Properties

Label 1386.2.ba.a.989.11
Level $1386$
Weight $2$
Character 1386.989
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 989.11
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.42385 + 0.822059i) q^{5} +(2.58759 - 0.551706i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.42385 + 0.822059i) q^{5} +(2.58759 - 0.551706i) q^{7} +1.00000 q^{8} +(-1.42385 + 0.822059i) q^{10} +(2.53893 + 2.13397i) q^{11} +1.29335i q^{13} +(-0.816004 + 2.51677i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.68534 + 2.91910i) q^{17} +(-0.340140 - 0.196380i) q^{19} -1.64412i q^{20} +(-3.11754 + 1.13179i) q^{22} +(0.455476 + 0.262969i) q^{23} +(-1.14844 - 1.98915i) q^{25} +(-1.12007 - 0.646675i) q^{26} +(-1.77159 - 1.96507i) q^{28} -1.33002 q^{29} +(-2.86951 - 4.97013i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.37069 q^{34} +(4.13787 + 1.34161i) q^{35} +(1.50973 - 2.61493i) q^{37} +(0.340140 - 0.196380i) q^{38} +(1.42385 + 0.822059i) q^{40} +10.9253 q^{41} +10.5847i q^{43} +(0.578609 - 3.26576i) q^{44} +(-0.455476 + 0.262969i) q^{46} +(4.48768 + 2.59096i) q^{47} +(6.39124 - 2.85518i) q^{49} +2.29687 q^{50} +(1.12007 - 0.646675i) q^{52} +(1.43915 - 0.830895i) q^{53} +(1.86080 + 5.12560i) q^{55} +(2.58759 - 0.551706i) q^{56} +(0.665012 - 1.15183i) q^{58} +(-8.26233 + 4.77026i) q^{59} +(-3.32010 - 1.91686i) q^{61} +5.73902 q^{62} +1.00000 q^{64} +(-1.06321 + 1.84153i) q^{65} +(-6.80137 - 11.7803i) q^{67} +(1.68534 - 2.91910i) q^{68} +(-3.23080 + 2.91270i) q^{70} -1.62169i q^{71} +(-8.82651 + 5.09599i) q^{73} +(1.50973 + 2.61493i) q^{74} +0.392760i q^{76} +(7.74703 + 4.12110i) q^{77} +(7.22793 + 4.17305i) q^{79} +(-1.42385 + 0.822059i) q^{80} +(-5.46264 + 9.46156i) q^{82} +5.98532 q^{83} +5.54181i q^{85} +(-9.16665 - 5.29237i) q^{86} +(2.53893 + 2.13397i) q^{88} +(8.32280 + 4.80517i) q^{89} +(0.713549 + 3.34666i) q^{91} -0.525938i q^{92} +(-4.48768 + 2.59096i) q^{94} +(-0.322872 - 0.559231i) q^{95} +8.31783 q^{97} +(-0.722965 + 6.96257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(5\) 1.42385 + 0.822059i 0.636764 + 0.367636i 0.783367 0.621559i \(-0.213501\pi\)
−0.146603 + 0.989195i \(0.546834\pi\)
\(6\) 0 0
\(7\) 2.58759 0.551706i 0.978017 0.208525i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.42385 + 0.822059i −0.450260 + 0.259958i
\(11\) 2.53893 + 2.13397i 0.765516 + 0.643417i
\(12\) 0 0
\(13\) 1.29335i 0.358711i 0.983784 + 0.179355i \(0.0574012\pi\)
−0.983784 + 0.179355i \(0.942599\pi\)
\(14\) −0.816004 + 2.51677i −0.218086 + 0.672635i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.68534 + 2.91910i 0.408756 + 0.707986i 0.994751 0.102329i \(-0.0326294\pi\)
−0.585995 + 0.810315i \(0.699296\pi\)
\(18\) 0 0
\(19\) −0.340140 0.196380i −0.0780335 0.0450527i 0.460476 0.887672i \(-0.347679\pi\)
−0.538509 + 0.842620i \(0.681012\pi\)
\(20\) 1.64412i 0.367636i
\(21\) 0 0
\(22\) −3.11754 + 1.13179i −0.664661 + 0.241299i
\(23\) 0.455476 + 0.262969i 0.0949733 + 0.0548329i 0.546734 0.837306i \(-0.315871\pi\)
−0.451761 + 0.892139i \(0.649204\pi\)
\(24\) 0 0
\(25\) −1.14844 1.98915i −0.229687 0.397830i
\(26\) −1.12007 0.646675i −0.219665 0.126823i
\(27\) 0 0
\(28\) −1.77159 1.96507i −0.334798 0.371362i
\(29\) −1.33002 −0.246979 −0.123490 0.992346i \(-0.539409\pi\)
−0.123490 + 0.992346i \(0.539409\pi\)
\(30\) 0 0
\(31\) −2.86951 4.97013i −0.515379 0.892662i −0.999841 0.0178500i \(-0.994318\pi\)
0.484462 0.874812i \(-0.339015\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.37069 −0.578068
\(35\) 4.13787 + 1.34161i 0.699428 + 0.226773i
\(36\) 0 0
\(37\) 1.50973 2.61493i 0.248198 0.429892i −0.714828 0.699300i \(-0.753495\pi\)
0.963026 + 0.269409i \(0.0868283\pi\)
\(38\) 0.340140 0.196380i 0.0551780 0.0318570i
\(39\) 0 0
\(40\) 1.42385 + 0.822059i 0.225130 + 0.129979i
\(41\) 10.9253 1.70624 0.853120 0.521714i \(-0.174707\pi\)
0.853120 + 0.521714i \(0.174707\pi\)
\(42\) 0 0
\(43\) 10.5847i 1.61416i 0.590444 + 0.807079i \(0.298953\pi\)
−0.590444 + 0.807079i \(0.701047\pi\)
\(44\) 0.578609 3.26576i 0.0872286 0.492332i
\(45\) 0 0
\(46\) −0.455476 + 0.262969i −0.0671563 + 0.0387727i
\(47\) 4.48768 + 2.59096i 0.654595 + 0.377931i 0.790215 0.612830i \(-0.209969\pi\)
−0.135619 + 0.990761i \(0.543302\pi\)
\(48\) 0 0
\(49\) 6.39124 2.85518i 0.913034 0.407882i
\(50\) 2.29687 0.324827
\(51\) 0 0
\(52\) 1.12007 0.646675i 0.155326 0.0896777i
\(53\) 1.43915 0.830895i 0.197683 0.114132i −0.397891 0.917433i \(-0.630258\pi\)
0.595574 + 0.803300i \(0.296925\pi\)
\(54\) 0 0
\(55\) 1.86080 + 5.12560i 0.250910 + 0.691136i
\(56\) 2.58759 0.551706i 0.345781 0.0737248i
\(57\) 0 0
\(58\) 0.665012 1.15183i 0.0873203 0.151243i
\(59\) −8.26233 + 4.77026i −1.07566 + 0.621035i −0.929724 0.368258i \(-0.879954\pi\)
−0.145941 + 0.989293i \(0.546621\pi\)
\(60\) 0 0
\(61\) −3.32010 1.91686i −0.425095 0.245429i 0.272160 0.962252i \(-0.412262\pi\)
−0.697255 + 0.716823i \(0.745595\pi\)
\(62\) 5.73902 0.728856
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.06321 + 1.84153i −0.131875 + 0.228414i
\(66\) 0 0
\(67\) −6.80137 11.7803i −0.830919 1.43919i −0.897310 0.441401i \(-0.854482\pi\)
0.0663907 0.997794i \(-0.478852\pi\)
\(68\) 1.68534 2.91910i 0.204378 0.353993i
\(69\) 0 0
\(70\) −3.23080 + 2.91270i −0.386155 + 0.348134i
\(71\) 1.62169i 0.192459i −0.995359 0.0962296i \(-0.969322\pi\)
0.995359 0.0962296i \(-0.0306783\pi\)
\(72\) 0 0
\(73\) −8.82651 + 5.09599i −1.03307 + 0.596440i −0.917861 0.396901i \(-0.870085\pi\)
−0.115204 + 0.993342i \(0.536752\pi\)
\(74\) 1.50973 + 2.61493i 0.175503 + 0.303979i
\(75\) 0 0
\(76\) 0.392760i 0.0450527i
\(77\) 7.74703 + 4.12110i 0.882856 + 0.469643i
\(78\) 0 0
\(79\) 7.22793 + 4.17305i 0.813206 + 0.469505i 0.848068 0.529887i \(-0.177766\pi\)
−0.0348619 + 0.999392i \(0.511099\pi\)
\(80\) −1.42385 + 0.822059i −0.159191 + 0.0919090i
\(81\) 0 0
\(82\) −5.46264 + 9.46156i −0.603247 + 1.04485i
\(83\) 5.98532 0.656975 0.328487 0.944508i \(-0.393461\pi\)
0.328487 + 0.944508i \(0.393461\pi\)
\(84\) 0 0
\(85\) 5.54181i 0.601094i
\(86\) −9.16665 5.29237i −0.988466 0.570691i
\(87\) 0 0
\(88\) 2.53893 + 2.13397i 0.270651 + 0.227482i
\(89\) 8.32280 + 4.80517i 0.882215 + 0.509347i 0.871388 0.490594i \(-0.163220\pi\)
0.0108269 + 0.999941i \(0.496554\pi\)
\(90\) 0 0
\(91\) 0.713549 + 3.34666i 0.0748003 + 0.350825i
\(92\) 0.525938i 0.0548329i
\(93\) 0 0
\(94\) −4.48768 + 2.59096i −0.462869 + 0.267237i
\(95\) −0.322872 0.559231i −0.0331260 0.0573759i
\(96\) 0 0
\(97\) 8.31783 0.844548 0.422274 0.906468i \(-0.361232\pi\)
0.422274 + 0.906468i \(0.361232\pi\)
\(98\) −0.722965 + 6.96257i −0.0730305 + 0.703325i
\(99\) 0 0
\(100\) −1.14844 + 1.98915i −0.114844 + 0.198915i
\(101\) −2.53452 4.38992i −0.252194 0.436813i 0.711935 0.702245i \(-0.247819\pi\)
−0.964130 + 0.265432i \(0.914485\pi\)
\(102\) 0 0
\(103\) −3.64472 + 6.31283i −0.359124 + 0.622022i −0.987815 0.155634i \(-0.950258\pi\)
0.628690 + 0.777656i \(0.283591\pi\)
\(104\) 1.29335i 0.126823i
\(105\) 0 0
\(106\) 1.66179i 0.161407i
\(107\) 2.16028 3.74171i 0.208842 0.361725i −0.742508 0.669837i \(-0.766364\pi\)
0.951350 + 0.308112i \(0.0996972\pi\)
\(108\) 0 0
\(109\) −5.84618 + 3.37529i −0.559962 + 0.323294i −0.753130 0.657871i \(-0.771457\pi\)
0.193168 + 0.981166i \(0.438124\pi\)
\(110\) −5.36930 0.951302i −0.511943 0.0907030i
\(111\) 0 0
\(112\) −0.816004 + 2.51677i −0.0771051 + 0.237813i
\(113\) 18.2771i 1.71936i 0.510831 + 0.859681i \(0.329338\pi\)
−0.510831 + 0.859681i \(0.670662\pi\)
\(114\) 0 0
\(115\) 0.432353 + 0.748857i 0.0403171 + 0.0698312i
\(116\) 0.665012 + 1.15183i 0.0617448 + 0.106945i
\(117\) 0 0
\(118\) 9.54052i 0.878276i
\(119\) 5.97146 + 6.62362i 0.547403 + 0.607186i
\(120\) 0 0
\(121\) 1.89233 + 10.8360i 0.172030 + 0.985092i
\(122\) 3.32010 1.91686i 0.300588 0.173544i
\(123\) 0 0
\(124\) −2.86951 + 4.97013i −0.257689 + 0.446331i
\(125\) 11.9969i 1.07304i
\(126\) 0 0
\(127\) 9.84411i 0.873524i −0.899577 0.436762i \(-0.856125\pi\)
0.899577 0.436762i \(-0.143875\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.06321 1.84153i −0.0932497 0.161513i
\(131\) −3.20488 + 5.55101i −0.280011 + 0.484994i −0.971387 0.237501i \(-0.923672\pi\)
0.691376 + 0.722495i \(0.257005\pi\)
\(132\) 0 0
\(133\) −0.988487 0.320494i −0.0857127 0.0277903i
\(134\) 13.6027 1.17510
\(135\) 0 0
\(136\) 1.68534 + 2.91910i 0.144517 + 0.250311i
\(137\) −14.4951 + 8.36876i −1.23840 + 0.714992i −0.968767 0.247971i \(-0.920236\pi\)
−0.269634 + 0.962963i \(0.586903\pi\)
\(138\) 0 0
\(139\) 3.66143i 0.310559i −0.987871 0.155279i \(-0.950372\pi\)
0.987871 0.155279i \(-0.0496278\pi\)
\(140\) −0.907070 4.25430i −0.0766614 0.359554i
\(141\) 0 0
\(142\) 1.40442 + 0.810845i 0.117857 + 0.0680446i
\(143\) −2.75997 + 3.28373i −0.230801 + 0.274599i
\(144\) 0 0
\(145\) −1.89375 1.09336i −0.157268 0.0907984i
\(146\) 10.1920i 0.843494i
\(147\) 0 0
\(148\) −3.01946 −0.248198
\(149\) −7.35277 + 12.7354i −0.602363 + 1.04332i 0.390100 + 0.920773i \(0.372441\pi\)
−0.992462 + 0.122550i \(0.960893\pi\)
\(150\) 0 0
\(151\) 8.55083 4.93683i 0.695857 0.401753i −0.109946 0.993938i \(-0.535068\pi\)
0.805802 + 0.592184i \(0.201734\pi\)
\(152\) −0.340140 0.196380i −0.0275890 0.0159285i
\(153\) 0 0
\(154\) −7.44249 + 4.64858i −0.599733 + 0.374593i
\(155\) 9.43562i 0.757887i
\(156\) 0 0
\(157\) 4.33551 + 7.50933i 0.346012 + 0.599310i 0.985537 0.169460i \(-0.0542025\pi\)
−0.639525 + 0.768770i \(0.720869\pi\)
\(158\) −7.22793 + 4.17305i −0.575024 + 0.331990i
\(159\) 0 0
\(160\) 1.64412i 0.129979i
\(161\) 1.32367 + 0.429168i 0.104320 + 0.0338232i
\(162\) 0 0
\(163\) 6.06457 10.5041i 0.475014 0.822748i −0.524577 0.851363i \(-0.675776\pi\)
0.999591 + 0.0286150i \(0.00910968\pi\)
\(164\) −5.46264 9.46156i −0.426560 0.738824i
\(165\) 0 0
\(166\) −2.99266 + 5.18344i −0.232276 + 0.402313i
\(167\) 1.42411 0.110201 0.0551006 0.998481i \(-0.482452\pi\)
0.0551006 + 0.998481i \(0.482452\pi\)
\(168\) 0 0
\(169\) 11.3272 0.871327
\(170\) −4.79935 2.77090i −0.368093 0.212519i
\(171\) 0 0
\(172\) 9.16665 5.29237i 0.698951 0.403539i
\(173\) 2.13167 3.69216i 0.162068 0.280709i −0.773542 0.633745i \(-0.781517\pi\)
0.935610 + 0.353035i \(0.114850\pi\)
\(174\) 0 0
\(175\) −4.06911 4.51351i −0.307596 0.341189i
\(176\) −3.11754 + 1.13179i −0.234993 + 0.0853120i
\(177\) 0 0
\(178\) −8.32280 + 4.80517i −0.623820 + 0.360163i
\(179\) 1.32093 0.762640i 0.0987311 0.0570024i −0.449821 0.893118i \(-0.648512\pi\)
0.548553 + 0.836116i \(0.315179\pi\)
\(180\) 0 0
\(181\) 19.7414 1.46736 0.733682 0.679493i \(-0.237800\pi\)
0.733682 + 0.679493i \(0.237800\pi\)
\(182\) −3.25507 1.05538i −0.241282 0.0782299i
\(183\) 0 0
\(184\) 0.455476 + 0.262969i 0.0335781 + 0.0193864i
\(185\) 4.29925 2.48217i 0.316087 0.182493i
\(186\) 0 0
\(187\) −1.95031 + 11.0079i −0.142621 + 0.804975i
\(188\) 5.18193i 0.377931i
\(189\) 0 0
\(190\) 0.645744 0.0468472
\(191\) −12.9424 7.47229i −0.936478 0.540676i −0.0476233 0.998865i \(-0.515165\pi\)
−0.888854 + 0.458190i \(0.848498\pi\)
\(192\) 0 0
\(193\) 3.47593 2.00683i 0.250203 0.144455i −0.369654 0.929169i \(-0.620524\pi\)
0.619857 + 0.784715i \(0.287190\pi\)
\(194\) −4.15892 + 7.20346i −0.298593 + 0.517178i
\(195\) 0 0
\(196\) −5.66828 4.10739i −0.404877 0.293385i
\(197\) −21.4340 −1.52711 −0.763554 0.645744i \(-0.776547\pi\)
−0.763554 + 0.645744i \(0.776547\pi\)
\(198\) 0 0
\(199\) −11.7097 20.2818i −0.830079 1.43774i −0.897975 0.440047i \(-0.854962\pi\)
0.0678951 0.997692i \(-0.478372\pi\)
\(200\) −1.14844 1.98915i −0.0812068 0.140654i
\(201\) 0 0
\(202\) 5.06904 0.356656
\(203\) −3.44156 + 0.733782i −0.241550 + 0.0515014i
\(204\) 0 0
\(205\) 15.5559 + 8.98122i 1.08647 + 0.627276i
\(206\) −3.64472 6.31283i −0.253939 0.439836i
\(207\) 0 0
\(208\) −1.12007 0.646675i −0.0776632 0.0448389i
\(209\) −0.444523 1.22444i −0.0307483 0.0846966i
\(210\) 0 0
\(211\) 2.15572i 0.148406i 0.997243 + 0.0742028i \(0.0236412\pi\)
−0.997243 + 0.0742028i \(0.976359\pi\)
\(212\) −1.43915 0.830895i −0.0988414 0.0570661i
\(213\) 0 0
\(214\) 2.16028 + 3.74171i 0.147674 + 0.255778i
\(215\) −8.70128 + 15.0711i −0.593423 + 1.02784i
\(216\) 0 0
\(217\) −10.1672 11.2775i −0.690192 0.765569i
\(218\) 6.75058i 0.457207i
\(219\) 0 0
\(220\) 3.50850 4.17430i 0.236543 0.281431i
\(221\) −3.77542 + 2.17974i −0.253962 + 0.146625i
\(222\) 0 0
\(223\) 7.01103 0.469493 0.234747 0.972057i \(-0.424574\pi\)
0.234747 + 0.972057i \(0.424574\pi\)
\(224\) −1.77159 1.96507i −0.118369 0.131296i
\(225\) 0 0
\(226\) −15.8284 9.13854i −1.05289 0.607886i
\(227\) −10.0653 17.4337i −0.668060 1.15711i −0.978446 0.206503i \(-0.933792\pi\)
0.310387 0.950610i \(-0.399542\pi\)
\(228\) 0 0
\(229\) 4.19825 7.27158i 0.277428 0.480520i −0.693317 0.720633i \(-0.743851\pi\)
0.970745 + 0.240113i \(0.0771846\pi\)
\(230\) −0.864705 −0.0570170
\(231\) 0 0
\(232\) −1.33002 −0.0873203
\(233\) 6.15876 10.6673i 0.403474 0.698838i −0.590669 0.806914i \(-0.701136\pi\)
0.994143 + 0.108077i \(0.0344692\pi\)
\(234\) 0 0
\(235\) 4.25985 + 7.37828i 0.277882 + 0.481306i
\(236\) 8.26233 + 4.77026i 0.537832 + 0.310518i
\(237\) 0 0
\(238\) −8.72196 + 1.85963i −0.565360 + 0.120542i
\(239\) −6.66725 −0.431268 −0.215634 0.976474i \(-0.569182\pi\)
−0.215634 + 0.976474i \(0.569182\pi\)
\(240\) 0 0
\(241\) 4.40382 2.54255i 0.283675 0.163780i −0.351411 0.936221i \(-0.614298\pi\)
0.635086 + 0.772441i \(0.280965\pi\)
\(242\) −10.3304 3.77920i −0.664065 0.242936i
\(243\) 0 0
\(244\) 3.83372i 0.245429i
\(245\) 11.4473 + 1.18864i 0.731340 + 0.0759394i
\(246\) 0 0
\(247\) 0.253988 0.439920i 0.0161609 0.0279915i
\(248\) −2.86951 4.97013i −0.182214 0.315604i
\(249\) 0 0
\(250\) 10.3896 + 5.99846i 0.657099 + 0.379376i
\(251\) 15.5033i 0.978563i −0.872126 0.489281i \(-0.837259\pi\)
0.872126 0.489281i \(-0.162741\pi\)
\(252\) 0 0
\(253\) 0.595253 + 1.63963i 0.0374232 + 0.103083i
\(254\) 8.52525 + 4.92206i 0.534922 + 0.308837i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 11.4588 + 6.61574i 0.714780 + 0.412678i 0.812828 0.582503i \(-0.197927\pi\)
−0.0980485 + 0.995182i \(0.531260\pi\)
\(258\) 0 0
\(259\) 2.46389 7.59929i 0.153099 0.472197i
\(260\) 2.12642 0.131875
\(261\) 0 0
\(262\) −3.20488 5.55101i −0.197998 0.342942i
\(263\) 2.38841 + 4.13684i 0.147275 + 0.255088i 0.930220 0.367004i \(-0.119616\pi\)
−0.782944 + 0.622092i \(0.786283\pi\)
\(264\) 0 0
\(265\) 2.73218 0.167837
\(266\) 0.771799 0.695808i 0.0473220 0.0426627i
\(267\) 0 0
\(268\) −6.80137 + 11.7803i −0.415460 + 0.719597i
\(269\) −9.14107 + 5.27760i −0.557341 + 0.321781i −0.752077 0.659075i \(-0.770948\pi\)
0.194737 + 0.980856i \(0.437615\pi\)
\(270\) 0 0
\(271\) −21.4275 12.3712i −1.30163 0.751496i −0.320946 0.947098i \(-0.604001\pi\)
−0.980683 + 0.195602i \(0.937334\pi\)
\(272\) −3.37069 −0.204378
\(273\) 0 0
\(274\) 16.7375i 1.01115i
\(275\) 1.32899 7.50105i 0.0801412 0.452330i
\(276\) 0 0
\(277\) 10.2245 5.90312i 0.614331 0.354684i −0.160328 0.987064i \(-0.551255\pi\)
0.774659 + 0.632380i \(0.217922\pi\)
\(278\) 3.17089 + 1.83072i 0.190178 + 0.109799i
\(279\) 0 0
\(280\) 4.13787 + 1.34161i 0.247285 + 0.0801763i
\(281\) −16.1488 −0.963359 −0.481680 0.876347i \(-0.659973\pi\)
−0.481680 + 0.876347i \(0.659973\pi\)
\(282\) 0 0
\(283\) −11.4555 + 6.61385i −0.680960 + 0.393153i −0.800217 0.599711i \(-0.795282\pi\)
0.119257 + 0.992863i \(0.461949\pi\)
\(284\) −1.40442 + 0.810845i −0.0833373 + 0.0481148i
\(285\) 0 0
\(286\) −1.46380 4.03207i −0.0865565 0.238421i
\(287\) 28.2701 6.02754i 1.66873 0.355794i
\(288\) 0 0
\(289\) 2.81923 4.88306i 0.165837 0.287239i
\(290\) 1.89375 1.09336i 0.111205 0.0642042i
\(291\) 0 0
\(292\) 8.82651 + 5.09599i 0.516533 + 0.298220i
\(293\) −14.9415 −0.872894 −0.436447 0.899730i \(-0.643763\pi\)
−0.436447 + 0.899730i \(0.643763\pi\)
\(294\) 0 0
\(295\) −15.6857 −0.913260
\(296\) 1.50973 2.61493i 0.0877513 0.151990i
\(297\) 0 0
\(298\) −7.35277 12.7354i −0.425935 0.737741i
\(299\) −0.340111 + 0.589090i −0.0196691 + 0.0340680i
\(300\) 0 0
\(301\) 5.83966 + 27.3890i 0.336593 + 1.57867i
\(302\) 9.87365i 0.568165i
\(303\) 0 0
\(304\) 0.340140 0.196380i 0.0195084 0.0112632i
\(305\) −3.15154 5.45863i −0.180457 0.312561i
\(306\) 0 0
\(307\) 32.9465i 1.88036i −0.340683 0.940178i \(-0.610658\pi\)
0.340683 0.940178i \(-0.389342\pi\)
\(308\) −0.304539 8.76968i −0.0173527 0.499699i
\(309\) 0 0
\(310\) 8.17149 + 4.71781i 0.464109 + 0.267954i
\(311\) 16.8425 9.72400i 0.955049 0.551398i 0.0604031 0.998174i \(-0.480761\pi\)
0.894646 + 0.446776i \(0.147428\pi\)
\(312\) 0 0
\(313\) −4.28905 + 7.42885i −0.242431 + 0.419904i −0.961406 0.275132i \(-0.911278\pi\)
0.718975 + 0.695036i \(0.244612\pi\)
\(314\) −8.67102 −0.489334
\(315\) 0 0
\(316\) 8.34610i 0.469505i
\(317\) 1.74470 + 1.00730i 0.0979923 + 0.0565759i 0.548195 0.836350i \(-0.315315\pi\)
−0.450203 + 0.892926i \(0.648648\pi\)
\(318\) 0 0
\(319\) −3.37684 2.83823i −0.189067 0.158911i
\(320\) 1.42385 + 0.822059i 0.0795955 + 0.0459545i
\(321\) 0 0
\(322\) −1.03350 + 0.931745i −0.0575949 + 0.0519241i
\(323\) 1.32387i 0.0736622i
\(324\) 0 0
\(325\) 2.57267 1.48533i 0.142706 0.0823914i
\(326\) 6.06457 + 10.5041i 0.335886 + 0.581771i
\(327\) 0 0
\(328\) 10.9253 0.603247
\(329\) 13.0417 + 4.22847i 0.719013 + 0.233123i
\(330\) 0 0
\(331\) 9.13936 15.8298i 0.502345 0.870086i −0.497652 0.867377i \(-0.665804\pi\)
0.999996 0.00270934i \(-0.000862412\pi\)
\(332\) −2.99266 5.18344i −0.164244 0.284478i
\(333\) 0 0
\(334\) −0.712056 + 1.23332i −0.0389620 + 0.0674841i
\(335\) 22.3645i 1.22190i
\(336\) 0 0
\(337\) 1.04529i 0.0569406i −0.999595 0.0284703i \(-0.990936\pi\)
0.999595 0.0284703i \(-0.00906361\pi\)
\(338\) −5.66362 + 9.80968i −0.308060 + 0.533576i
\(339\) 0 0
\(340\) 4.79935 2.77090i 0.260281 0.150273i
\(341\) 3.32065 18.7423i 0.179823 1.01495i
\(342\) 0 0
\(343\) 14.9627 10.9141i 0.807909 0.589307i
\(344\) 10.5847i 0.570691i
\(345\) 0 0
\(346\) 2.13167 + 3.69216i 0.114599 + 0.198492i
\(347\) −12.0831 20.9286i −0.648657 1.12351i −0.983444 0.181212i \(-0.941998\pi\)
0.334787 0.942294i \(-0.391336\pi\)
\(348\) 0 0
\(349\) 30.8063i 1.64902i 0.565846 + 0.824511i \(0.308550\pi\)
−0.565846 + 0.824511i \(0.691450\pi\)
\(350\) 5.94337 1.26720i 0.317686 0.0677346i
\(351\) 0 0
\(352\) 0.578609 3.26576i 0.0308400 0.174066i
\(353\) 8.94782 5.16602i 0.476244 0.274960i −0.242606 0.970125i \(-0.578002\pi\)
0.718850 + 0.695165i \(0.244669\pi\)
\(354\) 0 0
\(355\) 1.33313 2.30904i 0.0707549 0.122551i
\(356\) 9.61034i 0.509347i
\(357\) 0 0
\(358\) 1.52528i 0.0806136i
\(359\) −10.1350 + 17.5542i −0.534902 + 0.926478i 0.464266 + 0.885696i \(0.346318\pi\)
−0.999168 + 0.0407819i \(0.987015\pi\)
\(360\) 0 0
\(361\) −9.42287 16.3209i −0.495941 0.858994i
\(362\) −9.87068 + 17.0965i −0.518792 + 0.898573i
\(363\) 0 0
\(364\) 2.54152 2.29128i 0.133212 0.120096i
\(365\) −16.7568 −0.877092
\(366\) 0 0
\(367\) −4.97708 8.62055i −0.259801 0.449989i 0.706387 0.707826i \(-0.250324\pi\)
−0.966189 + 0.257836i \(0.916990\pi\)
\(368\) −0.455476 + 0.262969i −0.0237433 + 0.0137082i
\(369\) 0 0
\(370\) 4.96435i 0.258084i
\(371\) 3.26553 2.94401i 0.169538 0.152845i
\(372\) 0 0
\(373\) 10.3112 + 5.95317i 0.533894 + 0.308244i 0.742601 0.669735i \(-0.233592\pi\)
−0.208707 + 0.977978i \(0.566925\pi\)
\(374\) −8.55794 7.19295i −0.442520 0.371939i
\(375\) 0 0
\(376\) 4.48768 + 2.59096i 0.231434 + 0.133619i
\(377\) 1.72019i 0.0885941i
\(378\) 0 0
\(379\) −18.3862 −0.944437 −0.472218 0.881482i \(-0.656547\pi\)
−0.472218 + 0.881482i \(0.656547\pi\)
\(380\) −0.322872 + 0.559231i −0.0165630 + 0.0286879i
\(381\) 0 0
\(382\) 12.9424 7.47229i 0.662190 0.382315i
\(383\) 33.5005 + 19.3415i 1.71180 + 0.988306i 0.932141 + 0.362096i \(0.117939\pi\)
0.779655 + 0.626209i \(0.215394\pi\)
\(384\) 0 0
\(385\) 7.64281 + 12.2363i 0.389514 + 0.623622i
\(386\) 4.01366i 0.204290i
\(387\) 0 0
\(388\) −4.15892 7.20346i −0.211137 0.365700i
\(389\) −27.7566 + 16.0253i −1.40731 + 0.812513i −0.995128 0.0985872i \(-0.968568\pi\)
−0.412185 + 0.911100i \(0.635234\pi\)
\(390\) 0 0
\(391\) 1.77277i 0.0896530i
\(392\) 6.39124 2.85518i 0.322806 0.144208i
\(393\) 0 0
\(394\) 10.7170 18.5624i 0.539914 0.935159i
\(395\) 6.86099 + 11.8836i 0.345214 + 0.597928i
\(396\) 0 0
\(397\) 16.4657 28.5193i 0.826387 1.43134i −0.0744670 0.997223i \(-0.523726\pi\)
0.900854 0.434121i \(-0.142941\pi\)
\(398\) 23.4194 1.17391
\(399\) 0 0
\(400\) 2.29687 0.114844
\(401\) −8.94782 5.16602i −0.446833 0.257979i 0.259659 0.965700i \(-0.416390\pi\)
−0.706492 + 0.707721i \(0.749723\pi\)
\(402\) 0 0
\(403\) 6.42812 3.71128i 0.320208 0.184872i
\(404\) −2.53452 + 4.38992i −0.126097 + 0.218407i
\(405\) 0 0
\(406\) 1.08530 3.34736i 0.0538627 0.166127i
\(407\) 9.41328 3.41740i 0.466599 0.169394i
\(408\) 0 0
\(409\) 13.7011 7.91033i 0.677476 0.391141i −0.121428 0.992600i \(-0.538747\pi\)
0.798903 + 0.601459i \(0.205414\pi\)
\(410\) −15.5559 + 8.98122i −0.768253 + 0.443551i
\(411\) 0 0
\(412\) 7.28943 0.359124
\(413\) −18.7478 + 16.9019i −0.922516 + 0.831686i
\(414\) 0 0
\(415\) 8.52220 + 4.92029i 0.418338 + 0.241528i
\(416\) 1.12007 0.646675i 0.0549162 0.0317059i
\(417\) 0 0
\(418\) 1.28266 + 0.227254i 0.0627370 + 0.0111154i
\(419\) 32.3275i 1.57930i −0.613556 0.789651i \(-0.710261\pi\)
0.613556 0.789651i \(-0.289739\pi\)
\(420\) 0 0
\(421\) −10.8176 −0.527217 −0.263609 0.964630i \(-0.584913\pi\)
−0.263609 + 0.964630i \(0.584913\pi\)
\(422\) −1.86691 1.07786i −0.0908795 0.0524693i
\(423\) 0 0
\(424\) 1.43915 0.830895i 0.0698914 0.0403518i
\(425\) 3.87102 6.70481i 0.187772 0.325231i
\(426\) 0 0
\(427\) −9.64859 3.12833i −0.466928 0.151390i
\(428\) −4.32056 −0.208842
\(429\) 0 0
\(430\) −8.70128 15.0711i −0.419613 0.726791i
\(431\) −17.9409 31.0745i −0.864183 1.49681i −0.867856 0.496815i \(-0.834503\pi\)
0.00367384 0.999993i \(-0.498831\pi\)
\(432\) 0 0
\(433\) 23.8240 1.14491 0.572454 0.819937i \(-0.305991\pi\)
0.572454 + 0.819937i \(0.305991\pi\)
\(434\) 14.8502 3.16625i 0.712833 0.151985i
\(435\) 0 0
\(436\) 5.84618 + 3.37529i 0.279981 + 0.161647i
\(437\) −0.103284 0.178893i −0.00494074 0.00855760i
\(438\) 0 0
\(439\) −18.4555 10.6553i −0.880834 0.508550i −0.00990091 0.999951i \(-0.503152\pi\)
−0.870933 + 0.491401i \(0.836485\pi\)
\(440\) 1.86080 + 5.12560i 0.0887102 + 0.244354i
\(441\) 0 0
\(442\) 4.35948i 0.207359i
\(443\) −27.1827 15.6939i −1.29149 0.745642i −0.312571 0.949894i \(-0.601190\pi\)
−0.978918 + 0.204252i \(0.934524\pi\)
\(444\) 0 0
\(445\) 7.90027 + 13.6837i 0.374509 + 0.648668i
\(446\) −3.50552 + 6.07173i −0.165991 + 0.287505i
\(447\) 0 0
\(448\) 2.58759 0.551706i 0.122252 0.0260657i
\(449\) 20.7653i 0.979973i −0.871730 0.489987i \(-0.837002\pi\)
0.871730 0.489987i \(-0.162998\pi\)
\(450\) 0 0
\(451\) 27.7385 + 23.3142i 1.30616 + 1.09782i
\(452\) 15.8284 9.13854i 0.744506 0.429841i
\(453\) 0 0
\(454\) 20.1307 0.944779
\(455\) −1.73517 + 5.35172i −0.0813459 + 0.250892i
\(456\) 0 0
\(457\) 3.43048 + 1.98059i 0.160471 + 0.0926479i 0.578085 0.815977i \(-0.303800\pi\)
−0.417614 + 0.908625i \(0.637134\pi\)
\(458\) 4.19825 + 7.27158i 0.196171 + 0.339779i
\(459\) 0 0
\(460\) 0.432353 0.748857i 0.0201585 0.0349156i
\(461\) 4.46540 0.207975 0.103987 0.994579i \(-0.466840\pi\)
0.103987 + 0.994579i \(0.466840\pi\)
\(462\) 0 0
\(463\) −33.8033 −1.57097 −0.785486 0.618879i \(-0.787587\pi\)
−0.785486 + 0.618879i \(0.787587\pi\)
\(464\) 0.665012 1.15183i 0.0308724 0.0534726i
\(465\) 0 0
\(466\) 6.15876 + 10.6673i 0.285299 + 0.494153i
\(467\) 2.67151 + 1.54240i 0.123623 + 0.0713735i 0.560536 0.828130i \(-0.310595\pi\)
−0.436914 + 0.899504i \(0.643928\pi\)
\(468\) 0 0
\(469\) −24.0984 26.7303i −1.11276 1.23429i
\(470\) −8.51970 −0.392984
\(471\) 0 0
\(472\) −8.26233 + 4.77026i −0.380305 + 0.219569i
\(473\) −22.5875 + 26.8739i −1.03858 + 1.23566i
\(474\) 0 0
\(475\) 0.902120i 0.0413921i
\(476\) 2.75049 8.48325i 0.126069 0.388829i
\(477\) 0 0
\(478\) 3.33362 5.77400i 0.152476 0.264097i
\(479\) 7.85049 + 13.5974i 0.358698 + 0.621283i 0.987744 0.156085i \(-0.0498875\pi\)
−0.629046 + 0.777368i \(0.716554\pi\)
\(480\) 0 0
\(481\) 3.38202 + 1.95261i 0.154207 + 0.0890313i
\(482\) 5.08510i 0.231620i
\(483\) 0 0
\(484\) 8.43809 7.05681i 0.383550 0.320764i
\(485\) 11.8433 + 6.83775i 0.537778 + 0.310486i
\(486\) 0 0
\(487\) −14.0970 24.4167i −0.638795 1.10643i −0.985698 0.168524i \(-0.946100\pi\)
0.346903 0.937901i \(-0.387233\pi\)
\(488\) −3.32010 1.91686i −0.150294 0.0867722i
\(489\) 0 0
\(490\) −6.75303 + 9.31932i −0.305071 + 0.421004i
\(491\) −14.6613 −0.661655 −0.330828 0.943691i \(-0.607328\pi\)
−0.330828 + 0.943691i \(0.607328\pi\)
\(492\) 0 0
\(493\) −2.24155 3.88247i −0.100954 0.174858i
\(494\) 0.253988 + 0.439920i 0.0114275 + 0.0197930i
\(495\) 0 0
\(496\) 5.73902 0.257689
\(497\) −0.894696 4.19627i −0.0401326 0.188228i
\(498\) 0 0
\(499\) −19.5576 + 33.8747i −0.875517 + 1.51644i −0.0193055 + 0.999814i \(0.506146\pi\)
−0.856211 + 0.516626i \(0.827188\pi\)
\(500\) −10.3896 + 5.99846i −0.464639 + 0.268259i
\(501\) 0 0
\(502\) 13.4263 + 7.75167i 0.599245 + 0.345974i
\(503\) 39.2496 1.75005 0.875027 0.484074i \(-0.160844\pi\)
0.875027 + 0.484074i \(0.160844\pi\)
\(504\) 0 0
\(505\) 8.33410i 0.370863i
\(506\) −1.71759 0.304313i −0.0763562 0.0135283i
\(507\) 0 0
\(508\) −8.52525 + 4.92206i −0.378247 + 0.218381i
\(509\) −3.76989 2.17655i −0.167098 0.0964738i 0.414119 0.910223i \(-0.364090\pi\)
−0.581217 + 0.813749i \(0.697423\pi\)
\(510\) 0 0
\(511\) −20.0279 + 18.0560i −0.885982 + 0.798749i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −11.4588 + 6.61574i −0.505426 + 0.291808i
\(515\) −10.3790 + 5.99234i −0.457355 + 0.264054i
\(516\) 0 0
\(517\) 5.86486 + 16.1549i 0.257936 + 0.710490i
\(518\) 5.34923 + 5.93344i 0.235032 + 0.260700i
\(519\) 0 0
\(520\) −1.06321 + 1.84153i −0.0466249 + 0.0807566i
\(521\) −17.8760 + 10.3207i −0.783161 + 0.452158i −0.837549 0.546362i \(-0.816012\pi\)
0.0543883 + 0.998520i \(0.482679\pi\)
\(522\) 0 0
\(523\) −23.0273 13.2948i −1.00691 0.581343i −0.0966280 0.995321i \(-0.530806\pi\)
−0.910287 + 0.413978i \(0.864139\pi\)
\(524\) 6.40975 0.280011
\(525\) 0 0
\(526\) −4.77681 −0.208279
\(527\) 9.67221 16.7528i 0.421328 0.729762i
\(528\) 0 0
\(529\) −11.3617 19.6790i −0.493987 0.855610i
\(530\) −1.36609 + 2.36614i −0.0593392 + 0.102778i
\(531\) 0 0
\(532\) 0.216688 + 1.01630i 0.00939462 + 0.0440623i
\(533\) 14.1302i 0.612047i
\(534\) 0 0
\(535\) 6.15182 3.55175i 0.265966 0.153556i
\(536\) −6.80137 11.7803i −0.293774 0.508832i
\(537\) 0 0
\(538\) 10.5552i 0.455067i
\(539\) 22.3198 + 6.38963i 0.961381 + 0.275221i
\(540\) 0 0
\(541\) −22.7295 13.1229i −0.977218 0.564197i −0.0757888 0.997124i \(-0.524147\pi\)
−0.901429 + 0.432927i \(0.857481\pi\)
\(542\) 21.4275 12.3712i 0.920391 0.531388i
\(543\) 0 0
\(544\) 1.68534 2.91910i 0.0722585 0.125155i
\(545\) −11.0988 −0.475419
\(546\) 0 0
\(547\) 37.4556i 1.60149i 0.599008 + 0.800743i \(0.295562\pi\)
−0.599008 + 0.800743i \(0.704438\pi\)
\(548\) 14.4951 + 8.36876i 0.619201 + 0.357496i
\(549\) 0 0
\(550\) 5.83160 + 4.90146i 0.248660 + 0.208999i
\(551\) 0.452394 + 0.261190i 0.0192727 + 0.0111271i
\(552\) 0 0
\(553\) 21.0052 + 6.81045i 0.893233 + 0.289610i
\(554\) 11.8062i 0.501599i
\(555\) 0 0
\(556\) −3.17089 + 1.83072i −0.134476 + 0.0776397i
\(557\) −6.80146 11.7805i −0.288187 0.499155i 0.685190 0.728365i \(-0.259719\pi\)
−0.973377 + 0.229210i \(0.926386\pi\)
\(558\) 0 0
\(559\) −13.6898 −0.579016
\(560\) −3.23080 + 2.91270i −0.136526 + 0.123084i
\(561\) 0 0
\(562\) 8.07442 13.9853i 0.340599 0.589935i
\(563\) 6.85190 + 11.8678i 0.288773 + 0.500170i 0.973517 0.228614i \(-0.0734193\pi\)
−0.684744 + 0.728784i \(0.740086\pi\)
\(564\) 0 0
\(565\) −15.0248 + 26.0238i −0.632100 + 1.09483i
\(566\) 13.2277i 0.556002i
\(567\) 0 0
\(568\) 1.62169i 0.0680446i
\(569\) −16.1147 + 27.9115i −0.675565 + 1.17011i 0.300738 + 0.953707i \(0.402767\pi\)
−0.976303 + 0.216406i \(0.930566\pi\)
\(570\) 0 0
\(571\) −26.5520 + 15.3298i −1.11117 + 0.641532i −0.939131 0.343558i \(-0.888368\pi\)
−0.172035 + 0.985091i \(0.555034\pi\)
\(572\) 4.22378 + 0.748344i 0.176605 + 0.0312898i
\(573\) 0 0
\(574\) −8.91506 + 27.4964i −0.372107 + 1.14768i
\(575\) 1.20801i 0.0503777i
\(576\) 0 0
\(577\) 17.7360 + 30.7197i 0.738360 + 1.27888i 0.953233 + 0.302235i \(0.0977329\pi\)
−0.214873 + 0.976642i \(0.568934\pi\)
\(578\) 2.81923 + 4.88306i 0.117265 + 0.203108i
\(579\) 0 0
\(580\) 2.18672i 0.0907984i
\(581\) 15.4876 3.30214i 0.642532 0.136996i
\(582\) 0 0
\(583\) 5.42702 + 0.961527i 0.224764 + 0.0398224i
\(584\) −8.82651 + 5.09599i −0.365244 + 0.210874i
\(585\) 0 0
\(586\) 7.47077 12.9398i 0.308615 0.534536i
\(587\) 17.6758i 0.729557i 0.931094 + 0.364778i \(0.118855\pi\)
−0.931094 + 0.364778i \(0.881145\pi\)
\(588\) 0 0
\(589\) 2.25406i 0.0928768i
\(590\) 7.84287 13.5843i 0.322886 0.559255i
\(591\) 0 0
\(592\) 1.50973 + 2.61493i 0.0620495 + 0.107473i
\(593\) −1.53418 + 2.65729i −0.0630014 + 0.109122i −0.895806 0.444446i \(-0.853401\pi\)
0.832804 + 0.553568i \(0.186734\pi\)
\(594\) 0 0
\(595\) 3.05745 + 14.3399i 0.125343 + 0.587880i
\(596\) 14.7055 0.602363
\(597\) 0 0
\(598\) −0.340111 0.589090i −0.0139082 0.0240897i
\(599\) 1.84155 1.06322i 0.0752436 0.0434419i −0.461906 0.886929i \(-0.652834\pi\)
0.537150 + 0.843487i \(0.319501\pi\)
\(600\) 0 0
\(601\) 3.74930i 0.152937i −0.997072 0.0764686i \(-0.975635\pi\)
0.997072 0.0764686i \(-0.0243645\pi\)
\(602\) −26.6394 8.63718i −1.08574 0.352025i
\(603\) 0 0
\(604\) −8.55083 4.93683i −0.347928 0.200877i
\(605\) −6.21345 + 16.9844i −0.252613 + 0.690516i
\(606\) 0 0
\(607\) 16.2817 + 9.40025i 0.660855 + 0.381545i 0.792602 0.609739i \(-0.208726\pi\)
−0.131748 + 0.991283i \(0.542059\pi\)
\(608\) 0.392760i 0.0159285i
\(609\) 0 0
\(610\) 6.30309 0.255205
\(611\) −3.35102 + 5.80414i −0.135568 + 0.234810i
\(612\) 0 0
\(613\) −17.7160 + 10.2283i −0.715542 + 0.413118i −0.813110 0.582110i \(-0.802227\pi\)
0.0975676 + 0.995229i \(0.468894\pi\)
\(614\) 28.5325 + 16.4733i 1.15148 + 0.664806i
\(615\) 0 0
\(616\) 7.74703 + 4.12110i 0.312137 + 0.166044i
\(617\) 29.3351i 1.18099i 0.807043 + 0.590493i \(0.201067\pi\)
−0.807043 + 0.590493i \(0.798933\pi\)
\(618\) 0 0
\(619\) −6.16332 10.6752i −0.247725 0.429072i 0.715169 0.698951i \(-0.246350\pi\)
−0.962894 + 0.269879i \(0.913016\pi\)
\(620\) −8.17149 + 4.71781i −0.328175 + 0.189472i
\(621\) 0 0
\(622\) 19.4480i 0.779794i
\(623\) 24.1870 + 7.84207i 0.969033 + 0.314186i
\(624\) 0 0
\(625\) 4.12000 7.13605i 0.164800 0.285442i
\(626\) −4.28905 7.42885i −0.171425 0.296917i
\(627\) 0 0
\(628\) 4.33551 7.50933i 0.173006 0.299655i
\(629\) 10.1777 0.405810
\(630\) 0 0
\(631\) −14.7738 −0.588136 −0.294068 0.955784i \(-0.595009\pi\)
−0.294068 + 0.955784i \(0.595009\pi\)
\(632\) 7.22793 + 4.17305i 0.287512 + 0.165995i
\(633\) 0 0
\(634\) −1.74470 + 1.00730i −0.0692910 + 0.0400052i
\(635\) 8.09244 14.0165i 0.321139 0.556229i
\(636\) 0 0
\(637\) 3.69274 + 8.26611i 0.146312 + 0.327515i
\(638\) 4.14640 1.50531i 0.164158 0.0595958i
\(639\) 0 0
\(640\) −1.42385 + 0.822059i −0.0562826 + 0.0324947i
\(641\) −17.1907 + 9.92508i −0.678994 + 0.392017i −0.799476 0.600698i \(-0.794889\pi\)
0.120482 + 0.992716i \(0.461556\pi\)
\(642\) 0 0
\(643\) 2.60504 0.102733 0.0513664 0.998680i \(-0.483642\pi\)
0.0513664 + 0.998680i \(0.483642\pi\)
\(644\) −0.290163 1.36091i −0.0114340 0.0536275i
\(645\) 0 0
\(646\) 1.14651 + 0.661936i 0.0451087 + 0.0260435i
\(647\) 11.2756 6.50996i 0.443289 0.255933i −0.261703 0.965149i \(-0.584284\pi\)
0.704992 + 0.709216i \(0.250951\pi\)
\(648\) 0 0
\(649\) −31.1571 5.52023i −1.22302 0.216688i
\(650\) 2.97066i 0.116519i
\(651\) 0 0
\(652\) −12.1291 −0.475014
\(653\) −34.0245 19.6441i −1.33148 0.768732i −0.345956 0.938251i \(-0.612446\pi\)
−0.985527 + 0.169518i \(0.945779\pi\)
\(654\) 0 0
\(655\) −9.12652 + 5.26920i −0.356602 + 0.205885i
\(656\) −5.46264 + 9.46156i −0.213280 + 0.369412i
\(657\) 0 0
\(658\) −10.1828 + 9.18023i −0.396968 + 0.357883i
\(659\) 21.8725 0.852033 0.426017 0.904715i \(-0.359917\pi\)
0.426017 + 0.904715i \(0.359917\pi\)
\(660\) 0 0
\(661\) −14.6974 25.4567i −0.571665 0.990152i −0.996395 0.0848322i \(-0.972965\pi\)
0.424731 0.905320i \(-0.360369\pi\)
\(662\) 9.13936 + 15.8298i 0.355211 + 0.615244i
\(663\) 0 0
\(664\) 5.98532 0.232276
\(665\) −1.14399 1.26893i −0.0443621 0.0492070i
\(666\) 0 0
\(667\) −0.605794 0.349755i −0.0234564 0.0135426i
\(668\) −0.712056 1.23332i −0.0275503 0.0477185i
\(669\) 0 0
\(670\) 19.3682 + 11.1823i 0.748260 + 0.432008i
\(671\) −4.33897 11.9518i −0.167504 0.461393i
\(672\) 0 0
\(673\) 18.0026i 0.693949i 0.937875 + 0.346975i \(0.112791\pi\)
−0.937875 + 0.346975i \(0.887209\pi\)
\(674\) 0.905249 + 0.522645i 0.0348689 + 0.0201316i
\(675\) 0 0
\(676\) −5.66362 9.80968i −0.217832 0.377295i
\(677\) 17.7248 30.7003i 0.681219 1.17991i −0.293390 0.955993i \(-0.594783\pi\)
0.974609 0.223914i \(-0.0718834\pi\)
\(678\) 0 0
\(679\) 21.5231 4.58900i 0.825982 0.176110i
\(680\) 5.54181i 0.212519i
\(681\) 0 0
\(682\) 14.5710 + 12.2469i 0.557951 + 0.468958i
\(683\) 4.85527 2.80319i 0.185782 0.107261i −0.404225 0.914660i \(-0.632459\pi\)
0.590006 + 0.807399i \(0.299125\pi\)
\(684\) 0 0
\(685\) −27.5185 −1.05143
\(686\) 1.97055 + 18.4151i 0.0752360 + 0.703093i
\(687\) 0 0
\(688\) −9.16665 5.29237i −0.349475 0.201770i
\(689\) 1.07464 + 1.86133i 0.0409405 + 0.0709110i
\(690\) 0 0
\(691\) −16.7993 + 29.0972i −0.639074 + 1.10691i 0.346562 + 0.938027i \(0.387349\pi\)
−0.985636 + 0.168882i \(0.945984\pi\)
\(692\) −4.26333 −0.162068
\(693\) 0 0
\(694\) 24.1663 0.917339
\(695\) 3.00992 5.21333i 0.114173 0.197753i
\(696\) 0 0
\(697\) 18.4128 + 31.8920i 0.697436 + 1.20799i
\(698\) −26.6790 15.4031i −1.00982 0.583017i
\(699\) 0 0
\(700\) −1.87426 + 5.78071i −0.0708403 + 0.218490i
\(701\) 43.4126 1.63967 0.819835 0.572600i \(-0.194065\pi\)
0.819835 + 0.572600i \(0.194065\pi\)
\(702\) 0 0
\(703\) −1.02704 + 0.592962i −0.0387355 + 0.0223640i
\(704\) 2.53893 + 2.13397i 0.0956895 + 0.0804271i
\(705\) 0 0
\(706\) 10.3320i 0.388852i
\(707\) −8.98024 9.96100i −0.337737 0.374622i
\(708\) 0 0
\(709\) −1.34801 + 2.33482i −0.0506255 + 0.0876859i −0.890228 0.455516i \(-0.849455\pi\)
0.839602 + 0.543202i \(0.182788\pi\)
\(710\) 1.33313 + 2.30904i 0.0500313 + 0.0866567i
\(711\) 0 0
\(712\) 8.32280 + 4.80517i 0.311910 + 0.180081i
\(713\) 3.01837i 0.113039i
\(714\) 0 0
\(715\) −6.62920 + 2.40667i −0.247918 + 0.0900042i
\(716\) −1.32093 0.762640i −0.0493655 0.0285012i
\(717\) 0 0
\(718\) −10.1350 17.5542i −0.378233 0.655119i
\(719\) 6.61138 + 3.81708i 0.246563 + 0.142353i 0.618189 0.786029i \(-0.287866\pi\)
−0.371627 + 0.928382i \(0.621200\pi\)
\(720\) 0 0
\(721\) −5.94820 + 18.3458i −0.221523 + 0.683234i
\(722\) 18.8457 0.701366
\(723\) 0 0
\(724\) −9.87068 17.0965i −0.366841 0.635387i
\(725\) 1.52745 + 2.64562i 0.0567280 + 0.0982558i
\(726\) 0 0
\(727\) 16.8096 0.623435 0.311717 0.950175i \(-0.399096\pi\)
0.311717 + 0.950175i \(0.399096\pi\)
\(728\) 0.713549 + 3.34666i 0.0264459 + 0.124035i
\(729\) 0 0
\(730\) 8.37841 14.5118i 0.310099 0.537107i
\(731\) −30.8979 + 17.8389i −1.14280 + 0.659796i
\(732\) 0 0
\(733\) 2.28623 + 1.31996i 0.0844440 + 0.0487537i 0.541627 0.840619i \(-0.317808\pi\)
−0.457183 + 0.889372i \(0.651142\pi\)
\(734\) 9.95416 0.367415
\(735\) 0 0
\(736\) 0.525938i 0.0193864i
\(737\) 7.87066 44.4233i 0.289920 1.63635i
\(738\) 0 0
\(739\) −2.14077 + 1.23598i −0.0787496 + 0.0454661i −0.538858 0.842397i \(-0.681144\pi\)
0.460108 + 0.887863i \(0.347811\pi\)
\(740\) −4.29925 2.48217i −0.158044 0.0912465i
\(741\) 0 0
\(742\) 0.916820 + 4.30003i 0.0336575 + 0.157859i
\(743\) 9.82643 0.360497 0.180248 0.983621i \(-0.442310\pi\)
0.180248 + 0.983621i \(0.442310\pi\)
\(744\) 0 0
\(745\) −20.9385 + 12.0888i −0.767126 + 0.442901i
\(746\) −10.3112 + 5.95317i −0.377520 + 0.217961i
\(747\) 0 0
\(748\) 10.5082 3.81492i 0.384220 0.139487i
\(749\) 3.52559 10.8739i 0.128822 0.397322i
\(750\) 0 0
\(751\) −5.78977 + 10.0282i −0.211272 + 0.365934i −0.952113 0.305747i \(-0.901094\pi\)
0.740841 + 0.671680i \(0.234427\pi\)
\(752\) −4.48768 + 2.59096i −0.163649 + 0.0944827i
\(753\) 0 0
\(754\) 1.48973 + 0.860093i 0.0542526 + 0.0313227i
\(755\) 16.2335 0.590796
\(756\) 0 0
\(757\) 25.5191 0.927507 0.463753 0.885964i \(-0.346502\pi\)
0.463753 + 0.885964i \(0.346502\pi\)
\(758\) 9.19311 15.9229i 0.333909 0.578347i
\(759\) 0 0
\(760\) −0.322872 0.559231i −0.0117118 0.0202854i
\(761\) 5.09089 8.81767i 0.184544 0.319640i −0.758878 0.651232i \(-0.774252\pi\)
0.943423 + 0.331592i \(0.107586\pi\)
\(762\) 0 0
\(763\) −13.2653 + 11.9592i −0.480237 + 0.432954i
\(764\) 14.9446i 0.540676i
\(765\) 0 0
\(766\) −33.5005 + 19.3415i −1.21042 + 0.698838i
\(767\) −6.16962 10.6861i −0.222772 0.385852i
\(768\) 0 0
\(769\) 22.7648i 0.820921i 0.911878 + 0.410461i \(0.134632\pi\)
−0.911878 + 0.410461i \(0.865368\pi\)
\(770\) −14.4184 + 0.500698i −0.519603 + 0.0180439i
\(771\) 0 0
\(772\) −3.47593 2.00683i −0.125102 0.0722274i
\(773\) 1.09140 0.630122i 0.0392551 0.0226639i −0.480244 0.877135i \(-0.659452\pi\)
0.519499 + 0.854471i \(0.326119\pi\)
\(774\) 0 0
\(775\) −6.59090 + 11.4158i −0.236752 + 0.410067i
\(776\) 8.31783 0.298593
\(777\) 0 0
\(778\) 32.0505i 1.14907i
\(779\) −3.71612 2.14551i −0.133144 0.0768707i
\(780\) 0 0
\(781\) 3.46064 4.11736i 0.123831 0.147331i
\(782\) −1.53527 0.886387i −0.0549010 0.0316971i
\(783\) 0 0
\(784\) −0.722965 + 6.96257i −0.0258202 + 0.248663i
\(785\) 14.2562i 0.508825i
\(786\) 0 0
\(787\) 39.6470 22.8902i 1.41326 0.815948i 0.417568 0.908646i \(-0.362882\pi\)
0.995694 + 0.0926980i \(0.0295491\pi\)
\(788\) 10.7170 + 18.5624i 0.381777 + 0.661257i
\(789\) 0 0
\(790\) −13.7220 −0.488206
\(791\)