Properties

Label 8018.2.a.d.1.12
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.14046 q^{3}\) \(+1.00000 q^{4}\) \(+1.90163 q^{5}\) \(-1.14046 q^{6}\) \(+2.39414 q^{7}\) \(+1.00000 q^{8}\) \(-1.69934 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.14046 q^{3}\) \(+1.00000 q^{4}\) \(+1.90163 q^{5}\) \(-1.14046 q^{6}\) \(+2.39414 q^{7}\) \(+1.00000 q^{8}\) \(-1.69934 q^{9}\) \(+1.90163 q^{10}\) \(-4.82094 q^{11}\) \(-1.14046 q^{12}\) \(-2.93868 q^{13}\) \(+2.39414 q^{14}\) \(-2.16874 q^{15}\) \(+1.00000 q^{16}\) \(-2.32516 q^{17}\) \(-1.69934 q^{18}\) \(+1.00000 q^{19}\) \(+1.90163 q^{20}\) \(-2.73043 q^{21}\) \(-4.82094 q^{22}\) \(+3.20197 q^{23}\) \(-1.14046 q^{24}\) \(-1.38379 q^{25}\) \(-2.93868 q^{26}\) \(+5.35943 q^{27}\) \(+2.39414 q^{28}\) \(-0.604936 q^{29}\) \(-2.16874 q^{30}\) \(-2.02761 q^{31}\) \(+1.00000 q^{32}\) \(+5.49810 q^{33}\) \(-2.32516 q^{34}\) \(+4.55278 q^{35}\) \(-1.69934 q^{36}\) \(+3.52215 q^{37}\) \(+1.00000 q^{38}\) \(+3.35146 q^{39}\) \(+1.90163 q^{40}\) \(+7.60182 q^{41}\) \(-2.73043 q^{42}\) \(-3.42519 q^{43}\) \(-4.82094 q^{44}\) \(-3.23153 q^{45}\) \(+3.20197 q^{46}\) \(+5.77575 q^{47}\) \(-1.14046 q^{48}\) \(-1.26809 q^{49}\) \(-1.38379 q^{50}\) \(+2.65176 q^{51}\) \(-2.93868 q^{52}\) \(+6.56721 q^{53}\) \(+5.35943 q^{54}\) \(-9.16766 q^{55}\) \(+2.39414 q^{56}\) \(-1.14046 q^{57}\) \(-0.604936 q^{58}\) \(-8.44960 q^{59}\) \(-2.16874 q^{60}\) \(-4.08156 q^{61}\) \(-2.02761 q^{62}\) \(-4.06847 q^{63}\) \(+1.00000 q^{64}\) \(-5.58830 q^{65}\) \(+5.49810 q^{66}\) \(-4.70179 q^{67}\) \(-2.32516 q^{68}\) \(-3.65173 q^{69}\) \(+4.55278 q^{70}\) \(-2.73075 q^{71}\) \(-1.69934 q^{72}\) \(+9.55631 q^{73}\) \(+3.52215 q^{74}\) \(+1.57816 q^{75}\) \(+1.00000 q^{76}\) \(-11.5420 q^{77}\) \(+3.35146 q^{78}\) \(-15.4282 q^{79}\) \(+1.90163 q^{80}\) \(-1.01421 q^{81}\) \(+7.60182 q^{82}\) \(-3.58775 q^{83}\) \(-2.73043 q^{84}\) \(-4.42161 q^{85}\) \(-3.42519 q^{86}\) \(+0.689908 q^{87}\) \(-4.82094 q^{88}\) \(-15.9989 q^{89}\) \(-3.23153 q^{90}\) \(-7.03562 q^{91}\) \(+3.20197 q^{92}\) \(+2.31242 q^{93}\) \(+5.77575 q^{94}\) \(+1.90163 q^{95}\) \(-1.14046 q^{96}\) \(-4.53892 q^{97}\) \(-1.26809 q^{98}\) \(+8.19242 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.14046 −0.658447 −0.329224 0.944252i \(-0.606787\pi\)
−0.329224 + 0.944252i \(0.606787\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.90163 0.850437 0.425218 0.905091i \(-0.360197\pi\)
0.425218 + 0.905091i \(0.360197\pi\)
\(6\) −1.14046 −0.465592
\(7\) 2.39414 0.904900 0.452450 0.891790i \(-0.350550\pi\)
0.452450 + 0.891790i \(0.350550\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.69934 −0.566447
\(10\) 1.90163 0.601350
\(11\) −4.82094 −1.45357 −0.726783 0.686867i \(-0.758986\pi\)
−0.726783 + 0.686867i \(0.758986\pi\)
\(12\) −1.14046 −0.329224
\(13\) −2.93868 −0.815044 −0.407522 0.913195i \(-0.633607\pi\)
−0.407522 + 0.913195i \(0.633607\pi\)
\(14\) 2.39414 0.639861
\(15\) −2.16874 −0.559968
\(16\) 1.00000 0.250000
\(17\) −2.32516 −0.563934 −0.281967 0.959424i \(-0.590987\pi\)
−0.281967 + 0.959424i \(0.590987\pi\)
\(18\) −1.69934 −0.400539
\(19\) 1.00000 0.229416
\(20\) 1.90163 0.425218
\(21\) −2.73043 −0.595829
\(22\) −4.82094 −1.02783
\(23\) 3.20197 0.667657 0.333829 0.942634i \(-0.391659\pi\)
0.333829 + 0.942634i \(0.391659\pi\)
\(24\) −1.14046 −0.232796
\(25\) −1.38379 −0.276758
\(26\) −2.93868 −0.576323
\(27\) 5.35943 1.03142
\(28\) 2.39414 0.452450
\(29\) −0.604936 −0.112334 −0.0561669 0.998421i \(-0.517888\pi\)
−0.0561669 + 0.998421i \(0.517888\pi\)
\(30\) −2.16874 −0.395957
\(31\) −2.02761 −0.364170 −0.182085 0.983283i \(-0.558285\pi\)
−0.182085 + 0.983283i \(0.558285\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.49810 0.957097
\(34\) −2.32516 −0.398762
\(35\) 4.55278 0.769560
\(36\) −1.69934 −0.283224
\(37\) 3.52215 0.579037 0.289519 0.957172i \(-0.406505\pi\)
0.289519 + 0.957172i \(0.406505\pi\)
\(38\) 1.00000 0.162221
\(39\) 3.35146 0.536663
\(40\) 1.90163 0.300675
\(41\) 7.60182 1.18721 0.593603 0.804758i \(-0.297705\pi\)
0.593603 + 0.804758i \(0.297705\pi\)
\(42\) −2.73043 −0.421315
\(43\) −3.42519 −0.522337 −0.261168 0.965293i \(-0.584108\pi\)
−0.261168 + 0.965293i \(0.584108\pi\)
\(44\) −4.82094 −0.726783
\(45\) −3.23153 −0.481728
\(46\) 3.20197 0.472105
\(47\) 5.77575 0.842480 0.421240 0.906949i \(-0.361595\pi\)
0.421240 + 0.906949i \(0.361595\pi\)
\(48\) −1.14046 −0.164612
\(49\) −1.26809 −0.181155
\(50\) −1.38379 −0.195697
\(51\) 2.65176 0.371321
\(52\) −2.93868 −0.407522
\(53\) 6.56721 0.902075 0.451038 0.892505i \(-0.351054\pi\)
0.451038 + 0.892505i \(0.351054\pi\)
\(54\) 5.35943 0.729326
\(55\) −9.16766 −1.23617
\(56\) 2.39414 0.319931
\(57\) −1.14046 −0.151058
\(58\) −0.604936 −0.0794320
\(59\) −8.44960 −1.10004 −0.550022 0.835150i \(-0.685381\pi\)
−0.550022 + 0.835150i \(0.685381\pi\)
\(60\) −2.16874 −0.279984
\(61\) −4.08156 −0.522590 −0.261295 0.965259i \(-0.584150\pi\)
−0.261295 + 0.965259i \(0.584150\pi\)
\(62\) −2.02761 −0.257507
\(63\) −4.06847 −0.512579
\(64\) 1.00000 0.125000
\(65\) −5.58830 −0.693143
\(66\) 5.49810 0.676770
\(67\) −4.70179 −0.574415 −0.287207 0.957868i \(-0.592727\pi\)
−0.287207 + 0.957868i \(0.592727\pi\)
\(68\) −2.32516 −0.281967
\(69\) −3.65173 −0.439617
\(70\) 4.55278 0.544161
\(71\) −2.73075 −0.324080 −0.162040 0.986784i \(-0.551807\pi\)
−0.162040 + 0.986784i \(0.551807\pi\)
\(72\) −1.69934 −0.200269
\(73\) 9.55631 1.11848 0.559241 0.829005i \(-0.311093\pi\)
0.559241 + 0.829005i \(0.311093\pi\)
\(74\) 3.52215 0.409441
\(75\) 1.57816 0.182230
\(76\) 1.00000 0.114708
\(77\) −11.5420 −1.31533
\(78\) 3.35146 0.379478
\(79\) −15.4282 −1.73581 −0.867905 0.496729i \(-0.834534\pi\)
−0.867905 + 0.496729i \(0.834534\pi\)
\(80\) 1.90163 0.212609
\(81\) −1.01421 −0.112690
\(82\) 7.60182 0.839481
\(83\) −3.58775 −0.393807 −0.196904 0.980423i \(-0.563089\pi\)
−0.196904 + 0.980423i \(0.563089\pi\)
\(84\) −2.73043 −0.297915
\(85\) −4.42161 −0.479590
\(86\) −3.42519 −0.369348
\(87\) 0.689908 0.0739659
\(88\) −4.82094 −0.513913
\(89\) −15.9989 −1.69588 −0.847942 0.530088i \(-0.822159\pi\)
−0.847942 + 0.530088i \(0.822159\pi\)
\(90\) −3.23153 −0.340633
\(91\) −7.03562 −0.737534
\(92\) 3.20197 0.333829
\(93\) 2.31242 0.239787
\(94\) 5.77575 0.595723
\(95\) 1.90163 0.195104
\(96\) −1.14046 −0.116398
\(97\) −4.53892 −0.460857 −0.230429 0.973089i \(-0.574013\pi\)
−0.230429 + 0.973089i \(0.574013\pi\)
\(98\) −1.26809 −0.128096
\(99\) 8.19242 0.823369
\(100\) −1.38379 −0.138379
\(101\) −6.86289 −0.682883 −0.341442 0.939903i \(-0.610915\pi\)
−0.341442 + 0.939903i \(0.610915\pi\)
\(102\) 2.65176 0.262564
\(103\) −2.54820 −0.251082 −0.125541 0.992088i \(-0.540067\pi\)
−0.125541 + 0.992088i \(0.540067\pi\)
\(104\) −2.93868 −0.288162
\(105\) −5.19228 −0.506715
\(106\) 6.56721 0.637863
\(107\) −12.0545 −1.16535 −0.582675 0.812705i \(-0.697994\pi\)
−0.582675 + 0.812705i \(0.697994\pi\)
\(108\) 5.35943 0.515711
\(109\) −9.42618 −0.902865 −0.451432 0.892305i \(-0.649087\pi\)
−0.451432 + 0.892305i \(0.649087\pi\)
\(110\) −9.16766 −0.874102
\(111\) −4.01688 −0.381265
\(112\) 2.39414 0.226225
\(113\) −7.92859 −0.745859 −0.372930 0.927860i \(-0.621647\pi\)
−0.372930 + 0.927860i \(0.621647\pi\)
\(114\) −1.14046 −0.106814
\(115\) 6.08898 0.567800
\(116\) −0.604936 −0.0561669
\(117\) 4.99383 0.461680
\(118\) −8.44960 −0.777849
\(119\) −5.56676 −0.510304
\(120\) −2.16874 −0.197978
\(121\) 12.2414 1.11286
\(122\) −4.08156 −0.369527
\(123\) −8.66960 −0.781712
\(124\) −2.02761 −0.182085
\(125\) −12.1396 −1.08580
\(126\) −4.06847 −0.362448
\(127\) 13.0827 1.16090 0.580451 0.814295i \(-0.302876\pi\)
0.580451 + 0.814295i \(0.302876\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.90630 0.343931
\(130\) −5.58830 −0.490126
\(131\) −19.5141 −1.70495 −0.852475 0.522767i \(-0.824900\pi\)
−0.852475 + 0.522767i \(0.824900\pi\)
\(132\) 5.49810 0.478548
\(133\) 2.39414 0.207598
\(134\) −4.70179 −0.406173
\(135\) 10.1917 0.877160
\(136\) −2.32516 −0.199381
\(137\) −23.3673 −1.99641 −0.998203 0.0599229i \(-0.980915\pi\)
−0.998203 + 0.0599229i \(0.980915\pi\)
\(138\) −3.65173 −0.310856
\(139\) −11.4619 −0.972187 −0.486093 0.873907i \(-0.661579\pi\)
−0.486093 + 0.873907i \(0.661579\pi\)
\(140\) 4.55278 0.384780
\(141\) −6.58703 −0.554728
\(142\) −2.73075 −0.229159
\(143\) 14.1672 1.18472
\(144\) −1.69934 −0.141612
\(145\) −1.15037 −0.0955328
\(146\) 9.55631 0.790886
\(147\) 1.44621 0.119281
\(148\) 3.52215 0.289519
\(149\) 9.50817 0.778939 0.389470 0.921039i \(-0.372658\pi\)
0.389470 + 0.921039i \(0.372658\pi\)
\(150\) 1.57816 0.128856
\(151\) −7.87999 −0.641264 −0.320632 0.947204i \(-0.603895\pi\)
−0.320632 + 0.947204i \(0.603895\pi\)
\(152\) 1.00000 0.0811107
\(153\) 3.95124 0.319439
\(154\) −11.5420 −0.930081
\(155\) −3.85578 −0.309704
\(156\) 3.35146 0.268332
\(157\) −0.647215 −0.0516533 −0.0258267 0.999666i \(-0.508222\pi\)
−0.0258267 + 0.999666i \(0.508222\pi\)
\(158\) −15.4282 −1.22740
\(159\) −7.48966 −0.593969
\(160\) 1.90163 0.150337
\(161\) 7.66598 0.604164
\(162\) −1.01421 −0.0796838
\(163\) 10.3531 0.810919 0.405459 0.914113i \(-0.367112\pi\)
0.405459 + 0.914113i \(0.367112\pi\)
\(164\) 7.60182 0.593603
\(165\) 10.4554 0.813950
\(166\) −3.58775 −0.278464
\(167\) 12.9384 1.00120 0.500602 0.865677i \(-0.333112\pi\)
0.500602 + 0.865677i \(0.333112\pi\)
\(168\) −2.73043 −0.210657
\(169\) −4.36414 −0.335703
\(170\) −4.42161 −0.339122
\(171\) −1.69934 −0.129952
\(172\) −3.42519 −0.261168
\(173\) −20.1901 −1.53503 −0.767514 0.641032i \(-0.778507\pi\)
−0.767514 + 0.641032i \(0.778507\pi\)
\(174\) 0.689908 0.0523018
\(175\) −3.31298 −0.250438
\(176\) −4.82094 −0.363392
\(177\) 9.63647 0.724321
\(178\) −15.9989 −1.19917
\(179\) 4.10847 0.307082 0.153541 0.988142i \(-0.450932\pi\)
0.153541 + 0.988142i \(0.450932\pi\)
\(180\) −3.23153 −0.240864
\(181\) −7.52973 −0.559681 −0.279840 0.960047i \(-0.590282\pi\)
−0.279840 + 0.960047i \(0.590282\pi\)
\(182\) −7.03562 −0.521515
\(183\) 4.65487 0.344098
\(184\) 3.20197 0.236053
\(185\) 6.69783 0.492434
\(186\) 2.31242 0.169555
\(187\) 11.2095 0.819716
\(188\) 5.77575 0.421240
\(189\) 12.8312 0.933335
\(190\) 1.90163 0.137959
\(191\) −12.1894 −0.881997 −0.440998 0.897508i \(-0.645376\pi\)
−0.440998 + 0.897508i \(0.645376\pi\)
\(192\) −1.14046 −0.0823059
\(193\) 19.5976 1.41067 0.705334 0.708875i \(-0.250797\pi\)
0.705334 + 0.708875i \(0.250797\pi\)
\(194\) −4.53892 −0.325875
\(195\) 6.37325 0.456398
\(196\) −1.26809 −0.0905776
\(197\) 8.20442 0.584541 0.292270 0.956336i \(-0.405589\pi\)
0.292270 + 0.956336i \(0.405589\pi\)
\(198\) 8.19242 0.582210
\(199\) 6.16300 0.436883 0.218442 0.975850i \(-0.429903\pi\)
0.218442 + 0.975850i \(0.429903\pi\)
\(200\) −1.38379 −0.0978486
\(201\) 5.36222 0.378222
\(202\) −6.86289 −0.482871
\(203\) −1.44830 −0.101651
\(204\) 2.65176 0.185660
\(205\) 14.4559 1.00964
\(206\) −2.54820 −0.177542
\(207\) −5.44125 −0.378193
\(208\) −2.93868 −0.203761
\(209\) −4.82094 −0.333471
\(210\) −5.19228 −0.358302
\(211\) −1.00000 −0.0688428
\(212\) 6.56721 0.451038
\(213\) 3.11432 0.213390
\(214\) −12.0545 −0.824027
\(215\) −6.51346 −0.444214
\(216\) 5.35943 0.364663
\(217\) −4.85439 −0.329538
\(218\) −9.42618 −0.638422
\(219\) −10.8986 −0.736461
\(220\) −9.16766 −0.618083
\(221\) 6.83291 0.459631
\(222\) −4.01688 −0.269595
\(223\) −1.96378 −0.131505 −0.0657523 0.997836i \(-0.520945\pi\)
−0.0657523 + 0.997836i \(0.520945\pi\)
\(224\) 2.39414 0.159965
\(225\) 2.35153 0.156769
\(226\) −7.92859 −0.527402
\(227\) 4.30234 0.285556 0.142778 0.989755i \(-0.454396\pi\)
0.142778 + 0.989755i \(0.454396\pi\)
\(228\) −1.14046 −0.0755291
\(229\) 0.785254 0.0518910 0.0259455 0.999663i \(-0.491740\pi\)
0.0259455 + 0.999663i \(0.491740\pi\)
\(230\) 6.08898 0.401495
\(231\) 13.1632 0.866077
\(232\) −0.604936 −0.0397160
\(233\) −1.33349 −0.0873598 −0.0436799 0.999046i \(-0.513908\pi\)
−0.0436799 + 0.999046i \(0.513908\pi\)
\(234\) 4.99383 0.326457
\(235\) 10.9834 0.716476
\(236\) −8.44960 −0.550022
\(237\) 17.5953 1.14294
\(238\) −5.56676 −0.360840
\(239\) 0.532759 0.0344613 0.0172307 0.999852i \(-0.494515\pi\)
0.0172307 + 0.999852i \(0.494515\pi\)
\(240\) −2.16874 −0.139992
\(241\) 7.29043 0.469618 0.234809 0.972042i \(-0.424554\pi\)
0.234809 + 0.972042i \(0.424554\pi\)
\(242\) 12.2414 0.786908
\(243\) −14.9216 −0.957222
\(244\) −4.08156 −0.261295
\(245\) −2.41144 −0.154061
\(246\) −8.66960 −0.552754
\(247\) −2.93868 −0.186984
\(248\) −2.02761 −0.128754
\(249\) 4.09170 0.259301
\(250\) −12.1396 −0.767778
\(251\) 6.16285 0.388996 0.194498 0.980903i \(-0.437692\pi\)
0.194498 + 0.980903i \(0.437692\pi\)
\(252\) −4.06847 −0.256289
\(253\) −15.4365 −0.970485
\(254\) 13.0827 0.820882
\(255\) 5.04268 0.315785
\(256\) 1.00000 0.0625000
\(257\) −1.07167 −0.0668489 −0.0334245 0.999441i \(-0.510641\pi\)
−0.0334245 + 0.999441i \(0.510641\pi\)
\(258\) 3.90630 0.243196
\(259\) 8.43251 0.523971
\(260\) −5.58830 −0.346572
\(261\) 1.02799 0.0636312
\(262\) −19.5141 −1.20558
\(263\) 21.6730 1.33641 0.668207 0.743976i \(-0.267062\pi\)
0.668207 + 0.743976i \(0.267062\pi\)
\(264\) 5.49810 0.338385
\(265\) 12.4884 0.767158
\(266\) 2.39414 0.146794
\(267\) 18.2462 1.11665
\(268\) −4.70179 −0.287207
\(269\) −1.69256 −0.103197 −0.0515985 0.998668i \(-0.516432\pi\)
−0.0515985 + 0.998668i \(0.516432\pi\)
\(270\) 10.1917 0.620246
\(271\) −9.57448 −0.581608 −0.290804 0.956783i \(-0.593923\pi\)
−0.290804 + 0.956783i \(0.593923\pi\)
\(272\) −2.32516 −0.140984
\(273\) 8.02387 0.485627
\(274\) −23.3673 −1.41167
\(275\) 6.67115 0.402286
\(276\) −3.65173 −0.219809
\(277\) 3.19515 0.191978 0.0959889 0.995382i \(-0.469399\pi\)
0.0959889 + 0.995382i \(0.469399\pi\)
\(278\) −11.4619 −0.687440
\(279\) 3.44561 0.206283
\(280\) 4.55278 0.272081
\(281\) −15.6841 −0.935637 −0.467819 0.883825i \(-0.654960\pi\)
−0.467819 + 0.883825i \(0.654960\pi\)
\(282\) −6.58703 −0.392252
\(283\) −14.9308 −0.887542 −0.443771 0.896140i \(-0.646360\pi\)
−0.443771 + 0.896140i \(0.646360\pi\)
\(284\) −2.73075 −0.162040
\(285\) −2.16874 −0.128465
\(286\) 14.1672 0.837724
\(287\) 18.1998 1.07430
\(288\) −1.69934 −0.100135
\(289\) −11.5936 −0.681978
\(290\) −1.15037 −0.0675519
\(291\) 5.17647 0.303450
\(292\) 9.55631 0.559241
\(293\) 2.03761 0.119038 0.0595191 0.998227i \(-0.481043\pi\)
0.0595191 + 0.998227i \(0.481043\pi\)
\(294\) 1.44621 0.0843445
\(295\) −16.0681 −0.935518
\(296\) 3.52215 0.204721
\(297\) −25.8375 −1.49924
\(298\) 9.50817 0.550793
\(299\) −9.40958 −0.544170
\(300\) 1.57816 0.0911151
\(301\) −8.20039 −0.472663
\(302\) −7.87999 −0.453442
\(303\) 7.82688 0.449642
\(304\) 1.00000 0.0573539
\(305\) −7.76163 −0.444430
\(306\) 3.95124 0.225878
\(307\) −1.06385 −0.0607171 −0.0303585 0.999539i \(-0.509665\pi\)
−0.0303585 + 0.999539i \(0.509665\pi\)
\(308\) −11.5420 −0.657667
\(309\) 2.90613 0.165324
\(310\) −3.85578 −0.218994
\(311\) 18.1752 1.03062 0.515309 0.857004i \(-0.327677\pi\)
0.515309 + 0.857004i \(0.327677\pi\)
\(312\) 3.35146 0.189739
\(313\) −7.37917 −0.417095 −0.208548 0.978012i \(-0.566874\pi\)
−0.208548 + 0.978012i \(0.566874\pi\)
\(314\) −0.647215 −0.0365244
\(315\) −7.73673 −0.435916
\(316\) −15.4282 −0.867905
\(317\) 8.65810 0.486287 0.243144 0.969990i \(-0.421821\pi\)
0.243144 + 0.969990i \(0.421821\pi\)
\(318\) −7.48966 −0.419999
\(319\) 2.91636 0.163285
\(320\) 1.90163 0.106305
\(321\) 13.7477 0.767322
\(322\) 7.66598 0.427208
\(323\) −2.32516 −0.129375
\(324\) −1.01421 −0.0563450
\(325\) 4.06651 0.225570
\(326\) 10.3531 0.573406
\(327\) 10.7502 0.594489
\(328\) 7.60182 0.419740
\(329\) 13.8280 0.762360
\(330\) 10.4554 0.575550
\(331\) −10.5891 −0.582029 −0.291014 0.956719i \(-0.593993\pi\)
−0.291014 + 0.956719i \(0.593993\pi\)
\(332\) −3.58775 −0.196904
\(333\) −5.98533 −0.327994
\(334\) 12.9384 0.707959
\(335\) −8.94108 −0.488504
\(336\) −2.73043 −0.148957
\(337\) 24.4995 1.33457 0.667285 0.744802i \(-0.267456\pi\)
0.667285 + 0.744802i \(0.267456\pi\)
\(338\) −4.36414 −0.237378
\(339\) 9.04227 0.491109
\(340\) −4.42161 −0.239795
\(341\) 9.77500 0.529346
\(342\) −1.69934 −0.0918899
\(343\) −19.7950 −1.06883
\(344\) −3.42519 −0.184674
\(345\) −6.94426 −0.373867
\(346\) −20.1901 −1.08543
\(347\) −16.7123 −0.897163 −0.448581 0.893742i \(-0.648071\pi\)
−0.448581 + 0.893742i \(0.648071\pi\)
\(348\) 0.689908 0.0369830
\(349\) −22.3433 −1.19601 −0.598004 0.801493i \(-0.704039\pi\)
−0.598004 + 0.801493i \(0.704039\pi\)
\(350\) −3.31298 −0.177086
\(351\) −15.7497 −0.840655
\(352\) −4.82094 −0.256957
\(353\) 18.0206 0.959140 0.479570 0.877503i \(-0.340793\pi\)
0.479570 + 0.877503i \(0.340793\pi\)
\(354\) 9.63647 0.512172
\(355\) −5.19288 −0.275610
\(356\) −15.9989 −0.847942
\(357\) 6.34869 0.336009
\(358\) 4.10847 0.217139
\(359\) −4.74870 −0.250627 −0.125313 0.992117i \(-0.539994\pi\)
−0.125313 + 0.992117i \(0.539994\pi\)
\(360\) −3.23153 −0.170316
\(361\) 1.00000 0.0526316
\(362\) −7.52973 −0.395754
\(363\) −13.9609 −0.732757
\(364\) −7.03562 −0.368767
\(365\) 18.1726 0.951198
\(366\) 4.65487 0.243314
\(367\) −31.3401 −1.63594 −0.817969 0.575262i \(-0.804900\pi\)
−0.817969 + 0.575262i \(0.804900\pi\)
\(368\) 3.20197 0.166914
\(369\) −12.9181 −0.672489
\(370\) 6.69783 0.348204
\(371\) 15.7228 0.816288
\(372\) 2.31242 0.119893
\(373\) 15.4360 0.799244 0.399622 0.916680i \(-0.369141\pi\)
0.399622 + 0.916680i \(0.369141\pi\)
\(374\) 11.2095 0.579627
\(375\) 13.8448 0.714943
\(376\) 5.77575 0.297862
\(377\) 1.77772 0.0915571
\(378\) 12.8312 0.659967
\(379\) 20.4755 1.05175 0.525877 0.850560i \(-0.323737\pi\)
0.525877 + 0.850560i \(0.323737\pi\)
\(380\) 1.90163 0.0975518
\(381\) −14.9204 −0.764393
\(382\) −12.1894 −0.623666
\(383\) 22.8696 1.16858 0.584290 0.811545i \(-0.301373\pi\)
0.584290 + 0.811545i \(0.301373\pi\)
\(384\) −1.14046 −0.0581991
\(385\) −21.9487 −1.11861
\(386\) 19.5976 0.997493
\(387\) 5.82057 0.295876
\(388\) −4.53892 −0.230429
\(389\) 14.4768 0.734005 0.367003 0.930220i \(-0.380384\pi\)
0.367003 + 0.930220i \(0.380384\pi\)
\(390\) 6.37325 0.322722
\(391\) −7.44510 −0.376515
\(392\) −1.26809 −0.0640480
\(393\) 22.2551 1.12262
\(394\) 8.20442 0.413333
\(395\) −29.3388 −1.47620
\(396\) 8.19242 0.411685
\(397\) −5.73317 −0.287739 −0.143870 0.989597i \(-0.545955\pi\)
−0.143870 + 0.989597i \(0.545955\pi\)
\(398\) 6.16300 0.308923
\(399\) −2.73043 −0.136693
\(400\) −1.38379 −0.0691894
\(401\) −37.7760 −1.88644 −0.943220 0.332167i \(-0.892220\pi\)
−0.943220 + 0.332167i \(0.892220\pi\)
\(402\) 5.36222 0.267443
\(403\) 5.95852 0.296815
\(404\) −6.86289 −0.341442
\(405\) −1.92865 −0.0958356
\(406\) −1.44830 −0.0718781
\(407\) −16.9800 −0.841669
\(408\) 2.65176 0.131282
\(409\) −13.0004 −0.642828 −0.321414 0.946939i \(-0.604158\pi\)
−0.321414 + 0.946939i \(0.604158\pi\)
\(410\) 14.4559 0.713925
\(411\) 26.6496 1.31453
\(412\) −2.54820 −0.125541
\(413\) −20.2295 −0.995431
\(414\) −5.44125 −0.267423
\(415\) −6.82259 −0.334908
\(416\) −2.93868 −0.144081
\(417\) 13.0719 0.640134
\(418\) −4.82094 −0.235800
\(419\) 38.6433 1.88785 0.943925 0.330159i \(-0.107102\pi\)
0.943925 + 0.330159i \(0.107102\pi\)
\(420\) −5.19228 −0.253357
\(421\) −4.82061 −0.234942 −0.117471 0.993076i \(-0.537479\pi\)
−0.117471 + 0.993076i \(0.537479\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −9.81498 −0.477220
\(424\) 6.56721 0.318932
\(425\) 3.21753 0.156073
\(426\) 3.11432 0.150889
\(427\) −9.77183 −0.472892
\(428\) −12.0545 −0.582675
\(429\) −16.1572 −0.780076
\(430\) −6.51346 −0.314107
\(431\) 16.7088 0.804833 0.402416 0.915457i \(-0.368170\pi\)
0.402416 + 0.915457i \(0.368170\pi\)
\(432\) 5.35943 0.257856
\(433\) 14.2112 0.682947 0.341474 0.939891i \(-0.389074\pi\)
0.341474 + 0.939891i \(0.389074\pi\)
\(434\) −4.85439 −0.233018
\(435\) 1.31195 0.0629033
\(436\) −9.42618 −0.451432
\(437\) 3.20197 0.153171
\(438\) −10.8986 −0.520756
\(439\) 23.6895 1.13064 0.565318 0.824873i \(-0.308753\pi\)
0.565318 + 0.824873i \(0.308753\pi\)
\(440\) −9.16766 −0.437051
\(441\) 2.15491 0.102615
\(442\) 6.83291 0.325008
\(443\) 3.91211 0.185870 0.0929350 0.995672i \(-0.470375\pi\)
0.0929350 + 0.995672i \(0.470375\pi\)
\(444\) −4.01688 −0.190633
\(445\) −30.4241 −1.44224
\(446\) −1.96378 −0.0929879
\(447\) −10.8437 −0.512890
\(448\) 2.39414 0.113113
\(449\) 8.41883 0.397309 0.198655 0.980070i \(-0.436343\pi\)
0.198655 + 0.980070i \(0.436343\pi\)
\(450\) 2.35153 0.110852
\(451\) −36.6479 −1.72568
\(452\) −7.92859 −0.372930
\(453\) 8.98684 0.422239
\(454\) 4.30234 0.201919
\(455\) −13.3792 −0.627226
\(456\) −1.14046 −0.0534071
\(457\) −24.5193 −1.14696 −0.573482 0.819218i \(-0.694408\pi\)
−0.573482 + 0.819218i \(0.694408\pi\)
\(458\) 0.785254 0.0366925
\(459\) −12.4615 −0.581655
\(460\) 6.08898 0.283900
\(461\) 22.0623 1.02754 0.513771 0.857927i \(-0.328248\pi\)
0.513771 + 0.857927i \(0.328248\pi\)
\(462\) 13.1632 0.612409
\(463\) 17.4055 0.808903 0.404452 0.914559i \(-0.367462\pi\)
0.404452 + 0.914559i \(0.367462\pi\)
\(464\) −0.604936 −0.0280835
\(465\) 4.39738 0.203924
\(466\) −1.33349 −0.0617727
\(467\) 16.1044 0.745222 0.372611 0.927988i \(-0.378463\pi\)
0.372611 + 0.927988i \(0.378463\pi\)
\(468\) 4.99383 0.230840
\(469\) −11.2567 −0.519788
\(470\) 10.9834 0.506625
\(471\) 0.738125 0.0340110
\(472\) −8.44960 −0.388925
\(473\) 16.5126 0.759251
\(474\) 17.5953 0.808180
\(475\) −1.38379 −0.0634925
\(476\) −5.56676 −0.255152
\(477\) −11.1599 −0.510978
\(478\) 0.532759 0.0243678
\(479\) 0.611032 0.0279188 0.0139594 0.999903i \(-0.495556\pi\)
0.0139594 + 0.999903i \(0.495556\pi\)
\(480\) −2.16874 −0.0989892
\(481\) −10.3505 −0.471941
\(482\) 7.29043 0.332070
\(483\) −8.74277 −0.397810
\(484\) 12.2414 0.556428
\(485\) −8.63136 −0.391930
\(486\) −14.9216 −0.676858
\(487\) 30.5937 1.38633 0.693166 0.720778i \(-0.256215\pi\)
0.693166 + 0.720778i \(0.256215\pi\)
\(488\) −4.08156 −0.184764
\(489\) −11.8074 −0.533947
\(490\) −2.41144 −0.108938
\(491\) 10.4501 0.471608 0.235804 0.971801i \(-0.424228\pi\)
0.235804 + 0.971801i \(0.424228\pi\)
\(492\) −8.66960 −0.390856
\(493\) 1.40657 0.0633489
\(494\) −2.93868 −0.132218
\(495\) 15.5790 0.700223
\(496\) −2.02761 −0.0910426
\(497\) −6.53780 −0.293260
\(498\) 4.09170 0.183354
\(499\) 38.1008 1.70563 0.852813 0.522217i \(-0.174895\pi\)
0.852813 + 0.522217i \(0.174895\pi\)
\(500\) −12.1396 −0.542901
\(501\) −14.7558 −0.659240
\(502\) 6.16285 0.275061
\(503\) 22.8274 1.01782 0.508912 0.860819i \(-0.330048\pi\)
0.508912 + 0.860819i \(0.330048\pi\)
\(504\) −4.06847 −0.181224
\(505\) −13.0507 −0.580749
\(506\) −15.4365 −0.686236
\(507\) 4.97714 0.221043
\(508\) 13.0827 0.580451
\(509\) −5.93351 −0.262998 −0.131499 0.991316i \(-0.541979\pi\)
−0.131499 + 0.991316i \(0.541979\pi\)
\(510\) 5.04268 0.223294
\(511\) 22.8792 1.01211
\(512\) 1.00000 0.0441942
\(513\) 5.35943 0.236625
\(514\) −1.07167 −0.0472693
\(515\) −4.84574 −0.213529
\(516\) 3.90630 0.171965
\(517\) −27.8445 −1.22460
\(518\) 8.43251 0.370503
\(519\) 23.0261 1.01074
\(520\) −5.58830 −0.245063
\(521\) −39.8184 −1.74448 −0.872238 0.489082i \(-0.837332\pi\)
−0.872238 + 0.489082i \(0.837332\pi\)
\(522\) 1.02799 0.0449941
\(523\) −32.2310 −1.40936 −0.704681 0.709524i \(-0.748910\pi\)
−0.704681 + 0.709524i \(0.748910\pi\)
\(524\) −19.5141 −0.852475
\(525\) 3.77834 0.164900
\(526\) 21.6730 0.944987
\(527\) 4.71453 0.205368
\(528\) 5.49810 0.239274
\(529\) −12.7474 −0.554233
\(530\) 12.4884 0.542462
\(531\) 14.3588 0.623117
\(532\) 2.39414 0.103799
\(533\) −22.3393 −0.967625
\(534\) 18.2462 0.789591
\(535\) −22.9232 −0.991057
\(536\) −4.70179 −0.203086
\(537\) −4.68556 −0.202197
\(538\) −1.69256 −0.0729714
\(539\) 6.11336 0.263321
\(540\) 10.1917 0.438580
\(541\) −41.3741 −1.77881 −0.889407 0.457117i \(-0.848882\pi\)
−0.889407 + 0.457117i \(0.848882\pi\)
\(542\) −9.57448 −0.411259
\(543\) 8.58739 0.368520
\(544\) −2.32516 −0.0996905
\(545\) −17.9252 −0.767829
\(546\) 8.02387 0.343390
\(547\) 25.1939 1.07721 0.538606 0.842558i \(-0.318951\pi\)
0.538606 + 0.842558i \(0.318951\pi\)
\(548\) −23.3673 −0.998203
\(549\) 6.93597 0.296020
\(550\) 6.67115 0.284459
\(551\) −0.604936 −0.0257712
\(552\) −3.65173 −0.155428
\(553\) −36.9374 −1.57074
\(554\) 3.19515 0.135749
\(555\) −7.63863 −0.324242
\(556\) −11.4619 −0.486093
\(557\) −14.3011 −0.605957 −0.302978 0.952997i \(-0.597981\pi\)
−0.302978 + 0.952997i \(0.597981\pi\)
\(558\) 3.44561 0.145864
\(559\) 10.0655 0.425727
\(560\) 4.55278 0.192390
\(561\) −12.7840 −0.539740
\(562\) −15.6841 −0.661595
\(563\) 1.56987 0.0661620 0.0330810 0.999453i \(-0.489468\pi\)
0.0330810 + 0.999453i \(0.489468\pi\)
\(564\) −6.58703 −0.277364
\(565\) −15.0773 −0.634306
\(566\) −14.9308 −0.627587
\(567\) −2.42816 −0.101973
\(568\) −2.73075 −0.114580
\(569\) −32.7189 −1.37165 −0.685825 0.727767i \(-0.740558\pi\)
−0.685825 + 0.727767i \(0.740558\pi\)
\(570\) −2.16874 −0.0908387
\(571\) −23.9621 −1.00278 −0.501390 0.865221i \(-0.667178\pi\)
−0.501390 + 0.865221i \(0.667178\pi\)
\(572\) 14.1672 0.592361
\(573\) 13.9016 0.580748
\(574\) 18.1998 0.759647
\(575\) −4.43085 −0.184779
\(576\) −1.69934 −0.0708059
\(577\) 34.8472 1.45071 0.725354 0.688376i \(-0.241676\pi\)
0.725354 + 0.688376i \(0.241676\pi\)
\(578\) −11.5936 −0.482231
\(579\) −22.3504 −0.928851
\(580\) −1.15037 −0.0477664
\(581\) −8.58959 −0.356356
\(582\) 5.17647 0.214572
\(583\) −31.6601 −1.31123
\(584\) 9.55631 0.395443
\(585\) 9.49644 0.392629
\(586\) 2.03761 0.0841727
\(587\) 0.683958 0.0282300 0.0141150 0.999900i \(-0.495507\pi\)
0.0141150 + 0.999900i \(0.495507\pi\)
\(588\) 1.44621 0.0596406
\(589\) −2.02761 −0.0835464
\(590\) −16.0681 −0.661511
\(591\) −9.35684 −0.384889
\(592\) 3.52215 0.144759
\(593\) 19.2060 0.788696 0.394348 0.918961i \(-0.370970\pi\)
0.394348 + 0.918961i \(0.370970\pi\)
\(594\) −25.8375 −1.06012
\(595\) −10.5859 −0.433982
\(596\) 9.50817 0.389470
\(597\) −7.02868 −0.287665
\(598\) −9.40958 −0.384787
\(599\) 29.9674 1.22443 0.612217 0.790690i \(-0.290278\pi\)
0.612217 + 0.790690i \(0.290278\pi\)
\(600\) 1.57816 0.0644281
\(601\) −23.4925 −0.958281 −0.479140 0.877738i \(-0.659051\pi\)
−0.479140 + 0.877738i \(0.659051\pi\)
\(602\) −8.20039 −0.334223
\(603\) 7.98995 0.325376
\(604\) −7.87999 −0.320632
\(605\) 23.2787 0.946414
\(606\) 7.82688 0.317945
\(607\) 26.8321 1.08908 0.544541 0.838734i \(-0.316704\pi\)
0.544541 + 0.838734i \(0.316704\pi\)
\(608\) 1.00000 0.0405554
\(609\) 1.65174 0.0669318
\(610\) −7.76163 −0.314259
\(611\) −16.9731 −0.686658
\(612\) 3.95124 0.159720
\(613\) 25.2794 1.02102 0.510512 0.859871i \(-0.329456\pi\)
0.510512 + 0.859871i \(0.329456\pi\)
\(614\) −1.06385 −0.0429334
\(615\) −16.4864 −0.664796
\(616\) −11.5420 −0.465041
\(617\) 35.2161 1.41775 0.708873 0.705336i \(-0.249204\pi\)
0.708873 + 0.705336i \(0.249204\pi\)
\(618\) 2.90613 0.116902
\(619\) 45.6522 1.83492 0.917459 0.397830i \(-0.130237\pi\)
0.917459 + 0.397830i \(0.130237\pi\)
\(620\) −3.85578 −0.154852
\(621\) 17.1607 0.688637
\(622\) 18.1752 0.728757
\(623\) −38.3037 −1.53461
\(624\) 3.35146 0.134166
\(625\) −16.1662 −0.646648
\(626\) −7.37917 −0.294931
\(627\) 5.49810 0.219573
\(628\) −0.647215 −0.0258267
\(629\) −8.18955 −0.326539
\(630\) −7.73673 −0.308239
\(631\) −26.8790 −1.07004 −0.535019 0.844840i \(-0.679695\pi\)
−0.535019 + 0.844840i \(0.679695\pi\)
\(632\) −15.4282 −0.613702
\(633\) 1.14046 0.0453294
\(634\) 8.65810 0.343857
\(635\) 24.8785 0.987274
\(636\) −7.48966 −0.296984
\(637\) 3.72650 0.147649
\(638\) 2.91636 0.115460
\(639\) 4.64048 0.183574
\(640\) 1.90163 0.0751687
\(641\) −21.3245 −0.842268 −0.421134 0.906998i \(-0.638368\pi\)
−0.421134 + 0.906998i \(0.638368\pi\)
\(642\) 13.7477 0.542578
\(643\) −9.78045 −0.385703 −0.192852 0.981228i \(-0.561774\pi\)
−0.192852 + 0.981228i \(0.561774\pi\)
\(644\) 7.66598 0.302082
\(645\) 7.42836 0.292491
\(646\) −2.32516 −0.0914822
\(647\) −43.7024 −1.71812 −0.859060 0.511875i \(-0.828951\pi\)
−0.859060 + 0.511875i \(0.828951\pi\)
\(648\) −1.01421 −0.0398419
\(649\) 40.7350 1.59899
\(650\) 4.06651 0.159502
\(651\) 5.53626 0.216983
\(652\) 10.3531 0.405459
\(653\) −2.38643 −0.0933881 −0.0466941 0.998909i \(-0.514869\pi\)
−0.0466941 + 0.998909i \(0.514869\pi\)
\(654\) 10.7502 0.420367
\(655\) −37.1086 −1.44995
\(656\) 7.60182 0.296801
\(657\) −16.2394 −0.633561
\(658\) 13.8280 0.539070
\(659\) 38.4464 1.49766 0.748831 0.662762i \(-0.230616\pi\)
0.748831 + 0.662762i \(0.230616\pi\)
\(660\) 10.4554 0.406975
\(661\) −26.1296 −1.01632 −0.508161 0.861262i \(-0.669675\pi\)
−0.508161 + 0.861262i \(0.669675\pi\)
\(662\) −10.5891 −0.411557
\(663\) −7.79269 −0.302643
\(664\) −3.58775 −0.139232
\(665\) 4.55278 0.176549
\(666\) −5.98533 −0.231927
\(667\) −1.93699 −0.0750005
\(668\) 12.9384 0.500602
\(669\) 2.23962 0.0865889
\(670\) −8.94108 −0.345424
\(671\) 19.6769 0.759620
\(672\) −2.73043 −0.105329
\(673\) 44.6219 1.72005 0.860025 0.510252i \(-0.170448\pi\)
0.860025 + 0.510252i \(0.170448\pi\)
\(674\) 24.4995 0.943684
\(675\) −7.41631 −0.285454
\(676\) −4.36414 −0.167852
\(677\) −17.0043 −0.653528 −0.326764 0.945106i \(-0.605958\pi\)
−0.326764 + 0.945106i \(0.605958\pi\)
\(678\) 9.04227 0.347266
\(679\) −10.8668 −0.417030
\(680\) −4.42161 −0.169561
\(681\) −4.90666 −0.188024
\(682\) 9.77500 0.374304
\(683\) 13.4028 0.512843 0.256422 0.966565i \(-0.417456\pi\)
0.256422 + 0.966565i \(0.417456\pi\)
\(684\) −1.69934 −0.0649760
\(685\) −44.4361 −1.69782
\(686\) −19.7950 −0.755775
\(687\) −0.895553 −0.0341675
\(688\) −3.42519 −0.130584
\(689\) −19.2989 −0.735231
\(690\) −6.94426 −0.264364
\(691\) 11.2690 0.428695 0.214347 0.976757i \(-0.431238\pi\)
0.214347 + 0.976757i \(0.431238\pi\)
\(692\) −20.1901 −0.767514
\(693\) 19.6138 0.745067
\(694\) −16.7123 −0.634390
\(695\) −21.7964 −0.826783
\(696\) 0.689908 0.0261509
\(697\) −17.6755 −0.669506
\(698\) −22.3433 −0.845706
\(699\) 1.52080 0.0575218
\(700\) −3.31298 −0.125219
\(701\) 20.6079 0.778349 0.389175 0.921164i \(-0.372760\pi\)
0.389175 + 0.921164i \(0.372760\pi\)
\(702\) −15.7497 −0.594433
\(703\) 3.52215 0.132840
\(704\) −4.82094 −0.181696
\(705\) −12.5261 −0.471761
\(706\) 18.0206 0.678215
\(707\) −16.4307 −0.617941
\(708\) 9.63647 0.362161
\(709\) −7.23701 −0.271792 −0.135896 0.990723i \(-0.543391\pi\)
−0.135896 + 0.990723i \(0.543391\pi\)
\(710\) −5.19288 −0.194885
\(711\) 26.2178 0.983246
\(712\) −15.9989 −0.599586
\(713\) −6.49236 −0.243141
\(714\) 6.34869 0.237594
\(715\) 26.9408 1.00753
\(716\) 4.10847 0.153541
\(717\) −0.607593 −0.0226910
\(718\) −4.74870 −0.177220
\(719\) −10.4831 −0.390953 −0.195476 0.980708i \(-0.562625\pi\)
−0.195476 + 0.980708i \(0.562625\pi\)
\(720\) −3.23153 −0.120432
\(721\) −6.10075 −0.227204
\(722\) 1.00000 0.0372161
\(723\) −8.31448 −0.309219
\(724\) −7.52973 −0.279840
\(725\) 0.837103 0.0310892
\(726\) −13.9609 −0.518138
\(727\) 21.1004 0.782569 0.391285 0.920270i \(-0.372031\pi\)
0.391285 + 0.920270i \(0.372031\pi\)
\(728\) −7.03562 −0.260758
\(729\) 20.0602 0.742970
\(730\) 18.1726 0.672598
\(731\) 7.96412 0.294564
\(732\) 4.65487 0.172049
\(733\) −39.4051 −1.45546 −0.727729 0.685864i \(-0.759424\pi\)
−0.727729 + 0.685864i \(0.759424\pi\)
\(734\) −31.3401 −1.15678
\(735\) 2.75016 0.101441
\(736\) 3.20197 0.118026
\(737\) 22.6670 0.834951
\(738\) −12.9181 −0.475522
\(739\) −36.8284 −1.35476 −0.677378 0.735635i \(-0.736884\pi\)
−0.677378 + 0.735635i \(0.736884\pi\)
\(740\) 6.69783 0.246217
\(741\) 3.35146 0.123119
\(742\) 15.7228 0.577203
\(743\) 40.8084 1.49711 0.748557 0.663070i \(-0.230747\pi\)
0.748557 + 0.663070i \(0.230747\pi\)
\(744\) 2.31242 0.0847774
\(745\) 18.0811 0.662439
\(746\) 15.4360 0.565151
\(747\) 6.09682 0.223071
\(748\) 11.2095 0.409858
\(749\) −28.8601 −1.05453
\(750\) 13.8448 0.505541
\(751\) −7.84625 −0.286314 −0.143157 0.989700i \(-0.545725\pi\)
−0.143157 + 0.989700i \(0.545725\pi\)
\(752\) 5.77575 0.210620
\(753\) −7.02851 −0.256133
\(754\) 1.77772 0.0647406
\(755\) −14.9849 −0.545355
\(756\) 12.8312 0.466667
\(757\) −50.0526 −1.81919 −0.909597 0.415491i \(-0.863610\pi\)
−0.909597 + 0.415491i \(0.863610\pi\)
\(758\) 20.4755 0.743703
\(759\) 17.6048 0.639013
\(760\) 1.90163 0.0689795
\(761\) −51.7645 −1.87646 −0.938231 0.346010i \(-0.887536\pi\)
−0.938231 + 0.346010i \(0.887536\pi\)
\(762\) −14.9204 −0.540507
\(763\) −22.5676 −0.817003
\(764\) −12.1894 −0.440998
\(765\) 7.51382 0.271663
\(766\) 22.8696 0.826311
\(767\) 24.8307 0.896585
\(768\) −1.14046 −0.0411529
\(769\) −10.7044 −0.386012 −0.193006 0.981198i \(-0.561824\pi\)
−0.193006 + 0.981198i \(0.561824\pi\)
\(770\) −21.9487 −0.790975
\(771\) 1.22220 0.0440165
\(772\) 19.5976 0.705334
\(773\) −38.8711 −1.39810 −0.699049 0.715074i \(-0.746393\pi\)
−0.699049 + 0.715074i \(0.746393\pi\)
\(774\) 5.82057 0.209216
\(775\) 2.80579 0.100787
\(776\) −4.53892 −0.162938
\(777\) −9.61698 −0.345007
\(778\) 14.4768 0.519020
\(779\) 7.60182 0.272364
\(780\) 6.37325 0.228199
\(781\) 13.1648 0.471072
\(782\) −7.44510 −0.266236
\(783\) −3.24211 −0.115864
\(784\) −1.26809 −0.0452888
\(785\) −1.23077 −0.0439279
\(786\) 22.2551 0.793812
\(787\) 38.3829 1.36820 0.684102 0.729387i \(-0.260194\pi\)
0.684102 + 0.729387i \(0.260194\pi\)
\(788\) 8.20442 0.292270
\(789\) −24.7173 −0.879958
\(790\) −29.3388 −1.04383
\(791\) −18.9822 −0.674928
\(792\) 8.19242 0.291105
\(793\) 11.9944 0.425934
\(794\) −5.73317 −0.203462
\(795\) −14.2426 −0.505133
\(796\) 6.16300 0.218442
\(797\) 53.6289 1.89963 0.949816 0.312808i \(-0.101270\pi\)
0.949816 + 0.312808i \(0.101270\pi\)
\(798\) −2.73043 −0.0966562
\(799\) −13.4295 −0.475103
\(800\) −1.38379 −0.0489243
\(801\) 27.1877 0.960630
\(802\) −37.7760 −1.33392
\(803\) −46.0704 −1.62579
\(804\) 5.36222 0.189111
\(805\) 14.5779 0.513803
\(806\) 5.95852 0.209880
\(807\) 1.93030 0.0679498
\(808\) −6.86289 −0.241436
\(809\) −20.9760 −0.737476 −0.368738 0.929533i \(-0.620210\pi\)
−0.368738 + 0.929533i \(0.620210\pi\)
\(810\) −1.92865 −0.0677660
\(811\) −2.41901 −0.0849429 −0.0424714 0.999098i \(-0.513523\pi\)
−0.0424714 + 0.999098i \(0.513523\pi\)
\(812\) −1.44830 −0.0508255
\(813\) 10.9194 0.382958
\(814\) −16.9800 −0.595150
\(815\) 19.6878 0.689635
\(816\) 2.65176 0.0928302
\(817\) −3.42519 −0.119832
\(818\) −13.0004 −0.454548
\(819\) 11.9559 0.417774
\(820\) 14.4559 0.504821
\(821\) −36.0004 −1.25642 −0.628211 0.778043i \(-0.716213\pi\)
−0.628211 + 0.778043i \(0.716213\pi\)
\(822\) 26.6496 0.929511
\(823\) −16.5293 −0.576176 −0.288088 0.957604i \(-0.593020\pi\)
−0.288088 + 0.957604i \(0.593020\pi\)
\(824\) −2.54820 −0.0887708
\(825\) −7.60821 −0.264884
\(826\) −20.2295 −0.703876
\(827\) −36.9663 −1.28544 −0.642722 0.766099i \(-0.722195\pi\)
−0.642722 + 0.766099i \(0.722195\pi\)
\(828\) −5.44125 −0.189096
\(829\) 29.6178 1.02867 0.514335 0.857589i \(-0.328039\pi\)
0.514335 + 0.857589i \(0.328039\pi\)
\(830\) −6.82259 −0.236816
\(831\) −3.64395 −0.126407
\(832\) −2.93868 −0.101881
\(833\) 2.94850 0.102160
\(834\) 13.0719 0.452643
\(835\) 24.6041 0.851461
\(836\) −4.82094 −0.166736
\(837\) −10.8669 −0.375613
\(838\) 38.6433 1.33491
\(839\) 12.7919 0.441625 0.220813 0.975316i \(-0.429129\pi\)
0.220813 + 0.975316i \(0.429129\pi\)
\(840\) −5.19228 −0.179151
\(841\) −28.6341 −0.987381
\(842\) −4.82061 −0.166129
\(843\) 17.8872 0.616068
\(844\) −1.00000 −0.0344214
\(845\) −8.29900 −0.285494
\(846\) −9.81498 −0.337446
\(847\) 29.3077 1.00702
\(848\) 6.56721 0.225519
\(849\) 17.0280 0.584399
\(850\) 3.21753 0.110360
\(851\) 11.2778 0.386598
\(852\) 3.11432 0.106695
\(853\) −28.1712 −0.964564 −0.482282 0.876016i \(-0.660192\pi\)
−0.482282 + 0.876016i \(0.660192\pi\)
\(854\) −9.77183 −0.334385
\(855\) −3.23153 −0.110516
\(856\) −12.0545 −0.412014
\(857\) 23.6406 0.807549 0.403775 0.914858i \(-0.367698\pi\)
0.403775 + 0.914858i \(0.367698\pi\)
\(858\) −16.1572 −0.551597
\(859\) 28.4571 0.970943 0.485472 0.874252i \(-0.338648\pi\)
0.485472 + 0.874252i \(0.338648\pi\)
\(860\) −6.51346 −0.222107
\(861\) −20.7563 −0.707371
\(862\) 16.7088 0.569103
\(863\) 44.4196 1.51206 0.756030 0.654537i \(-0.227136\pi\)
0.756030 + 0.654537i \(0.227136\pi\)
\(864\) 5.35943 0.182332
\(865\) −38.3943 −1.30544
\(866\) 14.2112 0.482917
\(867\) 13.2221 0.449046
\(868\) −4.85439 −0.164769
\(869\) 74.3785 2.52312
\(870\) 1.31195 0.0444794
\(871\) 13.8171 0.468174
\(872\) −9.42618 −0.319211
\(873\) 7.71317 0.261051
\(874\) 3.20197 0.108308
\(875\) −29.0640 −0.982542
\(876\) −10.8986 −0.368230
\(877\) −36.0516 −1.21737 −0.608687 0.793410i \(-0.708304\pi\)
−0.608687 + 0.793410i \(0.708304\pi\)
\(878\) 23.6895 0.799481
\(879\) −2.32382 −0.0783804
\(880\) −9.16766 −0.309042
\(881\) 53.9762 1.81851 0.909253 0.416244i \(-0.136654\pi\)
0.909253 + 0.416244i \(0.136654\pi\)
\(882\) 2.15491 0.0725597
\(883\) −43.1784 −1.45307 −0.726534 0.687131i \(-0.758870\pi\)
−0.726534 + 0.687131i \(0.758870\pi\)
\(884\) 6.83291 0.229816
\(885\) 18.3250 0.615989
\(886\) 3.91211 0.131430
\(887\) 30.4025 1.02082 0.510408 0.859932i \(-0.329494\pi\)
0.510408 + 0.859932i \(0.329494\pi\)
\(888\) −4.01688 −0.134798
\(889\) 31.3218 1.05050
\(890\) −30.4241 −1.01982
\(891\) 4.88944 0.163802
\(892\) −1.96378 −0.0657523
\(893\) 5.77575 0.193278
\(894\) −10.8437 −0.362668
\(895\) 7.81281 0.261153
\(896\) 2.39414 0.0799827
\(897\) 10.7313 0.358307
\(898\) 8.41883 0.280940
\(899\) 1.22658 0.0409086
\(900\) 2.35153 0.0783843
\(901\) −15.2698 −0.508711
\(902\) −36.6479 −1.22024
\(903\) 9.35225 0.311223
\(904\) −7.92859 −0.263701
\(905\) −14.3188 −0.475973
\(906\) 8.98684 0.298568
\(907\) 5.61217 0.186349 0.0931745 0.995650i \(-0.470299\pi\)
0.0931745 + 0.995650i \(0.470299\pi\)
\(908\) 4.30234 0.142778
\(909\) 11.6624 0.386817
\(910\) −13.3792 −0.443516
\(911\) −30.4107 −1.00755 −0.503776 0.863834i \(-0.668056\pi\)
−0.503776 + 0.863834i \(0.668056\pi\)
\(912\) −1.14046 −0.0377645
\(913\) 17.2963 0.572425
\(914\) −24.5193 −0.811026
\(915\) 8.85186 0.292634
\(916\) 0.785254 0.0259455
\(917\) −46.7194 −1.54281
\(918\) −12.4615 −0.411292
\(919\) 37.0728 1.22292 0.611460 0.791275i \(-0.290583\pi\)
0.611460 + 0.791275i \(0.290583\pi\)
\(920\) 6.08898 0.200748
\(921\) 1.21328 0.0399790
\(922\) 22.0623 0.726582
\(923\) 8.02480 0.264140
\(924\) 13.1632 0.433039
\(925\) −4.87390 −0.160253
\(926\) 17.4055 0.571981
\(927\) 4.33026 0.142225
\(928\) −0.604936 −0.0198580
\(929\) −37.9929 −1.24651 −0.623253 0.782021i \(-0.714189\pi\)
−0.623253 + 0.782021i \(0.714189\pi\)
\(930\) 4.39738 0.144196
\(931\) −1.26809 −0.0415599
\(932\) −1.33349 −0.0436799
\(933\) −20.7281 −0.678608
\(934\) 16.1044 0.526952
\(935\) 21.3163 0.697117
\(936\) 4.99383 0.163228
\(937\) 44.1192 1.44131 0.720656 0.693293i \(-0.243841\pi\)
0.720656 + 0.693293i \(0.243841\pi\)
\(938\) −11.2567 −0.367546
\(939\) 8.41567 0.274635
\(940\) 10.9834 0.358238
\(941\) −54.7029 −1.78326 −0.891632 0.452760i \(-0.850439\pi\)
−0.891632 + 0.452760i \(0.850439\pi\)
\(942\) 0.738125 0.0240494
\(943\) 24.3408 0.792646
\(944\) −8.44960 −0.275011
\(945\) 24.4003 0.793742
\(946\) 16.5126 0.536872
\(947\) 17.1841 0.558410 0.279205 0.960232i \(-0.409929\pi\)
0.279205 + 0.960232i \(0.409929\pi\)
\(948\) 17.5953 0.571470
\(949\) −28.0830 −0.911612
\(950\) −1.38379 −0.0448960
\(951\) −9.87424 −0.320194
\(952\) −5.56676 −0.180420
\(953\) 48.6572 1.57616 0.788081 0.615571i \(-0.211075\pi\)
0.788081 + 0.615571i \(0.211075\pi\)
\(954\) −11.1599 −0.361316
\(955\) −23.1798 −0.750082
\(956\) 0.532759 0.0172307
\(957\) −3.32600 −0.107514
\(958\) 0.611032 0.0197415
\(959\) −55.9447 −1.80655
\(960\) −2.16874 −0.0699959
\(961\) −26.8888 −0.867380
\(962\) −10.3505 −0.333713
\(963\) 20.4847 0.660110
\(964\) 7.29043 0.234809
\(965\) 37.2675 1.19968
\(966\) −8.74277 −0.281294
\(967\) −39.8318 −1.28090 −0.640451 0.767999i \(-0.721253\pi\)
−0.640451 + 0.767999i \(0.721253\pi\)
\(968\) 12.2414 0.393454
\(969\) 2.65176 0.0851869
\(970\) −8.63136 −0.277136
\(971\) 6.54264 0.209963 0.104982 0.994474i \(-0.466522\pi\)
0.104982 + 0.994474i \(0.466522\pi\)
\(972\) −14.9216 −0.478611
\(973\) −27.4414 −0.879732
\(974\) 30.5937 0.980284
\(975\) −4.63771 −0.148526
\(976\) −4.08156 −0.130648
\(977\) 29.8224 0.954103 0.477052 0.878875i \(-0.341706\pi\)
0.477052 + 0.878875i \(0.341706\pi\)
\(978\) −11.8074 −0.377558
\(979\) 77.1299 2.46508
\(980\) −2.41144 −0.0770305
\(981\) 16.0183 0.511425
\(982\) 10.4501 0.333477
\(983\) 14.0035 0.446643 0.223322 0.974745i \(-0.428310\pi\)
0.223322 + 0.974745i \(0.428310\pi\)
\(984\) −8.66960 −0.276377
\(985\) 15.6018 0.497115
\(986\) 1.40657 0.0447945
\(987\) −15.7703 −0.501974
\(988\) −2.93868 −0.0934920
\(989\) −10.9674 −0.348742
\(990\) 15.5790 0.495133
\(991\) −16.8095 −0.533971 −0.266986 0.963700i \(-0.586028\pi\)
−0.266986 + 0.963700i \(0.586028\pi\)
\(992\) −2.02761 −0.0643768
\(993\) 12.0765 0.383235
\(994\) −6.53780 −0.207366
\(995\) 11.7198 0.371542
\(996\) 4.09170 0.129651
\(997\) −31.9755 −1.01267 −0.506336 0.862336i \(-0.669001\pi\)
−0.506336 + 0.862336i \(0.669001\pi\)
\(998\) 38.1008 1.20606
\(999\) 18.8767 0.597232
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 \(a_p\))