Properties

Label 1200.3.bg.o.1057.2
Level $1200$
Weight $3$
Character 1200.1057
Analytic conductor $32.698$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1057.2
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.1057
Dual form 1200.3.bg.o.193.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 1.22474i) q^{3} +(2.55051 + 2.55051i) q^{7} -3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 - 1.22474i) q^{3} +(2.55051 + 2.55051i) q^{7} -3.00000i q^{9} -8.24745 q^{11} +(12.2474 - 12.2474i) q^{13} +(12.4495 + 12.4495i) q^{17} -34.4949i q^{19} +6.24745 q^{21} +(-17.3485 + 17.3485i) q^{23} +(-3.67423 - 3.67423i) q^{27} -9.75255i q^{29} -28.4949 q^{31} +(-10.1010 + 10.1010i) q^{33} +(7.34847 + 7.34847i) q^{37} -30.0000i q^{39} +74.4949 q^{41} +(34.8990 - 34.8990i) q^{43} +(-22.0454 - 22.0454i) q^{47} -35.9898i q^{49} +30.4949 q^{51} +(64.6969 - 64.6969i) q^{53} +(-42.2474 - 42.2474i) q^{57} +15.2577i q^{59} -53.5051 q^{61} +(7.65153 - 7.65153i) q^{63} +(4.69694 + 4.69694i) q^{67} +42.4949i q^{69} +117.980 q^{71} +(-34.1918 + 34.1918i) q^{73} +(-21.0352 - 21.0352i) q^{77} -0.494897i q^{79} -9.00000 q^{81} +(-18.3587 + 18.3587i) q^{83} +(-11.9444 - 11.9444i) q^{87} -136.969i q^{89} +62.4745 q^{91} +(-34.8990 + 34.8990i) q^{93} +(-94.5959 - 94.5959i) q^{97} +24.7423i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 20 q^{7} + O(q^{10}) \) \( 4 q + 20 q^{7} + 16 q^{11} + 40 q^{17} - 24 q^{21} - 40 q^{23} - 16 q^{31} - 60 q^{33} + 200 q^{41} + 120 q^{43} + 24 q^{51} + 200 q^{53} - 120 q^{57} - 312 q^{61} + 60 q^{63} - 40 q^{67} + 80 q^{71} + 20 q^{73} + 200 q^{77} - 36 q^{81} - 240 q^{83} + 60 q^{87} - 240 q^{91} - 120 q^{93} - 300 q^{97} + O(q^{100}) \)

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
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.55051 + 2.55051i 0.364359 + 0.364359i 0.865415 0.501056i \(-0.167055\pi\)
−0.501056 + 0.865415i \(0.667055\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −8.24745 −0.749768 −0.374884 0.927072i \(-0.622317\pi\)
−0.374884 + 0.927072i \(0.622317\pi\)
\(12\) 0 0
\(13\) 12.2474 12.2474i 0.942111 0.942111i −0.0563023 0.998414i \(-0.517931\pi\)
0.998414 + 0.0563023i \(0.0179311\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 12.4495 + 12.4495i 0.732323 + 0.732323i 0.971079 0.238757i \(-0.0767398\pi\)
−0.238757 + 0.971079i \(0.576740\pi\)
\(18\) 0 0
\(19\) 34.4949i 1.81552i −0.419489 0.907760i \(-0.637791\pi\)
0.419489 0.907760i \(-0.362209\pi\)
\(20\) 0 0
\(21\) 6.24745 0.297498
\(22\) 0 0
\(23\) −17.3485 + 17.3485i −0.754281 + 0.754281i −0.975275 0.220994i \(-0.929070\pi\)
0.220994 + 0.975275i \(0.429070\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 0 0
\(29\) 9.75255i 0.336295i −0.985762 0.168147i \(-0.946222\pi\)
0.985762 0.168147i \(-0.0537785\pi\)
\(30\) 0 0
\(31\) −28.4949 −0.919190 −0.459595 0.888129i \(-0.652005\pi\)
−0.459595 + 0.888129i \(0.652005\pi\)
\(32\) 0 0
\(33\) −10.1010 + 10.1010i −0.306092 + 0.306092i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.34847 + 7.34847i 0.198607 + 0.198607i 0.799403 0.600795i \(-0.205149\pi\)
−0.600795 + 0.799403i \(0.705149\pi\)
\(38\) 0 0
\(39\) 30.0000i 0.769231i
\(40\) 0 0
\(41\) 74.4949 1.81695 0.908474 0.417941i \(-0.137248\pi\)
0.908474 + 0.417941i \(0.137248\pi\)
\(42\) 0 0
\(43\) 34.8990 34.8990i 0.811604 0.811604i −0.173270 0.984874i \(-0.555433\pi\)
0.984874 + 0.173270i \(0.0554334\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −22.0454 22.0454i −0.469051 0.469051i 0.432556 0.901607i \(-0.357612\pi\)
−0.901607 + 0.432556i \(0.857612\pi\)
\(48\) 0 0
\(49\) 35.9898i 0.734486i
\(50\) 0 0
\(51\) 30.4949 0.597939
\(52\) 0 0
\(53\) 64.6969 64.6969i 1.22070 1.22070i 0.253312 0.967385i \(-0.418480\pi\)
0.967385 0.253312i \(-0.0815201\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −42.2474 42.2474i −0.741183 0.741183i
\(58\) 0 0
\(59\) 15.2577i 0.258604i 0.991605 + 0.129302i \(0.0412737\pi\)
−0.991605 + 0.129302i \(0.958726\pi\)
\(60\) 0 0
\(61\) −53.5051 −0.877133 −0.438566 0.898699i \(-0.644514\pi\)
−0.438566 + 0.898699i \(0.644514\pi\)
\(62\) 0 0
\(63\) 7.65153 7.65153i 0.121453 0.121453i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.69694 + 4.69694i 0.0701036 + 0.0701036i 0.741289 0.671186i \(-0.234215\pi\)
−0.671186 + 0.741289i \(0.734215\pi\)
\(68\) 0 0
\(69\) 42.4949i 0.615868i
\(70\) 0 0
\(71\) 117.980 1.66168 0.830842 0.556508i \(-0.187859\pi\)
0.830842 + 0.556508i \(0.187859\pi\)
\(72\) 0 0
\(73\) −34.1918 + 34.1918i −0.468381 + 0.468381i −0.901390 0.433009i \(-0.857452\pi\)
0.433009 + 0.901390i \(0.357452\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −21.0352 21.0352i −0.273184 0.273184i
\(78\) 0 0
\(79\) 0.494897i 0.00626452i −0.999995 0.00313226i \(-0.999003\pi\)
0.999995 0.00313226i \(-0.000997032\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) −18.3587 + 18.3587i −0.221189 + 0.221189i −0.808999 0.587810i \(-0.799990\pi\)
0.587810 + 0.808999i \(0.299990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −11.9444 11.9444i −0.137292 0.137292i
\(88\) 0 0
\(89\) 136.969i 1.53898i −0.638658 0.769491i \(-0.720510\pi\)
0.638658 0.769491i \(-0.279490\pi\)
\(90\) 0 0
\(91\) 62.4745 0.686533
\(92\) 0 0
\(93\) −34.8990 + 34.8990i −0.375258 + 0.375258i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −94.5959 94.5959i −0.975216 0.975216i 0.0244846 0.999700i \(-0.492206\pi\)
−0.999700 + 0.0244846i \(0.992206\pi\)
\(98\) 0 0
\(99\) 24.7423i 0.249923i
\(100\) 0 0
\(101\) 70.2474 0.695519 0.347760 0.937584i \(-0.386943\pi\)
0.347760 + 0.937584i \(0.386943\pi\)
\(102\) 0 0
\(103\) 86.8434 86.8434i 0.843139 0.843139i −0.146126 0.989266i \(-0.546681\pi\)
0.989266 + 0.146126i \(0.0466806\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −96.3383 96.3383i −0.900358 0.900358i 0.0951092 0.995467i \(-0.469680\pi\)
−0.995467 + 0.0951092i \(0.969680\pi\)
\(108\) 0 0
\(109\) 12.5153i 0.114819i 0.998351 + 0.0574097i \(0.0182841\pi\)
−0.998351 + 0.0574097i \(0.981716\pi\)
\(110\) 0 0
\(111\) 18.0000 0.162162
\(112\) 0 0
\(113\) −66.9444 + 66.9444i −0.592428 + 0.592428i −0.938287 0.345858i \(-0.887588\pi\)
0.345858 + 0.938287i \(0.387588\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −36.7423 36.7423i −0.314037 0.314037i
\(118\) 0 0
\(119\) 63.5051i 0.533656i
\(120\) 0 0
\(121\) −52.9796 −0.437848
\(122\) 0 0
\(123\) 91.2372 91.2372i 0.741766 0.741766i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.55051 + 2.55051i 0.0200828 + 0.0200828i 0.717077 0.696994i \(-0.245480\pi\)
−0.696994 + 0.717077i \(0.745480\pi\)
\(128\) 0 0
\(129\) 85.4847i 0.662672i
\(130\) 0 0
\(131\) −44.2474 −0.337767 −0.168883 0.985636i \(-0.554016\pi\)
−0.168883 + 0.985636i \(0.554016\pi\)
\(132\) 0 0
\(133\) 87.9796 87.9796i 0.661501 0.661501i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 18.3587 + 18.3587i 0.134005 + 0.134005i 0.770928 0.636923i \(-0.219793\pi\)
−0.636923 + 0.770928i \(0.719793\pi\)
\(138\) 0 0
\(139\) 219.980i 1.58259i −0.611437 0.791293i \(-0.709408\pi\)
0.611437 0.791293i \(-0.290592\pi\)
\(140\) 0 0
\(141\) −54.0000 −0.382979
\(142\) 0 0
\(143\) −101.010 + 101.010i −0.706365 + 0.706365i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −44.0783 44.0783i −0.299852 0.299852i
\(148\) 0 0
\(149\) 28.2679i 0.189717i −0.995491 0.0948586i \(-0.969760\pi\)
0.995491 0.0948586i \(-0.0302399\pi\)
\(150\) 0 0
\(151\) 61.0102 0.404041 0.202021 0.979381i \(-0.435249\pi\)
0.202021 + 0.979381i \(0.435249\pi\)
\(152\) 0 0
\(153\) 37.3485 37.3485i 0.244108 0.244108i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 22.6515 + 22.6515i 0.144277 + 0.144277i 0.775556 0.631279i \(-0.217470\pi\)
−0.631279 + 0.775556i \(0.717470\pi\)
\(158\) 0 0
\(159\) 158.474i 0.996695i
\(160\) 0 0
\(161\) −88.4949 −0.549658
\(162\) 0 0
\(163\) −88.9898 + 88.9898i −0.545950 + 0.545950i −0.925267 0.379317i \(-0.876159\pi\)
0.379317 + 0.925267i \(0.376159\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 171.641 + 171.641i 1.02779 + 1.02779i 0.999603 + 0.0281898i \(0.00897427\pi\)
0.0281898 + 0.999603i \(0.491026\pi\)
\(168\) 0 0
\(169\) 131.000i 0.775148i
\(170\) 0 0
\(171\) −103.485 −0.605174
\(172\) 0 0
\(173\) 10.6311 10.6311i 0.0614516 0.0614516i −0.675713 0.737165i \(-0.736164\pi\)
0.737165 + 0.675713i \(0.236164\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 18.6867 + 18.6867i 0.105575 + 0.105575i
\(178\) 0 0
\(179\) 100.247i 0.560042i −0.959994 0.280021i \(-0.909659\pi\)
0.959994 0.280021i \(-0.0903414\pi\)
\(180\) 0 0
\(181\) 259.444 1.43339 0.716696 0.697386i \(-0.245654\pi\)
0.716696 + 0.697386i \(0.245654\pi\)
\(182\) 0 0
\(183\) −65.5301 + 65.5301i −0.358088 + 0.358088i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −102.677 102.677i −0.549072 0.549072i
\(188\) 0 0
\(189\) 18.7423i 0.0991659i
\(190\) 0 0
\(191\) −77.4847 −0.405679 −0.202840 0.979212i \(-0.565017\pi\)
−0.202840 + 0.979212i \(0.565017\pi\)
\(192\) 0 0
\(193\) −83.5857 + 83.5857i −0.433087 + 0.433087i −0.889677 0.456590i \(-0.849070\pi\)
0.456590 + 0.889677i \(0.349070\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 200.252 + 200.252i 1.01651 + 1.01651i 0.999861 + 0.0166464i \(0.00529894\pi\)
0.0166464 + 0.999861i \(0.494701\pi\)
\(198\) 0 0
\(199\) 162.990i 0.819044i 0.912300 + 0.409522i \(0.134305\pi\)
−0.912300 + 0.409522i \(0.865695\pi\)
\(200\) 0 0
\(201\) 11.5051 0.0572393
\(202\) 0 0
\(203\) 24.8740 24.8740i 0.122532 0.122532i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 52.0454 + 52.0454i 0.251427 + 0.251427i
\(208\) 0 0
\(209\) 284.495i 1.36122i
\(210\) 0 0
\(211\) −207.980 −0.985685 −0.492843 0.870118i \(-0.664042\pi\)
−0.492843 + 0.870118i \(0.664042\pi\)
\(212\) 0 0
\(213\) 144.495 144.495i 0.678380 0.678380i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −72.6765 72.6765i −0.334915 0.334915i
\(218\) 0 0
\(219\) 83.7526i 0.382432i
\(220\) 0 0
\(221\) 304.949 1.37986
\(222\) 0 0
\(223\) 29.7219 29.7219i 0.133282 0.133282i −0.637318 0.770601i \(-0.719956\pi\)
0.770601 + 0.637318i \(0.219956\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 197.980 + 197.980i 0.872157 + 0.872157i 0.992707 0.120550i \(-0.0384659\pi\)
−0.120550 + 0.992707i \(0.538466\pi\)
\(228\) 0 0
\(229\) 8.96938i 0.0391676i 0.999808 + 0.0195838i \(0.00623412\pi\)
−0.999808 + 0.0195838i \(0.993766\pi\)
\(230\) 0 0
\(231\) −51.5255 −0.223054
\(232\) 0 0
\(233\) −28.7628 + 28.7628i −0.123445 + 0.123445i −0.766130 0.642685i \(-0.777820\pi\)
0.642685 + 0.766130i \(0.277820\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.606123 0.606123i −0.00255748 0.00255748i
\(238\) 0 0
\(239\) 242.969i 1.01661i −0.861178 0.508304i \(-0.830273\pi\)
0.861178 0.508304i \(-0.169727\pi\)
\(240\) 0 0
\(241\) −32.0000 −0.132780 −0.0663900 0.997794i \(-0.521148\pi\)
−0.0663900 + 0.997794i \(0.521148\pi\)
\(242\) 0 0
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −422.474 422.474i −1.71042 1.71042i
\(248\) 0 0
\(249\) 44.9694i 0.180600i
\(250\) 0 0
\(251\) 250.763 0.999055 0.499527 0.866298i \(-0.333507\pi\)
0.499527 + 0.866298i \(0.333507\pi\)
\(252\) 0 0
\(253\) 143.081 143.081i 0.565536 0.565536i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 73.8638 + 73.8638i 0.287408 + 0.287408i 0.836054 0.548647i \(-0.184857\pi\)
−0.548647 + 0.836054i \(0.684857\pi\)
\(258\) 0 0
\(259\) 37.4847i 0.144729i
\(260\) 0 0
\(261\) −29.2577 −0.112098
\(262\) 0 0
\(263\) 49.1668 49.1668i 0.186946 0.186946i −0.607428 0.794374i \(-0.707799\pi\)
0.794374 + 0.607428i \(0.207799\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −167.753 167.753i −0.628287 0.628287i
\(268\) 0 0
\(269\) 278.742i 1.03622i 0.855315 + 0.518108i \(0.173364\pi\)
−0.855315 + 0.518108i \(0.826636\pi\)
\(270\) 0 0
\(271\) 66.0000 0.243542 0.121771 0.992558i \(-0.461143\pi\)
0.121771 + 0.992558i \(0.461143\pi\)
\(272\) 0 0
\(273\) 76.5153 76.5153i 0.280276 0.280276i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −211.843 211.843i −0.764777 0.764777i 0.212404 0.977182i \(-0.431871\pi\)
−0.977182 + 0.212404i \(0.931871\pi\)
\(278\) 0 0
\(279\) 85.4847i 0.306397i
\(280\) 0 0
\(281\) −312.434 −1.11186 −0.555932 0.831228i \(-0.687638\pi\)
−0.555932 + 0.831228i \(0.687638\pi\)
\(282\) 0 0
\(283\) −204.747 + 204.747i −0.723487 + 0.723487i −0.969314 0.245826i \(-0.920941\pi\)
0.245826 + 0.969314i \(0.420941\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 190.000 + 190.000i 0.662021 + 0.662021i
\(288\) 0 0
\(289\) 20.9796i 0.0725937i
\(290\) 0 0
\(291\) −231.712 −0.796260
\(292\) 0 0
\(293\) −325.151 + 325.151i −1.10973 + 1.10973i −0.116545 + 0.993185i \(0.537182\pi\)
−0.993185 + 0.116545i \(0.962818\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 30.3031 + 30.3031i 0.102031 + 0.102031i
\(298\) 0 0
\(299\) 424.949i 1.42123i
\(300\) 0 0
\(301\) 178.020 0.591430
\(302\) 0 0
\(303\) 86.0352 86.0352i 0.283945 0.283945i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 179.394 + 179.394i 0.584345 + 0.584345i 0.936094 0.351749i \(-0.114413\pi\)
−0.351749 + 0.936094i \(0.614413\pi\)
\(308\) 0 0
\(309\) 212.722i 0.688421i
\(310\) 0 0
\(311\) 213.980 0.688037 0.344019 0.938963i \(-0.388212\pi\)
0.344019 + 0.938963i \(0.388212\pi\)
\(312\) 0 0
\(313\) 186.414 186.414i 0.595573 0.595573i −0.343558 0.939131i \(-0.611632\pi\)
0.939131 + 0.343558i \(0.111632\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −57.5505 57.5505i −0.181547 0.181547i 0.610482 0.792030i \(-0.290976\pi\)
−0.792030 + 0.610482i \(0.790976\pi\)
\(318\) 0 0
\(319\) 80.4337i 0.252143i
\(320\) 0 0
\(321\) −235.980 −0.735139
\(322\) 0 0
\(323\) 429.444 429.444i 1.32955 1.32955i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 15.3281 + 15.3281i 0.0468748 + 0.0468748i
\(328\) 0 0
\(329\) 112.454i 0.341806i
\(330\) 0 0
\(331\) 214.413 0.647774 0.323887 0.946096i \(-0.395010\pi\)
0.323887 + 0.946096i \(0.395010\pi\)
\(332\) 0 0
\(333\) 22.0454 22.0454i 0.0662024 0.0662024i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 94.5959 + 94.5959i 0.280700 + 0.280700i 0.833388 0.552688i \(-0.186398\pi\)
−0.552688 + 0.833388i \(0.686398\pi\)
\(338\) 0 0
\(339\) 163.980i 0.483716i
\(340\) 0 0
\(341\) 235.010 0.689179
\(342\) 0 0
\(343\) 216.767 216.767i 0.631975 0.631975i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 226.919 + 226.919i 0.653946 + 0.653946i 0.953941 0.299995i \(-0.0969849\pi\)
−0.299995 + 0.953941i \(0.596985\pi\)
\(348\) 0 0
\(349\) 182.454i 0.522791i 0.965232 + 0.261396i \(0.0841827\pi\)
−0.965232 + 0.261396i \(0.915817\pi\)
\(350\) 0 0
\(351\) −90.0000 −0.256410
\(352\) 0 0
\(353\) −263.914 + 263.914i −0.747631 + 0.747631i −0.974034 0.226403i \(-0.927303\pi\)
0.226403 + 0.974034i \(0.427303\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 77.7775 + 77.7775i 0.217864 + 0.217864i
\(358\) 0 0
\(359\) 285.485i 0.795222i 0.917554 + 0.397611i \(0.130161\pi\)
−0.917554 + 0.397611i \(0.869839\pi\)
\(360\) 0 0
\(361\) −828.898 −2.29612
\(362\) 0 0
\(363\) −64.8865 + 64.8865i −0.178751 + 0.178751i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 418.964 + 418.964i 1.14159 + 1.14159i 0.988159 + 0.153431i \(0.0490324\pi\)
0.153431 + 0.988159i \(0.450968\pi\)
\(368\) 0 0
\(369\) 223.485i 0.605650i
\(370\) 0 0
\(371\) 330.020 0.889543
\(372\) 0 0
\(373\) −283.106 + 283.106i −0.758996 + 0.758996i −0.976140 0.217143i \(-0.930326\pi\)
0.217143 + 0.976140i \(0.430326\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −119.444 119.444i −0.316827 0.316827i
\(378\) 0 0
\(379\) 194.000i 0.511873i 0.966694 + 0.255937i \(0.0823839\pi\)
−0.966694 + 0.255937i \(0.917616\pi\)
\(380\) 0 0
\(381\) 6.24745 0.0163975
\(382\) 0 0
\(383\) −531.489 + 531.489i −1.38770 + 1.38770i −0.557572 + 0.830129i \(0.688267\pi\)
−0.830129 + 0.557572i \(0.811733\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −104.697 104.697i −0.270535 0.270535i
\(388\) 0 0
\(389\) 479.196i 1.23187i 0.787798 + 0.615934i \(0.211221\pi\)
−0.787798 + 0.615934i \(0.788779\pi\)
\(390\) 0 0
\(391\) −431.959 −1.10475
\(392\) 0 0
\(393\) −54.1918 + 54.1918i −0.137893 + 0.137893i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 389.267 + 389.267i 0.980521 + 0.980521i 0.999814 0.0192929i \(-0.00614150\pi\)
−0.0192929 + 0.999814i \(0.506142\pi\)
\(398\) 0 0
\(399\) 215.505i 0.540113i
\(400\) 0 0
\(401\) −603.898 −1.50598 −0.752990 0.658032i \(-0.771389\pi\)
−0.752990 + 0.658032i \(0.771389\pi\)
\(402\) 0 0
\(403\) −348.990 + 348.990i −0.865980 + 0.865980i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −60.6061 60.6061i −0.148909 0.148909i
\(408\) 0 0
\(409\) 183.959i 0.449778i −0.974384 0.224889i \(-0.927798\pi\)
0.974384 0.224889i \(-0.0722019\pi\)
\(410\) 0 0
\(411\) 44.9694 0.109415
\(412\) 0 0
\(413\) −38.9148 + 38.9148i −0.0942247 + 0.0942247i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −269.419 269.419i −0.646088 0.646088i
\(418\) 0 0
\(419\) 197.814i 0.472109i −0.971740 0.236055i \(-0.924146\pi\)
0.971740 0.236055i \(-0.0758544\pi\)
\(420\) 0 0
\(421\) −114.041 −0.270881 −0.135440 0.990785i \(-0.543245\pi\)
−0.135440 + 0.990785i \(0.543245\pi\)
\(422\) 0 0
\(423\) −66.1362 + 66.1362i −0.156350 + 0.156350i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −136.465 136.465i −0.319591 0.319591i
\(428\) 0 0
\(429\) 247.423i 0.576745i
\(430\) 0 0
\(431\) −348.454 −0.808478 −0.404239 0.914653i \(-0.632464\pi\)
−0.404239 + 0.914653i \(0.632464\pi\)
\(432\) 0 0
\(433\) −60.1010 + 60.1010i −0.138801 + 0.138801i −0.773094 0.634292i \(-0.781292\pi\)
0.634292 + 0.773094i \(0.281292\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 598.434 + 598.434i 1.36941 + 1.36941i
\(438\) 0 0
\(439\) 556.929i 1.26863i 0.773075 + 0.634315i \(0.218718\pi\)
−0.773075 + 0.634315i \(0.781282\pi\)
\(440\) 0 0
\(441\) −107.969 −0.244829
\(442\) 0 0
\(443\) 95.5551 95.5551i 0.215700 0.215700i −0.590984 0.806684i \(-0.701260\pi\)
0.806684 + 0.590984i \(0.201260\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −34.6209 34.6209i −0.0774517 0.0774517i
\(448\) 0 0
\(449\) 213.423i 0.475331i 0.971347 + 0.237665i \(0.0763821\pi\)
−0.971347 + 0.237665i \(0.923618\pi\)
\(450\) 0 0
\(451\) −614.393 −1.36229
\(452\) 0 0
\(453\) 74.7219 74.7219i 0.164949 0.164949i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 38.9388 + 38.9388i 0.0852052 + 0.0852052i 0.748425 0.663220i \(-0.230810\pi\)
−0.663220 + 0.748425i \(0.730810\pi\)
\(458\) 0 0
\(459\) 91.4847i 0.199313i
\(460\) 0 0
\(461\) 509.712 1.10567 0.552833 0.833292i \(-0.313547\pi\)
0.552833 + 0.833292i \(0.313547\pi\)
\(462\) 0 0
\(463\) 492.955 492.955i 1.06470 1.06470i 0.0669397 0.997757i \(-0.478676\pi\)
0.997757 0.0669397i \(-0.0213235\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 647.044 + 647.044i 1.38553 + 1.38553i 0.834449 + 0.551085i \(0.185786\pi\)
0.551085 + 0.834449i \(0.314214\pi\)
\(468\) 0 0
\(469\) 23.9592i 0.0510857i
\(470\) 0 0
\(471\) 55.4847 0.117802
\(472\) 0 0
\(473\) −287.828 + 287.828i −0.608515 + 0.608515i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −194.091 194.091i −0.406899 0.406899i
\(478\) 0 0
\(479\) 198.969i 0.415385i 0.978194 + 0.207692i \(0.0665953\pi\)
−0.978194 + 0.207692i \(0.933405\pi\)
\(480\) 0 0
\(481\) 180.000 0.374220
\(482\) 0 0
\(483\) −108.384 + 108.384i −0.224397 + 0.224397i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −34.6209 34.6209i −0.0710902 0.0710902i 0.670668 0.741758i \(-0.266008\pi\)
−0.741758 + 0.670668i \(0.766008\pi\)
\(488\) 0 0
\(489\) 217.980i 0.445766i
\(490\) 0 0
\(491\) 155.217 0.316124 0.158062 0.987429i \(-0.449475\pi\)
0.158062 + 0.987429i \(0.449475\pi\)
\(492\) 0 0
\(493\) 121.414 121.414i 0.246276 0.246276i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 300.908 + 300.908i 0.605449 + 0.605449i
\(498\) 0 0
\(499\) 547.444i 1.09708i −0.836124 0.548541i \(-0.815183\pi\)
0.836124 0.548541i \(-0.184817\pi\)
\(500\) 0 0
\(501\) 420.434 0.839189
\(502\) 0 0
\(503\) −526.590 + 526.590i −1.04690 + 1.04690i −0.0480545 + 0.998845i \(0.515302\pi\)
−0.998845 + 0.0480545i \(0.984698\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −160.442 160.442i −0.316453 0.316453i
\(508\) 0 0
\(509\) 115.773i 0.227452i −0.993512 0.113726i \(-0.963721\pi\)
0.993512 0.113726i \(-0.0362786\pi\)
\(510\) 0 0
\(511\) −174.413 −0.341318
\(512\) 0 0
\(513\) −126.742 + 126.742i −0.247061 + 0.247061i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 181.818 + 181.818i 0.351680 + 0.351680i
\(518\) 0 0
\(519\) 26.0408i 0.0501750i
\(520\) 0 0
\(521\) 791.444 1.51909 0.759543 0.650457i \(-0.225423\pi\)
0.759543 + 0.650457i \(0.225423\pi\)
\(522\) 0 0
\(523\) 93.6867 93.6867i 0.179133 0.179133i −0.611845 0.790978i \(-0.709572\pi\)
0.790978 + 0.611845i \(0.209572\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −354.747 354.747i −0.673144 0.673144i
\(528\) 0 0
\(529\) 72.9388i 0.137880i
\(530\) 0 0
\(531\) 45.7730 0.0862014
\(532\) 0 0
\(533\) 912.372 912.372i 1.71177 1.71177i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −122.778 122.778i −0.228636 0.228636i
\(538\) 0 0
\(539\) 296.824i 0.550694i
\(540\) 0 0
\(541\) −359.526 −0.664557 −0.332279 0.943181i \(-0.607817\pi\)
−0.332279 + 0.943181i \(0.607817\pi\)
\(542\) 0 0
\(543\) 317.753 317.753i 0.585180 0.585180i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 164.647 + 164.647i 0.301000 + 0.301000i 0.841405 0.540405i \(-0.181729\pi\)
−0.540405 + 0.841405i \(0.681729\pi\)
\(548\) 0 0
\(549\) 160.515i 0.292378i
\(550\) 0 0
\(551\) −336.413 −0.610550
\(552\) 0 0
\(553\) 1.26224 1.26224i 0.00228253 0.00228253i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −139.040 139.040i −0.249623 0.249623i 0.571193 0.820816i \(-0.306481\pi\)
−0.820816 + 0.571193i \(0.806481\pi\)
\(558\) 0 0
\(559\) 854.847i 1.52924i
\(560\) 0 0
\(561\) −251.505 −0.448316
\(562\) 0 0
\(563\) −787.423 + 787.423i −1.39862 + 1.39862i −0.594596 + 0.804024i \(0.702688\pi\)
−0.804024 + 0.594596i \(0.797312\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −22.9546 22.9546i −0.0404843 0.0404843i
\(568\) 0 0
\(569\) 4.92856i 0.00866180i 0.999991 + 0.00433090i \(0.00137857\pi\)
−0.999991 + 0.00433090i \(0.998621\pi\)
\(570\) 0 0
\(571\) −205.505 −0.359904 −0.179952 0.983675i \(-0.557594\pi\)
−0.179952 + 0.983675i \(0.557594\pi\)
\(572\) 0 0
\(573\) −94.8990 + 94.8990i −0.165618 + 0.165618i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −689.999 689.999i −1.19584 1.19584i −0.975401 0.220438i \(-0.929251\pi\)
−0.220438 0.975401i \(-0.570749\pi\)
\(578\) 0 0
\(579\) 204.742i 0.353614i
\(580\) 0 0
\(581\) −93.6480 −0.161184
\(582\) 0 0
\(583\) −533.585 + 533.585i −0.915240 + 0.915240i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −672.347 672.347i −1.14540 1.14540i −0.987447 0.157949i \(-0.949512\pi\)
−0.157949 0.987447i \(-0.550488\pi\)
\(588\) 0 0
\(589\) 982.929i 1.66881i
\(590\) 0 0
\(591\) 490.515 0.829975
\(592\) 0 0
\(593\) −344.570 + 344.570i −0.581062 + 0.581062i −0.935195 0.354133i \(-0.884776\pi\)
0.354133 + 0.935195i \(0.384776\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 199.621 + 199.621i 0.334373 + 0.334373i
\(598\) 0 0
\(599\) 739.464i 1.23450i 0.786768 + 0.617249i \(0.211753\pi\)
−0.786768 + 0.617249i \(0.788247\pi\)
\(600\) 0 0
\(601\) −642.908 −1.06973 −0.534865 0.844937i \(-0.679638\pi\)
−0.534865 + 0.844937i \(0.679638\pi\)
\(602\) 0 0
\(603\) 14.0908 14.0908i 0.0233679 0.0233679i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −362.803 362.803i −0.597698 0.597698i 0.342002 0.939699i \(-0.388895\pi\)
−0.939699 + 0.342002i \(0.888895\pi\)
\(608\) 0 0
\(609\) 60.9286i 0.100047i
\(610\) 0 0
\(611\) −540.000 −0.883797
\(612\) 0 0
\(613\) 721.943 721.943i 1.17772 1.17772i 0.197398 0.980323i \(-0.436751\pi\)
0.980323 0.197398i \(-0.0632492\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −72.9036 72.9036i −0.118158 0.118158i 0.645555 0.763713i \(-0.276626\pi\)
−0.763713 + 0.645555i \(0.776626\pi\)
\(618\) 0 0
\(619\) 228.061i 0.368435i 0.982886 + 0.184217i \(0.0589751\pi\)
−0.982886 + 0.184217i \(0.941025\pi\)
\(620\) 0 0
\(621\) 127.485 0.205289
\(622\) 0 0
\(623\) 349.342 349.342i 0.560741 0.560741i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 348.434 + 348.434i 0.555716 + 0.555716i
\(628\) 0 0
\(629\) 182.969i 0.290889i
\(630\) 0 0
\(631\) 86.4337 0.136979 0.0684894 0.997652i \(-0.478182\pi\)
0.0684894 + 0.997652i \(0.478182\pi\)
\(632\) 0 0
\(633\) −254.722 + 254.722i −0.402404 + 0.402404i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −440.783 440.783i −0.691967 0.691967i
\(638\) 0 0
\(639\) 353.939i 0.553895i
\(640\) 0 0
\(641\) 340.061 0.530517 0.265258 0.964177i \(-0.414543\pi\)
0.265258 + 0.964177i \(0.414543\pi\)
\(642\) 0 0
\(643\) 769.040 769.040i 1.19602 1.19602i 0.220670 0.975349i \(-0.429176\pi\)
0.975349 0.220670i \(-0.0708243\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −602.854 602.854i −0.931767 0.931767i 0.0660489 0.997816i \(-0.478961\pi\)
−0.997816 + 0.0660489i \(0.978961\pi\)
\(648\) 0 0
\(649\) 125.837i 0.193893i
\(650\) 0 0
\(651\) −178.020 −0.273457
\(652\) 0 0
\(653\) 75.8842 75.8842i 0.116209 0.116209i −0.646611 0.762820i \(-0.723814\pi\)
0.762820 + 0.646611i \(0.223814\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 102.576 + 102.576i 0.156127 + 0.156127i
\(658\) 0 0
\(659\) 61.1964i 0.0928626i 0.998921 + 0.0464313i \(0.0147849\pi\)
−0.998921 + 0.0464313i \(0.985215\pi\)
\(660\) 0 0
\(661\) 1158.45 1.75258 0.876289 0.481786i \(-0.160012\pi\)
0.876289 + 0.481786i \(0.160012\pi\)
\(662\) 0 0
\(663\) 373.485 373.485i 0.563325 0.563325i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 169.192 + 169.192i 0.253661 + 0.253661i
\(668\) 0 0
\(669\) 72.8036i 0.108824i
\(670\) 0 0
\(671\) 441.281 0.657646
\(672\) 0 0
\(673\) −711.413 + 711.413i −1.05708 + 1.05708i −0.0588084 + 0.998269i \(0.518730\pi\)
−0.998269 + 0.0588084i \(0.981270\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −351.943 351.943i −0.519857 0.519857i 0.397671 0.917528i \(-0.369819\pi\)
−0.917528 + 0.397671i \(0.869819\pi\)
\(678\) 0 0
\(679\) 482.536i 0.710656i
\(680\) 0 0
\(681\) 484.949 0.712113
\(682\) 0 0
\(683\) 277.905 277.905i 0.406888 0.406888i −0.473764 0.880652i \(-0.657105\pi\)
0.880652 + 0.473764i \(0.157105\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 10.9852 + 10.9852i 0.0159901 + 0.0159901i
\(688\) 0 0
\(689\) 1584.74i 2.30007i
\(690\) 0 0
\(691\) 1097.51 1.58829 0.794143 0.607731i \(-0.207920\pi\)
0.794143 + 0.607731i \(0.207920\pi\)
\(692\) 0 0
\(693\) −63.1056 + 63.1056i −0.0910615 + 0.0910615i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 927.423 + 927.423i 1.33059 + 1.33059i
\(698\) 0 0
\(699\) 70.4541i 0.100793i
\(700\) 0 0
\(701\) −354.783 −0.506110 −0.253055 0.967452i \(-0.581435\pi\)
−0.253055 + 0.967452i \(0.581435\pi\)
\(702\) 0 0
\(703\) 253.485 253.485i 0.360576 0.360576i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 179.167 + 179.167i 0.253418 + 0.253418i
\(708\) 0 0
\(709\) 368.061i 0.519127i −0.965726 0.259564i \(-0.916421\pi\)
0.965726 0.259564i \(-0.0835787\pi\)
\(710\) 0 0
\(711\) −1.48469 −0.00208817
\(712\) 0 0
\(713\) 494.343 494.343i 0.693328 0.693328i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −297.576 297.576i −0.415029 0.415029i
\(718\) 0 0
\(719\) 382.969i 0.532642i −0.963884 0.266321i \(-0.914192\pi\)
0.963884 0.266321i \(-0.0858081\pi\)
\(720\) 0 0
\(721\) 442.990 0.614410
\(722\) 0 0
\(723\) −39.1918 + 39.1918i −0.0542072 + 0.0542072i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 837.297 + 837.297i 1.15172 + 1.15172i 0.986209 + 0.165507i \(0.0529261\pi\)
0.165507 + 0.986209i \(0.447074\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 868.949 1.18871
\(732\) 0 0
\(733\) 29.8230 29.8230i 0.0406862 0.0406862i −0.686471 0.727157i \(-0.740841\pi\)
0.727157 + 0.686471i \(0.240841\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −38.7378 38.7378i −0.0525614 0.0525614i
\(738\) 0 0
\(739\) 1183.28i 1.60119i 0.599205 + 0.800596i \(0.295484\pi\)
−0.599205 + 0.800596i \(0.704516\pi\)
\(740\) 0 0
\(741\) −1034.85 −1.39655
\(742\) 0 0
\(743\) 65.7821 65.7821i 0.0885358 0.0885358i −0.661452 0.749988i \(-0.730059\pi\)
0.749988 + 0.661452i \(0.230059\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 55.0760 + 55.0760i 0.0737296 + 0.0737296i
\(748\) 0 0
\(749\) 491.423i 0.656106i
\(750\) 0 0
\(751\) 850.270 1.13218 0.566092 0.824342i \(-0.308455\pi\)
0.566092 + 0.824342i \(0.308455\pi\)
\(752\) 0 0
\(753\) 307.120 307.120i 0.407862 0.407862i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −145.832 145.832i −0.192645 0.192645i 0.604193 0.796838i \(-0.293496\pi\)
−0.796838 + 0.604193i \(0.793496\pi\)
\(758\) 0 0
\(759\) 350.474i 0.461758i
\(760\) 0 0
\(761\) 157.505 0.206971 0.103486 0.994631i \(-0.467000\pi\)
0.103486 + 0.994631i \(0.467000\pi\)
\(762\) 0 0
\(763\) −31.9204 + 31.9204i −0.0418354 + 0.0418354i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 186.867 + 186.867i 0.243634 + 0.243634i
\(768\) 0 0
\(769\) 559.031i 0.726958i −0.931602 0.363479i \(-0.881589\pi\)
0.931602 0.363479i \(-0.118411\pi\)
\(770\) 0 0
\(771\) 180.929 0.234667
\(772\) 0 0
\(773\) 348.965 348.965i 0.451442 0.451442i −0.444391 0.895833i \(-0.646580\pi\)
0.895833 + 0.444391i \(0.146580\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 45.9092 + 45.9092i 0.0590852 + 0.0590852i
\(778\) 0 0
\(779\) 2569.69i 3.29871i
\(780\) 0 0
\(781\) −973.031 −1.24588
\(782\) 0 0
\(783\) −35.8332 + 35.8332i −0.0457639 + 0.0457639i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −821.414 821.414i −1.04373 1.04373i −0.998999 0.0447293i \(-0.985757\pi\)
−0.0447293 0.998999i \(-0.514243\pi\)
\(788\) 0 0
\(789\) 120.434i 0.152641i
\(790\) 0 0
\(791\) −341.485 −0.431713
\(792\) 0 0
\(793\) −655.301 + 655.301i −0.826357 + 0.826357i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 649.065 + 649.065i 0.814385 + 0.814385i 0.985288 0.170903i \(-0.0546685\pi\)
−0.170903 + 0.985288i \(0.554668\pi\)
\(798\) 0 0
\(799\) 548.908i