Properties

Label 8007.2.a.j.1.4
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.54273 q^{2}\) \(-1.00000 q^{3}\) \(+4.46545 q^{4}\) \(-2.67798 q^{5}\) \(+2.54273 q^{6}\) \(+2.94599 q^{7}\) \(-6.26898 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.54273 q^{2}\) \(-1.00000 q^{3}\) \(+4.46545 q^{4}\) \(-2.67798 q^{5}\) \(+2.54273 q^{6}\) \(+2.94599 q^{7}\) \(-6.26898 q^{8}\) \(+1.00000 q^{9}\) \(+6.80937 q^{10}\) \(+1.14862 q^{11}\) \(-4.46545 q^{12}\) \(+5.66604 q^{13}\) \(-7.49086 q^{14}\) \(+2.67798 q^{15}\) \(+7.00938 q^{16}\) \(+1.00000 q^{17}\) \(-2.54273 q^{18}\) \(+6.65907 q^{19}\) \(-11.9584 q^{20}\) \(-2.94599 q^{21}\) \(-2.92063 q^{22}\) \(-4.86607 q^{23}\) \(+6.26898 q^{24}\) \(+2.17158 q^{25}\) \(-14.4072 q^{26}\) \(-1.00000 q^{27}\) \(+13.1552 q^{28}\) \(+7.98328 q^{29}\) \(-6.80937 q^{30}\) \(+8.48950 q^{31}\) \(-5.28497 q^{32}\) \(-1.14862 q^{33}\) \(-2.54273 q^{34}\) \(-7.88932 q^{35}\) \(+4.46545 q^{36}\) \(+1.03093 q^{37}\) \(-16.9322 q^{38}\) \(-5.66604 q^{39}\) \(+16.7882 q^{40}\) \(-9.73755 q^{41}\) \(+7.49086 q^{42}\) \(+3.63622 q^{43}\) \(+5.12913 q^{44}\) \(-2.67798 q^{45}\) \(+12.3731 q^{46}\) \(+9.61783 q^{47}\) \(-7.00938 q^{48}\) \(+1.67889 q^{49}\) \(-5.52174 q^{50}\) \(-1.00000 q^{51}\) \(+25.3014 q^{52}\) \(+13.7771 q^{53}\) \(+2.54273 q^{54}\) \(-3.07599 q^{55}\) \(-18.4684 q^{56}\) \(-6.65907 q^{57}\) \(-20.2993 q^{58}\) \(+14.9266 q^{59}\) \(+11.9584 q^{60}\) \(-5.54929 q^{61}\) \(-21.5865 q^{62}\) \(+2.94599 q^{63}\) \(-0.580516 q^{64}\) \(-15.1735 q^{65}\) \(+2.92063 q^{66}\) \(+10.3001 q^{67}\) \(+4.46545 q^{68}\) \(+4.86607 q^{69}\) \(+20.0604 q^{70}\) \(+10.3559 q^{71}\) \(-6.26898 q^{72}\) \(+1.44898 q^{73}\) \(-2.62138 q^{74}\) \(-2.17158 q^{75}\) \(+29.7358 q^{76}\) \(+3.38384 q^{77}\) \(+14.4072 q^{78}\) \(-1.75552 q^{79}\) \(-18.7710 q^{80}\) \(+1.00000 q^{81}\) \(+24.7599 q^{82}\) \(+14.2150 q^{83}\) \(-13.1552 q^{84}\) \(-2.67798 q^{85}\) \(-9.24590 q^{86}\) \(-7.98328 q^{87}\) \(-7.20069 q^{88}\) \(-4.33431 q^{89}\) \(+6.80937 q^{90}\) \(+16.6921 q^{91}\) \(-21.7292 q^{92}\) \(-8.48950 q^{93}\) \(-24.4555 q^{94}\) \(-17.8329 q^{95}\) \(+5.28497 q^{96}\) \(-6.00271 q^{97}\) \(-4.26895 q^{98}\) \(+1.14862 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54273 −1.79798 −0.898989 0.437970i \(-0.855697\pi\)
−0.898989 + 0.437970i \(0.855697\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.46545 2.23273
\(5\) −2.67798 −1.19763 −0.598815 0.800888i \(-0.704361\pi\)
−0.598815 + 0.800888i \(0.704361\pi\)
\(6\) 2.54273 1.03806
\(7\) 2.94599 1.11348 0.556741 0.830686i \(-0.312052\pi\)
0.556741 + 0.830686i \(0.312052\pi\)
\(8\) −6.26898 −2.21642
\(9\) 1.00000 0.333333
\(10\) 6.80937 2.15331
\(11\) 1.14862 0.346323 0.173161 0.984893i \(-0.444602\pi\)
0.173161 + 0.984893i \(0.444602\pi\)
\(12\) −4.46545 −1.28907
\(13\) 5.66604 1.57148 0.785738 0.618559i \(-0.212283\pi\)
0.785738 + 0.618559i \(0.212283\pi\)
\(14\) −7.49086 −2.00202
\(15\) 2.67798 0.691452
\(16\) 7.00938 1.75234
\(17\) 1.00000 0.242536
\(18\) −2.54273 −0.599326
\(19\) 6.65907 1.52769 0.763847 0.645397i \(-0.223308\pi\)
0.763847 + 0.645397i \(0.223308\pi\)
\(20\) −11.9584 −2.67398
\(21\) −2.94599 −0.642869
\(22\) −2.92063 −0.622681
\(23\) −4.86607 −1.01465 −0.507323 0.861756i \(-0.669365\pi\)
−0.507323 + 0.861756i \(0.669365\pi\)
\(24\) 6.26898 1.27965
\(25\) 2.17158 0.434316
\(26\) −14.4072 −2.82548
\(27\) −1.00000 −0.192450
\(28\) 13.1552 2.48610
\(29\) 7.98328 1.48246 0.741229 0.671252i \(-0.234243\pi\)
0.741229 + 0.671252i \(0.234243\pi\)
\(30\) −6.80937 −1.24322
\(31\) 8.48950 1.52476 0.762380 0.647130i \(-0.224031\pi\)
0.762380 + 0.647130i \(0.224031\pi\)
\(32\) −5.28497 −0.934260
\(33\) −1.14862 −0.199950
\(34\) −2.54273 −0.436074
\(35\) −7.88932 −1.33354
\(36\) 4.46545 0.744242
\(37\) 1.03093 0.169485 0.0847423 0.996403i \(-0.472993\pi\)
0.0847423 + 0.996403i \(0.472993\pi\)
\(38\) −16.9322 −2.74676
\(39\) −5.66604 −0.907292
\(40\) 16.7882 2.65445
\(41\) −9.73755 −1.52075 −0.760375 0.649484i \(-0.774985\pi\)
−0.760375 + 0.649484i \(0.774985\pi\)
\(42\) 7.49086 1.15586
\(43\) 3.63622 0.554518 0.277259 0.960795i \(-0.410574\pi\)
0.277259 + 0.960795i \(0.410574\pi\)
\(44\) 5.12913 0.773245
\(45\) −2.67798 −0.399210
\(46\) 12.3731 1.82431
\(47\) 9.61783 1.40290 0.701452 0.712717i \(-0.252535\pi\)
0.701452 + 0.712717i \(0.252535\pi\)
\(48\) −7.00938 −1.01172
\(49\) 1.67889 0.239841
\(50\) −5.52174 −0.780891
\(51\) −1.00000 −0.140028
\(52\) 25.3014 3.50868
\(53\) 13.7771 1.89242 0.946212 0.323546i \(-0.104875\pi\)
0.946212 + 0.323546i \(0.104875\pi\)
\(54\) 2.54273 0.346021
\(55\) −3.07599 −0.414767
\(56\) −18.4684 −2.46794
\(57\) −6.65907 −0.882015
\(58\) −20.2993 −2.66543
\(59\) 14.9266 1.94328 0.971638 0.236472i \(-0.0759911\pi\)
0.971638 + 0.236472i \(0.0759911\pi\)
\(60\) 11.9584 1.54382
\(61\) −5.54929 −0.710514 −0.355257 0.934769i \(-0.615607\pi\)
−0.355257 + 0.934769i \(0.615607\pi\)
\(62\) −21.5865 −2.74148
\(63\) 2.94599 0.371160
\(64\) −0.580516 −0.0725645
\(65\) −15.1735 −1.88205
\(66\) 2.92063 0.359505
\(67\) 10.3001 1.25836 0.629178 0.777261i \(-0.283392\pi\)
0.629178 + 0.777261i \(0.283392\pi\)
\(68\) 4.46545 0.541516
\(69\) 4.86607 0.585806
\(70\) 20.0604 2.39767
\(71\) 10.3559 1.22902 0.614510 0.788909i \(-0.289354\pi\)
0.614510 + 0.788909i \(0.289354\pi\)
\(72\) −6.26898 −0.738806
\(73\) 1.44898 0.169590 0.0847949 0.996398i \(-0.472976\pi\)
0.0847949 + 0.996398i \(0.472976\pi\)
\(74\) −2.62138 −0.304730
\(75\) −2.17158 −0.250753
\(76\) 29.7358 3.41093
\(77\) 3.38384 0.385624
\(78\) 14.4072 1.63129
\(79\) −1.75552 −0.197512 −0.0987559 0.995112i \(-0.531486\pi\)
−0.0987559 + 0.995112i \(0.531486\pi\)
\(80\) −18.7710 −2.09866
\(81\) 1.00000 0.111111
\(82\) 24.7599 2.73428
\(83\) 14.2150 1.56030 0.780149 0.625593i \(-0.215143\pi\)
0.780149 + 0.625593i \(0.215143\pi\)
\(84\) −13.1552 −1.43535
\(85\) −2.67798 −0.290468
\(86\) −9.24590 −0.997011
\(87\) −7.98328 −0.855898
\(88\) −7.20069 −0.767596
\(89\) −4.33431 −0.459436 −0.229718 0.973257i \(-0.573780\pi\)
−0.229718 + 0.973257i \(0.573780\pi\)
\(90\) 6.80937 0.717771
\(91\) 16.6921 1.74981
\(92\) −21.7292 −2.26543
\(93\) −8.48950 −0.880320
\(94\) −24.4555 −2.52239
\(95\) −17.8329 −1.82961
\(96\) 5.28497 0.539395
\(97\) −6.00271 −0.609483 −0.304742 0.952435i \(-0.598570\pi\)
−0.304742 + 0.952435i \(0.598570\pi\)
\(98\) −4.26895 −0.431229
\(99\) 1.14862 0.115441
\(100\) 9.69710 0.969710
\(101\) −3.33028 −0.331375 −0.165687 0.986178i \(-0.552984\pi\)
−0.165687 + 0.986178i \(0.552984\pi\)
\(102\) 2.54273 0.251767
\(103\) −0.902439 −0.0889199 −0.0444600 0.999011i \(-0.514157\pi\)
−0.0444600 + 0.999011i \(0.514157\pi\)
\(104\) −35.5203 −3.48305
\(105\) 7.88932 0.769919
\(106\) −35.0313 −3.40254
\(107\) 10.9399 1.05760 0.528801 0.848746i \(-0.322642\pi\)
0.528801 + 0.848746i \(0.322642\pi\)
\(108\) −4.46545 −0.429689
\(109\) 14.5605 1.39464 0.697321 0.716759i \(-0.254375\pi\)
0.697321 + 0.716759i \(0.254375\pi\)
\(110\) 7.82140 0.745741
\(111\) −1.03093 −0.0978520
\(112\) 20.6496 1.95120
\(113\) 6.44854 0.606628 0.303314 0.952891i \(-0.401907\pi\)
0.303314 + 0.952891i \(0.401907\pi\)
\(114\) 16.9322 1.58584
\(115\) 13.0312 1.21517
\(116\) 35.6490 3.30992
\(117\) 5.66604 0.523826
\(118\) −37.9542 −3.49397
\(119\) 2.94599 0.270059
\(120\) −16.7882 −1.53255
\(121\) −9.68066 −0.880060
\(122\) 14.1103 1.27749
\(123\) 9.73755 0.878006
\(124\) 37.9095 3.40437
\(125\) 7.57445 0.677480
\(126\) −7.49086 −0.667339
\(127\) −8.02012 −0.711671 −0.355835 0.934549i \(-0.615804\pi\)
−0.355835 + 0.934549i \(0.615804\pi\)
\(128\) 12.0460 1.06473
\(129\) −3.63622 −0.320151
\(130\) 38.5822 3.38388
\(131\) 11.2240 0.980648 0.490324 0.871540i \(-0.336878\pi\)
0.490324 + 0.871540i \(0.336878\pi\)
\(132\) −5.12913 −0.446433
\(133\) 19.6176 1.70106
\(134\) −26.1903 −2.26250
\(135\) 2.67798 0.230484
\(136\) −6.26898 −0.537560
\(137\) 13.1733 1.12547 0.562734 0.826638i \(-0.309749\pi\)
0.562734 + 0.826638i \(0.309749\pi\)
\(138\) −12.3731 −1.05327
\(139\) −20.3308 −1.72444 −0.862218 0.506537i \(-0.830925\pi\)
−0.862218 + 0.506537i \(0.830925\pi\)
\(140\) −35.2294 −2.97743
\(141\) −9.61783 −0.809967
\(142\) −26.3322 −2.20975
\(143\) 6.50814 0.544238
\(144\) 7.00938 0.584115
\(145\) −21.3791 −1.77544
\(146\) −3.68435 −0.304919
\(147\) −1.67889 −0.138472
\(148\) 4.60359 0.378413
\(149\) −4.27599 −0.350303 −0.175151 0.984542i \(-0.556041\pi\)
−0.175151 + 0.984542i \(0.556041\pi\)
\(150\) 5.52174 0.450848
\(151\) −18.5641 −1.51072 −0.755361 0.655309i \(-0.772538\pi\)
−0.755361 + 0.655309i \(0.772538\pi\)
\(152\) −41.7455 −3.38601
\(153\) 1.00000 0.0808452
\(154\) −8.60417 −0.693344
\(155\) −22.7347 −1.82610
\(156\) −25.3014 −2.02574
\(157\) −1.00000 −0.0798087
\(158\) 4.46381 0.355122
\(159\) −13.7771 −1.09259
\(160\) 14.1531 1.11890
\(161\) −14.3354 −1.12979
\(162\) −2.54273 −0.199775
\(163\) −11.5849 −0.907397 −0.453699 0.891155i \(-0.649896\pi\)
−0.453699 + 0.891155i \(0.649896\pi\)
\(164\) −43.4826 −3.39542
\(165\) 3.07599 0.239466
\(166\) −36.1448 −2.80538
\(167\) −3.97649 −0.307710 −0.153855 0.988093i \(-0.549169\pi\)
−0.153855 + 0.988093i \(0.549169\pi\)
\(168\) 18.4684 1.42487
\(169\) 19.1040 1.46954
\(170\) 6.80937 0.522255
\(171\) 6.65907 0.509232
\(172\) 16.2374 1.23809
\(173\) 9.89085 0.751987 0.375994 0.926622i \(-0.377301\pi\)
0.375994 + 0.926622i \(0.377301\pi\)
\(174\) 20.2993 1.53889
\(175\) 6.39747 0.483603
\(176\) 8.05113 0.606877
\(177\) −14.9266 −1.12195
\(178\) 11.0210 0.826056
\(179\) 3.11527 0.232846 0.116423 0.993200i \(-0.462857\pi\)
0.116423 + 0.993200i \(0.462857\pi\)
\(180\) −11.9584 −0.891327
\(181\) −13.3295 −0.990775 −0.495387 0.868672i \(-0.664974\pi\)
−0.495387 + 0.868672i \(0.664974\pi\)
\(182\) −42.4435 −3.14612
\(183\) 5.54929 0.410215
\(184\) 30.5053 2.24888
\(185\) −2.76082 −0.202980
\(186\) 21.5865 1.58280
\(187\) 1.14862 0.0839957
\(188\) 42.9480 3.13230
\(189\) −2.94599 −0.214290
\(190\) 45.3441 3.28960
\(191\) −8.78858 −0.635919 −0.317959 0.948104i \(-0.602998\pi\)
−0.317959 + 0.948104i \(0.602998\pi\)
\(192\) 0.580516 0.0418952
\(193\) 20.7784 1.49566 0.747831 0.663889i \(-0.231095\pi\)
0.747831 + 0.663889i \(0.231095\pi\)
\(194\) 15.2633 1.09584
\(195\) 15.1735 1.08660
\(196\) 7.49699 0.535499
\(197\) −23.7695 −1.69351 −0.846753 0.531986i \(-0.821446\pi\)
−0.846753 + 0.531986i \(0.821446\pi\)
\(198\) −2.92063 −0.207560
\(199\) 15.2002 1.07751 0.538756 0.842462i \(-0.318894\pi\)
0.538756 + 0.842462i \(0.318894\pi\)
\(200\) −13.6136 −0.962626
\(201\) −10.3001 −0.726512
\(202\) 8.46798 0.595805
\(203\) 23.5187 1.65069
\(204\) −4.46545 −0.312644
\(205\) 26.0770 1.82130
\(206\) 2.29465 0.159876
\(207\) −4.86607 −0.338215
\(208\) 39.7154 2.75377
\(209\) 7.64876 0.529076
\(210\) −20.0604 −1.38430
\(211\) 15.7713 1.08574 0.542869 0.839817i \(-0.317338\pi\)
0.542869 + 0.839817i \(0.317338\pi\)
\(212\) 61.5208 4.22527
\(213\) −10.3559 −0.709575
\(214\) −27.8172 −1.90154
\(215\) −9.73772 −0.664107
\(216\) 6.26898 0.426550
\(217\) 25.0100 1.69779
\(218\) −37.0233 −2.50754
\(219\) −1.44898 −0.0979127
\(220\) −13.7357 −0.926061
\(221\) 5.66604 0.381139
\(222\) 2.62138 0.175936
\(223\) 9.15149 0.612829 0.306415 0.951898i \(-0.400871\pi\)
0.306415 + 0.951898i \(0.400871\pi\)
\(224\) −15.5695 −1.04028
\(225\) 2.17158 0.144772
\(226\) −16.3969 −1.09070
\(227\) −20.5423 −1.36344 −0.681720 0.731613i \(-0.738768\pi\)
−0.681720 + 0.731613i \(0.738768\pi\)
\(228\) −29.7358 −1.96930
\(229\) −14.8520 −0.981448 −0.490724 0.871315i \(-0.663268\pi\)
−0.490724 + 0.871315i \(0.663268\pi\)
\(230\) −33.1349 −2.18485
\(231\) −3.38384 −0.222640
\(232\) −50.0470 −3.28575
\(233\) −6.18493 −0.405188 −0.202594 0.979263i \(-0.564937\pi\)
−0.202594 + 0.979263i \(0.564937\pi\)
\(234\) −14.4072 −0.941827
\(235\) −25.7564 −1.68016
\(236\) 66.6540 4.33881
\(237\) 1.75552 0.114033
\(238\) −7.49086 −0.485560
\(239\) −8.90165 −0.575800 −0.287900 0.957660i \(-0.592957\pi\)
−0.287900 + 0.957660i \(0.592957\pi\)
\(240\) 18.7710 1.21166
\(241\) −9.59092 −0.617805 −0.308903 0.951094i \(-0.599962\pi\)
−0.308903 + 0.951094i \(0.599962\pi\)
\(242\) 24.6153 1.58233
\(243\) −1.00000 −0.0641500
\(244\) −24.7801 −1.58638
\(245\) −4.49602 −0.287240
\(246\) −24.7599 −1.57864
\(247\) 37.7305 2.40074
\(248\) −53.2205 −3.37950
\(249\) −14.2150 −0.900839
\(250\) −19.2598 −1.21809
\(251\) −12.8153 −0.808898 −0.404449 0.914561i \(-0.632537\pi\)
−0.404449 + 0.914561i \(0.632537\pi\)
\(252\) 13.1552 0.828700
\(253\) −5.58928 −0.351395
\(254\) 20.3930 1.27957
\(255\) 2.67798 0.167702
\(256\) −29.4687 −1.84180
\(257\) −18.2418 −1.13789 −0.568945 0.822375i \(-0.692648\pi\)
−0.568945 + 0.822375i \(0.692648\pi\)
\(258\) 9.24590 0.575625
\(259\) 3.03713 0.188718
\(260\) −67.7568 −4.20210
\(261\) 7.98328 0.494153
\(262\) −28.5396 −1.76318
\(263\) 12.8203 0.790531 0.395266 0.918567i \(-0.370653\pi\)
0.395266 + 0.918567i \(0.370653\pi\)
\(264\) 7.20069 0.443172
\(265\) −36.8947 −2.26642
\(266\) −49.8821 −3.05847
\(267\) 4.33431 0.265256
\(268\) 45.9946 2.80957
\(269\) 14.0139 0.854440 0.427220 0.904148i \(-0.359493\pi\)
0.427220 + 0.904148i \(0.359493\pi\)
\(270\) −6.80937 −0.414405
\(271\) 1.72927 0.105046 0.0525230 0.998620i \(-0.483274\pi\)
0.0525230 + 0.998620i \(0.483274\pi\)
\(272\) 7.00938 0.425006
\(273\) −16.6921 −1.01025
\(274\) −33.4960 −2.02357
\(275\) 2.49433 0.150414
\(276\) 21.7292 1.30794
\(277\) −20.2522 −1.21684 −0.608419 0.793616i \(-0.708196\pi\)
−0.608419 + 0.793616i \(0.708196\pi\)
\(278\) 51.6957 3.10050
\(279\) 8.48950 0.508253
\(280\) 49.4579 2.95568
\(281\) 5.78300 0.344985 0.172492 0.985011i \(-0.444818\pi\)
0.172492 + 0.985011i \(0.444818\pi\)
\(282\) 24.4555 1.45630
\(283\) −11.5004 −0.683630 −0.341815 0.939767i \(-0.611042\pi\)
−0.341815 + 0.939767i \(0.611042\pi\)
\(284\) 46.2438 2.74407
\(285\) 17.8329 1.05633
\(286\) −16.5484 −0.978529
\(287\) −28.6868 −1.69333
\(288\) −5.28497 −0.311420
\(289\) 1.00000 0.0588235
\(290\) 54.3611 3.19219
\(291\) 6.00271 0.351885
\(292\) 6.47034 0.378648
\(293\) 5.66538 0.330975 0.165488 0.986212i \(-0.447080\pi\)
0.165488 + 0.986212i \(0.447080\pi\)
\(294\) 4.26895 0.248970
\(295\) −39.9731 −2.32733
\(296\) −6.46290 −0.375649
\(297\) −1.14862 −0.0666499
\(298\) 10.8727 0.629837
\(299\) −27.5713 −1.59449
\(300\) −9.69710 −0.559862
\(301\) 10.7123 0.617445
\(302\) 47.2033 2.71625
\(303\) 3.33028 0.191319
\(304\) 46.6759 2.67705
\(305\) 14.8609 0.850932
\(306\) −2.54273 −0.145358
\(307\) 24.2299 1.38288 0.691438 0.722436i \(-0.256978\pi\)
0.691438 + 0.722436i \(0.256978\pi\)
\(308\) 15.1104 0.860994
\(309\) 0.902439 0.0513379
\(310\) 57.8082 3.28328
\(311\) −1.55255 −0.0880371 −0.0440185 0.999031i \(-0.514016\pi\)
−0.0440185 + 0.999031i \(0.514016\pi\)
\(312\) 35.5203 2.01094
\(313\) −22.4840 −1.27087 −0.635436 0.772153i \(-0.719180\pi\)
−0.635436 + 0.772153i \(0.719180\pi\)
\(314\) 2.54273 0.143494
\(315\) −7.88932 −0.444513
\(316\) −7.83921 −0.440990
\(317\) −24.6033 −1.38186 −0.690929 0.722922i \(-0.742798\pi\)
−0.690929 + 0.722922i \(0.742798\pi\)
\(318\) 35.0313 1.96446
\(319\) 9.16978 0.513409
\(320\) 1.55461 0.0869054
\(321\) −10.9399 −0.610606
\(322\) 36.4510 2.03134
\(323\) 6.65907 0.370520
\(324\) 4.46545 0.248081
\(325\) 12.3043 0.682518
\(326\) 29.4572 1.63148
\(327\) −14.5605 −0.805197
\(328\) 61.0445 3.37062
\(329\) 28.3341 1.56211
\(330\) −7.82140 −0.430554
\(331\) −9.42272 −0.517920 −0.258960 0.965888i \(-0.583380\pi\)
−0.258960 + 0.965888i \(0.583380\pi\)
\(332\) 63.4764 3.48372
\(333\) 1.03093 0.0564949
\(334\) 10.1111 0.553256
\(335\) −27.5834 −1.50704
\(336\) −20.6496 −1.12653
\(337\) −9.58223 −0.521977 −0.260989 0.965342i \(-0.584048\pi\)
−0.260989 + 0.965342i \(0.584048\pi\)
\(338\) −48.5762 −2.64220
\(339\) −6.44854 −0.350237
\(340\) −11.9584 −0.648535
\(341\) 9.75124 0.528059
\(342\) −16.9322 −0.915588
\(343\) −15.6760 −0.846423
\(344\) −22.7954 −1.22904
\(345\) −13.0312 −0.701578
\(346\) −25.1497 −1.35206
\(347\) −27.3762 −1.46963 −0.734816 0.678267i \(-0.762731\pi\)
−0.734816 + 0.678267i \(0.762731\pi\)
\(348\) −35.6490 −1.91099
\(349\) 17.9630 0.961540 0.480770 0.876847i \(-0.340357\pi\)
0.480770 + 0.876847i \(0.340357\pi\)
\(350\) −16.2670 −0.869508
\(351\) −5.66604 −0.302431
\(352\) −6.07044 −0.323556
\(353\) −27.5292 −1.46523 −0.732615 0.680644i \(-0.761700\pi\)
−0.732615 + 0.680644i \(0.761700\pi\)
\(354\) 37.9542 2.01724
\(355\) −27.7329 −1.47191
\(356\) −19.3547 −1.02580
\(357\) −2.94599 −0.155919
\(358\) −7.92127 −0.418652
\(359\) 11.4062 0.601995 0.300998 0.953625i \(-0.402680\pi\)
0.300998 + 0.953625i \(0.402680\pi\)
\(360\) 16.7882 0.884816
\(361\) 25.3432 1.33385
\(362\) 33.8933 1.78139
\(363\) 9.68066 0.508103
\(364\) 74.5379 3.90685
\(365\) −3.88033 −0.203106
\(366\) −14.1103 −0.737559
\(367\) 18.3147 0.956021 0.478010 0.878354i \(-0.341358\pi\)
0.478010 + 0.878354i \(0.341358\pi\)
\(368\) −34.1081 −1.77801
\(369\) −9.73755 −0.506917
\(370\) 7.02001 0.364953
\(371\) 40.5872 2.10718
\(372\) −37.9095 −1.96551
\(373\) 20.9121 1.08279 0.541394 0.840769i \(-0.317897\pi\)
0.541394 + 0.840769i \(0.317897\pi\)
\(374\) −2.92063 −0.151022
\(375\) −7.57445 −0.391143
\(376\) −60.2939 −3.10942
\(377\) 45.2336 2.32965
\(378\) 7.49086 0.385288
\(379\) 2.98218 0.153184 0.0765922 0.997063i \(-0.475596\pi\)
0.0765922 + 0.997063i \(0.475596\pi\)
\(380\) −79.6318 −4.08503
\(381\) 8.02012 0.410883
\(382\) 22.3469 1.14337
\(383\) 32.8908 1.68064 0.840322 0.542088i \(-0.182366\pi\)
0.840322 + 0.542088i \(0.182366\pi\)
\(384\) −12.0460 −0.614722
\(385\) −9.06185 −0.461835
\(386\) −52.8338 −2.68917
\(387\) 3.63622 0.184839
\(388\) −26.8048 −1.36081
\(389\) −32.0896 −1.62701 −0.813505 0.581558i \(-0.802443\pi\)
−0.813505 + 0.581558i \(0.802443\pi\)
\(390\) −38.5822 −1.95368
\(391\) −4.86607 −0.246088
\(392\) −10.5249 −0.531587
\(393\) −11.2240 −0.566177
\(394\) 60.4393 3.04489
\(395\) 4.70126 0.236546
\(396\) 5.12913 0.257748
\(397\) −23.8666 −1.19783 −0.598914 0.800813i \(-0.704401\pi\)
−0.598914 + 0.800813i \(0.704401\pi\)
\(398\) −38.6499 −1.93734
\(399\) −19.6176 −0.982107
\(400\) 15.2214 0.761072
\(401\) −27.9994 −1.39822 −0.699112 0.715012i \(-0.746421\pi\)
−0.699112 + 0.715012i \(0.746421\pi\)
\(402\) 26.1903 1.30625
\(403\) 48.1018 2.39612
\(404\) −14.8712 −0.739870
\(405\) −2.67798 −0.133070
\(406\) −59.8016 −2.96790
\(407\) 1.18416 0.0586964
\(408\) 6.26898 0.310361
\(409\) −9.86637 −0.487861 −0.243930 0.969793i \(-0.578437\pi\)
−0.243930 + 0.969793i \(0.578437\pi\)
\(410\) −66.3066 −3.27465
\(411\) −13.1733 −0.649790
\(412\) −4.02980 −0.198534
\(413\) 43.9737 2.16380
\(414\) 12.3731 0.608104
\(415\) −38.0675 −1.86866
\(416\) −29.9449 −1.46817
\(417\) 20.3308 0.995604
\(418\) −19.4487 −0.951267
\(419\) 10.3559 0.505919 0.252959 0.967477i \(-0.418596\pi\)
0.252959 + 0.967477i \(0.418596\pi\)
\(420\) 35.2294 1.71902
\(421\) 17.7266 0.863940 0.431970 0.901888i \(-0.357819\pi\)
0.431970 + 0.901888i \(0.357819\pi\)
\(422\) −40.1020 −1.95213
\(423\) 9.61783 0.467635
\(424\) −86.3681 −4.19440
\(425\) 2.17158 0.105337
\(426\) 26.3322 1.27580
\(427\) −16.3482 −0.791144
\(428\) 48.8517 2.36133
\(429\) −6.50814 −0.314216
\(430\) 24.7603 1.19405
\(431\) 5.07575 0.244490 0.122245 0.992500i \(-0.460991\pi\)
0.122245 + 0.992500i \(0.460991\pi\)
\(432\) −7.00938 −0.337239
\(433\) −1.50363 −0.0722599 −0.0361300 0.999347i \(-0.511503\pi\)
−0.0361300 + 0.999347i \(0.511503\pi\)
\(434\) −63.5936 −3.05259
\(435\) 21.3791 1.02505
\(436\) 65.0192 3.11386
\(437\) −32.4035 −1.55007
\(438\) 3.68435 0.176045
\(439\) −14.2046 −0.677949 −0.338975 0.940796i \(-0.610080\pi\)
−0.338975 + 0.940796i \(0.610080\pi\)
\(440\) 19.2833 0.919296
\(441\) 1.67889 0.0799469
\(442\) −14.4072 −0.685280
\(443\) −36.1147 −1.71586 −0.857932 0.513764i \(-0.828251\pi\)
−0.857932 + 0.513764i \(0.828251\pi\)
\(444\) −4.60359 −0.218477
\(445\) 11.6072 0.550234
\(446\) −23.2697 −1.10185
\(447\) 4.27599 0.202247
\(448\) −1.71020 −0.0807993
\(449\) −9.30746 −0.439246 −0.219623 0.975585i \(-0.570483\pi\)
−0.219623 + 0.975585i \(0.570483\pi\)
\(450\) −5.52174 −0.260297
\(451\) −11.1848 −0.526671
\(452\) 28.7957 1.35444
\(453\) 18.5641 0.872216
\(454\) 52.2334 2.45144
\(455\) −44.7012 −2.09562
\(456\) 41.7455 1.95491
\(457\) 22.4678 1.05100 0.525499 0.850794i \(-0.323879\pi\)
0.525499 + 0.850794i \(0.323879\pi\)
\(458\) 37.7646 1.76462
\(459\) −1.00000 −0.0466760
\(460\) 58.1904 2.71314
\(461\) 11.1532 0.519457 0.259729 0.965682i \(-0.416367\pi\)
0.259729 + 0.965682i \(0.416367\pi\)
\(462\) 8.60417 0.400302
\(463\) −6.37371 −0.296211 −0.148106 0.988972i \(-0.547318\pi\)
−0.148106 + 0.988972i \(0.547318\pi\)
\(464\) 55.9578 2.59778
\(465\) 22.7347 1.05430
\(466\) 15.7266 0.728520
\(467\) −4.10325 −0.189876 −0.0949379 0.995483i \(-0.530265\pi\)
−0.0949379 + 0.995483i \(0.530265\pi\)
\(468\) 25.3014 1.16956
\(469\) 30.3440 1.40116
\(470\) 65.4914 3.02089
\(471\) 1.00000 0.0460776
\(472\) −93.5744 −4.30711
\(473\) 4.17664 0.192042
\(474\) −4.46381 −0.205030
\(475\) 14.4607 0.663503
\(476\) 13.1552 0.602968
\(477\) 13.7771 0.630808
\(478\) 22.6345 1.03528
\(479\) −25.2367 −1.15309 −0.576547 0.817064i \(-0.695600\pi\)
−0.576547 + 0.817064i \(0.695600\pi\)
\(480\) −14.1531 −0.645996
\(481\) 5.84131 0.266341
\(482\) 24.3871 1.11080
\(483\) 14.3354 0.652284
\(484\) −43.2286 −1.96494
\(485\) 16.0751 0.729935
\(486\) 2.54273 0.115340
\(487\) −38.9121 −1.76328 −0.881638 0.471926i \(-0.843559\pi\)
−0.881638 + 0.471926i \(0.843559\pi\)
\(488\) 34.7884 1.57480
\(489\) 11.5849 0.523886
\(490\) 11.4322 0.516452
\(491\) −29.8868 −1.34877 −0.674387 0.738378i \(-0.735592\pi\)
−0.674387 + 0.738378i \(0.735592\pi\)
\(492\) 43.4826 1.96035
\(493\) 7.98328 0.359549
\(494\) −95.9384 −4.31647
\(495\) −3.07599 −0.138256
\(496\) 59.5061 2.67190
\(497\) 30.5085 1.36849
\(498\) 36.1448 1.61969
\(499\) −33.6178 −1.50494 −0.752469 0.658628i \(-0.771137\pi\)
−0.752469 + 0.658628i \(0.771137\pi\)
\(500\) 33.8234 1.51263
\(501\) 3.97649 0.177657
\(502\) 32.5859 1.45438
\(503\) −21.6655 −0.966018 −0.483009 0.875616i \(-0.660456\pi\)
−0.483009 + 0.875616i \(0.660456\pi\)
\(504\) −18.4684 −0.822647
\(505\) 8.91842 0.396864
\(506\) 14.2120 0.631801
\(507\) −19.1040 −0.848438
\(508\) −35.8135 −1.58897
\(509\) −30.7088 −1.36114 −0.680571 0.732682i \(-0.738268\pi\)
−0.680571 + 0.732682i \(0.738268\pi\)
\(510\) −6.80937 −0.301524
\(511\) 4.26868 0.188835
\(512\) 50.8389 2.24678
\(513\) −6.65907 −0.294005
\(514\) 46.3838 2.04590
\(515\) 2.41671 0.106493
\(516\) −16.2374 −0.714810
\(517\) 11.0473 0.485858
\(518\) −7.72258 −0.339311
\(519\) −9.89085 −0.434160
\(520\) 95.1226 4.17140
\(521\) −21.0919 −0.924052 −0.462026 0.886866i \(-0.652877\pi\)
−0.462026 + 0.886866i \(0.652877\pi\)
\(522\) −20.2993 −0.888476
\(523\) 28.9815 1.26727 0.633637 0.773631i \(-0.281561\pi\)
0.633637 + 0.773631i \(0.281561\pi\)
\(524\) 50.1204 2.18952
\(525\) −6.39747 −0.279208
\(526\) −32.5984 −1.42136
\(527\) 8.48950 0.369808
\(528\) −8.05113 −0.350381
\(529\) 0.678634 0.0295058
\(530\) 93.8131 4.07498
\(531\) 14.9266 0.647759
\(532\) 87.6014 3.79800
\(533\) −55.1734 −2.38982
\(534\) −11.0210 −0.476924
\(535\) −29.2969 −1.26661
\(536\) −64.5710 −2.78904
\(537\) −3.11527 −0.134434
\(538\) −35.6334 −1.53626
\(539\) 1.92841 0.0830624
\(540\) 11.9584 0.514608
\(541\) −39.1386 −1.68270 −0.841351 0.540490i \(-0.818239\pi\)
−0.841351 + 0.540490i \(0.818239\pi\)
\(542\) −4.39707 −0.188870
\(543\) 13.3295 0.572024
\(544\) −5.28497 −0.226591
\(545\) −38.9927 −1.67026
\(546\) 42.4435 1.81641
\(547\) 13.0844 0.559450 0.279725 0.960080i \(-0.409757\pi\)
0.279725 + 0.960080i \(0.409757\pi\)
\(548\) 58.8247 2.51286
\(549\) −5.54929 −0.236838
\(550\) −6.34239 −0.270441
\(551\) 53.1612 2.26474
\(552\) −30.5053 −1.29839
\(553\) −5.17176 −0.219926
\(554\) 51.4958 2.18785
\(555\) 2.76082 0.117190
\(556\) −90.7863 −3.85020
\(557\) 1.86466 0.0790082 0.0395041 0.999219i \(-0.487422\pi\)
0.0395041 + 0.999219i \(0.487422\pi\)
\(558\) −21.5865 −0.913828
\(559\) 20.6029 0.871412
\(560\) −55.2992 −2.33682
\(561\) −1.14862 −0.0484949
\(562\) −14.7046 −0.620275
\(563\) −37.2297 −1.56905 −0.784523 0.620099i \(-0.787092\pi\)
−0.784523 + 0.620099i \(0.787092\pi\)
\(564\) −42.9480 −1.80844
\(565\) −17.2691 −0.726516
\(566\) 29.2425 1.22915
\(567\) 2.94599 0.123720
\(568\) −64.9209 −2.72402
\(569\) −13.1522 −0.551367 −0.275683 0.961248i \(-0.588904\pi\)
−0.275683 + 0.961248i \(0.588904\pi\)
\(570\) −45.3441 −1.89925
\(571\) 6.97925 0.292073 0.146036 0.989279i \(-0.453348\pi\)
0.146036 + 0.989279i \(0.453348\pi\)
\(572\) 29.0618 1.21514
\(573\) 8.78858 0.367148
\(574\) 72.9426 3.04457
\(575\) −10.5671 −0.440677
\(576\) −0.580516 −0.0241882
\(577\) 31.6789 1.31881 0.659405 0.751788i \(-0.270808\pi\)
0.659405 + 0.751788i \(0.270808\pi\)
\(578\) −2.54273 −0.105763
\(579\) −20.7784 −0.863521
\(580\) −95.4673 −3.96406
\(581\) 41.8773 1.73736
\(582\) −15.2633 −0.632682
\(583\) 15.8247 0.655390
\(584\) −9.08359 −0.375882
\(585\) −15.1735 −0.627349
\(586\) −14.4055 −0.595086
\(587\) 4.00509 0.165308 0.0826538 0.996578i \(-0.473660\pi\)
0.0826538 + 0.996578i \(0.473660\pi\)
\(588\) −7.49699 −0.309171
\(589\) 56.5322 2.32937
\(590\) 101.641 4.18448
\(591\) 23.7695 0.977746
\(592\) 7.22621 0.296995
\(593\) −0.572225 −0.0234985 −0.0117492 0.999931i \(-0.503740\pi\)
−0.0117492 + 0.999931i \(0.503740\pi\)
\(594\) 2.92063 0.119835
\(595\) −7.88932 −0.323430
\(596\) −19.0942 −0.782131
\(597\) −15.2002 −0.622102
\(598\) 70.1064 2.86686
\(599\) 6.26893 0.256141 0.128071 0.991765i \(-0.459122\pi\)
0.128071 + 0.991765i \(0.459122\pi\)
\(600\) 13.6136 0.555772
\(601\) 3.24638 0.132422 0.0662112 0.997806i \(-0.478909\pi\)
0.0662112 + 0.997806i \(0.478909\pi\)
\(602\) −27.2384 −1.11015
\(603\) 10.3001 0.419452
\(604\) −82.8970 −3.37303
\(605\) 25.9246 1.05399
\(606\) −8.46798 −0.343988
\(607\) 15.5336 0.630489 0.315245 0.949010i \(-0.397913\pi\)
0.315245 + 0.949010i \(0.397913\pi\)
\(608\) −35.1930 −1.42726
\(609\) −23.5187 −0.953026
\(610\) −37.7872 −1.52996
\(611\) 54.4950 2.20463
\(612\) 4.46545 0.180505
\(613\) −8.94320 −0.361212 −0.180606 0.983556i \(-0.557806\pi\)
−0.180606 + 0.983556i \(0.557806\pi\)
\(614\) −61.6101 −2.48638
\(615\) −26.0770 −1.05153
\(616\) −21.2132 −0.854704
\(617\) 42.5049 1.71118 0.855592 0.517651i \(-0.173193\pi\)
0.855592 + 0.517651i \(0.173193\pi\)
\(618\) −2.29465 −0.0923045
\(619\) 29.8724 1.20067 0.600337 0.799747i \(-0.295033\pi\)
0.600337 + 0.799747i \(0.295033\pi\)
\(620\) −101.521 −4.07718
\(621\) 4.86607 0.195269
\(622\) 3.94771 0.158289
\(623\) −12.7689 −0.511573
\(624\) −39.7154 −1.58989
\(625\) −31.1421 −1.24569
\(626\) 57.1707 2.28500
\(627\) −7.64876 −0.305462
\(628\) −4.46545 −0.178191
\(629\) 1.03093 0.0411060
\(630\) 20.0604 0.799224
\(631\) 37.2974 1.48479 0.742394 0.669964i \(-0.233690\pi\)
0.742394 + 0.669964i \(0.233690\pi\)
\(632\) 11.0053 0.437768
\(633\) −15.7713 −0.626851
\(634\) 62.5594 2.48455
\(635\) 21.4777 0.852318
\(636\) −61.5208 −2.43946
\(637\) 9.51263 0.376904
\(638\) −23.3162 −0.923099
\(639\) 10.3559 0.409673
\(640\) −32.2591 −1.27515
\(641\) −45.8235 −1.80992 −0.904959 0.425498i \(-0.860099\pi\)
−0.904959 + 0.425498i \(0.860099\pi\)
\(642\) 27.8172 1.09786
\(643\) −40.5538 −1.59928 −0.799642 0.600477i \(-0.794977\pi\)
−0.799642 + 0.600477i \(0.794977\pi\)
\(644\) −64.0142 −2.52251
\(645\) 9.73772 0.383422
\(646\) −16.9322 −0.666188
\(647\) 40.4860 1.59167 0.795834 0.605514i \(-0.207033\pi\)
0.795834 + 0.605514i \(0.207033\pi\)
\(648\) −6.26898 −0.246269
\(649\) 17.1450 0.673001
\(650\) −31.2864 −1.22715
\(651\) −25.0100 −0.980220
\(652\) −51.7317 −2.02597
\(653\) −14.6748 −0.574270 −0.287135 0.957890i \(-0.592703\pi\)
−0.287135 + 0.957890i \(0.592703\pi\)
\(654\) 37.0233 1.44773
\(655\) −30.0577 −1.17445
\(656\) −68.2542 −2.66488
\(657\) 1.44898 0.0565299
\(658\) −72.0458 −2.80864
\(659\) −33.7038 −1.31291 −0.656457 0.754363i \(-0.727946\pi\)
−0.656457 + 0.754363i \(0.727946\pi\)
\(660\) 13.7357 0.534661
\(661\) −13.3403 −0.518876 −0.259438 0.965760i \(-0.583537\pi\)
−0.259438 + 0.965760i \(0.583537\pi\)
\(662\) 23.9594 0.931209
\(663\) −5.66604 −0.220051
\(664\) −89.1135 −3.45827
\(665\) −52.5355 −2.03724
\(666\) −2.62138 −0.101577
\(667\) −38.8472 −1.50417
\(668\) −17.7568 −0.687033
\(669\) −9.15149 −0.353817
\(670\) 70.1371 2.70963
\(671\) −6.37405 −0.246067
\(672\) 15.5695 0.600607
\(673\) 15.8351 0.610397 0.305198 0.952289i \(-0.401277\pi\)
0.305198 + 0.952289i \(0.401277\pi\)
\(674\) 24.3650 0.938504
\(675\) −2.17158 −0.0835842
\(676\) 85.3080 3.28108
\(677\) 48.2236 1.85338 0.926692 0.375821i \(-0.122639\pi\)
0.926692 + 0.375821i \(0.122639\pi\)
\(678\) 16.3969 0.629718
\(679\) −17.6840 −0.678648
\(680\) 16.7882 0.643798
\(681\) 20.5423 0.787183
\(682\) −24.7947 −0.949439
\(683\) 46.9093 1.79493 0.897467 0.441082i \(-0.145405\pi\)
0.897467 + 0.441082i \(0.145405\pi\)
\(684\) 29.7358 1.13698
\(685\) −35.2778 −1.34789
\(686\) 39.8597 1.52185
\(687\) 14.8520 0.566639
\(688\) 25.4876 0.971706
\(689\) 78.0614 2.97390
\(690\) 33.1349 1.26142
\(691\) 40.8271 1.55314 0.776569 0.630033i \(-0.216959\pi\)
0.776569 + 0.630033i \(0.216959\pi\)
\(692\) 44.1671 1.67898
\(693\) 3.38384 0.128541
\(694\) 69.6102 2.64237
\(695\) 54.4455 2.06524
\(696\) 50.0470 1.89703
\(697\) −9.73755 −0.368836
\(698\) −45.6751 −1.72883
\(699\) 6.18493 0.233936
\(700\) 28.5676 1.07975
\(701\) −32.2668 −1.21870 −0.609351 0.792901i \(-0.708570\pi\)
−0.609351 + 0.792901i \(0.708570\pi\)
\(702\) 14.4072 0.543764
\(703\) 6.86506 0.258921
\(704\) −0.666794 −0.0251308
\(705\) 25.7564 0.970041
\(706\) 69.9991 2.63445
\(707\) −9.81098 −0.368980
\(708\) −66.6540 −2.50501
\(709\) −10.9244 −0.410276 −0.205138 0.978733i \(-0.565764\pi\)
−0.205138 + 0.978733i \(0.565764\pi\)
\(710\) 70.5172 2.64646
\(711\) −1.75552 −0.0658372
\(712\) 27.1717 1.01830
\(713\) −41.3105 −1.54709
\(714\) 7.49086 0.280338
\(715\) −17.4287 −0.651796
\(716\) 13.9111 0.519882
\(717\) 8.90165 0.332438
\(718\) −29.0028 −1.08237
\(719\) 2.81368 0.104933 0.0524663 0.998623i \(-0.483292\pi\)
0.0524663 + 0.998623i \(0.483292\pi\)
\(720\) −18.7710 −0.699553
\(721\) −2.65858 −0.0990107
\(722\) −64.4407 −2.39824
\(723\) 9.59092 0.356690
\(724\) −59.5223 −2.21213
\(725\) 17.3363 0.643856
\(726\) −24.6153 −0.913559
\(727\) −11.0598 −0.410185 −0.205092 0.978743i \(-0.565749\pi\)
−0.205092 + 0.978743i \(0.565749\pi\)
\(728\) −104.643 −3.87831
\(729\) 1.00000 0.0370370
\(730\) 9.86661 0.365180
\(731\) 3.63622 0.134490
\(732\) 24.7801 0.915899
\(733\) 21.0413 0.777178 0.388589 0.921411i \(-0.372963\pi\)
0.388589 + 0.921411i \(0.372963\pi\)
\(734\) −46.5693 −1.71890
\(735\) 4.49602 0.165838
\(736\) 25.7170 0.947943
\(737\) 11.8309 0.435797
\(738\) 24.7599 0.911426
\(739\) −3.50290 −0.128856 −0.0644281 0.997922i \(-0.520522\pi\)
−0.0644281 + 0.997922i \(0.520522\pi\)
\(740\) −12.3283 −0.453198
\(741\) −37.7305 −1.38607
\(742\) −103.202 −3.78866
\(743\) 17.3606 0.636899 0.318450 0.947940i \(-0.396838\pi\)
0.318450 + 0.947940i \(0.396838\pi\)
\(744\) 53.2205 1.95116
\(745\) 11.4510 0.419533
\(746\) −53.1738 −1.94683
\(747\) 14.2150 0.520100
\(748\) 5.12913 0.187539
\(749\) 32.2289 1.17762
\(750\) 19.2598 0.703267
\(751\) −3.73919 −0.136445 −0.0682225 0.997670i \(-0.521733\pi\)
−0.0682225 + 0.997670i \(0.521733\pi\)
\(752\) 67.4150 2.45837
\(753\) 12.8153 0.467017
\(754\) −115.017 −4.18866
\(755\) 49.7142 1.80928
\(756\) −13.1552 −0.478450
\(757\) −1.88287 −0.0684341 −0.0342170 0.999414i \(-0.510894\pi\)
−0.0342170 + 0.999414i \(0.510894\pi\)
\(758\) −7.58287 −0.275422
\(759\) 5.58928 0.202878
\(760\) 111.794 4.05518
\(761\) 47.0097 1.70410 0.852050 0.523460i \(-0.175359\pi\)
0.852050 + 0.523460i \(0.175359\pi\)
\(762\) −20.3930 −0.738760
\(763\) 42.8951 1.55291
\(764\) −39.2450 −1.41983
\(765\) −2.67798 −0.0968226
\(766\) −83.6324 −3.02176
\(767\) 84.5747 3.05381
\(768\) 29.4687 1.06336
\(769\) 3.99993 0.144241 0.0721205 0.997396i \(-0.477023\pi\)
0.0721205 + 0.997396i \(0.477023\pi\)
\(770\) 23.0418 0.830369
\(771\) 18.2418 0.656961
\(772\) 92.7850 3.33941
\(773\) 45.8037 1.64745 0.823723 0.566992i \(-0.191893\pi\)
0.823723 + 0.566992i \(0.191893\pi\)
\(774\) −9.24590 −0.332337
\(775\) 18.4356 0.662228
\(776\) 37.6309 1.35087
\(777\) −3.03713 −0.108956
\(778\) 81.5952 2.92533
\(779\) −64.8430 −2.32324
\(780\) 67.7568 2.42608
\(781\) 11.8950 0.425638
\(782\) 12.3731 0.442460
\(783\) −7.98328 −0.285299
\(784\) 11.7679 0.420284
\(785\) 2.67798 0.0955812
\(786\) 28.5396 1.01797
\(787\) −37.0113 −1.31931 −0.659655 0.751568i \(-0.729298\pi\)
−0.659655 + 0.751568i \(0.729298\pi\)
\(788\) −106.142 −3.78114
\(789\) −12.8203 −0.456413
\(790\) −11.9540 −0.425304
\(791\) 18.9974 0.675469
\(792\) −7.20069 −0.255865
\(793\) −31.4425 −1.11656
\(794\) 60.6862 2.15367
\(795\) 36.8947 1.30852
\(796\) 67.8757 2.40579
\(797\) −31.2415 −1.10663 −0.553315 0.832972i \(-0.686637\pi\)
−0.553315 + 0.832972i \(0.686637\pi\)
\(798\) 49.8821 1.76581
\(799\) 9.61783 0.340254
\(800\) −11.4767 −0.405764
\(801\) −4.33431 −0.153145
\(802\) 71.1948 2.51398
\(803\) 1.66433 0.0587328
\(804\) −45.9946 −1.62210
\(805\) 38.3900 1.35307
\(806\) −122.310 −4.30818
\(807\) −14.0139 −0.493311
\(808\) 20.8774 0.734465
\(809\) −9.29265 −0.326712 −0.163356 0.986567i \(-0.552232\pi\)
−0.163356 + 0.986567i \(0.552232\pi\)
\(810\) 6.80937 0.239257
\(811\) −21.9752 −0.771654 −0.385827 0.922571i \(-0.626084\pi\)
−0.385827 + 0.922571i \(0.626084\pi\)
\(812\) 105.022 3.68554
\(813\) −1.72927 −0.0606483
\(814\) −3.01098 −0.105535
\(815\) 31.0241 1.08673
\(816\) −7.00938 −0.245377
\(817\) 24.2138 0.847134
\(818\) 25.0875 0.877163
\(819\) 16.6921 0.583270
\(820\) 116.446 4.06646
\(821\) 1.19974 0.0418710 0.0209355 0.999781i \(-0.493336\pi\)
0.0209355 + 0.999781i \(0.493336\pi\)
\(822\) 33.4960 1.16831
\(823\) 41.0775 1.43187 0.715936 0.698166i \(-0.246000\pi\)
0.715936 + 0.698166i \(0.246000\pi\)
\(824\) 5.65737 0.197084
\(825\) −2.49433 −0.0868414
\(826\) −111.813 −3.89047
\(827\) 7.45083 0.259091 0.129545 0.991573i \(-0.458648\pi\)
0.129545 + 0.991573i \(0.458648\pi\)
\(828\) −21.7292 −0.755142
\(829\) 7.04979 0.244849 0.122425 0.992478i \(-0.460933\pi\)
0.122425 + 0.992478i \(0.460933\pi\)
\(830\) 96.7952 3.35981
\(831\) 20.2522 0.702542
\(832\) −3.28923 −0.114033
\(833\) 1.67889 0.0581699
\(834\) −51.6957 −1.79007
\(835\) 10.6490 0.368523
\(836\) 34.1552 1.18128
\(837\) −8.48950 −0.293440
\(838\) −26.3322 −0.909631
\(839\) 15.2193 0.525428 0.262714 0.964874i \(-0.415382\pi\)
0.262714 + 0.964874i \(0.415382\pi\)
\(840\) −49.4579 −1.70646
\(841\) 34.7328 1.19768
\(842\) −45.0738 −1.55335
\(843\) −5.78300 −0.199177
\(844\) 70.4259 2.42416
\(845\) −51.1601 −1.75996
\(846\) −24.4555 −0.840797
\(847\) −28.5192 −0.979931
\(848\) 96.5686 3.31618
\(849\) 11.5004 0.394694
\(850\) −5.52174 −0.189394
\(851\) −5.01660 −0.171967
\(852\) −46.2438 −1.58429
\(853\) 44.8014 1.53397 0.766985 0.641665i \(-0.221756\pi\)
0.766985 + 0.641665i \(0.221756\pi\)
\(854\) 41.5690 1.42246
\(855\) −17.8329 −0.609871
\(856\) −68.5820 −2.34409
\(857\) 8.04126 0.274684 0.137342 0.990524i \(-0.456144\pi\)
0.137342 + 0.990524i \(0.456144\pi\)
\(858\) 16.5484 0.564954
\(859\) 18.6670 0.636910 0.318455 0.947938i \(-0.396836\pi\)
0.318455 + 0.947938i \(0.396836\pi\)
\(860\) −43.4833 −1.48277
\(861\) 28.6868 0.977643
\(862\) −12.9062 −0.439588
\(863\) −23.4954 −0.799794 −0.399897 0.916560i \(-0.630954\pi\)
−0.399897 + 0.916560i \(0.630954\pi\)
\(864\) 5.28497 0.179798
\(865\) −26.4875 −0.900602
\(866\) 3.82332 0.129922
\(867\) −1.00000 −0.0339618
\(868\) 111.681 3.79070
\(869\) −2.01643 −0.0684028
\(870\) −54.3611 −1.84301
\(871\) 58.3607 1.97748
\(872\) −91.2794 −3.09111
\(873\) −6.00271 −0.203161
\(874\) 82.3932 2.78699
\(875\) 22.3143 0.754361
\(876\) −6.47034 −0.218612
\(877\) 2.98976 0.100957 0.0504786 0.998725i \(-0.483925\pi\)
0.0504786 + 0.998725i \(0.483925\pi\)
\(878\) 36.1184 1.21894
\(879\) −5.66538 −0.191089
\(880\) −21.5608 −0.726814
\(881\) −44.9227 −1.51348 −0.756742 0.653714i \(-0.773210\pi\)
−0.756742 + 0.653714i \(0.773210\pi\)
\(882\) −4.26895 −0.143743
\(883\) 6.73305 0.226585 0.113293 0.993562i \(-0.463860\pi\)
0.113293 + 0.993562i \(0.463860\pi\)
\(884\) 25.3014 0.850980
\(885\) 39.9731 1.34368
\(886\) 91.8299 3.08509
\(887\) 8.95244 0.300594 0.150297 0.988641i \(-0.451977\pi\)
0.150297 + 0.988641i \(0.451977\pi\)
\(888\) 6.46290 0.216881
\(889\) −23.6272 −0.792432
\(890\) −29.5139 −0.989309
\(891\) 1.14862 0.0384803
\(892\) 40.8656 1.36828
\(893\) 64.0458 2.14321
\(894\) −10.8727 −0.363637
\(895\) −8.34263 −0.278863
\(896\) 35.4876 1.18556
\(897\) 27.5713 0.920580
\(898\) 23.6663 0.789755
\(899\) 67.7741 2.26039
\(900\) 9.69710 0.323237
\(901\) 13.7771 0.458980
\(902\) 28.4398 0.946943
\(903\) −10.7123 −0.356482
\(904\) −40.4258 −1.34454
\(905\) 35.6962 1.18658
\(906\) −47.2033 −1.56822
\(907\) 7.36387 0.244513 0.122257 0.992499i \(-0.460987\pi\)
0.122257 + 0.992499i \(0.460987\pi\)
\(908\) −91.7307 −3.04419
\(909\) −3.33028 −0.110458
\(910\) 113.663 3.76789
\(911\) 3.85375 0.127680 0.0638402 0.997960i \(-0.479665\pi\)
0.0638402 + 0.997960i \(0.479665\pi\)
\(912\) −46.6759 −1.54559
\(913\) 16.3277 0.540367
\(914\) −57.1294 −1.88967
\(915\) −14.8609 −0.491286
\(916\) −66.3210 −2.19131
\(917\) 33.0659 1.09193
\(918\) 2.54273 0.0839225
\(919\) 15.5684 0.513553 0.256777 0.966471i \(-0.417340\pi\)
0.256777 + 0.966471i \(0.417340\pi\)
\(920\) −81.6925 −2.69332
\(921\) −24.2299 −0.798403
\(922\) −28.3596 −0.933973
\(923\) 58.6770 1.93138
\(924\) −15.1104 −0.497095
\(925\) 2.23876 0.0736099
\(926\) 16.2066 0.532582
\(927\) −0.902439 −0.0296400
\(928\) −42.1914 −1.38500
\(929\) −19.5795 −0.642382 −0.321191 0.947014i \(-0.604083\pi\)
−0.321191 + 0.947014i \(0.604083\pi\)
\(930\) −57.8082 −1.89560
\(931\) 11.1798 0.366404
\(932\) −27.6185 −0.904675
\(933\) 1.55255 0.0508282
\(934\) 10.4334 0.341392
\(935\) −3.07599 −0.100596
\(936\) −35.5203 −1.16102
\(937\) −46.2258 −1.51013 −0.755066 0.655649i \(-0.772395\pi\)
−0.755066 + 0.655649i \(0.772395\pi\)
\(938\) −77.1565 −2.51925
\(939\) 22.4840 0.733739
\(940\) −115.014 −3.75134
\(941\) 15.7648 0.513917 0.256958 0.966422i \(-0.417280\pi\)
0.256958 + 0.966422i \(0.417280\pi\)
\(942\) −2.54273 −0.0828465
\(943\) 47.3836 1.54302
\(944\) 104.626 3.40529
\(945\) 7.88932 0.256640
\(946\) −10.6201 −0.345288
\(947\) 37.4702 1.21762 0.608809 0.793317i \(-0.291648\pi\)
0.608809 + 0.793317i \(0.291648\pi\)
\(948\) 7.83921 0.254606
\(949\) 8.20995 0.266506
\(950\) −36.7696 −1.19296
\(951\) 24.6033 0.797816
\(952\) −18.4684 −0.598563
\(953\) −13.1411 −0.425683 −0.212842 0.977087i \(-0.568272\pi\)
−0.212842 + 0.977087i \(0.568272\pi\)
\(954\) −35.0313 −1.13418
\(955\) 23.5356 0.761595
\(956\) −39.7499 −1.28560
\(957\) −9.16978 −0.296417
\(958\) 64.1700 2.07324
\(959\) 38.8084 1.25319
\(960\) −1.55461 −0.0501749
\(961\) 41.0716 1.32489
\(962\) −14.8529 −0.478875
\(963\) 10.9399 0.352534
\(964\) −42.8278 −1.37939
\(965\) −55.6442 −1.79125
\(966\) −36.4510 −1.17279
\(967\) 38.3319 1.23267 0.616335 0.787484i \(-0.288617\pi\)
0.616335 + 0.787484i \(0.288617\pi\)
\(968\) 60.6879 1.95058
\(969\) −6.65907 −0.213920
\(970\) −40.8747 −1.31241
\(971\) −36.8988 −1.18414 −0.592070 0.805886i \(-0.701689\pi\)
−0.592070 + 0.805886i \(0.701689\pi\)
\(972\) −4.46545 −0.143230
\(973\) −59.8944 −1.92013
\(974\) 98.9429 3.17033
\(975\) −12.3043 −0.394052
\(976\) −38.8971 −1.24507
\(977\) −25.1925 −0.805981 −0.402990 0.915204i \(-0.632029\pi\)
−0.402990 + 0.915204i \(0.632029\pi\)
\(978\) −29.4572 −0.941936
\(979\) −4.97849 −0.159113
\(980\) −20.0768 −0.641330
\(981\) 14.5605 0.464881
\(982\) 75.9941 2.42507
\(983\) 37.1597 1.18521 0.592606 0.805493i \(-0.298099\pi\)
0.592606 + 0.805493i \(0.298099\pi\)
\(984\) −61.0445 −1.94603
\(985\) 63.6542 2.02819
\(986\) −20.2993 −0.646461
\(987\) −28.3341 −0.901883
\(988\) 168.484 5.36019
\(989\) −17.6941 −0.562639
\(990\) 7.82140 0.248580
\(991\) −41.6746 −1.32384 −0.661919 0.749576i \(-0.730258\pi\)
−0.661919 + 0.749576i \(0.730258\pi\)
\(992\) −44.8668 −1.42452
\(993\) 9.42272 0.299021
\(994\) −77.5746 −2.46052
\(995\) −40.7058 −1.29046
\(996\) −63.4764 −2.01133
\(997\) −21.4095 −0.678045 −0.339022 0.940778i \(-0.610096\pi\)
−0.339022 + 0.940778i \(0.610096\pi\)
\(998\) 85.4807 2.70585
\(999\) −1.03093 −0.0326173
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 \(a_p\))