LMFDB - Embedded newform 2303.4.a.n.1.8

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			1.8
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)

$f(q)$	$=$	$q-4.80817 q^{2} +9.29565 q^{3} +15.1185 q^{4} +20.1348 q^{5} -44.6951 q^{6} -34.2269 q^{8} +59.4092 q^{9} +O(q^{10})$	\(q-4.80817 q^{2} +9.29565 q^{3} +15.1185 q^{4} +20.1348 q^{5} -44.6951 q^{6} -34.2269 q^{8} +59.4092 q^{9} -96.8114 q^{10} +48.0604 q^{11} +140.536 q^{12} +55.0599 q^{13} +187.166 q^{15} +43.6207 q^{16} +20.3777 q^{17} -285.649 q^{18} -76.7396 q^{19} +304.407 q^{20} -231.082 q^{22} +1.94841 q^{23} -318.161 q^{24} +280.409 q^{25} -264.737 q^{26} +301.265 q^{27} +269.818 q^{29} -899.925 q^{30} -28.1774 q^{31} +64.0793 q^{32} +446.753 q^{33} -97.9792 q^{34} +898.177 q^{36} -354.681 q^{37} +368.977 q^{38} +511.818 q^{39} -689.150 q^{40} +490.885 q^{41} -214.131 q^{43} +726.600 q^{44} +1196.19 q^{45} -9.36828 q^{46} -47.0000 q^{47} +405.483 q^{48} -1348.25 q^{50} +189.424 q^{51} +832.422 q^{52} -343.485 q^{53} -1448.53 q^{54} +967.685 q^{55} -713.345 q^{57} -1297.33 q^{58} -183.883 q^{59} +2829.66 q^{60} -165.396 q^{61} +135.481 q^{62} -657.070 q^{64} +1108.62 q^{65} -2148.06 q^{66} +94.2883 q^{67} +308.079 q^{68} +18.1117 q^{69} -920.939 q^{71} -2033.39 q^{72} -518.579 q^{73} +1705.36 q^{74} +2606.58 q^{75} -1160.19 q^{76} -2460.90 q^{78} -1009.05 q^{79} +878.293 q^{80} +1196.40 q^{81} -2360.26 q^{82} +687.182 q^{83} +410.299 q^{85} +1029.58 q^{86} +2508.13 q^{87} -1644.96 q^{88} -1033.97 q^{89} -5751.49 q^{90} +29.4570 q^{92} -261.927 q^{93} +225.984 q^{94} -1545.13 q^{95} +595.659 q^{96} +931.178 q^{97} +2855.23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.80817	−1.69994	−0.849972	−	0.526828i	$-0.823381\pi$
$2$	−4.80817	−1.69994	−0.849972	+	0.526828i	$0.823381\pi$
$3$	9.29565	1.78895	0.894475	−	0.447118i	$-0.147550\pi$
$3$	9.29565	1.78895	0.894475	+	0.447118i	$0.147550\pi$
$4$	15.1185	1.88981
$5$	20.1348	1.80091	0.900454	−	0.434951i	$-0.143234\pi$
$5$	20.1348	1.80091	0.900454	+	0.434951i	$0.143234\pi$
$6$	−44.6951	−3.04111
$7$	0	0
$7$	0	0
$8$	−34.2269	−1.51263
$9$	59.4092	2.20034
$10$	−96.8114	−3.06144
$11$	48.0604	1.31734	0.658671	−	0.752431i	$-0.271119\pi$
$11$	48.0604	1.31734	0.658671	+	0.752431i	$0.271119\pi$
$12$	140.536	3.38078
$13$	55.0599	1.17468	0.587341	−	0.809340i	$-0.300175\pi$
$13$	55.0599	1.17468	0.587341	+	0.809340i	$0.300175\pi$
$14$	0	0
$15$	187.166	3.22173
$16$	43.6207	0.681573
$17$	20.3777	0.290724	0.145362	−	0.989379i	$-0.453565\pi$
$17$	20.3777	0.290724	0.145362	+	0.989379i	$0.453565\pi$
$18$	−285.649	−3.74046
$19$	−76.7396	−0.926593	−0.463297	−	0.886203i	$-0.653334\pi$
$19$	−76.7396	−0.926593	−0.463297	+	0.886203i	$0.653334\pi$
$20$	304.407	3.40338
$21$	0	0
$22$	−231.082	−2.23941
$23$	1.94841	0.0176640	0.00883199	−	0.999961i	$-0.497189\pi$
$23$	1.94841	0.0176640	0.00883199	+	0.999961i	$0.497189\pi$
$24$	−318.161	−2.70602
$25$	280.409	2.24327
$26$	−264.737	−1.99689
$27$	301.265	2.14735
$28$	0	0
$29$	269.818	1.72772	0.863861	−	0.503731i	$-0.168040\pi$
$29$	269.818	1.72772	0.863861	+	0.503731i	$0.168040\pi$
$30$	−899.925	−5.47677
$31$	−28.1774	−0.163252	−0.0816258	−	0.996663i	$-0.526011\pi$
$31$	−28.1774	−0.163252	−0.0816258	+	0.996663i	$0.526011\pi$
$32$	64.0793	0.353992
$33$	446.753	2.35666
$34$	−97.9792	−0.494214
$35$	0	0
$36$	898.177	4.15823
$37$	−354.681	−1.57592	−0.787962	−	0.615724i	$-0.788863\pi$
$37$	−354.681	−1.57592	−0.787962	+	0.615724i	$0.788863\pi$
$38$	368.977	1.57516
$39$	511.818	2.10145
$40$	−689.150	−2.72411
$41$	490.885	1.86984	0.934918	−	0.354863i	$-0.115472\pi$
$41$	490.885	1.86984	0.934918	+	0.354863i	$0.115472\pi$
$42$	0	0
$43$	−214.131	−0.759410	−0.379705	−	0.925108i	$-0.623975\pi$
$43$	−214.131	−0.759410	−0.379705	+	0.925108i	$0.623975\pi$
$44$	726.600	2.48953
$45$	1196.19	3.96261
$46$	−9.36828	−0.0300278
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	405.483	1.21930
$49$	0	0
$50$	−1348.25	−3.81344
$51$	189.424	0.520090
$52$	832.422	2.21993
$53$	−343.485	−0.890212	−0.445106	−	0.895478i	$-0.646834\pi$
$53$	−343.485	−0.890212	−0.445106	+	0.895478i	$0.646834\pi$
$54$	−1448.53	−3.65037
$55$	967.685	2.37241
$56$	0	0
$57$	−713.345	−1.65763
$58$	−1297.33	−2.93703
$59$	−183.883	−0.405755	−0.202878	−	0.979204i	$-0.565029\pi$
$59$	−183.883	−0.405755	−0.202878	+	0.979204i	$0.565029\pi$
$60$	2829.66	6.08847
$61$	−165.396	−0.347161	−0.173580	−	0.984820i	$-0.555534\pi$
$61$	−165.396	−0.347161	−0.173580	+	0.984820i	$0.555534\pi$
$62$	135.481	0.277519
$63$	0	0
$64$	−657.070	−1.28334
$65$	1108.62	2.11549
$66$	−2148.06	−4.00619
$67$	94.2883	0.171928	0.0859638	−	0.996298i	$-0.472603\pi$
$67$	94.2883	0.171928	0.0859638	+	0.996298i	$0.472603\pi$
$68$	308.079	0.549413
$69$	18.1117	0.0316000
$70$	0	0
$71$	−920.939	−1.53937	−0.769686	−	0.638423i	$-0.779587\pi$
$71$	−920.939	−1.53937	−0.769686	+	0.638423i	$0.779587\pi$
$72$	−2033.39	−3.32830
$73$	−518.579	−0.831439	−0.415720	−	0.909493i	$-0.636470\pi$
$73$	−518.579	−0.831439	−0.415720	+	0.909493i	$0.636470\pi$
$74$	1705.36	2.67898
$75$	2606.58	4.01310
$76$	−1160.19	−1.75109
$77$	0	0
$78$	−2460.90	−3.57234
$79$	−1009.05	−1.43705	−0.718527	−	0.695499i	$-0.755184\pi$
$79$	−1009.05	−1.43705	−0.718527	+	0.695499i	$0.755184\pi$
$80$	878.293	1.22745
$81$	1196.40	1.64116
$82$	−2360.26	−3.17862
$83$	687.182	0.908772	0.454386	−	0.890805i	$-0.349859\pi$
$83$	687.182	0.908772	0.454386	+	0.890805i	$0.349859\pi$
$84$	0	0
$85$	410.299	0.523567
$86$	1029.58	1.29095
$87$	2508.13	3.09081
$88$	−1644.96	−1.99265
$89$	−1033.97	−1.23146	−0.615732	−	0.787956i	$-0.711139\pi$
$89$	−1033.97	−1.23146	−0.615732	+	0.787956i	$0.711139\pi$
$90$	−5751.49	−6.73622
$91$	0	0
$92$	29.4570	0.0333816
$93$	−261.927	−0.292049
$94$	225.984	0.247962
$95$	−1545.13	−1.66871
$96$	595.659	0.633273
$97$	931.178	0.974710	0.487355	−	0.873204i	$-0.337962\pi$
$97$	931.178	0.974710	0.487355	+	0.873204i	$0.337962\pi$
$98$	0	0
$99$	2855.23	2.89860
$100$	4239.36	4.23936
$101$	−1288.89	−1.26980	−0.634898	−	0.772596i	$-0.718958\pi$
$101$	−1288.89	−1.26980	−0.634898	+	0.772596i	$0.718958\pi$
$102$	−910.781	−0.884125
$103$	−621.127	−0.594189	−0.297095	−	0.954848i	$-0.596018\pi$
$103$	−621.127	−0.594189	−0.297095	+	0.954848i	$0.596018\pi$
$104$	−1884.53	−1.77686
$105$	0	0
$106$	1651.53	1.51331
$107$	988.220	0.892849	0.446424	−	0.894821i	$-0.352697\pi$
$107$	988.220	0.892849	0.446424	+	0.894821i	$0.352697\pi$
$108$	4554.67	4.05808
$109$	631.018	0.554500	0.277250	−	0.960798i	$-0.410577\pi$
$109$	631.018	0.554500	0.277250	+	0.960798i	$0.410577\pi$
$110$	−4652.79	−4.03297
$111$	−3296.99	−2.81925
$112$	0	0
$113$	1599.79	1.33182	0.665909	−	0.746033i	$-0.268044\pi$
$113$	1599.79	1.33182	0.665909	+	0.746033i	$0.268044\pi$
$114$	3429.88	2.81788
$115$	39.2308	0.0318112
$116$	4079.24	3.26507
$117$	3271.06	2.58470
$118$	884.142	0.689761
$119$	0	0
$120$	−6406.10	−4.87329
$121$	978.802	0.735388
$122$	795.253	0.590154
$123$	4563.09	3.34504
$124$	−425.999	−0.308515
$125$	3129.12	2.23902
$126$	0	0
$127$	−782.936	−0.547042	−0.273521	−	0.961866i	$-0.588188\pi$
$127$	−782.936	−0.547042	−0.273521	+	0.961866i	$0.588188\pi$
$128$	2646.67	1.82761
$129$	−1990.49	−1.35855
$130$	−5330.42	−3.59622
$131$	1694.45	1.13011	0.565055	−	0.825053i	$-0.308855\pi$
$131$	1694.45	1.13011	0.565055	+	0.825053i	$0.308855\pi$
$132$	6754.23	4.45364
$133$	0	0
$134$	−453.354	−0.292267
$135$	6065.90	3.86718
$136$	−697.463	−0.439757
$137$	−588.517	−0.367010	−0.183505	−	0.983019i	$-0.558744\pi$
$137$	−588.517	−0.367010	−0.183505	+	0.983019i	$0.558744\pi$
$138$	−87.0843	−0.0537182
$139$	−1310.31	−0.799559	−0.399780	−	0.916611i	$-0.630913\pi$
$139$	−1310.31	−0.799559	−0.399780	+	0.916611i	$0.630913\pi$
$140$	0	0
$141$	−436.896	−0.260945
$142$	4428.03	2.61685
$143$	2646.20	1.54746
$144$	2591.47	1.49969
$145$	5432.72	3.11147
$146$	2493.41	1.41340
$147$	0	0
$148$	−5362.24	−2.97820
$149$	1268.65	0.697531	0.348765	−	0.937210i	$-0.386601\pi$
$149$	1268.65	0.697531	0.348765	+	0.937210i	$0.386601\pi$
$150$	−12532.9	−6.82204
$151$	−2729.25	−1.47088	−0.735440	−	0.677590i	$-0.763025\pi$
$151$	−2729.25	−1.47088	−0.735440	+	0.677590i	$0.763025\pi$
$152$	2626.56	1.40159
$153$	1210.62	0.639692
$154$	0	0
$155$	−567.344	−0.294001
$156$	7737.91	3.97133
$157$	−12.7727	−0.00649282	−0.00324641	−	0.999995i	$-0.501033\pi$
$157$	−12.7727	−0.00649282	−0.00324641	+	0.999995i	$0.501033\pi$
$158$	4851.70	2.44291
$159$	−3192.92	−1.59255
$160$	1290.22	0.637506
$161$	0	0
$162$	−5752.51	−2.78988
$163$	−2403.78	−1.15508	−0.577541	−	0.816361i	$-0.695988\pi$
$163$	−2403.78	−1.15508	−0.577541	+	0.816361i	$0.695988\pi$
$164$	7421.43	3.53364
$165$	8995.27	4.24412
$166$	−3304.09	−1.54486
$167$	−3222.25	−1.49308	−0.746542	−	0.665338i	$-0.768287\pi$
$167$	−3222.25	−1.49308	−0.746542	+	0.665338i	$0.768287\pi$
$168$	0	0
$169$	834.589	0.379877
$170$	−1972.79	−0.890035
$171$	−4559.04	−2.03882
$172$	−3237.33	−1.43514
$173$	−2620.91	−1.15182	−0.575908	−	0.817514i	$-0.695351\pi$
$173$	−2620.91	−1.15182	−0.575908	+	0.817514i	$0.695351\pi$
$174$	−12059.5	−5.25420
$175$	0	0
$176$	2096.43	0.897865
$177$	−1709.32	−0.725876
$178$	4971.49	2.09342
$179$	3995.47	1.66835	0.834176	−	0.551498i	$-0.185943\pi$
$179$	3995.47	1.66835	0.834176	+	0.551498i	$0.185943\pi$
$180$	18084.6	7.48859
$181$	−1971.99	−0.809817	−0.404908	−	0.914357i	$-0.632697\pi$
$181$	−1971.99	−0.809817	−0.404908	+	0.914357i	$0.632697\pi$
$182$	0	0
$183$	−1537.47	−0.621053
$184$	−66.6880	−0.0267190
$185$	−7141.41	−2.83809
$186$	1259.39	0.496467
$187$	979.358	0.382983
$188$	−710.569	−0.275657
$189$	0	0
$190$	7429.27	2.83671
$191$	−2581.79	−0.978073	−0.489037	−	0.872263i	$-0.662652\pi$
$191$	−2581.79	−0.978073	−0.489037	+	0.872263i	$0.662652\pi$
$192$	−6107.89	−2.29583
$193$	782.414	0.291810	0.145905	−	0.989299i	$-0.453391\pi$
$193$	782.414	0.291810	0.145905	+	0.989299i	$0.453391\pi$
$194$	−4477.26	−1.65695
$195$	10305.3	3.78451
$196$	0	0
$197$	4320.86	1.56268	0.781342	−	0.624103i	$-0.214535\pi$
$197$	4320.86	1.56268	0.781342	+	0.624103i	$0.214535\pi$
$198$	−13728.4	−4.92746
$199$	−211.210	−0.0752374	−0.0376187	−	0.999292i	$-0.511977\pi$
$199$	−211.210	−0.0752374	−0.0376187	+	0.999292i	$0.511977\pi$
$200$	−9597.52	−3.39324
$201$	876.471	0.307570
$202$	6197.20	2.15858
$203$	0	0
$204$	2863.80	0.982872
$205$	9883.85	3.36740
$206$	2986.49	1.01009
$207$	115.753	0.0388668
$208$	2401.75	0.800632
$209$	−3688.14	−1.22064
$210$	0	0
$211$	−4064.93	−1.32626	−0.663130	−	0.748504i	$-0.730773\pi$
$211$	−4064.93	−1.32626	−0.663130	+	0.748504i	$0.730773\pi$
$212$	−5192.97	−1.68233
$213$	−8560.73	−2.75386
$214$	−4751.53	−1.51779
$215$	−4311.47	−1.36763
$216$	−10311.3	−3.24814
$217$	0	0
$218$	−3034.04	−0.942619
$219$	−4820.53	−1.48740
$220$	14629.9	4.48341
$221$	1121.99	0.341508
$222$	15852.5	4.79256
$223$	−3155.99	−0.947717	−0.473859	−	0.880601i	$-0.657139\pi$
$223$	−3155.99	−0.947717	−0.473859	+	0.880601i	$0.657139\pi$
$224$	0	0
$225$	16658.9	4.93596
$226$	−7692.05	−2.26402
$227$	2609.40	0.762959	0.381480	−	0.924377i	$-0.375415\pi$
$227$	2609.40	0.762959	0.381480	+	0.924377i	$0.375415\pi$
$228$	−10784.7	−3.13260
$229$	4684.48	1.35179	0.675893	−	0.737000i	$-0.263758\pi$
$229$	4684.48	1.35179	0.675893	+	0.737000i	$0.263758\pi$
$230$	−188.628	−0.0540773
$231$	0	0
$232$	−9235.02	−2.61340
$233$	−4206.67	−1.18278	−0.591391	−	0.806385i	$-0.701421\pi$
$233$	−4206.67	−1.18278	−0.591391	+	0.806385i	$0.701421\pi$
$234$	−15727.8	−4.39384
$235$	−946.334	−0.262689
$236$	−2780.04	−0.766800
$237$	−9379.81	−2.57082
$238$	0	0
$239$	2731.18	0.739184	0.369592	−	0.929194i	$-0.379497\pi$
$239$	2731.18	0.739184	0.369592	+	0.929194i	$0.379497\pi$
$240$	8164.30	2.19585
$241$	4132.58	1.10458	0.552288	−	0.833653i	$-0.313755\pi$
$241$	4132.58	1.10458	0.552288	+	0.833653i	$0.313755\pi$
$242$	−4706.24	−1.25012
$243$	2987.21	0.788601
$244$	−2500.54	−0.656068
$245$	0	0
$246$	−21940.1	−5.68639
$247$	−4225.27	−1.08845
$248$	964.423	0.246939
$249$	6387.81	1.62575
$250$	−15045.3	−3.80620
$251$	1057.28	0.265876	0.132938	−	0.991124i	$-0.457559\pi$
$251$	1057.28	0.265876	0.132938	+	0.991124i	$0.457559\pi$
$252$	0	0
$253$	93.6414	0.0232695
$254$	3764.49	0.929941
$255$	3814.00	0.936635
$256$	−7469.07	−1.82350
$257$	−4807.90	−1.16696	−0.583479	−	0.812128i	$-0.698309\pi$
$257$	−4807.90	−1.16696	−0.583479	+	0.812128i	$0.698309\pi$
$258$	9570.59	2.30945
$259$	0	0
$260$	16760.6	3.99788
$261$	16029.7	3.80158
$262$	−8147.18	−1.92112
$263$	3635.57	0.852392	0.426196	−	0.904631i	$-0.359853\pi$
$263$	3635.57	0.852392	0.426196	+	0.904631i	$0.359853\pi$
$264$	−15291.0	−3.56475
$265$	−6915.99	−1.60319
$266$	0	0
$267$	−9611.40	−2.20303
$268$	1425.50	0.324910
$269$	−31.6259	−0.00716828	−0.00358414	−	0.999994i	$-0.501141\pi$
$269$	−31.6259	−0.00716828	−0.00358414	+	0.999994i	$0.501141\pi$
$270$	−29165.8	−6.57399
$271$	−3082.61	−0.690979	−0.345490	−	0.938423i	$-0.612287\pi$
$271$	−3082.61	−0.690979	−0.345490	+	0.938423i	$0.612287\pi$
$272$	888.887	0.198150
$273$	0	0
$274$	2829.69	0.623897
$275$	13476.6	2.95515
$276$	273.822	0.0597180
$277$	6276.38	1.36141	0.680706	−	0.732557i	$-0.261673\pi$
$277$	6276.38	1.36141	0.680706	+	0.732557i	$0.261673\pi$
$278$	6300.17	1.35921
$279$	−1673.99	−0.359209
$280$	0	0
$281$	−8364.25	−1.77569	−0.887846	−	0.460141i	$-0.847799\pi$
$281$	−8364.25	−1.77569	−0.887846	+	0.460141i	$0.847799\pi$
$282$	2100.67	0.443592
$283$	−5728.97	−1.20336	−0.601681	−	0.798736i	$-0.705502\pi$
$283$	−5728.97	−1.20336	−0.601681	+	0.798736i	$0.705502\pi$
$284$	−13923.2	−2.90912
$285$	−14363.0	−2.98524
$286$	−12723.4	−2.63059
$287$	0	0
$288$	3806.90	0.778902
$289$	−4497.75	−0.915480
$290$	−26121.4	−5.28932
$291$	8655.91	1.74371
$292$	−7840.13	−1.57126
$293$	−3768.29	−0.751350	−0.375675	−	0.926751i	$-0.622589\pi$
$293$	−3768.29	−0.751350	−0.375675	+	0.926751i	$0.622589\pi$
$294$	0	0
$295$	−3702.45	−0.730728
$296$	12139.6	2.38379
$297$	14478.9	2.82879
$298$	−6099.90	−1.18576
$299$	107.279	0.0207496
$300$	39407.6	7.58400
$301$	0	0
$302$	13122.7	2.50041
$303$	−11981.1	−2.27160
$304$	−3347.43	−0.631541
$305$	−3330.21	−0.625205
$306$	−5820.86	−1.08744
$307$	4701.26	0.873990	0.436995	−	0.899464i	$-0.356043\pi$
$307$	4701.26	0.873990	0.436995	+	0.899464i	$0.356043\pi$
$308$	0	0
$309$	−5773.79	−1.06297
$310$	2727.89	0.499786
$311$	−1346.03	−0.245422	−0.122711	−	0.992442i	$-0.539159\pi$
$311$	−1346.03	−0.245422	−0.122711	+	0.992442i	$0.539159\pi$
$312$	−17517.9	−3.17871
$313$	2797.18	0.505131	0.252565	−	0.967580i	$-0.418726\pi$
$313$	2797.18	0.505131	0.252565	+	0.967580i	$0.418726\pi$
$314$	61.4133	0.0110374
$315$	0	0
$316$	−15255.4	−2.71576
$317$	−338.438	−0.0599640	−0.0299820	−	0.999550i	$-0.509545\pi$
$317$	−338.438	−0.0599640	−0.0299820	+	0.999550i	$0.509545\pi$
$318$	15352.1	2.70724
$319$	12967.6	2.27600
$320$	−13229.9	−2.31118
$321$	9186.15	1.59726
$322$	0	0
$323$	−1563.77	−0.269383
$324$	18087.8	3.10148
$325$	15439.3	2.63513
$326$	11557.8	1.96358
$327$	5865.72	0.991973
$328$	−16801.4	−2.82837
$329$	0	0
$330$	−43250.8	−7.21477
$331$	−7476.00	−1.24145	−0.620723	−	0.784030i	$-0.713161\pi$
$331$	−7476.00	−1.24145	−0.620723	+	0.784030i	$0.713161\pi$
$332$	10389.2	1.71741
$333$	−21071.3	−3.46757
$334$	15493.1	2.53816
$335$	1898.47	0.309626
$336$	0	0
$337$	3860.73	0.624058	0.312029	−	0.950073i	$-0.398991\pi$
$337$	3860.73	0.624058	0.312029	+	0.950073i	$0.398991\pi$
$338$	−4012.84	−0.645769
$339$	14871.1	2.38255
$340$	6203.10	0.989443
$341$	−1354.21	−0.215058
$342$	21920.6	3.46588
$343$	0	0
$344$	7329.03	1.14871
$345$	364.676	0.0569087
$346$	12601.8	1.95802
$347$	−1852.24	−0.286552	−0.143276	−	0.989683i	$-0.545764\pi$
$347$	−1852.24	−0.286552	−0.143276	+	0.989683i	$0.545764\pi$
$348$	37919.2	5.84104
$349$	−11548.8	−1.77133	−0.885665	−	0.464325i	$-0.846297\pi$
$349$	−11548.8	−1.77133	−0.885665	+	0.464325i	$0.846297\pi$
$350$	0	0
$351$	16587.6	2.52245
$352$	3079.68	0.466328
$353$	−3619.47	−0.545736	−0.272868	−	0.962051i	$-0.587972\pi$
$353$	−3619.47	−0.545736	−0.272868	+	0.962051i	$0.587972\pi$
$354$	8218.67	1.23395
$355$	−18542.9	−2.77227
$356$	−15632.0	−2.32723
$357$	0	0
$358$	−19210.9	−2.83611
$359$	−19.6361	−0.00288678	−0.00144339	−	0.999999i	$-0.500459\pi$
$359$	−19.6361	−0.00288678	−0.00144339	+	0.999999i	$0.500459\pi$
$360$	−40941.9	−5.99396
$361$	−970.033	−0.141425
$362$	9481.66	1.37664
$363$	9098.60	1.31557
$364$	0	0
$365$	−10441.5	−1.49735
$366$	7392.39	1.05576
$367$	−4558.82	−0.648415	−0.324208	−	0.945986i	$-0.605098\pi$
$367$	−4558.82	−0.648415	−0.324208	+	0.945986i	$0.605098\pi$
$368$	84.9910	0.0120393
$369$	29163.1	4.11428
$370$	34337.1	4.82460
$371$	0	0
$372$	−3959.94	−0.551917
$373$	6345.65	0.880872	0.440436	−	0.897784i	$-0.354824\pi$
$373$	6345.65	0.880872	0.440436	+	0.897784i	$0.354824\pi$
$374$	−4708.92	−0.651049
$375$	29087.2	4.00549
$376$	1608.66	0.220640
$377$	14856.1	2.02952
$378$	0	0
$379$	8831.30	1.19692	0.598461	−	0.801152i	$-0.295779\pi$
$379$	8831.30	1.19692	0.598461	+	0.801152i	$0.295779\pi$
$380$	−23360.1	−3.15355
$381$	−7277.90	−0.978631
$382$	12413.7	1.66267
$383$	−1935.07	−0.258166	−0.129083	−	0.991634i	$-0.541203\pi$
$383$	−1935.07	−0.258166	−0.129083	+	0.991634i	$0.541203\pi$
$384$	24602.5	3.26951
$385$	0	0
$386$	−3761.98	−0.496061
$387$	−12721.3	−1.67096
$388$	14078.0	1.84202
$389$	−10221.2	−1.33223	−0.666114	−	0.745850i	$-0.732044\pi$
$389$	−10221.2	−1.33223	−0.666114	+	0.745850i	$0.732044\pi$
$390$	−49549.7	−6.43346
$391$	39.7040	0.00513534
$392$	0	0
$393$	15751.0	2.02171
$394$	−20775.4	−2.65648
$395$	−20317.0	−2.58800
$396$	43166.7	5.47780
$397$	1576.02	0.199240	0.0996201	−	0.995026i	$-0.468237\pi$
$397$	1576.02	0.199240	0.0996201	+	0.995026i	$0.468237\pi$
$398$	1015.53	0.127899
$399$	0	0
$400$	12231.6	1.52895
$401$	−3546.43	−0.441647	−0.220823	−	0.975314i	$-0.570874\pi$
$401$	−3546.43	−0.441647	−0.220823	+	0.975314i	$0.570874\pi$
$402$	−4214.22	−0.522851
$403$	−1551.44	−0.191769
$404$	−19486.1	−2.39967
$405$	24089.3	2.95558
$406$	0	0
$407$	−17046.1	−2.07603
$408$	−6483.38	−0.786703
$409$	8237.98	0.995946	0.497973	−	0.867193i	$-0.334078\pi$
$409$	8237.98	0.995946	0.497973	+	0.867193i	$0.334078\pi$
$410$	−47523.2	−5.72440
$411$	−5470.65	−0.656563
$412$	−9390.50	−1.12291
$413$	0	0
$414$	−556.562	−0.0660714
$415$	13836.3	1.63661
$416$	3528.20	0.415827
$417$	−12180.2	−1.43037
$418$	17733.2	2.07502
$419$	−6331.56	−0.738226	−0.369113	−	0.929385i	$-0.620338\pi$
$419$	−6331.56	−0.738226	−0.369113	+	0.929385i	$0.620338\pi$
$420$	0	0
$421$	−11065.5	−1.28100	−0.640498	−	0.767960i	$-0.721272\pi$
$421$	−11065.5	−1.28100	−0.640498	+	0.767960i	$0.721272\pi$
$422$	19544.9	2.25457
$423$	−2792.23	−0.320953
$424$	11756.4	1.34656
$425$	5714.07	0.652173
$426$	41161.4	4.68140
$427$	0	0
$428$	14940.4	1.68732
$429$	24598.2	2.76832
$430$	20730.3	2.32489
$431$	10331.0	1.15459	0.577295	−	0.816535i	$-0.304108\pi$
$431$	10331.0	1.15459	0.577295	+	0.816535i	$0.304108\pi$
$432$	13141.4	1.46358
$433$	9743.31	1.08137	0.540685	−	0.841225i	$-0.318165\pi$
$433$	9743.31	1.08137	0.540685	+	0.841225i	$0.318165\pi$
$434$	0	0
$435$	50500.7	5.56626
$436$	9540.03	1.04790
$437$	−149.520	−0.0163673
$438$	23177.9	2.52850
$439$	15102.0	1.64187	0.820935	−	0.571022i	$-0.193453\pi$
$439$	15102.0	1.64187	0.820935	+	0.571022i	$0.193453\pi$
$440$	−33120.8	−3.58858
$441$	0	0
$442$	−5394.72	−0.580545
$443$	−1073.69	−0.115153	−0.0575764	−	0.998341i	$-0.518337\pi$
$443$	−1073.69	−0.115153	−0.0575764	+	0.998341i	$0.518337\pi$
$444$	−49845.5	−5.32784
$445$	−20818.7	−2.21775
$446$	15174.6	1.61107
$447$	11793.0	1.24785
$448$	0	0
$449$	13378.8	1.40620	0.703100	−	0.711091i	$-0.251799\pi$
$449$	13378.8	1.40620	0.703100	+	0.711091i	$0.251799\pi$
$450$	−80098.6	−8.39086
$451$	23592.1	2.46321
$452$	24186.4	2.51688
$453$	−25370.1	−2.63133
$454$	−12546.4	−1.29699
$455$	0	0
$456$	24415.6	2.50738
$457$	−668.635	−0.0684407	−0.0342204	−	0.999414i	$-0.510895\pi$
$457$	−668.635	−0.0684407	−0.0342204	+	0.999414i	$0.510895\pi$
$458$	−22523.8	−2.29796
$459$	6139.07	0.624286
$460$	593.110	0.0601172
$461$	10259.5	1.03651	0.518255	−	0.855226i	$-0.326582\pi$
$461$	10259.5	1.03651	0.518255	+	0.855226i	$0.326582\pi$
$462$	0	0
$463$	−12104.7	−1.21502	−0.607510	−	0.794312i	$-0.707831\pi$
$463$	−12104.7	−1.21502	−0.607510	+	0.794312i	$0.707831\pi$
$464$	11769.6	1.17757
$465$	−5273.84	−0.525954
$466$	20226.4	2.01066
$467$	−587.995	−0.0582637	−0.0291319	−	0.999576i	$-0.509274\pi$
$467$	−587.995	−0.0582637	−0.0291319	+	0.999576i	$0.509274\pi$
$468$	49453.5	4.88459
$469$	0	0
$470$	4550.13	0.446557
$471$	−118.731	−0.0116153
$472$	6293.75	0.613757
$473$	−10291.2	−1.00040
$474$	45099.7	4.37025
$475$	−21518.5	−2.07860
$476$	0	0
$477$	−20406.2	−1.95877
$478$	−13132.0	−1.25657
$479$	−14932.5	−1.42439	−0.712195	−	0.701982i	$-0.752299\pi$
$479$	−14932.5	−1.42439	−0.712195	+	0.701982i	$0.752299\pi$
$480$	11993.5	1.14047
$481$	−19528.7	−1.85121
$482$	−19870.1	−1.87772
$483$	0	0
$484$	14798.0	1.38974
$485$	18749.1	1.75536
$486$	−14363.0	−1.34058
$487$	−13078.7	−1.21695	−0.608474	−	0.793574i	$-0.708218\pi$
$487$	−13078.7	−1.21695	−0.608474	+	0.793574i	$0.708218\pi$
$488$	5660.99	0.525125
$489$	−22344.7	−2.06638
$490$	0	0
$491$	19436.0	1.78642	0.893211	−	0.449638i	$-0.148447\pi$
$491$	19436.0	1.78642	0.893211	+	0.449638i	$0.148447\pi$
$492$	68987.1	6.32150
$493$	5498.25	0.502290
$494$	20315.8	1.85031
$495$	57489.4	5.22011
$496$	−1229.12	−0.111268
$497$	0	0
$498$	−30713.7	−2.76368
$499$	−12758.3	−1.14457	−0.572284	−	0.820055i	$-0.693943\pi$
$499$	−12758.3	−1.14457	−0.572284	+	0.820055i	$0.693943\pi$
$500$	47307.6	4.23132
$501$	−29952.9	−2.67105
$502$	−5083.58	−0.451975
$503$	−14229.8	−1.26138	−0.630691	−	0.776034i	$-0.717228\pi$
$503$	−14229.8	−1.26138	−0.630691	+	0.776034i	$0.717228\pi$
$504$	0	0
$505$	−25951.5	−2.28679
$506$	−450.243	−0.0395568
$507$	7758.05	0.679580
$508$	−11836.8	−1.03381
$509$	−489.016	−0.0425840	−0.0212920	−	0.999773i	$-0.506778\pi$
$509$	−489.016	−0.0425840	−0.0212920	+	0.999773i	$0.506778\pi$
$510$	−18338.4	−1.59223
$511$	0	0
$512$	14739.2	1.27224
$513$	−23118.9	−1.98972
$514$	23117.2	1.98376
$515$	−12506.3	−1.07008
$516$	−30093.1	−2.56740
$517$	−2258.84	−0.192154
$518$	0	0
$519$	−24363.1	−2.06054
$520$	−37944.5	−3.19996
$521$	4734.80	0.398148	0.199074	−	0.979984i	$-0.436207\pi$
$521$	4734.80	0.398148	0.199074	+	0.979984i	$0.436207\pi$
$522$	−77073.3	−6.46247
$523$	7706.19	0.644299	0.322149	−	0.946689i	$-0.395595\pi$
$523$	7706.19	0.644299	0.322149	+	0.946689i	$0.395595\pi$
$524$	25617.4	2.13569
$525$	0	0
$526$	−17480.5	−1.44902
$527$	−574.188	−0.0474612
$528$	19487.7	1.60623
$529$	−12163.2	−0.999688
$530$	33253.2	2.72534
$531$	−10924.4	−0.892800
$532$	0	0
$533$	27028.0	2.19646
$534$	46213.2	3.74502
$535$	19897.6	1.60794
$536$	−3227.19	−0.260062
$537$	37140.5	2.98460
$538$	152.063	0.0121857
$539$	0	0
$540$	91707.1	7.30824
$541$	17907.2	1.42309	0.711545	−	0.702641i	$-0.247996\pi$
$541$	17907.2	1.42309	0.711545	+	0.702641i	$0.247996\pi$
$542$	14821.7	1.17463
$543$	−18330.9	−1.44872
$544$	1305.79	0.102914
$545$	12705.4	0.998604
$546$	0	0
$547$	−4769.44	−0.372809	−0.186404	−	0.982473i	$-0.559683\pi$
$547$	−4769.44	−0.372809	−0.186404	+	0.982473i	$0.559683\pi$
$548$	−8897.48	−0.693580
$549$	−9826.05	−0.763872
$550$	−64797.6	−5.02360
$551$	−20705.7	−1.60089
$552$	−619.908	−0.0477990
$553$	0	0
$554$	−30177.9	−2.31433
$555$	−66384.1	−5.07721
$556$	−19809.8	−1.51102
$557$	13747.5	1.04578	0.522891	−	0.852400i	$-0.324854\pi$
$557$	13747.5	1.04578	0.522891	+	0.852400i	$0.324854\pi$
$558$	8048.84	0.610636
$559$	−11790.0	−0.892065
$560$	0	0
$561$	9103.77	0.685137
$562$	40216.7	3.01858
$563$	1450.75	0.108600	0.0543000	−	0.998525i	$-0.482707\pi$
$563$	1450.75	0.108600	0.0543000	+	0.998525i	$0.482707\pi$
$564$	−6605.20	−0.493137
$565$	32211.4	2.39848
$566$	27545.8	2.04565
$567$	0	0
$568$	31520.9	2.32850
$569$	−5774.95	−0.425481	−0.212740	−	0.977109i	$-0.568239\pi$
$569$	−5774.95	−0.425481	−0.212740	+	0.977109i	$0.568239\pi$
$570$	69059.9	5.07474
$571$	14762.9	1.08198	0.540989	−	0.841030i	$-0.318050\pi$
$571$	14762.9	1.08198	0.540989	+	0.841030i	$0.318050\pi$
$572$	40006.5	2.92440
$573$	−23999.5	−1.74972
$574$	0	0
$575$	546.351	0.0396251
$576$	−39036.0	−2.82378
$577$	6895.06	0.497479	0.248739	−	0.968570i	$-0.419984\pi$
$577$	6895.06	0.497479	0.248739	+	0.968570i	$0.419984\pi$
$578$	21625.9	1.55626
$579$	7273.05	0.522034
$580$	82134.5	5.88008
$581$	0	0
$582$	−41619.1	−2.96420
$583$	−16508.0	−1.17271
$584$	17749.3	1.25766
$585$	65862.1	4.65481
$586$	18118.6	1.27725
$587$	8776.02	0.617079	0.308539	−	0.951212i	$-0.400160\pi$
$587$	8776.02	0.617079	0.308539	+	0.951212i	$0.400160\pi$
$588$	0	0
$589$	2162.32	0.151268
$590$	17802.0	1.24220
$591$	40165.3	2.79556
$592$	−15471.4	−1.07411
$593$	9647.87	0.668112	0.334056	−	0.942553i	$-0.391583\pi$
$593$	9647.87	0.668112	0.334056	+	0.942553i	$0.391583\pi$
$594$	−69617.0	−4.80879
$595$	0	0
$596$	19180.1	1.31820
$597$	−1963.33	−0.134596
$598$	−515.816	−0.0352731
$599$	14436.4	0.984731	0.492366	−	0.870388i	$-0.336132\pi$
$599$	14436.4	0.984731	0.492366	+	0.870388i	$0.336132\pi$
$600$	−89215.2	−6.07033
$601$	−7186.82	−0.487781	−0.243891	−	0.969803i	$-0.578424\pi$
$601$	−7186.82	−0.487781	−0.243891	+	0.969803i	$0.578424\pi$
$602$	0	0
$603$	5601.59	0.378299
$604$	−41262.1	−2.77969
$605$	19707.9	1.32437
$606$	57607.0	3.86159
$607$	16058.0	1.07376	0.536880	−	0.843658i	$-0.319603\pi$
$607$	16058.0	1.07376	0.536880	+	0.843658i	$0.319603\pi$
$608$	−4917.42	−0.328006
$609$	0	0
$610$	16012.2	1.06281
$611$	−2587.81	−0.171345
$612$	18302.7	1.20890
$613$	21912.8	1.44380	0.721900	−	0.691997i	$-0.243269\pi$
$613$	21912.8	1.44380	0.721900	+	0.691997i	$0.243269\pi$
$614$	−22604.4	−1.48573
$615$	91876.8	6.02412
$616$	0	0
$617$	10754.2	0.701699	0.350849	−	0.936432i	$-0.385893\pi$
$617$	10754.2	0.701699	0.350849	+	0.936432i	$0.385893\pi$
$618$	27761.3	1.80700
$619$	−22172.4	−1.43971	−0.719857	−	0.694122i	$-0.755793\pi$
$619$	−22172.4	−1.43971	−0.719857	+	0.694122i	$0.755793\pi$
$620$	−8577.39	−0.555607
$621$	586.987	0.0379307
$622$	6471.92	0.417203
$623$	0	0
$624$	22325.8	1.43229
$625$	27953.0	1.78899
$626$	−13449.3	−0.858694
$627$	−34283.6	−2.18366
$628$	−193.104	−0.0122702
$629$	−7227.56	−0.458158
$630$	0	0
$631$	30866.5	1.94735	0.973673	−	0.227947i	$-0.0732014\pi$
$631$	30866.5	1.94735	0.973673	+	0.227947i	$0.0732014\pi$
$632$	34536.7	2.17373
$633$	−37786.2	−2.37261
$634$	1627.27	0.101935
$635$	−15764.2	−0.985173
$636$	−48272.0	−3.00961
$637$	0	0
$638$	−62350.2	−3.86907
$639$	−54712.3	−3.38714
$640$	53290.0	3.29137
$641$	14422.7	0.888709	0.444354	−	0.895851i	$-0.353433\pi$
$641$	14422.7	0.888709	0.444354	+	0.895851i	$0.353433\pi$
$642$	−44168.6	−2.71526
$643$	−515.480	−0.0316152	−0.0158076	−	0.999875i	$-0.505032\pi$
$643$	−515.480	−0.0316152	−0.0158076	+	0.999875i	$0.505032\pi$
$644$	0	0
$645$	−40078.0	−2.44662
$646$	7518.88	0.457936
$647$	3307.41	0.200970	0.100485	−	0.994939i	$-0.467961\pi$
$647$	3307.41	0.200970	0.100485	+	0.994939i	$0.467961\pi$
$648$	−40949.2	−2.48246
$649$	−8837.50	−0.534518
$650$	−74234.6	−4.47957
$651$	0	0
$652$	−36341.5	−2.18289
$653$	7194.89	0.431176	0.215588	−	0.976484i	$-0.430833\pi$
$653$	7194.89	0.431176	0.215588	+	0.976484i	$0.430833\pi$
$654$	−28203.4	−1.68630
$655$	34117.3	2.03522
$656$	21412.7	1.27443
$657$	−30808.4	−1.82945
$658$	0	0
$659$	−13715.7	−0.810753	−0.405376	−	0.914150i	$-0.632860\pi$
$659$	−13715.7	−0.810753	−0.405376	+	0.914150i	$0.632860\pi$
$660$	135995.	8.02059
$661$	8291.50	0.487900	0.243950	−	0.969788i	$-0.421557\pi$
$661$	8291.50	0.487900	0.243950	+	0.969788i	$0.421557\pi$
$662$	35945.9	2.11039
$663$	10429.6	0.610941
$664$	−23520.1	−1.37463
$665$	0	0
$666$	101314.	5.89467
$667$	525.716	0.0305184
$668$	−48715.5	−2.82165
$669$	−29337.0	−1.69542
$670$	−9128.17	−0.526346
$671$	−7949.01	−0.457329
$672$	0	0
$673$	6689.50	0.383152	0.191576	−	0.981478i	$-0.438640\pi$
$673$	6689.50	0.383152	0.191576	+	0.981478i	$0.438640\pi$
$674$	−18563.1	−1.06086
$675$	84477.3	4.81709
$676$	12617.7	0.717895
$677$	23755.6	1.34860	0.674300	−	0.738458i	$-0.264446\pi$
$677$	23755.6	1.34860	0.674300	+	0.738458i	$0.264446\pi$
$678$	−71502.6	−4.05021
$679$	0	0
$680$	−14043.3	−0.791962
$681$	24256.0	1.36490
$682$	6511.29	0.365587
$683$	27233.9	1.52573	0.762867	−	0.646556i	$-0.223791\pi$
$683$	27233.9	1.52573	0.762867	+	0.646556i	$0.223791\pi$
$684$	−68925.7	−3.85299
$685$	−11849.7	−0.660952
$686$	0	0
$687$	43545.3	2.41828
$688$	−9340.53	−0.517594
$689$	−18912.2	−1.04572
$690$	−1753.42	−0.0967415
$691$	9072.45	0.499468	0.249734	−	0.968314i	$-0.419657\pi$
$691$	9072.45	0.499468	0.249734	+	0.968314i	$0.419657\pi$
$692$	−39624.2	−2.17671
$693$	0	0
$694$	8905.90	0.487123
$695$	−26382.7	−1.43993
$696$	−85845.6	−4.67524
$697$	10003.1	0.543606
$698$	55528.7	3.01116
$699$	−39103.8	−2.11594
$700$	0	0
$701$	12766.6	0.687855	0.343927	−	0.938996i	$-0.388243\pi$
$701$	12766.6	0.687855	0.343927	+	0.938996i	$0.388243\pi$
$702$	−79755.9	−4.28803
$703$	27218.1	1.46024
$704$	−31579.0	−1.69060
$705$	−8796.80	−0.469938
$706$	17403.0	0.927721
$707$	0	0
$708$	−25842.3	−1.37177
$709$	23443.7	1.24181	0.620907	−	0.783884i	$-0.286765\pi$
$709$	23443.7	1.24181	0.620907	+	0.783884i	$0.286765\pi$
$710$	89157.4	4.71270
$711$	−59947.0	−3.16201
$712$	35389.4	1.86275
$713$	−54.9010	−0.00288367
$714$	0	0
$715$	53280.6	2.78683
$716$	60405.4	3.15287
$717$	25388.1	1.32236
$718$	94.4139	0.00490737
$719$	−6016.16	−0.312051	−0.156026	−	0.987753i	$-0.549868\pi$
$719$	−6016.16	−0.312051	−0.156026	+	0.987753i	$0.549868\pi$
$720$	52178.7	2.70081
$721$	0	0
$722$	4664.08	0.240414
$723$	38415.0	1.97603
$724$	−29813.5	−1.53040
$725$	75659.3	3.87575
$726$	−43747.6	−2.23640
$727$	−12346.1	−0.629837	−0.314919	−	0.949119i	$-0.601977\pi$
$727$	−12346.1	−0.629837	−0.314919	+	0.949119i	$0.601977\pi$
$728$	0	0
$729$	−4534.80	−0.230392
$730$	50204.3	2.54540
$731$	−4363.48	−0.220779
$732$	−23244.1	−1.17367
$733$	−8283.56	−0.417408	−0.208704	−	0.977979i	$-0.566925\pi$
$733$	−8283.56	−0.417408	−0.208704	+	0.977979i	$0.566925\pi$
$734$	21919.6	1.10227
$735$	0	0
$736$	124.853	0.00625290
$737$	4531.53	0.226487
$738$	−140221.	−6.99404
$739$	22716.7	1.13078	0.565392	−	0.824823i	$-0.308725\pi$
$739$	22716.7	1.13078	0.565392	+	0.824823i	$0.308725\pi$
$740$	−107967.	−5.36346
$741$	−39276.7	−1.94719
$742$	0	0
$743$	−9746.52	−0.481245	−0.240623	−	0.970619i	$-0.577352\pi$
$743$	−9746.52	−0.481245	−0.240623	+	0.970619i	$0.577352\pi$
$744$	8964.94	0.441762
$745$	25544.0	1.25619
$746$	−30511.0	−1.49743
$747$	40825.0	1.99961
$748$	14806.4	0.723765
$749$	0	0
$750$	−139856.	−6.80911
$751$	24670.1	1.19870	0.599351	−	0.800486i	$-0.295425\pi$
$751$	24670.1	1.19870	0.599351	+	0.800486i	$0.295425\pi$
$752$	−2050.17	−0.0994177
$753$	9828.12	0.475639
$754$	−71430.8	−3.45007
$755$	−54952.7	−2.64892
$756$	0	0
$757$	36509.2	1.75290	0.876452	−	0.481490i	$-0.159904\pi$
$757$	36509.2	1.75290	0.876452	+	0.481490i	$0.159904\pi$
$758$	−42462.4	−2.03470
$759$	870.458	0.0416280
$760$	52885.1	2.52414
$761$	11491.0	0.547369	0.273684	−	0.961820i	$-0.411758\pi$
$761$	11491.0	0.547369	0.273684	+	0.961820i	$0.411758\pi$
$762$	34993.4	1.66362
$763$	0	0
$764$	−39032.8	−1.84837
$765$	24375.6	1.15203
$766$	9304.14	0.438867
$767$	−10124.6	−0.476633
$768$	−69429.9	−3.26215
$769$	−6136.32	−0.287752	−0.143876	−	0.989596i	$-0.545957\pi$
$769$	−6136.32	−0.287752	−0.143876	+	0.989596i	$0.545957\pi$
$770$	0	0
$771$	−44692.6	−2.08763
$772$	11828.9	0.551466
$773$	−2191.91	−0.101989	−0.0509944	−	0.998699i	$-0.516239\pi$
$773$	−2191.91	−0.101989	−0.0509944	+	0.998699i	$0.516239\pi$
$774$	61166.3	2.84054
$775$	−7901.18	−0.366218
$776$	−31871.3	−1.47437
$777$	0	0
$778$	49145.4	2.26472
$779$	−37670.3	−1.73258
$780$	155801.	7.15201
$781$	−44260.7	−2.02788
$782$	−190.904	−0.00872979
$783$	81286.6	3.71002
$784$	0	0
$785$	−257.175	−0.0116930
$786$	−75733.4	−3.43679
$787$	−24920.8	−1.12876	−0.564378	−	0.825516i	$-0.690884\pi$
$787$	−24920.8	−1.12876	−0.564378	+	0.825516i	$0.690884\pi$
$788$	65324.9	2.95318
$789$	33795.0	1.52489
$790$	97687.8	4.39946
$791$	0	0
$792$	−97725.6	−4.38450
$793$	−9106.69	−0.407803
$794$	−7577.79	−0.338697
$795$	−64288.6	−2.86803
$796$	−3193.17	−0.142184
$797$	−41502.4	−1.84453	−0.922265	−	0.386558i	$-0.873664\pi$
$797$	−41502.4	−1.84453	−0.922265	+	0.386558i	$0.873664\pi$
$798$	0	0
$799$	−957.750	−0.0424064
$800$	17968.4	0.794099
$801$	−61427.1	−2.70964
$802$	17051.8	0.750775
$803$	−24923.1	−1.09529
$804$	13250.9	0.581248
$805$	0	0
$806$	7459.59	0.325996
$807$	−293.984	−0.0128237
$808$	44114.7	1.92073
$809$	−14638.1	−0.636152	−0.318076	−	0.948065i	$-0.603037\pi$
$809$	−14638.1	−0.636152	−0.318076	+	0.948065i	$0.603037\pi$
$810$	−115826.	−5.02431
$811$	33346.2	1.44383	0.721913	−	0.691984i	$-0.243263\pi$
$811$	33346.2	1.44383	0.721913	+	0.691984i	$0.243263\pi$
$812$	0	0
$813$	−28654.9	−1.23613
$814$	81960.5	3.52913
$815$	−48399.5	−2.08020
$816$	8262.79	0.354480
$817$	16432.3	0.703664
$818$	−39609.6	−1.69305
$819$	0	0
$820$	149429.	6.36376
$821$	−11868.3	−0.504514	−0.252257	−	0.967660i	$-0.581173\pi$
$821$	−11868.3	−0.504514	−0.252257	+	0.967660i	$0.581173\pi$
$822$	26303.8	1.11612
$823$	−12383.5	−0.524497	−0.262249	−	0.965000i	$-0.584464\pi$
$823$	−12383.5	−0.524497	−0.262249	+	0.965000i	$0.584464\pi$
$824$	21259.2	0.898788
$825$	125273.	5.28662
$826$	0	0
$827$	−18602.4	−0.782187	−0.391094	−	0.920351i	$-0.627903\pi$
$827$	−18602.4	−0.782187	−0.391094	+	0.920351i	$0.627903\pi$
$828$	1750.02	0.0734508
$829$	11288.3	0.472930	0.236465	−	0.971640i	$-0.424011\pi$
$829$	11288.3	0.472930	0.236465	+	0.971640i	$0.424011\pi$
$830$	−66527.1	−2.78215
$831$	58343.1	2.43550
$832$	−36178.2	−1.50752
$833$	0	0
$834$	58564.2	2.43155
$835$	−64879.2	−2.68891
$836$	−55759.0	−2.30678
$837$	−8488.84	−0.350558
$838$	30443.2	1.25494
$839$	26459.5	1.08878	0.544388	−	0.838833i	$-0.316762\pi$
$839$	26459.5	1.08878	0.544388	+	0.838833i	$0.316762\pi$
$840$	0	0
$841$	48412.7	1.98502
$842$	53204.8	2.17762
$843$	−77751.2	−3.17662
$844$	−61455.5	−2.50638
$845$	16804.3	0.684123
$846$	13425.5	0.545602
$847$	0	0
$848$	−14983.0	−0.606745
$849$	−53254.5	−2.15276
$850$	−27474.2	−1.10866
$851$	−691.063	−0.0278371
$852$	−129425.	−5.20427
$853$	13195.8	0.529679	0.264840	−	0.964292i	$-0.414681\pi$
$853$	13195.8	0.529679	0.264840	+	0.964292i	$0.414681\pi$
$854$	0	0
$855$	−91795.2	−3.67173
$856$	−33823.7	−1.35055
$857$	25336.6	1.00990	0.504949	−	0.863149i	$-0.331511\pi$
$857$	25336.6	1.00990	0.504949	+	0.863149i	$0.331511\pi$
$858$	−118272.	−4.70599
$859$	−19607.7	−0.778818	−0.389409	−	0.921065i	$-0.627321\pi$
$859$	−19607.7	−0.778818	−0.389409	+	0.921065i	$0.627321\pi$
$860$	−65182.9	−2.58456
$861$	0	0
$862$	−49673.4	−1.96274
$863$	−18443.5	−0.727490	−0.363745	−	0.931499i	$-0.618502\pi$
$863$	−18443.5	−0.727490	−0.363745	+	0.931499i	$0.618502\pi$
$864$	19304.8	0.760143
$865$	−52771.4	−2.07432
$866$	−46847.5	−1.83827
$867$	−41809.5	−1.63775
$868$	0	0
$869$	−48495.5	−1.89309
$870$	−242816.	−9.46233
$871$	5191.50	0.201960
$872$	−21597.8	−0.838753
$873$	55320.6	2.14469
$874$	718.918	0.0278235
$875$	0	0
$876$	−72879.1	−2.81091
$877$	34485.8	1.32782	0.663912	−	0.747811i	$-0.268895\pi$
$877$	34485.8	1.32782	0.663912	+	0.747811i	$0.268895\pi$
$878$	−72613.1	−2.79109
$879$	−35028.7	−1.34413
$880$	42211.1	1.61697
$881$	−14977.5	−0.572766	−0.286383	−	0.958115i	$-0.592453\pi$
$881$	−14977.5	−0.572766	−0.286383	+	0.958115i	$0.592453\pi$
$882$	0	0
$883$	−18200.0	−0.693634	−0.346817	−	0.937933i	$-0.612737\pi$
$883$	−18200.0	−0.693634	−0.346817	+	0.937933i	$0.612737\pi$
$884$	16962.8	0.645385
$885$	−34416.7	−1.30724
$886$	5162.49	0.195753
$887$	−35272.0	−1.33519	−0.667597	−	0.744523i	$-0.732677\pi$
$887$	−35272.0	−1.33519	−0.667597	+	0.744523i	$0.732677\pi$
$888$	112846.	4.26447
$889$	0	0
$890$	100100.	3.77006
$891$	57499.7	2.16197
$892$	−47713.8	−1.79101
$893$	3606.76	0.135158
$894$	−56702.5	−2.12127
$895$	80447.8	3.00455
$896$	0	0
$897$	997.230	0.0371199
$898$	−64327.5	−2.39046
$899$	−7602.75	−0.282053
$900$	251857.	9.32803
$901$	−6999.41	−0.258806
$902$	−113435.	−4.18733
$903$	0	0
$904$	−54755.7	−2.01455
$905$	−39705.5	−1.45841
$906$	121984.	4.47312
$907$	27752.9	1.01601	0.508005	−	0.861354i	$-0.330383\pi$
$907$	27752.9	1.01601	0.508005	+	0.861354i	$0.330383\pi$
$908$	39450.1	1.44185
$909$	−76571.9	−2.79398
$910$	0	0
$911$	19444.1	0.707149	0.353575	−	0.935406i	$-0.384966\pi$
$911$	19444.1	0.707149	0.353575	+	0.935406i	$0.384966\pi$
$912$	−31116.6	−1.12980
$913$	33026.3	1.19716
$914$	3214.91	0.116345
$915$	−30956.5	−1.11846
$916$	70822.2	2.55462
$917$	0	0
$918$	−29517.7	−1.06125
$919$	7281.42	0.261362	0.130681	−	0.991424i	$-0.458284\pi$
$919$	7281.42	0.261362	0.130681	+	0.991424i	$0.458284\pi$
$920$	−1342.75	−0.0481185
$921$	43701.2	1.56352
$922$	−49329.3	−1.76201
$923$	−50706.8	−1.80827
$924$	0	0
$925$	−99455.6	−3.53522
$926$	58201.5	2.06547
$927$	−36900.7	−1.30742
$928$	17289.7	0.611599
$929$	−10325.8	−0.364670	−0.182335	−	0.983237i	$-0.558365\pi$
$929$	−10325.8	−0.364670	−0.182335	+	0.983237i	$0.558365\pi$
$930$	25357.5	0.894092
$931$	0	0
$932$	−63598.5	−2.23523
$933$	−12512.2	−0.439047
$934$	2827.18	0.0990451
$935$	19719.1	0.689717
$936$	−111958.	−3.90969
$937$	−14489.6	−0.505181	−0.252591	−	0.967573i	$-0.581283\pi$
$937$	−14489.6	−0.505181	−0.252591	+	0.967573i	$0.581283\pi$
$938$	0	0
$939$	26001.6	0.903654
$940$	−14307.1	−0.496433
$941$	−12228.1	−0.423620	−0.211810	−	0.977311i	$-0.567936\pi$
$941$	−12228.1	−0.423620	−0.211810	+	0.977311i	$0.567936\pi$
$942$	570.877	0.0197454
$943$	956.445	0.0330288
$944$	−8021.11	−0.276552
$945$	0	0
$946$	49481.9	1.70063
$947$	−18903.2	−0.648649	−0.324325	−	0.945946i	$-0.605137\pi$
$947$	−18903.2	−0.648649	−0.324325	+	0.945946i	$0.605137\pi$
$948$	−141808.	−4.85836
$949$	−28552.9	−0.976676
$950$	103464.	3.53350
$951$	−3146.01	−0.107273
$952$	0	0
$953$	10677.8	0.362946	0.181473	−	0.983396i	$-0.441914\pi$
$953$	10677.8	0.362946	0.181473	+	0.983396i	$0.441914\pi$
$954$	98116.2	3.32980
$955$	−51983.8	−1.76142
$956$	41291.2	1.39692
$957$	120542.	4.07165
$958$	71797.9	2.42138
$959$	0	0
$960$	−122981.	−4.13458
$961$	−28997.0	−0.973349
$962$	93897.2	3.14695
$963$	58709.4	1.96457
$964$	62478.4	2.08744
$965$	15753.7	0.525524
$966$	0	0
$967$	20608.0	0.685323	0.342662	−	0.939459i	$-0.388672\pi$
$967$	20608.0	0.685323	0.342662	+	0.939459i	$0.388672\pi$
$968$	−33501.3	−1.11237
$969$	−14536.3	−0.481912
$970$	−90148.6	−2.98402
$971$	31888.8	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$971$	31888.8	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$972$	45162.2	1.49031
$973$	0	0
$974$	62884.7	2.06874
$975$	143518.	4.71411
$976$	−7214.70	−0.236616
$977$	−41985.1	−1.37485	−0.687423	−	0.726258i	$-0.741258\pi$
$977$	−41985.1	−1.37485	−0.687423	+	0.726258i	$0.741258\pi$
$978$	107437.	3.51274
$979$	−49692.8	−1.62226
$980$	0	0
$981$	37488.2	1.22009
$982$	−93451.4	−3.03682
$983$	10162.5	0.329740	0.164870	−	0.986315i	$-0.447279\pi$
$983$	10162.5	0.329740	0.164870	+	0.986315i	$0.447279\pi$
$984$	−156180.	−5.05981
$985$	86999.6	2.81425
$986$	−26436.5	−0.853865
$987$	0	0
$988$	−63879.7	−2.05697
$989$	−417.215	−0.0134142
$990$	−276419.	−8.87390
$991$	23954.0	0.767834	0.383917	−	0.923368i	$-0.374575\pi$
$991$	23954.0	0.767834	0.383917	+	0.923368i	$0.374575\pi$
$992$	−1805.59	−0.0577897
$993$	−69494.4	−2.22088
$994$	0	0
$995$	−4252.65	−0.135496
$996$	96574.0	3.07235
$997$	20462.5	0.650003	0.325001	−	0.945714i	$-0.394635\pi$
$997$	20462.5	0.650003	0.325001	+	0.945714i	$0.394635\pi$
$998$	61344.1	1.94570
$999$	−106853.	−3.38406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.8	yes	68
7.6	odd	2		2303.4.a.m.1.8	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.8	✓	68	7.6	odd	2
2303.4.a.n.1.8	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)

\(f(q)\)	\(=\)	\(q-4.80817 q^{2} +9.29565 q^{3} +15.1185 q^{4} +20.1348 q^{5} -44.6951 q^{6} -34.2269 q^{8} +59.4092 q^{9} +O(q^{10})\)	\(q-4.80817 q^{2} +9.29565 q^{3} +15.1185 q^{4} +20.1348 q^{5} -44.6951 q^{6} -34.2269 q^{8} +59.4092 q^{9} -96.8114 q^{10} +48.0604 q^{11} +140.536 q^{12} +55.0599 q^{13} +187.166 q^{15} +43.6207 q^{16} +20.3777 q^{17} -285.649 q^{18} -76.7396 q^{19} +304.407 q^{20} -231.082 q^{22} +1.94841 q^{23} -318.161 q^{24} +280.409 q^{25} -264.737 q^{26} +301.265 q^{27} +269.818 q^{29} -899.925 q^{30} -28.1774 q^{31} +64.0793 q^{32} +446.753 q^{33} -97.9792 q^{34} +898.177 q^{36} -354.681 q^{37} +368.977 q^{38} +511.818 q^{39} -689.150 q^{40} +490.885 q^{41} -214.131 q^{43} +726.600 q^{44} +1196.19 q^{45} -9.36828 q^{46} -47.0000 q^{47} +405.483 q^{48} -1348.25 q^{50} +189.424 q^{51} +832.422 q^{52} -343.485 q^{53} -1448.53 q^{54} +967.685 q^{55} -713.345 q^{57} -1297.33 q^{58} -183.883 q^{59} +2829.66 q^{60} -165.396 q^{61} +135.481 q^{62} -657.070 q^{64} +1108.62 q^{65} -2148.06 q^{66} +94.2883 q^{67} +308.079 q^{68} +18.1117 q^{69} -920.939 q^{71} -2033.39 q^{72} -518.579 q^{73} +1705.36 q^{74} +2606.58 q^{75} -1160.19 q^{76} -2460.90 q^{78} -1009.05 q^{79} +878.293 q^{80} +1196.40 q^{81} -2360.26 q^{82} +687.182 q^{83} +410.299 q^{85} +1029.58 q^{86} +2508.13 q^{87} -1644.96 q^{88} -1033.97 q^{89} -5751.49 q^{90} +29.4570 q^{92} -261.927 q^{93} +225.984 q^{94} -1545.13 q^{95} +595.659 q^{96} +931.178 q^{97} +2855.23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 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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