Properties

Label 108.2.b.b.107.2
Level 108
Weight 2
Character 108.107
Analytic conductor 0.862
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.862384341830\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.2
Root \(-1.22474 + 0.707107i\)
Character \(\chi\) = 108.107
Dual form 108.2.b.b.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} -2.82843i q^{5} -1.73205i q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} -2.82843i q^{5} -1.73205i q^{7} +2.82843i q^{8} +(2.00000 + 3.46410i) q^{10} +4.89898 q^{11} -1.00000 q^{13} +(1.22474 + 2.12132i) q^{14} +(-2.00000 - 3.46410i) q^{16} -2.82843i q^{17} +5.19615i q^{19} +(-4.89898 - 2.82843i) q^{20} +(-6.00000 + 3.46410i) q^{22} -4.89898 q^{23} -3.00000 q^{25} +(1.22474 - 0.707107i) q^{26} +(-3.00000 - 1.73205i) q^{28} +5.65685i q^{29} -3.46410i q^{31} +(4.89898 + 2.82843i) q^{32} +(2.00000 + 3.46410i) q^{34} -4.89898 q^{35} -1.00000 q^{37} +(-3.67423 - 6.36396i) q^{38} +8.00000 q^{40} +5.65685i q^{41} +3.46410i q^{43} +(4.89898 - 8.48528i) q^{44} +(6.00000 - 3.46410i) q^{46} +4.89898 q^{47} +4.00000 q^{49} +(3.67423 - 2.12132i) q^{50} +(-1.00000 + 1.73205i) q^{52} +5.65685i q^{53} -13.8564i q^{55} +4.89898 q^{56} +(-4.00000 - 6.92820i) q^{58} -4.89898 q^{59} +11.0000 q^{61} +(2.44949 + 4.24264i) q^{62} -8.00000 q^{64} +2.82843i q^{65} +12.1244i q^{67} +(-4.89898 - 2.82843i) q^{68} +(6.00000 - 3.46410i) q^{70} -1.00000 q^{73} +(1.22474 - 0.707107i) q^{74} +(9.00000 + 5.19615i) q^{76} -8.48528i q^{77} -1.73205i q^{79} +(-9.79796 + 5.65685i) q^{80} +(-4.00000 - 6.92820i) q^{82} -9.79796 q^{83} -8.00000 q^{85} +(-2.44949 - 4.24264i) q^{86} +13.8564i q^{88} -2.82843i q^{89} +1.73205i q^{91} +(-4.89898 + 8.48528i) q^{92} +(-6.00000 + 3.46410i) q^{94} +14.6969 q^{95} -13.0000 q^{97} +(-4.89898 + 2.82843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{4} + O(q^{10}) \) \( 4q + 4q^{4} + 8q^{10} - 4q^{13} - 8q^{16} - 24q^{22} - 12q^{25} - 12q^{28} + 8q^{34} - 4q^{37} + 32q^{40} + 24q^{46} + 16q^{49} - 4q^{52} - 16q^{58} + 44q^{61} - 32q^{64} + 24q^{70} - 4q^{73} + 36q^{76} - 16q^{82} - 32q^{85} - 24q^{94} - 52q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.866025 + 0.500000i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 2.82843i 1.26491i −0.774597 0.632456i \(-0.782047\pi\)
0.774597 0.632456i \(-0.217953\pi\)
\(6\) 0 0
\(7\) 1.73205i 0.654654i −0.944911 0.327327i \(-0.893852\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 2.00000 + 3.46410i 0.632456 + 1.09545i
\(11\) 4.89898 1.47710 0.738549 0.674200i \(-0.235511\pi\)
0.738549 + 0.674200i \(0.235511\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 1.22474 + 2.12132i 0.327327 + 0.566947i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) 0 0
\(19\) 5.19615i 1.19208i 0.802955 + 0.596040i \(0.203260\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −4.89898 2.82843i −1.09545 0.632456i
\(21\) 0 0
\(22\) −6.00000 + 3.46410i −1.27920 + 0.738549i
\(23\) −4.89898 −1.02151 −0.510754 0.859727i \(-0.670634\pi\)
−0.510754 + 0.859727i \(0.670634\pi\)
\(24\) 0 0
\(25\) −3.00000 −0.600000
\(26\) 1.22474 0.707107i 0.240192 0.138675i
\(27\) 0 0
\(28\) −3.00000 1.73205i −0.566947 0.327327i
\(29\) 5.65685i 1.05045i 0.850963 + 0.525226i \(0.176019\pi\)
−0.850963 + 0.525226i \(0.823981\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i −0.950382 0.311086i \(-0.899307\pi\)
0.950382 0.311086i \(-0.100693\pi\)
\(32\) 4.89898 + 2.82843i 0.866025 + 0.500000i
\(33\) 0 0
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) −4.89898 −0.828079
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −3.67423 6.36396i −0.596040 1.03237i
\(39\) 0 0
\(40\) 8.00000 1.26491
\(41\) 5.65685i 0.883452i 0.897150 + 0.441726i \(0.145634\pi\)
−0.897150 + 0.441726i \(0.854366\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i 0.964486 + 0.264135i \(0.0850865\pi\)
−0.964486 + 0.264135i \(0.914913\pi\)
\(44\) 4.89898 8.48528i 0.738549 1.27920i
\(45\) 0 0
\(46\) 6.00000 3.46410i 0.884652 0.510754i
\(47\) 4.89898 0.714590 0.357295 0.933992i \(-0.383699\pi\)
0.357295 + 0.933992i \(0.383699\pi\)
\(48\) 0 0
\(49\) 4.00000 0.571429
\(50\) 3.67423 2.12132i 0.519615 0.300000i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 5.65685i 0.777029i 0.921443 + 0.388514i \(0.127012\pi\)
−0.921443 + 0.388514i \(0.872988\pi\)
\(54\) 0 0
\(55\) 13.8564i 1.86840i
\(56\) 4.89898 0.654654
\(57\) 0 0
\(58\) −4.00000 6.92820i −0.525226 0.909718i
\(59\) −4.89898 −0.637793 −0.318896 0.947790i \(-0.603312\pi\)
−0.318896 + 0.947790i \(0.603312\pi\)
\(60\) 0 0
\(61\) 11.0000 1.40841 0.704203 0.709999i \(-0.251305\pi\)
0.704203 + 0.709999i \(0.251305\pi\)
\(62\) 2.44949 + 4.24264i 0.311086 + 0.538816i
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 2.82843i 0.350823i
\(66\) 0 0
\(67\) 12.1244i 1.48123i 0.671932 + 0.740613i \(0.265465\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) −4.89898 2.82843i −0.594089 0.342997i
\(69\) 0 0
\(70\) 6.00000 3.46410i 0.717137 0.414039i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −1.00000 −0.117041 −0.0585206 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) 1.22474 0.707107i 0.142374 0.0821995i
\(75\) 0 0
\(76\) 9.00000 + 5.19615i 1.03237 + 0.596040i
\(77\) 8.48528i 0.966988i
\(78\) 0 0
\(79\) 1.73205i 0.194871i −0.995242 0.0974355i \(-0.968936\pi\)
0.995242 0.0974355i \(-0.0310640\pi\)
\(80\) −9.79796 + 5.65685i −1.09545 + 0.632456i
\(81\) 0 0
\(82\) −4.00000 6.92820i −0.441726 0.765092i
\(83\) −9.79796 −1.07547 −0.537733 0.843115i \(-0.680719\pi\)
−0.537733 + 0.843115i \(0.680719\pi\)
\(84\) 0 0
\(85\) −8.00000 −0.867722
\(86\) −2.44949 4.24264i −0.264135 0.457496i
\(87\) 0 0
\(88\) 13.8564i 1.47710i
\(89\) 2.82843i 0.299813i −0.988700 0.149906i \(-0.952103\pi\)
0.988700 0.149906i \(-0.0478972\pi\)
\(90\) 0 0
\(91\) 1.73205i 0.181568i
\(92\) −4.89898 + 8.48528i −0.510754 + 0.884652i
\(93\) 0 0
\(94\) −6.00000 + 3.46410i −0.618853 + 0.357295i
\(95\) 14.6969 1.50787
\(96\) 0 0
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) −4.89898 + 2.82843i −0.494872 + 0.285714i
\(99\) 0 0
\(100\) −3.00000 + 5.19615i −0.300000 + 0.519615i
\(101\) 11.3137i 1.12576i −0.826540 0.562878i \(-0.809694\pi\)
0.826540 0.562878i \(-0.190306\pi\)
\(102\) 0 0
\(103\) 8.66025i 0.853320i −0.904412 0.426660i \(-0.859690\pi\)
0.904412 0.426660i \(-0.140310\pi\)
\(104\) 2.82843i 0.277350i
\(105\) 0 0
\(106\) −4.00000 6.92820i −0.388514 0.672927i
\(107\) 14.6969 1.42081 0.710403 0.703795i \(-0.248513\pi\)
0.710403 + 0.703795i \(0.248513\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 9.79796 + 16.9706i 0.934199 + 1.61808i
\(111\) 0 0
\(112\) −6.00000 + 3.46410i −0.566947 + 0.327327i
\(113\) 2.82843i 0.266076i −0.991111 0.133038i \(-0.957527\pi\)
0.991111 0.133038i \(-0.0424732\pi\)
\(114\) 0 0
\(115\) 13.8564i 1.29212i
\(116\) 9.79796 + 5.65685i 0.909718 + 0.525226i
\(117\) 0 0
\(118\) 6.00000 3.46410i 0.552345 0.318896i
\(119\) −4.89898 −0.449089
\(120\) 0 0
\(121\) 13.0000 1.18182
\(122\) −13.4722 + 7.77817i −1.21972 + 0.704203i
\(123\) 0 0
\(124\) −6.00000 3.46410i −0.538816 0.311086i
\(125\) 5.65685i 0.505964i
\(126\) 0 0
\(127\) 10.3923i 0.922168i 0.887357 + 0.461084i \(0.152539\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 9.79796 5.65685i 0.866025 0.500000i
\(129\) 0 0
\(130\) −2.00000 3.46410i −0.175412 0.303822i
\(131\) 9.79796 0.856052 0.428026 0.903767i \(-0.359209\pi\)
0.428026 + 0.903767i \(0.359209\pi\)
\(132\) 0 0
\(133\) 9.00000 0.780399
\(134\) −8.57321 14.8492i −0.740613 1.28278i
\(135\) 0 0
\(136\) 8.00000 0.685994
\(137\) 19.7990i 1.69154i −0.533546 0.845771i \(-0.679141\pi\)
0.533546 0.845771i \(-0.320859\pi\)
\(138\) 0 0
\(139\) 8.66025i 0.734553i −0.930112 0.367277i \(-0.880290\pi\)
0.930112 0.367277i \(-0.119710\pi\)
\(140\) −4.89898 + 8.48528i −0.414039 + 0.717137i
\(141\) 0 0
\(142\) 0 0
\(143\) −4.89898 −0.409673
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 1.22474 0.707107i 0.101361 0.0585206i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) 22.6274i 1.85371i 0.375419 + 0.926855i \(0.377499\pi\)
−0.375419 + 0.926855i \(0.622501\pi\)
\(150\) 0 0
\(151\) 22.5167i 1.83238i −0.400744 0.916190i \(-0.631248\pi\)
0.400744 0.916190i \(-0.368752\pi\)
\(152\) −14.6969 −1.19208
\(153\) 0 0
\(154\) 6.00000 + 10.3923i 0.483494 + 0.837436i
\(155\) −9.79796 −0.786991
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 1.22474 + 2.12132i 0.0974355 + 0.168763i
\(159\) 0 0
\(160\) 8.00000 13.8564i 0.632456 1.09545i
\(161\) 8.48528i 0.668734i
\(162\) 0 0
\(163\) 5.19615i 0.406994i 0.979076 + 0.203497i \(0.0652307\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 9.79796 + 5.65685i 0.765092 + 0.441726i
\(165\) 0 0
\(166\) 12.0000 6.92820i 0.931381 0.537733i
\(167\) −4.89898 −0.379094 −0.189547 0.981872i \(-0.560702\pi\)
−0.189547 + 0.981872i \(0.560702\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 9.79796 5.65685i 0.751469 0.433861i
\(171\) 0 0
\(172\) 6.00000 + 3.46410i 0.457496 + 0.264135i
\(173\) 5.65685i 0.430083i 0.976605 + 0.215041i \(0.0689886\pi\)
−0.976605 + 0.215041i \(0.931011\pi\)
\(174\) 0 0
\(175\) 5.19615i 0.392792i
\(176\) −9.79796 16.9706i −0.738549 1.27920i
\(177\) 0 0
\(178\) 2.00000 + 3.46410i 0.149906 + 0.259645i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) −1.22474 2.12132i −0.0907841 0.157243i
\(183\) 0 0
\(184\) 13.8564i 1.02151i
\(185\) 2.82843i 0.207950i
\(186\) 0 0
\(187\) 13.8564i 1.01328i
\(188\) 4.89898 8.48528i 0.357295 0.618853i
\(189\) 0 0
\(190\) −18.0000 + 10.3923i −1.30586 + 0.753937i
\(191\) −24.4949 −1.77239 −0.886194 0.463314i \(-0.846660\pi\)
−0.886194 + 0.463314i \(0.846660\pi\)
\(192\) 0 0
\(193\) −1.00000 −0.0719816 −0.0359908 0.999352i \(-0.511459\pi\)
−0.0359908 + 0.999352i \(0.511459\pi\)
\(194\) 15.9217 9.19239i 1.14311 0.659975i
\(195\) 0 0
\(196\) 4.00000 6.92820i 0.285714 0.494872i
\(197\) 2.82843i 0.201517i −0.994911 0.100759i \(-0.967873\pi\)
0.994911 0.100759i \(-0.0321270\pi\)
\(198\) 0 0
\(199\) 5.19615i 0.368345i 0.982894 + 0.184173i \(0.0589606\pi\)
−0.982894 + 0.184173i \(0.941039\pi\)
\(200\) 8.48528i 0.600000i
\(201\) 0 0
\(202\) 8.00000 + 13.8564i 0.562878 + 0.974933i
\(203\) 9.79796 0.687682
\(204\) 0 0
\(205\) 16.0000 1.11749
\(206\) 6.12372 + 10.6066i 0.426660 + 0.738997i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 25.4558i 1.76082i
\(210\) 0 0
\(211\) 12.1244i 0.834675i 0.908752 + 0.417338i \(0.137037\pi\)
−0.908752 + 0.417338i \(0.862963\pi\)
\(212\) 9.79796 + 5.65685i 0.672927 + 0.388514i
\(213\) 0 0
\(214\) −18.0000 + 10.3923i −1.23045 + 0.710403i
\(215\) 9.79796 0.668215
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 12.2474 7.07107i 0.829502 0.478913i
\(219\) 0 0
\(220\) −24.0000 13.8564i −1.61808 0.934199i
\(221\) 2.82843i 0.190261i
\(222\) 0 0
\(223\) 24.2487i 1.62381i 0.583787 + 0.811907i \(0.301570\pi\)
−0.583787 + 0.811907i \(0.698430\pi\)
\(224\) 4.89898 8.48528i 0.327327 0.566947i
\(225\) 0 0
\(226\) 2.00000 + 3.46410i 0.133038 + 0.230429i
\(227\) 19.5959 1.30063 0.650313 0.759666i \(-0.274638\pi\)
0.650313 + 0.759666i \(0.274638\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) −9.79796 16.9706i −0.646058 1.11901i
\(231\) 0 0
\(232\) −16.0000 −1.05045
\(233\) 22.6274i 1.48237i 0.671300 + 0.741186i \(0.265736\pi\)
−0.671300 + 0.741186i \(0.734264\pi\)
\(234\) 0 0
\(235\) 13.8564i 0.903892i
\(236\) −4.89898 + 8.48528i −0.318896 + 0.552345i
\(237\) 0 0
\(238\) 6.00000 3.46410i 0.388922 0.224544i
\(239\) −19.5959 −1.26755 −0.633777 0.773516i \(-0.718496\pi\)
−0.633777 + 0.773516i \(0.718496\pi\)
\(240\) 0 0
\(241\) −25.0000 −1.61039 −0.805196 0.593009i \(-0.797940\pi\)
−0.805196 + 0.593009i \(0.797940\pi\)
\(242\) −15.9217 + 9.19239i −1.02348 + 0.590909i
\(243\) 0 0
\(244\) 11.0000 19.0526i 0.704203 1.21972i
\(245\) 11.3137i 0.722806i
\(246\) 0 0
\(247\) 5.19615i 0.330623i
\(248\) 9.79796 0.622171
\(249\) 0 0
\(250\) 4.00000 + 6.92820i 0.252982 + 0.438178i
\(251\) −29.3939 −1.85533 −0.927663 0.373420i \(-0.878185\pi\)
−0.927663 + 0.373420i \(0.878185\pi\)
\(252\) 0 0
\(253\) −24.0000 −1.50887
\(254\) −7.34847 12.7279i −0.461084 0.798621i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 28.2843i 1.76432i −0.470946 0.882162i \(-0.656087\pi\)
0.470946 0.882162i \(-0.343913\pi\)
\(258\) 0 0
\(259\) 1.73205i 0.107624i
\(260\) 4.89898 + 2.82843i 0.303822 + 0.175412i
\(261\) 0 0
\(262\) −12.0000 + 6.92820i −0.741362 + 0.428026i
\(263\) 19.5959 1.20834 0.604168 0.796857i \(-0.293506\pi\)
0.604168 + 0.796857i \(0.293506\pi\)
\(264\) 0 0
\(265\) 16.0000 0.982872
\(266\) −11.0227 + 6.36396i −0.675845 + 0.390199i
\(267\) 0 0
\(268\) 21.0000 + 12.1244i 1.28278 + 0.740613i
\(269\) 2.82843i 0.172452i −0.996276 0.0862261i \(-0.972519\pi\)
0.996276 0.0862261i \(-0.0274808\pi\)
\(270\) 0 0
\(271\) 5.19615i 0.315644i 0.987468 + 0.157822i \(0.0504472\pi\)
−0.987468 + 0.157822i \(0.949553\pi\)
\(272\) −9.79796 + 5.65685i −0.594089 + 0.342997i
\(273\) 0 0
\(274\) 14.0000 + 24.2487i 0.845771 + 1.46492i
\(275\) −14.6969 −0.886259
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 6.12372 + 10.6066i 0.367277 + 0.636142i
\(279\) 0 0
\(280\) 13.8564i 0.828079i
\(281\) 5.65685i 0.337460i 0.985662 + 0.168730i \(0.0539665\pi\)
−0.985662 + 0.168730i \(0.946033\pi\)
\(282\) 0 0
\(283\) 24.2487i 1.44144i −0.693228 0.720718i \(-0.743812\pi\)
0.693228 0.720718i \(-0.256188\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 6.00000 3.46410i 0.354787 0.204837i
\(287\) 9.79796 0.578355
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) −19.5959 + 11.3137i −1.15071 + 0.664364i
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) 2.82843i 0.165238i −0.996581 0.0826192i \(-0.973671\pi\)
0.996581 0.0826192i \(-0.0263285\pi\)
\(294\) 0 0
\(295\) 13.8564i 0.806751i
\(296\) 2.82843i 0.164399i
\(297\) 0 0
\(298\) −16.0000 27.7128i −0.926855 1.60536i
\(299\) 4.89898 0.283315
\(300\) 0 0
\(301\) 6.00000 0.345834
\(302\) 15.9217 + 27.5772i 0.916190 + 1.58689i
\(303\) 0 0
\(304\) 18.0000 10.3923i 1.03237 0.596040i
\(305\) 31.1127i 1.78151i
\(306\) 0 0
\(307\) 10.3923i 0.593120i −0.955014 0.296560i \(-0.904160\pi\)
0.955014 0.296560i \(-0.0958395\pi\)
\(308\) −14.6969 8.48528i −0.837436 0.483494i
\(309\) 0 0
\(310\) 12.0000 6.92820i 0.681554 0.393496i
\(311\) 24.4949 1.38898 0.694489 0.719503i \(-0.255630\pi\)
0.694489 + 0.719503i \(0.255630\pi\)
\(312\) 0 0
\(313\) 11.0000 0.621757 0.310878 0.950450i \(-0.399377\pi\)
0.310878 + 0.950450i \(0.399377\pi\)
\(314\) 12.2474 7.07107i 0.691164 0.399043i
\(315\) 0 0
\(316\) −3.00000 1.73205i −0.168763 0.0974355i
\(317\) 5.65685i 0.317721i 0.987301 + 0.158860i \(0.0507819\pi\)
−0.987301 + 0.158860i \(0.949218\pi\)
\(318\) 0 0
\(319\) 27.7128i 1.55162i
\(320\) 22.6274i 1.26491i
\(321\) 0 0
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) 14.6969 0.817760
\(324\) 0 0
\(325\) 3.00000 0.166410
\(326\) −3.67423 6.36396i −0.203497 0.352467i
\(327\) 0 0
\(328\) −16.0000 −0.883452
\(329\) 8.48528i 0.467809i
\(330\) 0 0
\(331\) 22.5167i 1.23763i −0.785538 0.618814i \(-0.787614\pi\)
0.785538 0.618814i \(-0.212386\pi\)
\(332\) −9.79796 + 16.9706i −0.537733 + 0.931381i
\(333\) 0 0
\(334\) 6.00000 3.46410i 0.328305 0.189547i
\(335\) 34.2929 1.87362
\(336\) 0 0
\(337\) 11.0000 0.599208 0.299604 0.954064i \(-0.403145\pi\)
0.299604 + 0.954064i \(0.403145\pi\)
\(338\) 14.6969 8.48528i 0.799408 0.461538i
\(339\) 0 0
\(340\) −8.00000 + 13.8564i −0.433861 + 0.751469i
\(341\) 16.9706i 0.919007i
\(342\) 0 0
\(343\) 19.0526i 1.02874i
\(344\) −9.79796 −0.528271
\(345\) 0 0
\(346\) −4.00000 6.92820i −0.215041 0.372463i
\(347\) −19.5959 −1.05196 −0.525982 0.850496i \(-0.676302\pi\)
−0.525982 + 0.850496i \(0.676302\pi\)
\(348\) 0 0
\(349\) 23.0000 1.23116 0.615581 0.788074i \(-0.288921\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) −3.67423 6.36396i −0.196396 0.340168i
\(351\) 0 0
\(352\) 24.0000 + 13.8564i 1.27920 + 0.738549i
\(353\) 11.3137i 0.602168i −0.953598 0.301084i \(-0.902652\pi\)
0.953598 0.301084i \(-0.0973484\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −4.89898 2.82843i −0.259645 0.149906i
\(357\) 0 0
\(358\) 0 0
\(359\) −14.6969 −0.775675 −0.387837 0.921728i \(-0.626778\pi\)
−0.387837 + 0.921728i \(0.626778\pi\)
\(360\) 0 0
\(361\) −8.00000 −0.421053
\(362\) −13.4722 + 7.77817i −0.708083 + 0.408812i
\(363\) 0 0
\(364\) 3.00000 + 1.73205i 0.157243 + 0.0907841i
\(365\) 2.82843i 0.148047i
\(366\) 0 0
\(367\) 19.0526i 0.994535i 0.867597 + 0.497268i \(0.165663\pi\)
−0.867597 + 0.497268i \(0.834337\pi\)
\(368\) 9.79796 + 16.9706i 0.510754 + 0.884652i
\(369\) 0 0
\(370\) −2.00000 3.46410i −0.103975 0.180090i
\(371\) 9.79796 0.508685
\(372\) 0 0
\(373\) −25.0000 −1.29445 −0.647225 0.762299i \(-0.724071\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 9.79796 + 16.9706i 0.506640 + 0.877527i
\(375\) 0 0
\(376\) 13.8564i 0.714590i
\(377\) 5.65685i 0.291343i
\(378\) 0 0
\(379\) 15.5885i 0.800725i −0.916357 0.400363i \(-0.868884\pi\)
0.916357 0.400363i \(-0.131116\pi\)
\(380\) 14.6969 25.4558i 0.753937 1.30586i
\(381\) 0 0
\(382\) 30.0000 17.3205i 1.53493 0.886194i
\(383\) −19.5959 −1.00130 −0.500652 0.865648i \(-0.666906\pi\)
−0.500652 + 0.865648i \(0.666906\pi\)
\(384\) 0 0
\(385\) −24.0000 −1.22315
\(386\) 1.22474 0.707107i 0.0623379 0.0359908i
\(387\) 0 0
\(388\) −13.0000 + 22.5167i −0.659975 + 1.14311i
\(389\) 14.1421i 0.717035i 0.933523 + 0.358517i \(0.116718\pi\)
−0.933523 + 0.358517i \(0.883282\pi\)
\(390\) 0 0
\(391\) 13.8564i 0.700749i
\(392\) 11.3137i 0.571429i
\(393\) 0 0
\(394\) 2.00000 + 3.46410i 0.100759 + 0.174519i
\(395\) −4.89898 −0.246494
\(396\) 0 0
\(397\) −10.0000 −0.501886 −0.250943 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) −3.67423 6.36396i −0.184173 0.318997i
\(399\) 0 0
\(400\) 6.00000 + 10.3923i 0.300000 + 0.519615i
\(401\) 22.6274i 1.12996i 0.825105 + 0.564980i \(0.191116\pi\)
−0.825105 + 0.564980i \(0.808884\pi\)
\(402\) 0 0
\(403\) 3.46410i 0.172559i
\(404\) −19.5959 11.3137i −0.974933 0.562878i
\(405\) 0 0
\(406\) −12.0000 + 6.92820i −0.595550 + 0.343841i
\(407\) −4.89898 −0.242833
\(408\) 0 0
\(409\) −1.00000 −0.0494468 −0.0247234 0.999694i \(-0.507871\pi\)
−0.0247234 + 0.999694i \(0.507871\pi\)
\(410\) −19.5959 + 11.3137i −0.967773 + 0.558744i
\(411\) 0 0
\(412\) −15.0000 8.66025i −0.738997 0.426660i
\(413\) 8.48528i 0.417533i
\(414\) 0 0
\(415\) 27.7128i 1.36037i
\(416\) −4.89898 2.82843i −0.240192 0.138675i
\(417\) 0 0
\(418\) −18.0000 31.1769i −0.880409 1.52491i
\(419\) −4.89898 −0.239331 −0.119665 0.992814i \(-0.538182\pi\)
−0.119665 + 0.992814i \(0.538182\pi\)
\(420\) 0 0
\(421\) −25.0000 −1.21843 −0.609213 0.793007i \(-0.708514\pi\)
−0.609213 + 0.793007i \(0.708514\pi\)
\(422\) −8.57321 14.8492i −0.417338 0.722850i
\(423\) 0 0
\(424\) −16.0000 −0.777029
\(425\) 8.48528i 0.411597i
\(426\) 0 0
\(427\) 19.0526i 0.922018i
\(428\) 14.6969 25.4558i 0.710403 1.23045i
\(429\) 0 0
\(430\) −12.0000 + 6.92820i −0.578691 + 0.334108i
\(431\) −14.6969 −0.707927 −0.353963 0.935259i \(-0.615166\pi\)
−0.353963 + 0.935259i \(0.615166\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 7.34847 4.24264i 0.352738 0.203653i
\(435\) 0 0
\(436\) −10.0000 + 17.3205i −0.478913 + 0.829502i
\(437\) 25.4558i 1.21772i
\(438\) 0 0
\(439\) 17.3205i 0.826663i −0.910581 0.413331i \(-0.864365\pi\)
0.910581 0.413331i \(-0.135635\pi\)
\(440\) 39.1918 1.86840
\(441\) 0 0
\(442\) −2.00000 3.46410i −0.0951303 0.164771i
\(443\) −9.79796 −0.465515 −0.232758 0.972535i \(-0.574775\pi\)
−0.232758 + 0.972535i \(0.574775\pi\)
\(444\) 0 0
\(445\) −8.00000 −0.379236
\(446\) −17.1464 29.6985i −0.811907 1.40626i
\(447\) 0 0
\(448\) 13.8564i 0.654654i
\(449\) 31.1127i 1.46830i 0.678988 + 0.734150i \(0.262419\pi\)
−0.678988 + 0.734150i \(0.737581\pi\)
\(450\) 0 0
\(451\) 27.7128i 1.30495i
\(452\) −4.89898 2.82843i −0.230429 0.133038i
\(453\) 0 0
\(454\) −24.0000 + 13.8564i −1.12638 + 0.650313i
\(455\) 4.89898 0.229668
\(456\) 0 0
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) 12.2474 7.07107i 0.572286 0.330409i
\(459\) 0 0
\(460\) 24.0000 + 13.8564i 1.11901 + 0.646058i
\(461\) 14.1421i 0.658665i 0.944214 + 0.329332i \(0.106824\pi\)
−0.944214 + 0.329332i \(0.893176\pi\)
\(462\) 0 0
\(463\) 12.1244i 0.563467i 0.959493 + 0.281733i \(0.0909093\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(464\) 19.5959 11.3137i 0.909718 0.525226i
\(465\) 0 0
\(466\) −16.0000 27.7128i −0.741186 1.28377i
\(467\) 14.6969 0.680093 0.340047 0.940409i \(-0.389557\pi\)
0.340047 + 0.940409i \(0.389557\pi\)
\(468\) 0 0
\(469\) 21.0000 0.969690
\(470\) 9.79796 + 16.9706i 0.451946 + 0.782794i
\(471\) 0 0
\(472\) 13.8564i 0.637793i
\(473\) 16.9706i 0.780307i
\(474\) 0 0
\(475\) 15.5885i 0.715247i
\(476\) −4.89898 + 8.48528i −0.224544 + 0.388922i
\(477\) 0 0
\(478\) 24.0000 13.8564i 1.09773 0.633777i
\(479\) −9.79796 −0.447680 −0.223840 0.974626i \(-0.571859\pi\)
−0.223840 + 0.974626i \(0.571859\pi\)
\(480\) 0 0
\(481\) 1.00000 0.0455961
\(482\) 30.6186 17.6777i 1.39464 0.805196i
\(483\) 0 0
\(484\) 13.0000 22.5167i 0.590909 1.02348i
\(485\) 36.7696i 1.66962i
\(486\) 0 0
\(487\) 25.9808i 1.17730i 0.808388 + 0.588650i \(0.200341\pi\)
−0.808388 + 0.588650i \(0.799659\pi\)
\(488\) 31.1127i 1.40841i
\(489\) 0 0
\(490\) 8.00000 + 13.8564i 0.361403 + 0.625969i
\(491\) 24.4949 1.10544 0.552720 0.833367i \(-0.313590\pi\)
0.552720 + 0.833367i \(0.313590\pi\)
\(492\) 0 0
\(493\) 16.0000 0.720604
\(494\) 3.67423 + 6.36396i 0.165312 + 0.286328i
\(495\) 0 0
\(496\) −12.0000 + 6.92820i −0.538816 + 0.311086i
\(497\) 0 0
\(498\) 0 0
\(499\) 24.2487i 1.08552i −0.839887 0.542761i \(-0.817379\pi\)
0.839887 0.542761i \(-0.182621\pi\)
\(500\) −9.79796 5.65685i −0.438178 0.252982i
\(501\) 0 0
\(502\) 36.0000 20.7846i 1.60676 0.927663i
\(503\) −14.6969 −0.655304 −0.327652 0.944798i \(-0.606257\pi\)
−0.327652 + 0.944798i \(0.606257\pi\)
\(504\) 0 0
\(505\) −32.0000 −1.42398
\(506\) 29.3939 16.9706i 1.30672 0.754434i
\(507\) 0 0
\(508\) 18.0000 + 10.3923i 0.798621 + 0.461084i
\(509\) 19.7990i 0.877575i −0.898591 0.438787i \(-0.855408\pi\)
0.898591 0.438787i \(-0.144592\pi\)
\(510\) 0 0
\(511\) 1.73205i 0.0766214i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 20.0000 + 34.6410i 0.882162 + 1.52795i
\(515\) −24.4949 −1.07937
\(516\) 0 0
\(517\) 24.0000 1.05552
\(518\) −1.22474 2.12132i −0.0538122 0.0932055i
\(519\) 0 0
\(520\) −8.00000 −0.350823
\(521\) 19.7990i 0.867409i −0.901055 0.433705i \(-0.857206\pi\)
0.901055 0.433705i \(-0.142794\pi\)
\(522\) 0 0
\(523\) 15.5885i 0.681636i −0.940129 0.340818i \(-0.889296\pi\)
0.940129 0.340818i \(-0.110704\pi\)
\(524\) 9.79796 16.9706i 0.428026 0.741362i
\(525\) 0 0
\(526\) −24.0000 + 13.8564i −1.04645 + 0.604168i
\(527\) −9.79796 −0.426806
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −19.5959 + 11.3137i −0.851192 + 0.491436i
\(531\) 0 0
\(532\) 9.00000 15.5885i 0.390199 0.675845i
\(533\) 5.65685i 0.245026i
\(534\) 0 0
\(535\) 41.5692i 1.79719i
\(536\) −34.2929 −1.48123
\(537\) 0 0
\(538\) 2.00000 + 3.46410i 0.0862261 + 0.149348i
\(539\) 19.5959 0.844056
\(540\) 0 0
\(541\) −1.00000 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(542\) −3.67423 6.36396i −0.157822 0.273356i
\(543\) 0 0
\(544\) 8.00000 13.8564i 0.342997 0.594089i
\(545\) 28.2843i 1.21157i
\(546\) 0 0
\(547\) 22.5167i 0.962743i −0.876517 0.481371i \(-0.840139\pi\)
0.876517 0.481371i \(-0.159861\pi\)
\(548\) −34.2929 19.7990i −1.46492 0.845771i
\(549\) 0 0
\(550\) 18.0000 10.3923i 0.767523 0.443129i
\(551\) −29.3939 −1.25222
\(552\) 0 0
\(553\) −3.00000 −0.127573
\(554\) −17.1464 + 9.89949i −0.728482 + 0.420589i
\(555\) 0 0
\(556\) −15.0000 8.66025i −0.636142 0.367277i
\(557\) 2.82843i 0.119844i −0.998203 0.0599222i \(-0.980915\pi\)
0.998203 0.0599222i \(-0.0190852\pi\)
\(558\) 0 0
\(559\) 3.46410i 0.146516i
\(560\) 9.79796 + 16.9706i 0.414039 + 0.717137i
\(561\) 0 0
\(562\) −4.00000 6.92820i −0.168730 0.292249i
\(563\) 9.79796 0.412935 0.206467 0.978453i \(-0.433803\pi\)
0.206467 + 0.978453i \(0.433803\pi\)
\(564\) 0 0
\(565\) −8.00000 −0.336563
\(566\) 17.1464 + 29.6985i 0.720718 + 1.24832i
\(567\) 0 0
\(568\) 0 0
\(569\) 19.7990i 0.830017i −0.909818 0.415008i \(-0.863779\pi\)
0.909818 0.415008i \(-0.136221\pi\)
\(570\) 0 0
\(571\) 32.9090i 1.37720i 0.725143 + 0.688599i \(0.241774\pi\)
−0.725143 + 0.688599i \(0.758226\pi\)
\(572\) −4.89898 + 8.48528i −0.204837 + 0.354787i
\(573\) 0 0
\(574\) −12.0000 + 6.92820i −0.500870 + 0.289178i
\(575\) 14.6969 0.612905
\(576\) 0 0
\(577\) 35.0000 1.45707 0.728535 0.685009i \(-0.240202\pi\)
0.728535 + 0.685009i \(0.240202\pi\)
\(578\) −11.0227 + 6.36396i −0.458484 + 0.264706i
\(579\) 0 0
\(580\) 16.0000 27.7128i 0.664364 1.15071i
\(581\) 16.9706i 0.704058i
\(582\) 0 0
\(583\) 27.7128i 1.14775i
\(584\) 2.82843i 0.117041i
\(585\) 0 0
\(586\) 2.00000 + 3.46410i 0.0826192 + 0.143101i
\(587\) 4.89898 0.202203 0.101101 0.994876i \(-0.467763\pi\)
0.101101 + 0.994876i \(0.467763\pi\)
\(588\) 0 0
\(589\) 18.0000 0.741677
\(590\) −9.79796 16.9706i −0.403376 0.698667i
\(591\) 0 0
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) 28.2843i 1.16150i −0.814083 0.580748i \(-0.802760\pi\)
0.814083 0.580748i \(-0.197240\pi\)
\(594\) 0 0
\(595\) 13.8564i 0.568057i
\(596\) 39.1918 + 22.6274i 1.60536 + 0.926855i
\(597\) 0 0
\(598\) −6.00000 + 3.46410i −0.245358 + 0.141658i
\(599\) 9.79796 0.400334 0.200167 0.979762i \(-0.435852\pi\)
0.200167 + 0.979762i \(0.435852\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −7.34847 + 4.24264i −0.299501 + 0.172917i
\(603\) 0 0
\(604\) −39.0000 22.5167i −1.58689 0.916190i
\(605\) 36.7696i 1.49489i
\(606\) 0 0
\(607\) 12.1244i 0.492112i 0.969256 + 0.246056i \(0.0791348\pi\)
−0.969256 + 0.246056i \(0.920865\pi\)
\(608\) −14.6969 + 25.4558i −0.596040 + 1.03237i
\(609\) 0 0
\(610\) 22.0000 + 38.1051i 0.890754 + 1.54283i
\(611\) −4.89898 −0.198191
\(612\) 0 0
\(613\) 11.0000 0.444286 0.222143 0.975014i \(-0.428695\pi\)
0.222143 + 0.975014i \(0.428695\pi\)
\(614\) 7.34847 + 12.7279i 0.296560 + 0.513657i
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) 2.82843i 0.113868i −0.998378 0.0569341i \(-0.981868\pi\)
0.998378 0.0569341i \(-0.0181325\pi\)
\(618\) 0 0
\(619\) 19.0526i 0.765787i 0.923792 + 0.382893i \(0.125072\pi\)
−0.923792 + 0.382893i \(0.874928\pi\)
\(620\) −9.79796 + 16.9706i −0.393496 + 0.681554i
\(621\) 0 0
\(622\) −30.0000 + 17.3205i −1.20289 + 0.694489i
\(623\) −4.89898 −0.196273
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) −13.4722 + 7.77817i −0.538457 + 0.310878i
\(627\) 0 0
\(628\) −10.0000 + 17.3205i −0.399043 + 0.691164i
\(629\) 2.82843i 0.112777i
\(630\) 0 0
\(631\) 36.3731i 1.44799i −0.689806 0.723994i \(-0.742304\pi\)
0.689806 0.723994i \(-0.257696\pi\)
\(632\) 4.89898 0.194871
\(633\) 0 0
\(634\) −4.00000 6.92820i −0.158860 0.275154i
\(635\) 29.3939 1.16646
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) −19.5959 33.9411i −0.775810 1.34374i
\(639\) 0 0
\(640\) −16.0000 27.7128i −0.632456 1.09545i
\(641\) 45.2548i 1.78746i −0.448607 0.893729i \(-0.648080\pi\)
0.448607 0.893729i \(-0.351920\pi\)
\(642\) 0 0
\(643\) 17.3205i 0.683054i 0.939872 + 0.341527i \(0.110944\pi\)
−0.939872 + 0.341527i \(0.889056\pi\)
\(644\) 14.6969 + 8.48528i 0.579141 + 0.334367i
\(645\) 0 0
\(646\) −18.0000 + 10.3923i −0.708201 + 0.408880i
\(647\) 29.3939 1.15559 0.577796 0.816181i \(-0.303913\pi\)
0.577796 + 0.816181i \(0.303913\pi\)
\(648\) 0 0
\(649\) −24.0000 −0.942082
\(650\) −3.67423 + 2.12132i −0.144115 + 0.0832050i
\(651\) 0 0
\(652\) 9.00000 + 5.19615i 0.352467 + 0.203497i
\(653\) 5.65685i 0.221370i 0.993856 + 0.110685i \(0.0353044\pi\)
−0.993856 + 0.110685i \(0.964696\pi\)
\(654\) 0 0
\(655\) 27.7128i 1.08283i
\(656\) 19.5959 11.3137i 0.765092 0.441726i
\(657\) 0 0
\(658\) 6.00000 + 10.3923i 0.233904 + 0.405134i
\(659\) −9.79796 −0.381674 −0.190837 0.981622i \(-0.561120\pi\)
−0.190837 + 0.981622i \(0.561120\pi\)
\(660\) 0 0
\(661\) −37.0000 −1.43913 −0.719567 0.694423i \(-0.755660\pi\)
−0.719567 + 0.694423i \(0.755660\pi\)
\(662\) 15.9217 + 27.5772i 0.618814 + 1.07182i
\(663\) 0 0
\(664\) 27.7128i 1.07547i
\(665\) 25.4558i 0.987135i
\(666\) 0 0
\(667\) 27.7128i 1.07304i
\(668\) −4.89898 + 8.48528i −0.189547 + 0.328305i
\(669\) 0 0
\(670\) −42.0000 + 24.2487i −1.62260 + 0.936809i
\(671\) 53.8888 2.08035
\(672\) 0 0
\(673\) 11.0000 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) −13.4722 + 7.77817i −0.518930 + 0.299604i
\(675\) 0 0
\(676\) −12.0000 + 20.7846i −0.461538 + 0.799408i
\(677\) 14.1421i 0.543526i 0.962364 + 0.271763i \(0.0876068\pi\)
−0.962364 + 0.271763i \(0.912393\pi\)
\(678\) 0 0
\(679\) 22.5167i 0.864110i
\(680\) 22.6274i 0.867722i
\(681\) 0 0
\(682\) 12.0000 + 20.7846i 0.459504 + 0.795884i
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) −56.0000 −2.13965
\(686\) 13.4722 + 23.3345i 0.514371 + 0.890916i
\(687\) 0 0
\(688\) 12.0000 6.92820i 0.457496 0.264135i
\(689\) 5.65685i 0.215509i
\(690\) 0 0
\(691\) 45.0333i 1.71315i 0.516024 + 0.856574i \(0.327412\pi\)
−0.516024 + 0.856574i \(0.672588\pi\)
\(692\) 9.79796 + 5.65685i 0.372463 + 0.215041i
\(693\) 0 0
\(694\) 24.0000 13.8564i 0.911028 0.525982i
\(695\) −24.4949 −0.929144
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) −28.1691 + 16.2635i −1.06622 + 0.615581i
\(699\) 0 0
\(700\) 9.00000 + 5.19615i 0.340168 + 0.196396i
\(701\) 2.82843i 0.106828i −0.998572 0.0534141i \(-0.982990\pi\)
0.998572 0.0534141i \(-0.0170103\pi\)
\(702\) 0 0
\(703\) 5.19615i 0.195977i
\(704\) −39.1918 −1.47710
\(705\) 0 0
\(706\) 8.00000 + 13.8564i 0.301084 + 0.521493i
\(707\) −19.5959 −0.736980
\(708\) 0 0
\(709\) −25.0000 −0.938895 −0.469447 0.882960i \(-0.655547\pi\)
−0.469447 + 0.882960i \(0.655547\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 8.00000 0.299813
\(713\) 16.9706i 0.635553i
\(714\) 0 0
\(715\) 13.8564i 0.518200i
\(716\) 0 0
\(717\) 0 0
\(718\) 18.0000 10.3923i 0.671754 0.387837i
\(719\) 29.3939 1.09621 0.548103 0.836411i \(-0.315350\pi\)
0.548103 + 0.836411i \(0.315350\pi\)
\(720\) 0 0
\(721\) −15.0000 −0.558629
\(722\) 9.79796 5.65685i 0.364642 0.210526i
\(723\) 0 0
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) 16.9706i 0.630271i
\(726\) 0 0
\(727\) 17.3205i 0.642382i −0.947014 0.321191i \(-0.895917\pi\)
0.947014 0.321191i \(-0.104083\pi\)
\(728\) −4.89898 −0.181568
\(729\) 0 0
\(730\) −2.00000 3.46410i −0.0740233 0.128212i
\(731\) 9.79796 0.362391
\(732\) 0 0
\(733\) 38.0000 1.40356 0.701781 0.712393i \(-0.252388\pi\)
0.701781 + 0.712393i \(0.252388\pi\)
\(734\) −13.4722 23.3345i −0.497268 0.861293i
\(735\) 0 0
\(736\) −24.0000 13.8564i −0.884652 0.510754i
\(737\) 59.3970i 2.18792i
\(738\) 0 0
\(739\) 10.3923i 0.382287i −0.981562 0.191144i \(-0.938780\pi\)
0.981562 0.191144i \(-0.0612196\pi\)
\(740\) 4.89898 + 2.82843i 0.180090 + 0.103975i
\(741\) 0 0
\(742\) −12.0000 + 6.92820i −0.440534 + 0.254342i
\(743\) −34.2929 −1.25808 −0.629041 0.777372i \(-0.716552\pi\)
−0.629041 + 0.777372i \(0.716552\pi\)
\(744\) 0 0
\(745\) 64.0000 2.34478
\(746\) 30.6186 17.6777i 1.12103 0.647225i
\(747\) 0 0
\(748\) −24.0000 13.8564i −0.877527 0.506640i
\(749\) 25.4558i 0.930136i
\(750\) 0 0
\(751\) 29.4449i 1.07446i −0.843436 0.537229i \(-0.819471\pi\)
0.843436 0.537229i \(-0.180529\pi\)
\(752\) −9.79796 16.9706i −0.357295 0.618853i
\(753\) 0 0
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) −63.6867 −2.31780
\(756\) 0 0
\(757\) 47.0000 1.70824 0.854122 0.520073i \(-0.174095\pi\)
0.854122 + 0.520073i \(0.174095\pi\)
\(758\) 11.0227 + 19.0919i 0.400363 + 0.693448i
\(759\) 0 0
\(760\) 41.5692i 1.50787i
\(761\) 2.82843i 0.102530i −0.998685 0.0512652i \(-0.983675\pi\)
0.998685 0.0512652i \(-0.0163254\pi\)
\(762\) 0 0
\(763\) 17.3205i 0.627044i
\(764\) −24.4949 + 42.4264i −0.886194 + 1.53493i
\(765\) 0 0
\(766\) 24.0000 13.8564i 0.867155 0.500652i
\(767\) 4.89898 0.176892
\(768\) 0 0
\(769\) −1.00000 −0.0360609 −0.0180305 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 29.3939 16.9706i 1.05928 0.611577i
\(771\) 0 0
\(772\) −1.00000 + 1.73205i −0.0359908 + 0.0623379i
\(773\) 28.2843i 1.01731i −0.860969 0.508657i \(-0.830142\pi\)
0.860969 0.508657i \(-0.169858\pi\)
\(774\) 0 0
\(775\) 10.3923i 0.373303i
\(776\) 36.7696i 1.31995i
\(777\) 0 0
\(778\) −10.0000 17.3205i −0.358517 0.620970i
\(779\) −29.3939 −1.05314
\(780\) 0 0
\(781\) 0 0
\(782\) −9.79796 16.9706i −0.350374 0.606866i
\(783\) 0 0
\(784\) −8.00000 13.8564i −0.285714 0.494872i
\(785\) 28.2843i 1.00951i
\(786\) 0 0
\(787\) 8.66025i 0.308705i −0.988016 0.154352i \(-0.950671\pi\)
0.988016 0.154352i \(-0.0493291\pi\)
\(788\) −4.89898 2.82843i −0.174519 0.100759i
\(789\) 0 0
\(790\) 6.00000 3.46410i 0.213470 0.123247i
\(791\) −4.89898 −0.174188
\(792\) 0 0
\(793\) −11.0000 −0.390621
\(794\) 12.2474 7.07107i 0.434646 0.250943i
\(795\) 0 0
\(796\) 9.00000 + 5.19615i 0.318997 + 0.184173i
\(797\) 22.6274i 0.801504i 0.916187 + 0.400752i \(0.131251\pi\)
−0.916187 + 0.400752i \(0.868749\pi\)
\(798\) 0 0
\(799\) 13.8564i 0.490204i
\(800\) −14.6969 8.48528i −0.519615 0.300000i
\(801\) 0 0