Properties

Label 1148.2.k.b.337.5
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.5
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.38781 - 1.38781i) q^{3} +2.11167i q^{5} +(0.707107 + 0.707107i) q^{7} +0.852014i q^{9} +O(q^{10})\) \(q+(-1.38781 - 1.38781i) q^{3} +2.11167i q^{5} +(0.707107 + 0.707107i) q^{7} +0.852014i q^{9} +(-0.520395 - 0.520395i) q^{11} +(0.612447 + 0.612447i) q^{13} +(2.93059 - 2.93059i) q^{15} +(1.16252 - 1.16252i) q^{17} +(-2.68768 + 2.68768i) q^{19} -1.96265i q^{21} -3.65691 q^{23} +0.540846 q^{25} +(-2.98099 + 2.98099i) q^{27} +(3.93269 + 3.93269i) q^{29} -4.96601 q^{31} +1.44442i q^{33} +(-1.49318 + 1.49318i) q^{35} -1.57189 q^{37} -1.69992i q^{39} +(1.38487 + 6.25157i) q^{41} +8.44151i q^{43} -1.79917 q^{45} +(-1.57218 + 1.57218i) q^{47} +1.00000i q^{49} -3.22672 q^{51} +(2.25691 + 2.25691i) q^{53} +(1.09890 - 1.09890i) q^{55} +7.45997 q^{57} +6.36540 q^{59} +8.42809i q^{61} +(-0.602465 + 0.602465i) q^{63} +(-1.29329 + 1.29329i) q^{65} +(-0.439215 + 0.439215i) q^{67} +(5.07508 + 5.07508i) q^{69} +(-1.13798 - 1.13798i) q^{71} +0.278184i q^{73} +(-0.750589 - 0.750589i) q^{75} -0.735950i q^{77} +(-3.94424 - 3.94424i) q^{79} +10.8301 q^{81} +8.17699 q^{83} +(2.45487 + 2.45487i) q^{85} -10.9156i q^{87} +(11.2391 + 11.2391i) q^{89} +0.866131i q^{91} +(6.89187 + 6.89187i) q^{93} +(-5.67550 - 5.67550i) q^{95} +(-9.32999 + 9.32999i) q^{97} +(0.443384 - 0.443384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −1.38781 1.38781i −0.801250 0.801250i 0.182041 0.983291i \(-0.441730\pi\)
−0.983291 + 0.182041i \(0.941730\pi\)
\(4\) 0 0
\(5\) 2.11167i 0.944368i 0.881500 + 0.472184i \(0.156534\pi\)
−0.881500 + 0.472184i \(0.843466\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 0.852014i 0.284005i
\(10\) 0 0
\(11\) −0.520395 0.520395i −0.156905 0.156905i 0.624289 0.781194i \(-0.285389\pi\)
−0.781194 + 0.624289i \(0.785389\pi\)
\(12\) 0 0
\(13\) 0.612447 + 0.612447i 0.169862 + 0.169862i 0.786919 0.617057i \(-0.211675\pi\)
−0.617057 + 0.786919i \(0.711675\pi\)
\(14\) 0 0
\(15\) 2.93059 2.93059i 0.756675 0.756675i
\(16\) 0 0
\(17\) 1.16252 1.16252i 0.281954 0.281954i −0.551934 0.833888i \(-0.686110\pi\)
0.833888 + 0.551934i \(0.186110\pi\)
\(18\) 0 0
\(19\) −2.68768 + 2.68768i −0.616597 + 0.616597i −0.944657 0.328060i \(-0.893605\pi\)
0.328060 + 0.944657i \(0.393605\pi\)
\(20\) 0 0
\(21\) 1.96265i 0.428286i
\(22\) 0 0
\(23\) −3.65691 −0.762518 −0.381259 0.924468i \(-0.624509\pi\)
−0.381259 + 0.924468i \(0.624509\pi\)
\(24\) 0 0
\(25\) 0.540846 0.108169
\(26\) 0 0
\(27\) −2.98099 + 2.98099i −0.573692 + 0.573692i
\(28\) 0 0
\(29\) 3.93269 + 3.93269i 0.730282 + 0.730282i 0.970676 0.240393i \(-0.0772764\pi\)
−0.240393 + 0.970676i \(0.577276\pi\)
\(30\) 0 0
\(31\) −4.96601 −0.891922 −0.445961 0.895052i \(-0.647138\pi\)
−0.445961 + 0.895052i \(0.647138\pi\)
\(32\) 0 0
\(33\) 1.44442i 0.251441i
\(34\) 0 0
\(35\) −1.49318 + 1.49318i −0.252393 + 0.252393i
\(36\) 0 0
\(37\) −1.57189 −0.258417 −0.129208 0.991617i \(-0.541244\pi\)
−0.129208 + 0.991617i \(0.541244\pi\)
\(38\) 0 0
\(39\) 1.69992i 0.272204i
\(40\) 0 0
\(41\) 1.38487 + 6.25157i 0.216281 + 0.976331i
\(42\) 0 0
\(43\) 8.44151i 1.28732i 0.765313 + 0.643659i \(0.222584\pi\)
−0.765313 + 0.643659i \(0.777416\pi\)
\(44\) 0 0
\(45\) −1.79917 −0.268205
\(46\) 0 0
\(47\) −1.57218 + 1.57218i −0.229326 + 0.229326i −0.812411 0.583085i \(-0.801845\pi\)
0.583085 + 0.812411i \(0.301845\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −3.22672 −0.451831
\(52\) 0 0
\(53\) 2.25691 + 2.25691i 0.310011 + 0.310011i 0.844914 0.534903i \(-0.179652\pi\)
−0.534903 + 0.844914i \(0.679652\pi\)
\(54\) 0 0
\(55\) 1.09890 1.09890i 0.148176 0.148176i
\(56\) 0 0
\(57\) 7.45997 0.988097
\(58\) 0 0
\(59\) 6.36540 0.828704 0.414352 0.910117i \(-0.364008\pi\)
0.414352 + 0.910117i \(0.364008\pi\)
\(60\) 0 0
\(61\) 8.42809i 1.07911i 0.841952 + 0.539553i \(0.181407\pi\)
−0.841952 + 0.539553i \(0.818593\pi\)
\(62\) 0 0
\(63\) −0.602465 + 0.602465i −0.0759034 + 0.0759034i
\(64\) 0 0
\(65\) −1.29329 + 1.29329i −0.160413 + 0.160413i
\(66\) 0 0
\(67\) −0.439215 + 0.439215i −0.0536586 + 0.0536586i −0.733427 0.679768i \(-0.762080\pi\)
0.679768 + 0.733427i \(0.262080\pi\)
\(68\) 0 0
\(69\) 5.07508 + 5.07508i 0.610968 + 0.610968i
\(70\) 0 0
\(71\) −1.13798 1.13798i −0.135054 0.135054i 0.636348 0.771402i \(-0.280444\pi\)
−0.771402 + 0.636348i \(0.780444\pi\)
\(72\) 0 0
\(73\) 0.278184i 0.0325590i 0.999867 + 0.0162795i \(0.00518215\pi\)
−0.999867 + 0.0162795i \(0.994818\pi\)
\(74\) 0 0
\(75\) −0.750589 0.750589i −0.0866706 0.0866706i
\(76\) 0 0
\(77\) 0.735950i 0.0838693i
\(78\) 0 0
\(79\) −3.94424 3.94424i −0.443762 0.443762i 0.449512 0.893274i \(-0.351598\pi\)
−0.893274 + 0.449512i \(0.851598\pi\)
\(80\) 0 0
\(81\) 10.8301 1.20335
\(82\) 0 0
\(83\) 8.17699 0.897541 0.448771 0.893647i \(-0.351862\pi\)
0.448771 + 0.893647i \(0.351862\pi\)
\(84\) 0 0
\(85\) 2.45487 + 2.45487i 0.266268 + 0.266268i
\(86\) 0 0
\(87\) 10.9156i 1.17028i
\(88\) 0 0
\(89\) 11.2391 + 11.2391i 1.19134 + 1.19134i 0.976691 + 0.214652i \(0.0688617\pi\)
0.214652 + 0.976691i \(0.431138\pi\)
\(90\) 0 0
\(91\) 0.866131i 0.0907952i
\(92\) 0 0
\(93\) 6.89187 + 6.89187i 0.714653 + 0.714653i
\(94\) 0 0
\(95\) −5.67550 5.67550i −0.582294 0.582294i
\(96\) 0 0
\(97\) −9.32999 + 9.32999i −0.947317 + 0.947317i −0.998680 0.0513627i \(-0.983644\pi\)
0.0513627 + 0.998680i \(0.483644\pi\)
\(98\) 0 0
\(99\) 0.443384 0.443384i 0.0445618 0.0445618i
\(100\) 0 0
\(101\) −8.06655 + 8.06655i −0.802652 + 0.802652i −0.983509 0.180857i \(-0.942113\pi\)
0.180857 + 0.983509i \(0.442113\pi\)
\(102\) 0 0
\(103\) 8.71515i 0.858729i 0.903131 + 0.429364i \(0.141262\pi\)
−0.903131 + 0.429364i \(0.858738\pi\)
\(104\) 0 0
\(105\) 4.14448 0.404460
\(106\) 0 0
\(107\) 12.4476 1.20336 0.601678 0.798738i \(-0.294499\pi\)
0.601678 + 0.798738i \(0.294499\pi\)
\(108\) 0 0
\(109\) −0.538916 + 0.538916i −0.0516188 + 0.0516188i −0.732445 0.680826i \(-0.761621\pi\)
0.680826 + 0.732445i \(0.261621\pi\)
\(110\) 0 0
\(111\) 2.18148 + 2.18148i 0.207057 + 0.207057i
\(112\) 0 0
\(113\) −3.47377 −0.326785 −0.163393 0.986561i \(-0.552244\pi\)
−0.163393 + 0.986561i \(0.552244\pi\)
\(114\) 0 0
\(115\) 7.72218i 0.720097i
\(116\) 0 0
\(117\) −0.521814 + 0.521814i −0.0482417 + 0.0482417i
\(118\) 0 0
\(119\) 1.64406 0.150711
\(120\) 0 0
\(121\) 10.4584i 0.950762i
\(122\) 0 0
\(123\) 6.75403 10.5979i 0.608991 0.955581i
\(124\) 0 0
\(125\) 11.7004i 1.04652i
\(126\) 0 0
\(127\) −0.723418 −0.0641930 −0.0320965 0.999485i \(-0.510218\pi\)
−0.0320965 + 0.999485i \(0.510218\pi\)
\(128\) 0 0
\(129\) 11.7152 11.7152i 1.03146 1.03146i
\(130\) 0 0
\(131\) 13.8945i 1.21397i 0.794715 + 0.606983i \(0.207620\pi\)
−0.794715 + 0.606983i \(0.792380\pi\)
\(132\) 0 0
\(133\) −3.80096 −0.329585
\(134\) 0 0
\(135\) −6.29487 6.29487i −0.541776 0.541776i
\(136\) 0 0
\(137\) −1.45697 + 1.45697i −0.124477 + 0.124477i −0.766601 0.642124i \(-0.778053\pi\)
0.642124 + 0.766601i \(0.278053\pi\)
\(138\) 0 0
\(139\) −0.798436 −0.0677225 −0.0338612 0.999427i \(-0.510780\pi\)
−0.0338612 + 0.999427i \(0.510780\pi\)
\(140\) 0 0
\(141\) 4.36375 0.367494
\(142\) 0 0
\(143\) 0.637429i 0.0533045i
\(144\) 0 0
\(145\) −8.30455 + 8.30455i −0.689655 + 0.689655i
\(146\) 0 0
\(147\) 1.38781 1.38781i 0.114464 0.114464i
\(148\) 0 0
\(149\) 2.04524 2.04524i 0.167553 0.167553i −0.618350 0.785903i \(-0.712199\pi\)
0.785903 + 0.618350i \(0.212199\pi\)
\(150\) 0 0
\(151\) −7.07106 7.07106i −0.575435 0.575435i 0.358207 0.933642i \(-0.383388\pi\)
−0.933642 + 0.358207i \(0.883388\pi\)
\(152\) 0 0
\(153\) 0.990487 + 0.990487i 0.0800762 + 0.0800762i
\(154\) 0 0
\(155\) 10.4866i 0.842303i
\(156\) 0 0
\(157\) −11.5420 11.5420i −0.921148 0.921148i 0.0759626 0.997111i \(-0.475797\pi\)
−0.997111 + 0.0759626i \(0.975797\pi\)
\(158\) 0 0
\(159\) 6.26432i 0.496793i
\(160\) 0 0
\(161\) −2.58582 2.58582i −0.203791 0.203791i
\(162\) 0 0
\(163\) −5.12099 −0.401107 −0.200553 0.979683i \(-0.564274\pi\)
−0.200553 + 0.979683i \(0.564274\pi\)
\(164\) 0 0
\(165\) −3.05013 −0.237452
\(166\) 0 0
\(167\) −14.9884 14.9884i −1.15984 1.15984i −0.984511 0.175325i \(-0.943902\pi\)
−0.175325 0.984511i \(-0.556098\pi\)
\(168\) 0 0
\(169\) 12.2498i 0.942294i
\(170\) 0 0
\(171\) −2.28994 2.28994i −0.175116 0.175116i
\(172\) 0 0
\(173\) 7.58618i 0.576767i 0.957515 + 0.288383i \(0.0931177\pi\)
−0.957515 + 0.288383i \(0.906882\pi\)
\(174\) 0 0
\(175\) 0.382436 + 0.382436i 0.0289094 + 0.0289094i
\(176\) 0 0
\(177\) −8.83394 8.83394i −0.664000 0.664000i
\(178\) 0 0
\(179\) 1.75522 1.75522i 0.131191 0.131191i −0.638462 0.769653i \(-0.720429\pi\)
0.769653 + 0.638462i \(0.220429\pi\)
\(180\) 0 0
\(181\) 0.764776 0.764776i 0.0568454 0.0568454i −0.678113 0.734958i \(-0.737202\pi\)
0.734958 + 0.678113i \(0.237202\pi\)
\(182\) 0 0
\(183\) 11.6966 11.6966i 0.864634 0.864634i
\(184\) 0 0
\(185\) 3.31931i 0.244041i
\(186\) 0 0
\(187\) −1.20995 −0.0884800
\(188\) 0 0
\(189\) −4.21576 −0.306651
\(190\) 0 0
\(191\) −6.87828 + 6.87828i −0.497695 + 0.497695i −0.910720 0.413025i \(-0.864472\pi\)
0.413025 + 0.910720i \(0.364472\pi\)
\(192\) 0 0
\(193\) 0.863929 + 0.863929i 0.0621870 + 0.0621870i 0.737516 0.675329i \(-0.235999\pi\)
−0.675329 + 0.737516i \(0.735999\pi\)
\(194\) 0 0
\(195\) 3.58966 0.257061
\(196\) 0 0
\(197\) 8.98320i 0.640026i −0.947413 0.320013i \(-0.896313\pi\)
0.947413 0.320013i \(-0.103687\pi\)
\(198\) 0 0
\(199\) −1.06602 + 1.06602i −0.0755679 + 0.0755679i −0.743881 0.668313i \(-0.767017\pi\)
0.668313 + 0.743881i \(0.267017\pi\)
\(200\) 0 0
\(201\) 1.21909 0.0859880
\(202\) 0 0
\(203\) 5.56166i 0.390352i
\(204\) 0 0
\(205\) −13.2013 + 2.92440i −0.922016 + 0.204249i
\(206\) 0 0
\(207\) 3.11574i 0.216559i
\(208\) 0 0
\(209\) 2.79732 0.193494
\(210\) 0 0
\(211\) 9.61928 9.61928i 0.662218 0.662218i −0.293684 0.955903i \(-0.594881\pi\)
0.955903 + 0.293684i \(0.0948814\pi\)
\(212\) 0 0
\(213\) 3.15860i 0.216424i
\(214\) 0 0
\(215\) −17.8257 −1.21570
\(216\) 0 0
\(217\) −3.51150 3.51150i −0.238376 0.238376i
\(218\) 0 0
\(219\) 0.386065 0.386065i 0.0260879 0.0260879i
\(220\) 0 0
\(221\) 1.42397 0.0957866
\(222\) 0 0
\(223\) −27.4521 −1.83833 −0.919165 0.393873i \(-0.871135\pi\)
−0.919165 + 0.393873i \(0.871135\pi\)
\(224\) 0 0
\(225\) 0.460808i 0.0307205i
\(226\) 0 0
\(227\) 4.14726 4.14726i 0.275263 0.275263i −0.555952 0.831215i \(-0.687646\pi\)
0.831215 + 0.555952i \(0.187646\pi\)
\(228\) 0 0
\(229\) −2.45124 + 2.45124i −0.161983 + 0.161983i −0.783444 0.621462i \(-0.786539\pi\)
0.621462 + 0.783444i \(0.286539\pi\)
\(230\) 0 0
\(231\) −1.02136 + 1.02136i −0.0672003 + 0.0672003i
\(232\) 0 0
\(233\) −4.11812 4.11812i −0.269787 0.269787i 0.559227 0.829014i \(-0.311098\pi\)
−0.829014 + 0.559227i \(0.811098\pi\)
\(234\) 0 0
\(235\) −3.31992 3.31992i −0.216568 0.216568i
\(236\) 0 0
\(237\) 10.9477i 0.711129i
\(238\) 0 0
\(239\) −1.41383 1.41383i −0.0914532 0.0914532i 0.659900 0.751353i \(-0.270599\pi\)
−0.751353 + 0.659900i \(0.770599\pi\)
\(240\) 0 0
\(241\) 3.30462i 0.212870i −0.994320 0.106435i \(-0.966056\pi\)
0.994320 0.106435i \(-0.0339435\pi\)
\(242\) 0 0
\(243\) −6.08714 6.08714i −0.390490 0.390490i
\(244\) 0 0
\(245\) −2.11167 −0.134910
\(246\) 0 0
\(247\) −3.29213 −0.209473
\(248\) 0 0
\(249\) −11.3481 11.3481i −0.719155 0.719155i
\(250\) 0 0
\(251\) 2.78594i 0.175847i 0.996127 + 0.0879236i \(0.0280231\pi\)
−0.996127 + 0.0879236i \(0.971977\pi\)
\(252\) 0 0
\(253\) 1.90304 + 1.90304i 0.119643 + 0.119643i
\(254\) 0 0
\(255\) 6.81377i 0.426695i
\(256\) 0 0
\(257\) 1.00595 + 1.00595i 0.0627496 + 0.0627496i 0.737785 0.675036i \(-0.235872\pi\)
−0.675036 + 0.737785i \(0.735872\pi\)
\(258\) 0 0
\(259\) −1.11149 1.11149i −0.0690648 0.0690648i
\(260\) 0 0
\(261\) −3.35071 + 3.35071i −0.207404 + 0.207404i
\(262\) 0 0
\(263\) 15.3098 15.3098i 0.944044 0.944044i −0.0544715 0.998515i \(-0.517347\pi\)
0.998515 + 0.0544715i \(0.0173474\pi\)
\(264\) 0 0
\(265\) −4.76586 + 4.76586i −0.292764 + 0.292764i
\(266\) 0 0
\(267\) 31.1954i 1.90913i
\(268\) 0 0
\(269\) 6.79639 0.414383 0.207192 0.978300i \(-0.433568\pi\)
0.207192 + 0.978300i \(0.433568\pi\)
\(270\) 0 0
\(271\) 8.93799 0.542944 0.271472 0.962446i \(-0.412490\pi\)
0.271472 + 0.962446i \(0.412490\pi\)
\(272\) 0 0
\(273\) 1.20202 1.20202i 0.0727497 0.0727497i
\(274\) 0 0
\(275\) −0.281454 0.281454i −0.0169723 0.0169723i
\(276\) 0 0
\(277\) −16.7403 −1.00583 −0.502914 0.864337i \(-0.667739\pi\)
−0.502914 + 0.864337i \(0.667739\pi\)
\(278\) 0 0
\(279\) 4.23111i 0.253310i
\(280\) 0 0
\(281\) 7.83300 7.83300i 0.467278 0.467278i −0.433754 0.901032i \(-0.642811\pi\)
0.901032 + 0.433754i \(0.142811\pi\)
\(282\) 0 0
\(283\) 7.10090 0.422105 0.211052 0.977475i \(-0.432311\pi\)
0.211052 + 0.977475i \(0.432311\pi\)
\(284\) 0 0
\(285\) 15.7530i 0.933127i
\(286\) 0 0
\(287\) −3.44127 + 5.39978i −0.203132 + 0.318739i
\(288\) 0 0
\(289\) 14.2971i 0.841004i
\(290\) 0 0
\(291\) 25.8965 1.51808
\(292\) 0 0
\(293\) 17.2745 17.2745i 1.00919 1.00919i 0.00922862 0.999957i \(-0.497062\pi\)
0.999957 0.00922862i \(-0.00293760\pi\)
\(294\) 0 0
\(295\) 13.4416i 0.782602i
\(296\) 0 0
\(297\) 3.10259 0.180030
\(298\) 0 0
\(299\) −2.23966 2.23966i −0.129523 0.129523i
\(300\) 0 0
\(301\) −5.96905 + 5.96905i −0.344050 + 0.344050i
\(302\) 0 0
\(303\) 22.3896 1.28625
\(304\) 0 0
\(305\) −17.7974 −1.01907
\(306\) 0 0
\(307\) 6.19217i 0.353406i −0.984264 0.176703i \(-0.943457\pi\)
0.984264 0.176703i \(-0.0565432\pi\)
\(308\) 0 0
\(309\) 12.0949 12.0949i 0.688057 0.688057i
\(310\) 0 0
\(311\) 12.6559 12.6559i 0.717649 0.717649i −0.250474 0.968123i \(-0.580587\pi\)
0.968123 + 0.250474i \(0.0805866\pi\)
\(312\) 0 0
\(313\) 0.840639 0.840639i 0.0475157 0.0475157i −0.682950 0.730465i \(-0.739303\pi\)
0.730465 + 0.682950i \(0.239303\pi\)
\(314\) 0 0
\(315\) −1.27221 1.27221i −0.0716808 0.0716808i
\(316\) 0 0
\(317\) −8.19168 8.19168i −0.460090 0.460090i 0.438595 0.898685i \(-0.355476\pi\)
−0.898685 + 0.438595i \(0.855476\pi\)
\(318\) 0 0
\(319\) 4.09311i 0.229170i
\(320\) 0 0
\(321\) −17.2749 17.2749i −0.964190 0.964190i
\(322\) 0 0
\(323\) 6.24900i 0.347703i
\(324\) 0 0
\(325\) 0.331239 + 0.331239i 0.0183739 + 0.0183739i
\(326\) 0 0
\(327\) 1.49582 0.0827192
\(328\) 0 0
\(329\) −2.22339 −0.122580
\(330\) 0 0
\(331\) 19.0714 + 19.0714i 1.04826 + 1.04826i 0.998775 + 0.0494840i \(0.0157577\pi\)
0.0494840 + 0.998775i \(0.484242\pi\)
\(332\) 0 0
\(333\) 1.33927i 0.0733916i
\(334\) 0 0
\(335\) −0.927477 0.927477i −0.0506735 0.0506735i
\(336\) 0 0
\(337\) 24.1450i 1.31526i −0.753341 0.657630i \(-0.771559\pi\)
0.753341 0.657630i \(-0.228441\pi\)
\(338\) 0 0
\(339\) 4.82093 + 4.82093i 0.261837 + 0.261837i
\(340\) 0 0
\(341\) 2.58429 + 2.58429i 0.139947 + 0.139947i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) −10.7169 + 10.7169i −0.576978 + 0.576978i
\(346\) 0 0
\(347\) 8.46341 8.46341i 0.454340 0.454340i −0.442452 0.896792i \(-0.645891\pi\)
0.896792 + 0.442452i \(0.145891\pi\)
\(348\) 0 0
\(349\) 26.1570i 1.40015i 0.714069 + 0.700075i \(0.246850\pi\)
−0.714069 + 0.700075i \(0.753150\pi\)
\(350\) 0 0
\(351\) −3.65140 −0.194897
\(352\) 0 0
\(353\) 30.1016 1.60215 0.801074 0.598565i \(-0.204262\pi\)
0.801074 + 0.598565i \(0.204262\pi\)
\(354\) 0 0
\(355\) 2.40305 2.40305i 0.127541 0.127541i
\(356\) 0 0
\(357\) −2.28164 2.28164i −0.120757 0.120757i
\(358\) 0 0
\(359\) 6.71114 0.354200 0.177100 0.984193i \(-0.443328\pi\)
0.177100 + 0.984193i \(0.443328\pi\)
\(360\) 0 0
\(361\) 4.55272i 0.239617i
\(362\) 0 0
\(363\) −14.5142 + 14.5142i −0.761798 + 0.761798i
\(364\) 0 0
\(365\) −0.587433 −0.0307476
\(366\) 0 0
\(367\) 18.0624i 0.942847i 0.881907 + 0.471424i \(0.156260\pi\)
−0.881907 + 0.471424i \(0.843740\pi\)
\(368\) 0 0
\(369\) −5.32642 + 1.17993i −0.277283 + 0.0614248i
\(370\) 0 0
\(371\) 3.19176i 0.165708i
\(372\) 0 0
\(373\) 15.3347 0.794000 0.397000 0.917819i \(-0.370051\pi\)
0.397000 + 0.917819i \(0.370051\pi\)
\(374\) 0 0
\(375\) 16.2380 16.2380i 0.838524 0.838524i
\(376\) 0 0
\(377\) 4.81713i 0.248095i
\(378\) 0 0
\(379\) −7.86104 −0.403794 −0.201897 0.979407i \(-0.564711\pi\)
−0.201897 + 0.979407i \(0.564711\pi\)
\(380\) 0 0
\(381\) 1.00396 + 1.00396i 0.0514346 + 0.0514346i
\(382\) 0 0
\(383\) −7.82055 + 7.82055i −0.399612 + 0.399612i −0.878096 0.478484i \(-0.841186\pi\)
0.478484 + 0.878096i \(0.341186\pi\)
\(384\) 0 0
\(385\) 1.55408 0.0792035
\(386\) 0 0
\(387\) −7.19228 −0.365604
\(388\) 0 0
\(389\) 5.90513i 0.299402i 0.988731 + 0.149701i \(0.0478311\pi\)
−0.988731 + 0.149701i \(0.952169\pi\)
\(390\) 0 0
\(391\) −4.25124 + 4.25124i −0.214995 + 0.214995i
\(392\) 0 0
\(393\) 19.2828 19.2828i 0.972691 0.972691i
\(394\) 0 0
\(395\) 8.32894 8.32894i 0.419075 0.419075i
\(396\) 0 0
\(397\) −20.3757 20.3757i −1.02263 1.02263i −0.999738 0.0228914i \(-0.992713\pi\)
−0.0228914 0.999738i \(-0.507287\pi\)
\(398\) 0 0
\(399\) 5.27499 + 5.27499i 0.264080 + 0.264080i
\(400\) 0 0
\(401\) 10.3889i 0.518798i 0.965770 + 0.259399i \(0.0835245\pi\)
−0.965770 + 0.259399i \(0.916476\pi\)
\(402\) 0 0
\(403\) −3.04142 3.04142i −0.151504 0.151504i
\(404\) 0 0
\(405\) 22.8696i 1.13640i
\(406\) 0 0
\(407\) 0.818004 + 0.818004i 0.0405469 + 0.0405469i
\(408\) 0 0
\(409\) 22.8922 1.13195 0.565974 0.824423i \(-0.308500\pi\)
0.565974 + 0.824423i \(0.308500\pi\)
\(410\) 0 0
\(411\) 4.04397 0.199474
\(412\) 0 0
\(413\) 4.50102 + 4.50102i 0.221481 + 0.221481i
\(414\) 0 0
\(415\) 17.2671i 0.847609i
\(416\) 0 0
\(417\) 1.10808 + 1.10808i 0.0542627 + 0.0542627i
\(418\) 0 0
\(419\) 5.91881i 0.289153i 0.989494 + 0.144576i \(0.0461819\pi\)
−0.989494 + 0.144576i \(0.953818\pi\)
\(420\) 0 0
\(421\) −4.46517 4.46517i −0.217619 0.217619i 0.589875 0.807494i \(-0.299177\pi\)
−0.807494 + 0.589875i \(0.799177\pi\)
\(422\) 0 0
\(423\) −1.33952 1.33952i −0.0651295 0.0651295i
\(424\) 0 0
\(425\) 0.628746 0.628746i 0.0304987 0.0304987i
\(426\) 0 0
\(427\) −5.95956 + 5.95956i −0.288403 + 0.288403i
\(428\) 0 0
\(429\) −0.884629 + 0.884629i −0.0427103 + 0.0427103i
\(430\) 0 0
\(431\) 9.00868i 0.433933i 0.976179 + 0.216966i \(0.0696162\pi\)
−0.976179 + 0.216966i \(0.930384\pi\)
\(432\) 0 0
\(433\) −8.47139 −0.407109 −0.203555 0.979064i \(-0.565249\pi\)
−0.203555 + 0.979064i \(0.565249\pi\)
\(434\) 0 0
\(435\) 23.0502 1.10517
\(436\) 0 0
\(437\) 9.82861 9.82861i 0.470166 0.470166i
\(438\) 0 0
\(439\) −2.29786 2.29786i −0.109671 0.109671i 0.650142 0.759813i \(-0.274709\pi\)
−0.759813 + 0.650142i \(0.774709\pi\)
\(440\) 0 0
\(441\) −0.852014 −0.0405721
\(442\) 0 0
\(443\) 1.31899i 0.0626673i −0.999509 0.0313336i \(-0.990025\pi\)
0.999509 0.0313336i \(-0.00997544\pi\)
\(444\) 0 0
\(445\) −23.7333 + 23.7333i −1.12507 + 1.12507i
\(446\) 0 0
\(447\) −5.67680 −0.268504
\(448\) 0 0
\(449\) 20.9279i 0.987649i −0.869561 0.493825i \(-0.835598\pi\)
0.869561 0.493825i \(-0.164402\pi\)
\(450\) 0 0
\(451\) 2.53261 3.97397i 0.119256 0.187127i
\(452\) 0 0
\(453\) 19.6265i 0.922135i
\(454\) 0 0
\(455\) −1.82898 −0.0857441
\(456\) 0 0
\(457\) 13.6067 13.6067i 0.636493 0.636493i −0.313196 0.949689i \(-0.601400\pi\)
0.949689 + 0.313196i \(0.101400\pi\)
\(458\) 0 0
\(459\) 6.93095i 0.323509i
\(460\) 0 0
\(461\) 29.5007 1.37398 0.686992 0.726665i \(-0.258931\pi\)
0.686992 + 0.726665i \(0.258931\pi\)
\(462\) 0 0
\(463\) −20.4091 20.4091i −0.948490 0.948490i 0.0502464 0.998737i \(-0.483999\pi\)
−0.998737 + 0.0502464i \(0.983999\pi\)
\(464\) 0 0
\(465\) −14.5534 + 14.5534i −0.674896 + 0.674896i
\(466\) 0 0
\(467\) 15.6883 0.725969 0.362984 0.931795i \(-0.381758\pi\)
0.362984 + 0.931795i \(0.381758\pi\)
\(468\) 0 0
\(469\) −0.621143 −0.0286817
\(470\) 0 0
\(471\) 32.0360i 1.47614i
\(472\) 0 0
\(473\) 4.39292 4.39292i 0.201987 0.201987i
\(474\) 0 0
\(475\) −1.45362 + 1.45362i −0.0666967 + 0.0666967i
\(476\) 0 0
\(477\) −1.92292 + 1.92292i −0.0880446 + 0.0880446i
\(478\) 0 0
\(479\) −7.85693 7.85693i −0.358992 0.358992i 0.504449 0.863441i \(-0.331696\pi\)
−0.863441 + 0.504449i \(0.831696\pi\)
\(480\) 0 0
\(481\) −0.962699 0.962699i −0.0438953 0.0438953i
\(482\) 0 0
\(483\) 7.17725i 0.326576i
\(484\) 0 0
\(485\) −19.7019 19.7019i −0.894616 0.894616i
\(486\) 0 0
\(487\) 6.60885i 0.299476i −0.988726 0.149738i \(-0.952157\pi\)
0.988726 0.149738i \(-0.0478430\pi\)
\(488\) 0 0
\(489\) 7.10694 + 7.10694i 0.321387 + 0.321387i
\(490\) 0 0
\(491\) −13.0898 −0.590733 −0.295367 0.955384i \(-0.595442\pi\)
−0.295367 + 0.955384i \(0.595442\pi\)
\(492\) 0 0
\(493\) 9.14370 0.411812
\(494\) 0 0
\(495\) 0.936282 + 0.936282i 0.0420827 + 0.0420827i
\(496\) 0 0
\(497\) 1.60935i 0.0721893i
\(498\) 0 0
\(499\) 18.6689 + 18.6689i 0.835734 + 0.835734i 0.988294 0.152560i \(-0.0487518\pi\)
−0.152560 + 0.988294i \(0.548752\pi\)
\(500\) 0 0
\(501\) 41.6019i 1.85864i
\(502\) 0 0
\(503\) −28.7586 28.7586i −1.28228 1.28228i −0.939367 0.342914i \(-0.888586\pi\)
−0.342914 0.939367i \(-0.611414\pi\)
\(504\) 0 0
\(505\) −17.0339 17.0339i −0.757999 0.757999i
\(506\) 0 0
\(507\) −17.0004 + 17.0004i −0.755013 + 0.755013i
\(508\) 0 0
\(509\) 1.29529 1.29529i 0.0574128 0.0574128i −0.677817 0.735230i \(-0.737074\pi\)
0.735230 + 0.677817i \(0.237074\pi\)
\(510\) 0 0
\(511\) −0.196706 + 0.196706i −0.00870175 + 0.00870175i
\(512\) 0 0
\(513\) 16.0239i 0.707473i
\(514\) 0 0
\(515\) −18.4035 −0.810956
\(516\) 0 0
\(517\) 1.63631 0.0719647
\(518\) 0 0
\(519\) 10.5282 10.5282i 0.462135 0.462135i
\(520\) 0 0
\(521\) 10.6591 + 10.6591i 0.466983 + 0.466983i 0.900936 0.433953i \(-0.142882\pi\)
−0.433953 + 0.900936i \(0.642882\pi\)
\(522\) 0 0
\(523\) −20.5879 −0.900245 −0.450123 0.892967i \(-0.648620\pi\)
−0.450123 + 0.892967i \(0.648620\pi\)
\(524\) 0 0
\(525\) 1.06149i 0.0463274i
\(526\) 0 0
\(527\) −5.77311 + 5.77311i −0.251481 + 0.251481i
\(528\) 0 0
\(529\) −9.62703 −0.418567
\(530\) 0 0
\(531\) 5.42341i 0.235356i
\(532\) 0 0
\(533\) −2.98059 + 4.67692i −0.129104 + 0.202580i
\(534\) 0 0
\(535\) 26.2853i 1.13641i
\(536\) 0 0
\(537\) −4.87180 −0.210234
\(538\) 0 0
\(539\) 0.520395 0.520395i 0.0224150 0.0224150i
\(540\) 0 0
\(541\) 22.2711i 0.957508i 0.877949 + 0.478754i \(0.158911\pi\)
−0.877949 + 0.478754i \(0.841089\pi\)
\(542\) 0 0
\(543\) −2.12272 −0.0910948
\(544\) 0 0
\(545\) −1.13801 1.13801i −0.0487472 0.0487472i
\(546\) 0 0
\(547\) −28.8837 + 28.8837i −1.23498 + 1.23498i −0.272951 + 0.962028i \(0.588000\pi\)
−0.962028 + 0.272951i \(0.912000\pi\)
\(548\) 0 0
\(549\) −7.18085 −0.306471
\(550\) 0 0
\(551\) −21.1397 −0.900580
\(552\) 0 0
\(553\) 5.57800i 0.237201i
\(554\) 0 0
\(555\) −4.60656 + 4.60656i −0.195538 + 0.195538i
\(556\) 0 0
\(557\) 5.69310 5.69310i 0.241224 0.241224i −0.576132 0.817357i \(-0.695439\pi\)
0.817357 + 0.576132i \(0.195439\pi\)
\(558\) 0 0
\(559\) −5.16998 + 5.16998i −0.218667 + 0.218667i
\(560\) 0 0
\(561\) 1.67917 + 1.67917i 0.0708946 + 0.0708946i
\(562\) 0 0
\(563\) 17.2253 + 17.2253i 0.725960 + 0.725960i 0.969812 0.243852i \(-0.0784111\pi\)
−0.243852 + 0.969812i \(0.578411\pi\)
\(564\) 0 0
\(565\) 7.33547i 0.308605i
\(566\) 0 0
\(567\) 7.65805 + 7.65805i 0.321608 + 0.321608i
\(568\) 0 0
\(569\) 42.3445i 1.77517i 0.460640 + 0.887587i \(0.347620\pi\)
−0.460640 + 0.887587i \(0.652380\pi\)
\(570\) 0 0
\(571\) −5.34409 5.34409i −0.223643 0.223643i 0.586388 0.810031i \(-0.300550\pi\)
−0.810031 + 0.586388i \(0.800550\pi\)
\(572\) 0 0
\(573\) 19.0914 0.797557
\(574\) 0 0
\(575\) −1.97782 −0.0824809
\(576\) 0 0
\(577\) −32.9190 32.9190i −1.37044 1.37044i −0.859790 0.510648i \(-0.829406\pi\)
−0.510648 0.859790i \(-0.670594\pi\)
\(578\) 0 0
\(579\) 2.39793i 0.0996547i
\(580\) 0 0
\(581\) 5.78201 + 5.78201i 0.239878 + 0.239878i
\(582\) 0 0
\(583\) 2.34898i 0.0972846i
\(584\) 0 0
\(585\) −1.10190 1.10190i −0.0455579 0.0455579i
\(586\) 0 0
\(587\) −20.6815 20.6815i −0.853616 0.853616i 0.136960 0.990577i \(-0.456267\pi\)
−0.990577 + 0.136960i \(0.956267\pi\)
\(588\) 0 0
\(589\) 13.3471 13.3471i 0.549957 0.549957i
\(590\) 0 0
\(591\) −12.4669 + 12.4669i −0.512822 + 0.512822i
\(592\) 0 0
\(593\) 4.00333 4.00333i 0.164397 0.164397i −0.620114 0.784511i \(-0.712914\pi\)
0.784511 + 0.620114i \(0.212914\pi\)
\(594\) 0 0
\(595\) 3.47171i 0.142326i
\(596\) 0 0
\(597\) 2.95885 0.121098
\(598\) 0 0
\(599\) 47.6272 1.94600 0.972998 0.230812i \(-0.0741383\pi\)
0.972998 + 0.230812i \(0.0741383\pi\)
\(600\) 0 0
\(601\) −8.81011 + 8.81011i −0.359372 + 0.359372i −0.863581 0.504210i \(-0.831784\pi\)
0.504210 + 0.863581i \(0.331784\pi\)
\(602\) 0 0
\(603\) −0.374217 0.374217i −0.0152393 0.0152393i
\(604\) 0 0
\(605\) 22.0847 0.897869
\(606\) 0 0
\(607\) 36.5165i 1.48216i −0.671418 0.741078i \(-0.734315\pi\)
0.671418 0.741078i \(-0.265685\pi\)
\(608\) 0 0
\(609\) 7.71851 7.71851i 0.312770 0.312770i
\(610\) 0 0
\(611\) −1.92575 −0.0779075
\(612\) 0 0
\(613\) 32.2352i 1.30197i 0.759092 + 0.650984i \(0.225643\pi\)
−0.759092 + 0.650984i \(0.774357\pi\)
\(614\) 0 0
\(615\) 22.3793 + 14.2623i 0.902420 + 0.575111i
\(616\) 0 0
\(617\) 18.8966i 0.760749i −0.924833 0.380374i \(-0.875795\pi\)
0.924833 0.380374i \(-0.124205\pi\)
\(618\) 0 0
\(619\) −7.32834 −0.294551 −0.147275 0.989096i \(-0.547050\pi\)
−0.147275 + 0.989096i \(0.547050\pi\)
\(620\) 0 0
\(621\) 10.9012 10.9012i 0.437450 0.437450i
\(622\) 0 0
\(623\) 15.8945i 0.636799i
\(624\) 0 0
\(625\) −22.0033 −0.880130
\(626\) 0 0
\(627\) −3.88213 3.88213i −0.155037 0.155037i
\(628\) 0 0
\(629\) −1.82736 + 1.82736i −0.0728616 + 0.0728616i
\(630\) 0 0
\(631\) 39.8793 1.58757 0.793785 0.608198i \(-0.208107\pi\)
0.793785 + 0.608198i \(0.208107\pi\)
\(632\) 0 0
\(633\) −26.6994 −1.06121
\(634\) 0 0
\(635\) 1.52762i 0.0606218i
\(636\) 0 0
\(637\) −0.612447 + 0.612447i −0.0242660 + 0.0242660i
\(638\) 0 0
\(639\) 0.969578 0.969578i 0.0383559 0.0383559i
\(640\) 0 0
\(641\) −9.47633 + 9.47633i −0.374292 + 0.374292i −0.869038 0.494745i \(-0.835261\pi\)
0.494745 + 0.869038i \(0.335261\pi\)
\(642\) 0 0
\(643\) 14.2664 + 14.2664i 0.562614 + 0.562614i 0.930049 0.367435i \(-0.119764\pi\)
−0.367435 + 0.930049i \(0.619764\pi\)
\(644\) 0 0
\(645\) 24.7386 + 24.7386i 0.974081 + 0.974081i
\(646\) 0 0
\(647\) 17.0892i 0.671846i −0.941889 0.335923i \(-0.890952\pi\)
0.941889 0.335923i \(-0.109048\pi\)
\(648\) 0 0
\(649\) −3.31252 3.31252i −0.130028 0.130028i
\(650\) 0 0
\(651\) 9.74657i 0.381998i
\(652\) 0 0
\(653\) 11.1468 + 11.1468i 0.436207 + 0.436207i 0.890733 0.454526i \(-0.150191\pi\)
−0.454526 + 0.890733i \(0.650191\pi\)
\(654\) 0 0
\(655\) −29.3406 −1.14643
\(656\) 0 0
\(657\) −0.237017 −0.00924690
\(658\) 0 0
\(659\) 0.418356 + 0.418356i 0.0162968 + 0.0162968i 0.715208 0.698911i \(-0.246332\pi\)
−0.698911 + 0.715208i \(0.746332\pi\)
\(660\) 0 0
\(661\) 5.10196i 0.198443i −0.995065 0.0992216i \(-0.968365\pi\)
0.995065 0.0992216i \(-0.0316353\pi\)
\(662\) 0 0
\(663\) −1.97620 1.97620i −0.0767491 0.0767491i
\(664\) 0 0
\(665\) 8.02637i 0.311249i
\(666\) 0 0
\(667\) −14.3815 14.3815i −0.556853 0.556853i
\(668\) 0 0
\(669\) 38.0982 + 38.0982i 1.47296 + 1.47296i
\(670\) 0 0
\(671\) 4.38594 4.38594i 0.169317 0.169317i
\(672\) 0 0
\(673\) 18.9106 18.9106i 0.728952 0.728952i −0.241459 0.970411i \(-0.577626\pi\)
0.970411 + 0.241459i \(0.0776261\pi\)
\(674\) 0 0
\(675\) −1.61225 + 1.61225i −0.0620557 + 0.0620557i
\(676\) 0 0
\(677\) 22.4278i 0.861969i −0.902359 0.430984i \(-0.858166\pi\)
0.902359 0.430984i \(-0.141834\pi\)
\(678\) 0 0
\(679\) −13.1946 −0.506362
\(680\) 0 0
\(681\) −11.5112 −0.441109
\(682\) 0 0
\(683\) 16.6486 16.6486i 0.637040 0.637040i −0.312784 0.949824i \(-0.601262\pi\)
0.949824 + 0.312784i \(0.101262\pi\)
\(684\) 0 0
\(685\) −3.07663 3.07663i −0.117552 0.117552i
\(686\) 0 0
\(687\) 6.80370 0.259577
\(688\) 0 0
\(689\) 2.76448i 0.105318i
\(690\) 0 0
\(691\) −19.3720 + 19.3720i −0.736945 + 0.736945i −0.971986 0.235040i \(-0.924478\pi\)
0.235040 + 0.971986i \(0.424478\pi\)
\(692\) 0 0
\(693\) 0.627040 0.0238193
\(694\) 0 0
\(695\) 1.68603i 0.0639549i
\(696\) 0 0
\(697\) 8.87756 + 5.65765i 0.336261 + 0.214299i
\(698\) 0 0
\(699\) 11.4303i 0.432334i
\(700\) 0 0
\(701\) 7.05364 0.266412 0.133206 0.991088i \(-0.457473\pi\)
0.133206 + 0.991088i \(0.457473\pi\)
\(702\) 0 0
\(703\) 4.22474 4.22474i 0.159339 0.159339i
\(704\) 0 0
\(705\) 9.21481i 0.347050i
\(706\) 0 0
\(707\) −11.4078 −0.429036
\(708\) 0 0
\(709\) −13.3339 13.3339i −0.500767 0.500767i 0.410909 0.911676i \(-0.365211\pi\)
−0.911676 + 0.410909i \(0.865211\pi\)
\(710\) 0 0
\(711\) 3.36055 3.36055i 0.126030 0.126030i
\(712\) 0 0
\(713\) 18.1603 0.680107
\(714\) 0 0
\(715\) 1.34604 0.0503391
\(716\) 0 0
\(717\) 3.92425i 0.146554i
\(718\) 0 0
\(719\) 21.6670 21.6670i 0.808044 0.808044i −0.176294 0.984338i \(-0.556411\pi\)
0.984338 + 0.176294i \(0.0564109\pi\)
\(720\) 0 0
\(721\) −6.16254 + 6.16254i −0.229505 + 0.229505i
\(722\) 0 0
\(723\) −4.58618 + 4.58618i −0.170562 + 0.170562i
\(724\) 0 0
\(725\) 2.12698 + 2.12698i 0.0789940 + 0.0789940i
\(726\) 0 0
\(727\) 4.23623 + 4.23623i 0.157113 + 0.157113i 0.781286 0.624173i \(-0.214564\pi\)
−0.624173 + 0.781286i \(0.714564\pi\)
\(728\) 0 0
\(729\) 15.5948i 0.577585i
\(730\) 0 0
\(731\) 9.81346 + 9.81346i 0.362964 + 0.362964i
\(732\) 0 0
\(733\) 48.0360i 1.77425i 0.461531 + 0.887124i \(0.347300\pi\)
−0.461531 + 0.887124i \(0.652700\pi\)
\(734\) 0 0
\(735\) 2.93059 + 2.93059i 0.108096 + 0.108096i
\(736\) 0 0
\(737\) 0.457131 0.0168386
\(738\) 0 0
\(739\) 25.0807 0.922608 0.461304 0.887242i \(-0.347382\pi\)
0.461304 + 0.887242i \(0.347382\pi\)
\(740\) 0 0
\(741\) 4.56884 + 4.56884i 0.167840 + 0.167840i
\(742\) 0 0
\(743\) 23.1665i 0.849897i 0.905218 + 0.424948i \(0.139708\pi\)
−0.905218 + 0.424948i \(0.860292\pi\)
\(744\) 0 0
\(745\) 4.31888 + 4.31888i 0.158232 + 0.158232i
\(746\) 0 0
\(747\) 6.96691i 0.254906i
\(748\) 0 0
\(749\) 8.80180 + 8.80180i 0.321611 + 0.321611i
\(750\) 0 0
\(751\) 22.4974 + 22.4974i 0.820942 + 0.820942i 0.986243 0.165301i \(-0.0528595\pi\)
−0.165301 + 0.986243i \(0.552860\pi\)
\(752\) 0 0
\(753\) 3.86635 3.86635i 0.140898 0.140898i
\(754\) 0 0
\(755\) 14.9318 14.9318i 0.543422 0.543422i
\(756\) 0 0
\(757\) −8.62170 + 8.62170i −0.313361 + 0.313361i −0.846210 0.532849i \(-0.821121\pi\)
0.532849 + 0.846210i \(0.321121\pi\)
\(758\) 0 0
\(759\) 5.28210i 0.191728i
\(760\) 0 0
\(761\) −4.67890 −0.169610 −0.0848049 0.996398i \(-0.527027\pi\)
−0.0848049 + 0.996398i \(0.527027\pi\)
\(762\) 0 0
\(763\) −0.762143 −0.0275914
\(764\) 0 0
\(765\) −2.09158 + 2.09158i −0.0756214 + 0.0756214i
\(766\) 0 0
\(767\) 3.89847 + 3.89847i 0.140766 + 0.140766i
\(768\) 0 0
\(769\) 7.68935 0.277285 0.138643 0.990342i \(-0.455726\pi\)
0.138643 + 0.990342i \(0.455726\pi\)
\(770\) 0 0
\(771\) 2.79214i 0.100556i
\(772\) 0 0
\(773\) 6.51065 6.51065i 0.234172 0.234172i −0.580260 0.814432i \(-0.697049\pi\)
0.814432 + 0.580260i \(0.197049\pi\)
\(774\) 0 0
\(775\) −2.68585 −0.0964785
\(776\) 0 0
\(777\) 3.08507i 0.110676i
\(778\) 0 0
\(779\) −20.5243 13.0801i −0.735361 0.468644i
\(780\) 0 0
\(781\) 1.18440i 0.0423813i
\(782\) 0 0
\(783\) −23.4466 −0.837914
\(784\) 0 0
\(785\) 24.3728 24.3728i 0.869903 0.869903i
\(786\) 0 0
\(787\) 38.8016i 1.38313i 0.722314 + 0.691565i \(0.243078\pi\)
−0.722314 + 0.691565i \(0.756922\pi\)
\(788\) 0 0
\(789\) −42.4941 −1.51283
\(790\) 0 0
\(791\) −2.45633 2.45633i −0.0873370 0.0873370i
\(792\) 0 0
\(793\) −5.16176 + 5.16176i −0.183299 + 0.183299i
\(794\) 0 0
\(795\) 13.2282 0.469155
\(796\) 0 0
\(797\) −39.6615 −1.40488 −0.702441 0.711742i \(-0.747907\pi\)
−0.702441 + 0.711742i \(0.747907\pi\)
\(798\) 0 0
\(799\) 3.65539i 0.129318i
\(800\) 0 0
\(801\)