Properties

Label 3150.2.bp.g.899.8
Level 3150
Weight 2
Character 3150.899
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 899.8
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.g.1349.8

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

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

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 0.774935 0.632041i \(-0.217782\pi\)
−0.159896 + 0.987134i \(0.551116\pi\)
\(12\) 0 0
\(13\) 4.64698 1.28884 0.644420 0.764672i \(-0.277099\pi\)
0.644420 + 0.764672i \(0.277099\pi\)
\(14\) −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 \(-0.146722\pi\)
0.0626158 + 0.998038i \(0.480056\pi\)
\(18\) 0 0
\(19\) −0.491268 + 0.283634i −0.112705 + 0.0650700i −0.555293 0.831655i \(-0.687394\pi\)
0.442588 + 0.896725i \(0.354060\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.35542i 0.502178i
\(23\) 2.91324 + 5.04588i 0.607453 + 1.05214i 0.991659 + 0.128891i \(0.0411419\pi\)
−0.384206 + 0.923247i \(0.625525\pi\)
\(24\) 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 \(0.0761893\pi\)
−0.971491 + 0.237077i \(0.923811\pi\)
\(30\) 0 0
\(31\) −1.89659 1.09500i −0.340638 0.196667i 0.319916 0.947446i \(-0.396345\pi\)
−0.660554 + 0.750778i \(0.729679\pi\)
\(32\) −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 \(-0.942326\pi\)
−0.335760 + 0.941948i \(0.608993\pi\)
\(38\) 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 \(-0.514382\pi\)
0.842558 + 0.538606i \(0.181049\pi\)
\(48\) 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 0.0599168 + 0.998203i \(0.480916\pi\)
−0.894428 + 0.447212i \(0.852417\pi\)
\(54\) 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 −0.954312 0.298812i \(-0.903410\pi\)
0.735935 + 0.677053i \(0.236743\pi\)
\(60\) 0 0
\(61\) −6.85523 + 3.95787i −0.877722 + 0.506753i −0.869907 0.493216i \(-0.835821\pi\)
−0.00781543 + 0.999969i \(0.502488\pi\)
\(62\) 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 \(-0.254705\pi\)
−0.273068 + 0.961995i \(0.588039\pi\)
\(68\) −3.95097 + 2.28109i −0.479125 + 0.276623i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.02720i 0.240585i −0.992738 0.120292i \(-0.961617\pi\)
0.992738 0.120292i \(-0.0383832\pi\)
\(72\) 0 0
\(73\) 4.10801 7.11528i 0.480806 0.832780i −0.518952 0.854804i \(-0.673678\pi\)
0.999757 + 0.0220235i \(0.00701086\pi\)
\(74\) 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 0.534297 0.845297i \(-0.320576\pi\)
−0.999197 + 0.0400666i \(0.987243\pi\)
\(80\) 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 0.973646 0.228065i \(-0.0732397\pi\)
−0.684333 + 0.729170i \(0.739906\pi\)
\(90\) 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 \(-0.685811\pi\)
−0.551151 + 0.834406i \(0.685811\pi\)
\(98\) −2.99518 + 6.32684i −0.302559 + 0.639107i
\(99\) 0 0
\(100\) 0 0
\(101\) −5.74827 + 9.95630i −0.571975 + 0.990689i 0.424388 + 0.905480i \(0.360489\pi\)
−0.996363 + 0.0852090i \(0.972844\pi\)
\(102\) 0 0
\(103\) 9.68690 + 16.7782i 0.954478 + 1.65320i 0.735558 + 0.677462i \(0.236920\pi\)
0.218920 + 0.975743i \(0.429747\pi\)
\(104\) 4.64698 0.455674
\(105\) 0 0
\(106\) 12.1507 1.18018
\(107\) −5.36029 9.28430i −0.518199 0.897547i −0.999776 0.0211436i \(-0.993269\pi\)
0.481577 0.876404i \(-0.340064\pi\)
\(108\) 0 0
\(109\) 5.41186 9.37362i 0.518363 0.897830i −0.481410 0.876496i \(-0.659875\pi\)
0.999772 0.0213347i \(-0.00679157\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.64356 + 0.107718i −0.249793 + 0.0101784i
\(113\) 18.4343 1.73415 0.867076 0.498176i \(-0.165997\pi\)
0.867076 + 0.498176i \(0.165997\pi\)
\(114\) 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 0.988745 + 0.149608i \(0.0478012\pi\)
−0.364808 + 0.931083i \(0.618866\pi\)
\(132\) 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 \(-0.905032\pi\)
0.732475 + 0.680794i \(0.238365\pi\)
\(138\) 0 0
\(139\) 19.4726i 1.65164i −0.563933 0.825820i \(-0.690712\pi\)
0.563933 0.825820i \(-0.309288\pi\)
\(140\) 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 −0.683493 0.729957i \(-0.739540\pi\)
0.290414 + 0.956901i \(0.406207\pi\)
\(150\) 0 0
\(151\) 4.23984 7.34362i 0.345033 0.597615i −0.640327 0.768103i \(-0.721201\pi\)
0.985360 + 0.170488i \(0.0545343\pi\)
\(152\) −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 \(-0.819090\pi\)
0.887524 + 0.460762i \(0.152424\pi\)
\(158\) −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 \(-0.581962\pi\)
0.710147 + 0.704053i \(0.248628\pi\)
\(164\) −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 \(-0.842456\pi\)
−0.0286558 + 0.999589i \(0.509123\pi\)
\(174\) 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 0.410794 0.911728i \(-0.365252\pi\)
−0.584183 + 0.811622i \(0.698585\pi\)
\(180\) 0 0
\(181\) 6.88082i 0.511447i −0.966750 0.255724i \(-0.917686\pi\)
0.966750 0.255724i \(-0.0823137\pi\)
\(182\) −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 −0.153110 0.988209i \(-0.548929\pi\)
0.779260 + 0.626701i \(0.215595\pi\)
\(192\) 0 0
\(193\) 21.7620 + 12.5643i 1.56646 + 0.904398i 0.996577 + 0.0826753i \(0.0263464\pi\)
0.569887 + 0.821723i \(0.306987\pi\)
\(194\) 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 \(-0.246263\pi\)
0.715359 + 0.698757i \(0.246263\pi\)
\(198\) 0 0
\(199\) 10.3028 + 5.94834i 0.730348 + 0.421667i 0.818550 0.574436i \(-0.194779\pi\)
−0.0882014 + 0.996103i \(0.528112\pi\)
\(200\) 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 \(-0.0865763\pi\)
0.963239 + 0.268646i \(0.0865763\pi\)
\(224\) 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 \(-0.355574\pi\)
−0.559241 + 0.829005i \(0.688907\pi\)
\(228\) 0 0
\(229\) 14.0269 8.09841i 0.926920 0.535158i 0.0410842 0.999156i \(-0.486919\pi\)
0.885836 + 0.463998i \(0.153585\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.55339i 0.167639i
\(233\) −4.00569 6.93805i −0.262421 0.454527i 0.704464 0.709740i \(-0.251188\pi\)
−0.966885 + 0.255213i \(0.917854\pi\)
\(234\) 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 \(-0.831384\pi\)
0.862947 0.505294i \(-0.168616\pi\)
\(240\) 0 0
\(241\) −3.54491 2.04665i −0.228348 0.131837i 0.381462 0.924385i \(-0.375421\pi\)
−0.609809 + 0.792548i \(0.708754\pi\)
\(242\) −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 \(-0.885472\pi\)
−0.163067 + 0.986615i \(0.552139\pi\)
\(258\) 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 \(-0.797772\pi\)
0.916370 + 0.400333i \(0.131105\pi\)
\(264\) 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 −0.336410 0.941716i \(-0.609213\pi\)
0.983755 0.179518i \(-0.0574539\pi\)
\(270\) 0 0
\(271\) −18.9957 + 10.9672i −1.15390 + 0.666207i −0.949836 0.312749i \(-0.898750\pi\)
−0.204069 + 0.978956i \(0.565417\pi\)
\(272\) 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 \(-0.236917\pi\)
−0.218912 + 0.975745i \(0.570251\pi\)
\(278\) −16.8637 + 9.73628i −1.01142 + 0.583943i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.0696i 0.660358i 0.943918 + 0.330179i \(0.107109\pi\)
−0.943918 + 0.330179i \(0.892891\pi\)
\(282\) 0 0
\(283\) 11.3387 19.6392i 0.674014 1.16743i −0.302742 0.953072i \(-0.597902\pi\)
0.976756 0.214354i \(-0.0687646\pi\)
\(284\) 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 \(-0.573900\pi\)
−0.230082 + 0.973171i \(0.573900\pi\)
\(308\) 0.253721 + 6.22670i 0.0144571 + 0.354799i
\(309\) 0 0
\(310\) 0 0
\(311\) −13.2215 + 22.9003i −0.749721 + 1.29855i 0.198236 + 0.980154i \(0.436479\pi\)
−0.947956 + 0.318400i \(0.896854\pi\)
\(312\) 0 0
\(313\) −8.26650 14.3180i −0.467250 0.809301i 0.532050 0.846713i \(-0.321422\pi\)
−0.999300 + 0.0374122i \(0.988089\pi\)
\(314\) −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 \(-0.0547773\pi\)
−0.640913 + 0.767614i \(0.721444\pi\)
\(318\) 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 −0.755598 0.655036i \(-0.772654\pi\)
−0.189479 0.981885i \(-0.560680\pi\)
\(332\) 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 −0.167013 0.985955i \(-0.553412\pi\)
0.937368 0.348340i \(-0.113254\pi\)
\(348\) 0 0
\(349\) 3.57176i 0.191192i −0.995420 0.0955960i \(-0.969524\pi\)
0.995420 0.0955960i \(-0.0304757\pi\)
\(350\) 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 \(-0.225033\pi\)
−0.182337 + 0.983236i \(0.558366\pi\)
\(354\) 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 −0.0930190 0.995664i \(-0.529652\pi\)
0.815761 + 0.578389i \(0.196318\pi\)
\(360\) 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 0.148867 0.988857i \(-0.452437\pi\)
0.781942 0.623351i \(-0.214229\pi\)
\(368\) 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 \(-0.870321\pi\)
−0.115939 + 0.993256i \(0.536988\pi\)
\(374\) 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 \(-0.628903\pi\)
0.598989 + 0.800757i \(0.295569\pi\)
\(384\) 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 −0.471860 0.881673i \(-0.656417\pi\)
−0.999482 + 0.0321938i \(0.989751\pi\)
\(390\) 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 \(-0.0124368\pi\)
−0.533447 + 0.845834i \(0.679103\pi\)
\(398\) 11.8967i 0.596327i
\(399\) 0 0
\(400\) 0 0
\(401\) 12.1377 7.00770i 0.606128 0.349948i −0.165321 0.986240i \(-0.552866\pi\)
0.771448 + 0.636292i \(0.219533\pi\)
\(402\) 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 −0.105474 0.994422i \(-0.533636\pi\)
−0.913932 + 0.405868i \(0.866969\pi\)
\(410\) 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 −0.325456 0.945557i \(-0.605518\pi\)
−0.981605 + 0.190925i \(0.938851\pi\)
\(432\) 0 0
\(433\) −5.21564 −0.250648 −0.125324 0.992116i \(-0.539997\pi\)
−0.125324 + 0.992116i \(0.539997\pi\)
\(434\) 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 −0.271828 0.962346i \(-0.587628\pi\)
0.697502 + 0.716583i \(0.254295\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 21.2004i 1.00840i
\(443\) −20.7828 35.9968i −0.987419 1.71026i −0.630651 0.776067i \(-0.717212\pi\)
−0.356768 0.934193i \(-0.616121\pi\)
\(444\) 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 \(-0.810335\pi\)
0.827672 0.561212i \(-0.189665\pi\)
\(450\) 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 \(-0.811379\pi\)
0.0689182 + 0.997622i \(0.478045\pi\)
\(458\) −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 \(-0.466614\pi\)
0.913613 + 0.406585i \(0.133280\pi\)
\(468\) 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 0.457304 + 0.889311i \(0.348815\pi\)
−0.998817 + 0.0486188i \(0.984518\pi\)
\(480\) 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 \(-0.258985\pi\)
−0.285979 + 0.958236i \(0.592319\pi\)
\(488\) −6.85523 + 3.95787i −0.310322 + 0.179164i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.25910i 0.101952i 0.998700 + 0.0509758i \(0.0162331\pi\)
−0.998700 + 0.0509758i \(0.983767\pi\)
\(492\) 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 0.925028 + 0.379900i \(0.124042\pi\)
−0.133511 + 0.991047i \(0.542625\pi\)
\(500\) 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 0.888138 0.459577i \(-0.151999\pi\)
−0.842074 + 0.539362i \(0.818666\pi\)
\(510\) 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 −0.952652 0.304062i \(-0.901657\pi\)
0.739652 + 0.672990i \(0.234990\pi\)
\(522\) 0 0
\(523\) −0.695001 1.20378i −0.0303903 0.0526375i 0.850430 0.526088i \(-0.176342\pi\)
−0.880821 + 0.473450i \(0.843008\pi\)
\(524\) −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 −0.696884 0.717184i \(-0.745431\pi\)
−0.272658 0.962111i \(-0.587903\pi\)
\(542\) 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 −0.413919 0.910314i \(-0.635840\pi\)
0.995314 0.0966925i \(-0.0308263\pi\)
\(558\) 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 \(-0.580753\pi\)
−0.963796 + 0.266640i \(0.914086\pi\)
\(564\) 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 −0.917610 0.397482i \(-0.869884\pi\)
−0.114575 + 0.993415i \(0.536551\pi\)
\(570\) 0 0
\(571\) −14.0784 + 24.3845i −0.589162 + 1.02046i 0.405181 + 0.914237i \(0.367209\pi\)
−0.994343 + 0.106221i \(0.966125\pi\)
\(572\) −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 \(-0.819741\pi\)
0.886580 + 0.462575i \(0.153075\pi\)
\(578\) 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 \(-0.919878\pi\)
−0.268551 + 0.963265i \(0.586545\pi\)
\(594\) 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 0.979188 0.202956i \(-0.0650547\pi\)
0.313829 + 0.949479i \(0.398388\pi\)
\(600\) 0 0
\(601\) 45.5137i 1.85654i 0.371902 + 0.928272i \(0.378706\pi\)
−0.371902 + 0.928272i \(0.621294\pi\)
\(602\) −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 0.949647 + 0.313323i \(0.101442\pi\)
−0.203478 + 0.979080i \(0.565224\pi\)
\(608\) 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 \(-0.563031\pi\)
−0.947465 + 0.319860i \(0.896364\pi\)
\(614\) 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 \(-0.635770\pi\)
−0.413717 + 0.910405i \(0.635770\pi\)
\(618\) 0 0
\(619\) −14.9593 8.63675i −0.601265 0.347140i 0.168274 0.985740i \(-0.446181\pi\)
−0.769539 + 0.638600i \(0.779514\pi\)
\(620\) 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 0.824858 0.565340i \(-0.191255\pi\)
−0.0771698 + 0.997018i \(0.524588\pi\)
\(642\) 0 0
\(643\) 4.13643 0.163125 0.0815624 0.996668i \(-0.474009\pi\)
0.0815624 + 0.996668i \(0.474009\pi\)
\(644\) −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 \(-0.126259\pi\)
0.126603 + 0.991953i \(0.459593\pi\)
\(648\) 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 \(-0.123547\pi\)
−0.790565 + 0.612378i \(0.790213\pi\)
\(654\) 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 \(0.0692986\pi\)
−0.976395 + 0.215992i \(0.930701\pi\)
\(660\) 0 0
\(661\) 13.7077 + 7.91416i 0.533169 + 0.307825i 0.742306 0.670061i \(-0.233732\pi\)
−0.209137 + 0.977886i \(0.567065\pi\)
\(662\) −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 \(-0.870925\pi\)
−0.117823 + 0.993035i \(0.537592\pi\)
\(678\) 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 \(-0.673254\pi\)
0.999786 + 0.0206948i \(0.00658782\pi\)
\(684\) 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 −0.918933 0.394414i \(-0.870948\pi\)
−0.117894 + 0.993026i \(0.537614\pi\)
\(692\) 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 \(0.0312721\pi\)
−0.995178 + 0.0980864i \(0.968728\pi\)
\(702\) 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 0.976788 + 0.214207i \(0.0687167\pi\)
−0.302885 + 0.953027i \(0.597950\pi\)
\(710\) 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 0.513025 0.858374i \(-0.328525\pi\)
−0.999886 + 0.0151058i \(0.995191\pi\)
\(720\) 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 \(-0.385266\pi\)
0.352693 + 0.935739i \(0.385266\pi\)
\(728\) 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 \(-0.114468\pi\)
−0.772780 + 0.634674i \(0.781134\pi\)
\(734\) −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 −0.976553 0.215276i \(-0.930935\pi\)
0.674711 + 0.738082i \(0.264268\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 14.9270 28.4720i 0.547987 1.04524i
\(743\) 47.4829 1.74198 0.870989 0.491302i \(-0.163479\pi\)
0.870989 + 0.491302i \(0.163479\pi\)
\(744\) 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 0.986492 + 0.163809i \(0.0523781\pi\)
−0.351383 + 0.936232i \(0.614289\pi\)
\(752\) −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 −0.915882 0.401448i \(-0.868507\pi\)
0.110277 0.993901i \(-0.464826\pi\)
\(762\) 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 \(-0.734934\pi\)
0.672858 0.739771i \(-0.265066\pi\)
\(770\) 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 \(-0.116664\pi\)
0.156443 + 0.987687i \(0.449997\pi\)
\(774\) 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 &m