LMFDB - Embedded newform 2303.4.a.h.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.67304 q^{2} -8.29020 q^{3} -5.20094 q^{4} +3.53349 q^{5} +13.8698 q^{6} +22.0857 q^{8} +41.7274 q^{9} +O(q^{10})$	\(q-1.67304 q^{2} -8.29020 q^{3} -5.20094 q^{4} +3.53349 q^{5} +13.8698 q^{6} +22.0857 q^{8} +41.7274 q^{9} -5.91167 q^{10} -44.0944 q^{11} +43.1168 q^{12} -48.8892 q^{13} -29.2934 q^{15} +4.65731 q^{16} -65.5376 q^{17} -69.8116 q^{18} +16.8759 q^{19} -18.3775 q^{20} +73.7716 q^{22} +10.1138 q^{23} -183.095 q^{24} -112.514 q^{25} +81.7936 q^{26} -122.093 q^{27} -107.909 q^{29} +49.0090 q^{30} +98.8608 q^{31} -184.477 q^{32} +365.551 q^{33} +109.647 q^{34} -217.022 q^{36} -68.8163 q^{37} -28.2340 q^{38} +405.301 q^{39} +78.0397 q^{40} +224.820 q^{41} +126.620 q^{43} +229.332 q^{44} +147.444 q^{45} -16.9207 q^{46} +47.0000 q^{47} -38.6101 q^{48} +188.241 q^{50} +543.320 q^{51} +254.270 q^{52} +164.575 q^{53} +204.267 q^{54} -155.807 q^{55} -139.904 q^{57} +180.535 q^{58} -159.239 q^{59} +152.353 q^{60} -686.360 q^{61} -165.398 q^{62} +271.379 q^{64} -172.750 q^{65} -611.581 q^{66} -894.405 q^{67} +340.857 q^{68} -83.8453 q^{69} -1046.74 q^{71} +921.579 q^{72} +303.579 q^{73} +115.132 q^{74} +932.767 q^{75} -87.7703 q^{76} -678.085 q^{78} +444.430 q^{79} +16.4566 q^{80} -114.463 q^{81} -376.133 q^{82} -1247.24 q^{83} -231.577 q^{85} -211.841 q^{86} +894.584 q^{87} -973.854 q^{88} -1207.58 q^{89} -246.679 q^{90} -52.6012 q^{92} -819.576 q^{93} -78.6328 q^{94} +59.6308 q^{95} +1529.35 q^{96} -167.597 q^{97} -1839.94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.67304	−0.591509	−0.295754	−	0.955264i	$-0.595571\pi$
$2$	−1.67304	−0.591509	−0.295754	+	0.955264i	$0.595571\pi$
$3$	−8.29020	−1.59545	−0.797725	−	0.603022i	$-0.793963\pi$
$3$	−8.29020	−1.59545	−0.797725	+	0.603022i	$0.793963\pi$
$4$	−5.20094	−0.650118
$5$	3.53349	0.316045	0.158023	−	0.987435i	$-0.449488\pi$
$5$	3.53349	0.316045	0.158023	+	0.987435i	$0.449488\pi$
$6$	13.8698	0.943722
$7$	0	0
$7$	0	0
$8$	22.0857	0.976059
$9$	41.7274	1.54546
$10$	−5.91167	−0.186944
$11$	−44.0944	−1.20863	−0.604316	−	0.796745i	$-0.706553\pi$
$11$	−44.0944	−1.20863	−0.604316	+	0.796745i	$0.706553\pi$
$12$	43.1168	1.03723
$13$	−48.8892	−1.04303	−0.521517	−	0.853241i	$-0.674634\pi$
$13$	−48.8892	−1.04303	−0.521517	+	0.853241i	$0.674634\pi$
$14$	0	0
$15$	−29.2934	−0.504235
$16$	4.65731	0.0727705
$17$	−65.5376	−0.935012	−0.467506	−	0.883990i	$-0.654847\pi$
$17$	−65.5376	−0.935012	−0.467506	+	0.883990i	$0.654847\pi$
$18$	−69.8116	−0.914153
$19$	16.8759	0.203768	0.101884	−	0.994796i	$-0.467513\pi$
$19$	16.8759	0.203768	0.101884	+	0.994796i	$0.467513\pi$
$20$	−18.3775	−0.205467
$21$	0	0
$22$	73.7716	0.714916
$23$	10.1138	0.0916900	0.0458450	−	0.998949i	$-0.485402\pi$
$23$	10.1138	0.0916900	0.0458450	+	0.998949i	$0.485402\pi$
$24$	−183.095	−1.55725
$25$	−112.514	−0.900115
$26$	81.7936	0.616963
$27$	−122.093	−0.870253
$28$	0	0
$29$	−107.909	−0.690970	−0.345485	−	0.938424i	$-0.612286\pi$
$29$	−107.909	−0.690970	−0.345485	+	0.938424i	$0.612286\pi$
$30$	49.0090	0.298259
$31$	98.8608	0.572772	0.286386	−	0.958114i	$-0.407546\pi$
$31$	98.8608	0.572772	0.286386	+	0.958114i	$0.407546\pi$
$32$	−184.477	−1.01910
$33$	365.551	1.92831
$34$	109.647	0.553068
$35$	0	0
$36$	−217.022	−1.00473
$37$	−68.8163	−0.305766	−0.152883	−	0.988244i	$-0.548856\pi$
$37$	−68.8163	−0.305766	−0.152883	+	0.988244i	$0.548856\pi$
$38$	−28.2340	−0.120530
$39$	405.301	1.66411
$40$	78.0397	0.308479
$41$	224.820	0.856367	0.428184	−	0.903692i	$-0.359154\pi$
$41$	224.820	0.856367	0.428184	+	0.903692i	$0.359154\pi$
$42$	0	0
$43$	126.620	0.449056	0.224528	−	0.974468i	$-0.427916\pi$
$43$	126.620	0.449056	0.224528	+	0.974468i	$0.427916\pi$
$44$	229.332	0.785753
$45$	147.444	0.488435
$46$	−16.9207	−0.0542354
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−38.6101	−0.116102
$49$	0	0
$50$	188.241	0.532426
$51$	543.320	1.49177
$52$	254.270	0.678094
$53$	164.575	0.426530	0.213265	−	0.976994i	$-0.431590\pi$
$53$	164.575	0.426530	0.213265	+	0.976994i	$0.431590\pi$
$54$	204.267	0.514762
$55$	−155.807	−0.381983
$56$	0	0
$57$	−139.904	−0.325101
$58$	180.535	0.408715
$59$	−159.239	−0.351375	−0.175687	−	0.984446i	$-0.556215\pi$
$59$	−159.239	−0.351375	−0.175687	+	0.984446i	$0.556215\pi$
$60$	152.353	0.327812
$61$	−686.360	−1.44065	−0.720323	−	0.693639i	$-0.756006\pi$
$61$	−686.360	−1.44065	−0.720323	+	0.693639i	$0.756006\pi$
$62$	−165.398	−0.338799
$63$	0	0
$64$	271.379	0.530038
$65$	−172.750	−0.329646
$66$	−611.581	−1.14061
$67$	−894.405	−1.63088	−0.815440	−	0.578842i	$-0.803505\pi$
$67$	−894.405	−1.63088	−0.815440	+	0.578842i	$0.803505\pi$
$68$	340.857	0.607868
$69$	−83.8453	−0.146287
$70$	0	0
$71$	−1046.74	−1.74966	−0.874828	−	0.484434i	$-0.839025\pi$
$71$	−1046.74	−1.74966	−0.874828	+	0.484434i	$0.839025\pi$
$72$	921.579	1.50846
$73$	303.579	0.486730	0.243365	−	0.969935i	$-0.421749\pi$
$73$	303.579	0.486730	0.243365	+	0.969935i	$0.421749\pi$
$74$	115.132	0.180863
$75$	932.767	1.43609
$76$	−87.7703	−0.132473
$77$	0	0
$78$	−678.085	−0.984333
$79$	444.430	0.632940	0.316470	−	0.948603i	$-0.397502\pi$
$79$	444.430	0.632940	0.316470	+	0.948603i	$0.397502\pi$
$80$	16.4566	0.0229988
$81$	−114.463	−0.157014
$82$	−376.133	−0.506548
$83$	−1247.24	−1.64942	−0.824710	−	0.565556i	$-0.808662\pi$
$83$	−1247.24	−1.64942	−0.824710	+	0.565556i	$0.808662\pi$
$84$	0	0
$85$	−231.577	−0.295506
$86$	−211.841	−0.265621
$87$	894.584	1.10241
$88$	−973.854	−1.17970
$89$	−1207.58	−1.43824	−0.719118	−	0.694888i	$-0.755454\pi$
$89$	−1207.58	−1.43824	−0.719118	+	0.694888i	$0.755454\pi$
$90$	−246.679	−0.288914
$91$	0	0
$92$	−52.6012	−0.0596093
$93$	−819.576	−0.913828
$94$	−78.6328	−0.0862804
$95$	59.6308	0.0643999
$96$	1529.35	1.62593
$97$	−167.597	−0.175431	−0.0877157	−	0.996146i	$-0.527957\pi$
$97$	−167.597	−0.175431	−0.0877157	+	0.996146i	$0.527957\pi$
$98$	0	0
$99$	−1839.94	−1.86789
$100$	585.181	0.585181
$101$	446.196	0.439586	0.219793	−	0.975547i	$-0.429462\pi$
$101$	446.196	0.439586	0.219793	+	0.975547i	$0.429462\pi$
$102$	−908.996	−0.882392
$103$	−135.753	−0.129866	−0.0649328	−	0.997890i	$-0.520683\pi$
$103$	−135.753	−0.129866	−0.0649328	+	0.997890i	$0.520683\pi$
$104$	−1079.75	−1.01806
$105$	0	0
$106$	−275.340	−0.252296
$107$	73.2449	0.0661762	0.0330881	−	0.999452i	$-0.489466\pi$
$107$	73.2449	0.0661762	0.0330881	+	0.999452i	$0.489466\pi$
$108$	634.999	0.565767
$109$	−87.2962	−0.0767106	−0.0383553	−	0.999264i	$-0.512212\pi$
$109$	−87.2962	−0.0767106	−0.0383553	+	0.999264i	$0.512212\pi$
$110$	260.671	0.225946
$111$	570.501	0.487834
$112$	0	0
$113$	−44.5416	−0.0370807	−0.0185403	−	0.999828i	$-0.505902\pi$
$113$	−44.5416	−0.0370807	−0.0185403	+	0.999828i	$0.505902\pi$
$114$	234.065	0.192300
$115$	35.7370	0.0289782
$116$	561.226	0.449212
$117$	−2040.02	−1.61197
$118$	266.412	0.207841
$119$	0	0
$120$	−646.964	−0.492163
$121$	613.312	0.460791
$122$	1148.31	0.852154
$123$	−1863.81	−1.36629
$124$	−514.169	−0.372369
$125$	−839.256	−0.600523
$126$	0	0
$127$	−851.653	−0.595055	−0.297527	−	0.954713i	$-0.596162\pi$
$127$	−851.653	−0.595055	−0.297527	+	0.954713i	$0.596162\pi$
$128$	1021.79	0.705581
$129$	−1049.71	−0.716447
$130$	289.017	0.194988
$131$	−2538.72	−1.69320	−0.846601	−	0.532229i	$-0.821355\pi$
$131$	−2538.72	−1.69320	−0.846601	+	0.532229i	$0.821355\pi$
$132$	−1901.21	−1.25363
$133$	0	0
$134$	1496.37	0.964679
$135$	−431.416	−0.275040
$136$	−1447.44	−0.912627
$137$	−2402.39	−1.49817	−0.749087	−	0.662472i	$-0.769507\pi$
$137$	−2402.39	−1.49817	−0.749087	+	0.662472i	$0.769507\pi$
$138$	140.276	0.0865298
$139$	110.428	0.0673837	0.0336919	−	0.999432i	$-0.489274\pi$
$139$	110.428	0.0673837	0.0336919	+	0.999432i	$0.489274\pi$
$140$	0	0
$141$	−389.639	−0.232720
$142$	1751.24	1.03494
$143$	2155.74	1.26064
$144$	194.338	0.112464
$145$	−381.295	−0.218378
$146$	−507.900	−0.287905
$147$	0	0
$148$	357.910	0.198784
$149$	−940.060	−0.516864	−0.258432	−	0.966029i	$-0.583206\pi$
$149$	−940.060	−0.516864	−0.258432	+	0.966029i	$0.583206\pi$
$150$	−1560.56	−0.849459
$151$	−2454.65	−1.32289	−0.661446	−	0.749993i	$-0.730057\pi$
$151$	−2454.65	−1.32289	−0.661446	+	0.749993i	$0.730057\pi$
$152$	372.715	0.198889
$153$	−2734.72	−1.44502
$154$	0	0
$155$	349.324	0.181022
$156$	−2107.95	−1.08187
$157$	352.610	0.179244	0.0896221	−	0.995976i	$-0.471434\pi$
$157$	352.610	0.179244	0.0896221	+	0.995976i	$0.471434\pi$
$158$	−743.548	−0.374389
$159$	−1364.36	−0.680507
$160$	−651.850	−0.322083
$161$	0	0
$162$	191.502	0.0928752
$163$	−3711.30	−1.78338	−0.891692	−	0.452643i	$-0.850481\pi$
$163$	−3711.30	−1.78338	−0.891692	+	0.452643i	$0.850481\pi$
$164$	−1169.28	−0.556739
$165$	1291.67	0.609434
$166$	2086.67	0.975646
$167$	2392.35	1.10853	0.554267	−	0.832339i	$-0.312999\pi$
$167$	2392.35	1.10853	0.554267	+	0.832339i	$0.312999\pi$
$168$	0	0
$169$	193.156	0.0879179
$170$	387.437	0.174795
$171$	704.186	0.314915
$172$	−658.545	−0.291939
$173$	1933.62	0.849773	0.424886	−	0.905247i	$-0.360314\pi$
$173$	1933.62	0.849773	0.424886	+	0.905247i	$0.360314\pi$
$174$	−1496.67	−0.652084
$175$	0	0
$176$	−205.361	−0.0879528
$177$	1320.12	0.560600
$178$	2020.32	0.850728
$179$	−3292.09	−1.37465	−0.687326	−	0.726349i	$-0.741216\pi$
$179$	−3292.09	−1.37465	−0.687326	+	0.726349i	$0.741216\pi$
$180$	−766.845	−0.317540
$181$	350.728	0.144030	0.0720148	−	0.997404i	$-0.477057\pi$
$181$	350.728	0.144030	0.0720148	+	0.997404i	$0.477057\pi$
$182$	0	0
$183$	5690.06	2.29848
$184$	223.370	0.0894948
$185$	−243.162	−0.0966358
$186$	1371.18	0.540537
$187$	2889.84	1.13009
$188$	−244.444	−0.0948294
$189$	0	0
$190$	−99.7646	−0.0380931
$191$	−2691.04	−1.01946	−0.509730	−	0.860335i	$-0.670255\pi$
$191$	−2691.04	−1.01946	−0.509730	+	0.860335i	$0.670255\pi$
$192$	−2249.79	−0.845648
$193$	−1624.12	−0.605735	−0.302867	−	0.953033i	$-0.597944\pi$
$193$	−1624.12	−0.605735	−0.302867	+	0.953033i	$0.597944\pi$
$194$	280.396	0.103769
$195$	1432.13	0.525933
$196$	0	0
$197$	−3109.67	−1.12465	−0.562323	−	0.826918i	$-0.690092\pi$
$197$	−3109.67	−1.12465	−0.562323	+	0.826918i	$0.690092\pi$
$198$	3078.30	1.10487
$199$	1088.39	0.387709	0.193855	−	0.981030i	$-0.437901\pi$
$199$	1088.39	0.387709	0.193855	+	0.981030i	$0.437901\pi$
$200$	−2484.96	−0.878565
$201$	7414.79	2.60199
$202$	−746.504	−0.260019
$203$	0	0
$204$	−2825.78	−0.969823
$205$	794.402	0.270651
$206$	227.120	0.0768166
$207$	422.022	0.141703
$208$	−227.692	−0.0759021
$209$	−744.130	−0.246280
$210$	0	0
$211$	226.377	0.0738600	0.0369300	−	0.999318i	$-0.488242\pi$
$211$	226.377	0.0738600	0.0369300	+	0.999318i	$0.488242\pi$
$212$	−855.944	−0.277295
$213$	8677.71	2.79149
$214$	−122.542	−0.0391438
$215$	447.412	0.141922
$216$	−2696.51	−0.849418
$217$	0	0
$218$	146.050	0.0453750
$219$	−2516.73	−0.776553
$220$	810.344	0.248334
$221$	3204.08	0.975249
$222$	−954.470	−0.288558
$223$	−1050.67	−0.315508	−0.157754	−	0.987478i	$-0.550425\pi$
$223$	−1050.67	−0.315508	−0.157754	+	0.987478i	$0.550425\pi$
$224$	0	0
$225$	−4694.94	−1.39109
$226$	74.5198	0.0219335
$227$	1296.69	0.379138	0.189569	−	0.981867i	$-0.439291\pi$
$227$	1296.69	0.379138	0.189569	+	0.981867i	$0.439291\pi$
$228$	727.634	0.211354
$229$	1452.63	0.419181	0.209591	−	0.977789i	$-0.432787\pi$
$229$	1452.63	0.419181	0.209591	+	0.977789i	$0.432787\pi$
$230$	−59.7894	−0.0171408
$231$	0	0
$232$	−2383.24	−0.674427
$233$	483.645	0.135986	0.0679928	−	0.997686i	$-0.478340\pi$
$233$	483.645	0.135986	0.0679928	+	0.997686i	$0.478340\pi$
$234$	3413.03	0.953491
$235$	166.074	0.0461000
$236$	828.190	0.228435
$237$	−3684.41	−1.00982
$238$	0	0
$239$	−2732.88	−0.739646	−0.369823	−	0.929102i	$-0.620582\pi$
$239$	−2732.88	−0.739646	−0.369823	+	0.929102i	$0.620582\pi$
$240$	−136.428	−0.0366934
$241$	2928.84	0.782834	0.391417	−	0.920213i	$-0.371985\pi$
$241$	2928.84	0.782834	0.391417	+	0.920213i	$0.371985\pi$
$242$	−1026.10	−0.272562
$243$	4245.44	1.12076
$244$	3569.72	0.936589
$245$	0	0
$246$	3118.22	0.808173
$247$	−825.047	−0.212536
$248$	2183.41	0.559059
$249$	10339.8	2.63157
$250$	1404.11	0.355214
$251$	2490.06	0.626179	0.313090	−	0.949724i	$-0.398636\pi$
$251$	2490.06	0.626179	0.313090	+	0.949724i	$0.398636\pi$
$252$	0	0
$253$	−445.961	−0.110819
$254$	1424.85	0.351980
$255$	1919.82	0.471466
$256$	−3880.53	−0.947395
$257$	−2244.33	−0.544737	−0.272369	−	0.962193i	$-0.587807\pi$
$257$	−2244.33	−0.544737	−0.272369	+	0.962193i	$0.587807\pi$
$258$	1756.20	0.423784
$259$	0	0
$260$	898.462	0.214309
$261$	−4502.75	−1.06787
$262$	4247.38	1.00154
$263$	6512.18	1.52684	0.763418	−	0.645905i	$-0.223520\pi$
$263$	6512.18	1.52684	0.763418	+	0.645905i	$0.223520\pi$
$264$	8073.45	1.88214
$265$	581.524	0.134803
$266$	0	0
$267$	10011.1	2.29463
$268$	4651.75	1.06026
$269$	−2590.06	−0.587059	−0.293530	−	0.955950i	$-0.594830\pi$
$269$	−2590.06	−0.587059	−0.293530	+	0.955950i	$0.594830\pi$
$270$	721.775	0.162688
$271$	−603.780	−0.135340	−0.0676698	−	0.997708i	$-0.521556\pi$
$271$	−603.780	−0.135340	−0.0676698	+	0.997708i	$0.521556\pi$
$272$	−305.229	−0.0680414
$273$	0	0
$274$	4019.29	0.886183
$275$	4961.25	1.08791
$276$	436.074	0.0951036
$277$	−1373.97	−0.298029	−0.149014	−	0.988835i	$-0.547610\pi$
$277$	−1373.97	−0.298029	−0.149014	+	0.988835i	$0.547610\pi$
$278$	−184.750	−0.0398581
$279$	4125.20	0.885196
$280$	0	0
$281$	2824.70	0.599672	0.299836	−	0.953991i	$-0.403068\pi$
$281$	2824.70	0.599672	0.299836	+	0.953991i	$0.403068\pi$
$282$	651.882	0.137656
$283$	−6229.62	−1.30853	−0.654263	−	0.756267i	$-0.727021\pi$
$283$	−6229.62	−1.30853	−0.654263	+	0.756267i	$0.727021\pi$
$284$	5444.05	1.13748
$285$	−494.351	−0.102747
$286$	−3606.63	−0.745681
$287$	0	0
$288$	−7697.76	−1.57498
$289$	−617.818	−0.125752
$290$	637.921	0.129172
$291$	1389.41	0.279892
$292$	−1578.90	−0.316432
$293$	2839.07	0.566077	0.283038	−	0.959109i	$-0.408658\pi$
$293$	2839.07	0.566077	0.283038	+	0.959109i	$0.408658\pi$
$294$	0	0
$295$	−562.669	−0.111050
$296$	−1519.86	−0.298445
$297$	5383.62	1.05182
$298$	1572.76	0.305730
$299$	−494.455	−0.0956357
$300$	−4851.27	−0.933627
$301$	0	0
$302$	4106.73	0.782502
$303$	−3699.06	−0.701338
$304$	78.5962	0.0148283
$305$	−2425.25	−0.455309
$306$	4575.29	0.854744
$307$	−9209.22	−1.71205	−0.856023	−	0.516938i	$-0.827072\pi$
$307$	−9209.22	−1.71205	−0.856023	+	0.516938i	$0.827072\pi$
$308$	0	0
$309$	1125.42	0.207194
$310$	−584.433	−0.107076
$311$	6054.03	1.10383	0.551917	−	0.833899i	$-0.313897\pi$
$311$	6054.03	1.10383	0.551917	+	0.833899i	$0.313897\pi$
$312$	8951.36	1.62427
$313$	6150.51	1.11069	0.555347	−	0.831618i	$-0.312585\pi$
$313$	6150.51	1.11069	0.555347	+	0.831618i	$0.312585\pi$
$314$	−589.930	−0.106025
$315$	0	0
$316$	−2311.45	−0.411485
$317$	−4399.07	−0.779421	−0.389711	−	0.920937i	$-0.627425\pi$
$317$	−4399.07	−0.779421	−0.389711	+	0.920937i	$0.627425\pi$
$318$	2282.62	0.402526
$319$	4758.16	0.835128
$320$	958.917	0.167516
$321$	−607.215	−0.105581
$322$	0	0
$323$	−1106.00	−0.190525
$324$	595.317	0.102078
$325$	5500.74	0.938850
$326$	6209.15	1.05489
$327$	723.703	0.122388
$328$	4965.31	0.835865
$329$	0	0
$330$	−2161.02	−0.360485
$331$	−8726.37	−1.44908	−0.724539	−	0.689234i	$-0.757947\pi$
$331$	−8726.37	−1.44908	−0.724539	+	0.689234i	$0.757947\pi$
$332$	6486.80	1.07232
$333$	−2871.53	−0.472549
$334$	−4002.49	−0.655708
$335$	−3160.37	−0.515432
$336$	0	0
$337$	−4533.26	−0.732767	−0.366383	−	0.930464i	$-0.619404\pi$
$337$	−4533.26	−0.732767	−0.366383	+	0.930464i	$0.619404\pi$
$338$	−323.157	−0.0520042
$339$	369.258	0.0591604
$340$	1204.42	0.192114
$341$	−4359.20	−0.692270
$342$	−1178.13	−0.186275
$343$	0	0
$344$	2796.50	0.438305
$345$	−296.267	−0.0462332
$346$	−3235.03	−0.502648
$347$	−2758.20	−0.426709	−0.213354	−	0.976975i	$-0.568439\pi$
$347$	−2758.20	−0.426709	−0.213354	+	0.976975i	$0.568439\pi$
$348$	−4652.68	−0.716695
$349$	3056.95	0.468868	0.234434	−	0.972132i	$-0.424676\pi$
$349$	3056.95	0.468868	0.234434	+	0.972132i	$0.424676\pi$
$350$	0	0
$351$	5969.04	0.907703
$352$	8134.41	1.23172
$353$	10165.0	1.53266	0.766331	−	0.642446i	$-0.222080\pi$
$353$	10165.0	1.53266	0.766331	+	0.642446i	$0.222080\pi$
$354$	−2208.61	−0.331600
$355$	−3698.66	−0.552970
$356$	6280.54	0.935022
$357$	0	0
$358$	5507.80	0.813118
$359$	8322.59	1.22354	0.611768	−	0.791037i	$-0.290459\pi$
$359$	8322.59	1.22354	0.611768	+	0.791037i	$0.290459\pi$
$360$	3256.39	0.476742
$361$	−6574.21	−0.958479
$362$	−586.781	−0.0851948
$363$	−5084.48	−0.735168
$364$	0	0
$365$	1072.70	0.153829
$366$	−9519.69	−1.35957
$367$	−785.922	−0.111784	−0.0558921	−	0.998437i	$-0.517800\pi$
$367$	−785.922	−0.111784	−0.0558921	+	0.998437i	$0.517800\pi$
$368$	47.1031	0.00667233
$369$	9381.17	1.32348
$370$	406.820	0.0571609
$371$	0	0
$372$	4262.56	0.594096
$373$	−1673.47	−0.232302	−0.116151	−	0.993232i	$-0.537056\pi$
$373$	−1673.47	−0.232302	−0.116151	+	0.993232i	$0.537056\pi$
$374$	−4834.81	−0.668455
$375$	6957.60	0.958104
$376$	1038.03	0.142373
$377$	5275.57	0.720704
$378$	0	0
$379$	−982.880	−0.133211	−0.0666057	−	0.997779i	$-0.521217\pi$
$379$	−982.880	−0.133211	−0.0666057	+	0.997779i	$0.521217\pi$
$380$	−310.136	−0.0418675
$381$	7060.37	0.949380
$382$	4502.21	0.603019
$383$	−13771.7	−1.83734	−0.918670	−	0.395025i	$-0.870736\pi$
$383$	−13771.7	−1.83734	−0.918670	+	0.395025i	$0.870736\pi$
$384$	−8470.85	−1.12572
$385$	0	0
$386$	2717.22	0.358297
$387$	5283.54	0.693998
$388$	871.660	0.114051
$389$	3481.40	0.453764	0.226882	−	0.973922i	$-0.427147\pi$
$389$	3481.40	0.453764	0.226882	+	0.973922i	$0.427147\pi$
$390$	−2396.01	−0.311094
$391$	−662.833	−0.0857313
$392$	0	0
$393$	21046.5	2.70142
$394$	5202.61	0.665237
$395$	1570.39	0.200038
$396$	9569.44	1.21435
$397$	14933.6	1.88790	0.943952	−	0.330084i	$-0.107077\pi$
$397$	14933.6	1.88790	0.943952	+	0.330084i	$0.107077\pi$
$398$	−1820.92	−0.229333
$399$	0	0
$400$	−524.015	−0.0655019
$401$	3731.69	0.464718	0.232359	−	0.972630i	$-0.425356\pi$
$401$	3731.69	0.464718	0.232359	+	0.972630i	$0.425356\pi$
$402$	−12405.2	−1.53910
$403$	−4833.23	−0.597420
$404$	−2320.64	−0.285783
$405$	−404.455	−0.0496236
$406$	0	0
$407$	3034.41	0.369558
$408$	11999.6	1.45605
$409$	−10067.2	−1.21710	−0.608548	−	0.793517i	$-0.708248\pi$
$409$	−10067.2	−1.21710	−0.608548	+	0.793517i	$0.708248\pi$
$410$	−1329.07	−0.160092
$411$	19916.3	2.39026
$412$	706.044	0.0844279
$413$	0	0
$414$	−706.059	−0.0838186
$415$	−4407.10	−0.521292
$416$	9018.95	1.06296
$417$	−915.466	−0.107507
$418$	1244.96	0.145677
$419$	−9856.84	−1.14926	−0.574628	−	0.818415i	$-0.694853\pi$
$419$	−9856.84	−1.14926	−0.574628	+	0.818415i	$0.694853\pi$
$420$	0	0
$421$	−2541.00	−0.294158	−0.147079	−	0.989125i	$-0.546987\pi$
$421$	−2541.00	−0.294158	−0.147079	+	0.989125i	$0.546987\pi$
$422$	−378.738	−0.0436888
$423$	1961.19	0.225428
$424$	3634.75	0.416318
$425$	7373.93	0.841619
$426$	−14518.1	−1.65119
$427$	0	0
$428$	−380.943	−0.0430223
$429$	−17871.5	−2.01129
$430$	−748.538	−0.0839482
$431$	−968.879	−0.108281	−0.0541407	−	0.998533i	$-0.517242\pi$
$431$	−968.879	−0.108281	−0.0541407	+	0.998533i	$0.517242\pi$
$432$	−568.626	−0.0633288
$433$	−11558.9	−1.28287	−0.641436	−	0.767177i	$-0.721661\pi$
$433$	−11558.9	−1.28287	−0.641436	+	0.767177i	$0.721661\pi$
$434$	0	0
$435$	3161.01	0.348411
$436$	454.022	0.0498709
$437$	170.679	0.0186835
$438$	4210.59	0.459338
$439$	−6453.38	−0.701602	−0.350801	−	0.936450i	$-0.614091\pi$
$439$	−6453.38	−0.701602	−0.350801	+	0.936450i	$0.614091\pi$
$440$	−3441.11	−0.372837
$441$	0	0
$442$	−5360.56	−0.576868
$443$	−12809.4	−1.37379	−0.686897	−	0.726755i	$-0.741028\pi$
$443$	−12809.4	−1.37379	−0.686897	+	0.726755i	$0.741028\pi$
$444$	−2967.14	−0.317149
$445$	−4266.97	−0.454548
$446$	1757.82	0.186625
$447$	7793.29	0.824631
$448$	0	0
$449$	7601.70	0.798989	0.399495	−	0.916736i	$-0.369186\pi$
$449$	7601.70	0.798989	0.399495	+	0.916736i	$0.369186\pi$
$450$	7854.81	0.822843
$451$	−9913.31	−1.03503
$452$	231.658	0.0241068
$453$	20349.5	2.11061
$454$	−2169.41	−0.224264
$455$	0	0
$456$	−3089.88	−0.317318
$457$	1098.44	0.112435	0.0562175	−	0.998419i	$-0.482096\pi$
$457$	1098.44	0.112435	0.0562175	+	0.998419i	$0.482096\pi$
$458$	−2430.31	−0.247949
$459$	8001.70	0.813698
$460$	−185.866	−0.0188392
$461$	6974.03	0.704584	0.352292	−	0.935890i	$-0.385402\pi$
$461$	6974.03	0.704584	0.352292	+	0.935890i	$0.385402\pi$
$462$	0	0
$463$	13171.5	1.32210	0.661050	−	0.750342i	$-0.270111\pi$
$463$	13171.5	1.32210	0.661050	+	0.750342i	$0.270111\pi$
$464$	−502.564	−0.0502822
$465$	−2895.97	−0.288811
$466$	−809.158	−0.0804367
$467$	14146.4	1.40175	0.700877	−	0.713282i	$-0.252792\pi$
$467$	14146.4	1.40175	0.700877	+	0.713282i	$0.252792\pi$
$468$	10610.0	1.04797
$469$	0	0
$470$	−277.849	−0.0272685
$471$	−2923.21	−0.285975
$472$	−3516.89	−0.342962
$473$	−5583.24	−0.542744
$474$	6164.16	0.597319
$475$	−1898.78	−0.183414
$476$	0	0
$477$	6867.28	0.659185
$478$	4572.22	0.437507
$479$	−8164.31	−0.778783	−0.389391	−	0.921072i	$-0.627315\pi$
$479$	−8164.31	−0.778783	−0.389391	+	0.921072i	$0.627315\pi$
$480$	5403.97	0.513867
$481$	3364.38	0.318924
$482$	−4900.06	−0.463053
$483$	0	0
$484$	−3189.80	−0.299568
$485$	−592.202	−0.0554443
$486$	−7102.78	−0.662940
$487$	8570.51	0.797468	0.398734	−	0.917067i	$-0.369450\pi$
$487$	8570.51	0.797468	0.398734	+	0.917067i	$0.369450\pi$
$488$	−15158.7	−1.40615
$489$	30767.4	2.84530
$490$	0	0
$491$	2598.27	0.238816	0.119408	−	0.992845i	$-0.461900\pi$
$491$	2598.27	0.238816	0.119408	+	0.992845i	$0.461900\pi$
$492$	9693.55	0.888250
$493$	7072.08	0.646065
$494$	1380.34	0.125717
$495$	−6501.43	−0.590339
$496$	460.426	0.0416809
$497$	0	0
$498$	−17298.9	−1.55659
$499$	7493.28	0.672235	0.336117	−	0.941820i	$-0.390886\pi$
$499$	7493.28	0.672235	0.336117	+	0.941820i	$0.390886\pi$
$500$	4364.92	0.390410
$501$	−19833.0	−1.76861
$502$	−4165.96	−0.370391
$503$	−9225.57	−0.817789	−0.408894	−	0.912582i	$-0.634086\pi$
$503$	−9225.57	−0.817789	−0.408894	+	0.912582i	$0.634086\pi$
$504$	0	0
$505$	1576.63	0.138929
$506$	746.110	0.0655506
$507$	−1601.30	−0.140269
$508$	4429.40	0.386856
$509$	16912.8	1.47279	0.736393	−	0.676554i	$-0.236527\pi$
$509$	16912.8	1.47279	0.736393	+	0.676554i	$0.236527\pi$
$510$	−3211.93	−0.278876
$511$	0	0
$512$	−1682.05	−0.145189
$513$	−2060.43	−0.177330
$514$	3754.85	0.322217
$515$	−479.683	−0.0410434
$516$	5459.47	0.465775
$517$	−2072.43	−0.176297
$518$	0	0
$519$	−16030.1	−1.35577
$520$	−3815.30	−0.321754
$521$	5361.21	0.450823	0.225412	−	0.974264i	$-0.427627\pi$
$521$	5361.21	0.450823	0.225412	+	0.974264i	$0.427627\pi$
$522$	7533.27	0.631652
$523$	2225.04	0.186031	0.0930156	−	0.995665i	$-0.470349\pi$
$523$	2225.04	0.186031	0.0930156	+	0.995665i	$0.470349\pi$
$524$	13203.8	1.10078
$525$	0	0
$526$	−10895.1	−0.903137
$527$	−6479.10	−0.535549
$528$	1702.49	0.140324
$529$	−12064.7	−0.991593
$530$	−972.913	−0.0797370
$531$	−6644.61	−0.543035
$532$	0	0
$533$	−10991.3	−0.893219
$534$	−16748.9	−1.35729
$535$	258.811	0.0209147
$536$	−19753.5	−1.59183
$537$	27292.1	2.19319
$538$	4333.28	0.347250
$539$	0	0
$540$	2243.77	0.178808
$541$	−22060.2	−1.75313	−0.876564	−	0.481285i	$-0.840170\pi$
$541$	−22060.2	−1.75313	−0.876564	+	0.481285i	$0.840170\pi$
$542$	1010.15	0.0800546
$543$	−2907.60	−0.229792
$544$	12090.2	0.952874
$545$	−308.461	−0.0242440
$546$	0	0
$547$	21989.1	1.71881	0.859403	−	0.511299i	$-0.170836\pi$
$547$	21989.1	1.71881	0.859403	+	0.511299i	$0.170836\pi$
$548$	12494.7	0.973989
$549$	−28640.0	−2.22646
$550$	−8300.37	−0.643507
$551$	−1821.05	−0.140797
$552$	−1851.78	−0.142784
$553$	0	0
$554$	2298.71	0.176287
$555$	2015.86	0.154178
$556$	−574.327	−0.0438074
$557$	−15230.2	−1.15857	−0.579287	−	0.815124i	$-0.696669\pi$
$557$	−15230.2	−1.15857	−0.579287	+	0.815124i	$0.696669\pi$
$558$	−6901.63	−0.523601
$559$	−6190.37	−0.468380
$560$	0	0
$561$	−23957.4	−1.80299
$562$	−4725.84	−0.354711
$563$	−14027.0	−1.05003	−0.525017	−	0.851092i	$-0.675941\pi$
$563$	−14027.0	−1.05003	−0.525017	+	0.851092i	$0.675941\pi$
$564$	2026.49	0.151296
$565$	−157.387	−0.0117192
$566$	10422.4	0.774004
$567$	0	0
$568$	−23118.0	−1.70777
$569$	22501.0	1.65780	0.828901	−	0.559395i	$-0.188966\pi$
$569$	22501.0	1.65780	0.828901	+	0.559395i	$0.188966\pi$
$570$	827.068	0.0607756
$571$	−1016.23	−0.0744799	−0.0372399	−	0.999306i	$-0.511857\pi$
$571$	−1016.23	−0.0744799	−0.0372399	+	0.999306i	$0.511857\pi$
$572$	−11211.9	−0.819566
$573$	22309.2	1.62650
$574$	0	0
$575$	−1137.95	−0.0825315
$576$	11324.0	0.819152
$577$	13244.3	0.955577	0.477789	−	0.878475i	$-0.341438\pi$
$577$	13244.3	0.955577	0.477789	+	0.878475i	$0.341438\pi$
$578$	1033.63	0.0743832
$579$	13464.3	0.966419
$580$	1983.09	0.141971
$581$	0	0
$582$	−2324.53	−0.165559
$583$	−7256.82	−0.515518
$584$	6704.76	0.475077
$585$	−7208.40	−0.509454
$586$	−4749.88	−0.334839
$587$	−1270.39	−0.0893266	−0.0446633	−	0.999002i	$-0.514222\pi$
$587$	−1270.39	−0.0893266	−0.0446633	+	0.999002i	$0.514222\pi$
$588$	0	0
$589$	1668.36	0.116712
$590$	941.367	0.0656872
$591$	25779.8	1.79431
$592$	−320.499	−0.0222507
$593$	792.861	0.0549054	0.0274527	−	0.999623i	$-0.491260\pi$
$593$	792.861	0.0549054	0.0274527	+	0.999623i	$0.491260\pi$
$594$	−9007.01	−0.622158
$595$	0	0
$596$	4889.20	0.336022
$597$	−9022.99	−0.618570
$598$	827.242	0.0565693
$599$	−13516.0	−0.921949	−0.460975	−	0.887413i	$-0.652500\pi$
$599$	−13516.0	−0.921949	−0.460975	+	0.887413i	$0.652500\pi$
$600$	20600.8	1.40171
$601$	6505.18	0.441517	0.220759	−	0.975328i	$-0.429147\pi$
$601$	6505.18	0.441517	0.220759	+	0.975328i	$0.429147\pi$
$602$	0	0
$603$	−37321.2	−2.52046
$604$	12766.5	0.860035
$605$	2167.14	0.145631
$606$	6188.67	0.414847
$607$	−3158.66	−0.211212	−0.105606	−	0.994408i	$-0.533678\pi$
$607$	−3158.66	−0.211212	−0.105606	+	0.994408i	$0.533678\pi$
$608$	−3113.21	−0.207660
$609$	0	0
$610$	4057.54	0.269319
$611$	−2297.79	−0.152142
$612$	14223.1	0.939436
$613$	−12608.7	−0.830771	−0.415385	−	0.909645i	$-0.636353\pi$
$613$	−12608.7	−0.830771	−0.415385	+	0.909645i	$0.636353\pi$
$614$	15407.4	1.01269
$615$	−6585.75	−0.431810
$616$	0	0
$617$	16416.6	1.07116	0.535580	−	0.844484i	$-0.320093\pi$
$617$	16416.6	1.07116	0.535580	+	0.844484i	$0.320093\pi$
$618$	−1882.87	−0.122557
$619$	4560.92	0.296153	0.148077	−	0.988976i	$-0.452692\pi$
$619$	4560.92	0.296153	0.148077	+	0.988976i	$0.452692\pi$
$620$	−1816.81	−0.117685
$621$	−1234.82	−0.0797935
$622$	−10128.6	−0.652927
$623$	0	0
$624$	1887.62	0.121098
$625$	11098.8	0.710323
$626$	−10290.0	−0.656986
$627$	6168.99	0.392928
$628$	−1833.90	−0.116530
$629$	4510.06	0.285895
$630$	0	0
$631$	3564.10	0.224857	0.112428	−	0.993660i	$-0.464137\pi$
$631$	3564.10	0.224857	0.112428	+	0.993660i	$0.464137\pi$
$632$	9815.53	0.617786
$633$	−1876.71	−0.117840
$634$	7359.82	0.461034
$635$	−3009.31	−0.188064
$636$	7095.95	0.442410
$637$	0	0
$638$	−7960.59	−0.493985
$639$	−43677.9	−2.70402
$640$	3610.49	0.222996
$641$	−11159.9	−0.687658	−0.343829	−	0.939032i	$-0.611724\pi$
$641$	−11159.9	−0.687658	−0.343829	+	0.939032i	$0.611724\pi$
$642$	1015.89	0.0624520
$643$	28441.1	1.74433	0.872167	−	0.489208i	$-0.162714\pi$
$643$	28441.1	1.74433	0.872167	+	0.489208i	$0.162714\pi$
$644$	0	0
$645$	−3709.14	−0.226430
$646$	1850.39	0.112697
$647$	−24081.7	−1.46329	−0.731647	−	0.681684i	$-0.761248\pi$
$647$	−24081.7	−1.46329	−0.731647	+	0.681684i	$0.761248\pi$
$648$	−2528.00	−0.153255
$649$	7021.52	0.424682
$650$	−9202.95	−0.555338
$651$	0	0
$652$	19302.3	1.15941
$653$	21261.4	1.27415	0.637076	−	0.770801i	$-0.280144\pi$
$653$	21261.4	1.27415	0.637076	+	0.770801i	$0.280144\pi$
$654$	−1210.78	−0.0723935
$655$	−8970.57	−0.535128
$656$	1047.06	0.0623183
$657$	12667.6	0.752222
$658$	0	0
$659$	−13231.7	−0.782147	−0.391073	−	0.920360i	$-0.627896\pi$
$659$	−13231.7	−0.782147	−0.391073	+	0.920360i	$0.627896\pi$
$660$	−6717.91	−0.396204
$661$	26556.0	1.56265	0.781324	−	0.624126i	$-0.214545\pi$
$661$	26556.0	1.56265	0.781324	+	0.624126i	$0.214545\pi$
$662$	14599.6	0.857142
$663$	−26562.5	−1.55596
$664$	−27546.0	−1.60993
$665$	0	0
$666$	4804.18	0.279517
$667$	−1091.36	−0.0633550
$668$	−12442.4	−0.720678
$669$	8710.28	0.503377
$670$	5287.43	0.304882
$671$	30264.6	1.74121
$672$	0	0
$673$	17736.7	1.01590	0.507950	−	0.861386i	$-0.330403\pi$
$673$	17736.7	1.01590	0.507950	+	0.861386i	$0.330403\pi$
$674$	7584.32	0.433438
$675$	13737.2	0.783328
$676$	−1004.59	−0.0571570
$677$	6698.01	0.380244	0.190122	−	0.981760i	$-0.439112\pi$
$677$	6698.01	0.380244	0.190122	+	0.981760i	$0.439112\pi$
$678$	−617.784	−0.0349939
$679$	0	0
$680$	−5114.54	−0.288432
$681$	−10749.8	−0.604896
$682$	7293.12	0.409484
$683$	−9038.48	−0.506366	−0.253183	−	0.967418i	$-0.581477\pi$
$683$	−9038.48	−0.506366	−0.253183	+	0.967418i	$0.581477\pi$
$684$	−3662.43	−0.204732
$685$	−8488.82	−0.473491
$686$	0	0
$687$	−12042.6	−0.668783
$688$	589.710	0.0326781
$689$	−8045.93	−0.444885
$690$	495.666	0.0273474
$691$	−7123.45	−0.392169	−0.196085	−	0.980587i	$-0.562823\pi$
$691$	−7123.45	−0.392169	−0.196085	+	0.980587i	$0.562823\pi$
$692$	−10056.7	−0.552452
$693$	0	0
$694$	4614.58	0.252402
$695$	390.195	0.0212963
$696$	19757.5	1.07601
$697$	−14734.2	−0.800714
$698$	−5114.40	−0.277339
$699$	−4009.52	−0.216958
$700$	0	0
$701$	2225.48	0.119908	0.0599538	−	0.998201i	$-0.480905\pi$
$701$	2225.48	0.119908	0.0599538	+	0.998201i	$0.480905\pi$
$702$	−9986.44	−0.536914
$703$	−1161.33	−0.0623052
$704$	−11966.3	−0.640620
$705$	−1376.79	−0.0735502
$706$	−17006.5	−0.906582
$707$	0	0
$708$	−6865.86	−0.364456
$709$	−936.862	−0.0496257	−0.0248128	−	0.999692i	$-0.507899\pi$
$709$	−936.862	−0.0496257	−0.0248128	+	0.999692i	$0.507899\pi$
$710$	6188.00	0.327087
$711$	18544.9	0.978183
$712$	−26670.2	−1.40380
$713$	999.856	0.0525174
$714$	0	0
$715$	7617.29	0.398420
$716$	17122.0	0.893685
$717$	22656.1	1.18007
$718$	−13924.0	−0.723732
$719$	6033.28	0.312939	0.156470	−	0.987683i	$-0.449989\pi$
$719$	6033.28	0.312939	0.156470	+	0.987683i	$0.449989\pi$
$720$	686.691	0.0355437
$721$	0	0
$722$	10998.9	0.566948
$723$	−24280.6	−1.24897
$724$	−1824.11	−0.0936362
$725$	12141.3	0.621953
$726$	8506.54	0.434858
$727$	22844.9	1.16543	0.582717	−	0.812675i	$-0.301989\pi$
$727$	22844.9	1.16543	0.582717	+	0.812675i	$0.301989\pi$
$728$	0	0
$729$	−32105.0	−1.63110
$730$	−1794.66	−0.0909910
$731$	−8298.40	−0.419873
$732$	−29593.7	−1.49428
$733$	−30960.9	−1.56012	−0.780059	−	0.625706i	$-0.784811\pi$
$733$	−30960.9	−1.56012	−0.780059	+	0.625706i	$0.784811\pi$
$734$	1314.88	0.0661213
$735$	0	0
$736$	−1865.76	−0.0934415
$737$	39438.2	1.97113
$738$	−15695.1	−0.782850
$739$	−17634.5	−0.877804	−0.438902	−	0.898535i	$-0.644632\pi$
$739$	−17634.5	−0.877804	−0.438902	+	0.898535i	$0.644632\pi$
$740$	1264.67	0.0628247
$741$	6839.81	0.339091
$742$	0	0
$743$	−35924.8	−1.77382	−0.886912	−	0.461938i	$-0.847154\pi$
$743$	−35924.8	−1.77382	−0.886912	+	0.461938i	$0.847154\pi$
$744$	−18100.9	−0.891950
$745$	−3321.70	−0.163353
$746$	2799.77	0.137409
$747$	−52043.9	−2.54911
$748$	−15029.9	−0.734689
$749$	0	0
$750$	−11640.3	−0.566727
$751$	29382.7	1.42768	0.713842	−	0.700307i	$-0.246953\pi$
$751$	29382.7	1.42768	0.713842	+	0.700307i	$0.246953\pi$
$752$	218.894	0.0106147
$753$	−20643.1	−0.999038
$754$	−8826.23	−0.426303
$755$	−8673.50	−0.418094
$756$	0	0
$757$	24544.4	1.17844	0.589221	−	0.807972i	$-0.299435\pi$
$757$	24544.4	1.17844	0.589221	+	0.807972i	$0.299435\pi$
$758$	1644.40	0.0787957
$759$	3697.10	0.176807
$760$	1316.99	0.0628580
$761$	3378.20	0.160919	0.0804597	−	0.996758i	$-0.474361\pi$
$761$	3378.20	0.160919	0.0804597	+	0.996758i	$0.474361\pi$
$762$	−11812.3	−0.561567
$763$	0	0
$764$	13995.9	0.662768
$765$	−9663.11	−0.456693
$766$	23040.6	1.08680
$767$	7785.05	0.366495
$768$	32170.4	1.51152
$769$	−20261.5	−0.950126	−0.475063	−	0.879952i	$-0.657575\pi$
$769$	−20261.5	−0.950126	−0.475063	+	0.879952i	$0.657575\pi$
$770$	0	0
$771$	18605.9	0.869101
$772$	8446.96	0.393799
$773$	−14495.6	−0.674476	−0.337238	−	0.941419i	$-0.609493\pi$
$773$	−14495.6	−0.674476	−0.337238	+	0.941419i	$0.609493\pi$
$774$	−8839.56	−0.410506
$775$	−11123.3	−0.515561
$776$	−3701.48	−0.171231
$777$	0	0
$778$	−5824.52	−0.268405
$779$	3794.04	0.174500
$780$	−7448.43	−0.341918
$781$	46155.5	2.11469
$782$	1108.95	0.0507108
$783$	13174.9	0.601319
$784$	0	0
$785$	1245.95	0.0566493
$786$	−35211.7	−1.59791
$787$	−30625.1	−1.38713	−0.693563	−	0.720396i	$-0.743960\pi$
$787$	−30625.1	−1.38713	−0.693563	+	0.720396i	$0.743960\pi$
$788$	16173.2	0.731152
$789$	−53987.2	−2.43599
$790$	−2627.32	−0.118324
$791$	0	0
$792$	−40636.4	−1.82317
$793$	33555.6	1.50264
$794$	−24984.5	−1.11671
$795$	−4820.95	−0.215071
$796$	−5660.67	−0.252056
$797$	28558.3	1.26924	0.634621	−	0.772824i	$-0.281156\pi$
$797$	28558.3	1.26924	0.634621	+	0.772824i	$0.281156\pi$
$798$	0	0
$799$	−3080.27	−0.136386
$800$	20756.4	0.917310
$801$	−50389.1	−2.22273
$802$	−6243.27	−0.274885
$803$	−13386.1	−0.588277
$804$	−38563.9	−1.69160
$805$	0	0
$806$	8086.18	0.353379
$807$	21472.1	0.936623
$808$	9854.55	0.429062
$809$	−34768.8	−1.51101	−0.755504	−	0.655144i	$-0.772608\pi$
$809$	−34768.8	−1.51101	−0.755504	+	0.655144i	$0.772608\pi$
$810$	676.670	0.0293528
$811$	−4624.03	−0.200212	−0.100106	−	0.994977i	$-0.531918\pi$
$811$	−4624.03	−0.200212	−0.100106	+	0.994977i	$0.531918\pi$
$812$	0	0
$813$	5005.46	0.215928
$814$	−5076.69	−0.218597
$815$	−13113.9	−0.563630
$816$	2530.41	0.108557
$817$	2136.83	0.0915032
$818$	16842.9	0.719922
$819$	0	0
$820$	−4131.64	−0.175955
$821$	20626.2	0.876809	0.438405	−	0.898778i	$-0.355544\pi$
$821$	20626.2	0.876809	0.438405	+	0.898778i	$0.355544\pi$
$822$	−33320.7	−1.41386
$823$	−34121.9	−1.44522	−0.722610	−	0.691256i	$-0.757058\pi$
$823$	−34121.9	−1.44522	−0.722610	+	0.691256i	$0.757058\pi$
$824$	−2998.20	−0.126756
$825$	−41129.8	−1.73570
$826$	0	0
$827$	−8323.42	−0.349980	−0.174990	−	0.984570i	$-0.555989\pi$
$827$	−8323.42	−0.349980	−0.174990	+	0.984570i	$0.555989\pi$
$828$	−2194.91	−0.0921237
$829$	2385.15	0.0999272	0.0499636	−	0.998751i	$-0.484089\pi$
$829$	2385.15	0.0999272	0.0499636	+	0.998751i	$0.484089\pi$
$830$	7373.25	0.308348
$831$	11390.5	0.475490
$832$	−13267.5	−0.552847
$833$	0	0
$834$	1531.61	0.0635915
$835$	8453.34	0.350347
$836$	3870.18	0.160111
$837$	−12070.2	−0.498457
$838$	16490.9	0.679794
$839$	16627.0	0.684183	0.342091	−	0.939667i	$-0.388865\pi$
$839$	16627.0	0.684183	0.342091	+	0.939667i	$0.388865\pi$
$840$	0	0
$841$	−12744.7	−0.522561
$842$	4251.19	0.173997
$843$	−23417.4	−0.956746
$844$	−1177.37	−0.0480177
$845$	682.514	0.0277860
$846$	−3281.14	−0.133343
$847$	0	0
$848$	766.477	0.0310388
$849$	51644.8	2.08769
$850$	−12336.9	−0.497825
$851$	−695.993	−0.0280356
$852$	−45132.2	−1.81479
$853$	15114.5	0.606696	0.303348	−	0.952880i	$-0.401895\pi$
$853$	15114.5	0.606696	0.303348	+	0.952880i	$0.401895\pi$
$854$	0	0
$855$	2488.24	0.0995274
$856$	1617.66	0.0645919
$857$	−10092.8	−0.402289	−0.201145	−	0.979562i	$-0.564466\pi$
$857$	−10092.8	−0.402289	−0.201145	+	0.979562i	$0.564466\pi$
$858$	29899.7	1.18970
$859$	−8944.14	−0.355262	−0.177631	−	0.984097i	$-0.556843\pi$
$859$	−8944.14	−0.355262	−0.177631	+	0.984097i	$0.556843\pi$
$860$	−2326.96	−0.0922661
$861$	0	0
$862$	1620.97	0.0640494
$863$	18657.4	0.735926	0.367963	−	0.929840i	$-0.380055\pi$
$863$	18657.4	0.735926	0.367963	+	0.929840i	$0.380055\pi$
$864$	22523.4	0.886878
$865$	6832.45	0.268567
$866$	19338.4	0.758830
$867$	5121.83	0.200630
$868$	0	0
$869$	−19596.8	−0.764991
$870$	−5288.49	−0.206088
$871$	43726.7	1.70106
$872$	−1928.00	−0.0748741
$873$	−6993.37	−0.271122
$874$	−285.552	−0.0110514
$875$	0	0
$876$	13089.4	0.504851
$877$	47721.9	1.83746	0.918731	−	0.394883i	$-0.129215\pi$
$877$	47721.9	1.83746	0.918731	+	0.394883i	$0.129215\pi$
$878$	10796.8	0.415003
$879$	−23536.5	−0.903147
$880$	−725.643	−0.0277971
$881$	9953.26	0.380629	0.190314	−	0.981723i	$-0.439049\pi$
$881$	9953.26	0.380629	0.190314	+	0.981723i	$0.439049\pi$
$882$	0	0
$883$	−27519.0	−1.04880	−0.524398	−	0.851473i	$-0.675710\pi$
$883$	−27519.0	−1.04880	−0.524398	+	0.851473i	$0.675710\pi$
$884$	−16664.3	−0.634026
$885$	4664.64	0.177175
$886$	21430.5	0.812611
$887$	−9666.90	−0.365933	−0.182967	−	0.983119i	$-0.558570\pi$
$887$	−9666.90	−0.365933	−0.182967	+	0.983119i	$0.558570\pi$
$888$	12599.9	0.476154
$889$	0	0
$890$	7138.80	0.268869
$891$	5047.18	0.189772
$892$	5464.48	0.205117
$893$	793.165	0.0297226
$894$	−13038.5	−0.487776
$895$	−11632.6	−0.434452
$896$	0	0
$897$	4099.13	0.152582
$898$	−12717.9	−0.472609
$899$	−10667.9	−0.395768
$900$	24418.1	0.904373
$901$	−10785.8	−0.398811
$902$	16585.4	0.612231
$903$	0	0
$904$	−983.731	−0.0361929
$905$	1239.29	0.0455199
$906$	−34045.6	−1.24844
$907$	24028.6	0.879665	0.439833	−	0.898080i	$-0.355038\pi$
$907$	24028.6	0.879665	0.439833	+	0.898080i	$0.355038\pi$
$908$	−6744.01	−0.246484
$909$	18618.6	0.679363
$910$	0	0
$911$	6055.02	0.220210	0.110105	−	0.993920i	$-0.464881\pi$
$911$	6055.02	0.220210	0.110105	+	0.993920i	$0.464881\pi$
$912$	−651.578	−0.0236578
$913$	54996.0	1.99354
$914$	−1837.73	−0.0665062
$915$	20105.8	0.726423
$916$	−7555.05	−0.272517
$917$	0	0
$918$	−13387.2	−0.481309
$919$	−14697.8	−0.527570	−0.263785	−	0.964582i	$-0.584971\pi$
$919$	−14697.8	−0.527570	−0.263785	+	0.964582i	$0.584971\pi$
$920$	789.276	0.0282844
$921$	76346.3	2.73148
$922$	−11667.8	−0.416767
$923$	51174.4	1.82495
$924$	0	0
$925$	7742.83	0.275224
$926$	−22036.5	−0.782033
$927$	−5664.63	−0.200702
$928$	19906.7	0.704170
$929$	25916.0	0.915261	0.457631	−	0.889142i	$-0.348698\pi$
$929$	25916.0	0.915261	0.457631	+	0.889142i	$0.348698\pi$
$930$	4845.06	0.170834
$931$	0	0
$932$	−2515.41	−0.0884067
$933$	−50189.1	−1.76111
$934$	−23667.6	−0.829150
$935$	10211.2	0.357158
$936$	−45055.3	−1.57337
$937$	32087.4	1.11873	0.559365	−	0.828922i	$-0.311045\pi$
$937$	32087.4	1.11873	0.559365	+	0.828922i	$0.311045\pi$
$938$	0	0
$939$	−50989.0	−1.77206
$940$	−863.742	−0.0299704
$941$	−2844.34	−0.0985366	−0.0492683	−	0.998786i	$-0.515689\pi$
$941$	−2844.34	−0.0985366	−0.0492683	+	0.998786i	$0.515689\pi$
$942$	4890.64	0.169157
$943$	2273.78	0.0785203
$944$	−741.624	−0.0255697
$945$	0	0
$946$	9340.98	0.321037
$947$	−44491.6	−1.52670	−0.763349	−	0.645986i	$-0.776446\pi$
$947$	−44491.6	−1.52670	−0.763349	+	0.645986i	$0.776446\pi$
$948$	19162.4	0.656504
$949$	−14841.8	−0.507675
$950$	3176.73	0.108491
$951$	36469.2	1.24353
$952$	0	0
$953$	50417.4	1.71372	0.856862	−	0.515546i	$-0.172411\pi$
$953$	50417.4	1.71372	0.856862	+	0.515546i	$0.172411\pi$
$954$	−11489.2	−0.389913
$955$	−9508.77	−0.322195
$956$	14213.6	0.480857
$957$	−39446.1	−1.33240
$958$	13659.2	0.460657
$959$	0	0
$960$	−7949.62	−0.267263
$961$	−20017.5	−0.671933
$962$	−5628.73	−0.188646
$963$	3056.32	0.102273
$964$	−15232.7	−0.508934
$965$	−5738.82	−0.191440
$966$	0	0
$967$	27956.1	0.929687	0.464844	−	0.885393i	$-0.346111\pi$
$967$	27956.1	0.929687	0.464844	+	0.885393i	$0.346111\pi$
$968$	13545.4	0.449759
$969$	9168.99	0.303974
$970$	990.776	0.0327958
$971$	−40302.5	−1.33200	−0.665998	−	0.745953i	$-0.731994\pi$
$971$	−40302.5	−1.33200	−0.665998	+	0.745953i	$0.731994\pi$
$972$	−22080.3	−0.728627
$973$	0	0
$974$	−14338.8	−0.471709
$975$	−45602.2	−1.49789
$976$	−3196.59	−0.104837
$977$	−2677.80	−0.0876871	−0.0438436	−	0.999038i	$-0.513960\pi$
$977$	−2677.80	−0.0876871	−0.0438436	+	0.999038i	$0.513960\pi$
$978$	−51475.1	−1.68302
$979$	53247.3	1.73830
$980$	0	0
$981$	−3642.64	−0.118553
$982$	−4347.01	−0.141262
$983$	−21852.8	−0.709051	−0.354526	−	0.935046i	$-0.615358\pi$
$983$	−21852.8	−0.709051	−0.354526	+	0.935046i	$0.615358\pi$
$984$	−41163.4	−1.33358
$985$	−10988.0	−0.355439
$986$	−11831.9	−0.382153
$987$	0	0
$988$	4291.02	0.138174
$989$	1280.61	0.0411739
$990$	10877.1	0.349190
$991$	44298.8	1.41998	0.709989	−	0.704213i	$-0.248700\pi$
$991$	44298.8	1.41998	0.709989	+	0.704213i	$0.248700\pi$
$992$	−18237.6	−0.583713
$993$	72343.4	2.31193
$994$	0	0
$995$	3845.83	0.122534
$996$	−53776.8	−1.71083
$997$	32423.6	1.02996	0.514978	−	0.857204i	$-0.327800\pi$
$997$	32423.6	1.02996	0.514978	+	0.857204i	$0.327800\pi$
$998$	−12536.5	−0.397633
$999$	8402.00	0.266094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.13	yes	35
7.6	odd	2		2303.4.a.g.1.13	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.13	✓	35	7.6	odd	2
2303.4.a.h.1.13	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)

\(f(q)\)	\(=\)	\(q-1.67304 q^{2} -8.29020 q^{3} -5.20094 q^{4} +3.53349 q^{5} +13.8698 q^{6} +22.0857 q^{8} +41.7274 q^{9} +O(q^{10})\)	\(q-1.67304 q^{2} -8.29020 q^{3} -5.20094 q^{4} +3.53349 q^{5} +13.8698 q^{6} +22.0857 q^{8} +41.7274 q^{9} -5.91167 q^{10} -44.0944 q^{11} +43.1168 q^{12} -48.8892 q^{13} -29.2934 q^{15} +4.65731 q^{16} -65.5376 q^{17} -69.8116 q^{18} +16.8759 q^{19} -18.3775 q^{20} +73.7716 q^{22} +10.1138 q^{23} -183.095 q^{24} -112.514 q^{25} +81.7936 q^{26} -122.093 q^{27} -107.909 q^{29} +49.0090 q^{30} +98.8608 q^{31} -184.477 q^{32} +365.551 q^{33} +109.647 q^{34} -217.022 q^{36} -68.8163 q^{37} -28.2340 q^{38} +405.301 q^{39} +78.0397 q^{40} +224.820 q^{41} +126.620 q^{43} +229.332 q^{44} +147.444 q^{45} -16.9207 q^{46} +47.0000 q^{47} -38.6101 q^{48} +188.241 q^{50} +543.320 q^{51} +254.270 q^{52} +164.575 q^{53} +204.267 q^{54} -155.807 q^{55} -139.904 q^{57} +180.535 q^{58} -159.239 q^{59} +152.353 q^{60} -686.360 q^{61} -165.398 q^{62} +271.379 q^{64} -172.750 q^{65} -611.581 q^{66} -894.405 q^{67} +340.857 q^{68} -83.8453 q^{69} -1046.74 q^{71} +921.579 q^{72} +303.579 q^{73} +115.132 q^{74} +932.767 q^{75} -87.7703 q^{76} -678.085 q^{78} +444.430 q^{79} +16.4566 q^{80} -114.463 q^{81} -376.133 q^{82} -1247.24 q^{83} -231.577 q^{85} -211.841 q^{86} +894.584 q^{87} -973.854 q^{88} -1207.58 q^{89} -246.679 q^{90} -52.6012 q^{92} -819.576 q^{93} -78.6328 q^{94} +59.6308 q^{95} +1529.35 q^{96} -167.597 q^{97} -1839.94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 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

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Database

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