LMFDB - Embedded Newform 6047.2.a.a.1.7

Newspace parameters

Level:	$ N $	=	$ 6047 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	6047.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$48.2855381023$
Analytic rank:	$1$
Dimension:	$217$
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	=	6047.1

$q$-expansion

$f(q)$	$=$	$q-2.65722 q^{2} +0.109936 q^{3} +5.06084 q^{4} +0.753739 q^{5} -0.292126 q^{6} +3.98656 q^{7} -8.13334 q^{8} -2.98791 q^{9} +O(q^{10})$	\(q-2.65722 q^{2} +0.109936 q^{3} +5.06084 q^{4} +0.753739 q^{5} -0.292126 q^{6} +3.98656 q^{7} -8.13334 q^{8} -2.98791 q^{9} -2.00285 q^{10} +0.383918 q^{11} +0.556370 q^{12} +2.64293 q^{13} -10.5932 q^{14} +0.0828634 q^{15} +11.4904 q^{16} +8.14277 q^{17} +7.93956 q^{18} -5.99205 q^{19} +3.81456 q^{20} +0.438268 q^{21} -1.02016 q^{22} -1.73696 q^{23} -0.894150 q^{24} -4.43188 q^{25} -7.02285 q^{26} -0.658289 q^{27} +20.1753 q^{28} +5.51678 q^{29} -0.220187 q^{30} -10.8615 q^{31} -14.2660 q^{32} +0.0422065 q^{33} -21.6372 q^{34} +3.00483 q^{35} -15.1214 q^{36} +2.46709 q^{37} +15.9222 q^{38} +0.290554 q^{39} -6.13042 q^{40} -11.2355 q^{41} -1.16458 q^{42} -9.53031 q^{43} +1.94295 q^{44} -2.25211 q^{45} +4.61548 q^{46} +9.71406 q^{47} +1.26322 q^{48} +8.89264 q^{49} +11.7765 q^{50} +0.895187 q^{51} +13.3754 q^{52} -6.80202 q^{53} +1.74922 q^{54} +0.289374 q^{55} -32.4240 q^{56} -0.658744 q^{57} -14.6593 q^{58} -1.90748 q^{59} +0.419358 q^{60} -11.7282 q^{61} +28.8615 q^{62} -11.9115 q^{63} +14.9270 q^{64} +1.99208 q^{65} -0.112152 q^{66} -6.26307 q^{67} +41.2093 q^{68} -0.190955 q^{69} -7.98450 q^{70} +3.63989 q^{71} +24.3017 q^{72} +4.38284 q^{73} -6.55561 q^{74} -0.487224 q^{75} -30.3248 q^{76} +1.53051 q^{77} -0.772067 q^{78} -13.0161 q^{79} +8.66079 q^{80} +8.89137 q^{81} +29.8553 q^{82} -4.10504 q^{83} +2.21800 q^{84} +6.13753 q^{85} +25.3242 q^{86} +0.606495 q^{87} -3.12254 q^{88} -1.79972 q^{89} +5.98436 q^{90} +10.5362 q^{91} -8.79046 q^{92} -1.19408 q^{93} -25.8124 q^{94} -4.51645 q^{95} -1.56835 q^{96} -11.3226 q^{97} -23.6297 q^{98} -1.14711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) $	\( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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 $

$2$	−2.65722	−1.87894	−0.939471	−	0.342629i	$-0.888683\pi$
$2$	−2.65722	−1.87894	−0.939471	+	0.342629i	$0.888683\pi$
$3$	0.109936	0.0634718	0.0317359	−	0.999496i	$-0.489896\pi$
$3$	0.109936	0.0634718	0.0317359	+	0.999496i	$0.489896\pi$
$4$	5.06084	2.53042
$5$	0.753739	0.337083	0.168541	−	0.985695i	$-0.446094\pi$
$5$	0.753739	0.337083	0.168541	+	0.985695i	$0.446094\pi$
$6$	−0.292126	−0.119260
$7$	3.98656	1.50678	0.753389	−	0.657576i	$-0.228418\pi$
$7$	3.98656	1.50678	0.753389	+	0.657576i	$0.228418\pi$
$8$	−8.13334	−2.87557
$9$	−2.98791	−0.995971
$10$	−2.00285	−0.633358
$11$	0.383918	0.115756	0.0578778	−	0.998324i	$-0.481567\pi$
$11$	0.383918	0.115756	0.0578778	+	0.998324i	$0.481567\pi$
$12$	0.556370	0.160610
$13$	2.64293	0.733016	0.366508	−	0.930415i	$-0.380553\pi$
$13$	2.64293	0.733016	0.366508	+	0.930415i	$0.380553\pi$
$14$	−10.5932	−2.83115
$15$	0.0828634	0.0213952
$16$	11.4904	2.87261
$17$	8.14277	1.97491	0.987456	−	0.157891i	$-0.0504696\pi$
$17$	8.14277	1.97491	0.987456	+	0.157891i	$0.0504696\pi$
$18$	7.93956	1.87137
$19$	−5.99205	−1.37467	−0.687336	−	0.726340i	$-0.741220\pi$
$19$	−5.99205	−1.37467	−0.687336	+	0.726340i	$0.741220\pi$
$20$	3.81456	0.852961
$21$	0.438268	0.0956378
$22$	−1.02016	−0.217498
$23$	−1.73696	−0.362180	−0.181090	−	0.983467i	$-0.557963\pi$
$23$	−1.73696	−0.362180	−0.181090	+	0.983467i	$0.557963\pi$
$24$	−0.894150	−0.182518
$25$	−4.43188	−0.886375
$26$	−7.02285	−1.37729
$27$	−0.658289	−0.126688
$28$	20.1753	3.81278
$29$	5.51678	1.02444	0.512220	−	0.858854i	$-0.328823\pi$
$29$	5.51678	1.02444	0.512220	+	0.858854i	$0.328823\pi$
$30$	−0.220187	−0.0402004
$31$	−10.8615	−1.95079	−0.975394	−	0.220471i	$-0.929241\pi$
$31$	−10.8615	−1.95079	−0.975394	+	0.220471i	$0.929241\pi$
$32$	−14.2660	−2.52189
$33$	0.0422065	0.00734721
$34$	−21.6372	−3.71075
$35$	3.00483	0.507908
$36$	−15.1214	−2.52023
$37$	2.46709	0.405587	0.202793	−	0.979222i	$-0.434998\pi$
$37$	2.46709	0.405587	0.202793	+	0.979222i	$0.434998\pi$
$38$	15.9222	2.58293
$39$	0.290554	0.0465258
$40$	−6.13042	−0.969305
$41$	−11.2355	−1.75469	−0.877345	−	0.479859i	$-0.840688\pi$
$41$	−11.2355	−1.75469	−0.877345	+	0.479859i	$0.840688\pi$
$42$	−1.16458	−0.179698
$43$	−9.53031	−1.45336	−0.726679	−	0.686977i	$-0.758937\pi$
$43$	−9.53031	−1.45336	−0.726679	+	0.686977i	$0.758937\pi$
$44$	1.94295	0.292910
$45$	−2.25211	−0.335725
$46$	4.61548	0.680516
$47$	9.71406	1.41694	0.708470	−	0.705740i	$-0.249386\pi$
$47$	9.71406	1.41694	0.708470	+	0.705740i	$0.249386\pi$
$48$	1.26322	0.182330
$49$	8.89264	1.27038
$50$	11.7765	1.66545
$51$	0.895187	0.125351
$52$	13.3754	1.85484
$53$	−6.80202	−0.934329	−0.467164	−	0.884170i	$-0.654724\pi$
$53$	−6.80202	−0.934329	−0.467164	+	0.884170i	$0.654724\pi$
$54$	1.74922	0.238039
$55$	0.289374	0.0390192
$56$	−32.4240	−4.33285
$57$	−0.658744	−0.0872528
$58$	−14.6593	−1.92486
$59$	−1.90748	−0.248332	−0.124166	−	0.992261i	$-0.539626\pi$
$59$	−1.90748	−0.248332	−0.124166	+	0.992261i	$0.539626\pi$
$60$	0.419358	0.0541389
$61$	−11.7282	−1.50164	−0.750819	−	0.660509i	$-0.770341\pi$
$61$	−11.7282	−1.50164	−0.750819	+	0.660509i	$0.770341\pi$
$62$	28.8615	3.66541
$63$	−11.9115	−1.50071
$64$	14.9270	1.86588
$65$	1.99208	0.247087
$66$	−0.112152	−0.0138050
$67$	−6.26307	−0.765156	−0.382578	−	0.923923i	$-0.624964\pi$
$67$	−6.26307	−0.765156	−0.382578	+	0.923923i	$0.624964\pi$
$68$	41.2093	4.99736
$69$	−0.190955	−0.0229882
$70$	−7.98450	−0.954330
$71$	3.63989	0.431976	0.215988	−	0.976396i	$-0.430703\pi$
$71$	3.63989	0.431976	0.215988	+	0.976396i	$0.430703\pi$
$72$	24.3017	2.86399
$73$	4.38284	0.512972	0.256486	−	0.966548i	$-0.417435\pi$
$73$	4.38284	0.512972	0.256486	+	0.966548i	$0.417435\pi$
$74$	−6.55561	−0.762074
$75$	−0.487224	−0.0562598
$76$	−30.3248	−3.47850
$77$	1.53051	0.174418
$78$	−0.772067	−0.0874193
$79$	−13.0161	−1.46442	−0.732211	−	0.681078i	$-0.761511\pi$
$79$	−13.0161	−1.46442	−0.732211	+	0.681078i	$0.761511\pi$
$80$	8.66079	0.968306
$81$	8.89137	0.987930
$82$	29.8553	3.29696
$83$	−4.10504	−0.450587	−0.225293	−	0.974291i	$-0.572334\pi$
$83$	−4.10504	−0.450587	−0.225293	+	0.974291i	$0.572334\pi$
$84$	2.21800	0.242004
$85$	6.13753	0.665709
$86$	25.3242	2.73078
$87$	0.606495	0.0650230
$88$	−3.12254	−0.332863
$89$	−1.79972	−0.190770	−0.0953850	−	0.995440i	$-0.530408\pi$
$89$	−1.79972	−0.190770	−0.0953850	+	0.995440i	$0.530408\pi$
$90$	5.98436	0.630807
$91$	10.5362	1.10449
$92$	−8.79046	−0.916469
$93$	−1.19408	−0.123820
$94$	−25.8124	−2.66235
$95$	−4.51645	−0.463378
$96$	−1.56835	−0.160069
$97$	−11.3226	−1.14964	−0.574819	−	0.818281i	$-0.694928\pi$
$97$	−11.3226	−1.14964	−0.574819	+	0.818281i	$0.694928\pi$
$98$	−23.6297	−2.38697
$99$	−1.14711	−0.115289
$100$	−22.4290	−2.24290
$101$	−14.2990	−1.42281	−0.711403	−	0.702784i	$-0.751940\pi$
$101$	−14.2990	−1.42281	−0.711403	+	0.702784i	$0.751940\pi$
$102$	−2.37871	−0.235528
$103$	11.1978	1.10335	0.551677	−	0.834058i	$-0.313988\pi$
$103$	11.1978	1.10335	0.551677	+	0.834058i	$0.313988\pi$
$104$	−21.4958	−2.10784
$105$	0.330340	0.0322378
$106$	18.0745	1.75555
$107$	14.1082	1.36389	0.681946	−	0.731403i	$-0.261134\pi$
$107$	14.1082	1.36389	0.681946	+	0.731403i	$0.261134\pi$
$108$	−3.33150	−0.320574
$109$	2.33398	0.223555	0.111777	−	0.993733i	$-0.464346\pi$
$109$	2.33398	0.223555	0.111777	+	0.993733i	$0.464346\pi$
$110$	−0.768932	−0.0733147
$111$	0.271223	0.0257433
$112$	45.8073	4.32838
$113$	−11.9901	−1.12794	−0.563968	−	0.825797i	$-0.690726\pi$
$113$	−11.9901	−1.12794	−0.563968	+	0.825797i	$0.690726\pi$
$114$	1.75043	0.163943
$115$	−1.30921	−0.122085
$116$	27.9195	2.59226
$117$	−7.89684	−0.730063
$118$	5.06859	0.466602
$119$	32.4616	2.97575
$120$	−0.673956	−0.0615235
$121$	−10.8526	−0.986601
$122$	31.1644	2.82149
$123$	−1.23519	−0.111373
$124$	−54.9684	−4.93631
$125$	−7.10918	−0.635864
$126$	31.6515	2.81974
$127$	9.95970	0.883781	0.441890	−	0.897069i	$-0.354308\pi$
$127$	9.95970	0.883781	0.441890	+	0.897069i	$0.354308\pi$
$128$	−11.1325	−0.983986
$129$	−1.04773	−0.0922473
$130$	−5.29340	−0.464262
$131$	−16.6878	−1.45802	−0.729012	−	0.684501i	$-0.760020\pi$
$131$	−16.6878	−1.45802	−0.729012	+	0.684501i	$0.760020\pi$
$132$	0.213600	0.0185915
$133$	−23.8877	−2.07132
$134$	16.6424	1.43768
$135$	−0.496179	−0.0427043
$136$	−66.2280	−5.67900
$137$	−20.9167	−1.78703	−0.893517	−	0.449030i	$-0.851770\pi$
$137$	−20.9167	−1.78703	−0.893517	+	0.449030i	$0.851770\pi$
$138$	0.507409	0.0431935
$139$	−1.43452	−0.121674	−0.0608371	−	0.998148i	$-0.519377\pi$
$139$	−1.43452	−0.121674	−0.0608371	+	0.998148i	$0.519377\pi$
$140$	15.2069	1.28522
$141$	1.06793	0.0899358
$142$	−9.67201	−0.811657
$143$	1.01467	0.0848507
$144$	−34.3324	−2.86104
$145$	4.15821	0.345321
$146$	−11.6462	−0.963845
$147$	0.977625	0.0806331
$148$	12.4855	1.02631
$149$	−6.60260	−0.540906	−0.270453	−	0.962733i	$-0.587174\pi$
$149$	−6.60260	−0.540906	−0.270453	+	0.962733i	$0.587174\pi$
$150$	1.29466	0.105709
$151$	−19.6075	−1.59564	−0.797819	−	0.602896i	$-0.794013\pi$
$151$	−19.6075	−1.59564	−0.797819	+	0.602896i	$0.794013\pi$
$152$	48.7354	3.95296
$153$	−24.3299	−1.96696
$154$	−4.06691	−0.327721
$155$	−8.18676	−0.657576
$156$	1.47045	0.117730
$157$	−19.8002	−1.58023	−0.790113	−	0.612961i	$-0.789978\pi$
$157$	−19.8002	−1.58023	−0.790113	+	0.612961i	$0.789978\pi$
$158$	34.5866	2.75156
$159$	−0.747789	−0.0593035
$160$	−10.7528	−0.850086
$161$	−6.92447	−0.545725
$162$	−23.6264	−1.85626
$163$	17.3114	1.35594	0.677968	−	0.735092i	$-0.262861\pi$
$163$	17.3114	1.35594	0.677968	+	0.735092i	$0.262861\pi$
$164$	−56.8611	−4.44011
$165$	0.0318127	0.00247662
$166$	10.9080	0.846627
$167$	2.80771	0.217267	0.108634	−	0.994082i	$-0.465352\pi$
$167$	2.80771	0.217267	0.108634	+	0.994082i	$0.465352\pi$
$168$	−3.56458	−0.275013
$169$	−6.01494	−0.462687
$170$	−16.3088	−1.25083
$171$	17.9037	1.36913
$172$	−48.2314	−3.67761
$173$	7.99607	0.607930	0.303965	−	0.952683i	$-0.401689\pi$
$173$	7.99607	0.607930	0.303965	+	0.952683i	$0.401689\pi$
$174$	−1.61159	−0.122174
$175$	−17.6679	−1.33557
$176$	4.41138	0.332520
$177$	−0.209701	−0.0157621
$178$	4.78226	0.358446
$179$	15.4206	1.15259	0.576296	−	0.817241i	$-0.304497\pi$
$179$	15.4206	1.15259	0.576296	+	0.817241i	$0.304497\pi$
$180$	−11.3976	−0.849524
$181$	−6.42159	−0.477313	−0.238657	−	0.971104i	$-0.576707\pi$
$181$	−6.42159	−0.477313	−0.238657	+	0.971104i	$0.576707\pi$
$182$	−27.9970	−2.07528
$183$	−1.28935	−0.0953116
$184$	14.1273	1.04148
$185$	1.85954	0.136716
$186$	3.17293	0.232650
$187$	3.12616	0.228607
$188$	49.1613	3.58546
$189$	−2.62431	−0.190890
$190$	12.0012	0.870659
$191$	8.44303	0.610916	0.305458	−	0.952206i	$-0.401190\pi$
$191$	8.44303	0.610916	0.305458	+	0.952206i	$0.401190\pi$
$192$	1.64102	0.118431
$193$	−21.2931	−1.53271	−0.766357	−	0.642415i	$-0.777933\pi$
$193$	−21.2931	−1.53271	−0.766357	+	0.642415i	$0.777933\pi$
$194$	30.0867	2.16010
$195$	0.219002	0.0156830
$196$	45.0043	3.21459
$197$	12.1670	0.866864	0.433432	−	0.901186i	$-0.357302\pi$
$197$	12.1670	0.866864	0.433432	+	0.901186i	$0.357302\pi$
$198$	3.04814	0.216622
$199$	2.76874	0.196271	0.0981354	−	0.995173i	$-0.468712\pi$
$199$	2.76874	0.196271	0.0981354	+	0.995173i	$0.468712\pi$
$200$	36.0460	2.54884
$201$	−0.688539	−0.0485658
$202$	37.9957	2.67337
$203$	21.9930	1.54360
$204$	4.53040	0.317191
$205$	−8.46864	−0.591476
$206$	−29.7551	−2.07314
$207$	5.18987	0.360721
$208$	30.3684	2.10567
$209$	−2.30046	−0.159126
$210$	−0.877786	−0.0605730
$211$	−14.6582	−1.00911	−0.504557	−	0.863378i	$-0.668344\pi$
$211$	−14.6582	−1.00911	−0.504557	+	0.863378i	$0.668344\pi$
$212$	−34.4239	−2.36425
$213$	0.400156	0.0274183
$214$	−37.4887	−2.56267
$215$	−7.18337	−0.489902
$216$	5.35409	0.364300
$217$	−43.3001	−2.93940
$218$	−6.20191	−0.420046
$219$	0.481833	0.0325593
$220$	1.46448	0.0987349
$221$	21.5208	1.44764
$222$	−0.720699	−0.0483702
$223$	11.5641	0.774390	0.387195	−	0.921998i	$-0.373444\pi$
$223$	11.5641	0.774390	0.387195	+	0.921998i	$0.373444\pi$
$224$	−56.8721	−3.79993
$225$	13.2421	0.882804
$226$	31.8604	2.11932
$227$	−11.3874	−0.755807	−0.377904	−	0.925845i	$-0.623355\pi$
$227$	−11.3874	−0.755807	−0.377904	+	0.925845i	$0.623355\pi$
$228$	−3.33380	−0.220786
$229$	17.8075	1.17675	0.588376	−	0.808587i	$-0.299767\pi$
$229$	17.8075	1.17675	0.588376	+	0.808587i	$0.299767\pi$
$230$	3.47887	0.229390
$231$	0.168259	0.0110706
$232$	−44.8699	−2.94585
$233$	17.3767	1.13838	0.569192	−	0.822204i	$-0.307256\pi$
$233$	17.3767	1.13838	0.569192	+	0.822204i	$0.307256\pi$
$234$	20.9837	1.37175
$235$	7.32187	0.477626
$236$	−9.65343	−0.628385
$237$	−1.43094	−0.0929495
$238$	−86.2579	−5.59127
$239$	−19.5310	−1.26335	−0.631677	−	0.775232i	$-0.717633\pi$
$239$	−19.5310	−1.26335	−0.631677	+	0.775232i	$0.717633\pi$
$240$	0.952136	0.0614601
$241$	19.6798	1.26769	0.633845	−	0.773460i	$-0.281476\pi$
$241$	19.6798	1.26769	0.633845	+	0.773460i	$0.281476\pi$
$242$	28.8378	1.85376
$243$	2.95235	0.189394
$244$	−59.3544	−3.79977
$245$	6.70274	0.428222
$246$	3.28218	0.209264
$247$	−15.8366	−1.00766
$248$	88.3405	5.60963
$249$	−0.451293	−0.0285996
$250$	18.8907	1.19475
$251$	17.6413	1.11351	0.556756	−	0.830676i	$-0.312046\pi$
$251$	17.6413	1.11351	0.556756	+	0.830676i	$0.312046\pi$
$252$	−60.2822	−3.79742
$253$	−0.666848	−0.0419244
$254$	−26.4652	−1.66057
$255$	0.674738	0.0422537
$256$	−0.272444	−0.0170278
$257$	8.66961	0.540796	0.270398	−	0.962749i	$-0.412845\pi$
$257$	8.66961	0.540796	0.270398	+	0.962749i	$0.412845\pi$
$258$	2.78405	0.173327
$259$	9.83519	0.611129
$260$	10.0816	0.625234
$261$	−16.4837	−1.02031
$262$	44.3434	2.73954
$263$	6.35897	0.392111	0.196056	−	0.980593i	$-0.437187\pi$
$263$	6.35897	0.392111	0.196056	+	0.980593i	$0.437187\pi$
$264$	−0.343280	−0.0211274
$265$	−5.12695	−0.314946
$266$	63.4749	3.89190
$267$	−0.197855	−0.0121085
$268$	−31.6964	−1.93617
$269$	6.45664	0.393668	0.196834	−	0.980437i	$-0.436934\pi$
$269$	6.45664	0.393668	0.196834	+	0.980437i	$0.436934\pi$
$270$	1.31846	0.0802388
$271$	−5.59309	−0.339756	−0.169878	−	0.985465i	$-0.554337\pi$
$271$	−5.59309	−0.339756	−0.169878	+	0.985465i	$0.554337\pi$
$272$	93.5640	5.67315
$273$	1.15831	0.0701041
$274$	55.5804	3.35773
$275$	−1.70148	−0.102603
$276$	−0.966391	−0.0581699
$277$	18.3752	1.10406	0.552031	−	0.833824i	$-0.313853\pi$
$277$	18.3752	1.10406	0.552031	+	0.833824i	$0.313853\pi$
$278$	3.81184	0.228619
$279$	32.4533	1.94293
$280$	−24.4393	−1.46053
$281$	10.0851	0.601629	0.300815	−	0.953683i	$-0.402741\pi$
$281$	10.0851	0.601629	0.300815	+	0.953683i	$0.402741\pi$
$282$	−2.83772	−0.168984
$283$	13.7718	0.818649	0.409324	−	0.912389i	$-0.365764\pi$
$283$	13.7718	0.818649	0.409324	+	0.912389i	$0.365764\pi$
$284$	18.4209	1.09308
$285$	−0.496522	−0.0294114
$286$	−2.69620	−0.159429
$287$	−44.7910	−2.64393
$288$	42.6255	2.51173
$289$	49.3048	2.90028
$290$	−11.0493	−0.648838
$291$	−1.24477	−0.0729696
$292$	22.1808	1.29804
$293$	3.78930	0.221374	0.110687	−	0.993855i	$-0.464695\pi$
$293$	3.78930	0.221374	0.110687	+	0.993855i	$0.464695\pi$
$294$	−2.59777	−0.151505
$295$	−1.43774	−0.0837084
$296$	−20.0657	−1.16629
$297$	−0.252729	−0.0146648
$298$	17.5446	1.01633
$299$	−4.59065	−0.265484
$300$	−2.46577	−0.142361
$301$	−37.9931	−2.18989
$302$	52.1016	2.99811
$303$	−1.57198	−0.0903080
$304$	−68.8513	−3.94889
$305$	−8.83998	−0.506176
$306$	64.6500	3.69580
$307$	8.74445	0.499072	0.249536	−	0.968366i	$-0.419722\pi$
$307$	8.74445	0.499072	0.249536	+	0.968366i	$0.419722\pi$
$308$	7.74567	0.441351
$309$	1.23105	0.0700318
$310$	21.7541	1.23555
$311$	3.24763	0.184156	0.0920782	−	0.995752i	$-0.470649\pi$
$311$	3.24763	0.184156	0.0920782	+	0.995752i	$0.470649\pi$
$312$	−2.36317	−0.133788
$313$	9.96281	0.563131	0.281566	−	0.959542i	$-0.409146\pi$
$313$	9.96281	0.563131	0.281566	+	0.959542i	$0.409146\pi$
$314$	52.6135	2.96915
$315$	−8.97816	−0.505862
$316$	−65.8722	−3.70560
$317$	17.1522	0.963366	0.481683	−	0.876345i	$-0.340026\pi$
$317$	17.1522	0.963366	0.481683	+	0.876345i	$0.340026\pi$
$318$	1.98704	0.111428
$319$	2.11799	0.118585
$320$	11.2511	0.628955
$321$	1.55100	0.0865686
$322$	18.3999	1.02539
$323$	−48.7919	−2.71486
$324$	44.9978	2.49988
$325$	−11.7131	−0.649727
$326$	−46.0003	−2.54772
$327$	0.256589	0.0141894
$328$	91.3822	5.04574
$329$	38.7257	2.13501
$330$	−0.0845335	−0.00465342
$331$	−31.9960	−1.75866	−0.879328	−	0.476216i	$-0.842008\pi$
$331$	−31.9960	−1.75866	−0.879328	+	0.476216i	$0.842008\pi$
$332$	−20.7750	−1.14017
$333$	−7.37145	−0.403953
$334$	−7.46072	−0.408232
$335$	−4.72072	−0.257921
$336$	5.03589	0.274730
$337$	−23.8337	−1.29830	−0.649151	−	0.760660i	$-0.724876\pi$
$337$	−23.8337	−1.29830	−0.649151	+	0.760660i	$0.724876\pi$
$338$	15.9830	0.869363
$339$	−1.31815	−0.0715921
$340$	31.0611	1.68452
$341$	−4.16993	−0.225814
$342$	−47.5743	−2.57252
$343$	7.54513	0.407399
$344$	77.5133	4.17924
$345$	−0.143930	−0.00774893
$346$	−21.2474	−1.14226
$347$	13.6207	0.731198	0.365599	−	0.930772i	$-0.380864\pi$
$347$	13.6207	0.731198	0.365599	+	0.930772i	$0.380864\pi$
$348$	3.06937	0.164536
$349$	0.298770	0.0159928	0.00799638	−	0.999968i	$-0.497455\pi$
$349$	0.298770	0.0159928	0.00799638	+	0.999968i	$0.497455\pi$
$350$	46.9477	2.50946
$351$	−1.73981	−0.0928642
$352$	−5.47696	−0.291923
$353$	−4.86633	−0.259009	−0.129504	−	0.991579i	$-0.541339\pi$
$353$	−4.86633	−0.259009	−0.129504	+	0.991579i	$0.541339\pi$
$354$	0.557222	0.0296160
$355$	2.74353	0.145611
$356$	−9.10810	−0.482728
$357$	3.56871	0.188876
$358$	−40.9761	−2.16565
$359$	−1.85735	−0.0980273	−0.0490136	−	0.998798i	$-0.515608\pi$
$359$	−1.85735	−0.0980273	−0.0490136	+	0.998798i	$0.515608\pi$
$360$	18.3172	0.965400
$361$	16.9047	0.889721
$362$	17.0636	0.896844
$363$	−1.19310	−0.0626213
$364$	53.3219	2.79483
$365$	3.30352	0.172914
$366$	3.42610	0.179085
$367$	19.9137	1.03949	0.519745	−	0.854322i	$-0.326027\pi$
$367$	19.9137	1.03949	0.519745	+	0.854322i	$0.326027\pi$
$368$	−19.9584	−1.04040
$369$	33.5707	1.74762
$370$	−4.94122	−0.256882
$371$	−27.1166	−1.40783
$372$	−6.04303	−0.313317
$373$	−19.0628	−0.987036	−0.493518	−	0.869736i	$-0.664289\pi$
$373$	−19.0628	−0.987036	−0.493518	+	0.869736i	$0.664289\pi$
$374$	−8.30690	−0.429539
$375$	−0.781557	−0.0403594
$376$	−79.0078	−4.07451
$377$	14.5804	0.750931
$378$	6.97338	0.358672
$379$	7.18360	0.368997	0.184498	−	0.982833i	$-0.440934\pi$
$379$	7.18360	0.368997	0.184498	+	0.982833i	$0.440934\pi$
$380$	−22.8570	−1.17254
$381$	1.09493	0.0560951
$382$	−22.4350	−1.14788
$383$	−20.1213	−1.02815	−0.514075	−	0.857745i	$-0.671865\pi$
$383$	−20.1213	−1.02815	−0.514075	+	0.857745i	$0.671865\pi$
$384$	−1.22387	−0.0624553
$385$	1.15361	0.0587932
$386$	56.5807	2.87988
$387$	28.4757	1.44750
$388$	−57.3020	−2.90907
$389$	−5.47602	−0.277645	−0.138823	−	0.990317i	$-0.544332\pi$
$389$	−5.47602	−0.277645	−0.138823	+	0.990317i	$0.544332\pi$
$390$	−0.581937	−0.0294675
$391$	−14.1436	−0.715275
$392$	−72.3269	−3.65306
$393$	−1.83460	−0.0925434
$394$	−32.3305	−1.62879
$395$	−9.81072	−0.493631
$396$	−5.80536	−0.291730
$397$	−21.0567	−1.05680	−0.528402	−	0.848994i	$-0.677209\pi$
$397$	−21.0567	−1.05680	−0.528402	+	0.848994i	$0.677209\pi$
$398$	−7.35716	−0.368781
$399$	−2.62612	−0.131471
$400$	−50.9242	−2.54621
$401$	2.83248	0.141447	0.0707237	−	0.997496i	$-0.477469\pi$
$401$	2.83248	0.141447	0.0707237	+	0.997496i	$0.477469\pi$
$402$	1.82960	0.0912523
$403$	−28.7062	−1.42996
$404$	−72.3651	−3.60030
$405$	6.70178	0.333014
$406$	−58.4402	−2.90034
$407$	0.947159	0.0469489
$408$	−7.28086	−0.360456
$409$	0.484995	0.0239815	0.0119907	−	0.999928i	$-0.496183\pi$
$409$	0.484995	0.0239815	0.0119907	+	0.999928i	$0.496183\pi$
$410$	22.5031	1.11135
$411$	−2.29950	−0.113426
$412$	56.6704	2.79195
$413$	−7.60426	−0.374181
$414$	−13.7907	−0.677774
$415$	−3.09413	−0.151885
$416$	−37.7039	−1.84859
$417$	−0.157706	−0.00772288
$418$	6.11283	0.298988
$419$	37.0157	1.80833	0.904167	−	0.427179i	$-0.140492\pi$
$419$	37.0157	1.80833	0.904167	+	0.427179i	$0.140492\pi$
$420$	1.67180	0.0815753
$421$	17.7645	0.865789	0.432895	−	0.901445i	$-0.357492\pi$
$421$	17.7645	0.865789	0.432895	+	0.901445i	$0.357492\pi$
$422$	38.9502	1.89607
$423$	−29.0248	−1.41123
$424$	55.3231	2.68673
$425$	−36.0878	−1.75051
$426$	−1.06331	−0.0515173
$427$	−46.7550	−2.26263
$428$	71.3994	3.45122
$429$	0.111549	0.00538562
$430$	19.0878	0.920497
$431$	−29.4236	−1.41729	−0.708644	−	0.705567i	$-0.750693\pi$
$431$	−29.4236	−1.41729	−0.708644	+	0.705567i	$0.750693\pi$
$432$	−7.56403	−0.363925
$433$	18.5214	0.890081	0.445040	−	0.895510i	$-0.353189\pi$
$433$	18.5214	0.890081	0.445040	+	0.895510i	$0.353189\pi$
$434$	115.058	5.52296
$435$	0.457139	0.0219181
$436$	11.8119	0.565687
$437$	10.4079	0.497879
$438$	−1.28034	−0.0611770
$439$	17.5923	0.839635	0.419817	−	0.907609i	$-0.362094\pi$
$439$	17.5923	0.839635	0.419817	+	0.907609i	$0.362094\pi$
$440$	−2.35358	−0.112202
$441$	−26.5705	−1.26526
$442$	−57.1855	−2.72004
$443$	7.12922	0.338719	0.169360	−	0.985554i	$-0.445830\pi$
$443$	7.12922	0.338719	0.169360	+	0.985554i	$0.445830\pi$
$444$	1.37261	0.0651414
$445$	−1.35652	−0.0643052
$446$	−30.7284	−1.45503
$447$	−0.725866	−0.0343323
$448$	59.5075	2.81146
$449$	−1.20234	−0.0567419	−0.0283709	−	0.999597i	$-0.509032\pi$
$449$	−1.20234	−0.0567419	−0.0283709	+	0.999597i	$0.509032\pi$
$450$	−35.1871	−1.65874
$451$	−4.31351	−0.203115
$452$	−60.6801	−2.85415
$453$	−2.15558	−0.101278
$454$	30.2588	1.42012
$455$	7.94154	0.372305
$456$	5.35779	0.250902
$457$	−12.9134	−0.604064	−0.302032	−	0.953298i	$-0.597665\pi$
$457$	−12.9134	−0.604064	−0.302032	+	0.953298i	$0.597665\pi$
$458$	−47.3185	−2.21105
$459$	−5.36030	−0.250197
$460$	−6.62571	−0.308926
$461$	30.6969	1.42970	0.714849	−	0.699279i	$-0.246495\pi$
$461$	30.6969	1.42970	0.714849	+	0.699279i	$0.246495\pi$
$462$	−0.447101	−0.0208010
$463$	34.0402	1.58198	0.790992	−	0.611827i	$-0.209565\pi$
$463$	34.0402	1.58198	0.790992	+	0.611827i	$0.209565\pi$
$464$	63.3902	2.94282
$465$	−0.900022	−0.0417375
$466$	−46.1738	−2.13896
$467$	−25.6968	−1.18911	−0.594554	−	0.804056i	$-0.702671\pi$
$467$	−25.6968	−1.18911	−0.594554	+	0.804056i	$0.702671\pi$
$468$	−39.9647	−1.84737
$469$	−24.9681	−1.15292
$470$	−19.4558	−0.897431
$471$	−2.17676	−0.100300
$472$	15.5142	0.714097
$473$	−3.65886	−0.168234
$474$	3.80233	0.174647
$475$	26.5560	1.21847
$476$	164.283	7.52991
$477$	20.3238	0.930565
$478$	51.8982	2.37377
$479$	18.3110	0.836650	0.418325	−	0.908297i	$-0.362617\pi$
$479$	18.3110	0.836650	0.418325	+	0.908297i	$0.362617\pi$
$480$	−1.18213	−0.0539565
$481$	6.52033	0.297302
$482$	−52.2937	−2.38191
$483$	−0.761251	−0.0346381
$484$	−54.9233	−2.49651
$485$	−8.53431	−0.387523
$486$	−7.84506	−0.355859
$487$	1.48411	0.0672513	0.0336257	−	0.999434i	$-0.489295\pi$
$487$	1.48411	0.0672513	0.0336257	+	0.999434i	$0.489295\pi$
$488$	95.3892	4.31806
$489$	1.90315	0.0860636
$490$	−17.8107	−0.804604
$491$	7.06142	0.318677	0.159339	−	0.987224i	$-0.449064\pi$
$491$	7.06142	0.318677	0.159339	+	0.987224i	$0.449064\pi$
$492$	−6.25110	−0.281821
$493$	44.9219	2.02318
$494$	42.0813	1.89333
$495$	−0.864624	−0.0388620
$496$	−124.804	−5.60385
$497$	14.5106	0.650891
$498$	1.19919	0.0537369
$499$	39.4725	1.76703	0.883516	−	0.468401i	$-0.155170\pi$
$499$	39.4725	1.76703	0.883516	+	0.468401i	$0.155170\pi$
$500$	−35.9784	−1.60900
$501$	0.308670	0.0137903
$502$	−46.8770	−2.09222
$503$	−3.32698	−0.148343	−0.0741714	−	0.997246i	$-0.523631\pi$
$503$	−3.32698	−0.148343	−0.0741714	+	0.997246i	$0.523631\pi$
$504$	96.8803	4.31539
$505$	−10.7777	−0.479603
$506$	1.77197	0.0787735
$507$	−0.661260	−0.0293676
$508$	50.4045	2.23634
$509$	−42.1004	−1.86607	−0.933033	−	0.359791i	$-0.882848\pi$
$509$	−42.1004	−1.86607	−0.933033	+	0.359791i	$0.882848\pi$
$510$	−1.79293	−0.0793922
$511$	17.4724	0.772935
$512$	22.9890	1.01598
$513$	3.94450	0.174154
$514$	−23.0371	−1.01612
$515$	8.44024	0.371921
$516$	−5.30238	−0.233424
$517$	3.72940	0.164019
$518$	−26.1343	−1.14828
$519$	0.879059	0.0385864
$520$	−16.2023	−0.710516
$521$	−22.4586	−0.983929	−0.491965	−	0.870615i	$-0.663721\pi$
$521$	−22.4586	−0.983929	−0.491965	+	0.870615i	$0.663721\pi$
$522$	43.8008	1.91711
$523$	26.6651	1.16599	0.582993	−	0.812477i	$-0.301882\pi$
$523$	26.6651	1.16599	0.582993	+	0.812477i	$0.301882\pi$
$524$	−84.4546	−3.68941
$525$	−1.94235	−0.0847710
$526$	−16.8972	−0.736754
$527$	−88.4429	−3.85263
$528$	0.484971	0.0211057
$529$	−19.9830	−0.868825
$530$	13.6235	0.591765
$531$	5.69937	0.247332
$532$	−120.892	−5.24132
$533$	−29.6946	−1.28622
$534$	0.525744	0.0227512
$535$	10.6339	0.459744
$536$	50.9397	2.20026
$537$	1.69529	0.0731571
$538$	−17.1567	−0.739679
$539$	3.41404	0.147053
$540$	−2.51108	−0.108060
$541$	31.6347	1.36008	0.680040	−	0.733175i	$-0.261962\pi$
$541$	31.6347	1.36008	0.680040	+	0.733175i	$0.261962\pi$
$542$	14.8621	0.638382
$543$	−0.705967	−0.0302959
$544$	−116.165	−4.98052
$545$	1.75921	0.0753564
$546$	−3.07789	−0.131721
$547$	10.7409	0.459248	0.229624	−	0.973279i	$-0.426250\pi$
$547$	10.7409	0.459248	0.229624	+	0.973279i	$0.426250\pi$
$548$	−105.856	−4.52195
$549$	35.0427	1.49559
$550$	4.52120	0.192785
$551$	−33.0568	−1.40827
$552$	1.55310	0.0661043
$553$	−51.8893	−2.20656
$554$	−48.8271	−2.07447
$555$	0.204431	0.00867762
$556$	−7.25987	−0.307887
$557$	−17.0507	−0.722461	−0.361230	−	0.932477i	$-0.617643\pi$
$557$	−17.0507	−0.722461	−0.361230	+	0.932477i	$0.617643\pi$
$558$	−86.2357	−3.65065
$559$	−25.1879	−1.06534
$560$	34.5268	1.45902
$561$	0.343678	0.0145101
$562$	−26.7985	−1.13043
$563$	−36.3197	−1.53069	−0.765345	−	0.643620i	$-0.777432\pi$
$563$	−36.3197	−1.53069	−0.765345	+	0.643620i	$0.777432\pi$
$564$	5.40461	0.227575
$565$	−9.03742	−0.380207
$566$	−36.5948	−1.53819
$567$	35.4460	1.48859
$568$	−29.6045	−1.24218
$569$	−2.42060	−0.101477	−0.0507384	−	0.998712i	$-0.516157\pi$
$569$	−2.42060	−0.101477	−0.0507384	+	0.998712i	$0.516157\pi$
$570$	1.31937	0.0552623
$571$	33.6527	1.40832	0.704161	−	0.710040i	$-0.251323\pi$
$571$	33.6527	1.40832	0.704161	+	0.710040i	$0.251323\pi$
$572$	5.13507	0.214708
$573$	0.928195	0.0387759
$574$	119.020	4.96779
$575$	7.69797	0.321028
$576$	−44.6007	−1.85836
$577$	−0.640483	−0.0266637	−0.0133318	−	0.999911i	$-0.504244\pi$
$577$	−0.640483	−0.0266637	−0.0133318	+	0.999911i	$0.504244\pi$
$578$	−131.014	−5.44946
$579$	−2.34089	−0.0972841
$580$	21.0441	0.873807
$581$	−16.3650	−0.678934
$582$	3.30763	0.137106
$583$	−2.61142	−0.108154
$584$	−35.6471	−1.47509
$585$	−5.95216	−0.246091
$586$	−10.0690	−0.415948
$587$	−5.56835	−0.229831	−0.114915	−	0.993375i	$-0.536660\pi$
$587$	−5.56835	−0.229831	−0.114915	+	0.993375i	$0.536660\pi$
$588$	4.94760	0.204036
$589$	65.0828	2.68169
$590$	3.82040	0.157283
$591$	1.33760	0.0550214
$592$	28.3479	1.16509
$593$	−19.6020	−0.804957	−0.402479	−	0.915429i	$-0.631851\pi$
$593$	−19.6020	−0.804957	−0.402479	+	0.915429i	$0.631851\pi$
$594$	0.671558	0.0275543
$595$	24.4676	1.00307
$596$	−33.4147	−1.36872
$597$	0.304385	0.0124577
$598$	12.1984	0.498829
$599$	18.3350	0.749147	0.374574	−	0.927197i	$-0.377789\pi$
$599$	18.3350	0.749147	0.374574	+	0.927197i	$0.377789\pi$
$600$	3.96276	0.161779
$601$	15.5256	0.633302	0.316651	−	0.948542i	$-0.397442\pi$
$601$	15.5256	0.633302	0.316651	+	0.948542i	$0.397442\pi$
$602$	100.956	4.11467
$603$	18.7135	0.762073
$604$	−99.2306	−4.03764
$605$	−8.18004	−0.332566
$606$	4.17711	0.169684
$607$	−10.6175	−0.430953	−0.215476	−	0.976509i	$-0.569130\pi$
$607$	−10.6175	−0.430953	−0.215476	+	0.976509i	$0.569130\pi$
$608$	85.4825	3.46677
$609$	2.41783	0.0979752
$610$	23.4898	0.951074
$611$	25.6735	1.03864
$612$	−123.130	−4.97723
$613$	28.0835	1.13428	0.567141	−	0.823621i	$-0.308050\pi$
$613$	28.0835	1.13428	0.567141	+	0.823621i	$0.308050\pi$
$614$	−23.2360	−0.937727
$615$	−0.931011	−0.0375420
$616$	−12.4482	−0.501551
$617$	39.4781	1.58933	0.794665	−	0.607049i	$-0.207647\pi$
$617$	39.4781	1.58933	0.794665	+	0.607049i	$0.207647\pi$
$618$	−3.27117	−0.131586
$619$	−7.02842	−0.282496	−0.141248	−	0.989974i	$-0.545112\pi$
$619$	−7.02842	−0.282496	−0.141248	+	0.989974i	$0.545112\pi$
$620$	−41.4319	−1.66394
$621$	1.14342	0.0458838
$622$	−8.62969	−0.346019
$623$	−7.17469	−0.287448
$624$	3.33859	0.133651
$625$	16.8009	0.672037
$626$	−26.4734	−1.05809
$627$	−0.252904	−0.0101000
$628$	−100.206	−3.99864
$629$	20.0889	0.800999
$630$	23.8570	0.950485
$631$	−31.8567	−1.26820	−0.634098	−	0.773252i	$-0.718629\pi$
$631$	−31.8567	−1.26820	−0.634098	+	0.773252i	$0.718629\pi$
$632$	105.864	4.21105
$633$	−1.61147	−0.0640503
$634$	−45.5774	−1.81011
$635$	7.50702	0.297907
$636$	−3.78444	−0.150063
$637$	23.5026	0.931207
$638$	−5.62797	−0.222814
$639$	−10.8757	−0.430235
$640$	−8.39103	−0.331684
$641$	−38.0304	−1.50211	−0.751055	−	0.660240i	$-0.770455\pi$
$641$	−38.0304	−1.50211	−0.751055	+	0.660240i	$0.770455\pi$
$642$	−4.12137	−0.162657
$643$	−30.0898	−1.18662	−0.593312	−	0.804973i	$-0.702180\pi$
$643$	−30.0898	−1.18662	−0.593312	+	0.804973i	$0.702180\pi$
$644$	−35.0437	−1.38091
$645$	−0.789713	−0.0310949
$646$	129.651	5.10106
$647$	−23.8488	−0.937593	−0.468796	−	0.883306i	$-0.655312\pi$
$647$	−23.8488	−0.937593	−0.468796	+	0.883306i	$0.655312\pi$
$648$	−72.3166	−2.84086
$649$	−0.732314	−0.0287458
$650$	31.1244	1.22080
$651$	−4.76025	−0.186569
$652$	87.6104	3.43109
$653$	26.3396	1.03075	0.515374	−	0.856965i	$-0.327653\pi$
$653$	26.3396	1.03075	0.515374	+	0.856965i	$0.327653\pi$
$654$	−0.681815	−0.0266611
$655$	−12.5783	−0.491474
$656$	−129.101	−5.04054
$657$	−13.0955	−0.510906
$658$	−102.903	−4.01157
$659$	−25.9335	−1.01023	−0.505113	−	0.863053i	$-0.668549\pi$
$659$	−25.9335	−1.01023	−0.505113	+	0.863053i	$0.668549\pi$
$660$	0.160999	0.00626688
$661$	−8.14032	−0.316622	−0.158311	−	0.987389i	$-0.550605\pi$
$661$	−8.14032	−0.316622	−0.158311	+	0.987389i	$0.550605\pi$
$662$	85.0204	3.30441
$663$	2.36591	0.0918845
$664$	33.3877	1.29569
$665$	−18.0051	−0.698207
$666$	19.5876	0.759004
$667$	−9.58240	−0.371032
$668$	14.2094	0.549778
$669$	1.27132	0.0491519
$670$	12.5440	0.484618
$671$	−4.50265	−0.173823
$672$	−6.25232	−0.241188
$673$	−45.6503	−1.75969	−0.879845	−	0.475261i	$-0.842354\pi$
$673$	−45.6503	−1.75969	−0.879845	+	0.475261i	$0.842354\pi$
$674$	63.3314	2.43943
$675$	2.91746	0.112293
$676$	−30.4406	−1.17079
$677$	−25.6800	−0.986964	−0.493482	−	0.869756i	$-0.664276\pi$
$677$	−25.6800	−0.986964	−0.493482	+	0.869756i	$0.664276\pi$
$678$	3.50262	0.134517
$679$	−45.1383	−1.73225
$680$	−49.9186	−1.91429
$681$	−1.25189	−0.0479724
$682$	11.0804	0.424292
$683$	4.08897	0.156460	0.0782300	−	0.996935i	$-0.475073\pi$
$683$	4.08897	0.156460	0.0782300	+	0.996935i	$0.475073\pi$
$684$	90.6080	3.46448
$685$	−15.7657	−0.602378
$686$	−20.0491	−0.765478
$687$	1.95769	0.0746906
$688$	−109.507	−4.17493
$689$	−17.9772	−0.684878
$690$	0.382454	0.0145598
$691$	12.6631	0.481728	0.240864	−	0.970559i	$-0.422569\pi$
$691$	12.6631	0.481728	0.240864	+	0.970559i	$0.422569\pi$
$692$	40.4668	1.53832
$693$	−4.57303	−0.173715
$694$	−36.1933	−1.37388
$695$	−1.08125	−0.0410143
$696$	−4.93283	−0.186978
$697$	−91.4882	−3.46536
$698$	−0.793898	−0.0300495
$699$	1.91033	0.0722553
$700$	−89.4146	−3.37955
$701$	−39.6328	−1.49691	−0.748455	−	0.663185i	$-0.769204\pi$
$701$	−39.6328	−1.49691	−0.748455	+	0.663185i	$0.769204\pi$
$702$	4.62307	0.174486
$703$	−14.7829	−0.557548
$704$	5.73075	0.215986
$705$	0.804939	0.0303158
$706$	12.9309	0.486662
$707$	−57.0039	−2.14385
$708$	−1.06126	−0.0398847
$709$	−35.5949	−1.33679	−0.668397	−	0.743804i	$-0.733019\pi$
$709$	−35.5949	−1.33679	−0.668397	+	0.743804i	$0.733019\pi$
$710$	−7.29018	−0.273595
$711$	38.8909	1.45852
$712$	14.6377	0.548573
$713$	18.8660	0.706537
$714$	−9.48287	−0.354888
$715$	0.764794	0.0286017
$716$	78.0414	2.91654
$717$	−2.14716	−0.0801873
$718$	4.93540	0.184188
$719$	−17.3147	−0.645731	−0.322866	−	0.946445i	$-0.604646\pi$
$719$	−17.3147	−0.645731	−0.322866	+	0.946445i	$0.604646\pi$
$720$	−25.8777	−0.964405
$721$	44.6408	1.66251
$722$	−44.9196	−1.67173
$723$	2.16353	0.0804625
$724$	−32.4987	−1.20780
$725$	−24.4497	−0.908039
$726$	3.17032	0.117662
$727$	33.3354	1.23634	0.618170	−	0.786044i	$-0.287874\pi$
$727$	33.3354	1.23634	0.618170	+	0.786044i	$0.287874\pi$
$728$	−85.6944	−3.17605
$729$	−26.3495	−0.975909
$730$	−8.77819	−0.324895
$731$	−77.6032	−2.87026
$732$	−6.52520	−0.241178
$733$	−46.6450	−1.72287	−0.861436	−	0.507866i	$-0.830435\pi$
$733$	−46.6450	−1.72287	−0.861436	+	0.507866i	$0.830435\pi$
$734$	−52.9153	−1.95314
$735$	0.736874	0.0271800
$736$	24.7794	0.913380
$737$	−2.40450	−0.0885711
$738$	−89.2049	−3.28368
$739$	1.85287	0.0681589	0.0340795	−	0.999419i	$-0.489150\pi$
$739$	1.85287	0.0681589	0.0340795	+	0.999419i	$0.489150\pi$
$740$	9.41085	0.345950
$741$	−1.74101	−0.0639577
$742$	72.0550	2.64522
$743$	−4.21611	−0.154674	−0.0773370	−	0.997005i	$-0.524642\pi$
$743$	−4.21611	−0.154674	−0.0773370	+	0.997005i	$0.524642\pi$
$744$	9.71183	0.356053
$745$	−4.97664	−0.182330
$746$	50.6542	1.85458
$747$	12.2655	0.448772
$748$	15.8210	0.578472
$749$	56.2432	2.05508
$750$	2.07677	0.0758330
$751$	−14.8585	−0.542195	−0.271097	−	0.962552i	$-0.587387\pi$
$751$	−14.8585	−0.542195	−0.271097	+	0.962552i	$0.587387\pi$
$752$	111.619	4.07032
$753$	1.93943	0.0706766
$754$	−38.7435	−1.41096
$755$	−14.7790	−0.537862
$756$	−13.2812	−0.483033
$757$	−24.4764	−0.889610	−0.444805	−	0.895627i	$-0.646727\pi$
$757$	−24.4764	−0.889610	−0.444805	+	0.895627i	$0.646727\pi$
$758$	−19.0884	−0.693323
$759$	−0.0733108	−0.00266102
$760$	36.7338	1.33248
$761$	38.1800	1.38402	0.692012	−	0.721886i	$-0.256725\pi$
$761$	38.1800	1.38402	0.692012	+	0.721886i	$0.256725\pi$
$762$	−2.90948	−0.105399
$763$	9.30454	0.336847
$764$	42.7288	1.54587
$765$	−18.3384	−0.663027
$766$	53.4668	1.93183
$767$	−5.04132	−0.182031
$768$	−0.0299515	−0.00108078
$769$	−47.9659	−1.72969	−0.864847	−	0.502035i	$-0.832585\pi$
$769$	−47.9659	−1.72969	−0.864847	+	0.502035i	$0.832585\pi$
$770$	−3.06539	−0.110469
$771$	0.953106	0.0343253
$772$	−107.761	−3.87841
$773$	22.4050	0.805852	0.402926	−	0.915233i	$-0.367993\pi$
$773$	22.4050	0.805852	0.402926	+	0.915233i	$0.367993\pi$
$774$	−75.6665	−2.71977
$775$	48.1369	1.72913
$776$	92.0908	3.30587
$777$	1.08124	0.0387894
$778$	14.5510	0.521679
$779$	67.3237	2.41212
$780$	1.10833	0.0396847
$781$	1.39742	0.0500036
$782$	37.5828	1.34396
$783$	−3.63164	−0.129784
$784$	102.180	3.64930
$785$	−14.9242	−0.532666
$786$	4.87495	0.173884
$787$	9.22688	0.328903	0.164451	−	0.986385i	$-0.447415\pi$
$787$	9.22688	0.328903	0.164451	+	0.986385i	$0.447415\pi$
$788$	61.5754	2.19353
$789$	0.699082	0.0248880
$790$	26.0693	0.927504
$791$	−47.7993	−1.69955
$792$	9.32987	0.331522
$793$	−30.9967	−1.10072
$794$	55.9523	1.98567
$795$	−0.563638	−0.0199902
$796$	14.0122	0.496648
$797$	25.7836	0.913303	0.456652	−	0.889646i	$-0.349049\pi$
$797$	25.7836	0.913303	0.456652	+	0.889646i	$0.349049\pi$
$798$	6.97820	0.247025
$799$	79.0994	2.79834
$800$	63.2251	2.23534
$801$	5.37741	0.190001
$802$	−7.52654	−0.265772
$803$	1.68265	0.0593794
$804$	−3.48459	−0.122892
$805$	−5.21925	−0.183954
$806$	76.2789	2.68681
$807$	0.709819	0.0249868
$808$	116.299	4.09138
$809$	19.3004	0.678564	0.339282	−	0.940685i	$-0.389816\pi$
$809$	19.3004	0.678564	0.339282	+	0.940685i	$0.389816\pi$
$810$	−17.8081	−0.625714
$811$	7.77316	0.272953	0.136476	−	0.990643i	$-0.456422\pi$
$811$	7.77316	0.272953	0.136476	+	0.990643i	$0.456422\pi$
$812$	111.303	3.90597
$813$	−0.614884	−0.0215649
$814$	−2.51681	−0.0882143
$815$	13.0483	0.457062
$816$	10.2861	0.360085
$817$	57.1061	1.99789
$818$	−1.28874	−0.0450598
$819$	−31.4812	−1.10004
$820$	−42.8585	−1.49668
$821$	4.82228	0.168299	0.0841494	−	0.996453i	$-0.473183\pi$
$821$	4.82228	0.168299	0.0841494	+	0.996453i	$0.473183\pi$
$822$	6.11030	0.213121
$823$	−31.0432	−1.08210	−0.541048	−	0.840991i	$-0.681972\pi$
$823$	−31.0432	−1.08210	−0.541048	+	0.840991i	$0.681972\pi$
$824$	−91.0757	−3.17277
$825$	−0.187054	−0.00651239
$826$	20.2062	0.703065
$827$	38.3255	1.33271	0.666354	−	0.745636i	$-0.267854\pi$
$827$	38.3255	1.33271	0.666354	+	0.745636i	$0.267854\pi$
$828$	26.2651	0.912776
$829$	−13.5111	−0.469261	−0.234631	−	0.972085i	$-0.575388\pi$
$829$	−13.5111	−0.469261	−0.234631	+	0.972085i	$0.575388\pi$
$830$	8.22180	0.285383
$831$	2.02011	0.0700767
$832$	39.4511	1.36772
$833$	72.4108	2.50889
$834$	0.419059	0.0145108
$835$	2.11628	0.0732370
$836$	−11.6422	−0.402655
$837$	7.15003	0.247141
$838$	−98.3590	−3.39775
$839$	−19.9246	−0.687872	−0.343936	−	0.938993i	$-0.611760\pi$
$839$	−19.9246	−0.687872	−0.343936	+	0.938993i	$0.611760\pi$
$840$	−2.68676	−0.0927022
$841$	1.43486	0.0494778
$842$	−47.2043	−1.62677
$843$	1.10872	0.0381865
$844$	−74.1830	−2.55348
$845$	−4.53369	−0.155964
$846$	77.1253	2.65162
$847$	−43.2645	−1.48659
$848$	−78.1581	−2.68396
$849$	1.51402	0.0519611
$850$	95.8933	3.28911
$851$	−4.28522	−0.146896
$852$	2.02513	0.0693798
$853$	47.2304	1.61714	0.808569	−	0.588401i	$-0.200242\pi$
$853$	47.2304	1.61714	0.808569	+	0.588401i	$0.200242\pi$
$854$	124.239	4.25135
$855$	13.4948	0.461511
$856$	−114.747	−3.92197
$857$	−11.4042	−0.389561	−0.194780	−	0.980847i	$-0.562399\pi$
$857$	−11.4042	−0.389561	−0.194780	+	0.980847i	$0.562399\pi$
$858$	−0.296410	−0.0101193
$859$	0.357189	0.0121871	0.00609356	−	0.999981i	$-0.498060\pi$
$859$	0.357189	0.0121871	0.00609356	+	0.999981i	$0.498060\pi$
$860$	−36.3539	−1.23966
$861$	−4.92416	−0.167815
$862$	78.1852	2.66300
$863$	21.2027	0.721750	0.360875	−	0.932614i	$-0.382478\pi$
$863$	21.2027	0.721750	0.360875	+	0.932614i	$0.382478\pi$
$864$	9.39114	0.319493
$865$	6.02695	0.204923
$866$	−49.2155	−1.67241
$867$	5.42039	0.184086
$868$	−219.135	−7.43792
$869$	−4.99710	−0.169515
$870$	−1.21472	−0.0411829
$871$	−16.5528	−0.560872
$872$	−18.9831	−0.642847
$873$	33.8310	1.14501
$874$	−27.6562	−0.935485
$875$	−28.3411	−0.958106
$876$	2.43848	0.0823886
$877$	−57.1829	−1.93093	−0.965464	−	0.260537i	$-0.916100\pi$
$877$	−57.1829	−1.93093	−0.965464	+	0.260537i	$0.916100\pi$
$878$	−46.7467	−1.57762
$879$	0.416582	0.0140510
$880$	3.32503	0.112087
$881$	33.6427	1.13345	0.566726	−	0.823906i	$-0.308210\pi$
$881$	33.6427	1.13345	0.566726	+	0.823906i	$0.308210\pi$
$882$	70.6037	2.37735
$883$	−19.8361	−0.667538	−0.333769	−	0.942655i	$-0.608321\pi$
$883$	−19.8361	−0.667538	−0.333769	+	0.942655i	$0.608321\pi$
$884$	108.913	3.66315
$885$	−0.158060	−0.00531312
$886$	−18.9439	−0.636434
$887$	18.1013	0.607782	0.303891	−	0.952707i	$-0.401714\pi$
$887$	18.1013	0.607782	0.303891	+	0.952707i	$0.401714\pi$
$888$	−2.20595	−0.0740267
$889$	39.7049	1.33166
$890$	3.60458	0.120826
$891$	3.41356	0.114358
$892$	58.5241	1.95953
$893$	−58.2071	−1.94783
$894$	1.92879	0.0645084
$895$	11.6231	0.388519
$896$	−44.3805	−1.48265
$897$	−0.504679	−0.0168507
$898$	3.19488	0.106615
$899$	−59.9206	−1.99846
$900$	67.0160	2.23387
$901$	−55.3873	−1.84522
$902$	11.4620	0.381642
$903$	−4.17683	−0.138996
$904$	97.5197	3.24346
$905$	−4.84021	−0.160894
$906$	5.72786	0.190295
$907$	−19.0079	−0.631148	−0.315574	−	0.948901i	$-0.602197\pi$
$907$	−19.0079	−0.631148	−0.315574	+	0.948901i	$0.602197\pi$
$908$	−57.6298	−1.91251
$909$	42.7243	1.41707
$910$	−21.1024	−0.699539
$911$	0.969427	0.0321185	0.0160593	−	0.999871i	$-0.494888\pi$
$911$	0.969427	0.0321185	0.0160593	+	0.999871i	$0.494888\pi$
$912$	−7.56926	−0.250643
$913$	−1.57600	−0.0521580
$914$	34.3138	1.13500
$915$	−0.971835	−0.0321279
$916$	90.1210	2.97768
$917$	−66.5271	−2.19692
$918$	14.2435	0.470106
$919$	21.5416	0.710593	0.355296	−	0.934754i	$-0.384380\pi$
$919$	21.5416	0.710593	0.355296	+	0.934754i	$0.384380\pi$
$920$	10.6483	0.351063
$921$	0.961332	0.0316770
$922$	−81.5686	−2.68632
$923$	9.61997	0.316645
$924$	0.851531	0.0280133
$925$	−10.9338	−0.359502
$926$	−90.4525	−2.97245
$927$	−33.4581	−1.09891
$928$	−78.7023	−2.58353
$929$	37.2927	1.22353	0.611767	−	0.791038i	$-0.290459\pi$
$929$	37.2927	1.22353	0.611767	+	0.791038i	$0.290459\pi$
$930$	2.39156	0.0784224
$931$	−53.2852	−1.74635
$932$	87.9407	2.88059
$933$	0.357033	0.0116887
$934$	68.2822	2.23426
$935$	2.35631	0.0770595
$936$	64.2277	2.09935
$937$	−39.3489	−1.28547	−0.642737	−	0.766087i	$-0.722201\pi$
$937$	−39.3489	−1.28547	−0.642737	+	0.766087i	$0.722201\pi$
$938$	66.3458	2.16627
$939$	1.09528	0.0357430
$940$	37.0548	1.20859
$941$	−3.93865	−0.128396	−0.0641982	−	0.997937i	$-0.520449\pi$
$941$	−3.93865	−0.128396	−0.0641982	+	0.997937i	$0.520449\pi$
$942$	5.78414	0.188457
$943$	19.5156	0.635514
$944$	−21.9177	−0.713361
$945$	−1.97804	−0.0643458
$946$	9.72240	0.316103
$947$	−31.7228	−1.03085	−0.515427	−	0.856934i	$-0.672367\pi$
$947$	−31.7228	−1.03085	−0.515427	+	0.856934i	$0.672367\pi$
$948$	−7.24175	−0.235201
$949$	11.5835	0.376017
$950$	−70.5654	−2.28944
$951$	1.88566	0.0611466
$952$	−264.022	−8.55699
$953$	−13.8767	−0.449510	−0.224755	−	0.974415i	$-0.572158\pi$
$953$	−13.8767	−0.449510	−0.224755	+	0.974415i	$0.572158\pi$
$954$	−54.0050	−1.74848
$955$	6.36384	0.205929
$956$	−98.8431	−3.19682
$957$	0.232844	0.00752678
$958$	−48.6564	−1.57202
$959$	−83.3856	−2.69266
$960$	1.23690	0.0399209
$961$	86.9727	2.80557
$962$	−17.3260	−0.558612
$963$	−42.1541	−1.35840
$964$	99.5965	3.20779
$965$	−16.0495	−0.516651
$966$	2.02282	0.0650830
$967$	23.6917	0.761873	0.380937	−	0.924601i	$-0.375602\pi$
$967$	23.6917	0.761873	0.380937	+	0.924601i	$0.375602\pi$
$968$	88.2680	2.83704
$969$	−5.36401	−0.172317
$970$	22.6776	0.728133
$971$	−3.61344	−0.115961	−0.0579804	−	0.998318i	$-0.518466\pi$
$971$	−3.61344	−0.115961	−0.0579804	+	0.998318i	$0.518466\pi$
$972$	14.9414	0.479245
$973$	−5.71879	−0.183336
$974$	−3.94361	−0.126361
$975$	−1.28770	−0.0412394
$976$	−134.762	−4.31362
$977$	11.5946	0.370944	0.185472	−	0.982650i	$-0.440619\pi$
$977$	11.5946	0.370944	0.185472	+	0.982650i	$0.440619\pi$
$978$	−5.05711	−0.161708
$979$	−0.690945	−0.0220827
$980$	33.9215	1.08358
$981$	−6.97373	−0.222654
$982$	−18.7638	−0.598776
$983$	−54.5626	−1.74028	−0.870138	−	0.492807i	$-0.835971\pi$
$983$	−54.5626	−1.74028	−0.870138	+	0.492807i	$0.835971\pi$
$984$	10.0462	0.320262
$985$	9.17076	0.292205
$986$	−119.368	−3.80144
$987$	4.25736	0.135513
$988$	−80.1463	−2.54979
$989$	16.5537	0.526378
$990$	2.29750	0.0730194
$991$	−12.1881	−0.387166	−0.193583	−	0.981084i	$-0.562011\pi$
$991$	−12.1881	−0.387166	−0.193583	+	0.981084i	$0.562011\pi$
$992$	154.950	4.91968
$993$	−3.51752	−0.111625
$994$	−38.5580	−1.22299
$995$	2.08691	0.0661595
$996$	−2.28392	−0.0723689
$997$	23.6592	0.749293	0.374647	−	0.927168i	$-0.377764\pi$
$997$	23.6592	0.749293	0.374647	+	0.927168i	$0.377764\pi$
$998$	−104.887	−3.32015
$999$	−1.62406	−0.0513829

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 6047 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65722 q^{2} +0.109936 q^{3} +5.06084 q^{4} +0.753739 q^{5} -0.292126 q^{6} +3.98656 q^{7} -8.13334 q^{8} -2.98791 q^{9} +O(q^{10})\)	\(q-2.65722 q^{2} +0.109936 q^{3} +5.06084 q^{4} +0.753739 q^{5} -0.292126 q^{6} +3.98656 q^{7} -8.13334 q^{8} -2.98791 q^{9} -2.00285 q^{10} +0.383918 q^{11} +0.556370 q^{12} +2.64293 q^{13} -10.5932 q^{14} +0.0828634 q^{15} +11.4904 q^{16} +8.14277 q^{17} +7.93956 q^{18} -5.99205 q^{19} +3.81456 q^{20} +0.438268 q^{21} -1.02016 q^{22} -1.73696 q^{23} -0.894150 q^{24} -4.43188 q^{25} -7.02285 q^{26} -0.658289 q^{27} +20.1753 q^{28} +5.51678 q^{29} -0.220187 q^{30} -10.8615 q^{31} -14.2660 q^{32} +0.0422065 q^{33} -21.6372 q^{34} +3.00483 q^{35} -15.1214 q^{36} +2.46709 q^{37} +15.9222 q^{38} +0.290554 q^{39} -6.13042 q^{40} -11.2355 q^{41} -1.16458 q^{42} -9.53031 q^{43} +1.94295 q^{44} -2.25211 q^{45} +4.61548 q^{46} +9.71406 q^{47} +1.26322 q^{48} +8.89264 q^{49} +11.7765 q^{50} +0.895187 q^{51} +13.3754 q^{52} -6.80202 q^{53} +1.74922 q^{54} +0.289374 q^{55} -32.4240 q^{56} -0.658744 q^{57} -14.6593 q^{58} -1.90748 q^{59} +0.419358 q^{60} -11.7282 q^{61} +28.8615 q^{62} -11.9115 q^{63} +14.9270 q^{64} +1.99208 q^{65} -0.112152 q^{66} -6.26307 q^{67} +41.2093 q^{68} -0.190955 q^{69} -7.98450 q^{70} +3.63989 q^{71} +24.3017 q^{72} +4.38284 q^{73} -6.55561 q^{74} -0.487224 q^{75} -30.3248 q^{76} +1.53051 q^{77} -0.772067 q^{78} -13.0161 q^{79} +8.66079 q^{80} +8.89137 q^{81} +29.8553 q^{82} -4.10504 q^{83} +2.21800 q^{84} +6.13753 q^{85} +25.3242 q^{86} +0.606495 q^{87} -3.12254 q^{88} -1.79972 q^{89} +5.98436 q^{90} +10.5362 q^{91} -8.79046 q^{92} -1.19408 q^{93} -25.8124 q^{94} -4.51645 q^{95} -1.56835 q^{96} -11.3226 q^{97} -23.6297 q^{98} -1.14711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \)	\( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

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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	6047.2.a.a.1.7

Level	6047
Weight	2
Character	6047.1
Self dual	Yes
Analytic conductor	48.286
Analytic rank	1
Dimension	217
CM	No

Self dual:	Yes
Analytic conductor:	\(48.2855381023\)
Analytic rank:	\(1\)
Dimension:	\(217\)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$