Properties

Label 1170.2.b.g.181.7
Level $1170$
Weight $2$
Character 1170.181
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3057647616.6
Defining polynomial: \(x^{8} + 30 x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.7
Root \(1.65068 - 1.65068i\) of defining polynomial
Character \(\chi\) \(=\) 1170.181
Dual form 1170.2.b.g.181.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +1.00000i q^{5} +1.48393i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +1.00000i q^{5} +1.48393i q^{7} -1.00000i q^{8} -1.00000 q^{10} -4.89898i q^{11} +(1.44949 - 3.30136i) q^{13} -1.48393 q^{14} +1.00000 q^{16} +8.08665 q^{17} +5.11879i q^{19} -1.00000i q^{20} +4.89898 q^{22} +1.48393 q^{23} -1.00000 q^{25} +(3.30136 + 1.44949i) q^{26} -1.48393i q^{28} +5.11879 q^{29} +6.60272i q^{31} +1.00000i q^{32} +8.08665i q^{34} -1.48393 q^{35} +3.63487i q^{37} -5.11879 q^{38} +1.00000 q^{40} +1.10102i q^{41} -4.00000 q^{43} +4.89898i q^{44} +1.48393i q^{46} -9.79796i q^{47} +4.79796 q^{49} -1.00000i q^{50} +(-1.44949 + 3.30136i) q^{52} -6.60272 q^{53} +4.89898 q^{55} +1.48393 q^{56} +5.11879i q^{58} +4.89898i q^{59} -2.00000 q^{61} -6.60272 q^{62} -1.00000 q^{64} +(3.30136 + 1.44949i) q^{65} +9.57058i q^{67} -8.08665 q^{68} -1.48393i q^{70} +4.45178i q^{73} -3.63487 q^{74} -5.11879i q^{76} +7.26973 q^{77} +13.7980 q^{79} +1.00000i q^{80} -1.10102 q^{82} +9.79796i q^{83} +8.08665i q^{85} -4.00000i q^{86} -4.89898 q^{88} -10.8990i q^{89} +(4.89898 + 2.15094i) q^{91} -1.48393 q^{92} +9.79796 q^{94} -5.11879 q^{95} -17.6572i q^{97} +4.79796i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + O(q^{10}) \) \( 8 q - 8 q^{4} - 8 q^{10} - 8 q^{13} + 8 q^{16} - 8 q^{25} + 8 q^{40} - 32 q^{43} - 40 q^{49} + 8 q^{52} - 16 q^{61} - 8 q^{64} + 32 q^{79} - 48 q^{82} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 1.48393i 0.560872i 0.959873 + 0.280436i \(0.0904790\pi\)
−0.959873 + 0.280436i \(0.909521\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) 4.89898i 1.47710i −0.674200 0.738549i \(-0.735511\pi\)
0.674200 0.738549i \(-0.264489\pi\)
\(12\) 0 0
\(13\) 1.44949 3.30136i 0.402016 0.915633i
\(14\) −1.48393 −0.396596
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 8.08665 1.96130 0.980650 0.195769i \(-0.0627201\pi\)
0.980650 + 0.195769i \(0.0627201\pi\)
\(18\) 0 0
\(19\) 5.11879i 1.17433i 0.809467 + 0.587166i \(0.199756\pi\)
−0.809467 + 0.587166i \(0.800244\pi\)
\(20\) 1.00000i 0.223607i
\(21\) 0 0
\(22\) 4.89898 1.04447
\(23\) 1.48393 0.309420 0.154710 0.987960i \(-0.450556\pi\)
0.154710 + 0.987960i \(0.450556\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.30136 + 1.44949i 0.647450 + 0.284268i
\(27\) 0 0
\(28\) 1.48393i 0.280436i
\(29\) 5.11879 0.950536 0.475268 0.879841i \(-0.342351\pi\)
0.475268 + 0.879841i \(0.342351\pi\)
\(30\) 0 0
\(31\) 6.60272i 1.18588i 0.805245 + 0.592942i \(0.202034\pi\)
−0.805245 + 0.592942i \(0.797966\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 8.08665i 1.38685i
\(35\) −1.48393 −0.250830
\(36\) 0 0
\(37\) 3.63487i 0.597568i 0.954321 + 0.298784i \(0.0965810\pi\)
−0.954321 + 0.298784i \(0.903419\pi\)
\(38\) −5.11879 −0.830378
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 1.10102i 0.171951i 0.996297 + 0.0859753i \(0.0274006\pi\)
−0.996297 + 0.0859753i \(0.972599\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 4.89898i 0.738549i
\(45\) 0 0
\(46\) 1.48393i 0.218793i
\(47\) 9.79796i 1.42918i −0.699544 0.714590i \(-0.746613\pi\)
0.699544 0.714590i \(-0.253387\pi\)
\(48\) 0 0
\(49\) 4.79796 0.685423
\(50\) 1.00000i 0.141421i
\(51\) 0 0
\(52\) −1.44949 + 3.30136i −0.201008 + 0.457816i
\(53\) −6.60272 −0.906953 −0.453477 0.891268i \(-0.649816\pi\)
−0.453477 + 0.891268i \(0.649816\pi\)
\(54\) 0 0
\(55\) 4.89898 0.660578
\(56\) 1.48393 0.198298
\(57\) 0 0
\(58\) 5.11879i 0.672130i
\(59\) 4.89898i 0.637793i 0.947790 + 0.318896i \(0.103312\pi\)
−0.947790 + 0.318896i \(0.896688\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) −6.60272 −0.838546
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.30136 + 1.44949i 0.409483 + 0.179787i
\(66\) 0 0
\(67\) 9.57058i 1.16923i 0.811310 + 0.584616i \(0.198755\pi\)
−0.811310 + 0.584616i \(0.801245\pi\)
\(68\) −8.08665 −0.980650
\(69\) 0 0
\(70\) 1.48393i 0.177363i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 4.45178i 0.521042i 0.965468 + 0.260521i \(0.0838943\pi\)
−0.965468 + 0.260521i \(0.916106\pi\)
\(74\) −3.63487 −0.422545
\(75\) 0 0
\(76\) 5.11879i 0.587166i
\(77\) 7.26973 0.828463
\(78\) 0 0
\(79\) 13.7980 1.55239 0.776196 0.630492i \(-0.217147\pi\)
0.776196 + 0.630492i \(0.217147\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 0 0
\(82\) −1.10102 −0.121587
\(83\) 9.79796i 1.07547i 0.843115 + 0.537733i \(0.180719\pi\)
−0.843115 + 0.537733i \(0.819281\pi\)
\(84\) 0 0
\(85\) 8.08665i 0.877120i
\(86\) 4.00000i 0.431331i
\(87\) 0 0
\(88\) −4.89898 −0.522233
\(89\) 10.8990i 1.15529i −0.816288 0.577645i \(-0.803972\pi\)
0.816288 0.577645i \(-0.196028\pi\)
\(90\) 0 0
\(91\) 4.89898 + 2.15094i 0.513553 + 0.225480i
\(92\) −1.48393 −0.154710
\(93\) 0 0
\(94\) 9.79796 1.01058
\(95\) −5.11879 −0.525177
\(96\) 0 0
\(97\) 17.6572i 1.79282i −0.443226 0.896410i \(-0.646166\pi\)
0.443226 0.896410i \(-0.353834\pi\)
\(98\) 4.79796i 0.484667i
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 18.3242 1.82333 0.911665 0.410935i \(-0.134798\pi\)
0.911665 + 0.410935i \(0.134798\pi\)
\(102\) 0 0
\(103\) 12.8990 1.27097 0.635487 0.772111i \(-0.280799\pi\)
0.635487 + 0.772111i \(0.280799\pi\)
\(104\) −3.30136 1.44949i −0.323725 0.142134i
\(105\) 0 0
\(106\) 6.60272i 0.641313i
\(107\) 5.93571 0.573827 0.286913 0.957957i \(-0.407371\pi\)
0.286913 + 0.957957i \(0.407371\pi\)
\(108\) 0 0
\(109\) 17.6572i 1.69126i 0.533773 + 0.845628i \(0.320774\pi\)
−0.533773 + 0.845628i \(0.679226\pi\)
\(110\) 4.89898i 0.467099i
\(111\) 0 0
\(112\) 1.48393i 0.140218i
\(113\) −5.11879 −0.481536 −0.240768 0.970583i \(-0.577399\pi\)
−0.240768 + 0.970583i \(0.577399\pi\)
\(114\) 0 0
\(115\) 1.48393i 0.138377i
\(116\) −5.11879 −0.475268
\(117\) 0 0
\(118\) −4.89898 −0.450988
\(119\) 12.0000i 1.10004i
\(120\) 0 0
\(121\) −13.0000 −1.18182
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) 6.60272i 0.592942i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −12.8990 −1.14460 −0.572300 0.820045i \(-0.693949\pi\)
−0.572300 + 0.820045i \(0.693949\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −1.44949 + 3.30136i −0.127129 + 0.289548i
\(131\) 11.0545 0.965836 0.482918 0.875665i \(-0.339577\pi\)
0.482918 + 0.875665i \(0.339577\pi\)
\(132\) 0 0
\(133\) −7.59592 −0.658650
\(134\) −9.57058 −0.826772
\(135\) 0 0
\(136\) 8.08665i 0.693424i
\(137\) 3.79796i 0.324482i −0.986751 0.162241i \(-0.948128\pi\)
0.986751 0.162241i \(-0.0518721\pi\)
\(138\) 0 0
\(139\) −13.7980 −1.17033 −0.585164 0.810915i \(-0.698970\pi\)
−0.585164 + 0.810915i \(0.698970\pi\)
\(140\) 1.48393 0.125415
\(141\) 0 0
\(142\) 0 0
\(143\) −16.1733 7.10102i −1.35248 0.593817i
\(144\) 0 0
\(145\) 5.11879i 0.425093i
\(146\) −4.45178 −0.368432
\(147\) 0 0
\(148\) 3.63487i 0.298784i
\(149\) 15.7980i 1.29422i −0.762397 0.647110i \(-0.775978\pi\)
0.762397 0.647110i \(-0.224022\pi\)
\(150\) 0 0
\(151\) 6.60272i 0.537322i −0.963235 0.268661i \(-0.913419\pi\)
0.963235 0.268661i \(-0.0865811\pi\)
\(152\) 5.11879 0.415189
\(153\) 0 0
\(154\) 7.26973i 0.585812i
\(155\) −6.60272 −0.530343
\(156\) 0 0
\(157\) 9.10102 0.726341 0.363170 0.931723i \(-0.381694\pi\)
0.363170 + 0.931723i \(0.381694\pi\)
\(158\) 13.7980i 1.09771i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 2.20204i 0.173545i
\(162\) 0 0
\(163\) 6.60272i 0.517165i −0.965989 0.258582i \(-0.916745\pi\)
0.965989 0.258582i \(-0.0832554\pi\)
\(164\) 1.10102i 0.0859753i
\(165\) 0 0
\(166\) −9.79796 −0.760469
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −8.79796 9.57058i −0.676766 0.736198i
\(170\) −8.08665 −0.620218
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) −12.5384 −0.953279 −0.476640 0.879099i \(-0.658145\pi\)
−0.476640 + 0.879099i \(0.658145\pi\)
\(174\) 0 0
\(175\) 1.48393i 0.112174i
\(176\) 4.89898i 0.369274i
\(177\) 0 0
\(178\) 10.8990 0.816913
\(179\) −21.2921 −1.59145 −0.795723 0.605661i \(-0.792909\pi\)
−0.795723 + 0.605661i \(0.792909\pi\)
\(180\) 0 0
\(181\) 23.7980 1.76889 0.884444 0.466646i \(-0.154538\pi\)
0.884444 + 0.466646i \(0.154538\pi\)
\(182\) −2.15094 + 4.89898i −0.159438 + 0.363137i
\(183\) 0 0
\(184\) 1.48393i 0.109397i
\(185\) −3.63487 −0.267241
\(186\) 0 0
\(187\) 39.6163i 2.89703i
\(188\) 9.79796i 0.714590i
\(189\) 0 0
\(190\) 5.11879i 0.371356i
\(191\) 20.4752 1.48153 0.740766 0.671763i \(-0.234463\pi\)
0.740766 + 0.671763i \(0.234463\pi\)
\(192\) 0 0
\(193\) 17.6572i 1.27099i −0.772103 0.635497i \(-0.780795\pi\)
0.772103 0.635497i \(-0.219205\pi\)
\(194\) 17.6572 1.26771
\(195\) 0 0
\(196\) −4.79796 −0.342711
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 18.3242i 1.28929i
\(203\) 7.59592i 0.533129i
\(204\) 0 0
\(205\) −1.10102 −0.0768986
\(206\) 12.8990i 0.898714i
\(207\) 0 0
\(208\) 1.44949 3.30136i 0.100504 0.228908i
\(209\) 25.0769 1.73460
\(210\) 0 0
\(211\) −5.79796 −0.399148 −0.199574 0.979883i \(-0.563956\pi\)
−0.199574 + 0.979883i \(0.563956\pi\)
\(212\) 6.60272 0.453477
\(213\) 0 0
\(214\) 5.93571i 0.405757i
\(215\) 4.00000i 0.272798i
\(216\) 0 0
\(217\) −9.79796 −0.665129
\(218\) −17.6572 −1.19590
\(219\) 0 0
\(220\) −4.89898 −0.330289
\(221\) 11.7215 26.6969i 0.788474 1.79583i
\(222\) 0 0
\(223\) 17.6572i 1.18242i −0.806519 0.591208i \(-0.798651\pi\)
0.806519 0.591208i \(-0.201349\pi\)
\(224\) −1.48393 −0.0991491
\(225\) 0 0
\(226\) 5.11879i 0.340497i
\(227\) 2.20204i 0.146155i −0.997326 0.0730773i \(-0.976718\pi\)
0.997326 0.0730773i \(-0.0232820\pi\)
\(228\) 0 0
\(229\) 1.48393i 0.0980607i 0.998797 + 0.0490303i \(0.0156131\pi\)
−0.998797 + 0.0490303i \(0.984387\pi\)
\(230\) −1.48393 −0.0978473
\(231\) 0 0
\(232\) 5.11879i 0.336065i
\(233\) −5.11879 −0.335343 −0.167672 0.985843i \(-0.553625\pi\)
−0.167672 + 0.985843i \(0.553625\pi\)
\(234\) 0 0
\(235\) 9.79796 0.639148
\(236\) 4.89898i 0.318896i
\(237\) 0 0
\(238\) −12.0000 −0.777844
\(239\) 2.20204i 0.142438i 0.997461 + 0.0712191i \(0.0226890\pi\)
−0.997461 + 0.0712191i \(0.977311\pi\)
\(240\) 0 0
\(241\) 5.93571i 0.382353i 0.981556 + 0.191176i \(0.0612302\pi\)
−0.981556 + 0.191176i \(0.938770\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 4.79796i 0.306530i
\(246\) 0 0
\(247\) 16.8990 + 7.41964i 1.07526 + 0.472100i
\(248\) 6.60272 0.419273
\(249\) 0 0
\(250\) 1.00000 0.0632456
\(251\) −8.08665 −0.510425 −0.255212 0.966885i \(-0.582145\pi\)
−0.255212 + 0.966885i \(0.582145\pi\)
\(252\) 0 0
\(253\) 7.26973i 0.457044i
\(254\) 12.8990i 0.809354i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 11.0545 0.689561 0.344780 0.938683i \(-0.387953\pi\)
0.344780 + 0.938683i \(0.387953\pi\)
\(258\) 0 0
\(259\) −5.39388 −0.335159
\(260\) −3.30136 1.44949i −0.204742 0.0898935i
\(261\) 0 0
\(262\) 11.0545i 0.682949i
\(263\) −11.7215 −0.722779 −0.361390 0.932415i \(-0.617698\pi\)
−0.361390 + 0.932415i \(0.617698\pi\)
\(264\) 0 0
\(265\) 6.60272i 0.405602i
\(266\) 7.59592i 0.465736i
\(267\) 0 0
\(268\) 9.57058i 0.584616i
\(269\) 14.0224 0.854958 0.427479 0.904025i \(-0.359402\pi\)
0.427479 + 0.904025i \(0.359402\pi\)
\(270\) 0 0
\(271\) 12.5384i 0.761655i 0.924646 + 0.380828i \(0.124361\pi\)
−0.924646 + 0.380828i \(0.875639\pi\)
\(272\) 8.08665 0.490325
\(273\) 0 0
\(274\) 3.79796 0.229443
\(275\) 4.89898i 0.295420i
\(276\) 0 0
\(277\) −24.6969 −1.48390 −0.741948 0.670458i \(-0.766098\pi\)
−0.741948 + 0.670458i \(0.766098\pi\)
\(278\) 13.7980i 0.827547i
\(279\) 0 0
\(280\) 1.48393i 0.0886816i
\(281\) 8.69694i 0.518816i −0.965768 0.259408i \(-0.916473\pi\)
0.965768 0.259408i \(-0.0835274\pi\)
\(282\) 0 0
\(283\) −29.7980 −1.77130 −0.885652 0.464349i \(-0.846288\pi\)
−0.885652 + 0.464349i \(0.846288\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 7.10102 16.1733i 0.419892 0.956347i
\(287\) −1.63383 −0.0964422
\(288\) 0 0
\(289\) 48.3939 2.84670
\(290\) −5.11879 −0.300586
\(291\) 0 0
\(292\) 4.45178i 0.260521i
\(293\) 18.0000i 1.05157i 0.850617 + 0.525786i \(0.176229\pi\)
−0.850617 + 0.525786i \(0.823771\pi\)
\(294\) 0 0
\(295\) −4.89898 −0.285230
\(296\) 3.63487 0.211272
\(297\) 0 0
\(298\) 15.7980 0.915151
\(299\) 2.15094 4.89898i 0.124392 0.283315i
\(300\) 0 0
\(301\) 5.93571i 0.342129i
\(302\) 6.60272 0.379944
\(303\) 0 0
\(304\) 5.11879i 0.293583i
\(305\) 2.00000i 0.114520i
\(306\) 0 0
\(307\) 9.57058i 0.546222i −0.961983 0.273111i \(-0.911947\pi\)
0.961983 0.273111i \(-0.0880526\pi\)
\(308\) −7.26973 −0.414231
\(309\) 0 0
\(310\) 6.60272i 0.375009i
\(311\) 5.93571 0.336583 0.168292 0.985737i \(-0.446175\pi\)
0.168292 + 0.985737i \(0.446175\pi\)
\(312\) 0 0
\(313\) −31.3939 −1.77449 −0.887243 0.461302i \(-0.847383\pi\)
−0.887243 + 0.461302i \(0.847383\pi\)
\(314\) 9.10102i 0.513600i
\(315\) 0 0
\(316\) −13.7980 −0.776196
\(317\) 13.5959i 0.763623i −0.924240 0.381811i \(-0.875300\pi\)
0.924240 0.381811i \(-0.124700\pi\)
\(318\) 0 0
\(319\) 25.0769i 1.40403i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −2.20204 −0.122715
\(323\) 41.3939i 2.30322i
\(324\) 0 0
\(325\) −1.44949 + 3.30136i −0.0804032 + 0.183127i
\(326\) 6.60272 0.365691
\(327\) 0 0
\(328\) 1.10102 0.0607937
\(329\) 14.5395 0.801586
\(330\) 0 0
\(331\) 24.2599i 1.33345i 0.745305 + 0.666724i \(0.232304\pi\)
−0.745305 + 0.666724i \(0.767696\pi\)
\(332\) 9.79796i 0.537733i
\(333\) 0 0
\(334\) 0 0
\(335\) −9.57058 −0.522896
\(336\) 0 0
\(337\) 10.0000 0.544735 0.272367 0.962193i \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) 9.57058 8.79796i 0.520571 0.478546i
\(339\) 0 0
\(340\) 8.08665i 0.438560i
\(341\) 32.3466 1.75167
\(342\) 0 0
\(343\) 17.5073i 0.945306i
\(344\) 4.00000i 0.215666i
\(345\) 0 0
\(346\) 12.5384i 0.674070i
\(347\) −35.3144 −1.89578 −0.947889 0.318599i \(-0.896788\pi\)
−0.947889 + 0.318599i \(0.896788\pi\)
\(348\) 0 0
\(349\) 18.9912i 1.01658i −0.861187 0.508289i \(-0.830278\pi\)
0.861187 0.508289i \(-0.169722\pi\)
\(350\) 1.48393 0.0793193
\(351\) 0 0
\(352\) 4.89898 0.261116
\(353\) 6.00000i 0.319348i −0.987170 0.159674i \(-0.948956\pi\)
0.987170 0.159674i \(-0.0510443\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.8990i 0.577645i
\(357\) 0 0
\(358\) 21.2921i 1.12532i
\(359\) 9.79796i 0.517116i 0.965996 + 0.258558i \(0.0832474\pi\)
−0.965996 + 0.258558i \(0.916753\pi\)
\(360\) 0 0
\(361\) −7.20204 −0.379055
\(362\) 23.7980i 1.25079i
\(363\) 0 0
\(364\) −4.89898 2.15094i −0.256776 0.112740i
\(365\) −4.45178 −0.233017
\(366\) 0 0
\(367\) −6.69694 −0.349577 −0.174789 0.984606i \(-0.555924\pi\)
−0.174789 + 0.984606i \(0.555924\pi\)
\(368\) 1.48393 0.0773551
\(369\) 0 0
\(370\) 3.63487i 0.188968i
\(371\) 9.79796i 0.508685i
\(372\) 0 0
\(373\) 12.6969 0.657423 0.328711 0.944430i \(-0.393386\pi\)
0.328711 + 0.944430i \(0.393386\pi\)
\(374\) 39.6163 2.04851
\(375\) 0 0
\(376\) −9.79796 −0.505291
\(377\) 7.41964 16.8990i 0.382131 0.870342i
\(378\) 0 0
\(379\) 12.3885i 0.636356i −0.948031 0.318178i \(-0.896929\pi\)
0.948031 0.318178i \(-0.103071\pi\)
\(380\) 5.11879 0.262589
\(381\) 0 0
\(382\) 20.4752i 1.04760i
\(383\) 33.7980i 1.72700i −0.504353 0.863498i \(-0.668269\pi\)
0.504353 0.863498i \(-0.331731\pi\)
\(384\) 0 0
\(385\) 7.26973i 0.370500i
\(386\) 17.6572 0.898729
\(387\) 0 0
\(388\) 17.6572i 0.896410i
\(389\) −14.0224 −0.710962 −0.355481 0.934684i \(-0.615683\pi\)
−0.355481 + 0.934684i \(0.615683\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) 4.79796i 0.242334i
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) 13.7980i 0.694251i
\(396\) 0 0
\(397\) 9.57058i 0.480333i −0.970732 0.240167i \(-0.922798\pi\)
0.970732 0.240167i \(-0.0772021\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 8.69694i 0.434304i −0.976138 0.217152i \(-0.930323\pi\)
0.976138 0.217152i \(-0.0696768\pi\)
\(402\) 0 0
\(403\) 21.7980 + 9.57058i 1.08583 + 0.476744i
\(404\) −18.3242 −0.911665
\(405\) 0 0
\(406\) −7.59592 −0.376979
\(407\) 17.8071 0.882667
\(408\) 0 0
\(409\) 10.2376i 0.506216i 0.967438 + 0.253108i \(0.0814528\pi\)
−0.967438 + 0.253108i \(0.918547\pi\)
\(410\) 1.10102i 0.0543755i
\(411\) 0 0
\(412\) −12.8990 −0.635487
\(413\) −7.26973 −0.357720
\(414\) 0 0
\(415\) −9.79796 −0.480963
\(416\) 3.30136 + 1.44949i 0.161863 + 0.0710671i
\(417\) 0 0
\(418\) 25.0769i 1.22655i
\(419\) −27.2278 −1.33017 −0.665083 0.746770i \(-0.731604\pi\)
−0.665083 + 0.746770i \(0.731604\pi\)
\(420\) 0 0
\(421\) 4.45178i 0.216967i −0.994098 0.108483i \(-0.965401\pi\)
0.994098 0.108483i \(-0.0345994\pi\)
\(422\) 5.79796i 0.282240i
\(423\) 0 0
\(424\) 6.60272i 0.320656i
\(425\) −8.08665 −0.392260
\(426\) 0 0
\(427\) 2.96786i 0.143625i
\(428\) −5.93571 −0.286913
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) 7.59592i 0.365882i 0.983124 + 0.182941i \(0.0585618\pi\)
−0.983124 + 0.182941i \(0.941438\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 9.79796i 0.470317i
\(435\) 0 0
\(436\) 17.6572i 0.845628i
\(437\) 7.59592i 0.363362i
\(438\) 0 0
\(439\) −11.5959 −0.553443 −0.276721 0.960950i \(-0.589248\pi\)
−0.276721 + 0.960950i \(0.589248\pi\)
\(440\) 4.89898i 0.233550i
\(441\) 0 0
\(442\) 26.6969 + 11.7215i 1.26984 + 0.557536i
\(443\) −30.7128 −1.45921 −0.729604 0.683870i \(-0.760295\pi\)
−0.729604 + 0.683870i \(0.760295\pi\)
\(444\) 0 0
\(445\) 10.8990 0.516661
\(446\) 17.6572 0.836094
\(447\) 0 0
\(448\) 1.48393i 0.0701090i
\(449\) 10.8990i 0.514355i −0.966364 0.257177i \(-0.917208\pi\)
0.966364 0.257177i \(-0.0827924\pi\)
\(450\) 0 0
\(451\) 5.39388 0.253988
\(452\) 5.11879 0.240768
\(453\) 0 0
\(454\) 2.20204 0.103347
\(455\) −2.15094 + 4.89898i −0.100838 + 0.229668i
\(456\) 0 0
\(457\) 11.7215i 0.548309i −0.961686 0.274155i \(-0.911602\pi\)
0.961686 0.274155i \(-0.0883980\pi\)
\(458\) −1.48393 −0.0693394
\(459\) 0 0
\(460\) 1.48393i 0.0691885i
\(461\) 15.7980i 0.735784i 0.929868 + 0.367892i \(0.119920\pi\)
−0.929868 + 0.367892i \(0.880080\pi\)
\(462\) 0 0
\(463\) 11.7215i 0.544745i 0.962192 + 0.272372i \(0.0878083\pi\)
−0.962192 + 0.272372i \(0.912192\pi\)
\(464\) 5.11879 0.237634
\(465\) 0 0
\(466\) 5.11879i 0.237124i
\(467\) −13.2054 −0.611075 −0.305537 0.952180i \(-0.598836\pi\)
−0.305537 + 0.952180i \(0.598836\pi\)
\(468\) 0 0
\(469\) −14.2020 −0.655789
\(470\) 9.79796i 0.451946i
\(471\) 0 0
\(472\) 4.89898 0.225494
\(473\) 19.5959i 0.901021i
\(474\) 0 0
\(475\) 5.11879i 0.234866i
\(476\) 12.0000i 0.550019i
\(477\) 0 0
\(478\) −2.20204 −0.100719
\(479\) 2.20204i 0.100614i −0.998734 0.0503069i \(-0.983980\pi\)
0.998734 0.0503069i \(-0.0160199\pi\)
\(480\) 0 0
\(481\) 12.0000 + 5.26870i 0.547153 + 0.240232i
\(482\) −5.93571 −0.270364
\(483\) 0 0
\(484\) 13.0000 0.590909
\(485\) 17.6572 0.801773
\(486\) 0 0
\(487\) 10.3875i 0.470702i 0.971910 + 0.235351i \(0.0756240\pi\)
−0.971910 + 0.235351i \(0.924376\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 0 0
\(490\) −4.79796 −0.216750
\(491\) −18.3242 −0.826961 −0.413481 0.910513i \(-0.635687\pi\)
−0.413481 + 0.910513i \(0.635687\pi\)
\(492\) 0 0
\(493\) 41.3939 1.86429
\(494\) −7.41964 + 16.8990i −0.333825 + 0.760321i
\(495\) 0 0
\(496\) 6.60272i 0.296471i
\(497\) 0 0
\(498\) 0 0
\(499\) 5.11879i 0.229149i −0.993415 0.114574i \(-0.963450\pi\)
0.993415 0.114574i \(-0.0365504\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 0 0
\(502\) 8.08665i 0.360925i
\(503\) −17.6572 −0.787297 −0.393648 0.919261i \(-0.628787\pi\)
−0.393648 + 0.919261i \(0.628787\pi\)
\(504\) 0 0
\(505\) 18.3242i 0.815418i
\(506\) 7.26973 0.323179
\(507\) 0 0
\(508\) 12.8990 0.572300
\(509\) 30.0000i 1.32973i 0.746965 + 0.664863i \(0.231510\pi\)
−0.746965 + 0.664863i \(0.768490\pi\)
\(510\) 0 0
\(511\) −6.60612 −0.292238
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 11.0545i 0.487593i
\(515\) 12.8990i 0.568397i
\(516\) 0 0
\(517\) −48.0000 −2.11104
\(518\) 5.39388i 0.236993i
\(519\) 0 0
\(520\) 1.44949 3.30136i 0.0635643 0.144774i
\(521\) −35.3144 −1.54715 −0.773577 0.633702i \(-0.781534\pi\)
−0.773577 + 0.633702i \(0.781534\pi\)
\(522\) 0 0
\(523\) 41.7980 1.82770 0.913849 0.406055i \(-0.133096\pi\)
0.913849 + 0.406055i \(0.133096\pi\)
\(524\) −11.0545 −0.482918
\(525\) 0 0
\(526\) 11.7215i 0.511082i
\(527\) 53.3939i 2.32587i
\(528\) 0 0
\(529\) −20.7980 −0.904259
\(530\) 6.60272 0.286804
\(531\) 0 0
\(532\) 7.59592 0.329325
\(533\) 3.63487 + 1.59592i 0.157443 + 0.0691269i
\(534\) 0 0
\(535\) 5.93571i 0.256623i
\(536\) 9.57058 0.413386
\(537\) 0 0
\(538\) 14.0224i 0.604547i
\(539\) 23.5051i 1.01244i
\(540\) 0 0
\(541\) 32.1967i 1.38424i 0.721781 + 0.692122i \(0.243324\pi\)
−0.721781 + 0.692122i \(0.756676\pi\)
\(542\) −12.5384 −0.538572
\(543\) 0 0
\(544\) 8.08665i 0.346712i
\(545\) −17.6572 −0.756352
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 3.79796i 0.162241i
\(549\) 0 0
\(550\) −4.89898 −0.208893
\(551\) 26.2020i 1.11624i
\(552\) 0 0
\(553\) 20.4752i 0.870693i
\(554\) 24.6969i 1.04927i
\(555\) 0 0
\(556\) 13.7980 0.585164
\(557\) 13.5959i 0.576078i −0.957619 0.288039i \(-0.906997\pi\)
0.957619 0.288039i \(-0.0930032\pi\)
\(558\) 0 0
\(559\) −5.79796 + 13.2054i −0.245228 + 0.558531i
\(560\) −1.48393 −0.0627074
\(561\) 0 0
\(562\) 8.69694 0.366858
\(563\) −36.6485 −1.54455 −0.772274 0.635289i \(-0.780881\pi\)
−0.772274 + 0.635289i \(0.780881\pi\)
\(564\) 0 0
\(565\) 5.11879i 0.215349i
\(566\) 29.7980i 1.25250i
\(567\) 0 0
\(568\) 0 0
\(569\) 2.96786 0.124419 0.0622095 0.998063i \(-0.480185\pi\)
0.0622095 + 0.998063i \(0.480185\pi\)
\(570\) 0 0
\(571\) 23.5959 0.987458 0.493729 0.869616i \(-0.335633\pi\)
0.493729 + 0.869616i \(0.335633\pi\)
\(572\) 16.1733 + 7.10102i 0.676239 + 0.296909i
\(573\) 0 0
\(574\) 1.63383i 0.0681949i
\(575\) −1.48393 −0.0618841
\(576\) 0 0
\(577\) 24.9270i 1.03772i 0.854858 + 0.518861i \(0.173644\pi\)
−0.854858 + 0.518861i \(0.826356\pi\)
\(578\) 48.3939i 2.01292i
\(579\) 0 0
\(580\) 5.11879i 0.212546i
\(581\) −14.5395 −0.603199
\(582\) 0 0
\(583\) 32.3466i 1.33966i
\(584\) 4.45178 0.184216
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −33.7980 −1.39262
\(590\) 4.89898i 0.201688i
\(591\) 0 0
\(592\) 3.63487i 0.149392i
\(593\) 25.5959i 1.05110i −0.850763 0.525549i \(-0.823860\pi\)
0.850763 0.525549i \(-0.176140\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 15.7980i 0.647110i
\(597\) 0 0
\(598\) 4.89898 + 2.15094i 0.200334 + 0.0879584i
\(599\) 11.8714 0.485053 0.242527 0.970145i \(-0.422024\pi\)
0.242527 + 0.970145i \(0.422024\pi\)
\(600\) 0 0
\(601\) 39.3939 1.60691 0.803455 0.595366i \(-0.202993\pi\)
0.803455 + 0.595366i \(0.202993\pi\)
\(602\) 5.93571 0.241921
\(603\) 0 0
\(604\) 6.60272i 0.268661i
\(605\) 13.0000i 0.528525i
\(606\) 0 0
\(607\) −1.30306 −0.0528896 −0.0264448 0.999650i \(-0.508419\pi\)
−0.0264448 + 0.999650i \(0.508419\pi\)
\(608\) −5.11879 −0.207594
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) −32.3466 14.2020i −1.30860 0.574553i
\(612\) 0 0
\(613\) 3.63487i 0.146811i 0.997302 + 0.0734054i \(0.0233867\pi\)
−0.997302 + 0.0734054i \(0.976613\pi\)
\(614\) 9.57058 0.386237
\(615\) 0 0
\(616\) 7.26973i 0.292906i
\(617\) 39.7980i 1.60221i −0.598527 0.801103i \(-0.704247\pi\)
0.598527 0.801103i \(-0.295753\pi\)
\(618\) 0 0
\(619\) 46.3690i 1.86373i −0.362811 0.931863i \(-0.618183\pi\)
0.362811 0.931863i \(-0.381817\pi\)
\(620\) 6.60272 0.265172
\(621\) 0 0
\(622\) 5.93571i 0.238000i
\(623\) 16.1733 0.647969
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 31.3939i 1.25475i
\(627\) 0 0
\(628\) −9.10102 −0.363170
\(629\) 29.3939i 1.17201i
\(630\) 0 0
\(631\) 30.0457i 1.19610i 0.801458 + 0.598051i \(0.204058\pi\)
−0.801458 + 0.598051i \(0.795942\pi\)
\(632\) 13.7980i 0.548853i
\(633\) 0 0
\(634\) 13.5959 0.539963
\(635\) 12.8990i 0.511880i
\(636\) 0 0
\(637\) 6.95459 15.8398i 0.275551 0.627595i
\(638\) 25.0769 0.992802
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 20.4752 0.808721 0.404360 0.914600i \(-0.367494\pi\)
0.404360 + 0.914600i \(0.367494\pi\)
\(642\) 0 0
\(643\) 35.9815i 1.41897i 0.704720 + 0.709485i \(0.251072\pi\)
−0.704720 + 0.709485i \(0.748928\pi\)
\(644\) 2.20204i 0.0867726i
\(645\) 0 0
\(646\) −41.3939 −1.62862
\(647\) 11.7215 0.460820 0.230410 0.973094i \(-0.425993\pi\)
0.230410 + 0.973094i \(0.425993\pi\)
\(648\) 0 0
\(649\) 24.0000 0.942082
\(650\) −3.30136 1.44949i −0.129490 0.0568537i
\(651\) 0 0
\(652\) 6.60272i 0.258582i
\(653\) 10.9046 0.426730 0.213365 0.976973i \(-0.431558\pi\)
0.213365 + 0.976973i \(0.431558\pi\)
\(654\) 0 0
\(655\) 11.0545i 0.431935i
\(656\) 1.10102i 0.0429876i
\(657\) 0 0
\(658\) 14.5395i 0.566807i
\(659\) −2.15094 −0.0837886 −0.0418943 0.999122i \(-0.513339\pi\)
−0.0418943 + 0.999122i \(0.513339\pi\)
\(660\) 0 0
\(661\) 18.9912i 0.738674i 0.929296 + 0.369337i \(0.120415\pi\)
−0.929296 + 0.369337i \(0.879585\pi\)
\(662\) −24.2599 −0.942890
\(663\) 0 0
\(664\) 9.79796 0.380235
\(665\) 7.59592i 0.294557i
\(666\) 0 0
\(667\) 7.59592 0.294115
\(668\) 0 0
\(669\) 0 0
\(670\) 9.57058i 0.369744i
\(671\) 9.79796i 0.378246i
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 10.0000i 0.385186i
\(675\) 0 0
\(676\) 8.79796 + 9.57058i 0.338383 + 0.368099i
\(677\) −2.30084 −0.0884287 −0.0442143 0.999022i \(-0.514078\pi\)
−0.0442143 + 0.999022i \(0.514078\pi\)
\(678\) 0 0
\(679\) 26.2020 1.00554
\(680\) 8.08665 0.310109
\(681\) 0 0
\(682\) 32.3466i 1.23862i
\(683\) 33.7980i 1.29324i 0.762811 + 0.646621i \(0.223819\pi\)
−0.762811 + 0.646621i \(0.776181\pi\)
\(684\) 0 0
\(685\) 3.79796 0.145113
\(686\) −17.5073 −0.668432
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) −9.57058 + 21.7980i −0.364610 + 0.830436i
\(690\) 0 0
\(691\) 38.7994i 1.47600i 0.674801 + 0.737999i \(0.264229\pi\)
−0.674801 + 0.737999i \(0.735771\pi\)
\(692\) 12.5384 0.476640
\(693\) 0 0
\(694\) 35.3144i 1.34052i
\(695\) 13.7980i 0.523386i
\(696\) 0 0
\(697\) 8.90357i 0.337247i
\(698\) 18.9912 0.718829
\(699\) 0 0
\(700\) 1.48393i 0.0560872i
\(701\) 25.5940 0.966671 0.483335 0.875435i \(-0.339425\pi\)
0.483335 + 0.875435i \(0.339425\pi\)
\(702\) 0 0
\(703\) −18.6061 −0.701743
\(704\) 4.89898i 0.184637i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 27.1918i 1.02265i
\(708\) 0 0
\(709\) 33.8305i 1.27053i 0.772293 + 0.635266i \(0.219110\pi\)
−0.772293 + 0.635266i \(0.780890\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.8990 −0.408457
\(713\) 9.79796i 0.366936i
\(714\) 0 0
\(715\) 7.10102 16.1733i 0.265563 0.604847i
\(716\) 21.2921 0.795723
\(717\) 0 0
\(718\) −9.79796 −0.365657
\(719\) −10.2376 −0.381798 −0.190899 0.981610i \(-0.561140\pi\)
−0.190899 + 0.981610i \(0.561140\pi\)
\(720\) 0 0
\(721\) 19.1412i 0.712854i
\(722\) 7.20204i 0.268032i
\(723\) 0 0
\(724\) −23.7980 −0.884444
\(725\) −5.11879 −0.190107
\(726\) 0 0
\(727\) −22.6969 −0.841783 −0.420891 0.907111i \(-0.638283\pi\)
−0.420891 + 0.907111i \(0.638283\pi\)
\(728\) 2.15094 4.89898i 0.0797191 0.181568i
\(729\) 0 0
\(730\) 4.45178i 0.164768i
\(731\) −32.3466 −1.19638
\(732\) 0 0
\(733\) 43.2512i 1.59752i −0.601650 0.798760i \(-0.705490\pi\)
0.601650 0.798760i \(-0.294510\pi\)
\(734\) 6.69694i 0.247189i
\(735\) 0 0
\(736\) 1.48393i 0.0546983i
\(737\) 46.8861 1.72707
\(738\) 0 0
\(739\) 8.08665i 0.297472i −0.988877 0.148736i \(-0.952480\pi\)
0.988877 0.148736i \(-0.0475205\pi\)
\(740\) 3.63487 0.133620
\(741\) 0 0
\(742\) 9.79796 0.359694
\(743\) 43.5959i 1.59938i −0.600414 0.799690i \(-0.704997\pi\)
0.600414 0.799690i \(-0.295003\pi\)
\(744\) 0 0
\(745\) 15.7980 0.578792
\(746\) 12.6969i 0.464868i
\(747\) 0 0
\(748\) 39.6163i 1.44852i
\(749\) 8.80816i 0.321843i
\(750\) 0 0
\(751\) −25.7980 −0.941381 −0.470690 0.882298i \(-0.655995\pi\)
−0.470690 + 0.882298i \(0.655995\pi\)
\(752\) 9.79796i 0.357295i
\(753\) 0 0
\(754\) 16.8990 + 7.41964i 0.615425 + 0.270207i
\(755\) 6.60272 0.240298
\(756\) 0 0
\(757\) 38.8990 1.41381 0.706904 0.707310i \(-0.250091\pi\)
0.706904 + 0.707310i \(0.250091\pi\)
\(758\) 12.3885 0.449971
\(759\) 0 0
\(760\) 5.11879i 0.185678i
\(761\) 52.2929i 1.89561i 0.318844 + 0.947807i \(0.396705\pi\)
−0.318844 + 0.947807i \(0.603295\pi\)
\(762\) 0 0
\(763\) −26.2020 −0.948578
\(764\) −20.4752 −0.740766
\(765\) 0 0
\(766\) 33.7980 1.22117
\(767\) 16.1733 + 7.10102i 0.583984 + 0.256403i
\(768\) 0 0
\(769\) 31.0126i 1.11834i 0.829052 + 0.559171i \(0.188880\pi\)
−0.829052 + 0.559171i \(0.811120\pi\)
\(770\) −7.26973 −0.261983
\(771\) 0 0
\(772\) 17.6572i 0.635497i
\(773\) 13.5959i 0.489011i −0.969648 0.244506i \(-0.921374\pi\)
0.969648 0.244506i \(-0.0786257\pi\)
\(774\) 0 0
\(775\) 6.60272i 0.237177i
\(776\) −17.6572 −0.633857
\(777\) 0 0
\(778\) 14.0224i 0.502726i
\(779\) −5.63590 −0.201927
\(780\) 0 0
\(781\) 0 0
\(782\) 12.0000i 0.429119i
\(783\) 0 0
\(784\) 4.79796 0.171356
\(785\) 9.10102i 0.324829i
\(786\) 0 0
\(787\) 25.7439i 0.917670i −0.888522 0.458835i \(-0.848267\pi\)
0.888522 0.458835i \(-0.151733\pi\)
\(788\) 18.0000i 0.641223i
\(789\) 0 0
\(790\) −13.7980 −0.490909
\(791\) 7.59592i 0.270080i
\(792\) 0 0
\(793\) −2.89898 + 6.60272i −0.102946 + 0.234469i
\(794\) 9.57058 0.339647
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) −46.2190 −1.63716 −0.818581 0.574391i \(-0.805239\pi\)
−0.818581 + 0.574391i \(0.805239\pi\)
\(798\) 0 0
\(799\) 79.2326i 2.80305i
\(800\) 1.00000i 0.0353553i