Properties

Label 4017.2.a.j.1.2
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36961 q^{2} -1.00000 q^{3} +3.61506 q^{4} -2.39998 q^{5} +2.36961 q^{6} -0.116274 q^{7} -3.82707 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.36961 q^{2} -1.00000 q^{3} +3.61506 q^{4} -2.39998 q^{5} +2.36961 q^{6} -0.116274 q^{7} -3.82707 q^{8} +1.00000 q^{9} +5.68703 q^{10} +6.13402 q^{11} -3.61506 q^{12} +1.00000 q^{13} +0.275524 q^{14} +2.39998 q^{15} +1.83856 q^{16} +2.09587 q^{17} -2.36961 q^{18} -7.41857 q^{19} -8.67609 q^{20} +0.116274 q^{21} -14.5353 q^{22} -1.40898 q^{23} +3.82707 q^{24} +0.759917 q^{25} -2.36961 q^{26} -1.00000 q^{27} -0.420338 q^{28} +7.01793 q^{29} -5.68703 q^{30} +0.944662 q^{31} +3.29748 q^{32} -6.13402 q^{33} -4.96640 q^{34} +0.279056 q^{35} +3.61506 q^{36} +6.01036 q^{37} +17.5791 q^{38} -1.00000 q^{39} +9.18491 q^{40} +7.72190 q^{41} -0.275524 q^{42} +10.3949 q^{43} +22.1749 q^{44} -2.39998 q^{45} +3.33874 q^{46} +11.7311 q^{47} -1.83856 q^{48} -6.98648 q^{49} -1.80071 q^{50} -2.09587 q^{51} +3.61506 q^{52} +2.14660 q^{53} +2.36961 q^{54} -14.7215 q^{55} +0.444989 q^{56} +7.41857 q^{57} -16.6298 q^{58} +5.08541 q^{59} +8.67609 q^{60} -11.4265 q^{61} -2.23848 q^{62} -0.116274 q^{63} -11.4909 q^{64} -2.39998 q^{65} +14.5353 q^{66} +8.27795 q^{67} +7.57671 q^{68} +1.40898 q^{69} -0.661254 q^{70} -13.4824 q^{71} -3.82707 q^{72} -1.99101 q^{73} -14.2422 q^{74} -0.759917 q^{75} -26.8186 q^{76} -0.713228 q^{77} +2.36961 q^{78} +1.94350 q^{79} -4.41251 q^{80} +1.00000 q^{81} -18.2979 q^{82} -3.21526 q^{83} +0.420338 q^{84} -5.03005 q^{85} -24.6319 q^{86} -7.01793 q^{87} -23.4754 q^{88} -6.25664 q^{89} +5.68703 q^{90} -0.116274 q^{91} -5.09356 q^{92} -0.944662 q^{93} -27.7982 q^{94} +17.8044 q^{95} -3.29748 q^{96} -6.94282 q^{97} +16.5553 q^{98} +6.13402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36961 −1.67557 −0.837785 0.546001i \(-0.816149\pi\)
−0.837785 + 0.546001i \(0.816149\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.61506 1.80753
\(5\) −2.39998 −1.07330 −0.536652 0.843803i \(-0.680311\pi\)
−0.536652 + 0.843803i \(0.680311\pi\)
\(6\) 2.36961 0.967390
\(7\) −0.116274 −0.0439474 −0.0219737 0.999759i \(-0.506995\pi\)
−0.0219737 + 0.999759i \(0.506995\pi\)
\(8\) −3.82707 −1.35308
\(9\) 1.00000 0.333333
\(10\) 5.68703 1.79840
\(11\) 6.13402 1.84948 0.924739 0.380602i \(-0.124283\pi\)
0.924739 + 0.380602i \(0.124283\pi\)
\(12\) −3.61506 −1.04358
\(13\) 1.00000 0.277350
\(14\) 0.275524 0.0736370
\(15\) 2.39998 0.619673
\(16\) 1.83856 0.459639
\(17\) 2.09587 0.508323 0.254162 0.967162i \(-0.418200\pi\)
0.254162 + 0.967162i \(0.418200\pi\)
\(18\) −2.36961 −0.558523
\(19\) −7.41857 −1.70194 −0.850969 0.525216i \(-0.823984\pi\)
−0.850969 + 0.525216i \(0.823984\pi\)
\(20\) −8.67609 −1.94003
\(21\) 0.116274 0.0253731
\(22\) −14.5353 −3.09893
\(23\) −1.40898 −0.293793 −0.146897 0.989152i \(-0.546928\pi\)
−0.146897 + 0.989152i \(0.546928\pi\)
\(24\) 3.82707 0.781198
\(25\) 0.759917 0.151983
\(26\) −2.36961 −0.464719
\(27\) −1.00000 −0.192450
\(28\) −0.420338 −0.0794364
\(29\) 7.01793 1.30320 0.651599 0.758564i \(-0.274099\pi\)
0.651599 + 0.758564i \(0.274099\pi\)
\(30\) −5.68703 −1.03830
\(31\) 0.944662 0.169666 0.0848332 0.996395i \(-0.472964\pi\)
0.0848332 + 0.996395i \(0.472964\pi\)
\(32\) 3.29748 0.582918
\(33\) −6.13402 −1.06780
\(34\) −4.96640 −0.851731
\(35\) 0.279056 0.0471690
\(36\) 3.61506 0.602511
\(37\) 6.01036 0.988096 0.494048 0.869435i \(-0.335517\pi\)
0.494048 + 0.869435i \(0.335517\pi\)
\(38\) 17.5791 2.85171
\(39\) −1.00000 −0.160128
\(40\) 9.18491 1.45226
\(41\) 7.72190 1.20596 0.602979 0.797757i \(-0.293980\pi\)
0.602979 + 0.797757i \(0.293980\pi\)
\(42\) −0.275524 −0.0425143
\(43\) 10.3949 1.58521 0.792605 0.609736i \(-0.208724\pi\)
0.792605 + 0.609736i \(0.208724\pi\)
\(44\) 22.1749 3.34299
\(45\) −2.39998 −0.357768
\(46\) 3.33874 0.492271
\(47\) 11.7311 1.71116 0.855580 0.517671i \(-0.173201\pi\)
0.855580 + 0.517671i \(0.173201\pi\)
\(48\) −1.83856 −0.265373
\(49\) −6.98648 −0.998069
\(50\) −1.80071 −0.254659
\(51\) −2.09587 −0.293481
\(52\) 3.61506 0.501319
\(53\) 2.14660 0.294858 0.147429 0.989073i \(-0.452900\pi\)
0.147429 + 0.989073i \(0.452900\pi\)
\(54\) 2.36961 0.322463
\(55\) −14.7215 −1.98505
\(56\) 0.444989 0.0594642
\(57\) 7.41857 0.982614
\(58\) −16.6298 −2.18360
\(59\) 5.08541 0.662064 0.331032 0.943619i \(-0.392603\pi\)
0.331032 + 0.943619i \(0.392603\pi\)
\(60\) 8.67609 1.12008
\(61\) −11.4265 −1.46302 −0.731509 0.681832i \(-0.761183\pi\)
−0.731509 + 0.681832i \(0.761183\pi\)
\(62\) −2.23848 −0.284288
\(63\) −0.116274 −0.0146491
\(64\) −11.4909 −1.43636
\(65\) −2.39998 −0.297681
\(66\) 14.5353 1.78917
\(67\) 8.27795 1.01131 0.505656 0.862735i \(-0.331250\pi\)
0.505656 + 0.862735i \(0.331250\pi\)
\(68\) 7.57671 0.918811
\(69\) 1.40898 0.169621
\(70\) −0.661254 −0.0790349
\(71\) −13.4824 −1.60007 −0.800035 0.599953i \(-0.795186\pi\)
−0.800035 + 0.599953i \(0.795186\pi\)
\(72\) −3.82707 −0.451025
\(73\) −1.99101 −0.233030 −0.116515 0.993189i \(-0.537172\pi\)
−0.116515 + 0.993189i \(0.537172\pi\)
\(74\) −14.2422 −1.65562
\(75\) −0.759917 −0.0877477
\(76\) −26.8186 −3.07631
\(77\) −0.713228 −0.0812798
\(78\) 2.36961 0.268306
\(79\) 1.94350 0.218661 0.109331 0.994005i \(-0.465129\pi\)
0.109331 + 0.994005i \(0.465129\pi\)
\(80\) −4.41251 −0.493333
\(81\) 1.00000 0.111111
\(82\) −18.2979 −2.02067
\(83\) −3.21526 −0.352921 −0.176460 0.984308i \(-0.556465\pi\)
−0.176460 + 0.984308i \(0.556465\pi\)
\(84\) 0.420338 0.0458626
\(85\) −5.03005 −0.545586
\(86\) −24.6319 −2.65613
\(87\) −7.01793 −0.752401
\(88\) −23.4754 −2.50248
\(89\) −6.25664 −0.663203 −0.331601 0.943420i \(-0.607589\pi\)
−0.331601 + 0.943420i \(0.607589\pi\)
\(90\) 5.68703 0.599466
\(91\) −0.116274 −0.0121888
\(92\) −5.09356 −0.531040
\(93\) −0.944662 −0.0979569
\(94\) −27.7982 −2.86717
\(95\) 17.8044 1.82670
\(96\) −3.29748 −0.336548
\(97\) −6.94282 −0.704936 −0.352468 0.935824i \(-0.614658\pi\)
−0.352468 + 0.935824i \(0.614658\pi\)
\(98\) 16.5553 1.67233
\(99\) 6.13402 0.616493
\(100\) 2.74715 0.274715
\(101\) −10.2226 −1.01719 −0.508593 0.861007i \(-0.669834\pi\)
−0.508593 + 0.861007i \(0.669834\pi\)
\(102\) 4.96640 0.491747
\(103\) −1.00000 −0.0985329
\(104\) −3.82707 −0.375276
\(105\) −0.279056 −0.0272330
\(106\) −5.08660 −0.494054
\(107\) −4.67454 −0.451905 −0.225952 0.974138i \(-0.572549\pi\)
−0.225952 + 0.974138i \(0.572549\pi\)
\(108\) −3.61506 −0.347860
\(109\) 3.41075 0.326691 0.163346 0.986569i \(-0.447771\pi\)
0.163346 + 0.986569i \(0.447771\pi\)
\(110\) 34.8844 3.32609
\(111\) −6.01036 −0.570478
\(112\) −0.213776 −0.0202000
\(113\) −5.88948 −0.554036 −0.277018 0.960865i \(-0.589346\pi\)
−0.277018 + 0.960865i \(0.589346\pi\)
\(114\) −17.5791 −1.64644
\(115\) 3.38153 0.315330
\(116\) 25.3703 2.35557
\(117\) 1.00000 0.0924500
\(118\) −12.0505 −1.10933
\(119\) −0.243695 −0.0223395
\(120\) −9.18491 −0.838464
\(121\) 26.6262 2.42057
\(122\) 27.0765 2.45139
\(123\) −7.72190 −0.696261
\(124\) 3.41501 0.306677
\(125\) 10.1761 0.910180
\(126\) 0.275524 0.0245457
\(127\) −6.02610 −0.534730 −0.267365 0.963595i \(-0.586153\pi\)
−0.267365 + 0.963595i \(0.586153\pi\)
\(128\) 20.6339 1.82380
\(129\) −10.3949 −0.915221
\(130\) 5.68703 0.498785
\(131\) −15.5972 −1.36273 −0.681365 0.731944i \(-0.738613\pi\)
−0.681365 + 0.731944i \(0.738613\pi\)
\(132\) −22.1749 −1.93008
\(133\) 0.862587 0.0747958
\(134\) −19.6155 −1.69452
\(135\) 2.39998 0.206558
\(136\) −8.02105 −0.687800
\(137\) 1.52562 0.130342 0.0651710 0.997874i \(-0.479241\pi\)
0.0651710 + 0.997874i \(0.479241\pi\)
\(138\) −3.33874 −0.284213
\(139\) −9.77054 −0.828726 −0.414363 0.910112i \(-0.635996\pi\)
−0.414363 + 0.910112i \(0.635996\pi\)
\(140\) 1.00880 0.0852595
\(141\) −11.7311 −0.987939
\(142\) 31.9481 2.68103
\(143\) 6.13402 0.512953
\(144\) 1.83856 0.153213
\(145\) −16.8429 −1.39873
\(146\) 4.71792 0.390458
\(147\) 6.98648 0.576235
\(148\) 21.7278 1.78602
\(149\) 11.5754 0.948293 0.474146 0.880446i \(-0.342757\pi\)
0.474146 + 0.880446i \(0.342757\pi\)
\(150\) 1.80071 0.147027
\(151\) −2.15749 −0.175574 −0.0877870 0.996139i \(-0.527979\pi\)
−0.0877870 + 0.996139i \(0.527979\pi\)
\(152\) 28.3914 2.30285
\(153\) 2.09587 0.169441
\(154\) 1.69007 0.136190
\(155\) −2.26717 −0.182104
\(156\) −3.61506 −0.289437
\(157\) −2.58005 −0.205911 −0.102955 0.994686i \(-0.532830\pi\)
−0.102955 + 0.994686i \(0.532830\pi\)
\(158\) −4.60535 −0.366382
\(159\) −2.14660 −0.170236
\(160\) −7.91390 −0.625648
\(161\) 0.163828 0.0129115
\(162\) −2.36961 −0.186174
\(163\) 16.0762 1.25919 0.629593 0.776925i \(-0.283222\pi\)
0.629593 + 0.776925i \(0.283222\pi\)
\(164\) 27.9152 2.17981
\(165\) 14.7215 1.14607
\(166\) 7.61892 0.591343
\(167\) −0.398337 −0.0308242 −0.0154121 0.999881i \(-0.504906\pi\)
−0.0154121 + 0.999881i \(0.504906\pi\)
\(168\) −0.444989 −0.0343317
\(169\) 1.00000 0.0769231
\(170\) 11.9193 0.914167
\(171\) −7.41857 −0.567312
\(172\) 37.5783 2.86532
\(173\) 0.645860 0.0491038 0.0245519 0.999699i \(-0.492184\pi\)
0.0245519 + 0.999699i \(0.492184\pi\)
\(174\) 16.6298 1.26070
\(175\) −0.0883586 −0.00667929
\(176\) 11.2778 0.850093
\(177\) −5.08541 −0.382243
\(178\) 14.8258 1.11124
\(179\) −13.3349 −0.996696 −0.498348 0.866977i \(-0.666060\pi\)
−0.498348 + 0.866977i \(0.666060\pi\)
\(180\) −8.67609 −0.646678
\(181\) −7.65395 −0.568914 −0.284457 0.958689i \(-0.591813\pi\)
−0.284457 + 0.958689i \(0.591813\pi\)
\(182\) 0.275524 0.0204232
\(183\) 11.4265 0.844674
\(184\) 5.39228 0.397524
\(185\) −14.4248 −1.06053
\(186\) 2.23848 0.164134
\(187\) 12.8561 0.940133
\(188\) 42.4087 3.09298
\(189\) 0.116274 0.00845769
\(190\) −42.1896 −3.06076
\(191\) 20.8707 1.51015 0.755076 0.655638i \(-0.227600\pi\)
0.755076 + 0.655638i \(0.227600\pi\)
\(192\) 11.4909 0.829282
\(193\) −2.98729 −0.215030 −0.107515 0.994203i \(-0.534289\pi\)
−0.107515 + 0.994203i \(0.534289\pi\)
\(194\) 16.4518 1.18117
\(195\) 2.39998 0.171866
\(196\) −25.2566 −1.80404
\(197\) 14.1735 1.00982 0.504911 0.863171i \(-0.331525\pi\)
0.504911 + 0.863171i \(0.331525\pi\)
\(198\) −14.5353 −1.03298
\(199\) −16.2594 −1.15260 −0.576300 0.817238i \(-0.695504\pi\)
−0.576300 + 0.817238i \(0.695504\pi\)
\(200\) −2.90826 −0.205645
\(201\) −8.27795 −0.583882
\(202\) 24.2236 1.70437
\(203\) −0.816003 −0.0572722
\(204\) −7.57671 −0.530476
\(205\) −18.5324 −1.29436
\(206\) 2.36961 0.165099
\(207\) −1.40898 −0.0979310
\(208\) 1.83856 0.127481
\(209\) −45.5057 −3.14770
\(210\) 0.661254 0.0456308
\(211\) 15.7417 1.08370 0.541850 0.840475i \(-0.317724\pi\)
0.541850 + 0.840475i \(0.317724\pi\)
\(212\) 7.76008 0.532965
\(213\) 13.4824 0.923801
\(214\) 11.0768 0.757198
\(215\) −24.9476 −1.70141
\(216\) 3.82707 0.260399
\(217\) −0.109840 −0.00745640
\(218\) −8.08217 −0.547393
\(219\) 1.99101 0.134540
\(220\) −53.2193 −3.58805
\(221\) 2.09587 0.140984
\(222\) 14.2422 0.955875
\(223\) −2.35632 −0.157791 −0.0788954 0.996883i \(-0.525139\pi\)
−0.0788954 + 0.996883i \(0.525139\pi\)
\(224\) −0.383411 −0.0256177
\(225\) 0.759917 0.0506612
\(226\) 13.9558 0.928326
\(227\) 0.0550758 0.00365551 0.00182775 0.999998i \(-0.499418\pi\)
0.00182775 + 0.999998i \(0.499418\pi\)
\(228\) 26.8186 1.77611
\(229\) −17.8185 −1.17748 −0.588741 0.808322i \(-0.700376\pi\)
−0.588741 + 0.808322i \(0.700376\pi\)
\(230\) −8.01292 −0.528356
\(231\) 0.713228 0.0469269
\(232\) −26.8581 −1.76332
\(233\) 18.3560 1.20254 0.601271 0.799045i \(-0.294661\pi\)
0.601271 + 0.799045i \(0.294661\pi\)
\(234\) −2.36961 −0.154906
\(235\) −28.1545 −1.83660
\(236\) 18.3841 1.19670
\(237\) −1.94350 −0.126244
\(238\) 0.577463 0.0374314
\(239\) 6.73765 0.435822 0.217911 0.975969i \(-0.430076\pi\)
0.217911 + 0.975969i \(0.430076\pi\)
\(240\) 4.41251 0.284826
\(241\) 14.4248 0.929180 0.464590 0.885526i \(-0.346202\pi\)
0.464590 + 0.885526i \(0.346202\pi\)
\(242\) −63.0939 −4.05583
\(243\) −1.00000 −0.0641500
\(244\) −41.3076 −2.64445
\(245\) 16.7674 1.07123
\(246\) 18.2979 1.16663
\(247\) −7.41857 −0.472033
\(248\) −3.61529 −0.229571
\(249\) 3.21526 0.203759
\(250\) −24.1135 −1.52507
\(251\) −3.33272 −0.210360 −0.105180 0.994453i \(-0.533542\pi\)
−0.105180 + 0.994453i \(0.533542\pi\)
\(252\) −0.420338 −0.0264788
\(253\) −8.64273 −0.543364
\(254\) 14.2795 0.895977
\(255\) 5.03005 0.314994
\(256\) −25.9127 −1.61954
\(257\) 17.1817 1.07177 0.535883 0.844292i \(-0.319979\pi\)
0.535883 + 0.844292i \(0.319979\pi\)
\(258\) 24.6319 1.53352
\(259\) −0.698848 −0.0434243
\(260\) −8.67609 −0.538068
\(261\) 7.01793 0.434399
\(262\) 36.9592 2.28335
\(263\) 4.03724 0.248947 0.124473 0.992223i \(-0.460276\pi\)
0.124473 + 0.992223i \(0.460276\pi\)
\(264\) 23.4754 1.44481
\(265\) −5.15179 −0.316472
\(266\) −2.04400 −0.125326
\(267\) 6.25664 0.382900
\(268\) 29.9253 1.82798
\(269\) 23.3134 1.42144 0.710721 0.703474i \(-0.248369\pi\)
0.710721 + 0.703474i \(0.248369\pi\)
\(270\) −5.68703 −0.346102
\(271\) 26.0550 1.58273 0.791364 0.611345i \(-0.209371\pi\)
0.791364 + 0.611345i \(0.209371\pi\)
\(272\) 3.85338 0.233645
\(273\) 0.116274 0.00703722
\(274\) −3.61512 −0.218397
\(275\) 4.66135 0.281090
\(276\) 5.09356 0.306596
\(277\) 30.8306 1.85243 0.926215 0.376995i \(-0.123043\pi\)
0.926215 + 0.376995i \(0.123043\pi\)
\(278\) 23.1524 1.38859
\(279\) 0.944662 0.0565554
\(280\) −1.06797 −0.0638232
\(281\) −25.8182 −1.54018 −0.770092 0.637933i \(-0.779790\pi\)
−0.770092 + 0.637933i \(0.779790\pi\)
\(282\) 27.7982 1.65536
\(283\) 6.88462 0.409248 0.204624 0.978841i \(-0.434403\pi\)
0.204624 + 0.978841i \(0.434403\pi\)
\(284\) −48.7398 −2.89218
\(285\) −17.8044 −1.05464
\(286\) −14.5353 −0.859488
\(287\) −0.897857 −0.0529988
\(288\) 3.29748 0.194306
\(289\) −12.6073 −0.741607
\(290\) 39.9112 2.34367
\(291\) 6.94282 0.406995
\(292\) −7.19763 −0.421209
\(293\) −28.1257 −1.64312 −0.821561 0.570121i \(-0.806896\pi\)
−0.821561 + 0.570121i \(0.806896\pi\)
\(294\) −16.5553 −0.965522
\(295\) −12.2049 −0.710597
\(296\) −23.0021 −1.33697
\(297\) −6.13402 −0.355932
\(298\) −27.4292 −1.58893
\(299\) −1.40898 −0.0814835
\(300\) −2.74715 −0.158607
\(301\) −1.20866 −0.0696659
\(302\) 5.11241 0.294186
\(303\) 10.2226 0.587273
\(304\) −13.6395 −0.782278
\(305\) 27.4235 1.57026
\(306\) −4.96640 −0.283910
\(307\) 18.1931 1.03833 0.519166 0.854673i \(-0.326243\pi\)
0.519166 + 0.854673i \(0.326243\pi\)
\(308\) −2.57836 −0.146916
\(309\) 1.00000 0.0568880
\(310\) 5.37232 0.305127
\(311\) 24.1152 1.36745 0.683725 0.729740i \(-0.260359\pi\)
0.683725 + 0.729740i \(0.260359\pi\)
\(312\) 3.82707 0.216665
\(313\) 5.78369 0.326913 0.163457 0.986551i \(-0.447736\pi\)
0.163457 + 0.986551i \(0.447736\pi\)
\(314\) 6.11373 0.345018
\(315\) 0.279056 0.0157230
\(316\) 7.02589 0.395237
\(317\) 7.27734 0.408736 0.204368 0.978894i \(-0.434486\pi\)
0.204368 + 0.978894i \(0.434486\pi\)
\(318\) 5.08660 0.285242
\(319\) 43.0481 2.41023
\(320\) 27.5779 1.54165
\(321\) 4.67454 0.260907
\(322\) −0.388209 −0.0216340
\(323\) −15.5484 −0.865134
\(324\) 3.61506 0.200837
\(325\) 0.759917 0.0421526
\(326\) −38.0944 −2.10985
\(327\) −3.41075 −0.188615
\(328\) −29.5523 −1.63175
\(329\) −1.36402 −0.0752011
\(330\) −34.8844 −1.92032
\(331\) −0.00818240 −0.000449745 0 −0.000224873 1.00000i \(-0.500072\pi\)
−0.000224873 1.00000i \(0.500072\pi\)
\(332\) −11.6234 −0.637916
\(333\) 6.01036 0.329365
\(334\) 0.943904 0.0516481
\(335\) −19.8669 −1.08545
\(336\) 0.213776 0.0116625
\(337\) 14.9787 0.815942 0.407971 0.912995i \(-0.366237\pi\)
0.407971 + 0.912995i \(0.366237\pi\)
\(338\) −2.36961 −0.128890
\(339\) 5.88948 0.319873
\(340\) −18.1840 −0.986164
\(341\) 5.79458 0.313794
\(342\) 17.5791 0.950571
\(343\) 1.62626 0.0878100
\(344\) −39.7821 −2.14491
\(345\) −3.38153 −0.182056
\(346\) −1.53044 −0.0822769
\(347\) −15.0237 −0.806512 −0.403256 0.915087i \(-0.632122\pi\)
−0.403256 + 0.915087i \(0.632122\pi\)
\(348\) −25.3703 −1.35999
\(349\) −11.8939 −0.636668 −0.318334 0.947979i \(-0.603123\pi\)
−0.318334 + 0.947979i \(0.603123\pi\)
\(350\) 0.209376 0.0111916
\(351\) −1.00000 −0.0533761
\(352\) 20.2268 1.07809
\(353\) 4.60173 0.244926 0.122463 0.992473i \(-0.460921\pi\)
0.122463 + 0.992473i \(0.460921\pi\)
\(354\) 12.0505 0.640475
\(355\) 32.3576 1.71736
\(356\) −22.6182 −1.19876
\(357\) 0.243695 0.0128977
\(358\) 31.5985 1.67003
\(359\) −2.12663 −0.112239 −0.0561195 0.998424i \(-0.517873\pi\)
−0.0561195 + 0.998424i \(0.517873\pi\)
\(360\) 9.18491 0.484087
\(361\) 36.0352 1.89659
\(362\) 18.1369 0.953254
\(363\) −26.6262 −1.39752
\(364\) −0.420338 −0.0220317
\(365\) 4.77839 0.250112
\(366\) −27.0765 −1.41531
\(367\) −18.7710 −0.979838 −0.489919 0.871768i \(-0.662974\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(368\) −2.59049 −0.135039
\(369\) 7.72190 0.401986
\(370\) 34.1811 1.77699
\(371\) −0.249593 −0.0129582
\(372\) −3.41501 −0.177060
\(373\) 2.94927 0.152707 0.0763536 0.997081i \(-0.475672\pi\)
0.0763536 + 0.997081i \(0.475672\pi\)
\(374\) −30.4640 −1.57526
\(375\) −10.1761 −0.525493
\(376\) −44.8959 −2.31533
\(377\) 7.01793 0.361442
\(378\) −0.275524 −0.0141714
\(379\) −29.8273 −1.53213 −0.766064 0.642764i \(-0.777787\pi\)
−0.766064 + 0.642764i \(0.777787\pi\)
\(380\) 64.3642 3.30181
\(381\) 6.02610 0.308726
\(382\) −49.4555 −2.53036
\(383\) −3.24483 −0.165803 −0.0829014 0.996558i \(-0.526419\pi\)
−0.0829014 + 0.996558i \(0.526419\pi\)
\(384\) −20.6339 −1.05297
\(385\) 1.71173 0.0872380
\(386\) 7.07871 0.360297
\(387\) 10.3949 0.528403
\(388\) −25.0987 −1.27420
\(389\) −33.9431 −1.72098 −0.860491 0.509466i \(-0.829843\pi\)
−0.860491 + 0.509466i \(0.829843\pi\)
\(390\) −5.68703 −0.287974
\(391\) −2.95304 −0.149342
\(392\) 26.7378 1.35046
\(393\) 15.5972 0.786772
\(394\) −33.5858 −1.69203
\(395\) −4.66437 −0.234690
\(396\) 22.1749 1.11433
\(397\) 22.9989 1.15428 0.577142 0.816644i \(-0.304168\pi\)
0.577142 + 0.816644i \(0.304168\pi\)
\(398\) 38.5286 1.93126
\(399\) −0.862587 −0.0431834
\(400\) 1.39715 0.0698576
\(401\) −3.15596 −0.157601 −0.0788006 0.996890i \(-0.525109\pi\)
−0.0788006 + 0.996890i \(0.525109\pi\)
\(402\) 19.6155 0.978334
\(403\) 0.944662 0.0470570
\(404\) −36.9553 −1.83860
\(405\) −2.39998 −0.119256
\(406\) 1.93361 0.0959635
\(407\) 36.8677 1.82746
\(408\) 8.02105 0.397101
\(409\) 28.6686 1.41757 0.708785 0.705425i \(-0.249244\pi\)
0.708785 + 0.705425i \(0.249244\pi\)
\(410\) 43.9147 2.16879
\(411\) −1.52562 −0.0752530
\(412\) −3.61506 −0.178101
\(413\) −0.591301 −0.0290960
\(414\) 3.33874 0.164090
\(415\) 7.71657 0.378792
\(416\) 3.29748 0.161672
\(417\) 9.77054 0.478465
\(418\) 107.831 5.27418
\(419\) 9.68642 0.473212 0.236606 0.971606i \(-0.423965\pi\)
0.236606 + 0.971606i \(0.423965\pi\)
\(420\) −1.00880 −0.0492246
\(421\) 6.86042 0.334356 0.167178 0.985927i \(-0.446534\pi\)
0.167178 + 0.985927i \(0.446534\pi\)
\(422\) −37.3016 −1.81582
\(423\) 11.7311 0.570387
\(424\) −8.21518 −0.398965
\(425\) 1.59269 0.0772567
\(426\) −31.9481 −1.54789
\(427\) 1.32861 0.0642959
\(428\) −16.8988 −0.816832
\(429\) −6.13402 −0.296153
\(430\) 59.1162 2.85084
\(431\) 34.0110 1.63825 0.819127 0.573613i \(-0.194459\pi\)
0.819127 + 0.573613i \(0.194459\pi\)
\(432\) −1.83856 −0.0884576
\(433\) −17.7135 −0.851256 −0.425628 0.904898i \(-0.639947\pi\)
−0.425628 + 0.904898i \(0.639947\pi\)
\(434\) 0.260277 0.0124937
\(435\) 16.8429 0.807556
\(436\) 12.3301 0.590504
\(437\) 10.4526 0.500017
\(438\) −4.71792 −0.225431
\(439\) 4.41143 0.210546 0.105273 0.994443i \(-0.466428\pi\)
0.105273 + 0.994443i \(0.466428\pi\)
\(440\) 56.3405 2.68593
\(441\) −6.98648 −0.332690
\(442\) −4.96640 −0.236228
\(443\) −16.1742 −0.768460 −0.384230 0.923237i \(-0.625533\pi\)
−0.384230 + 0.923237i \(0.625533\pi\)
\(444\) −21.7278 −1.03116
\(445\) 15.0158 0.711819
\(446\) 5.58356 0.264389
\(447\) −11.5754 −0.547497
\(448\) 1.33609 0.0631243
\(449\) 15.8538 0.748187 0.374093 0.927391i \(-0.377954\pi\)
0.374093 + 0.927391i \(0.377954\pi\)
\(450\) −1.80071 −0.0848863
\(451\) 47.3663 2.23039
\(452\) −21.2909 −1.00144
\(453\) 2.15749 0.101368
\(454\) −0.130508 −0.00612506
\(455\) 0.279056 0.0130823
\(456\) −28.3914 −1.32955
\(457\) −21.8320 −1.02126 −0.510629 0.859801i \(-0.670588\pi\)
−0.510629 + 0.859801i \(0.670588\pi\)
\(458\) 42.2230 1.97295
\(459\) −2.09587 −0.0978269
\(460\) 12.2245 0.569968
\(461\) 22.9270 1.06782 0.533908 0.845543i \(-0.320723\pi\)
0.533908 + 0.845543i \(0.320723\pi\)
\(462\) −1.69007 −0.0786293
\(463\) 21.4577 0.997223 0.498611 0.866826i \(-0.333843\pi\)
0.498611 + 0.866826i \(0.333843\pi\)
\(464\) 12.9029 0.599001
\(465\) 2.26717 0.105138
\(466\) −43.4966 −2.01494
\(467\) −18.3118 −0.847368 −0.423684 0.905810i \(-0.639263\pi\)
−0.423684 + 0.905810i \(0.639263\pi\)
\(468\) 3.61506 0.167106
\(469\) −0.962510 −0.0444446
\(470\) 66.7152 3.07734
\(471\) 2.58005 0.118883
\(472\) −19.4623 −0.895823
\(473\) 63.7627 2.93181
\(474\) 4.60535 0.211531
\(475\) −5.63750 −0.258666
\(476\) −0.880974 −0.0403794
\(477\) 2.14660 0.0982859
\(478\) −15.9656 −0.730250
\(479\) 6.66562 0.304560 0.152280 0.988337i \(-0.451338\pi\)
0.152280 + 0.988337i \(0.451338\pi\)
\(480\) 7.91390 0.361218
\(481\) 6.01036 0.274049
\(482\) −34.1811 −1.55691
\(483\) −0.163828 −0.00745443
\(484\) 96.2555 4.37525
\(485\) 16.6626 0.756612
\(486\) 2.36961 0.107488
\(487\) 39.6562 1.79699 0.898496 0.438981i \(-0.144660\pi\)
0.898496 + 0.438981i \(0.144660\pi\)
\(488\) 43.7302 1.97957
\(489\) −16.0762 −0.726992
\(490\) −39.7323 −1.79492
\(491\) 2.41411 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(492\) −27.9152 −1.25851
\(493\) 14.7087 0.662445
\(494\) 17.5791 0.790923
\(495\) −14.7215 −0.661684
\(496\) 1.73682 0.0779853
\(497\) 1.56766 0.0703190
\(498\) −7.61892 −0.341412
\(499\) 10.4716 0.468775 0.234388 0.972143i \(-0.424692\pi\)
0.234388 + 0.972143i \(0.424692\pi\)
\(500\) 36.7873 1.64518
\(501\) 0.398337 0.0177964
\(502\) 7.89726 0.352472
\(503\) −20.7218 −0.923937 −0.461969 0.886896i \(-0.652857\pi\)
−0.461969 + 0.886896i \(0.652857\pi\)
\(504\) 0.444989 0.0198214
\(505\) 24.5341 1.09175
\(506\) 20.4799 0.910443
\(507\) −1.00000 −0.0444116
\(508\) −21.7847 −0.966541
\(509\) 29.3660 1.30163 0.650813 0.759238i \(-0.274428\pi\)
0.650813 + 0.759238i \(0.274428\pi\)
\(510\) −11.9193 −0.527794
\(511\) 0.231503 0.0102411
\(512\) 20.1352 0.889859
\(513\) 7.41857 0.327538
\(514\) −40.7140 −1.79582
\(515\) 2.39998 0.105756
\(516\) −37.5783 −1.65429
\(517\) 71.9590 3.16475
\(518\) 1.65600 0.0727604
\(519\) −0.645860 −0.0283501
\(520\) 9.18491 0.402785
\(521\) −15.6956 −0.687635 −0.343817 0.939037i \(-0.611720\pi\)
−0.343817 + 0.939037i \(0.611720\pi\)
\(522\) −16.6298 −0.727866
\(523\) −37.7153 −1.64917 −0.824587 0.565735i \(-0.808593\pi\)
−0.824587 + 0.565735i \(0.808593\pi\)
\(524\) −56.3847 −2.46318
\(525\) 0.0883586 0.00385629
\(526\) −9.56670 −0.417128
\(527\) 1.97989 0.0862453
\(528\) −11.2778 −0.490801
\(529\) −21.0148 −0.913686
\(530\) 12.2078 0.530271
\(531\) 5.08541 0.220688
\(532\) 3.11831 0.135196
\(533\) 7.72190 0.334473
\(534\) −14.8258 −0.641576
\(535\) 11.2188 0.485032
\(536\) −31.6803 −1.36838
\(537\) 13.3349 0.575443
\(538\) −55.2437 −2.38172
\(539\) −42.8552 −1.84591
\(540\) 8.67609 0.373359
\(541\) −28.6810 −1.23309 −0.616546 0.787319i \(-0.711469\pi\)
−0.616546 + 0.787319i \(0.711469\pi\)
\(542\) −61.7402 −2.65197
\(543\) 7.65395 0.328462
\(544\) 6.91109 0.296311
\(545\) −8.18575 −0.350639
\(546\) −0.275524 −0.0117914
\(547\) 18.8589 0.806346 0.403173 0.915124i \(-0.367907\pi\)
0.403173 + 0.915124i \(0.367907\pi\)
\(548\) 5.51520 0.235597
\(549\) −11.4265 −0.487673
\(550\) −11.0456 −0.470986
\(551\) −52.0630 −2.21796
\(552\) −5.39228 −0.229511
\(553\) −0.225979 −0.00960960
\(554\) −73.0565 −3.10387
\(555\) 14.4248 0.612297
\(556\) −35.3211 −1.49795
\(557\) 32.3709 1.37160 0.685799 0.727791i \(-0.259453\pi\)
0.685799 + 0.727791i \(0.259453\pi\)
\(558\) −2.23848 −0.0947625
\(559\) 10.3949 0.439658
\(560\) 0.513060 0.0216807
\(561\) −12.8561 −0.542786
\(562\) 61.1791 2.58068
\(563\) 36.1358 1.52294 0.761472 0.648198i \(-0.224477\pi\)
0.761472 + 0.648198i \(0.224477\pi\)
\(564\) −42.4087 −1.78573
\(565\) 14.1347 0.594650
\(566\) −16.3139 −0.685724
\(567\) −0.116274 −0.00488305
\(568\) 51.5983 2.16502
\(569\) 25.5231 1.06998 0.534992 0.844857i \(-0.320315\pi\)
0.534992 + 0.844857i \(0.320315\pi\)
\(570\) 42.1896 1.76713
\(571\) −13.9219 −0.582612 −0.291306 0.956630i \(-0.594090\pi\)
−0.291306 + 0.956630i \(0.594090\pi\)
\(572\) 22.1749 0.927178
\(573\) −20.8707 −0.871886
\(574\) 2.12757 0.0888032
\(575\) −1.07071 −0.0446517
\(576\) −11.4909 −0.478786
\(577\) −17.7906 −0.740633 −0.370316 0.928906i \(-0.620751\pi\)
−0.370316 + 0.928906i \(0.620751\pi\)
\(578\) 29.8745 1.24261
\(579\) 2.98729 0.124147
\(580\) −60.8882 −2.52824
\(581\) 0.373851 0.0155100
\(582\) −16.4518 −0.681949
\(583\) 13.1673 0.545333
\(584\) 7.61974 0.315307
\(585\) −2.39998 −0.0992271
\(586\) 66.6470 2.75316
\(587\) 20.7514 0.856503 0.428251 0.903660i \(-0.359130\pi\)
0.428251 + 0.903660i \(0.359130\pi\)
\(588\) 25.2566 1.04156
\(589\) −7.00804 −0.288761
\(590\) 28.9209 1.19065
\(591\) −14.1735 −0.583022
\(592\) 11.0504 0.454168
\(593\) 8.47324 0.347954 0.173977 0.984750i \(-0.444338\pi\)
0.173977 + 0.984750i \(0.444338\pi\)
\(594\) 14.5353 0.596389
\(595\) 0.584865 0.0239771
\(596\) 41.8458 1.71407
\(597\) 16.2594 0.665454
\(598\) 3.33874 0.136531
\(599\) −18.8081 −0.768479 −0.384239 0.923234i \(-0.625536\pi\)
−0.384239 + 0.923234i \(0.625536\pi\)
\(600\) 2.90826 0.118729
\(601\) 25.0414 1.02146 0.510729 0.859742i \(-0.329375\pi\)
0.510729 + 0.859742i \(0.329375\pi\)
\(602\) 2.86405 0.116730
\(603\) 8.27795 0.337104
\(604\) −7.79946 −0.317356
\(605\) −63.9025 −2.59801
\(606\) −24.2236 −0.984017
\(607\) −15.6860 −0.636673 −0.318337 0.947978i \(-0.603124\pi\)
−0.318337 + 0.947978i \(0.603124\pi\)
\(608\) −24.4626 −0.992090
\(609\) 0.816003 0.0330661
\(610\) −64.9830 −2.63109
\(611\) 11.7311 0.474590
\(612\) 7.57671 0.306270
\(613\) −21.7968 −0.880364 −0.440182 0.897909i \(-0.645086\pi\)
−0.440182 + 0.897909i \(0.645086\pi\)
\(614\) −43.1105 −1.73980
\(615\) 18.5324 0.747300
\(616\) 2.72958 0.109978
\(617\) 11.1706 0.449710 0.224855 0.974392i \(-0.427809\pi\)
0.224855 + 0.974392i \(0.427809\pi\)
\(618\) −2.36961 −0.0953198
\(619\) 3.13589 0.126042 0.0630211 0.998012i \(-0.479926\pi\)
0.0630211 + 0.998012i \(0.479926\pi\)
\(620\) −8.19597 −0.329158
\(621\) 1.40898 0.0565405
\(622\) −57.1438 −2.29126
\(623\) 0.727485 0.0291461
\(624\) −1.83856 −0.0736012
\(625\) −28.2221 −1.12888
\(626\) −13.7051 −0.547766
\(627\) 45.5057 1.81732
\(628\) −9.32706 −0.372190
\(629\) 12.5969 0.502272
\(630\) −0.661254 −0.0263450
\(631\) −46.2876 −1.84268 −0.921340 0.388758i \(-0.872904\pi\)
−0.921340 + 0.388758i \(0.872904\pi\)
\(632\) −7.43793 −0.295865
\(633\) −15.7417 −0.625675
\(634\) −17.2445 −0.684865
\(635\) 14.4625 0.573928
\(636\) −7.76008 −0.307707
\(637\) −6.98648 −0.276814
\(638\) −102.007 −4.03851
\(639\) −13.4824 −0.533357
\(640\) −49.5211 −1.95749
\(641\) 17.7990 0.703020 0.351510 0.936184i \(-0.385668\pi\)
0.351510 + 0.936184i \(0.385668\pi\)
\(642\) −11.0768 −0.437168
\(643\) −25.9758 −1.02438 −0.512192 0.858871i \(-0.671166\pi\)
−0.512192 + 0.858871i \(0.671166\pi\)
\(644\) 0.592249 0.0233379
\(645\) 24.9476 0.982312
\(646\) 36.8436 1.44959
\(647\) 32.8205 1.29031 0.645153 0.764053i \(-0.276794\pi\)
0.645153 + 0.764053i \(0.276794\pi\)
\(648\) −3.82707 −0.150342
\(649\) 31.1940 1.22447
\(650\) −1.80071 −0.0706296
\(651\) 0.109840 0.00430496
\(652\) 58.1165 2.27602
\(653\) −15.8081 −0.618619 −0.309309 0.950961i \(-0.600098\pi\)
−0.309309 + 0.950961i \(0.600098\pi\)
\(654\) 8.08217 0.316038
\(655\) 37.4329 1.46262
\(656\) 14.1972 0.554306
\(657\) −1.99101 −0.0776767
\(658\) 3.23221 0.126005
\(659\) −5.78413 −0.225318 −0.112659 0.993634i \(-0.535937\pi\)
−0.112659 + 0.993634i \(0.535937\pi\)
\(660\) 53.2193 2.07156
\(661\) 34.7299 1.35084 0.675418 0.737435i \(-0.263963\pi\)
0.675418 + 0.737435i \(0.263963\pi\)
\(662\) 0.0193891 0.000753579 0
\(663\) −2.09587 −0.0813969
\(664\) 12.3050 0.477528
\(665\) −2.07019 −0.0802787
\(666\) −14.2422 −0.551875
\(667\) −9.88814 −0.382870
\(668\) −1.44001 −0.0557158
\(669\) 2.35632 0.0911005
\(670\) 47.0769 1.81874
\(671\) −70.0906 −2.70582
\(672\) 0.383411 0.0147904
\(673\) −42.3818 −1.63370 −0.816849 0.576852i \(-0.804281\pi\)
−0.816849 + 0.576852i \(0.804281\pi\)
\(674\) −35.4937 −1.36717
\(675\) −0.759917 −0.0292492
\(676\) 3.61506 0.139041
\(677\) −1.48246 −0.0569754 −0.0284877 0.999594i \(-0.509069\pi\)
−0.0284877 + 0.999594i \(0.509069\pi\)
\(678\) −13.9558 −0.535969
\(679\) 0.807270 0.0309802
\(680\) 19.2504 0.738219
\(681\) −0.0550758 −0.00211051
\(682\) −13.7309 −0.525784
\(683\) 41.9200 1.60403 0.802013 0.597307i \(-0.203762\pi\)
0.802013 + 0.597307i \(0.203762\pi\)
\(684\) −26.8186 −1.02544
\(685\) −3.66145 −0.139897
\(686\) −3.85362 −0.147132
\(687\) 17.8185 0.679820
\(688\) 19.1117 0.728625
\(689\) 2.14660 0.0817788
\(690\) 8.01292 0.305047
\(691\) 46.4261 1.76613 0.883066 0.469249i \(-0.155475\pi\)
0.883066 + 0.469249i \(0.155475\pi\)
\(692\) 2.33483 0.0887568
\(693\) −0.713228 −0.0270933
\(694\) 35.6003 1.35137
\(695\) 23.4491 0.889476
\(696\) 26.8581 1.01806
\(697\) 16.1841 0.613017
\(698\) 28.1840 1.06678
\(699\) −18.3560 −0.694288
\(700\) −0.319422 −0.0120730
\(701\) 16.6390 0.628445 0.314222 0.949349i \(-0.398256\pi\)
0.314222 + 0.949349i \(0.398256\pi\)
\(702\) 2.36961 0.0894353
\(703\) −44.5883 −1.68168
\(704\) −70.4852 −2.65651
\(705\) 28.1545 1.06036
\(706\) −10.9043 −0.410390
\(707\) 1.18862 0.0447028
\(708\) −18.3841 −0.690917
\(709\) −14.9418 −0.561149 −0.280575 0.959832i \(-0.590525\pi\)
−0.280575 + 0.959832i \(0.590525\pi\)
\(710\) −76.6750 −2.87756
\(711\) 1.94350 0.0728871
\(712\) 23.9446 0.897363
\(713\) −1.33101 −0.0498468
\(714\) −0.577463 −0.0216110
\(715\) −14.7215 −0.550555
\(716\) −48.2064 −1.80156
\(717\) −6.73765 −0.251622
\(718\) 5.03928 0.188064
\(719\) 32.1728 1.19984 0.599922 0.800058i \(-0.295198\pi\)
0.599922 + 0.800058i \(0.295198\pi\)
\(720\) −4.41251 −0.164444
\(721\) 0.116274 0.00433027
\(722\) −85.3895 −3.17787
\(723\) −14.4248 −0.536463
\(724\) −27.6695 −1.02833
\(725\) 5.33305 0.198064
\(726\) 63.0939 2.34163
\(727\) 4.20568 0.155980 0.0779900 0.996954i \(-0.475150\pi\)
0.0779900 + 0.996954i \(0.475150\pi\)
\(728\) 0.444989 0.0164924
\(729\) 1.00000 0.0370370
\(730\) −11.3229 −0.419081
\(731\) 21.7864 0.805799
\(732\) 41.3076 1.52677
\(733\) 9.58797 0.354140 0.177070 0.984198i \(-0.443338\pi\)
0.177070 + 0.984198i \(0.443338\pi\)
\(734\) 44.4800 1.64179
\(735\) −16.7674 −0.618476
\(736\) −4.64609 −0.171257
\(737\) 50.7771 1.87040
\(738\) −18.2979 −0.673556
\(739\) 31.4808 1.15804 0.579020 0.815313i \(-0.303435\pi\)
0.579020 + 0.815313i \(0.303435\pi\)
\(740\) −52.1464 −1.91694
\(741\) 7.41857 0.272528
\(742\) 0.591440 0.0217124
\(743\) 29.9663 1.09936 0.549678 0.835377i \(-0.314750\pi\)
0.549678 + 0.835377i \(0.314750\pi\)
\(744\) 3.61529 0.132543
\(745\) −27.7807 −1.01781
\(746\) −6.98862 −0.255871
\(747\) −3.21526 −0.117640
\(748\) 46.4757 1.69932
\(749\) 0.543528 0.0198601
\(750\) 24.1135 0.880500
\(751\) −3.48987 −0.127347 −0.0636735 0.997971i \(-0.520282\pi\)
−0.0636735 + 0.997971i \(0.520282\pi\)
\(752\) 21.5683 0.786516
\(753\) 3.33272 0.121451
\(754\) −16.6298 −0.605621
\(755\) 5.17794 0.188444
\(756\) 0.420338 0.0152875
\(757\) −44.1066 −1.60308 −0.801542 0.597939i \(-0.795986\pi\)
−0.801542 + 0.597939i \(0.795986\pi\)
\(758\) 70.6793 2.56719
\(759\) 8.64273 0.313711
\(760\) −68.1390 −2.47166
\(761\) 24.1692 0.876134 0.438067 0.898942i \(-0.355663\pi\)
0.438067 + 0.898942i \(0.355663\pi\)
\(762\) −14.2795 −0.517292
\(763\) −0.396582 −0.0143572
\(764\) 75.4489 2.72965
\(765\) −5.03005 −0.181862
\(766\) 7.68898 0.277814
\(767\) 5.08541 0.183624
\(768\) 25.9127 0.935044
\(769\) −8.22778 −0.296701 −0.148351 0.988935i \(-0.547396\pi\)
−0.148351 + 0.988935i \(0.547396\pi\)
\(770\) −4.05615 −0.146173
\(771\) −17.1817 −0.618785
\(772\) −10.7992 −0.388673
\(773\) 14.0889 0.506742 0.253371 0.967369i \(-0.418461\pi\)
0.253371 + 0.967369i \(0.418461\pi\)
\(774\) −24.6319 −0.885376
\(775\) 0.717865 0.0257865
\(776\) 26.5707 0.953832
\(777\) 0.698848 0.0250710
\(778\) 80.4319 2.88362
\(779\) −57.2855 −2.05247
\(780\) 8.67609 0.310654
\(781\) −82.7015 −2.95929
\(782\) 6.99757 0.250233
\(783\) −7.01793 −0.250800
\(784\) −12.8450 −0.458752
\(785\) 6.19208 0.221005
\(786\) −36.9592 −1.31829
\(787\) 4.07590 0.145290 0.0726451 0.997358i \(-0.476856\pi\)
0.0726451 + 0.997358i \(0.476856\pi\)
\(788\) 51.2382 1.82529
\(789\) −4.03724 −0.143730
\(790\) 11.0528 0.393239
\(791\) 0.684794 0.0243485
\(792\) −23.4754 −0.834161
\(793\) −11.4265 −0.405768
\(794\) −54.4985 −1.93408
\(795\) 5.15179 0.182715
\(796\) −58.7789 −2.08336
\(797\) 11.6042 0.411043 0.205521 0.978653i \(-0.434111\pi\)
0.205521 + 0.978653i \(0.434111\pi\)
\(798\) 2.04400 0.0723567
\(799\) 24.5869 0.869822
\(800\) 2.50581 0.0885939
\(801\) −6.25664 −0.221068
\(802\) 7.47840 0.264072
\(803\) −12.2129 −0.430984
\(804\) −29.9253 −1.05538
\(805\) −0.393184 −0.0138579
\(806\) −2.23848 −0.0788472
\(807\) −23.3134 −0.820670
\(808\) 39.1227 1.37633
\(809\) 33.0718 1.16274 0.581372 0.813638i \(-0.302516\pi\)
0.581372 + 0.813638i \(0.302516\pi\)
\(810\) 5.68703 0.199822
\(811\) −3.75191 −0.131747 −0.0658737 0.997828i \(-0.520983\pi\)
−0.0658737 + 0.997828i \(0.520983\pi\)
\(812\) −2.94990 −0.103521
\(813\) −26.0550 −0.913788
\(814\) −87.3621 −3.06204
\(815\) −38.5826 −1.35149
\(816\) −3.85338 −0.134895
\(817\) −77.1154 −2.69793
\(818\) −67.9334 −2.37524
\(819\) −0.116274 −0.00406294
\(820\) −66.9959 −2.33960
\(821\) −2.24654 −0.0784046 −0.0392023 0.999231i \(-0.512482\pi\)
−0.0392023 + 0.999231i \(0.512482\pi\)
\(822\) 3.61512 0.126092
\(823\) 52.2548 1.82149 0.910743 0.412973i \(-0.135510\pi\)
0.910743 + 0.412973i \(0.135510\pi\)
\(824\) 3.82707 0.133322
\(825\) −4.66135 −0.162287
\(826\) 1.40116 0.0487524
\(827\) 18.9886 0.660298 0.330149 0.943929i \(-0.392901\pi\)
0.330149 + 0.943929i \(0.392901\pi\)
\(828\) −5.09356 −0.177013
\(829\) 51.3792 1.78447 0.892236 0.451569i \(-0.149135\pi\)
0.892236 + 0.451569i \(0.149135\pi\)
\(830\) −18.2853 −0.634692
\(831\) −30.8306 −1.06950
\(832\) −11.4909 −0.398374
\(833\) −14.6428 −0.507342
\(834\) −23.1524 −0.801702
\(835\) 0.956002 0.0330838
\(836\) −164.506 −5.68956
\(837\) −0.944662 −0.0326523
\(838\) −22.9531 −0.792900
\(839\) −2.44169 −0.0842965 −0.0421483 0.999111i \(-0.513420\pi\)
−0.0421483 + 0.999111i \(0.513420\pi\)
\(840\) 1.06797 0.0368484
\(841\) 20.2514 0.698322
\(842\) −16.2565 −0.560237
\(843\) 25.8182 0.889225
\(844\) 56.9071 1.95882
\(845\) −2.39998 −0.0825619
\(846\) −27.7982 −0.955722
\(847\) −3.09594 −0.106378
\(848\) 3.94664 0.135528
\(849\) −6.88462 −0.236280
\(850\) −3.77405 −0.129449
\(851\) −8.46848 −0.290296
\(852\) 48.7398 1.66980
\(853\) −48.1007 −1.64694 −0.823469 0.567361i \(-0.807964\pi\)
−0.823469 + 0.567361i \(0.807964\pi\)
\(854\) −3.14829 −0.107732
\(855\) 17.8044 0.608899
\(856\) 17.8898 0.611461
\(857\) 4.66589 0.159384 0.0796920 0.996820i \(-0.474606\pi\)
0.0796920 + 0.996820i \(0.474606\pi\)
\(858\) 14.5353 0.496226
\(859\) 54.9984 1.87652 0.938261 0.345928i \(-0.112436\pi\)
0.938261 + 0.345928i \(0.112436\pi\)
\(860\) −90.1872 −3.07536
\(861\) 0.897857 0.0305989
\(862\) −80.5929 −2.74501
\(863\) 8.41035 0.286292 0.143146 0.989702i \(-0.454278\pi\)
0.143146 + 0.989702i \(0.454278\pi\)
\(864\) −3.29748 −0.112183
\(865\) −1.55005 −0.0527034
\(866\) 41.9741 1.42634
\(867\) 12.6073 0.428167
\(868\) −0.397077 −0.0134777
\(869\) 11.9215 0.404409
\(870\) −39.9112 −1.35312
\(871\) 8.27795 0.280488
\(872\) −13.0532 −0.442038
\(873\) −6.94282 −0.234979
\(874\) −24.7687 −0.837814
\(875\) −1.18322 −0.0400001
\(876\) 7.19763 0.243185
\(877\) 8.40319 0.283756 0.141878 0.989884i \(-0.454686\pi\)
0.141878 + 0.989884i \(0.454686\pi\)
\(878\) −10.4534 −0.352784
\(879\) 28.1257 0.948656
\(880\) −27.0664 −0.912409
\(881\) 10.1955 0.343496 0.171748 0.985141i \(-0.445059\pi\)
0.171748 + 0.985141i \(0.445059\pi\)
\(882\) 16.5553 0.557444
\(883\) 2.57833 0.0867677 0.0433838 0.999058i \(-0.486186\pi\)
0.0433838 + 0.999058i \(0.486186\pi\)
\(884\) 7.57671 0.254832
\(885\) 12.2049 0.410263
\(886\) 38.3266 1.28761
\(887\) 4.83824 0.162452 0.0812261 0.996696i \(-0.474116\pi\)
0.0812261 + 0.996696i \(0.474116\pi\)
\(888\) 23.0021 0.771899
\(889\) 0.700679 0.0235000
\(890\) −35.5817 −1.19270
\(891\) 6.13402 0.205498
\(892\) −8.51824 −0.285212
\(893\) −87.0282 −2.91229
\(894\) 27.4292 0.917369
\(895\) 32.0035 1.06976
\(896\) −2.39919 −0.0801514
\(897\) 1.40898 0.0470445
\(898\) −37.5673 −1.25364
\(899\) 6.62957 0.221109
\(900\) 2.74715 0.0915717
\(901\) 4.49899 0.149883
\(902\) −112.240 −3.73718
\(903\) 1.20866 0.0402216
\(904\) 22.5395 0.749653
\(905\) 18.3694 0.610618
\(906\) −5.11241 −0.169849
\(907\) −31.3535 −1.04108 −0.520538 0.853839i \(-0.674268\pi\)
−0.520538 + 0.853839i \(0.674268\pi\)
\(908\) 0.199102 0.00660745
\(909\) −10.2226 −0.339062
\(910\) −0.661254 −0.0219203
\(911\) −48.9811 −1.62282 −0.811408 0.584480i \(-0.801299\pi\)
−0.811408 + 0.584480i \(0.801299\pi\)
\(912\) 13.6395 0.451648
\(913\) −19.7225 −0.652719
\(914\) 51.7334 1.71119
\(915\) −27.4235 −0.906592
\(916\) −64.4151 −2.12834
\(917\) 1.81354 0.0598885
\(918\) 4.96640 0.163916
\(919\) 27.6423 0.911836 0.455918 0.890022i \(-0.349311\pi\)
0.455918 + 0.890022i \(0.349311\pi\)
\(920\) −12.9414 −0.426665
\(921\) −18.1931 −0.599482
\(922\) −54.3280 −1.78920
\(923\) −13.4824 −0.443780
\(924\) 2.57836 0.0848219
\(925\) 4.56737 0.150174
\(926\) −50.8464 −1.67092
\(927\) −1.00000 −0.0328443
\(928\) 23.1415 0.759657
\(929\) 56.6574 1.85887 0.929435 0.368986i \(-0.120295\pi\)
0.929435 + 0.368986i \(0.120295\pi\)
\(930\) −5.37232 −0.176165
\(931\) 51.8297 1.69865
\(932\) 66.3582 2.17363
\(933\) −24.1152 −0.789498
\(934\) 43.3918 1.41982
\(935\) −30.8545 −1.00905
\(936\) −3.82707 −0.125092
\(937\) 32.6711 1.06732 0.533658 0.845700i \(-0.320817\pi\)
0.533658 + 0.845700i \(0.320817\pi\)
\(938\) 2.28078 0.0744700
\(939\) −5.78369 −0.188744
\(940\) −101.780 −3.31971
\(941\) 20.9401 0.682628 0.341314 0.939949i \(-0.389128\pi\)
0.341314 + 0.939949i \(0.389128\pi\)
\(942\) −6.11373 −0.199196
\(943\) −10.8800 −0.354302
\(944\) 9.34983 0.304311
\(945\) −0.279056 −0.00907768
\(946\) −151.093 −4.91245
\(947\) 19.8558 0.645228 0.322614 0.946531i \(-0.395438\pi\)
0.322614 + 0.946531i \(0.395438\pi\)
\(948\) −7.02589 −0.228190
\(949\) −1.99101 −0.0646309
\(950\) 13.3587 0.433413
\(951\) −7.27734 −0.235984
\(952\) 0.932640 0.0302270
\(953\) 34.3986 1.11428 0.557140 0.830418i \(-0.311898\pi\)
0.557140 + 0.830418i \(0.311898\pi\)
\(954\) −5.08660 −0.164685
\(955\) −50.0893 −1.62085
\(956\) 24.3570 0.787763
\(957\) −43.0481 −1.39155
\(958\) −15.7949 −0.510311
\(959\) −0.177389 −0.00572820
\(960\) −27.5779 −0.890072
\(961\) −30.1076 −0.971213
\(962\) −14.2422 −0.459187
\(963\) −4.67454 −0.150635
\(964\) 52.1464 1.67952
\(965\) 7.16944 0.230792
\(966\) 0.388209 0.0124904
\(967\) 25.3380 0.814814 0.407407 0.913247i \(-0.366433\pi\)
0.407407 + 0.913247i \(0.366433\pi\)
\(968\) −101.901 −3.27521
\(969\) 15.5484 0.499486
\(970\) −39.4840 −1.26776
\(971\) −21.0796 −0.676476 −0.338238 0.941061i \(-0.609831\pi\)
−0.338238 + 0.941061i \(0.609831\pi\)
\(972\) −3.61506 −0.115953
\(973\) 1.13606 0.0364204
\(974\) −93.9698 −3.01099
\(975\) −0.759917 −0.0243368
\(976\) −21.0083 −0.672461
\(977\) −46.4442 −1.48588 −0.742941 0.669357i \(-0.766570\pi\)
−0.742941 + 0.669357i \(0.766570\pi\)
\(978\) 38.0944 1.21812
\(979\) −38.3784 −1.22658
\(980\) 60.6153 1.93629
\(981\) 3.41075 0.108897
\(982\) −5.72050 −0.182548
\(983\) 4.77287 0.152231 0.0761155 0.997099i \(-0.475748\pi\)
0.0761155 + 0.997099i \(0.475748\pi\)
\(984\) 29.5523 0.942093
\(985\) −34.0163 −1.08385
\(986\) −34.8539 −1.10997
\(987\) 1.36402 0.0434174
\(988\) −26.8186 −0.853214
\(989\) −14.6462 −0.465724
\(990\) 34.8844 1.10870
\(991\) 16.1603 0.513348 0.256674 0.966498i \(-0.417373\pi\)
0.256674 + 0.966498i \(0.417373\pi\)
\(992\) 3.11500 0.0989015
\(993\) 0.00818240 0.000259660 0
\(994\) −3.71474 −0.117824
\(995\) 39.0224 1.23709
\(996\) 11.6234 0.368301
\(997\) −53.0022 −1.67860 −0.839298 0.543672i \(-0.817033\pi\)
−0.839298 + 0.543672i \(0.817033\pi\)
\(998\) −24.8137 −0.785465
\(999\) −6.01036 −0.190159
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 \(a_p\))