Properties

Label 4030.2.a.n.1.6
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.447568\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.447568 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.447568 q^{6} +1.86515 q^{7} +1.00000 q^{8} -2.79968 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.447568 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.447568 q^{6} +1.86515 q^{7} +1.00000 q^{8} -2.79968 q^{9} -1.00000 q^{10} -4.77230 q^{11} +0.447568 q^{12} -1.00000 q^{13} +1.86515 q^{14} -0.447568 q^{15} +1.00000 q^{16} +0.778658 q^{17} -2.79968 q^{18} +1.72026 q^{19} -1.00000 q^{20} +0.834782 q^{21} -4.77230 q^{22} +7.35604 q^{23} +0.447568 q^{24} +1.00000 q^{25} -1.00000 q^{26} -2.59575 q^{27} +1.86515 q^{28} +4.16592 q^{29} -0.447568 q^{30} -1.00000 q^{31} +1.00000 q^{32} -2.13593 q^{33} +0.778658 q^{34} -1.86515 q^{35} -2.79968 q^{36} +3.34010 q^{37} +1.72026 q^{38} -0.447568 q^{39} -1.00000 q^{40} +9.99536 q^{41} +0.834782 q^{42} +3.66184 q^{43} -4.77230 q^{44} +2.79968 q^{45} +7.35604 q^{46} +13.1874 q^{47} +0.447568 q^{48} -3.52121 q^{49} +1.00000 q^{50} +0.348503 q^{51} -1.00000 q^{52} +4.43178 q^{53} -2.59575 q^{54} +4.77230 q^{55} +1.86515 q^{56} +0.769933 q^{57} +4.16592 q^{58} +0.881231 q^{59} -0.447568 q^{60} +10.9344 q^{61} -1.00000 q^{62} -5.22183 q^{63} +1.00000 q^{64} +1.00000 q^{65} -2.13593 q^{66} +12.5130 q^{67} +0.778658 q^{68} +3.29233 q^{69} -1.86515 q^{70} -11.6243 q^{71} -2.79968 q^{72} -3.07944 q^{73} +3.34010 q^{74} +0.447568 q^{75} +1.72026 q^{76} -8.90107 q^{77} -0.447568 q^{78} -6.67559 q^{79} -1.00000 q^{80} +7.23727 q^{81} +9.99536 q^{82} +9.02853 q^{83} +0.834782 q^{84} -0.778658 q^{85} +3.66184 q^{86} +1.86453 q^{87} -4.77230 q^{88} +1.00767 q^{89} +2.79968 q^{90} -1.86515 q^{91} +7.35604 q^{92} -0.447568 q^{93} +13.1874 q^{94} -1.72026 q^{95} +0.447568 q^{96} -0.347181 q^{97} -3.52121 q^{98} +13.3609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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
\(3\) 0.447568 0.258404 0.129202 0.991618i \(-0.458758\pi\)
0.129202 + 0.991618i \(0.458758\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.447568 0.182719
\(7\) 1.86515 0.704961 0.352480 0.935819i \(-0.385338\pi\)
0.352480 + 0.935819i \(0.385338\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.79968 −0.933228
\(10\) −1.00000 −0.316228
\(11\) −4.77230 −1.43890 −0.719452 0.694542i \(-0.755607\pi\)
−0.719452 + 0.694542i \(0.755607\pi\)
\(12\) 0.447568 0.129202
\(13\) −1.00000 −0.277350
\(14\) 1.86515 0.498482
\(15\) −0.447568 −0.115562
\(16\) 1.00000 0.250000
\(17\) 0.778658 0.188852 0.0944262 0.995532i \(-0.469898\pi\)
0.0944262 + 0.995532i \(0.469898\pi\)
\(18\) −2.79968 −0.659892
\(19\) 1.72026 0.394654 0.197327 0.980338i \(-0.436774\pi\)
0.197327 + 0.980338i \(0.436774\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0.834782 0.182164
\(22\) −4.77230 −1.01746
\(23\) 7.35604 1.53384 0.766920 0.641742i \(-0.221788\pi\)
0.766920 + 0.641742i \(0.221788\pi\)
\(24\) 0.447568 0.0913595
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) −2.59575 −0.499553
\(28\) 1.86515 0.352480
\(29\) 4.16592 0.773591 0.386796 0.922165i \(-0.373582\pi\)
0.386796 + 0.922165i \(0.373582\pi\)
\(30\) −0.447568 −0.0817144
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −2.13593 −0.371818
\(34\) 0.778658 0.133539
\(35\) −1.86515 −0.315268
\(36\) −2.79968 −0.466614
\(37\) 3.34010 0.549109 0.274554 0.961572i \(-0.411470\pi\)
0.274554 + 0.961572i \(0.411470\pi\)
\(38\) 1.72026 0.279063
\(39\) −0.447568 −0.0716683
\(40\) −1.00000 −0.158114
\(41\) 9.99536 1.56101 0.780507 0.625147i \(-0.214961\pi\)
0.780507 + 0.625147i \(0.214961\pi\)
\(42\) 0.834782 0.128810
\(43\) 3.66184 0.558426 0.279213 0.960229i \(-0.409926\pi\)
0.279213 + 0.960229i \(0.409926\pi\)
\(44\) −4.77230 −0.719452
\(45\) 2.79968 0.417352
\(46\) 7.35604 1.08459
\(47\) 13.1874 1.92358 0.961789 0.273793i \(-0.0882783\pi\)
0.961789 + 0.273793i \(0.0882783\pi\)
\(48\) 0.447568 0.0646009
\(49\) −3.52121 −0.503030
\(50\) 1.00000 0.141421
\(51\) 0.348503 0.0488001
\(52\) −1.00000 −0.138675
\(53\) 4.43178 0.608751 0.304376 0.952552i \(-0.401552\pi\)
0.304376 + 0.952552i \(0.401552\pi\)
\(54\) −2.59575 −0.353237
\(55\) 4.77230 0.643497
\(56\) 1.86515 0.249241
\(57\) 0.769933 0.101980
\(58\) 4.16592 0.547012
\(59\) 0.881231 0.114726 0.0573632 0.998353i \(-0.481731\pi\)
0.0573632 + 0.998353i \(0.481731\pi\)
\(60\) −0.447568 −0.0577808
\(61\) 10.9344 1.40001 0.700003 0.714140i \(-0.253182\pi\)
0.700003 + 0.714140i \(0.253182\pi\)
\(62\) −1.00000 −0.127000
\(63\) −5.22183 −0.657889
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) −2.13593 −0.262915
\(67\) 12.5130 1.52870 0.764350 0.644801i \(-0.223060\pi\)
0.764350 + 0.644801i \(0.223060\pi\)
\(68\) 0.778658 0.0944262
\(69\) 3.29233 0.396350
\(70\) −1.86515 −0.222928
\(71\) −11.6243 −1.37955 −0.689776 0.724023i \(-0.742291\pi\)
−0.689776 + 0.724023i \(0.742291\pi\)
\(72\) −2.79968 −0.329946
\(73\) −3.07944 −0.360421 −0.180211 0.983628i \(-0.557678\pi\)
−0.180211 + 0.983628i \(0.557678\pi\)
\(74\) 3.34010 0.388278
\(75\) 0.447568 0.0516807
\(76\) 1.72026 0.197327
\(77\) −8.90107 −1.01437
\(78\) −0.447568 −0.0506771
\(79\) −6.67559 −0.751063 −0.375531 0.926810i \(-0.622540\pi\)
−0.375531 + 0.926810i \(0.622540\pi\)
\(80\) −1.00000 −0.111803
\(81\) 7.23727 0.804141
\(82\) 9.99536 1.10380
\(83\) 9.02853 0.991010 0.495505 0.868605i \(-0.334983\pi\)
0.495505 + 0.868605i \(0.334983\pi\)
\(84\) 0.834782 0.0910822
\(85\) −0.778658 −0.0844573
\(86\) 3.66184 0.394867
\(87\) 1.86453 0.199899
\(88\) −4.77230 −0.508729
\(89\) 1.00767 0.106813 0.0534065 0.998573i \(-0.482992\pi\)
0.0534065 + 0.998573i \(0.482992\pi\)
\(90\) 2.79968 0.295112
\(91\) −1.86515 −0.195521
\(92\) 7.35604 0.766920
\(93\) −0.447568 −0.0464107
\(94\) 13.1874 1.36017
\(95\) −1.72026 −0.176495
\(96\) 0.447568 0.0456797
\(97\) −0.347181 −0.0352509 −0.0176255 0.999845i \(-0.505611\pi\)
−0.0176255 + 0.999845i \(0.505611\pi\)
\(98\) −3.52121 −0.355696
\(99\) 13.3609 1.34282
\(100\) 1.00000 0.100000
\(101\) −13.2052 −1.31396 −0.656982 0.753906i \(-0.728167\pi\)
−0.656982 + 0.753906i \(0.728167\pi\)
\(102\) 0.348503 0.0345069
\(103\) −4.60964 −0.454202 −0.227101 0.973871i \(-0.572925\pi\)
−0.227101 + 0.973871i \(0.572925\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −0.834782 −0.0814664
\(106\) 4.43178 0.430452
\(107\) 9.36385 0.905237 0.452619 0.891704i \(-0.350490\pi\)
0.452619 + 0.891704i \(0.350490\pi\)
\(108\) −2.59575 −0.249777
\(109\) 0.494017 0.0473182 0.0236591 0.999720i \(-0.492468\pi\)
0.0236591 + 0.999720i \(0.492468\pi\)
\(110\) 4.77230 0.455021
\(111\) 1.49492 0.141892
\(112\) 1.86515 0.176240
\(113\) 5.70682 0.536852 0.268426 0.963300i \(-0.413496\pi\)
0.268426 + 0.963300i \(0.413496\pi\)
\(114\) 0.769933 0.0721108
\(115\) −7.35604 −0.685954
\(116\) 4.16592 0.386796
\(117\) 2.79968 0.258831
\(118\) 0.881231 0.0811239
\(119\) 1.45231 0.133133
\(120\) −0.447568 −0.0408572
\(121\) 11.7749 1.07044
\(122\) 10.9344 0.989954
\(123\) 4.47361 0.403372
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −5.22183 −0.465198
\(127\) 13.5704 1.20418 0.602088 0.798430i \(-0.294336\pi\)
0.602088 + 0.798430i \(0.294336\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.63892 0.144299
\(130\) 1.00000 0.0877058
\(131\) −11.4293 −0.998587 −0.499293 0.866433i \(-0.666407\pi\)
−0.499293 + 0.866433i \(0.666407\pi\)
\(132\) −2.13593 −0.185909
\(133\) 3.20854 0.278216
\(134\) 12.5130 1.08095
\(135\) 2.59575 0.223407
\(136\) 0.778658 0.0667694
\(137\) −3.83202 −0.327392 −0.163696 0.986511i \(-0.552342\pi\)
−0.163696 + 0.986511i \(0.552342\pi\)
\(138\) 3.29233 0.280262
\(139\) −5.95360 −0.504977 −0.252489 0.967600i \(-0.581249\pi\)
−0.252489 + 0.967600i \(0.581249\pi\)
\(140\) −1.86515 −0.157634
\(141\) 5.90225 0.497059
\(142\) −11.6243 −0.975491
\(143\) 4.77230 0.399080
\(144\) −2.79968 −0.233307
\(145\) −4.16592 −0.345961
\(146\) −3.07944 −0.254856
\(147\) −1.57598 −0.129985
\(148\) 3.34010 0.274554
\(149\) −1.40807 −0.115354 −0.0576769 0.998335i \(-0.518369\pi\)
−0.0576769 + 0.998335i \(0.518369\pi\)
\(150\) 0.447568 0.0365438
\(151\) −17.8726 −1.45445 −0.727227 0.686397i \(-0.759191\pi\)
−0.727227 + 0.686397i \(0.759191\pi\)
\(152\) 1.72026 0.139531
\(153\) −2.18000 −0.176242
\(154\) −8.90107 −0.717268
\(155\) 1.00000 0.0803219
\(156\) −0.447568 −0.0358341
\(157\) 3.24145 0.258696 0.129348 0.991599i \(-0.458712\pi\)
0.129348 + 0.991599i \(0.458712\pi\)
\(158\) −6.67559 −0.531082
\(159\) 1.98352 0.157303
\(160\) −1.00000 −0.0790569
\(161\) 13.7201 1.08130
\(162\) 7.23727 0.568614
\(163\) −8.73810 −0.684420 −0.342210 0.939623i \(-0.611176\pi\)
−0.342210 + 0.939623i \(0.611176\pi\)
\(164\) 9.99536 0.780507
\(165\) 2.13593 0.166282
\(166\) 9.02853 0.700750
\(167\) −19.0952 −1.47763 −0.738817 0.673907i \(-0.764615\pi\)
−0.738817 + 0.673907i \(0.764615\pi\)
\(168\) 0.834782 0.0644048
\(169\) 1.00000 0.0769231
\(170\) −0.778658 −0.0597204
\(171\) −4.81618 −0.368302
\(172\) 3.66184 0.279213
\(173\) 4.53336 0.344665 0.172333 0.985039i \(-0.444870\pi\)
0.172333 + 0.985039i \(0.444870\pi\)
\(174\) 1.86453 0.141350
\(175\) 1.86515 0.140992
\(176\) −4.77230 −0.359726
\(177\) 0.394411 0.0296457
\(178\) 1.00767 0.0755282
\(179\) 0.428265 0.0320100 0.0160050 0.999872i \(-0.494905\pi\)
0.0160050 + 0.999872i \(0.494905\pi\)
\(180\) 2.79968 0.208676
\(181\) −25.2013 −1.87320 −0.936598 0.350407i \(-0.886043\pi\)
−0.936598 + 0.350407i \(0.886043\pi\)
\(182\) −1.86515 −0.138254
\(183\) 4.89389 0.361767
\(184\) 7.35604 0.542295
\(185\) −3.34010 −0.245569
\(186\) −0.447568 −0.0328173
\(187\) −3.71599 −0.271740
\(188\) 13.1874 0.961789
\(189\) −4.84147 −0.352165
\(190\) −1.72026 −0.124801
\(191\) −22.3986 −1.62071 −0.810353 0.585942i \(-0.800724\pi\)
−0.810353 + 0.585942i \(0.800724\pi\)
\(192\) 0.447568 0.0323005
\(193\) 7.83137 0.563714 0.281857 0.959456i \(-0.409050\pi\)
0.281857 + 0.959456i \(0.409050\pi\)
\(194\) −0.347181 −0.0249262
\(195\) 0.447568 0.0320510
\(196\) −3.52121 −0.251515
\(197\) −0.917816 −0.0653917 −0.0326959 0.999465i \(-0.510409\pi\)
−0.0326959 + 0.999465i \(0.510409\pi\)
\(198\) 13.3609 0.949521
\(199\) −1.53767 −0.109003 −0.0545014 0.998514i \(-0.517357\pi\)
−0.0545014 + 0.998514i \(0.517357\pi\)
\(200\) 1.00000 0.0707107
\(201\) 5.60040 0.395022
\(202\) −13.2052 −0.929113
\(203\) 7.77006 0.545352
\(204\) 0.348503 0.0244001
\(205\) −9.99536 −0.698107
\(206\) −4.60964 −0.321169
\(207\) −20.5946 −1.43142
\(208\) −1.00000 −0.0693375
\(209\) −8.20959 −0.567869
\(210\) −0.834782 −0.0576054
\(211\) −11.8224 −0.813889 −0.406944 0.913453i \(-0.633406\pi\)
−0.406944 + 0.913453i \(0.633406\pi\)
\(212\) 4.43178 0.304376
\(213\) −5.20267 −0.356481
\(214\) 9.36385 0.640099
\(215\) −3.66184 −0.249736
\(216\) −2.59575 −0.176619
\(217\) −1.86515 −0.126615
\(218\) 0.494017 0.0334590
\(219\) −1.37826 −0.0931341
\(220\) 4.77230 0.321749
\(221\) −0.778658 −0.0523782
\(222\) 1.49492 0.100333
\(223\) −0.987764 −0.0661456 −0.0330728 0.999453i \(-0.510529\pi\)
−0.0330728 + 0.999453i \(0.510529\pi\)
\(224\) 1.86515 0.124621
\(225\) −2.79968 −0.186646
\(226\) 5.70682 0.379612
\(227\) 29.3711 1.94943 0.974713 0.223462i \(-0.0717358\pi\)
0.974713 + 0.223462i \(0.0717358\pi\)
\(228\) 0.769933 0.0509900
\(229\) 22.0436 1.45668 0.728342 0.685214i \(-0.240291\pi\)
0.728342 + 0.685214i \(0.240291\pi\)
\(230\) −7.35604 −0.485043
\(231\) −3.98383 −0.262117
\(232\) 4.16592 0.273506
\(233\) 29.9428 1.96162 0.980808 0.194977i \(-0.0624632\pi\)
0.980808 + 0.194977i \(0.0624632\pi\)
\(234\) 2.79968 0.183021
\(235\) −13.1874 −0.860250
\(236\) 0.881231 0.0573632
\(237\) −2.98778 −0.194077
\(238\) 1.45231 0.0941396
\(239\) −2.20402 −0.142566 −0.0712830 0.997456i \(-0.522709\pi\)
−0.0712830 + 0.997456i \(0.522709\pi\)
\(240\) −0.447568 −0.0288904
\(241\) −2.96453 −0.190962 −0.0954812 0.995431i \(-0.530439\pi\)
−0.0954812 + 0.995431i \(0.530439\pi\)
\(242\) 11.7749 0.756919
\(243\) 11.0264 0.707346
\(244\) 10.9344 0.700003
\(245\) 3.52121 0.224962
\(246\) 4.47361 0.285227
\(247\) −1.72026 −0.109457
\(248\) −1.00000 −0.0635001
\(249\) 4.04088 0.256081
\(250\) −1.00000 −0.0632456
\(251\) 13.3033 0.839695 0.419848 0.907595i \(-0.362084\pi\)
0.419848 + 0.907595i \(0.362084\pi\)
\(252\) −5.22183 −0.328944
\(253\) −35.1053 −2.20705
\(254\) 13.5704 0.851481
\(255\) −0.348503 −0.0218241
\(256\) 1.00000 0.0625000
\(257\) −19.2191 −1.19885 −0.599426 0.800430i \(-0.704605\pi\)
−0.599426 + 0.800430i \(0.704605\pi\)
\(258\) 1.63892 0.102035
\(259\) 6.22978 0.387100
\(260\) 1.00000 0.0620174
\(261\) −11.6632 −0.721937
\(262\) −11.4293 −0.706107
\(263\) 4.55763 0.281036 0.140518 0.990078i \(-0.455123\pi\)
0.140518 + 0.990078i \(0.455123\pi\)
\(264\) −2.13593 −0.131458
\(265\) −4.43178 −0.272242
\(266\) 3.20854 0.196728
\(267\) 0.451002 0.0276009
\(268\) 12.5130 0.764350
\(269\) 20.1656 1.22952 0.614759 0.788715i \(-0.289253\pi\)
0.614759 + 0.788715i \(0.289253\pi\)
\(270\) 2.59575 0.157973
\(271\) −7.81439 −0.474690 −0.237345 0.971425i \(-0.576277\pi\)
−0.237345 + 0.971425i \(0.576277\pi\)
\(272\) 0.778658 0.0472131
\(273\) −0.834782 −0.0505233
\(274\) −3.83202 −0.231501
\(275\) −4.77230 −0.287781
\(276\) 3.29233 0.198175
\(277\) −20.2372 −1.21593 −0.607967 0.793962i \(-0.708015\pi\)
−0.607967 + 0.793962i \(0.708015\pi\)
\(278\) −5.95360 −0.357073
\(279\) 2.79968 0.167613
\(280\) −1.86515 −0.111464
\(281\) −4.54675 −0.271236 −0.135618 0.990761i \(-0.543302\pi\)
−0.135618 + 0.990761i \(0.543302\pi\)
\(282\) 5.90225 0.351474
\(283\) −7.74070 −0.460137 −0.230068 0.973174i \(-0.573895\pi\)
−0.230068 + 0.973174i \(0.573895\pi\)
\(284\) −11.6243 −0.689776
\(285\) −0.769933 −0.0456069
\(286\) 4.77230 0.282192
\(287\) 18.6429 1.10045
\(288\) −2.79968 −0.164973
\(289\) −16.3937 −0.964335
\(290\) −4.16592 −0.244631
\(291\) −0.155387 −0.00910896
\(292\) −3.07944 −0.180211
\(293\) 27.0373 1.57954 0.789769 0.613405i \(-0.210201\pi\)
0.789769 + 0.613405i \(0.210201\pi\)
\(294\) −1.57598 −0.0919132
\(295\) −0.881231 −0.0513072
\(296\) 3.34010 0.194139
\(297\) 12.3877 0.718809
\(298\) −1.40807 −0.0815675
\(299\) −7.35604 −0.425411
\(300\) 0.447568 0.0258404
\(301\) 6.82989 0.393668
\(302\) −17.8726 −1.02845
\(303\) −5.91022 −0.339533
\(304\) 1.72026 0.0986635
\(305\) −10.9344 −0.626102
\(306\) −2.18000 −0.124622
\(307\) 21.7107 1.23909 0.619546 0.784960i \(-0.287317\pi\)
0.619546 + 0.784960i \(0.287317\pi\)
\(308\) −8.90107 −0.507185
\(309\) −2.06313 −0.117367
\(310\) 1.00000 0.0567962
\(311\) 12.3391 0.699686 0.349843 0.936808i \(-0.386235\pi\)
0.349843 + 0.936808i \(0.386235\pi\)
\(312\) −0.447568 −0.0253386
\(313\) 15.3649 0.868476 0.434238 0.900798i \(-0.357018\pi\)
0.434238 + 0.900798i \(0.357018\pi\)
\(314\) 3.24145 0.182926
\(315\) 5.22183 0.294217
\(316\) −6.67559 −0.375531
\(317\) 15.9180 0.894043 0.447022 0.894523i \(-0.352485\pi\)
0.447022 + 0.894523i \(0.352485\pi\)
\(318\) 1.98352 0.111230
\(319\) −19.8810 −1.11312
\(320\) −1.00000 −0.0559017
\(321\) 4.19096 0.233917
\(322\) 13.7201 0.764593
\(323\) 1.33949 0.0745314
\(324\) 7.23727 0.402071
\(325\) −1.00000 −0.0554700
\(326\) −8.73810 −0.483958
\(327\) 0.221106 0.0122272
\(328\) 9.99536 0.551902
\(329\) 24.5965 1.35605
\(330\) 2.13593 0.117579
\(331\) 18.4853 1.01604 0.508021 0.861345i \(-0.330377\pi\)
0.508021 + 0.861345i \(0.330377\pi\)
\(332\) 9.02853 0.495505
\(333\) −9.35121 −0.512443
\(334\) −19.0952 −1.04484
\(335\) −12.5130 −0.683656
\(336\) 0.834782 0.0455411
\(337\) −16.4309 −0.895050 −0.447525 0.894271i \(-0.647695\pi\)
−0.447525 + 0.894271i \(0.647695\pi\)
\(338\) 1.00000 0.0543928
\(339\) 2.55419 0.138725
\(340\) −0.778658 −0.0422287
\(341\) 4.77230 0.258435
\(342\) −4.81618 −0.260429
\(343\) −19.6236 −1.05958
\(344\) 3.66184 0.197433
\(345\) −3.29233 −0.177253
\(346\) 4.53336 0.243715
\(347\) 7.61718 0.408912 0.204456 0.978876i \(-0.434458\pi\)
0.204456 + 0.978876i \(0.434458\pi\)
\(348\) 1.86453 0.0999494
\(349\) 22.4423 1.20131 0.600655 0.799508i \(-0.294906\pi\)
0.600655 + 0.799508i \(0.294906\pi\)
\(350\) 1.86515 0.0996965
\(351\) 2.59575 0.138551
\(352\) −4.77230 −0.254365
\(353\) −3.91489 −0.208369 −0.104184 0.994558i \(-0.533223\pi\)
−0.104184 + 0.994558i \(0.533223\pi\)
\(354\) 0.394411 0.0209627
\(355\) 11.6243 0.616955
\(356\) 1.00767 0.0534065
\(357\) 0.650010 0.0344022
\(358\) 0.428265 0.0226345
\(359\) 27.3518 1.44357 0.721787 0.692116i \(-0.243321\pi\)
0.721787 + 0.692116i \(0.243321\pi\)
\(360\) 2.79968 0.147556
\(361\) −16.0407 −0.844248
\(362\) −25.2013 −1.32455
\(363\) 5.27007 0.276607
\(364\) −1.86515 −0.0977605
\(365\) 3.07944 0.161185
\(366\) 4.89389 0.255808
\(367\) −16.1452 −0.842771 −0.421386 0.906881i \(-0.638456\pi\)
−0.421386 + 0.906881i \(0.638456\pi\)
\(368\) 7.35604 0.383460
\(369\) −27.9839 −1.45678
\(370\) −3.34010 −0.173643
\(371\) 8.26593 0.429146
\(372\) −0.447568 −0.0232053
\(373\) −21.2717 −1.10141 −0.550703 0.834701i \(-0.685640\pi\)
−0.550703 + 0.834701i \(0.685640\pi\)
\(374\) −3.71599 −0.192149
\(375\) −0.447568 −0.0231123
\(376\) 13.1874 0.680087
\(377\) −4.16592 −0.214556
\(378\) −4.84147 −0.249018
\(379\) 26.2908 1.35047 0.675234 0.737604i \(-0.264043\pi\)
0.675234 + 0.737604i \(0.264043\pi\)
\(380\) −1.72026 −0.0882474
\(381\) 6.07367 0.311163
\(382\) −22.3986 −1.14601
\(383\) −11.4722 −0.586204 −0.293102 0.956081i \(-0.594687\pi\)
−0.293102 + 0.956081i \(0.594687\pi\)
\(384\) 0.447568 0.0228399
\(385\) 8.90107 0.453640
\(386\) 7.83137 0.398606
\(387\) −10.2520 −0.521138
\(388\) −0.347181 −0.0176255
\(389\) −2.58562 −0.131096 −0.0655481 0.997849i \(-0.520880\pi\)
−0.0655481 + 0.997849i \(0.520880\pi\)
\(390\) 0.447568 0.0226635
\(391\) 5.72784 0.289669
\(392\) −3.52121 −0.177848
\(393\) −5.11541 −0.258038
\(394\) −0.917816 −0.0462389
\(395\) 6.67559 0.335885
\(396\) 13.3609 0.671412
\(397\) 7.28233 0.365490 0.182745 0.983160i \(-0.441502\pi\)
0.182745 + 0.983160i \(0.441502\pi\)
\(398\) −1.53767 −0.0770766
\(399\) 1.43604 0.0718919
\(400\) 1.00000 0.0500000
\(401\) 9.87129 0.492948 0.246474 0.969149i \(-0.420728\pi\)
0.246474 + 0.969149i \(0.420728\pi\)
\(402\) 5.60040 0.279323
\(403\) 1.00000 0.0498135
\(404\) −13.2052 −0.656982
\(405\) −7.23727 −0.359623
\(406\) 7.77006 0.385622
\(407\) −15.9400 −0.790114
\(408\) 0.348503 0.0172535
\(409\) −7.54987 −0.373317 −0.186658 0.982425i \(-0.559766\pi\)
−0.186658 + 0.982425i \(0.559766\pi\)
\(410\) −9.99536 −0.493636
\(411\) −1.71509 −0.0845992
\(412\) −4.60964 −0.227101
\(413\) 1.64363 0.0808777
\(414\) −20.5946 −1.01217
\(415\) −9.02853 −0.443193
\(416\) −1.00000 −0.0490290
\(417\) −2.66464 −0.130488
\(418\) −8.20959 −0.401544
\(419\) 3.67874 0.179718 0.0898591 0.995954i \(-0.471358\pi\)
0.0898591 + 0.995954i \(0.471358\pi\)
\(420\) −0.834782 −0.0407332
\(421\) 25.5642 1.24592 0.622961 0.782253i \(-0.285930\pi\)
0.622961 + 0.782253i \(0.285930\pi\)
\(422\) −11.8224 −0.575506
\(423\) −36.9205 −1.79514
\(424\) 4.43178 0.215226
\(425\) 0.778658 0.0377705
\(426\) −5.20267 −0.252070
\(427\) 20.3943 0.986949
\(428\) 9.36385 0.452619
\(429\) 2.13593 0.103124
\(430\) −3.66184 −0.176590
\(431\) 6.61648 0.318705 0.159352 0.987222i \(-0.449059\pi\)
0.159352 + 0.987222i \(0.449059\pi\)
\(432\) −2.59575 −0.124888
\(433\) 34.7456 1.66977 0.834883 0.550428i \(-0.185535\pi\)
0.834883 + 0.550428i \(0.185535\pi\)
\(434\) −1.86515 −0.0895301
\(435\) −1.86453 −0.0893975
\(436\) 0.494017 0.0236591
\(437\) 12.6543 0.605337
\(438\) −1.37826 −0.0658558
\(439\) 2.41999 0.115500 0.0577499 0.998331i \(-0.481607\pi\)
0.0577499 + 0.998331i \(0.481607\pi\)
\(440\) 4.77230 0.227511
\(441\) 9.85828 0.469442
\(442\) −0.778658 −0.0370370
\(443\) −1.74933 −0.0831130 −0.0415565 0.999136i \(-0.513232\pi\)
−0.0415565 + 0.999136i \(0.513232\pi\)
\(444\) 1.49492 0.0709458
\(445\) −1.00767 −0.0477682
\(446\) −0.987764 −0.0467720
\(447\) −0.630209 −0.0298079
\(448\) 1.86515 0.0881201
\(449\) −10.9051 −0.514644 −0.257322 0.966326i \(-0.582840\pi\)
−0.257322 + 0.966326i \(0.582840\pi\)
\(450\) −2.79968 −0.131978
\(451\) −47.7009 −2.24615
\(452\) 5.70682 0.268426
\(453\) −7.99922 −0.375836
\(454\) 29.3711 1.37845
\(455\) 1.86515 0.0874396
\(456\) 0.769933 0.0360554
\(457\) −10.9185 −0.510744 −0.255372 0.966843i \(-0.582198\pi\)
−0.255372 + 0.966843i \(0.582198\pi\)
\(458\) 22.0436 1.03003
\(459\) −2.02120 −0.0943418
\(460\) −7.35604 −0.342977
\(461\) 8.49891 0.395834 0.197917 0.980219i \(-0.436582\pi\)
0.197917 + 0.980219i \(0.436582\pi\)
\(462\) −3.98383 −0.185345
\(463\) −4.70088 −0.218469 −0.109234 0.994016i \(-0.534840\pi\)
−0.109234 + 0.994016i \(0.534840\pi\)
\(464\) 4.16592 0.193398
\(465\) 0.447568 0.0207555
\(466\) 29.9428 1.38707
\(467\) 35.0427 1.62158 0.810791 0.585336i \(-0.199038\pi\)
0.810791 + 0.585336i \(0.199038\pi\)
\(468\) 2.79968 0.129415
\(469\) 23.3385 1.07767
\(470\) −13.1874 −0.608289
\(471\) 1.45077 0.0668479
\(472\) 0.881231 0.0405619
\(473\) −17.4754 −0.803521
\(474\) −2.98778 −0.137233
\(475\) 1.72026 0.0789308
\(476\) 1.45231 0.0665667
\(477\) −12.4076 −0.568103
\(478\) −2.20402 −0.100809
\(479\) −7.61684 −0.348022 −0.174011 0.984744i \(-0.555673\pi\)
−0.174011 + 0.984744i \(0.555673\pi\)
\(480\) −0.447568 −0.0204286
\(481\) −3.34010 −0.152295
\(482\) −2.96453 −0.135031
\(483\) 6.14069 0.279411
\(484\) 11.7749 0.535222
\(485\) 0.347181 0.0157647
\(486\) 11.0264 0.500169
\(487\) −18.2794 −0.828319 −0.414160 0.910204i \(-0.635924\pi\)
−0.414160 + 0.910204i \(0.635924\pi\)
\(488\) 10.9344 0.494977
\(489\) −3.91089 −0.176857
\(490\) 3.52121 0.159072
\(491\) 16.4804 0.743748 0.371874 0.928283i \(-0.378715\pi\)
0.371874 + 0.928283i \(0.378715\pi\)
\(492\) 4.47361 0.201686
\(493\) 3.24383 0.146095
\(494\) −1.72026 −0.0773980
\(495\) −13.3609 −0.600530
\(496\) −1.00000 −0.0449013
\(497\) −21.6811 −0.972530
\(498\) 4.04088 0.181076
\(499\) −15.8554 −0.709787 −0.354894 0.934907i \(-0.615483\pi\)
−0.354894 + 0.934907i \(0.615483\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −8.54642 −0.381826
\(502\) 13.3033 0.593754
\(503\) 30.0903 1.34166 0.670830 0.741611i \(-0.265938\pi\)
0.670830 + 0.741611i \(0.265938\pi\)
\(504\) −5.22183 −0.232599
\(505\) 13.2052 0.587623
\(506\) −35.1053 −1.56062
\(507\) 0.447568 0.0198772
\(508\) 13.5704 0.602088
\(509\) −14.0717 −0.623716 −0.311858 0.950129i \(-0.600951\pi\)
−0.311858 + 0.950129i \(0.600951\pi\)
\(510\) −0.348503 −0.0154320
\(511\) −5.74362 −0.254083
\(512\) 1.00000 0.0441942
\(513\) −4.46536 −0.197151
\(514\) −19.2191 −0.847717
\(515\) 4.60964 0.203125
\(516\) 1.63892 0.0721496
\(517\) −62.9342 −2.76784
\(518\) 6.22978 0.273721
\(519\) 2.02899 0.0890627
\(520\) 1.00000 0.0438529
\(521\) −39.8181 −1.74446 −0.872230 0.489095i \(-0.837327\pi\)
−0.872230 + 0.489095i \(0.837327\pi\)
\(522\) −11.6632 −0.510486
\(523\) −30.3377 −1.32658 −0.663288 0.748364i \(-0.730840\pi\)
−0.663288 + 0.748364i \(0.730840\pi\)
\(524\) −11.4293 −0.499293
\(525\) 0.834782 0.0364329
\(526\) 4.55763 0.198722
\(527\) −0.778658 −0.0339189
\(528\) −2.13593 −0.0929545
\(529\) 31.1113 1.35267
\(530\) −4.43178 −0.192504
\(531\) −2.46717 −0.107066
\(532\) 3.20854 0.139108
\(533\) −9.99536 −0.432947
\(534\) 0.451002 0.0195168
\(535\) −9.36385 −0.404834
\(536\) 12.5130 0.540477
\(537\) 0.191678 0.00827151
\(538\) 20.1656 0.869401
\(539\) 16.8043 0.723813
\(540\) 2.59575 0.111703
\(541\) 3.36965 0.144873 0.0724363 0.997373i \(-0.476923\pi\)
0.0724363 + 0.997373i \(0.476923\pi\)
\(542\) −7.81439 −0.335657
\(543\) −11.2793 −0.484040
\(544\) 0.778658 0.0333847
\(545\) −0.494017 −0.0211614
\(546\) −0.834782 −0.0357254
\(547\) −7.31261 −0.312664 −0.156332 0.987705i \(-0.549967\pi\)
−0.156332 + 0.987705i \(0.549967\pi\)
\(548\) −3.83202 −0.163696
\(549\) −30.6128 −1.30652
\(550\) −4.77230 −0.203492
\(551\) 7.16645 0.305301
\(552\) 3.29233 0.140131
\(553\) −12.4510 −0.529470
\(554\) −20.2372 −0.859795
\(555\) −1.49492 −0.0634559
\(556\) −5.95360 −0.252489
\(557\) −16.7686 −0.710509 −0.355255 0.934770i \(-0.615606\pi\)
−0.355255 + 0.934770i \(0.615606\pi\)
\(558\) 2.79968 0.118520
\(559\) −3.66184 −0.154879
\(560\) −1.86515 −0.0788170
\(561\) −1.66316 −0.0702187
\(562\) −4.54675 −0.191793
\(563\) −27.3655 −1.15332 −0.576659 0.816985i \(-0.695644\pi\)
−0.576659 + 0.816985i \(0.695644\pi\)
\(564\) 5.90225 0.248530
\(565\) −5.70682 −0.240088
\(566\) −7.74070 −0.325366
\(567\) 13.4986 0.566888
\(568\) −11.6243 −0.487745
\(569\) 8.59225 0.360206 0.180103 0.983648i \(-0.442357\pi\)
0.180103 + 0.983648i \(0.442357\pi\)
\(570\) −0.769933 −0.0322489
\(571\) −1.01112 −0.0423142 −0.0211571 0.999776i \(-0.506735\pi\)
−0.0211571 + 0.999776i \(0.506735\pi\)
\(572\) 4.77230 0.199540
\(573\) −10.0249 −0.418796
\(574\) 18.6429 0.778138
\(575\) 7.35604 0.306768
\(576\) −2.79968 −0.116653
\(577\) −31.4920 −1.31103 −0.655514 0.755183i \(-0.727548\pi\)
−0.655514 + 0.755183i \(0.727548\pi\)
\(578\) −16.3937 −0.681888
\(579\) 3.50507 0.145666
\(580\) −4.16592 −0.172980
\(581\) 16.8396 0.698623
\(582\) −0.155387 −0.00644101
\(583\) −21.1498 −0.875934
\(584\) −3.07944 −0.127428
\(585\) −2.79968 −0.115753
\(586\) 27.0373 1.11690
\(587\) −13.0002 −0.536577 −0.268289 0.963339i \(-0.586458\pi\)
−0.268289 + 0.963339i \(0.586458\pi\)
\(588\) −1.57598 −0.0649924
\(589\) −1.72026 −0.0708820
\(590\) −0.881231 −0.0362797
\(591\) −0.410785 −0.0168975
\(592\) 3.34010 0.137277
\(593\) 8.86766 0.364151 0.182076 0.983285i \(-0.441718\pi\)
0.182076 + 0.983285i \(0.441718\pi\)
\(594\) 12.3877 0.508275
\(595\) −1.45231 −0.0595391
\(596\) −1.40807 −0.0576769
\(597\) −0.688213 −0.0281667
\(598\) −7.35604 −0.300811
\(599\) 9.02508 0.368755 0.184377 0.982856i \(-0.440973\pi\)
0.184377 + 0.982856i \(0.440973\pi\)
\(600\) 0.447568 0.0182719
\(601\) −20.2693 −0.826803 −0.413401 0.910549i \(-0.635659\pi\)
−0.413401 + 0.910549i \(0.635659\pi\)
\(602\) 6.82989 0.278365
\(603\) −35.0323 −1.42663
\(604\) −17.8726 −0.727227
\(605\) −11.7749 −0.478718
\(606\) −5.91022 −0.240086
\(607\) −28.9615 −1.17551 −0.587756 0.809038i \(-0.699988\pi\)
−0.587756 + 0.809038i \(0.699988\pi\)
\(608\) 1.72026 0.0697657
\(609\) 3.47763 0.140921
\(610\) −10.9344 −0.442721
\(611\) −13.1874 −0.533504
\(612\) −2.18000 −0.0881211
\(613\) 19.1521 0.773545 0.386773 0.922175i \(-0.373590\pi\)
0.386773 + 0.922175i \(0.373590\pi\)
\(614\) 21.7107 0.876171
\(615\) −4.47361 −0.180393
\(616\) −8.90107 −0.358634
\(617\) −48.6447 −1.95836 −0.979180 0.202992i \(-0.934933\pi\)
−0.979180 + 0.202992i \(0.934933\pi\)
\(618\) −2.06313 −0.0829913
\(619\) 12.5591 0.504794 0.252397 0.967624i \(-0.418781\pi\)
0.252397 + 0.967624i \(0.418781\pi\)
\(620\) 1.00000 0.0401610
\(621\) −19.0945 −0.766235
\(622\) 12.3391 0.494753
\(623\) 1.87946 0.0752989
\(624\) −0.447568 −0.0179171
\(625\) 1.00000 0.0400000
\(626\) 15.3649 0.614106
\(627\) −3.67435 −0.146740
\(628\) 3.24145 0.129348
\(629\) 2.60079 0.103700
\(630\) 5.22183 0.208043
\(631\) −11.0498 −0.439886 −0.219943 0.975513i \(-0.570587\pi\)
−0.219943 + 0.975513i \(0.570587\pi\)
\(632\) −6.67559 −0.265541
\(633\) −5.29134 −0.210312
\(634\) 15.9180 0.632184
\(635\) −13.5704 −0.538524
\(636\) 1.98352 0.0786517
\(637\) 3.52121 0.139516
\(638\) −19.8810 −0.787097
\(639\) 32.5444 1.28744
\(640\) −1.00000 −0.0395285
\(641\) −10.0605 −0.397367 −0.198683 0.980064i \(-0.563667\pi\)
−0.198683 + 0.980064i \(0.563667\pi\)
\(642\) 4.19096 0.165404
\(643\) −4.39066 −0.173151 −0.0865754 0.996245i \(-0.527592\pi\)
−0.0865754 + 0.996245i \(0.527592\pi\)
\(644\) 13.7201 0.540649
\(645\) −1.63892 −0.0645326
\(646\) 1.33949 0.0527016
\(647\) −26.0147 −1.02274 −0.511372 0.859359i \(-0.670863\pi\)
−0.511372 + 0.859359i \(0.670863\pi\)
\(648\) 7.23727 0.284307
\(649\) −4.20550 −0.165080
\(650\) −1.00000 −0.0392232
\(651\) −0.834782 −0.0327177
\(652\) −8.73810 −0.342210
\(653\) 33.9554 1.32878 0.664388 0.747388i \(-0.268692\pi\)
0.664388 + 0.747388i \(0.268692\pi\)
\(654\) 0.221106 0.00864594
\(655\) 11.4293 0.446582
\(656\) 9.99536 0.390253
\(657\) 8.62145 0.336355
\(658\) 24.5965 0.958870
\(659\) 35.9335 1.39977 0.699886 0.714255i \(-0.253234\pi\)
0.699886 + 0.714255i \(0.253234\pi\)
\(660\) 2.13593 0.0831410
\(661\) −24.1467 −0.939197 −0.469598 0.882880i \(-0.655601\pi\)
−0.469598 + 0.882880i \(0.655601\pi\)
\(662\) 18.4853 0.718450
\(663\) −0.348503 −0.0135347
\(664\) 9.02853 0.350375
\(665\) −3.20854 −0.124422
\(666\) −9.35121 −0.362352
\(667\) 30.6447 1.18657
\(668\) −19.0952 −0.738817
\(669\) −0.442092 −0.0170923
\(670\) −12.5130 −0.483417
\(671\) −52.1823 −2.01447
\(672\) 0.834782 0.0322024
\(673\) −4.55474 −0.175572 −0.0877861 0.996139i \(-0.527979\pi\)
−0.0877861 + 0.996139i \(0.527979\pi\)
\(674\) −16.4309 −0.632896
\(675\) −2.59575 −0.0999106
\(676\) 1.00000 0.0384615
\(677\) 24.0091 0.922744 0.461372 0.887207i \(-0.347357\pi\)
0.461372 + 0.887207i \(0.347357\pi\)
\(678\) 2.55419 0.0980931
\(679\) −0.647545 −0.0248505
\(680\) −0.778658 −0.0298602
\(681\) 13.1456 0.503739
\(682\) 4.77230 0.182741
\(683\) 31.4528 1.20351 0.601754 0.798682i \(-0.294469\pi\)
0.601754 + 0.798682i \(0.294469\pi\)
\(684\) −4.81618 −0.184151
\(685\) 3.83202 0.146414
\(686\) −19.6236 −0.749234
\(687\) 9.86602 0.376412
\(688\) 3.66184 0.139606
\(689\) −4.43178 −0.168837
\(690\) −3.29233 −0.125337
\(691\) −6.27565 −0.238737 −0.119369 0.992850i \(-0.538087\pi\)
−0.119369 + 0.992850i \(0.538087\pi\)
\(692\) 4.53336 0.172333
\(693\) 24.9202 0.946639
\(694\) 7.61718 0.289144
\(695\) 5.95360 0.225833
\(696\) 1.86453 0.0706749
\(697\) 7.78297 0.294801
\(698\) 22.4423 0.849455
\(699\) 13.4014 0.506889
\(700\) 1.86515 0.0704961
\(701\) −0.574070 −0.0216823 −0.0108412 0.999941i \(-0.503451\pi\)
−0.0108412 + 0.999941i \(0.503451\pi\)
\(702\) 2.59575 0.0979704
\(703\) 5.74583 0.216708
\(704\) −4.77230 −0.179863
\(705\) −5.90225 −0.222292
\(706\) −3.91489 −0.147339
\(707\) −24.6296 −0.926293
\(708\) 0.394411 0.0148229
\(709\) −27.9485 −1.04963 −0.524815 0.851216i \(-0.675865\pi\)
−0.524815 + 0.851216i \(0.675865\pi\)
\(710\) 11.6243 0.436253
\(711\) 18.6895 0.700912
\(712\) 1.00767 0.0377641
\(713\) −7.35604 −0.275486
\(714\) 0.650010 0.0243260
\(715\) −4.77230 −0.178474
\(716\) 0.428265 0.0160050
\(717\) −0.986448 −0.0368396
\(718\) 27.3518 1.02076
\(719\) 41.4300 1.54508 0.772540 0.634966i \(-0.218986\pi\)
0.772540 + 0.634966i \(0.218986\pi\)
\(720\) 2.79968 0.104338
\(721\) −8.59768 −0.320194
\(722\) −16.0407 −0.596974
\(723\) −1.32683 −0.0493453
\(724\) −25.2013 −0.936598
\(725\) 4.16592 0.154718
\(726\) 5.27007 0.195591
\(727\) −34.8225 −1.29150 −0.645748 0.763551i \(-0.723454\pi\)
−0.645748 + 0.763551i \(0.723454\pi\)
\(728\) −1.86515 −0.0691271
\(729\) −16.7767 −0.621360
\(730\) 3.07944 0.113975
\(731\) 2.85132 0.105460
\(732\) 4.89389 0.180883
\(733\) −18.3137 −0.676433 −0.338216 0.941068i \(-0.609824\pi\)
−0.338216 + 0.941068i \(0.609824\pi\)
\(734\) −16.1452 −0.595929
\(735\) 1.57598 0.0581310
\(736\) 7.35604 0.271147
\(737\) −59.7156 −2.19965
\(738\) −27.9839 −1.03010
\(739\) 21.5968 0.794450 0.397225 0.917721i \(-0.369973\pi\)
0.397225 + 0.917721i \(0.369973\pi\)
\(740\) −3.34010 −0.122784
\(741\) −0.769933 −0.0282842
\(742\) 8.26593 0.303452
\(743\) 12.1199 0.444636 0.222318 0.974974i \(-0.428638\pi\)
0.222318 + 0.974974i \(0.428638\pi\)
\(744\) −0.447568 −0.0164086
\(745\) 1.40807 0.0515878
\(746\) −21.2717 −0.778812
\(747\) −25.2770 −0.924838
\(748\) −3.71599 −0.135870
\(749\) 17.4650 0.638157
\(750\) −0.447568 −0.0163429
\(751\) 53.1822 1.94065 0.970324 0.241810i \(-0.0777412\pi\)
0.970324 + 0.241810i \(0.0777412\pi\)
\(752\) 13.1874 0.480894
\(753\) 5.95412 0.216980
\(754\) −4.16592 −0.151714
\(755\) 17.8726 0.650452
\(756\) −4.84147 −0.176083
\(757\) −23.9118 −0.869091 −0.434545 0.900650i \(-0.643091\pi\)
−0.434545 + 0.900650i \(0.643091\pi\)
\(758\) 26.2908 0.954925
\(759\) −15.7120 −0.570310
\(760\) −1.72026 −0.0624003
\(761\) −20.9029 −0.757729 −0.378864 0.925452i \(-0.623685\pi\)
−0.378864 + 0.925452i \(0.623685\pi\)
\(762\) 6.07367 0.220026
\(763\) 0.921416 0.0333575
\(764\) −22.3986 −0.810353
\(765\) 2.18000 0.0788179
\(766\) −11.4722 −0.414509
\(767\) −0.881231 −0.0318194
\(768\) 0.447568 0.0161502
\(769\) 34.3679 1.23934 0.619670 0.784863i \(-0.287267\pi\)
0.619670 + 0.784863i \(0.287267\pi\)
\(770\) 8.90107 0.320772
\(771\) −8.60184 −0.309788
\(772\) 7.83137 0.281857
\(773\) −19.7225 −0.709368 −0.354684 0.934986i \(-0.615412\pi\)
−0.354684 + 0.934986i \(0.615412\pi\)
\(774\) −10.2520 −0.368500
\(775\) −1.00000 −0.0359211
\(776\) −0.347181 −0.0124631
\(777\) 2.78825 0.100028
\(778\) −2.58562 −0.0926990
\(779\) 17.1946 0.616061
\(780\) 0.447568 0.0160255
\(781\) 55.4748 1.98504
\(782\) 5.72784 0.204827
\(783\) −10.8137 −0.386450
\(784\) −3.52121 −0.125758
\(785\) −3.24145 −0.115692
\(786\) −5.11541 −0.182461
\(787\) 41.5231 1.48014 0.740069 0.672531i \(-0.234793\pi\)
0.740069 + 0.672531i \(0.234793\pi\)
\(788\) −0.917816 −0.0326959
\(789\) 2.03985 0.0726206
\(790\) 6.67559 0.237507
\(791\) 10.6441 0.378460
\(792\) 13.3609 0.474760
\(793\) −10.9344 −0.388292
\(794\) 7.28233 0.258440
\(795\) −1.98352 −0.0703483
\(796\) −1.53767 −0.0545014
\(797\) 46.4075 1.64384 0.821919 0.569605i \(-0.192904\pi\)
0.821919 + 0.569605i \(0.192904\pi\)
\(798\) 1.43604 0.0508353
\(799\) 10.2685 0.363272
\(800\) 1.00000 0.0353553
\(801\) −2.82116 −0.0996808
\(802\) 9.87129 0.348567
\(803\) 14.6960 0.518611
\(804\) 5.60040 0.197511
\(805\) −13.7201 −0.483571
\(806\) 1.00000 0.0352235
\(807\) 9.02549 0.317712
\(808\) −13.2052 −0.464557
\(809\) 4.22007 0.148370 0.0741848 0.997245i \(-0.476365\pi\)
0.0741848 + 0.997245i \(0.476365\pi\)
\(810\) −7.23727 −0.254292
\(811\) −35.4098 −1.24341 −0.621704 0.783252i \(-0.713559\pi\)
−0.621704 + 0.783252i \(0.713559\pi\)
\(812\) 7.77006 0.272676
\(813\) −3.49747 −0.122662
\(814\) −15.9400 −0.558695
\(815\) 8.73810 0.306082
\(816\) 0.348503 0.0122000
\(817\) 6.29931 0.220385
\(818\) −7.54987 −0.263975
\(819\) 5.22183 0.182466
\(820\) −9.99536 −0.349053
\(821\) −30.9267 −1.07935 −0.539675 0.841873i \(-0.681453\pi\)
−0.539675 + 0.841873i \(0.681453\pi\)
\(822\) −1.71509 −0.0598207
\(823\) 52.9075 1.84424 0.922120 0.386904i \(-0.126456\pi\)
0.922120 + 0.386904i \(0.126456\pi\)
\(824\) −4.60964 −0.160585
\(825\) −2.13593 −0.0743636
\(826\) 1.64363 0.0571891
\(827\) −37.9031 −1.31802 −0.659009 0.752135i \(-0.729024\pi\)
−0.659009 + 0.752135i \(0.729024\pi\)
\(828\) −20.5946 −0.715711
\(829\) 22.5811 0.784273 0.392136 0.919907i \(-0.371736\pi\)
0.392136 + 0.919907i \(0.371736\pi\)
\(830\) −9.02853 −0.313385
\(831\) −9.05752 −0.314202
\(832\) −1.00000 −0.0346688
\(833\) −2.74182 −0.0949985
\(834\) −2.66464 −0.0922690
\(835\) 19.0952 0.660818
\(836\) −8.20959 −0.283935
\(837\) 2.59575 0.0897224
\(838\) 3.67874 0.127080
\(839\) 26.2954 0.907818 0.453909 0.891048i \(-0.350029\pi\)
0.453909 + 0.891048i \(0.350029\pi\)
\(840\) −0.834782 −0.0288027
\(841\) −11.6451 −0.401556
\(842\) 25.5642 0.881000
\(843\) −2.03498 −0.0700884
\(844\) −11.8224 −0.406944
\(845\) −1.00000 −0.0344010
\(846\) −36.9205 −1.26935
\(847\) 21.9620 0.754622
\(848\) 4.43178 0.152188
\(849\) −3.46449 −0.118901
\(850\) 0.778658 0.0267078
\(851\) 24.5699 0.842245
\(852\) −5.20267 −0.178241
\(853\) −43.2843 −1.48203 −0.741014 0.671490i \(-0.765655\pi\)
−0.741014 + 0.671490i \(0.765655\pi\)
\(854\) 20.3943 0.697878
\(855\) 4.81618 0.164710
\(856\) 9.36385 0.320050
\(857\) 6.22499 0.212642 0.106321 0.994332i \(-0.466093\pi\)
0.106321 + 0.994332i \(0.466093\pi\)
\(858\) 2.13593 0.0729195
\(859\) −56.3879 −1.92393 −0.961965 0.273173i \(-0.911927\pi\)
−0.961965 + 0.273173i \(0.911927\pi\)
\(860\) −3.66184 −0.124868
\(861\) 8.34395 0.284361
\(862\) 6.61648 0.225358
\(863\) 31.7152 1.07960 0.539799 0.841794i \(-0.318500\pi\)
0.539799 + 0.841794i \(0.318500\pi\)
\(864\) −2.59575 −0.0883093
\(865\) −4.53336 −0.154139
\(866\) 34.7456 1.18070
\(867\) −7.33729 −0.249188
\(868\) −1.86515 −0.0633073
\(869\) 31.8580 1.08071
\(870\) −1.86453 −0.0632136
\(871\) −12.5130 −0.423985
\(872\) 0.494017 0.0167295
\(873\) 0.971997 0.0328971
\(874\) 12.6543 0.428038
\(875\) −1.86515 −0.0630536
\(876\) −1.37826 −0.0465671
\(877\) 49.8873 1.68457 0.842287 0.539029i \(-0.181209\pi\)
0.842287 + 0.539029i \(0.181209\pi\)
\(878\) 2.41999 0.0816706
\(879\) 12.1010 0.408158
\(880\) 4.77230 0.160874
\(881\) 44.7380 1.50726 0.753631 0.657297i \(-0.228300\pi\)
0.753631 + 0.657297i \(0.228300\pi\)
\(882\) 9.85828 0.331946
\(883\) −53.3699 −1.79604 −0.898020 0.439954i \(-0.854995\pi\)
−0.898020 + 0.439954i \(0.854995\pi\)
\(884\) −0.778658 −0.0261891
\(885\) −0.394411 −0.0132580
\(886\) −1.74933 −0.0587698
\(887\) −21.8610 −0.734020 −0.367010 0.930217i \(-0.619618\pi\)
−0.367010 + 0.930217i \(0.619618\pi\)
\(888\) 1.49492 0.0501663
\(889\) 25.3108 0.848897
\(890\) −1.00767 −0.0337772
\(891\) −34.5385 −1.15708
\(892\) −0.987764 −0.0330728
\(893\) 22.6857 0.759148
\(894\) −0.630209 −0.0210773
\(895\) −0.428265 −0.0143153
\(896\) 1.86515 0.0623103
\(897\) −3.29233 −0.109928
\(898\) −10.9051 −0.363908
\(899\) −4.16592 −0.138941
\(900\) −2.79968 −0.0933228
\(901\) 3.45084 0.114964
\(902\) −47.7009 −1.58827
\(903\) 3.05684 0.101725
\(904\) 5.70682 0.189806
\(905\) 25.2013 0.837718
\(906\) −7.99922 −0.265756
\(907\) −50.0962 −1.66342 −0.831709 0.555212i \(-0.812637\pi\)
−0.831709 + 0.555212i \(0.812637\pi\)
\(908\) 29.3711 0.974713
\(909\) 36.9703 1.22623
\(910\) 1.86515 0.0618291
\(911\) −46.3166 −1.53454 −0.767269 0.641326i \(-0.778385\pi\)
−0.767269 + 0.641326i \(0.778385\pi\)
\(912\) 0.769933 0.0254950
\(913\) −43.0869 −1.42597
\(914\) −10.9185 −0.361151
\(915\) −4.89389 −0.161787
\(916\) 22.0436 0.728342
\(917\) −21.3175 −0.703964
\(918\) −2.02120 −0.0667097
\(919\) 2.41549 0.0796798 0.0398399 0.999206i \(-0.487315\pi\)
0.0398399 + 0.999206i \(0.487315\pi\)
\(920\) −7.35604 −0.242521
\(921\) 9.71700 0.320186
\(922\) 8.49891 0.279897
\(923\) 11.6243 0.382619
\(924\) −3.98383 −0.131059
\(925\) 3.34010 0.109822
\(926\) −4.70088 −0.154481
\(927\) 12.9055 0.423874
\(928\) 4.16592 0.136753
\(929\) −2.38825 −0.0783561 −0.0391780 0.999232i \(-0.512474\pi\)
−0.0391780 + 0.999232i \(0.512474\pi\)
\(930\) 0.447568 0.0146763
\(931\) −6.05739 −0.198523
\(932\) 29.9428 0.980808
\(933\) 5.52259 0.180801
\(934\) 35.0427 1.14663
\(935\) 3.71599 0.121526
\(936\) 2.79968 0.0915105
\(937\) 10.4567 0.341605 0.170802 0.985305i \(-0.445364\pi\)
0.170802 + 0.985305i \(0.445364\pi\)
\(938\) 23.3385 0.762030
\(939\) 6.87685 0.224417
\(940\) −13.1874 −0.430125
\(941\) −39.2641 −1.27997 −0.639987 0.768386i \(-0.721060\pi\)
−0.639987 + 0.768386i \(0.721060\pi\)
\(942\) 1.45077 0.0472686
\(943\) 73.5263 2.39435
\(944\) 0.881231 0.0286816
\(945\) 4.84147 0.157493
\(946\) −17.4754 −0.568175
\(947\) 45.8543 1.49006 0.745032 0.667029i \(-0.232434\pi\)
0.745032 + 0.667029i \(0.232434\pi\)
\(948\) −2.98778 −0.0970387
\(949\) 3.07944 0.0999628
\(950\) 1.72026 0.0558125
\(951\) 7.12438 0.231024
\(952\) 1.45231 0.0470698
\(953\) −45.6183 −1.47772 −0.738860 0.673859i \(-0.764636\pi\)
−0.738860 + 0.673859i \(0.764636\pi\)
\(954\) −12.4076 −0.401710
\(955\) 22.3986 0.724801
\(956\) −2.20402 −0.0712830
\(957\) −8.89812 −0.287635
\(958\) −7.61684 −0.246089
\(959\) −7.14730 −0.230798
\(960\) −0.447568 −0.0144452
\(961\) 1.00000 0.0322581
\(962\) −3.34010 −0.107689
\(963\) −26.2158 −0.844792
\(964\) −2.96453 −0.0954812
\(965\) −7.83137 −0.252101
\(966\) 6.14069 0.197574
\(967\) −3.28378 −0.105599 −0.0527996 0.998605i \(-0.516814\pi\)
−0.0527996 + 0.998605i \(0.516814\pi\)
\(968\) 11.7749 0.378459
\(969\) 0.599514 0.0192592
\(970\) 0.347181 0.0111473
\(971\) −36.7536 −1.17948 −0.589740 0.807593i \(-0.700770\pi\)
−0.589740 + 0.807593i \(0.700770\pi\)
\(972\) 11.0264 0.353673
\(973\) −11.1044 −0.355989
\(974\) −18.2794 −0.585710
\(975\) −0.447568 −0.0143337
\(976\) 10.9344 0.350001
\(977\) 3.93943 0.126033 0.0630167 0.998012i \(-0.479928\pi\)
0.0630167 + 0.998012i \(0.479928\pi\)
\(978\) −3.91089 −0.125057
\(979\) −4.80892 −0.153694
\(980\) 3.52121 0.112481
\(981\) −1.38309 −0.0441587
\(982\) 16.4804 0.525909
\(983\) −39.5430 −1.26123 −0.630613 0.776097i \(-0.717197\pi\)
−0.630613 + 0.776097i \(0.717197\pi\)
\(984\) 4.47361 0.142613
\(985\) 0.917816 0.0292441
\(986\) 3.24383 0.103304
\(987\) 11.0086 0.350407
\(988\) −1.72026 −0.0547287
\(989\) 26.9367 0.856536
\(990\) −13.3609 −0.424639
\(991\) 10.2319 0.325027 0.162513 0.986706i \(-0.448040\pi\)
0.162513 + 0.986706i \(0.448040\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 8.27342 0.262549
\(994\) −21.6811 −0.687683
\(995\) 1.53767 0.0487475
\(996\) 4.04088 0.128040
\(997\) −27.3618 −0.866556 −0.433278 0.901260i \(-0.642643\pi\)
−0.433278 + 0.901260i \(0.642643\pi\)
\(998\) −15.8554 −0.501895
\(999\) −8.67007 −0.274309
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 \(a_p\))