Properties

Label 1050.2.bc.f.943.2
Level $1050$
Weight $2$
Character 1050.943
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 943.2
Root \(2.35727 + 1.36097i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.f.157.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.46313 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.46313 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.92471 + 3.33369i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-4.42535 + 4.42535i) q^{13} +(0.295509 - 2.62920i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.364671 - 1.36097i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-1.76317 + 3.05390i) q^{19} +(2.12920 + 1.57052i) q^{21} +(2.72194 - 2.72194i) q^{22} +(-1.36097 + 0.364671i) q^{23} +(0.500000 + 0.866025i) q^{24} +(5.41993 + 3.12920i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.61609 + 0.395046i) q^{28} +6.66738i q^{29} +(-4.55390 + 2.62920i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.996301 + 3.71825i) q^{33} -1.40898 q^{34} -1.00000 q^{36} +(-2.63283 - 9.82586i) q^{37} +(3.40619 + 0.912685i) q^{38} +(-5.41993 + 3.12920i) q^{39} -0.741607i q^{41} +(0.965926 - 2.46313i) q^{42} +(1.52070 + 1.52070i) q^{43} +(-3.33369 - 1.92471i) q^{44} +(0.704491 + 1.22021i) q^{46} +(5.07922 - 1.36097i) q^{47} +(0.707107 - 0.707107i) q^{48} +(5.13397 + 4.75839i) q^{49} +(0.704491 - 1.22021i) q^{51} +(1.61979 - 6.04514i) q^{52} +(2.54922 - 9.51380i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.05868 + 2.42471i) q^{56} +(-2.49350 + 2.49350i) q^{57} +(6.44019 - 1.72564i) q^{58} +(6.84941 + 11.8635i) q^{59} +(-0.857750 - 0.495222i) q^{61} +(3.71825 + 3.71825i) q^{62} +(1.65017 + 2.06808i) q^{63} +1.00000i q^{64} +(3.33369 - 1.92471i) q^{66} +(7.39689 + 1.98199i) q^{67} +(0.364671 + 1.36097i) q^{68} -1.40898 q^{69} +11.2584 q^{71} +(0.258819 + 0.965926i) q^{72} +(-10.2878 - 2.75660i) q^{73} +(-8.80963 + 5.08624i) q^{74} -3.52634i q^{76} +(1.52070 + 10.0704i) q^{77} +(4.42535 + 4.42535i) q^{78} +(2.72849 + 1.57529i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.716337 + 0.191942i) q^{82} +(0.471906 - 0.471906i) q^{83} +(-2.62920 - 0.295509i) q^{84} +(1.07529 - 1.86246i) q^{86} +(-1.72564 + 6.44019i) q^{87} +(-0.996301 + 3.71825i) q^{88} +(6.97594 - 12.0827i) q^{89} +(-15.1748 + 6.62564i) q^{91} +(0.996301 - 0.996301i) q^{92} +(-5.07922 + 1.36097i) q^{93} +(-2.62920 - 4.55390i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(6.98682 + 6.98682i) q^{97} +(3.26748 - 6.19060i) 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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 0.965926 + 0.258819i 0.557678 + 0.149429i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.46313 + 0.965926i 0.930974 + 0.365086i
\(8\) 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 \(0.636261\pi\)
\(12\) −0.965926 + 0.258819i −0.278839 + 0.0747146i
\(13\) −4.42535 + 4.42535i −1.22737 + 1.22737i −0.262417 + 0.964954i \(0.584520\pi\)
−0.964954 + 0.262417i \(0.915480\pi\)
\(14\) 0.295509 2.62920i 0.0789781 0.702682i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.364671 1.36097i 0.0884458 0.330084i −0.907499 0.420055i \(-0.862011\pi\)
0.995944 + 0.0899709i \(0.0286774\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) −1.76317 + 3.05390i −0.404499 + 0.700613i −0.994263 0.106963i \(-0.965887\pi\)
0.589764 + 0.807576i \(0.299221\pi\)
\(20\) 0 0
\(21\) 2.12920 + 1.57052i 0.464629 + 0.342715i
\(22\) 2.72194 2.72194i 0.580321 0.580321i
\(23\) −1.36097 + 0.364671i −0.283782 + 0.0760392i −0.397903 0.917428i \(-0.630262\pi\)
0.114120 + 0.993467i \(0.463595\pi\)
\(24\) 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
\(28\) −2.61609 + 0.395046i −0.494395 + 0.0746568i
\(29\) 6.66738i 1.23810i 0.785351 + 0.619050i \(0.212482\pi\)
−0.785351 + 0.619050i \(0.787518\pi\)
\(30\) 0 0
\(31\) −4.55390 + 2.62920i −0.817905 + 0.472218i −0.849693 0.527277i \(-0.823213\pi\)
0.0317885 + 0.999495i \(0.489880\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 0.996301 + 3.71825i 0.173434 + 0.647263i
\(34\) −1.40898 −0.241638
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −2.63283 9.82586i −0.432835 1.61536i −0.746195 0.665727i \(-0.768121\pi\)
0.313360 0.949634i \(-0.398545\pi\)
\(38\) 3.40619 + 0.912685i 0.552556 + 0.148057i
\(39\) −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 \(-0.0184436\pi\)
\(42\) 0.965926 2.46313i 0.149046 0.380069i
\(43\) 1.52070 + 1.52070i 0.231904 + 0.231904i 0.813487 0.581583i \(-0.197566\pi\)
−0.581583 + 0.813487i \(0.697566\pi\)
\(44\) −3.33369 1.92471i −0.502572 0.290160i
\(45\) 0 0
\(46\) 0.704491 + 1.22021i 0.103872 + 0.179911i
\(47\) 5.07922 1.36097i 0.740880 0.198518i 0.131411 0.991328i \(-0.458049\pi\)
0.609469 + 0.792810i \(0.291383\pi\)
\(48\) 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
\(52\) 1.61979 6.04514i 0.224625 0.838311i
\(53\) 2.54922 9.51380i 0.350162 1.30682i −0.536303 0.844025i \(-0.680180\pi\)
0.886465 0.462796i \(-0.153154\pi\)
\(54\) 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
\(58\) 6.44019 1.72564i 0.845638 0.226588i
\(59\) 6.84941 + 11.8635i 0.891717 + 1.54450i 0.837815 + 0.545954i \(0.183832\pi\)
0.0539019 + 0.998546i \(0.482834\pi\)
\(60\) 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
\(63\) 1.65017 + 2.06808i 0.207901 + 0.260553i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 3.33369 1.92471i 0.410349 0.236915i
\(67\) 7.39689 + 1.98199i 0.903673 + 0.242139i 0.680593 0.732662i \(-0.261722\pi\)
0.223080 + 0.974800i \(0.428389\pi\)
\(68\) 0.364671 + 1.36097i 0.0442229 + 0.165042i
\(69\) −1.40898 −0.169622
\(70\) 0 0
\(71\) 11.2584 1.33613 0.668063 0.744105i \(-0.267124\pi\)
0.668063 + 0.744105i \(0.267124\pi\)
\(72\) 0.258819 + 0.965926i 0.0305021 + 0.113835i
\(73\) −10.2878 2.75660i −1.20409 0.322636i −0.399652 0.916667i \(-0.630869\pi\)
−0.804442 + 0.594031i \(0.797536\pi\)
\(74\) −8.80963 + 5.08624i −1.02410 + 0.591263i
\(75\) 0 0
\(76\) 3.52634i 0.404499i
\(77\) 1.52070 + 10.0704i 0.173299 + 1.14763i
\(78\) 4.42535 + 4.42535i 0.501072 + 0.501072i
\(79\) 2.72849 + 1.57529i 0.306979 + 0.177234i 0.645574 0.763698i \(-0.276618\pi\)
−0.338595 + 0.940932i \(0.609952\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −0.716337 + 0.191942i −0.0791062 + 0.0211964i
\(83\) 0.471906 0.471906i 0.0517984 0.0517984i −0.680733 0.732532i \(-0.738339\pi\)
0.732532 + 0.680733i \(0.238339\pi\)
\(84\) −2.62920 0.295509i −0.286869 0.0322427i
\(85\) 0 0
\(86\) 1.07529 1.86246i 0.115952 0.200835i
\(87\) −1.72564 + 6.44019i −0.185008 + 0.690461i
\(88\) −0.996301 + 3.71825i −0.106206 + 0.396366i
\(89\) 6.97594 12.0827i 0.739448 1.28076i −0.213296 0.976988i \(-0.568420\pi\)
0.952744 0.303774i \(-0.0982467\pi\)
\(90\) 0 0
\(91\) −15.1748 + 6.62564i −1.59075 + 0.694555i
\(92\) 0.996301 0.996301i 0.103872 0.103872i
\(93\) −5.07922 + 1.36097i −0.526690 + 0.141126i
\(94\) −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 0.966410 0.257006i \(-0.0827359\pi\)
−0.257006 + 0.966410i \(0.582736\pi\)
\(98\) 3.26748 6.19060i 0.330066 0.625345i
\(99\) 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 \(0.0798761\pi\)
\(102\) −1.36097 0.364671i −0.134756 0.0361079i
\(103\) −3.97706 14.8426i −0.391872 1.46249i −0.827043 0.562138i \(-0.809979\pi\)
0.435172 0.900348i \(-0.356688\pi\)
\(104\) −6.25839 −0.613686
\(105\) 0 0
\(106\) −9.84941 −0.956659
\(107\) −0.697125 2.60170i −0.0673936 0.251516i 0.924008 0.382374i \(-0.124893\pi\)
−0.991401 + 0.130858i \(0.958227\pi\)
\(108\) −0.965926 0.258819i −0.0929463 0.0249049i
\(109\) −14.5503 + 8.40064i −1.39367 + 0.804636i −0.993719 0.111901i \(-0.964306\pi\)
−0.399951 + 0.916537i \(0.630973\pi\)
\(110\) 0 0
\(111\) 10.1725i 0.965529i
\(112\) 2.06808 1.65017i 0.195415 0.155926i
\(113\) 10.2109 + 10.2109i 0.960563 + 0.960563i 0.999251 0.0386883i \(-0.0123179\pi\)
−0.0386883 + 0.999251i \(0.512318\pi\)
\(114\) 3.05390 + 1.76317i 0.286024 + 0.165136i
\(115\) 0 0
\(116\) −3.33369 5.77412i −0.309525 0.536113i
\(117\) −6.04514 + 1.61979i −0.558874 + 0.149750i
\(118\) 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
\(122\) −0.256346 + 0.956695i −0.0232085 + 0.0866151i
\(123\) 0.191942 0.716337i 0.0173068 0.0645900i
\(124\) 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 0.357936 0.933746i \(-0.383481\pi\)
0.933746 0.357936i \(-0.116519\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) 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
\(133\) −7.29275 + 5.81905i −0.632362 + 0.504576i
\(134\) 7.65782i 0.661535i
\(135\) 0 0
\(136\) 1.22021 0.704491i 0.104633 0.0604096i
\(137\) −10.9950 2.94610i −0.939367 0.251703i −0.243523 0.969895i \(-0.578303\pi\)
−0.695845 + 0.718192i \(0.744970\pi\)
\(138\) 0.364671 + 1.36097i 0.0310429 + 0.115854i
\(139\) −3.50510 −0.297299 −0.148650 0.988890i \(-0.547493\pi\)
−0.148650 + 0.988890i \(0.547493\pi\)
\(140\) 0 0
\(141\) 5.25839 0.442837
\(142\) −2.91389 10.8748i −0.244528 0.912591i
\(143\) −23.2702 6.23524i −1.94596 0.521417i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 10.6507i 0.881458i
\(147\) 3.72748 + 5.92503i 0.307437 + 0.488688i
\(148\) 7.19303 + 7.19303i 0.591263 + 0.591263i
\(149\) 11.9713 + 6.91165i 0.980730 + 0.566225i 0.902490 0.430710i \(-0.141737\pi\)
0.0782393 + 0.996935i \(0.475070\pi\)
\(150\) 0 0
\(151\) −2.97861 5.15910i −0.242396 0.419842i 0.719001 0.695010i \(-0.244600\pi\)
−0.961396 + 0.275168i \(0.911267\pi\)
\(152\) −3.40619 + 0.912685i −0.276278 + 0.0740285i
\(153\) 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
\(157\) −2.58387 + 9.64315i −0.206216 + 0.769607i 0.782860 + 0.622198i \(0.213760\pi\)
−0.989076 + 0.147409i \(0.952907\pi\)
\(158\) 0.815432 3.04324i 0.0648723 0.242107i
\(159\) 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
\(163\) −1.32888 + 0.356071i −0.104086 + 0.0278896i −0.310486 0.950578i \(-0.600492\pi\)
0.206400 + 0.978468i \(0.433825\pi\)
\(164\) 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 0.343704 0.939078i \(-0.388318\pi\)
−0.939078 + 0.343704i \(0.888318\pi\)
\(168\) 0.395046 + 2.61609i 0.0304785 + 0.201836i
\(169\) 26.1675i 2.01288i
\(170\) 0 0
\(171\) −3.05390 + 1.76317i −0.233538 + 0.134833i
\(172\) −2.07731 0.556613i −0.158393 0.0424414i
\(173\) 0.439687 + 1.64094i 0.0334288 + 0.124758i 0.980624 0.195900i \(-0.0627627\pi\)
−0.947195 + 0.320658i \(0.896096\pi\)
\(174\) 6.66738 0.505452
\(175\) 0 0
\(176\) 3.84941 0.290160
\(177\) 3.54552 + 13.2320i 0.266497 + 0.994581i
\(178\) −13.4765 3.61101i −1.01010 0.270657i
\(179\) 11.9713 6.91165i 0.894779 0.516601i 0.0192766 0.999814i \(-0.493864\pi\)
0.875503 + 0.483213i \(0.160530\pi\)
\(180\) 0 0
\(181\) 3.36086i 0.249811i −0.992169 0.124905i \(-0.960137\pi\)
0.992169 0.124905i \(-0.0398627\pi\)
\(182\) 10.3274 + 12.9429i 0.765517 + 0.959388i
\(183\) −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
\(187\) 5.23894 1.40377i 0.383109 0.102654i
\(188\) −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 \(0.175208\pi\)
\(192\) −0.258819 + 0.965926i −0.0186787 + 0.0697097i
\(193\) 1.91759 7.15653i 0.138031 0.515138i −0.861936 0.507017i \(-0.830748\pi\)
0.999967 0.00812132i \(-0.00258513\pi\)
\(194\) 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 \(-0.967561\pi\)
0.101735 + 0.994811i \(0.467561\pi\)
\(198\) 3.71825 0.996301i 0.264244 0.0708040i
\(199\) 0.350302 + 0.606741i 0.0248323 + 0.0430107i 0.878174 0.478340i \(-0.158762\pi\)
−0.853342 + 0.521351i \(0.825428\pi\)
\(200\) 0 0
\(201\) 6.63187 + 3.82891i 0.467776 + 0.270070i
\(202\) −10.1584 10.1584i −0.714745 0.714745i
\(203\) −6.44019 + 16.4226i −0.452013 + 1.15264i
\(204\) 1.40898i 0.0986485i
\(205\) 0 0
\(206\) −13.3075 + 7.68310i −0.927179 + 0.535307i
\(207\) −1.36097 0.364671i −0.0945941 0.0253464i
\(208\) 1.61979 + 6.04514i 0.112312 + 0.419155i
\(209\) −13.5743 −0.938957
\(210\) 0 0
\(211\) −15.4426 −1.06311 −0.531555 0.847024i \(-0.678392\pi\)
−0.531555 + 0.847024i \(0.678392\pi\)
\(212\) 2.54922 + 9.51380i 0.175081 + 0.653410i
\(213\) 10.8748 + 2.91389i 0.745127 + 0.199656i
\(214\) −2.33262 + 1.34674i −0.159455 + 0.0920614i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −13.7564 + 2.07731i −0.933848 + 0.141017i
\(218\) 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
\(222\) −9.82586 + 2.63283i −0.659469 + 0.176704i
\(223\) 1.17901 1.17901i 0.0789525 0.0789525i −0.666528 0.745480i \(-0.732220\pi\)
0.745480 + 0.666528i \(0.232220\pi\)
\(224\) −2.12920 1.57052i −0.142263 0.104935i
\(225\) 0 0
\(226\) 7.22021 12.5058i 0.480282 0.831872i
\(227\) −2.97938 + 11.1192i −0.197749 + 0.738008i 0.793790 + 0.608192i \(0.208105\pi\)
−0.991538 + 0.129815i \(0.958562\pi\)
\(228\) 0.912685 3.40619i 0.0604440 0.225580i
\(229\) 7.80873 13.5251i 0.516016 0.893765i −0.483811 0.875172i \(-0.660748\pi\)
0.999827 0.0185931i \(-0.00591872\pi\)
\(230\) 0 0
\(231\) −1.13754 + 10.1209i −0.0748443 + 0.665904i
\(232\) −4.71455 + 4.71455i −0.309525 + 0.309525i
\(233\) 28.7141 7.69393i 1.88113 0.504046i 0.881641 0.471920i \(-0.156439\pi\)
0.999484 0.0321261i \(-0.0102278\pi\)
\(234\) 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
\(238\) −3.47050 1.36097i −0.224959 0.0882187i
\(239\) 7.95188i 0.514364i −0.966363 0.257182i \(-0.917206\pi\)
0.966363 0.257182i \(-0.0827940\pi\)
\(240\) 0 0
\(241\) −9.81069 + 5.66420i −0.631962 + 0.364863i −0.781512 0.623891i \(-0.785551\pi\)
0.149550 + 0.988754i \(0.452218\pi\)
\(242\) 3.68787 + 0.988162i 0.237065 + 0.0635215i
\(243\) 0.258819 + 0.965926i 0.0166032 + 0.0619642i
\(244\) 0.990444 0.0634067
\(245\) 0 0
\(246\) −0.741607 −0.0472831
\(247\) −5.71194 21.3172i −0.363442 1.35638i
\(248\) −5.07922 1.36097i −0.322531 0.0864218i
\(249\) 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 \(-0.231063\pi\)
\(252\) −2.46313 0.965926i −0.155162 0.0608476i
\(253\) −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
\(257\) −25.0314 + 6.70715i −1.56142 + 0.418380i −0.933112 0.359587i \(-0.882918\pi\)
−0.628305 + 0.777967i \(0.716251\pi\)
\(258\) 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
\(262\) −1.69343 + 6.31995i −0.104620 + 0.390448i
\(263\) 4.29407 16.0257i 0.264784 0.988187i −0.697599 0.716489i \(-0.745748\pi\)
0.962383 0.271698i \(-0.0875852\pi\)
\(264\) −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
\(268\) −7.39689 + 1.98199i −0.451837 + 0.121069i
\(269\) 13.6804 + 23.6952i 0.834110 + 1.44472i 0.894753 + 0.446562i \(0.147352\pi\)
−0.0606421 + 0.998160i \(0.519315\pi\)
\(270\) 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
\(273\) −16.3725 + 2.47236i −0.990911 + 0.149634i
\(274\) 11.3829i 0.687665i
\(275\) 0 0
\(276\) 1.22021 0.704491i 0.0734483 0.0424054i
\(277\) −20.1045 5.38699i −1.20796 0.323673i −0.402001 0.915639i \(-0.631685\pi\)
−0.805963 + 0.591966i \(0.798352\pi\)
\(278\) 0.907188 + 3.38567i 0.0544095 + 0.203059i
\(279\) −5.25839 −0.314812
\(280\) 0 0
\(281\) 2.89220 0.172534 0.0862670 0.996272i \(-0.472506\pi\)
0.0862670 + 0.996272i \(0.472506\pi\)
\(282\) −1.36097 5.07922i −0.0810447 0.302463i
\(283\) −20.4714 5.48531i −1.21690 0.326068i −0.407435 0.913234i \(-0.633577\pi\)
−0.809466 + 0.587167i \(0.800243\pi\)
\(284\) −9.75005 + 5.62920i −0.578559 + 0.334031i
\(285\) 0 0
\(286\) 24.0911i 1.42454i
\(287\) 0.716337 1.82667i 0.0422841 0.107825i
\(288\) −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
\(292\) 10.2878 2.75660i 0.602047 0.161318i
\(293\) −14.1436 + 14.1436i −0.826280 + 0.826280i −0.987000 0.160720i \(-0.948618\pi\)
0.160720 + 0.987000i \(0.448618\pi\)
\(294\) 4.75839 5.13397i 0.277515 0.299419i
\(295\) 0 0
\(296\) 5.08624 8.80963i 0.295632 0.512049i
\(297\) −0.996301 + 3.71825i −0.0578112 + 0.215754i
\(298\) 3.57773 13.3523i 0.207253 0.773477i
\(299\) 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
\(303\) 13.8767 3.71825i 0.797194 0.213608i
\(304\) 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 0.874286 0.485411i \(-0.161330\pi\)
−0.485411 + 0.874286i \(0.661330\pi\)
\(308\) −6.35217 7.96089i −0.361948 0.453614i
\(309\) 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 \(0.532084\pi\)
\(312\) −6.04514 1.61979i −0.342239 0.0917026i
\(313\) 4.26240 + 15.9075i 0.240925 + 0.899145i 0.975388 + 0.220496i \(0.0707677\pi\)
−0.734463 + 0.678649i \(0.762566\pi\)
\(314\) 9.98332 0.563391
\(315\) 0 0
\(316\) −3.15059 −0.177234
\(317\) −6.87988 25.6761i −0.386412 1.44211i −0.835928 0.548838i \(-0.815070\pi\)
0.449516 0.893272i \(-0.351596\pi\)
\(318\) −9.51380 2.54922i −0.533507 0.142953i
\(319\) −22.2269 + 12.8327i −1.24447 + 0.718495i
\(320\) 0 0
\(321\) 2.69348i 0.150336i
\(322\) 0.556613 + 3.68603i 0.0310189 + 0.205414i
\(323\) 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
\(327\) −16.2288 + 4.34849i −0.897455 + 0.240472i
\(328\) 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 \(0.226032\pi\)
\(332\) −0.172729 + 0.644635i −0.00947976 + 0.0353789i
\(333\) 2.63283 9.82586i 0.144278 0.538454i
\(334\) −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 \(-0.776976\pi\)
0.644715 + 0.764423i \(0.276976\pi\)
\(338\) −25.2758 + 6.77264i −1.37482 + 0.368383i
\(339\) 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
\(343\) 8.04937 + 16.6796i 0.434625 + 0.900611i
\(344\) 2.15059i 0.115952i
\(345\) 0 0
\(346\) 1.47122 0.849411i 0.0790934 0.0456646i
\(347\) 12.7957 + 3.42859i 0.686908 + 0.184056i 0.585359 0.810774i \(-0.300954\pi\)
0.101549 + 0.994831i \(0.467620\pi\)
\(348\) −1.72564 6.44019i −0.0925042 0.345230i
\(349\) −18.1788 −0.973090 −0.486545 0.873655i \(-0.661743\pi\)
−0.486545 + 0.873655i \(0.661743\pi\)
\(350\) 0 0
\(351\) −6.25839 −0.334048
\(352\) −0.996301 3.71825i −0.0531030 0.198183i
\(353\) 21.0687 + 5.64535i 1.12138 + 0.300472i 0.771440 0.636302i \(-0.219537\pi\)
0.349936 + 0.936774i \(0.386203\pi\)
\(354\) 11.8635 6.84941i 0.630539 0.364042i
\(355\) 0 0
\(356\) 13.9519i 0.739448i
\(357\) 2.91389 2.32505i 0.154219 0.123055i
\(358\) −9.77455 9.77455i −0.516601 0.516601i
\(359\) −24.7752 14.3040i −1.30758 0.754934i −0.325892 0.945407i \(-0.605664\pi\)
−0.981692 + 0.190473i \(0.938998\pi\)
\(360\) 0 0
\(361\) 3.28246 + 5.68538i 0.172761 + 0.299230i
\(362\) −3.24634 + 0.869854i −0.170624 + 0.0457185i
\(363\) −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
\(367\) −8.40733 + 31.3766i −0.438859 + 1.63784i 0.292800 + 0.956174i \(0.405413\pi\)
−0.731659 + 0.681671i \(0.761254\pi\)
\(368\) −0.364671 + 1.36097i −0.0190098 + 0.0709456i
\(369\) 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
\(373\) 21.3172 5.71194i 1.10377 0.295753i 0.339468 0.940618i \(-0.389753\pi\)
0.764297 + 0.644865i \(0.223086\pi\)
\(374\) −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
\(378\) 2.06808 1.65017i 0.106371 0.0848754i
\(379\) 15.8588i 0.814614i −0.913291 0.407307i \(-0.866468\pi\)
0.913291 0.407307i \(-0.133532\pi\)
\(380\) 0 0
\(381\) 17.8280 10.2930i 0.913357 0.527327i
\(382\) 0.716337 + 0.191942i 0.0366510 + 0.00982061i
\(383\) −4.59325 17.1422i −0.234704 0.875927i −0.978282 0.207278i \(-0.933540\pi\)
0.743578 0.668649i \(-0.233127\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −7.40898 −0.377107
\(387\) 0.556613 + 2.07731i 0.0282942 + 0.105596i
\(388\) −9.54418 2.55735i −0.484532 0.129830i
\(389\) −30.2340 + 17.4556i −1.53292 + 0.885034i −0.533700 + 0.845674i \(0.679199\pi\)
−0.999225 + 0.0393604i \(0.987468\pi\)
\(390\) 0 0
\(391\) 1.98523i 0.100397i
\(392\) 0.265576 + 6.99496i 0.0134136 + 0.353299i
\(393\) −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
\(397\) 34.8886 9.34838i 1.75101 0.469182i 0.766169 0.642640i \(-0.222161\pi\)
0.984841 + 0.173458i \(0.0554941\pi\)
\(398\) 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 \(0.178458\pi\)
\(402\) 1.98199 7.39689i 0.0988526 0.368923i
\(403\) 8.51750 31.7877i 0.424287 1.58346i
\(404\) −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
\(408\) 1.36097 0.364671i 0.0673782 0.0180539i
\(409\) 1.51216 + 2.61914i 0.0747716 + 0.129508i 0.900987 0.433846i \(-0.142844\pi\)
−0.826215 + 0.563354i \(0.809511\pi\)
\(410\) 0 0
\(411\) −9.85786 5.69144i −0.486252 0.280738i
\(412\) 10.8655 + 10.8655i 0.535307 + 0.535307i
\(413\) 5.41167 + 35.8374i 0.266291 + 1.76344i
\(414\) 1.40898i 0.0692477i
\(415\) 0 0
\(416\) 5.41993 3.12920i 0.265734 0.153421i
\(417\) −3.38567 0.907188i −0.165797 0.0444252i
\(418\) 3.51330 + 13.1118i 0.171841 + 0.641319i
\(419\) 14.8547 0.725702 0.362851 0.931847i \(-0.381803\pi\)
0.362851 + 0.931847i \(0.381803\pi\)
\(420\) 0 0
\(421\) 27.2920 1.33013 0.665065 0.746786i \(-0.268404\pi\)
0.665065 + 0.746786i \(0.268404\pi\)
\(422\) 3.99683 + 14.9164i 0.194563 + 0.726117i
\(423\) 5.07922 + 1.36097i 0.246960 + 0.0661727i
\(424\) 8.52984 4.92471i 0.414246 0.239165i
\(425\) 0 0
\(426\) 11.2584i 0.545471i
\(427\) −1.63440 2.04832i −0.0790940 0.0991250i
\(428\) 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 \(-0.517561\pi\)
\(432\) 0.965926 0.258819i 0.0464731 0.0124524i
\(433\) 7.65990 7.65990i 0.368111 0.368111i −0.498677 0.866788i \(-0.666181\pi\)
0.866788 + 0.498677i \(0.166181\pi\)
\(434\) 5.56696 + 12.7501i 0.267222 + 0.612022i
\(435\) 0 0
\(436\) 8.40064 14.5503i 0.402318 0.696835i
\(437\) 1.28596 4.79925i 0.0615156 0.229579i
\(438\) −2.75660 + 10.2878i −0.131716 + 0.491569i
\(439\) −10.1375 + 17.5586i −0.483835 + 0.838027i −0.999828 0.0185660i \(-0.994090\pi\)
0.515992 + 0.856593i \(0.327423\pi\)
\(440\) 0 0
\(441\) 2.06696 + 6.68788i 0.0984265 + 0.318470i
\(442\) 6.23524 6.23524i 0.296580 0.296580i
\(443\) 6.79186 1.81987i 0.322691 0.0864647i −0.0938374 0.995588i \(-0.529913\pi\)
0.416528 + 0.909123i \(0.363247\pi\)
\(444\) 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
\(448\) −0.965926 + 2.46313i −0.0456357 + 0.116372i
\(449\) 4.46654i 0.210789i −0.994430 0.105394i \(-0.966389\pi\)
0.994430 0.105394i \(-0.0336105\pi\)
\(450\) 0 0
\(451\) 2.47229 1.42737i 0.116415 0.0672125i
\(452\) −13.9484 3.73746i −0.656077 0.175795i
\(453\) −1.54184 5.75423i −0.0724420 0.270357i
\(454\) 11.5114 0.540259
\(455\) 0 0
\(456\) −3.52634 −0.165136
\(457\) 6.28043 + 23.4389i 0.293786 + 1.09643i 0.942176 + 0.335117i \(0.108776\pi\)
−0.648390 + 0.761308i \(0.724557\pi\)
\(458\) −15.0853 4.04210i −0.704891 0.188875i
\(459\) 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 \(0.934168\pi\)
\(462\) 10.0704 1.52070i 0.468518 0.0707492i
\(463\) 1.05131 + 1.05131i 0.0488583 + 0.0488583i 0.731114 0.682256i \(-0.239001\pi\)
−0.682256 + 0.731114i \(0.739001\pi\)
\(464\) 5.77412 + 3.33369i 0.268057 + 0.154763i
\(465\) 0 0
\(466\) −14.8635 25.7444i −0.688540 1.19259i
\(467\) 35.7465 9.57824i 1.65415 0.443228i 0.693379 0.720573i \(-0.256121\pi\)
0.960770 + 0.277345i \(0.0894546\pi\)
\(468\) 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
\(472\) −3.54552 + 13.2320i −0.163196 + 0.609054i
\(473\) −2.14263 + 7.99642i −0.0985184 + 0.367676i
\(474\) 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
\(478\) −7.68092 + 2.05810i −0.351317 + 0.0941352i
\(479\) 0.778723 + 1.34879i 0.0355807 + 0.0616277i 0.883267 0.468870i \(-0.155339\pi\)
−0.847687 + 0.530497i \(0.822005\pi\)
\(480\) 0 0
\(481\) 55.1341 + 31.8317i 2.51390 + 1.45140i
\(482\) 8.01039 + 8.01039i 0.364863 + 0.364863i
\(483\) −3.47050 1.36097i −0.157913 0.0619264i
\(484\) 3.81796i 0.173544i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −7.56068 2.02588i −0.342607 0.0918013i 0.0834127 0.996515i \(-0.473418\pi\)
−0.426020 + 0.904714i \(0.640085\pi\)
\(488\) −0.256346 0.956695i −0.0116042 0.0433076i
\(489\) −1.37575 −0.0622137
\(490\) 0 0
\(491\) 43.8776 1.98017 0.990085 0.140468i \(-0.0448608\pi\)
0.990085 + 0.140468i \(0.0448608\pi\)
\(492\) 0.191942 + 0.716337i 0.00865341 + 0.0322950i
\(493\) 9.07411 + 2.43140i 0.408677 + 0.109505i
\(494\) −19.1125 + 11.0346i −0.859913 + 0.496471i
\(495\) 0 0
\(496\) 5.25839i 0.236109i
\(497\) 27.7308 + 10.8748i 1.24390 + 0.487800i
\(498\) −0.471906 0.471906i −0.0211466 0.0211466i
\(499\) 29.9024 + 17.2642i 1.33862 + 0.772850i 0.986602 0.163144i \(-0.0521636\pi\)
0.352014 + 0.935995i \(0.385497\pi\)
\(500\) 0 0
\(501\) −5.44043 9.42310i −0.243060 0.420993i
\(502\) −20.3169 + 5.44389i −0.906786 + 0.242973i
\(503\) 16.9300 16.9300i 0.754872 0.754872i −0.220512 0.975384i \(-0.570773\pi\)
0.975384 + 0.220512i \(0.0707728\pi\)
\(504\) −0.295509 + 2.62920i −0.0131630 + 0.117114i
\(505\) 0 0
\(506\) −2.71188 + 4.69711i −0.120558 + 0.208812i
\(507\) 6.77264 25.2758i 0.300784 1.12254i
\(508\) −5.32805 + 19.8846i −0.236394 + 0.882235i
\(509\) 5.10674 8.84514i 0.226352 0.392054i −0.730372 0.683050i \(-0.760653\pi\)
0.956724 + 0.290996i \(0.0939866\pi\)
\(510\) 0 0
\(511\) −22.6774 16.7271i −1.00319 0.739963i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −3.40619 + 0.912685i −0.150387 + 0.0402960i
\(514\) 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
\(518\) −26.6121 + 4.01860i −1.16927 + 0.176567i
\(519\) 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 \(0.457426\pi\)
\(522\) 6.44019 + 1.72564i 0.281879 + 0.0755294i
\(523\) 10.9108 + 40.7197i 0.477097 + 1.78055i 0.613281 + 0.789865i \(0.289849\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(524\) 6.54289 0.285828
\(525\) 0 0
\(526\) −16.5910 −0.723403
\(527\) 1.91759 + 7.15653i 0.0835313 + 0.311743i
\(528\) 3.71825 + 0.996301i 0.161816 + 0.0433584i
\(529\) −18.1993 + 10.5074i −0.791275 + 0.456843i
\(530\) 0 0
\(531\) 13.6988i 0.594478i
\(532\) 3.40619 8.68582i 0.147677 0.376578i
\(533\) 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
\(537\) 13.3523 3.57773i 0.576194 0.154391i
\(538\) 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 \(0.00407455\pi\)
\(542\) −0.247745 + 0.924599i −0.0106416 + 0.0397149i
\(543\) 0.869854 3.24634i 0.0373290 0.139314i
\(544\) −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 \(-0.629415\pi\)
0.918483 + 0.395462i \(0.129415\pi\)
\(548\) 10.9950 2.94610i 0.469684 0.125851i
\(549\) −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
\(553\) 5.19900 + 6.51567i 0.221084 + 0.277074i
\(554\) 20.8137i 0.884291i
\(555\) 0 0
\(556\) 3.03551 1.75255i 0.128734 0.0743248i
\(557\) 34.7179 + 9.30265i 1.47105 + 0.394166i 0.903290 0.429031i \(-0.141145\pi\)
0.567757 + 0.823196i \(0.307811\pi\)
\(558\) 1.36097 + 5.07922i 0.0576146 + 0.215020i
\(559\) −13.4592 −0.569265
\(560\) 0 0
\(561\) 5.42375 0.228991
\(562\) −0.748555 2.79365i −0.0315759 0.117843i
\(563\) −31.9435 8.55924i −1.34626 0.360729i −0.487506 0.873120i \(-0.662093\pi\)
−0.858752 + 0.512391i \(0.828760\pi\)
\(564\) −4.55390 + 2.62920i −0.191754 + 0.110709i
\(565\) 0 0
\(566\) 21.1936i 0.890833i
\(567\) 0.395046 + 2.61609i 0.0165904 + 0.109866i
\(568\) 7.96089 + 7.96089i 0.334031 + 0.334031i
\(569\) −14.4472 8.34107i −0.605656 0.349676i 0.165607 0.986192i \(-0.447042\pi\)
−0.771264 + 0.636516i \(0.780375\pi\)
\(570\) 0 0
\(571\) −1.21754 2.10885i −0.0509527 0.0882526i 0.839424 0.543477i \(-0.182892\pi\)
−0.890377 + 0.455224i \(0.849559\pi\)
\(572\) 23.2702 6.23524i 0.972978 0.260709i
\(573\) −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
\(577\) 0.464598 1.73390i 0.0193415 0.0721834i −0.955581 0.294730i \(-0.904770\pi\)
0.974922 + 0.222547i \(0.0714370\pi\)
\(578\) 3.88611 14.5032i 0.161641 0.603252i
\(579\) 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
\(583\) 36.6225 9.81298i 1.51675 0.406412i
\(584\) −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 −0.982622 0.185619i \(-0.940571\pi\)
−0.185619 0.982622i \(-0.559429\pi\)
\(588\) −6.19060 3.26748i −0.255296 0.134749i
\(589\) 18.5429i 0.764047i
\(590\) 0 0
\(591\) −15.3521 + 8.86353i −0.631500 + 0.364597i
\(592\) −9.82586 2.63283i −0.403840 0.108209i
\(593\) 0.710130 + 2.65024i 0.0291616 + 0.108832i 0.978973 0.203992i \(-0.0653916\pi\)
−0.949811 + 0.312824i \(0.898725\pi\)
\(594\) 3.84941 0.157943
\(595\) 0 0
\(596\) −13.8233 −0.566225
\(597\) 0.181330 + 0.676732i 0.00742133 + 0.0276968i
\(598\) −8.51750 2.28226i −0.348306 0.0933284i
\(599\) 27.3558 15.7939i 1.11773 0.645321i 0.176909 0.984227i \(-0.443390\pi\)
0.940820 + 0.338906i \(0.110057\pi\)
\(600\) 0 0
\(601\) 4.59089i 0.187266i −0.995607 0.0936332i \(-0.970152\pi\)
0.995607 0.0936332i \(-0.0298481\pi\)
\(602\) 4.44759 3.54883i 0.181270 0.144640i
\(603\) 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
\(607\) 16.4732 4.41399i 0.668628 0.179158i 0.0914911 0.995806i \(-0.470837\pi\)
0.577137 + 0.816648i \(0.304170\pi\)
\(608\) 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
\(612\) −0.364671 + 1.36097i −0.0147410 + 0.0550140i
\(613\) −2.92689 + 10.9233i −0.118216 + 0.441188i −0.999507 0.0313851i \(-0.990008\pi\)
0.881291 + 0.472573i \(0.156675\pi\)
\(614\) 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 \(-0.779808\pi\)
0.637889 + 0.770128i \(0.279808\pi\)
\(618\) −14.8426 + 3.97706i −0.597057 + 0.159981i
\(619\) −12.8766 22.3029i −0.517554 0.896429i −0.999792 0.0203891i \(-0.993510\pi\)
0.482239 0.876040i \(-0.339824\pi\)
\(620\) 0 0
\(621\) −1.22021 0.704491i −0.0489655 0.0282703i
\(622\) 14.5800 + 14.5800i 0.584605 + 0.584605i
\(623\) 28.8536 23.0229i 1.15599 0.922394i
\(624\) 6.25839i 0.250536i
\(625\) 0 0
\(626\) 14.2623 8.23433i 0.570035 0.329110i
\(627\) −13.1118 3.51330i −0.523635 0.140308i
\(628\) −2.58387 9.64315i −0.103108 0.384804i
\(629\) −14.3328 −0.571488
\(630\) 0 0
\(631\) 35.5189 1.41399 0.706993 0.707221i \(-0.250051\pi\)
0.706993 + 0.707221i \(0.250051\pi\)
\(632\) 0.815432 + 3.04324i 0.0324362 + 0.121053i
\(633\) −14.9164 3.99683i −0.592872 0.158860i
\(634\) −23.0205 + 13.2909i −0.914262 + 0.527849i
\(635\) 0 0
\(636\) 9.84941i 0.390555i
\(637\) −43.7772 + 1.66208i −1.73452 + 0.0658540i
\(638\) 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 \(0.755297\pi\)
\(642\) −2.60170 + 0.697125i −0.102681 + 0.0275133i
\(643\) −25.5136 + 25.5136i −1.00616 + 1.00616i −0.00617772 + 0.999981i \(0.501966\pi\)
−0.999981 + 0.00617772i \(0.998034\pi\)
\(644\) 3.41637 1.49166i 0.134624 0.0587797i
\(645\) 0 0
\(646\) 2.48428 4.30289i 0.0977426 0.169295i
\(647\) 8.44686 31.5241i 0.332080 1.23934i −0.574920 0.818210i \(-0.694967\pi\)
0.907000 0.421130i \(-0.138367\pi\)
\(648\) −0.258819 + 0.965926i −0.0101674 + 0.0379452i
\(649\) −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
\(653\) −18.0668 + 4.84099i −0.707010 + 0.189443i −0.594368 0.804193i \(-0.702598\pi\)
−0.112642 + 0.993636i \(0.535931\pi\)
\(654\) 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
\(658\) −2.07731 13.7564i −0.0809820 0.536282i
\(659\) 43.5871i 1.69791i −0.528462 0.848957i \(-0.677231\pi\)
0.528462 0.848957i \(-0.322769\pi\)
\(660\) 0 0
\(661\) 21.3300 12.3149i 0.829642 0.478994i −0.0240879 0.999710i \(-0.507668\pi\)
0.853730 + 0.520716i \(0.174335\pi\)
\(662\) 6.51705 + 1.74624i 0.253292 + 0.0678695i
\(663\) 2.28226 + 8.51750i 0.0886355 + 0.330792i
\(664\) 0.667375 0.0258992
\(665\) 0 0
\(666\) −10.1725 −0.394176
\(667\) −2.43140 9.07411i −0.0941442 0.351351i
\(668\) 10.5101 + 2.81617i 0.406648 + 0.108961i
\(669\) 1.44399 0.833688i 0.0558279 0.0322322i
\(670\) 0 0
\(671\) 3.81263i 0.147185i
\(672\) −1.65017 2.06808i −0.0636565 0.0797779i
\(673\) −11.4796 11.4796i −0.442506 0.442506i 0.450348 0.892853i \(-0.351300\pi\)
−0.892853 + 0.450348i \(0.851300\pi\)
\(674\) 2.69144 + 1.55390i 0.103670 + 0.0598541i
\(675\) 0 0
\(676\) 13.0837 + 22.6617i 0.503221 + 0.871604i
\(677\) −16.0065 + 4.28892i −0.615179 + 0.164837i −0.552935 0.833224i \(-0.686492\pi\)
−0.0622438 + 0.998061i \(0.519826\pi\)
\(678\) 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
\(682\) −5.23894 + 19.5520i −0.200609 + 0.748685i
\(683\) 3.60132 13.4403i 0.137801 0.514279i −0.862170 0.506619i \(-0.830895\pi\)
0.999971 0.00765999i \(-0.00243827\pi\)
\(684\) 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
\(688\) 2.07731 0.556613i 0.0791967 0.0212207i
\(689\) 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
\(693\) −3.71825 + 9.48158i −0.141244 + 0.360176i
\(694\) 13.2471i 0.502851i
\(695\) 0 0
\(696\) −5.77412 + 3.33369i −0.218867 + 0.126363i
\(697\) −1.00931 0.270443i −0.0382302 0.0102438i
\(698\) 4.70503 + 17.5594i 0.178088 + 0.664633i
\(699\) 29.7271 1.12438
\(700\) 0 0
\(701\) 27.2732 1.03009 0.515047 0.857162i \(-0.327775\pi\)
0.515047 + 0.857162i \(0.327775\pi\)
\(702\) 1.61979 + 6.04514i 0.0611351 + 0.228159i
\(703\) 34.6493 + 9.28426i 1.30682 + 0.350163i
\(704\) −3.33369 + 1.92471i −0.125643 + 0.0725401i
\(705\) 0 0
\(706\) 21.8120i 0.820904i
\(707\) 37.5833 5.67532i 1.41347 0.213442i
\(708\) −9.68653 9.68653i −0.364042 0.364042i
\(709\) −22.7497 13.1345i −0.854382 0.493278i 0.00774478 0.999970i \(-0.497535\pi\)
−0.862127 + 0.506692i \(0.830868\pi\)
\(710\) 0 0
\(711\) 1.57529 + 2.72849i 0.0590782 + 0.102326i
\(712\) 13.4765 3.61101i 0.505052 0.135328i
\(713\) 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
\(717\) 2.05810 7.68092i 0.0768610 0.286849i
\(718\) −7.40427 + 27.6331i −0.276325 + 1.03126i
\(719\) −10.2929 + 17.8279i −0.383862 + 0.664869i −0.991611 0.129261i \(-0.958740\pi\)
0.607748 + 0.794130i \(0.292073\pi\)
\(720\) 0 0
\(721\) 4.54085 40.4008i 0.169110 1.50460i
\(722\) 4.64209 4.64209i 0.172761 0.172761i
\(723\) −10.9424 + 2.93201i −0.406952 + 0.109043i
\(724\) 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 0.551209 0.834367i \(-0.314167\pi\)
−0.834367 + 0.551209i \(0.814167\pi\)
\(728\) −15.4152 6.04514i −0.571326 0.224048i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 2.62418 1.51507i 0.0970588 0.0560369i
\(732\) 0.956695 + 0.256346i 0.0353605 + 0.00947481i
\(733\) 3.65082 + 13.6250i 0.134846 + 0.503252i 0.999998 + 0.00174331i \(0.000554912\pi\)
−0.865152 + 0.501509i \(0.832778\pi\)
\(734\) 32.4834 1.19899
\(735\) 0 0
\(736\) 1.40898 0.0519358
\(737\) 7.62949 + 28.4737i 0.281036 + 1.04884i
\(738\) −0.716337 0.191942i −0.0263687 0.00706548i
\(739\) 17.0208 9.82696i 0.626120 0.361490i −0.153128 0.988206i \(-0.548935\pi\)
0.779248 + 0.626716i \(0.215601\pi\)
\(740\) 0 0
\(741\) 22.0692i 0.810734i
\(742\) −24.2603 9.51380i −0.890625 0.349263i
\(743\) −20.7983 20.7983i −0.763016 0.763016i 0.213851 0.976866i \(-0.431399\pi\)
−0.976866 + 0.213851i \(0.931399\pi\)
\(744\) −4.55390 2.62920i −0.166954 0.0963910i
\(745\) 0 0
\(746\) −11.0346 19.1125i −0.404006 0.699759i
\(747\) 0.644635 0.172729i 0.0235860 0.00631984i
\(748\) −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 \(0.0232915\pi\)
\(752\) 1.36097 5.07922i 0.0496296 0.185220i
\(753\) 5.44389 20.3169i 0.198386 0.740388i
\(754\) −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 −0.110699 + 0.993854i \(0.535309\pi\)
−0.993854 + 0.110699i \(0.964691\pi\)
\(758\) −15.3185 + 4.10457i −0.556392 + 0.149085i
\(759\) −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
\(763\) −43.9537 + 6.63729i −1.59123 + 0.240286i
\(764\) 0.741607i 0.0268304i
\(765\) 0 0
\(766\) −15.3693 + 8.87347i −0.555316 + 0.320612i
\(767\) −82.8113 22.1892i −2.99014 0.801207i
\(768\) −0.258819 0.965926i −0.00933933 0.0348548i
\(769\) −27.3976 −0.987984 −0.493992 0.869466i \(-0.664463\pi\)
−0.493992 + 0.869466i \(0.664463\pi\)
\(770\) 0 0
\(771\) −25.9144 −0.933285
\(772\) 1.91759 + 7.15653i 0.0690154 + 0.257569i
\(773\) −4.67901 1.25374i −0.168292 0.0450938i 0.173689 0.984801i \(-0.444431\pi\)
−0.341981 + 0.939707i \(0.611098\pi\)
\(774\) 1.86246 1.07529i 0.0669449 0.0386507i
\(775\) 0 0
\(776\) 9.88086i 0.354702i
\(777\) 9.82586 25.0561i 0.352501 0.898882i
\(778\) 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
\(782\) 1.91759 0.513816i 0.0685727 0.0183740i
\(783\)