Properties

Label 6013.2.a.e.1.10
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31924 q^{2}\) \(+3.03113 q^{3}\) \(+3.37885 q^{4}\) \(+1.64684 q^{5}\) \(-7.02991 q^{6}\) \(+1.00000 q^{7}\) \(-3.19788 q^{8}\) \(+6.18776 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31924 q^{2}\) \(+3.03113 q^{3}\) \(+3.37885 q^{4}\) \(+1.64684 q^{5}\) \(-7.02991 q^{6}\) \(+1.00000 q^{7}\) \(-3.19788 q^{8}\) \(+6.18776 q^{9}\) \(-3.81941 q^{10}\) \(+1.18478 q^{11}\) \(+10.2417 q^{12}\) \(+5.12534 q^{13}\) \(-2.31924 q^{14}\) \(+4.99179 q^{15}\) \(+0.658941 q^{16}\) \(-6.39433 q^{17}\) \(-14.3509 q^{18}\) \(+6.08738 q^{19}\) \(+5.56443 q^{20}\) \(+3.03113 q^{21}\) \(-2.74778 q^{22}\) \(+5.34244 q^{23}\) \(-9.69321 q^{24}\) \(-2.28792 q^{25}\) \(-11.8869 q^{26}\) \(+9.66251 q^{27}\) \(+3.37885 q^{28}\) \(+7.62059 q^{29}\) \(-11.5771 q^{30}\) \(-10.7372 q^{31}\) \(+4.86753 q^{32}\) \(+3.59122 q^{33}\) \(+14.8300 q^{34}\) \(+1.64684 q^{35}\) \(+20.9075 q^{36}\) \(+7.75870 q^{37}\) \(-14.1181 q^{38}\) \(+15.5356 q^{39}\) \(-5.26640 q^{40}\) \(-2.27736 q^{41}\) \(-7.02991 q^{42}\) \(-10.2084 q^{43}\) \(+4.00320 q^{44}\) \(+10.1902 q^{45}\) \(-12.3904 q^{46}\) \(-5.91309 q^{47}\) \(+1.99734 q^{48}\) \(+1.00000 q^{49}\) \(+5.30622 q^{50}\) \(-19.3821 q^{51}\) \(+17.3178 q^{52}\) \(+5.89523 q^{53}\) \(-22.4096 q^{54}\) \(+1.95114 q^{55}\) \(-3.19788 q^{56}\) \(+18.4516 q^{57}\) \(-17.6739 q^{58}\) \(+6.73270 q^{59}\) \(+16.8665 q^{60}\) \(+4.52365 q^{61}\) \(+24.9022 q^{62}\) \(+6.18776 q^{63}\) \(-12.6068 q^{64}\) \(+8.44062 q^{65}\) \(-8.32889 q^{66}\) \(-0.200977 q^{67}\) \(-21.6055 q^{68}\) \(+16.1936 q^{69}\) \(-3.81941 q^{70}\) \(+7.70302 q^{71}\) \(-19.7877 q^{72}\) \(-2.54847 q^{73}\) \(-17.9942 q^{74}\) \(-6.93498 q^{75}\) \(+20.5683 q^{76}\) \(+1.18478 q^{77}\) \(-36.0307 q^{78}\) \(+5.43372 q^{79}\) \(+1.08517 q^{80}\) \(+10.7251 q^{81}\) \(+5.28172 q^{82}\) \(+4.01327 q^{83}\) \(+10.2417 q^{84}\) \(-10.5304 q^{85}\) \(+23.6758 q^{86}\) \(+23.0990 q^{87}\) \(-3.78879 q^{88}\) \(-10.7483 q^{89}\) \(-23.6336 q^{90}\) \(+5.12534 q^{91}\) \(+18.0513 q^{92}\) \(-32.5460 q^{93}\) \(+13.7139 q^{94}\) \(+10.0249 q^{95}\) \(+14.7541 q^{96}\) \(-6.33525 q^{97}\) \(-2.31924 q^{98}\) \(+7.33113 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31924 −1.63995 −0.819974 0.572401i \(-0.806012\pi\)
−0.819974 + 0.572401i \(0.806012\pi\)
\(3\) 3.03113 1.75002 0.875012 0.484101i \(-0.160853\pi\)
0.875012 + 0.484101i \(0.160853\pi\)
\(4\) 3.37885 1.68943
\(5\) 1.64684 0.736489 0.368245 0.929729i \(-0.379959\pi\)
0.368245 + 0.929729i \(0.379959\pi\)
\(6\) −7.02991 −2.86995
\(7\) 1.00000 0.377964
\(8\) −3.19788 −1.13062
\(9\) 6.18776 2.06259
\(10\) −3.81941 −1.20780
\(11\) 1.18478 0.357225 0.178612 0.983920i \(-0.442839\pi\)
0.178612 + 0.983920i \(0.442839\pi\)
\(12\) 10.2417 2.95654
\(13\) 5.12534 1.42151 0.710757 0.703438i \(-0.248353\pi\)
0.710757 + 0.703438i \(0.248353\pi\)
\(14\) −2.31924 −0.619842
\(15\) 4.99179 1.28887
\(16\) 0.658941 0.164735
\(17\) −6.39433 −1.55085 −0.775426 0.631438i \(-0.782465\pi\)
−0.775426 + 0.631438i \(0.782465\pi\)
\(18\) −14.3509 −3.38253
\(19\) 6.08738 1.39654 0.698270 0.715835i \(-0.253954\pi\)
0.698270 + 0.715835i \(0.253954\pi\)
\(20\) 5.56443 1.24424
\(21\) 3.03113 0.661447
\(22\) −2.74778 −0.585829
\(23\) 5.34244 1.11398 0.556988 0.830521i \(-0.311957\pi\)
0.556988 + 0.830521i \(0.311957\pi\)
\(24\) −9.69321 −1.97862
\(25\) −2.28792 −0.457584
\(26\) −11.8869 −2.33121
\(27\) 9.66251 1.85955
\(28\) 3.37885 0.638543
\(29\) 7.62059 1.41511 0.707554 0.706659i \(-0.249798\pi\)
0.707554 + 0.706659i \(0.249798\pi\)
\(30\) −11.5771 −2.11369
\(31\) −10.7372 −1.92847 −0.964233 0.265057i \(-0.914609\pi\)
−0.964233 + 0.265057i \(0.914609\pi\)
\(32\) 4.86753 0.860466
\(33\) 3.59122 0.625152
\(34\) 14.8300 2.54332
\(35\) 1.64684 0.278367
\(36\) 20.9075 3.48459
\(37\) 7.75870 1.27552 0.637761 0.770234i \(-0.279861\pi\)
0.637761 + 0.770234i \(0.279861\pi\)
\(38\) −14.1181 −2.29025
\(39\) 15.5356 2.48768
\(40\) −5.26640 −0.832692
\(41\) −2.27736 −0.355663 −0.177832 0.984061i \(-0.556908\pi\)
−0.177832 + 0.984061i \(0.556908\pi\)
\(42\) −7.02991 −1.08474
\(43\) −10.2084 −1.55677 −0.778386 0.627786i \(-0.783961\pi\)
−0.778386 + 0.627786i \(0.783961\pi\)
\(44\) 4.00320 0.603505
\(45\) 10.1902 1.51907
\(46\) −12.3904 −1.82686
\(47\) −5.91309 −0.862513 −0.431257 0.902229i \(-0.641930\pi\)
−0.431257 + 0.902229i \(0.641930\pi\)
\(48\) 1.99734 0.288291
\(49\) 1.00000 0.142857
\(50\) 5.30622 0.750413
\(51\) −19.3821 −2.71403
\(52\) 17.3178 2.40154
\(53\) 5.89523 0.809773 0.404886 0.914367i \(-0.367311\pi\)
0.404886 + 0.914367i \(0.367311\pi\)
\(54\) −22.4096 −3.04957
\(55\) 1.95114 0.263092
\(56\) −3.19788 −0.427335
\(57\) 18.4516 2.44398
\(58\) −17.6739 −2.32070
\(59\) 6.73270 0.876523 0.438261 0.898848i \(-0.355594\pi\)
0.438261 + 0.898848i \(0.355594\pi\)
\(60\) 16.8665 2.17746
\(61\) 4.52365 0.579195 0.289597 0.957149i \(-0.406479\pi\)
0.289597 + 0.957149i \(0.406479\pi\)
\(62\) 24.9022 3.16258
\(63\) 6.18776 0.779584
\(64\) −12.6068 −1.57585
\(65\) 8.44062 1.04693
\(66\) −8.32889 −1.02522
\(67\) −0.200977 −0.0245532 −0.0122766 0.999925i \(-0.503908\pi\)
−0.0122766 + 0.999925i \(0.503908\pi\)
\(68\) −21.6055 −2.62005
\(69\) 16.1936 1.94949
\(70\) −3.81941 −0.456507
\(71\) 7.70302 0.914181 0.457090 0.889420i \(-0.348892\pi\)
0.457090 + 0.889420i \(0.348892\pi\)
\(72\) −19.7877 −2.33201
\(73\) −2.54847 −0.298276 −0.149138 0.988816i \(-0.547650\pi\)
−0.149138 + 0.988816i \(0.547650\pi\)
\(74\) −17.9942 −2.09179
\(75\) −6.93498 −0.800782
\(76\) 20.5683 2.35935
\(77\) 1.18478 0.135018
\(78\) −36.0307 −4.07967
\(79\) 5.43372 0.611341 0.305670 0.952137i \(-0.401119\pi\)
0.305670 + 0.952137i \(0.401119\pi\)
\(80\) 1.08517 0.121326
\(81\) 10.7251 1.19168
\(82\) 5.28172 0.583269
\(83\) 4.01327 0.440513 0.220257 0.975442i \(-0.429311\pi\)
0.220257 + 0.975442i \(0.429311\pi\)
\(84\) 10.2417 1.11747
\(85\) −10.5304 −1.14219
\(86\) 23.6758 2.55302
\(87\) 23.0990 2.47647
\(88\) −3.78879 −0.403886
\(89\) −10.7483 −1.13932 −0.569661 0.821880i \(-0.692925\pi\)
−0.569661 + 0.821880i \(0.692925\pi\)
\(90\) −23.6336 −2.49120
\(91\) 5.12534 0.537282
\(92\) 18.0513 1.88198
\(93\) −32.5460 −3.37486
\(94\) 13.7139 1.41448
\(95\) 10.0249 1.02854
\(96\) 14.7541 1.50584
\(97\) −6.33525 −0.643247 −0.321624 0.946868i \(-0.604229\pi\)
−0.321624 + 0.946868i \(0.604229\pi\)
\(98\) −2.31924 −0.234278
\(99\) 7.33113 0.736807
\(100\) −7.73054 −0.773054
\(101\) 5.01109 0.498622 0.249311 0.968424i \(-0.419796\pi\)
0.249311 + 0.968424i \(0.419796\pi\)
\(102\) 44.9515 4.45087
\(103\) −6.24112 −0.614955 −0.307478 0.951555i \(-0.599485\pi\)
−0.307478 + 0.951555i \(0.599485\pi\)
\(104\) −16.3902 −1.60720
\(105\) 4.99179 0.487149
\(106\) −13.6724 −1.32798
\(107\) 11.2229 1.08496 0.542478 0.840070i \(-0.317486\pi\)
0.542478 + 0.840070i \(0.317486\pi\)
\(108\) 32.6482 3.14158
\(109\) −13.0611 −1.25103 −0.625515 0.780212i \(-0.715111\pi\)
−0.625515 + 0.780212i \(0.715111\pi\)
\(110\) −4.52516 −0.431457
\(111\) 23.5176 2.23219
\(112\) 0.658941 0.0622640
\(113\) 2.34478 0.220578 0.110289 0.993900i \(-0.464822\pi\)
0.110289 + 0.993900i \(0.464822\pi\)
\(114\) −42.7937 −4.00800
\(115\) 8.79814 0.820431
\(116\) 25.7489 2.39072
\(117\) 31.7144 2.93200
\(118\) −15.6147 −1.43745
\(119\) −6.39433 −0.586167
\(120\) −15.9632 −1.45723
\(121\) −9.59630 −0.872391
\(122\) −10.4914 −0.949848
\(123\) −6.90296 −0.622419
\(124\) −36.2796 −3.25800
\(125\) −12.0020 −1.07349
\(126\) −14.3509 −1.27848
\(127\) −14.0360 −1.24549 −0.622747 0.782423i \(-0.713983\pi\)
−0.622747 + 0.782423i \(0.713983\pi\)
\(128\) 19.5031 1.72385
\(129\) −30.9431 −2.72439
\(130\) −19.5758 −1.71691
\(131\) 3.60801 0.315234 0.157617 0.987500i \(-0.449619\pi\)
0.157617 + 0.987500i \(0.449619\pi\)
\(132\) 12.1342 1.05615
\(133\) 6.08738 0.527842
\(134\) 0.466112 0.0402659
\(135\) 15.9126 1.36954
\(136\) 20.4483 1.75343
\(137\) 9.12559 0.779651 0.389826 0.920889i \(-0.372535\pi\)
0.389826 + 0.920889i \(0.372535\pi\)
\(138\) −37.5569 −3.19705
\(139\) −14.4230 −1.22334 −0.611670 0.791113i \(-0.709502\pi\)
−0.611670 + 0.791113i \(0.709502\pi\)
\(140\) 5.56443 0.470280
\(141\) −17.9234 −1.50942
\(142\) −17.8651 −1.49921
\(143\) 6.07240 0.507800
\(144\) 4.07736 0.339780
\(145\) 12.5499 1.04221
\(146\) 5.91051 0.489157
\(147\) 3.03113 0.250004
\(148\) 26.2155 2.15490
\(149\) −7.11121 −0.582573 −0.291286 0.956636i \(-0.594083\pi\)
−0.291286 + 0.956636i \(0.594083\pi\)
\(150\) 16.0838 1.31324
\(151\) −17.0462 −1.38720 −0.693601 0.720360i \(-0.743977\pi\)
−0.693601 + 0.720360i \(0.743977\pi\)
\(152\) −19.4667 −1.57896
\(153\) −39.5666 −3.19877
\(154\) −2.74778 −0.221423
\(155\) −17.6825 −1.42029
\(156\) 52.4925 4.20276
\(157\) 19.5705 1.56190 0.780948 0.624596i \(-0.214736\pi\)
0.780948 + 0.624596i \(0.214736\pi\)
\(158\) −12.6021 −1.00257
\(159\) 17.8692 1.41712
\(160\) 8.01604 0.633724
\(161\) 5.34244 0.421043
\(162\) −24.8740 −1.95428
\(163\) 14.7845 1.15801 0.579006 0.815323i \(-0.303441\pi\)
0.579006 + 0.815323i \(0.303441\pi\)
\(164\) −7.69485 −0.600867
\(165\) 5.91417 0.460418
\(166\) −9.30771 −0.722418
\(167\) 7.23587 0.559928 0.279964 0.960010i \(-0.409677\pi\)
0.279964 + 0.960010i \(0.409677\pi\)
\(168\) −9.69321 −0.747847
\(169\) 13.2691 1.02070
\(170\) 24.4226 1.87313
\(171\) 37.6672 2.88048
\(172\) −34.4928 −2.63005
\(173\) −17.1092 −1.30079 −0.650394 0.759597i \(-0.725396\pi\)
−0.650394 + 0.759597i \(0.725396\pi\)
\(174\) −53.5721 −4.06129
\(175\) −2.28792 −0.172950
\(176\) 0.780700 0.0588474
\(177\) 20.4077 1.53394
\(178\) 24.9279 1.86843
\(179\) 1.24969 0.0934065 0.0467032 0.998909i \(-0.485128\pi\)
0.0467032 + 0.998909i \(0.485128\pi\)
\(180\) 34.4313 2.56636
\(181\) 17.9073 1.33104 0.665521 0.746379i \(-0.268209\pi\)
0.665521 + 0.746379i \(0.268209\pi\)
\(182\) −11.8869 −0.881114
\(183\) 13.7118 1.01360
\(184\) −17.0845 −1.25949
\(185\) 12.7773 0.939408
\(186\) 75.4818 5.53460
\(187\) −7.57587 −0.554003
\(188\) −19.9795 −1.45715
\(189\) 9.66251 0.702845
\(190\) −23.2502 −1.68675
\(191\) 13.4239 0.971323 0.485661 0.874147i \(-0.338579\pi\)
0.485661 + 0.874147i \(0.338579\pi\)
\(192\) −38.2130 −2.75778
\(193\) −11.6318 −0.837278 −0.418639 0.908153i \(-0.637493\pi\)
−0.418639 + 0.908153i \(0.637493\pi\)
\(194\) 14.6929 1.05489
\(195\) 25.5846 1.83215
\(196\) 3.37885 0.241347
\(197\) −3.38305 −0.241032 −0.120516 0.992711i \(-0.538455\pi\)
−0.120516 + 0.992711i \(0.538455\pi\)
\(198\) −17.0026 −1.20832
\(199\) 27.2690 1.93305 0.966526 0.256570i \(-0.0825925\pi\)
0.966526 + 0.256570i \(0.0825925\pi\)
\(200\) 7.31650 0.517354
\(201\) −0.609186 −0.0429687
\(202\) −11.6219 −0.817713
\(203\) 7.62059 0.534861
\(204\) −65.4891 −4.58515
\(205\) −3.75044 −0.261942
\(206\) 14.4746 1.00849
\(207\) 33.0577 2.29767
\(208\) 3.37730 0.234173
\(209\) 7.21220 0.498878
\(210\) −11.5771 −0.798898
\(211\) 7.66551 0.527716 0.263858 0.964562i \(-0.415005\pi\)
0.263858 + 0.964562i \(0.415005\pi\)
\(212\) 19.9191 1.36805
\(213\) 23.3489 1.59984
\(214\) −26.0285 −1.77927
\(215\) −16.8117 −1.14655
\(216\) −30.8996 −2.10245
\(217\) −10.7372 −0.728891
\(218\) 30.2918 2.05162
\(219\) −7.72476 −0.521991
\(220\) 6.59263 0.444475
\(221\) −32.7731 −2.20456
\(222\) −54.5429 −3.66068
\(223\) −15.3162 −1.02565 −0.512825 0.858493i \(-0.671401\pi\)
−0.512825 + 0.858493i \(0.671401\pi\)
\(224\) 4.86753 0.325226
\(225\) −14.1571 −0.943805
\(226\) −5.43809 −0.361736
\(227\) 20.9724 1.39199 0.695994 0.718047i \(-0.254964\pi\)
0.695994 + 0.718047i \(0.254964\pi\)
\(228\) 62.3454 4.12892
\(229\) 26.3555 1.74162 0.870810 0.491620i \(-0.163595\pi\)
0.870810 + 0.491620i \(0.163595\pi\)
\(230\) −20.4050 −1.34546
\(231\) 3.59122 0.236285
\(232\) −24.3698 −1.59995
\(233\) 0.159976 0.0104804 0.00524019 0.999986i \(-0.498332\pi\)
0.00524019 + 0.999986i \(0.498332\pi\)
\(234\) −73.5531 −4.80832
\(235\) −9.73792 −0.635232
\(236\) 22.7488 1.48082
\(237\) 16.4703 1.06986
\(238\) 14.8300 0.961283
\(239\) −5.14720 −0.332945 −0.166472 0.986046i \(-0.553238\pi\)
−0.166472 + 0.986046i \(0.553238\pi\)
\(240\) 3.28929 0.212323
\(241\) −15.1274 −0.974444 −0.487222 0.873278i \(-0.661990\pi\)
−0.487222 + 0.873278i \(0.661990\pi\)
\(242\) 22.2561 1.43067
\(243\) 3.52158 0.225909
\(244\) 15.2848 0.978507
\(245\) 1.64684 0.105213
\(246\) 16.0096 1.02073
\(247\) 31.1999 1.98520
\(248\) 34.3365 2.18037
\(249\) 12.1647 0.770909
\(250\) 27.8355 1.76047
\(251\) −20.8228 −1.31433 −0.657163 0.753749i \(-0.728244\pi\)
−0.657163 + 0.753749i \(0.728244\pi\)
\(252\) 20.9075 1.31705
\(253\) 6.32962 0.397940
\(254\) 32.5528 2.04254
\(255\) −31.9191 −1.99885
\(256\) −20.0187 −1.25117
\(257\) −27.7150 −1.72882 −0.864408 0.502791i \(-0.832306\pi\)
−0.864408 + 0.502791i \(0.832306\pi\)
\(258\) 71.7644 4.46785
\(259\) 7.75870 0.482102
\(260\) 28.5196 1.76871
\(261\) 47.1544 2.91878
\(262\) −8.36783 −0.516967
\(263\) 20.3314 1.25368 0.626842 0.779146i \(-0.284347\pi\)
0.626842 + 0.779146i \(0.284347\pi\)
\(264\) −11.4843 −0.706811
\(265\) 9.70851 0.596389
\(266\) −14.1181 −0.865634
\(267\) −32.5796 −1.99384
\(268\) −0.679070 −0.0414808
\(269\) −2.93400 −0.178889 −0.0894447 0.995992i \(-0.528509\pi\)
−0.0894447 + 0.995992i \(0.528509\pi\)
\(270\) −36.9051 −2.24597
\(271\) −14.1314 −0.858419 −0.429209 0.903205i \(-0.641208\pi\)
−0.429209 + 0.903205i \(0.641208\pi\)
\(272\) −4.21348 −0.255480
\(273\) 15.5356 0.940256
\(274\) −21.1644 −1.27859
\(275\) −2.71068 −0.163460
\(276\) 54.7159 3.29351
\(277\) −19.4136 −1.16645 −0.583226 0.812310i \(-0.698210\pi\)
−0.583226 + 0.812310i \(0.698210\pi\)
\(278\) 33.4502 2.00621
\(279\) −66.4395 −3.97763
\(280\) −5.26640 −0.314728
\(281\) −25.2475 −1.50614 −0.753069 0.657941i \(-0.771428\pi\)
−0.753069 + 0.657941i \(0.771428\pi\)
\(282\) 41.5685 2.47537
\(283\) −22.5169 −1.33849 −0.669244 0.743042i \(-0.733382\pi\)
−0.669244 + 0.743042i \(0.733382\pi\)
\(284\) 26.0274 1.54444
\(285\) 30.3869 1.79996
\(286\) −14.0833 −0.832765
\(287\) −2.27736 −0.134428
\(288\) 30.1191 1.77478
\(289\) 23.8875 1.40514
\(290\) −29.1062 −1.70917
\(291\) −19.2030 −1.12570
\(292\) −8.61092 −0.503916
\(293\) 30.0825 1.75744 0.878718 0.477341i \(-0.158399\pi\)
0.878718 + 0.477341i \(0.158399\pi\)
\(294\) −7.02991 −0.409993
\(295\) 11.0877 0.645550
\(296\) −24.8114 −1.44213
\(297\) 11.4480 0.664278
\(298\) 16.4926 0.955389
\(299\) 27.3818 1.58353
\(300\) −23.4323 −1.35286
\(301\) −10.2084 −0.588404
\(302\) 39.5342 2.27494
\(303\) 15.1893 0.872600
\(304\) 4.01122 0.230059
\(305\) 7.44973 0.426571
\(306\) 91.7642 5.24581
\(307\) 5.68328 0.324362 0.162181 0.986761i \(-0.448147\pi\)
0.162181 + 0.986761i \(0.448147\pi\)
\(308\) 4.00320 0.228103
\(309\) −18.9176 −1.07619
\(310\) 41.0099 2.32921
\(311\) −2.28904 −0.129799 −0.0648997 0.997892i \(-0.520673\pi\)
−0.0648997 + 0.997892i \(0.520673\pi\)
\(312\) −49.6810 −2.81263
\(313\) 4.65374 0.263045 0.131522 0.991313i \(-0.458013\pi\)
0.131522 + 0.991313i \(0.458013\pi\)
\(314\) −45.3886 −2.56143
\(315\) 10.1902 0.574155
\(316\) 18.3597 1.03282
\(317\) 17.2308 0.967777 0.483889 0.875130i \(-0.339224\pi\)
0.483889 + 0.875130i \(0.339224\pi\)
\(318\) −41.4430 −2.32401
\(319\) 9.02873 0.505512
\(320\) −20.7614 −1.16060
\(321\) 34.0180 1.89870
\(322\) −12.3904 −0.690489
\(323\) −38.9247 −2.16583
\(324\) 36.2385 2.01325
\(325\) −11.7264 −0.650461
\(326\) −34.2887 −1.89908
\(327\) −39.5900 −2.18933
\(328\) 7.28272 0.402121
\(329\) −5.91309 −0.325999
\(330\) −13.7164 −0.755061
\(331\) 22.4834 1.23580 0.617900 0.786257i \(-0.287984\pi\)
0.617900 + 0.786257i \(0.287984\pi\)
\(332\) 13.5602 0.744215
\(333\) 48.0089 2.63087
\(334\) −16.7817 −0.918253
\(335\) −0.330976 −0.0180832
\(336\) 1.99734 0.108964
\(337\) −28.8038 −1.56904 −0.784521 0.620102i \(-0.787091\pi\)
−0.784521 + 0.620102i \(0.787091\pi\)
\(338\) −30.7742 −1.67390
\(339\) 7.10732 0.386017
\(340\) −35.5808 −1.92964
\(341\) −12.7213 −0.688895
\(342\) −87.3591 −4.72384
\(343\) 1.00000 0.0539949
\(344\) 32.6454 1.76012
\(345\) 26.6683 1.43577
\(346\) 39.6802 2.13322
\(347\) −10.8197 −0.580834 −0.290417 0.956900i \(-0.593794\pi\)
−0.290417 + 0.956900i \(0.593794\pi\)
\(348\) 78.0482 4.18382
\(349\) 17.8549 0.955752 0.477876 0.878427i \(-0.341407\pi\)
0.477876 + 0.878427i \(0.341407\pi\)
\(350\) 5.30622 0.283629
\(351\) 49.5237 2.64338
\(352\) 5.76695 0.307380
\(353\) −12.8811 −0.685594 −0.342797 0.939410i \(-0.611374\pi\)
−0.342797 + 0.939410i \(0.611374\pi\)
\(354\) −47.3302 −2.51557
\(355\) 12.6856 0.673284
\(356\) −36.3171 −1.92480
\(357\) −19.3821 −1.02581
\(358\) −2.89833 −0.153182
\(359\) −30.1383 −1.59064 −0.795319 0.606191i \(-0.792697\pi\)
−0.795319 + 0.606191i \(0.792697\pi\)
\(360\) −32.5872 −1.71750
\(361\) 18.0561 0.950323
\(362\) −41.5313 −2.18284
\(363\) −29.0876 −1.52670
\(364\) 17.3178 0.907698
\(365\) −4.19693 −0.219677
\(366\) −31.8009 −1.66226
\(367\) −19.1210 −0.998110 −0.499055 0.866570i \(-0.666319\pi\)
−0.499055 + 0.866570i \(0.666319\pi\)
\(368\) 3.52035 0.183511
\(369\) −14.0917 −0.733586
\(370\) −29.6336 −1.54058
\(371\) 5.89523 0.306065
\(372\) −109.968 −5.70158
\(373\) −0.983259 −0.0509112 −0.0254556 0.999676i \(-0.508104\pi\)
−0.0254556 + 0.999676i \(0.508104\pi\)
\(374\) 17.5702 0.908535
\(375\) −36.3797 −1.87864
\(376\) 18.9094 0.975177
\(377\) 39.0581 2.01160
\(378\) −22.4096 −1.15263
\(379\) −31.5450 −1.62036 −0.810178 0.586184i \(-0.800629\pi\)
−0.810178 + 0.586184i \(0.800629\pi\)
\(380\) 33.8728 1.73764
\(381\) −42.5450 −2.17965
\(382\) −31.1333 −1.59292
\(383\) 15.8326 0.809007 0.404504 0.914536i \(-0.367444\pi\)
0.404504 + 0.914536i \(0.367444\pi\)
\(384\) 59.1166 3.01678
\(385\) 1.95114 0.0994395
\(386\) 26.9770 1.37309
\(387\) −63.1673 −3.21098
\(388\) −21.4059 −1.08672
\(389\) −1.70292 −0.0863416 −0.0431708 0.999068i \(-0.513746\pi\)
−0.0431708 + 0.999068i \(0.513746\pi\)
\(390\) −59.3368 −3.00463
\(391\) −34.1613 −1.72761
\(392\) −3.19788 −0.161518
\(393\) 10.9364 0.551667
\(394\) 7.84608 0.395280
\(395\) 8.94846 0.450246
\(396\) 24.7708 1.24478
\(397\) −4.08442 −0.204991 −0.102496 0.994733i \(-0.532683\pi\)
−0.102496 + 0.994733i \(0.532683\pi\)
\(398\) −63.2433 −3.17010
\(399\) 18.4516 0.923737
\(400\) −1.50760 −0.0753801
\(401\) −31.7083 −1.58344 −0.791719 0.610885i \(-0.790814\pi\)
−0.791719 + 0.610885i \(0.790814\pi\)
\(402\) 1.41285 0.0704664
\(403\) −55.0320 −2.74134
\(404\) 16.9317 0.842385
\(405\) 17.6625 0.877656
\(406\) −17.6739 −0.877143
\(407\) 9.19235 0.455648
\(408\) 61.9816 3.06854
\(409\) −0.419241 −0.0207301 −0.0103651 0.999946i \(-0.503299\pi\)
−0.0103651 + 0.999946i \(0.503299\pi\)
\(410\) 8.69815 0.429571
\(411\) 27.6609 1.36441
\(412\) −21.0878 −1.03892
\(413\) 6.73270 0.331294
\(414\) −76.6687 −3.76806
\(415\) 6.60921 0.324433
\(416\) 24.9478 1.22316
\(417\) −43.7179 −2.14087
\(418\) −16.7268 −0.818134
\(419\) 7.30320 0.356785 0.178392 0.983959i \(-0.442910\pi\)
0.178392 + 0.983959i \(0.442910\pi\)
\(420\) 16.8665 0.823002
\(421\) 11.3649 0.553893 0.276947 0.960885i \(-0.410678\pi\)
0.276947 + 0.960885i \(0.410678\pi\)
\(422\) −17.7781 −0.865426
\(423\) −36.5888 −1.77901
\(424\) −18.8523 −0.915548
\(425\) 14.6297 0.709645
\(426\) −54.1515 −2.62365
\(427\) 4.52365 0.218915
\(428\) 37.9204 1.83295
\(429\) 18.4063 0.888662
\(430\) 38.9902 1.88027
\(431\) −10.1198 −0.487454 −0.243727 0.969844i \(-0.578370\pi\)
−0.243727 + 0.969844i \(0.578370\pi\)
\(432\) 6.36702 0.306334
\(433\) 3.84773 0.184910 0.0924550 0.995717i \(-0.470529\pi\)
0.0924550 + 0.995717i \(0.470529\pi\)
\(434\) 24.9022 1.19534
\(435\) 38.0404 1.82390
\(436\) −44.1316 −2.11352
\(437\) 32.5214 1.55571
\(438\) 17.9155 0.856037
\(439\) 20.1952 0.963864 0.481932 0.876209i \(-0.339935\pi\)
0.481932 + 0.876209i \(0.339935\pi\)
\(440\) −6.23953 −0.297458
\(441\) 6.18776 0.294655
\(442\) 76.0086 3.61536
\(443\) −6.50705 −0.309159 −0.154580 0.987980i \(-0.549402\pi\)
−0.154580 + 0.987980i \(0.549402\pi\)
\(444\) 79.4626 3.77113
\(445\) −17.7008 −0.839098
\(446\) 35.5219 1.68201
\(447\) −21.5550 −1.01952
\(448\) −12.6068 −0.595617
\(449\) 1.79501 0.0847117 0.0423558 0.999103i \(-0.486514\pi\)
0.0423558 + 0.999103i \(0.486514\pi\)
\(450\) 32.8336 1.54779
\(451\) −2.69817 −0.127052
\(452\) 7.92265 0.372650
\(453\) −51.6693 −2.42764
\(454\) −48.6400 −2.28279
\(455\) 8.44062 0.395702
\(456\) −59.0062 −2.76322
\(457\) −36.3229 −1.69911 −0.849557 0.527498i \(-0.823130\pi\)
−0.849557 + 0.527498i \(0.823130\pi\)
\(458\) −61.1246 −2.85616
\(459\) −61.7853 −2.88389
\(460\) 29.7276 1.38606
\(461\) 6.84375 0.318745 0.159373 0.987218i \(-0.449053\pi\)
0.159373 + 0.987218i \(0.449053\pi\)
\(462\) −8.32889 −0.387495
\(463\) −33.6672 −1.56465 −0.782324 0.622872i \(-0.785966\pi\)
−0.782324 + 0.622872i \(0.785966\pi\)
\(464\) 5.02152 0.233118
\(465\) −53.5980 −2.48555
\(466\) −0.371022 −0.0171873
\(467\) 35.8138 1.65727 0.828633 0.559792i \(-0.189119\pi\)
0.828633 + 0.559792i \(0.189119\pi\)
\(468\) 107.158 4.95339
\(469\) −0.200977 −0.00928023
\(470\) 22.5845 1.04175
\(471\) 59.3208 2.73336
\(472\) −21.5304 −0.991017
\(473\) −12.0948 −0.556117
\(474\) −38.1985 −1.75452
\(475\) −13.9274 −0.639034
\(476\) −21.6055 −0.990286
\(477\) 36.4783 1.67023
\(478\) 11.9376 0.546012
\(479\) 0.588134 0.0268725 0.0134363 0.999910i \(-0.495723\pi\)
0.0134363 + 0.999910i \(0.495723\pi\)
\(480\) 24.2977 1.10903
\(481\) 39.7660 1.81317
\(482\) 35.0841 1.59804
\(483\) 16.1936 0.736836
\(484\) −32.4245 −1.47384
\(485\) −10.4331 −0.473745
\(486\) −8.16737 −0.370479
\(487\) −3.94727 −0.178868 −0.0894340 0.995993i \(-0.528506\pi\)
−0.0894340 + 0.995993i \(0.528506\pi\)
\(488\) −14.4661 −0.654851
\(489\) 44.8138 2.02655
\(490\) −3.81941 −0.172543
\(491\) −13.3365 −0.601868 −0.300934 0.953645i \(-0.597298\pi\)
−0.300934 + 0.953645i \(0.597298\pi\)
\(492\) −23.3241 −1.05153
\(493\) −48.7286 −2.19463
\(494\) −72.3599 −3.25562
\(495\) 12.0732 0.542650
\(496\) −7.07520 −0.317686
\(497\) 7.70302 0.345528
\(498\) −28.2129 −1.26425
\(499\) 21.3624 0.956312 0.478156 0.878275i \(-0.341305\pi\)
0.478156 + 0.878275i \(0.341305\pi\)
\(500\) −40.5531 −1.81359
\(501\) 21.9329 0.979888
\(502\) 48.2930 2.15542
\(503\) 0.837181 0.0373280 0.0186640 0.999826i \(-0.494059\pi\)
0.0186640 + 0.999826i \(0.494059\pi\)
\(504\) −19.7877 −0.881416
\(505\) 8.25246 0.367230
\(506\) −14.6799 −0.652600
\(507\) 40.2205 1.78625
\(508\) −47.4256 −2.10417
\(509\) 7.41482 0.328656 0.164328 0.986406i \(-0.447454\pi\)
0.164328 + 0.986406i \(0.447454\pi\)
\(510\) 74.0280 3.27802
\(511\) −2.54847 −0.112738
\(512\) 7.42184 0.328002
\(513\) 58.8194 2.59694
\(514\) 64.2777 2.83517
\(515\) −10.2781 −0.452908
\(516\) −104.552 −4.60265
\(517\) −7.00571 −0.308111
\(518\) −17.9942 −0.790622
\(519\) −51.8602 −2.27641
\(520\) −26.9921 −1.18368
\(521\) 14.7867 0.647815 0.323908 0.946089i \(-0.395003\pi\)
0.323908 + 0.946089i \(0.395003\pi\)
\(522\) −109.362 −4.78665
\(523\) 6.56218 0.286944 0.143472 0.989654i \(-0.454173\pi\)
0.143472 + 0.989654i \(0.454173\pi\)
\(524\) 12.1909 0.532564
\(525\) −6.93498 −0.302667
\(526\) −47.1532 −2.05598
\(527\) 68.6575 2.99077
\(528\) 2.36640 0.102984
\(529\) 5.54167 0.240942
\(530\) −22.5163 −0.978046
\(531\) 41.6603 1.80790
\(532\) 20.5683 0.891751
\(533\) −11.6722 −0.505580
\(534\) 75.5598 3.26979
\(535\) 18.4823 0.799059
\(536\) 0.642700 0.0277604
\(537\) 3.78799 0.163464
\(538\) 6.80465 0.293369
\(539\) 1.18478 0.0510321
\(540\) 53.7664 2.31374
\(541\) 14.9973 0.644784 0.322392 0.946606i \(-0.395513\pi\)
0.322392 + 0.946606i \(0.395513\pi\)
\(542\) 32.7739 1.40776
\(543\) 54.2795 2.32936
\(544\) −31.1246 −1.33446
\(545\) −21.5096 −0.921370
\(546\) −36.0307 −1.54197
\(547\) −31.7740 −1.35856 −0.679279 0.733880i \(-0.737707\pi\)
−0.679279 + 0.733880i \(0.737707\pi\)
\(548\) 30.8340 1.31716
\(549\) 27.9913 1.19464
\(550\) 6.28670 0.268066
\(551\) 46.3894 1.97626
\(552\) −51.7854 −2.20413
\(553\) 5.43372 0.231065
\(554\) 45.0248 1.91292
\(555\) 38.7298 1.64399
\(556\) −48.7331 −2.06674
\(557\) −3.74638 −0.158739 −0.0793696 0.996845i \(-0.525291\pi\)
−0.0793696 + 0.996845i \(0.525291\pi\)
\(558\) 154.089 6.52310
\(559\) −52.3217 −2.21297
\(560\) 1.08517 0.0458568
\(561\) −22.9635 −0.969519
\(562\) 58.5549 2.46999
\(563\) −5.16990 −0.217885 −0.108943 0.994048i \(-0.534747\pi\)
−0.108943 + 0.994048i \(0.534747\pi\)
\(564\) −60.5604 −2.55005
\(565\) 3.86147 0.162453
\(566\) 52.2219 2.19505
\(567\) 10.7251 0.450411
\(568\) −24.6334 −1.03359
\(569\) 10.9253 0.458013 0.229007 0.973425i \(-0.426452\pi\)
0.229007 + 0.973425i \(0.426452\pi\)
\(570\) −70.4744 −2.95185
\(571\) −4.07348 −0.170470 −0.0852350 0.996361i \(-0.527164\pi\)
−0.0852350 + 0.996361i \(0.527164\pi\)
\(572\) 20.5178 0.857890
\(573\) 40.6897 1.69984
\(574\) 5.28172 0.220455
\(575\) −12.2231 −0.509737
\(576\) −78.0080 −3.25033
\(577\) 17.5048 0.728733 0.364366 0.931256i \(-0.381286\pi\)
0.364366 + 0.931256i \(0.381286\pi\)
\(578\) −55.4006 −2.30436
\(579\) −35.2576 −1.46526
\(580\) 42.4043 1.76074
\(581\) 4.01327 0.166498
\(582\) 44.5362 1.84609
\(583\) 6.98456 0.289271
\(584\) 8.14972 0.337238
\(585\) 52.2285 2.15938
\(586\) −69.7683 −2.88210
\(587\) −7.45946 −0.307885 −0.153943 0.988080i \(-0.549197\pi\)
−0.153943 + 0.988080i \(0.549197\pi\)
\(588\) 10.2417 0.422363
\(589\) −65.3616 −2.69318
\(590\) −25.7149 −1.05867
\(591\) −10.2545 −0.421812
\(592\) 5.11252 0.210123
\(593\) 35.2783 1.44871 0.724353 0.689429i \(-0.242139\pi\)
0.724353 + 0.689429i \(0.242139\pi\)
\(594\) −26.5505 −1.08938
\(595\) −10.5304 −0.431706
\(596\) −24.0277 −0.984214
\(597\) 82.6561 3.38289
\(598\) −63.5049 −2.59691
\(599\) −29.7386 −1.21509 −0.607543 0.794287i \(-0.707845\pi\)
−0.607543 + 0.794287i \(0.707845\pi\)
\(600\) 22.1773 0.905383
\(601\) −15.0481 −0.613825 −0.306913 0.951738i \(-0.599296\pi\)
−0.306913 + 0.951738i \(0.599296\pi\)
\(602\) 23.6758 0.964952
\(603\) −1.24359 −0.0506431
\(604\) −57.5966 −2.34357
\(605\) −15.8036 −0.642506
\(606\) −35.2275 −1.43102
\(607\) 5.36717 0.217847 0.108923 0.994050i \(-0.465260\pi\)
0.108923 + 0.994050i \(0.465260\pi\)
\(608\) 29.6305 1.20167
\(609\) 23.0990 0.936020
\(610\) −17.2777 −0.699553
\(611\) −30.3066 −1.22607
\(612\) −133.690 −5.40408
\(613\) 24.4031 0.985631 0.492815 0.870134i \(-0.335968\pi\)
0.492815 + 0.870134i \(0.335968\pi\)
\(614\) −13.1809 −0.531936
\(615\) −11.3681 −0.458405
\(616\) −3.78879 −0.152655
\(617\) 35.1737 1.41604 0.708019 0.706193i \(-0.249589\pi\)
0.708019 + 0.706193i \(0.249589\pi\)
\(618\) 43.8745 1.76489
\(619\) −6.19250 −0.248898 −0.124449 0.992226i \(-0.539716\pi\)
−0.124449 + 0.992226i \(0.539716\pi\)
\(620\) −59.7466 −2.39948
\(621\) 51.6214 2.07150
\(622\) 5.30882 0.212864
\(623\) −10.7483 −0.430623
\(624\) 10.2370 0.409809
\(625\) −8.32584 −0.333034
\(626\) −10.7931 −0.431380
\(627\) 21.8611 0.873049
\(628\) 66.1259 2.63871
\(629\) −49.6117 −1.97815
\(630\) −23.6336 −0.941585
\(631\) −0.275267 −0.0109582 −0.00547911 0.999985i \(-0.501744\pi\)
−0.00547911 + 0.999985i \(0.501744\pi\)
\(632\) −17.3764 −0.691196
\(633\) 23.2352 0.923516
\(634\) −39.9623 −1.58710
\(635\) −23.1151 −0.917293
\(636\) 60.3775 2.39412
\(637\) 5.12534 0.203073
\(638\) −20.9397 −0.829012
\(639\) 47.6644 1.88558
\(640\) 32.1186 1.26960
\(641\) −21.9951 −0.868752 −0.434376 0.900732i \(-0.643031\pi\)
−0.434376 + 0.900732i \(0.643031\pi\)
\(642\) −78.8958 −3.11377
\(643\) 24.9184 0.982684 0.491342 0.870967i \(-0.336507\pi\)
0.491342 + 0.870967i \(0.336507\pi\)
\(644\) 18.0513 0.711322
\(645\) −50.9584 −2.00648
\(646\) 90.2755 3.55184
\(647\) 6.26837 0.246435 0.123217 0.992380i \(-0.460679\pi\)
0.123217 + 0.992380i \(0.460679\pi\)
\(648\) −34.2976 −1.34734
\(649\) 7.97677 0.313115
\(650\) 27.1962 1.06672
\(651\) −32.5460 −1.27558
\(652\) 49.9547 1.95638
\(653\) −2.31739 −0.0906863 −0.0453431 0.998971i \(-0.514438\pi\)
−0.0453431 + 0.998971i \(0.514438\pi\)
\(654\) 91.8185 3.59039
\(655\) 5.94182 0.232166
\(656\) −1.50064 −0.0585902
\(657\) −15.7693 −0.615221
\(658\) 13.7139 0.534622
\(659\) −23.0499 −0.897896 −0.448948 0.893558i \(-0.648201\pi\)
−0.448948 + 0.893558i \(0.648201\pi\)
\(660\) 19.9831 0.777842
\(661\) 34.4082 1.33832 0.669162 0.743116i \(-0.266653\pi\)
0.669162 + 0.743116i \(0.266653\pi\)
\(662\) −52.1443 −2.02665
\(663\) −99.3397 −3.85803
\(664\) −12.8340 −0.498054
\(665\) 10.0249 0.388750
\(666\) −111.344 −4.31449
\(667\) 40.7126 1.57640
\(668\) 24.4489 0.945958
\(669\) −46.4255 −1.79491
\(670\) 0.767612 0.0296554
\(671\) 5.35953 0.206903
\(672\) 14.7541 0.569153
\(673\) −28.2861 −1.09035 −0.545175 0.838322i \(-0.683537\pi\)
−0.545175 + 0.838322i \(0.683537\pi\)
\(674\) 66.8027 2.57315
\(675\) −22.1070 −0.850900
\(676\) 44.8344 1.72440
\(677\) −7.83501 −0.301124 −0.150562 0.988601i \(-0.548108\pi\)
−0.150562 + 0.988601i \(0.548108\pi\)
\(678\) −16.4836 −0.633047
\(679\) −6.33525 −0.243125
\(680\) 33.6751 1.29138
\(681\) 63.5702 2.43601
\(682\) 29.5036 1.12975
\(683\) 49.3746 1.88927 0.944634 0.328126i \(-0.106417\pi\)
0.944634 + 0.328126i \(0.106417\pi\)
\(684\) 127.272 4.86636
\(685\) 15.0284 0.574205
\(686\) −2.31924 −0.0885488
\(687\) 79.8870 3.04788
\(688\) −6.72675 −0.256455
\(689\) 30.2151 1.15110
\(690\) −61.8501 −2.35459
\(691\) −32.1810 −1.22422 −0.612111 0.790772i \(-0.709679\pi\)
−0.612111 + 0.790772i \(0.709679\pi\)
\(692\) −57.8094 −2.19758
\(693\) 7.33113 0.278487
\(694\) 25.0935 0.952538
\(695\) −23.7523 −0.900976
\(696\) −73.8680 −2.79996
\(697\) 14.5622 0.551581
\(698\) −41.4098 −1.56738
\(699\) 0.484908 0.0183409
\(700\) −7.73054 −0.292187
\(701\) −14.1053 −0.532748 −0.266374 0.963870i \(-0.585826\pi\)
−0.266374 + 0.963870i \(0.585826\pi\)
\(702\) −114.857 −4.33500
\(703\) 47.2301 1.78132
\(704\) −14.9363 −0.562934
\(705\) −29.5169 −1.11167
\(706\) 29.8744 1.12434
\(707\) 5.01109 0.188461
\(708\) 68.9546 2.59147
\(709\) −43.3902 −1.62955 −0.814776 0.579775i \(-0.803140\pi\)
−0.814776 + 0.579775i \(0.803140\pi\)
\(710\) −29.4210 −1.10415
\(711\) 33.6225 1.26094
\(712\) 34.3719 1.28814
\(713\) −57.3631 −2.14826
\(714\) 44.9515 1.68227
\(715\) 10.0003 0.373989
\(716\) 4.22253 0.157803
\(717\) −15.6019 −0.582662
\(718\) 69.8978 2.60856
\(719\) 7.94878 0.296439 0.148220 0.988954i \(-0.452646\pi\)
0.148220 + 0.988954i \(0.452646\pi\)
\(720\) 6.71477 0.250245
\(721\) −6.24112 −0.232431
\(722\) −41.8764 −1.55848
\(723\) −45.8533 −1.70530
\(724\) 60.5063 2.24870
\(725\) −17.4353 −0.647530
\(726\) 67.4611 2.50372
\(727\) −41.6980 −1.54649 −0.773247 0.634106i \(-0.781368\pi\)
−0.773247 + 0.634106i \(0.781368\pi\)
\(728\) −16.3902 −0.607463
\(729\) −21.5009 −0.796328
\(730\) 9.73367 0.360259
\(731\) 65.2761 2.41432
\(732\) 46.3301 1.71241
\(733\) 5.45241 0.201389 0.100695 0.994917i \(-0.467894\pi\)
0.100695 + 0.994917i \(0.467894\pi\)
\(734\) 44.3462 1.63685
\(735\) 4.99179 0.184125
\(736\) 26.0045 0.958538
\(737\) −0.238113 −0.00877100
\(738\) 32.6820 1.20304
\(739\) −24.5090 −0.901577 −0.450789 0.892631i \(-0.648857\pi\)
−0.450789 + 0.892631i \(0.648857\pi\)
\(740\) 43.1727 1.58706
\(741\) 94.5709 3.47415
\(742\) −13.6724 −0.501931
\(743\) 48.5534 1.78125 0.890626 0.454737i \(-0.150267\pi\)
0.890626 + 0.454737i \(0.150267\pi\)
\(744\) 104.078 3.81570
\(745\) −11.7110 −0.429059
\(746\) 2.28041 0.0834917
\(747\) 24.8331 0.908597
\(748\) −25.5978 −0.935947
\(749\) 11.2229 0.410075
\(750\) 84.3732 3.08087
\(751\) 44.2012 1.61292 0.806462 0.591286i \(-0.201380\pi\)
0.806462 + 0.591286i \(0.201380\pi\)
\(752\) −3.89638 −0.142086
\(753\) −63.1167 −2.30010
\(754\) −90.5850 −3.29891
\(755\) −28.0724 −1.02166
\(756\) 32.6482 1.18740
\(757\) 10.4023 0.378077 0.189038 0.981970i \(-0.439463\pi\)
0.189038 + 0.981970i \(0.439463\pi\)
\(758\) 73.1602 2.65730
\(759\) 19.1859 0.696404
\(760\) −32.0586 −1.16289
\(761\) −0.343218 −0.0124417 −0.00622083 0.999981i \(-0.501980\pi\)
−0.00622083 + 0.999981i \(0.501980\pi\)
\(762\) 98.6718 3.57450
\(763\) −13.0611 −0.472845
\(764\) 45.3575 1.64098
\(765\) −65.1598 −2.35586
\(766\) −36.7195 −1.32673
\(767\) 34.5074 1.24599
\(768\) −60.6794 −2.18958
\(769\) 44.3665 1.59990 0.799948 0.600069i \(-0.204860\pi\)
0.799948 + 0.600069i \(0.204860\pi\)
\(770\) −4.52516 −0.163075
\(771\) −84.0079 −3.02547
\(772\) −39.3023 −1.41452
\(773\) 12.9482 0.465713 0.232857 0.972511i \(-0.425193\pi\)
0.232857 + 0.972511i \(0.425193\pi\)
\(774\) 146.500 5.26583
\(775\) 24.5659 0.882434
\(776\) 20.2594 0.727270
\(777\) 23.5176 0.843690
\(778\) 3.94948 0.141596
\(779\) −13.8631 −0.496698
\(780\) 86.4467 3.09529
\(781\) 9.12639 0.326568
\(782\) 79.2282 2.83319
\(783\) 73.6341 2.63147
\(784\) 0.658941 0.0235336
\(785\) 32.2295 1.15032
\(786\) −25.3640 −0.904704
\(787\) −13.2914 −0.473789 −0.236894 0.971535i \(-0.576129\pi\)
−0.236894 + 0.971535i \(0.576129\pi\)
\(788\) −11.4308 −0.407206
\(789\) 61.6270 2.19398
\(790\) −20.7536 −0.738380
\(791\) 2.34478 0.0833706
\(792\) −23.4441 −0.833050
\(793\) 23.1853 0.823333
\(794\) 9.47274 0.336175
\(795\) 29.4278 1.04370
\(796\) 92.1381 3.26575
\(797\) 6.29706 0.223053 0.111527 0.993761i \(-0.464426\pi\)
0.111527 + 0.993761i \(0.464426\pi\)
\(798\) −42.7937 −1.51488
\(799\) 37.8103 1.33763
\(800\) −11.1365 −0.393735
\(801\) −66.5081 −2.34995
\(802\) 73.5391 2.59675
\(803\) −3.01938 −0.106552
\(804\) −2.05835 −0.0725924
\(805\) 8.79814 0.310094
\(806\) 127.632 4.49565
\(807\) −8.89335 −0.313061
\(808\) −16.0249 −0.563753
\(809\) −4.36705 −0.153537 −0.0767687 0.997049i \(-0.524460\pi\)
−0.0767687 + 0.997049i \(0.524460\pi\)
\(810\) −40.9635 −1.43931
\(811\) 29.7660 1.04523 0.522613 0.852570i \(-0.324957\pi\)
0.522613 + 0.852570i \(0.324957\pi\)
\(812\) 25.7489 0.903608
\(813\) −42.8340 −1.50225
\(814\) −21.3192 −0.747238
\(815\) 24.3477 0.852863
\(816\) −12.7716 −0.447096
\(817\) −62.1426 −2.17409
\(818\) 0.972318 0.0339963
\(819\) 31.7144 1.10819
\(820\) −12.6722 −0.442532
\(821\) −4.31901 −0.150735 −0.0753673 0.997156i \(-0.524013\pi\)
−0.0753673 + 0.997156i \(0.524013\pi\)
\(822\) −64.1520 −2.23756
\(823\) 5.15417 0.179663 0.0898315 0.995957i \(-0.471367\pi\)
0.0898315 + 0.995957i \(0.471367\pi\)
\(824\) 19.9584 0.695283
\(825\) −8.21643 −0.286059
\(826\) −15.6147 −0.543305
\(827\) −7.72863 −0.268751 −0.134375 0.990931i \(-0.542903\pi\)
−0.134375 + 0.990931i \(0.542903\pi\)
\(828\) 111.697 3.88175
\(829\) 1.29865 0.0451040 0.0225520 0.999746i \(-0.492821\pi\)
0.0225520 + 0.999746i \(0.492821\pi\)
\(830\) −15.3283 −0.532053
\(831\) −58.8452 −2.04132
\(832\) −64.6143 −2.24010
\(833\) −6.39433 −0.221550
\(834\) 101.392 3.51092
\(835\) 11.9163 0.412381
\(836\) 24.3690 0.842818
\(837\) −103.749 −3.58608
\(838\) −16.9378 −0.585108
\(839\) 57.2421 1.97622 0.988108 0.153761i \(-0.0491386\pi\)
0.988108 + 0.153761i \(0.0491386\pi\)
\(840\) −15.9632 −0.550781
\(841\) 29.0734 1.00253
\(842\) −26.3580 −0.908355
\(843\) −76.5284 −2.63578
\(844\) 25.9006 0.891537
\(845\) 21.8521 0.751736
\(846\) 84.8580 2.91748
\(847\) −9.59630 −0.329733
\(848\) 3.88461 0.133398
\(849\) −68.2516 −2.34239
\(850\) −33.9297 −1.16378
\(851\) 41.4504 1.42090
\(852\) 78.8924 2.70281
\(853\) −37.9841 −1.30055 −0.650275 0.759699i \(-0.725346\pi\)
−0.650275 + 0.759699i \(0.725346\pi\)
\(854\) −10.4914 −0.359009
\(855\) 62.0319 2.12145
\(856\) −35.8894 −1.22668
\(857\) 42.2812 1.44430 0.722149 0.691738i \(-0.243155\pi\)
0.722149 + 0.691738i \(0.243155\pi\)
\(858\) −42.6884 −1.45736
\(859\) −1.00000 −0.0341196
\(860\) −56.8041 −1.93700
\(861\) −6.90296 −0.235252
\(862\) 23.4702 0.799399
\(863\) −15.7211 −0.535151 −0.267576 0.963537i \(-0.586223\pi\)
−0.267576 + 0.963537i \(0.586223\pi\)
\(864\) 47.0326 1.60008
\(865\) −28.1761 −0.958016
\(866\) −8.92378 −0.303242
\(867\) 72.4060 2.45904
\(868\) −36.2796 −1.23141
\(869\) 6.43776 0.218386
\(870\) −88.2246 −2.99109
\(871\) −1.03007 −0.0349027
\(872\) 41.7680 1.41444
\(873\) −39.2010 −1.32675
\(874\) −75.4249 −2.55128
\(875\) −12.0020 −0.405743
\(876\) −26.1008 −0.881865
\(877\) 13.1111 0.442731 0.221365 0.975191i \(-0.428949\pi\)
0.221365 + 0.975191i \(0.428949\pi\)
\(878\) −46.8374 −1.58069
\(879\) 91.1839 3.07556
\(880\) 1.28569 0.0433405
\(881\) −32.5518 −1.09670 −0.548349 0.836249i \(-0.684744\pi\)
−0.548349 + 0.836249i \(0.684744\pi\)
\(882\) −14.3509 −0.483219
\(883\) 5.76480 0.194001 0.0970005 0.995284i \(-0.469075\pi\)
0.0970005 + 0.995284i \(0.469075\pi\)
\(884\) −110.736 −3.72444
\(885\) 33.6082 1.12973
\(886\) 15.0914 0.507005
\(887\) 15.1647 0.509181 0.254591 0.967049i \(-0.418059\pi\)
0.254591 + 0.967049i \(0.418059\pi\)
\(888\) −75.2067 −2.52377
\(889\) −14.0360 −0.470753
\(890\) 41.0523 1.37608
\(891\) 12.7069 0.425696
\(892\) −51.7513 −1.73276
\(893\) −35.9952 −1.20453
\(894\) 49.9911 1.67195
\(895\) 2.05805 0.0687929
\(896\) 19.5031 0.651554
\(897\) 82.9979 2.77122
\(898\) −4.16305 −0.138923
\(899\) −81.8242 −2.72899
\(900\) −47.8347 −1.59449
\(901\) −37.6961 −1.25584
\(902\) 6.25768 0.208358
\(903\) −30.9431 −1.02972
\(904\) −7.49832 −0.249390
\(905\) 29.4905 0.980298
\(906\) 119.833 3.98120
\(907\) 7.77814 0.258269 0.129134 0.991627i \(-0.458780\pi\)
0.129134 + 0.991627i \(0.458780\pi\)
\(908\) 70.8627 2.35166
\(909\) 31.0074 1.02845
\(910\) −19.5758 −0.648931
\(911\) −6.93044 −0.229616 −0.114808 0.993388i \(-0.536625\pi\)
−0.114808 + 0.993388i \(0.536625\pi\)
\(912\) 12.1585 0.402609
\(913\) 4.75484 0.157362
\(914\) 84.2413 2.78646
\(915\) 22.5811 0.746509
\(916\) 89.0513 2.94234
\(917\) 3.60801 0.119147
\(918\) 143.295 4.72943
\(919\) −41.7806 −1.37822 −0.689108 0.724659i \(-0.741998\pi\)
−0.689108 + 0.724659i \(0.741998\pi\)
\(920\) −28.1354 −0.927598
\(921\) 17.2268 0.567641
\(922\) −15.8723 −0.522725
\(923\) 39.4806 1.29952
\(924\) 12.1342 0.399186
\(925\) −17.7513 −0.583658
\(926\) 78.0822 2.56594
\(927\) −38.6185 −1.26840
\(928\) 37.0935 1.21765
\(929\) −16.8225 −0.551928 −0.275964 0.961168i \(-0.588997\pi\)
−0.275964 + 0.961168i \(0.588997\pi\)
\(930\) 124.306 4.07617
\(931\) 6.08738 0.199506
\(932\) 0.540535 0.0177058
\(933\) −6.93838 −0.227152
\(934\) −83.0607 −2.71783
\(935\) −12.4763 −0.408017
\(936\) −101.419 −3.31498
\(937\) 39.5364 1.29160 0.645799 0.763508i \(-0.276524\pi\)
0.645799 + 0.763508i \(0.276524\pi\)
\(938\) 0.466112 0.0152191
\(939\) 14.1061 0.460335
\(940\) −32.9030 −1.07318
\(941\) −3.46219 −0.112864 −0.0564320 0.998406i \(-0.517972\pi\)
−0.0564320 + 0.998406i \(0.517972\pi\)
\(942\) −137.579 −4.48256
\(943\) −12.1666 −0.396200
\(944\) 4.43645 0.144394
\(945\) 15.9126 0.517637
\(946\) 28.0506 0.912003
\(947\) 39.0736 1.26972 0.634861 0.772626i \(-0.281057\pi\)
0.634861 + 0.772626i \(0.281057\pi\)
\(948\) 55.6508 1.80745
\(949\) −13.0618 −0.424004
\(950\) 32.3010 1.04798
\(951\) 52.2288 1.69363
\(952\) 20.4483 0.662734
\(953\) −23.2234 −0.752278 −0.376139 0.926563i \(-0.622749\pi\)
−0.376139 + 0.926563i \(0.622749\pi\)
\(954\) −84.6017 −2.73908
\(955\) 22.1071 0.715369
\(956\) −17.3916 −0.562486
\(957\) 27.3673 0.884658
\(958\) −1.36402 −0.0440695
\(959\) 9.12559 0.294681
\(960\) −62.9306 −2.03108
\(961\) 84.2884 2.71898
\(962\) −92.2267 −2.97351
\(963\) 69.4444 2.23782
\(964\) −51.1134 −1.64625
\(965\) −19.1558 −0.616646
\(966\) −37.5569 −1.20837
\(967\) 23.8746 0.767755 0.383877 0.923384i \(-0.374589\pi\)
0.383877 + 0.923384i \(0.374589\pi\)
\(968\) 30.6878 0.986345
\(969\) −117.986 −3.79025
\(970\) 24.1969 0.776916
\(971\) 30.0242 0.963523 0.481762 0.876302i \(-0.339997\pi\)
0.481762 + 0.876302i \(0.339997\pi\)
\(972\) 11.8989 0.381657
\(973\) −14.4230 −0.462379
\(974\) 9.15465 0.293334
\(975\) −35.5441 −1.13832
\(976\) 2.98082 0.0954137
\(977\) 44.4253 1.42129 0.710646 0.703550i \(-0.248403\pi\)
0.710646 + 0.703550i \(0.248403\pi\)
\(978\) −103.934 −3.32343
\(979\) −12.7344 −0.406994
\(980\) 5.56443 0.177749
\(981\) −80.8191 −2.58036
\(982\) 30.9305 0.987031
\(983\) −28.4577 −0.907659 −0.453830 0.891089i \(-0.649942\pi\)
−0.453830 + 0.891089i \(0.649942\pi\)
\(984\) 22.0749 0.703721
\(985\) −5.57134 −0.177518
\(986\) 113.013 3.59907
\(987\) −17.9234 −0.570507
\(988\) 105.420 3.35385
\(989\) −54.5380 −1.73421
\(990\) −28.0006 −0.889917
\(991\) −29.1700 −0.926617 −0.463308 0.886197i \(-0.653338\pi\)
−0.463308 + 0.886197i \(0.653338\pi\)
\(992\) −52.2638 −1.65938
\(993\) 68.1502 2.16268
\(994\) −17.8651 −0.566647
\(995\) 44.9078 1.42367
\(996\) 41.1029 1.30239
\(997\) 23.5922 0.747173 0.373587 0.927595i \(-0.378128\pi\)
0.373587 + 0.927595i \(0.378128\pi\)
\(998\) −49.5444 −1.56830
\(999\) 74.9685 2.37190
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 \(a_p\))