Properties

Label 6001.2.a.b.1.15
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 1.15
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.29894 q^{2}\) \(+0.676824 q^{3}\) \(+3.28511 q^{4}\) \(-3.14176 q^{5}\) \(-1.55598 q^{6}\) \(-3.61058 q^{7}\) \(-2.95439 q^{8}\) \(-2.54191 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.29894 q^{2}\) \(+0.676824 q^{3}\) \(+3.28511 q^{4}\) \(-3.14176 q^{5}\) \(-1.55598 q^{6}\) \(-3.61058 q^{7}\) \(-2.95439 q^{8}\) \(-2.54191 q^{9}\) \(+7.22271 q^{10}\) \(-5.00307 q^{11}\) \(+2.22344 q^{12}\) \(+3.46811 q^{13}\) \(+8.30050 q^{14}\) \(-2.12642 q^{15}\) \(+0.221727 q^{16}\) \(+1.00000 q^{17}\) \(+5.84369 q^{18}\) \(-2.21471 q^{19}\) \(-10.3210 q^{20}\) \(-2.44373 q^{21}\) \(+11.5017 q^{22}\) \(-4.03171 q^{23}\) \(-1.99960 q^{24}\) \(+4.87066 q^{25}\) \(-7.97297 q^{26}\) \(-3.75090 q^{27}\) \(-11.8612 q^{28}\) \(+6.02696 q^{29}\) \(+4.88850 q^{30}\) \(+7.26825 q^{31}\) \(+5.39904 q^{32}\) \(-3.38620 q^{33}\) \(-2.29894 q^{34}\) \(+11.3436 q^{35}\) \(-8.35045 q^{36}\) \(+8.52411 q^{37}\) \(+5.09147 q^{38}\) \(+2.34730 q^{39}\) \(+9.28197 q^{40}\) \(-3.54127 q^{41}\) \(+5.61797 q^{42}\) \(-4.72382 q^{43}\) \(-16.4356 q^{44}\) \(+7.98607 q^{45}\) \(+9.26866 q^{46}\) \(+2.95722 q^{47}\) \(+0.150070 q^{48}\) \(+6.03629 q^{49}\) \(-11.1973 q^{50}\) \(+0.676824 q^{51}\) \(+11.3931 q^{52}\) \(-1.45415 q^{53}\) \(+8.62307 q^{54}\) \(+15.7184 q^{55}\) \(+10.6671 q^{56}\) \(-1.49897 q^{57}\) \(-13.8556 q^{58}\) \(-4.01062 q^{59}\) \(-6.98552 q^{60}\) \(+7.07630 q^{61}\) \(-16.7093 q^{62}\) \(+9.17777 q^{63}\) \(-12.8555 q^{64}\) \(-10.8960 q^{65}\) \(+7.78465 q^{66}\) \(+2.33224 q^{67}\) \(+3.28511 q^{68}\) \(-2.72876 q^{69}\) \(-26.0782 q^{70}\) \(-4.74504 q^{71}\) \(+7.50978 q^{72}\) \(-2.40867 q^{73}\) \(-19.5964 q^{74}\) \(+3.29658 q^{75}\) \(-7.27555 q^{76}\) \(+18.0640 q^{77}\) \(-5.39629 q^{78}\) \(+10.8731 q^{79}\) \(-0.696615 q^{80}\) \(+5.08703 q^{81}\) \(+8.14116 q^{82}\) \(-0.0418311 q^{83}\) \(-8.02791 q^{84}\) \(-3.14176 q^{85}\) \(+10.8598 q^{86}\) \(+4.07919 q^{87}\) \(+14.7810 q^{88}\) \(+4.18620 q^{89}\) \(-18.3595 q^{90}\) \(-12.5219 q^{91}\) \(-13.2446 q^{92}\) \(+4.91933 q^{93}\) \(-6.79846 q^{94}\) \(+6.95808 q^{95}\) \(+3.65420 q^{96}\) \(-0.739229 q^{97}\) \(-13.8771 q^{98}\) \(+12.7173 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29894 −1.62559 −0.812797 0.582547i \(-0.802056\pi\)
−0.812797 + 0.582547i \(0.802056\pi\)
\(3\) 0.676824 0.390764 0.195382 0.980727i \(-0.437405\pi\)
0.195382 + 0.980727i \(0.437405\pi\)
\(4\) 3.28511 1.64255
\(5\) −3.14176 −1.40504 −0.702519 0.711665i \(-0.747941\pi\)
−0.702519 + 0.711665i \(0.747941\pi\)
\(6\) −1.55598 −0.635224
\(7\) −3.61058 −1.36467 −0.682336 0.731039i \(-0.739036\pi\)
−0.682336 + 0.731039i \(0.739036\pi\)
\(8\) −2.95439 −1.04453
\(9\) −2.54191 −0.847303
\(10\) 7.22271 2.28402
\(11\) −5.00307 −1.50848 −0.754241 0.656598i \(-0.771995\pi\)
−0.754241 + 0.656598i \(0.771995\pi\)
\(12\) 2.22344 0.641852
\(13\) 3.46811 0.961881 0.480940 0.876753i \(-0.340295\pi\)
0.480940 + 0.876753i \(0.340295\pi\)
\(14\) 8.30050 2.21840
\(15\) −2.12642 −0.549039
\(16\) 0.221727 0.0554319
\(17\) 1.00000 0.242536
\(18\) 5.84369 1.37737
\(19\) −2.21471 −0.508089 −0.254044 0.967193i \(-0.581761\pi\)
−0.254044 + 0.967193i \(0.581761\pi\)
\(20\) −10.3210 −2.30785
\(21\) −2.44373 −0.533265
\(22\) 11.5017 2.45218
\(23\) −4.03171 −0.840671 −0.420335 0.907369i \(-0.638088\pi\)
−0.420335 + 0.907369i \(0.638088\pi\)
\(24\) −1.99960 −0.408166
\(25\) 4.87066 0.974131
\(26\) −7.97297 −1.56363
\(27\) −3.75090 −0.721860
\(28\) −11.8612 −2.24155
\(29\) 6.02696 1.11918 0.559589 0.828770i \(-0.310959\pi\)
0.559589 + 0.828770i \(0.310959\pi\)
\(30\) 4.88850 0.892514
\(31\) 7.26825 1.30542 0.652708 0.757609i \(-0.273633\pi\)
0.652708 + 0.757609i \(0.273633\pi\)
\(32\) 5.39904 0.954424
\(33\) −3.38620 −0.589461
\(34\) −2.29894 −0.394264
\(35\) 11.3436 1.91741
\(36\) −8.35045 −1.39174
\(37\) 8.52411 1.40135 0.700677 0.713478i \(-0.252881\pi\)
0.700677 + 0.713478i \(0.252881\pi\)
\(38\) 5.09147 0.825946
\(39\) 2.34730 0.375869
\(40\) 9.28197 1.46761
\(41\) −3.54127 −0.553054 −0.276527 0.961006i \(-0.589184\pi\)
−0.276527 + 0.961006i \(0.589184\pi\)
\(42\) 5.61797 0.866872
\(43\) −4.72382 −0.720376 −0.360188 0.932880i \(-0.617288\pi\)
−0.360188 + 0.932880i \(0.617288\pi\)
\(44\) −16.4356 −2.47776
\(45\) 7.98607 1.19049
\(46\) 9.26866 1.36659
\(47\) 2.95722 0.431355 0.215677 0.976465i \(-0.430804\pi\)
0.215677 + 0.976465i \(0.430804\pi\)
\(48\) 0.150070 0.0216608
\(49\) 6.03629 0.862328
\(50\) −11.1973 −1.58354
\(51\) 0.676824 0.0947743
\(52\) 11.3931 1.57994
\(53\) −1.45415 −0.199743 −0.0998714 0.995000i \(-0.531843\pi\)
−0.0998714 + 0.995000i \(0.531843\pi\)
\(54\) 8.62307 1.17345
\(55\) 15.7184 2.11947
\(56\) 10.6671 1.42544
\(57\) −1.49897 −0.198543
\(58\) −13.8556 −1.81933
\(59\) −4.01062 −0.522138 −0.261069 0.965320i \(-0.584075\pi\)
−0.261069 + 0.965320i \(0.584075\pi\)
\(60\) −6.98552 −0.901826
\(61\) 7.07630 0.906028 0.453014 0.891503i \(-0.350349\pi\)
0.453014 + 0.891503i \(0.350349\pi\)
\(62\) −16.7093 −2.12208
\(63\) 9.17777 1.15629
\(64\) −12.8555 −1.60694
\(65\) −10.8960 −1.35148
\(66\) 7.78465 0.958224
\(67\) 2.33224 0.284928 0.142464 0.989800i \(-0.454497\pi\)
0.142464 + 0.989800i \(0.454497\pi\)
\(68\) 3.28511 0.398378
\(69\) −2.72876 −0.328504
\(70\) −26.0782 −3.11694
\(71\) −4.74504 −0.563133 −0.281566 0.959542i \(-0.590854\pi\)
−0.281566 + 0.959542i \(0.590854\pi\)
\(72\) 7.50978 0.885036
\(73\) −2.40867 −0.281914 −0.140957 0.990016i \(-0.545018\pi\)
−0.140957 + 0.990016i \(0.545018\pi\)
\(74\) −19.5964 −2.27803
\(75\) 3.29658 0.380656
\(76\) −7.27555 −0.834563
\(77\) 18.0640 2.05858
\(78\) −5.39629 −0.611010
\(79\) 10.8731 1.22332 0.611662 0.791119i \(-0.290501\pi\)
0.611662 + 0.791119i \(0.290501\pi\)
\(80\) −0.696615 −0.0778839
\(81\) 5.08703 0.565226
\(82\) 8.14116 0.899041
\(83\) −0.0418311 −0.00459156 −0.00229578 0.999997i \(-0.500731\pi\)
−0.00229578 + 0.999997i \(0.500731\pi\)
\(84\) −8.02791 −0.875917
\(85\) −3.14176 −0.340772
\(86\) 10.8598 1.17104
\(87\) 4.07919 0.437335
\(88\) 14.7810 1.57566
\(89\) 4.18620 0.443737 0.221868 0.975077i \(-0.428784\pi\)
0.221868 + 0.975077i \(0.428784\pi\)
\(90\) −18.3595 −1.93526
\(91\) −12.5219 −1.31265
\(92\) −13.2446 −1.38085
\(93\) 4.91933 0.510110
\(94\) −6.79846 −0.701208
\(95\) 6.95808 0.713884
\(96\) 3.65420 0.372955
\(97\) −0.739229 −0.0750573 −0.0375286 0.999296i \(-0.511949\pi\)
−0.0375286 + 0.999296i \(0.511949\pi\)
\(98\) −13.8771 −1.40179
\(99\) 12.7173 1.27814
\(100\) 16.0006 1.60006
\(101\) 17.2598 1.71741 0.858707 0.512468i \(-0.171269\pi\)
0.858707 + 0.512468i \(0.171269\pi\)
\(102\) −1.55598 −0.154064
\(103\) 17.1913 1.69391 0.846956 0.531664i \(-0.178433\pi\)
0.846956 + 0.531664i \(0.178433\pi\)
\(104\) −10.2461 −1.00472
\(105\) 7.67760 0.749257
\(106\) 3.34300 0.324701
\(107\) −7.85975 −0.759831 −0.379916 0.925021i \(-0.624047\pi\)
−0.379916 + 0.925021i \(0.624047\pi\)
\(108\) −12.3221 −1.18570
\(109\) 6.61226 0.633340 0.316670 0.948536i \(-0.397435\pi\)
0.316670 + 0.948536i \(0.397435\pi\)
\(110\) −36.1357 −3.44540
\(111\) 5.76932 0.547600
\(112\) −0.800565 −0.0756463
\(113\) −0.0902512 −0.00849012 −0.00424506 0.999991i \(-0.501351\pi\)
−0.00424506 + 0.999991i \(0.501351\pi\)
\(114\) 3.44603 0.322750
\(115\) 12.6667 1.18117
\(116\) 19.7992 1.83831
\(117\) −8.81562 −0.815005
\(118\) 9.22016 0.848784
\(119\) −3.61058 −0.330981
\(120\) 6.28226 0.573489
\(121\) 14.0307 1.27552
\(122\) −16.2680 −1.47283
\(123\) −2.39682 −0.216114
\(124\) 23.8770 2.14422
\(125\) 0.406364 0.0363463
\(126\) −21.0991 −1.87966
\(127\) −22.0076 −1.95286 −0.976429 0.215839i \(-0.930751\pi\)
−0.976429 + 0.215839i \(0.930751\pi\)
\(128\) 18.7559 1.65780
\(129\) −3.19720 −0.281497
\(130\) 25.0492 2.19696
\(131\) 9.51275 0.831133 0.415566 0.909563i \(-0.363583\pi\)
0.415566 + 0.909563i \(0.363583\pi\)
\(132\) −11.1240 −0.968222
\(133\) 7.99638 0.693374
\(134\) −5.36166 −0.463177
\(135\) 11.7844 1.01424
\(136\) −2.95439 −0.253337
\(137\) −13.4583 −1.14982 −0.574911 0.818216i \(-0.694963\pi\)
−0.574911 + 0.818216i \(0.694963\pi\)
\(138\) 6.27325 0.534014
\(139\) −20.4663 −1.73593 −0.867966 0.496623i \(-0.834573\pi\)
−0.867966 + 0.496623i \(0.834573\pi\)
\(140\) 37.2649 3.14946
\(141\) 2.00152 0.168558
\(142\) 10.9086 0.915425
\(143\) −17.3512 −1.45098
\(144\) −0.563611 −0.0469676
\(145\) −18.9353 −1.57249
\(146\) 5.53739 0.458277
\(147\) 4.08551 0.336967
\(148\) 28.0026 2.30180
\(149\) −0.129244 −0.0105881 −0.00529404 0.999986i \(-0.501685\pi\)
−0.00529404 + 0.999986i \(0.501685\pi\)
\(150\) −7.57862 −0.618792
\(151\) 23.6820 1.92722 0.963608 0.267319i \(-0.0861376\pi\)
0.963608 + 0.267319i \(0.0861376\pi\)
\(152\) 6.54310 0.530715
\(153\) −2.54191 −0.205501
\(154\) −41.5279 −3.34642
\(155\) −22.8351 −1.83416
\(156\) 7.71114 0.617385
\(157\) 13.1085 1.04617 0.523085 0.852280i \(-0.324781\pi\)
0.523085 + 0.852280i \(0.324781\pi\)
\(158\) −24.9967 −1.98863
\(159\) −0.984203 −0.0780524
\(160\) −16.9625 −1.34100
\(161\) 14.5568 1.14724
\(162\) −11.6948 −0.918828
\(163\) −0.653299 −0.0511703 −0.0255852 0.999673i \(-0.508145\pi\)
−0.0255852 + 0.999673i \(0.508145\pi\)
\(164\) −11.6335 −0.908422
\(165\) 10.6386 0.828215
\(166\) 0.0961671 0.00746401
\(167\) −16.7110 −1.29313 −0.646567 0.762858i \(-0.723796\pi\)
−0.646567 + 0.762858i \(0.723796\pi\)
\(168\) 7.21971 0.557013
\(169\) −0.972207 −0.0747852
\(170\) 7.22271 0.553956
\(171\) 5.62958 0.430505
\(172\) −15.5183 −1.18326
\(173\) 3.02851 0.230254 0.115127 0.993351i \(-0.463273\pi\)
0.115127 + 0.993351i \(0.463273\pi\)
\(174\) −9.37780 −0.710929
\(175\) −17.5859 −1.32937
\(176\) −1.10932 −0.0836180
\(177\) −2.71448 −0.204033
\(178\) −9.62382 −0.721336
\(179\) −1.50324 −0.112358 −0.0561789 0.998421i \(-0.517892\pi\)
−0.0561789 + 0.998421i \(0.517892\pi\)
\(180\) 26.2351 1.95545
\(181\) −6.54968 −0.486834 −0.243417 0.969922i \(-0.578268\pi\)
−0.243417 + 0.969922i \(0.578268\pi\)
\(182\) 28.7870 2.13384
\(183\) 4.78941 0.354043
\(184\) 11.9112 0.878108
\(185\) −26.7807 −1.96896
\(186\) −11.3092 −0.829232
\(187\) −5.00307 −0.365861
\(188\) 9.71479 0.708524
\(189\) 13.5429 0.985102
\(190\) −15.9962 −1.16048
\(191\) 1.71593 0.124160 0.0620801 0.998071i \(-0.480227\pi\)
0.0620801 + 0.998071i \(0.480227\pi\)
\(192\) −8.70091 −0.627934
\(193\) −11.2622 −0.810671 −0.405335 0.914168i \(-0.632845\pi\)
−0.405335 + 0.914168i \(0.632845\pi\)
\(194\) 1.69944 0.122013
\(195\) −7.37465 −0.528110
\(196\) 19.8299 1.41642
\(197\) −19.1442 −1.36397 −0.681983 0.731368i \(-0.738882\pi\)
−0.681983 + 0.731368i \(0.738882\pi\)
\(198\) −29.2364 −2.07774
\(199\) −17.9354 −1.27140 −0.635702 0.771934i \(-0.719289\pi\)
−0.635702 + 0.771934i \(0.719289\pi\)
\(200\) −14.3898 −1.01751
\(201\) 1.57851 0.111340
\(202\) −39.6792 −2.79182
\(203\) −21.7608 −1.52731
\(204\) 2.22344 0.155672
\(205\) 11.1258 0.777062
\(206\) −39.5218 −2.75361
\(207\) 10.2483 0.712303
\(208\) 0.768975 0.0533189
\(209\) 11.0803 0.766442
\(210\) −17.6503 −1.21799
\(211\) −1.89961 −0.130774 −0.0653872 0.997860i \(-0.520828\pi\)
−0.0653872 + 0.997860i \(0.520828\pi\)
\(212\) −4.77704 −0.328088
\(213\) −3.21156 −0.220052
\(214\) 18.0691 1.23518
\(215\) 14.8411 1.01216
\(216\) 11.0816 0.754007
\(217\) −26.2426 −1.78146
\(218\) −15.2012 −1.02955
\(219\) −1.63025 −0.110162
\(220\) 51.6368 3.48135
\(221\) 3.46811 0.233290
\(222\) −13.2633 −0.890174
\(223\) 10.6679 0.714375 0.357187 0.934033i \(-0.383736\pi\)
0.357187 + 0.934033i \(0.383736\pi\)
\(224\) −19.4937 −1.30247
\(225\) −12.3808 −0.825385
\(226\) 0.207482 0.0138015
\(227\) −25.3126 −1.68005 −0.840027 0.542545i \(-0.817461\pi\)
−0.840027 + 0.542545i \(0.817461\pi\)
\(228\) −4.92427 −0.326118
\(229\) 7.39467 0.488653 0.244327 0.969693i \(-0.421433\pi\)
0.244327 + 0.969693i \(0.421433\pi\)
\(230\) −29.1199 −1.92011
\(231\) 12.2261 0.804420
\(232\) −17.8060 −1.16902
\(233\) 19.3484 1.26756 0.633779 0.773515i \(-0.281503\pi\)
0.633779 + 0.773515i \(0.281503\pi\)
\(234\) 20.2666 1.32487
\(235\) −9.29087 −0.606070
\(236\) −13.1753 −0.857640
\(237\) 7.35920 0.478031
\(238\) 8.30050 0.538041
\(239\) 1.37499 0.0889404 0.0444702 0.999011i \(-0.485840\pi\)
0.0444702 + 0.999011i \(0.485840\pi\)
\(240\) −0.471485 −0.0304342
\(241\) −9.27995 −0.597774 −0.298887 0.954288i \(-0.596615\pi\)
−0.298887 + 0.954288i \(0.596615\pi\)
\(242\) −32.2557 −2.07347
\(243\) 14.6957 0.942730
\(244\) 23.2464 1.48820
\(245\) −18.9646 −1.21160
\(246\) 5.51013 0.351313
\(247\) −7.68085 −0.488721
\(248\) −21.4732 −1.36355
\(249\) −0.0283123 −0.00179422
\(250\) −0.934206 −0.0590844
\(251\) −13.4357 −0.848052 −0.424026 0.905650i \(-0.639383\pi\)
−0.424026 + 0.905650i \(0.639383\pi\)
\(252\) 30.1500 1.89927
\(253\) 20.1709 1.26814
\(254\) 50.5941 3.17455
\(255\) −2.12642 −0.133161
\(256\) −17.4076 −1.08798
\(257\) 27.1753 1.69515 0.847574 0.530677i \(-0.178062\pi\)
0.847574 + 0.530677i \(0.178062\pi\)
\(258\) 7.35015 0.457601
\(259\) −30.7770 −1.91239
\(260\) −35.7945 −2.21988
\(261\) −15.3200 −0.948283
\(262\) −21.8692 −1.35108
\(263\) 23.5773 1.45384 0.726919 0.686723i \(-0.240951\pi\)
0.726919 + 0.686723i \(0.240951\pi\)
\(264\) 10.0041 0.615712
\(265\) 4.56859 0.280646
\(266\) −18.3832 −1.12714
\(267\) 2.83332 0.173397
\(268\) 7.66165 0.468010
\(269\) −23.9470 −1.46008 −0.730038 0.683406i \(-0.760498\pi\)
−0.730038 + 0.683406i \(0.760498\pi\)
\(270\) −27.0916 −1.64874
\(271\) −12.4315 −0.755161 −0.377581 0.925977i \(-0.623244\pi\)
−0.377581 + 0.925977i \(0.623244\pi\)
\(272\) 0.221727 0.0134442
\(273\) −8.47512 −0.512937
\(274\) 30.9398 1.86914
\(275\) −24.3682 −1.46946
\(276\) −8.96428 −0.539586
\(277\) 23.7653 1.42792 0.713959 0.700188i \(-0.246900\pi\)
0.713959 + 0.700188i \(0.246900\pi\)
\(278\) 47.0508 2.82192
\(279\) −18.4752 −1.10608
\(280\) −33.5133 −2.00280
\(281\) 21.0050 1.25306 0.626528 0.779399i \(-0.284475\pi\)
0.626528 + 0.779399i \(0.284475\pi\)
\(282\) −4.60136 −0.274007
\(283\) 11.4954 0.683331 0.341666 0.939822i \(-0.389009\pi\)
0.341666 + 0.939822i \(0.389009\pi\)
\(284\) −15.5880 −0.924977
\(285\) 4.70939 0.278960
\(286\) 39.8893 2.35870
\(287\) 12.7861 0.754737
\(288\) −13.7239 −0.808686
\(289\) 1.00000 0.0588235
\(290\) 43.5310 2.55623
\(291\) −0.500328 −0.0293297
\(292\) −7.91275 −0.463059
\(293\) −18.7639 −1.09620 −0.548098 0.836414i \(-0.684648\pi\)
−0.548098 + 0.836414i \(0.684648\pi\)
\(294\) −9.39232 −0.547771
\(295\) 12.6004 0.733624
\(296\) −25.1835 −1.46376
\(297\) 18.7660 1.08891
\(298\) 0.297124 0.0172119
\(299\) −13.9824 −0.808625
\(300\) 10.8296 0.625248
\(301\) 17.0557 0.983077
\(302\) −54.4435 −3.13287
\(303\) 11.6818 0.671104
\(304\) −0.491061 −0.0281643
\(305\) −22.2321 −1.27300
\(306\) 5.84369 0.334061
\(307\) 8.95426 0.511047 0.255523 0.966803i \(-0.417752\pi\)
0.255523 + 0.966803i \(0.417752\pi\)
\(308\) 59.3422 3.38133
\(309\) 11.6355 0.661920
\(310\) 52.4965 2.98160
\(311\) −4.87181 −0.276255 −0.138128 0.990414i \(-0.544108\pi\)
−0.138128 + 0.990414i \(0.544108\pi\)
\(312\) −6.93483 −0.392608
\(313\) 18.9843 1.07305 0.536527 0.843883i \(-0.319736\pi\)
0.536527 + 0.843883i \(0.319736\pi\)
\(314\) −30.1356 −1.70065
\(315\) −28.8344 −1.62463
\(316\) 35.7194 2.00938
\(317\) −24.5905 −1.38114 −0.690571 0.723264i \(-0.742641\pi\)
−0.690571 + 0.723264i \(0.742641\pi\)
\(318\) 2.26262 0.126881
\(319\) −30.1533 −1.68826
\(320\) 40.3889 2.25781
\(321\) −5.31967 −0.296915
\(322\) −33.4652 −1.86494
\(323\) −2.21471 −0.123230
\(324\) 16.7115 0.928415
\(325\) 16.8920 0.936998
\(326\) 1.50189 0.0831822
\(327\) 4.47533 0.247487
\(328\) 10.4623 0.577683
\(329\) −10.6773 −0.588657
\(330\) −24.4575 −1.34634
\(331\) −20.5671 −1.13047 −0.565236 0.824929i \(-0.691215\pi\)
−0.565236 + 0.824929i \(0.691215\pi\)
\(332\) −0.137420 −0.00754189
\(333\) −21.6675 −1.18737
\(334\) 38.4174 2.10211
\(335\) −7.32733 −0.400335
\(336\) −0.541841 −0.0295599
\(337\) 19.6308 1.06936 0.534679 0.845055i \(-0.320433\pi\)
0.534679 + 0.845055i \(0.320433\pi\)
\(338\) 2.23504 0.121570
\(339\) −0.0610842 −0.00331764
\(340\) −10.3210 −0.559736
\(341\) −36.3636 −1.96920
\(342\) −12.9421 −0.699826
\(343\) 3.47954 0.187878
\(344\) 13.9560 0.752457
\(345\) 8.57311 0.461561
\(346\) −6.96236 −0.374299
\(347\) −17.9500 −0.963604 −0.481802 0.876280i \(-0.660018\pi\)
−0.481802 + 0.876280i \(0.660018\pi\)
\(348\) 13.4006 0.718347
\(349\) −11.8813 −0.635992 −0.317996 0.948092i \(-0.603010\pi\)
−0.317996 + 0.948092i \(0.603010\pi\)
\(350\) 40.4289 2.16101
\(351\) −13.0085 −0.694344
\(352\) −27.0117 −1.43973
\(353\) 1.00000 0.0532246
\(354\) 6.24042 0.331675
\(355\) 14.9078 0.791223
\(356\) 13.7521 0.728862
\(357\) −2.44373 −0.129336
\(358\) 3.45586 0.182648
\(359\) −23.7131 −1.25153 −0.625765 0.780011i \(-0.715213\pi\)
−0.625765 + 0.780011i \(0.715213\pi\)
\(360\) −23.5939 −1.24351
\(361\) −14.0951 −0.741846
\(362\) 15.0573 0.791394
\(363\) 9.49630 0.498427
\(364\) −41.1358 −2.15610
\(365\) 7.56747 0.396100
\(366\) −11.0106 −0.575531
\(367\) 0.638015 0.0333041 0.0166521 0.999861i \(-0.494699\pi\)
0.0166521 + 0.999861i \(0.494699\pi\)
\(368\) −0.893942 −0.0465999
\(369\) 9.00160 0.468604
\(370\) 61.5671 3.20072
\(371\) 5.25032 0.272583
\(372\) 16.1605 0.837884
\(373\) 3.01159 0.155934 0.0779671 0.996956i \(-0.475157\pi\)
0.0779671 + 0.996956i \(0.475157\pi\)
\(374\) 11.5017 0.594741
\(375\) 0.275037 0.0142028
\(376\) −8.73677 −0.450564
\(377\) 20.9022 1.07652
\(378\) −31.1343 −1.60138
\(379\) 24.4279 1.25478 0.627389 0.778706i \(-0.284124\pi\)
0.627389 + 0.778706i \(0.284124\pi\)
\(380\) 22.8580 1.17259
\(381\) −14.8953 −0.763107
\(382\) −3.94481 −0.201834
\(383\) 2.65014 0.135416 0.0677078 0.997705i \(-0.478431\pi\)
0.0677078 + 0.997705i \(0.478431\pi\)
\(384\) 12.6944 0.647810
\(385\) −56.7527 −2.89239
\(386\) 25.8911 1.31782
\(387\) 12.0075 0.610377
\(388\) −2.42845 −0.123286
\(389\) 36.1883 1.83482 0.917409 0.397946i \(-0.130277\pi\)
0.917409 + 0.397946i \(0.130277\pi\)
\(390\) 16.9539 0.858492
\(391\) −4.03171 −0.203893
\(392\) −17.8335 −0.900730
\(393\) 6.43846 0.324777
\(394\) 44.0113 2.21726
\(395\) −34.1608 −1.71882
\(396\) 41.7779 2.09942
\(397\) 28.4096 1.42584 0.712918 0.701247i \(-0.247373\pi\)
0.712918 + 0.701247i \(0.247373\pi\)
\(398\) 41.2323 2.06679
\(399\) 5.41214 0.270946
\(400\) 1.07996 0.0539979
\(401\) −14.3720 −0.717702 −0.358851 0.933395i \(-0.616831\pi\)
−0.358851 + 0.933395i \(0.616831\pi\)
\(402\) −3.62890 −0.180993
\(403\) 25.2071 1.25566
\(404\) 56.7003 2.82095
\(405\) −15.9822 −0.794164
\(406\) 50.0267 2.48279
\(407\) −42.6467 −2.11392
\(408\) −1.99960 −0.0989949
\(409\) 13.6809 0.676479 0.338240 0.941060i \(-0.390169\pi\)
0.338240 + 0.941060i \(0.390169\pi\)
\(410\) −25.5776 −1.26319
\(411\) −9.10892 −0.449310
\(412\) 56.4754 2.78234
\(413\) 14.4807 0.712547
\(414\) −23.5601 −1.15792
\(415\) 0.131423 0.00645132
\(416\) 18.7245 0.918042
\(417\) −13.8521 −0.678341
\(418\) −25.4730 −1.24592
\(419\) −0.0799622 −0.00390641 −0.00195320 0.999998i \(-0.500622\pi\)
−0.00195320 + 0.999998i \(0.500622\pi\)
\(420\) 25.2218 1.23070
\(421\) 8.39663 0.409227 0.204613 0.978843i \(-0.434406\pi\)
0.204613 + 0.978843i \(0.434406\pi\)
\(422\) 4.36708 0.212586
\(423\) −7.51698 −0.365488
\(424\) 4.29612 0.208638
\(425\) 4.87066 0.236262
\(426\) 7.38317 0.357716
\(427\) −25.5496 −1.23643
\(428\) −25.8202 −1.24806
\(429\) −11.7437 −0.566991
\(430\) −34.1188 −1.64535
\(431\) 4.95307 0.238581 0.119291 0.992859i \(-0.461938\pi\)
0.119291 + 0.992859i \(0.461938\pi\)
\(432\) −0.831677 −0.0400141
\(433\) 39.0135 1.87487 0.937436 0.348159i \(-0.113193\pi\)
0.937436 + 0.348159i \(0.113193\pi\)
\(434\) 60.3301 2.89594
\(435\) −12.8158 −0.614472
\(436\) 21.7220 1.04030
\(437\) 8.92906 0.427135
\(438\) 3.74783 0.179078
\(439\) −25.8330 −1.23294 −0.616472 0.787377i \(-0.711439\pi\)
−0.616472 + 0.787377i \(0.711439\pi\)
\(440\) −46.4383 −2.21386
\(441\) −15.3437 −0.730653
\(442\) −7.97297 −0.379235
\(443\) 19.1949 0.911978 0.455989 0.889986i \(-0.349286\pi\)
0.455989 + 0.889986i \(0.349286\pi\)
\(444\) 18.9528 0.899462
\(445\) −13.1520 −0.623467
\(446\) −24.5248 −1.16128
\(447\) −0.0874754 −0.00413744
\(448\) 46.4158 2.19294
\(449\) −30.7152 −1.44954 −0.724770 0.688991i \(-0.758054\pi\)
−0.724770 + 0.688991i \(0.758054\pi\)
\(450\) 28.4626 1.34174
\(451\) 17.7172 0.834272
\(452\) −0.296485 −0.0139455
\(453\) 16.0286 0.753088
\(454\) 58.1920 2.73109
\(455\) 39.3408 1.84432
\(456\) 4.42853 0.207385
\(457\) −6.61176 −0.309285 −0.154643 0.987970i \(-0.549423\pi\)
−0.154643 + 0.987970i \(0.549423\pi\)
\(458\) −16.9999 −0.794352
\(459\) −3.75090 −0.175077
\(460\) 41.6114 1.94014
\(461\) −14.2456 −0.663485 −0.331742 0.943370i \(-0.607637\pi\)
−0.331742 + 0.943370i \(0.607637\pi\)
\(462\) −28.1071 −1.30766
\(463\) −40.9274 −1.90206 −0.951029 0.309103i \(-0.899971\pi\)
−0.951029 + 0.309103i \(0.899971\pi\)
\(464\) 1.33634 0.0620381
\(465\) −15.4553 −0.716724
\(466\) −44.4808 −2.06053
\(467\) 5.55279 0.256952 0.128476 0.991713i \(-0.458991\pi\)
0.128476 + 0.991713i \(0.458991\pi\)
\(468\) −28.9603 −1.33869
\(469\) −8.42073 −0.388833
\(470\) 21.3591 0.985223
\(471\) 8.87213 0.408806
\(472\) 11.8489 0.545390
\(473\) 23.6336 1.08667
\(474\) −16.9183 −0.777085
\(475\) −10.7871 −0.494945
\(476\) −11.8612 −0.543655
\(477\) 3.69632 0.169243
\(478\) −3.16100 −0.144581
\(479\) −23.9135 −1.09264 −0.546319 0.837577i \(-0.683971\pi\)
−0.546319 + 0.837577i \(0.683971\pi\)
\(480\) −11.4806 −0.524016
\(481\) 29.5626 1.34794
\(482\) 21.3340 0.971738
\(483\) 9.85241 0.448300
\(484\) 46.0923 2.09511
\(485\) 2.32248 0.105458
\(486\) −33.7845 −1.53250
\(487\) 11.9983 0.543695 0.271848 0.962340i \(-0.412365\pi\)
0.271848 + 0.962340i \(0.412365\pi\)
\(488\) −20.9061 −0.946376
\(489\) −0.442168 −0.0199955
\(490\) 43.5984 1.96957
\(491\) 12.9861 0.586056 0.293028 0.956104i \(-0.405337\pi\)
0.293028 + 0.956104i \(0.405337\pi\)
\(492\) −7.87381 −0.354979
\(493\) 6.02696 0.271440
\(494\) 17.6578 0.794461
\(495\) −39.9549 −1.79584
\(496\) 1.61157 0.0723617
\(497\) 17.1324 0.768491
\(498\) 0.0650881 0.00291667
\(499\) −19.0751 −0.853919 −0.426960 0.904271i \(-0.640415\pi\)
−0.426960 + 0.904271i \(0.640415\pi\)
\(500\) 1.33495 0.0597008
\(501\) −11.3104 −0.505310
\(502\) 30.8877 1.37859
\(503\) 27.4287 1.22298 0.611492 0.791251i \(-0.290570\pi\)
0.611492 + 0.791251i \(0.290570\pi\)
\(504\) −27.1147 −1.20778
\(505\) −54.2261 −2.41303
\(506\) −46.3717 −2.06147
\(507\) −0.658013 −0.0292234
\(508\) −72.2974 −3.20768
\(509\) 10.8322 0.480130 0.240065 0.970757i \(-0.422831\pi\)
0.240065 + 0.970757i \(0.422831\pi\)
\(510\) 4.88850 0.216466
\(511\) 8.69671 0.384720
\(512\) 2.50725 0.110806
\(513\) 8.30713 0.366769
\(514\) −62.4743 −2.75562
\(515\) −54.0110 −2.38001
\(516\) −10.5031 −0.462375
\(517\) −14.7952 −0.650691
\(518\) 70.7543 3.10877
\(519\) 2.04977 0.0899749
\(520\) 32.1909 1.41166
\(521\) 10.3149 0.451906 0.225953 0.974138i \(-0.427450\pi\)
0.225953 + 0.974138i \(0.427450\pi\)
\(522\) 35.2197 1.54152
\(523\) 12.1984 0.533399 0.266699 0.963780i \(-0.414067\pi\)
0.266699 + 0.963780i \(0.414067\pi\)
\(524\) 31.2504 1.36518
\(525\) −11.9026 −0.519470
\(526\) −54.2027 −2.36335
\(527\) 7.26825 0.316610
\(528\) −0.750813 −0.0326749
\(529\) −6.74528 −0.293273
\(530\) −10.5029 −0.456217
\(531\) 10.1946 0.442409
\(532\) 26.2690 1.13890
\(533\) −12.2815 −0.531972
\(534\) −6.51363 −0.281872
\(535\) 24.6935 1.06759
\(536\) −6.89033 −0.297617
\(537\) −1.01743 −0.0439054
\(538\) 55.0527 2.37349
\(539\) −30.2000 −1.30081
\(540\) 38.7131 1.66595
\(541\) −28.4394 −1.22271 −0.611353 0.791358i \(-0.709374\pi\)
−0.611353 + 0.791358i \(0.709374\pi\)
\(542\) 28.5793 1.22759
\(543\) −4.43298 −0.190237
\(544\) 5.39904 0.231482
\(545\) −20.7741 −0.889866
\(546\) 19.4838 0.833828
\(547\) 3.91466 0.167379 0.0836893 0.996492i \(-0.473330\pi\)
0.0836893 + 0.996492i \(0.473330\pi\)
\(548\) −44.2121 −1.88865
\(549\) −17.9873 −0.767680
\(550\) 56.0210 2.38874
\(551\) −13.3479 −0.568641
\(552\) 8.06181 0.343134
\(553\) −39.2583 −1.66943
\(554\) −54.6349 −2.32121
\(555\) −18.1258 −0.769398
\(556\) −67.2342 −2.85137
\(557\) 29.5323 1.25132 0.625662 0.780095i \(-0.284829\pi\)
0.625662 + 0.780095i \(0.284829\pi\)
\(558\) 42.4734 1.79804
\(559\) −16.3827 −0.692916
\(560\) 2.51518 0.106286
\(561\) −3.38620 −0.142965
\(562\) −48.2893 −2.03696
\(563\) −3.30634 −0.139345 −0.0696727 0.997570i \(-0.522196\pi\)
−0.0696727 + 0.997570i \(0.522196\pi\)
\(564\) 6.57520 0.276866
\(565\) 0.283548 0.0119289
\(566\) −26.4272 −1.11082
\(567\) −18.3671 −0.771347
\(568\) 14.0187 0.588211
\(569\) 16.3949 0.687311 0.343655 0.939096i \(-0.388335\pi\)
0.343655 + 0.939096i \(0.388335\pi\)
\(570\) −10.8266 −0.453476
\(571\) −32.4486 −1.35793 −0.678965 0.734171i \(-0.737571\pi\)
−0.678965 + 0.734171i \(0.737571\pi\)
\(572\) −57.0006 −2.38331
\(573\) 1.16138 0.0485174
\(574\) −29.3943 −1.22690
\(575\) −19.6371 −0.818924
\(576\) 32.6775 1.36156
\(577\) 43.3846 1.80612 0.903061 0.429512i \(-0.141314\pi\)
0.903061 + 0.429512i \(0.141314\pi\)
\(578\) −2.29894 −0.0956232
\(579\) −7.62252 −0.316781
\(580\) −62.2044 −2.58290
\(581\) 0.151035 0.00626597
\(582\) 1.15022 0.0476782
\(583\) 7.27521 0.301308
\(584\) 7.11615 0.294468
\(585\) 27.6966 1.14511
\(586\) 43.1369 1.78197
\(587\) −1.31121 −0.0541195 −0.0270598 0.999634i \(-0.508614\pi\)
−0.0270598 + 0.999634i \(0.508614\pi\)
\(588\) 13.4213 0.553487
\(589\) −16.0970 −0.663267
\(590\) −28.9675 −1.19257
\(591\) −12.9572 −0.532990
\(592\) 1.89003 0.0776797
\(593\) −28.3916 −1.16590 −0.582952 0.812506i \(-0.698103\pi\)
−0.582952 + 0.812506i \(0.698103\pi\)
\(594\) −43.1418 −1.77013
\(595\) 11.3436 0.465041
\(596\) −0.424581 −0.0173915
\(597\) −12.1391 −0.496820
\(598\) 32.1447 1.31450
\(599\) 0.907711 0.0370881 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(600\) −9.73936 −0.397608
\(601\) 15.2212 0.620884 0.310442 0.950592i \(-0.399523\pi\)
0.310442 + 0.950592i \(0.399523\pi\)
\(602\) −39.2101 −1.59808
\(603\) −5.92833 −0.241420
\(604\) 77.7981 3.16556
\(605\) −44.0811 −1.79215
\(606\) −26.8558 −1.09094
\(607\) −7.57408 −0.307423 −0.153711 0.988116i \(-0.549123\pi\)
−0.153711 + 0.988116i \(0.549123\pi\)
\(608\) −11.9573 −0.484932
\(609\) −14.7282 −0.596818
\(610\) 51.1101 2.06939
\(611\) 10.2560 0.414912
\(612\) −8.35045 −0.337547
\(613\) −15.3428 −0.619688 −0.309844 0.950787i \(-0.600277\pi\)
−0.309844 + 0.950787i \(0.600277\pi\)
\(614\) −20.5853 −0.830754
\(615\) 7.53023 0.303648
\(616\) −53.3680 −2.15026
\(617\) −13.4506 −0.541499 −0.270749 0.962650i \(-0.587271\pi\)
−0.270749 + 0.962650i \(0.587271\pi\)
\(618\) −26.7493 −1.07601
\(619\) 29.0423 1.16731 0.583654 0.812003i \(-0.301623\pi\)
0.583654 + 0.812003i \(0.301623\pi\)
\(620\) −75.0158 −3.01271
\(621\) 15.1225 0.606847
\(622\) 11.2000 0.449079
\(623\) −15.1146 −0.605555
\(624\) 0.520461 0.0208351
\(625\) −25.6300 −1.02520
\(626\) −43.6437 −1.74435
\(627\) 7.49943 0.299498
\(628\) 43.0628 1.71839
\(629\) 8.52411 0.339878
\(630\) 66.2883 2.64099
\(631\) −27.7666 −1.10537 −0.552685 0.833390i \(-0.686397\pi\)
−0.552685 + 0.833390i \(0.686397\pi\)
\(632\) −32.1234 −1.27780
\(633\) −1.28570 −0.0511020
\(634\) 56.5321 2.24518
\(635\) 69.1426 2.74384
\(636\) −3.23321 −0.128205
\(637\) 20.9345 0.829456
\(638\) 69.3205 2.74442
\(639\) 12.0615 0.477144
\(640\) −58.9265 −2.32928
\(641\) −11.2254 −0.443378 −0.221689 0.975117i \(-0.571157\pi\)
−0.221689 + 0.975117i \(0.571157\pi\)
\(642\) 12.2296 0.482663
\(643\) 38.8931 1.53379 0.766897 0.641770i \(-0.221800\pi\)
0.766897 + 0.641770i \(0.221800\pi\)
\(644\) 47.8208 1.88440
\(645\) 10.0448 0.395515
\(646\) 5.09147 0.200321
\(647\) 12.2230 0.480537 0.240269 0.970706i \(-0.422764\pi\)
0.240269 + 0.970706i \(0.422764\pi\)
\(648\) −15.0291 −0.590397
\(649\) 20.0654 0.787636
\(650\) −38.8336 −1.52318
\(651\) −17.7616 −0.696133
\(652\) −2.14616 −0.0840501
\(653\) −30.9004 −1.20923 −0.604613 0.796519i \(-0.706672\pi\)
−0.604613 + 0.796519i \(0.706672\pi\)
\(654\) −10.2885 −0.402313
\(655\) −29.8868 −1.16777
\(656\) −0.785198 −0.0306568
\(657\) 6.12263 0.238866
\(658\) 24.5464 0.956918
\(659\) −7.30415 −0.284529 −0.142265 0.989829i \(-0.545438\pi\)
−0.142265 + 0.989829i \(0.545438\pi\)
\(660\) 34.9490 1.36039
\(661\) −30.6933 −1.19383 −0.596916 0.802303i \(-0.703608\pi\)
−0.596916 + 0.802303i \(0.703608\pi\)
\(662\) 47.2825 1.83769
\(663\) 2.34730 0.0911616
\(664\) 0.123585 0.00479604
\(665\) −25.1227 −0.974216
\(666\) 49.8122 1.93019
\(667\) −24.2990 −0.940860
\(668\) −54.8973 −2.12404
\(669\) 7.22028 0.279152
\(670\) 16.8451 0.650782
\(671\) −35.4032 −1.36673
\(672\) −13.1938 −0.508961
\(673\) 25.0745 0.966552 0.483276 0.875468i \(-0.339447\pi\)
0.483276 + 0.875468i \(0.339447\pi\)
\(674\) −45.1300 −1.73834
\(675\) −18.2693 −0.703187
\(676\) −3.19381 −0.122839
\(677\) −13.4478 −0.516840 −0.258420 0.966033i \(-0.583202\pi\)
−0.258420 + 0.966033i \(0.583202\pi\)
\(678\) 0.140429 0.00539313
\(679\) 2.66904 0.102429
\(680\) 9.28197 0.355947
\(681\) −17.1321 −0.656505
\(682\) 83.5975 3.20111
\(683\) −43.9040 −1.67994 −0.839971 0.542632i \(-0.817428\pi\)
−0.839971 + 0.542632i \(0.817428\pi\)
\(684\) 18.4938 0.707128
\(685\) 42.2828 1.61554
\(686\) −7.99925 −0.305413
\(687\) 5.00489 0.190948
\(688\) −1.04740 −0.0399318
\(689\) −5.04315 −0.192129
\(690\) −19.7090 −0.750310
\(691\) 38.9391 1.48131 0.740656 0.671884i \(-0.234515\pi\)
0.740656 + 0.671884i \(0.234515\pi\)
\(692\) 9.94900 0.378204
\(693\) −45.9170 −1.74424
\(694\) 41.2658 1.56643
\(695\) 64.3004 2.43905
\(696\) −12.0515 −0.456811
\(697\) −3.54127 −0.134135
\(698\) 27.3144 1.03386
\(699\) 13.0955 0.495316
\(700\) −57.7716 −2.18356
\(701\) −5.69168 −0.214972 −0.107486 0.994207i \(-0.534280\pi\)
−0.107486 + 0.994207i \(0.534280\pi\)
\(702\) 29.9058 1.12872
\(703\) −18.8784 −0.712012
\(704\) 64.3169 2.42403
\(705\) −6.28828 −0.236831
\(706\) −2.29894 −0.0865216
\(707\) −62.3179 −2.34370
\(708\) −8.91737 −0.335135
\(709\) −0.603496 −0.0226648 −0.0113324 0.999936i \(-0.503607\pi\)
−0.0113324 + 0.999936i \(0.503607\pi\)
\(710\) −34.2721 −1.28621
\(711\) −27.6385 −1.03653
\(712\) −12.3677 −0.463498
\(713\) −29.3035 −1.09743
\(714\) 5.61797 0.210247
\(715\) 54.5133 2.03868
\(716\) −4.93832 −0.184554
\(717\) 0.930623 0.0347547
\(718\) 54.5150 2.03448
\(719\) 28.9927 1.08124 0.540622 0.841266i \(-0.318189\pi\)
0.540622 + 0.841266i \(0.318189\pi\)
\(720\) 1.77073 0.0659913
\(721\) −62.0707 −2.31163
\(722\) 32.4037 1.20594
\(723\) −6.28089 −0.233589
\(724\) −21.5164 −0.799651
\(725\) 29.3552 1.09023
\(726\) −21.8314 −0.810239
\(727\) −28.1318 −1.04335 −0.521676 0.853144i \(-0.674693\pi\)
−0.521676 + 0.853144i \(0.674693\pi\)
\(728\) 36.9945 1.37111
\(729\) −5.31469 −0.196840
\(730\) −17.3971 −0.643897
\(731\) −4.72382 −0.174717
\(732\) 15.7337 0.581536
\(733\) −29.6995 −1.09698 −0.548489 0.836158i \(-0.684797\pi\)
−0.548489 + 0.836158i \(0.684797\pi\)
\(734\) −1.46676 −0.0541390
\(735\) −12.8357 −0.473451
\(736\) −21.7674 −0.802356
\(737\) −11.6683 −0.429809
\(738\) −20.6941 −0.761760
\(739\) 30.6203 1.12639 0.563194 0.826325i \(-0.309573\pi\)
0.563194 + 0.826325i \(0.309573\pi\)
\(740\) −87.9776 −3.23412
\(741\) −5.19858 −0.190975
\(742\) −12.0702 −0.443110
\(743\) −8.73139 −0.320324 −0.160162 0.987091i \(-0.551202\pi\)
−0.160162 + 0.987091i \(0.551202\pi\)
\(744\) −14.5336 −0.532827
\(745\) 0.406053 0.0148766
\(746\) −6.92346 −0.253486
\(747\) 0.106331 0.00389044
\(748\) −16.4356 −0.600946
\(749\) 28.3783 1.03692
\(750\) −0.632293 −0.0230881
\(751\) 4.57804 0.167055 0.0835275 0.996505i \(-0.473381\pi\)
0.0835275 + 0.996505i \(0.473381\pi\)
\(752\) 0.655697 0.0239108
\(753\) −9.09358 −0.331388
\(754\) −48.0527 −1.74998
\(755\) −74.4033 −2.70781
\(756\) 44.4900 1.61808
\(757\) −10.4326 −0.379181 −0.189590 0.981863i \(-0.560716\pi\)
−0.189590 + 0.981863i \(0.560716\pi\)
\(758\) −56.1582 −2.03976
\(759\) 13.6522 0.495542
\(760\) −20.5568 −0.745675
\(761\) 0.724565 0.0262655 0.0131327 0.999914i \(-0.495820\pi\)
0.0131327 + 0.999914i \(0.495820\pi\)
\(762\) 34.2433 1.24050
\(763\) −23.8741 −0.864300
\(764\) 5.63701 0.203940
\(765\) 7.98607 0.288737
\(766\) −6.09249 −0.220131
\(767\) −13.9093 −0.502235
\(768\) −11.7819 −0.425143
\(769\) 0.441772 0.0159307 0.00796535 0.999968i \(-0.497465\pi\)
0.00796535 + 0.999968i \(0.497465\pi\)
\(770\) 130.471 4.70184
\(771\) 18.3929 0.662404
\(772\) −36.9976 −1.33157
\(773\) −20.0461 −0.721007 −0.360503 0.932758i \(-0.617395\pi\)
−0.360503 + 0.932758i \(0.617395\pi\)
\(774\) −27.6046 −0.992225
\(775\) 35.4012 1.27165
\(776\) 2.18397 0.0783998
\(777\) −20.8306 −0.747293
\(778\) −83.1945 −2.98267
\(779\) 7.84288 0.281000
\(780\) −24.2265 −0.867450
\(781\) 23.7398 0.849476
\(782\) 9.26866 0.331446
\(783\) −22.6065 −0.807890
\(784\) 1.33841 0.0478004
\(785\) −41.1837 −1.46991
\(786\) −14.8016 −0.527956
\(787\) −11.4148 −0.406892 −0.203446 0.979086i \(-0.565214\pi\)
−0.203446 + 0.979086i \(0.565214\pi\)
\(788\) −62.8908 −2.24039
\(789\) 15.9577 0.568108
\(790\) 78.5335 2.79410
\(791\) 0.325859 0.0115862
\(792\) −37.5720 −1.33506
\(793\) 24.5414 0.871491
\(794\) −65.3118 −2.31783
\(795\) 3.09213 0.109667
\(796\) −58.9196 −2.08835
\(797\) 43.3706 1.53626 0.768132 0.640291i \(-0.221186\pi\)
0.768132 + 0.640291i \(0.221186\pi\)
\(798\) −12.4422 −0.440448
\(799\) 2.95722 0.104619
\(800\) 26.2969 0.929734
\(801\) −10.6410 −0.375980
\(802\) 33.0403 1.16669
\(803\) 12.0508 0.425262
\(804\) 5.18559 0.182882
\(805\) −45.7341 −1.61191
\(806\) −57.9495 −2.04119
\(807\) −16.2079 −0.570546
\(808\) −50.9921 −1.79390
\(809\) −26.6505 −0.936982 −0.468491 0.883468i \(-0.655202\pi\)
−0.468491 + 0.883468i \(0.655202\pi\)
\(810\) 36.7422 1.29099
\(811\) −50.9075 −1.78761 −0.893803 0.448460i \(-0.851973\pi\)
−0.893803 + 0.448460i \(0.851973\pi\)
\(812\) −71.4867 −2.50869
\(813\) −8.41395 −0.295090
\(814\) 98.0420 3.43637
\(815\) 2.05251 0.0718963
\(816\) 0.150070 0.00525352
\(817\) 10.4619 0.366015
\(818\) −31.4516 −1.09968
\(819\) 31.8295 1.11221
\(820\) 36.5496 1.27637
\(821\) 4.18614 0.146097 0.0730487 0.997328i \(-0.476727\pi\)
0.0730487 + 0.997328i \(0.476727\pi\)
\(822\) 20.9408 0.730395
\(823\) 31.6078 1.10178 0.550889 0.834578i \(-0.314289\pi\)
0.550889 + 0.834578i \(0.314289\pi\)
\(824\) −50.7898 −1.76935
\(825\) −16.4930 −0.574212
\(826\) −33.2901 −1.15831
\(827\) 19.9084 0.692284 0.346142 0.938182i \(-0.387492\pi\)
0.346142 + 0.938182i \(0.387492\pi\)
\(828\) 33.6666 1.17000
\(829\) −20.2717 −0.704064 −0.352032 0.935988i \(-0.614509\pi\)
−0.352032 + 0.935988i \(0.614509\pi\)
\(830\) −0.302134 −0.0104872
\(831\) 16.0849 0.557980
\(832\) −44.5843 −1.54568
\(833\) 6.03629 0.209145
\(834\) 31.8451 1.10271
\(835\) 52.5018 1.81690
\(836\) 36.4001 1.25892
\(837\) −27.2625 −0.942329
\(838\) 0.183828 0.00635023
\(839\) 31.2137 1.07761 0.538807 0.842429i \(-0.318875\pi\)
0.538807 + 0.842429i \(0.318875\pi\)
\(840\) −22.6826 −0.782624
\(841\) 7.32421 0.252559
\(842\) −19.3033 −0.665237
\(843\) 14.2167 0.489650
\(844\) −6.24042 −0.214804
\(845\) 3.05444 0.105076
\(846\) 17.2811 0.594135
\(847\) −50.6589 −1.74066
\(848\) −0.322425 −0.0110721
\(849\) 7.78037 0.267022
\(850\) −11.1973 −0.384065
\(851\) −34.3668 −1.17808
\(852\) −10.5503 −0.361448
\(853\) 33.6167 1.15101 0.575507 0.817797i \(-0.304805\pi\)
0.575507 + 0.817797i \(0.304805\pi\)
\(854\) 58.7368 2.00993
\(855\) −17.6868 −0.604876
\(856\) 23.2208 0.793669
\(857\) 8.88779 0.303601 0.151801 0.988411i \(-0.451493\pi\)
0.151801 + 0.988411i \(0.451493\pi\)
\(858\) 26.9980 0.921697
\(859\) −29.8631 −1.01892 −0.509458 0.860496i \(-0.670154\pi\)
−0.509458 + 0.860496i \(0.670154\pi\)
\(860\) 48.7547 1.66252
\(861\) 8.65391 0.294924
\(862\) −11.3868 −0.387836
\(863\) −26.2242 −0.892683 −0.446341 0.894863i \(-0.647273\pi\)
−0.446341 + 0.894863i \(0.647273\pi\)
\(864\) −20.2512 −0.688961
\(865\) −9.51486 −0.323515
\(866\) −89.6897 −3.04778
\(867\) 0.676824 0.0229861
\(868\) −86.2099 −2.92615
\(869\) −54.3990 −1.84536
\(870\) 29.4628 0.998882
\(871\) 8.08845 0.274067
\(872\) −19.5352 −0.661544
\(873\) 1.87905 0.0635963
\(874\) −20.5274 −0.694348
\(875\) −1.46721 −0.0496008
\(876\) −5.35554 −0.180947
\(877\) −36.4614 −1.23121 −0.615606 0.788054i \(-0.711089\pi\)
−0.615606 + 0.788054i \(0.711089\pi\)
\(878\) 59.3885 2.00427
\(879\) −12.6998 −0.428354
\(880\) 3.48521 0.117486
\(881\) −46.5762 −1.56919 −0.784595 0.620008i \(-0.787129\pi\)
−0.784595 + 0.620008i \(0.787129\pi\)
\(882\) 35.2742 1.18774
\(883\) 26.9522 0.907013 0.453507 0.891253i \(-0.350173\pi\)
0.453507 + 0.891253i \(0.350173\pi\)
\(884\) 11.3931 0.383192
\(885\) 8.52825 0.286674
\(886\) −44.1279 −1.48251
\(887\) 53.4339 1.79413 0.897067 0.441895i \(-0.145694\pi\)
0.897067 + 0.441895i \(0.145694\pi\)
\(888\) −17.0448 −0.571986
\(889\) 79.4602 2.66501
\(890\) 30.2357 1.01350
\(891\) −25.4508 −0.852633
\(892\) 35.0452 1.17340
\(893\) −6.54937 −0.219166
\(894\) 0.201100 0.00672580
\(895\) 4.72283 0.157867
\(896\) −67.7197 −2.26236
\(897\) −9.46364 −0.315982
\(898\) 70.6123 2.35636
\(899\) 43.8054 1.46099
\(900\) −40.6722 −1.35574
\(901\) −1.45415 −0.0484447
\(902\) −40.7308 −1.35619
\(903\) 11.5437 0.384151
\(904\) 0.266637 0.00886821
\(905\) 20.5775 0.684020
\(906\) −36.8487 −1.22421
\(907\) 20.4132 0.677809 0.338904 0.940821i \(-0.389944\pi\)
0.338904 + 0.940821i \(0.389944\pi\)
\(908\) −83.1546 −2.75958
\(909\) −43.8728 −1.45517
\(910\) −90.4420 −2.99812
\(911\) −14.8722 −0.492737 −0.246369 0.969176i \(-0.579237\pi\)
−0.246369 + 0.969176i \(0.579237\pi\)
\(912\) −0.332362 −0.0110056
\(913\) 0.209284 0.00692628
\(914\) 15.2000 0.502772
\(915\) −15.0472 −0.497445
\(916\) 24.2923 0.802640
\(917\) −34.3466 −1.13422
\(918\) 8.62307 0.284604
\(919\) −43.6636 −1.44033 −0.720165 0.693803i \(-0.755934\pi\)
−0.720165 + 0.693803i \(0.755934\pi\)
\(920\) −37.4223 −1.23378
\(921\) 6.06046 0.199699
\(922\) 32.7498 1.07856
\(923\) −16.4563 −0.541667
\(924\) 40.1642 1.32130
\(925\) 41.5180 1.36510
\(926\) 94.0895 3.09197
\(927\) −43.6988 −1.43526
\(928\) 32.5398 1.06817
\(929\) 8.52875 0.279819 0.139910 0.990164i \(-0.455319\pi\)
0.139910 + 0.990164i \(0.455319\pi\)
\(930\) 35.5309 1.16510
\(931\) −13.3686 −0.438139
\(932\) 63.5617 2.08203
\(933\) −3.29736 −0.107951
\(934\) −12.7655 −0.417700
\(935\) 15.7184 0.514048
\(936\) 26.0448 0.851300
\(937\) −9.45609 −0.308917 −0.154458 0.987999i \(-0.549363\pi\)
−0.154458 + 0.987999i \(0.549363\pi\)
\(938\) 19.3587 0.632085
\(939\) 12.8490 0.419312
\(940\) −30.5215 −0.995503
\(941\) 37.6423 1.22710 0.613551 0.789655i \(-0.289740\pi\)
0.613551 + 0.789655i \(0.289740\pi\)
\(942\) −20.3965 −0.664553
\(943\) 14.2774 0.464936
\(944\) −0.889264 −0.0289431
\(945\) −42.5486 −1.38411
\(946\) −54.3322 −1.76649
\(947\) 31.5419 1.02497 0.512486 0.858695i \(-0.328725\pi\)
0.512486 + 0.858695i \(0.328725\pi\)
\(948\) 24.1758 0.785193
\(949\) −8.35354 −0.271167
\(950\) 24.7988 0.804580
\(951\) −16.6435 −0.539701
\(952\) 10.6671 0.345721
\(953\) 21.0411 0.681588 0.340794 0.940138i \(-0.389304\pi\)
0.340794 + 0.940138i \(0.389304\pi\)
\(954\) −8.49760 −0.275120
\(955\) −5.39103 −0.174450
\(956\) 4.51698 0.146089
\(957\) −20.4085 −0.659712
\(958\) 54.9757 1.77618
\(959\) 48.5924 1.56913
\(960\) 27.3362 0.882271
\(961\) 21.8275 0.704113
\(962\) −67.9624 −2.19120
\(963\) 19.9788 0.643807
\(964\) −30.4857 −0.981877
\(965\) 35.3831 1.13902
\(966\) −22.6501 −0.728754
\(967\) 4.58049 0.147299 0.0736493 0.997284i \(-0.476535\pi\)
0.0736493 + 0.997284i \(0.476535\pi\)
\(968\) −41.4521 −1.33232
\(969\) −1.49897 −0.0481537
\(970\) −5.33923 −0.171432
\(971\) −4.26831 −0.136976 −0.0684882 0.997652i \(-0.521818\pi\)
−0.0684882 + 0.997652i \(0.521818\pi\)
\(972\) 48.2770 1.54849
\(973\) 73.8954 2.36898
\(974\) −27.5834 −0.883828
\(975\) 11.4329 0.366146
\(976\) 1.56901 0.0502228
\(977\) −6.20038 −0.198368 −0.0991838 0.995069i \(-0.531623\pi\)
−0.0991838 + 0.995069i \(0.531623\pi\)
\(978\) 1.01652 0.0325046
\(979\) −20.9439 −0.669369
\(980\) −62.3007 −1.99012
\(981\) −16.8078 −0.536631
\(982\) −29.8543 −0.952688
\(983\) 21.5731 0.688076 0.344038 0.938956i \(-0.388205\pi\)
0.344038 + 0.938956i \(0.388205\pi\)
\(984\) 7.08113 0.225738
\(985\) 60.1464 1.91642
\(986\) −13.8556 −0.441252
\(987\) −7.22664 −0.230026
\(988\) −25.2324 −0.802751
\(989\) 19.0451 0.605599
\(990\) 91.8537 2.91930
\(991\) −2.23436 −0.0709766 −0.0354883 0.999370i \(-0.511299\pi\)
−0.0354883 + 0.999370i \(0.511299\pi\)
\(992\) 39.2416 1.24592
\(993\) −13.9203 −0.441748
\(994\) −39.3862 −1.24925
\(995\) 56.3486 1.78637
\(996\) −0.0930090 −0.00294710
\(997\) −23.3745 −0.740278 −0.370139 0.928976i \(-0.620690\pi\)
−0.370139 + 0.928976i \(0.620690\pi\)
\(998\) 43.8525 1.38813
\(999\) −31.9730 −1.01158
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 \(a_p\))