Properties

Label 136.3.p.a.19.1
Level $136$
Weight $3$
Character 136.19
Analytic conductor $3.706$
Analytic rank $0$
Dimension $4$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.p (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.70573159530\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{8}]$

Embedding invariants

Embedding label 19.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 136.19
Dual form 136.3.p.a.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +O(q^{10})\) \(q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +(-17.9497 - 7.43503i) q^{11} +(-9.17157 - 22.1421i) q^{12} -16.0000 q^{16} +(-11.2929 + 12.7071i) q^{17} +53.7990 q^{18} +(12.0000 + 12.0000i) q^{19} +(-14.8701 - 35.8995i) q^{22} +(18.3431 - 44.2843i) q^{24} +(-17.6777 + 17.6777i) q^{25} +(-41.0416 + 99.0833i) q^{27} +(-22.6274 - 22.6274i) q^{32} +116.409 q^{33} +(-33.9411 + 2.00000i) q^{34} +(76.0833 + 76.0833i) q^{36} +33.9411i q^{38} +(-6.32233 + 15.2635i) q^{41} +(-35.4264 + 35.4264i) q^{43} +(29.7401 - 71.7990i) q^{44} +(88.5685 - 36.6863i) q^{48} +(-34.6482 - 34.6482i) q^{49} -50.0000 q^{50} +(33.3762 - 96.2340i) q^{51} +(-198.167 + 82.0833i) q^{54} +(-93.9411 - 38.9117i) q^{57} +(-1.42641 + 1.42641i) q^{59} -64.0000i q^{64} +(164.627 + 164.627i) q^{66} +127.841 q^{67} +(-50.8284 - 45.1716i) q^{68} +215.196i q^{72} +(45.2340 + 109.205i) q^{73} +(57.3223 - 138.388i) q^{75} +(-48.0000 + 48.0000i) q^{76} -400.487i q^{81} +(-30.5269 + 12.6447i) q^{82} +(53.5442 + 53.5442i) q^{83} -100.201 q^{86} +(143.598 - 59.4802i) q^{88} +31.2376i q^{89} +(177.137 + 73.3726i) q^{96} +(73.7660 + 178.087i) q^{97} -98.0000i q^{98} +(-482.839 + 199.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9} + O(q^{10}) \) \( 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9} - 52 q^{11} - 48 q^{12} - 64 q^{16} - 48 q^{17} + 136 q^{18} + 48 q^{19} + 48 q^{22} + 96 q^{24} - 68 q^{27} + 64 q^{33} + 112 q^{36} - 96 q^{41} + 28 q^{43} - 96 q^{44} + 128 q^{48} - 200 q^{50} - 56 q^{51} - 408 q^{54} - 240 q^{57} + 164 q^{59} + 568 q^{66} + 336 q^{67} - 192 q^{68} + 48 q^{73} + 300 q^{75} - 192 q^{76} + 8 q^{82} + 316 q^{83} - 480 q^{86} + 416 q^{88} + 256 q^{96} + 428 q^{97} - 1080 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 + 1.41421i 0.707107 + 0.707107i
\(3\) −5.53553 + 2.29289i −1.84518 + 0.764298i −0.902369 + 0.430964i \(0.858173\pi\)
−0.942809 + 0.333333i \(0.891827\pi\)
\(4\) 4.00000i 1.00000i
\(5\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(6\) −11.0711 4.58579i −1.84518 0.764298i
\(7\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(8\) −5.65685 + 5.65685i −0.707107 + 0.707107i
\(9\) 19.0208 19.0208i 2.11342 2.11342i
\(10\) 0 0
\(11\) −17.9497 7.43503i −1.63180 0.675912i −0.636364 0.771389i \(-0.719562\pi\)
−0.995432 + 0.0954775i \(0.969562\pi\)
\(12\) −9.17157 22.1421i −0.764298 1.84518i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −16.0000 −1.00000
\(17\) −11.2929 + 12.7071i −0.664288 + 0.747477i
\(18\) 53.7990 2.98883
\(19\) 12.0000 + 12.0000i 0.631579 + 0.631579i 0.948464 0.316885i \(-0.102637\pi\)
−0.316885 + 0.948464i \(0.602637\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −14.8701 35.8995i −0.675912 1.63180i
\(23\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(24\) 18.3431 44.2843i 0.764298 1.84518i
\(25\) −17.6777 + 17.6777i −0.707107 + 0.707107i
\(26\) 0 0
\(27\) −41.0416 + 99.0833i −1.52006 + 3.66975i
\(28\) 0 0
\(29\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(30\) 0 0
\(31\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(32\) −22.6274 22.6274i −0.707107 0.707107i
\(33\) 116.409 3.52755
\(34\) −33.9411 + 2.00000i −0.998268 + 0.0588235i
\(35\) 0 0
\(36\) 76.0833 + 76.0833i 2.11342 + 2.11342i
\(37\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(38\) 33.9411i 0.893188i
\(39\) 0 0
\(40\) 0 0
\(41\) −6.32233 + 15.2635i −0.154203 + 0.372279i −0.982036 0.188696i \(-0.939574\pi\)
0.827832 + 0.560976i \(0.189574\pi\)
\(42\) 0 0
\(43\) −35.4264 + 35.4264i −0.823870 + 0.823870i −0.986661 0.162791i \(-0.947950\pi\)
0.162791 + 0.986661i \(0.447950\pi\)
\(44\) 29.7401 71.7990i 0.675912 1.63180i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 88.5685 36.6863i 1.84518 0.764298i
\(49\) −34.6482 34.6482i −0.707107 0.707107i
\(50\) −50.0000 −1.00000
\(51\) 33.3762 96.2340i 0.654434 1.88694i
\(52\) 0 0
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) −198.167 + 82.0833i −3.66975 + 1.52006i
\(55\) 0 0
\(56\) 0 0
\(57\) −93.9411 38.9117i −1.64809 0.682661i
\(58\) 0 0
\(59\) −1.42641 + 1.42641i −0.0241764 + 0.0241764i −0.719092 0.694915i \(-0.755442\pi\)
0.694915 + 0.719092i \(0.255442\pi\)
\(60\) 0 0
\(61\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 64.0000i 1.00000i
\(65\) 0 0
\(66\) 164.627 + 164.627i 2.49435 + 2.49435i
\(67\) 127.841 1.90807 0.954034 0.299697i \(-0.0968855\pi\)
0.954034 + 0.299697i \(0.0968855\pi\)
\(68\) −50.8284 45.1716i −0.747477 0.664288i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(72\) 215.196i 2.98883i
\(73\) 45.2340 + 109.205i 0.619644 + 1.49595i 0.852118 + 0.523350i \(0.175318\pi\)
−0.232473 + 0.972603i \(0.574682\pi\)
\(74\) 0 0
\(75\) 57.3223 138.388i 0.764298 1.84518i
\(76\) −48.0000 + 48.0000i −0.631579 + 0.631579i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(80\) 0 0
\(81\) 400.487i 4.94429i
\(82\) −30.5269 + 12.6447i −0.372279 + 0.154203i
\(83\) 53.5442 + 53.5442i 0.645110 + 0.645110i 0.951807 0.306697i \(-0.0992238\pi\)
−0.306697 + 0.951807i \(0.599224\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −100.201 −1.16513
\(87\) 0 0
\(88\) 143.598 59.4802i 1.63180 0.675912i
\(89\) 31.2376i 0.350984i 0.984481 + 0.175492i \(0.0561516\pi\)
−0.984481 + 0.175492i \(0.943848\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 177.137 + 73.3726i 1.84518 + 0.764298i
\(97\) 73.7660 + 178.087i 0.760474 + 1.83595i 0.484536 + 0.874771i \(0.338988\pi\)
0.275938 + 0.961175i \(0.411012\pi\)
\(98\) 98.0000i 1.00000i
\(99\) −482.839 + 199.999i −4.87716 + 2.02019i
\(100\) −70.7107 70.7107i −0.707107 0.707107i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 183.296 88.8944i 1.79702 0.871514i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −68.0675 164.329i −0.636145 1.53579i −0.831776 0.555112i \(-0.812675\pi\)
0.195631 0.980678i \(-0.437325\pi\)
\(108\) −396.333 164.167i −3.66975 1.52006i
\(109\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −139.175 57.6482i −1.23164 0.510161i −0.330547 0.943790i \(-0.607233\pi\)
−0.901092 + 0.433628i \(0.857233\pi\)
\(114\) −77.8234 187.882i −0.682661 1.64809i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −4.03449 −0.0341906
\(119\) 0 0
\(120\) 0 0
\(121\) 181.354 + 181.354i 1.49879 + 1.49879i
\(122\) 0 0
\(123\) 98.9878i 0.804779i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 90.5097 90.5097i 0.707107 0.707107i
\(129\) 114.875 277.333i 0.890505 2.14987i
\(130\) 0 0
\(131\) 15.3589 + 37.0797i 0.117244 + 0.283051i 0.971597 0.236641i \(-0.0760466\pi\)
−0.854354 + 0.519692i \(0.826047\pi\)
\(132\) 465.637i 3.52755i
\(133\) 0 0
\(134\) 180.794 + 180.794i 1.34921 + 1.34921i
\(135\) 0 0
\(136\) −8.00000 135.765i −0.0588235 0.998268i
\(137\) −135.765 −0.990982 −0.495491 0.868613i \(-0.665012\pi\)
−0.495491 + 0.868613i \(0.665012\pi\)
\(138\) 0 0
\(139\) 86.5061 35.8320i 0.622346 0.257784i −0.0491511 0.998791i \(-0.515652\pi\)
0.671497 + 0.741007i \(0.265652\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −304.333 + 304.333i −2.11342 + 2.11342i
\(145\) 0 0
\(146\) −90.4680 + 218.409i −0.619644 + 1.49595i
\(147\) 271.241 + 112.352i 1.84518 + 0.764298i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 276.777 114.645i 1.84518 0.764298i
\(151\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(152\) −135.765 −0.893188
\(153\) 26.8995 + 456.500i 0.175814 + 2.98366i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 566.375 566.375i 3.49614 3.49614i
\(163\) 29.1558 70.3883i 0.178870 0.431830i −0.808860 0.588001i \(-0.799915\pi\)
0.987730 + 0.156171i \(0.0499150\pi\)
\(164\) −61.0538 25.2893i −0.372279 0.154203i
\(165\) 0 0
\(166\) 151.446i 0.912324i
\(167\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 0 0
\(171\) 456.500 2.66959
\(172\) −141.706 141.706i −0.823870 0.823870i
\(173\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 287.196 + 118.960i 1.63180 + 0.675912i
\(177\) 4.62532 11.1665i 0.0261318 0.0630877i
\(178\) −44.1766 + 44.1766i −0.248183 + 0.248183i
\(179\) −252.000 + 252.000i −1.40782 + 1.40782i −0.636755 + 0.771066i \(0.719724\pi\)
−0.771066 + 0.636755i \(0.780276\pi\)
\(180\) 0 0
\(181\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 297.182 144.126i 1.58921 0.770729i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 146.745 + 354.274i 0.764298 + 1.84518i
\(193\) 353.324 + 146.352i 1.83070 + 0.758299i 0.967234 + 0.253886i \(0.0817088\pi\)
0.863462 + 0.504413i \(0.168291\pi\)
\(194\) −147.532 + 356.174i −0.760474 + 1.83595i
\(195\) 0 0
\(196\) 138.593 138.593i 0.707107 0.707107i
\(197\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(198\) −965.678 399.997i −4.87716 2.02019i
\(199\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(200\) 200.000i 1.00000i
\(201\) −707.666 + 293.125i −3.52073 + 1.45833i
\(202\) 0 0
\(203\) 0 0
\(204\) 384.936 + 133.505i 1.88694 + 0.654434i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −126.177 304.617i −0.603716 1.45750i
\(210\) 0 0
\(211\) 132.094 318.903i 0.626038 1.51139i −0.218469 0.975844i \(-0.570106\pi\)
0.844507 0.535545i \(-0.179894\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 136.135 328.659i 0.636145 1.53579i
\(215\) 0 0
\(216\) −328.333 792.666i −1.52006 3.66975i
\(217\) 0 0
\(218\) 0 0
\(219\) −500.789 500.789i −2.28671 2.28671i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 0 0
\(225\) 672.487i 2.98883i
\(226\) −115.296 278.350i −0.510161 1.23164i
\(227\) −85.2584 35.3152i −0.375588 0.155574i 0.186900 0.982379i \(-0.440156\pi\)
−0.562488 + 0.826805i \(0.690156\pi\)
\(228\) 155.647 375.765i 0.682661 1.64809i
\(229\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 123.558 + 298.295i 0.530291 + 1.28024i 0.931330 + 0.364175i \(0.118649\pi\)
−0.401039 + 0.916061i \(0.631351\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.70563 5.70563i −0.0241764 0.0241764i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −321.589 + 133.207i −1.33440 + 0.552725i −0.931906 0.362700i \(-0.881855\pi\)
−0.402490 + 0.915425i \(0.631855\pi\)
\(242\) 512.946i 2.11961i
\(243\) 548.900 + 1325.16i 2.25885 + 5.45334i
\(244\) 0 0
\(245\) 0 0
\(246\) 139.990 139.990i 0.569065 0.569065i
\(247\) 0 0
\(248\) 0 0
\(249\) −419.167 173.624i −1.68340 0.697287i
\(250\) 0 0
\(251\) 197.512i 0.786899i −0.919346 0.393450i \(-0.871282\pi\)
0.919346 0.393450i \(-0.128718\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) −362.706 362.706i −1.41131 1.41131i −0.750973 0.660333i \(-0.770415\pi\)
−0.660333 0.750973i \(-0.729585\pi\)
\(258\) 554.666 229.750i 2.14987 0.890505i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −30.7178 + 74.1594i −0.117244 + 0.283051i
\(263\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(264\) −658.510 + 658.510i −2.49435 + 2.49435i
\(265\) 0 0
\(266\) 0 0
\(267\) −71.6245 172.917i −0.268256 0.647628i
\(268\) 511.362i 1.90807i
\(269\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 180.686 203.314i 0.664288 0.747477i
\(273\) 0 0
\(274\) −192.000 192.000i −0.700730 0.700730i
\(275\) 448.744 185.876i 1.63180 0.675912i
\(276\) 0 0
\(277\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(278\) 173.012 + 71.6640i 0.622346 + 0.257784i
\(279\) 0 0
\(280\) 0 0
\(281\) 360.000 360.000i 1.28114 1.28114i 0.341118 0.940020i \(-0.389194\pi\)
0.940020 0.341118i \(-0.110806\pi\)
\(282\) 0 0
\(283\) 128.009 + 53.0229i 0.452327 + 0.187360i 0.597204 0.802090i \(-0.296278\pi\)
−0.144876 + 0.989450i \(0.546278\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −860.784 −2.98883
\(289\) −33.9411 287.000i −0.117443 0.993080i
\(290\) 0 0
\(291\) −816.668 816.668i −2.80642 2.80642i
\(292\) −436.818 + 180.936i −1.49595 + 0.619644i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 224.704 + 542.482i 0.764298 + 1.84518i
\(295\) 0 0
\(296\) 0 0
\(297\) 1473.37 1473.37i 4.96085 4.96085i
\(298\) 0 0
\(299\) 0 0
\(300\) 553.553 + 229.289i 1.84518 + 0.764298i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −192.000 192.000i −0.631579 0.631579i
\(305\) 0 0
\(306\) −607.546 + 683.630i −1.98545 + 2.23408i
\(307\) −542.000 −1.76547 −0.882736 0.469869i \(-0.844301\pi\)
−0.882736 + 0.469869i \(0.844301\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(312\) 0 0
\(313\) −42.9691 + 103.737i −0.137281 + 0.331427i −0.977537 0.210764i \(-0.932405\pi\)
0.840256 + 0.542191i \(0.182405\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 753.580 + 753.580i 2.34760 + 2.34760i
\(322\) 0 0
\(323\) −288.000 + 16.9706i −0.891641 + 0.0525404i
\(324\) 1601.95 4.94429
\(325\) 0 0
\(326\) 140.777 58.3116i 0.431830 0.178870i
\(327\) 0 0
\(328\) −50.5786 122.108i −0.154203 0.372279i
\(329\) 0 0
\(330\) 0 0
\(331\) −323.926 + 323.926i −0.978628 + 0.978628i −0.999776 0.0211480i \(-0.993268\pi\)
0.0211480 + 0.999776i \(0.493268\pi\)
\(332\) −214.177 + 214.177i −0.645110 + 0.645110i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 236.589 97.9985i 0.702046 0.290797i −0.00296297 0.999996i \(-0.500943\pi\)
0.705009 + 0.709199i \(0.250943\pi\)
\(338\) −239.002 239.002i −0.707107 0.707107i
\(339\) 902.590 2.66251
\(340\) 0 0
\(341\) 0 0
\(342\) 645.588 + 645.588i 1.88768 + 1.88768i
\(343\) 0 0
\(344\) 400.804i 1.16513i
\(345\) 0 0
\(346\) 0 0
\(347\) −264.947 + 639.638i −0.763535 + 1.84334i −0.317892 + 0.948127i \(0.602975\pi\)
−0.445643 + 0.895211i \(0.647025\pi\)
\(348\) 0 0
\(349\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 237.921 + 574.392i 0.675912 + 1.63180i
\(353\) 617.179i 1.74838i −0.485583 0.874191i \(-0.661392\pi\)
0.485583 0.874191i \(-0.338608\pi\)
\(354\) 22.3330 9.25065i 0.0630877 0.0261318i
\(355\) 0 0
\(356\) −124.950 −0.350984
\(357\) 0 0
\(358\) −712.764 −1.99096
\(359\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(360\) 0 0
\(361\) 73.0000i 0.202216i
\(362\) 0 0
\(363\) −1419.72 588.065i −3.91106 1.62001i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(368\) 0 0
\(369\) 170.067 + 410.579i 0.460888 + 1.11268i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 624.105 + 216.454i 1.66873 + 0.578753i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 195.317 + 471.538i 0.515349 + 1.24416i 0.940733 + 0.339149i \(0.110139\pi\)
−0.425383 + 0.905013i \(0.639861\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) −293.490 + 708.548i −0.764298 + 1.84518i
\(385\) 0 0
\(386\) 292.704 + 706.649i 0.758299 + 1.83070i
\(387\) 1347.68i 3.48237i
\(388\) −712.347 + 295.064i −1.83595 + 0.760474i
\(389\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 392.000 1.00000
\(393\) −170.040 170.040i −0.432671 0.432671i
\(394\) 0 0
\(395\) 0 0
\(396\) −799.994 1931.36i −2.02019 4.87716i
\(397\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 282.843 282.843i 0.707107 0.707107i
\(401\) −28.1781 + 68.0280i −0.0702696 + 0.169646i −0.955112 0.296244i \(-0.904266\pi\)
0.884843 + 0.465890i \(0.154266\pi\)
\(402\) −1415.33 586.250i −3.52073 1.45833i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 355.578 + 733.186i 0.871514 + 1.79702i
\(409\) −291.826 −0.713512 −0.356756 0.934198i \(-0.616117\pi\)
−0.356756 + 0.934198i \(0.616117\pi\)
\(410\) 0 0
\(411\) 751.529 311.294i 1.82854 0.757405i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −396.698 + 396.698i −0.951315 + 0.951315i
\(418\) 252.353 609.235i 0.603716 1.45750i
\(419\) 383.200 + 158.726i 0.914557 + 0.378822i 0.789799 0.613365i \(-0.210185\pi\)
0.124758 + 0.992187i \(0.460185\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 637.806 264.188i 1.51139 0.626038i
\(423\) 0 0
\(424\) 0 0
\(425\) −25.0000 424.264i −0.0588235 0.998268i
\(426\) 0 0
\(427\) 0 0
\(428\) 657.318 272.270i 1.53579 0.636145i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(432\) 656.666 1585.33i 1.52006 3.66975i
\(433\) −456.000 + 456.000i −1.05312 + 1.05312i −0.0546100 + 0.998508i \(0.517392\pi\)
−0.998508 + 0.0546100i \(0.982608\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1416.44i 3.23389i
\(439\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(440\) 0 0
\(441\) −1318.08 −2.98883
\(442\) 0 0
\(443\) 704.840 1.59106 0.795530 0.605914i \(-0.207192\pi\)
0.795530 + 0.605914i \(0.207192\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 210.823 508.971i 0.469538 1.13357i −0.494827 0.868992i \(-0.664769\pi\)
0.964365 0.264574i \(-0.0852315\pi\)
\(450\) −951.041 + 951.041i −2.11342 + 2.11342i
\(451\) 226.968 226.968i 0.503256 0.503256i
\(452\) 230.593 556.701i 0.510161 1.23164i
\(453\) 0 0
\(454\) −70.6304 170.517i −0.155574 0.375588i
\(455\) 0 0
\(456\) 751.529 311.294i 1.64809 0.682661i
\(457\) 624.000 + 624.000i 1.36543 + 1.36543i 0.866840 + 0.498587i \(0.166148\pi\)
0.498587 + 0.866840i \(0.333852\pi\)
\(458\) 0 0
\(459\) −795.583 1640.46i −1.73330 3.57398i
\(460\) 0 0
\(461\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −247.116 + 596.590i −0.530291 + 1.28024i
\(467\) −660.000 + 660.000i −1.41328 + 1.41328i −0.680898 + 0.732379i \(0.738410\pi\)
−0.732379 + 0.680898i \(0.761590\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 16.1380i 0.0341906i
\(473\) 899.291 372.499i 1.90125 0.787524i
\(474\) 0 0
\(475\) −424.264 −0.893188
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −643.179 266.413i −1.33440 0.552725i
\(483\) 0 0
\(484\) −725.415 + 725.415i −1.49879 + 1.49879i
\(485\) 0 0
\(486\) −1097.80 + 2650.32i −2.25885 + 5.45334i
\(487\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(488\) 0 0
\(489\) 456.488i 0.933514i
\(490\) 0 0
\(491\) 420.000 + 420.000i 0.855397 + 0.855397i 0.990792 0.135395i \(-0.0432302\pi\)
−0.135395 + 0.990792i \(0.543230\pi\)
\(492\) 395.951 0.804779
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −347.249 838.333i −0.697287 1.68340i
\(499\) 474.550 + 196.565i 0.951002 + 0.393918i 0.803607 0.595160i \(-0.202911\pi\)
0.147394 + 0.989078i \(0.452911\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 279.324 279.324i 0.556422 0.556422i
\(503\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 935.505 387.499i 1.84518 0.764298i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 362.039 + 362.039i 0.707107 + 0.707107i
\(513\) −1681.50 + 696.500i −3.27778 + 1.35770i
\(514\) 1025.89i 1.99589i
\(515\) 0 0
\(516\) 1109.33 + 459.500i 2.14987 + 0.890505i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 954.675 + 395.439i 1.83239 + 0.759000i 0.965451 + 0.260584i \(0.0839152\pi\)
0.866938 + 0.498416i \(0.166085\pi\)
\(522\) 0 0
\(523\) 965.428i 1.84594i −0.384868 0.922972i \(-0.625753\pi\)
0.384868 0.922972i \(-0.374247\pi\)
\(524\) −148.319 + 61.4356i −0.283051 + 0.117244i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1862.55 −3.52755
\(529\) 374.059 + 374.059i 0.707107 + 0.707107i
\(530\) 0 0
\(531\) 54.2628i 0.102190i
\(532\) 0 0
\(533\) 0 0
\(534\) 143.249 345.833i 0.268256 0.647628i
\(535\) 0 0
\(536\) −723.176 + 723.176i −1.34921 + 1.34921i
\(537\) 817.145 1972.76i 1.52169 3.67368i
\(538\) 0 0
\(539\) 364.316 + 879.538i 0.675912 + 1.63180i
\(540\) 0 0
\(541\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 543.058 32.0000i 0.998268 0.0588235i
\(545\) 0 0
\(546\) 0 0
\(547\) −694.493 + 287.668i −1.26964 + 0.525902i −0.912855 0.408284i \(-0.866127\pi\)
−0.356785 + 0.934186i \(0.616127\pi\)
\(548\) 543.058i 0.990982i
\(549\) 0 0
\(550\) 897.487 + 371.751i 1.63180 + 0.675912i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 143.328 + 346.024i 0.257784 + 0.622346i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −1314.60 + 1479.22i −2.34331 + 2.63676i
\(562\) 1018.23 1.81180
\(563\) 664.543 + 664.543i 1.18036 + 1.18036i 0.979651 + 0.200710i \(0.0643251\pi\)
0.200710 + 0.979651i \(0.435675\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 106.046 + 256.017i 0.187360 + 0.452327i
\(567\) 0 0
\(568\) 0 0
\(569\) −162.176 + 162.176i −0.285019 + 0.285019i −0.835107 0.550088i \(-0.814594\pi\)
0.550088 + 0.835107i \(0.314594\pi\)
\(570\) 0 0
\(571\) −95.9477 + 231.638i −0.168034 + 0.405671i −0.985356 0.170511i \(-0.945458\pi\)
0.817321 + 0.576182i \(0.195458\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −1217.33 1217.33i −2.11342 2.11342i
\(577\) 2.00000 0.00346620 0.00173310 0.999998i \(-0.499448\pi\)
0.00173310 + 0.999998i \(0.499448\pi\)
\(578\) 357.879 453.879i 0.619168 0.785258i
\(579\) −2291.41 −3.95753
\(580\) 0 0
\(581\) 0 0
\(582\) 2309.89i 3.96888i
\(583\) 0 0
\(584\) −873.637 361.872i −1.49595 0.619644i
\(585\) 0 0
\(586\) 0 0
\(587\) −804.688 + 804.688i −1.37085 + 1.37085i −0.511659 + 0.859189i \(0.670969\pi\)
−0.859189 + 0.511659i \(0.829031\pi\)
\(588\) −449.407 + 1084.96i −0.764298 + 1.84518i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −23.7065 23.7065i −0.0399772 0.0399772i 0.686836 0.726813i \(-0.258999\pi\)
−0.726813 + 0.686836i \(0.758999\pi\)
\(594\) 4167.33 7.01571
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 458.579 + 1107.11i 0.764298 + 1.84518i
\(601\) −343.175 142.148i −0.571007 0.236519i 0.0784489 0.996918i \(-0.475003\pi\)
−0.649456 + 0.760399i \(0.725003\pi\)
\(602\) 0 0
\(603\) 2431.63 2431.63i 4.03256 4.03256i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(608\) 543.058i 0.893188i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1826.00 + 107.598i −2.98366 + 0.175814i
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −766.504 766.504i −1.24838 1.24838i
\(615\) 0 0
\(616\) 0 0
\(617\) −292.057 705.087i −0.473349 1.14277i −0.962674 0.270665i \(-0.912757\pi\)
0.489324 0.872102i \(-0.337243\pi\)
\(618\) 0 0
\(619\) 307.697 742.846i 0.497087 1.20007i −0.453958 0.891023i \(-0.649988\pi\)
0.951045 0.309052i \(-0.100012\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000i 1.00000i
\(626\) −207.473 + 85.9382i −0.331427 + 0.137281i
\(627\) 1396.91 + 1396.91i 2.22793 + 2.22793i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(632\) 0 0
\(633\) 2068.18i 3.26726i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.55696 8.58727i −0.00554908 0.0133967i 0.921081 0.389372i \(-0.127308\pi\)
−0.926630 + 0.375975i \(0.877308\pi\)
\(642\) 2131.45i 3.32001i
\(643\) −886.214 + 367.082i −1.37825 + 0.570889i −0.944012 0.329910i \(-0.892982\pi\)
−0.434236 + 0.900799i \(0.642982\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −431.294 383.294i −0.667637 0.593334i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 2265.50 + 2265.50i 3.49614 + 3.49614i
\(649\) 36.2090 14.9983i 0.0557920 0.0231098i
\(650\) 0 0
\(651\) 0 0
\(652\) 281.553 + 116.623i 0.431830 + 0.178870i
\(653\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 101.157 244.215i 0.154203 0.372279i
\(657\) 2937.55 + 1216.77i 4.47115 + 1.85201i
\(658\) 0 0
\(659\) 994.000i 1.50835i 0.656676 + 0.754173i \(0.271962\pi\)
−0.656676 + 0.754173i \(0.728038\pi\)
\(660\) 0 0
\(661\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(662\) −916.201 −1.38399
\(663\) 0 0
\(664\) −605.783 −0.912324
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 365.969 883.528i 0.543788 1.31282i −0.378244 0.925706i \(-0.623472\pi\)
0.922032 0.387114i \(-0.126528\pi\)
\(674\) 473.179 + 195.997i 0.702046 + 0.290797i
\(675\) −1026.04 2477.08i −1.52006 3.66975i
\(676\) 676.000i 1.00000i
\(677\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(678\) 1276.45 + 1276.45i 1.88268 + 1.88268i
\(679\) 0 0
\(680\) 0 0
\(681\) 552.925 0.811931
\(682\) 0 0
\(683\) −801.714 + 332.081i −1.17381 + 0.486209i −0.882451 0.470404i \(-0.844108\pi\)
−0.291362 + 0.956613i \(0.594108\pi\)
\(684\) 1826.00i 2.66959i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 566.823 566.823i 0.823870 0.823870i
\(689\) 0 0
\(690\) 0 0
\(691\) 212.508 + 88.0238i 0.307537 + 0.127386i 0.531114 0.847300i \(-0.321773\pi\)
−0.223577 + 0.974686i \(0.571773\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1279.28 + 529.894i −1.84334 + 0.763535i
\(695\) 0 0
\(696\) 0 0
\(697\) −122.557 252.707i −0.175835 0.362564i
\(698\) 0 0
\(699\) −1367.92 1367.92i −1.95696 1.95696i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −475.842 + 1148.78i −0.675912 + 1.63180i
\(705\) 0 0
\(706\) 872.823 872.823i 1.23629 1.23629i
\(707\) 0 0
\(708\) 44.6661 + 18.5013i 0.0630877 + 0.0261318i
\(709\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −176.706 176.706i −0.248183 0.248183i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1008.00 1008.00i −1.40782 1.40782i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 103.238 103.238i 0.142988 0.142988i
\(723\) 1474.74 1474.74i 2.03975 2.03975i
\(724\) 0 0
\(725\) 0 0
\(726\) −1176.13 2839.43i −1.62001 3.91106i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −3528.22 3528.22i −4.83981 4.83981i
\(730\) 0 0
\(731\) −50.1005 850.234i −0.0685369 1.16311i
\(732\) 0 0
\(733\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2294.71 950.499i −3.11358 1.28969i
\(738\) −340.135 + 821.159i −0.460888 + 1.11268i
\(739\) −227.688 + 227.688i −0.308103 + 0.308103i −0.844173 0.536070i \(-0.819908\pi\)
0.536070 + 0.844173i \(0.319908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2036.91 2.72678
\(748\) 576.505 + 1188.73i 0.770729 + 1.58921i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(752\) 0 0
\(753\) 452.873 + 1093.33i 0.601425 + 1.45197i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) −390.635 + 943.075i −0.515349 + 1.24416i
\(759\) 0 0
\(760\) 0 0
\(761\) 610.940i 0.802812i 0.915900 + 0.401406i \(0.131478\pi\)
−0.915900 + 0.401406i \(0.868522\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1417.10 + 586.981i −1.84518 + 0.764298i
\(769\) 1120.06i 1.45651i −0.685306 0.728256i \(-0.740331\pi\)
0.685306 0.728256i \(-0.259669\pi\)
\(770\) 0 0
\(771\) 2839.41 + 1176.12i 3.68277 + 1.52545i
\(772\) −585.407 + 1413.30i −0.758299 + 1.83070i
\(773\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(774\) −1905.90 + 1905.90i −2.46241 + 2.46241i
\(775\) 0 0
\(776\) −1424.69 590.128i −1.83595 0.760474i
\(777\) 0 0
\(778\) 0 0
\(779\) −259.029 + 107.294i −0.332515 + 0.137732i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 554.372 + 554.372i 0.707107 + 0.707107i
\(785\) 0 0
\(786\) 480.944i 0.611889i
\(787\) −585.610 1413.79i −0.744104 1.79643i −0.588310 0.808635i \(-0.700207\pi\)
−0.155794 0.987790i \(-0.549793\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1599.99 3862.71i 2.02019 4.87716i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0