LMFDB - Embedded newform 1078.2.i.b.1011.1

Newspace parameters

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.162447943996702457856.1
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.1
Root			$1.14839 + 0.825348i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.b.901.1

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-2.68085 - 1.54779i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.559525 - 0.323042i) q^{5} +3.09557 q^{6} +1.00000i q^{8} +(3.29129 + 5.70068i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.68085 - 1.54779i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.559525 - 0.323042i) q^{5} +3.09557 q^{6} +1.00000i q^{8} +(3.29129 + 5.70068i) q^{9} +(-0.323042 + 0.559525i) q^{10} +(-2.94694 + 1.52168i) q^{11} +(-2.68085 + 1.54779i) q^{12} +3.09557 q^{13} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87083 - 3.24037i) q^{17} +(-5.70068 - 3.29129i) q^{18} +(-2.77253 - 4.80217i) q^{19} -0.646084i q^{20} +(1.79129 - 2.79129i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(1.54779 - 2.68085i) q^{24} +(-2.29129 + 3.96863i) q^{25} +(-2.68085 + 1.54779i) q^{26} -11.0901i q^{27} -7.58258i q^{29} +(1.73205 - 1.00000i) q^{30} +(-1.00227 - 0.578661i) q^{31} +(0.866025 + 0.500000i) q^{32} +(10.2555 + 0.481847i) q^{33} +3.74166i q^{34} +6.58258 q^{36} +(2.79129 + 4.83465i) q^{37} +(4.80217 + 2.77253i) q^{38} +(-8.29875 - 4.79129i) q^{39} +(0.323042 + 0.559525i) q^{40} -5.03383 q^{41} +11.1652i q^{43} +(-0.155657 + 3.31297i) q^{44} +(3.68312 + 2.12645i) q^{45} +(3.46410 + 2.00000i) q^{46} +(-4.35942 + 2.51691i) q^{47} +3.09557i q^{48} -4.58258i q^{50} +(-10.0308 + 5.79129i) q^{51} +(1.54779 - 2.68085i) q^{52} +(1.20871 - 2.09355i) q^{53} +(5.54506 + 9.60433i) q^{54} +(-1.15732 + 1.80341i) q^{55} +17.1652i q^{57} +(3.79129 + 6.56670i) q^{58} +(2.68085 + 1.54779i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-4.64336 - 8.04254i) q^{61} +1.15732 q^{62} -1.00000 q^{64} +(1.73205 - 1.00000i) q^{65} +(-9.12248 + 4.71048i) q^{66} +(-0.791288 + 1.37055i) q^{67} +(-1.87083 - 3.24037i) q^{68} +12.3823i q^{69} +2.00000 q^{71} +(-5.70068 + 3.29129i) q^{72} +(-3.16300 + 5.47847i) q^{73} +(-4.83465 - 2.79129i) q^{74} +(12.2852 - 7.09285i) q^{75} -5.54506 q^{76} +9.58258 q^{78} +(-3.46410 + 2.00000i) q^{79} +(-0.559525 - 0.323042i) q^{80} +(-7.29129 + 12.6289i) q^{81} +(4.35942 - 2.51691i) q^{82} -9.15188 q^{83} -2.41742i q^{85} +(-5.58258 - 9.66930i) q^{86} +(-11.7362 + 20.3277i) q^{87} +(-1.52168 - 2.94694i) q^{88} +(-8.48528 + 4.89898i) q^{89} -4.25290 q^{90} -4.00000 q^{92} +(1.79129 + 3.10260i) q^{93} +(2.51691 - 4.35942i) q^{94} +(-3.10260 - 1.79129i) q^{95} +(-1.54779 - 2.68085i) q^{96} +15.9891i q^{97} +(-18.3739 - 11.7913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 16 * q^9	$ 16 q + 8 q^{4} + 16 q^{9} - 4 q^{11} - 32 q^{15} - 8 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 8 q^{37} + 4 q^{44} + 56 q^{53} + 24 q^{58} - 16 q^{60} - 16 q^{64} + 24 q^{67} + 32 q^{71} + 80 q^{78} - 80 q^{81} - 16 q^{86} - 4 q^{88} - 64 q^{92} - 8 q^{93} - 184 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 16 * q^9 - 4 * q^11 - 32 * q^15 - 8 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 8 * q^37 + 4 * q^44 + 56 * q^53 + 24 * q^58 - 16 * q^60 - 16 * q^64 + 24 * q^67 + 32 * q^71 + 80 * q^78 - 80 * q^81 - 16 * q^86 - 4 * q^88 - 64 * q^92 - 8 * q^93 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−2.68085	−	1.54779i	−1.54779	−	0.893615i	−0.998310	−	0.0581058i	$-0.981494\pi$
$3$	−2.68085	−	1.54779i	−1.54779	−	0.893615i	−0.549476	−	0.835509i	$-0.685173\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.559525	−	0.323042i	0.250227	−	0.144469i	−0.369641	−	0.929175i	$-0.620519\pi$
$5$	0.559525	−	0.323042i	0.250227	−	0.144469i	0.619868	+	0.784706i	$0.287186\pi$
$6$	3.09557			1.26376
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	3.29129	+	5.70068i	1.09710	+	1.90023i
$10$	−0.323042	+	0.559525i	−0.102155	+	0.176937i
$11$	−2.94694	+	1.52168i	−0.888537	+	0.458804i
$11$	−2.94694	+	1.52168i	−0.888537	+	0.458804i
$12$	−2.68085	+	1.54779i	−0.773893	+	0.446808i
$13$	3.09557			0.858558			0.429279	−	0.903172i	$-0.358768\pi$
$13$	3.09557			0.858558			0.429279	+	0.903172i	$0.358768\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.87083	−	3.24037i	0.453743	−	0.785905i	−0.544872	−	0.838519i	$-0.683422\pi$
$17$	1.87083	−	3.24037i	0.453743	−	0.785905i	0.998615	+	0.0526138i	$0.0167552\pi$
$18$	−5.70068	−	3.29129i	−1.34366	−	0.775764i
$19$	−2.77253	−	4.80217i	−0.636062	−	1.10169i	−0.986289	−	0.165027i	$-0.947229\pi$
$19$	−2.77253	−	4.80217i	−0.636062	−	1.10169i	0.350227	−	0.936665i	$-0.386105\pi$
$20$		−	0.646084i		−	0.144469i
$21$		0			0
$22$	1.79129	−	2.79129i	0.381904	−	0.595105i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	1.54779	−	2.68085i	0.315941	−	0.547225i
$25$	−2.29129	+	3.96863i	−0.458258	+	0.793725i
$26$	−2.68085	+	1.54779i	−0.525757	+	0.303546i
$27$		−	11.0901i		−	2.13430i
$28$		0			0
$29$		−	7.58258i		−	1.40805i	−0.710176	−	0.704024i	$-0.751385\pi$
$29$		−	7.58258i		−	1.40805i	0.710176	−	0.704024i	$-0.248615\pi$
$30$	1.73205	−	1.00000i	0.316228	−	0.182574i
$31$	−1.00227	−	0.578661i	−0.180013	−	0.103931i	0.407286	−	0.913301i	$-0.366475\pi$
$31$	−1.00227	−	0.578661i	−0.180013	−	0.103931i	−0.587299	+	0.809370i	$0.699809\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	10.2555	+	0.481847i	1.78526	+	0.0838788i
$34$			3.74166i			0.641689i
$35$		0			0
$36$	6.58258			1.09710
$37$	2.79129	+	4.83465i	0.458885	+	0.794812i	0.998902	−	0.0468419i	$-0.0149157\pi$
$37$	2.79129	+	4.83465i	0.458885	+	0.794812i	−0.540017	+	0.841654i	$0.681582\pi$
$38$	4.80217	+	2.77253i	0.779014	+	0.449764i
$39$	−8.29875	−	4.79129i	−1.32886	−	0.767220i
$40$	0.323042	+	0.559525i	0.0510774	+	0.0884687i
$41$	−5.03383			−0.786151			−0.393076	−	0.919506i	$-0.628589\pi$
$41$	−5.03383			−0.786151			−0.393076	+	0.919506i	$0.628589\pi$
$42$		0			0
$43$			11.1652i			1.70267i	0.524623	+	0.851335i	$0.324206\pi$
$43$			11.1652i			1.70267i	−0.524623	+	0.851335i	$0.675794\pi$
$44$	−0.155657	+	3.31297i	−0.0234662	+	0.499449i
$45$	3.68312	+	2.12645i	0.549046	+	0.316992i
$46$	3.46410	+	2.00000i	0.510754	+	0.294884i
$47$	−4.35942	+	2.51691i	−0.635887	+	0.367129i	−0.783028	−	0.621986i	$-0.786326\pi$
$47$	−4.35942	+	2.51691i	−0.635887	+	0.367129i	0.147142	+	0.989115i	$0.452993\pi$
$48$			3.09557i			0.446808i
$49$		0			0
$50$		−	4.58258i		−	0.648074i
$51$	−10.0308	+	5.79129i	−1.40459	+	0.810943i
$52$	1.54779	−	2.68085i	0.214639	−	0.371766i
$53$	1.20871	−	2.09355i	0.166029	−	0.287571i	−0.770991	−	0.636846i	$-0.780239\pi$
$53$	1.20871	−	2.09355i	0.166029	−	0.287571i	0.937020	+	0.349275i	$0.113572\pi$
$54$	5.54506	+	9.60433i	0.754588	+	1.30698i
$55$	−1.15732	+	1.80341i	−0.156053	+	0.243171i
$56$		0			0
$57$			17.1652i			2.27358i
$58$	3.79129	+	6.56670i	0.497820	+	0.862250i
$59$	2.68085	+	1.54779i	0.349016	+	0.201505i	0.664252	−	0.747509i	$-0.268750\pi$
$59$	2.68085	+	1.54779i	0.349016	+	0.201505i	−0.315236	+	0.949013i	$0.602084\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	−4.64336	−	8.04254i	−0.594521	−	1.02974i	−0.993614	−	0.112831i	$-0.964008\pi$
$61$	−4.64336	−	8.04254i	−0.594521	−	1.02974i	0.399093	−	0.916911i	$-0.369325\pi$
$62$	1.15732			0.146980
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.73205	−	1.00000i	0.214834	−	0.124035i
$66$	−9.12248	+	4.71048i	−1.12290	+	0.579820i
$67$	−0.791288	+	1.37055i	−0.0966712	+	0.167439i	−0.910305	−	0.413938i	$-0.864153\pi$
$67$	−0.791288	+	1.37055i	−0.0966712	+	0.167439i	0.813634	+	0.581378i	$0.197486\pi$
$68$	−1.87083	−	3.24037i	−0.226871	−	0.392953i
$69$			12.3823i			1.49065i
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−5.70068	+	3.29129i	−0.671831	+	0.387882i
$73$	−3.16300	+	5.47847i	−0.370201	+	0.641206i	−0.989596	−	0.143873i	$-0.954044\pi$
$73$	−3.16300	+	5.47847i	−0.370201	+	0.641206i	0.619395	+	0.785079i	$0.287378\pi$
$74$	−4.83465	−	2.79129i	−0.562017	−	0.324481i
$75$	12.2852	−	7.09285i	1.41857	−	0.819012i
$76$	−5.54506			−0.636062
$77$		0			0
$78$	9.58258			1.08501
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$	−0.559525	−	0.323042i	−0.0625568	−	0.0361172i
$81$	−7.29129	+	12.6289i	−0.810143	+	1.40321i
$82$	4.35942	−	2.51691i	0.481417	−	0.277946i
$83$	−9.15188			−1.00455			−0.502274	−	0.864708i	$-0.667503\pi$
$83$	−9.15188			−1.00455			−0.502274	+	0.864708i	$0.667503\pi$
$84$		0			0
$85$		−	2.41742i		−	0.262206i
$86$	−5.58258	−	9.66930i	−0.601985	−	1.04267i
$87$	−11.7362	+	20.3277i	−1.25825	+	2.17936i
$88$	−1.52168	−	2.94694i	−0.162212	−	0.314145i
$89$	−8.48528	+	4.89898i	−0.899438	+	0.519291i	−0.877018	−	0.480458i	$-0.840471\pi$
$89$	−8.48528	+	4.89898i	−0.899438	+	0.519291i	−0.0224202	+	0.999749i	$0.507137\pi$
$90$	−4.25290			−0.448295
$91$		0			0
$92$	−4.00000			−0.417029
$93$	1.79129	+	3.10260i	0.185748	+	0.321725i
$94$	2.51691	−	4.35942i	0.259600	−	0.449640i
$95$	−3.10260	−	1.79129i	−0.318320	−	0.183782i
$96$	−1.54779	−	2.68085i	−0.157970	−	0.273613i
$97$			15.9891i			1.62345i	0.584041	+	0.811724i	$0.301471\pi$
$97$			15.9891i			1.62345i	−0.584041	+	0.811724i	$0.698529\pi$
$98$		0			0
$99$	−18.3739	−	11.7913i	−1.84664	−	1.18507i
$100$	2.29129	+	3.96863i	0.229129	+	0.396863i
$101$	−0.255619	+	0.442745i	−0.0254351	+	0.0440548i	−0.878463	−	0.477811i	$-0.841430\pi$
$101$	−0.255619	+	0.442745i	−0.0254351	+	0.0440548i	0.853028	+	0.521866i	$0.174764\pi$
$102$	5.79129	−	10.0308i	0.573423	−	0.993198i
$103$	−11.7257	+	6.76981i	−1.15536	+	0.667049i	−0.950188	−	0.311676i	$-0.899110\pi$
$103$	−11.7257	+	6.76981i	−1.15536	+	0.667049i	−0.205174	+	0.978725i	$0.565776\pi$
$104$			3.09557i			0.303546i
$105$		0			0
$106$			2.41742i			0.234801i
$107$	7.28970	−	4.20871i	0.704722	−	0.406872i	−0.104382	−	0.994537i	$-0.533286\pi$
$107$	7.28970	−	4.20871i	0.704722	−	0.406872i	0.809104	+	0.587666i	$0.199953\pi$
$108$	−9.60433	−	5.54506i	−0.924177	−	0.533574i
$109$	1.00905	+	0.582576i	0.0966495	+	0.0558006i	0.547546	−	0.836776i	$-0.315562\pi$
$109$	1.00905	+	0.582576i	0.0966495	+	0.0558006i	−0.450896	+	0.892576i	$0.648896\pi$
$110$	0.100567	−	2.14046i	0.00958872	−	0.204085i
$111$		−	17.2813i		−	1.64027i
$112$		0			0
$113$	−16.7477			−1.57549			−0.787747	−	0.615999i	$-0.788752\pi$
$113$	−16.7477			−1.57549			−0.787747	+	0.615999i	$0.788752\pi$
$114$	−8.58258	−	14.8655i	−0.803832	−	1.39228i
$115$	−2.23810	−	1.29217i	−0.208704	−	0.120495i
$116$	−6.56670	−	3.79129i	−0.609703	−	0.352012i
$117$	10.1884	+	17.6469i	0.941920	+	1.63145i
$118$	−3.09557			−0.284971
$119$		0			0
$120$		−	2.00000i		−	0.182574i
$121$	6.36897	−	8.96863i	0.578997	−	0.815330i
$122$	8.04254	+	4.64336i	0.728137	+	0.420390i
$123$	13.4949	+	7.79129i	1.21679	+	0.702517i
$124$	−1.00227	+	0.578661i	−0.0900065	+	0.0519653i
$125$			6.19115i			0.553753i
$126$		0			0
$127$			5.58258i			0.495373i	0.968840	+	0.247687i	$0.0796704\pi$
$127$			5.58258i			0.495373i	−0.968840	+	0.247687i	$0.920330\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	17.2813	−	29.9320i	1.52153	−	2.63537i
$130$	−1.00000	+	1.73205i	−0.0877058	+	0.151911i
$131$	4.71078	+	8.15932i	0.411583	+	0.712883i	0.995063	−	0.0992448i	$-0.0316427\pi$
$131$	4.71078	+	8.15932i	0.411583	+	0.712883i	−0.583480	+	0.812127i	$0.698309\pi$
$132$	5.54506	−	8.64064i	0.482636	−	0.752071i
$133$		0			0
$134$		−	1.58258i		−	0.136714i
$135$	−3.58258	−	6.20520i	−0.308339	−	0.534059i
$136$	3.24037	+	1.87083i	0.277859	+	0.160422i
$137$	−7.58258	+	13.1334i	−0.647823	+	1.12206i	0.335819	+	0.941927i	$0.390987\pi$
$137$	−7.58258	+	13.1334i	−0.647823	+	1.12206i	−0.983642	+	0.180136i	$0.942346\pi$
$138$	−6.19115	−	10.7234i	−0.527025	−	0.912835i
$139$	−3.23042			−0.274001			−0.137000	−	0.990571i	$-0.543746\pi$
$139$	−3.23042			−0.274001			−0.137000	+	0.990571i	$0.543746\pi$
$140$		0			0
$141$	15.5826			1.31229
$142$	−1.73205	+	1.00000i	−0.145350	+	0.0839181i
$143$	−9.12248	+	4.71048i	−0.762860	+	0.393910i
$144$	3.29129	−	5.70068i	0.274274	−	0.475056i
$145$	−2.44949	−	4.24264i	−0.203419	−	0.352332i
$146$		−	6.32599i		−	0.523543i
$147$		0			0
$148$	5.58258			0.458885
$149$	−12.1244	+	7.00000i	−0.993266	+	0.573462i	−0.906249	−	0.422744i	$-0.861067\pi$
$149$	−12.1244	+	7.00000i	−0.993266	+	0.573462i	−0.0870170	+	0.996207i	$0.527733\pi$
$150$	−7.09285	+	12.2852i	−0.579129	+	1.00308i
$151$	3.10260	+	1.79129i	0.252486	+	0.145773i	0.620902	−	0.783888i	$-0.286766\pi$
$151$	3.10260	+	1.79129i	0.252486	+	0.145773i	−0.368416	+	0.929661i	$0.620100\pi$
$152$	4.80217	−	2.77253i	0.389507	−	0.224882i
$153$	24.6297			1.99120
$154$		0			0
$155$	−0.747727			−0.0600589
$156$	−8.29875	+	4.79129i	−0.664432	+	0.383610i
$157$	17.7636	+	10.2558i	1.41769	+	0.818506i	0.996096	−	0.0882774i	$-0.0281362\pi$
$157$	17.7636	+	10.2558i	1.41769	+	0.818506i	0.421597	+	0.906783i	$0.361470\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−6.48074	+	3.74166i	−0.513956	+	0.296733i
$160$	0.646084			0.0510774
$161$		0			0
$162$		−	14.5826i		−	1.14572i
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−2.51691	+	4.35942i	−0.196538	+	0.340414i
$165$	5.89389	−	3.04336i	0.458839	−	0.236926i
$166$	7.92576	−	4.57594i	0.615158	−	0.355162i
$167$	6.19115			0.479085			0.239543	−	0.970886i	$-0.423002\pi$
$167$	6.19115			0.479085			0.239543	+	0.970886i	$0.423002\pi$
$168$		0			0
$169$	−3.41742			−0.262879
$170$	1.20871	+	2.09355i	0.0927040	+	0.160568i
$171$	18.2504	−	31.6106i	1.39564	−	2.41732i
$172$	9.66930	+	5.58258i	0.737278	+	0.425667i
$173$	−11.4806	−	19.8850i	−0.872853	−	1.51183i	−0.859032	−	0.511922i	$-0.828934\pi$
$173$	−11.4806	−	19.8850i	−0.872853	−	1.51183i	−0.0138210	−	0.999904i	$-0.504400\pi$
$174$		−	23.4724i		−	1.77944i
$175$		0			0
$176$	2.79129	+	1.79129i	0.210401	+	0.135023i
$177$	−4.79129	−	8.29875i	−0.360135	−	0.623773i
$178$	4.89898	−	8.48528i	0.367194	−	0.635999i
$179$	3.58258	−	6.20520i	0.267774	−	0.463799i	−0.700512	−	0.713640i	$-0.747045\pi$
$179$	3.58258	−	6.20520i	0.267774	−	0.463799i	0.968287	+	0.249842i	$0.0803785\pi$
$180$	3.68312	−	2.12645i	0.274523	−	0.158496i
$181$		−	16.6352i		−	1.23648i	−0.785988	−	0.618242i	$-0.787845\pi$
$181$		−	16.6352i		−	1.23648i	0.785988	−	0.618242i	$-0.212155\pi$
$182$		0			0
$183$			28.7477i			2.12509i
$184$	3.46410	−	2.00000i	0.255377	−	0.147442i
$185$	3.12359	+	1.80341i	0.229651	+	0.132589i
$186$	−3.10260	−	1.79129i	−0.227494	−	0.131344i
$187$	−0.582415	+	12.3960i	−0.0425904	+	0.906485i
$188$			5.03383i			0.367129i
$189$		0			0
$190$	3.58258			0.259907
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$	2.68085	+	1.54779i	0.193473	+	0.111702i
$193$	17.6066	+	10.1652i	1.26735	+	0.731704i	0.974485	−	0.224451i	$-0.0720589\pi$
$193$	17.6066	+	10.1652i	1.26735	+	0.731704i	0.292862	+	0.956155i	$0.405392\pi$
$194$	−7.99455	−	13.8470i	−0.573975	−	0.994155i
$195$	−6.19115			−0.443357
$196$		0			0
$197$		−	18.7477i		−	1.33572i	−0.744287	−	0.667860i	$-0.767210\pi$
$197$		−	18.7477i		−	1.33572i	0.744287	−	0.667860i	$-0.232790\pi$
$198$	21.8079	+	1.02462i	1.54982	+	0.0728168i
$199$	−21.3300	−	12.3149i	−1.51204	−	0.872978i	−0.999901	−	0.0140770i	$-0.995519\pi$
$199$	−21.3300	−	12.3149i	−1.51204	−	0.872978i	−0.512141	−	0.858901i	$-0.671148\pi$
$200$	−3.96863	−	2.29129i	−0.280624	−	0.162019i
$201$	4.24264	−	2.44949i	0.299253	−	0.172774i
$202$		−	0.511238i		−	0.0359706i
$203$		0			0
$204$			11.5826i			0.810943i
$205$	−2.81655	+	1.62614i	−0.196716	+	0.113574i
$206$	6.76981	−	11.7257i	0.471675	−	0.816965i
$207$	13.1652	−	22.8027i	0.915041	−	1.58490i
$208$	−1.54779	−	2.68085i	−0.107320	−	0.185883i
$209$	15.4779	+	9.93280i	1.07063	+	0.687066i
$210$		0			0
$211$		−	10.7477i		−	0.739904i	−0.929051	−	0.369952i	$-0.879374\pi$
$211$		−	10.7477i		−	0.739904i	0.929051	−	0.369952i	$-0.120626\pi$
$212$	−1.20871	−	2.09355i	−0.0830147	−	0.143786i
$213$	−5.36169	−	3.09557i	−0.367377	−	0.212105i
$214$	−4.20871	+	7.28970i	−0.287702	+	0.498314i
$215$	3.60681	+	6.24718i	0.245983	+	0.426054i
$216$	11.0901			0.754588
$217$		0			0
$218$	−1.16515			−0.0789140
$219$	16.9590	−	9.79129i	1.14598	−	0.661634i
$220$	0.983134	+	1.90397i	0.0662829	+	0.128366i
$221$	5.79129	−	10.0308i	0.389564	−	0.674745i
$222$	8.64064	+	14.9660i	0.579922	+	1.00445i
$223$			6.32599i			0.423620i	0.977311	+	0.211810i	$0.0679358\pi$
$223$			6.32599i			0.423620i	−0.977311	+	0.211810i	$0.932064\pi$
$224$		0			0
$225$	−30.1652			−2.01101
$226$	14.5040	−	8.37386i	0.964789	−	0.557021i
$227$	−5.86811	+	10.1639i	−0.389480	+	0.674599i	−0.992380	−	0.123218i	$-0.960679\pi$
$227$	−5.86811	+	10.1639i	−0.389480	+	0.674599i	0.602900	+	0.797817i	$0.294012\pi$
$228$	14.8655	+	8.58258i	0.984489	+	0.568395i
$229$	−11.2829	+	6.51419i	−0.745595	+	0.430470i	−0.824100	−	0.566444i	$-0.808319\pi$
$229$	−11.2829	+	6.51419i	−0.745595	+	0.430470i	0.0785048	+	0.996914i	$0.474985\pi$
$230$	2.58434			0.170406
$231$		0			0
$232$	7.58258			0.497820
$233$	−7.65120	+	4.41742i	−0.501247	+	0.289395i	−0.729228	−	0.684270i	$-0.760121\pi$
$233$	−7.65120	+	4.41742i	−0.501247	+	0.289395i	0.227981	+	0.973665i	$0.426787\pi$
$234$	−17.6469	−	10.1884i	−1.15361	−	0.666038i
$235$	−1.62614	+	2.81655i	−0.106077	+	0.183732i
$236$	2.68085	−	1.54779i	0.174508	−	0.100752i
$237$	12.3823			0.804316
$238$		0			0
$239$		−	17.5826i		−	1.13732i	−0.822572	−	0.568661i	$-0.807462\pi$
$239$		−	17.5826i		−	1.13732i	0.822572	−	0.568661i	$-0.192538\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	−12.9610	+	22.4490i	−0.834889	+	1.44607i	0.0592326	+	0.998244i	$0.481135\pi$
$241$	−12.9610	+	22.4490i	−0.834889	+	1.44607i	−0.894121	+	0.447825i	$0.852199\pi$
$242$	−1.03137	+	10.9515i	−0.0662992	+	0.703992i
$243$	10.2806	−	5.93553i	0.659503	−	0.380764i
$244$	−9.28672			−0.594521
$245$		0			0
$246$	−15.5826			−0.993509
$247$	−8.58258	−	14.8655i	−0.546096	−	0.945866i
$248$	0.578661	−	1.00227i	0.0367450	−	0.0636442i
$249$	24.5348	+	14.1652i	1.55483	+	0.897680i
$250$	−3.09557	−	5.36169i	−0.195781	−	0.339103i
$251$			2.07310i			0.130853i	0.997857	+	0.0654264i	$0.0208407\pi$
$251$			2.07310i			0.130853i	−0.997857	+	0.0654264i	$0.979159\pi$
$252$		0			0
$253$	11.1652	+	7.16515i	0.701947	+	0.450469i
$254$	−2.79129	−	4.83465i	−0.175141	−	0.303353i
$255$	−3.74166	+	6.48074i	−0.234312	+	0.405840i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.24264	−	2.44949i	0.264649	−	0.152795i	−0.361805	−	0.932254i	$-0.617839\pi$
$257$	4.24264	−	2.44949i	0.264649	−	0.152795i	0.626453	+	0.779459i	$0.284506\pi$
$258$			34.5625i			2.15177i
$259$		0			0
$260$		−	2.00000i		−	0.124035i
$261$	43.2258	−	24.9564i	2.67561	−	1.54476i
$262$	−8.15932	−	4.71078i	−0.504084	−	0.291033i
$263$	−24.5348	−	14.1652i	−1.51288	−	0.873461i	−0.999886	−	0.0150671i	$-0.995204\pi$
$263$	−24.5348	−	14.1652i	−1.51288	−	0.873461i	−0.512992	−	0.858394i	$-0.671463\pi$
$264$	−0.481847	+	10.2555i	−0.0296556	+	0.631185i
$265$		−	1.56186i		−	0.0959442i
$266$		0			0
$267$	30.3303			1.85618
$268$	0.791288	+	1.37055i	0.0483356	+	0.0837197i
$269$	−17.5301	−	10.1210i	−1.06883	−	0.617088i	−0.140967	−	0.990014i	$-0.545021\pi$
$269$	−17.5301	−	10.1210i	−1.06883	−	0.617088i	−0.927861	+	0.372926i	$0.878355\pi$
$270$	6.20520	+	3.58258i	0.377637	+	0.218029i
$271$	−2.44949	−	4.24264i	−0.148796	−	0.257722i	0.781987	−	0.623295i	$-0.214206\pi$
$271$	−2.44949	−	4.24264i	−0.148796	−	0.257722i	−0.930783	+	0.365573i	$0.880873\pi$
$272$	−3.74166			−0.226871
$273$		0			0
$274$		−	15.1652i		−	0.916160i
$275$	0.713309	−	15.1819i	0.0430142	−	0.915505i
$276$	10.7234	+	6.19115i	0.645472	+	0.372663i
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$	2.79763	−	1.61521i	0.167790	−	0.0968738i
$279$		−	7.61816i		−	0.456087i
$280$		0			0
$281$		−	7.16515i		−	0.427437i	−0.976895	−	0.213719i	$-0.931442\pi$
$281$		−	7.16515i		−	0.427437i	0.976895	−	0.213719i	$-0.0685575\pi$
$282$	−13.4949	+	7.79129i	−0.803610	+	0.463964i
$283$	7.80636	−	13.5210i	0.464040	−	0.803740i	−0.535118	−	0.844777i	$-0.679733\pi$
$283$	7.80636	−	13.5210i	0.464040	−	0.803740i	0.999158	+	0.0410370i	$0.0130661\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	5.54506	+	9.60433i	0.328461	+	0.568911i
$286$	5.54506	−	8.64064i	0.327886	−	0.510932i
$287$		0			0
$288$			6.58258i			0.387882i
$289$	1.50000	+	2.59808i	0.0882353	+	0.152828i
$290$	4.24264	+	2.44949i	0.249136	+	0.143839i
$291$	24.7477	−	42.8643i	1.45074	−	2.51275i
$292$	3.16300	+	5.47847i	0.185100	+	0.320603i
$293$	−21.3993			−1.25016			−0.625081	−	0.780560i	$-0.714934\pi$
$293$	−21.3993			−1.25016			−0.625081	+	0.780560i	$0.714934\pi$
$294$		0			0
$295$	2.00000			0.116445
$296$	−4.83465	+	2.79129i	−0.281008	+	0.162240i
$297$	16.8756	+	32.6820i	0.979224	+	1.89640i
$298$	7.00000	−	12.1244i	0.405499	−	0.702345i
$299$	−6.19115	−	10.7234i	−0.358043	−	0.620149i
$300$		−	14.1857i		−	0.819012i
$301$		0			0
$302$	−3.58258			−0.206154
$303$	1.37055	−	0.791288i	0.0787361	−	0.0454583i
$304$	−2.77253	+	4.80217i	−0.159016	+	0.275423i
$305$	−5.19615	−	3.00000i	−0.297531	−	0.171780i
$306$	−21.3300	+	12.3149i	−1.21935	+	0.703994i
$307$	−8.12940			−0.463969			−0.231985	−	0.972719i	$-0.574522\pi$
$307$	−8.12940			−0.463969			−0.231985	+	0.972719i	$0.574522\pi$
$308$		0			0
$309$	41.9129			2.38434
$310$	0.647551	−	0.373864i	0.0367784	−	0.0212340i
$311$	−8.60206	−	4.96640i	−0.487778	−	0.281619i	0.235874	−	0.971784i	$-0.424205\pi$
$311$	−8.60206	−	4.96640i	−0.487778	−	0.281619i	−0.723652	+	0.690165i	$0.757538\pi$
$312$	4.79129	−	8.29875i	0.271253	−	0.469824i
$313$	0.885491	−	0.511238i	0.0500509	−	0.0288969i	−0.474766	−	0.880112i	$-0.657467\pi$
$313$	0.885491	−	0.511238i	0.0500509	−	0.0288969i	0.524817	+	0.851215i	$0.324134\pi$
$314$	−20.5117			−1.15754
$315$		0			0
$316$			4.00000i			0.225018i
$317$	4.58258	+	7.93725i	0.257383	+	0.445801i	0.965540	−	0.260254i	$-0.0838064\pi$
$317$	4.58258	+	7.93725i	0.257383	+	0.445801i	−0.708157	+	0.706055i	$0.750473\pi$
$318$	3.74166	−	6.48074i	0.209822	−	0.363422i
$319$	11.5383	+	22.3454i	0.646019	+	1.25110i
$320$	−0.559525	+	0.323042i	−0.0312784	+	0.0180586i
$321$	−26.0568			−1.45435
$322$		0			0
$323$	−20.7477			−1.15443
$324$	7.29129	+	12.6289i	0.405072	+	0.701605i
$325$	−7.09285	+	12.2852i	−0.393441	+	0.681459i
$326$	3.46410	+	2.00000i	0.191859	+	0.110770i
$327$	−1.80341	−	3.12359i	−0.0997286	−	0.172735i
$328$		−	5.03383i		−	0.277946i
$329$		0			0
$330$	−3.58258	+	5.58258i	−0.197214	+	0.307311i
$331$	7.20871	+	12.4859i	0.396227	+	0.686285i	0.993257	−	0.115934i	$-0.0369861\pi$
$331$	7.20871	+	12.4859i	0.396227	+	0.686285i	−0.597030	+	0.802219i	$0.703653\pi$
$332$	−4.57594	+	7.92576i	−0.251137	+	0.434982i
$333$	−18.3739	+	31.8245i	−1.00688	+	1.74397i
$334$	−5.36169	+	3.09557i	−0.293379	+	0.169382i
$335$			1.02248i			0.0558639i
$336$		0			0
$337$			29.1652i			1.58873i	0.607443	+	0.794364i	$0.292195\pi$
$337$			29.1652i			1.58873i	−0.607443	+	0.794364i	$0.707805\pi$
$338$	2.95958	−	1.70871i	0.160980	−	0.0929417i
$339$	44.8981	+	25.9219i	2.43853	+	1.40788i
$340$	−2.09355	−	1.20871i	−0.113539	−	0.0655516i
$341$	3.83417	+	0.180145i	0.207632	+	0.00975541i
$342$			36.5008i			1.97374i
$343$		0			0
$344$	−11.1652			−0.601985
$345$	4.00000	+	6.92820i	0.215353	+	0.373002i
$346$	19.8850	+	11.4806i	1.06902	+	0.617200i
$347$	0.723000	+	0.417424i	0.0388127	+	0.0224085i	0.519281	−	0.854604i	$-0.326200\pi$
$347$	0.723000	+	0.417424i	0.0388127	+	0.0224085i	−0.480468	+	0.877012i	$0.659533\pi$
$348$	11.7362	+	20.3277i	0.629127	+	1.08968i
$349$	2.07310			0.110970			0.0554852	−	0.998460i	$-0.482329\pi$
$349$	2.07310			0.110970			0.0554852	+	0.998460i	$0.482329\pi$
$350$		0			0
$351$		−	34.3303i		−	1.83242i
$352$	−3.31297	−	0.155657i	−0.176582	−	0.00829654i
$353$	−6.48074	−	3.74166i	−0.344935	−	0.199148i	0.317517	−	0.948253i	$-0.397151\pi$
$353$	−6.48074	−	3.74166i	−0.344935	−	0.199148i	−0.662452	+	0.749104i	$0.730484\pi$
$354$	8.29875	+	4.79129i	0.441074	+	0.254654i
$355$	1.11905	−	0.646084i	0.0593930	−	0.0342906i
$356$			9.79796i			0.519291i
$357$		0			0
$358$			7.16515i			0.378690i
$359$	−0.361500	+	0.208712i	−0.0190792	+	0.0110154i	−0.509509	−	0.860465i	$-0.670173\pi$
$359$	−0.361500	+	0.208712i	−0.0190792	+	0.0110154i	0.490430	+	0.871481i	$0.336840\pi$
$360$	−2.12645	+	3.68312i	−0.112074	+	0.194117i
$361$	−5.87386	+	10.1738i	−0.309151	+	0.535465i
$362$	8.31759	+	14.4065i	0.437163	+	0.757189i
$363$	−30.9557	+	14.1857i	−1.62475	+	0.744556i
$364$		0			0
$365$			4.08712i			0.213930i
$366$	−14.3739	−	24.8963i	−0.751334	−	1.30135i
$367$	−1.23583	−	0.713507i	−0.0645098	−	0.0372447i	0.467398	−	0.884047i	$-0.345191\pi$
$367$	−1.23583	−	0.713507i	−0.0645098	−	0.0372447i	−0.531908	+	0.846802i	$0.678525\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	−16.5678	−	28.6962i	−0.862484	−	1.49387i
$370$	−3.60681			−0.187509
$371$		0			0
$372$	3.58258			0.185748
$373$	0.361500	−	0.208712i	0.0187178	−	0.0108067i	−0.490612	−	0.871378i	$-0.663227\pi$
$373$	0.361500	−	0.208712i	0.0187178	−	0.0108067i	0.509330	+	0.860571i	$0.329893\pi$
$374$	−5.69361	−	11.0265i	−0.294410	−	0.570165i
$375$	9.58258	−	16.5975i	0.494842	−	0.857092i
$376$	−2.51691	−	4.35942i	−0.129800	−	0.224820i
$377$		−	23.4724i		−	1.20889i
$378$		0			0
$379$	14.3303			0.736098			0.368049	−	0.929806i	$-0.380026\pi$
$379$	14.3303			0.736098			0.368049	+	0.929806i	$0.380026\pi$
$380$	−3.10260	+	1.79129i	−0.159160	+	0.0918911i
$381$	8.64064	−	14.9660i	0.442673	−	0.766733i
$382$	−15.5885	−	9.00000i	−0.797575	−	0.460480i
$383$	−4.12586	+	2.38207i	−0.210822	+	0.121718i	−0.601693	−	0.798727i	$-0.705507\pi$
$383$	−4.12586	+	2.38207i	−0.210822	+	0.121718i	0.390872	+	0.920445i	$0.372174\pi$
$384$	−3.09557			−0.157970
$385$		0			0
$386$	−20.3303			−1.03479
$387$	−63.6489	+	36.7477i	−3.23546	+	1.86799i
$388$	13.8470	+	7.99455i	0.702973	+	0.405862i
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$	5.36169	−	3.09557i	0.271500	−	0.156750i
$391$	−14.9666			−0.756895
$392$		0			0
$393$		−	29.1652i		−	1.47119i
$394$	9.37386	+	16.2360i	0.472248	+	0.817958i
$395$	−1.29217	+	2.23810i	−0.0650160	+	0.112611i
$396$	−19.3985	+	10.0166i	−0.974811	+	0.503353i
$397$	20.6537	−	11.9244i	1.03658	−	0.598469i	0.117716	−	0.993047i	$-0.462443\pi$
$397$	20.6537	−	11.9244i	1.03658	−	0.598469i	0.918862	+	0.394578i	$0.129109\pi$
$398$	24.6297			1.23458
$399$		0			0
$400$	4.58258			0.229129
$401$	0.791288	+	1.37055i	0.0395150	+	0.0684420i	0.885107	−	0.465388i	$-0.154085\pi$
$401$	0.791288	+	1.37055i	0.0395150	+	0.0684420i	−0.845592	+	0.533831i	$0.820752\pi$
$402$	−2.44949	+	4.24264i	−0.122169	+	0.211604i
$403$	−3.10260	−	1.79129i	−0.154552	−	0.0892304i
$404$	0.255619	+	0.442745i	0.0127175	+	0.0220274i
$405$			9.42157i			0.468161i
$406$		0			0
$407$	−15.5826	−	10.0000i	−0.772400	−	0.495682i
$408$	−5.79129	−	10.0308i	−0.286711	−	0.496599i
$409$	4.96640	−	8.60206i	0.245573	−	0.425345i	−0.716720	−	0.697361i	$-0.754357\pi$
$409$	4.96640	−	8.60206i	0.245573	−	0.425345i	0.962293	+	0.272017i	$0.0876906\pi$
$410$	1.62614	−	2.81655i	0.0803092	−	0.139100i
$411$	40.6554	−	23.4724i	2.00538	−	1.15781i
$412$			13.5396i			0.667049i
$413$		0			0
$414$			26.3303i			1.29406i
$415$	−5.12070	+	2.95644i	−0.251365	+	0.145126i
$416$	2.68085	+	1.54779i	0.131439	+	0.0758865i
$417$	8.66025	+	5.00000i	0.424094	+	0.244851i
$418$	−18.3706	−	0.863127i	−0.898537	−	0.0422169i
$419$			5.67991i			0.277482i	0.990329	+	0.138741i	$0.0443055\pi$
$419$			5.67991i			0.277482i	−0.990329	+	0.138741i	$0.955694\pi$
$420$		0			0
$421$	−1.58258			−0.0771300			−0.0385650	−	0.999256i	$-0.512279\pi$
$421$	−1.58258			−0.0771300			−0.0385650	+	0.999256i	$0.512279\pi$
$422$	5.37386	+	9.30780i	0.261596	+	0.453097i
$423$	−28.6962	−	16.5678i	−1.39526	−	0.805552i
$424$	2.09355	+	1.20871i	0.101672	+	0.0587003i
$425$	8.57321	+	14.8492i	0.415862	+	0.720294i
$426$	6.19115			0.299962
$427$		0			0
$428$		−	8.41742i		−	0.406872i
$429$	31.7468	+	1.49159i	1.53275	+	0.0720148i
$430$	−6.24718	−	3.60681i	−0.301266	−	0.173936i
$431$	−15.5130	−	8.95644i	−0.747235	−	0.431416i	0.0774588	−	0.996996i	$-0.475319\pi$
$431$	−15.5130	−	8.95644i	−0.747235	−	0.431416i	−0.824694	+	0.565579i	$0.808653\pi$
$432$	−9.60433	+	5.54506i	−0.462089	+	0.266787i
$433$		−	28.1017i		−	1.35048i	−0.737597	−	0.675241i	$-0.764040\pi$
$433$		−	28.1017i		−	1.35048i	0.737597	−	0.675241i	$-0.235960\pi$
$434$		0			0
$435$			15.1652i			0.727113i
$436$	1.00905	−	0.582576i	0.0483248	−	0.0279003i
$437$	−11.0901	+	19.2087i	−0.530513	+	0.918875i
$438$	−9.79129	+	16.9590i	−0.467846	+	0.810333i
$439$	1.15732	+	2.00454i	0.0552360	+	0.0956715i	0.892321	−	0.451401i	$-0.149076\pi$
$439$	1.15732	+	2.00454i	0.0552360	+	0.0956715i	−0.837085	+	0.547072i	$0.815742\pi$
$440$	−1.80341	−	1.15732i	−0.0859740	−	0.0551732i
$441$		0			0
$442$			11.5826i			0.550927i
$443$	1.58258	+	2.74110i	0.0751904	+	0.130234i	0.901169	−	0.433468i	$-0.142710\pi$
$443$	1.58258	+	2.74110i	0.0751904	+	0.130234i	−0.825979	+	0.563701i	$0.809377\pi$
$444$	−14.9660	−	8.64064i	−0.710256	−	0.410066i
$445$	−3.16515	+	5.48220i	−0.150043	+	0.259881i
$446$	−3.16300	−	5.47847i	−0.149772	−	0.259413i
$447$	43.3380			2.04982
$448$		0			0
$449$	12.8348			0.605714			0.302857	−	0.953036i	$-0.402060\pi$
$449$	12.8348			0.605714			0.302857	+	0.953036i	$0.402060\pi$
$450$	26.1238	−	15.0826i	1.23149	−	0.710999i
$451$	14.8344	−	7.65988i	0.698525	−	0.360690i
$452$	−8.37386	+	14.5040i	−0.393873	+	0.682209i
$453$	−5.54506	−	9.60433i	−0.260530	−	0.451251i
$454$		−	11.7362i		−	0.550808i
$455$		0			0
$456$	−17.1652			−0.803832
$457$	12.8474	−	7.41742i	0.600974	−	0.346972i	−0.168451	−	0.985710i	$-0.553876\pi$
$457$	12.8474	−	7.41742i	0.600974	−	0.346972i	0.769425	+	0.638738i	$0.220543\pi$
$458$	6.51419	−	11.2829i	0.304388	−	0.527216i
$459$	−35.9361	−	20.7477i	−1.67735	−	0.968421i
$460$	−2.23810	+	1.29217i	−0.104352	+	0.0602476i
$461$	−26.2983			−1.22483			−0.612417	−	0.790535i	$-0.709803\pi$
$461$	−26.2983			−1.22483			−0.612417	+	0.790535i	$0.709803\pi$
$462$		0			0
$463$	−13.1652			−0.611836			−0.305918	−	0.952058i	$-0.598963\pi$
$463$	−13.1652			−0.611836			−0.305918	+	0.952058i	$0.598963\pi$
$464$	−6.56670	+	3.79129i	−0.304852	+	0.176006i
$465$	2.00454	+	1.15732i	0.0929583	+	0.0536695i
$466$	4.41742	−	7.65120i	0.204633	−	0.354435i
$467$	0.442745	−	0.255619i	0.0204878	−	0.0118286i	−0.489721	−	0.871879i	$-0.662901\pi$
$467$	0.442745	−	0.255619i	0.0204878	−	0.0118286i	0.510209	+	0.860050i	$0.329568\pi$
$468$	20.3768			0.941920
$469$		0			0
$470$		−	3.25227i		−	0.150016i
$471$	−31.7477	−	54.9887i	−1.46286	−	2.53374i
$472$	−1.54779	+	2.68085i	−0.0712427	+	0.123396i
$473$	−16.9898	−	32.9031i	−0.781192	−	1.51289i
$474$	−10.7234	+	6.19115i	−0.492541	+	0.284369i
$475$	25.4107			1.16592
$476$		0			0
$477$	15.9129			0.728601
$478$	8.79129	+	15.2270i	0.402104	+	0.696465i
$479$	−3.23042	+	5.59525i	−0.147602	+	0.255653i	−0.930341	−	0.366697i	$-0.880489\pi$
$479$	−3.23042	+	5.59525i	−0.147602	+	0.255653i	0.782739	+	0.622350i	$0.213822\pi$
$480$	−1.73205	−	1.00000i	−0.0790569	−	0.0456435i
$481$	8.64064	+	14.9660i	0.393979	+	0.682392i
$482$		−	25.9219i		−	1.18071i
$483$		0			0
$484$	−4.58258	−	10.0000i	−0.208299	−	0.454545i
$485$	5.16515	+	8.94630i	0.234537	+	0.406231i
$486$	−5.93553	+	10.2806i	−0.269241	+	0.466339i
$487$	16.7477	−	29.0079i	0.758912	−	1.31447i	−0.184494	−	0.982834i	$-0.559065\pi$
$487$	16.7477	−	29.0079i	0.758912	−	1.31447i	0.943406	−	0.331640i	$-0.107602\pi$
$488$	8.04254	−	4.64336i	0.364069	−	0.210195i
$489$			12.3823i			0.559947i
$490$		0			0
$491$		−	21.4955i		−	0.970076i	−0.874493	−	0.485038i	$-0.838806\pi$
$491$		−	21.4955i		−	0.970076i	0.874493	−	0.485038i	$-0.161194\pi$
$492$	13.4949	−	7.79129i	0.608397	−	0.351258i
$493$	−24.5704	−	14.1857i	−1.10659	−	0.638892i
$494$	14.8655	+	8.58258i	0.668829	+	0.386148i
$495$	−14.0897	−	0.661992i	−0.633286	−	0.0297543i
$496$			1.15732i			0.0519653i
$497$		0			0
$498$	−28.3303			−1.26951
$499$	−13.9564	−	24.1733i	−0.624776	−	1.08214i	−0.988584	−	0.150670i	$-0.951857\pi$
$499$	−13.9564	−	24.1733i	−0.624776	−	1.08214i	0.363808	−	0.931474i	$-0.381476\pi$
$500$	5.36169	+	3.09557i	0.239782	+	0.138438i
$501$	−16.5975	−	9.58258i	−0.741522	−	0.428118i
$502$	−1.03655	−	1.79535i	−0.0462634	−	0.0801306i
$503$	31.9782			1.42584			0.712919	−	0.701246i	$-0.247373\pi$
$503$	31.9782			1.42584			0.712919	+	0.701246i	$0.247373\pi$
$504$		0			0
$505$			0.330303i			0.0146983i
$506$	−13.2519	−	0.622627i	−0.589118	−	0.0276792i
$507$	9.16159	+	5.28944i	0.406880	+	0.234912i
$508$	4.83465	+	2.79129i	0.214503	+	0.123843i
$509$	15.5255	−	8.96368i	0.688158	−	0.397308i	−0.114764	−	0.993393i	$-0.536611\pi$
$509$	15.5255	−	8.96368i	0.688158	−	0.397308i	0.802922	+	0.596085i	$0.203278\pi$
$510$		−	7.48331i		−	0.331367i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−53.2566	+	30.7477i	−2.35134	+	1.35755i
$514$	−2.44949	+	4.24264i	−0.108042	+	0.187135i
$515$	−4.37386	+	7.57575i	−0.192735	+	0.333828i
$516$	−17.2813	−	29.9320i	−0.760766	−	1.31768i
$517$	9.01703	−	14.0509i	0.396569	−	0.617956i
$518$		0			0
$519$			71.0780i			3.11998i
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	−30.8175	−	17.7925i	−1.35014	−	0.779504i	−0.361872	−	0.932228i	$-0.617862\pi$
$521$	−30.8175	−	17.7925i	−1.35014	−	0.779504i	−0.988269	+	0.152724i	$0.951196\pi$
$522$	−24.9564	+	43.2258i	−1.09231	+	1.89194i
$523$	13.3514	+	23.1253i	0.583817	+	1.01120i	0.995022	+	0.0996575i	$0.0317747\pi$
$523$	13.3514	+	23.1253i	0.583817	+	1.01120i	−0.411205	+	0.911543i	$0.634892\pi$
$524$	9.42157			0.411583
$525$		0			0
$526$	28.3303			1.23526
$527$	−3.75015	+	2.16515i	−0.163359	+	0.0943155i
$528$	−4.71048	−	9.12248i	−0.204997	−	0.397005i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	0.780929	+	1.35261i	0.0339214	+	0.0587536i
$531$			20.3768i			0.884280i
$532$		0			0
$533$	−15.5826			−0.674956
$534$	−26.2668	+	15.1652i	−1.13668	+	0.656260i
$535$	2.71918	−	4.70976i	0.117560	−	0.203621i
$536$	−1.37055	−	0.791288i	−0.0591988	−	0.0341784i
$537$	−19.2087	+	11.0901i	−0.828915	+	0.478574i
$538$	20.2420			0.872695
$539$		0			0
$540$	−7.16515			−0.308339
$541$	−8.01270	+	4.62614i	−0.344493	+	0.198893i	−0.662257	−	0.749277i	$-0.730401\pi$
$541$	−8.01270	+	4.62614i	−0.344493	+	0.198893i	0.317764	+	0.948170i	$0.397068\pi$
$542$	4.24264	+	2.44949i	0.182237	+	0.105215i
$543$	−25.7477	+	44.5964i	−1.10494	+	1.91381i
$544$	3.24037	−	1.87083i	0.138930	−	0.0802111i
$545$	0.752785			0.0322458
$546$		0			0
$547$			2.74773i			0.117484i	0.998273	+	0.0587422i	$0.0187090\pi$
$547$			2.74773i			0.117484i	−0.998273	+	0.0587422i	$0.981291\pi$
$548$	7.58258	+	13.1334i	0.323912	+	0.561031i
$549$	30.5653	−	52.9406i	1.30449	−	2.25945i
$550$	6.97322	+	13.5046i	0.297339	+	0.575838i
$551$	−36.4128	+	21.0229i	−1.55124	+	0.895607i
$552$	−12.3823			−0.527025
$553$		0			0
$554$	2.00000			0.0849719
$555$	−5.58258	−	9.66930i	−0.236967	−	0.410439i
$556$	−1.61521	+	2.79763i	−0.0685001	+	0.118646i
$557$	−8.58480	−	4.95644i	−0.363750	−	0.210011i	0.306975	−	0.951718i	$-0.400683\pi$
$557$	−8.58480	−	4.95644i	−0.363750	−	0.210011i	−0.670724	+	0.741707i	$0.734017\pi$
$558$	3.80908	+	6.59752i	0.161251	+	0.279295i
$559$			34.5625i			1.46184i
$560$		0			0
$561$	20.7477	−	32.3303i	0.875970	−	1.36499i
$562$	3.58258	+	6.20520i	0.151122	+	0.261751i
$563$	21.2111	−	36.7388i	0.893942	−	1.54835i	0.0588344	−	0.998268i	$-0.481262\pi$
$563$	21.2111	−	36.7388i	0.893942	−	1.54835i	0.835108	−	0.550086i	$-0.185405\pi$
$564$	7.79129	−	13.4949i	0.328072	−	0.568238i
$565$	−9.37077	+	5.41022i	−0.394231	+	0.227610i
$566$			15.6127i			0.656251i
$567$		0			0
$568$			2.00000i			0.0839181i
$569$	−13.4195	+	7.74773i	−0.562573	+	0.324802i	−0.754178	−	0.656671i	$-0.771964\pi$
$569$	−13.4195	+	7.74773i	−0.562573	+	0.324802i	0.191605	+	0.981472i	$0.438631\pi$
$570$	−9.60433	−	5.54506i	−0.402281	−	0.232257i
$571$	−3.10260	−	1.79129i	−0.129840	−	0.0749631i	0.433673	−	0.901070i	$-0.357217\pi$
$571$	−3.10260	−	1.79129i	−0.129840	−	0.0749631i	−0.563513	+	0.826107i	$0.690551\pi$
$572$	−0.481847	+	10.2555i	−0.0201470	+	0.428806i
$573$		−	55.7203i		−	2.32775i
$574$		0			0
$575$	18.3303			0.764426
$576$	−3.29129	−	5.70068i	−0.137137	−	0.237528i
$577$	−0.233559	−	0.134846i	−0.00972320	−	0.00561369i	0.495131	−	0.868819i	$-0.335120\pi$
$577$	−0.233559	−	0.134846i	−0.00972320	−	0.00561369i	−0.504854	+	0.863205i	$0.668454\pi$
$578$	−2.59808	−	1.50000i	−0.108066	−	0.0623918i
$579$	−31.4670	−	54.5024i	−1.30772	−	2.26504i
$580$	−4.89898			−0.203419
$581$		0			0
$582$			49.4955i			2.05165i
$583$	−0.376289	+	8.00885i	−0.0155843	+	0.331693i
$584$	−5.47847	−	3.16300i	−0.226701	−	0.130886i
$585$	11.4014	+	6.58258i	0.471388	+	0.272156i
$586$	18.5324	−	10.6997i	0.765565	−	0.441999i
$587$		−	17.0397i		−	0.703305i	−0.936131	−	0.351652i	$-0.885620\pi$
$587$		−	17.0397i		−	0.703305i	0.936131	−	0.351652i	$-0.114380\pi$
$588$		0			0
$589$			6.41742i			0.264425i
$590$	−1.73205	+	1.00000i	−0.0713074	+	0.0411693i
$591$	−29.0175	+	50.2598i	−1.19362	+	2.06741i
$592$	2.79129	−	4.83465i	0.114721	−	0.198703i
$593$	0.0674228	+	0.116780i	0.00276872	+	0.00479557i	0.867406	−	0.497600i	$-0.165785\pi$
$593$	0.0674228	+	0.116780i	0.00276872	+	0.00479557i	−0.864638	+	0.502396i	$0.832452\pi$
$594$	−30.9557	−	19.8656i	−1.27013	−	0.815096i
$595$		0			0
$596$			14.0000i			0.573462i
$597$	38.1216	+	66.0285i	1.56021	+	2.70237i
$598$	10.7234	+	6.19115i	0.438512	+	0.253175i
$599$	1.41742	−	2.45505i	0.0579144	−	0.100311i	−0.835615	−	0.549316i	$-0.814888\pi$
$599$	1.41742	−	2.45505i	0.0579144	−	0.100311i	0.893529	+	0.449005i	$0.148222\pi$
$600$	7.09285	+	12.2852i	0.289564	+	0.501540i
$601$	1.42701			0.0582091			0.0291045	−	0.999576i	$-0.490734\pi$
$601$	1.42701			0.0582091			0.0291045	+	0.999576i	$0.490734\pi$
$602$		0			0
$603$	−10.4174			−0.424230
$604$	3.10260	−	1.79129i	0.126243	−	0.0728865i
$605$	0.666353	−	7.07561i	0.0270911	−	0.287665i
$606$	−0.791288	+	1.37055i	−0.0321439	+	0.0556748i
$607$	23.4724	+	40.6554i	0.952716	+	1.65015i	0.739510	+	0.673146i	$0.235057\pi$
$607$	23.4724	+	40.6554i	0.952716	+	1.65015i	0.213206	+	0.977007i	$0.431609\pi$
$608$		−	5.54506i		−	0.224882i
$609$		0			0
$610$	6.00000			0.242933
$611$	−13.4949	+	7.79129i	−0.545945	+	0.315202i
$612$	12.3149	−	21.3300i	0.497799	−	0.862213i
$613$	12.0489	+	6.95644i	0.486651	+	0.280968i	0.723184	−	0.690655i	$-0.242678\pi$
$613$	12.0489	+	6.95644i	0.486651	+	0.280968i	−0.236533	+	0.971623i	$0.576011\pi$
$614$	7.04027	−	4.06470i	0.284122	−	0.164038i
$615$	10.0677			0.405967
$616$		0			0
$617$	25.9129			1.04321			0.521607	−	0.853186i	$-0.325333\pi$
$617$	25.9129			1.04321			0.521607	+	0.853186i	$0.325333\pi$
$618$	−36.2976	+	20.9564i	−1.46010	+	0.842992i
$619$	0.676305	+	0.390465i	0.0271830	+	0.0156941i	0.513530	−	0.858072i	$-0.328338\pi$
$619$	0.676305	+	0.390465i	0.0271830	+	0.0156941i	−0.486347	+	0.873766i	$0.661671\pi$
$620$	−0.373864	+	0.647551i	−0.0150147	+	0.0260063i
$621$	−38.4173	+	22.1803i	−1.54163	+	0.890063i
$622$	9.93280			0.398269
$623$		0			0
$624$			9.58258i			0.383610i
$625$	−9.45644	−	16.3790i	−0.378258	−	0.655161i
$626$	−0.511238	+	0.885491i	−0.0204332	+	0.0353913i
$627$	−26.1199	−	50.5848i	−1.04313	−	2.02016i
$628$	17.7636	−	10.2558i	0.708847	−	0.409253i
$629$	20.8881			0.832863
$630$		0			0
$631$	−5.16515			−0.205621			−0.102811	−	0.994701i	$-0.532784\pi$
$631$	−5.16515			−0.205621			−0.102811	+	0.994701i	$0.532784\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	−16.6352	+	28.8130i	−0.661189	+	1.14521i
$634$	−7.93725	−	4.58258i	−0.315229	−	0.181997i
$635$	1.80341	+	3.12359i	0.0715660	+	0.123956i
$636$			7.48331i			0.296733i
$637$		0			0
$638$	−21.1652	−	13.5826i	−0.837936	−	0.537739i
$639$	6.58258	+	11.4014i	0.260403	+	0.451031i
$640$	0.323042	−	0.559525i	0.0127694	−	0.0221172i
$641$	−14.9564	+	25.9053i	−0.590744	+	1.02320i	0.403389	+	0.915029i	$0.367832\pi$
$641$	−14.9564	+	25.9053i	−0.590744	+	1.02320i	−0.994132	+	0.108170i	$0.965501\pi$
$642$	22.5658	−	13.0284i	0.890602	−	0.514189i
$643$		−	16.7700i		−	0.661346i	−0.943745	−	0.330673i	$-0.892724\pi$
$643$		−	16.7700i		−	0.661346i	0.943745	−	0.330673i	$-0.107276\pi$
$644$		0			0
$645$		−	22.3303i		−	0.879255i
$646$	17.9681	−	10.3739i	0.706944	−	0.408154i
$647$	38.7677	+	22.3825i	1.52411	+	0.879948i	0.999592	+	0.0285507i	$0.00908921\pi$
$647$	38.7677	+	22.3825i	1.52411	+	0.879948i	0.524522	+	0.851397i	$0.324244\pi$
$648$	−12.6289	−	7.29129i	−0.496109	−	0.286429i
$649$	−10.2555	−	0.481847i	−0.402565	−	0.0189142i
$650$		−	14.1857i		−	0.556409i
$651$		0			0
$652$	−4.00000			−0.156652
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	3.12359	+	1.80341i	0.122142	+	0.0705188i
$655$	5.27160	+	3.04356i	0.205979	+	0.118922i
$656$	2.51691	+	4.35942i	0.0982689	+	0.170207i
$657$	−41.6413			−1.62458
$658$		0			0
$659$			30.3303i			1.18150i	0.806854	+	0.590750i	$0.201168\pi$
$659$			30.3303i			1.18150i	−0.806854	+	0.590750i	$0.798832\pi$
$660$	0.311314	−	6.62594i	0.0121179	−	0.257914i
$661$	−22.0063	−	12.7053i	−0.855945	−	0.494180i	0.00670702	−	0.999978i	$-0.497865\pi$
$661$	−22.0063	−	12.7053i	−0.855945	−	0.494180i	−0.862652	+	0.505797i	$0.831198\pi$
$662$	−12.4859	−	7.20871i	−0.485277	−	0.280175i
$663$	−31.0511	+	17.9274i	−1.20592	+	0.696241i
$664$		−	9.15188i		−	0.355162i
$665$		0			0
$666$		−	36.7477i		−	1.42395i
$667$	−26.2668	+	15.1652i	−1.01706	+	0.587197i
$668$	3.09557	−	5.36169i	0.119771	−	0.207450i
$669$	9.79129	−	16.9590i	0.378553	−	0.655673i
$670$	−0.511238	−	0.885491i	−0.0197509	−	0.0342095i
$671$	25.9219	+	16.6352i	1.00070	+	0.642194i
$672$		0			0
$673$			18.3303i			0.706581i	0.935514	+	0.353291i	$0.114937\pi$
$673$			18.3303i			0.706581i	−0.935514	+	0.353291i	$0.885063\pi$
$674$	−14.5826	−	25.2578i	−0.561700	−	0.972893i
$675$	44.0126	+	25.4107i	1.69404	+	0.978057i
$676$	−1.70871	+	2.95958i	−0.0657197	+	0.113830i
$677$	15.7335	+	27.2512i	0.604687	+	1.04735i	0.992101	+	0.125443i	$0.0400351\pi$
$677$	15.7335	+	27.2512i	0.604687	+	1.04735i	−0.387414	+	0.921906i	$0.626632\pi$
$678$	−51.8438			−1.99105
$679$		0			0
$680$	2.41742			0.0927040
$681$	31.4630	−	18.1652i	1.20566	−	0.696090i
$682$	−3.41056	+	1.76108i	−0.130597	+	0.0674351i
$683$	−22.7477	+	39.4002i	−0.870418	+	1.50761i	−0.00885223	+	0.999961i	$0.502818\pi$
$683$	−22.7477	+	39.4002i	−0.870418	+	1.50761i	−0.861565	+	0.507647i	$0.830516\pi$
$684$	−18.2504	−	31.6106i	−0.697821	−	1.20866i
$685$			9.79796i			0.374361i
$686$		0			0
$687$	40.3303			1.53870
$688$	9.66930	−	5.58258i	0.368639	−	0.212834i
$689$	3.74166	−	6.48074i	0.142546	−	0.246897i
$690$	−6.92820	−	4.00000i	−0.263752	−	0.152277i
$691$	32.6129	−	18.8291i	1.24065	−	0.716291i	0.271426	−	0.962459i	$-0.412505\pi$
$691$	32.6129	−	18.8291i	1.24065	−	0.716291i	0.969227	+	0.246168i	$0.0791716\pi$
$692$	−22.9612			−0.872853
$693$		0			0
$694$	−0.834849			−0.0316904
$695$	−1.80750	+	1.04356i	−0.0685624	+	0.0395845i
$696$	−20.3277	−	11.7362i	−0.770520	−	0.444860i
$697$	−9.41742	+	16.3115i	−0.356710	+	0.617841i
$698$	−1.79535	+	1.03655i	−0.0679552	+	0.0392339i
$699$	27.3489			1.03443
$700$		0			0
$701$		−	24.3303i		−	0.918943i	−0.888193	−	0.459471i	$-0.848039\pi$
$701$		−	24.3303i		−	0.918943i	0.888193	−	0.459471i	$-0.151961\pi$
$702$	17.1652	+	29.7309i	0.647857	+	1.12212i
$703$	15.4779	−	26.8085i	0.583759	−	1.01110i
$704$	2.94694	−	1.52168i	0.111067	−	0.0573506i
$705$	8.71884	−	5.03383i	0.328371	−	0.189585i
$706$	7.48331			0.281638
$707$		0			0
$708$	−9.58258			−0.360135
$709$	−7.83485	−	13.5704i	−0.294244	−	0.509645i	0.680565	−	0.732688i	$-0.261734\pi$
$709$	−7.83485	−	13.5704i	−0.294244	−	0.509645i	−0.974809	+	0.223042i	$0.928401\pi$
$710$	−0.646084	+	1.11905i	−0.0242471	+	0.0419972i
$711$	−22.8027	−	13.1652i	−0.855168	−	0.493732i
$712$	−4.89898	−	8.48528i	−0.183597	−	0.317999i
$713$			4.62929i			0.173368i
$714$		0			0
$715$	−3.58258	+	5.58258i	−0.133981	+	0.208776i
$716$	−3.58258	−	6.20520i	−0.133887	−	0.231899i
$717$	−27.2141	+	47.1362i	−1.01633	+	1.76033i
$718$	0.208712	−	0.361500i	0.00778907	−	0.0134911i
$719$	13.7302	−	7.92713i	0.512050	−	0.295632i	−0.221626	−	0.975132i	$-0.571136\pi$
$719$	13.7302	−	7.92713i	0.512050	−	0.295632i	0.733676	+	0.679500i	$0.237803\pi$
$720$		−	4.25290i		−	0.158496i
$721$		0			0
$722$		−	11.7477i		−	0.437205i
$723$	69.4926	−	40.1216i	2.58446	−	1.49214i
$724$	−14.4065	−	8.31759i	−0.535413	−	0.309121i
$725$	30.0924	+	17.3739i	1.11760	+	0.645249i
$726$	19.7156	−	27.7630i	0.731715	−	1.03038i
$727$			52.2484i			1.93778i	0.247483	+	0.968892i	$0.420396\pi$
$727$			52.2484i			1.93778i	−0.247483	+	0.968892i	$0.579604\pi$
$728$		0			0
$729$	7.00000			0.259259
$730$	−2.04356	−	3.53955i	−0.0756356	−	0.131005i
$731$	36.1792	+	20.8881i	1.33814	+	0.772574i
$732$	24.8963	+	14.3739i	0.920192	+	0.531273i
$733$	−11.4806	−	19.8850i	−0.424045	−	0.734468i	0.572285	−	0.820055i	$-0.306057\pi$
$733$	−11.4806	−	19.8850i	−0.424045	−	0.734468i	−0.996331	+	0.0855865i	$0.972724\pi$
$734$	1.42701			0.0526720
$735$		0			0
$736$		−	4.00000i		−	0.147442i
$737$	0.246339	−	5.24303i	0.00907400	−	0.193129i
$738$	28.6962	+	16.5678i	1.05632	+	0.609868i
$739$	6.56670	+	3.79129i	0.241560	+	0.139465i	0.615894	−	0.787829i	$-0.288795\pi$
$739$	6.56670	+	3.79129i	0.241560	+	0.139465i	−0.374333	+	0.927294i	$0.622128\pi$
$740$	3.12359	−	1.80341i	0.114825	−	0.0662945i
$741$			53.1360i			1.95200i
$742$		0			0
$743$		−	43.9129i		−	1.61101i	−0.592591	−	0.805504i	$-0.701895\pi$
$743$		−	43.9129i		−	1.61101i	0.592591	−	0.805504i	$-0.298105\pi$
$744$	−3.10260	+	1.79129i	−0.113747	+	0.0656718i
$745$	−4.52259	+	7.83335i	−0.165695	+	0.286992i
$746$	−0.208712	+	0.361500i	−0.00764149	+	0.0132355i
$747$	−30.1215	−	52.1719i	−1.10209	−	1.90887i
$748$	10.4440	+	6.70239i	0.381872	+	0.245063i
$749$		0			0
$750$			19.1652i			0.699812i
$751$	−6.74773	−	11.6874i	−0.246228	−	0.426480i	0.716248	−	0.697846i	$-0.245858\pi$
$751$	−6.74773	−	11.6874i	−0.246228	−	0.426480i	−0.962476	+	0.271366i	$0.912525\pi$
$752$	4.35942	+	2.51691i	0.158972	+	0.0917824i
$753$	3.20871	−	5.55765i	0.116932	−	0.202532i
$754$	11.7362	+	20.3277i	0.427408	+	0.740292i
$755$	2.31464			0.0842385
$756$		0			0
$757$	−49.1652			−1.78694			−0.893469	−	0.449125i	$-0.851736\pi$
$757$	−49.1652			−1.78694			−0.893469	+	0.449125i	$0.851736\pi$
$758$	−12.4104	+	7.16515i	−0.450766	+	0.260250i
$759$	−18.8419	−	36.4899i	−0.683918	−	1.32450i
$760$	1.79129	−	3.10260i	0.0649768	−	0.112543i
$761$	10.3766	+	17.9728i	0.376152	+	0.651515i	0.990499	−	0.137522i	$-0.0439137\pi$
$761$	10.3766	+	17.9728i	0.376152	+	0.651515i	−0.614347	+	0.789036i	$0.710580\pi$
$762$			17.2813i			0.626034i
$763$		0			0
$764$	18.0000			0.651217
$765$	13.7810	−	7.95644i	0.498252	−	0.287666i
$766$	2.38207	−	4.12586i	0.0860676	−	0.149073i
$767$	8.29875	+	4.79129i	0.299651	+	0.173003i
$768$	2.68085	−	1.54779i	0.0967367	−	0.0558509i
$769$	−29.7984			−1.07456			−0.537279	−	0.843404i	$-0.680548\pi$
$769$	−29.7984			−1.07456			−0.537279	+	0.843404i	$0.680548\pi$
$770$		0			0
$771$	−15.1652			−0.546160
$772$	17.6066	−	10.1652i	0.633674	−	0.365852i
$773$	44.3385	+	25.5989i	1.59475	+	0.920727i	0.992477	+	0.122435i	$0.0390702\pi$
$773$	44.3385	+	25.5989i	1.59475	+	0.920727i	0.602270	+	0.798293i	$0.294263\pi$
$774$	36.7477	−	63.6489i	1.32087	−	2.28781i
$775$	4.59298	−	2.65176i	0.164985	−	0.0952540i
$776$	−15.9891			−0.573975
$777$		0			0
$778$		−	10.0000i		−	0.358517i
$779$	13.9564	+	24.1733i	0.500041	+	0.866097i
$780$	−3.09557	+	5.36169i	−0.110839	+	0.191979i
$781$	−5.89389

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.68085 - 1.54779i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.559525 - 0.323042i) q^{5} +3.09557 q^{6} +1.00000i q^{8} +(3.29129 + 5.70068i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.68085 - 1.54779i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.559525 - 0.323042i) q^{5} +3.09557 q^{6} +1.00000i q^{8} +(3.29129 + 5.70068i) q^{9} +(-0.323042 + 0.559525i) q^{10} +(-2.94694 + 1.52168i) q^{11} +(-2.68085 + 1.54779i) q^{12} +3.09557 q^{13} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87083 - 3.24037i) q^{17} +(-5.70068 - 3.29129i) q^{18} +(-2.77253 - 4.80217i) q^{19} -0.646084i q^{20} +(1.79129 - 2.79129i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(1.54779 - 2.68085i) q^{24} +(-2.29129 + 3.96863i) q^{25} +(-2.68085 + 1.54779i) q^{26} -11.0901i q^{27} -7.58258i q^{29} +(1.73205 - 1.00000i) q^{30} +(-1.00227 - 0.578661i) q^{31} +(0.866025 + 0.500000i) q^{32} +(10.2555 + 0.481847i) q^{33} +3.74166i q^{34} +6.58258 q^{36} +(2.79129 + 4.83465i) q^{37} +(4.80217 + 2.77253i) q^{38} +(-8.29875 - 4.79129i) q^{39} +(0.323042 + 0.559525i) q^{40} -5.03383 q^{41} +11.1652i q^{43} +(-0.155657 + 3.31297i) q^{44} +(3.68312 + 2.12645i) q^{45} +(3.46410 + 2.00000i) q^{46} +(-4.35942 + 2.51691i) q^{47} +3.09557i q^{48} -4.58258i q^{50} +(-10.0308 + 5.79129i) q^{51} +(1.54779 - 2.68085i) q^{52} +(1.20871 - 2.09355i) q^{53} +(5.54506 + 9.60433i) q^{54} +(-1.15732 + 1.80341i) q^{55} +17.1652i q^{57} +(3.79129 + 6.56670i) q^{58} +(2.68085 + 1.54779i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-4.64336 - 8.04254i) q^{61} +1.15732 q^{62} -1.00000 q^{64} +(1.73205 - 1.00000i) q^{65} +(-9.12248 + 4.71048i) q^{66} +(-0.791288 + 1.37055i) q^{67} +(-1.87083 - 3.24037i) q^{68} +12.3823i q^{69} +2.00000 q^{71} +(-5.70068 + 3.29129i) q^{72} +(-3.16300 + 5.47847i) q^{73} +(-4.83465 - 2.79129i) q^{74} +(12.2852 - 7.09285i) q^{75} -5.54506 q^{76} +9.58258 q^{78} +(-3.46410 + 2.00000i) q^{79} +(-0.559525 - 0.323042i) q^{80} +(-7.29129 + 12.6289i) q^{81} +(4.35942 - 2.51691i) q^{82} -9.15188 q^{83} -2.41742i q^{85} +(-5.58258 - 9.66930i) q^{86} +(-11.7362 + 20.3277i) q^{87} +(-1.52168 - 2.94694i) q^{88} +(-8.48528 + 4.89898i) q^{89} -4.25290 q^{90} -4.00000 q^{92} +(1.79129 + 3.10260i) q^{93} +(2.51691 - 4.35942i) q^{94} +(-3.10260 - 1.79129i) q^{95} +(-1.54779 - 2.68085i) q^{96} +15.9891i q^{97} +(-18.3739 - 11.7913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 16 * q^9	\( 16 q + 8 q^{4} + 16 q^{9} - 4 q^{11} - 32 q^{15} - 8 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 8 q^{37} + 4 q^{44} + 56 q^{53} + 24 q^{58} - 16 q^{60} - 16 q^{64} + 24 q^{67} + 32 q^{71} + 80 q^{78} - 80 q^{81} - 16 q^{86} - 4 q^{88} - 64 q^{92} - 8 q^{93} - 184 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 16 * q^9 - 4 * q^11 - 32 * q^15 - 8 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 8 * q^37 + 4 * q^44 + 56 * q^53 + 24 * q^58 - 16 * q^60 - 16 * q^64 + 24 * q^67 + 32 * q^71 + 80 * q^78 - 80 * q^81 - 16 * q^86 - 4 * q^88 - 64 * q^92 - 8 * q^93 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more