Properties

Label 4010.2.a.k.1.6
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.71302\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.21181 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.21181 q^{6} +0.441519 q^{7} -1.00000 q^{8} -1.53151 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.21181 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.21181 q^{6} +0.441519 q^{7} -1.00000 q^{8} -1.53151 q^{9} +1.00000 q^{10} +0.781934 q^{11} -1.21181 q^{12} -4.67597 q^{13} -0.441519 q^{14} +1.21181 q^{15} +1.00000 q^{16} +0.347476 q^{17} +1.53151 q^{18} +0.947001 q^{19} -1.00000 q^{20} -0.535038 q^{21} -0.781934 q^{22} -2.26644 q^{23} +1.21181 q^{24} +1.00000 q^{25} +4.67597 q^{26} +5.49134 q^{27} +0.441519 q^{28} +8.38155 q^{29} -1.21181 q^{30} +7.83398 q^{31} -1.00000 q^{32} -0.947558 q^{33} -0.347476 q^{34} -0.441519 q^{35} -1.53151 q^{36} +7.03784 q^{37} -0.947001 q^{38} +5.66640 q^{39} +1.00000 q^{40} -4.97470 q^{41} +0.535038 q^{42} +1.53149 q^{43} +0.781934 q^{44} +1.53151 q^{45} +2.26644 q^{46} +2.09399 q^{47} -1.21181 q^{48} -6.80506 q^{49} -1.00000 q^{50} -0.421076 q^{51} -4.67597 q^{52} -9.21875 q^{53} -5.49134 q^{54} -0.781934 q^{55} -0.441519 q^{56} -1.14759 q^{57} -8.38155 q^{58} +7.20809 q^{59} +1.21181 q^{60} -13.0437 q^{61} -7.83398 q^{62} -0.676190 q^{63} +1.00000 q^{64} +4.67597 q^{65} +0.947558 q^{66} -11.2388 q^{67} +0.347476 q^{68} +2.74650 q^{69} +0.441519 q^{70} +9.64673 q^{71} +1.53151 q^{72} -5.47699 q^{73} -7.03784 q^{74} -1.21181 q^{75} +0.947001 q^{76} +0.345238 q^{77} -5.66640 q^{78} -1.92618 q^{79} -1.00000 q^{80} -2.05995 q^{81} +4.97470 q^{82} +8.36611 q^{83} -0.535038 q^{84} -0.347476 q^{85} -1.53149 q^{86} -10.1569 q^{87} -0.781934 q^{88} +7.27170 q^{89} -1.53151 q^{90} -2.06453 q^{91} -2.26644 q^{92} -9.49332 q^{93} -2.09399 q^{94} -0.947001 q^{95} +1.21181 q^{96} +11.6018 q^{97} +6.80506 q^{98} -1.19754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −1.21181 −0.699641 −0.349820 0.936817i \(-0.613757\pi\)
−0.349820 + 0.936817i \(0.613757\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.21181 0.494721
\(7\) 0.441519 0.166878 0.0834392 0.996513i \(-0.473410\pi\)
0.0834392 + 0.996513i \(0.473410\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.53151 −0.510503
\(10\) 1.00000 0.316228
\(11\) 0.781934 0.235762 0.117881 0.993028i \(-0.462390\pi\)
0.117881 + 0.993028i \(0.462390\pi\)
\(12\) −1.21181 −0.349820
\(13\) −4.67597 −1.29688 −0.648441 0.761265i \(-0.724579\pi\)
−0.648441 + 0.761265i \(0.724579\pi\)
\(14\) −0.441519 −0.118001
\(15\) 1.21181 0.312889
\(16\) 1.00000 0.250000
\(17\) 0.347476 0.0842753 0.0421376 0.999112i \(-0.486583\pi\)
0.0421376 + 0.999112i \(0.486583\pi\)
\(18\) 1.53151 0.360980
\(19\) 0.947001 0.217257 0.108628 0.994082i \(-0.465354\pi\)
0.108628 + 0.994082i \(0.465354\pi\)
\(20\) −1.00000 −0.223607
\(21\) −0.535038 −0.116755
\(22\) −0.781934 −0.166709
\(23\) −2.26644 −0.472585 −0.236292 0.971682i \(-0.575932\pi\)
−0.236292 + 0.971682i \(0.575932\pi\)
\(24\) 1.21181 0.247360
\(25\) 1.00000 0.200000
\(26\) 4.67597 0.917034
\(27\) 5.49134 1.05681
\(28\) 0.441519 0.0834392
\(29\) 8.38155 1.55642 0.778208 0.628007i \(-0.216129\pi\)
0.778208 + 0.628007i \(0.216129\pi\)
\(30\) −1.21181 −0.221246
\(31\) 7.83398 1.40703 0.703513 0.710683i \(-0.251614\pi\)
0.703513 + 0.710683i \(0.251614\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.947558 −0.164949
\(34\) −0.347476 −0.0595916
\(35\) −0.441519 −0.0746303
\(36\) −1.53151 −0.255252
\(37\) 7.03784 1.15701 0.578507 0.815678i \(-0.303636\pi\)
0.578507 + 0.815678i \(0.303636\pi\)
\(38\) −0.947001 −0.153624
\(39\) 5.66640 0.907351
\(40\) 1.00000 0.158114
\(41\) −4.97470 −0.776918 −0.388459 0.921466i \(-0.626993\pi\)
−0.388459 + 0.921466i \(0.626993\pi\)
\(42\) 0.535038 0.0825582
\(43\) 1.53149 0.233550 0.116775 0.993158i \(-0.462744\pi\)
0.116775 + 0.993158i \(0.462744\pi\)
\(44\) 0.781934 0.117881
\(45\) 1.53151 0.228304
\(46\) 2.26644 0.334168
\(47\) 2.09399 0.305440 0.152720 0.988270i \(-0.451197\pi\)
0.152720 + 0.988270i \(0.451197\pi\)
\(48\) −1.21181 −0.174910
\(49\) −6.80506 −0.972152
\(50\) −1.00000 −0.141421
\(51\) −0.421076 −0.0589624
\(52\) −4.67597 −0.648441
\(53\) −9.21875 −1.26629 −0.633147 0.774032i \(-0.718237\pi\)
−0.633147 + 0.774032i \(0.718237\pi\)
\(54\) −5.49134 −0.747277
\(55\) −0.781934 −0.105436
\(56\) −0.441519 −0.0590004
\(57\) −1.14759 −0.152002
\(58\) −8.38155 −1.10055
\(59\) 7.20809 0.938414 0.469207 0.883088i \(-0.344540\pi\)
0.469207 + 0.883088i \(0.344540\pi\)
\(60\) 1.21181 0.156444
\(61\) −13.0437 −1.67008 −0.835038 0.550193i \(-0.814554\pi\)
−0.835038 + 0.550193i \(0.814554\pi\)
\(62\) −7.83398 −0.994917
\(63\) −0.676190 −0.0851919
\(64\) 1.00000 0.125000
\(65\) 4.67597 0.579983
\(66\) 0.947558 0.116636
\(67\) −11.2388 −1.37304 −0.686522 0.727109i \(-0.740863\pi\)
−0.686522 + 0.727109i \(0.740863\pi\)
\(68\) 0.347476 0.0421376
\(69\) 2.74650 0.330639
\(70\) 0.441519 0.0527716
\(71\) 9.64673 1.14486 0.572428 0.819955i \(-0.306001\pi\)
0.572428 + 0.819955i \(0.306001\pi\)
\(72\) 1.53151 0.180490
\(73\) −5.47699 −0.641034 −0.320517 0.947243i \(-0.603857\pi\)
−0.320517 + 0.947243i \(0.603857\pi\)
\(74\) −7.03784 −0.818132
\(75\) −1.21181 −0.139928
\(76\) 0.947001 0.108628
\(77\) 0.345238 0.0393436
\(78\) −5.66640 −0.641594
\(79\) −1.92618 −0.216712 −0.108356 0.994112i \(-0.534559\pi\)
−0.108356 + 0.994112i \(0.534559\pi\)
\(80\) −1.00000 −0.111803
\(81\) −2.05995 −0.228883
\(82\) 4.97470 0.549364
\(83\) 8.36611 0.918300 0.459150 0.888359i \(-0.348154\pi\)
0.459150 + 0.888359i \(0.348154\pi\)
\(84\) −0.535038 −0.0583774
\(85\) −0.347476 −0.0376891
\(86\) −1.53149 −0.165144
\(87\) −10.1569 −1.08893
\(88\) −0.781934 −0.0833544
\(89\) 7.27170 0.770798 0.385399 0.922750i \(-0.374064\pi\)
0.385399 + 0.922750i \(0.374064\pi\)
\(90\) −1.53151 −0.161435
\(91\) −2.06453 −0.216421
\(92\) −2.26644 −0.236292
\(93\) −9.49332 −0.984412
\(94\) −2.09399 −0.215978
\(95\) −0.947001 −0.0971602
\(96\) 1.21181 0.123680
\(97\) 11.6018 1.17798 0.588992 0.808139i \(-0.299525\pi\)
0.588992 + 0.808139i \(0.299525\pi\)
\(98\) 6.80506 0.687415
\(99\) −1.19754 −0.120357
\(100\) 1.00000 0.100000
\(101\) 1.12415 0.111857 0.0559286 0.998435i \(-0.482188\pi\)
0.0559286 + 0.998435i \(0.482188\pi\)
\(102\) 0.421076 0.0416927
\(103\) −4.02781 −0.396872 −0.198436 0.980114i \(-0.563586\pi\)
−0.198436 + 0.980114i \(0.563586\pi\)
\(104\) 4.67597 0.458517
\(105\) 0.535038 0.0522144
\(106\) 9.21875 0.895405
\(107\) 0.728772 0.0704530 0.0352265 0.999379i \(-0.488785\pi\)
0.0352265 + 0.999379i \(0.488785\pi\)
\(108\) 5.49134 0.528405
\(109\) 9.42649 0.902894 0.451447 0.892298i \(-0.350908\pi\)
0.451447 + 0.892298i \(0.350908\pi\)
\(110\) 0.781934 0.0745545
\(111\) −8.52855 −0.809494
\(112\) 0.441519 0.0417196
\(113\) −3.90239 −0.367106 −0.183553 0.983010i \(-0.558760\pi\)
−0.183553 + 0.983010i \(0.558760\pi\)
\(114\) 1.14759 0.107481
\(115\) 2.26644 0.211346
\(116\) 8.38155 0.778208
\(117\) 7.16130 0.662062
\(118\) −7.20809 −0.663559
\(119\) 0.153417 0.0140637
\(120\) −1.21181 −0.110623
\(121\) −10.3886 −0.944416
\(122\) 13.0437 1.18092
\(123\) 6.02841 0.543563
\(124\) 7.83398 0.703513
\(125\) −1.00000 −0.0894427
\(126\) 0.676190 0.0602398
\(127\) −17.5384 −1.55628 −0.778139 0.628092i \(-0.783836\pi\)
−0.778139 + 0.628092i \(0.783836\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.85588 −0.163401
\(130\) −4.67597 −0.410110
\(131\) −2.83317 −0.247536 −0.123768 0.992311i \(-0.539498\pi\)
−0.123768 + 0.992311i \(0.539498\pi\)
\(132\) −0.947558 −0.0824743
\(133\) 0.418118 0.0362555
\(134\) 11.2388 0.970888
\(135\) −5.49134 −0.472619
\(136\) −0.347476 −0.0297958
\(137\) 10.1243 0.864975 0.432488 0.901640i \(-0.357636\pi\)
0.432488 + 0.901640i \(0.357636\pi\)
\(138\) −2.74650 −0.233797
\(139\) 6.29885 0.534262 0.267131 0.963660i \(-0.413924\pi\)
0.267131 + 0.963660i \(0.413924\pi\)
\(140\) −0.441519 −0.0373151
\(141\) −2.53752 −0.213698
\(142\) −9.64673 −0.809536
\(143\) −3.65630 −0.305755
\(144\) −1.53151 −0.127626
\(145\) −8.38155 −0.696050
\(146\) 5.47699 0.453279
\(147\) 8.24646 0.680157
\(148\) 7.03784 0.578507
\(149\) 3.54263 0.290223 0.145112 0.989415i \(-0.453646\pi\)
0.145112 + 0.989415i \(0.453646\pi\)
\(150\) 1.21181 0.0989441
\(151\) 6.03883 0.491433 0.245716 0.969342i \(-0.420977\pi\)
0.245716 + 0.969342i \(0.420977\pi\)
\(152\) −0.947001 −0.0768119
\(153\) −0.532163 −0.0430228
\(154\) −0.345238 −0.0278201
\(155\) −7.83398 −0.629241
\(156\) 5.66640 0.453675
\(157\) −9.79188 −0.781477 −0.390738 0.920502i \(-0.627780\pi\)
−0.390738 + 0.920502i \(0.627780\pi\)
\(158\) 1.92618 0.153239
\(159\) 11.1714 0.885950
\(160\) 1.00000 0.0790569
\(161\) −1.00067 −0.0788642
\(162\) 2.05995 0.161845
\(163\) −15.1332 −1.18532 −0.592661 0.805452i \(-0.701923\pi\)
−0.592661 + 0.805452i \(0.701923\pi\)
\(164\) −4.97470 −0.388459
\(165\) 0.947558 0.0737673
\(166\) −8.36611 −0.649336
\(167\) −19.9819 −1.54625 −0.773124 0.634255i \(-0.781307\pi\)
−0.773124 + 0.634255i \(0.781307\pi\)
\(168\) 0.535038 0.0412791
\(169\) 8.86473 0.681902
\(170\) 0.347476 0.0266502
\(171\) −1.45034 −0.110910
\(172\) 1.53149 0.116775
\(173\) −2.42866 −0.184648 −0.0923238 0.995729i \(-0.529430\pi\)
−0.0923238 + 0.995729i \(0.529430\pi\)
\(174\) 10.1569 0.769991
\(175\) 0.441519 0.0333757
\(176\) 0.781934 0.0589405
\(177\) −8.73486 −0.656552
\(178\) −7.27170 −0.545037
\(179\) −24.5676 −1.83627 −0.918134 0.396271i \(-0.870304\pi\)
−0.918134 + 0.396271i \(0.870304\pi\)
\(180\) 1.53151 0.114152
\(181\) −5.73582 −0.426340 −0.213170 0.977015i \(-0.568379\pi\)
−0.213170 + 0.977015i \(0.568379\pi\)
\(182\) 2.06453 0.153033
\(183\) 15.8065 1.16845
\(184\) 2.26644 0.167084
\(185\) −7.03784 −0.517432
\(186\) 9.49332 0.696084
\(187\) 0.271703 0.0198689
\(188\) 2.09399 0.152720
\(189\) 2.42453 0.176359
\(190\) 0.947001 0.0687027
\(191\) −11.5893 −0.838571 −0.419285 0.907854i \(-0.637719\pi\)
−0.419285 + 0.907854i \(0.637719\pi\)
\(192\) −1.21181 −0.0874551
\(193\) 1.55342 0.111818 0.0559088 0.998436i \(-0.482194\pi\)
0.0559088 + 0.998436i \(0.482194\pi\)
\(194\) −11.6018 −0.832960
\(195\) −5.66640 −0.405780
\(196\) −6.80506 −0.486076
\(197\) −10.9813 −0.782383 −0.391191 0.920309i \(-0.627937\pi\)
−0.391191 + 0.920309i \(0.627937\pi\)
\(198\) 1.19754 0.0851054
\(199\) 13.9734 0.990546 0.495273 0.868737i \(-0.335068\pi\)
0.495273 + 0.868737i \(0.335068\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 13.6194 0.960637
\(202\) −1.12415 −0.0790950
\(203\) 3.70061 0.259732
\(204\) −0.421076 −0.0294812
\(205\) 4.97470 0.347448
\(206\) 4.02781 0.280631
\(207\) 3.47107 0.241256
\(208\) −4.67597 −0.324220
\(209\) 0.740492 0.0512209
\(210\) −0.535038 −0.0369211
\(211\) 2.91823 0.200899 0.100449 0.994942i \(-0.467972\pi\)
0.100449 + 0.994942i \(0.467972\pi\)
\(212\) −9.21875 −0.633147
\(213\) −11.6900 −0.800988
\(214\) −0.728772 −0.0498178
\(215\) −1.53149 −0.104447
\(216\) −5.49134 −0.373638
\(217\) 3.45885 0.234802
\(218\) −9.42649 −0.638442
\(219\) 6.63709 0.448493
\(220\) −0.781934 −0.0527180
\(221\) −1.62479 −0.109295
\(222\) 8.52855 0.572398
\(223\) −17.8176 −1.19315 −0.596576 0.802557i \(-0.703473\pi\)
−0.596576 + 0.802557i \(0.703473\pi\)
\(224\) −0.441519 −0.0295002
\(225\) −1.53151 −0.102101
\(226\) 3.90239 0.259583
\(227\) 15.5741 1.03369 0.516845 0.856079i \(-0.327106\pi\)
0.516845 + 0.856079i \(0.327106\pi\)
\(228\) −1.14759 −0.0760009
\(229\) 8.00310 0.528860 0.264430 0.964405i \(-0.414816\pi\)
0.264430 + 0.964405i \(0.414816\pi\)
\(230\) −2.26644 −0.149444
\(231\) −0.418364 −0.0275264
\(232\) −8.38155 −0.550276
\(233\) 14.7387 0.965565 0.482782 0.875740i \(-0.339626\pi\)
0.482782 + 0.875740i \(0.339626\pi\)
\(234\) −7.16130 −0.468149
\(235\) −2.09399 −0.136597
\(236\) 7.20809 0.469207
\(237\) 2.33417 0.151621
\(238\) −0.153417 −0.00994455
\(239\) 0.273552 0.0176946 0.00884732 0.999961i \(-0.497184\pi\)
0.00884732 + 0.999961i \(0.497184\pi\)
\(240\) 1.21181 0.0782222
\(241\) 0.940060 0.0605546 0.0302773 0.999542i \(-0.490361\pi\)
0.0302773 + 0.999542i \(0.490361\pi\)
\(242\) 10.3886 0.667803
\(243\) −13.9778 −0.896673
\(244\) −13.0437 −0.835038
\(245\) 6.80506 0.434759
\(246\) −6.02841 −0.384357
\(247\) −4.42815 −0.281756
\(248\) −7.83398 −0.497459
\(249\) −10.1382 −0.642480
\(250\) 1.00000 0.0632456
\(251\) 3.17592 0.200462 0.100231 0.994964i \(-0.468042\pi\)
0.100231 + 0.994964i \(0.468042\pi\)
\(252\) −0.676190 −0.0425960
\(253\) −1.77220 −0.111418
\(254\) 17.5384 1.10045
\(255\) 0.421076 0.0263688
\(256\) 1.00000 0.0625000
\(257\) −18.2747 −1.13995 −0.569973 0.821663i \(-0.693046\pi\)
−0.569973 + 0.821663i \(0.693046\pi\)
\(258\) 1.85588 0.115542
\(259\) 3.10734 0.193081
\(260\) 4.67597 0.289992
\(261\) −12.8364 −0.794555
\(262\) 2.83317 0.175034
\(263\) 22.1564 1.36622 0.683111 0.730315i \(-0.260627\pi\)
0.683111 + 0.730315i \(0.260627\pi\)
\(264\) 0.947558 0.0583181
\(265\) 9.21875 0.566304
\(266\) −0.418118 −0.0256365
\(267\) −8.81194 −0.539282
\(268\) −11.2388 −0.686522
\(269\) −30.9675 −1.88812 −0.944060 0.329774i \(-0.893027\pi\)
−0.944060 + 0.329774i \(0.893027\pi\)
\(270\) 5.49134 0.334192
\(271\) −0.286023 −0.0173747 −0.00868734 0.999962i \(-0.502765\pi\)
−0.00868734 + 0.999962i \(0.502765\pi\)
\(272\) 0.347476 0.0210688
\(273\) 2.50182 0.151417
\(274\) −10.1243 −0.611630
\(275\) 0.781934 0.0471524
\(276\) 2.74650 0.165320
\(277\) −16.2895 −0.978739 −0.489370 0.872076i \(-0.662773\pi\)
−0.489370 + 0.872076i \(0.662773\pi\)
\(278\) −6.29885 −0.377780
\(279\) −11.9978 −0.718291
\(280\) 0.441519 0.0263858
\(281\) −6.11821 −0.364982 −0.182491 0.983208i \(-0.558416\pi\)
−0.182491 + 0.983208i \(0.558416\pi\)
\(282\) 2.53752 0.151107
\(283\) −29.3709 −1.74592 −0.872959 0.487793i \(-0.837802\pi\)
−0.872959 + 0.487793i \(0.837802\pi\)
\(284\) 9.64673 0.572428
\(285\) 1.14759 0.0679772
\(286\) 3.65630 0.216202
\(287\) −2.19642 −0.129651
\(288\) 1.53151 0.0902451
\(289\) −16.8793 −0.992898
\(290\) 8.38155 0.492182
\(291\) −14.0592 −0.824165
\(292\) −5.47699 −0.320517
\(293\) −1.39480 −0.0814854 −0.0407427 0.999170i \(-0.512972\pi\)
−0.0407427 + 0.999170i \(0.512972\pi\)
\(294\) −8.24646 −0.480943
\(295\) −7.20809 −0.419671
\(296\) −7.03784 −0.409066
\(297\) 4.29387 0.249155
\(298\) −3.54263 −0.205219
\(299\) 10.5978 0.612887
\(300\) −1.21181 −0.0699641
\(301\) 0.676180 0.0389744
\(302\) −6.03883 −0.347495
\(303\) −1.36226 −0.0782599
\(304\) 0.947001 0.0543142
\(305\) 13.0437 0.746880
\(306\) 0.532163 0.0304217
\(307\) 14.3901 0.821286 0.410643 0.911796i \(-0.365304\pi\)
0.410643 + 0.911796i \(0.365304\pi\)
\(308\) 0.345238 0.0196718
\(309\) 4.88096 0.277668
\(310\) 7.83398 0.444940
\(311\) 10.3774 0.588448 0.294224 0.955736i \(-0.404939\pi\)
0.294224 + 0.955736i \(0.404939\pi\)
\(312\) −5.66640 −0.320797
\(313\) −1.21333 −0.0685817 −0.0342908 0.999412i \(-0.510917\pi\)
−0.0342908 + 0.999412i \(0.510917\pi\)
\(314\) 9.79188 0.552588
\(315\) 0.676190 0.0380990
\(316\) −1.92618 −0.108356
\(317\) −12.8494 −0.721694 −0.360847 0.932625i \(-0.617512\pi\)
−0.360847 + 0.932625i \(0.617512\pi\)
\(318\) −11.1714 −0.626461
\(319\) 6.55382 0.366944
\(320\) −1.00000 −0.0559017
\(321\) −0.883135 −0.0492918
\(322\) 1.00067 0.0557654
\(323\) 0.329060 0.0183094
\(324\) −2.05995 −0.114442
\(325\) −4.67597 −0.259376
\(326\) 15.1332 0.838149
\(327\) −11.4231 −0.631701
\(328\) 4.97470 0.274682
\(329\) 0.924535 0.0509712
\(330\) −0.947558 −0.0521613
\(331\) −8.01850 −0.440737 −0.220368 0.975417i \(-0.570726\pi\)
−0.220368 + 0.975417i \(0.570726\pi\)
\(332\) 8.36611 0.459150
\(333\) −10.7785 −0.590659
\(334\) 19.9819 1.09336
\(335\) 11.2388 0.614044
\(336\) −0.535038 −0.0291887
\(337\) 13.1570 0.716708 0.358354 0.933586i \(-0.383338\pi\)
0.358354 + 0.933586i \(0.383338\pi\)
\(338\) −8.86473 −0.482178
\(339\) 4.72897 0.256842
\(340\) −0.347476 −0.0188445
\(341\) 6.12566 0.331723
\(342\) 1.45034 0.0784254
\(343\) −6.09519 −0.329109
\(344\) −1.53149 −0.0825722
\(345\) −2.74650 −0.147866
\(346\) 2.42866 0.130566
\(347\) −15.7431 −0.845132 −0.422566 0.906332i \(-0.638870\pi\)
−0.422566 + 0.906332i \(0.638870\pi\)
\(348\) −10.1569 −0.544466
\(349\) −4.78445 −0.256106 −0.128053 0.991767i \(-0.540873\pi\)
−0.128053 + 0.991767i \(0.540873\pi\)
\(350\) −0.441519 −0.0236002
\(351\) −25.6774 −1.37056
\(352\) −0.781934 −0.0416772
\(353\) 5.67180 0.301880 0.150940 0.988543i \(-0.451770\pi\)
0.150940 + 0.988543i \(0.451770\pi\)
\(354\) 8.73486 0.464252
\(355\) −9.64673 −0.511995
\(356\) 7.27170 0.385399
\(357\) −0.185913 −0.00983955
\(358\) 24.5676 1.29844
\(359\) −3.45971 −0.182597 −0.0912983 0.995824i \(-0.529102\pi\)
−0.0912983 + 0.995824i \(0.529102\pi\)
\(360\) −1.53151 −0.0807176
\(361\) −18.1032 −0.952799
\(362\) 5.73582 0.301468
\(363\) 12.5890 0.660752
\(364\) −2.06453 −0.108211
\(365\) 5.47699 0.286679
\(366\) −15.8065 −0.826221
\(367\) −19.2846 −1.00665 −0.503325 0.864097i \(-0.667890\pi\)
−0.503325 + 0.864097i \(0.667890\pi\)
\(368\) −2.26644 −0.118146
\(369\) 7.61880 0.396619
\(370\) 7.03784 0.365880
\(371\) −4.07025 −0.211317
\(372\) −9.49332 −0.492206
\(373\) −21.5390 −1.11525 −0.557623 0.830094i \(-0.688287\pi\)
−0.557623 + 0.830094i \(0.688287\pi\)
\(374\) −0.271703 −0.0140494
\(375\) 1.21181 0.0625778
\(376\) −2.09399 −0.107989
\(377\) −39.1919 −2.01849
\(378\) −2.42453 −0.124704
\(379\) 4.78597 0.245839 0.122920 0.992417i \(-0.460774\pi\)
0.122920 + 0.992417i \(0.460774\pi\)
\(380\) −0.947001 −0.0485801
\(381\) 21.2532 1.08884
\(382\) 11.5893 0.592959
\(383\) 6.11975 0.312705 0.156352 0.987701i \(-0.450026\pi\)
0.156352 + 0.987701i \(0.450026\pi\)
\(384\) 1.21181 0.0618401
\(385\) −0.345238 −0.0175950
\(386\) −1.55342 −0.0790670
\(387\) −2.34549 −0.119228
\(388\) 11.6018 0.588992
\(389\) 3.87667 0.196555 0.0982775 0.995159i \(-0.468667\pi\)
0.0982775 + 0.995159i \(0.468667\pi\)
\(390\) 5.66640 0.286930
\(391\) −0.787532 −0.0398272
\(392\) 6.80506 0.343708
\(393\) 3.43328 0.173186
\(394\) 10.9813 0.553228
\(395\) 1.92618 0.0969167
\(396\) −1.19754 −0.0601786
\(397\) −28.6478 −1.43779 −0.718896 0.695118i \(-0.755352\pi\)
−0.718896 + 0.695118i \(0.755352\pi\)
\(398\) −13.9734 −0.700422
\(399\) −0.506681 −0.0253658
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −13.6194 −0.679273
\(403\) −36.6315 −1.82475
\(404\) 1.12415 0.0559286
\(405\) 2.05995 0.102360
\(406\) −3.70061 −0.183658
\(407\) 5.50313 0.272780
\(408\) 0.421076 0.0208464
\(409\) −5.74096 −0.283872 −0.141936 0.989876i \(-0.545333\pi\)
−0.141936 + 0.989876i \(0.545333\pi\)
\(410\) −4.97470 −0.245683
\(411\) −12.2687 −0.605172
\(412\) −4.02781 −0.198436
\(413\) 3.18251 0.156601
\(414\) −3.47107 −0.170594
\(415\) −8.36611 −0.410676
\(416\) 4.67597 0.229258
\(417\) −7.63303 −0.373791
\(418\) −0.740492 −0.0362187
\(419\) −3.90764 −0.190901 −0.0954505 0.995434i \(-0.530429\pi\)
−0.0954505 + 0.995434i \(0.530429\pi\)
\(420\) 0.535038 0.0261072
\(421\) 18.4802 0.900668 0.450334 0.892860i \(-0.351305\pi\)
0.450334 + 0.892860i \(0.351305\pi\)
\(422\) −2.91823 −0.142057
\(423\) −3.20696 −0.155928
\(424\) 9.21875 0.447702
\(425\) 0.347476 0.0168551
\(426\) 11.6900 0.566384
\(427\) −5.75904 −0.278699
\(428\) 0.728772 0.0352265
\(429\) 4.43075 0.213919
\(430\) 1.53149 0.0738548
\(431\) −38.8156 −1.86968 −0.934841 0.355067i \(-0.884458\pi\)
−0.934841 + 0.355067i \(0.884458\pi\)
\(432\) 5.49134 0.264202
\(433\) 9.40605 0.452026 0.226013 0.974124i \(-0.427431\pi\)
0.226013 + 0.974124i \(0.427431\pi\)
\(434\) −3.45885 −0.166030
\(435\) 10.1569 0.486985
\(436\) 9.42649 0.451447
\(437\) −2.14632 −0.102672
\(438\) −6.63709 −0.317132
\(439\) −2.85365 −0.136197 −0.0680987 0.997679i \(-0.521693\pi\)
−0.0680987 + 0.997679i \(0.521693\pi\)
\(440\) 0.781934 0.0372772
\(441\) 10.4220 0.496286
\(442\) 1.62479 0.0772833
\(443\) −18.8725 −0.896660 −0.448330 0.893868i \(-0.647981\pi\)
−0.448330 + 0.893868i \(0.647981\pi\)
\(444\) −8.52855 −0.404747
\(445\) −7.27170 −0.344711
\(446\) 17.8176 0.843686
\(447\) −4.29300 −0.203052
\(448\) 0.441519 0.0208598
\(449\) 21.0421 0.993038 0.496519 0.868026i \(-0.334611\pi\)
0.496519 + 0.868026i \(0.334611\pi\)
\(450\) 1.53151 0.0721960
\(451\) −3.88989 −0.183168
\(452\) −3.90239 −0.183553
\(453\) −7.31793 −0.343826
\(454\) −15.5741 −0.730929
\(455\) 2.06453 0.0967866
\(456\) 1.14759 0.0537407
\(457\) −8.24588 −0.385726 −0.192863 0.981226i \(-0.561777\pi\)
−0.192863 + 0.981226i \(0.561777\pi\)
\(458\) −8.00310 −0.373960
\(459\) 1.90811 0.0890629
\(460\) 2.26644 0.105673
\(461\) 28.0292 1.30545 0.652724 0.757596i \(-0.273626\pi\)
0.652724 + 0.757596i \(0.273626\pi\)
\(462\) 0.418364 0.0194641
\(463\) −28.1590 −1.30866 −0.654329 0.756210i \(-0.727049\pi\)
−0.654329 + 0.756210i \(0.727049\pi\)
\(464\) 8.38155 0.389104
\(465\) 9.49332 0.440242
\(466\) −14.7387 −0.682758
\(467\) −1.74732 −0.0808565 −0.0404282 0.999182i \(-0.512872\pi\)
−0.0404282 + 0.999182i \(0.512872\pi\)
\(468\) 7.16130 0.331031
\(469\) −4.96216 −0.229131
\(470\) 2.09399 0.0965885
\(471\) 11.8659 0.546753
\(472\) −7.20809 −0.331779
\(473\) 1.19752 0.0550621
\(474\) −2.33417 −0.107212
\(475\) 0.947001 0.0434514
\(476\) 0.153417 0.00703186
\(477\) 14.1186 0.646447
\(478\) −0.273552 −0.0125120
\(479\) 26.2763 1.20059 0.600297 0.799777i \(-0.295049\pi\)
0.600297 + 0.799777i \(0.295049\pi\)
\(480\) −1.21181 −0.0553114
\(481\) −32.9087 −1.50051
\(482\) −0.940060 −0.0428185
\(483\) 1.21263 0.0551766
\(484\) −10.3886 −0.472208
\(485\) −11.6018 −0.526810
\(486\) 13.9778 0.634044
\(487\) −23.8805 −1.08213 −0.541065 0.840981i \(-0.681979\pi\)
−0.541065 + 0.840981i \(0.681979\pi\)
\(488\) 13.0437 0.590461
\(489\) 18.3386 0.829299
\(490\) −6.80506 −0.307421
\(491\) −8.48580 −0.382959 −0.191479 0.981497i \(-0.561328\pi\)
−0.191479 + 0.981497i \(0.561328\pi\)
\(492\) 6.02841 0.271782
\(493\) 2.91239 0.131167
\(494\) 4.42815 0.199232
\(495\) 1.19754 0.0538254
\(496\) 7.83398 0.351756
\(497\) 4.25921 0.191052
\(498\) 10.1382 0.454302
\(499\) −15.8989 −0.711731 −0.355866 0.934537i \(-0.615814\pi\)
−0.355866 + 0.934537i \(0.615814\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 24.2144 1.08182
\(502\) −3.17592 −0.141748
\(503\) −1.89612 −0.0845440 −0.0422720 0.999106i \(-0.513460\pi\)
−0.0422720 + 0.999106i \(0.513460\pi\)
\(504\) 0.676190 0.0301199
\(505\) −1.12415 −0.0500241
\(506\) 1.77220 0.0787841
\(507\) −10.7424 −0.477086
\(508\) −17.5384 −0.778139
\(509\) 34.6656 1.53653 0.768263 0.640134i \(-0.221121\pi\)
0.768263 + 0.640134i \(0.221121\pi\)
\(510\) −0.421076 −0.0186456
\(511\) −2.41819 −0.106975
\(512\) −1.00000 −0.0441942
\(513\) 5.20031 0.229599
\(514\) 18.2747 0.806064
\(515\) 4.02781 0.177487
\(516\) −1.85588 −0.0817004
\(517\) 1.63736 0.0720110
\(518\) −3.10734 −0.136529
\(519\) 2.94308 0.129187
\(520\) −4.67597 −0.205055
\(521\) 23.1428 1.01391 0.506953 0.861974i \(-0.330772\pi\)
0.506953 + 0.861974i \(0.330772\pi\)
\(522\) 12.8364 0.561835
\(523\) 18.2417 0.797656 0.398828 0.917026i \(-0.369417\pi\)
0.398828 + 0.917026i \(0.369417\pi\)
\(524\) −2.83317 −0.123768
\(525\) −0.535038 −0.0233510
\(526\) −22.1564 −0.966065
\(527\) 2.72212 0.118577
\(528\) −0.947558 −0.0412372
\(529\) −17.8633 −0.776664
\(530\) −9.21875 −0.400437
\(531\) −11.0393 −0.479063
\(532\) 0.418118 0.0181277
\(533\) 23.2616 1.00757
\(534\) 8.81194 0.381330
\(535\) −0.728772 −0.0315075
\(536\) 11.2388 0.485444
\(537\) 29.7713 1.28473
\(538\) 30.9675 1.33510
\(539\) −5.32111 −0.229196
\(540\) −5.49134 −0.236310
\(541\) 4.08936 0.175815 0.0879077 0.996129i \(-0.471982\pi\)
0.0879077 + 0.996129i \(0.471982\pi\)
\(542\) 0.286023 0.0122858
\(543\) 6.95074 0.298285
\(544\) −0.347476 −0.0148979
\(545\) −9.42649 −0.403786
\(546\) −2.50182 −0.107068
\(547\) −0.598670 −0.0255973 −0.0127986 0.999918i \(-0.504074\pi\)
−0.0127986 + 0.999918i \(0.504074\pi\)
\(548\) 10.1243 0.432488
\(549\) 19.9766 0.852579
\(550\) −0.781934 −0.0333418
\(551\) 7.93734 0.338142
\(552\) −2.74650 −0.116899
\(553\) −0.850445 −0.0361646
\(554\) 16.2895 0.692073
\(555\) 8.52855 0.362017
\(556\) 6.29885 0.267131
\(557\) 2.59015 0.109748 0.0548740 0.998493i \(-0.482524\pi\)
0.0548740 + 0.998493i \(0.482524\pi\)
\(558\) 11.9978 0.507908
\(559\) −7.16119 −0.302886
\(560\) −0.441519 −0.0186576
\(561\) −0.329254 −0.0139011
\(562\) 6.11821 0.258081
\(563\) −27.6580 −1.16565 −0.582823 0.812599i \(-0.698052\pi\)
−0.582823 + 0.812599i \(0.698052\pi\)
\(564\) −2.53752 −0.106849
\(565\) 3.90239 0.164175
\(566\) 29.3709 1.23455
\(567\) −0.909507 −0.0381957
\(568\) −9.64673 −0.404768
\(569\) 39.1870 1.64280 0.821401 0.570351i \(-0.193193\pi\)
0.821401 + 0.570351i \(0.193193\pi\)
\(570\) −1.14759 −0.0480672
\(571\) −41.8064 −1.74954 −0.874772 0.484536i \(-0.838989\pi\)
−0.874772 + 0.484536i \(0.838989\pi\)
\(572\) −3.65630 −0.152878
\(573\) 14.0440 0.586698
\(574\) 2.19642 0.0916770
\(575\) −2.26644 −0.0945170
\(576\) −1.53151 −0.0638129
\(577\) −37.4265 −1.55808 −0.779042 0.626971i \(-0.784294\pi\)
−0.779042 + 0.626971i \(0.784294\pi\)
\(578\) 16.8793 0.702085
\(579\) −1.88245 −0.0782321
\(580\) −8.38155 −0.348025
\(581\) 3.69379 0.153244
\(582\) 14.0592 0.582773
\(583\) −7.20846 −0.298544
\(584\) 5.47699 0.226640
\(585\) −7.16130 −0.296083
\(586\) 1.39480 0.0576188
\(587\) 18.2023 0.751289 0.375645 0.926764i \(-0.377421\pi\)
0.375645 + 0.926764i \(0.377421\pi\)
\(588\) 8.24646 0.340078
\(589\) 7.41879 0.305686
\(590\) 7.20809 0.296752
\(591\) 13.3072 0.547387
\(592\) 7.03784 0.289253
\(593\) 12.1539 0.499099 0.249550 0.968362i \(-0.419717\pi\)
0.249550 + 0.968362i \(0.419717\pi\)
\(594\) −4.29387 −0.176179
\(595\) −0.153417 −0.00628949
\(596\) 3.54263 0.145112
\(597\) −16.9331 −0.693026
\(598\) −10.5978 −0.433376
\(599\) 24.6183 1.00588 0.502938 0.864323i \(-0.332252\pi\)
0.502938 + 0.864323i \(0.332252\pi\)
\(600\) 1.21181 0.0494721
\(601\) −5.83318 −0.237940 −0.118970 0.992898i \(-0.537959\pi\)
−0.118970 + 0.992898i \(0.537959\pi\)
\(602\) −0.676180 −0.0275590
\(603\) 17.2124 0.700943
\(604\) 6.03883 0.245716
\(605\) 10.3886 0.422356
\(606\) 1.36226 0.0553381
\(607\) 5.32952 0.216319 0.108159 0.994134i \(-0.465504\pi\)
0.108159 + 0.994134i \(0.465504\pi\)
\(608\) −0.947001 −0.0384060
\(609\) −4.48445 −0.181719
\(610\) −13.0437 −0.528124
\(611\) −9.79143 −0.396119
\(612\) −0.532163 −0.0215114
\(613\) 3.17924 0.128408 0.0642041 0.997937i \(-0.479549\pi\)
0.0642041 + 0.997937i \(0.479549\pi\)
\(614\) −14.3901 −0.580737
\(615\) −6.02841 −0.243089
\(616\) −0.345238 −0.0139101
\(617\) 26.6755 1.07391 0.536957 0.843609i \(-0.319574\pi\)
0.536957 + 0.843609i \(0.319574\pi\)
\(618\) −4.88096 −0.196341
\(619\) −27.3184 −1.09802 −0.549010 0.835816i \(-0.684995\pi\)
−0.549010 + 0.835816i \(0.684995\pi\)
\(620\) −7.83398 −0.314620
\(621\) −12.4458 −0.499432
\(622\) −10.3774 −0.416096
\(623\) 3.21059 0.128630
\(624\) 5.66640 0.226838
\(625\) 1.00000 0.0400000
\(626\) 1.21333 0.0484946
\(627\) −0.897338 −0.0358362
\(628\) −9.79188 −0.390738
\(629\) 2.44548 0.0975077
\(630\) −0.676190 −0.0269400
\(631\) 12.0937 0.481444 0.240722 0.970594i \(-0.422616\pi\)
0.240722 + 0.970594i \(0.422616\pi\)
\(632\) 1.92618 0.0766194
\(633\) −3.53634 −0.140557
\(634\) 12.8494 0.510315
\(635\) 17.5384 0.695989
\(636\) 11.1714 0.442975
\(637\) 31.8203 1.26077
\(638\) −6.55382 −0.259468
\(639\) −14.7741 −0.584453
\(640\) 1.00000 0.0395285
\(641\) −20.5534 −0.811809 −0.405905 0.913915i \(-0.633044\pi\)
−0.405905 + 0.913915i \(0.633044\pi\)
\(642\) 0.883135 0.0348546
\(643\) −29.4893 −1.16294 −0.581472 0.813567i \(-0.697523\pi\)
−0.581472 + 0.813567i \(0.697523\pi\)
\(644\) −1.00067 −0.0394321
\(645\) 1.85588 0.0730750
\(646\) −0.329060 −0.0129467
\(647\) 14.6520 0.576029 0.288014 0.957626i \(-0.407005\pi\)
0.288014 + 0.957626i \(0.407005\pi\)
\(648\) 2.05995 0.0809225
\(649\) 5.63625 0.221242
\(650\) 4.67597 0.183407
\(651\) −4.19148 −0.164277
\(652\) −15.1332 −0.592661
\(653\) −4.47836 −0.175252 −0.0876260 0.996153i \(-0.527928\pi\)
−0.0876260 + 0.996153i \(0.527928\pi\)
\(654\) 11.4231 0.446680
\(655\) 2.83317 0.110701
\(656\) −4.97470 −0.194230
\(657\) 8.38807 0.327250
\(658\) −0.924535 −0.0360421
\(659\) −7.32171 −0.285213 −0.142607 0.989779i \(-0.545548\pi\)
−0.142607 + 0.989779i \(0.545548\pi\)
\(660\) 0.947558 0.0368836
\(661\) 38.1544 1.48403 0.742017 0.670381i \(-0.233869\pi\)
0.742017 + 0.670381i \(0.233869\pi\)
\(662\) 8.01850 0.311648
\(663\) 1.96894 0.0764673
\(664\) −8.36611 −0.324668
\(665\) −0.418118 −0.0162139
\(666\) 10.7785 0.417659
\(667\) −18.9963 −0.735538
\(668\) −19.9819 −0.773124
\(669\) 21.5915 0.834777
\(670\) −11.2388 −0.434195
\(671\) −10.1993 −0.393740
\(672\) 0.535038 0.0206395
\(673\) −0.557535 −0.0214914 −0.0107457 0.999942i \(-0.503421\pi\)
−0.0107457 + 0.999942i \(0.503421\pi\)
\(674\) −13.1570 −0.506789
\(675\) 5.49134 0.211362
\(676\) 8.86473 0.340951
\(677\) −25.7037 −0.987872 −0.493936 0.869498i \(-0.664442\pi\)
−0.493936 + 0.869498i \(0.664442\pi\)
\(678\) −4.72897 −0.181615
\(679\) 5.12241 0.196580
\(680\) 0.347476 0.0133251
\(681\) −18.8729 −0.723212
\(682\) −6.12566 −0.234564
\(683\) −11.4197 −0.436961 −0.218480 0.975841i \(-0.570110\pi\)
−0.218480 + 0.975841i \(0.570110\pi\)
\(684\) −1.45034 −0.0554552
\(685\) −10.1243 −0.386829
\(686\) 6.09519 0.232715
\(687\) −9.69826 −0.370012
\(688\) 1.53149 0.0583874
\(689\) 43.1066 1.64223
\(690\) 2.74650 0.104557
\(691\) −28.2101 −1.07316 −0.536582 0.843848i \(-0.680285\pi\)
−0.536582 + 0.843848i \(0.680285\pi\)
\(692\) −2.42866 −0.0923238
\(693\) −0.528736 −0.0200850
\(694\) 15.7431 0.597598
\(695\) −6.29885 −0.238929
\(696\) 10.1569 0.384995
\(697\) −1.72859 −0.0654750
\(698\) 4.78445 0.181094
\(699\) −17.8606 −0.675548
\(700\) 0.441519 0.0166878
\(701\) −25.3329 −0.956812 −0.478406 0.878139i \(-0.658785\pi\)
−0.478406 + 0.878139i \(0.658785\pi\)
\(702\) 25.6774 0.969130
\(703\) 6.66484 0.251369
\(704\) 0.781934 0.0294702
\(705\) 2.53752 0.0955686
\(706\) −5.67180 −0.213461
\(707\) 0.496334 0.0186666
\(708\) −8.73486 −0.328276
\(709\) −40.4961 −1.52086 −0.760432 0.649418i \(-0.775013\pi\)
−0.760432 + 0.649418i \(0.775013\pi\)
\(710\) 9.64673 0.362035
\(711\) 2.94997 0.110632
\(712\) −7.27170 −0.272518
\(713\) −17.7552 −0.664939
\(714\) 0.185913 0.00695761
\(715\) 3.65630 0.136738
\(716\) −24.5676 −0.918134
\(717\) −0.331494 −0.0123799
\(718\) 3.45971 0.129115
\(719\) −22.3153 −0.832221 −0.416111 0.909314i \(-0.636607\pi\)
−0.416111 + 0.909314i \(0.636607\pi\)
\(720\) 1.53151 0.0570760
\(721\) −1.77835 −0.0662294
\(722\) 18.1032 0.673731
\(723\) −1.13918 −0.0423664
\(724\) −5.73582 −0.213170
\(725\) 8.38155 0.311283
\(726\) −12.5890 −0.467222
\(727\) 23.5195 0.872289 0.436145 0.899877i \(-0.356344\pi\)
0.436145 + 0.899877i \(0.356344\pi\)
\(728\) 2.06453 0.0765165
\(729\) 23.1183 0.856232
\(730\) −5.47699 −0.202713
\(731\) 0.532155 0.0196825
\(732\) 15.8065 0.584226
\(733\) 47.5357 1.75577 0.877885 0.478872i \(-0.158954\pi\)
0.877885 + 0.478872i \(0.158954\pi\)
\(734\) 19.2846 0.711809
\(735\) −8.24646 −0.304175
\(736\) 2.26644 0.0835420
\(737\) −8.78804 −0.323711
\(738\) −7.61880 −0.280452
\(739\) 9.07806 0.333942 0.166971 0.985962i \(-0.446601\pi\)
0.166971 + 0.985962i \(0.446601\pi\)
\(740\) −7.03784 −0.258716
\(741\) 5.36609 0.197128
\(742\) 4.07025 0.149424
\(743\) 28.6060 1.04945 0.524725 0.851272i \(-0.324168\pi\)
0.524725 + 0.851272i \(0.324168\pi\)
\(744\) 9.49332 0.348042
\(745\) −3.54263 −0.129792
\(746\) 21.5390 0.788598
\(747\) −12.8128 −0.468795
\(748\) 0.271703 0.00993445
\(749\) 0.321766 0.0117571
\(750\) −1.21181 −0.0442492
\(751\) −22.6726 −0.827335 −0.413668 0.910428i \(-0.635752\pi\)
−0.413668 + 0.910428i \(0.635752\pi\)
\(752\) 2.09399 0.0763599
\(753\) −3.84862 −0.140251
\(754\) 39.1919 1.42729
\(755\) −6.03883 −0.219775
\(756\) 2.42453 0.0881793
\(757\) 22.3643 0.812843 0.406421 0.913686i \(-0.366777\pi\)
0.406421 + 0.913686i \(0.366777\pi\)
\(758\) −4.78597 −0.173834
\(759\) 2.14758 0.0779522
\(760\) 0.947001 0.0343513
\(761\) 2.61429 0.0947680 0.0473840 0.998877i \(-0.484912\pi\)
0.0473840 + 0.998877i \(0.484912\pi\)
\(762\) −21.2532 −0.769923
\(763\) 4.16197 0.150673
\(764\) −11.5893 −0.419285
\(765\) 0.532163 0.0192404
\(766\) −6.11975 −0.221116
\(767\) −33.7048 −1.21701
\(768\) −1.21181 −0.0437275
\(769\) 11.3662 0.409875 0.204938 0.978775i \(-0.434301\pi\)
0.204938 + 0.978775i \(0.434301\pi\)
\(770\) 0.345238 0.0124415
\(771\) 22.1456 0.797553
\(772\) 1.55342 0.0559088
\(773\) −17.5362 −0.630734 −0.315367 0.948970i \(-0.602128\pi\)
−0.315367 + 0.948970i \(0.602128\pi\)
\(774\) 2.34549 0.0843068
\(775\) 7.83398 0.281405
\(776\) −11.6018 −0.416480
\(777\) −3.76551 −0.135087
\(778\) −3.87667 −0.138985
\(779\) −4.71105 −0.168791
\(780\) −5.66640 −0.202890
\(781\) 7.54311 0.269914
\(782\) 0.787532 0.0281621
\(783\) 46.0260 1.64483
\(784\) −6.80506 −0.243038
\(785\) 9.79188 0.349487
\(786\) −3.43328 −0.122461
\(787\) 7.48945 0.266970 0.133485 0.991051i \(-0.457383\pi\)
0.133485 + 0.991051i \(0.457383\pi\)
\(788\) −10.9813 −0.391191
\(789\) −26.8494 −0.955864
\(790\) −1.92618 −0.0685305
\(791\) −1.72298 −0.0612620
\(792\) 1.19754 0.0425527
\(793\) 60.9920 2.16589
\(794\) 28.6478 1.01667
\(795\) −11.1714 −0.396209
\(796\) 13.9734 0.495273
\(797\) 0.761516 0.0269743 0.0134871 0.999909i \(-0.495707\pi\)
0.0134871 + 0.999909i \(0.495707\pi\)
\(798\) 0.506681 0.0179363
\(799\) 0.727610 0.0257410
\(800\) −1.00000 −0.0353553
\(801\) −11.1367 −0.393495
\(802\) 1.00000 0.0353112
\(803\) −4.28265 −0.151131
\(804\) 13.6194 0.480318
\(805\) 1.00067 0.0352691
\(806\) 36.6315 1.29029
\(807\) 37.5268 1.32101
\(808\) −1.12415 −0.0395475
\(809\) −11.2517 −0.395587 −0.197794 0.980244i \(-0.563378\pi\)
−0.197794 + 0.980244i \(0.563378\pi\)
\(810\) −2.05995 −0.0723793
\(811\) −46.7416 −1.64132 −0.820661 0.571416i \(-0.806394\pi\)
−0.820661 + 0.571416i \(0.806394\pi\)
\(812\) 3.70061 0.129866
\(813\) 0.346607 0.0121560
\(814\) −5.50313 −0.192884
\(815\) 15.1332 0.530092
\(816\) −0.421076 −0.0147406
\(817\) 1.45032 0.0507402
\(818\) 5.74096 0.200728
\(819\) 3.16185 0.110484
\(820\) 4.97470 0.173724
\(821\) −20.4555 −0.713904 −0.356952 0.934123i \(-0.616184\pi\)
−0.356952 + 0.934123i \(0.616184\pi\)
\(822\) 12.2687 0.427921
\(823\) −29.6757 −1.03443 −0.517214 0.855856i \(-0.673031\pi\)
−0.517214 + 0.855856i \(0.673031\pi\)
\(824\) 4.02781 0.140316
\(825\) −0.947558 −0.0329897
\(826\) −3.18251 −0.110734
\(827\) 1.06553 0.0370520 0.0185260 0.999828i \(-0.494103\pi\)
0.0185260 + 0.999828i \(0.494103\pi\)
\(828\) 3.47107 0.120628
\(829\) 56.0850 1.94791 0.973957 0.226735i \(-0.0728050\pi\)
0.973957 + 0.226735i \(0.0728050\pi\)
\(830\) 8.36611 0.290392
\(831\) 19.7398 0.684766
\(832\) −4.67597 −0.162110
\(833\) −2.36460 −0.0819284
\(834\) 7.63303 0.264310
\(835\) 19.9819 0.691503
\(836\) 0.740492 0.0256105
\(837\) 43.0191 1.48696
\(838\) 3.90764 0.134987
\(839\) 36.8965 1.27381 0.636905 0.770942i \(-0.280214\pi\)
0.636905 + 0.770942i \(0.280214\pi\)
\(840\) −0.535038 −0.0184606
\(841\) 41.2504 1.42243
\(842\) −18.4802 −0.636868
\(843\) 7.41413 0.255356
\(844\) 2.91823 0.100449
\(845\) −8.86473 −0.304956
\(846\) 3.20696 0.110258
\(847\) −4.58675 −0.157603
\(848\) −9.21875 −0.316573
\(849\) 35.5920 1.22152
\(850\) −0.347476 −0.0119183
\(851\) −15.9508 −0.546787
\(852\) −11.6900 −0.400494
\(853\) 21.5303 0.737182 0.368591 0.929592i \(-0.379840\pi\)
0.368591 + 0.929592i \(0.379840\pi\)
\(854\) 5.75904 0.197070
\(855\) 1.45034 0.0496006
\(856\) −0.728772 −0.0249089
\(857\) 4.60168 0.157191 0.0785953 0.996907i \(-0.474957\pi\)
0.0785953 + 0.996907i \(0.474957\pi\)
\(858\) −4.43075 −0.151263
\(859\) −42.9929 −1.46690 −0.733450 0.679744i \(-0.762091\pi\)
−0.733450 + 0.679744i \(0.762091\pi\)
\(860\) −1.53149 −0.0522233
\(861\) 2.66166 0.0907090
\(862\) 38.8156 1.32206
\(863\) 19.4634 0.662543 0.331272 0.943535i \(-0.392522\pi\)
0.331272 + 0.943535i \(0.392522\pi\)
\(864\) −5.49134 −0.186819
\(865\) 2.42866 0.0825770
\(866\) −9.40605 −0.319631
\(867\) 20.4545 0.694671
\(868\) 3.45885 0.117401
\(869\) −1.50615 −0.0510925
\(870\) −10.1569 −0.344350
\(871\) 52.5525 1.78067
\(872\) −9.42649 −0.319221
\(873\) −17.7683 −0.601364
\(874\) 2.14632 0.0726003
\(875\) −0.441519 −0.0149261
\(876\) 6.63709 0.224247
\(877\) 7.50383 0.253386 0.126693 0.991942i \(-0.459564\pi\)
0.126693 + 0.991942i \(0.459564\pi\)
\(878\) 2.85365 0.0963061
\(879\) 1.69024 0.0570105
\(880\) −0.781934 −0.0263590
\(881\) −30.2278 −1.01840 −0.509200 0.860648i \(-0.670059\pi\)
−0.509200 + 0.860648i \(0.670059\pi\)
\(882\) −10.4220 −0.350928
\(883\) −38.4664 −1.29450 −0.647249 0.762279i \(-0.724081\pi\)
−0.647249 + 0.762279i \(0.724081\pi\)
\(884\) −1.62479 −0.0546475
\(885\) 8.73486 0.293619
\(886\) 18.8725 0.634035
\(887\) −22.3512 −0.750479 −0.375239 0.926928i \(-0.622439\pi\)
−0.375239 + 0.926928i \(0.622439\pi\)
\(888\) 8.52855 0.286199
\(889\) −7.74351 −0.259709
\(890\) 7.27170 0.243748
\(891\) −1.61075 −0.0539620
\(892\) −17.8176 −0.596576
\(893\) 1.98301 0.0663588
\(894\) 4.29300 0.143579
\(895\) 24.5676 0.821204
\(896\) −0.441519 −0.0147501
\(897\) −12.8425 −0.428800
\(898\) −21.0421 −0.702184
\(899\) 65.6610 2.18992
\(900\) −1.53151 −0.0510503
\(901\) −3.20330 −0.106717
\(902\) 3.88989 0.129519
\(903\) −0.819403 −0.0272680
\(904\) 3.90239 0.129792
\(905\) 5.73582 0.190665
\(906\) 7.31793 0.243122
\(907\) 15.0899 0.501051 0.250526 0.968110i \(-0.419397\pi\)
0.250526 + 0.968110i \(0.419397\pi\)
\(908\) 15.5741 0.516845
\(909\) −1.72165 −0.0571035
\(910\) −2.06453 −0.0684385
\(911\) 54.6511 1.81067 0.905336 0.424696i \(-0.139619\pi\)
0.905336 + 0.424696i \(0.139619\pi\)
\(912\) −1.14759 −0.0380004
\(913\) 6.54175 0.216500
\(914\) 8.24588 0.272749
\(915\) −15.8065 −0.522548
\(916\) 8.00310 0.264430
\(917\) −1.25090 −0.0413083
\(918\) −1.90811 −0.0629770
\(919\) −1.10681 −0.0365104 −0.0182552 0.999833i \(-0.505811\pi\)
−0.0182552 + 0.999833i \(0.505811\pi\)
\(920\) −2.26644 −0.0747222
\(921\) −17.4381 −0.574605
\(922\) −28.0292 −0.923091
\(923\) −45.1079 −1.48474
\(924\) −0.418364 −0.0137632
\(925\) 7.03784 0.231403
\(926\) 28.1590 0.925361
\(927\) 6.16863 0.202605
\(928\) −8.38155 −0.275138
\(929\) 29.9498 0.982620 0.491310 0.870985i \(-0.336518\pi\)
0.491310 + 0.870985i \(0.336518\pi\)
\(930\) −9.49332 −0.311298
\(931\) −6.44440 −0.211207
\(932\) 14.7387 0.482782
\(933\) −12.5755 −0.411702
\(934\) 1.74732 0.0571742
\(935\) −0.271703 −0.00888565
\(936\) −7.16130 −0.234074
\(937\) 60.4497 1.97480 0.987402 0.158232i \(-0.0505793\pi\)
0.987402 + 0.158232i \(0.0505793\pi\)
\(938\) 4.96216 0.162020
\(939\) 1.47033 0.0479825
\(940\) −2.09399 −0.0682984
\(941\) 19.9986 0.651937 0.325968 0.945381i \(-0.394310\pi\)
0.325968 + 0.945381i \(0.394310\pi\)
\(942\) −11.8659 −0.386613
\(943\) 11.2749 0.367160
\(944\) 7.20809 0.234603
\(945\) −2.42453 −0.0788700
\(946\) −1.19752 −0.0389348
\(947\) 24.5867 0.798960 0.399480 0.916742i \(-0.369191\pi\)
0.399480 + 0.916742i \(0.369191\pi\)
\(948\) 2.33417 0.0758104
\(949\) 25.6103 0.831345
\(950\) −0.947001 −0.0307248
\(951\) 15.5711 0.504927
\(952\) −0.153417 −0.00497228
\(953\) 53.7109 1.73987 0.869934 0.493169i \(-0.164161\pi\)
0.869934 + 0.493169i \(0.164161\pi\)
\(954\) −14.1186 −0.457107
\(955\) 11.5893 0.375020
\(956\) 0.273552 0.00884732
\(957\) −7.94201 −0.256729
\(958\) −26.2763 −0.848949
\(959\) 4.47006 0.144346
\(960\) 1.21181 0.0391111
\(961\) 30.3713 0.979720
\(962\) 32.9087 1.06102
\(963\) −1.11612 −0.0359665
\(964\) 0.940060 0.0302773
\(965\) −1.55342 −0.0500064
\(966\) −1.21263 −0.0390157
\(967\) −33.7710 −1.08600 −0.543000 0.839732i \(-0.682712\pi\)
−0.543000 + 0.839732i \(0.682712\pi\)
\(968\) 10.3886 0.333902
\(969\) −0.398759 −0.0128100
\(970\) 11.6018 0.372511
\(971\) 7.98673 0.256306 0.128153 0.991754i \(-0.459095\pi\)
0.128153 + 0.991754i \(0.459095\pi\)
\(972\) −13.9778 −0.448337
\(973\) 2.78106 0.0891567
\(974\) 23.8805 0.765181
\(975\) 5.66640 0.181470
\(976\) −13.0437 −0.417519
\(977\) −15.7017 −0.502341 −0.251171 0.967943i \(-0.580816\pi\)
−0.251171 + 0.967943i \(0.580816\pi\)
\(978\) −18.3386 −0.586403
\(979\) 5.68599 0.181725
\(980\) 6.80506 0.217380
\(981\) −14.4368 −0.460930
\(982\) 8.48580 0.270793
\(983\) −0.551020 −0.0175748 −0.00878740 0.999961i \(-0.502797\pi\)
−0.00878740 + 0.999961i \(0.502797\pi\)
\(984\) −6.02841 −0.192179
\(985\) 10.9813 0.349892
\(986\) −2.91239 −0.0927493
\(987\) −1.12036 −0.0356616
\(988\) −4.42815 −0.140878
\(989\) −3.47102 −0.110372
\(990\) −1.19754 −0.0380603
\(991\) 4.47988 0.142308 0.0711540 0.997465i \(-0.477332\pi\)
0.0711540 + 0.997465i \(0.477332\pi\)
\(992\) −7.83398 −0.248729
\(993\) 9.71693 0.308357
\(994\) −4.25921 −0.135094
\(995\) −13.9734 −0.442986
\(996\) −10.1382 −0.321240
\(997\) 14.7494 0.467119 0.233559 0.972343i \(-0.424963\pi\)
0.233559 + 0.972343i \(0.424963\pi\)
\(998\) 15.8989 0.503270
\(999\) 38.6472 1.22274
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 \(a_p\))