LMFDB - Embedded newform 2303.4.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.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:	$135.881398743$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.44134 q^{2} +7.09644 q^{3} +11.7255 q^{4} -11.0798 q^{5} -31.5177 q^{6} -16.5462 q^{8} +23.3594 q^{9} +O(q^{10})$	\(q-4.44134 q^{2} +7.09644 q^{3} +11.7255 q^{4} -11.0798 q^{5} -31.5177 q^{6} -16.5462 q^{8} +23.3594 q^{9} +49.2091 q^{10} -48.6924 q^{11} +83.2092 q^{12} +84.3157 q^{13} -78.6270 q^{15} -20.3167 q^{16} +18.3648 q^{17} -103.747 q^{18} -98.4234 q^{19} -129.916 q^{20} +216.259 q^{22} -74.5738 q^{23} -117.419 q^{24} -2.23839 q^{25} -374.475 q^{26} -25.8353 q^{27} -3.41029 q^{29} +349.209 q^{30} -86.0926 q^{31} +222.603 q^{32} -345.542 q^{33} -81.5645 q^{34} +273.901 q^{36} +153.101 q^{37} +437.132 q^{38} +598.341 q^{39} +183.328 q^{40} +4.10594 q^{41} -205.072 q^{43} -570.942 q^{44} -258.817 q^{45} +331.207 q^{46} -47.0000 q^{47} -144.176 q^{48} +9.94145 q^{50} +130.325 q^{51} +988.643 q^{52} +694.228 q^{53} +114.743 q^{54} +539.501 q^{55} -698.456 q^{57} +15.1463 q^{58} +187.775 q^{59} -921.940 q^{60} -14.9526 q^{61} +382.366 q^{62} -826.122 q^{64} -934.200 q^{65} +1534.67 q^{66} +37.6004 q^{67} +215.337 q^{68} -529.208 q^{69} -182.449 q^{71} -386.509 q^{72} +124.371 q^{73} -679.974 q^{74} -15.8846 q^{75} -1154.06 q^{76} -2657.43 q^{78} +898.236 q^{79} +225.105 q^{80} -814.042 q^{81} -18.2359 q^{82} -427.028 q^{83} -203.479 q^{85} +910.794 q^{86} -24.2009 q^{87} +805.673 q^{88} -114.070 q^{89} +1149.49 q^{90} -874.414 q^{92} -610.951 q^{93} +208.743 q^{94} +1090.51 q^{95} +1579.69 q^{96} -293.765 q^{97} -1137.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) $ 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * 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 $

$2$	−4.44134	−1.57025	−0.785125	−	0.619337i	$-0.787401\pi$
$2$	−4.44134	−1.57025	−0.785125	+	0.619337i	$0.787401\pi$
$3$	7.09644	1.36571	0.682855	−	0.730554i	$-0.260738\pi$
$3$	7.09644	1.36571	0.682855	+	0.730554i	$0.260738\pi$
$4$	11.7255	1.46569
$5$	−11.0798	−0.991006	−0.495503	−	0.868606i	$-0.665016\pi$
$5$	−11.0798	−0.991006	−0.495503	+	0.868606i	$0.665016\pi$
$6$	−31.5177	−2.14451
$7$	0	0
$7$	0	0
$8$	−16.5462	−0.731245
$9$	23.3594	0.865163
$10$	49.2091	1.55613
$11$	−48.6924	−1.33466	−0.667332	−	0.744761i	$-0.732564\pi$
$11$	−48.6924	−1.33466	−0.667332	+	0.744761i	$0.732564\pi$
$12$	83.2092	2.00170
$13$	84.3157	1.79884	0.899422	−	0.437082i	$-0.143988\pi$
$13$	84.3157	1.79884	0.899422	+	0.437082i	$0.143988\pi$
$14$	0	0
$15$	−78.6270	−1.35343
$16$	−20.3167	−0.317449
$17$	18.3648	0.262008	0.131004	−	0.991382i	$-0.458180\pi$
$17$	18.3648	0.262008	0.131004	+	0.991382i	$0.458180\pi$
$18$	−103.747	−1.35852
$19$	−98.4234	−1.18842	−0.594208	−	0.804312i	$-0.702534\pi$
$19$	−98.4234	−1.18842	−0.594208	+	0.804312i	$0.702534\pi$
$20$	−129.916	−1.45250
$21$	0	0
$22$	216.259	2.09576
$23$	−74.5738	−0.676074	−0.338037	−	0.941133i	$-0.609763\pi$
$23$	−74.5738	−0.676074	−0.338037	+	0.941133i	$0.609763\pi$
$24$	−117.419	−0.998668
$25$	−2.23839	−0.0179071
$26$	−374.475	−2.82463
$27$	−25.8353	−0.184148
$28$	0	0
$29$	−3.41029	−0.0218371	−0.0109185	−	0.999940i	$-0.503476\pi$
$29$	−3.41029	−0.0218371	−0.0109185	+	0.999940i	$0.503476\pi$
$30$	349.209	2.12522
$31$	−86.0926	−0.498796	−0.249398	−	0.968401i	$-0.580233\pi$
$31$	−86.0926	−0.498796	−0.249398	+	0.968401i	$0.580233\pi$
$32$	222.603	1.22972
$33$	−345.542	−1.82276
$34$	−81.5645	−0.411418
$35$	0	0
$36$	273.901	1.26806
$37$	153.101	0.680261	0.340131	−	0.940378i	$-0.389529\pi$
$37$	153.101	0.680261	0.340131	+	0.940378i	$0.389529\pi$
$38$	437.132	1.86611
$39$	598.341	2.45670
$40$	183.328	0.724668
$41$	4.10594	0.0156400	0.00782000	−	0.999969i	$-0.497511\pi$
$41$	4.10594	0.0156400	0.00782000	+	0.999969i	$0.497511\pi$
$42$	0	0
$43$	−205.072	−0.727283	−0.363641	−	0.931539i	$-0.618467\pi$
$43$	−205.072	−0.727283	−0.363641	+	0.931539i	$0.618467\pi$
$44$	−570.942	−1.95620
$45$	−258.817	−0.857382
$46$	331.207	1.06161
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	−144.176	−0.433543
$49$	0	0
$50$	9.94145	0.0281187
$51$	130.325	0.357826
$52$	988.643	2.63654
$53$	694.228	1.79924	0.899618	−	0.436677i	$-0.143845\pi$
$53$	694.228	1.79924	0.899618	+	0.436677i	$0.143845\pi$
$54$	114.743	0.289159
$55$	539.501	1.32266
$56$	0	0
$57$	−698.456	−1.62303
$58$	15.1463	0.0342897
$59$	187.775	0.414342	0.207171	−	0.978305i	$-0.433574\pi$
$59$	187.775	0.414342	0.207171	+	0.978305i	$0.433574\pi$
$60$	−921.940	−1.98370
$61$	−14.9526	−0.0313850	−0.0156925	−	0.999877i	$-0.504995\pi$
$61$	−14.9526	−0.0313850	−0.0156925	+	0.999877i	$0.504995\pi$
$62$	382.366	0.783235
$63$	0	0
$64$	−826.122	−1.61352
$65$	−934.200	−1.78266
$66$	1534.67	2.86219
$67$	37.6004	0.0685615	0.0342807	−	0.999412i	$-0.489086\pi$
$67$	37.6004	0.0685615	0.0342807	+	0.999412i	$0.489086\pi$
$68$	215.337	0.384021
$69$	−529.208	−0.923321
$70$	0	0
$71$	−182.449	−0.304967	−0.152484	−	0.988306i	$-0.548727\pi$
$71$	−182.449	−0.304967	−0.152484	+	0.988306i	$0.548727\pi$
$72$	−386.509	−0.632646
$73$	124.371	0.199404	0.0997020	−	0.995017i	$-0.468211\pi$
$73$	124.371	0.199404	0.0997020	+	0.995017i	$0.468211\pi$
$74$	−679.974	−1.06818
$75$	−15.8846	−0.0244559
$76$	−1154.06	−1.74184
$77$	0	0
$78$	−2657.43	−3.85763
$79$	898.236	1.27923	0.639617	−	0.768694i	$-0.279093\pi$
$79$	898.236	1.27923	0.639617	+	0.768694i	$0.279093\pi$
$80$	225.105	0.314594
$81$	−814.042	−1.11666
$82$	−18.2359	−0.0245587
$83$	−427.028	−0.564728	−0.282364	−	0.959307i	$-0.591119\pi$
$83$	−427.028	−0.564728	−0.282364	+	0.959307i	$0.591119\pi$
$84$	0	0
$85$	−203.479	−0.259651
$86$	910.794	1.14202
$87$	−24.2009	−0.0298231
$88$	805.673	0.975966
$89$	−114.070	−0.135859	−0.0679293	−	0.997690i	$-0.521639\pi$
$89$	−114.070	−0.135859	−0.0679293	+	0.997690i	$0.521639\pi$
$90$	1149.49	1.34630
$91$	0	0
$92$	−874.414	−0.990913
$93$	−610.951	−0.681211
$94$	208.743	0.229045
$95$	1090.51	1.17773
$96$	1579.69	1.67944
$97$	−293.765	−0.307498	−0.153749	−	0.988110i	$-0.549135\pi$
$97$	−293.765	−0.307498	−0.153749	+	0.988110i	$0.549135\pi$
$98$	0	0
$99$	−1137.42	−1.15470
$100$	−26.2462	−0.0262462
$101$	−1076.09	−1.06015	−0.530075	−	0.847950i	$-0.677836\pi$
$101$	−1076.09	−1.06015	−0.530075	+	0.847950i	$0.677836\pi$
$102$	−578.817	−0.561877
$103$	810.737	0.775575	0.387788	−	0.921749i	$-0.373239\pi$
$103$	810.737	0.775575	0.387788	+	0.921749i	$0.373239\pi$
$104$	−1395.10	−1.31539
$105$	0	0
$106$	−3083.30	−2.82525
$107$	−1341.55	−1.21208	−0.606042	−	0.795433i	$-0.707244\pi$
$107$	−1341.55	−1.21208	−0.606042	+	0.795433i	$0.707244\pi$
$108$	−302.931	−0.269904
$109$	1630.56	1.43284	0.716418	−	0.697671i	$-0.245780\pi$
$109$	1630.56	1.43284	0.716418	+	0.697671i	$0.245780\pi$
$110$	−2396.11	−2.07691
$111$	1086.47	0.929039
$112$	0	0
$113$	−2277.50	−1.89601	−0.948003	−	0.318260i	$-0.896901\pi$
$113$	−2277.50	−1.89601	−0.948003	+	0.318260i	$0.896901\pi$
$114$	3102.08	2.54856
$115$	826.261	0.669993
$116$	−39.9873	−0.0320063
$117$	1969.56	1.55629
$118$	−833.971	−0.650620
$119$	0	0
$120$	1300.98	0.989686
$121$	1039.95	0.781327
$122$	66.4096	0.0492823
$123$	29.1375	0.0213597
$124$	−1009.48	−0.731079
$125$	1409.77	1.00875
$126$	0	0
$127$	1975.75	1.38047	0.690233	−	0.723587i	$-0.257508\pi$
$127$	1975.75	1.38047	0.690233	+	0.723587i	$0.257508\pi$
$128$	1888.26	1.30391
$129$	−1455.28	−0.993257
$130$	4149.10	2.79923
$131$	−2478.01	−1.65271	−0.826355	−	0.563150i	$-0.809589\pi$
$131$	−2478.01	−1.65271	−0.826355	+	0.563150i	$0.809589\pi$
$132$	−4051.65	−2.67160
$133$	0	0
$134$	−166.996	−0.107659
$135$	286.249	0.182492
$136$	−303.868	−0.191592
$137$	2695.36	1.68088	0.840439	−	0.541906i	$-0.182297\pi$
$137$	2695.36	1.68088	0.840439	+	0.541906i	$0.182297\pi$
$138$	2350.39	1.44984
$139$	556.820	0.339776	0.169888	−	0.985463i	$-0.445659\pi$
$139$	556.820	0.339776	0.169888	+	0.985463i	$0.445659\pi$
$140$	0	0
$141$	−333.532	−0.199209
$142$	810.317	0.478875
$143$	−4105.53	−2.40085
$144$	−474.587	−0.274645
$145$	37.7853	0.0216407
$146$	−552.373	−0.313114
$147$	0	0
$148$	1795.19	0.997050
$149$	67.7150	0.0372311	0.0186155	−	0.999827i	$-0.494074\pi$
$149$	67.7150	0.0372311	0.0186155	+	0.999827i	$0.494074\pi$
$150$	70.5489	0.0384019
$151$	2934.81	1.58167	0.790833	−	0.612032i	$-0.209648\pi$
$151$	2934.81	1.58167	0.790833	+	0.612032i	$0.209648\pi$
$152$	1628.53	0.869022
$153$	428.992	0.226679
$154$	0	0
$155$	953.887	0.494310
$156$	7015.84	3.60075
$157$	3243.08	1.64857	0.824287	−	0.566173i	$-0.191577\pi$
$157$	3243.08	1.64857	0.824287	+	0.566173i	$0.191577\pi$
$158$	−3989.37	−2.00872
$159$	4926.54	2.45723
$160$	−2466.39	−1.21866
$161$	0	0
$162$	3615.44	1.75343
$163$	−172.305	−0.0827974	−0.0413987	−	0.999143i	$-0.513181\pi$
$163$	−172.305	−0.0827974	−0.0413987	+	0.999143i	$0.513181\pi$
$164$	48.1442	0.0229233
$165$	3828.53	1.80637
$166$	1896.58	0.886764
$167$	1519.03	0.703871	0.351935	−	0.936024i	$-0.385524\pi$
$167$	1519.03	0.703871	0.351935	+	0.936024i	$0.385524\pi$
$168$	0	0
$169$	4912.14	2.23584
$170$	903.717	0.407717
$171$	−2299.11	−1.02817
$172$	−2404.57	−1.06597
$173$	−2421.56	−1.06421	−0.532104	−	0.846679i	$-0.678598\pi$
$173$	−2421.56	−1.06421	−0.532104	+	0.846679i	$0.678598\pi$
$174$	107.484	0.0468297
$175$	0	0
$176$	989.270	0.423688
$177$	1332.53	0.565871
$178$	506.624	0.213332
$179$	−163.485	−0.0682650	−0.0341325	−	0.999417i	$-0.510867\pi$
$179$	−163.485	−0.0682650	−0.0341325	+	0.999417i	$0.510867\pi$
$180$	−3034.76	−1.25665
$181$	1802.00	0.740011	0.370005	−	0.929030i	$-0.379356\pi$
$181$	1802.00	0.740011	0.370005	+	0.929030i	$0.379356\pi$
$182$	0	0
$183$	−106.110	−0.0428628
$184$	1233.91	0.494376
$185$	−1696.33	−0.674143
$186$	2713.44	1.06967
$187$	−894.228	−0.349692
$188$	−551.098	−0.213792
$189$	0	0
$190$	−4843.33	−1.84933
$191$	−1196.60	−0.453312	−0.226656	−	0.973975i	$-0.572779\pi$
$191$	−1196.60	−0.453312	−0.226656	+	0.973975i	$0.572779\pi$
$192$	−5862.52	−2.20360
$193$	−24.7669	−0.00923711	−0.00461855	−	0.999989i	$-0.501470\pi$
$193$	−24.7669	−0.00923711	−0.00461855	+	0.999989i	$0.501470\pi$
$194$	1304.71	0.482850
$195$	−6629.49	−2.43460
$196$	0	0
$197$	−5105.90	−1.84660	−0.923299	−	0.384081i	$-0.874518\pi$
$197$	−5105.90	−1.84660	−0.923299	+	0.384081i	$0.874518\pi$
$198$	5051.69	1.81317
$199$	−3050.29	−1.08658	−0.543290	−	0.839545i	$-0.682821\pi$
$199$	−3050.29	−1.08658	−0.543290	+	0.839545i	$0.682821\pi$
$200$	37.0368	0.0130945
$201$	266.829	0.0936351
$202$	4779.29	1.66470
$203$	0	0
$204$	1528.12	0.524461
$205$	−45.4929	−0.0154993
$206$	−3600.76	−1.21785
$207$	−1742.00	−0.584914
$208$	−1713.02	−0.571041
$209$	4792.47	1.58613
$210$	0	0
$211$	−1026.63	−0.334957	−0.167478	−	0.985876i	$-0.553562\pi$
$211$	−1026.63	−0.334957	−0.167478	+	0.985876i	$0.553562\pi$
$212$	8140.17	2.63712
$213$	−1294.74	−0.416497
$214$	5958.30	1.90327
$215$	2272.15	0.720742
$216$	427.475	0.134657
$217$	0	0
$218$	−7241.86	−2.24991
$219$	882.589	0.272328
$220$	6325.91	1.93860
$221$	1548.44	0.471311
$222$	−4825.39	−1.45882
$223$	3345.06	1.00449	0.502246	−	0.864725i	$-0.332507\pi$
$223$	3345.06	1.00449	0.502246	+	0.864725i	$0.332507\pi$
$224$	0	0
$225$	−52.2874	−0.0154926
$226$	10115.1	2.97721
$227$	1332.61	0.389640	0.194820	−	0.980839i	$-0.437588\pi$
$227$	1332.61	0.389640	0.194820	+	0.980839i	$0.437588\pi$
$228$	−8189.74	−2.37885
$229$	3052.46	0.880839	0.440420	−	0.897792i	$-0.354830\pi$
$229$	3052.46	0.880839	0.440420	+	0.897792i	$0.354830\pi$
$230$	−3669.71	−1.05206
$231$	0	0
$232$	56.4273	0.0159682
$233$	4844.57	1.36214	0.681069	−	0.732220i	$-0.261515\pi$
$233$	4844.57	1.36214	0.681069	+	0.732220i	$0.261515\pi$
$234$	−8747.50	−2.44377
$235$	520.750	0.144553
$236$	2201.75	0.607295
$237$	6374.27	1.74706
$238$	0	0
$239$	6467.94	1.75053	0.875264	−	0.483646i	$-0.160688\pi$
$239$	6467.94	1.75053	0.875264	+	0.483646i	$0.160688\pi$
$240$	1597.44	0.429644
$241$	5658.34	1.51239	0.756194	−	0.654347i	$-0.227056\pi$
$241$	5658.34	1.51239	0.756194	+	0.654347i	$0.227056\pi$
$242$	−4618.75	−1.22688
$243$	−5079.25	−1.34088
$244$	−175.327	−0.0460006
$245$	0	0
$246$	−129.410	−0.0335401
$247$	−8298.64	−2.13777
$248$	1424.50	0.364742
$249$	−3030.38	−0.771254
$250$	−6261.28	−1.58399
$251$	−2879.61	−0.724141	−0.362071	−	0.932151i	$-0.617930\pi$
$251$	−2879.61	−0.724141	−0.362071	+	0.932151i	$0.617930\pi$
$252$	0	0
$253$	3631.17	0.902331
$254$	−8774.96	−2.16768
$255$	−1443.97	−0.354608
$256$	−1777.44	−0.433945
$257$	−1748.00	−0.424271	−0.212135	−	0.977240i	$-0.568042\pi$
$257$	−1748.00	−0.424271	−0.212135	+	0.977240i	$0.568042\pi$
$258$	6463.39	1.55966
$259$	0	0
$260$	−10954.0	−2.61283
$261$	−79.6623	−0.0188926
$262$	11005.7	2.59517
$263$	−3716.96	−0.871474	−0.435737	−	0.900074i	$-0.643512\pi$
$263$	−3716.96	−0.871474	−0.435737	+	0.900074i	$0.643512\pi$
$264$	5717.40	1.33289
$265$	−7691.90	−1.78305
$266$	0	0
$267$	−809.491	−0.185543
$268$	440.883	0.100490
$269$	1759.59	0.398825	0.199412	−	0.979916i	$-0.436097\pi$
$269$	1759.59	0.398825	0.199412	+	0.979916i	$0.436097\pi$
$270$	−1271.33	−0.286558
$271$	−8432.40	−1.89016	−0.945078	−	0.326846i	$-0.894014\pi$
$271$	−8432.40	−1.89016	−0.945078	+	0.326846i	$0.894014\pi$
$272$	−373.114	−0.0831741
$273$	0	0
$274$	−11971.0	−2.63940
$275$	108.992	0.0239000
$276$	−6205.22	−1.35330
$277$	−3836.63	−0.832206	−0.416103	−	0.909318i	$-0.636604\pi$
$277$	−3836.63	−0.832206	−0.416103	+	0.909318i	$0.636604\pi$
$278$	−2473.03	−0.533534
$279$	−2011.07	−0.431540
$280$	0	0
$281$	−295.161	−0.0626614	−0.0313307	−	0.999509i	$-0.509975\pi$
$281$	−295.161	−0.0626614	−0.0313307	+	0.999509i	$0.509975\pi$
$282$	1481.33	0.312808
$283$	−6307.73	−1.32493	−0.662465	−	0.749093i	$-0.730490\pi$
$283$	−6307.73	−1.32493	−0.662465	+	0.749093i	$0.730490\pi$
$284$	−2139.30	−0.446986
$285$	7738.74	1.60843
$286$	18234.1	3.76994
$287$	0	0
$288$	5199.87	1.06391
$289$	−4575.73	−0.931352
$290$	−167.817	−0.0339813
$291$	−2084.69	−0.419954
$292$	1458.31	0.292264
$293$	−331.608	−0.0661186	−0.0330593	−	0.999453i	$-0.510525\pi$
$293$	−331.608	−0.0661186	−0.0330593	+	0.999453i	$0.510525\pi$
$294$	0	0
$295$	−2080.50	−0.410615
$296$	−2533.24	−0.497437
$297$	1257.98	0.245776
$298$	−300.745	−0.0584621
$299$	−6287.74	−1.21615
$300$	−186.255	−0.0358447
$301$	0	0
$302$	−13034.5	−2.48361
$303$	−7636.42	−1.44786
$304$	1999.64	0.377261
$305$	165.672	0.0311027
$306$	−1905.30	−0.355943
$307$	2417.76	0.449475	0.224737	−	0.974419i	$-0.427848\pi$
$307$	2417.76	0.449475	0.224737	+	0.974419i	$0.427848\pi$
$308$	0	0
$309$	5753.34	1.05921
$310$	−4236.54	−0.776191
$311$	6536.15	1.19174	0.595870	−	0.803081i	$-0.296807\pi$
$311$	6536.15	1.19174	0.595870	+	0.803081i	$0.296807\pi$
$312$	−9900.26	−1.79645
$313$	−461.541	−0.0833477	−0.0416739	−	0.999131i	$-0.513269\pi$
$313$	−461.541	−0.0833477	−0.0416739	+	0.999131i	$0.513269\pi$
$314$	−14403.6	−2.58867
$315$	0	0
$316$	10532.3	1.87496
$317$	10488.8	1.85838	0.929192	−	0.369597i	$-0.120504\pi$
$317$	10488.8	1.85838	0.929192	+	0.369597i	$0.120504\pi$
$318$	−21880.5	−3.85847
$319$	166.055	0.0291451
$320$	9153.25	1.59901
$321$	−9520.25	−1.65535
$322$	0	0
$323$	−1807.53	−0.311374
$324$	−9545.05	−1.63667
$325$	−188.731	−0.0322121
$326$	765.266	0.130013
$327$	11571.2	1.95684
$328$	−67.9376	−0.0114367
$329$	0	0
$330$	−17003.8	−2.83645
$331$	6224.36	1.03360	0.516801	−	0.856106i	$-0.327123\pi$
$331$	6224.36	1.03360	0.516801	+	0.856106i	$0.327123\pi$
$332$	−5007.11	−0.827714
$333$	3576.35	0.588537
$334$	−6746.55	−1.10525
$335$	−416.604	−0.0679448
$336$	0	0
$337$	4093.75	0.661724	0.330862	−	0.943679i	$-0.392661\pi$
$337$	4093.75	0.661724	0.330862	+	0.943679i	$0.392661\pi$
$338$	−21816.5	−3.51083
$339$	−16162.1	−2.58939
$340$	−2385.89	−0.380567
$341$	4192.05	0.665725
$342$	10211.1	1.61449
$343$	0	0
$344$	3393.16	0.531822
$345$	5863.51	0.915016
$346$	10755.0	1.67107
$347$	−8025.26	−1.24155	−0.620776	−	0.783988i	$-0.713182\pi$
$347$	−8025.26	−1.24155	−0.620776	+	0.783988i	$0.713182\pi$
$348$	−283.768	−0.0437113
$349$	9514.03	1.45924	0.729619	−	0.683854i	$-0.239697\pi$
$349$	9514.03	1.45924	0.729619	+	0.683854i	$0.239697\pi$
$350$	0	0
$351$	−2178.32	−0.331254
$352$	−10839.1	−1.64126
$353$	−6341.54	−0.956165	−0.478083	−	0.878315i	$-0.658668\pi$
$353$	−6341.54	−0.956165	−0.478083	+	0.878315i	$0.658668\pi$
$354$	−5918.22	−0.888559
$355$	2021.49	0.302224
$356$	−1337.53	−0.199126
$357$	0	0
$358$	726.092	0.107193
$359$	3372.24	0.495766	0.247883	−	0.968790i	$-0.420265\pi$
$359$	3372.24	0.495766	0.247883	+	0.968790i	$0.420265\pi$
$360$	4282.43	0.626956
$361$	2828.17	0.412330
$362$	−8003.31	−1.16200
$363$	7379.91	1.06707
$364$	0	0
$365$	−1378.00	−0.197611
$366$	471.271	0.0673053
$367$	−1419.56	−0.201909	−0.100955	−	0.994891i	$-0.532190\pi$
$367$	−1419.56	−0.201909	−0.100955	+	0.994891i	$0.532190\pi$
$368$	1515.10	0.214619
$369$	95.9123	0.0135311
$370$	7533.96	1.05857
$371$	0	0
$372$	−7163.70	−0.998442
$373$	11274.7	1.56510	0.782550	−	0.622588i	$-0.213919\pi$
$373$	11274.7	1.56510	0.782550	+	0.622588i	$0.213919\pi$
$374$	3971.57	0.549104
$375$	10004.4	1.37766
$376$	777.671	0.106663
$377$	−287.541	−0.0392815
$378$	0	0
$379$	8600.82	1.16568	0.582842	−	0.812585i	$-0.301941\pi$
$379$	8600.82	1.16568	0.582842	+	0.812585i	$0.301941\pi$
$380$	12786.8	1.72618
$381$	14020.8	1.88532
$382$	5314.49	0.711814
$383$	9374.49	1.25069	0.625345	−	0.780348i	$-0.284958\pi$
$383$	9374.49	1.25069	0.625345	+	0.780348i	$0.284958\pi$
$384$	13399.9	1.78076
$385$	0	0
$386$	109.998	0.0145046
$387$	−4790.36	−0.629218
$388$	−3444.54	−0.450696
$389$	980.173	0.127755	0.0638775	−	0.997958i	$-0.479653\pi$
$389$	980.173	0.127755	0.0638775	+	0.997958i	$0.479653\pi$
$390$	29443.8	3.82294
$391$	−1369.54	−0.177137
$392$	0	0
$393$	−17585.1	−2.25712
$394$	22677.0	2.89962
$395$	−9952.26	−1.26773
$396$	−13336.9	−1.69243
$397$	11327.2	1.43198	0.715992	−	0.698108i	$-0.245975\pi$
$397$	11327.2	1.43198	0.715992	+	0.698108i	$0.245975\pi$
$398$	13547.4	1.70620
$399$	0	0
$400$	45.4768	0.00568460
$401$	3106.32	0.386838	0.193419	−	0.981116i	$-0.438042\pi$
$401$	3106.32	0.386838	0.193419	+	0.981116i	$0.438042\pi$
$402$	−1185.08	−0.147031
$403$	−7258.96	−0.897257
$404$	−12617.7	−1.55385
$405$	9019.41	1.10661
$406$	0	0
$407$	−7454.85	−0.907920
$408$	−2156.38	−0.261659
$409$	9364.58	1.13215	0.566074	−	0.824354i	$-0.308462\pi$
$409$	9364.58	1.13215	0.566074	+	0.824354i	$0.308462\pi$
$410$	202.049	0.0243378
$411$	19127.5	2.29559
$412$	9506.29	1.13675
$413$	0	0
$414$	7736.80	0.918462
$415$	4731.38	0.559649
$416$	18768.9	2.21207
$417$	3951.44	0.464036
$418$	−21285.0	−2.49063
$419$	7493.99	0.873760	0.436880	−	0.899520i	$-0.356083\pi$
$419$	7493.99	0.873760	0.436880	+	0.899520i	$0.356083\pi$
$420$	0	0
$421$	2724.62	0.315416	0.157708	−	0.987486i	$-0.449590\pi$
$421$	2724.62	0.315416	0.157708	+	0.987486i	$0.449590\pi$
$422$	4559.60	0.525966
$423$	−1097.89	−0.126197
$424$	−11486.8	−1.31568
$425$	−41.1077	−0.00469180
$426$	5750.36	0.654004
$427$	0	0
$428$	−15730.4	−1.77653
$429$	−29134.6	−3.27887
$430$	−10091.4	−1.13175
$431$	6269.43	0.700668	0.350334	−	0.936625i	$-0.386068\pi$
$431$	6269.43	0.700668	0.350334	+	0.936625i	$0.386068\pi$
$432$	524.889	0.0584577
$433$	−4656.21	−0.516774	−0.258387	−	0.966041i	$-0.583191\pi$
$433$	−4656.21	−0.516774	−0.258387	+	0.966041i	$0.583191\pi$
$434$	0	0
$435$	268.141	0.0295549
$436$	19119.1	2.10009
$437$	7339.81	0.803457
$438$	−3919.88	−0.427623
$439$	300.034	0.0326193	0.0163096	−	0.999867i	$-0.494808\pi$
$439$	300.034	0.0326193	0.0163096	+	0.999867i	$0.494808\pi$
$440$	−8926.68	−0.967188
$441$	0	0
$442$	−6877.17	−0.740076
$443$	−3513.48	−0.376819	−0.188409	−	0.982091i	$-0.560333\pi$
$443$	−3513.48	−0.376819	−0.188409	+	0.982091i	$0.560333\pi$
$444$	12739.4	1.36168
$445$	1263.87	0.134637
$446$	−14856.6	−1.57731
$447$	480.535	0.0508468
$448$	0	0
$449$	16840.4	1.77003	0.885017	−	0.465559i	$-0.154147\pi$
$449$	16840.4	1.77003	0.885017	+	0.465559i	$0.154147\pi$
$450$	232.226	0.0243272
$451$	−199.928	−0.0208741
$452$	−26704.8	−2.77895
$453$	20826.7	2.16010
$454$	−5918.56	−0.611832
$455$	0	0
$456$	11556.8	1.18683
$457$	−9978.07	−1.02134	−0.510672	−	0.859775i	$-0.670603\pi$
$457$	−9978.07	−1.02134	−0.510672	+	0.859775i	$0.670603\pi$
$458$	−13557.0	−1.38314
$459$	−474.461	−0.0482482
$460$	9688.32	0.982000
$461$	17291.5	1.74696	0.873478	−	0.486864i	$-0.161859\pi$
$461$	17291.5	1.74696	0.873478	+	0.486864i	$0.161859\pi$
$462$	0	0
$463$	1671.45	0.167773	0.0838864	−	0.996475i	$-0.473267\pi$
$463$	1671.45	0.167773	0.0838864	+	0.996475i	$0.473267\pi$
$464$	69.2860	0.00693216
$465$	6769.20	0.675084
$466$	−21516.4	−2.13890
$467$	−8875.93	−0.879505	−0.439753	−	0.898119i	$-0.644934\pi$
$467$	−8875.93	−0.879505	−0.439753	+	0.898119i	$0.644934\pi$
$468$	23094.1	2.28104
$469$	0	0
$470$	−2312.83	−0.226985
$471$	23014.3	2.25147
$472$	−3106.95	−0.302985
$473$	9985.43	0.970678
$474$	−28310.3	−2.74332
$475$	220.310	0.0212811
$476$	0	0
$477$	16216.7	1.55663
$478$	−28726.3	−2.74877
$479$	−15552.8	−1.48356	−0.741782	−	0.670641i	$-0.766019\pi$
$479$	−15552.8	−1.48356	−0.741782	+	0.670641i	$0.766019\pi$
$480$	−17502.6	−1.66433
$481$	12908.8	1.22368
$482$	−25130.6	−2.37483
$483$	0	0
$484$	12193.9	1.14518
$485$	3254.86	0.304733
$486$	22558.7	2.10552
$487$	−10528.4	−0.979647	−0.489824	−	0.871822i	$-0.662939\pi$
$487$	−10528.4	−0.979647	−0.489824	+	0.871822i	$0.662939\pi$
$488$	247.408	0.0229501
$489$	−1222.75	−0.113077
$490$	0	0
$491$	2267.78	0.208439	0.104220	−	0.994554i	$-0.466766\pi$
$491$	2267.78	0.208439	0.104220	+	0.994554i	$0.466766\pi$
$492$	341.652	0.0313066
$493$	−62.6295	−0.00572148
$494$	36857.1	3.35684
$495$	12602.4	1.14432
$496$	1749.12	0.158342
$497$	0	0
$498$	13458.9	1.21106
$499$	7889.84	0.707811	0.353906	−	0.935281i	$-0.384853\pi$
$499$	7889.84	0.707811	0.353906	+	0.935281i	$0.384853\pi$
$500$	16530.3	1.47851
$501$	10779.7	0.961283
$502$	12789.3	1.13708
$503$	−3605.45	−0.319601	−0.159800	−	0.987149i	$-0.551085\pi$
$503$	−3605.45	−0.319601	−0.159800	+	0.987149i	$0.551085\pi$
$504$	0	0
$505$	11922.9	1.05062
$506$	−16127.3	−1.41689
$507$	34858.7	3.05351
$508$	23166.6	2.02333
$509$	−5166.11	−0.449870	−0.224935	−	0.974374i	$-0.572217\pi$
$509$	−5166.11	−0.449870	−0.224935	+	0.974374i	$0.572217\pi$
$510$	6413.17	0.556823
$511$	0	0
$512$	−7211.89	−0.622506
$513$	2542.80	0.218844
$514$	7763.48	0.666211
$515$	−8982.79	−0.768600
$516$	−17063.9	−1.45580
$517$	2288.54	0.194681
$518$	0	0
$519$	−17184.5	−1.45340
$520$	15457.4	1.30356
$521$	18706.5	1.57302	0.786512	−	0.617575i	$-0.211885\pi$
$521$	18706.5	1.57302	0.786512	+	0.617575i	$0.211885\pi$
$522$	353.807	0.0296662
$523$	18868.4	1.57755	0.788773	−	0.614684i	$-0.210717\pi$
$523$	18868.4	1.57755	0.788773	+	0.614684i	$0.210717\pi$
$524$	−29055.9	−2.42235
$525$	0	0
$526$	16508.3	1.36843
$527$	−1581.08	−0.130688
$528$	7020.29	0.578635
$529$	−6605.76	−0.542924
$530$	34162.3	2.79984
$531$	4386.30	0.358473
$532$	0	0
$533$	346.195	0.0281339
$534$	3595.23	0.291349
$535$	14864.1	1.20118
$536$	−622.143	−0.0501352
$537$	−1160.16	−0.0932302
$538$	−7814.92	−0.626255
$539$	0	0
$540$	3356.41	0.267476
$541$	−4760.43	−0.378312	−0.189156	−	0.981947i	$-0.560575\pi$
$541$	−4760.43	−0.378312	−0.189156	+	0.981947i	$0.560575\pi$
$542$	37451.2	2.96802
$543$	12787.8	1.01064
$544$	4088.07	0.322196
$545$	−18066.2	−1.41995
$546$	0	0
$547$	−3298.64	−0.257842	−0.128921	−	0.991655i	$-0.541151\pi$
$547$	−3298.64	−0.257842	−0.128921	+	0.991655i	$0.541151\pi$
$548$	31604.5	2.46364
$549$	−349.284	−0.0271531
$550$	−484.073	−0.0375290
$551$	335.653	0.0259515
$552$	8756.37	0.675174
$553$	0	0
$554$	17039.8	1.30677
$555$	−12037.9	−0.920683
$556$	6528.99	0.498006
$557$	−12259.2	−0.932568	−0.466284	−	0.884635i	$-0.654407\pi$
$557$	−12259.2	−0.932568	−0.466284	+	0.884635i	$0.654407\pi$
$558$	8931.85	0.677626
$559$	−17290.8	−1.30827
$560$	0	0
$561$	−6345.83	−0.477578
$562$	1310.91	0.0983941
$563$	−4369.28	−0.327075	−0.163537	−	0.986537i	$-0.552290\pi$
$563$	−4369.28	−0.327075	−0.163537	+	0.986537i	$0.552290\pi$
$564$	−3910.83	−0.291978
$565$	25234.2	1.87895
$566$	28014.8	2.08047
$567$	0	0
$568$	3018.83	0.223006
$569$	18284.7	1.34716	0.673580	−	0.739114i	$-0.264756\pi$
$569$	18284.7	1.34716	0.673580	+	0.739114i	$0.264756\pi$
$570$	−34370.4	−2.52564
$571$	5651.31	0.414185	0.207093	−	0.978321i	$-0.433600\pi$
$571$	5651.31	0.414185	0.207093	+	0.978321i	$0.433600\pi$
$572$	−48139.4	−3.51890
$573$	−8491.57	−0.619093
$574$	0	0
$575$	166.925	0.0121065
$576$	−19297.7	−1.39596
$577$	7668.64	0.553293	0.276646	−	0.960972i	$-0.410777\pi$
$577$	7668.64	0.553293	0.276646	+	0.960972i	$0.410777\pi$
$578$	20322.4	1.46246
$579$	−175.757	−0.0126152
$580$	443.051	0.0317184
$581$	0	0
$582$	9258.80	0.659432
$583$	−33803.6	−2.40138
$584$	−2057.86	−0.145813
$585$	−21822.3	−1.54230
$586$	1472.78	0.103823
$587$	2728.28	0.191837	0.0959185	−	0.995389i	$-0.469421\pi$
$587$	2728.28	0.191837	0.0959185	+	0.995389i	$0.469421\pi$
$588$	0	0
$589$	8473.53	0.592777
$590$	9240.21	0.644769
$591$	−36233.7	−2.52192
$592$	−3110.52	−0.215948
$593$	18355.3	1.27110	0.635548	−	0.772061i	$-0.280774\pi$
$593$	18355.3	1.27110	0.635548	+	0.772061i	$0.280774\pi$
$594$	−5587.12	−0.385930
$595$	0	0
$596$	793.992	0.0545691
$597$	−21646.2	−1.48395
$598$	27926.0	1.90966
$599$	9618.15	0.656072	0.328036	−	0.944665i	$-0.393613\pi$
$599$	9618.15	0.656072	0.328036	+	0.944665i	$0.393613\pi$
$600$	262.829	0.0178833
$601$	18605.6	1.26279	0.631395	−	0.775462i	$-0.282483\pi$
$601$	18605.6	1.26279	0.631395	+	0.775462i	$0.282483\pi$
$602$	0	0
$603$	878.323	0.0593169
$604$	34412.1	2.31823
$605$	−11522.4	−0.774300
$606$	33916.0	2.27350
$607$	26138.8	1.74785	0.873923	−	0.486065i	$-0.161568\pi$
$607$	26138.8	1.74785	0.873923	+	0.486065i	$0.161568\pi$
$608$	−21909.4	−1.46142
$609$	0	0
$610$	−735.804	−0.0488390
$611$	−3962.84	−0.262388
$612$	5030.14	0.332241
$613$	−25475.7	−1.67855	−0.839276	−	0.543706i	$-0.817021\pi$
$613$	−25475.7	−1.67855	−0.839276	+	0.543706i	$0.817021\pi$
$614$	−10738.1	−0.705788
$615$	−322.838	−0.0211676
$616$	0	0
$617$	23786.5	1.55204	0.776019	−	0.630709i	$-0.217236\pi$
$617$	23786.5	1.55204	0.776019	+	0.630709i	$0.217236\pi$
$618$	−25552.5	−1.66323
$619$	1265.73	0.0821875	0.0410937	−	0.999155i	$-0.486916\pi$
$619$	1265.73	0.0821875	0.0410937	+	0.999155i	$0.486916\pi$
$620$	11184.8	0.724504
$621$	1926.63	0.124498
$622$	−29029.3	−1.87133
$623$	0	0
$624$	−12156.3	−0.779877
$625$	−15340.2	−0.981772
$626$	2049.86	0.130877
$627$	34009.5	2.16620
$628$	38026.7	2.41629
$629$	2811.68	0.178234
$630$	0	0
$631$	8836.65	0.557499	0.278749	−	0.960364i	$-0.410080\pi$
$631$	8836.65	0.557499	0.278749	+	0.960364i	$0.410080\pi$
$632$	−14862.4	−0.935433
$633$	−7285.39	−0.457454
$634$	−46584.2	−2.91813
$635$	−21890.9	−1.36805
$636$	57766.2	3.60154
$637$	0	0
$638$	−737.507	−0.0457652
$639$	−4261.89	−0.263846
$640$	−20921.5	−1.29218
$641$	284.696	0.0175426	0.00877131	−	0.999962i	$-0.497208\pi$
$641$	284.696	0.0175426	0.00877131	+	0.999962i	$0.497208\pi$
$642$	42282.7	2.59932
$643$	−13421.8	−0.823179	−0.411589	−	0.911369i	$-0.635026\pi$
$643$	−13421.8	−0.823179	−0.411589	+	0.911369i	$0.635026\pi$
$644$	0	0
$645$	16124.2	0.984324
$646$	8027.86	0.488935
$647$	5623.70	0.341716	0.170858	−	0.985296i	$-0.445346\pi$
$647$	5623.70	0.341716	0.170858	+	0.985296i	$0.445346\pi$
$648$	13469.3	0.816549
$649$	−9143.19	−0.553007
$650$	838.220	0.0505811
$651$	0	0
$652$	−2020.36	−0.121355
$653$	−1615.23	−0.0967979	−0.0483989	−	0.998828i	$-0.515412\pi$
$653$	−1615.23	−0.0967979	−0.0483989	+	0.998828i	$0.515412\pi$
$654$	−51391.4	−3.07273
$655$	27455.8	1.63785
$656$	−83.4193	−0.00496490
$657$	2905.23	0.172517
$658$	0	0
$659$	1499.60	0.0886435	0.0443217	−	0.999017i	$-0.485887\pi$
$659$	1499.60	0.0886435	0.0443217	+	0.999017i	$0.485887\pi$
$660$	44891.4	2.64757
$661$	27229.2	1.60226	0.801131	−	0.598489i	$-0.204232\pi$
$661$	27229.2	1.60226	0.801131	+	0.598489i	$0.204232\pi$
$662$	−27644.5	−1.62301
$663$	10988.4	0.643674
$664$	7065.68	0.412954
$665$	0	0
$666$	−15883.8	−0.924150
$667$	254.318	0.0147635
$668$	17811.4	1.03165
$669$	23738.0	1.37185
$670$	1850.28	0.106690
$671$	728.077	0.0418884
$672$	0	0
$673$	−13623.9	−0.780330	−0.390165	−	0.920745i	$-0.627582\pi$
$673$	−13623.9	−0.780330	−0.390165	+	0.920745i	$0.627582\pi$
$674$	−18181.7	−1.03907
$675$	57.8294	0.00329756
$676$	57597.2	3.27704
$677$	−7128.35	−0.404675	−0.202337	−	0.979316i	$-0.564854\pi$
$677$	−7128.35	−0.404675	−0.202337	+	0.979316i	$0.564854\pi$
$678$	71781.4	4.06600
$679$	0	0
$680$	3366.79	0.189869
$681$	9456.76	0.532135
$682$	−18618.3	−1.04536
$683$	16012.1	0.897053	0.448527	−	0.893770i	$-0.351949\pi$
$683$	16012.1	0.897053	0.448527	+	0.893770i	$0.351949\pi$
$684$	−26958.2	−1.50698
$685$	−29864.0	−1.66576
$686$	0	0
$687$	21661.6	1.20297
$688$	4166.39	0.230875
$689$	58534.3	3.23654
$690$	−26041.8	−1.43681
$691$	−20790.2	−1.14457	−0.572285	−	0.820055i	$-0.693943\pi$
$691$	−20790.2	−1.14457	−0.572285	+	0.820055i	$0.693943\pi$
$692$	−28394.0	−1.55979
$693$	0	0
$694$	35642.9	1.94955
$695$	−6169.45	−0.336720
$696$	400.433	0.0218080
$697$	75.4049	0.00409780
$698$	−42255.0	−2.29137
$699$	34379.1	1.86028
$700$	0	0
$701$	21409.5	1.15353	0.576765	−	0.816910i	$-0.304315\pi$
$701$	21409.5	1.15353	0.576765	+	0.816910i	$0.304315\pi$
$702$	9674.65	0.520151
$703$	−15068.7	−0.808432
$704$	40225.8	2.15350
$705$	3695.47	0.197418
$706$	28164.9	1.50142
$707$	0	0
$708$	15624.6	0.829389
$709$	12697.7	0.672597	0.336299	−	0.941755i	$-0.390825\pi$
$709$	12697.7	0.672597	0.336299	+	0.941755i	$0.390825\pi$
$710$	−8978.13	−0.474568
$711$	20982.3	1.10675
$712$	1887.42	0.0993458
$713$	6420.25	0.337223
$714$	0	0
$715$	45488.4	2.37926
$716$	−1916.94	−0.100055
$717$	45899.3	2.39071
$718$	−14977.2	−0.778476
$719$	−26299.1	−1.36410	−0.682052	−	0.731304i	$-0.738912\pi$
$719$	−26299.1	−1.36410	−0.682052	+	0.731304i	$0.738912\pi$
$720$	5258.32	0.272175
$721$	0	0
$722$	−12560.9	−0.647462
$723$	40154.0	2.06548
$724$	21129.4	1.08462
$725$	7.63356	0.000391039 0
$726$	−32776.7	−1.67556
$727$	8946.91	0.456427	0.228214	−	0.973611i	$-0.426712\pi$
$727$	8946.91	0.456427	0.228214	+	0.973611i	$0.426712\pi$
$728$	0	0
$729$	−14065.4	−0.714596
$730$	6120.17	0.310298
$731$	−3766.11	−0.190554
$732$	−1244.19	−0.0628234
$733$	−8530.89	−0.429871	−0.214936	−	0.976628i	$-0.568954\pi$
$733$	−8530.89	−0.429871	−0.214936	+	0.976628i	$0.568954\pi$
$734$	6304.77	0.317048
$735$	0	0
$736$	−16600.3	−0.831381
$737$	−1830.85	−0.0915065
$738$	−425.979	−0.0212473
$739$	−28533.2	−1.42031	−0.710157	−	0.704044i	$-0.751376\pi$
$739$	−28533.2	−1.42031	−0.710157	+	0.704044i	$0.751376\pi$
$740$	−19890.3	−0.988082
$741$	−58890.8	−2.91958
$742$	0	0
$743$	16037.7	0.791881	0.395940	−	0.918276i	$-0.370419\pi$
$743$	16037.7	0.791881	0.395940	+	0.918276i	$0.370419\pi$
$744$	10108.9	0.498132
$745$	−750.267	−0.0368962
$746$	−50074.8	−2.45760
$747$	−9975.12	−0.488582
$748$	−10485.3	−0.512539
$749$	0	0
$750$	−44432.8	−2.16328
$751$	−21196.0	−1.02990	−0.514948	−	0.857222i	$-0.672189\pi$
$751$	−21196.0	−1.02990	−0.514948	+	0.857222i	$0.672189\pi$
$752$	954.887	0.0463047
$753$	−20435.0	−0.988967
$754$	1277.07	0.0616817
$755$	−32517.1	−1.56744
$756$	0	0
$757$	−16858.4	−0.809420	−0.404710	−	0.914445i	$-0.632627\pi$
$757$	−16858.4	−0.809420	−0.404710	+	0.914445i	$0.632627\pi$
$758$	−38199.2	−1.83042
$759$	25768.4	1.23232
$760$	−18043.8	−0.861206
$761$	−17868.5	−0.851159	−0.425579	−	0.904921i	$-0.639930\pi$
$761$	−17868.5	−0.851159	−0.425579	+	0.904921i	$0.639930\pi$
$762$	−62271.0	−2.96042
$763$	0	0
$764$	−14030.7	−0.664414
$765$	−4753.14	−0.224641
$766$	−41635.3	−1.96390
$767$	15832.3	0.745336
$768$	−12613.5	−0.592643
$769$	20004.1	0.938056	0.469028	−	0.883183i	$-0.344604\pi$
$769$	20004.1	0.938056	0.469028	+	0.883183i	$0.344604\pi$
$770$	0	0
$771$	−12404.6	−0.579430
$772$	−290.404	−0.0135387
$773$	−27197.4	−1.26549	−0.632744	−	0.774361i	$-0.718071\pi$
$773$	−27197.4	−1.26549	−0.632744	+	0.774361i	$0.718071\pi$
$774$	21275.6	0.988030
$775$	192.709	0.00893201
$776$	4860.69	0.224857
$777$	0	0
$778$	−4353.28	−0.200607
$779$	−404.121	−0.0185868
$780$	−77734.0	−3.56836
$781$	8883.86	0.407029
$782$	6082.57	0.278149
$783$	88.1058	0.00402126
$784$	0	0
$785$	−35932.6	−1.63375
$786$	78101.2	3.54425
$787$	26179.4	1.18576	0.592882	−	0.805289i	$-0.297990\pi$
$787$	26179.4	1.18576	0.592882	+	0.805289i	$0.297990\pi$
$788$	−59869.1	−2.70654
$789$	−26377.2	−1.19018
$790$	44201.4	1.99065
$791$	0	0
$792$	18820.0	0.844370
$793$	−1260.74	−0.0564567
$794$	−50308.1	−2.24857
$795$	−54585.0	−2.43513
$796$	−35766.1	−1.59258
$797$	35289.6	1.56841	0.784203	−	0.620504i	$-0.213072\pi$
$797$	35289.6	1.56841	0.784203	+	0.620504i	$0.213072\pi$
$798$	0	0
$799$	−863.148	−0.0382177
$800$	−498.272	−0.0220207
$801$	−2664.61	−0.117540
$802$	−13796.2	−0.607433
$803$	−6055.91	−0.266137
$804$	3128.70	0.137240
$805$	0	0
$806$	32239.5	1.40892
$807$	12486.8	0.544679
$808$	17805.2	0.775230
$809$	−24881.8	−1.08133	−0.540666	−	0.841237i	$-0.681828\pi$
$809$	−24881.8	−1.08133	−0.540666	+	0.841237i	$0.681828\pi$
$810$	−40058.3	−1.73766
$811$	−10101.5	−0.437375	−0.218688	−	0.975795i	$-0.570178\pi$
$811$	−10101.5	−0.437375	−0.218688	+	0.975795i	$0.570178\pi$
$812$	0	0
$813$	−59840.0	−2.58140
$814$	33109.5	1.42566
$815$	1909.10	0.0820527
$816$	−2647.78	−0.113592
$817$	20183.9	0.864314
$818$	−41591.3	−1.77776
$819$	0	0
$820$	−533.427	−0.0227172
$821$	−12650.7	−0.537773	−0.268886	−	0.963172i	$-0.586656\pi$
$821$	−12650.7	−0.537773	−0.268886	+	0.963172i	$0.586656\pi$
$822$	−84951.6	−3.60465
$823$	40177.2	1.70169	0.850845	−	0.525417i	$-0.176091\pi$
$823$	40177.2	1.70169	0.850845	+	0.525417i	$0.176091\pi$
$824$	−13414.6	−0.567135
$825$	773.458	0.0326404
$826$	0	0
$827$	3339.15	0.140403	0.0702017	−	0.997533i	$-0.477636\pi$
$827$	3339.15	0.140403	0.0702017	+	0.997533i	$0.477636\pi$
$828$	−20425.8	−0.857301
$829$	34367.6	1.43985	0.719926	−	0.694051i	$-0.244176\pi$
$829$	34367.6	1.43985	0.719926	+	0.694051i	$0.244176\pi$
$830$	−21013.6	−0.878788
$831$	−27226.4	−1.13655
$832$	−69655.0	−2.90247
$833$	0	0
$834$	−17549.7	−0.728652
$835$	−16830.6	−0.697540
$836$	56194.1	2.32478
$837$	2224.23	0.0918524
$838$	−33283.3	−1.37202
$839$	−26114.0	−1.07456	−0.537279	−	0.843405i	$-0.680548\pi$
$839$	−26114.0	−1.07456	−0.537279	+	0.843405i	$0.680548\pi$
$840$	0	0
$841$	−24377.4	−0.999523
$842$	−12101.0	−0.495282
$843$	−2094.59	−0.0855773
$844$	−12037.7	−0.490942
$845$	−54425.4	−2.21573
$846$	4876.11	0.198161
$847$	0	0
$848$	−14104.5	−0.571166
$849$	−44762.4	−1.80947
$850$	182.573	0.00736730
$851$	−11417.3	−0.459907
$852$	−15181.4	−0.610454
$853$	24982.1	1.00278	0.501389	−	0.865222i	$-0.332822\pi$
$853$	24982.1	1.00278	0.501389	+	0.865222i	$0.332822\pi$
$854$	0	0
$855$	25473.7	1.01893
$856$	22197.6	0.886330
$857$	18151.1	0.723490	0.361745	−	0.932277i	$-0.382181\pi$
$857$	18151.1	0.723490	0.361745	+	0.932277i	$0.382181\pi$
$858$	129397.	5.14864
$859$	41575.1	1.65137	0.825683	−	0.564134i	$-0.190790\pi$
$859$	41575.1	1.65137	0.825683	+	0.564134i	$0.190790\pi$
$860$	26642.1	1.05638
$861$	0	0
$862$	−27844.7	−1.10022
$863$	−17545.4	−0.692065	−0.346032	−	0.938223i	$-0.612471\pi$
$863$	−17545.4	−0.692065	−0.346032	+	0.938223i	$0.612471\pi$
$864$	−5751.01	−0.226451
$865$	26830.4	1.05464
$866$	20679.8	0.811465
$867$	−32471.4	−1.27196
$868$	0	0
$869$	−43737.2	−1.70735
$870$	−1190.90	−0.0464085
$871$	3170.30	0.123331
$872$	−26979.5	−1.04775
$873$	−6862.18	−0.266036
$874$	−32598.6	−1.26163
$875$	0	0
$876$	10348.8	0.399148
$877$	18060.8	0.695407	0.347703	−	0.937605i	$-0.386962\pi$
$877$	18060.8	0.695407	0.347703	+	0.937605i	$0.386962\pi$
$878$	−1332.55	−0.0512204
$879$	−2353.23	−0.0902988
$880$	−10960.9	−0.419877
$881$	−17023.1	−0.650991	−0.325496	−	0.945544i	$-0.605531\pi$
$881$	−17023.1	−0.650991	−0.325496	+	0.945544i	$0.605531\pi$
$882$	0	0
$883$	32552.3	1.24062	0.620312	−	0.784355i	$-0.287006\pi$
$883$	32552.3	1.24062	0.620312	+	0.784355i	$0.287006\pi$
$884$	18156.3	0.690794
$885$	−14764.1	−0.560781
$886$	15604.6	0.591700
$887$	39204.2	1.48405	0.742023	−	0.670374i	$-0.233867\pi$
$887$	39204.2	1.48405	0.742023	+	0.670374i	$0.233867\pi$
$888$	−17977.0	−0.679355
$889$	0	0
$890$	−5613.29	−0.211413
$891$	39637.6	1.49036
$892$	39222.5	1.47227
$893$	4625.90	0.173348
$894$	−2134.22	−0.0798422
$895$	1811.38	0.0676510
$896$	0	0
$897$	−44620.5	−1.66091
$898$	−74793.7	−2.77940
$899$	293.601	0.0108923
$900$	−613.096	−0.0227073
$901$	12749.4	0.471414
$902$	887.947	0.0327776
$903$	0	0
$904$	37683.9	1.38645
$905$	−19965.8	−0.733355
$906$	−92498.5	−3.39189
$907$	−33847.2	−1.23912	−0.619558	−	0.784951i	$-0.712688\pi$
$907$	−33847.2	−1.23912	−0.619558	+	0.784951i	$0.712688\pi$
$908$	15625.5	0.571090
$909$	−25136.9	−0.917203
$910$	0	0
$911$	545.316	0.0198322	0.00991609	−	0.999951i	$-0.496844\pi$
$911$	545.316	0.0198322	0.00991609	+	0.999951i	$0.496844\pi$
$912$	14190.3	0.515229
$913$	20793.0	0.753722
$914$	44316.0	1.60377
$915$	1175.68	0.0424773
$916$	35791.6	1.29103
$917$	0	0
$918$	2107.24	0.0757618
$919$	−7903.69	−0.283698	−0.141849	−	0.989888i	$-0.545305\pi$
$919$	−7903.69	−0.283698	−0.141849	+	0.989888i	$0.545305\pi$
$920$	−13671.5	−0.489929
$921$	17157.5	0.613852
$922$	−76797.5	−2.74316
$923$	−15383.3	−0.548588
$924$	0	0
$925$	−342.700	−0.0121815
$926$	−7423.47	−0.263445
$927$	18938.3	0.670999
$928$	−759.141	−0.0268535
$929$	−42973.2	−1.51766	−0.758830	−	0.651289i	$-0.774229\pi$
$929$	−42973.2	−1.51766	−0.758830	+	0.651289i	$0.774229\pi$
$930$	−30064.3	−1.06005
$931$	0	0
$932$	56804.9	1.99647
$933$	46383.4	1.62757
$934$	39421.0	1.38104
$935$	9907.85	0.346547
$936$	−32588.8	−1.13803
$937$	6760.44	0.235703	0.117852	−	0.993031i	$-0.462399\pi$
$937$	6760.44	0.235703	0.117852	+	0.993031i	$0.462399\pi$
$938$	0	0
$939$	−3275.30	−0.113829
$940$	6106.05	0.211870
$941$	17703.6	0.613307	0.306653	−	0.951821i	$-0.400791\pi$
$941$	17703.6	0.613307	0.306653	+	0.951821i	$0.400791\pi$
$942$	−102214.	−3.53538
$943$	−306.195	−0.0105738
$944$	−3814.97	−0.131532
$945$	0	0
$946$	−44348.7	−1.52421
$947$	22592.8	0.775255	0.387628	−	0.921816i	$-0.373295\pi$
$947$	22592.8	0.775255	0.387628	+	0.921816i	$0.373295\pi$
$948$	74741.5	2.56064
$949$	10486.4	0.358697
$950$	−978.472	−0.0334166
$951$	74432.9	2.53801
$952$	0	0
$953$	−52013.1	−1.76796	−0.883981	−	0.467522i	$-0.845147\pi$
$953$	−52013.1	−1.76796	−0.883981	+	0.467522i	$0.845147\pi$
$954$	−72024.1	−2.44430
$955$	13258.0	0.449235
$956$	75839.7	2.56572
$957$	1178.40	0.0398038
$958$	69075.4	2.32957
$959$	0	0
$960$	64955.4	2.18378
$961$	−22379.1	−0.751202
$962$	−57332.4	−1.92149
$963$	−31337.9	−1.04865
$964$	66346.8	2.21669
$965$	274.412	0.00915403
$966$	0	0
$967$	−26579.6	−0.883913	−0.441956	−	0.897037i	$-0.645715\pi$
$967$	−26579.6	−0.883913	−0.441956	+	0.897037i	$0.645715\pi$
$968$	−17207.1	−0.571341
$969$	−12827.0	−0.425246
$970$	−14455.9	−0.478507
$971$	30539.4	1.00933	0.504664	−	0.863316i	$-0.331616\pi$
$971$	30539.4	1.00933	0.504664	+	0.863316i	$0.331616\pi$
$972$	−59556.7	−1.96531
$973$	0	0
$974$	46760.3	1.53829
$975$	−1339.32	−0.0439924
$976$	303.788	0.00996314
$977$	5345.63	0.175048	0.0875240	−	0.996162i	$-0.472105\pi$
$977$	5345.63	0.175048	0.0875240	+	0.996162i	$0.472105\pi$
$978$	5430.66	0.177560
$979$	5554.34	0.181325
$980$	0	0
$981$	38088.9	1.23964
$982$	−10072.0	−0.327302
$983$	−20492.5	−0.664911	−0.332456	−	0.943119i	$-0.607877\pi$
$983$	−20492.5	−0.664911	−0.332456	+	0.943119i	$0.607877\pi$
$984$	−482.115	−0.0156192
$985$	56572.2	1.82999
$986$	278.159	0.00898415
$987$	0	0
$988$	−97305.7	−3.13330
$989$	15293.0	0.491697
$990$	−55971.6	−1.79686
$991$	−22554.0	−0.722959	−0.361480	−	0.932380i	$-0.617728\pi$
$991$	−22554.0	−0.722959	−0.361480	+	0.932380i	$0.617728\pi$
$992$	−19164.5	−0.613380
$993$	44170.8	1.41160
$994$	0	0
$995$	33796.5	1.07681
$996$	−35532.7	−1.13042
$997$	−4993.62	−0.158625	−0.0793126	−	0.996850i	$-0.525273\pi$
$997$	−4993.62	−0.158625	−0.0793126	+	0.996850i	$0.525273\pi$
$998$	−35041.5	−1.11144
$999$	−3955.41	−0.125269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.9	yes	68
7.6	odd	2		2303.4.a.m.1.9	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.9	✓	68	7.6	odd	2
2303.4.a.n.1.9	yes	68	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:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-4.44134 q^{2} +7.09644 q^{3} +11.7255 q^{4} -11.0798 q^{5} -31.5177 q^{6} -16.5462 q^{8} +23.3594 q^{9} +O(q^{10})\)	\(q-4.44134 q^{2} +7.09644 q^{3} +11.7255 q^{4} -11.0798 q^{5} -31.5177 q^{6} -16.5462 q^{8} +23.3594 q^{9} +49.2091 q^{10} -48.6924 q^{11} +83.2092 q^{12} +84.3157 q^{13} -78.6270 q^{15} -20.3167 q^{16} +18.3648 q^{17} -103.747 q^{18} -98.4234 q^{19} -129.916 q^{20} +216.259 q^{22} -74.5738 q^{23} -117.419 q^{24} -2.23839 q^{25} -374.475 q^{26} -25.8353 q^{27} -3.41029 q^{29} +349.209 q^{30} -86.0926 q^{31} +222.603 q^{32} -345.542 q^{33} -81.5645 q^{34} +273.901 q^{36} +153.101 q^{37} +437.132 q^{38} +598.341 q^{39} +183.328 q^{40} +4.10594 q^{41} -205.072 q^{43} -570.942 q^{44} -258.817 q^{45} +331.207 q^{46} -47.0000 q^{47} -144.176 q^{48} +9.94145 q^{50} +130.325 q^{51} +988.643 q^{52} +694.228 q^{53} +114.743 q^{54} +539.501 q^{55} -698.456 q^{57} +15.1463 q^{58} +187.775 q^{59} -921.940 q^{60} -14.9526 q^{61} +382.366 q^{62} -826.122 q^{64} -934.200 q^{65} +1534.67 q^{66} +37.6004 q^{67} +215.337 q^{68} -529.208 q^{69} -182.449 q^{71} -386.509 q^{72} +124.371 q^{73} -679.974 q^{74} -15.8846 q^{75} -1154.06 q^{76} -2657.43 q^{78} +898.236 q^{79} +225.105 q^{80} -814.042 q^{81} -18.2359 q^{82} -427.028 q^{83} -203.479 q^{85} +910.794 q^{86} -24.2009 q^{87} +805.673 q^{88} -114.070 q^{89} +1149.49 q^{90} -874.414 q^{92} -610.951 q^{93} +208.743 q^{94} +1090.51 q^{95} +1579.69 q^{96} -293.765 q^{97} -1137.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * q^99

Introduction

L-functions

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Database

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