Properties

Label 6026.2.a.i.1.16
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.694821 q^{3}\) \(+1.00000 q^{4}\) \(+0.658132 q^{5}\) \(-0.694821 q^{6}\) \(-2.75018 q^{7}\) \(-1.00000 q^{8}\) \(-2.51722 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.694821 q^{3}\) \(+1.00000 q^{4}\) \(+0.658132 q^{5}\) \(-0.694821 q^{6}\) \(-2.75018 q^{7}\) \(-1.00000 q^{8}\) \(-2.51722 q^{9}\) \(-0.658132 q^{10}\) \(-3.14857 q^{11}\) \(+0.694821 q^{12}\) \(-1.49529 q^{13}\) \(+2.75018 q^{14}\) \(+0.457284 q^{15}\) \(+1.00000 q^{16}\) \(+7.27942 q^{17}\) \(+2.51722 q^{18}\) \(+5.41346 q^{19}\) \(+0.658132 q^{20}\) \(-1.91089 q^{21}\) \(+3.14857 q^{22}\) \(+1.00000 q^{23}\) \(-0.694821 q^{24}\) \(-4.56686 q^{25}\) \(+1.49529 q^{26}\) \(-3.83348 q^{27}\) \(-2.75018 q^{28}\) \(+7.88069 q^{29}\) \(-0.457284 q^{30}\) \(-1.13470 q^{31}\) \(-1.00000 q^{32}\) \(-2.18769 q^{33}\) \(-7.27942 q^{34}\) \(-1.80998 q^{35}\) \(-2.51722 q^{36}\) \(-0.745843 q^{37}\) \(-5.41346 q^{38}\) \(-1.03896 q^{39}\) \(-0.658132 q^{40}\) \(+0.571803 q^{41}\) \(+1.91089 q^{42}\) \(+5.56529 q^{43}\) \(-3.14857 q^{44}\) \(-1.65666 q^{45}\) \(-1.00000 q^{46}\) \(+0.938950 q^{47}\) \(+0.694821 q^{48}\) \(+0.563515 q^{49}\) \(+4.56686 q^{50}\) \(+5.05790 q^{51}\) \(-1.49529 q^{52}\) \(-10.5215 q^{53}\) \(+3.83348 q^{54}\) \(-2.07217 q^{55}\) \(+2.75018 q^{56}\) \(+3.76139 q^{57}\) \(-7.88069 q^{58}\) \(-6.71876 q^{59}\) \(+0.457284 q^{60}\) \(+12.7225 q^{61}\) \(+1.13470 q^{62}\) \(+6.92283 q^{63}\) \(+1.00000 q^{64}\) \(-0.984094 q^{65}\) \(+2.18769 q^{66}\) \(+6.08507 q^{67}\) \(+7.27942 q^{68}\) \(+0.694821 q^{69}\) \(+1.80998 q^{70}\) \(-8.32793 q^{71}\) \(+2.51722 q^{72}\) \(+8.52483 q^{73}\) \(+0.745843 q^{74}\) \(-3.17315 q^{75}\) \(+5.41346 q^{76}\) \(+8.65916 q^{77}\) \(+1.03896 q^{78}\) \(+0.159145 q^{79}\) \(+0.658132 q^{80}\) \(+4.88809 q^{81}\) \(-0.571803 q^{82}\) \(-1.60969 q^{83}\) \(-1.91089 q^{84}\) \(+4.79082 q^{85}\) \(-5.56529 q^{86}\) \(+5.47567 q^{87}\) \(+3.14857 q^{88}\) \(-15.4922 q^{89}\) \(+1.65666 q^{90}\) \(+4.11231 q^{91}\) \(+1.00000 q^{92}\) \(-0.788414 q^{93}\) \(-0.938950 q^{94}\) \(+3.56277 q^{95}\) \(-0.694821 q^{96}\) \(-9.93497 q^{97}\) \(-0.563515 q^{98}\) \(+7.92566 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.694821 0.401155 0.200578 0.979678i \(-0.435718\pi\)
0.200578 + 0.979678i \(0.435718\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.658132 0.294325 0.147163 0.989112i \(-0.452986\pi\)
0.147163 + 0.989112i \(0.452986\pi\)
\(6\) −0.694821 −0.283660
\(7\) −2.75018 −1.03947 −0.519736 0.854327i \(-0.673970\pi\)
−0.519736 + 0.854327i \(0.673970\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.51722 −0.839075
\(10\) −0.658132 −0.208119
\(11\) −3.14857 −0.949330 −0.474665 0.880166i \(-0.657431\pi\)
−0.474665 + 0.880166i \(0.657431\pi\)
\(12\) 0.694821 0.200578
\(13\) −1.49529 −0.414718 −0.207359 0.978265i \(-0.566487\pi\)
−0.207359 + 0.978265i \(0.566487\pi\)
\(14\) 2.75018 0.735018
\(15\) 0.457284 0.118070
\(16\) 1.00000 0.250000
\(17\) 7.27942 1.76552 0.882759 0.469825i \(-0.155683\pi\)
0.882759 + 0.469825i \(0.155683\pi\)
\(18\) 2.51722 0.593315
\(19\) 5.41346 1.24193 0.620967 0.783837i \(-0.286740\pi\)
0.620967 + 0.783837i \(0.286740\pi\)
\(20\) 0.658132 0.147163
\(21\) −1.91089 −0.416990
\(22\) 3.14857 0.671278
\(23\) 1.00000 0.208514
\(24\) −0.694821 −0.141830
\(25\) −4.56686 −0.913373
\(26\) 1.49529 0.293250
\(27\) −3.83348 −0.737754
\(28\) −2.75018 −0.519736
\(29\) 7.88069 1.46341 0.731703 0.681623i \(-0.238726\pi\)
0.731703 + 0.681623i \(0.238726\pi\)
\(30\) −0.457284 −0.0834882
\(31\) −1.13470 −0.203798 −0.101899 0.994795i \(-0.532492\pi\)
−0.101899 + 0.994795i \(0.532492\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.18769 −0.380829
\(34\) −7.27942 −1.24841
\(35\) −1.80998 −0.305943
\(36\) −2.51722 −0.419537
\(37\) −0.745843 −0.122616 −0.0613079 0.998119i \(-0.519527\pi\)
−0.0613079 + 0.998119i \(0.519527\pi\)
\(38\) −5.41346 −0.878179
\(39\) −1.03896 −0.166366
\(40\) −0.658132 −0.104060
\(41\) 0.571803 0.0893006 0.0446503 0.999003i \(-0.485783\pi\)
0.0446503 + 0.999003i \(0.485783\pi\)
\(42\) 1.91089 0.294856
\(43\) 5.56529 0.848698 0.424349 0.905499i \(-0.360503\pi\)
0.424349 + 0.905499i \(0.360503\pi\)
\(44\) −3.14857 −0.474665
\(45\) −1.65666 −0.246961
\(46\) −1.00000 −0.147442
\(47\) 0.938950 0.136960 0.0684799 0.997652i \(-0.478185\pi\)
0.0684799 + 0.997652i \(0.478185\pi\)
\(48\) 0.694821 0.100289
\(49\) 0.563515 0.0805022
\(50\) 4.56686 0.645852
\(51\) 5.05790 0.708247
\(52\) −1.49529 −0.207359
\(53\) −10.5215 −1.44523 −0.722617 0.691248i \(-0.757061\pi\)
−0.722617 + 0.691248i \(0.757061\pi\)
\(54\) 3.83348 0.521671
\(55\) −2.07217 −0.279412
\(56\) 2.75018 0.367509
\(57\) 3.76139 0.498208
\(58\) −7.88069 −1.03478
\(59\) −6.71876 −0.874707 −0.437354 0.899290i \(-0.644084\pi\)
−0.437354 + 0.899290i \(0.644084\pi\)
\(60\) 0.457284 0.0590351
\(61\) 12.7225 1.62895 0.814473 0.580201i \(-0.197026\pi\)
0.814473 + 0.580201i \(0.197026\pi\)
\(62\) 1.13470 0.144107
\(63\) 6.92283 0.872195
\(64\) 1.00000 0.125000
\(65\) −0.984094 −0.122062
\(66\) 2.18769 0.269287
\(67\) 6.08507 0.743410 0.371705 0.928351i \(-0.378773\pi\)
0.371705 + 0.928351i \(0.378773\pi\)
\(68\) 7.27942 0.882759
\(69\) 0.694821 0.0836466
\(70\) 1.80998 0.216334
\(71\) −8.32793 −0.988343 −0.494172 0.869364i \(-0.664529\pi\)
−0.494172 + 0.869364i \(0.664529\pi\)
\(72\) 2.51722 0.296658
\(73\) 8.52483 0.997756 0.498878 0.866672i \(-0.333746\pi\)
0.498878 + 0.866672i \(0.333746\pi\)
\(74\) 0.745843 0.0867025
\(75\) −3.17315 −0.366404
\(76\) 5.41346 0.620967
\(77\) 8.65916 0.986802
\(78\) 1.03896 0.117639
\(79\) 0.159145 0.0179053 0.00895263 0.999960i \(-0.497150\pi\)
0.00895263 + 0.999960i \(0.497150\pi\)
\(80\) 0.658132 0.0735813
\(81\) 4.88809 0.543121
\(82\) −0.571803 −0.0631451
\(83\) −1.60969 −0.176687 −0.0883433 0.996090i \(-0.528157\pi\)
−0.0883433 + 0.996090i \(0.528157\pi\)
\(84\) −1.91089 −0.208495
\(85\) 4.79082 0.519637
\(86\) −5.56529 −0.600120
\(87\) 5.47567 0.587053
\(88\) 3.14857 0.335639
\(89\) −15.4922 −1.64217 −0.821084 0.570808i \(-0.806630\pi\)
−0.821084 + 0.570808i \(0.806630\pi\)
\(90\) 1.65666 0.174628
\(91\) 4.11231 0.431087
\(92\) 1.00000 0.104257
\(93\) −0.788414 −0.0817548
\(94\) −0.938950 −0.0968452
\(95\) 3.56277 0.365532
\(96\) −0.694821 −0.0709149
\(97\) −9.93497 −1.00874 −0.504372 0.863487i \(-0.668276\pi\)
−0.504372 + 0.863487i \(0.668276\pi\)
\(98\) −0.563515 −0.0569236
\(99\) 7.92566 0.796559
\(100\) −4.56686 −0.456686
\(101\) 13.8875 1.38186 0.690931 0.722921i \(-0.257201\pi\)
0.690931 + 0.722921i \(0.257201\pi\)
\(102\) −5.05790 −0.500806
\(103\) −5.75577 −0.567133 −0.283566 0.958953i \(-0.591518\pi\)
−0.283566 + 0.958953i \(0.591518\pi\)
\(104\) 1.49529 0.146625
\(105\) −1.25761 −0.122731
\(106\) 10.5215 1.02194
\(107\) −16.1338 −1.55971 −0.779856 0.625959i \(-0.784708\pi\)
−0.779856 + 0.625959i \(0.784708\pi\)
\(108\) −3.83348 −0.368877
\(109\) −8.74861 −0.837965 −0.418983 0.907994i \(-0.637613\pi\)
−0.418983 + 0.907994i \(0.637613\pi\)
\(110\) 2.07217 0.197574
\(111\) −0.518227 −0.0491880
\(112\) −2.75018 −0.259868
\(113\) −5.92802 −0.557661 −0.278831 0.960340i \(-0.589947\pi\)
−0.278831 + 0.960340i \(0.589947\pi\)
\(114\) −3.76139 −0.352286
\(115\) 0.658132 0.0613711
\(116\) 7.88069 0.731703
\(117\) 3.76397 0.347979
\(118\) 6.71876 0.618512
\(119\) −20.0198 −1.83521
\(120\) −0.457284 −0.0417441
\(121\) −1.08649 −0.0987720
\(122\) −12.7225 −1.15184
\(123\) 0.397301 0.0358234
\(124\) −1.13470 −0.101899
\(125\) −6.29625 −0.563154
\(126\) −6.92283 −0.616735
\(127\) 5.50278 0.488293 0.244146 0.969738i \(-0.421492\pi\)
0.244146 + 0.969738i \(0.421492\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.86688 0.340460
\(130\) 0.984094 0.0863108
\(131\) 1.00000 0.0873704
\(132\) −2.18769 −0.190414
\(133\) −14.8880 −1.29095
\(134\) −6.08507 −0.525670
\(135\) −2.52294 −0.217140
\(136\) −7.27942 −0.624205
\(137\) 4.71028 0.402426 0.201213 0.979547i \(-0.435512\pi\)
0.201213 + 0.979547i \(0.435512\pi\)
\(138\) −0.694821 −0.0591471
\(139\) −7.19628 −0.610380 −0.305190 0.952291i \(-0.598720\pi\)
−0.305190 + 0.952291i \(0.598720\pi\)
\(140\) −1.80998 −0.152972
\(141\) 0.652402 0.0549422
\(142\) 8.32793 0.698864
\(143\) 4.70801 0.393704
\(144\) −2.51722 −0.209769
\(145\) 5.18653 0.430718
\(146\) −8.52483 −0.705520
\(147\) 0.391542 0.0322939
\(148\) −0.745843 −0.0613079
\(149\) −21.7636 −1.78295 −0.891473 0.453074i \(-0.850327\pi\)
−0.891473 + 0.453074i \(0.850327\pi\)
\(150\) 3.17315 0.259087
\(151\) −24.1261 −1.96336 −0.981678 0.190548i \(-0.938974\pi\)
−0.981678 + 0.190548i \(0.938974\pi\)
\(152\) −5.41346 −0.439090
\(153\) −18.3239 −1.48140
\(154\) −8.65916 −0.697775
\(155\) −0.746783 −0.0599830
\(156\) −1.03896 −0.0831830
\(157\) 4.29518 0.342793 0.171396 0.985202i \(-0.445172\pi\)
0.171396 + 0.985202i \(0.445172\pi\)
\(158\) −0.159145 −0.0126609
\(159\) −7.31054 −0.579763
\(160\) −0.658132 −0.0520299
\(161\) −2.75018 −0.216745
\(162\) −4.88809 −0.384044
\(163\) −12.5454 −0.982628 −0.491314 0.870983i \(-0.663483\pi\)
−0.491314 + 0.870983i \(0.663483\pi\)
\(164\) 0.571803 0.0446503
\(165\) −1.43979 −0.112088
\(166\) 1.60969 0.124936
\(167\) −0.118125 −0.00914077 −0.00457038 0.999990i \(-0.501455\pi\)
−0.00457038 + 0.999990i \(0.501455\pi\)
\(168\) 1.91089 0.147428
\(169\) −10.7641 −0.828009
\(170\) −4.79082 −0.367439
\(171\) −13.6269 −1.04207
\(172\) 5.56529 0.424349
\(173\) 1.22616 0.0932232 0.0466116 0.998913i \(-0.485158\pi\)
0.0466116 + 0.998913i \(0.485158\pi\)
\(174\) −5.47567 −0.415109
\(175\) 12.5597 0.949425
\(176\) −3.14857 −0.237333
\(177\) −4.66833 −0.350893
\(178\) 15.4922 1.16119
\(179\) 21.1353 1.57972 0.789862 0.613284i \(-0.210152\pi\)
0.789862 + 0.613284i \(0.210152\pi\)
\(180\) −1.65666 −0.123480
\(181\) 3.70932 0.275712 0.137856 0.990452i \(-0.455979\pi\)
0.137856 + 0.990452i \(0.455979\pi\)
\(182\) −4.11231 −0.304825
\(183\) 8.83985 0.653460
\(184\) −1.00000 −0.0737210
\(185\) −0.490863 −0.0360890
\(186\) 0.788414 0.0578093
\(187\) −22.9198 −1.67606
\(188\) 0.938950 0.0684799
\(189\) 10.5428 0.766875
\(190\) −3.56277 −0.258470
\(191\) −14.9726 −1.08338 −0.541689 0.840579i \(-0.682215\pi\)
−0.541689 + 0.840579i \(0.682215\pi\)
\(192\) 0.694821 0.0501444
\(193\) 4.67809 0.336736 0.168368 0.985724i \(-0.446150\pi\)
0.168368 + 0.985724i \(0.446150\pi\)
\(194\) 9.93497 0.713290
\(195\) −0.683770 −0.0489658
\(196\) 0.563515 0.0402511
\(197\) −16.3000 −1.16133 −0.580664 0.814144i \(-0.697207\pi\)
−0.580664 + 0.814144i \(0.697207\pi\)
\(198\) −7.92566 −0.563252
\(199\) −27.1378 −1.92375 −0.961875 0.273490i \(-0.911822\pi\)
−0.961875 + 0.273490i \(0.911822\pi\)
\(200\) 4.56686 0.322926
\(201\) 4.22804 0.298223
\(202\) −13.8875 −0.977124
\(203\) −21.6733 −1.52117
\(204\) 5.05790 0.354124
\(205\) 0.376322 0.0262834
\(206\) 5.75577 0.401023
\(207\) −2.51722 −0.174959
\(208\) −1.49529 −0.103679
\(209\) −17.0447 −1.17900
\(210\) 1.25761 0.0867837
\(211\) 13.6348 0.938658 0.469329 0.883023i \(-0.344496\pi\)
0.469329 + 0.883023i \(0.344496\pi\)
\(212\) −10.5215 −0.722617
\(213\) −5.78642 −0.396479
\(214\) 16.1338 1.10288
\(215\) 3.66269 0.249793
\(216\) 3.83348 0.260836
\(217\) 3.12064 0.211843
\(218\) 8.74861 0.592531
\(219\) 5.92323 0.400255
\(220\) −2.07217 −0.139706
\(221\) −10.8848 −0.732192
\(222\) 0.518227 0.0347811
\(223\) −21.2600 −1.42367 −0.711836 0.702346i \(-0.752136\pi\)
−0.711836 + 0.702346i \(0.752136\pi\)
\(224\) 2.75018 0.183754
\(225\) 11.4958 0.766388
\(226\) 5.92802 0.394326
\(227\) −0.670276 −0.0444878 −0.0222439 0.999753i \(-0.507081\pi\)
−0.0222439 + 0.999753i \(0.507081\pi\)
\(228\) 3.76139 0.249104
\(229\) 11.9142 0.787314 0.393657 0.919257i \(-0.371210\pi\)
0.393657 + 0.919257i \(0.371210\pi\)
\(230\) −0.658132 −0.0433959
\(231\) 6.01656 0.395861
\(232\) −7.88069 −0.517392
\(233\) −0.864723 −0.0566499 −0.0283250 0.999599i \(-0.509017\pi\)
−0.0283250 + 0.999599i \(0.509017\pi\)
\(234\) −3.76397 −0.246058
\(235\) 0.617952 0.0403108
\(236\) −6.71876 −0.437354
\(237\) 0.110578 0.00718279
\(238\) 20.0198 1.29769
\(239\) 22.8758 1.47971 0.739855 0.672767i \(-0.234894\pi\)
0.739855 + 0.672767i \(0.234894\pi\)
\(240\) 0.457284 0.0295175
\(241\) −11.8143 −0.761025 −0.380513 0.924776i \(-0.624252\pi\)
−0.380513 + 0.924776i \(0.624252\pi\)
\(242\) 1.08649 0.0698423
\(243\) 14.8968 0.955630
\(244\) 12.7225 0.814473
\(245\) 0.370867 0.0236938
\(246\) −0.397301 −0.0253310
\(247\) −8.09467 −0.515051
\(248\) 1.13470 0.0720536
\(249\) −1.11845 −0.0708787
\(250\) 6.29625 0.398210
\(251\) −20.0470 −1.26536 −0.632679 0.774414i \(-0.718045\pi\)
−0.632679 + 0.774414i \(0.718045\pi\)
\(252\) 6.92283 0.436097
\(253\) −3.14857 −0.197949
\(254\) −5.50278 −0.345275
\(255\) 3.32876 0.208455
\(256\) 1.00000 0.0625000
\(257\) −3.31472 −0.206767 −0.103383 0.994642i \(-0.532967\pi\)
−0.103383 + 0.994642i \(0.532967\pi\)
\(258\) −3.86688 −0.240741
\(259\) 2.05121 0.127456
\(260\) −0.984094 −0.0610309
\(261\) −19.8374 −1.22791
\(262\) −1.00000 −0.0617802
\(263\) −13.7906 −0.850366 −0.425183 0.905107i \(-0.639790\pi\)
−0.425183 + 0.905107i \(0.639790\pi\)
\(264\) 2.18769 0.134643
\(265\) −6.92451 −0.425369
\(266\) 14.8880 0.912843
\(267\) −10.7643 −0.658764
\(268\) 6.08507 0.371705
\(269\) 5.73083 0.349415 0.174708 0.984620i \(-0.444102\pi\)
0.174708 + 0.984620i \(0.444102\pi\)
\(270\) 2.52294 0.153541
\(271\) −2.53205 −0.153811 −0.0769056 0.997038i \(-0.524504\pi\)
−0.0769056 + 0.997038i \(0.524504\pi\)
\(272\) 7.27942 0.441380
\(273\) 2.85732 0.172933
\(274\) −4.71028 −0.284558
\(275\) 14.3791 0.867092
\(276\) 0.694821 0.0418233
\(277\) 4.29884 0.258292 0.129146 0.991626i \(-0.458776\pi\)
0.129146 + 0.991626i \(0.458776\pi\)
\(278\) 7.19628 0.431604
\(279\) 2.85630 0.171002
\(280\) 1.80998 0.108167
\(281\) 1.97574 0.117863 0.0589314 0.998262i \(-0.481231\pi\)
0.0589314 + 0.998262i \(0.481231\pi\)
\(282\) −0.652402 −0.0388500
\(283\) −12.8507 −0.763893 −0.381946 0.924185i \(-0.624746\pi\)
−0.381946 + 0.924185i \(0.624746\pi\)
\(284\) −8.32793 −0.494172
\(285\) 2.47549 0.146635
\(286\) −4.70801 −0.278391
\(287\) −1.57256 −0.0928255
\(288\) 2.51722 0.148329
\(289\) 35.9900 2.11706
\(290\) −5.18653 −0.304563
\(291\) −6.90303 −0.404663
\(292\) 8.52483 0.498878
\(293\) 29.0896 1.69943 0.849717 0.527239i \(-0.176773\pi\)
0.849717 + 0.527239i \(0.176773\pi\)
\(294\) −0.391542 −0.0228352
\(295\) −4.42183 −0.257449
\(296\) 0.745843 0.0433512
\(297\) 12.0700 0.700372
\(298\) 21.7636 1.26073
\(299\) −1.49529 −0.0864746
\(300\) −3.17315 −0.183202
\(301\) −15.3056 −0.882198
\(302\) 24.1261 1.38830
\(303\) 9.64936 0.554341
\(304\) 5.41346 0.310483
\(305\) 8.37306 0.479440
\(306\) 18.3239 1.04751
\(307\) 0.792769 0.0452457 0.0226228 0.999744i \(-0.492798\pi\)
0.0226228 + 0.999744i \(0.492798\pi\)
\(308\) 8.65916 0.493401
\(309\) −3.99923 −0.227508
\(310\) 0.746783 0.0424144
\(311\) 13.7086 0.777346 0.388673 0.921376i \(-0.372934\pi\)
0.388673 + 0.921376i \(0.372934\pi\)
\(312\) 1.03896 0.0588193
\(313\) 20.3914 1.15259 0.576295 0.817241i \(-0.304498\pi\)
0.576295 + 0.817241i \(0.304498\pi\)
\(314\) −4.29518 −0.242391
\(315\) 4.55613 0.256709
\(316\) 0.159145 0.00895263
\(317\) 18.9589 1.06484 0.532420 0.846481i \(-0.321283\pi\)
0.532420 + 0.846481i \(0.321283\pi\)
\(318\) 7.31054 0.409955
\(319\) −24.8129 −1.38926
\(320\) 0.658132 0.0367907
\(321\) −11.2101 −0.625687
\(322\) 2.75018 0.153262
\(323\) 39.4069 2.19266
\(324\) 4.88809 0.271560
\(325\) 6.82876 0.378792
\(326\) 12.5454 0.694823
\(327\) −6.07872 −0.336154
\(328\) −0.571803 −0.0315725
\(329\) −2.58228 −0.142366
\(330\) 1.43979 0.0792579
\(331\) −30.7041 −1.68765 −0.843825 0.536619i \(-0.819701\pi\)
−0.843825 + 0.536619i \(0.819701\pi\)
\(332\) −1.60969 −0.0883433
\(333\) 1.87745 0.102884
\(334\) 0.118125 0.00646350
\(335\) 4.00478 0.218804
\(336\) −1.91089 −0.104247
\(337\) −32.2210 −1.75519 −0.877594 0.479405i \(-0.840853\pi\)
−0.877594 + 0.479405i \(0.840853\pi\)
\(338\) 10.7641 0.585491
\(339\) −4.11891 −0.223709
\(340\) 4.79082 0.259819
\(341\) 3.57269 0.193472
\(342\) 13.6269 0.736858
\(343\) 17.7015 0.955792
\(344\) −5.56529 −0.300060
\(345\) 0.457284 0.0246193
\(346\) −1.22616 −0.0659187
\(347\) −20.2439 −1.08675 −0.543374 0.839491i \(-0.682853\pi\)
−0.543374 + 0.839491i \(0.682853\pi\)
\(348\) 5.47567 0.293527
\(349\) −11.9773 −0.641133 −0.320566 0.947226i \(-0.603873\pi\)
−0.320566 + 0.947226i \(0.603873\pi\)
\(350\) −12.5597 −0.671345
\(351\) 5.73215 0.305960
\(352\) 3.14857 0.167819
\(353\) −5.21454 −0.277542 −0.138771 0.990325i \(-0.544315\pi\)
−0.138771 + 0.990325i \(0.544315\pi\)
\(354\) 4.66833 0.248119
\(355\) −5.48087 −0.290894
\(356\) −15.4922 −0.821084
\(357\) −13.9101 −0.736203
\(358\) −21.1353 −1.11703
\(359\) 25.9486 1.36951 0.684757 0.728772i \(-0.259908\pi\)
0.684757 + 0.728772i \(0.259908\pi\)
\(360\) 1.65666 0.0873139
\(361\) 10.3056 0.542398
\(362\) −3.70932 −0.194958
\(363\) −0.754917 −0.0396229
\(364\) 4.11231 0.215544
\(365\) 5.61046 0.293665
\(366\) −8.83985 −0.462066
\(367\) −25.0750 −1.30891 −0.654453 0.756103i \(-0.727101\pi\)
−0.654453 + 0.756103i \(0.727101\pi\)
\(368\) 1.00000 0.0521286
\(369\) −1.43936 −0.0749299
\(370\) 0.490863 0.0255187
\(371\) 28.9360 1.50228
\(372\) −0.788414 −0.0408774
\(373\) 24.6352 1.27556 0.637782 0.770217i \(-0.279852\pi\)
0.637782 + 0.770217i \(0.279852\pi\)
\(374\) 22.9198 1.18515
\(375\) −4.37477 −0.225912
\(376\) −0.938950 −0.0484226
\(377\) −11.7839 −0.606900
\(378\) −10.5428 −0.542262
\(379\) −22.2957 −1.14525 −0.572626 0.819817i \(-0.694075\pi\)
−0.572626 + 0.819817i \(0.694075\pi\)
\(380\) 3.56277 0.182766
\(381\) 3.82345 0.195881
\(382\) 14.9726 0.766064
\(383\) 4.31212 0.220339 0.110169 0.993913i \(-0.464861\pi\)
0.110169 + 0.993913i \(0.464861\pi\)
\(384\) −0.694821 −0.0354574
\(385\) 5.69886 0.290441
\(386\) −4.67809 −0.238108
\(387\) −14.0091 −0.712121
\(388\) −9.93497 −0.504372
\(389\) 1.19665 0.0606723 0.0303362 0.999540i \(-0.490342\pi\)
0.0303362 + 0.999540i \(0.490342\pi\)
\(390\) 0.683770 0.0346240
\(391\) 7.27942 0.368136
\(392\) −0.563515 −0.0284618
\(393\) 0.694821 0.0350491
\(394\) 16.3000 0.821182
\(395\) 0.104739 0.00526997
\(396\) 7.92566 0.398279
\(397\) 1.15769 0.0581026 0.0290513 0.999578i \(-0.490751\pi\)
0.0290513 + 0.999578i \(0.490751\pi\)
\(398\) 27.1378 1.36030
\(399\) −10.3445 −0.517873
\(400\) −4.56686 −0.228343
\(401\) −5.23220 −0.261284 −0.130642 0.991430i \(-0.541704\pi\)
−0.130642 + 0.991430i \(0.541704\pi\)
\(402\) −4.22804 −0.210875
\(403\) 1.69670 0.0845187
\(404\) 13.8875 0.690931
\(405\) 3.21700 0.159854
\(406\) 21.6733 1.07563
\(407\) 2.34834 0.116403
\(408\) −5.05790 −0.250403
\(409\) 16.2341 0.802724 0.401362 0.915919i \(-0.368537\pi\)
0.401362 + 0.915919i \(0.368537\pi\)
\(410\) −0.376322 −0.0185852
\(411\) 3.27280 0.161435
\(412\) −5.75577 −0.283566
\(413\) 18.4778 0.909234
\(414\) 2.51722 0.123715
\(415\) −1.05939 −0.0520033
\(416\) 1.49529 0.0733124
\(417\) −5.00012 −0.244857
\(418\) 17.0447 0.833682
\(419\) 0.0219989 0.00107472 0.000537359 1.00000i \(-0.499829\pi\)
0.000537359 1.00000i \(0.499829\pi\)
\(420\) −1.25761 −0.0613653
\(421\) −37.9389 −1.84903 −0.924514 0.381149i \(-0.875529\pi\)
−0.924514 + 0.381149i \(0.875529\pi\)
\(422\) −13.6348 −0.663731
\(423\) −2.36355 −0.114920
\(424\) 10.5215 0.510968
\(425\) −33.2441 −1.61258
\(426\) 5.78642 0.280353
\(427\) −34.9892 −1.69324
\(428\) −16.1338 −0.779856
\(429\) 3.27123 0.157936
\(430\) −3.66269 −0.176631
\(431\) 20.0758 0.967015 0.483508 0.875340i \(-0.339363\pi\)
0.483508 + 0.875340i \(0.339363\pi\)
\(432\) −3.83348 −0.184439
\(433\) −13.8363 −0.664928 −0.332464 0.943116i \(-0.607880\pi\)
−0.332464 + 0.943116i \(0.607880\pi\)
\(434\) −3.12064 −0.149795
\(435\) 3.60371 0.172785
\(436\) −8.74861 −0.418983
\(437\) 5.41346 0.258961
\(438\) −5.92323 −0.283023
\(439\) 0.455439 0.0217369 0.0108685 0.999941i \(-0.496540\pi\)
0.0108685 + 0.999941i \(0.496540\pi\)
\(440\) 2.07217 0.0987871
\(441\) −1.41849 −0.0675473
\(442\) 10.8848 0.517738
\(443\) 22.5855 1.07307 0.536534 0.843879i \(-0.319733\pi\)
0.536534 + 0.843879i \(0.319733\pi\)
\(444\) −0.518227 −0.0245940
\(445\) −10.1959 −0.483332
\(446\) 21.2600 1.00669
\(447\) −15.1218 −0.715238
\(448\) −2.75018 −0.129934
\(449\) 28.3401 1.33745 0.668725 0.743510i \(-0.266840\pi\)
0.668725 + 0.743510i \(0.266840\pi\)
\(450\) −11.4958 −0.541918
\(451\) −1.80036 −0.0847758
\(452\) −5.92802 −0.278831
\(453\) −16.7633 −0.787610
\(454\) 0.670276 0.0314576
\(455\) 2.70644 0.126880
\(456\) −3.76139 −0.176143
\(457\) 1.31355 0.0614455 0.0307227 0.999528i \(-0.490219\pi\)
0.0307227 + 0.999528i \(0.490219\pi\)
\(458\) −11.9142 −0.556715
\(459\) −27.9055 −1.30252
\(460\) 0.658132 0.0306855
\(461\) −28.5051 −1.32761 −0.663807 0.747904i \(-0.731060\pi\)
−0.663807 + 0.747904i \(0.731060\pi\)
\(462\) −6.01656 −0.279916
\(463\) −14.6572 −0.681178 −0.340589 0.940212i \(-0.610626\pi\)
−0.340589 + 0.940212i \(0.610626\pi\)
\(464\) 7.88069 0.365852
\(465\) −0.518880 −0.0240625
\(466\) 0.864723 0.0400575
\(467\) −14.3089 −0.662136 −0.331068 0.943607i \(-0.607409\pi\)
−0.331068 + 0.943607i \(0.607409\pi\)
\(468\) 3.76397 0.173989
\(469\) −16.7351 −0.772754
\(470\) −0.617952 −0.0285040
\(471\) 2.98438 0.137513
\(472\) 6.71876 0.309256
\(473\) −17.5227 −0.805695
\(474\) −0.110578 −0.00507900
\(475\) −24.7225 −1.13435
\(476\) −20.0198 −0.917604
\(477\) 26.4849 1.21266
\(478\) −22.8758 −1.04631
\(479\) −31.9334 −1.45907 −0.729537 0.683942i \(-0.760264\pi\)
−0.729537 + 0.683942i \(0.760264\pi\)
\(480\) −0.457284 −0.0208721
\(481\) 1.11525 0.0508509
\(482\) 11.8143 0.538126
\(483\) −1.91089 −0.0869483
\(484\) −1.08649 −0.0493860
\(485\) −6.53852 −0.296899
\(486\) −14.8968 −0.675732
\(487\) 16.7752 0.760156 0.380078 0.924954i \(-0.375897\pi\)
0.380078 + 0.924954i \(0.375897\pi\)
\(488\) −12.7225 −0.575919
\(489\) −8.71677 −0.394186
\(490\) −0.370867 −0.0167541
\(491\) 7.83418 0.353552 0.176776 0.984251i \(-0.443433\pi\)
0.176776 + 0.984251i \(0.443433\pi\)
\(492\) 0.397301 0.0179117
\(493\) 57.3668 2.58367
\(494\) 8.09467 0.364196
\(495\) 5.21613 0.234448
\(496\) −1.13470 −0.0509496
\(497\) 22.9033 1.02735
\(498\) 1.11845 0.0501188
\(499\) −23.9829 −1.07362 −0.536811 0.843703i \(-0.680371\pi\)
−0.536811 + 0.843703i \(0.680371\pi\)
\(500\) −6.29625 −0.281577
\(501\) −0.0820756 −0.00366687
\(502\) 20.0470 0.894743
\(503\) 17.6562 0.787253 0.393626 0.919271i \(-0.371220\pi\)
0.393626 + 0.919271i \(0.371220\pi\)
\(504\) −6.92283 −0.308367
\(505\) 9.13983 0.406717
\(506\) 3.14857 0.139971
\(507\) −7.47914 −0.332160
\(508\) 5.50278 0.244146
\(509\) 32.5101 1.44098 0.720492 0.693464i \(-0.243916\pi\)
0.720492 + 0.693464i \(0.243916\pi\)
\(510\) −3.32876 −0.147400
\(511\) −23.4449 −1.03714
\(512\) −1.00000 −0.0441942
\(513\) −20.7524 −0.916241
\(514\) 3.31472 0.146206
\(515\) −3.78805 −0.166922
\(516\) 3.86688 0.170230
\(517\) −2.95635 −0.130020
\(518\) −2.05121 −0.0901248
\(519\) 0.851962 0.0373970
\(520\) 0.984094 0.0431554
\(521\) −19.2640 −0.843973 −0.421987 0.906602i \(-0.638667\pi\)
−0.421987 + 0.906602i \(0.638667\pi\)
\(522\) 19.8374 0.868261
\(523\) 8.62009 0.376930 0.188465 0.982080i \(-0.439649\pi\)
0.188465 + 0.982080i \(0.439649\pi\)
\(524\) 1.00000 0.0436852
\(525\) 8.72676 0.380867
\(526\) 13.7906 0.601300
\(527\) −8.25997 −0.359810
\(528\) −2.18769 −0.0952072
\(529\) 1.00000 0.0434783
\(530\) 6.92451 0.300782
\(531\) 16.9126 0.733945
\(532\) −14.8880 −0.645477
\(533\) −0.855009 −0.0370345
\(534\) 10.7643 0.465816
\(535\) −10.6182 −0.459063
\(536\) −6.08507 −0.262835
\(537\) 14.6852 0.633715
\(538\) −5.73083 −0.247074
\(539\) −1.77427 −0.0764232
\(540\) −2.52294 −0.108570
\(541\) −27.5731 −1.18546 −0.592730 0.805401i \(-0.701950\pi\)
−0.592730 + 0.805401i \(0.701950\pi\)
\(542\) 2.53205 0.108761
\(543\) 2.57732 0.110603
\(544\) −7.27942 −0.312103
\(545\) −5.75774 −0.246634
\(546\) −2.85732 −0.122282
\(547\) −13.4317 −0.574300 −0.287150 0.957886i \(-0.592708\pi\)
−0.287150 + 0.957886i \(0.592708\pi\)
\(548\) 4.71028 0.201213
\(549\) −32.0253 −1.36681
\(550\) −14.3791 −0.613127
\(551\) 42.6618 1.81745
\(552\) −0.694821 −0.0295736
\(553\) −0.437679 −0.0186120
\(554\) −4.29884 −0.182640
\(555\) −0.341062 −0.0144773
\(556\) −7.19628 −0.305190
\(557\) 19.0470 0.807049 0.403525 0.914969i \(-0.367785\pi\)
0.403525 + 0.914969i \(0.367785\pi\)
\(558\) −2.85630 −0.120917
\(559\) −8.32169 −0.351970
\(560\) −1.80998 −0.0764858
\(561\) −15.9252 −0.672360
\(562\) −1.97574 −0.0833415
\(563\) −16.4054 −0.691407 −0.345704 0.938344i \(-0.612360\pi\)
−0.345704 + 0.938344i \(0.612360\pi\)
\(564\) 0.652402 0.0274711
\(565\) −3.90142 −0.164134
\(566\) 12.8507 0.540154
\(567\) −13.4431 −0.564559
\(568\) 8.32793 0.349432
\(569\) 17.2800 0.724413 0.362207 0.932098i \(-0.382023\pi\)
0.362207 + 0.932098i \(0.382023\pi\)
\(570\) −2.47549 −0.103687
\(571\) 45.6655 1.91104 0.955521 0.294922i \(-0.0952937\pi\)
0.955521 + 0.294922i \(0.0952937\pi\)
\(572\) 4.70801 0.196852
\(573\) −10.4033 −0.434603
\(574\) 1.57256 0.0656375
\(575\) −4.56686 −0.190451
\(576\) −2.51722 −0.104884
\(577\) −24.0912 −1.00293 −0.501465 0.865178i \(-0.667205\pi\)
−0.501465 + 0.865178i \(0.667205\pi\)
\(578\) −35.9900 −1.49699
\(579\) 3.25044 0.135083
\(580\) 5.18653 0.215359
\(581\) 4.42695 0.183661
\(582\) 6.90303 0.286140
\(583\) 33.1276 1.37201
\(584\) −8.52483 −0.352760
\(585\) 2.47719 0.102419
\(586\) −29.0896 −1.20168
\(587\) 15.1134 0.623797 0.311899 0.950115i \(-0.399035\pi\)
0.311899 + 0.950115i \(0.399035\pi\)
\(588\) 0.391542 0.0161469
\(589\) −6.14266 −0.253104
\(590\) 4.42183 0.182044
\(591\) −11.3256 −0.465872
\(592\) −0.745843 −0.0306540
\(593\) −23.9030 −0.981578 −0.490789 0.871278i \(-0.663291\pi\)
−0.490789 + 0.871278i \(0.663291\pi\)
\(594\) −12.0700 −0.495238
\(595\) −13.1756 −0.540148
\(596\) −21.7636 −0.891473
\(597\) −18.8559 −0.771722
\(598\) 1.49529 0.0611468
\(599\) −17.9812 −0.734692 −0.367346 0.930084i \(-0.619734\pi\)
−0.367346 + 0.930084i \(0.619734\pi\)
\(600\) 3.17315 0.129543
\(601\) −21.4257 −0.873971 −0.436986 0.899469i \(-0.643954\pi\)
−0.436986 + 0.899469i \(0.643954\pi\)
\(602\) 15.3056 0.623808
\(603\) −15.3175 −0.623777
\(604\) −24.1261 −0.981678
\(605\) −0.715054 −0.0290711
\(606\) −9.64936 −0.391978
\(607\) 8.29982 0.336879 0.168440 0.985712i \(-0.446127\pi\)
0.168440 + 0.985712i \(0.446127\pi\)
\(608\) −5.41346 −0.219545
\(609\) −15.0591 −0.610225
\(610\) −8.37306 −0.339015
\(611\) −1.40400 −0.0567997
\(612\) −18.3239 −0.740701
\(613\) −12.5208 −0.505709 −0.252854 0.967504i \(-0.581369\pi\)
−0.252854 + 0.967504i \(0.581369\pi\)
\(614\) −0.792769 −0.0319935
\(615\) 0.261476 0.0105437
\(616\) −8.65916 −0.348887
\(617\) −17.7025 −0.712675 −0.356337 0.934357i \(-0.615975\pi\)
−0.356337 + 0.934357i \(0.615975\pi\)
\(618\) 3.99923 0.160873
\(619\) 16.2196 0.651920 0.325960 0.945384i \(-0.394313\pi\)
0.325960 + 0.945384i \(0.394313\pi\)
\(620\) −0.746783 −0.0299915
\(621\) −3.83348 −0.153832
\(622\) −13.7086 −0.549667
\(623\) 42.6063 1.70699
\(624\) −1.03896 −0.0415915
\(625\) 18.6905 0.747622
\(626\) −20.3914 −0.815005
\(627\) −11.8430 −0.472964
\(628\) 4.29518 0.171396
\(629\) −5.42930 −0.216481
\(630\) −4.55613 −0.181521
\(631\) −23.3358 −0.928984 −0.464492 0.885577i \(-0.653763\pi\)
−0.464492 + 0.885577i \(0.653763\pi\)
\(632\) −0.159145 −0.00633047
\(633\) 9.47374 0.376547
\(634\) −18.9589 −0.752955
\(635\) 3.62155 0.143717
\(636\) −7.31054 −0.289882
\(637\) −0.842616 −0.0333857
\(638\) 24.8129 0.982352
\(639\) 20.9633 0.829293
\(640\) −0.658132 −0.0260149
\(641\) 39.9053 1.57617 0.788083 0.615570i \(-0.211074\pi\)
0.788083 + 0.615570i \(0.211074\pi\)
\(642\) 11.2101 0.442427
\(643\) −34.2542 −1.35085 −0.675426 0.737427i \(-0.736040\pi\)
−0.675426 + 0.737427i \(0.736040\pi\)
\(644\) −2.75018 −0.108372
\(645\) 2.54492 0.100206
\(646\) −39.4069 −1.55044
\(647\) −35.6578 −1.40185 −0.700926 0.713234i \(-0.747230\pi\)
−0.700926 + 0.713234i \(0.747230\pi\)
\(648\) −4.88809 −0.192022
\(649\) 21.1545 0.830386
\(650\) −6.82876 −0.267846
\(651\) 2.16829 0.0849818
\(652\) −12.5454 −0.491314
\(653\) −29.8576 −1.16842 −0.584210 0.811603i \(-0.698596\pi\)
−0.584210 + 0.811603i \(0.698596\pi\)
\(654\) 6.07872 0.237697
\(655\) 0.658132 0.0257153
\(656\) 0.571803 0.0223252
\(657\) −21.4589 −0.837192
\(658\) 2.58228 0.100668
\(659\) 33.4901 1.30459 0.652295 0.757966i \(-0.273807\pi\)
0.652295 + 0.757966i \(0.273807\pi\)
\(660\) −1.43979 −0.0560438
\(661\) 33.6795 1.30998 0.654991 0.755637i \(-0.272672\pi\)
0.654991 + 0.755637i \(0.272672\pi\)
\(662\) 30.7041 1.19335
\(663\) −7.56300 −0.293722
\(664\) 1.60969 0.0624681
\(665\) −9.79827 −0.379961
\(666\) −1.87745 −0.0727498
\(667\) 7.88069 0.305141
\(668\) −0.118125 −0.00457038
\(669\) −14.7719 −0.571114
\(670\) −4.00478 −0.154718
\(671\) −40.0576 −1.54641
\(672\) 1.91089 0.0737140
\(673\) 0.514315 0.0198254 0.00991270 0.999951i \(-0.496845\pi\)
0.00991270 + 0.999951i \(0.496845\pi\)
\(674\) 32.2210 1.24111
\(675\) 17.5070 0.673845
\(676\) −10.7641 −0.414005
\(677\) 48.4923 1.86371 0.931856 0.362829i \(-0.118189\pi\)
0.931856 + 0.362829i \(0.118189\pi\)
\(678\) 4.11891 0.158186
\(679\) 27.3230 1.04856
\(680\) −4.79082 −0.183719
\(681\) −0.465722 −0.0178465
\(682\) −3.57269 −0.136805
\(683\) −18.3406 −0.701784 −0.350892 0.936416i \(-0.614122\pi\)
−0.350892 + 0.936416i \(0.614122\pi\)
\(684\) −13.6269 −0.521037
\(685\) 3.09998 0.118444
\(686\) −17.7015 −0.675847
\(687\) 8.27825 0.315835
\(688\) 5.56529 0.212175
\(689\) 15.7326 0.599364
\(690\) −0.457284 −0.0174085
\(691\) −6.76233 −0.257251 −0.128625 0.991693i \(-0.541057\pi\)
−0.128625 + 0.991693i \(0.541057\pi\)
\(692\) 1.22616 0.0466116
\(693\) −21.7970 −0.828001
\(694\) 20.2439 0.768447
\(695\) −4.73610 −0.179650
\(696\) −5.47567 −0.207555
\(697\) 4.16239 0.157662
\(698\) 11.9773 0.453349
\(699\) −0.600828 −0.0227254
\(700\) 12.5597 0.474713
\(701\) 11.8954 0.449284 0.224642 0.974441i \(-0.427879\pi\)
0.224642 + 0.974441i \(0.427879\pi\)
\(702\) −5.73215 −0.216346
\(703\) −4.03759 −0.152281
\(704\) −3.14857 −0.118666
\(705\) 0.429366 0.0161709
\(706\) 5.21454 0.196252
\(707\) −38.1933 −1.43641
\(708\) −4.66833 −0.175447
\(709\) −29.8736 −1.12193 −0.560963 0.827841i \(-0.689569\pi\)
−0.560963 + 0.827841i \(0.689569\pi\)
\(710\) 5.48087 0.205693
\(711\) −0.400605 −0.0150239
\(712\) 15.4922 0.580594
\(713\) −1.13470 −0.0424949
\(714\) 13.9101 0.520574
\(715\) 3.09849 0.115877
\(716\) 21.1353 0.789862
\(717\) 15.8946 0.593593
\(718\) −25.9486 −0.968392
\(719\) 10.2261 0.381368 0.190684 0.981651i \(-0.438929\pi\)
0.190684 + 0.981651i \(0.438929\pi\)
\(720\) −1.65666 −0.0617402
\(721\) 15.8294 0.589519
\(722\) −10.3056 −0.383533
\(723\) −8.20882 −0.305289
\(724\) 3.70932 0.137856
\(725\) −35.9900 −1.33664
\(726\) 0.754917 0.0280176
\(727\) −28.7802 −1.06740 −0.533700 0.845674i \(-0.679199\pi\)
−0.533700 + 0.845674i \(0.679199\pi\)
\(728\) −4.11231 −0.152412
\(729\) −4.31365 −0.159765
\(730\) −5.61046 −0.207653
\(731\) 40.5121 1.49839
\(732\) 8.83985 0.326730
\(733\) 3.54184 0.130821 0.0654104 0.997858i \(-0.479164\pi\)
0.0654104 + 0.997858i \(0.479164\pi\)
\(734\) 25.0750 0.925536
\(735\) 0.257686 0.00950491
\(736\) −1.00000 −0.0368605
\(737\) −19.1593 −0.705742
\(738\) 1.43936 0.0529834
\(739\) −29.6310 −1.08999 −0.544997 0.838438i \(-0.683469\pi\)
−0.544997 + 0.838438i \(0.683469\pi\)
\(740\) −0.490863 −0.0180445
\(741\) −5.62435 −0.206616
\(742\) −28.9360 −1.06227
\(743\) 46.9697 1.72315 0.861576 0.507629i \(-0.169478\pi\)
0.861576 + 0.507629i \(0.169478\pi\)
\(744\) 0.788414 0.0289047
\(745\) −14.3233 −0.524766
\(746\) −24.6352 −0.901960
\(747\) 4.05195 0.148253
\(748\) −22.9198 −0.838030
\(749\) 44.3709 1.62128
\(750\) 4.37477 0.159744
\(751\) −12.1831 −0.444567 −0.222284 0.974982i \(-0.571351\pi\)
−0.222284 + 0.974982i \(0.571351\pi\)
\(752\) 0.938950 0.0342400
\(753\) −13.9291 −0.507605
\(754\) 11.7839 0.429143
\(755\) −15.8782 −0.577865
\(756\) 10.5428 0.383437
\(757\) 37.3316 1.35684 0.678419 0.734675i \(-0.262665\pi\)
0.678419 + 0.734675i \(0.262665\pi\)
\(758\) 22.2957 0.809815
\(759\) −2.18769 −0.0794083
\(760\) −3.56277 −0.129235
\(761\) 18.3068 0.663620 0.331810 0.943346i \(-0.392341\pi\)
0.331810 + 0.943346i \(0.392341\pi\)
\(762\) −3.82345 −0.138509
\(763\) 24.0603 0.871041
\(764\) −14.9726 −0.541689
\(765\) −12.0596 −0.436014
\(766\) −4.31212 −0.155803
\(767\) 10.0465 0.362756
\(768\) 0.694821 0.0250722
\(769\) 43.7609 1.57806 0.789029 0.614356i \(-0.210584\pi\)
0.789029 + 0.614356i \(0.210584\pi\)
\(770\) −5.69886 −0.205373
\(771\) −2.30314 −0.0829455
\(772\) 4.67809 0.168368
\(773\) −34.1896 −1.22972 −0.614858 0.788638i \(-0.710787\pi\)
−0.614858 + 0.788638i \(0.710787\pi\)
\(774\) 14.0091 0.503546
\(775\) 5.18202 0.186144
\(776\) 9.93497 0.356645
\(777\) 1.42522 0.0511295
\(778\) −1.19665 −0.0429018
\(779\) 3.09543 0.110905
\(780\) −0.683770 −0.0244829
\(781\) 26.2211 0.938264
\(782\) −7.27942 −0.260312
\(783\) −30.2105 −1.07963
\(784\) 0.563515 0.0201255
\(785\) 2.82679 0.100893
\(786\) −0.694821 −0.0247834
\(787\) 21.7507 0.775328 0.387664 0.921801i \(-0.373282\pi\)
0.387664 + 0.921801i \(0.373282\pi\)
\(788\) −16.3000 −0.580664
\(789\) −9.58201 −0.341129
\(790\) −0.104739 −0.00372643
\(791\) 16.3031 0.579673
\(792\) −7.92566 −0.281626
\(793\) −19.0237 −0.675552
\(794\) −1.15769 −0.0410847
\(795\) −4.81130 −0.170639
\(796\) −27.1378 −0.961875
\(797\) 50.4341 1.78647 0.893234 0.449592i \(-0.148431\pi\)
0.893234 + 0.449592i \(0.148431\pi\)
\(798\) 10.3445 0.366192
\(799\) 6.83501 0.241805
\(800\) 4.56686 0.161463
\(801\) 38.9973 1.37790
\(802\) 5.23220 0.184755
\(803\) −26.8411 −0.947200
\(804\) 4.22804 0.149111
\(805\) −1.80998 −0.0637935
\(806\) −1.69670 −0.0597638
\(807\) 3.98190 0.140170
\(808\) −13.8875 −0.488562
\(809\) −36.9337 −1.29852 −0.649260 0.760567i \(-0.724921\pi\)
−0.649260 + 0.760567i \(0.724921\pi\)
\(810\) −3.21700 −0.113034
\(811\) 10.1298 0.355706 0.177853 0.984057i \(-0.443085\pi\)
0.177853 + 0.984057i \(0.443085\pi\)
\(812\) −21.6733 −0.760585
\(813\) −1.75932 −0.0617021
\(814\) −2.34834 −0.0823093
\(815\) −8.25649 −0.289212
\(816\) 5.05790 0.177062
\(817\) 30.1275 1.05403
\(818\) −16.2341 −0.567612
\(819\) −10.3516 −0.361714
\(820\) 0.376322 0.0131417
\(821\) 9.05774 0.316117 0.158059 0.987430i \(-0.449477\pi\)
0.158059 + 0.987430i \(0.449477\pi\)
\(822\) −3.27280 −0.114152
\(823\) 23.9357 0.834346 0.417173 0.908827i \(-0.363021\pi\)
0.417173 + 0.908827i \(0.363021\pi\)
\(824\) 5.75577 0.200512
\(825\) 9.99090 0.347839
\(826\) −18.4778 −0.642925
\(827\) 15.7423 0.547412 0.273706 0.961813i \(-0.411750\pi\)
0.273706 + 0.961813i \(0.411750\pi\)
\(828\) −2.51722 −0.0874796
\(829\) 32.4219 1.12606 0.563030 0.826436i \(-0.309636\pi\)
0.563030 + 0.826436i \(0.309636\pi\)
\(830\) 1.05939 0.0367719
\(831\) 2.98692 0.103615
\(832\) −1.49529 −0.0518397
\(833\) 4.10206 0.142128
\(834\) 5.00012 0.173140
\(835\) −0.0777416 −0.00269036
\(836\) −17.0447 −0.589502
\(837\) 4.34986 0.150353
\(838\) −0.0219989 −0.000759940 0
\(839\) −22.8462 −0.788739 −0.394370 0.918952i \(-0.629037\pi\)
−0.394370 + 0.918952i \(0.629037\pi\)
\(840\) 1.25761 0.0433918
\(841\) 33.1052 1.14156
\(842\) 37.9389 1.30746
\(843\) 1.37279 0.0472812
\(844\) 13.6348 0.469329
\(845\) −7.08421 −0.243704
\(846\) 2.36355 0.0812604
\(847\) 2.98805 0.102671
\(848\) −10.5215 −0.361309
\(849\) −8.92891 −0.306439
\(850\) 33.2441 1.14026
\(851\) −0.745843 −0.0255672
\(852\) −5.78642 −0.198239
\(853\) 24.8542 0.850993 0.425496 0.904960i \(-0.360099\pi\)
0.425496 + 0.904960i \(0.360099\pi\)
\(854\) 34.9892 1.19730
\(855\) −8.96829 −0.306709
\(856\) 16.1338 0.551441
\(857\) −3.63255 −0.124086 −0.0620428 0.998073i \(-0.519762\pi\)
−0.0620428 + 0.998073i \(0.519762\pi\)
\(858\) −3.27123 −0.111678
\(859\) −20.6635 −0.705031 −0.352515 0.935806i \(-0.614674\pi\)
−0.352515 + 0.935806i \(0.614674\pi\)
\(860\) 3.66269 0.124897
\(861\) −1.09265 −0.0372374
\(862\) −20.0758 −0.683783
\(863\) 3.63896 0.123872 0.0619358 0.998080i \(-0.480273\pi\)
0.0619358 + 0.998080i \(0.480273\pi\)
\(864\) 3.83348 0.130418
\(865\) 0.806974 0.0274379
\(866\) 13.8363 0.470175
\(867\) 25.0066 0.849268
\(868\) 3.12064 0.105921
\(869\) −0.501081 −0.0169980
\(870\) −3.60371 −0.122177
\(871\) −9.09892 −0.308305
\(872\) 8.74861 0.296265
\(873\) 25.0086 0.846411
\(874\) −5.41346 −0.183113
\(875\) 17.3159 0.585383
\(876\) 5.92323 0.200128
\(877\) 8.42961 0.284648 0.142324 0.989820i \(-0.454543\pi\)
0.142324 + 0.989820i \(0.454543\pi\)
\(878\) −0.455439 −0.0153703
\(879\) 20.2121 0.681737
\(880\) −2.07217 −0.0698530
\(881\) −35.6407 −1.20077 −0.600383 0.799713i \(-0.704985\pi\)
−0.600383 + 0.799713i \(0.704985\pi\)
\(882\) 1.41849 0.0477632
\(883\) 2.87396 0.0967166 0.0483583 0.998830i \(-0.484601\pi\)
0.0483583 + 0.998830i \(0.484601\pi\)
\(884\) −10.8848 −0.366096
\(885\) −3.07238 −0.103277
\(886\) −22.5855 −0.758773
\(887\) −18.9107 −0.634960 −0.317480 0.948265i \(-0.602837\pi\)
−0.317480 + 0.948265i \(0.602837\pi\)
\(888\) 0.518227 0.0173906
\(889\) −15.1337 −0.507567
\(890\) 10.1959 0.341767
\(891\) −15.3905 −0.515601
\(892\) −21.2600 −0.711836
\(893\) 5.08297 0.170095
\(894\) 15.1218 0.505750
\(895\) 13.9098 0.464953
\(896\) 2.75018 0.0918772
\(897\) −1.03896 −0.0346897
\(898\) −28.3401 −0.945720
\(899\) −8.94222 −0.298240
\(900\) 11.4958 0.383194
\(901\) −76.5902 −2.55159
\(902\) 1.80036 0.0599455
\(903\) −10.6346 −0.353898
\(904\) 5.92802 0.197163
\(905\) 2.44122 0.0811490
\(906\) 16.7633 0.556925
\(907\) −50.3508 −1.67187 −0.835935 0.548829i \(-0.815074\pi\)
−0.835935 + 0.548829i \(0.815074\pi\)
\(908\) −0.670276 −0.0222439
\(909\) −34.9580 −1.15948
\(910\) −2.70644 −0.0897177
\(911\) 26.6345 0.882441 0.441221 0.897399i \(-0.354546\pi\)
0.441221 + 0.897399i \(0.354546\pi\)
\(912\) 3.76139 0.124552
\(913\) 5.06823 0.167734
\(914\) −1.31355 −0.0434485
\(915\) 5.81778 0.192330
\(916\) 11.9142 0.393657
\(917\) −2.75018 −0.0908191
\(918\) 27.9055 0.921020
\(919\) −45.9429 −1.51552 −0.757759 0.652535i \(-0.773706\pi\)
−0.757759 + 0.652535i \(0.773706\pi\)
\(920\) −0.658132 −0.0216980
\(921\) 0.550832 0.0181505
\(922\) 28.5051 0.938764
\(923\) 12.4526 0.409883
\(924\) 6.01656 0.197930
\(925\) 3.40616 0.111994
\(926\) 14.6572 0.481665
\(927\) 14.4886 0.475867
\(928\) −7.88069 −0.258696
\(929\) −48.2511 −1.58307 −0.791533 0.611126i \(-0.790717\pi\)
−0.791533 + 0.611126i \(0.790717\pi\)
\(930\) 0.518880 0.0170148
\(931\) 3.05057 0.0999783
\(932\) −0.864723 −0.0283250
\(933\) 9.52506 0.311836
\(934\) 14.3089 0.468201
\(935\) −15.0842 −0.493307
\(936\) −3.76397 −0.123029
\(937\) −37.0743 −1.21116 −0.605582 0.795783i \(-0.707060\pi\)
−0.605582 + 0.795783i \(0.707060\pi\)
\(938\) 16.7351 0.546420
\(939\) 14.1684 0.462368
\(940\) 0.617952 0.0201554
\(941\) −33.1354 −1.08018 −0.540092 0.841606i \(-0.681610\pi\)
−0.540092 + 0.841606i \(0.681610\pi\)
\(942\) −2.98438 −0.0972364
\(943\) 0.571803 0.0186205
\(944\) −6.71876 −0.218677
\(945\) 6.93854 0.225711
\(946\) 17.5227 0.569712
\(947\) −47.0830 −1.52999 −0.764996 0.644035i \(-0.777259\pi\)
−0.764996 + 0.644035i \(0.777259\pi\)
\(948\) 0.110578 0.00359139
\(949\) −12.7471 −0.413787
\(950\) 24.7225 0.802105
\(951\) 13.1731 0.427166
\(952\) 20.0198 0.648844
\(953\) −19.1754 −0.621153 −0.310576 0.950548i \(-0.600522\pi\)
−0.310576 + 0.950548i \(0.600522\pi\)
\(954\) −26.4849 −0.857480
\(955\) −9.85393 −0.318866
\(956\) 22.8758 0.739855
\(957\) −17.2405 −0.557307
\(958\) 31.9334 1.03172
\(959\) −12.9541 −0.418311
\(960\) 0.457284 0.0147588
\(961\) −29.7125 −0.958466
\(962\) −1.11525 −0.0359570
\(963\) 40.6123 1.30871
\(964\) −11.8143 −0.380513
\(965\) 3.07880 0.0991100
\(966\) 1.91089 0.0614818
\(967\) −1.68616 −0.0542232 −0.0271116 0.999632i \(-0.508631\pi\)
−0.0271116 + 0.999632i \(0.508631\pi\)
\(968\) 1.08649 0.0349212
\(969\) 27.3807 0.879595
\(970\) 6.53852 0.209939
\(971\) −34.8390 −1.11804 −0.559018 0.829155i \(-0.688822\pi\)
−0.559018 + 0.829155i \(0.688822\pi\)
\(972\) 14.8968 0.477815
\(973\) 19.7911 0.634473
\(974\) −16.7752 −0.537511
\(975\) 4.74477 0.151954
\(976\) 12.7225 0.407237
\(977\) 24.0490 0.769396 0.384698 0.923042i \(-0.374306\pi\)
0.384698 + 0.923042i \(0.374306\pi\)
\(978\) 8.71677 0.278732
\(979\) 48.7782 1.55896
\(980\) 0.370867 0.0118469
\(981\) 22.0222 0.703115
\(982\) −7.83418 −0.249999
\(983\) −37.5531 −1.19776 −0.598878 0.800840i \(-0.704387\pi\)
−0.598878 + 0.800840i \(0.704387\pi\)
\(984\) −0.397301 −0.0126655
\(985\) −10.7275 −0.341808
\(986\) −57.3668 −1.82693
\(987\) −1.79423 −0.0571108
\(988\) −8.09467 −0.257526
\(989\) 5.56529 0.176966
\(990\) −5.21613 −0.165779
\(991\) 14.1581 0.449748 0.224874 0.974388i \(-0.427803\pi\)
0.224874 + 0.974388i \(0.427803\pi\)
\(992\) 1.13470 0.0360268
\(993\) −21.3339 −0.677009
\(994\) −22.9033 −0.726450
\(995\) −17.8603 −0.566208
\(996\) −1.11845 −0.0354394
\(997\) 28.2854 0.895808 0.447904 0.894082i \(-0.352171\pi\)
0.447904 + 0.894082i \(0.352171\pi\)
\(998\) 23.9829 0.759165
\(999\) 2.85918 0.0904603
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 \(a_p\))