Properties

Label 1386.2.ba.a.989.9
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 989.9
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.346303 + 0.199938i) q^{5} +(-1.03937 + 2.43304i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.346303 + 0.199938i) q^{5} +(-1.03937 + 2.43304i) q^{7} +1.00000 q^{8} +(-0.346303 + 0.199938i) q^{10} +(-2.70584 + 1.91792i) q^{11} +0.164753i q^{13} +(-1.58739 - 2.11664i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.906908 + 1.57081i) q^{17} +(5.41372 + 3.12561i) q^{19} -0.399877i q^{20} +(-0.308042 - 3.30229i) q^{22} +(-3.76546 - 2.17399i) q^{23} +(-2.42005 - 4.19165i) q^{25} +(-0.142681 - 0.0823767i) q^{26} +(2.62676 - 0.316401i) q^{28} -4.12269 q^{29} +(-0.141785 - 0.245579i) q^{31} +(-0.500000 - 0.866025i) q^{32} -1.81382 q^{34} +(-0.846396 + 0.634761i) q^{35} +(2.40479 - 4.16521i) q^{37} +(-5.41372 + 3.12561i) q^{38} +(0.346303 + 0.199938i) q^{40} -9.23554 q^{41} +2.07944i q^{43} +(3.01389 + 1.38437i) q^{44} +(3.76546 - 2.17399i) q^{46} +(-0.367808 - 0.212354i) q^{47} +(-4.83941 - 5.05767i) q^{49} +4.84010 q^{50} +(0.142681 - 0.0823767i) q^{52} +(-7.71343 + 4.45335i) q^{53} +(-1.32051 + 0.123179i) q^{55} +(-1.03937 + 2.43304i) q^{56} +(2.06135 - 3.57036i) q^{58} +(-6.92731 + 3.99948i) q^{59} +(6.10939 + 3.52726i) q^{61} +0.283570 q^{62} +1.00000 q^{64} +(-0.0329405 + 0.0570546i) q^{65} +(0.0327874 + 0.0567894i) q^{67} +(0.906908 - 1.57081i) q^{68} +(-0.126521 - 1.05038i) q^{70} +6.43763i q^{71} +(-7.21457 + 4.16533i) q^{73} +(2.40479 + 4.16521i) q^{74} -6.25122i q^{76} +(-1.85400 - 8.57687i) q^{77} +(-0.531141 - 0.306654i) q^{79} +(-0.346303 + 0.199938i) q^{80} +(4.61777 - 7.99822i) q^{82} +1.91649 q^{83} +0.725302i q^{85} +(-1.80085 - 1.03972i) q^{86} +(-2.70584 + 1.91792i) q^{88} +(-8.89851 - 5.13756i) q^{89} +(-0.400852 - 0.171240i) q^{91} +4.34798i q^{92} +(0.367808 - 0.212354i) q^{94} +(1.24986 + 2.16482i) q^{95} -15.3888 q^{97} +(6.79978 - 1.66222i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

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
\(5\) 0.346303 + 0.199938i 0.154872 + 0.0894151i 0.575433 0.817849i \(-0.304834\pi\)
−0.420561 + 0.907264i \(0.638167\pi\)
\(6\) 0 0
\(7\) −1.03937 + 2.43304i −0.392845 + 0.919605i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.346303 + 0.199938i −0.109511 + 0.0632260i
\(11\) −2.70584 + 1.91792i −0.815843 + 0.578274i
\(12\) 0 0
\(13\) 0.164753i 0.0456944i 0.999739 + 0.0228472i \(0.00727312\pi\)
−0.999739 + 0.0228472i \(0.992727\pi\)
\(14\) −1.58739 2.11664i −0.424249 0.565697i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.906908 + 1.57081i 0.219957 + 0.380977i 0.954795 0.297266i \(-0.0960748\pi\)
−0.734837 + 0.678243i \(0.762742\pi\)
\(18\) 0 0
\(19\) 5.41372 + 3.12561i 1.24199 + 0.717065i 0.969499 0.245093i \(-0.0788186\pi\)
0.272493 + 0.962158i \(0.412152\pi\)
\(20\) 0.399877i 0.0894151i
\(21\) 0 0
\(22\) −0.308042 3.30229i −0.0656748 0.704050i
\(23\) −3.76546 2.17399i −0.785153 0.453309i 0.0531002 0.998589i \(-0.483090\pi\)
−0.838254 + 0.545281i \(0.816423\pi\)
\(24\) 0 0
\(25\) −2.42005 4.19165i −0.484010 0.838330i
\(26\) −0.142681 0.0823767i −0.0279820 0.0161554i
\(27\) 0 0
\(28\) 2.62676 0.316401i 0.496412 0.0597941i
\(29\) −4.12269 −0.765565 −0.382782 0.923839i \(-0.625034\pi\)
−0.382782 + 0.923839i \(0.625034\pi\)
\(30\) 0 0
\(31\) −0.141785 0.245579i −0.0254653 0.0441072i 0.853012 0.521891i \(-0.174773\pi\)
−0.878477 + 0.477784i \(0.841440\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.81382 −0.311067
\(35\) −0.846396 + 0.634761i −0.143067 + 0.107294i
\(36\) 0 0
\(37\) 2.40479 4.16521i 0.395344 0.684756i −0.597801 0.801645i \(-0.703959\pi\)
0.993145 + 0.116888i \(0.0372919\pi\)
\(38\) −5.41372 + 3.12561i −0.878221 + 0.507041i
\(39\) 0 0
\(40\) 0.346303 + 0.199938i 0.0547554 + 0.0316130i
\(41\) −9.23554 −1.44235 −0.721175 0.692753i \(-0.756398\pi\)
−0.721175 + 0.692753i \(0.756398\pi\)
\(42\) 0 0
\(43\) 2.07944i 0.317112i 0.987350 + 0.158556i \(0.0506839\pi\)
−0.987350 + 0.158556i \(0.949316\pi\)
\(44\) 3.01389 + 1.38437i 0.454361 + 0.208702i
\(45\) 0 0
\(46\) 3.76546 2.17399i 0.555187 0.320538i
\(47\) −0.367808 0.212354i −0.0536503 0.0309750i 0.472935 0.881097i \(-0.343195\pi\)
−0.526585 + 0.850122i \(0.676528\pi\)
\(48\) 0 0
\(49\) −4.83941 5.05767i −0.691345 0.722525i
\(50\) 4.84010 0.684493
\(51\) 0 0
\(52\) 0.142681 0.0823767i 0.0197862 0.0114236i
\(53\) −7.71343 + 4.45335i −1.05952 + 0.611714i −0.925300 0.379237i \(-0.876187\pi\)
−0.134221 + 0.990951i \(0.542853\pi\)
\(54\) 0 0
\(55\) −1.32051 + 0.123179i −0.178057 + 0.0166094i
\(56\) −1.03937 + 2.43304i −0.138892 + 0.325129i
\(57\) 0 0
\(58\) 2.06135 3.57036i 0.270668 0.468811i
\(59\) −6.92731 + 3.99948i −0.901858 + 0.520688i −0.877803 0.479022i \(-0.840991\pi\)
−0.0240557 + 0.999711i \(0.507658\pi\)
\(60\) 0 0
\(61\) 6.10939 + 3.52726i 0.782227 + 0.451619i 0.837219 0.546868i \(-0.184180\pi\)
−0.0549920 + 0.998487i \(0.517513\pi\)
\(62\) 0.283570 0.0360134
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.0329405 + 0.0570546i −0.00408577 + 0.00707676i
\(66\) 0 0
\(67\) 0.0327874 + 0.0567894i 0.00400562 + 0.00693793i 0.868021 0.496527i \(-0.165392\pi\)
−0.864016 + 0.503465i \(0.832058\pi\)
\(68\) 0.906908 1.57081i 0.109979 0.190489i
\(69\) 0 0
\(70\) −0.126521 1.05038i −0.0151222 0.125545i
\(71\) 6.43763i 0.764006i 0.924161 + 0.382003i \(0.124766\pi\)
−0.924161 + 0.382003i \(0.875234\pi\)
\(72\) 0 0
\(73\) −7.21457 + 4.16533i −0.844402 + 0.487515i −0.858758 0.512381i \(-0.828763\pi\)
0.0143564 + 0.999897i \(0.495430\pi\)
\(74\) 2.40479 + 4.16521i 0.279551 + 0.484196i
\(75\) 0 0
\(76\) 6.25122i 0.717065i
\(77\) −1.85400 8.57687i −0.211283 0.977425i
\(78\) 0 0
\(79\) −0.531141 0.306654i −0.0597580 0.0345013i 0.469823 0.882760i \(-0.344318\pi\)
−0.529581 + 0.848259i \(0.677651\pi\)
\(80\) −0.346303 + 0.199938i −0.0387179 + 0.0223538i
\(81\) 0 0
\(82\) 4.61777 7.99822i 0.509948 0.883255i
\(83\) 1.91649 0.210362 0.105181 0.994453i \(-0.466458\pi\)
0.105181 + 0.994453i \(0.466458\pi\)
\(84\) 0 0
\(85\) 0.725302i 0.0786701i
\(86\) −1.80085 1.03972i −0.194191 0.112116i
\(87\) 0 0
\(88\) −2.70584 + 1.91792i −0.288444 + 0.204451i
\(89\) −8.89851 5.13756i −0.943241 0.544580i −0.0522659 0.998633i \(-0.516644\pi\)
−0.890975 + 0.454053i \(0.849978\pi\)
\(90\) 0 0
\(91\) −0.400852 0.171240i −0.0420207 0.0179508i
\(92\) 4.34798i 0.453309i
\(93\) 0 0
\(94\) 0.367808 0.212354i 0.0379365 0.0219027i
\(95\) 1.24986 + 2.16482i 0.128233 + 0.222106i
\(96\) 0 0
\(97\) −15.3888 −1.56249 −0.781246 0.624223i \(-0.785416\pi\)
−0.781246 + 0.624223i \(0.785416\pi\)
\(98\) 6.79978 1.66222i 0.686882 0.167909i
\(99\) 0 0
\(100\) −2.42005 + 4.19165i −0.242005 + 0.419165i
\(101\) −1.20313 2.08388i −0.119716 0.207354i 0.799939 0.600081i \(-0.204865\pi\)
−0.919655 + 0.392727i \(0.871532\pi\)
\(102\) 0 0
\(103\) 2.10989 3.65443i 0.207893 0.360082i −0.743157 0.669117i \(-0.766673\pi\)
0.951051 + 0.309035i \(0.100006\pi\)
\(104\) 0.164753i 0.0161554i
\(105\) 0 0
\(106\) 8.90670i 0.865095i
\(107\) −6.05913 + 10.4947i −0.585758 + 1.01456i 0.409022 + 0.912524i \(0.365870\pi\)
−0.994780 + 0.102039i \(0.967463\pi\)
\(108\) 0 0
\(109\) −14.5861 + 8.42128i −1.39709 + 0.806613i −0.994087 0.108584i \(-0.965368\pi\)
−0.403007 + 0.915197i \(0.632035\pi\)
\(110\) 0.553578 1.20518i 0.0527816 0.114910i
\(111\) 0 0
\(112\) −1.58739 2.11664i −0.149995 0.200004i
\(113\) 3.04275i 0.286238i 0.989705 + 0.143119i \(0.0457131\pi\)
−0.989705 + 0.143119i \(0.954287\pi\)
\(114\) 0 0
\(115\) −0.869328 1.50572i −0.0810653 0.140409i
\(116\) 2.06135 + 3.57036i 0.191391 + 0.331499i
\(117\) 0 0
\(118\) 7.99896i 0.736364i
\(119\) −4.76446 + 0.573892i −0.436758 + 0.0526086i
\(120\) 0 0
\(121\) 3.64319 10.3792i 0.331199 0.943561i
\(122\) −6.10939 + 3.52726i −0.553118 + 0.319343i
\(123\) 0 0
\(124\) −0.141785 + 0.245579i −0.0127327 + 0.0220536i
\(125\) 3.93482i 0.351941i
\(126\) 0 0
\(127\) 10.8250i 0.960561i 0.877115 + 0.480281i \(0.159465\pi\)
−0.877115 + 0.480281i \(0.840535\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.0329405 0.0570546i −0.00288907 0.00500402i
\(131\) 7.68882 13.3174i 0.671775 1.16355i −0.305625 0.952152i \(-0.598866\pi\)
0.977400 0.211396i \(-0.0678011\pi\)
\(132\) 0 0
\(133\) −13.2316 + 9.92315i −1.14733 + 0.860446i
\(134\) −0.0655748 −0.00566480
\(135\) 0 0
\(136\) 0.906908 + 1.57081i 0.0777667 + 0.134696i
\(137\) 14.9235 8.61608i 1.27500 0.736121i 0.299075 0.954230i \(-0.403322\pi\)
0.975924 + 0.218109i \(0.0699887\pi\)
\(138\) 0 0
\(139\) 7.87238i 0.667726i −0.942622 0.333863i \(-0.891648\pi\)
0.942622 0.333863i \(-0.108352\pi\)
\(140\) 0.972918 + 0.415620i 0.0822265 + 0.0351263i
\(141\) 0 0
\(142\) −5.57515 3.21881i −0.467856 0.270117i
\(143\) −0.315983 0.445797i −0.0264238 0.0372794i
\(144\) 0 0
\(145\) −1.42770 0.824284i −0.118564 0.0684531i
\(146\) 8.33067i 0.689451i
\(147\) 0 0
\(148\) −4.80957 −0.395344
\(149\) 0.346336 0.599872i 0.0283730 0.0491435i −0.851490 0.524370i \(-0.824301\pi\)
0.879863 + 0.475227i \(0.157634\pi\)
\(150\) 0 0
\(151\) 7.27714 4.20146i 0.592205 0.341910i −0.173764 0.984787i \(-0.555593\pi\)
0.765969 + 0.642877i \(0.222260\pi\)
\(152\) 5.41372 + 3.12561i 0.439111 + 0.253521i
\(153\) 0 0
\(154\) 8.35479 + 2.68282i 0.673248 + 0.216188i
\(155\) 0.113393i 0.00910794i
\(156\) 0 0
\(157\) 1.21224 + 2.09967i 0.0967477 + 0.167572i 0.910337 0.413869i \(-0.135823\pi\)
−0.813589 + 0.581440i \(0.802489\pi\)
\(158\) 0.531141 0.306654i 0.0422553 0.0243961i
\(159\) 0 0
\(160\) 0.399877i 0.0316130i
\(161\) 9.20313 6.90196i 0.725308 0.543950i
\(162\) 0 0
\(163\) 5.60153 9.70213i 0.438746 0.759930i −0.558848 0.829270i \(-0.688756\pi\)
0.997593 + 0.0693409i \(0.0220896\pi\)
\(164\) 4.61777 + 7.99822i 0.360587 + 0.624556i
\(165\) 0 0
\(166\) −0.958245 + 1.65973i −0.0743742 + 0.128820i
\(167\) −17.7532 −1.37378 −0.686892 0.726760i \(-0.741025\pi\)
−0.686892 + 0.726760i \(0.741025\pi\)
\(168\) 0 0
\(169\) 12.9729 0.997912
\(170\) −0.628130 0.362651i −0.0481754 0.0278141i
\(171\) 0 0
\(172\) 1.80085 1.03972i 0.137314 0.0792781i
\(173\) 7.75760 13.4366i 0.589799 1.02156i −0.404459 0.914556i \(-0.632540\pi\)
0.994258 0.107006i \(-0.0341265\pi\)
\(174\) 0 0
\(175\) 12.7138 1.53141i 0.961073 0.115764i
\(176\) −0.308042 3.30229i −0.0232195 0.248919i
\(177\) 0 0
\(178\) 8.89851 5.13756i 0.666972 0.385076i
\(179\) −1.11782 + 0.645375i −0.0835500 + 0.0482376i −0.541193 0.840898i \(-0.682027\pi\)
0.457643 + 0.889136i \(0.348694\pi\)
\(180\) 0 0
\(181\) 20.0823 1.49271 0.746354 0.665549i \(-0.231803\pi\)
0.746354 + 0.665549i \(0.231803\pi\)
\(182\) 0.348724 0.261528i 0.0258492 0.0193858i
\(183\) 0 0
\(184\) −3.76546 2.17399i −0.277594 0.160269i
\(185\) 1.66557 0.961617i 0.122455 0.0706995i
\(186\) 0 0
\(187\) −5.46663 2.51099i −0.399760 0.183622i
\(188\) 0.424708i 0.0309750i
\(189\) 0 0
\(190\) −2.49972 −0.181349
\(191\) 12.4810 + 7.20591i 0.903094 + 0.521402i 0.878203 0.478289i \(-0.158743\pi\)
0.0248912 + 0.999690i \(0.492076\pi\)
\(192\) 0 0
\(193\) −15.7143 + 9.07265i −1.13114 + 0.653064i −0.944221 0.329312i \(-0.893183\pi\)
−0.186918 + 0.982376i \(0.559850\pi\)
\(194\) 7.69438 13.3271i 0.552424 0.956827i
\(195\) 0 0
\(196\) −1.96037 + 6.71989i −0.140026 + 0.479992i
\(197\) −3.45410 −0.246095 −0.123047 0.992401i \(-0.539267\pi\)
−0.123047 + 0.992401i \(0.539267\pi\)
\(198\) 0 0
\(199\) 12.7513 + 22.0860i 0.903918 + 1.56563i 0.822363 + 0.568963i \(0.192655\pi\)
0.0815547 + 0.996669i \(0.474011\pi\)
\(200\) −2.42005 4.19165i −0.171123 0.296394i
\(201\) 0 0
\(202\) 2.40626 0.169304
\(203\) 4.28501 10.0307i 0.300749 0.704017i
\(204\) 0 0
\(205\) −3.19830 1.84654i −0.223379 0.128968i
\(206\) 2.10989 + 3.65443i 0.147003 + 0.254616i
\(207\) 0 0
\(208\) −0.142681 0.0823767i −0.00989312 0.00571180i
\(209\) −20.6433 + 1.92564i −1.42793 + 0.133199i
\(210\) 0 0
\(211\) 4.16072i 0.286436i −0.989691 0.143218i \(-0.954255\pi\)
0.989691 0.143218i \(-0.0457450\pi\)
\(212\) 7.71343 + 4.45335i 0.529760 + 0.305857i
\(213\) 0 0
\(214\) −6.05913 10.4947i −0.414194 0.717404i
\(215\) −0.415761 + 0.720119i −0.0283546 + 0.0491117i
\(216\) 0 0
\(217\) 0.744871 0.0897216i 0.0505651 0.00609070i
\(218\) 16.8426i 1.14072i
\(219\) 0 0
\(220\) 0.766930 + 1.08200i 0.0517064 + 0.0729487i
\(221\) −0.258796 + 0.149416i −0.0174085 + 0.0100508i
\(222\) 0 0
\(223\) −10.8608 −0.727292 −0.363646 0.931537i \(-0.618468\pi\)
−0.363646 + 0.931537i \(0.618468\pi\)
\(224\) 2.62676 0.316401i 0.175508 0.0211404i
\(225\) 0 0
\(226\) −2.63510 1.52138i −0.175284 0.101200i
\(227\) 6.56574 + 11.3722i 0.435783 + 0.754799i 0.997359 0.0726263i \(-0.0231380\pi\)
−0.561576 + 0.827425i \(0.689805\pi\)
\(228\) 0 0
\(229\) −12.7878 + 22.1491i −0.845040 + 1.46365i 0.0405465 + 0.999178i \(0.487090\pi\)
−0.885586 + 0.464475i \(0.846243\pi\)
\(230\) 1.73866 0.114644
\(231\) 0 0
\(232\) −4.12269 −0.270668
\(233\) −5.30687 + 9.19177i −0.347664 + 0.602173i −0.985834 0.167723i \(-0.946359\pi\)
0.638170 + 0.769896i \(0.279692\pi\)
\(234\) 0 0
\(235\) −0.0849155 0.147078i −0.00553927 0.00959430i
\(236\) 6.92731 + 3.99948i 0.450929 + 0.260344i
\(237\) 0 0
\(238\) 1.88523 4.41309i 0.122201 0.286058i
\(239\) −6.19484 −0.400711 −0.200355 0.979723i \(-0.564210\pi\)
−0.200355 + 0.979723i \(0.564210\pi\)
\(240\) 0 0
\(241\) −8.85163 + 5.11049i −0.570183 + 0.329196i −0.757223 0.653157i \(-0.773444\pi\)
0.187039 + 0.982352i \(0.440111\pi\)
\(242\) 7.16703 + 8.34468i 0.460714 + 0.536416i
\(243\) 0 0
\(244\) 7.05451i 0.451619i
\(245\) −0.664683 2.71907i −0.0424650 0.173715i
\(246\) 0 0
\(247\) −0.514955 + 0.891928i −0.0327658 + 0.0567520i
\(248\) −0.141785 0.245579i −0.00900335 0.0155943i
\(249\) 0 0
\(250\) 3.40766 + 1.96741i 0.215519 + 0.124430i
\(251\) 12.9208i 0.815556i −0.913081 0.407778i \(-0.866304\pi\)
0.913081 0.407778i \(-0.133696\pi\)
\(252\) 0 0
\(253\) 14.3583 1.33936i 0.902698 0.0842049i
\(254\) −9.37471 5.41249i −0.588221 0.339610i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 23.0048 + 13.2818i 1.43500 + 0.828498i 0.997496 0.0707192i \(-0.0225294\pi\)
0.437504 + 0.899217i \(0.355863\pi\)
\(258\) 0 0
\(259\) 7.63468 + 10.1802i 0.474396 + 0.632564i
\(260\) 0.0658810 0.00408577
\(261\) 0 0
\(262\) 7.68882 + 13.3174i 0.475017 + 0.822753i
\(263\) 8.38615 + 14.5252i 0.517112 + 0.895664i 0.999803 + 0.0198733i \(0.00632629\pi\)
−0.482690 + 0.875791i \(0.660340\pi\)
\(264\) 0 0
\(265\) −3.56158 −0.218786
\(266\) −1.97789 16.4205i −0.121272 1.00680i
\(267\) 0 0
\(268\) 0.0327874 0.0567894i 0.00200281 0.00346897i
\(269\) 0.0333496 0.0192544i 0.00203336 0.00117396i −0.498983 0.866612i \(-0.666293\pi\)
0.501016 + 0.865438i \(0.332960\pi\)
\(270\) 0 0
\(271\) 10.9630 + 6.32950i 0.665956 + 0.384490i 0.794543 0.607208i \(-0.207711\pi\)
−0.128587 + 0.991698i \(0.541044\pi\)
\(272\) −1.81382 −0.109979
\(273\) 0 0
\(274\) 17.2322i 1.04103i
\(275\) 14.5875 + 6.70050i 0.879660 + 0.404055i
\(276\) 0 0
\(277\) −15.7022 + 9.06569i −0.943456 + 0.544705i −0.891042 0.453921i \(-0.850025\pi\)
−0.0524139 + 0.998625i \(0.516692\pi\)
\(278\) 6.81768 + 3.93619i 0.408897 + 0.236077i
\(279\) 0 0
\(280\) −0.846396 + 0.634761i −0.0505819 + 0.0379342i
\(281\) 29.7454 1.77446 0.887231 0.461326i \(-0.152626\pi\)
0.887231 + 0.461326i \(0.152626\pi\)
\(282\) 0 0
\(283\) −4.03054 + 2.32703i −0.239591 + 0.138328i −0.614989 0.788536i \(-0.710839\pi\)
0.375398 + 0.926864i \(0.377506\pi\)
\(284\) 5.57515 3.21881i 0.330824 0.191001i
\(285\) 0 0
\(286\) 0.544063 0.0507510i 0.0321711 0.00300097i
\(287\) 9.59916 22.4705i 0.566620 1.32639i
\(288\) 0 0
\(289\) 6.85504 11.8733i 0.403238 0.698428i
\(290\) 1.42770 0.824284i 0.0838375 0.0484036i
\(291\) 0 0
\(292\) 7.21457 + 4.16533i 0.422201 + 0.243758i
\(293\) −18.1852 −1.06239 −0.531197 0.847249i \(-0.678257\pi\)
−0.531197 + 0.847249i \(0.678257\pi\)
\(294\) 0 0
\(295\) −3.19860 −0.186230
\(296\) 2.40479 4.16521i 0.139775 0.242098i
\(297\) 0 0
\(298\) 0.346336 + 0.599872i 0.0200627 + 0.0347497i
\(299\) 0.358172 0.620373i 0.0207136 0.0358771i
\(300\) 0 0
\(301\) −5.05938 2.16132i −0.291618 0.124576i
\(302\) 8.40292i 0.483534i
\(303\) 0 0
\(304\) −5.41372 + 3.12561i −0.310498 + 0.179266i
\(305\) 1.41047 + 2.44300i 0.0807631 + 0.139886i
\(306\) 0 0
\(307\) 11.6702i 0.666051i −0.942918 0.333025i \(-0.891931\pi\)
0.942918 0.333025i \(-0.108069\pi\)
\(308\) −6.50079 + 5.89405i −0.370417 + 0.335844i
\(309\) 0 0
\(310\) 0.0982011 + 0.0566965i 0.00557745 + 0.00322014i
\(311\) 21.3421 12.3218i 1.21020 0.698708i 0.247395 0.968915i \(-0.420425\pi\)
0.962802 + 0.270207i \(0.0870922\pi\)
\(312\) 0 0
\(313\) 0.450517 0.780318i 0.0254647 0.0441062i −0.853012 0.521891i \(-0.825227\pi\)
0.878477 + 0.477785i \(0.158560\pi\)
\(314\) −2.42449 −0.136822
\(315\) 0 0
\(316\) 0.613309i 0.0345013i
\(317\) 4.22112 + 2.43707i 0.237082 + 0.136879i 0.613835 0.789435i \(-0.289626\pi\)
−0.376753 + 0.926314i \(0.622959\pi\)
\(318\) 0 0
\(319\) 11.1554 7.90698i 0.624581 0.442706i
\(320\) 0.346303 + 0.199938i 0.0193589 + 0.0111769i
\(321\) 0 0
\(322\) 1.37570 + 11.4211i 0.0766650 + 0.636474i
\(323\) 11.3386i 0.630895i
\(324\) 0 0
\(325\) 0.690588 0.398711i 0.0383069 0.0221165i
\(326\) 5.60153 + 9.70213i 0.310240 + 0.537351i
\(327\) 0 0
\(328\) −9.23554 −0.509948
\(329\) 0.898956 0.674179i 0.0495611 0.0371687i
\(330\) 0 0
\(331\) −16.9428 + 29.3457i −0.931259 + 1.61299i −0.150085 + 0.988673i \(0.547955\pi\)
−0.781173 + 0.624314i \(0.785379\pi\)
\(332\) −0.958245 1.65973i −0.0525905 0.0910894i
\(333\) 0 0
\(334\) 8.87660 15.3747i 0.485706 0.841267i
\(335\) 0.0262218i 0.00143265i
\(336\) 0 0
\(337\) 25.0659i 1.36542i 0.730687 + 0.682712i \(0.239200\pi\)
−0.730687 + 0.682712i \(0.760800\pi\)
\(338\) −6.48643 + 11.2348i −0.352815 + 0.611094i
\(339\) 0 0
\(340\) 0.628130 0.362651i 0.0340651 0.0196675i
\(341\) 0.854647 + 0.392566i 0.0462817 + 0.0212586i
\(342\) 0 0
\(343\) 17.3355 6.51771i 0.936029 0.351923i
\(344\) 2.07944i 0.112116i
\(345\) 0 0
\(346\) 7.75760 + 13.4366i 0.417051 + 0.722354i
\(347\) 11.0467 + 19.1335i 0.593021 + 1.02714i 0.993823 + 0.110977i \(0.0353981\pi\)
−0.400802 + 0.916165i \(0.631269\pi\)
\(348\) 0 0
\(349\) 12.3244i 0.659709i −0.944032 0.329854i \(-0.893000\pi\)
0.944032 0.329854i \(-0.107000\pi\)
\(350\) −5.03066 + 11.7762i −0.268900 + 0.629463i
\(351\) 0 0
\(352\) 3.01389 + 1.38437i 0.160641 + 0.0737873i
\(353\) −10.9072 + 6.29726i −0.580531 + 0.335169i −0.761344 0.648348i \(-0.775460\pi\)
0.180814 + 0.983517i \(0.442127\pi\)
\(354\) 0 0
\(355\) −1.28713 + 2.22937i −0.0683136 + 0.118323i
\(356\) 10.2751i 0.544580i
\(357\) 0 0
\(358\) 1.29075i 0.0682183i
\(359\) −13.0266 + 22.5628i −0.687520 + 1.19082i 0.285118 + 0.958493i \(0.407967\pi\)
−0.972638 + 0.232327i \(0.925366\pi\)
\(360\) 0 0
\(361\) 10.0389 + 17.3879i 0.528363 + 0.915152i
\(362\) −10.0412 + 17.3918i −0.527752 + 0.914093i
\(363\) 0 0
\(364\) 0.0521281 + 0.432768i 0.00273225 + 0.0226832i
\(365\) −3.33124 −0.174365
\(366\) 0 0
\(367\) −7.79109 13.4946i −0.406692 0.704411i 0.587825 0.808988i \(-0.299984\pi\)
−0.994517 + 0.104577i \(0.966651\pi\)
\(368\) 3.76546 2.17399i 0.196288 0.113327i
\(369\) 0 0
\(370\) 1.92323i 0.0999842i
\(371\) −2.81808 23.3958i −0.146308 1.21465i
\(372\) 0 0
\(373\) 10.9916 + 6.34599i 0.569123 + 0.328583i 0.756799 0.653648i \(-0.226762\pi\)
−0.187676 + 0.982231i \(0.560096\pi\)
\(374\) 4.90790 3.47875i 0.253782 0.179882i
\(375\) 0 0
\(376\) −0.367808 0.212354i −0.0189683 0.0109513i
\(377\) 0.679227i 0.0349820i
\(378\) 0 0
\(379\) 22.9946 1.18115 0.590577 0.806981i \(-0.298900\pi\)
0.590577 + 0.806981i \(0.298900\pi\)
\(380\) 1.24986 2.16482i 0.0641164 0.111053i
\(381\) 0 0
\(382\) −12.4810 + 7.20591i −0.638584 + 0.368687i
\(383\) −21.6145 12.4791i −1.10445 0.637653i −0.167062 0.985946i \(-0.553428\pi\)
−0.937386 + 0.348293i \(0.886761\pi\)
\(384\) 0 0
\(385\) 1.07280 3.34088i 0.0546749 0.170267i
\(386\) 18.1453i 0.923571i
\(387\) 0 0
\(388\) 7.69438 + 13.3271i 0.390623 + 0.676579i
\(389\) 15.6436 9.03184i 0.793162 0.457932i −0.0479125 0.998852i \(-0.515257\pi\)
0.841075 + 0.540919i \(0.181924\pi\)
\(390\) 0 0
\(391\) 7.88644i 0.398834i
\(392\) −4.83941 5.05767i −0.244427 0.255451i
\(393\) 0 0
\(394\) 1.72705 2.99134i 0.0870075 0.150701i
\(395\) −0.122624 0.212391i −0.00616988 0.0106865i
\(396\) 0 0
\(397\) −15.5641 + 26.9578i −0.781138 + 1.35297i 0.150141 + 0.988665i \(0.452027\pi\)
−0.931279 + 0.364306i \(0.881306\pi\)
\(398\) −25.5027 −1.27833
\(399\) 0 0
\(400\) 4.84010 0.242005
\(401\) 10.9072 + 6.29726i 0.544678 + 0.314470i 0.746973 0.664854i \(-0.231506\pi\)
−0.202294 + 0.979325i \(0.564840\pi\)
\(402\) 0 0
\(403\) 0.0404599 0.0233595i 0.00201545 0.00116362i
\(404\) −1.20313 + 2.08388i −0.0598580 + 0.103677i
\(405\) 0 0
\(406\) 6.54433 + 8.72627i 0.324790 + 0.433078i
\(407\) 1.48155 + 15.8826i 0.0734377 + 0.787271i
\(408\) 0 0
\(409\) −4.95999 + 2.86365i −0.245256 + 0.141598i −0.617590 0.786500i \(-0.711891\pi\)
0.372334 + 0.928099i \(0.378557\pi\)
\(410\) 3.19830 1.84654i 0.157953 0.0911941i
\(411\) 0 0
\(412\) −4.21977 −0.207893
\(413\) −2.53088 21.0114i −0.124536 1.03390i
\(414\) 0 0
\(415\) 0.663687 + 0.383180i 0.0325791 + 0.0188095i
\(416\) 0.142681 0.0823767i 0.00699549 0.00403885i
\(417\) 0 0
\(418\) 8.65402 18.8405i 0.423282 0.921518i
\(419\) 16.5405i 0.808055i −0.914747 0.404027i \(-0.867610\pi\)
0.914747 0.404027i \(-0.132390\pi\)
\(420\) 0 0
\(421\) −9.41277 −0.458751 −0.229375 0.973338i \(-0.573668\pi\)
−0.229375 + 0.973338i \(0.573668\pi\)
\(422\) 3.60329 + 2.08036i 0.175405 + 0.101270i
\(423\) 0 0
\(424\) −7.71343 + 4.45335i −0.374597 + 0.216274i
\(425\) 4.38952 7.60287i 0.212923 0.368794i
\(426\) 0 0
\(427\) −14.9319 + 11.1983i −0.722605 + 0.541923i
\(428\) 12.1183 0.585758
\(429\) 0 0
\(430\) −0.415761 0.720119i −0.0200498 0.0347272i
\(431\) 17.0304 + 29.4975i 0.820326 + 1.42085i 0.905440 + 0.424475i \(0.139541\pi\)
−0.0851140 + 0.996371i \(0.527125\pi\)
\(432\) 0 0
\(433\) 30.8495 1.48253 0.741266 0.671211i \(-0.234226\pi\)
0.741266 + 0.671211i \(0.234226\pi\)
\(434\) −0.294734 + 0.689938i −0.0141477 + 0.0331181i
\(435\) 0 0
\(436\) 14.5861 + 8.42128i 0.698547 + 0.403306i
\(437\) −13.5901 23.5388i −0.650103 1.12601i
\(438\) 0 0
\(439\) 31.6900 + 18.2962i 1.51248 + 0.873232i 0.999893 + 0.0145970i \(0.00464654\pi\)
0.512588 + 0.858635i \(0.328687\pi\)
\(440\) −1.32051 + 0.123179i −0.0629527 + 0.00587232i
\(441\) 0 0
\(442\) 0.298832i 0.0142140i
\(443\) −4.85111 2.80079i −0.230483 0.133070i 0.380312 0.924858i \(-0.375817\pi\)
−0.610795 + 0.791789i \(0.709150\pi\)
\(444\) 0 0
\(445\) −2.05439 3.55831i −0.0973874 0.168680i
\(446\) 5.43039 9.40572i 0.257137 0.445374i
\(447\) 0 0
\(448\) −1.03937 + 2.43304i −0.0491057 + 0.114951i
\(449\) 6.07297i 0.286601i −0.989679 0.143301i \(-0.954228\pi\)
0.989679 0.143301i \(-0.0457716\pi\)
\(450\) 0 0
\(451\) 24.9900 17.7130i 1.17673 0.834073i
\(452\) 2.63510 1.52138i 0.123945 0.0715595i
\(453\) 0 0
\(454\) −13.1315 −0.616291
\(455\) −0.104579 0.139447i −0.00490274 0.00653736i
\(456\) 0 0
\(457\) −21.4636 12.3920i −1.00402 0.579674i −0.0945879 0.995517i \(-0.530153\pi\)
−0.909437 + 0.415843i \(0.863487\pi\)
\(458\) −12.7878 22.1491i −0.597534 1.03496i
\(459\) 0 0
\(460\) −0.869328 + 1.50572i −0.0405326 + 0.0702046i
\(461\) 1.67869 0.0781842 0.0390921 0.999236i \(-0.487553\pi\)
0.0390921 + 0.999236i \(0.487553\pi\)
\(462\) 0 0
\(463\) −13.3190 −0.618987 −0.309494 0.950902i \(-0.600160\pi\)
−0.309494 + 0.950902i \(0.600160\pi\)
\(464\) 2.06135 3.57036i 0.0956956 0.165750i
\(465\) 0 0
\(466\) −5.30687 9.19177i −0.245836 0.425800i
\(467\) 20.9573 + 12.0997i 0.969787 + 0.559907i 0.899171 0.437597i \(-0.144170\pi\)
0.0706157 + 0.997504i \(0.477504\pi\)
\(468\) 0 0
\(469\) −0.172250 + 0.0207479i −0.00795374 + 0.000958049i
\(470\) 0.169831 0.00783372
\(471\) 0 0
\(472\) −6.92731 + 3.99948i −0.318855 + 0.184091i
\(473\) −3.98820 5.62666i −0.183378 0.258714i
\(474\) 0 0
\(475\) 30.2565i 1.38827i
\(476\) 2.87924 + 3.83920i 0.131970 + 0.175970i
\(477\) 0 0
\(478\) 3.09742 5.36489i 0.141673 0.245384i
\(479\) 13.3087 + 23.0514i 0.608092 + 1.05325i 0.991555 + 0.129690i \(0.0413982\pi\)
−0.383462 + 0.923556i \(0.625268\pi\)
\(480\) 0 0
\(481\) 0.686233 + 0.396197i 0.0312895 + 0.0180650i
\(482\) 10.2210i 0.465553i
\(483\) 0 0
\(484\) −10.8102 + 2.03449i −0.491374 + 0.0924767i
\(485\) −5.32918 3.07680i −0.241986 0.139710i
\(486\) 0 0
\(487\) 10.7456 + 18.6119i 0.486929 + 0.843387i 0.999887 0.0150274i \(-0.00478355\pi\)
−0.512958 + 0.858414i \(0.671450\pi\)
\(488\) 6.10939 + 3.52726i 0.276559 + 0.159671i
\(489\) 0 0
\(490\) 2.68713 + 0.783905i 0.121392 + 0.0354132i
\(491\) 27.9035 1.25927 0.629633 0.776893i \(-0.283205\pi\)
0.629633 + 0.776893i \(0.283205\pi\)
\(492\) 0 0
\(493\) −3.73890 6.47597i −0.168392 0.291663i
\(494\) −0.514955 0.891928i −0.0231689 0.0401298i
\(495\) 0 0
\(496\) 0.283570 0.0127327
\(497\) −15.6630 6.69108i −0.702583 0.300136i
\(498\) 0 0
\(499\) 18.4160 31.8975i 0.824415 1.42793i −0.0779511 0.996957i \(-0.524838\pi\)
0.902366 0.430971i \(-0.141829\pi\)
\(500\) −3.40766 + 1.96741i −0.152395 + 0.0879854i
\(501\) 0 0
\(502\) 11.1898 + 6.46042i 0.499424 + 0.288342i
\(503\) −7.07546 −0.315479 −0.157740 0.987481i \(-0.550421\pi\)
−0.157740 + 0.987481i \(0.550421\pi\)
\(504\) 0 0
\(505\) 0.962208i 0.0428177i
\(506\) −6.01923 + 13.1043i −0.267587 + 0.582558i
\(507\) 0 0
\(508\) 9.37471 5.41249i 0.415935 0.240140i
\(509\) −33.9365 19.5933i −1.50421 0.868456i −0.999988 0.00488238i \(-0.998446\pi\)
−0.504222 0.863574i \(-0.668221\pi\)
\(510\) 0 0
\(511\) −2.63583 21.8827i −0.116602 0.968034i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −23.0048 + 13.2818i −1.01470 + 0.585836i
\(515\) 1.46132 0.843694i 0.0643935 0.0371776i
\(516\) 0 0
\(517\) 1.40251 0.130828i 0.0616823 0.00575381i
\(518\) −12.6336 + 1.52175i −0.555089 + 0.0668619i
\(519\) 0 0
\(520\) −0.0329405 + 0.0570546i −0.00144454 + 0.00250201i
\(521\) 1.11383 0.643068i 0.0487976 0.0281733i −0.475403 0.879768i \(-0.657698\pi\)
0.524200 + 0.851595i \(0.324364\pi\)
\(522\) 0 0
\(523\) −19.0077 10.9741i −0.831150 0.479865i 0.0230963 0.999733i \(-0.492648\pi\)
−0.854246 + 0.519869i \(0.825981\pi\)
\(524\) −15.3776 −0.671775
\(525\) 0 0
\(526\) −16.7723 −0.731307
\(527\) 0.257172 0.445434i 0.0112026 0.0194034i
\(528\) 0 0
\(529\) −2.04752 3.54642i −0.0890228 0.154192i
\(530\) 1.78079 3.08442i 0.0773526 0.133979i
\(531\) 0 0
\(532\) 15.2095 + 6.49734i 0.659416 + 0.281695i
\(533\) 1.52159i 0.0659073i
\(534\) 0 0
\(535\) −4.19659 + 2.42290i −0.181435 + 0.104751i
\(536\) 0.0327874 + 0.0567894i 0.00141620 + 0.00245293i
\(537\) 0 0
\(538\) 0.0385088i 0.00166023i
\(539\) 22.7949 + 4.40369i 0.981846 + 0.189680i
\(540\) 0 0
\(541\) −37.6161 21.7177i −1.61724 0.933716i −0.987629 0.156809i \(-0.949879\pi\)
−0.629615 0.776907i \(-0.716787\pi\)
\(542\) −10.9630 + 6.32950i −0.470902 + 0.271875i
\(543\) 0 0
\(544\) 0.906908 1.57081i 0.0388833 0.0673479i
\(545\) −6.73495 −0.288493
\(546\) 0 0
\(547\) 15.0701i 0.644351i −0.946680 0.322176i \(-0.895586\pi\)
0.946680 0.322176i \(-0.104414\pi\)
\(548\) −14.9235 8.61608i −0.637500 0.368061i
\(549\) 0 0
\(550\) −13.0966 + 9.28291i −0.558439 + 0.395824i
\(551\) −22.3191 12.8859i −0.950825 0.548959i
\(552\) 0 0
\(553\) 1.29816 0.973562i 0.0552032 0.0414001i
\(554\) 18.1314i 0.770328i
\(555\) 0 0
\(556\) −6.81768 + 3.93619i −0.289134 + 0.166932i
\(557\) 16.9504 + 29.3590i 0.718213 + 1.24398i 0.961707 + 0.274080i \(0.0883732\pi\)
−0.243494 + 0.969902i \(0.578294\pi\)
\(558\) 0 0
\(559\) −0.342596 −0.0144902
\(560\) −0.126521 1.05038i −0.00534649 0.0443867i
\(561\) 0 0
\(562\) −14.8727 + 25.7603i −0.627367 + 1.08663i
\(563\) 7.23496 + 12.5313i 0.304917 + 0.528132i 0.977243 0.212123i \(-0.0680379\pi\)
−0.672326 + 0.740256i \(0.734705\pi\)
\(564\) 0 0
\(565\) −0.608362 + 1.05371i −0.0255940 + 0.0443301i
\(566\) 4.65407i 0.195625i
\(567\) 0 0
\(568\) 6.43763i 0.270117i
\(569\) 12.8626 22.2787i 0.539229 0.933973i −0.459716 0.888066i \(-0.652049\pi\)
0.998946 0.0459069i \(-0.0146178\pi\)
\(570\) 0 0
\(571\) −12.6298 + 7.29182i −0.528541 + 0.305153i −0.740422 0.672142i \(-0.765374\pi\)
0.211881 + 0.977295i \(0.432041\pi\)
\(572\) −0.228080 + 0.496548i −0.00953650 + 0.0207617i
\(573\) 0 0
\(574\) 14.6604 + 19.5484i 0.611915 + 0.815933i
\(575\) 21.0447i 0.877623i
\(576\) 0 0
\(577\) −6.12595 10.6104i −0.255026 0.441719i 0.709876 0.704326i \(-0.248751\pi\)
−0.964903 + 0.262608i \(0.915418\pi\)
\(578\) 6.85504 + 11.8733i 0.285132 + 0.493863i
\(579\) 0 0
\(580\) 1.64857i 0.0684531i
\(581\) −1.99194 + 4.66291i −0.0826398 + 0.193450i
\(582\) 0 0
\(583\) 12.3302 26.8438i 0.510664 1.11176i
\(584\) −7.21457 + 4.16533i −0.298541 + 0.172363i
\(585\) 0 0
\(586\) 9.09262 15.7489i 0.375613 0.650580i
\(587\) 11.4407i 0.472207i 0.971728 + 0.236104i \(0.0758705\pi\)
−0.971728 + 0.236104i \(0.924129\pi\)
\(588\) 0 0
\(589\) 1.77266i 0.0730411i
\(590\) 1.59930 2.77007i 0.0658421 0.114042i
\(591\) 0 0
\(592\) 2.40479 + 4.16521i 0.0988361 + 0.171189i
\(593\) 4.71698 8.17005i 0.193703 0.335504i −0.752771 0.658282i \(-0.771283\pi\)
0.946475 + 0.322778i \(0.104617\pi\)
\(594\) 0 0
\(595\) −1.76469 0.753858i −0.0723453 0.0309052i
\(596\) −0.692673 −0.0283730
\(597\) 0 0
\(598\) 0.358172 + 0.620373i 0.0146468 + 0.0253689i
\(599\) −29.3273 + 16.9321i −1.19828 + 0.691827i −0.960171 0.279411i \(-0.909861\pi\)
−0.238108 + 0.971239i \(0.576527\pi\)
\(600\) 0 0
\(601\) 26.4610i 1.07937i −0.841868 0.539683i \(-0.818544\pi\)
0.841868 0.539683i \(-0.181456\pi\)
\(602\) 4.40145 3.30090i 0.179390 0.134534i
\(603\) 0 0
\(604\) −7.27714 4.20146i −0.296103 0.170955i
\(605\) 3.33684 2.86593i 0.135662 0.116516i
\(606\) 0 0
\(607\) 9.68966 + 5.59433i 0.393291 + 0.227067i 0.683585 0.729871i \(-0.260420\pi\)
−0.290294 + 0.956938i \(0.593753\pi\)
\(608\) 6.25122i 0.253521i
\(609\) 0 0
\(610\) −2.82093 −0.114216
\(611\) 0.0349861 0.0605976i 0.00141538 0.00245152i
\(612\) 0 0
\(613\) −1.83466 + 1.05924i −0.0741014 + 0.0427824i −0.536593 0.843841i \(-0.680289\pi\)
0.462492 + 0.886624i \(0.346956\pi\)
\(614\) 10.1066 + 5.83508i 0.407871 + 0.235485i
\(615\) 0 0
\(616\) −1.85400 8.57687i −0.0746998 0.345572i
\(617\) 15.0359i 0.605321i 0.953098 + 0.302660i \(0.0978748\pi\)
−0.953098 + 0.302660i \(0.902125\pi\)
\(618\) 0 0
\(619\) −3.78009 6.54731i −0.151935 0.263159i 0.780004 0.625775i \(-0.215217\pi\)
−0.931939 + 0.362616i \(0.881884\pi\)
\(620\) −0.0982011 + 0.0566965i −0.00394385 + 0.00227698i
\(621\) 0 0
\(622\) 24.6437i 0.988122i
\(623\) 21.7488 16.3107i 0.871346 0.653472i
\(624\) 0 0
\(625\) −11.3135 + 19.5956i −0.452541 + 0.783824i
\(626\) 0.450517 + 0.780318i 0.0180063 + 0.0311878i
\(627\) 0 0
\(628\) 1.21224 2.09967i 0.0483738 0.0837859i
\(629\) 8.72367 0.347836
\(630\) 0 0
\(631\) 47.5404 1.89255 0.946276 0.323359i \(-0.104812\pi\)
0.946276 + 0.323359i \(0.104812\pi\)
\(632\) −0.531141 0.306654i −0.0211277 0.0121981i
\(633\) 0 0
\(634\) −4.22112 + 2.43707i −0.167642 + 0.0967882i
\(635\) −2.16433 + 3.74872i −0.0858887 + 0.148764i
\(636\) 0 0
\(637\) 0.833269 0.797310i 0.0330153 0.0315906i
\(638\) 1.26996 + 13.6143i 0.0502783 + 0.538996i
\(639\) 0 0
\(640\) −0.346303 + 0.199938i −0.0136888 + 0.00790325i
\(641\) −24.4173 + 14.0974i −0.964427 + 0.556812i −0.897533 0.440948i \(-0.854642\pi\)
−0.0668942 + 0.997760i \(0.521309\pi\)
\(642\) 0 0
\(643\) −0.930892 −0.0367108 −0.0183554 0.999832i \(-0.505843\pi\)
−0.0183554 + 0.999832i \(0.505843\pi\)
\(644\) −10.5788 4.51917i −0.416865 0.178080i
\(645\) 0 0
\(646\) −9.81948 5.66928i −0.386342 0.223055i
\(647\) −15.9156 + 9.18888i −0.625707 + 0.361252i −0.779088 0.626915i \(-0.784317\pi\)
0.153381 + 0.988167i \(0.450984\pi\)
\(648\) 0 0
\(649\) 11.0735 24.1080i 0.434674 0.946321i
\(650\) 0.797423i 0.0312775i
\(651\) 0 0
\(652\) −11.2031 −0.438746
\(653\) 1.93226 + 1.11559i 0.0756150 + 0.0436564i 0.537331 0.843372i \(-0.319433\pi\)
−0.461716 + 0.887028i \(0.652766\pi\)
\(654\) 0 0
\(655\) 5.32532 3.07458i 0.208078 0.120134i
\(656\) 4.61777 7.99822i 0.180294 0.312278i
\(657\) 0 0
\(658\) 0.134378 + 1.11561i 0.00523860 + 0.0434910i
\(659\) 24.8756 0.969015 0.484508 0.874787i \(-0.338999\pi\)
0.484508 + 0.874787i \(0.338999\pi\)
\(660\) 0 0
\(661\) −16.4995 28.5780i −0.641756 1.11155i −0.985041 0.172323i \(-0.944873\pi\)
0.343284 0.939232i \(-0.388461\pi\)
\(662\) −16.9428 29.3457i −0.658499 1.14055i
\(663\) 0 0
\(664\) 1.91649 0.0743742
\(665\) −6.56617 + 0.790912i −0.254625 + 0.0306703i
\(666\) 0 0
\(667\) 15.5238 + 8.96270i 0.601086 + 0.347037i
\(668\) 8.87660 + 15.3747i 0.343446 + 0.594866i
\(669\) 0 0
\(670\) −0.0227088 0.0131109i −0.000877316 0.000506519i
\(671\) −23.2960 + 2.17309i −0.899334 + 0.0838911i
\(672\) 0 0
\(673\) 1.74912i 0.0674236i 0.999432 + 0.0337118i \(0.0107328\pi\)
−0.999432 + 0.0337118i \(0.989267\pi\)
\(674\) −21.7077 12.5329i −0.836148 0.482750i
\(675\) 0 0
\(676\) −6.48643 11.2348i −0.249478 0.432109i
\(677\) 15.5773 26.9808i 0.598686 1.03695i −0.394329 0.918969i \(-0.629023\pi\)
0.993015 0.117985i \(-0.0376436\pi\)
\(678\) 0 0
\(679\) 15.9946 37.4416i 0.613818 1.43687i
\(680\) 0.725302i 0.0278141i
\(681\) 0 0
\(682\) −0.767296 + 0.543863i −0.0293813 + 0.0208256i
\(683\) −37.1098 + 21.4253i −1.41997 + 0.819817i −0.996295 0.0859990i \(-0.972592\pi\)
−0.423670 + 0.905816i \(0.639258\pi\)
\(684\) 0 0
\(685\) 6.89073 0.263281
\(686\) −3.02324 + 18.2718i −0.115428 + 0.697622i
\(687\) 0 0
\(688\) −1.80085 1.03972i −0.0686568 0.0396390i
\(689\) −0.733704 1.27081i −0.0279519 0.0484141i
\(690\) 0 0
\(691\) −12.9688 + 22.4626i −0.493356 + 0.854518i −0.999971 0.00765487i \(-0.997563\pi\)
0.506615 + 0.862173i \(0.330897\pi\)
\(692\) −15.5152 −0.589799
\(693\) 0 0
\(694\) −22.0935 −0.838658
\(695\) 1.57399 2.72623i 0.0597048 0.103412i
\(696\) 0 0
\(697\) −8.37578 14.5073i −0.317255 0.549503i
\(698\) 10.6732 + 6.16219i 0.403987 + 0.233242i
\(699\) 0 0
\(700\) −7.68314 10.2448i −0.290395 0.387216i
\(701\) 0.324170 0.0122437 0.00612186 0.999981i \(-0.498051\pi\)
0.00612186 + 0.999981i \(0.498051\pi\)
\(702\) 0 0
\(703\) 26.0377 15.0329i 0.982029 0.566975i
\(704\) −2.70584 + 1.91792i −0.101980 + 0.0722842i
\(705\) 0 0
\(706\) 12.5945i 0.474001i
\(707\) 6.32068 0.761343i 0.237714 0.0286332i
\(708\) 0 0
\(709\) 8.36850 14.4947i 0.314285 0.544358i −0.665000 0.746843i \(-0.731568\pi\)
0.979285 + 0.202485i \(0.0649018\pi\)
\(710\) −1.28713 2.22937i −0.0483050 0.0836668i
\(711\) 0 0
\(712\) −8.89851 5.13756i −0.333486 0.192538i
\(713\) 1.23296i 0.0461746i
\(714\) 0 0
\(715\) −0.0202941 0.217558i −0.000758957 0.00813621i
\(716\) 1.11782 + 0.645375i 0.0417750 + 0.0241188i
\(717\) 0 0
\(718\) −13.0266 22.5628i −0.486150 0.842037i
\(719\) 3.90390 + 2.25392i 0.145591 + 0.0840570i 0.571026 0.820932i \(-0.306546\pi\)
−0.425435 + 0.904989i \(0.639879\pi\)
\(720\) 0 0
\(721\) 6.69843 + 8.93175i 0.249463 + 0.332636i
\(722\) −20.0778 −0.747218
\(723\) 0 0
\(724\) −10.0412 17.3918i −0.373177 0.646362i
\(725\) 9.97712 + 17.2809i 0.370541 + 0.641796i
\(726\) 0 0
\(727\) −38.4312 −1.42534 −0.712668 0.701502i \(-0.752513\pi\)
−0.712668 + 0.701502i \(0.752513\pi\)
\(728\) −0.400852 0.171240i −0.0148566 0.00634657i
\(729\) 0 0
\(730\) 1.66562 2.88494i 0.0616473 0.106776i
\(731\) −3.26641 + 1.88586i −0.120813 + 0.0697512i
\(732\) 0 0
\(733\) −42.5297 24.5546i −1.57087 0.906943i −0.996062 0.0886556i \(-0.971743\pi\)
−0.574809 0.818287i \(-0.694924\pi\)
\(734\) 15.5822 0.575149
\(735\) 0 0
\(736\) 4.34798i 0.160269i
\(737\) −0.197635 0.0907799i −0.00727998 0.00334392i
\(738\) 0 0
\(739\) −28.4872 + 16.4471i −1.04792 + 0.605016i −0.922066 0.387033i \(-0.873500\pi\)
−0.125852 + 0.992049i \(0.540167\pi\)
\(740\) −1.66557 0.961617i −0.0612276 0.0353498i
\(741\) 0 0
\(742\) 21.6704 + 9.25736i 0.795545 + 0.339849i
\(743\) 0.0301484 0.00110604 0.000553019 1.00000i \(-0.499824\pi\)
0.000553019 1.00000i \(0.499824\pi\)
\(744\) 0 0
\(745\) 0.239875 0.138492i 0.00878834 0.00507395i
\(746\) −10.9916 + 6.34599i −0.402430 + 0.232343i
\(747\) 0 0
\(748\) 0.558731 + 5.98974i 0.0204292 + 0.219007i
\(749\) −19.2364 25.6501i −0.702884 0.937232i
\(750\) 0 0
\(751\) −21.1744 + 36.6752i −0.772666 + 1.33830i 0.163432 + 0.986555i \(0.447744\pi\)
−0.936097 + 0.351741i \(0.885590\pi\)
\(752\) 0.367808 0.212354i 0.0134126 0.00774376i
\(753\) 0 0
\(754\) 0.588228 + 0.339614i 0.0214220 + 0.0123680i
\(755\) 3.36013 0.122288
\(756\) 0 0
\(757\) 4.32399 0.157158 0.0785790 0.996908i \(-0.474962\pi\)
0.0785790 + 0.996908i \(0.474962\pi\)
\(758\) −11.4973 + 19.9139i −0.417601 + 0.723307i
\(759\) 0 0
\(760\) 1.24986 + 2.16482i 0.0453371 + 0.0785262i
\(761\) 0.217251 0.376290i 0.00787535 0.0136405i −0.862061 0.506805i \(-0.830827\pi\)
0.869936 + 0.493164i \(0.164160\pi\)
\(762\) 0 0
\(763\) −5.32900 44.2415i −0.192923 1.60165i
\(764\) 14.4118i 0.521402i
\(765\) 0 0
\(766\) 21.6145 12.4791i 0.780963 0.450889i
\(767\) −0.658928 1.14130i −0.0237925 0.0412098i
\(768\) 0 0
\(769\) 33.3122i 1.20127i −0.799524 0.600634i \(-0.794915\pi\)
0.799524 0.600634i \(-0.205085\pi\)
\(770\) 2.35689 + 2.59951i 0.0849364 + 0.0936799i
\(771\) 0 0
\(772\) 15.7143 + 9.07265i 0.565570 + 0.326532i
\(773\) 9.83462 5.67802i 0.353727 0.204224i −0.312599 0.949885i \(-0.601199\pi\)
0.666325 + 0.745661i \(0.267866\pi\)
\(774\) 0 0
\(775\) −0.686253 + 1.18862i −0.0246509 + 0.0426967i
\(776\) −15.3888 −0.552424
\(777\) 0 0
\(778\) 18.0637i 0.647614i
\(779\) −49.9986 28.8667i −1.79139 1.03426i
\(780\) 0 0
\(781\) −12.3468 17.4192i −0.441804 0.623308i
\(782\) 6.82985 + 3.94322i 0.244235 + 0.141009i
\(783\) 0 0
\(784\) 6.79978 1.66222i 0.242849 0.0593650i
\(785\) 0.969497i 0.0346028i
\(786\) 0 0
\(787\) 11.3772 6.56865i 0.405555 0.234147i −0.283323 0.959024i \(-0.591437\pi\)
0.688878 + 0.724877i \(0.258104\pi\)
\(788\) 1.72705 + 2.99134i 0.0615236 + 0.106562i
\(789\) 0 0
\(790\) 0.245248 0.00872553