Properties

Label 4033.2.a.d.1.18
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.80025 q^{2}\) \(+1.41167 q^{3}\) \(+1.24090 q^{4}\) \(+0.213559 q^{5}\) \(-2.54136 q^{6}\) \(-2.54704 q^{7}\) \(+1.36657 q^{8}\) \(-1.00719 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.80025 q^{2}\) \(+1.41167 q^{3}\) \(+1.24090 q^{4}\) \(+0.213559 q^{5}\) \(-2.54136 q^{6}\) \(-2.54704 q^{7}\) \(+1.36657 q^{8}\) \(-1.00719 q^{9}\) \(-0.384459 q^{10}\) \(+1.24725 q^{11}\) \(+1.75174 q^{12}\) \(+1.90462 q^{13}\) \(+4.58531 q^{14}\) \(+0.301474 q^{15}\) \(-4.94197 q^{16}\) \(-3.92660 q^{17}\) \(+1.81319 q^{18}\) \(+5.27048 q^{19}\) \(+0.265005 q^{20}\) \(-3.59558 q^{21}\) \(-2.24537 q^{22}\) \(+2.59275 q^{23}\) \(+1.92914 q^{24}\) \(-4.95439 q^{25}\) \(-3.42880 q^{26}\) \(-5.65683 q^{27}\) \(-3.16063 q^{28}\) \(+4.85757 q^{29}\) \(-0.542729 q^{30}\) \(+1.57742 q^{31}\) \(+6.16365 q^{32}\) \(+1.76071 q^{33}\) \(+7.06886 q^{34}\) \(-0.543942 q^{35}\) \(-1.24983 q^{36}\) \(-1.00000 q^{37}\) \(-9.48819 q^{38}\) \(+2.68870 q^{39}\) \(+0.291842 q^{40}\) \(-7.59622 q^{41}\) \(+6.47294 q^{42}\) \(-3.23107 q^{43}\) \(+1.54772 q^{44}\) \(-0.215094 q^{45}\) \(-4.66760 q^{46}\) \(-1.14828 q^{47}\) \(-6.97642 q^{48}\) \(-0.512597 q^{49}\) \(+8.91915 q^{50}\) \(-5.54305 q^{51}\) \(+2.36345 q^{52}\) \(+11.3924 q^{53}\) \(+10.1837 q^{54}\) \(+0.266362 q^{55}\) \(-3.48069 q^{56}\) \(+7.44018 q^{57}\) \(-8.74484 q^{58}\) \(+4.17419 q^{59}\) \(+0.374100 q^{60}\) \(+4.10910 q^{61}\) \(-2.83975 q^{62}\) \(+2.56535 q^{63}\) \(-1.21218 q^{64}\) \(+0.406749 q^{65}\) \(-3.16972 q^{66}\) \(-5.17598 q^{67}\) \(-4.87252 q^{68}\) \(+3.66010 q^{69}\) \(+0.979232 q^{70}\) \(-16.1412 q^{71}\) \(-1.37639 q^{72}\) \(-4.41986 q^{73}\) \(+1.80025 q^{74}\) \(-6.99396 q^{75}\) \(+6.54016 q^{76}\) \(-3.17680 q^{77}\) \(-4.84033 q^{78}\) \(-2.92425 q^{79}\) \(-1.05540 q^{80}\) \(-4.96400 q^{81}\) \(+13.6751 q^{82}\) \(+7.83025 q^{83}\) \(-4.46176 q^{84}\) \(-0.838558 q^{85}\) \(+5.81673 q^{86}\) \(+6.85727 q^{87}\) \(+1.70445 q^{88}\) \(+4.91950 q^{89}\) \(+0.387223 q^{90}\) \(-4.85115 q^{91}\) \(+3.21735 q^{92}\) \(+2.22679 q^{93}\) \(+2.06719 q^{94}\) \(+1.12556 q^{95}\) \(+8.70103 q^{96}\) \(+11.2210 q^{97}\) \(+0.922803 q^{98}\) \(-1.25622 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80025 −1.27297 −0.636485 0.771289i \(-0.719612\pi\)
−0.636485 + 0.771289i \(0.719612\pi\)
\(3\) 1.41167 0.815028 0.407514 0.913199i \(-0.366396\pi\)
0.407514 + 0.913199i \(0.366396\pi\)
\(4\) 1.24090 0.620451
\(5\) 0.213559 0.0955063 0.0477532 0.998859i \(-0.484794\pi\)
0.0477532 + 0.998859i \(0.484794\pi\)
\(6\) −2.54136 −1.03751
\(7\) −2.54704 −0.962690 −0.481345 0.876531i \(-0.659852\pi\)
−0.481345 + 0.876531i \(0.659852\pi\)
\(8\) 1.36657 0.483154
\(9\) −1.00719 −0.335730
\(10\) −0.384459 −0.121577
\(11\) 1.24725 0.376061 0.188030 0.982163i \(-0.439790\pi\)
0.188030 + 0.982163i \(0.439790\pi\)
\(12\) 1.75174 0.505685
\(13\) 1.90462 0.528247 0.264124 0.964489i \(-0.414917\pi\)
0.264124 + 0.964489i \(0.414917\pi\)
\(14\) 4.58531 1.22547
\(15\) 0.301474 0.0778403
\(16\) −4.94197 −1.23549
\(17\) −3.92660 −0.952339 −0.476170 0.879353i \(-0.657975\pi\)
−0.476170 + 0.879353i \(0.657975\pi\)
\(18\) 1.81319 0.427374
\(19\) 5.27048 1.20913 0.604566 0.796555i \(-0.293347\pi\)
0.604566 + 0.796555i \(0.293347\pi\)
\(20\) 0.265005 0.0592570
\(21\) −3.59558 −0.784619
\(22\) −2.24537 −0.478714
\(23\) 2.59275 0.540625 0.270313 0.962773i \(-0.412873\pi\)
0.270313 + 0.962773i \(0.412873\pi\)
\(24\) 1.92914 0.393784
\(25\) −4.95439 −0.990879
\(26\) −3.42880 −0.672443
\(27\) −5.65683 −1.08866
\(28\) −3.16063 −0.597302
\(29\) 4.85757 0.902027 0.451014 0.892517i \(-0.351063\pi\)
0.451014 + 0.892517i \(0.351063\pi\)
\(30\) −0.542729 −0.0990883
\(31\) 1.57742 0.283313 0.141656 0.989916i \(-0.454757\pi\)
0.141656 + 0.989916i \(0.454757\pi\)
\(32\) 6.16365 1.08959
\(33\) 1.76071 0.306500
\(34\) 7.06886 1.21230
\(35\) −0.543942 −0.0919430
\(36\) −1.24983 −0.208304
\(37\) −1.00000 −0.164399
\(38\) −9.48819 −1.53919
\(39\) 2.68870 0.430536
\(40\) 0.291842 0.0461442
\(41\) −7.59622 −1.18633 −0.593165 0.805081i \(-0.702122\pi\)
−0.593165 + 0.805081i \(0.702122\pi\)
\(42\) 6.47294 0.998796
\(43\) −3.23107 −0.492733 −0.246366 0.969177i \(-0.579237\pi\)
−0.246366 + 0.969177i \(0.579237\pi\)
\(44\) 1.54772 0.233328
\(45\) −0.215094 −0.0320643
\(46\) −4.66760 −0.688199
\(47\) −1.14828 −0.167494 −0.0837469 0.996487i \(-0.526689\pi\)
−0.0837469 + 0.996487i \(0.526689\pi\)
\(48\) −6.97642 −1.00696
\(49\) −0.512597 −0.0732282
\(50\) 8.91915 1.26136
\(51\) −5.54305 −0.776183
\(52\) 2.36345 0.327752
\(53\) 11.3924 1.56486 0.782430 0.622738i \(-0.213980\pi\)
0.782430 + 0.622738i \(0.213980\pi\)
\(54\) 10.1837 1.38583
\(55\) 0.266362 0.0359162
\(56\) −3.48069 −0.465127
\(57\) 7.44018 0.985476
\(58\) −8.74484 −1.14825
\(59\) 4.17419 0.543434 0.271717 0.962377i \(-0.412409\pi\)
0.271717 + 0.962377i \(0.412409\pi\)
\(60\) 0.374100 0.0482961
\(61\) 4.10910 0.526117 0.263058 0.964780i \(-0.415269\pi\)
0.263058 + 0.964780i \(0.415269\pi\)
\(62\) −2.83975 −0.360649
\(63\) 2.56535 0.323204
\(64\) −1.21218 −0.151522
\(65\) 0.406749 0.0504510
\(66\) −3.16972 −0.390165
\(67\) −5.17598 −0.632346 −0.316173 0.948701i \(-0.602398\pi\)
−0.316173 + 0.948701i \(0.602398\pi\)
\(68\) −4.87252 −0.590880
\(69\) 3.66010 0.440624
\(70\) 0.979232 0.117041
\(71\) −16.1412 −1.91560 −0.957802 0.287429i \(-0.907199\pi\)
−0.957802 + 0.287429i \(0.907199\pi\)
\(72\) −1.37639 −0.162209
\(73\) −4.41986 −0.517305 −0.258653 0.965970i \(-0.583279\pi\)
−0.258653 + 0.965970i \(0.583279\pi\)
\(74\) 1.80025 0.209275
\(75\) −6.99396 −0.807593
\(76\) 6.54016 0.750207
\(77\) −3.17680 −0.362030
\(78\) −4.84033 −0.548059
\(79\) −2.92425 −0.329004 −0.164502 0.986377i \(-0.552602\pi\)
−0.164502 + 0.986377i \(0.552602\pi\)
\(80\) −1.05540 −0.117997
\(81\) −4.96400 −0.551555
\(82\) 13.6751 1.51016
\(83\) 7.83025 0.859482 0.429741 0.902952i \(-0.358605\pi\)
0.429741 + 0.902952i \(0.358605\pi\)
\(84\) −4.46176 −0.486818
\(85\) −0.838558 −0.0909544
\(86\) 5.81673 0.627234
\(87\) 6.85727 0.735177
\(88\) 1.70445 0.181695
\(89\) 4.91950 0.521466 0.260733 0.965411i \(-0.416036\pi\)
0.260733 + 0.965411i \(0.416036\pi\)
\(90\) 0.387223 0.0408169
\(91\) −4.85115 −0.508538
\(92\) 3.21735 0.335432
\(93\) 2.22679 0.230908
\(94\) 2.06719 0.213214
\(95\) 1.12556 0.115480
\(96\) 8.70103 0.888045
\(97\) 11.2210 1.13932 0.569662 0.821879i \(-0.307074\pi\)
0.569662 + 0.821879i \(0.307074\pi\)
\(98\) 0.922803 0.0932172
\(99\) −1.25622 −0.126255
\(100\) −6.14792 −0.614792
\(101\) 6.77092 0.673732 0.336866 0.941553i \(-0.390633\pi\)
0.336866 + 0.941553i \(0.390633\pi\)
\(102\) 9.97889 0.988057
\(103\) 2.91963 0.287679 0.143840 0.989601i \(-0.454055\pi\)
0.143840 + 0.989601i \(0.454055\pi\)
\(104\) 2.60279 0.255225
\(105\) −0.767866 −0.0749360
\(106\) −20.5091 −1.99202
\(107\) −8.02324 −0.775636 −0.387818 0.921736i \(-0.626771\pi\)
−0.387818 + 0.921736i \(0.626771\pi\)
\(108\) −7.01957 −0.675459
\(109\) −1.00000 −0.0957826
\(110\) −0.479518 −0.0457202
\(111\) −1.41167 −0.133990
\(112\) 12.5874 1.18940
\(113\) −11.1729 −1.05106 −0.525530 0.850775i \(-0.676133\pi\)
−0.525530 + 0.850775i \(0.676133\pi\)
\(114\) −13.3942 −1.25448
\(115\) 0.553703 0.0516331
\(116\) 6.02777 0.559664
\(117\) −1.91832 −0.177349
\(118\) −7.51460 −0.691775
\(119\) 10.0012 0.916807
\(120\) 0.411984 0.0376088
\(121\) −9.44436 −0.858578
\(122\) −7.39742 −0.669731
\(123\) −10.7234 −0.966892
\(124\) 1.95742 0.175782
\(125\) −2.12585 −0.190141
\(126\) −4.61828 −0.411429
\(127\) −20.4583 −1.81538 −0.907690 0.419641i \(-0.862156\pi\)
−0.907690 + 0.419641i \(0.862156\pi\)
\(128\) −10.1451 −0.896706
\(129\) −4.56120 −0.401591
\(130\) −0.732250 −0.0642225
\(131\) −15.9608 −1.39450 −0.697250 0.716828i \(-0.745593\pi\)
−0.697250 + 0.716828i \(0.745593\pi\)
\(132\) 2.18487 0.190168
\(133\) −13.4241 −1.16402
\(134\) 9.31806 0.804958
\(135\) −1.20806 −0.103974
\(136\) −5.36595 −0.460126
\(137\) −13.2797 −1.13456 −0.567282 0.823524i \(-0.692005\pi\)
−0.567282 + 0.823524i \(0.692005\pi\)
\(138\) −6.58910 −0.560901
\(139\) 21.2954 1.80625 0.903124 0.429380i \(-0.141268\pi\)
0.903124 + 0.429380i \(0.141268\pi\)
\(140\) −0.674979 −0.0570461
\(141\) −1.62099 −0.136512
\(142\) 29.0581 2.43851
\(143\) 2.37555 0.198653
\(144\) 4.97750 0.414792
\(145\) 1.03737 0.0861493
\(146\) 7.95686 0.658514
\(147\) −0.723618 −0.0596830
\(148\) −1.24090 −0.102002
\(149\) −18.6716 −1.52963 −0.764817 0.644247i \(-0.777171\pi\)
−0.764817 + 0.644247i \(0.777171\pi\)
\(150\) 12.5909 1.02804
\(151\) −1.68125 −0.136818 −0.0684090 0.997657i \(-0.521792\pi\)
−0.0684090 + 0.997657i \(0.521792\pi\)
\(152\) 7.20246 0.584196
\(153\) 3.95483 0.319729
\(154\) 5.71904 0.460853
\(155\) 0.336871 0.0270582
\(156\) 3.33641 0.267127
\(157\) −20.7802 −1.65844 −0.829221 0.558921i \(-0.811216\pi\)
−0.829221 + 0.558921i \(0.811216\pi\)
\(158\) 5.26439 0.418812
\(159\) 16.0822 1.27540
\(160\) 1.31630 0.104063
\(161\) −6.60383 −0.520454
\(162\) 8.93644 0.702113
\(163\) −1.41071 −0.110495 −0.0552475 0.998473i \(-0.517595\pi\)
−0.0552475 + 0.998473i \(0.517595\pi\)
\(164\) −9.42618 −0.736061
\(165\) 0.376014 0.0292727
\(166\) −14.0964 −1.09409
\(167\) 17.5776 1.36020 0.680100 0.733120i \(-0.261937\pi\)
0.680100 + 0.733120i \(0.261937\pi\)
\(168\) −4.91359 −0.379092
\(169\) −9.37241 −0.720955
\(170\) 1.50961 0.115782
\(171\) −5.30838 −0.405942
\(172\) −4.00944 −0.305717
\(173\) −14.5096 −1.10314 −0.551572 0.834127i \(-0.685972\pi\)
−0.551572 + 0.834127i \(0.685972\pi\)
\(174\) −12.3448 −0.935858
\(175\) 12.6190 0.953909
\(176\) −6.16388 −0.464620
\(177\) 5.89258 0.442914
\(178\) −8.85634 −0.663810
\(179\) 12.3478 0.922918 0.461459 0.887161i \(-0.347326\pi\)
0.461459 + 0.887161i \(0.347326\pi\)
\(180\) −0.266911 −0.0198944
\(181\) 22.1524 1.64657 0.823287 0.567626i \(-0.192138\pi\)
0.823287 + 0.567626i \(0.192138\pi\)
\(182\) 8.73328 0.647354
\(183\) 5.80069 0.428800
\(184\) 3.54316 0.261205
\(185\) −0.213559 −0.0157011
\(186\) −4.00879 −0.293938
\(187\) −4.89746 −0.358138
\(188\) −1.42490 −0.103922
\(189\) 14.4082 1.04804
\(190\) −2.02628 −0.147002
\(191\) 15.1479 1.09607 0.548033 0.836456i \(-0.315377\pi\)
0.548033 + 0.836456i \(0.315377\pi\)
\(192\) −1.71120 −0.123495
\(193\) −23.5997 −1.69874 −0.849372 0.527794i \(-0.823019\pi\)
−0.849372 + 0.527794i \(0.823019\pi\)
\(194\) −20.2007 −1.45032
\(195\) 0.574195 0.0411189
\(196\) −0.636083 −0.0454345
\(197\) −18.6758 −1.33060 −0.665298 0.746578i \(-0.731696\pi\)
−0.665298 + 0.746578i \(0.731696\pi\)
\(198\) 2.26151 0.160719
\(199\) 6.98773 0.495347 0.247674 0.968844i \(-0.420334\pi\)
0.247674 + 0.968844i \(0.420334\pi\)
\(200\) −6.77050 −0.478747
\(201\) −7.30677 −0.515380
\(202\) −12.1894 −0.857640
\(203\) −12.3724 −0.868372
\(204\) −6.87839 −0.481584
\(205\) −1.62224 −0.113302
\(206\) −5.25606 −0.366207
\(207\) −2.61139 −0.181504
\(208\) −9.41258 −0.652645
\(209\) 6.57363 0.454707
\(210\) 1.38235 0.0953913
\(211\) −12.7140 −0.875266 −0.437633 0.899154i \(-0.644183\pi\)
−0.437633 + 0.899154i \(0.644183\pi\)
\(212\) 14.1368 0.970920
\(213\) −22.7860 −1.56127
\(214\) 14.4438 0.987361
\(215\) −0.690022 −0.0470591
\(216\) −7.73042 −0.525989
\(217\) −4.01775 −0.272742
\(218\) 1.80025 0.121928
\(219\) −6.23938 −0.421618
\(220\) 0.330529 0.0222843
\(221\) −7.47868 −0.503071
\(222\) 2.54136 0.170565
\(223\) 16.6781 1.11685 0.558425 0.829555i \(-0.311406\pi\)
0.558425 + 0.829555i \(0.311406\pi\)
\(224\) −15.6990 −1.04894
\(225\) 4.99002 0.332668
\(226\) 20.1140 1.33797
\(227\) −13.6199 −0.903982 −0.451991 0.892023i \(-0.649286\pi\)
−0.451991 + 0.892023i \(0.649286\pi\)
\(228\) 9.23254 0.611440
\(229\) −15.5217 −1.02571 −0.512853 0.858477i \(-0.671411\pi\)
−0.512853 + 0.858477i \(0.671411\pi\)
\(230\) −0.996805 −0.0657274
\(231\) −4.48459 −0.295065
\(232\) 6.63818 0.435818
\(233\) −0.525509 −0.0344273 −0.0172136 0.999852i \(-0.505480\pi\)
−0.0172136 + 0.999852i \(0.505480\pi\)
\(234\) 3.45345 0.225759
\(235\) −0.245225 −0.0159967
\(236\) 5.17977 0.337174
\(237\) −4.12808 −0.268148
\(238\) −18.0046 −1.16707
\(239\) −25.9358 −1.67765 −0.838824 0.544403i \(-0.816756\pi\)
−0.838824 + 0.544403i \(0.816756\pi\)
\(240\) −1.48987 −0.0961710
\(241\) −1.29649 −0.0835143 −0.0417572 0.999128i \(-0.513296\pi\)
−0.0417572 + 0.999128i \(0.513296\pi\)
\(242\) 17.0022 1.09294
\(243\) 9.96296 0.639124
\(244\) 5.09900 0.326430
\(245\) −0.109470 −0.00699375
\(246\) 19.3047 1.23082
\(247\) 10.0383 0.638721
\(248\) 2.15565 0.136884
\(249\) 11.0537 0.700501
\(250\) 3.82706 0.242044
\(251\) 22.6741 1.43117 0.715587 0.698524i \(-0.246159\pi\)
0.715587 + 0.698524i \(0.246159\pi\)
\(252\) 3.18335 0.200532
\(253\) 3.23381 0.203308
\(254\) 36.8301 2.31092
\(255\) −1.18377 −0.0741303
\(256\) 20.6880 1.29300
\(257\) 5.53155 0.345049 0.172524 0.985005i \(-0.444808\pi\)
0.172524 + 0.985005i \(0.444808\pi\)
\(258\) 8.21130 0.511213
\(259\) 2.54704 0.158265
\(260\) 0.504736 0.0313024
\(261\) −4.89249 −0.302838
\(262\) 28.7334 1.77516
\(263\) −24.3064 −1.49880 −0.749398 0.662119i \(-0.769657\pi\)
−0.749398 + 0.662119i \(0.769657\pi\)
\(264\) 2.40612 0.148087
\(265\) 2.43293 0.149454
\(266\) 24.1668 1.48176
\(267\) 6.94471 0.425009
\(268\) −6.42289 −0.392340
\(269\) 2.16670 0.132106 0.0660531 0.997816i \(-0.478959\pi\)
0.0660531 + 0.997816i \(0.478959\pi\)
\(270\) 2.17482 0.132355
\(271\) −5.39620 −0.327796 −0.163898 0.986477i \(-0.552407\pi\)
−0.163898 + 0.986477i \(0.552407\pi\)
\(272\) 19.4051 1.17661
\(273\) −6.84822 −0.414473
\(274\) 23.9068 1.44426
\(275\) −6.17938 −0.372631
\(276\) 4.54183 0.273386
\(277\) 3.88107 0.233191 0.116595 0.993179i \(-0.462802\pi\)
0.116595 + 0.993179i \(0.462802\pi\)
\(278\) −38.3370 −2.29930
\(279\) −1.58876 −0.0951166
\(280\) −0.743332 −0.0444226
\(281\) −10.8055 −0.644603 −0.322302 0.946637i \(-0.604457\pi\)
−0.322302 + 0.946637i \(0.604457\pi\)
\(282\) 2.91819 0.173776
\(283\) 5.45346 0.324175 0.162087 0.986776i \(-0.448177\pi\)
0.162087 + 0.986776i \(0.448177\pi\)
\(284\) −20.0296 −1.18854
\(285\) 1.58891 0.0941191
\(286\) −4.27658 −0.252880
\(287\) 19.3479 1.14207
\(288\) −6.20797 −0.365808
\(289\) −1.58185 −0.0930500
\(290\) −1.86753 −0.109665
\(291\) 15.8404 0.928580
\(292\) −5.48462 −0.320963
\(293\) 6.74315 0.393939 0.196970 0.980410i \(-0.436890\pi\)
0.196970 + 0.980410i \(0.436890\pi\)
\(294\) 1.30269 0.0759746
\(295\) 0.891435 0.0519014
\(296\) −1.36657 −0.0794300
\(297\) −7.05550 −0.409401
\(298\) 33.6135 1.94718
\(299\) 4.93821 0.285584
\(300\) −8.67883 −0.501072
\(301\) 8.22965 0.474349
\(302\) 3.02667 0.174165
\(303\) 9.55830 0.549110
\(304\) −26.0465 −1.49387
\(305\) 0.877534 0.0502475
\(306\) −7.11968 −0.407005
\(307\) −7.00194 −0.399622 −0.199811 0.979834i \(-0.564033\pi\)
−0.199811 + 0.979834i \(0.564033\pi\)
\(308\) −3.94210 −0.224622
\(309\) 4.12155 0.234467
\(310\) −0.606453 −0.0344442
\(311\) 6.95327 0.394284 0.197142 0.980375i \(-0.436834\pi\)
0.197142 + 0.980375i \(0.436834\pi\)
\(312\) 3.67428 0.208015
\(313\) 23.7959 1.34502 0.672512 0.740086i \(-0.265215\pi\)
0.672512 + 0.740086i \(0.265215\pi\)
\(314\) 37.4096 2.11115
\(315\) 0.547853 0.0308680
\(316\) −3.62872 −0.204131
\(317\) 0.222151 0.0124773 0.00623863 0.999981i \(-0.498014\pi\)
0.00623863 + 0.999981i \(0.498014\pi\)
\(318\) −28.9521 −1.62355
\(319\) 6.05861 0.339217
\(320\) −0.258871 −0.0144713
\(321\) −11.3262 −0.632165
\(322\) 11.8885 0.662523
\(323\) −20.6950 −1.15150
\(324\) −6.15984 −0.342213
\(325\) −9.43625 −0.523429
\(326\) 2.53962 0.140657
\(327\) −1.41167 −0.0780655
\(328\) −10.3807 −0.573180
\(329\) 2.92471 0.161245
\(330\) −0.676920 −0.0372632
\(331\) −28.7581 −1.58069 −0.790343 0.612665i \(-0.790098\pi\)
−0.790343 + 0.612665i \(0.790098\pi\)
\(332\) 9.71658 0.533267
\(333\) 1.00719 0.0551937
\(334\) −31.6442 −1.73149
\(335\) −1.10537 −0.0603931
\(336\) 17.7692 0.969390
\(337\) 1.70024 0.0926181 0.0463090 0.998927i \(-0.485254\pi\)
0.0463090 + 0.998927i \(0.485254\pi\)
\(338\) 16.8727 0.917753
\(339\) −15.7725 −0.856642
\(340\) −1.04057 −0.0564328
\(341\) 1.96744 0.106543
\(342\) 9.55641 0.516752
\(343\) 19.1349 1.03319
\(344\) −4.41546 −0.238066
\(345\) 0.781646 0.0420824
\(346\) 26.1209 1.40427
\(347\) −28.8999 −1.55143 −0.775714 0.631085i \(-0.782610\pi\)
−0.775714 + 0.631085i \(0.782610\pi\)
\(348\) 8.50921 0.456142
\(349\) 14.5565 0.779194 0.389597 0.920985i \(-0.372614\pi\)
0.389597 + 0.920985i \(0.372614\pi\)
\(350\) −22.7174 −1.21430
\(351\) −10.7741 −0.575080
\(352\) 7.68763 0.409752
\(353\) 0.608885 0.0324077 0.0162038 0.999869i \(-0.494842\pi\)
0.0162038 + 0.999869i \(0.494842\pi\)
\(354\) −10.6081 −0.563815
\(355\) −3.44708 −0.182952
\(356\) 6.10462 0.323544
\(357\) 14.1184 0.747223
\(358\) −22.2291 −1.17485
\(359\) 4.48611 0.236768 0.118384 0.992968i \(-0.462229\pi\)
0.118384 + 0.992968i \(0.462229\pi\)
\(360\) −0.293940 −0.0154920
\(361\) 8.77798 0.461999
\(362\) −39.8798 −2.09604
\(363\) −13.3323 −0.699765
\(364\) −6.01980 −0.315523
\(365\) −0.943899 −0.0494059
\(366\) −10.4427 −0.545849
\(367\) −11.0145 −0.574952 −0.287476 0.957788i \(-0.592816\pi\)
−0.287476 + 0.957788i \(0.592816\pi\)
\(368\) −12.8133 −0.667938
\(369\) 7.65084 0.398287
\(370\) 0.384459 0.0199871
\(371\) −29.0168 −1.50648
\(372\) 2.76323 0.143267
\(373\) 7.38632 0.382449 0.191225 0.981546i \(-0.438754\pi\)
0.191225 + 0.981546i \(0.438754\pi\)
\(374\) 8.81665 0.455898
\(375\) −3.00099 −0.154971
\(376\) −1.56920 −0.0809252
\(377\) 9.25183 0.476494
\(378\) −25.9383 −1.33412
\(379\) 22.1161 1.13603 0.568013 0.823019i \(-0.307712\pi\)
0.568013 + 0.823019i \(0.307712\pi\)
\(380\) 1.39671 0.0716495
\(381\) −28.8803 −1.47959
\(382\) −27.2701 −1.39526
\(383\) −17.9409 −0.916735 −0.458367 0.888763i \(-0.651566\pi\)
−0.458367 + 0.888763i \(0.651566\pi\)
\(384\) −14.3215 −0.730840
\(385\) −0.678433 −0.0345762
\(386\) 42.4854 2.16245
\(387\) 3.25430 0.165425
\(388\) 13.9242 0.706895
\(389\) −2.56891 −0.130249 −0.0651244 0.997877i \(-0.520744\pi\)
−0.0651244 + 0.997877i \(0.520744\pi\)
\(390\) −1.03369 −0.0523431
\(391\) −10.1807 −0.514859
\(392\) −0.700497 −0.0353805
\(393\) −22.5313 −1.13656
\(394\) 33.6211 1.69381
\(395\) −0.624500 −0.0314220
\(396\) −1.55885 −0.0783351
\(397\) −5.25847 −0.263915 −0.131958 0.991255i \(-0.542126\pi\)
−0.131958 + 0.991255i \(0.542126\pi\)
\(398\) −12.5797 −0.630562
\(399\) −18.9504 −0.948707
\(400\) 24.4844 1.22422
\(401\) −26.7064 −1.33366 −0.666828 0.745212i \(-0.732348\pi\)
−0.666828 + 0.745212i \(0.732348\pi\)
\(402\) 13.1540 0.656063
\(403\) 3.00439 0.149659
\(404\) 8.40205 0.418018
\(405\) −1.06010 −0.0526770
\(406\) 22.2734 1.10541
\(407\) −1.24725 −0.0618240
\(408\) −7.57494 −0.375016
\(409\) 7.22754 0.357379 0.178689 0.983906i \(-0.442814\pi\)
0.178689 + 0.983906i \(0.442814\pi\)
\(410\) 2.92044 0.144230
\(411\) −18.7466 −0.924701
\(412\) 3.62297 0.178491
\(413\) −10.6318 −0.523158
\(414\) 4.70116 0.231049
\(415\) 1.67222 0.0820859
\(416\) 11.7394 0.575573
\(417\) 30.0620 1.47214
\(418\) −11.8342 −0.578828
\(419\) −30.1586 −1.47335 −0.736673 0.676249i \(-0.763604\pi\)
−0.736673 + 0.676249i \(0.763604\pi\)
\(420\) −0.952847 −0.0464942
\(421\) −38.2342 −1.86342 −0.931711 0.363201i \(-0.881684\pi\)
−0.931711 + 0.363201i \(0.881684\pi\)
\(422\) 22.8883 1.11419
\(423\) 1.15654 0.0562327
\(424\) 15.5684 0.756068
\(425\) 19.4539 0.943652
\(426\) 41.0205 1.98745
\(427\) −10.4660 −0.506487
\(428\) −9.95606 −0.481244
\(429\) 3.35349 0.161908
\(430\) 1.24221 0.0599048
\(431\) 29.8305 1.43688 0.718441 0.695588i \(-0.244856\pi\)
0.718441 + 0.695588i \(0.244856\pi\)
\(432\) 27.9558 1.34503
\(433\) −39.4970 −1.89810 −0.949052 0.315120i \(-0.897955\pi\)
−0.949052 + 0.315120i \(0.897955\pi\)
\(434\) 7.23295 0.347193
\(435\) 1.46443 0.0702140
\(436\) −1.24090 −0.0594285
\(437\) 13.6650 0.653687
\(438\) 11.2324 0.536707
\(439\) −6.49411 −0.309947 −0.154974 0.987919i \(-0.549529\pi\)
−0.154974 + 0.987919i \(0.549529\pi\)
\(440\) 0.364001 0.0173530
\(441\) 0.516283 0.0245849
\(442\) 13.4635 0.640394
\(443\) −30.9260 −1.46934 −0.734669 0.678426i \(-0.762663\pi\)
−0.734669 + 0.678426i \(0.762663\pi\)
\(444\) −1.75174 −0.0831341
\(445\) 1.05060 0.0498033
\(446\) −30.0248 −1.42172
\(447\) −26.3581 −1.24669
\(448\) 3.08747 0.145869
\(449\) −25.2817 −1.19312 −0.596559 0.802570i \(-0.703466\pi\)
−0.596559 + 0.802570i \(0.703466\pi\)
\(450\) −8.98328 −0.423476
\(451\) −9.47441 −0.446133
\(452\) −13.8645 −0.652131
\(453\) −2.37336 −0.111510
\(454\) 24.5192 1.15074
\(455\) −1.03600 −0.0485686
\(456\) 10.1675 0.476136
\(457\) 38.5460 1.80310 0.901552 0.432671i \(-0.142429\pi\)
0.901552 + 0.432671i \(0.142429\pi\)
\(458\) 27.9430 1.30569
\(459\) 22.2121 1.03677
\(460\) 0.687092 0.0320358
\(461\) −37.5321 −1.74805 −0.874023 0.485884i \(-0.838498\pi\)
−0.874023 + 0.485884i \(0.838498\pi\)
\(462\) 8.07339 0.375608
\(463\) 40.8846 1.90007 0.950033 0.312149i \(-0.101049\pi\)
0.950033 + 0.312149i \(0.101049\pi\)
\(464\) −24.0059 −1.11445
\(465\) 0.475551 0.0220531
\(466\) 0.946049 0.0438249
\(467\) 23.3733 1.08159 0.540794 0.841155i \(-0.318124\pi\)
0.540794 + 0.841155i \(0.318124\pi\)
\(468\) −2.38045 −0.110036
\(469\) 13.1834 0.608753
\(470\) 0.441466 0.0203633
\(471\) −29.3348 −1.35168
\(472\) 5.70431 0.262562
\(473\) −4.02996 −0.185298
\(474\) 7.43158 0.341344
\(475\) −26.1120 −1.19810
\(476\) 12.4105 0.568834
\(477\) −11.4743 −0.525371
\(478\) 46.6909 2.13559
\(479\) −38.0047 −1.73648 −0.868240 0.496144i \(-0.834749\pi\)
−0.868240 + 0.496144i \(0.834749\pi\)
\(480\) 1.85818 0.0848139
\(481\) −1.90462 −0.0868433
\(482\) 2.33401 0.106311
\(483\) −9.32242 −0.424185
\(484\) −11.7195 −0.532706
\(485\) 2.39635 0.108813
\(486\) −17.9358 −0.813586
\(487\) −13.8591 −0.628015 −0.314007 0.949421i \(-0.601672\pi\)
−0.314007 + 0.949421i \(0.601672\pi\)
\(488\) 5.61536 0.254195
\(489\) −1.99145 −0.0900565
\(490\) 0.197073 0.00890283
\(491\) 29.9389 1.35112 0.675562 0.737303i \(-0.263901\pi\)
0.675562 + 0.737303i \(0.263901\pi\)
\(492\) −13.3066 −0.599910
\(493\) −19.0737 −0.859036
\(494\) −18.0714 −0.813072
\(495\) −0.268277 −0.0120581
\(496\) −7.79555 −0.350030
\(497\) 41.1122 1.84413
\(498\) −19.8995 −0.891717
\(499\) −16.9268 −0.757745 −0.378873 0.925449i \(-0.623688\pi\)
−0.378873 + 0.925449i \(0.623688\pi\)
\(500\) −2.63797 −0.117974
\(501\) 24.8138 1.10860
\(502\) −40.8190 −1.82184
\(503\) −38.7637 −1.72839 −0.864193 0.503161i \(-0.832170\pi\)
−0.864193 + 0.503161i \(0.832170\pi\)
\(504\) 3.50572 0.156157
\(505\) 1.44599 0.0643456
\(506\) −5.82167 −0.258805
\(507\) −13.2307 −0.587598
\(508\) −25.3868 −1.12636
\(509\) −17.6837 −0.783816 −0.391908 0.920004i \(-0.628185\pi\)
−0.391908 + 0.920004i \(0.628185\pi\)
\(510\) 2.13108 0.0943657
\(511\) 11.2575 0.498005
\(512\) −16.9535 −0.749246
\(513\) −29.8142 −1.31633
\(514\) −9.95818 −0.439237
\(515\) 0.623511 0.0274752
\(516\) −5.66000 −0.249168
\(517\) −1.43220 −0.0629879
\(518\) −4.58531 −0.201467
\(519\) −20.4827 −0.899092
\(520\) 0.555849 0.0243756
\(521\) 5.32183 0.233154 0.116577 0.993182i \(-0.462808\pi\)
0.116577 + 0.993182i \(0.462808\pi\)
\(522\) 8.80771 0.385503
\(523\) 8.01136 0.350312 0.175156 0.984541i \(-0.443957\pi\)
0.175156 + 0.984541i \(0.443957\pi\)
\(524\) −19.8058 −0.865219
\(525\) 17.8139 0.777462
\(526\) 43.7576 1.90792
\(527\) −6.19388 −0.269810
\(528\) −8.70136 −0.378678
\(529\) −16.2777 −0.707724
\(530\) −4.37989 −0.190250
\(531\) −4.20421 −0.182447
\(532\) −16.6580 −0.722217
\(533\) −14.4679 −0.626676
\(534\) −12.5022 −0.541024
\(535\) −1.71343 −0.0740781
\(536\) −7.07331 −0.305521
\(537\) 17.4310 0.752204
\(538\) −3.90061 −0.168167
\(539\) −0.639338 −0.0275383
\(540\) −1.49909 −0.0645106
\(541\) 41.5949 1.78831 0.894153 0.447762i \(-0.147779\pi\)
0.894153 + 0.447762i \(0.147779\pi\)
\(542\) 9.71451 0.417274
\(543\) 31.2718 1.34200
\(544\) −24.2021 −1.03766
\(545\) −0.213559 −0.00914784
\(546\) 12.3285 0.527611
\(547\) −2.56527 −0.109683 −0.0548416 0.998495i \(-0.517465\pi\)
−0.0548416 + 0.998495i \(0.517465\pi\)
\(548\) −16.4789 −0.703942
\(549\) −4.13865 −0.176633
\(550\) 11.1244 0.474348
\(551\) 25.6017 1.09067
\(552\) 5.00177 0.212889
\(553\) 7.44819 0.316729
\(554\) −6.98690 −0.296845
\(555\) −0.301474 −0.0127969
\(556\) 26.4255 1.12069
\(557\) 4.01493 0.170118 0.0850590 0.996376i \(-0.472892\pi\)
0.0850590 + 0.996376i \(0.472892\pi\)
\(558\) 2.86017 0.121081
\(559\) −6.15396 −0.260285
\(560\) 2.68814 0.113595
\(561\) −6.91359 −0.291892
\(562\) 19.4526 0.820560
\(563\) 5.53414 0.233236 0.116618 0.993177i \(-0.462795\pi\)
0.116618 + 0.993177i \(0.462795\pi\)
\(564\) −2.01149 −0.0846991
\(565\) −2.38607 −0.100383
\(566\) −9.81760 −0.412665
\(567\) 12.6435 0.530977
\(568\) −22.0580 −0.925531
\(569\) −4.96786 −0.208263 −0.104132 0.994564i \(-0.533206\pi\)
−0.104132 + 0.994564i \(0.533206\pi\)
\(570\) −2.86044 −0.119811
\(571\) 0.262219 0.0109735 0.00548676 0.999985i \(-0.498253\pi\)
0.00548676 + 0.999985i \(0.498253\pi\)
\(572\) 2.94782 0.123255
\(573\) 21.3839 0.893325
\(574\) −34.8310 −1.45382
\(575\) −12.8455 −0.535694
\(576\) 1.22090 0.0508706
\(577\) −27.1979 −1.13226 −0.566131 0.824315i \(-0.691560\pi\)
−0.566131 + 0.824315i \(0.691560\pi\)
\(578\) 2.84773 0.118450
\(579\) −33.3150 −1.38452
\(580\) 1.28728 0.0534514
\(581\) −19.9439 −0.827414
\(582\) −28.5167 −1.18205
\(583\) 14.2091 0.588483
\(584\) −6.04003 −0.249938
\(585\) −0.409673 −0.0169379
\(586\) −12.1394 −0.501472
\(587\) −39.4103 −1.62664 −0.813319 0.581818i \(-0.802341\pi\)
−0.813319 + 0.581818i \(0.802341\pi\)
\(588\) −0.897939 −0.0370304
\(589\) 8.31376 0.342562
\(590\) −1.60481 −0.0660688
\(591\) −26.3641 −1.08447
\(592\) 4.94197 0.203114
\(593\) 41.0366 1.68517 0.842586 0.538562i \(-0.181032\pi\)
0.842586 + 0.538562i \(0.181032\pi\)
\(594\) 12.7017 0.521155
\(595\) 2.13584 0.0875609
\(596\) −23.1696 −0.949064
\(597\) 9.86437 0.403722
\(598\) −8.89001 −0.363540
\(599\) −30.6206 −1.25112 −0.625562 0.780175i \(-0.715130\pi\)
−0.625562 + 0.780175i \(0.715130\pi\)
\(600\) −9.55771 −0.390192
\(601\) 19.2508 0.785257 0.392629 0.919697i \(-0.371566\pi\)
0.392629 + 0.919697i \(0.371566\pi\)
\(602\) −14.8154 −0.603832
\(603\) 5.21319 0.212298
\(604\) −2.08626 −0.0848889
\(605\) −2.01692 −0.0819996
\(606\) −17.2073 −0.699000
\(607\) −15.0844 −0.612257 −0.306128 0.951990i \(-0.599034\pi\)
−0.306128 + 0.951990i \(0.599034\pi\)
\(608\) 32.4854 1.31746
\(609\) −17.4657 −0.707747
\(610\) −1.57978 −0.0639635
\(611\) −2.18704 −0.0884782
\(612\) 4.90756 0.198376
\(613\) −11.2684 −0.455128 −0.227564 0.973763i \(-0.573076\pi\)
−0.227564 + 0.973763i \(0.573076\pi\)
\(614\) 12.6053 0.508707
\(615\) −2.29006 −0.0923443
\(616\) −4.34131 −0.174916
\(617\) −46.9949 −1.89194 −0.945972 0.324247i \(-0.894889\pi\)
−0.945972 + 0.324247i \(0.894889\pi\)
\(618\) −7.41982 −0.298469
\(619\) −41.6769 −1.67514 −0.837569 0.546332i \(-0.816024\pi\)
−0.837569 + 0.546332i \(0.816024\pi\)
\(620\) 0.418025 0.0167883
\(621\) −14.6667 −0.588555
\(622\) −12.5176 −0.501911
\(623\) −12.5302 −0.502010
\(624\) −13.2875 −0.531924
\(625\) 24.3180 0.972719
\(626\) −42.8386 −1.71217
\(627\) 9.27978 0.370599
\(628\) −25.7862 −1.02898
\(629\) 3.92660 0.156564
\(630\) −0.986273 −0.0392940
\(631\) 45.7407 1.82091 0.910454 0.413610i \(-0.135732\pi\)
0.910454 + 0.413610i \(0.135732\pi\)
\(632\) −3.99618 −0.158960
\(633\) −17.9479 −0.713366
\(634\) −0.399928 −0.0158832
\(635\) −4.36904 −0.173380
\(636\) 19.9565 0.791326
\(637\) −0.976305 −0.0386826
\(638\) −10.9070 −0.431813
\(639\) 16.2572 0.643126
\(640\) −2.16657 −0.0856411
\(641\) −21.0365 −0.830893 −0.415447 0.909618i \(-0.636375\pi\)
−0.415447 + 0.909618i \(0.636375\pi\)
\(642\) 20.3899 0.804726
\(643\) 46.3141 1.82645 0.913224 0.407458i \(-0.133585\pi\)
0.913224 + 0.407458i \(0.133585\pi\)
\(644\) −8.19471 −0.322917
\(645\) −0.974083 −0.0383545
\(646\) 37.2563 1.46583
\(647\) 40.7174 1.60077 0.800383 0.599489i \(-0.204630\pi\)
0.800383 + 0.599489i \(0.204630\pi\)
\(648\) −6.78363 −0.266486
\(649\) 5.20628 0.204364
\(650\) 16.9876 0.666309
\(651\) −5.67173 −0.222293
\(652\) −1.75055 −0.0685568
\(653\) −46.9420 −1.83698 −0.918491 0.395442i \(-0.870591\pi\)
−0.918491 + 0.395442i \(0.870591\pi\)
\(654\) 2.54136 0.0993750
\(655\) −3.40856 −0.133184
\(656\) 37.5403 1.46570
\(657\) 4.45164 0.173675
\(658\) −5.26521 −0.205259
\(659\) 15.0726 0.587147 0.293573 0.955937i \(-0.405156\pi\)
0.293573 + 0.955937i \(0.405156\pi\)
\(660\) 0.466597 0.0181623
\(661\) 14.8072 0.575933 0.287967 0.957640i \(-0.407021\pi\)
0.287967 + 0.957640i \(0.407021\pi\)
\(662\) 51.7717 2.01216
\(663\) −10.5574 −0.410017
\(664\) 10.7005 0.415262
\(665\) −2.86684 −0.111171
\(666\) −1.81319 −0.0702599
\(667\) 12.5944 0.487659
\(668\) 21.8122 0.843938
\(669\) 23.5440 0.910263
\(670\) 1.98995 0.0768785
\(671\) 5.12509 0.197852
\(672\) −22.1619 −0.854912
\(673\) 46.0429 1.77482 0.887412 0.460978i \(-0.152501\pi\)
0.887412 + 0.460978i \(0.152501\pi\)
\(674\) −3.06086 −0.117900
\(675\) 28.0261 1.07873
\(676\) −11.6303 −0.447317
\(677\) 20.6941 0.795339 0.397669 0.917529i \(-0.369819\pi\)
0.397669 + 0.917529i \(0.369819\pi\)
\(678\) 28.3944 1.09048
\(679\) −28.5804 −1.09682
\(680\) −1.14594 −0.0439450
\(681\) −19.2267 −0.736770
\(682\) −3.54189 −0.135626
\(683\) −20.2855 −0.776202 −0.388101 0.921617i \(-0.626869\pi\)
−0.388101 + 0.921617i \(0.626869\pi\)
\(684\) −6.58718 −0.251867
\(685\) −2.83600 −0.108358
\(686\) −34.4476 −1.31521
\(687\) −21.9116 −0.835978
\(688\) 15.9678 0.608767
\(689\) 21.6981 0.826633
\(690\) −1.40716 −0.0535696
\(691\) 3.13865 0.119400 0.0596999 0.998216i \(-0.480986\pi\)
0.0596999 + 0.998216i \(0.480986\pi\)
\(692\) −18.0050 −0.684447
\(693\) 3.19964 0.121544
\(694\) 52.0271 1.97492
\(695\) 4.54781 0.172508
\(696\) 9.37091 0.355204
\(697\) 29.8273 1.12979
\(698\) −26.2054 −0.991890
\(699\) −0.741845 −0.0280592
\(700\) 15.6590 0.591854
\(701\) −2.61768 −0.0988684 −0.0494342 0.998777i \(-0.515742\pi\)
−0.0494342 + 0.998777i \(0.515742\pi\)
\(702\) 19.3961 0.732060
\(703\) −5.27048 −0.198780
\(704\) −1.51189 −0.0569817
\(705\) −0.346176 −0.0130378
\(706\) −1.09615 −0.0412540
\(707\) −17.2458 −0.648595
\(708\) 7.31212 0.274806
\(709\) 3.07494 0.115482 0.0577408 0.998332i \(-0.481610\pi\)
0.0577408 + 0.998332i \(0.481610\pi\)
\(710\) 6.20562 0.232893
\(711\) 2.94528 0.110457
\(712\) 6.72282 0.251948
\(713\) 4.08985 0.153166
\(714\) −25.4166 −0.951192
\(715\) 0.507319 0.0189726
\(716\) 15.3224 0.572626
\(717\) −36.6128 −1.36733
\(718\) −8.07612 −0.301398
\(719\) −46.9200 −1.74982 −0.874910 0.484285i \(-0.839080\pi\)
−0.874910 + 0.484285i \(0.839080\pi\)
\(720\) 1.06299 0.0396152
\(721\) −7.43640 −0.276946
\(722\) −15.8026 −0.588111
\(723\) −1.83022 −0.0680665
\(724\) 27.4889 1.02162
\(725\) −24.0663 −0.893799
\(726\) 24.0015 0.890779
\(727\) 23.0194 0.853743 0.426871 0.904312i \(-0.359616\pi\)
0.426871 + 0.904312i \(0.359616\pi\)
\(728\) −6.62941 −0.245702
\(729\) 28.9564 1.07246
\(730\) 1.69925 0.0628922
\(731\) 12.6871 0.469249
\(732\) 7.19810 0.266049
\(733\) −14.8495 −0.548478 −0.274239 0.961662i \(-0.588426\pi\)
−0.274239 + 0.961662i \(0.588426\pi\)
\(734\) 19.8288 0.731896
\(735\) −0.154535 −0.00570010
\(736\) 15.9808 0.589059
\(737\) −6.45576 −0.237801
\(738\) −13.7734 −0.507007
\(739\) 18.8250 0.692488 0.346244 0.938145i \(-0.387457\pi\)
0.346244 + 0.938145i \(0.387457\pi\)
\(740\) −0.265005 −0.00974179
\(741\) 14.1707 0.520575
\(742\) 52.2374 1.91770
\(743\) 13.5052 0.495458 0.247729 0.968829i \(-0.420316\pi\)
0.247729 + 0.968829i \(0.420316\pi\)
\(744\) 3.04306 0.111564
\(745\) −3.98747 −0.146090
\(746\) −13.2972 −0.486846
\(747\) −7.88655 −0.288554
\(748\) −6.07727 −0.222207
\(749\) 20.4355 0.746697
\(750\) 5.40254 0.197273
\(751\) −24.1608 −0.881640 −0.440820 0.897596i \(-0.645312\pi\)
−0.440820 + 0.897596i \(0.645312\pi\)
\(752\) 5.67476 0.206937
\(753\) 32.0083 1.16645
\(754\) −16.6556 −0.606562
\(755\) −0.359045 −0.0130670
\(756\) 17.8791 0.650257
\(757\) 17.1605 0.623710 0.311855 0.950130i \(-0.399050\pi\)
0.311855 + 0.950130i \(0.399050\pi\)
\(758\) −39.8145 −1.44613
\(759\) 4.56507 0.165702
\(760\) 1.53815 0.0557944
\(761\) −8.22391 −0.298117 −0.149058 0.988828i \(-0.547624\pi\)
−0.149058 + 0.988828i \(0.547624\pi\)
\(762\) 51.9919 1.88347
\(763\) 2.54704 0.0922090
\(764\) 18.7971 0.680056
\(765\) 0.844588 0.0305361
\(766\) 32.2980 1.16698
\(767\) 7.95027 0.287068
\(768\) 29.2046 1.05383
\(769\) 31.8215 1.14751 0.573757 0.819026i \(-0.305485\pi\)
0.573757 + 0.819026i \(0.305485\pi\)
\(770\) 1.22135 0.0440144
\(771\) 7.80872 0.281224
\(772\) −29.2849 −1.05399
\(773\) 36.9921 1.33051 0.665257 0.746614i \(-0.268322\pi\)
0.665257 + 0.746614i \(0.268322\pi\)
\(774\) −5.85855 −0.210581
\(775\) −7.81515 −0.280729
\(776\) 15.3343 0.550468
\(777\) 3.59558 0.128991
\(778\) 4.62468 0.165803
\(779\) −40.0358 −1.43443
\(780\) 0.712520 0.0255123
\(781\) −20.1321 −0.720384
\(782\) 18.3278 0.655399
\(783\) −27.4784 −0.981998
\(784\) 2.53324 0.0904728
\(785\) −4.43779 −0.158392
\(786\) 40.5621 1.44680
\(787\) 39.0593 1.39231 0.696156 0.717890i \(-0.254892\pi\)
0.696156 + 0.717890i \(0.254892\pi\)
\(788\) −23.1749 −0.825570
\(789\) −34.3126 −1.22156
\(790\) 1.12426 0.0399992
\(791\) 28.4578 1.01184
\(792\) −1.71671 −0.0610006
\(793\) 7.82629 0.277920
\(794\) 9.46657 0.335956
\(795\) 3.43450 0.121809
\(796\) 8.67110 0.307339
\(797\) −33.8021 −1.19733 −0.598666 0.800999i \(-0.704302\pi\)
−0.598666 + 0.800999i \(0.704302\pi\)
\(798\) 34.1155 1.20768
\(799\) 4.50883 0.159511
\(800\) −30.5371 −1.07965
\(801\) −4.95487 −0.175072
\(802\) 48.0783 1.69770
\(803\) −5.51268 −0.194538
\(804\) −9.06699 −0.319768
\(805\) −1.41030 −0.0497067
\(806\) −5.40865 −0.190512
\(807\) 3.05867 0.107670
\(808\) 9.25290 0.325516
\(809\) 16.1064 0.566272 0.283136 0.959080i \(-0.408625\pi\)
0.283136 + 0.959080i \(0.408625\pi\)
\(810\) 1.90845 0.0670562
\(811\) −19.2934 −0.677482 −0.338741 0.940880i \(-0.610001\pi\)
−0.338741 + 0.940880i \(0.610001\pi\)
\(812\) −15.3530 −0.538783
\(813\) −7.61765 −0.267163
\(814\) 2.24537 0.0787001
\(815\) −0.301268 −0.0105530
\(816\) 27.3936 0.958967
\(817\) −17.0293 −0.595779
\(818\) −13.0114 −0.454932
\(819\) 4.88603 0.170732
\(820\) −2.01304 −0.0702984
\(821\) 17.1033 0.596908 0.298454 0.954424i \(-0.403529\pi\)
0.298454 + 0.954424i \(0.403529\pi\)
\(822\) 33.7485 1.17712
\(823\) 19.2070 0.669516 0.334758 0.942304i \(-0.391345\pi\)
0.334758 + 0.942304i \(0.391345\pi\)
\(824\) 3.98986 0.138993
\(825\) −8.72324 −0.303704
\(826\) 19.1400 0.665964
\(827\) 8.31783 0.289239 0.144620 0.989487i \(-0.453804\pi\)
0.144620 + 0.989487i \(0.453804\pi\)
\(828\) −3.24048 −0.112614
\(829\) 35.2352 1.22377 0.611884 0.790947i \(-0.290412\pi\)
0.611884 + 0.790947i \(0.290412\pi\)
\(830\) −3.01041 −0.104493
\(831\) 5.47879 0.190057
\(832\) −2.30875 −0.0800413
\(833\) 2.01276 0.0697381
\(834\) −54.1191 −1.87399
\(835\) 3.75386 0.129908
\(836\) 8.15723 0.282124
\(837\) −8.92318 −0.308430
\(838\) 54.2931 1.87552
\(839\) 52.8401 1.82424 0.912122 0.409919i \(-0.134443\pi\)
0.912122 + 0.409919i \(0.134443\pi\)
\(840\) −1.04934 −0.0362056
\(841\) −5.40406 −0.186347
\(842\) 68.8312 2.37208
\(843\) −15.2538 −0.525369
\(844\) −15.7768 −0.543060
\(845\) −2.00156 −0.0688557
\(846\) −2.08205 −0.0715825
\(847\) 24.0551 0.826545
\(848\) −56.3006 −1.93337
\(849\) 7.69849 0.264211
\(850\) −35.0219 −1.20124
\(851\) −2.59275 −0.0888782
\(852\) −28.2752 −0.968692
\(853\) 36.0002 1.23262 0.616311 0.787503i \(-0.288626\pi\)
0.616311 + 0.787503i \(0.288626\pi\)
\(854\) 18.8415 0.644743
\(855\) −1.13365 −0.0387700
\(856\) −10.9643 −0.374751
\(857\) 14.7071 0.502386 0.251193 0.967937i \(-0.419177\pi\)
0.251193 + 0.967937i \(0.419177\pi\)
\(858\) −6.03712 −0.206104
\(859\) −1.52695 −0.0520990 −0.0260495 0.999661i \(-0.508293\pi\)
−0.0260495 + 0.999661i \(0.508293\pi\)
\(860\) −0.856250 −0.0291979
\(861\) 27.3128 0.930818
\(862\) −53.7023 −1.82911
\(863\) −33.0974 −1.12665 −0.563324 0.826236i \(-0.690478\pi\)
−0.563324 + 0.826236i \(0.690478\pi\)
\(864\) −34.8667 −1.18619
\(865\) −3.09865 −0.105357
\(866\) 71.1045 2.41623
\(867\) −2.23305 −0.0758384
\(868\) −4.98563 −0.169223
\(869\) −3.64729 −0.123726
\(870\) −2.63634 −0.0893803
\(871\) −9.85829 −0.334035
\(872\) −1.36657 −0.0462777
\(873\) −11.3017 −0.382505
\(874\) −24.6005 −0.832124
\(875\) 5.41461 0.183047
\(876\) −7.74246 −0.261594
\(877\) 41.9607 1.41691 0.708457 0.705754i \(-0.249392\pi\)
0.708457 + 0.705754i \(0.249392\pi\)
\(878\) 11.6910 0.394553
\(879\) 9.51910 0.321071
\(880\) −1.31635 −0.0443741
\(881\) 12.1140 0.408130 0.204065 0.978957i \(-0.434585\pi\)
0.204065 + 0.978957i \(0.434585\pi\)
\(882\) −0.929439 −0.0312958
\(883\) 6.11719 0.205860 0.102930 0.994689i \(-0.467178\pi\)
0.102930 + 0.994689i \(0.467178\pi\)
\(884\) −9.28032 −0.312131
\(885\) 1.25841 0.0423010
\(886\) 55.6745 1.87042
\(887\) −42.9961 −1.44367 −0.721834 0.692066i \(-0.756701\pi\)
−0.721834 + 0.692066i \(0.756701\pi\)
\(888\) −1.92914 −0.0647376
\(889\) 52.1081 1.74765
\(890\) −1.89135 −0.0633981
\(891\) −6.19136 −0.207418
\(892\) 20.6959 0.692951
\(893\) −6.05199 −0.202522
\(894\) 47.4511 1.58700
\(895\) 2.63698 0.0881445
\(896\) 25.8399 0.863250
\(897\) 6.97111 0.232759
\(898\) 45.5134 1.51880
\(899\) 7.66241 0.255556
\(900\) 6.19213 0.206404
\(901\) −44.7332 −1.49028
\(902\) 17.0563 0.567913
\(903\) 11.6175 0.386608
\(904\) −15.2685 −0.507823
\(905\) 4.73083 0.157258
\(906\) 4.27265 0.141949
\(907\) −46.6362 −1.54853 −0.774265 0.632861i \(-0.781880\pi\)
−0.774265 + 0.632861i \(0.781880\pi\)
\(908\) −16.9009 −0.560877
\(909\) −6.81961 −0.226192
\(910\) 1.86507 0.0618264
\(911\) −4.25752 −0.141058 −0.0705289 0.997510i \(-0.522469\pi\)
−0.0705289 + 0.997510i \(0.522469\pi\)
\(912\) −36.7691 −1.21755
\(913\) 9.76630 0.323217
\(914\) −69.3924 −2.29530
\(915\) 1.23879 0.0409531
\(916\) −19.2610 −0.636400
\(917\) 40.6527 1.34247
\(918\) −39.9873 −1.31978
\(919\) −53.8262 −1.77556 −0.887782 0.460264i \(-0.847755\pi\)
−0.887782 + 0.460264i \(0.847755\pi\)
\(920\) 0.756672 0.0249467
\(921\) −9.88443 −0.325703
\(922\) 67.5673 2.22521
\(923\) −30.7428 −1.01191
\(924\) −5.56494 −0.183073
\(925\) 4.95439 0.162899
\(926\) −73.6025 −2.41873
\(927\) −2.94062 −0.0965826
\(928\) 29.9403 0.982839
\(929\) 4.32903 0.142031 0.0710154 0.997475i \(-0.477376\pi\)
0.0710154 + 0.997475i \(0.477376\pi\)
\(930\) −0.856111 −0.0280730
\(931\) −2.70163 −0.0885425
\(932\) −0.652106 −0.0213604
\(933\) 9.81571 0.321352
\(934\) −42.0778 −1.37683
\(935\) −1.04589 −0.0342044
\(936\) −2.62151 −0.0856866
\(937\) 9.44016 0.308397 0.154198 0.988040i \(-0.450721\pi\)
0.154198 + 0.988040i \(0.450721\pi\)
\(938\) −23.7335 −0.774925
\(939\) 33.5919 1.09623
\(940\) −0.304300 −0.00992518
\(941\) 54.0288 1.76129 0.880644 0.473779i \(-0.157110\pi\)
0.880644 + 0.473779i \(0.157110\pi\)
\(942\) 52.8100 1.72064
\(943\) −19.6951 −0.641360
\(944\) −20.6287 −0.671408
\(945\) 3.07698 0.100094
\(946\) 7.25493 0.235878
\(947\) −13.1895 −0.428602 −0.214301 0.976768i \(-0.568747\pi\)
−0.214301 + 0.976768i \(0.568747\pi\)
\(948\) −5.12255 −0.166373
\(949\) −8.41817 −0.273265
\(950\) 47.0082 1.52515
\(951\) 0.313604 0.0101693
\(952\) 13.6673 0.442959
\(953\) 40.4313 1.30970 0.654850 0.755759i \(-0.272732\pi\)
0.654850 + 0.755759i \(0.272732\pi\)
\(954\) 20.6566 0.668781
\(955\) 3.23497 0.104681
\(956\) −32.1838 −1.04090
\(957\) 8.55276 0.276471
\(958\) 68.4180 2.21049
\(959\) 33.8240 1.09223
\(960\) −0.365441 −0.0117945
\(961\) −28.5118 −0.919734
\(962\) 3.42880 0.110549
\(963\) 8.08093 0.260404
\(964\) −1.60882 −0.0518166
\(965\) −5.03992 −0.162241
\(966\) 16.7827 0.539974
\(967\) −16.8395 −0.541522 −0.270761 0.962647i \(-0.587275\pi\)
−0.270761 + 0.962647i \(0.587275\pi\)
\(968\) −12.9063 −0.414825
\(969\) −29.2146 −0.938507
\(970\) −4.31403 −0.138515
\(971\) 13.1838 0.423087 0.211544 0.977369i \(-0.432151\pi\)
0.211544 + 0.977369i \(0.432151\pi\)
\(972\) 12.3631 0.396545
\(973\) −54.2401 −1.73886
\(974\) 24.9498 0.799444
\(975\) −13.3209 −0.426609
\(976\) −20.3070 −0.650013
\(977\) −47.5642 −1.52171 −0.760856 0.648921i \(-0.775221\pi\)
−0.760856 + 0.648921i \(0.775221\pi\)
\(978\) 3.58511 0.114639
\(979\) 6.13586 0.196103
\(980\) −0.135841 −0.00433928
\(981\) 1.00719 0.0321571
\(982\) −53.8976 −1.71994
\(983\) −47.5978 −1.51813 −0.759067 0.651013i \(-0.774344\pi\)
−0.759067 + 0.651013i \(0.774344\pi\)
\(984\) −14.6542 −0.467158
\(985\) −3.98838 −0.127080
\(986\) 34.3374 1.09353
\(987\) 4.12872 0.131419
\(988\) 12.4565 0.396295
\(989\) −8.37734 −0.266384
\(990\) 0.482966 0.0153497
\(991\) 12.2593 0.389429 0.194715 0.980860i \(-0.437622\pi\)
0.194715 + 0.980860i \(0.437622\pi\)
\(992\) 9.72265 0.308695
\(993\) −40.5969 −1.28830
\(994\) −74.0122 −2.34752
\(995\) 1.49229 0.0473088
\(996\) 13.7166 0.434627
\(997\) 21.3222 0.675281 0.337641 0.941275i \(-0.390371\pi\)
0.337641 + 0.941275i \(0.390371\pi\)
\(998\) 30.4724 0.964587
\(999\) 5.65683 0.178974
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 \(a_p\))