Properties

Label 1050.2.bc.h.943.2
Level $1050$
Weight $2$
Character 1050.943
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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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: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 943.2
Root \(0.117630 - 0.893490i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.h.157.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.55046 - 0.703686i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.55046 - 0.703686i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.989376 + 1.71365i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-2.19222 + 2.19222i) q^{13} +(-1.33981 - 2.28142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.19130 + 4.44599i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-2.10939 + 3.65357i) q^{19} +(-2.64568 + 0.0196015i) q^{21} +(1.39919 - 1.39919i) q^{22} +(-5.68202 + 1.52249i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.68491 + 1.55013i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.85692 + 1.88464i) q^{28} -8.94996i q^{29} +(-1.50157 + 0.866930i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.512139 - 1.91133i) q^{33} +4.60282 q^{34} -1.00000 q^{36} +(0.717425 + 2.67747i) q^{37} +(4.07503 + 1.09190i) q^{38} +(2.68491 - 1.55013i) q^{39} +6.55691i q^{41} +(0.703686 + 2.55046i) q^{42} +(6.33724 + 6.33724i) q^{43} +(-1.71365 - 0.989376i) q^{44} +(2.94123 + 5.09436i) q^{46} +(-5.87298 + 1.57366i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(6.00965 - 3.58944i) q^{49} +(2.30141 - 3.98616i) q^{51} +(0.802407 - 2.99462i) q^{52} +(-2.95926 + 11.0441i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.30103 + 1.30586i) q^{56} +(2.98313 - 2.98313i) q^{57} +(-8.64500 + 2.31642i) q^{58} +(2.10351 + 3.64339i) q^{59} +(9.63018 + 5.55999i) q^{61} +(1.22602 + 1.22602i) q^{62} +(2.56060 + 0.665818i) q^{63} +1.00000i q^{64} +(-1.71365 + 0.989376i) q^{66} +(5.32434 + 1.42665i) q^{67} +(-1.19130 - 4.44599i) q^{68} +5.88246 q^{69} -3.86002 q^{71} +(0.258819 + 0.965926i) q^{72} +(14.7013 + 3.93920i) q^{73} +(2.40055 - 1.38596i) q^{74} -4.21878i q^{76} +(3.72923 + 3.67438i) q^{77} +(-2.19222 - 2.19222i) q^{78} +(-2.21282 - 1.27757i) q^{79} +(0.500000 + 0.866025i) q^{81} +(6.33349 - 1.69705i) q^{82} +(9.52969 - 9.52969i) q^{83} +(2.28142 - 1.33981i) q^{84} +(4.48111 - 7.76151i) q^{86} +(-2.31642 + 8.64500i) q^{87} +(-0.512139 + 1.91133i) q^{88} +(-3.09593 + 5.36231i) q^{89} +(-4.04852 + 7.13378i) q^{91} +(4.15953 - 4.15953i) q^{92} +(1.67478 - 0.448756i) q^{93} +(3.04008 + 5.26557i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-1.48031 - 1.48031i) q^{97} +(-5.02254 - 4.87586i) q^{98} +1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 4q^{11} + 16q^{13} + 16q^{14} + 8q^{16} + 12q^{17} - 8q^{19} + 8q^{21} - 4q^{22} - 32q^{23} - 8q^{24} - 12q^{26} + 8q^{28} - 24q^{31} - 8q^{33} + 16q^{34} - 16q^{36} + 8q^{37} + 28q^{38} - 12q^{39} + 4q^{42} + 24q^{43} - 4q^{46} + 24q^{47} + 52q^{49} + 8q^{51} + 8q^{52} - 44q^{53} - 8q^{54} + 8q^{56} + 8q^{57} - 48q^{58} + 8q^{59} + 24q^{61} - 8q^{62} - 4q^{63} - 36q^{67} + 12q^{68} - 8q^{69} - 32q^{71} + 40q^{73} - 24q^{74} + 44q^{77} + 16q^{78} + 12q^{79} + 8q^{81} - 12q^{82} + 16q^{83} + 4q^{84} - 8q^{86} - 12q^{87} - 8q^{88} - 16q^{89} + 8q^{91} - 8q^{92} - 40q^{93} + 8q^{94} - 44q^{97} + 8q^{98} + O(q^{100}) \)

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
\(7\) 2.55046 0.703686i 0.963982 0.265968i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0 0
\(11\) 0.989376 + 1.71365i 0.298308 + 0.516685i 0.975749 0.218892i \(-0.0702443\pi\)
−0.677441 + 0.735577i \(0.736911\pi\)
\(12\) 0.965926 0.258819i 0.278839 0.0747146i
\(13\) −2.19222 + 2.19222i −0.608011 + 0.608011i −0.942426 0.334415i \(-0.891461\pi\)
0.334415 + 0.942426i \(0.391461\pi\)
\(14\) −1.33981 2.28142i −0.358081 0.609736i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.19130 + 4.44599i −0.288932 + 1.07831i 0.656985 + 0.753903i \(0.271831\pi\)
−0.945918 + 0.324407i \(0.894835\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) −2.10939 + 3.65357i −0.483928 + 0.838188i −0.999830 0.0184602i \(-0.994124\pi\)
0.515902 + 0.856648i \(0.327457\pi\)
\(20\) 0 0
\(21\) −2.64568 + 0.0196015i −0.577334 + 0.00427740i
\(22\) 1.39919 1.39919i 0.298308 0.298308i
\(23\) −5.68202 + 1.52249i −1.18478 + 0.317462i −0.796822 0.604214i \(-0.793487\pi\)
−0.387961 + 0.921676i \(0.626821\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 2.68491 + 1.55013i 0.526553 + 0.304006i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −1.85692 + 1.88464i −0.350924 + 0.356163i
\(29\) 8.94996i 1.66197i −0.556298 0.830983i \(-0.687779\pi\)
0.556298 0.830983i \(-0.312221\pi\)
\(30\) 0 0
\(31\) −1.50157 + 0.866930i −0.269689 + 0.155705i −0.628747 0.777610i \(-0.716432\pi\)
0.359057 + 0.933316i \(0.383098\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) −0.512139 1.91133i −0.0891519 0.332720i
\(34\) 4.60282 0.789378
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 0.717425 + 2.67747i 0.117944 + 0.440173i 0.999490 0.0319248i \(-0.0101637\pi\)
−0.881546 + 0.472097i \(0.843497\pi\)
\(38\) 4.07503 + 1.09190i 0.661058 + 0.177130i
\(39\) 2.68491 1.55013i 0.429929 0.248220i
\(40\) 0 0
\(41\) 6.55691i 1.02402i 0.858980 + 0.512008i \(0.171098\pi\)
−0.858980 + 0.512008i \(0.828902\pi\)
\(42\) 0.703686 + 2.55046i 0.108581 + 0.393544i
\(43\) 6.33724 + 6.33724i 0.966421 + 0.966421i 0.999454 0.0330335i \(-0.0105168\pi\)
−0.0330335 + 0.999454i \(0.510517\pi\)
\(44\) −1.71365 0.989376i −0.258342 0.149154i
\(45\) 0 0
\(46\) 2.94123 + 5.09436i 0.433661 + 0.751122i
\(47\) −5.87298 + 1.57366i −0.856663 + 0.229542i −0.660312 0.750992i \(-0.729576\pi\)
−0.196351 + 0.980534i \(0.562909\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 6.00965 3.58944i 0.858522 0.512777i
\(50\) 0 0
\(51\) 2.30141 3.98616i 0.322262 0.558174i
\(52\) 0.802407 2.99462i 0.111274 0.415280i
\(53\) −2.95926 + 11.0441i −0.406485 + 1.51702i 0.394814 + 0.918761i \(0.370809\pi\)
−0.801300 + 0.598263i \(0.795858\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 2.30103 + 1.30586i 0.307487 + 0.174503i
\(57\) 2.98313 2.98313i 0.395125 0.395125i
\(58\) −8.64500 + 2.31642i −1.13514 + 0.304161i
\(59\) 2.10351 + 3.64339i 0.273854 + 0.474329i 0.969845 0.243721i \(-0.0783682\pi\)
−0.695991 + 0.718050i \(0.745035\pi\)
\(60\) 0 0
\(61\) 9.63018 + 5.55999i 1.23302 + 0.711883i 0.967658 0.252266i \(-0.0811759\pi\)
0.265360 + 0.964149i \(0.414509\pi\)
\(62\) 1.22602 + 1.22602i 0.155705 + 0.155705i
\(63\) 2.56060 + 0.665818i 0.322606 + 0.0838852i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −1.71365 + 0.989376i −0.210936 + 0.121784i
\(67\) 5.32434 + 1.42665i 0.650472 + 0.174294i 0.568942 0.822377i \(-0.307353\pi\)
0.0815298 + 0.996671i \(0.474019\pi\)
\(68\) −1.19130 4.44599i −0.144466 0.539155i
\(69\) 5.88246 0.708165
\(70\) 0 0
\(71\) −3.86002 −0.458100 −0.229050 0.973415i \(-0.573562\pi\)
−0.229050 + 0.973415i \(0.573562\pi\)
\(72\) 0.258819 + 0.965926i 0.0305021 + 0.113835i
\(73\) 14.7013 + 3.93920i 1.72066 + 0.461048i 0.977997 0.208621i \(-0.0668974\pi\)
0.742660 + 0.669669i \(0.233564\pi\)
\(74\) 2.40055 1.38596i 0.279058 0.161114i
\(75\) 0 0
\(76\) 4.21878i 0.483928i
\(77\) 3.72923 + 3.67438i 0.424985 + 0.418734i
\(78\) −2.19222 2.19222i −0.248220 0.248220i
\(79\) −2.21282 1.27757i −0.248962 0.143738i 0.370327 0.928901i \(-0.379246\pi\)
−0.619289 + 0.785163i \(0.712579\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 6.33349 1.69705i 0.699416 0.187408i
\(83\) 9.52969 9.52969i 1.04602 1.04602i 0.0471311 0.998889i \(-0.484992\pi\)
0.998889 0.0471311i \(-0.0150078\pi\)
\(84\) 2.28142 1.33981i 0.248924 0.146186i
\(85\) 0 0
\(86\) 4.48111 7.76151i 0.483210 0.836945i
\(87\) −2.31642 + 8.64500i −0.248346 + 0.926841i
\(88\) −0.512139 + 1.91133i −0.0545942 + 0.203748i
\(89\) −3.09593 + 5.36231i −0.328168 + 0.568404i −0.982148 0.188108i \(-0.939765\pi\)
0.653980 + 0.756512i \(0.273098\pi\)
\(90\) 0 0
\(91\) −4.04852 + 7.13378i −0.424400 + 0.747824i
\(92\) 4.15953 4.15953i 0.433661 0.433661i
\(93\) 1.67478 0.448756i 0.173667 0.0465339i
\(94\) 3.04008 + 5.26557i 0.313560 + 0.543102i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) −1.48031 1.48031i −0.150303 0.150303i 0.627951 0.778253i \(-0.283894\pi\)
−0.778253 + 0.627951i \(0.783894\pi\)
\(98\) −5.02254 4.87586i −0.507354 0.492537i
\(99\) 1.97875i 0.198872i
\(100\) 0 0
\(101\) −8.70112 + 5.02360i −0.865794 + 0.499866i −0.865948 0.500134i \(-0.833284\pi\)
0.000154194 1.00000i \(0.499951\pi\)
\(102\) −4.44599 1.19130i −0.440218 0.117956i
\(103\) −1.29095 4.81790i −0.127201 0.474722i 0.872707 0.488244i \(-0.162362\pi\)
−0.999909 + 0.0135219i \(0.995696\pi\)
\(104\) −3.10026 −0.304006
\(105\) 0 0
\(106\) 11.4337 1.11054
\(107\) −1.56576 5.84351i −0.151368 0.564913i −0.999389 0.0349507i \(-0.988873\pi\)
0.848021 0.529963i \(-0.177794\pi\)
\(108\) 0.965926 + 0.258819i 0.0929463 + 0.0249049i
\(109\) −8.44287 + 4.87449i −0.808680 + 0.466892i −0.846497 0.532393i \(-0.821293\pi\)
0.0378171 + 0.999285i \(0.487960\pi\)
\(110\) 0 0
\(111\) 2.77192i 0.263099i
\(112\) 0.665818 2.56060i 0.0629139 0.241954i
\(113\) −6.02504 6.02504i −0.566788 0.566788i 0.364439 0.931227i \(-0.381261\pi\)
−0.931227 + 0.364439i \(0.881261\pi\)
\(114\) −3.65357 2.10939i −0.342189 0.197563i
\(115\) 0 0
\(116\) 4.47498 + 7.75089i 0.415491 + 0.719652i
\(117\) −2.99462 + 0.802407i −0.276853 + 0.0741826i
\(118\) 2.97481 2.97481i 0.273854 0.273854i
\(119\) 0.0902224 + 12.1776i 0.00827067 + 1.11632i
\(120\) 0 0
\(121\) 3.54227 6.13539i 0.322024 0.557763i
\(122\) 2.87806 10.7411i 0.260567 0.972451i
\(123\) 1.69705 6.33349i 0.153018 0.571071i
\(124\) 0.866930 1.50157i 0.0778527 0.134845i
\(125\) 0 0
\(126\) −0.0196015 2.64568i −0.00174624 0.235696i
\(127\) 8.92770 8.92770i 0.792205 0.792205i −0.189647 0.981852i \(-0.560734\pi\)
0.981852 + 0.189647i \(0.0607345\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −4.48111 7.76151i −0.394540 0.683363i
\(130\) 0 0
\(131\) −4.43543 2.56080i −0.387526 0.223738i 0.293562 0.955940i \(-0.405159\pi\)
−0.681087 + 0.732202i \(0.738493\pi\)
\(132\) 1.39919 + 1.39919i 0.121784 + 0.121784i
\(133\) −2.80894 + 10.8026i −0.243566 + 0.936707i
\(134\) 5.51217i 0.476179i
\(135\) 0 0
\(136\) −3.98616 + 2.30141i −0.341811 + 0.197344i
\(137\) −11.1877 2.99773i −0.955829 0.256114i −0.252995 0.967468i \(-0.581416\pi\)
−0.702834 + 0.711354i \(0.748082\pi\)
\(138\) −1.52249 5.68202i −0.129603 0.483686i
\(139\) −2.87054 −0.243476 −0.121738 0.992562i \(-0.538847\pi\)
−0.121738 + 0.992562i \(0.538847\pi\)
\(140\) 0 0
\(141\) 6.08016 0.512042
\(142\) 0.999046 + 3.72849i 0.0838381 + 0.312888i
\(143\) −5.92562 1.58776i −0.495525 0.132776i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 15.2199i 1.25961i
\(147\) −6.73389 + 1.91172i −0.555402 + 0.157676i
\(148\) −1.96004 1.96004i −0.161114 0.161114i
\(149\) 13.4924 + 7.78982i 1.10534 + 0.638167i 0.937618 0.347668i \(-0.113026\pi\)
0.167720 + 0.985835i \(0.446360\pi\)
\(150\) 0 0
\(151\) −10.5953 18.3516i −0.862232 1.49343i −0.869769 0.493459i \(-0.835732\pi\)
0.00753703 0.999972i \(-0.497601\pi\)
\(152\) −4.07503 + 1.09190i −0.330529 + 0.0885649i
\(153\) −3.25469 + 3.25469i −0.263126 + 0.263126i
\(154\) 2.58398 4.55316i 0.208223 0.366904i
\(155\) 0 0
\(156\) −1.55013 + 2.68491i −0.124110 + 0.214965i
\(157\) −3.92974 + 14.6660i −0.313627 + 1.17047i 0.611633 + 0.791141i \(0.290513\pi\)
−0.925261 + 0.379332i \(0.876154\pi\)
\(158\) −0.661320 + 2.46808i −0.0526118 + 0.196350i
\(159\) 5.71685 9.90187i 0.453375 0.785269i
\(160\) 0 0
\(161\) −13.4204 + 7.88141i −1.05767 + 0.621142i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 21.5624 5.77762i 1.68890 0.452538i 0.718792 0.695225i \(-0.244695\pi\)
0.970105 + 0.242687i \(0.0780288\pi\)
\(164\) −3.27845 5.67845i −0.256004 0.443412i
\(165\) 0 0
\(166\) −11.6714 6.73851i −0.905880 0.523010i
\(167\) −6.91224 6.91224i −0.534885 0.534885i 0.387137 0.922022i \(-0.373464\pi\)
−0.922022 + 0.387137i \(0.873464\pi\)
\(168\) −1.88464 1.85692i −0.145403 0.143264i
\(169\) 3.38837i 0.260644i
\(170\) 0 0
\(171\) −3.65357 + 2.10939i −0.279396 + 0.161309i
\(172\) −8.65684 2.31959i −0.660078 0.176867i
\(173\) 1.17183 + 4.37334i 0.0890928 + 0.332499i 0.996058 0.0887072i \(-0.0282735\pi\)
−0.906965 + 0.421206i \(0.861607\pi\)
\(174\) 8.94996 0.678495
\(175\) 0 0
\(176\) 1.97875 0.149154
\(177\) −1.08886 4.06367i −0.0818436 0.305444i
\(178\) 5.98088 + 1.60257i 0.448286 + 0.120118i
\(179\) −1.79084 + 1.03394i −0.133853 + 0.0772803i −0.565431 0.824795i \(-0.691290\pi\)
0.431578 + 0.902076i \(0.357957\pi\)
\(180\) 0 0
\(181\) 6.13199i 0.455787i 0.973686 + 0.227894i \(0.0731839\pi\)
−0.973686 + 0.227894i \(0.926816\pi\)
\(182\) 7.93854 + 2.06421i 0.588444 + 0.153010i
\(183\) −7.86301 7.86301i −0.581250 0.581250i
\(184\) −5.09436 2.94123i −0.375561 0.216830i
\(185\) 0 0
\(186\) −0.866930 1.50157i −0.0635664 0.110100i
\(187\) −8.79751 + 2.35728i −0.643337 + 0.172382i
\(188\) 4.29932 4.29932i 0.313560 0.313560i
\(189\) −2.30103 1.30586i −0.167375 0.0949876i
\(190\) 0 0
\(191\) 8.08306 14.0003i 0.584869 1.01302i −0.410022 0.912075i \(-0.634479\pi\)
0.994892 0.100948i \(-0.0321876\pi\)
\(192\) 0.258819 0.965926i 0.0186787 0.0697097i
\(193\) −5.63991 + 21.0484i −0.405969 + 1.51510i 0.396292 + 0.918125i \(0.370297\pi\)
−0.802261 + 0.596973i \(0.796370\pi\)
\(194\) −1.04674 + 1.81300i −0.0751514 + 0.130166i
\(195\) 0 0
\(196\) −3.40979 + 6.11337i −0.243557 + 0.436669i
\(197\) 0.628120 0.628120i 0.0447517 0.0447517i −0.684377 0.729129i \(-0.739926\pi\)
0.729129 + 0.684377i \(0.239926\pi\)
\(198\) 1.91133 0.512139i 0.135832 0.0363961i
\(199\) 4.81248 + 8.33546i 0.341147 + 0.590885i 0.984646 0.174563i \(-0.0558511\pi\)
−0.643499 + 0.765447i \(0.722518\pi\)
\(200\) 0 0
\(201\) −4.77368 2.75608i −0.336709 0.194399i
\(202\) 7.10444 + 7.10444i 0.499866 + 0.499866i
\(203\) −6.29796 22.8265i −0.442030 1.60210i
\(204\) 4.60282i 0.322262i
\(205\) 0 0
\(206\) −4.31961 + 2.49393i −0.300962 + 0.173760i
\(207\) −5.68202 1.52249i −0.394928 0.105821i
\(208\) 0.802407 + 2.99462i 0.0556369 + 0.207640i
\(209\) −8.34793 −0.577439
\(210\) 0 0
\(211\) 11.2669 0.775648 0.387824 0.921733i \(-0.373227\pi\)
0.387824 + 0.921733i \(0.373227\pi\)
\(212\) −2.95926 11.0441i −0.203243 0.758512i
\(213\) 3.72849 + 0.999046i 0.255472 + 0.0684535i
\(214\) −5.23915 + 3.02482i −0.358141 + 0.206773i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −3.21964 + 3.26770i −0.218563 + 0.221826i
\(218\) 6.89357 + 6.89357i 0.466892 + 0.466892i
\(219\) −13.1808 7.60995i −0.890677 0.514233i
\(220\) 0 0
\(221\) −7.13498 12.3581i −0.479951 0.831299i
\(222\) −2.67747 + 0.717425i −0.179700 + 0.0481504i
\(223\) −13.1718 + 13.1718i −0.882048 + 0.882048i −0.993743 0.111694i \(-0.964372\pi\)
0.111694 + 0.993743i \(0.464372\pi\)
\(224\) −2.64568 + 0.0196015i −0.176772 + 0.00130968i
\(225\) 0 0
\(226\) −4.26035 + 7.37914i −0.283394 + 0.490853i
\(227\) −6.96589 + 25.9971i −0.462343 + 1.72549i 0.203210 + 0.979135i \(0.434863\pi\)
−0.665552 + 0.746351i \(0.731804\pi\)
\(228\) −1.09190 + 4.07503i −0.0723130 + 0.269876i
\(229\) −13.4452 + 23.2878i −0.888486 + 1.53890i −0.0468199 + 0.998903i \(0.514909\pi\)
−0.841666 + 0.539999i \(0.818425\pi\)
\(230\) 0 0
\(231\) −2.65116 4.51437i −0.174434 0.297024i
\(232\) 6.32858 6.32858i 0.415491 0.415491i
\(233\) −0.889853 + 0.238436i −0.0582962 + 0.0156204i −0.287849 0.957676i \(-0.592940\pi\)
0.229553 + 0.973296i \(0.426274\pi\)
\(234\) 1.55013 + 2.68491i 0.101335 + 0.175518i
\(235\) 0 0
\(236\) −3.64339 2.10351i −0.237164 0.136927i
\(237\) 1.80676 + 1.80676i 0.117362 + 0.117362i
\(238\) 11.7393 3.23894i 0.760946 0.209949i
\(239\) 25.3432i 1.63931i −0.572856 0.819656i \(-0.694164\pi\)
0.572856 0.819656i \(-0.305836\pi\)
\(240\) 0 0
\(241\) 18.2905 10.5600i 1.17819 0.680230i 0.222597 0.974911i \(-0.428547\pi\)
0.955596 + 0.294681i \(0.0952134\pi\)
\(242\) −6.84314 1.83361i −0.439894 0.117869i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) −11.1200 −0.711883
\(245\) 0 0
\(246\) −6.55691 −0.418053
\(247\) −3.38518 12.6337i −0.215394 0.803861i
\(248\) −1.67478 0.448756i −0.106349 0.0284960i
\(249\) −11.6714 + 6.73851i −0.739648 + 0.427036i
\(250\) 0 0
\(251\) 2.70623i 0.170816i 0.996346 + 0.0854078i \(0.0272193\pi\)
−0.996346 + 0.0854078i \(0.972781\pi\)
\(252\) −2.55046 + 0.703686i −0.160664 + 0.0443280i
\(253\) −8.23068 8.23068i −0.517458 0.517458i
\(254\) −10.9342 6.31283i −0.686070 0.396102i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 23.2035 6.21737i 1.44740 0.387829i 0.552279 0.833660i \(-0.313758\pi\)
0.895117 + 0.445831i \(0.147092\pi\)
\(258\) −6.33724 + 6.33724i −0.394540 + 0.394540i
\(259\) 3.71385 + 6.32392i 0.230768 + 0.392949i
\(260\) 0 0
\(261\) 4.47498 7.75089i 0.276994 0.479768i
\(262\) −1.32557 + 4.94708i −0.0818938 + 0.305632i
\(263\) −0.220080 + 0.821351i −0.0135707 + 0.0506467i −0.972379 0.233407i \(-0.925013\pi\)
0.958808 + 0.284053i \(0.0916793\pi\)
\(264\) 0.989376 1.71365i 0.0608919 0.105468i
\(265\) 0 0
\(266\) 11.1615 0.0826946i 0.684359 0.00507033i
\(267\) 4.37831 4.37831i 0.267948 0.267948i
\(268\) −5.32434 + 1.42665i −0.325236 + 0.0871468i
\(269\) 5.82171 + 10.0835i 0.354956 + 0.614802i 0.987110 0.160041i \(-0.0511625\pi\)
−0.632154 + 0.774842i \(0.717829\pi\)
\(270\) 0 0
\(271\) −20.2171 11.6724i −1.22810 0.709046i −0.261471 0.965211i \(-0.584208\pi\)
−0.966633 + 0.256165i \(0.917541\pi\)
\(272\) 3.25469 + 3.25469i 0.197344 + 0.197344i
\(273\) 5.75693 5.84287i 0.348425 0.353627i
\(274\) 11.5824i 0.699715i
\(275\) 0 0
\(276\) −5.09436 + 2.94123i −0.306644 + 0.177041i
\(277\) 9.12775 + 2.44577i 0.548433 + 0.146952i 0.522387 0.852708i \(-0.325042\pi\)
0.0260462 + 0.999661i \(0.491708\pi\)
\(278\) 0.742949 + 2.77273i 0.0445591 + 0.166297i
\(279\) −1.73386 −0.103804
\(280\) 0 0
\(281\) −11.7320 −0.699871 −0.349935 0.936774i \(-0.613796\pi\)
−0.349935 + 0.936774i \(0.613796\pi\)
\(282\) −1.57366 5.87298i −0.0937101 0.349731i
\(283\) −3.52349 0.944117i −0.209450 0.0561219i 0.152568 0.988293i \(-0.451246\pi\)
−0.362018 + 0.932171i \(0.617912\pi\)
\(284\) 3.34287 1.93001i 0.198363 0.114525i
\(285\) 0 0
\(286\) 6.13465i 0.362750i
\(287\) 4.61400 + 16.7231i 0.272356 + 0.987133i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) −3.62517 2.09299i −0.213245 0.123117i
\(290\) 0 0
\(291\) 1.04674 + 1.81300i 0.0613609 + 0.106280i
\(292\) −14.7013 + 3.93920i −0.860328 + 0.230524i
\(293\) 8.62354 8.62354i 0.503793 0.503793i −0.408822 0.912614i \(-0.634060\pi\)
0.912614 + 0.408822i \(0.134060\pi\)
\(294\) 3.58944 + 6.00965i 0.209340 + 0.350490i
\(295\) 0 0
\(296\) −1.38596 + 2.40055i −0.0805572 + 0.139529i
\(297\) 0.512139 1.91133i 0.0297173 0.110907i
\(298\) 4.03231 15.0488i 0.233585 0.871752i
\(299\) 9.11859 15.7939i 0.527341 0.913382i
\(300\) 0 0
\(301\) 20.6223 + 11.7034i 1.18865 + 0.674575i
\(302\) −14.9840 + 14.9840i −0.862232 + 0.862232i
\(303\) 9.70484 2.60040i 0.557529 0.149389i
\(304\) 2.10939 + 3.65357i 0.120982 + 0.209547i
\(305\) 0 0
\(306\) 3.98616 + 2.30141i 0.227874 + 0.131563i
\(307\) −15.9933 15.9933i −0.912785 0.912785i 0.0837060 0.996490i \(-0.473324\pi\)
−0.996490 + 0.0837060i \(0.973324\pi\)
\(308\) −5.06680 1.31749i −0.288708 0.0750710i
\(309\) 4.98786i 0.283750i
\(310\) 0 0
\(311\) 6.70522 3.87126i 0.380218 0.219519i −0.297695 0.954661i \(-0.596218\pi\)
0.677913 + 0.735142i \(0.262885\pi\)
\(312\) 2.99462 + 0.802407i 0.169537 + 0.0454273i
\(313\) −5.18810 19.3623i −0.293249 1.09442i −0.942598 0.333929i \(-0.891625\pi\)
0.649349 0.760490i \(-0.275041\pi\)
\(314\) 15.1833 0.856846
\(315\) 0 0
\(316\) 2.55514 0.143738
\(317\) 0.771364 + 2.87877i 0.0433241 + 0.161688i 0.984199 0.177067i \(-0.0566609\pi\)
−0.940875 + 0.338755i \(0.889994\pi\)
\(318\) −11.0441 2.95926i −0.619322 0.165947i
\(319\) 15.3371 8.85488i 0.858713 0.495778i
\(320\) 0 0
\(321\) 6.04965i 0.337658i
\(322\) 11.0863 + 10.9232i 0.617816 + 0.608728i
\(323\) −13.7308 13.7308i −0.764004 0.764004i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) 0 0
\(326\) −11.1615 19.3323i −0.618179 1.07072i
\(327\) 9.41680 2.52322i 0.520750 0.139535i
\(328\) −4.63643 + 4.63643i −0.256004 + 0.256004i
\(329\) −13.8714 + 8.14629i −0.764756 + 0.449119i
\(330\) 0 0
\(331\) −13.9186 + 24.1077i −0.765035 + 1.32508i 0.175194 + 0.984534i \(0.443945\pi\)
−0.940228 + 0.340545i \(0.889388\pi\)
\(332\) −3.48811 + 13.0178i −0.191435 + 0.714445i
\(333\) −0.717425 + 2.67747i −0.0393146 + 0.146724i
\(334\) −4.88769 + 8.46573i −0.267442 + 0.463224i
\(335\) 0 0
\(336\) −1.30586 + 2.30103i −0.0712407 + 0.125531i
\(337\) 17.1567 17.1567i 0.934583 0.934583i −0.0634051 0.997988i \(-0.520196\pi\)
0.997988 + 0.0634051i \(0.0201960\pi\)
\(338\) 3.27292 0.876975i 0.178023 0.0477012i
\(339\) 4.26035 + 7.37914i 0.231390 + 0.400780i
\(340\) 0 0
\(341\) −2.97123 1.71544i −0.160901 0.0928963i
\(342\) 2.98313 + 2.98313i 0.161309 + 0.161309i
\(343\) 12.8015 13.3836i 0.691217 0.722647i
\(344\) 8.96222i 0.483210i
\(345\) 0 0
\(346\) 3.92103 2.26381i 0.210796 0.121703i
\(347\) −24.1895 6.48156i −1.29856 0.347948i −0.457655 0.889130i \(-0.651311\pi\)
−0.840906 + 0.541181i \(0.817977\pi\)
\(348\) −2.31642 8.64500i −0.124173 0.463421i
\(349\) −18.0130 −0.964212 −0.482106 0.876113i \(-0.660128\pi\)
−0.482106 + 0.876113i \(0.660128\pi\)
\(350\) 0 0
\(351\) 3.10026 0.165480
\(352\) −0.512139 1.91133i −0.0272971 0.101874i
\(353\) −7.33911 1.96651i −0.390621 0.104667i 0.0581623 0.998307i \(-0.481476\pi\)
−0.448784 + 0.893641i \(0.648143\pi\)
\(354\) −3.64339 + 2.10351i −0.193644 + 0.111800i
\(355\) 0 0
\(356\) 6.19187i 0.328168i
\(357\) 3.06464 11.7860i 0.162198 0.623781i
\(358\) 1.46221 + 1.46221i 0.0772803 + 0.0772803i
\(359\) −2.84638 1.64336i −0.150226 0.0867332i 0.423003 0.906128i \(-0.360976\pi\)
−0.573229 + 0.819395i \(0.694309\pi\)
\(360\) 0 0
\(361\) 0.600927 + 1.04084i 0.0316277 + 0.0547808i
\(362\) 5.92305 1.58708i 0.311309 0.0834149i
\(363\) −5.00952 + 5.00952i −0.262932 + 0.262932i
\(364\) −0.0607699 8.20230i −0.00318521 0.429917i
\(365\) 0 0
\(366\) −5.55999 + 9.63018i −0.290625 + 0.503377i
\(367\) 0.840538 3.13693i 0.0438757 0.163746i −0.940512 0.339761i \(-0.889654\pi\)
0.984388 + 0.176014i \(0.0563205\pi\)
\(368\) −1.52249 + 5.68202i −0.0793654 + 0.296196i
\(369\) −3.27845 + 5.67845i −0.170669 + 0.295608i
\(370\) 0 0
\(371\) 0.224118 + 30.2499i 0.0116356 + 1.57050i
\(372\) −1.22602 + 1.22602i −0.0635664 + 0.0635664i
\(373\) −15.2290 + 4.08060i −0.788529 + 0.211286i −0.630542 0.776156i \(-0.717167\pi\)
−0.157987 + 0.987441i \(0.550500\pi\)
\(374\) 4.55392 + 7.88763i 0.235478 + 0.407860i
\(375\) 0 0
\(376\) −5.26557 3.04008i −0.271551 0.156780i
\(377\) 19.6203 + 19.6203i 1.01049 + 1.01049i
\(378\) −0.665818 + 2.56060i −0.0342460 + 0.131703i
\(379\) 21.7428i 1.11685i −0.829555 0.558426i \(-0.811406\pi\)
0.829555 0.558426i \(-0.188594\pi\)
\(380\) 0 0
\(381\) −10.9342 + 6.31283i −0.560174 + 0.323416i
\(382\) −15.6153 4.18410i −0.798946 0.214077i
\(383\) 4.62973 + 17.2784i 0.236568 + 0.882883i 0.977436 + 0.211233i \(0.0677478\pi\)
−0.740868 + 0.671651i \(0.765586\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 21.7909 1.10913
\(387\) 2.31959 + 8.65684i 0.117912 + 0.440052i
\(388\) 2.02214 + 0.541831i 0.102659 + 0.0275073i
\(389\) 4.36130 2.51800i 0.221127 0.127667i −0.385345 0.922772i \(-0.625918\pi\)
0.606472 + 0.795105i \(0.292584\pi\)
\(390\) 0 0
\(391\) 27.0759i 1.36929i
\(392\) 6.78758 + 1.71135i 0.342825 + 0.0864362i
\(393\) 3.62152 + 3.62152i 0.182681 + 0.182681i
\(394\) −0.769287 0.444148i −0.0387561 0.0223759i
\(395\) 0 0
\(396\) −0.989376 1.71365i −0.0497180 0.0861142i
\(397\) 14.2520 3.81880i 0.715285 0.191660i 0.117218 0.993106i \(-0.462602\pi\)
0.598067 + 0.801446i \(0.295936\pi\)
\(398\) 6.80587 6.80587i 0.341147 0.341147i
\(399\) 5.50916 9.70753i 0.275803 0.485984i
\(400\) 0 0
\(401\) 4.34686 7.52897i 0.217072 0.375979i −0.736840 0.676067i \(-0.763683\pi\)
0.953911 + 0.300088i \(0.0970162\pi\)
\(402\) −1.42665 + 5.32434i −0.0711550 + 0.265554i
\(403\) 1.39126 5.19226i 0.0693037 0.258645i
\(404\) 5.02360 8.70112i 0.249933 0.432897i
\(405\) 0 0
\(406\) −20.4187 + 11.9913i −1.01336 + 0.595118i
\(407\) −3.87844 + 3.87844i −0.192247 + 0.192247i
\(408\) 4.44599 1.19130i 0.220109 0.0589781i
\(409\) −9.49095 16.4388i −0.469297 0.812847i 0.530087 0.847944i \(-0.322159\pi\)
−0.999384 + 0.0350966i \(0.988826\pi\)
\(410\) 0 0
\(411\) 10.0306 + 5.79118i 0.494774 + 0.285658i
\(412\) 3.52695 + 3.52695i 0.173760 + 0.173760i
\(413\) 7.92871 + 7.81209i 0.390147 + 0.384408i
\(414\) 5.88246i 0.289107i
\(415\) 0 0
\(416\) 2.68491 1.55013i 0.131638 0.0760014i
\(417\) 2.77273 + 0.742949i 0.135781 + 0.0363824i
\(418\) 2.16060 + 8.06348i 0.105679 + 0.394398i
\(419\) 11.9171 0.582188 0.291094 0.956695i \(-0.405981\pi\)
0.291094 + 0.956695i \(0.405981\pi\)
\(420\) 0 0
\(421\) 6.95263 0.338850 0.169425 0.985543i \(-0.445809\pi\)
0.169425 + 0.985543i \(0.445809\pi\)
\(422\) −2.91610 10.8830i −0.141953 0.529778i
\(423\) −5.87298 1.57366i −0.285554 0.0765140i
\(424\) −9.90187 + 5.71685i −0.480877 + 0.277635i
\(425\) 0 0
\(426\) 3.86002i 0.187018i
\(427\) 28.4738 + 7.40388i 1.37795 + 0.358299i
\(428\) 4.27775 + 4.27775i 0.206773 + 0.206773i
\(429\) 5.31277 + 3.06733i 0.256503 + 0.148092i
\(430\) 0 0
\(431\) −3.12392 5.41078i −0.150474 0.260628i 0.780928 0.624621i \(-0.214747\pi\)
−0.931402 + 0.363993i \(0.881413\pi\)
\(432\) −0.965926 + 0.258819i −0.0464731 + 0.0124524i
\(433\) −15.1544 + 15.1544i −0.728274 + 0.728274i −0.970276 0.242002i \(-0.922196\pi\)
0.242002 + 0.970276i \(0.422196\pi\)
\(434\) 3.98966 + 2.26419i 0.191510 + 0.108684i
\(435\) 0 0
\(436\) 4.87449 8.44287i 0.233446 0.404340i
\(437\) 6.42307 23.9712i 0.307257 1.14670i
\(438\) −3.93920 + 14.7013i −0.188222 + 0.702455i
\(439\) 16.3729 28.3588i 0.781438 1.35349i −0.149666 0.988737i \(-0.547820\pi\)
0.931104 0.364753i \(-0.118847\pi\)
\(440\) 0 0
\(441\) 6.99923 0.103719i 0.333297 0.00493899i
\(442\) −10.0904 + 10.0904i −0.479951 + 0.479951i
\(443\) 29.7032 7.95895i 1.41124 0.378141i 0.528874 0.848701i \(-0.322615\pi\)
0.882368 + 0.470559i \(0.155948\pi\)
\(444\) 1.38596 + 2.40055i 0.0657747 + 0.113925i
\(445\) 0 0
\(446\) 16.1321 + 9.31386i 0.763876 + 0.441024i
\(447\) −11.0165 11.0165i −0.521061 0.521061i
\(448\) 0.703686 + 2.55046i 0.0332460 + 0.120498i
\(449\) 16.8713i 0.796207i −0.917341 0.398103i \(-0.869669\pi\)
0.917341 0.398103i \(-0.130331\pi\)
\(450\) 0 0
\(451\) −11.2362 + 6.48725i −0.529094 + 0.305473i
\(452\) 8.23036 + 2.20532i 0.387123 + 0.103729i
\(453\) 5.48452 + 20.4685i 0.257685 + 0.961695i
\(454\) 26.9142 1.26314
\(455\) 0 0
\(456\) 4.21878 0.197563
\(457\) −5.13696 19.1714i −0.240297 0.896800i −0.975689 0.219158i \(-0.929669\pi\)
0.735393 0.677641i \(-0.236998\pi\)
\(458\) 25.9742 + 6.95976i 1.21369 + 0.325208i
\(459\) 3.98616 2.30141i 0.186058 0.107421i
\(460\) 0 0
\(461\) 15.7775i 0.734830i 0.930057 + 0.367415i \(0.119757\pi\)
−0.930057 + 0.367415i \(0.880243\pi\)
\(462\) −3.67438 + 3.72923i −0.170948 + 0.173500i
\(463\) −4.48617 4.48617i −0.208490 0.208490i 0.595135 0.803625i \(-0.297098\pi\)
−0.803625 + 0.595135i \(0.797098\pi\)
\(464\) −7.75089 4.47498i −0.359826 0.207746i
\(465\) 0 0
\(466\) 0.460622 + 0.797821i 0.0213379 + 0.0369583i
\(467\) 16.8554 4.51639i 0.779975 0.208994i 0.153201 0.988195i \(-0.451042\pi\)
0.626774 + 0.779201i \(0.284375\pi\)
\(468\) 2.19222 2.19222i 0.101335 0.101335i
\(469\) 14.5834 0.108047i 0.673400 0.00498914i
\(470\) 0 0
\(471\) 7.59167 13.1492i 0.349806 0.605881i
\(472\) −1.08886 + 4.06367i −0.0501187 + 0.187046i
\(473\) −4.58990 + 17.1297i −0.211044 + 0.787626i
\(474\) 1.27757 2.21282i 0.0586808 0.101638i
\(475\) 0 0
\(476\) −6.16693 10.5010i −0.282661 0.481312i
\(477\) −8.08484 + 8.08484i −0.370180 + 0.370180i
\(478\) −24.4796 + 6.55929i −1.11967 + 0.300015i
\(479\) 15.8748 + 27.4960i 0.725339 + 1.25632i 0.958834 + 0.283966i \(0.0916503\pi\)
−0.233495 + 0.972358i \(0.575016\pi\)
\(480\) 0 0
\(481\) −7.44233 4.29683i −0.339341 0.195919i
\(482\) −14.9341 14.9341i −0.680230 0.680230i
\(483\) 15.0030 4.13940i 0.682658 0.188349i
\(484\) 7.08454i 0.322024i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) −28.8890 7.74077i −1.30908 0.350768i −0.464206 0.885727i \(-0.653660\pi\)
−0.844878 + 0.534960i \(0.820327\pi\)
\(488\) 2.87806 + 10.7411i 0.130284 + 0.486225i
\(489\) −22.3230 −1.00948
\(490\) 0 0
\(491\) 1.57179 0.0709340 0.0354670 0.999371i \(-0.488708\pi\)
0.0354670 + 0.999371i \(0.488708\pi\)
\(492\) 1.69705 + 6.33349i 0.0765090 + 0.285536i
\(493\) 39.7914 + 10.6621i 1.79211 + 0.480196i
\(494\) −11.3270 + 6.53967i −0.509628 + 0.294234i
\(495\) 0 0
\(496\) 1.73386i 0.0778527i
\(497\) −9.84480 + 2.71624i −0.441600 + 0.121840i
\(498\) 9.52969 + 9.52969i 0.427036 + 0.427036i
\(499\) 12.3491 + 7.12977i 0.552823 + 0.319172i 0.750260 0.661143i \(-0.229928\pi\)
−0.197437 + 0.980316i \(0.563262\pi\)
\(500\) 0 0
\(501\) 4.88769 + 8.46573i 0.218366 + 0.378221i
\(502\) 2.61401 0.700423i 0.116669 0.0312614i
\(503\) −28.7896 + 28.7896i −1.28367 + 1.28367i −0.345100 + 0.938566i \(0.612155\pi\)
−0.938566 + 0.345100i \(0.887845\pi\)
\(504\) 1.33981 + 2.28142i 0.0596801 + 0.101623i
\(505\) 0 0
\(506\) −5.81997 + 10.0805i −0.258729 + 0.448132i
\(507\) 0.876975 3.27292i 0.0389478 0.145355i
\(508\) −3.26776 + 12.1955i −0.144984 + 0.541086i
\(509\) 7.30942 12.6603i 0.323984 0.561157i −0.657322 0.753610i \(-0.728311\pi\)
0.981306 + 0.192453i \(0.0616442\pi\)
\(510\) 0 0
\(511\) 40.2670 0.298333i 1.78131 0.0131975i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 4.07503 1.09190i 0.179917 0.0482086i
\(514\) −12.0110 20.8037i −0.529784 0.917612i
\(515\) 0 0
\(516\) 7.76151 + 4.48111i 0.341681 + 0.197270i
\(517\) −8.50729 8.50729i −0.374150 0.374150i
\(518\) 5.14722 5.22406i 0.226156 0.229532i
\(519\) 4.52762i 0.198740i
\(520\) 0 0
\(521\) −13.3153 + 7.68757i −0.583352 + 0.336798i −0.762464 0.647030i \(-0.776011\pi\)
0.179112 + 0.983829i \(0.442677\pi\)
\(522\) −8.64500 2.31642i −0.378381 0.101387i
\(523\) −6.06041 22.6178i −0.265003 0.989006i −0.962248 0.272173i \(-0.912258\pi\)
0.697245 0.716833i \(-0.254409\pi\)
\(524\) 5.12160 0.223738
\(525\) 0 0
\(526\) 0.850325 0.0370759
\(527\) −2.06555 7.70872i −0.0899766 0.335797i
\(528\) −1.91133 0.512139i −0.0831799 0.0222880i
\(529\) 10.0488 5.80167i 0.436904 0.252247i
\(530\) 0 0
\(531\) 4.20702i 0.182569i
\(532\) −2.96870 10.7598i −0.128709 0.466498i
\(533\) −14.3742 14.3742i −0.622614 0.622614i
\(534\) −5.36231 3.09593i −0.232050 0.133974i
\(535\) 0 0
\(536\) 2.75608 + 4.77368i 0.119045 + 0.206191i
\(537\) 1.99742 0.535206i 0.0861949 0.0230959i
\(538\) 8.23314 8.23314i 0.354956 0.354956i
\(539\) 12.0969 + 6.74714i 0.521048 + 0.290620i
\(540\) 0 0
\(541\) −3.98437 + 6.90113i −0.171301 + 0.296703i −0.938875 0.344258i \(-0.888131\pi\)
0.767574 + 0.640961i \(0.221464\pi\)
\(542\) −6.04206 + 22.5493i −0.259529 + 0.968575i
\(543\) 1.58708 5.92305i 0.0681080 0.254182i
\(544\) 2.30141 3.98616i 0.0986722 0.170905i
\(545\) 0 0
\(546\) −7.13378 4.04852i −0.305298 0.173261i
\(547\) 5.88082 5.88082i 0.251446 0.251446i −0.570117 0.821563i \(-0.693102\pi\)
0.821563 + 0.570117i \(0.193102\pi\)
\(548\) 11.1877 2.99773i 0.477915 0.128057i
\(549\) 5.55999 + 9.63018i 0.237294 + 0.411006i
\(550\) 0 0
\(551\) 32.6994 + 18.8790i 1.39304 + 0.804272i
\(552\) 4.15953 + 4.15953i 0.177041 + 0.177041i
\(553\) −6.54271 1.70126i −0.278224 0.0723450i
\(554\) 9.44974i 0.401481i
\(555\) 0 0
\(556\) 2.48596 1.43527i 0.105428 0.0608689i
\(557\) 25.3198 + 6.78443i 1.07284 + 0.287466i 0.751658 0.659553i \(-0.229254\pi\)
0.321178 + 0.947019i \(0.395921\pi\)
\(558\) 0.448756 + 1.67478i 0.0189974 + 0.0708991i
\(559\) −27.7852 −1.17519
\(560\) 0 0
\(561\) 9.10785 0.384534
\(562\) 3.03646 + 11.3322i 0.128085 + 0.478020i
\(563\) −0.844624 0.226316i −0.0355967 0.00953810i 0.240977 0.970531i \(-0.422532\pi\)
−0.276573 + 0.960993i \(0.589199\pi\)
\(564\) −5.26557 + 3.04008i −0.221721 + 0.128010i
\(565\) 0 0
\(566\) 3.64779i 0.153328i
\(567\) 1.88464 + 1.85692i 0.0791473 + 0.0779832i
\(568\) −2.72944 2.72944i −0.114525 0.114525i
\(569\) 28.5877 + 16.5051i 1.19846 + 0.691929i 0.960211 0.279275i \(-0.0900943\pi\)
0.238246 + 0.971205i \(0.423428\pi\)
\(570\) 0 0
\(571\) −2.39594 4.14989i −0.100267 0.173668i 0.811528 0.584314i \(-0.198636\pi\)
−0.911795 + 0.410646i \(0.865303\pi\)
\(572\) 5.92562 1.58776i 0.247763 0.0663878i
\(573\) −11.4312 + 11.4312i −0.477544 + 0.477544i
\(574\) 14.9591 8.78504i 0.624380 0.366680i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −8.45046 + 31.5375i −0.351797 + 1.31293i 0.532670 + 0.846323i \(0.321189\pi\)
−0.884467 + 0.466602i \(0.845478\pi\)
\(578\) −1.08341 + 4.04335i −0.0450640 + 0.168181i
\(579\) 10.8955 18.8715i 0.452800 0.784272i
\(580\) 0 0
\(581\) 17.5992 31.0110i 0.730136 1.28655i
\(582\) 1.48031 1.48031i 0.0613609 0.0613609i
\(583\) −21.8535 + 5.85564i −0.905081 + 0.242516i
\(584\) 7.60995 + 13.1808i 0.314902 + 0.545426i
\(585\) 0 0
\(586\) −10.5616 6.09777i −0.436297 0.251896i
\(587\) −6.03856 6.03856i −0.249238 0.249238i 0.571420 0.820658i \(-0.306393\pi\)
−0.820658 + 0.571420i \(0.806393\pi\)
\(588\) 4.87586 5.02254i 0.201077 0.207126i
\(589\) 7.31479i 0.301401i
\(590\) 0 0
\(591\) −0.769287 + 0.444148i −0.0316442 + 0.0182698i
\(592\) 2.67747 + 0.717425i 0.110043 + 0.0294860i
\(593\) −1.05350 3.93171i −0.0432620 0.161456i 0.940915 0.338642i \(-0.109967\pi\)
−0.984177 + 0.177186i \(0.943301\pi\)
\(594\) −1.97875 −0.0811892
\(595\) 0 0
\(596\) −15.5796 −0.638167
\(597\) −2.49112 9.29699i −0.101955 0.380501i
\(598\) −17.6158 4.72013i −0.720362 0.193020i
\(599\) −29.5547 + 17.0634i −1.20757 + 0.697193i −0.962229 0.272243i \(-0.912235\pi\)
−0.245345 + 0.969436i \(0.578901\pi\)
\(600\) 0 0
\(601\) 9.99405i 0.407666i 0.979006 + 0.203833i \(0.0653399\pi\)
−0.979006 + 0.203833i \(0.934660\pi\)
\(602\) 5.96721 22.9487i 0.243205 0.935318i
\(603\) 3.89769 + 3.89769i 0.158726 + 0.158726i
\(604\) 18.3516 + 10.5953i 0.746715 + 0.431116i
\(605\) 0 0
\(606\) −5.02360 8.70112i −0.204070 0.353459i
\(607\) −17.6567 + 4.73109i −0.716662 + 0.192029i −0.598682 0.800987i \(-0.704309\pi\)
−0.117980 + 0.993016i \(0.537642\pi\)
\(608\) 2.98313 2.98313i 0.120982 0.120982i
\(609\) 0.175433 + 23.6787i 0.00710890 + 0.959510i
\(610\) 0 0
\(611\) 9.42504 16.3247i 0.381296 0.660425i
\(612\) 1.19130 4.44599i 0.0481554 0.179718i
\(613\) 7.72109 28.8155i 0.311852 1.16385i −0.615033 0.788501i \(-0.710857\pi\)
0.926885 0.375346i \(-0.122476\pi\)
\(614\) −11.3090 + 19.5877i −0.456392 + 0.790495i
\(615\) 0 0
\(616\) 0.0387866 + 5.23514i 0.00156276 + 0.210930i
\(617\) 35.0246 35.0246i 1.41004 1.41004i 0.650721 0.759317i \(-0.274467\pi\)
0.759317 0.650721i \(-0.225533\pi\)
\(618\) 4.81790 1.29095i 0.193805 0.0519298i
\(619\) −5.75770 9.97263i −0.231422 0.400834i 0.726805 0.686844i \(-0.241004\pi\)
−0.958227 + 0.286010i \(0.907671\pi\)
\(620\) 0 0
\(621\) 5.09436 + 2.94123i 0.204430 + 0.118028i
\(622\) −5.47479 5.47479i −0.219519 0.219519i
\(623\) −4.12266 + 15.8549i −0.165171 + 0.635214i
\(624\) 3.10026i 0.124110i
\(625\) 0 0
\(626\) −17.3597 + 10.0226i −0.693834 + 0.400585i
\(627\) 8.06348 + 2.16060i 0.322024 + 0.0862862i
\(628\) −3.92974 14.6660i −0.156814 0.585237i
\(629\) −12.7586 −0.508720
\(630\) 0 0
\(631\) 18.4477 0.734390 0.367195 0.930144i \(-0.380318\pi\)
0.367195 + 0.930144i \(0.380318\pi\)
\(632\) −0.661320 2.46808i −0.0263059 0.0981749i
\(633\) −10.8830 2.91610i −0.432562 0.115905i
\(634\) 2.58104 1.49016i 0.102506 0.0591819i
\(635\) 0 0
\(636\) 11.4337i 0.453375i
\(637\) −5.30563 + 21.0433i −0.210217 + 0.833765i
\(638\) −12.5227 12.5227i −0.495778 0.495778i
\(639\) −3.34287 1.93001i −0.132242 0.0763499i
\(640\) 0 0
\(641\) 9.74229 + 16.8741i 0.384797 + 0.666488i 0.991741 0.128256i \(-0.0409380\pi\)
−0.606944 + 0.794745i \(0.707605\pi\)
\(642\) 5.84351 1.56576i 0.230625 0.0617958i
\(643\) 28.2707 28.2707i 1.11489 1.11489i 0.122408 0.992480i \(-0.460938\pi\)
0.992480 0.122408i \(-0.0390615\pi\)
\(644\) 7.68169 13.5357i 0.302701 0.533381i
\(645\) 0 0
\(646\) −9.70916 + 16.8168i −0.382002 + 0.661647i
\(647\) 6.45214 24.0797i 0.253660 0.946672i −0.715171 0.698949i \(-0.753651\pi\)
0.968831 0.247722i \(-0.0796821\pi\)
\(648\) −0.258819 + 0.965926i −0.0101674 + 0.0379452i
\(649\) −4.16233 + 7.20937i −0.163386 + 0.282992i
\(650\) 0 0
\(651\) 3.95567 2.32305i 0.155035 0.0910476i
\(652\) −15.7848 + 15.7848i −0.618179 + 0.618179i
\(653\) −48.0477 + 12.8743i −1.88025 + 0.503812i −0.880705 + 0.473666i \(0.842930\pi\)
−0.999546 + 0.0301458i \(0.990403\pi\)
\(654\) −4.87449 8.44287i −0.190608 0.330142i
\(655\) 0 0
\(656\) 5.67845 + 3.27845i 0.221706 + 0.128002i
\(657\) 10.7621 + 10.7621i 0.419869 + 0.419869i
\(658\) 11.4589 + 11.2903i 0.446714 + 0.440144i
\(659\) 39.5644i 1.54121i 0.637312 + 0.770606i \(0.280046\pi\)
−0.637312 + 0.770606i \(0.719954\pi\)
\(660\) 0 0
\(661\) −1.74995 + 1.01033i −0.0680651 + 0.0392974i −0.533646 0.845708i \(-0.679179\pi\)
0.465581 + 0.885005i \(0.345845\pi\)
\(662\) 26.8886 + 7.20479i 1.04506 + 0.280022i
\(663\) 3.69334 + 13.7837i 0.143437 + 0.535315i
\(664\) 13.4770 0.523010
\(665\) 0 0
\(666\) 2.77192 0.107410
\(667\) 13.6263 + 50.8539i 0.527611 + 1.96907i
\(668\) 9.44229 + 2.53005i 0.365333 + 0.0978907i
\(669\) 16.1321 9.31386i 0.623702 0.360095i
\(670\) 0 0
\(671\) 22.0037i 0.849442i
\(672\) 2.56060 + 0.665818i 0.0987774 + 0.0256845i
\(673\) 19.7775 + 19.7775i 0.762366 + 0.762366i 0.976750 0.214383i \(-0.0687742\pi\)
−0.214383 + 0.976750i \(0.568774\pi\)
\(674\) −21.0125 12.1316i −0.809372 0.467291i
\(675\) 0 0
\(676\) −1.69419 2.93442i −0.0651610 0.112862i
\(677\) 16.5748 4.44120i 0.637021 0.170689i 0.0741672 0.997246i \(-0.476370\pi\)
0.562854 + 0.826557i \(0.309703\pi\)
\(678\) 6.02504 6.02504i 0.231390 0.231390i
\(679\) −4.81714 2.73379i −0.184865 0.104913i
\(680\) 0 0
\(681\) 13.4571 23.3083i 0.515676 0.893177i
\(682\) −0.887978 + 3.31398i −0.0340024 + 0.126899i
\(683\) −0.130540 + 0.487181i −0.00499496 + 0.0186414i −0.968378 0.249486i \(-0.919738\pi\)
0.963383 + 0.268128i \(0.0864049\pi\)
\(684\) 2.10939 3.65357i 0.0806546 0.139698i
\(685\) 0 0
\(686\) −16.2409 8.90138i −0.620079 0.339856i
\(687\) 19.0144 19.0144i 0.725445 0.725445i
\(688\) 8.65684 2.31959i 0.330039 0.0884336i
\(689\) −17.7237 30.6984i −0.675220 1.16952i
\(690\) 0 0
\(691\) 13.5396 + 7.81710i 0.515071 + 0.297376i 0.734916 0.678158i \(-0.237222\pi\)
−0.219845 + 0.975535i \(0.570555\pi\)
\(692\) −3.20151 3.20151i −0.121703 0.121703i
\(693\) 1.39242 + 5.04672i 0.0528937 + 0.191709i
\(694\) 25.0428i 0.950613i
\(695\) 0 0
\(696\) −7.75089 + 4.47498i −0.293797 + 0.169624i
\(697\) −29.1519 7.81123i −1.10421 0.295871i
\(698\) 4.66210 + 17.3992i 0.176463 + 0.658569i
\(699\) 0.921244 0.0348447
\(700\) 0 0
\(701\) 8.02724 0.303185 0.151592 0.988443i \(-0.451560\pi\)
0.151592 + 0.988443i \(0.451560\pi\)
\(702\) −0.802407 2.99462i −0.0302849 0.113025i
\(703\) −11.2956 3.02666i −0.426023 0.114153i
\(704\) −1.71365 + 0.989376i −0.0645856 + 0.0372885i
\(705\) 0 0
\(706\) 7.59800i 0.285955i
\(707\) −18.6568 + 18.9353i −0.701661 + 0.712136i
\(708\) 2.97481 + 2.97481i 0.111800 + 0.111800i
\(709\) 11.8457 + 6.83914i 0.444876 + 0.256849i 0.705664 0.708547i \(-0.250649\pi\)
−0.260788 + 0.965396i \(0.583982\pi\)
\(710\) 0 0
\(711\) −1.27757 2.21282i −0.0479127 0.0829872i
\(712\) −5.98088 + 1.60257i −0.224143 + 0.0600590i
\(713\) 7.21204 7.21204i 0.270093 0.270093i
\(714\) −12.1776 + 0.0902224i −0.455735 + 0.00337649i
\(715\) 0 0
\(716\) 1.03394 1.79084i 0.0386401 0.0669267i
\(717\) −6.55929 + 24.4796i −0.244961 + 0.914208i
\(718\) −0.850665 + 3.17473i −0.0317465 + 0.118480i
\(719\) −10.5235 + 18.2273i −0.392462 + 0.679764i −0.992774 0.120002i \(-0.961710\pi\)
0.600312 + 0.799766i \(0.295043\pi\)
\(720\) 0 0
\(721\) −6.68281 11.3794i −0.248881 0.423792i
\(722\) 0.849839 0.849839i 0.0316277 0.0316277i
\(723\) −20.4004 + 5.46626i −0.758698 + 0.203292i
\(724\) −3.06600 5.31046i −0.113947 0.197362i
\(725\) 0 0
\(726\) 6.13539 + 3.54227i 0.227706 + 0.131466i
\(727\) 11.2251 + 11.2251i 0.416317 + 0.416317i 0.883932 0.467615i \(-0.154887\pi\)
−0.467615 + 0.883932i \(0.654887\pi\)
\(728\) −7.90708 + 2.18161i −0.293056 + 0.0808559i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −35.7248 + 20.6258i −1.32133 + 0.762871i
\(732\) 10.7411 + 2.87806i 0.397001 + 0.106376i
\(733\) −7.44145 27.7719i −0.274856 1.02578i −0.955938 0.293570i \(-0.905157\pi\)
0.681081 0.732208i \(-0.261510\pi\)
\(734\) −3.24759 −0.119871
\(735\) 0 0
\(736\) 5.88246 0.216830
\(737\) 2.82300 + 10.5356i 0.103986 + 0.388082i
\(738\) 6.33349 + 1.69705i 0.233139 + 0.0624694i
\(739\) 36.3593 20.9921i 1.33750 0.772205i 0.351063 0.936352i \(-0.385820\pi\)
0.986436 + 0.164147i \(0.0524871\pi\)
\(740\) 0 0
\(741\) 13.0793i 0.480482i
\(742\) 29.1611 8.04573i 1.07054 0.295368i
\(743\) −8.63799 8.63799i −0.316897 0.316897i 0.530677 0.847574i \(-0.321938\pi\)
−0.847574 + 0.530677i \(0.821938\pi\)
\(744\) 1.50157 + 0.866930i 0.0550501 + 0.0317832i
\(745\) 0 0
\(746\) 7.88312 + 13.6540i 0.288622 + 0.499907i
\(747\) 13.0178 3.48811i 0.476297 0.127623i
\(748\) 6.44022 6.44022i 0.235478 0.235478i
\(749\) −8.10541 13.8018i −0.296165 0.504307i
\(750\) 0 0
\(751\) −15.8723 + 27.4916i −0.579188 + 1.00318i 0.416384 + 0.909189i \(0.363297\pi\)
−0.995573 + 0.0939948i \(0.970036\pi\)
\(752\) −1.57366 + 5.87298i −0.0573855 + 0.214166i
\(753\) 0.700423 2.61401i 0.0255248 0.0952600i
\(754\) 13.8736 24.0298i 0.505247 0.875114i
\(755\) 0 0
\(756\) 2.64568 0.0196015i 0.0962224 0.000712901i
\(757\) 9.81959 9.81959i 0.356899 0.356899i −0.505770 0.862669i \(-0.668791\pi\)
0.862669 + 0.505770i \(0.168791\pi\)
\(758\) −21.0019 + 5.62744i −0.762824 + 0.204398i
\(759\) 5.81997 + 10.0805i 0.211251 + 0.365898i
\(760\) 0 0
\(761\) 27.6636 + 15.9716i 1.00280 + 0.578970i 0.909077 0.416628i \(-0.136788\pi\)
0.0937278 + 0.995598i \(0.470122\pi\)
\(762\) 8.92770 + 8.92770i 0.323416 + 0.323416i
\(763\) −18.1031 + 18.3733i −0.655375 + 0.665158i
\(764\) 16.1661i 0.584869i
\(765\) 0 0
\(766\) 15.4914 8.94394i 0.559726 0.323158i
\(767\) −12.5985 3.37574i −0.454904 0.121891i
\(768\) 0.258819 + 0.965926i 0.00933933 + 0.0348548i
\(769\) −26.3715 −0.950981 −0.475490 0.879721i \(-0.657729\pi\)
−0.475490 + 0.879721i \(0.657729\pi\)
\(770\) 0 0
\(771\) −24.0221 −0.865133
\(772\) −5.63991 21.0484i −0.202985 0.757549i
\(773\) 44.4561 + 11.9120i 1.59898 + 0.428444i 0.944733 0.327841i \(-0.106321\pi\)
0.654242 + 0.756285i \(0.272988\pi\)
\(774\) 7.76151 4.48111i 0.278982 0.161070i
\(775\) 0 0
\(776\) 2.09348i 0.0751514i
\(777\) −1.95056 7.06965i −0.0699759 0.253622i
\(778\) −3.56098 3.56098i −0.127667 0.127667i
\(779\) −23.9561 13.8311i −0.858318 0.495550i
\(780\) 0 0
\(781\) −3.81901 6.61472i −0.136655 0.236693i