Properties

Label 804.2.q.b.241.3
Level 804
Weight 2
Character 804.241
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 241.3
Character \(\chi\) = 804.241
Dual form 804.2.q.b.397.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(-0.960253 - 0.281956i) q^{5} +(0.00738542 + 0.00852322i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(-0.960253 - 0.281956i) q^{5} +(0.00738542 + 0.00852322i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.0286737 - 0.00841935i) q^{11} +(-0.796658 - 0.511981i) q^{13} +(0.655379 - 0.756348i) q^{15} +(1.11543 + 7.75799i) q^{17} +(-0.720395 + 0.831380i) q^{19} +(-0.0108210 + 0.00317734i) q^{21} +(-2.46117 + 5.38921i) q^{23} +(-3.36368 - 2.16171i) q^{25} +(0.959493 - 0.281733i) q^{27} +0.886974 q^{29} +(-7.56934 + 4.86452i) q^{31} +(0.0195700 - 0.0225850i) q^{33} +(-0.00468869 - 0.0102668i) q^{35} -6.19364 q^{37} +(0.796658 - 0.511981i) q^{39} +(-0.919259 - 6.39359i) q^{41} +(0.139722 + 0.971788i) q^{43} +(0.415744 + 0.910352i) q^{45} +(-2.18150 + 4.77681i) q^{47} +(0.996186 - 6.92862i) q^{49} +(-7.52028 - 2.20815i) q^{51} +(-0.980545 + 6.81984i) q^{53} +(0.0251601 + 0.0161694i) q^{55} +(-0.456987 - 1.00066i) q^{57} +(-8.10432 + 5.20833i) q^{59} +(6.93827 - 2.03726i) q^{61} +(0.00160500 - 0.0111630i) q^{63} +(0.620637 + 0.716253i) q^{65} +(7.38311 - 3.53408i) q^{67} +(-3.87979 - 4.47751i) q^{69} +(-1.67456 + 11.6468i) q^{71} +(-9.65633 + 2.83536i) q^{73} +(3.36368 - 2.16171i) q^{75} +(-0.000140007 - 0.000306573i) q^{77} +(5.45532 + 3.50592i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(7.98130 + 2.34352i) q^{83} +(1.11631 - 7.76413i) q^{85} +(-0.368462 + 0.806820i) q^{87} +(-4.02122 - 8.80524i) q^{89} +(-0.00151992 - 0.0105713i) q^{91} +(-1.28050 - 8.90611i) q^{93} +(0.926173 - 0.595215i) q^{95} -13.0928 q^{97} +(0.0124143 + 0.0271836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(1\)

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 0
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) 0 0
\(5\) −0.960253 0.281956i −0.429438 0.126094i 0.0598685 0.998206i \(-0.480932\pi\)
−0.489307 + 0.872112i \(0.662750\pi\)
\(6\) 0 0
\(7\) 0.00738542 + 0.00852322i 0.00279142 + 0.00322148i 0.757144 0.653249i \(-0.226594\pi\)
−0.754352 + 0.656470i \(0.772049\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) −0.0286737 0.00841935i −0.00864544 0.00253853i 0.277407 0.960753i \(-0.410525\pi\)
−0.286052 + 0.958214i \(0.592343\pi\)
\(12\) 0 0
\(13\) −0.796658 0.511981i −0.220953 0.141998i 0.425482 0.904967i \(-0.360105\pi\)
−0.646435 + 0.762969i \(0.723741\pi\)
\(14\) 0 0
\(15\) 0.655379 0.756348i 0.169218 0.195288i
\(16\) 0 0
\(17\) 1.11543 + 7.75799i 0.270532 + 1.88159i 0.442921 + 0.896560i \(0.353942\pi\)
−0.172390 + 0.985029i \(0.555149\pi\)
\(18\) 0 0
\(19\) −0.720395 + 0.831380i −0.165270 + 0.190732i −0.832343 0.554260i \(-0.813001\pi\)
0.667074 + 0.744992i \(0.267547\pi\)
\(20\) 0 0
\(21\) −0.0108210 + 0.00317734i −0.00236134 + 0.000693351i
\(22\) 0 0
\(23\) −2.46117 + 5.38921i −0.513189 + 1.12373i 0.458765 + 0.888557i \(0.348292\pi\)
−0.971954 + 0.235170i \(0.924435\pi\)
\(24\) 0 0
\(25\) −3.36368 2.16171i −0.672736 0.432341i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) 0.886974 0.164707 0.0823535 0.996603i \(-0.473756\pi\)
0.0823535 + 0.996603i \(0.473756\pi\)
\(30\) 0 0
\(31\) −7.56934 + 4.86452i −1.35949 + 0.873693i −0.998271 0.0587864i \(-0.981277\pi\)
−0.361223 + 0.932480i \(0.617641\pi\)
\(32\) 0 0
\(33\) 0.0195700 0.0225850i 0.00340670 0.00393154i
\(34\) 0 0
\(35\) −0.00468869 0.0102668i −0.000792534 0.00173541i
\(36\) 0 0
\(37\) −6.19364 −1.01823 −0.509114 0.860699i \(-0.670027\pi\)
−0.509114 + 0.860699i \(0.670027\pi\)
\(38\) 0 0
\(39\) 0.796658 0.511981i 0.127567 0.0819826i
\(40\) 0 0
\(41\) −0.919259 6.39359i −0.143564 0.998510i −0.926470 0.376370i \(-0.877172\pi\)
0.782905 0.622141i \(-0.213737\pi\)
\(42\) 0 0
\(43\) 0.139722 + 0.971788i 0.0213074 + 0.148196i 0.997698 0.0678174i \(-0.0216035\pi\)
−0.976390 + 0.216014i \(0.930694\pi\)
\(44\) 0 0
\(45\) 0.415744 + 0.910352i 0.0619754 + 0.135707i
\(46\) 0 0
\(47\) −2.18150 + 4.77681i −0.318204 + 0.696770i −0.999375 0.0353548i \(-0.988744\pi\)
0.681171 + 0.732125i \(0.261471\pi\)
\(48\) 0 0
\(49\) 0.996186 6.92862i 0.142312 0.989803i
\(50\) 0 0
\(51\) −7.52028 2.20815i −1.05305 0.309203i
\(52\) 0 0
\(53\) −0.980545 + 6.81984i −0.134688 + 0.936777i 0.804641 + 0.593761i \(0.202358\pi\)
−0.939330 + 0.343016i \(0.888551\pi\)
\(54\) 0 0
\(55\) 0.0251601 + 0.0161694i 0.00339259 + 0.00218028i
\(56\) 0 0
\(57\) −0.456987 1.00066i −0.0605294 0.132541i
\(58\) 0 0
\(59\) −8.10432 + 5.20833i −1.05509 + 0.678067i −0.948674 0.316254i \(-0.897575\pi\)
−0.106419 + 0.994321i \(0.533938\pi\)
\(60\) 0 0
\(61\) 6.93827 2.03726i 0.888355 0.260845i 0.194451 0.980912i \(-0.437707\pi\)
0.693904 + 0.720068i \(0.255889\pi\)
\(62\) 0 0
\(63\) 0.00160500 0.0111630i 0.000202212 0.00140641i
\(64\) 0 0
\(65\) 0.620637 + 0.716253i 0.0769805 + 0.0888403i
\(66\) 0 0
\(67\) 7.38311 3.53408i 0.901990 0.431756i
\(68\) 0 0
\(69\) −3.87979 4.47751i −0.467072 0.539029i
\(70\) 0 0
\(71\) −1.67456 + 11.6468i −0.198734 + 1.38222i 0.609231 + 0.792993i \(0.291478\pi\)
−0.807964 + 0.589231i \(0.799431\pi\)
\(72\) 0 0
\(73\) −9.65633 + 2.83536i −1.13019 + 0.331853i −0.792782 0.609506i \(-0.791368\pi\)
−0.337407 + 0.941359i \(0.609550\pi\)
\(74\) 0 0
\(75\) 3.36368 2.16171i 0.388404 0.249612i
\(76\) 0 0
\(77\) −0.000140007 0 0.000306573i −1.59553e−5 0 3.49372e-5i
\(78\) 0 0
\(79\) 5.45532 + 3.50592i 0.613771 + 0.394447i 0.810270 0.586057i \(-0.199321\pi\)
−0.196498 + 0.980504i \(0.562957\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) 7.98130 + 2.34352i 0.876062 + 0.257235i 0.688692 0.725054i \(-0.258185\pi\)
0.187370 + 0.982289i \(0.440004\pi\)
\(84\) 0 0
\(85\) 1.11631 7.76413i 0.121081 0.842139i
\(86\) 0 0
\(87\) −0.368462 + 0.806820i −0.0395033 + 0.0865002i
\(88\) 0 0
\(89\) −4.02122 8.80524i −0.426248 0.933354i −0.993921 0.110099i \(-0.964883\pi\)
0.567672 0.823255i \(-0.307844\pi\)
\(90\) 0 0
\(91\) −0.00151992 0.0105713i −0.000159331 0.00110817i
\(92\) 0 0
\(93\) −1.28050 8.90611i −0.132782 0.923520i
\(94\) 0 0
\(95\) 0.926173 0.595215i 0.0950233 0.0610678i
\(96\) 0 0
\(97\) −13.0928 −1.32937 −0.664687 0.747122i \(-0.731435\pi\)
−0.664687 + 0.747122i \(0.731435\pi\)
\(98\) 0 0
\(99\) 0.0124143 + 0.0271836i 0.00124769 + 0.00273206i
\(100\) 0 0
\(101\) −2.54029 + 2.93165i −0.252768 + 0.291710i −0.867926 0.496694i \(-0.834547\pi\)
0.615157 + 0.788404i \(0.289092\pi\)
\(102\) 0 0
\(103\) 1.68237 1.08119i 0.165769 0.106533i −0.455126 0.890427i \(-0.650406\pi\)
0.620895 + 0.783894i \(0.286769\pi\)
\(104\) 0 0
\(105\) 0.0112868 0.00110148
\(106\) 0 0
\(107\) 8.53327 2.50559i 0.824942 0.242225i 0.158099 0.987423i \(-0.449463\pi\)
0.666843 + 0.745198i \(0.267645\pi\)
\(108\) 0 0
\(109\) 11.6058 + 7.45861i 1.11164 + 0.714405i 0.961649 0.274283i \(-0.0884404\pi\)
0.149987 + 0.988688i \(0.452077\pi\)
\(110\) 0 0
\(111\) 2.57293 5.63393i 0.244212 0.534749i
\(112\) 0 0
\(113\) 16.7838 4.92817i 1.57889 0.463603i 0.629316 0.777150i \(-0.283335\pi\)
0.949573 + 0.313546i \(0.101517\pi\)
\(114\) 0 0
\(115\) 3.88286 4.48106i 0.362079 0.417861i
\(116\) 0 0
\(117\) 0.134771 + 0.937350i 0.0124595 + 0.0866581i
\(118\) 0 0
\(119\) −0.0578852 + 0.0668031i −0.00530633 + 0.00612383i
\(120\) 0 0
\(121\) −9.25304 5.94657i −0.841185 0.540597i
\(122\) 0 0
\(123\) 6.19768 + 1.81980i 0.558826 + 0.164086i
\(124\) 0 0
\(125\) 5.89737 + 6.80593i 0.527477 + 0.608741i
\(126\) 0 0
\(127\) −2.41350 2.78532i −0.214163 0.247158i 0.638496 0.769625i \(-0.279557\pi\)
−0.852659 + 0.522468i \(0.825012\pi\)
\(128\) 0 0
\(129\) −0.942012 0.276600i −0.0829395 0.0243532i
\(130\) 0 0
\(131\) −6.78648 + 14.8603i −0.592938 + 1.29835i 0.340713 + 0.940167i \(0.389332\pi\)
−0.933651 + 0.358185i \(0.883396\pi\)
\(132\) 0 0
\(133\) −0.0124064 −0.00107578
\(134\) 0 0
\(135\) −1.00079 −0.0861344
\(136\) 0 0
\(137\) −1.73337 + 3.79556i −0.148092 + 0.324277i −0.969111 0.246624i \(-0.920679\pi\)
0.821019 + 0.570901i \(0.193406\pi\)
\(138\) 0 0
\(139\) 20.9716 + 6.15783i 1.77879 + 0.522300i 0.995102 0.0988538i \(-0.0315176\pi\)
0.783689 + 0.621154i \(0.213336\pi\)
\(140\) 0 0
\(141\) −3.43892 3.96872i −0.289609 0.334227i
\(142\) 0 0
\(143\) 0.0185326 + 0.0213877i 0.00154977 + 0.00178853i
\(144\) 0 0
\(145\) −0.851719 0.250087i −0.0707315 0.0207686i
\(146\) 0 0
\(147\) 5.88867 + 3.78442i 0.485689 + 0.312133i
\(148\) 0 0
\(149\) 3.32893 3.84179i 0.272717 0.314732i −0.602826 0.797873i \(-0.705959\pi\)
0.875543 + 0.483141i \(0.160504\pi\)
\(150\) 0 0
\(151\) −1.55503 10.8155i −0.126547 0.880150i −0.949885 0.312600i \(-0.898800\pi\)
0.823338 0.567551i \(-0.192109\pi\)
\(152\) 0 0
\(153\) 5.13265 5.92339i 0.414950 0.478878i
\(154\) 0 0
\(155\) 8.64005 2.53695i 0.693986 0.203773i
\(156\) 0 0
\(157\) −1.14967 + 2.51742i −0.0917534 + 0.200912i −0.949945 0.312418i \(-0.898861\pi\)
0.858191 + 0.513330i \(0.171588\pi\)
\(158\) 0 0
\(159\) −5.79621 3.72500i −0.459670 0.295412i
\(160\) 0 0
\(161\) −0.0641102 + 0.0188244i −0.00505259 + 0.00148357i
\(162\) 0 0
\(163\) 7.47422 0.585426 0.292713 0.956200i \(-0.405442\pi\)
0.292713 + 0.956200i \(0.405442\pi\)
\(164\) 0 0
\(165\) −0.0251601 + 0.0161694i −0.00195871 + 0.00125879i
\(166\) 0 0
\(167\) −6.46153 + 7.45700i −0.500008 + 0.577040i −0.948512 0.316741i \(-0.897412\pi\)
0.448504 + 0.893781i \(0.351957\pi\)
\(168\) 0 0
\(169\) −5.02786 11.0095i −0.386758 0.846882i
\(170\) 0 0
\(171\) 1.10007 0.0841247
\(172\) 0 0
\(173\) 10.3702 6.66449i 0.788428 0.506692i −0.0833928 0.996517i \(-0.526576\pi\)
0.871821 + 0.489825i \(0.162939\pi\)
\(174\) 0 0
\(175\) −0.00641747 0.0446345i −0.000485115 0.00337405i
\(176\) 0 0
\(177\) −1.37101 9.53557i −0.103051 0.716738i
\(178\) 0 0
\(179\) 7.15402 + 15.6651i 0.534716 + 1.17087i 0.963561 + 0.267487i \(0.0861934\pi\)
−0.428845 + 0.903378i \(0.641079\pi\)
\(180\) 0 0
\(181\) 4.31046 9.43859i 0.320394 0.701565i −0.679078 0.734066i \(-0.737620\pi\)
0.999472 + 0.0325013i \(0.0103473\pi\)
\(182\) 0 0
\(183\) −1.02911 + 7.15759i −0.0760737 + 0.529104i
\(184\) 0 0
\(185\) 5.94746 + 1.74633i 0.437266 + 0.128393i
\(186\) 0 0
\(187\) 0.0333338 0.231841i 0.00243761 0.0169539i
\(188\) 0 0
\(189\) 0.00948752 + 0.00609726i 0.000690116 + 0.000443511i
\(190\) 0 0
\(191\) −5.14173 11.2588i −0.372042 0.814659i −0.999356 0.0358921i \(-0.988573\pi\)
0.627313 0.778767i \(-0.284155\pi\)
\(192\) 0 0
\(193\) 13.6948 8.80109i 0.985770 0.633516i 0.0547564 0.998500i \(-0.482562\pi\)
0.931014 + 0.364984i \(0.118925\pi\)
\(194\) 0 0
\(195\) −0.909349 + 0.267009i −0.0651198 + 0.0191209i
\(196\) 0 0
\(197\) 0.582925 4.05433i 0.0415317 0.288859i −0.958462 0.285221i \(-0.907933\pi\)
0.999993 0.00363791i \(-0.00115799\pi\)
\(198\) 0 0
\(199\) −0.892500 1.03000i −0.0632677 0.0730148i 0.723233 0.690604i \(-0.242655\pi\)
−0.786501 + 0.617589i \(0.788110\pi\)
\(200\) 0 0
\(201\) 0.147655 + 8.18402i 0.0104148 + 0.577256i
\(202\) 0 0
\(203\) 0.00655067 + 0.00755988i 0.000459767 + 0.000530600i
\(204\) 0 0
\(205\) −0.919987 + 6.39865i −0.0642547 + 0.446901i
\(206\) 0 0
\(207\) 5.68461 1.66915i 0.395108 0.116014i
\(208\) 0 0
\(209\) 0.0276560 0.0177735i 0.00191301 0.00122942i
\(210\) 0 0
\(211\) −3.96139 8.67423i −0.272713 0.597158i 0.722876 0.690978i \(-0.242820\pi\)
−0.995589 + 0.0938192i \(0.970092\pi\)
\(212\) 0 0
\(213\) −9.89869 6.36150i −0.678247 0.435883i
\(214\) 0 0
\(215\) 0.139833 0.972557i 0.00953651 0.0663279i
\(216\) 0 0
\(217\) −0.0973641 0.0285887i −0.00660950 0.00194073i
\(218\) 0 0
\(219\) 1.43226 9.96156i 0.0967829 0.673140i
\(220\) 0 0
\(221\) 3.08333 6.75154i 0.207407 0.454158i
\(222\) 0 0
\(223\) 3.76060 + 8.23458i 0.251829 + 0.551428i 0.992755 0.120159i \(-0.0383404\pi\)
−0.740926 + 0.671587i \(0.765613\pi\)
\(224\) 0 0
\(225\) 0.569034 + 3.95772i 0.0379356 + 0.263848i
\(226\) 0 0
\(227\) −0.0393316 0.273557i −0.00261053 0.0181566i 0.988475 0.151387i \(-0.0483740\pi\)
−0.991085 + 0.133231i \(0.957465\pi\)
\(228\) 0 0
\(229\) −10.3283 + 6.63757i −0.682511 + 0.438623i −0.835416 0.549618i \(-0.814773\pi\)
0.152906 + 0.988241i \(0.451137\pi\)
\(230\) 0 0
\(231\) 0.000337029 0 2.21749e−5 0
\(232\) 0 0
\(233\) −0.417140 0.913410i −0.0273278 0.0598395i 0.895476 0.445110i \(-0.146835\pi\)
−0.922804 + 0.385271i \(0.874108\pi\)
\(234\) 0 0
\(235\) 3.44164 3.97186i 0.224508 0.259096i
\(236\) 0 0
\(237\) −5.45532 + 3.50592i −0.354361 + 0.227734i
\(238\) 0 0
\(239\) 2.24067 0.144937 0.0724684 0.997371i \(-0.476912\pi\)
0.0724684 + 0.997371i \(0.476912\pi\)
\(240\) 0 0
\(241\) 20.5581 6.03642i 1.32427 0.388840i 0.458236 0.888831i \(-0.348481\pi\)
0.866031 + 0.499991i \(0.166663\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) −2.91015 + 6.37235i −0.185923 + 0.407114i
\(246\) 0 0
\(247\) 0.999559 0.293497i 0.0636004 0.0186748i
\(248\) 0 0
\(249\) −5.44730 + 6.28652i −0.345208 + 0.398392i
\(250\) 0 0
\(251\) −2.21729 15.4216i −0.139954 0.973401i −0.931876 0.362778i \(-0.881828\pi\)
0.791922 0.610623i \(-0.209081\pi\)
\(252\) 0 0
\(253\) 0.115944 0.133807i 0.00728936 0.00841237i
\(254\) 0 0
\(255\) 6.59877 + 4.24077i 0.413231 + 0.265567i
\(256\) 0 0
\(257\) 18.7580 + 5.50786i 1.17010 + 0.343571i 0.808348 0.588705i \(-0.200362\pi\)
0.361747 + 0.932276i \(0.382180\pi\)
\(258\) 0 0
\(259\) −0.0457426 0.0527898i −0.00284231 0.00328020i
\(260\) 0 0
\(261\) −0.580845 0.670330i −0.0359534 0.0414924i
\(262\) 0 0
\(263\) −9.64233 2.83124i −0.594572 0.174582i −0.0294174 0.999567i \(-0.509365\pi\)
−0.565154 + 0.824985i \(0.691183\pi\)
\(264\) 0 0
\(265\) 2.86446 6.27230i 0.175963 0.385304i
\(266\) 0 0
\(267\) 9.68000 0.592407
\(268\) 0 0
\(269\) −14.1374 −0.861971 −0.430985 0.902359i \(-0.641834\pi\)
−0.430985 + 0.902359i \(0.641834\pi\)
\(270\) 0 0
\(271\) −7.69386 + 16.8472i −0.467369 + 1.02340i 0.518377 + 0.855152i \(0.326537\pi\)
−0.985746 + 0.168243i \(0.946191\pi\)
\(272\) 0 0
\(273\) 0.0102474 + 0.00300890i 0.000620200 + 0.000182107i
\(274\) 0 0
\(275\) 0.0782490 + 0.0903041i 0.00471859 + 0.00544554i
\(276\) 0 0
\(277\) −20.8043 24.0094i −1.25001 1.44259i −0.850599 0.525815i \(-0.823760\pi\)
−0.399410 0.916772i \(-0.630785\pi\)
\(278\) 0 0
\(279\) 8.63322 + 2.53494i 0.516857 + 0.151763i
\(280\) 0 0
\(281\) −18.5128 11.8975i −1.10438 0.709744i −0.144321 0.989531i \(-0.546100\pi\)
−0.960062 + 0.279787i \(0.909736\pi\)
\(282\) 0 0
\(283\) 10.6618 12.3044i 0.633780 0.731421i −0.344482 0.938793i \(-0.611945\pi\)
0.978262 + 0.207372i \(0.0664909\pi\)
\(284\) 0 0
\(285\) 0.156681 + 1.08974i 0.00928096 + 0.0645505i
\(286\) 0 0
\(287\) 0.0477049 0.0550543i 0.00281593 0.00324975i
\(288\) 0 0
\(289\) −42.6309 + 12.5176i −2.50770 + 0.736327i
\(290\) 0 0
\(291\) 5.43895 11.9096i 0.318837 0.698156i
\(292\) 0 0
\(293\) 13.5477 + 8.70659i 0.791466 + 0.508644i 0.872821 0.488041i \(-0.162288\pi\)
−0.0813548 + 0.996685i \(0.525925\pi\)
\(294\) 0 0
\(295\) 9.25072 2.71626i 0.538598 0.158147i
\(296\) 0 0
\(297\) −0.0298842 −0.00173406
\(298\) 0 0
\(299\) 4.71988 3.03328i 0.272958 0.175419i
\(300\) 0 0
\(301\) −0.00725086 + 0.00836794i −0.000417933 + 0.000482320i
\(302\) 0 0
\(303\) −1.61145 3.52858i −0.0925752 0.202711i
\(304\) 0 0
\(305\) −7.23691 −0.414384
\(306\) 0 0
\(307\) −8.35460 + 5.36917i −0.476822 + 0.306435i −0.756887 0.653546i \(-0.773280\pi\)
0.280065 + 0.959981i \(0.409644\pi\)
\(308\) 0 0
\(309\) 0.284606 + 1.97948i 0.0161907 + 0.112609i
\(310\) 0 0
\(311\) 0.373970 + 2.60102i 0.0212059 + 0.147490i 0.997673 0.0681743i \(-0.0217174\pi\)
−0.976468 + 0.215664i \(0.930808\pi\)
\(312\) 0 0
\(313\) −2.44696 5.35810i −0.138311 0.302858i 0.827784 0.561047i \(-0.189601\pi\)
−0.966094 + 0.258189i \(0.916874\pi\)
\(314\) 0 0
\(315\) −0.00468869 + 0.0102668i −0.000264178 + 0.000578469i
\(316\) 0 0
\(317\) −1.40646 + 9.78213i −0.0789946 + 0.549419i 0.911440 + 0.411434i \(0.134972\pi\)
−0.990434 + 0.137986i \(0.955937\pi\)
\(318\) 0 0
\(319\) −0.0254328 0.00746775i −0.00142396 0.000418114i
\(320\) 0 0
\(321\) −1.26568 + 8.80300i −0.0706434 + 0.491335i
\(322\) 0 0
\(323\) −7.25339 4.66147i −0.403589 0.259371i
\(324\) 0 0
\(325\) 1.57295 + 3.44428i 0.0872516 + 0.191054i
\(326\) 0 0
\(327\) −11.6058 + 7.45861i −0.641804 + 0.412462i
\(328\) 0 0
\(329\) −0.0568251 + 0.0166854i −0.00313287 + 0.000919894i
\(330\) 0 0
\(331\) −2.25469 + 15.6817i −0.123929 + 0.861947i 0.829107 + 0.559090i \(0.188849\pi\)
−0.953036 + 0.302857i \(0.902060\pi\)
\(332\) 0 0
\(333\) 4.05597 + 4.68084i 0.222266 + 0.256508i
\(334\) 0 0
\(335\) −8.08610 + 1.31190i −0.441791 + 0.0716766i
\(336\) 0 0
\(337\) 8.32107 + 9.60303i 0.453278 + 0.523110i 0.935685 0.352837i \(-0.114783\pi\)
−0.482407 + 0.875947i \(0.660237\pi\)
\(338\) 0 0
\(339\) −2.48943 + 17.3143i −0.135207 + 0.940385i
\(340\) 0 0
\(341\) 0.257997 0.0757547i 0.0139713 0.00410235i
\(342\) 0 0
\(343\) 0.132824 0.0853609i 0.00717183 0.00460905i
\(344\) 0 0
\(345\) 2.46312 + 5.39347i 0.132610 + 0.290375i
\(346\) 0 0
\(347\) −4.77003 3.06551i −0.256068 0.164565i 0.406308 0.913736i \(-0.366816\pi\)
−0.662377 + 0.749171i \(0.730452\pi\)
\(348\) 0 0
\(349\) −2.01607 + 14.0221i −0.107918 + 0.750585i 0.861957 + 0.506981i \(0.169239\pi\)
−0.969875 + 0.243603i \(0.921670\pi\)
\(350\) 0 0
\(351\) −0.908629 0.266798i −0.0484991 0.0142406i
\(352\) 0 0
\(353\) 0.442471 3.07746i 0.0235504 0.163796i −0.974652 0.223725i \(-0.928178\pi\)
0.998203 + 0.0599286i \(0.0190873\pi\)
\(354\) 0 0
\(355\) 4.89189 10.7117i 0.259635 0.568521i
\(356\) 0 0
\(357\) −0.0367198 0.0804052i −0.00194342 0.00425549i
\(358\) 0 0
\(359\) −2.28215 15.8727i −0.120447 0.837728i −0.957051 0.289920i \(-0.906371\pi\)
0.836604 0.547808i \(-0.184538\pi\)
\(360\) 0 0
\(361\) 2.53176 + 17.6088i 0.133250 + 0.926777i
\(362\) 0 0
\(363\) 9.25304 5.94657i 0.485659 0.312114i
\(364\) 0 0
\(365\) 10.0720 0.527191
\(366\) 0 0
\(367\) 12.2314 + 26.7831i 0.638476 + 1.39807i 0.901288 + 0.433221i \(0.142623\pi\)
−0.262812 + 0.964847i \(0.584650\pi\)
\(368\) 0 0
\(369\) −4.22996 + 4.88164i −0.220203 + 0.254128i
\(370\) 0 0
\(371\) −0.0653688 + 0.0420100i −0.00339378 + 0.00218105i
\(372\) 0 0
\(373\) 19.0550 0.986628 0.493314 0.869851i \(-0.335785\pi\)
0.493314 + 0.869851i \(0.335785\pi\)
\(374\) 0 0
\(375\) −8.64075 + 2.53715i −0.446207 + 0.131018i
\(376\) 0 0
\(377\) −0.706615 0.454114i −0.0363925 0.0233881i
\(378\) 0 0
\(379\) −10.6665 + 23.3564i −0.547903 + 1.19974i 0.409852 + 0.912152i \(0.365580\pi\)
−0.957754 + 0.287588i \(0.907147\pi\)
\(380\) 0 0
\(381\) 3.53622 1.03833i 0.181166 0.0531952i
\(382\) 0 0
\(383\) −23.5322 + 27.1576i −1.20244 + 1.38769i −0.301659 + 0.953416i \(0.597540\pi\)
−0.900781 + 0.434273i \(0.857005\pi\)
\(384\) 0 0
\(385\) 4.80023e−5 0 0.000333863i 2.44642e−6 0 1.70152e-5i
\(386\) 0 0
\(387\) 0.642930 0.741981i 0.0326820 0.0377170i
\(388\) 0 0
\(389\) 23.4324 + 15.0591i 1.18807 + 0.763526i 0.976853 0.213914i \(-0.0686211\pi\)
0.211217 + 0.977439i \(0.432257\pi\)
\(390\) 0 0
\(391\) −44.5547 13.0824i −2.25323 0.661607i
\(392\) 0 0
\(393\) −10.6982 12.3464i −0.539654 0.622794i
\(394\) 0 0
\(395\) −4.24997 4.90473i −0.213839 0.246784i
\(396\) 0 0
\(397\) −7.12812 2.09300i −0.357750 0.105045i 0.0979185 0.995194i \(-0.468782\pi\)
−0.455668 + 0.890150i \(0.650600\pi\)
\(398\) 0 0
\(399\) 0.00515382 0.0112853i 0.000258014 0.000564972i
\(400\) 0 0
\(401\) −19.1740 −0.957503 −0.478752 0.877950i \(-0.658911\pi\)
−0.478752 + 0.877950i \(0.658911\pi\)
\(402\) 0 0
\(403\) 8.52071 0.424447
\(404\) 0 0
\(405\) 0.415744 0.910352i 0.0206585 0.0452358i
\(406\) 0 0
\(407\) 0.177594 + 0.0521464i 0.00880303 + 0.00258480i
\(408\) 0 0
\(409\) 7.99494 + 9.22665i 0.395324 + 0.456229i 0.918163 0.396203i \(-0.129672\pi\)
−0.522838 + 0.852432i \(0.675127\pi\)
\(410\) 0 0
\(411\) −2.73249 3.15347i −0.134784 0.155549i
\(412\) 0 0
\(413\) −0.104246 0.0306093i −0.00512959 0.00150618i
\(414\) 0 0
\(415\) −7.00330 4.50075i −0.343778 0.220933i
\(416\) 0 0
\(417\) −14.3133 + 16.5184i −0.700925 + 0.808910i
\(418\) 0 0
\(419\) −2.71180 18.8610i −0.132480 0.921421i −0.942307 0.334751i \(-0.891348\pi\)
0.809826 0.586670i \(-0.199561\pi\)
\(420\) 0 0
\(421\) −7.24193 + 8.35763i −0.352950 + 0.407326i −0.904265 0.426971i \(-0.859581\pi\)
0.551315 + 0.834297i \(0.314126\pi\)
\(422\) 0 0
\(423\) 5.03865 1.47948i 0.244988 0.0719349i
\(424\) 0 0
\(425\) 13.0185 28.5066i 0.631492 1.38278i
\(426\) 0 0
\(427\) 0.0686061 + 0.0440904i 0.00332008 + 0.00213369i
\(428\) 0 0
\(429\) −0.0271537 + 0.00797304i −0.00131099 + 0.000384942i
\(430\) 0 0
\(431\) −31.2358 −1.50458 −0.752288 0.658835i \(-0.771050\pi\)
−0.752288 + 0.658835i \(0.771050\pi\)
\(432\) 0 0
\(433\) −1.84774 + 1.18747i −0.0887969 + 0.0570663i −0.584286 0.811548i \(-0.698625\pi\)
0.495489 + 0.868614i \(0.334989\pi\)
\(434\) 0 0
\(435\) 0.581305 0.670861i 0.0278714 0.0321653i
\(436\) 0 0
\(437\) −2.70746 5.92852i −0.129516 0.283600i
\(438\) 0 0
\(439\) 8.00230 0.381929 0.190964 0.981597i \(-0.438838\pi\)
0.190964 + 0.981597i \(0.438838\pi\)
\(440\) 0 0
\(441\) −5.88867 + 3.78442i −0.280413 + 0.180210i
\(442\) 0 0
\(443\) −2.76791 19.2512i −0.131507 0.914653i −0.943591 0.331112i \(-0.892576\pi\)
0.812084 0.583540i \(-0.198333\pi\)
\(444\) 0 0
\(445\) 1.37870 + 9.58906i 0.0653566 + 0.454565i
\(446\) 0 0
\(447\) 2.11173 + 4.62404i 0.0998814 + 0.218710i
\(448\) 0 0
\(449\) 7.65959 16.7722i 0.361478 0.791527i −0.638286 0.769800i \(-0.720356\pi\)
0.999764 0.0217273i \(-0.00691657\pi\)
\(450\) 0 0
\(451\) −0.0274713 + 0.191067i −0.00129357 + 0.00899701i
\(452\) 0 0
\(453\) 10.4841 + 3.07840i 0.492585 + 0.144636i
\(454\) 0 0
\(455\) −0.00152113 + 0.0105797i −7.13114e−5 + 0.000495982i
\(456\) 0 0
\(457\) 12.8510 + 8.25885i 0.601146 + 0.386333i 0.805528 0.592558i \(-0.201882\pi\)
−0.204382 + 0.978891i \(0.565518\pi\)
\(458\) 0 0
\(459\) 3.25593 + 7.12949i 0.151974 + 0.332776i
\(460\) 0 0
\(461\) −5.62452 + 3.61466i −0.261960 + 0.168351i −0.665028 0.746819i \(-0.731580\pi\)
0.403068 + 0.915170i \(0.367944\pi\)
\(462\) 0 0
\(463\) 13.5187 3.96945i 0.628268 0.184476i 0.0479282 0.998851i \(-0.484738\pi\)
0.580339 + 0.814375i \(0.302920\pi\)
\(464\) 0 0
\(465\) −1.28152 + 8.91316i −0.0594290 + 0.413338i
\(466\) 0 0
\(467\) −6.54900 7.55795i −0.303052 0.349740i 0.583714 0.811959i \(-0.301599\pi\)
−0.886766 + 0.462219i \(0.847053\pi\)
\(468\) 0 0
\(469\) 0.0846491 + 0.0368273i 0.00390873 + 0.00170053i
\(470\) 0 0
\(471\) −1.81234 2.09155i −0.0835080 0.0963734i
\(472\) 0 0
\(473\) 0.00417548 0.0290411i 0.000191989 0.00133531i
\(474\) 0 0
\(475\) 4.22038 1.23921i 0.193644 0.0568591i
\(476\) 0 0
\(477\) 5.79621 3.72500i 0.265390 0.170556i
\(478\) 0 0
\(479\) 8.60830 + 18.8495i 0.393323 + 0.861258i 0.997904 + 0.0647137i \(0.0206134\pi\)
−0.604581 + 0.796544i \(0.706659\pi\)
\(480\) 0 0
\(481\) 4.93421 + 3.17102i 0.224981 + 0.144586i
\(482\) 0 0
\(483\) 0.00950901 0.0661366i 0.000432675 0.00300932i
\(484\) 0 0
\(485\) 12.5724 + 3.69159i 0.570884 + 0.167627i
\(486\) 0 0
\(487\) −4.92647 + 34.2643i −0.223239 + 1.55266i 0.502428 + 0.864619i \(0.332440\pi\)
−0.725668 + 0.688046i \(0.758469\pi\)
\(488\) 0 0
\(489\) −3.10491 + 6.79879i −0.140409 + 0.307452i
\(490\) 0 0
\(491\) −2.01649 4.41550i −0.0910030 0.199269i 0.858657 0.512550i \(-0.171299\pi\)
−0.949660 + 0.313281i \(0.898572\pi\)
\(492\) 0 0
\(493\) 0.989358 + 6.88114i 0.0445585 + 0.309911i
\(494\) 0 0
\(495\) −0.00425633 0.0296035i −0.000191308 0.00133058i
\(496\) 0 0
\(497\) −0.111636 + 0.0717440i −0.00500755 + 0.00321816i
\(498\) 0 0
\(499\) 10.6616 0.477278 0.238639 0.971108i \(-0.423299\pi\)
0.238639 + 0.971108i \(0.423299\pi\)
\(500\) 0 0
\(501\) −4.09891 8.97536i −0.183126 0.400990i
\(502\) 0 0
\(503\) −23.7443 + 27.4024i −1.05871 + 1.22181i −0.0844385 + 0.996429i \(0.526910\pi\)
−0.974270 + 0.225386i \(0.927636\pi\)
\(504\) 0 0
\(505\) 3.26591 2.09887i 0.145331 0.0933987i
\(506\) 0 0
\(507\) 12.1032 0.537522
\(508\) 0 0
\(509\) −12.2768 + 3.60480i −0.544160 + 0.159780i −0.542248 0.840218i \(-0.682427\pi\)
−0.00191189 + 0.999998i \(0.500609\pi\)
\(510\) 0 0
\(511\) −0.0954824 0.0613628i −0.00422389 0.00271453i
\(512\) 0 0
\(513\) −0.456987 + 1.00066i −0.0201765 + 0.0441803i
\(514\) 0 0
\(515\) −1.92035 + 0.563865i −0.0846207 + 0.0248469i
\(516\) 0 0
\(517\) 0.102769 0.118602i 0.00451979 0.00521611i
\(518\) 0 0
\(519\) 1.75432 + 12.2016i 0.0770060 + 0.535589i
\(520\) 0 0
\(521\) 6.77537 7.81920i 0.296835 0.342565i −0.587667 0.809103i \(-0.699953\pi\)
0.884501 + 0.466538i \(0.154499\pi\)
\(522\) 0 0
\(523\) 14.9373 + 9.59960i 0.653161 + 0.419761i 0.824820 0.565395i \(-0.191276\pi\)
−0.171659 + 0.985156i \(0.554913\pi\)
\(524\) 0 0
\(525\) 0.0432669 + 0.0127043i 0.00188832 + 0.000554461i
\(526\) 0 0
\(527\) −46.1820 53.2968i −2.01172 2.32165i
\(528\) 0 0
\(529\) −7.92440 9.14524i −0.344539 0.397619i
\(530\) 0 0
\(531\) 9.24340 + 2.71411i 0.401129 + 0.117782i
\(532\) 0 0
\(533\) −2.54106 + 5.56414i −0.110066 + 0.241010i
\(534\) 0 0
\(535\) −8.90056 −0.384805
\(536\) 0 0
\(537\) −17.2214 −0.743157
\(538\) 0 0
\(539\) −0.0868989 + 0.190282i −0.00374300 + 0.00819602i
\(540\) 0 0
\(541\) −41.3501 12.1415i −1.77778 0.522003i −0.782816 0.622253i \(-0.786217\pi\)
−0.994962 + 0.100251i \(0.968036\pi\)
\(542\) 0 0
\(543\) 6.79502 + 7.84187i 0.291602 + 0.336527i
\(544\) 0 0
\(545\) −9.04153 10.4345i −0.387296 0.446964i
\(546\) 0 0
\(547\) −12.6909 3.72638i −0.542623 0.159328i −0.00107671 0.999999i \(-0.500343\pi\)
−0.541546 + 0.840671i \(0.682161\pi\)
\(548\) 0 0
\(549\) −6.08326 3.90948i −0.259627 0.166852i
\(550\) 0 0
\(551\) −0.638971 + 0.737412i −0.0272211 + 0.0314148i
\(552\) 0 0
\(553\) 0.0104081 + 0.0723896i 0.000442595 + 0.00307832i
\(554\) 0 0
\(555\) −4.05918 + 4.68455i −0.172303 + 0.198848i
\(556\) 0 0
\(557\) −1.74596 + 0.512660i −0.0739786 + 0.0217221i −0.318512 0.947919i \(-0.603183\pi\)
0.244534 + 0.969641i \(0.421365\pi\)
\(558\) 0 0
\(559\) 0.386226 0.845718i 0.0163356 0.0357700i
\(560\) 0 0
\(561\) 0.197043 + 0.126632i 0.00831916 + 0.00534640i
\(562\) 0 0
\(563\) 31.3250 9.19785i 1.32019 0.387643i 0.455629 0.890170i \(-0.349414\pi\)
0.864562 + 0.502527i \(0.167596\pi\)
\(564\) 0 0
\(565\) −17.5062 −0.736493
\(566\) 0 0
\(567\) −0.00948752 + 0.00609726i −0.000398439 + 0.000256061i
\(568\) 0 0
\(569\) 19.7860 22.8343i 0.829473 0.957263i −0.170130 0.985422i \(-0.554419\pi\)
0.999603 + 0.0281584i \(0.00896429\pi\)
\(570\) 0 0
\(571\) −14.6984 32.1851i −0.615111 1.34690i −0.919023 0.394205i \(-0.871020\pi\)
0.303912 0.952700i \(-0.401707\pi\)
\(572\) 0 0
\(573\) 12.3773 0.517070
\(574\) 0 0
\(575\) 19.9285 12.8072i 0.831075 0.534099i
\(576\) 0 0
\(577\) 5.54781 + 38.5859i 0.230958 + 1.60635i 0.693974 + 0.720000i \(0.255858\pi\)
−0.463016 + 0.886350i \(0.653233\pi\)
\(578\) 0 0
\(579\) 2.31674 + 16.1133i 0.0962805 + 0.669646i
\(580\) 0 0
\(581\) 0.0389709 + 0.0853343i 0.00161678 + 0.00354026i
\(582\) 0 0
\(583\) 0.0855345 0.187294i 0.00354248 0.00775694i
\(584\) 0 0
\(585\) 0.134877 0.938092i 0.00557649 0.0387853i
\(586\) 0 0
\(587\) −4.97576 1.46102i −0.205372 0.0603026i 0.177429 0.984134i \(-0.443222\pi\)
−0.382800 + 0.923831i \(0.625040\pi\)
\(588\) 0 0
\(589\) 1.40865 9.79736i 0.0580423 0.403693i
\(590\) 0 0
\(591\) 3.44579 + 2.21448i 0.141741 + 0.0910914i
\(592\) 0 0
\(593\) 12.4797 + 27.3266i 0.512478 + 1.12217i 0.972210 + 0.234112i \(0.0752184\pi\)
−0.459731 + 0.888058i \(0.652054\pi\)
\(594\) 0 0
\(595\) 0.0744199 0.0478268i 0.00305092 0.00196071i
\(596\) 0 0
\(597\) 1.30768 0.383969i 0.0535197 0.0157148i
\(598\) 0 0
\(599\) 4.85638 33.7769i 0.198426 1.38009i −0.610425 0.792074i \(-0.709002\pi\)
0.808852 0.588012i \(-0.200089\pi\)
\(600\) 0 0
\(601\) 9.82729 + 11.3413i 0.400864 + 0.462621i 0.919913 0.392123i \(-0.128259\pi\)
−0.519049 + 0.854744i \(0.673714\pi\)
\(602\) 0 0
\(603\) −7.50579 3.26545i −0.305659 0.132980i
\(604\) 0 0
\(605\) 7.20859 + 8.31915i 0.293071 + 0.338222i
\(606\) 0 0
\(607\) 4.90935 34.1453i 0.199265 1.38592i −0.607161 0.794579i \(-0.707692\pi\)
0.806425 0.591336i \(-0.201399\pi\)
\(608\) 0 0
\(609\) −0.00959796 + 0.00281821i −0.000388929 + 0.000114200i
\(610\) 0 0
\(611\) 4.18355 2.68860i 0.169248 0.108769i
\(612\) 0 0
\(613\) 16.9415 + 37.0967i 0.684261 + 1.49832i 0.858064 + 0.513542i \(0.171667\pi\)
−0.173803 + 0.984780i \(0.555606\pi\)
\(614\) 0 0
\(615\) −5.43824 3.49494i −0.219291 0.140930i
\(616\) 0 0
\(617\) 1.50370 10.4585i 0.0605366 0.421042i −0.936907 0.349580i \(-0.886324\pi\)
0.997443 0.0714620i \(-0.0227665\pi\)
\(618\) 0 0
\(619\) −25.0025 7.34141i −1.00494 0.295076i −0.262457 0.964944i \(-0.584533\pi\)
−0.742480 + 0.669868i \(0.766351\pi\)
\(620\) 0 0
\(621\) −0.843159 + 5.86430i −0.0338348 + 0.235326i
\(622\) 0 0
\(623\) 0.0453507 0.0993041i 0.00181694 0.00397854i
\(624\) 0 0
\(625\) 4.56101 + 9.98722i 0.182440 + 0.399489i
\(626\) 0 0
\(627\) 0.00467857 + 0.0325402i 0.000186844 + 0.00129953i
\(628\) 0 0
\(629\) −6.90857 48.0502i −0.275463 1.91589i
\(630\) 0 0
\(631\) −34.3799 + 22.0946i −1.36864 + 0.879573i −0.998774 0.0495107i \(-0.984234\pi\)
−0.369869 + 0.929084i \(0.620597\pi\)
\(632\) 0 0
\(633\) 9.53597 0.379021
\(634\) 0 0
\(635\) 1.53223 + 3.35511i 0.0608047 + 0.133144i
\(636\) 0 0
\(637\) −4.34094 + 5.00972i −0.171994 + 0.198492i
\(638\) 0 0
\(639\) 9.89869 6.36150i 0.391586 0.251657i
\(640\) 0 0
\(641\) −7.87182 −0.310918 −0.155459 0.987842i \(-0.549686\pi\)
−0.155459 + 0.987842i \(0.549686\pi\)
\(642\) 0 0
\(643\) 45.3101 13.3042i 1.78685 0.524668i 0.790694 0.612212i \(-0.209720\pi\)
0.996161 + 0.0875443i \(0.0279019\pi\)
\(644\) 0 0
\(645\) 0.826581 + 0.531211i 0.0325466 + 0.0209164i
\(646\) 0 0
\(647\) −8.61308 + 18.8600i −0.338615 + 0.741463i −0.999963 0.00861598i \(-0.997257\pi\)
0.661348 + 0.750079i \(0.269985\pi\)
\(648\) 0 0
\(649\) 0.276232 0.0811089i 0.0108430 0.00318380i
\(650\) 0 0
\(651\) 0.0664517 0.0766893i 0.00260445 0.00300569i
\(652\) 0 0
\(653\) 2.90942 + 20.2355i 0.113855 + 0.791876i 0.964110 + 0.265505i \(0.0855386\pi\)
−0.850255 + 0.526371i \(0.823552\pi\)
\(654\) 0 0
\(655\) 10.7067 12.3562i 0.418345 0.482796i
\(656\) 0 0
\(657\) 8.46637 + 5.44101i 0.330305 + 0.212274i
\(658\) 0 0
\(659\) −36.6412 10.7588i −1.42734 0.419105i −0.525358 0.850881i \(-0.676069\pi\)
−0.901981 + 0.431776i \(0.857887\pi\)
\(660\) 0 0
\(661\) 2.39916 + 2.76878i 0.0933165 + 0.107693i 0.800487 0.599350i \(-0.204574\pi\)
−0.707171 + 0.707043i \(0.750029\pi\)
\(662\) 0 0
\(663\) 4.86056 + 5.60939i 0.188769 + 0.217851i
\(664\) 0 0
\(665\) 0.0119133 + 0.00349807i 0.000461979 + 0.000135649i
\(666\) 0 0
\(667\) −2.18299 + 4.78009i −0.0845258 + 0.185086i
\(668\) 0 0
\(669\) −9.05264 −0.349995
\(670\) 0 0
\(671\) −0.216098 −0.00834238
\(672\) 0 0
\(673\) −4.02010 + 8.80280i −0.154964 + 0.339323i −0.971151 0.238464i \(-0.923356\pi\)
0.816188 + 0.577787i \(0.196083\pi\)
\(674\) 0 0
\(675\) −3.83645 1.12648i −0.147665 0.0433584i
\(676\) 0 0
\(677\) 19.7694 + 22.8152i 0.759802 + 0.876858i 0.995480 0.0949734i \(-0.0302766\pi\)
−0.235678 + 0.971831i \(0.575731\pi\)
\(678\) 0 0
\(679\) −0.0966959 0.111593i −0.00371085 0.00428255i
\(680\) 0 0
\(681\) 0.265175 + 0.0778625i 0.0101615 + 0.00298370i
\(682\) 0 0
\(683\) 29.5280 + 18.9765i 1.12986 + 0.726116i 0.965531 0.260290i \(-0.0838181\pi\)
0.164328 + 0.986406i \(0.447454\pi\)
\(684\) 0 0
\(685\) 2.73466 3.15596i 0.104486 0.120583i
\(686\) 0 0
\(687\) −1.74723 12.1523i −0.0666610 0.463638i
\(688\) 0 0
\(689\) 4.27279 4.93106i 0.162780 0.187858i
\(690\) 0 0
\(691\) 22.9955 6.75209i 0.874790 0.256862i 0.186639 0.982429i \(-0.440241\pi\)
0.688151 + 0.725567i \(0.258422\pi\)
\(692\) 0 0
\(693\) −0.000140007 0 0.000306573i −5.31843e−6 0 1.16457e-5i
\(694\) 0 0
\(695\) −18.4018 11.8261i −0.698021 0.448591i
\(696\) 0 0
\(697\) 48.5760 14.2632i 1.83995 0.540257i
\(698\) 0 0
\(699\) 1.00415 0.0379806
\(700\) 0 0
\(701\) 18.2215 11.7102i 0.688216 0.442289i −0.149235 0.988802i \(-0.547681\pi\)
0.837451 + 0.546512i \(0.184045\pi\)
\(702\) 0 0
\(703\) 4.46186 5.14926i 0.168282 0.194208i
\(704\) 0 0
\(705\) 2.18322 + 4.78060i 0.0822250 + 0.180048i
\(706\) 0 0
\(707\) −0.0437482 −0.00164532
\(708\) 0 0
\(709\) 27.0150 17.3615i 1.01457 0.652024i 0.0759968 0.997108i \(-0.475786\pi\)
0.938572 + 0.345085i \(0.112150\pi\)
\(710\) 0 0
\(711\) −0.922876 6.41874i −0.0346106 0.240722i
\(712\) 0 0
\(713\) −7.58648 52.7651i −0.284116 1.97607i
\(714\) 0 0
\(715\) −0.0117656 0.0257630i −0.000440007 0.000963481i
\(716\) 0 0
\(717\) −0.930807 + 2.03818i −0.0347616 + 0.0761173i
\(718\) 0 0
\(719\) 1.66081 11.5512i 0.0619378 0.430787i −0.935133 0.354298i \(-0.884720\pi\)
0.997070 0.0764891i \(-0.0243710\pi\)
\(720\) 0 0
\(721\) 0.0216403 + 0.00635415i 0.000805925 + 0.000236641i
\(722\) 0 0
\(723\) −3.04925 + 21.2080i −0.113403 + 0.788733i
\(724\) 0 0
\(725\) −2.98350 1.91738i −0.110804 0.0712096i
\(726\) 0 0
\(727\) −7.82175 17.1273i −0.290093 0.635215i 0.707336 0.706877i \(-0.249897\pi\)
−0.997429 + 0.0716627i \(0.977169\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) −7.38327 + 2.16792i −0.273080 + 0.0801836i
\(732\) 0 0
\(733\) 2.43652 16.9464i 0.0899950 0.625929i −0.894044 0.447978i \(-0.852144\pi\)
0.984039 0.177951i \(-0.0569468\pi\)
\(734\) 0 0
\(735\) −4.58757 5.29434i −0.169215 0.195285i
\(736\) 0 0
\(737\) −0.241456 + 0.0391740i −0.00889413 + 0.00144299i
\(738\) 0 0
\(739\) −4.71923 5.44629i −0.173600 0.200345i 0.662281 0.749255i \(-0.269588\pi\)
−0.835881 + 0.548910i \(0.815043\pi\)
\(740\) 0 0
\(741\) −0.148257 + 1.03115i −0.00544637 + 0.0378804i
\(742\) 0 0
\(743\) 11.2729 3.31002i 0.413563 0.121433i −0.0683309 0.997663i \(-0.521767\pi\)
0.481894 + 0.876230i \(0.339949\pi\)
\(744\) 0 0
\(745\) −4.27983 + 2.75048i −0.156801 + 0.100770i
\(746\) 0 0
\(747\) −3.45553 7.56655i −0.126431 0.276846i
\(748\) 0 0
\(749\) 0.0843775 + 0.0542261i 0.00308309 + 0.00198138i
\(750\) 0 0
\(751\) 3.02810 21.0609i 0.110497 0.768523i −0.856941 0.515415i \(-0.827638\pi\)
0.967438 0.253109i \(-0.0814530\pi\)
\(752\) 0 0
\(753\) 14.9490 + 4.38944i 0.544773 + 0.159960i
\(754\) 0 0
\(755\) −1.55626 + 10.8240i −0.0566381 + 0.393927i
\(756\) 0 0
\(757\) 15.9434 34.9112i 0.579474 1.26887i −0.362123 0.932130i \(-0.617948\pi\)
0.941597 0.336741i \(-0.109325\pi\)
\(758\) 0 0
\(759\) 0.0735501 + 0.161052i 0.00266970 + 0.00584582i
\(760\) 0 0
\(761\) 3.51530 + 24.4495i 0.127430 + 0.886292i 0.948796 + 0.315891i \(0.102303\pi\)
−0.821366 + 0.570402i \(0.806788\pi\)
\(762\) 0 0
\(763\) 0.0221424 + 0.154004i 0.000801610 + 0.00557532i
\(764\) 0 0
\(765\) −6.59877 + 4.24077i −0.238579 + 0.153325i
\(766\) 0 0
\(767\) 9.12294 0.329410
\(768\) 0 0
\(769\) 9.07294 + 19.8670i 0.327179 + 0.716421i 0.999721 0.0236378i \(-0.00752484\pi\)
−0.672542 + 0.740059i \(0.734798\pi\)
\(770\) 0 0
\(771\) −12.8025 + 14.7749i −0.461071 + 0.532104i
\(772\) 0 0
\(773\) 10.4607 6.72266i 0.376244 0.241797i −0.338828 0.940848i \(-0.610030\pi\)
0.715072 + 0.699051i \(0.246394\pi\)
\(774\) 0 0
\(775\) 35.9765 1.29231
\(776\) 0 0
\(777\) 0.0670214 0.0196793i 0.00240438 0.000705990i
\(778\) 0 0
\(779\) 5.97773 + 3.84165i 0.214174 + 0.137641i
\(780\) 0 0
\(781\) 0.146075 0.319859i