Properties

Label 3150.2.bp.h.1349.5
Level 3150
Weight 2
Character 3150.1349
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.5
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.h.899.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22849 - 2.34325i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22849 - 2.34325i) q^{7} -1.00000 q^{8} +(2.03986 - 1.17771i) q^{11} -4.64698 q^{13} +(-2.64356 - 0.107718i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.95097 + 2.28109i) q^{17} +(-0.491268 - 0.283634i) q^{19} -2.35542i q^{22} +(-2.91324 + 5.04588i) q^{23} +(-2.32349 + 4.02440i) q^{26} +(-1.41507 + 2.23553i) q^{28} -2.55339i q^{29} +(-1.89659 + 1.09500i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.56218i q^{34} +(8.02554 + 4.63355i) q^{37} +(-0.491268 + 0.283634i) q^{38} +8.68451 q^{41} +6.57695i q^{43} +(-2.03986 - 1.17771i) q^{44} +(2.91324 + 5.04588i) q^{46} +(-5.46663 - 3.15616i) q^{47} +(-3.98161 + 5.75732i) q^{49} +(2.32349 + 4.02440i) q^{52} +(6.07533 + 10.5228i) q^{53} +(1.22849 + 2.34325i) q^{56} +(-2.21130 - 1.27670i) q^{58} +(-1.67739 - 2.90532i) q^{59} +(-6.85523 - 3.95787i) q^{61} +2.18999i q^{62} +1.00000 q^{64} +(-3.46657 + 2.00143i) q^{67} +(3.95097 + 2.28109i) q^{68} +2.02720i q^{71} +(-4.10801 - 7.11528i) q^{73} +(8.02554 - 4.63355i) q^{74} +0.567267i q^{76} +(-5.26562 - 3.33308i) q^{77} +(-4.13212 + 7.15704i) q^{79} +(4.34226 - 7.52101i) q^{82} -0.171637i q^{83} +(5.69581 + 3.28848i) q^{86} +(-2.03986 + 1.17771i) q^{88} +(2.72938 - 4.72742i) q^{89} +(5.70878 + 10.8890i) q^{91} +5.82648 q^{92} +(-5.46663 + 3.15616i) q^{94} +10.8564 q^{97} +(2.99518 + 6.32684i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{2} - 12q^{4} - 24q^{8} + O(q^{10}) \) \( 24q + 12q^{2} - 12q^{4} - 24q^{8} - 12q^{16} - 24q^{17} - 12q^{19} + 8q^{23} + 12q^{32} - 12q^{38} - 8q^{46} + 24q^{47} + 52q^{49} + 32q^{53} - 12q^{61} + 24q^{64} + 24q^{68} + 16q^{77} - 4q^{79} + 68q^{91} - 16q^{92} + 24q^{94} + 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.22849 2.34325i −0.464326 0.885664i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 2.03986 1.17771i 0.615040 0.355093i −0.159896 0.987134i \(-0.551116\pi\)
0.774935 + 0.632041i \(0.217782\pi\)
\(12\) 0 0
\(13\) −4.64698 −1.28884 −0.644420 0.764672i \(-0.722901\pi\)
−0.644420 + 0.764672i \(0.722901\pi\)
\(14\) −2.64356 0.107718i −0.706520 0.0287888i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.95097 + 2.28109i −0.958250 + 0.553246i −0.895634 0.444792i \(-0.853278\pi\)
−0.0626158 + 0.998038i \(0.519944\pi\)
\(18\) 0 0
\(19\) −0.491268 0.283634i −0.112705 0.0650700i 0.442588 0.896725i \(-0.354060\pi\)
−0.555293 + 0.831655i \(0.687394\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.35542i 0.502178i
\(23\) −2.91324 + 5.04588i −0.607453 + 1.05214i 0.384206 + 0.923247i \(0.374475\pi\)
−0.991659 + 0.128891i \(0.958858\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.32349 + 4.02440i −0.455674 + 0.789250i
\(27\) 0 0
\(28\) −1.41507 + 2.23553i −0.267422 + 0.422475i
\(29\) 2.55339i 0.474153i −0.971491 0.237077i \(-0.923811\pi\)
0.971491 0.237077i \(-0.0761893\pi\)
\(30\) 0 0
\(31\) −1.89659 + 1.09500i −0.340638 + 0.196667i −0.660554 0.750778i \(-0.729679\pi\)
0.319916 + 0.947446i \(0.396345\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 4.56218i 0.782408i
\(35\) 0 0
\(36\) 0 0
\(37\) 8.02554 + 4.63355i 1.31939 + 0.761750i 0.983630 0.180197i \(-0.0576736\pi\)
0.335760 + 0.941948i \(0.391007\pi\)
\(38\) −0.491268 + 0.283634i −0.0796942 + 0.0460114i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.68451 1.35629 0.678147 0.734927i \(-0.262783\pi\)
0.678147 + 0.734927i \(0.262783\pi\)
\(42\) 0 0
\(43\) 6.57695i 1.00298i 0.865165 + 0.501488i \(0.167214\pi\)
−0.865165 + 0.501488i \(0.832786\pi\)
\(44\) −2.03986 1.17771i −0.307520 0.177547i
\(45\) 0 0
\(46\) 2.91324 + 5.04588i 0.429534 + 0.743975i
\(47\) −5.46663 3.15616i −0.797391 0.460374i 0.0451673 0.998979i \(-0.485618\pi\)
−0.842558 + 0.538606i \(0.818951\pi\)
\(48\) 0 0
\(49\) −3.98161 + 5.75732i −0.568802 + 0.822475i
\(50\) 0 0
\(51\) 0 0
\(52\) 2.32349 + 4.02440i 0.322210 + 0.558084i
\(53\) 6.07533 + 10.5228i 0.834511 + 1.44542i 0.894428 + 0.447212i \(0.147583\pi\)
−0.0599168 + 0.998203i \(0.519084\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.22849 + 2.34325i 0.164164 + 0.313130i
\(57\) 0 0
\(58\) −2.21130 1.27670i −0.290359 0.167639i
\(59\) −1.67739 2.90532i −0.218377 0.378241i 0.735935 0.677053i \(-0.236743\pi\)
−0.954312 + 0.298812i \(0.903410\pi\)
\(60\) 0 0
\(61\) −6.85523 3.95787i −0.877722 0.506753i −0.00781543 0.999969i \(-0.502488\pi\)
−0.869907 + 0.493216i \(0.835821\pi\)
\(62\) 2.18999i 0.278130i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −3.46657 + 2.00143i −0.423509 + 0.244513i −0.696578 0.717481i \(-0.745295\pi\)
0.273068 + 0.961995i \(0.411961\pi\)
\(68\) 3.95097 + 2.28109i 0.479125 + 0.276623i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.02720i 0.240585i 0.992738 + 0.120292i \(0.0383832\pi\)
−0.992738 + 0.120292i \(0.961617\pi\)
\(72\) 0 0
\(73\) −4.10801 7.11528i −0.480806 0.832780i 0.518952 0.854804i \(-0.326322\pi\)
−0.999757 + 0.0220235i \(0.992989\pi\)
\(74\) 8.02554 4.63355i 0.932950 0.538639i
\(75\) 0 0
\(76\) 0.567267i 0.0650700i
\(77\) −5.26562 3.33308i −0.600073 0.379839i
\(78\) 0 0
\(79\) −4.13212 + 7.15704i −0.464900 + 0.805230i −0.999197 0.0400666i \(-0.987243\pi\)
0.534297 + 0.845297i \(0.320576\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 4.34226 7.52101i 0.479522 0.830556i
\(83\) 0.171637i 0.0188396i −0.999956 0.00941978i \(-0.997002\pi\)
0.999956 0.00941978i \(-0.00299845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.69581 + 3.28848i 0.614195 + 0.354606i
\(87\) 0 0
\(88\) −2.03986 + 1.17771i −0.217449 + 0.125544i
\(89\) 2.72938 4.72742i 0.289313 0.501105i −0.684333 0.729170i \(-0.739906\pi\)
0.973646 + 0.228065i \(0.0732397\pi\)
\(90\) 0 0
\(91\) 5.70878 + 10.8890i 0.598443 + 1.14148i
\(92\) 5.82648 0.607453
\(93\) 0 0
\(94\) −5.46663 + 3.15616i −0.563840 + 0.325533i
\(95\) 0 0
\(96\) 0 0
\(97\) 10.8564 1.10230 0.551151 0.834406i \(-0.314189\pi\)
0.551151 + 0.834406i \(0.314189\pi\)
\(98\) 2.99518 + 6.32684i 0.302559 + 0.639107i
\(99\) 0 0
\(100\) 0 0
\(101\) −5.74827 9.95630i −0.571975 0.990689i −0.996363 0.0852090i \(-0.972844\pi\)
0.424388 0.905480i \(-0.360489\pi\)
\(102\) 0 0
\(103\) −9.68690 + 16.7782i −0.954478 + 1.65320i −0.218920 + 0.975743i \(0.570253\pi\)
−0.735558 + 0.677462i \(0.763080\pi\)
\(104\) 4.64698 0.455674
\(105\) 0 0
\(106\) 12.1507 1.18018
\(107\) 5.36029 9.28430i 0.518199 0.897547i −0.481577 0.876404i \(-0.659936\pi\)
0.999776 0.0211436i \(-0.00673071\pi\)
\(108\) 0 0
\(109\) 5.41186 + 9.37362i 0.518363 + 0.897830i 0.999772 + 0.0213347i \(0.00679157\pi\)
−0.481410 + 0.876496i \(0.659875\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.64356 + 0.107718i 0.249793 + 0.0101784i
\(113\) −18.4343 −1.73415 −0.867076 0.498176i \(-0.834003\pi\)
−0.867076 + 0.498176i \(0.834003\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.21130 + 1.27670i −0.205314 + 0.118538i
\(117\) 0 0
\(118\) −3.35478 −0.308832
\(119\) 10.1989 + 6.45578i 0.934931 + 0.591801i
\(120\) 0 0
\(121\) −2.72599 + 4.72156i −0.247817 + 0.429232i
\(122\) −6.85523 + 3.95787i −0.620643 + 0.358329i
\(123\) 0 0
\(124\) 1.89659 + 1.09500i 0.170319 + 0.0983337i
\(125\) 0 0
\(126\) 0 0
\(127\) 4.04880i 0.359273i 0.983733 + 0.179637i \(0.0574922\pi\)
−0.983733 + 0.179637i \(0.942508\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.14129 12.3691i 0.623937 1.08069i −0.364808 0.931083i \(-0.618866\pi\)
0.988745 0.149608i \(-0.0478012\pi\)
\(132\) 0 0
\(133\) −0.0611049 + 1.49960i −0.00529846 + 0.130032i
\(134\) 4.00285i 0.345794i
\(135\) 0 0
\(136\) 3.95097 2.28109i 0.338792 0.195602i
\(137\) 2.61421 + 4.52794i 0.223347 + 0.386848i 0.955822 0.293945i \(-0.0949684\pi\)
−0.732475 + 0.680794i \(0.761635\pi\)
\(138\) 0 0
\(139\) 19.4726i 1.65164i 0.563933 + 0.825820i \(0.309288\pi\)
−0.563933 + 0.825820i \(0.690712\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.75561 + 1.01360i 0.147328 + 0.0850596i
\(143\) −9.47917 + 5.47280i −0.792688 + 0.457659i
\(144\) 0 0
\(145\) 0 0
\(146\) −8.21601 −0.679962
\(147\) 0 0
\(148\) 9.26709i 0.761750i
\(149\) −4.79814 2.77021i −0.393079 0.226944i 0.290414 0.956901i \(-0.406207\pi\)
−0.683493 + 0.729957i \(0.739540\pi\)
\(150\) 0 0
\(151\) 4.23984 + 7.34362i 0.345033 + 0.597615i 0.985360 0.170488i \(-0.0545343\pi\)
−0.640327 + 0.768103i \(0.721201\pi\)
\(152\) 0.491268 + 0.283634i 0.0398471 + 0.0230057i
\(153\) 0 0
\(154\) −5.51934 + 2.89362i −0.444761 + 0.233174i
\(155\) 0 0
\(156\) 0 0
\(157\) −0.560470 0.970763i −0.0447304 0.0774753i 0.842793 0.538237i \(-0.180910\pi\)
−0.887524 + 0.460762i \(0.847576\pi\)
\(158\) 4.13212 + 7.15704i 0.328734 + 0.569384i
\(159\) 0 0
\(160\) 0 0
\(161\) 15.4026 + 0.627617i 1.21390 + 0.0494631i
\(162\) 0 0
\(163\) −5.81534 3.35749i −0.455493 0.262979i 0.254654 0.967032i \(-0.418038\pi\)
−0.710147 + 0.704053i \(0.751372\pi\)
\(164\) −4.34226 7.52101i −0.339073 0.587292i
\(165\) 0 0
\(166\) −0.148642 0.0858183i −0.0115368 0.00666079i
\(167\) 2.80110i 0.216756i −0.994110 0.108378i \(-0.965434\pi\)
0.994110 0.108378i \(-0.0345657\pi\)
\(168\) 0 0
\(169\) 8.59442 0.661109
\(170\) 0 0
\(171\) 0 0
\(172\) 5.69581 3.28848i 0.434301 0.250744i
\(173\) 11.9515 + 6.90018i 0.908653 + 0.524611i 0.879998 0.474978i \(-0.157544\pi\)
0.0286558 + 0.999589i \(0.490877\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.35542i 0.177547i
\(177\) 0 0
\(178\) −2.72938 4.72742i −0.204575 0.354335i
\(179\) −2.31980 + 1.33933i −0.173390 + 0.100107i −0.584183 0.811622i \(-0.698585\pi\)
0.410794 + 0.911728i \(0.365252\pi\)
\(180\) 0 0
\(181\) 6.88082i 0.511447i 0.966750 + 0.255724i \(0.0823137\pi\)
−0.966750 + 0.255724i \(0.917686\pi\)
\(182\) 12.2846 + 0.500563i 0.910592 + 0.0371042i
\(183\) 0 0
\(184\) 2.91324 5.04588i 0.214767 0.371987i
\(185\) 0 0
\(186\) 0 0
\(187\) −5.37293 + 9.30619i −0.392908 + 0.680536i
\(188\) 6.31233i 0.460374i
\(189\) 0 0
\(190\) 0 0
\(191\) 8.65356 + 4.99614i 0.626150 + 0.361508i 0.779260 0.626701i \(-0.215595\pi\)
−0.153110 + 0.988209i \(0.548929\pi\)
\(192\) 0 0
\(193\) −21.7620 + 12.5643i −1.56646 + 0.904398i −0.569887 + 0.821723i \(0.693013\pi\)
−0.996577 + 0.0826753i \(0.973654\pi\)
\(194\) 5.42821 9.40193i 0.389723 0.675019i
\(195\) 0 0
\(196\) 6.97679 + 0.569517i 0.498342 + 0.0406798i
\(197\) −20.0811 −1.43072 −0.715359 0.698757i \(-0.753737\pi\)
−0.715359 + 0.698757i \(0.753737\pi\)
\(198\) 0 0
\(199\) 10.3028 5.94834i 0.730348 0.421667i −0.0882014 0.996103i \(-0.528112\pi\)
0.818550 + 0.574436i \(0.194779\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −11.4965 −0.808894
\(203\) −5.98323 + 3.13683i −0.419941 + 0.220162i
\(204\) 0 0
\(205\) 0 0
\(206\) 9.68690 + 16.7782i 0.674918 + 1.16899i
\(207\) 0 0
\(208\) 2.32349 4.02440i 0.161105 0.279042i
\(209\) −1.33615 −0.0924237
\(210\) 0 0
\(211\) −6.78640 −0.467195 −0.233597 0.972333i \(-0.575050\pi\)
−0.233597 + 0.972333i \(0.575050\pi\)
\(212\) 6.07533 10.5228i 0.417256 0.722708i
\(213\) 0 0
\(214\) −5.36029 9.28430i −0.366422 0.634662i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.89580 + 3.09899i 0.332348 + 0.210373i
\(218\) 10.8237 0.733075
\(219\) 0 0
\(220\) 0 0
\(221\) 18.3601 10.6002i 1.23503 0.713045i
\(222\) 0 0
\(223\) −28.7684 −1.92648 −0.963239 0.268646i \(-0.913424\pi\)
−0.963239 + 0.268646i \(0.913424\pi\)
\(224\) 1.41507 2.23553i 0.0945480 0.149368i
\(225\) 0 0
\(226\) −9.21714 + 15.9646i −0.613115 + 1.06195i
\(227\) 1.82186 1.05185i 0.120921 0.0698140i −0.438319 0.898819i \(-0.644426\pi\)
0.559241 + 0.829005i \(0.311093\pi\)
\(228\) 0 0
\(229\) 14.0269 + 8.09841i 0.926920 + 0.535158i 0.885836 0.463998i \(-0.153585\pi\)
0.0410842 + 0.999156i \(0.486919\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.55339i 0.167639i
\(233\) 4.00569 6.93805i 0.262421 0.454527i −0.704464 0.709740i \(-0.748812\pi\)
0.966885 + 0.255213i \(0.0821457\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.67739 + 2.90532i −0.109189 + 0.189120i
\(237\) 0 0
\(238\) 10.6903 5.60460i 0.692950 0.363293i
\(239\) 15.6233i 1.01059i 0.862947 + 0.505294i \(0.168616\pi\)
−0.862947 + 0.505294i \(0.831384\pi\)
\(240\) 0 0
\(241\) −3.54491 + 2.04665i −0.228348 + 0.131837i −0.609809 0.792548i \(-0.708754\pi\)
0.381462 + 0.924385i \(0.375421\pi\)
\(242\) 2.72599 + 4.72156i 0.175233 + 0.303513i
\(243\) 0 0
\(244\) 7.91574i 0.506753i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.28291 + 1.31804i 0.145258 + 0.0838648i
\(248\) 1.89659 1.09500i 0.120434 0.0695324i
\(249\) 0 0
\(250\) 0 0
\(251\) −19.9413 −1.25869 −0.629343 0.777128i \(-0.716676\pi\)
−0.629343 + 0.777128i \(0.716676\pi\)
\(252\) 0 0
\(253\) 13.7238i 0.862810i
\(254\) 3.50637 + 2.02440i 0.220009 + 0.127022i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 17.6188 + 10.1722i 1.09903 + 0.634527i 0.935967 0.352088i \(-0.114528\pi\)
0.163067 + 0.986615i \(0.447861\pi\)
\(258\) 0 0
\(259\) 0.998233 24.4981i 0.0620272 1.52224i
\(260\) 0 0
\(261\) 0 0
\(262\) −7.14129 12.3691i −0.441190 0.764164i
\(263\) −1.80801 3.13156i −0.111487 0.193100i 0.804883 0.593433i \(-0.202228\pi\)
−0.916370 + 0.400333i \(0.868895\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.26814 + 0.802720i 0.0777548 + 0.0492179i
\(267\) 0 0
\(268\) 3.46657 + 2.00143i 0.211755 + 0.122257i
\(269\) 10.6172 + 18.3896i 0.647345 + 1.12123i 0.983755 + 0.179518i \(0.0574539\pi\)
−0.336410 + 0.941716i \(0.609213\pi\)
\(270\) 0 0
\(271\) −18.9957 10.9672i −1.15390 0.666207i −0.204069 0.978956i \(-0.565417\pi\)
−0.949836 + 0.312749i \(0.898750\pi\)
\(272\) 4.56218i 0.276623i
\(273\) 0 0
\(274\) 5.22842 0.315860
\(275\) 0 0
\(276\) 0 0
\(277\) −8.59880 + 4.96452i −0.516652 + 0.298289i −0.735564 0.677456i \(-0.763083\pi\)
0.218912 + 0.975745i \(0.429749\pi\)
\(278\) 16.8637 + 9.73628i 1.01142 + 0.583943i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.0696i 0.660358i −0.943918 0.330179i \(-0.892891\pi\)
0.943918 0.330179i \(-0.107109\pi\)
\(282\) 0 0
\(283\) −11.3387 19.6392i −0.674014 1.16743i −0.976756 0.214354i \(-0.931235\pi\)
0.302742 0.953072i \(-0.402098\pi\)
\(284\) 1.75561 1.01360i 0.104176 0.0601462i
\(285\) 0 0
\(286\) 10.9456i 0.647227i
\(287\) −10.6689 20.3500i −0.629763 1.20122i
\(288\) 0 0
\(289\) 1.90675 3.30259i 0.112162 0.194270i
\(290\) 0 0
\(291\) 0 0
\(292\) −4.10801 + 7.11528i −0.240403 + 0.416390i
\(293\) 12.3248i 0.720020i −0.932949 0.360010i \(-0.882773\pi\)
0.932949 0.360010i \(-0.117227\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −8.02554 4.63355i −0.466475 0.269319i
\(297\) 0 0
\(298\) −4.79814 + 2.77021i −0.277949 + 0.160474i
\(299\) 13.5378 23.4481i 0.782909 1.35604i
\(300\) 0 0
\(301\) 15.4114 8.07974i 0.888300 0.465708i
\(302\) 8.47968 0.487951
\(303\) 0 0
\(304\) 0.491268 0.283634i 0.0281761 0.0162675i
\(305\) 0 0
\(306\) 0 0
\(307\) 8.06274 0.460165 0.230082 0.973171i \(-0.426100\pi\)
0.230082 + 0.973171i \(0.426100\pi\)
\(308\) −0.253721 + 6.22670i −0.0144571 + 0.354799i
\(309\) 0 0
\(310\) 0 0
\(311\) −13.2215 22.9003i −0.749721 1.29855i −0.947956 0.318400i \(-0.896854\pi\)
0.198236 0.980154i \(-0.436479\pi\)
\(312\) 0 0
\(313\) 8.26650 14.3180i 0.467250 0.809301i −0.532050 0.846713i \(-0.678578\pi\)
0.999300 + 0.0374122i \(0.0119114\pi\)
\(314\) −1.12094 −0.0632583
\(315\) 0 0
\(316\) 8.26424 0.464900
\(317\) −6.13038 + 10.6181i −0.344317 + 0.596374i −0.985229 0.171240i \(-0.945223\pi\)
0.640913 + 0.767614i \(0.278556\pi\)
\(318\) 0 0
\(319\) −3.00716 5.20856i −0.168369 0.291623i
\(320\) 0 0
\(321\) 0 0
\(322\) 8.24485 13.0253i 0.459468 0.725870i
\(323\) 2.58798 0.143999
\(324\) 0 0
\(325\) 0 0
\(326\) −5.81534 + 3.35749i −0.322082 + 0.185954i
\(327\) 0 0
\(328\) −8.68451 −0.479522
\(329\) −0.679951 + 16.6870i −0.0374869 + 0.919984i
\(330\) 0 0
\(331\) −17.1942 + 29.7812i −0.945077 + 1.63692i −0.189479 + 0.981885i \(0.560680\pi\)
−0.755598 + 0.655036i \(0.772654\pi\)
\(332\) −0.148642 + 0.0858183i −0.00815777 + 0.00470989i
\(333\) 0 0
\(334\) −2.42583 1.40055i −0.132735 0.0766348i
\(335\) 0 0
\(336\) 0 0
\(337\) 23.9536i 1.30484i −0.757860 0.652418i \(-0.773755\pi\)
0.757860 0.652418i \(-0.226245\pi\)
\(338\) 4.29721 7.44298i 0.233737 0.404845i
\(339\) 0 0
\(340\) 0 0
\(341\) −2.57918 + 4.46727i −0.139671 + 0.241916i
\(342\) 0 0
\(343\) 18.3822 + 2.25708i 0.992546 + 0.121871i
\(344\) 6.57695i 0.354606i
\(345\) 0 0
\(346\) 11.9515 6.90018i 0.642515 0.370956i
\(347\) −14.3501 24.8552i −0.770355 1.33429i −0.937368 0.348340i \(-0.886746\pi\)
0.167013 0.985955i \(-0.446588\pi\)
\(348\) 0 0
\(349\) 3.57176i 0.191192i 0.995420 + 0.0955960i \(0.0304757\pi\)
−0.995420 + 0.0955960i \(0.969524\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.03986 + 1.17771i 0.108725 + 0.0627722i
\(353\) −10.8597 + 6.26984i −0.578003 + 0.333710i −0.760339 0.649526i \(-0.774967\pi\)
0.182337 + 0.983236i \(0.441634\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −5.45875 −0.289313
\(357\) 0 0
\(358\) 2.67867i 0.141572i
\(359\) 13.6940 + 7.90624i 0.722742 + 0.417275i 0.815761 0.578389i \(-0.196318\pi\)
−0.0930190 + 0.995664i \(0.529652\pi\)
\(360\) 0 0
\(361\) −9.33910 16.1758i −0.491532 0.851358i
\(362\) 5.95896 + 3.44041i 0.313196 + 0.180824i
\(363\) 0 0
\(364\) 6.57578 10.3885i 0.344664 0.544503i
\(365\) 0 0
\(366\) 0 0
\(367\) −17.8317 30.8855i −0.930809 1.61221i −0.781942 0.623351i \(-0.785771\pi\)
−0.148867 0.988857i \(-0.547563\pi\)
\(368\) −2.91324 5.04588i −0.151863 0.263035i
\(369\) 0 0
\(370\) 0 0
\(371\) 17.1940 27.1632i 0.892667 1.41024i
\(372\) 0 0
\(373\) 19.9717 + 11.5306i 1.03409 + 0.597034i 0.918155 0.396222i \(-0.129679\pi\)
0.115939 + 0.993256i \(0.463012\pi\)
\(374\) 5.37293 + 9.30619i 0.277828 + 0.481212i
\(375\) 0 0
\(376\) 5.46663 + 3.15616i 0.281920 + 0.162767i
\(377\) 11.8656i 0.611108i
\(378\) 0 0
\(379\) −8.20110 −0.421262 −0.210631 0.977566i \(-0.567552\pi\)
−0.210631 + 0.977566i \(0.567552\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8.65356 4.99614i 0.442755 0.255625i
\(383\) −4.01207 2.31637i −0.205007 0.118361i 0.393982 0.919118i \(-0.371097\pi\)
−0.598989 + 0.800757i \(0.704431\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 25.1286i 1.27901i
\(387\) 0 0
\(388\) −5.42821 9.40193i −0.275575 0.477311i
\(389\) −29.0194 + 16.7544i −1.47134 + 0.849480i −0.999482 0.0321938i \(-0.989751\pi\)
−0.471860 + 0.881673i \(0.656417\pi\)
\(390\) 0 0
\(391\) 26.5815i 1.34428i
\(392\) 3.98161 5.75732i 0.201102 0.290789i
\(393\) 0 0
\(394\) −10.0405 + 17.3907i −0.505835 + 0.876132i
\(395\) 0 0
\(396\) 0 0
\(397\) −9.28081 + 16.0748i −0.465790 + 0.806772i −0.999237 0.0390613i \(-0.987563\pi\)
0.533447 + 0.845834i \(0.320897\pi\)
\(398\) 11.8967i 0.596327i
\(399\) 0 0
\(400\) 0 0
\(401\) 12.1377 + 7.00770i 0.606128 + 0.349948i 0.771448 0.636292i \(-0.219533\pi\)
−0.165321 + 0.986240i \(0.552866\pi\)
\(402\) 0 0
\(403\) 8.81342 5.08843i 0.439028 0.253473i
\(404\) −5.74827 + 9.95630i −0.285987 + 0.495345i
\(405\) 0 0
\(406\) −0.275047 + 6.75005i −0.0136503 + 0.334999i
\(407\) 21.8279 1.08197
\(408\) 0 0
\(409\) −20.6162 + 11.9028i −1.01941 + 0.588555i −0.913932 0.405868i \(-0.866969\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 19.3738 0.954478
\(413\) −4.74723 + 7.49970i −0.233596 + 0.369036i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.32349 4.02440i −0.113918 0.197313i
\(417\) 0 0
\(418\) −0.668077 + 1.15714i −0.0326767 + 0.0565977i
\(419\) 18.1374 0.886068 0.443034 0.896505i \(-0.353902\pi\)
0.443034 + 0.896505i \(0.353902\pi\)
\(420\) 0 0
\(421\) 7.98092 0.388966 0.194483 0.980906i \(-0.437697\pi\)
0.194483 + 0.980906i \(0.437697\pi\)
\(422\) −3.39320 + 5.87719i −0.165178 + 0.286097i
\(423\) 0 0
\(424\) −6.07533 10.5228i −0.295044 0.511032i
\(425\) 0 0
\(426\) 0 0
\(427\) −0.852667 + 20.9257i −0.0412635 + 1.01267i
\(428\) −10.7206 −0.518199
\(429\) 0 0
\(430\) 0 0
\(431\) −27.1353 + 15.6666i −1.30706 + 0.754632i −0.981605 0.190925i \(-0.938851\pi\)
−0.325456 + 0.945557i \(0.605518\pi\)
\(432\) 0 0
\(433\) 5.21564 0.250648 0.125324 0.992116i \(-0.460003\pi\)
0.125324 + 0.992116i \(0.460003\pi\)
\(434\) 5.13170 2.69039i 0.246329 0.129143i
\(435\) 0 0
\(436\) 5.41186 9.37362i 0.259181 0.448915i
\(437\) 2.86236 1.65259i 0.136925 0.0790539i
\(438\) 0 0
\(439\) 8.91887 + 5.14931i 0.425675 + 0.245763i 0.697502 0.716583i \(-0.254295\pi\)
−0.271828 + 0.962346i \(0.587628\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 21.2004i 1.00840i
\(443\) 20.7828 35.9968i 0.987419 1.71026i 0.356768 0.934193i \(-0.383879\pi\)
0.630651 0.776067i \(-0.282788\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −14.3842 + 24.9142i −0.681113 + 1.17972i
\(447\) 0 0
\(448\) −1.22849 2.34325i −0.0580408 0.110708i
\(449\) 23.7838i 1.12242i 0.827672 + 0.561212i \(0.189665\pi\)
−0.827672 + 0.561212i \(0.810335\pi\)
\(450\) 0 0
\(451\) 17.7152 10.2279i 0.834174 0.481611i
\(452\) 9.21714 + 15.9646i 0.433538 + 0.750910i
\(453\) 0 0
\(454\) 2.10371i 0.0987319i
\(455\) 0 0
\(456\) 0 0
\(457\) 16.2595 + 9.38745i 0.760589 + 0.439126i 0.829507 0.558496i \(-0.188621\pi\)
−0.0689182 + 0.997622i \(0.521955\pi\)
\(458\) 14.0269 8.09841i 0.655432 0.378414i
\(459\) 0 0
\(460\) 0 0
\(461\) −17.4662 −0.813484 −0.406742 0.913543i \(-0.633335\pi\)
−0.406742 + 0.913543i \(0.633335\pi\)
\(462\) 0 0
\(463\) 2.99345i 0.139117i 0.997578 + 0.0695586i \(0.0221591\pi\)
−0.997578 + 0.0695586i \(0.977841\pi\)
\(464\) 2.21130 + 1.27670i 0.102657 + 0.0592692i
\(465\) 0 0
\(466\) −4.00569 6.93805i −0.185560 0.321399i
\(467\) −22.0058 12.7050i −1.01831 0.587920i −0.104694 0.994505i \(-0.533386\pi\)
−0.913613 + 0.406585i \(0.866720\pi\)
\(468\) 0 0
\(469\) 8.94849 + 5.66430i 0.413203 + 0.261553i
\(470\) 0 0
\(471\) 0 0
\(472\) 1.67739 + 2.90532i 0.0772081 + 0.133728i
\(473\) 7.74575 + 13.4160i 0.356150 + 0.616870i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.491429 12.0604i 0.0225246 0.552787i
\(477\) 0 0
\(478\) 13.5302 + 7.81165i 0.618856 + 0.357297i
\(479\) −11.8516 20.5276i −0.541514 0.937929i −0.998817 0.0486188i \(-0.984518\pi\)
0.457304 0.889311i \(-0.348815\pi\)
\(480\) 0 0
\(481\) −37.2945 21.5320i −1.70048 0.981774i
\(482\) 4.09331i 0.186445i
\(483\) 0 0
\(484\) 5.45198 0.247817
\(485\) 0 0
\(486\) 0 0
\(487\) −8.84683 + 5.10772i −0.400888 + 0.231453i −0.686867 0.726783i \(-0.741015\pi\)
0.285979 + 0.958236i \(0.407681\pi\)
\(488\) 6.85523 + 3.95787i 0.310322 + 0.179164i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.25910i 0.101952i −0.998700 0.0509758i \(-0.983767\pi\)
0.998700 0.0509758i \(-0.0162331\pi\)
\(492\) 0 0
\(493\) 5.82452 + 10.0884i 0.262323 + 0.454357i
\(494\) 2.28291 1.31804i 0.102713 0.0593014i
\(495\) 0 0
\(496\) 2.18999i 0.0983337i
\(497\) 4.75024 2.49041i 0.213077 0.111710i
\(498\) 0 0
\(499\) 17.6811 30.6246i 0.791517 1.37095i −0.133511 0.991047i \(-0.542625\pi\)
0.925028 0.379900i \(-0.124042\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −9.97066 + 17.2697i −0.445012 + 0.770784i
\(503\) 30.7297i 1.37017i −0.728464 0.685084i \(-0.759766\pi\)
0.728464 0.685084i \(-0.240234\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 11.8852 + 6.86191i 0.528361 + 0.305049i
\(507\) 0 0
\(508\) 3.50637 2.02440i 0.155570 0.0898183i
\(509\) 1.03925 1.80003i 0.0460637 0.0797847i −0.842074 0.539362i \(-0.818666\pi\)
0.888138 + 0.459577i \(0.151999\pi\)
\(510\) 0 0
\(511\) −11.6262 + 18.3671i −0.514313 + 0.812514i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 17.6188 10.1722i 0.777134 0.448679i
\(515\) 0 0
\(516\) 0 0
\(517\) −14.8682 −0.653903
\(518\) −20.7169 13.1135i −0.910246 0.576176i
\(519\) 0 0
\(520\) 0 0
\(521\) −4.86182 8.42093i −0.213000 0.368927i 0.739652 0.672990i \(-0.234990\pi\)
−0.952652 + 0.304062i \(0.901657\pi\)
\(522\) 0 0
\(523\) 0.695001 1.20378i 0.0303903 0.0526375i −0.850430 0.526088i \(-0.823658\pi\)
0.880821 + 0.473450i \(0.156992\pi\)
\(524\) −14.2826 −0.623937
\(525\) 0 0
\(526\) −3.61602 −0.157666
\(527\) 4.99558 8.65259i 0.217611 0.376913i
\(528\) 0 0
\(529\) −5.47394 9.48114i −0.237997 0.412224i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.32925 0.696883i 0.0576302 0.0302137i
\(533\) −40.3568 −1.74805
\(534\) 0 0
\(535\) 0 0
\(536\) 3.46657 2.00143i 0.149733 0.0864485i
\(537\) 0 0
\(538\) 21.2345 0.915484
\(539\) −1.34145 + 16.4333i −0.0577805 + 0.707832i
\(540\) 0 0
\(541\) −22.5510 + 39.0594i −0.969541 + 1.67930i −0.272658 + 0.962111i \(0.587903\pi\)
−0.696884 + 0.717184i \(0.745431\pi\)
\(542\) −18.9957 + 10.9672i −0.815934 + 0.471080i
\(543\) 0 0
\(544\) −3.95097 2.28109i −0.169396 0.0978010i
\(545\) 0 0
\(546\) 0 0
\(547\) 11.1372i 0.476193i −0.971242 0.238096i \(-0.923477\pi\)
0.971242 0.238096i \(-0.0765234\pi\)
\(548\) 2.61421 4.52794i 0.111673 0.193424i
\(549\) 0 0
\(550\) 0 0
\(551\) −0.724228 + 1.25440i −0.0308532 + 0.0534393i
\(552\) 0 0
\(553\) 21.8470 + 0.890207i 0.929029 + 0.0378555i
\(554\) 9.92903i 0.421844i
\(555\) 0 0
\(556\) 16.8637 9.73628i 0.715181 0.412910i
\(557\) −13.7214 23.7662i −0.581395 1.00701i −0.995314 0.0966925i \(-0.969174\pi\)
0.413919 0.910314i \(-0.364160\pi\)
\(558\) 0 0
\(559\) 30.5630i 1.29268i
\(560\) 0 0
\(561\) 0 0
\(562\) −9.58656 5.53481i −0.404385 0.233472i
\(563\) 28.8238 16.6414i 1.21478 0.701352i 0.250981 0.967992i \(-0.419247\pi\)
0.963796 + 0.266640i \(0.0859136\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −22.6773 −0.953200
\(567\) 0 0
\(568\) 2.02720i 0.0850596i
\(569\) −24.6215 14.2152i −1.03219 0.595932i −0.114575 0.993415i \(-0.536551\pi\)
−0.917610 + 0.397482i \(0.869884\pi\)
\(570\) 0 0
\(571\) −14.0784 24.3845i −0.589162 1.02046i −0.994343 0.106221i \(-0.966125\pi\)
0.405181 0.914237i \(-0.367209\pi\)
\(572\) 9.47917 + 5.47280i 0.396344 + 0.228829i
\(573\) 0 0
\(574\) −22.9580 0.935478i −0.958249 0.0390461i
\(575\) 0 0
\(576\) 0 0
\(577\) −1.02540 1.77604i −0.0426879 0.0739377i 0.843892 0.536513i \(-0.180259\pi\)
−0.886580 + 0.462575i \(0.846925\pi\)
\(578\) −1.90675 3.30259i −0.0793103 0.137370i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.402187 + 0.210854i −0.0166855 + 0.00874771i
\(582\) 0 0
\(583\) 24.7856 + 14.3100i 1.02652 + 0.592659i
\(584\) 4.10801 + 7.11528i 0.169991 + 0.294432i
\(585\) 0 0
\(586\) −10.6735 6.16238i −0.440920 0.254565i
\(587\) 36.2336i 1.49552i 0.663968 + 0.747761i \(0.268871\pi\)
−0.663968 + 0.747761i \(0.731129\pi\)
\(588\) 0 0
\(589\) 1.24231 0.0511886
\(590\) 0 0
\(591\) 0 0
\(592\) −8.02554 + 4.63355i −0.329848 + 0.190438i
\(593\) 30.1239 + 17.3920i 1.23704 + 0.714205i 0.968488 0.249061i \(-0.0801219\pi\)
0.268551 + 0.963265i \(0.413455\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.54041i 0.226944i
\(597\) 0 0
\(598\) −13.5378 23.4481i −0.553601 0.958864i
\(599\) 31.6459 18.2708i 1.29302 0.746524i 0.313829 0.949479i \(-0.398388\pi\)
0.979188 + 0.202956i \(0.0650547\pi\)
\(600\) 0 0
\(601\) 45.5137i 1.85654i −0.371902 0.928272i \(-0.621294\pi\)
0.371902 0.928272i \(-0.378706\pi\)
\(602\) 0.708456 17.3866i 0.0288745 0.708623i
\(603\) 0 0
\(604\) 4.23984 7.34362i 0.172517 0.298807i
\(605\) 0 0
\(606\) 0 0
\(607\) −18.3836 + 31.8414i −0.746169 + 1.29240i 0.203478 + 0.979080i \(0.434776\pi\)
−0.949647 + 0.313323i \(0.898558\pi\)
\(608\) 0.567267i 0.0230057i
\(609\) 0 0
\(610\) 0 0
\(611\) 25.4033 + 14.6666i 1.02771 + 0.593348i
\(612\) 0 0
\(613\) 28.3288 16.3557i 1.14419 0.660599i 0.196726 0.980459i \(-0.436969\pi\)
0.947465 + 0.319860i \(0.103636\pi\)
\(614\) 4.03137 6.98254i 0.162693 0.281792i
\(615\) 0 0
\(616\) 5.26562 + 3.33308i 0.212158 + 0.134294i
\(617\) 20.5530 0.827435 0.413717 0.910405i \(-0.364230\pi\)
0.413717 + 0.910405i \(0.364230\pi\)
\(618\) 0 0
\(619\) −14.9593 + 8.63675i −0.601265 + 0.347140i −0.769539 0.638600i \(-0.779514\pi\)
0.168274 + 0.985740i \(0.446181\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −26.4429 −1.06027
\(623\) −14.4305 0.588006i −0.578147 0.0235580i
\(624\) 0 0
\(625\) 0 0
\(626\) −8.26650 14.3180i −0.330396 0.572262i
\(627\) 0 0
\(628\) −0.560470 + 0.970763i −0.0223652 + 0.0387377i
\(629\) −42.2782 −1.68574
\(630\) 0 0
\(631\) 32.7501 1.30376 0.651880 0.758322i \(-0.273981\pi\)
0.651880 + 0.758322i \(0.273981\pi\)
\(632\) 4.13212 7.15704i 0.164367 0.284692i
\(633\) 0 0
\(634\) 6.13038 + 10.6181i 0.243469 + 0.421700i
\(635\) 0 0
\(636\) 0 0
\(637\) 18.5025 26.7542i 0.733095 1.06004i
\(638\) −6.01432 −0.238109
\(639\) 0 0
\(640\) 0 0
\(641\) 18.9300 10.9292i 0.747688 0.431678i −0.0771698 0.997018i \(-0.524588\pi\)
0.824858 + 0.565340i \(0.191255\pi\)
\(642\) 0 0
\(643\) −4.13643 −0.163125 −0.0815624 0.996668i \(-0.525991\pi\)
−0.0815624 + 0.996668i \(0.525991\pi\)
\(644\) −7.15779 13.6529i −0.282056 0.537999i
\(645\) 0 0
\(646\) 1.29399 2.24125i 0.0509113 0.0881809i
\(647\) −26.6816 + 15.4046i −1.04896 + 0.605618i −0.922358 0.386335i \(-0.873741\pi\)
−0.126603 + 0.991953i \(0.540407\pi\)
\(648\) 0 0
\(649\) −6.84327 3.95096i −0.268622 0.155089i
\(650\) 0 0
\(651\) 0 0
\(652\) 6.71498i 0.262979i
\(653\) −3.45110 + 5.97747i −0.135052 + 0.233917i −0.925617 0.378461i \(-0.876453\pi\)
0.790565 + 0.612378i \(0.209787\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.34226 + 7.52101i −0.169537 + 0.293646i
\(657\) 0 0
\(658\) 14.1114 + 8.93235i 0.550119 + 0.348219i
\(659\) 11.0895i 0.431985i −0.976395 0.215992i \(-0.930701\pi\)
0.976395 0.215992i \(-0.0692986\pi\)
\(660\) 0 0
\(661\) 13.7077 7.91416i 0.533169 0.307825i −0.209137 0.977886i \(-0.567065\pi\)
0.742306 + 0.670061i \(0.233732\pi\)
\(662\) 17.1942 + 29.7812i 0.668270 + 1.15748i
\(663\) 0 0
\(664\) 0.171637i 0.00666079i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.8841 + 7.43865i 0.498875 + 0.288026i
\(668\) −2.42583 + 1.40055i −0.0938581 + 0.0541890i
\(669\) 0 0
\(670\) 0 0
\(671\) −18.6449 −0.719779
\(672\) 0 0
\(673\) 27.8980i 1.07539i −0.843139 0.537695i \(-0.819295\pi\)
0.843139 0.537695i \(-0.180705\pi\)
\(674\) −20.7444 11.9768i −0.799045 0.461329i
\(675\) 0 0
\(676\) −4.29721 7.44298i −0.165277 0.286269i
\(677\) 26.9749 + 15.5739i 1.03673 + 0.598555i 0.918905 0.394479i \(-0.129075\pi\)
0.117823 + 0.993035i \(0.462408\pi\)
\(678\) 0 0
\(679\) −13.3370 25.4393i −0.511828 0.976269i
\(680\) 0 0
\(681\) 0 0
\(682\) 2.57918 + 4.46727i 0.0987620 + 0.171061i
\(683\) −12.5960 21.8168i −0.481971 0.834798i 0.517815 0.855493i \(-0.326746\pi\)
−0.999786 + 0.0206948i \(0.993412\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 11.1458 14.7909i 0.425548 0.564720i
\(687\) 0 0
\(688\) −5.69581 3.28848i −0.217151 0.125372i
\(689\) −28.2319 48.8992i −1.07555 1.86291i
\(690\) 0 0
\(691\) −27.2549 15.7356i −1.03683 0.598612i −0.117894 0.993026i \(-0.537614\pi\)
−0.918933 + 0.394414i \(0.870948\pi\)
\(692\) 13.8004i 0.524611i
\(693\) 0 0
\(694\) −28.7003 −1.08945
\(695\) 0 0
\(696\) 0 0
\(697\) −34.3122 + 19.8102i −1.29967 + 0.750363i
\(698\) 3.09324 + 1.78588i 0.117081 + 0.0675966i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.19395i 0.196173i −0.995178 0.0980864i \(-0.968728\pi\)
0.995178 0.0980864i \(-0.0312721\pi\)
\(702\) 0 0
\(703\) −2.62846 4.55262i −0.0991342 0.171705i
\(704\) 2.03986 1.17771i 0.0768800 0.0443867i
\(705\) 0 0
\(706\) 12.5397i 0.471937i
\(707\) −16.2684 + 25.7009i −0.611835 + 0.966581i
\(708\) 0 0
\(709\) 17.9440 31.0800i 0.673903 1.16723i −0.302885 0.953027i \(-0.597950\pi\)
0.976788 0.214207i \(-0.0687167\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −2.72938 + 4.72742i −0.102288 + 0.177167i
\(713\) 12.7600i 0.477864i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.31980 + 1.33933i 0.0866948 + 0.0500533i
\(717\) 0 0
\(718\) 13.6940 7.90624i 0.511056 0.295058i
\(719\) −13.0548 + 22.6115i −0.486861 + 0.843268i −0.999886 0.0151058i \(-0.995191\pi\)
0.513025 + 0.858374i \(0.328525\pi\)
\(720\) 0 0
\(721\) 51.2157 + 2.08691i 1.90737 + 0.0777204i
\(722\) −18.6782 −0.695131
\(723\) 0 0
\(724\) 5.95896 3.44041i 0.221463 0.127862i
\(725\) 0 0
\(726\) 0 0
\(727\) −19.0193 −0.705386 −0.352693 0.935739i \(-0.614734\pi\)
−0.352693 + 0.935739i \(0.614734\pi\)
\(728\) −5.70878 10.8890i −0.211581 0.403574i
\(729\) 0 0
\(730\) 0 0
\(731\) −15.0026 25.9853i −0.554892 0.961101i
\(732\) 0 0
\(733\) −4.41992 + 7.65553i −0.163254 + 0.282763i −0.936034 0.351910i \(-0.885532\pi\)
0.772780 + 0.634674i \(0.218866\pi\)
\(734\) −35.6635 −1.31636
\(735\) 0 0
\(736\) −5.82648 −0.214767
\(737\) −4.71421 + 8.16524i −0.173650 + 0.300771i
\(738\) 0 0
\(739\) −8.20546 14.2123i −0.301843 0.522807i 0.674711 0.738082i \(-0.264268\pi\)
−0.976553 + 0.215276i \(0.930935\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −14.9270 28.4720i −0.547987 1.04524i
\(743\) −47.4829 −1.74198 −0.870989 0.491302i \(-0.836521\pi\)
−0.870989 + 0.491302i \(0.836521\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 19.9717 11.5306i 0.731214 0.422167i
\(747\) 0 0
\(748\) 10.7459 0.392908
\(749\) −28.3405 1.15480i −1.03554 0.0421955i
\(750\) 0 0
\(751\) 17.4048 30.1459i 0.635109 1.10004i −0.351383 0.936232i \(-0.614289\pi\)
0.986492 0.163809i \(-0.0523781\pi\)
\(752\) 5.46663 3.15616i 0.199348 0.115093i
\(753\) 0 0
\(754\) 10.2759 + 5.93279i 0.374226 + 0.216059i
\(755\) 0 0
\(756\) 0 0
\(757\) 9.68581i 0.352037i 0.984387 + 0.176018i \(0.0563218\pi\)
−0.984387 + 0.176018i \(0.943678\pi\)
\(758\) −4.10055 + 7.10236i −0.148939 + 0.257969i
\(759\) 0 0
\(760\) 0 0
\(761\) −22.2236 + 38.4924i −0.805605 + 1.39535i 0.110277 + 0.993901i \(0.464826\pi\)
−0.915882 + 0.401448i \(0.868507\pi\)
\(762\) 0 0
\(763\) 15.3163 24.1968i 0.554487 0.875982i
\(764\) 9.99228i 0.361508i
\(765\) 0 0
\(766\) −4.01207 + 2.31637i −0.144962 + 0.0836939i
\(767\) 7.79479 + 13.5010i 0.281454 + 0.487492i
\(768\) 0 0
\(769\) 41.0290i 1.47954i 0.672858 + 0.739771i \(0.265066\pi\)
−0.672858 + 0.739771i \(0.734934\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 21.7620 + 12.5643i 0.783232 + 0.452199i
\(773\) −30.3059 + 17.4971i −1.09003 + 0.629327i −0.933583 0.358360i \(-0.883336\pi\)
−0.156443 + 0.987687i \(0.550003\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.8564 −0.389723
\(777\) 0 0
\(778\) 33.5087i 1.20135i
\(779\) −4.26642 2.46322i −0.152860 0.0882540i
\(780\) 0 0
\(781\) 2.38746 + 4.13521i 0.0854301 + 0.147969i
\(782\) −23.0202 13.2907i −0.823201 0.475276i
\(783\) 0 0
\(784\) −2.99518 6.32684i −0.106971 0.225959i
\(785\) 0 0
\(786\) 0 0
\(787\) −11.1509 19.3139i −0.397485 0.688465i 0.595930 0.803037i \(-0.296784\pi\)