Properties

Label 8035.2.a.e.1.17
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31112 q^{2}\) \(+3.30909 q^{3}\) \(+3.34126 q^{4}\) \(+1.00000 q^{5}\) \(-7.64768 q^{6}\) \(+0.225615 q^{7}\) \(-3.09980 q^{8}\) \(+7.95005 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31112 q^{2}\) \(+3.30909 q^{3}\) \(+3.34126 q^{4}\) \(+1.00000 q^{5}\) \(-7.64768 q^{6}\) \(+0.225615 q^{7}\) \(-3.09980 q^{8}\) \(+7.95005 q^{9}\) \(-2.31112 q^{10}\) \(+0.662342 q^{11}\) \(+11.0565 q^{12}\) \(+2.92402 q^{13}\) \(-0.521423 q^{14}\) \(+3.30909 q^{15}\) \(+0.481483 q^{16}\) \(-5.12902 q^{17}\) \(-18.3735 q^{18}\) \(+3.17639 q^{19}\) \(+3.34126 q^{20}\) \(+0.746580 q^{21}\) \(-1.53075 q^{22}\) \(-4.47644 q^{23}\) \(-10.2575 q^{24}\) \(+1.00000 q^{25}\) \(-6.75775 q^{26}\) \(+16.3801 q^{27}\) \(+0.753838 q^{28}\) \(+7.05047 q^{29}\) \(-7.64768 q^{30}\) \(+6.45822 q^{31}\) \(+5.08684 q^{32}\) \(+2.19175 q^{33}\) \(+11.8538 q^{34}\) \(+0.225615 q^{35}\) \(+26.5632 q^{36}\) \(-8.74995 q^{37}\) \(-7.34099 q^{38}\) \(+9.67584 q^{39}\) \(-3.09980 q^{40}\) \(+7.33300 q^{41}\) \(-1.72543 q^{42}\) \(-3.51990 q^{43}\) \(+2.21305 q^{44}\) \(+7.95005 q^{45}\) \(+10.3456 q^{46}\) \(-1.72056 q^{47}\) \(+1.59327 q^{48}\) \(-6.94910 q^{49}\) \(-2.31112 q^{50}\) \(-16.9724 q^{51}\) \(+9.76991 q^{52}\) \(+1.12992 q^{53}\) \(-37.8564 q^{54}\) \(+0.662342 q^{55}\) \(-0.699362 q^{56}\) \(+10.5109 q^{57}\) \(-16.2945 q^{58}\) \(+4.26722 q^{59}\) \(+11.0565 q^{60}\) \(+2.82564 q^{61}\) \(-14.9257 q^{62}\) \(+1.79365 q^{63}\) \(-12.7192 q^{64}\) \(+2.92402 q^{65}\) \(-5.06538 q^{66}\) \(+9.95420 q^{67}\) \(-17.1374 q^{68}\) \(-14.8129 q^{69}\) \(-0.521423 q^{70}\) \(+12.4929 q^{71}\) \(-24.6436 q^{72}\) \(-14.9405 q^{73}\) \(+20.2221 q^{74}\) \(+3.30909 q^{75}\) \(+10.6131 q^{76}\) \(+0.149434 q^{77}\) \(-22.3620 q^{78}\) \(-9.47426 q^{79}\) \(+0.481483 q^{80}\) \(+30.3531 q^{81}\) \(-16.9474 q^{82}\) \(+10.2318 q^{83}\) \(+2.49452 q^{84}\) \(-5.12902 q^{85}\) \(+8.13489 q^{86}\) \(+23.3306 q^{87}\) \(-2.05313 q^{88}\) \(+4.22567 q^{89}\) \(-18.3735 q^{90}\) \(+0.659704 q^{91}\) \(-14.9569 q^{92}\) \(+21.3708 q^{93}\) \(+3.97642 q^{94}\) \(+3.17639 q^{95}\) \(+16.8328 q^{96}\) \(-5.40434 q^{97}\) \(+16.0602 q^{98}\) \(+5.26565 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31112 −1.63421 −0.817103 0.576492i \(-0.804421\pi\)
−0.817103 + 0.576492i \(0.804421\pi\)
\(3\) 3.30909 1.91050 0.955251 0.295797i \(-0.0955852\pi\)
0.955251 + 0.295797i \(0.0955852\pi\)
\(4\) 3.34126 1.67063
\(5\) 1.00000 0.447214
\(6\) −7.64768 −3.12215
\(7\) 0.225615 0.0852745 0.0426373 0.999091i \(-0.486424\pi\)
0.0426373 + 0.999091i \(0.486424\pi\)
\(8\) −3.09980 −1.09594
\(9\) 7.95005 2.65002
\(10\) −2.31112 −0.730839
\(11\) 0.662342 0.199703 0.0998517 0.995002i \(-0.468163\pi\)
0.0998517 + 0.995002i \(0.468163\pi\)
\(12\) 11.0565 3.19174
\(13\) 2.92402 0.810978 0.405489 0.914100i \(-0.367101\pi\)
0.405489 + 0.914100i \(0.367101\pi\)
\(14\) −0.521423 −0.139356
\(15\) 3.30909 0.854402
\(16\) 0.481483 0.120371
\(17\) −5.12902 −1.24397 −0.621985 0.783029i \(-0.713674\pi\)
−0.621985 + 0.783029i \(0.713674\pi\)
\(18\) −18.3735 −4.33067
\(19\) 3.17639 0.728713 0.364356 0.931260i \(-0.381289\pi\)
0.364356 + 0.931260i \(0.381289\pi\)
\(20\) 3.34126 0.747128
\(21\) 0.746580 0.162917
\(22\) −1.53075 −0.326357
\(23\) −4.47644 −0.933403 −0.466701 0.884415i \(-0.654558\pi\)
−0.466701 + 0.884415i \(0.654558\pi\)
\(24\) −10.2575 −2.09380
\(25\) 1.00000 0.200000
\(26\) −6.75775 −1.32530
\(27\) 16.3801 3.15236
\(28\) 0.753838 0.142462
\(29\) 7.05047 1.30924 0.654620 0.755958i \(-0.272829\pi\)
0.654620 + 0.755958i \(0.272829\pi\)
\(30\) −7.64768 −1.39627
\(31\) 6.45822 1.15993 0.579965 0.814641i \(-0.303066\pi\)
0.579965 + 0.814641i \(0.303066\pi\)
\(32\) 5.08684 0.899234
\(33\) 2.19175 0.381534
\(34\) 11.8538 2.03290
\(35\) 0.225615 0.0381359
\(36\) 26.5632 4.42719
\(37\) −8.74995 −1.43848 −0.719241 0.694761i \(-0.755510\pi\)
−0.719241 + 0.694761i \(0.755510\pi\)
\(38\) −7.34099 −1.19087
\(39\) 9.67584 1.54937
\(40\) −3.09980 −0.490121
\(41\) 7.33300 1.14522 0.572611 0.819827i \(-0.305930\pi\)
0.572611 + 0.819827i \(0.305930\pi\)
\(42\) −1.72543 −0.266240
\(43\) −3.51990 −0.536779 −0.268390 0.963310i \(-0.586491\pi\)
−0.268390 + 0.963310i \(0.586491\pi\)
\(44\) 2.21305 0.333630
\(45\) 7.95005 1.18512
\(46\) 10.3456 1.52537
\(47\) −1.72056 −0.250970 −0.125485 0.992096i \(-0.540049\pi\)
−0.125485 + 0.992096i \(0.540049\pi\)
\(48\) 1.59327 0.229968
\(49\) −6.94910 −0.992728
\(50\) −2.31112 −0.326841
\(51\) −16.9724 −2.37661
\(52\) 9.76991 1.35484
\(53\) 1.12992 0.155207 0.0776036 0.996984i \(-0.475273\pi\)
0.0776036 + 0.996984i \(0.475273\pi\)
\(54\) −37.8564 −5.15160
\(55\) 0.662342 0.0893101
\(56\) −0.699362 −0.0934562
\(57\) 10.5109 1.39221
\(58\) −16.2945 −2.13957
\(59\) 4.26722 0.555545 0.277772 0.960647i \(-0.410404\pi\)
0.277772 + 0.960647i \(0.410404\pi\)
\(60\) 11.0565 1.42739
\(61\) 2.82564 0.361786 0.180893 0.983503i \(-0.442101\pi\)
0.180893 + 0.983503i \(0.442101\pi\)
\(62\) −14.9257 −1.89556
\(63\) 1.79365 0.225979
\(64\) −12.7192 −1.58990
\(65\) 2.92402 0.362680
\(66\) −5.06538 −0.623505
\(67\) 9.95420 1.21610 0.608050 0.793899i \(-0.291952\pi\)
0.608050 + 0.793899i \(0.291952\pi\)
\(68\) −17.1374 −2.07821
\(69\) −14.8129 −1.78327
\(70\) −0.521423 −0.0623220
\(71\) 12.4929 1.48264 0.741320 0.671152i \(-0.234200\pi\)
0.741320 + 0.671152i \(0.234200\pi\)
\(72\) −24.6436 −2.90427
\(73\) −14.9405 −1.74865 −0.874327 0.485337i \(-0.838697\pi\)
−0.874327 + 0.485337i \(0.838697\pi\)
\(74\) 20.2221 2.35078
\(75\) 3.30909 0.382100
\(76\) 10.6131 1.21741
\(77\) 0.149434 0.0170296
\(78\) −22.3620 −2.53200
\(79\) −9.47426 −1.06594 −0.532969 0.846135i \(-0.678924\pi\)
−0.532969 + 0.846135i \(0.678924\pi\)
\(80\) 0.481483 0.0538314
\(81\) 30.3531 3.37257
\(82\) −16.9474 −1.87153
\(83\) 10.2318 1.12309 0.561545 0.827447i \(-0.310207\pi\)
0.561545 + 0.827447i \(0.310207\pi\)
\(84\) 2.49452 0.272174
\(85\) −5.12902 −0.556320
\(86\) 8.13489 0.877208
\(87\) 23.3306 2.50130
\(88\) −2.05313 −0.218864
\(89\) 4.22567 0.447920 0.223960 0.974598i \(-0.428102\pi\)
0.223960 + 0.974598i \(0.428102\pi\)
\(90\) −18.3735 −1.93674
\(91\) 0.659704 0.0691558
\(92\) −14.9569 −1.55937
\(93\) 21.3708 2.21605
\(94\) 3.97642 0.410136
\(95\) 3.17639 0.325890
\(96\) 16.8328 1.71799
\(97\) −5.40434 −0.548728 −0.274364 0.961626i \(-0.588467\pi\)
−0.274364 + 0.961626i \(0.588467\pi\)
\(98\) 16.0602 1.62232
\(99\) 5.26565 0.529218
\(100\) 3.34126 0.334126
\(101\) 3.35238 0.333575 0.166787 0.985993i \(-0.446661\pi\)
0.166787 + 0.985993i \(0.446661\pi\)
\(102\) 39.2251 3.88386
\(103\) 4.92484 0.485259 0.242630 0.970119i \(-0.421990\pi\)
0.242630 + 0.970119i \(0.421990\pi\)
\(104\) −9.06388 −0.888787
\(105\) 0.746580 0.0728588
\(106\) −2.61139 −0.253640
\(107\) 14.6250 1.41385 0.706926 0.707288i \(-0.250082\pi\)
0.706926 + 0.707288i \(0.250082\pi\)
\(108\) 54.7302 5.26642
\(109\) 12.6180 1.20858 0.604292 0.796763i \(-0.293456\pi\)
0.604292 + 0.796763i \(0.293456\pi\)
\(110\) −1.53075 −0.145951
\(111\) −28.9543 −2.74822
\(112\) 0.108630 0.0102646
\(113\) −14.5656 −1.37021 −0.685107 0.728442i \(-0.740245\pi\)
−0.685107 + 0.728442i \(0.740245\pi\)
\(114\) −24.2920 −2.27515
\(115\) −4.47644 −0.417430
\(116\) 23.5574 2.18725
\(117\) 23.2461 2.14910
\(118\) −9.86204 −0.907875
\(119\) −1.15719 −0.106079
\(120\) −10.2575 −0.936378
\(121\) −10.5613 −0.960119
\(122\) −6.53037 −0.591232
\(123\) 24.2655 2.18795
\(124\) 21.5786 1.93781
\(125\) 1.00000 0.0894427
\(126\) −4.14534 −0.369296
\(127\) −2.27723 −0.202072 −0.101036 0.994883i \(-0.532216\pi\)
−0.101036 + 0.994883i \(0.532216\pi\)
\(128\) 19.2220 1.69900
\(129\) −11.6476 −1.02552
\(130\) −6.75775 −0.592694
\(131\) 14.1540 1.23664 0.618318 0.785928i \(-0.287814\pi\)
0.618318 + 0.785928i \(0.287814\pi\)
\(132\) 7.32318 0.637401
\(133\) 0.716641 0.0621406
\(134\) −23.0053 −1.98736
\(135\) 16.3801 1.40978
\(136\) 15.8989 1.36332
\(137\) 13.2361 1.13084 0.565419 0.824804i \(-0.308715\pi\)
0.565419 + 0.824804i \(0.308715\pi\)
\(138\) 34.2344 2.91423
\(139\) −10.1535 −0.861210 −0.430605 0.902541i \(-0.641700\pi\)
−0.430605 + 0.902541i \(0.641700\pi\)
\(140\) 0.753838 0.0637110
\(141\) −5.69349 −0.479478
\(142\) −28.8726 −2.42294
\(143\) 1.93670 0.161955
\(144\) 3.82781 0.318984
\(145\) 7.05047 0.585510
\(146\) 34.5292 2.85766
\(147\) −22.9952 −1.89661
\(148\) −29.2358 −2.40317
\(149\) −6.37237 −0.522045 −0.261022 0.965333i \(-0.584060\pi\)
−0.261022 + 0.965333i \(0.584060\pi\)
\(150\) −7.64768 −0.624431
\(151\) 1.73913 0.141529 0.0707643 0.997493i \(-0.477456\pi\)
0.0707643 + 0.997493i \(0.477456\pi\)
\(152\) −9.84616 −0.798629
\(153\) −40.7760 −3.29654
\(154\) −0.345360 −0.0278299
\(155\) 6.45822 0.518737
\(156\) 32.3295 2.58843
\(157\) 5.73893 0.458016 0.229008 0.973425i \(-0.426452\pi\)
0.229008 + 0.973425i \(0.426452\pi\)
\(158\) 21.8961 1.74196
\(159\) 3.73902 0.296523
\(160\) 5.08684 0.402150
\(161\) −1.00995 −0.0795955
\(162\) −70.1496 −5.51147
\(163\) −19.2470 −1.50754 −0.753770 0.657138i \(-0.771767\pi\)
−0.753770 + 0.657138i \(0.771767\pi\)
\(164\) 24.5014 1.91324
\(165\) 2.19175 0.170627
\(166\) −23.6469 −1.83536
\(167\) 7.23110 0.559559 0.279780 0.960064i \(-0.409739\pi\)
0.279780 + 0.960064i \(0.409739\pi\)
\(168\) −2.31425 −0.178548
\(169\) −4.45009 −0.342315
\(170\) 11.8538 0.909142
\(171\) 25.2524 1.93110
\(172\) −11.7609 −0.896759
\(173\) −20.4893 −1.55778 −0.778888 0.627163i \(-0.784216\pi\)
−0.778888 + 0.627163i \(0.784216\pi\)
\(174\) −53.9197 −4.08764
\(175\) 0.225615 0.0170549
\(176\) 0.318906 0.0240384
\(177\) 14.1206 1.06137
\(178\) −9.76601 −0.731993
\(179\) −24.4419 −1.82687 −0.913435 0.406984i \(-0.866580\pi\)
−0.913435 + 0.406984i \(0.866580\pi\)
\(180\) 26.5632 1.97990
\(181\) 3.86698 0.287430 0.143715 0.989619i \(-0.454095\pi\)
0.143715 + 0.989619i \(0.454095\pi\)
\(182\) −1.52465 −0.113015
\(183\) 9.35027 0.691192
\(184\) 13.8761 1.02296
\(185\) −8.74995 −0.643309
\(186\) −49.3904 −3.62148
\(187\) −3.39716 −0.248425
\(188\) −5.74884 −0.419277
\(189\) 3.69561 0.268816
\(190\) −7.34099 −0.532572
\(191\) 10.6811 0.772860 0.386430 0.922319i \(-0.373708\pi\)
0.386430 + 0.922319i \(0.373708\pi\)
\(192\) −42.0890 −3.03751
\(193\) 12.3256 0.887216 0.443608 0.896221i \(-0.353698\pi\)
0.443608 + 0.896221i \(0.353698\pi\)
\(194\) 12.4901 0.896734
\(195\) 9.67584 0.692901
\(196\) −23.2187 −1.65848
\(197\) −1.42548 −0.101561 −0.0507807 0.998710i \(-0.516171\pi\)
−0.0507807 + 0.998710i \(0.516171\pi\)
\(198\) −12.1695 −0.864850
\(199\) 21.4388 1.51975 0.759877 0.650067i \(-0.225259\pi\)
0.759877 + 0.650067i \(0.225259\pi\)
\(200\) −3.09980 −0.219189
\(201\) 32.9393 2.32336
\(202\) −7.74775 −0.545130
\(203\) 1.59069 0.111645
\(204\) −56.7090 −3.97043
\(205\) 7.33300 0.512159
\(206\) −11.3819 −0.793014
\(207\) −35.5879 −2.47353
\(208\) 1.40787 0.0976180
\(209\) 2.10385 0.145526
\(210\) −1.72543 −0.119066
\(211\) 21.4673 1.47787 0.738936 0.673776i \(-0.235329\pi\)
0.738936 + 0.673776i \(0.235329\pi\)
\(212\) 3.77537 0.259293
\(213\) 41.3402 2.83258
\(214\) −33.8000 −2.31052
\(215\) −3.51990 −0.240055
\(216\) −50.7751 −3.45481
\(217\) 1.45707 0.0989125
\(218\) −29.1616 −1.97507
\(219\) −49.4394 −3.34081
\(220\) 2.21305 0.149204
\(221\) −14.9974 −1.00883
\(222\) 66.9168 4.49116
\(223\) 5.27802 0.353442 0.176721 0.984261i \(-0.443451\pi\)
0.176721 + 0.984261i \(0.443451\pi\)
\(224\) 1.14767 0.0766818
\(225\) 7.95005 0.530003
\(226\) 33.6628 2.23921
\(227\) 23.3398 1.54912 0.774560 0.632501i \(-0.217972\pi\)
0.774560 + 0.632501i \(0.217972\pi\)
\(228\) 35.1197 2.32586
\(229\) −10.1097 −0.668070 −0.334035 0.942561i \(-0.608410\pi\)
−0.334035 + 0.942561i \(0.608410\pi\)
\(230\) 10.3456 0.682167
\(231\) 0.494491 0.0325351
\(232\) −21.8550 −1.43485
\(233\) 20.8152 1.36365 0.681826 0.731515i \(-0.261186\pi\)
0.681826 + 0.731515i \(0.261186\pi\)
\(234\) −53.7245 −3.51208
\(235\) −1.72056 −0.112237
\(236\) 14.2579 0.928109
\(237\) −31.3512 −2.03648
\(238\) 2.67439 0.173355
\(239\) −25.2186 −1.63125 −0.815627 0.578578i \(-0.803608\pi\)
−0.815627 + 0.578578i \(0.803608\pi\)
\(240\) 1.59327 0.102845
\(241\) −6.81361 −0.438903 −0.219451 0.975623i \(-0.570427\pi\)
−0.219451 + 0.975623i \(0.570427\pi\)
\(242\) 24.4084 1.56903
\(243\) 51.3007 3.29094
\(244\) 9.44118 0.604409
\(245\) −6.94910 −0.443962
\(246\) −56.0805 −3.57556
\(247\) 9.28782 0.590970
\(248\) −20.0192 −1.27122
\(249\) 33.8580 2.14566
\(250\) −2.31112 −0.146168
\(251\) 9.58678 0.605112 0.302556 0.953132i \(-0.402160\pi\)
0.302556 + 0.953132i \(0.402160\pi\)
\(252\) 5.99305 0.377527
\(253\) −2.96493 −0.186404
\(254\) 5.26295 0.330227
\(255\) −16.9724 −1.06285
\(256\) −18.9857 −1.18661
\(257\) −3.40766 −0.212564 −0.106282 0.994336i \(-0.533895\pi\)
−0.106282 + 0.994336i \(0.533895\pi\)
\(258\) 26.9191 1.67591
\(259\) −1.97412 −0.122666
\(260\) 9.76991 0.605904
\(261\) 56.0516 3.46951
\(262\) −32.7114 −2.02092
\(263\) 2.32345 0.143270 0.0716351 0.997431i \(-0.477178\pi\)
0.0716351 + 0.997431i \(0.477178\pi\)
\(264\) −6.79397 −0.418140
\(265\) 1.12992 0.0694107
\(266\) −1.65624 −0.101551
\(267\) 13.9831 0.855752
\(268\) 33.2595 2.03165
\(269\) −5.66317 −0.345289 −0.172645 0.984984i \(-0.555231\pi\)
−0.172645 + 0.984984i \(0.555231\pi\)
\(270\) −37.8564 −2.30387
\(271\) 10.5749 0.642380 0.321190 0.947015i \(-0.395917\pi\)
0.321190 + 0.947015i \(0.395917\pi\)
\(272\) −2.46953 −0.149738
\(273\) 2.18302 0.132122
\(274\) −30.5902 −1.84802
\(275\) 0.662342 0.0399407
\(276\) −49.4938 −2.97918
\(277\) 32.6854 1.96387 0.981937 0.189208i \(-0.0605921\pi\)
0.981937 + 0.189208i \(0.0605921\pi\)
\(278\) 23.4659 1.40739
\(279\) 51.3431 3.07383
\(280\) −0.699362 −0.0417949
\(281\) −4.04722 −0.241437 −0.120718 0.992687i \(-0.538520\pi\)
−0.120718 + 0.992687i \(0.538520\pi\)
\(282\) 13.1583 0.783566
\(283\) 9.52245 0.566051 0.283025 0.959112i \(-0.408662\pi\)
0.283025 + 0.959112i \(0.408662\pi\)
\(284\) 41.7421 2.47694
\(285\) 10.5109 0.622614
\(286\) −4.47594 −0.264668
\(287\) 1.65444 0.0976584
\(288\) 40.4406 2.38299
\(289\) 9.30684 0.547461
\(290\) −16.2945 −0.956843
\(291\) −17.8834 −1.04835
\(292\) −49.9201 −2.92135
\(293\) −14.7634 −0.862486 −0.431243 0.902236i \(-0.641925\pi\)
−0.431243 + 0.902236i \(0.641925\pi\)
\(294\) 53.1445 3.09945
\(295\) 4.26722 0.248447
\(296\) 27.1231 1.57650
\(297\) 10.8492 0.629537
\(298\) 14.7273 0.853129
\(299\) −13.0892 −0.756969
\(300\) 11.0565 0.638348
\(301\) −0.794143 −0.0457736
\(302\) −4.01934 −0.231287
\(303\) 11.0933 0.637295
\(304\) 1.52937 0.0877157
\(305\) 2.82564 0.161795
\(306\) 94.2380 5.38723
\(307\) −21.9498 −1.25274 −0.626370 0.779526i \(-0.715460\pi\)
−0.626370 + 0.779526i \(0.715460\pi\)
\(308\) 0.499299 0.0284502
\(309\) 16.2967 0.927089
\(310\) −14.9257 −0.847722
\(311\) −29.6950 −1.68385 −0.841923 0.539597i \(-0.818577\pi\)
−0.841923 + 0.539597i \(0.818577\pi\)
\(312\) −29.9932 −1.69803
\(313\) −11.2115 −0.633712 −0.316856 0.948474i \(-0.602627\pi\)
−0.316856 + 0.948474i \(0.602627\pi\)
\(314\) −13.2633 −0.748493
\(315\) 1.79365 0.101061
\(316\) −31.6559 −1.78079
\(317\) −19.4230 −1.09090 −0.545452 0.838142i \(-0.683642\pi\)
−0.545452 + 0.838142i \(0.683642\pi\)
\(318\) −8.64131 −0.484580
\(319\) 4.66982 0.261460
\(320\) −12.7192 −0.711027
\(321\) 48.3954 2.70117
\(322\) 2.33412 0.130075
\(323\) −16.2917 −0.906497
\(324\) 101.418 5.63431
\(325\) 2.92402 0.162196
\(326\) 44.4820 2.46363
\(327\) 41.7540 2.30900
\(328\) −22.7308 −1.25510
\(329\) −0.388185 −0.0214013
\(330\) −5.06538 −0.278840
\(331\) 9.31017 0.511733 0.255867 0.966712i \(-0.417639\pi\)
0.255867 + 0.966712i \(0.417639\pi\)
\(332\) 34.1872 1.87626
\(333\) −69.5625 −3.81200
\(334\) −16.7119 −0.914435
\(335\) 9.95420 0.543856
\(336\) 0.359466 0.0196105
\(337\) 22.4068 1.22058 0.610289 0.792179i \(-0.291053\pi\)
0.610289 + 0.792179i \(0.291053\pi\)
\(338\) 10.2847 0.559413
\(339\) −48.1988 −2.61780
\(340\) −17.1374 −0.929404
\(341\) 4.27755 0.231642
\(342\) −58.3613 −3.15582
\(343\) −3.14713 −0.169929
\(344\) 10.9110 0.588281
\(345\) −14.8129 −0.797502
\(346\) 47.3532 2.54573
\(347\) 19.2454 1.03315 0.516574 0.856243i \(-0.327207\pi\)
0.516574 + 0.856243i \(0.327207\pi\)
\(348\) 77.9535 4.17875
\(349\) −3.73826 −0.200104 −0.100052 0.994982i \(-0.531901\pi\)
−0.100052 + 0.994982i \(0.531901\pi\)
\(350\) −0.521423 −0.0278712
\(351\) 47.8959 2.55649
\(352\) 3.36922 0.179580
\(353\) −26.1822 −1.39354 −0.696770 0.717295i \(-0.745380\pi\)
−0.696770 + 0.717295i \(0.745380\pi\)
\(354\) −32.6343 −1.73450
\(355\) 12.4929 0.663056
\(356\) 14.1190 0.748308
\(357\) −3.82922 −0.202664
\(358\) 56.4880 2.98548
\(359\) 8.67859 0.458038 0.229019 0.973422i \(-0.426448\pi\)
0.229019 + 0.973422i \(0.426448\pi\)
\(360\) −24.6436 −1.29883
\(361\) −8.91058 −0.468978
\(362\) −8.93704 −0.469720
\(363\) −34.9483 −1.83431
\(364\) 2.20424 0.115534
\(365\) −14.9405 −0.782022
\(366\) −21.6096 −1.12955
\(367\) 10.0849 0.526427 0.263214 0.964738i \(-0.415218\pi\)
0.263214 + 0.964738i \(0.415218\pi\)
\(368\) −2.15533 −0.112354
\(369\) 58.2977 3.03486
\(370\) 20.2221 1.05130
\(371\) 0.254928 0.0132352
\(372\) 71.4053 3.70219
\(373\) −8.60598 −0.445601 −0.222800 0.974864i \(-0.571520\pi\)
−0.222800 + 0.974864i \(0.571520\pi\)
\(374\) 7.85124 0.405978
\(375\) 3.30909 0.170880
\(376\) 5.33340 0.275049
\(377\) 20.6157 1.06176
\(378\) −8.54098 −0.439301
\(379\) −7.84429 −0.402934 −0.201467 0.979495i \(-0.564571\pi\)
−0.201467 + 0.979495i \(0.564571\pi\)
\(380\) 10.6131 0.544441
\(381\) −7.53555 −0.386058
\(382\) −24.6853 −1.26301
\(383\) −26.5585 −1.35708 −0.678539 0.734565i \(-0.737386\pi\)
−0.678539 + 0.734565i \(0.737386\pi\)
\(384\) 63.6071 3.24594
\(385\) 0.149434 0.00761588
\(386\) −28.4859 −1.44989
\(387\) −27.9834 −1.42247
\(388\) −18.0573 −0.916720
\(389\) 25.0323 1.26919 0.634595 0.772845i \(-0.281167\pi\)
0.634595 + 0.772845i \(0.281167\pi\)
\(390\) −22.3620 −1.13234
\(391\) 22.9598 1.16113
\(392\) 21.5408 1.08798
\(393\) 46.8366 2.36260
\(394\) 3.29445 0.165972
\(395\) −9.47426 −0.476702
\(396\) 17.5939 0.884126
\(397\) −37.3083 −1.87245 −0.936224 0.351403i \(-0.885705\pi\)
−0.936224 + 0.351403i \(0.885705\pi\)
\(398\) −49.5475 −2.48359
\(399\) 2.37143 0.118720
\(400\) 0.481483 0.0240741
\(401\) 5.91908 0.295585 0.147792 0.989018i \(-0.452783\pi\)
0.147792 + 0.989018i \(0.452783\pi\)
\(402\) −76.1266 −3.79685
\(403\) 18.8840 0.940678
\(404\) 11.2012 0.557279
\(405\) 30.3531 1.50826
\(406\) −3.67628 −0.182451
\(407\) −5.79545 −0.287270
\(408\) 52.6109 2.60463
\(409\) −27.3500 −1.35237 −0.676186 0.736731i \(-0.736369\pi\)
−0.676186 + 0.736731i \(0.736369\pi\)
\(410\) −16.9474 −0.836974
\(411\) 43.7994 2.16047
\(412\) 16.4552 0.810688
\(413\) 0.962750 0.0473738
\(414\) 82.2479 4.04226
\(415\) 10.2318 0.502261
\(416\) 14.8740 0.729259
\(417\) −33.5988 −1.64534
\(418\) −4.86225 −0.237820
\(419\) 24.8756 1.21525 0.607625 0.794224i \(-0.292122\pi\)
0.607625 + 0.794224i \(0.292122\pi\)
\(420\) 2.49452 0.121720
\(421\) 3.94585 0.192309 0.0961544 0.995366i \(-0.469346\pi\)
0.0961544 + 0.995366i \(0.469346\pi\)
\(422\) −49.6135 −2.41515
\(423\) −13.6786 −0.665074
\(424\) −3.50254 −0.170098
\(425\) −5.12902 −0.248794
\(426\) −95.5420 −4.62903
\(427\) 0.637507 0.0308511
\(428\) 48.8658 2.36202
\(429\) 6.40871 0.309416
\(430\) 8.13489 0.392299
\(431\) −7.80234 −0.375825 −0.187913 0.982186i \(-0.560172\pi\)
−0.187913 + 0.982186i \(0.560172\pi\)
\(432\) 7.88675 0.379452
\(433\) 6.55691 0.315105 0.157553 0.987511i \(-0.449640\pi\)
0.157553 + 0.987511i \(0.449640\pi\)
\(434\) −3.36746 −0.161643
\(435\) 23.3306 1.11862
\(436\) 42.1599 2.01909
\(437\) −14.2189 −0.680183
\(438\) 114.260 5.45957
\(439\) −15.1347 −0.722342 −0.361171 0.932500i \(-0.617623\pi\)
−0.361171 + 0.932500i \(0.617623\pi\)
\(440\) −2.05313 −0.0978789
\(441\) −55.2457 −2.63075
\(442\) 34.6607 1.64864
\(443\) 29.7347 1.41274 0.706370 0.707843i \(-0.250332\pi\)
0.706370 + 0.707843i \(0.250332\pi\)
\(444\) −96.7438 −4.59126
\(445\) 4.22567 0.200316
\(446\) −12.1981 −0.577598
\(447\) −21.0867 −0.997367
\(448\) −2.86965 −0.135578
\(449\) 37.3183 1.76116 0.880580 0.473898i \(-0.157153\pi\)
0.880580 + 0.473898i \(0.157153\pi\)
\(450\) −18.3735 −0.866134
\(451\) 4.85695 0.228705
\(452\) −48.6674 −2.28912
\(453\) 5.75494 0.270391
\(454\) −53.9411 −2.53158
\(455\) 0.659704 0.0309274
\(456\) −32.5818 −1.52578
\(457\) −10.3689 −0.485035 −0.242517 0.970147i \(-0.577973\pi\)
−0.242517 + 0.970147i \(0.577973\pi\)
\(458\) 23.3648 1.09176
\(459\) −84.0141 −3.92144
\(460\) −14.9569 −0.697371
\(461\) 9.35487 0.435700 0.217850 0.975982i \(-0.430096\pi\)
0.217850 + 0.975982i \(0.430096\pi\)
\(462\) −1.14283 −0.0531691
\(463\) −25.1692 −1.16971 −0.584856 0.811137i \(-0.698849\pi\)
−0.584856 + 0.811137i \(0.698849\pi\)
\(464\) 3.39468 0.157594
\(465\) 21.3708 0.991047
\(466\) −48.1064 −2.22849
\(467\) −11.2776 −0.521863 −0.260931 0.965357i \(-0.584030\pi\)
−0.260931 + 0.965357i \(0.584030\pi\)
\(468\) 77.6713 3.59036
\(469\) 2.24582 0.103702
\(470\) 3.97642 0.183419
\(471\) 18.9906 0.875041
\(472\) −13.2275 −0.608846
\(473\) −2.33137 −0.107197
\(474\) 72.4561 3.32802
\(475\) 3.17639 0.145743
\(476\) −3.86645 −0.177219
\(477\) 8.98296 0.411301
\(478\) 58.2831 2.66581
\(479\) 37.6092 1.71841 0.859204 0.511634i \(-0.170959\pi\)
0.859204 + 0.511634i \(0.170959\pi\)
\(480\) 16.8328 0.768308
\(481\) −25.5850 −1.16658
\(482\) 15.7470 0.717258
\(483\) −3.34202 −0.152067
\(484\) −35.2880 −1.60400
\(485\) −5.40434 −0.245399
\(486\) −118.562 −5.37808
\(487\) −14.3116 −0.648520 −0.324260 0.945968i \(-0.605115\pi\)
−0.324260 + 0.945968i \(0.605115\pi\)
\(488\) −8.75891 −0.396497
\(489\) −63.6899 −2.88016
\(490\) 16.0602 0.725525
\(491\) −7.95400 −0.358959 −0.179480 0.983762i \(-0.557441\pi\)
−0.179480 + 0.983762i \(0.557441\pi\)
\(492\) 81.0774 3.65525
\(493\) −36.1620 −1.62865
\(494\) −21.4652 −0.965766
\(495\) 5.26565 0.236673
\(496\) 3.10952 0.139622
\(497\) 2.81860 0.126431
\(498\) −78.2498 −3.50646
\(499\) −27.9701 −1.25211 −0.626057 0.779777i \(-0.715332\pi\)
−0.626057 + 0.779777i \(0.715332\pi\)
\(500\) 3.34126 0.149426
\(501\) 23.9283 1.06904
\(502\) −22.1562 −0.988878
\(503\) −9.69723 −0.432378 −0.216189 0.976352i \(-0.569363\pi\)
−0.216189 + 0.976352i \(0.569363\pi\)
\(504\) −5.55996 −0.247660
\(505\) 3.35238 0.149179
\(506\) 6.85231 0.304622
\(507\) −14.7257 −0.653993
\(508\) −7.60882 −0.337587
\(509\) −24.5393 −1.08768 −0.543842 0.839188i \(-0.683031\pi\)
−0.543842 + 0.839188i \(0.683031\pi\)
\(510\) 39.2251 1.73692
\(511\) −3.37081 −0.149116
\(512\) 5.43422 0.240161
\(513\) 52.0296 2.29716
\(514\) 7.87549 0.347373
\(515\) 4.92484 0.217015
\(516\) −38.9178 −1.71326
\(517\) −1.13960 −0.0501195
\(518\) 4.56242 0.200461
\(519\) −67.8010 −2.97613
\(520\) −9.06388 −0.397478
\(521\) 11.4183 0.500243 0.250122 0.968214i \(-0.419529\pi\)
0.250122 + 0.968214i \(0.419529\pi\)
\(522\) −129.542 −5.66989
\(523\) 9.98169 0.436469 0.218235 0.975896i \(-0.429970\pi\)
0.218235 + 0.975896i \(0.429970\pi\)
\(524\) 47.2920 2.06596
\(525\) 0.746580 0.0325834
\(526\) −5.36977 −0.234133
\(527\) −33.1243 −1.44292
\(528\) 1.05529 0.0459255
\(529\) −2.96146 −0.128759
\(530\) −2.61139 −0.113431
\(531\) 33.9246 1.47220
\(532\) 2.39448 0.103814
\(533\) 21.4419 0.928750
\(534\) −32.3166 −1.39847
\(535\) 14.6250 0.632294
\(536\) −30.8560 −1.33278
\(537\) −80.8802 −3.49024
\(538\) 13.0882 0.564274
\(539\) −4.60268 −0.198251
\(540\) 54.7302 2.35521
\(541\) −6.19835 −0.266488 −0.133244 0.991083i \(-0.542539\pi\)
−0.133244 + 0.991083i \(0.542539\pi\)
\(542\) −24.4399 −1.04978
\(543\) 12.7962 0.549136
\(544\) −26.0905 −1.11862
\(545\) 12.6180 0.540495
\(546\) −5.04521 −0.215915
\(547\) 32.6315 1.39522 0.697610 0.716477i \(-0.254247\pi\)
0.697610 + 0.716477i \(0.254247\pi\)
\(548\) 44.2252 1.88921
\(549\) 22.4640 0.958738
\(550\) −1.53075 −0.0652713
\(551\) 22.3950 0.954059
\(552\) 45.9171 1.95436
\(553\) −2.13754 −0.0908974
\(554\) −75.5397 −3.20937
\(555\) −28.9543 −1.22904
\(556\) −33.9255 −1.43876
\(557\) 2.34294 0.0992736 0.0496368 0.998767i \(-0.484194\pi\)
0.0496368 + 0.998767i \(0.484194\pi\)
\(558\) −118.660 −5.02328
\(559\) −10.2923 −0.435316
\(560\) 0.108630 0.00459045
\(561\) −11.2415 −0.474617
\(562\) 9.35360 0.394558
\(563\) −9.26229 −0.390359 −0.195180 0.980768i \(-0.562529\pi\)
−0.195180 + 0.980768i \(0.562529\pi\)
\(564\) −19.0234 −0.801030
\(565\) −14.5656 −0.612779
\(566\) −22.0075 −0.925043
\(567\) 6.84813 0.287594
\(568\) −38.7256 −1.62489
\(569\) 0.671669 0.0281578 0.0140789 0.999901i \(-0.495518\pi\)
0.0140789 + 0.999901i \(0.495518\pi\)
\(570\) −24.2920 −1.01748
\(571\) −5.61658 −0.235047 −0.117523 0.993070i \(-0.537495\pi\)
−0.117523 + 0.993070i \(0.537495\pi\)
\(572\) 6.47102 0.270567
\(573\) 35.3448 1.47655
\(574\) −3.82360 −0.159594
\(575\) −4.47644 −0.186681
\(576\) −101.119 −4.21327
\(577\) −41.5967 −1.73169 −0.865846 0.500311i \(-0.833219\pi\)
−0.865846 + 0.500311i \(0.833219\pi\)
\(578\) −21.5092 −0.894665
\(579\) 40.7865 1.69503
\(580\) 23.5574 0.978169
\(581\) 2.30846 0.0957709
\(582\) 41.3307 1.71321
\(583\) 0.748396 0.0309954
\(584\) 46.3126 1.91643
\(585\) 23.2461 0.961109
\(586\) 34.1199 1.40948
\(587\) 21.4839 0.886737 0.443368 0.896340i \(-0.353783\pi\)
0.443368 + 0.896340i \(0.353783\pi\)
\(588\) −76.8327 −3.16853
\(589\) 20.5138 0.845256
\(590\) −9.86204 −0.406014
\(591\) −4.71704 −0.194033
\(592\) −4.21295 −0.173151
\(593\) 20.6112 0.846401 0.423200 0.906036i \(-0.360907\pi\)
0.423200 + 0.906036i \(0.360907\pi\)
\(594\) −25.0739 −1.02879
\(595\) −1.15719 −0.0474400
\(596\) −21.2917 −0.872143
\(597\) 70.9428 2.90349
\(598\) 30.2507 1.23704
\(599\) −5.66772 −0.231577 −0.115788 0.993274i \(-0.536939\pi\)
−0.115788 + 0.993274i \(0.536939\pi\)
\(600\) −10.2575 −0.418761
\(601\) −30.6898 −1.25186 −0.625931 0.779878i \(-0.715281\pi\)
−0.625931 + 0.779878i \(0.715281\pi\)
\(602\) 1.83536 0.0748035
\(603\) 79.1364 3.22268
\(604\) 5.81089 0.236442
\(605\) −10.5613 −0.429378
\(606\) −25.6380 −1.04147
\(607\) 2.82351 0.114603 0.0573015 0.998357i \(-0.481750\pi\)
0.0573015 + 0.998357i \(0.481750\pi\)
\(608\) 16.1578 0.655283
\(609\) 5.26374 0.213298
\(610\) −6.53037 −0.264407
\(611\) −5.03096 −0.203531
\(612\) −136.243 −5.50729
\(613\) −11.7612 −0.475031 −0.237516 0.971384i \(-0.576333\pi\)
−0.237516 + 0.971384i \(0.576333\pi\)
\(614\) 50.7285 2.04724
\(615\) 24.2655 0.978481
\(616\) −0.463217 −0.0186635
\(617\) −12.9423 −0.521037 −0.260518 0.965469i \(-0.583893\pi\)
−0.260518 + 0.965469i \(0.583893\pi\)
\(618\) −37.6636 −1.51505
\(619\) −30.6994 −1.23391 −0.616956 0.786997i \(-0.711634\pi\)
−0.616956 + 0.786997i \(0.711634\pi\)
\(620\) 21.5786 0.866616
\(621\) −73.3248 −2.94242
\(622\) 68.6285 2.75175
\(623\) 0.953375 0.0381962
\(624\) 4.65875 0.186499
\(625\) 1.00000 0.0400000
\(626\) 25.9111 1.03562
\(627\) 6.96183 0.278029
\(628\) 19.1752 0.765175
\(629\) 44.8786 1.78943
\(630\) −4.14534 −0.165154
\(631\) 30.5620 1.21665 0.608326 0.793687i \(-0.291841\pi\)
0.608326 + 0.793687i \(0.291841\pi\)
\(632\) 29.3683 1.16821
\(633\) 71.0372 2.82348
\(634\) 44.8888 1.78276
\(635\) −2.27723 −0.0903692
\(636\) 12.4930 0.495380
\(637\) −20.3193 −0.805081
\(638\) −10.7925 −0.427279
\(639\) 99.3195 3.92902
\(640\) 19.2220 0.759814
\(641\) −36.3265 −1.43481 −0.717404 0.696657i \(-0.754670\pi\)
−0.717404 + 0.696657i \(0.754670\pi\)
\(642\) −111.847 −4.41426
\(643\) −45.5057 −1.79457 −0.897285 0.441451i \(-0.854464\pi\)
−0.897285 + 0.441451i \(0.854464\pi\)
\(644\) −3.37451 −0.132975
\(645\) −11.6476 −0.458626
\(646\) 37.6521 1.48140
\(647\) 2.30197 0.0904997 0.0452498 0.998976i \(-0.485592\pi\)
0.0452498 + 0.998976i \(0.485592\pi\)
\(648\) −94.0886 −3.69615
\(649\) 2.82636 0.110944
\(650\) −6.75775 −0.265061
\(651\) 4.82158 0.188973
\(652\) −64.3091 −2.51854
\(653\) 8.56360 0.335119 0.167560 0.985862i \(-0.446411\pi\)
0.167560 + 0.985862i \(0.446411\pi\)
\(654\) −96.4983 −3.77338
\(655\) 14.1540 0.553041
\(656\) 3.53072 0.137851
\(657\) −118.778 −4.63396
\(658\) 0.897141 0.0349742
\(659\) −40.9908 −1.59677 −0.798387 0.602144i \(-0.794313\pi\)
−0.798387 + 0.602144i \(0.794313\pi\)
\(660\) 7.32318 0.285054
\(661\) 0.871646 0.0339031 0.0169516 0.999856i \(-0.494604\pi\)
0.0169516 + 0.999856i \(0.494604\pi\)
\(662\) −21.5169 −0.836278
\(663\) −49.6276 −1.92738
\(664\) −31.7166 −1.23084
\(665\) 0.716641 0.0277901
\(666\) 160.767 6.22959
\(667\) −31.5610 −1.22205
\(668\) 24.1609 0.934815
\(669\) 17.4654 0.675252
\(670\) −23.0053 −0.888773
\(671\) 1.87154 0.0722499
\(672\) 3.79773 0.146501
\(673\) 22.7876 0.878397 0.439198 0.898390i \(-0.355263\pi\)
0.439198 + 0.898390i \(0.355263\pi\)
\(674\) −51.7848 −1.99468
\(675\) 16.3801 0.630472
\(676\) −14.8689 −0.571881
\(677\) −24.1464 −0.928022 −0.464011 0.885829i \(-0.653590\pi\)
−0.464011 + 0.885829i \(0.653590\pi\)
\(678\) 111.393 4.27802
\(679\) −1.21930 −0.0467925
\(680\) 15.8989 0.609696
\(681\) 77.2335 2.95959
\(682\) −9.88590 −0.378551
\(683\) −46.0159 −1.76075 −0.880375 0.474278i \(-0.842709\pi\)
−0.880375 + 0.474278i \(0.842709\pi\)
\(684\) 84.3748 3.22615
\(685\) 13.2361 0.505726
\(686\) 7.27338 0.277699
\(687\) −33.4540 −1.27635
\(688\) −1.69477 −0.0646125
\(689\) 3.30393 0.125870
\(690\) 34.2344 1.30328
\(691\) −24.0957 −0.916645 −0.458323 0.888786i \(-0.651550\pi\)
−0.458323 + 0.888786i \(0.651550\pi\)
\(692\) −68.4601 −2.60246
\(693\) 1.18801 0.0451288
\(694\) −44.4784 −1.68838
\(695\) −10.1535 −0.385145
\(696\) −72.3202 −2.74129
\(697\) −37.6111 −1.42462
\(698\) 8.63954 0.327011
\(699\) 68.8794 2.60526
\(700\) 0.753838 0.0284924
\(701\) 38.1729 1.44177 0.720884 0.693055i \(-0.243736\pi\)
0.720884 + 0.693055i \(0.243736\pi\)
\(702\) −110.693 −4.17784
\(703\) −27.7932 −1.04824
\(704\) −8.42448 −0.317509
\(705\) −5.69349 −0.214429
\(706\) 60.5101 2.27733
\(707\) 0.756349 0.0284454
\(708\) 47.1806 1.77315
\(709\) 6.44294 0.241970 0.120985 0.992654i \(-0.461395\pi\)
0.120985 + 0.992654i \(0.461395\pi\)
\(710\) −28.8726 −1.08357
\(711\) −75.3209 −2.82475
\(712\) −13.0987 −0.490896
\(713\) −28.9098 −1.08268
\(714\) 8.84978 0.331195
\(715\) 1.93670 0.0724285
\(716\) −81.6665 −3.05202
\(717\) −83.4505 −3.11651
\(718\) −20.0572 −0.748529
\(719\) 36.3833 1.35687 0.678435 0.734661i \(-0.262659\pi\)
0.678435 + 0.734661i \(0.262659\pi\)
\(720\) 3.82781 0.142654
\(721\) 1.11112 0.0413803
\(722\) 20.5934 0.766406
\(723\) −22.5468 −0.838525
\(724\) 12.9206 0.480189
\(725\) 7.05047 0.261848
\(726\) 80.7695 2.99764
\(727\) 13.1092 0.486193 0.243096 0.970002i \(-0.421837\pi\)
0.243096 + 0.970002i \(0.421837\pi\)
\(728\) −2.04495 −0.0757909
\(729\) 78.6991 2.91478
\(730\) 34.5292 1.27798
\(731\) 18.0536 0.667738
\(732\) 31.2417 1.15473
\(733\) −2.82047 −0.104176 −0.0520881 0.998642i \(-0.516588\pi\)
−0.0520881 + 0.998642i \(0.516588\pi\)
\(734\) −23.3074 −0.860291
\(735\) −22.9952 −0.848189
\(736\) −22.7709 −0.839348
\(737\) 6.59308 0.242859
\(738\) −134.733 −4.95958
\(739\) 20.9038 0.768960 0.384480 0.923133i \(-0.374381\pi\)
0.384480 + 0.923133i \(0.374381\pi\)
\(740\) −29.2358 −1.07473
\(741\) 30.7342 1.12905
\(742\) −0.589169 −0.0216291
\(743\) −22.3935 −0.821539 −0.410770 0.911739i \(-0.634740\pi\)
−0.410770 + 0.911739i \(0.634740\pi\)
\(744\) −66.2452 −2.42867
\(745\) −6.37237 −0.233466
\(746\) 19.8894 0.728203
\(747\) 81.3435 2.97620
\(748\) −11.3508 −0.415026
\(749\) 3.29962 0.120566
\(750\) −7.64768 −0.279254
\(751\) −23.0525 −0.841198 −0.420599 0.907247i \(-0.638180\pi\)
−0.420599 + 0.907247i \(0.638180\pi\)
\(752\) −0.828421 −0.0302094
\(753\) 31.7235 1.15607
\(754\) −47.6453 −1.73514
\(755\) 1.73913 0.0632935
\(756\) 12.3480 0.449092
\(757\) 48.5058 1.76297 0.881487 0.472208i \(-0.156543\pi\)
0.881487 + 0.472208i \(0.156543\pi\)
\(758\) 18.1291 0.658477
\(759\) −9.81122 −0.356125
\(760\) −9.84616 −0.357158
\(761\) −15.5658 −0.564260 −0.282130 0.959376i \(-0.591041\pi\)
−0.282130 + 0.959376i \(0.591041\pi\)
\(762\) 17.4155 0.630898
\(763\) 2.84681 0.103061
\(764\) 35.6884 1.29116
\(765\) −40.7760 −1.47426
\(766\) 61.3798 2.21774
\(767\) 12.4775 0.450535
\(768\) −62.8253 −2.26701
\(769\) 8.82432 0.318213 0.159106 0.987261i \(-0.449139\pi\)
0.159106 + 0.987261i \(0.449139\pi\)
\(770\) −0.345360 −0.0124459
\(771\) −11.2762 −0.406103
\(772\) 41.1830 1.48221
\(773\) 15.4901 0.557139 0.278569 0.960416i \(-0.410140\pi\)
0.278569 + 0.960416i \(0.410140\pi\)
\(774\) 64.6728 2.32462
\(775\) 6.45822 0.231986
\(776\) 16.7524 0.601375
\(777\) −6.53254 −0.234353
\(778\) −57.8526 −2.07412
\(779\) 23.2924 0.834538
\(780\) 32.3295 1.15758
\(781\) 8.27459 0.296088
\(782\) −53.0627 −1.89752
\(783\) 115.488 4.12719
\(784\) −3.34587 −0.119495
\(785\) 5.73893 0.204831
\(786\) −108.245 −3.86097
\(787\) −44.3325 −1.58028 −0.790142 0.612924i \(-0.789993\pi\)
−0.790142 + 0.612924i \(0.789993\pi\)
\(788\) −4.76290 −0.169671
\(789\) 7.68851 0.273718
\(790\) 21.8961 0.779029
\(791\) −3.28622 −0.116844
\(792\) −16.3225 −0.579993
\(793\) 8.26223 0.293400
\(794\) 86.2237 3.05997
\(795\) 3.73902 0.132609
\(796\) 71.6325 2.53895
\(797\) 48.0054 1.70044 0.850220 0.526428i \(-0.176469\pi\)
0.850220 + 0.526428i \(0.176469\pi\)
\(798\) −5.48064 −0.194013
\(799\) 8.82480 0.312199
\(800\) 5.08684 0.179847
\(801\) 33.5943 1.18700
\(802\) −13.6797 −0.483047
\(803\) −9.89572 −0.349212
\(804\) 110.059 3.88147
\(805\) −1.00995 −0.0355962
\(806\) −43.6431 −1.53726
\(807\) −18.7399 −0.659676
\(808\) −10.3917 −0.365579
\(809\) 29.3435 1.03166 0.515831 0.856690i \(-0.327483\pi\)
0.515831 + 0.856690i \(0.327483\pi\)
\(810\) −70.1496 −2.46481
\(811\) −55.4109 −1.94574 −0.972870 0.231353i \(-0.925685\pi\)
−0.972870 + 0.231353i \(0.925685\pi\)
\(812\) 5.31491 0.186517
\(813\) 34.9933 1.22727
\(814\) 13.3940 0.469458
\(815\) −19.2470 −0.674192
\(816\) −8.17190 −0.286074
\(817\) −11.1806 −0.391158
\(818\) 63.2091 2.21006
\(819\) 5.24468 0.183264
\(820\) 24.5014 0.855628
\(821\) −42.5043 −1.48341 −0.741705 0.670726i \(-0.765983\pi\)
−0.741705 + 0.670726i \(0.765983\pi\)
\(822\) −101.226 −3.53065
\(823\) −50.0174 −1.74350 −0.871748 0.489954i \(-0.837014\pi\)
−0.871748 + 0.489954i \(0.837014\pi\)
\(824\) −15.2660 −0.531817
\(825\) 2.19175 0.0763068
\(826\) −2.22503 −0.0774186
\(827\) −43.5673 −1.51498 −0.757492 0.652844i \(-0.773576\pi\)
−0.757492 + 0.652844i \(0.773576\pi\)
\(828\) −118.908 −4.13235
\(829\) 15.8103 0.549113 0.274557 0.961571i \(-0.411469\pi\)
0.274557 + 0.961571i \(0.411469\pi\)
\(830\) −23.6469 −0.820797
\(831\) 108.159 3.75198
\(832\) −37.1913 −1.28938
\(833\) 35.6421 1.23492
\(834\) 77.6508 2.68883
\(835\) 7.23110 0.250242
\(836\) 7.02951 0.243121
\(837\) 105.786 3.65652
\(838\) −57.4903 −1.98597
\(839\) −40.8609 −1.41068 −0.705338 0.708871i \(-0.749205\pi\)
−0.705338 + 0.708871i \(0.749205\pi\)
\(840\) −2.31425 −0.0798492
\(841\) 20.7091 0.714107
\(842\) −9.11931 −0.314272
\(843\) −13.3926 −0.461266
\(844\) 71.7278 2.46897
\(845\) −4.45009 −0.153088
\(846\) 31.6127 1.08687
\(847\) −2.38279 −0.0818737
\(848\) 0.544039 0.0186824
\(849\) 31.5106 1.08144
\(850\) 11.8538 0.406581
\(851\) 39.1686 1.34268
\(852\) 138.128 4.73220
\(853\) 47.3049 1.61969 0.809845 0.586644i \(-0.199551\pi\)
0.809845 + 0.586644i \(0.199551\pi\)
\(854\) −1.47335 −0.0504171
\(855\) 25.2524 0.863614
\(856\) −45.3345 −1.54950
\(857\) −9.44951 −0.322789 −0.161395 0.986890i \(-0.551599\pi\)
−0.161395 + 0.986890i \(0.551599\pi\)
\(858\) −14.8113 −0.505649
\(859\) −53.6953 −1.83206 −0.916029 0.401111i \(-0.868624\pi\)
−0.916029 + 0.401111i \(0.868624\pi\)
\(860\) −11.7609 −0.401043
\(861\) 5.47468 0.186576
\(862\) 18.0321 0.614176
\(863\) 2.69643 0.0917876 0.0458938 0.998946i \(-0.485386\pi\)
0.0458938 + 0.998946i \(0.485386\pi\)
\(864\) 83.3231 2.83471
\(865\) −20.4893 −0.696658
\(866\) −15.1538 −0.514946
\(867\) 30.7971 1.04593
\(868\) 4.86845 0.165246
\(869\) −6.27520 −0.212872
\(870\) −53.9197 −1.82805
\(871\) 29.1063 0.986230
\(872\) −39.1132 −1.32454
\(873\) −42.9648 −1.45414
\(874\) 32.8615 1.11156
\(875\) 0.225615 0.00762719
\(876\) −165.190 −5.58125
\(877\) 39.5679 1.33611 0.668057 0.744110i \(-0.267126\pi\)
0.668057 + 0.744110i \(0.267126\pi\)
\(878\) 34.9781 1.18045
\(879\) −48.8533 −1.64778
\(880\) 0.318906 0.0107503
\(881\) 36.2384 1.22090 0.610452 0.792054i \(-0.290988\pi\)
0.610452 + 0.792054i \(0.290988\pi\)
\(882\) 127.679 4.29918
\(883\) −20.8483 −0.701601 −0.350801 0.936450i \(-0.614090\pi\)
−0.350801 + 0.936450i \(0.614090\pi\)
\(884\) −50.1101 −1.68538
\(885\) 14.1206 0.474659
\(886\) −68.7204 −2.30871
\(887\) 46.2253 1.55209 0.776047 0.630675i \(-0.217222\pi\)
0.776047 + 0.630675i \(0.217222\pi\)
\(888\) 89.7526 3.01190
\(889\) −0.513778 −0.0172316
\(890\) −9.76601 −0.327357
\(891\) 20.1041 0.673514
\(892\) 17.6352 0.590471
\(893\) −5.46517 −0.182885
\(894\) 48.7338 1.62990
\(895\) −24.4419 −0.817001
\(896\) 4.33677 0.144881
\(897\) −43.3134 −1.44619
\(898\) −86.2469 −2.87810
\(899\) 45.5335 1.51863
\(900\) 26.5632 0.885438
\(901\) −5.79541 −0.193073
\(902\) −11.2250 −0.373751
\(903\) −2.62789 −0.0874506
\(904\) 45.1504 1.50168
\(905\) 3.86698 0.128543
\(906\) −13.3003 −0.441874
\(907\) 20.9887 0.696920 0.348460 0.937324i \(-0.386705\pi\)
0.348460 + 0.937324i \(0.386705\pi\)
\(908\) 77.9844 2.58800
\(909\) 26.6516 0.883978
\(910\) −1.52465 −0.0505417
\(911\) 15.3498 0.508561 0.254280 0.967131i \(-0.418161\pi\)
0.254280 + 0.967131i \(0.418161\pi\)
\(912\) 5.06083 0.167581
\(913\) 6.77696 0.224285
\(914\) 23.9636 0.792647
\(915\) 9.35027 0.309111
\(916\) −33.7792 −1.11610
\(917\) 3.19335 0.105454
\(918\) 194.166 6.40844
\(919\) −23.3000 −0.768595 −0.384298 0.923209i \(-0.625556\pi\)
−0.384298 + 0.923209i \(0.625556\pi\)
\(920\) 13.8761 0.457481
\(921\) −72.6337 −2.39336
\(922\) −21.6202 −0.712023
\(923\) 36.5296 1.20239
\(924\) 1.65222 0.0543541
\(925\) −8.74995 −0.287696
\(926\) 58.1689 1.91155
\(927\) 39.1528 1.28595
\(928\) 35.8646 1.17731
\(929\) 34.8454 1.14324 0.571621 0.820518i \(-0.306315\pi\)
0.571621 + 0.820518i \(0.306315\pi\)
\(930\) −49.3904 −1.61957
\(931\) −22.0730 −0.723414
\(932\) 69.5490 2.27815
\(933\) −98.2632 −3.21699
\(934\) 26.0637 0.852831
\(935\) −3.39716 −0.111099
\(936\) −72.0583 −2.35530
\(937\) 18.5328 0.605441 0.302720 0.953079i \(-0.402105\pi\)
0.302720 + 0.953079i \(0.402105\pi\)
\(938\) −5.19035 −0.169471
\(939\) −37.0999 −1.21071
\(940\) −5.74884 −0.187506
\(941\) 42.2418 1.37704 0.688521 0.725216i \(-0.258260\pi\)
0.688521 + 0.725216i \(0.258260\pi\)
\(942\) −43.8895 −1.43000
\(943\) −32.8258 −1.06895
\(944\) 2.05459 0.0668713
\(945\) 3.69561 0.120218
\(946\) 5.38808 0.175181
\(947\) 2.17240 0.0705936 0.0352968 0.999377i \(-0.488762\pi\)
0.0352968 + 0.999377i \(0.488762\pi\)
\(948\) −104.752 −3.40219
\(949\) −43.6864 −1.41812
\(950\) −7.34099 −0.238173
\(951\) −64.2723 −2.08417
\(952\) 3.58704 0.116257
\(953\) −29.4304 −0.953343 −0.476672 0.879081i \(-0.658157\pi\)
−0.476672 + 0.879081i \(0.658157\pi\)
\(954\) −20.7607 −0.672151
\(955\) 10.6811 0.345633
\(956\) −84.2618 −2.72522
\(957\) 15.4528 0.499519
\(958\) −86.9192 −2.80823
\(959\) 2.98627 0.0964316
\(960\) −42.0890 −1.35842
\(961\) 10.7086 0.345438
\(962\) 59.1300 1.90643
\(963\) 116.269 3.74673
\(964\) −22.7660 −0.733244
\(965\) 12.3256 0.396775
\(966\) 7.72380 0.248509
\(967\) 59.8725 1.92537 0.962685 0.270624i \(-0.0872299\pi\)
0.962685 + 0.270624i \(0.0872299\pi\)
\(968\) 32.7379 1.05224
\(969\) −53.9108 −1.73186
\(970\) 12.4901 0.401032
\(971\) −23.6822 −0.759999 −0.379999 0.924987i \(-0.624076\pi\)
−0.379999 + 0.924987i \(0.624076\pi\)
\(972\) 171.409 5.49794
\(973\) −2.29079 −0.0734393
\(974\) 33.0757 1.05981
\(975\) 9.67584 0.309875
\(976\) 1.36050 0.0435484
\(977\) −28.5080 −0.912051 −0.456026 0.889967i \(-0.650727\pi\)
−0.456026 + 0.889967i \(0.650727\pi\)
\(978\) 147.195 4.70677
\(979\) 2.79884 0.0894512
\(980\) −23.2187 −0.741695
\(981\) 100.314 3.20277
\(982\) 18.3826 0.586613
\(983\) 2.79693 0.0892083 0.0446041 0.999005i \(-0.485797\pi\)
0.0446041 + 0.999005i \(0.485797\pi\)
\(984\) −75.2183 −2.39787
\(985\) −1.42548 −0.0454196
\(986\) 83.5746 2.66156
\(987\) −1.28454 −0.0408873
\(988\) 31.0330 0.987291
\(989\) 15.7566 0.501031
\(990\) −12.1695 −0.386773
\(991\) −30.1293 −0.957087 −0.478544 0.878064i \(-0.658835\pi\)
−0.478544 + 0.878064i \(0.658835\pi\)
\(992\) 32.8519 1.04305
\(993\) 30.8082 0.977667
\(994\) −6.51411 −0.206615
\(995\) 21.4388 0.679655
\(996\) 113.128 3.58461
\(997\) 43.4325 1.37552 0.687761 0.725937i \(-0.258594\pi\)
0.687761 + 0.725937i \(0.258594\pi\)
\(998\) 64.6422 2.04621
\(999\) −143.325 −4.53461
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 \(a_p\))