Properties

Label 6034.2.a.n.1.9
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.797155 q^{3} +1.00000 q^{4} +1.40867 q^{5} +0.797155 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.36454 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.797155 q^{3} +1.00000 q^{4} +1.40867 q^{5} +0.797155 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.36454 q^{9} -1.40867 q^{10} -4.26652 q^{11} -0.797155 q^{12} +0.799192 q^{13} +1.00000 q^{14} -1.12293 q^{15} +1.00000 q^{16} -3.62976 q^{17} +2.36454 q^{18} -6.70269 q^{19} +1.40867 q^{20} +0.797155 q^{21} +4.26652 q^{22} -4.59211 q^{23} +0.797155 q^{24} -3.01565 q^{25} -0.799192 q^{26} +4.27637 q^{27} -1.00000 q^{28} -6.21178 q^{29} +1.12293 q^{30} -6.61866 q^{31} -1.00000 q^{32} +3.40108 q^{33} +3.62976 q^{34} -1.40867 q^{35} -2.36454 q^{36} +5.42018 q^{37} +6.70269 q^{38} -0.637080 q^{39} -1.40867 q^{40} -4.51614 q^{41} -0.797155 q^{42} +0.780925 q^{43} -4.26652 q^{44} -3.33086 q^{45} +4.59211 q^{46} +11.1285 q^{47} -0.797155 q^{48} +1.00000 q^{49} +3.01565 q^{50} +2.89348 q^{51} +0.799192 q^{52} -3.36589 q^{53} -4.27637 q^{54} -6.01012 q^{55} +1.00000 q^{56} +5.34309 q^{57} +6.21178 q^{58} +5.39532 q^{59} -1.12293 q^{60} -5.80734 q^{61} +6.61866 q^{62} +2.36454 q^{63} +1.00000 q^{64} +1.12580 q^{65} -3.40108 q^{66} -4.88292 q^{67} -3.62976 q^{68} +3.66063 q^{69} +1.40867 q^{70} +9.37398 q^{71} +2.36454 q^{72} -3.99440 q^{73} -5.42018 q^{74} +2.40394 q^{75} -6.70269 q^{76} +4.26652 q^{77} +0.637080 q^{78} +5.28980 q^{79} +1.40867 q^{80} +3.68470 q^{81} +4.51614 q^{82} +14.1032 q^{83} +0.797155 q^{84} -5.11313 q^{85} -0.780925 q^{86} +4.95175 q^{87} +4.26652 q^{88} -13.9685 q^{89} +3.33086 q^{90} -0.799192 q^{91} -4.59211 q^{92} +5.27610 q^{93} -11.1285 q^{94} -9.44188 q^{95} +0.797155 q^{96} -3.54831 q^{97} -1.00000 q^{98} +10.0884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} + O(q^{10}) \) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} - 8q^{10} + 15q^{11} + 7q^{12} - 7q^{13} + 24q^{14} + 13q^{15} + 24q^{16} - 5q^{17} - 19q^{18} + 6q^{19} + 8q^{20} - 7q^{21} - 15q^{22} + 3q^{23} - 7q^{24} + 12q^{25} + 7q^{26} + 22q^{27} - 24q^{28} + 5q^{29} - 13q^{30} + 13q^{31} - 24q^{32} - 8q^{33} + 5q^{34} - 8q^{35} + 19q^{36} + 2q^{37} - 6q^{38} + 7q^{39} - 8q^{40} + 25q^{41} + 7q^{42} - 15q^{43} + 15q^{44} + 41q^{45} - 3q^{46} + 35q^{47} + 7q^{48} + 24q^{49} - 12q^{50} + 31q^{51} - 7q^{52} + 2q^{53} - 22q^{54} + 14q^{55} + 24q^{56} - 13q^{57} - 5q^{58} + 35q^{59} + 13q^{60} - 7q^{61} - 13q^{62} - 19q^{63} + 24q^{64} - 4q^{65} + 8q^{66} + 10q^{67} - 5q^{68} + 6q^{69} + 8q^{70} + 58q^{71} - 19q^{72} + 9q^{73} - 2q^{74} + 7q^{75} + 6q^{76} - 15q^{77} - 7q^{78} + 31q^{79} + 8q^{80} + 16q^{81} - 25q^{82} - q^{83} - 7q^{84} - 4q^{85} + 15q^{86} + 30q^{87} - 15q^{88} + 45q^{89} - 41q^{90} + 7q^{91} + 3q^{92} + 25q^{93} - 35q^{94} - 10q^{95} - 7q^{96} - 9q^{97} - 24q^{98} + 64q^{99} + O(q^{100}) \)

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
\(3\) −0.797155 −0.460238 −0.230119 0.973163i \(-0.573912\pi\)
−0.230119 + 0.973163i \(0.573912\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.40867 0.629976 0.314988 0.949096i \(-0.397999\pi\)
0.314988 + 0.949096i \(0.397999\pi\)
\(6\) 0.797155 0.325437
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.36454 −0.788181
\(10\) −1.40867 −0.445460
\(11\) −4.26652 −1.28640 −0.643202 0.765696i \(-0.722394\pi\)
−0.643202 + 0.765696i \(0.722394\pi\)
\(12\) −0.797155 −0.230119
\(13\) 0.799192 0.221656 0.110828 0.993840i \(-0.464650\pi\)
0.110828 + 0.993840i \(0.464650\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.12293 −0.289939
\(16\) 1.00000 0.250000
\(17\) −3.62976 −0.880345 −0.440173 0.897913i \(-0.645083\pi\)
−0.440173 + 0.897913i \(0.645083\pi\)
\(18\) 2.36454 0.557328
\(19\) −6.70269 −1.53770 −0.768851 0.639427i \(-0.779171\pi\)
−0.768851 + 0.639427i \(0.779171\pi\)
\(20\) 1.40867 0.314988
\(21\) 0.797155 0.173954
\(22\) 4.26652 0.909625
\(23\) −4.59211 −0.957522 −0.478761 0.877945i \(-0.658914\pi\)
−0.478761 + 0.877945i \(0.658914\pi\)
\(24\) 0.797155 0.162719
\(25\) −3.01565 −0.603130
\(26\) −0.799192 −0.156734
\(27\) 4.27637 0.822989
\(28\) −1.00000 −0.188982
\(29\) −6.21178 −1.15350 −0.576749 0.816921i \(-0.695679\pi\)
−0.576749 + 0.816921i \(0.695679\pi\)
\(30\) 1.12293 0.205018
\(31\) −6.61866 −1.18875 −0.594373 0.804189i \(-0.702600\pi\)
−0.594373 + 0.804189i \(0.702600\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.40108 0.592052
\(34\) 3.62976 0.622498
\(35\) −1.40867 −0.238109
\(36\) −2.36454 −0.394091
\(37\) 5.42018 0.891072 0.445536 0.895264i \(-0.353013\pi\)
0.445536 + 0.895264i \(0.353013\pi\)
\(38\) 6.70269 1.08732
\(39\) −0.637080 −0.102014
\(40\) −1.40867 −0.222730
\(41\) −4.51614 −0.705303 −0.352652 0.935755i \(-0.614720\pi\)
−0.352652 + 0.935755i \(0.614720\pi\)
\(42\) −0.797155 −0.123004
\(43\) 0.780925 0.119090 0.0595450 0.998226i \(-0.481035\pi\)
0.0595450 + 0.998226i \(0.481035\pi\)
\(44\) −4.26652 −0.643202
\(45\) −3.33086 −0.496535
\(46\) 4.59211 0.677070
\(47\) 11.1285 1.62325 0.811627 0.584176i \(-0.198582\pi\)
0.811627 + 0.584176i \(0.198582\pi\)
\(48\) −0.797155 −0.115059
\(49\) 1.00000 0.142857
\(50\) 3.01565 0.426477
\(51\) 2.89348 0.405168
\(52\) 0.799192 0.110828
\(53\) −3.36589 −0.462341 −0.231170 0.972913i \(-0.574255\pi\)
−0.231170 + 0.972913i \(0.574255\pi\)
\(54\) −4.27637 −0.581941
\(55\) −6.01012 −0.810404
\(56\) 1.00000 0.133631
\(57\) 5.34309 0.707709
\(58\) 6.21178 0.815646
\(59\) 5.39532 0.702410 0.351205 0.936298i \(-0.385772\pi\)
0.351205 + 0.936298i \(0.385772\pi\)
\(60\) −1.12293 −0.144969
\(61\) −5.80734 −0.743554 −0.371777 0.928322i \(-0.621251\pi\)
−0.371777 + 0.928322i \(0.621251\pi\)
\(62\) 6.61866 0.840571
\(63\) 2.36454 0.297904
\(64\) 1.00000 0.125000
\(65\) 1.12580 0.139638
\(66\) −3.40108 −0.418644
\(67\) −4.88292 −0.596543 −0.298272 0.954481i \(-0.596410\pi\)
−0.298272 + 0.954481i \(0.596410\pi\)
\(68\) −3.62976 −0.440173
\(69\) 3.66063 0.440688
\(70\) 1.40867 0.168368
\(71\) 9.37398 1.11249 0.556243 0.831020i \(-0.312242\pi\)
0.556243 + 0.831020i \(0.312242\pi\)
\(72\) 2.36454 0.278664
\(73\) −3.99440 −0.467510 −0.233755 0.972296i \(-0.575101\pi\)
−0.233755 + 0.972296i \(0.575101\pi\)
\(74\) −5.42018 −0.630083
\(75\) 2.40394 0.277583
\(76\) −6.70269 −0.768851
\(77\) 4.26652 0.486215
\(78\) 0.637080 0.0721351
\(79\) 5.28980 0.595149 0.297575 0.954699i \(-0.403822\pi\)
0.297575 + 0.954699i \(0.403822\pi\)
\(80\) 1.40867 0.157494
\(81\) 3.68470 0.409411
\(82\) 4.51614 0.498725
\(83\) 14.1032 1.54803 0.774015 0.633168i \(-0.218246\pi\)
0.774015 + 0.633168i \(0.218246\pi\)
\(84\) 0.797155 0.0869768
\(85\) −5.11313 −0.554596
\(86\) −0.780925 −0.0842093
\(87\) 4.95175 0.530883
\(88\) 4.26652 0.454813
\(89\) −13.9685 −1.48066 −0.740328 0.672246i \(-0.765330\pi\)
−0.740328 + 0.672246i \(0.765330\pi\)
\(90\) 3.33086 0.351104
\(91\) −0.799192 −0.0837781
\(92\) −4.59211 −0.478761
\(93\) 5.27610 0.547106
\(94\) −11.1285 −1.14781
\(95\) −9.44188 −0.968716
\(96\) 0.797155 0.0813593
\(97\) −3.54831 −0.360277 −0.180138 0.983641i \(-0.557655\pi\)
−0.180138 + 0.983641i \(0.557655\pi\)
\(98\) −1.00000 −0.101015
\(99\) 10.0884 1.01392
\(100\) −3.01565 −0.301565
\(101\) 9.29483 0.924870 0.462435 0.886653i \(-0.346976\pi\)
0.462435 + 0.886653i \(0.346976\pi\)
\(102\) −2.89348 −0.286497
\(103\) 8.45408 0.833005 0.416503 0.909134i \(-0.363256\pi\)
0.416503 + 0.909134i \(0.363256\pi\)
\(104\) −0.799192 −0.0783672
\(105\) 1.12293 0.109587
\(106\) 3.36589 0.326924
\(107\) 12.0908 1.16886 0.584430 0.811444i \(-0.301318\pi\)
0.584430 + 0.811444i \(0.301318\pi\)
\(108\) 4.27637 0.411494
\(109\) −5.51476 −0.528218 −0.264109 0.964493i \(-0.585078\pi\)
−0.264109 + 0.964493i \(0.585078\pi\)
\(110\) 6.01012 0.573042
\(111\) −4.32072 −0.410105
\(112\) −1.00000 −0.0944911
\(113\) 5.38250 0.506343 0.253171 0.967421i \(-0.418526\pi\)
0.253171 + 0.967421i \(0.418526\pi\)
\(114\) −5.34309 −0.500426
\(115\) −6.46877 −0.603216
\(116\) −6.21178 −0.576749
\(117\) −1.88972 −0.174705
\(118\) −5.39532 −0.496679
\(119\) 3.62976 0.332739
\(120\) 1.12293 0.102509
\(121\) 7.20319 0.654836
\(122\) 5.80734 0.525772
\(123\) 3.60007 0.324607
\(124\) −6.61866 −0.594373
\(125\) −11.2914 −1.00993
\(126\) −2.36454 −0.210650
\(127\) 13.0689 1.15968 0.579839 0.814731i \(-0.303115\pi\)
0.579839 + 0.814731i \(0.303115\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.622518 −0.0548097
\(130\) −1.12580 −0.0987390
\(131\) 5.75249 0.502597 0.251299 0.967910i \(-0.419142\pi\)
0.251299 + 0.967910i \(0.419142\pi\)
\(132\) 3.40108 0.296026
\(133\) 6.70269 0.581197
\(134\) 4.88292 0.421820
\(135\) 6.02400 0.518463
\(136\) 3.62976 0.311249
\(137\) 7.21273 0.616225 0.308113 0.951350i \(-0.400303\pi\)
0.308113 + 0.951350i \(0.400303\pi\)
\(138\) −3.66063 −0.311613
\(139\) −3.15380 −0.267502 −0.133751 0.991015i \(-0.542702\pi\)
−0.133751 + 0.991015i \(0.542702\pi\)
\(140\) −1.40867 −0.119054
\(141\) −8.87112 −0.747083
\(142\) −9.37398 −0.786647
\(143\) −3.40977 −0.285139
\(144\) −2.36454 −0.197045
\(145\) −8.75034 −0.726676
\(146\) 3.99440 0.330579
\(147\) −0.797155 −0.0657483
\(148\) 5.42018 0.445536
\(149\) 16.0083 1.31145 0.655726 0.754999i \(-0.272363\pi\)
0.655726 + 0.754999i \(0.272363\pi\)
\(150\) −2.40394 −0.196281
\(151\) 9.62444 0.783226 0.391613 0.920130i \(-0.371917\pi\)
0.391613 + 0.920130i \(0.371917\pi\)
\(152\) 6.70269 0.543660
\(153\) 8.58272 0.693871
\(154\) −4.26652 −0.343806
\(155\) −9.32351 −0.748882
\(156\) −0.637080 −0.0510072
\(157\) −2.78528 −0.222289 −0.111145 0.993804i \(-0.535452\pi\)
−0.111145 + 0.993804i \(0.535452\pi\)
\(158\) −5.28980 −0.420834
\(159\) 2.68314 0.212787
\(160\) −1.40867 −0.111365
\(161\) 4.59211 0.361909
\(162\) −3.68470 −0.289497
\(163\) 7.65399 0.599507 0.299753 0.954017i \(-0.403096\pi\)
0.299753 + 0.954017i \(0.403096\pi\)
\(164\) −4.51614 −0.352652
\(165\) 4.79100 0.372979
\(166\) −14.1032 −1.09462
\(167\) 8.70855 0.673888 0.336944 0.941525i \(-0.390607\pi\)
0.336944 + 0.941525i \(0.390607\pi\)
\(168\) −0.797155 −0.0615019
\(169\) −12.3613 −0.950869
\(170\) 5.11313 0.392159
\(171\) 15.8488 1.21199
\(172\) 0.780925 0.0595450
\(173\) 0.799481 0.0607834 0.0303917 0.999538i \(-0.490325\pi\)
0.0303917 + 0.999538i \(0.490325\pi\)
\(174\) −4.95175 −0.375391
\(175\) 3.01565 0.227962
\(176\) −4.26652 −0.321601
\(177\) −4.30091 −0.323276
\(178\) 13.9685 1.04698
\(179\) −7.40805 −0.553704 −0.276852 0.960913i \(-0.589291\pi\)
−0.276852 + 0.960913i \(0.589291\pi\)
\(180\) −3.33086 −0.248268
\(181\) −11.7333 −0.872126 −0.436063 0.899916i \(-0.643628\pi\)
−0.436063 + 0.899916i \(0.643628\pi\)
\(182\) 0.799192 0.0592400
\(183\) 4.62935 0.342211
\(184\) 4.59211 0.338535
\(185\) 7.63524 0.561354
\(186\) −5.27610 −0.386863
\(187\) 15.4864 1.13248
\(188\) 11.1285 0.811627
\(189\) −4.27637 −0.311060
\(190\) 9.44188 0.684986
\(191\) 8.22734 0.595309 0.297655 0.954674i \(-0.403796\pi\)
0.297655 + 0.954674i \(0.403796\pi\)
\(192\) −0.797155 −0.0575297
\(193\) −18.7582 −1.35024 −0.675121 0.737707i \(-0.735909\pi\)
−0.675121 + 0.737707i \(0.735909\pi\)
\(194\) 3.54831 0.254754
\(195\) −0.897435 −0.0642667
\(196\) 1.00000 0.0714286
\(197\) −20.4237 −1.45512 −0.727562 0.686041i \(-0.759347\pi\)
−0.727562 + 0.686041i \(0.759347\pi\)
\(198\) −10.0884 −0.716949
\(199\) −13.8409 −0.981152 −0.490576 0.871398i \(-0.663214\pi\)
−0.490576 + 0.871398i \(0.663214\pi\)
\(200\) 3.01565 0.213239
\(201\) 3.89244 0.274552
\(202\) −9.29483 −0.653982
\(203\) 6.21178 0.435981
\(204\) 2.89348 0.202584
\(205\) −6.36175 −0.444324
\(206\) −8.45408 −0.589024
\(207\) 10.8582 0.754701
\(208\) 0.799192 0.0554140
\(209\) 28.5972 1.97811
\(210\) −1.12293 −0.0774894
\(211\) 22.7593 1.56681 0.783407 0.621509i \(-0.213480\pi\)
0.783407 + 0.621509i \(0.213480\pi\)
\(212\) −3.36589 −0.231170
\(213\) −7.47251 −0.512008
\(214\) −12.0908 −0.826509
\(215\) 1.10007 0.0750238
\(216\) −4.27637 −0.290970
\(217\) 6.61866 0.449304
\(218\) 5.51476 0.373507
\(219\) 3.18416 0.215166
\(220\) −6.01012 −0.405202
\(221\) −2.90087 −0.195134
\(222\) 4.32072 0.289988
\(223\) −8.70757 −0.583102 −0.291551 0.956555i \(-0.594171\pi\)
−0.291551 + 0.956555i \(0.594171\pi\)
\(224\) 1.00000 0.0668153
\(225\) 7.13063 0.475376
\(226\) −5.38250 −0.358038
\(227\) −16.8011 −1.11513 −0.557564 0.830134i \(-0.688264\pi\)
−0.557564 + 0.830134i \(0.688264\pi\)
\(228\) 5.34309 0.353854
\(229\) 24.0920 1.59205 0.796023 0.605267i \(-0.206934\pi\)
0.796023 + 0.605267i \(0.206934\pi\)
\(230\) 6.46877 0.426538
\(231\) −3.40108 −0.223775
\(232\) 6.21178 0.407823
\(233\) −12.7964 −0.838321 −0.419160 0.907912i \(-0.637676\pi\)
−0.419160 + 0.907912i \(0.637676\pi\)
\(234\) 1.88972 0.123535
\(235\) 15.6763 1.02261
\(236\) 5.39532 0.351205
\(237\) −4.21680 −0.273910
\(238\) −3.62976 −0.235282
\(239\) 2.87318 0.185851 0.0929253 0.995673i \(-0.470378\pi\)
0.0929253 + 0.995673i \(0.470378\pi\)
\(240\) −1.12293 −0.0724847
\(241\) −8.19163 −0.527669 −0.263835 0.964568i \(-0.584987\pi\)
−0.263835 + 0.964568i \(0.584987\pi\)
\(242\) −7.20319 −0.463039
\(243\) −15.7664 −1.01141
\(244\) −5.80734 −0.371777
\(245\) 1.40867 0.0899966
\(246\) −3.60007 −0.229532
\(247\) −5.35674 −0.340841
\(248\) 6.61866 0.420285
\(249\) −11.2425 −0.712462
\(250\) 11.2914 0.714131
\(251\) −14.2956 −0.902332 −0.451166 0.892440i \(-0.648992\pi\)
−0.451166 + 0.892440i \(0.648992\pi\)
\(252\) 2.36454 0.148952
\(253\) 19.5923 1.23176
\(254\) −13.0689 −0.820017
\(255\) 4.07596 0.255246
\(256\) 1.00000 0.0625000
\(257\) 8.61994 0.537697 0.268849 0.963182i \(-0.413357\pi\)
0.268849 + 0.963182i \(0.413357\pi\)
\(258\) 0.622518 0.0387563
\(259\) −5.42018 −0.336793
\(260\) 1.12580 0.0698190
\(261\) 14.6880 0.909165
\(262\) −5.75249 −0.355390
\(263\) −22.6467 −1.39646 −0.698228 0.715875i \(-0.746028\pi\)
−0.698228 + 0.715875i \(0.746028\pi\)
\(264\) −3.40108 −0.209322
\(265\) −4.74143 −0.291264
\(266\) −6.70269 −0.410968
\(267\) 11.1350 0.681454
\(268\) −4.88292 −0.298272
\(269\) −1.14346 −0.0697182 −0.0348591 0.999392i \(-0.511098\pi\)
−0.0348591 + 0.999392i \(0.511098\pi\)
\(270\) −6.02400 −0.366609
\(271\) −26.5613 −1.61349 −0.806743 0.590903i \(-0.798772\pi\)
−0.806743 + 0.590903i \(0.798772\pi\)
\(272\) −3.62976 −0.220086
\(273\) 0.637080 0.0385578
\(274\) −7.21273 −0.435737
\(275\) 12.8663 0.775869
\(276\) 3.66063 0.220344
\(277\) −17.7413 −1.06597 −0.532987 0.846124i \(-0.678930\pi\)
−0.532987 + 0.846124i \(0.678930\pi\)
\(278\) 3.15380 0.189152
\(279\) 15.6501 0.936948
\(280\) 1.40867 0.0841841
\(281\) 3.28356 0.195881 0.0979404 0.995192i \(-0.468775\pi\)
0.0979404 + 0.995192i \(0.468775\pi\)
\(282\) 8.87112 0.528267
\(283\) 15.1321 0.899508 0.449754 0.893152i \(-0.351512\pi\)
0.449754 + 0.893152i \(0.351512\pi\)
\(284\) 9.37398 0.556243
\(285\) 7.52664 0.445840
\(286\) 3.40977 0.201624
\(287\) 4.51614 0.266580
\(288\) 2.36454 0.139332
\(289\) −3.82487 −0.224993
\(290\) 8.75034 0.513838
\(291\) 2.82856 0.165813
\(292\) −3.99440 −0.233755
\(293\) 3.09226 0.180652 0.0903259 0.995912i \(-0.471209\pi\)
0.0903259 + 0.995912i \(0.471209\pi\)
\(294\) 0.797155 0.0464910
\(295\) 7.60022 0.442502
\(296\) −5.42018 −0.315041
\(297\) −18.2452 −1.05870
\(298\) −16.0083 −0.927337
\(299\) −3.66998 −0.212240
\(300\) 2.40394 0.138792
\(301\) −0.780925 −0.0450118
\(302\) −9.62444 −0.553825
\(303\) −7.40942 −0.425660
\(304\) −6.70269 −0.384426
\(305\) −8.18062 −0.468421
\(306\) −8.58272 −0.490641
\(307\) 12.4885 0.712754 0.356377 0.934342i \(-0.384012\pi\)
0.356377 + 0.934342i \(0.384012\pi\)
\(308\) 4.26652 0.243108
\(309\) −6.73922 −0.383381
\(310\) 9.32351 0.529540
\(311\) −17.8336 −1.01125 −0.505624 0.862754i \(-0.668738\pi\)
−0.505624 + 0.862754i \(0.668738\pi\)
\(312\) 0.637080 0.0360676
\(313\) −28.9134 −1.63428 −0.817142 0.576437i \(-0.804443\pi\)
−0.817142 + 0.576437i \(0.804443\pi\)
\(314\) 2.78528 0.157182
\(315\) 3.33086 0.187673
\(316\) 5.28980 0.297575
\(317\) −7.35728 −0.413226 −0.206613 0.978423i \(-0.566244\pi\)
−0.206613 + 0.978423i \(0.566244\pi\)
\(318\) −2.68314 −0.150463
\(319\) 26.5027 1.48386
\(320\) 1.40867 0.0787470
\(321\) −9.63823 −0.537954
\(322\) −4.59211 −0.255908
\(323\) 24.3291 1.35371
\(324\) 3.68470 0.204705
\(325\) −2.41008 −0.133687
\(326\) −7.65399 −0.423915
\(327\) 4.39612 0.243106
\(328\) 4.51614 0.249362
\(329\) −11.1285 −0.613532
\(330\) −4.79100 −0.263736
\(331\) −6.60868 −0.363246 −0.181623 0.983368i \(-0.558135\pi\)
−0.181623 + 0.983368i \(0.558135\pi\)
\(332\) 14.1032 0.774015
\(333\) −12.8162 −0.702326
\(334\) −8.70855 −0.476511
\(335\) −6.87841 −0.375808
\(336\) 0.797155 0.0434884
\(337\) −13.4528 −0.732821 −0.366411 0.930453i \(-0.619413\pi\)
−0.366411 + 0.930453i \(0.619413\pi\)
\(338\) 12.3613 0.672366
\(339\) −4.29069 −0.233038
\(340\) −5.11313 −0.277298
\(341\) 28.2387 1.52921
\(342\) −15.8488 −0.857005
\(343\) −1.00000 −0.0539949
\(344\) −0.780925 −0.0421046
\(345\) 5.15661 0.277623
\(346\) −0.799481 −0.0429803
\(347\) −13.0592 −0.701052 −0.350526 0.936553i \(-0.613997\pi\)
−0.350526 + 0.936553i \(0.613997\pi\)
\(348\) 4.95175 0.265442
\(349\) −32.8893 −1.76052 −0.880262 0.474488i \(-0.842633\pi\)
−0.880262 + 0.474488i \(0.842633\pi\)
\(350\) −3.01565 −0.161193
\(351\) 3.41764 0.182420
\(352\) 4.26652 0.227406
\(353\) 33.8962 1.80411 0.902056 0.431620i \(-0.142058\pi\)
0.902056 + 0.431620i \(0.142058\pi\)
\(354\) 4.30091 0.228591
\(355\) 13.2048 0.700840
\(356\) −13.9685 −0.740328
\(357\) −2.89348 −0.153139
\(358\) 7.40805 0.391528
\(359\) −20.3577 −1.07444 −0.537219 0.843442i \(-0.680525\pi\)
−0.537219 + 0.843442i \(0.680525\pi\)
\(360\) 3.33086 0.175552
\(361\) 25.9261 1.36453
\(362\) 11.7333 0.616686
\(363\) −5.74206 −0.301380
\(364\) −0.799192 −0.0418890
\(365\) −5.62680 −0.294520
\(366\) −4.62935 −0.241980
\(367\) 23.4757 1.22542 0.612710 0.790308i \(-0.290079\pi\)
0.612710 + 0.790308i \(0.290079\pi\)
\(368\) −4.59211 −0.239380
\(369\) 10.6786 0.555907
\(370\) −7.63524 −0.396937
\(371\) 3.36589 0.174748
\(372\) 5.27610 0.273553
\(373\) 7.31132 0.378566 0.189283 0.981923i \(-0.439384\pi\)
0.189283 + 0.981923i \(0.439384\pi\)
\(374\) −15.4864 −0.800784
\(375\) 9.00100 0.464810
\(376\) −11.1285 −0.573907
\(377\) −4.96440 −0.255680
\(378\) 4.27637 0.219953
\(379\) −15.8034 −0.811766 −0.405883 0.913925i \(-0.633036\pi\)
−0.405883 + 0.913925i \(0.633036\pi\)
\(380\) −9.44188 −0.484358
\(381\) −10.4180 −0.533728
\(382\) −8.22734 −0.420947
\(383\) 13.1987 0.674424 0.337212 0.941429i \(-0.390516\pi\)
0.337212 + 0.941429i \(0.390516\pi\)
\(384\) 0.797155 0.0406797
\(385\) 6.01012 0.306304
\(386\) 18.7582 0.954765
\(387\) −1.84653 −0.0938644
\(388\) −3.54831 −0.180138
\(389\) 33.1194 1.67922 0.839609 0.543191i \(-0.182784\pi\)
0.839609 + 0.543191i \(0.182784\pi\)
\(390\) 0.897435 0.0454434
\(391\) 16.6682 0.842949
\(392\) −1.00000 −0.0505076
\(393\) −4.58563 −0.231314
\(394\) 20.4237 1.02893
\(395\) 7.45159 0.374930
\(396\) 10.0884 0.506960
\(397\) −17.0911 −0.857777 −0.428888 0.903358i \(-0.641095\pi\)
−0.428888 + 0.903358i \(0.641095\pi\)
\(398\) 13.8409 0.693779
\(399\) −5.34309 −0.267489
\(400\) −3.01565 −0.150782
\(401\) −20.1721 −1.00735 −0.503673 0.863894i \(-0.668018\pi\)
−0.503673 + 0.863894i \(0.668018\pi\)
\(402\) −3.89244 −0.194137
\(403\) −5.28958 −0.263493
\(404\) 9.29483 0.462435
\(405\) 5.19052 0.257919
\(406\) −6.21178 −0.308285
\(407\) −23.1253 −1.14628
\(408\) −2.89348 −0.143249
\(409\) 32.3193 1.59809 0.799043 0.601274i \(-0.205340\pi\)
0.799043 + 0.601274i \(0.205340\pi\)
\(410\) 6.36175 0.314185
\(411\) −5.74967 −0.283610
\(412\) 8.45408 0.416503
\(413\) −5.39532 −0.265486
\(414\) −10.8582 −0.533654
\(415\) 19.8668 0.975222
\(416\) −0.799192 −0.0391836
\(417\) 2.51407 0.123114
\(418\) −28.5972 −1.39873
\(419\) −22.7045 −1.10919 −0.554594 0.832121i \(-0.687126\pi\)
−0.554594 + 0.832121i \(0.687126\pi\)
\(420\) 1.12293 0.0547933
\(421\) 16.2815 0.793513 0.396756 0.917924i \(-0.370136\pi\)
0.396756 + 0.917924i \(0.370136\pi\)
\(422\) −22.7593 −1.10790
\(423\) −26.3137 −1.27942
\(424\) 3.36589 0.163462
\(425\) 10.9461 0.530962
\(426\) 7.47251 0.362044
\(427\) 5.80734 0.281037
\(428\) 12.0908 0.584430
\(429\) 2.71811 0.131232
\(430\) −1.10007 −0.0530499
\(431\) 1.00000 0.0481683
\(432\) 4.27637 0.205747
\(433\) 5.04478 0.242437 0.121218 0.992626i \(-0.461320\pi\)
0.121218 + 0.992626i \(0.461320\pi\)
\(434\) −6.61866 −0.317706
\(435\) 6.97538 0.334444
\(436\) −5.51476 −0.264109
\(437\) 30.7795 1.47238
\(438\) −3.18416 −0.152145
\(439\) 12.8675 0.614132 0.307066 0.951688i \(-0.400653\pi\)
0.307066 + 0.951688i \(0.400653\pi\)
\(440\) 6.01012 0.286521
\(441\) −2.36454 −0.112597
\(442\) 2.90087 0.137980
\(443\) 7.97797 0.379045 0.189522 0.981876i \(-0.439306\pi\)
0.189522 + 0.981876i \(0.439306\pi\)
\(444\) −4.32072 −0.205052
\(445\) −19.6770 −0.932778
\(446\) 8.70757 0.412315
\(447\) −12.7611 −0.603580
\(448\) −1.00000 −0.0472456
\(449\) 33.4115 1.57679 0.788394 0.615171i \(-0.210913\pi\)
0.788394 + 0.615171i \(0.210913\pi\)
\(450\) −7.13063 −0.336141
\(451\) 19.2682 0.907305
\(452\) 5.38250 0.253171
\(453\) −7.67218 −0.360470
\(454\) 16.8011 0.788515
\(455\) −1.12580 −0.0527782
\(456\) −5.34309 −0.250213
\(457\) 14.1064 0.659871 0.329935 0.944004i \(-0.392973\pi\)
0.329935 + 0.944004i \(0.392973\pi\)
\(458\) −24.0920 −1.12575
\(459\) −15.5222 −0.724514
\(460\) −6.46877 −0.301608
\(461\) 12.0170 0.559688 0.279844 0.960046i \(-0.409717\pi\)
0.279844 + 0.960046i \(0.409717\pi\)
\(462\) 3.40108 0.158233
\(463\) −11.9976 −0.557575 −0.278787 0.960353i \(-0.589932\pi\)
−0.278787 + 0.960353i \(0.589932\pi\)
\(464\) −6.21178 −0.288375
\(465\) 7.43228 0.344664
\(466\) 12.7964 0.592782
\(467\) 11.6270 0.538035 0.269018 0.963135i \(-0.413301\pi\)
0.269018 + 0.963135i \(0.413301\pi\)
\(468\) −1.88972 −0.0873525
\(469\) 4.88292 0.225472
\(470\) −15.6763 −0.723095
\(471\) 2.22030 0.102306
\(472\) −5.39532 −0.248340
\(473\) −3.33183 −0.153198
\(474\) 4.21680 0.193684
\(475\) 20.2130 0.927435
\(476\) 3.62976 0.166370
\(477\) 7.95880 0.364408
\(478\) −2.87318 −0.131416
\(479\) 2.99665 0.136921 0.0684603 0.997654i \(-0.478191\pi\)
0.0684603 + 0.997654i \(0.478191\pi\)
\(480\) 1.12293 0.0512544
\(481\) 4.33176 0.197511
\(482\) 8.19163 0.373118
\(483\) −3.66063 −0.166564
\(484\) 7.20319 0.327418
\(485\) −4.99840 −0.226966
\(486\) 15.7664 0.715178
\(487\) −18.3844 −0.833079 −0.416539 0.909118i \(-0.636757\pi\)
−0.416539 + 0.909118i \(0.636757\pi\)
\(488\) 5.80734 0.262886
\(489\) −6.10142 −0.275916
\(490\) −1.40867 −0.0636372
\(491\) 21.2906 0.960832 0.480416 0.877041i \(-0.340486\pi\)
0.480416 + 0.877041i \(0.340486\pi\)
\(492\) 3.60007 0.162304
\(493\) 22.5472 1.01548
\(494\) 5.35674 0.241011
\(495\) 14.2112 0.638745
\(496\) −6.61866 −0.297187
\(497\) −9.37398 −0.420480
\(498\) 11.2425 0.503787
\(499\) 39.7003 1.77723 0.888614 0.458655i \(-0.151669\pi\)
0.888614 + 0.458655i \(0.151669\pi\)
\(500\) −11.2914 −0.504967
\(501\) −6.94207 −0.310149
\(502\) 14.2956 0.638045
\(503\) −24.7499 −1.10354 −0.551772 0.833995i \(-0.686048\pi\)
−0.551772 + 0.833995i \(0.686048\pi\)
\(504\) −2.36454 −0.105325
\(505\) 13.0933 0.582646
\(506\) −19.5923 −0.870986
\(507\) 9.85387 0.437626
\(508\) 13.0689 0.579839
\(509\) 16.9879 0.752977 0.376489 0.926421i \(-0.377131\pi\)
0.376489 + 0.926421i \(0.377131\pi\)
\(510\) −4.07596 −0.180486
\(511\) 3.99440 0.176702
\(512\) −1.00000 −0.0441942
\(513\) −28.6632 −1.26551
\(514\) −8.61994 −0.380209
\(515\) 11.9090 0.524774
\(516\) −0.622518 −0.0274048
\(517\) −47.4798 −2.08816
\(518\) 5.42018 0.238149
\(519\) −0.637310 −0.0279748
\(520\) −1.12580 −0.0493695
\(521\) −0.356556 −0.0156210 −0.00781050 0.999969i \(-0.502486\pi\)
−0.00781050 + 0.999969i \(0.502486\pi\)
\(522\) −14.6880 −0.642877
\(523\) 0.463689 0.0202757 0.0101379 0.999949i \(-0.496773\pi\)
0.0101379 + 0.999949i \(0.496773\pi\)
\(524\) 5.75249 0.251299
\(525\) −2.40394 −0.104917
\(526\) 22.6467 0.987444
\(527\) 24.0241 1.04651
\(528\) 3.40108 0.148013
\(529\) −1.91250 −0.0831523
\(530\) 4.74143 0.205955
\(531\) −12.7575 −0.553627
\(532\) 6.70269 0.290599
\(533\) −3.60927 −0.156335
\(534\) −11.1350 −0.481861
\(535\) 17.0319 0.736354
\(536\) 4.88292 0.210910
\(537\) 5.90537 0.254835
\(538\) 1.14346 0.0492982
\(539\) −4.26652 −0.183772
\(540\) 6.02400 0.259232
\(541\) −18.7910 −0.807888 −0.403944 0.914784i \(-0.632361\pi\)
−0.403944 + 0.914784i \(0.632361\pi\)
\(542\) 26.5613 1.14091
\(543\) 9.35323 0.401385
\(544\) 3.62976 0.155624
\(545\) −7.76848 −0.332765
\(546\) −0.637080 −0.0272645
\(547\) 22.4507 0.959923 0.479962 0.877290i \(-0.340651\pi\)
0.479962 + 0.877290i \(0.340651\pi\)
\(548\) 7.21273 0.308113
\(549\) 13.7317 0.586055
\(550\) −12.8663 −0.548622
\(551\) 41.6356 1.77374
\(552\) −3.66063 −0.155807
\(553\) −5.28980 −0.224945
\(554\) 17.7413 0.753757
\(555\) −6.08647 −0.258356
\(556\) −3.15380 −0.133751
\(557\) 26.9804 1.14320 0.571599 0.820533i \(-0.306323\pi\)
0.571599 + 0.820533i \(0.306323\pi\)
\(558\) −15.6501 −0.662522
\(559\) 0.624109 0.0263970
\(560\) −1.40867 −0.0595272
\(561\) −12.3451 −0.521210
\(562\) −3.28356 −0.138509
\(563\) 9.44939 0.398244 0.199122 0.979975i \(-0.436191\pi\)
0.199122 + 0.979975i \(0.436191\pi\)
\(564\) −8.87112 −0.373541
\(565\) 7.58216 0.318984
\(566\) −15.1321 −0.636048
\(567\) −3.68470 −0.154743
\(568\) −9.37398 −0.393323
\(569\) −22.8688 −0.958710 −0.479355 0.877621i \(-0.659129\pi\)
−0.479355 + 0.877621i \(0.659129\pi\)
\(570\) −7.52664 −0.315256
\(571\) 33.7728 1.41335 0.706674 0.707539i \(-0.250195\pi\)
0.706674 + 0.707539i \(0.250195\pi\)
\(572\) −3.40977 −0.142570
\(573\) −6.55847 −0.273984
\(574\) −4.51614 −0.188500
\(575\) 13.8482 0.577510
\(576\) −2.36454 −0.0985226
\(577\) 30.0463 1.25084 0.625422 0.780286i \(-0.284927\pi\)
0.625422 + 0.780286i \(0.284927\pi\)
\(578\) 3.82487 0.159094
\(579\) 14.9532 0.621432
\(580\) −8.75034 −0.363338
\(581\) −14.1032 −0.585100
\(582\) −2.82856 −0.117247
\(583\) 14.3606 0.594757
\(584\) 3.99440 0.165290
\(585\) −2.66200 −0.110060
\(586\) −3.09226 −0.127740
\(587\) −3.46068 −0.142838 −0.0714189 0.997446i \(-0.522753\pi\)
−0.0714189 + 0.997446i \(0.522753\pi\)
\(588\) −0.797155 −0.0328741
\(589\) 44.3628 1.82794
\(590\) −7.60022 −0.312896
\(591\) 16.2808 0.669703
\(592\) 5.42018 0.222768
\(593\) 10.4962 0.431029 0.215514 0.976501i \(-0.430857\pi\)
0.215514 + 0.976501i \(0.430857\pi\)
\(594\) 18.2452 0.748611
\(595\) 5.11313 0.209618
\(596\) 16.0083 0.655726
\(597\) 11.0333 0.451563
\(598\) 3.66998 0.150077
\(599\) 6.44694 0.263415 0.131707 0.991289i \(-0.457954\pi\)
0.131707 + 0.991289i \(0.457954\pi\)
\(600\) −2.40394 −0.0981405
\(601\) −8.45631 −0.344940 −0.172470 0.985015i \(-0.555175\pi\)
−0.172470 + 0.985015i \(0.555175\pi\)
\(602\) 0.780925 0.0318281
\(603\) 11.5459 0.470184
\(604\) 9.62444 0.391613
\(605\) 10.1469 0.412531
\(606\) 7.40942 0.300987
\(607\) −25.4777 −1.03411 −0.517053 0.855953i \(-0.672971\pi\)
−0.517053 + 0.855953i \(0.672971\pi\)
\(608\) 6.70269 0.271830
\(609\) −4.95175 −0.200655
\(610\) 8.18062 0.331224
\(611\) 8.89378 0.359804
\(612\) 8.58272 0.346936
\(613\) −37.4831 −1.51393 −0.756964 0.653456i \(-0.773318\pi\)
−0.756964 + 0.653456i \(0.773318\pi\)
\(614\) −12.4885 −0.503993
\(615\) 5.07131 0.204495
\(616\) −4.26652 −0.171903
\(617\) 44.3768 1.78654 0.893271 0.449518i \(-0.148404\pi\)
0.893271 + 0.449518i \(0.148404\pi\)
\(618\) 6.73922 0.271091
\(619\) 23.0916 0.928131 0.464066 0.885801i \(-0.346390\pi\)
0.464066 + 0.885801i \(0.346390\pi\)
\(620\) −9.32351 −0.374441
\(621\) −19.6376 −0.788029
\(622\) 17.8336 0.715060
\(623\) 13.9685 0.559635
\(624\) −0.637080 −0.0255036
\(625\) −0.827608 −0.0331043
\(626\) 28.9134 1.15561
\(627\) −22.7964 −0.910400
\(628\) −2.78528 −0.111145
\(629\) −19.6739 −0.784451
\(630\) −3.33086 −0.132705
\(631\) −0.164653 −0.00655472 −0.00327736 0.999995i \(-0.501043\pi\)
−0.00327736 + 0.999995i \(0.501043\pi\)
\(632\) −5.28980 −0.210417
\(633\) −18.1427 −0.721107
\(634\) 7.35728 0.292195
\(635\) 18.4098 0.730570
\(636\) 2.68314 0.106393
\(637\) 0.799192 0.0316651
\(638\) −26.5027 −1.04925
\(639\) −22.1652 −0.876841
\(640\) −1.40867 −0.0556826
\(641\) 5.09320 0.201169 0.100585 0.994928i \(-0.467929\pi\)
0.100585 + 0.994928i \(0.467929\pi\)
\(642\) 9.63823 0.380391
\(643\) −27.0878 −1.06824 −0.534119 0.845409i \(-0.679357\pi\)
−0.534119 + 0.845409i \(0.679357\pi\)
\(644\) 4.59211 0.180955
\(645\) −0.876923 −0.0345288
\(646\) −24.3291 −0.957217
\(647\) 9.90929 0.389574 0.194787 0.980846i \(-0.437598\pi\)
0.194787 + 0.980846i \(0.437598\pi\)
\(648\) −3.68470 −0.144749
\(649\) −23.0192 −0.903584
\(650\) 2.41008 0.0945312
\(651\) −5.27610 −0.206787
\(652\) 7.65399 0.299753
\(653\) 10.1183 0.395961 0.197980 0.980206i \(-0.436562\pi\)
0.197980 + 0.980206i \(0.436562\pi\)
\(654\) −4.39612 −0.171902
\(655\) 8.10335 0.316624
\(656\) −4.51614 −0.176326
\(657\) 9.44494 0.368482
\(658\) 11.1285 0.433833
\(659\) −22.7802 −0.887392 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(660\) 4.79100 0.186489
\(661\) −29.7642 −1.15769 −0.578846 0.815437i \(-0.696497\pi\)
−0.578846 + 0.815437i \(0.696497\pi\)
\(662\) 6.60868 0.256854
\(663\) 2.31244 0.0898079
\(664\) −14.1032 −0.547311
\(665\) 9.44188 0.366140
\(666\) 12.8162 0.496619
\(667\) 28.5252 1.10450
\(668\) 8.70855 0.336944
\(669\) 6.94128 0.268365
\(670\) 6.87841 0.265736
\(671\) 24.7771 0.956510
\(672\) −0.797155 −0.0307509
\(673\) 5.64016 0.217412 0.108706 0.994074i \(-0.465329\pi\)
0.108706 + 0.994074i \(0.465329\pi\)
\(674\) 13.4528 0.518183
\(675\) −12.8960 −0.496369
\(676\) −12.3613 −0.475434
\(677\) −31.1155 −1.19586 −0.597932 0.801547i \(-0.704011\pi\)
−0.597932 + 0.801547i \(0.704011\pi\)
\(678\) 4.29069 0.164783
\(679\) 3.54831 0.136172
\(680\) 5.11313 0.196079
\(681\) 13.3931 0.513224
\(682\) −28.2387 −1.08131
\(683\) −0.451659 −0.0172822 −0.00864112 0.999963i \(-0.502751\pi\)
−0.00864112 + 0.999963i \(0.502751\pi\)
\(684\) 15.8488 0.605994
\(685\) 10.1604 0.388207
\(686\) 1.00000 0.0381802
\(687\) −19.2051 −0.732719
\(688\) 0.780925 0.0297725
\(689\) −2.68999 −0.102481
\(690\) −5.15661 −0.196309
\(691\) −40.4771 −1.53982 −0.769910 0.638152i \(-0.779699\pi\)
−0.769910 + 0.638152i \(0.779699\pi\)
\(692\) 0.799481 0.0303917
\(693\) −10.0884 −0.383226
\(694\) 13.0592 0.495719
\(695\) −4.44266 −0.168520
\(696\) −4.95175 −0.187696
\(697\) 16.3925 0.620910
\(698\) 32.8893 1.24488
\(699\) 10.2007 0.385827
\(700\) 3.01565 0.113981
\(701\) 9.36340 0.353651 0.176825 0.984242i \(-0.443417\pi\)
0.176825 + 0.984242i \(0.443417\pi\)
\(702\) −3.41764 −0.128991
\(703\) −36.3298 −1.37020
\(704\) −4.26652 −0.160801
\(705\) −12.4965 −0.470644
\(706\) −33.8962 −1.27570
\(707\) −9.29483 −0.349568
\(708\) −4.30091 −0.161638
\(709\) 42.8899 1.61076 0.805381 0.592757i \(-0.201961\pi\)
0.805381 + 0.592757i \(0.201961\pi\)
\(710\) −13.2048 −0.495569
\(711\) −12.5080 −0.469086
\(712\) 13.9685 0.523491
\(713\) 30.3936 1.13825
\(714\) 2.89348 0.108286
\(715\) −4.80324 −0.179631
\(716\) −7.40805 −0.276852
\(717\) −2.29037 −0.0855354
\(718\) 20.3577 0.759743
\(719\) 42.3347 1.57882 0.789409 0.613867i \(-0.210387\pi\)
0.789409 + 0.613867i \(0.210387\pi\)
\(720\) −3.33086 −0.124134
\(721\) −8.45408 −0.314846
\(722\) −25.9261 −0.964869
\(723\) 6.53000 0.242853
\(724\) −11.7333 −0.436063
\(725\) 18.7325 0.695709
\(726\) 5.74206 0.213108
\(727\) 50.0598 1.85661 0.928307 0.371814i \(-0.121264\pi\)
0.928307 + 0.371814i \(0.121264\pi\)
\(728\) 0.799192 0.0296200
\(729\) 1.51418 0.0560806
\(730\) 5.62680 0.208257
\(731\) −2.83457 −0.104840
\(732\) 4.62935 0.171106
\(733\) −42.7236 −1.57803 −0.789016 0.614372i \(-0.789409\pi\)
−0.789016 + 0.614372i \(0.789409\pi\)
\(734\) −23.4757 −0.866503
\(735\) −1.12293 −0.0414198
\(736\) 4.59211 0.169268
\(737\) 20.8331 0.767395
\(738\) −10.6786 −0.393085
\(739\) −17.5227 −0.644583 −0.322292 0.946640i \(-0.604453\pi\)
−0.322292 + 0.946640i \(0.604453\pi\)
\(740\) 7.63524 0.280677
\(741\) 4.27015 0.156868
\(742\) −3.36589 −0.123566
\(743\) −19.0604 −0.699259 −0.349629 0.936888i \(-0.613693\pi\)
−0.349629 + 0.936888i \(0.613693\pi\)
\(744\) −5.27610 −0.193431
\(745\) 22.5504 0.826184
\(746\) −7.31132 −0.267686
\(747\) −33.3477 −1.22013
\(748\) 15.4864 0.566240
\(749\) −12.0908 −0.441788
\(750\) −9.00100 −0.328670
\(751\) 39.7034 1.44880 0.724398 0.689382i \(-0.242118\pi\)
0.724398 + 0.689382i \(0.242118\pi\)
\(752\) 11.1285 0.405813
\(753\) 11.3958 0.415287
\(754\) 4.96440 0.180793
\(755\) 13.5577 0.493414
\(756\) −4.27637 −0.155530
\(757\) 29.3432 1.06650 0.533248 0.845959i \(-0.320971\pi\)
0.533248 + 0.845959i \(0.320971\pi\)
\(758\) 15.8034 0.574005
\(759\) −15.6181 −0.566902
\(760\) 9.44188 0.342493
\(761\) 8.77351 0.318039 0.159020 0.987275i \(-0.449167\pi\)
0.159020 + 0.987275i \(0.449167\pi\)
\(762\) 10.4180 0.377403
\(763\) 5.51476 0.199648
\(764\) 8.22734 0.297655
\(765\) 12.0902 0.437122
\(766\) −13.1987 −0.476890
\(767\) 4.31189 0.155693
\(768\) −0.797155 −0.0287649
\(769\) −2.17784 −0.0785349 −0.0392675 0.999229i \(-0.512502\pi\)
−0.0392675 + 0.999229i \(0.512502\pi\)
\(770\) −6.01012 −0.216590
\(771\) −6.87143 −0.247469
\(772\) −18.7582 −0.675121
\(773\) 16.9098 0.608204 0.304102 0.952639i \(-0.401644\pi\)
0.304102 + 0.952639i \(0.401644\pi\)
\(774\) 1.84653 0.0663722
\(775\) 19.9596 0.716969
\(776\) 3.54831 0.127377
\(777\) 4.32072 0.155005
\(778\) −33.1194 −1.18739
\(779\) 30.2703 1.08455
\(780\) −0.897435 −0.0321333
\(781\) −39.9943 −1.43111
\(782\) −16.6682 −0.596055
\(783\) −26.5639 −0.949316
\(784\) 1.00000 0.0357143
\(785\) −3.92354 −0.140037
\(786\) 4.58563 0.163564
\(787\) −0.623669 −0.0222314 −0.0111157 0.999938i \(-0.503538\pi\)
−0.0111157 + 0.999938i \(0.503538\pi\)
\(788\) −20.4237 −0.727562
\(789\) 18.0530 0.642702
\(790\) −7.45159 −0.265116
\(791\) −5.38250 −0.191380
\(792\) −10.0884 −0.358475
\(793\) −4.64118 −0.164813
\(794\) 17.0911 0.606540
\(795\) 3.77966 0.134051
\(796\) −13.8409 −0.490576
\(797\) 35.5372 1.25879 0.629396 0.777084i \(-0.283302\pi\)
0.629396 + 0.777084i \(0.283302\pi\)
\(798\) 5.34309 0.189143
\(799\) −40.3936 −1.42902
\(800\) 3.01565 0.106619
\(801\) 33.0291 1.16702
\(802\) 20.1721 0.712301
\(803\) 17.0422 0.601406
\(804\) 3.89244 0.137276
\(805\) 6.46877 0.227994
\(806\) 5.28958 0.186318
\(807\) 0.911518 0.0320870
\(808\) −9.29483 −0.326991
\(809\) 15.9061 0.559227 0.279614 0.960113i \(-0.409794\pi\)
0.279614 + 0.960113i \(0.409794\pi\)
\(810\) −5.19052 −0.182376
\(811\) 21.1041 0.741064 0.370532 0.928820i \(-0.379175\pi\)
0.370532 + 0.928820i \(0.379175\pi\)
\(812\) 6.21178 0.217991
\(813\) 21.1735 0.742587
\(814\) 23.1253 0.810541
\(815\) 10.7819 0.377675
\(816\) 2.89348 0.101292
\(817\) −5.23430 −0.183125
\(818\) −32.3193 −1.13002
\(819\) 1.88972 0.0660323
\(820\) −6.36175 −0.222162
\(821\) 14.3095 0.499405 0.249702 0.968323i \(-0.419667\pi\)
0.249702 + 0.968323i \(0.419667\pi\)
\(822\) 5.74967 0.200543
\(823\) −45.2039 −1.57571 −0.787854 0.615862i \(-0.788808\pi\)
−0.787854 + 0.615862i \(0.788808\pi\)
\(824\) −8.45408 −0.294512
\(825\) −10.2565 −0.357084
\(826\) 5.39532 0.187727
\(827\) −1.63444 −0.0568352 −0.0284176 0.999596i \(-0.509047\pi\)
−0.0284176 + 0.999596i \(0.509047\pi\)
\(828\) 10.8582 0.377350
\(829\) −6.78874 −0.235783 −0.117891 0.993026i \(-0.537613\pi\)
−0.117891 + 0.993026i \(0.537613\pi\)
\(830\) −19.8668 −0.689586
\(831\) 14.1426 0.490601
\(832\) 0.799192 0.0277070
\(833\) −3.62976 −0.125764
\(834\) −2.51407 −0.0870550
\(835\) 12.2675 0.424533
\(836\) 28.5972 0.989054
\(837\) −28.3039 −0.978325
\(838\) 22.7045 0.784314
\(839\) −13.8355 −0.477656 −0.238828 0.971062i \(-0.576763\pi\)
−0.238828 + 0.971062i \(0.576763\pi\)
\(840\) −1.12293 −0.0387447
\(841\) 9.58617 0.330558
\(842\) −16.2815 −0.561098
\(843\) −2.61751 −0.0901518
\(844\) 22.7593 0.783407
\(845\) −17.4130 −0.599025
\(846\) 26.3137 0.904685
\(847\) −7.20319 −0.247505
\(848\) −3.36589 −0.115585
\(849\) −12.0626 −0.413988
\(850\) −10.9461 −0.375447
\(851\) −24.8901 −0.853221
\(852\) −7.47251 −0.256004
\(853\) −34.3220 −1.17516 −0.587582 0.809165i \(-0.699920\pi\)
−0.587582 + 0.809165i \(0.699920\pi\)
\(854\) −5.80734 −0.198723
\(855\) 22.3257 0.763524
\(856\) −12.0908 −0.413254
\(857\) 1.08984 0.0372282 0.0186141 0.999827i \(-0.494075\pi\)
0.0186141 + 0.999827i \(0.494075\pi\)
\(858\) −2.71811 −0.0927949
\(859\) 54.4606 1.85817 0.929086 0.369863i \(-0.120595\pi\)
0.929086 + 0.369863i \(0.120595\pi\)
\(860\) 1.10007 0.0375119
\(861\) −3.60007 −0.122690
\(862\) −1.00000 −0.0340601
\(863\) 1.23710 0.0421113 0.0210557 0.999778i \(-0.493297\pi\)
0.0210557 + 0.999778i \(0.493297\pi\)
\(864\) −4.27637 −0.145485
\(865\) 1.12620 0.0382921
\(866\) −5.04478 −0.171429
\(867\) 3.04902 0.103550
\(868\) 6.61866 0.224652
\(869\) −22.5691 −0.765603
\(870\) −6.97538 −0.236488
\(871\) −3.90239 −0.132227
\(872\) 5.51476 0.186753
\(873\) 8.39014 0.283963
\(874\) −30.7795 −1.04113
\(875\) 11.2914 0.381719
\(876\) 3.18416 0.107583
\(877\) −55.8532 −1.88603 −0.943014 0.332753i \(-0.892022\pi\)
−0.943014 + 0.332753i \(0.892022\pi\)
\(878\) −12.8675 −0.434257
\(879\) −2.46501 −0.0831428
\(880\) −6.01012 −0.202601
\(881\) 3.74474 0.126164 0.0630818 0.998008i \(-0.479907\pi\)
0.0630818 + 0.998008i \(0.479907\pi\)
\(882\) 2.36454 0.0796183
\(883\) 31.3669 1.05558 0.527789 0.849375i \(-0.323021\pi\)
0.527789 + 0.849375i \(0.323021\pi\)
\(884\) −2.90087 −0.0975669
\(885\) −6.05856 −0.203656
\(886\) −7.97797 −0.268025
\(887\) −9.21818 −0.309516 −0.154758 0.987952i \(-0.549460\pi\)
−0.154758 + 0.987952i \(0.549460\pi\)
\(888\) 4.32072 0.144994
\(889\) −13.0689 −0.438317
\(890\) 19.6770 0.659574
\(891\) −15.7208 −0.526668
\(892\) −8.70757 −0.291551
\(893\) −74.5907 −2.49608
\(894\) 12.7611 0.426796
\(895\) −10.4355 −0.348820
\(896\) 1.00000 0.0334077
\(897\) 2.92554 0.0976810
\(898\) −33.4115 −1.11496
\(899\) 41.1137 1.37122
\(900\) 7.13063 0.237688
\(901\) 12.2174 0.407019
\(902\) −19.2682 −0.641561
\(903\) 0.622518 0.0207161
\(904\) −5.38250 −0.179019
\(905\) −16.5283 −0.549419
\(906\) 7.67218 0.254891
\(907\) −55.8219 −1.85353 −0.926767 0.375637i \(-0.877424\pi\)
−0.926767 + 0.375637i \(0.877424\pi\)
\(908\) −16.8011 −0.557564
\(909\) −21.9780 −0.728965
\(910\) 1.12580 0.0373198
\(911\) −52.2580 −1.73139 −0.865693 0.500576i \(-0.833122\pi\)
−0.865693 + 0.500576i \(0.833122\pi\)
\(912\) 5.34309 0.176927
\(913\) −60.1717 −1.99139
\(914\) −14.1064 −0.466599
\(915\) 6.52123 0.215585
\(916\) 24.0920 0.796023
\(917\) −5.75249 −0.189964
\(918\) 15.5222 0.512309
\(919\) −26.2785 −0.866847 −0.433423 0.901190i \(-0.642694\pi\)
−0.433423 + 0.901190i \(0.642694\pi\)
\(920\) 6.46877 0.213269
\(921\) −9.95524 −0.328036
\(922\) −12.0170 −0.395759
\(923\) 7.49161 0.246589
\(924\) −3.40108 −0.111887
\(925\) −16.3454 −0.537432
\(926\) 11.9976 0.394265
\(927\) −19.9900 −0.656559
\(928\) 6.21178 0.203912
\(929\) 59.5011 1.95217 0.976084 0.217396i \(-0.0697561\pi\)
0.976084 + 0.217396i \(0.0697561\pi\)
\(930\) −7.43228 −0.243714
\(931\) −6.70269 −0.219672
\(932\) −12.7964 −0.419160
\(933\) 14.2161 0.465415
\(934\) −11.6270 −0.380448
\(935\) 21.8153 0.713435
\(936\) 1.88972 0.0617676
\(937\) 28.4226 0.928527 0.464263 0.885697i \(-0.346319\pi\)
0.464263 + 0.885697i \(0.346319\pi\)
\(938\) −4.88292 −0.159433
\(939\) 23.0485 0.752159
\(940\) 15.6763 0.511306
\(941\) −5.91289 −0.192755 −0.0963773 0.995345i \(-0.530726\pi\)
−0.0963773 + 0.995345i \(0.530726\pi\)
\(942\) −2.22030 −0.0723413
\(943\) 20.7386 0.675343
\(944\) 5.39532 0.175603
\(945\) −6.02400 −0.195961
\(946\) 3.33183 0.108327
\(947\) 10.4490 0.339547 0.169774 0.985483i \(-0.445696\pi\)
0.169774 + 0.985483i \(0.445696\pi\)
\(948\) −4.21680 −0.136955
\(949\) −3.19229 −0.103626
\(950\) −20.2130 −0.655795
\(951\) 5.86490 0.190182
\(952\) −3.62976 −0.117641
\(953\) 22.5565 0.730677 0.365338 0.930875i \(-0.380953\pi\)
0.365338 + 0.930875i \(0.380953\pi\)
\(954\) −7.95880 −0.257676
\(955\) 11.5896 0.375031
\(956\) 2.87318 0.0929253
\(957\) −21.1267 −0.682931
\(958\) −2.99665 −0.0968174
\(959\) −7.21273 −0.232911
\(960\) −1.12293 −0.0362424
\(961\) 12.8067 0.413119
\(962\) −4.33176 −0.139662
\(963\) −28.5892 −0.921274
\(964\) −8.19163 −0.263835
\(965\) −26.4241 −0.850620
\(966\) 3.66063 0.117779
\(967\) −55.7314 −1.79220 −0.896101 0.443851i \(-0.853612\pi\)
−0.896101 + 0.443851i \(0.853612\pi\)
\(968\) −7.20319 −0.231519
\(969\) −19.3941 −0.623028
\(970\) 4.99840 0.160489
\(971\) 9.35061 0.300075 0.150038 0.988680i \(-0.452061\pi\)
0.150038 + 0.988680i \(0.452061\pi\)
\(972\) −15.7664 −0.505707
\(973\) 3.15380 0.101106
\(974\) 18.3844 0.589076
\(975\) 1.92121 0.0615280
\(976\) −5.80734 −0.185888
\(977\) −59.4553 −1.90214 −0.951072 0.308969i \(-0.900016\pi\)
−0.951072 + 0.308969i \(0.900016\pi\)
\(978\) 6.10142 0.195102
\(979\) 59.5968 1.90472
\(980\) 1.40867 0.0449983
\(981\) 13.0399 0.416332
\(982\) −21.2906 −0.679411
\(983\) −4.33086 −0.138133 −0.0690665 0.997612i \(-0.522002\pi\)
−0.0690665 + 0.997612i \(0.522002\pi\)
\(984\) −3.60007 −0.114766
\(985\) −28.7702 −0.916694
\(986\) −22.5472 −0.718050
\(987\) 8.87112 0.282371
\(988\) −5.35674 −0.170420
\(989\) −3.58609 −0.114031
\(990\) −14.2112 −0.451661
\(991\) −50.8695 −1.61592 −0.807961 0.589236i \(-0.799429\pi\)
−0.807961 + 0.589236i \(0.799429\pi\)
\(992\) 6.61866 0.210143
\(993\) 5.26814 0.167179
\(994\) 9.37398 0.297324
\(995\) −19.4972 −0.618103
\(996\) −11.2425 −0.356231
\(997\) −34.9720 −1.10757 −0.553787 0.832658i \(-0.686818\pi\)
−0.553787 + 0.832658i \(0.686818\pi\)
\(998\) −39.7003 −1.25669
\(999\) 23.1787 0.733342
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 \(a_p\))