LMFDB - Embedded Newform 8013.2.a.d.1.2

Newspace parameters

Level:	$ N $	=	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	8013.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	=	8013.1

$q$-expansion

$f(q)$	$=$	$q-2.75607 q^{2} +1.00000 q^{3} +5.59595 q^{4} +0.110089 q^{5} -2.75607 q^{6} +1.43985 q^{7} -9.91070 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.75607 q^{2} +1.00000 q^{3} +5.59595 q^{4} +0.110089 q^{5} -2.75607 q^{6} +1.43985 q^{7} -9.91070 q^{8} +1.00000 q^{9} -0.303413 q^{10} -0.0788383 q^{11} +5.59595 q^{12} -1.19203 q^{13} -3.96832 q^{14} +0.110089 q^{15} +16.1227 q^{16} +0.781615 q^{17} -2.75607 q^{18} -2.26675 q^{19} +0.616051 q^{20} +1.43985 q^{21} +0.217284 q^{22} -5.36820 q^{23} -9.91070 q^{24} -4.98788 q^{25} +3.28531 q^{26} +1.00000 q^{27} +8.05730 q^{28} -0.140154 q^{29} -0.303413 q^{30} +6.90226 q^{31} -24.6140 q^{32} -0.0788383 q^{33} -2.15419 q^{34} +0.158511 q^{35} +5.59595 q^{36} +0.903661 q^{37} +6.24734 q^{38} -1.19203 q^{39} -1.09106 q^{40} -1.92438 q^{41} -3.96832 q^{42} -2.72015 q^{43} -0.441175 q^{44} +0.110089 q^{45} +14.7951 q^{46} -0.0476025 q^{47} +16.1227 q^{48} -4.92684 q^{49} +13.7470 q^{50} +0.781615 q^{51} -6.67051 q^{52} +3.74754 q^{53} -2.75607 q^{54} -0.00867922 q^{55} -14.2699 q^{56} -2.26675 q^{57} +0.386276 q^{58} -11.1497 q^{59} +0.616051 q^{60} +6.72295 q^{61} -19.0231 q^{62} +1.43985 q^{63} +35.5927 q^{64} -0.131229 q^{65} +0.217284 q^{66} +9.41624 q^{67} +4.37388 q^{68} -5.36820 q^{69} -0.436868 q^{70} -2.32642 q^{71} -9.91070 q^{72} +15.4500 q^{73} -2.49056 q^{74} -4.98788 q^{75} -12.6846 q^{76} -0.113515 q^{77} +3.28531 q^{78} +7.02174 q^{79} +1.77493 q^{80} +1.00000 q^{81} +5.30373 q^{82} +14.7129 q^{83} +8.05730 q^{84} +0.0860472 q^{85} +7.49693 q^{86} -0.140154 q^{87} +0.781342 q^{88} -16.0404 q^{89} -0.303413 q^{90} -1.71633 q^{91} -30.0401 q^{92} +6.90226 q^{93} +0.131196 q^{94} -0.249544 q^{95} -24.6140 q^{96} -3.16445 q^{97} +13.5787 q^{98} -0.0788383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) $	\( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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 $

$2$	−2.75607	−1.94884	−0.974419	−	0.224737i	$-0.927848\pi$
$2$	−2.75607	−1.94884	−0.974419	+	0.224737i	$0.927848\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.59595	2.79797
$5$	0.110089	0.0492332	0.0246166	−	0.999697i	$-0.492163\pi$
$5$	0.110089	0.0492332	0.0246166	+	0.999697i	$0.492163\pi$
$6$	−2.75607	−1.12516
$7$	1.43985	0.544211	0.272105	−	0.962267i	$-0.412280\pi$
$7$	1.43985	0.544211	0.272105	+	0.962267i	$0.412280\pi$
$8$	−9.91070	−3.50396
$9$	1.00000	0.333333
$10$	−0.303413	−0.0959477
$11$	−0.0788383	−0.0237706	−0.0118853	−	0.999929i	$-0.503783\pi$
$11$	−0.0788383	−0.0237706	−0.0118853	+	0.999929i	$0.503783\pi$
$12$	5.59595	1.61541
$13$	−1.19203	−0.330608	−0.165304	−	0.986243i	$-0.552861\pi$
$13$	−1.19203	−0.330608	−0.165304	+	0.986243i	$0.552861\pi$
$14$	−3.96832	−1.06058
$15$	0.110089	0.0284248
$16$	16.1227	4.03068
$17$	0.781615	0.189570	0.0947848	−	0.995498i	$-0.469784\pi$
$17$	0.781615	0.189570	0.0947848	+	0.995498i	$0.469784\pi$
$18$	−2.75607	−0.649613
$19$	−2.26675	−0.520029	−0.260015	−	0.965605i	$-0.583727\pi$
$19$	−2.26675	−0.520029	−0.260015	+	0.965605i	$0.583727\pi$
$20$	0.616051	0.137753
$21$	1.43985	0.314200
$22$	0.217284	0.0463252
$23$	−5.36820	−1.11935	−0.559673	−	0.828714i	$-0.689073\pi$
$23$	−5.36820	−1.11935	−0.559673	+	0.828714i	$0.689073\pi$
$24$	−9.91070	−2.02301
$25$	−4.98788	−0.997576
$26$	3.28531	0.644302
$27$	1.00000	0.192450
$28$	8.05730	1.52269
$29$	−0.140154	−0.0260260	−0.0130130	−	0.999915i	$-0.504142\pi$
$29$	−0.140154	−0.0260260	−0.0130130	+	0.999915i	$0.504142\pi$
$30$	−0.303413	−0.0553954
$31$	6.90226	1.23968	0.619841	−	0.784728i	$-0.287197\pi$
$31$	6.90226	1.23968	0.619841	+	0.784728i	$0.287197\pi$
$32$	−24.6140	−4.35119
$33$	−0.0788383	−0.0137240
$34$	−2.15419	−0.369441
$35$	0.158511	0.0267932
$36$	5.59595	0.932658
$37$	0.903661	0.148561	0.0742805	−	0.997237i	$-0.476334\pi$
$37$	0.903661	0.148561	0.0742805	+	0.997237i	$0.476334\pi$
$38$	6.24734	1.01345
$39$	−1.19203	−0.190877
$40$	−1.09106	−0.172511
$41$	−1.92438	−0.300537	−0.150269	−	0.988645i	$-0.548014\pi$
$41$	−1.92438	−0.300537	−0.150269	+	0.988645i	$0.548014\pi$
$42$	−3.96832	−0.612325
$43$	−2.72015	−0.414819	−0.207409	−	0.978254i	$-0.566503\pi$
$43$	−2.72015	−0.414819	−0.207409	+	0.978254i	$0.566503\pi$
$44$	−0.441175	−0.0665096
$45$	0.110089	0.0164111
$46$	14.7951	2.18143
$47$	−0.0476025	−0.00694354	−0.00347177	−	0.999994i	$-0.501105\pi$
$47$	−0.0476025	−0.00694354	−0.00347177	+	0.999994i	$0.501105\pi$
$48$	16.1227	2.32711
$49$	−4.92684	−0.703835
$50$	13.7470	1.94412
$51$	0.781615	0.109448
$52$	−6.67051	−0.925033
$53$	3.74754	0.514764	0.257382	−	0.966310i	$-0.417140\pi$
$53$	3.74754	0.514764	0.257382	+	0.966310i	$0.417140\pi$
$54$	−2.75607	−0.375054
$55$	−0.00867922	−0.00117031
$56$	−14.2699	−1.90689
$57$	−2.26675	−0.300239
$58$	0.386276	0.0507205
$59$	−11.1497	−1.45157	−0.725784	−	0.687923i	$-0.758523\pi$
$59$	−11.1497	−1.45157	−0.725784	+	0.687923i	$0.758523\pi$
$60$	0.616051	0.0795319
$61$	6.72295	0.860785	0.430393	−	0.902642i	$-0.358375\pi$
$61$	6.72295	0.860785	0.430393	+	0.902642i	$0.358375\pi$
$62$	−19.0231	−2.41594
$63$	1.43985	0.181404
$64$	35.5927	4.44908
$65$	−0.131229	−0.0162769
$66$	0.217284	0.0267458
$67$	9.41624	1.15038	0.575188	−	0.818021i	$-0.304929\pi$
$67$	9.41624	1.15038	0.575188	+	0.818021i	$0.304929\pi$
$68$	4.37388	0.530411
$69$	−5.36820	−0.646255
$70$	−0.436868	−0.0522157
$71$	−2.32642	−0.276095	−0.138047	−	0.990426i	$-0.544083\pi$
$71$	−2.32642	−0.276095	−0.138047	+	0.990426i	$0.544083\pi$
$72$	−9.91070	−1.16799
$73$	15.4500	1.80829	0.904143	−	0.427231i	$-0.140511\pi$
$73$	15.4500	1.80829	0.904143	+	0.427231i	$0.140511\pi$
$74$	−2.49056	−0.289521
$75$	−4.98788	−0.575951
$76$	−12.6846	−1.45503
$77$	−0.113515	−0.0129362
$78$	3.28531	0.371988
$79$	7.02174	0.790008	0.395004	−	0.918679i	$-0.370743\pi$
$79$	7.02174	0.790008	0.395004	+	0.918679i	$0.370743\pi$
$80$	1.77493	0.198444
$81$	1.00000	0.111111
$82$	5.30373	0.585699
$83$	14.7129	1.61495	0.807474	−	0.589904i	$-0.200834\pi$
$83$	14.7129	1.61495	0.807474	+	0.589904i	$0.200834\pi$
$84$	8.05730	0.879123
$85$	0.0860472	0.00933312
$86$	7.49693	0.808415
$87$	−0.140154	−0.0150261
$88$	0.781342	0.0832914
$89$	−16.0404	−1.70028	−0.850138	−	0.526560i	$-0.823482\pi$
$89$	−16.0404	−1.70028	−0.850138	+	0.526560i	$0.823482\pi$
$90$	−0.303413	−0.0319826
$91$	−1.71633	−0.179920
$92$	−30.0401	−3.13190
$93$	6.90226	0.715731
$94$	0.131196	0.0135318
$95$	−0.249544	−0.0256027
$96$	−24.6140	−2.51216
$97$	−3.16445	−0.321302	−0.160651	−	0.987011i	$-0.551359\pi$
$97$	−3.16445	−0.321302	−0.160651	+	0.987011i	$0.551359\pi$
$98$	13.5787	1.37166
$99$	−0.0788383	−0.00792355
$100$	−27.9119	−2.79119
$101$	14.7029	1.46299	0.731495	−	0.681847i	$-0.238823\pi$
$101$	14.7029	1.46299	0.731495	+	0.681847i	$0.238823\pi$
$102$	−2.15419	−0.213297
$103$	7.32325	0.721582	0.360791	−	0.932647i	$-0.382507\pi$
$103$	7.32325	0.721582	0.360791	+	0.932647i	$0.382507\pi$
$104$	11.8138	1.15844
$105$	0.158511	0.0154691
$106$	−10.3285	−1.00319
$107$	−19.2573	−1.86167	−0.930837	−	0.365434i	$-0.880921\pi$
$107$	−19.2573	−1.86167	−0.930837	+	0.365434i	$0.880921\pi$
$108$	5.59595	0.538470
$109$	2.09641	0.200800	0.100400	−	0.994947i	$-0.467988\pi$
$109$	2.09641	0.200800	0.100400	+	0.994947i	$0.467988\pi$
$110$	0.0239206	0.00228074
$111$	0.903661	0.0857717
$112$	23.2142	2.19354
$113$	13.8910	1.30675	0.653377	−	0.757032i	$-0.273352\pi$
$113$	13.8910	1.30675	0.653377	+	0.757032i	$0.273352\pi$
$114$	6.24734	0.585117
$115$	−0.590979	−0.0551090
$116$	−0.784296	−0.0728200
$117$	−1.19203	−0.110203
$118$	30.7294	2.82887
$119$	1.12541	0.103166
$120$	−1.09106	−0.0995995
$121$	−10.9938	−0.999435
$122$	−18.5289	−1.67753
$123$	−1.92438	−0.173515
$124$	38.6247	3.46860
$125$	−1.09955	−0.0983471
$126$	−3.96832	−0.353526
$127$	14.6191	1.29723	0.648616	−	0.761116i	$-0.275348\pi$
$127$	14.6191	1.29723	0.648616	+	0.761116i	$0.275348\pi$
$128$	−48.8680	−4.31936
$129$	−2.72015	−0.239496
$130$	0.361676	0.0317211
$131$	−0.117046	−0.0102263	−0.00511316	−	0.999987i	$-0.501628\pi$
$131$	−0.117046	−0.0102263	−0.00511316	+	0.999987i	$0.501628\pi$
$132$	−0.441175	−0.0383993
$133$	−3.26378	−0.283005
$134$	−25.9519	−2.24190
$135$	0.110089	0.00947494
$136$	−7.74635	−0.664244
$137$	17.2615	1.47475	0.737376	−	0.675482i	$-0.236065\pi$
$137$	17.2615	1.47475	0.737376	+	0.675482i	$0.236065\pi$
$138$	14.7951	1.25945
$139$	4.71172	0.399643	0.199821	−	0.979832i	$-0.435964\pi$
$139$	4.71172	0.399643	0.199821	+	0.979832i	$0.435964\pi$
$140$	0.887019	0.0749668
$141$	−0.0476025	−0.00400885
$142$	6.41178	0.538065
$143$	0.0939772	0.00785877
$144$	16.1227	1.34356
$145$	−0.0154294	−0.00128134
$146$	−42.5813	−3.52406
$147$	−4.92684	−0.406359
$148$	5.05684	0.415669
$149$	−14.3317	−1.17410	−0.587048	−	0.809552i	$-0.699710\pi$
$149$	−14.3317	−1.17410	−0.587048	+	0.809552i	$0.699710\pi$
$150$	13.7470	1.12244
$151$	−18.5093	−1.50627	−0.753134	−	0.657867i	$-0.771459\pi$
$151$	−18.5093	−1.50627	−0.753134	+	0.657867i	$0.771459\pi$
$152$	22.4651	1.82216
$153$	0.781615	0.0631899
$154$	0.312856	0.0252106
$155$	0.759862	0.0610336
$156$	−6.67051	−0.534068
$157$	−8.08169	−0.644989	−0.322494	−	0.946571i	$-0.604521\pi$
$157$	−8.08169	−0.644989	−0.322494	+	0.946571i	$0.604521\pi$
$158$	−19.3524	−1.53960
$159$	3.74754	0.297199
$160$	−2.70973	−0.214223
$161$	−7.72937	−0.609160
$162$	−2.75607	−0.216538
$163$	23.1826	1.81580	0.907902	−	0.419182i	$-0.137683\pi$
$163$	23.1826	1.81580	0.907902	+	0.419182i	$0.137683\pi$
$164$	−10.7687	−0.840896
$165$	−0.00867922	−0.000675676 0
$166$	−40.5498	−3.14727
$167$	6.08845	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$167$	6.08845	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$168$	−14.2699	−1.10094
$169$	−11.5791	−0.890698
$170$	−0.237152	−0.0181888
$171$	−2.26675	−0.173343
$172$	−15.2218	−1.16065
$173$	11.1913	0.850856	0.425428	−	0.904992i	$-0.360124\pi$
$173$	11.1913	0.850856	0.425428	+	0.904992i	$0.360124\pi$
$174$	0.386276	0.0292835
$175$	−7.18178	−0.542891
$176$	−1.27109	−0.0958119
$177$	−11.1497	−0.838063
$178$	44.2085	3.31356
$179$	2.79118	0.208622	0.104311	−	0.994545i	$-0.466736\pi$
$179$	2.79118	0.208622	0.104311	+	0.994545i	$0.466736\pi$
$180$	0.616051	0.0459178
$181$	24.8091	1.84405	0.922023	−	0.387134i	$-0.126535\pi$
$181$	24.8091	1.84405	0.922023	+	0.387134i	$0.126535\pi$
$182$	4.73034	0.350636
$183$	6.72295	0.496975
$184$	53.2026	3.92214
$185$	0.0994830	0.00731414
$186$	−19.0231	−1.39484
$187$	−0.0616212	−0.00450619
$188$	−0.266381	−0.0194278
$189$	1.43985	0.104733
$190$	0.687763	0.0498956
$191$	9.31265	0.673840	0.336920	−	0.941533i	$-0.390615\pi$
$191$	9.31265	0.673840	0.336920	+	0.941533i	$0.390615\pi$
$192$	35.5927	2.56868
$193$	5.43914	0.391518	0.195759	−	0.980652i	$-0.437283\pi$
$193$	5.43914	0.391518	0.195759	+	0.980652i	$0.437283\pi$
$194$	8.72147	0.626165
$195$	−0.131229	−0.00939748
$196$	−27.5704	−1.96931
$197$	13.1030	0.933550	0.466775	−	0.884376i	$-0.345416\pi$
$197$	13.1030	0.933550	0.466775	+	0.884376i	$0.345416\pi$
$198$	0.217284	0.0154417
$199$	19.9869	1.41683	0.708415	−	0.705796i	$-0.249410\pi$
$199$	19.9869	1.41683	0.708415	+	0.705796i	$0.249410\pi$
$200$	49.4334	3.49547
$201$	9.41624	0.664170
$202$	−40.5222	−2.85113
$203$	−0.201801	−0.0141636
$204$	4.37388	0.306233
$205$	−0.211853	−0.0147964
$206$	−20.1834	−1.40625
$207$	−5.36820	−0.373115
$208$	−19.2187	−1.33258
$209$	0.178707	0.0123614
$210$	−0.436868	−0.0301468
$211$	18.8138	1.29519	0.647596	−	0.761984i	$-0.275774\pi$
$211$	18.8138	1.29519	0.647596	+	0.761984i	$0.275774\pi$
$212$	20.9710	1.44030
$213$	−2.32642	−0.159403
$214$	53.0746	3.62810
$215$	−0.299458	−0.0204229
$216$	−9.91070	−0.674337
$217$	9.93818	0.674648
$218$	−5.77786	−0.391326
$219$	15.4500	1.04401
$220$	−0.0485685	−0.00327448
$221$	−0.931705	−0.0626733
$222$	−2.49056	−0.167155
$223$	4.35219	0.291444	0.145722	−	0.989326i	$-0.453449\pi$
$223$	4.35219	0.291444	0.145722	+	0.989326i	$0.453449\pi$
$224$	−35.4404	−2.36796
$225$	−4.98788	−0.332525
$226$	−38.2846	−2.54665
$227$	−3.16005	−0.209740	−0.104870	−	0.994486i	$-0.533443\pi$
$227$	−3.16005	−0.209740	−0.104870	+	0.994486i	$0.533443\pi$
$228$	−12.6846	−0.840061
$229$	9.94671	0.657297	0.328648	−	0.944452i	$-0.393407\pi$
$229$	9.94671	0.657297	0.328648	+	0.944452i	$0.393407\pi$
$230$	1.62878	0.107399
$231$	−0.113515	−0.00746874
$232$	1.38903	0.0911941
$233$	21.4661	1.40629	0.703144	−	0.711048i	$-0.251779\pi$
$233$	21.4661	1.40629	0.703144	+	0.711048i	$0.251779\pi$
$234$	3.28531	0.214767
$235$	−0.00524050	−0.000341853 0
$236$	−62.3931	−4.06145
$237$	7.02174	0.456111
$238$	−3.10170	−0.201053
$239$	7.65270	0.495012	0.247506	−	0.968886i	$-0.420389\pi$
$239$	7.65270	0.495012	0.247506	+	0.968886i	$0.420389\pi$
$240$	1.77493	0.114571
$241$	17.1582	1.10526	0.552628	−	0.833428i	$-0.313625\pi$
$241$	17.1582	1.10526	0.552628	+	0.833428i	$0.313625\pi$
$242$	30.2997	1.94774
$243$	1.00000	0.0641500
$244$	37.6213	2.40845
$245$	−0.542391	−0.0346521
$246$	5.30373	0.338153
$247$	2.70203	0.171926
$248$	−68.4062	−4.34380
$249$	14.7129	0.932390
$250$	3.03045	0.191663
$251$	7.62276	0.481144	0.240572	−	0.970631i	$-0.422665\pi$
$251$	7.62276	0.481144	0.240572	+	0.970631i	$0.422665\pi$
$252$	8.05730	0.507562
$253$	0.423219	0.0266076
$254$	−40.2912	−2.52810
$255$	0.0860472	0.00538848
$256$	63.4984	3.96865
$257$	21.4895	1.34048	0.670241	−	0.742144i	$-0.266191\pi$
$257$	21.4895	1.34048	0.670241	+	0.742144i	$0.266191\pi$
$258$	7.49693	0.466739
$259$	1.30113	0.0808484
$260$	−0.734349	−0.0455424
$261$	−0.140154	−0.00867533
$262$	0.322586	0.0199294
$263$	−2.73623	−0.168723	−0.0843614	−	0.996435i	$-0.526885\pi$
$263$	−2.73623	−0.168723	−0.0843614	+	0.996435i	$0.526885\pi$
$264$	0.781342	0.0480883
$265$	0.412563	0.0253435
$266$	8.99521	0.551532
$267$	−16.0404	−0.981655
$268$	52.6928	3.21872
$269$	−25.7350	−1.56909	−0.784546	−	0.620071i	$-0.787104\pi$
$269$	−25.7350	−1.56909	−0.784546	+	0.620071i	$0.787104\pi$
$270$	−0.303413	−0.0184651
$271$	26.7687	1.62608	0.813042	−	0.582205i	$-0.197810\pi$
$271$	26.7687	1.62608	0.813042	+	0.582205i	$0.197810\pi$
$272$	12.6018	0.764094
$273$	−1.71633	−0.103877
$274$	−47.5741	−2.87406
$275$	0.393236	0.0237130
$276$	−30.0401	−1.80820
$277$	−21.8169	−1.31085	−0.655425	−	0.755260i	$-0.727510\pi$
$277$	−21.8169	−1.31085	−0.655425	+	0.755260i	$0.727510\pi$
$278$	−12.9858	−0.778839
$279$	6.90226	0.413227
$280$	−1.57095	−0.0938825
$281$	−5.15863	−0.307738	−0.153869	−	0.988091i	$-0.549173\pi$
$281$	−5.15863	−0.307738	−0.153869	+	0.988091i	$0.549173\pi$
$282$	0.131196	0.00781261
$283$	−13.2745	−0.789090	−0.394545	−	0.918877i	$-0.629098\pi$
$283$	−13.2745	−0.789090	−0.394545	+	0.918877i	$0.629098\pi$
$284$	−13.0185	−0.772506
$285$	−0.249544	−0.0147817
$286$	−0.259008	−0.0153155
$287$	−2.77081	−0.163556
$288$	−24.6140	−1.45040
$289$	−16.3891	−0.964063
$290$	0.0425246	0.00249713
$291$	−3.16445	−0.185504
$292$	86.4573	5.05953
$293$	25.2928	1.47762	0.738810	−	0.673914i	$-0.235388\pi$
$293$	25.2928	1.47762	0.738810	+	0.673914i	$0.235388\pi$
$294$	13.5787	0.791929
$295$	−1.22746	−0.0714654
$296$	−8.95591	−0.520552
$297$	−0.0788383	−0.00457466
$298$	39.4992	2.28812
$299$	6.39902	0.370065
$300$	−27.9119	−1.61150
$301$	−3.91660	−0.225749
$302$	51.0131	2.93547
$303$	14.7029	0.844658
$304$	−36.5463	−2.09607
$305$	0.740122	0.0423793
$306$	−2.15419	−0.123147
$307$	8.87263	0.506388	0.253194	−	0.967416i	$-0.418519\pi$
$307$	8.87263	0.506388	0.253194	+	0.967416i	$0.418519\pi$
$308$	−0.635224	−0.0361952
$309$	7.32325	0.416605
$310$	−2.09424	−0.118945
$311$	−12.6628	−0.718043	−0.359022	−	0.933329i	$-0.616890\pi$
$311$	−12.6628	−0.718043	−0.359022	+	0.933329i	$0.616890\pi$
$312$	11.8138	0.668825
$313$	3.64883	0.206244	0.103122	−	0.994669i	$-0.467117\pi$
$313$	3.64883	0.206244	0.103122	+	0.994669i	$0.467117\pi$
$314$	22.2737	1.25698
$315$	0.158511	0.00893108
$316$	39.2933	2.21042
$317$	18.4750	1.03766	0.518829	−	0.854878i	$-0.326368\pi$
$317$	18.4750	1.03766	0.518829	+	0.854878i	$0.326368\pi$
$318$	−10.3285	−0.579194
$319$	0.0110495	0.000618655 0
$320$	3.91836	0.219043
$321$	−19.2573	−1.07484
$322$	21.3027	1.18715
$323$	−1.77173	−0.0985817
$324$	5.59595	0.310886
$325$	5.94568	0.329807
$326$	−63.8931	−3.53871
$327$	2.09641	0.115932
$328$	19.0719	1.05307
$329$	−0.0685402	−0.00377875
$330$	0.0239206	0.00131678
$331$	−32.1696	−1.76820	−0.884101	−	0.467296i	$-0.845228\pi$
$331$	−32.1696	−1.76820	−0.884101	+	0.467296i	$0.845228\pi$
$332$	82.3324	4.51858
$333$	0.903661	0.0495203
$334$	−16.7802	−0.918173
$335$	1.03662	0.0566368
$336$	23.2142	1.26644
$337$	−19.3712	−1.05522	−0.527609	−	0.849487i	$-0.676912\pi$
$337$	−19.3712	−1.05522	−0.527609	+	0.849487i	$0.676912\pi$
$338$	31.9128	1.73583
$339$	13.8910	0.754455
$340$	0.481515	0.0261138
$341$	−0.544162	−0.0294680
$342$	6.24734	0.337818
$343$	−17.1728	−0.927245
$344$	26.9586	1.45351
$345$	−0.590979	−0.0318172
$346$	−30.8439	−1.65818
$347$	3.43557	0.184431	0.0922155	−	0.995739i	$-0.470605\pi$
$347$	3.43557	0.184431	0.0922155	+	0.995739i	$0.470605\pi$
$348$	−0.784296	−0.0420427
$349$	17.0909	0.914857	0.457429	−	0.889246i	$-0.348771\pi$
$349$	17.0909	0.914857	0.457429	+	0.889246i	$0.348771\pi$
$350$	19.7935	1.05801
$351$	−1.19203	−0.0636256
$352$	1.94053	0.103431
$353$	28.3332	1.50803	0.754013	−	0.656859i	$-0.228115\pi$
$353$	28.3332	1.50803	0.754013	+	0.656859i	$0.228115\pi$
$354$	30.7294	1.63325
$355$	−0.256113	−0.0135930
$356$	−89.7611	−4.75733
$357$	1.12541	0.0595628
$358$	−7.69269	−0.406571
$359$	9.50107	0.501447	0.250724	−	0.968059i	$-0.419331\pi$
$359$	9.50107	0.501447	0.250724	+	0.968059i	$0.419331\pi$
$360$	−1.09106	−0.0575038
$361$	−13.8618	−0.729570
$362$	−68.3758	−3.59375
$363$	−10.9938	−0.577024
$364$	−9.60450	−0.503413
$365$	1.70087	0.0890277
$366$	−18.5289	−0.968524
$367$	−22.7474	−1.18740	−0.593702	−	0.804685i	$-0.702334\pi$
$367$	−22.7474	−1.18740	−0.593702	+	0.804685i	$0.702334\pi$
$368$	−86.5499	−4.51173
$369$	−1.92438	−0.100179
$370$	−0.274183	−0.0142541
$371$	5.39588	0.280140
$372$	38.6247	2.00260
$373$	20.8796	1.08111	0.540553	−	0.841310i	$-0.318215\pi$
$373$	20.8796	1.08111	0.540553	+	0.841310i	$0.318215\pi$
$374$	0.169833	0.00878184
$375$	−1.09955	−0.0567808
$376$	0.471774	0.0243299
$377$	0.167067	0.00860441
$378$	−3.96832	−0.204108
$379$	−26.8200	−1.37765	−0.688826	−	0.724927i	$-0.741874\pi$
$379$	−26.8200	−1.37765	−0.688826	+	0.724927i	$0.741874\pi$
$380$	−1.39644	−0.0716357
$381$	14.6191	0.748957
$382$	−25.6664	−1.31321
$383$	27.3799	1.39905	0.699523	−	0.714610i	$-0.253396\pi$
$383$	27.3799	1.39905	0.699523	+	0.714610i	$0.253396\pi$
$384$	−48.8680	−2.49378
$385$	−0.0124967	−0.000636893 0
$386$	−14.9907	−0.763006
$387$	−2.72015	−0.138273
$388$	−17.7081	−0.898994
$389$	−17.4782	−0.886180	−0.443090	−	0.896477i	$-0.646118\pi$
$389$	−17.4782	−0.886180	−0.443090	+	0.896477i	$0.646118\pi$
$390$	0.361676	0.0183142
$391$	−4.19586	−0.212194
$392$	48.8285	2.46621
$393$	−0.117046	−0.00590416
$394$	−36.1128	−1.81934
$395$	0.773016	0.0388946
$396$	−0.441175	−0.0221699
$397$	−6.92519	−0.347565	−0.173783	−	0.984784i	$-0.555599\pi$
$397$	−6.92519	−0.347565	−0.173783	+	0.984784i	$0.555599\pi$
$398$	−55.0853	−2.76118
$399$	−3.26378	−0.163393
$400$	−80.4182	−4.02091
$401$	5.37106	0.268218	0.134109	−	0.990967i	$-0.457183\pi$
$401$	5.37106	0.268218	0.134109	+	0.990967i	$0.457183\pi$
$402$	−25.9519	−1.29436
$403$	−8.22766	−0.409849
$404$	82.2765	4.09341
$405$	0.110089	0.00547036
$406$	0.556177	0.0276026
$407$	−0.0712431	−0.00353139
$408$	−7.74635	−0.383502
$409$	−7.39223	−0.365522	−0.182761	−	0.983157i	$-0.558503\pi$
$409$	−7.39223	−0.365522	−0.182761	+	0.983157i	$0.558503\pi$
$410$	0.583882	0.0288359
$411$	17.2615	0.851449
$412$	40.9805	2.01897
$413$	−16.0538	−0.789958
$414$	14.7951	0.727142
$415$	1.61972	0.0795091
$416$	29.3405	1.43854
$417$	4.71172	0.230734
$418$	−0.492530	−0.0240904
$419$	17.6677	0.863124	0.431562	−	0.902083i	$-0.357963\pi$
$419$	17.6677	0.863124	0.431562	+	0.902083i	$0.357963\pi$
$420$	0.887019	0.0432821
$421$	−2.31305	−0.112731	−0.0563657	−	0.998410i	$-0.517951\pi$
$421$	−2.31305	−0.112731	−0.0563657	+	0.998410i	$0.517951\pi$
$422$	−51.8521	−2.52412
$423$	−0.0476025	−0.00231451
$424$	−37.1407	−1.80371
$425$	−3.89860	−0.189110
$426$	6.41178	0.310652
$427$	9.68001	0.468449
$428$	−107.763	−5.20892
$429$	0.0939772	0.00453726
$430$	0.825329	0.0398009
$431$	−11.1812	−0.538577	−0.269289	−	0.963060i	$-0.586789\pi$
$431$	−11.1812	−0.538577	−0.269289	+	0.963060i	$0.586789\pi$
$432$	16.1227	0.775705
$433$	−32.0607	−1.54074	−0.770369	−	0.637598i	$-0.779928\pi$
$433$	−32.0607	−1.54074	−0.770369	+	0.637598i	$0.779928\pi$
$434$	−27.3904	−1.31478
$435$	−0.0154294	−0.000739784 0
$436$	11.7314	0.561832
$437$	12.1684	0.582093
$438$	−42.5813	−2.03461
$439$	27.4159	1.30849	0.654246	−	0.756282i	$-0.272986\pi$
$439$	27.4159	1.30849	0.654246	+	0.756282i	$0.272986\pi$
$440$	0.0860171	0.00410071
$441$	−4.92684	−0.234612
$442$	2.56785	0.122140
$443$	−20.3313	−0.965971	−0.482985	−	0.875628i	$-0.660448\pi$
$443$	−20.3313	−0.965971	−0.482985	+	0.875628i	$0.660448\pi$
$444$	5.05684	0.239987
$445$	−1.76587	−0.0837101
$446$	−11.9950	−0.567978
$447$	−14.3317	−0.677865
$448$	51.2480	2.42124
$449$	26.5362	1.25232	0.626160	−	0.779694i	$-0.284626\pi$
$449$	26.5362	1.25232	0.626160	+	0.779694i	$0.284626\pi$
$450$	13.7470	0.648038
$451$	0.151715	0.00714397
$452$	77.7333	3.65626
$453$	−18.5093	−0.869645
$454$	8.70932	0.408749
$455$	−0.188949	−0.00885807
$456$	22.4651	1.05203
$457$	−15.0585	−0.704408	−0.352204	−	0.935923i	$-0.614568\pi$
$457$	−15.0585	−0.704408	−0.352204	+	0.935923i	$0.614568\pi$
$458$	−27.4139	−1.28097
$459$	0.781615	0.0364827
$460$	−3.30708	−0.154194
$461$	−7.96082	−0.370772	−0.185386	−	0.982666i	$-0.559354\pi$
$461$	−7.96082	−0.370772	−0.185386	+	0.982666i	$0.559354\pi$
$462$	0.312856	0.0145554
$463$	−20.1588	−0.936861	−0.468431	−	0.883500i	$-0.655180\pi$
$463$	−20.1588	−0.936861	−0.468431	+	0.883500i	$0.655180\pi$
$464$	−2.25967	−0.104902
$465$	0.759862	0.0352377
$466$	−59.1620	−2.74063
$467$	−6.00211	−0.277745	−0.138872	−	0.990310i	$-0.544348\pi$
$467$	−6.00211	−0.277745	−0.138872	+	0.990310i	$0.544348\pi$
$468$	−6.67051	−0.308344
$469$	13.5579	0.626047
$470$	0.0144432	0.000666216 0
$471$	−8.08169	−0.372384
$472$	110.501	5.08623
$473$	0.214452	0.00986051
$474$	−19.3524	−0.888887
$475$	11.3063	0.518769
$476$	6.29771	0.288655
$477$	3.74754	0.171588
$478$	−21.0914	−0.964699
$479$	−12.5656	−0.574137	−0.287069	−	0.957910i	$-0.592681\pi$
$479$	−12.5656	−0.574137	−0.287069	+	0.957910i	$0.592681\pi$
$480$	−2.70973	−0.123682
$481$	−1.07719	−0.0491155
$482$	−47.2892	−2.15397
$483$	−7.72937	−0.351699
$484$	−61.5206	−2.79639
$485$	−0.348371	−0.0158187
$486$	−2.75607	−0.125018
$487$	2.12392	0.0962441	0.0481221	−	0.998841i	$-0.484676\pi$
$487$	2.12392	0.0962441	0.0481221	+	0.998841i	$0.484676\pi$
$488$	−66.6291	−3.01616
$489$	23.1826	1.04836
$490$	1.49487	0.0675313
$491$	13.4654	0.607683	0.303842	−	0.952723i	$-0.401731\pi$
$491$	13.4654	0.607683	0.303842	+	0.952723i	$0.401731\pi$
$492$	−10.7687	−0.485491
$493$	−0.109547	−0.00493374
$494$	−7.44699	−0.335056
$495$	−0.00867922	−0.000390102 0
$496$	111.283	4.99676
$497$	−3.34968	−0.150254
$498$	−40.5498	−1.81708
$499$	25.7652	1.15341	0.576705	−	0.816953i	$-0.304338\pi$
$499$	25.7652	1.15341	0.576705	+	0.816953i	$0.304338\pi$
$500$	−6.15305	−0.275173
$501$	6.08845	0.272012
$502$	−21.0089	−0.937673
$503$	−18.4764	−0.823820	−0.411910	−	0.911224i	$-0.635138\pi$
$503$	−18.4764	−0.823820	−0.411910	+	0.911224i	$0.635138\pi$
$504$	−14.2699	−0.635631
$505$	1.61862	0.0720278
$506$	−1.16642	−0.0518539
$507$	−11.5791	−0.514245
$508$	81.8075	3.62962
$509$	−27.5480	−1.22104	−0.610522	−	0.791999i	$-0.709041\pi$
$509$	−27.5480	−1.22104	−0.610522	+	0.791999i	$0.709041\pi$
$510$	−0.237152	−0.0105013
$511$	22.2456	0.984088
$512$	−77.2705	−3.41491
$513$	−2.26675	−0.100080
$514$	−59.2268	−2.61238
$515$	0.806209	0.0355258
$516$	−15.2218	−0.670103
$517$	0.00375290	0.000165052 0
$518$	−3.58602	−0.157561
$519$	11.1913	0.491242
$520$	1.30057	0.0570337
$521$	−15.0611	−0.659840	−0.329920	−	0.944009i	$-0.607022\pi$
$521$	−15.0611	−0.659840	−0.329920	+	0.944009i	$0.607022\pi$
$522$	0.386276	0.0169068
$523$	−29.6345	−1.29583	−0.647914	−	0.761713i	$-0.724358\pi$
$523$	−29.6345	−1.29583	−0.647914	+	0.761713i	$0.724358\pi$
$524$	−0.654980	−0.0286130
$525$	−7.18178	−0.313439
$526$	7.54124	0.328814
$527$	5.39491	0.235006
$528$	−1.27109	−0.0553170
$529$	5.81752	0.252936
$530$	−1.13705	−0.0493904
$531$	−11.1497	−0.483856
$532$	−18.2639	−0.791841
$533$	2.29391	0.0993601
$534$	44.2085	1.91309
$535$	−2.12002	−0.0916563
$536$	−93.3215	−4.03087
$537$	2.79118	0.120448
$538$	70.9276	3.05791
$539$	0.388424	0.0167306
$540$	0.616051	0.0265106
$541$	1.52676	0.0656406	0.0328203	−	0.999461i	$-0.489551\pi$
$541$	1.52676	0.0656406	0.0328203	+	0.999461i	$0.489551\pi$
$542$	−73.7766	−3.16898
$543$	24.8091	1.06466
$544$	−19.2387	−0.824853
$545$	0.230792	0.00988602
$546$	4.73034	0.202440
$547$	−7.58831	−0.324453	−0.162226	−	0.986754i	$-0.551867\pi$
$547$	−7.58831	−0.324453	−0.162226	+	0.986754i	$0.551867\pi$
$548$	96.5946	4.12632
$549$	6.72295	0.286928
$550$	−1.08379	−0.0462129
$551$	0.317695	0.0135343
$552$	53.2026	2.26445
$553$	10.1102	0.429931
$554$	60.1290	2.55464
$555$	0.0994830	0.00422282
$556$	26.3665	1.11819
$557$	15.6551	0.663328	0.331664	−	0.943398i	$-0.392390\pi$
$557$	15.6551	0.663328	0.331664	+	0.943398i	$0.392390\pi$
$558$	−19.0231	−0.805313
$559$	3.24249	0.137143
$560$	2.55563	0.107995
$561$	−0.0616212	−0.00260165
$562$	14.2176	0.599732
$563$	−6.05473	−0.255177	−0.127588	−	0.991827i	$-0.540724\pi$
$563$	−6.05473	−0.255177	−0.127588	+	0.991827i	$0.540724\pi$
$564$	−0.266381	−0.0112167
$565$	1.52924	0.0643358
$566$	36.5856	1.53781
$567$	1.43985	0.0604678
$568$	23.0564	0.967426
$569$	9.67767	0.405709	0.202855	−	0.979209i	$-0.434978\pi$
$569$	9.67767	0.405709	0.202855	+	0.979209i	$0.434978\pi$
$570$	0.687763	0.0288072
$571$	−22.3562	−0.935577	−0.467788	−	0.883841i	$-0.654949\pi$
$571$	−22.3562	−0.935577	−0.467788	+	0.883841i	$0.654949\pi$
$572$	0.525892	0.0219886
$573$	9.31265	0.389042
$574$	7.63655	0.318744
$575$	26.7759	1.11663
$576$	35.5927	1.48303
$577$	−13.5877	−0.565665	−0.282832	−	0.959169i	$-0.591274\pi$
$577$	−13.5877	−0.565665	−0.282832	+	0.959169i	$0.591274\pi$
$578$	45.1695	1.87880
$579$	5.43914	0.226043
$580$	−0.0863422	−0.00358517
$581$	21.1843	0.878871
$582$	8.72147	0.361517
$583$	−0.295450	−0.0122363
$584$	−153.120	−6.33616
$585$	−0.131229	−0.00542564
$586$	−69.7088	−2.87964
$587$	−5.20905	−0.215000	−0.107500	−	0.994205i	$-0.534285\pi$
$587$	−5.20905	−0.215000	−0.107500	+	0.994205i	$0.534285\pi$
$588$	−27.5704	−1.13698
$589$	−15.6457	−0.644671
$590$	3.38297	0.139274
$591$	13.1030	0.538985
$592$	14.5695	0.598802
$593$	−9.26031	−0.380275	−0.190138	−	0.981757i	$-0.560893\pi$
$593$	−9.26031	−0.380275	−0.190138	+	0.981757i	$0.560893\pi$
$594$	0.217284	0.00891528
$595$	0.123895	0.00507918
$596$	−80.1993	−3.28509
$597$	19.9869	0.818008
$598$	−17.6362	−0.721197
$599$	1.24840	0.0510084	0.0255042	−	0.999675i	$-0.491881\pi$
$599$	1.24840	0.0510084	0.0255042	+	0.999675i	$0.491881\pi$
$600$	49.4334	2.01811
$601$	4.53374	0.184935	0.0924675	−	0.995716i	$-0.470525\pi$
$601$	4.53374	0.184935	0.0924675	+	0.995716i	$0.470525\pi$
$602$	10.7944	0.439948
$603$	9.41624	0.383459
$604$	−103.577	−4.21450
$605$	−1.21029	−0.0492054
$606$	−40.5222	−1.64610
$607$	16.1967	0.657403	0.328701	−	0.944434i	$-0.393389\pi$
$607$	16.1967	0.657403	0.328701	+	0.944434i	$0.393389\pi$
$608$	55.7940	2.26274
$609$	−0.201801	−0.00817737
$610$	−2.03983	−0.0825903
$611$	0.0567434	0.00229559
$612$	4.37388	0.176804
$613$	2.44721	0.0988417	0.0494209	−	0.998778i	$-0.484262\pi$
$613$	2.44721	0.0988417	0.0494209	+	0.998778i	$0.484262\pi$
$614$	−24.4536	−0.986869
$615$	−0.211853	−0.00854272
$616$	1.12501	0.0453281
$617$	−13.6207	−0.548350	−0.274175	−	0.961680i	$-0.588405\pi$
$617$	−13.6207	−0.548350	−0.274175	+	0.961680i	$0.588405\pi$
$618$	−20.1834	−0.811897
$619$	−11.0613	−0.444590	−0.222295	−	0.974979i	$-0.571355\pi$
$619$	−11.0613	−0.444590	−0.222295	+	0.974979i	$0.571355\pi$
$620$	4.25214	0.170770
$621$	−5.36820	−0.215418
$622$	34.8997	1.39935
$623$	−23.0957	−0.925308
$624$	−19.2187	−0.769363
$625$	24.8184	0.992734
$626$	−10.0565	−0.401937
$627$	0.178707	0.00713687
$628$	−45.2247	−1.80466
$629$	0.706315	0.0281626
$630$	−0.436868	−0.0174052
$631$	24.5623	0.977811	0.488906	−	0.872337i	$-0.337396\pi$
$631$	24.5623	0.977811	0.488906	+	0.872337i	$0.337396\pi$
$632$	−69.5904	−2.76816
$633$	18.8138	0.747780
$634$	−50.9184	−2.02223
$635$	1.60940	0.0638669
$636$	20.9710	0.831556
$637$	5.87292	0.232694
$638$	−0.0304533	−0.00120566
$639$	−2.32642	−0.0920316
$640$	−5.37982	−0.212656
$641$	−38.5614	−1.52309	−0.761543	−	0.648115i	$-0.775558\pi$
$641$	−38.5614	−1.52309	−0.761543	+	0.648115i	$0.775558\pi$
$642$	53.0746	2.09469
$643$	33.4818	1.32039	0.660196	−	0.751094i	$-0.270473\pi$
$643$	33.4818	1.32039	0.660196	+	0.751094i	$0.270473\pi$
$644$	−43.2532	−1.70441
$645$	−0.299458	−0.0117912
$646$	4.88302	0.192120
$647$	−26.2525	−1.03209	−0.516046	−	0.856561i	$-0.672597\pi$
$647$	−26.2525	−1.03209	−0.516046	+	0.856561i	$0.672597\pi$
$648$	−9.91070	−0.389329
$649$	0.879023	0.0345047
$650$	−16.3867	−0.642741
$651$	9.93818	0.389508
$652$	129.729	5.08057
$653$	14.1512	0.553781	0.276890	−	0.960902i	$-0.410696\pi$
$653$	14.1512	0.553781	0.276890	+	0.960902i	$0.410696\pi$
$654$	−5.77786	−0.225932
$655$	−0.0128854	−0.000503475 0
$656$	−31.0262	−1.21137
$657$	15.4500	0.602762
$658$	0.188902	0.00736417
$659$	29.4226	1.14614	0.573072	−	0.819505i	$-0.305752\pi$
$659$	29.4226	1.14614	0.573072	+	0.819505i	$0.305752\pi$
$660$	−0.0485685	−0.00189052
$661$	−30.0095	−1.16724	−0.583618	−	0.812029i	$-0.698363\pi$
$661$	−30.0095	−1.16724	−0.583618	+	0.812029i	$0.698363\pi$
$662$	88.6619	3.44594
$663$	−0.931705	−0.0361844
$664$	−145.815	−5.65871
$665$	−0.359306	−0.0139333
$666$	−2.49056	−0.0965071
$667$	0.752375	0.0291321
$668$	34.0706	1.31823
$669$	4.35219	0.168266
$670$	−2.85701	−0.110376
$671$	−0.530026	−0.0204614
$672$	−35.4404	−1.36714
$673$	38.7015	1.49183	0.745916	−	0.666040i	$-0.232012\pi$
$673$	38.7015	1.49183	0.745916	+	0.666040i	$0.232012\pi$
$674$	53.3886	2.05645
$675$	−4.98788	−0.191984
$676$	−64.7959	−2.49215
$677$	17.5453	0.674320	0.337160	−	0.941447i	$-0.390534\pi$
$677$	17.5453	0.674320	0.337160	+	0.941447i	$0.390534\pi$
$678$	−38.2846	−1.47031
$679$	−4.55633	−0.174856
$680$	−0.852787	−0.0327029
$681$	−3.16005	−0.121093
$682$	1.49975	0.0574284
$683$	−51.3379	−1.96439	−0.982195	−	0.187864i	$-0.939844\pi$
$683$	−51.3379	−1.96439	−0.982195	+	0.187864i	$0.939844\pi$
$684$	−12.6846	−0.485009
$685$	1.90030	0.0726068
$686$	47.3296	1.80705
$687$	9.94671	0.379491
$688$	−43.8562	−1.67200
$689$	−4.46716	−0.170185
$690$	1.62878	0.0620066
$691$	38.6423	1.47002	0.735010	−	0.678056i	$-0.237177\pi$
$691$	38.6423	1.47002	0.735010	+	0.678056i	$0.237177\pi$
$692$	62.6257	2.38067
$693$	−0.113515	−0.00431208
$694$	−9.46868	−0.359426
$695$	0.518708	0.0196757
$696$	1.38903	0.0526509
$697$	−1.50412	−0.0569727
$698$	−47.1039	−1.78291
$699$	21.4661	0.811921
$700$	−40.1888	−1.51900
$701$	14.1508	0.534467	0.267233	−	0.963632i	$-0.413891\pi$
$701$	14.1508	0.534467	0.267233	+	0.963632i	$0.413891\pi$
$702$	3.28531	0.123996
$703$	−2.04838	−0.0772560
$704$	−2.80607	−0.105758
$705$	−0.00524050	−0.000197369 0
$706$	−78.0885	−2.93890
$707$	21.1699	0.796175
$708$	−62.3931	−2.34488
$709$	−17.2232	−0.646831	−0.323415	−	0.946257i	$-0.604831\pi$
$709$	−17.2232	−0.646831	−0.323415	+	0.946257i	$0.604831\pi$
$710$	0.705866	0.0264907
$711$	7.02174	0.263336
$712$	158.971	5.95770
$713$	−37.0527	−1.38763
$714$	−3.10170	−0.116078
$715$	0.0103458	0.000386913 0
$716$	15.6193	0.583720
$717$	7.65270	0.285795
$718$	−26.1857	−0.977240
$719$	35.8461	1.33683	0.668417	−	0.743787i	$-0.266972\pi$
$719$	35.8461	1.33683	0.668417	+	0.743787i	$0.266972\pi$
$720$	1.77493	0.0661478
$721$	10.5444	0.392692
$722$	38.2042	1.42181
$723$	17.1582	0.638120
$724$	138.830	5.15959
$725$	0.699073	0.0259629
$726$	30.2997	1.12453
$727$	4.64883	0.172415	0.0862077	−	0.996277i	$-0.472525\pi$
$727$	4.64883	0.172415	0.0862077	+	0.996277i	$0.472525\pi$
$728$	17.0100	0.630434
$729$	1.00000	0.0370370
$730$	−4.68773	−0.173501
$731$	−2.12611	−0.0786370
$732$	37.6213	1.39052
$733$	−12.5447	−0.463349	−0.231674	−	0.972793i	$-0.574420\pi$
$733$	−12.5447	−0.463349	−0.231674	+	0.972793i	$0.574420\pi$
$734$	62.6935	2.31406
$735$	−0.542391	−0.0200064
$736$	132.133	4.87049
$737$	−0.742360	−0.0273452
$738$	5.30373	0.195233
$739$	−20.2421	−0.744620	−0.372310	−	0.928109i	$-0.621434\pi$
$739$	−20.2421	−0.744620	−0.372310	+	0.928109i	$0.621434\pi$
$740$	0.556702	0.0204648
$741$	2.70203	0.0992615
$742$	−14.8715	−0.545948
$743$	39.8075	1.46040	0.730198	−	0.683235i	$-0.239428\pi$
$743$	39.8075	1.46040	0.730198	+	0.683235i	$0.239428\pi$
$744$	−68.4062	−2.50789
$745$	−1.57776	−0.0578046
$746$	−57.5458	−2.10690
$747$	14.7129	0.538316
$748$	−0.344829	−0.0126082
$749$	−27.7276	−1.01314
$750$	3.03045	0.110657
$751$	14.8689	0.542573	0.271287	−	0.962499i	$-0.412551\pi$
$751$	14.8689	0.542573	0.271287	+	0.962499i	$0.412551\pi$
$752$	−0.767482	−0.0279872
$753$	7.62276	0.277789
$754$	−0.460450	−0.0167686
$755$	−2.03767	−0.0741585
$756$	8.05730	0.293041
$757$	−22.8113	−0.829092	−0.414546	−	0.910028i	$-0.636060\pi$
$757$	−22.8113	−0.829092	−0.414546	+	0.910028i	$0.636060\pi$
$758$	73.9180	2.68482
$759$	0.423219	0.0153619
$760$	2.47316	0.0897109
$761$	42.1584	1.52824	0.764121	−	0.645073i	$-0.223173\pi$
$761$	42.1584	1.52824	0.764121	+	0.645073i	$0.223173\pi$
$762$	−40.2912	−1.45960
$763$	3.01851	0.109277
$764$	52.1131	1.88539
$765$	0.0860472	0.00311104
$766$	−75.4610	−2.72652
$767$	13.2907	0.479900
$768$	63.4984	2.29130
$769$	7.39667	0.266731	0.133365	−	0.991067i	$-0.457422\pi$
$769$	7.39667	0.266731	0.133365	+	0.991067i	$0.457422\pi$
$770$	0.0344419	0.00124120
$771$	21.4895	0.773927
$772$	30.4372	1.09546
$773$	5.29348	0.190393	0.0951965	−	0.995458i	$-0.469652\pi$
$773$	5.29348	0.190393	0.0951965	+	0.995458i	$0.469652\pi$
$774$	7.49693	0.269472
$775$	−34.4276	−1.23668
$776$	31.3620	1.12583
$777$	1.30113	0.0466779
$778$	48.1712	1.72702
$779$	4.36209	0.156288
$780$	−0.734349	−0.0262939
$781$	0.183411	0.00656295
$782$	11.5641	0.413532
$783$	−0.140154	−0.00500870
$784$	−79.4342	−2.83693
$785$	−0.889704	−0.0317549
$786$	0.322586	0.0115063
$787$	14.0069	0.499294	0.249647	−	0.968337i	$-0.419685\pi$
$787$	14.0069	0.499294	0.249647	+	0.968337i	$0.419685\pi$
$788$	73.3237	2.61205
$789$	−2.73623	−0.0974122
$790$	−2.13049	−0.0757994
$791$	20.0009	0.711150
$792$	0.781342	0.0277638
$793$	−8.01392	−0.284583
$794$	19.0863	0.677349
$795$	0.412563	0.0146321
$796$	111.845	3.96425
$797$	3.45035	0.122218	0.0611088	−	0.998131i	$-0.480536\pi$
$797$	3.45035	0.122218	0.0611088	+	0.998131i	$0.480536\pi$
$798$	8.99521	0.318427
$799$	−0.0372068	−0.00131628
$800$	122.772	4.34064
$801$	−16.0404	−0.566759
$802$	−14.8030	−0.522713
$803$	−1.21805	−0.0429841
$804$	52.6928	1.85833
$805$	−0.850918	−0.0299909
$806$	22.6760	0.798730
$807$	−25.7350	−0.905916
$808$	−145.716	−5.12626
$809$	−15.0161	−0.527937	−0.263969	−	0.964531i	$-0.585032\pi$
$809$	−15.0161	−0.527937	−0.263969	+	0.964531i	$0.585032\pi$
$810$	−0.303413	−0.0106609
$811$	−52.1260	−1.83039	−0.915195	−	0.403010i	$-0.867964\pi$
$811$	−52.1260	−1.83039	−0.915195	+	0.403010i	$0.867964\pi$
$812$	−1.12926	−0.0396294
$813$	26.7687	0.938820
$814$	0.196351	0.00688211
$815$	2.55215	0.0893979
$816$	12.6018	0.441150
$817$	6.16591	0.215718
$818$	20.3735	0.712344
$819$	−1.71633	−0.0599735
$820$	−1.18552	−0.0414000
$821$	24.8891	0.868636	0.434318	−	0.900760i	$-0.356989\pi$
$821$	24.8891	0.868636	0.434318	+	0.900760i	$0.356989\pi$
$822$	−47.5741	−1.65934
$823$	4.90950	0.171134	0.0855671	−	0.996332i	$-0.472730\pi$
$823$	4.90950	0.171134	0.0855671	+	0.996332i	$0.472730\pi$
$824$	−72.5786	−2.52839
$825$	0.393236	0.0136907
$826$	44.2456	1.53950
$827$	−5.56030	−0.193351	−0.0966753	−	0.995316i	$-0.530821\pi$
$827$	−5.56030	−0.193351	−0.0966753	+	0.995316i	$0.530821\pi$
$828$	−30.0401	−1.04397
$829$	2.76310	0.0959665	0.0479833	−	0.998848i	$-0.484721\pi$
$829$	2.76310	0.0959665	0.0479833	+	0.998848i	$0.484721\pi$
$830$	−4.46408	−0.154950
$831$	−21.8169	−0.756820
$832$	−42.4274	−1.47090
$833$	−3.85090	−0.133426
$834$	−12.9858	−0.449663
$835$	0.670271	0.0231957
$836$	1.00004	0.0345869
$837$	6.90226	0.238577
$838$	−48.6935	−1.68209
$839$	30.5576	1.05497	0.527483	−	0.849565i	$-0.323136\pi$
$839$	30.5576	1.05497	0.527483	+	0.849565i	$0.323136\pi$
$840$	−1.57095	−0.0542031
$841$	−28.9804	−0.999323
$842$	6.37495	0.219695
$843$	−5.15863	−0.177673
$844$	105.281	3.62391
$845$	−1.27473	−0.0438520
$846$	0.131196	0.00451061
$847$	−15.8294	−0.543903
$848$	60.4206	2.07485
$849$	−13.2745	−0.455581
$850$	10.7448	0.368545
$851$	−4.85103	−0.166291
$852$	−13.0185	−0.446007
$853$	−15.7416	−0.538981	−0.269490	−	0.963003i	$-0.586855\pi$
$853$	−15.7416	−0.538981	−0.269490	+	0.963003i	$0.586855\pi$
$854$	−26.6788	−0.912931
$855$	−0.249544	−0.00853424
$856$	190.853	6.52323
$857$	15.8132	0.540168	0.270084	−	0.962837i	$-0.412949\pi$
$857$	15.8132	0.540168	0.270084	+	0.962837i	$0.412949\pi$
$858$	−0.259008	−0.00884240
$859$	19.7235	0.672956	0.336478	−	0.941691i	$-0.390764\pi$
$859$	19.7235	0.672956	0.336478	+	0.941691i	$0.390764\pi$
$860$	−1.67575	−0.0571427
$861$	−2.77081	−0.0944289
$862$	30.8161	1.04960
$863$	21.0077	0.715110	0.357555	−	0.933892i	$-0.383610\pi$
$863$	21.0077	0.715110	0.357555	+	0.933892i	$0.383610\pi$
$864$	−24.6140	−0.837387
$865$	1.23203	0.0418904
$866$	88.3617	3.00265
$867$	−16.3891	−0.556602
$868$	55.6135	1.88765
$869$	−0.553582	−0.0187790
$870$	0.0425246	0.00144172
$871$	−11.2244	−0.380324
$872$	−20.7769	−0.703594
$873$	−3.16445	−0.107101
$874$	−33.5370	−1.13440
$875$	−1.58319	−0.0535216
$876$	86.4573	2.92112
$877$	55.6593	1.87948	0.939741	−	0.341887i	$-0.111066\pi$
$877$	55.6593	1.87948	0.939741	+	0.341887i	$0.111066\pi$
$878$	−75.5604	−2.55004
$879$	25.2928	0.853104
$880$	−0.139933	−0.00471713
$881$	42.5623	1.43396	0.716980	−	0.697094i	$-0.245524\pi$
$881$	42.5623	1.43396	0.716980	+	0.697094i	$0.245524\pi$
$882$	13.5787	0.457220
$883$	2.58016	0.0868294	0.0434147	−	0.999057i	$-0.486176\pi$
$883$	2.58016	0.0868294	0.0434147	+	0.999057i	$0.486176\pi$
$884$	−5.21377	−0.175358
$885$	−1.22746	−0.0412605
$886$	56.0347	1.88252
$887$	−55.0465	−1.84828	−0.924140	−	0.382054i	$-0.875217\pi$
$887$	−55.0465	−1.84828	−0.924140	+	0.382054i	$0.875217\pi$
$888$	−8.95591	−0.300541
$889$	21.0492	0.705967
$890$	4.86686	0.163138
$891$	−0.0788383	−0.00264118
$892$	24.3546	0.815454
$893$	0.107903	0.00361084
$894$	39.4992	1.32105
$895$	0.307278	0.0102712
$896$	−70.3624	−2.35064
$897$	6.39902	0.213657
$898$	−73.1357	−2.44057
$899$	−0.967381	−0.0322639
$900$	−27.9119	−0.930397
$901$	2.92914	0.0975837
$902$	−0.418137	−0.0139224
$903$	−3.91660	−0.130336
$904$	−137.669	−4.57882
$905$	2.73121	0.0907884
$906$	51.0131	1.69480
$907$	37.2310	1.23624	0.618118	−	0.786085i	$-0.287895\pi$
$907$	37.2310	1.23624	0.618118	+	0.786085i	$0.287895\pi$
$908$	−17.6834	−0.586846
$909$	14.7029	0.487663
$910$	0.520758	0.0172630
$911$	−30.5379	−1.01177	−0.505883	−	0.862602i	$-0.668833\pi$
$911$	−30.5379	−1.01177	−0.505883	+	0.862602i	$0.668833\pi$
$912$	−36.5463	−1.21017
$913$	−1.15994	−0.0383883
$914$	41.5024	1.37278
$915$	0.740122	0.0244677
$916$	55.6612	1.83910
$917$	−0.168527	−0.00556527
$918$	−2.15419	−0.0710989
$919$	−13.7697	−0.454221	−0.227111	−	0.973869i	$-0.572928\pi$
$919$	−13.7697	−0.454221	−0.227111	+	0.973869i	$0.572928\pi$
$920$	5.85701	0.193100
$921$	8.87263	0.292363
$922$	21.9406	0.722576
$923$	2.77315	0.0912793
$924$	−0.635224	−0.0208973
$925$	−4.50735	−0.148201
$926$	55.5593	1.82579
$927$	7.32325	0.240527
$928$	3.44976	0.113244
$929$	11.7525	0.385587	0.192794	−	0.981239i	$-0.438245\pi$
$929$	11.7525	0.385587	0.192794	+	0.981239i	$0.438245\pi$
$930$	−2.09424	−0.0686727
$931$	11.1679	0.366015
$932$	120.123	3.93476
$933$	−12.6628	−0.414563
$934$	16.5423	0.541279
$935$	−0.00678381	−0.000221854 0
$936$	11.8138	0.386146
$937$	33.5421	1.09577	0.547887	−	0.836552i	$-0.315432\pi$
$937$	33.5421	1.09577	0.547887	+	0.836552i	$0.315432\pi$
$938$	−37.3667	−1.22006
$939$	3.64883	0.119075
$940$	−0.0293256	−0.000956495 0
$941$	9.94975	0.324353	0.162176	−	0.986762i	$-0.448149\pi$
$941$	9.94975	0.324353	0.162176	+	0.986762i	$0.448149\pi$
$942$	22.2737	0.725717
$943$	10.3304	0.336405
$944$	−179.764	−5.85080
$945$	0.158511	0.00515636
$946$	−0.591046	−0.0192165
$947$	24.5295	0.797102	0.398551	−	0.917146i	$-0.369513\pi$
$947$	24.5295	0.797102	0.398551	+	0.917146i	$0.369513\pi$
$948$	39.2933	1.27619
$949$	−18.4168	−0.597834
$950$	−31.1610	−1.01100
$951$	18.4750	0.599092
$952$	−11.1536	−0.361489
$953$	41.0257	1.32895	0.664477	−	0.747309i	$-0.268654\pi$
$953$	41.0257	1.32895	0.664477	+	0.747309i	$0.268654\pi$
$954$	−10.3285	−0.334398
$955$	1.02522	0.0331753
$956$	42.8241	1.38503
$957$	0.0110495	0.000357180 0
$958$	34.6318	1.11890
$959$	24.8539	0.802576
$960$	3.91836	0.126464
$961$	16.6411	0.536811
$962$	2.96881	0.0957181
$963$	−19.2573	−0.620558
$964$	96.0163	3.09248
$965$	0.598789	0.0192757
$966$	21.3027	0.685404
$967$	47.5391	1.52875	0.764377	−	0.644769i	$-0.223047\pi$
$967$	47.5391	1.52875	0.764377	+	0.644769i	$0.223047\pi$
$968$	108.956	3.50198
$969$	−1.77173	−0.0569162
$970$	0.960137	0.0308281
$971$	−7.41369	−0.237917	−0.118958	−	0.992899i	$-0.537956\pi$
$971$	−7.41369	−0.237917	−0.118958	+	0.992899i	$0.537956\pi$
$972$	5.59595	0.179490
$973$	6.78414	0.217490
$974$	−5.85369	−0.187564
$975$	5.94568	0.190414
$976$	108.392	3.46955
$977$	−25.1269	−0.803882	−0.401941	−	0.915666i	$-0.631664\pi$
$977$	−25.1269	−0.803882	−0.401941	+	0.915666i	$0.631664\pi$
$978$	−63.8931	−2.04308
$979$	1.26460	0.0404167
$980$	−3.03519	−0.0969556
$981$	2.09641	0.0669333
$982$	−37.1115	−1.18428
$983$	35.6650	1.13754	0.568769	−	0.822497i	$-0.307420\pi$
$983$	35.6650	1.13754	0.568769	+	0.822497i	$0.307420\pi$
$984$	19.0719	0.607991
$985$	1.44249	0.0459617
$986$	0.301919	0.00961506
$987$	−0.0685402	−0.00218166
$988$	15.1204	0.481044
$989$	14.6023	0.464326
$990$	0.0239206	0.000760246 0
$991$	−44.8419	−1.42445	−0.712224	−	0.701952i	$-0.752312\pi$
$991$	−44.8419	−1.42445	−0.712224	+	0.701952i	$0.752312\pi$
$992$	−169.892	−5.39409
$993$	−32.1696	−1.02087
$994$	9.23197	0.292820
$995$	2.20033	0.0697552
$996$	82.3324	2.60880
$997$	−17.6539	−0.559105	−0.279552	−	0.960130i	$-0.590186\pi$
$997$	−17.6539	−0.559105	−0.279552	+	0.960130i	$0.590186\pi$
$998$	−71.0109	−2.24781
$999$	0.903661	0.0285906

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75607 q^{2} +1.00000 q^{3} +5.59595 q^{4} +0.110089 q^{5} -2.75607 q^{6} +1.43985 q^{7} -9.91070 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.75607 q^{2} +1.00000 q^{3} +5.59595 q^{4} +0.110089 q^{5} -2.75607 q^{6} +1.43985 q^{7} -9.91070 q^{8} +1.00000 q^{9} -0.303413 q^{10} -0.0788383 q^{11} +5.59595 q^{12} -1.19203 q^{13} -3.96832 q^{14} +0.110089 q^{15} +16.1227 q^{16} +0.781615 q^{17} -2.75607 q^{18} -2.26675 q^{19} +0.616051 q^{20} +1.43985 q^{21} +0.217284 q^{22} -5.36820 q^{23} -9.91070 q^{24} -4.98788 q^{25} +3.28531 q^{26} +1.00000 q^{27} +8.05730 q^{28} -0.140154 q^{29} -0.303413 q^{30} +6.90226 q^{31} -24.6140 q^{32} -0.0788383 q^{33} -2.15419 q^{34} +0.158511 q^{35} +5.59595 q^{36} +0.903661 q^{37} +6.24734 q^{38} -1.19203 q^{39} -1.09106 q^{40} -1.92438 q^{41} -3.96832 q^{42} -2.72015 q^{43} -0.441175 q^{44} +0.110089 q^{45} +14.7951 q^{46} -0.0476025 q^{47} +16.1227 q^{48} -4.92684 q^{49} +13.7470 q^{50} +0.781615 q^{51} -6.67051 q^{52} +3.74754 q^{53} -2.75607 q^{54} -0.00867922 q^{55} -14.2699 q^{56} -2.26675 q^{57} +0.386276 q^{58} -11.1497 q^{59} +0.616051 q^{60} +6.72295 q^{61} -19.0231 q^{62} +1.43985 q^{63} +35.5927 q^{64} -0.131229 q^{65} +0.217284 q^{66} +9.41624 q^{67} +4.37388 q^{68} -5.36820 q^{69} -0.436868 q^{70} -2.32642 q^{71} -9.91070 q^{72} +15.4500 q^{73} -2.49056 q^{74} -4.98788 q^{75} -12.6846 q^{76} -0.113515 q^{77} +3.28531 q^{78} +7.02174 q^{79} +1.77493 q^{80} +1.00000 q^{81} +5.30373 q^{82} +14.7129 q^{83} +8.05730 q^{84} +0.0860472 q^{85} +7.49693 q^{86} -0.140154 q^{87} +0.781342 q^{88} -16.0404 q^{89} -0.303413 q^{90} -1.71633 q^{91} -30.0401 q^{92} +6.90226 q^{93} +0.131196 q^{94} -0.249544 q^{95} -24.6140 q^{96} -3.16445 q^{97} +13.5787 q^{98} -0.0788383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \)	\( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

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Learn more about

Newspace parameters

Newform invariants

Embedding invariants

$q$-expansion

Coefficient data

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	8013.2.a.d.1.2

Level	8013
Weight	2
Character	8013.1
Self dual	Yes
Analytic conductor	63.984
Analytic rank	0
Dimension	129
CM	No

Self dual:	Yes
Analytic conductor:	\(63.9841271397\)
Analytic rank:	\(0\)
Dimension:	\(129\)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$