Properties

Label 1216.2.i.i.577.1
Level $1216$
Weight $2$
Character 1216.577
Analytic conductor $9.710$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.70980888579\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 577.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1216.577
Dual form 1216.2.i.i.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +4.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(2.50000 + 4.33013i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +4.00000 q^{31} +(2.00000 + 3.46410i) q^{33} -2.00000 q^{37} -5.00000 q^{39} +(2.50000 + 4.33013i) q^{41} +(-5.50000 - 9.52628i) q^{43} +6.00000 q^{45} +(2.50000 - 4.33013i) q^{47} -7.00000 q^{49} +(-2.50000 + 4.33013i) q^{51} +(-4.50000 + 7.79423i) q^{53} +(6.00000 + 10.3923i) q^{55} +(-0.500000 - 4.33013i) q^{57} +(6.50000 + 11.2583i) q^{59} +(-0.500000 + 0.866025i) q^{61} -15.0000 q^{65} +(-2.50000 + 4.33013i) q^{67} +1.00000 q^{69} +(-0.500000 - 0.866025i) q^{71} +(4.50000 + 7.79423i) q^{73} -4.00000 q^{75} +(-8.50000 - 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{81} -16.0000 q^{83} +(-7.50000 + 12.9904i) q^{85} +3.00000 q^{87} +(-1.50000 + 2.59808i) q^{89} +(2.00000 + 3.46410i) q^{93} +(-1.50000 - 12.9904i) q^{95} +(6.50000 + 11.2583i) q^{97} +(4.00000 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + 3q^{5} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} + 3q^{5} + 2q^{9} + 8q^{11} - 5q^{13} - 3q^{15} + 5q^{17} - 8q^{19} + q^{23} - 4q^{25} + 10q^{27} + 3q^{29} + 8q^{31} + 4q^{33} - 4q^{37} - 10q^{39} + 5q^{41} - 11q^{43} + 12q^{45} + 5q^{47} - 14q^{49} - 5q^{51} - 9q^{53} + 12q^{55} - q^{57} + 13q^{59} - q^{61} - 30q^{65} - 5q^{67} + 2q^{69} - q^{71} + 9q^{73} - 8q^{75} - 17q^{79} - q^{81} - 32q^{83} - 15q^{85} + 6q^{87} - 3q^{89} + 4q^{93} - 3q^{95} + 13q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(705\) \(837\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 0 0
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) 0 0
\(17\) 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i \(0.0406959\pi\)
−0.385499 + 0.922708i \(0.625971\pi\)
\(18\) 0 0
\(19\) −4.00000 1.73205i −0.917663 0.397360i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 2.00000 + 3.46410i 0.348155 + 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) −5.00000 −0.800641
\(40\) 0 0
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 0 0
\(43\) −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i \(-0.849958\pi\)
0.0522047 0.998636i \(-0.483375\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) 0 0
\(47\) 2.50000 4.33013i 0.364662 0.631614i −0.624059 0.781377i \(-0.714518\pi\)
0.988722 + 0.149763i \(0.0478510\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) −2.50000 + 4.33013i −0.350070 + 0.606339i
\(52\) 0 0
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 0 0
\(55\) 6.00000 + 10.3923i 0.809040 + 1.40130i
\(56\) 0 0
\(57\) −0.500000 4.33013i −0.0662266 0.573539i
\(58\) 0 0
\(59\) 6.50000 + 11.2583i 0.846228 + 1.46571i 0.884551 + 0.466444i \(0.154465\pi\)
−0.0383226 + 0.999265i \(0.512201\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −15.0000 −1.86052
\(66\) 0 0
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −0.500000 0.866025i −0.0593391 0.102778i 0.834830 0.550508i \(-0.185566\pi\)
−0.894169 + 0.447730i \(0.852233\pi\)
\(72\) 0 0
\(73\) 4.50000 + 7.79423i 0.526685 + 0.912245i 0.999517 + 0.0310925i \(0.00989865\pi\)
−0.472831 + 0.881153i \(0.656768\pi\)
\(74\) 0 0
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.50000 14.7224i −0.956325 1.65640i −0.731307 0.682048i \(-0.761089\pi\)
−0.225018 0.974355i \(-0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −16.0000 −1.75623 −0.878114 0.478451i \(-0.841198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 0 0
\(85\) −7.50000 + 12.9904i −0.813489 + 1.40900i
\(86\) 0 0
\(87\) 3.00000 0.321634
\(88\) 0 0
\(89\) −1.50000 + 2.59808i −0.159000 + 0.275396i −0.934508 0.355942i \(-0.884160\pi\)
0.775509 + 0.631337i \(0.217494\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 0 0
\(95\) −1.50000 12.9904i −0.153897 1.33278i
\(96\) 0 0
\(97\) 6.50000 + 11.2583i 0.659975 + 1.14311i 0.980622 + 0.195911i \(0.0627665\pi\)
−0.320647 + 0.947199i \(0.603900\pi\)
\(98\) 0 0
\(99\) 4.00000 6.92820i 0.402015 0.696311i
\(100\) 0 0
\(101\) 9.50000 16.4545i 0.945285 1.63728i 0.190106 0.981763i \(-0.439117\pi\)
0.755179 0.655519i \(-0.227550\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i \(-0.0578495\pi\)
−0.648292 + 0.761392i \(0.724516\pi\)
\(110\) 0 0
\(111\) −1.00000 1.73205i −0.0949158 0.164399i
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 3.00000 0.279751
\(116\) 0 0
\(117\) 5.00000 + 8.66025i 0.462250 + 0.800641i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −2.50000 + 4.33013i −0.225417 + 0.390434i
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −7.50000 + 12.9904i −0.665517 + 1.15271i 0.313627 + 0.949546i \(0.398456\pi\)
−0.979145 + 0.203164i \(0.934878\pi\)
\(128\) 0 0
\(129\) 5.50000 9.52628i 0.484248 0.838742i
\(130\) 0 0
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 7.50000 + 12.9904i 0.645497 + 1.11803i
\(136\) 0 0
\(137\) 2.50000 4.33013i 0.213589 0.369948i −0.739246 0.673436i \(-0.764818\pi\)
0.952835 + 0.303488i \(0.0981512\pi\)
\(138\) 0 0
\(139\) 7.50000 12.9904i 0.636142 1.10183i −0.350130 0.936701i \(-0.613863\pi\)
0.986272 0.165129i \(-0.0528040\pi\)
\(140\) 0 0
\(141\) 5.00000 0.421076
\(142\) 0 0
\(143\) −10.0000 + 17.3205i −0.836242 + 1.44841i
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) −3.50000 6.06218i −0.288675 0.500000i
\(148\) 0 0
\(149\) −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i \(-0.921474\pi\)
0.273377 0.961907i \(-0.411859\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 10.0000 0.808452
\(154\) 0 0
\(155\) 6.00000 + 10.3923i 0.481932 + 0.834730i
\(156\) 0 0
\(157\) −6.50000 11.2583i −0.518756 0.898513i −0.999762 0.0217953i \(-0.993062\pi\)
0.481006 0.876717i \(-0.340272\pi\)
\(158\) 0 0
\(159\) −9.00000 −0.713746
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 0 0
\(165\) −6.00000 + 10.3923i −0.467099 + 0.809040i
\(166\) 0 0
\(167\) 2.50000 4.33013i 0.193456 0.335075i −0.752937 0.658092i \(-0.771364\pi\)
0.946393 + 0.323017i \(0.104697\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −7.00000 + 5.19615i −0.535303 + 0.397360i
\(172\) 0 0
\(173\) −2.50000 4.33013i −0.190071 0.329213i 0.755202 0.655492i \(-0.227539\pi\)
−0.945274 + 0.326278i \(0.894205\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.50000 + 11.2583i −0.488570 + 0.846228i
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 3.50000 6.06218i 0.260153 0.450598i −0.706129 0.708083i \(-0.749560\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 0 0
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) 10.0000 + 17.3205i 0.731272 + 1.26660i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −7.50000 12.9904i −0.539862 0.935068i −0.998911 0.0466572i \(-0.985143\pi\)
0.459049 0.888411i \(-0.348190\pi\)
\(194\) 0 0
\(195\) −7.50000 12.9904i −0.537086 0.930261i
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) −1.50000 + 2.59808i −0.106332 + 0.184173i −0.914282 0.405079i \(-0.867244\pi\)
0.807950 + 0.589252i \(0.200577\pi\)
\(200\) 0 0
\(201\) −5.00000 −0.352673
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −7.50000 + 12.9904i −0.523823 + 0.907288i
\(206\) 0 0
\(207\) −1.00000 1.73205i −0.0695048 0.120386i
\(208\) 0 0
\(209\) −16.0000 6.92820i −1.10674 0.479234i
\(210\) 0 0
\(211\) 4.50000 + 7.79423i 0.309793 + 0.536577i 0.978317 0.207114i \(-0.0664070\pi\)
−0.668524 + 0.743690i \(0.733074\pi\)
\(212\) 0 0
\(213\) 0.500000 0.866025i 0.0342594 0.0593391i
\(214\) 0 0
\(215\) 16.5000 28.5788i 1.12529 1.94906i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −4.50000 + 7.79423i −0.304082 + 0.526685i
\(220\) 0 0
\(221\) −25.0000 −1.68168
\(222\) 0 0
\(223\) 5.50000 + 9.52628i 0.368307 + 0.637927i 0.989301 0.145889i \(-0.0466041\pi\)
−0.620994 + 0.783815i \(0.713271\pi\)
\(224\) 0 0
\(225\) 4.00000 + 6.92820i 0.266667 + 0.461880i
\(226\) 0 0
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.50000 9.52628i −0.360317 0.624087i 0.627696 0.778459i \(-0.283998\pi\)
−0.988013 + 0.154371i \(0.950665\pi\)
\(234\) 0 0
\(235\) 15.0000 0.978492
\(236\) 0 0
\(237\) 8.50000 14.7224i 0.552134 0.956325i
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 10.5000 18.1865i 0.676364 1.17150i −0.299704 0.954032i \(-0.596888\pi\)
0.976068 0.217465i \(-0.0697789\pi\)
\(242\) 0 0
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) 0 0
\(245\) −10.5000 18.1865i −0.670820 1.16190i
\(246\) 0 0
\(247\) 17.5000 12.9904i 1.11350 0.826558i
\(248\) 0 0
\(249\) −8.00000 13.8564i −0.506979 0.878114i
\(250\) 0 0
\(251\) −4.50000 + 7.79423i −0.284037 + 0.491967i −0.972375 0.233423i \(-0.925007\pi\)
0.688338 + 0.725390i \(0.258341\pi\)
\(252\) 0 0
\(253\) 2.00000 3.46410i 0.125739 0.217786i
\(254\) 0 0
\(255\) −15.0000 −0.939336
\(256\) 0 0
\(257\) 12.5000 21.6506i 0.779729 1.35053i −0.152370 0.988324i \(-0.548690\pi\)
0.932098 0.362206i \(-0.117976\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 0 0
\(263\) 9.50000 + 16.4545i 0.585795 + 1.01463i 0.994776 + 0.102084i \(0.0325510\pi\)
−0.408981 + 0.912543i \(0.634116\pi\)
\(264\) 0 0
\(265\) −27.0000 −1.65860
\(266\) 0 0
\(267\) −3.00000 −0.183597
\(268\) 0 0
\(269\) −8.50000 14.7224i −0.518254 0.897643i −0.999775 0.0212079i \(-0.993249\pi\)
0.481521 0.876435i \(-0.340085\pi\)
\(270\) 0 0
\(271\) −14.5000 25.1147i −0.880812 1.52561i −0.850439 0.526073i \(-0.823664\pi\)
−0.0303728 0.999539i \(-0.509669\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.00000 + 13.8564i −0.482418 + 0.835573i
\(276\) 0 0
\(277\) 30.0000 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) 0 0
\(279\) 4.00000 6.92820i 0.239474 0.414781i
\(280\) 0 0
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) 0 0
\(283\) −7.50000 12.9904i −0.445829 0.772198i 0.552281 0.833658i \(-0.313758\pi\)
−0.998110 + 0.0614601i \(0.980424\pi\)
\(284\) 0 0
\(285\) 10.5000 7.79423i 0.621966 0.461690i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) −6.50000 + 11.2583i −0.381037 + 0.659975i
\(292\) 0 0
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) −19.5000 + 33.7750i −1.13533 + 1.96646i
\(296\) 0 0
\(297\) 20.0000 1.16052
\(298\) 0 0
\(299\) 2.50000 + 4.33013i 0.144579 + 0.250418i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 19.0000 1.09152
\(304\) 0 0
\(305\) −3.00000 −0.171780
\(306\) 0 0
\(307\) −1.50000 2.59808i −0.0856095 0.148280i 0.820041 0.572304i \(-0.193950\pi\)
−0.905651 + 0.424024i \(0.860617\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) 2.50000 4.33013i 0.141308 0.244753i −0.786681 0.617359i \(-0.788202\pi\)
0.927990 + 0.372606i \(0.121536\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.5000 23.3827i 0.758236 1.31330i −0.185514 0.982642i \(-0.559395\pi\)
0.943750 0.330661i \(-0.107272\pi\)
\(318\) 0 0
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 0 0
\(323\) −2.50000 21.6506i −0.139104 1.20467i
\(324\) 0 0
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) 0 0
\(327\) −3.50000 + 6.06218i −0.193550 + 0.335239i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 0 0
\(333\) −2.00000 + 3.46410i −0.109599 + 0.189832i
\(334\) 0 0
\(335\) −15.0000 −0.819538
\(336\) 0 0
\(337\) −1.50000 2.59808i −0.0817102 0.141526i 0.822274 0.569091i \(-0.192705\pi\)
−0.903985 + 0.427565i \(0.859372\pi\)
\(338\) 0 0
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.50000 + 2.59808i 0.0807573 + 0.139876i
\(346\) 0 0
\(347\) 2.50000 + 4.33013i 0.134207 + 0.232453i 0.925294 0.379250i \(-0.123818\pi\)
−0.791087 + 0.611703i \(0.790485\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −12.5000 + 21.6506i −0.667201 + 1.15563i
\(352\) 0 0
\(353\) −10.0000 −0.532246 −0.266123 0.963939i \(-0.585743\pi\)
−0.266123 + 0.963939i \(0.585743\pi\)
\(354\) 0 0
\(355\) 1.50000 2.59808i 0.0796117 0.137892i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.50000 4.33013i −0.131945 0.228535i 0.792481 0.609896i \(-0.208789\pi\)
−0.924426 + 0.381361i \(0.875456\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 0 0
\(363\) 2.50000 + 4.33013i 0.131216 + 0.227273i
\(364\) 0 0
\(365\) −13.5000 + 23.3827i −0.706622 + 1.22391i
\(366\) 0 0
\(367\) 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i \(-0.791675\pi\)
0.923869 + 0.382709i \(0.125009\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) 1.50000 + 2.59808i 0.0774597 + 0.134164i
\(376\) 0 0
\(377\) 7.50000 + 12.9904i 0.386270 + 0.669039i
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) −15.0000 −0.768473
\(382\) 0 0
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −22.0000 −1.11832
\(388\) 0 0
\(389\) −8.50000 + 14.7224i −0.430967 + 0.746457i −0.996957 0.0779554i \(-0.975161\pi\)
0.565990 + 0.824412i \(0.308494\pi\)
\(390\) 0 0
\(391\) 5.00000 0.252861
\(392\) 0 0
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) 0 0
\(395\) 25.5000 44.1673i 1.28304 2.22230i
\(396\) 0 0
\(397\) 17.5000 + 30.3109i 0.878300 + 1.52126i 0.853206 + 0.521575i \(0.174655\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.50000 9.52628i −0.274657 0.475720i 0.695392 0.718631i \(-0.255231\pi\)
−0.970049 + 0.242911i \(0.921898\pi\)
\(402\) 0 0
\(403\) −10.0000 + 17.3205i −0.498135 + 0.862796i
\(404\) 0 0
\(405\) 1.50000 2.59808i 0.0745356 0.129099i
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) −3.50000 + 6.06218i −0.173064 + 0.299755i −0.939490 0.342578i \(-0.888700\pi\)
0.766426 + 0.642333i \(0.222033\pi\)
\(410\) 0 0
\(411\) 5.00000 0.246632
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −24.0000 41.5692i −1.17811 2.04055i
\(416\) 0 0
\(417\) 15.0000 0.734553
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −14.5000 25.1147i −0.706687 1.22402i −0.966079 0.258245i \(-0.916856\pi\)
0.259393 0.965772i \(-0.416478\pi\)
\(422\) 0 0
\(423\) −5.00000 8.66025i −0.243108 0.421076i
\(424\) 0 0
\(425\) −20.0000 −0.970143
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −20.0000 −0.965609
\(430\) 0 0
\(431\) 4.50000 7.79423i 0.216757 0.375435i −0.737057 0.675830i \(-0.763785\pi\)
0.953815 + 0.300395i \(0.0971186\pi\)
\(432\) 0 0
\(433\) 12.5000 21.6506i 0.600712 1.04046i −0.392002 0.919964i \(-0.628217\pi\)
0.992713 0.120499i \(-0.0384494\pi\)
\(434\) 0 0
\(435\) 4.50000 + 7.79423i 0.215758 + 0.373705i
\(436\) 0 0
\(437\) −3.50000 + 2.59808i −0.167428 + 0.124283i
\(438\) 0 0
\(439\) 3.50000 + 6.06218i 0.167046 + 0.289332i 0.937380 0.348309i \(-0.113244\pi\)
−0.770334 + 0.637641i \(0.779911\pi\)
\(440\) 0 0
\(441\) −7.00000 + 12.1244i −0.333333 + 0.577350i
\(442\) 0 0
\(443\) 7.50000 12.9904i 0.356336 0.617192i −0.631010 0.775775i \(-0.717359\pi\)
0.987346 + 0.158583i \(0.0506926\pi\)
\(444\) 0 0
\(445\) −9.00000 −0.426641
\(446\) 0 0
\(447\) 8.50000 14.7224i 0.402036 0.696347i
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 10.0000 + 17.3205i 0.470882 + 0.815591i
\(452\) 0 0
\(453\) 8.00000 + 13.8564i 0.375873 + 0.651031i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 0 0
\(459\) 12.5000 + 21.6506i 0.583450 + 1.01057i
\(460\) 0 0
\(461\) −0.500000 0.866025i −0.0232873 0.0403348i 0.854147 0.520032i \(-0.174080\pi\)
−0.877434 + 0.479697i \(0.840747\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 0 0
\(465\) −6.00000 + 10.3923i −0.278243 + 0.481932i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 6.50000 11.2583i 0.299504 0.518756i
\(472\) 0 0
\(473\) −22.0000 38.1051i −1.01156 1.75208i
\(474\) 0 0
\(475\) 14.0000 10.3923i 0.642364 0.476832i
\(476\) 0 0
\(477\) 9.00000 + 15.5885i 0.412082 + 0.713746i
\(478\) 0 0
\(479\) −13.5000 + 23.3827i −0.616831 + 1.06838i 0.373230 + 0.927739i \(0.378250\pi\)
−0.990060 + 0.140643i \(0.955083\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −19.5000 + 33.7750i −0.885449 + 1.53364i
\(486\) 0 0
\(487\) −40.0000 −1.81257 −0.906287 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 0 0
\(489\) 2.00000 + 3.46410i 0.0904431 + 0.156652i
\(490\) 0 0
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 24.0000 1.07872
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −17.5000 30.3109i −0.783408 1.35690i −0.929946 0.367697i \(-0.880146\pi\)
0.146538 0.989205i \(-0.453187\pi\)
\(500\) 0 0
\(501\) 5.00000 0.223384
\(502\) 0 0
\(503\) −7.50000 + 12.9904i −0.334408 + 0.579212i −0.983371 0.181608i \(-0.941870\pi\)
0.648963 + 0.760820i \(0.275203\pi\)
\(504\) 0 0
\(505\) 57.0000 2.53647
\(506\) 0 0
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 0 0
\(509\) −2.50000 + 4.33013i −0.110811 + 0.191930i −0.916097 0.400956i \(-0.868678\pi\)
0.805287 + 0.592886i \(0.202011\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −20.0000 8.66025i −0.883022 0.382360i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.0000 17.3205i 0.439799 0.761755i
\(518\) 0 0
\(519\) 2.50000 4.33013i 0.109738 0.190071i
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −14.5000 + 25.1147i −0.634041 + 1.09819i 0.352677 + 0.935745i \(0.385272\pi\)
−0.986718 + 0.162446i \(0.948062\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0000 + 17.3205i 0.435607 + 0.754493i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 26.0000 1.12830
\(532\) 0 0
\(533\) −25.0000 −1.08287
\(534\) 0 0
\(535\) 18.0000 + 31.1769i 0.778208 + 1.34790i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) −28.0000 −1.20605
\(540\) 0 0
\(541\) 5.50000 9.52628i 0.236463 0.409567i −0.723234 0.690604i \(-0.757345\pi\)
0.959697 + 0.281037i \(0.0906783\pi\)
\(542\) 0 0
\(543\) 7.00000 0.300399
\(544\) 0 0
\(545\) −10.5000 + 18.1865i −0.449771 + 0.779026i
\(546\) 0 0
\(547\) 3.50000 6.06218i 0.149649 0.259200i −0.781449 0.623970i \(-0.785519\pi\)
0.931098 + 0.364770i \(0.118852\pi\)
\(548\) 0 0
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) −10.5000 + 7.79423i −0.447315 + 0.332045i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 3.00000 5.19615i 0.127343 0.220564i
\(556\) 0 0
\(557\) −16.5000 + 28.5788i −0.699127 + 1.21092i 0.269642 + 0.962961i \(0.413095\pi\)
−0.968769 + 0.247964i \(0.920239\pi\)
\(558\) 0 0
\(559\) 55.0000 2.32625
\(560\) 0 0
\(561\) −10.0000 + 17.3205i −0.422200 + 0.731272i
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 9.00000 + 15.5885i 0.378633 + 0.655811i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) −8.00000 13.8564i −0.334205 0.578860i
\(574\) 0 0
\(575\) 2.00000 + 3.46410i 0.0834058 + 0.144463i
\(576\) 0 0
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 0 0
\(579\) 7.50000 12.9904i 0.311689 0.539862i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) 0 0
\(585\) −15.0000 + 25.9808i −0.620174 + 1.07417i
\(586\) 0 0
\(587\) 12.5000 + 21.6506i 0.515930 + 0.893617i 0.999829 + 0.0184934i \(0.00588696\pi\)
−0.483899 + 0.875124i \(0.660780\pi\)
\(588\) 0 0
\(589\) −16.0000 6.92820i −0.659269 0.285472i
\(590\) 0 0
\(591\) −5.00000 8.66025i −0.205673 0.356235i
\(592\) 0 0
\(593\) −17.5000 + 30.3109i −0.718639 + 1.24472i 0.242900 + 0.970051i \(0.421901\pi\)
−0.961539 + 0.274668i \(0.911432\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3.00000 −0.122782
\(598\) 0 0
\(599\) 12.5000 21.6506i 0.510736 0.884621i −0.489186 0.872179i \(-0.662706\pi\)
0.999923 0.0124417i \(-0.00396043\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 5.00000 + 8.66025i 0.203616 + 0.352673i
\(604\) 0 0
\(605\) 7.50000 + 12.9904i 0.304918 + 0.528134i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.5000 + 21.6506i 0.505696 + 0.875891i
\(612\) 0 0
\(613\) −0.500000 0.866025i −0.0201948 0.0349784i 0.855751 0.517387i \(-0.173095\pi\)
−0.875946 + 0.482409i \(0.839762\pi\)
\(614\) 0 0
\(615\) −15.0000 −0.604858
\(616\) 0 0
\(617\) −1.50000 + 2.59808i −0.0603877 + 0.104595i −0.894639 0.446790i \(-0.852567\pi\)
0.834251 + 0.551385i \(0.185900\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 2.50000 4.33013i 0.100322 0.173762i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) −2.00000 17.3205i −0.0798723 0.691714i
\(628\) 0 0
\(629\) −5.00000 8.66025i −0.199363 0.345307i
\(630\) 0 0
\(631\) 14.5000 25.1147i 0.577236 0.999802i −0.418559 0.908190i \(-0.637465\pi\)
0.995795 0.0916122i \(-0.0292020\pi\)
\(632\) 0 0
\(633\) −4.50000 + 7.79423i −0.178859 + 0.309793i
\(634\) 0 0
\(635\) −45.0000 −1.78577
\(636\) 0 0
\(637\) 17.5000 30.3109i 0.693375 1.20096i
\(638\) 0 0
\(639\) −2.00000 −0.0791188
\(640\) 0 0
\(641\) 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) 0 0
\(643\) 2.50000 + 4.33013i 0.0985904 + 0.170764i 0.911101 0.412182i \(-0.135233\pi\)
−0.812511 + 0.582946i \(0.801900\pi\)
\(644\) 0 0
\(645\) 33.0000 1.29937
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 26.0000 + 45.0333i 1.02059 + 1.76771i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 22.5000 38.9711i 0.879148 1.52273i
\(656\) 0 0
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) 9.50000 16.4545i 0.370067 0.640976i −0.619508 0.784990i \(-0.712668\pi\)
0.989576 + 0.144015i \(0.0460012\pi\)
\(660\) 0 0
\(661\) −14.5000 + 25.1147i −0.563985 + 0.976850i 0.433159 + 0.901318i \(0.357399\pi\)
−0.997143 + 0.0755324i \(0.975934\pi\)
\(662\) 0 0
\(663\) −12.5000 21.6506i −0.485460 0.840841i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.50000 2.59808i −0.0580802 0.100598i
\(668\) 0 0
\(669\) −5.50000 + 9.52628i −0.212642 + 0.368307i
\(670\) 0 0
\(671\) −2.00000 + 3.46410i −0.0772091 + 0.133730i
\(672\) 0 0
\(673\) 30.0000 1.15642 0.578208 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(674\) 0 0
\(675\) −10.0000 + 17.3205i −0.384900 + 0.666667i
\(676\) 0 0
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −6.00000 10.3923i −0.229920 0.398234i
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 15.0000 0.573121
\(686\) 0 0
\(687\) 11.0000 + 19.0526i 0.419676 + 0.726900i
\(688\) 0 0
\(689\) −22.5000 38.9711i −0.857182 1.48468i
\(690\) 0 0
\(691\) −36.0000 −1.36950 −0.684752 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 45.0000 1.70695
\(696\) 0 0
\(697\) −12.5000 + 21.6506i −0.473471 + 0.820076i
\(698\) 0 0
\(699\) 5.50000 9.52628i 0.208029 0.360317i
\(700\) 0 0
\(701\) 11.5000 + 19.9186i 0.434349 + 0.752315i 0.997242 0.0742151i \(-0.0236451\pi\)
−0.562893 + 0.826530i \(0.690312\pi\)
\(702\) 0 0
\(703\) 8.00000 + 3.46410i 0.301726 + 0.130651i
\(704\) 0 0
\(705\) 7.50000 + 12.9904i 0.282466 + 0.489246i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −8.50000 + 14.7224i −0.319224 + 0.552913i −0.980326 0.197383i \(-0.936756\pi\)
0.661102 + 0.750296i \(0.270089\pi\)
\(710\) 0 0
\(711\) −34.0000 −1.27510
\(712\) 0 0
\(713\) 2.00000 3.46410i 0.0749006 0.129732i
\(714\) 0 0
\(715\) −60.0000 −2.24387
\(716\) 0 0
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) 0 0
\(719\) 13.5000 + 23.3827i 0.503465 + 0.872027i 0.999992 + 0.00400572i \(0.00127506\pi\)
−0.496527 + 0.868021i \(0.665392\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 21.0000 0.780998
\(724\) 0 0
\(725\) 6.00000 + 10.3923i 0.222834 + 0.385961i
\(726\) 0 0
\(727\) −6.50000 11.2583i −0.241072 0.417548i 0.719948 0.694028i \(-0.244166\pi\)
−0.961020 + 0.276479i \(0.910832\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 27.5000 47.6314i 1.01712 1.76171i
\(732\) 0 0
\(733\) 6.00000 0.221615 0.110808 0.993842i \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) 0 0
\(735\) 10.5000 18.1865i 0.387298 0.670820i
\(736\) 0 0
\(737\) −10.0000 + 17.3205i −0.368355 + 0.638009i
\(738\) 0 0
\(739\) 18.5000 + 32.0429i 0.680534 + 1.17872i 0.974818 + 0.223001i \(0.0715853\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) 20.0000 + 8.66025i 0.734718 + 0.318142i
\(742\) 0 0
\(743\) −14.5000 25.1147i −0.531953 0.921370i −0.999304 0.0372984i \(-0.988125\pi\)
0.467351 0.884072i \(-0.345209\pi\)
\(744\) 0 0
\(745\) 25.5000 44.1673i 0.934248 1.61816i
\(746\) 0 0
\(747\) −16.0000 + 27.7128i −0.585409 + 1.01396i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) 0 0
\(753\) −9.00000 −0.327978
\(754\) 0 0
\(755\) 24.0000 + 41.5692i 0.873449 + 1.51286i
\(756\) 0 0
\(757\) 17.5000 + 30.3109i 0.636048 + 1.10167i 0.986292 + 0.165009i \(0.0527654\pi\)
−0.350244 + 0.936659i \(0.613901\pi\)
\(758\) 0 0
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 38.0000 1.37750 0.688749 0.724999i \(-0.258160\pi\)
0.688749 + 0.724999i \(0.258160\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 15.0000 + 25.9808i 0.542326 + 0.939336i
\(766\) 0 0
\(767\) −65.0000 −2.34701
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 0 0
\(771\) 25.0000 0.900353
\(772\) 0 0
\(773\) −12.5000 + 21.6506i −0.449594 + 0.778719i −0.998359 0.0572570i \(-0.981765\pi\)
0.548766 + 0.835976i \(0.315098\pi\)
\(774\) 0 0
\(775\) −8.00000 + 13.8564i −0.287368 + 0.497737i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.50000 21.6506i −0.0895718 0.775715i
\(780\) 0 0
\(781\) −2.00000 3.46410i −0.0715656 0.123955i
\(782\) 0 0
\(783\) 7.50000 12.9904i 0.268028 0.464238i
\(784\) 0 0
\(785\) 19.5000 33.7750i 0.695985 1.20548i
\(786\) 0 0
\(787\) −20.0000 −0.712923 −0.356462 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) 0 0
\(789\) −9.50000 + 16.4545i −0.338209 + 0.585795i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.50000 4.33013i −0.0887776 0.153767i
\(794\) 0 0
\(795\) −13.5000 23.3827i −0.478796 0.829298i
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 25.0000 0.884436