Properties

Label 6013.2.a.e.1.5
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 1.5
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.53130 q^{2}\) \(+1.72523 q^{3}\) \(+4.40746 q^{4}\) \(-1.30306 q^{5}\) \(-4.36707 q^{6}\) \(+1.00000 q^{7}\) \(-6.09399 q^{8}\) \(-0.0235740 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.53130 q^{2}\) \(+1.72523 q^{3}\) \(+4.40746 q^{4}\) \(-1.30306 q^{5}\) \(-4.36707 q^{6}\) \(+1.00000 q^{7}\) \(-6.09399 q^{8}\) \(-0.0235740 q^{9}\) \(+3.29843 q^{10}\) \(-0.721143 q^{11}\) \(+7.60389 q^{12}\) \(+0.841919 q^{13}\) \(-2.53130 q^{14}\) \(-2.24808 q^{15}\) \(+6.61079 q^{16}\) \(+7.21849 q^{17}\) \(+0.0596727 q^{18}\) \(-3.82019 q^{19}\) \(-5.74318 q^{20}\) \(+1.72523 q^{21}\) \(+1.82543 q^{22}\) \(+0.353318 q^{23}\) \(-10.5136 q^{24}\) \(-3.30204 q^{25}\) \(-2.13115 q^{26}\) \(-5.21637 q^{27}\) \(+4.40746 q^{28}\) \(+3.12979 q^{29}\) \(+5.69055 q^{30}\) \(+5.64160 q^{31}\) \(-4.54587 q^{32}\) \(-1.24414 q^{33}\) \(-18.2721 q^{34}\) \(-1.30306 q^{35}\) \(-0.103901 q^{36}\) \(+0.891975 q^{37}\) \(+9.67003 q^{38}\) \(+1.45251 q^{39}\) \(+7.94083 q^{40}\) \(+5.49875 q^{41}\) \(-4.36707 q^{42}\) \(-8.06585 q^{43}\) \(-3.17841 q^{44}\) \(+0.0307183 q^{45}\) \(-0.894353 q^{46}\) \(-3.08589 q^{47}\) \(+11.4051 q^{48}\) \(+1.00000 q^{49}\) \(+8.35844 q^{50}\) \(+12.4536 q^{51}\) \(+3.71072 q^{52}\) \(+9.23293 q^{53}\) \(+13.2042 q^{54}\) \(+0.939691 q^{55}\) \(-6.09399 q^{56}\) \(-6.59071 q^{57}\) \(-7.92242 q^{58}\) \(+2.08753 q^{59}\) \(-9.90832 q^{60}\) \(-5.39601 q^{61}\) \(-14.2806 q^{62}\) \(-0.0235740 q^{63}\) \(-1.71464 q^{64}\) \(-1.09707 q^{65}\) \(+3.14928 q^{66}\) \(+4.81531 q^{67}\) \(+31.8152 q^{68}\) \(+0.609556 q^{69}\) \(+3.29843 q^{70}\) \(+1.37071 q^{71}\) \(+0.143660 q^{72}\) \(+6.46357 q^{73}\) \(-2.25785 q^{74}\) \(-5.69678 q^{75}\) \(-16.8373 q^{76}\) \(-0.721143 q^{77}\) \(-3.67672 q^{78}\) \(+8.56828 q^{79}\) \(-8.61424 q^{80}\) \(-8.92872 q^{81}\) \(-13.9190 q^{82}\) \(+2.89335 q^{83}\) \(+7.60389 q^{84}\) \(-9.40611 q^{85}\) \(+20.4171 q^{86}\) \(+5.39961 q^{87}\) \(+4.39464 q^{88}\) \(-5.28524 q^{89}\) \(-0.0777571 q^{90}\) \(+0.841919 q^{91}\) \(+1.55724 q^{92}\) \(+9.73306 q^{93}\) \(+7.81131 q^{94}\) \(+4.97793 q^{95}\) \(-7.84267 q^{96}\) \(-13.9376 q^{97}\) \(-2.53130 q^{98}\) \(+0.0170002 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53130 −1.78990 −0.894948 0.446170i \(-0.852788\pi\)
−0.894948 + 0.446170i \(0.852788\pi\)
\(3\) 1.72523 0.996063 0.498032 0.867159i \(-0.334056\pi\)
0.498032 + 0.867159i \(0.334056\pi\)
\(4\) 4.40746 2.20373
\(5\) −1.30306 −0.582745 −0.291373 0.956610i \(-0.594112\pi\)
−0.291373 + 0.956610i \(0.594112\pi\)
\(6\) −4.36707 −1.78285
\(7\) 1.00000 0.377964
\(8\) −6.09399 −2.15455
\(9\) −0.0235740 −0.00785799
\(10\) 3.29843 1.04305
\(11\) −0.721143 −0.217433 −0.108716 0.994073i \(-0.534674\pi\)
−0.108716 + 0.994073i \(0.534674\pi\)
\(12\) 7.60389 2.19505
\(13\) 0.841919 0.233506 0.116753 0.993161i \(-0.462751\pi\)
0.116753 + 0.993161i \(0.462751\pi\)
\(14\) −2.53130 −0.676517
\(15\) −2.24808 −0.580451
\(16\) 6.61079 1.65270
\(17\) 7.21849 1.75074 0.875371 0.483453i \(-0.160617\pi\)
0.875371 + 0.483453i \(0.160617\pi\)
\(18\) 0.0596727 0.0140650
\(19\) −3.82019 −0.876412 −0.438206 0.898875i \(-0.644386\pi\)
−0.438206 + 0.898875i \(0.644386\pi\)
\(20\) −5.74318 −1.28421
\(21\) 1.72523 0.376477
\(22\) 1.82543 0.389182
\(23\) 0.353318 0.0736720 0.0368360 0.999321i \(-0.488272\pi\)
0.0368360 + 0.999321i \(0.488272\pi\)
\(24\) −10.5136 −2.14607
\(25\) −3.30204 −0.660408
\(26\) −2.13115 −0.417952
\(27\) −5.21637 −1.00389
\(28\) 4.40746 0.832932
\(29\) 3.12979 0.581187 0.290593 0.956847i \(-0.406147\pi\)
0.290593 + 0.956847i \(0.406147\pi\)
\(30\) 5.69055 1.03895
\(31\) 5.64160 1.01326 0.506630 0.862163i \(-0.330891\pi\)
0.506630 + 0.862163i \(0.330891\pi\)
\(32\) −4.54587 −0.803603
\(33\) −1.24414 −0.216577
\(34\) −18.2721 −3.13365
\(35\) −1.30306 −0.220257
\(36\) −0.103901 −0.0173169
\(37\) 0.891975 0.146640 0.0733199 0.997308i \(-0.476641\pi\)
0.0733199 + 0.997308i \(0.476641\pi\)
\(38\) 9.67003 1.56869
\(39\) 1.45251 0.232587
\(40\) 7.94083 1.25556
\(41\) 5.49875 0.858761 0.429380 0.903124i \(-0.358732\pi\)
0.429380 + 0.903124i \(0.358732\pi\)
\(42\) −4.36707 −0.673854
\(43\) −8.06585 −1.23003 −0.615015 0.788515i \(-0.710850\pi\)
−0.615015 + 0.788515i \(0.710850\pi\)
\(44\) −3.17841 −0.479163
\(45\) 0.0307183 0.00457921
\(46\) −0.894353 −0.131865
\(47\) −3.08589 −0.450124 −0.225062 0.974344i \(-0.572258\pi\)
−0.225062 + 0.974344i \(0.572258\pi\)
\(48\) 11.4051 1.64619
\(49\) 1.00000 0.142857
\(50\) 8.35844 1.18206
\(51\) 12.4536 1.74385
\(52\) 3.71072 0.514585
\(53\) 9.23293 1.26824 0.634120 0.773235i \(-0.281362\pi\)
0.634120 + 0.773235i \(0.281362\pi\)
\(54\) 13.2042 1.79686
\(55\) 0.939691 0.126708
\(56\) −6.09399 −0.814344
\(57\) −6.59071 −0.872961
\(58\) −7.92242 −1.04026
\(59\) 2.08753 0.271773 0.135887 0.990724i \(-0.456612\pi\)
0.135887 + 0.990724i \(0.456612\pi\)
\(60\) −9.90832 −1.27916
\(61\) −5.39601 −0.690888 −0.345444 0.938439i \(-0.612272\pi\)
−0.345444 + 0.938439i \(0.612272\pi\)
\(62\) −14.2806 −1.81363
\(63\) −0.0235740 −0.00297004
\(64\) −1.71464 −0.214330
\(65\) −1.09707 −0.136075
\(66\) 3.14928 0.387650
\(67\) 4.81531 0.588284 0.294142 0.955762i \(-0.404966\pi\)
0.294142 + 0.955762i \(0.404966\pi\)
\(68\) 31.8152 3.85816
\(69\) 0.609556 0.0733819
\(70\) 3.29843 0.394237
\(71\) 1.37071 0.162674 0.0813368 0.996687i \(-0.474081\pi\)
0.0813368 + 0.996687i \(0.474081\pi\)
\(72\) 0.143660 0.0169305
\(73\) 6.46357 0.756503 0.378252 0.925703i \(-0.376525\pi\)
0.378252 + 0.925703i \(0.376525\pi\)
\(74\) −2.25785 −0.262470
\(75\) −5.69678 −0.657808
\(76\) −16.8373 −1.93137
\(77\) −0.721143 −0.0821818
\(78\) −3.67672 −0.416307
\(79\) 8.56828 0.964007 0.482003 0.876169i \(-0.339909\pi\)
0.482003 + 0.876169i \(0.339909\pi\)
\(80\) −8.61424 −0.963101
\(81\) −8.92872 −0.992080
\(82\) −13.9190 −1.53709
\(83\) 2.89335 0.317586 0.158793 0.987312i \(-0.449240\pi\)
0.158793 + 0.987312i \(0.449240\pi\)
\(84\) 7.60389 0.829653
\(85\) −9.40611 −1.02024
\(86\) 20.4171 2.20163
\(87\) 5.39961 0.578899
\(88\) 4.39464 0.468470
\(89\) −5.28524 −0.560235 −0.280117 0.959966i \(-0.590373\pi\)
−0.280117 + 0.959966i \(0.590373\pi\)
\(90\) −0.0777571 −0.00819631
\(91\) 0.841919 0.0882571
\(92\) 1.55724 0.162353
\(93\) 9.73306 1.00927
\(94\) 7.81131 0.805675
\(95\) 4.97793 0.510725
\(96\) −7.84267 −0.800440
\(97\) −13.9376 −1.41515 −0.707576 0.706637i \(-0.750211\pi\)
−0.707576 + 0.706637i \(0.750211\pi\)
\(98\) −2.53130 −0.255700
\(99\) 0.0170002 0.00170859
\(100\) −14.5536 −1.45536
\(101\) 10.3686 1.03171 0.515855 0.856676i \(-0.327474\pi\)
0.515855 + 0.856676i \(0.327474\pi\)
\(102\) −31.5237 −3.12131
\(103\) −15.6779 −1.54479 −0.772397 0.635140i \(-0.780942\pi\)
−0.772397 + 0.635140i \(0.780942\pi\)
\(104\) −5.13065 −0.503102
\(105\) −2.24808 −0.219390
\(106\) −23.3713 −2.27002
\(107\) −17.4175 −1.68381 −0.841907 0.539622i \(-0.818567\pi\)
−0.841907 + 0.539622i \(0.818567\pi\)
\(108\) −22.9909 −2.21230
\(109\) 3.01641 0.288920 0.144460 0.989511i \(-0.453856\pi\)
0.144460 + 0.989511i \(0.453856\pi\)
\(110\) −2.37864 −0.226794
\(111\) 1.53886 0.146062
\(112\) 6.61079 0.624661
\(113\) 5.61041 0.527783 0.263891 0.964552i \(-0.414994\pi\)
0.263891 + 0.964552i \(0.414994\pi\)
\(114\) 16.6830 1.56251
\(115\) −0.460394 −0.0429320
\(116\) 13.7944 1.28078
\(117\) −0.0198474 −0.00183489
\(118\) −5.28416 −0.486446
\(119\) 7.21849 0.661718
\(120\) 13.6998 1.25061
\(121\) −10.4800 −0.952723
\(122\) 13.6589 1.23662
\(123\) 9.48662 0.855380
\(124\) 24.8651 2.23295
\(125\) 10.8180 0.967595
\(126\) 0.0596727 0.00531607
\(127\) 3.02753 0.268650 0.134325 0.990937i \(-0.457113\pi\)
0.134325 + 0.990937i \(0.457113\pi\)
\(128\) 13.4320 1.18723
\(129\) −13.9155 −1.22519
\(130\) 2.77701 0.243560
\(131\) 10.3355 0.903016 0.451508 0.892267i \(-0.350886\pi\)
0.451508 + 0.892267i \(0.350886\pi\)
\(132\) −5.48349 −0.477277
\(133\) −3.82019 −0.331252
\(134\) −12.1890 −1.05297
\(135\) 6.79723 0.585012
\(136\) −43.9894 −3.77206
\(137\) 10.6889 0.913214 0.456607 0.889668i \(-0.349064\pi\)
0.456607 + 0.889668i \(0.349064\pi\)
\(138\) −1.54297 −0.131346
\(139\) 22.0592 1.87104 0.935519 0.353277i \(-0.114933\pi\)
0.935519 + 0.353277i \(0.114933\pi\)
\(140\) −5.74318 −0.485387
\(141\) −5.32388 −0.448352
\(142\) −3.46968 −0.291169
\(143\) −0.607144 −0.0507719
\(144\) −0.155843 −0.0129869
\(145\) −4.07829 −0.338684
\(146\) −16.3612 −1.35406
\(147\) 1.72523 0.142295
\(148\) 3.93134 0.323154
\(149\) −4.94614 −0.405204 −0.202602 0.979261i \(-0.564940\pi\)
−0.202602 + 0.979261i \(0.564940\pi\)
\(150\) 14.4202 1.17741
\(151\) 5.57117 0.453375 0.226688 0.973968i \(-0.427210\pi\)
0.226688 + 0.973968i \(0.427210\pi\)
\(152\) 23.2802 1.88827
\(153\) −0.170169 −0.0137573
\(154\) 1.82543 0.147097
\(155\) −7.35133 −0.590473
\(156\) 6.40186 0.512559
\(157\) 1.46140 0.116633 0.0583163 0.998298i \(-0.481427\pi\)
0.0583163 + 0.998298i \(0.481427\pi\)
\(158\) −21.6889 −1.72547
\(159\) 15.9289 1.26325
\(160\) 5.92353 0.468296
\(161\) 0.353318 0.0278454
\(162\) 22.6012 1.77572
\(163\) 14.8377 1.16218 0.581091 0.813839i \(-0.302626\pi\)
0.581091 + 0.813839i \(0.302626\pi\)
\(164\) 24.2355 1.89248
\(165\) 1.62119 0.126209
\(166\) −7.32392 −0.568447
\(167\) 20.2138 1.56419 0.782094 0.623161i \(-0.214152\pi\)
0.782094 + 0.623161i \(0.214152\pi\)
\(168\) −10.5136 −0.811138
\(169\) −12.2912 −0.945475
\(170\) 23.8097 1.82612
\(171\) 0.0900571 0.00688684
\(172\) −35.5499 −2.71066
\(173\) −19.3943 −1.47452 −0.737259 0.675610i \(-0.763880\pi\)
−0.737259 + 0.675610i \(0.763880\pi\)
\(174\) −13.6680 −1.03617
\(175\) −3.30204 −0.249611
\(176\) −4.76732 −0.359350
\(177\) 3.60147 0.270703
\(178\) 13.3785 1.00276
\(179\) 16.3504 1.22209 0.611043 0.791598i \(-0.290750\pi\)
0.611043 + 0.791598i \(0.290750\pi\)
\(180\) 0.135390 0.0100913
\(181\) 12.6634 0.941266 0.470633 0.882329i \(-0.344026\pi\)
0.470633 + 0.882329i \(0.344026\pi\)
\(182\) −2.13115 −0.157971
\(183\) −9.30937 −0.688168
\(184\) −2.15312 −0.158730
\(185\) −1.16230 −0.0854536
\(186\) −24.6373 −1.80649
\(187\) −5.20556 −0.380668
\(188\) −13.6009 −0.991951
\(189\) −5.21637 −0.379435
\(190\) −12.6006 −0.914145
\(191\) −10.1547 −0.734766 −0.367383 0.930070i \(-0.619746\pi\)
−0.367383 + 0.930070i \(0.619746\pi\)
\(192\) −2.95815 −0.213486
\(193\) 8.35507 0.601411 0.300706 0.953717i \(-0.402778\pi\)
0.300706 + 0.953717i \(0.402778\pi\)
\(194\) 35.2803 2.53298
\(195\) −1.89270 −0.135539
\(196\) 4.40746 0.314819
\(197\) −11.5488 −0.822816 −0.411408 0.911451i \(-0.634963\pi\)
−0.411408 + 0.911451i \(0.634963\pi\)
\(198\) −0.0430326 −0.00305819
\(199\) −12.1635 −0.862250 −0.431125 0.902292i \(-0.641883\pi\)
−0.431125 + 0.902292i \(0.641883\pi\)
\(200\) 20.1226 1.42288
\(201\) 8.30753 0.585968
\(202\) −26.2459 −1.84665
\(203\) 3.12979 0.219668
\(204\) 54.8886 3.84297
\(205\) −7.16519 −0.500439
\(206\) 39.6855 2.76502
\(207\) −0.00832912 −0.000578914 0
\(208\) 5.56575 0.385915
\(209\) 2.75490 0.190561
\(210\) 5.69055 0.392685
\(211\) −4.71501 −0.324595 −0.162297 0.986742i \(-0.551890\pi\)
−0.162297 + 0.986742i \(0.551890\pi\)
\(212\) 40.6938 2.79486
\(213\) 2.36480 0.162033
\(214\) 44.0889 3.01385
\(215\) 10.5103 0.716795
\(216\) 31.7885 2.16293
\(217\) 5.64160 0.382977
\(218\) −7.63543 −0.517136
\(219\) 11.1512 0.753525
\(220\) 4.14165 0.279230
\(221\) 6.07738 0.408809
\(222\) −3.89532 −0.261437
\(223\) 10.8126 0.724066 0.362033 0.932165i \(-0.382083\pi\)
0.362033 + 0.932165i \(0.382083\pi\)
\(224\) −4.54587 −0.303733
\(225\) 0.0778422 0.00518948
\(226\) −14.2016 −0.944677
\(227\) 14.3050 0.949457 0.474729 0.880132i \(-0.342546\pi\)
0.474729 + 0.880132i \(0.342546\pi\)
\(228\) −29.0483 −1.92377
\(229\) 21.2236 1.40249 0.701246 0.712920i \(-0.252628\pi\)
0.701246 + 0.712920i \(0.252628\pi\)
\(230\) 1.16539 0.0768438
\(231\) −1.24414 −0.0818583
\(232\) −19.0729 −1.25220
\(233\) 22.4807 1.47276 0.736380 0.676568i \(-0.236534\pi\)
0.736380 + 0.676568i \(0.236534\pi\)
\(234\) 0.0502396 0.00328427
\(235\) 4.02110 0.262307
\(236\) 9.20070 0.598915
\(237\) 14.7823 0.960212
\(238\) −18.2721 −1.18441
\(239\) 25.7090 1.66298 0.831489 0.555541i \(-0.187489\pi\)
0.831489 + 0.555541i \(0.187489\pi\)
\(240\) −14.8616 −0.959310
\(241\) −29.5350 −1.90252 −0.951259 0.308392i \(-0.900209\pi\)
−0.951259 + 0.308392i \(0.900209\pi\)
\(242\) 26.5279 1.70528
\(243\) 0.244982 0.0157156
\(244\) −23.7827 −1.52253
\(245\) −1.30306 −0.0832493
\(246\) −24.0135 −1.53104
\(247\) −3.21629 −0.204648
\(248\) −34.3799 −2.18312
\(249\) 4.99170 0.316336
\(250\) −27.3837 −1.73190
\(251\) −16.3953 −1.03486 −0.517431 0.855725i \(-0.673112\pi\)
−0.517431 + 0.855725i \(0.673112\pi\)
\(252\) −0.103901 −0.00654517
\(253\) −0.254793 −0.0160187
\(254\) −7.66358 −0.480856
\(255\) −16.2277 −1.01622
\(256\) −30.5711 −1.91069
\(257\) 29.9290 1.86692 0.933459 0.358683i \(-0.116774\pi\)
0.933459 + 0.358683i \(0.116774\pi\)
\(258\) 35.2242 2.19296
\(259\) 0.891975 0.0554246
\(260\) −4.83529 −0.299872
\(261\) −0.0737815 −0.00456696
\(262\) −26.1622 −1.61631
\(263\) 24.2003 1.49226 0.746128 0.665802i \(-0.231911\pi\)
0.746128 + 0.665802i \(0.231911\pi\)
\(264\) 7.58177 0.466626
\(265\) −12.0310 −0.739061
\(266\) 9.67003 0.592908
\(267\) −9.11827 −0.558029
\(268\) 21.2233 1.29642
\(269\) −17.0955 −1.04233 −0.521165 0.853456i \(-0.674502\pi\)
−0.521165 + 0.853456i \(0.674502\pi\)
\(270\) −17.2058 −1.04711
\(271\) 29.5525 1.79519 0.897593 0.440824i \(-0.145314\pi\)
0.897593 + 0.440824i \(0.145314\pi\)
\(272\) 47.7199 2.89344
\(273\) 1.45251 0.0879096
\(274\) −27.0568 −1.63456
\(275\) 2.38124 0.143594
\(276\) 2.68659 0.161714
\(277\) −4.45754 −0.267828 −0.133914 0.990993i \(-0.542755\pi\)
−0.133914 + 0.990993i \(0.542755\pi\)
\(278\) −55.8384 −3.34896
\(279\) −0.132995 −0.00796220
\(280\) 7.94083 0.474555
\(281\) 16.2924 0.971921 0.485961 0.873981i \(-0.338470\pi\)
0.485961 + 0.873981i \(0.338470\pi\)
\(282\) 13.4763 0.802503
\(283\) −7.23941 −0.430338 −0.215169 0.976577i \(-0.569030\pi\)
−0.215169 + 0.976577i \(0.569030\pi\)
\(284\) 6.04136 0.358489
\(285\) 8.58809 0.508714
\(286\) 1.53686 0.0908765
\(287\) 5.49875 0.324581
\(288\) 0.107164 0.00631471
\(289\) 35.1066 2.06509
\(290\) 10.3234 0.606209
\(291\) −24.0457 −1.40958
\(292\) 28.4879 1.66713
\(293\) −17.3033 −1.01087 −0.505435 0.862865i \(-0.668668\pi\)
−0.505435 + 0.862865i \(0.668668\pi\)
\(294\) −4.36707 −0.254693
\(295\) −2.72017 −0.158375
\(296\) −5.43569 −0.315943
\(297\) 3.76175 0.218279
\(298\) 12.5201 0.725272
\(299\) 0.297465 0.0172029
\(300\) −25.1083 −1.44963
\(301\) −8.06585 −0.464908
\(302\) −14.1023 −0.811495
\(303\) 17.8882 1.02765
\(304\) −25.2545 −1.44844
\(305\) 7.03132 0.402612
\(306\) 0.430747 0.0246242
\(307\) −7.64360 −0.436243 −0.218122 0.975922i \(-0.569993\pi\)
−0.218122 + 0.975922i \(0.569993\pi\)
\(308\) −3.17841 −0.181107
\(309\) −27.0481 −1.53871
\(310\) 18.6084 1.05689
\(311\) 21.0490 1.19358 0.596789 0.802398i \(-0.296443\pi\)
0.596789 + 0.802398i \(0.296443\pi\)
\(312\) −8.85156 −0.501121
\(313\) −25.1947 −1.42409 −0.712043 0.702135i \(-0.752230\pi\)
−0.712043 + 0.702135i \(0.752230\pi\)
\(314\) −3.69924 −0.208760
\(315\) 0.0307183 0.00173078
\(316\) 37.7643 2.12441
\(317\) 23.8691 1.34062 0.670312 0.742080i \(-0.266160\pi\)
0.670312 + 0.742080i \(0.266160\pi\)
\(318\) −40.3209 −2.26108
\(319\) −2.25702 −0.126369
\(320\) 2.23427 0.124900
\(321\) −30.0493 −1.67719
\(322\) −0.894353 −0.0498404
\(323\) −27.5760 −1.53437
\(324\) −39.3530 −2.18628
\(325\) −2.78005 −0.154209
\(326\) −37.5587 −2.08018
\(327\) 5.20401 0.287782
\(328\) −33.5094 −1.85024
\(329\) −3.08589 −0.170131
\(330\) −4.10370 −0.225901
\(331\) 26.3966 1.45089 0.725444 0.688282i \(-0.241635\pi\)
0.725444 + 0.688282i \(0.241635\pi\)
\(332\) 12.7523 0.699875
\(333\) −0.0210274 −0.00115229
\(334\) −51.1670 −2.79973
\(335\) −6.27463 −0.342820
\(336\) 11.4051 0.622201
\(337\) −17.0247 −0.927396 −0.463698 0.885993i \(-0.653478\pi\)
−0.463698 + 0.885993i \(0.653478\pi\)
\(338\) 31.1126 1.69230
\(339\) 9.67926 0.525705
\(340\) −41.4571 −2.24833
\(341\) −4.06840 −0.220316
\(342\) −0.227961 −0.0123267
\(343\) 1.00000 0.0539949
\(344\) 49.1533 2.65017
\(345\) −0.794287 −0.0427630
\(346\) 49.0926 2.63924
\(347\) −4.94361 −0.265387 −0.132693 0.991157i \(-0.542363\pi\)
−0.132693 + 0.991157i \(0.542363\pi\)
\(348\) 23.7986 1.27574
\(349\) 17.3781 0.930229 0.465114 0.885251i \(-0.346013\pi\)
0.465114 + 0.885251i \(0.346013\pi\)
\(350\) 8.35844 0.446777
\(351\) −4.39176 −0.234415
\(352\) 3.27822 0.174730
\(353\) −1.25769 −0.0669400 −0.0334700 0.999440i \(-0.510656\pi\)
−0.0334700 + 0.999440i \(0.510656\pi\)
\(354\) −9.11640 −0.484531
\(355\) −1.78612 −0.0947972
\(356\) −23.2945 −1.23461
\(357\) 12.4536 0.659113
\(358\) −41.3877 −2.18741
\(359\) −31.2615 −1.64992 −0.824958 0.565193i \(-0.808802\pi\)
−0.824958 + 0.565193i \(0.808802\pi\)
\(360\) −0.187197 −0.00986615
\(361\) −4.40615 −0.231903
\(362\) −32.0549 −1.68477
\(363\) −18.0804 −0.948972
\(364\) 3.71072 0.194495
\(365\) −8.42241 −0.440849
\(366\) 23.5648 1.23175
\(367\) −24.2682 −1.26679 −0.633395 0.773828i \(-0.718339\pi\)
−0.633395 + 0.773828i \(0.718339\pi\)
\(368\) 2.33571 0.121757
\(369\) −0.129627 −0.00674814
\(370\) 2.94211 0.152953
\(371\) 9.23293 0.479350
\(372\) 42.8981 2.22416
\(373\) 23.2261 1.20260 0.601302 0.799022i \(-0.294649\pi\)
0.601302 + 0.799022i \(0.294649\pi\)
\(374\) 13.1768 0.681357
\(375\) 18.6636 0.963786
\(376\) 18.8054 0.969815
\(377\) 2.63503 0.135711
\(378\) 13.2042 0.679149
\(379\) 33.1981 1.70527 0.852635 0.522507i \(-0.175003\pi\)
0.852635 + 0.522507i \(0.175003\pi\)
\(380\) 21.9400 1.12550
\(381\) 5.22320 0.267592
\(382\) 25.7045 1.31516
\(383\) −1.70574 −0.0871592 −0.0435796 0.999050i \(-0.513876\pi\)
−0.0435796 + 0.999050i \(0.513876\pi\)
\(384\) 23.1733 1.18256
\(385\) 0.939691 0.0478911
\(386\) −21.1492 −1.07646
\(387\) 0.190144 0.00966558
\(388\) −61.4296 −3.11861
\(389\) −1.99761 −0.101283 −0.0506414 0.998717i \(-0.516127\pi\)
−0.0506414 + 0.998717i \(0.516127\pi\)
\(390\) 4.79098 0.242601
\(391\) 2.55042 0.128981
\(392\) −6.09399 −0.307793
\(393\) 17.8311 0.899461
\(394\) 29.2334 1.47276
\(395\) −11.1650 −0.561770
\(396\) 0.0749277 0.00376526
\(397\) −20.7005 −1.03893 −0.519465 0.854492i \(-0.673869\pi\)
−0.519465 + 0.854492i \(0.673869\pi\)
\(398\) 30.7895 1.54334
\(399\) −6.59071 −0.329948
\(400\) −21.8291 −1.09145
\(401\) 8.40382 0.419667 0.209833 0.977737i \(-0.432708\pi\)
0.209833 + 0.977737i \(0.432708\pi\)
\(402\) −21.0288 −1.04882
\(403\) 4.74977 0.236603
\(404\) 45.6990 2.27361
\(405\) 11.6346 0.578130
\(406\) −7.92242 −0.393183
\(407\) −0.643241 −0.0318843
\(408\) −75.8920 −3.75721
\(409\) −37.1213 −1.83553 −0.917765 0.397125i \(-0.870008\pi\)
−0.917765 + 0.397125i \(0.870008\pi\)
\(410\) 18.1372 0.895734
\(411\) 18.4408 0.909619
\(412\) −69.0999 −3.40431
\(413\) 2.08753 0.102721
\(414\) 0.0210835 0.00103620
\(415\) −3.77020 −0.185072
\(416\) −3.82725 −0.187646
\(417\) 38.0572 1.86367
\(418\) −6.97347 −0.341084
\(419\) 17.3588 0.848032 0.424016 0.905655i \(-0.360620\pi\)
0.424016 + 0.905655i \(0.360620\pi\)
\(420\) −9.90832 −0.483476
\(421\) 6.83181 0.332962 0.166481 0.986045i \(-0.446760\pi\)
0.166481 + 0.986045i \(0.446760\pi\)
\(422\) 11.9351 0.580991
\(423\) 0.0727468 0.00353707
\(424\) −56.2654 −2.73249
\(425\) −23.8357 −1.15620
\(426\) −5.98600 −0.290023
\(427\) −5.39601 −0.261131
\(428\) −76.7670 −3.71067
\(429\) −1.04746 −0.0505720
\(430\) −26.6046 −1.28299
\(431\) −23.6055 −1.13704 −0.568518 0.822671i \(-0.692483\pi\)
−0.568518 + 0.822671i \(0.692483\pi\)
\(432\) −34.4843 −1.65913
\(433\) 18.9735 0.911808 0.455904 0.890029i \(-0.349316\pi\)
0.455904 + 0.890029i \(0.349316\pi\)
\(434\) −14.2806 −0.685488
\(435\) −7.03600 −0.337351
\(436\) 13.2947 0.636701
\(437\) −1.34974 −0.0645670
\(438\) −28.2269 −1.34873
\(439\) −10.5105 −0.501638 −0.250819 0.968034i \(-0.580700\pi\)
−0.250819 + 0.968034i \(0.580700\pi\)
\(440\) −5.72647 −0.272999
\(441\) −0.0235740 −0.00112257
\(442\) −15.3837 −0.731726
\(443\) 4.48793 0.213228 0.106614 0.994300i \(-0.465999\pi\)
0.106614 + 0.994300i \(0.465999\pi\)
\(444\) 6.78248 0.321882
\(445\) 6.88698 0.326474
\(446\) −27.3699 −1.29600
\(447\) −8.53324 −0.403608
\(448\) −1.71464 −0.0810090
\(449\) −31.2102 −1.47290 −0.736449 0.676493i \(-0.763499\pi\)
−0.736449 + 0.676493i \(0.763499\pi\)
\(450\) −0.197042 −0.00928863
\(451\) −3.96538 −0.186723
\(452\) 24.7276 1.16309
\(453\) 9.61156 0.451590
\(454\) −36.2102 −1.69943
\(455\) −1.09707 −0.0514314
\(456\) 40.1638 1.88084
\(457\) −6.27089 −0.293340 −0.146670 0.989185i \(-0.546856\pi\)
−0.146670 + 0.989185i \(0.546856\pi\)
\(458\) −53.7231 −2.51032
\(459\) −37.6543 −1.75755
\(460\) −2.02917 −0.0946105
\(461\) 11.6575 0.542944 0.271472 0.962446i \(-0.412490\pi\)
0.271472 + 0.962446i \(0.412490\pi\)
\(462\) 3.14928 0.146518
\(463\) 12.6268 0.586818 0.293409 0.955987i \(-0.405210\pi\)
0.293409 + 0.955987i \(0.405210\pi\)
\(464\) 20.6903 0.960525
\(465\) −12.6828 −0.588148
\(466\) −56.9053 −2.63609
\(467\) −40.3467 −1.86702 −0.933510 0.358550i \(-0.883271\pi\)
−0.933510 + 0.358550i \(0.883271\pi\)
\(468\) −0.0874766 −0.00404361
\(469\) 4.81531 0.222350
\(470\) −10.1786 −0.469503
\(471\) 2.52126 0.116173
\(472\) −12.7214 −0.585550
\(473\) 5.81663 0.267449
\(474\) −37.4183 −1.71868
\(475\) 12.6144 0.578789
\(476\) 31.8152 1.45825
\(477\) −0.217657 −0.00996582
\(478\) −65.0771 −2.97656
\(479\) 38.8981 1.77730 0.888650 0.458586i \(-0.151644\pi\)
0.888650 + 0.458586i \(0.151644\pi\)
\(480\) 10.2195 0.466452
\(481\) 0.750971 0.0342413
\(482\) 74.7619 3.40531
\(483\) 0.609556 0.0277358
\(484\) −46.1900 −2.09954
\(485\) 18.1615 0.824673
\(486\) −0.620123 −0.0281293
\(487\) 8.00409 0.362700 0.181350 0.983419i \(-0.441953\pi\)
0.181350 + 0.983419i \(0.441953\pi\)
\(488\) 32.8833 1.48856
\(489\) 25.5985 1.15761
\(490\) 3.29843 0.149008
\(491\) 8.27877 0.373616 0.186808 0.982396i \(-0.440186\pi\)
0.186808 + 0.982396i \(0.440186\pi\)
\(492\) 41.8119 1.88503
\(493\) 22.5923 1.01751
\(494\) 8.14138 0.366298
\(495\) −0.0221523 −0.000995670 0
\(496\) 37.2954 1.67461
\(497\) 1.37071 0.0614848
\(498\) −12.6355 −0.566209
\(499\) 27.0555 1.21117 0.605586 0.795780i \(-0.292939\pi\)
0.605586 + 0.795780i \(0.292939\pi\)
\(500\) 47.6801 2.13232
\(501\) 34.8734 1.55803
\(502\) 41.5013 1.85230
\(503\) −0.897705 −0.0400267 −0.0200133 0.999800i \(-0.506371\pi\)
−0.0200133 + 0.999800i \(0.506371\pi\)
\(504\) 0.143660 0.00639911
\(505\) −13.5108 −0.601224
\(506\) 0.644956 0.0286718
\(507\) −21.2051 −0.941753
\(508\) 13.3437 0.592032
\(509\) 7.86666 0.348684 0.174342 0.984685i \(-0.444220\pi\)
0.174342 + 0.984685i \(0.444220\pi\)
\(510\) 41.0772 1.81893
\(511\) 6.46357 0.285931
\(512\) 50.5204 2.23271
\(513\) 19.9275 0.879821
\(514\) −75.7591 −3.34159
\(515\) 20.4293 0.900221
\(516\) −61.3319 −2.69998
\(517\) 2.22537 0.0978716
\(518\) −2.25785 −0.0992043
\(519\) −33.4596 −1.46871
\(520\) 6.68554 0.293180
\(521\) −17.6662 −0.773969 −0.386985 0.922086i \(-0.626483\pi\)
−0.386985 + 0.922086i \(0.626483\pi\)
\(522\) 0.186763 0.00817439
\(523\) −39.5190 −1.72805 −0.864023 0.503452i \(-0.832063\pi\)
−0.864023 + 0.503452i \(0.832063\pi\)
\(524\) 45.5533 1.99000
\(525\) −5.69678 −0.248628
\(526\) −61.2582 −2.67099
\(527\) 40.7238 1.77396
\(528\) −8.22473 −0.357936
\(529\) −22.8752 −0.994572
\(530\) 30.4541 1.32284
\(531\) −0.0492114 −0.00213559
\(532\) −16.8373 −0.729991
\(533\) 4.62950 0.200526
\(534\) 23.0811 0.998815
\(535\) 22.6960 0.981235
\(536\) −29.3445 −1.26749
\(537\) 28.2082 1.21727
\(538\) 43.2738 1.86566
\(539\) −0.721143 −0.0310618
\(540\) 29.9585 1.28921
\(541\) 24.4309 1.05037 0.525184 0.850989i \(-0.323996\pi\)
0.525184 + 0.850989i \(0.323996\pi\)
\(542\) −74.8061 −3.21320
\(543\) 21.8474 0.937561
\(544\) −32.8143 −1.40690
\(545\) −3.93056 −0.168367
\(546\) −3.67672 −0.157349
\(547\) 37.7618 1.61458 0.807289 0.590156i \(-0.200934\pi\)
0.807289 + 0.590156i \(0.200934\pi\)
\(548\) 47.1109 2.01248
\(549\) 0.127205 0.00542900
\(550\) −6.02763 −0.257019
\(551\) −11.9564 −0.509359
\(552\) −3.71463 −0.158105
\(553\) 8.56828 0.364360
\(554\) 11.2834 0.479384
\(555\) −2.00523 −0.0851172
\(556\) 97.2251 4.12326
\(557\) 11.4267 0.484164 0.242082 0.970256i \(-0.422170\pi\)
0.242082 + 0.970256i \(0.422170\pi\)
\(558\) 0.336649 0.0142515
\(559\) −6.79079 −0.287220
\(560\) −8.61424 −0.364018
\(561\) −8.98080 −0.379170
\(562\) −41.2408 −1.73964
\(563\) 2.97078 0.125203 0.0626017 0.998039i \(-0.480060\pi\)
0.0626017 + 0.998039i \(0.480060\pi\)
\(564\) −23.4648 −0.988046
\(565\) −7.31069 −0.307563
\(566\) 18.3251 0.770261
\(567\) −8.92872 −0.374971
\(568\) −8.35311 −0.350489
\(569\) −34.4412 −1.44385 −0.721924 0.691972i \(-0.756742\pi\)
−0.721924 + 0.691972i \(0.756742\pi\)
\(570\) −21.7390 −0.910546
\(571\) 13.1595 0.550707 0.275353 0.961343i \(-0.411205\pi\)
0.275353 + 0.961343i \(0.411205\pi\)
\(572\) −2.67596 −0.111888
\(573\) −17.5192 −0.731874
\(574\) −13.9190 −0.580966
\(575\) −1.16667 −0.0486535
\(576\) 0.0404208 0.00168420
\(577\) −17.7916 −0.740673 −0.370336 0.928898i \(-0.620758\pi\)
−0.370336 + 0.928898i \(0.620758\pi\)
\(578\) −88.8652 −3.69631
\(579\) 14.4144 0.599044
\(580\) −17.9749 −0.746368
\(581\) 2.89335 0.120036
\(582\) 60.8667 2.52300
\(583\) −6.65826 −0.275757
\(584\) −39.3889 −1.62993
\(585\) 0.0258623 0.00106927
\(586\) 43.7998 1.80935
\(587\) 31.6925 1.30809 0.654044 0.756456i \(-0.273071\pi\)
0.654044 + 0.756456i \(0.273071\pi\)
\(588\) 7.60389 0.313579
\(589\) −21.5520 −0.888033
\(590\) 6.88556 0.283474
\(591\) −19.9243 −0.819577
\(592\) 5.89665 0.242351
\(593\) 29.0118 1.19137 0.595686 0.803217i \(-0.296880\pi\)
0.595686 + 0.803217i \(0.296880\pi\)
\(594\) −9.52209 −0.390696
\(595\) −9.40611 −0.385613
\(596\) −21.7999 −0.892959
\(597\) −20.9849 −0.858855
\(598\) −0.752973 −0.0307914
\(599\) −38.7779 −1.58442 −0.792211 0.610247i \(-0.791070\pi\)
−0.792211 + 0.610247i \(0.791070\pi\)
\(600\) 34.7162 1.41728
\(601\) 10.7421 0.438181 0.219090 0.975705i \(-0.429691\pi\)
0.219090 + 0.975705i \(0.429691\pi\)
\(602\) 20.4171 0.832137
\(603\) −0.113516 −0.00462273
\(604\) 24.5547 0.999116
\(605\) 13.6560 0.555195
\(606\) −45.2803 −1.83938
\(607\) 40.7250 1.65298 0.826489 0.562952i \(-0.190335\pi\)
0.826489 + 0.562952i \(0.190335\pi\)
\(608\) 17.3661 0.704287
\(609\) 5.39961 0.218803
\(610\) −17.7983 −0.720634
\(611\) −2.59807 −0.105107
\(612\) −0.750011 −0.0303174
\(613\) −30.1012 −1.21578 −0.607889 0.794022i \(-0.707983\pi\)
−0.607889 + 0.794022i \(0.707983\pi\)
\(614\) 19.3482 0.780831
\(615\) −12.3616 −0.498469
\(616\) 4.39464 0.177065
\(617\) 32.6160 1.31307 0.656534 0.754296i \(-0.272022\pi\)
0.656534 + 0.754296i \(0.272022\pi\)
\(618\) 68.4667 2.75414
\(619\) 22.3052 0.896521 0.448261 0.893903i \(-0.352044\pi\)
0.448261 + 0.893903i \(0.352044\pi\)
\(620\) −32.4007 −1.30124
\(621\) −1.84304 −0.0739586
\(622\) −53.2812 −2.13638
\(623\) −5.28524 −0.211749
\(624\) 9.60220 0.384396
\(625\) 2.41366 0.0965462
\(626\) 63.7752 2.54897
\(627\) 4.75285 0.189810
\(628\) 6.44107 0.257027
\(629\) 6.43871 0.256728
\(630\) −0.0777571 −0.00309792
\(631\) −15.8887 −0.632517 −0.316259 0.948673i \(-0.602427\pi\)
−0.316259 + 0.948673i \(0.602427\pi\)
\(632\) −52.2150 −2.07700
\(633\) −8.13448 −0.323317
\(634\) −60.4198 −2.39958
\(635\) −3.94505 −0.156555
\(636\) 70.2062 2.78386
\(637\) 0.841919 0.0333580
\(638\) 5.71319 0.226187
\(639\) −0.0323131 −0.00127829
\(640\) −17.5027 −0.691854
\(641\) 10.7468 0.424473 0.212237 0.977218i \(-0.431925\pi\)
0.212237 + 0.977218i \(0.431925\pi\)
\(642\) 76.0636 3.00199
\(643\) 19.4609 0.767465 0.383732 0.923444i \(-0.374638\pi\)
0.383732 + 0.923444i \(0.374638\pi\)
\(644\) 1.55724 0.0613637
\(645\) 18.1327 0.713973
\(646\) 69.8030 2.74636
\(647\) 50.1856 1.97300 0.986500 0.163760i \(-0.0523622\pi\)
0.986500 + 0.163760i \(0.0523622\pi\)
\(648\) 54.4116 2.13749
\(649\) −1.50541 −0.0590924
\(650\) 7.03713 0.276019
\(651\) 9.73306 0.381469
\(652\) 65.3967 2.56113
\(653\) 10.3850 0.406395 0.203197 0.979138i \(-0.434867\pi\)
0.203197 + 0.979138i \(0.434867\pi\)
\(654\) −13.1729 −0.515100
\(655\) −13.4677 −0.526229
\(656\) 36.3511 1.41927
\(657\) −0.152372 −0.00594460
\(658\) 7.81131 0.304516
\(659\) 0.140891 0.00548833 0.00274416 0.999996i \(-0.499127\pi\)
0.00274416 + 0.999996i \(0.499127\pi\)
\(660\) 7.14531 0.278131
\(661\) −3.30832 −0.128679 −0.0643395 0.997928i \(-0.520494\pi\)
−0.0643395 + 0.997928i \(0.520494\pi\)
\(662\) −66.8176 −2.59694
\(663\) 10.4849 0.407200
\(664\) −17.6321 −0.684256
\(665\) 4.97793 0.193036
\(666\) 0.0532266 0.00206249
\(667\) 1.10581 0.0428172
\(668\) 89.0913 3.44705
\(669\) 18.6543 0.721216
\(670\) 15.8829 0.613612
\(671\) 3.89129 0.150222
\(672\) −7.84267 −0.302538
\(673\) 18.0308 0.695037 0.347519 0.937673i \(-0.387024\pi\)
0.347519 + 0.937673i \(0.387024\pi\)
\(674\) 43.0946 1.65994
\(675\) 17.2246 0.662977
\(676\) −54.1729 −2.08357
\(677\) 1.73646 0.0667374 0.0333687 0.999443i \(-0.489376\pi\)
0.0333687 + 0.999443i \(0.489376\pi\)
\(678\) −24.5011 −0.940958
\(679\) −13.9376 −0.534877
\(680\) 57.3208 2.19815
\(681\) 24.6795 0.945720
\(682\) 10.2983 0.394343
\(683\) 20.6257 0.789221 0.394610 0.918849i \(-0.370880\pi\)
0.394610 + 0.918849i \(0.370880\pi\)
\(684\) 0.396923 0.0151767
\(685\) −13.9283 −0.532172
\(686\) −2.53130 −0.0966453
\(687\) 36.6156 1.39697
\(688\) −53.3216 −2.03287
\(689\) 7.77338 0.296142
\(690\) 2.01058 0.0765413
\(691\) 4.11720 0.156626 0.0783128 0.996929i \(-0.475047\pi\)
0.0783128 + 0.996929i \(0.475047\pi\)
\(692\) −85.4794 −3.24944
\(693\) 0.0170002 0.000645784 0
\(694\) 12.5137 0.475015
\(695\) −28.7444 −1.09034
\(696\) −32.9052 −1.24727
\(697\) 39.6927 1.50347
\(698\) −43.9891 −1.66501
\(699\) 38.7844 1.46696
\(700\) −14.5536 −0.550075
\(701\) 24.5896 0.928735 0.464368 0.885642i \(-0.346282\pi\)
0.464368 + 0.885642i \(0.346282\pi\)
\(702\) 11.1168 0.419578
\(703\) −3.40751 −0.128517
\(704\) 1.23650 0.0466023
\(705\) 6.93733 0.261275
\(706\) 3.18358 0.119816
\(707\) 10.3686 0.389950
\(708\) 15.8734 0.596557
\(709\) 22.9289 0.861114 0.430557 0.902563i \(-0.358317\pi\)
0.430557 + 0.902563i \(0.358317\pi\)
\(710\) 4.52119 0.169677
\(711\) −0.201988 −0.00757516
\(712\) 32.2083 1.20706
\(713\) 1.99328 0.0746489
\(714\) −31.5237 −1.17974
\(715\) 0.791144 0.0295871
\(716\) 72.0637 2.69315
\(717\) 44.3540 1.65643
\(718\) 79.1320 2.95318
\(719\) 27.3228 1.01897 0.509485 0.860480i \(-0.329836\pi\)
0.509485 + 0.860480i \(0.329836\pi\)
\(720\) 0.203072 0.00756804
\(721\) −15.6779 −0.583877
\(722\) 11.1533 0.415082
\(723\) −50.9548 −1.89503
\(724\) 55.8136 2.07430
\(725\) −10.3347 −0.383820
\(726\) 45.7667 1.69856
\(727\) 6.59392 0.244555 0.122277 0.992496i \(-0.460980\pi\)
0.122277 + 0.992496i \(0.460980\pi\)
\(728\) −5.13065 −0.190155
\(729\) 27.2088 1.00773
\(730\) 21.3196 0.789074
\(731\) −58.2233 −2.15347
\(732\) −41.0307 −1.51654
\(733\) −10.6378 −0.392914 −0.196457 0.980512i \(-0.562944\pi\)
−0.196457 + 0.980512i \(0.562944\pi\)
\(734\) 61.4300 2.26742
\(735\) −2.24808 −0.0829216
\(736\) −1.60614 −0.0592030
\(737\) −3.47253 −0.127912
\(738\) 0.328126 0.0120785
\(739\) 20.2306 0.744194 0.372097 0.928194i \(-0.378639\pi\)
0.372097 + 0.928194i \(0.378639\pi\)
\(740\) −5.12277 −0.188317
\(741\) −5.54885 −0.203842
\(742\) −23.3713 −0.857986
\(743\) −32.8780 −1.20618 −0.603088 0.797675i \(-0.706063\pi\)
−0.603088 + 0.797675i \(0.706063\pi\)
\(744\) −59.3132 −2.17453
\(745\) 6.44511 0.236131
\(746\) −58.7922 −2.15254
\(747\) −0.0682078 −0.00249559
\(748\) −22.9433 −0.838890
\(749\) −17.4175 −0.636422
\(750\) −47.2432 −1.72508
\(751\) 28.1426 1.02694 0.513469 0.858108i \(-0.328360\pi\)
0.513469 + 0.858108i \(0.328360\pi\)
\(752\) −20.4002 −0.743918
\(753\) −28.2857 −1.03079
\(754\) −6.67003 −0.242908
\(755\) −7.25956 −0.264202
\(756\) −22.9909 −0.836172
\(757\) 11.7670 0.427678 0.213839 0.976869i \(-0.431403\pi\)
0.213839 + 0.976869i \(0.431403\pi\)
\(758\) −84.0341 −3.05226
\(759\) −0.439577 −0.0159556
\(760\) −30.3355 −1.10038
\(761\) −25.4656 −0.923128 −0.461564 0.887107i \(-0.652712\pi\)
−0.461564 + 0.887107i \(0.652712\pi\)
\(762\) −13.2215 −0.478963
\(763\) 3.01641 0.109201
\(764\) −44.7563 −1.61923
\(765\) 0.221740 0.00801701
\(766\) 4.31773 0.156006
\(767\) 1.75753 0.0634608
\(768\) −52.7422 −1.90317
\(769\) −26.6857 −0.962310 −0.481155 0.876635i \(-0.659783\pi\)
−0.481155 + 0.876635i \(0.659783\pi\)
\(770\) −2.37864 −0.0857201
\(771\) 51.6344 1.85957
\(772\) 36.8247 1.32535
\(773\) 51.7495 1.86130 0.930650 0.365912i \(-0.119243\pi\)
0.930650 + 0.365912i \(0.119243\pi\)
\(774\) −0.481311 −0.0173004
\(775\) −18.6288 −0.669165
\(776\) 84.9359 3.04902
\(777\) 1.53886 0.0552064
\(778\) 5.05654 0.181286
\(779\) −21.0063 −0.752628
\(780\) −8.34200 −0.298691
\(781\) −0.988479 −0.0353705
\(782\) −6.45588 −0.230862
\(783\) −16.3261 −0.583448
\(784\) 6.61079 0.236099
\(785\) −1.90429 −0.0679671
\(786\) −45.1359 −1.60994
\(787\) 15.2801 0.544676 0.272338 0.962202i \(-0.412203\pi\)
0.272338 + 0.962202i \(0.412203\pi\)
\(788\) −50.9008 −1.81327
\(789\) 41.7512 1.48638
\(790\) 28.2618 1.00551
\(791\) 5.61041 0.199483
\(792\) −0.103599 −0.00368124
\(793\) −4.54300 −0.161327
\(794\) 52.3992 1.85958
\(795\) −20.7563 −0.736152
\(796\) −53.6103 −1.90017
\(797\) 12.2004 0.432159 0.216080 0.976376i \(-0.430673\pi\)
0.216080 + 0.976376i \(0.430673\pi\)
\(798\) 16.6830 0.590574
\(799\) −22.2755 −0.788050
\(800\) 15.0106 0.530706
\(801\) 0.124594 0.00440232
\(802\) −21.2726 −0.751160
\(803\) −4.66115 −0.164489
\(804\) 36.6151 1.29131
\(805\) −0.460394 −0.0162268
\(806\) −12.0231 −0.423495
\(807\) −29.4937 −1.03823
\(808\) −63.1859 −2.22287
\(809\) 10.9534 0.385101 0.192550 0.981287i \(-0.438324\pi\)
0.192550 + 0.981287i \(0.438324\pi\)
\(810\) −29.4507 −1.03479
\(811\) 36.0109 1.26451 0.632257 0.774759i \(-0.282129\pi\)
0.632257 + 0.774759i \(0.282129\pi\)
\(812\) 13.7944 0.484089
\(813\) 50.9849 1.78812
\(814\) 1.62823 0.0570696
\(815\) −19.3344 −0.677256
\(816\) 82.3279 2.88205
\(817\) 30.8131 1.07801
\(818\) 93.9649 3.28541
\(819\) −0.0198474 −0.000693524 0
\(820\) −31.5803 −1.10283
\(821\) 12.3969 0.432656 0.216328 0.976321i \(-0.430592\pi\)
0.216328 + 0.976321i \(0.430592\pi\)
\(822\) −46.6792 −1.62812
\(823\) −17.9161 −0.624515 −0.312258 0.949997i \(-0.601085\pi\)
−0.312258 + 0.949997i \(0.601085\pi\)
\(824\) 95.5413 3.32834
\(825\) 4.10819 0.143029
\(826\) −5.28416 −0.183859
\(827\) −31.9229 −1.11007 −0.555034 0.831828i \(-0.687295\pi\)
−0.555034 + 0.831828i \(0.687295\pi\)
\(828\) −0.0367103 −0.00127577
\(829\) −18.1689 −0.631031 −0.315515 0.948920i \(-0.602177\pi\)
−0.315515 + 0.948920i \(0.602177\pi\)
\(830\) 9.54350 0.331260
\(831\) −7.69029 −0.266773
\(832\) −1.44359 −0.0500474
\(833\) 7.21849 0.250106
\(834\) −96.3342 −3.33578
\(835\) −26.3397 −0.911523
\(836\) 12.1421 0.419944
\(837\) −29.4286 −1.01720
\(838\) −43.9402 −1.51789
\(839\) −39.2360 −1.35458 −0.677289 0.735717i \(-0.736845\pi\)
−0.677289 + 0.735717i \(0.736845\pi\)
\(840\) 13.6998 0.472687
\(841\) −19.2044 −0.662222
\(842\) −17.2933 −0.595968
\(843\) 28.1081 0.968095
\(844\) −20.7812 −0.715319
\(845\) 16.0161 0.550971
\(846\) −0.184144 −0.00633099
\(847\) −10.4800 −0.360095
\(848\) 61.0369 2.09602
\(849\) −12.4897 −0.428644
\(850\) 60.3353 2.06948
\(851\) 0.315151 0.0108032
\(852\) 10.4227 0.357077
\(853\) 3.92968 0.134550 0.0672748 0.997734i \(-0.478570\pi\)
0.0672748 + 0.997734i \(0.478570\pi\)
\(854\) 13.6589 0.467398
\(855\) −0.117350 −0.00401327
\(856\) 106.142 3.62787
\(857\) −4.29732 −0.146794 −0.0733968 0.997303i \(-0.523384\pi\)
−0.0733968 + 0.997303i \(0.523384\pi\)
\(858\) 2.65144 0.0905187
\(859\) −1.00000 −0.0341196
\(860\) 46.3236 1.57962
\(861\) 9.48662 0.323303
\(862\) 59.7525 2.03518
\(863\) 35.6307 1.21288 0.606441 0.795129i \(-0.292597\pi\)
0.606441 + 0.795129i \(0.292597\pi\)
\(864\) 23.7129 0.806729
\(865\) 25.2719 0.859269
\(866\) −48.0275 −1.63204
\(867\) 60.5670 2.05696
\(868\) 24.8651 0.843977
\(869\) −6.17895 −0.209607
\(870\) 17.8102 0.603823
\(871\) 4.05410 0.137368
\(872\) −18.3820 −0.622492
\(873\) 0.328566 0.0111203
\(874\) 3.41660 0.115568
\(875\) 10.8180 0.365717
\(876\) 49.1483 1.66057
\(877\) −10.0328 −0.338785 −0.169392 0.985549i \(-0.554181\pi\)
−0.169392 + 0.985549i \(0.554181\pi\)
\(878\) 26.6052 0.897881
\(879\) −29.8522 −1.00689
\(880\) 6.21210 0.209410
\(881\) 13.5260 0.455703 0.227851 0.973696i \(-0.426830\pi\)
0.227851 + 0.973696i \(0.426830\pi\)
\(882\) 0.0596727 0.00200929
\(883\) 35.9934 1.21127 0.605637 0.795741i \(-0.292919\pi\)
0.605637 + 0.795741i \(0.292919\pi\)
\(884\) 26.7858 0.900905
\(885\) −4.69293 −0.157751
\(886\) −11.3603 −0.381656
\(887\) −54.7566 −1.83855 −0.919273 0.393620i \(-0.871222\pi\)
−0.919273 + 0.393620i \(0.871222\pi\)
\(888\) −9.37783 −0.314699
\(889\) 3.02753 0.101540
\(890\) −17.4330 −0.584355
\(891\) 6.43888 0.215711
\(892\) 47.6562 1.59565
\(893\) 11.7887 0.394494
\(894\) 21.6002 0.722417
\(895\) −21.3055 −0.712165
\(896\) 13.4320 0.448731
\(897\) 0.513197 0.0171351
\(898\) 79.0021 2.63634
\(899\) 17.6570 0.588894
\(900\) 0.343086 0.0114362
\(901\) 66.6478 2.22036
\(902\) 10.0376 0.334214
\(903\) −13.9155 −0.463078
\(904\) −34.1898 −1.13714
\(905\) −16.5012 −0.548519
\(906\) −24.3297 −0.808300
\(907\) 4.93892 0.163994 0.0819971 0.996633i \(-0.473870\pi\)
0.0819971 + 0.996633i \(0.473870\pi\)
\(908\) 63.0488 2.09235
\(909\) −0.244428 −0.00810717
\(910\) 2.77701 0.0920569
\(911\) −39.7087 −1.31561 −0.657803 0.753190i \(-0.728514\pi\)
−0.657803 + 0.753190i \(0.728514\pi\)
\(912\) −43.5698 −1.44274
\(913\) −2.08652 −0.0690537
\(914\) 15.8735 0.525048
\(915\) 12.1307 0.401027
\(916\) 93.5420 3.09071
\(917\) 10.3355 0.341308
\(918\) 95.3142 3.14584
\(919\) −34.2537 −1.12992 −0.564962 0.825117i \(-0.691109\pi\)
−0.564962 + 0.825117i \(0.691109\pi\)
\(920\) 2.80564 0.0924992
\(921\) −13.1870 −0.434526
\(922\) −29.5086 −0.971813
\(923\) 1.15403 0.0379853
\(924\) −5.48349 −0.180394
\(925\) −2.94534 −0.0968420
\(926\) −31.9622 −1.05034
\(927\) 0.369592 0.0121390
\(928\) −14.2276 −0.467044
\(929\) 35.0451 1.14979 0.574896 0.818226i \(-0.305042\pi\)
0.574896 + 0.818226i \(0.305042\pi\)
\(930\) 32.1038 1.05272
\(931\) −3.82019 −0.125202
\(932\) 99.0828 3.24557
\(933\) 36.3144 1.18888
\(934\) 102.129 3.34177
\(935\) 6.78315 0.221833
\(936\) 0.120950 0.00395337
\(937\) 61.0833 1.99550 0.997752 0.0670201i \(-0.0213492\pi\)
0.997752 + 0.0670201i \(0.0213492\pi\)
\(938\) −12.1890 −0.397984
\(939\) −43.4666 −1.41848
\(940\) 17.7228 0.578055
\(941\) 0.806963 0.0263063 0.0131531 0.999913i \(-0.495813\pi\)
0.0131531 + 0.999913i \(0.495813\pi\)
\(942\) −6.38205 −0.207938
\(943\) 1.94281 0.0632666
\(944\) 13.8002 0.449159
\(945\) 6.79723 0.221114
\(946\) −14.7236 −0.478706
\(947\) −4.22403 −0.137263 −0.0686313 0.997642i \(-0.521863\pi\)
−0.0686313 + 0.997642i \(0.521863\pi\)
\(948\) 65.1523 2.11605
\(949\) 5.44180 0.176648
\(950\) −31.9308 −1.03597
\(951\) 41.1798 1.33535
\(952\) −43.9894 −1.42571
\(953\) 21.7187 0.703538 0.351769 0.936087i \(-0.385580\pi\)
0.351769 + 0.936087i \(0.385580\pi\)
\(954\) 0.550954 0.0178378
\(955\) 13.2321 0.428182
\(956\) 113.311 3.66475
\(957\) −3.89389 −0.125872
\(958\) −98.4627 −3.18118
\(959\) 10.6889 0.345163
\(960\) 3.85464 0.124408
\(961\) 0.827611 0.0266971
\(962\) −1.90093 −0.0612884
\(963\) 0.410600 0.0132314
\(964\) −130.174 −4.19264
\(965\) −10.8871 −0.350470
\(966\) −1.54297 −0.0496441
\(967\) 14.4520 0.464746 0.232373 0.972627i \(-0.425351\pi\)
0.232373 + 0.972627i \(0.425351\pi\)
\(968\) 63.8648 2.05269
\(969\) −47.5750 −1.52833
\(970\) −45.9723 −1.47608
\(971\) 17.4354 0.559528 0.279764 0.960069i \(-0.409744\pi\)
0.279764 + 0.960069i \(0.409744\pi\)
\(972\) 1.07975 0.0346330
\(973\) 22.0592 0.707186
\(974\) −20.2607 −0.649196
\(975\) −4.79623 −0.153602
\(976\) −35.6719 −1.14183
\(977\) −0.920220 −0.0294404 −0.0147202 0.999892i \(-0.504686\pi\)
−0.0147202 + 0.999892i \(0.504686\pi\)
\(978\) −64.7975 −2.07200
\(979\) 3.81142 0.121813
\(980\) −5.74318 −0.183459
\(981\) −0.0711088 −0.00227033
\(982\) −20.9560 −0.668733
\(983\) −41.2655 −1.31616 −0.658082 0.752946i \(-0.728632\pi\)
−0.658082 + 0.752946i \(0.728632\pi\)
\(984\) −57.8114 −1.84296
\(985\) 15.0487 0.479493
\(986\) −57.1879 −1.82123
\(987\) −5.32388 −0.169461
\(988\) −14.1757 −0.450988
\(989\) −2.84981 −0.0906188
\(990\) 0.0560739 0.00178215
\(991\) 4.49250 0.142709 0.0713544 0.997451i \(-0.477268\pi\)
0.0713544 + 0.997451i \(0.477268\pi\)
\(992\) −25.6459 −0.814259
\(993\) 45.5402 1.44518
\(994\) −3.46968 −0.110051
\(995\) 15.8498 0.502472
\(996\) 22.0007 0.697119
\(997\) 29.1720 0.923886 0.461943 0.886910i \(-0.347153\pi\)
0.461943 + 0.886910i \(0.347153\pi\)
\(998\) −68.4855 −2.16787
\(999\) −4.65287 −0.147210
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 \(a_p\))