Properties

Label 1050.2.bc.g.607.4
Level $1050$
Weight $2$
Character 1050.607
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 607.4
Root \(0.117630 - 0.893490i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.g.493.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.703686 + 2.55046i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.703686 + 2.55046i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.989376 + 1.71365i) q^{11} +(0.258819 + 0.965926i) q^{12} +(2.19222 + 2.19222i) q^{13} +(1.33981 + 2.28142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.44599 - 1.19130i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.10939 - 3.65357i) q^{19} +(-2.64568 + 0.0196015i) q^{21} +(1.39919 + 1.39919i) q^{22} +(1.52249 + 5.68202i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.68491 + 1.55013i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.88464 + 1.85692i) q^{28} +8.94996i q^{29} +(-1.50157 + 0.866930i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.91133 + 0.512139i) q^{33} -4.60282 q^{34} -1.00000 q^{36} +(-2.67747 + 0.717425i) q^{37} +(1.09190 - 4.07503i) q^{38} +(-2.68491 + 1.55013i) q^{39} +6.55691i q^{41} +(-2.55046 + 0.703686i) q^{42} +(6.33724 - 6.33724i) q^{43} +(1.71365 + 0.989376i) q^{44} +(2.94123 + 5.09436i) q^{46} +(-1.57366 - 5.87298i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.00965 + 3.58944i) q^{49} +(2.30141 - 3.98616i) q^{51} +(2.99462 + 0.802407i) q^{52} +(11.0441 + 2.95926i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.30103 + 1.30586i) q^{56} +(2.98313 + 2.98313i) q^{57} +(2.31642 + 8.64500i) q^{58} +(-2.10351 - 3.64339i) q^{59} +(9.63018 + 5.55999i) q^{61} +(-1.22602 + 1.22602i) q^{62} +(0.665818 - 2.56060i) q^{63} -1.00000i q^{64} +(-1.71365 + 0.989376i) q^{66} +(-1.42665 + 5.32434i) q^{67} +(-4.44599 + 1.19130i) q^{68} -5.88246 q^{69} -3.86002 q^{71} +(-0.965926 + 0.258819i) q^{72} +(3.93920 - 14.7013i) q^{73} +(-2.40055 + 1.38596i) q^{74} -4.21878i q^{76} +(-3.67438 + 3.72923i) q^{77} +(-2.19222 + 2.19222i) q^{78} +(2.21282 + 1.27757i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.69705 + 6.33349i) q^{82} +(-9.52969 - 9.52969i) q^{83} +(-2.28142 + 1.33981i) q^{84} +(4.48111 - 7.76151i) q^{86} +(-8.64500 - 2.31642i) q^{87} +(1.91133 + 0.512139i) q^{88} +(3.09593 - 5.36231i) q^{89} +(-4.04852 + 7.13378i) q^{91} +(4.15953 + 4.15953i) q^{92} +(-0.448756 - 1.67478i) q^{93} +(-3.04008 - 5.26557i) q^{94} +(0.866025 + 0.500000i) q^{96} +(1.48031 - 1.48031i) q^{97} +(-4.87586 + 5.02254i) q^{98} -1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 4q^{11} - 16q^{13} - 16q^{14} + 8q^{16} - 12q^{17} + 8q^{19} + 8q^{21} - 4q^{22} + 40q^{23} + 8q^{24} - 12q^{26} + 4q^{28} - 24q^{31} - 4q^{33} - 16q^{34} - 16q^{36} + 8q^{37} + 20q^{38} + 12q^{39} - 8q^{42} + 24q^{43} - 4q^{46} - 52q^{49} + 8q^{51} - 8q^{52} + 28q^{53} + 8q^{54} + 8q^{56} + 8q^{57} + 12q^{58} - 8q^{59} + 24q^{61} + 8q^{62} + 4q^{63} + 84q^{67} - 12q^{68} + 8q^{69} - 32q^{71} - 16q^{73} + 24q^{74} - 44q^{77} + 16q^{78} - 12q^{79} + 8q^{81} - 36q^{82} - 16q^{83} - 4q^{84} - 8q^{86} - 48q^{87} + 4q^{88} + 16q^{89} + 8q^{91} - 8q^{92} + 32q^{93} - 8q^{94} + 44q^{97} - 24q^{98} + O(q^{100}) \)

Character values

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

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

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
\(7\) 0.703686 + 2.55046i 0.265968 + 0.963982i
\(8\) 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 \(0.736911\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) 2.19222 + 2.19222i 0.608011 + 0.608011i 0.942426 0.334415i \(-0.108539\pi\)
−0.334415 + 0.942426i \(0.608539\pi\)
\(14\) 1.33981 + 2.28142i 0.358081 + 0.609736i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −4.44599 1.19130i −1.07831 0.288932i −0.324407 0.945918i \(-0.605165\pi\)
−0.753903 + 0.656985i \(0.771831\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) 2.10939 3.65357i 0.483928 0.838188i −0.515902 0.856648i \(-0.672543\pi\)
0.999830 + 0.0184602i \(0.00587639\pi\)
\(20\) 0 0
\(21\) −2.64568 + 0.0196015i −0.577334 + 0.00427740i
\(22\) 1.39919 + 1.39919i 0.298308 + 0.298308i
\(23\) 1.52249 + 5.68202i 0.317462 + 1.18478i 0.921676 + 0.387961i \(0.126821\pi\)
−0.604214 + 0.796822i \(0.706513\pi\)
\(24\) 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
\(28\) 1.88464 + 1.85692i 0.356163 + 0.350924i
\(29\) 8.94996i 1.66197i 0.556298 + 0.830983i \(0.312221\pi\)
−0.556298 + 0.830983i \(0.687779\pi\)
\(30\) 0 0
\(31\) −1.50157 + 0.866930i −0.269689 + 0.155705i −0.628747 0.777610i \(-0.716432\pi\)
0.359057 + 0.933316i \(0.383098\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −1.91133 + 0.512139i −0.332720 + 0.0891519i
\(34\) −4.60282 −0.789378
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −2.67747 + 0.717425i −0.440173 + 0.117944i −0.472097 0.881546i \(-0.656503\pi\)
0.0319248 + 0.999490i \(0.489836\pi\)
\(38\) 1.09190 4.07503i 0.177130 0.661058i
\(39\) −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 \(0.828902\pi\)
\(42\) −2.55046 + 0.703686i −0.393544 + 0.108581i
\(43\) 6.33724 6.33724i 0.966421 0.966421i −0.0330335 0.999454i \(-0.510517\pi\)
0.999454 + 0.0330335i \(0.0105168\pi\)
\(44\) 1.71365 + 0.989376i 0.258342 + 0.149154i
\(45\) 0 0
\(46\) 2.94123 + 5.09436i 0.433661 + 0.751122i
\(47\) −1.57366 5.87298i −0.229542 0.856663i −0.980534 0.196351i \(-0.937091\pi\)
0.750992 0.660312i \(-0.229576\pi\)
\(48\) 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
\(52\) 2.99462 + 0.802407i 0.415280 + 0.111274i
\(53\) 11.0441 + 2.95926i 1.51702 + 0.406485i 0.918761 0.394814i \(-0.129191\pi\)
0.598263 + 0.801300i \(0.295858\pi\)
\(54\) 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
\(58\) 2.31642 + 8.64500i 0.304161 + 1.13514i
\(59\) −2.10351 3.64339i −0.273854 0.474329i 0.695991 0.718050i \(-0.254965\pi\)
−0.969845 + 0.243721i \(0.921632\pi\)
\(60\) 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
\(63\) 0.665818 2.56060i 0.0838852 0.322606i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −1.71365 + 0.989376i −0.210936 + 0.121784i
\(67\) −1.42665 + 5.32434i −0.174294 + 0.650472i 0.822377 + 0.568942i \(0.192647\pi\)
−0.996671 + 0.0815298i \(0.974019\pi\)
\(68\) −4.44599 + 1.19130i −0.539155 + 0.144466i
\(69\) −5.88246 −0.708165
\(70\) 0 0
\(71\) −3.86002 −0.458100 −0.229050 0.973415i \(-0.573562\pi\)
−0.229050 + 0.973415i \(0.573562\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) 3.93920 14.7013i 0.461048 1.72066i −0.208621 0.977997i \(-0.566897\pi\)
0.669669 0.742660i \(-0.266436\pi\)
\(74\) −2.40055 + 1.38596i −0.279058 + 0.161114i
\(75\) 0 0
\(76\) 4.21878i 0.483928i
\(77\) −3.67438 + 3.72923i −0.418734 + 0.424985i
\(78\) −2.19222 + 2.19222i −0.248220 + 0.248220i
\(79\) 2.21282 + 1.27757i 0.248962 + 0.143738i 0.619289 0.785163i \(-0.287421\pi\)
−0.370327 + 0.928901i \(0.620754\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 1.69705 + 6.33349i 0.187408 + 0.699416i
\(83\) −9.52969 9.52969i −1.04602 1.04602i −0.998889 0.0471311i \(-0.984992\pi\)
−0.0471311 0.998889i \(-0.515008\pi\)
\(84\) −2.28142 + 1.33981i −0.248924 + 0.146186i
\(85\) 0 0
\(86\) 4.48111 7.76151i 0.483210 0.836945i
\(87\) −8.64500 2.31642i −0.926841 0.248346i
\(88\) 1.91133 + 0.512139i 0.203748 + 0.0545942i
\(89\) 3.09593 5.36231i 0.328168 0.568404i −0.653980 0.756512i \(-0.726902\pi\)
0.982148 + 0.188108i \(0.0602354\pi\)
\(90\) 0 0
\(91\) −4.04852 + 7.13378i −0.424400 + 0.747824i
\(92\) 4.15953 + 4.15953i 0.433661 + 0.433661i
\(93\) −0.448756 1.67478i −0.0465339 0.173667i
\(94\) −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 \(-0.716106\pi\)
0.778253 + 0.627951i \(0.216106\pi\)
\(98\) −4.87586 + 5.02254i −0.492537 + 0.507354i
\(99\) 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 \(0.499951\pi\)
\(102\) 1.19130 4.44599i 0.117956 0.440218i
\(103\) −4.81790 + 1.29095i −0.474722 + 0.127201i −0.488244 0.872707i \(-0.662362\pi\)
0.0135219 + 0.999909i \(0.495696\pi\)
\(104\) 3.10026 0.304006
\(105\) 0 0
\(106\) 11.4337 1.11054
\(107\) 5.84351 1.56576i 0.564913 0.151368i 0.0349507 0.999389i \(-0.488873\pi\)
0.529963 + 0.848021i \(0.322206\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) 8.44287 4.87449i 0.808680 0.466892i −0.0378171 0.999285i \(-0.512040\pi\)
0.846497 + 0.532393i \(0.178707\pi\)
\(110\) 0 0
\(111\) 2.77192i 0.263099i
\(112\) 2.56060 + 0.665818i 0.241954 + 0.0629139i
\(113\) −6.02504 + 6.02504i −0.566788 + 0.566788i −0.931227 0.364439i \(-0.881261\pi\)
0.364439 + 0.931227i \(0.381261\pi\)
\(114\) 3.65357 + 2.10939i 0.342189 + 0.197563i
\(115\) 0 0
\(116\) 4.47498 + 7.75089i 0.415491 + 0.719652i
\(117\) −0.802407 2.99462i −0.0741826 0.276853i
\(118\) −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
\(122\) 10.7411 + 2.87806i 0.972451 + 0.260567i
\(123\) −6.33349 1.69705i −0.571071 0.153018i
\(124\) −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 0.981852 0.189647i \(-0.0607345\pi\)
−0.189647 + 0.981852i \(0.560734\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 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
\(133\) 10.8026 + 2.80894i 0.936707 + 0.243566i
\(134\) 5.51217i 0.476179i
\(135\) 0 0
\(136\) −3.98616 + 2.30141i −0.341811 + 0.197344i
\(137\) 2.99773 11.1877i 0.256114 0.955829i −0.711354 0.702834i \(-0.751918\pi\)
0.967468 0.252995i \(-0.0814157\pi\)
\(138\) −5.68202 + 1.52249i −0.483686 + 0.129603i
\(139\) 2.87054 0.243476 0.121738 0.992562i \(-0.461153\pi\)
0.121738 + 0.992562i \(0.461153\pi\)
\(140\) 0 0
\(141\) 6.08016 0.512042
\(142\) −3.72849 + 0.999046i −0.312888 + 0.0838381i
\(143\) −1.58776 + 5.92562i −0.132776 + 0.495525i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 15.2199i 1.25961i
\(147\) −1.91172 6.73389i −0.157676 0.555402i
\(148\) −1.96004 + 1.96004i −0.161114 + 0.161114i
\(149\) −13.4924 7.78982i −1.10534 0.638167i −0.167720 0.985835i \(-0.553640\pi\)
−0.937618 + 0.347668i \(0.886974\pi\)
\(150\) 0 0
\(151\) −10.5953 18.3516i −0.862232 1.49343i −0.869769 0.493459i \(-0.835732\pi\)
0.00753703 0.999972i \(-0.497601\pi\)
\(152\) −1.09190 4.07503i −0.0885649 0.330529i
\(153\) 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
\(157\) −14.6660 3.92974i −1.17047 0.313627i −0.379332 0.925261i \(-0.623846\pi\)
−0.791141 + 0.611633i \(0.790513\pi\)
\(158\) 2.46808 + 0.661320i 0.196350 + 0.0526118i
\(159\) −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
\(163\) −5.77762 21.5624i −0.452538 1.68890i −0.695225 0.718792i \(-0.744695\pi\)
0.242687 0.970105i \(-0.421971\pi\)
\(164\) 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 \(-0.626536\pi\)
0.922022 + 0.387137i \(0.126536\pi\)
\(168\) −1.85692 + 1.88464i −0.143264 + 0.145403i
\(169\) 3.38837i 0.260644i
\(170\) 0 0
\(171\) −3.65357 + 2.10939i −0.279396 + 0.161309i
\(172\) 2.31959 8.65684i 0.176867 0.660078i
\(173\) 4.37334 1.17183i 0.332499 0.0890928i −0.0887072 0.996058i \(-0.528274\pi\)
0.421206 + 0.906965i \(0.361607\pi\)
\(174\) −8.94996 −0.678495
\(175\) 0 0
\(176\) 1.97875 0.149154
\(177\) 4.06367 1.08886i 0.305444 0.0818436i
\(178\) 1.60257 5.98088i 0.120118 0.448286i
\(179\) 1.79084 1.03394i 0.133853 0.0772803i −0.431578 0.902076i \(-0.642043\pi\)
0.565431 + 0.824795i \(0.308710\pi\)
\(180\) 0 0
\(181\) 6.13199i 0.455787i 0.973686 + 0.227894i \(0.0731839\pi\)
−0.973686 + 0.227894i \(0.926816\pi\)
\(182\) −2.06421 + 7.93854i −0.153010 + 0.588444i
\(183\) −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
\(187\) −2.35728 8.79751i −0.172382 0.643337i
\(188\) −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 \(-0.0321876\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) 21.0484 + 5.63991i 1.51510 + 0.405969i 0.918125 0.396292i \(-0.129703\pi\)
0.596973 + 0.802261i \(0.296370\pi\)
\(194\) 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 0.729129 0.684377i \(-0.239926\pi\)
−0.684377 + 0.729129i \(0.739926\pi\)
\(198\) −0.512139 1.91133i −0.0363961 0.135832i
\(199\) −4.81248 8.33546i −0.341147 0.590885i 0.643499 0.765447i \(-0.277482\pi\)
−0.984646 + 0.174563i \(0.944149\pi\)
\(200\) 0 0
\(201\) −4.77368 2.75608i −0.336709 0.194399i
\(202\) −7.10444 + 7.10444i −0.499866 + 0.499866i
\(203\) −22.8265 + 6.29796i −1.60210 + 0.442030i
\(204\) 4.60282i 0.322262i
\(205\) 0 0
\(206\) −4.31961 + 2.49393i −0.300962 + 0.173760i
\(207\) 1.52249 5.68202i 0.105821 0.394928i
\(208\) 2.99462 0.802407i 0.207640 0.0556369i
\(209\) 8.34793 0.577439
\(210\) 0 0
\(211\) 11.2669 0.775648 0.387824 0.921733i \(-0.373227\pi\)
0.387824 + 0.921733i \(0.373227\pi\)
\(212\) 11.0441 2.95926i 0.758512 0.203243i
\(213\) 0.999046 3.72849i 0.0684535 0.255472i
\(214\) 5.23915 3.02482i 0.358141 0.206773i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −3.26770 3.21964i −0.221826 0.218563i
\(218\) 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
\(222\) −0.717425 2.67747i −0.0481504 0.179700i
\(223\) 13.1718 + 13.1718i 0.882048 + 0.882048i 0.993743 0.111694i \(-0.0356277\pi\)
−0.111694 + 0.993743i \(0.535628\pi\)
\(224\) 2.64568 0.0196015i 0.176772 0.00130968i
\(225\) 0 0
\(226\) −4.26035 + 7.37914i −0.283394 + 0.490853i
\(227\) −25.9971 6.96589i −1.72549 0.462343i −0.746351 0.665552i \(-0.768196\pi\)
−0.979135 + 0.203210i \(0.934863\pi\)
\(228\) 4.07503 + 1.09190i 0.269876 + 0.0723130i
\(229\) 13.4452 23.2878i 0.888486 1.53890i 0.0468199 0.998903i \(-0.485091\pi\)
0.841666 0.539999i \(-0.181575\pi\)
\(230\) 0 0
\(231\) −2.65116 4.51437i −0.174434 0.297024i
\(232\) 6.32858 + 6.32858i 0.415491 + 0.415491i
\(233\) 0.238436 + 0.889853i 0.0156204 + 0.0582962i 0.973296 0.229553i \(-0.0737264\pi\)
−0.957676 + 0.287849i \(0.907060\pi\)
\(234\) −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
\(238\) −3.23894 11.7393i −0.209949 0.760946i
\(239\) 25.3432i 1.63931i 0.572856 + 0.819656i \(0.305836\pi\)
−0.572856 + 0.819656i \(0.694164\pi\)
\(240\) 0 0
\(241\) 18.2905 10.5600i 1.17819 0.680230i 0.222597 0.974911i \(-0.428547\pi\)
0.955596 + 0.294681i \(0.0952134\pi\)
\(242\) 1.83361 6.84314i 0.117869 0.439894i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) 11.1200 0.711883
\(245\) 0 0
\(246\) −6.55691 −0.418053
\(247\) 12.6337 3.38518i 0.803861 0.215394i
\(248\) −0.448756 + 1.67478i −0.0284960 + 0.106349i
\(249\) 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 \(0.972781\pi\)
\(252\) −0.703686 2.55046i −0.0443280 0.160664i
\(253\) −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
\(257\) 6.21737 + 23.2035i 0.387829 + 1.44740i 0.833660 + 0.552279i \(0.186242\pi\)
−0.445831 + 0.895117i \(0.647092\pi\)
\(258\) 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
\(262\) −4.94708 1.32557i −0.305632 0.0818938i
\(263\) 0.821351 + 0.220080i 0.0506467 + 0.0135707i 0.284053 0.958808i \(-0.408321\pi\)
−0.233407 + 0.972379i \(0.574987\pi\)
\(264\) −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
\(268\) 1.42665 + 5.32434i 0.0871468 + 0.325236i
\(269\) −5.82171 10.0835i −0.354956 0.614802i 0.632154 0.774842i \(-0.282171\pi\)
−0.987110 + 0.160041i \(0.948837\pi\)
\(270\) 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
\(273\) −5.84287 5.75693i −0.353627 0.348425i
\(274\) 11.5824i 0.699715i
\(275\) 0 0
\(276\) −5.09436 + 2.94123i −0.306644 + 0.177041i
\(277\) −2.44577 + 9.12775i −0.146952 + 0.548433i 0.852708 + 0.522387i \(0.174958\pi\)
−0.999661 + 0.0260462i \(0.991708\pi\)
\(278\) 2.77273 0.742949i 0.166297 0.0445591i
\(279\) 1.73386 0.103804
\(280\) 0 0
\(281\) −11.7320 −0.699871 −0.349935 0.936774i \(-0.613796\pi\)
−0.349935 + 0.936774i \(0.613796\pi\)
\(282\) 5.87298 1.57366i 0.349731 0.0937101i
\(283\) −0.944117 + 3.52349i −0.0561219 + 0.209450i −0.988293 0.152568i \(-0.951246\pi\)
0.932171 + 0.362018i \(0.117912\pi\)
\(284\) −3.34287 + 1.93001i −0.198363 + 0.114525i
\(285\) 0 0
\(286\) 6.13465i 0.362750i
\(287\) −16.7231 + 4.61400i −0.987133 + 0.272356i
\(288\) −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
\(292\) −3.93920 14.7013i −0.230524 0.860328i
\(293\) −8.62354 8.62354i −0.503793 0.503793i 0.408822 0.912614i \(-0.365940\pi\)
−0.912614 + 0.408822i \(0.865940\pi\)
\(294\) −3.58944 6.00965i −0.209340 0.350490i
\(295\) 0 0
\(296\) −1.38596 + 2.40055i −0.0805572 + 0.139529i
\(297\) 1.91133 + 0.512139i 0.110907 + 0.0297173i
\(298\) −15.0488 4.03231i −0.871752 0.233585i
\(299\) −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
\(303\) −2.60040 9.70484i −0.149389 0.557529i
\(304\) −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 \(-0.526676\pi\)
0.996490 + 0.0837060i \(0.0266757\pi\)
\(308\) −1.31749 + 5.06680i −0.0750710 + 0.288708i
\(309\) 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 \(0.262885\pi\)
\(312\) −0.802407 + 2.99462i −0.0454273 + 0.169537i
\(313\) −19.3623 + 5.18810i −1.09442 + 0.293249i −0.760490 0.649349i \(-0.775041\pi\)
−0.333929 + 0.942598i \(0.608375\pi\)
\(314\) −15.1833 −0.856846
\(315\) 0 0
\(316\) 2.55514 0.143738
\(317\) −2.87877 + 0.771364i −0.161688 + 0.0433241i −0.338755 0.940875i \(-0.610006\pi\)
0.177067 + 0.984199i \(0.443339\pi\)
\(318\) −2.95926 + 11.0441i −0.165947 + 0.619322i
\(319\) −15.3371 + 8.85488i −0.858713 + 0.495778i
\(320\) 0 0
\(321\) 6.04965i 0.337658i
\(322\) −10.9232 + 11.0863i −0.608728 + 0.617816i
\(323\) −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
\(327\) 2.52322 + 9.41680i 0.139535 + 0.520750i
\(328\) 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 \(0.889388\pi\)
\(332\) −13.0178 3.48811i −0.714445 0.191435i
\(333\) 2.67747 + 0.717425i 0.146724 + 0.0393146i
\(334\) 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 0.997988 0.0634051i \(-0.0201960\pi\)
−0.0634051 + 0.997988i \(0.520196\pi\)
\(338\) −0.876975 3.27292i −0.0477012 0.178023i
\(339\) −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
\(343\) −13.3836 12.8015i −0.722647 0.691217i
\(344\) 8.96222i 0.483210i
\(345\) 0 0
\(346\) 3.92103 2.26381i 0.210796 0.121703i
\(347\) 6.48156 24.1895i 0.347948 1.29856i −0.541181 0.840906i \(-0.682023\pi\)
0.889130 0.457655i \(-0.151311\pi\)
\(348\) −8.64500 + 2.31642i −0.463421 + 0.124173i
\(349\) 18.0130 0.964212 0.482106 0.876113i \(-0.339872\pi\)
0.482106 + 0.876113i \(0.339872\pi\)
\(350\) 0 0
\(351\) 3.10026 0.165480
\(352\) 1.91133 0.512139i 0.101874 0.0272971i
\(353\) −1.96651 + 7.33911i −0.104667 + 0.390621i −0.998307 0.0581623i \(-0.981476\pi\)
0.893641 + 0.448784i \(0.148143\pi\)
\(354\) 3.64339 2.10351i 0.193644 0.111800i
\(355\) 0 0
\(356\) 6.19187i 0.328168i
\(357\) 11.7860 + 3.06464i 0.623781 + 0.162198i
\(358\) 1.46221 1.46221i 0.0772803 0.0772803i
\(359\) 2.84638 + 1.64336i 0.150226 + 0.0867332i 0.573229 0.819395i \(-0.305691\pi\)
−0.423003 + 0.906128i \(0.639024\pi\)
\(360\) 0 0
\(361\) 0.600927 + 1.04084i 0.0316277 + 0.0547808i
\(362\) 1.58708 + 5.92305i 0.0834149 + 0.311309i
\(363\) 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
\(367\) 3.13693 + 0.840538i 0.163746 + 0.0438757i 0.339761 0.940512i \(-0.389654\pi\)
−0.176014 + 0.984388i \(0.556321\pi\)
\(368\) 5.68202 + 1.52249i 0.296196 + 0.0793654i
\(369\) 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
\(373\) 4.08060 + 15.2290i 0.211286 + 0.788529i 0.987441 + 0.157987i \(0.0505005\pi\)
−0.776156 + 0.630542i \(0.782833\pi\)
\(374\) −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
\(378\) 2.56060 + 0.665818i 0.131703 + 0.0342460i
\(379\) 21.7428i 1.11685i 0.829555 + 0.558426i \(0.188594\pi\)
−0.829555 + 0.558426i \(0.811406\pi\)
\(380\) 0 0
\(381\) −10.9342 + 6.31283i −0.560174 + 0.323416i
\(382\) 4.18410 15.6153i 0.214077 0.798946i
\(383\) 17.2784 4.62973i 0.882883 0.236568i 0.211233 0.977436i \(-0.432252\pi\)
0.671651 + 0.740868i \(0.265586\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 21.7909 1.10913
\(387\) −8.65684 + 2.31959i −0.440052 + 0.117912i
\(388\) 0.541831 2.02214i 0.0275073 0.102659i
\(389\) −4.36130 + 2.51800i −0.221127 + 0.127667i −0.606472 0.795105i \(-0.707416\pi\)
0.385345 + 0.922772i \(0.374082\pi\)
\(390\) 0 0
\(391\) 27.0759i 1.36929i
\(392\) −1.71135 + 6.78758i −0.0864362 + 0.342825i
\(393\) 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
\(397\) 3.81880 + 14.2520i 0.191660 + 0.715285i 0.993106 + 0.117218i \(0.0373977\pi\)
−0.801446 + 0.598067i \(0.795936\pi\)
\(398\) −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 \(0.0970162\pi\)
\(402\) −5.32434 1.42665i −0.265554 0.0711550i
\(403\) −5.19226 1.39126i −0.258645 0.0693037i
\(404\) −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
\(408\) −1.19130 4.44599i −0.0589781 0.220109i
\(409\) 9.49095 + 16.4388i 0.469297 + 0.812847i 0.999384 0.0350966i \(-0.0111739\pi\)
−0.530087 + 0.847944i \(0.677841\pi\)
\(410\) 0 0
\(411\) 10.0306 + 5.79118i 0.494774 + 0.285658i
\(412\) −3.52695 + 3.52695i −0.173760 + 0.173760i
\(413\) 7.81209 7.92871i 0.384408 0.390147i
\(414\) 5.88246i 0.289107i
\(415\) 0 0
\(416\) 2.68491 1.55013i 0.131638 0.0760014i
\(417\) −0.742949 + 2.77273i −0.0363824 + 0.135781i
\(418\) 8.06348 2.16060i 0.394398 0.105679i
\(419\) −11.9171 −0.582188 −0.291094 0.956695i \(-0.594019\pi\)
−0.291094 + 0.956695i \(0.594019\pi\)
\(420\) 0 0
\(421\) 6.95263 0.338850 0.169425 0.985543i \(-0.445809\pi\)
0.169425 + 0.985543i \(0.445809\pi\)
\(422\) 10.8830 2.91610i 0.529778 0.141953i
\(423\) −1.57366 + 5.87298i −0.0765140 + 0.285554i
\(424\) 9.90187 5.71685i 0.480877 0.277635i
\(425\) 0 0
\(426\) 3.86002i 0.187018i
\(427\) −7.40388 + 28.4738i −0.358299 + 1.37795i
\(428\) 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 \(0.881413\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) 15.1544 + 15.1544i 0.728274 + 0.728274i 0.970276 0.242002i \(-0.0778040\pi\)
−0.242002 + 0.970276i \(0.577804\pi\)
\(434\) −3.98966 2.26419i −0.191510 0.108684i
\(435\) 0 0
\(436\) 4.87449 8.44287i 0.233446 0.404340i
\(437\) 23.9712 + 6.42307i 1.14670 + 0.307257i
\(438\) 14.7013 + 3.93920i 0.702455 + 0.188222i
\(439\) −16.3729 + 28.3588i −0.781438 + 1.35349i 0.149666 + 0.988737i \(0.452180\pi\)
−0.931104 + 0.364753i \(0.881153\pi\)
\(440\) 0 0
\(441\) 6.99923 0.103719i 0.333297 0.00493899i
\(442\) −10.0904 10.0904i −0.479951 0.479951i
\(443\) −7.95895 29.7032i −0.378141 1.41124i −0.848701 0.528874i \(-0.822615\pi\)
0.470559 0.882368i \(-0.344052\pi\)
\(444\) −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
\(448\) 2.55046 0.703686i 0.120498 0.0332460i
\(449\) 16.8713i 0.796207i 0.917341 + 0.398103i \(0.130331\pi\)
−0.917341 + 0.398103i \(0.869669\pi\)
\(450\) 0 0
\(451\) −11.2362 + 6.48725i −0.529094 + 0.305473i
\(452\) −2.20532 + 8.23036i −0.103729 + 0.387123i
\(453\) 20.4685 5.48452i 0.961695 0.257685i
\(454\) −26.9142 −1.26314
\(455\) 0 0
\(456\) 4.21878 0.197563
\(457\) 19.1714 5.13696i 0.896800 0.240297i 0.219158 0.975689i \(-0.429669\pi\)
0.677641 + 0.735393i \(0.263002\pi\)
\(458\) 6.95976 25.9742i 0.325208 1.21369i
\(459\) −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 \(0.880243\pi\)
\(462\) −3.72923 3.67438i −0.173500 0.170948i
\(463\) −4.48617 + 4.48617i −0.208490 + 0.208490i −0.803625 0.595135i \(-0.797098\pi\)
0.595135 + 0.803625i \(0.297098\pi\)
\(464\) 7.75089 + 4.47498i 0.359826 + 0.207746i
\(465\) 0 0
\(466\) 0.460622 + 0.797821i 0.0213379 + 0.0369583i
\(467\) 4.51639 + 16.8554i 0.208994 + 0.779975i 0.988195 + 0.153201i \(0.0489583\pi\)
−0.779201 + 0.626774i \(0.784375\pi\)
\(468\) −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
\(472\) −4.06367 1.08886i −0.187046 0.0501187i
\(473\) 17.1297 + 4.58990i 0.787626 + 0.211044i
\(474\) −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
\(478\) 6.55929 + 24.4796i 0.300015 + 1.11967i
\(479\) −15.8748 27.4960i −0.725339 1.25632i −0.958834 0.283966i \(-0.908350\pi\)
0.233495 0.972358i \(-0.424984\pi\)
\(480\) 0 0
\(481\) −7.44233 4.29683i −0.339341 0.195919i
\(482\) 14.9341 14.9341i 0.680230 0.680230i
\(483\) −4.13940 15.0030i −0.188349 0.682658i
\(484\) 7.08454i 0.322024i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 7.74077 28.8890i 0.350768 1.30908i −0.534960 0.844878i \(-0.679673\pi\)
0.885727 0.464206i \(-0.153660\pi\)
\(488\) 10.7411 2.87806i 0.486225 0.130284i
\(489\) 22.3230 1.00948
\(490\) 0 0
\(491\) 1.57179 0.0709340 0.0354670 0.999371i \(-0.488708\pi\)
0.0354670 + 0.999371i \(0.488708\pi\)
\(492\) −6.33349 + 1.69705i −0.285536 + 0.0765090i
\(493\) 10.6621 39.7914i 0.480196 1.79211i
\(494\) 11.3270 6.53967i 0.509628 0.294234i
\(495\) 0 0
\(496\) 1.73386i 0.0778527i
\(497\) −2.71624 9.84480i −0.121840 0.441600i
\(498\) 9.52969 9.52969i 0.427036 0.427036i
\(499\) −12.3491 7.12977i −0.552823 0.319172i 0.197437 0.980316i \(-0.436738\pi\)
−0.750260 + 0.661143i \(0.770072\pi\)
\(500\) 0 0
\(501\) 4.88769 + 8.46573i 0.218366 + 0.378221i
\(502\) 0.700423 + 2.61401i 0.0312614 + 0.116669i
\(503\) 28.7896 + 28.7896i 1.28367 + 1.28367i 0.938566 + 0.345100i \(0.112155\pi\)
0.345100 + 0.938566i \(0.387845\pi\)
\(504\) −1.33981 2.28142i −0.0596801 0.101623i
\(505\) 0 0
\(506\) −5.81997 + 10.0805i −0.258729 + 0.448132i
\(507\) 3.27292 + 0.876975i 0.145355 + 0.0389478i
\(508\) 12.1955 + 3.26776i 0.541086 + 0.144984i
\(509\) −7.30942 + 12.6603i −0.323984 + 0.561157i −0.981306 0.192453i \(-0.938356\pi\)
0.657322 + 0.753610i \(0.271689\pi\)
\(510\) 0 0
\(511\) 40.2670 0.298333i 1.78131 0.0131975i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −1.09190 4.07503i −0.0482086 0.179917i
\(514\) 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
\(518\) −5.22406 5.14722i −0.229532 0.226156i
\(519\) 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 \(0.442677\pi\)
\(522\) 2.31642 8.64500i 0.101387 0.378381i
\(523\) −22.6178 + 6.06041i −0.989006 + 0.265003i −0.716833 0.697245i \(-0.754409\pi\)
−0.272173 + 0.962248i \(0.587742\pi\)
\(524\) −5.12160 −0.223738
\(525\) 0 0
\(526\) 0.850325 0.0370759
\(527\) 7.70872 2.06555i 0.335797 0.0899766i
\(528\) −0.512139 + 1.91133i −0.0222880 + 0.0831799i
\(529\) −10.0488 + 5.80167i −0.436904 + 0.252247i
\(530\) 0 0
\(531\) 4.20702i 0.182569i
\(532\) 10.7598 2.96870i 0.466498 0.128709i
\(533\) −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
\(537\) 0.535206 + 1.99742i 0.0230959 + 0.0861949i
\(538\) −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 \(0.221464\pi\)
\(542\) −22.5493 6.04206i −0.968575 0.259529i
\(543\) −5.92305 1.58708i −0.254182 0.0681080i
\(544\) −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 0.821563 0.570117i \(-0.193102\pi\)
−0.570117 + 0.821563i \(0.693102\pi\)
\(548\) −2.99773 11.1877i −0.128057 0.477915i
\(549\) −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
\(553\) −1.70126 + 6.54271i −0.0723450 + 0.278224i
\(554\) 9.44974i 0.401481i
\(555\) 0 0
\(556\) 2.48596 1.43527i 0.105428 0.0608689i
\(557\) −6.78443 + 25.3198i −0.287466 + 1.07284i 0.659553 + 0.751658i \(0.270746\pi\)
−0.947019 + 0.321178i \(0.895921\pi\)
\(558\) 1.67478 0.448756i 0.0708991 0.0189974i
\(559\) 27.7852 1.17519
\(560\) 0 0
\(561\) 9.10785 0.384534
\(562\) −11.3322 + 3.03646i −0.478020 + 0.128085i
\(563\) −0.226316 + 0.844624i −0.00953810 + 0.0355967i −0.970531 0.240977i \(-0.922532\pi\)
0.960993 + 0.276573i \(0.0891989\pi\)
\(564\) 5.26557 3.04008i 0.221721 0.128010i
\(565\) 0 0
\(566\) 3.64779i 0.153328i
\(567\) −1.85692 + 1.88464i −0.0779832 + 0.0791473i
\(568\) −2.72944 + 2.72944i −0.114525 + 0.114525i
\(569\) −28.5877 16.5051i −1.19846 0.691929i −0.238246 0.971205i \(-0.576572\pi\)
−0.960211 + 0.279275i \(0.909906\pi\)
\(570\) 0 0
\(571\) −2.39594 4.14989i −0.100267 0.173668i 0.811528 0.584314i \(-0.198636\pi\)
−0.911795 + 0.410646i \(0.865303\pi\)
\(572\) 1.58776 + 5.92562i 0.0663878 + 0.247763i
\(573\) 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
\(577\) −31.5375 8.45046i −1.31293 0.351797i −0.466602 0.884467i \(-0.654522\pi\)
−0.846323 + 0.532670i \(0.821189\pi\)
\(578\) 4.04335 + 1.08341i 0.168181 + 0.0450640i
\(579\) −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
\(583\) 5.85564 + 21.8535i 0.242516 + 0.905081i
\(584\) −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 \(-0.693607\pi\)
0.820658 + 0.571420i \(0.193607\pi\)
\(588\) −5.02254 4.87586i −0.207126 0.201077i
\(589\) 7.31479i 0.301401i
\(590\) 0 0
\(591\) −0.769287 + 0.444148i −0.0316442 + 0.0182698i
\(592\) −0.717425 + 2.67747i −0.0294860 + 0.110043i
\(593\) −3.93171 + 1.05350i −0.161456 + 0.0432620i −0.338642 0.940915i \(-0.609967\pi\)
0.177186 + 0.984177i \(0.443301\pi\)
\(594\) 1.97875 0.0811892
\(595\) 0 0
\(596\) −15.5796 −0.638167
\(597\) 9.29699 2.49112i 0.380501 0.101955i
\(598\) −4.72013 + 17.6158i −0.193020 + 0.720362i
\(599\) 29.5547 17.0634i 1.20757 0.697193i 0.245345 0.969436i \(-0.421099\pi\)
0.962229 + 0.272243i \(0.0877654\pi\)
\(600\) 0 0
\(601\) 9.99405i 0.407666i 0.979006 + 0.203833i \(0.0653399\pi\)
−0.979006 + 0.203833i \(0.934660\pi\)
\(602\) 22.9487 + 5.96721i 0.935318 + 0.243205i
\(603\) 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
\(607\) −4.73109 17.6567i −0.192029 0.716662i −0.993016 0.117980i \(-0.962358\pi\)
0.800987 0.598682i \(-0.204309\pi\)
\(608\) −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
\(612\) 4.44599 + 1.19130i 0.179718 + 0.0481554i
\(613\) −28.8155 7.72109i −1.16385 0.311852i −0.375346 0.926885i \(-0.622476\pi\)
−0.788501 + 0.615033i \(0.789143\pi\)
\(614\) 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 0.759317 + 0.650721i \(0.225533\pi\)
0.650721 + 0.759317i \(0.274467\pi\)
\(618\) −1.29095 4.81790i −0.0519298 0.193805i
\(619\) 5.75770 + 9.97263i 0.231422 + 0.400834i 0.958227 0.286010i \(-0.0923290\pi\)
−0.726805 + 0.686844i \(0.758996\pi\)
\(620\) 0 0
\(621\) 5.09436 + 2.94123i 0.204430 + 0.118028i
\(622\) 5.47479 5.47479i 0.219519 0.219519i
\(623\) 15.8549 + 4.12266i 0.635214 + 0.165171i
\(624\) 3.10026i 0.124110i
\(625\) 0 0
\(626\) −17.3597 + 10.0226i −0.693834 + 0.400585i
\(627\) −2.16060 + 8.06348i −0.0862862 + 0.322024i
\(628\) −14.6660 + 3.92974i −0.585237 + 0.156814i
\(629\) 12.7586 0.508720
\(630\) 0 0
\(631\) 18.4477 0.734390 0.367195 0.930144i \(-0.380318\pi\)
0.367195 + 0.930144i \(0.380318\pi\)
\(632\) 2.46808 0.661320i 0.0981749 0.0263059i
\(633\) −2.91610 + 10.8830i −0.115905 + 0.432562i
\(634\) −2.58104 + 1.49016i −0.102506 + 0.0591819i
\(635\) 0 0
\(636\) 11.4337i 0.453375i
\(637\) −21.0433 5.30563i −0.833765 0.210217i
\(638\) −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 \(0.707605\pi\)
\(642\) 1.56576 + 5.84351i 0.0617958 + 0.230625i
\(643\) −28.2707 28.2707i −1.11489 1.11489i −0.992480 0.122408i \(-0.960938\pi\)
−0.122408 0.992480i \(-0.539062\pi\)
\(644\) −7.68169 + 13.5357i −0.302701 + 0.533381i
\(645\) 0 0
\(646\) −9.70916 + 16.8168i −0.382002 + 0.661647i
\(647\) 24.0797 + 6.45214i 0.946672 + 0.253660i 0.698949 0.715171i \(-0.253651\pi\)
0.247722 + 0.968831i \(0.420318\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) 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
\(653\) 12.8743 + 48.0477i 0.503812 + 1.88025i 0.473666 + 0.880705i \(0.342930\pi\)
0.0301458 + 0.999546i \(0.490403\pi\)
\(654\) 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
\(658\) 11.2903 11.4589i 0.440144 0.446714i
\(659\) 39.5644i 1.54121i −0.637312 0.770606i \(-0.719954\pi\)
0.637312 0.770606i \(-0.280046\pi\)
\(660\) 0 0
\(661\) −1.74995 + 1.01033i −0.0680651 + 0.0392974i −0.533646 0.845708i \(-0.679179\pi\)
0.465581 + 0.885005i \(0.345845\pi\)
\(662\) −7.20479 + 26.8886i −0.280022 + 1.04506i
\(663\) 13.7837 3.69334i 0.535315 0.143437i
\(664\) −13.4770 −0.523010
\(665\) 0 0
\(666\) 2.77192 0.107410
\(667\) −50.8539 + 13.6263i −1.96907 + 0.527611i
\(668\) 2.53005 9.44229i 0.0978907 0.365333i
\(669\) −16.1321 + 9.31386i −0.623702 + 0.360095i
\(670\) 0 0
\(671\) 22.0037i 0.849442i
\(672\) −0.665818 + 2.56060i −0.0256845 + 0.0987774i
\(673\) 19.7775 19.7775i 0.762366 0.762366i −0.214383 0.976750i \(-0.568774\pi\)
0.976750 + 0.214383i \(0.0687742\pi\)
\(674\) 21.0125 + 12.1316i 0.809372 + 0.467291i
\(675\) 0 0
\(676\) −1.69419 2.93442i −0.0651610 0.112862i
\(677\) 4.44120 + 16.5748i 0.170689 + 0.637021i 0.997246 + 0.0741672i \(0.0236298\pi\)
−0.826557 + 0.562854i \(0.809703\pi\)
\(678\) −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
\(682\) −3.31398 0.887978i −0.126899 0.0340024i
\(683\) 0.487181 + 0.130540i 0.0186414 + 0.00499496i 0.268128 0.963383i \(-0.413595\pi\)
−0.249486 + 0.968378i \(0.580262\pi\)
\(684\) −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
\(688\) −2.31959 8.65684i −0.0884336 0.330039i
\(689\) 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
\(693\) 5.04672 1.39242i 0.191709 0.0528937i
\(694\) 25.0428i 0.950613i
\(695\) 0 0
\(696\) −7.75089 + 4.47498i −0.293797 + 0.169624i
\(697\) 7.81123 29.1519i 0.295871 1.10421i
\(698\) 17.3992 4.66210i 0.658569 0.176463i
\(699\) −0.921244 −0.0348447
\(700\) 0 0
\(701\) 8.02724 0.303185 0.151592 0.988443i \(-0.451560\pi\)
0.151592 + 0.988443i \(0.451560\pi\)
\(702\) 2.99462 0.802407i 0.113025 0.0302849i
\(703\) −3.02666 + 11.2956i −0.114153 + 0.426023i
\(704\) 1.71365 0.989376i 0.0645856 0.0372885i
\(705\) 0 0
\(706\) 7.59800i 0.285955i
\(707\) −18.9353 18.6568i −0.712136 0.701661i
\(708\) 2.97481 2.97481i 0.111800 0.111800i
\(709\) −11.8457 6.83914i −0.444876 0.256849i 0.260788 0.965396i \(-0.416018\pi\)
−0.705664 + 0.708547i \(0.749351\pi\)
\(710\) 0 0
\(711\) −1.27757 2.21282i −0.0479127 0.0829872i
\(712\) −1.60257 5.98088i −0.0600590 0.224143i
\(713\) −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
\(717\) −24.4796 6.55929i −0.914208 0.244961i
\(718\) 3.17473 + 0.850665i 0.118480 + 0.0317465i
\(719\) 10.5235 18.2273i 0.392462 0.679764i −0.600312 0.799766i \(-0.704957\pi\)
0.992774 + 0.120002i \(0.0382901\pi\)
\(720\) 0 0
\(721\) −6.68281 11.3794i −0.248881 0.423792i
\(722\) 0.849839 + 0.849839i 0.0316277 + 0.0316277i
\(723\) 5.46626 + 20.4004i 0.203292 + 0.758698i
\(724\) 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 \(-0.845113\pi\)
0.467615 + 0.883932i \(0.345113\pi\)
\(728\) 2.18161 + 7.90708i 0.0808559 + 0.293056i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −35.7248 + 20.6258i −1.32133 + 0.762871i
\(732\) −2.87806 + 10.7411i −0.106376 + 0.397001i
\(733\) −27.7719 + 7.44145i −1.02578 + 0.274856i −0.732208 0.681081i \(-0.761510\pi\)
−0.293570 + 0.955938i \(0.594843\pi\)
\(734\) 3.24759 0.119871
\(735\) 0 0
\(736\) 5.88246 0.216830
\(737\) −10.5356 + 2.82300i −0.388082 + 0.103986i
\(738\) 1.69705 6.33349i 0.0624694 0.233139i
\(739\) −36.3593 + 20.9921i −1.33750 + 0.772205i −0.986436 0.164147i \(-0.947513\pi\)
−0.351063 + 0.936352i \(0.614180\pi\)
\(740\) 0 0
\(741\) 13.0793i 0.480482i
\(742\) 8.04573 + 29.1611i 0.295368 + 1.07054i
\(743\) −8.63799 + 8.63799i −0.316897 + 0.316897i −0.847574 0.530677i \(-0.821938\pi\)
0.530677 + 0.847574i \(0.321938\pi\)
\(744\) −1.50157 0.866930i −0.0550501 0.0317832i
\(745\) 0 0
\(746\) 7.88312 + 13.6540i 0.288622 + 0.499907i
\(747\) 3.48811 + 13.0178i 0.127623 + 0.476297i
\(748\) −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 \(0.970036\pi\)
\(752\) −5.87298 1.57366i −0.214166 0.0573855i
\(753\) −2.61401 0.700423i −0.0952600 0.0255248i
\(754\) −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 0.862669 0.505770i \(-0.168791\pi\)
−0.505770 + 0.862669i \(0.668791\pi\)
\(758\) 5.62744 + 21.0019i 0.204398 + 0.762824i
\(759\) −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
\(763\) 18.3733 + 18.1031i 0.665158 + 0.655375i
\(764\) 16.1661i 0.584869i
\(765\) 0 0
\(766\) 15.4914 8.94394i 0.559726 0.323158i
\(767\) 3.37574 12.5985i 0.121891 0.454904i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) 26.3715 0.950981 0.475490 0.879721i \(-0.342271\pi\)
0.475490 + 0.879721i \(0.342271\pi\)
\(770\) 0 0
\(771\) −24.0221 −0.865133
\(772\) 21.0484 5.63991i 0.757549 0.202985i
\(773\) 11.9120 44.4561i 0.428444 1.59898i −0.327841 0.944733i \(-0.606321\pi\)
0.756285 0.654242i \(-0.227012\pi\)
\(774\) −7.76151 + 4.48111i −0.278982 + 0.161070i
\(775\) 0 0
\(776\) 2.09348i 0.0751514i
\(777\) 7.06965 1.95056i 0.253622 0.0699759i
\(778\) −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
\(782\) −7.00777