LMFDB - Embedded Newform 4030.2.a.f.1.4

Newspace parameters

Level:	$ N $	=	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	4030.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.4418197.1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.59064$
Character	$\chi$	=	4030.1

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} -0.252625 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.252625 q^{6} -1.23948 q^{7} +1.00000 q^{8} -2.93618 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.252625 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.252625 q^{6} -1.23948 q^{7} +1.00000 q^{8} -2.93618 q^{9} -1.00000 q^{10} +4.08674 q^{11} -0.252625 q^{12} +1.00000 q^{13} -1.23948 q^{14} +0.252625 q^{15} +1.00000 q^{16} -1.06781 q^{17} -2.93618 q^{18} -8.14236 q^{19} -1.00000 q^{20} +0.313125 q^{21} +4.08674 q^{22} +6.59643 q^{23} -0.252625 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.49963 q^{27} -1.23948 q^{28} -1.85322 q^{29} +0.252625 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.03241 q^{33} -1.06781 q^{34} +1.23948 q^{35} -2.93618 q^{36} -0.537878 q^{37} -8.14236 q^{38} -0.252625 q^{39} -1.00000 q^{40} -0.693843 q^{41} +0.313125 q^{42} -12.5556 q^{43} +4.08674 q^{44} +2.93618 q^{45} +6.59643 q^{46} +6.79817 q^{47} -0.252625 q^{48} -5.46368 q^{49} +1.00000 q^{50} +0.269755 q^{51} +1.00000 q^{52} -11.4271 q^{53} +1.49963 q^{54} -4.08674 q^{55} -1.23948 q^{56} +2.05697 q^{57} -1.85322 q^{58} +4.92227 q^{59} +0.252625 q^{60} +4.53622 q^{61} -1.00000 q^{62} +3.63935 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.03241 q^{66} -7.82519 q^{67} -1.06781 q^{68} -1.66643 q^{69} +1.23948 q^{70} +2.45442 q^{71} -2.93618 q^{72} -14.2626 q^{73} -0.537878 q^{74} -0.252625 q^{75} -8.14236 q^{76} -5.06544 q^{77} -0.252625 q^{78} +0.819624 q^{79} -1.00000 q^{80} +8.42970 q^{81} -0.693843 q^{82} -16.3989 q^{83} +0.313125 q^{84} +1.06781 q^{85} -12.5556 q^{86} +0.468169 q^{87} +4.08674 q^{88} +9.66762 q^{89} +2.93618 q^{90} -1.23948 q^{91} +6.59643 q^{92} +0.252625 q^{93} +6.79817 q^{94} +8.14236 q^{95} -0.252625 q^{96} -4.14428 q^{97} -5.46368 q^{98} -11.9994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) $	$ 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.252625	−0.145853	−0.0729266	−	0.997337i	$-0.523234\pi$
$3$	−0.252625	−0.145853	−0.0729266	+	0.997337i	$0.523234\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.252625	−0.103134
$7$	−1.23948	−0.468481	−0.234240	−	0.972179i	$-0.575260\pi$
$7$	−1.23948	−0.468481	−0.234240	+	0.972179i	$0.575260\pi$
$8$	1.00000	0.353553
$9$	−2.93618	−0.978727
$10$	−1.00000	−0.316228
$11$	4.08674	1.23220	0.616099	−	0.787669i	$-0.288712\pi$
$11$	4.08674	1.23220	0.616099	+	0.787669i	$0.288712\pi$
$12$	−0.252625	−0.0729266
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.23948	−0.331266
$15$	0.252625	0.0652276
$16$	1.00000	0.250000
$17$	−1.06781	−0.258981	−0.129491	−	0.991581i	$-0.541334\pi$
$17$	−1.06781	−0.258981	−0.129491	+	0.991581i	$0.541334\pi$
$18$	−2.93618	−0.692064
$19$	−8.14236	−1.86798	−0.933992	−	0.357293i	$-0.883700\pi$
$19$	−8.14236	−1.86798	−0.933992	+	0.357293i	$0.883700\pi$
$20$	−1.00000	−0.223607
$21$	0.313125	0.0683294
$22$	4.08674	0.871295
$23$	6.59643	1.37545	0.687725	−	0.725971i	$-0.258609\pi$
$23$	6.59643	1.37545	0.687725	+	0.725971i	$0.258609\pi$
$24$	−0.252625	−0.0515669
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	1.49963	0.288604
$28$	−1.23948	−0.234240
$29$	−1.85322	−0.344134	−0.172067	−	0.985085i	$-0.555044\pi$
$29$	−1.85322	−0.344134	−0.172067	+	0.985085i	$0.555044\pi$
$30$	0.252625	0.0461229
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−1.03241	−0.179720
$34$	−1.06781	−0.183127
$35$	1.23948	0.209511
$36$	−2.93618	−0.489363
$37$	−0.537878	−0.0884266	−0.0442133	−	0.999022i	$-0.514078\pi$
$37$	−0.537878	−0.0884266	−0.0442133	+	0.999022i	$0.514078\pi$
$38$	−8.14236	−1.32086
$39$	−0.252625	−0.0404524
$40$	−1.00000	−0.158114
$41$	−0.693843	−0.108360	−0.0541800	−	0.998531i	$-0.517254\pi$
$41$	−0.693843	−0.108360	−0.0541800	+	0.998531i	$0.517254\pi$
$42$	0.313125	0.0483162
$43$	−12.5556	−1.91471	−0.957356	−	0.288912i	$-0.906707\pi$
$43$	−12.5556	−1.91471	−0.957356	+	0.288912i	$0.906707\pi$
$44$	4.08674	0.616099
$45$	2.93618	0.437700
$46$	6.59643	0.972591
$47$	6.79817	0.991614	0.495807	−	0.868433i	$-0.334872\pi$
$47$	6.79817	0.991614	0.495807	+	0.868433i	$0.334872\pi$
$48$	−0.252625	−0.0364633
$49$	−5.46368	−0.780526
$50$	1.00000	0.141421
$51$	0.269755	0.0377733
$52$	1.00000	0.138675
$53$	−11.4271	−1.56963	−0.784817	−	0.619727i	$-0.787243\pi$
$53$	−11.4271	−1.56963	−0.784817	+	0.619727i	$0.787243\pi$
$54$	1.49963	0.204074
$55$	−4.08674	−0.551056
$56$	−1.23948	−0.165633
$57$	2.05697	0.272452
$58$	−1.85322	−0.243339
$59$	4.92227	0.640825	0.320413	−	0.947278i	$-0.396178\pi$
$59$	4.92227	0.640825	0.320413	+	0.947278i	$0.396178\pi$
$60$	0.252625	0.0326138
$61$	4.53622	0.580803	0.290402	−	0.956905i	$-0.406211\pi$
$61$	4.53622	0.580803	0.290402	+	0.956905i	$0.406211\pi$
$62$	−1.00000	−0.127000
$63$	3.63935	0.458514
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−1.03241	−0.127081
$67$	−7.82519	−0.955999	−0.478000	−	0.878360i	$-0.658638\pi$
$67$	−7.82519	−0.955999	−0.478000	+	0.878360i	$0.658638\pi$
$68$	−1.06781	−0.129491
$69$	−1.66643	−0.200614
$70$	1.23948	0.148147
$71$	2.45442	0.291286	0.145643	−	0.989337i	$-0.453475\pi$
$71$	2.45442	0.291286	0.145643	+	0.989337i	$0.453475\pi$
$72$	−2.93618	−0.346032
$73$	−14.2626	−1.66931	−0.834654	−	0.550775i	$-0.814332\pi$
$73$	−14.2626	−1.66931	−0.834654	+	0.550775i	$0.814332\pi$
$74$	−0.537878	−0.0625270
$75$	−0.252625	−0.0291707
$76$	−8.14236	−0.933992
$77$	−5.06544	−0.577261
$78$	−0.252625	−0.0286042
$79$	0.819624	0.0922149	0.0461074	−	0.998936i	$-0.485318\pi$
$79$	0.819624	0.0922149	0.0461074	+	0.998936i	$0.485318\pi$
$80$	−1.00000	−0.111803
$81$	8.42970	0.936633
$82$	−0.693843	−0.0766221
$83$	−16.3989	−1.80001	−0.900005	−	0.435880i	$-0.856437\pi$
$83$	−16.3989	−1.80001	−0.900005	+	0.435880i	$0.856437\pi$
$84$	0.313125	0.0341647
$85$	1.06781	0.115820
$86$	−12.5556	−1.35391
$87$	0.468169	0.0501930
$88$	4.08674	0.435648
$89$	9.66762	1.02477	0.512383	−	0.858757i	$-0.328763\pi$
$89$	9.66762	1.02477	0.512383	+	0.858757i	$0.328763\pi$
$90$	2.93618	0.309501
$91$	−1.23948	−0.129933
$92$	6.59643	0.687725
$93$	0.252625	0.0261960
$94$	6.79817	0.701177
$95$	8.14236	0.835388
$96$	−0.252625	−0.0257835
$97$	−4.14428	−0.420788	−0.210394	−	0.977617i	$-0.567475\pi$
$97$	−4.14428	−0.420788	−0.210394	+	0.977617i	$0.567475\pi$
$98$	−5.46368	−0.551915
$99$	−11.9994	−1.20599
$100$	1.00000	0.100000
$101$	−6.09882	−0.606855	−0.303428	−	0.952854i	$-0.598131\pi$
$101$	−6.09882	−0.606855	−0.303428	+	0.952854i	$0.598131\pi$
$102$	0.269755	0.0267097
$103$	4.89812	0.482626	0.241313	−	0.970447i	$-0.422422\pi$
$103$	4.89812	0.482626	0.241313	+	0.970447i	$0.422422\pi$
$104$	1.00000	0.0980581
$105$	−0.313125	−0.0305578
$106$	−11.4271	−1.10990
$107$	7.34568	0.710134	0.355067	−	0.934841i	$-0.384458\pi$
$107$	7.34568	0.710134	0.355067	+	0.934841i	$0.384458\pi$
$108$	1.49963	0.144302
$109$	−19.2327	−1.84216	−0.921081	−	0.389370i	$-0.872693\pi$
$109$	−19.2327	−1.84216	−0.921081	+	0.389370i	$0.872693\pi$
$110$	−4.08674	−0.389655
$111$	0.135882	0.0128973
$112$	−1.23948	−0.117120
$113$	−16.4569	−1.54813	−0.774065	−	0.633106i	$-0.781780\pi$
$113$	−16.4569	−1.54813	−0.774065	+	0.633106i	$0.781780\pi$
$114$	2.05697	0.192652
$115$	−6.59643	−0.615120
$116$	−1.85322	−0.172067
$117$	−2.93618	−0.271450
$118$	4.92227	0.453132
$119$	1.32353	0.121328
$120$	0.252625	0.0230614
$121$	5.70143	0.518311
$122$	4.53622	0.410690
$123$	0.175282	0.0158047
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	3.63935	0.324219
$127$	−17.7965	−1.57918	−0.789590	−	0.613635i	$-0.789707\pi$
$127$	−17.7965	−1.57918	−0.789590	+	0.613635i	$0.789707\pi$
$128$	1.00000	0.0883883
$129$	3.17186	0.279267
$130$	−1.00000	−0.0877058
$131$	−7.32944	−0.640376	−0.320188	−	0.947354i	$-0.603746\pi$
$131$	−7.32944	−0.640376	−0.320188	+	0.947354i	$0.603746\pi$
$132$	−1.03241	−0.0898601
$133$	10.0923	0.875114
$134$	−7.82519	−0.675994
$135$	−1.49963	−0.129068
$136$	−1.06781	−0.0915637
$137$	17.0050	1.45283	0.726417	−	0.687254i	$-0.241184\pi$
$137$	17.0050	1.45283	0.726417	+	0.687254i	$0.241184\pi$
$138$	−1.66643	−0.141856
$139$	6.80321	0.577040	0.288520	−	0.957474i	$-0.406837\pi$
$139$	6.80321	0.577040	0.288520	+	0.957474i	$0.406837\pi$
$140$	1.23948	0.104755
$141$	−1.71739	−0.144630
$142$	2.45442	0.205971
$143$	4.08674	0.341750
$144$	−2.93618	−0.244682
$145$	1.85322	0.153901
$146$	−14.2626	−1.18038
$147$	1.38026	0.113842
$148$	−0.537878	−0.0442133
$149$	−10.7988	−0.884671	−0.442336	−	0.896850i	$-0.645850\pi$
$149$	−10.7988	−0.884671	−0.442336	+	0.896850i	$0.645850\pi$
$150$	−0.252625	−0.0206268
$151$	−1.77076	−0.144102	−0.0720511	−	0.997401i	$-0.522954\pi$
$151$	−1.77076	−0.144102	−0.0720511	+	0.997401i	$0.522954\pi$
$152$	−8.14236	−0.660432
$153$	3.13527	0.253472
$154$	−5.06544	−0.408185
$155$	1.00000	0.0803219
$156$	−0.252625	−0.0202262
$157$	22.1053	1.76420	0.882099	−	0.471064i	$-0.156130\pi$
$157$	22.1053	1.76420	0.882099	+	0.471064i	$0.156130\pi$
$158$	0.819624	0.0652058
$159$	2.88678	0.228936
$160$	−1.00000	−0.0790569
$161$	−8.17616	−0.644372
$162$	8.42970	0.662300
$163$	−17.9197	−1.40358	−0.701788	−	0.712385i	$-0.747615\pi$
$163$	−17.9197	−1.40358	−0.701788	+	0.712385i	$0.747615\pi$
$164$	−0.693843	−0.0541800
$165$	1.03241	0.0803733
$166$	−16.3989	−1.27280
$167$	12.0670	0.933775	0.466887	−	0.884317i	$-0.345375\pi$
$167$	12.0670	0.933775	0.466887	+	0.884317i	$0.345375\pi$
$168$	0.313125	0.0241581
$169$	1.00000	0.0769231
$170$	1.06781	0.0818970
$171$	23.9074	1.82825
$172$	−12.5556	−0.957356
$173$	21.4481	1.63067	0.815335	−	0.578989i	$-0.196553\pi$
$173$	21.4481	1.63067	0.815335	+	0.578989i	$0.196553\pi$
$174$	0.468169	0.0354918
$175$	−1.23948	−0.0936961
$176$	4.08674	0.308049
$177$	−1.24349	−0.0934664
$178$	9.66762	0.724619
$179$	−18.8075	−1.40574	−0.702871	−	0.711318i	$-0.748099\pi$
$179$	−18.8075	−1.40574	−0.702871	+	0.711318i	$0.748099\pi$
$180$	2.93618	0.218850
$181$	−19.2383	−1.42997	−0.714986	−	0.699138i	$-0.753567\pi$
$181$	−19.2383	−1.42997	−0.714986	+	0.699138i	$0.753567\pi$
$182$	−1.23948	−0.0918766
$183$	−1.14596	−0.0847120
$184$	6.59643	0.486295
$185$	0.537878	0.0395456
$186$	0.252625	0.0185234
$187$	−4.36385	−0.319116
$188$	6.79817	0.495807
$189$	−1.85877	−0.135205
$190$	8.14236	0.590709
$191$	3.25410	0.235458	0.117729	−	0.993046i	$-0.462439\pi$
$191$	3.25410	0.235458	0.117729	+	0.993046i	$0.462439\pi$
$192$	−0.252625	−0.0182317
$193$	4.75236	0.342082	0.171041	−	0.985264i	$-0.445287\pi$
$193$	4.75236	0.342082	0.171041	+	0.985264i	$0.445287\pi$
$194$	−4.14428	−0.297542
$195$	0.252625	0.0180909
$196$	−5.46368	−0.390263
$197$	−20.7562	−1.47882	−0.739410	−	0.673255i	$-0.764896\pi$
$197$	−20.7562	−1.47882	−0.739410	+	0.673255i	$0.764896\pi$
$198$	−11.9994	−0.852760
$199$	−12.6687	−0.898057	−0.449028	−	0.893517i	$-0.648230\pi$
$199$	−12.6687	−0.898057	−0.449028	+	0.893517i	$0.648230\pi$
$200$	1.00000	0.0707107
$201$	1.97684	0.139436
$202$	−6.09882	−0.429111
$203$	2.29703	0.161220
$204$	0.269755	0.0188866
$205$	0.693843	0.0484601
$206$	4.89812	0.341268
$207$	−19.3683	−1.34619
$208$	1.00000	0.0693375
$209$	−33.2757	−2.30173
$210$	−0.313125	−0.0216077
$211$	5.59342	0.385067	0.192534	−	0.981290i	$-0.438330\pi$
$211$	5.59342	0.385067	0.192534	+	0.981290i	$0.438330\pi$
$212$	−11.4271	−0.784817
$213$	−0.620049	−0.0424851
$214$	7.34568	0.502140
$215$	12.5556	0.856285
$216$	1.49963	0.102037
$217$	1.23948	0.0841416
$218$	−19.2327	−1.30261
$219$	3.60309	0.243474
$220$	−4.08674	−0.275528
$221$	−1.06781	−0.0718285
$222$	0.135882	0.00911977
$223$	25.1249	1.68249	0.841243	−	0.540657i	$-0.181824\pi$
$223$	25.1249	1.68249	0.841243	+	0.540657i	$0.181824\pi$
$224$	−1.23948	−0.0828164
$225$	−2.93618	−0.195745
$226$	−16.4569	−1.09469
$227$	13.2454	0.879131	0.439565	−	0.898211i	$-0.355132\pi$
$227$	13.2454	0.879131	0.439565	+	0.898211i	$0.355132\pi$
$228$	2.05697	0.136226
$229$	−6.93174	−0.458063	−0.229031	−	0.973419i	$-0.573556\pi$
$229$	−6.93174	−0.458063	−0.229031	+	0.973419i	$0.573556\pi$
$230$	−6.59643	−0.434956
$231$	1.27966	0.0841954
$232$	−1.85322	−0.121670
$233$	−21.5947	−1.41471	−0.707357	−	0.706856i	$-0.750113\pi$
$233$	−21.5947	−1.41471	−0.707357	+	0.706856i	$0.750113\pi$
$234$	−2.93618	−0.191944
$235$	−6.79817	−0.443463
$236$	4.92227	0.320413
$237$	−0.207058	−0.0134498
$238$	1.32353	0.0857916
$239$	−20.6583	−1.33628	−0.668139	−	0.744037i	$-0.732909\pi$
$239$	−20.6583	−1.33628	−0.668139	+	0.744037i	$0.732909\pi$
$240$	0.252625	0.0163069
$241$	−21.7353	−1.40010	−0.700048	−	0.714096i	$-0.746838\pi$
$241$	−21.7353	−1.40010	−0.700048	+	0.714096i	$0.746838\pi$
$242$	5.70143	0.366502
$243$	−6.62844	−0.425215
$244$	4.53622	0.290402
$245$	5.46368	0.349062
$246$	0.175282	0.0111756
$247$	−8.14236	−0.518086
$248$	−1.00000	−0.0635001
$249$	4.14277	0.262537
$250$	−1.00000	−0.0632456
$251$	12.7871	0.807117	0.403558	−	0.914954i	$-0.367773\pi$
$251$	12.7871	0.807117	0.403558	+	0.914954i	$0.367773\pi$
$252$	3.63935	0.229257
$253$	26.9579	1.69483
$254$	−17.7965	−1.11665
$255$	−0.269755	−0.0168927
$256$	1.00000	0.0625000
$257$	−6.88832	−0.429681	−0.214841	−	0.976649i	$-0.568923\pi$
$257$	−6.88832	−0.429681	−0.214841	+	0.976649i	$0.568923\pi$
$258$	3.17186	0.197472
$259$	0.666690	0.0414261
$260$	−1.00000	−0.0620174
$261$	5.44138	0.336813
$262$	−7.32944	−0.452814
$263$	17.9601	1.10747	0.553733	−	0.832694i	$-0.313203\pi$
$263$	17.9601	1.10747	0.553733	+	0.832694i	$0.313203\pi$
$264$	−1.03241	−0.0635407
$265$	11.4271	0.701962
$266$	10.0923	0.618799
$267$	−2.44229	−0.149465
$268$	−7.82519	−0.478000
$269$	3.72219	0.226946	0.113473	−	0.993541i	$-0.463802\pi$
$269$	3.72219	0.226946	0.113473	+	0.993541i	$0.463802\pi$
$270$	−1.49963	−0.0912645
$271$	3.22237	0.195745	0.0978726	−	0.995199i	$-0.468796\pi$
$271$	3.22237	0.195745	0.0978726	+	0.995199i	$0.468796\pi$
$272$	−1.06781	−0.0647453
$273$	0.313125	0.0189512
$274$	17.0050	1.02731
$275$	4.08674	0.246440
$276$	−1.66643	−0.100307
$277$	24.9074	1.49654	0.748271	−	0.663394i	$-0.230884\pi$
$277$	24.9074	1.49654	0.748271	+	0.663394i	$0.230884\pi$
$278$	6.80321	0.408029
$279$	2.93618	0.175785
$280$	1.23948	0.0740733
$281$	18.3523	1.09481	0.547403	−	0.836869i	$-0.315616\pi$
$281$	18.3523	1.09481	0.547403	+	0.836869i	$0.315616\pi$
$282$	−1.71739	−0.102269
$283$	−9.33022	−0.554624	−0.277312	−	0.960780i	$-0.589444\pi$
$283$	−9.33022	−0.554624	−0.277312	+	0.960780i	$0.589444\pi$
$284$	2.45442	0.145643
$285$	−2.05697	−0.121844
$286$	4.08674	0.241654
$287$	0.860006	0.0507646
$288$	−2.93618	−0.173016
$289$	−15.8598	−0.932929
$290$	1.85322	0.108825
$291$	1.04695	0.0613733
$292$	−14.2626	−0.834654
$293$	21.5474	1.25881	0.629406	−	0.777077i	$-0.283298\pi$
$293$	21.5474	1.25881	0.629406	+	0.777077i	$0.283298\pi$
$294$	1.38026	0.0804987
$295$	−4.92227	−0.286586
$296$	−0.537878	−0.0312635
$297$	6.12859	0.355617
$298$	−10.7988	−0.625557
$299$	6.59643	0.381481
$300$	−0.252625	−0.0145853
$301$	15.5625	0.897005
$302$	−1.77076	−0.101896
$303$	1.54072	0.0885118
$304$	−8.14236	−0.466996
$305$	−4.53622	−0.259743
$306$	3.13527	0.179232
$307$	15.4675	0.882779	0.441389	−	0.897316i	$-0.354486\pi$
$307$	15.4675	0.882779	0.441389	+	0.897316i	$0.354486\pi$
$308$	−5.06544	−0.288630
$309$	−1.23739	−0.0703926
$310$	1.00000	0.0567962
$311$	−20.4847	−1.16158	−0.580789	−	0.814054i	$-0.697256\pi$
$311$	−20.4847	−1.16158	−0.580789	+	0.814054i	$0.697256\pi$
$312$	−0.252625	−0.0143021
$313$	25.7248	1.45405	0.727026	−	0.686610i	$-0.240902\pi$
$313$	25.7248	1.45405	0.727026	+	0.686610i	$0.240902\pi$
$314$	22.1053	1.24748
$315$	−3.63935	−0.205054
$316$	0.819624	0.0461074
$317$	−0.411304	−0.0231011	−0.0115506	−	0.999933i	$-0.503677\pi$
$317$	−0.411304	−0.0231011	−0.0115506	+	0.999933i	$0.503677\pi$
$318$	2.88678	0.161882
$319$	−7.57361	−0.424041
$320$	−1.00000	−0.0559017
$321$	−1.85570	−0.103575
$322$	−8.17616	−0.455640
$323$	8.69446	0.483773
$324$	8.42970	0.468316
$325$	1.00000	0.0554700
$326$	−17.9197	−0.992479
$327$	4.85868	0.268685
$328$	−0.693843	−0.0383110
$329$	−8.42621	−0.464552
$330$	1.03241	0.0568325
$331$	−19.5537	−1.07477	−0.537383	−	0.843338i	$-0.680587\pi$
$331$	−19.5537	−1.07477	−0.537383	+	0.843338i	$0.680587\pi$
$332$	−16.3989	−0.900005
$333$	1.57931	0.0865455
$334$	12.0670	0.660278
$335$	7.82519	0.427536
$336$	0.313125	0.0170824
$337$	−24.8159	−1.35181	−0.675904	−	0.736989i	$-0.736247\pi$
$337$	−24.8159	−1.35181	−0.675904	+	0.736989i	$0.736247\pi$
$338$	1.00000	0.0543928
$339$	4.15742	0.225800
$340$	1.06781	0.0579100
$341$	−4.08674	−0.221309
$342$	23.9074	1.29277
$343$	15.4485	0.834142
$344$	−12.5556	−0.676953
$345$	1.66643	0.0897173
$346$	21.4481	1.15306
$347$	−12.2109	−0.655518	−0.327759	−	0.944761i	$-0.606293\pi$
$347$	−12.2109	−0.655518	−0.327759	+	0.944761i	$0.606293\pi$
$348$	0.468169	0.0250965
$349$	31.9548	1.71050	0.855249	−	0.518217i	$-0.173404\pi$
$349$	31.9548	1.71050	0.855249	+	0.518217i	$0.173404\pi$
$350$	−1.23948	−0.0662531
$351$	1.49963	0.0800443
$352$	4.08674	0.217824
$353$	23.4863	1.25005	0.625024	−	0.780606i	$-0.285089\pi$
$353$	23.4863	1.25005	0.625024	+	0.780606i	$0.285089\pi$
$354$	−1.24349	−0.0660908
$355$	−2.45442	−0.130267
$356$	9.66762	0.512383
$357$	−0.334357	−0.0176960
$358$	−18.8075	−0.994009
$359$	−4.71759	−0.248985	−0.124493	−	0.992221i	$-0.539730\pi$
$359$	−4.71759	−0.248985	−0.124493	+	0.992221i	$0.539730\pi$
$360$	2.93618	0.154750
$361$	47.2980	2.48937
$362$	−19.2383	−1.01114
$363$	−1.44032	−0.0755974
$364$	−1.23948	−0.0649666
$365$	14.2626	0.746537
$366$	−1.14596	−0.0599005
$367$	−2.37279	−0.123859	−0.0619294	−	0.998081i	$-0.519725\pi$
$367$	−2.37279	−0.123859	−0.0619294	+	0.998081i	$0.519725\pi$
$368$	6.59643	0.343863
$369$	2.03725	0.106055
$370$	0.537878	0.0279629
$371$	14.1637	0.735343
$372$	0.252625	0.0130980
$373$	−14.2652	−0.738623	−0.369312	−	0.929306i	$-0.620406\pi$
$373$	−14.2652	−0.738623	−0.369312	+	0.929306i	$0.620406\pi$
$374$	−4.36385	−0.225649
$375$	0.252625	0.0130455
$376$	6.79817	0.350589
$377$	−1.85322	−0.0954455
$378$	−1.85877	−0.0956046
$379$	26.9056	1.38205	0.691023	−	0.722832i	$-0.257160\pi$
$379$	26.9056	1.38205	0.691023	+	0.722832i	$0.257160\pi$
$380$	8.14236	0.417694
$381$	4.49584	0.230329
$382$	3.25410	0.166494
$383$	32.3812	1.65460	0.827301	−	0.561759i	$-0.189875\pi$
$383$	32.3812	1.65460	0.827301	+	0.561759i	$0.189875\pi$
$384$	−0.252625	−0.0128917
$385$	5.06544	0.258159
$386$	4.75236	0.241889
$387$	36.8655	1.87398
$388$	−4.14428	−0.210394
$389$	7.42585	0.376506	0.188253	−	0.982121i	$-0.439718\pi$
$389$	7.42585	0.376506	0.188253	+	0.982121i	$0.439718\pi$
$390$	0.252625	0.0127922
$391$	−7.04371	−0.356216
$392$	−5.46368	−0.275958
$393$	1.85160	0.0934009
$394$	−20.7562	−1.04568
$395$	−0.819624	−0.0412398
$396$	−11.9994	−0.602993
$397$	−0.532290	−0.0267149	−0.0133574	−	0.999911i	$-0.504252\pi$
$397$	−0.532290	−0.0267149	−0.0133574	+	0.999911i	$0.504252\pi$
$398$	−12.6687	−0.635022
$399$	−2.54957	−0.127638
$400$	1.00000	0.0500000
$401$	5.08171	0.253768	0.126884	−	0.991918i	$-0.459502\pi$
$401$	5.08171	0.253768	0.126884	+	0.991918i	$0.459502\pi$
$402$	1.97684	0.0985959
$403$	−1.00000	−0.0498135
$404$	−6.09882	−0.303428
$405$	−8.42970	−0.418875
$406$	2.29703	0.114000
$407$	−2.19817	−0.108959
$408$	0.269755	0.0133549
$409$	−11.9445	−0.590617	−0.295308	−	0.955402i	$-0.595422\pi$
$409$	−11.9445	−0.590617	−0.295308	+	0.955402i	$0.595422\pi$
$410$	0.693843	0.0342664
$411$	−4.29589	−0.211901
$412$	4.89812	0.241313
$413$	−6.10107	−0.300214
$414$	−19.3683	−0.951901
$415$	16.3989	0.804989
$416$	1.00000	0.0490290
$417$	−1.71866	−0.0841632
$418$	−33.2757	−1.62757
$419$	29.6890	1.45040	0.725200	−	0.688538i	$-0.241747\pi$
$419$	29.6890	1.45040	0.725200	+	0.688538i	$0.241747\pi$
$420$	−0.313125	−0.0152789
$421$	−8.84383	−0.431022	−0.215511	−	0.976501i	$-0.569142\pi$
$421$	−8.84383	−0.431022	−0.215511	+	0.976501i	$0.569142\pi$
$422$	5.59342	0.272284
$423$	−19.9606	−0.970520
$424$	−11.4271	−0.554950
$425$	−1.06781	−0.0517962
$426$	−0.620049	−0.0300415
$427$	−5.62256	−0.272095
$428$	7.34568	0.355067
$429$	−1.03241	−0.0498454
$430$	12.5556	0.605485
$431$	−27.1853	−1.30947	−0.654734	−	0.755860i	$-0.727219\pi$
$431$	−27.1853	−1.30947	−0.654734	+	0.755860i	$0.727219\pi$
$432$	1.49963	0.0721510
$433$	28.8950	1.38860	0.694301	−	0.719684i	$-0.255713\pi$
$433$	28.8950	1.38860	0.694301	+	0.719684i	$0.255713\pi$
$434$	1.23948	0.0594971
$435$	−0.468169	−0.0224470
$436$	−19.2327	−0.921081
$437$	−53.7105	−2.56932
$438$	3.60309	0.172162
$439$	−27.7820	−1.32596	−0.662981	−	0.748636i	$-0.730709\pi$
$439$	−27.7820	−1.32596	−0.662981	+	0.748636i	$0.730709\pi$
$440$	−4.08674	−0.194828
$441$	16.0424	0.763922
$442$	−1.06781	−0.0507904
$443$	14.8814	0.707036	0.353518	−	0.935428i	$-0.384985\pi$
$443$	14.8814	0.707036	0.353518	+	0.935428i	$0.384985\pi$
$444$	0.135882	0.00644865
$445$	−9.66762	−0.458289
$446$	25.1249	1.18970
$447$	2.72805	0.129032
$448$	−1.23948	−0.0585601
$449$	6.47878	0.305753	0.152876	−	0.988245i	$-0.451146\pi$
$449$	6.47878	0.305753	0.152876	+	0.988245i	$0.451146\pi$
$450$	−2.93618	−0.138413
$451$	−2.83555	−0.133521
$452$	−16.4569	−0.774065
$453$	0.447338	0.0210178
$454$	13.2454	0.621639
$455$	1.23948	0.0581079
$456$	2.05697	0.0963262
$457$	4.98112	0.233007	0.116504	−	0.993190i	$-0.462831\pi$
$457$	4.98112	0.233007	0.116504	+	0.993190i	$0.462831\pi$
$458$	−6.93174	−0.323899
$459$	−1.60131	−0.0747430
$460$	−6.59643	−0.307560
$461$	−18.0686	−0.841539	−0.420769	−	0.907168i	$-0.638240\pi$
$461$	−18.0686	−0.841539	−0.420769	+	0.907168i	$0.638240\pi$
$462$	1.27966	0.0595351
$463$	−0.522460	−0.0242808	−0.0121404	−	0.999926i	$-0.503865\pi$
$463$	−0.522460	−0.0242808	−0.0121404	+	0.999926i	$0.503865\pi$
$464$	−1.85322	−0.0860334
$465$	−0.252625	−0.0117152
$466$	−21.5947	−1.00035
$467$	8.97422	0.415277	0.207639	−	0.978206i	$-0.433422\pi$
$467$	8.97422	0.415277	0.207639	+	0.978206i	$0.433422\pi$
$468$	−2.93618	−0.135725
$469$	9.69919	0.447867
$470$	−6.79817	−0.313576
$471$	−5.58437	−0.257314
$472$	4.92227	0.226566
$473$	−51.3115	−2.35930
$474$	−0.207058	−0.00951048
$475$	−8.14236	−0.373597
$476$	1.32353	0.0606638
$477$	33.5521	1.53624
$478$	−20.6583	−0.944891
$479$	11.3765	0.519805	0.259902	−	0.965635i	$-0.416310\pi$
$479$	11.3765	0.519805	0.259902	+	0.965635i	$0.416310\pi$
$480$	0.252625	0.0115307
$481$	−0.537878	−0.0245251
$482$	−21.7353	−0.990018
$483$	2.06551	0.0939838
$484$	5.70143	0.259156
$485$	4.14428	0.188182
$486$	−6.62844	−0.300672
$487$	5.50411	0.249415	0.124707	−	0.992194i	$-0.460201\pi$
$487$	5.50411	0.249415	0.124707	+	0.992194i	$0.460201\pi$
$488$	4.53622	0.205345
$489$	4.52696	0.204716
$490$	5.46368	0.246824
$491$	−39.8235	−1.79721	−0.898604	−	0.438761i	$-0.855418\pi$
$491$	−39.8235	−1.79721	−0.898604	+	0.438761i	$0.855418\pi$
$492$	0.175282	0.00790233
$493$	1.97888	0.0891241
$494$	−8.14236	−0.366342
$495$	11.9994	0.539333
$496$	−1.00000	−0.0449013
$497$	−3.04221	−0.136462
$498$	4.14277	0.185642
$499$	−12.4798	−0.558675	−0.279337	−	0.960193i	$-0.590115\pi$
$499$	−12.4798	−0.558675	−0.279337	+	0.960193i	$0.590115\pi$
$500$	−1.00000	−0.0447214
$501$	−3.04844	−0.136194
$502$	12.7871	0.570718
$503$	−25.0994	−1.11913	−0.559563	−	0.828788i	$-0.689031\pi$
$503$	−25.0994	−1.11913	−0.559563	+	0.828788i	$0.689031\pi$
$504$	3.63935	0.162109
$505$	6.09882	0.271394
$506$	26.9579	1.19842
$507$	−0.252625	−0.0112195
$508$	−17.7965	−0.789590
$509$	−29.1914	−1.29389	−0.646944	−	0.762538i	$-0.723953\pi$
$509$	−29.1914	−1.29389	−0.646944	+	0.762538i	$0.723953\pi$
$510$	−0.269755	−0.0119450
$511$	17.6782	0.782038
$512$	1.00000	0.0441942
$513$	−12.2105	−0.539108
$514$	−6.88832	−0.303831
$515$	−4.89812	−0.215837
$516$	3.17186	0.139633
$517$	27.7823	1.22186
$518$	0.666690	0.0292927
$519$	−5.41834	−0.237839
$520$	−1.00000	−0.0438529
$521$	23.9008	1.04711	0.523557	−	0.851991i	$-0.324605\pi$
$521$	23.9008	1.04711	0.523557	+	0.851991i	$0.324605\pi$
$522$	5.44138	0.238163
$523$	−14.9556	−0.653963	−0.326982	−	0.945031i	$-0.606032\pi$
$523$	−14.9556	−0.653963	−0.326982	+	0.945031i	$0.606032\pi$
$524$	−7.32944	−0.320188
$525$	0.313125	0.0136659
$526$	17.9601	0.783097
$527$	1.06781	0.0465144
$528$	−1.03241	−0.0449300
$529$	20.5129	0.891865
$530$	11.4271	0.496362
$531$	−14.4527	−0.627193
$532$	10.0923	0.437557
$533$	−0.693843	−0.0300537
$534$	−2.44229	−0.105688
$535$	−7.34568	−0.317581
$536$	−7.82519	−0.337997
$537$	4.75126	0.205032
$538$	3.72219	0.160475
$539$	−22.3286	−0.961762
$540$	−1.49963	−0.0645338
$541$	26.1527	1.12439	0.562196	−	0.827004i	$-0.309957\pi$
$541$	26.1527	1.12439	0.562196	+	0.827004i	$0.309957\pi$
$542$	3.22237	0.138413
$543$	4.86009	0.208566
$544$	−1.06781	−0.0457818
$545$	19.2327	0.823840
$546$	0.313125	0.0134005
$547$	17.1760	0.734392	0.367196	−	0.930144i	$-0.380318\pi$
$547$	17.1760	0.734392	0.367196	+	0.930144i	$0.380318\pi$
$548$	17.0050	0.726417
$549$	−13.3192	−0.568448
$550$	4.08674	0.174259
$551$	15.0895	0.642836
$552$	−1.66643	−0.0709278
$553$	−1.01591	−0.0432009
$554$	24.9074	1.05821
$555$	−0.135882	−0.00576785
$556$	6.80321	0.288520
$557$	−12.7916	−0.541999	−0.270999	−	0.962580i	$-0.587354\pi$
$557$	−12.7916	−0.541999	−0.270999	+	0.962580i	$0.587354\pi$
$558$	2.93618	0.124298
$559$	−12.5556	−0.531045
$560$	1.23948	0.0523777
$561$	1.10242	0.0465441
$562$	18.3523	0.774145
$563$	14.3652	0.605423	0.302711	−	0.953082i	$-0.402108\pi$
$563$	14.3652	0.605423	0.302711	+	0.953082i	$0.402108\pi$
$564$	−1.71739	−0.0723151
$565$	16.4569	0.692345
$566$	−9.33022	−0.392178
$567$	−10.4485	−0.438794
$568$	2.45442	0.102985
$569$	−22.5054	−0.943475	−0.471737	−	0.881739i	$-0.656373\pi$
$569$	−22.5054	−0.943475	−0.471737	+	0.881739i	$0.656373\pi$
$570$	−2.05697	−0.0861568
$571$	22.2032	0.929176	0.464588	−	0.885527i	$-0.346202\pi$
$571$	22.2032	0.929176	0.464588	+	0.885527i	$0.346202\pi$
$572$	4.08674	0.170875
$573$	−0.822067	−0.0343423
$574$	0.860006	0.0358960
$575$	6.59643	0.275090
$576$	−2.93618	−0.122341
$577$	9.89301	0.411852	0.205926	−	0.978568i	$-0.433979\pi$
$577$	9.89301	0.411852	0.205926	+	0.978568i	$0.433979\pi$
$578$	−15.8598	−0.659680
$579$	−1.20057	−0.0498938
$580$	1.85322	0.0769506
$581$	20.3261	0.843270
$582$	1.04695	0.0433974
$583$	−46.6996	−1.93410
$584$	−14.2626	−0.590189
$585$	2.93618	0.121396
$586$	21.5474	0.890114
$587$	−15.4613	−0.638155	−0.319078	−	0.947729i	$-0.603373\pi$
$587$	−15.4613	−0.638155	−0.319078	+	0.947729i	$0.603373\pi$
$588$	1.38026	0.0569211
$589$	8.14236	0.335500
$590$	−4.92227	−0.202647
$591$	5.24355	0.215691
$592$	−0.537878	−0.0221066
$593$	37.1204	1.52435	0.762177	−	0.647369i	$-0.224131\pi$
$593$	37.1204	1.52435	0.762177	+	0.647369i	$0.224131\pi$
$594$	6.12859	0.251459
$595$	−1.32353	−0.0542594
$596$	−10.7988	−0.442336
$597$	3.20042	0.130985
$598$	6.59643	0.269748
$599$	−0.998753	−0.0408079	−0.0204040	−	0.999792i	$-0.506495\pi$
$599$	−0.998753	−0.0408079	−0.0204040	+	0.999792i	$0.506495\pi$
$600$	−0.252625	−0.0103134
$601$	−24.7299	−1.00875	−0.504377	−	0.863484i	$-0.668278\pi$
$601$	−24.7299	−1.00875	−0.504377	+	0.863484i	$0.668278\pi$
$602$	15.5625	0.634278
$603$	22.9762	0.935662
$604$	−1.77076	−0.0720511
$605$	−5.70143	−0.231796
$606$	1.54072	0.0625873
$607$	−32.7085	−1.32760	−0.663798	−	0.747912i	$-0.731056\pi$
$607$	−32.7085	−1.32760	−0.663798	+	0.747912i	$0.731056\pi$
$608$	−8.14236	−0.330216
$609$	−0.580288	−0.0235145
$610$	−4.53622	−0.183666
$611$	6.79817	0.275024
$612$	3.13527	0.126736
$613$	−14.3331	−0.578910	−0.289455	−	0.957192i	$-0.593474\pi$
$613$	−14.3331	−0.578910	−0.289455	+	0.957192i	$0.593474\pi$
$614$	15.4675	0.624219
$615$	−0.175282	−0.00706806
$616$	−5.06544	−0.204092
$617$	10.3893	0.418256	0.209128	−	0.977888i	$-0.432938\pi$
$617$	10.3893	0.418256	0.209128	+	0.977888i	$0.432938\pi$
$618$	−1.23739	−0.0497751
$619$	−16.4954	−0.663005	−0.331503	−	0.943454i	$-0.607556\pi$
$619$	−16.4954	−0.663005	−0.331503	+	0.943454i	$0.607556\pi$
$620$	1.00000	0.0401610
$621$	9.89220	0.396960
$622$	−20.4847	−0.821360
$623$	−11.9828	−0.480083
$624$	−0.252625	−0.0101131
$625$	1.00000	0.0400000
$626$	25.7248	1.02817
$627$	8.40628	0.335714
$628$	22.1053	0.882099
$629$	0.574350	0.0229008
$630$	−3.63935	−0.144995
$631$	−11.7825	−0.469053	−0.234527	−	0.972110i	$-0.575354\pi$
$631$	−11.7825	−0.469053	−0.234527	+	0.972110i	$0.575354\pi$
$632$	0.819624	0.0326029
$633$	−1.41304	−0.0561633
$634$	−0.411304	−0.0163350
$635$	17.7965	0.706231
$636$	2.88678	0.114468
$637$	−5.46368	−0.216479
$638$	−7.57361	−0.299842
$639$	−7.20663	−0.285090
$640$	−1.00000	−0.0395285
$641$	37.2059	1.46954	0.734772	−	0.678314i	$-0.237289\pi$
$641$	37.2059	1.46954	0.734772	+	0.678314i	$0.237289\pi$
$642$	−1.85570	−0.0732388
$643$	22.9318	0.904343	0.452171	−	0.891931i	$-0.350650\pi$
$643$	22.9318	0.904343	0.452171	+	0.891931i	$0.350650\pi$
$644$	−8.17616	−0.322186
$645$	−3.17186	−0.124892
$646$	8.69446	0.342079
$647$	7.39363	0.290674	0.145337	−	0.989382i	$-0.453573\pi$
$647$	7.39363	0.290674	0.145337	+	0.989382i	$0.453573\pi$
$648$	8.42970	0.331150
$649$	20.1160	0.789623
$650$	1.00000	0.0392232
$651$	−0.313125	−0.0122723
$652$	−17.9197	−0.701788
$653$	1.32955	0.0520292	0.0260146	−	0.999662i	$-0.491718\pi$
$653$	1.32955	0.0520292	0.0260146	+	0.999662i	$0.491718\pi$
$654$	4.85868	0.189989
$655$	7.32944	0.286385
$656$	−0.693843	−0.0270900
$657$	41.8775	1.63380
$658$	−8.42621	−0.328488
$659$	−17.5624	−0.684136	−0.342068	−	0.939675i	$-0.611127\pi$
$659$	−17.5624	−0.684136	−0.342068	+	0.939675i	$0.611127\pi$
$660$	1.03241	0.0401866
$661$	45.0340	1.75162	0.875810	−	0.482657i	$-0.160328\pi$
$661$	45.0340	1.75162	0.875810	+	0.482657i	$0.160328\pi$
$662$	−19.5537	−0.759974
$663$	0.269755	0.0104764
$664$	−16.3989	−0.636400
$665$	−10.0923	−0.391363
$666$	1.57931	0.0611969
$667$	−12.2246	−0.473339
$668$	12.0670	0.466887
$669$	−6.34718	−0.245396
$670$	7.82519	0.302314
$671$	18.5383	0.715664
$672$	0.313125	0.0120790
$673$	35.5859	1.37173	0.685867	−	0.727727i	$-0.259423\pi$
$673$	35.5859	1.37173	0.685867	+	0.727727i	$0.259423\pi$
$674$	−24.8159	−0.955873
$675$	1.49963	0.0577208
$676$	1.00000	0.0384615
$677$	−11.3157	−0.434899	−0.217449	−	0.976072i	$-0.569774\pi$
$677$	−11.3157	−0.434899	−0.217449	+	0.976072i	$0.569774\pi$
$678$	4.15742	0.159665
$679$	5.13676	0.197131
$680$	1.06781	0.0409485
$681$	−3.34613	−0.128224
$682$	−4.08674	−0.156489
$683$	−36.7408	−1.40585	−0.702924	−	0.711265i	$-0.748123\pi$
$683$	−36.7408	−1.40585	−0.702924	+	0.711265i	$0.748123\pi$
$684$	23.9074	0.914123
$685$	−17.0050	−0.649727
$686$	15.4485	0.589827
$687$	1.75113	0.0668099
$688$	−12.5556	−0.478678
$689$	−11.4271	−0.435338
$690$	1.66643	0.0634397
$691$	0.889761	0.0338481	0.0169241	−	0.999857i	$-0.494613\pi$
$691$	0.889761	0.0338481	0.0169241	+	0.999857i	$0.494613\pi$
$692$	21.4481	0.815335
$693$	14.8731	0.564980
$694$	−12.2109	−0.463521
$695$	−6.80321	−0.258060
$696$	0.468169	0.0177459
$697$	0.740890	0.0280632
$698$	31.9548	1.20951
$699$	5.45536	0.206341
$700$	−1.23948	−0.0468481
$701$	8.29197	0.313183	0.156592	−	0.987663i	$-0.449949\pi$
$701$	8.29197	0.313183	0.156592	+	0.987663i	$0.449949\pi$
$702$	1.49963	0.0565999
$703$	4.37959	0.165180
$704$	4.08674	0.154025
$705$	1.71739	0.0646806
$706$	23.4863	0.883917
$707$	7.55938	0.284300
$708$	−1.24349	−0.0467332
$709$	20.9812	0.787964	0.393982	−	0.919118i	$-0.371097\pi$
$709$	20.9812	0.787964	0.393982	+	0.919118i	$0.371097\pi$
$710$	−2.45442	−0.0921128
$711$	−2.40656	−0.0902532
$712$	9.66762	0.362309
$713$	−6.59643	−0.247038
$714$	−0.334357	−0.0125130
$715$	−4.08674	−0.152835
$716$	−18.8075	−0.702871
$717$	5.21882	0.194900
$718$	−4.71759	−0.176059
$719$	−34.7957	−1.29766	−0.648829	−	0.760934i	$-0.724741\pi$
$719$	−34.7957	−1.29766	−0.648829	+	0.760934i	$0.724741\pi$
$720$	2.93618	0.109425
$721$	−6.07114	−0.226101
$722$	47.2980	1.76025
$723$	5.49090	0.204209
$724$	−19.2383	−0.714986
$725$	−1.85322	−0.0688267
$726$	−1.44032	−0.0534555
$727$	41.1678	1.52683	0.763415	−	0.645909i	$-0.223521\pi$
$727$	41.1678	1.52683	0.763415	+	0.645909i	$0.223521\pi$
$728$	−1.23948	−0.0459383
$729$	−23.6146	−0.874614
$730$	14.2626	0.527881
$731$	13.4070	0.495874
$732$	−1.14596	−0.0423560
$733$	47.7243	1.76274	0.881368	−	0.472431i	$-0.156623\pi$
$733$	47.7243	1.76274	0.881368	+	0.472431i	$0.156623\pi$
$734$	−2.37279	−0.0875814
$735$	−1.38026	−0.0509118
$736$	6.59643	0.243148
$737$	−31.9795	−1.17798
$738$	2.03725	0.0749921
$739$	−31.0167	−1.14097	−0.570485	−	0.821308i	$-0.693245\pi$
$739$	−31.0167	−1.14097	−0.570485	+	0.821308i	$0.693245\pi$
$740$	0.537878	0.0197728
$741$	2.05697	0.0755645
$742$	14.1637	0.519966
$743$	25.5923	0.938891	0.469446	−	0.882961i	$-0.344454\pi$
$743$	25.5923	0.938891	0.469446	+	0.882961i	$0.344454\pi$
$744$	0.252625	0.00926169
$745$	10.7988	0.395637
$746$	−14.2652	−0.522285
$747$	48.1500	1.76172
$748$	−4.36385	−0.159558
$749$	−9.10484	−0.332684
$750$	0.252625	0.00922457
$751$	−18.1625	−0.662759	−0.331379	−	0.943498i	$-0.607514\pi$
$751$	−18.1625	−0.662759	−0.331379	+	0.943498i	$0.607514\pi$
$752$	6.79817	0.247904
$753$	−3.23035	−0.117721
$754$	−1.85322	−0.0674902
$755$	1.77076	0.0644445
$756$	−1.85877	−0.0676026
$757$	49.7137	1.80687	0.903437	−	0.428721i	$-0.141036\pi$
$757$	49.7137	1.80687	0.903437	+	0.428721i	$0.141036\pi$
$758$	26.9056	0.977255
$759$	−6.81024	−0.247196
$760$	8.14236	0.295354
$761$	−42.8571	−1.55357	−0.776784	−	0.629767i	$-0.783150\pi$
$761$	−42.8571	−1.55357	−0.776784	+	0.629767i	$0.783150\pi$
$762$	4.49584	0.162867
$763$	23.8387	0.863017
$764$	3.25410	0.117729
$765$	−3.13527	−0.113356
$766$	32.3812	1.16998
$767$	4.92227	0.177733
$768$	−0.252625	−0.00911583
$769$	−4.05252	−0.146138	−0.0730689	−	0.997327i	$-0.523279\pi$
$769$	−4.05252	−0.146138	−0.0730689	+	0.997327i	$0.523279\pi$
$770$	5.06544	0.182546
$771$	1.74016	0.0626704
$772$	4.75236	0.171041
$773$	−42.4579	−1.52711	−0.763553	−	0.645745i	$-0.776547\pi$
$773$	−42.4579	−1.52711	−0.763553	+	0.645745i	$0.776547\pi$
$774$	36.8655	1.32510
$775$	−1.00000	−0.0359211
$776$	−4.14428	−0.148771
$777$	−0.168423	−0.00604214
$778$	7.42585	0.266230
$779$	5.64951	0.202415
$780$	0.252625	0.00904544
$781$	10.0306	0.358922
$782$	−7.04371	−0.251883
$783$	−2.77914	−0.0993183
$784$	−5.46368	−0.195132
$785$	−22.1053	−0.788974
$786$	1.85160	0.0660444
$787$	−42.3030	−1.50794	−0.753970	−	0.656908i	$-0.771864\pi$
$787$	−42.3030	−1.50794	−0.753970	+	0.656908i	$0.771864\pi$
$788$	−20.7562	−0.739410
$789$	−4.53717	−0.161528
$790$	−0.819624	−0.0291609
$791$	20.3980	0.725269
$792$	−11.9994	−0.426380
$793$	4.53622	0.161086
$794$	−0.532290	−0.0188903
$795$	−2.88678	−0.102383
$796$	−12.6687	−0.449028
$797$	30.6478	1.08560	0.542800	−	0.839862i	$-0.317364\pi$
$797$	30.6478	1.08560	0.542800	+	0.839862i	$0.317364\pi$
$798$	−2.54957	−0.0902539
$799$	−7.25913	−0.256809
$800$	1.00000	0.0353553
$801$	−28.3859	−1.00297
$802$	5.08171	0.179441
$803$	−58.2874	−2.05692
$804$	1.97684	0.0697178
$805$	8.17616	0.288172
$806$	−1.00000	−0.0352235
$807$	−0.940321	−0.0331009
$808$	−6.09882	−0.214556
$809$	31.8304	1.11910	0.559548	−	0.828798i	$-0.310975\pi$
$809$	31.8304	1.11910	0.559548	+	0.828798i	$0.310975\pi$
$810$	−8.42970	−0.296189
$811$	−28.4738	−0.999850	−0.499925	−	0.866069i	$-0.666639\pi$
$811$	−28.4738	−0.999850	−0.499925	+	0.866069i	$0.666639\pi$
$812$	2.29703	0.0806099
$813$	−0.814053	−0.0285501
$814$	−2.19817	−0.0770457
$815$	17.9197	0.627699
$816$	0.269755	0.00944332
$817$	102.232	3.57665
$818$	−11.9445	−0.417629
$819$	3.63935	0.127169
$820$	0.693843	0.0242300
$821$	−21.3139	−0.743860	−0.371930	−	0.928261i	$-0.621304\pi$
$821$	−21.3139	−0.743860	−0.371930	+	0.928261i	$0.621304\pi$
$822$	−4.29589	−0.149836
$823$	51.4546	1.79359	0.896797	−	0.442442i	$-0.145888\pi$
$823$	51.4546	1.79359	0.896797	+	0.442442i	$0.145888\pi$
$824$	4.89812	0.170634
$825$	−1.03241	−0.0359440
$826$	−6.10107	−0.212283
$827$	49.3955	1.71765	0.858825	−	0.512269i	$-0.171195\pi$
$827$	49.3955	1.71765	0.858825	+	0.512269i	$0.171195\pi$
$828$	−19.3683	−0.673095
$829$	−32.0823	−1.11426	−0.557132	−	0.830424i	$-0.688098\pi$
$829$	−32.0823	−1.11426	−0.557132	+	0.830424i	$0.688098\pi$
$830$	16.3989	0.569213
$831$	−6.29224	−0.218275
$832$	1.00000	0.0346688
$833$	5.83416	0.202142
$834$	−1.71866	−0.0595124
$835$	−12.0670	−0.417597
$836$	−33.2757	−1.15086
$837$	−1.49963	−0.0518348
$838$	29.6890	1.02559
$839$	−9.12410	−0.314999	−0.157500	−	0.987519i	$-0.550343\pi$
$839$	−9.12410	−0.314999	−0.157500	+	0.987519i	$0.550343\pi$
$840$	−0.313125	−0.0108038
$841$	−25.5656	−0.881572
$842$	−8.84383	−0.304778
$843$	−4.63626	−0.159681
$844$	5.59342	0.192534
$845$	−1.00000	−0.0344010
$846$	−19.9606	−0.686261
$847$	−7.06682	−0.242819
$848$	−11.4271	−0.392409
$849$	2.35705	0.0808937
$850$	−1.06781	−0.0366255
$851$	−3.54807	−0.121626
$852$	−0.620049	−0.0212425
$853$	−13.8725	−0.474986	−0.237493	−	0.971389i	$-0.576326\pi$
$853$	−13.8725	−0.474986	−0.237493	+	0.971389i	$0.576326\pi$
$854$	−5.62256	−0.192400
$855$	−23.9074	−0.817617
$856$	7.34568	0.251070
$857$	−9.35314	−0.319497	−0.159749	−	0.987158i	$-0.551068\pi$
$857$	−9.35314	−0.319497	−0.159749	+	0.987158i	$0.551068\pi$
$858$	−1.03241	−0.0352460
$859$	10.8291	0.369483	0.184742	−	0.982787i	$-0.440855\pi$
$859$	10.8291	0.369483	0.184742	+	0.982787i	$0.440855\pi$
$860$	12.5556	0.428143
$861$	−0.217259	−0.00740418
$862$	−27.1853	−0.925933
$863$	1.57292	0.0535428	0.0267714	−	0.999642i	$-0.491477\pi$
$863$	1.57292	0.0535428	0.0267714	+	0.999642i	$0.491477\pi$
$864$	1.49963	0.0510184
$865$	−21.4481	−0.729258
$866$	28.8950	0.981890
$867$	4.00658	0.136071
$868$	1.23948	0.0420708
$869$	3.34959	0.113627
$870$	−0.468169	−0.0158724
$871$	−7.82519	−0.265146
$872$	−19.2327	−0.651303
$873$	12.1683	0.411836
$874$	−53.7105	−1.81678
$875$	1.23948	0.0419022
$876$	3.60309	0.121737
$877$	18.5215	0.625427	0.312713	−	0.949847i	$-0.398762\pi$
$877$	18.5215	0.625427	0.312713	+	0.949847i	$0.398762\pi$
$878$	−27.7820	−0.937596
$879$	−5.44341	−0.183602
$880$	−4.08674	−0.137764
$881$	37.0775	1.24917	0.624587	−	0.780956i	$-0.285267\pi$
$881$	37.0775	1.24917	0.624587	+	0.780956i	$0.285267\pi$
$882$	16.0424	0.540174
$883$	−7.31224	−0.246076	−0.123038	−	0.992402i	$-0.539264\pi$
$883$	−7.31224	−0.246076	−0.123038	+	0.992402i	$0.539264\pi$
$884$	−1.06781	−0.0359142
$885$	1.24349	0.0417995
$886$	14.8814	0.499950
$887$	−45.9674	−1.54343	−0.771717	−	0.635967i	$-0.780602\pi$
$887$	−45.9674	−1.54343	−0.771717	+	0.635967i	$0.780602\pi$
$888$	0.135882	0.00455989
$889$	22.0584	0.739815
$890$	−9.66762	−0.324059
$891$	34.4500	1.15412
$892$	25.1249	0.841243
$893$	−55.3531	−1.85232
$894$	2.72805	0.0912396
$895$	18.8075	0.628667
$896$	−1.23948	−0.0414082
$897$	−1.66643	−0.0556403
$898$	6.47878	0.216200
$899$	1.85322	0.0618082
$900$	−2.93618	−0.0978727
$901$	12.2019	0.406506
$902$	−2.83555	−0.0944136
$903$	−3.93147	−0.130831
$904$	−16.4569	−0.547347
$905$	19.2383	0.639503
$906$	0.447338	0.0148618
$907$	−35.1358	−1.16667	−0.583333	−	0.812233i	$-0.698252\pi$
$907$	−35.1358	−1.16667	−0.583333	+	0.812233i	$0.698252\pi$
$908$	13.2454	0.439565
$909$	17.9072	0.593946
$910$	1.23948	0.0410885
$911$	−24.2580	−0.803703	−0.401851	−	0.915705i	$-0.631633\pi$
$911$	−24.2580	−0.803703	−0.401851	+	0.915705i	$0.631633\pi$
$912$	2.05697	0.0681129
$913$	−67.0179	−2.21797
$914$	4.98112	0.164761
$915$	1.14596	0.0378844
$916$	−6.93174	−0.229031
$917$	9.08471	0.300004
$918$	−1.60131	−0.0528513
$919$	−47.9168	−1.58063	−0.790315	−	0.612701i	$-0.790083\pi$
$919$	−47.9168	−1.58063	−0.790315	+	0.612701i	$0.790083\pi$
$920$	−6.59643	−0.217478
$921$	−3.90749	−0.128756
$922$	−18.0686	−0.595058
$923$	2.45442	0.0807883
$924$	1.27966	0.0420977
$925$	−0.537878	−0.0176853
$926$	−0.522460	−0.0171691
$927$	−14.3818	−0.472359
$928$	−1.85322	−0.0608348
$929$	5.33547	0.175051	0.0875256	−	0.996162i	$-0.472104\pi$
$929$	5.33547	0.175051	0.0875256	+	0.996162i	$0.472104\pi$
$930$	−0.252625	−0.00828391
$931$	44.4873	1.45801
$932$	−21.5947	−0.707357
$933$	5.17494	0.169420
$934$	8.97422	0.293645
$935$	4.36385	0.142713
$936$	−2.93618	−0.0959721
$937$	−32.1668	−1.05084	−0.525422	−	0.850842i	$-0.676092\pi$
$937$	−32.1668	−1.05084	−0.525422	+	0.850842i	$0.676092\pi$
$938$	9.69919	0.316690
$939$	−6.49874	−0.212078
$940$	−6.79817	−0.221732
$941$	29.3481	0.956721	0.478360	−	0.878164i	$-0.341231\pi$
$941$	29.3481	0.956721	0.478360	+	0.878164i	$0.341231\pi$
$942$	−5.58437	−0.181949
$943$	−4.57688	−0.149044
$944$	4.92227	0.160206
$945$	1.85877	0.0604656
$946$	−51.3115	−1.66828
$947$	14.7608	0.479663	0.239831	−	0.970815i	$-0.422908\pi$
$947$	14.7608	0.479663	0.239831	+	0.970815i	$0.422908\pi$
$948$	−0.207058	−0.00672492
$949$	−14.2626	−0.462983
$950$	−8.14236	−0.264173
$951$	0.103906	0.00336938
$952$	1.32353	0.0428958
$953$	39.9727	1.29484	0.647421	−	0.762132i	$-0.275847\pi$
$953$	39.9727	1.29484	0.647421	+	0.762132i	$0.275847\pi$
$954$	33.5521	1.08629
$955$	−3.25410	−0.105300
$956$	−20.6583	−0.668139
$957$	1.91329	0.0618477
$958$	11.3765	0.367557
$959$	−21.0774	−0.680625
$960$	0.252625	0.00815345
$961$	1.00000	0.0322581
$962$	−0.537878	−0.0173419
$963$	−21.5682	−0.695027
$964$	−21.7353	−0.700048
$965$	−4.75236	−0.152984
$966$	2.06551	0.0664566
$967$	32.8199	1.05542	0.527709	−	0.849425i	$-0.323051\pi$
$967$	32.8199	1.05542	0.527709	+	0.849425i	$0.323051\pi$
$968$	5.70143	0.183251
$969$	−2.19644	−0.0705599
$970$	4.14428	0.133065
$971$	−30.7539	−0.986940	−0.493470	−	0.869763i	$-0.664272\pi$
$971$	−30.7539	−0.986940	−0.493470	+	0.869763i	$0.664272\pi$
$972$	−6.62844	−0.212607
$973$	−8.43246	−0.270332
$974$	5.50411	0.176363
$975$	−0.252625	−0.00809049
$976$	4.53622	0.145201
$977$	40.3591	1.29120	0.645601	−	0.763675i	$-0.276607\pi$
$977$	40.3591	1.29120	0.645601	+	0.763675i	$0.276607\pi$
$978$	4.52696	0.144756
$979$	39.5090	1.26271
$980$	5.46368	0.174531
$981$	56.4708	1.80297
$982$	−39.8235	−1.27082
$983$	−33.6357	−1.07281	−0.536407	−	0.843960i	$-0.680219\pi$
$983$	−33.6357	−1.07281	−0.536407	+	0.843960i	$0.680219\pi$
$984$	0.175282	0.00558779
$985$	20.7562	0.661349
$986$	1.97888	0.0630203
$987$	2.12867	0.0677564
$988$	−8.14236	−0.259043
$989$	−82.8222	−2.63359
$990$	11.9994	0.381366
$991$	−31.0175	−0.985303	−0.492652	−	0.870227i	$-0.663972\pi$
$991$	−31.0175	−0.985303	−0.492652	+	0.870227i	$0.663972\pi$
$992$	−1.00000	−0.0317500
$993$	4.93975	0.156758
$994$	−3.04221	−0.0964932
$995$	12.6687	0.401623
$996$	4.14277	0.131269
$997$	23.5340	0.745330	0.372665	−	0.927966i	$-0.378444\pi$
$997$	23.5340	0.745330	0.372665	+	0.927966i	$0.378444\pi$
$998$	−12.4798	−0.395043
$999$	−0.806617	−0.0255202

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.252625 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.252625 q^{6} -1.23948 q^{7} +1.00000 q^{8} -2.93618 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.252625 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.252625 q^{6} -1.23948 q^{7} +1.00000 q^{8} -2.93618 q^{9} -1.00000 q^{10} +4.08674 q^{11} -0.252625 q^{12} +1.00000 q^{13} -1.23948 q^{14} +0.252625 q^{15} +1.00000 q^{16} -1.06781 q^{17} -2.93618 q^{18} -8.14236 q^{19} -1.00000 q^{20} +0.313125 q^{21} +4.08674 q^{22} +6.59643 q^{23} -0.252625 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.49963 q^{27} -1.23948 q^{28} -1.85322 q^{29} +0.252625 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.03241 q^{33} -1.06781 q^{34} +1.23948 q^{35} -2.93618 q^{36} -0.537878 q^{37} -8.14236 q^{38} -0.252625 q^{39} -1.00000 q^{40} -0.693843 q^{41} +0.313125 q^{42} -12.5556 q^{43} +4.08674 q^{44} +2.93618 q^{45} +6.59643 q^{46} +6.79817 q^{47} -0.252625 q^{48} -5.46368 q^{49} +1.00000 q^{50} +0.269755 q^{51} +1.00000 q^{52} -11.4271 q^{53} +1.49963 q^{54} -4.08674 q^{55} -1.23948 q^{56} +2.05697 q^{57} -1.85322 q^{58} +4.92227 q^{59} +0.252625 q^{60} +4.53622 q^{61} -1.00000 q^{62} +3.63935 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.03241 q^{66} -7.82519 q^{67} -1.06781 q^{68} -1.66643 q^{69} +1.23948 q^{70} +2.45442 q^{71} -2.93618 q^{72} -14.2626 q^{73} -0.537878 q^{74} -0.252625 q^{75} -8.14236 q^{76} -5.06544 q^{77} -0.252625 q^{78} +0.819624 q^{79} -1.00000 q^{80} +8.42970 q^{81} -0.693843 q^{82} -16.3989 q^{83} +0.313125 q^{84} +1.06781 q^{85} -12.5556 q^{86} +0.468169 q^{87} +4.08674 q^{88} +9.66762 q^{89} +2.93618 q^{90} -1.23948 q^{91} +6.59643 q^{92} +0.252625 q^{93} +6.79817 q^{94} +8.14236 q^{95} -0.252625 q^{96} -4.14428 q^{97} -5.46368 q^{98} -11.9994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \)	\( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

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Knowledge

Properties

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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	4030.2.a.f.1.4

Level	4030
Weight	2
Character	4030.1
Self dual	Yes
Analytic conductor	32.180
Analytic rank	1
Dimension	6
CM	No
Inner twists	1

Self dual:	Yes
Analytic conductor:	\(32.1797120146\)
Analytic rank:	\(1\)
Dimension:	\(6\)
Coefficient field:	6.6.4418197.1
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$