LMFDB - Embedded newform 2303.4.a.n.1.14

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			1.14
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)

$f(q)$	$=$	$q-3.74103 q^{2} -10.2661 q^{3} +5.99534 q^{4} +7.67916 q^{5} +38.4059 q^{6} +7.49951 q^{8} +78.3932 q^{9} +O(q^{10})$	\(q-3.74103 q^{2} -10.2661 q^{3} +5.99534 q^{4} +7.67916 q^{5} +38.4059 q^{6} +7.49951 q^{8} +78.3932 q^{9} -28.7280 q^{10} -49.7867 q^{11} -61.5489 q^{12} +25.5311 q^{13} -78.8352 q^{15} -76.0186 q^{16} -1.23727 q^{17} -293.272 q^{18} +54.8055 q^{19} +46.0392 q^{20} +186.254 q^{22} -152.057 q^{23} -76.9908 q^{24} -66.0305 q^{25} -95.5126 q^{26} -527.609 q^{27} +284.866 q^{29} +294.925 q^{30} -340.282 q^{31} +224.392 q^{32} +511.116 q^{33} +4.62865 q^{34} +469.994 q^{36} +100.957 q^{37} -205.029 q^{38} -262.105 q^{39} +57.5899 q^{40} -177.371 q^{41} +324.564 q^{43} -298.488 q^{44} +601.994 q^{45} +568.851 q^{46} -47.0000 q^{47} +780.416 q^{48} +247.022 q^{50} +12.7019 q^{51} +153.067 q^{52} +152.288 q^{53} +1973.80 q^{54} -382.320 q^{55} -562.639 q^{57} -1065.69 q^{58} +550.709 q^{59} -472.644 q^{60} +475.472 q^{61} +1273.01 q^{62} -231.310 q^{64} +196.057 q^{65} -1912.10 q^{66} -476.820 q^{67} -7.41783 q^{68} +1561.04 q^{69} -676.863 q^{71} +587.910 q^{72} +517.966 q^{73} -377.682 q^{74} +677.877 q^{75} +328.577 q^{76} +980.543 q^{78} -745.459 q^{79} -583.759 q^{80} +3299.88 q^{81} +663.550 q^{82} -376.785 q^{83} -9.50116 q^{85} -1214.20 q^{86} -2924.47 q^{87} -373.376 q^{88} -921.074 q^{89} -2252.08 q^{90} -911.634 q^{92} +3493.38 q^{93} +175.829 q^{94} +420.860 q^{95} -2303.64 q^{96} +1186.39 q^{97} -3902.94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.74103	−1.32266	−0.661328	−	0.750097i	$-0.730007\pi$
$2$	−3.74103	−1.32266	−0.661328	+	0.750097i	$0.730007\pi$
$3$	−10.2661	−1.97572	−0.987858	−	0.155361i	$-0.950346\pi$
$3$	−10.2661	−1.97572	−0.987858	+	0.155361i	$0.950346\pi$
$4$	5.99534	0.749417
$5$	7.67916	0.686845	0.343422	−	0.939181i	$-0.388414\pi$
$5$	7.67916	0.686845	0.343422	+	0.939181i	$0.388414\pi$
$6$	38.4059	2.61319
$7$	0	0
$7$	0	0
$8$	7.49951	0.331434
$9$	78.3932	2.90345
$10$	−28.7280	−0.908459
$11$	−49.7867	−1.36466	−0.682330	−	0.731045i	$-0.739033\pi$
$11$	−49.7867	−1.36466	−0.682330	+	0.731045i	$0.739033\pi$
$12$	−61.5489	−1.48064
$13$	25.5311	0.544695	0.272348	−	0.962199i	$-0.412200\pi$
$13$	25.5311	0.544695	0.272348	+	0.962199i	$0.412200\pi$
$14$	0	0
$15$	−78.8352	−1.35701
$16$	−76.0186	−1.18779
$17$	−1.23727	−0.0176518	−0.00882591	−	0.999961i	$-0.502809\pi$
$17$	−1.23727	−0.0176518	−0.00882591	+	0.999961i	$0.502809\pi$
$18$	−293.272	−3.84027
$19$	54.8055	0.661749	0.330875	−	0.943675i	$-0.392656\pi$
$19$	54.8055	0.661749	0.330875	+	0.943675i	$0.392656\pi$
$20$	46.0392	0.514733
$21$	0	0
$22$	186.254	1.80497
$23$	−152.057	−1.37853	−0.689263	−	0.724511i	$-0.742066\pi$
$23$	−152.057	−1.37853	−0.689263	+	0.724511i	$0.742066\pi$
$24$	−76.9908	−0.654820
$25$	−66.0305	−0.528244
$26$	−95.5126	−0.720444
$27$	−527.609	−3.76068
$28$	0	0
$29$	284.866	1.82408	0.912040	−	0.410101i	$-0.134507\pi$
$29$	284.866	1.82408	0.912040	+	0.410101i	$0.134507\pi$
$30$	294.925	1.79486
$31$	−340.282	−1.97150	−0.985750	−	0.168219i	$-0.946198\pi$
$31$	−340.282	−1.97150	−0.985750	+	0.168219i	$0.946198\pi$
$32$	224.392	1.23960
$33$	511.116	2.69618
$34$	4.62865	0.0233473
$35$	0	0
$36$	469.994	2.17590
$37$	100.957	0.448572	0.224286	−	0.974523i	$-0.427995\pi$
$37$	100.957	0.448572	0.224286	+	0.974523i	$0.427995\pi$
$38$	−205.029	−0.875266
$39$	−262.105	−1.07616
$40$	57.5899	0.227644
$41$	−177.371	−0.675625	−0.337813	−	0.941213i	$-0.609687\pi$
$41$	−177.371	−0.675625	−0.337813	+	0.941213i	$0.609687\pi$
$42$	0	0
$43$	324.564	1.15106	0.575529	−	0.817781i	$-0.304796\pi$
$43$	324.564	1.15106	0.575529	+	0.817781i	$0.304796\pi$
$44$	−298.488	−1.02270
$45$	601.994	1.99422
$46$	568.851	1.82332
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	780.416	2.34674
$49$	0	0
$50$	247.022	0.698685
$51$	12.7019	0.0348750
$52$	153.067	0.408204
$53$	152.288	0.394687	0.197343	−	0.980334i	$-0.436769\pi$
$53$	152.288	0.394687	0.197343	+	0.980334i	$0.436769\pi$
$54$	1973.80	4.97408
$55$	−382.320	−0.937309
$56$	0	0
$57$	−562.639	−1.30743
$58$	−1065.69	−2.41263
$59$	550.709	1.21519	0.607595	−	0.794247i	$-0.292134\pi$
$59$	550.709	1.21519	0.607595	+	0.794247i	$0.292134\pi$
$60$	−472.644	−1.01697
$61$	475.472	0.997998	0.498999	−	0.866602i	$-0.333701\pi$
$61$	475.472	0.997998	0.498999	+	0.866602i	$0.333701\pi$
$62$	1273.01	2.60761
$63$	0	0
$64$	−231.310	−0.451778
$65$	196.057	0.374121
$66$	−1912.10	−3.56612
$67$	−476.820	−0.869446	−0.434723	−	0.900564i	$-0.643154\pi$
$67$	−476.820	−0.869446	−0.434723	+	0.900564i	$0.643154\pi$
$68$	−7.41783	−0.0132286
$69$	1561.04	2.72358
$70$	0	0
$71$	−676.863	−1.13139	−0.565697	−	0.824614i	$-0.691393\pi$
$71$	−676.863	−1.13139	−0.565697	+	0.824614i	$0.691393\pi$
$72$	587.910	0.962304
$73$	517.966	0.830457	0.415228	−	0.909717i	$-0.363702\pi$
$73$	517.966	0.830457	0.415228	+	0.909717i	$0.363702\pi$
$74$	−377.682	−0.593306
$75$	677.877	1.04366
$76$	328.577	0.495926
$77$	0	0
$78$	980.543	1.42339
$79$	−745.459	−1.06165	−0.530827	−	0.847480i	$-0.678119\pi$
$79$	−745.459	−1.06165	−0.530827	+	0.847480i	$0.678119\pi$
$80$	−583.759	−0.815828
$81$	3299.88	4.52658
$82$	663.550	0.893619
$83$	−376.785	−0.498284	−0.249142	−	0.968467i	$-0.580149\pi$
$83$	−376.785	−0.498284	−0.249142	+	0.968467i	$0.580149\pi$
$84$	0	0
$85$	−9.50116	−0.0121241
$86$	−1214.20	−1.52245
$87$	−2924.47	−3.60386
$88$	−373.376	−0.452295
$89$	−921.074	−1.09701	−0.548504	−	0.836148i	$-0.684802\pi$
$89$	−921.074	−1.09701	−0.548504	+	0.836148i	$0.684802\pi$
$90$	−2252.08	−2.63767
$91$	0	0
$92$	−911.634	−1.03309
$93$	3493.38	3.89512
$94$	175.829	0.192929
$95$	420.860	0.454519
$96$	−2303.64	−2.44910
$97$	1186.39	1.24185	0.620926	−	0.783869i	$-0.286757\pi$
$97$	1186.39	1.24185	0.620926	+	0.783869i	$0.286757\pi$
$98$	0	0
$99$	−3902.94	−3.96222
$100$	−395.875	−0.395875
$101$	1045.47	1.02998	0.514991	−	0.857196i	$-0.327795\pi$
$101$	1045.47	1.02998	0.514991	+	0.857196i	$0.327795\pi$
$102$	−47.5183	−0.0461276
$103$	1338.10	1.28007	0.640033	−	0.768347i	$-0.278921\pi$
$103$	1338.10	1.28007	0.640033	+	0.768347i	$0.278921\pi$
$104$	191.470	0.180531
$105$	0	0
$106$	−569.716	−0.522035
$107$	−130.465	−0.117874	−0.0589371	−	0.998262i	$-0.518771\pi$
$107$	−130.465	−0.117874	−0.0589371	+	0.998262i	$0.518771\pi$
$108$	−3163.19	−2.81832
$109$	−277.090	−0.243490	−0.121745	−	0.992561i	$-0.538849\pi$
$109$	−277.090	−0.243490	−0.121745	+	0.992561i	$0.538849\pi$
$110$	1430.27	1.23974
$111$	−1036.43	−0.886250
$112$	0	0
$113$	37.3186	0.0310676	0.0155338	−	0.999879i	$-0.495055\pi$
$113$	37.3186	0.0310676	0.0155338	+	0.999879i	$0.495055\pi$
$114$	2104.85	1.72928
$115$	−1167.67	−0.946834
$116$	1707.87	1.36700
$117$	2001.46	1.58150
$118$	−2060.22	−1.60728
$119$	0	0
$120$	−591.225	−0.449760
$121$	1147.71	0.862295
$122$	−1778.76	−1.32001
$123$	1820.91	1.33484
$124$	−2040.11	−1.47748
$125$	−1466.95	−1.04967
$126$	0	0
$127$	−1779.42	−1.24329	−0.621647	−	0.783297i	$-0.713536\pi$
$127$	−1779.42	−1.24329	−0.621647	+	0.783297i	$0.713536\pi$
$128$	−929.799	−0.642058
$129$	−3332.01	−2.27416
$130$	−733.456	−0.494834
$131$	1242.91	0.828956	0.414478	−	0.910059i	$-0.363964\pi$
$131$	1242.91	0.828956	0.414478	+	0.910059i	$0.363964\pi$
$132$	3064.31	2.02056
$133$	0	0
$134$	1783.80	1.14998
$135$	−4051.59	−2.58300
$136$	−9.27888	−0.00585042
$137$	−1904.32	−1.18757	−0.593786	−	0.804623i	$-0.702367\pi$
$137$	−1904.32	−1.18757	−0.593786	+	0.804623i	$0.702367\pi$
$138$	−5839.89	−3.60235
$139$	−974.368	−0.594567	−0.297284	−	0.954789i	$-0.596081\pi$
$139$	−974.368	−0.594567	−0.297284	+	0.954789i	$0.596081\pi$
$140$	0	0
$141$	482.508	0.288188
$142$	2532.17	1.49644
$143$	−1271.11	−0.743324
$144$	−5959.34	−3.44869
$145$	2187.53	1.25286
$146$	−1937.73	−1.09841
$147$	0	0
$148$	605.269	0.336167
$149$	−2684.06	−1.47575	−0.737874	−	0.674938i	$-0.764170\pi$
$149$	−2684.06	−1.47575	−0.737874	+	0.674938i	$0.764170\pi$
$150$	−2535.96	−1.38040
$151$	634.552	0.341981	0.170990	−	0.985273i	$-0.445303\pi$
$151$	634.552	0.341981	0.170990	+	0.985273i	$0.445303\pi$
$152$	411.014	0.219327
$153$	−96.9932	−0.0512512
$154$	0	0
$155$	−2613.08	−1.35411
$156$	−1571.41	−0.806496
$157$	1717.63	0.873135	0.436567	−	0.899672i	$-0.356194\pi$
$157$	1717.63	0.873135	0.436567	+	0.899672i	$0.356194\pi$
$158$	2788.79	1.40420
$159$	−1563.41	−0.779789
$160$	1723.14	0.851415
$161$	0	0
$162$	−12345.0	−5.98711
$163$	−2614.30	−1.25624	−0.628122	−	0.778114i	$-0.716176\pi$
$163$	−2614.30	−1.25624	−0.628122	+	0.778114i	$0.716176\pi$
$164$	−1063.40	−0.506325
$165$	3924.94	1.85186
$166$	1409.57	0.659058
$167$	2247.82	1.04157	0.520783	−	0.853689i	$-0.325640\pi$
$167$	2247.82	1.04157	0.520783	+	0.853689i	$0.325640\pi$
$168$	0	0
$169$	−1545.17	−0.703307
$170$	35.5442	0.0160360
$171$	4296.38	1.92136
$172$	1945.87	0.862624
$173$	−1678.01	−0.737440	−0.368720	−	0.929541i	$-0.620204\pi$
$173$	−1678.01	−0.737440	−0.368720	+	0.929541i	$0.620204\pi$
$174$	10940.5	4.76667
$175$	0	0
$176$	3784.72	1.62093
$177$	−5653.64	−2.40087
$178$	3445.77	1.45096
$179$	1862.84	0.777850	0.388925	−	0.921270i	$-0.372847\pi$
$179$	1862.84	0.777850	0.388925	+	0.921270i	$0.372847\pi$
$180$	3609.16	1.49450
$181$	−4027.95	−1.65412	−0.827059	−	0.562115i	$-0.809988\pi$
$181$	−4027.95	−1.65412	−0.827059	+	0.562115i	$0.809988\pi$
$182$	0	0
$183$	−4881.25	−1.97176
$184$	−1140.35	−0.456891
$185$	775.261	0.308099
$186$	−13068.8	−5.15190
$187$	61.5994	0.0240887
$188$	−281.781	−0.109314
$189$	0	0
$190$	−1574.45	−0.601172
$191$	320.759	0.121515	0.0607574	−	0.998153i	$-0.480648\pi$
$191$	320.759	0.121515	0.0607574	+	0.998153i	$0.480648\pi$
$192$	2374.66	0.892584
$193$	521.866	0.194636	0.0973180	−	0.995253i	$-0.468974\pi$
$193$	521.866	0.194636	0.0973180	+	0.995253i	$0.468974\pi$
$194$	−4438.32	−1.64254
$195$	−2012.75	−0.739157
$196$	0	0
$197$	−3966.45	−1.43451	−0.717254	−	0.696812i	$-0.754601\pi$
$197$	−3966.45	−1.43451	−0.717254	+	0.696812i	$0.754601\pi$
$198$	14601.0	5.24065
$199$	929.061	0.330952	0.165476	−	0.986214i	$-0.447084\pi$
$199$	929.061	0.330952	0.165476	+	0.986214i	$0.447084\pi$
$200$	−495.196	−0.175078
$201$	4895.09	1.71778
$202$	−3911.14	−1.36231
$203$	0	0
$204$	76.1523	0.0261359
$205$	−1362.06	−0.464050
$206$	−5005.87	−1.69309
$207$	−11920.2	−4.00249
$208$	−1940.84	−0.646984
$209$	−2728.58	−0.903062
$210$	0	0
$211$	3169.52	1.03412	0.517059	−	0.855950i	$-0.327027\pi$
$211$	3169.52	1.03412	0.517059	+	0.855950i	$0.327027\pi$
$212$	913.020	0.295785
$213$	6948.76	2.23531
$214$	488.075	0.155907
$215$	2492.38	0.790599
$216$	−3956.80	−1.24642
$217$	0	0
$218$	1036.60	0.322054
$219$	−5317.50	−1.64075
$220$	−2292.14	−0.702436
$221$	−31.5887	−0.00961487
$222$	3877.33	1.17220
$223$	3834.74	1.15154	0.575769	−	0.817612i	$-0.304703\pi$
$223$	3834.74	1.15154	0.575769	+	0.817612i	$0.304703\pi$
$224$	0	0
$225$	−5176.34	−1.53373
$226$	−139.610	−0.0410917
$227$	4410.52	1.28959	0.644794	−	0.764356i	$-0.276943\pi$
$227$	4410.52	1.28959	0.644794	+	0.764356i	$0.276943\pi$
$228$	−3373.21	−0.979810
$229$	−2519.44	−0.727026	−0.363513	−	0.931589i	$-0.618423\pi$
$229$	−2519.44	−0.727026	−0.363513	+	0.931589i	$0.618423\pi$
$230$	4368.30	1.25234
$231$	0	0
$232$	2136.36	0.604563
$233$	1452.10	0.408286	0.204143	−	0.978941i	$-0.434559\pi$
$233$	1452.10	0.408286	0.204143	+	0.978941i	$0.434559\pi$
$234$	−7487.54	−2.09178
$235$	−360.920	−0.100187
$236$	3301.69	0.910684
$237$	7652.97	2.09753
$238$	0	0
$239$	1166.39	0.315680	0.157840	−	0.987465i	$-0.449547\pi$
$239$	1166.39	0.315680	0.157840	+	0.987465i	$0.449547\pi$
$240$	5992.94	1.61184
$241$	−3085.15	−0.824615	−0.412307	−	0.911045i	$-0.635277\pi$
$241$	−3085.15	−0.824615	−0.412307	+	0.911045i	$0.635277\pi$
$242$	−4293.64	−1.14052
$243$	−19631.5	−5.18256
$244$	2850.61	0.747917
$245$	0	0
$246$	−6812.08	−1.76554
$247$	1399.24	0.360452
$248$	−2551.95	−0.653423
$249$	3868.12	0.984467
$250$	5487.92	1.38835
$251$	5125.26	1.28886	0.644429	−	0.764664i	$-0.277095\pi$
$251$	5125.26	1.28886	0.644429	+	0.764664i	$0.277095\pi$
$252$	0	0
$253$	7570.42	1.88122
$254$	6656.89	1.64445
$255$	97.5401	0.0239537
$256$	5328.89	1.30100
$257$	−178.292	−0.0432744	−0.0216372	−	0.999766i	$-0.506888\pi$
$257$	−178.292	−0.0432744	−0.0216372	+	0.999766i	$0.506888\pi$
$258$	12465.2	3.00794
$259$	0	0
$260$	1175.43	0.280373
$261$	22331.6	5.29613
$262$	−4649.76	−1.09642
$263$	4855.60	1.13844	0.569218	−	0.822186i	$-0.307246\pi$
$263$	4855.60	1.13844	0.569218	+	0.822186i	$0.307246\pi$
$264$	3833.12	0.893606
$265$	1169.45	0.271089
$266$	0	0
$267$	9455.86	2.16737
$268$	−2858.70	−0.651578
$269$	−1231.58	−0.279148	−0.139574	−	0.990212i	$-0.544573\pi$
$269$	−1231.58	−0.279148	−0.139574	+	0.990212i	$0.544573\pi$
$270$	15157.1	3.41642
$271$	4215.97	0.945026	0.472513	−	0.881324i	$-0.343347\pi$
$271$	4215.97	0.945026	0.472513	+	0.881324i	$0.343347\pi$
$272$	94.0553	0.0209667
$273$	0	0
$274$	7124.14	1.57075
$275$	3287.44	0.720873
$276$	9358.95	2.04110
$277$	−5099.64	−1.10617	−0.553083	−	0.833126i	$-0.686549\pi$
$277$	−5099.64	−1.10617	−0.553083	+	0.833126i	$0.686549\pi$
$278$	3645.14	0.786407
$279$	−26675.8	−5.72415
$280$	0	0
$281$	−4791.09	−1.01713	−0.508563	−	0.861025i	$-0.669823\pi$
$281$	−4791.09	−1.01713	−0.508563	+	0.861025i	$0.669823\pi$
$282$	−1805.08	−0.381173
$283$	2491.57	0.523352	0.261676	−	0.965156i	$-0.415725\pi$
$283$	2491.57	0.523352	0.261676	+	0.965156i	$0.415725\pi$
$284$	−4058.03	−0.847886
$285$	−4320.60	−0.898000
$286$	4755.25	0.983161
$287$	0	0
$288$	17590.8	3.59913
$289$	−4911.47	−0.999688
$290$	−8183.63	−1.65710
$291$	−12179.6	−2.45355
$292$	3105.38	0.622359
$293$	−829.808	−0.165454	−0.0827268	−	0.996572i	$-0.526363\pi$
$293$	−829.808	−0.165454	−0.0827268	+	0.996572i	$0.526363\pi$
$294$	0	0
$295$	4228.98	0.834647
$296$	757.124	0.148672
$297$	26267.9	5.13205
$298$	10041.1	1.95191
$299$	−3882.18	−0.750877
$300$	4064.10	0.782137
$301$	0	0
$302$	−2373.88	−0.452323
$303$	−10732.9	−2.03495
$304$	−4166.24	−0.786020
$305$	3651.22	0.685470
$306$	362.855	0.0677877
$307$	−102.728	−0.0190976	−0.00954882	−	0.999954i	$-0.503040\pi$
$307$	−102.728	−0.0190976	−0.00954882	+	0.999954i	$0.503040\pi$
$308$	0	0
$309$	−13737.1	−2.52905
$310$	9775.63	1.79103
$311$	−9464.06	−1.72559	−0.862793	−	0.505557i	$-0.831287\pi$
$311$	−9464.06	−1.72559	−0.862793	+	0.505557i	$0.831287\pi$
$312$	−1965.66	−0.356678
$313$	5666.33	1.02326	0.511629	−	0.859206i	$-0.329042\pi$
$313$	5666.33	1.02326	0.511629	+	0.859206i	$0.329042\pi$
$314$	−6425.73	−1.15486
$315$	0	0
$316$	−4469.28	−0.795622
$317$	5281.27	0.935727	0.467864	−	0.883801i	$-0.345024\pi$
$317$	5281.27	0.935727	0.467864	+	0.883801i	$0.345024\pi$
$318$	5848.77	1.03139
$319$	−14182.5	−2.48925
$320$	−1776.27	−0.310301
$321$	1339.37	0.232886
$322$	0	0
$323$	−67.8089	−0.0116811
$324$	19783.9	3.39230
$325$	−1685.83	−0.287732
$326$	9780.19	1.66158
$327$	2844.64	0.481068
$328$	−1330.19	−0.223926
$329$	0	0
$330$	−14683.3	−2.44937
$331$	−6292.09	−1.04485	−0.522424	−	0.852686i	$-0.674972\pi$
$331$	−6292.09	−1.04485	−0.522424	+	0.852686i	$0.674972\pi$
$332$	−2258.96	−0.373423
$333$	7914.30	1.30241
$334$	−8409.18	−1.37763
$335$	−3661.58	−0.597174
$336$	0	0
$337$	−4070.82	−0.658017	−0.329009	−	0.944327i	$-0.606714\pi$
$337$	−4070.82	−0.658017	−0.329009	+	0.944327i	$0.606714\pi$
$338$	5780.52	0.930233
$339$	−383.117	−0.0613807
$340$	−56.9627	−0.00908599
$341$	16941.5	2.69042
$342$	−16072.9	−2.54129
$343$	0	0
$344$	2434.07	0.381501
$345$	11987.5	1.87067
$346$	6277.51	0.975378
$347$	5381.19	0.832500	0.416250	−	0.909250i	$-0.363344\pi$
$347$	5381.19	0.832500	0.416250	+	0.909250i	$0.363344\pi$
$348$	−17533.2	−2.70080
$349$	3140.41	0.481669	0.240835	−	0.970566i	$-0.422579\pi$
$349$	3140.41	0.481669	0.240835	+	0.970566i	$0.422579\pi$
$350$	0	0
$351$	−13470.4	−2.04842
$352$	−11171.7	−1.69164
$353$	−2844.09	−0.428827	−0.214413	−	0.976743i	$-0.568784\pi$
$353$	−2844.09	−0.428827	−0.214413	+	0.976743i	$0.568784\pi$
$354$	21150.5	3.17552
$355$	−5197.74	−0.777092
$356$	−5522.15	−0.822116
$357$	0	0
$358$	−6968.94	−1.02883
$359$	4327.70	0.636232	0.318116	−	0.948052i	$-0.396950\pi$
$359$	4327.70	0.636232	0.318116	+	0.948052i	$0.396950\pi$
$360$	4514.66	0.660954
$361$	−3855.36	−0.562088
$362$	15068.7	2.18783
$363$	−11782.6	−1.70365
$364$	0	0
$365$	3977.54	0.570395
$366$	18260.9	2.60796
$367$	−4466.11	−0.635229	−0.317614	−	0.948220i	$-0.602882\pi$
$367$	−4466.11	−0.635229	−0.317614	+	0.948220i	$0.602882\pi$
$368$	11559.2	1.63740
$369$	−13904.7	−1.96165
$370$	−2900.28	−0.407509
$371$	0	0
$372$	20944.0	2.91907
$373$	−9664.52	−1.34158	−0.670791	−	0.741646i	$-0.734045\pi$
$373$	−9664.52	−1.34158	−0.670791	+	0.741646i	$0.734045\pi$
$374$	−230.445	−0.0318611
$375$	15059.9	2.07384
$376$	−352.477	−0.0483447
$377$	7272.93	0.993568
$378$	0	0
$379$	3308.36	0.448388	0.224194	−	0.974544i	$-0.428025\pi$
$379$	3308.36	0.448388	0.224194	+	0.974544i	$0.428025\pi$
$380$	2523.20	0.340625
$381$	18267.8	2.45640
$382$	−1199.97	−0.160722
$383$	1128.80	0.150598	0.0752989	−	0.997161i	$-0.476009\pi$
$383$	1128.80	0.150598	0.0752989	+	0.997161i	$0.476009\pi$
$384$	9545.42	1.26852
$385$	0	0
$386$	−1952.32	−0.257436
$387$	25443.6	3.34204
$388$	7112.81	0.930665
$389$	−14181.2	−1.84837	−0.924183	−	0.381949i	$-0.875253\pi$
$389$	−14181.2	−1.84837	−0.924183	+	0.381949i	$0.875253\pi$
$390$	7529.75	0.977650
$391$	188.135	0.0243335
$392$	0	0
$393$	−12759.8	−1.63778
$394$	14838.6	1.89736
$395$	−5724.50	−0.729192
$396$	−23399.4	−2.96936
$397$	11060.5	1.39826	0.699131	−	0.714994i	$-0.253570\pi$
$397$	11060.5	1.39826	0.699131	+	0.714994i	$0.253570\pi$
$398$	−3475.65	−0.437735
$399$	0	0
$400$	5019.55	0.627444
$401$	−12872.6	−1.60305	−0.801527	−	0.597958i	$-0.795979\pi$
$401$	−12872.6	−1.60305	−0.801527	+	0.597958i	$0.795979\pi$
$402$	−18312.7	−2.27203
$403$	−8687.76	−1.07387
$404$	6267.95	0.771886
$405$	25340.3	3.10906
$406$	0	0
$407$	−5026.29	−0.612147
$408$	95.2581	0.0115588
$409$	12242.8	1.48011	0.740056	−	0.672545i	$-0.234799\pi$
$409$	12242.8	1.48011	0.740056	+	0.672545i	$0.234799\pi$
$410$	5095.50	0.613778
$411$	19550.0	2.34630
$412$	8022.36	0.959304
$413$	0	0
$414$	44594.1	5.29391
$415$	−2893.39	−0.342244
$416$	5728.97	0.675207
$417$	10003.0	1.17470
$418$	10207.7	1.19444
$419$	−3672.25	−0.428166	−0.214083	−	0.976816i	$-0.568676\pi$
$419$	−3672.25	−0.428166	−0.214083	+	0.976816i	$0.568676\pi$
$420$	0	0
$421$	2308.92	0.267292	0.133646	−	0.991029i	$-0.457331\pi$
$421$	2308.92	0.267292	0.133646	+	0.991029i	$0.457331\pi$
$422$	−11857.3	−1.36778
$423$	−3684.48	−0.423512
$424$	1142.09	0.130813
$425$	81.6973	0.00932447
$426$	−25995.6	−2.95655
$427$	0	0
$428$	−782.183	−0.0883370
$429$	13049.3	1.46860
$430$	−9324.07	−1.04569
$431$	−3268.97	−0.365339	−0.182669	−	0.983174i	$-0.558474\pi$
$431$	−3268.97	−0.365339	−0.182669	+	0.983174i	$0.558474\pi$
$432$	40108.1	4.46690
$433$	13321.4	1.47849	0.739245	−	0.673437i	$-0.235183\pi$
$433$	13321.4	1.47849	0.739245	+	0.673437i	$0.235183\pi$
$434$	0	0
$435$	−22457.5	−2.47529
$436$	−1661.25	−0.182476
$437$	−8333.56	−0.912239
$438$	19893.0	2.17014
$439$	−2156.28	−0.234427	−0.117214	−	0.993107i	$-0.537396\pi$
$439$	−2156.28	−0.234427	−0.117214	+	0.993107i	$0.537396\pi$
$440$	−2867.21	−0.310657
$441$	0	0
$442$	118.174	0.0127172
$443$	10634.4	1.14053	0.570264	−	0.821462i	$-0.306841\pi$
$443$	10634.4	1.14053	0.570264	+	0.821462i	$0.306841\pi$
$444$	−6213.76	−0.664171
$445$	−7073.07	−0.753474
$446$	−14345.9	−1.52309
$447$	27554.8	2.91566
$448$	0	0
$449$	645.647	0.0678619	0.0339309	−	0.999424i	$-0.489197\pi$
$449$	645.647	0.0678619	0.0339309	+	0.999424i	$0.489197\pi$
$450$	19364.9	2.02860
$451$	8830.70	0.921998
$452$	223.738	0.0232826
$453$	−6514.39	−0.675657
$454$	−16499.9	−1.70568
$455$	0	0
$456$	−4219.52	−0.433327
$457$	13655.3	1.39774	0.698871	−	0.715248i	$-0.253686\pi$
$457$	13655.3	1.39774	0.698871	+	0.715248i	$0.253686\pi$
$458$	9425.29	0.961605
$459$	652.792	0.0663829
$460$	−7000.58	−0.709574
$461$	5348.60	0.540367	0.270184	−	0.962809i	$-0.412916\pi$
$461$	5348.60	0.540367	0.270184	+	0.962809i	$0.412916\pi$
$462$	0	0
$463$	7970.42	0.800036	0.400018	−	0.916507i	$-0.369004\pi$
$463$	7970.42	0.800036	0.400018	+	0.916507i	$0.369004\pi$
$464$	−21655.1	−2.16663
$465$	26826.2	2.67534
$466$	−5432.37	−0.540021
$467$	−6451.83	−0.639304	−0.319652	−	0.947535i	$-0.603566\pi$
$467$	−6451.83	−0.639304	−0.319652	+	0.947535i	$0.603566\pi$
$468$	11999.4	1.18520
$469$	0	0
$470$	1350.22	0.132512
$471$	−17633.4	−1.72507
$472$	4130.04	0.402756
$473$	−16159.0	−1.57080
$474$	−28630.0	−2.77430
$475$	−3618.83	−0.349565
$476$	0	0
$477$	11938.4	1.14595
$478$	−4363.51	−0.417536
$479$	−19952.7	−1.90326	−0.951632	−	0.307239i	$-0.900595\pi$
$479$	−19952.7	−1.90326	−0.951632	+	0.307239i	$0.900595\pi$
$480$	−17690.0	−1.68215
$481$	2577.53	0.244335
$482$	11541.7	1.09068
$483$	0	0
$484$	6880.94	0.646219
$485$	9110.47	0.852959
$486$	73442.1	6.85474
$487$	1150.54	0.107055	0.0535277	−	0.998566i	$-0.482953\pi$
$487$	1150.54	0.107055	0.0535277	+	0.998566i	$0.482953\pi$
$488$	3565.80	0.330771
$489$	26838.7	2.48198
$490$	0	0
$491$	20392.6	1.87434	0.937172	−	0.348868i	$-0.113434\pi$
$491$	20392.6	1.87434	0.937172	+	0.348868i	$0.113434\pi$
$492$	10917.0	1.00035
$493$	−352.455	−0.0321983
$494$	−5234.61	−0.476754
$495$	−29971.3	−2.72143
$496$	25867.8	2.34173
$497$	0	0
$498$	−14470.8	−1.30211
$499$	−10706.4	−0.960485	−0.480243	−	0.877136i	$-0.659451\pi$
$499$	−10706.4	−0.960485	−0.480243	+	0.877136i	$0.659451\pi$
$500$	−8794.89	−0.786638
$501$	−23076.4	−2.05784
$502$	−19173.8	−1.70472
$503$	−12769.0	−1.13189	−0.565944	−	0.824444i	$-0.691488\pi$
$503$	−12769.0	−1.13189	−0.565944	+	0.824444i	$0.691488\pi$
$504$	0	0
$505$	8028.33	0.707438
$506$	−28321.2	−2.48820
$507$	15862.8	1.38953
$508$	−10668.3	−0.931747
$509$	−10851.5	−0.944960	−0.472480	−	0.881341i	$-0.656641\pi$
$509$	−10851.5	−0.944960	−0.472480	+	0.881341i	$0.656641\pi$
$510$	−364.901	−0.0316825
$511$	0	0
$512$	−12497.2	−1.07872
$513$	−28915.8	−2.48863
$514$	666.995	0.0572371
$515$	10275.5	0.879207
$516$	−19976.5	−1.70430
$517$	2339.97	0.199056
$518$	0	0
$519$	17226.7	1.45697
$520$	1470.33	0.123997
$521$	−18616.0	−1.56542	−0.782710	−	0.622387i	$-0.786163\pi$
$521$	−18616.0	−1.56542	−0.782710	+	0.622387i	$0.786163\pi$
$522$	−83543.2	−7.00495
$523$	−12060.7	−1.00837	−0.504185	−	0.863596i	$-0.668207\pi$
$523$	−12060.7	−1.00837	−0.504185	+	0.863596i	$0.668207\pi$
$524$	7451.65	0.621234
$525$	0	0
$526$	−18165.0	−1.50576
$527$	421.020	0.0348006
$528$	−38854.3	−3.20250
$529$	10954.4	0.900336
$530$	−4374.94	−0.358557
$531$	43171.8	3.52824
$532$	0	0
$533$	−4528.46	−0.368010
$534$	−35374.7	−2.86669
$535$	−1001.86	−0.0809613
$536$	−3575.92	−0.288164
$537$	−19124.1	−1.53681
$538$	4607.38	0.369216
$539$	0	0
$540$	−24290.7	−1.93575
$541$	6831.78	0.542923	0.271461	−	0.962449i	$-0.412493\pi$
$541$	6831.78	0.542923	0.271461	+	0.962449i	$0.412493\pi$
$542$	−15772.1	−1.24994
$543$	41351.4	3.26807
$544$	−277.633	−0.0218813
$545$	−2127.82	−0.167240
$546$	0	0
$547$	−8611.05	−0.673093	−0.336546	−	0.941667i	$-0.609259\pi$
$547$	−8611.05	−0.673093	−0.336546	+	0.941667i	$0.609259\pi$
$548$	−11417.1	−0.889987
$549$	37273.7	2.89764
$550$	−12298.4	−0.953467
$551$	15612.2	1.20708
$552$	11707.0	0.902687
$553$	0	0
$554$	19077.9	1.46308
$555$	−7958.92	−0.608716
$556$	−5841.67	−0.445579
$557$	−522.735	−0.0397648	−0.0198824	−	0.999802i	$-0.506329\pi$
$557$	−522.735	−0.0397648	−0.0198824	+	0.999802i	$0.506329\pi$
$558$	99795.1	7.57108
$559$	8286.46	0.626977
$560$	0	0
$561$	−632.387	−0.0475925
$562$	17923.6	1.34531
$563$	11017.7	0.824760	0.412380	−	0.911012i	$-0.364698\pi$
$563$	11017.7	0.824760	0.412380	+	0.911012i	$0.364698\pi$
$564$	2892.80	0.215973
$565$	286.575	0.0213386
$566$	−9321.05	−0.692214
$567$	0	0
$568$	−5076.14	−0.374983
$569$	−12548.3	−0.924522	−0.462261	−	0.886744i	$-0.652962\pi$
$569$	−12548.3	−0.924522	−0.462261	+	0.886744i	$0.652962\pi$
$570$	16163.5	1.18775
$571$	−4291.56	−0.314530	−0.157265	−	0.987556i	$-0.550268\pi$
$571$	−4291.56	−0.314530	−0.157265	+	0.987556i	$0.550268\pi$
$572$	−7620.72	−0.557060
$573$	−3292.95	−0.240079
$574$	0	0
$575$	10040.4	0.728199
$576$	−18133.1	−1.31171
$577$	−10547.3	−0.760990	−0.380495	−	0.924783i	$-0.624246\pi$
$577$	−10547.3	−0.760990	−0.380495	+	0.924783i	$0.624246\pi$
$578$	18374.0	1.32224
$579$	−5357.54	−0.384545
$580$	13115.0	0.938915
$581$	0	0
$582$	45564.4	3.24520
$583$	−7581.93	−0.538613
$584$	3884.49	0.275242
$585$	15369.5	1.08624
$586$	3104.34	0.218838
$587$	19414.4	1.36511	0.682553	−	0.730836i	$-0.260870\pi$
$587$	19414.4	1.36511	0.682553	+	0.730836i	$0.260870\pi$
$588$	0	0
$589$	−18649.3	−1.30464
$590$	−15820.8	−1.10395
$591$	40720.1	2.83418
$592$	−7674.57	−0.532809
$593$	−9935.34	−0.688019	−0.344010	−	0.938966i	$-0.611785\pi$
$593$	−9935.34	−0.688019	−0.344010	+	0.938966i	$0.611785\pi$
$594$	−98269.1	−6.78793
$595$	0	0
$596$	−16091.8	−1.10595
$597$	−9537.85	−0.653866
$598$	14523.4	0.993152
$599$	4041.52	0.275680	0.137840	−	0.990455i	$-0.455984\pi$
$599$	4041.52	0.275680	0.137840	+	0.990455i	$0.455984\pi$
$600$	5083.74	0.345905
$601$	5444.23	0.369509	0.184754	−	0.982785i	$-0.440851\pi$
$601$	5444.23	0.369509	0.184754	+	0.982785i	$0.440851\pi$
$602$	0	0
$603$	−37379.5	−2.52439
$604$	3804.36	0.256286
$605$	8813.48	0.592263
$606$	40152.2	2.69154
$607$	−4471.40	−0.298993	−0.149496	−	0.988762i	$-0.547765\pi$
$607$	−4471.40	−0.298993	−0.149496	+	0.988762i	$0.547765\pi$
$608$	12297.9	0.820307
$609$	0	0
$610$	−13659.3	−0.906641
$611$	−1199.96	−0.0794520
$612$	−581.507	−0.0384086
$613$	14314.5	0.943161	0.471581	−	0.881823i	$-0.343684\pi$
$613$	14314.5	0.943161	0.471581	+	0.881823i	$0.343684\pi$
$614$	384.308	0.0252596
$615$	13983.0	0.916830
$616$	0	0
$617$	−13431.2	−0.876372	−0.438186	−	0.898884i	$-0.644379\pi$
$617$	−13431.2	−0.876372	−0.438186	+	0.898884i	$0.644379\pi$
$618$	51390.9	3.34506
$619$	3082.23	0.200138	0.100069	−	0.994981i	$-0.468094\pi$
$619$	3082.23	0.200138	0.100069	+	0.994981i	$0.468094\pi$
$620$	−15666.3	−1.01480
$621$	80226.7	5.18420
$622$	35405.4	2.28236
$623$	0	0
$624$	19924.9	1.27826
$625$	−3011.16	−0.192714
$626$	−21197.9	−1.35342
$627$	28012.0	1.78419
$628$	10297.8	0.654342
$629$	−124.910	−0.00791811
$630$	0	0
$631$	16357.4	1.03198	0.515990	−	0.856595i	$-0.327424\pi$
$631$	16357.4	1.03198	0.515990	+	0.856595i	$0.327424\pi$
$632$	−5590.57	−0.351869
$633$	−32538.7	−2.04312
$634$	−19757.4	−1.23764
$635$	−13664.5	−0.853951
$636$	−9373.17	−0.584387
$637$	0	0
$638$	53057.4	3.29242
$639$	−53061.5	−3.28495
$640$	−7140.07	−0.440994
$641$	−14912.1	−0.918863	−0.459431	−	0.888213i	$-0.651947\pi$
$641$	−14912.1	−0.918863	−0.459431	+	0.888213i	$0.651947\pi$
$642$	−5010.63	−0.308028
$643$	14514.6	0.890200	0.445100	−	0.895481i	$-0.353168\pi$
$643$	14514.6	0.890200	0.445100	+	0.895481i	$0.353168\pi$
$644$	0	0
$645$	−25587.0	−1.56200
$646$	253.676	0.0154500
$647$	8032.87	0.488106	0.244053	−	0.969762i	$-0.421523\pi$
$647$	8032.87	0.488106	0.244053	+	0.969762i	$0.421523\pi$
$648$	24747.4	1.50026
$649$	−27418.0	−1.65832
$650$	6306.74	0.380571
$651$	0	0
$652$	−15673.6	−0.941452
$653$	−4303.70	−0.257912	−0.128956	−	0.991650i	$-0.541163\pi$
$653$	−4303.70	−0.257912	−0.128956	+	0.991650i	$0.541163\pi$
$654$	−10641.9	−0.636287
$655$	9544.48	0.569364
$656$	13483.5	0.802502
$657$	40605.0	2.41119
$658$	0	0
$659$	−19629.5	−1.16033	−0.580165	−	0.814499i	$-0.697012\pi$
$659$	−19629.5	−1.16033	−0.580165	+	0.814499i	$0.697012\pi$
$660$	23531.4	1.38781
$661$	−15193.3	−0.894025	−0.447012	−	0.894528i	$-0.647512\pi$
$661$	−15193.3	−0.894025	−0.447012	+	0.894528i	$0.647512\pi$
$662$	23538.9	1.38197
$663$	324.293	0.0189962
$664$	−2825.70	−0.165148
$665$	0	0
$666$	−29607.7	−1.72263
$667$	−43315.9	−2.51454
$668$	13476.5	0.780568
$669$	−39367.9	−2.27511
$670$	13698.1	0.789856
$671$	−23672.2	−1.36193
$672$	0	0
$673$	24068.2	1.37855	0.689273	−	0.724502i	$-0.257930\pi$
$673$	24068.2	1.37855	0.689273	+	0.724502i	$0.257930\pi$
$674$	15229.1	0.870330
$675$	34838.3	1.98656
$676$	−9263.79	−0.527070
$677$	2367.28	0.134390	0.0671950	−	0.997740i	$-0.478595\pi$
$677$	2367.28	0.134390	0.0671950	+	0.997740i	$0.478595\pi$
$678$	1433.25	0.0811855
$679$	0	0
$680$	−71.2540	−0.00401833
$681$	−45278.9	−2.54786
$682$	−63378.8	−3.55851
$683$	26092.0	1.46176	0.730881	−	0.682505i	$-0.239110\pi$
$683$	26092.0	1.46176	0.730881	+	0.682505i	$0.239110\pi$
$684$	25758.2	1.43990
$685$	−14623.6	−0.815677
$686$	0	0
$687$	25864.8	1.43640
$688$	−24672.9	−1.36722
$689$	3888.08	0.214984
$690$	−44845.5	−2.47426
$691$	−2942.18	−0.161977	−0.0809883	−	0.996715i	$-0.525808\pi$
$691$	−2942.18	−0.161977	−0.0809883	+	0.996715i	$0.525808\pi$
$692$	−10060.3	−0.552650
$693$	0	0
$694$	−20131.2	−1.10111
$695$	−7482.33	−0.408375
$696$	−21932.1	−1.19444
$697$	219.455	0.0119260
$698$	−11748.4	−0.637082
$699$	−14907.5	−0.806656
$700$	0	0
$701$	13371.4	0.720443	0.360221	−	0.932867i	$-0.382701\pi$
$701$	13371.4	0.720443	0.360221	+	0.932867i	$0.382701\pi$
$702$	50393.3	2.70936
$703$	5532.97	0.296842
$704$	11516.2	0.616523
$705$	3705.25	0.197940
$706$	10639.9	0.567190
$707$	0	0
$708$	−33895.5	−1.79925
$709$	−9851.75	−0.521848	−0.260924	−	0.965359i	$-0.584027\pi$
$709$	−9851.75	−0.521848	−0.260924	+	0.965359i	$0.584027\pi$
$710$	19444.9	1.02782
$711$	−58438.9	−3.08246
$712$	−6907.60	−0.363586
$713$	51742.3	2.71776
$714$	0	0
$715$	−9761.03	−0.510548
$716$	11168.3	0.582934
$717$	−11974.3	−0.623694
$718$	−16190.1	−0.841515
$719$	15259.8	0.791507	0.395753	−	0.918357i	$-0.370484\pi$
$719$	15259.8	0.791507	0.395753	+	0.918357i	$0.370484\pi$
$720$	−45762.7	−2.36872
$721$	0	0
$722$	14423.0	0.743449
$723$	31672.6	1.62920
$724$	−24148.9	−1.23963
$725$	−18809.9	−0.963560
$726$	44079.0	2.25334
$727$	−38325.3	−1.95517	−0.977585	−	0.210543i	$-0.932477\pi$
$727$	−38325.3	−1.95517	−0.977585	+	0.210543i	$0.932477\pi$
$728$	0	0
$729$	112443.	5.71268
$730$	−14880.1	−0.754436
$731$	−401.572	−0.0203183
$732$	−29264.7	−1.47767
$733$	38601.7	1.94514	0.972570	−	0.232610i	$-0.0747265\pi$
$733$	38601.7	1.94514	0.972570	+	0.232610i	$0.0747265\pi$
$734$	16707.9	0.840189
$735$	0	0
$736$	−34120.4	−1.70883
$737$	23739.3	1.18650
$738$	52017.8	2.59458
$739$	−21969.9	−1.09361	−0.546805	−	0.837260i	$-0.684156\pi$
$739$	−21969.9	−1.09361	−0.546805	+	0.837260i	$0.684156\pi$
$740$	4647.95	0.230895
$741$	−14364.8	−0.712150
$742$	0	0
$743$	1586.14	0.0783175	0.0391587	−	0.999233i	$-0.487532\pi$
$743$	1586.14	0.0783175	0.0391587	+	0.999233i	$0.487532\pi$
$744$	26198.6	1.29098
$745$	−20611.3	−1.01361
$746$	36155.3	1.77445
$747$	−29537.4	−1.44674
$748$	369.309	0.0180525
$749$	0	0
$750$	−56339.7	−2.74298
$751$	21202.0	1.03019	0.515094	−	0.857133i	$-0.327757\pi$
$751$	21202.0	1.03019	0.515094	+	0.857133i	$0.327757\pi$
$752$	3572.88	0.173257
$753$	−52616.5	−2.54642
$754$	−27208.3	−1.31415
$755$	4872.83	0.234888
$756$	0	0
$757$	−24261.4	−1.16486	−0.582428	−	0.812882i	$-0.697897\pi$
$757$	−24261.4	−1.16486	−0.582428	+	0.812882i	$0.697897\pi$
$758$	−12376.7	−0.593063
$759$	−77718.9	−3.71675
$760$	3156.24	0.150643
$761$	−30566.3	−1.45601	−0.728007	−	0.685569i	$-0.759553\pi$
$761$	−30566.3	−1.45601	−0.728007	+	0.685569i	$0.759553\pi$
$762$	−68340.4	−3.24897
$763$	0	0
$764$	1923.06	0.0910653
$765$	−744.826	−0.0352016
$766$	−4222.88	−0.199189
$767$	14060.2	0.661908
$768$	−54707.0	−2.57040
$769$	13995.6	0.656298	0.328149	−	0.944626i	$-0.393575\pi$
$769$	13995.6	0.656298	0.328149	+	0.944626i	$0.393575\pi$
$770$	0	0
$771$	1830.36	0.0854979
$772$	3128.76	0.145864
$773$	−5305.69	−0.246872	−0.123436	−	0.992353i	$-0.539391\pi$
$773$	−5305.69	−0.246872	−0.123436	+	0.992353i	$0.539391\pi$
$774$	−95185.4	−4.42037
$775$	22469.0	1.04143
$776$	8897.33	0.411592
$777$	0	0
$778$	53052.3	2.44475
$779$	−9720.88	−0.447095
$780$	−12067.1	−0.553937
$781$	33698.8	1.54397
$782$	−703.820	−0.0321849
$783$	−150298.	−6.85978
$784$	0	0
$785$	13190.0	0.599708
$786$	47735.0	2.16622
$787$	34454.8	1.56058	0.780292	−	0.625416i	$-0.215071\pi$
$787$	34454.8	1.56058	0.780292	+	0.625416i	$0.215071\pi$
$788$	−23780.2	−1.07504
$789$	−49848.1	−2.24923
$790$	21415.5	0.964469
$791$	0	0
$792$	−29270.1	−1.31322
$793$	12139.3	0.543605
$794$	−41377.7	−1.84942
$795$	−12005.7	−0.535594
$796$	5570.04	0.248021
$797$	−19991.2	−0.888489	−0.444245	−	0.895905i	$-0.646528\pi$
$797$	−19991.2	−0.888489	−0.444245	+	0.895905i	$0.646528\pi$
$798$	0	0
$799$	58.1515	0.00257478
$800$	−14816.7	−0.654813
$801$	−72205.9	−3.18511
$802$	48156.7	2.12029
$803$	−25787.8	−1.13329
$804$	29347.7	1.28733
$805$	0	0
$806$	32501.2	1.42036
$807$	12643.5	0.551516
$808$	7840.51	0.341371
$809$	24197.7	1.05160	0.525801	−	0.850608i	$-0.323766\pi$
$809$	24197.7	1.05160	0.525801	+	0.850608i	$0.323766\pi$
$810$	−94798.9	−4.11221
$811$	7706.13	0.333661	0.166830	−	0.985986i	$-0.446647\pi$
$811$	7706.13	0.333661	0.166830	+	0.985986i	$0.446647\pi$
$812$	0	0
$813$	−43281.7	−1.86710
$814$	18803.5	0.809660
$815$	−20075.6	−0.862845
$816$	−965.582	−0.0414242
$817$	17787.9	0.761712
$818$	−45800.6	−1.95768
$819$	0	0
$820$	−8166.00	−0.347767
$821$	3815.48	0.162194	0.0810969	−	0.996706i	$-0.474158\pi$
$821$	3815.48	0.162194	0.0810969	+	0.996706i	$0.474158\pi$
$822$	−73137.3	−3.10335
$823$	31278.4	1.32478	0.662391	−	0.749158i	$-0.269542\pi$
$823$	31278.4	1.32478	0.662391	+	0.749158i	$0.269542\pi$
$824$	10035.1	0.424258
$825$	−33749.3	−1.42424
$826$	0	0
$827$	−4910.31	−0.206467	−0.103234	−	0.994657i	$-0.532919\pi$
$827$	−4910.31	−0.206467	−0.103234	+	0.994657i	$0.532919\pi$
$828$	−71465.9	−2.99953
$829$	−11796.6	−0.494225	−0.247112	−	0.968987i	$-0.579482\pi$
$829$	−11796.6	−0.494225	−0.247112	+	0.968987i	$0.579482\pi$
$830$	10824.3	0.452671
$831$	52353.6	2.18547
$832$	−5905.59	−0.246081
$833$	0	0
$834$	−37421.5	−1.55372
$835$	17261.4	0.715395
$836$	−16358.8	−0.676771
$837$	179536.	7.41418
$838$	13738.0	0.566316
$839$	−27416.0	−1.12813	−0.564067	−	0.825729i	$-0.690764\pi$
$839$	−27416.0	−1.12813	−0.564067	+	0.825729i	$0.690764\pi$
$840$	0	0
$841$	56759.7	2.32727
$842$	−8637.76	−0.353536
$843$	49185.9	2.00955
$844$	19002.3	0.774985
$845$	−11865.6	−0.483063
$846$	13783.8	0.560160
$847$	0	0
$848$	−11576.7	−0.468805
$849$	−25578.8	−1.03399
$850$	−305.632	−0.0123331
$851$	−15351.2	−0.618368
$852$	41660.2	1.67518
$853$	21683.6	0.870378	0.435189	−	0.900339i	$-0.356682\pi$
$853$	21683.6	0.870378	0.435189	+	0.900339i	$0.356682\pi$
$854$	0	0
$855$	32992.6	1.31967
$856$	−978.424	−0.0390676
$857$	34397.3	1.37105	0.685526	−	0.728048i	$-0.259572\pi$
$857$	34397.3	1.37105	0.685526	+	0.728048i	$0.259572\pi$
$858$	−48818.0	−1.94245
$859$	32492.9	1.29062	0.645311	−	0.763920i	$-0.276728\pi$
$859$	32492.9	1.29062	0.645311	+	0.763920i	$0.276728\pi$
$860$	14942.7	0.592489
$861$	0	0
$862$	12229.3	0.483217
$863$	15944.3	0.628913	0.314456	−	0.949272i	$-0.398178\pi$
$863$	15944.3	0.628913	0.314456	+	0.949272i	$0.398178\pi$
$864$	−118391.	−4.66175
$865$	−12885.7	−0.506507
$866$	−49835.8	−1.95553
$867$	50421.7	1.97510
$868$	0	0
$869$	37113.9	1.44880
$870$	84014.2	3.27396
$871$	−12173.7	−0.473583
$872$	−2078.04	−0.0807011
$873$	93004.9	3.60566
$874$	31176.2	1.20658
$875$	0	0
$876$	−31880.2	−1.22960
$877$	−23468.7	−0.903627	−0.451814	−	0.892112i	$-0.649223\pi$
$877$	−23468.7	−0.903627	−0.451814	+	0.892112i	$0.649223\pi$
$878$	8066.72	0.310067
$879$	8518.91	0.326889
$880$	29063.4	1.11333
$881$	7967.20	0.304679	0.152339	−	0.988328i	$-0.451319\pi$
$881$	7967.20	0.304679	0.152339	+	0.988328i	$0.451319\pi$
$882$	0	0
$883$	11982.5	0.456673	0.228337	−	0.973582i	$-0.426671\pi$
$883$	11982.5	0.456673	0.228337	+	0.973582i	$0.426671\pi$
$884$	−189.385	−0.00720555
$885$	−43415.2	−1.64902
$886$	−39783.5	−1.50852
$887$	−23767.7	−0.899708	−0.449854	−	0.893102i	$-0.648524\pi$
$887$	−23767.7	−0.899708	−0.449854	+	0.893102i	$0.648524\pi$
$888$	−7772.72	−0.293734
$889$	0	0
$890$	26460.6	0.996586
$891$	−164290.	−6.17724
$892$	22990.6	0.862983
$893$	−2575.86	−0.0965261
$894$	−103084.	−3.85641
$895$	14305.0	0.534262
$896$	0	0
$897$	39854.9	1.48352
$898$	−2415.39	−0.0897579
$899$	−96934.9	−3.59617
$900$	−31033.9	−1.14940
$901$	−188.421	−0.00696694
$902$	−33035.9	−1.21949
$903$	0	0
$904$	279.871	0.0102969
$905$	−30931.3	−1.13612
$906$	24370.5	0.893661
$907$	45097.4	1.65097	0.825487	−	0.564421i	$-0.190901\pi$
$907$	45097.4	1.65097	0.825487	+	0.564421i	$0.190901\pi$
$908$	26442.6	0.966440
$909$	81957.7	2.99050
$910$	0	0
$911$	4781.57	0.173897	0.0869487	−	0.996213i	$-0.472288\pi$
$911$	4781.57	0.173897	0.0869487	+	0.996213i	$0.472288\pi$
$912$	42771.1	1.55295
$913$	18758.9	0.679988
$914$	−51084.9	−1.84873
$915$	−37483.9	−1.35429
$916$	−15104.9	−0.544846
$917$	0	0
$918$	−2442.12	−0.0878017
$919$	−12442.3	−0.446608	−0.223304	−	0.974749i	$-0.571684\pi$
$919$	−12442.3	−0.446608	−0.223304	+	0.974749i	$0.571684\pi$
$920$	−8756.96	−0.313813
$921$	1054.61	0.0377315
$922$	−20009.3	−0.714720
$923$	−17281.0	−0.616265
$924$	0	0
$925$	−6666.21	−0.236955
$926$	−29817.6	−1.05817
$927$	104898.	3.71661
$928$	63921.8	2.26114
$929$	37692.8	1.33118	0.665588	−	0.746320i	$-0.268181\pi$
$929$	37692.8	1.33118	0.665588	+	0.746320i	$0.268181\pi$
$930$	−100358.	−3.53856
$931$	0	0
$932$	8705.86	0.305976
$933$	97159.1	3.40927
$934$	24136.5	0.845579
$935$	473.031	0.0165452
$936$	15010.0	0.524163
$937$	24024.4	0.837614	0.418807	−	0.908075i	$-0.362448\pi$
$937$	24024.4	0.837614	0.418807	+	0.908075i	$0.362448\pi$
$938$	0	0
$939$	−58171.2	−2.02167
$940$	−2163.84	−0.0750816
$941$	23013.5	0.797259	0.398629	−	0.917112i	$-0.369486\pi$
$941$	23013.5	0.797259	0.398629	+	0.917112i	$0.369486\pi$
$942$	65967.3	2.28167
$943$	26970.5	0.931367
$944$	−41864.1	−1.44339
$945$	0	0
$946$	60451.2	2.07763
$947$	25878.7	0.888009	0.444005	−	0.896024i	$-0.353557\pi$
$947$	25878.7	0.888009	0.444005	+	0.896024i	$0.353557\pi$
$948$	45882.1	1.57192
$949$	13224.2	0.452346
$950$	13538.2	0.462354
$951$	−54218.1	−1.84873
$952$	0	0
$953$	−10902.2	−0.370573	−0.185286	−	0.982685i	$-0.559321\pi$
$953$	−10902.2	−0.370573	−0.185286	+	0.982685i	$0.559321\pi$
$954$	−44661.8	−1.51570
$955$	2463.16	0.0834618
$956$	6992.91	0.236576
$957$	145600.	4.91805
$958$	74643.9	2.51736
$959$	0	0
$960$	18235.4	0.613067
$961$	86000.9	2.88681
$962$	−9642.62	−0.323171
$963$	−10227.6	−0.342242
$964$	−18496.5	−0.617981
$965$	4007.49	0.133685
$966$	0	0
$967$	−12796.8	−0.425562	−0.212781	−	0.977100i	$-0.568252\pi$
$967$	−12796.8	−0.425562	−0.212781	+	0.977100i	$0.568252\pi$
$968$	8607.29	0.285794
$969$	696.135	0.0230785
$970$	−34082.6	−1.12817
$971$	12612.7	0.416850	0.208425	−	0.978038i	$-0.433166\pi$
$971$	12612.7	0.416850	0.208425	+	0.978038i	$0.433166\pi$
$972$	−117697.	−3.88390
$973$	0	0
$974$	−4304.21	−0.141597
$975$	17306.9	0.568477
$976$	−36144.7	−1.18541
$977$	25303.4	0.828585	0.414292	−	0.910144i	$-0.364029\pi$
$977$	25303.4	0.828585	0.414292	+	0.910144i	$0.364029\pi$
$978$	−100405.	−3.28281
$979$	45857.2	1.49704
$980$	0	0
$981$	−21722.0	−0.706963
$982$	−76289.2	−2.47911
$983$	−11240.1	−0.364705	−0.182352	−	0.983233i	$-0.558371\pi$
$983$	−11240.1	−0.364705	−0.182352	+	0.983233i	$0.558371\pi$
$984$	13655.9	0.442413
$985$	−30459.0	−0.985284
$986$	1318.55	0.0425873
$987$	0	0
$988$	8388.93	0.270129
$989$	−49352.3	−1.58677
$990$	112124.	3.59952
$991$	40782.9	1.30728	0.653639	−	0.756807i	$-0.273242\pi$
$991$	40782.9	1.30728	0.653639	+	0.756807i	$0.273242\pi$
$992$	−76356.7	−2.44388
$993$	64595.4	2.06432
$994$	0	0
$995$	7134.41	0.227312
$996$	23190.7	0.737777
$997$	2567.79	0.0815673	0.0407836	−	0.999168i	$-0.487015\pi$
$997$	2567.79	0.0815673	0.0407836	+	0.999168i	$0.487015\pi$
$998$	40052.8	1.27039
$999$	−53265.5	−1.68693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.14	yes	68
7.6	odd	2		2303.4.a.m.1.14	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.14	✓	68	7.6	odd	2
2303.4.a.n.1.14	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)

\(f(q)\)	\(=\)	\(q-3.74103 q^{2} -10.2661 q^{3} +5.99534 q^{4} +7.67916 q^{5} +38.4059 q^{6} +7.49951 q^{8} +78.3932 q^{9} +O(q^{10})\)	\(q-3.74103 q^{2} -10.2661 q^{3} +5.99534 q^{4} +7.67916 q^{5} +38.4059 q^{6} +7.49951 q^{8} +78.3932 q^{9} -28.7280 q^{10} -49.7867 q^{11} -61.5489 q^{12} +25.5311 q^{13} -78.8352 q^{15} -76.0186 q^{16} -1.23727 q^{17} -293.272 q^{18} +54.8055 q^{19} +46.0392 q^{20} +186.254 q^{22} -152.057 q^{23} -76.9908 q^{24} -66.0305 q^{25} -95.5126 q^{26} -527.609 q^{27} +284.866 q^{29} +294.925 q^{30} -340.282 q^{31} +224.392 q^{32} +511.116 q^{33} +4.62865 q^{34} +469.994 q^{36} +100.957 q^{37} -205.029 q^{38} -262.105 q^{39} +57.5899 q^{40} -177.371 q^{41} +324.564 q^{43} -298.488 q^{44} +601.994 q^{45} +568.851 q^{46} -47.0000 q^{47} +780.416 q^{48} +247.022 q^{50} +12.7019 q^{51} +153.067 q^{52} +152.288 q^{53} +1973.80 q^{54} -382.320 q^{55} -562.639 q^{57} -1065.69 q^{58} +550.709 q^{59} -472.644 q^{60} +475.472 q^{61} +1273.01 q^{62} -231.310 q^{64} +196.057 q^{65} -1912.10 q^{66} -476.820 q^{67} -7.41783 q^{68} +1561.04 q^{69} -676.863 q^{71} +587.910 q^{72} +517.966 q^{73} -377.682 q^{74} +677.877 q^{75} +328.577 q^{76} +980.543 q^{78} -745.459 q^{79} -583.759 q^{80} +3299.88 q^{81} +663.550 q^{82} -376.785 q^{83} -9.50116 q^{85} -1214.20 q^{86} -2924.47 q^{87} -373.376 q^{88} -921.074 q^{89} -2252.08 q^{90} -911.634 q^{92} +3493.38 q^{93} +175.829 q^{94} +420.860 q^{95} -2303.64 q^{96} +1186.39 q^{97} -3902.94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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