Properties

Label 1078.2.i.b.1011.8
Level $1078$
Weight $2$
Character 1078.1011
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

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: \(x^{16} - x^{12} - 15 x^{8} - 16 x^{4} + 256\)
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 1011.8
Root \(-0.825348 + 1.14839i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1011
Dual form 1078.2.i.b.901.8

$q$-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} +(0.155657 + 3.31297i) 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} +(-4.71048 + 9.12248i) 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} +(2.94694 + 1.52168i) 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} +(0.481847 + 10.2555i) 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} +(3.31297 - 0.155657i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 16 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{4} + 16 q^{9} - 4 q^{11} - 32 q^{15} - 8 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 8 q^{37} + 4 q^{44} + 56 q^{53} + 24 q^{58} - 16 q^{60} - 16 q^{64} + 24 q^{67} + 32 q^{71} + 80 q^{78} - 80 q^{81} - 16 q^{86} - 4 q^{88} - 64 q^{92} - 8 q^{93} - 184 q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 2.68085 + 1.54779i 1.54779 + 0.893615i 0.998310 + 0.0581058i \(0.0185061\pi\)
0.549476 + 0.835509i \(0.314827\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.559525 + 0.323042i −0.250227 + 0.144469i −0.619868 0.784706i \(-0.712814\pi\)
0.369641 + 0.929175i \(0.379481\pi\)
\(6\) 3.09557 1.26376
\(7\) 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
\(11\) 0.155657 + 3.31297i 0.0469323 + 0.998898i
\(12\) 2.68085 1.54779i 0.773893 0.446808i
\(13\) 3.09557 0.858558 0.429279 0.903172i \(-0.358768\pi\)
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 \(-0.683422\pi\)
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 \(-0.947229\pi\)
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 \(-0.303595\pi\)
−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 \(0.248615\pi\)
−0.710176 + 0.704024i \(0.751385\pi\)
\(30\) −1.73205 + 1.00000i −0.316228 + 0.182574i
\(31\) 1.00227 + 0.578661i 0.180013 + 0.103931i 0.587299 0.809370i \(-0.300191\pi\)
−0.407286 + 0.913301i \(0.633525\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −4.71048 + 9.12248i −0.819989 + 1.58802i
\(34\) 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 \(-0.0149157\pi\)
−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 \(-0.628589\pi\)
−0.393076 + 0.919506i \(0.628589\pi\)
\(42\) 0 0
\(43\) 11.1652i 1.70267i −0.524623 0.851335i \(-0.675794\pi\)
0.524623 0.851335i \(-0.324206\pi\)
\(44\) 2.94694 + 1.52168i 0.444269 + 0.229402i
\(45\) −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 −0.147142 0.989115i \(-0.547007\pi\)
0.783028 + 0.621986i \(0.213674\pi\)
\(48\) 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 \(-0.780239\pi\)
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 0.315236 0.949013i \(-0.397916\pi\)
−0.664252 + 0.747509i \(0.731250\pi\)
\(60\) −1.00000 + 1.73205i −0.129099 + 0.223607i
\(61\) −4.64336 8.04254i −0.594521 1.02974i −0.993614 0.112831i \(-0.964008\pi\)
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
\(66\) 0.481847 + 10.2555i 0.0593113 + 1.26237i
\(67\) −0.791288 + 1.37055i −0.0966712 + 0.167439i −0.910305 0.413938i \(-0.864153\pi\)
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 \(-0.462134\pi\)
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 \(-0.954044\pi\)
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 −0.292306 0.956325i \(-0.594423\pi\)
0.682048 + 0.731307i \(0.261089\pi\)
\(80\) 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 \(-0.667503\pi\)
−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
\(88\) 3.31297 0.155657i 0.353164 0.0165931i
\(89\) 8.48528 4.89898i 0.899438 0.519291i 0.0224202 0.999749i \(-0.492863\pi\)
0.877018 + 0.480458i \(0.159529\pi\)
\(90\) −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 \(-0.698529\pi\)
0.584041 0.811724i \(-0.301471\pi\)
\(98\) 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 \(-0.841430\pi\)
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 0.205174 0.978725i \(-0.434224\pi\)
0.950188 + 0.311676i \(0.100890\pi\)
\(104\) 3.09557i 0.303546i
\(105\) 0 0
\(106\) 2.41742i 0.234801i
\(107\) −7.28970 + 4.20871i −0.704722 + 0.406872i −0.809104 0.587666i \(-0.800047\pi\)
0.104382 + 0.994537i \(0.466714\pi\)
\(108\) 9.60433 + 5.54506i 0.924177 + 0.533574i
\(109\) −1.00905 0.582576i −0.0966495 0.0558006i 0.450896 0.892576i \(-0.351104\pi\)
−0.547546 + 0.836776i \(0.684438\pi\)
\(110\) −1.90397 0.983134i −0.181537 0.0937382i
\(111\) 17.2813i 1.64027i
\(112\) 0 0
\(113\) −16.7477 −1.57549 −0.787747 0.615999i \(-0.788752\pi\)
−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
\(121\) −10.9515 + 1.03137i −0.995595 + 0.0937612i
\(122\) −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 \(-0.920330\pi\)
0.968840 0.247687i \(-0.0796704\pi\)
\(128\) −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 \(-0.0316427\pi\)
−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 \(0.390987\pi\)
−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 \(-0.543746\pi\)
−0.137000 + 0.990571i \(0.543746\pi\)
\(140\) 0 0
\(141\) 15.5826 1.31229
\(142\) 1.73205 1.00000i 0.145350 0.0839181i
\(143\) 0.481847 + 10.2555i 0.0402941 + 0.857612i
\(144\) 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 0.0870170 0.996207i \(-0.472267\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(150\) −7.09285 + 12.2852i −0.579129 + 1.00308i
\(151\) −3.10260 1.79129i −0.252486 0.145773i 0.368416 0.929661i \(-0.379900\pi\)
−0.620902 + 0.783888i \(0.713234\pi\)
\(152\) −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 −0.421597 0.906783i \(-0.638530\pi\)
−0.996096 + 0.0882774i \(0.971864\pi\)
\(158\) 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 \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) −2.51691 + 4.35942i −0.196538 + 0.340414i
\(165\) −0.311314 6.62594i −0.0242357 0.515829i
\(166\) −7.92576 + 4.57594i −0.615158 + 0.355162i
\(167\) 6.19115 0.479085 0.239543 0.970886i \(-0.423002\pi\)
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 \(-0.828934\pi\)
−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 \(-0.747045\pi\)
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 \(0.212155\pi\)
−0.785988 + 0.618242i \(0.787845\pi\)
\(182\) 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
\(187\) 11.0265 + 5.69361i 0.806334 + 0.416358i
\(188\) 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 \(0.0590746\pi\)
−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 −0.292862 0.956155i \(-0.594608\pi\)
−0.974485 + 0.224451i \(0.927941\pi\)
\(194\) −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 \(0.232790\pi\)
−0.744287 + 0.667860i \(0.767210\pi\)
\(198\) −10.0166 + 19.3985i −0.711848 + 1.37859i
\(199\) 21.3300 + 12.3149i 1.51204 + 0.872978i 0.999901 + 0.0140770i \(0.00448100\pi\)
0.512141 + 0.858901i \(0.328852\pi\)
\(200\) 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 \(0.120626\pi\)
−0.929051 + 0.369952i \(0.879374\pi\)
\(212\) −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
\(220\) −2.14046 + 0.100567i −0.144310 + 0.00678025i
\(221\) 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 \(-0.932064\pi\)
0.977311 0.211810i \(-0.0679358\pi\)
\(224\) 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 \(-0.960679\pi\)
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 −0.0785048 0.996914i \(-0.525015\pi\)
0.824100 + 0.566444i \(0.191681\pi\)
\(230\) 2.58434 0.170406
\(231\) 0 0
\(232\) 7.58258 0.497820
\(233\) 7.65120 4.41742i 0.501247 0.289395i −0.227981 0.973665i \(-0.573213\pi\)
0.729228 + 0.684270i \(0.239879\pi\)
\(234\) 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 \(0.192538\pi\)
−0.822572 + 0.568661i \(0.807462\pi\)
\(240\) 1.00000 + 1.73205i 0.0645497 + 0.111803i
\(241\) −12.9610 + 22.4490i −0.834889 + 1.44607i 0.0592326 + 0.998244i \(0.481135\pi\)
−0.894121 + 0.447825i \(0.852199\pi\)
\(242\) −8.96863 + 6.36897i −0.576525 + 0.409413i
\(243\) −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 \(-0.979159\pi\)
0.997857 0.0654264i \(-0.0208407\pi\)
\(252\) 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 −0.626453 0.779459i \(-0.715494\pi\)
0.361805 + 0.932254i \(0.382161\pi\)
\(258\) 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 \(0.00479619\pi\)
0.512992 + 0.858394i \(0.328537\pi\)
\(264\) 9.12248 + 4.71048i 0.561450 + 0.289910i
\(265\) 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 0.927861 0.372926i \(-0.121645\pi\)
0.140967 + 0.990014i \(0.454979\pi\)
\(270\) −6.20520 3.58258i −0.377637 0.218029i
\(271\) −2.44949 4.24264i −0.148796 0.257722i 0.781987 0.623295i \(-0.214206\pi\)
−0.930783 + 0.365573i \(0.880873\pi\)
\(272\) −3.74166 −0.226871
\(273\) 0 0
\(274\) 15.1652i 0.916160i
\(275\) −13.5046 6.97322i −0.814358 0.420501i
\(276\) −10.7234 6.19115i −0.645472 0.372663i
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) −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 \(0.0685575\pi\)
−0.976895 + 0.213719i \(0.931442\pi\)
\(282\) 13.4949 7.79129i 0.803610 0.463964i
\(283\) 7.80636 13.5210i 0.464040 0.803740i −0.535118 0.844777i \(-0.679733\pi\)
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 \(-0.714934\pi\)
−0.625081 + 0.780560i \(0.714934\pi\)
\(294\) 0 0
\(295\) 2.00000 0.116445
\(296\) 4.83465 2.79129i 0.281008 0.162240i
\(297\) −36.7413 + 1.72625i −2.13194 + 0.100167i
\(298\) 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 \(-0.574522\pi\)
−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 0.723652 0.690165i \(-0.242462\pi\)
−0.235874 + 0.971784i \(0.575795\pi\)
\(312\) 4.79129 8.29875i 0.271253 0.469824i
\(313\) −0.885491 + 0.511238i −0.0500509 + 0.0288969i −0.524817 0.851215i \(-0.675866\pi\)
0.474766 + 0.880112i \(0.342533\pi\)
\(314\) −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 \(-0.0838064\pi\)
−0.708157 + 0.706055i \(0.750473\pi\)
\(318\) 3.74166 6.48074i 0.209822 0.363422i
\(319\) −25.1208 + 1.18028i −1.40650 + 0.0660830i
\(320\) 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 \(-0.0369861\pi\)
−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 \(-0.707805\pi\)
0.607443 0.794364i \(-0.292195\pi\)
\(338\) −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
\(341\) −1.76108 + 3.41056i −0.0953676 + 0.184692i
\(342\) 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 0.480468 0.877012i \(-0.340467\pi\)
−0.519281 + 0.854604i \(0.673800\pi\)
\(348\) 11.7362 + 20.3277i 0.629127 + 1.08968i
\(349\) 2.07310 0.110970 0.0554852 0.998460i \(-0.482329\pi\)
0.0554852 + 0.998460i \(0.482329\pi\)
\(350\) 0 0
\(351\) 34.3303i 1.83242i
\(352\) 1.52168 2.94694i 0.0811059 0.157073i
\(353\) 6.48074 + 3.74166i 0.344935 + 0.199148i 0.662452 0.749104i \(-0.269516\pi\)
−0.317517 + 0.948253i \(0.602849\pi\)
\(354\) −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 −0.490430 0.871481i \(-0.663160\pi\)
0.509509 + 0.860465i \(0.329827\pi\)
\(360\) −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 0.531908 0.846802i \(-0.321475\pi\)
−0.467398 + 0.884047i \(0.654809\pi\)
\(368\) −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 −0.509330 0.860571i \(-0.670107\pi\)
0.490612 + 0.871378i \(0.336773\pi\)
\(374\) 12.3960 0.582415i 0.640982 0.0301159i
\(375\) 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 \(-0.380026\pi\)
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 −0.390872 0.920445i \(-0.627826\pi\)
0.601693 + 0.798727i \(0.294493\pi\)
\(384\) −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 \(-0.914918\pi\)
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
\(396\) 1.02462 + 21.8079i 0.0514892 + 1.09589i
\(397\) −20.6537 + 11.9244i −1.03658 + 0.598469i −0.918862 0.394578i \(-0.870891\pi\)
−0.117716 + 0.993047i \(0.537557\pi\)
\(398\) 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 \(-0.154085\pi\)
−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 \(-0.754357\pi\)
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
\(418\) 8.43782 16.3410i 0.412707 0.799264i
\(419\) 5.67991i 0.277482i −0.990329 0.138741i \(-0.955694\pi\)
0.990329 0.138741i \(-0.0443055\pi\)
\(420\) 0 0
\(421\) −1.58258 −0.0771300 −0.0385650 0.999256i \(-0.512279\pi\)
−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
\(429\) −14.5816 + 28.2393i −0.704008 + 1.36341i
\(430\) 6.24718 + 3.60681i 0.301266 + 0.173936i
\(431\) 15.5130 + 8.95644i 0.747235 + 0.431416i 0.824694 0.565579i \(-0.191347\pi\)
−0.0774588 + 0.996996i \(0.524681\pi\)
\(432\) 9.60433 5.54506i 0.462089 0.266787i
\(433\) 28.1017i 1.35048i 0.737597 + 0.675241i \(0.235960\pi\)
−0.737597 + 0.675241i \(0.764040\pi\)
\(434\) 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 \(-0.149076\pi\)
−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 \(-0.142710\pi\)
−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 \(-0.402060\pi\)
0.302857 + 0.953036i \(0.402060\pi\)
\(450\) −26.1238 + 15.0826i −1.23149 + 0.710999i
\(451\) −0.783549 16.6769i −0.0368959 0.785285i
\(452\) −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 −0.769425 0.638738i \(-0.779457\pi\)
0.168451 + 0.985710i \(0.446124\pi\)
\(458\) 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 \(-0.709803\pi\)
−0.612417 + 0.790535i \(0.709803\pi\)
\(462\) 0 0
\(463\) −13.1652 −0.611836 −0.305918 0.952058i \(-0.598963\pi\)
−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 −0.510209 0.860050i \(-0.670432\pi\)
0.489721 + 0.871879i \(0.337099\pi\)
\(468\) 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
\(473\) 36.9898 1.73793i 1.70079 0.0799102i
\(474\) 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 \(-0.880489\pi\)
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 \(-0.559065\pi\)
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 \(0.161194\pi\)
−0.874493 + 0.485038i \(0.838806\pi\)
\(492\) −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
\(495\) 6.47156 12.5330i 0.290875 0.563319i
\(496\) 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 \(-0.951857\pi\)
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 \(-0.247373\pi\)
0.712919 + 0.701246i \(0.247373\pi\)
\(504\) 0 0
\(505\) 0.330303i 0.0146983i
\(506\) 6.08673 11.7878i 0.270588 0.524031i
\(507\) −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 −0.802922 0.596085i \(-0.796722\pi\)
0.114764 + 0.993393i \(0.463389\pi\)
\(510\) 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 0.988269 0.152724i \(-0.0488045\pi\)
0.361872 + 0.932228i \(0.382138\pi\)
\(522\) −24.9564 + 43.2258i −1.09231 + 1.89194i
\(523\) 13.3514 + 23.1253i 0.583817 + 1.01120i 0.995022 + 0.0996575i \(0.0317747\pi\)
−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
\(528\) 10.2555 0.481847i 0.446315 0.0209697i
\(529\) 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 −0.317764 0.948170i \(-0.602932\pi\)
0.662257 + 0.749277i \(0.269599\pi\)
\(542\) −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 \(-0.981291\pi\)
0.998273 0.0587422i \(-0.0187090\pi\)
\(548\) 7.58258 + 13.1334i 0.323912 + 0.561031i
\(549\) 30.5653 52.9406i 1.30449 2.25945i
\(550\) −15.1819 + 0.713309i −0.647360 + 0.0304156i
\(551\) 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 0.670724 0.741707i \(-0.265983\pi\)
−0.306975 + 0.951718i \(0.599317\pi\)
\(558\) 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 \(-0.481262\pi\)
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 −0.191605 0.981472i \(-0.561369\pi\)
0.754178 + 0.656671i \(0.228036\pi\)
\(570\) 9.60433 + 5.54506i 0.402281 + 0.232257i
\(571\) 3.10260 + 1.79129i 0.129840 + 0.0749631i 0.563513 0.826107i \(-0.309449\pi\)
−0.433673 + 0.901070i \(0.642783\pi\)
\(572\) 9.12248 + 4.71048i 0.381430 + 0.196955i
\(573\) 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 0.504854 0.863205i \(-0.331546\pi\)
−0.495131 + 0.868819i \(0.664880\pi\)
\(578\) 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
\(583\) 7.12402 + 3.67855i 0.295047 + 0.152350i
\(584\) 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 \(0.114380\pi\)
−0.936131 + 0.351652i \(0.885620\pi\)
\(588\) 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 \(-0.165785\pi\)
−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 \(-0.814888\pi\)
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 \(-0.490734\pi\)
0.0291045 + 0.999576i \(0.490734\pi\)
\(602\) 0 0
\(603\) −10.4174 −0.424230
\(604\) −3.10260 + 1.79129i −0.126243 + 0.0728865i
\(605\) 5.79448 4.11489i 0.235579 0.167294i
\(606\) −0.791288 + 1.37055i −0.0321439 + 0.0556748i
\(607\) 23.4724 + 40.6554i 0.952716 + 1.65015i 0.739510 + 0.673146i \(0.235057\pi\)
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 0.236533 0.971623i \(-0.423989\pi\)
−0.723184 + 0.690655i \(0.757322\pi\)
\(614\) −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 \(-0.325333\pi\)
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 0.486347 0.873766i \(-0.338329\pi\)
−0.513530 + 0.858072i \(0.671662\pi\)
\(620\) −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
\(627\) 56.8676 2.67187i 2.27107 0.106704i
\(628\) −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 \(-0.532784\pi\)
−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 \(0.367832\pi\)
−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 \(0.107276\pi\)
−0.943745 + 0.330673i \(0.892724\pi\)
\(644\) 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 \(-0.990911\pi\)
−0.524522 0.851397i \(-0.675756\pi\)
\(648\) 12.6289 + 7.29129i 0.496109 + 0.286429i
\(649\) 4.71048 9.12248i 0.184902 0.358089i
\(650\) 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 \(-0.129211\pi\)
−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 \(-0.798832\pi\)
0.806854 0.590750i \(-0.201168\pi\)
\(660\) −5.89389 3.04336i −0.229419 0.118463i
\(661\) 22.0063 + 12.7053i 0.855945 + 0.494180i 0.862652 0.505797i \(-0.168802\pi\)
−0.00670702 + 0.999978i \(0.502135\pi\)
\(662\) 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 \(-0.885063\pi\)
0.935514 0.353291i \(-0.114937\pi\)
\(674\) −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 \(0.0400351\pi\)
−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
\(682\) 0.180145 + 3.83417i 0.00689811 + 0.146818i
\(683\) −22.7477 + 39.4002i −0.870418 + 1.50761i −0.00885223 + 0.999961i \(0.502818\pi\)
−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 −0.969227 0.246168i \(-0.920828\pi\)
−0.271426 + 0.962459i \(0.587495\pi\)
\(692\) −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 \(0.151961\pi\)
−0.888193 + 0.459471i \(0.848039\pi\)
\(702\) 17.1652 + 29.7309i 0.647857 + 1.12212i
\(703\) 15.4779 26.8085i 0.583759 1.01110i
\(704\) −0.155657 3.31297i −0.00586654 0.124862i
\(705\) −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 \(-0.261734\pi\)
−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 −0.733676 0.679500i \(-0.762197\pi\)
0.221626 + 0.975132i \(0.428864\pi\)
\(720\) 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
\(726\) −33.9013 + 3.19269i −1.25820 + 0.118492i
\(727\) 52.2484i 1.93778i −0.247483 0.968892i \(-0.579604\pi\)
0.247483 0.968892i \(-0.420396\pi\)
\(728\) 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 \(-0.306057\pi\)
−0.996331 + 0.0855865i \(0.972724\pi\)
\(734\) 1.42701 0.0526720
\(735\) 0 0
\(736\) 4.00000i 0.147442i
\(737\) −4.66376 2.40818i −0.171792 0.0887064i
\(738\) −28.6962 16.5678i −1.05632 0.609868i
\(739\) −6.56670 3.79129i −0.241560 0.139465i 0.374333 0.927294i \(-0.377872\pi\)
−0.615894 + 0.787829i \(0.711205\pi\)
\(740\) −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 \(0.298105\pi\)
−0.592591 + 0.805504i \(0.701895\pi\)
\(744\) 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 \(-0.245858\pi\)
−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 \(-0.851736\pi\)
−0.893469 + 0.449125i \(0.851736\pi\)
\(758\) 12.4104 7.16515i 0.450766 0.260250i
\(759\) 41.0222 1.92739i 1.48901 0.0699598i
\(760\) 1.79129 3.10260i 0.0649768 0.112543i
\(761\) 10.3766 + 17.9728i 0.376152 + 0.651515i 0.990499 0.137522i \(-0.0439137\pi\)
−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 \(-0.680548\pi\)
−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 \(-0.960930\pi\)
−0.602270 0.798293i \(-0.705737\pi\)
\(774\) 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
\(781\) 0.311314 + 6.62594i 0.0111397 + 0.237095i
\(782\) −12.9615 + 7.48331i −0.463502 + 0.267603i