Properties

Label 1386.2.ba.a.989.6
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 989.6
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.42385 - 0.822059i) q^{5} +(-2.58759 + 0.551706i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.42385 - 0.822059i) q^{5} +(-2.58759 + 0.551706i) q^{7} +1.00000 q^{8} +(1.42385 - 0.822059i) q^{10} +(0.578609 + 3.26576i) q^{11} -1.29335i q^{13} +(0.816004 - 2.51677i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.68534 + 2.91910i) q^{17} +(0.340140 + 0.196380i) q^{19} +1.64412i q^{20} +(-3.11754 - 1.13179i) q^{22} +(-0.455476 - 0.262969i) q^{23} +(-1.14844 - 1.98915i) q^{25} +(1.12007 + 0.646675i) q^{26} +(1.77159 + 1.96507i) q^{28} -1.33002 q^{29} +(-2.86951 - 4.97013i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.37069 q^{34} +(4.13787 + 1.34161i) q^{35} +(1.50973 - 2.61493i) q^{37} +(-0.340140 + 0.196380i) q^{38} +(-1.42385 - 0.822059i) q^{40} +10.9253 q^{41} -10.5847i q^{43} +(2.53893 - 2.13397i) q^{44} +(0.455476 - 0.262969i) q^{46} +(-4.48768 - 2.59096i) q^{47} +(6.39124 - 2.85518i) q^{49} +2.29687 q^{50} +(-1.12007 + 0.646675i) q^{52} +(-1.43915 + 0.830895i) q^{53} +(1.86080 - 5.12560i) q^{55} +(-2.58759 + 0.551706i) q^{56} +(0.665012 - 1.15183i) q^{58} +(8.26233 - 4.77026i) q^{59} +(3.32010 + 1.91686i) q^{61} +5.73902 q^{62} +1.00000 q^{64} +(-1.06321 + 1.84153i) q^{65} +(-6.80137 - 11.7803i) q^{67} +(1.68534 - 2.91910i) q^{68} +(-3.23080 + 2.91270i) q^{70} +1.62169i q^{71} +(8.82651 - 5.09599i) q^{73} +(1.50973 + 2.61493i) q^{74} -0.392760i q^{76} +(-3.29894 - 8.13123i) q^{77} +(-7.22793 - 4.17305i) q^{79} +(1.42385 - 0.822059i) q^{80} +(-5.46264 + 9.46156i) q^{82} +5.98532 q^{83} -5.54181i q^{85} +(9.16665 + 5.29237i) q^{86} +(0.578609 + 3.26576i) q^{88} +(-8.32280 - 4.80517i) q^{89} +(0.713549 + 3.34666i) q^{91} +0.525938i q^{92} +(4.48768 - 2.59096i) q^{94} +(-0.322872 - 0.559231i) q^{95} +8.31783 q^{97} +(-0.722965 + 6.96257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

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 0.146603 0.989195i \(-0.453166\pi\)
−0.783367 + 0.621559i \(0.786499\pi\)
\(6\) 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
\(11\) 0.578609 + 3.26576i 0.174457 + 0.984665i
\(12\) 0 0
\(13\) 1.29335i 0.358711i −0.983784 0.179355i \(-0.942599\pi\)
0.983784 0.179355i \(-0.0574012\pi\)
\(14\) 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 0.538509 0.842620i \(-0.318988\pi\)
−0.460476 + 0.887672i \(0.652321\pi\)
\(20\) 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 0.451761 0.892139i \(-0.350796\pi\)
−0.546734 + 0.837306i \(0.684129\pi\)
\(24\) 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 \(-0.701047\pi\)
0.590444 0.807079i \(-0.298953\pi\)
\(44\) 2.53893 2.13397i 0.382758 0.321708i
\(45\) 0 0
\(46\) 0.455476 0.262969i 0.0671563 0.0387727i
\(47\) −4.48768 2.59096i −0.654595 0.377931i 0.135619 0.990761i \(-0.456698\pi\)
−0.790215 + 0.612830i \(0.790031\pi\)
\(48\) 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 −0.595574 0.803300i \(-0.703075\pi\)
0.397891 + 0.917433i \(0.369742\pi\)
\(54\) 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 0.145941 0.989293i \(-0.453379\pi\)
0.929724 + 0.368258i \(0.120046\pi\)
\(60\) 0 0
\(61\) 3.32010 + 1.91686i 0.425095 + 0.245429i 0.697255 0.716823i \(-0.254405\pi\)
−0.272160 + 0.962252i \(0.587738\pi\)
\(62\) 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 \(0.0306783\pi\)
−0.995359 + 0.0962296i \(0.969322\pi\)
\(72\) 0 0
\(73\) 8.82651 5.09599i 1.03307 0.596440i 0.115204 0.993342i \(-0.463248\pi\)
0.917861 + 0.396901i \(0.129915\pi\)
\(74\) 1.50973 + 2.61493i 0.175503 + 0.303979i
\(75\) 0 0
\(76\) 0.392760i 0.0450527i
\(77\) −3.29894 8.13123i −0.375949 0.926640i
\(78\) 0 0
\(79\) −7.22793 4.17305i −0.813206 0.469505i 0.0348619 0.999392i \(-0.488901\pi\)
−0.848068 + 0.529887i \(0.822234\pi\)
\(80\) 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
\(88\) 0.578609 + 3.26576i 0.0616799 + 0.348132i
\(89\) −8.32280 4.80517i −0.882215 0.509347i −0.0108269 0.999941i \(-0.503446\pi\)
−0.871388 + 0.490594i \(0.836780\pi\)
\(90\) 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 −0.193168 0.981166i \(-0.561876\pi\)
0.753130 + 0.657871i \(0.228543\pi\)
\(110\) 3.50850 + 4.17430i 0.334523 + 0.398004i
\(111\) 0 0
\(112\) 0.816004 2.51677i 0.0771051 0.237813i
\(113\) 18.2771i 1.71936i −0.510831 0.859681i \(-0.670662\pi\)
0.510831 0.859681i \(-0.329338\pi\)
\(114\) 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
\(121\) −10.3304 + 3.77920i −0.939129 + 0.343564i
\(122\) −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 \(0.143875\pi\)
−0.899577 + 0.436762i \(0.856125\pi\)
\(128\) −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 0.269634 0.962963i \(-0.413097\pi\)
0.968767 + 0.247971i \(0.0797639\pi\)
\(138\) 0 0
\(139\) 3.66143i 0.310559i 0.987871 + 0.155279i \(0.0496278\pi\)
−0.987871 + 0.155279i \(0.950372\pi\)
\(140\) −0.907070 4.25430i −0.0766614 0.359554i
\(141\) 0 0
\(142\) −1.40442 0.810845i −0.117857 0.0680446i
\(143\) 4.22378 0.748344i 0.353210 0.0625797i
\(144\) 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 −0.805802 0.592184i \(-0.798266\pi\)
0.109946 + 0.993938i \(0.464932\pi\)
\(152\) 0.340140 + 0.196380i 0.0275890 + 0.0159285i
\(153\) 0 0
\(154\) 8.69133 + 1.20865i 0.700367 + 0.0973957i
\(155\) 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 −0.548553 0.836116i \(-0.684821\pi\)
0.449821 + 0.893118i \(0.351488\pi\)
\(180\) 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
\(187\) −8.55794 + 7.19295i −0.625818 + 0.526001i
\(188\) 5.18193i 0.377931i
\(189\) 0 0
\(190\) 0.645744 0.0468472
\(191\) 12.9424 + 7.47229i 0.936478 + 0.540676i 0.888854 0.458190i \(-0.151502\pi\)
0.0476233 + 0.998865i \(0.484835\pi\)
\(192\) 0 0
\(193\) −3.47593 + 2.00683i −0.250203 + 0.144455i −0.619857 0.784715i \(-0.712810\pi\)
0.369654 + 0.929169i \(0.379476\pi\)
\(194\) −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 \(-0.976359\pi\)
0.997243 0.0742028i \(-0.0236412\pi\)
\(212\) 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
\(220\) −5.36930 + 0.951302i −0.361998 + 0.0641367i
\(221\) 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 −0.635086 0.772441i \(-0.719035\pi\)
0.351411 + 0.936221i \(0.385702\pi\)
\(242\) 1.89233 10.8360i 0.121644 0.696565i
\(243\) 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 \(0.162741\pi\)
−0.872126 + 0.489281i \(0.837259\pi\)
\(252\) 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 0.0980485 0.995182i \(-0.468740\pi\)
−0.812828 + 0.582503i \(0.802073\pi\)
\(258\) 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 −0.194737 0.980856i \(-0.562385\pi\)
0.752077 + 0.659075i \(0.229052\pi\)
\(270\) 0 0
\(271\) 21.4275 + 12.3712i 1.30163 + 0.751496i 0.980683 0.195602i \(-0.0626660\pi\)
0.320946 + 0.947098i \(0.395999\pi\)
\(272\) −3.37069 −0.204378
\(273\) 0 0
\(274\) 16.7375i 1.01115i
\(275\) 5.83160 4.90146i 0.351659 0.295569i
\(276\) 0 0
\(277\) −10.2245 + 5.90312i −0.614331 + 0.354684i −0.774659 0.632380i \(-0.782078\pi\)
0.160328 + 0.987064i \(0.448745\pi\)
\(278\) −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 −0.119257 0.992863i \(-0.538051\pi\)
0.800217 + 0.599711i \(0.204718\pi\)
\(284\) 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 \(0.389342\pi\)
−0.340683 + 0.940178i \(0.610658\pi\)
\(308\) −5.39238 + 6.92259i −0.307260 + 0.394451i
\(309\) 0 0
\(310\) −8.17149 4.71781i −0.464109 0.267954i
\(311\) −16.8425 + 9.72400i −0.955049 + 0.551398i −0.894646 0.446776i \(-0.852572\pi\)
−0.0604031 + 0.998174i \(0.519239\pi\)
\(312\) 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 0.450203 0.892926i \(-0.351352\pi\)
−0.548195 + 0.836350i \(0.684685\pi\)
\(318\) 0 0
\(319\) −0.769563 4.34354i −0.0430873 0.243192i
\(320\) −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 \(0.00906361\pi\)
−0.999595 + 0.0284703i \(0.990936\pi\)
\(338\) −5.66362 + 9.80968i −0.308060 + 0.533576i
\(339\) 0 0
\(340\) −4.79935 + 2.77090i −0.260281 + 0.150273i
\(341\) 14.5710 12.2469i 0.789062 0.663207i
\(342\) 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 \(-0.691450\pi\)
0.565846 0.824511i \(-0.308550\pi\)
\(350\) −5.94337 + 1.26720i −0.317686 + 0.0677346i
\(351\) 0 0
\(352\) 2.53893 2.13397i 0.135325 0.113741i
\(353\) −8.94782 + 5.16602i −0.476244 + 0.274960i −0.718850 0.695165i \(-0.755331\pi\)
0.242606 + 0.970125i \(0.421998\pi\)
\(354\) 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 0.208707 0.977978i \(-0.433075\pi\)
−0.742601 + 0.669735i \(0.766408\pi\)
\(374\) −1.95031 11.0079i −0.100848 0.569203i
\(375\) 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 \(-0.882061\pi\)
−0.779655 0.626209i \(-0.784606\pi\)
\(384\) 0 0
\(385\) −1.98716 + 14.2896i −0.101275 + 0.728264i
\(386\) 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 0.412185 0.911100i \(-0.364766\pi\)
0.995128 + 0.0985872i \(0.0314323\pi\)
\(390\) 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 0.706492 0.707721i \(-0.250277\pi\)
−0.259659 + 0.965700i \(0.583610\pi\)
\(402\) 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 −0.798903 0.601459i \(-0.794586\pi\)
0.121428 + 0.992600i \(0.461253\pi\)
\(410\) 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
\(418\) −0.838139 0.997190i −0.0409947 0.0487742i
\(419\) 32.3275i 1.57930i 0.613556 + 0.789651i \(0.289739\pi\)
−0.613556 + 0.789651i \(0.710261\pi\)
\(420\) 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 0.870933 0.491401i \(-0.163515\pi\)
0.00990091 + 0.999951i \(0.496848\pi\)
\(440\) 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 0.978918 0.204252i \(-0.0654763\pi\)
0.312571 + 0.949894i \(0.398810\pi\)
\(444\) 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 \(0.162998\pi\)
−0.871730 + 0.489987i \(0.837002\pi\)
\(450\) 0 0
\(451\) 6.32146 + 35.6794i 0.297666 + 1.68008i
\(452\) −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 0.417614 0.908625i \(-0.362866\pi\)
−0.578085 + 0.815977i \(0.696200\pi\)
\(458\) 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 0.436914 0.899504i \(-0.356072\pi\)
−0.560536 + 0.828130i \(0.689405\pi\)
\(468\) 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
\(473\) 34.5673 6.12442i 1.58940 0.281601i
\(474\) 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
\(506\) 1.12234 + 1.33532i 0.0498940 + 0.0593623i
\(507\) 0 0
\(508\) 8.52525 4.92206i 0.378247 0.218381i
\(509\) 3.76989 + 2.17655i 0.167098 + 0.0964738i 0.581217 0.813749i \(-0.302577\pi\)
−0.414119 + 0.910223i \(0.635910\pi\)
\(510\) 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 −0.0543883 0.998520i \(-0.517321\pi\)
0.837549 + 0.546362i \(0.183988\pi\)
\(522\) 0 0
\(523\) 23.0273 + 13.2948i 1.00691 + 0.581343i 0.910287 0.413978i \(-0.135861\pi\)
0.0966280 + 0.995321i \(0.469194\pi\)
\(524\) 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
\(539\) 13.0224 + 19.2203i 0.560913 + 0.827875i
\(540\) 0 0
\(541\) 22.7295 + 13.1229i 0.977218 + 0.564197i 0.901429 0.432927i \(-0.142519\pi\)
0.0757888 + 0.997124i \(0.475853\pi\)
\(542\) −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 \(-0.704438\pi\)
0.599008 0.800743i \(-0.295562\pi\)
\(548\) −14.4951 8.36876i −0.619201 0.357496i
\(549\) 0 0
\(550\) 1.32899 + 7.50105i 0.0566684 + 0.319846i
\(551\) −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 0.172035 0.985091i \(-0.444966\pi\)
0.939131 + 0.343558i \(0.111632\pi\)
\(572\) −2.75997 3.28373i −0.115400 0.137299i
\(573\) 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
\(583\) −3.54621 4.21917i −0.146869 0.174740i
\(584\) 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 \(-0.881145\pi\)
0.931094 0.364778i \(-0.118855\pi\)
\(588\) 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 −0.537150 0.843487i \(-0.680499\pi\)
0.461906 + 0.886929i \(0.347166\pi\)
\(600\) 0 0
\(601\) 3.74930i 0.152937i 0.997072 + 0.0764686i \(0.0243645\pi\)
−0.997072 + 0.0764686i \(0.975635\pi\)
\(602\) −26.6394 8.63718i −1.08574 0.352025i
\(603\) 0 0
\(604\) 8.55083 + 4.93683i 0.347928 + 0.200877i
\(605\) 17.8157 + 3.11121i 0.724311 + 0.126489i
\(606\) 0 0
\(607\) −16.2817 9.40025i −0.660855 0.381545i 0.131748 0.991283i \(-0.457941\pi\)
−0.792602 + 0.609739i \(0.791274\pi\)
\(608\) 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 −0.0975676 0.995229i \(-0.531106\pi\)
0.813110 + 0.582110i \(0.197773\pi\)
\(614\) −28.5325 16.4733i −1.15148 0.664806i
\(615\) 0 0
\(616\) −3.29894 8.13123i −0.132918 0.327617i
\(617\) 29.3351i 1.18099i −0.807043 0.590493i \(-0.798933\pi\)
0.807043 0.590493i \(-0.201067\pi\)
\(618\) 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 −0.120482 0.992716i \(-0.538444\pi\)
0.799476 + 0.600698i \(0.205111\pi\)
\(642\) 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 −0.704992 0.709216i \(-0.749049\pi\)
0.261703 + 0.965149i \(0.415716\pi\)
\(648\) 0 0
\(649\) 20.3592 + 24.2227i 0.799169 + 0.950825i
\(650\) 2.97066i 0.116519i
\(651\) 0 0
\(652\) −12.1291 −0.475014
\(653\) 34.0245 + 19.6441i 1.33148 + 0.768732i 0.985527 0.169518i \(-0.0542212\pi\)
0.345956 + 0.938251i \(0.387554\pi\)
\(654\) 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 \(-0.887209\pi\)
0.937875 0.346975i \(-0.112791\pi\)
\(674\) −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
\(682\) 3.32065 + 18.7423i 0.127154 + 0.717679i
\(683\) −4.85527 + 2.80319i −0.185782 + 0.107261i −0.590006 0.807399i \(-0.700875\pi\)
0.404225 + 0.914660i \(0.367541\pi\)
\(684\) 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
\(704\) 0.578609 + 3.26576i 0.0218071 + 0.123083i
\(705\) 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 0.371627 0.928382i \(-0.378800\pi\)
−0.618189 + 0.786029i \(0.712134\pi\)
\(720\) 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 0.457183 0.889372i \(-0.348858\pi\)
−0.541627 + 0.840619i \(0.682192\pi\)
\(734\) 9.95416 0.367415
\(735\) 0 0
\(736\) 0.525938i 0.0193864i
\(737\) 34.5364 29.0279i 1.27216 1.06925i
\(738\) 0 0
\(739\) 2.14077 1.23598i 0.0787496 0.0454661i −0.460108 0.887863i \(-0.652189\pi\)
0.538858 + 0.842397i \(0.318856\pi\)
\(740\) 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 \(-0.865368\pi\)
0.911878 0.410461i \(-0.134632\pi\)
\(770\) −11.3816 8.86572i −0.410163 0.319498i
\(771\) 0 0
\(772\) 3.47593 + 2.00683i 0.125102 + 0.0722274i
\(773\) −1.09140 + 0.630122i −0.0392551 + 0.0226639i −0.519499 0.854471i \(-0.673881\pi\)
0.480244 + 0.877135i \(0.340548\pi\)
\(774\) 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
\(781\) −5.29606 + 0.938324i −0.189508 + 0.0335759i
\(782\) 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 −0.995694 0.0926980i \(-0.970451\pi\)
−0.417568 + 0.908646i \(0.637118\pi\)
\(788\) 10.7170 + 18.5624i 0.381777 + 0.661257i
\(789\) 0 0
\(790\) −13.7220 −0.488206
\(791\)