Properties

Label 1200.2.v.k.257.2
Level $1200$
Weight $2$
Character 1200.257
Analytic conductor $9.582$
Analytic rank $0$
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: \(0\)
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 257.2
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1200.257
Dual form 1200.2.v.k.593.2

$q$-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 0.975579 0.219650i \(-0.0704915\pi\)
−0.219650 + 0.975579i \(0.570491\pi\)
\(8\) 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 −0.275350 0.961344i \(-0.588794\pi\)
0.961344 + 0.275350i \(0.0887937\pi\)
\(18\) 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 0.109351 0.994003i \(-0.465123\pi\)
−0.994003 + 0.109351i \(0.965123\pi\)
\(24\) 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 \(0.130177\pi\)
0.397658 + 0.917534i \(0.369823\pi\)
\(38\) 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 −0.537968 0.842965i \(-0.680808\pi\)
0.842965 + 0.537968i \(0.180808\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.41421 1.41421i 0.206284 0.206284i −0.596402 0.802686i \(-0.703403\pi\)
0.802686 + 0.596402i \(0.203403\pi\)
\(48\) 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 0.979324 0.202296i \(-0.0648402\pi\)
−0.202296 + 0.979324i \(0.564840\pi\)
\(54\) 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 0.971216 0.238200i \(-0.0765572\pi\)
−0.238200 + 0.971216i \(0.576557\pi\)
\(68\) 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 −0.0617617 0.998091i \(-0.519672\pi\)
0.998091 + 0.0617617i \(0.0196719\pi\)
\(74\) 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 \(-0.971078\pi\)
−0.0907357 0.995875i \(-0.528922\pi\)
\(84\) 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 0.172698 0.984975i \(-0.444752\pi\)
−0.984975 + 0.172698i \(0.944752\pi\)
\(98\) 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 −0.346757 0.937955i \(-0.612717\pi\)
0.937955 + 0.346757i \(0.112717\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.24264 + 4.24264i −0.410152 + 0.410152i −0.881791 0.471640i \(-0.843662\pi\)
0.471640 + 0.881791i \(0.343662\pi\)
\(108\) 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 0.561441 0.827517i \(-0.310247\pi\)
−0.827517 + 0.561441i \(0.810247\pi\)
\(114\) 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 0.612781 0.790253i \(-0.290051\pi\)
−0.790253 + 0.612781i \(0.790051\pi\)
\(128\) 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 −0.969608 0.244662i \(-0.921323\pi\)
0.244662 + 0.969608i \(0.421323\pi\)
\(138\) 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 0.950178 0.311708i \(-0.100901\pi\)
−0.311708 + 0.950178i \(0.600901\pi\)
\(158\) 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 −0.781081 0.624429i \(-0.785332\pi\)
0.624429 + 0.781081i \(0.285332\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.07107 + 7.07107i −0.547176 + 0.547176i −0.925623 0.378447i \(-0.876458\pi\)
0.378447 + 0.925623i \(0.376458\pi\)
\(168\) 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 \(0.115729\pi\)
0.355616 + 0.934632i \(0.384271\pi\)
\(174\) 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 −0.357905 0.933758i \(-0.616509\pi\)
0.933758 + 0.357905i \(0.116509\pi\)
\(194\) 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 \(0.574808\pi\)
−0.972511 + 0.232859i \(0.925192\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.89949 9.89949i 0.657053 0.657053i −0.297629 0.954682i \(-0.596196\pi\)
0.954682 + 0.297629i \(0.0961959\pi\)
\(228\) 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 0.0709946 0.997477i \(-0.477383\pi\)
−0.997477 + 0.0709946i \(0.977383\pi\)
\(234\) 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 −0.920363 0.391066i \(-0.872107\pi\)
0.391066 + 0.920363i \(0.372107\pi\)
\(258\) 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 0.825709 0.564096i \(-0.190775\pi\)
−0.564096 + 0.825709i \(0.690775\pi\)
\(264\) 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 0.424673 0.905347i \(-0.360389\pi\)
−0.905347 + 0.424673i \(0.860389\pi\)
\(278\) 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 −0.862581 0.505918i \(-0.831154\pi\)
0.505918 + 0.862581i \(0.331154\pi\)
\(284\) 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 0.522291 0.852768i \(-0.325078\pi\)
−0.852768 + 0.522291i \(0.825078\pi\)
\(294\) 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 0.932332 0.361602i \(-0.117770\pi\)
−0.361602 + 0.932332i \(0.617770\pi\)
\(308\) 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 \(0.605451\pi\)
−0.945626 + 0.325257i \(0.894549\pi\)
\(318\) 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 −0.988210 0.153102i \(-0.951074\pi\)
0.153102 + 0.988210i \(0.451074\pi\)
\(348\) 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 0.627818 0.778360i \(-0.283948\pi\)
−0.778360 + 0.627818i \(0.783948\pi\)
\(354\) 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 0.0586842 0.998277i \(-0.481309\pi\)
−0.998277 + 0.0586842i \(0.981309\pi\)
\(368\) 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 −0.883207 0.468983i \(-0.844621\pi\)
0.468983 + 0.883207i \(0.344621\pi\)
\(374\) 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 \(0.0279857\pi\)
0.0878065 + 0.996138i \(0.472014\pi\)
\(384\) 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 \(-0.446433\pi\)
0.985873 0.167493i \(-0.0535672\pi\)
\(434\) 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 0.518887 0.854843i \(-0.326347\pi\)
−0.854843 + 0.518887i \(0.826347\pi\)
\(444\) 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 0.974188 0.225739i \(-0.0724798\pi\)
−0.225739 + 0.974188i \(0.572480\pi\)
\(458\) 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 −0.832647 0.553804i \(-0.813176\pi\)
0.553804 + 0.832647i \(0.313176\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.89949 9.89949i 0.458094 0.458094i −0.439935 0.898029i \(-0.644999\pi\)
0.898029 + 0.439935i \(0.144999\pi\)
\(468\) 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 0.985476 0.169818i \(-0.0543179\pi\)
−0.169818 + 0.985476i \(0.554318\pi\)
\(488\) 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 0.606167 0.795337i \(-0.292706\pi\)
−0.795337 + 0.606167i \(0.792706\pi\)
\(504\) 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 −0.563651 0.826013i \(-0.690604\pi\)
0.826013 + 0.563651i \(0.190604\pi\)
\(524\) 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 \(0.111642\pi\)
0.343586 + 0.939121i \(0.388358\pi\)
\(548\) 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 −0.249348 0.968414i \(-0.580216\pi\)
0.968414 + 0.249348i \(0.0802163\pi\)
\(558\) 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 0.884242 0.467028i \(-0.154675\pi\)
−0.467028 + 0.884242i \(0.654675\pi\)
\(564\) 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 0.956808 0.290720i \(-0.0938947\pi\)
−0.290720 + 0.956808i \(0.593895\pi\)
\(578\) 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 −0.308987 0.951066i \(-0.599990\pi\)
0.951066 + 0.308987i \(0.0999900\pi\)
\(588\) 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 0.511083 0.859532i \(-0.329245\pi\)
−0.859532 + 0.511083i \(0.829245\pi\)
\(594\) 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 0.880302 0.474414i \(-0.157340\pi\)
−0.474414 + 0.880302i \(0.657340\pi\)
\(608\) 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 \(-0.492000\pi\)
0.999684 0.0251295i \(-0.00799981\pi\)
\(618\) 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 −0.124610 0.992206i \(-0.539768\pi\)
0.992206 + 0.124610i \(0.0397681\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.24264 4.24264i 0.166795 0.166795i −0.618774 0.785569i \(-0.712370\pi\)
0.785569 + 0.618774i \(0.212370\pi\)
\(648\) 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 0.292237 0.956346i \(-0.405601\pi\)
−0.956346 + 0.292237i \(0.905601\pi\)
\(654\) 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 −0.997386 0.0722542i \(-0.976981\pi\)
0.0722542 + 0.997386i \(0.476981\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.9706 + 16.9706i −0.652232 + 0.652232i −0.953530 0.301298i \(-0.902580\pi\)
0.301298 + 0.953530i \(0.402580\pi\)
\(678\) 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 0.783603 0.621262i \(-0.213380\pi\)
−0.621262 + 0.783603i \(0.713380\pi\)
\(684\) 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 \(0.0382401\pi\)
0.119846 + 0.992793i \(0.461760\pi\)
\(728\) 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 −0.107721 0.994181i \(-0.534355\pi\)
0.994181 + 0.107721i \(0.0343553\pi\)
\(734\) 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 0.284272 0.958744i \(-0.408248\pi\)
−0.958744 + 0.284272i \(0.908248\pi\)
\(744\) 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 0.992722 0.120427i \(-0.0384265\pi\)
−0.120427 + 0.992722i \(0.538426\pi\)
\(758\) 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 0.880665 0.473739i \(-0.157096\pi\)
−0.473739 + 0.880665i \(0.657096\pi\)
\(774\) 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 0.980539 0.196324i \(-0.0629004\pi\)
−0.196324 + 0.980539i \(0.562900\pi\)
\(788\) 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
\(800\) 0 0
\(801\)