LMFDB - Embedded newform 2303.4.a.h.1.7

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:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-3.81980 q^{2} -8.81241 q^{3} +6.59091 q^{4} +14.5625 q^{5} +33.6617 q^{6} +5.38246 q^{8} +50.6586 q^{9} +O(q^{10})$	\(q-3.81980 q^{2} -8.81241 q^{3} +6.59091 q^{4} +14.5625 q^{5} +33.6617 q^{6} +5.38246 q^{8} +50.6586 q^{9} -55.6259 q^{10} +26.7052 q^{11} -58.0818 q^{12} +15.0765 q^{13} -128.331 q^{15} -73.2872 q^{16} +5.84327 q^{17} -193.506 q^{18} +35.8038 q^{19} +95.9800 q^{20} -102.009 q^{22} +32.7893 q^{23} -47.4325 q^{24} +87.0661 q^{25} -57.5893 q^{26} -208.489 q^{27} -160.185 q^{29} +490.198 q^{30} -77.8725 q^{31} +236.883 q^{32} -235.337 q^{33} -22.3202 q^{34} +333.886 q^{36} +423.969 q^{37} -136.764 q^{38} -132.860 q^{39} +78.3821 q^{40} +6.86430 q^{41} -371.336 q^{43} +176.011 q^{44} +737.715 q^{45} -125.249 q^{46} +47.0000 q^{47} +645.837 q^{48} -332.576 q^{50} -51.4933 q^{51} +99.3678 q^{52} +150.902 q^{53} +796.387 q^{54} +388.894 q^{55} -315.518 q^{57} +611.877 q^{58} +661.770 q^{59} -845.815 q^{60} +554.886 q^{61} +297.458 q^{62} -318.549 q^{64} +219.551 q^{65} +898.942 q^{66} +326.777 q^{67} +38.5125 q^{68} -288.953 q^{69} +351.513 q^{71} +272.668 q^{72} +223.273 q^{73} -1619.48 q^{74} -767.262 q^{75} +235.979 q^{76} +507.500 q^{78} +354.488 q^{79} -1067.24 q^{80} +469.509 q^{81} -26.2203 q^{82} +637.261 q^{83} +85.0926 q^{85} +1418.43 q^{86} +1411.62 q^{87} +143.740 q^{88} +431.551 q^{89} -2817.93 q^{90} +216.111 q^{92} +686.245 q^{93} -179.531 q^{94} +521.392 q^{95} -2087.51 q^{96} -783.612 q^{97} +1352.85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * 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 $

$2$	−3.81980	−1.35050	−0.675252	−	0.737587i	$-0.735965\pi$
$2$	−3.81980	−1.35050	−0.675252	+	0.737587i	$0.735965\pi$
$3$	−8.81241	−1.69595	−0.847975	−	0.530037i	$-0.822178\pi$
$3$	−8.81241	−1.69595	−0.847975	+	0.530037i	$0.822178\pi$
$4$	6.59091	0.823863
$5$	14.5625	1.30251	0.651254	−	0.758860i	$-0.274243\pi$
$5$	14.5625	1.30251	0.651254	+	0.758860i	$0.274243\pi$
$6$	33.6617	2.29039
$7$	0	0
$7$	0	0
$8$	5.38246	0.237874
$9$	50.6586	1.87624
$10$	−55.6259	−1.75904
$11$	26.7052	0.731993	0.365996	−	0.930616i	$-0.380728\pi$
$11$	26.7052	0.731993	0.365996	+	0.930616i	$0.380728\pi$
$12$	−58.0818	−1.39723
$13$	15.0765	0.321651	0.160826	−	0.986983i	$-0.448584\pi$
$13$	15.0765	0.321651	0.160826	+	0.986983i	$0.448584\pi$
$14$	0	0
$15$	−128.331	−2.20899
$16$	−73.2872	−1.14511
$17$	5.84327	0.0833648	0.0416824	−	0.999131i	$-0.486728\pi$
$17$	5.84327	0.0833648	0.0416824	+	0.999131i	$0.486728\pi$
$18$	−193.506	−2.53388
$19$	35.8038	0.432313	0.216157	−	0.976359i	$-0.430648\pi$
$19$	35.8038	0.432313	0.216157	+	0.976359i	$0.430648\pi$
$20$	95.9800	1.07309
$21$	0	0
$22$	−102.009	−0.988560
$23$	32.7893	0.297263	0.148631	−	0.988893i	$-0.452513\pi$
$23$	32.7893	0.297263	0.148631	+	0.988893i	$0.452513\pi$
$24$	−47.4325	−0.403421
$25$	87.0661	0.696529
$26$	−57.5893	−0.434392
$27$	−208.489	−1.48606
$28$	0	0
$29$	−160.185	−1.02571	−0.512856	−	0.858474i	$-0.671413\pi$
$29$	−160.185	−1.02571	−0.512856	+	0.858474i	$0.671413\pi$
$30$	490.198	2.98325
$31$	−77.8725	−0.451172	−0.225586	−	0.974223i	$-0.572430\pi$
$31$	−77.8725	−0.451172	−0.225586	+	0.974223i	$0.572430\pi$
$32$	236.883	1.30861
$33$	−235.337	−1.24142
$34$	−22.3202	−0.112585
$35$	0	0
$36$	333.886	1.54577
$37$	423.969	1.88378	0.941892	−	0.335915i	$-0.109045\pi$
$37$	423.969	1.88378	0.941892	+	0.335915i	$0.109045\pi$
$38$	−136.764	−0.583841
$39$	−132.860	−0.545504
$40$	78.3821	0.309832
$41$	6.86430	0.0261469	0.0130735	−	0.999915i	$-0.495838\pi$
$41$	6.86430	0.0261469	0.0130735	+	0.999915i	$0.495838\pi$
$42$	0	0
$43$	−371.336	−1.31694	−0.658468	−	0.752609i	$-0.728795\pi$
$43$	−371.336	−1.31694	−0.658468	+	0.752609i	$0.728795\pi$
$44$	176.011	0.603062
$45$	737.715	2.44382
$46$	−125.249	−0.401455
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	645.837	1.94205
$49$	0	0
$50$	−332.576	−0.940666
$51$	−51.4933	−0.141382
$52$	99.3678	0.264997
$53$	150.902	0.391093	0.195547	−	0.980694i	$-0.437352\pi$
$53$	150.902	0.391093	0.195547	+	0.980694i	$0.437352\pi$
$54$	796.387	2.00694
$55$	388.894	0.953427
$56$	0	0
$57$	−315.518	−0.733181
$58$	611.877	1.38523
$59$	661.770	1.46026	0.730128	−	0.683311i	$-0.239461\pi$
$59$	661.770	1.46026	0.730128	+	0.683311i	$0.239461\pi$
$60$	−845.815	−1.81990
$61$	554.886	1.16469	0.582343	−	0.812943i	$-0.302136\pi$
$61$	554.886	1.16469	0.582343	+	0.812943i	$0.302136\pi$
$62$	297.458	0.609309
$63$	0	0
$64$	−318.549	−0.622167
$65$	219.551	0.418954
$66$	898.942	1.67655
$67$	326.777	0.595854	0.297927	−	0.954589i	$-0.403705\pi$
$67$	326.777	0.595854	0.297927	+	0.954589i	$0.403705\pi$
$68$	38.5125	0.0686812
$69$	−288.953	−0.504142
$70$	0	0
$71$	351.513	0.587562	0.293781	−	0.955873i	$-0.405086\pi$
$71$	351.513	0.587562	0.293781	+	0.955873i	$0.405086\pi$
$72$	272.668	0.446309
$73$	223.273	0.357974	0.178987	−	0.983851i	$-0.442718\pi$
$73$	223.273	0.357974	0.178987	+	0.983851i	$0.442718\pi$
$74$	−1619.48	−2.54406
$75$	−767.262	−1.18128
$76$	235.979	0.356167
$77$	0	0
$78$	507.500	0.736706
$79$	354.488	0.504848	0.252424	−	0.967617i	$-0.418772\pi$
$79$	354.488	0.504848	0.252424	+	0.967617i	$0.418772\pi$
$80$	−1067.24	−1.49152
$81$	469.509	0.644045
$82$	−26.2203	−0.0353115
$83$	637.261	0.842753	0.421376	−	0.906886i	$-0.361547\pi$
$83$	637.261	0.842753	0.421376	+	0.906886i	$0.361547\pi$
$84$	0	0
$85$	85.0926	0.108583
$86$	1418.43	1.77853
$87$	1411.62	1.73956
$88$	143.740	0.174122
$89$	431.551	0.513981	0.256991	−	0.966414i	$-0.417269\pi$
$89$	431.551	0.513981	0.256991	+	0.966414i	$0.417269\pi$
$90$	−2817.93	−3.30039
$91$	0	0
$92$	216.111	0.244904
$93$	686.245	0.765164
$94$	−179.531	−0.196991
$95$	521.392	0.563092
$96$	−2087.51	−2.21933
$97$	−783.612	−0.820244	−0.410122	−	0.912031i	$-0.634514\pi$
$97$	−783.612	−0.820244	−0.410122	+	0.912031i	$0.634514\pi$
$98$	0	0
$99$	1352.85	1.37340
$100$	573.845	0.573845
$101$	1007.52	0.992590	0.496295	−	0.868154i	$-0.334693\pi$
$101$	1007.52	0.992590	0.496295	+	0.868154i	$0.334693\pi$
$102$	196.694	0.190938
$103$	−1701.12	−1.62734	−0.813669	−	0.581328i	$-0.802533\pi$
$103$	−1701.12	−1.62734	−0.813669	+	0.581328i	$0.802533\pi$
$104$	81.1487	0.0765124
$105$	0	0
$106$	−576.415	−0.528174
$107$	662.316	0.598398	0.299199	−	0.954191i	$-0.403281\pi$
$107$	662.316	0.598398	0.299199	+	0.954191i	$0.403281\pi$
$108$	−1374.13	−1.22431
$109$	−554.818	−0.487540	−0.243770	−	0.969833i	$-0.578384\pi$
$109$	−554.818	−0.487540	−0.243770	+	0.969833i	$0.578384\pi$
$110$	−1485.50	−1.28761
$111$	−3736.19	−3.19480
$112$	0	0
$113$	1179.97	0.982322	0.491161	−	0.871069i	$-0.336573\pi$
$113$	1179.97	0.982322	0.491161	+	0.871069i	$0.336573\pi$
$114$	1205.22	0.990165
$115$	477.494	0.387187
$116$	−1055.77	−0.845047
$117$	763.754	0.603496
$118$	−2527.83	−1.97208
$119$	0	0
$120$	−690.735	−0.525460
$121$	−617.833	−0.464187
$122$	−2119.56	−1.57291
$123$	−60.4910	−0.0443438
$124$	−513.250	−0.371704
$125$	−552.412	−0.395274
$126$	0	0
$127$	−2712.10	−1.89496	−0.947481	−	0.319812i	$-0.896380\pi$
$127$	−2712.10	−1.89496	−0.947481	+	0.319812i	$0.896380\pi$
$128$	−678.268	−0.468367
$129$	3272.37	2.23346
$130$	−838.643	−0.565799
$131$	93.5545	0.0623962	0.0311981	−	0.999513i	$-0.490068\pi$
$131$	93.5545	0.0623962	0.0311981	+	0.999513i	$0.490068\pi$
$132$	−1551.08	−1.02276
$133$	0	0
$134$	−1248.23	−0.804703
$135$	−3036.12	−1.93561
$136$	31.4512	0.0198303
$137$	1264.26	0.788414	0.394207	−	0.919022i	$-0.371019\pi$
$137$	1264.26	0.788414	0.394207	+	0.919022i	$0.371019\pi$
$138$	1103.74	0.680847
$139$	409.831	0.250082	0.125041	−	0.992152i	$-0.460094\pi$
$139$	409.831	0.250082	0.125041	+	0.992152i	$0.460094\pi$
$140$	0	0
$141$	−414.183	−0.247380
$142$	−1342.71	−0.793505
$143$	402.621	0.235446
$144$	−3712.62	−2.14851
$145$	−2332.70	−1.33600
$146$	−852.859	−0.483446
$147$	0	0
$148$	2794.34	1.55198
$149$	−717.855	−0.394691	−0.197346	−	0.980334i	$-0.563232\pi$
$149$	−717.855	−0.394691	−0.197346	+	0.980334i	$0.563232\pi$
$150$	2930.79	1.59532
$151$	−363.428	−0.195863	−0.0979317	−	0.995193i	$-0.531223\pi$
$151$	−363.428	−0.195863	−0.0979317	+	0.995193i	$0.531223\pi$
$152$	192.713	0.102836
$153$	296.012	0.156413
$154$	0	0
$155$	−1134.02	−0.587655
$156$	−875.670	−0.449421
$157$	746.536	0.379491	0.189745	−	0.981833i	$-0.439234\pi$
$157$	746.536	0.379491	0.189745	+	0.981833i	$0.439234\pi$
$158$	−1354.07	−0.681799
$159$	−1329.81	−0.663274
$160$	3449.61	1.70447
$161$	0	0
$162$	−1793.43	−0.869786
$163$	147.936	0.0710873	0.0355437	−	0.999368i	$-0.488684\pi$
$163$	147.936	0.0710873	0.0355437	+	0.999368i	$0.488684\pi$
$164$	45.2420	0.0215415
$165$	−3427.09	−1.61696
$166$	−2434.21	−1.13814
$167$	2803.93	1.29925	0.649624	−	0.760255i	$-0.274926\pi$
$167$	2803.93	1.29925	0.649624	+	0.760255i	$0.274926\pi$
$168$	0	0
$169$	−1969.70	−0.896540
$170$	−325.037	−0.146642
$171$	1813.77	0.811125
$172$	−2447.44	−1.08497
$173$	−1310.87	−0.576090	−0.288045	−	0.957617i	$-0.593005\pi$
$173$	−1310.87	−0.576090	−0.288045	+	0.957617i	$0.593005\pi$
$174$	−5392.11	−2.34928
$175$	0	0
$176$	−1957.15	−0.838214
$177$	−5831.78	−2.47652
$178$	−1648.44	−0.694134
$179$	921.204	0.384659	0.192330	−	0.981330i	$-0.438396\pi$
$179$	921.204	0.384659	0.192330	+	0.981330i	$0.438396\pi$
$180$	4862.21	2.01338
$181$	2947.72	1.21051	0.605254	−	0.796032i	$-0.293071\pi$
$181$	2947.72	1.21051	0.605254	+	0.796032i	$0.293071\pi$
$182$	0	0
$183$	−4889.88	−1.97525
$184$	176.487	0.0707110
$185$	6174.04	2.45365
$186$	−2621.32	−1.03336
$187$	156.046	0.0610224
$188$	309.773	0.120173
$189$	0	0
$190$	−1991.62	−0.760458
$191$	−95.4560	−0.0361621	−0.0180810	−	0.999837i	$-0.505756\pi$
$191$	−95.4560	−0.0361621	−0.0180810	+	0.999837i	$0.505756\pi$
$192$	2807.19	1.05516
$193$	958.128	0.357345	0.178672	−	0.983909i	$-0.442820\pi$
$193$	958.128	0.357345	0.178672	+	0.983909i	$0.442820\pi$
$194$	2993.24	1.10774
$195$	−1934.78	−0.710524
$196$	0	0
$197$	4557.70	1.64834	0.824169	−	0.566345i	$-0.191643\pi$
$197$	4557.70	1.64834	0.824169	+	0.566345i	$0.191643\pi$
$198$	−5167.61	−1.85478
$199$	−4803.45	−1.71109	−0.855547	−	0.517725i	$-0.826779\pi$
$199$	−4803.45	−1.71109	−0.855547	+	0.517725i	$0.826779\pi$
$200$	468.630	0.165686
$201$	−2879.70	−1.01054
$202$	−3848.51	−1.34050
$203$	0	0
$204$	−339.388	−0.116480
$205$	99.9613	0.0340566
$206$	6497.93	2.19773
$207$	1661.06	0.557737
$208$	−1104.91	−0.368327
$209$	956.147	0.316450
$210$	0	0
$211$	−5260.71	−1.71641	−0.858204	−	0.513308i	$-0.828420\pi$
$211$	−5260.71	−1.71641	−0.858204	+	0.513308i	$0.828420\pi$
$212$	994.579	0.322207
$213$	−3097.67	−0.996475
$214$	−2529.92	−0.808139
$215$	−5407.58	−1.71532
$216$	−1122.18	−0.353495
$217$	0	0
$218$	2119.30	0.658426
$219$	−1967.57	−0.607106
$220$	2563.16	0.785493
$221$	88.0961	0.0268144
$222$	14271.5	4.31460
$223$	155.124	0.0465824	0.0232912	−	0.999729i	$-0.492586\pi$
$223$	155.124	0.0465824	0.0232912	+	0.999729i	$0.492586\pi$
$224$	0	0
$225$	4410.64	1.30686
$226$	−4507.26	−1.32663
$227$	−1910.71	−0.558671	−0.279335	−	0.960194i	$-0.590114\pi$
$227$	−1910.71	−0.558671	−0.279335	+	0.960194i	$0.590114\pi$
$228$	−2079.55	−0.604041
$229$	5308.63	1.53190	0.765948	−	0.642903i	$-0.222270\pi$
$229$	5308.63	1.53190	0.765948	+	0.642903i	$0.222270\pi$
$230$	−1823.93	−0.522898
$231$	0	0
$232$	−862.192	−0.243990
$233$	1171.44	0.329371	0.164685	−	0.986346i	$-0.447339\pi$
$233$	1171.44	0.329371	0.164685	+	0.986346i	$0.447339\pi$
$234$	−2917.39	−0.815025
$235$	684.437	0.189990
$236$	4361.66	1.20305
$237$	−3123.89	−0.856196
$238$	0	0
$239$	−164.089	−0.0444103	−0.0222051	−	0.999753i	$-0.507069\pi$
$239$	−164.089	−0.0444103	−0.0222051	+	0.999753i	$0.507069\pi$
$240$	9404.99	2.52954
$241$	5436.70	1.45315	0.726573	−	0.687089i	$-0.241112\pi$
$241$	5436.70	1.45315	0.726573	+	0.687089i	$0.241112\pi$
$242$	2360.00	0.626887
$243$	1491.70	0.393796
$244$	3657.20	0.959542
$245$	0	0
$246$	231.064	0.0598866
$247$	539.796	0.139054
$248$	−419.146	−0.107322
$249$	−5615.80	−1.42927
$250$	2110.10	0.533819
$251$	−5767.02	−1.45024	−0.725122	−	0.688620i	$-0.758217\pi$
$251$	−5767.02	−1.45024	−0.725122	+	0.688620i	$0.758217\pi$
$252$	0	0
$253$	875.645	0.217594
$254$	10359.7	2.55916
$255$	−749.871	−0.184152
$256$	5139.25	1.25470
$257$	7495.03	1.81917	0.909585	−	0.415517i	$-0.136399\pi$
$257$	7495.03	1.81917	0.909585	+	0.415517i	$0.136399\pi$
$258$	−12499.8	−3.01629
$259$	0	0
$260$	1447.04	0.345161
$261$	−8114.76	−1.92449
$262$	−357.360	−0.0842663
$263$	−4832.56	−1.13304	−0.566518	−	0.824049i	$-0.691710\pi$
$263$	−4832.56	−1.13304	−0.566518	+	0.824049i	$0.691710\pi$
$264$	−1266.69	−0.295302
$265$	2197.51	0.509403
$266$	0	0
$267$	−3803.01	−0.871686
$268$	2153.76	0.490902
$269$	−2858.16	−0.647826	−0.323913	−	0.946087i	$-0.604998\pi$
$269$	−2858.16	−0.647826	−0.323913	+	0.946087i	$0.604998\pi$
$270$	11597.4	2.61405
$271$	3364.93	0.754263	0.377131	−	0.926160i	$-0.376911\pi$
$271$	3364.93	0.754263	0.377131	+	0.926160i	$0.376911\pi$
$272$	−428.237	−0.0954621
$273$	0	0
$274$	−4829.22	−1.06476
$275$	2325.12	0.509854
$276$	−1904.46	−0.415344
$277$	7499.96	1.62682	0.813410	−	0.581691i	$-0.197609\pi$
$277$	7499.96	1.62682	0.813410	+	0.581691i	$0.197609\pi$
$278$	−1565.47	−0.337737
$279$	−3944.91	−0.846508
$280$	0	0
$281$	−6977.98	−1.48139	−0.740697	−	0.671839i	$-0.765504\pi$
$281$	−6977.98	−1.48139	−0.740697	+	0.671839i	$0.765504\pi$
$282$	1582.10	0.334087
$283$	−488.946	−0.102703	−0.0513513	−	0.998681i	$-0.516353\pi$
$283$	−488.946	−0.102703	−0.0513513	+	0.998681i	$0.516353\pi$
$284$	2316.79	0.484070
$285$	−4594.72	−0.954975
$286$	−1537.93	−0.317972
$287$	0	0
$288$	12000.2	2.45526
$289$	−4878.86	−0.993050
$290$	8910.45	1.80427
$291$	6905.51	1.39109
$292$	1471.57	0.294922
$293$	1249.39	0.249114	0.124557	−	0.992212i	$-0.460249\pi$
$293$	1249.39	0.249114	0.124557	+	0.992212i	$0.460249\pi$
$294$	0	0
$295$	9637.01	1.90200
$296$	2282.00	0.448103
$297$	−5567.74	−1.08779
$298$	2742.07	0.533032
$299$	494.348	0.0956150
$300$	−5056.95	−0.973211
$301$	0	0
$302$	1388.23	0.264515
$303$	−8878.64	−1.68338
$304$	−2623.96	−0.495048
$305$	8080.52	1.51701
$306$	−1130.71	−0.211236
$307$	5001.86	0.929873	0.464937	−	0.885344i	$-0.346077\pi$
$307$	5001.86	0.929873	0.464937	+	0.885344i	$0.346077\pi$
$308$	0	0
$309$	14990.9	2.75988
$310$	4331.73	0.793631
$311$	−8655.98	−1.57825	−0.789124	−	0.614234i	$-0.789465\pi$
$311$	−8655.98	−1.57825	−0.789124	+	0.614234i	$0.789465\pi$
$312$	−715.116	−0.129761
$313$	−1014.63	−0.183227	−0.0916137	−	0.995795i	$-0.529202\pi$
$313$	−1014.63	−0.183227	−0.0916137	+	0.995795i	$0.529202\pi$
$314$	−2851.62	−0.512504
$315$	0	0
$316$	2336.39	0.415925
$317$	−2701.94	−0.478726	−0.239363	−	0.970930i	$-0.576939\pi$
$317$	−2701.94	−0.478726	−0.239363	+	0.970930i	$0.576939\pi$
$318$	5079.61	0.895755
$319$	−4277.78	−0.750814
$320$	−4638.87	−0.810378
$321$	−5836.60	−1.01485
$322$	0	0
$323$	209.211	0.0360397
$324$	3094.49	0.530605
$325$	1312.65	0.224040
$326$	−565.086	−0.0960038
$327$	4889.28	0.826844
$328$	36.9469	0.00621966
$329$	0	0
$330$	13090.8	2.18372
$331$	−7236.73	−1.20171	−0.600856	−	0.799357i	$-0.705173\pi$
$331$	−7236.73	−1.20171	−0.600856	+	0.799357i	$0.705173\pi$
$332$	4200.13	0.694313
$333$	21477.6	3.53444
$334$	−10710.5	−1.75464
$335$	4758.69	0.776105
$336$	0	0
$337$	−5786.02	−0.935266	−0.467633	−	0.883923i	$-0.654893\pi$
$337$	−5786.02	−0.935266	−0.467633	+	0.883923i	$0.654893\pi$
$338$	7523.87	1.21078
$339$	−10398.4	−1.66597
$340$	560.837	0.0894579
$341$	−2079.60	−0.330254
$342$	−6928.24	−1.09543
$343$	0	0
$344$	−1998.70	−0.313264
$345$	−4207.87	−0.656650
$346$	5007.27	0.778013
$347$	−9502.27	−1.47005	−0.735027	−	0.678038i	$-0.762830\pi$
$347$	−9502.27	−1.47005	−0.735027	+	0.678038i	$0.762830\pi$
$348$	9303.84	1.43316
$349$	3841.75	0.589239	0.294619	−	0.955615i	$-0.404807\pi$
$349$	3841.75	0.589239	0.294619	+	0.955615i	$0.404807\pi$
$350$	0	0
$351$	−3143.28	−0.477995
$352$	6326.01	0.957890
$353$	3316.28	0.500022	0.250011	−	0.968243i	$-0.419566\pi$
$353$	3316.28	0.500022	0.250011	+	0.968243i	$0.419566\pi$
$354$	22276.3	3.34455
$355$	5118.90	0.765304
$356$	2844.31	0.423450
$357$	0	0
$358$	−3518.82	−0.519484
$359$	−934.649	−0.137406	−0.0687032	−	0.997637i	$-0.521886\pi$
$359$	−934.649	−0.137406	−0.0687032	+	0.997637i	$0.521886\pi$
$360$	3970.72	0.581321
$361$	−5577.09	−0.813105
$362$	−11259.7	−1.63480
$363$	5444.59	0.787237
$364$	0	0
$365$	3251.41	0.466264
$366$	18678.4	2.66758
$367$	7983.86	1.13557	0.567785	−	0.823177i	$-0.307801\pi$
$367$	7983.86	1.13557	0.567785	+	0.823177i	$0.307801\pi$
$368$	−2403.04	−0.340399
$369$	347.736	0.0490580
$370$	−23583.6	−3.31366
$371$	0	0
$372$	4522.97	0.630390
$373$	6096.00	0.846217	0.423109	−	0.906079i	$-0.360939\pi$
$373$	6096.00	0.846217	0.423109	+	0.906079i	$0.360939\pi$
$374$	−596.064	−0.0824111
$375$	4868.08	0.670364
$376$	252.976	0.0346974
$377$	−2415.03	−0.329922
$378$	0	0
$379$	3074.92	0.416750	0.208375	−	0.978049i	$-0.433183\pi$
$379$	3074.92	0.416750	0.208375	+	0.978049i	$0.433183\pi$
$380$	3436.45	0.463911
$381$	23900.2	3.21376
$382$	364.623	0.0488371
$383$	8464.68	1.12931	0.564654	−	0.825328i	$-0.309010\pi$
$383$	8464.68	1.12931	0.564654	+	0.825328i	$0.309010\pi$
$384$	5977.18	0.794327
$385$	0	0
$386$	−3659.86	−0.482596
$387$	−18811.4	−2.47089
$388$	−5164.71	−0.675769
$389$	−3281.77	−0.427743	−0.213872	−	0.976862i	$-0.568607\pi$
$389$	−3281.77	−0.427743	−0.213872	+	0.976862i	$0.568607\pi$
$390$	7390.47	0.959566
$391$	191.597	0.0247813
$392$	0	0
$393$	−824.441	−0.105821
$394$	−17409.5	−2.22609
$395$	5162.22	0.657568
$396$	8916.49	1.13149
$397$	11022.8	1.39349	0.696747	−	0.717317i	$-0.254630\pi$
$397$	11022.8	1.39349	0.696747	+	0.717317i	$0.254630\pi$
$398$	18348.3	2.31084
$399$	0	0
$400$	−6380.83	−0.797604
$401$	8274.64	1.03046	0.515232	−	0.857051i	$-0.327706\pi$
$401$	8274.64	1.03046	0.515232	+	0.857051i	$0.327706\pi$
$402$	10999.9	1.36474
$403$	−1174.05	−0.145120
$404$	6640.44	0.817758
$405$	6837.22	0.838874
$406$	0	0
$407$	11322.2	1.37892
$408$	−277.161	−0.0336312
$409$	742.792	0.0898012	0.0449006	−	0.998991i	$-0.485703\pi$
$409$	742.792	0.0898012	0.0449006	+	0.998991i	$0.485703\pi$
$410$	−381.833	−0.0459936
$411$	−11141.2	−1.33711
$412$	−11211.9	−1.34070
$413$	0	0
$414$	−6344.92	−0.753227
$415$	9280.10	1.09769
$416$	3571.37	0.420915
$417$	−3611.60	−0.424127
$418$	−3652.30	−0.427368
$419$	−1934.96	−0.225606	−0.112803	−	0.993617i	$-0.535983\pi$
$419$	−1934.96	−0.225606	−0.112803	+	0.993617i	$0.535983\pi$
$420$	0	0
$421$	−5825.89	−0.674433	−0.337217	−	0.941427i	$-0.609485\pi$
$421$	−5825.89	−0.674433	−0.337217	+	0.941427i	$0.609485\pi$
$422$	20094.9	2.31802
$423$	2380.95	0.273678
$424$	812.223	0.0930308
$425$	508.751	0.0580660
$426$	11832.5	1.34574
$427$	0	0
$428$	4365.27	0.492998
$429$	−3548.06	−0.399305
$430$	20655.9	2.31655
$431$	15769.7	1.76241	0.881205	−	0.472734i	$-0.156733\pi$
$431$	15769.7	1.76241	0.881205	+	0.472734i	$0.156733\pi$
$432$	15279.6	1.70171
$433$	10804.9	1.19919	0.599594	−	0.800304i	$-0.295329\pi$
$433$	10804.9	1.19919	0.599594	+	0.800304i	$0.295329\pi$
$434$	0	0
$435$	20556.7	2.26579
$436$	−3656.75	−0.401667
$437$	1173.98	0.128511
$438$	7515.74	0.819899
$439$	10255.8	1.11500	0.557498	−	0.830178i	$-0.311761\pi$
$439$	10255.8	1.11500	0.557498	+	0.830178i	$0.311761\pi$
$440$	2093.21	0.226795
$441$	0	0
$442$	−336.510	−0.0362130
$443$	13605.9	1.45923	0.729613	−	0.683860i	$-0.239700\pi$
$443$	13605.9	1.45923	0.729613	+	0.683860i	$0.239700\pi$
$444$	−24624.9	−2.63208
$445$	6284.46	0.669465
$446$	−592.543	−0.0629097
$447$	6326.03	0.669376
$448$	0	0
$449$	−16651.8	−1.75022	−0.875109	−	0.483926i	$-0.839210\pi$
$449$	−16651.8	−1.75022	−0.875109	+	0.483926i	$0.839210\pi$
$450$	−16847.8	−1.76492
$451$	183.312	0.0191393
$452$	7777.08	0.809299
$453$	3202.68	0.332174
$454$	7298.54	0.754487
$455$	0	0
$456$	−1698.26	−0.174405
$457$	2153.93	0.220474	0.110237	−	0.993905i	$-0.464839\pi$
$457$	2153.93	0.220474	0.110237	+	0.993905i	$0.464839\pi$
$458$	−20277.9	−2.06883
$459$	−1218.26	−0.123885
$460$	3147.12	0.318989
$461$	5931.12	0.599218	0.299609	−	0.954062i	$-0.403144\pi$
$461$	5931.12	0.599218	0.299609	+	0.954062i	$0.403144\pi$
$462$	0	0
$463$	−3387.98	−0.340071	−0.170035	−	0.985438i	$-0.554388\pi$
$463$	−3387.98	−0.340071	−0.170035	+	0.985438i	$0.554388\pi$
$464$	11739.5	1.17456
$465$	9993.43	0.996633
$466$	−4474.66	−0.444816
$467$	12026.0	1.19164	0.595819	−	0.803119i	$-0.296828\pi$
$467$	12026.0	1.19164	0.595819	+	0.803119i	$0.296828\pi$
$468$	5033.83	0.497198
$469$	0	0
$470$	−2614.42	−0.256583
$471$	−6578.78	−0.643597
$472$	3561.95	0.347356
$473$	−9916.60	−0.963987
$474$	11932.6	1.15630
$475$	3117.30	0.301119
$476$	0	0
$477$	7644.47	0.733786
$478$	626.789	0.0599763
$479$	−9070.88	−0.865259	−0.432629	−	0.901572i	$-0.642414\pi$
$479$	−9070.88	−0.865259	−0.432629	+	0.901572i	$0.642414\pi$
$480$	−30399.4	−2.89070
$481$	6391.97	0.605922
$482$	−20767.1	−1.96248
$483$	0	0
$484$	−4072.08	−0.382426
$485$	−11411.3	−1.06838
$486$	−5697.99	−0.531823
$487$	−15453.3	−1.43790	−0.718949	−	0.695063i	$-0.755377\pi$
$487$	−15453.3	−1.43790	−0.718949	+	0.695063i	$0.755377\pi$
$488$	2986.65	0.277048
$489$	−1303.67	−0.120560
$490$	0	0
$491$	−540.846	−0.0497109	−0.0248554	−	0.999691i	$-0.507913\pi$
$491$	−540.846	−0.0497109	−0.0248554	+	0.999691i	$0.507913\pi$
$492$	−398.691	−0.0365333
$493$	−936.006	−0.0855083
$494$	−2061.91	−0.187793
$495$	19700.8	1.78886
$496$	5707.06	0.516642
$497$	0	0
$498$	21451.3	1.93023
$499$	−13957.7	−1.25217	−0.626083	−	0.779757i	$-0.715343\pi$
$499$	−13957.7	−1.25217	−0.626083	+	0.779757i	$0.715343\pi$
$500$	−3640.89	−0.325651
$501$	−24709.4	−2.20346
$502$	22028.9	1.95856
$503$	7277.65	0.645118	0.322559	−	0.946549i	$-0.395457\pi$
$503$	7277.65	0.645118	0.322559	+	0.946549i	$0.395457\pi$
$504$	0	0
$505$	14671.9	1.29286
$506$	−3344.79	−0.293862
$507$	17357.8	1.52049
$508$	−17875.2	−1.56119
$509$	−9896.52	−0.861798	−0.430899	−	0.902400i	$-0.641804\pi$
$509$	−9896.52	−0.861798	−0.430899	+	0.902400i	$0.641804\pi$
$510$	2864.36	0.248698
$511$	0	0
$512$	−14204.8	−1.22611
$513$	−7464.70	−0.642445
$514$	−28629.5	−2.45680
$515$	−24772.5	−2.11962
$516$	21567.9	1.84006
$517$	1255.14	0.106772
$518$	0	0
$519$	11551.9	0.977020
$520$	1181.73	0.0996580
$521$	−13444.5	−1.13054	−0.565272	−	0.824904i	$-0.691229\pi$
$521$	−13444.5	−1.13054	−0.565272	+	0.824904i	$0.691229\pi$
$522$	30996.8	2.59903
$523$	−17606.5	−1.47204	−0.736020	−	0.676959i	$-0.763297\pi$
$523$	−17606.5	−1.47204	−0.736020	+	0.676959i	$0.763297\pi$
$524$	616.609	0.0514059
$525$	0	0
$526$	18459.4	1.53017
$527$	−455.030	−0.0376118
$528$	17247.2	1.42157
$529$	−11091.9	−0.911635
$530$	−8394.04	−0.687951
$531$	33524.3	2.73979
$532$	0	0
$533$	103.490	0.00841019
$534$	14526.7	1.17722
$535$	9644.98	0.779418
$536$	1758.87	0.141738
$537$	−8118.03	−0.652363
$538$	10917.6	0.874891
$539$	0	0
$540$	−20010.8	−1.59468
$541$	−11773.9	−0.935673	−0.467836	−	0.883815i	$-0.654966\pi$
$541$	−11773.9	−0.935673	−0.467836	+	0.883815i	$0.654966\pi$
$542$	−12853.4	−1.01864
$543$	−25976.5	−2.05296
$544$	1384.17	0.109092
$545$	−8079.53	−0.635026
$546$	0	0
$547$	13048.5	1.01995	0.509976	−	0.860189i	$-0.329654\pi$
$547$	13048.5	1.01995	0.509976	+	0.860189i	$0.329654\pi$
$548$	8332.60	0.649546
$549$	28109.7	2.18523
$550$	−8881.49	−0.688560
$551$	−5735.24	−0.443429
$552$	−1555.28	−0.119922
$553$	0	0
$554$	−28648.4	−2.19703
$555$	−54408.2	−4.16126
$556$	2701.16	0.206033
$557$	−17474.3	−1.32928	−0.664639	−	0.747165i	$-0.731415\pi$
$557$	−17474.3	−1.32928	−0.664639	+	0.747165i	$0.731415\pi$
$558$	15068.8	1.14321
$559$	−5598.45	−0.423594
$560$	0	0
$561$	−1375.14	−0.103491
$562$	26654.5	2.00063
$563$	−4414.12	−0.330431	−0.165216	−	0.986257i	$-0.552832\pi$
$563$	−4414.12	−0.330431	−0.165216	+	0.986257i	$0.552832\pi$
$564$	−2729.84	−0.203807
$565$	17183.3	1.27948
$566$	1867.68	0.138700
$567$	0	0
$568$	1892.00	0.139765
$569$	23356.4	1.72083	0.860415	−	0.509594i	$-0.170204\pi$
$569$	23356.4	1.72083	0.860415	+	0.509594i	$0.170204\pi$
$570$	17550.9	1.28970
$571$	−577.932	−0.0423567	−0.0211784	−	0.999776i	$-0.506742\pi$
$571$	−577.932	−0.0423567	−0.0211784	+	0.999776i	$0.506742\pi$
$572$	2653.64	0.193976
$573$	841.198	0.0613290
$574$	0	0
$575$	2854.84	0.207052
$576$	−16137.3	−1.16734
$577$	19314.3	1.39352	0.696762	−	0.717302i	$-0.254623\pi$
$577$	19314.3	1.39352	0.696762	+	0.717302i	$0.254623\pi$
$578$	18636.3	1.34112
$579$	−8443.41	−0.606039
$580$	−15374.6	−1.10068
$581$	0	0
$582$	−26377.7	−1.87868
$583$	4029.86	0.286277
$584$	1201.76	0.0851526
$585$	11122.2	0.786059
$586$	−4772.43	−0.336429
$587$	−138.263	−0.00972185	−0.00486093	−	0.999988i	$-0.501547\pi$
$587$	−138.263	−0.00972185	−0.00486093	+	0.999988i	$0.501547\pi$
$588$	0	0
$589$	−2788.13	−0.195048
$590$	−36811.5	−2.56865
$591$	−40164.3	−2.79550
$592$	−31071.5	−2.15715
$593$	7388.43	0.511646	0.255823	−	0.966724i	$-0.417654\pi$
$593$	7388.43	0.511646	0.255823	+	0.966724i	$0.417654\pi$
$594$	21267.7	1.46906
$595$	0	0
$596$	−4731.32	−0.325172
$597$	42330.0	2.90193
$598$	−1888.31	−0.129129
$599$	1453.08	0.0991175	0.0495587	−	0.998771i	$-0.484219\pi$
$599$	1453.08	0.0991175	0.0495587	+	0.998771i	$0.484219\pi$
$600$	−4129.76	−0.280995
$601$	16144.3	1.09574	0.547870	−	0.836564i	$-0.315439\pi$
$601$	16144.3	1.09574	0.547870	+	0.836564i	$0.315439\pi$
$602$	0	0
$603$	16554.1	1.11797
$604$	−2395.32	−0.161365
$605$	−8997.18	−0.604607
$606$	33914.7	2.27342
$607$	6997.24	0.467890	0.233945	−	0.972250i	$-0.424836\pi$
$607$	6997.24	0.467890	0.233945	+	0.972250i	$0.424836\pi$
$608$	8481.31	0.565728
$609$	0	0
$610$	−30866.0	−2.04873
$611$	708.595	0.0469177
$612$	1950.99	0.128863
$613$	3306.98	0.217892	0.108946	−	0.994048i	$-0.465252\pi$
$613$	3306.98	0.217892	0.108946	+	0.994048i	$0.465252\pi$
$614$	−19106.1	−1.25580
$615$	−880.900	−0.0577582
$616$	0	0
$617$	2081.45	0.135812	0.0679062	−	0.997692i	$-0.478368\pi$
$617$	2081.45	0.135812	0.0679062	+	0.997692i	$0.478368\pi$
$618$	−57262.4	−3.72724
$619$	−27667.8	−1.79655	−0.898275	−	0.439433i	$-0.855179\pi$
$619$	−27667.8	−1.79655	−0.898275	+	0.439433i	$0.855179\pi$
$620$	−7474.21	−0.484147
$621$	−6836.21	−0.441751
$622$	33064.1	2.13143
$623$	0	0
$624$	9736.96	0.624664
$625$	−18927.8	−1.21138
$626$	3875.68	0.247450
$627$	−8425.96	−0.536683
$628$	4920.35	0.312649
$629$	2477.37	0.157041
$630$	0	0
$631$	−25752.5	−1.62471	−0.812355	−	0.583163i	$-0.801815\pi$
$631$	−25752.5	−1.62471	−0.812355	+	0.583163i	$0.801815\pi$
$632$	1908.02	0.120090
$633$	46359.5	2.91094
$634$	10320.9	0.646522
$635$	−39495.0	−2.46820
$636$	−8764.64	−0.546447
$637$	0	0
$638$	16340.3	1.01398
$639$	17807.1	1.10241
$640$	−9877.28	−0.610053
$641$	−22980.4	−1.41602	−0.708011	−	0.706202i	$-0.750407\pi$
$641$	−22980.4	−1.41602	−0.708011	+	0.706202i	$0.750407\pi$
$642$	22294.7	1.37056
$643$	−6493.95	−0.398283	−0.199142	−	0.979971i	$-0.563815\pi$
$643$	−6493.95	−0.398283	−0.199142	+	0.979971i	$0.563815\pi$
$644$	0	0
$645$	47653.8	2.90910
$646$	−799.146	−0.0486718
$647$	−22379.8	−1.35988	−0.679940	−	0.733268i	$-0.737994\pi$
$647$	−22379.8	−1.35988	−0.679940	+	0.733268i	$0.737994\pi$
$648$	2527.11	0.153201
$649$	17672.7	1.06890
$650$	−5014.08	−0.302566
$651$	0	0
$652$	975.032	0.0585662
$653$	13008.7	0.779585	0.389793	−	0.920903i	$-0.372547\pi$
$653$	13008.7	0.779585	0.389793	+	0.920903i	$0.372547\pi$
$654$	−18676.1	−1.11666
$655$	1362.39	0.0812716
$656$	−503.065	−0.0299412
$657$	11310.7	0.671646
$658$	0	0
$659$	14524.9	0.858588	0.429294	−	0.903165i	$-0.358762\pi$
$659$	14524.9	0.858588	0.429294	+	0.903165i	$0.358762\pi$
$660$	−22587.7	−1.33216
$661$	−11479.8	−0.675508	−0.337754	−	0.941234i	$-0.609667\pi$
$661$	−11479.8	−0.675508	−0.337754	+	0.941234i	$0.609667\pi$
$662$	27642.9	1.62292
$663$	−776.339	−0.0454759
$664$	3430.03	0.200469
$665$	0	0
$666$	−82040.4	−4.77328
$667$	−5252.37	−0.304906
$668$	18480.4	1.07040
$669$	−1367.02	−0.0790013
$670$	−18177.3	−1.04813
$671$	14818.3	0.852542
$672$	0	0
$673$	−9643.44	−0.552344	−0.276172	−	0.961108i	$-0.589066\pi$
$673$	−9643.44	−0.552344	−0.276172	+	0.961108i	$0.589066\pi$
$674$	22101.5	1.26308
$675$	−18152.3	−1.03509
$676$	−12982.1	−0.738627
$677$	−27255.1	−1.54726	−0.773632	−	0.633635i	$-0.781562\pi$
$677$	−27255.1	−1.54726	−0.773632	+	0.633635i	$0.781562\pi$
$678$	39719.8	2.24990
$679$	0	0
$680$	458.008	0.0258291
$681$	16838.0	0.947477
$682$	7943.67	0.446010
$683$	11025.1	0.617660	0.308830	−	0.951117i	$-0.400063\pi$
$683$	11025.1	0.617660	0.308830	+	0.951117i	$0.400063\pi$
$684$	11954.4	0.668256
$685$	18410.7	1.02692
$686$	0	0
$687$	−46781.8	−2.59802
$688$	27214.2	1.50804
$689$	2275.07	0.125796
$690$	16073.2	0.886809
$691$	33688.5	1.85466	0.927330	−	0.374245i	$-0.122098\pi$
$691$	33688.5	1.85466	0.927330	+	0.374245i	$0.122098\pi$
$692$	−8639.82	−0.474620
$693$	0	0
$694$	36296.8	1.98531
$695$	5968.16	0.325734
$696$	7597.99	0.413794
$697$	40.1100	0.00217973
$698$	−14674.7	−0.795769
$699$	−10323.2	−0.558596
$700$	0	0
$701$	−6022.37	−0.324482	−0.162241	−	0.986751i	$-0.551872\pi$
$701$	−6022.37	−0.324482	−0.162241	+	0.986751i	$0.551872\pi$
$702$	12006.7	0.645534
$703$	15179.7	0.814385
$704$	−8506.92	−0.455421
$705$	−6031.54	−0.322214
$706$	−12667.5	−0.675282
$707$	0	0
$708$	−38436.7	−2.04031
$709$	34919.8	1.84971	0.924853	−	0.380324i	$-0.124188\pi$
$709$	34919.8	1.84971	0.924853	+	0.380324i	$0.124188\pi$
$710$	−19553.2	−1.03355
$711$	17957.8	0.947217
$712$	2322.81	0.122263
$713$	−2553.39	−0.134117
$714$	0	0
$715$	5863.16	0.306671
$716$	6071.57	0.316907
$717$	1446.02	0.0753176
$718$	3570.18	0.185568
$719$	−18882.1	−0.979393	−0.489696	−	0.871893i	$-0.662892\pi$
$719$	−18882.1	−0.979393	−0.489696	+	0.871893i	$0.662892\pi$
$720$	−54065.1	−2.79845
$721$	0	0
$722$	21303.4	1.09810
$723$	−47910.4	−2.46446
$724$	19428.1	0.997293
$725$	−13946.7	−0.714438
$726$	−20797.3	−1.06317
$727$	−5549.58	−0.283112	−0.141556	−	0.989930i	$-0.545211\pi$
$727$	−5549.58	−0.283112	−0.141556	+	0.989930i	$0.545211\pi$
$728$	0	0
$729$	−25822.2	−1.31190
$730$	−12419.7	−0.629692
$731$	−2169.82	−0.109786
$732$	−32228.8	−1.62733
$733$	27238.5	1.37254	0.686272	−	0.727345i	$-0.259246\pi$
$733$	27238.5	1.37254	0.686272	+	0.727345i	$0.259246\pi$
$734$	−30496.8	−1.53359
$735$	0	0
$736$	7767.23	0.389000
$737$	8726.65	0.436161
$738$	−1328.28	−0.0662530
$739$	−35022.9	−1.74335	−0.871677	−	0.490081i	$-0.836967\pi$
$739$	−35022.9	−1.74335	−0.871677	+	0.490081i	$0.836967\pi$
$740$	40692.5	2.02147
$741$	−4756.90	−0.235829
$742$	0	0
$743$	−30866.6	−1.52407	−0.762035	−	0.647536i	$-0.775800\pi$
$743$	−30866.6	−1.52407	−0.762035	+	0.647536i	$0.775800\pi$
$744$	3693.69	0.182012
$745$	−10453.8	−0.514089
$746$	−23285.5	−1.14282
$747$	32282.7	1.58121
$748$	1028.48	0.0502741
$749$	0	0
$750$	−18595.1	−0.905330
$751$	−2422.93	−0.117728	−0.0588642	−	0.998266i	$-0.518748\pi$
$751$	−2422.93	−0.117728	−0.0588642	+	0.998266i	$0.518748\pi$
$752$	−3444.50	−0.167032
$753$	50821.4	2.45954
$754$	9224.96	0.445561
$755$	−5292.42	−0.255114
$756$	0	0
$757$	19538.4	0.938092	0.469046	−	0.883174i	$-0.344598\pi$
$757$	19538.4	0.938092	0.469046	+	0.883174i	$0.344598\pi$
$758$	−11745.6	−0.562822
$759$	−7716.54	−0.369029
$760$	2806.38	0.133945
$761$	16835.8	0.801967	0.400983	−	0.916085i	$-0.368668\pi$
$761$	16835.8	0.801967	0.400983	+	0.916085i	$0.368668\pi$
$762$	−91293.9	−4.34020
$763$	0	0
$764$	−629.142	−0.0297926
$765$	4310.67	0.203729
$766$	−32333.4	−1.52514
$767$	9977.17	0.469693
$768$	−45289.2	−2.12791
$769$	−5556.48	−0.260562	−0.130281	−	0.991477i	$-0.541588\pi$
$769$	−5556.48	−0.260562	−0.130281	+	0.991477i	$0.541588\pi$
$770$	0	0
$771$	−66049.2	−3.08522
$772$	6314.93	0.294403
$773$	−140.894	−0.00655578	−0.00327789	−	0.999995i	$-0.501043\pi$
$773$	−140.894	−0.00655578	−0.00327789	+	0.999995i	$0.501043\pi$
$774$	71855.7	3.33695
$775$	−6780.06	−0.314254
$776$	−4217.76	−0.195114
$777$	0	0
$778$	12535.7	0.577669
$779$	245.768	0.0113037
$780$	−12751.9	−0.585375
$781$	9387.21	0.430091
$782$	−731.863	−0.0334672
$783$	33396.9	1.52427
$784$	0	0
$785$	10871.4	0.494290
$786$	3149.20	0.142911
$787$	2271.00	0.102862	0.0514311	−	0.998677i	$-0.483622\pi$
$787$	2271.00	0.102862	0.0514311	+	0.998677i	$0.483622\pi$
$788$	30039.3	1.35800
$789$	42586.5	1.92157
$790$	−19718.7	−0.888049
$791$	0	0
$792$	7281.65	0.326695
$793$	8365.74	0.374623
$794$	−42104.9	−1.88192
$795$	−19365.3	−0.863921
$796$	−31659.1	−1.40971
$797$	−38957.6	−1.73143	−0.865714	−	0.500539i	$-0.833135\pi$
$797$	−38957.6	−1.73143	−0.865714	+	0.500539i	$0.833135\pi$
$798$	0	0
$799$	274.634	0.0121600
$800$	20624.5	0.911482
$801$	21861.8	0.964354
$802$	−31607.5	−1.39165
$803$	5962.54	0.262034
$804$	−18979.8	−0.832545
$805$	0	0
$806$	4484.62	0.195985
$807$	25187.3	1.09868
$808$	5422.92	0.236111
$809$	−16138.1	−0.701340	−0.350670	−	0.936499i	$-0.614046\pi$
$809$	−16138.1	−0.701340	−0.350670	+	0.936499i	$0.614046\pi$
$810$	−26116.8	−1.13290
$811$	11201.8	0.485018	0.242509	−	0.970149i	$-0.422030\pi$
$811$	11201.8	0.485018	0.242509	+	0.970149i	$0.422030\pi$
$812$	0	0
$813$	−29653.2	−1.27919
$814$	−43248.5	−1.86223
$815$	2154.32	0.0925919
$816$	3773.80	0.161899
$817$	−13295.2	−0.569329
$818$	−2837.32	−0.121277
$819$	0	0
$820$	658.835	0.0280580
$821$	13583.8	0.577442	0.288721	−	0.957413i	$-0.406770\pi$
$821$	13583.8	0.577442	0.288721	+	0.957413i	$0.406770\pi$
$822$	42557.0	1.80577
$823$	32809.9	1.38965	0.694824	−	0.719180i	$-0.255482\pi$
$823$	32809.9	1.38965	0.694824	+	0.719180i	$0.255482\pi$
$824$	−9156.20	−0.387101
$825$	−20489.9	−0.864686
$826$	0	0
$827$	26678.0	1.12175	0.560874	−	0.827901i	$-0.310465\pi$
$827$	26678.0	1.12175	0.560874	+	0.827901i	$0.310465\pi$
$828$	10947.9	0.459499
$829$	34077.3	1.42769	0.713844	−	0.700305i	$-0.246953\pi$
$829$	34077.3	1.42769	0.713844	+	0.700305i	$0.246953\pi$
$830$	−35448.2	−1.48244
$831$	−66092.7	−2.75900
$832$	−4802.61	−0.200121
$833$	0	0
$834$	13795.6	0.572785
$835$	40832.2	1.69228
$836$	6301.88	0.260712
$837$	16235.6	0.670470
$838$	7391.16	0.304682
$839$	40636.3	1.67213	0.836067	−	0.548628i	$-0.184850\pi$
$839$	40636.3	1.67213	0.836067	+	0.548628i	$0.184850\pi$
$840$	0	0
$841$	1270.33	0.0520862
$842$	22253.7	0.910825
$843$	61492.8	2.51237
$844$	−34672.9	−1.41409
$845$	−28683.7	−1.16775
$846$	−9094.77	−0.369604
$847$	0	0
$848$	−11059.2	−0.447846
$849$	4308.80	0.174178
$850$	−1943.33	−0.0784184
$851$	13901.6	0.559979
$852$	−20416.5	−0.820959
$853$	22772.2	0.914073	0.457036	−	0.889448i	$-0.348911\pi$
$853$	22772.2	0.914073	0.457036	+	0.889448i	$0.348911\pi$
$854$	0	0
$855$	26413.0	1.05650
$856$	3564.90	0.142343
$857$	9716.24	0.387282	0.193641	−	0.981072i	$-0.437970\pi$
$857$	9716.24	0.387282	0.193641	+	0.981072i	$0.437970\pi$
$858$	13552.9	0.539264
$859$	12271.1	0.487411	0.243706	−	0.969849i	$-0.421637\pi$
$859$	12271.1	0.487411	0.243706	+	0.969849i	$0.421637\pi$
$860$	−35640.8	−1.41319
$861$	0	0
$862$	−60237.1	−2.38014
$863$	−6213.88	−0.245102	−0.122551	−	0.992462i	$-0.539107\pi$
$863$	−6213.88	−0.245102	−0.122551	+	0.992462i	$0.539107\pi$
$864$	−49387.5	−1.94467
$865$	−19089.5	−0.750363
$866$	−41272.4	−1.61951
$867$	42994.5	1.68416
$868$	0	0
$869$	9466.66	0.369545
$870$	−78522.5	−3.05996
$871$	4926.66	0.191657
$872$	−2986.29	−0.115973
$873$	−39696.6	−1.53898
$874$	−4484.38	−0.173554
$875$	0	0
$876$	−12968.1	−0.500172
$877$	31162.8	1.19988	0.599939	−	0.800046i	$-0.295191\pi$
$877$	31162.8	1.19988	0.599939	+	0.800046i	$0.295191\pi$
$878$	−39175.2	−1.50581
$879$	−11010.2	−0.422484
$880$	−28501.0	−1.09178
$881$	24246.7	0.927234	0.463617	−	0.886036i	$-0.346551\pi$
$881$	24246.7	0.927234	0.463617	+	0.886036i	$0.346551\pi$
$882$	0	0
$883$	28950.5	1.10335	0.551677	−	0.834058i	$-0.313988\pi$
$883$	28950.5	1.10335	0.551677	+	0.834058i	$0.313988\pi$
$884$	580.633	0.0220914
$885$	−84925.3	−3.22569
$886$	−51972.0	−1.97069
$887$	11425.1	0.432489	0.216245	−	0.976339i	$-0.430619\pi$
$887$	11425.1	0.432489	0.216245	+	0.976339i	$0.430619\pi$
$888$	−20109.9	−0.759959
$889$	0	0
$890$	−24005.4	−0.904116
$891$	12538.3	0.471436
$892$	1022.41	0.0383775
$893$	1682.78	0.0630594
$894$	−24164.2	−0.903996
$895$	13415.0	0.501022
$896$	0	0
$897$	−4356.40	−0.162158
$898$	63606.7	2.36368
$899$	12474.0	0.462772
$900$	29070.1	1.07667
$901$	881.760	0.0326034
$902$	−700.218	−0.0258478
$903$	0	0
$904$	6351.15	0.233668
$905$	42926.1	1.57670
$906$	−12233.6	−0.448603
$907$	−5525.48	−0.202283	−0.101141	−	0.994872i	$-0.532249\pi$
$907$	−5525.48	−0.202283	−0.101141	+	0.994872i	$0.532249\pi$
$908$	−12593.3	−0.460268
$909$	51039.3	1.86234
$910$	0	0
$911$	−25935.4	−0.943226	−0.471613	−	0.881806i	$-0.656328\pi$
$911$	−25935.4	−0.943226	−0.471613	+	0.881806i	$0.656328\pi$
$912$	23123.4	0.839575
$913$	17018.2	0.616889
$914$	−8227.59	−0.297751
$915$	−71208.9	−2.57278
$916$	34988.7	1.26207
$917$	0	0
$918$	4653.51	0.167308
$919$	−16601.3	−0.595895	−0.297948	−	0.954582i	$-0.596302\pi$
$919$	−16601.3	−0.595895	−0.297948	+	0.954582i	$0.596302\pi$
$920$	2570.09	0.0921016
$921$	−44078.4	−1.57702
$922$	−22655.7	−0.809247
$923$	5299.58	0.188990
$924$	0	0
$925$	36913.3	1.31211
$926$	12941.4	0.459267
$927$	−86176.1	−3.05328
$928$	−37945.2	−1.34225
$929$	−8856.50	−0.312780	−0.156390	−	0.987695i	$-0.549986\pi$
$929$	−8856.50	−0.312780	−0.156390	+	0.987695i	$0.549986\pi$
$930$	−38172.9	−1.34596
$931$	0	0
$932$	7720.83	0.271356
$933$	76280.0	2.67663
$934$	−45936.8	−1.60931
$935$	2272.41	0.0794822
$936$	4110.88	0.143556
$937$	−7855.34	−0.273877	−0.136938	−	0.990580i	$-0.543726\pi$
$937$	−7855.34	−0.273877	−0.136938	+	0.990580i	$0.543726\pi$
$938$	0	0
$939$	8941.32	0.310744
$940$	4511.06	0.156526
$941$	41921.7	1.45229	0.726146	−	0.687540i	$-0.241309\pi$
$941$	41921.7	1.45229	0.726146	+	0.687540i	$0.241309\pi$
$942$	25129.7	0.869181
$943$	225.076	0.00777250
$944$	−48499.2	−1.67216
$945$	0	0
$946$	37879.5	1.30187
$947$	1246.38	0.0427688	0.0213844	−	0.999771i	$-0.493193\pi$
$947$	1246.38	0.0427688	0.0213844	+	0.999771i	$0.493193\pi$
$948$	−20589.3	−0.705388
$949$	3366.17	0.115143
$950$	−11907.5	−0.406662
$951$	23810.6	0.811896
$952$	0	0
$953$	29916.7	1.01689	0.508446	−	0.861094i	$-0.330220\pi$
$953$	29916.7	1.01689	0.508446	+	0.861094i	$0.330220\pi$
$954$	−29200.4	−0.990982
$955$	−1390.08	−0.0471014
$956$	−1081.50	−0.0365880
$957$	37697.5	1.27334
$958$	34649.0	1.16854
$959$	0	0
$960$	40879.6	1.37436
$961$	−23726.9	−0.796444
$962$	−24416.1	−0.818301
$963$	33552.0	1.12274
$964$	35832.7	1.19719
$965$	13952.7	0.465445
$966$	0	0
$967$	26866.7	0.893459	0.446729	−	0.894669i	$-0.352589\pi$
$967$	26866.7	0.893459	0.446729	+	0.894669i	$0.352589\pi$
$968$	−3325.46	−0.110418
$969$	−1843.66	−0.0611215
$970$	43589.1	1.44285
$971$	24344.8	0.804595	0.402297	−	0.915509i	$-0.368212\pi$
$971$	24344.8	0.804595	0.402297	+	0.915509i	$0.368212\pi$
$972$	9831.64	0.324434
$973$	0	0
$974$	59028.6	1.94189
$975$	−11567.6	−0.379960
$976$	−40666.0	−1.33370
$977$	33267.7	1.08938	0.544692	−	0.838636i	$-0.316647\pi$
$977$	33267.7	1.08938	0.544692	+	0.838636i	$0.316647\pi$
$978$	4979.77	0.162818
$979$	11524.7	0.376230
$980$	0	0
$981$	−28106.3	−0.914744
$982$	2065.93	0.0671348
$983$	57659.4	1.87085	0.935427	−	0.353520i	$-0.115015\pi$
$983$	57659.4	1.87085	0.935427	+	0.353520i	$0.115015\pi$
$984$	−325.591	−0.0105482
$985$	66371.4	2.14697
$986$	3575.36	0.115479
$987$	0	0
$988$	3557.74	0.114562
$989$	−12175.9	−0.391476
$990$	−75253.3	−2.41586
$991$	−12444.7	−0.398910	−0.199455	−	0.979907i	$-0.563917\pi$
$991$	−12444.7	−0.398910	−0.199455	+	0.979907i	$0.563917\pi$
$992$	−18446.7	−0.590406
$993$	63773.0	2.03804
$994$	0	0
$995$	−69950.3	−2.22872
$996$	−37013.2	−1.17752
$997$	−3553.90	−0.112892	−0.0564460	−	0.998406i	$-0.517977\pi$
$997$	−3553.90	−0.112892	−0.0564460	+	0.998406i	$0.517977\pi$
$998$	53315.5	1.69106
$999$	−88392.8	−2.79942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.7	yes	35
7.6	odd	2		2303.4.a.g.1.7	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.7	✓	35	7.6	odd	2
2303.4.a.h.1.7	yes	35	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)

\(f(q)\)	\(=\)	\(q-3.81980 q^{2} -8.81241 q^{3} +6.59091 q^{4} +14.5625 q^{5} +33.6617 q^{6} +5.38246 q^{8} +50.6586 q^{9} +O(q^{10})\)	\(q-3.81980 q^{2} -8.81241 q^{3} +6.59091 q^{4} +14.5625 q^{5} +33.6617 q^{6} +5.38246 q^{8} +50.6586 q^{9} -55.6259 q^{10} +26.7052 q^{11} -58.0818 q^{12} +15.0765 q^{13} -128.331 q^{15} -73.2872 q^{16} +5.84327 q^{17} -193.506 q^{18} +35.8038 q^{19} +95.9800 q^{20} -102.009 q^{22} +32.7893 q^{23} -47.4325 q^{24} +87.0661 q^{25} -57.5893 q^{26} -208.489 q^{27} -160.185 q^{29} +490.198 q^{30} -77.8725 q^{31} +236.883 q^{32} -235.337 q^{33} -22.3202 q^{34} +333.886 q^{36} +423.969 q^{37} -136.764 q^{38} -132.860 q^{39} +78.3821 q^{40} +6.86430 q^{41} -371.336 q^{43} +176.011 q^{44} +737.715 q^{45} -125.249 q^{46} +47.0000 q^{47} +645.837 q^{48} -332.576 q^{50} -51.4933 q^{51} +99.3678 q^{52} +150.902 q^{53} +796.387 q^{54} +388.894 q^{55} -315.518 q^{57} +611.877 q^{58} +661.770 q^{59} -845.815 q^{60} +554.886 q^{61} +297.458 q^{62} -318.549 q^{64} +219.551 q^{65} +898.942 q^{66} +326.777 q^{67} +38.5125 q^{68} -288.953 q^{69} +351.513 q^{71} +272.668 q^{72} +223.273 q^{73} -1619.48 q^{74} -767.262 q^{75} +235.979 q^{76} +507.500 q^{78} +354.488 q^{79} -1067.24 q^{80} +469.509 q^{81} -26.2203 q^{82} +637.261 q^{83} +85.0926 q^{85} +1418.43 q^{86} +1411.62 q^{87} +143.740 q^{88} +431.551 q^{89} -2817.93 q^{90} +216.111 q^{92} +686.245 q^{93} -179.531 q^{94} +521.392 q^{95} -2087.51 q^{96} -783.612 q^{97} +1352.85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

Modular forms

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Database

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