	−0.276397
$637$	0	0
$638$	56.1570	2.22328
$639$	1.81594	0.0718374
$640$	−1.19806	−0.0473576
$641$	−1.71618	−0.0677852	−0.0338926	−	0.999425i	$-0.510790\pi$
$641$	−1.71618	−0.0677852	−0.0338926	+	0.999425i	$0.510790\pi$
$642$	−26.2030	−1.03415
$643$	−10.7278	−0.423063	−0.211531	−	0.977371i	$-0.567845\pi$
$643$	−10.7278	−0.423063	−0.211531	+	0.977371i	$0.567845\pi$
$644$	−2.69202	−0.106081
$645$	2.67111	0.105175
$646$	−46.7851	−1.84073
$647$	−41.1377	−1.61729	−0.808644	−	0.588298i	$-0.799798\pi$
$647$	−41.1377	−1.61729	−0.808644	+	0.588298i	$0.799798\pi$
$648$	−4.18060	−0.164230
$649$	32.8635	1.29001
$650$	0	0
$651$	8.55927	0.335464
$652$	0.571352	0.0223759
$653$	−20.5985	−0.806082	−0.403041	−	0.915182i	$-0.632047\pi$
$653$	−20.5985	−0.806082	−0.403041	+	0.915182i	$0.632047\pi$
$654$	4.99330	0.195253
$655$	−2.32304	−0.0907688
$656$	8.78986	0.343186
$657$	1.69979	0.0663152
$658$	5.55496	0.216555
$659$	0.0639828	0.00249242	0.00124621	−	0.999999i	$-0.499603\pi$
$659$	0.0639828	0.00249242	0.00124621	+	0.999999i	$0.499603\pi$
$660$	9.83340	0.382764
$661$	34.0944	1.32612	0.663059	−	0.748567i	$-0.269258\pi$
$661$	34.0944	1.32612	0.663059	+	0.748567i	$0.269258\pi$
$662$	16.5646	0.643803
$663$	0	0
$664$	−11.7778	−0.457066
$665$	−8.20775	−0.318283
$666$	−10.3134	−0.399634
$667$	−24.9922	−0.967703
$668$	11.9269	0.461466
$669$	−27.5730	−1.06603
$670$	2.61250	0.100930
$671$	−23.4252	−0.904319
$672$	−1.35690	−0.0523434
$673$	−4.37627	−0.168693	−0.0843465	−	0.996436i	$-0.526880\pi$
$673$	−4.37627	−0.168693	−0.0843465	+	0.996436i	$0.526880\pi$
$674$	−6.54288	−0.252022
$675$	20.1157	0.774253
$676$	0	0
$677$	41.5967	1.59869	0.799345	−	0.600872i	$-0.205180\pi$
$677$	41.5967	1.59869	0.799345	+	0.600872i	$0.205180\pi$
$678$	17.8756	0.686509
$679$	−7.30798	−0.280454
$680$	−8.18167	−0.313753
$681$	12.7036	0.486804
$682$	38.1564	1.46109
$683$	3.41683	0.130741	0.0653707	−	0.997861i	$-0.479177\pi$
$683$	3.41683	0.130741	0.0653707	+	0.997861i	$0.479177\pi$
$684$	7.93900	0.303555
$685$	5.10620	0.195098
$686$	−1.00000	−0.0381802
$687$	−18.5714	−0.708541
$688$	−1.64310	−0.0626428
$689$	0	0
$690$	−4.37627	−0.166602
$691$	−40.5153	−1.54127	−0.770636	−	0.637275i	$-0.780062\pi$
$691$	−40.5153	−1.54127	−0.770636	+	0.637275i	$0.780062\pi$
$692$	−11.4993	−0.437139
$693$	−7.00969	−0.266276
$694$	6.55496	0.248823
$695$	−20.3526	−0.772018
$696$	−12.5972	−0.477495
$697$	60.0267	2.27367
$698$	−19.9782	−0.756187
$699$	−16.7948	−0.635236
$700$	3.56465	0.134731
$701$	39.1608	1.47908	0.739541	−	0.673112i	$-0.235043\pi$
$701$	39.1608	1.47908	0.739541	+	0.673112i	$0.235043\pi$
$702$	0	0
$703$	−60.9711	−2.29957
$704$	−6.04892	−0.227977
$705$	9.03039	0.340104
$706$	8.10560	0.305058
$707$	−6.58211	−0.247546
$708$	−7.37196	−0.277055
$709$	−16.5453	−0.621371	−0.310685	−	0.950513i	$-0.600559\pi$
$709$	−16.5453	−0.621371	−0.310685	+	0.950513i	$0.600559\pi$
$710$	1.87741	0.0704580
$711$	12.1013	0.453834
$712$	−1.91185	−0.0716498
$713$	−16.9812	−0.635951
$714$	−9.26636	−0.346785
$715$	0	0
$716$	16.6775	0.623269
$717$	40.6799	1.51922
$718$	9.16315	0.341966
$719$	25.0767	0.935201	0.467601	−	0.883940i	$-0.345119\pi$
$719$	25.0767	0.935201	0.467601	+	0.883940i	$0.345119\pi$
$720$	1.38835	0.0517409
$721$	−5.16852	−0.192486
$722$	27.9342	1.03960
$723$	−30.3196	−1.12760
$724$	−10.0543	−0.373665
$725$	33.0935	1.22906
$726$	34.7222	1.28866
$727$	−40.4620	−1.50065	−0.750327	−	0.661067i	$-0.770104\pi$
$727$	−40.4620	−1.50065	−0.750327	+	0.661067i	$0.770104\pi$
$728$	0	0
$729$	27.8159	1.03022
$730$	1.75733	0.0650418
$731$	−11.2209	−0.415020
$732$	5.25475	0.194221
$733$	−50.8654	−1.87876	−0.939379	−	0.342880i	$-0.888597\pi$
$733$	−50.8654	−1.87876	−0.939379	+	0.342880i	$0.888597\pi$
$734$	2.67456	0.0987199
$735$	−1.62565	−0.0599628
$736$	2.69202	0.0992292
$737$	13.1903	0.485871
$738$	−10.1860	−0.374951
$739$	−23.4601	−0.862994	−0.431497	−	0.902114i	$-0.642014\pi$
$739$	−23.4601	−0.862994	−0.431497	+	0.902114i	$0.642014\pi$
$740$	−10.6625	−0.391961
$741$	0	0
$742$	5.13706	0.188588
$743$	−0.706496	−0.0259188	−0.0129594	−	0.999916i	$-0.504125\pi$
$743$	−0.706496	−0.0259188	−0.0129594	+	0.999916i	$0.504125\pi$
$744$	−8.55927	−0.313798
$745$	−4.99702	−0.183077
$746$	−11.6165	−0.425312
$747$	13.6485	0.499372
$748$	−41.3086	−1.51039
$749$	19.3110	0.705607
$750$	13.9231	0.508399
$751$	−13.9855	−0.510339	−0.255170	−	0.966896i	$-0.582131\pi$
$751$	−13.9855	−0.510339	−0.255170	+	0.966896i	$0.582131\pi$
$752$	−5.55496	−0.202568
$753$	−17.3217	−0.631238
$754$	0	0
$755$	−1.04546	−0.0380482
$756$	5.64310	0.205238
$757$	18.1927	0.661224	0.330612	−	0.943767i	$-0.392745\pi$
$757$	18.1927	0.661224	0.330612	+	0.943767i	$0.392745\pi$
$758$	2.76271	0.100346
$759$	−22.0954	−0.802014
$760$	8.20775	0.297726
$761$	−33.7222	−1.22243	−0.611214	−	0.791466i	$-0.709318\pi$
$761$	−33.7222	−1.22243	−0.611214	+	0.791466i	$0.709318\pi$
$762$	19.1497	0.693722
$763$	−3.67994	−0.133223
$764$	17.1075	0.618928
$765$	9.48119	0.342793
$766$	16.8877	0.610177
$767$	0	0
$768$	1.35690	0.0489628
$769$	22.7356	0.819865	0.409933	−	0.912116i	$-0.365552\pi$
$769$	22.7356	0.819865	0.409933	+	0.912116i	$0.365552\pi$
$770$	−7.24698	−0.261163
$771$	−6.78123	−0.244220
$772$	−12.2687	−0.441562
$773$	−1.06744	−0.0383932	−0.0191966	−	0.999816i	$-0.506111\pi$
$773$	−1.06744	−0.0383932	−0.0191966	+	0.999816i	$0.506111\pi$
$774$	1.90408	0.0684409
$775$	22.4857	0.807711
$776$	7.30798	0.262341
$777$	−12.0761	−0.433226
$778$	−4.07739	−0.146182
$779$	−60.2180	−2.15753
$780$	0	0
$781$	9.47889	0.339181
$782$	18.3840	0.657412
$783$	52.3895	1.87225
$784$	1.00000	0.0357143
$785$	22.8270	0.814729
$786$	2.63102	0.0938455
$787$	47.4379	1.69098	0.845489	−	0.533993i	$-0.179309\pi$
$787$	47.4379	1.69098	0.845489	+	0.533993i	$0.179309\pi$
$788$	14.0043	0.498883
$789$	−7.84164	−0.279170
$790$	12.5109	0.445119
$791$	−13.1739	−0.468410
$792$	7.00969	0.249078
$793$	0	0
$794$	4.46548	0.158474
$795$	8.35105	0.296181
$796$	−0.188374	−0.00667672
$797$	−36.0170	−1.27579	−0.637894	−	0.770125i	$-0.720194\pi$
$797$	−36.0170	−1.27579	−0.637894	+	0.770125i	$0.720194\pi$
$798$	9.29590	0.329071
$799$	−37.9353	−1.34205
$800$	−3.56465	−0.126029
$801$	2.21552	0.0782816
$802$	28.2349	0.997009
$803$	8.87263	0.313108
$804$	−2.95885	−0.104351
$805$	3.22521	0.113674
$806$	0	0
$807$	−29.8043	−1.04916
$808$	6.58211	0.231558
$809$	−43.8447	−1.54150	−0.770750	−	0.637138i	$-0.780118\pi$
$809$	−43.8447	−1.54150	−0.770750	+	0.637138i	$0.780118\pi$
$810$	5.00862	0.175985
$811$	39.7101	1.39441	0.697205	−	0.716872i	$-0.254427\pi$
$811$	39.7101	1.39441	0.697205	+	0.716872i	$0.254427\pi$
$812$	9.28382	0.325798
$813$	−19.9724	−0.700462
$814$	−53.8340	−1.88688
$815$	−0.684515	−0.0239775
$816$	9.26636	0.324387
$817$	11.2567	0.393821
$818$	−22.7004	−0.793700
$819$	0	0
$820$	−10.5308	−0.367751
$821$	−33.1366	−1.15647	−0.578237	−	0.815869i	$-0.696259\pi$
$821$	−33.1366	−1.15647	−0.578237	+	0.815869i	$0.696259\pi$
$822$	−5.78315	−0.201711
$823$	−32.2495	−1.12415	−0.562073	−	0.827087i	$-0.689996\pi$
$823$	−32.2495	−1.12415	−0.562073	+	0.827087i	$0.689996\pi$
$824$	5.16852	0.180054
$825$	29.2577	1.01862
$826$	5.43296	0.189037
$827$	4.41119	0.153392	0.0766961	−	0.997055i	$-0.475563\pi$
$827$	4.41119	0.153392	0.0766961	+	0.997055i	$0.475563\pi$
$828$	−3.11960	−0.108414
$829$	−51.0465	−1.77292	−0.886460	−	0.462806i	$-0.846843\pi$
$829$	−51.0465	−1.77292	−0.886460	+	0.462806i	$0.846843\pi$
$830$	14.1105	0.489783
$831$	−3.13574	−0.108777
$832$	0	0
$833$	6.82908	0.236614
$834$	23.0508	0.798185
$835$	−14.2892	−0.494498
$836$	41.4403	1.43324
$837$	35.5966	1.23040
$838$	14.1933	0.490299
$839$	−0.256668	−0.00886117	−0.00443059	−	0.999990i	$-0.501410\pi$
$839$	−0.256668	−0.00886117	−0.00443059	+	0.999990i	$0.501410\pi$
$840$	1.62565	0.0560901
$841$	57.1892	1.97204
$842$	−30.7899	−1.06109
$843$	44.4819	1.53204
$844$	−10.2131	−0.351550
$845$	0	0
$846$	6.43727	0.221318
$847$	−25.5894	−0.879262
$848$	−5.13706	−0.176407
$849$	−2.55735	−0.0877681
$850$	−24.3433	−0.834967
$851$	23.9584	0.821283
$852$	−2.12631	−0.0728462
$853$	29.5217	1.01080	0.505402	−	0.862884i	$-0.331344\pi$
$853$	29.5217	1.01080	0.505402	+	0.862884i	$0.331344\pi$
$854$	−3.87263	−0.132519
$855$	−9.51142	−0.325284
$856$	−19.3110	−0.660035
$857$	42.6534	1.45701	0.728506	−	0.685040i	$-0.240215\pi$
$857$	42.6534	1.45701	0.728506	+	0.685040i	$0.240215\pi$
$858$	0	0
$859$	−46.3430	−1.58120	−0.790602	−	0.612331i	$-0.790232\pi$
$859$	−46.3430	−1.58120	−0.790602	+	0.612331i	$0.790232\pi$
$860$	1.96854	0.0671267
$861$	−11.9269	−0.406468
$862$	−24.4456	−0.832622
$863$	−12.4397	−0.423451	−0.211726	−	0.977329i	$-0.567908\pi$
$863$	−12.4397	−0.423451	−0.211726	+	0.977329i	$0.567908\pi$
$864$	−5.64310	−0.191982
$865$	13.7769	0.468429
$866$	−18.5633	−0.630807
$867$	40.2135	1.36572
$868$	6.30798	0.214107
$869$	63.1667	2.14278
$870$	15.0922	0.511673
$871$	0	0
$872$	3.67994	0.124618
$873$	−8.46873	−0.286623
$874$	−18.4426	−0.623832
$875$	−10.2610	−0.346884
$876$	−1.99031	−0.0672464
$877$	−19.3752	−0.654254	−0.327127	−	0.944980i	$-0.606081\pi$
$877$	−19.3752	−0.654254	−0.327127	+	0.944980i	$0.606081\pi$
$878$	−14.7748	−0.498625
$879$	1.45426	0.0490509
$880$	7.24698	0.244296
$881$	−10.3314	−0.348074	−0.174037	−	0.984739i	$-0.555681\pi$
$881$	−10.3314	−0.348074	−0.174037	+	0.984739i	$0.555681\pi$
$882$	−1.15883	−0.0390200
$883$	29.6142	0.996596	0.498298	−	0.867006i	$-0.333959\pi$
$883$	29.6142	0.996596	0.498298	+	0.867006i	$0.333959\pi$
$884$	0	0
$885$	8.83207	0.296887
$886$	−27.1588	−0.912419
$887$	−18.0696	−0.606719	−0.303359	−	0.952876i	$-0.598108\pi$
$887$	−18.0696	−0.606719	−0.303359	+	0.952876i	$0.598108\pi$
$888$	12.0761	0.405246
$889$	−14.1129	−0.473331
$890$	2.29052	0.0767784
$891$	25.2881	0.847184
$892$	−20.3207	−0.680386
$893$	38.0562	1.27350
$894$	5.65950	0.189282
$895$	−19.9807	−0.667882
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	24.1521	0.805967
$899$	58.5621	1.95316
$900$	4.13083	0.137694
$901$	−35.0814	−1.16873
$902$	−53.1691	−1.77034
$903$	2.22952	0.0741938
$904$	13.1739	0.438157
$905$	12.0457	0.400412
$906$	1.18406	0.0393378
$907$	32.8549	1.09093	0.545465	−	0.838134i	$-0.316353\pi$
$907$	32.8549	1.09093	0.545465	+	0.838134i	$0.316353\pi$
$908$	9.36227	0.310698
$909$	−7.62756	−0.252990
$910$	0	0
$911$	−14.6039	−0.483848	−0.241924	−	0.970295i	$-0.577778\pi$
$911$	−14.6039	−0.483848	−0.241924	+	0.970295i	$0.577778\pi$
$912$	−9.29590	−0.307818
$913$	71.2428	2.35779
$914$	11.4470	0.378632
$915$	−6.29552	−0.208123
$916$	−13.6866	−0.452219
$917$	−1.93900	−0.0640315
$918$	−38.5372	−1.27192
$919$	−17.2222	−0.568109	−0.284054	−	0.958808i	$-0.591680\pi$
$919$	−17.2222	−0.568109	−0.284054	+	0.958808i	$0.591680\pi$
$920$	−3.22521	−0.106332
$921$	−30.4097	−1.00203
$922$	−17.1728	−0.565557
$923$	0	0
$924$	8.20775	0.270015
$925$	−31.7245	−1.04310
$926$	−8.36360	−0.274845
$927$	−5.98946	−0.196720
$928$	−9.28382	−0.304756
$929$	−0.510353	−0.0167441	−0.00837206	−	0.999965i	$-0.502665\pi$
$929$	−0.510353	−0.0167441	−0.00837206	+	0.999965i	$0.502665\pi$
$930$	10.2545	0.336260
$931$	−6.85086	−0.224528
$932$	−12.3773	−0.405433
$933$	−14.9259	−0.488651
$934$	4.05621	0.132723
$935$	49.4902	1.61850
$936$	0	0
$937$	−19.4776	−0.636304	−0.318152	−	0.948040i	$-0.603062\pi$
$937$	−19.4776	−0.636304	−0.318152	+	0.948040i	$0.603062\pi$
$938$	2.18060	0.0711992
$939$	−9.43514	−0.307904
$940$	6.65519	0.217068
$941$	−41.4392	−1.35088	−0.675440	−	0.737415i	$-0.736046\pi$
$941$	−41.4392	−1.35088	−0.675440	+	0.737415i	$0.736046\pi$
$942$	−25.8532	−0.842344
$943$	23.6625	0.770556
$944$	−5.43296	−0.176828
$945$	−6.76079	−0.219929
$946$	9.93900	0.323145
$947$	19.8103	0.643748	0.321874	−	0.946782i	$-0.395687\pi$
$947$	19.8103	0.643748	0.321874	+	0.946782i	$0.395687\pi$
$948$	−14.1696	−0.460207
$949$	0	0
$950$	24.4209	0.792318
$951$	−24.8151	−0.804684
$952$	−6.82908	−0.221332
$953$	10.0392	0.325203	0.162601	−	0.986692i	$-0.448012\pi$
$953$	10.0392	0.325203	0.162601	+	0.986692i	$0.448012\pi$
$954$	5.95300	0.192736
$955$	−20.4959	−0.663231
$956$	29.9801	0.969627
$957$	76.1992	2.46317
$958$	1.79225	0.0579049
$959$	4.26205	0.137629
$960$	−1.62565	−0.0524675
$961$	8.79059	0.283568
$962$	0	0
$963$	22.3782	0.721127
$964$	−22.3448	−0.719678
$965$	14.6987	0.473169
$966$	−3.65279	−0.117527
$967$	−58.6540	−1.88618	−0.943092	−	0.332531i	$-0.892097\pi$
$967$	−58.6540	−1.88618	−0.943092	+	0.332531i	$0.892097\pi$
$968$	25.5894	0.822474
$969$	−63.4825	−2.03935
$970$	−8.75541	−0.281119
$971$	−10.1599	−0.326047	−0.163023	−	0.986622i	$-0.552125\pi$
$971$	−10.1599	−0.326047	−0.163023	+	0.986622i	$0.552125\pi$
$972$	11.2567	0.361058
$973$	−16.9879	−0.544608
$974$	−9.83579	−0.315159
$975$	0	0
$976$	3.87263	0.123960
$977$	−16.0810	−0.514476	−0.257238	−	0.966348i	$-0.582812\pi$
$977$	−16.0810	−0.514476	−0.257238	+	0.966348i	$0.582812\pi$
$978$	0.775265	0.0247902
$979$	11.5646	0.369608
$980$	−1.19806	−0.0382707
$981$	−4.26444	−0.136153
$982$	−4.21983	−0.134660
$983$	−48.4946	−1.54674	−0.773368	−	0.633957i	$-0.781429\pi$
$983$	−48.4946	−1.54674	−0.773368	+	0.633957i	$0.781429\pi$
$984$	11.9269	0.380216
$985$	−16.7780	−0.534593
$986$	−63.4000	−2.01907
$987$	7.53750	0.239921
$988$	0	0
$989$	−4.42327	−0.140652
$990$	−8.39804	−0.266907
$991$	−6.69335	−0.212621	−0.106311	−	0.994333i	$-0.533904\pi$
$991$	−6.69335	−0.212621	−0.106311	+	0.994333i	$0.533904\pi$
$992$	−6.30798	−0.200279
$993$	22.4765	0.713270
$994$	1.56704	0.0497035
$995$	0.225683	0.00715464
$996$	−15.9812	−0.506384
$997$	−55.6738	−1.76321	−0.881604	−	0.471990i	$-0.843536\pi$
$997$	−55.6738	−1.76321	−0.881604	+	0.471990i	$0.843536\pi$
$998$	5.44696	0.172421
$999$	−50.2223	−1.58896

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bb.1.2	yes	3
13.5	odd	4		2366.2.d.o.337.2		6
13.8	odd	4		2366.2.d.o.337.5		6
13.12	even	2		2366.2.a.w.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.w.1.2	✓	3	13.12	even	2
2366.2.a.bb.1.2	yes	3	1.1	even	1	trivial
2366.2.d.o.337.2		6	13.5	odd	4
2366.2.d.o.337.5		6	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.35690 q^{3} +1.00000 q^{4} -1.19806 q^{5} +1.35690 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.15883 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.35690 q^{3} +1.00000 q^{4} -1.19806 q^{5} +1.35690 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.15883 q^{9} -1.19806 q^{10} -6.04892 q^{11} +1.35690 q^{12} -1.00000 q^{14} -1.62565 q^{15} +1.00000 q^{16} +6.82908 q^{17} -1.15883 q^{18} -6.85086 q^{19} -1.19806 q^{20} -1.35690 q^{21} -6.04892 q^{22} +2.69202 q^{23} +1.35690 q^{24} -3.56465 q^{25} -5.64310 q^{27} -1.00000 q^{28} -9.28382 q^{29} -1.62565 q^{30} -6.30798 q^{31} +1.00000 q^{32} -8.20775 q^{33} +6.82908 q^{34} +1.19806 q^{35} -1.15883 q^{36} +8.89977 q^{37} -6.85086 q^{38} -1.19806 q^{40} +8.78986 q^{41} -1.35690 q^{42} -1.64310 q^{43} -6.04892 q^{44} +1.38835 q^{45} +2.69202 q^{46} -5.55496 q^{47} +1.35690 q^{48} +1.00000 q^{49} -3.56465 q^{50} +9.26636 q^{51} -5.13706 q^{53} -5.64310 q^{54} +7.24698 q^{55} -1.00000 q^{56} -9.29590 q^{57} -9.28382 q^{58} -5.43296 q^{59} -1.62565 q^{60} +3.87263 q^{61} -6.30798 q^{62} +1.15883 q^{63} +1.00000 q^{64} -8.20775 q^{66} -2.18060 q^{67} +6.82908 q^{68} +3.65279 q^{69} +1.19806 q^{70} -1.56704 q^{71} -1.15883 q^{72} -1.46681 q^{73} +8.89977 q^{74} -4.83685 q^{75} -6.85086 q^{76} +6.04892 q^{77} -10.4426 q^{79} -1.19806 q^{80} -4.18060 q^{81} +8.78986 q^{82} -11.7778 q^{83} -1.35690 q^{84} -8.18167 q^{85} -1.64310 q^{86} -12.5972 q^{87} -6.04892 q^{88} -1.91185 q^{89} +1.38835 q^{90} +2.69202 q^{92} -8.55927 q^{93} -5.55496 q^{94} +8.20775 q^{95} +1.35690 q^{96} +7.30798 q^{97} +1.00000 q^{98} +7.00969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 8 q^{5} - 3 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 8 * q^5 - 3 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 8 q^{5} - 3 q^{7} + 3 q^{8} + 5 q^{9} - 8 q^{10} - 9 q^{11} - 3 q^{14} + 7 q^{15} + 3 q^{16} + 10 q^{17} + 5 q^{18} - 7 q^{19} - 8 q^{20} - 9 q^{22} + 3 q^{23} + 11 q^{25} - 21 q^{27} - 3 q^{28} + 5 q^{29} + 7 q^{30} - 24 q^{31} + 3 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{35} + 5 q^{36} + 4 q^{37} - 7 q^{38} - 8 q^{40} + 3 q^{41} - 9 q^{43} - 9 q^{44} - 25 q^{45} + 3 q^{46} - 17 q^{47} + 3 q^{49} + 11 q^{50} - 21 q^{51} - 10 q^{53} - 21 q^{54} + 17 q^{55} - 3 q^{56} - 14 q^{57} + 5 q^{58} + 3 q^{59} + 7 q^{60} - 5 q^{61} - 24 q^{62} - 5 q^{63} + 3 q^{64} - 7 q^{66} + 5 q^{67} + 10 q^{68} - 7 q^{69} + 8 q^{70} - 24 q^{71} + 5 q^{72} - q^{73} + 4 q^{74} - 42 q^{75} - 7 q^{76} + 9 q^{77} + 10 q^{79} - 8 q^{80} - q^{81} + 3 q^{82} + 7 q^{83} - 29 q^{85} - 9 q^{86} - 7 q^{87} - 9 q^{88} - 2 q^{89} - 25 q^{90} + 3 q^{92} - 7 q^{93} - 17 q^{94} + 7 q^{95} + 27 q^{97} + 3 q^{98} - q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 8 * q^5 - 3 * q^7 + 3 * q^8 + 5 * q^9 - 8 * q^10 - 9 * q^11 - 3 * q^14 + 7 * q^15 + 3 * q^16 + 10 * q^17 + 5 * q^18 - 7 * q^19 - 8 * q^20 - 9 * q^22 + 3 * q^23 + 11 * q^25 - 21 * q^27 - 3 * q^28 + 5 * q^29 + 7 * q^30 - 24 * q^31 + 3 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^35 + 5 * q^36 + 4 * q^37 - 7 * q^38 - 8 * q^40 + 3 * q^41 - 9 * q^43 - 9 * q^44 - 25 * q^45 + 3 * q^46 - 17 * q^47 + 3 * q^49 + 11 * q^50 - 21 * q^51 - 10 * q^53 - 21 * q^54 + 17 * q^55 - 3 * q^56 - 14 * q^57 + 5 * q^58 + 3 * q^59 + 7 * q^60 - 5 * q^61 - 24 * q^62 - 5 * q^63 + 3 * q^64 - 7 * q^66 + 5 * q^67 + 10 * q^68 - 7 * q^69 + 8 * q^70 - 24 * q^71 + 5 * q^72 - q^73 + 4 * q^74 - 42 * q^75 - 7 * q^76 + 9 * q^77 + 10 * q^79 - 8 * q^80 - q^81 + 3 * q^82 + 7 * q^83 - 29 * q^85 - 9 * q^86 - 7 * q^87 - 9 * q^88 - 2 * q^89 - 25 * q^90 + 3 * q^92 - 7 * q^93 - 17 * q^94 + 7 * q^95 + 27 * q^97 + 3 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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