Properties

Label 6027.2.a.s.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.34292\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -0.853635 q^{5} +2.34292 q^{6} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -0.853635 q^{5} +2.34292 q^{6} +3.48929 q^{8} +1.00000 q^{9} -2.00000 q^{10} -3.34292 q^{11} +3.48929 q^{12} -3.14637 q^{13} -0.853635 q^{15} +1.19656 q^{16} -3.63565 q^{17} +2.34292 q^{18} -1.14637 q^{19} -2.97858 q^{20} -7.83221 q^{22} -2.85363 q^{23} +3.48929 q^{24} -4.27131 q^{25} -7.37169 q^{26} +1.00000 q^{27} -8.02877 q^{29} -2.00000 q^{30} -9.86098 q^{31} -4.17513 q^{32} -3.34292 q^{33} -8.51806 q^{34} +3.48929 q^{36} +8.19656 q^{37} -2.68585 q^{38} -3.14637 q^{39} -2.97858 q^{40} -1.00000 q^{41} +11.7606 q^{43} -11.6644 q^{44} -0.853635 q^{45} -6.68585 q^{46} -8.32150 q^{47} +1.19656 q^{48} -10.0073 q^{50} -3.63565 q^{51} -10.9786 q^{52} +1.60688 q^{53} +2.34292 q^{54} +2.85363 q^{55} -1.14637 q^{57} -18.8108 q^{58} +11.6644 q^{59} -2.97858 q^{60} +4.19656 q^{61} -23.1035 q^{62} -12.1751 q^{64} +2.68585 q^{65} -7.83221 q^{66} +6.10038 q^{67} -12.6858 q^{68} -2.85363 q^{69} -8.65708 q^{71} +3.48929 q^{72} +10.1537 q^{73} +19.2039 q^{74} -4.27131 q^{75} -4.00000 q^{76} -7.37169 q^{78} -3.60688 q^{79} -1.02142 q^{80} +1.00000 q^{81} -2.34292 q^{82} +10.1249 q^{83} +3.10352 q^{85} +27.5542 q^{86} -8.02877 q^{87} -11.6644 q^{88} +3.37169 q^{89} -2.00000 q^{90} -9.95715 q^{92} -9.86098 q^{93} -19.4966 q^{94} +0.978577 q^{95} -4.17513 q^{96} +7.53948 q^{97} -3.34292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + q^{2} + 3q^{3} + 3q^{4} - 4q^{5} + q^{6} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + q^{2} + 3q^{3} + 3q^{4} - 4q^{5} + q^{6} + 3q^{8} + 3q^{9} - 6q^{10} - 4q^{11} + 3q^{12} - 8q^{13} - 4q^{15} - q^{16} - 2q^{17} + q^{18} - 2q^{19} + 6q^{20} - 10q^{22} - 10q^{23} + 3q^{24} + 5q^{25} + 2q^{26} + 3q^{27} - 6q^{29} - 6q^{30} + 2q^{31} + 7q^{32} - 4q^{33} + 3q^{36} + 20q^{37} + 4q^{38} - 8q^{39} + 6q^{40} - 3q^{41} + 10q^{43} - 8q^{44} - 4q^{45} - 8q^{46} - 4q^{47} - q^{48} + 3q^{50} - 2q^{51} - 18q^{52} + 14q^{53} + q^{54} + 10q^{55} - 2q^{57} - 28q^{58} + 8q^{59} + 6q^{60} + 8q^{61} - 38q^{62} - 17q^{64} - 4q^{65} - 10q^{66} + 12q^{67} - 26q^{68} - 10q^{69} - 32q^{71} + 3q^{72} - 4q^{73} + 20q^{74} + 5q^{75} - 12q^{76} + 2q^{78} - 20q^{79} - 18q^{80} + 3q^{81} - q^{82} + 14q^{83} - 22q^{85} + 6q^{86} - 6q^{87} - 8q^{88} - 14q^{89} - 6q^{90} + 2q^{93} - 18q^{94} - 12q^{95} + 7q^{96} + 12q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.34292 1.65670 0.828348 0.560213i \(-0.189281\pi\)
0.828348 + 0.560213i \(0.189281\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.48929 1.74464
\(5\) −0.853635 −0.381757 −0.190878 0.981614i \(-0.561134\pi\)
−0.190878 + 0.981614i \(0.561134\pi\)
\(6\) 2.34292 0.956494
\(7\) 0 0
\(8\) 3.48929 1.23365
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) −3.34292 −1.00793 −0.503965 0.863724i \(-0.668126\pi\)
−0.503965 + 0.863724i \(0.668126\pi\)
\(12\) 3.48929 1.00727
\(13\) −3.14637 −0.872645 −0.436322 0.899790i \(-0.643719\pi\)
−0.436322 + 0.899790i \(0.643719\pi\)
\(14\) 0 0
\(15\) −0.853635 −0.220407
\(16\) 1.19656 0.299139
\(17\) −3.63565 −0.881776 −0.440888 0.897562i \(-0.645336\pi\)
−0.440888 + 0.897562i \(0.645336\pi\)
\(18\) 2.34292 0.552232
\(19\) −1.14637 −0.262994 −0.131497 0.991317i \(-0.541978\pi\)
−0.131497 + 0.991317i \(0.541978\pi\)
\(20\) −2.97858 −0.666030
\(21\) 0 0
\(22\) −7.83221 −1.66983
\(23\) −2.85363 −0.595024 −0.297512 0.954718i \(-0.596157\pi\)
−0.297512 + 0.954718i \(0.596157\pi\)
\(24\) 3.48929 0.712248
\(25\) −4.27131 −0.854262
\(26\) −7.37169 −1.44571
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.02877 −1.49091 −0.745453 0.666559i \(-0.767767\pi\)
−0.745453 + 0.666559i \(0.767767\pi\)
\(30\) −2.00000 −0.365148
\(31\) −9.86098 −1.77108 −0.885542 0.464559i \(-0.846213\pi\)
−0.885542 + 0.464559i \(0.846213\pi\)
\(32\) −4.17513 −0.738067
\(33\) −3.34292 −0.581928
\(34\) −8.51806 −1.46083
\(35\) 0 0
\(36\) 3.48929 0.581548
\(37\) 8.19656 1.34751 0.673753 0.738957i \(-0.264681\pi\)
0.673753 + 0.738957i \(0.264681\pi\)
\(38\) −2.68585 −0.435702
\(39\) −3.14637 −0.503822
\(40\) −2.97858 −0.470954
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 11.7606 1.79347 0.896737 0.442564i \(-0.145931\pi\)
0.896737 + 0.442564i \(0.145931\pi\)
\(44\) −11.6644 −1.75848
\(45\) −0.853635 −0.127252
\(46\) −6.68585 −0.985774
\(47\) −8.32150 −1.21382 −0.606908 0.794772i \(-0.707590\pi\)
−0.606908 + 0.794772i \(0.707590\pi\)
\(48\) 1.19656 0.172708
\(49\) 0 0
\(50\) −10.0073 −1.41525
\(51\) −3.63565 −0.509093
\(52\) −10.9786 −1.52245
\(53\) 1.60688 0.220723 0.110361 0.993892i \(-0.464799\pi\)
0.110361 + 0.993892i \(0.464799\pi\)
\(54\) 2.34292 0.318831
\(55\) 2.85363 0.384784
\(56\) 0 0
\(57\) −1.14637 −0.151840
\(58\) −18.8108 −2.46998
\(59\) 11.6644 1.51858 0.759289 0.650753i \(-0.225547\pi\)
0.759289 + 0.650753i \(0.225547\pi\)
\(60\) −2.97858 −0.384533
\(61\) 4.19656 0.537314 0.268657 0.963236i \(-0.413420\pi\)
0.268657 + 0.963236i \(0.413420\pi\)
\(62\) −23.1035 −2.93415
\(63\) 0 0
\(64\) −12.1751 −1.52189
\(65\) 2.68585 0.333138
\(66\) −7.83221 −0.964079
\(67\) 6.10038 0.745281 0.372640 0.927976i \(-0.378453\pi\)
0.372640 + 0.927976i \(0.378453\pi\)
\(68\) −12.6858 −1.53838
\(69\) −2.85363 −0.343537
\(70\) 0 0
\(71\) −8.65708 −1.02741 −0.513703 0.857968i \(-0.671727\pi\)
−0.513703 + 0.857968i \(0.671727\pi\)
\(72\) 3.48929 0.411217
\(73\) 10.1537 1.18840 0.594201 0.804317i \(-0.297468\pi\)
0.594201 + 0.804317i \(0.297468\pi\)
\(74\) 19.2039 2.23241
\(75\) −4.27131 −0.493208
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) −7.37169 −0.834680
\(79\) −3.60688 −0.405806 −0.202903 0.979199i \(-0.565038\pi\)
−0.202903 + 0.979199i \(0.565038\pi\)
\(80\) −1.02142 −0.114199
\(81\) 1.00000 0.111111
\(82\) −2.34292 −0.258733
\(83\) 10.1249 1.11136 0.555678 0.831397i \(-0.312459\pi\)
0.555678 + 0.831397i \(0.312459\pi\)
\(84\) 0 0
\(85\) 3.10352 0.336624
\(86\) 27.5542 2.97124
\(87\) −8.02877 −0.860774
\(88\) −11.6644 −1.24343
\(89\) 3.37169 0.357399 0.178699 0.983904i \(-0.442811\pi\)
0.178699 + 0.983904i \(0.442811\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −9.95715 −1.03811
\(93\) −9.86098 −1.02254
\(94\) −19.4966 −2.01092
\(95\) 0.978577 0.100400
\(96\) −4.17513 −0.426123
\(97\) 7.53948 0.765518 0.382759 0.923848i \(-0.374974\pi\)
0.382759 + 0.923848i \(0.374974\pi\)
\(98\) 0 0
\(99\) −3.34292 −0.335976
\(100\) −14.9038 −1.49038
\(101\) −5.00735 −0.498250 −0.249125 0.968471i \(-0.580143\pi\)
−0.249125 + 0.968471i \(0.580143\pi\)
\(102\) −8.51806 −0.843413
\(103\) −1.21798 −0.120011 −0.0600056 0.998198i \(-0.519112\pi\)
−0.0600056 + 0.998198i \(0.519112\pi\)
\(104\) −10.9786 −1.07654
\(105\) 0 0
\(106\) 3.76481 0.365670
\(107\) 13.7648 1.33069 0.665347 0.746534i \(-0.268284\pi\)
0.665347 + 0.746534i \(0.268284\pi\)
\(108\) 3.48929 0.335757
\(109\) 3.14637 0.301367 0.150684 0.988582i \(-0.451853\pi\)
0.150684 + 0.988582i \(0.451853\pi\)
\(110\) 6.68585 0.637470
\(111\) 8.19656 0.777983
\(112\) 0 0
\(113\) −7.73183 −0.727349 −0.363675 0.931526i \(-0.618478\pi\)
−0.363675 + 0.931526i \(0.618478\pi\)
\(114\) −2.68585 −0.251553
\(115\) 2.43596 0.227155
\(116\) −28.0147 −2.60110
\(117\) −3.14637 −0.290882
\(118\) 27.3288 2.51582
\(119\) 0 0
\(120\) −2.97858 −0.271906
\(121\) 0.175135 0.0159213
\(122\) 9.83221 0.890167
\(123\) −1.00000 −0.0901670
\(124\) −34.4078 −3.08991
\(125\) 7.91431 0.707877
\(126\) 0 0
\(127\) −12.0575 −1.06993 −0.534967 0.844873i \(-0.679676\pi\)
−0.534967 + 0.844873i \(0.679676\pi\)
\(128\) −20.1751 −1.78325
\(129\) 11.7606 1.03546
\(130\) 6.29273 0.551909
\(131\) −12.2253 −1.06813 −0.534066 0.845443i \(-0.679337\pi\)
−0.534066 + 0.845443i \(0.679337\pi\)
\(132\) −11.6644 −1.01526
\(133\) 0 0
\(134\) 14.2927 1.23470
\(135\) −0.853635 −0.0734692
\(136\) −12.6858 −1.08780
\(137\) 7.69319 0.657274 0.328637 0.944456i \(-0.393411\pi\)
0.328637 + 0.944456i \(0.393411\pi\)
\(138\) −6.68585 −0.569137
\(139\) 18.0147 1.52799 0.763993 0.645224i \(-0.223236\pi\)
0.763993 + 0.645224i \(0.223236\pi\)
\(140\) 0 0
\(141\) −8.32150 −0.700797
\(142\) −20.2829 −1.70210
\(143\) 10.5181 0.879564
\(144\) 1.19656 0.0997131
\(145\) 6.85363 0.569163
\(146\) 23.7894 1.96882
\(147\) 0 0
\(148\) 28.6002 2.35092
\(149\) 12.5426 1.02753 0.513766 0.857931i \(-0.328250\pi\)
0.513766 + 0.857931i \(0.328250\pi\)
\(150\) −10.0073 −0.817096
\(151\) 2.62831 0.213889 0.106944 0.994265i \(-0.465893\pi\)
0.106944 + 0.994265i \(0.465893\pi\)
\(152\) −4.00000 −0.324443
\(153\) −3.63565 −0.293925
\(154\) 0 0
\(155\) 8.41767 0.676124
\(156\) −10.9786 −0.878990
\(157\) −20.1579 −1.60878 −0.804389 0.594103i \(-0.797507\pi\)
−0.804389 + 0.594103i \(0.797507\pi\)
\(158\) −8.45065 −0.672298
\(159\) 1.60688 0.127434
\(160\) 3.56404 0.281762
\(161\) 0 0
\(162\) 2.34292 0.184077
\(163\) 18.2541 1.42977 0.714886 0.699241i \(-0.246479\pi\)
0.714886 + 0.699241i \(0.246479\pi\)
\(164\) −3.48929 −0.272468
\(165\) 2.85363 0.222155
\(166\) 23.7220 1.84118
\(167\) −1.31415 −0.101692 −0.0508461 0.998706i \(-0.516192\pi\)
−0.0508461 + 0.998706i \(0.516192\pi\)
\(168\) 0 0
\(169\) −3.10038 −0.238491
\(170\) 7.27131 0.557684
\(171\) −1.14637 −0.0876648
\(172\) 41.0361 3.12897
\(173\) −1.18921 −0.0904141 −0.0452070 0.998978i \(-0.514395\pi\)
−0.0452070 + 0.998978i \(0.514395\pi\)
\(174\) −18.8108 −1.42604
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 11.6644 0.876752
\(178\) 7.89962 0.592101
\(179\) −19.0073 −1.42068 −0.710338 0.703861i \(-0.751458\pi\)
−0.710338 + 0.703861i \(0.751458\pi\)
\(180\) −2.97858 −0.222010
\(181\) −10.3931 −0.772514 −0.386257 0.922391i \(-0.626232\pi\)
−0.386257 + 0.922391i \(0.626232\pi\)
\(182\) 0 0
\(183\) 4.19656 0.310218
\(184\) −9.95715 −0.734051
\(185\) −6.99686 −0.514420
\(186\) −23.1035 −1.69403
\(187\) 12.1537 0.888767
\(188\) −29.0361 −2.11768
\(189\) 0 0
\(190\) 2.29273 0.166332
\(191\) −6.87819 −0.497689 −0.248844 0.968544i \(-0.580051\pi\)
−0.248844 + 0.968544i \(0.580051\pi\)
\(192\) −12.1751 −0.878665
\(193\) −19.5970 −1.41062 −0.705312 0.708897i \(-0.749193\pi\)
−0.705312 + 0.708897i \(0.749193\pi\)
\(194\) 17.6644 1.26823
\(195\) 2.68585 0.192337
\(196\) 0 0
\(197\) −24.7679 −1.76464 −0.882321 0.470647i \(-0.844020\pi\)
−0.882321 + 0.470647i \(0.844020\pi\)
\(198\) −7.83221 −0.556611
\(199\) −12.8108 −0.908133 −0.454066 0.890968i \(-0.650027\pi\)
−0.454066 + 0.890968i \(0.650027\pi\)
\(200\) −14.9038 −1.05386
\(201\) 6.10038 0.430288
\(202\) −11.7318 −0.825448
\(203\) 0 0
\(204\) −12.6858 −0.888187
\(205\) 0.853635 0.0596204
\(206\) −2.85363 −0.198822
\(207\) −2.85363 −0.198341
\(208\) −3.76481 −0.261042
\(209\) 3.83221 0.265080
\(210\) 0 0
\(211\) 3.66442 0.252269 0.126135 0.992013i \(-0.459743\pi\)
0.126135 + 0.992013i \(0.459743\pi\)
\(212\) 5.60688 0.385082
\(213\) −8.65708 −0.593173
\(214\) 32.2499 2.20456
\(215\) −10.0393 −0.684671
\(216\) 3.48929 0.237416
\(217\) 0 0
\(218\) 7.37169 0.499274
\(219\) 10.1537 0.686124
\(220\) 9.95715 0.671311
\(221\) 11.4391 0.769477
\(222\) 19.2039 1.28888
\(223\) −9.17092 −0.614130 −0.307065 0.951688i \(-0.599347\pi\)
−0.307065 + 0.951688i \(0.599347\pi\)
\(224\) 0 0
\(225\) −4.27131 −0.284754
\(226\) −18.1151 −1.20500
\(227\) −0.263962 −0.0175198 −0.00875988 0.999962i \(-0.502788\pi\)
−0.00875988 + 0.999962i \(0.502788\pi\)
\(228\) −4.00000 −0.264906
\(229\) −7.20390 −0.476047 −0.238024 0.971259i \(-0.576500\pi\)
−0.238024 + 0.971259i \(0.576500\pi\)
\(230\) 5.70727 0.376326
\(231\) 0 0
\(232\) −28.0147 −1.83925
\(233\) 16.1579 1.05854 0.529270 0.848453i \(-0.322466\pi\)
0.529270 + 0.848453i \(0.322466\pi\)
\(234\) −7.37169 −0.481903
\(235\) 7.10352 0.463383
\(236\) 40.7005 2.64938
\(237\) −3.60688 −0.234292
\(238\) 0 0
\(239\) −15.6644 −1.01325 −0.506624 0.862167i \(-0.669107\pi\)
−0.506624 + 0.862167i \(0.669107\pi\)
\(240\) −1.02142 −0.0659326
\(241\) −10.5468 −0.679381 −0.339690 0.940537i \(-0.610322\pi\)
−0.339690 + 0.940537i \(0.610322\pi\)
\(242\) 0.410327 0.0263768
\(243\) 1.00000 0.0641500
\(244\) 14.6430 0.937422
\(245\) 0 0
\(246\) −2.34292 −0.149379
\(247\) 3.60688 0.229501
\(248\) −34.4078 −2.18490
\(249\) 10.1249 0.641642
\(250\) 18.5426 1.17274
\(251\) −21.4292 −1.35260 −0.676301 0.736626i \(-0.736418\pi\)
−0.676301 + 0.736626i \(0.736418\pi\)
\(252\) 0 0
\(253\) 9.53948 0.599742
\(254\) −28.2499 −1.77256
\(255\) 3.10352 0.194350
\(256\) −22.9185 −1.43241
\(257\) 7.10773 0.443368 0.221684 0.975119i \(-0.428845\pi\)
0.221684 + 0.975119i \(0.428845\pi\)
\(258\) 27.5542 1.71545
\(259\) 0 0
\(260\) 9.37169 0.581208
\(261\) −8.02877 −0.496968
\(262\) −28.6430 −1.76957
\(263\) −9.97123 −0.614852 −0.307426 0.951572i \(-0.599468\pi\)
−0.307426 + 0.951572i \(0.599468\pi\)
\(264\) −11.6644 −0.717896
\(265\) −1.37169 −0.0842624
\(266\) 0 0
\(267\) 3.37169 0.206344
\(268\) 21.2860 1.30025
\(269\) 0.685846 0.0418168 0.0209084 0.999781i \(-0.493344\pi\)
0.0209084 + 0.999781i \(0.493344\pi\)
\(270\) −2.00000 −0.121716
\(271\) −13.8034 −0.838499 −0.419250 0.907871i \(-0.637707\pi\)
−0.419250 + 0.907871i \(0.637707\pi\)
\(272\) −4.35027 −0.263774
\(273\) 0 0
\(274\) 18.0246 1.08890
\(275\) 14.2787 0.861035
\(276\) −9.95715 −0.599350
\(277\) 22.2113 1.33454 0.667272 0.744814i \(-0.267462\pi\)
0.667272 + 0.744814i \(0.267462\pi\)
\(278\) 42.2070 2.53141
\(279\) −9.86098 −0.590361
\(280\) 0 0
\(281\) 4.61423 0.275262 0.137631 0.990484i \(-0.456051\pi\)
0.137631 + 0.990484i \(0.456051\pi\)
\(282\) −19.4966 −1.16101
\(283\) −9.13229 −0.542858 −0.271429 0.962458i \(-0.587496\pi\)
−0.271429 + 0.962458i \(0.587496\pi\)
\(284\) −30.2070 −1.79246
\(285\) 0.978577 0.0579659
\(286\) 24.6430 1.45717
\(287\) 0 0
\(288\) −4.17513 −0.246022
\(289\) −3.78202 −0.222472
\(290\) 16.0575 0.942931
\(291\) 7.53948 0.441972
\(292\) 35.4292 2.07334
\(293\) −23.4433 −1.36957 −0.684786 0.728744i \(-0.740104\pi\)
−0.684786 + 0.728744i \(0.740104\pi\)
\(294\) 0 0
\(295\) −9.95715 −0.579728
\(296\) 28.6002 1.66235
\(297\) −3.34292 −0.193976
\(298\) 29.3864 1.70231
\(299\) 8.97858 0.519245
\(300\) −14.9038 −0.860473
\(301\) 0 0
\(302\) 6.15792 0.354349
\(303\) −5.00735 −0.287665
\(304\) −1.37169 −0.0786720
\(305\) −3.58233 −0.205123
\(306\) −8.51806 −0.486945
\(307\) −18.2541 −1.04182 −0.520908 0.853613i \(-0.674407\pi\)
−0.520908 + 0.853613i \(0.674407\pi\)
\(308\) 0 0
\(309\) −1.21798 −0.0692885
\(310\) 19.7220 1.12013
\(311\) −14.8782 −0.843665 −0.421832 0.906674i \(-0.638613\pi\)
−0.421832 + 0.906674i \(0.638613\pi\)
\(312\) −10.9786 −0.621540
\(313\) 26.4752 1.49647 0.748234 0.663435i \(-0.230902\pi\)
0.748234 + 0.663435i \(0.230902\pi\)
\(314\) −47.2285 −2.66526
\(315\) 0 0
\(316\) −12.5855 −0.707988
\(317\) 29.6503 1.66533 0.832665 0.553777i \(-0.186814\pi\)
0.832665 + 0.553777i \(0.186814\pi\)
\(318\) 3.76481 0.211120
\(319\) 26.8396 1.50273
\(320\) 10.3931 0.580993
\(321\) 13.7648 0.768277
\(322\) 0 0
\(323\) 4.16779 0.231902
\(324\) 3.48929 0.193849
\(325\) 13.4391 0.745467
\(326\) 42.7679 2.36870
\(327\) 3.14637 0.173994
\(328\) −3.48929 −0.192664
\(329\) 0 0
\(330\) 6.68585 0.368044
\(331\) 2.60375 0.143115 0.0715575 0.997436i \(-0.477203\pi\)
0.0715575 + 0.997436i \(0.477203\pi\)
\(332\) 35.3288 1.93892
\(333\) 8.19656 0.449169
\(334\) −3.07896 −0.168473
\(335\) −5.20750 −0.284516
\(336\) 0 0
\(337\) −1.51071 −0.0822937 −0.0411468 0.999153i \(-0.513101\pi\)
−0.0411468 + 0.999153i \(0.513101\pi\)
\(338\) −7.26396 −0.395107
\(339\) −7.73183 −0.419935
\(340\) 10.8291 0.587289
\(341\) 32.9645 1.78513
\(342\) −2.68585 −0.145234
\(343\) 0 0
\(344\) 41.0361 2.21252
\(345\) 2.43596 0.131148
\(346\) −2.78623 −0.149789
\(347\) −14.2787 −0.766518 −0.383259 0.923641i \(-0.625198\pi\)
−0.383259 + 0.923641i \(0.625198\pi\)
\(348\) −28.0147 −1.50175
\(349\) 16.2541 0.870062 0.435031 0.900416i \(-0.356737\pi\)
0.435031 + 0.900416i \(0.356737\pi\)
\(350\) 0 0
\(351\) −3.14637 −0.167941
\(352\) 13.9572 0.743919
\(353\) −11.1709 −0.594568 −0.297284 0.954789i \(-0.596081\pi\)
−0.297284 + 0.954789i \(0.596081\pi\)
\(354\) 27.3288 1.45251
\(355\) 7.38998 0.392219
\(356\) 11.7648 0.623534
\(357\) 0 0
\(358\) −44.5328 −2.35363
\(359\) −16.2253 −0.856340 −0.428170 0.903698i \(-0.640842\pi\)
−0.428170 + 0.903698i \(0.640842\pi\)
\(360\) −2.97858 −0.156985
\(361\) −17.6858 −0.930834
\(362\) −24.3503 −1.27982
\(363\) 0.175135 0.00919219
\(364\) 0 0
\(365\) −8.66756 −0.453681
\(366\) 9.83221 0.513938
\(367\) −0.431750 −0.0225372 −0.0112686 0.999937i \(-0.503587\pi\)
−0.0112686 + 0.999937i \(0.503587\pi\)
\(368\) −3.41454 −0.177995
\(369\) −1.00000 −0.0520579
\(370\) −16.3931 −0.852237
\(371\) 0 0
\(372\) −34.4078 −1.78396
\(373\) −3.66863 −0.189955 −0.0949773 0.995479i \(-0.530278\pi\)
−0.0949773 + 0.995479i \(0.530278\pi\)
\(374\) 28.4752 1.47242
\(375\) 7.91431 0.408693
\(376\) −29.0361 −1.49742
\(377\) 25.2614 1.30103
\(378\) 0 0
\(379\) −9.89962 −0.508509 −0.254255 0.967137i \(-0.581830\pi\)
−0.254255 + 0.967137i \(0.581830\pi\)
\(380\) 3.41454 0.175162
\(381\) −12.0575 −0.617726
\(382\) −16.1151 −0.824519
\(383\) 31.3148 1.60011 0.800055 0.599927i \(-0.204804\pi\)
0.800055 + 0.599927i \(0.204804\pi\)
\(384\) −20.1751 −1.02956
\(385\) 0 0
\(386\) −45.9143 −2.33698
\(387\) 11.7606 0.597825
\(388\) 26.3074 1.33556
\(389\) 7.39625 0.375005 0.187502 0.982264i \(-0.439961\pi\)
0.187502 + 0.982264i \(0.439961\pi\)
\(390\) 6.29273 0.318645
\(391\) 10.3748 0.524678
\(392\) 0 0
\(393\) −12.2253 −0.616686
\(394\) −58.0294 −2.92348
\(395\) 3.07896 0.154919
\(396\) −11.6644 −0.586159
\(397\) −11.9326 −0.598880 −0.299440 0.954115i \(-0.596800\pi\)
−0.299440 + 0.954115i \(0.596800\pi\)
\(398\) −30.0147 −1.50450
\(399\) 0 0
\(400\) −5.11087 −0.255543
\(401\) −15.7648 −0.787257 −0.393628 0.919270i \(-0.628780\pi\)
−0.393628 + 0.919270i \(0.628780\pi\)
\(402\) 14.2927 0.712857
\(403\) 31.0263 1.54553
\(404\) −17.4721 −0.869268
\(405\) −0.853635 −0.0424174
\(406\) 0 0
\(407\) −27.4005 −1.35819
\(408\) −12.6858 −0.628043
\(409\) 7.55356 0.373499 0.186750 0.982408i \(-0.440205\pi\)
0.186750 + 0.982408i \(0.440205\pi\)
\(410\) 2.00000 0.0987730
\(411\) 7.69319 0.379477
\(412\) −4.24989 −0.209377
\(413\) 0 0
\(414\) −6.68585 −0.328591
\(415\) −8.64300 −0.424268
\(416\) 13.1365 0.644070
\(417\) 18.0147 0.882183
\(418\) 8.97858 0.439157
\(419\) −9.59702 −0.468845 −0.234423 0.972135i \(-0.575320\pi\)
−0.234423 + 0.972135i \(0.575320\pi\)
\(420\) 0 0
\(421\) 12.3503 0.601915 0.300958 0.953638i \(-0.402694\pi\)
0.300958 + 0.953638i \(0.402694\pi\)
\(422\) 8.58546 0.417934
\(423\) −8.32150 −0.404605
\(424\) 5.60688 0.272294
\(425\) 15.5290 0.753267
\(426\) −20.2829 −0.982708
\(427\) 0 0
\(428\) 48.0294 2.32159
\(429\) 10.5181 0.507817
\(430\) −23.5212 −1.13429
\(431\) 5.14637 0.247892 0.123946 0.992289i \(-0.460445\pi\)
0.123946 + 0.992289i \(0.460445\pi\)
\(432\) 1.19656 0.0575694
\(433\) −17.0894 −0.821266 −0.410633 0.911801i \(-0.634692\pi\)
−0.410633 + 0.911801i \(0.634692\pi\)
\(434\) 0 0
\(435\) 6.85363 0.328607
\(436\) 10.9786 0.525778
\(437\) 3.27131 0.156488
\(438\) 23.7894 1.13670
\(439\) 22.3503 1.06672 0.533360 0.845888i \(-0.320929\pi\)
0.533360 + 0.845888i \(0.320929\pi\)
\(440\) 9.95715 0.474689
\(441\) 0 0
\(442\) 26.8009 1.27479
\(443\) 23.4145 1.11246 0.556229 0.831029i \(-0.312248\pi\)
0.556229 + 0.831029i \(0.312248\pi\)
\(444\) 28.6002 1.35730
\(445\) −2.87819 −0.136439
\(446\) −21.4868 −1.01743
\(447\) 12.5426 0.593245
\(448\) 0 0
\(449\) −33.2713 −1.57017 −0.785085 0.619388i \(-0.787381\pi\)
−0.785085 + 0.619388i \(0.787381\pi\)
\(450\) −10.0073 −0.471751
\(451\) 3.34292 0.157412
\(452\) −26.9786 −1.26897
\(453\) 2.62831 0.123489
\(454\) −0.618442 −0.0290249
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −26.3931 −1.23462 −0.617309 0.786721i \(-0.711777\pi\)
−0.617309 + 0.786721i \(0.711777\pi\)
\(458\) −16.8782 −0.788666
\(459\) −3.63565 −0.169698
\(460\) 8.49977 0.396304
\(461\) −2.20077 −0.102500 −0.0512500 0.998686i \(-0.516321\pi\)
−0.0512500 + 0.998686i \(0.516321\pi\)
\(462\) 0 0
\(463\) 24.5328 1.14013 0.570067 0.821598i \(-0.306917\pi\)
0.570067 + 0.821598i \(0.306917\pi\)
\(464\) −9.60688 −0.445988
\(465\) 8.41767 0.390360
\(466\) 37.8568 1.75368
\(467\) 22.9357 1.06134 0.530670 0.847579i \(-0.321941\pi\)
0.530670 + 0.847579i \(0.321941\pi\)
\(468\) −10.9786 −0.507485
\(469\) 0 0
\(470\) 16.6430 0.767684
\(471\) −20.1579 −0.928828
\(472\) 40.7005 1.87339
\(473\) −39.3148 −1.80770
\(474\) −8.45065 −0.388151
\(475\) 4.89648 0.224666
\(476\) 0 0
\(477\) 1.60688 0.0735742
\(478\) −36.7005 −1.67864
\(479\) −41.6075 −1.90110 −0.950548 0.310579i \(-0.899477\pi\)
−0.950548 + 0.310579i \(0.899477\pi\)
\(480\) 3.56404 0.162675
\(481\) −25.7894 −1.17589
\(482\) −24.7104 −1.12553
\(483\) 0 0
\(484\) 0.611096 0.0277771
\(485\) −6.43596 −0.292242
\(486\) 2.34292 0.106277
\(487\) 40.4036 1.83086 0.915431 0.402475i \(-0.131850\pi\)
0.915431 + 0.402475i \(0.131850\pi\)
\(488\) 14.6430 0.662857
\(489\) 18.2541 0.825479
\(490\) 0 0
\(491\) −16.6184 −0.749980 −0.374990 0.927029i \(-0.622354\pi\)
−0.374990 + 0.927029i \(0.622354\pi\)
\(492\) −3.48929 −0.157309
\(493\) 29.1898 1.31464
\(494\) 8.45065 0.380213
\(495\) 2.85363 0.128261
\(496\) −11.7992 −0.529801
\(497\) 0 0
\(498\) 23.7220 1.06301
\(499\) −0.921039 −0.0412314 −0.0206157 0.999787i \(-0.506563\pi\)
−0.0206157 + 0.999787i \(0.506563\pi\)
\(500\) 27.6153 1.23499
\(501\) −1.31415 −0.0587121
\(502\) −50.2070 −2.24085
\(503\) −18.9217 −0.843675 −0.421837 0.906671i \(-0.638615\pi\)
−0.421837 + 0.906671i \(0.638615\pi\)
\(504\) 0 0
\(505\) 4.27444 0.190210
\(506\) 22.3503 0.993591
\(507\) −3.10038 −0.137693
\(508\) −42.0722 −1.86665
\(509\) −27.8855 −1.23600 −0.618002 0.786176i \(-0.712058\pi\)
−0.618002 + 0.786176i \(0.712058\pi\)
\(510\) 7.27131 0.321979
\(511\) 0 0
\(512\) −13.3461 −0.589818
\(513\) −1.14637 −0.0506133
\(514\) 16.6529 0.734526
\(515\) 1.03971 0.0458151
\(516\) 41.0361 1.80651
\(517\) 27.8181 1.22344
\(518\) 0 0
\(519\) −1.18921 −0.0522006
\(520\) 9.37169 0.410976
\(521\) −9.93681 −0.435339 −0.217670 0.976022i \(-0.569846\pi\)
−0.217670 + 0.976022i \(0.569846\pi\)
\(522\) −18.8108 −0.823326
\(523\) 35.9718 1.57294 0.786470 0.617629i \(-0.211907\pi\)
0.786470 + 0.617629i \(0.211907\pi\)
\(524\) −42.6577 −1.86351
\(525\) 0 0
\(526\) −23.3618 −1.01862
\(527\) 35.8511 1.56170
\(528\) −4.00000 −0.174078
\(529\) −14.8568 −0.645947
\(530\) −3.21377 −0.139597
\(531\) 11.6644 0.506193
\(532\) 0 0
\(533\) 3.14637 0.136284
\(534\) 7.89962 0.341850
\(535\) −11.7501 −0.508002
\(536\) 21.2860 0.919415
\(537\) −19.0073 −0.820228
\(538\) 1.60688 0.0692777
\(539\) 0 0
\(540\) −2.97858 −0.128178
\(541\) 9.79923 0.421302 0.210651 0.977561i \(-0.432442\pi\)
0.210651 + 0.977561i \(0.432442\pi\)
\(542\) −32.3404 −1.38914
\(543\) −10.3931 −0.446011
\(544\) 15.1793 0.650809
\(545\) −2.68585 −0.115049
\(546\) 0 0
\(547\) −33.8223 −1.44614 −0.723070 0.690775i \(-0.757269\pi\)
−0.723070 + 0.690775i \(0.757269\pi\)
\(548\) 26.8438 1.14671
\(549\) 4.19656 0.179105
\(550\) 33.4538 1.42647
\(551\) 9.20390 0.392099
\(552\) −9.95715 −0.423805
\(553\) 0 0
\(554\) 52.0393 2.21094
\(555\) −6.99686 −0.297000
\(556\) 62.8585 2.66579
\(557\) −20.9217 −0.886479 −0.443239 0.896403i \(-0.646171\pi\)
−0.443239 + 0.896403i \(0.646171\pi\)
\(558\) −23.1035 −0.978050
\(559\) −37.0031 −1.56507
\(560\) 0 0
\(561\) 12.1537 0.513130
\(562\) 10.8108 0.456026
\(563\) 28.6289 1.20657 0.603283 0.797527i \(-0.293859\pi\)
0.603283 + 0.797527i \(0.293859\pi\)
\(564\) −29.0361 −1.22264
\(565\) 6.60015 0.277671
\(566\) −21.3963 −0.899352
\(567\) 0 0
\(568\) −30.2070 −1.26746
\(569\) −20.9603 −0.878701 −0.439351 0.898316i \(-0.644791\pi\)
−0.439351 + 0.898316i \(0.644791\pi\)
\(570\) 2.29273 0.0960319
\(571\) −13.2860 −0.556002 −0.278001 0.960581i \(-0.589672\pi\)
−0.278001 + 0.960581i \(0.589672\pi\)
\(572\) 36.7005 1.53453
\(573\) −6.87819 −0.287341
\(574\) 0 0
\(575\) 12.1888 0.508306
\(576\) −12.1751 −0.507297
\(577\) −1.35700 −0.0564926 −0.0282463 0.999601i \(-0.508992\pi\)
−0.0282463 + 0.999601i \(0.508992\pi\)
\(578\) −8.86098 −0.368568
\(579\) −19.5970 −0.814424
\(580\) 23.9143 0.992988
\(581\) 0 0
\(582\) 17.6644 0.732214
\(583\) −5.37169 −0.222473
\(584\) 35.4292 1.46607
\(585\) 2.68585 0.111046
\(586\) −54.9259 −2.26897
\(587\) −29.9431 −1.23588 −0.617942 0.786224i \(-0.712033\pi\)
−0.617942 + 0.786224i \(0.712033\pi\)
\(588\) 0 0
\(589\) 11.3043 0.465785
\(590\) −23.3288 −0.960433
\(591\) −24.7679 −1.01882
\(592\) 9.80765 0.403092
\(593\) 6.01408 0.246969 0.123484 0.992347i \(-0.460593\pi\)
0.123484 + 0.992347i \(0.460593\pi\)
\(594\) −7.83221 −0.321360
\(595\) 0 0
\(596\) 43.7648 1.79268
\(597\) −12.8108 −0.524311
\(598\) 21.0361 0.860231
\(599\) 30.0477 1.22771 0.613857 0.789417i \(-0.289617\pi\)
0.613857 + 0.789417i \(0.289617\pi\)
\(600\) −14.9038 −0.608446
\(601\) 38.1642 1.55675 0.778375 0.627800i \(-0.216044\pi\)
0.778375 + 0.627800i \(0.216044\pi\)
\(602\) 0 0
\(603\) 6.10038 0.248427
\(604\) 9.17092 0.373160
\(605\) −0.149501 −0.00607808
\(606\) −11.7318 −0.476573
\(607\) −35.7220 −1.44991 −0.724955 0.688796i \(-0.758139\pi\)
−0.724955 + 0.688796i \(0.758139\pi\)
\(608\) 4.78623 0.194107
\(609\) 0 0
\(610\) −8.39312 −0.339827
\(611\) 26.1825 1.05923
\(612\) −12.6858 −0.512795
\(613\) −8.68585 −0.350818 −0.175409 0.984496i \(-0.556125\pi\)
−0.175409 + 0.984496i \(0.556125\pi\)
\(614\) −42.7679 −1.72597
\(615\) 0.853635 0.0344219
\(616\) 0 0
\(617\) 25.4391 1.02414 0.512070 0.858944i \(-0.328879\pi\)
0.512070 + 0.858944i \(0.328879\pi\)
\(618\) −2.85363 −0.114790
\(619\) −4.28852 −0.172370 −0.0861851 0.996279i \(-0.527468\pi\)
−0.0861851 + 0.996279i \(0.527468\pi\)
\(620\) 29.3717 1.17960
\(621\) −2.85363 −0.114512
\(622\) −34.8585 −1.39770
\(623\) 0 0
\(624\) −3.76481 −0.150713
\(625\) 14.6006 0.584025
\(626\) 62.0294 2.47919
\(627\) 3.83221 0.153044
\(628\) −70.3368 −2.80674
\(629\) −29.7998 −1.18820
\(630\) 0 0
\(631\) −3.17513 −0.126400 −0.0632001 0.998001i \(-0.520131\pi\)
−0.0632001 + 0.998001i \(0.520131\pi\)
\(632\) −12.5855 −0.500623
\(633\) 3.66442 0.145648
\(634\) 69.4685 2.75895
\(635\) 10.2927 0.408455
\(636\) 5.60688 0.222327
\(637\) 0 0
\(638\) 62.8830 2.48956
\(639\) −8.65708 −0.342469
\(640\) 17.2222 0.680767
\(641\) −21.0565 −0.831680 −0.415840 0.909438i \(-0.636512\pi\)
−0.415840 + 0.909438i \(0.636512\pi\)
\(642\) 32.2499 1.27280
\(643\) 18.2070 0.718016 0.359008 0.933335i \(-0.383115\pi\)
0.359008 + 0.933335i \(0.383115\pi\)
\(644\) 0 0
\(645\) −10.0393 −0.395295
\(646\) 9.76481 0.384191
\(647\) 19.6890 0.774054 0.387027 0.922068i \(-0.373502\pi\)
0.387027 + 0.922068i \(0.373502\pi\)
\(648\) 3.48929 0.137072
\(649\) −38.9933 −1.53062
\(650\) 31.4868 1.23501
\(651\) 0 0
\(652\) 63.6938 2.49444
\(653\) −2.80031 −0.109584 −0.0547922 0.998498i \(-0.517450\pi\)
−0.0547922 + 0.998498i \(0.517450\pi\)
\(654\) 7.37169 0.288256
\(655\) 10.4360 0.407767
\(656\) −1.19656 −0.0467177
\(657\) 10.1537 0.396134
\(658\) 0 0
\(659\) −7.07896 −0.275757 −0.137879 0.990449i \(-0.544028\pi\)
−0.137879 + 0.990449i \(0.544028\pi\)
\(660\) 9.95715 0.387582
\(661\) 15.6791 0.609847 0.304923 0.952377i \(-0.401369\pi\)
0.304923 + 0.952377i \(0.401369\pi\)
\(662\) 6.10038 0.237098
\(663\) 11.4391 0.444258
\(664\) 35.3288 1.37103
\(665\) 0 0
\(666\) 19.2039 0.744136
\(667\) 22.9112 0.887124
\(668\) −4.58546 −0.177417
\(669\) −9.17092 −0.354568
\(670\) −12.2008 −0.471357
\(671\) −14.0288 −0.541575
\(672\) 0 0
\(673\) −12.2070 −0.470547 −0.235273 0.971929i \(-0.575599\pi\)
−0.235273 + 0.971929i \(0.575599\pi\)
\(674\) −3.53948 −0.136336
\(675\) −4.27131 −0.164403
\(676\) −10.8181 −0.416082
\(677\) 39.7121 1.52626 0.763130 0.646245i \(-0.223662\pi\)
0.763130 + 0.646245i \(0.223662\pi\)
\(678\) −18.1151 −0.695705
\(679\) 0 0
\(680\) 10.8291 0.415276
\(681\) −0.263962 −0.0101150
\(682\) 77.2333 2.95742
\(683\) 9.22846 0.353117 0.176559 0.984290i \(-0.443503\pi\)
0.176559 + 0.984290i \(0.443503\pi\)
\(684\) −4.00000 −0.152944
\(685\) −6.56717 −0.250919
\(686\) 0 0
\(687\) −7.20390 −0.274846
\(688\) 14.0722 0.536499
\(689\) −5.05585 −0.192612
\(690\) 5.70727 0.217272
\(691\) 4.75325 0.180822 0.0904111 0.995905i \(-0.471182\pi\)
0.0904111 + 0.995905i \(0.471182\pi\)
\(692\) −4.14950 −0.157740
\(693\) 0 0
\(694\) −33.4538 −1.26989
\(695\) −15.3780 −0.583319
\(696\) −28.0147 −1.06189
\(697\) 3.63565 0.137710
\(698\) 38.0821 1.44143
\(699\) 16.1579 0.611149
\(700\) 0 0
\(701\) −21.0790 −0.796141 −0.398071 0.917355i \(-0.630320\pi\)
−0.398071 + 0.917355i \(0.630320\pi\)
\(702\) −7.37169 −0.278227
\(703\) −9.39625 −0.354386
\(704\) 40.7005 1.53396
\(705\) 7.10352 0.267534
\(706\) −26.1726 −0.985019
\(707\) 0 0
\(708\) 40.7005 1.52962
\(709\) 42.7497 1.60550 0.802749 0.596318i \(-0.203370\pi\)
0.802749 + 0.596318i \(0.203370\pi\)
\(710\) 17.3142 0.649789
\(711\) −3.60688 −0.135269
\(712\) 11.7648 0.440905
\(713\) 28.1396 1.05384
\(714\) 0 0
\(715\) −8.97858 −0.335780
\(716\) −66.3221 −2.47857
\(717\) −15.6644 −0.584999
\(718\) −38.0147 −1.41870
\(719\) 7.00735 0.261330 0.130665 0.991427i \(-0.458289\pi\)
0.130665 + 0.991427i \(0.458289\pi\)
\(720\) −1.02142 −0.0380662
\(721\) 0 0
\(722\) −41.4366 −1.54211
\(723\) −10.5468 −0.392241
\(724\) −36.2646 −1.34776
\(725\) 34.2933 1.27362
\(726\) 0.410327 0.0152287
\(727\) 33.3963 1.23860 0.619299 0.785155i \(-0.287417\pi\)
0.619299 + 0.785155i \(0.287417\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −20.3074 −0.751611
\(731\) −42.7575 −1.58144
\(732\) 14.6430 0.541221
\(733\) −13.1176 −0.484509 −0.242255 0.970213i \(-0.577887\pi\)
−0.242255 + 0.970213i \(0.577887\pi\)
\(734\) −1.01156 −0.0373373
\(735\) 0 0
\(736\) 11.9143 0.439167
\(737\) −20.3931 −0.751190
\(738\) −2.34292 −0.0862442
\(739\) −47.2902 −1.73960 −0.869799 0.493406i \(-0.835752\pi\)
−0.869799 + 0.493406i \(0.835752\pi\)
\(740\) −24.4141 −0.897479
\(741\) 3.60688 0.132502
\(742\) 0 0
\(743\) −18.5510 −0.680572 −0.340286 0.940322i \(-0.610524\pi\)
−0.340286 + 0.940322i \(0.610524\pi\)
\(744\) −34.4078 −1.26145
\(745\) −10.7068 −0.392267
\(746\) −8.59533 −0.314697
\(747\) 10.1249 0.370452
\(748\) 42.4078 1.55058
\(749\) 0 0
\(750\) 18.5426 0.677081
\(751\) −13.6791 −0.499158 −0.249579 0.968354i \(-0.580292\pi\)
−0.249579 + 0.968354i \(0.580292\pi\)
\(752\) −9.95715 −0.363100
\(753\) −21.4292 −0.780925
\(754\) 59.1856 2.15541
\(755\) −2.24361 −0.0816535
\(756\) 0 0
\(757\) −23.0031 −0.836063 −0.418032 0.908432i \(-0.637280\pi\)
−0.418032 + 0.908432i \(0.637280\pi\)
\(758\) −23.1940 −0.842445
\(759\) 9.53948 0.346261
\(760\) 3.41454 0.123858
\(761\) −20.4851 −0.742583 −0.371292 0.928516i \(-0.621085\pi\)
−0.371292 + 0.928516i \(0.621085\pi\)
\(762\) −28.2499 −1.02339
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 3.10352 0.112208
\(766\) 73.3681 2.65090
\(767\) −36.7005 −1.32518
\(768\) −22.9185 −0.827001
\(769\) 17.5107 0.631452 0.315726 0.948850i \(-0.397752\pi\)
0.315726 + 0.948850i \(0.397752\pi\)
\(770\) 0 0
\(771\) 7.10773 0.255979
\(772\) −68.3797 −2.46104
\(773\) 31.8083 1.14406 0.572032 0.820231i \(-0.306155\pi\)
0.572032 + 0.820231i \(0.306155\pi\)
\(774\) 27.5542 0.990414
\(775\) 42.1193 1.51297
\(776\) 26.3074 0.944381
\(777\) 0 0
\(778\) 17.3288 0.621269
\(779\) 1.14637 0.0410728
\(780\) 9.37169 0.335560
\(781\) 28.9399 1.03555
\(782\) 24.3074 0.869232
\(783\) −8.02877 −0.286925
\(784\) 0 0
\(785\) 17.2075 0.614162
\(786\) −28.6430 −1.02166
\(787\) −14.5040 −0.517011 −0.258506 0.966010i \(-0.583230\pi\)
−0.258506 + 0.966010i \(0.583230\pi\)
\(788\) −86.4225 −3.07867
\(789\) −9.97123 −0.354985
\(790\) 7.21377 0.256654
\(791\) 0 0
\(792\) −11.6644 −0.414477
\(793\) −13.2039 −0.468884
\(794\) −27.9572 −0.992162
\(795\) −1.37169 −0.0486489
\(796\) −44.7005 −1.58437
\(797\) −50.3650 −1.78402 −0.892009 0.452017i \(-0.850705\pi\)
−0.892009 + 0.452017i \(0.850705\pi\)
\(798\) 0 0
\(799\) 30.2541 1.07031
\(800\) 17.8333 0.630502
\(801\) 3.37169 0.119133
\(802\) −36.9357 −1.30425
\(803\) −33.9431 −1.19783
\(804\) 21.2860 0.750699
\(805\) 0 0
\(806\) 72.6921 2.56047
\(807\) 0.685846 0.0241429
\(808\) −17.4721 −0.614666
\(809\) 35.2369 1.23886 0.619431 0.785051i \(-0.287363\pi\)
0.619431 + 0.785051i \(0.287363\pi\)
\(810\) −2.00000 −0.0702728
\(811\) 13.8610 0.486725 0.243362 0.969935i \(-0.421750\pi\)
0.243362 + 0.969935i \(0.421750\pi\)
\(812\) 0 0
\(813\) −13.8034 −0.484108
\(814\) −64.1972 −2.25011
\(815\) −15.5823 −0.545825
\(816\) −4.35027 −0.152290
\(817\) −13.4819 −0.471673
\(818\) 17.6974 0.618775
\(819\) 0 0
\(820\) 2.97858 0.104016
\(821\) 7.20390 0.251418 0.125709 0.992067i \(-0.459879\pi\)
0.125709 + 0.992067i \(0.459879\pi\)
\(822\) 18.0246 0.628679
\(823\) −9.81392 −0.342092 −0.171046 0.985263i \(-0.554715\pi\)
−0.171046 + 0.985263i \(0.554715\pi\)
\(824\) −4.24989 −0.148052
\(825\) 14.2787 0.497119
\(826\) 0 0
\(827\) 24.8788 0.865121 0.432560 0.901605i \(-0.357610\pi\)
0.432560 + 0.901605i \(0.357610\pi\)
\(828\) −9.95715 −0.346035
\(829\) −13.3759 −0.464564 −0.232282 0.972648i \(-0.574619\pi\)
−0.232282 + 0.972648i \(0.574619\pi\)
\(830\) −20.2499 −0.702884
\(831\) 22.2113 0.770500
\(832\) 38.3074 1.32807
\(833\) 0 0
\(834\) 42.2070 1.46151
\(835\) 1.12181 0.0388217
\(836\) 13.3717 0.462470
\(837\) −9.86098 −0.340845
\(838\) −22.4851 −0.776734
\(839\) 12.9210 0.446084 0.223042 0.974809i \(-0.428401\pi\)
0.223042 + 0.974809i \(0.428401\pi\)
\(840\) 0 0
\(841\) 35.4611 1.22280
\(842\) 28.9357 0.997191
\(843\) 4.61423 0.158923
\(844\) 12.7862 0.440120
\(845\) 2.64659 0.0910456
\(846\) −19.4966 −0.670308
\(847\) 0 0
\(848\) 1.92273 0.0660268
\(849\) −9.13229 −0.313419
\(850\) 36.3832 1.24794
\(851\) −23.3900 −0.801798
\(852\) −30.2070 −1.03488
\(853\) −16.4851 −0.564438 −0.282219 0.959350i \(-0.591071\pi\)
−0.282219 + 0.959350i \(0.591071\pi\)
\(854\) 0 0
\(855\) 0.978577 0.0334666
\(856\) 48.0294 1.64161
\(857\) 11.5149 0.393342 0.196671 0.980470i \(-0.436987\pi\)
0.196671 + 0.980470i \(0.436987\pi\)
\(858\) 24.6430 0.841298
\(859\) 28.7392 0.980568 0.490284 0.871563i \(-0.336893\pi\)
0.490284 + 0.871563i \(0.336893\pi\)
\(860\) −35.0298 −1.19451
\(861\) 0 0
\(862\) 12.0575 0.410681
\(863\) 51.1611 1.74154 0.870771 0.491688i \(-0.163620\pi\)
0.870771 + 0.491688i \(0.163620\pi\)
\(864\) −4.17513 −0.142041
\(865\) 1.01515 0.0345162
\(866\) −40.0393 −1.36059
\(867\) −3.78202 −0.128444
\(868\) 0 0
\(869\) 12.0575 0.409024
\(870\) 16.0575 0.544402
\(871\) −19.1940 −0.650365
\(872\) 10.9786 0.371782
\(873\) 7.53948 0.255173
\(874\) 7.66442 0.259253
\(875\) 0 0
\(876\) 35.4292 1.19704
\(877\) 34.3179 1.15883 0.579417 0.815031i \(-0.303280\pi\)
0.579417 + 0.815031i \(0.303280\pi\)
\(878\) 52.3650 1.76723
\(879\) −23.4433 −0.790723
\(880\) 3.41454 0.115104
\(881\) 38.9786 1.31322 0.656611 0.754230i \(-0.271989\pi\)
0.656611 + 0.754230i \(0.271989\pi\)
\(882\) 0 0
\(883\) −28.2253 −0.949858 −0.474929 0.880024i \(-0.657526\pi\)
−0.474929 + 0.880024i \(0.657526\pi\)
\(884\) 39.9143 1.34246
\(885\) −9.95715 −0.334706
\(886\) 54.8585 1.84301
\(887\) 30.1438 1.01213 0.506066 0.862495i \(-0.331099\pi\)
0.506066 + 0.862495i \(0.331099\pi\)
\(888\) 28.6002 0.959758
\(889\) 0 0
\(890\) −6.74338 −0.226039
\(891\) −3.34292 −0.111992
\(892\) −32.0000 −1.07144
\(893\) 9.53948 0.319227
\(894\) 29.3864 0.982828
\(895\) 16.2253 0.542353
\(896\) 0 0
\(897\) 8.97858 0.299786
\(898\) −77.9521 −2.60130
\(899\) 79.1715 2.64052
\(900\) −14.9038 −0.496794
\(901\) −5.84208 −0.194628
\(902\) 7.83221 0.260784
\(903\) 0 0
\(904\) −26.9786 −0.897294
\(905\) 8.87192 0.294913
\(906\) 6.15792 0.204583
\(907\) 41.3435 1.37279 0.686395 0.727229i \(-0.259192\pi\)
0.686395 + 0.727229i \(0.259192\pi\)
\(908\) −0.921039 −0.0305657
\(909\) −5.00735 −0.166083
\(910\) 0 0
\(911\) −1.23206 −0.0408199 −0.0204099 0.999792i \(-0.506497\pi\)
−0.0204099 + 0.999792i \(0.506497\pi\)
\(912\) −1.37169 −0.0454213
\(913\) −33.8469 −1.12017
\(914\) −61.8370 −2.04539
\(915\) −3.58233 −0.118428
\(916\) −25.1365 −0.830533
\(917\) 0 0
\(918\) −8.51806 −0.281138
\(919\) −21.4047 −0.706075 −0.353037 0.935609i \(-0.614851\pi\)
−0.353037 + 0.935609i \(0.614851\pi\)
\(920\) 8.49977 0.280229
\(921\) −18.2541 −0.601493
\(922\) −5.15623 −0.169811
\(923\) 27.2383 0.896560
\(924\) 0 0
\(925\) −35.0100 −1.15112
\(926\) 57.4783 1.88886
\(927\) −1.21798 −0.0400037
\(928\) 33.5212 1.10039
\(929\) −32.8150 −1.07663 −0.538313 0.842745i \(-0.680938\pi\)
−0.538313 + 0.842745i \(0.680938\pi\)
\(930\) 19.7220 0.646709
\(931\) 0 0
\(932\) 56.3797 1.84678
\(933\) −14.8782 −0.487090
\(934\) 53.7367 1.75832
\(935\) −10.3748 −0.339293
\(936\) −10.9786 −0.358846
\(937\) −27.4783 −0.897678 −0.448839 0.893613i \(-0.648162\pi\)
−0.448839 + 0.893613i \(0.648162\pi\)
\(938\) 0 0
\(939\) 26.4752 0.863986
\(940\) 24.7862 0.808438
\(941\) −38.1151 −1.24252 −0.621258 0.783606i \(-0.713378\pi\)
−0.621258 + 0.783606i \(0.713378\pi\)
\(942\) −47.2285 −1.53879
\(943\) 2.85363 0.0929271
\(944\) 13.9572 0.454267
\(945\) 0 0
\(946\) −92.1115 −2.99480
\(947\) −9.85050 −0.320098 −0.160049 0.987109i \(-0.551165\pi\)
−0.160049 + 0.987109i \(0.551165\pi\)
\(948\) −12.5855 −0.408757
\(949\) −31.9473 −1.03705
\(950\) 11.4721 0.372203
\(951\) 29.6503 0.961478
\(952\) 0 0
\(953\) 3.92417 0.127116 0.0635582 0.997978i \(-0.479755\pi\)
0.0635582 + 0.997978i \(0.479755\pi\)
\(954\) 3.76481 0.121890
\(955\) 5.87146 0.189996
\(956\) −54.6577 −1.76776
\(957\) 26.8396 0.867600
\(958\) −97.4832 −3.14954
\(959\) 0 0
\(960\) 10.3931 0.335436
\(961\) 66.2389 2.13674
\(962\) −60.4225 −1.94810
\(963\) 13.7648 0.443565
\(964\) −36.8009 −1.18528
\(965\) 16.7287 0.538516
\(966\) 0 0
\(967\) −40.3074 −1.29620 −0.648100 0.761556i \(-0.724436\pi\)
−0.648100 + 0.761556i \(0.724436\pi\)
\(968\) 0.611096 0.0196414
\(969\) 4.16779 0.133889
\(970\) −15.0790 −0.484156
\(971\) −37.8280 −1.21396 −0.606979 0.794718i \(-0.707619\pi\)
−0.606979 + 0.794718i \(0.707619\pi\)
\(972\) 3.48929 0.111919
\(973\) 0 0
\(974\) 94.6625 3.03318
\(975\) 13.4391 0.430396
\(976\) 5.02142 0.160732
\(977\) 8.89227 0.284489 0.142244 0.989832i \(-0.454568\pi\)
0.142244 + 0.989832i \(0.454568\pi\)
\(978\) 42.7679 1.36757
\(979\) −11.2713 −0.360233
\(980\) 0 0
\(981\) 3.14637 0.100456
\(982\) −38.9357 −1.24249
\(983\) 30.6247 0.976777 0.488388 0.872626i \(-0.337585\pi\)
0.488388 + 0.872626i \(0.337585\pi\)
\(984\) −3.48929 −0.111234
\(985\) 21.1428 0.673665
\(986\) 68.3895 2.17797
\(987\) 0 0
\(988\) 12.5855 0.400397
\(989\) −33.5604 −1.06716
\(990\) 6.68585 0.212490
\(991\) −53.1512 −1.68840 −0.844202 0.536026i \(-0.819925\pi\)
−0.844202 + 0.536026i \(0.819925\pi\)
\(992\) 41.1709 1.30718
\(993\) 2.60375 0.0826275
\(994\) 0 0
\(995\) 10.9357 0.346686
\(996\) 35.3288 1.11944
\(997\) 44.5181 1.40990 0.704951 0.709256i \(-0.250969\pi\)
0.704951 + 0.709256i \(0.250969\pi\)
\(998\) −2.15792 −0.0683078
\(999\) 8.19656 0.259328
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 \(a_p\))