Properties

Label 1200.2.v.a.257.1
Level $1200$
Weight $2$
Character 1200.257
Analytic conductor $9.582$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.58204824255\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 257.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1200.257
Dual form 1200.2.v.a.593.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70711 + 0.292893i) q^{3} +(-2.00000 - 2.00000i) q^{7} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(-1.70711 + 0.292893i) q^{3} +(-2.00000 - 2.00000i) q^{7} +(2.82843 - 1.00000i) q^{9} -5.65685i q^{11} +(-2.82843 + 2.82843i) q^{17} +4.00000i q^{19} +(4.00000 + 2.82843i) q^{21} +(4.24264 + 4.24264i) q^{23} +(-4.53553 + 2.53553i) q^{27} +5.65685 q^{29} -8.00000 q^{31} +(1.65685 + 9.65685i) q^{33} +(-8.00000 - 8.00000i) q^{37} +5.65685i q^{41} +(-2.00000 + 2.00000i) q^{43} +(-1.41421 + 1.41421i) q^{47} +1.00000i q^{49} +(4.00000 - 5.65685i) q^{51} +(-5.65685 - 5.65685i) q^{53} +(-1.17157 - 6.82843i) q^{57} -5.65685 q^{59} -6.00000 q^{61} +(-7.65685 - 3.65685i) q^{63} +(-6.00000 - 6.00000i) q^{67} +(-8.48528 - 6.00000i) q^{69} +11.3137i q^{71} +(-8.00000 + 8.00000i) q^{73} +(-11.3137 + 11.3137i) q^{77} +(7.00000 - 5.65685i) q^{81} +(9.89949 + 9.89949i) q^{83} +(-9.65685 + 1.65685i) q^{87} -11.3137 q^{89} +(13.6569 - 2.34315i) q^{93} +(8.00000 + 8.00000i) q^{97} +(-5.65685 - 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 8 q^{7} + 16 q^{21} - 4 q^{27} - 32 q^{31} - 16 q^{33} - 32 q^{37} - 8 q^{43} + 16 q^{51} - 16 q^{57} - 24 q^{61} - 8 q^{63} - 24 q^{67} - 32 q^{73} + 28 q^{81} - 16 q^{87} + 32 q^{93} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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
\(3\) −1.70711 + 0.292893i −0.985599 + 0.169102i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.00000 2.00000i −0.755929 0.755929i 0.219650 0.975579i \(-0.429509\pi\)
−0.975579 + 0.219650i \(0.929509\pi\)
\(8\) 0 0
\(9\) 2.82843 1.00000i 0.942809 0.333333i
\(10\) 0 0
\(11\) 5.65685i 1.70561i −0.522233 0.852803i \(-0.674901\pi\)
0.522233 0.852803i \(-0.325099\pi\)
\(12\) 0 0
\(13\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.82843 + 2.82843i −0.685994 + 0.685994i −0.961344 0.275350i \(-0.911206\pi\)
0.275350 + 0.961344i \(0.411206\pi\)
\(18\) 0 0
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 0 0
\(21\) 4.00000 + 2.82843i 0.872872 + 0.617213i
\(22\) 0 0
\(23\) 4.24264 + 4.24264i 0.884652 + 0.884652i 0.994003 0.109351i \(-0.0348774\pi\)
−0.109351 + 0.994003i \(0.534877\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.53553 + 2.53553i −0.872864 + 0.487964i
\(28\) 0 0
\(29\) 5.65685 1.05045 0.525226 0.850963i \(-0.323981\pi\)
0.525226 + 0.850963i \(0.323981\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 0 0
\(33\) 1.65685 + 9.65685i 0.288421 + 1.68104i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.00000 8.00000i −1.31519 1.31519i −0.917534 0.397658i \(-0.869823\pi\)
−0.397658 0.917534i \(-0.630177\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.65685i 0.883452i 0.897150 + 0.441726i \(0.145634\pi\)
−0.897150 + 0.441726i \(0.854366\pi\)
\(42\) 0 0
\(43\) −2.00000 + 2.00000i −0.304997 + 0.304997i −0.842965 0.537968i \(-0.819192\pi\)
0.537968 + 0.842965i \(0.319192\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.41421 + 1.41421i −0.206284 + 0.206284i −0.802686 0.596402i \(-0.796597\pi\)
0.596402 + 0.802686i \(0.296597\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 4.00000 5.65685i 0.560112 0.792118i
\(52\) 0 0
\(53\) −5.65685 5.65685i −0.777029 0.777029i 0.202296 0.979324i \(-0.435160\pi\)
−0.979324 + 0.202296i \(0.935160\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.17157 6.82843i −0.155179 0.904447i
\(58\) 0 0
\(59\) −5.65685 −0.736460 −0.368230 0.929735i \(-0.620036\pi\)
−0.368230 + 0.929735i \(0.620036\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) −7.65685 3.65685i −0.964673 0.460720i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.00000 6.00000i −0.733017 0.733017i 0.238200 0.971216i \(-0.423443\pi\)
−0.971216 + 0.238200i \(0.923443\pi\)
\(68\) 0 0
\(69\) −8.48528 6.00000i −1.02151 0.722315i
\(70\) 0 0
\(71\) 11.3137i 1.34269i 0.741145 + 0.671345i \(0.234283\pi\)
−0.741145 + 0.671345i \(0.765717\pi\)
\(72\) 0 0
\(73\) −8.00000 + 8.00000i −0.936329 + 0.936329i −0.998091 0.0617617i \(-0.980328\pi\)
0.0617617 + 0.998091i \(0.480328\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.3137 + 11.3137i −1.28932 + 1.28932i
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 7.00000 5.65685i 0.777778 0.628539i
\(82\) 0 0
\(83\) 9.89949 + 9.89949i 1.08661 + 1.08661i 0.995875 + 0.0907357i \(0.0289219\pi\)
0.0907357 + 0.995875i \(0.471078\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.65685 + 1.65685i −1.03532 + 0.177633i
\(88\) 0 0
\(89\) −11.3137 −1.19925 −0.599625 0.800281i \(-0.704684\pi\)
−0.599625 + 0.800281i \(0.704684\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 13.6569 2.34315i 1.41615 0.242973i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.00000 + 8.00000i 0.812277 + 0.812277i 0.984975 0.172698i \(-0.0552484\pi\)
−0.172698 + 0.984975i \(0.555248\pi\)
\(98\) 0 0
\(99\) −5.65685 16.0000i −0.568535 1.60806i
\(100\) 0 0
\(101\) 5.65685i 0.562878i −0.959579 0.281439i \(-0.909188\pi\)
0.959579 0.281439i \(-0.0908117\pi\)
\(102\) 0 0
\(103\) −6.00000 + 6.00000i −0.591198 + 0.591198i −0.937955 0.346757i \(-0.887283\pi\)
0.346757 + 0.937955i \(0.387283\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.24264 4.24264i 0.410152 0.410152i −0.471640 0.881791i \(-0.656338\pi\)
0.881791 + 0.471640i \(0.156338\pi\)
\(108\) 0 0
\(109\) 10.0000i 0.957826i 0.877862 + 0.478913i \(0.158969\pi\)
−0.877862 + 0.478913i \(0.841031\pi\)
\(110\) 0 0
\(111\) 16.0000 + 11.3137i 1.51865 + 1.07385i
\(112\) 0 0
\(113\) 2.82843 + 2.82843i 0.266076 + 0.266076i 0.827517 0.561441i \(-0.189753\pi\)
−0.561441 + 0.827517i \(0.689753\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 11.3137 1.03713
\(120\) 0 0
\(121\) −21.0000 −1.90909
\(122\) 0 0
\(123\) −1.65685 9.65685i −0.149394 0.870729i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 + 2.00000i 0.177471 + 0.177471i 0.790253 0.612781i \(-0.209949\pi\)
−0.612781 + 0.790253i \(0.709949\pi\)
\(128\) 0 0
\(129\) 2.82843 4.00000i 0.249029 0.352180i
\(130\) 0 0
\(131\) 5.65685i 0.494242i 0.968985 + 0.247121i \(0.0794845\pi\)
−0.968985 + 0.247121i \(0.920516\pi\)
\(132\) 0 0
\(133\) 8.00000 8.00000i 0.693688 0.693688i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.48528 8.48528i 0.724947 0.724947i −0.244662 0.969608i \(-0.578677\pi\)
0.969608 + 0.244662i \(0.0786770\pi\)
\(138\) 0 0
\(139\) 4.00000i 0.339276i 0.985506 + 0.169638i \(0.0542598\pi\)
−0.985506 + 0.169638i \(0.945740\pi\)
\(140\) 0 0
\(141\) 2.00000 2.82843i 0.168430 0.238197i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.292893 1.70711i −0.0241574 0.140800i
\(148\) 0 0
\(149\) −11.3137 −0.926855 −0.463428 0.886135i \(-0.653381\pi\)
−0.463428 + 0.886135i \(0.653381\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) −5.17157 + 10.8284i −0.418097 + 0.875426i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.00000 8.00000i −0.638470 0.638470i 0.311708 0.950178i \(-0.399099\pi\)
−0.950178 + 0.311708i \(0.899099\pi\)
\(158\) 0 0
\(159\) 11.3137 + 8.00000i 0.897235 + 0.634441i
\(160\) 0 0
\(161\) 16.9706i 1.33747i
\(162\) 0 0
\(163\) 2.00000 2.00000i 0.156652 0.156652i −0.624429 0.781081i \(-0.714668\pi\)
0.781081 + 0.624429i \(0.214668\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.07107 7.07107i 0.547176 0.547176i −0.378447 0.925623i \(-0.623542\pi\)
0.925623 + 0.378447i \(0.123542\pi\)
\(168\) 0 0
\(169\) 13.0000i 1.00000i
\(170\) 0 0
\(171\) 4.00000 + 11.3137i 0.305888 + 0.865181i
\(172\) 0 0
\(173\) −16.9706 16.9706i −1.29025 1.29025i −0.934632 0.355616i \(-0.884271\pi\)
−0.355616 0.934632i \(-0.615729\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 9.65685 1.65685i 0.725854 0.124537i
\(178\) 0 0
\(179\) 5.65685 0.422813 0.211407 0.977398i \(-0.432196\pi\)
0.211407 + 0.977398i \(0.432196\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 10.2426 1.75736i 0.757158 0.129908i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 16.0000 + 16.0000i 1.17004 + 1.17004i
\(188\) 0 0
\(189\) 14.1421 + 4.00000i 1.02869 + 0.290957i
\(190\) 0 0
\(191\) 11.3137i 0.818631i −0.912393 0.409316i \(-0.865768\pi\)
0.912393 0.409316i \(-0.134232\pi\)
\(192\) 0 0
\(193\) −8.00000 + 8.00000i −0.575853 + 0.575853i −0.933758 0.357905i \(-0.883491\pi\)
0.357905 + 0.933758i \(0.383491\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 12.0000 + 8.48528i 0.846415 + 0.598506i
\(202\) 0 0
\(203\) −11.3137 11.3137i −0.794067 0.794067i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 16.2426 + 7.75736i 1.12894 + 0.539174i
\(208\) 0 0
\(209\) 22.6274 1.56517
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −3.31371 19.3137i −0.227052 1.32335i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.0000 + 16.0000i 1.08615 + 1.08615i
\(218\) 0 0
\(219\) 11.3137 16.0000i 0.764510 1.08118i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 18.0000 18.0000i 1.20537 1.20537i 0.232859 0.972511i \(-0.425192\pi\)
0.972511 0.232859i \(-0.0748079\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.89949 + 9.89949i −0.657053 + 0.657053i −0.954682 0.297629i \(-0.903804\pi\)
0.297629 + 0.954682i \(0.403804\pi\)
\(228\) 0 0
\(229\) 6.00000i 0.396491i −0.980152 0.198246i \(-0.936476\pi\)
0.980152 0.198246i \(-0.0635244\pi\)
\(230\) 0 0
\(231\) 16.0000 22.6274i 1.05272 1.48877i
\(232\) 0 0
\(233\) 14.1421 + 14.1421i 0.926482 + 0.926482i 0.997477 0.0709946i \(-0.0226173\pi\)
−0.0709946 + 0.997477i \(0.522617\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.3137 −0.731823 −0.365911 0.930650i \(-0.619243\pi\)
−0.365911 + 0.930650i \(0.619243\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) −10.2929 + 11.7071i −0.660289 + 0.751011i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −19.7990 14.0000i −1.25471 0.887214i
\(250\) 0 0
\(251\) 5.65685i 0.357057i −0.983935 0.178529i \(-0.942866\pi\)
0.983935 0.178529i \(-0.0571337\pi\)
\(252\) 0 0
\(253\) 24.0000 24.0000i 1.50887 1.50887i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.48528 8.48528i 0.529297 0.529297i −0.391066 0.920363i \(-0.627893\pi\)
0.920363 + 0.391066i \(0.127893\pi\)
\(258\) 0 0
\(259\) 32.0000i 1.98838i
\(260\) 0 0
\(261\) 16.0000 5.65685i 0.990375 0.350150i
\(262\) 0 0
\(263\) −4.24264 4.24264i −0.261612 0.261612i 0.564096 0.825709i \(-0.309225\pi\)
−0.825709 + 0.564096i \(0.809225\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 19.3137 3.31371i 1.18198 0.202796i
\(268\) 0 0
\(269\) 11.3137 0.689809 0.344904 0.938638i \(-0.387911\pi\)
0.344904 + 0.938638i \(0.387911\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000 + 8.00000i 0.480673 + 0.480673i 0.905347 0.424673i \(-0.139611\pi\)
−0.424673 + 0.905347i \(0.639611\pi\)
\(278\) 0 0
\(279\) −22.6274 + 8.00000i −1.35467 + 0.478947i
\(280\) 0 0
\(281\) 16.9706i 1.01238i 0.862422 + 0.506189i \(0.168946\pi\)
−0.862422 + 0.506189i \(0.831054\pi\)
\(282\) 0 0
\(283\) 6.00000 6.00000i 0.356663 0.356663i −0.505918 0.862581i \(-0.668846\pi\)
0.862581 + 0.505918i \(0.168846\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11.3137 11.3137i 0.667827 0.667827i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) −16.0000 11.3137i −0.937937 0.663221i
\(292\) 0 0
\(293\) 5.65685 + 5.65685i 0.330477 + 0.330477i 0.852768 0.522291i \(-0.174922\pi\)
−0.522291 + 0.852768i \(0.674922\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 14.3431 + 25.6569i 0.832274 + 1.48876i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 1.65685 + 9.65685i 0.0951838 + 0.554772i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −10.0000 10.0000i −0.570730 0.570730i 0.361602 0.932332i \(-0.382230\pi\)
−0.932332 + 0.361602i \(0.882230\pi\)
\(308\) 0 0
\(309\) 8.48528 12.0000i 0.482711 0.682656i
\(310\) 0 0
\(311\) 11.3137i 0.641542i −0.947157 0.320771i \(-0.896058\pi\)
0.947157 0.320771i \(-0.103942\pi\)
\(312\) 0 0
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.6274 22.6274i 1.27088 1.27088i 0.325257 0.945626i \(-0.394549\pi\)
0.945626 0.325257i \(-0.105451\pi\)
\(318\) 0 0
\(319\) 32.0000i 1.79166i
\(320\) 0 0
\(321\) −6.00000 + 8.48528i −0.334887 + 0.473602i
\(322\) 0 0
\(323\) −11.3137 11.3137i −0.629512 0.629512i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.92893 17.0711i −0.161970 0.944032i
\(328\) 0 0
\(329\) 5.65685 0.311872
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 0 0
\(333\) −30.6274 14.6274i −1.67837 0.801578i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 0 0
\(339\) −5.65685 4.00000i −0.307238 0.217250i
\(340\) 0 0
\(341\) 45.2548i 2.45069i
\(342\) 0 0
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.5563 15.5563i 0.835109 0.835109i −0.153102 0.988210i \(-0.548926\pi\)
0.988210 + 0.153102i \(0.0489263\pi\)
\(348\) 0 0
\(349\) 2.00000i 0.107058i −0.998566 0.0535288i \(-0.982953\pi\)
0.998566 0.0535288i \(-0.0170469\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.82843 + 2.82843i 0.150542 + 0.150542i 0.778360 0.627818i \(-0.216052\pi\)
−0.627818 + 0.778360i \(0.716052\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −19.3137 + 3.31371i −1.02219 + 0.175380i
\(358\) 0 0
\(359\) −22.6274 −1.19423 −0.597115 0.802156i \(-0.703686\pi\)
−0.597115 + 0.802156i \(0.703686\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 0 0
\(363\) 35.8492 6.15076i 1.88160 0.322831i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 18.0000 + 18.0000i 0.939592 + 0.939592i 0.998277 0.0586842i \(-0.0186905\pi\)
−0.0586842 + 0.998277i \(0.518691\pi\)
\(368\) 0 0
\(369\) 5.65685 + 16.0000i 0.294484 + 0.832927i
\(370\) 0 0
\(371\) 22.6274i 1.17476i
\(372\) 0 0
\(373\) 8.00000 8.00000i 0.414224 0.414224i −0.468983 0.883207i \(-0.655379\pi\)
0.883207 + 0.468983i \(0.155379\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 36.0000i 1.84920i 0.380945 + 0.924598i \(0.375599\pi\)
−0.380945 + 0.924598i \(0.624401\pi\)
\(380\) 0 0
\(381\) −4.00000 2.82843i −0.204926 0.144905i
\(382\) 0 0
\(383\) −21.2132 21.2132i −1.08394 1.08394i −0.996138 0.0878065i \(-0.972014\pi\)
−0.0878065 0.996138i \(-0.527986\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.65685 + 7.65685i −0.185888 + 0.389220i
\(388\) 0 0
\(389\) −33.9411 −1.72088 −0.860442 0.509549i \(-0.829812\pi\)
−0.860442 + 0.509549i \(0.829812\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 0 0
\(393\) −1.65685 9.65685i −0.0835772 0.487124i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 0 0
\(399\) −11.3137 + 16.0000i −0.566394 + 0.801002i
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −45.2548 + 45.2548i −2.24320 + 2.24320i
\(408\) 0 0
\(409\) 30.0000i 1.48340i −0.670729 0.741702i \(-0.734019\pi\)
0.670729 0.741702i \(-0.265981\pi\)
\(410\) 0 0
\(411\) −12.0000 + 16.9706i −0.591916 + 0.837096i
\(412\) 0 0
\(413\) 11.3137 + 11.3137i 0.556711 + 0.556711i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.17157 6.82843i −0.0573722 0.334390i
\(418\) 0 0
\(419\) 16.9706 0.829066 0.414533 0.910034i \(-0.363945\pi\)
0.414533 + 0.910034i \(0.363945\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 0 0
\(423\) −2.58579 + 5.41421i −0.125725 + 0.263248i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 12.0000 + 12.0000i 0.580721 + 0.580721i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 22.6274i 1.08992i −0.838461 0.544962i \(-0.816544\pi\)
0.838461 0.544962i \(-0.183456\pi\)
\(432\) 0 0
\(433\) −24.0000 + 24.0000i −1.15337 + 1.15337i −0.167493 + 0.985873i \(0.553567\pi\)
−0.985873 + 0.167493i \(0.946433\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −16.9706 + 16.9706i −0.811812 + 0.811812i
\(438\) 0 0
\(439\) 32.0000i 1.52728i −0.645644 0.763638i \(-0.723411\pi\)
0.645644 0.763638i \(-0.276589\pi\)
\(440\) 0 0
\(441\) 1.00000 + 2.82843i 0.0476190 + 0.134687i
\(442\) 0 0
\(443\) 7.07107 + 7.07107i 0.335957 + 0.335957i 0.854843 0.518887i \(-0.173653\pi\)
−0.518887 + 0.854843i \(0.673653\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 19.3137 3.31371i 0.913507 0.156733i
\(448\) 0 0
\(449\) −5.65685 −0.266963 −0.133482 0.991051i \(-0.542616\pi\)
−0.133482 + 0.991051i \(0.542616\pi\)
\(450\) 0 0
\(451\) 32.0000 1.50682
\(452\) 0 0
\(453\) 13.6569 2.34315i 0.641655 0.110091i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.0000 16.0000i −0.748448 0.748448i 0.225739 0.974188i \(-0.427520\pi\)
−0.974188 + 0.225739i \(0.927520\pi\)
\(458\) 0 0
\(459\) 5.65685 20.0000i 0.264039 0.933520i
\(460\) 0 0
\(461\) 39.5980i 1.84426i −0.386878 0.922131i \(-0.626447\pi\)
0.386878 0.922131i \(-0.373553\pi\)
\(462\) 0 0
\(463\) 6.00000 6.00000i 0.278844 0.278844i −0.553804 0.832647i \(-0.686824\pi\)
0.832647 + 0.553804i \(0.186824\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.89949 + 9.89949i −0.458094 + 0.458094i −0.898029 0.439935i \(-0.855001\pi\)
0.439935 + 0.898029i \(0.355001\pi\)
\(468\) 0 0
\(469\) 24.0000i 1.10822i
\(470\) 0 0
\(471\) 16.0000 + 11.3137i 0.737241 + 0.521308i
\(472\) 0 0
\(473\) 11.3137 + 11.3137i 0.520205 + 0.520205i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −21.6569 10.3431i −0.991599 0.473580i
\(478\) 0 0
\(479\) −11.3137 −0.516937 −0.258468 0.966020i \(-0.583218\pi\)
−0.258468 + 0.966020i \(0.583218\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 4.97056 + 28.9706i 0.226168 + 1.31821i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −18.0000 18.0000i −0.815658 0.815658i 0.169818 0.985476i \(-0.445682\pi\)
−0.985476 + 0.169818i \(0.945682\pi\)
\(488\) 0 0
\(489\) −2.82843 + 4.00000i −0.127906 + 0.180886i
\(490\) 0 0
\(491\) 5.65685i 0.255290i 0.991820 + 0.127645i \(0.0407419\pi\)
−0.991820 + 0.127645i \(0.959258\pi\)
\(492\) 0 0
\(493\) −16.0000 + 16.0000i −0.720604 + 0.720604i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.6274 22.6274i 1.01498 1.01498i
\(498\) 0 0
\(499\) 20.0000i 0.895323i −0.894203 0.447661i \(-0.852257\pi\)
0.894203 0.447661i \(-0.147743\pi\)
\(500\) 0 0
\(501\) −10.0000 + 14.1421i −0.446767 + 0.631824i
\(502\) 0 0
\(503\) 4.24264 + 4.24264i 0.189170 + 0.189170i 0.795337 0.606167i \(-0.207294\pi\)
−0.606167 + 0.795337i \(0.707294\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.80761 22.1924i −0.169102 0.985599i
\(508\) 0 0
\(509\) 16.9706 0.752207 0.376103 0.926578i \(-0.377264\pi\)
0.376103 + 0.926578i \(0.377264\pi\)
\(510\) 0 0
\(511\) 32.0000 1.41560
\(512\) 0 0
\(513\) −10.1421 18.1421i −0.447786 0.800995i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.00000 + 8.00000i 0.351840 + 0.351840i
\(518\) 0 0
\(519\) 33.9411 + 24.0000i 1.48985 + 1.05348i
\(520\) 0 0
\(521\) 33.9411i 1.48699i −0.668743 0.743494i \(-0.733167\pi\)
0.668743 0.743494i \(-0.266833\pi\)
\(522\) 0 0
\(523\) −6.00000 + 6.00000i −0.262362 + 0.262362i −0.826013 0.563651i \(-0.809396\pi\)
0.563651 + 0.826013i \(0.309396\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.6274 22.6274i 0.985666 0.985666i
\(528\) 0 0
\(529\) 13.0000i 0.565217i
\(530\) 0 0
\(531\) −16.0000 + 5.65685i −0.694341 + 0.245487i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.65685 + 1.65685i −0.416724 + 0.0714985i
\(538\) 0 0
\(539\) 5.65685 0.243658
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 0 0
\(543\) 17.0711 2.92893i 0.732590 0.125693i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −30.0000 30.0000i −1.28271 1.28271i −0.939121 0.343586i \(-0.888358\pi\)
−0.343586 0.939121i \(-0.611642\pi\)
\(548\) 0 0
\(549\) −16.9706 + 6.00000i −0.724286 + 0.256074i
\(550\) 0 0
\(551\) 22.6274i 0.963960i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.9706 + 16.9706i −0.719066 + 0.719066i −0.968414 0.249348i \(-0.919784\pi\)
0.249348 + 0.968414i \(0.419784\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −32.0000 22.6274i −1.35104 0.955330i
\(562\) 0 0
\(563\) −9.89949 9.89949i −0.417214 0.417214i 0.467028 0.884242i \(-0.345325\pi\)
−0.884242 + 0.467028i \(0.845325\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −25.3137 2.68629i −1.06308 0.112814i
\(568\) 0 0
\(569\) −28.2843 −1.18574 −0.592869 0.805299i \(-0.702005\pi\)
−0.592869 + 0.805299i \(0.702005\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 3.31371 + 19.3137i 0.138432 + 0.806842i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −16.0000 16.0000i −0.666089 0.666089i 0.290720 0.956808i \(-0.406105\pi\)
−0.956808 + 0.290720i \(0.906105\pi\)
\(578\) 0 0
\(579\) 11.3137 16.0000i 0.470182 0.664937i
\(580\) 0 0
\(581\) 39.5980i 1.64280i
\(582\) 0 0
\(583\) −32.0000 + 32.0000i −1.32530 + 1.32530i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.5563 + 15.5563i −0.642079 + 0.642079i −0.951066 0.308987i \(-0.900010\pi\)
0.308987 + 0.951066i \(0.400010\pi\)
\(588\) 0 0
\(589\) 32.0000i 1.31854i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.48528 + 8.48528i 0.348449 + 0.348449i 0.859532 0.511083i \(-0.170755\pi\)
−0.511083 + 0.859532i \(0.670755\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 45.2548 1.84906 0.924531 0.381106i \(-0.124457\pi\)
0.924531 + 0.381106i \(0.124457\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) −22.9706 10.9706i −0.935434 0.446756i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −10.0000 10.0000i −0.405887 0.405887i 0.474414 0.880302i \(-0.342660\pi\)
−0.880302 + 0.474414i \(0.842660\pi\)
\(608\) 0 0
\(609\) 22.6274 + 16.0000i 0.916909 + 0.648353i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −25.4558 + 25.4558i −1.02481 + 1.02481i −0.0251295 + 0.999684i \(0.508000\pi\)
−0.999684 + 0.0251295i \(0.992000\pi\)
\(618\) 0 0
\(619\) 12.0000i 0.482321i 0.970485 + 0.241160i \(0.0775280\pi\)
−0.970485 + 0.241160i \(0.922472\pi\)
\(620\) 0 0
\(621\) −30.0000 8.48528i −1.20386 0.340503i
\(622\) 0 0
\(623\) 22.6274 + 22.6274i 0.906548 + 0.906548i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −38.6274 + 6.62742i −1.54263 + 0.264674i
\(628\) 0 0
\(629\) 45.2548 1.80443
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 6.82843 1.17157i 0.271406 0.0465658i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 11.3137 + 32.0000i 0.447563 + 1.26590i
\(640\) 0 0
\(641\) 28.2843i 1.11716i 0.829450 + 0.558581i \(0.188654\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(642\) 0 0
\(643\) −22.0000 + 22.0000i −0.867595 + 0.867595i −0.992206 0.124610i \(-0.960232\pi\)
0.124610 + 0.992206i \(0.460232\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.24264 + 4.24264i −0.166795 + 0.166795i −0.785569 0.618774i \(-0.787630\pi\)
0.618774 + 0.785569i \(0.287630\pi\)
\(648\) 0 0
\(649\) 32.0000i 1.25611i
\(650\) 0 0
\(651\) −32.0000 22.6274i −1.25418 0.886838i
\(652\) 0 0
\(653\) 16.9706 + 16.9706i 0.664109 + 0.664109i 0.956346 0.292237i \(-0.0943995\pi\)
−0.292237 + 0.956346i \(0.594399\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −14.6274 + 30.6274i −0.570670 + 1.19489i
\(658\) 0 0
\(659\) −16.9706 −0.661079 −0.330540 0.943792i \(-0.607231\pi\)
−0.330540 + 0.943792i \(0.607231\pi\)
\(660\) 0 0
\(661\) −34.0000 −1.32245 −0.661223 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 24.0000 + 24.0000i 0.929284 + 0.929284i
\(668\) 0 0
\(669\) −25.4558 + 36.0000i −0.984180 + 1.39184i
\(670\) 0 0
\(671\) 33.9411i 1.31028i
\(672\) 0 0
\(673\) 24.0000 24.0000i 0.925132 0.925132i −0.0722542 0.997386i \(-0.523019\pi\)
0.997386 + 0.0722542i \(0.0230193\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16.9706 16.9706i 0.652232 0.652232i −0.301298 0.953530i \(-0.597420\pi\)
0.953530 + 0.301298i \(0.0974200\pi\)
\(678\) 0 0
\(679\) 32.0000i 1.22805i
\(680\) 0 0
\(681\) 14.0000 19.7990i 0.536481 0.758699i
\(682\) 0 0
\(683\) −4.24264 4.24264i −0.162340 0.162340i 0.621262 0.783603i \(-0.286620\pi\)
−0.783603 + 0.621262i \(0.786620\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.75736 + 10.2426i 0.0670474 + 0.390781i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 0 0
\(693\) −20.6863 + 43.3137i −0.785807 + 1.64535i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −16.0000 16.0000i −0.606043 0.606043i
\(698\) 0 0
\(699\) −28.2843 20.0000i −1.06981 0.756469i
\(700\) 0 0
\(701\) 22.6274i 0.854626i 0.904104 + 0.427313i \(0.140540\pi\)
−0.904104 + 0.427313i \(0.859460\pi\)
\(702\) 0 0
\(703\) 32.0000 32.0000i 1.20690 1.20690i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −11.3137 + 11.3137i −0.425496 + 0.425496i
\(708\) 0 0
\(709\) 6.00000i 0.225335i −0.993633 0.112667i \(-0.964061\pi\)
0.993633 0.112667i \(-0.0359394\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −33.9411 33.9411i −1.27111 1.27111i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 19.3137 3.31371i 0.721284 0.123753i
\(718\) 0 0
\(719\) 45.2548 1.68772 0.843860 0.536563i \(-0.180278\pi\)
0.843860 + 0.536563i \(0.180278\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 0 0
\(723\) −17.0711 + 2.92893i −0.634880 + 0.108928i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −30.0000 30.0000i −1.11264 1.11264i −0.992793 0.119846i \(-0.961760\pi\)
−0.119846 0.992793i \(-0.538240\pi\)
\(728\) 0 0
\(729\) 14.1421 23.0000i 0.523783 0.851852i
\(730\) 0 0
\(731\) 11.3137i 0.418453i
\(732\) 0 0
\(733\) −24.0000 + 24.0000i −0.886460 + 0.886460i −0.994181 0.107721i \(-0.965645\pi\)
0.107721 + 0.994181i \(0.465645\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −33.9411 + 33.9411i −1.25024 + 1.25024i
\(738\) 0 0
\(739\) 4.00000i 0.147142i 0.997290 + 0.0735712i \(0.0234396\pi\)
−0.997290 + 0.0735712i \(0.976560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.3848 + 18.3848i 0.674472 + 0.674472i 0.958744 0.284272i \(-0.0917518\pi\)
−0.284272 + 0.958744i \(0.591752\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 37.8995 + 18.1005i 1.38667 + 0.662263i
\(748\) 0 0
\(749\) −16.9706 −0.620091
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 0 0
\(753\) 1.65685 + 9.65685i 0.0603791 + 0.351915i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −24.0000 24.0000i −0.872295 0.872295i 0.120427 0.992722i \(-0.461574\pi\)
−0.992722 + 0.120427i \(0.961574\pi\)
\(758\) 0 0
\(759\) −33.9411 + 48.0000i −1.23198 + 1.74229i
\(760\) 0 0
\(761\) 22.6274i 0.820243i 0.912031 + 0.410122i \(0.134514\pi\)
−0.912031 + 0.410122i \(0.865486\pi\)
\(762\) 0 0
\(763\) 20.0000 20.0000i 0.724049 0.724049i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 50.0000i 1.80305i −0.432731 0.901523i \(-0.642450\pi\)
0.432731 0.901523i \(-0.357550\pi\)
\(770\) 0 0
\(771\) −12.0000 + 16.9706i −0.432169 + 0.611180i
\(772\) 0 0
\(773\) −11.3137 11.3137i −0.406926 0.406926i 0.473739 0.880665i \(-0.342904\pi\)
−0.880665 + 0.473739i \(0.842904\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −9.37258 54.6274i −0.336240 1.95975i
\(778\) 0 0
\(779\) −22.6274 −0.810711
\(780\) 0 0
\(781\) 64.0000 2.29010
\(782\) 0 0
\(783\) −25.6569 + 14.3431i −0.916901 + 0.512582i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −22.0000 22.0000i −0.784215 0.784215i 0.196324 0.980539i \(-0.437100\pi\)
−0.980539 + 0.196324i \(0.937100\pi\)
\(788\) 0 0
\(789\) 8.48528 + 6.00000i 0.302084 + 0.213606i
\(790\) 0 0
\(791\) 11.3137i 0.402269i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 0 0
\(799\) 8.00000i 0.283020i