Properties

Label 4030.2.a.f.1.6
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 1
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4418197.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.14519\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.43620 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.43620 q^{6} -3.35900 q^{7} +1.00000 q^{8} +2.93509 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.43620 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.43620 q^{6} -3.35900 q^{7} +1.00000 q^{8} +2.93509 q^{9} -1.00000 q^{10} -3.03476 q^{11} +2.43620 q^{12} +1.00000 q^{13} -3.35900 q^{14} -2.43620 q^{15} +1.00000 q^{16} -4.12272 q^{17} +2.93509 q^{18} -2.24877 q^{19} -1.00000 q^{20} -8.18321 q^{21} -3.03476 q^{22} -2.50746 q^{23} +2.43620 q^{24} +1.00000 q^{25} +1.00000 q^{26} -0.158129 q^{27} -3.35900 q^{28} -10.2379 q^{29} -2.43620 q^{30} -1.00000 q^{31} +1.00000 q^{32} -7.39331 q^{33} -4.12272 q^{34} +3.35900 q^{35} +2.93509 q^{36} +8.42975 q^{37} -2.24877 q^{38} +2.43620 q^{39} -1.00000 q^{40} +3.29306 q^{41} -8.18321 q^{42} -2.39832 q^{43} -3.03476 q^{44} -2.93509 q^{45} -2.50746 q^{46} -5.72331 q^{47} +2.43620 q^{48} +4.28288 q^{49} +1.00000 q^{50} -10.0438 q^{51} +1.00000 q^{52} -12.1017 q^{53} -0.158129 q^{54} +3.03476 q^{55} -3.35900 q^{56} -5.47846 q^{57} -10.2379 q^{58} +2.41542 q^{59} -2.43620 q^{60} -1.65628 q^{61} -1.00000 q^{62} -9.85898 q^{63} +1.00000 q^{64} -1.00000 q^{65} -7.39331 q^{66} +10.9975 q^{67} -4.12272 q^{68} -6.10869 q^{69} +3.35900 q^{70} -6.06828 q^{71} +2.93509 q^{72} -1.74115 q^{73} +8.42975 q^{74} +2.43620 q^{75} -2.24877 q^{76} +10.1938 q^{77} +2.43620 q^{78} +9.95863 q^{79} -1.00000 q^{80} -9.19051 q^{81} +3.29306 q^{82} +0.183069 q^{83} -8.18321 q^{84} +4.12272 q^{85} -2.39832 q^{86} -24.9417 q^{87} -3.03476 q^{88} +12.8811 q^{89} -2.93509 q^{90} -3.35900 q^{91} -2.50746 q^{92} -2.43620 q^{93} -5.72331 q^{94} +2.24877 q^{95} +2.43620 q^{96} +5.54896 q^{97} +4.28288 q^{98} -8.90731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.43620 1.40654 0.703272 0.710921i \(-0.251722\pi\)
0.703272 + 0.710921i \(0.251722\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.43620 0.994576
\(7\) −3.35900 −1.26958 −0.634791 0.772684i \(-0.718914\pi\)
−0.634791 + 0.772684i \(0.718914\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.93509 0.978364
\(10\) −1.00000 −0.316228
\(11\) −3.03476 −0.915016 −0.457508 0.889206i \(-0.651258\pi\)
−0.457508 + 0.889206i \(0.651258\pi\)
\(12\) 2.43620 0.703272
\(13\) 1.00000 0.277350
\(14\) −3.35900 −0.897731
\(15\) −2.43620 −0.629025
\(16\) 1.00000 0.250000
\(17\) −4.12272 −0.999906 −0.499953 0.866053i \(-0.666649\pi\)
−0.499953 + 0.866053i \(0.666649\pi\)
\(18\) 2.93509 0.691808
\(19\) −2.24877 −0.515903 −0.257951 0.966158i \(-0.583047\pi\)
−0.257951 + 0.966158i \(0.583047\pi\)
\(20\) −1.00000 −0.223607
\(21\) −8.18321 −1.78572
\(22\) −3.03476 −0.647014
\(23\) −2.50746 −0.522842 −0.261421 0.965225i \(-0.584191\pi\)
−0.261421 + 0.965225i \(0.584191\pi\)
\(24\) 2.43620 0.497288
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) −0.158129 −0.0304320
\(28\) −3.35900 −0.634791
\(29\) −10.2379 −1.90114 −0.950570 0.310512i \(-0.899500\pi\)
−0.950570 + 0.310512i \(0.899500\pi\)
\(30\) −2.43620 −0.444788
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −7.39331 −1.28701
\(34\) −4.12272 −0.707040
\(35\) 3.35900 0.567775
\(36\) 2.93509 0.489182
\(37\) 8.42975 1.38584 0.692921 0.721013i \(-0.256323\pi\)
0.692921 + 0.721013i \(0.256323\pi\)
\(38\) −2.24877 −0.364798
\(39\) 2.43620 0.390105
\(40\) −1.00000 −0.158114
\(41\) 3.29306 0.514289 0.257144 0.966373i \(-0.417218\pi\)
0.257144 + 0.966373i \(0.417218\pi\)
\(42\) −8.18321 −1.26270
\(43\) −2.39832 −0.365741 −0.182870 0.983137i \(-0.558539\pi\)
−0.182870 + 0.983137i \(0.558539\pi\)
\(44\) −3.03476 −0.457508
\(45\) −2.93509 −0.437538
\(46\) −2.50746 −0.369705
\(47\) −5.72331 −0.834831 −0.417416 0.908716i \(-0.637064\pi\)
−0.417416 + 0.908716i \(0.637064\pi\)
\(48\) 2.43620 0.351636
\(49\) 4.28288 0.611840
\(50\) 1.00000 0.141421
\(51\) −10.0438 −1.40641
\(52\) 1.00000 0.138675
\(53\) −12.1017 −1.66230 −0.831148 0.556052i \(-0.812316\pi\)
−0.831148 + 0.556052i \(0.812316\pi\)
\(54\) −0.158129 −0.0215187
\(55\) 3.03476 0.409207
\(56\) −3.35900 −0.448865
\(57\) −5.47846 −0.725639
\(58\) −10.2379 −1.34431
\(59\) 2.41542 0.314461 0.157231 0.987562i \(-0.449743\pi\)
0.157231 + 0.987562i \(0.449743\pi\)
\(60\) −2.43620 −0.314513
\(61\) −1.65628 −0.212065 −0.106033 0.994363i \(-0.533815\pi\)
−0.106033 + 0.994363i \(0.533815\pi\)
\(62\) −1.00000 −0.127000
\(63\) −9.85898 −1.24211
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −7.39331 −0.910053
\(67\) 10.9975 1.34355 0.671777 0.740753i \(-0.265531\pi\)
0.671777 + 0.740753i \(0.265531\pi\)
\(68\) −4.12272 −0.499953
\(69\) −6.10869 −0.735400
\(70\) 3.35900 0.401477
\(71\) −6.06828 −0.720173 −0.360086 0.932919i \(-0.617253\pi\)
−0.360086 + 0.932919i \(0.617253\pi\)
\(72\) 2.93509 0.345904
\(73\) −1.74115 −0.203786 −0.101893 0.994795i \(-0.532490\pi\)
−0.101893 + 0.994795i \(0.532490\pi\)
\(74\) 8.42975 0.979939
\(75\) 2.43620 0.281309
\(76\) −2.24877 −0.257951
\(77\) 10.1938 1.16169
\(78\) 2.43620 0.275846
\(79\) 9.95863 1.12043 0.560217 0.828346i \(-0.310718\pi\)
0.560217 + 0.828346i \(0.310718\pi\)
\(80\) −1.00000 −0.111803
\(81\) −9.19051 −1.02117
\(82\) 3.29306 0.363657
\(83\) 0.183069 0.0200944 0.0100472 0.999950i \(-0.496802\pi\)
0.0100472 + 0.999950i \(0.496802\pi\)
\(84\) −8.18321 −0.892862
\(85\) 4.12272 0.447172
\(86\) −2.39832 −0.258618
\(87\) −24.9417 −2.67403
\(88\) −3.03476 −0.323507
\(89\) 12.8811 1.36540 0.682698 0.730700i \(-0.260806\pi\)
0.682698 + 0.730700i \(0.260806\pi\)
\(90\) −2.93509 −0.309386
\(91\) −3.35900 −0.352119
\(92\) −2.50746 −0.261421
\(93\) −2.43620 −0.252623
\(94\) −5.72331 −0.590315
\(95\) 2.24877 0.230719
\(96\) 2.43620 0.248644
\(97\) 5.54896 0.563412 0.281706 0.959501i \(-0.409100\pi\)
0.281706 + 0.959501i \(0.409100\pi\)
\(98\) 4.28288 0.432637
\(99\) −8.90731 −0.895218
\(100\) 1.00000 0.100000
\(101\) −0.0361924 −0.00360128 −0.00180064 0.999998i \(-0.500573\pi\)
−0.00180064 + 0.999998i \(0.500573\pi\)
\(102\) −10.0438 −0.994483
\(103\) −1.74255 −0.171699 −0.0858493 0.996308i \(-0.527360\pi\)
−0.0858493 + 0.996308i \(0.527360\pi\)
\(104\) 1.00000 0.0980581
\(105\) 8.18321 0.798600
\(106\) −12.1017 −1.17542
\(107\) 5.43366 0.525292 0.262646 0.964892i \(-0.415405\pi\)
0.262646 + 0.964892i \(0.415405\pi\)
\(108\) −0.158129 −0.0152160
\(109\) 17.9444 1.71876 0.859379 0.511339i \(-0.170850\pi\)
0.859379 + 0.511339i \(0.170850\pi\)
\(110\) 3.03476 0.289353
\(111\) 20.5366 1.94925
\(112\) −3.35900 −0.317396
\(113\) −8.66105 −0.814763 −0.407381 0.913258i \(-0.633558\pi\)
−0.407381 + 0.913258i \(0.633558\pi\)
\(114\) −5.47846 −0.513104
\(115\) 2.50746 0.233822
\(116\) −10.2379 −0.950570
\(117\) 2.93509 0.271349
\(118\) 2.41542 0.222358
\(119\) 13.8482 1.26946
\(120\) −2.43620 −0.222394
\(121\) −1.79021 −0.162746
\(122\) −1.65628 −0.149953
\(123\) 8.02256 0.723369
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −9.85898 −0.878307
\(127\) 0.876232 0.0777530 0.0388765 0.999244i \(-0.487622\pi\)
0.0388765 + 0.999244i \(0.487622\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.84280 −0.514430
\(130\) −1.00000 −0.0877058
\(131\) −13.2381 −1.15662 −0.578309 0.815818i \(-0.696287\pi\)
−0.578309 + 0.815818i \(0.696287\pi\)
\(132\) −7.39331 −0.643505
\(133\) 7.55361 0.654981
\(134\) 10.9975 0.950036
\(135\) 0.158129 0.0136096
\(136\) −4.12272 −0.353520
\(137\) 7.15307 0.611128 0.305564 0.952172i \(-0.401155\pi\)
0.305564 + 0.952172i \(0.401155\pi\)
\(138\) −6.10869 −0.520006
\(139\) −9.98682 −0.847071 −0.423536 0.905879i \(-0.639211\pi\)
−0.423536 + 0.905879i \(0.639211\pi\)
\(140\) 3.35900 0.283887
\(141\) −13.9432 −1.17423
\(142\) −6.06828 −0.509239
\(143\) −3.03476 −0.253780
\(144\) 2.93509 0.244591
\(145\) 10.2379 0.850215
\(146\) −1.74115 −0.144098
\(147\) 10.4340 0.860580
\(148\) 8.42975 0.692921
\(149\) −16.7269 −1.37032 −0.685159 0.728394i \(-0.740267\pi\)
−0.685159 + 0.728394i \(0.740267\pi\)
\(150\) 2.43620 0.198915
\(151\) −7.14948 −0.581817 −0.290908 0.956751i \(-0.593957\pi\)
−0.290908 + 0.956751i \(0.593957\pi\)
\(152\) −2.24877 −0.182399
\(153\) −12.1006 −0.978272
\(154\) 10.1938 0.821438
\(155\) 1.00000 0.0803219
\(156\) 2.43620 0.195052
\(157\) −10.6518 −0.850107 −0.425054 0.905168i \(-0.639745\pi\)
−0.425054 + 0.905168i \(0.639745\pi\)
\(158\) 9.95863 0.792266
\(159\) −29.4822 −2.33809
\(160\) −1.00000 −0.0790569
\(161\) 8.42257 0.663791
\(162\) −9.19051 −0.722075
\(163\) −13.4807 −1.05589 −0.527944 0.849279i \(-0.677037\pi\)
−0.527944 + 0.849279i \(0.677037\pi\)
\(164\) 3.29306 0.257144
\(165\) 7.39331 0.575568
\(166\) 0.183069 0.0142089
\(167\) −6.54893 −0.506772 −0.253386 0.967365i \(-0.581544\pi\)
−0.253386 + 0.967365i \(0.581544\pi\)
\(168\) −8.18321 −0.631348
\(169\) 1.00000 0.0769231
\(170\) 4.12272 0.316198
\(171\) −6.60034 −0.504740
\(172\) −2.39832 −0.182870
\(173\) −4.25742 −0.323686 −0.161843 0.986817i \(-0.551744\pi\)
−0.161843 + 0.986817i \(0.551744\pi\)
\(174\) −24.9417 −1.89083
\(175\) −3.35900 −0.253917
\(176\) −3.03476 −0.228754
\(177\) 5.88446 0.442303
\(178\) 12.8811 0.965481
\(179\) 5.65679 0.422809 0.211404 0.977399i \(-0.432196\pi\)
0.211404 + 0.977399i \(0.432196\pi\)
\(180\) −2.93509 −0.218769
\(181\) 13.3560 0.992743 0.496371 0.868110i \(-0.334665\pi\)
0.496371 + 0.868110i \(0.334665\pi\)
\(182\) −3.35900 −0.248986
\(183\) −4.03504 −0.298279
\(184\) −2.50746 −0.184853
\(185\) −8.42975 −0.619768
\(186\) −2.43620 −0.178631
\(187\) 12.5115 0.914930
\(188\) −5.72331 −0.417416
\(189\) 0.531156 0.0386359
\(190\) 2.24877 0.163143
\(191\) −13.0306 −0.942865 −0.471432 0.881902i \(-0.656263\pi\)
−0.471432 + 0.881902i \(0.656263\pi\)
\(192\) 2.43620 0.175818
\(193\) 1.17390 0.0844990 0.0422495 0.999107i \(-0.486548\pi\)
0.0422495 + 0.999107i \(0.486548\pi\)
\(194\) 5.54896 0.398392
\(195\) −2.43620 −0.174460
\(196\) 4.28288 0.305920
\(197\) 11.0487 0.787187 0.393593 0.919285i \(-0.371232\pi\)
0.393593 + 0.919285i \(0.371232\pi\)
\(198\) −8.90731 −0.633015
\(199\) 16.0984 1.14119 0.570593 0.821233i \(-0.306713\pi\)
0.570593 + 0.821233i \(0.306713\pi\)
\(200\) 1.00000 0.0707107
\(201\) 26.7921 1.88977
\(202\) −0.0361924 −0.00254649
\(203\) 34.3893 2.41365
\(204\) −10.0438 −0.703205
\(205\) −3.29306 −0.229997
\(206\) −1.74255 −0.121409
\(207\) −7.35963 −0.511530
\(208\) 1.00000 0.0693375
\(209\) 6.82448 0.472059
\(210\) 8.18321 0.564695
\(211\) −19.9570 −1.37389 −0.686947 0.726708i \(-0.741049\pi\)
−0.686947 + 0.726708i \(0.741049\pi\)
\(212\) −12.1017 −0.831148
\(213\) −14.7836 −1.01295
\(214\) 5.43366 0.371438
\(215\) 2.39832 0.163564
\(216\) −0.158129 −0.0107593
\(217\) 3.35900 0.228024
\(218\) 17.9444 1.21535
\(219\) −4.24179 −0.286634
\(220\) 3.03476 0.204604
\(221\) −4.12272 −0.277324
\(222\) 20.5366 1.37833
\(223\) −19.1316 −1.28115 −0.640574 0.767896i \(-0.721304\pi\)
−0.640574 + 0.767896i \(0.721304\pi\)
\(224\) −3.35900 −0.224433
\(225\) 2.93509 0.195673
\(226\) −8.66105 −0.576124
\(227\) 8.34873 0.554124 0.277062 0.960852i \(-0.410639\pi\)
0.277062 + 0.960852i \(0.410639\pi\)
\(228\) −5.47846 −0.362820
\(229\) 6.74983 0.446041 0.223021 0.974814i \(-0.428408\pi\)
0.223021 + 0.974814i \(0.428408\pi\)
\(230\) 2.50746 0.165337
\(231\) 24.8341 1.63396
\(232\) −10.2379 −0.672154
\(233\) 12.0158 0.787180 0.393590 0.919286i \(-0.371233\pi\)
0.393590 + 0.919286i \(0.371233\pi\)
\(234\) 2.93509 0.191873
\(235\) 5.72331 0.373348
\(236\) 2.41542 0.157231
\(237\) 24.2613 1.57594
\(238\) 13.8482 0.897646
\(239\) −4.03837 −0.261220 −0.130610 0.991434i \(-0.541694\pi\)
−0.130610 + 0.991434i \(0.541694\pi\)
\(240\) −2.43620 −0.157256
\(241\) −0.722061 −0.0465120 −0.0232560 0.999730i \(-0.507403\pi\)
−0.0232560 + 0.999730i \(0.507403\pi\)
\(242\) −1.79021 −0.115079
\(243\) −21.9156 −1.40588
\(244\) −1.65628 −0.106033
\(245\) −4.28288 −0.273623
\(246\) 8.02256 0.511499
\(247\) −2.24877 −0.143086
\(248\) −1.00000 −0.0635001
\(249\) 0.445993 0.0282637
\(250\) −1.00000 −0.0632456
\(251\) −2.24540 −0.141729 −0.0708643 0.997486i \(-0.522576\pi\)
−0.0708643 + 0.997486i \(0.522576\pi\)
\(252\) −9.85898 −0.621057
\(253\) 7.60956 0.478409
\(254\) 0.876232 0.0549797
\(255\) 10.0438 0.628966
\(256\) 1.00000 0.0625000
\(257\) 17.6813 1.10293 0.551464 0.834199i \(-0.314069\pi\)
0.551464 + 0.834199i \(0.314069\pi\)
\(258\) −5.84280 −0.363757
\(259\) −28.3155 −1.75944
\(260\) −1.00000 −0.0620174
\(261\) −30.0493 −1.86001
\(262\) −13.2381 −0.817853
\(263\) 7.81814 0.482087 0.241043 0.970514i \(-0.422510\pi\)
0.241043 + 0.970514i \(0.422510\pi\)
\(264\) −7.39331 −0.455026
\(265\) 12.1017 0.743401
\(266\) 7.55361 0.463141
\(267\) 31.3811 1.92049
\(268\) 10.9975 0.671777
\(269\) −8.89811 −0.542527 −0.271264 0.962505i \(-0.587442\pi\)
−0.271264 + 0.962505i \(0.587442\pi\)
\(270\) 0.158129 0.00962344
\(271\) −21.4495 −1.30296 −0.651481 0.758665i \(-0.725852\pi\)
−0.651481 + 0.758665i \(0.725852\pi\)
\(272\) −4.12272 −0.249976
\(273\) −8.18321 −0.495270
\(274\) 7.15307 0.432132
\(275\) −3.03476 −0.183003
\(276\) −6.10869 −0.367700
\(277\) 11.5867 0.696175 0.348087 0.937462i \(-0.386831\pi\)
0.348087 + 0.937462i \(0.386831\pi\)
\(278\) −9.98682 −0.598970
\(279\) −2.93509 −0.175719
\(280\) 3.35900 0.200739
\(281\) 8.81499 0.525858 0.262929 0.964815i \(-0.415311\pi\)
0.262929 + 0.964815i \(0.415311\pi\)
\(282\) −13.9432 −0.830303
\(283\) −7.85274 −0.466797 −0.233399 0.972381i \(-0.574985\pi\)
−0.233399 + 0.972381i \(0.574985\pi\)
\(284\) −6.06828 −0.360086
\(285\) 5.47846 0.324516
\(286\) −3.03476 −0.179449
\(287\) −11.0614 −0.652932
\(288\) 2.93509 0.172952
\(289\) −0.00319780 −0.000188106 0
\(290\) 10.2379 0.601193
\(291\) 13.5184 0.792463
\(292\) −1.74115 −0.101893
\(293\) −30.1225 −1.75978 −0.879889 0.475180i \(-0.842383\pi\)
−0.879889 + 0.475180i \(0.842383\pi\)
\(294\) 10.4340 0.608522
\(295\) −2.41542 −0.140631
\(296\) 8.42975 0.489969
\(297\) 0.479885 0.0278457
\(298\) −16.7269 −0.968961
\(299\) −2.50746 −0.145010
\(300\) 2.43620 0.140654
\(301\) 8.05596 0.464338
\(302\) −7.14948 −0.411407
\(303\) −0.0881722 −0.00506536
\(304\) −2.24877 −0.128976
\(305\) 1.65628 0.0948384
\(306\) −12.1006 −0.691743
\(307\) 27.0815 1.54562 0.772811 0.634636i \(-0.218850\pi\)
0.772811 + 0.634636i \(0.218850\pi\)
\(308\) 10.1938 0.580844
\(309\) −4.24521 −0.241502
\(310\) 1.00000 0.0567962
\(311\) −4.24696 −0.240823 −0.120411 0.992724i \(-0.538421\pi\)
−0.120411 + 0.992724i \(0.538421\pi\)
\(312\) 2.43620 0.137923
\(313\) 7.03699 0.397754 0.198877 0.980024i \(-0.436271\pi\)
0.198877 + 0.980024i \(0.436271\pi\)
\(314\) −10.6518 −0.601117
\(315\) 9.85898 0.555490
\(316\) 9.95863 0.560217
\(317\) 1.52411 0.0856027 0.0428013 0.999084i \(-0.486372\pi\)
0.0428013 + 0.999084i \(0.486372\pi\)
\(318\) −29.4822 −1.65328
\(319\) 31.0698 1.73957
\(320\) −1.00000 −0.0559017
\(321\) 13.2375 0.738846
\(322\) 8.42257 0.469371
\(323\) 9.27103 0.515854
\(324\) −9.19051 −0.510584
\(325\) 1.00000 0.0554700
\(326\) −13.4807 −0.746625
\(327\) 43.7161 2.41751
\(328\) 3.29306 0.181829
\(329\) 19.2246 1.05989
\(330\) 7.39331 0.406988
\(331\) 32.6478 1.79448 0.897242 0.441539i \(-0.145567\pi\)
0.897242 + 0.441539i \(0.145567\pi\)
\(332\) 0.183069 0.0100472
\(333\) 24.7421 1.35586
\(334\) −6.54893 −0.358342
\(335\) −10.9975 −0.600856
\(336\) −8.18321 −0.446431
\(337\) 15.4088 0.839370 0.419685 0.907670i \(-0.362140\pi\)
0.419685 + 0.907670i \(0.362140\pi\)
\(338\) 1.00000 0.0543928
\(339\) −21.1001 −1.14600
\(340\) 4.12272 0.223586
\(341\) 3.03476 0.164342
\(342\) −6.60034 −0.356905
\(343\) 9.12680 0.492801
\(344\) −2.39832 −0.129309
\(345\) 6.10869 0.328881
\(346\) −4.25742 −0.228881
\(347\) −27.4585 −1.47405 −0.737025 0.675865i \(-0.763770\pi\)
−0.737025 + 0.675865i \(0.763770\pi\)
\(348\) −24.9417 −1.33702
\(349\) −22.3226 −1.19490 −0.597450 0.801906i \(-0.703819\pi\)
−0.597450 + 0.801906i \(0.703819\pi\)
\(350\) −3.35900 −0.179546
\(351\) −0.158129 −0.00844031
\(352\) −3.03476 −0.161753
\(353\) 11.9457 0.635808 0.317904 0.948123i \(-0.397021\pi\)
0.317904 + 0.948123i \(0.397021\pi\)
\(354\) 5.88446 0.312756
\(355\) 6.06828 0.322071
\(356\) 12.8811 0.682698
\(357\) 33.7371 1.78556
\(358\) 5.65679 0.298971
\(359\) 3.30894 0.174639 0.0873196 0.996180i \(-0.472170\pi\)
0.0873196 + 0.996180i \(0.472170\pi\)
\(360\) −2.93509 −0.154693
\(361\) −13.9430 −0.733845
\(362\) 13.3560 0.701975
\(363\) −4.36131 −0.228910
\(364\) −3.35900 −0.176059
\(365\) 1.74115 0.0911358
\(366\) −4.03504 −0.210915
\(367\) 10.1283 0.528692 0.264346 0.964428i \(-0.414844\pi\)
0.264346 + 0.964428i \(0.414844\pi\)
\(368\) −2.50746 −0.130711
\(369\) 9.66542 0.503162
\(370\) −8.42975 −0.438242
\(371\) 40.6496 2.11042
\(372\) −2.43620 −0.126311
\(373\) −9.56233 −0.495119 −0.247559 0.968873i \(-0.579628\pi\)
−0.247559 + 0.968873i \(0.579628\pi\)
\(374\) 12.5115 0.646953
\(375\) −2.43620 −0.125805
\(376\) −5.72331 −0.295157
\(377\) −10.2379 −0.527281
\(378\) 0.531156 0.0273197
\(379\) −17.3898 −0.893252 −0.446626 0.894721i \(-0.647375\pi\)
−0.446626 + 0.894721i \(0.647375\pi\)
\(380\) 2.24877 0.115359
\(381\) 2.13468 0.109363
\(382\) −13.0306 −0.666706
\(383\) −25.2403 −1.28972 −0.644859 0.764301i \(-0.723084\pi\)
−0.644859 + 0.764301i \(0.723084\pi\)
\(384\) 2.43620 0.124322
\(385\) −10.1938 −0.519523
\(386\) 1.17390 0.0597498
\(387\) −7.03929 −0.357827
\(388\) 5.54896 0.281706
\(389\) −7.15457 −0.362751 −0.181375 0.983414i \(-0.558055\pi\)
−0.181375 + 0.983414i \(0.558055\pi\)
\(390\) −2.43620 −0.123362
\(391\) 10.3376 0.522793
\(392\) 4.28288 0.216318
\(393\) −32.2507 −1.62683
\(394\) 11.0487 0.556625
\(395\) −9.95863 −0.501073
\(396\) −8.90731 −0.447609
\(397\) 11.0021 0.552178 0.276089 0.961132i \(-0.410962\pi\)
0.276089 + 0.961132i \(0.410962\pi\)
\(398\) 16.0984 0.806941
\(399\) 18.4021 0.921259
\(400\) 1.00000 0.0500000
\(401\) 11.6998 0.584260 0.292130 0.956379i \(-0.405636\pi\)
0.292130 + 0.956379i \(0.405636\pi\)
\(402\) 26.7921 1.33627
\(403\) −1.00000 −0.0498135
\(404\) −0.0361924 −0.00180064
\(405\) 9.19051 0.456680
\(406\) 34.3893 1.70671
\(407\) −25.5823 −1.26807
\(408\) −10.0438 −0.497241
\(409\) −12.3151 −0.608942 −0.304471 0.952522i \(-0.598480\pi\)
−0.304471 + 0.952522i \(0.598480\pi\)
\(410\) −3.29306 −0.162632
\(411\) 17.4263 0.859577
\(412\) −1.74255 −0.0858493
\(413\) −8.11340 −0.399234
\(414\) −7.35963 −0.361706
\(415\) −0.183069 −0.00898650
\(416\) 1.00000 0.0490290
\(417\) −24.3299 −1.19144
\(418\) 6.82448 0.333796
\(419\) 25.3245 1.23718 0.618592 0.785712i \(-0.287703\pi\)
0.618592 + 0.785712i \(0.287703\pi\)
\(420\) 8.18321 0.399300
\(421\) 1.35698 0.0661353 0.0330676 0.999453i \(-0.489472\pi\)
0.0330676 + 0.999453i \(0.489472\pi\)
\(422\) −19.9570 −0.971489
\(423\) −16.7985 −0.816769
\(424\) −12.1017 −0.587710
\(425\) −4.12272 −0.199981
\(426\) −14.7836 −0.716267
\(427\) 5.56345 0.269234
\(428\) 5.43366 0.262646
\(429\) −7.39331 −0.356952
\(430\) 2.39832 0.115657
\(431\) 36.9462 1.77964 0.889819 0.456314i \(-0.150831\pi\)
0.889819 + 0.456314i \(0.150831\pi\)
\(432\) −0.158129 −0.00760799
\(433\) 40.0004 1.92230 0.961149 0.276030i \(-0.0890191\pi\)
0.961149 + 0.276030i \(0.0890191\pi\)
\(434\) 3.35900 0.161237
\(435\) 24.9417 1.19586
\(436\) 17.9444 0.859379
\(437\) 5.63870 0.269736
\(438\) −4.24179 −0.202681
\(439\) 4.80749 0.229449 0.114724 0.993397i \(-0.463402\pi\)
0.114724 + 0.993397i \(0.463402\pi\)
\(440\) 3.03476 0.144677
\(441\) 12.5707 0.598603
\(442\) −4.12272 −0.196098
\(443\) 26.0549 1.23791 0.618954 0.785427i \(-0.287557\pi\)
0.618954 + 0.785427i \(0.287557\pi\)
\(444\) 20.5366 0.974624
\(445\) −12.8811 −0.610624
\(446\) −19.1316 −0.905909
\(447\) −40.7500 −1.92741
\(448\) −3.35900 −0.158698
\(449\) 29.5530 1.39469 0.697346 0.716735i \(-0.254364\pi\)
0.697346 + 0.716735i \(0.254364\pi\)
\(450\) 2.93509 0.138362
\(451\) −9.99365 −0.470582
\(452\) −8.66105 −0.407381
\(453\) −17.4176 −0.818351
\(454\) 8.34873 0.391825
\(455\) 3.35900 0.157472
\(456\) −5.47846 −0.256552
\(457\) 2.43980 0.114129 0.0570646 0.998370i \(-0.481826\pi\)
0.0570646 + 0.998370i \(0.481826\pi\)
\(458\) 6.74983 0.315399
\(459\) 0.651922 0.0304291
\(460\) 2.50746 0.116911
\(461\) 2.61924 0.121990 0.0609950 0.998138i \(-0.480573\pi\)
0.0609950 + 0.998138i \(0.480573\pi\)
\(462\) 24.8341 1.15539
\(463\) −27.1193 −1.26034 −0.630171 0.776457i \(-0.717015\pi\)
−0.630171 + 0.776457i \(0.717015\pi\)
\(464\) −10.2379 −0.475285
\(465\) 2.43620 0.112976
\(466\) 12.0158 0.556620
\(467\) 5.74393 0.265798 0.132899 0.991130i \(-0.457571\pi\)
0.132899 + 0.991130i \(0.457571\pi\)
\(468\) 2.93509 0.135675
\(469\) −36.9405 −1.70575
\(470\) 5.72331 0.263997
\(471\) −25.9500 −1.19571
\(472\) 2.41542 0.111179
\(473\) 7.27834 0.334658
\(474\) 24.2613 1.11436
\(475\) −2.24877 −0.103181
\(476\) 13.8482 0.634732
\(477\) −35.5196 −1.62633
\(478\) −4.03837 −0.184711
\(479\) 21.0537 0.961968 0.480984 0.876729i \(-0.340280\pi\)
0.480984 + 0.876729i \(0.340280\pi\)
\(480\) −2.43620 −0.111197
\(481\) 8.42975 0.384364
\(482\) −0.722061 −0.0328890
\(483\) 20.5191 0.933651
\(484\) −1.79021 −0.0813731
\(485\) −5.54896 −0.251965
\(486\) −21.9156 −0.994111
\(487\) −27.1324 −1.22949 −0.614743 0.788727i \(-0.710740\pi\)
−0.614743 + 0.788727i \(0.710740\pi\)
\(488\) −1.65628 −0.0749763
\(489\) −32.8417 −1.48515
\(490\) −4.28288 −0.193481
\(491\) −6.10977 −0.275730 −0.137865 0.990451i \(-0.544024\pi\)
−0.137865 + 0.990451i \(0.544024\pi\)
\(492\) 8.02256 0.361685
\(493\) 42.2082 1.90096
\(494\) −2.24877 −0.101177
\(495\) 8.90731 0.400354
\(496\) −1.00000 −0.0449013
\(497\) 20.3834 0.914319
\(498\) 0.445993 0.0199854
\(499\) −28.4020 −1.27145 −0.635724 0.771917i \(-0.719298\pi\)
−0.635724 + 0.771917i \(0.719298\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −15.9545 −0.712796
\(502\) −2.24540 −0.100217
\(503\) −11.6760 −0.520606 −0.260303 0.965527i \(-0.583822\pi\)
−0.260303 + 0.965527i \(0.583822\pi\)
\(504\) −9.85898 −0.439154
\(505\) 0.0361924 0.00161054
\(506\) 7.60956 0.338286
\(507\) 2.43620 0.108196
\(508\) 0.876232 0.0388765
\(509\) 27.2652 1.20851 0.604254 0.796792i \(-0.293471\pi\)
0.604254 + 0.796792i \(0.293471\pi\)
\(510\) 10.0438 0.444746
\(511\) 5.84851 0.258723
\(512\) 1.00000 0.0441942
\(513\) 0.355596 0.0156999
\(514\) 17.6813 0.779888
\(515\) 1.74255 0.0767860
\(516\) −5.84280 −0.257215
\(517\) 17.3689 0.763884
\(518\) −28.3155 −1.24411
\(519\) −10.3720 −0.455278
\(520\) −1.00000 −0.0438529
\(521\) −21.0802 −0.923540 −0.461770 0.887000i \(-0.652785\pi\)
−0.461770 + 0.887000i \(0.652785\pi\)
\(522\) −30.0493 −1.31522
\(523\) 1.12503 0.0491942 0.0245971 0.999697i \(-0.492170\pi\)
0.0245971 + 0.999697i \(0.492170\pi\)
\(524\) −13.2381 −0.578309
\(525\) −8.18321 −0.357145
\(526\) 7.81814 0.340887
\(527\) 4.12272 0.179588
\(528\) −7.39331 −0.321752
\(529\) −16.7126 −0.726636
\(530\) 12.1017 0.525664
\(531\) 7.08948 0.307657
\(532\) 7.55361 0.327490
\(533\) 3.29306 0.142638
\(534\) 31.3811 1.35799
\(535\) −5.43366 −0.234918
\(536\) 10.9975 0.475018
\(537\) 13.7811 0.594699
\(538\) −8.89811 −0.383625
\(539\) −12.9975 −0.559844
\(540\) 0.158129 0.00680480
\(541\) −11.4740 −0.493305 −0.246652 0.969104i \(-0.579331\pi\)
−0.246652 + 0.969104i \(0.579331\pi\)
\(542\) −21.4495 −0.921333
\(543\) 32.5379 1.39634
\(544\) −4.12272 −0.176760
\(545\) −17.9444 −0.768652
\(546\) −8.18321 −0.350209
\(547\) 8.65652 0.370126 0.185063 0.982727i \(-0.440751\pi\)
0.185063 + 0.982727i \(0.440751\pi\)
\(548\) 7.15307 0.305564
\(549\) −4.86134 −0.207477
\(550\) −3.03476 −0.129403
\(551\) 23.0228 0.980803
\(552\) −6.10869 −0.260003
\(553\) −33.4510 −1.42248
\(554\) 11.5867 0.492270
\(555\) −20.5366 −0.871730
\(556\) −9.98682 −0.423536
\(557\) −10.0807 −0.427133 −0.213566 0.976929i \(-0.568508\pi\)
−0.213566 + 0.976929i \(0.568508\pi\)
\(558\) −2.93509 −0.124252
\(559\) −2.39832 −0.101438
\(560\) 3.35900 0.141944
\(561\) 30.4805 1.28689
\(562\) 8.81499 0.371838
\(563\) −33.9166 −1.42942 −0.714708 0.699423i \(-0.753440\pi\)
−0.714708 + 0.699423i \(0.753440\pi\)
\(564\) −13.9432 −0.587113
\(565\) 8.66105 0.364373
\(566\) −7.85274 −0.330075
\(567\) 30.8709 1.29646
\(568\) −6.06828 −0.254620
\(569\) −30.1231 −1.26283 −0.631414 0.775446i \(-0.717525\pi\)
−0.631414 + 0.775446i \(0.717525\pi\)
\(570\) 5.47846 0.229467
\(571\) −31.6253 −1.32348 −0.661739 0.749734i \(-0.730181\pi\)
−0.661739 + 0.749734i \(0.730181\pi\)
\(572\) −3.03476 −0.126890
\(573\) −31.7453 −1.32618
\(574\) −11.0614 −0.461693
\(575\) −2.50746 −0.104568
\(576\) 2.93509 0.122295
\(577\) −43.4210 −1.80764 −0.903819 0.427915i \(-0.859248\pi\)
−0.903819 + 0.427915i \(0.859248\pi\)
\(578\) −0.00319780 −0.000133011 0
\(579\) 2.85985 0.118851
\(580\) 10.2379 0.425108
\(581\) −0.614928 −0.0255115
\(582\) 13.5184 0.560356
\(583\) 36.7258 1.52103
\(584\) −1.74115 −0.0720492
\(585\) −2.93509 −0.121351
\(586\) −30.1225 −1.24435
\(587\) 8.71175 0.359572 0.179786 0.983706i \(-0.442459\pi\)
0.179786 + 0.983706i \(0.442459\pi\)
\(588\) 10.4340 0.430290
\(589\) 2.24877 0.0926588
\(590\) −2.41542 −0.0994413
\(591\) 26.9169 1.10721
\(592\) 8.42975 0.346461
\(593\) −30.7163 −1.26137 −0.630683 0.776041i \(-0.717225\pi\)
−0.630683 + 0.776041i \(0.717225\pi\)
\(594\) 0.479885 0.0196899
\(595\) −13.8482 −0.567721
\(596\) −16.7269 −0.685159
\(597\) 39.2190 1.60513
\(598\) −2.50746 −0.102538
\(599\) 11.2583 0.460004 0.230002 0.973190i \(-0.426127\pi\)
0.230002 + 0.973190i \(0.426127\pi\)
\(600\) 2.43620 0.0994576
\(601\) 20.8697 0.851293 0.425646 0.904890i \(-0.360047\pi\)
0.425646 + 0.904890i \(0.360047\pi\)
\(602\) 8.05596 0.328336
\(603\) 32.2786 1.31449
\(604\) −7.14948 −0.290908
\(605\) 1.79021 0.0727823
\(606\) −0.0881722 −0.00358175
\(607\) −12.3754 −0.502302 −0.251151 0.967948i \(-0.580809\pi\)
−0.251151 + 0.967948i \(0.580809\pi\)
\(608\) −2.24877 −0.0911995
\(609\) 83.7793 3.39491
\(610\) 1.65628 0.0670609
\(611\) −5.72331 −0.231540
\(612\) −12.1006 −0.489136
\(613\) 38.1498 1.54085 0.770427 0.637528i \(-0.220043\pi\)
0.770427 + 0.637528i \(0.220043\pi\)
\(614\) 27.0815 1.09292
\(615\) −8.02256 −0.323501
\(616\) 10.1938 0.410719
\(617\) −5.99730 −0.241442 −0.120721 0.992686i \(-0.538521\pi\)
−0.120721 + 0.992686i \(0.538521\pi\)
\(618\) −4.24521 −0.170767
\(619\) 28.2065 1.13371 0.566857 0.823816i \(-0.308159\pi\)
0.566857 + 0.823816i \(0.308159\pi\)
\(620\) 1.00000 0.0401610
\(621\) 0.396503 0.0159111
\(622\) −4.24696 −0.170288
\(623\) −43.2677 −1.73348
\(624\) 2.43620 0.0975262
\(625\) 1.00000 0.0400000
\(626\) 7.03699 0.281255
\(627\) 16.6258 0.663971
\(628\) −10.6518 −0.425054
\(629\) −34.7535 −1.38571
\(630\) 9.85898 0.392791
\(631\) −18.6210 −0.741289 −0.370644 0.928775i \(-0.620863\pi\)
−0.370644 + 0.928775i \(0.620863\pi\)
\(632\) 9.95863 0.396133
\(633\) −48.6192 −1.93244
\(634\) 1.52411 0.0605302
\(635\) −0.876232 −0.0347722
\(636\) −29.4822 −1.16905
\(637\) 4.28288 0.169694
\(638\) 31.0698 1.23006
\(639\) −17.8110 −0.704591
\(640\) −1.00000 −0.0395285
\(641\) 6.00870 0.237329 0.118665 0.992934i \(-0.462139\pi\)
0.118665 + 0.992934i \(0.462139\pi\)
\(642\) 13.2375 0.522443
\(643\) −10.3531 −0.408284 −0.204142 0.978941i \(-0.565441\pi\)
−0.204142 + 0.978941i \(0.565441\pi\)
\(644\) 8.42257 0.331896
\(645\) 5.84280 0.230060
\(646\) 9.27103 0.364764
\(647\) 29.8176 1.17225 0.586125 0.810221i \(-0.300653\pi\)
0.586125 + 0.810221i \(0.300653\pi\)
\(648\) −9.19051 −0.361037
\(649\) −7.33023 −0.287737
\(650\) 1.00000 0.0392232
\(651\) 8.18321 0.320725
\(652\) −13.4807 −0.527944
\(653\) −29.4076 −1.15081 −0.575405 0.817869i \(-0.695155\pi\)
−0.575405 + 0.817869i \(0.695155\pi\)
\(654\) 43.7161 1.70944
\(655\) 13.2381 0.517256
\(656\) 3.29306 0.128572
\(657\) −5.11043 −0.199377
\(658\) 19.2246 0.749453
\(659\) −4.16954 −0.162422 −0.0812110 0.996697i \(-0.525879\pi\)
−0.0812110 + 0.996697i \(0.525879\pi\)
\(660\) 7.39331 0.287784
\(661\) −1.97703 −0.0768976 −0.0384488 0.999261i \(-0.512242\pi\)
−0.0384488 + 0.999261i \(0.512242\pi\)
\(662\) 32.6478 1.26889
\(663\) −10.0438 −0.390068
\(664\) 0.183069 0.00710445
\(665\) −7.55361 −0.292916
\(666\) 24.7421 0.958737
\(667\) 25.6713 0.993996
\(668\) −6.54893 −0.253386
\(669\) −46.6086 −1.80199
\(670\) −10.9975 −0.424869
\(671\) 5.02642 0.194043
\(672\) −8.18321 −0.315674
\(673\) 15.8420 0.610664 0.305332 0.952246i \(-0.401233\pi\)
0.305332 + 0.952246i \(0.401233\pi\)
\(674\) 15.4088 0.593524
\(675\) −0.158129 −0.00608639
\(676\) 1.00000 0.0384615
\(677\) −12.6540 −0.486334 −0.243167 0.969984i \(-0.578186\pi\)
−0.243167 + 0.969984i \(0.578186\pi\)
\(678\) −21.1001 −0.810344
\(679\) −18.6390 −0.715298
\(680\) 4.12272 0.158099
\(681\) 20.3392 0.779400
\(682\) 3.03476 0.116207
\(683\) 38.9291 1.48958 0.744790 0.667298i \(-0.232549\pi\)
0.744790 + 0.667298i \(0.232549\pi\)
\(684\) −6.60034 −0.252370
\(685\) −7.15307 −0.273305
\(686\) 9.12680 0.348463
\(687\) 16.4440 0.627376
\(688\) −2.39832 −0.0914351
\(689\) −12.1017 −0.461038
\(690\) 6.10869 0.232554
\(691\) −24.6483 −0.937664 −0.468832 0.883287i \(-0.655325\pi\)
−0.468832 + 0.883287i \(0.655325\pi\)
\(692\) −4.25742 −0.161843
\(693\) 29.9197 1.13655
\(694\) −27.4585 −1.04231
\(695\) 9.98682 0.378822
\(696\) −24.9417 −0.945414
\(697\) −13.5763 −0.514240
\(698\) −22.3226 −0.844921
\(699\) 29.2729 1.10720
\(700\) −3.35900 −0.126958
\(701\) −31.1921 −1.17811 −0.589054 0.808094i \(-0.700500\pi\)
−0.589054 + 0.808094i \(0.700500\pi\)
\(702\) −0.158129 −0.00596820
\(703\) −18.9566 −0.714960
\(704\) −3.03476 −0.114377
\(705\) 13.9432 0.525130
\(706\) 11.9457 0.449584
\(707\) 0.121570 0.00457212
\(708\) 5.88446 0.221152
\(709\) −8.52821 −0.320284 −0.160142 0.987094i \(-0.551195\pi\)
−0.160142 + 0.987094i \(0.551195\pi\)
\(710\) 6.06828 0.227739
\(711\) 29.2295 1.09619
\(712\) 12.8811 0.482741
\(713\) 2.50746 0.0939052
\(714\) 33.7371 1.26258
\(715\) 3.03476 0.113494
\(716\) 5.65679 0.211404
\(717\) −9.83829 −0.367418
\(718\) 3.30894 0.123489
\(719\) 39.8054 1.48449 0.742246 0.670128i \(-0.233761\pi\)
0.742246 + 0.670128i \(0.233761\pi\)
\(720\) −2.93509 −0.109384
\(721\) 5.85323 0.217986
\(722\) −13.9430 −0.518906
\(723\) −1.75909 −0.0654212
\(724\) 13.3560 0.496371
\(725\) −10.2379 −0.380228
\(726\) −4.36131 −0.161864
\(727\) −49.3121 −1.82889 −0.914443 0.404715i \(-0.867371\pi\)
−0.914443 + 0.404715i \(0.867371\pi\)
\(728\) −3.35900 −0.124493
\(729\) −25.8193 −0.956270
\(730\) 1.74115 0.0644428
\(731\) 9.88760 0.365706
\(732\) −4.03504 −0.149139
\(733\) 17.6417 0.651609 0.325805 0.945437i \(-0.394365\pi\)
0.325805 + 0.945437i \(0.394365\pi\)
\(734\) 10.1283 0.373842
\(735\) −10.4340 −0.384863
\(736\) −2.50746 −0.0924263
\(737\) −33.3747 −1.22937
\(738\) 9.66542 0.355789
\(739\) 19.4391 0.715080 0.357540 0.933898i \(-0.383616\pi\)
0.357540 + 0.933898i \(0.383616\pi\)
\(740\) −8.42975 −0.309884
\(741\) −5.47846 −0.201256
\(742\) 40.6496 1.49229
\(743\) −9.93362 −0.364429 −0.182215 0.983259i \(-0.558327\pi\)
−0.182215 + 0.983259i \(0.558327\pi\)
\(744\) −2.43620 −0.0893156
\(745\) 16.7269 0.612824
\(746\) −9.56233 −0.350102
\(747\) 0.537324 0.0196597
\(748\) 12.5115 0.457465
\(749\) −18.2517 −0.666902
\(750\) −2.43620 −0.0889576
\(751\) −19.7638 −0.721190 −0.360595 0.932722i \(-0.617426\pi\)
−0.360595 + 0.932722i \(0.617426\pi\)
\(752\) −5.72331 −0.208708
\(753\) −5.47026 −0.199348
\(754\) −10.2379 −0.372844
\(755\) 7.14948 0.260196
\(756\) 0.531156 0.0193180
\(757\) −33.5781 −1.22042 −0.610208 0.792241i \(-0.708914\pi\)
−0.610208 + 0.792241i \(0.708914\pi\)
\(758\) −17.3898 −0.631625
\(759\) 18.5384 0.672903
\(760\) 2.24877 0.0815714
\(761\) −25.0735 −0.908912 −0.454456 0.890769i \(-0.650166\pi\)
−0.454456 + 0.890769i \(0.650166\pi\)
\(762\) 2.13468 0.0773313
\(763\) −60.2751 −2.18211
\(764\) −13.0306 −0.471432
\(765\) 12.1006 0.437497
\(766\) −25.2403 −0.911969
\(767\) 2.41542 0.0872158
\(768\) 2.43620 0.0879090
\(769\) −52.3243 −1.88686 −0.943432 0.331566i \(-0.892423\pi\)
−0.943432 + 0.331566i \(0.892423\pi\)
\(770\) −10.1938 −0.367358
\(771\) 43.0752 1.55132
\(772\) 1.17390 0.0422495
\(773\) −35.5117 −1.27727 −0.638634 0.769511i \(-0.720500\pi\)
−0.638634 + 0.769511i \(0.720500\pi\)
\(774\) −7.03929 −0.253022
\(775\) −1.00000 −0.0359211
\(776\) 5.54896 0.199196
\(777\) −68.9825 −2.47473
\(778\) −7.15457 −0.256504
\(779\) −7.40531 −0.265323
\(780\) −2.43620 −0.0872301
\(781\) 18.4158 0.658969
\(782\) 10.3376 0.369670
\(783\) 1.61892 0.0578554
\(784\) 4.28288 0.152960
\(785\) 10.6518 0.380179
\(786\) −32.2507 −1.15035
\(787\) −34.4764 −1.22895 −0.614476 0.788936i \(-0.710632\pi\)
−0.614476 + 0.788936i \(0.710632\pi\)
\(788\) 11.0487 0.393593
\(789\) 19.0466 0.678076
\(790\) −9.95863 −0.354312
\(791\) 29.0925 1.03441
\(792\) −8.90731 −0.316508
\(793\) −1.65628 −0.0588163
\(794\) 11.0021 0.390449
\(795\) 29.4822 1.04563
\(796\) 16.0984 0.570593
\(797\) 1.91643 0.0678834 0.0339417 0.999424i \(-0.489194\pi\)
0.0339417 + 0.999424i \(0.489194\pi\)
\(798\) 18.4021 0.651429
\(799\) 23.5956 0.834753
\(800\) 1.00000 0.0353553
\(801\) 37.8073 1.33585
\(802\) 11.6998 0.413134
\(803\) 5.28397 0.186467
\(804\) 26.7921 0.944884
\(805\) −8.42257 −0.296857
\(806\) −1.00000 −0.0352235
\(807\) −21.6776 −0.763088
\(808\) −0.0361924 −0.00127325
\(809\) −30.8924 −1.08612 −0.543059 0.839695i \(-0.682734\pi\)
−0.543059 + 0.839695i \(0.682734\pi\)
\(810\) 9.19051 0.322922
\(811\) 29.0271 1.01928 0.509640 0.860388i \(-0.329779\pi\)
0.509640 + 0.860388i \(0.329779\pi\)
\(812\) 34.3893 1.20683
\(813\) −52.2553 −1.83267
\(814\) −25.5823 −0.896660
\(815\) 13.4807 0.472207
\(816\) −10.0438 −0.351603
\(817\) 5.39327 0.188686
\(818\) −12.3151 −0.430587
\(819\) −9.85898 −0.344500
\(820\) −3.29306 −0.114998
\(821\) −2.28902 −0.0798873 −0.0399436 0.999202i \(-0.512718\pi\)
−0.0399436 + 0.999202i \(0.512718\pi\)
\(822\) 17.4263 0.607813
\(823\) 7.21273 0.251420 0.125710 0.992067i \(-0.459879\pi\)
0.125710 + 0.992067i \(0.459879\pi\)
\(824\) −1.74255 −0.0607046
\(825\) −7.39331 −0.257402
\(826\) −8.11340 −0.282301
\(827\) −26.2776 −0.913761 −0.456880 0.889528i \(-0.651033\pi\)
−0.456880 + 0.889528i \(0.651033\pi\)
\(828\) −7.35963 −0.255765
\(829\) −47.9819 −1.66648 −0.833240 0.552911i \(-0.813517\pi\)
−0.833240 + 0.552911i \(0.813517\pi\)
\(830\) −0.183069 −0.00635441
\(831\) 28.2275 0.979200
\(832\) 1.00000 0.0346688
\(833\) −17.6571 −0.611783
\(834\) −24.3299 −0.842477
\(835\) 6.54893 0.226635
\(836\) 6.82448 0.236029
\(837\) 0.158129 0.00546574
\(838\) 25.3245 0.874822
\(839\) 16.9904 0.586572 0.293286 0.956025i \(-0.405251\pi\)
0.293286 + 0.956025i \(0.405251\pi\)
\(840\) 8.18321 0.282348
\(841\) 75.8156 2.61433
\(842\) 1.35698 0.0467647
\(843\) 21.4751 0.739643
\(844\) −19.9570 −0.686947
\(845\) −1.00000 −0.0344010
\(846\) −16.7985 −0.577543
\(847\) 6.01331 0.206620
\(848\) −12.1017 −0.415574
\(849\) −19.1309 −0.656570
\(850\) −4.12272 −0.141408
\(851\) −21.1373 −0.724577
\(852\) −14.7836 −0.506477
\(853\) −8.69427 −0.297686 −0.148843 0.988861i \(-0.547555\pi\)
−0.148843 + 0.988861i \(0.547555\pi\)
\(854\) 5.56345 0.190377
\(855\) 6.60034 0.225727
\(856\) 5.43366 0.185719
\(857\) −4.35394 −0.148728 −0.0743639 0.997231i \(-0.523693\pi\)
−0.0743639 + 0.997231i \(0.523693\pi\)
\(858\) −7.39331 −0.252403
\(859\) 48.9514 1.67020 0.835099 0.550099i \(-0.185410\pi\)
0.835099 + 0.550099i \(0.185410\pi\)
\(860\) 2.39832 0.0817821
\(861\) −26.9478 −0.918377
\(862\) 36.9462 1.25839
\(863\) −53.1037 −1.80767 −0.903835 0.427880i \(-0.859260\pi\)
−0.903835 + 0.427880i \(0.859260\pi\)
\(864\) −0.158129 −0.00537966
\(865\) 4.25742 0.144757
\(866\) 40.0004 1.35927
\(867\) −0.00779049 −0.000264579 0
\(868\) 3.35900 0.114012
\(869\) −30.2221 −1.02521
\(870\) 24.9417 0.845604
\(871\) 10.9975 0.372635
\(872\) 17.9444 0.607673
\(873\) 16.2867 0.551222
\(874\) 5.63870 0.190732
\(875\) 3.35900 0.113555
\(876\) −4.24179 −0.143317
\(877\) 19.3537 0.653529 0.326764 0.945106i \(-0.394042\pi\)
0.326764 + 0.945106i \(0.394042\pi\)
\(878\) 4.80749 0.162245
\(879\) −73.3846 −2.47520
\(880\) 3.03476 0.102302
\(881\) 38.5377 1.29837 0.649183 0.760632i \(-0.275111\pi\)
0.649183 + 0.760632i \(0.275111\pi\)
\(882\) 12.5707 0.423276
\(883\) 23.6231 0.794980 0.397490 0.917606i \(-0.369881\pi\)
0.397490 + 0.917606i \(0.369881\pi\)
\(884\) −4.12272 −0.138662
\(885\) −5.88446 −0.197804
\(886\) 26.0549 0.875333
\(887\) −33.6482 −1.12980 −0.564899 0.825160i \(-0.691085\pi\)
−0.564899 + 0.825160i \(0.691085\pi\)
\(888\) 20.5366 0.689163
\(889\) −2.94326 −0.0987139
\(890\) −12.8811 −0.431776
\(891\) 27.8910 0.934385
\(892\) −19.1316 −0.640574
\(893\) 12.8704 0.430691
\(894\) −40.7500 −1.36288
\(895\) −5.65679 −0.189086
\(896\) −3.35900 −0.112216
\(897\) −6.10869 −0.203963
\(898\) 29.5530 0.986196
\(899\) 10.2379 0.341455
\(900\) 2.93509 0.0978364
\(901\) 49.8919 1.66214
\(902\) −9.99365 −0.332752
\(903\) 19.6260 0.653111
\(904\) −8.66105 −0.288062
\(905\) −13.3560 −0.443968
\(906\) −17.4176 −0.578661
\(907\) 29.4763 0.978744 0.489372 0.872075i \(-0.337226\pi\)
0.489372 + 0.872075i \(0.337226\pi\)
\(908\) 8.34873 0.277062
\(909\) −0.106228 −0.00352336
\(910\) 3.35900 0.111350
\(911\) −48.8748 −1.61929 −0.809647 0.586917i \(-0.800341\pi\)
−0.809647 + 0.586917i \(0.800341\pi\)
\(912\) −5.47846 −0.181410
\(913\) −0.555571 −0.0183867
\(914\) 2.43980 0.0807015
\(915\) 4.03504 0.133394
\(916\) 6.74983 0.223021
\(917\) 44.4668 1.46842
\(918\) 0.651922 0.0215166
\(919\) −45.9552 −1.51592 −0.757961 0.652300i \(-0.773804\pi\)
−0.757961 + 0.652300i \(0.773804\pi\)
\(920\) 2.50746 0.0826686
\(921\) 65.9761 2.17399
\(922\) 2.61924 0.0862600
\(923\) −6.06828 −0.199740
\(924\) 24.8341 0.816982
\(925\) 8.42975 0.277169
\(926\) −27.1193 −0.891196
\(927\) −5.11455 −0.167984
\(928\) −10.2379 −0.336077
\(929\) −36.5650 −1.19966 −0.599829 0.800128i \(-0.704765\pi\)
−0.599829 + 0.800128i \(0.704765\pi\)
\(930\) 2.43620 0.0798863
\(931\) −9.63121 −0.315650
\(932\) 12.0158 0.393590
\(933\) −10.3465 −0.338728
\(934\) 5.74393 0.187947
\(935\) −12.5115 −0.409169
\(936\) 2.93509 0.0959365
\(937\) 16.0311 0.523714 0.261857 0.965107i \(-0.415665\pi\)
0.261857 + 0.965107i \(0.415665\pi\)
\(938\) −36.9405 −1.20615
\(939\) 17.1436 0.559459
\(940\) 5.72331 0.186674
\(941\) 5.87792 0.191615 0.0958074 0.995400i \(-0.469457\pi\)
0.0958074 + 0.995400i \(0.469457\pi\)
\(942\) −25.9500 −0.845496
\(943\) −8.25721 −0.268892
\(944\) 2.41542 0.0786153
\(945\) −0.531156 −0.0172785
\(946\) 7.27834 0.236639
\(947\) 3.00412 0.0976209 0.0488105 0.998808i \(-0.484457\pi\)
0.0488105 + 0.998808i \(0.484457\pi\)
\(948\) 24.2613 0.787969
\(949\) −1.74115 −0.0565200
\(950\) −2.24877 −0.0729596
\(951\) 3.71305 0.120404
\(952\) 13.8482 0.448823
\(953\) 41.1703 1.33364 0.666819 0.745220i \(-0.267655\pi\)
0.666819 + 0.745220i \(0.267655\pi\)
\(954\) −35.5196 −1.14999
\(955\) 13.0306 0.421662
\(956\) −4.03837 −0.130610
\(957\) 75.6923 2.44678
\(958\) 21.0537 0.680214
\(959\) −24.0272 −0.775877
\(960\) −2.43620 −0.0786282
\(961\) 1.00000 0.0322581
\(962\) 8.42975 0.271786
\(963\) 15.9483 0.513927
\(964\) −0.722061 −0.0232560
\(965\) −1.17390 −0.0377891
\(966\) 20.5191 0.660191
\(967\) −13.3776 −0.430194 −0.215097 0.976593i \(-0.569007\pi\)
−0.215097 + 0.976593i \(0.569007\pi\)
\(968\) −1.79021 −0.0575395
\(969\) 22.5861 0.725571
\(970\) −5.54896 −0.178167
\(971\) 47.8948 1.53702 0.768509 0.639839i \(-0.220999\pi\)
0.768509 + 0.639839i \(0.220999\pi\)
\(972\) −21.9156 −0.702942
\(973\) 33.5457 1.07543
\(974\) −27.1324 −0.869378
\(975\) 2.43620 0.0780210
\(976\) −1.65628 −0.0530163
\(977\) 4.38759 0.140371 0.0701857 0.997534i \(-0.477641\pi\)
0.0701857 + 0.997534i \(0.477641\pi\)
\(978\) −32.8417 −1.05016
\(979\) −39.0912 −1.24936
\(980\) −4.28288 −0.136812
\(981\) 52.6684 1.68157
\(982\) −6.10977 −0.194971
\(983\) 8.83016 0.281638 0.140819 0.990035i \(-0.455026\pi\)
0.140819 + 0.990035i \(0.455026\pi\)
\(984\) 8.02256 0.255750
\(985\) −11.0487 −0.352041
\(986\) 42.2082 1.34418
\(987\) 46.8351 1.49078
\(988\) −2.24877 −0.0715428
\(989\) 6.01370 0.191225
\(990\) 8.90731 0.283093
\(991\) 23.6041 0.749810 0.374905 0.927063i \(-0.377675\pi\)
0.374905 + 0.927063i \(0.377675\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 79.5367 2.52402
\(994\) 20.3834 0.646521
\(995\) −16.0984 −0.510354
\(996\) 0.445993 0.0141318
\(997\) 56.6238 1.79329 0.896647 0.442747i \(-0.145996\pi\)
0.896647 + 0.442747i \(0.145996\pi\)
\(998\) −28.4020 −0.899049
\(999\) −1.33299 −0.0421739
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 \(a_p\))