LMFDB - Embedded newform 9295.2.a.bh.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9295,2,Mod(1,9295)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9295, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9295.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9295 = 5 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9295.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:	$74.2209486788$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	9295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.140494 q^{2} +1.29629 q^{3} -1.98026 q^{4} +1.00000 q^{5} +0.182121 q^{6} +4.03393 q^{7} -0.559204 q^{8} -1.31963 q^{9} +O(q^{10})$	\(q+0.140494 q^{2} +1.29629 q^{3} -1.98026 q^{4} +1.00000 q^{5} +0.182121 q^{6} +4.03393 q^{7} -0.559204 q^{8} -1.31963 q^{9} +0.140494 q^{10} -1.00000 q^{11} -2.56699 q^{12} +0.566744 q^{14} +1.29629 q^{15} +3.88196 q^{16} +1.47921 q^{17} -0.185400 q^{18} +0.0361554 q^{19} -1.98026 q^{20} +5.22914 q^{21} -0.140494 q^{22} -0.964365 q^{23} -0.724890 q^{24} +1.00000 q^{25} -5.59950 q^{27} -7.98824 q^{28} +3.63260 q^{29} +0.182121 q^{30} -0.326459 q^{31} +1.66380 q^{32} -1.29629 q^{33} +0.207820 q^{34} +4.03393 q^{35} +2.61321 q^{36} +9.09484 q^{37} +0.00507963 q^{38} -0.559204 q^{40} -10.4713 q^{41} +0.734664 q^{42} +8.17151 q^{43} +1.98026 q^{44} -1.31963 q^{45} -0.135488 q^{46} -6.95718 q^{47} +5.03215 q^{48} +9.27259 q^{49} +0.140494 q^{50} +1.91749 q^{51} +12.3702 q^{53} -0.786697 q^{54} -1.00000 q^{55} -2.25579 q^{56} +0.0468679 q^{57} +0.510359 q^{58} +6.41881 q^{59} -2.56699 q^{60} +6.05128 q^{61} -0.0458656 q^{62} -5.32330 q^{63} -7.53016 q^{64} -0.182121 q^{66} -14.0232 q^{67} -2.92922 q^{68} -1.25010 q^{69} +0.566744 q^{70} -10.3449 q^{71} +0.737942 q^{72} +10.5177 q^{73} +1.27777 q^{74} +1.29629 q^{75} -0.0715972 q^{76} -4.03393 q^{77} -17.1575 q^{79} +3.88196 q^{80} -3.29968 q^{81} -1.47116 q^{82} +11.0221 q^{83} -10.3551 q^{84} +1.47921 q^{85} +1.14805 q^{86} +4.70890 q^{87} +0.559204 q^{88} +15.3854 q^{89} -0.185400 q^{90} +1.90969 q^{92} -0.423186 q^{93} -0.977443 q^{94} +0.0361554 q^{95} +2.15677 q^{96} +1.24365 q^{97} +1.30274 q^{98} +1.31963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 8 q^{2} + 20 q^{4} + 27 q^{5} - 8 q^{6} + 6 q^{7} + 21 q^{8} + 23 q^{9}+O(q^{10}) $ 27 * q + 8 * q^2 + 20 * q^4 + 27 * q^5 - 8 * q^6 + 6 * q^7 + 21 * q^8 + 23 * q^9	\( 27 q + 8 q^{2} + 20 q^{4} + 27 q^{5} - 8 q^{6} + 6 q^{7} + 21 q^{8} + 23 q^{9} + 8 q^{10} - 27 q^{11} + 2 q^{12} - 11 q^{14} + 2 q^{16} + 13 q^{17} + 28 q^{18} + 8 q^{19} + 20 q^{20} + 23 q^{21} - 8 q^{22} - 9 q^{23} + 16 q^{24} + 27 q^{25} + 6 q^{27} - 7 q^{28} - 5 q^{29} - 8 q^{30} + 23 q^{31} + 5 q^{32} + 49 q^{34} + 6 q^{35} + 18 q^{36} + 16 q^{37} + 28 q^{38} + 21 q^{40} + 54 q^{41} - 7 q^{42} + 8 q^{43} - 20 q^{44} + 23 q^{45} + 31 q^{46} - 4 q^{47} + 58 q^{48} + 5 q^{49} + 8 q^{50} - 13 q^{51} + 11 q^{53} - 26 q^{54} - 27 q^{55} - 12 q^{56} + 30 q^{57} + 15 q^{58} + 42 q^{59} + 2 q^{60} + 12 q^{61} + 46 q^{62} - 14 q^{63} - 15 q^{64} + 8 q^{66} + 24 q^{67} + 34 q^{68} - 36 q^{69} - 11 q^{70} + 49 q^{71} + 74 q^{72} + 45 q^{73} + 26 q^{74} - 18 q^{76} - 6 q^{77} - 2 q^{79} + 2 q^{80} - 33 q^{81} - 32 q^{82} + 60 q^{83} + 57 q^{84} + 13 q^{85} + 53 q^{86} + 64 q^{87} - 21 q^{88} + 59 q^{89} + 28 q^{90} + 29 q^{92} + 2 q^{93} - 32 q^{94} + 8 q^{95} + 77 q^{96} + 18 q^{97} + 16 q^{98} - 23 q^{99}+O(q^{100}) \) 27 * q + 8 * q^2 + 20 * q^4 + 27 * q^5 - 8 * q^6 + 6 * q^7 + 21 * q^8 + 23 * q^9 + 8 * q^10 - 27 * q^11 + 2 * q^12 - 11 * q^14 + 2 * q^16 + 13 * q^17 + 28 * q^18 + 8 * q^19 + 20 * q^20 + 23 * q^21 - 8 * q^22 - 9 * q^23 + 16 * q^24 + 27 * q^25 + 6 * q^27 - 7 * q^28 - 5 * q^29 - 8 * q^30 + 23 * q^31 + 5 * q^32 + 49 * q^34 + 6 * q^35 + 18 * q^36 + 16 * q^37 + 28 * q^38 + 21 * q^40 + 54 * q^41 - 7 * q^42 + 8 * q^43 - 20 * q^44 + 23 * q^45 + 31 * q^46 - 4 * q^47 + 58 * q^48 + 5 * q^49 + 8 * q^50 - 13 * q^51 + 11 * q^53 - 26 * q^54 - 27 * q^55 - 12 * q^56 + 30 * q^57 + 15 * q^58 + 42 * q^59 + 2 * q^60 + 12 * q^61 + 46 * q^62 - 14 * q^63 - 15 * q^64 + 8 * q^66 + 24 * q^67 + 34 * q^68 - 36 * q^69 - 11 * q^70 + 49 * q^71 + 74 * q^72 + 45 * q^73 + 26 * q^74 - 18 * q^76 - 6 * q^77 - 2 * q^79 + 2 * q^80 - 33 * q^81 - 32 * q^82 + 60 * q^83 + 57 * q^84 + 13 * q^85 + 53 * q^86 + 64 * q^87 - 21 * q^88 + 59 * q^89 + 28 * q^90 + 29 * q^92 + 2 * q^93 - 32 * q^94 + 8 * q^95 + 77 * q^96 + 18 * q^97 + 16 * q^98 - 23 * 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 $

$2$	0.140494	0.0993444	0.0496722	−	0.998766i	$-0.484182\pi$
$2$	0.140494	0.0993444	0.0496722	+	0.998766i	$0.484182\pi$
$3$	1.29629	0.748414	0.374207	−	0.927345i	$-0.377915\pi$
$3$	1.29629	0.748414	0.374207	+	0.927345i	$0.377915\pi$
$4$	−1.98026	−0.990131
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.182121	0.0743507
$7$	4.03393	1.52468	0.762341	−	0.647175i	$-0.224050\pi$
$7$	4.03393	1.52468	0.762341	+	0.647175i	$0.224050\pi$
$8$	−0.559204	−0.197708
$9$	−1.31963	−0.439877
$10$	0.140494	0.0444282
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.56699	−0.741027
$13$	0	0
$13$	0	0
$14$	0.566744	0.151469
$15$	1.29629	0.334701
$16$	3.88196	0.970489
$17$	1.47921	0.358761	0.179381	−	0.983780i	$-0.442591\pi$
$17$	1.47921	0.358761	0.179381	+	0.983780i	$0.442591\pi$
$18$	−0.185400	−0.0436993
$19$	0.0361554	0.00829462	0.00414731	−	0.999991i	$-0.498680\pi$
$19$	0.0361554	0.00829462	0.00414731	+	0.999991i	$0.498680\pi$
$20$	−1.98026	−0.442800
$21$	5.22914	1.14109
$22$	−0.140494	−0.0299535
$23$	−0.964365	−0.201084	−0.100542	−	0.994933i	$-0.532058\pi$
$23$	−0.964365	−0.201084	−0.100542	+	0.994933i	$0.532058\pi$
$24$	−0.724890	−0.147968
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.59950	−1.07762
$28$	−7.98824	−1.50963
$29$	3.63260	0.674556	0.337278	−	0.941405i	$-0.390494\pi$
$29$	3.63260	0.674556	0.337278	+	0.941405i	$0.390494\pi$
$30$	0.182121	0.0332506
$31$	−0.326459	−0.0586338	−0.0293169	−	0.999570i	$-0.509333\pi$
$31$	−0.326459	−0.0586338	−0.0293169	+	0.999570i	$0.509333\pi$
$32$	1.66380	0.294121
$33$	−1.29629	−0.225655
$34$	0.207820	0.0356409
$35$	4.03393	0.681859
$36$	2.61321	0.435536
$37$	9.09484	1.49518	0.747591	−	0.664159i	$-0.231210\pi$
$37$	9.09484	1.49518	0.747591	+	0.664159i	$0.231210\pi$
$38$	0.00507963	0.000824024 0
$39$	0	0
$40$	−0.559204	−0.0884178
$41$	−10.4713	−1.63535	−0.817674	−	0.575681i	$-0.804737\pi$
$41$	−10.4713	−1.63535	−0.817674	+	0.575681i	$0.804737\pi$
$42$	0.734664	0.113361
$43$	8.17151	1.24614	0.623072	−	0.782165i	$-0.285884\pi$
$43$	8.17151	1.24614	0.623072	+	0.782165i	$0.285884\pi$
$44$	1.98026	0.298536
$45$	−1.31963	−0.196719
$46$	−0.135488	−0.0199766
$47$	−6.95718	−1.01481	−0.507404	−	0.861708i	$-0.669395\pi$
$47$	−6.95718	−1.01481	−0.507404	+	0.861708i	$0.669395\pi$
$48$	5.03215	0.726328
$49$	9.27259	1.32466
$50$	0.140494	0.0198689
$51$	1.91749	0.268502
$52$	0	0
$53$	12.3702	1.69917	0.849586	−	0.527449i	$-0.176852\pi$
$53$	12.3702	1.69917	0.849586	+	0.527449i	$0.176852\pi$
$54$	−0.786697	−0.107056
$55$	−1.00000	−0.134840
$56$	−2.25579	−0.301442
$57$	0.0468679	0.00620781
$58$	0.510359	0.0670134
$59$	6.41881	0.835657	0.417829	−	0.908526i	$-0.362791\pi$
$59$	6.41881	0.835657	0.417829	+	0.908526i	$0.362791\pi$
$60$	−2.56699	−0.331398
$61$	6.05128	0.774787	0.387393	−	0.921914i	$-0.373376\pi$
$61$	6.05128	0.774787	0.387393	+	0.921914i	$0.373376\pi$
$62$	−0.0458656	−0.00582494
$63$	−5.32330	−0.670673
$64$	−7.53016	−0.941270
$65$	0	0
$66$	−0.182121	−0.0224176
$67$	−14.0232	−1.71320	−0.856602	−	0.515978i	$-0.827429\pi$
$67$	−14.0232	−1.71320	−0.856602	+	0.515978i	$0.827429\pi$
$68$	−2.92922	−0.355220
$69$	−1.25010	−0.150494
$70$	0.566744	0.0677388
$71$	−10.3449	−1.22771	−0.613855	−	0.789419i	$-0.710382\pi$
$71$	−10.3449	−1.22771	−0.613855	+	0.789419i	$0.710382\pi$
$72$	0.737942	0.0869673
$73$	10.5177	1.23100	0.615502	−	0.788135i	$-0.288953\pi$
$73$	10.5177	1.23100	0.615502	+	0.788135i	$0.288953\pi$
$74$	1.27777	0.148538
$75$	1.29629	0.149683
$76$	−0.0715972	−0.00821276
$77$	−4.03393	−0.459709
$78$	0	0
$79$	−17.1575	−1.93037	−0.965186	−	0.261565i	$-0.915761\pi$
$79$	−17.1575	−1.93037	−0.965186	+	0.261565i	$0.915761\pi$
$80$	3.88196	0.434016
$81$	−3.29968	−0.366631
$82$	−1.47116	−0.162463
$83$	11.0221	1.20983	0.604915	−	0.796290i	$-0.293207\pi$
$83$	11.0221	1.20983	0.604915	+	0.796290i	$0.293207\pi$
$84$	−10.3551	−1.12983
$85$	1.47921	0.160443
$86$	1.14805	0.123797
$87$	4.70890	0.504847
$88$	0.559204	0.0596113
$89$	15.3854	1.63085	0.815426	−	0.578861i	$-0.196502\pi$
$89$	15.3854	1.63085	0.815426	+	0.578861i	$0.196502\pi$
$90$	−0.185400	−0.0195429
$91$	0	0
$92$	1.90969	0.199099
$93$	−0.423186	−0.0438823
$94$	−0.977443	−0.100816
$95$	0.0361554	0.00370947
$96$	2.15677	0.220124
$97$	1.24365	0.126273	0.0631366	−	0.998005i	$-0.479890\pi$
$97$	1.24365	0.126273	0.0631366	+	0.998005i	$0.479890\pi$
$98$	1.30274	0.131597
$99$	1.31963	0.132628
$100$	−1.98026	−0.198026
$101$	7.12383	0.708848	0.354424	−	0.935085i	$-0.384677\pi$
$101$	7.12383	0.708848	0.354424	+	0.935085i	$0.384677\pi$
$102$	0.269395	0.0266741
$103$	−8.48672	−0.836221	−0.418110	−	0.908396i	$-0.637307\pi$
$103$	−8.48672	−0.836221	−0.418110	+	0.908396i	$0.637307\pi$
$104$	0	0
$105$	5.22914	0.510312
$106$	1.73794	0.168803
$107$	2.84252	0.274797	0.137399	−	0.990516i	$-0.456126\pi$
$107$	2.84252	0.274797	0.137399	+	0.990516i	$0.456126\pi$
$108$	11.0885	1.06699
$109$	17.9523	1.71952	0.859759	−	0.510700i	$-0.170614\pi$
$109$	17.9523	1.71952	0.859759	+	0.510700i	$0.170614\pi$
$110$	−0.140494	−0.0133956
$111$	11.7896	1.11902
$112$	15.6595	1.47969
$113$	11.6690	1.09773	0.548863	−	0.835913i	$-0.315061\pi$
$113$	11.6690	1.09773	0.548863	+	0.835913i	$0.315061\pi$
$114$	0.00658467	0.000616711 0
$115$	−0.964365	−0.0899275
$116$	−7.19349	−0.667899
$117$	0	0
$118$	0.901805	0.0830179
$119$	5.96703	0.546996
$120$	−0.724890	−0.0661731
$121$	1.00000	0.0909091
$122$	0.850169	0.0769707
$123$	−13.5739	−1.22392
$124$	0.646474	0.0580551
$125$	1.00000	0.0894427
$126$	−0.747892	−0.0666275
$127$	−6.54566	−0.580834	−0.290417	−	0.956900i	$-0.593794\pi$
$127$	−6.54566	−0.580834	−0.290417	+	0.956900i	$0.593794\pi$
$128$	−4.38554	−0.387631
$129$	10.5927	0.932631
$130$	0	0
$131$	2.09098	0.182690	0.0913449	−	0.995819i	$-0.470883\pi$
$131$	2.09098	0.182690	0.0913449	+	0.995819i	$0.470883\pi$
$132$	2.56699	0.223428
$133$	0.145848	0.0126467
$134$	−1.97017	−0.170197
$135$	−5.59950	−0.481928
$136$	−0.827179	−0.0709300
$137$	12.5045	1.06833	0.534166	−	0.845380i	$-0.320626\pi$
$137$	12.5045	1.06833	0.534166	+	0.845380i	$0.320626\pi$
$138$	−0.175631	−0.0149507
$139$	−4.81086	−0.408051	−0.204026	−	0.978966i	$-0.565403\pi$
$139$	−4.81086	−0.408051	−0.204026	+	0.978966i	$0.565403\pi$
$140$	−7.98824	−0.675129
$141$	−9.01852	−0.759497
$142$	−1.45339	−0.121966
$143$	0	0
$144$	−5.12275	−0.426896
$145$	3.63260	0.301671
$146$	1.47768	0.122293
$147$	12.0200	0.991390
$148$	−18.0102	−1.48043
$149$	16.2210	1.32887	0.664436	−	0.747345i	$-0.268672\pi$
$149$	16.2210	1.32887	0.664436	+	0.747345i	$0.268672\pi$
$150$	0.182121	0.0148701
$151$	−17.8901	−1.45588	−0.727938	−	0.685643i	$-0.759521\pi$
$151$	−17.8901	−1.45588	−0.727938	+	0.685643i	$0.759521\pi$
$152$	−0.0202182	−0.00163992
$153$	−1.95201	−0.157811
$154$	−0.566744	−0.0456695
$155$	−0.326459	−0.0262218
$156$	0	0
$157$	14.7262	1.17528	0.587638	−	0.809124i	$-0.300058\pi$
$157$	14.7262	1.17528	0.587638	+	0.809124i	$0.300058\pi$
$158$	−2.41053	−0.191772
$159$	16.0353	1.27168
$160$	1.66380	0.131535
$161$	−3.89018	−0.306589
$162$	−0.463586	−0.0364228
$163$	12.7983	1.00244	0.501222	−	0.865319i	$-0.332884\pi$
$163$	12.7983	1.00244	0.501222	+	0.865319i	$0.332884\pi$
$164$	20.7360	1.61921
$165$	−1.29629	−0.100916
$166$	1.54854	0.120190
$167$	−9.55131	−0.739103	−0.369551	−	0.929210i	$-0.620489\pi$
$167$	−9.55131	−0.739103	−0.369551	+	0.929210i	$0.620489\pi$
$168$	−2.92416	−0.225604
$169$	0	0
$170$	0.207820	0.0159391
$171$	−0.0477118	−0.00364861
$172$	−16.1817	−1.23385
$173$	−3.61792	−0.275065	−0.137533	−	0.990497i	$-0.543917\pi$
$173$	−3.61792	−0.275065	−0.137533	+	0.990497i	$0.543917\pi$
$174$	0.661573	0.0501537
$175$	4.03393	0.304936
$176$	−3.88196	−0.292614
$177$	8.32064	0.625417
$178$	2.16156	0.162016
$179$	−5.05904	−0.378131	−0.189065	−	0.981965i	$-0.560546\pi$
$179$	−5.05904	−0.378131	−0.189065	+	0.981965i	$0.560546\pi$
$180$	2.61321	0.194777
$181$	−7.75811	−0.576655	−0.288328	−	0.957532i	$-0.593099\pi$
$181$	−7.75811	−0.576655	−0.288328	+	0.957532i	$0.593099\pi$
$182$	0	0
$183$	7.84422	0.579861
$184$	0.539276	0.0397560
$185$	9.09484	0.668666
$186$	−0.0594551	−0.00435946
$187$	−1.47921	−0.108171
$188$	13.7770	1.00479
$189$	−22.5880	−1.64303
$190$	0.00507963	0.000368515 0
$191$	4.12002	0.298114	0.149057	−	0.988829i	$-0.452376\pi$
$191$	4.12002	0.298114	0.149057	+	0.988829i	$0.452376\pi$
$192$	−9.76128	−0.704460
$193$	−1.13049	−0.0813741	−0.0406871	−	0.999172i	$-0.512955\pi$
$193$	−1.13049	−0.0813741	−0.0406871	+	0.999172i	$0.512955\pi$
$194$	0.174725	0.0125445
$195$	0	0
$196$	−18.3621	−1.31158
$197$	−23.8120	−1.69653	−0.848266	−	0.529571i	$-0.822353\pi$
$197$	−23.8120	−1.69653	−0.848266	+	0.529571i	$0.822353\pi$
$198$	0.185400	0.0131758
$199$	13.7508	0.974765	0.487382	−	0.873189i	$-0.337952\pi$
$199$	13.7508	0.974765	0.487382	+	0.873189i	$0.337952\pi$
$200$	−0.559204	−0.0395417
$201$	−18.1781	−1.28218
$202$	1.00086	0.0704200
$203$	14.6536	1.02848
$204$	−3.79712	−0.265852
$205$	−10.4713	−0.731350
$206$	−1.19233	−0.0830738
$207$	1.27261	0.0884522
$208$	0	0
$209$	−0.0361554	−0.00250092
$210$	0.734664	0.0506967
$211$	−21.1993	−1.45942	−0.729710	−	0.683756i	$-0.760345\pi$
$211$	−21.1993	−1.45942	−0.729710	+	0.683756i	$0.760345\pi$
$212$	−24.4962	−1.68240
$213$	−13.4100	−0.918835
$214$	0.399358	0.0272996
$215$	8.17151	0.557292
$216$	3.13126	0.213055
$217$	−1.31691	−0.0893979
$218$	2.52219	0.170824
$219$	13.6340	0.921300
$220$	1.98026	0.133509
$221$	0	0
$222$	1.65636	0.111168
$223$	−6.86539	−0.459741	−0.229870	−	0.973221i	$-0.573830\pi$
$223$	−6.86539	−0.459741	−0.229870	+	0.973221i	$0.573830\pi$
$224$	6.71165	0.448441
$225$	−1.31963	−0.0879754
$226$	1.63942	0.109053
$227$	20.3351	1.34969	0.674845	−	0.737959i	$-0.264210\pi$
$227$	20.3351	1.34969	0.674845	+	0.737959i	$0.264210\pi$
$228$	−0.0928108	−0.00614654
$229$	9.32957	0.616515	0.308258	−	0.951303i	$-0.400254\pi$
$229$	9.32957	0.616515	0.308258	+	0.951303i	$0.400254\pi$
$230$	−0.135488	−0.00893379
$231$	−5.22914	−0.344052
$232$	−2.03136	−0.133365
$233$	10.2185	0.669437	0.334718	−	0.942318i	$-0.391359\pi$
$233$	10.2185	0.669437	0.334718	+	0.942318i	$0.391359\pi$
$234$	0	0
$235$	−6.95718	−0.453836
$236$	−12.7109	−0.827410
$237$	−22.2411	−1.44472
$238$	0.838333	0.0543410
$239$	−4.65520	−0.301120	−0.150560	−	0.988601i	$-0.548108\pi$
$239$	−4.65520	−0.301120	−0.150560	+	0.988601i	$0.548108\pi$
$240$	5.03215	0.324824
$241$	24.7376	1.59349	0.796746	−	0.604314i	$-0.206553\pi$
$241$	24.7376	1.59349	0.796746	+	0.604314i	$0.206553\pi$
$242$	0.140494	0.00903131
$243$	12.5211	0.803232
$244$	−11.9831	−0.767140
$245$	9.27259	0.592404
$246$	−1.90705	−0.121589
$247$	0	0
$248$	0.182557	0.0115924
$249$	14.2878	0.905453
$250$	0.140494	0.00888563
$251$	0.179238	0.0113134	0.00565670	−	0.999984i	$-0.498199\pi$
$251$	0.179238	0.0113134	0.00565670	+	0.999984i	$0.498199\pi$
$252$	10.5415	0.664053
$253$	0.964365	0.0606291
$254$	−0.919628	−0.0577026
$255$	1.91749	0.120078
$256$	14.4442	0.902761
$257$	7.73387	0.482426	0.241213	−	0.970472i	$-0.422455\pi$
$257$	7.73387	0.482426	0.241213	+	0.970472i	$0.422455\pi$
$258$	1.48821	0.0926517
$259$	36.6880	2.27968
$260$	0	0
$261$	−4.79369	−0.296722
$262$	0.293771	0.0181492
$263$	2.10030	0.129510	0.0647549	−	0.997901i	$-0.479373\pi$
$263$	2.10030	0.129510	0.0647549	+	0.997901i	$0.479373\pi$
$264$	0.724890	0.0446139
$265$	12.3702	0.759893
$266$	0.0204909	0.00125637
$267$	19.9440	1.22055
$268$	27.7696	1.69630
$269$	15.4839	0.944067	0.472034	−	0.881581i	$-0.343520\pi$
$269$	15.4839	0.944067	0.472034	+	0.881581i	$0.343520\pi$
$270$	−0.786697	−0.0478768
$271$	13.5458	0.822846	0.411423	−	0.911444i	$-0.365032\pi$
$271$	13.5458	0.822846	0.411423	+	0.911444i	$0.365032\pi$
$272$	5.74223	0.348174
$273$	0	0
$274$	1.75681	0.106133
$275$	−1.00000	−0.0603023
$276$	2.47552	0.149009
$277$	−5.91382	−0.355327	−0.177664	−	0.984091i	$-0.556854\pi$
$277$	−5.91382	−0.355327	−0.177664	+	0.984091i	$0.556854\pi$
$278$	−0.675897	−0.0405376
$279$	0.430806	0.0257917
$280$	−2.25579	−0.134809
$281$	18.1234	1.08115	0.540576	−	0.841295i	$-0.318206\pi$
$281$	18.1234	1.08115	0.540576	+	0.841295i	$0.318206\pi$
$282$	−1.26705	−0.0754517
$283$	2.36689	0.140697	0.0703485	−	0.997522i	$-0.477589\pi$
$283$	2.36689	0.140697	0.0703485	+	0.997522i	$0.477589\pi$
$284$	20.4855	1.21559
$285$	0.0468679	0.00277622
$286$	0	0
$287$	−42.2407	−2.49339
$288$	−2.19560	−0.129377
$289$	−14.8119	−0.871291
$290$	0.510359	0.0299693
$291$	1.61213	0.0945045
$292$	−20.8278	−1.21885
$293$	28.8166	1.68349	0.841743	−	0.539879i	$-0.181530\pi$
$293$	28.8166	1.68349	0.841743	+	0.539879i	$0.181530\pi$
$294$	1.68874	0.0984891
$295$	6.41881	0.373717
$296$	−5.08587	−0.295610
$297$	5.59950	0.324916
$298$	2.27895	0.132016
$299$	0	0
$300$	−2.56699	−0.148205
$301$	32.9633	1.89997
$302$	−2.51346	−0.144633
$303$	9.23455	0.530511
$304$	0.140354	0.00804984
$305$	6.05128	0.346495
$306$	−0.274246	−0.0156776
$307$	−23.4170	−1.33648	−0.668238	−	0.743947i	$-0.732951\pi$
$307$	−23.4170	−1.33648	−0.668238	+	0.743947i	$0.732951\pi$
$308$	7.98824	0.455172
$309$	−11.0012	−0.625839
$310$	−0.0458656	−0.00260499
$311$	3.07308	0.174259	0.0871293	−	0.996197i	$-0.472231\pi$
$311$	3.07308	0.174259	0.0871293	+	0.996197i	$0.472231\pi$
$312$	0	0
$313$	−24.2356	−1.36988	−0.684939	−	0.728600i	$-0.740171\pi$
$313$	−24.2356	−1.36988	−0.684939	+	0.728600i	$0.740171\pi$
$314$	2.06894	0.116757
$315$	−5.32330	−0.299934
$316$	33.9764	1.91132
$317$	−2.37087	−0.133161	−0.0665807	−	0.997781i	$-0.521209\pi$
$317$	−2.37087	−0.133161	−0.0665807	+	0.997781i	$0.521209\pi$
$318$	2.25287	0.126335
$319$	−3.63260	−0.203386
$320$	−7.53016	−0.420949
$321$	3.68474	0.205662
$322$	−0.546547	−0.0304579
$323$	0.0534814	0.00297579
$324$	6.53423	0.363013
$325$	0	0
$326$	1.79809	0.0995872
$327$	23.2714	1.28691
$328$	5.85561	0.323322
$329$	−28.0648	−1.54726
$330$	−0.182121	−0.0100254
$331$	11.5363	0.634092	0.317046	−	0.948410i	$-0.397309\pi$
$331$	11.5363	0.634092	0.317046	+	0.948410i	$0.397309\pi$
$332$	−21.8266	−1.19789
$333$	−12.0018	−0.657696
$334$	−1.34190	−0.0734257
$335$	−14.0232	−0.766168
$336$	20.2993	1.10742
$337$	−10.6496	−0.580122	−0.290061	−	0.957008i	$-0.593676\pi$
$337$	−10.6496	−0.580122	−0.290061	+	0.957008i	$0.593676\pi$
$338$	0	0
$339$	15.1264	0.821553
$340$	−2.92922	−0.158859
$341$	0.326459	0.0176788
$342$	−0.00670323	−0.000362469 0
$343$	9.16746	0.494996
$344$	−4.56954	−0.246373
$345$	−1.25010	−0.0673029
$346$	−0.508297	−0.0273262
$347$	−5.50837	−0.295705	−0.147852	−	0.989009i	$-0.547236\pi$
$347$	−5.50837	−0.295705	−0.147852	+	0.989009i	$0.547236\pi$
$348$	−9.32486	−0.499865
$349$	−12.8575	−0.688246	−0.344123	−	0.938925i	$-0.611824\pi$
$349$	−12.8575	−0.688246	−0.344123	+	0.938925i	$0.611824\pi$
$350$	0.566744	0.0302937
$351$	0	0
$352$	−1.66380	−0.0886808
$353$	−17.6042	−0.936977	−0.468489	−	0.883470i	$-0.655201\pi$
$353$	−17.6042	−0.936977	−0.468489	+	0.883470i	$0.655201\pi$
$354$	1.16900	0.0621317
$355$	−10.3449	−0.549049
$356$	−30.4672	−1.61476
$357$	7.73500	0.409380
$358$	−0.710766	−0.0375651
$359$	0.123722	0.00652981	0.00326490	−	0.999995i	$-0.498961\pi$
$359$	0.123722	0.00652981	0.00326490	+	0.999995i	$0.498961\pi$
$360$	0.737942	0.0388930
$361$	−18.9987	−0.999931
$362$	−1.08997	−0.0572875
$363$	1.29629	0.0680376
$364$	0	0
$365$	10.5177	0.550522
$366$	1.10207	0.0576059
$367$	−18.6358	−0.972783	−0.486391	−	0.873741i	$-0.661687\pi$
$367$	−18.6358	−0.972783	−0.486391	+	0.873741i	$0.661687\pi$
$368$	−3.74362	−0.195150
$369$	13.8183	0.719352
$370$	1.27777	0.0664282
$371$	49.9004	2.59070
$372$	0.838019	0.0434492
$373$	−2.16107	−0.111896	−0.0559481	−	0.998434i	$-0.517818\pi$
$373$	−2.16107	−0.111896	−0.0559481	+	0.998434i	$0.517818\pi$
$374$	−0.207820	−0.0107461
$375$	1.29629	0.0669402
$376$	3.89048	0.200636
$377$	0	0
$378$	−3.17348	−0.163226
$379$	11.2889	0.579872	0.289936	−	0.957046i	$-0.406366\pi$
$379$	11.2889	0.579872	0.289936	+	0.957046i	$0.406366\pi$
$380$	−0.0715972	−0.00367286
$381$	−8.48508	−0.434704
$382$	0.578839	0.0296160
$383$	−5.85045	−0.298944	−0.149472	−	0.988766i	$-0.547757\pi$
$383$	−5.85045	−0.298944	−0.149472	+	0.988766i	$0.547757\pi$
$384$	−5.68494	−0.290108
$385$	−4.03393	−0.205588
$386$	−0.158827	−0.00808406
$387$	−10.7834	−0.548150
$388$	−2.46274	−0.125027
$389$	38.6338	1.95881	0.979407	−	0.201897i	$-0.0647106\pi$
$389$	38.6338	1.95881	0.979407	+	0.201897i	$0.0647106\pi$
$390$	0	0
$391$	−1.42650	−0.0721411
$392$	−5.18526	−0.261895
$393$	2.71052	0.136728
$394$	−3.34544	−0.168541
$395$	−17.1575	−0.863288
$396$	−2.61321	−0.131319
$397$	−5.39727	−0.270881	−0.135441	−	0.990785i	$-0.543245\pi$
$397$	−5.39727	−0.270881	−0.135441	+	0.990785i	$0.543245\pi$
$398$	1.93190	0.0968374
$399$	0.189062	0.00946494
$400$	3.88196	0.194098
$401$	5.35655	0.267494	0.133747	−	0.991016i	$-0.457299\pi$
$401$	5.35655	0.267494	0.133747	+	0.991016i	$0.457299\pi$
$402$	−2.55392	−0.127378
$403$	0	0
$404$	−14.1070	−0.701852
$405$	−3.29968	−0.163963
$406$	2.05875	0.102174
$407$	−9.09484	−0.450815
$408$	−1.07226	−0.0530850
$409$	−17.1818	−0.849586	−0.424793	−	0.905291i	$-0.639653\pi$
$409$	−17.1818	−0.849586	−0.424793	+	0.905291i	$0.639653\pi$
$410$	−1.47116	−0.0726555
$411$	16.2095	0.799554
$412$	16.8059	0.827968
$413$	25.8930	1.27411
$414$	0.178794	0.00878723
$415$	11.0221	0.541052
$416$	0	0
$417$	−6.23627	−0.305391
$418$	−0.00507963	−0.000248453 0
$419$	24.0672	1.17576	0.587880	−	0.808948i	$-0.299963\pi$
$419$	24.0672	1.17576	0.587880	+	0.808948i	$0.299963\pi$
$420$	−10.3551	−0.505276
$421$	40.2482	1.96157	0.980787	−	0.195080i	$-0.0624965\pi$
$421$	40.2482	1.96157	0.980787	+	0.195080i	$0.0624965\pi$
$422$	−2.97838	−0.144985
$423$	9.18091	0.446391
$424$	−6.91744	−0.335941
$425$	1.47921	0.0717522
$426$	−1.88402	−0.0912811
$427$	24.4104	1.18130
$428$	−5.62894	−0.272085
$429$	0	0
$430$	1.14805	0.0553639
$431$	21.6499	1.04284	0.521419	−	0.853301i	$-0.325403\pi$
$431$	21.6499	1.04284	0.521419	+	0.853301i	$0.325403\pi$
$432$	−21.7370	−1.04582
$433$	−26.6264	−1.27958	−0.639792	−	0.768548i	$-0.720980\pi$
$433$	−26.6264	−1.27958	−0.639792	+	0.768548i	$0.720980\pi$
$434$	−0.185019	−0.00888118
$435$	4.70890	0.225775
$436$	−35.5502	−1.70255
$437$	−0.0348670	−0.00166792
$438$	1.91550	0.0915260
$439$	11.8536	0.565741	0.282871	−	0.959158i	$-0.408713\pi$
$439$	11.8536	0.565741	0.282871	+	0.959158i	$0.408713\pi$
$440$	0.559204	0.0266590
$441$	−12.2364	−0.582685
$442$	0	0
$443$	8.44012	0.401002	0.200501	−	0.979693i	$-0.435743\pi$
$443$	8.44012	0.401002	0.200501	+	0.979693i	$0.435743\pi$
$444$	−23.3464	−1.10797
$445$	15.3854	0.729340
$446$	−0.964548	−0.0456727
$447$	21.0271	0.994546
$448$	−30.3761	−1.43514
$449$	14.5297	0.685701	0.342851	−	0.939390i	$-0.388608\pi$
$449$	14.5297	0.685701	0.342851	+	0.939390i	$0.388608\pi$
$450$	−0.185400	−0.00873986
$451$	10.4713	0.493076
$452$	−23.1076	−1.08689
$453$	−23.1908	−1.08960
$454$	2.85697	0.134084
$455$	0	0
$456$	−0.0262087	−0.00122734
$457$	0.230926	0.0108023	0.00540113	−	0.999985i	$-0.498281\pi$
$457$	0.230926	0.0108023	0.00540113	+	0.999985i	$0.498281\pi$
$458$	1.31075	0.0612473
$459$	−8.28283	−0.386609
$460$	1.90969	0.0890399
$461$	−15.4867	−0.721289	−0.360645	−	0.932703i	$-0.617443\pi$
$461$	−15.4867	−0.721289	−0.360645	+	0.932703i	$0.617443\pi$
$462$	−0.734664	−0.0341797
$463$	29.4417	1.36827	0.684135	−	0.729356i	$-0.260180\pi$
$463$	29.4417	1.36827	0.684135	+	0.729356i	$0.260180\pi$
$464$	14.1016	0.654650
$465$	−0.423186	−0.0196248
$466$	1.43564	0.0665048
$467$	−6.46637	−0.299228	−0.149614	−	0.988745i	$-0.547803\pi$
$467$	−6.46637	−0.299228	−0.149614	+	0.988745i	$0.547803\pi$
$468$	0	0
$469$	−56.5685	−2.61209
$470$	−0.977443	−0.0450861
$471$	19.0894	0.879593
$472$	−3.58942	−0.165216
$473$	−8.17151	−0.375727
$474$	−3.12475	−0.143524
$475$	0.0361554	0.00165892
$476$	−11.8163	−0.541598
$477$	−16.3241	−0.747427
$478$	−0.654028	−0.0299145
$479$	−14.7758	−0.675122	−0.337561	−	0.941304i	$-0.609602\pi$
$479$	−14.7758	−0.675122	−0.337561	+	0.941304i	$0.609602\pi$
$480$	2.15677	0.0984425
$481$	0	0
$482$	3.47549	0.158304
$483$	−5.04280	−0.229455
$484$	−1.98026	−0.0900119
$485$	1.24365	0.0564711
$486$	1.75915	0.0797966
$487$	−11.2138	−0.508148	−0.254074	−	0.967185i	$-0.581771\pi$
$487$	−11.2138	−0.508148	−0.254074	+	0.967185i	$0.581771\pi$
$488$	−3.38390	−0.153182
$489$	16.5904	0.750243
$490$	1.30274	0.0588520
$491$	−4.26935	−0.192673	−0.0963365	−	0.995349i	$-0.530712\pi$
$491$	−4.26935	−0.192673	−0.0963365	+	0.995349i	$0.530712\pi$
$492$	26.8799	1.21184
$493$	5.37337	0.242005
$494$	0	0
$495$	1.31963	0.0593130
$496$	−1.26730	−0.0569035
$497$	−41.7305	−1.87187
$498$	2.00735	0.0899516
$499$	32.0124	1.43307	0.716535	−	0.697551i	$-0.245727\pi$
$499$	32.0124	1.43307	0.716535	+	0.697551i	$0.245727\pi$
$500$	−1.98026	−0.0885600
$501$	−12.3813	−0.553155
$502$	0.0251819	0.00112392
$503$	36.4077	1.62334	0.811670	−	0.584116i	$-0.198559\pi$
$503$	36.4077	1.62334	0.811670	+	0.584116i	$0.198559\pi$
$504$	2.97681	0.132598
$505$	7.12383	0.317006
$506$	0.135488	0.00602316
$507$	0	0
$508$	12.9621	0.575101
$509$	40.3123	1.78681	0.893406	−	0.449251i	$-0.148309\pi$
$509$	40.3123	1.78681	0.893406	+	0.449251i	$0.148309\pi$
$510$	0.269395	0.0119290
$511$	42.4277	1.87689
$512$	10.8004	0.477315
$513$	−0.202452	−0.00893848
$514$	1.08656	0.0479263
$515$	−8.48672	−0.373969
$516$	−20.9762	−0.923427
$517$	6.95718	0.305976
$518$	5.15444	0.226473
$519$	−4.68988	−0.205863
$520$	0	0
$521$	−20.1942	−0.884725	−0.442362	−	0.896836i	$-0.645860\pi$
$521$	−20.1942	−0.884725	−0.442362	+	0.896836i	$0.645860\pi$
$522$	−0.673485	−0.0294776
$523$	−28.0166	−1.22508	−0.612540	−	0.790439i	$-0.709852\pi$
$523$	−28.0166	−1.22508	−0.612540	+	0.790439i	$0.709852\pi$
$524$	−4.14069	−0.180887
$525$	5.22914	0.228219
$526$	0.295079	0.0128661
$527$	−0.482901	−0.0210355
$528$	−5.03215	−0.218996
$529$	−22.0700	−0.959565
$530$	1.73794	0.0754911
$531$	−8.47045	−0.367586
$532$	−0.288818	−0.0125218
$533$	0	0
$534$	2.80201	0.121255
$535$	2.84252	0.122893
$536$	7.84181	0.338715
$537$	−6.55799	−0.282998
$538$	2.17539	0.0937878
$539$	−9.27259	−0.399399
$540$	11.0885	0.477172
$541$	−4.70299	−0.202197	−0.101099	−	0.994876i	$-0.532236\pi$
$541$	−4.70299	−0.202197	−0.101099	+	0.994876i	$0.532236\pi$
$542$	1.90310	0.0817451
$543$	−10.0568	−0.431577
$544$	2.46111	0.105519
$545$	17.9523	0.768992
$546$	0	0
$547$	17.6776	0.755842	0.377921	−	0.925838i	$-0.376639\pi$
$547$	17.6776	0.755842	0.377921	+	0.925838i	$0.376639\pi$
$548$	−24.7622	−1.05779
$549$	−7.98545	−0.340811
$550$	−0.140494	−0.00599069
$551$	0.131338	0.00559519
$552$	0.699058	0.0297539
$553$	−69.2122	−2.94320
$554$	−0.830857	−0.0352997
$555$	11.7896	0.500439
$556$	9.52675	0.404024
$557$	−1.38952	−0.0588758	−0.0294379	−	0.999567i	$-0.509372\pi$
$557$	−1.38952	−0.0588758	−0.0294379	+	0.999567i	$0.509372\pi$
$558$	0.0605257	0.00256226
$559$	0	0
$560$	15.6595	0.661737
$561$	−1.91749	−0.0809563
$562$	2.54623	0.107406
$563$	−37.1255	−1.56465	−0.782326	−	0.622869i	$-0.785967\pi$
$563$	−37.1255	−1.56465	−0.782326	+	0.622869i	$0.785967\pi$
$564$	17.8590	0.752001
$565$	11.6690	0.490918
$566$	0.332534	0.0139775
$567$	−13.3107	−0.558996
$568$	5.78489	0.242728
$569$	0.122647	0.00514162	0.00257081	−	0.999997i	$-0.499182\pi$
$569$	0.122647	0.00514162	0.00257081	+	0.999997i	$0.499182\pi$
$570$	0.00658467	0.000275802 0
$571$	−7.87757	−0.329666	−0.164833	−	0.986321i	$-0.552709\pi$
$571$	−7.87757	−0.329666	−0.164833	+	0.986321i	$0.552709\pi$
$572$	0	0
$573$	5.34074	0.223113
$574$	−5.93457	−0.247704
$575$	−0.964365	−0.0402168
$576$	9.93703	0.414043
$577$	24.2131	1.00800	0.504002	−	0.863703i	$-0.331861\pi$
$577$	24.2131	1.00800	0.504002	+	0.863703i	$0.331861\pi$
$578$	−2.08099	−0.0865578
$579$	−1.46544	−0.0609015
$580$	−7.19349	−0.298694
$581$	44.4622	1.84460
$582$	0.226494	0.00938849
$583$	−12.3702	−0.512320
$584$	−5.88154	−0.243380
$585$	0	0
$586$	4.04857	0.167245
$587$	−16.0680	−0.663199	−0.331600	−	0.943420i	$-0.607588\pi$
$587$	−16.0680	−0.663199	−0.331600	+	0.943420i	$0.607588\pi$
$588$	−23.8027	−0.981606
$589$	−0.0118033	−0.000486345 0
$590$	0.901805	0.0371267
$591$	−30.8672	−1.26971
$592$	35.3058	1.45106
$593$	−6.39964	−0.262802	−0.131401	−	0.991329i	$-0.541948\pi$
$593$	−6.39964	−0.262802	−0.131401	+	0.991329i	$0.541948\pi$
$594$	0.786697	0.0322786
$595$	5.96703	0.244624
$596$	−32.1217	−1.31576
$597$	17.8250	0.729527
$598$	0	0
$599$	28.2707	1.15511	0.577554	−	0.816353i	$-0.304007\pi$
$599$	28.2707	1.15511	0.577554	+	0.816353i	$0.304007\pi$
$600$	−0.724890	−0.0295935
$601$	28.2409	1.15197	0.575985	−	0.817460i	$-0.304619\pi$
$601$	28.2409	1.15197	0.575985	+	0.817460i	$0.304619\pi$
$602$	4.63115	0.188752
$603$	18.5054	0.753599
$604$	35.4271	1.44151
$605$	1.00000	0.0406558
$606$	1.29740	0.0527033
$607$	4.90166	0.198952	0.0994761	−	0.995040i	$-0.468283\pi$
$607$	4.90166	0.198952	0.0994761	+	0.995040i	$0.468283\pi$
$608$	0.0601554	0.00243962
$609$	18.9954	0.769732
$610$	0.850169	0.0344224
$611$	0	0
$612$	3.86549	0.156253
$613$	39.0195	1.57598	0.787992	−	0.615686i	$-0.211121\pi$
$613$	39.0195	1.57598	0.787992	+	0.615686i	$0.211121\pi$
$614$	−3.28995	−0.132771
$615$	−13.5739	−0.547352
$616$	2.25579	0.0908883
$617$	25.2717	1.01740	0.508701	−	0.860943i	$-0.330126\pi$
$617$	25.2717	1.01740	0.508701	+	0.860943i	$0.330126\pi$
$618$	−1.54561	−0.0621736
$619$	−12.9733	−0.521442	−0.260721	−	0.965414i	$-0.583960\pi$
$619$	−12.9733	−0.521442	−0.260721	+	0.965414i	$0.583960\pi$
$620$	0.646474	0.0259630
$621$	5.39996	0.216693
$622$	0.431750	0.0173116
$623$	62.0638	2.48653
$624$	0	0
$625$	1.00000	0.0400000
$626$	−3.40496	−0.136090
$627$	−0.0468679	−0.00187172
$628$	−29.1617	−1.16368
$629$	13.4532	0.536413
$630$	−0.747892	−0.0297967
$631$	−13.5546	−0.539599	−0.269800	−	0.962916i	$-0.586957\pi$
$631$	−13.5546	−0.539599	−0.269800	+	0.962916i	$0.586957\pi$
$632$	9.59454	0.381650
$633$	−27.4805	−1.09225
$634$	−0.333094	−0.0132288
$635$	−6.54566	−0.259757
$636$	−31.7541	−1.25913
$637$	0	0
$638$	−0.510359	−0.0202053
$639$	13.6514	0.540041
$640$	−4.38554	−0.173354
$641$	−8.87438	−0.350517	−0.175258	−	0.984522i	$-0.556076\pi$
$641$	−8.87438	−0.350517	−0.175258	+	0.984522i	$0.556076\pi$
$642$	0.517684	0.0204314
$643$	19.0855	0.752660	0.376330	−	0.926486i	$-0.377186\pi$
$643$	19.0855	0.752660	0.376330	+	0.926486i	$0.377186\pi$
$644$	7.70357	0.303563
$645$	10.5927	0.417085
$646$	0.00751383	0.000295628 0
$647$	−48.2801	−1.89809	−0.949043	−	0.315147i	$-0.897946\pi$
$647$	−48.2801	−1.89809	−0.949043	+	0.315147i	$0.897946\pi$
$648$	1.84519	0.0724861
$649$	−6.41881	−0.251960
$650$	0	0
$651$	−1.70710	−0.0669066
$652$	−25.3441	−0.992551
$653$	25.6531	1.00388	0.501941	−	0.864902i	$-0.332619\pi$
$653$	25.6531	1.00388	0.501941	+	0.864902i	$0.332619\pi$
$654$	3.26949	0.127847
$655$	2.09098	0.0817014
$656$	−40.6493	−1.58709
$657$	−13.8795	−0.541490
$658$	−3.94294	−0.153712
$659$	−29.1605	−1.13593	−0.567967	−	0.823052i	$-0.692270\pi$
$659$	−29.1605	−1.13593	−0.567967	+	0.823052i	$0.692270\pi$
$660$	2.56699	0.0999201
$661$	12.0926	0.470348	0.235174	−	0.971953i	$-0.424434\pi$
$661$	12.0926	0.470348	0.235174	+	0.971953i	$0.424434\pi$
$662$	1.62078	0.0629935
$663$	0	0
$664$	−6.16358	−0.239193
$665$	0.145848	0.00565576
$666$	−1.68619	−0.0653384
$667$	−3.50315	−0.135642
$668$	18.9141	0.731809
$669$	−8.89955	−0.344076
$670$	−1.97017	−0.0761145
$671$	−6.05128	−0.233607
$672$	8.70025	0.335619
$673$	11.2920	0.435273	0.217637	−	0.976030i	$-0.430165\pi$
$673$	11.2920	0.435273	0.217637	+	0.976030i	$0.430165\pi$
$674$	−1.49621	−0.0576319
$675$	−5.59950	−0.215525
$676$	0	0
$677$	−5.91918	−0.227492	−0.113746	−	0.993510i	$-0.536285\pi$
$677$	−5.91918	−0.227492	−0.113746	+	0.993510i	$0.536285\pi$
$678$	2.12517	0.0816166
$679$	5.01678	0.192526
$680$	−0.827179	−0.0317209
$681$	26.3602	1.01013
$682$	0.0458656	0.00175628
$683$	−40.2519	−1.54019	−0.770097	−	0.637926i	$-0.779792\pi$
$683$	−40.2519	−1.54019	−0.770097	+	0.637926i	$0.779792\pi$
$684$	0.0944819	0.00361260
$685$	12.5045	0.477773
$686$	1.28797	0.0491751
$687$	12.0938	0.461408
$688$	31.7215	1.20937
$689$	0	0
$690$	−0.175631	−0.00668617
$691$	37.5033	1.42669	0.713346	−	0.700812i	$-0.247179\pi$
$691$	37.5033	1.42669	0.713346	+	0.700812i	$0.247179\pi$
$692$	7.16443	0.272351
$693$	5.32330	0.202215
$694$	−0.773894	−0.0293766
$695$	−4.81086	−0.182486
$696$	−2.63323	−0.0998125
$697$	−15.4893	−0.586699
$698$	−1.80640	−0.0683733
$699$	13.2462	0.501015
$700$	−7.98824	−0.301927
$701$	45.6241	1.72320	0.861599	−	0.507589i	$-0.169463\pi$
$701$	45.6241	1.72320	0.861599	+	0.507589i	$0.169463\pi$
$702$	0	0
$703$	0.328828	0.0124020
$704$	7.53016	0.283804
$705$	−9.01852	−0.339657
$706$	−2.47329	−0.0930834
$707$	28.7370	1.08077
$708$	−16.4770	−0.619245
$709$	15.2686	0.573423	0.286712	−	0.958017i	$-0.407438\pi$
$709$	15.2686	0.573423	0.286712	+	0.958017i	$0.407438\pi$
$710$	−1.45339	−0.0545449
$711$	22.6416	0.849126
$712$	−8.60359	−0.322433
$713$	0.314826	0.0117903
$714$	1.08672	0.0406696
$715$	0	0
$716$	10.0182	0.374399
$717$	−6.03449	−0.225362
$718$	0.0173822	0.000648700 0
$719$	−1.06339	−0.0396579	−0.0198289	−	0.999803i	$-0.506312\pi$
$719$	−1.06339	−0.0396579	−0.0198289	+	0.999803i	$0.506312\pi$
$720$	−5.12275	−0.190914
$721$	−34.2348	−1.27497
$722$	−2.66921	−0.0993375
$723$	32.0672	1.19259
$724$	15.3631	0.570964
$725$	3.63260	0.134911
$726$	0.182121	0.00675915
$727$	−41.4387	−1.53688	−0.768438	−	0.639925i	$-0.778966\pi$
$727$	−41.4387	−1.53688	−0.768438	+	0.639925i	$0.778966\pi$
$728$	0	0
$729$	26.1301	0.967781
$730$	1.47768	0.0546912
$731$	12.0874	0.447068
$732$	−15.5336	−0.574138
$733$	−39.3482	−1.45336	−0.726679	−	0.686977i	$-0.758937\pi$
$733$	−39.3482	−1.45336	−0.726679	+	0.686977i	$0.758937\pi$
$734$	−2.61823	−0.0966405
$735$	12.0200	0.443363
$736$	−1.60451	−0.0591430
$737$	14.0232	0.516550
$738$	1.94139	0.0714636
$739$	−20.2425	−0.744633	−0.372317	−	0.928106i	$-0.621436\pi$
$739$	−20.2425	−0.744633	−0.372317	+	0.928106i	$0.621436\pi$
$740$	−18.0102	−0.662067
$741$	0	0
$742$	7.01071	0.257371
$743$	−29.7891	−1.09286	−0.546428	−	0.837506i	$-0.684013\pi$
$743$	−29.7891	−1.09286	−0.546428	+	0.837506i	$0.684013\pi$
$744$	0.236647	0.00867590
$745$	16.2210	0.594290
$746$	−0.303618	−0.0111163
$747$	−14.5451	−0.532176
$748$	2.92922	0.107103
$749$	11.4665	0.418978
$750$	0.182121	0.00665013
$751$	−46.7581	−1.70623	−0.853113	−	0.521726i	$-0.825288\pi$
$751$	−46.7581	−1.70623	−0.853113	+	0.521726i	$0.825288\pi$
$752$	−27.0075	−0.984861
$753$	0.232345	0.00846711
$754$	0	0
$755$	−17.8901	−0.651088
$756$	44.7301	1.62682
$757$	4.68089	0.170130	0.0850649	−	0.996375i	$-0.472890\pi$
$757$	4.68089	0.170130	0.0850649	+	0.996375i	$0.472890\pi$
$758$	1.58603	0.0576071
$759$	1.25010	0.0453756
$760$	−0.0202182	−0.000733393 0
$761$	13.0629	0.473531	0.236765	−	0.971567i	$-0.423913\pi$
$761$	13.0629	0.473531	0.236765	+	0.971567i	$0.423913\pi$
$762$	−1.19210	−0.0431854
$763$	72.4183	2.62172
$764$	−8.15872	−0.295172
$765$	−1.95201	−0.0705751
$766$	−0.821954	−0.0296984
$767$	0	0
$768$	18.7239	0.675639
$769$	−45.2855	−1.63304	−0.816518	−	0.577320i	$-0.804099\pi$
$769$	−45.2855	−1.63304	−0.816518	+	0.577320i	$0.804099\pi$
$770$	−0.566744	−0.0204240
$771$	10.0253	0.361054
$772$	2.23866	0.0805710
$773$	52.2130	1.87797	0.938986	−	0.343956i	$-0.111767\pi$
$773$	52.2130	1.87797	0.938986	+	0.343956i	$0.111767\pi$
$774$	−1.51500	−0.0544556
$775$	−0.326459	−0.0117268
$776$	−0.695451	−0.0249652
$777$	47.5582	1.70614
$778$	5.42783	0.194597
$779$	−0.378596	−0.0135646
$780$	0	0
$781$	10.3449	0.370168
$782$	−0.200415	−0.00716681
$783$	−20.3407	−0.726918
$784$	35.9958	1.28556
$785$	14.7262	0.525600
$786$	0.380812	0.0135831
$787$	−16.1248	−0.574789	−0.287394	−	0.957812i	$-0.592789\pi$
$787$	−16.1248	−0.574789	−0.287394	+	0.957812i	$0.592789\pi$
$788$	47.1539	1.67979
$789$	2.72259	0.0969269
$790$	−2.41053	−0.0857629
$791$	47.0718	1.67368
$792$	−0.737942	−0.0262216
$793$	0	0
$794$	−0.758285	−0.0269105
$795$	16.0353	0.568715
$796$	−27.2301	−0.965145
$797$	21.7344	0.769871	0.384936	−	0.922943i	$-0.374224\pi$
$797$	21.7344	0.769871	0.384936	+	0.922943i	$0.374224\pi$
$798$	0.0265621	0.000940288 0
$799$	−10.2911	−0.364074
$800$	1.66380	0.0588242
$801$	−20.3031	−0.717375
$802$	0.752565	0.0265740
$803$	−10.5177	−0.371162
$804$	35.9974	1.26953
$805$	−3.89018	−0.137111
$806$	0	0
$807$	20.0716	0.706553
$808$	−3.98367	−0.140145
$809$	7.17878	0.252393	0.126196	−	0.992005i	$-0.459723\pi$
$809$	7.17878	0.252393	0.126196	+	0.992005i	$0.459723\pi$
$810$	−0.463586	−0.0162888
$811$	16.1417	0.566813	0.283406	−	0.959000i	$-0.408536\pi$
$811$	16.1417	0.566813	0.283406	+	0.959000i	$0.408536\pi$
$812$	−29.0180	−1.01833
$813$	17.5592	0.615829
$814$	−1.27777	−0.0447859
$815$	12.7983	0.448307
$816$	7.44360	0.260578
$817$	0.295444	0.0103363
$818$	−2.41394	−0.0844016
$819$	0	0
$820$	20.7360	0.724132
$821$	20.7154	0.722973	0.361486	−	0.932377i	$-0.382269\pi$
$821$	20.7154	0.722973	0.361486	+	0.932377i	$0.382269\pi$
$822$	2.27734	0.0794312
$823$	1.02015	0.0355603	0.0177802	−	0.999842i	$-0.494340\pi$
$823$	1.02015	0.0355603	0.0177802	+	0.999842i	$0.494340\pi$
$824$	4.74580	0.165328
$825$	−1.29629	−0.0451310
$826$	3.63782	0.126576
$827$	−21.1096	−0.734052	−0.367026	−	0.930211i	$-0.619624\pi$
$827$	−21.1096	−0.734052	−0.367026	+	0.930211i	$0.619624\pi$
$828$	−2.52009	−0.0875792
$829$	40.0995	1.39271	0.696356	−	0.717696i	$-0.254803\pi$
$829$	40.0995	1.39271	0.696356	+	0.717696i	$0.254803\pi$
$830$	1.54854	0.0537505
$831$	−7.66603	−0.265932
$832$	0	0
$833$	13.7161	0.475235
$834$	−0.876159	−0.0303389
$835$	−9.55131	−0.330537
$836$	0.0715972	0.00247624
$837$	1.82801	0.0631852
$838$	3.38130	0.116805
$839$	0.405482	0.0139988	0.00699940	−	0.999976i	$-0.497772\pi$
$839$	0.405482	0.0139988	0.00699940	+	0.999976i	$0.497772\pi$
$840$	−2.92416	−0.100893
$841$	−15.8042	−0.544974
$842$	5.65463	0.194871
$843$	23.4932	0.809149
$844$	41.9802	1.44502
$845$	0	0
$846$	1.28986	0.0443464
$847$	4.03393	0.138607
$848$	48.0205	1.64903
$849$	3.06818	0.105300
$850$	0.207820	0.00712818
$851$	−8.77074	−0.300657
$852$	26.5552	0.909767
$853$	−13.4778	−0.461473	−0.230736	−	0.973016i	$-0.574113\pi$
$853$	−13.4778	−0.461473	−0.230736	+	0.973016i	$0.574113\pi$
$854$	3.42952	0.117356
$855$	−0.0477118	−0.00163171
$856$	−1.58955	−0.0543297
$857$	−17.0751	−0.583276	−0.291638	−	0.956529i	$-0.594200\pi$
$857$	−17.0751	−0.583276	−0.291638	+	0.956529i	$0.594200\pi$
$858$	0	0
$859$	−32.6937	−1.11549	−0.557747	−	0.830011i	$-0.688334\pi$
$859$	−32.6937	−1.11549	−0.557747	+	0.830011i	$0.688334\pi$
$860$	−16.1817	−0.551792
$861$	−54.7562	−1.86608
$862$	3.04168	0.103600
$863$	−10.0425	−0.341851	−0.170926	−	0.985284i	$-0.554676\pi$
$863$	−10.0425	−0.341851	−0.170926	+	0.985284i	$0.554676\pi$
$864$	−9.31644	−0.316952
$865$	−3.61792	−0.123013
$866$	−3.74086	−0.127119
$867$	−19.2006	−0.652086
$868$	2.60783	0.0885156
$869$	17.1575	0.582029
$870$	0.661573	0.0224294
$871$	0	0
$872$	−10.0390	−0.339963
$873$	−1.64115	−0.0555446
$874$	−0.00489861	−0.000165698 0
$875$	4.03393	0.136372
$876$	−26.9989	−0.912208
$877$	3.69975	0.124932	0.0624658	−	0.998047i	$-0.480104\pi$
$877$	3.69975	0.124932	0.0624658	+	0.998047i	$0.480104\pi$
$878$	1.66536	0.0562032
$879$	37.3547	1.25994
$880$	−3.88196	−0.130861
$881$	9.04527	0.304743	0.152371	−	0.988323i	$-0.451309\pi$
$881$	9.04527	0.304743	0.152371	+	0.988323i	$0.451309\pi$
$882$	−1.71914	−0.0578865
$883$	2.23100	0.0750792	0.0375396	−	0.999295i	$-0.488048\pi$
$883$	2.23100	0.0750792	0.0375396	+	0.999295i	$0.488048\pi$
$884$	0	0
$885$	8.32064	0.279695
$886$	1.18579	0.0398373
$887$	53.1937	1.78607	0.893036	−	0.449986i	$-0.148571\pi$
$887$	53.1937	1.78607	0.893036	+	0.449986i	$0.148571\pi$
$888$	−6.59276	−0.221239
$889$	−26.4047	−0.885587
$890$	2.16156	0.0724558
$891$	3.29968	0.110544
$892$	13.5953	0.455203
$893$	−0.251540	−0.00841746
$894$	2.95418	0.0988026
$895$	−5.05904	−0.169105
$896$	−17.6910	−0.591014
$897$	0	0
$898$	2.04134	0.0681206
$899$	−1.18589	−0.0395518
$900$	2.61321	0.0871071
$901$	18.2981	0.609597
$902$	1.47116	0.0489843
$903$	42.7300	1.42197
$904$	−6.52533	−0.217029
$905$	−7.75811	−0.257888
$906$	−3.25817	−0.108245
$907$	17.3711	0.576799	0.288399	−	0.957510i	$-0.406877\pi$
$907$	17.3711	0.576799	0.288399	+	0.957510i	$0.406877\pi$
$908$	−40.2689	−1.33637
$909$	−9.40083	−0.311806
$910$	0	0
$911$	−37.4284	−1.24006	−0.620029	−	0.784579i	$-0.712879\pi$
$911$	−37.4284	−1.24006	−0.620029	+	0.784579i	$0.712879\pi$
$912$	0.181939	0.00602461
$913$	−11.0221	−0.364777
$914$	0.0324438	0.00107314
$915$	7.84422	0.259322
$916$	−18.4750	−0.610430
$917$	8.43487	0.278544
$918$	−1.16369	−0.0384075
$919$	8.59426	0.283499	0.141749	−	0.989903i	$-0.454727\pi$
$919$	8.59426	0.283499	0.141749	+	0.989903i	$0.454727\pi$
$920$	0.539276	0.0177794
$921$	−30.3552	−1.00024
$922$	−2.17580	−0.0716561
$923$	0	0
$924$	10.3551	0.340657
$925$	9.09484	0.299037
$926$	4.13638	0.135930
$927$	11.1993	0.367834
$928$	6.04391	0.198401
$929$	7.16282	0.235004	0.117502	−	0.993073i	$-0.462511\pi$
$929$	7.16282	0.235004	0.117502	+	0.993073i	$0.462511\pi$
$930$	−0.0594551	−0.00194961
$931$	0.335254	0.0109875
$932$	−20.2353	−0.662830
$933$	3.98361	0.130418
$934$	−0.908487	−0.0297266
$935$	−1.47921	−0.0483753
$936$	0	0
$937$	−18.3693	−0.600100	−0.300050	−	0.953923i	$-0.597003\pi$
$937$	−18.3693	−0.600100	−0.300050	+	0.953923i	$0.597003\pi$
$938$	−7.94754	−0.259497
$939$	−31.4164	−1.02524
$940$	13.7770	0.449357
$941$	18.3977	0.599747	0.299874	−	0.953979i	$-0.403056\pi$
$941$	18.3977	0.599747	0.299874	+	0.953979i	$0.403056\pi$
$942$	2.68195	0.0873826
$943$	10.0982	0.328842
$944$	24.9175	0.810997
$945$	−22.5880	−0.734787
$946$	−1.14805	−0.0373263
$947$	52.5400	1.70732	0.853660	−	0.520831i	$-0.174378\pi$
$947$	52.5400	1.70732	0.853660	+	0.520831i	$0.174378\pi$
$948$	44.0432	1.43046
$949$	0	0
$950$	0.00507963	0.000164805 0
$951$	−3.07334	−0.0996598
$952$	−3.33678	−0.108146
$953$	−30.8793	−1.00028	−0.500139	−	0.865945i	$-0.666718\pi$
$953$	−30.8793	−1.00028	−0.500139	+	0.865945i	$0.666718\pi$
$954$	−2.29343	−0.0742527
$955$	4.12002	0.133321
$956$	9.21850	0.298148
$957$	−4.70890	−0.152217
$958$	−2.07591	−0.0670696
$959$	50.4423	1.62887
$960$	−9.76128	−0.315044
$961$	−30.8934	−0.996562
$962$	0	0
$963$	−3.75108	−0.120877
$964$	−48.9870	−1.57777
$965$	−1.13049	−0.0363916
$966$	−0.708484	−0.0227951
$967$	9.98884	0.321219	0.160610	−	0.987018i	$-0.448654\pi$
$967$	9.98884	0.321219	0.160610	+	0.987018i	$0.448654\pi$
$968$	−0.559204	−0.0179735
$969$	0.0693275	0.00222712
$970$	0.174725	0.00561008
$971$	30.6699	0.984245	0.492123	−	0.870526i	$-0.336221\pi$
$971$	30.6699	0.984245	0.492123	+	0.870526i	$0.336221\pi$
$972$	−24.7951	−0.795304
$973$	−19.4067	−0.622149
$974$	−1.57548	−0.0504816
$975$	0	0
$976$	23.4908	0.751923
$977$	−3.08391	−0.0986629	−0.0493315	−	0.998782i	$-0.515709\pi$
$977$	−3.08391	−0.0986629	−0.0493315	+	0.998782i	$0.515709\pi$
$978$	2.33085	0.0745324
$979$	−15.3854	−0.491721
$980$	−18.3621	−0.586557
$981$	−23.6904	−0.756376
$982$	−0.599818	−0.0191410
$983$	−9.33457	−0.297726	−0.148863	−	0.988858i	$-0.547561\pi$
$983$	−9.33457	−0.297726	−0.148863	+	0.988858i	$0.547561\pi$
$984$	7.59057	0.241979
$985$	−23.8120	−0.758712
$986$	0.754928	0.0240418
$987$	−36.3801	−1.15799
$988$	0	0
$989$	−7.88032	−0.250579
$990$	0.185400	0.00589241
$991$	−32.4964	−1.03228	−0.516141	−	0.856504i	$-0.672632\pi$
$991$	−32.4964	−1.03228	−0.516141	+	0.856504i	$0.672632\pi$
$992$	−0.543163	−0.0172454
$993$	14.9544	0.474563
$994$	−5.86289	−0.185959
$995$	13.7508	0.435928
$996$	−28.2936	−0.896517
$997$	−29.5246	−0.935054	−0.467527	−	0.883979i	$-0.654855\pi$
$997$	−29.5246	−0.935054	−0.467527	+	0.883979i	$0.654855\pi$
$998$	4.49755	0.142367
$999$	−50.9265	−1.61124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9295.2.a.bh.1.13	yes	27
13.12	even	2		9295.2.a.bg.1.15	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9295.2.a.bg.1.15	✓	27	13.12	even	2
9295.2.a.bh.1.13	yes	27	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:	\( N \)	\(=\)	\( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9295.a (trivial)

\(f(q)\)	\(=\)	\(q+0.140494 q^{2} +1.29629 q^{3} -1.98026 q^{4} +1.00000 q^{5} +0.182121 q^{6} +4.03393 q^{7} -0.559204 q^{8} -1.31963 q^{9} +O(q^{10})\)	\(q+0.140494 q^{2} +1.29629 q^{3} -1.98026 q^{4} +1.00000 q^{5} +0.182121 q^{6} +4.03393 q^{7} -0.559204 q^{8} -1.31963 q^{9} +0.140494 q^{10} -1.00000 q^{11} -2.56699 q^{12} +0.566744 q^{14} +1.29629 q^{15} +3.88196 q^{16} +1.47921 q^{17} -0.185400 q^{18} +0.0361554 q^{19} -1.98026 q^{20} +5.22914 q^{21} -0.140494 q^{22} -0.964365 q^{23} -0.724890 q^{24} +1.00000 q^{25} -5.59950 q^{27} -7.98824 q^{28} +3.63260 q^{29} +0.182121 q^{30} -0.326459 q^{31} +1.66380 q^{32} -1.29629 q^{33} +0.207820 q^{34} +4.03393 q^{35} +2.61321 q^{36} +9.09484 q^{37} +0.00507963 q^{38} -0.559204 q^{40} -10.4713 q^{41} +0.734664 q^{42} +8.17151 q^{43} +1.98026 q^{44} -1.31963 q^{45} -0.135488 q^{46} -6.95718 q^{47} +5.03215 q^{48} +9.27259 q^{49} +0.140494 q^{50} +1.91749 q^{51} +12.3702 q^{53} -0.786697 q^{54} -1.00000 q^{55} -2.25579 q^{56} +0.0468679 q^{57} +0.510359 q^{58} +6.41881 q^{59} -2.56699 q^{60} +6.05128 q^{61} -0.0458656 q^{62} -5.32330 q^{63} -7.53016 q^{64} -0.182121 q^{66} -14.0232 q^{67} -2.92922 q^{68} -1.25010 q^{69} +0.566744 q^{70} -10.3449 q^{71} +0.737942 q^{72} +10.5177 q^{73} +1.27777 q^{74} +1.29629 q^{75} -0.0715972 q^{76} -4.03393 q^{77} -17.1575 q^{79} +3.88196 q^{80} -3.29968 q^{81} -1.47116 q^{82} +11.0221 q^{83} -10.3551 q^{84} +1.47921 q^{85} +1.14805 q^{86} +4.70890 q^{87} +0.559204 q^{88} +15.3854 q^{89} -0.185400 q^{90} +1.90969 q^{92} -0.423186 q^{93} -0.977443 q^{94} +0.0361554 q^{95} +2.15677 q^{96} +1.24365 q^{97} +1.30274 q^{98} +1.31963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 8 q^{2} + 20 q^{4} + 27 q^{5} - 8 q^{6} + 6 q^{7} + 21 q^{8} + 23 q^{9}+O(q^{10}) \) 27 * q + 8 * q^2 + 20 * q^4 + 27 * q^5 - 8 * q^6 + 6 * q^7 + 21 * q^8 + 23 * q^9	\( 27 q + 8 q^{2} + 20 q^{4} + 27 q^{5} - 8 q^{6} + 6 q^{7} + 21 q^{8} + 23 q^{9} + 8 q^{10} - 27 q^{11} + 2 q^{12} - 11 q^{14} + 2 q^{16} + 13 q^{17} + 28 q^{18} + 8 q^{19} + 20 q^{20} + 23 q^{21} - 8 q^{22} - 9 q^{23} + 16 q^{24} + 27 q^{25} + 6 q^{27} - 7 q^{28} - 5 q^{29} - 8 q^{30} + 23 q^{31} + 5 q^{32} + 49 q^{34} + 6 q^{35} + 18 q^{36} + 16 q^{37} + 28 q^{38} + 21 q^{40} + 54 q^{41} - 7 q^{42} + 8 q^{43} - 20 q^{44} + 23 q^{45} + 31 q^{46} - 4 q^{47} + 58 q^{48} + 5 q^{49} + 8 q^{50} - 13 q^{51} + 11 q^{53} - 26 q^{54} - 27 q^{55} - 12 q^{56} + 30 q^{57} + 15 q^{58} + 42 q^{59} + 2 q^{60} + 12 q^{61} + 46 q^{62} - 14 q^{63} - 15 q^{64} + 8 q^{66} + 24 q^{67} + 34 q^{68} - 36 q^{69} - 11 q^{70} + 49 q^{71} + 74 q^{72} + 45 q^{73} + 26 q^{74} - 18 q^{76} - 6 q^{77} - 2 q^{79} + 2 q^{80} - 33 q^{81} - 32 q^{82} + 60 q^{83} + 57 q^{84} + 13 q^{85} + 53 q^{86} + 64 q^{87} - 21 q^{88} + 59 q^{89} + 28 q^{90} + 29 q^{92} + 2 q^{93} - 32 q^{94} + 8 q^{95} + 77 q^{96} + 18 q^{97} + 16 q^{98} - 23 q^{99}+O(q^{100}) \) 27 * q + 8 * q^2 + 20 * q^4 + 27 * q^5 - 8 * q^6 + 6 * q^7 + 21 * q^8 + 23 * q^9 + 8 * q^10 - 27 * q^11 + 2 * q^12 - 11 * q^14 + 2 * q^16 + 13 * q^17 + 28 * q^18 + 8 * q^19 + 20 * q^20 + 23 * q^21 - 8 * q^22 - 9 * q^23 + 16 * q^24 + 27 * q^25 + 6 * q^27 - 7 * q^28 - 5 * q^29 - 8 * q^30 + 23 * q^31 + 5 * q^32 + 49 * q^34 + 6 * q^35 + 18 * q^36 + 16 * q^37 + 28 * q^38 + 21 * q^40 + 54 * q^41 - 7 * q^42 + 8 * q^43 - 20 * q^44 + 23 * q^45 + 31 * q^46 - 4 * q^47 + 58 * q^48 + 5 * q^49 + 8 * q^50 - 13 * q^51 + 11 * q^53 - 26 * q^54 - 27 * q^55 - 12 * q^56 + 30 * q^57 + 15 * q^58 + 42 * q^59 + 2 * q^60 + 12 * q^61 + 46 * q^62 - 14 * q^63 - 15 * q^64 + 8 * q^66 + 24 * q^67 + 34 * q^68 - 36 * q^69 - 11 * q^70 + 49 * q^71 + 74 * q^72 + 45 * q^73 + 26 * q^74 - 18 * q^76 - 6 * q^77 - 2 * q^79 + 2 * q^80 - 33 * q^81 - 32 * q^82 + 60 * q^83 + 57 * q^84 + 13 * q^85 + 53 * q^86 + 64 * q^87 - 21 * q^88 + 59 * q^89 + 28 * q^90 + 29 * q^92 + 2 * q^93 - 32 * q^94 + 8 * q^95 + 77 * q^96 + 18 * q^97 + 16 * q^98 - 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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