Properties

Label 8002.2.a.d.1.1
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.43715 q^{3} +1.00000 q^{4} -2.28285 q^{5} -3.43715 q^{6} -3.85963 q^{7} +1.00000 q^{8} +8.81400 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.43715 q^{3} +1.00000 q^{4} -2.28285 q^{5} -3.43715 q^{6} -3.85963 q^{7} +1.00000 q^{8} +8.81400 q^{9} -2.28285 q^{10} +0.361008 q^{11} -3.43715 q^{12} -4.38630 q^{13} -3.85963 q^{14} +7.84648 q^{15} +1.00000 q^{16} +1.54216 q^{17} +8.81400 q^{18} -7.18602 q^{19} -2.28285 q^{20} +13.2661 q^{21} +0.361008 q^{22} +6.47568 q^{23} -3.43715 q^{24} +0.211388 q^{25} -4.38630 q^{26} -19.9836 q^{27} -3.85963 q^{28} -4.60661 q^{29} +7.84648 q^{30} +9.01373 q^{31} +1.00000 q^{32} -1.24084 q^{33} +1.54216 q^{34} +8.81095 q^{35} +8.81400 q^{36} -0.704615 q^{37} -7.18602 q^{38} +15.0764 q^{39} -2.28285 q^{40} -1.54259 q^{41} +13.2661 q^{42} +6.07803 q^{43} +0.361008 q^{44} -20.1210 q^{45} +6.47568 q^{46} +6.06179 q^{47} -3.43715 q^{48} +7.89678 q^{49} +0.211388 q^{50} -5.30063 q^{51} -4.38630 q^{52} +2.49746 q^{53} -19.9836 q^{54} -0.824126 q^{55} -3.85963 q^{56} +24.6994 q^{57} -4.60661 q^{58} +9.64179 q^{59} +7.84648 q^{60} -5.89636 q^{61} +9.01373 q^{62} -34.0188 q^{63} +1.00000 q^{64} +10.0133 q^{65} -1.24084 q^{66} +9.47651 q^{67} +1.54216 q^{68} -22.2579 q^{69} +8.81095 q^{70} +10.4189 q^{71} +8.81400 q^{72} -13.9243 q^{73} -0.704615 q^{74} -0.726572 q^{75} -7.18602 q^{76} -1.39336 q^{77} +15.0764 q^{78} -16.0878 q^{79} -2.28285 q^{80} +42.2445 q^{81} -1.54259 q^{82} -10.7216 q^{83} +13.2661 q^{84} -3.52051 q^{85} +6.07803 q^{86} +15.8336 q^{87} +0.361008 q^{88} +18.3038 q^{89} -20.1210 q^{90} +16.9295 q^{91} +6.47568 q^{92} -30.9816 q^{93} +6.06179 q^{94} +16.4046 q^{95} -3.43715 q^{96} +1.80861 q^{97} +7.89678 q^{98} +3.18192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q + 69q^{2} - 25q^{3} + 69q^{4} - 33q^{5} - 25q^{6} - 19q^{7} + 69q^{8} + 54q^{9} + O(q^{10}) \) \( 69q + 69q^{2} - 25q^{3} + 69q^{4} - 33q^{5} - 25q^{6} - 19q^{7} + 69q^{8} + 54q^{9} - 33q^{10} - 30q^{11} - 25q^{12} - 58q^{13} - 19q^{14} + 2q^{15} + 69q^{16} - 80q^{17} + 54q^{18} - 40q^{19} - 33q^{20} - 32q^{21} - 30q^{22} - 45q^{23} - 25q^{24} + 42q^{25} - 58q^{26} - 76q^{27} - 19q^{28} - 44q^{29} + 2q^{30} - 12q^{31} + 69q^{32} - 41q^{33} - 80q^{34} - 49q^{35} + 54q^{36} - 47q^{37} - 40q^{38} - 14q^{39} - 33q^{40} - 94q^{41} - 32q^{42} - 10q^{43} - 30q^{44} - 89q^{45} - 45q^{46} - 85q^{47} - 25q^{48} + 32q^{49} + 42q^{50} - 10q^{51} - 58q^{52} - 41q^{53} - 76q^{54} - 27q^{55} - 19q^{56} - 72q^{57} - 44q^{58} - 75q^{59} + 2q^{60} - 98q^{61} - 12q^{62} - 61q^{63} + 69q^{64} - 47q^{65} - 41q^{66} - 22q^{67} - 80q^{68} - 74q^{69} - 49q^{70} - 22q^{71} + 54q^{72} - 129q^{73} - 47q^{74} - 106q^{75} - 40q^{76} - 108q^{77} - 14q^{78} + 21q^{79} - 33q^{80} + 13q^{81} - 94q^{82} - 111q^{83} - 32q^{84} - 67q^{85} - 10q^{86} - 38q^{87} - 30q^{88} - 112q^{89} - 89q^{90} - 55q^{91} - 45q^{92} - 90q^{93} - 85q^{94} - 38q^{95} - 25q^{96} - 98q^{97} + 32q^{98} - 51q^{99} + O(q^{100}) \)

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
\(3\) −3.43715 −1.98444 −0.992220 0.124501i \(-0.960267\pi\)
−0.992220 + 0.124501i \(0.960267\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.28285 −1.02092 −0.510460 0.859902i \(-0.670525\pi\)
−0.510460 + 0.859902i \(0.670525\pi\)
\(6\) −3.43715 −1.40321
\(7\) −3.85963 −1.45880 −0.729402 0.684085i \(-0.760202\pi\)
−0.729402 + 0.684085i \(0.760202\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.81400 2.93800
\(10\) −2.28285 −0.721899
\(11\) 0.361008 0.108848 0.0544240 0.998518i \(-0.482668\pi\)
0.0544240 + 0.998518i \(0.482668\pi\)
\(12\) −3.43715 −0.992220
\(13\) −4.38630 −1.21654 −0.608271 0.793730i \(-0.708137\pi\)
−0.608271 + 0.793730i \(0.708137\pi\)
\(14\) −3.85963 −1.03153
\(15\) 7.84648 2.02595
\(16\) 1.00000 0.250000
\(17\) 1.54216 0.374029 0.187014 0.982357i \(-0.440119\pi\)
0.187014 + 0.982357i \(0.440119\pi\)
\(18\) 8.81400 2.07748
\(19\) −7.18602 −1.64859 −0.824293 0.566164i \(-0.808427\pi\)
−0.824293 + 0.566164i \(0.808427\pi\)
\(20\) −2.28285 −0.510460
\(21\) 13.2661 2.89491
\(22\) 0.361008 0.0769672
\(23\) 6.47568 1.35027 0.675137 0.737693i \(-0.264085\pi\)
0.675137 + 0.737693i \(0.264085\pi\)
\(24\) −3.43715 −0.701605
\(25\) 0.211388 0.0422776
\(26\) −4.38630 −0.860225
\(27\) −19.9836 −3.84584
\(28\) −3.85963 −0.729402
\(29\) −4.60661 −0.855426 −0.427713 0.903915i \(-0.640681\pi\)
−0.427713 + 0.903915i \(0.640681\pi\)
\(30\) 7.84648 1.43257
\(31\) 9.01373 1.61891 0.809457 0.587179i \(-0.199761\pi\)
0.809457 + 0.587179i \(0.199761\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.24084 −0.216002
\(34\) 1.54216 0.264478
\(35\) 8.81095 1.48932
\(36\) 8.81400 1.46900
\(37\) −0.704615 −0.115838 −0.0579190 0.998321i \(-0.518447\pi\)
−0.0579190 + 0.998321i \(0.518447\pi\)
\(38\) −7.18602 −1.16573
\(39\) 15.0764 2.41415
\(40\) −2.28285 −0.360950
\(41\) −1.54259 −0.240912 −0.120456 0.992719i \(-0.538436\pi\)
−0.120456 + 0.992719i \(0.538436\pi\)
\(42\) 13.2661 2.04701
\(43\) 6.07803 0.926891 0.463445 0.886126i \(-0.346613\pi\)
0.463445 + 0.886126i \(0.346613\pi\)
\(44\) 0.361008 0.0544240
\(45\) −20.1210 −2.99946
\(46\) 6.47568 0.954787
\(47\) 6.06179 0.884203 0.442101 0.896965i \(-0.354233\pi\)
0.442101 + 0.896965i \(0.354233\pi\)
\(48\) −3.43715 −0.496110
\(49\) 7.89678 1.12811
\(50\) 0.211388 0.0298948
\(51\) −5.30063 −0.742237
\(52\) −4.38630 −0.608271
\(53\) 2.49746 0.343052 0.171526 0.985180i \(-0.445130\pi\)
0.171526 + 0.985180i \(0.445130\pi\)
\(54\) −19.9836 −2.71942
\(55\) −0.824126 −0.111125
\(56\) −3.85963 −0.515765
\(57\) 24.6994 3.27152
\(58\) −4.60661 −0.604878
\(59\) 9.64179 1.25525 0.627627 0.778514i \(-0.284026\pi\)
0.627627 + 0.778514i \(0.284026\pi\)
\(60\) 7.84648 1.01298
\(61\) −5.89636 −0.754951 −0.377476 0.926020i \(-0.623208\pi\)
−0.377476 + 0.926020i \(0.623208\pi\)
\(62\) 9.01373 1.14475
\(63\) −34.0188 −4.28597
\(64\) 1.00000 0.125000
\(65\) 10.0133 1.24199
\(66\) −1.24084 −0.152737
\(67\) 9.47651 1.15774 0.578870 0.815420i \(-0.303494\pi\)
0.578870 + 0.815420i \(0.303494\pi\)
\(68\) 1.54216 0.187014
\(69\) −22.2579 −2.67953
\(70\) 8.81095 1.05311
\(71\) 10.4189 1.23649 0.618247 0.785984i \(-0.287843\pi\)
0.618247 + 0.785984i \(0.287843\pi\)
\(72\) 8.81400 1.03874
\(73\) −13.9243 −1.62971 −0.814855 0.579664i \(-0.803184\pi\)
−0.814855 + 0.579664i \(0.803184\pi\)
\(74\) −0.704615 −0.0819098
\(75\) −0.726572 −0.0838973
\(76\) −7.18602 −0.824293
\(77\) −1.39336 −0.158788
\(78\) 15.0764 1.70706
\(79\) −16.0878 −1.81002 −0.905011 0.425389i \(-0.860137\pi\)
−0.905011 + 0.425389i \(0.860137\pi\)
\(80\) −2.28285 −0.255230
\(81\) 42.2445 4.69384
\(82\) −1.54259 −0.170350
\(83\) −10.7216 −1.17685 −0.588425 0.808552i \(-0.700252\pi\)
−0.588425 + 0.808552i \(0.700252\pi\)
\(84\) 13.2661 1.44745
\(85\) −3.52051 −0.381853
\(86\) 6.07803 0.655411
\(87\) 15.8336 1.69754
\(88\) 0.361008 0.0384836
\(89\) 18.3038 1.94020 0.970098 0.242715i \(-0.0780378\pi\)
0.970098 + 0.242715i \(0.0780378\pi\)
\(90\) −20.1210 −2.12094
\(91\) 16.9295 1.77470
\(92\) 6.47568 0.675137
\(93\) −30.9816 −3.21264
\(94\) 6.06179 0.625226
\(95\) 16.4046 1.68307
\(96\) −3.43715 −0.350803
\(97\) 1.80861 0.183636 0.0918180 0.995776i \(-0.470732\pi\)
0.0918180 + 0.995776i \(0.470732\pi\)
\(98\) 7.89678 0.797695
\(99\) 3.18192 0.319795
\(100\) 0.211388 0.0211388
\(101\) 20.0095 1.99102 0.995510 0.0946561i \(-0.0301752\pi\)
0.995510 + 0.0946561i \(0.0301752\pi\)
\(102\) −5.30063 −0.524841
\(103\) −1.48856 −0.146672 −0.0733361 0.997307i \(-0.523365\pi\)
−0.0733361 + 0.997307i \(0.523365\pi\)
\(104\) −4.38630 −0.430112
\(105\) −30.2846 −2.95547
\(106\) 2.49746 0.242574
\(107\) 4.37825 0.423261 0.211631 0.977350i \(-0.432123\pi\)
0.211631 + 0.977350i \(0.432123\pi\)
\(108\) −19.9836 −1.92292
\(109\) −13.2141 −1.26568 −0.632842 0.774281i \(-0.718112\pi\)
−0.632842 + 0.774281i \(0.718112\pi\)
\(110\) −0.824126 −0.0785773
\(111\) 2.42187 0.229873
\(112\) −3.85963 −0.364701
\(113\) 10.3975 0.978114 0.489057 0.872252i \(-0.337341\pi\)
0.489057 + 0.872252i \(0.337341\pi\)
\(114\) 24.6994 2.31331
\(115\) −14.7830 −1.37852
\(116\) −4.60661 −0.427713
\(117\) −38.6609 −3.57420
\(118\) 9.64179 0.887598
\(119\) −5.95217 −0.545635
\(120\) 7.84648 0.716283
\(121\) −10.8697 −0.988152
\(122\) −5.89636 −0.533831
\(123\) 5.30211 0.478075
\(124\) 9.01373 0.809457
\(125\) 10.9317 0.977758
\(126\) −34.0188 −3.03064
\(127\) 4.60505 0.408632 0.204316 0.978905i \(-0.434503\pi\)
0.204316 + 0.978905i \(0.434503\pi\)
\(128\) 1.00000 0.0883883
\(129\) −20.8911 −1.83936
\(130\) 10.0133 0.878221
\(131\) 15.2608 1.33335 0.666673 0.745351i \(-0.267718\pi\)
0.666673 + 0.745351i \(0.267718\pi\)
\(132\) −1.24084 −0.108001
\(133\) 27.7354 2.40496
\(134\) 9.47651 0.818645
\(135\) 45.6194 3.92629
\(136\) 1.54216 0.132239
\(137\) −1.15379 −0.0985748 −0.0492874 0.998785i \(-0.515695\pi\)
−0.0492874 + 0.998785i \(0.515695\pi\)
\(138\) −22.2579 −1.89472
\(139\) −4.42923 −0.375682 −0.187841 0.982199i \(-0.560149\pi\)
−0.187841 + 0.982199i \(0.560149\pi\)
\(140\) 8.81095 0.744661
\(141\) −20.8353 −1.75465
\(142\) 10.4189 0.874333
\(143\) −1.58349 −0.132418
\(144\) 8.81400 0.734500
\(145\) 10.5162 0.873322
\(146\) −13.9243 −1.15238
\(147\) −27.1424 −2.23867
\(148\) −0.704615 −0.0579190
\(149\) −10.6811 −0.875028 −0.437514 0.899212i \(-0.644141\pi\)
−0.437514 + 0.899212i \(0.644141\pi\)
\(150\) −0.726572 −0.0593244
\(151\) 17.9884 1.46387 0.731937 0.681372i \(-0.238616\pi\)
0.731937 + 0.681372i \(0.238616\pi\)
\(152\) −7.18602 −0.582863
\(153\) 13.5926 1.09890
\(154\) −1.39336 −0.112280
\(155\) −20.5770 −1.65278
\(156\) 15.0764 1.20708
\(157\) −7.37785 −0.588817 −0.294408 0.955680i \(-0.595123\pi\)
−0.294408 + 0.955680i \(0.595123\pi\)
\(158\) −16.0878 −1.27988
\(159\) −8.58413 −0.680766
\(160\) −2.28285 −0.180475
\(161\) −24.9938 −1.96978
\(162\) 42.2445 3.31904
\(163\) 3.42250 0.268071 0.134036 0.990977i \(-0.457206\pi\)
0.134036 + 0.990977i \(0.457206\pi\)
\(164\) −1.54259 −0.120456
\(165\) 2.83264 0.220521
\(166\) −10.7216 −0.832158
\(167\) 11.9050 0.921234 0.460617 0.887599i \(-0.347628\pi\)
0.460617 + 0.887599i \(0.347628\pi\)
\(168\) 13.2661 1.02350
\(169\) 6.23966 0.479973
\(170\) −3.52051 −0.270011
\(171\) −63.3375 −4.84354
\(172\) 6.07803 0.463445
\(173\) −21.8901 −1.66427 −0.832137 0.554570i \(-0.812883\pi\)
−0.832137 + 0.554570i \(0.812883\pi\)
\(174\) 15.8336 1.20034
\(175\) −0.815880 −0.0616748
\(176\) 0.361008 0.0272120
\(177\) −33.1403 −2.49097
\(178\) 18.3038 1.37193
\(179\) 4.15916 0.310870 0.155435 0.987846i \(-0.450322\pi\)
0.155435 + 0.987846i \(0.450322\pi\)
\(180\) −20.1210 −1.49973
\(181\) −1.08020 −0.0802908 −0.0401454 0.999194i \(-0.512782\pi\)
−0.0401454 + 0.999194i \(0.512782\pi\)
\(182\) 16.9295 1.25490
\(183\) 20.2667 1.49815
\(184\) 6.47568 0.477394
\(185\) 1.60853 0.118261
\(186\) −30.9816 −2.27168
\(187\) 0.556732 0.0407123
\(188\) 6.06179 0.442101
\(189\) 77.1293 5.61033
\(190\) 16.4046 1.19011
\(191\) −0.505220 −0.0365565 −0.0182782 0.999833i \(-0.505818\pi\)
−0.0182782 + 0.999833i \(0.505818\pi\)
\(192\) −3.43715 −0.248055
\(193\) −4.91064 −0.353475 −0.176738 0.984258i \(-0.556554\pi\)
−0.176738 + 0.984258i \(0.556554\pi\)
\(194\) 1.80861 0.129850
\(195\) −34.4171 −2.46466
\(196\) 7.89678 0.564056
\(197\) 6.63410 0.472660 0.236330 0.971673i \(-0.424055\pi\)
0.236330 + 0.971673i \(0.424055\pi\)
\(198\) 3.18192 0.226129
\(199\) 12.0176 0.851903 0.425952 0.904746i \(-0.359939\pi\)
0.425952 + 0.904746i \(0.359939\pi\)
\(200\) 0.211388 0.0149474
\(201\) −32.5722 −2.29746
\(202\) 20.0095 1.40786
\(203\) 17.7798 1.24790
\(204\) −5.30063 −0.371119
\(205\) 3.52149 0.245952
\(206\) −1.48856 −0.103713
\(207\) 57.0766 3.96710
\(208\) −4.38630 −0.304135
\(209\) −2.59421 −0.179445
\(210\) −30.2846 −2.08983
\(211\) 8.77979 0.604426 0.302213 0.953240i \(-0.402275\pi\)
0.302213 + 0.953240i \(0.402275\pi\)
\(212\) 2.49746 0.171526
\(213\) −35.8113 −2.45375
\(214\) 4.37825 0.299291
\(215\) −13.8752 −0.946281
\(216\) −19.9836 −1.35971
\(217\) −34.7897 −2.36168
\(218\) −13.2141 −0.894974
\(219\) 47.8597 3.23406
\(220\) −0.824126 −0.0555625
\(221\) −6.76438 −0.455022
\(222\) 2.42187 0.162545
\(223\) −4.16238 −0.278734 −0.139367 0.990241i \(-0.544507\pi\)
−0.139367 + 0.990241i \(0.544507\pi\)
\(224\) −3.85963 −0.257883
\(225\) 1.86317 0.124212
\(226\) 10.3975 0.691631
\(227\) −10.5565 −0.700658 −0.350329 0.936627i \(-0.613930\pi\)
−0.350329 + 0.936627i \(0.613930\pi\)
\(228\) 24.6994 1.63576
\(229\) 5.99864 0.396401 0.198201 0.980161i \(-0.436490\pi\)
0.198201 + 0.980161i \(0.436490\pi\)
\(230\) −14.7830 −0.974761
\(231\) 4.78918 0.315105
\(232\) −4.60661 −0.302439
\(233\) 12.9067 0.845548 0.422774 0.906235i \(-0.361056\pi\)
0.422774 + 0.906235i \(0.361056\pi\)
\(234\) −38.6609 −2.52734
\(235\) −13.8381 −0.902700
\(236\) 9.64179 0.627627
\(237\) 55.2962 3.59188
\(238\) −5.95217 −0.385822
\(239\) −19.8478 −1.28384 −0.641922 0.766770i \(-0.721863\pi\)
−0.641922 + 0.766770i \(0.721863\pi\)
\(240\) 7.84648 0.506488
\(241\) 2.71243 0.174723 0.0873616 0.996177i \(-0.472156\pi\)
0.0873616 + 0.996177i \(0.472156\pi\)
\(242\) −10.8697 −0.698729
\(243\) −85.2500 −5.46879
\(244\) −5.89636 −0.377476
\(245\) −18.0271 −1.15171
\(246\) 5.30211 0.338050
\(247\) 31.5201 2.00557
\(248\) 9.01373 0.572373
\(249\) 36.8518 2.33539
\(250\) 10.9317 0.691379
\(251\) 0.460861 0.0290893 0.0145447 0.999894i \(-0.495370\pi\)
0.0145447 + 0.999894i \(0.495370\pi\)
\(252\) −34.0188 −2.14298
\(253\) 2.33777 0.146975
\(254\) 4.60505 0.288946
\(255\) 12.1005 0.757765
\(256\) 1.00000 0.0625000
\(257\) −27.7877 −1.73335 −0.866676 0.498872i \(-0.833748\pi\)
−0.866676 + 0.498872i \(0.833748\pi\)
\(258\) −20.8911 −1.30062
\(259\) 2.71956 0.168985
\(260\) 10.0133 0.620996
\(261\) −40.6027 −2.51324
\(262\) 15.2608 0.942817
\(263\) −15.5040 −0.956016 −0.478008 0.878356i \(-0.658641\pi\)
−0.478008 + 0.878356i \(0.658641\pi\)
\(264\) −1.24084 −0.0763683
\(265\) −5.70131 −0.350229
\(266\) 27.7354 1.70057
\(267\) −62.9128 −3.85020
\(268\) 9.47651 0.578870
\(269\) −3.74935 −0.228602 −0.114301 0.993446i \(-0.536463\pi\)
−0.114301 + 0.993446i \(0.536463\pi\)
\(270\) 45.6194 2.77631
\(271\) −18.0585 −1.09698 −0.548489 0.836158i \(-0.684797\pi\)
−0.548489 + 0.836158i \(0.684797\pi\)
\(272\) 1.54216 0.0935072
\(273\) −58.1893 −3.52178
\(274\) −1.15379 −0.0697029
\(275\) 0.0763127 0.00460183
\(276\) −22.2579 −1.33977
\(277\) −17.6270 −1.05911 −0.529553 0.848277i \(-0.677640\pi\)
−0.529553 + 0.848277i \(0.677640\pi\)
\(278\) −4.42923 −0.265647
\(279\) 79.4470 4.75637
\(280\) 8.81095 0.526555
\(281\) 4.89388 0.291944 0.145972 0.989289i \(-0.453369\pi\)
0.145972 + 0.989289i \(0.453369\pi\)
\(282\) −20.8353 −1.24072
\(283\) −12.7271 −0.756546 −0.378273 0.925694i \(-0.623482\pi\)
−0.378273 + 0.925694i \(0.623482\pi\)
\(284\) 10.4189 0.618247
\(285\) −56.3850 −3.33996
\(286\) −1.58349 −0.0936337
\(287\) 5.95383 0.351443
\(288\) 8.81400 0.519370
\(289\) −14.6217 −0.860102
\(290\) 10.5162 0.617532
\(291\) −6.21645 −0.364415
\(292\) −13.9243 −0.814855
\(293\) −25.5441 −1.49230 −0.746151 0.665776i \(-0.768101\pi\)
−0.746151 + 0.665776i \(0.768101\pi\)
\(294\) −27.1424 −1.58298
\(295\) −22.0107 −1.28151
\(296\) −0.704615 −0.0409549
\(297\) −7.21423 −0.418612
\(298\) −10.6811 −0.618738
\(299\) −28.4043 −1.64266
\(300\) −0.726572 −0.0419487
\(301\) −23.4590 −1.35215
\(302\) 17.9884 1.03512
\(303\) −68.7757 −3.95106
\(304\) −7.18602 −0.412146
\(305\) 13.4605 0.770745
\(306\) 13.5926 0.777037
\(307\) −18.8491 −1.07578 −0.537888 0.843016i \(-0.680778\pi\)
−0.537888 + 0.843016i \(0.680778\pi\)
\(308\) −1.39336 −0.0793940
\(309\) 5.11640 0.291062
\(310\) −20.5770 −1.16869
\(311\) 23.3036 1.32143 0.660713 0.750639i \(-0.270254\pi\)
0.660713 + 0.750639i \(0.270254\pi\)
\(312\) 15.0764 0.853532
\(313\) −34.6503 −1.95855 −0.979274 0.202540i \(-0.935080\pi\)
−0.979274 + 0.202540i \(0.935080\pi\)
\(314\) −7.37785 −0.416356
\(315\) 77.6597 4.37563
\(316\) −16.0878 −0.905011
\(317\) −6.30150 −0.353928 −0.176964 0.984217i \(-0.556628\pi\)
−0.176964 + 0.984217i \(0.556628\pi\)
\(318\) −8.58413 −0.481374
\(319\) −1.66302 −0.0931114
\(320\) −2.28285 −0.127615
\(321\) −15.0487 −0.839936
\(322\) −24.9938 −1.39285
\(323\) −11.0820 −0.616618
\(324\) 42.2445 2.34692
\(325\) −0.927212 −0.0514325
\(326\) 3.42250 0.189555
\(327\) 45.4189 2.51167
\(328\) −1.54259 −0.0851752
\(329\) −23.3963 −1.28988
\(330\) 2.83264 0.155932
\(331\) −16.7890 −0.922804 −0.461402 0.887191i \(-0.652653\pi\)
−0.461402 + 0.887191i \(0.652653\pi\)
\(332\) −10.7216 −0.588425
\(333\) −6.21047 −0.340332
\(334\) 11.9050 0.651411
\(335\) −21.6334 −1.18196
\(336\) 13.2661 0.723727
\(337\) −8.49180 −0.462578 −0.231289 0.972885i \(-0.574294\pi\)
−0.231289 + 0.972885i \(0.574294\pi\)
\(338\) 6.23966 0.339393
\(339\) −35.7378 −1.94101
\(340\) −3.52051 −0.190927
\(341\) 3.25403 0.176216
\(342\) −63.3375 −3.42490
\(343\) −3.46124 −0.186889
\(344\) 6.07803 0.327705
\(345\) 50.8113 2.73559
\(346\) −21.8901 −1.17682
\(347\) −34.1733 −1.83452 −0.917258 0.398293i \(-0.869603\pi\)
−0.917258 + 0.398293i \(0.869603\pi\)
\(348\) 15.8336 0.848771
\(349\) 19.9392 1.06732 0.533661 0.845698i \(-0.320816\pi\)
0.533661 + 0.845698i \(0.320816\pi\)
\(350\) −0.815880 −0.0436106
\(351\) 87.6540 4.67862
\(352\) 0.361008 0.0192418
\(353\) −3.42769 −0.182437 −0.0912187 0.995831i \(-0.529076\pi\)
−0.0912187 + 0.995831i \(0.529076\pi\)
\(354\) −33.1403 −1.76138
\(355\) −23.7847 −1.26236
\(356\) 18.3038 0.970098
\(357\) 20.4585 1.08278
\(358\) 4.15916 0.219818
\(359\) 32.1213 1.69530 0.847649 0.530557i \(-0.178017\pi\)
0.847649 + 0.530557i \(0.178017\pi\)
\(360\) −20.1210 −1.06047
\(361\) 32.6389 1.71783
\(362\) −1.08020 −0.0567742
\(363\) 37.3607 1.96093
\(364\) 16.9295 0.887348
\(365\) 31.7869 1.66380
\(366\) 20.2667 1.05936
\(367\) −31.1725 −1.62719 −0.813595 0.581432i \(-0.802492\pi\)
−0.813595 + 0.581432i \(0.802492\pi\)
\(368\) 6.47568 0.337568
\(369\) −13.5964 −0.707799
\(370\) 1.60853 0.0836234
\(371\) −9.63927 −0.500446
\(372\) −30.9816 −1.60632
\(373\) 32.9584 1.70652 0.853259 0.521487i \(-0.174622\pi\)
0.853259 + 0.521487i \(0.174622\pi\)
\(374\) 0.556732 0.0287879
\(375\) −37.5738 −1.94030
\(376\) 6.06179 0.312613
\(377\) 20.2060 1.04066
\(378\) 77.1293 3.96710
\(379\) 5.03123 0.258437 0.129218 0.991616i \(-0.458753\pi\)
0.129218 + 0.991616i \(0.458753\pi\)
\(380\) 16.4046 0.841537
\(381\) −15.8282 −0.810905
\(382\) −0.505220 −0.0258493
\(383\) 18.1170 0.925737 0.462868 0.886427i \(-0.346820\pi\)
0.462868 + 0.886427i \(0.346820\pi\)
\(384\) −3.43715 −0.175401
\(385\) 3.18082 0.162110
\(386\) −4.91064 −0.249945
\(387\) 53.5717 2.72320
\(388\) 1.80861 0.0918180
\(389\) 4.36529 0.221329 0.110664 0.993858i \(-0.464702\pi\)
0.110664 + 0.993858i \(0.464702\pi\)
\(390\) −34.4171 −1.74278
\(391\) 9.98654 0.505041
\(392\) 7.89678 0.398848
\(393\) −52.4538 −2.64594
\(394\) 6.63410 0.334221
\(395\) 36.7260 1.84789
\(396\) 3.18192 0.159898
\(397\) −24.3276 −1.22097 −0.610485 0.792028i \(-0.709025\pi\)
−0.610485 + 0.792028i \(0.709025\pi\)
\(398\) 12.0176 0.602387
\(399\) −95.3307 −4.77251
\(400\) 0.211388 0.0105694
\(401\) −3.52602 −0.176081 −0.0880406 0.996117i \(-0.528061\pi\)
−0.0880406 + 0.996117i \(0.528061\pi\)
\(402\) −32.5722 −1.62455
\(403\) −39.5370 −1.96948
\(404\) 20.0095 0.995510
\(405\) −96.4378 −4.79203
\(406\) 17.7798 0.882399
\(407\) −0.254372 −0.0126087
\(408\) −5.30063 −0.262421
\(409\) −18.7840 −0.928807 −0.464403 0.885624i \(-0.653731\pi\)
−0.464403 + 0.885624i \(0.653731\pi\)
\(410\) 3.52149 0.173914
\(411\) 3.96574 0.195616
\(412\) −1.48856 −0.0733361
\(413\) −37.2138 −1.83117
\(414\) 57.0766 2.80516
\(415\) 24.4758 1.20147
\(416\) −4.38630 −0.215056
\(417\) 15.2239 0.745518
\(418\) −2.59421 −0.126887
\(419\) 24.8971 1.21630 0.608151 0.793822i \(-0.291912\pi\)
0.608151 + 0.793822i \(0.291912\pi\)
\(420\) −30.2846 −1.47774
\(421\) −3.33289 −0.162435 −0.0812175 0.996696i \(-0.525881\pi\)
−0.0812175 + 0.996696i \(0.525881\pi\)
\(422\) 8.77979 0.427393
\(423\) 53.4286 2.59779
\(424\) 2.49746 0.121287
\(425\) 0.325994 0.0158130
\(426\) −35.8113 −1.73506
\(427\) 22.7578 1.10133
\(428\) 4.37825 0.211631
\(429\) 5.44269 0.262776
\(430\) −13.8752 −0.669122
\(431\) 12.4942 0.601826 0.300913 0.953652i \(-0.402709\pi\)
0.300913 + 0.953652i \(0.402709\pi\)
\(432\) −19.9836 −0.961460
\(433\) −8.81737 −0.423736 −0.211868 0.977298i \(-0.567955\pi\)
−0.211868 + 0.977298i \(0.567955\pi\)
\(434\) −34.7897 −1.66996
\(435\) −36.1457 −1.73305
\(436\) −13.2141 −0.632842
\(437\) −46.5344 −2.22604
\(438\) 47.8597 2.28683
\(439\) 19.2818 0.920269 0.460135 0.887849i \(-0.347801\pi\)
0.460135 + 0.887849i \(0.347801\pi\)
\(440\) −0.824126 −0.0392887
\(441\) 69.6022 3.31439
\(442\) −6.76438 −0.321749
\(443\) 26.9186 1.27894 0.639471 0.768815i \(-0.279153\pi\)
0.639471 + 0.768815i \(0.279153\pi\)
\(444\) 2.42187 0.114937
\(445\) −41.7847 −1.98078
\(446\) −4.16238 −0.197095
\(447\) 36.7125 1.73644
\(448\) −3.85963 −0.182351
\(449\) −6.33393 −0.298916 −0.149458 0.988768i \(-0.547753\pi\)
−0.149458 + 0.988768i \(0.547753\pi\)
\(450\) 1.86317 0.0878308
\(451\) −0.556887 −0.0262228
\(452\) 10.3975 0.489057
\(453\) −61.8288 −2.90497
\(454\) −10.5565 −0.495440
\(455\) −38.6475 −1.81182
\(456\) 24.6994 1.15666
\(457\) −8.02585 −0.375434 −0.187717 0.982223i \(-0.560109\pi\)
−0.187717 + 0.982223i \(0.560109\pi\)
\(458\) 5.99864 0.280298
\(459\) −30.8179 −1.43845
\(460\) −14.7830 −0.689260
\(461\) 27.5375 1.28255 0.641276 0.767311i \(-0.278406\pi\)
0.641276 + 0.767311i \(0.278406\pi\)
\(462\) 4.78918 0.222813
\(463\) −40.8397 −1.89798 −0.948991 0.315302i \(-0.897894\pi\)
−0.948991 + 0.315302i \(0.897894\pi\)
\(464\) −4.60661 −0.213857
\(465\) 70.7261 3.27985
\(466\) 12.9067 0.597892
\(467\) 12.2630 0.567463 0.283731 0.958904i \(-0.408428\pi\)
0.283731 + 0.958904i \(0.408428\pi\)
\(468\) −38.6609 −1.78710
\(469\) −36.5759 −1.68892
\(470\) −13.8381 −0.638305
\(471\) 25.3588 1.16847
\(472\) 9.64179 0.443799
\(473\) 2.19422 0.100890
\(474\) 55.2962 2.53984
\(475\) −1.51904 −0.0696982
\(476\) −5.95217 −0.272817
\(477\) 22.0126 1.00789
\(478\) −19.8478 −0.907815
\(479\) 29.2475 1.33635 0.668175 0.744004i \(-0.267076\pi\)
0.668175 + 0.744004i \(0.267076\pi\)
\(480\) 7.84648 0.358141
\(481\) 3.09066 0.140922
\(482\) 2.71243 0.123548
\(483\) 85.9073 3.90892
\(484\) −10.8697 −0.494076
\(485\) −4.12877 −0.187478
\(486\) −85.2500 −3.86702
\(487\) −14.5335 −0.658576 −0.329288 0.944230i \(-0.606809\pi\)
−0.329288 + 0.944230i \(0.606809\pi\)
\(488\) −5.89636 −0.266916
\(489\) −11.7637 −0.531971
\(490\) −18.0271 −0.814383
\(491\) −7.66250 −0.345804 −0.172902 0.984939i \(-0.555314\pi\)
−0.172902 + 0.984939i \(0.555314\pi\)
\(492\) 5.30211 0.239038
\(493\) −7.10413 −0.319954
\(494\) 31.5201 1.41815
\(495\) −7.26384 −0.326485
\(496\) 9.01373 0.404729
\(497\) −40.2131 −1.80380
\(498\) 36.8518 1.65137
\(499\) −31.1742 −1.39555 −0.697774 0.716318i \(-0.745826\pi\)
−0.697774 + 0.716318i \(0.745826\pi\)
\(500\) 10.9317 0.488879
\(501\) −40.9192 −1.82813
\(502\) 0.460861 0.0205692
\(503\) −21.0971 −0.940673 −0.470337 0.882487i \(-0.655867\pi\)
−0.470337 + 0.882487i \(0.655867\pi\)
\(504\) −34.0188 −1.51532
\(505\) −45.6786 −2.03267
\(506\) 2.33777 0.103927
\(507\) −21.4466 −0.952478
\(508\) 4.60505 0.204316
\(509\) 12.4964 0.553893 0.276946 0.960885i \(-0.410678\pi\)
0.276946 + 0.960885i \(0.410678\pi\)
\(510\) 12.1005 0.535821
\(511\) 53.7425 2.37743
\(512\) 1.00000 0.0441942
\(513\) 143.602 6.34020
\(514\) −27.7877 −1.22566
\(515\) 3.39815 0.149741
\(516\) −20.8911 −0.919679
\(517\) 2.18835 0.0962437
\(518\) 2.71956 0.119490
\(519\) 75.2396 3.30265
\(520\) 10.0133 0.439110
\(521\) −36.2419 −1.58778 −0.793892 0.608058i \(-0.791949\pi\)
−0.793892 + 0.608058i \(0.791949\pi\)
\(522\) −40.6027 −1.77713
\(523\) 37.6417 1.64596 0.822978 0.568074i \(-0.192311\pi\)
0.822978 + 0.568074i \(0.192311\pi\)
\(524\) 15.2608 0.666673
\(525\) 2.80430 0.122390
\(526\) −15.5040 −0.676005
\(527\) 13.9006 0.605521
\(528\) −1.24084 −0.0540006
\(529\) 18.9345 0.823238
\(530\) −5.70131 −0.247649
\(531\) 84.9827 3.68793
\(532\) 27.7354 1.20248
\(533\) 6.76626 0.293079
\(534\) −62.9128 −2.72250
\(535\) −9.99487 −0.432116
\(536\) 9.47651 0.409323
\(537\) −14.2956 −0.616902
\(538\) −3.74935 −0.161646
\(539\) 2.85080 0.122793
\(540\) 45.6194 1.96315
\(541\) −8.58565 −0.369126 −0.184563 0.982821i \(-0.559087\pi\)
−0.184563 + 0.982821i \(0.559087\pi\)
\(542\) −18.0585 −0.775680
\(543\) 3.71282 0.159332
\(544\) 1.54216 0.0661196
\(545\) 30.1658 1.29216
\(546\) −58.1893 −2.49027
\(547\) 8.56072 0.366030 0.183015 0.983110i \(-0.441414\pi\)
0.183015 + 0.983110i \(0.441414\pi\)
\(548\) −1.15379 −0.0492874
\(549\) −51.9705 −2.21805
\(550\) 0.0763127 0.00325399
\(551\) 33.1032 1.41024
\(552\) −22.2579 −0.947359
\(553\) 62.0931 2.64047
\(554\) −17.6270 −0.748902
\(555\) −5.52875 −0.234682
\(556\) −4.42923 −0.187841
\(557\) −7.87206 −0.333550 −0.166775 0.985995i \(-0.553335\pi\)
−0.166775 + 0.985995i \(0.553335\pi\)
\(558\) 79.4470 3.36326
\(559\) −26.6601 −1.12760
\(560\) 8.81095 0.372331
\(561\) −1.91357 −0.0807910
\(562\) 4.89388 0.206436
\(563\) 4.78943 0.201850 0.100925 0.994894i \(-0.467820\pi\)
0.100925 + 0.994894i \(0.467820\pi\)
\(564\) −20.8353 −0.877323
\(565\) −23.7359 −0.998577
\(566\) −12.7271 −0.534959
\(567\) −163.048 −6.84739
\(568\) 10.4189 0.437167
\(569\) −34.3600 −1.44045 −0.720223 0.693742i \(-0.755961\pi\)
−0.720223 + 0.693742i \(0.755961\pi\)
\(570\) −56.3850 −2.36171
\(571\) 6.62622 0.277299 0.138649 0.990342i \(-0.455724\pi\)
0.138649 + 0.990342i \(0.455724\pi\)
\(572\) −1.58349 −0.0662091
\(573\) 1.73652 0.0725441
\(574\) 5.95383 0.248508
\(575\) 1.36888 0.0570863
\(576\) 8.81400 0.367250
\(577\) 18.4521 0.768170 0.384085 0.923298i \(-0.374517\pi\)
0.384085 + 0.923298i \(0.374517\pi\)
\(578\) −14.6217 −0.608184
\(579\) 16.8786 0.701450
\(580\) 10.5162 0.436661
\(581\) 41.3815 1.71679
\(582\) −6.21645 −0.257680
\(583\) 0.901601 0.0373405
\(584\) −13.9243 −0.576190
\(585\) 88.2568 3.64897
\(586\) −25.5441 −1.05522
\(587\) −25.4131 −1.04891 −0.524455 0.851438i \(-0.675731\pi\)
−0.524455 + 0.851438i \(0.675731\pi\)
\(588\) −27.1424 −1.11933
\(589\) −64.7729 −2.66892
\(590\) −22.0107 −0.906167
\(591\) −22.8024 −0.937965
\(592\) −0.704615 −0.0289595
\(593\) −38.3779 −1.57599 −0.787996 0.615681i \(-0.788881\pi\)
−0.787996 + 0.615681i \(0.788881\pi\)
\(594\) −7.21423 −0.296003
\(595\) 13.5879 0.557050
\(596\) −10.6811 −0.437514
\(597\) −41.3062 −1.69055
\(598\) −28.4043 −1.16154
\(599\) −20.7652 −0.848445 −0.424222 0.905558i \(-0.639452\pi\)
−0.424222 + 0.905558i \(0.639452\pi\)
\(600\) −0.726572 −0.0296622
\(601\) 26.8648 1.09584 0.547919 0.836531i \(-0.315420\pi\)
0.547919 + 0.836531i \(0.315420\pi\)
\(602\) −23.4590 −0.956116
\(603\) 83.5259 3.40144
\(604\) 17.9884 0.731937
\(605\) 24.8138 1.00882
\(606\) −68.7757 −2.79382
\(607\) 2.21155 0.0897641 0.0448820 0.998992i \(-0.485709\pi\)
0.0448820 + 0.998992i \(0.485709\pi\)
\(608\) −7.18602 −0.291432
\(609\) −61.1120 −2.47638
\(610\) 13.4605 0.544999
\(611\) −26.5888 −1.07567
\(612\) 13.5926 0.549448
\(613\) 30.7580 1.24231 0.621153 0.783690i \(-0.286665\pi\)
0.621153 + 0.783690i \(0.286665\pi\)
\(614\) −18.8491 −0.760689
\(615\) −12.1039 −0.488076
\(616\) −1.39336 −0.0561400
\(617\) 43.8140 1.76388 0.881942 0.471357i \(-0.156236\pi\)
0.881942 + 0.471357i \(0.156236\pi\)
\(618\) 5.11640 0.205812
\(619\) 18.2194 0.732301 0.366151 0.930556i \(-0.380676\pi\)
0.366151 + 0.930556i \(0.380676\pi\)
\(620\) −20.5770 −0.826391
\(621\) −129.407 −5.19293
\(622\) 23.3036 0.934389
\(623\) −70.6459 −2.83037
\(624\) 15.0764 0.603538
\(625\) −26.0123 −1.04049
\(626\) −34.6503 −1.38490
\(627\) 8.91669 0.356098
\(628\) −7.37785 −0.294408
\(629\) −1.08663 −0.0433267
\(630\) 77.6597 3.09404
\(631\) −3.30219 −0.131458 −0.0657292 0.997838i \(-0.520937\pi\)
−0.0657292 + 0.997838i \(0.520937\pi\)
\(632\) −16.0878 −0.639939
\(633\) −30.1774 −1.19945
\(634\) −6.30150 −0.250265
\(635\) −10.5126 −0.417180
\(636\) −8.58413 −0.340383
\(637\) −34.6377 −1.37239
\(638\) −1.66302 −0.0658397
\(639\) 91.8320 3.63282
\(640\) −2.28285 −0.0902374
\(641\) 14.1111 0.557354 0.278677 0.960385i \(-0.410104\pi\)
0.278677 + 0.960385i \(0.410104\pi\)
\(642\) −15.0487 −0.593925
\(643\) 31.1308 1.22768 0.613840 0.789431i \(-0.289624\pi\)
0.613840 + 0.789431i \(0.289624\pi\)
\(644\) −24.9938 −0.984892
\(645\) 47.6912 1.87784
\(646\) −11.0820 −0.436015
\(647\) 19.4766 0.765703 0.382851 0.923810i \(-0.374942\pi\)
0.382851 + 0.923810i \(0.374942\pi\)
\(648\) 42.2445 1.65952
\(649\) 3.48076 0.136632
\(650\) −0.927212 −0.0363682
\(651\) 119.577 4.68661
\(652\) 3.42250 0.134036
\(653\) 34.7814 1.36110 0.680550 0.732702i \(-0.261741\pi\)
0.680550 + 0.732702i \(0.261741\pi\)
\(654\) 45.4189 1.77602
\(655\) −34.8381 −1.36124
\(656\) −1.54259 −0.0602280
\(657\) −122.728 −4.78809
\(658\) −23.3963 −0.912082
\(659\) −24.0845 −0.938200 −0.469100 0.883145i \(-0.655422\pi\)
−0.469100 + 0.883145i \(0.655422\pi\)
\(660\) 2.83264 0.110260
\(661\) −18.6861 −0.726805 −0.363402 0.931632i \(-0.618385\pi\)
−0.363402 + 0.931632i \(0.618385\pi\)
\(662\) −16.7890 −0.652521
\(663\) 23.2502 0.902963
\(664\) −10.7216 −0.416079
\(665\) −63.3157 −2.45528
\(666\) −6.21047 −0.240651
\(667\) −29.8310 −1.15506
\(668\) 11.9050 0.460617
\(669\) 14.3067 0.553130
\(670\) −21.6334 −0.835772
\(671\) −2.12863 −0.0821749
\(672\) 13.2661 0.511752
\(673\) −39.9539 −1.54011 −0.770056 0.637977i \(-0.779772\pi\)
−0.770056 + 0.637977i \(0.779772\pi\)
\(674\) −8.49180 −0.327092
\(675\) −4.22429 −0.162593
\(676\) 6.23966 0.239987
\(677\) −14.3836 −0.552805 −0.276402 0.961042i \(-0.589142\pi\)
−0.276402 + 0.961042i \(0.589142\pi\)
\(678\) −35.7378 −1.37250
\(679\) −6.98056 −0.267889
\(680\) −3.52051 −0.135006
\(681\) 36.2842 1.39041
\(682\) 3.25403 0.124603
\(683\) 21.9011 0.838021 0.419011 0.907981i \(-0.362377\pi\)
0.419011 + 0.907981i \(0.362377\pi\)
\(684\) −63.3375 −2.42177
\(685\) 2.63392 0.100637
\(686\) −3.46124 −0.132151
\(687\) −20.6182 −0.786634
\(688\) 6.07803 0.231723
\(689\) −10.9546 −0.417337
\(690\) 50.8113 1.93435
\(691\) −23.5784 −0.896965 −0.448483 0.893792i \(-0.648035\pi\)
−0.448483 + 0.893792i \(0.648035\pi\)
\(692\) −21.8901 −0.832137
\(693\) −12.2811 −0.466519
\(694\) −34.1733 −1.29720
\(695\) 10.1112 0.383541
\(696\) 15.8336 0.600172
\(697\) −2.37892 −0.0901080
\(698\) 19.9392 0.754711
\(699\) −44.3623 −1.67794
\(700\) −0.815880 −0.0308374
\(701\) 45.1051 1.70360 0.851798 0.523870i \(-0.175512\pi\)
0.851798 + 0.523870i \(0.175512\pi\)
\(702\) 87.6540 3.30829
\(703\) 5.06338 0.190969
\(704\) 0.361008 0.0136060
\(705\) 47.5637 1.79135
\(706\) −3.42769 −0.129003
\(707\) −77.2294 −2.90451
\(708\) −33.1403 −1.24549
\(709\) −10.0490 −0.377397 −0.188699 0.982035i \(-0.560427\pi\)
−0.188699 + 0.982035i \(0.560427\pi\)
\(710\) −23.7847 −0.892625
\(711\) −141.798 −5.31784
\(712\) 18.3038 0.685963
\(713\) 58.3701 2.18598
\(714\) 20.4585 0.765641
\(715\) 3.61487 0.135188
\(716\) 4.15916 0.155435
\(717\) 68.2197 2.54771
\(718\) 32.1213 1.19876
\(719\) −7.74052 −0.288673 −0.144336 0.989529i \(-0.546105\pi\)
−0.144336 + 0.989529i \(0.546105\pi\)
\(720\) −20.1210 −0.749865
\(721\) 5.74530 0.213966
\(722\) 32.6389 1.21469
\(723\) −9.32304 −0.346727
\(724\) −1.08020 −0.0401454
\(725\) −0.973782 −0.0361654
\(726\) 37.3607 1.38659
\(727\) −41.5408 −1.54066 −0.770332 0.637643i \(-0.779909\pi\)
−0.770332 + 0.637643i \(0.779909\pi\)
\(728\) 16.9295 0.627450
\(729\) 166.284 6.15865
\(730\) 31.7869 1.17649
\(731\) 9.37329 0.346684
\(732\) 20.2667 0.749077
\(733\) 21.0349 0.776943 0.388471 0.921461i \(-0.373003\pi\)
0.388471 + 0.921461i \(0.373003\pi\)
\(734\) −31.1725 −1.15060
\(735\) 61.9620 2.28550
\(736\) 6.47568 0.238697
\(737\) 3.42109 0.126018
\(738\) −13.5964 −0.500489
\(739\) 6.94372 0.255429 0.127714 0.991811i \(-0.459236\pi\)
0.127714 + 0.991811i \(0.459236\pi\)
\(740\) 1.60853 0.0591307
\(741\) −108.339 −3.97994
\(742\) −9.63927 −0.353869
\(743\) −32.5720 −1.19495 −0.597475 0.801888i \(-0.703829\pi\)
−0.597475 + 0.801888i \(0.703829\pi\)
\(744\) −30.9816 −1.13584
\(745\) 24.3833 0.893333
\(746\) 32.9584 1.20669
\(747\) −94.5002 −3.45758
\(748\) 0.556732 0.0203561
\(749\) −16.8984 −0.617455
\(750\) −37.5738 −1.37200
\(751\) −7.20426 −0.262887 −0.131444 0.991324i \(-0.541961\pi\)
−0.131444 + 0.991324i \(0.541961\pi\)
\(752\) 6.06179 0.221051
\(753\) −1.58405 −0.0577260
\(754\) 20.2060 0.735859
\(755\) −41.0647 −1.49450
\(756\) 77.1293 2.80516
\(757\) 1.28789 0.0468090 0.0234045 0.999726i \(-0.492549\pi\)
0.0234045 + 0.999726i \(0.492549\pi\)
\(758\) 5.03123 0.182742
\(759\) −8.03527 −0.291662
\(760\) 16.4046 0.595056
\(761\) 33.8984 1.22882 0.614408 0.788988i \(-0.289395\pi\)
0.614408 + 0.788988i \(0.289395\pi\)
\(762\) −15.8282 −0.573396
\(763\) 51.0017 1.84639
\(764\) −0.505220 −0.0182782
\(765\) −31.0298 −1.12188
\(766\) 18.1170 0.654595
\(767\) −42.2918 −1.52707
\(768\) −3.43715 −0.124027
\(769\) 14.6411 0.527970 0.263985 0.964527i \(-0.414963\pi\)
0.263985 + 0.964527i \(0.414963\pi\)
\(770\) 3.18082 0.114629
\(771\) 95.5106 3.43973
\(772\) −4.91064 −0.176738
\(773\) 16.1390 0.580480 0.290240 0.956954i \(-0.406265\pi\)
0.290240 + 0.956954i \(0.406265\pi\)
\(774\) 53.5717 1.92560
\(775\) 1.90540 0.0684438
\(776\) 1.80861 0.0649251
\(777\) −9.34752 −0.335340
\(778\) 4.36529 0.156503
\(779\) 11.0851 0.397164
\(780\) −34.4171 −1.23233
\(781\) 3.76130 0.134590
\(782\) 9.98654 0.357118
\(783\) 92.0566 3.28983
\(784\) 7.89678 0.282028
\(785\) 16.8425 0.601135
\(786\) −52.4538 −1.87096
\(787\) 4.19515 0.149541 0.0747705 0.997201i \(-0.476178\pi\)
0.0747705 + 0.997201i \(0.476178\pi\)
\(788\) 6.63410 0.236330
\(789\) 53.2895 1.89716
\(790\) 36.7260 1.30665
\(791\) −40.1305 −1.42688
\(792\) 3.18192 0.113065
\(793\) 25.8632 0.918430
\(794\) −24.3276 −0.863356
\(795\) 19.5962 0.695007
\(796\) 12.0176 0.425952
\(797\) 45.9449 1.62745 0.813727 0.581248i \(-0.197435\pi\)
0.813727 + 0.581248i \(0.197435\pi\)
\(798\) −95.3307 −3.37467
\(799\) 9.34825 0.330717
\(800\) 0.211388 0.00747369
\(801\) 161.329 5.70029
\(802\) −3.52602 −0.124508
\(803\) −5.02677 −0.177391
\(804\) −32.5722 −1.14873
\(805\) 57.0569 2.01099
\(806\) −39.5370 −1.39263
\(807\) 12.8871 0.453647
\(808\) 20.0095 0.703932
\(809\) 39.0275 1.37213 0.686067 0.727538i \(-0.259335\pi\)
0.686067 + 0.727538i \(0.259335\pi\)
\(810\) −96.4378 −3.38848
\(811\) −15.6739 −0.550384 −0.275192 0.961389i \(-0.588741\pi\)
−0.275192 + 0.961389i \(0.588741\pi\)
\(812\) 17.7798 0.623950
\(813\) 62.0699 2.17689
\(814\) −0.254372 −0.00891572
\(815\) −7.81305 −0.273679
\(816\) −5.30063 −0.185559
\(817\) −43.6768 −1.52806
\(818\) −18.7840 −0.656766
\(819\) 149.217 5.21406
\(820\) 3.52149 0.122976
\(821\) −23.4399 −0.818059 −0.409029 0.912521i \(-0.634133\pi\)
−0.409029 + 0.912521i \(0.634133\pi\)
\(822\) 3.96574 0.138321
\(823\) −8.29980 −0.289313 −0.144656 0.989482i \(-0.546208\pi\)
−0.144656 + 0.989482i \(0.546208\pi\)
\(824\) −1.48856 −0.0518564
\(825\) −0.262298 −0.00913205
\(826\) −37.2138 −1.29483
\(827\) 36.7606 1.27829 0.639146 0.769085i \(-0.279288\pi\)
0.639146 + 0.769085i \(0.279288\pi\)
\(828\) 57.0766 1.98355
\(829\) −5.31370 −0.184553 −0.0922763 0.995733i \(-0.529414\pi\)
−0.0922763 + 0.995733i \(0.529414\pi\)
\(830\) 24.4758 0.849567
\(831\) 60.5868 2.10173
\(832\) −4.38630 −0.152068
\(833\) 12.1781 0.421946
\(834\) 15.2239 0.527161
\(835\) −27.1772 −0.940507
\(836\) −2.59421 −0.0897226
\(837\) −180.127 −6.22609
\(838\) 24.8971 0.860055
\(839\) −10.9768 −0.378961 −0.189480 0.981885i \(-0.560680\pi\)
−0.189480 + 0.981885i \(0.560680\pi\)
\(840\) −30.2846 −1.04492
\(841\) −7.77913 −0.268246
\(842\) −3.33289 −0.114859
\(843\) −16.8210 −0.579346
\(844\) 8.77979 0.302213
\(845\) −14.2442 −0.490015
\(846\) 53.4286 1.83691
\(847\) 41.9530 1.44152
\(848\) 2.49746 0.0857630
\(849\) 43.7448 1.50132
\(850\) 0.325994 0.0111815
\(851\) −4.56286 −0.156413
\(852\) −35.8113 −1.22687
\(853\) 7.04692 0.241282 0.120641 0.992696i \(-0.461505\pi\)
0.120641 + 0.992696i \(0.461505\pi\)
\(854\) 22.7578 0.778755
\(855\) 144.590 4.94487
\(856\) 4.37825 0.149645
\(857\) −25.5924 −0.874218 −0.437109 0.899408i \(-0.643998\pi\)
−0.437109 + 0.899408i \(0.643998\pi\)
\(858\) 5.44269 0.185810
\(859\) −25.6368 −0.874715 −0.437358 0.899288i \(-0.644086\pi\)
−0.437358 + 0.899288i \(0.644086\pi\)
\(860\) −13.8752 −0.473141
\(861\) −20.4642 −0.697418
\(862\) 12.4942 0.425555
\(863\) −3.39448 −0.115549 −0.0577747 0.998330i \(-0.518400\pi\)
−0.0577747 + 0.998330i \(0.518400\pi\)
\(864\) −19.9836 −0.679855
\(865\) 49.9717 1.69909
\(866\) −8.81737 −0.299626
\(867\) 50.2571 1.70682
\(868\) −34.7897 −1.18084
\(869\) −5.80783 −0.197017
\(870\) −36.1457 −1.22545
\(871\) −41.5668 −1.40844
\(872\) −13.2141 −0.447487
\(873\) 15.9410 0.539522
\(874\) −46.5344 −1.57405
\(875\) −42.1922 −1.42636
\(876\) 47.8597 1.61703
\(877\) 42.7031 1.44198 0.720991 0.692945i \(-0.243687\pi\)
0.720991 + 0.692945i \(0.243687\pi\)
\(878\) 19.2818 0.650729
\(879\) 87.7989 2.96138
\(880\) −0.824126 −0.0277813
\(881\) 39.9187 1.34490 0.672448 0.740144i \(-0.265243\pi\)
0.672448 + 0.740144i \(0.265243\pi\)
\(882\) 69.6022 2.34363
\(883\) 42.1911 1.41984 0.709921 0.704281i \(-0.248730\pi\)
0.709921 + 0.704281i \(0.248730\pi\)
\(884\) −6.76438 −0.227511
\(885\) 75.6541 2.54309
\(886\) 26.9186 0.904349
\(887\) 9.10136 0.305594 0.152797 0.988258i \(-0.451172\pi\)
0.152797 + 0.988258i \(0.451172\pi\)
\(888\) 2.42187 0.0812725
\(889\) −17.7738 −0.596114
\(890\) −41.7847 −1.40063
\(891\) 15.2506 0.510915
\(892\) −4.16238 −0.139367
\(893\) −43.5601 −1.45768
\(894\) 36.7125 1.22785
\(895\) −9.49472 −0.317373
\(896\) −3.85963 −0.128941
\(897\) 97.6298 3.25977
\(898\) −6.33393 −0.211366
\(899\) −41.5228 −1.38486
\(900\) 1.86317 0.0621058
\(901\) 3.85148 0.128311
\(902\) −0.556887 −0.0185423
\(903\) 80.6320 2.68326
\(904\) 10.3975 0.345816
\(905\) 2.46594 0.0819705
\(906\) −61.8288 −2.05412
\(907\) 28.9234 0.960386 0.480193 0.877163i \(-0.340567\pi\)
0.480193 + 0.877163i \(0.340567\pi\)
\(908\) −10.5565 −0.350329
\(909\) 176.364 5.84961
\(910\) −38.6475 −1.28115
\(911\) 16.0352 0.531271 0.265635 0.964074i \(-0.414418\pi\)
0.265635 + 0.964074i \(0.414418\pi\)
\(912\) 24.6994 0.817879
\(913\) −3.87058 −0.128098
\(914\) −8.02585 −0.265472
\(915\) −46.2657 −1.52950
\(916\) 5.99864 0.198201
\(917\) −58.9012 −1.94509
\(918\) −30.8179 −1.01714
\(919\) 39.9042 1.31632 0.658158 0.752879i \(-0.271336\pi\)
0.658158 + 0.752879i \(0.271336\pi\)
\(920\) −14.7830 −0.487381
\(921\) 64.7873 2.13481
\(922\) 27.5375 0.906901
\(923\) −45.7004 −1.50425
\(924\) 4.78918 0.157553
\(925\) −0.148947 −0.00489735
\(926\) −40.8397 −1.34208
\(927\) −13.1202 −0.430923
\(928\) −4.60661 −0.151219
\(929\) 29.4339 0.965696 0.482848 0.875704i \(-0.339602\pi\)
0.482848 + 0.875704i \(0.339602\pi\)
\(930\) 70.7261 2.31920
\(931\) −56.7464 −1.85979
\(932\) 12.9067 0.422774
\(933\) −80.0979 −2.62229
\(934\) 12.2630 0.401257
\(935\) −1.27093 −0.0415640
\(936\) −38.6609 −1.26367
\(937\) −38.8089 −1.26783 −0.633917 0.773401i \(-0.718554\pi\)
−0.633917 + 0.773401i \(0.718554\pi\)
\(938\) −36.5759 −1.19424
\(939\) 119.098 3.88662
\(940\) −13.8381 −0.451350
\(941\) 3.16882 0.103301 0.0516503 0.998665i \(-0.483552\pi\)
0.0516503 + 0.998665i \(0.483552\pi\)
\(942\) 25.3588 0.826234
\(943\) −9.98932 −0.325297
\(944\) 9.64179 0.313813
\(945\) −176.074 −5.72770
\(946\) 2.19422 0.0713401
\(947\) −48.4182 −1.57338 −0.786690 0.617349i \(-0.788207\pi\)
−0.786690 + 0.617349i \(0.788207\pi\)
\(948\) 55.2962 1.79594
\(949\) 61.0760 1.98261
\(950\) −1.51904 −0.0492841
\(951\) 21.6592 0.702348
\(952\) −5.95217 −0.192911
\(953\) 22.4957 0.728706 0.364353 0.931261i \(-0.381290\pi\)
0.364353 + 0.931261i \(0.381290\pi\)
\(954\) 22.0126 0.712683
\(955\) 1.15334 0.0373212
\(956\) −19.8478 −0.641922
\(957\) 5.71606 0.184774
\(958\) 29.2475 0.944942
\(959\) 4.45320 0.143801
\(960\) 7.84648 0.253244
\(961\) 50.2474 1.62088
\(962\) 3.09066 0.0996467
\(963\) 38.5899 1.24354
\(964\) 2.71243 0.0873616
\(965\) 11.2102 0.360870
\(966\) 85.9073 2.76402
\(967\) −37.9318 −1.21980 −0.609902 0.792477i \(-0.708791\pi\)
−0.609902 + 0.792477i \(0.708791\pi\)
\(968\) −10.8697 −0.349365
\(969\) 38.0905 1.22364
\(970\) −4.12877 −0.132567
\(971\) −42.8819 −1.37615 −0.688073 0.725642i \(-0.741543\pi\)
−0.688073 + 0.725642i \(0.741543\pi\)
\(972\) −85.2500 −2.73440
\(973\) 17.0952 0.548047
\(974\) −14.5335 −0.465683
\(975\) 3.18697 0.102065
\(976\) −5.89636 −0.188738
\(977\) 37.7232 1.20687 0.603436 0.797411i \(-0.293798\pi\)
0.603436 + 0.797411i \(0.293798\pi\)
\(978\) −11.7637 −0.376160
\(979\) 6.60781 0.211186
\(980\) −18.0271 −0.575856
\(981\) −116.469 −3.71858
\(982\) −7.66250 −0.244520
\(983\) −28.0142 −0.893514 −0.446757 0.894655i \(-0.647421\pi\)
−0.446757 + 0.894655i \(0.647421\pi\)
\(984\) 5.30211 0.169025
\(985\) −15.1446 −0.482548
\(986\) −7.10413 −0.226242
\(987\) 80.4165 2.55969
\(988\) 31.5201 1.00279
\(989\) 39.3594 1.25156
\(990\) −7.26384 −0.230860
\(991\) −38.3848 −1.21933 −0.609666 0.792658i \(-0.708696\pi\)
−0.609666 + 0.792658i \(0.708696\pi\)
\(992\) 9.01373 0.286186
\(993\) 57.7061 1.83125
\(994\) −40.2131 −1.27548
\(995\) −27.4343 −0.869725
\(996\) 36.8518 1.16769
\(997\) −0.718145 −0.0227439 −0.0113719 0.999935i \(-0.503620\pi\)
−0.0113719 + 0.999935i \(0.503620\pi\)
\(998\) −31.1742 −0.986801
\(999\) 14.0807 0.445494
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 \(a_p\))