Properties

Label 8015.2.a.l.1.8
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23328 q^{2}\) \(+1.54114 q^{3}\) \(+2.98754 q^{4}\) \(-1.00000 q^{5}\) \(-3.44181 q^{6}\) \(-1.00000 q^{7}\) \(-2.20546 q^{8}\) \(-0.624877 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23328 q^{2}\) \(+1.54114 q^{3}\) \(+2.98754 q^{4}\) \(-1.00000 q^{5}\) \(-3.44181 q^{6}\) \(-1.00000 q^{7}\) \(-2.20546 q^{8}\) \(-0.624877 q^{9}\) \(+2.23328 q^{10}\) \(-0.380972 q^{11}\) \(+4.60423 q^{12}\) \(-3.83163 q^{13}\) \(+2.23328 q^{14}\) \(-1.54114 q^{15}\) \(-1.04967 q^{16}\) \(-2.25256 q^{17}\) \(+1.39553 q^{18}\) \(-4.69167 q^{19}\) \(-2.98754 q^{20}\) \(-1.54114 q^{21}\) \(+0.850816 q^{22}\) \(+3.81705 q^{23}\) \(-3.39893 q^{24}\) \(+1.00000 q^{25}\) \(+8.55710 q^{26}\) \(-5.58646 q^{27}\) \(-2.98754 q^{28}\) \(-4.90178 q^{29}\) \(+3.44181 q^{30}\) \(-0.412751 q^{31}\) \(+6.75514 q^{32}\) \(-0.587132 q^{33}\) \(+5.03059 q^{34}\) \(+1.00000 q^{35}\) \(-1.86685 q^{36}\) \(-4.75791 q^{37}\) \(+10.4778 q^{38}\) \(-5.90509 q^{39}\) \(+2.20546 q^{40}\) \(+2.15652 q^{41}\) \(+3.44181 q^{42}\) \(-8.37449 q^{43}\) \(-1.13817 q^{44}\) \(+0.624877 q^{45}\) \(-8.52455 q^{46}\) \(+9.23317 q^{47}\) \(-1.61770 q^{48}\) \(+1.00000 q^{49}\) \(-2.23328 q^{50}\) \(-3.47151 q^{51}\) \(-11.4471 q^{52}\) \(-9.56310 q^{53}\) \(+12.4761 q^{54}\) \(+0.380972 q^{55}\) \(+2.20546 q^{56}\) \(-7.23054 q^{57}\) \(+10.9470 q^{58}\) \(-0.910238 q^{59}\) \(-4.60423 q^{60}\) \(+9.37004 q^{61}\) \(+0.921789 q^{62}\) \(+0.624877 q^{63}\) \(-12.9868 q^{64}\) \(+3.83163 q^{65}\) \(+1.31123 q^{66}\) \(+3.78810 q^{67}\) \(-6.72961 q^{68}\) \(+5.88262 q^{69}\) \(-2.23328 q^{70}\) \(-8.71837 q^{71}\) \(+1.37814 q^{72}\) \(-3.06051 q^{73}\) \(+10.6258 q^{74}\) \(+1.54114 q^{75}\) \(-14.0166 q^{76}\) \(+0.380972 q^{77}\) \(+13.1877 q^{78}\) \(+6.21476 q^{79}\) \(+1.04967 q^{80}\) \(-6.73490 q^{81}\) \(-4.81611 q^{82}\) \(-2.30591 q^{83}\) \(-4.60423 q^{84}\) \(+2.25256 q^{85}\) \(+18.7026 q^{86}\) \(-7.55434 q^{87}\) \(+0.840217 q^{88}\) \(-12.4143 q^{89}\) \(-1.39553 q^{90}\) \(+3.83163 q^{91}\) \(+11.4036 q^{92}\) \(-0.636109 q^{93}\) \(-20.6203 q^{94}\) \(+4.69167 q^{95}\) \(+10.4106 q^{96}\) \(-13.2234 q^{97}\) \(-2.23328 q^{98}\) \(+0.238060 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23328 −1.57917 −0.789584 0.613643i \(-0.789704\pi\)
−0.789584 + 0.613643i \(0.789704\pi\)
\(3\) 1.54114 0.889780 0.444890 0.895585i \(-0.353243\pi\)
0.444890 + 0.895585i \(0.353243\pi\)
\(4\) 2.98754 1.49377
\(5\) −1.00000 −0.447214
\(6\) −3.44181 −1.40511
\(7\) −1.00000 −0.377964
\(8\) −2.20546 −0.779748
\(9\) −0.624877 −0.208292
\(10\) 2.23328 0.706225
\(11\) −0.380972 −0.114867 −0.0574336 0.998349i \(-0.518292\pi\)
−0.0574336 + 0.998349i \(0.518292\pi\)
\(12\) 4.60423 1.32913
\(13\) −3.83163 −1.06270 −0.531351 0.847152i \(-0.678315\pi\)
−0.531351 + 0.847152i \(0.678315\pi\)
\(14\) 2.23328 0.596869
\(15\) −1.54114 −0.397922
\(16\) −1.04967 −0.262419
\(17\) −2.25256 −0.546325 −0.273163 0.961968i \(-0.588070\pi\)
−0.273163 + 0.961968i \(0.588070\pi\)
\(18\) 1.39553 0.328929
\(19\) −4.69167 −1.07634 −0.538171 0.842835i \(-0.680885\pi\)
−0.538171 + 0.842835i \(0.680885\pi\)
\(20\) −2.98754 −0.668035
\(21\) −1.54114 −0.336305
\(22\) 0.850816 0.181395
\(23\) 3.81705 0.795910 0.397955 0.917405i \(-0.369720\pi\)
0.397955 + 0.917405i \(0.369720\pi\)
\(24\) −3.39893 −0.693804
\(25\) 1.00000 0.200000
\(26\) 8.55710 1.67818
\(27\) −5.58646 −1.07511
\(28\) −2.98754 −0.564592
\(29\) −4.90178 −0.910237 −0.455118 0.890431i \(-0.650403\pi\)
−0.455118 + 0.890431i \(0.650403\pi\)
\(30\) 3.44181 0.628385
\(31\) −0.412751 −0.0741323 −0.0370661 0.999313i \(-0.511801\pi\)
−0.0370661 + 0.999313i \(0.511801\pi\)
\(32\) 6.75514 1.19415
\(33\) −0.587132 −0.102207
\(34\) 5.03059 0.862739
\(35\) 1.00000 0.169031
\(36\) −1.86685 −0.311141
\(37\) −4.75791 −0.782196 −0.391098 0.920349i \(-0.627905\pi\)
−0.391098 + 0.920349i \(0.627905\pi\)
\(38\) 10.4778 1.69973
\(39\) −5.90509 −0.945570
\(40\) 2.20546 0.348714
\(41\) 2.15652 0.336791 0.168396 0.985719i \(-0.446141\pi\)
0.168396 + 0.985719i \(0.446141\pi\)
\(42\) 3.44181 0.531082
\(43\) −8.37449 −1.27710 −0.638549 0.769581i \(-0.720465\pi\)
−0.638549 + 0.769581i \(0.720465\pi\)
\(44\) −1.13817 −0.171585
\(45\) 0.624877 0.0931512
\(46\) −8.52455 −1.25688
\(47\) 9.23317 1.34680 0.673398 0.739280i \(-0.264834\pi\)
0.673398 + 0.739280i \(0.264834\pi\)
\(48\) −1.61770 −0.233495
\(49\) 1.00000 0.142857
\(50\) −2.23328 −0.315834
\(51\) −3.47151 −0.486109
\(52\) −11.4471 −1.58743
\(53\) −9.56310 −1.31359 −0.656796 0.754068i \(-0.728089\pi\)
−0.656796 + 0.754068i \(0.728089\pi\)
\(54\) 12.4761 1.69779
\(55\) 0.380972 0.0513702
\(56\) 2.20546 0.294717
\(57\) −7.23054 −0.957708
\(58\) 10.9470 1.43742
\(59\) −0.910238 −0.118503 −0.0592514 0.998243i \(-0.518871\pi\)
−0.0592514 + 0.998243i \(0.518871\pi\)
\(60\) −4.60423 −0.594404
\(61\) 9.37004 1.19971 0.599855 0.800108i \(-0.295225\pi\)
0.599855 + 0.800108i \(0.295225\pi\)
\(62\) 0.921789 0.117067
\(63\) 0.624877 0.0787271
\(64\) −12.9868 −1.62335
\(65\) 3.83163 0.475255
\(66\) 1.31123 0.161401
\(67\) 3.78810 0.462790 0.231395 0.972860i \(-0.425671\pi\)
0.231395 + 0.972860i \(0.425671\pi\)
\(68\) −6.72961 −0.816085
\(69\) 5.88262 0.708185
\(70\) −2.23328 −0.266928
\(71\) −8.71837 −1.03468 −0.517340 0.855780i \(-0.673078\pi\)
−0.517340 + 0.855780i \(0.673078\pi\)
\(72\) 1.37814 0.162415
\(73\) −3.06051 −0.358206 −0.179103 0.983830i \(-0.557319\pi\)
−0.179103 + 0.983830i \(0.557319\pi\)
\(74\) 10.6258 1.23522
\(75\) 1.54114 0.177956
\(76\) −14.0166 −1.60781
\(77\) 0.380972 0.0434157
\(78\) 13.1877 1.49321
\(79\) 6.21476 0.699216 0.349608 0.936896i \(-0.386315\pi\)
0.349608 + 0.936896i \(0.386315\pi\)
\(80\) 1.04967 0.117357
\(81\) −6.73490 −0.748322
\(82\) −4.81611 −0.531850
\(83\) −2.30591 −0.253106 −0.126553 0.991960i \(-0.540391\pi\)
−0.126553 + 0.991960i \(0.540391\pi\)
\(84\) −4.60423 −0.502363
\(85\) 2.25256 0.244324
\(86\) 18.7026 2.01675
\(87\) −7.55434 −0.809910
\(88\) 0.840217 0.0895675
\(89\) −12.4143 −1.31591 −0.657955 0.753057i \(-0.728578\pi\)
−0.657955 + 0.753057i \(0.728578\pi\)
\(90\) −1.39553 −0.147101
\(91\) 3.83163 0.401664
\(92\) 11.4036 1.18891
\(93\) −0.636109 −0.0659614
\(94\) −20.6203 −2.12682
\(95\) 4.69167 0.481355
\(96\) 10.4106 1.06253
\(97\) −13.2234 −1.34263 −0.671315 0.741172i \(-0.734270\pi\)
−0.671315 + 0.741172i \(0.734270\pi\)
\(98\) −2.23328 −0.225595
\(99\) 0.238060 0.0239260
\(100\) 2.98754 0.298754
\(101\) −3.18741 −0.317159 −0.158579 0.987346i \(-0.550691\pi\)
−0.158579 + 0.987346i \(0.550691\pi\)
\(102\) 7.75286 0.767648
\(103\) 7.80859 0.769403 0.384702 0.923041i \(-0.374304\pi\)
0.384702 + 0.923041i \(0.374304\pi\)
\(104\) 8.45050 0.828639
\(105\) 1.54114 0.150400
\(106\) 21.3571 2.07438
\(107\) 5.06847 0.489988 0.244994 0.969525i \(-0.421214\pi\)
0.244994 + 0.969525i \(0.421214\pi\)
\(108\) −16.6898 −1.60597
\(109\) 18.4401 1.76624 0.883122 0.469143i \(-0.155437\pi\)
0.883122 + 0.469143i \(0.155437\pi\)
\(110\) −0.850816 −0.0811222
\(111\) −7.33263 −0.695982
\(112\) 1.04967 0.0991849
\(113\) 14.2113 1.33689 0.668446 0.743761i \(-0.266960\pi\)
0.668446 + 0.743761i \(0.266960\pi\)
\(114\) 16.1478 1.51238
\(115\) −3.81705 −0.355942
\(116\) −14.6443 −1.35969
\(117\) 2.39429 0.221353
\(118\) 2.03282 0.187136
\(119\) 2.25256 0.206492
\(120\) 3.39893 0.310278
\(121\) −10.8549 −0.986806
\(122\) −20.9259 −1.89454
\(123\) 3.32350 0.299670
\(124\) −1.23311 −0.110737
\(125\) −1.00000 −0.0894427
\(126\) −1.39553 −0.124323
\(127\) 2.02659 0.179831 0.0899153 0.995949i \(-0.471340\pi\)
0.0899153 + 0.995949i \(0.471340\pi\)
\(128\) 15.4928 1.36939
\(129\) −12.9063 −1.13634
\(130\) −8.55710 −0.750507
\(131\) 0.716254 0.0625794 0.0312897 0.999510i \(-0.490039\pi\)
0.0312897 + 0.999510i \(0.490039\pi\)
\(132\) −1.75408 −0.152673
\(133\) 4.69167 0.406819
\(134\) −8.45990 −0.730824
\(135\) 5.58646 0.480806
\(136\) 4.96792 0.425996
\(137\) 20.0041 1.70907 0.854534 0.519395i \(-0.173843\pi\)
0.854534 + 0.519395i \(0.173843\pi\)
\(138\) −13.1376 −1.11834
\(139\) 8.57697 0.727489 0.363745 0.931499i \(-0.381498\pi\)
0.363745 + 0.931499i \(0.381498\pi\)
\(140\) 2.98754 0.252493
\(141\) 14.2296 1.19835
\(142\) 19.4706 1.63393
\(143\) 1.45974 0.122070
\(144\) 0.655917 0.0546598
\(145\) 4.90178 0.407070
\(146\) 6.83498 0.565667
\(147\) 1.54114 0.127111
\(148\) −14.2145 −1.16842
\(149\) −20.2101 −1.65568 −0.827840 0.560965i \(-0.810430\pi\)
−0.827840 + 0.560965i \(0.810430\pi\)
\(150\) −3.44181 −0.281022
\(151\) 8.30709 0.676022 0.338011 0.941142i \(-0.390246\pi\)
0.338011 + 0.941142i \(0.390246\pi\)
\(152\) 10.3473 0.839276
\(153\) 1.40757 0.113795
\(154\) −0.850816 −0.0685607
\(155\) 0.412751 0.0331530
\(156\) −17.6417 −1.41247
\(157\) 13.4589 1.07414 0.537069 0.843538i \(-0.319531\pi\)
0.537069 + 0.843538i \(0.319531\pi\)
\(158\) −13.8793 −1.10418
\(159\) −14.7381 −1.16881
\(160\) −6.75514 −0.534040
\(161\) −3.81705 −0.300826
\(162\) 15.0409 1.18173
\(163\) −3.86110 −0.302425 −0.151212 0.988501i \(-0.548318\pi\)
−0.151212 + 0.988501i \(0.548318\pi\)
\(164\) 6.44269 0.503089
\(165\) 0.587132 0.0457081
\(166\) 5.14973 0.399697
\(167\) −6.59998 −0.510722 −0.255361 0.966846i \(-0.582194\pi\)
−0.255361 + 0.966846i \(0.582194\pi\)
\(168\) 3.39893 0.262233
\(169\) 1.68136 0.129335
\(170\) −5.03059 −0.385829
\(171\) 2.93172 0.224194
\(172\) −25.0192 −1.90769
\(173\) −20.3752 −1.54910 −0.774549 0.632514i \(-0.782023\pi\)
−0.774549 + 0.632514i \(0.782023\pi\)
\(174\) 16.8710 1.27898
\(175\) −1.00000 −0.0755929
\(176\) 0.399896 0.0301433
\(177\) −1.40281 −0.105441
\(178\) 27.7245 2.07804
\(179\) −10.4006 −0.777375 −0.388688 0.921370i \(-0.627071\pi\)
−0.388688 + 0.921370i \(0.627071\pi\)
\(180\) 1.86685 0.139147
\(181\) 5.23795 0.389334 0.194667 0.980869i \(-0.437637\pi\)
0.194667 + 0.980869i \(0.437637\pi\)
\(182\) −8.55710 −0.634294
\(183\) 14.4406 1.06748
\(184\) −8.41835 −0.620609
\(185\) 4.75791 0.349809
\(186\) 1.42061 0.104164
\(187\) 0.858160 0.0627549
\(188\) 27.5845 2.01181
\(189\) 5.58646 0.406355
\(190\) −10.4778 −0.760141
\(191\) 7.80441 0.564708 0.282354 0.959310i \(-0.408885\pi\)
0.282354 + 0.959310i \(0.408885\pi\)
\(192\) −20.0145 −1.44442
\(193\) 17.0029 1.22389 0.611946 0.790900i \(-0.290387\pi\)
0.611946 + 0.790900i \(0.290387\pi\)
\(194\) 29.5315 2.12024
\(195\) 5.90509 0.422872
\(196\) 2.98754 0.213396
\(197\) −9.63174 −0.686233 −0.343117 0.939293i \(-0.611483\pi\)
−0.343117 + 0.939293i \(0.611483\pi\)
\(198\) −0.531656 −0.0377831
\(199\) −8.90697 −0.631399 −0.315699 0.948859i \(-0.602239\pi\)
−0.315699 + 0.948859i \(0.602239\pi\)
\(200\) −2.20546 −0.155950
\(201\) 5.83801 0.411781
\(202\) 7.11838 0.500847
\(203\) 4.90178 0.344037
\(204\) −10.3713 −0.726136
\(205\) −2.15652 −0.150618
\(206\) −17.4388 −1.21502
\(207\) −2.38519 −0.165782
\(208\) 4.02196 0.278873
\(209\) 1.78739 0.123637
\(210\) −3.44181 −0.237507
\(211\) 7.26557 0.500183 0.250091 0.968222i \(-0.419539\pi\)
0.250091 + 0.968222i \(0.419539\pi\)
\(212\) −28.5702 −1.96221
\(213\) −13.4363 −0.920637
\(214\) −11.3193 −0.773773
\(215\) 8.37449 0.571136
\(216\) 12.3207 0.838318
\(217\) 0.412751 0.0280194
\(218\) −41.1820 −2.78920
\(219\) −4.71669 −0.318724
\(220\) 1.13817 0.0767353
\(221\) 8.63096 0.580581
\(222\) 16.3758 1.09907
\(223\) 21.9365 1.46898 0.734488 0.678622i \(-0.237422\pi\)
0.734488 + 0.678622i \(0.237422\pi\)
\(224\) −6.75514 −0.451347
\(225\) −0.624877 −0.0416585
\(226\) −31.7379 −2.11118
\(227\) −24.7687 −1.64396 −0.821980 0.569517i \(-0.807130\pi\)
−0.821980 + 0.569517i \(0.807130\pi\)
\(228\) −21.6015 −1.43060
\(229\) 1.00000 0.0660819
\(230\) 8.52455 0.562092
\(231\) 0.587132 0.0386304
\(232\) 10.8107 0.709755
\(233\) 24.6662 1.61593 0.807967 0.589227i \(-0.200568\pi\)
0.807967 + 0.589227i \(0.200568\pi\)
\(234\) −5.34713 −0.349553
\(235\) −9.23317 −0.602306
\(236\) −2.71937 −0.177016
\(237\) 9.57784 0.622148
\(238\) −5.03059 −0.326085
\(239\) 17.7292 1.14680 0.573402 0.819274i \(-0.305623\pi\)
0.573402 + 0.819274i \(0.305623\pi\)
\(240\) 1.61770 0.104422
\(241\) −9.54025 −0.614542 −0.307271 0.951622i \(-0.599416\pi\)
−0.307271 + 0.951622i \(0.599416\pi\)
\(242\) 24.2420 1.55833
\(243\) 6.37992 0.409272
\(244\) 27.9934 1.79209
\(245\) −1.00000 −0.0638877
\(246\) −7.42231 −0.473229
\(247\) 17.9767 1.14383
\(248\) 0.910306 0.0578045
\(249\) −3.55373 −0.225209
\(250\) 2.23328 0.141245
\(251\) 16.6146 1.04871 0.524353 0.851501i \(-0.324307\pi\)
0.524353 + 0.851501i \(0.324307\pi\)
\(252\) 1.86685 0.117600
\(253\) −1.45419 −0.0914240
\(254\) −4.52594 −0.283983
\(255\) 3.47151 0.217395
\(256\) −8.62629 −0.539143
\(257\) 17.5157 1.09260 0.546301 0.837589i \(-0.316035\pi\)
0.546301 + 0.837589i \(0.316035\pi\)
\(258\) 28.8234 1.79447
\(259\) 4.75791 0.295642
\(260\) 11.4471 0.709922
\(261\) 3.06301 0.189595
\(262\) −1.59960 −0.0988234
\(263\) −14.1019 −0.869561 −0.434780 0.900537i \(-0.643174\pi\)
−0.434780 + 0.900537i \(0.643174\pi\)
\(264\) 1.29490 0.0796953
\(265\) 9.56310 0.587457
\(266\) −10.4778 −0.642436
\(267\) −19.1322 −1.17087
\(268\) 11.3171 0.691303
\(269\) −24.2271 −1.47715 −0.738576 0.674170i \(-0.764501\pi\)
−0.738576 + 0.674170i \(0.764501\pi\)
\(270\) −12.4761 −0.759273
\(271\) 23.7745 1.44420 0.722100 0.691788i \(-0.243177\pi\)
0.722100 + 0.691788i \(0.243177\pi\)
\(272\) 2.36445 0.143366
\(273\) 5.90509 0.357392
\(274\) −44.6749 −2.69891
\(275\) −0.380972 −0.0229734
\(276\) 17.5746 1.05787
\(277\) −17.4180 −1.04654 −0.523272 0.852166i \(-0.675289\pi\)
−0.523272 + 0.852166i \(0.675289\pi\)
\(278\) −19.1548 −1.14883
\(279\) 0.257919 0.0154412
\(280\) −2.20546 −0.131801
\(281\) −19.9487 −1.19004 −0.595020 0.803711i \(-0.702856\pi\)
−0.595020 + 0.803711i \(0.702856\pi\)
\(282\) −31.7788 −1.89240
\(283\) 21.8565 1.29923 0.649617 0.760262i \(-0.274929\pi\)
0.649617 + 0.760262i \(0.274929\pi\)
\(284\) −26.0465 −1.54558
\(285\) 7.23054 0.428300
\(286\) −3.26001 −0.192768
\(287\) −2.15652 −0.127295
\(288\) −4.22113 −0.248732
\(289\) −11.9260 −0.701529
\(290\) −10.9470 −0.642832
\(291\) −20.3791 −1.19464
\(292\) −9.14341 −0.535077
\(293\) 20.0155 1.16932 0.584660 0.811279i \(-0.301228\pi\)
0.584660 + 0.811279i \(0.301228\pi\)
\(294\) −3.44181 −0.200730
\(295\) 0.910238 0.0529961
\(296\) 10.4934 0.609916
\(297\) 2.12828 0.123495
\(298\) 45.1349 2.61460
\(299\) −14.6255 −0.845815
\(300\) 4.60423 0.265825
\(301\) 8.37449 0.482698
\(302\) −18.5521 −1.06755
\(303\) −4.91225 −0.282201
\(304\) 4.92473 0.282452
\(305\) −9.37004 −0.536527
\(306\) −3.14350 −0.179702
\(307\) 9.51221 0.542890 0.271445 0.962454i \(-0.412498\pi\)
0.271445 + 0.962454i \(0.412498\pi\)
\(308\) 1.13817 0.0648532
\(309\) 12.0342 0.684599
\(310\) −0.921789 −0.0523541
\(311\) −3.04029 −0.172399 −0.0861996 0.996278i \(-0.527472\pi\)
−0.0861996 + 0.996278i \(0.527472\pi\)
\(312\) 13.0234 0.737306
\(313\) 26.1113 1.47590 0.737948 0.674858i \(-0.235795\pi\)
0.737948 + 0.674858i \(0.235795\pi\)
\(314\) −30.0575 −1.69624
\(315\) −0.624877 −0.0352078
\(316\) 18.5669 1.04447
\(317\) 13.1203 0.736909 0.368455 0.929646i \(-0.379887\pi\)
0.368455 + 0.929646i \(0.379887\pi\)
\(318\) 32.9143 1.84574
\(319\) 1.86744 0.104556
\(320\) 12.9868 0.725982
\(321\) 7.81124 0.435981
\(322\) 8.52455 0.475054
\(323\) 10.5683 0.588033
\(324\) −20.1208 −1.11782
\(325\) −3.83163 −0.212540
\(326\) 8.62292 0.477579
\(327\) 28.4189 1.57157
\(328\) −4.75611 −0.262612
\(329\) −9.23317 −0.509041
\(330\) −1.31123 −0.0721808
\(331\) 25.4724 1.40009 0.700044 0.714099i \(-0.253163\pi\)
0.700044 + 0.714099i \(0.253163\pi\)
\(332\) −6.88899 −0.378083
\(333\) 2.97311 0.162925
\(334\) 14.7396 0.806515
\(335\) −3.78810 −0.206966
\(336\) 1.61770 0.0882527
\(337\) −6.09729 −0.332141 −0.166070 0.986114i \(-0.553108\pi\)
−0.166070 + 0.986114i \(0.553108\pi\)
\(338\) −3.75495 −0.204242
\(339\) 21.9017 1.18954
\(340\) 6.72961 0.364964
\(341\) 0.157246 0.00851537
\(342\) −6.54734 −0.354040
\(343\) −1.00000 −0.0539949
\(344\) 18.4696 0.995815
\(345\) −5.88262 −0.316710
\(346\) 45.5036 2.44629
\(347\) −5.46481 −0.293366 −0.146683 0.989184i \(-0.546860\pi\)
−0.146683 + 0.989184i \(0.546860\pi\)
\(348\) −22.5689 −1.20982
\(349\) 5.83658 0.312425 0.156213 0.987723i \(-0.450072\pi\)
0.156213 + 0.987723i \(0.450072\pi\)
\(350\) 2.23328 0.119374
\(351\) 21.4052 1.14253
\(352\) −2.57352 −0.137169
\(353\) 36.0809 1.92039 0.960197 0.279323i \(-0.0901099\pi\)
0.960197 + 0.279323i \(0.0901099\pi\)
\(354\) 3.13286 0.166510
\(355\) 8.71837 0.462723
\(356\) −37.0881 −1.96567
\(357\) 3.47151 0.183732
\(358\) 23.2274 1.22761
\(359\) −30.6301 −1.61660 −0.808299 0.588773i \(-0.799611\pi\)
−0.808299 + 0.588773i \(0.799611\pi\)
\(360\) −1.37814 −0.0726344
\(361\) 3.01176 0.158514
\(362\) −11.6978 −0.614824
\(363\) −16.7289 −0.878039
\(364\) 11.4471 0.599994
\(365\) 3.06051 0.160194
\(366\) −32.2499 −1.68573
\(367\) −8.12487 −0.424115 −0.212057 0.977257i \(-0.568016\pi\)
−0.212057 + 0.977257i \(0.568016\pi\)
\(368\) −4.00666 −0.208862
\(369\) −1.34756 −0.0701511
\(370\) −10.6258 −0.552407
\(371\) 9.56310 0.496491
\(372\) −1.90040 −0.0985312
\(373\) −4.82394 −0.249774 −0.124887 0.992171i \(-0.539857\pi\)
−0.124887 + 0.992171i \(0.539857\pi\)
\(374\) −1.91651 −0.0991005
\(375\) −1.54114 −0.0795843
\(376\) −20.3634 −1.05016
\(377\) 18.7818 0.967310
\(378\) −12.4761 −0.641703
\(379\) 12.6207 0.648282 0.324141 0.946009i \(-0.394925\pi\)
0.324141 + 0.946009i \(0.394925\pi\)
\(380\) 14.0166 0.719034
\(381\) 3.12326 0.160010
\(382\) −17.4294 −0.891768
\(383\) 33.0414 1.68834 0.844168 0.536079i \(-0.180095\pi\)
0.844168 + 0.536079i \(0.180095\pi\)
\(384\) 23.8767 1.21845
\(385\) −0.380972 −0.0194161
\(386\) −37.9721 −1.93273
\(387\) 5.23303 0.266010
\(388\) −39.5054 −2.00558
\(389\) −2.33412 −0.118345 −0.0591724 0.998248i \(-0.518846\pi\)
−0.0591724 + 0.998248i \(0.518846\pi\)
\(390\) −13.1877 −0.667786
\(391\) −8.59813 −0.434826
\(392\) −2.20546 −0.111393
\(393\) 1.10385 0.0556819
\(394\) 21.5104 1.08368
\(395\) −6.21476 −0.312699
\(396\) 0.711215 0.0357399
\(397\) 30.7694 1.54427 0.772135 0.635459i \(-0.219189\pi\)
0.772135 + 0.635459i \(0.219189\pi\)
\(398\) 19.8918 0.997085
\(399\) 7.23054 0.361980
\(400\) −1.04967 −0.0524837
\(401\) −14.2027 −0.709249 −0.354625 0.935009i \(-0.615391\pi\)
−0.354625 + 0.935009i \(0.615391\pi\)
\(402\) −13.0379 −0.650272
\(403\) 1.58151 0.0787805
\(404\) −9.52252 −0.473763
\(405\) 6.73490 0.334660
\(406\) −10.9470 −0.543292
\(407\) 1.81263 0.0898487
\(408\) 7.65628 0.379042
\(409\) −38.7098 −1.91407 −0.957037 0.289965i \(-0.906356\pi\)
−0.957037 + 0.289965i \(0.906356\pi\)
\(410\) 4.81611 0.237851
\(411\) 30.8292 1.52069
\(412\) 23.3285 1.14931
\(413\) 0.910238 0.0447899
\(414\) 5.32679 0.261798
\(415\) 2.30591 0.113192
\(416\) −25.8832 −1.26903
\(417\) 13.2183 0.647305
\(418\) −3.99175 −0.195243
\(419\) −19.2477 −0.940312 −0.470156 0.882583i \(-0.655802\pi\)
−0.470156 + 0.882583i \(0.655802\pi\)
\(420\) 4.60423 0.224664
\(421\) 28.1700 1.37292 0.686460 0.727167i \(-0.259164\pi\)
0.686460 + 0.727167i \(0.259164\pi\)
\(422\) −16.2261 −0.789873
\(423\) −5.76960 −0.280527
\(424\) 21.0910 1.02427
\(425\) −2.25256 −0.109265
\(426\) 30.0069 1.45384
\(427\) −9.37004 −0.453448
\(428\) 15.1423 0.731930
\(429\) 2.24967 0.108615
\(430\) −18.7026 −0.901919
\(431\) 22.7563 1.09613 0.548065 0.836435i \(-0.315364\pi\)
0.548065 + 0.836435i \(0.315364\pi\)
\(432\) 5.86396 0.282130
\(433\) −10.6690 −0.512718 −0.256359 0.966582i \(-0.582523\pi\)
−0.256359 + 0.966582i \(0.582523\pi\)
\(434\) −0.921789 −0.0442473
\(435\) 7.55434 0.362203
\(436\) 55.0907 2.63837
\(437\) −17.9083 −0.856672
\(438\) 10.5337 0.503319
\(439\) 17.9960 0.858901 0.429450 0.903090i \(-0.358707\pi\)
0.429450 + 0.903090i \(0.358707\pi\)
\(440\) −0.840217 −0.0400558
\(441\) −0.624877 −0.0297560
\(442\) −19.2753 −0.916835
\(443\) 6.43490 0.305731 0.152866 0.988247i \(-0.451150\pi\)
0.152866 + 0.988247i \(0.451150\pi\)
\(444\) −21.9065 −1.03964
\(445\) 12.4143 0.588493
\(446\) −48.9903 −2.31976
\(447\) −31.1467 −1.47319
\(448\) 12.9868 0.613567
\(449\) −21.2567 −1.00316 −0.501582 0.865110i \(-0.667248\pi\)
−0.501582 + 0.865110i \(0.667248\pi\)
\(450\) 1.39553 0.0657857
\(451\) −0.821572 −0.0386863
\(452\) 42.4570 1.99701
\(453\) 12.8024 0.601510
\(454\) 55.3156 2.59609
\(455\) −3.83163 −0.179629
\(456\) 15.9467 0.746771
\(457\) 6.69014 0.312952 0.156476 0.987682i \(-0.449987\pi\)
0.156476 + 0.987682i \(0.449987\pi\)
\(458\) −2.23328 −0.104354
\(459\) 12.5838 0.587362
\(460\) −11.4036 −0.531696
\(461\) −10.0798 −0.469464 −0.234732 0.972060i \(-0.575421\pi\)
−0.234732 + 0.972060i \(0.575421\pi\)
\(462\) −1.31123 −0.0610039
\(463\) 1.39149 0.0646678 0.0323339 0.999477i \(-0.489706\pi\)
0.0323339 + 0.999477i \(0.489706\pi\)
\(464\) 5.14527 0.238863
\(465\) 0.636109 0.0294988
\(466\) −55.0865 −2.55183
\(467\) −9.02204 −0.417490 −0.208745 0.977970i \(-0.566938\pi\)
−0.208745 + 0.977970i \(0.566938\pi\)
\(468\) 7.15306 0.330650
\(469\) −3.78810 −0.174918
\(470\) 20.6203 0.951142
\(471\) 20.7421 0.955746
\(472\) 2.00749 0.0924023
\(473\) 3.19044 0.146697
\(474\) −21.3900 −0.982476
\(475\) −4.69167 −0.215269
\(476\) 6.72961 0.308451
\(477\) 5.97576 0.273611
\(478\) −39.5942 −1.81100
\(479\) −27.5480 −1.25870 −0.629351 0.777121i \(-0.716679\pi\)
−0.629351 + 0.777121i \(0.716679\pi\)
\(480\) −10.4106 −0.475178
\(481\) 18.2306 0.831242
\(482\) 21.3061 0.970465
\(483\) −5.88262 −0.267669
\(484\) −32.4294 −1.47406
\(485\) 13.2234 0.600442
\(486\) −14.2482 −0.646309
\(487\) −41.1581 −1.86505 −0.932526 0.361104i \(-0.882400\pi\)
−0.932526 + 0.361104i \(0.882400\pi\)
\(488\) −20.6652 −0.935472
\(489\) −5.95051 −0.269091
\(490\) 2.23328 0.100889
\(491\) 20.5104 0.925621 0.462810 0.886457i \(-0.346841\pi\)
0.462810 + 0.886457i \(0.346841\pi\)
\(492\) 9.92911 0.447639
\(493\) 11.0415 0.497285
\(494\) −40.1471 −1.80630
\(495\) −0.238060 −0.0107000
\(496\) 0.433254 0.0194537
\(497\) 8.71837 0.391072
\(498\) 7.93648 0.355642
\(499\) −35.1629 −1.57411 −0.787054 0.616884i \(-0.788395\pi\)
−0.787054 + 0.616884i \(0.788395\pi\)
\(500\) −2.98754 −0.133607
\(501\) −10.1715 −0.454430
\(502\) −37.1051 −1.65608
\(503\) −30.7471 −1.37095 −0.685473 0.728098i \(-0.740404\pi\)
−0.685473 + 0.728098i \(0.740404\pi\)
\(504\) −1.37814 −0.0613873
\(505\) 3.18741 0.141838
\(506\) 3.24761 0.144374
\(507\) 2.59122 0.115080
\(508\) 6.05452 0.268626
\(509\) −28.5293 −1.26454 −0.632270 0.774748i \(-0.717877\pi\)
−0.632270 + 0.774748i \(0.717877\pi\)
\(510\) −7.75286 −0.343303
\(511\) 3.06051 0.135389
\(512\) −11.7207 −0.517988
\(513\) 26.2098 1.15719
\(514\) −39.1176 −1.72540
\(515\) −7.80859 −0.344088
\(516\) −38.5581 −1.69743
\(517\) −3.51758 −0.154703
\(518\) −10.6258 −0.466869
\(519\) −31.4011 −1.37836
\(520\) −8.45050 −0.370579
\(521\) −15.4156 −0.675368 −0.337684 0.941260i \(-0.609643\pi\)
−0.337684 + 0.941260i \(0.609643\pi\)
\(522\) −6.84055 −0.299403
\(523\) 0.212709 0.00930113 0.00465056 0.999989i \(-0.498520\pi\)
0.00465056 + 0.999989i \(0.498520\pi\)
\(524\) 2.13984 0.0934793
\(525\) −1.54114 −0.0672610
\(526\) 31.4935 1.37318
\(527\) 0.929745 0.0405003
\(528\) 0.616297 0.0268209
\(529\) −8.43012 −0.366527
\(530\) −21.3571 −0.927693
\(531\) 0.568787 0.0246832
\(532\) 14.0166 0.607695
\(533\) −8.26297 −0.357909
\(534\) 42.7275 1.84900
\(535\) −5.06847 −0.219129
\(536\) −8.35451 −0.360860
\(537\) −16.0288 −0.691693
\(538\) 54.1059 2.33267
\(539\) −0.380972 −0.0164096
\(540\) 16.6898 0.718213
\(541\) 11.2131 0.482089 0.241044 0.970514i \(-0.422510\pi\)
0.241044 + 0.970514i \(0.422510\pi\)
\(542\) −53.0952 −2.28064
\(543\) 8.07243 0.346421
\(544\) −15.2163 −0.652395
\(545\) −18.4401 −0.789889
\(546\) −13.1877 −0.564382
\(547\) −3.37544 −0.144323 −0.0721617 0.997393i \(-0.522990\pi\)
−0.0721617 + 0.997393i \(0.522990\pi\)
\(548\) 59.7632 2.55296
\(549\) −5.85512 −0.249891
\(550\) 0.850816 0.0362789
\(551\) 22.9975 0.979727
\(552\) −12.9739 −0.552205
\(553\) −6.21476 −0.264279
\(554\) 38.8992 1.65267
\(555\) 7.33263 0.311253
\(556\) 25.6241 1.08670
\(557\) −25.7181 −1.08971 −0.544854 0.838531i \(-0.683415\pi\)
−0.544854 + 0.838531i \(0.683415\pi\)
\(558\) −0.576005 −0.0243842
\(559\) 32.0879 1.35717
\(560\) −1.04967 −0.0443568
\(561\) 1.32255 0.0558380
\(562\) 44.5510 1.87927
\(563\) −18.1389 −0.764463 −0.382231 0.924067i \(-0.624844\pi\)
−0.382231 + 0.924067i \(0.624844\pi\)
\(564\) 42.5117 1.79006
\(565\) −14.2113 −0.597876
\(566\) −48.8117 −2.05171
\(567\) 6.73490 0.282839
\(568\) 19.2280 0.806790
\(569\) −10.3828 −0.435268 −0.217634 0.976030i \(-0.569834\pi\)
−0.217634 + 0.976030i \(0.569834\pi\)
\(570\) −16.1478 −0.676358
\(571\) −3.08998 −0.129312 −0.0646558 0.997908i \(-0.520595\pi\)
−0.0646558 + 0.997908i \(0.520595\pi\)
\(572\) 4.36104 0.182344
\(573\) 12.0277 0.502465
\(574\) 4.81611 0.201020
\(575\) 3.81705 0.159182
\(576\) 8.11513 0.338130
\(577\) −18.0913 −0.753150 −0.376575 0.926386i \(-0.622898\pi\)
−0.376575 + 0.926386i \(0.622898\pi\)
\(578\) 26.6341 1.10783
\(579\) 26.2038 1.08899
\(580\) 14.6443 0.608070
\(581\) 2.30591 0.0956651
\(582\) 45.5123 1.88654
\(583\) 3.64327 0.150889
\(584\) 6.74983 0.279310
\(585\) −2.39429 −0.0989919
\(586\) −44.7003 −1.84655
\(587\) 30.1312 1.24365 0.621823 0.783158i \(-0.286392\pi\)
0.621823 + 0.783158i \(0.286392\pi\)
\(588\) 4.60423 0.189875
\(589\) 1.93649 0.0797918
\(590\) −2.03282 −0.0836897
\(591\) −14.8439 −0.610596
\(592\) 4.99426 0.205263
\(593\) 32.8192 1.34772 0.673861 0.738858i \(-0.264635\pi\)
0.673861 + 0.738858i \(0.264635\pi\)
\(594\) −4.75305 −0.195020
\(595\) −2.25256 −0.0923458
\(596\) −60.3787 −2.47321
\(597\) −13.7269 −0.561806
\(598\) 32.6629 1.33568
\(599\) 24.8317 1.01460 0.507299 0.861770i \(-0.330644\pi\)
0.507299 + 0.861770i \(0.330644\pi\)
\(600\) −3.39893 −0.138761
\(601\) 13.0088 0.530642 0.265321 0.964160i \(-0.414522\pi\)
0.265321 + 0.964160i \(0.414522\pi\)
\(602\) −18.7026 −0.762261
\(603\) −2.36710 −0.0963957
\(604\) 24.8178 1.00982
\(605\) 10.8549 0.441313
\(606\) 10.9704 0.445644
\(607\) −14.7777 −0.599807 −0.299904 0.953970i \(-0.596954\pi\)
−0.299904 + 0.953970i \(0.596954\pi\)
\(608\) −31.6929 −1.28532
\(609\) 7.55434 0.306117
\(610\) 20.9259 0.847266
\(611\) −35.3781 −1.43124
\(612\) 4.20518 0.169984
\(613\) −3.16953 −0.128016 −0.0640080 0.997949i \(-0.520388\pi\)
−0.0640080 + 0.997949i \(0.520388\pi\)
\(614\) −21.2434 −0.857315
\(615\) −3.32350 −0.134017
\(616\) −0.840217 −0.0338533
\(617\) −17.5745 −0.707521 −0.353761 0.935336i \(-0.615097\pi\)
−0.353761 + 0.935336i \(0.615097\pi\)
\(618\) −26.8757 −1.08110
\(619\) −23.9026 −0.960727 −0.480364 0.877069i \(-0.659495\pi\)
−0.480364 + 0.877069i \(0.659495\pi\)
\(620\) 1.23311 0.0495229
\(621\) −21.3238 −0.855694
\(622\) 6.78983 0.272247
\(623\) 12.4143 0.497367
\(624\) 6.19842 0.248135
\(625\) 1.00000 0.0400000
\(626\) −58.3138 −2.33069
\(627\) 2.75463 0.110009
\(628\) 40.2091 1.60452
\(629\) 10.7175 0.427334
\(630\) 1.39553 0.0555991
\(631\) 21.1444 0.841744 0.420872 0.907120i \(-0.361724\pi\)
0.420872 + 0.907120i \(0.361724\pi\)
\(632\) −13.7064 −0.545212
\(633\) 11.1973 0.445052
\(634\) −29.3013 −1.16370
\(635\) −2.02659 −0.0804227
\(636\) −44.0307 −1.74593
\(637\) −3.83163 −0.151815
\(638\) −4.17051 −0.165112
\(639\) 5.44791 0.215516
\(640\) −15.4928 −0.612408
\(641\) −16.0787 −0.635069 −0.317534 0.948247i \(-0.602855\pi\)
−0.317534 + 0.948247i \(0.602855\pi\)
\(642\) −17.4447 −0.688487
\(643\) 2.34504 0.0924795 0.0462398 0.998930i \(-0.485276\pi\)
0.0462398 + 0.998930i \(0.485276\pi\)
\(644\) −11.4036 −0.449365
\(645\) 12.9063 0.508185
\(646\) −23.6019 −0.928603
\(647\) 50.3655 1.98007 0.990037 0.140808i \(-0.0449700\pi\)
0.990037 + 0.140808i \(0.0449700\pi\)
\(648\) 14.8535 0.583502
\(649\) 0.346775 0.0136121
\(650\) 8.55710 0.335637
\(651\) 0.636109 0.0249311
\(652\) −11.5352 −0.451753
\(653\) −40.2477 −1.57501 −0.787506 0.616307i \(-0.788628\pi\)
−0.787506 + 0.616307i \(0.788628\pi\)
\(654\) −63.4674 −2.48177
\(655\) −0.716254 −0.0279864
\(656\) −2.26364 −0.0883803
\(657\) 1.91244 0.0746115
\(658\) 20.6203 0.803862
\(659\) 28.7884 1.12144 0.560719 0.828006i \(-0.310525\pi\)
0.560719 + 0.828006i \(0.310525\pi\)
\(660\) 1.75408 0.0682775
\(661\) 14.3056 0.556425 0.278213 0.960520i \(-0.410258\pi\)
0.278213 + 0.960520i \(0.410258\pi\)
\(662\) −56.8870 −2.21098
\(663\) 13.3015 0.516589
\(664\) 5.08558 0.197359
\(665\) −4.69167 −0.181935
\(666\) −6.63979 −0.257287
\(667\) −18.7103 −0.724467
\(668\) −19.7177 −0.762901
\(669\) 33.8073 1.30706
\(670\) 8.45990 0.326834
\(671\) −3.56972 −0.137807
\(672\) −10.4106 −0.401599
\(673\) 22.3913 0.863122 0.431561 0.902084i \(-0.357963\pi\)
0.431561 + 0.902084i \(0.357963\pi\)
\(674\) 13.6170 0.524506
\(675\) −5.58646 −0.215023
\(676\) 5.02313 0.193197
\(677\) −40.7403 −1.56578 −0.782889 0.622161i \(-0.786255\pi\)
−0.782889 + 0.622161i \(0.786255\pi\)
\(678\) −48.9127 −1.87848
\(679\) 13.2234 0.507467
\(680\) −4.96792 −0.190511
\(681\) −38.1722 −1.46276
\(682\) −0.351175 −0.0134472
\(683\) 28.6458 1.09610 0.548050 0.836446i \(-0.315370\pi\)
0.548050 + 0.836446i \(0.315370\pi\)
\(684\) 8.75863 0.334894
\(685\) −20.0041 −0.764319
\(686\) 2.23328 0.0852671
\(687\) 1.54114 0.0587983
\(688\) 8.79049 0.335134
\(689\) 36.6422 1.39596
\(690\) 13.1376 0.500138
\(691\) 11.8958 0.452537 0.226268 0.974065i \(-0.427347\pi\)
0.226268 + 0.974065i \(0.427347\pi\)
\(692\) −60.8718 −2.31400
\(693\) −0.238060 −0.00904316
\(694\) 12.2045 0.463275
\(695\) −8.57697 −0.325343
\(696\) 16.6608 0.631526
\(697\) −4.85768 −0.183998
\(698\) −13.0347 −0.493372
\(699\) 38.0141 1.43783
\(700\) −2.98754 −0.112918
\(701\) −43.0097 −1.62445 −0.812227 0.583341i \(-0.801745\pi\)
−0.812227 + 0.583341i \(0.801745\pi\)
\(702\) −47.8038 −1.80424
\(703\) 22.3226 0.841911
\(704\) 4.94759 0.186469
\(705\) −14.2296 −0.535919
\(706\) −80.5789 −3.03263
\(707\) 3.18741 0.119875
\(708\) −4.19095 −0.157505
\(709\) 27.5433 1.03441 0.517205 0.855862i \(-0.326972\pi\)
0.517205 + 0.855862i \(0.326972\pi\)
\(710\) −19.4706 −0.730717
\(711\) −3.88346 −0.145641
\(712\) 27.3792 1.02608
\(713\) −1.57549 −0.0590027
\(714\) −7.75286 −0.290144
\(715\) −1.45974 −0.0545912
\(716\) −31.0722 −1.16122
\(717\) 27.3232 1.02040
\(718\) 68.4057 2.55288
\(719\) 43.9234 1.63807 0.819034 0.573745i \(-0.194510\pi\)
0.819034 + 0.573745i \(0.194510\pi\)
\(720\) −0.655917 −0.0244446
\(721\) −7.80859 −0.290807
\(722\) −6.72611 −0.250320
\(723\) −14.7029 −0.546807
\(724\) 15.6486 0.581576
\(725\) −4.90178 −0.182047
\(726\) 37.3603 1.38657
\(727\) 39.2889 1.45714 0.728571 0.684970i \(-0.240185\pi\)
0.728571 + 0.684970i \(0.240185\pi\)
\(728\) −8.45050 −0.313196
\(729\) 30.0371 1.11248
\(730\) −6.83498 −0.252974
\(731\) 18.8640 0.697711
\(732\) 43.1418 1.59457
\(733\) −9.47636 −0.350017 −0.175009 0.984567i \(-0.555995\pi\)
−0.175009 + 0.984567i \(0.555995\pi\)
\(734\) 18.1451 0.669748
\(735\) −1.54114 −0.0568459
\(736\) 25.7847 0.950437
\(737\) −1.44316 −0.0531595
\(738\) 3.00948 0.110780
\(739\) −14.9002 −0.548114 −0.274057 0.961713i \(-0.588366\pi\)
−0.274057 + 0.961713i \(0.588366\pi\)
\(740\) 14.2145 0.522534
\(741\) 27.7047 1.01776
\(742\) −21.3571 −0.784043
\(743\) −36.8848 −1.35317 −0.676587 0.736363i \(-0.736542\pi\)
−0.676587 + 0.736363i \(0.736542\pi\)
\(744\) 1.40291 0.0514333
\(745\) 20.2101 0.740442
\(746\) 10.7732 0.394435
\(747\) 1.44091 0.0527200
\(748\) 2.56379 0.0937414
\(749\) −5.06847 −0.185198
\(750\) 3.44181 0.125677
\(751\) −0.259560 −0.00947148 −0.00473574 0.999989i \(-0.501507\pi\)
−0.00473574 + 0.999989i \(0.501507\pi\)
\(752\) −9.69183 −0.353425
\(753\) 25.6055 0.933117
\(754\) −41.9450 −1.52755
\(755\) −8.30709 −0.302326
\(756\) 16.6898 0.607001
\(757\) 26.7576 0.972521 0.486260 0.873814i \(-0.338361\pi\)
0.486260 + 0.873814i \(0.338361\pi\)
\(758\) −28.1856 −1.02375
\(759\) −2.24111 −0.0813472
\(760\) −10.3473 −0.375336
\(761\) 17.7603 0.643810 0.321905 0.946772i \(-0.395677\pi\)
0.321905 + 0.946772i \(0.395677\pi\)
\(762\) −6.97512 −0.252682
\(763\) −18.4401 −0.667578
\(764\) 23.3160 0.843544
\(765\) −1.40757 −0.0508908
\(766\) −73.7907 −2.66617
\(767\) 3.48769 0.125933
\(768\) −13.2943 −0.479719
\(769\) 47.4772 1.71207 0.856036 0.516917i \(-0.172920\pi\)
0.856036 + 0.516917i \(0.172920\pi\)
\(770\) 0.850816 0.0306613
\(771\) 26.9943 0.972175
\(772\) 50.7967 1.82821
\(773\) 32.7896 1.17936 0.589679 0.807638i \(-0.299254\pi\)
0.589679 + 0.807638i \(0.299254\pi\)
\(774\) −11.6868 −0.420074
\(775\) −0.412751 −0.0148265
\(776\) 29.1636 1.04691
\(777\) 7.33263 0.263057
\(778\) 5.21275 0.186886
\(779\) −10.1177 −0.362503
\(780\) 17.6417 0.631674
\(781\) 3.32145 0.118851
\(782\) 19.2020 0.686663
\(783\) 27.3835 0.978608
\(784\) −1.04967 −0.0374884
\(785\) −13.4589 −0.480369
\(786\) −2.46521 −0.0879310
\(787\) 5.67269 0.202210 0.101105 0.994876i \(-0.467762\pi\)
0.101105 + 0.994876i \(0.467762\pi\)
\(788\) −28.7752 −1.02508
\(789\) −21.7331 −0.773717
\(790\) 13.8793 0.493804
\(791\) −14.2113 −0.505297
\(792\) −0.525032 −0.0186562
\(793\) −35.9025 −1.27493
\(794\) −68.7166 −2.43866
\(795\) 14.7381 0.522707
\(796\) −26.6100 −0.943165
\(797\) 31.4624 1.11445 0.557227 0.830360i \(-0.311865\pi\)
0.557227 + 0.830360i \(0.311865\pi\)
\(798\) −16.1478 −0.571626
\(799\) −20.7982 −0.735789
\(800\) 6.75514 0.238830
\(801\) 7.75739 0.274094
\(802\) 31.7186 1.12002
\(803\) 1.16597 0.0411461
\(804\) 17.4413 0.615107
\(805\) 3.81705 0.134533
\(806\) −3.53195 −0.124408
\(807\) −37.3374 −1.31434
\(808\) 7.02970 0.247304
\(809\) 0.372042 0.0130803 0.00654015 0.999979i \(-0.497918\pi\)
0.00654015 + 0.999979i \(0.497918\pi\)
\(810\) −15.0409 −0.528484
\(811\) 13.6360 0.478826 0.239413 0.970918i \(-0.423045\pi\)
0.239413 + 0.970918i \(0.423045\pi\)
\(812\) 14.6443 0.513913
\(813\) 36.6400 1.28502
\(814\) −4.04811 −0.141886
\(815\) 3.86110 0.135248
\(816\) 3.64396 0.127564
\(817\) 39.2904 1.37460
\(818\) 86.4498 3.02265
\(819\) −2.39429 −0.0836634
\(820\) −6.44269 −0.224988
\(821\) 0.536072 0.0187090 0.00935452 0.999956i \(-0.497022\pi\)
0.00935452 + 0.999956i \(0.497022\pi\)
\(822\) −68.8504 −2.40143
\(823\) −21.3508 −0.744243 −0.372121 0.928184i \(-0.621369\pi\)
−0.372121 + 0.928184i \(0.621369\pi\)
\(824\) −17.2215 −0.599941
\(825\) −0.587132 −0.0204413
\(826\) −2.03282 −0.0707307
\(827\) 1.13907 0.0396094 0.0198047 0.999804i \(-0.493696\pi\)
0.0198047 + 0.999804i \(0.493696\pi\)
\(828\) −7.12585 −0.247640
\(829\) 0.933015 0.0324050 0.0162025 0.999869i \(-0.494842\pi\)
0.0162025 + 0.999869i \(0.494842\pi\)
\(830\) −5.14973 −0.178750
\(831\) −26.8436 −0.931194
\(832\) 49.7604 1.72513
\(833\) −2.25256 −0.0780465
\(834\) −29.5203 −1.02220
\(835\) 6.59998 0.228402
\(836\) 5.33991 0.184685
\(837\) 2.30582 0.0797006
\(838\) 42.9855 1.48491
\(839\) 23.9276 0.826071 0.413036 0.910715i \(-0.364469\pi\)
0.413036 + 0.910715i \(0.364469\pi\)
\(840\) −3.39893 −0.117274
\(841\) −4.97260 −0.171469
\(842\) −62.9114 −2.16807
\(843\) −30.7438 −1.05887
\(844\) 21.7062 0.747159
\(845\) −1.68136 −0.0578405
\(846\) 12.8851 0.443000
\(847\) 10.8549 0.372977
\(848\) 10.0381 0.344711
\(849\) 33.6840 1.15603
\(850\) 5.03059 0.172548
\(851\) −18.1612 −0.622558
\(852\) −40.1414 −1.37522
\(853\) −38.6365 −1.32289 −0.661444 0.749994i \(-0.730056\pi\)
−0.661444 + 0.749994i \(0.730056\pi\)
\(854\) 20.9259 0.716071
\(855\) −2.93172 −0.100263
\(856\) −11.1783 −0.382067
\(857\) 33.6508 1.14949 0.574745 0.818332i \(-0.305101\pi\)
0.574745 + 0.818332i \(0.305101\pi\)
\(858\) −5.02414 −0.171521
\(859\) 20.3792 0.695330 0.347665 0.937619i \(-0.386975\pi\)
0.347665 + 0.937619i \(0.386975\pi\)
\(860\) 25.0192 0.853146
\(861\) −3.32350 −0.113265
\(862\) −50.8211 −1.73097
\(863\) 34.0931 1.16054 0.580271 0.814424i \(-0.302947\pi\)
0.580271 + 0.814424i \(0.302947\pi\)
\(864\) −37.7373 −1.28385
\(865\) 20.3752 0.692778
\(866\) 23.8268 0.809668
\(867\) −18.3797 −0.624206
\(868\) 1.23311 0.0418545
\(869\) −2.36765 −0.0803170
\(870\) −16.8710 −0.571979
\(871\) −14.5146 −0.491808
\(872\) −40.6690 −1.37723
\(873\) 8.26298 0.279660
\(874\) 39.9944 1.35283
\(875\) 1.00000 0.0338062
\(876\) −14.0913 −0.476101
\(877\) 28.2374 0.953510 0.476755 0.879036i \(-0.341813\pi\)
0.476755 + 0.879036i \(0.341813\pi\)
\(878\) −40.1900 −1.35635
\(879\) 30.8468 1.04044
\(880\) −0.399896 −0.0134805
\(881\) −45.0761 −1.51865 −0.759326 0.650710i \(-0.774471\pi\)
−0.759326 + 0.650710i \(0.774471\pi\)
\(882\) 1.39553 0.0469898
\(883\) 34.0592 1.14618 0.573092 0.819491i \(-0.305744\pi\)
0.573092 + 0.819491i \(0.305744\pi\)
\(884\) 25.7853 0.867255
\(885\) 1.40281 0.0471548
\(886\) −14.3709 −0.482801
\(887\) −16.7922 −0.563828 −0.281914 0.959440i \(-0.590969\pi\)
−0.281914 + 0.959440i \(0.590969\pi\)
\(888\) 16.1718 0.542691
\(889\) −2.02659 −0.0679696
\(890\) −27.7245 −0.929329
\(891\) 2.56580 0.0859577
\(892\) 65.5362 2.19431
\(893\) −43.3190 −1.44962
\(894\) 69.5594 2.32641
\(895\) 10.4006 0.347653
\(896\) −15.4928 −0.517579
\(897\) −22.5400 −0.752589
\(898\) 47.4721 1.58416
\(899\) 2.02321 0.0674779
\(900\) −1.86685 −0.0622282
\(901\) 21.5414 0.717649
\(902\) 1.83480 0.0610922
\(903\) 12.9063 0.429495
\(904\) −31.3426 −1.04244
\(905\) −5.23795 −0.174115
\(906\) −28.5914 −0.949886
\(907\) 31.8896 1.05888 0.529439 0.848348i \(-0.322402\pi\)
0.529439 + 0.848348i \(0.322402\pi\)
\(908\) −73.9977 −2.45570
\(909\) 1.99174 0.0660618
\(910\) 8.55710 0.283665
\(911\) 46.7294 1.54822 0.774108 0.633054i \(-0.218199\pi\)
0.774108 + 0.633054i \(0.218199\pi\)
\(912\) 7.58971 0.251320
\(913\) 0.878484 0.0290736
\(914\) −14.9410 −0.494203
\(915\) −14.4406 −0.477391
\(916\) 2.98754 0.0987112
\(917\) −0.716254 −0.0236528
\(918\) −28.1032 −0.927543
\(919\) −9.96466 −0.328704 −0.164352 0.986402i \(-0.552553\pi\)
−0.164352 + 0.986402i \(0.552553\pi\)
\(920\) 8.41835 0.277545
\(921\) 14.6597 0.483053
\(922\) 22.5111 0.741363
\(923\) 33.4055 1.09956
\(924\) 1.75408 0.0577050
\(925\) −4.75791 −0.156439
\(926\) −3.10758 −0.102121
\(927\) −4.87941 −0.160261
\(928\) −33.1122 −1.08696
\(929\) −24.8109 −0.814019 −0.407010 0.913424i \(-0.633428\pi\)
−0.407010 + 0.913424i \(0.633428\pi\)
\(930\) −1.42061 −0.0465836
\(931\) −4.69167 −0.153763
\(932\) 73.6912 2.41384
\(933\) −4.68553 −0.153397
\(934\) 20.1487 0.659287
\(935\) −0.858160 −0.0280648
\(936\) −5.28052 −0.172599
\(937\) 12.7167 0.415438 0.207719 0.978189i \(-0.433396\pi\)
0.207719 + 0.978189i \(0.433396\pi\)
\(938\) 8.45990 0.276225
\(939\) 40.2412 1.31322
\(940\) −27.5845 −0.899707
\(941\) −31.2644 −1.01919 −0.509595 0.860415i \(-0.670205\pi\)
−0.509595 + 0.860415i \(0.670205\pi\)
\(942\) −46.3230 −1.50928
\(943\) 8.23154 0.268056
\(944\) 0.955453 0.0310974
\(945\) −5.58646 −0.181727
\(946\) −7.12516 −0.231659
\(947\) 8.72480 0.283518 0.141759 0.989901i \(-0.454724\pi\)
0.141759 + 0.989901i \(0.454724\pi\)
\(948\) 28.6142 0.929347
\(949\) 11.7267 0.380666
\(950\) 10.4778 0.339945
\(951\) 20.2203 0.655687
\(952\) −4.96792 −0.161011
\(953\) 44.2799 1.43437 0.717184 0.696884i \(-0.245431\pi\)
0.717184 + 0.696884i \(0.245431\pi\)
\(954\) −13.3456 −0.432078
\(955\) −7.80441 −0.252545
\(956\) 52.9666 1.71306
\(957\) 2.87799 0.0930321
\(958\) 61.5225 1.98770
\(959\) −20.0041 −0.645967
\(960\) 20.0145 0.645964
\(961\) −30.8296 −0.994504
\(962\) −40.7139 −1.31267
\(963\) −3.16717 −0.102061
\(964\) −28.5019 −0.917985
\(965\) −17.0029 −0.547341
\(966\) 13.1376 0.422694
\(967\) 21.6899 0.697499 0.348749 0.937216i \(-0.386606\pi\)
0.348749 + 0.937216i \(0.386606\pi\)
\(968\) 23.9400 0.769459
\(969\) 16.2872 0.523220
\(970\) −29.5315 −0.948199
\(971\) 0.927211 0.0297556 0.0148778 0.999889i \(-0.495264\pi\)
0.0148778 + 0.999889i \(0.495264\pi\)
\(972\) 19.0603 0.611359
\(973\) −8.57697 −0.274965
\(974\) 91.9176 2.94523
\(975\) −5.90509 −0.189114
\(976\) −9.83549 −0.314826
\(977\) 30.3914 0.972306 0.486153 0.873874i \(-0.338400\pi\)
0.486153 + 0.873874i \(0.338400\pi\)
\(978\) 13.2892 0.424940
\(979\) 4.72948 0.151155
\(980\) −2.98754 −0.0954335
\(981\) −11.5228 −0.367895
\(982\) −45.8055 −1.46171
\(983\) 47.8510 1.52621 0.763104 0.646275i \(-0.223674\pi\)
0.763104 + 0.646275i \(0.223674\pi\)
\(984\) −7.32985 −0.233667
\(985\) 9.63174 0.306893
\(986\) −24.6588 −0.785297
\(987\) −14.2296 −0.452935
\(988\) 53.7062 1.70862
\(989\) −31.9659 −1.01646
\(990\) 0.531656 0.0168971
\(991\) −44.0474 −1.39921 −0.699605 0.714529i \(-0.746641\pi\)
−0.699605 + 0.714529i \(0.746641\pi\)
\(992\) −2.78819 −0.0885251
\(993\) 39.2566 1.24577
\(994\) −19.4706 −0.617569
\(995\) 8.90697 0.282370
\(996\) −10.6169 −0.336410
\(997\) −29.6342 −0.938523 −0.469261 0.883059i \(-0.655480\pi\)
−0.469261 + 0.883059i \(0.655480\pi\)
\(998\) 78.5287 2.48578
\(999\) 26.5799 0.840950
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 \(a_p\))