Properties

Label 6001.2.a.b.1.9
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.39336 q^{2}\) \(+0.882221 q^{3}\) \(+3.72817 q^{4}\) \(+0.123030 q^{5}\) \(-2.11147 q^{6}\) \(-1.77301 q^{7}\) \(-4.13613 q^{8}\) \(-2.22169 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.39336 q^{2}\) \(+0.882221 q^{3}\) \(+3.72817 q^{4}\) \(+0.123030 q^{5}\) \(-2.11147 q^{6}\) \(-1.77301 q^{7}\) \(-4.13613 q^{8}\) \(-2.22169 q^{9}\) \(-0.294456 q^{10}\) \(+1.33826 q^{11}\) \(+3.28907 q^{12}\) \(+1.60065 q^{13}\) \(+4.24346 q^{14}\) \(+0.108540 q^{15}\) \(+2.44290 q^{16}\) \(+1.00000 q^{17}\) \(+5.31729 q^{18}\) \(+5.76795 q^{19}\) \(+0.458678 q^{20}\) \(-1.56419 q^{21}\) \(-3.20294 q^{22}\) \(+3.19803 q^{23}\) \(-3.64898 q^{24}\) \(-4.98486 q^{25}\) \(-3.83093 q^{26}\) \(-4.60668 q^{27}\) \(-6.61009 q^{28}\) \(-1.74173 q^{29}\) \(-0.259775 q^{30}\) \(+1.64454 q^{31}\) \(+2.42552 q^{32}\) \(+1.18064 q^{33}\) \(-2.39336 q^{34}\) \(-0.218135 q^{35}\) \(-8.28282 q^{36}\) \(+5.32254 q^{37}\) \(-13.8048 q^{38}\) \(+1.41213 q^{39}\) \(-0.508869 q^{40}\) \(-6.97762 q^{41}\) \(+3.74367 q^{42}\) \(-5.34754 q^{43}\) \(+4.98926 q^{44}\) \(-0.273335 q^{45}\) \(-7.65404 q^{46}\) \(-9.93182 q^{47}\) \(+2.15518 q^{48}\) \(-3.85642 q^{49}\) \(+11.9306 q^{50}\) \(+0.882221 q^{51}\) \(+5.96750 q^{52}\) \(-12.9838 q^{53}\) \(+11.0254 q^{54}\) \(+0.164647 q^{55}\) \(+7.33341 q^{56}\) \(+5.08861 q^{57}\) \(+4.16859 q^{58}\) \(+4.56078 q^{59}\) \(+0.404655 q^{60}\) \(+2.77929 q^{61}\) \(-3.93598 q^{62}\) \(+3.93908 q^{63}\) \(-10.6909 q^{64}\) \(+0.196929 q^{65}\) \(-2.82570 q^{66}\) \(+13.4500 q^{67}\) \(+3.72817 q^{68}\) \(+2.82137 q^{69}\) \(+0.522074 q^{70}\) \(+8.33793 q^{71}\) \(+9.18917 q^{72}\) \(-3.50164 q^{73}\) \(-12.7387 q^{74}\) \(-4.39775 q^{75}\) \(+21.5039 q^{76}\) \(-2.37275 q^{77}\) \(-3.37973 q^{78}\) \(-15.4312 q^{79}\) \(+0.300551 q^{80}\) \(+2.60095 q^{81}\) \(+16.7000 q^{82}\) \(+8.57409 q^{83}\) \(-5.83156 q^{84}\) \(+0.123030 q^{85}\) \(+12.7986 q^{86}\) \(-1.53659 q^{87}\) \(-5.53521 q^{88}\) \(-2.14066 q^{89}\) \(+0.654188 q^{90}\) \(-2.83798 q^{91}\) \(+11.9228 q^{92}\) \(+1.45085 q^{93}\) \(+23.7704 q^{94}\) \(+0.709633 q^{95}\) \(+2.13984 q^{96}\) \(+9.16315 q^{97}\) \(+9.22980 q^{98}\) \(-2.97319 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39336 −1.69236 −0.846180 0.532897i \(-0.821103\pi\)
−0.846180 + 0.532897i \(0.821103\pi\)
\(3\) 0.882221 0.509351 0.254675 0.967027i \(-0.418031\pi\)
0.254675 + 0.967027i \(0.418031\pi\)
\(4\) 3.72817 1.86408
\(5\) 0.123030 0.0550208 0.0275104 0.999622i \(-0.491242\pi\)
0.0275104 + 0.999622i \(0.491242\pi\)
\(6\) −2.11147 −0.862005
\(7\) −1.77301 −0.670136 −0.335068 0.942194i \(-0.608759\pi\)
−0.335068 + 0.942194i \(0.608759\pi\)
\(8\) −4.13613 −1.46234
\(9\) −2.22169 −0.740562
\(10\) −0.294456 −0.0931151
\(11\) 1.33826 0.403500 0.201750 0.979437i \(-0.435337\pi\)
0.201750 + 0.979437i \(0.435337\pi\)
\(12\) 3.28907 0.949472
\(13\) 1.60065 0.443941 0.221970 0.975053i \(-0.428751\pi\)
0.221970 + 0.975053i \(0.428751\pi\)
\(14\) 4.24346 1.13411
\(15\) 0.108540 0.0280249
\(16\) 2.44290 0.610725
\(17\) 1.00000 0.242536
\(18\) 5.31729 1.25330
\(19\) 5.76795 1.32326 0.661629 0.749831i \(-0.269865\pi\)
0.661629 + 0.749831i \(0.269865\pi\)
\(20\) 0.458678 0.102563
\(21\) −1.56419 −0.341334
\(22\) −3.20294 −0.682868
\(23\) 3.19803 0.666836 0.333418 0.942779i \(-0.391798\pi\)
0.333418 + 0.942779i \(0.391798\pi\)
\(24\) −3.64898 −0.744844
\(25\) −4.98486 −0.996973
\(26\) −3.83093 −0.751308
\(27\) −4.60668 −0.886556
\(28\) −6.61009 −1.24919
\(29\) −1.74173 −0.323432 −0.161716 0.986837i \(-0.551703\pi\)
−0.161716 + 0.986837i \(0.551703\pi\)
\(30\) −0.259775 −0.0474282
\(31\) 1.64454 0.295369 0.147684 0.989035i \(-0.452818\pi\)
0.147684 + 0.989035i \(0.452818\pi\)
\(32\) 2.42552 0.428775
\(33\) 1.18064 0.205523
\(34\) −2.39336 −0.410458
\(35\) −0.218135 −0.0368715
\(36\) −8.28282 −1.38047
\(37\) 5.32254 0.875020 0.437510 0.899214i \(-0.355861\pi\)
0.437510 + 0.899214i \(0.355861\pi\)
\(38\) −13.8048 −2.23943
\(39\) 1.41213 0.226121
\(40\) −0.508869 −0.0804593
\(41\) −6.97762 −1.08972 −0.544861 0.838527i \(-0.683417\pi\)
−0.544861 + 0.838527i \(0.683417\pi\)
\(42\) 3.74367 0.577661
\(43\) −5.34754 −0.815493 −0.407746 0.913095i \(-0.633685\pi\)
−0.407746 + 0.913095i \(0.633685\pi\)
\(44\) 4.98926 0.752159
\(45\) −0.273335 −0.0407463
\(46\) −7.65404 −1.12853
\(47\) −9.93182 −1.44870 −0.724352 0.689430i \(-0.757861\pi\)
−0.724352 + 0.689430i \(0.757861\pi\)
\(48\) 2.15518 0.311073
\(49\) −3.85642 −0.550917
\(50\) 11.9306 1.68724
\(51\) 0.882221 0.123536
\(52\) 5.96750 0.827543
\(53\) −12.9838 −1.78346 −0.891729 0.452571i \(-0.850507\pi\)
−0.891729 + 0.452571i \(0.850507\pi\)
\(54\) 11.0254 1.50037
\(55\) 0.164647 0.0222009
\(56\) 7.33341 0.979968
\(57\) 5.08861 0.674003
\(58\) 4.16859 0.547363
\(59\) 4.56078 0.593763 0.296881 0.954914i \(-0.404053\pi\)
0.296881 + 0.954914i \(0.404053\pi\)
\(60\) 0.404655 0.0522408
\(61\) 2.77929 0.355852 0.177926 0.984044i \(-0.443061\pi\)
0.177926 + 0.984044i \(0.443061\pi\)
\(62\) −3.93598 −0.499870
\(63\) 3.93908 0.496278
\(64\) −10.6909 −1.33637
\(65\) 0.196929 0.0244260
\(66\) −2.82570 −0.347819
\(67\) 13.4500 1.64317 0.821587 0.570083i \(-0.193089\pi\)
0.821587 + 0.570083i \(0.193089\pi\)
\(68\) 3.72817 0.452107
\(69\) 2.82137 0.339653
\(70\) 0.522074 0.0623998
\(71\) 8.33793 0.989530 0.494765 0.869027i \(-0.335254\pi\)
0.494765 + 0.869027i \(0.335254\pi\)
\(72\) 9.18917 1.08295
\(73\) −3.50164 −0.409836 −0.204918 0.978779i \(-0.565693\pi\)
−0.204918 + 0.978779i \(0.565693\pi\)
\(74\) −12.7387 −1.48085
\(75\) −4.39775 −0.507809
\(76\) 21.5039 2.46667
\(77\) −2.37275 −0.270400
\(78\) −3.37973 −0.382679
\(79\) −15.4312 −1.73615 −0.868075 0.496434i \(-0.834643\pi\)
−0.868075 + 0.496434i \(0.834643\pi\)
\(80\) 0.300551 0.0336026
\(81\) 2.60095 0.288994
\(82\) 16.7000 1.84420
\(83\) 8.57409 0.941129 0.470564 0.882366i \(-0.344050\pi\)
0.470564 + 0.882366i \(0.344050\pi\)
\(84\) −5.83156 −0.636276
\(85\) 0.123030 0.0133445
\(86\) 12.7986 1.38011
\(87\) −1.53659 −0.164740
\(88\) −5.53521 −0.590055
\(89\) −2.14066 −0.226910 −0.113455 0.993543i \(-0.536192\pi\)
−0.113455 + 0.993543i \(0.536192\pi\)
\(90\) 0.654188 0.0689575
\(91\) −2.83798 −0.297501
\(92\) 11.9228 1.24304
\(93\) 1.45085 0.150446
\(94\) 23.7704 2.45173
\(95\) 0.709633 0.0728068
\(96\) 2.13984 0.218397
\(97\) 9.16315 0.930377 0.465188 0.885212i \(-0.345987\pi\)
0.465188 + 0.885212i \(0.345987\pi\)
\(98\) 9.22980 0.932351
\(99\) −2.97319 −0.298817
\(100\) −18.5844 −1.85844
\(101\) 15.3396 1.52634 0.763172 0.646195i \(-0.223641\pi\)
0.763172 + 0.646195i \(0.223641\pi\)
\(102\) −2.11147 −0.209067
\(103\) 1.98584 0.195671 0.0978353 0.995203i \(-0.468808\pi\)
0.0978353 + 0.995203i \(0.468808\pi\)
\(104\) −6.62049 −0.649193
\(105\) −0.192443 −0.0187805
\(106\) 31.0748 3.01825
\(107\) −15.6668 −1.51457 −0.757284 0.653086i \(-0.773474\pi\)
−0.757284 + 0.653086i \(0.773474\pi\)
\(108\) −17.1745 −1.65262
\(109\) −9.18696 −0.879952 −0.439976 0.898010i \(-0.645013\pi\)
−0.439976 + 0.898010i \(0.645013\pi\)
\(110\) −0.394058 −0.0375720
\(111\) 4.69565 0.445692
\(112\) −4.33130 −0.409269
\(113\) 7.03963 0.662233 0.331117 0.943590i \(-0.392575\pi\)
0.331117 + 0.943590i \(0.392575\pi\)
\(114\) −12.1789 −1.14066
\(115\) 0.393455 0.0366899
\(116\) −6.49348 −0.602904
\(117\) −3.55614 −0.328766
\(118\) −10.9156 −1.00486
\(119\) −1.77301 −0.162532
\(120\) −0.448935 −0.0409820
\(121\) −9.20906 −0.837187
\(122\) −6.65184 −0.602229
\(123\) −6.15580 −0.555050
\(124\) 6.13113 0.550592
\(125\) −1.22844 −0.109875
\(126\) −9.42763 −0.839880
\(127\) 19.3547 1.71746 0.858728 0.512432i \(-0.171255\pi\)
0.858728 + 0.512432i \(0.171255\pi\)
\(128\) 20.7362 1.83284
\(129\) −4.71772 −0.415372
\(130\) −0.471321 −0.0413376
\(131\) −1.90329 −0.166291 −0.0831454 0.996537i \(-0.526497\pi\)
−0.0831454 + 0.996537i \(0.526497\pi\)
\(132\) 4.40163 0.383112
\(133\) −10.2267 −0.886764
\(134\) −32.1906 −2.78084
\(135\) −0.566762 −0.0487791
\(136\) −4.13613 −0.354670
\(137\) 5.40409 0.461702 0.230851 0.972989i \(-0.425849\pi\)
0.230851 + 0.972989i \(0.425849\pi\)
\(138\) −6.75256 −0.574816
\(139\) 14.0663 1.19309 0.596545 0.802579i \(-0.296540\pi\)
0.596545 + 0.802579i \(0.296540\pi\)
\(140\) −0.813242 −0.0687315
\(141\) −8.76206 −0.737898
\(142\) −19.9557 −1.67464
\(143\) 2.14209 0.179130
\(144\) −5.42736 −0.452280
\(145\) −0.214286 −0.0177955
\(146\) 8.38068 0.693590
\(147\) −3.40222 −0.280610
\(148\) 19.8433 1.63111
\(149\) 0.755096 0.0618598 0.0309299 0.999522i \(-0.490153\pi\)
0.0309299 + 0.999522i \(0.490153\pi\)
\(150\) 10.5254 0.859395
\(151\) 1.46087 0.118884 0.0594419 0.998232i \(-0.481068\pi\)
0.0594419 + 0.998232i \(0.481068\pi\)
\(152\) −23.8570 −1.93506
\(153\) −2.22169 −0.179613
\(154\) 5.67885 0.457615
\(155\) 0.202329 0.0162514
\(156\) 5.26465 0.421509
\(157\) −8.91025 −0.711116 −0.355558 0.934654i \(-0.615709\pi\)
−0.355558 + 0.934654i \(0.615709\pi\)
\(158\) 36.9325 2.93819
\(159\) −11.4546 −0.908405
\(160\) 0.298412 0.0235915
\(161\) −5.67016 −0.446871
\(162\) −6.22500 −0.489082
\(163\) 20.4245 1.59977 0.799886 0.600152i \(-0.204893\pi\)
0.799886 + 0.600152i \(0.204893\pi\)
\(164\) −26.0137 −2.03133
\(165\) 0.145255 0.0113081
\(166\) −20.5209 −1.59273
\(167\) −8.85599 −0.685297 −0.342649 0.939464i \(-0.611324\pi\)
−0.342649 + 0.939464i \(0.611324\pi\)
\(168\) 6.46969 0.499147
\(169\) −10.4379 −0.802917
\(170\) −0.294456 −0.0225837
\(171\) −12.8146 −0.979955
\(172\) −19.9365 −1.52015
\(173\) −11.5527 −0.878332 −0.439166 0.898406i \(-0.644726\pi\)
−0.439166 + 0.898406i \(0.644726\pi\)
\(174\) 3.67762 0.278800
\(175\) 8.83823 0.668108
\(176\) 3.26923 0.246428
\(177\) 4.02361 0.302433
\(178\) 5.12337 0.384013
\(179\) −19.9777 −1.49320 −0.746600 0.665273i \(-0.768315\pi\)
−0.746600 + 0.665273i \(0.768315\pi\)
\(180\) −1.01904 −0.0759546
\(181\) −5.00580 −0.372078 −0.186039 0.982542i \(-0.559565\pi\)
−0.186039 + 0.982542i \(0.559565\pi\)
\(182\) 6.79230 0.503479
\(183\) 2.45195 0.181253
\(184\) −13.2275 −0.975142
\(185\) 0.654833 0.0481443
\(186\) −3.47241 −0.254609
\(187\) 1.33826 0.0978632
\(188\) −37.0275 −2.70051
\(189\) 8.16771 0.594114
\(190\) −1.69841 −0.123215
\(191\) −8.04155 −0.581866 −0.290933 0.956743i \(-0.593966\pi\)
−0.290933 + 0.956743i \(0.593966\pi\)
\(192\) −9.43176 −0.680679
\(193\) −1.37559 −0.0990169 −0.0495084 0.998774i \(-0.515765\pi\)
−0.0495084 + 0.998774i \(0.515765\pi\)
\(194\) −21.9307 −1.57453
\(195\) 0.173735 0.0124414
\(196\) −14.3774 −1.02696
\(197\) −22.8788 −1.63005 −0.815024 0.579427i \(-0.803276\pi\)
−0.815024 + 0.579427i \(0.803276\pi\)
\(198\) 7.11592 0.505706
\(199\) 0.0299027 0.00211974 0.00105987 0.999999i \(-0.499663\pi\)
0.00105987 + 0.999999i \(0.499663\pi\)
\(200\) 20.6180 1.45791
\(201\) 11.8658 0.836952
\(202\) −36.7131 −2.58313
\(203\) 3.08812 0.216743
\(204\) 3.28907 0.230281
\(205\) −0.858459 −0.0599574
\(206\) −4.75283 −0.331145
\(207\) −7.10503 −0.493834
\(208\) 3.91023 0.271126
\(209\) 7.71902 0.533935
\(210\) 0.460585 0.0317834
\(211\) −22.8389 −1.57230 −0.786148 0.618039i \(-0.787928\pi\)
−0.786148 + 0.618039i \(0.787928\pi\)
\(212\) −48.4057 −3.32451
\(213\) 7.35590 0.504018
\(214\) 37.4963 2.56319
\(215\) −0.657910 −0.0448691
\(216\) 19.0538 1.29645
\(217\) −2.91580 −0.197937
\(218\) 21.9877 1.48920
\(219\) −3.08922 −0.208750
\(220\) 0.613830 0.0413844
\(221\) 1.60065 0.107671
\(222\) −11.2384 −0.754271
\(223\) −3.93567 −0.263552 −0.131776 0.991280i \(-0.542068\pi\)
−0.131776 + 0.991280i \(0.542068\pi\)
\(224\) −4.30047 −0.287338
\(225\) 11.0748 0.738320
\(226\) −16.8484 −1.12074
\(227\) 23.1926 1.53935 0.769674 0.638437i \(-0.220419\pi\)
0.769674 + 0.638437i \(0.220419\pi\)
\(228\) 18.9712 1.25640
\(229\) 8.96577 0.592475 0.296237 0.955114i \(-0.404268\pi\)
0.296237 + 0.955114i \(0.404268\pi\)
\(230\) −0.941680 −0.0620925
\(231\) −2.09329 −0.137729
\(232\) 7.20403 0.472968
\(233\) −27.1240 −1.77695 −0.888477 0.458920i \(-0.848236\pi\)
−0.888477 + 0.458920i \(0.848236\pi\)
\(234\) 8.51113 0.556390
\(235\) −1.22191 −0.0797089
\(236\) 17.0033 1.10682
\(237\) −13.6138 −0.884309
\(238\) 4.24346 0.275063
\(239\) −5.21028 −0.337025 −0.168513 0.985700i \(-0.553896\pi\)
−0.168513 + 0.985700i \(0.553896\pi\)
\(240\) 0.265152 0.0171155
\(241\) 0.981420 0.0632188 0.0316094 0.999500i \(-0.489937\pi\)
0.0316094 + 0.999500i \(0.489937\pi\)
\(242\) 22.0406 1.41682
\(243\) 16.1147 1.03376
\(244\) 10.3617 0.663337
\(245\) −0.474457 −0.0303119
\(246\) 14.7330 0.939345
\(247\) 9.23248 0.587448
\(248\) −6.80204 −0.431930
\(249\) 7.56424 0.479364
\(250\) 2.94010 0.185948
\(251\) −7.63378 −0.481840 −0.240920 0.970545i \(-0.577449\pi\)
−0.240920 + 0.970545i \(0.577449\pi\)
\(252\) 14.6856 0.925103
\(253\) 4.27980 0.269069
\(254\) −46.3229 −2.90655
\(255\) 0.108540 0.00679704
\(256\) −28.2473 −1.76546
\(257\) −17.6713 −1.10230 −0.551152 0.834405i \(-0.685812\pi\)
−0.551152 + 0.834405i \(0.685812\pi\)
\(258\) 11.2912 0.702959
\(259\) −9.43693 −0.586382
\(260\) 0.734183 0.0455321
\(261\) 3.86958 0.239521
\(262\) 4.55525 0.281424
\(263\) 2.88392 0.177830 0.0889151 0.996039i \(-0.471660\pi\)
0.0889151 + 0.996039i \(0.471660\pi\)
\(264\) −4.88328 −0.300545
\(265\) −1.59740 −0.0981273
\(266\) 24.4761 1.50072
\(267\) −1.88854 −0.115577
\(268\) 50.1437 3.06301
\(269\) 11.6444 0.709972 0.354986 0.934872i \(-0.384486\pi\)
0.354986 + 0.934872i \(0.384486\pi\)
\(270\) 1.35646 0.0825518
\(271\) −10.9744 −0.666648 −0.333324 0.942812i \(-0.608170\pi\)
−0.333324 + 0.942812i \(0.608170\pi\)
\(272\) 2.44290 0.148123
\(273\) −2.50372 −0.151532
\(274\) −12.9339 −0.781367
\(275\) −6.67104 −0.402279
\(276\) 10.5186 0.633143
\(277\) 12.4385 0.747354 0.373677 0.927559i \(-0.378097\pi\)
0.373677 + 0.927559i \(0.378097\pi\)
\(278\) −33.6658 −2.01914
\(279\) −3.65366 −0.218739
\(280\) 0.902232 0.0539187
\(281\) −27.1118 −1.61735 −0.808676 0.588254i \(-0.799816\pi\)
−0.808676 + 0.588254i \(0.799816\pi\)
\(282\) 20.9708 1.24879
\(283\) −4.89908 −0.291220 −0.145610 0.989342i \(-0.546514\pi\)
−0.145610 + 0.989342i \(0.546514\pi\)
\(284\) 31.0852 1.84457
\(285\) 0.626053 0.0370842
\(286\) −5.12678 −0.303153
\(287\) 12.3714 0.730262
\(288\) −5.38874 −0.317534
\(289\) 1.00000 0.0588235
\(290\) 0.512864 0.0301164
\(291\) 8.08392 0.473888
\(292\) −13.0547 −0.763968
\(293\) −13.0381 −0.761695 −0.380848 0.924638i \(-0.624368\pi\)
−0.380848 + 0.924638i \(0.624368\pi\)
\(294\) 8.14272 0.474893
\(295\) 0.561114 0.0326693
\(296\) −22.0147 −1.27958
\(297\) −6.16494 −0.357726
\(298\) −1.80721 −0.104689
\(299\) 5.11894 0.296036
\(300\) −16.3956 −0.946598
\(301\) 9.48127 0.546491
\(302\) −3.49638 −0.201194
\(303\) 13.5329 0.777445
\(304\) 14.0905 0.808147
\(305\) 0.341937 0.0195793
\(306\) 5.31729 0.303969
\(307\) −12.9970 −0.741779 −0.370889 0.928677i \(-0.620947\pi\)
−0.370889 + 0.928677i \(0.620947\pi\)
\(308\) −8.84602 −0.504049
\(309\) 1.75195 0.0996649
\(310\) −0.484245 −0.0275033
\(311\) 24.7999 1.40627 0.703135 0.711056i \(-0.251783\pi\)
0.703135 + 0.711056i \(0.251783\pi\)
\(312\) −5.84074 −0.330667
\(313\) 27.0158 1.52702 0.763511 0.645794i \(-0.223474\pi\)
0.763511 + 0.645794i \(0.223474\pi\)
\(314\) 21.3254 1.20346
\(315\) 0.484626 0.0273056
\(316\) −57.5302 −3.23633
\(317\) −1.28434 −0.0721359 −0.0360680 0.999349i \(-0.511483\pi\)
−0.0360680 + 0.999349i \(0.511483\pi\)
\(318\) 27.4149 1.53735
\(319\) −2.33089 −0.130505
\(320\) −1.31531 −0.0735280
\(321\) −13.8216 −0.771446
\(322\) 13.5707 0.756267
\(323\) 5.76795 0.320937
\(324\) 9.69676 0.538709
\(325\) −7.97903 −0.442597
\(326\) −48.8832 −2.70739
\(327\) −8.10493 −0.448204
\(328\) 28.8603 1.59354
\(329\) 17.6093 0.970830
\(330\) −0.347647 −0.0191373
\(331\) 13.5904 0.746996 0.373498 0.927631i \(-0.378158\pi\)
0.373498 + 0.927631i \(0.378158\pi\)
\(332\) 31.9656 1.75434
\(333\) −11.8250 −0.648006
\(334\) 21.1956 1.15977
\(335\) 1.65475 0.0904088
\(336\) −3.82116 −0.208461
\(337\) −27.0928 −1.47584 −0.737921 0.674887i \(-0.764192\pi\)
−0.737921 + 0.674887i \(0.764192\pi\)
\(338\) 24.9817 1.35882
\(339\) 6.21051 0.337309
\(340\) 0.458678 0.0248753
\(341\) 2.20082 0.119181
\(342\) 30.6699 1.65844
\(343\) 19.2486 1.03933
\(344\) 22.1181 1.19253
\(345\) 0.347115 0.0186880
\(346\) 27.6496 1.48645
\(347\) −12.7237 −0.683044 −0.341522 0.939874i \(-0.610942\pi\)
−0.341522 + 0.939874i \(0.610942\pi\)
\(348\) −5.72868 −0.307090
\(349\) 10.8860 0.582712 0.291356 0.956615i \(-0.405894\pi\)
0.291356 + 0.956615i \(0.405894\pi\)
\(350\) −21.1531 −1.13068
\(351\) −7.37369 −0.393578
\(352\) 3.24597 0.173011
\(353\) 1.00000 0.0532246
\(354\) −9.62995 −0.511826
\(355\) 1.02582 0.0544448
\(356\) −7.98075 −0.422979
\(357\) −1.56419 −0.0827857
\(358\) 47.8137 2.52703
\(359\) −26.3020 −1.38817 −0.694084 0.719894i \(-0.744190\pi\)
−0.694084 + 0.719894i \(0.744190\pi\)
\(360\) 1.13055 0.0595851
\(361\) 14.2693 0.751014
\(362\) 11.9807 0.629690
\(363\) −8.12443 −0.426422
\(364\) −10.5805 −0.554566
\(365\) −0.430808 −0.0225495
\(366\) −5.86839 −0.306746
\(367\) −14.6838 −0.766489 −0.383245 0.923647i \(-0.625193\pi\)
−0.383245 + 0.923647i \(0.625193\pi\)
\(368\) 7.81248 0.407254
\(369\) 15.5021 0.807006
\(370\) −1.56725 −0.0814775
\(371\) 23.0204 1.19516
\(372\) 5.40901 0.280444
\(373\) 11.8096 0.611476 0.305738 0.952116i \(-0.401097\pi\)
0.305738 + 0.952116i \(0.401097\pi\)
\(374\) −3.20294 −0.165620
\(375\) −1.08376 −0.0559650
\(376\) 41.0792 2.11850
\(377\) −2.78791 −0.143585
\(378\) −19.5483 −1.00545
\(379\) −0.242188 −0.0124404 −0.00622019 0.999981i \(-0.501980\pi\)
−0.00622019 + 0.999981i \(0.501980\pi\)
\(380\) 2.64563 0.135718
\(381\) 17.0752 0.874787
\(382\) 19.2463 0.984728
\(383\) −11.2947 −0.577131 −0.288565 0.957460i \(-0.593178\pi\)
−0.288565 + 0.957460i \(0.593178\pi\)
\(384\) 18.2939 0.933558
\(385\) −0.291921 −0.0148777
\(386\) 3.29227 0.167572
\(387\) 11.8806 0.603923
\(388\) 34.1618 1.73430
\(389\) −7.25377 −0.367781 −0.183890 0.982947i \(-0.558869\pi\)
−0.183890 + 0.982947i \(0.558869\pi\)
\(390\) −0.415809 −0.0210553
\(391\) 3.19803 0.161732
\(392\) 15.9506 0.805629
\(393\) −1.67912 −0.0847003
\(394\) 54.7572 2.75863
\(395\) −1.89851 −0.0955244
\(396\) −11.0846 −0.557020
\(397\) −30.2885 −1.52014 −0.760068 0.649843i \(-0.774834\pi\)
−0.760068 + 0.649843i \(0.774834\pi\)
\(398\) −0.0715679 −0.00358737
\(399\) −9.02218 −0.451674
\(400\) −12.1775 −0.608876
\(401\) −34.4278 −1.71924 −0.859622 0.510930i \(-0.829301\pi\)
−0.859622 + 0.510930i \(0.829301\pi\)
\(402\) −28.3992 −1.41642
\(403\) 2.63234 0.131126
\(404\) 57.1885 2.84523
\(405\) 0.319995 0.0159007
\(406\) −7.39098 −0.366808
\(407\) 7.12293 0.353071
\(408\) −3.64898 −0.180651
\(409\) 25.4054 1.25622 0.628108 0.778126i \(-0.283830\pi\)
0.628108 + 0.778126i \(0.283830\pi\)
\(410\) 2.05460 0.101469
\(411\) 4.76760 0.235168
\(412\) 7.40354 0.364746
\(413\) −8.08632 −0.397902
\(414\) 17.0049 0.835744
\(415\) 1.05487 0.0517817
\(416\) 3.88240 0.190351
\(417\) 12.4096 0.607702
\(418\) −18.4744 −0.903611
\(419\) 1.53694 0.0750843 0.0375421 0.999295i \(-0.488047\pi\)
0.0375421 + 0.999295i \(0.488047\pi\)
\(420\) −0.717459 −0.0350084
\(421\) −14.0713 −0.685793 −0.342897 0.939373i \(-0.611408\pi\)
−0.342897 + 0.939373i \(0.611408\pi\)
\(422\) 54.6617 2.66089
\(423\) 22.0654 1.07286
\(424\) 53.7025 2.60802
\(425\) −4.98486 −0.241801
\(426\) −17.6053 −0.852980
\(427\) −4.92772 −0.238469
\(428\) −58.4085 −2.82328
\(429\) 1.88979 0.0912401
\(430\) 1.57461 0.0759347
\(431\) −24.5700 −1.18349 −0.591747 0.806124i \(-0.701562\pi\)
−0.591747 + 0.806124i \(0.701562\pi\)
\(432\) −11.2537 −0.541442
\(433\) −1.27391 −0.0612200 −0.0306100 0.999531i \(-0.509745\pi\)
−0.0306100 + 0.999531i \(0.509745\pi\)
\(434\) 6.97855 0.334981
\(435\) −0.189048 −0.00906414
\(436\) −34.2505 −1.64030
\(437\) 18.4461 0.882397
\(438\) 7.39361 0.353280
\(439\) 24.6898 1.17838 0.589190 0.807995i \(-0.299447\pi\)
0.589190 + 0.807995i \(0.299447\pi\)
\(440\) −0.680999 −0.0324653
\(441\) 8.56776 0.407988
\(442\) −3.83093 −0.182219
\(443\) 4.09156 0.194396 0.0971979 0.995265i \(-0.469012\pi\)
0.0971979 + 0.995265i \(0.469012\pi\)
\(444\) 17.5062 0.830807
\(445\) −0.263366 −0.0124848
\(446\) 9.41948 0.446025
\(447\) 0.666161 0.0315083
\(448\) 18.9552 0.895548
\(449\) 3.25229 0.153485 0.0767426 0.997051i \(-0.475548\pi\)
0.0767426 + 0.997051i \(0.475548\pi\)
\(450\) −26.5060 −1.24950
\(451\) −9.33787 −0.439703
\(452\) 26.2449 1.23446
\(453\) 1.28881 0.0605535
\(454\) −55.5083 −2.60513
\(455\) −0.349157 −0.0163687
\(456\) −21.0471 −0.985622
\(457\) 33.9759 1.58933 0.794664 0.607050i \(-0.207647\pi\)
0.794664 + 0.607050i \(0.207647\pi\)
\(458\) −21.4583 −1.00268
\(459\) −4.60668 −0.215021
\(460\) 1.46687 0.0683930
\(461\) −38.8339 −1.80867 −0.904337 0.426819i \(-0.859634\pi\)
−0.904337 + 0.426819i \(0.859634\pi\)
\(462\) 5.01000 0.233086
\(463\) 8.43322 0.391925 0.195963 0.980611i \(-0.437217\pi\)
0.195963 + 0.980611i \(0.437217\pi\)
\(464\) −4.25488 −0.197528
\(465\) 0.178499 0.00827767
\(466\) 64.9176 3.00725
\(467\) −24.4175 −1.12991 −0.564954 0.825122i \(-0.691106\pi\)
−0.564954 + 0.825122i \(0.691106\pi\)
\(468\) −13.2579 −0.612847
\(469\) −23.8470 −1.10115
\(470\) 2.92448 0.134896
\(471\) −7.86081 −0.362207
\(472\) −18.8639 −0.868284
\(473\) −7.15640 −0.329052
\(474\) 32.5826 1.49657
\(475\) −28.7525 −1.31925
\(476\) −6.61009 −0.302973
\(477\) 28.8458 1.32076
\(478\) 12.4701 0.570368
\(479\) 23.3105 1.06509 0.532543 0.846403i \(-0.321237\pi\)
0.532543 + 0.846403i \(0.321237\pi\)
\(480\) 0.263265 0.0120164
\(481\) 8.51952 0.388457
\(482\) −2.34889 −0.106989
\(483\) −5.00234 −0.227614
\(484\) −34.3329 −1.56059
\(485\) 1.12735 0.0511901
\(486\) −38.5682 −1.74949
\(487\) −30.5097 −1.38252 −0.691262 0.722604i \(-0.742945\pi\)
−0.691262 + 0.722604i \(0.742945\pi\)
\(488\) −11.4955 −0.520377
\(489\) 18.0190 0.814845
\(490\) 1.13555 0.0512987
\(491\) −24.5234 −1.10672 −0.553362 0.832941i \(-0.686655\pi\)
−0.553362 + 0.832941i \(0.686655\pi\)
\(492\) −22.9499 −1.03466
\(493\) −1.74173 −0.0784437
\(494\) −22.0966 −0.994174
\(495\) −0.365793 −0.0164412
\(496\) 4.01745 0.180389
\(497\) −14.7833 −0.663120
\(498\) −18.1040 −0.811257
\(499\) −10.2987 −0.461034 −0.230517 0.973068i \(-0.574042\pi\)
−0.230517 + 0.973068i \(0.574042\pi\)
\(500\) −4.57983 −0.204816
\(501\) −7.81294 −0.349057
\(502\) 18.2704 0.815447
\(503\) −21.5652 −0.961544 −0.480772 0.876846i \(-0.659644\pi\)
−0.480772 + 0.876846i \(0.659644\pi\)
\(504\) −16.2925 −0.725727
\(505\) 1.88723 0.0839808
\(506\) −10.2431 −0.455361
\(507\) −9.20855 −0.408966
\(508\) 72.1577 3.20148
\(509\) −37.7273 −1.67223 −0.836116 0.548553i \(-0.815179\pi\)
−0.836116 + 0.548553i \(0.815179\pi\)
\(510\) −0.259775 −0.0115030
\(511\) 6.20846 0.274646
\(512\) 26.1336 1.15495
\(513\) −26.5711 −1.17314
\(514\) 42.2937 1.86550
\(515\) 0.244318 0.0107660
\(516\) −17.5884 −0.774288
\(517\) −13.2913 −0.584553
\(518\) 22.5860 0.992370
\(519\) −10.1920 −0.447379
\(520\) −0.814522 −0.0357191
\(521\) −3.26730 −0.143143 −0.0715714 0.997435i \(-0.522801\pi\)
−0.0715714 + 0.997435i \(0.522801\pi\)
\(522\) −9.26131 −0.405356
\(523\) 32.2982 1.41230 0.706150 0.708063i \(-0.250431\pi\)
0.706150 + 0.708063i \(0.250431\pi\)
\(524\) −7.09577 −0.309980
\(525\) 7.79728 0.340301
\(526\) −6.90226 −0.300953
\(527\) 1.64454 0.0716374
\(528\) 2.88419 0.125518
\(529\) −12.7726 −0.555329
\(530\) 3.82314 0.166067
\(531\) −10.1326 −0.439718
\(532\) −38.1267 −1.65300
\(533\) −11.1687 −0.483772
\(534\) 4.51995 0.195597
\(535\) −1.92749 −0.0833327
\(536\) −55.6307 −2.40288
\(537\) −17.6247 −0.760563
\(538\) −27.8693 −1.20153
\(539\) −5.16089 −0.222295
\(540\) −2.11298 −0.0909283
\(541\) −9.21622 −0.396236 −0.198118 0.980178i \(-0.563483\pi\)
−0.198118 + 0.980178i \(0.563483\pi\)
\(542\) 26.2657 1.12821
\(543\) −4.41622 −0.189518
\(544\) 2.42552 0.103993
\(545\) −1.13028 −0.0484157
\(546\) 5.99231 0.256447
\(547\) 3.74196 0.159995 0.0799973 0.996795i \(-0.474509\pi\)
0.0799973 + 0.996795i \(0.474509\pi\)
\(548\) 20.1473 0.860652
\(549\) −6.17471 −0.263530
\(550\) 15.9662 0.680801
\(551\) −10.0462 −0.427984
\(552\) −11.6696 −0.496689
\(553\) 27.3598 1.16346
\(554\) −29.7697 −1.26479
\(555\) 0.577708 0.0245223
\(556\) 52.4417 2.22402
\(557\) −37.3328 −1.58184 −0.790921 0.611919i \(-0.790398\pi\)
−0.790921 + 0.611919i \(0.790398\pi\)
\(558\) 8.74451 0.370185
\(559\) −8.55955 −0.362030
\(560\) −0.532881 −0.0225183
\(561\) 1.18064 0.0498467
\(562\) 64.8882 2.73714
\(563\) −18.8935 −0.796267 −0.398133 0.917328i \(-0.630342\pi\)
−0.398133 + 0.917328i \(0.630342\pi\)
\(564\) −32.6664 −1.37550
\(565\) 0.866089 0.0364366
\(566\) 11.7253 0.492849
\(567\) −4.61151 −0.193665
\(568\) −34.4867 −1.44703
\(569\) 14.2499 0.597386 0.298693 0.954349i \(-0.403449\pi\)
0.298693 + 0.954349i \(0.403449\pi\)
\(570\) −1.49837 −0.0627598
\(571\) −32.9788 −1.38012 −0.690060 0.723752i \(-0.742416\pi\)
−0.690060 + 0.723752i \(0.742416\pi\)
\(572\) 7.98606 0.333914
\(573\) −7.09443 −0.296374
\(574\) −29.6092 −1.23587
\(575\) −15.9418 −0.664818
\(576\) 23.7519 0.989662
\(577\) −38.1539 −1.58837 −0.794183 0.607679i \(-0.792101\pi\)
−0.794183 + 0.607679i \(0.792101\pi\)
\(578\) −2.39336 −0.0995506
\(579\) −1.21357 −0.0504343
\(580\) −0.798894 −0.0331723
\(581\) −15.2020 −0.630685
\(582\) −19.3477 −0.801989
\(583\) −17.3756 −0.719626
\(584\) 14.4832 0.599320
\(585\) −0.437514 −0.0180890
\(586\) 31.2049 1.28906
\(587\) −9.98957 −0.412314 −0.206157 0.978519i \(-0.566096\pi\)
−0.206157 + 0.978519i \(0.566096\pi\)
\(588\) −12.6840 −0.523081
\(589\) 9.48564 0.390849
\(590\) −1.34295 −0.0552883
\(591\) −20.1842 −0.830266
\(592\) 13.0024 0.534396
\(593\) −28.0243 −1.15082 −0.575409 0.817866i \(-0.695157\pi\)
−0.575409 + 0.817866i \(0.695157\pi\)
\(594\) 14.7549 0.605401
\(595\) −0.218135 −0.00894264
\(596\) 2.81512 0.115312
\(597\) 0.0263808 0.00107969
\(598\) −12.2515 −0.500999
\(599\) −7.66024 −0.312989 −0.156494 0.987679i \(-0.550019\pi\)
−0.156494 + 0.987679i \(0.550019\pi\)
\(600\) 18.1897 0.742590
\(601\) −9.01507 −0.367732 −0.183866 0.982951i \(-0.558861\pi\)
−0.183866 + 0.982951i \(0.558861\pi\)
\(602\) −22.6921 −0.924860
\(603\) −29.8816 −1.21687
\(604\) 5.44636 0.221609
\(605\) −1.13299 −0.0460628
\(606\) −32.3891 −1.31572
\(607\) 27.0189 1.09666 0.548331 0.836261i \(-0.315263\pi\)
0.548331 + 0.836261i \(0.315263\pi\)
\(608\) 13.9903 0.567380
\(609\) 2.72440 0.110398
\(610\) −0.818378 −0.0331352
\(611\) −15.8974 −0.643139
\(612\) −8.28282 −0.334813
\(613\) 23.6707 0.956049 0.478025 0.878346i \(-0.341353\pi\)
0.478025 + 0.878346i \(0.341353\pi\)
\(614\) 31.1065 1.25536
\(615\) −0.757351 −0.0305393
\(616\) 9.81401 0.395418
\(617\) 2.68488 0.108089 0.0540447 0.998539i \(-0.482789\pi\)
0.0540447 + 0.998539i \(0.482789\pi\)
\(618\) −4.19304 −0.168669
\(619\) −22.6814 −0.911643 −0.455822 0.890071i \(-0.650655\pi\)
−0.455822 + 0.890071i \(0.650655\pi\)
\(620\) 0.754315 0.0302940
\(621\) −14.7323 −0.591188
\(622\) −59.3550 −2.37992
\(623\) 3.79542 0.152060
\(624\) 3.44969 0.138098
\(625\) 24.7732 0.990927
\(626\) −64.6585 −2.58427
\(627\) 6.80988 0.271960
\(628\) −33.2189 −1.32558
\(629\) 5.32254 0.212223
\(630\) −1.15989 −0.0462109
\(631\) 3.17988 0.126589 0.0632946 0.997995i \(-0.479839\pi\)
0.0632946 + 0.997995i \(0.479839\pi\)
\(632\) 63.8255 2.53884
\(633\) −20.1490 −0.800850
\(634\) 3.07390 0.122080
\(635\) 2.38122 0.0944959
\(636\) −42.7045 −1.69334
\(637\) −6.17278 −0.244575
\(638\) 5.57866 0.220861
\(639\) −18.5243 −0.732808
\(640\) 2.55118 0.100844
\(641\) 7.35204 0.290388 0.145194 0.989403i \(-0.453619\pi\)
0.145194 + 0.989403i \(0.453619\pi\)
\(642\) 33.0800 1.30556
\(643\) 15.3946 0.607103 0.303551 0.952815i \(-0.401828\pi\)
0.303551 + 0.952815i \(0.401828\pi\)
\(644\) −21.1393 −0.833005
\(645\) −0.580422 −0.0228541
\(646\) −13.8048 −0.543142
\(647\) −0.189022 −0.00743123 −0.00371561 0.999993i \(-0.501183\pi\)
−0.00371561 + 0.999993i \(0.501183\pi\)
\(648\) −10.7578 −0.422608
\(649\) 6.10350 0.239583
\(650\) 19.0967 0.749033
\(651\) −2.57238 −0.100819
\(652\) 76.1461 2.98211
\(653\) −31.4016 −1.22884 −0.614420 0.788979i \(-0.710610\pi\)
−0.614420 + 0.788979i \(0.710610\pi\)
\(654\) 19.3980 0.758522
\(655\) −0.234162 −0.00914946
\(656\) −17.0456 −0.665520
\(657\) 7.77954 0.303509
\(658\) −42.1453 −1.64299
\(659\) −2.28881 −0.0891595 −0.0445798 0.999006i \(-0.514195\pi\)
−0.0445798 + 0.999006i \(0.514195\pi\)
\(660\) 0.541534 0.0210792
\(661\) 20.6718 0.804039 0.402019 0.915631i \(-0.368308\pi\)
0.402019 + 0.915631i \(0.368308\pi\)
\(662\) −32.5267 −1.26419
\(663\) 1.41213 0.0548425
\(664\) −35.4635 −1.37625
\(665\) −1.25819 −0.0487905
\(666\) 28.3015 1.09666
\(667\) −5.57012 −0.215676
\(668\) −33.0166 −1.27745
\(669\) −3.47213 −0.134240
\(670\) −3.96042 −0.153004
\(671\) 3.71941 0.143586
\(672\) −3.79397 −0.146356
\(673\) 43.9699 1.69491 0.847457 0.530865i \(-0.178133\pi\)
0.847457 + 0.530865i \(0.178133\pi\)
\(674\) 64.8429 2.49766
\(675\) 22.9637 0.883872
\(676\) −38.9143 −1.49670
\(677\) 42.3937 1.62932 0.814661 0.579937i \(-0.196923\pi\)
0.814661 + 0.579937i \(0.196923\pi\)
\(678\) −14.8640 −0.570848
\(679\) −16.2464 −0.623479
\(680\) −0.508869 −0.0195142
\(681\) 20.4610 0.784068
\(682\) −5.26736 −0.201698
\(683\) −23.9217 −0.915337 −0.457668 0.889123i \(-0.651315\pi\)
−0.457668 + 0.889123i \(0.651315\pi\)
\(684\) −47.7749 −1.82672
\(685\) 0.664867 0.0254032
\(686\) −46.0688 −1.75891
\(687\) 7.90979 0.301777
\(688\) −13.0635 −0.498042
\(689\) −20.7825 −0.791749
\(690\) −0.830770 −0.0316269
\(691\) −27.4096 −1.04271 −0.521355 0.853340i \(-0.674573\pi\)
−0.521355 + 0.853340i \(0.674573\pi\)
\(692\) −43.0702 −1.63728
\(693\) 5.27151 0.200248
\(694\) 30.4524 1.15596
\(695\) 1.73059 0.0656449
\(696\) 6.35555 0.240906
\(697\) −6.97762 −0.264296
\(698\) −26.0540 −0.986158
\(699\) −23.9294 −0.905093
\(700\) 32.9504 1.24541
\(701\) −16.2080 −0.612169 −0.306084 0.952004i \(-0.599019\pi\)
−0.306084 + 0.952004i \(0.599019\pi\)
\(702\) 17.6479 0.666077
\(703\) 30.7001 1.15788
\(704\) −14.3072 −0.539224
\(705\) −1.07800 −0.0405998
\(706\) −2.39336 −0.0900753
\(707\) −27.1973 −1.02286
\(708\) 15.0007 0.563761
\(709\) −32.7594 −1.23030 −0.615152 0.788408i \(-0.710905\pi\)
−0.615152 + 0.788408i \(0.710905\pi\)
\(710\) −2.45515 −0.0921402
\(711\) 34.2833 1.28573
\(712\) 8.85405 0.331819
\(713\) 5.25930 0.196962
\(714\) 3.74367 0.140103
\(715\) 0.263542 0.00985590
\(716\) −74.4801 −2.78345
\(717\) −4.59662 −0.171664
\(718\) 62.9502 2.34928
\(719\) −13.3415 −0.497553 −0.248777 0.968561i \(-0.580029\pi\)
−0.248777 + 0.968561i \(0.580029\pi\)
\(720\) −0.667729 −0.0248848
\(721\) −3.52092 −0.131126
\(722\) −34.1515 −1.27099
\(723\) 0.865830 0.0322005
\(724\) −18.6625 −0.693585
\(725\) 8.68230 0.322453
\(726\) 19.4447 0.721660
\(727\) −43.6640 −1.61941 −0.809704 0.586838i \(-0.800372\pi\)
−0.809704 + 0.586838i \(0.800372\pi\)
\(728\) 11.7382 0.435048
\(729\) 6.41385 0.237550
\(730\) 1.03108 0.0381619
\(731\) −5.34754 −0.197786
\(732\) 9.14128 0.337871
\(733\) 21.4406 0.791925 0.395962 0.918267i \(-0.370411\pi\)
0.395962 + 0.918267i \(0.370411\pi\)
\(734\) 35.1437 1.29718
\(735\) −0.418576 −0.0154394
\(736\) 7.75688 0.285923
\(737\) 17.9995 0.663021
\(738\) −37.1020 −1.36575
\(739\) 41.9140 1.54183 0.770916 0.636937i \(-0.219799\pi\)
0.770916 + 0.636937i \(0.219799\pi\)
\(740\) 2.44133 0.0897450
\(741\) 8.14509 0.299217
\(742\) −55.0961 −2.02264
\(743\) 40.4103 1.48251 0.741254 0.671224i \(-0.234231\pi\)
0.741254 + 0.671224i \(0.234231\pi\)
\(744\) −6.00090 −0.220004
\(745\) 0.0928997 0.00340358
\(746\) −28.2645 −1.03484
\(747\) −19.0489 −0.696964
\(748\) 4.98926 0.182425
\(749\) 27.7775 1.01497
\(750\) 2.59382 0.0947129
\(751\) 18.8097 0.686376 0.343188 0.939267i \(-0.388493\pi\)
0.343188 + 0.939267i \(0.388493\pi\)
\(752\) −24.2624 −0.884760
\(753\) −6.73468 −0.245426
\(754\) 6.67246 0.242997
\(755\) 0.179731 0.00654108
\(756\) 30.4506 1.10748
\(757\) 33.5789 1.22045 0.610223 0.792230i \(-0.291080\pi\)
0.610223 + 0.792230i \(0.291080\pi\)
\(758\) 0.579643 0.0210536
\(759\) 3.77573 0.137050
\(760\) −2.93513 −0.106468
\(761\) 43.6170 1.58112 0.790558 0.612387i \(-0.209791\pi\)
0.790558 + 0.612387i \(0.209791\pi\)
\(762\) −40.8670 −1.48046
\(763\) 16.2886 0.589688
\(764\) −29.9803 −1.08465
\(765\) −0.273335 −0.00988244
\(766\) 27.0322 0.976714
\(767\) 7.30021 0.263595
\(768\) −24.9204 −0.899237
\(769\) −35.7241 −1.28824 −0.644121 0.764923i \(-0.722777\pi\)
−0.644121 + 0.764923i \(0.722777\pi\)
\(770\) 0.698671 0.0251783
\(771\) −15.5900 −0.561459
\(772\) −5.12842 −0.184576
\(773\) 33.7598 1.21425 0.607127 0.794605i \(-0.292322\pi\)
0.607127 + 0.794605i \(0.292322\pi\)
\(774\) −28.4344 −1.02206
\(775\) −8.19782 −0.294474
\(776\) −37.8999 −1.36053
\(777\) −8.32546 −0.298674
\(778\) 17.3609 0.622417
\(779\) −40.2466 −1.44198
\(780\) 0.647712 0.0231918
\(781\) 11.1583 0.399276
\(782\) −7.65404 −0.273708
\(783\) 8.02361 0.286741
\(784\) −9.42085 −0.336459
\(785\) −1.09623 −0.0391262
\(786\) 4.01873 0.143344
\(787\) 0.0813139 0.00289853 0.00144926 0.999999i \(-0.499539\pi\)
0.00144926 + 0.999999i \(0.499539\pi\)
\(788\) −85.2960 −3.03855
\(789\) 2.54426 0.0905779
\(790\) 4.54381 0.161662
\(791\) −12.4814 −0.443786
\(792\) 12.2975 0.436973
\(793\) 4.44867 0.157977
\(794\) 72.4913 2.57262
\(795\) −1.40926 −0.0499812
\(796\) 0.111482 0.00395138
\(797\) −18.7502 −0.664167 −0.332083 0.943250i \(-0.607752\pi\)
−0.332083 + 0.943250i \(0.607752\pi\)
\(798\) 21.5933 0.764395
\(799\) −9.93182 −0.351362
\(800\) −12.0909 −0.427477
\(801\) 4.75588 0.168041
\(802\) 82.3982 2.90958
\(803\) −4.68610 −0.165369
\(804\) 44.2378 1.56015
\(805\) −0.697602 −0.0245872
\(806\) −6.30013 −0.221913
\(807\) 10.2729 0.361625
\(808\) −63.4464 −2.23204
\(809\) 6.47016 0.227479 0.113739 0.993511i \(-0.463717\pi\)
0.113739 + 0.993511i \(0.463717\pi\)
\(810\) −0.765864 −0.0269097
\(811\) 16.8686 0.592336 0.296168 0.955136i \(-0.404291\pi\)
0.296168 + 0.955136i \(0.404291\pi\)
\(812\) 11.5130 0.404028
\(813\) −9.68185 −0.339557
\(814\) −17.0477 −0.597523
\(815\) 2.51284 0.0880208
\(816\) 2.15518 0.0754463
\(817\) −30.8444 −1.07911
\(818\) −60.8042 −2.12597
\(819\) 6.30509 0.220318
\(820\) −3.20048 −0.111766
\(821\) −4.27083 −0.149053 −0.0745266 0.997219i \(-0.523745\pi\)
−0.0745266 + 0.997219i \(0.523745\pi\)
\(822\) −11.4106 −0.397990
\(823\) 18.9157 0.659361 0.329680 0.944093i \(-0.393059\pi\)
0.329680 + 0.944093i \(0.393059\pi\)
\(824\) −8.21368 −0.286137
\(825\) −5.88533 −0.204901
\(826\) 19.3535 0.673393
\(827\) −16.6223 −0.578012 −0.289006 0.957327i \(-0.593325\pi\)
−0.289006 + 0.957327i \(0.593325\pi\)
\(828\) −26.4887 −0.920547
\(829\) −46.5733 −1.61756 −0.808779 0.588113i \(-0.799871\pi\)
−0.808779 + 0.588113i \(0.799871\pi\)
\(830\) −2.52469 −0.0876333
\(831\) 10.9735 0.380665
\(832\) −17.1124 −0.593267
\(833\) −3.85642 −0.133617
\(834\) −29.7007 −1.02845
\(835\) −1.08956 −0.0377056
\(836\) 28.7778 0.995301
\(837\) −7.57588 −0.261861
\(838\) −3.67844 −0.127070
\(839\) −22.3118 −0.770290 −0.385145 0.922856i \(-0.625849\pi\)
−0.385145 + 0.922856i \(0.625849\pi\)
\(840\) 0.795968 0.0274635
\(841\) −25.9664 −0.895392
\(842\) 33.6777 1.16061
\(843\) −23.9186 −0.823799
\(844\) −85.1473 −2.93089
\(845\) −1.28418 −0.0441772
\(846\) −52.8104 −1.81566
\(847\) 16.3278 0.561030
\(848\) −31.7180 −1.08920
\(849\) −4.32207 −0.148333
\(850\) 11.9306 0.409215
\(851\) 17.0217 0.583495
\(852\) 27.4240 0.939531
\(853\) −47.9888 −1.64310 −0.821552 0.570133i \(-0.806892\pi\)
−0.821552 + 0.570133i \(0.806892\pi\)
\(854\) 11.7938 0.403576
\(855\) −1.57658 −0.0539180
\(856\) 64.7999 2.21481
\(857\) −12.6109 −0.430779 −0.215389 0.976528i \(-0.569102\pi\)
−0.215389 + 0.976528i \(0.569102\pi\)
\(858\) −4.52295 −0.154411
\(859\) −43.2642 −1.47616 −0.738078 0.674715i \(-0.764267\pi\)
−0.738078 + 0.674715i \(0.764267\pi\)
\(860\) −2.45280 −0.0836397
\(861\) 10.9143 0.371959
\(862\) 58.8048 2.00290
\(863\) −2.35486 −0.0801605 −0.0400803 0.999196i \(-0.512761\pi\)
−0.0400803 + 0.999196i \(0.512761\pi\)
\(864\) −11.1736 −0.380133
\(865\) −1.42133 −0.0483266
\(866\) 3.04892 0.103606
\(867\) 0.882221 0.0299618
\(868\) −10.8706 −0.368972
\(869\) −20.6510 −0.700537
\(870\) 0.452459 0.0153398
\(871\) 21.5287 0.729472
\(872\) 37.9984 1.28679
\(873\) −20.3576 −0.689002
\(874\) −44.1482 −1.49333
\(875\) 2.17804 0.0736313
\(876\) −11.5171 −0.389128
\(877\) 46.4181 1.56743 0.783714 0.621122i \(-0.213323\pi\)
0.783714 + 0.621122i \(0.213323\pi\)
\(878\) −59.0915 −1.99424
\(879\) −11.5025 −0.387970
\(880\) 0.402215 0.0135587
\(881\) −14.8706 −0.501002 −0.250501 0.968116i \(-0.580595\pi\)
−0.250501 + 0.968116i \(0.580595\pi\)
\(882\) −20.5057 −0.690463
\(883\) −5.33774 −0.179629 −0.0898146 0.995959i \(-0.528627\pi\)
−0.0898146 + 0.995959i \(0.528627\pi\)
\(884\) 5.96750 0.200709
\(885\) 0.495027 0.0166401
\(886\) −9.79257 −0.328988
\(887\) 9.26697 0.311154 0.155577 0.987824i \(-0.450276\pi\)
0.155577 + 0.987824i \(0.450276\pi\)
\(888\) −19.4218 −0.651753
\(889\) −34.3162 −1.15093
\(890\) 0.630330 0.0211287
\(891\) 3.48074 0.116609
\(892\) −14.6729 −0.491283
\(893\) −57.2862 −1.91701
\(894\) −1.59436 −0.0533235
\(895\) −2.45786 −0.0821571
\(896\) −36.7656 −1.22825
\(897\) 4.51603 0.150786
\(898\) −7.78390 −0.259752
\(899\) −2.86435 −0.0955316
\(900\) 41.2887 1.37629
\(901\) −12.9838 −0.432552
\(902\) 22.3489 0.744136
\(903\) 8.36458 0.278356
\(904\) −29.1168 −0.968411
\(905\) −0.615865 −0.0204720
\(906\) −3.08458 −0.102478
\(907\) −19.7093 −0.654437 −0.327218 0.944949i \(-0.606111\pi\)
−0.327218 + 0.944949i \(0.606111\pi\)
\(908\) 86.4660 2.86947
\(909\) −34.0797 −1.13035
\(910\) 0.835659 0.0277018
\(911\) 17.8572 0.591635 0.295817 0.955245i \(-0.404408\pi\)
0.295817 + 0.955245i \(0.404408\pi\)
\(912\) 12.4310 0.411630
\(913\) 11.4744 0.379746
\(914\) −81.3166 −2.68972
\(915\) 0.301664 0.00997271
\(916\) 33.4259 1.10442
\(917\) 3.37455 0.111438
\(918\) 11.0254 0.363894
\(919\) 24.6958 0.814638 0.407319 0.913286i \(-0.366464\pi\)
0.407319 + 0.913286i \(0.366464\pi\)
\(920\) −1.62738 −0.0536531
\(921\) −11.4662 −0.377826
\(922\) 92.9434 3.06093
\(923\) 13.3461 0.439293
\(924\) −7.80415 −0.256738
\(925\) −26.5321 −0.872371
\(926\) −20.1837 −0.663279
\(927\) −4.41191 −0.144906
\(928\) −4.22460 −0.138679
\(929\) −4.14132 −0.135872 −0.0679362 0.997690i \(-0.521641\pi\)
−0.0679362 + 0.997690i \(0.521641\pi\)
\(930\) −0.427211 −0.0140088
\(931\) −22.2436 −0.729006
\(932\) −101.123 −3.31239
\(933\) 21.8790 0.716285
\(934\) 58.4399 1.91221
\(935\) 0.164647 0.00538452
\(936\) 14.7087 0.480768
\(937\) −29.3178 −0.957772 −0.478886 0.877877i \(-0.658959\pi\)
−0.478886 + 0.877877i \(0.658959\pi\)
\(938\) 57.0744 1.86354
\(939\) 23.8339 0.777790
\(940\) −4.55550 −0.148584
\(941\) 10.0712 0.328312 0.164156 0.986434i \(-0.447510\pi\)
0.164156 + 0.986434i \(0.447510\pi\)
\(942\) 18.8138 0.612985
\(943\) −22.3147 −0.726666
\(944\) 11.1415 0.362626
\(945\) 1.00488 0.0326886
\(946\) 17.1278 0.556874
\(947\) −4.87194 −0.158317 −0.0791583 0.996862i \(-0.525223\pi\)
−0.0791583 + 0.996862i \(0.525223\pi\)
\(948\) −50.7544 −1.64843
\(949\) −5.60490 −0.181943
\(950\) 68.8149 2.23265
\(951\) −1.13308 −0.0367425
\(952\) 7.33341 0.237677
\(953\) 56.7348 1.83782 0.918911 0.394466i \(-0.129070\pi\)
0.918911 + 0.394466i \(0.129070\pi\)
\(954\) −69.0385 −2.23520
\(955\) −0.989355 −0.0320148
\(956\) −19.4248 −0.628243
\(957\) −2.05636 −0.0664727
\(958\) −55.7905 −1.80251
\(959\) −9.58152 −0.309403
\(960\) −1.16039 −0.0374515
\(961\) −28.2955 −0.912757
\(962\) −20.3903 −0.657409
\(963\) 34.8067 1.12163
\(964\) 3.65890 0.117845
\(965\) −0.169239 −0.00544799
\(966\) 11.9724 0.385205
\(967\) −1.71951 −0.0552958 −0.0276479 0.999618i \(-0.508802\pi\)
−0.0276479 + 0.999618i \(0.508802\pi\)
\(968\) 38.0898 1.22425
\(969\) 5.08861 0.163470
\(970\) −2.69814 −0.0866321
\(971\) −38.9313 −1.24937 −0.624683 0.780878i \(-0.714772\pi\)
−0.624683 + 0.780878i \(0.714772\pi\)
\(972\) 60.0781 1.92701
\(973\) −24.9398 −0.799534
\(974\) 73.0206 2.33973
\(975\) −7.03927 −0.225437
\(976\) 6.78953 0.217327
\(977\) −3.21251 −0.102777 −0.0513886 0.998679i \(-0.516365\pi\)
−0.0513886 + 0.998679i \(0.516365\pi\)
\(978\) −43.1258 −1.37901
\(979\) −2.86476 −0.0915581
\(980\) −1.76885 −0.0565040
\(981\) 20.4105 0.651659
\(982\) 58.6932 1.87298
\(983\) 8.65240 0.275969 0.137984 0.990434i \(-0.455938\pi\)
0.137984 + 0.990434i \(0.455938\pi\)
\(984\) 25.4612 0.811673
\(985\) −2.81479 −0.0896866
\(986\) 4.16859 0.132755
\(987\) 15.5353 0.494493
\(988\) 34.4202 1.09505
\(989\) −17.1016 −0.543800
\(990\) 0.875474 0.0278244
\(991\) −21.1868 −0.673022 −0.336511 0.941680i \(-0.609247\pi\)
−0.336511 + 0.941680i \(0.609247\pi\)
\(992\) 3.98886 0.126647
\(993\) 11.9897 0.380483
\(994\) 35.3817 1.12224
\(995\) 0.00367894 0.000116630 0
\(996\) 28.2008 0.893576
\(997\) 42.9369 1.35983 0.679913 0.733293i \(-0.262017\pi\)
0.679913 + 0.733293i \(0.262017\pi\)
\(998\) 24.6485 0.780235
\(999\) −24.5192 −0.775754
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 \(a_p\))