Properties

Label 4020.2.g.c.1609.10
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.10
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.29

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-0.504884 - 2.17832i) q^{5}\) \(-3.91807i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-0.504884 - 2.17832i) q^{5}\) \(-3.91807i q^{7}\) \(-1.00000 q^{9}\) \(+3.46196 q^{11}\) \(+6.46128i q^{13}\) \(+(-2.17832 + 0.504884i) q^{15}\) \(-0.603948i q^{17}\) \(-0.547912 q^{19}\) \(-3.91807 q^{21}\) \(+7.27671i q^{23}\) \(+(-4.49019 + 2.19960i) q^{25}\) \(+1.00000i q^{27}\) \(-5.89848 q^{29}\) \(-4.98609 q^{31}\) \(-3.46196i q^{33}\) \(+(-8.53483 + 1.97817i) q^{35}\) \(+2.50660i q^{37}\) \(+6.46128 q^{39}\) \(-10.9146 q^{41}\) \(-3.38640i q^{43}\) \(+(0.504884 + 2.17832i) q^{45}\) \(-5.74394i q^{47}\) \(-8.35128 q^{49}\) \(-0.603948 q^{51}\) \(+2.06027i q^{53}\) \(+(-1.74789 - 7.54127i) q^{55}\) \(+0.547912i q^{57}\) \(-11.6318 q^{59}\) \(-8.87755 q^{61}\) \(+3.91807i q^{63}\) \(+(14.0747 - 3.26219i) q^{65}\) \(-1.00000i q^{67}\) \(+7.27671 q^{69}\) \(+3.83462 q^{71}\) \(+15.6619i q^{73}\) \(+(2.19960 + 4.49019i) q^{75}\) \(-13.5642i q^{77}\) \(-8.63769 q^{79}\) \(+1.00000 q^{81}\) \(-3.96810i q^{83}\) \(+(-1.31559 + 0.304924i) q^{85}\) \(+5.89848i q^{87}\) \(-8.55112 q^{89}\) \(+25.3157 q^{91}\) \(+4.98609i q^{93}\) \(+(0.276632 + 1.19353i) q^{95}\) \(-6.10602i q^{97}\) \(-3.46196 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −0.504884 2.17832i −0.225791 0.974176i
\(6\) 0 0
\(7\) 3.91807i 1.48089i −0.672116 0.740446i \(-0.734614\pi\)
0.672116 0.740446i \(-0.265386\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.46196 1.04382 0.521910 0.853001i \(-0.325220\pi\)
0.521910 + 0.853001i \(0.325220\pi\)
\(12\) 0 0
\(13\) 6.46128i 1.79204i 0.444018 + 0.896018i \(0.353552\pi\)
−0.444018 + 0.896018i \(0.646448\pi\)
\(14\) 0 0
\(15\) −2.17832 + 0.504884i −0.562441 + 0.130360i
\(16\) 0 0
\(17\) 0.603948i 0.146479i −0.997314 0.0732395i \(-0.976666\pi\)
0.997314 0.0732395i \(-0.0233337\pi\)
\(18\) 0 0
\(19\) −0.547912 −0.125700 −0.0628498 0.998023i \(-0.520019\pi\)
−0.0628498 + 0.998023i \(0.520019\pi\)
\(20\) 0 0
\(21\) −3.91807 −0.854993
\(22\) 0 0
\(23\) 7.27671i 1.51730i 0.651499 + 0.758649i \(0.274140\pi\)
−0.651499 + 0.758649i \(0.725860\pi\)
\(24\) 0 0
\(25\) −4.49019 + 2.19960i −0.898037 + 0.439920i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −5.89848 −1.09532 −0.547660 0.836701i \(-0.684481\pi\)
−0.547660 + 0.836701i \(0.684481\pi\)
\(30\) 0 0
\(31\) −4.98609 −0.895529 −0.447765 0.894152i \(-0.647780\pi\)
−0.447765 + 0.894152i \(0.647780\pi\)
\(32\) 0 0
\(33\) 3.46196i 0.602650i
\(34\) 0 0
\(35\) −8.53483 + 1.97817i −1.44265 + 0.334372i
\(36\) 0 0
\(37\) 2.50660i 0.412082i 0.978543 + 0.206041i \(0.0660581\pi\)
−0.978543 + 0.206041i \(0.933942\pi\)
\(38\) 0 0
\(39\) 6.46128 1.03463
\(40\) 0 0
\(41\) −10.9146 −1.70458 −0.852288 0.523073i \(-0.824785\pi\)
−0.852288 + 0.523073i \(0.824785\pi\)
\(42\) 0 0
\(43\) 3.38640i 0.516420i −0.966089 0.258210i \(-0.916867\pi\)
0.966089 0.258210i \(-0.0831327\pi\)
\(44\) 0 0
\(45\) 0.504884 + 2.17832i 0.0752636 + 0.324725i
\(46\) 0 0
\(47\) 5.74394i 0.837839i −0.908023 0.418920i \(-0.862409\pi\)
0.908023 0.418920i \(-0.137591\pi\)
\(48\) 0 0
\(49\) −8.35128 −1.19304
\(50\) 0 0
\(51\) −0.603948 −0.0845697
\(52\) 0 0
\(53\) 2.06027i 0.283000i 0.989938 + 0.141500i \(0.0451925\pi\)
−0.989938 + 0.141500i \(0.954808\pi\)
\(54\) 0 0
\(55\) −1.74789 7.54127i −0.235685 1.01686i
\(56\) 0 0
\(57\) 0.547912i 0.0725727i
\(58\) 0 0
\(59\) −11.6318 −1.51433 −0.757164 0.653225i \(-0.773416\pi\)
−0.757164 + 0.653225i \(0.773416\pi\)
\(60\) 0 0
\(61\) −8.87755 −1.13665 −0.568327 0.822803i \(-0.692409\pi\)
−0.568327 + 0.822803i \(0.692409\pi\)
\(62\) 0 0
\(63\) 3.91807i 0.493631i
\(64\) 0 0
\(65\) 14.0747 3.26219i 1.74576 0.404625i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 7.27671 0.876013
\(70\) 0 0
\(71\) 3.83462 0.455086 0.227543 0.973768i \(-0.426931\pi\)
0.227543 + 0.973768i \(0.426931\pi\)
\(72\) 0 0
\(73\) 15.6619i 1.83309i 0.399936 + 0.916543i \(0.369032\pi\)
−0.399936 + 0.916543i \(0.630968\pi\)
\(74\) 0 0
\(75\) 2.19960 + 4.49019i 0.253988 + 0.518482i
\(76\) 0 0
\(77\) 13.5642i 1.54578i
\(78\) 0 0
\(79\) −8.63769 −0.971817 −0.485908 0.874010i \(-0.661511\pi\)
−0.485908 + 0.874010i \(0.661511\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.96810i 0.435556i −0.975998 0.217778i \(-0.930119\pi\)
0.975998 0.217778i \(-0.0698808\pi\)
\(84\) 0 0
\(85\) −1.31559 + 0.304924i −0.142696 + 0.0330736i
\(86\) 0 0
\(87\) 5.89848i 0.632383i
\(88\) 0 0
\(89\) −8.55112 −0.906417 −0.453209 0.891404i \(-0.649721\pi\)
−0.453209 + 0.891404i \(0.649721\pi\)
\(90\) 0 0
\(91\) 25.3157 2.65381
\(92\) 0 0
\(93\) 4.98609i 0.517034i
\(94\) 0 0
\(95\) 0.276632 + 1.19353i 0.0283818 + 0.122454i
\(96\) 0 0
\(97\) 6.10602i 0.619973i −0.950741 0.309986i \(-0.899676\pi\)
0.950741 0.309986i \(-0.100324\pi\)
\(98\) 0 0
\(99\) −3.46196 −0.347940
\(100\) 0 0
\(101\) 5.80936 0.578053 0.289027 0.957321i \(-0.406668\pi\)
0.289027 + 0.957321i \(0.406668\pi\)
\(102\) 0 0
\(103\) 8.89577i 0.876526i 0.898847 + 0.438263i \(0.144406\pi\)
−0.898847 + 0.438263i \(0.855594\pi\)
\(104\) 0 0
\(105\) 1.97817 + 8.53483i 0.193050 + 0.832914i
\(106\) 0 0
\(107\) 15.2578i 1.47503i 0.675333 + 0.737513i \(0.264000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(108\) 0 0
\(109\) −12.6445 −1.21112 −0.605560 0.795800i \(-0.707051\pi\)
−0.605560 + 0.795800i \(0.707051\pi\)
\(110\) 0 0
\(111\) 2.50660 0.237916
\(112\) 0 0
\(113\) 10.2895i 0.967956i −0.875080 0.483978i \(-0.839191\pi\)
0.875080 0.483978i \(-0.160809\pi\)
\(114\) 0 0
\(115\) 15.8510 3.67389i 1.47812 0.342592i
\(116\) 0 0
\(117\) 6.46128i 0.597345i
\(118\) 0 0
\(119\) −2.36631 −0.216920
\(120\) 0 0
\(121\) 0.985162 0.0895602
\(122\) 0 0
\(123\) 10.9146i 0.984137i
\(124\) 0 0
\(125\) 7.05846 + 8.67053i 0.631328 + 0.775516i
\(126\) 0 0
\(127\) 6.92997i 0.614935i −0.951559 0.307468i \(-0.900518\pi\)
0.951559 0.307468i \(-0.0994816\pi\)
\(128\) 0 0
\(129\) −3.38640 −0.298156
\(130\) 0 0
\(131\) 11.2951 0.986861 0.493430 0.869785i \(-0.335743\pi\)
0.493430 + 0.869785i \(0.335743\pi\)
\(132\) 0 0
\(133\) 2.14676i 0.186148i
\(134\) 0 0
\(135\) 2.17832 0.504884i 0.187480 0.0434535i
\(136\) 0 0
\(137\) 7.64778i 0.653394i 0.945129 + 0.326697i \(0.105936\pi\)
−0.945129 + 0.326697i \(0.894064\pi\)
\(138\) 0 0
\(139\) 3.12792 0.265306 0.132653 0.991163i \(-0.457650\pi\)
0.132653 + 0.991163i \(0.457650\pi\)
\(140\) 0 0
\(141\) −5.74394 −0.483727
\(142\) 0 0
\(143\) 22.3687i 1.87056i
\(144\) 0 0
\(145\) 2.97804 + 12.8488i 0.247313 + 1.06703i
\(146\) 0 0
\(147\) 8.35128i 0.688802i
\(148\) 0 0
\(149\) 13.5824 1.11271 0.556357 0.830943i \(-0.312199\pi\)
0.556357 + 0.830943i \(0.312199\pi\)
\(150\) 0 0
\(151\) −14.4695 −1.17751 −0.588756 0.808311i \(-0.700382\pi\)
−0.588756 + 0.808311i \(0.700382\pi\)
\(152\) 0 0
\(153\) 0.603948i 0.0488263i
\(154\) 0 0
\(155\) 2.51740 + 10.8613i 0.202202 + 0.872403i
\(156\) 0 0
\(157\) 12.0664i 0.963007i −0.876444 0.481504i \(-0.840091\pi\)
0.876444 0.481504i \(-0.159909\pi\)
\(158\) 0 0
\(159\) 2.06027 0.163390
\(160\) 0 0
\(161\) 28.5107 2.24695
\(162\) 0 0
\(163\) 3.01144i 0.235874i 0.993021 + 0.117937i \(0.0376281\pi\)
−0.993021 + 0.117937i \(0.962372\pi\)
\(164\) 0 0
\(165\) −7.54127 + 1.74789i −0.587087 + 0.136073i
\(166\) 0 0
\(167\) 6.13904i 0.475053i 0.971381 + 0.237527i \(0.0763367\pi\)
−0.971381 + 0.237527i \(0.923663\pi\)
\(168\) 0 0
\(169\) −28.7481 −2.21139
\(170\) 0 0
\(171\) 0.547912 0.0418999
\(172\) 0 0
\(173\) 0.831968i 0.0632533i 0.999500 + 0.0316267i \(0.0100688\pi\)
−0.999500 + 0.0316267i \(0.989931\pi\)
\(174\) 0 0
\(175\) 8.61819 + 17.5929i 0.651474 + 1.32990i
\(176\) 0 0
\(177\) 11.6318i 0.874298i
\(178\) 0 0
\(179\) 13.4026 1.00175 0.500877 0.865518i \(-0.333011\pi\)
0.500877 + 0.865518i \(0.333011\pi\)
\(180\) 0 0
\(181\) −2.84980 −0.211824 −0.105912 0.994375i \(-0.533776\pi\)
−0.105912 + 0.994375i \(0.533776\pi\)
\(182\) 0 0
\(183\) 8.87755i 0.656248i
\(184\) 0 0
\(185\) 5.46018 1.26554i 0.401441 0.0930444i
\(186\) 0 0
\(187\) 2.09084i 0.152898i
\(188\) 0 0
\(189\) 3.91807 0.284998
\(190\) 0 0
\(191\) 16.8329 1.21798 0.608992 0.793176i \(-0.291574\pi\)
0.608992 + 0.793176i \(0.291574\pi\)
\(192\) 0 0
\(193\) 25.5455i 1.83881i −0.393315 0.919404i \(-0.628672\pi\)
0.393315 0.919404i \(-0.371328\pi\)
\(194\) 0 0
\(195\) −3.26219 14.0747i −0.233610 1.00791i
\(196\) 0 0
\(197\) 12.3050i 0.876695i 0.898805 + 0.438348i \(0.144436\pi\)
−0.898805 + 0.438348i \(0.855564\pi\)
\(198\) 0 0
\(199\) 8.79978 0.623800 0.311900 0.950115i \(-0.399035\pi\)
0.311900 + 0.950115i \(0.399035\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 23.1107i 1.62205i
\(204\) 0 0
\(205\) 5.51061 + 23.7755i 0.384877 + 1.66056i
\(206\) 0 0
\(207\) 7.27671i 0.505766i
\(208\) 0 0
\(209\) −1.89685 −0.131208
\(210\) 0 0
\(211\) −11.6312 −0.800726 −0.400363 0.916357i \(-0.631116\pi\)
−0.400363 + 0.916357i \(0.631116\pi\)
\(212\) 0 0
\(213\) 3.83462i 0.262744i
\(214\) 0 0
\(215\) −7.37666 + 1.70974i −0.503084 + 0.116603i
\(216\) 0 0
\(217\) 19.5359i 1.32618i
\(218\) 0 0
\(219\) 15.6619 1.05833
\(220\) 0 0
\(221\) 3.90228 0.262495
\(222\) 0 0
\(223\) 18.7044i 1.25254i −0.779607 0.626269i \(-0.784581\pi\)
0.779607 0.626269i \(-0.215419\pi\)
\(224\) 0 0
\(225\) 4.49019 2.19960i 0.299346 0.146640i
\(226\) 0 0
\(227\) 10.1922i 0.676483i −0.941059 0.338241i \(-0.890168\pi\)
0.941059 0.338241i \(-0.109832\pi\)
\(228\) 0 0
\(229\) 0.810691 0.0535719 0.0267860 0.999641i \(-0.491473\pi\)
0.0267860 + 0.999641i \(0.491473\pi\)
\(230\) 0 0
\(231\) −13.5642 −0.892459
\(232\) 0 0
\(233\) 25.4579i 1.66780i −0.551913 0.833902i \(-0.686102\pi\)
0.551913 0.833902i \(-0.313898\pi\)
\(234\) 0 0
\(235\) −12.5122 + 2.90002i −0.816203 + 0.189176i
\(236\) 0 0
\(237\) 8.63769i 0.561079i
\(238\) 0 0
\(239\) −8.47427 −0.548155 −0.274077 0.961708i \(-0.588372\pi\)
−0.274077 + 0.961708i \(0.588372\pi\)
\(240\) 0 0
\(241\) −7.25751 −0.467497 −0.233749 0.972297i \(-0.575099\pi\)
−0.233749 + 0.972297i \(0.575099\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 4.21642 + 18.1918i 0.269378 + 1.16223i
\(246\) 0 0
\(247\) 3.54021i 0.225258i
\(248\) 0 0
\(249\) −3.96810 −0.251468
\(250\) 0 0
\(251\) −8.98355 −0.567037 −0.283518 0.958967i \(-0.591502\pi\)
−0.283518 + 0.958967i \(0.591502\pi\)
\(252\) 0 0
\(253\) 25.1917i 1.58379i
\(254\) 0 0
\(255\) 0.304924 + 1.31559i 0.0190951 + 0.0823857i
\(256\) 0 0
\(257\) 8.42681i 0.525650i −0.964843 0.262825i \(-0.915346\pi\)
0.964843 0.262825i \(-0.0846542\pi\)
\(258\) 0 0
\(259\) 9.82103 0.610249
\(260\) 0 0
\(261\) 5.89848 0.365107
\(262\) 0 0
\(263\) 10.4437i 0.643987i −0.946742 0.321994i \(-0.895647\pi\)
0.946742 0.321994i \(-0.104353\pi\)
\(264\) 0 0
\(265\) 4.48793 1.04020i 0.275691 0.0638987i
\(266\) 0 0
\(267\) 8.55112i 0.523320i
\(268\) 0 0
\(269\) −14.6313 −0.892083 −0.446042 0.895012i \(-0.647167\pi\)
−0.446042 + 0.895012i \(0.647167\pi\)
\(270\) 0 0
\(271\) −25.6460 −1.55788 −0.778940 0.627098i \(-0.784243\pi\)
−0.778940 + 0.627098i \(0.784243\pi\)
\(272\) 0 0
\(273\) 25.3157i 1.53218i
\(274\) 0 0
\(275\) −15.5448 + 7.61492i −0.937389 + 0.459197i
\(276\) 0 0
\(277\) 11.7897i 0.708373i 0.935175 + 0.354186i \(0.115242\pi\)
−0.935175 + 0.354186i \(0.884758\pi\)
\(278\) 0 0
\(279\) 4.98609 0.298510
\(280\) 0 0
\(281\) 33.1194 1.97573 0.987867 0.155299i \(-0.0496342\pi\)
0.987867 + 0.155299i \(0.0496342\pi\)
\(282\) 0 0
\(283\) 17.9719i 1.06832i −0.845384 0.534159i \(-0.820628\pi\)
0.845384 0.534159i \(-0.179372\pi\)
\(284\) 0 0
\(285\) 1.19353 0.276632i 0.0706986 0.0163863i
\(286\) 0 0
\(287\) 42.7642i 2.52429i
\(288\) 0 0
\(289\) 16.6352 0.978544
\(290\) 0 0
\(291\) −6.10602 −0.357941
\(292\) 0 0
\(293\) 5.64494i 0.329781i −0.986312 0.164890i \(-0.947273\pi\)
0.986312 0.164890i \(-0.0527271\pi\)
\(294\) 0 0
\(295\) 5.87269 + 25.3378i 0.341921 + 1.47522i
\(296\) 0 0
\(297\) 3.46196i 0.200883i
\(298\) 0 0
\(299\) −47.0168 −2.71905
\(300\) 0 0
\(301\) −13.2681 −0.764763
\(302\) 0 0
\(303\) 5.80936i 0.333739i
\(304\) 0 0
\(305\) 4.48213 + 19.3382i 0.256646 + 1.10730i
\(306\) 0 0
\(307\) 9.43241i 0.538336i −0.963093 0.269168i \(-0.913251\pi\)
0.963093 0.269168i \(-0.0867487\pi\)
\(308\) 0 0
\(309\) 8.89577 0.506062
\(310\) 0 0
\(311\) 14.9238 0.846251 0.423125 0.906071i \(-0.360933\pi\)
0.423125 + 0.906071i \(0.360933\pi\)
\(312\) 0 0
\(313\) 11.8081i 0.667436i −0.942673 0.333718i \(-0.891697\pi\)
0.942673 0.333718i \(-0.108303\pi\)
\(314\) 0 0
\(315\) 8.53483 1.97817i 0.480883 0.111457i
\(316\) 0 0
\(317\) 8.68438i 0.487764i −0.969805 0.243882i \(-0.921579\pi\)
0.969805 0.243882i \(-0.0784209\pi\)
\(318\) 0 0
\(319\) −20.4203 −1.14332
\(320\) 0 0
\(321\) 15.2578 0.851607
\(322\) 0 0
\(323\) 0.330911i 0.0184124i
\(324\) 0 0
\(325\) −14.2122 29.0123i −0.788352 1.60931i
\(326\) 0 0
\(327\) 12.6445i 0.699240i
\(328\) 0 0
\(329\) −22.5052 −1.24075
\(330\) 0 0
\(331\) −17.2191 −0.946446 −0.473223 0.880943i \(-0.656909\pi\)
−0.473223 + 0.880943i \(0.656909\pi\)
\(332\) 0 0
\(333\) 2.50660i 0.137361i
\(334\) 0 0
\(335\) −2.17832 + 0.504884i −0.119015 + 0.0275847i
\(336\) 0 0
\(337\) 0.800375i 0.0435992i 0.999762 + 0.0217996i \(0.00693958\pi\)
−0.999762 + 0.0217996i \(0.993060\pi\)
\(338\) 0 0
\(339\) −10.2895 −0.558850
\(340\) 0 0
\(341\) −17.2617 −0.934771
\(342\) 0 0
\(343\) 5.29442i 0.285872i
\(344\) 0 0
\(345\) −3.67389 15.8510i −0.197796 0.853390i
\(346\) 0 0
\(347\) 7.50758i 0.403028i −0.979486 0.201514i \(-0.935414\pi\)
0.979486 0.201514i \(-0.0645862\pi\)
\(348\) 0 0
\(349\) 10.4840 0.561194 0.280597 0.959826i \(-0.409468\pi\)
0.280597 + 0.959826i \(0.409468\pi\)
\(350\) 0 0
\(351\) −6.46128 −0.344877
\(352\) 0 0
\(353\) 35.7951i 1.90518i −0.304255 0.952591i \(-0.598408\pi\)
0.304255 0.952591i \(-0.401592\pi\)
\(354\) 0 0
\(355\) −1.93604 8.35305i −0.102754 0.443334i
\(356\) 0 0
\(357\) 2.36631i 0.125239i
\(358\) 0 0
\(359\) −29.9078 −1.57847 −0.789236 0.614090i \(-0.789523\pi\)
−0.789236 + 0.614090i \(0.789523\pi\)
\(360\) 0 0
\(361\) −18.6998 −0.984200
\(362\) 0 0
\(363\) 0.985162i 0.0517076i
\(364\) 0 0
\(365\) 34.1167 7.90743i 1.78575 0.413894i
\(366\) 0 0
\(367\) 23.6154i 1.23271i 0.787468 + 0.616356i \(0.211392\pi\)
−0.787468 + 0.616356i \(0.788608\pi\)
\(368\) 0 0
\(369\) 10.9146 0.568192
\(370\) 0 0
\(371\) 8.07228 0.419092
\(372\) 0 0
\(373\) 12.2685i 0.635238i 0.948218 + 0.317619i \(0.102883\pi\)
−0.948218 + 0.317619i \(0.897117\pi\)
\(374\) 0 0
\(375\) 8.67053 7.05846i 0.447744 0.364497i
\(376\) 0 0
\(377\) 38.1117i 1.96285i
\(378\) 0 0
\(379\) −11.4821 −0.589797 −0.294899 0.955529i \(-0.595286\pi\)
−0.294899 + 0.955529i \(0.595286\pi\)
\(380\) 0 0
\(381\) −6.92997 −0.355033
\(382\) 0 0
\(383\) 6.02874i 0.308054i −0.988067 0.154027i \(-0.950776\pi\)
0.988067 0.154027i \(-0.0492243\pi\)
\(384\) 0 0
\(385\) −29.5472 + 6.84834i −1.50587 + 0.349024i
\(386\) 0 0
\(387\) 3.38640i 0.172140i
\(388\) 0 0
\(389\) 8.23972 0.417770 0.208885 0.977940i \(-0.433017\pi\)
0.208885 + 0.977940i \(0.433017\pi\)
\(390\) 0 0
\(391\) 4.39475 0.222252
\(392\) 0 0
\(393\) 11.2951i 0.569764i
\(394\) 0 0
\(395\) 4.36103 + 18.8157i 0.219427 + 0.946720i
\(396\) 0 0
\(397\) 34.4987i 1.73144i −0.500530 0.865719i \(-0.666861\pi\)
0.500530 0.865719i \(-0.333139\pi\)
\(398\) 0 0
\(399\) 2.14676 0.107472
\(400\) 0 0
\(401\) −0.541548 −0.0270436 −0.0135218 0.999909i \(-0.504304\pi\)
−0.0135218 + 0.999909i \(0.504304\pi\)
\(402\) 0 0
\(403\) 32.2165i 1.60482i
\(404\) 0 0
\(405\) −0.504884 2.17832i −0.0250879 0.108242i
\(406\) 0 0
\(407\) 8.67775i 0.430140i
\(408\) 0 0
\(409\) −5.24012 −0.259107 −0.129554 0.991572i \(-0.541354\pi\)
−0.129554 + 0.991572i \(0.541354\pi\)
\(410\) 0 0
\(411\) 7.64778 0.377237
\(412\) 0 0
\(413\) 45.5741i 2.24256i
\(414\) 0 0
\(415\) −8.64381 + 2.00343i −0.424308 + 0.0983445i
\(416\) 0 0
\(417\) 3.12792i 0.153175i
\(418\) 0 0
\(419\) 23.5486 1.15042 0.575212 0.818004i \(-0.304919\pi\)
0.575212 + 0.818004i \(0.304919\pi\)
\(420\) 0 0
\(421\) 14.6193 0.712503 0.356252 0.934390i \(-0.384055\pi\)
0.356252 + 0.934390i \(0.384055\pi\)
\(422\) 0 0
\(423\) 5.74394i 0.279280i
\(424\) 0 0
\(425\) 1.32844 + 2.71184i 0.0644390 + 0.131544i
\(426\) 0 0
\(427\) 34.7829i 1.68326i
\(428\) 0 0
\(429\) 22.3687 1.07997
\(430\) 0 0
\(431\) 13.4405 0.647406 0.323703 0.946159i \(-0.395072\pi\)
0.323703 + 0.946159i \(0.395072\pi\)
\(432\) 0 0
\(433\) 1.12100i 0.0538718i 0.999637 + 0.0269359i \(0.00857500\pi\)
−0.999637 + 0.0269359i \(0.991425\pi\)
\(434\) 0 0
\(435\) 12.8488 2.97804i 0.616052 0.142786i
\(436\) 0 0
\(437\) 3.98700i 0.190724i
\(438\) 0 0
\(439\) −16.7882 −0.801258 −0.400629 0.916240i \(-0.631208\pi\)
−0.400629 + 0.916240i \(0.631208\pi\)
\(440\) 0 0
\(441\) 8.35128 0.397680
\(442\) 0 0
\(443\) 14.6154i 0.694399i 0.937791 + 0.347200i \(0.112867\pi\)
−0.937791 + 0.347200i \(0.887133\pi\)
\(444\) 0 0
\(445\) 4.31732 + 18.6271i 0.204661 + 0.883010i
\(446\) 0 0
\(447\) 13.5824i 0.642426i
\(448\) 0 0
\(449\) 19.7499 0.932055 0.466027 0.884770i \(-0.345685\pi\)
0.466027 + 0.884770i \(0.345685\pi\)
\(450\) 0 0
\(451\) −37.7859 −1.77927
\(452\) 0 0
\(453\) 14.4695i 0.679837i
\(454\) 0 0
\(455\) −12.7815 55.1459i −0.599206 2.58528i
\(456\) 0 0
\(457\) 32.6243i 1.52610i 0.646338 + 0.763051i \(0.276299\pi\)
−0.646338 + 0.763051i \(0.723701\pi\)
\(458\) 0 0
\(459\) 0.603948 0.0281899
\(460\) 0 0
\(461\) −0.0149658 −0.000697028 −0.000348514 1.00000i \(-0.500111\pi\)
−0.000348514 1.00000i \(0.500111\pi\)
\(462\) 0 0
\(463\) 41.8885i 1.94672i 0.229276 + 0.973361i \(0.426364\pi\)
−0.229276 + 0.973361i \(0.573636\pi\)
\(464\) 0 0
\(465\) 10.8613 2.51740i 0.503682 0.116742i
\(466\) 0 0
\(467\) 1.82257i 0.0843383i −0.999110 0.0421692i \(-0.986573\pi\)
0.999110 0.0421692i \(-0.0134268\pi\)
\(468\) 0 0
\(469\) −3.91807 −0.180920
\(470\) 0 0
\(471\) −12.0664 −0.555993
\(472\) 0 0
\(473\) 11.7236i 0.539050i
\(474\) 0 0
\(475\) 2.46023 1.20519i 0.112883 0.0552978i
\(476\) 0 0
\(477\) 2.06027i 0.0943332i
\(478\) 0 0
\(479\) 33.0426 1.50975 0.754877 0.655866i \(-0.227696\pi\)
0.754877 + 0.655866i \(0.227696\pi\)
\(480\) 0 0
\(481\) −16.1958 −0.738466
\(482\) 0 0
\(483\) 28.5107i 1.29728i
\(484\) 0 0
\(485\) −13.3009 + 3.08283i −0.603962 + 0.139984i
\(486\) 0 0
\(487\) 18.4966i 0.838161i 0.907949 + 0.419081i \(0.137648\pi\)
−0.907949 + 0.419081i \(0.862352\pi\)
\(488\) 0 0
\(489\) 3.01144 0.136182
\(490\) 0 0
\(491\) 22.9057 1.03372 0.516861 0.856069i \(-0.327100\pi\)
0.516861 + 0.856069i \(0.327100\pi\)
\(492\) 0 0
\(493\) 3.56238i 0.160441i
\(494\) 0 0
\(495\) 1.74789 + 7.54127i 0.0785617 + 0.338955i
\(496\) 0 0
\(497\) 15.0243i 0.673933i
\(498\) 0 0
\(499\) 6.99474 0.313127 0.156564 0.987668i \(-0.449958\pi\)
0.156564 + 0.987668i \(0.449958\pi\)
\(500\) 0 0
\(501\) 6.13904 0.274272
\(502\) 0 0
\(503\) 19.7114i 0.878887i 0.898270 + 0.439443i \(0.144824\pi\)
−0.898270 + 0.439443i \(0.855176\pi\)
\(504\) 0 0
\(505\) −2.93305 12.6547i −0.130519 0.563125i
\(506\) 0 0
\(507\) 28.7481i 1.27675i
\(508\) 0 0
\(509\) −10.6555 −0.472298 −0.236149 0.971717i \(-0.575885\pi\)
−0.236149 + 0.971717i \(0.575885\pi\)
\(510\) 0 0
\(511\) 61.3644 2.71460
\(512\) 0 0
\(513\) 0.547912i 0.0241909i
\(514\) 0 0
\(515\) 19.3779 4.49133i 0.853890 0.197911i
\(516\) 0 0
\(517\) 19.8853i 0.874554i
\(518\) 0 0
\(519\) 0.831968 0.0365193
\(520\) 0 0
\(521\) 30.2288 1.32435 0.662173 0.749351i \(-0.269634\pi\)
0.662173 + 0.749351i \(0.269634\pi\)
\(522\) 0 0
\(523\) 22.0987i 0.966307i −0.875536 0.483154i \(-0.839491\pi\)
0.875536 0.483154i \(-0.160509\pi\)
\(524\) 0 0
\(525\) 17.5929 8.61819i 0.767816 0.376129i
\(526\) 0 0
\(527\) 3.01134i 0.131176i
\(528\) 0 0
\(529\) −29.9505 −1.30219
\(530\) 0 0
\(531\) 11.6318 0.504776
\(532\) 0 0
\(533\) 70.5223i 3.05466i
\(534\) 0 0
\(535\) 33.2364 7.70341i 1.43693 0.333047i
\(536\) 0 0
\(537\) 13.4026i 0.578363i
\(538\) 0 0
\(539\) −28.9118 −1.24532
\(540\) 0 0
\(541\) 32.7919 1.40983 0.704917 0.709290i \(-0.250984\pi\)
0.704917 + 0.709290i \(0.250984\pi\)
\(542\) 0 0
\(543\) 2.84980i 0.122297i
\(544\) 0 0
\(545\) 6.38398 + 27.5437i 0.273460 + 1.17984i
\(546\) 0 0
\(547\) 3.72673i 0.159344i 0.996821 + 0.0796718i \(0.0253872\pi\)
−0.996821 + 0.0796718i \(0.974613\pi\)
\(548\) 0 0
\(549\) 8.87755 0.378885
\(550\) 0 0
\(551\) 3.23185 0.137681
\(552\) 0 0
\(553\) 33.8431i 1.43916i
\(554\) 0 0
\(555\) −1.26554 5.46018i −0.0537192 0.231772i
\(556\) 0 0
\(557\) 36.1249i 1.53066i 0.643637 + 0.765331i \(0.277425\pi\)
−0.643637 + 0.765331i \(0.722575\pi\)
\(558\) 0 0
\(559\) 21.8804 0.925444
\(560\) 0 0
\(561\) −2.09084 −0.0882755
\(562\) 0 0
\(563\) 17.1739i 0.723795i 0.932218 + 0.361897i \(0.117871\pi\)
−0.932218 + 0.361897i \(0.882129\pi\)
\(564\) 0 0
\(565\) −22.4139 + 5.19501i −0.942959 + 0.218556i
\(566\) 0 0
\(567\) 3.91807i 0.164544i
\(568\) 0 0
\(569\) −22.6756 −0.950611 −0.475306 0.879821i \(-0.657662\pi\)
−0.475306 + 0.879821i \(0.657662\pi\)
\(570\) 0 0
\(571\) −40.6790 −1.70236 −0.851181 0.524871i \(-0.824113\pi\)
−0.851181 + 0.524871i \(0.824113\pi\)
\(572\) 0 0
\(573\) 16.8329i 0.703203i
\(574\) 0 0
\(575\) −16.0058 32.6738i −0.667490 1.36259i
\(576\) 0 0
\(577\) 3.02853i 0.126079i −0.998011 0.0630397i \(-0.979921\pi\)
0.998011 0.0630397i \(-0.0200795\pi\)
\(578\) 0 0
\(579\) −25.5455 −1.06164
\(580\) 0 0
\(581\) −15.5473 −0.645011
\(582\) 0 0
\(583\) 7.13256i 0.295401i
\(584\) 0 0
\(585\) −14.0747 + 3.26219i −0.581919 + 0.134875i
\(586\) 0 0
\(587\) 10.9045i 0.450077i 0.974350 + 0.225038i \(0.0722508\pi\)
−0.974350 + 0.225038i \(0.927749\pi\)
\(588\) 0 0
\(589\) 2.73194 0.112568
\(590\) 0 0
\(591\) 12.3050 0.506160
\(592\) 0 0
\(593\) 32.8092i 1.34731i 0.739045 + 0.673656i \(0.235277\pi\)
−0.739045 + 0.673656i \(0.764723\pi\)
\(594\) 0 0
\(595\) 1.19471 + 5.15459i 0.0489784 + 0.211318i
\(596\) 0 0
\(597\) 8.79978i 0.360151i
\(598\) 0 0
\(599\) −6.48832 −0.265105 −0.132553 0.991176i \(-0.542317\pi\)
−0.132553 + 0.991176i \(0.542317\pi\)
\(600\) 0 0
\(601\) −34.7975 −1.41942 −0.709709 0.704495i \(-0.751174\pi\)
−0.709709 + 0.704495i \(0.751174\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −0.497392 2.14600i −0.0202219 0.0872474i
\(606\) 0 0
\(607\) 39.6684i 1.61009i 0.593214 + 0.805045i \(0.297859\pi\)
−0.593214 + 0.805045i \(0.702141\pi\)
\(608\) 0 0
\(609\) 23.1107 0.936491
\(610\) 0 0
\(611\) 37.1132 1.50144
\(612\) 0 0
\(613\) 39.2040i 1.58343i −0.610888 0.791717i \(-0.709187\pi\)
0.610888 0.791717i \(-0.290813\pi\)
\(614\) 0 0
\(615\) 23.7755 5.51061i 0.958723 0.222209i
\(616\) 0 0
\(617\) 7.92069i 0.318875i −0.987208 0.159438i \(-0.949032\pi\)
0.987208 0.159438i \(-0.0509681\pi\)
\(618\) 0 0
\(619\) −19.6071 −0.788075 −0.394038 0.919094i \(-0.628922\pi\)
−0.394038 + 0.919094i \(0.628922\pi\)
\(620\) 0 0
\(621\) −7.27671 −0.292004
\(622\) 0 0
\(623\) 33.5039i 1.34231i
\(624\) 0 0
\(625\) 15.3235 19.7532i 0.612941 0.790129i
\(626\) 0 0
\(627\) 1.89685i 0.0757529i
\(628\) 0 0
\(629\) 1.51386 0.0603614
\(630\) 0 0
\(631\) 34.0601 1.35591 0.677956 0.735103i \(-0.262866\pi\)
0.677956 + 0.735103i \(0.262866\pi\)
\(632\) 0 0
\(633\) 11.6312i 0.462300i
\(634\) 0 0
\(635\) −15.0957 + 3.49883i −0.599055 + 0.138847i
\(636\) 0 0
\(637\) 53.9599i 2.13797i
\(638\) 0 0
\(639\) −3.83462 −0.151695
\(640\) 0 0
\(641\) −12.5681 −0.496410 −0.248205 0.968708i \(-0.579841\pi\)
−0.248205 + 0.968708i \(0.579841\pi\)
\(642\) 0 0
\(643\) 32.1584i 1.26821i −0.773249 0.634103i \(-0.781370\pi\)
0.773249 0.634103i \(-0.218630\pi\)
\(644\) 0 0
\(645\) 1.70974 + 7.37666i 0.0673208 + 0.290456i
\(646\) 0 0
\(647\) 40.2256i 1.58143i 0.612183 + 0.790716i \(0.290291\pi\)
−0.612183 + 0.790716i \(0.709709\pi\)
\(648\) 0 0
\(649\) −40.2687 −1.58069
\(650\) 0 0
\(651\) 19.5359 0.765671
\(652\) 0 0
\(653\) 5.59191i 0.218828i 0.993996 + 0.109414i \(0.0348975\pi\)
−0.993996 + 0.109414i \(0.965103\pi\)
\(654\) 0 0
\(655\) −5.70273 24.6045i −0.222824 0.961376i
\(656\) 0 0
\(657\) 15.6619i 0.611029i
\(658\) 0 0
\(659\) −8.77383 −0.341780 −0.170890 0.985290i \(-0.554664\pi\)
−0.170890 + 0.985290i \(0.554664\pi\)
\(660\) 0 0
\(661\) −10.1677 −0.395476 −0.197738 0.980255i \(-0.563360\pi\)
−0.197738 + 0.980255i \(0.563360\pi\)
\(662\) 0 0
\(663\) 3.90228i 0.151552i
\(664\) 0 0
\(665\) 4.67633 1.08386i 0.181340 0.0420304i
\(666\) 0 0
\(667\) 42.9215i 1.66193i
\(668\) 0 0
\(669\) −18.7044 −0.723153
\(670\) 0 0
\(671\) −30.7337 −1.18646
\(672\) 0 0
\(673\) 40.4943i 1.56094i −0.625193 0.780470i \(-0.714980\pi\)
0.625193 0.780470i \(-0.285020\pi\)
\(674\) 0 0
\(675\) −2.19960 4.49019i −0.0846626 0.172827i
\(676\) 0 0
\(677\) 24.3471i 0.935736i −0.883798 0.467868i \(-0.845022\pi\)
0.883798 0.467868i \(-0.154978\pi\)
\(678\) 0 0
\(679\) −23.9238 −0.918112
\(680\) 0 0
\(681\) −10.1922 −0.390568
\(682\) 0 0
\(683\) 33.2757i 1.27326i −0.771170 0.636629i \(-0.780328\pi\)
0.771170 0.636629i \(-0.219672\pi\)
\(684\) 0 0
\(685\) 16.6593 3.86124i 0.636521 0.147530i
\(686\) 0 0
\(687\) 0.810691i 0.0309298i
\(688\) 0 0
\(689\) −13.3120 −0.507145
\(690\) 0 0
\(691\) −44.3331 −1.68651 −0.843254 0.537515i \(-0.819363\pi\)
−0.843254 + 0.537515i \(0.819363\pi\)
\(692\) 0 0
\(693\) 13.5642i 0.515261i
\(694\) 0 0
\(695\) −1.57923 6.81361i −0.0599037 0.258455i
\(696\) 0 0
\(697\) 6.59186i 0.249684i
\(698\) 0 0
\(699\) −25.4579 −0.962907
\(700\) 0 0
\(701\) −5.22873 −0.197486 −0.0987432 0.995113i \(-0.531482\pi\)
−0.0987432 + 0.995113i \(0.531482\pi\)
\(702\) 0 0
\(703\) 1.37340i 0.0517986i
\(704\) 0 0
\(705\) 2.90002 + 12.5122i 0.109221 + 0.471235i
\(706\) 0 0
\(707\) 22.7615i 0.856034i
\(708\) 0 0
\(709\) −15.0683 −0.565904 −0.282952 0.959134i \(-0.591314\pi\)
−0.282952 + 0.959134i \(0.591314\pi\)
\(710\) 0 0
\(711\) 8.63769 0.323939
\(712\) 0 0
\(713\) 36.2823i 1.35878i
\(714\) 0 0
\(715\) 48.7262 11.2936i 1.82226 0.422356i
\(716\) 0 0
\(717\) 8.47427i 0.316477i
\(718\) 0 0
\(719\) −32.7462 −1.22123 −0.610613 0.791929i \(-0.709077\pi\)
−0.610613 + 0.791929i \(0.709077\pi\)
\(720\) 0 0
\(721\) 34.8542 1.29804
\(722\) 0 0
\(723\) 7.25751i 0.269910i
\(724\) 0 0
\(725\) 26.4853 12.9743i 0.983638 0.481853i
\(726\) 0 0
\(727\) 27.0445i 1.00302i 0.865151 + 0.501512i \(0.167223\pi\)
−0.865151 + 0.501512i \(0.832777\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −2.04521 −0.0756447
\(732\) 0 0
\(733\) 48.5035i 1.79152i −0.444540 0.895759i \(-0.646633\pi\)
0.444540 0.895759i \(-0.353367\pi\)
\(734\) 0 0
\(735\) 18.1918 4.21642i 0.671014 0.155525i
\(736\) 0 0
\(737\) 3.46196i 0.127523i
\(738\) 0 0
\(739\) 22.1169 0.813585 0.406793 0.913521i \(-0.366647\pi\)
0.406793 + 0.913521i \(0.366647\pi\)
\(740\) 0 0
\(741\) −3.54021 −0.130053
\(742\) 0 0
\(743\) 35.8252i 1.31430i 0.753760 + 0.657149i \(0.228238\pi\)
−0.753760 + 0.657149i \(0.771762\pi\)
\(744\) 0 0
\(745\) −6.85754 29.5869i −0.251241 1.08398i
\(746\) 0 0
\(747\) 3.96810i 0.145185i
\(748\) 0 0
\(749\) 59.7811 2.18435
\(750\) 0 0
\(751\) −44.8290 −1.63583 −0.817916 0.575337i \(-0.804871\pi\)
−0.817916 + 0.575337i \(0.804871\pi\)
\(752\) 0 0
\(753\) 8.98355i 0.327379i
\(754\) 0 0
\(755\) 7.30542 + 31.5193i 0.265871 + 1.14710i
\(756\) 0 0
\(757\) 9.34434i 0.339626i −0.985476 0.169813i \(-0.945684\pi\)
0.985476 0.169813i \(-0.0543163\pi\)
\(758\) 0 0
\(759\) 25.1917 0.914399
\(760\) 0 0
\(761\) −15.3896 −0.557872 −0.278936 0.960310i \(-0.589982\pi\)
−0.278936 + 0.960310i \(0.589982\pi\)
\(762\) 0 0
\(763\) 49.5419i 1.79354i
\(764\) 0 0
\(765\) 1.31559 0.304924i 0.0475654 0.0110245i
\(766\) 0 0
\(767\) 75.1561i 2.71373i
\(768\) 0 0
\(769\) 0.737169 0.0265830 0.0132915 0.999912i \(-0.495769\pi\)
0.0132915 + 0.999912i \(0.495769\pi\)
\(770\) 0 0
\(771\) −8.42681 −0.303484
\(772\) 0 0
\(773\) 23.9712i 0.862183i −0.902308 0.431092i \(-0.858129\pi\)
0.902308 0.431092i \(-0.141871\pi\)
\(774\) 0 0
\(775\) 22.3885 10.9674i 0.804218 0.393961i
\(776\) 0 0
\(777\) 9.82103i 0.352328i
\(778\) 0 0
\(779\) 5.98025 0.214265
\(780\) 0 0
\(781\) 13.2753 0.475028
\(782\) 0 0
\(783\) 5.89848i 0.210794i
\(784\) 0 0
\(785\) −26.2846 + 6.09215i −0.938139 + 0.217438i
\(786\) 0 0
\(787\) 45.7716i 1.63158i 0.578348 + 0.815790i \(0.303698\pi\)
−0.578348 + 0.815790i \(0.696302\pi\)
\(788\) 0 0
\(789\) −10.4437 −0.371806
\(790\) 0 0
\(791\) −40.3150 −1.43344
\(792\) 0