Properties

Label 76.2.e.a.45.1
Level $76$
Weight $2$
Character 76.45
Analytic conductor $0.607$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 45.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.2.e.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} -4.00000 q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-2.50000 + 4.33013i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{27} +(-3.50000 + 6.06218i) q^{29} +4.00000 q^{31} +(-2.00000 - 3.46410i) q^{33} +10.0000 q^{37} +1.00000 q^{39} +(2.50000 + 4.33013i) q^{41} +(2.50000 + 4.33013i) q^{43} +2.00000 q^{45} +(3.50000 - 6.06218i) q^{47} -7.00000 q^{49} +(1.50000 - 2.59808i) q^{51} +(-5.50000 + 9.52628i) q^{53} +(-2.00000 - 3.46410i) q^{55} +(-0.500000 - 4.33013i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +1.00000 q^{65} +(1.50000 - 2.59808i) q^{67} -5.00000 q^{69} +(-5.50000 - 9.52628i) q^{71} +(-7.50000 - 12.9904i) q^{73} +4.00000 q^{75} +(6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{85} -7.00000 q^{87} +(-1.50000 + 2.59808i) q^{89} +(2.00000 + 3.46410i) q^{93} +(-0.500000 - 4.33013i) q^{95} +(2.50000 + 4.33013i) q^{97} +(-4.00000 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + q^{5} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} + q^{5} + 2 q^{9} - 8 q^{11} + q^{13} - q^{15} - 3 q^{17} - 8 q^{19} - 5 q^{23} + 4 q^{25} + 10 q^{27} - 7 q^{29} + 8 q^{31} - 4 q^{33} + 20 q^{37} + 2 q^{39} + 5 q^{41} + 5 q^{43} + 4 q^{45} + 7 q^{47} - 14 q^{49} + 3 q^{51} - 11 q^{53} - 4 q^{55} - q^{57} - 3 q^{59} - 11 q^{61} + 2 q^{65} + 3 q^{67} - 10 q^{69} - 11 q^{71} - 15 q^{73} + 8 q^{75} + 13 q^{79} - q^{81} + 3 q^{85} - 14 q^{87} - 3 q^{89} + 4 q^{93} - q^{95} + 5 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 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 \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) −0.500000 + 0.866025i −0.129099 + 0.223607i
\(16\) 0 0
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −4.00000 1.73205i −0.917663 0.397360i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.50000 + 4.33013i −0.521286 + 0.902894i 0.478407 + 0.878138i \(0.341214\pi\)
−0.999694 + 0.0247559i \(0.992119\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −3.50000 + 6.06218i −0.649934 + 1.12572i 0.333205 + 0.942855i \(0.391870\pi\)
−0.983138 + 0.182864i \(0.941463\pi\)
\(30\) 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
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 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
\(43\) 2.50000 + 4.33013i 0.381246 + 0.660338i 0.991241 0.132068i \(-0.0421616\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) 0 0
\(47\) 3.50000 6.06218i 0.510527 0.884260i −0.489398 0.872060i \(-0.662783\pi\)
0.999926 0.0121990i \(-0.00388317\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 1.50000 2.59808i 0.210042 0.363803i
\(52\) 0 0
\(53\) −5.50000 + 9.52628i −0.755483 + 1.30854i 0.189651 + 0.981852i \(0.439264\pi\)
−0.945134 + 0.326683i \(0.894069\pi\)
\(54\) 0 0
\(55\) −2.00000 3.46410i −0.269680 0.467099i
\(56\) 0 0
\(57\) −0.500000 4.33013i −0.0662266 0.573539i
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) 0 0
\(69\) −5.00000 −0.601929
\(70\) 0 0
\(71\) −5.50000 9.52628i −0.652730 1.13056i −0.982458 0.186485i \(-0.940290\pi\)
0.329728 0.944076i \(-0.393043\pi\)
\(72\) 0 0
\(73\) −7.50000 12.9904i −0.877809 1.52041i −0.853740 0.520699i \(-0.825671\pi\)
−0.0240681 0.999710i \(-0.507662\pi\)
\(74\) 0 0
\(75\) 4.00000 0.461880
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i \(0.0944227\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 1.50000 2.59808i 0.162698 0.281801i
\(86\) 0 0
\(87\) −7.00000 −0.750479
\(88\) 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
\(95\) −0.500000 4.33013i −0.0512989 0.444262i
\(96\) 0 0
\(97\) 2.50000 + 4.33013i 0.253837 + 0.439658i 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −4.00000 + 6.92820i −0.402015 + 0.696311i
\(100\) 0 0
\(101\) 0.500000 0.866025i 0.0497519 0.0861727i −0.840077 0.542467i \(-0.817490\pi\)
0.889829 + 0.456294i \(0.150824\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20.0000 1.93347 0.966736 0.255774i \(-0.0823304\pi\)
0.966736 + 0.255774i \(0.0823304\pi\)
\(108\) 0 0
\(109\) −1.50000 2.59808i −0.143674 0.248851i 0.785203 0.619238i \(-0.212558\pi\)
−0.928877 + 0.370387i \(0.879225\pi\)
\(110\) 0 0
\(111\) 5.00000 + 8.66025i 0.474579 + 0.821995i
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −5.00000 −0.466252
\(116\) 0 0
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) 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
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 1.50000 2.59808i 0.133103 0.230542i −0.791768 0.610822i \(-0.790839\pi\)
0.924871 + 0.380280i \(0.124172\pi\)
\(128\) 0 0
\(129\) −2.50000 + 4.33013i −0.220113 + 0.381246i
\(130\) 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
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 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
\(139\) −4.50000 + 7.79423i −0.381685 + 0.661098i −0.991303 0.131597i \(-0.957989\pi\)
0.609618 + 0.792695i \(0.291323\pi\)
\(140\) 0 0
\(141\) 7.00000 0.589506
\(142\) 0 0
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) 0 0
\(145\) −7.00000 −0.581318
\(146\) 0 0
\(147\) −3.50000 6.06218i −0.288675 0.500000i
\(148\) 0 0
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 2.00000 + 3.46410i 0.160644 + 0.278243i
\(156\) 0 0
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) 0 0
\(159\) −11.0000 −0.872357
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 2.00000 3.46410i 0.155700 0.269680i
\(166\) 0 0
\(167\) 7.50000 12.9904i 0.580367 1.00523i −0.415068 0.909790i \(-0.636242\pi\)
0.995436 0.0954356i \(-0.0304244\pi\)
\(168\) 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
\(173\) −7.50000 12.9904i −0.570214 0.987640i −0.996544 0.0830722i \(-0.973527\pi\)
0.426329 0.904568i \(-0.359807\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.50000 2.59808i 0.112747 0.195283i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.50000 4.33013i 0.185824 0.321856i −0.758030 0.652219i \(-0.773838\pi\)
0.943854 + 0.330364i \(0.107171\pi\)
\(182\) 0 0
\(183\) −11.0000 −0.813143
\(184\) 0 0
\(185\) 5.00000 + 8.66025i 0.367607 + 0.636715i
\(186\) 0 0
\(187\) 6.00000 + 10.3923i 0.438763 + 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 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
\(195\) 0.500000 + 0.866025i 0.0358057 + 0.0620174i
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) 3.00000 0.211604
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.50000 + 4.33013i −0.174608 + 0.302429i
\(206\) 0 0
\(207\) 5.00000 + 8.66025i 0.347524 + 0.601929i
\(208\) 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
\(213\) 5.50000 9.52628i 0.376854 0.652730i
\(214\) 0 0
\(215\) −2.50000 + 4.33013i −0.170499 + 0.295312i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 7.50000 12.9904i 0.506803 0.877809i
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 12.5000 + 21.6506i 0.837062 + 1.44983i 0.892341 + 0.451363i \(0.149062\pi\)
−0.0552786 + 0.998471i \(0.517605\pi\)
\(224\) 0 0
\(225\) −4.00000 6.92820i −0.266667 0.461880i
\(226\) 0 0
\(227\) −20.0000 −1.32745 −0.663723 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i \(0.0747909\pi\)
−0.284645 + 0.958633i \(0.591876\pi\)
\(234\) 0 0
\(235\) 7.00000 0.456630
\(236\) 0 0
\(237\) −6.50000 + 11.2583i −0.422220 + 0.731307i
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) 0 0
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) 0 0
\(245\) −3.50000 6.06218i −0.223607 0.387298i
\(246\) 0 0
\(247\) −3.50000 + 2.59808i −0.222700 + 0.165312i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.5000 26.8468i 0.978351 1.69455i 0.309951 0.950753i \(-0.399687\pi\)
0.668400 0.743802i \(-0.266979\pi\)
\(252\) 0 0
\(253\) 10.0000 17.3205i 0.628695 1.08893i
\(254\) 0 0
\(255\) 3.00000 0.187867
\(256\) 0 0
\(257\) −11.5000 + 19.9186i −0.717350 + 1.24249i 0.244696 + 0.969600i \(0.421312\pi\)
−0.962046 + 0.272887i \(0.912021\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 7.00000 + 12.1244i 0.433289 + 0.750479i
\(262\) 0 0
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 0 0
\(265\) −11.0000 −0.675725
\(266\) 0 0
\(267\) −3.00000 −0.183597
\(268\) 0 0
\(269\) −13.5000 23.3827i −0.823110 1.42567i −0.903356 0.428892i \(-0.858904\pi\)
0.0802460 0.996775i \(-0.474429\pi\)
\(270\) 0 0
\(271\) −15.5000 26.8468i −0.941558 1.63083i −0.762501 0.646988i \(-0.776029\pi\)
−0.179057 0.983839i \(-0.557305\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.00000 + 13.8564i −0.482418 + 0.835573i
\(276\) 0 0
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 0 0
\(279\) 4.00000 6.92820i 0.239474 0.414781i
\(280\) 0 0
\(281\) −3.50000 + 6.06218i −0.208792 + 0.361639i −0.951334 0.308160i \(-0.900287\pi\)
0.742542 + 0.669800i \(0.233620\pi\)
\(282\) 0 0
\(283\) 4.50000 + 7.79423i 0.267497 + 0.463319i 0.968215 0.250120i \(-0.0804700\pi\)
−0.700718 + 0.713439i \(0.747137\pi\)
\(284\) 0 0
\(285\) 3.50000 2.59808i 0.207322 0.153897i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) −2.50000 + 4.33013i −0.146553 + 0.253837i
\(292\) 0 0
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) 1.50000 2.59808i 0.0873334 0.151266i
\(296\) 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
\(303\) 1.00000 0.0574485
\(304\) 0 0
\(305\) −11.0000 −0.629858
\(306\) 0 0
\(307\) −13.5000 23.3827i −0.770486 1.33452i −0.937297 0.348532i \(-0.886680\pi\)
0.166811 0.985989i \(-0.446653\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) −5.50000 + 9.52628i −0.310878 + 0.538457i −0.978553 0.205996i \(-0.933957\pi\)
0.667674 + 0.744453i \(0.267290\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.50000 + 12.9904i −0.421242 + 0.729612i −0.996061 0.0886679i \(-0.971739\pi\)
0.574819 + 0.818280i \(0.305072\pi\)
\(318\) 0 0
\(319\) 14.0000 24.2487i 0.783850 1.35767i
\(320\) 0 0
\(321\) 10.0000 + 17.3205i 0.558146 + 0.966736i
\(322\) 0 0
\(323\) 1.50000 + 12.9904i 0.0834622 + 0.722804i
\(324\) 0 0
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) 0 0
\(327\) 1.50000 2.59808i 0.0829502 0.143674i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 10.0000 17.3205i 0.547997 0.949158i
\(334\) 0 0
\(335\) 3.00000 0.163908
\(336\) 0 0
\(337\) 2.50000 + 4.33013i 0.136184 + 0.235877i 0.926049 0.377403i \(-0.123183\pi\)
−0.789865 + 0.613280i \(0.789850\pi\)
\(338\) 0 0
\(339\) 7.00000 + 12.1244i 0.380188 + 0.658505i
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.50000 4.33013i −0.134595 0.233126i
\(346\) 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
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 2.50000 4.33013i 0.133440 0.231125i
\(352\) 0 0
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 0 0
\(355\) 5.50000 9.52628i 0.291910 0.505602i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.50000 12.9904i −0.395835 0.685606i 0.597372 0.801964i \(-0.296211\pi\)
−0.993207 + 0.116358i \(0.962878\pi\)
\(360\) 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
\(365\) 7.50000 12.9904i 0.392568 0.679948i
\(366\) 0 0
\(367\) −12.5000 + 21.6506i −0.652495 + 1.13015i 0.330021 + 0.943974i \(0.392944\pi\)
−0.982516 + 0.186180i \(0.940389\pi\)
\(368\) 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 \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 4.50000 + 7.79423i 0.232379 + 0.402492i
\(376\) 0 0
\(377\) 3.50000 + 6.06218i 0.180259 + 0.312218i
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 3.00000 0.153695
\(382\) 0 0
\(383\) 14.5000 + 25.1147i 0.740915 + 1.28330i 0.952079 + 0.305852i \(0.0989414\pi\)
−0.211164 + 0.977451i \(0.567725\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.0000 0.508329
\(388\) 0 0
\(389\) −1.50000 + 2.59808i −0.0760530 + 0.131728i −0.901544 0.432688i \(-0.857565\pi\)
0.825491 + 0.564416i \(0.190898\pi\)
\(390\) 0 0
\(391\) 15.0000 0.758583
\(392\) 0 0
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) 0 0
\(395\) −6.50000 + 11.2583i −0.327050 + 0.566468i
\(396\) 0 0
\(397\) 12.5000 + 21.6506i 0.627357 + 1.08661i 0.988080 + 0.153941i \(0.0491966\pi\)
−0.360723 + 0.932673i \(0.617470\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.50000 16.4545i −0.474407 0.821698i 0.525163 0.851002i \(-0.324004\pi\)
−0.999571 + 0.0293039i \(0.990671\pi\)
\(402\) 0 0
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) 0 0
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) 8.50000 14.7224i 0.420298 0.727977i −0.575670 0.817682i \(-0.695259\pi\)
0.995968 + 0.0897044i \(0.0285922\pi\)
\(410\) 0 0
\(411\) 5.00000 0.246632
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −9.00000 −0.440732
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) 0 0
\(423\) −7.00000 12.1244i −0.340352 0.589506i
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) −10.5000 + 18.1865i −0.505767 + 0.876014i 0.494211 + 0.869342i \(0.335457\pi\)
−0.999978 + 0.00667224i \(0.997876\pi\)
\(432\) 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
\(435\) −3.50000 6.06218i −0.167812 0.290659i
\(436\) 0 0
\(437\) 17.5000 12.9904i 0.837139 0.621414i
\(438\) 0 0
\(439\) 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) −7.00000 + 12.1244i −0.333333 + 0.577350i
\(442\) 0 0
\(443\) −12.5000 + 21.6506i −0.593893 + 1.02865i 0.399809 + 0.916598i \(0.369076\pi\)
−0.993702 + 0.112054i \(0.964257\pi\)
\(444\) 0 0
\(445\) −3.00000 −0.142214
\(446\) 0 0
\(447\) 1.50000 2.59808i 0.0709476 0.122885i
\(448\) 0 0
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) 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
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) −7.50000 12.9904i −0.350070 0.606339i
\(460\) 0 0
\(461\) −5.50000 9.52628i −0.256161 0.443683i 0.709050 0.705159i \(-0.249124\pi\)
−0.965210 + 0.261476i \(0.915791\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 0 0
\(465\) −2.00000 + 3.46410i −0.0927478 + 0.160644i
\(466\) 0 0
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.50000 6.06218i 0.161271 0.279330i
\(472\) 0 0
\(473\) −10.0000 17.3205i −0.459800 0.796398i
\(474\) 0 0
\(475\) −14.0000 + 10.3923i −0.642364 + 0.476832i
\(476\) 0 0
\(477\) 11.0000 + 19.0526i 0.503655 + 0.872357i
\(478\) 0 0
\(479\) 11.5000 19.9186i 0.525448 0.910103i −0.474112 0.880464i \(-0.657231\pi\)
0.999561 0.0296389i \(-0.00943575\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.50000 + 4.33013i −0.113519 + 0.196621i
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 0 0
\(489\) −2.00000 3.46410i −0.0904431 0.156652i
\(490\) 0 0
\(491\) 0.500000 + 0.866025i 0.0225647 + 0.0390832i 0.877087 0.480331i \(-0.159483\pi\)
−0.854523 + 0.519414i \(0.826150\pi\)
\(492\) 0 0
\(493\) 21.0000 0.945792
\(494\) 0 0
\(495\) −8.00000 −0.359573
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2.50000 + 4.33013i 0.111915 + 0.193843i 0.916542 0.399937i \(-0.130968\pi\)
−0.804627 + 0.593780i \(0.797635\pi\)
\(500\) 0 0
\(501\) 15.0000 0.670151
\(502\) 0 0
\(503\) −10.5000 + 18.1865i −0.468172 + 0.810897i −0.999338 0.0363700i \(-0.988421\pi\)
0.531167 + 0.847267i \(0.321754\pi\)
\(504\) 0 0
\(505\) 1.00000 0.0444994
\(506\) 0 0
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 0 0
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) 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
\(517\) −14.0000 + 24.2487i −0.615719 + 1.06646i
\(518\) 0 0
\(519\) 7.50000 12.9904i 0.329213 0.570214i
\(520\) 0 0
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 0 0
\(523\) 9.50000 16.4545i 0.415406 0.719504i −0.580065 0.814570i \(-0.696973\pi\)
0.995471 + 0.0950659i \(0.0303062\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 5.00000 0.216574
\(534\) 0 0
\(535\) 10.0000 + 17.3205i 0.432338 + 0.748831i
\(536\) 0 0
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 0 0
\(539\) 28.0000 1.20605
\(540\) 0 0
\(541\) 0.500000 0.866025i 0.0214967 0.0372333i −0.855077 0.518501i \(-0.826490\pi\)
0.876574 + 0.481268i \(0.159824\pi\)
\(542\) 0 0
\(543\) 5.00000 0.214571
\(544\) 0 0
\(545\) 1.50000 2.59808i 0.0642529 0.111289i
\(546\) 0 0
\(547\) −12.5000 + 21.6506i −0.534461 + 0.925714i 0.464728 + 0.885454i \(0.346152\pi\)
−0.999189 + 0.0402607i \(0.987181\pi\)
\(548\) 0 0
\(549\) 11.0000 + 19.0526i 0.469469 + 0.813143i
\(550\) 0 0
\(551\) 24.5000 18.1865i 1.04374 0.774772i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −5.00000 + 8.66025i −0.212238 + 0.367607i
\(556\) 0 0
\(557\) 2.50000 4.33013i 0.105928 0.183473i −0.808189 0.588924i \(-0.799552\pi\)
0.914117 + 0.405450i \(0.132885\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) 0 0
\(561\) −6.00000 + 10.3923i −0.253320 + 0.438763i
\(562\) 0 0
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) 7.00000 + 12.1244i 0.294492 + 0.510075i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 8.00000 + 13.8564i 0.334205 + 0.578860i
\(574\) 0 0
\(575\) 10.0000 + 17.3205i 0.417029 + 0.722315i
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) 7.50000 12.9904i 0.311689 0.539862i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 22.0000 38.1051i 0.911147 1.57815i
\(584\) 0 0
\(585\) 1.00000 1.73205i 0.0413449 0.0716115i
\(586\) 0 0
\(587\) −7.50000 12.9904i −0.309558 0.536170i 0.668708 0.743525i \(-0.266848\pi\)
−0.978266 + 0.207355i \(0.933514\pi\)
\(588\) 0 0
\(589\) −16.0000 6.92820i −0.659269 0.285472i
\(590\) 0 0
\(591\) 1.00000 + 1.73205i 0.0411345 + 0.0712470i
\(592\) 0 0
\(593\) 2.50000 4.33013i 0.102663 0.177817i −0.810118 0.586267i \(-0.800597\pi\)
0.912781 + 0.408450i \(0.133930\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.00000 0.286491
\(598\) 0 0
\(599\) −22.5000 + 38.9711i −0.919325 + 1.59232i −0.118882 + 0.992908i \(0.537931\pi\)
−0.800443 + 0.599409i \(0.795402\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) −3.00000 5.19615i −0.122169 0.211604i
\(604\) 0 0
\(605\) 2.50000 + 4.33013i 0.101639 + 0.176045i
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.50000 6.06218i −0.141595 0.245249i
\(612\) 0 0
\(613\) 14.5000 + 25.1147i 0.585649 + 1.01437i 0.994794 + 0.101905i \(0.0324938\pi\)
−0.409145 + 0.912470i \(0.634173\pi\)
\(614\) 0 0
\(615\) −5.00000 −0.201619
\(616\) 0 0
\(617\) 22.5000 38.9711i 0.905816 1.56892i 0.0859976 0.996295i \(-0.472592\pi\)
0.819818 0.572624i \(-0.194074\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) −12.5000 + 21.6506i −0.501608 + 0.868810i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 2.00000 + 17.3205i 0.0798723 + 0.691714i
\(628\) 0 0
\(629\) −15.0000 25.9808i −0.598089 1.03592i
\(630\) 0 0
\(631\) −20.5000 + 35.5070i −0.816092 + 1.41351i 0.0924489 + 0.995717i \(0.470531\pi\)
−0.908541 + 0.417796i \(0.862803\pi\)
\(632\) 0 0
\(633\) −4.50000 + 7.79423i −0.178859 + 0.309793i
\(634\) 0 0
\(635\) 3.00000 0.119051
\(636\) 0 0
\(637\) −3.50000 + 6.06218i −0.138675 + 0.240192i
\(638\) 0 0
\(639\) −22.0000 −0.870307
\(640\) 0 0
\(641\) −19.5000 33.7750i −0.770204 1.33403i −0.937451 0.348117i \(-0.886821\pi\)
0.167247 0.985915i \(-0.446512\pi\)
\(642\) 0 0
\(643\) −9.50000 16.4545i −0.374643 0.648901i 0.615630 0.788035i \(-0.288902\pi\)
−0.990274 + 0.139134i \(0.955568\pi\)
\(644\) 0 0
\(645\) −5.00000 −0.196875
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) 6.00000 + 10.3923i 0.235521 + 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 0 0
\(655\) 7.50000 12.9904i 0.293049 0.507576i
\(656\) 0 0
\(657\) −30.0000 −1.17041
\(658\) 0 0
\(659\) −2.50000 + 4.33013i −0.0973862 + 0.168678i −0.910602 0.413284i \(-0.864382\pi\)
0.813216 + 0.581962i \(0.197715\pi\)
\(660\) 0 0
\(661\) −15.5000 + 26.8468i −0.602880 + 1.04422i 0.389503 + 0.921025i \(0.372647\pi\)
−0.992383 + 0.123194i \(0.960686\pi\)
\(662\) 0 0
\(663\) −1.50000 2.59808i −0.0582552 0.100901i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −17.5000 30.3109i −0.677603 1.17364i
\(668\) 0 0
\(669\) −12.5000 + 21.6506i −0.483278 + 0.837062i
\(670\) 0 0
\(671\) 22.0000 38.1051i 0.849301 1.47103i
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 0 0
\(675\) 10.0000 17.3205i 0.384900 0.666667i
\(676\) 0 0
\(677\) 10.0000 0.384331 0.192166 0.981363i \(-0.438449\pi\)
0.192166 + 0.981363i \(0.438449\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −10.0000 17.3205i −0.383201 0.663723i
\(682\) 0 0
\(683\) 16.0000 0.612223 0.306111 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(684\) 0 0
\(685\) 5.00000 0.191040
\(686\) 0 0
\(687\) 1.00000 + 1.73205i 0.0381524 + 0.0660819i
\(688\) 0 0
\(689\) 5.50000 + 9.52628i 0.209533 + 0.362922i
\(690\) 0 0
\(691\) 36.0000 1.36950 0.684752 0.728776i \(-0.259910\pi\)
0.684752 + 0.728776i \(0.259910\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.00000 −0.341389
\(696\) 0 0
\(697\) 7.50000 12.9904i 0.284083 0.492046i
\(698\) 0 0
\(699\) −10.5000 + 18.1865i −0.397146 + 0.687878i
\(700\) 0 0
\(701\) −17.5000 30.3109i −0.660966 1.14483i −0.980362 0.197205i \(-0.936813\pi\)
0.319396 0.947621i \(-0.396520\pi\)
\(702\) 0 0
\(703\) −40.0000 17.3205i −1.50863 0.653255i
\(704\) 0 0
\(705\) 3.50000 + 6.06218i 0.131818 + 0.228315i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.50000 + 2.59808i −0.0563337 + 0.0975728i −0.892817 0.450420i \(-0.851274\pi\)
0.836483 + 0.547992i \(0.184608\pi\)
\(710\) 0 0
\(711\) 26.0000 0.975076
\(712\) 0 0
\(713\) −10.0000 + 17.3205i −0.374503 + 0.648658i
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 0 0
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) 0 0
\(719\) −3.50000 6.06218i −0.130528 0.226081i 0.793352 0.608763i \(-0.208334\pi\)
−0.923880 + 0.382682i \(0.875001\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −19.0000 −0.706618
\(724\) 0 0
\(725\) 14.0000 + 24.2487i 0.519947 + 0.900575i
\(726\) 0 0
\(727\) −3.50000 6.06218i −0.129808 0.224834i 0.793794 0.608186i \(-0.208103\pi\)
−0.923602 + 0.383353i \(0.874769\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 7.50000 12.9904i 0.277398 0.480467i
\(732\) 0 0
\(733\) −30.0000 −1.10808 −0.554038 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) 0 0
\(735\) 3.50000 6.06218i 0.129099 0.223607i
\(736\) 0 0
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) 0 0
\(739\) 6.50000 + 11.2583i 0.239106 + 0.414144i 0.960458 0.278425i \(-0.0898122\pi\)
−0.721352 + 0.692569i \(0.756479\pi\)
\(740\) 0 0
\(741\) −4.00000 1.73205i −0.146944 0.0636285i
\(742\) 0 0
\(743\) 12.5000 + 21.6506i 0.458581 + 0.794285i 0.998886 0.0471840i \(-0.0150247\pi\)
−0.540306 + 0.841469i \(0.681691\pi\)
\(744\) 0 0
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i \(0.344142\pi\)
−0.999424 + 0.0339490i \(0.989192\pi\)
\(752\) 0 0
\(753\) 31.0000 1.12970
\(754\) 0 0
\(755\) −8.00000 13.8564i −0.291150 0.504286i
\(756\) 0 0
\(757\) 8.50000 + 14.7224i 0.308938 + 0.535096i 0.978130 0.207993i \(-0.0666932\pi\)
−0.669193 + 0.743089i \(0.733360\pi\)
\(758\) 0 0
\(759\) 20.0000 0.725954
\(760\) 0 0
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) 0 0
\(767\) −3.00000 −0.108324
\(768\) 0 0
\(769\) −3.50000 + 6.06218i −0.126213 + 0.218608i −0.922207 0.386698i \(-0.873616\pi\)
0.795993 + 0.605305i \(0.206949\pi\)
\(770\) 0 0
\(771\) −23.0000 −0.828325
\(772\) 0 0
\(773\) 10.5000 18.1865i 0.377659 0.654124i −0.613062 0.790034i \(-0.710063\pi\)
0.990721 + 0.135910i \(0.0433959\pi\)
\(774\) 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
\(781\) 22.0000 + 38.1051i 0.787222 + 1.36351i
\(782\) 0 0
\(783\) −17.5000 + 30.3109i −0.625399 + 1.08322i
\(784\) 0 0
\(785\) 3.50000 6.06218i 0.124920 0.216368i
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 0 0
\(789\) −4.50000 + 7.79423i −0.160204 + 0.277482i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 5.50000 + 9.52628i 0.195311 + 0.338288i
\(794\) 0 0
\(795\) −5.50000 9.52628i −0.195065 0.337862i
\(796\) 0 0
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\)