Properties

Label 1050.2.bc.e.607.1
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 28 x^{14} + 519 x^{12} - 5404 x^{10} + 40705 x^{8} - 194544 x^{6} + 672624 x^{4} - 1306368 x^{2} + 1679616\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.1
Root \(-2.35727 + 1.36097i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.e.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(0.965926 - 2.46313i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(0.965926 - 2.46313i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.92471 + 3.33369i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-4.42535 - 4.42535i) q^{13} +(-0.295509 + 2.62920i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.36097 - 0.364671i) q^{17} +(0.965926 + 0.258819i) q^{18} +(1.76317 - 3.05390i) q^{19} +(2.12920 + 1.57052i) q^{21} +(-2.72194 - 2.72194i) q^{22} +(-0.364671 - 1.36097i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(5.41993 + 3.12920i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.395046 - 2.61609i) q^{28} -6.66738i q^{29} +(-4.55390 + 2.62920i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-3.71825 + 0.996301i) q^{33} +1.40898 q^{34} -1.00000 q^{36} +(-9.82586 + 2.63283i) q^{37} +(-0.912685 + 3.40619i) q^{38} +(5.41993 - 3.12920i) q^{39} -0.741607i q^{41} +(-2.46313 - 0.965926i) q^{42} +(-1.52070 + 1.52070i) q^{43} +(3.33369 + 1.92471i) q^{44} +(0.704491 + 1.22021i) q^{46} +(-1.36097 - 5.07922i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-5.13397 - 4.75839i) q^{49} +(0.704491 - 1.22021i) q^{51} +(-6.04514 - 1.61979i) q^{52} +(9.51380 + 2.54922i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.05868 + 2.42471i) q^{56} +(2.49350 + 2.49350i) q^{57} +(1.72564 + 6.44019i) q^{58} +(-6.84941 - 11.8635i) q^{59} +(-0.857750 - 0.495222i) q^{61} +(3.71825 - 3.71825i) q^{62} +(-2.06808 + 1.65017i) q^{63} -1.00000i q^{64} +(3.33369 - 1.92471i) q^{66} +(1.98199 - 7.39689i) q^{67} +(-1.36097 + 0.364671i) q^{68} +1.40898 q^{69} +11.2584 q^{71} +(0.965926 - 0.258819i) q^{72} +(2.75660 - 10.2878i) q^{73} +(8.80963 - 5.08624i) q^{74} -3.52634i q^{76} +(10.0704 - 1.52070i) q^{77} +(-4.42535 + 4.42535i) q^{78} +(-2.72849 - 1.57529i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.191942 + 0.716337i) q^{82} +(0.471906 + 0.471906i) q^{83} +(2.62920 + 0.295509i) q^{84} +(1.07529 - 1.86246i) q^{86} +(6.44019 + 1.72564i) q^{87} +(-3.71825 - 0.996301i) q^{88} +(-6.97594 + 12.0827i) q^{89} +(-15.1748 + 6.62564i) q^{91} +(-0.996301 - 0.996301i) q^{92} +(-1.36097 - 5.07922i) q^{93} +(2.62920 + 4.55390i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(6.98682 - 6.98682i) q^{97} +(6.19060 + 3.26748i) q^{98} -3.84941i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 4q^{11} - 8q^{14} + 8q^{16} + 4q^{19} - 4q^{21} - 8q^{24} + 16q^{34} - 16q^{36} + 12q^{44} + 8q^{46} - 96q^{49} + 8q^{51} - 8q^{54} - 4q^{56} - 40q^{59} - 24q^{61} + 12q^{66} + 16q^{69} + 104q^{71} + 48q^{74} + 12q^{79} + 8q^{81} + 4q^{84} + 52q^{86} - 60q^{89} - 52q^{91} + 4q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 0.965926 2.46313i 0.365086 0.930974i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) 1.92471 + 3.33369i 0.580321 + 1.00514i 0.995441 + 0.0953782i \(0.0304061\pi\)
−0.415121 + 0.909766i \(0.636261\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) −4.42535 4.42535i −1.22737 1.22737i −0.964954 0.262417i \(-0.915480\pi\)
−0.262417 0.964954i \(-0.584520\pi\)
\(14\) −0.295509 + 2.62920i −0.0789781 + 0.702682i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.36097 0.364671i −0.330084 0.0884458i 0.0899709 0.995944i \(-0.471323\pi\)
−0.420055 + 0.907499i \(0.637989\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) 1.76317 3.05390i 0.404499 0.700613i −0.589764 0.807576i \(-0.700779\pi\)
0.994263 + 0.106963i \(0.0341125\pi\)
\(20\) 0 0
\(21\) 2.12920 + 1.57052i 0.464629 + 0.342715i
\(22\) −2.72194 2.72194i −0.580321 0.580321i
\(23\) −0.364671 1.36097i −0.0760392 0.283782i 0.917428 0.397903i \(-0.130262\pi\)
−0.993467 + 0.114120i \(0.963595\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 5.41993 + 3.12920i 1.06294 + 0.613686i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.395046 2.61609i −0.0746568 0.494395i
\(29\) 6.66738i 1.23810i −0.785351 0.619050i \(-0.787518\pi\)
0.785351 0.619050i \(-0.212482\pi\)
\(30\) 0 0
\(31\) −4.55390 + 2.62920i −0.817905 + 0.472218i −0.849693 0.527277i \(-0.823213\pi\)
0.0317885 + 0.999495i \(0.489880\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −3.71825 + 0.996301i −0.647263 + 0.173434i
\(34\) 1.40898 0.241638
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −9.82586 + 2.63283i −1.61536 + 0.432835i −0.949634 0.313360i \(-0.898545\pi\)
−0.665727 + 0.746195i \(0.731879\pi\)
\(38\) −0.912685 + 3.40619i −0.148057 + 0.552556i
\(39\) 5.41993 3.12920i 0.867883 0.501072i
\(40\) 0 0
\(41\) 0.741607i 0.115820i −0.998322 0.0579098i \(-0.981556\pi\)
0.998322 0.0579098i \(-0.0184436\pi\)
\(42\) −2.46313 0.965926i −0.380069 0.149046i
\(43\) −1.52070 + 1.52070i −0.231904 + 0.231904i −0.813487 0.581583i \(-0.802434\pi\)
0.581583 + 0.813487i \(0.302434\pi\)
\(44\) 3.33369 + 1.92471i 0.502572 + 0.290160i
\(45\) 0 0
\(46\) 0.704491 + 1.22021i 0.103872 + 0.179911i
\(47\) −1.36097 5.07922i −0.198518 0.740880i −0.991328 0.131411i \(-0.958049\pi\)
0.792810 0.609469i \(-0.208617\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) −5.13397 4.75839i −0.733425 0.679770i
\(50\) 0 0
\(51\) 0.704491 1.22021i 0.0986485 0.170864i
\(52\) −6.04514 1.61979i −0.838311 0.224625i
\(53\) 9.51380 + 2.54922i 1.30682 + 0.350162i 0.844025 0.536303i \(-0.180180\pi\)
0.462796 + 0.886465i \(0.346846\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.05868 + 2.42471i 0.141472 + 0.324015i
\(57\) 2.49350 + 2.49350i 0.330272 + 0.330272i
\(58\) 1.72564 + 6.44019i 0.226588 + 0.845638i
\(59\) −6.84941 11.8635i −0.891717 1.54450i −0.837815 0.545954i \(-0.816168\pi\)
−0.0539019 0.998546i \(-0.517166\pi\)
\(60\) 0 0
\(61\) −0.857750 0.495222i −0.109824 0.0634067i 0.444082 0.895986i \(-0.353530\pi\)
−0.553906 + 0.832579i \(0.686863\pi\)
\(62\) 3.71825 3.71825i 0.472218 0.472218i
\(63\) −2.06808 + 1.65017i −0.260553 + 0.207901i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 3.33369 1.92471i 0.410349 0.236915i
\(67\) 1.98199 7.39689i 0.242139 0.903673i −0.732662 0.680593i \(-0.761722\pi\)
0.974800 0.223080i \(-0.0716112\pi\)
\(68\) −1.36097 + 0.364671i −0.165042 + 0.0442229i
\(69\) 1.40898 0.169622
\(70\) 0 0
\(71\) 11.2584 1.33613 0.668063 0.744105i \(-0.267124\pi\)
0.668063 + 0.744105i \(0.267124\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) 2.75660 10.2878i 0.322636 1.20409i −0.594031 0.804442i \(-0.702464\pi\)
0.916667 0.399652i \(-0.130869\pi\)
\(74\) 8.80963 5.08624i 1.02410 0.591263i
\(75\) 0 0
\(76\) 3.52634i 0.404499i
\(77\) 10.0704 1.52070i 1.14763 0.173299i
\(78\) −4.42535 + 4.42535i −0.501072 + 0.501072i
\(79\) −2.72849 1.57529i −0.306979 0.177234i 0.338595 0.940932i \(-0.390048\pi\)
−0.645574 + 0.763698i \(0.723382\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 0.191942 + 0.716337i 0.0211964 + 0.0791062i
\(83\) 0.471906 + 0.471906i 0.0517984 + 0.0517984i 0.732532 0.680733i \(-0.238339\pi\)
−0.680733 + 0.732532i \(0.738339\pi\)
\(84\) 2.62920 + 0.295509i 0.286869 + 0.0322427i
\(85\) 0 0
\(86\) 1.07529 1.86246i 0.115952 0.200835i
\(87\) 6.44019 + 1.72564i 0.690461 + 0.185008i
\(88\) −3.71825 0.996301i −0.396366 0.106206i
\(89\) −6.97594 + 12.0827i −0.739448 + 1.28076i 0.213296 + 0.976988i \(0.431580\pi\)
−0.952744 + 0.303774i \(0.901753\pi\)
\(90\) 0 0
\(91\) −15.1748 + 6.62564i −1.59075 + 0.694555i
\(92\) −0.996301 0.996301i −0.103872 0.103872i
\(93\) −1.36097 5.07922i −0.141126 0.526690i
\(94\) 2.62920 + 4.55390i 0.271181 + 0.469699i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 6.98682 6.98682i 0.709404 0.709404i −0.257006 0.966410i \(-0.582736\pi\)
0.966410 + 0.257006i \(0.0827359\pi\)
\(98\) 6.19060 + 3.26748i 0.625345 + 0.330066i
\(99\) 3.84941i 0.386880i
\(100\) 0 0
\(101\) 12.4415 7.18310i 1.23797 0.714745i 0.269295 0.963058i \(-0.413209\pi\)
0.968680 + 0.248313i \(0.0798761\pi\)
\(102\) −0.364671 + 1.36097i −0.0361079 + 0.134756i
\(103\) 14.8426 3.97706i 1.46249 0.391872i 0.562138 0.827043i \(-0.309979\pi\)
0.900348 + 0.435172i \(0.143312\pi\)
\(104\) 6.25839 0.613686
\(105\) 0 0
\(106\) −9.84941 −0.956659
\(107\) −2.60170 + 0.697125i −0.251516 + 0.0673936i −0.382374 0.924008i \(-0.624893\pi\)
0.130858 + 0.991401i \(0.458227\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) 14.5503 8.40064i 1.39367 0.804636i 0.399951 0.916537i \(-0.369027\pi\)
0.993719 + 0.111901i \(0.0356939\pi\)
\(110\) 0 0
\(111\) 10.1725i 0.965529i
\(112\) −1.65017 2.06808i −0.155926 0.195415i
\(113\) −10.2109 + 10.2109i −0.960563 + 0.960563i −0.999251 0.0386883i \(-0.987682\pi\)
0.0386883 + 0.999251i \(0.487682\pi\)
\(114\) −3.05390 1.76317i −0.286024 0.165136i
\(115\) 0 0
\(116\) −3.33369 5.77412i −0.309525 0.536113i
\(117\) 1.61979 + 6.04514i 0.149750 + 0.558874i
\(118\) 9.68653 + 9.68653i 0.891717 + 0.891717i
\(119\) −2.21283 + 3.00000i −0.202850 + 0.275010i
\(120\) 0 0
\(121\) −1.90898 + 3.30645i −0.173544 + 0.300587i
\(122\) 0.956695 + 0.256346i 0.0866151 + 0.0232085i
\(123\) 0.716337 + 0.191942i 0.0645900 + 0.0173068i
\(124\) −2.62920 + 4.55390i −0.236109 + 0.408952i
\(125\) 0 0
\(126\) 1.57052 2.12920i 0.139913 0.189684i
\(127\) −14.5565 14.5565i −1.29168 1.29168i −0.933746 0.357936i \(-0.883481\pi\)
−0.357936 0.933746i \(-0.616519\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −1.07529 1.86246i −0.0946744 0.163981i
\(130\) 0 0
\(131\) −5.66631 3.27145i −0.495068 0.285828i 0.231607 0.972810i \(-0.425602\pi\)
−0.726675 + 0.686982i \(0.758935\pi\)
\(132\) −2.72194 + 2.72194i −0.236915 + 0.236915i
\(133\) −5.81905 7.29275i −0.504576 0.632362i
\(134\) 7.65782i 0.661535i
\(135\) 0 0
\(136\) 1.22021 0.704491i 0.104633 0.0604096i
\(137\) −2.94610 + 10.9950i −0.251703 + 0.939367i 0.718192 + 0.695845i \(0.244970\pi\)
−0.969895 + 0.243523i \(0.921697\pi\)
\(138\) −1.36097 + 0.364671i −0.115854 + 0.0310429i
\(139\) 3.50510 0.297299 0.148650 0.988890i \(-0.452507\pi\)
0.148650 + 0.988890i \(0.452507\pi\)
\(140\) 0 0
\(141\) 5.25839 0.442837
\(142\) −10.8748 + 2.91389i −0.912591 + 0.244528i
\(143\) 6.23524 23.2702i 0.521417 1.94596i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 10.6507i 0.881458i
\(147\) 5.92503 3.72748i 0.488688 0.307437i
\(148\) −7.19303 + 7.19303i −0.591263 + 0.591263i
\(149\) −11.9713 6.91165i −0.980730 0.566225i −0.0782393 0.996935i \(-0.524930\pi\)
−0.902490 + 0.430710i \(0.858263\pi\)
\(150\) 0 0
\(151\) −2.97861 5.15910i −0.242396 0.419842i 0.719001 0.695010i \(-0.244600\pi\)
−0.961396 + 0.275168i \(0.911267\pi\)
\(152\) 0.912685 + 3.40619i 0.0740285 + 0.276278i
\(153\) 0.996301 + 0.996301i 0.0805462 + 0.0805462i
\(154\) −9.33369 + 4.07529i −0.752130 + 0.328397i
\(155\) 0 0
\(156\) 3.12920 5.41993i 0.250536 0.433941i
\(157\) 9.64315 + 2.58387i 0.769607 + 0.206216i 0.622198 0.782860i \(-0.286240\pi\)
0.147409 + 0.989076i \(0.452907\pi\)
\(158\) 3.04324 + 0.815432i 0.242107 + 0.0648723i
\(159\) −4.92471 + 8.52984i −0.390555 + 0.676460i
\(160\) 0 0
\(161\) −3.70449 0.416367i −0.291955 0.0328143i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) −0.356071 1.32888i −0.0278896 0.104086i 0.950578 0.310486i \(-0.100492\pi\)
−0.978468 + 0.206400i \(0.933825\pi\)
\(164\) −0.370803 0.642250i −0.0289549 0.0501513i
\(165\) 0 0
\(166\) −0.577964 0.333688i −0.0448587 0.0258992i
\(167\) −7.69393 + 7.69393i −0.595374 + 0.595374i −0.939078 0.343704i \(-0.888318\pi\)
0.343704 + 0.939078i \(0.388318\pi\)
\(168\) −2.61609 + 0.395046i −0.201836 + 0.0304785i
\(169\) 26.1675i 2.01288i
\(170\) 0 0
\(171\) −3.05390 + 1.76317i −0.233538 + 0.134833i
\(172\) −0.556613 + 2.07731i −0.0424414 + 0.158393i
\(173\) −1.64094 + 0.439687i −0.124758 + 0.0334288i −0.320658 0.947195i \(-0.603904\pi\)
0.195900 + 0.980624i \(0.437237\pi\)
\(174\) −6.66738 −0.505452
\(175\) 0 0
\(176\) 3.84941 0.290160
\(177\) 13.2320 3.54552i 0.994581 0.266497i
\(178\) 3.61101 13.4765i 0.270657 1.01010i
\(179\) −11.9713 + 6.91165i −0.894779 + 0.516601i −0.875503 0.483213i \(-0.839470\pi\)
−0.0192766 + 0.999814i \(0.506136\pi\)
\(180\) 0 0
\(181\) 3.36086i 0.249811i −0.992169 0.124905i \(-0.960137\pi\)
0.992169 0.124905i \(-0.0398627\pi\)
\(182\) 12.9429 10.3274i 0.959388 0.765517i
\(183\) 0.700350 0.700350i 0.0517713 0.0517713i
\(184\) 1.22021 + 0.704491i 0.0899554 + 0.0519358i
\(185\) 0 0
\(186\) 2.62920 + 4.55390i 0.192782 + 0.333908i
\(187\) −1.40377 5.23894i −0.102654 0.383109i
\(188\) −3.71825 3.71825i −0.271181 0.271181i
\(189\) −1.05868 2.42471i −0.0770076 0.176371i
\(190\) 0 0
\(191\) −0.370803 + 0.642250i −0.0268304 + 0.0464716i −0.879129 0.476584i \(-0.841875\pi\)
0.852298 + 0.523056i \(0.175208\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) 7.15653 + 1.91759i 0.515138 + 0.138031i 0.507017 0.861936i \(-0.330748\pi\)
0.00812132 + 0.999967i \(0.497415\pi\)
\(194\) −4.94043 + 8.55707i −0.354702 + 0.614362i
\(195\) 0 0
\(196\) −6.82535 1.55390i −0.487525 0.110993i
\(197\) 12.5349 + 12.5349i 0.893076 + 0.893076i 0.994811 0.101735i \(-0.0324395\pi\)
−0.101735 + 0.994811i \(0.532439\pi\)
\(198\) 0.996301 + 3.71825i 0.0708040 + 0.264244i
\(199\) −0.350302 0.606741i −0.0248323 0.0430107i 0.853342 0.521351i \(-0.174572\pi\)
−0.878174 + 0.478340i \(0.841238\pi\)
\(200\) 0 0
\(201\) 6.63187 + 3.82891i 0.467776 + 0.270070i
\(202\) −10.1584 + 10.1584i −0.714745 + 0.714745i
\(203\) −16.4226 6.44019i −1.15264 0.452013i
\(204\) 1.40898i 0.0986485i
\(205\) 0 0
\(206\) −13.3075 + 7.68310i −0.927179 + 0.535307i
\(207\) −0.364671 + 1.36097i −0.0253464 + 0.0945941i
\(208\) −6.04514 + 1.61979i −0.419155 + 0.112312i
\(209\) 13.5743 0.938957
\(210\) 0 0
\(211\) −15.4426 −1.06311 −0.531555 0.847024i \(-0.678392\pi\)
−0.531555 + 0.847024i \(0.678392\pi\)
\(212\) 9.51380 2.54922i 0.653410 0.175081i
\(213\) −2.91389 + 10.8748i −0.199656 + 0.745127i
\(214\) 2.33262 1.34674i 0.159455 0.0920614i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 2.07731 + 13.7564i 0.141017 + 0.933848i
\(218\) −11.8803 + 11.8803i −0.804636 + 0.804636i
\(219\) 9.22377 + 5.32535i 0.623285 + 0.359854i
\(220\) 0 0
\(221\) 4.40898 + 7.63658i 0.296580 + 0.513692i
\(222\) 2.63283 + 9.82586i 0.176704 + 0.659469i
\(223\) 1.17901 + 1.17901i 0.0789525 + 0.0789525i 0.745480 0.666528i \(-0.232220\pi\)
−0.666528 + 0.745480i \(0.732220\pi\)
\(224\) 2.12920 + 1.57052i 0.142263 + 0.104935i
\(225\) 0 0
\(226\) 7.22021 12.5058i 0.480282 0.831872i
\(227\) 11.1192 + 2.97938i 0.738008 + 0.197749i 0.608192 0.793790i \(-0.291895\pi\)
0.129815 + 0.991538i \(0.458562\pi\)
\(228\) 3.40619 + 0.912685i 0.225580 + 0.0604440i
\(229\) −7.80873 + 13.5251i −0.516016 + 0.893765i 0.483811 + 0.875172i \(0.339252\pi\)
−0.999827 + 0.0185931i \(0.994081\pi\)
\(230\) 0 0
\(231\) −1.13754 + 10.1209i −0.0748443 + 0.665904i
\(232\) 4.71455 + 4.71455i 0.309525 + 0.309525i
\(233\) 7.69393 + 28.7141i 0.504046 + 1.88113i 0.471920 + 0.881641i \(0.343561\pi\)
0.0321261 + 0.999484i \(0.489772\pi\)
\(234\) −3.12920 5.41993i −0.204562 0.354312i
\(235\) 0 0
\(236\) −11.8635 6.84941i −0.772250 0.445859i
\(237\) 2.22780 2.22780i 0.144711 0.144711i
\(238\) 1.36097 3.47050i 0.0882187 0.224959i
\(239\) 7.95188i 0.514364i 0.966363 + 0.257182i \(0.0827940\pi\)
−0.966363 + 0.257182i \(0.917206\pi\)
\(240\) 0 0
\(241\) −9.81069 + 5.66420i −0.631962 + 0.364863i −0.781512 0.623891i \(-0.785551\pi\)
0.149550 + 0.988754i \(0.452218\pi\)
\(242\) 0.988162 3.68787i 0.0635215 0.237065i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) −0.990444 −0.0634067
\(245\) 0 0
\(246\) −0.741607 −0.0472831
\(247\) −21.3172 + 5.71194i −1.35638 + 0.363442i
\(248\) 1.36097 5.07922i 0.0864218 0.322531i
\(249\) −0.577964 + 0.333688i −0.0366270 + 0.0211466i
\(250\) 0 0
\(251\) 21.0336i 1.32763i −0.747898 0.663814i \(-0.768937\pi\)
0.747898 0.663814i \(-0.231063\pi\)
\(252\) −0.965926 + 2.46313i −0.0608476 + 0.155162i
\(253\) 3.83517 3.83517i 0.241115 0.241115i
\(254\) 17.8280 + 10.2930i 1.11863 + 0.645841i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.70715 + 25.0314i 0.418380 + 1.56142i 0.777967 + 0.628305i \(0.216251\pi\)
−0.359587 + 0.933112i \(0.617082\pi\)
\(258\) 1.52070 + 1.52070i 0.0946744 + 0.0946744i
\(259\) −3.00606 + 26.7454i −0.186787 + 1.66188i
\(260\) 0 0
\(261\) −3.33369 + 5.77412i −0.206350 + 0.357409i
\(262\) 6.31995 + 1.69343i 0.390448 + 0.104620i
\(263\) 16.0257 + 4.29407i 0.988187 + 0.264784i 0.716489 0.697599i \(-0.245748\pi\)
0.271698 + 0.962383i \(0.412415\pi\)
\(264\) 1.92471 3.33369i 0.118457 0.205174i
\(265\) 0 0
\(266\) 7.50828 + 5.53818i 0.460362 + 0.339568i
\(267\) −9.86547 9.86547i −0.603757 0.603757i
\(268\) −1.98199 7.39689i −0.121069 0.451837i
\(269\) −13.6804 23.6952i −0.834110 1.44472i −0.894753 0.446562i \(-0.852648\pi\)
0.0606421 0.998160i \(-0.480685\pi\)
\(270\) 0 0
\(271\) −0.828972 0.478607i −0.0503565 0.0290733i 0.474610 0.880196i \(-0.342589\pi\)
−0.524967 + 0.851123i \(0.675922\pi\)
\(272\) −0.996301 + 0.996301i −0.0604096 + 0.0604096i
\(273\) −2.47236 16.3725i −0.149634 0.990911i
\(274\) 11.3829i 0.687665i
\(275\) 0 0
\(276\) 1.22021 0.704491i 0.0734483 0.0424054i
\(277\) −5.38699 + 20.1045i −0.323673 + 1.20796i 0.591966 + 0.805963i \(0.298352\pi\)
−0.915639 + 0.402001i \(0.868315\pi\)
\(278\) −3.38567 + 0.907188i −0.203059 + 0.0544095i
\(279\) 5.25839 0.314812
\(280\) 0 0
\(281\) 2.89220 0.172534 0.0862670 0.996272i \(-0.472506\pi\)
0.0862670 + 0.996272i \(0.472506\pi\)
\(282\) −5.07922 + 1.36097i −0.302463 + 0.0810447i
\(283\) 5.48531 20.4714i 0.326068 1.21690i −0.587167 0.809466i \(-0.699757\pi\)
0.913234 0.407435i \(-0.133577\pi\)
\(284\) 9.75005 5.62920i 0.578559 0.334031i
\(285\) 0 0
\(286\) 24.0911i 1.42454i
\(287\) −1.82667 0.716337i −0.107825 0.0422841i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) −13.0032 7.50738i −0.764892 0.441611i
\(290\) 0 0
\(291\) 4.94043 + 8.55707i 0.289613 + 0.501625i
\(292\) −2.75660 10.2878i −0.161318 0.602047i
\(293\) −14.1436 14.1436i −0.826280 0.826280i 0.160720 0.987000i \(-0.448618\pi\)
−0.987000 + 0.160720i \(0.948618\pi\)
\(294\) −4.75839 + 5.13397i −0.277515 + 0.299419i
\(295\) 0 0
\(296\) 5.08624 8.80963i 0.295632 0.512049i
\(297\) 3.71825 + 0.996301i 0.215754 + 0.0578112i
\(298\) 13.3523 + 3.57773i 0.773477 + 0.207253i
\(299\) −4.40898 + 7.63658i −0.254978 + 0.441635i
\(300\) 0 0
\(301\) 2.27679 + 5.21455i 0.131232 + 0.300561i
\(302\) 4.21239 + 4.21239i 0.242396 + 0.242396i
\(303\) 3.71825 + 13.8767i 0.213608 + 0.797194i
\(304\) −1.76317 3.05390i −0.101125 0.175153i
\(305\) 0 0
\(306\) −1.22021 0.704491i −0.0697550 0.0402731i
\(307\) 6.81363 6.81363i 0.388874 0.388874i −0.485411 0.874286i \(-0.661330\pi\)
0.874286 + 0.485411i \(0.161330\pi\)
\(308\) 7.96089 6.35217i 0.453614 0.361948i
\(309\) 15.3662i 0.874152i
\(310\) 0 0
\(311\) −17.8568 + 10.3096i −1.01257 + 0.584605i −0.911942 0.410319i \(-0.865417\pi\)
−0.100624 + 0.994925i \(0.532084\pi\)
\(312\) −1.61979 + 6.04514i −0.0917026 + 0.342239i
\(313\) −15.9075 + 4.26240i −0.899145 + 0.240925i −0.678649 0.734463i \(-0.737434\pi\)
−0.220496 + 0.975388i \(0.570768\pi\)
\(314\) −9.98332 −0.563391
\(315\) 0 0
\(316\) −3.15059 −0.177234
\(317\) −25.6761 + 6.87988i −1.44211 + 0.386412i −0.893272 0.449516i \(-0.851596\pi\)
−0.548838 + 0.835928i \(0.684930\pi\)
\(318\) 2.54922 9.51380i 0.142953 0.533507i
\(319\) 22.2269 12.8327i 1.24447 0.718495i
\(320\) 0 0
\(321\) 2.69348i 0.150336i
\(322\) 3.68603 0.556613i 0.205414 0.0310189i
\(323\) −3.51330 + 3.51330i −0.195485 + 0.195485i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 0.687877 + 1.19144i 0.0380980 + 0.0659876i
\(327\) 4.34849 + 16.2288i 0.240472 + 0.897455i
\(328\) 0.524395 + 0.524395i 0.0289549 + 0.0289549i
\(329\) −13.8253 1.55390i −0.762216 0.0856694i
\(330\) 0 0
\(331\) −3.37347 + 5.84303i −0.185423 + 0.321162i −0.943719 0.330749i \(-0.892699\pi\)
0.758296 + 0.651910i \(0.226032\pi\)
\(332\) 0.644635 + 0.172729i 0.0353789 + 0.00947976i
\(333\) 9.82586 + 2.63283i 0.538454 + 0.144278i
\(334\) 5.44043 9.42310i 0.297687 0.515609i
\(335\) 0 0
\(336\) 2.42471 1.05868i 0.132279 0.0577557i
\(337\) 2.19755 + 2.19755i 0.119708 + 0.119708i 0.764423 0.644715i \(-0.223024\pi\)
−0.644715 + 0.764423i \(0.723024\pi\)
\(338\) −6.77264 25.2758i −0.368383 1.37482i
\(339\) −7.22021 12.5058i −0.392148 0.679221i
\(340\) 0 0
\(341\) −17.5298 10.1209i −0.949294 0.548075i
\(342\) 2.49350 2.49350i 0.134833 0.134833i
\(343\) −16.6796 + 8.04937i −0.900611 + 0.434625i
\(344\) 2.15059i 0.115952i
\(345\) 0 0
\(346\) 1.47122 0.849411i 0.0790934 0.0456646i
\(347\) 3.42859 12.7957i 0.184056 0.686908i −0.810774 0.585359i \(-0.800954\pi\)
0.994831 0.101549i \(-0.0323798\pi\)
\(348\) 6.44019 1.72564i 0.345230 0.0925042i
\(349\) 18.1788 0.973090 0.486545 0.873655i \(-0.338257\pi\)
0.486545 + 0.873655i \(0.338257\pi\)
\(350\) 0 0
\(351\) −6.25839 −0.334048
\(352\) −3.71825 + 0.996301i −0.198183 + 0.0531030i
\(353\) −5.64535 + 21.0687i −0.300472 + 1.12138i 0.636302 + 0.771440i \(0.280463\pi\)
−0.936774 + 0.349936i \(0.886203\pi\)
\(354\) −11.8635 + 6.84941i −0.630539 + 0.364042i
\(355\) 0 0
\(356\) 13.9519i 0.739448i
\(357\) −2.32505 2.91389i −0.123055 0.154219i
\(358\) 9.77455 9.77455i 0.516601 0.516601i
\(359\) 24.7752 + 14.3040i 1.30758 + 0.754934i 0.981692 0.190473i \(-0.0610022\pi\)
0.325892 + 0.945407i \(0.394336\pi\)
\(360\) 0 0
\(361\) 3.28246 + 5.68538i 0.172761 + 0.299230i
\(362\) 0.869854 + 3.24634i 0.0457185 + 0.170624i
\(363\) −2.69971 2.69971i −0.141698 0.141698i
\(364\) −9.82891 + 13.3253i −0.515175 + 0.698438i
\(365\) 0 0
\(366\) −0.495222 + 0.857750i −0.0258857 + 0.0448353i
\(367\) 31.3766 + 8.40733i 1.63784 + 0.438859i 0.956174 0.292800i \(-0.0945870\pi\)
0.681671 + 0.731659i \(0.261254\pi\)
\(368\) −1.36097 0.364671i −0.0709456 0.0190098i
\(369\) −0.370803 + 0.642250i −0.0193033 + 0.0334342i
\(370\) 0 0
\(371\) 15.4687 20.9713i 0.803093 1.08878i
\(372\) −3.71825 3.71825i −0.192782 0.192782i
\(373\) 5.71194 + 21.3172i 0.295753 + 1.10377i 0.940618 + 0.339468i \(0.110247\pi\)
−0.644865 + 0.764297i \(0.723086\pi\)
\(374\) 2.71188 + 4.69711i 0.140228 + 0.242882i
\(375\) 0 0
\(376\) 4.55390 + 2.62920i 0.234850 + 0.135590i
\(377\) −29.5055 + 29.5055i −1.51961 + 1.51961i
\(378\) 1.65017 + 2.06808i 0.0848754 + 0.106371i
\(379\) 15.8588i 0.814614i 0.913291 + 0.407307i \(0.133532\pi\)
−0.913291 + 0.407307i \(0.866468\pi\)
\(380\) 0 0
\(381\) 17.8280 10.2930i 0.913357 0.527327i
\(382\) 0.191942 0.716337i 0.00982061 0.0366510i
\(383\) 17.1422 4.59325i 0.875927 0.234704i 0.207278 0.978282i \(-0.433540\pi\)
0.668649 + 0.743578i \(0.266873\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −7.40898 −0.377107
\(387\) 2.07731 0.556613i 0.105596 0.0282942i
\(388\) 2.55735 9.54418i 0.129830 0.484532i
\(389\) 30.2340 17.4556i 1.53292 0.885034i 0.533700 0.845674i \(-0.320801\pi\)
0.999225 0.0393604i \(-0.0125320\pi\)
\(390\) 0 0
\(391\) 1.98523i 0.100397i
\(392\) 6.99496 0.265576i 0.353299 0.0134136i
\(393\) 4.62652 4.62652i 0.233377 0.233377i
\(394\) −15.3521 8.86353i −0.773427 0.446538i
\(395\) 0 0
\(396\) −1.92471 3.33369i −0.0967201 0.167524i
\(397\) −9.34838 34.8886i −0.469182 1.75101i −0.642640 0.766169i \(-0.722161\pi\)
0.173458 0.984841i \(-0.444506\pi\)
\(398\) 0.495402 + 0.495402i 0.0248323 + 0.0248323i
\(399\) 8.55034 3.73327i 0.428052 0.186897i
\(400\) 0 0
\(401\) −0.741607 + 1.28450i −0.0370341 + 0.0641449i −0.883948 0.467585i \(-0.845124\pi\)
0.846914 + 0.531729i \(0.178458\pi\)
\(402\) −7.39689 1.98199i −0.368923 0.0988526i
\(403\) 31.7877 + 8.51750i 1.58346 + 0.424287i
\(404\) 7.18310 12.4415i 0.357373 0.618987i
\(405\) 0 0
\(406\) 17.5298 + 1.97027i 0.869991 + 0.0977828i
\(407\) −27.6889 27.6889i −1.37249 1.37249i
\(408\) 0.364671 + 1.36097i 0.0180539 + 0.0673782i
\(409\) −1.51216 2.61914i −0.0747716 0.129508i 0.826215 0.563354i \(-0.190489\pi\)
−0.900987 + 0.433846i \(0.857156\pi\)
\(410\) 0 0
\(411\) −9.85786 5.69144i −0.486252 0.280738i
\(412\) 10.8655 10.8655i 0.535307 0.535307i
\(413\) −35.8374 + 5.41167i −1.76344 + 0.266291i
\(414\) 1.40898i 0.0692477i
\(415\) 0 0
\(416\) 5.41993 3.12920i 0.265734 0.153421i
\(417\) −0.907188 + 3.38567i −0.0444252 + 0.165797i
\(418\) −13.1118 + 3.51330i −0.641319 + 0.171841i
\(419\) −14.8547 −0.725702 −0.362851 0.931847i \(-0.618197\pi\)
−0.362851 + 0.931847i \(0.618197\pi\)
\(420\) 0 0
\(421\) 27.2920 1.33013 0.665065 0.746786i \(-0.268404\pi\)
0.665065 + 0.746786i \(0.268404\pi\)
\(422\) 14.9164 3.99683i 0.726117 0.194563i
\(423\) −1.36097 + 5.07922i −0.0661727 + 0.246960i
\(424\) −8.52984 + 4.92471i −0.414246 + 0.239165i
\(425\) 0 0
\(426\) 11.2584i 0.545471i
\(427\) −2.04832 + 1.63440i −0.0991250 + 0.0790940i
\(428\) −1.90458 + 1.90458i −0.0920614 + 0.0920614i
\(429\) 20.8635 + 12.0456i 1.00730 + 0.581565i
\(430\) 0 0
\(431\) −18.5242 32.0848i −0.892278 1.54547i −0.837138 0.546992i \(-0.815773\pi\)
−0.0551401 0.998479i \(-0.517561\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) 7.65990 + 7.65990i 0.368111 + 0.368111i 0.866788 0.498677i \(-0.166181\pi\)
−0.498677 + 0.866788i \(0.666181\pi\)
\(434\) −5.56696 12.7501i −0.267222 0.612022i
\(435\) 0 0
\(436\) 8.40064 14.5503i 0.402318 0.696835i
\(437\) −4.79925 1.28596i −0.229579 0.0615156i
\(438\) −10.2878 2.75660i −0.491569 0.131716i
\(439\) 10.1375 17.5586i 0.483835 0.838027i −0.515992 0.856593i \(-0.672577\pi\)
0.999828 + 0.0185660i \(0.00591009\pi\)
\(440\) 0 0
\(441\) 2.06696 + 6.68788i 0.0984265 + 0.318470i
\(442\) −6.23524 6.23524i −0.296580 0.296580i
\(443\) 1.81987 + 6.79186i 0.0864647 + 0.322691i 0.995588 0.0938374i \(-0.0299134\pi\)
−0.909123 + 0.416528i \(0.863247\pi\)
\(444\) −5.08624 8.80963i −0.241382 0.418086i
\(445\) 0 0
\(446\) −1.44399 0.833688i −0.0683749 0.0394763i
\(447\) 9.77455 9.77455i 0.462320 0.462320i
\(448\) −2.46313 0.965926i −0.116372 0.0456357i
\(449\) 4.46654i 0.210789i 0.994430 + 0.105394i \(0.0336105\pi\)
−0.994430 + 0.105394i \(0.966389\pi\)
\(450\) 0 0
\(451\) 2.47229 1.42737i 0.116415 0.0672125i
\(452\) −3.73746 + 13.9484i −0.175795 + 0.656077i
\(453\) 5.75423 1.54184i 0.270357 0.0724420i
\(454\) −11.5114 −0.540259
\(455\) 0 0
\(456\) −3.52634 −0.165136
\(457\) 23.4389 6.28043i 1.09643 0.293786i 0.335117 0.942176i \(-0.391224\pi\)
0.761308 + 0.648390i \(0.224557\pi\)
\(458\) 4.04210 15.0853i 0.188875 0.704891i
\(459\) −1.22021 + 0.704491i −0.0569547 + 0.0328828i
\(460\) 0 0
\(461\) 8.81796i 0.410694i 0.978689 + 0.205347i \(0.0658322\pi\)
−0.978689 + 0.205347i \(0.934168\pi\)
\(462\) −1.52070 10.0704i −0.0707492 0.468518i
\(463\) −1.05131 + 1.05131i −0.0488583 + 0.0488583i −0.731114 0.682256i \(-0.760999\pi\)
0.682256 + 0.731114i \(0.260999\pi\)
\(464\) −5.77412 3.33369i −0.268057 0.154763i
\(465\) 0 0
\(466\) −14.8635 25.7444i −0.688540 1.19259i
\(467\) −9.57824 35.7465i −0.443228 1.65415i −0.720573 0.693379i \(-0.756121\pi\)
0.277345 0.960770i \(-0.410545\pi\)
\(468\) 4.42535 + 4.42535i 0.204562 + 0.204562i
\(469\) −16.3050 12.0267i −0.752895 0.555343i
\(470\) 0 0
\(471\) −4.99166 + 8.64581i −0.230004 + 0.398378i
\(472\) 13.2320 + 3.54552i 0.609054 + 0.163196i
\(473\) −7.99642 2.14263i −0.367676 0.0985184i
\(474\) −1.57529 + 2.72849i −0.0723557 + 0.125324i
\(475\) 0 0
\(476\) −0.416367 + 3.70449i −0.0190841 + 0.169795i
\(477\) −6.96459 6.96459i −0.318886 0.318886i
\(478\) −2.05810 7.68092i −0.0941352 0.351317i
\(479\) −0.778723 1.34879i −0.0355807 0.0616277i 0.847687 0.530497i \(-0.177995\pi\)
−0.883267 + 0.468870i \(0.844661\pi\)
\(480\) 0 0
\(481\) 55.1341 + 31.8317i 2.51390 + 1.45140i
\(482\) 8.01039 8.01039i 0.364863 0.364863i
\(483\) 1.36097 3.47050i 0.0619264 0.157913i
\(484\) 3.81796i 0.173544i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −2.02588 + 7.56068i −0.0918013 + 0.342607i −0.996515 0.0834127i \(-0.973418\pi\)
0.904714 + 0.426020i \(0.140085\pi\)
\(488\) 0.956695 0.256346i 0.0433076 0.0116042i
\(489\) 1.37575 0.0622137
\(490\) 0 0
\(491\) 43.8776 1.98017 0.990085 0.140468i \(-0.0448608\pi\)
0.990085 + 0.140468i \(0.0448608\pi\)
\(492\) 0.716337 0.191942i 0.0322950 0.00865341i
\(493\) −2.43140 + 9.07411i −0.109505 + 0.408677i
\(494\) 19.1125 11.0346i 0.859913 0.496471i
\(495\) 0 0
\(496\) 5.25839i 0.236109i
\(497\) 10.8748 27.7308i 0.487800 1.24390i
\(498\) 0.471906 0.471906i 0.0211466 0.0211466i
\(499\) −29.9024 17.2642i −1.33862 0.772850i −0.352014 0.935995i \(-0.614503\pi\)
−0.986602 + 0.163144i \(0.947836\pi\)
\(500\) 0 0
\(501\) −5.44043 9.42310i −0.243060 0.420993i
\(502\) 5.44389 + 20.3169i 0.242973 + 0.906786i
\(503\) 16.9300 + 16.9300i 0.754872 + 0.754872i 0.975384 0.220512i \(-0.0707728\pi\)
−0.220512 + 0.975384i \(0.570773\pi\)
\(504\) 0.295509 2.62920i 0.0131630 0.117114i
\(505\) 0 0
\(506\) −2.71188 + 4.69711i −0.120558 + 0.208812i
\(507\) −25.2758 6.77264i −1.12254 0.300784i
\(508\) −19.8846 5.32805i −0.882235 0.236394i
\(509\) −5.10674 + 8.84514i −0.226352 + 0.392054i −0.956724 0.290996i \(-0.906013\pi\)
0.730372 + 0.683050i \(0.239347\pi\)
\(510\) 0 0
\(511\) −22.6774 16.7271i −1.00319 0.739963i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −0.912685 3.40619i −0.0402960 0.150387i
\(514\) −12.9572 22.4426i −0.571518 0.989899i
\(515\) 0 0
\(516\) −1.86246 1.07529i −0.0819904 0.0473372i
\(517\) 14.3131 14.3131i 0.629487 0.629487i
\(518\) −4.01860 26.6121i −0.176567 1.16927i
\(519\) 1.69882i 0.0745700i
\(520\) 0 0
\(521\) −15.0251 + 8.67476i −0.658263 + 0.380048i −0.791615 0.611021i \(-0.790759\pi\)
0.133352 + 0.991069i \(0.457426\pi\)
\(522\) 1.72564 6.44019i 0.0755294 0.281879i
\(523\) −40.7197 + 10.9108i −1.78055 + 0.477097i −0.990684 0.136184i \(-0.956516\pi\)
−0.789865 + 0.613281i \(0.789849\pi\)
\(524\) −6.54289 −0.285828
\(525\) 0 0
\(526\) −16.5910 −0.723403
\(527\) 7.15653 1.91759i 0.311743 0.0835313i
\(528\) −0.996301 + 3.71825i −0.0433584 + 0.161816i
\(529\) 18.1993 10.5074i 0.791275 0.456843i
\(530\) 0 0
\(531\) 13.6988i 0.594478i
\(532\) −8.68582 3.40619i −0.376578 0.147677i
\(533\) −3.28187 + 3.28187i −0.142154 + 0.142154i
\(534\) 12.0827 + 6.97594i 0.522869 + 0.301878i
\(535\) 0 0
\(536\) 3.82891 + 6.63187i 0.165384 + 0.286453i
\(537\) −3.57773 13.3523i −0.154391 0.576194i
\(538\) 19.3470 + 19.3470i 0.834110 + 0.834110i
\(539\) 5.98161 26.2736i 0.257646 1.13168i
\(540\) 0 0
\(541\) 11.3709 19.6950i 0.488874 0.846754i −0.511044 0.859554i \(-0.670741\pi\)
0.999918 + 0.0128002i \(0.00407455\pi\)
\(542\) 0.924599 + 0.247745i 0.0397149 + 0.0106416i
\(543\) 3.24634 + 0.869854i 0.139314 + 0.0373290i
\(544\) 0.704491 1.22021i 0.0302048 0.0523163i
\(545\) 0 0
\(546\) 6.62564 + 15.1748i 0.283551 + 0.649420i
\(547\) −12.2324 12.2324i −0.523021 0.523021i 0.395462 0.918483i \(-0.370585\pi\)
−0.918483 + 0.395462i \(0.870585\pi\)
\(548\) 2.94610 + 10.9950i 0.125851 + 0.469684i
\(549\) 0.495222 + 0.857750i 0.0211356 + 0.0366079i
\(550\) 0 0
\(551\) −20.3615 11.7557i −0.867430 0.500811i
\(552\) −0.996301 + 0.996301i −0.0424054 + 0.0424054i
\(553\) −6.51567 + 5.19900i −0.277074 + 0.221084i
\(554\) 20.8137i 0.884291i
\(555\) 0 0
\(556\) 3.03551 1.75255i 0.128734 0.0743248i
\(557\) 9.30265 34.7179i 0.394166 1.47105i −0.429031 0.903290i \(-0.641145\pi\)
0.823196 0.567757i \(-0.192189\pi\)
\(558\) −5.07922 + 1.36097i −0.215020 + 0.0576146i
\(559\) 13.4592 0.569265
\(560\) 0 0
\(561\) 5.42375 0.228991
\(562\) −2.79365 + 0.748555i −0.117843 + 0.0315759i
\(563\) 8.55924 31.9435i 0.360729 1.34626i −0.512391 0.858752i \(-0.671240\pi\)
0.873120 0.487506i \(-0.162093\pi\)
\(564\) 4.55390 2.62920i 0.191754 0.110709i
\(565\) 0 0
\(566\) 21.1936i 0.890833i
\(567\) 2.61609 0.395046i 0.109866 0.0165904i
\(568\) −7.96089 + 7.96089i −0.334031 + 0.334031i
\(569\) 14.4472 + 8.34107i 0.605656 + 0.349676i 0.771264 0.636516i \(-0.219625\pi\)
−0.165607 + 0.986192i \(0.552958\pi\)
\(570\) 0 0
\(571\) −1.21754 2.10885i −0.0509527 0.0882526i 0.839424 0.543477i \(-0.182892\pi\)
−0.890377 + 0.455224i \(0.849559\pi\)
\(572\) −6.23524 23.2702i −0.260709 0.972978i
\(573\) −0.524395 0.524395i −0.0219069 0.0219069i
\(574\) 1.94983 + 0.219151i 0.0813843 + 0.00914720i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −1.73390 0.464598i −0.0721834 0.0193415i 0.222547 0.974922i \(-0.428563\pi\)
−0.294730 + 0.955581i \(0.595230\pi\)
\(578\) 14.5032 + 3.88611i 0.603252 + 0.161641i
\(579\) −3.70449 + 6.41637i −0.153953 + 0.266655i
\(580\) 0 0
\(581\) 1.61819 0.706537i 0.0671338 0.0293121i
\(582\) −6.98682 6.98682i −0.289613 0.289613i
\(583\) 9.81298 + 36.6225i 0.406412 + 1.51675i
\(584\) 5.32535 + 9.22377i 0.220365 + 0.381683i
\(585\) 0 0
\(586\) 17.3223 + 10.0011i 0.715580 + 0.413140i
\(587\) −28.3042 + 28.3042i −1.16824 + 1.16824i −0.185619 + 0.982622i \(0.559429\pi\)
−0.982622 + 0.185619i \(0.940571\pi\)
\(588\) 3.26748 6.19060i 0.134749 0.255296i
\(589\) 18.5429i 0.764047i
\(590\) 0 0
\(591\) −15.3521 + 8.86353i −0.631500 + 0.364597i
\(592\) −2.63283 + 9.82586i −0.108209 + 0.403840i
\(593\) −2.65024 + 0.710130i −0.108832 + 0.0291616i −0.312824 0.949811i \(-0.601275\pi\)
0.203992 + 0.978973i \(0.434608\pi\)
\(594\) −3.84941 −0.157943
\(595\) 0 0
\(596\) −13.8233 −0.566225
\(597\) 0.676732 0.181330i 0.0276968 0.00742133i
\(598\) 2.28226 8.51750i 0.0933284 0.348306i
\(599\) −27.3558 + 15.7939i −1.11773 + 0.645321i −0.940820 0.338906i \(-0.889943\pi\)
−0.176909 + 0.984227i \(0.556610\pi\)
\(600\) 0 0
\(601\) 4.59089i 0.187266i −0.995607 0.0936332i \(-0.970152\pi\)
0.995607 0.0936332i \(-0.0298481\pi\)
\(602\) −3.54883 4.44759i −0.144640 0.181270i
\(603\) −5.41490 + 5.41490i −0.220512 + 0.220512i
\(604\) −5.15910 2.97861i −0.209921 0.121198i
\(605\) 0 0
\(606\) −7.18310 12.4415i −0.291793 0.505401i
\(607\) −4.41399 16.4732i −0.179158 0.668628i −0.995806 0.0914911i \(-0.970837\pi\)
0.816648 0.577137i \(-0.195830\pi\)
\(608\) 2.49350 + 2.49350i 0.101125 + 0.101125i
\(609\) 10.4712 14.1962i 0.424315 0.575257i
\(610\) 0 0
\(611\) −16.4545 + 28.5001i −0.665680 + 1.15299i
\(612\) 1.36097 + 0.364671i 0.0550140 + 0.0147410i
\(613\) −10.9233 2.92689i −0.441188 0.118216i 0.0313851 0.999507i \(-0.490008\pi\)
−0.472573 + 0.881291i \(0.656675\pi\)
\(614\) −4.81796 + 8.34496i −0.194437 + 0.336775i
\(615\) 0 0
\(616\) −6.04556 + 8.19615i −0.243583 + 0.330232i
\(617\) 3.28476 + 3.28476i 0.132240 + 0.132240i 0.770128 0.637889i \(-0.220192\pi\)
−0.637889 + 0.770128i \(0.720192\pi\)
\(618\) −3.97706 14.8426i −0.159981 0.597057i
\(619\) 12.8766 + 22.3029i 0.517554 + 0.896429i 0.999792 + 0.0203891i \(0.00649049\pi\)
−0.482239 + 0.876040i \(0.660176\pi\)
\(620\) 0 0
\(621\) −1.22021 0.704491i −0.0489655 0.0282703i
\(622\) 14.5800 14.5800i 0.584605 0.584605i
\(623\) 23.0229 + 28.8536i 0.922394 + 1.15599i
\(624\) 6.25839i 0.250536i
\(625\) 0 0
\(626\) 14.2623 8.23433i 0.570035 0.329110i
\(627\) −3.51330 + 13.1118i −0.140308 + 0.523635i
\(628\) 9.64315 2.58387i 0.384804 0.103108i
\(629\) 14.3328 0.571488
\(630\) 0 0
\(631\) 35.5189 1.41399 0.706993 0.707221i \(-0.250051\pi\)
0.706993 + 0.707221i \(0.250051\pi\)
\(632\) 3.04324 0.815432i 0.121053 0.0324362i
\(633\) 3.99683 14.9164i 0.158860 0.592872i
\(634\) 23.0205 13.2909i 0.914262 0.527849i
\(635\) 0 0
\(636\) 9.84941i 0.390555i
\(637\) 1.66208 + 43.7772i 0.0658540 + 1.73452i
\(638\) −18.1482 + 18.1482i −0.718495 + 0.718495i
\(639\) −9.75005 5.62920i −0.385706 0.222688i
\(640\) 0 0
\(641\) 6.14492 + 10.6433i 0.242710 + 0.420386i 0.961485 0.274857i \(-0.0886304\pi\)
−0.718775 + 0.695242i \(0.755297\pi\)
\(642\) 0.697125 + 2.60170i 0.0275133 + 0.102681i
\(643\) −25.5136 25.5136i −1.00616 1.00616i −0.999981 0.00617772i \(-0.998034\pi\)
−0.00617772 0.999981i \(-0.501966\pi\)
\(644\) −3.41637 + 1.49166i −0.134624 + 0.0587797i
\(645\) 0 0
\(646\) 2.48428 4.30289i 0.0977426 0.169295i
\(647\) −31.5241 8.44686i −1.23934 0.332080i −0.421130 0.907000i \(-0.638367\pi\)
−0.818210 + 0.574920i \(0.805033\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) 26.3662 45.6676i 1.03496 1.79261i
\(650\) 0 0
\(651\) −13.8253 1.55390i −0.541858 0.0609022i
\(652\) −0.972804 0.972804i −0.0380980 0.0380980i
\(653\) −4.84099 18.0668i −0.189443 0.707010i −0.993636 0.112642i \(-0.964069\pi\)
0.804193 0.594368i \(-0.202598\pi\)
\(654\) −8.40064 14.5503i −0.328491 0.568963i
\(655\) 0 0
\(656\) −0.642250 0.370803i −0.0250757 0.0144774i
\(657\) −7.53118 + 7.53118i −0.293819 + 0.293819i
\(658\) 13.7564 2.07731i 0.536282 0.0809820i
\(659\) 43.5871i 1.69791i 0.528462 + 0.848957i \(0.322769\pi\)
−0.528462 + 0.848957i \(0.677231\pi\)
\(660\) 0 0
\(661\) 21.3300 12.3149i 0.829642 0.478994i −0.0240879 0.999710i \(-0.507668\pi\)
0.853730 + 0.520716i \(0.174335\pi\)
\(662\) 1.74624 6.51705i 0.0678695 0.253292i
\(663\) −8.51750 + 2.28226i −0.330792 + 0.0886355i
\(664\) −0.667375 −0.0258992
\(665\) 0 0
\(666\) −10.1725 −0.394176
\(667\) −9.07411 + 2.43140i −0.351351 + 0.0941442i
\(668\) −2.81617 + 10.5101i −0.108961 + 0.406648i
\(669\) −1.44399 + 0.833688i −0.0558279 + 0.0322322i
\(670\) 0 0
\(671\) 3.81263i 0.147185i
\(672\) −2.06808 + 1.65017i −0.0797779 + 0.0636565i
\(673\) 11.4796 11.4796i 0.442506 0.442506i −0.450348 0.892853i \(-0.648700\pi\)
0.892853 + 0.450348i \(0.148700\pi\)
\(674\) −2.69144 1.55390i −0.103670 0.0598541i
\(675\) 0 0
\(676\) 13.0837 + 22.6617i 0.503221 + 0.871604i
\(677\) 4.28892 + 16.0065i 0.164837 + 0.615179i 0.998061 + 0.0622438i \(0.0198256\pi\)
−0.833224 + 0.552935i \(0.813508\pi\)
\(678\) 10.2109 + 10.2109i 0.392148 + 0.392148i
\(679\) −10.4607 23.9582i −0.401444 0.919430i
\(680\) 0 0
\(681\) −5.75572 + 9.96921i −0.220560 + 0.382021i
\(682\) 19.5520 + 5.23894i 0.748685 + 0.200609i
\(683\) 13.4403 + 3.60132i 0.514279 + 0.137801i 0.506619 0.862170i \(-0.330895\pi\)
0.00765999 + 0.999971i \(0.497562\pi\)
\(684\) −1.76317 + 3.05390i −0.0674165 + 0.116769i
\(685\) 0 0
\(686\) 14.0279 12.0921i 0.535587 0.461678i
\(687\) −11.0432 11.0432i −0.421325 0.421325i
\(688\) 0.556613 + 2.07731i 0.0212207 + 0.0791967i
\(689\) −30.8207 53.3831i −1.17418 2.03373i
\(690\) 0 0
\(691\) 4.05178 + 2.33929i 0.154137 + 0.0889909i 0.575085 0.818094i \(-0.304969\pi\)
−0.420948 + 0.907085i \(0.638302\pi\)
\(692\) −1.20125 + 1.20125i −0.0456646 + 0.0456646i
\(693\) −9.48158 3.71825i −0.360176 0.141244i
\(694\) 13.2471i 0.502851i
\(695\) 0 0
\(696\) −5.77412 + 3.33369i −0.218867 + 0.126363i
\(697\) −0.270443 + 1.00931i −0.0102438 + 0.0382302i
\(698\) −17.5594 + 4.70503i −0.664633 + 0.178088i
\(699\) −29.7271 −1.12438
\(700\) 0 0
\(701\) 27.2732 1.03009 0.515047 0.857162i \(-0.327775\pi\)
0.515047 + 0.857162i \(0.327775\pi\)
\(702\) 6.04514 1.61979i 0.228159 0.0611351i
\(703\) −9.28426 + 34.6493i −0.350163 + 1.30682i
\(704\) 3.33369 1.92471i 0.125643 0.0725401i
\(705\) 0 0
\(706\) 21.8120i 0.820904i
\(707\) −5.67532 37.5833i −0.213442 1.41347i
\(708\) 9.68653 9.68653i 0.364042 0.364042i
\(709\) 22.7497 + 13.1345i 0.854382 + 0.493278i 0.862127 0.506692i \(-0.169132\pi\)
−0.00774478 + 0.999970i \(0.502465\pi\)
\(710\) 0 0
\(711\) 1.57529 + 2.72849i 0.0590782 + 0.102326i
\(712\) −3.61101 13.4765i −0.135328 0.505052i
\(713\) 5.23894 + 5.23894i 0.196200 + 0.196200i
\(714\) 3.00000 + 2.21283i 0.112272 + 0.0828131i
\(715\) 0 0
\(716\) −6.91165 + 11.9713i −0.258301 + 0.447390i
\(717\) −7.68092 2.05810i −0.286849 0.0768610i
\(718\) −27.6331 7.40427i −1.03126 0.276325i
\(719\) 10.2929 17.8279i 0.383862 0.664869i −0.607748 0.794130i \(-0.707927\pi\)
0.991611 + 0.129261i \(0.0412604\pi\)
\(720\) 0 0
\(721\) 4.54085 40.4008i 0.169110 1.50460i
\(722\) −4.64209 4.64209i −0.172761 0.172761i
\(723\) −2.93201 10.9424i −0.109043 0.406952i
\(724\) −1.68043 2.91059i −0.0624527 0.108171i
\(725\) 0 0
\(726\) 3.30645 + 1.90898i 0.122714 + 0.0708490i
\(727\) −7.63477 + 7.63477i −0.283158 + 0.283158i −0.834367 0.551209i \(-0.814167\pi\)
0.551209 + 0.834367i \(0.314167\pi\)
\(728\) 6.04514 15.4152i 0.224048 0.571326i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 2.62418 1.51507i 0.0970588 0.0560369i
\(732\) 0.256346 0.956695i 0.00947481 0.0353605i
\(733\) −13.6250 + 3.65082i −0.503252 + 0.134846i −0.501509 0.865152i \(-0.667222\pi\)
−0.00174331 + 0.999998i \(0.500555\pi\)
\(734\) −32.4834 −1.19899
\(735\) 0 0
\(736\) 1.40898 0.0519358
\(737\) 28.4737 7.62949i 1.04884 0.281036i
\(738\) 0.191942 0.716337i 0.00706548 0.0263687i
\(739\) −17.0208 + 9.82696i −0.626120 + 0.361490i −0.779248 0.626716i \(-0.784399\pi\)
0.153128 + 0.988206i \(0.451065\pi\)
\(740\) 0 0
\(741\) 22.0692i 0.810734i
\(742\) −9.51380 + 24.2603i −0.349263 + 0.890625i
\(743\) 20.7983 20.7983i 0.763016 0.763016i −0.213851 0.976866i \(-0.568601\pi\)
0.976866 + 0.213851i \(0.0686006\pi\)
\(744\) 4.55390 + 2.62920i 0.166954 + 0.0963910i
\(745\) 0 0
\(746\) −11.0346 19.1125i −0.404006 0.699759i
\(747\) −0.172729 0.644635i −0.00631984 0.0235860i
\(748\) −3.83517 3.83517i −0.140228 0.140228i
\(749\) −0.795948 + 7.08170i −0.0290833 + 0.258760i
\(750\) 0 0
\(751\) 11.9305 20.6642i 0.435350 0.754048i −0.561975 0.827155i \(-0.689958\pi\)
0.997324 + 0.0731070i \(0.0232915\pi\)
\(752\) −5.07922 1.36097i −0.185220 0.0496296i
\(753\) 20.3169 + 5.44389i 0.740388 + 0.198386i
\(754\) 20.8635 36.1367i 0.759805 1.31602i
\(755\) 0 0
\(756\) −2.12920 1.57052i −0.0774381 0.0571191i
\(757\) 30.3903 + 30.3903i 1.10455 + 1.10455i 0.993854 + 0.110699i \(0.0353090\pi\)
0.110699 + 0.993854i \(0.464691\pi\)
\(758\) −4.10457 15.3185i −0.149085 0.556392i
\(759\) 2.71188 + 4.69711i 0.0984349 + 0.170494i
\(760\) 0 0
\(761\) 0.111347 + 0.0642865i 0.00403634 + 0.00233038i 0.502017 0.864858i \(-0.332592\pi\)
−0.497980 + 0.867188i \(0.665925\pi\)
\(762\) −14.5565 + 14.5565i −0.527327 + 0.527327i
\(763\) −6.63729 43.9537i −0.240286 1.59123i
\(764\) 0.741607i 0.0268304i
\(765\) 0 0
\(766\) −15.3693 + 8.87347i −0.555316 + 0.320612i
\(767\) −22.1892 + 82.8113i −0.801207 + 2.99014i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) 27.3976 0.987984 0.493992 0.869466i \(-0.335537\pi\)
0.493992 + 0.869466i \(0.335537\pi\)
\(770\) 0 0
\(771\) −25.9144 −0.933285
\(772\) 7.15653 1.91759i 0.257569 0.0690154i
\(773\) 1.25374 4.67901i 0.0450938 0.168292i −0.939707 0.341981i \(-0.888902\pi\)
0.984801 + 0.173689i \(0.0555687\pi\)
\(774\) −1.86246 + 1.07529i −0.0669449 + 0.0386507i
\(775\) 0 0
\(776\) 9.88086i 0.354702i
\(777\) −25.0561 9.82586i −0.898882 0.352501i
\(778\) −24.6860 + 24.6860i −0.885034 + 0.885034i
\(779\) −2.26479 1.30758i −0.0811447 0.0468489i
\(780\) 0 0
\(781\) 21.6691 + 37.5320i 0.775381 + 1.34300i
\(782\) −0.513816 1.91759i −0.0183740 0.0685727i