LMFDB - Embedded newform 7381.2.a.p.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.365014 q^{2} +1.51817 q^{3} -1.86676 q^{4} +1.31702 q^{5} -0.554152 q^{6} -1.96303 q^{7} +1.41142 q^{8} -0.695170 q^{9} +O(q^{10})$	\(q-0.365014 q^{2} +1.51817 q^{3} -1.86676 q^{4} +1.31702 q^{5} -0.554152 q^{6} -1.96303 q^{7} +1.41142 q^{8} -0.695170 q^{9} -0.480730 q^{10} -2.83406 q^{12} -4.52655 q^{13} +0.716533 q^{14} +1.99945 q^{15} +3.21834 q^{16} +4.39779 q^{17} +0.253747 q^{18} -1.04283 q^{19} -2.45856 q^{20} -2.98021 q^{21} -3.67076 q^{23} +2.14278 q^{24} -3.26546 q^{25} +1.65225 q^{26} -5.60988 q^{27} +3.66451 q^{28} +4.74019 q^{29} -0.729829 q^{30} -5.61182 q^{31} -3.99758 q^{32} -1.60525 q^{34} -2.58535 q^{35} +1.29772 q^{36} -5.69112 q^{37} +0.380647 q^{38} -6.87206 q^{39} +1.85887 q^{40} +6.63013 q^{41} +1.08782 q^{42} +7.56831 q^{43} -0.915552 q^{45} +1.33988 q^{46} +7.94674 q^{47} +4.88598 q^{48} -3.14652 q^{49} +1.19194 q^{50} +6.67658 q^{51} +8.45001 q^{52} +0.108868 q^{53} +2.04769 q^{54} -2.77066 q^{56} -1.58319 q^{57} -1.73024 q^{58} -0.664835 q^{59} -3.73251 q^{60} +1.00000 q^{61} +2.04839 q^{62} +1.36464 q^{63} -4.97751 q^{64} -5.96156 q^{65} +10.9112 q^{67} -8.20964 q^{68} -5.57282 q^{69} +0.943687 q^{70} +3.60257 q^{71} -0.981178 q^{72} +15.6746 q^{73} +2.07734 q^{74} -4.95751 q^{75} +1.94672 q^{76} +2.50840 q^{78} +5.71388 q^{79} +4.23862 q^{80} -6.43123 q^{81} -2.42009 q^{82} -5.20151 q^{83} +5.56334 q^{84} +5.79197 q^{85} -2.76254 q^{86} +7.19640 q^{87} +8.02334 q^{89} +0.334189 q^{90} +8.88576 q^{91} +6.85244 q^{92} -8.51967 q^{93} -2.90067 q^{94} -1.37342 q^{95} -6.06900 q^{96} +3.46335 q^{97} +1.14852 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) $ 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9	$ 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} + 21 q^{16} + 8 q^{17} + 16 q^{19} - 16 q^{20} + 12 q^{21} + 3 q^{23} + 62 q^{24} + 26 q^{25} - 4 q^{26} - 13 q^{27} - 42 q^{28} + 28 q^{29} + 12 q^{30} - q^{31} + 35 q^{32} + 8 q^{34} + 62 q^{35} + 17 q^{36} - 7 q^{37} + 20 q^{38} - 27 q^{40} + 28 q^{41} - 34 q^{42} + 22 q^{43} + 58 q^{46} - 2 q^{47} + 10 q^{48} + 25 q^{49} - 15 q^{50} + 38 q^{51} + 12 q^{52} - 4 q^{53} + 24 q^{54} - 48 q^{56} + 40 q^{57} + 8 q^{58} + 9 q^{59} + 18 q^{60} + 25 q^{61} + 4 q^{62} + 30 q^{63} + 41 q^{64} + 32 q^{65} - 15 q^{67} + 112 q^{68} - q^{69} + 14 q^{70} - 9 q^{71} - 59 q^{72} - 8 q^{73} + 54 q^{74} - 4 q^{75} + 32 q^{76} + 20 q^{78} + 30 q^{79} - 18 q^{80} + 17 q^{81} + 10 q^{83} - 39 q^{84} + 52 q^{85} - 6 q^{86} + 24 q^{87} - 5 q^{89} + 110 q^{90} - 38 q^{92} - q^{93} - 120 q^{94} + 50 q^{95} + 130 q^{96} + 5 q^{97} + 35 q^{98}+O(q^{100}) $ 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9 + 6 * q^10 + 2 * q^12 + 4 * q^13 - 10 * q^14 + q^15 + 21 * q^16 + 8 * q^17 + 16 * q^19 - 16 * q^20 + 12 * q^21 + 3 * q^23 + 62 * q^24 + 26 * q^25 - 4 * q^26 - 13 * q^27 - 42 * q^28 + 28 * q^29 + 12 * q^30 - q^31 + 35 * q^32 + 8 * q^34 + 62 * q^35 + 17 * q^36 - 7 * q^37 + 20 * q^38 - 27 * q^40 + 28 * q^41 - 34 * q^42 + 22 * q^43 + 58 * q^46 - 2 * q^47 + 10 * q^48 + 25 * q^49 - 15 * q^50 + 38 * q^51 + 12 * q^52 - 4 * q^53 + 24 * q^54 - 48 * q^56 + 40 * q^57 + 8 * q^58 + 9 * q^59 + 18 * q^60 + 25 * q^61 + 4 * q^62 + 30 * q^63 + 41 * q^64 + 32 * q^65 - 15 * q^67 + 112 * q^68 - q^69 + 14 * q^70 - 9 * q^71 - 59 * q^72 - 8 * q^73 + 54 * q^74 - 4 * q^75 + 32 * q^76 + 20 * q^78 + 30 * q^79 - 18 * q^80 + 17 * q^81 + 10 * q^83 - 39 * q^84 + 52 * q^85 - 6 * q^86 + 24 * q^87 - 5 * q^89 + 110 * q^90 - 38 * q^92 - q^93 - 120 * q^94 + 50 * q^95 + 130 * q^96 + 5 * q^97 + 35 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.365014	−0.258104	−0.129052	−	0.991638i	$-0.541193\pi$
$2$	−0.365014	−0.258104	−0.129052	+	0.991638i	$0.541193\pi$
$3$	1.51817	0.876514	0.438257	−	0.898850i	$-0.355596\pi$
$3$	1.51817	0.876514	0.438257	+	0.898850i	$0.355596\pi$
$4$	−1.86676	−0.933382
$5$	1.31702	0.588989	0.294494	−	0.955653i	$-0.404849\pi$
$5$	1.31702	0.588989	0.294494	+	0.955653i	$0.404849\pi$
$6$	−0.554152	−0.226232
$7$	−1.96303	−0.741955	−0.370978	−	0.928642i	$-0.620977\pi$
$7$	−1.96303	−0.741955	−0.370978	+	0.928642i	$0.620977\pi$
$8$	1.41142	0.499013
$9$	−0.695170	−0.231723
$10$	−0.480730	−0.152020
$11$	0	0
$11$	0	0
$12$	−2.83406	−0.818123
$13$	−4.52655	−1.25544	−0.627720	−	0.778439i	$-0.716012\pi$
$13$	−4.52655	−1.25544	−0.627720	+	0.778439i	$0.716012\pi$
$14$	0.716533	0.191501
$15$	1.99945	0.516257
$16$	3.21834	0.804585
$17$	4.39779	1.06662	0.533311	−	0.845920i	$-0.320948\pi$
$17$	4.39779	1.06662	0.533311	+	0.845920i	$0.320948\pi$
$18$	0.253747	0.0598086
$19$	−1.04283	−0.239241	−0.119621	−	0.992820i	$-0.538168\pi$
$19$	−1.04283	−0.239241	−0.119621	+	0.992820i	$0.538168\pi$
$20$	−2.45856	−0.549752
$21$	−2.98021	−0.650334
$22$	0	0
$23$	−3.67076	−0.765406	−0.382703	−	0.923871i	$-0.625007\pi$
$23$	−3.67076	−0.765406	−0.382703	+	0.923871i	$0.625007\pi$
$24$	2.14278	0.437392
$25$	−3.26546	−0.653092
$26$	1.65225	0.324034
$27$	−5.60988	−1.07962
$28$	3.66451	0.692528
$29$	4.74019	0.880231	0.440116	−	0.897941i	$-0.354937\pi$
$29$	4.74019	0.880231	0.440116	+	0.897941i	$0.354937\pi$
$30$	−0.729829	−0.133248
$31$	−5.61182	−1.00791	−0.503956	−	0.863729i	$-0.668123\pi$
$31$	−5.61182	−1.00791	−0.503956	+	0.863729i	$0.668123\pi$
$32$	−3.99758	−0.706680
$33$	0	0
$34$	−1.60525	−0.275299
$35$	−2.58535	−0.437003
$36$	1.29772	0.216286
$37$	−5.69112	−0.935614	−0.467807	−	0.883831i	$-0.654956\pi$
$37$	−5.69112	−0.935614	−0.467807	+	0.883831i	$0.654956\pi$
$38$	0.380647	0.0617491
$39$	−6.87206	−1.10041
$40$	1.85887	0.293913
$41$	6.63013	1.03545	0.517726	−	0.855546i	$-0.326779\pi$
$41$	6.63013	1.03545	0.517726	+	0.855546i	$0.326779\pi$
$42$	1.08782	0.167854
$43$	7.56831	1.15416	0.577078	−	0.816689i	$-0.304193\pi$
$43$	7.56831	1.15416	0.577078	+	0.816689i	$0.304193\pi$
$44$	0	0
$45$	−0.915552	−0.136482
$46$	1.33988	0.197554
$47$	7.94674	1.15915	0.579575	−	0.814919i	$-0.303218\pi$
$47$	7.94674	1.15915	0.579575	+	0.814919i	$0.303218\pi$
$48$	4.88598	0.705230
$49$	−3.14652	−0.449502
$50$	1.19194	0.168566
$51$	6.67658	0.934908
$52$	8.45001	1.17181
$53$	0.108868	0.0149542	0.00747710	−	0.999972i	$-0.497620\pi$
$53$	0.108868	0.0149542	0.00747710	+	0.999972i	$0.497620\pi$
$54$	2.04769	0.278655
$55$	0	0
$56$	−2.77066	−0.370246
$57$	−1.58319	−0.209698
$58$	−1.73024	−0.227191
$59$	−0.664835	−0.0865542	−0.0432771	−	0.999063i	$-0.513780\pi$
$59$	−0.664835	−0.0865542	−0.0432771	+	0.999063i	$0.513780\pi$
$60$	−3.73251	−0.481865
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.04839	0.260146
$63$	1.36464	0.171928
$64$	−4.97751	−0.622189
$65$	−5.96156	−0.739440
$66$	0	0
$67$	10.9112	1.33302	0.666510	−	0.745496i	$-0.267787\pi$
$67$	10.9112	1.33302	0.666510	+	0.745496i	$0.267787\pi$
$68$	−8.20964	−0.995565
$69$	−5.57282	−0.670889
$70$	0.943687	0.112792
$71$	3.60257	0.427546	0.213773	−	0.976883i	$-0.431425\pi$
$71$	3.60257	0.427546	0.213773	+	0.976883i	$0.431425\pi$
$72$	−0.981178	−0.115633
$73$	15.6746	1.83457	0.917285	−	0.398232i	$-0.130376\pi$
$73$	15.6746	1.83457	0.917285	+	0.398232i	$0.130376\pi$
$74$	2.07734	0.241485
$75$	−4.95751	−0.572444
$76$	1.94672	0.223304
$77$	0	0
$78$	2.50840	0.284020
$79$	5.71388	0.642862	0.321431	−	0.946933i	$-0.395836\pi$
$79$	5.71388	0.642862	0.321431	+	0.946933i	$0.395836\pi$
$80$	4.23862	0.473892
$81$	−6.43123	−0.714581
$82$	−2.42009	−0.267254
$83$	−5.20151	−0.570940	−0.285470	−	0.958388i	$-0.592150\pi$
$83$	−5.20151	−0.570940	−0.285470	+	0.958388i	$0.592150\pi$
$84$	5.56334	0.607010
$85$	5.79197	0.628228
$86$	−2.76254	−0.297892
$87$	7.19640	0.771535
$88$	0	0
$89$	8.02334	0.850473	0.425236	−	0.905082i	$-0.360191\pi$
$89$	8.02334	0.850473	0.425236	+	0.905082i	$0.360191\pi$
$90$	0.334189	0.0352266
$91$	8.88576	0.931480
$92$	6.85244	0.714417
$93$	−8.51967	−0.883449
$94$	−2.90067	−0.299181
$95$	−1.37342	−0.140910
$96$	−6.06900	−0.619415
$97$	3.46335	0.351649	0.175825	−	0.984421i	$-0.443741\pi$
$97$	3.46335	0.351649	0.175825	+	0.984421i	$0.443741\pi$
$98$	1.14852	0.116018
$99$	0	0
$100$	6.09585	0.609585
$101$	−15.4358	−1.53592	−0.767959	−	0.640499i	$-0.778727\pi$
$101$	−15.4358	−1.53592	−0.767959	+	0.640499i	$0.778727\pi$
$102$	−2.43704	−0.241303
$103$	1.87764	0.185009	0.0925046	−	0.995712i	$-0.470513\pi$
$103$	1.87764	0.185009	0.0925046	+	0.995712i	$0.470513\pi$
$104$	−6.38888	−0.626481
$105$	−3.92499	−0.383040
$106$	−0.0397384	−0.00385974
$107$	9.75656	0.943203	0.471601	−	0.881812i	$-0.343676\pi$
$107$	9.75656	0.943203	0.471601	+	0.881812i	$0.343676\pi$
$108$	10.4723	1.00770
$109$	11.3825	1.09025	0.545123	−	0.838356i	$-0.316483\pi$
$109$	11.3825	1.09025	0.545123	+	0.838356i	$0.316483\pi$
$110$	0	0
$111$	−8.64006	−0.820079
$112$	−6.31770	−0.596966
$113$	−16.0608	−1.51088	−0.755438	−	0.655220i	$-0.772576\pi$
$113$	−16.0608	−1.51088	−0.755438	+	0.655220i	$0.772576\pi$
$114$	0.577885	0.0541239
$115$	−4.83446	−0.450816
$116$	−8.84882	−0.821593
$117$	3.14672	0.290915
$118$	0.242674	0.0223400
$119$	−8.63299	−0.791385
$120$	2.82208	0.257619
$121$	0	0
$122$	−0.365014	−0.0330468
$123$	10.0656	0.907589
$124$	10.4759	0.940767
$125$	−10.8858	−0.973653
$126$	−0.498112	−0.0443753
$127$	−16.1785	−1.43561	−0.717805	−	0.696244i	$-0.754853\pi$
$127$	−16.1785	−1.43561	−0.717805	+	0.696244i	$0.754853\pi$
$128$	9.81203	0.867269
$129$	11.4899	1.01163
$130$	2.17605	0.190852
$131$	−4.67548	−0.408498	−0.204249	−	0.978919i	$-0.565475\pi$
$131$	−4.67548	−0.408498	−0.204249	+	0.978919i	$0.565475\pi$
$132$	0	0
$133$	2.04710	0.177506
$134$	−3.98275	−0.344058
$135$	−7.38832	−0.635886
$136$	6.20714	0.532258
$137$	20.5046	1.75182	0.875912	−	0.482471i	$-0.160261\pi$
$137$	20.5046	1.75182	0.875912	+	0.482471i	$0.160261\pi$
$138$	2.03416	0.173159
$139$	−1.09518	−0.0928920	−0.0464460	−	0.998921i	$-0.514790\pi$
$139$	−1.09518	−0.0928920	−0.0464460	+	0.998921i	$0.514790\pi$
$140$	4.82623	0.407891
$141$	12.0645	1.01601
$142$	−1.31499	−0.110351
$143$	0	0
$144$	−2.23729	−0.186441
$145$	6.24292	0.518446
$146$	−5.72143	−0.473509
$147$	−4.77694	−0.393995
$148$	10.6240	0.873285
$149$	−7.24630	−0.593640	−0.296820	−	0.954933i	$-0.595926\pi$
$149$	−7.24630	−0.593640	−0.296820	+	0.954933i	$0.595926\pi$
$150$	1.80956	0.147750
$151$	1.35241	0.110057	0.0550286	−	0.998485i	$-0.482475\pi$
$151$	1.35241	0.110057	0.0550286	+	0.998485i	$0.482475\pi$
$152$	−1.47187	−0.119385
$153$	−3.05721	−0.247161
$154$	0	0
$155$	−7.39087	−0.593649
$156$	12.8285	1.02710
$157$	−14.1528	−1.12951	−0.564756	−	0.825258i	$-0.691030\pi$
$157$	−14.1528	−1.12951	−0.564756	+	0.825258i	$0.691030\pi$
$158$	−2.08565	−0.165925
$159$	0.165280	0.0131076
$160$	−5.26489	−0.416226
$161$	7.20581	0.567897
$162$	2.34749	0.184436
$163$	17.1087	1.34005	0.670027	−	0.742336i	$-0.266282\pi$
$163$	17.1087	1.34005	0.670027	+	0.742336i	$0.266282\pi$
$164$	−12.3769	−0.966473
$165$	0	0
$166$	1.89862	0.147362
$167$	−2.46595	−0.190821	−0.0954105	−	0.995438i	$-0.530416\pi$
$167$	−2.46595	−0.190821	−0.0954105	+	0.995438i	$0.530416\pi$
$168$	−4.20633	−0.324525
$169$	7.48969	0.576130
$170$	−2.11415	−0.162148
$171$	0.724943	0.0554378
$172$	−14.1282	−1.07727
$173$	19.5490	1.48628	0.743142	−	0.669134i	$-0.233335\pi$
$173$	19.5490	1.48628	0.743142	+	0.669134i	$0.233335\pi$
$174$	−2.62679	−0.199136
$175$	6.41019	0.484565
$176$	0	0
$177$	−1.00933	−0.0758660
$178$	−2.92863	−0.219510
$179$	11.7622	0.879148	0.439574	−	0.898206i	$-0.355129\pi$
$179$	11.7622	0.879148	0.439574	+	0.898206i	$0.355129\pi$
$180$	1.70912	0.127390
$181$	21.9857	1.63419	0.817093	−	0.576506i	$-0.195584\pi$
$181$	21.9857	1.63419	0.817093	+	0.576506i	$0.195584\pi$
$182$	−3.24342	−0.240419
$183$	1.51817	0.112226
$184$	−5.18099	−0.381948
$185$	−7.49531	−0.551066
$186$	3.10980	0.228021
$187$	0	0
$188$	−14.8347	−1.08193
$189$	11.0124	0.801032
$190$	0.501319	0.0363695
$191$	−21.6651	−1.56763	−0.783816	−	0.620993i	$-0.786730\pi$
$191$	−21.6651	−1.56763	−0.783816	+	0.620993i	$0.786730\pi$
$192$	−7.55669	−0.545357
$193$	3.58736	0.258224	0.129112	−	0.991630i	$-0.458787\pi$
$193$	3.58736	0.258224	0.129112	+	0.991630i	$0.458787\pi$
$194$	−1.26417	−0.0907621
$195$	−9.05064	−0.648130
$196$	5.87381	0.419558
$197$	22.3148	1.58987	0.794933	−	0.606697i	$-0.207506\pi$
$197$	22.3148	1.58987	0.794933	+	0.606697i	$0.207506\pi$
$198$	0	0
$199$	−2.00884	−0.142403	−0.0712014	−	0.997462i	$-0.522683\pi$
$199$	−2.00884	−0.142403	−0.0712014	+	0.997462i	$0.522683\pi$
$200$	−4.60895	−0.325902
$201$	16.5651	1.16841
$202$	5.63427	0.396426
$203$	−9.30513	−0.653092
$204$	−12.4636	−0.872627
$205$	8.73201	0.609870
$206$	−0.685364	−0.0477516
$207$	2.55180	0.177362
$208$	−14.5680	−1.01011
$209$	0	0
$210$	1.43267	0.0988639
$211$	9.85482	0.678433	0.339217	−	0.940708i	$-0.389838\pi$
$211$	9.85482	0.678433	0.339217	+	0.940708i	$0.389838\pi$
$212$	−0.203231	−0.0139580
$213$	5.46930	0.374750
$214$	−3.56128	−0.243444
$215$	9.96760	0.679785
$216$	−7.91792	−0.538746
$217$	11.0162	0.747825
$218$	−4.15477	−0.281397
$219$	23.7966	1.60803
$220$	0	0
$221$	−19.9068	−1.33908
$222$	3.15374	0.211665
$223$	11.1067	0.743760	0.371880	−	0.928281i	$-0.378713\pi$
$223$	11.1067	0.743760	0.371880	+	0.928281i	$0.378713\pi$
$224$	7.84737	0.524325
$225$	2.27005	0.151337
$226$	5.86243	0.389963
$227$	8.55147	0.567581	0.283791	−	0.958886i	$-0.408408\pi$
$227$	8.55147	0.567581	0.283791	+	0.958886i	$0.408408\pi$
$228$	2.95544	0.195729
$229$	−1.25760	−0.0831045	−0.0415522	−	0.999136i	$-0.513230\pi$
$229$	−1.25760	−0.0831045	−0.0415522	+	0.999136i	$0.513230\pi$
$230$	1.76464	0.116357
$231$	0	0
$232$	6.69041	0.439247
$233$	20.4635	1.34061	0.670306	−	0.742085i	$-0.266163\pi$
$233$	20.4635	1.34061	0.670306	+	0.742085i	$0.266163\pi$
$234$	−1.14860	−0.0750862
$235$	10.4660	0.682727
$236$	1.24109	0.0807882
$237$	8.67463	0.563478
$238$	3.15116	0.204259
$239$	13.6572	0.883410	0.441705	−	0.897160i	$-0.354374\pi$
$239$	13.6572	0.883410	0.441705	+	0.897160i	$0.354374\pi$
$240$	6.43493	0.415373
$241$	14.8204	0.954666	0.477333	−	0.878723i	$-0.341604\pi$
$241$	14.8204	0.954666	0.477333	+	0.878723i	$0.341604\pi$
$242$	0	0
$243$	7.06597	0.453282
$244$	−1.86676	−0.119507
$245$	−4.14402	−0.264752
$246$	−3.67410	−0.234252
$247$	4.72042	0.300353
$248$	−7.92064	−0.502961
$249$	−7.89677	−0.500437
$250$	3.97346	0.251303
$251$	−3.03277	−0.191427	−0.0957135	−	0.995409i	$-0.530513\pi$
$251$	−3.03277	−0.191427	−0.0957135	+	0.995409i	$0.530513\pi$
$252$	−2.54746	−0.160475
$253$	0	0
$254$	5.90538	0.370536
$255$	8.79318	0.550651
$256$	6.37349	0.398343
$257$	−9.01120	−0.562103	−0.281052	−	0.959693i	$-0.590683\pi$
$257$	−9.01120	−0.562103	−0.281052	+	0.959693i	$0.590683\pi$
$258$	−4.19399	−0.261106
$259$	11.1718	0.694183
$260$	11.1288	0.690180
$261$	−3.29524	−0.203970
$262$	1.70661	0.105435
$263$	9.92240	0.611841	0.305921	−	0.952057i	$-0.401036\pi$
$263$	9.92240	0.611841	0.305921	+	0.952057i	$0.401036\pi$
$264$	0	0
$265$	0.143382	0.00880786
$266$	−0.747221	−0.0458150
$267$	12.1808	0.745451
$268$	−20.3687	−1.24422
$269$	−12.3640	−0.753847	−0.376923	−	0.926244i	$-0.623018\pi$
$269$	−12.3640	−0.753847	−0.376923	+	0.926244i	$0.623018\pi$
$270$	2.69684	0.164124
$271$	28.0500	1.70391	0.851957	−	0.523612i	$-0.175416\pi$
$271$	28.0500	1.70391	0.851957	+	0.523612i	$0.175416\pi$
$272$	14.1536	0.858188
$273$	13.4901	0.816456
$274$	−7.48445	−0.452152
$275$	0	0
$276$	10.4032	0.626196
$277$	−28.3645	−1.70426	−0.852128	−	0.523333i	$-0.824688\pi$
$277$	−28.3645	−1.70426	−0.852128	+	0.523333i	$0.824688\pi$
$278$	0.399756	0.0239758
$279$	3.90116	0.233557
$280$	−3.64902	−0.218070
$281$	11.5046	0.686309	0.343154	−	0.939279i	$-0.388505\pi$
$281$	11.5046	0.686309	0.343154	+	0.939279i	$0.388505\pi$
$282$	−4.40370	−0.262237
$283$	22.0926	1.31327	0.656634	−	0.754209i	$-0.271980\pi$
$283$	22.0926	1.31327	0.656634	+	0.754209i	$0.271980\pi$
$284$	−6.72515	−0.399064
$285$	−2.08509	−0.123510
$286$	0	0
$287$	−13.0151	−0.768259
$288$	2.77900	0.163754
$289$	2.34057	0.137680
$290$	−2.27875	−0.133813
$291$	5.25794	0.308226
$292$	−29.2607	−1.71235
$293$	−8.54710	−0.499327	−0.249663	−	0.968333i	$-0.580320\pi$
$293$	−8.54710	−0.499327	−0.249663	+	0.968333i	$0.580320\pi$
$294$	1.74365	0.101692
$295$	−0.875601	−0.0509795
$296$	−8.03257	−0.466884
$297$	0	0
$298$	2.64500	0.153221
$299$	16.6159	0.960922
$300$	9.25451	0.534310
$301$	−14.8568	−0.856332
$302$	−0.493647	−0.0284062
$303$	−23.4341	−1.34625
$304$	−3.35618	−0.192490
$305$	1.31702	0.0754123
$306$	1.11592	0.0637931
$307$	2.37875	0.135762	0.0678812	−	0.997693i	$-0.478376\pi$
$307$	2.37875	0.135762	0.0678812	+	0.997693i	$0.478376\pi$
$308$	0	0
$309$	2.85057	0.162163
$310$	2.69777	0.153223
$311$	−5.89852	−0.334474	−0.167237	−	0.985917i	$-0.553485\pi$
$311$	−5.89852	−0.334474	−0.167237	+	0.985917i	$0.553485\pi$
$312$	−9.69939	−0.549120
$313$	−9.22664	−0.521520	−0.260760	−	0.965404i	$-0.583973\pi$
$313$	−9.22664	−0.521520	−0.260760	+	0.965404i	$0.583973\pi$
$314$	5.16595	0.291532
$315$	1.79725	0.101264
$316$	−10.6665	−0.600036
$317$	−12.7069	−0.713689	−0.356844	−	0.934164i	$-0.616147\pi$
$317$	−12.7069	−0.713689	−0.356844	+	0.934164i	$0.616147\pi$
$318$	−0.0603295	−0.00338311
$319$	0	0
$320$	−6.55547	−0.366462
$321$	14.8121	0.826730
$322$	−2.63022	−0.146576
$323$	−4.58614	−0.255180
$324$	12.0056	0.666977
$325$	14.7813	0.819918
$326$	−6.24490	−0.345873
$327$	17.2805	0.955616
$328$	9.35792	0.516704
$329$	−15.5997	−0.860038
$330$	0	0
$331$	−10.3368	−0.568162	−0.284081	−	0.958800i	$-0.591688\pi$
$331$	−10.3368	−0.568162	−0.284081	+	0.958800i	$0.591688\pi$
$332$	9.71000	0.532906
$333$	3.95629	0.216803
$334$	0.900106	0.0492516
$335$	14.3703	0.785134
$336$	−9.59132	−0.523249
$337$	−2.97328	−0.161965	−0.0809824	−	0.996716i	$-0.525806\pi$
$337$	−2.97328	−0.161965	−0.0809824	+	0.996716i	$0.525806\pi$
$338$	−2.73384	−0.148701
$339$	−24.3830	−1.32430
$340$	−10.8123	−0.586377
$341$	0	0
$342$	−0.264614	−0.0143087
$343$	19.9179	1.07547
$344$	10.6821	0.575939
$345$	−7.33952	−0.395146
$346$	−7.13566	−0.383615
$347$	−31.1126	−1.67021	−0.835107	−	0.550087i	$-0.814594\pi$
$347$	−31.1126	−1.67021	−0.835107	+	0.550087i	$0.814594\pi$
$348$	−13.4340	−0.720137
$349$	−35.2763	−1.88830	−0.944148	−	0.329522i	$-0.893113\pi$
$349$	−35.2763	−1.88830	−0.944148	+	0.329522i	$0.893113\pi$
$350$	−2.33981	−0.125068
$351$	25.3934	1.35540
$352$	0	0
$353$	0.631343	0.0336030	0.0168015	−	0.999859i	$-0.494652\pi$
$353$	0.631343	0.0336030	0.0168015	+	0.999859i	$0.494652\pi$
$354$	0.368420	0.0195813
$355$	4.74465	0.251820
$356$	−14.9777	−0.793816
$357$	−13.1063	−0.693660
$358$	−4.29336	−0.226911
$359$	−20.1657	−1.06431	−0.532153	−	0.846648i	$-0.678617\pi$
$359$	−20.1657	−1.06431	−0.532153	+	0.846648i	$0.678617\pi$
$360$	−1.29223	−0.0681065
$361$	−17.9125	−0.942764
$362$	−8.02509	−0.421790
$363$	0	0
$364$	−16.5876	−0.869427
$365$	20.6437	1.08054
$366$	−0.554152	−0.0289660
$367$	15.1802	0.792399	0.396199	−	0.918164i	$-0.370329\pi$
$367$	15.1802	0.792399	0.396199	+	0.918164i	$0.370329\pi$
$368$	−11.8138	−0.615834
$369$	−4.60907	−0.239938
$370$	2.73589	0.142232
$371$	−0.213712	−0.0110953
$372$	15.9042	0.824596
$373$	14.9459	0.773870	0.386935	−	0.922107i	$-0.373534\pi$
$373$	14.9459	0.773870	0.386935	+	0.922107i	$0.373534\pi$
$374$	0	0
$375$	−16.5264	−0.853420
$376$	11.2162	0.578432
$377$	−21.4567	−1.10508
$378$	−4.01967	−0.206749
$379$	29.0308	1.49121	0.745605	−	0.666388i	$-0.232161\pi$
$379$	29.0308	1.49121	0.745605	+	0.666388i	$0.232161\pi$
$380$	2.56386	0.131523
$381$	−24.5617	−1.25833
$382$	7.90807	0.404612
$383$	11.9582	0.611033	0.305517	−	0.952187i	$-0.401171\pi$
$383$	11.9582	0.611033	0.305517	+	0.952187i	$0.401171\pi$
$384$	14.8963	0.760173
$385$	0	0
$386$	−1.30944	−0.0666486
$387$	−5.26126	−0.267445
$388$	−6.46525	−0.328223
$389$	−0.612135	−0.0310365	−0.0155182	−	0.999880i	$-0.504940\pi$
$389$	−0.612135	−0.0310365	−0.0155182	+	0.999880i	$0.504940\pi$
$390$	3.30361	0.167285
$391$	−16.1432	−0.816398
$392$	−4.44107	−0.224308
$393$	−7.09816	−0.358055
$394$	−8.14522	−0.410350
$395$	7.52529	0.378639
$396$	0	0
$397$	1.83187	0.0919391	0.0459695	−	0.998943i	$-0.485362\pi$
$397$	1.83187	0.0919391	0.0459695	+	0.998943i	$0.485362\pi$
$398$	0.733254	0.0367547
$399$	3.10784	0.155587
$400$	−10.5094	−0.525468
$401$	5.70772	0.285030	0.142515	−	0.989793i	$-0.454481\pi$
$401$	5.70772	0.285030	0.142515	+	0.989793i	$0.454481\pi$
$402$	−6.04648	−0.301571
$403$	25.4022	1.26537
$404$	28.8150	1.43360
$405$	−8.47005	−0.420880
$406$	3.39650	0.168566
$407$	0	0
$408$	9.42348	0.466532
$409$	−12.6779	−0.626882	−0.313441	−	0.949608i	$-0.601482\pi$
$409$	−12.6779	−0.626882	−0.313441	+	0.949608i	$0.601482\pi$
$410$	−3.18730	−0.157410
$411$	31.1294	1.53550
$412$	−3.50511	−0.172684
$413$	1.30509	0.0642193
$414$	−0.931442	−0.0457779
$415$	−6.85049	−0.336277
$416$	18.0953	0.887194
$417$	−1.66267	−0.0814212
$418$	0	0
$419$	31.4897	1.53837	0.769187	−	0.639024i	$-0.220662\pi$
$419$	31.4897	1.53837	0.769187	+	0.639024i	$0.220662\pi$
$420$	7.32703	0.357522
$421$	24.8511	1.21117	0.605584	−	0.795782i	$-0.292940\pi$
$421$	24.8511	1.21117	0.605584	+	0.795782i	$0.292940\pi$
$422$	−3.59714	−0.175106
$423$	−5.52433	−0.268602
$424$	0.153659	0.00746235
$425$	−14.3608	−0.696602
$426$	−1.99637	−0.0967244
$427$	−1.96303	−0.0949976
$428$	−18.2132	−0.880369
$429$	0	0
$430$	−3.63831	−0.175455
$431$	16.7513	0.806884	0.403442	−	0.915005i	$-0.367814\pi$
$431$	16.7513	0.806884	0.403442	+	0.915005i	$0.367814\pi$
$432$	−18.0545	−0.868648
$433$	28.2861	1.35934	0.679672	−	0.733517i	$-0.262122\pi$
$433$	28.2861	1.35934	0.679672	+	0.733517i	$0.262122\pi$
$434$	−4.02105	−0.193017
$435$	9.47780	0.454426
$436$	−21.2485	−1.01762
$437$	3.82797	0.183117
$438$	−8.68609	−0.415037
$439$	17.9049	0.854552	0.427276	−	0.904121i	$-0.359473\pi$
$439$	17.9049	0.854552	0.427276	+	0.904121i	$0.359473\pi$
$440$	0	0
$441$	2.18736	0.104160
$442$	7.26627	0.345621
$443$	−14.3240	−0.680554	−0.340277	−	0.940325i	$-0.610521\pi$
$443$	−14.3240	−0.680554	−0.340277	+	0.940325i	$0.610521\pi$
$444$	16.1290	0.765447
$445$	10.5669	0.500919
$446$	−4.05410	−0.191967
$447$	−11.0011	−0.520334
$448$	9.77099	0.461636
$449$	7.46504	0.352297	0.176148	−	0.984364i	$-0.443636\pi$
$449$	7.46504	0.352297	0.176148	+	0.984364i	$0.443636\pi$
$450$	−0.828599	−0.0390606
$451$	0	0
$452$	29.9818	1.41023
$453$	2.05318	0.0964668
$454$	−3.12141	−0.146495
$455$	11.7027	0.548631
$456$	−2.23455	−0.104642
$457$	−27.9953	−1.30957	−0.654783	−	0.755817i	$-0.727240\pi$
$457$	−27.9953	−1.30957	−0.654783	+	0.755817i	$0.727240\pi$
$458$	0.459041	0.0214496
$459$	−24.6711	−1.15155
$460$	9.02480	0.420783
$461$	9.33439	0.434746	0.217373	−	0.976089i	$-0.430251\pi$
$461$	9.33439	0.434746	0.217373	+	0.976089i	$0.430251\pi$
$462$	0	0
$463$	37.0481	1.72177	0.860887	−	0.508797i	$-0.169910\pi$
$463$	37.0481	1.72177	0.860887	+	0.508797i	$0.169910\pi$
$464$	15.2556	0.708221
$465$	−11.2206	−0.520341
$466$	−7.46948	−0.346017
$467$	−15.1004	−0.698762	−0.349381	−	0.936981i	$-0.613608\pi$
$467$	−15.1004	−0.698762	−0.349381	+	0.936981i	$0.613608\pi$
$468$	−5.87419	−0.271535
$469$	−21.4191	−0.989041
$470$	−3.82024	−0.176214
$471$	−21.4862	−0.990034
$472$	−0.938364	−0.0431917
$473$	0	0
$474$	−3.16636	−0.145436
$475$	3.40532	0.156247
$476$	16.1158	0.738665
$477$	−0.0756819	−0.00346524
$478$	−4.98506	−0.228012
$479$	11.4818	0.524617	0.262308	−	0.964984i	$-0.415516\pi$
$479$	11.4818	0.524617	0.262308	+	0.964984i	$0.415516\pi$
$480$	−7.99299	−0.364828
$481$	25.7611	1.17461
$482$	−5.40965	−0.246403
$483$	10.9396	0.497770
$484$	0	0
$485$	4.56129	0.207118
$486$	−2.57918	−0.116994
$487$	−13.4681	−0.610299	−0.305150	−	0.952304i	$-0.598706\pi$
$487$	−13.4681	−0.610299	−0.305150	+	0.952304i	$0.598706\pi$
$488$	1.41142	0.0638921
$489$	25.9738	1.17458
$490$	1.51263	0.0683335
$491$	32.1829	1.45239	0.726196	−	0.687487i	$-0.241286\pi$
$491$	32.1829	1.45239	0.726196	+	0.687487i	$0.241286\pi$
$492$	−18.7902	−0.847127
$493$	20.8464	0.938873
$494$	−1.72302	−0.0775223
$495$	0	0
$496$	−18.0607	−0.810951
$497$	−7.07195	−0.317220
$498$	2.88243	0.129165
$499$	−0.527751	−0.0236254	−0.0118127	−	0.999930i	$-0.503760\pi$
$499$	−0.527751	−0.0236254	−0.0118127	+	0.999930i	$0.503760\pi$
$500$	20.3212	0.908790
$501$	−3.74373	−0.167257
$502$	1.10700	0.0494080
$503$	−25.1035	−1.11931	−0.559656	−	0.828725i	$-0.689067\pi$
$503$	−25.1035	−1.11931	−0.559656	+	0.828725i	$0.689067\pi$
$504$	1.92608	0.0857945
$505$	−20.3292	−0.904638
$506$	0	0
$507$	11.3706	0.504986
$508$	30.2015	1.33997
$509$	7.56794	0.335443	0.167722	−	0.985834i	$-0.446359\pi$
$509$	7.56794	0.335443	0.167722	+	0.985834i	$0.446359\pi$
$510$	−3.20963	−0.142125
$511$	−30.7696	−1.36117
$512$	−21.9505	−0.970083
$513$	5.85015	0.258290
$514$	3.28921	0.145081
$515$	2.47289	0.108968
$516$	−21.4490	−0.944241
$517$	0	0
$518$	−4.07787	−0.179171
$519$	29.6787	1.30275
$520$	−8.41428	−0.368990
$521$	10.2532	0.449200	0.224600	−	0.974451i	$-0.427892\pi$
$521$	10.2532	0.449200	0.224600	+	0.974451i	$0.427892\pi$
$522$	1.20281	0.0526454
$523$	−17.7984	−0.778268	−0.389134	−	0.921181i	$-0.627226\pi$
$523$	−17.7984	−0.778268	−0.389134	+	0.921181i	$0.627226\pi$
$524$	8.72802	0.381285
$525$	9.73174	0.424728
$526$	−3.62181	−0.157919
$527$	−24.6796	−1.07506
$528$	0	0
$529$	−9.52553	−0.414153
$530$	−0.0523362	−0.00227334
$531$	0.462173	0.0200566
$532$	−3.82146	−0.165681
$533$	−30.0116	−1.29995
$534$	−4.44615	−0.192404
$535$	12.8496	0.555536
$536$	15.4004	0.665195
$537$	17.8570	0.770585
$538$	4.51303	0.194571
$539$	0	0
$540$	13.7923	0.593525
$541$	23.6573	1.01711	0.508553	−	0.861031i	$-0.330181\pi$
$541$	23.6573	1.01711	0.508553	+	0.861031i	$0.330181\pi$
$542$	−10.2386	−0.439787
$543$	33.3780	1.43239
$544$	−17.5805	−0.753760
$545$	14.9910	0.642143
$546$	−4.92406	−0.210730
$547$	−3.29162	−0.140740	−0.0703698	−	0.997521i	$-0.522418\pi$
$547$	−3.29162	−0.140740	−0.0703698	+	0.997521i	$0.522418\pi$
$548$	−38.2772	−1.63512
$549$	−0.695170	−0.0296691
$550$	0	0
$551$	−4.94321	−0.210588
$552$	−7.86561	−0.334783
$553$	−11.2165	−0.476975
$554$	10.3534	0.439875
$555$	−11.3791	−0.483017
$556$	2.04444	0.0867038
$557$	25.6414	1.08646	0.543231	−	0.839583i	$-0.317201\pi$
$557$	25.6414	1.08646	0.543231	+	0.839583i	$0.317201\pi$
$558$	−1.42398	−0.0602818
$559$	−34.2583	−1.44897
$560$	−8.32053	−0.351606
$561$	0	0
$562$	−4.19935	−0.177139
$563$	8.93812	0.376697	0.188348	−	0.982102i	$-0.439687\pi$
$563$	8.93812	0.376697	0.188348	+	0.982102i	$0.439687\pi$
$564$	−22.5215	−0.948328
$565$	−21.1524	−0.889889
$566$	−8.06410	−0.338960
$567$	12.6247	0.530187
$568$	5.08475	0.213351
$569$	38.1684	1.60010	0.800051	−	0.599932i	$-0.204806\pi$
$569$	38.1684	1.60010	0.800051	+	0.599932i	$0.204806\pi$
$570$	0.761086	0.0318784
$571$	13.7023	0.573423	0.286711	−	0.958017i	$-0.407438\pi$
$571$	13.7023	0.573423	0.286711	+	0.958017i	$0.407438\pi$
$572$	0	0
$573$	−32.8913	−1.37405
$574$	4.75071	0.198291
$575$	11.9867	0.499881
$576$	3.46021	0.144176
$577$	36.1808	1.50623	0.753114	−	0.657891i	$-0.228551\pi$
$577$	36.1808	1.50623	0.753114	+	0.657891i	$0.228551\pi$
$578$	−0.854340	−0.0355359
$579$	5.44621	0.226337
$580$	−11.6541	−0.483909
$581$	10.2107	0.423612
$582$	−1.91922	−0.0795542
$583$	0	0
$584$	22.1234	0.915474
$585$	4.14429	0.171345
$586$	3.11981	0.128878
$587$	6.18397	0.255240	0.127620	−	0.991823i	$-0.459266\pi$
$587$	6.18397	0.255240	0.127620	+	0.991823i	$0.459266\pi$
$588$	8.91742	0.367748
$589$	5.85216	0.241134
$590$	0.319606	0.0131580
$591$	33.8776	1.39354
$592$	−18.3160	−0.752781
$593$	−38.6788	−1.58835	−0.794174	−	0.607691i	$-0.792096\pi$
$593$	−38.6788	−1.58835	−0.794174	+	0.607691i	$0.792096\pi$
$594$	0	0
$595$	−11.3698	−0.466117
$596$	13.5271	0.554093
$597$	−3.04975	−0.124818
$598$	−6.06503	−0.248017
$599$	−23.4679	−0.958874	−0.479437	−	0.877576i	$-0.659159\pi$
$599$	−23.4679	−0.958874	−0.479437	+	0.877576i	$0.659159\pi$
$600$	−6.99715	−0.285657
$601$	8.05607	0.328614	0.164307	−	0.986409i	$-0.447461\pi$
$601$	8.05607	0.328614	0.164307	+	0.986409i	$0.447461\pi$
$602$	5.42294	0.221022
$603$	−7.58516	−0.308892
$604$	−2.52463	−0.102726
$605$	0	0
$606$	8.55377	0.347473
$607$	−17.9824	−0.729883	−0.364942	−	0.931030i	$-0.618911\pi$
$607$	−17.9824	−0.729883	−0.364942	+	0.931030i	$0.618911\pi$
$608$	4.16879	0.169067
$609$	−14.1267	−0.572445
$610$	−0.480730	−0.0194642
$611$	−35.9713	−1.45524
$612$	5.70709	0.230696
$613$	34.9393	1.41118	0.705592	−	0.708619i	$-0.250681\pi$
$613$	34.9393	1.41118	0.705592	+	0.708619i	$0.250681\pi$
$614$	−0.868276	−0.0350408
$615$	13.2566	0.534559
$616$	0	0
$617$	−17.0697	−0.687198	−0.343599	−	0.939116i	$-0.611646\pi$
$617$	−17.0697	−0.687198	−0.343599	+	0.939116i	$0.611646\pi$
$618$	−1.04050	−0.0418549
$619$	−2.76309	−0.111058	−0.0555290	−	0.998457i	$-0.517685\pi$
$619$	−2.76309	−0.111058	−0.0555290	+	0.998457i	$0.517685\pi$
$620$	13.7970	0.554101
$621$	20.5925	0.826350
$622$	2.15304	0.0863291
$623$	−15.7501	−0.631013
$624$	−22.1166	−0.885374
$625$	1.99054	0.0796216
$626$	3.36785	0.134606
$627$	0	0
$628$	26.4199	1.05427
$629$	−25.0283	−0.997945
$630$	−0.656023	−0.0261366
$631$	29.8536	1.18845	0.594226	−	0.804298i	$-0.297459\pi$
$631$	29.8536	1.18845	0.594226	+	0.804298i	$0.297459\pi$
$632$	8.06470	0.320797
$633$	14.9613	0.594656
$634$	4.63818	0.184206
$635$	−21.3074	−0.845558
$636$	−0.308539	−0.0122344
$637$	14.2429	0.564323
$638$	0	0
$639$	−2.50440	−0.0990724
$640$	12.9226	0.510812
$641$	−7.02002	−0.277274	−0.138637	−	0.990343i	$-0.544272\pi$
$641$	−7.02002	−0.277274	−0.138637	+	0.990343i	$0.544272\pi$
$642$	−5.40662	−0.213382
$643$	−5.36010	−0.211382	−0.105691	−	0.994399i	$-0.533705\pi$
$643$	−5.36010	−0.211382	−0.105691	+	0.994399i	$0.533705\pi$
$644$	−13.4515	−0.530065
$645$	15.1325	0.595841
$646$	1.67401	0.0658629
$647$	6.34797	0.249565	0.124782	−	0.992184i	$-0.460177\pi$
$647$	6.34797	0.249565	0.124782	+	0.992184i	$0.460177\pi$
$648$	−9.07718	−0.356585
$649$	0	0
$650$	−5.39537	−0.211624
$651$	16.7244	0.655479
$652$	−31.9379	−1.25078
$653$	−7.08338	−0.277194	−0.138597	−	0.990349i	$-0.544259\pi$
$653$	−7.08338	−0.277194	−0.138597	+	0.990349i	$0.544259\pi$
$654$	−6.30764	−0.246648
$655$	−6.15769	−0.240601
$656$	21.3380	0.833110
$657$	−10.8965	−0.425112
$658$	5.69410	0.221979
$659$	−45.0629	−1.75540	−0.877701	−	0.479208i	$-0.840924\pi$
$659$	−45.0629	−1.75540	−0.877701	+	0.479208i	$0.840924\pi$
$660$	0	0
$661$	−0.199256	−0.00775016	−0.00387508	−	0.999992i	$-0.501233\pi$
$661$	−0.199256	−0.00775016	−0.00387508	+	0.999992i	$0.501233\pi$
$662$	3.77307	0.146645
$663$	−30.2219	−1.17372
$664$	−7.34154	−0.284907
$665$	2.69607	0.104549
$666$	−1.44410	−0.0559578
$667$	−17.4001	−0.673735
$668$	4.60335	0.178109
$669$	16.8618	0.651916
$670$	−5.24536	−0.202646
$671$	0	0
$672$	11.9136	0.459578
$673$	−37.8094	−1.45745	−0.728723	−	0.684809i	$-0.759886\pi$
$673$	−37.8094	−1.45745	−0.728723	+	0.684809i	$0.759886\pi$
$674$	1.08529	0.0418037
$675$	18.3189	0.705093
$676$	−13.9815	−0.537749
$677$	−16.6866	−0.641318	−0.320659	−	0.947195i	$-0.603904\pi$
$677$	−16.6866	−0.641318	−0.320659	+	0.947195i	$0.603904\pi$
$678$	8.90014	0.341808
$679$	−6.79865	−0.260908
$680$	8.17492	0.313494
$681$	12.9826	0.497493
$682$	0	0
$683$	−27.3464	−1.04638	−0.523191	−	0.852216i	$-0.675258\pi$
$683$	−27.3464	−1.04638	−0.523191	+	0.852216i	$0.675258\pi$
$684$	−1.35330	−0.0517446
$685$	27.0049	1.03180
$686$	−7.27031	−0.277582
$687$	−1.90925	−0.0728422
$688$	24.3574	0.928617
$689$	−0.492798	−0.0187741
$690$	2.67902	0.101989
$691$	38.2641	1.45563	0.727817	−	0.685771i	$-0.240535\pi$
$691$	38.2641	1.45563	0.727817	+	0.685771i	$0.240535\pi$
$692$	−36.4934	−1.38727
$693$	0	0
$694$	11.3565	0.431089
$695$	−1.44237	−0.0547124
$696$	10.1572	0.385006
$697$	29.1579	1.10444
$698$	12.8763	0.487376
$699$	31.0671	1.17506
$700$	−11.9663	−0.452285
$701$	3.21198	0.121315	0.0606573	−	0.998159i	$-0.480680\pi$
$701$	3.21198	0.121315	0.0606573	+	0.998159i	$0.480680\pi$
$702$	−9.26896	−0.349834
$703$	5.93486	0.223837
$704$	0	0
$705$	15.8891	0.598420
$706$	−0.230449	−0.00867306
$707$	30.3009	1.13958
$708$	1.88418	0.0708120
$709$	7.83769	0.294351	0.147175	−	0.989110i	$-0.452982\pi$
$709$	7.83769	0.294351	0.147175	+	0.989110i	$0.452982\pi$
$710$	−1.73186	−0.0649957
$711$	−3.97212	−0.148966
$712$	11.3243	0.424397
$713$	20.5996	0.771462
$714$	4.78399	0.179036
$715$	0	0
$716$	−21.9573	−0.820581
$717$	20.7339	0.774322
$718$	7.36077	0.274702
$719$	−43.7877	−1.63301	−0.816503	−	0.577340i	$-0.804091\pi$
$719$	−43.7877	−1.63301	−0.816503	+	0.577340i	$0.804091\pi$
$720$	−2.94656	−0.109812
$721$	−3.68586	−0.137269
$722$	6.53831	0.243331
$723$	22.4998	0.836778
$724$	−41.0422	−1.52532
$725$	−15.4789	−0.574872
$726$	0	0
$727$	−12.3166	−0.456799	−0.228400	−	0.973567i	$-0.573349\pi$
$727$	−12.3166	−0.456799	−0.228400	+	0.973567i	$0.573349\pi$
$728$	12.5416	0.464821
$729$	30.0210	1.11189
$730$	−7.53524	−0.278892
$731$	33.2838	1.23105
$732$	−2.83406	−0.104750
$733$	36.1267	1.33437	0.667186	−	0.744891i	$-0.267499\pi$
$733$	36.1267	1.33437	0.667186	+	0.744891i	$0.267499\pi$
$734$	−5.54097	−0.204521
$735$	−6.29132	−0.232059
$736$	14.6742	0.540897
$737$	0	0
$738$	1.68237	0.0619290
$739$	5.89351	0.216796	0.108398	−	0.994108i	$-0.465428\pi$
$739$	5.89351	0.216796	0.108398	+	0.994108i	$0.465428\pi$
$740$	13.9920	0.514355
$741$	7.16638	0.263264
$742$	0.0780077	0.00286375
$743$	52.9752	1.94347	0.971735	−	0.236073i	$-0.0758605\pi$
$743$	52.9752	1.94347	0.971735	+	0.236073i	$0.0758605\pi$
$744$	−12.0249	−0.440853
$745$	−9.54352	−0.349647
$746$	−5.45546	−0.199739
$747$	3.61594	0.132300
$748$	0	0
$749$	−19.1524	−0.699814
$750$	6.03237	0.220271
$751$	−20.6584	−0.753834	−0.376917	−	0.926247i	$-0.623016\pi$
$751$	−20.6584	−0.753834	−0.376917	+	0.926247i	$0.623016\pi$
$752$	25.5753	0.932636
$753$	−4.60426	−0.167788
$754$	7.83200	0.285225
$755$	1.78115	0.0648225
$756$	−20.5575	−0.747669
$757$	44.9657	1.63431	0.817153	−	0.576421i	$-0.195551\pi$
$757$	44.9657	1.63431	0.817153	+	0.576421i	$0.195551\pi$
$758$	−10.5966	−0.384887
$759$	0	0
$760$	−1.93848	−0.0703162
$761$	38.6870	1.40240	0.701202	−	0.712963i	$-0.252647\pi$
$761$	38.6870	1.40240	0.701202	+	0.712963i	$0.252647\pi$
$762$	8.96535	0.324780
$763$	−22.3442	−0.808914
$764$	40.4437	1.46320
$765$	−4.02641	−0.145575
$766$	−4.36489	−0.157710
$767$	3.00941	0.108664
$768$	9.67602	0.349153
$769$	−2.96731	−0.107004	−0.0535020	−	0.998568i	$-0.517038\pi$
$769$	−2.96731	−0.107004	−0.0535020	+	0.998568i	$0.517038\pi$
$770$	0	0
$771$	−13.6805	−0.492691
$772$	−6.69676	−0.241022
$773$	28.4862	1.02458	0.512289	−	0.858813i	$-0.328798\pi$
$773$	28.4862	1.02458	0.512289	+	0.858813i	$0.328798\pi$
$774$	1.92043	0.0690285
$775$	18.3252	0.658259
$776$	4.88824	0.175478
$777$	16.9607	0.608462
$778$	0.223438	0.00801063
$779$	−6.91409	−0.247723
$780$	16.8954	0.604953
$781$	0	0
$782$	5.89250	0.210715
$783$	−26.5919	−0.950318
$784$	−10.1266	−0.361663
$785$	−18.6395	−0.665271
$786$	2.59093	0.0924152
$787$	−26.3892	−0.940675	−0.470338	−	0.882487i	$-0.655868\pi$
$787$	−26.3892	−0.940675	−0.470338	+	0.882487i	$0.655868\pi$
$788$	−41.6566	−1.48395
$789$	15.0639	0.536287
$790$	−2.74684	−0.0977280
$791$	31.5279	1.12100
$792$	0	0
$793$	−4.52655	−0.160743
$794$	−0.668659	−0.0237298
$795$	0.217677	0.00772021
$796$	3.75003	0.132916
$797$	−51.7459	−1.83294	−0.916468	−	0.400109i	$-0.868972\pi$
$797$	−51.7459	−1.83294	−0.916468	+	0.400109i	$0.868972\pi$
$798$	−1.13441	−0.0401575
$799$	34.9481	1.23637
$800$	13.0540	0.461527
$801$	−5.57758	−0.197074
$802$	−2.08340	−0.0735673
$803$	0	0
$804$	−30.9231	−1.09057
$805$	9.49018	0.334485
$806$	−9.27215	−0.326597
$807$	−18.7706	−0.660757
$808$	−21.7864	−0.766443
$809$	14.6155	0.513854	0.256927	−	0.966431i	$-0.417290\pi$
$809$	14.6155	0.513854	0.256927	+	0.966431i	$0.417290\pi$
$810$	3.09169	0.108631
$811$	18.5981	0.653067	0.326533	−	0.945186i	$-0.394119\pi$
$811$	18.5981	0.653067	0.326533	+	0.945186i	$0.394119\pi$
$812$	17.3705	0.609585
$813$	42.5845	1.49350
$814$	0	0
$815$	22.5324	0.789277
$816$	21.4875	0.752213
$817$	−7.89244	−0.276122
$818$	4.62761	0.161801
$819$	−6.17711	−0.215846
$820$	−16.3006	−0.569242
$821$	−51.4514	−1.79567	−0.897834	−	0.440335i	$-0.854860\pi$
$821$	−51.4514	−1.79567	−0.897834	+	0.440335i	$0.854860\pi$
$822$	−11.3626	−0.396318
$823$	−7.79035	−0.271555	−0.135777	−	0.990739i	$-0.543353\pi$
$823$	−7.79035	−0.271555	−0.135777	+	0.990739i	$0.543353\pi$
$824$	2.65014	0.0923221
$825$	0	0
$826$	−0.476376	−0.0165753
$827$	−42.1646	−1.46621	−0.733103	−	0.680118i	$-0.761929\pi$
$827$	−42.1646	−1.46621	−0.733103	+	0.680118i	$0.761929\pi$
$828$	−4.76361	−0.165547
$829$	−35.2778	−1.22525	−0.612625	−	0.790374i	$-0.709886\pi$
$829$	−35.2778	−1.22525	−0.612625	+	0.790374i	$0.709886\pi$
$830$	2.50052	0.0867945
$831$	−43.0620	−1.49380
$832$	22.5310	0.781120
$833$	−13.8377	−0.479449
$834$	0.606896	0.0210151
$835$	−3.24771	−0.112391
$836$	0	0
$837$	31.4816	1.08816
$838$	−11.4942	−0.397060
$839$	−35.0886	−1.21139	−0.605697	−	0.795696i	$-0.707105\pi$
$839$	−35.0886	−1.21139	−0.605697	+	0.795696i	$0.707105\pi$
$840$	−5.53982	−0.191142
$841$	−6.53058	−0.225193
$842$	−9.07099	−0.312607
$843$	17.4659	0.601559
$844$	−18.3966	−0.633238
$845$	9.86406	0.339334
$846$	2.01646	0.0693272
$847$	0	0
$848$	0.350375	0.0120319
$849$	33.5402	1.15110
$850$	5.24190	0.179796
$851$	20.8907	0.716124
$852$	−10.2099	−0.349785
$853$	10.6490	0.364614	0.182307	−	0.983242i	$-0.441644\pi$
$853$	10.6490	0.364614	0.182307	+	0.983242i	$0.441644\pi$
$854$	0.716533	0.0245192
$855$	0.954763	0.0326522
$856$	13.7706	0.470671
$857$	−34.0672	−1.16371	−0.581857	−	0.813291i	$-0.697674\pi$
$857$	−34.0672	−1.16371	−0.581857	+	0.813291i	$0.697674\pi$
$858$	0	0
$859$	26.0040	0.887244	0.443622	−	0.896214i	$-0.353693\pi$
$859$	26.0040	0.887244	0.443622	+	0.896214i	$0.353693\pi$
$860$	−18.6072	−0.634499
$861$	−19.7591	−0.673390
$862$	−6.11447	−0.208260
$863$	−6.11331	−0.208100	−0.104050	−	0.994572i	$-0.533180\pi$
$863$	−6.11331	−0.208100	−0.104050	+	0.994572i	$0.533180\pi$
$864$	22.4260	0.762947
$865$	25.7464	0.875405
$866$	−10.3248	−0.350852
$867$	3.55337	0.120679
$868$	−20.5646	−0.698007
$869$	0	0
$870$	−3.45953	−0.117289
$871$	−49.3903	−1.67353
$872$	16.0655	0.544048
$873$	−2.40761	−0.0814854
$874$	−1.39726	−0.0472631
$875$	21.3691	0.722407
$876$	−44.4227	−1.50090
$877$	−37.2297	−1.25716	−0.628579	−	0.777745i	$-0.716363\pi$
$877$	−37.2297	−1.25716	−0.628579	+	0.777745i	$0.716363\pi$
$878$	−6.53552	−0.220563
$879$	−12.9759	−0.437667
$880$	0	0
$881$	4.49506	0.151443	0.0757213	−	0.997129i	$-0.475874\pi$
$881$	4.49506	0.151443	0.0757213	+	0.997129i	$0.475874\pi$
$882$	−0.798418	−0.0268841
$883$	24.0183	0.808279	0.404139	−	0.914697i	$-0.367571\pi$
$883$	24.0183	0.808279	0.404139	+	0.914697i	$0.367571\pi$
$884$	37.1614	1.24987
$885$	−1.32931	−0.0446842
$886$	5.22846	0.175654
$887$	18.4402	0.619162	0.309581	−	0.950873i	$-0.399811\pi$
$887$	18.4402	0.619162	0.309581	+	0.950873i	$0.399811\pi$
$888$	−12.1948	−0.409230
$889$	31.7589	1.06516
$890$	−3.85706	−0.129289
$891$	0	0
$892$	−20.7336	−0.694213
$893$	−8.28708	−0.277317
$894$	4.01555	0.134300
$895$	15.4910	0.517808
$896$	−19.2613	−0.643475
$897$	25.2257	0.842261
$898$	−2.72484	−0.0909292
$899$	−26.6011	−0.887196
$900$	−4.23765	−0.141255
$901$	0.478780	0.0159505
$902$	0	0
$903$	−22.5551	−0.750587
$904$	−22.6686	−0.753947
$905$	28.9556	0.962517
$906$	−0.749439	−0.0248984
$907$	21.5745	0.716369	0.358185	−	0.933651i	$-0.383396\pi$
$907$	21.5745	0.716369	0.358185	+	0.933651i	$0.383396\pi$
$908$	−15.9636	−0.529770
$909$	10.7305	0.355908
$910$	−4.27165	−0.141604
$911$	−7.73129	−0.256149	−0.128075	−	0.991765i	$-0.540880\pi$
$911$	−7.73129	−0.256149	−0.128075	+	0.991765i	$0.540880\pi$
$912$	−5.09524	−0.168720
$913$	0	0
$914$	10.2187	0.338004
$915$	1.99945	0.0660999
$916$	2.34764	0.0775683
$917$	9.17810	0.303088
$918$	9.00529	0.297219
$919$	−6.66041	−0.219707	−0.109853	−	0.993948i	$-0.535038\pi$
$919$	−6.66041	−0.219707	−0.109853	+	0.993948i	$0.535038\pi$
$920$	−6.82347	−0.224963
$921$	3.61134	0.118998
$922$	−3.40718	−0.112210
$923$	−16.3072	−0.536759
$924$	0	0
$925$	18.5841	0.611042
$926$	−13.5231	−0.444396
$927$	−1.30528	−0.0428709
$928$	−18.9493	−0.622042
$929$	−32.7907	−1.07583	−0.537914	−	0.843000i	$-0.680788\pi$
$929$	−32.7907	−1.07583	−0.537914	+	0.843000i	$0.680788\pi$
$930$	4.09566	0.134302
$931$	3.28128	0.107540
$932$	−38.2006	−1.25130
$933$	−8.95494	−0.293171
$934$	5.51184	0.180353
$935$	0	0
$936$	4.44136	0.145170
$937$	−16.1135	−0.526405	−0.263202	−	0.964741i	$-0.584779\pi$
$937$	−16.1135	−0.526405	−0.263202	+	0.964741i	$0.584779\pi$
$938$	7.81826	0.255275
$939$	−14.0076	−0.457120
$940$	−19.5376	−0.637245
$941$	3.35936	0.109512	0.0547561	−	0.998500i	$-0.482562\pi$
$941$	3.35936	0.109512	0.0547561	+	0.998500i	$0.482562\pi$
$942$	7.84278	0.255531
$943$	−24.3376	−0.792542
$944$	−2.13967	−0.0696402
$945$	14.5035	0.471799
$946$	0	0
$947$	52.1111	1.69338	0.846692	−	0.532084i	$-0.178591\pi$
$947$	52.1111	1.69338	0.846692	+	0.532084i	$0.178591\pi$
$948$	−16.1935	−0.525940
$949$	−70.9518	−2.30319
$950$	−1.24299	−0.0403278
$951$	−19.2911	−0.625558
$952$	−12.1848	−0.394912
$953$	33.1370	1.07341	0.536706	−	0.843770i	$-0.319669\pi$
$953$	33.1370	1.07341	0.536706	+	0.843770i	$0.319669\pi$
$954$	0.0276249	0.000894390 0
$955$	−28.5334	−0.923318
$956$	−25.4948	−0.824560
$957$	0	0
$958$	−4.19102	−0.135406
$959$	−40.2511	−1.29978
$960$	−9.95230	−0.321209
$961$	0.492472	0.0158862
$962$	−9.40317	−0.303170
$963$	−6.78247	−0.218562
$964$	−27.6662	−0.891068
$965$	4.72462	0.152091
$966$	−3.99311	−0.128476
$967$	23.6560	0.760725	0.380363	−	0.924837i	$-0.375799\pi$
$967$	23.6560	0.760725	0.380363	+	0.924837i	$0.375799\pi$
$968$	0	0
$969$	−6.96253	−0.223669
$970$	−1.66493	−0.0534578
$971$	52.6306	1.68900	0.844498	−	0.535559i	$-0.179899\pi$
$971$	52.6306	1.68900	0.844498	+	0.535559i	$0.179899\pi$
$972$	−13.1905	−0.423086
$973$	2.14987	0.0689217
$974$	4.91605	0.157521
$975$	22.4405	0.718670
$976$	3.21834	0.103017
$977$	−40.0154	−1.28020	−0.640102	−	0.768290i	$-0.721108\pi$
$977$	−40.0154	−1.28020	−0.640102	+	0.768290i	$0.721108\pi$
$978$	−9.48080	−0.303163
$979$	0	0
$980$	7.73592	0.247115
$981$	−7.91277	−0.252635
$982$	−11.7472	−0.374868
$983$	−43.8294	−1.39794	−0.698971	−	0.715150i	$-0.746358\pi$
$983$	−43.8294	−1.39794	−0.698971	+	0.715150i	$0.746358\pi$
$984$	14.2069	0.452899
$985$	29.3891	0.936413
$986$	−7.60921	−0.242327
$987$	−23.6829	−0.753835
$988$	−8.81191	−0.280344
$989$	−27.7814	−0.883398
$990$	0	0
$991$	22.6704	0.720148	0.360074	−	0.932924i	$-0.382751\pi$
$991$	22.6704	0.720148	0.360074	+	0.932924i	$0.382751\pi$
$992$	22.4337	0.712271
$993$	−15.6930	−0.498002
$994$	2.58136	0.0818757
$995$	−2.64568	−0.0838736
$996$	14.7414	0.467099
$997$	32.0949	1.01646	0.508228	−	0.861223i	$-0.330301\pi$
$997$	32.0949	1.01646	0.508228	+	0.861223i	$0.330301\pi$
$998$	0.192637	0.00609780
$999$	31.9265	1.01011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.p.1.11	yes	25
11.10	odd	2		7381.2.a.m.1.15	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.m.1.15	✓	25	11.10	odd	2
7381.2.a.p.1.11	yes	25	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.365014 q^{2} +1.51817 q^{3} -1.86676 q^{4} +1.31702 q^{5} -0.554152 q^{6} -1.96303 q^{7} +1.41142 q^{8} -0.695170 q^{9} +O(q^{10})\)	\(q-0.365014 q^{2} +1.51817 q^{3} -1.86676 q^{4} +1.31702 q^{5} -0.554152 q^{6} -1.96303 q^{7} +1.41142 q^{8} -0.695170 q^{9} -0.480730 q^{10} -2.83406 q^{12} -4.52655 q^{13} +0.716533 q^{14} +1.99945 q^{15} +3.21834 q^{16} +4.39779 q^{17} +0.253747 q^{18} -1.04283 q^{19} -2.45856 q^{20} -2.98021 q^{21} -3.67076 q^{23} +2.14278 q^{24} -3.26546 q^{25} +1.65225 q^{26} -5.60988 q^{27} +3.66451 q^{28} +4.74019 q^{29} -0.729829 q^{30} -5.61182 q^{31} -3.99758 q^{32} -1.60525 q^{34} -2.58535 q^{35} +1.29772 q^{36} -5.69112 q^{37} +0.380647 q^{38} -6.87206 q^{39} +1.85887 q^{40} +6.63013 q^{41} +1.08782 q^{42} +7.56831 q^{43} -0.915552 q^{45} +1.33988 q^{46} +7.94674 q^{47} +4.88598 q^{48} -3.14652 q^{49} +1.19194 q^{50} +6.67658 q^{51} +8.45001 q^{52} +0.108868 q^{53} +2.04769 q^{54} -2.77066 q^{56} -1.58319 q^{57} -1.73024 q^{58} -0.664835 q^{59} -3.73251 q^{60} +1.00000 q^{61} +2.04839 q^{62} +1.36464 q^{63} -4.97751 q^{64} -5.96156 q^{65} +10.9112 q^{67} -8.20964 q^{68} -5.57282 q^{69} +0.943687 q^{70} +3.60257 q^{71} -0.981178 q^{72} +15.6746 q^{73} +2.07734 q^{74} -4.95751 q^{75} +1.94672 q^{76} +2.50840 q^{78} +5.71388 q^{79} +4.23862 q^{80} -6.43123 q^{81} -2.42009 q^{82} -5.20151 q^{83} +5.56334 q^{84} +5.79197 q^{85} -2.76254 q^{86} +7.19640 q^{87} +8.02334 q^{89} +0.334189 q^{90} +8.88576 q^{91} +6.85244 q^{92} -8.51967 q^{93} -2.90067 q^{94} -1.37342 q^{95} -6.06900 q^{96} +3.46335 q^{97} +1.14852 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \) 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9	\( 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} + 21 q^{16} + 8 q^{17} + 16 q^{19} - 16 q^{20} + 12 q^{21} + 3 q^{23} + 62 q^{24} + 26 q^{25} - 4 q^{26} - 13 q^{27} - 42 q^{28} + 28 q^{29} + 12 q^{30} - q^{31} + 35 q^{32} + 8 q^{34} + 62 q^{35} + 17 q^{36} - 7 q^{37} + 20 q^{38} - 27 q^{40} + 28 q^{41} - 34 q^{42} + 22 q^{43} + 58 q^{46} - 2 q^{47} + 10 q^{48} + 25 q^{49} - 15 q^{50} + 38 q^{51} + 12 q^{52} - 4 q^{53} + 24 q^{54} - 48 q^{56} + 40 q^{57} + 8 q^{58} + 9 q^{59} + 18 q^{60} + 25 q^{61} + 4 q^{62} + 30 q^{63} + 41 q^{64} + 32 q^{65} - 15 q^{67} + 112 q^{68} - q^{69} + 14 q^{70} - 9 q^{71} - 59 q^{72} - 8 q^{73} + 54 q^{74} - 4 q^{75} + 32 q^{76} + 20 q^{78} + 30 q^{79} - 18 q^{80} + 17 q^{81} + 10 q^{83} - 39 q^{84} + 52 q^{85} - 6 q^{86} + 24 q^{87} - 5 q^{89} + 110 q^{90} - 38 q^{92} - q^{93} - 120 q^{94} + 50 q^{95} + 130 q^{96} + 5 q^{97} + 35 q^{98}+O(q^{100}) \) 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9 + 6 * q^10 + 2 * q^12 + 4 * q^13 - 10 * q^14 + q^15 + 21 * q^16 + 8 * q^17 + 16 * q^19 - 16 * q^20 + 12 * q^21 + 3 * q^23 + 62 * q^24 + 26 * q^25 - 4 * q^26 - 13 * q^27 - 42 * q^28 + 28 * q^29 + 12 * q^30 - q^31 + 35 * q^32 + 8 * q^34 + 62 * q^35 + 17 * q^36 - 7 * q^37 + 20 * q^38 - 27 * q^40 + 28 * q^41 - 34 * q^42 + 22 * q^43 + 58 * q^46 - 2 * q^47 + 10 * q^48 + 25 * q^49 - 15 * q^50 + 38 * q^51 + 12 * q^52 - 4 * q^53 + 24 * q^54 - 48 * q^56 + 40 * q^57 + 8 * q^58 + 9 * q^59 + 18 * q^60 + 25 * q^61 + 4 * q^62 + 30 * q^63 + 41 * q^64 + 32 * q^65 - 15 * q^67 + 112 * q^68 - q^69 + 14 * q^70 - 9 * q^71 - 59 * q^72 - 8 * q^73 + 54 * q^74 - 4 * q^75 + 32 * q^76 + 20 * q^78 + 30 * q^79 - 18 * q^80 + 17 * q^81 + 10 * q^83 - 39 * q^84 + 52 * q^85 - 6 * q^86 + 24 * q^87 - 5 * q^89 + 110 * q^90 - 38 * q^92 - q^93 - 120 * q^94 + 50 * q^95 + 130 * q^96 + 5 * q^97 + 35 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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