Properties

Label 6010.2.a.c.1.12
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
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 1.12
Root \(1.74152\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.741521 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.741521 q^{6} -2.92320 q^{7} +1.00000 q^{8} -2.45015 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.741521 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.741521 q^{6} -2.92320 q^{7} +1.00000 q^{8} -2.45015 q^{9} +1.00000 q^{10} +3.78605 q^{11} +0.741521 q^{12} -1.20674 q^{13} -2.92320 q^{14} +0.741521 q^{15} +1.00000 q^{16} +2.24040 q^{17} -2.45015 q^{18} -6.75626 q^{19} +1.00000 q^{20} -2.16761 q^{21} +3.78605 q^{22} -2.16212 q^{23} +0.741521 q^{24} +1.00000 q^{25} -1.20674 q^{26} -4.04140 q^{27} -2.92320 q^{28} -7.43472 q^{29} +0.741521 q^{30} +2.54924 q^{31} +1.00000 q^{32} +2.80743 q^{33} +2.24040 q^{34} -2.92320 q^{35} -2.45015 q^{36} -2.16013 q^{37} -6.75626 q^{38} -0.894820 q^{39} +1.00000 q^{40} -4.79426 q^{41} -2.16761 q^{42} +2.62620 q^{43} +3.78605 q^{44} -2.45015 q^{45} -2.16212 q^{46} -9.28939 q^{47} +0.741521 q^{48} +1.54507 q^{49} +1.00000 q^{50} +1.66131 q^{51} -1.20674 q^{52} -4.24197 q^{53} -4.04140 q^{54} +3.78605 q^{55} -2.92320 q^{56} -5.00990 q^{57} -7.43472 q^{58} -2.50293 q^{59} +0.741521 q^{60} -2.21161 q^{61} +2.54924 q^{62} +7.16226 q^{63} +1.00000 q^{64} -1.20674 q^{65} +2.80743 q^{66} -6.47843 q^{67} +2.24040 q^{68} -1.60326 q^{69} -2.92320 q^{70} +3.13750 q^{71} -2.45015 q^{72} +7.55686 q^{73} -2.16013 q^{74} +0.741521 q^{75} -6.75626 q^{76} -11.0674 q^{77} -0.894820 q^{78} -7.16658 q^{79} +1.00000 q^{80} +4.35366 q^{81} -4.79426 q^{82} +14.7455 q^{83} -2.16761 q^{84} +2.24040 q^{85} +2.62620 q^{86} -5.51300 q^{87} +3.78605 q^{88} +10.3519 q^{89} -2.45015 q^{90} +3.52753 q^{91} -2.16212 q^{92} +1.89031 q^{93} -9.28939 q^{94} -6.75626 q^{95} +0.741521 q^{96} -6.45797 q^{97} +1.54507 q^{98} -9.27637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + O(q^{10}) \) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + 16q^{10} - 14q^{11} - 8q^{12} - 20q^{13} - 10q^{14} - 8q^{15} + 16q^{16} - 27q^{17} - 2q^{18} - 17q^{19} + 16q^{20} - 12q^{21} - 14q^{22} - 9q^{23} - 8q^{24} + 16q^{25} - 20q^{26} - 11q^{27} - 10q^{28} - 23q^{29} - 8q^{30} - 21q^{31} + 16q^{32} - 9q^{33} - 27q^{34} - 10q^{35} - 2q^{36} - 16q^{37} - 17q^{38} - 6q^{39} + 16q^{40} - 35q^{41} - 12q^{42} + 3q^{43} - 14q^{44} - 2q^{45} - 9q^{46} - 25q^{47} - 8q^{48} - 24q^{49} + 16q^{50} - q^{51} - 20q^{52} - 39q^{53} - 11q^{54} - 14q^{55} - 10q^{56} - 6q^{57} - 23q^{58} - 32q^{59} - 8q^{60} - 38q^{61} - 21q^{62} + q^{63} + 16q^{64} - 20q^{65} - 9q^{66} + 5q^{67} - 27q^{68} - 25q^{69} - 10q^{70} - 16q^{71} - 2q^{72} - 17q^{73} - 16q^{74} - 8q^{75} - 17q^{76} - 34q^{77} - 6q^{78} - 40q^{79} + 16q^{80} - 28q^{81} - 35q^{82} - 22q^{83} - 12q^{84} - 27q^{85} + 3q^{86} + 10q^{87} - 14q^{88} - 46q^{89} - 2q^{90} - q^{91} - 9q^{92} + 14q^{93} - 25q^{94} - 17q^{95} - 8q^{96} - 21q^{97} - 24q^{98} + 15q^{99} + O(q^{100}) \)

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
\(3\) 0.741521 0.428117 0.214059 0.976821i \(-0.431332\pi\)
0.214059 + 0.976821i \(0.431332\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.741521 0.302725
\(7\) −2.92320 −1.10486 −0.552432 0.833558i \(-0.686300\pi\)
−0.552432 + 0.833558i \(0.686300\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.45015 −0.816716
\(10\) 1.00000 0.316228
\(11\) 3.78605 1.14154 0.570768 0.821111i \(-0.306646\pi\)
0.570768 + 0.821111i \(0.306646\pi\)
\(12\) 0.741521 0.214059
\(13\) −1.20674 −0.334688 −0.167344 0.985899i \(-0.553519\pi\)
−0.167344 + 0.985899i \(0.553519\pi\)
\(14\) −2.92320 −0.781257
\(15\) 0.741521 0.191460
\(16\) 1.00000 0.250000
\(17\) 2.24040 0.543378 0.271689 0.962385i \(-0.412418\pi\)
0.271689 + 0.962385i \(0.412418\pi\)
\(18\) −2.45015 −0.577505
\(19\) −6.75626 −1.54999 −0.774996 0.631967i \(-0.782248\pi\)
−0.774996 + 0.631967i \(0.782248\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.16761 −0.473011
\(22\) 3.78605 0.807188
\(23\) −2.16212 −0.450833 −0.225416 0.974263i \(-0.572374\pi\)
−0.225416 + 0.974263i \(0.572374\pi\)
\(24\) 0.741521 0.151362
\(25\) 1.00000 0.200000
\(26\) −1.20674 −0.236660
\(27\) −4.04140 −0.777767
\(28\) −2.92320 −0.552432
\(29\) −7.43472 −1.38059 −0.690297 0.723527i \(-0.742520\pi\)
−0.690297 + 0.723527i \(0.742520\pi\)
\(30\) 0.741521 0.135383
\(31\) 2.54924 0.457856 0.228928 0.973443i \(-0.426478\pi\)
0.228928 + 0.973443i \(0.426478\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.80743 0.488711
\(34\) 2.24040 0.384226
\(35\) −2.92320 −0.494110
\(36\) −2.45015 −0.408358
\(37\) −2.16013 −0.355124 −0.177562 0.984110i \(-0.556821\pi\)
−0.177562 + 0.984110i \(0.556821\pi\)
\(38\) −6.75626 −1.09601
\(39\) −0.894820 −0.143286
\(40\) 1.00000 0.158114
\(41\) −4.79426 −0.748737 −0.374369 0.927280i \(-0.622141\pi\)
−0.374369 + 0.927280i \(0.622141\pi\)
\(42\) −2.16761 −0.334470
\(43\) 2.62620 0.400492 0.200246 0.979746i \(-0.435826\pi\)
0.200246 + 0.979746i \(0.435826\pi\)
\(44\) 3.78605 0.570768
\(45\) −2.45015 −0.365246
\(46\) −2.16212 −0.318787
\(47\) −9.28939 −1.35500 −0.677499 0.735524i \(-0.736936\pi\)
−0.677499 + 0.735524i \(0.736936\pi\)
\(48\) 0.741521 0.107029
\(49\) 1.54507 0.220724
\(50\) 1.00000 0.141421
\(51\) 1.66131 0.232629
\(52\) −1.20674 −0.167344
\(53\) −4.24197 −0.582680 −0.291340 0.956620i \(-0.594101\pi\)
−0.291340 + 0.956620i \(0.594101\pi\)
\(54\) −4.04140 −0.549965
\(55\) 3.78605 0.510510
\(56\) −2.92320 −0.390628
\(57\) −5.00990 −0.663578
\(58\) −7.43472 −0.976227
\(59\) −2.50293 −0.325854 −0.162927 0.986638i \(-0.552094\pi\)
−0.162927 + 0.986638i \(0.552094\pi\)
\(60\) 0.741521 0.0957299
\(61\) −2.21161 −0.283167 −0.141584 0.989926i \(-0.545219\pi\)
−0.141584 + 0.989926i \(0.545219\pi\)
\(62\) 2.54924 0.323753
\(63\) 7.16226 0.902359
\(64\) 1.00000 0.125000
\(65\) −1.20674 −0.149677
\(66\) 2.80743 0.345571
\(67\) −6.47843 −0.791467 −0.395733 0.918365i \(-0.629510\pi\)
−0.395733 + 0.918365i \(0.629510\pi\)
\(68\) 2.24040 0.271689
\(69\) −1.60326 −0.193009
\(70\) −2.92320 −0.349389
\(71\) 3.13750 0.372352 0.186176 0.982516i \(-0.440390\pi\)
0.186176 + 0.982516i \(0.440390\pi\)
\(72\) −2.45015 −0.288753
\(73\) 7.55686 0.884464 0.442232 0.896901i \(-0.354187\pi\)
0.442232 + 0.896901i \(0.354187\pi\)
\(74\) −2.16013 −0.251110
\(75\) 0.741521 0.0856235
\(76\) −6.75626 −0.774996
\(77\) −11.0674 −1.26124
\(78\) −0.894820 −0.101318
\(79\) −7.16658 −0.806303 −0.403152 0.915133i \(-0.632085\pi\)
−0.403152 + 0.915133i \(0.632085\pi\)
\(80\) 1.00000 0.111803
\(81\) 4.35366 0.483740
\(82\) −4.79426 −0.529437
\(83\) 14.7455 1.61852 0.809262 0.587447i \(-0.199867\pi\)
0.809262 + 0.587447i \(0.199867\pi\)
\(84\) −2.16761 −0.236506
\(85\) 2.24040 0.243006
\(86\) 2.62620 0.283191
\(87\) −5.51300 −0.591056
\(88\) 3.78605 0.403594
\(89\) 10.3519 1.09730 0.548652 0.836051i \(-0.315141\pi\)
0.548652 + 0.836051i \(0.315141\pi\)
\(90\) −2.45015 −0.258268
\(91\) 3.52753 0.369785
\(92\) −2.16212 −0.225416
\(93\) 1.89031 0.196016
\(94\) −9.28939 −0.958128
\(95\) −6.75626 −0.693177
\(96\) 0.741521 0.0756812
\(97\) −6.45797 −0.655708 −0.327854 0.944728i \(-0.606325\pi\)
−0.327854 + 0.944728i \(0.606325\pi\)
\(98\) 1.54507 0.156076
\(99\) −9.27637 −0.932310
\(100\) 1.00000 0.100000
\(101\) 3.69551 0.367717 0.183858 0.982953i \(-0.441141\pi\)
0.183858 + 0.982953i \(0.441141\pi\)
\(102\) 1.66131 0.164494
\(103\) 6.19576 0.610487 0.305243 0.952274i \(-0.401262\pi\)
0.305243 + 0.952274i \(0.401262\pi\)
\(104\) −1.20674 −0.118330
\(105\) −2.16761 −0.211537
\(106\) −4.24197 −0.412017
\(107\) −4.26814 −0.412617 −0.206309 0.978487i \(-0.566145\pi\)
−0.206309 + 0.978487i \(0.566145\pi\)
\(108\) −4.04140 −0.388884
\(109\) −6.78094 −0.649496 −0.324748 0.945800i \(-0.605280\pi\)
−0.324748 + 0.945800i \(0.605280\pi\)
\(110\) 3.78605 0.360985
\(111\) −1.60178 −0.152035
\(112\) −2.92320 −0.276216
\(113\) −12.8387 −1.20776 −0.603881 0.797075i \(-0.706380\pi\)
−0.603881 + 0.797075i \(0.706380\pi\)
\(114\) −5.00990 −0.469221
\(115\) −2.16212 −0.201619
\(116\) −7.43472 −0.690297
\(117\) 2.95668 0.273345
\(118\) −2.50293 −0.230414
\(119\) −6.54914 −0.600358
\(120\) 0.741521 0.0676913
\(121\) 3.33415 0.303105
\(122\) −2.21161 −0.200229
\(123\) −3.55504 −0.320547
\(124\) 2.54924 0.228928
\(125\) 1.00000 0.0894427
\(126\) 7.16226 0.638065
\(127\) −21.5834 −1.91522 −0.957610 0.288069i \(-0.906987\pi\)
−0.957610 + 0.288069i \(0.906987\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.94739 0.171458
\(130\) −1.20674 −0.105838
\(131\) −1.86617 −0.163048 −0.0815242 0.996671i \(-0.525979\pi\)
−0.0815242 + 0.996671i \(0.525979\pi\)
\(132\) 2.80743 0.244356
\(133\) 19.7499 1.71253
\(134\) −6.47843 −0.559651
\(135\) −4.04140 −0.347828
\(136\) 2.24040 0.192113
\(137\) 16.5456 1.41358 0.706792 0.707421i \(-0.250141\pi\)
0.706792 + 0.707421i \(0.250141\pi\)
\(138\) −1.60326 −0.136478
\(139\) 17.7109 1.50222 0.751111 0.660176i \(-0.229518\pi\)
0.751111 + 0.660176i \(0.229518\pi\)
\(140\) −2.92320 −0.247055
\(141\) −6.88828 −0.580098
\(142\) 3.13750 0.263293
\(143\) −4.56876 −0.382059
\(144\) −2.45015 −0.204179
\(145\) −7.43472 −0.617420
\(146\) 7.55686 0.625410
\(147\) 1.14570 0.0944958
\(148\) −2.16013 −0.177562
\(149\) −6.38704 −0.523246 −0.261623 0.965170i \(-0.584258\pi\)
−0.261623 + 0.965170i \(0.584258\pi\)
\(150\) 0.741521 0.0605449
\(151\) −3.63992 −0.296213 −0.148106 0.988971i \(-0.547318\pi\)
−0.148106 + 0.988971i \(0.547318\pi\)
\(152\) −6.75626 −0.548005
\(153\) −5.48932 −0.443785
\(154\) −11.0674 −0.891833
\(155\) 2.54924 0.204760
\(156\) −0.894820 −0.0716430
\(157\) −3.48148 −0.277852 −0.138926 0.990303i \(-0.544365\pi\)
−0.138926 + 0.990303i \(0.544365\pi\)
\(158\) −7.16658 −0.570142
\(159\) −3.14551 −0.249455
\(160\) 1.00000 0.0790569
\(161\) 6.32029 0.498109
\(162\) 4.35366 0.342056
\(163\) −7.48872 −0.586562 −0.293281 0.956026i \(-0.594747\pi\)
−0.293281 + 0.956026i \(0.594747\pi\)
\(164\) −4.79426 −0.374369
\(165\) 2.80743 0.218558
\(166\) 14.7455 1.14447
\(167\) 0.756944 0.0585741 0.0292870 0.999571i \(-0.490676\pi\)
0.0292870 + 0.999571i \(0.490676\pi\)
\(168\) −2.16761 −0.167235
\(169\) −11.5438 −0.887984
\(170\) 2.24040 0.171831
\(171\) 16.5538 1.26590
\(172\) 2.62620 0.200246
\(173\) −18.3173 −1.39264 −0.696321 0.717730i \(-0.745181\pi\)
−0.696321 + 0.717730i \(0.745181\pi\)
\(174\) −5.51300 −0.417940
\(175\) −2.92320 −0.220973
\(176\) 3.78605 0.285384
\(177\) −1.85598 −0.139504
\(178\) 10.3519 0.775911
\(179\) 2.24990 0.168166 0.0840829 0.996459i \(-0.473204\pi\)
0.0840829 + 0.996459i \(0.473204\pi\)
\(180\) −2.45015 −0.182623
\(181\) −9.62422 −0.715363 −0.357681 0.933844i \(-0.616433\pi\)
−0.357681 + 0.933844i \(0.616433\pi\)
\(182\) 3.52753 0.261478
\(183\) −1.63995 −0.121229
\(184\) −2.16212 −0.159393
\(185\) −2.16013 −0.158816
\(186\) 1.89031 0.138604
\(187\) 8.48227 0.620285
\(188\) −9.28939 −0.677499
\(189\) 11.8138 0.859327
\(190\) −6.75626 −0.490150
\(191\) 1.03740 0.0750638 0.0375319 0.999295i \(-0.488050\pi\)
0.0375319 + 0.999295i \(0.488050\pi\)
\(192\) 0.741521 0.0535147
\(193\) −12.0456 −0.867064 −0.433532 0.901138i \(-0.642733\pi\)
−0.433532 + 0.901138i \(0.642733\pi\)
\(194\) −6.45797 −0.463656
\(195\) −0.894820 −0.0640794
\(196\) 1.54507 0.110362
\(197\) 15.0764 1.07415 0.537073 0.843536i \(-0.319530\pi\)
0.537073 + 0.843536i \(0.319530\pi\)
\(198\) −9.27637 −0.659243
\(199\) 0.396256 0.0280899 0.0140449 0.999901i \(-0.495529\pi\)
0.0140449 + 0.999901i \(0.495529\pi\)
\(200\) 1.00000 0.0707107
\(201\) −4.80390 −0.338841
\(202\) 3.69551 0.260015
\(203\) 21.7331 1.52537
\(204\) 1.66131 0.116315
\(205\) −4.79426 −0.334846
\(206\) 6.19576 0.431679
\(207\) 5.29751 0.368202
\(208\) −1.20674 −0.0836721
\(209\) −25.5795 −1.76937
\(210\) −2.16761 −0.149579
\(211\) 18.2045 1.25325 0.626624 0.779322i \(-0.284436\pi\)
0.626624 + 0.779322i \(0.284436\pi\)
\(212\) −4.24197 −0.291340
\(213\) 2.32652 0.159410
\(214\) −4.26814 −0.291764
\(215\) 2.62620 0.179106
\(216\) −4.04140 −0.274982
\(217\) −7.45192 −0.505869
\(218\) −6.78094 −0.459263
\(219\) 5.60357 0.378654
\(220\) 3.78605 0.255255
\(221\) −2.70358 −0.181862
\(222\) −1.60178 −0.107505
\(223\) −9.99886 −0.669573 −0.334787 0.942294i \(-0.608664\pi\)
−0.334787 + 0.942294i \(0.608664\pi\)
\(224\) −2.92320 −0.195314
\(225\) −2.45015 −0.163343
\(226\) −12.8387 −0.854016
\(227\) −8.02690 −0.532764 −0.266382 0.963868i \(-0.585828\pi\)
−0.266382 + 0.963868i \(0.585828\pi\)
\(228\) −5.00990 −0.331789
\(229\) −25.6126 −1.69253 −0.846264 0.532763i \(-0.821154\pi\)
−0.846264 + 0.532763i \(0.821154\pi\)
\(230\) −2.16212 −0.142566
\(231\) −8.20667 −0.539960
\(232\) −7.43472 −0.488113
\(233\) 8.36069 0.547727 0.273864 0.961769i \(-0.411698\pi\)
0.273864 + 0.961769i \(0.411698\pi\)
\(234\) 2.95668 0.193284
\(235\) −9.28939 −0.605973
\(236\) −2.50293 −0.162927
\(237\) −5.31417 −0.345192
\(238\) −6.54914 −0.424517
\(239\) −5.94177 −0.384341 −0.192171 0.981362i \(-0.561553\pi\)
−0.192171 + 0.981362i \(0.561553\pi\)
\(240\) 0.741521 0.0478650
\(241\) −28.2635 −1.82061 −0.910307 0.413933i \(-0.864155\pi\)
−0.910307 + 0.413933i \(0.864155\pi\)
\(242\) 3.33415 0.214327
\(243\) 15.3525 0.984865
\(244\) −2.21161 −0.141584
\(245\) 1.54507 0.0987108
\(246\) −3.55504 −0.226661
\(247\) 8.15302 0.518764
\(248\) 2.54924 0.161877
\(249\) 10.9341 0.692919
\(250\) 1.00000 0.0632456
\(251\) 1.54250 0.0973619 0.0486810 0.998814i \(-0.484498\pi\)
0.0486810 + 0.998814i \(0.484498\pi\)
\(252\) 7.16226 0.451180
\(253\) −8.18588 −0.514642
\(254\) −21.5834 −1.35426
\(255\) 1.66131 0.104035
\(256\) 1.00000 0.0625000
\(257\) 12.2344 0.763159 0.381580 0.924336i \(-0.375380\pi\)
0.381580 + 0.924336i \(0.375380\pi\)
\(258\) 1.94739 0.121239
\(259\) 6.31449 0.392363
\(260\) −1.20674 −0.0748386
\(261\) 18.2162 1.12755
\(262\) −1.86617 −0.115293
\(263\) 6.05174 0.373167 0.186583 0.982439i \(-0.440259\pi\)
0.186583 + 0.982439i \(0.440259\pi\)
\(264\) 2.80743 0.172786
\(265\) −4.24197 −0.260582
\(266\) 19.7499 1.21094
\(267\) 7.67618 0.469775
\(268\) −6.47843 −0.395733
\(269\) 15.8007 0.963388 0.481694 0.876339i \(-0.340022\pi\)
0.481694 + 0.876339i \(0.340022\pi\)
\(270\) −4.04140 −0.245952
\(271\) 5.49046 0.333522 0.166761 0.985997i \(-0.446669\pi\)
0.166761 + 0.985997i \(0.446669\pi\)
\(272\) 2.24040 0.135844
\(273\) 2.61573 0.158311
\(274\) 16.5456 0.999556
\(275\) 3.78605 0.228307
\(276\) −1.60326 −0.0965046
\(277\) 12.6922 0.762601 0.381301 0.924451i \(-0.375476\pi\)
0.381301 + 0.924451i \(0.375476\pi\)
\(278\) 17.7109 1.06223
\(279\) −6.24600 −0.373938
\(280\) −2.92320 −0.174694
\(281\) −11.4113 −0.680739 −0.340369 0.940292i \(-0.610552\pi\)
−0.340369 + 0.940292i \(0.610552\pi\)
\(282\) −6.88828 −0.410191
\(283\) −2.68041 −0.159334 −0.0796668 0.996822i \(-0.525386\pi\)
−0.0796668 + 0.996822i \(0.525386\pi\)
\(284\) 3.13750 0.186176
\(285\) −5.00990 −0.296761
\(286\) −4.56876 −0.270156
\(287\) 14.0146 0.827253
\(288\) −2.45015 −0.144376
\(289\) −11.9806 −0.704741
\(290\) −7.43472 −0.436582
\(291\) −4.78872 −0.280720
\(292\) 7.55686 0.442232
\(293\) 20.4478 1.19457 0.597285 0.802029i \(-0.296246\pi\)
0.597285 + 0.802029i \(0.296246\pi\)
\(294\) 1.14570 0.0668187
\(295\) −2.50293 −0.145726
\(296\) −2.16013 −0.125555
\(297\) −15.3009 −0.887850
\(298\) −6.38704 −0.369991
\(299\) 2.60911 0.150888
\(300\) 0.741521 0.0428117
\(301\) −7.67691 −0.442490
\(302\) −3.63992 −0.209454
\(303\) 2.74030 0.157426
\(304\) −6.75626 −0.387498
\(305\) −2.21161 −0.126636
\(306\) −5.48932 −0.313803
\(307\) −21.7246 −1.23989 −0.619943 0.784647i \(-0.712844\pi\)
−0.619943 + 0.784647i \(0.712844\pi\)
\(308\) −11.0674 −0.630621
\(309\) 4.59429 0.261360
\(310\) 2.54924 0.144787
\(311\) −21.9236 −1.24317 −0.621586 0.783346i \(-0.713511\pi\)
−0.621586 + 0.783346i \(0.713511\pi\)
\(312\) −0.894820 −0.0506592
\(313\) −13.4995 −0.763039 −0.381520 0.924361i \(-0.624599\pi\)
−0.381520 + 0.924361i \(0.624599\pi\)
\(314\) −3.48148 −0.196471
\(315\) 7.16226 0.403547
\(316\) −7.16658 −0.403152
\(317\) 22.9412 1.28851 0.644254 0.764811i \(-0.277168\pi\)
0.644254 + 0.764811i \(0.277168\pi\)
\(318\) −3.14551 −0.176391
\(319\) −28.1482 −1.57600
\(320\) 1.00000 0.0559017
\(321\) −3.16492 −0.176649
\(322\) 6.32029 0.352216
\(323\) −15.1367 −0.842231
\(324\) 4.35366 0.241870
\(325\) −1.20674 −0.0669377
\(326\) −7.48872 −0.414762
\(327\) −5.02821 −0.278061
\(328\) −4.79426 −0.264719
\(329\) 27.1547 1.49709
\(330\) 2.80743 0.154544
\(331\) −20.8164 −1.14417 −0.572086 0.820194i \(-0.693866\pi\)
−0.572086 + 0.820194i \(0.693866\pi\)
\(332\) 14.7455 0.809262
\(333\) 5.29264 0.290035
\(334\) 0.756944 0.0414181
\(335\) −6.47843 −0.353955
\(336\) −2.16761 −0.118253
\(337\) 13.2746 0.723114 0.361557 0.932350i \(-0.382245\pi\)
0.361557 + 0.932350i \(0.382245\pi\)
\(338\) −11.5438 −0.627899
\(339\) −9.52015 −0.517063
\(340\) 2.24040 0.121503
\(341\) 9.65153 0.522660
\(342\) 16.5538 0.895128
\(343\) 15.9458 0.860994
\(344\) 2.62620 0.141595
\(345\) −1.60326 −0.0863164
\(346\) −18.3173 −0.984747
\(347\) 2.90152 0.155762 0.0778809 0.996963i \(-0.475185\pi\)
0.0778809 + 0.996963i \(0.475185\pi\)
\(348\) −5.51300 −0.295528
\(349\) −2.22064 −0.118868 −0.0594341 0.998232i \(-0.518930\pi\)
−0.0594341 + 0.998232i \(0.518930\pi\)
\(350\) −2.92320 −0.156251
\(351\) 4.87690 0.260310
\(352\) 3.78605 0.201797
\(353\) 18.6751 0.993974 0.496987 0.867758i \(-0.334440\pi\)
0.496987 + 0.867758i \(0.334440\pi\)
\(354\) −1.85598 −0.0986441
\(355\) 3.13750 0.166521
\(356\) 10.3519 0.548652
\(357\) −4.85632 −0.257024
\(358\) 2.24990 0.118911
\(359\) 10.0962 0.532856 0.266428 0.963855i \(-0.414157\pi\)
0.266428 + 0.963855i \(0.414157\pi\)
\(360\) −2.45015 −0.129134
\(361\) 26.6470 1.40247
\(362\) −9.62422 −0.505838
\(363\) 2.47234 0.129764
\(364\) 3.52753 0.184893
\(365\) 7.55686 0.395544
\(366\) −1.63995 −0.0857217
\(367\) 13.3188 0.695236 0.347618 0.937636i \(-0.386991\pi\)
0.347618 + 0.937636i \(0.386991\pi\)
\(368\) −2.16212 −0.112708
\(369\) 11.7466 0.611505
\(370\) −2.16013 −0.112300
\(371\) 12.4001 0.643782
\(372\) 1.89031 0.0980081
\(373\) −7.01034 −0.362981 −0.181491 0.983393i \(-0.558092\pi\)
−0.181491 + 0.983393i \(0.558092\pi\)
\(374\) 8.48227 0.438608
\(375\) 0.741521 0.0382920
\(376\) −9.28939 −0.479064
\(377\) 8.97175 0.462069
\(378\) 11.8138 0.607636
\(379\) −11.3530 −0.583166 −0.291583 0.956546i \(-0.594182\pi\)
−0.291583 + 0.956546i \(0.594182\pi\)
\(380\) −6.75626 −0.346589
\(381\) −16.0046 −0.819939
\(382\) 1.03740 0.0530781
\(383\) −1.90171 −0.0971729 −0.0485865 0.998819i \(-0.515472\pi\)
−0.0485865 + 0.998819i \(0.515472\pi\)
\(384\) 0.741521 0.0378406
\(385\) −11.0674 −0.564045
\(386\) −12.0456 −0.613107
\(387\) −6.43459 −0.327088
\(388\) −6.45797 −0.327854
\(389\) 16.4178 0.832418 0.416209 0.909269i \(-0.363358\pi\)
0.416209 + 0.909269i \(0.363358\pi\)
\(390\) −0.894820 −0.0453110
\(391\) −4.84402 −0.244972
\(392\) 1.54507 0.0780378
\(393\) −1.38381 −0.0698038
\(394\) 15.0764 0.759536
\(395\) −7.16658 −0.360590
\(396\) −9.27637 −0.466155
\(397\) 0.399823 0.0200666 0.0100333 0.999950i \(-0.496806\pi\)
0.0100333 + 0.999950i \(0.496806\pi\)
\(398\) 0.396256 0.0198625
\(399\) 14.6449 0.733163
\(400\) 1.00000 0.0500000
\(401\) 12.1723 0.607856 0.303928 0.952695i \(-0.401702\pi\)
0.303928 + 0.952695i \(0.401702\pi\)
\(402\) −4.80390 −0.239597
\(403\) −3.07626 −0.153239
\(404\) 3.69551 0.183858
\(405\) 4.35366 0.216335
\(406\) 21.7331 1.07860
\(407\) −8.17836 −0.405386
\(408\) 1.66131 0.0822469
\(409\) −33.4856 −1.65575 −0.827877 0.560909i \(-0.810452\pi\)
−0.827877 + 0.560909i \(0.810452\pi\)
\(410\) −4.79426 −0.236772
\(411\) 12.2689 0.605180
\(412\) 6.19576 0.305243
\(413\) 7.31656 0.360025
\(414\) 5.29751 0.260358
\(415\) 14.7455 0.723826
\(416\) −1.20674 −0.0591651
\(417\) 13.1330 0.643127
\(418\) −25.5795 −1.25113
\(419\) 9.60020 0.469001 0.234500 0.972116i \(-0.424655\pi\)
0.234500 + 0.972116i \(0.424655\pi\)
\(420\) −2.16761 −0.105769
\(421\) −5.78529 −0.281958 −0.140979 0.990013i \(-0.545025\pi\)
−0.140979 + 0.990013i \(0.545025\pi\)
\(422\) 18.2045 0.886180
\(423\) 22.7604 1.10665
\(424\) −4.24197 −0.206008
\(425\) 2.24040 0.108676
\(426\) 2.32652 0.112720
\(427\) 6.46496 0.312861
\(428\) −4.26814 −0.206309
\(429\) −3.38783 −0.163566
\(430\) 2.62620 0.126647
\(431\) 19.4632 0.937509 0.468754 0.883329i \(-0.344703\pi\)
0.468754 + 0.883329i \(0.344703\pi\)
\(432\) −4.04140 −0.194442
\(433\) −2.27704 −0.109428 −0.0547138 0.998502i \(-0.517425\pi\)
−0.0547138 + 0.998502i \(0.517425\pi\)
\(434\) −7.45192 −0.357703
\(435\) −5.51300 −0.264328
\(436\) −6.78094 −0.324748
\(437\) 14.6078 0.698787
\(438\) 5.60357 0.267749
\(439\) 4.72610 0.225565 0.112782 0.993620i \(-0.464024\pi\)
0.112782 + 0.993620i \(0.464024\pi\)
\(440\) 3.78605 0.180493
\(441\) −3.78565 −0.180269
\(442\) −2.70358 −0.128596
\(443\) 26.4606 1.25718 0.628590 0.777736i \(-0.283632\pi\)
0.628590 + 0.777736i \(0.283632\pi\)
\(444\) −1.60178 −0.0760173
\(445\) 10.3519 0.490729
\(446\) −9.99886 −0.473460
\(447\) −4.73612 −0.224011
\(448\) −2.92320 −0.138108
\(449\) 6.77324 0.319649 0.159825 0.987145i \(-0.448907\pi\)
0.159825 + 0.987145i \(0.448907\pi\)
\(450\) −2.45015 −0.115501
\(451\) −18.1513 −0.854711
\(452\) −12.8387 −0.603881
\(453\) −2.69908 −0.126814
\(454\) −8.02690 −0.376721
\(455\) 3.52753 0.165373
\(456\) −5.00990 −0.234610
\(457\) 26.8513 1.25605 0.628026 0.778193i \(-0.283863\pi\)
0.628026 + 0.778193i \(0.283863\pi\)
\(458\) −25.6126 −1.19680
\(459\) −9.05436 −0.422621
\(460\) −2.16212 −0.100809
\(461\) −5.33116 −0.248297 −0.124148 0.992264i \(-0.539620\pi\)
−0.124148 + 0.992264i \(0.539620\pi\)
\(462\) −8.20667 −0.381809
\(463\) 23.2851 1.08215 0.541076 0.840974i \(-0.318017\pi\)
0.541076 + 0.840974i \(0.318017\pi\)
\(464\) −7.43472 −0.345148
\(465\) 1.89031 0.0876611
\(466\) 8.36069 0.387302
\(467\) −3.15723 −0.146099 −0.0730495 0.997328i \(-0.523273\pi\)
−0.0730495 + 0.997328i \(0.523273\pi\)
\(468\) 2.95668 0.136673
\(469\) 18.9377 0.874463
\(470\) −9.28939 −0.428488
\(471\) −2.58159 −0.118953
\(472\) −2.50293 −0.115207
\(473\) 9.94293 0.457177
\(474\) −5.31417 −0.244088
\(475\) −6.75626 −0.309998
\(476\) −6.54914 −0.300179
\(477\) 10.3935 0.475883
\(478\) −5.94177 −0.271770
\(479\) 17.2512 0.788226 0.394113 0.919062i \(-0.371052\pi\)
0.394113 + 0.919062i \(0.371052\pi\)
\(480\) 0.741521 0.0338456
\(481\) 2.60671 0.118856
\(482\) −28.2635 −1.28737
\(483\) 4.68663 0.213249
\(484\) 3.33415 0.151552
\(485\) −6.45797 −0.293242
\(486\) 15.3525 0.696405
\(487\) 14.1137 0.639555 0.319777 0.947493i \(-0.396392\pi\)
0.319777 + 0.947493i \(0.396392\pi\)
\(488\) −2.21161 −0.100115
\(489\) −5.55305 −0.251117
\(490\) 1.54507 0.0697991
\(491\) 5.58698 0.252137 0.126068 0.992022i \(-0.459764\pi\)
0.126068 + 0.992022i \(0.459764\pi\)
\(492\) −3.55504 −0.160274
\(493\) −16.6568 −0.750184
\(494\) 8.15302 0.366822
\(495\) −9.27637 −0.416942
\(496\) 2.54924 0.114464
\(497\) −9.17151 −0.411399
\(498\) 10.9341 0.489967
\(499\) 31.5338 1.41165 0.705824 0.708387i \(-0.250577\pi\)
0.705824 + 0.708387i \(0.250577\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0.561290 0.0250766
\(502\) 1.54250 0.0688453
\(503\) −33.9558 −1.51402 −0.757008 0.653406i \(-0.773339\pi\)
−0.757008 + 0.653406i \(0.773339\pi\)
\(504\) 7.16226 0.319032
\(505\) 3.69551 0.164448
\(506\) −8.18588 −0.363907
\(507\) −8.55996 −0.380161
\(508\) −21.5834 −0.957610
\(509\) −25.9636 −1.15081 −0.575407 0.817867i \(-0.695156\pi\)
−0.575407 + 0.817867i \(0.695156\pi\)
\(510\) 1.66131 0.0735639
\(511\) −22.0902 −0.977212
\(512\) 1.00000 0.0441942
\(513\) 27.3047 1.20553
\(514\) 12.2344 0.539635
\(515\) 6.19576 0.273018
\(516\) 1.94739 0.0857289
\(517\) −35.1701 −1.54678
\(518\) 6.31449 0.277443
\(519\) −13.5827 −0.596214
\(520\) −1.20674 −0.0529189
\(521\) 19.3369 0.847165 0.423582 0.905858i \(-0.360772\pi\)
0.423582 + 0.905858i \(0.360772\pi\)
\(522\) 18.2162 0.797300
\(523\) 21.9848 0.961328 0.480664 0.876905i \(-0.340396\pi\)
0.480664 + 0.876905i \(0.340396\pi\)
\(524\) −1.86617 −0.0815242
\(525\) −2.16761 −0.0946023
\(526\) 6.05174 0.263869
\(527\) 5.71132 0.248789
\(528\) 2.80743 0.122178
\(529\) −18.3252 −0.796750
\(530\) −4.24197 −0.184259
\(531\) 6.13256 0.266130
\(532\) 19.7499 0.856265
\(533\) 5.78541 0.250594
\(534\) 7.67618 0.332181
\(535\) −4.26814 −0.184528
\(536\) −6.47843 −0.279826
\(537\) 1.66835 0.0719947
\(538\) 15.8007 0.681218
\(539\) 5.84970 0.251965
\(540\) −4.04140 −0.173914
\(541\) −1.17590 −0.0505558 −0.0252779 0.999680i \(-0.508047\pi\)
−0.0252779 + 0.999680i \(0.508047\pi\)
\(542\) 5.49046 0.235835
\(543\) −7.13656 −0.306259
\(544\) 2.24040 0.0960565
\(545\) −6.78094 −0.290464
\(546\) 2.61573 0.111943
\(547\) −1.59787 −0.0683201 −0.0341601 0.999416i \(-0.510876\pi\)
−0.0341601 + 0.999416i \(0.510876\pi\)
\(548\) 16.5456 0.706792
\(549\) 5.41876 0.231267
\(550\) 3.78605 0.161438
\(551\) 50.2309 2.13991
\(552\) −1.60326 −0.0682391
\(553\) 20.9493 0.890855
\(554\) 12.6922 0.539241
\(555\) −1.60178 −0.0679919
\(556\) 17.7109 0.751111
\(557\) 6.99965 0.296585 0.148292 0.988944i \(-0.452622\pi\)
0.148292 + 0.988944i \(0.452622\pi\)
\(558\) −6.24600 −0.264414
\(559\) −3.16914 −0.134040
\(560\) −2.92320 −0.123528
\(561\) 6.28978 0.265555
\(562\) −11.4113 −0.481355
\(563\) −0.539470 −0.0227359 −0.0113680 0.999935i \(-0.503619\pi\)
−0.0113680 + 0.999935i \(0.503619\pi\)
\(564\) −6.88828 −0.290049
\(565\) −12.8387 −0.540127
\(566\) −2.68041 −0.112666
\(567\) −12.7266 −0.534467
\(568\) 3.13750 0.131646
\(569\) −21.5821 −0.904770 −0.452385 0.891823i \(-0.649427\pi\)
−0.452385 + 0.891823i \(0.649427\pi\)
\(570\) −5.00990 −0.209842
\(571\) 28.9663 1.21220 0.606102 0.795387i \(-0.292732\pi\)
0.606102 + 0.795387i \(0.292732\pi\)
\(572\) −4.56876 −0.191029
\(573\) 0.769255 0.0321361
\(574\) 14.0146 0.584956
\(575\) −2.16212 −0.0901665
\(576\) −2.45015 −0.102089
\(577\) 28.1175 1.17055 0.585273 0.810837i \(-0.300987\pi\)
0.585273 + 0.810837i \(0.300987\pi\)
\(578\) −11.9806 −0.498327
\(579\) −8.93209 −0.371205
\(580\) −7.43472 −0.308710
\(581\) −43.1039 −1.78825
\(582\) −4.78872 −0.198499
\(583\) −16.0603 −0.665150
\(584\) 7.55686 0.312705
\(585\) 2.95668 0.122244
\(586\) 20.4478 0.844689
\(587\) 5.04201 0.208106 0.104053 0.994572i \(-0.466819\pi\)
0.104053 + 0.994572i \(0.466819\pi\)
\(588\) 1.14570 0.0472479
\(589\) −17.2233 −0.709673
\(590\) −2.50293 −0.103044
\(591\) 11.1794 0.459861
\(592\) −2.16013 −0.0887809
\(593\) 15.1369 0.621597 0.310799 0.950476i \(-0.399403\pi\)
0.310799 + 0.950476i \(0.399403\pi\)
\(594\) −15.3009 −0.627804
\(595\) −6.54914 −0.268488
\(596\) −6.38704 −0.261623
\(597\) 0.293832 0.0120258
\(598\) 2.60911 0.106694
\(599\) 20.9884 0.857563 0.428782 0.903408i \(-0.358943\pi\)
0.428782 + 0.903408i \(0.358943\pi\)
\(600\) 0.741521 0.0302725
\(601\) −1.00000 −0.0407909
\(602\) −7.67691 −0.312887
\(603\) 15.8731 0.646403
\(604\) −3.63992 −0.148106
\(605\) 3.33415 0.135552
\(606\) 2.74030 0.111317
\(607\) 26.7289 1.08489 0.542446 0.840091i \(-0.317498\pi\)
0.542446 + 0.840091i \(0.317498\pi\)
\(608\) −6.75626 −0.274002
\(609\) 16.1156 0.653036
\(610\) −2.21161 −0.0895453
\(611\) 11.2098 0.453502
\(612\) −5.48932 −0.221893
\(613\) 5.68225 0.229504 0.114752 0.993394i \(-0.463393\pi\)
0.114752 + 0.993394i \(0.463393\pi\)
\(614\) −21.7246 −0.876732
\(615\) −3.55504 −0.143353
\(616\) −11.0674 −0.445916
\(617\) 37.6119 1.51420 0.757099 0.653300i \(-0.226616\pi\)
0.757099 + 0.653300i \(0.226616\pi\)
\(618\) 4.59429 0.184809
\(619\) 20.0050 0.804069 0.402035 0.915624i \(-0.368303\pi\)
0.402035 + 0.915624i \(0.368303\pi\)
\(620\) 2.54924 0.102380
\(621\) 8.73798 0.350643
\(622\) −21.9236 −0.879055
\(623\) −30.2607 −1.21237
\(624\) −0.894820 −0.0358215
\(625\) 1.00000 0.0400000
\(626\) −13.4995 −0.539550
\(627\) −18.9677 −0.757498
\(628\) −3.48148 −0.138926
\(629\) −4.83957 −0.192966
\(630\) 7.16226 0.285351
\(631\) 0.0444024 0.00176763 0.000883817 1.00000i \(-0.499719\pi\)
0.000883817 1.00000i \(0.499719\pi\)
\(632\) −7.16658 −0.285071
\(633\) 13.4990 0.536537
\(634\) 22.9412 0.911113
\(635\) −21.5834 −0.856512
\(636\) −3.14551 −0.124728
\(637\) −1.86449 −0.0738738
\(638\) −28.1482 −1.11440
\(639\) −7.68733 −0.304106
\(640\) 1.00000 0.0395285
\(641\) −23.1116 −0.912852 −0.456426 0.889761i \(-0.650871\pi\)
−0.456426 + 0.889761i \(0.650871\pi\)
\(642\) −3.16492 −0.124909
\(643\) −6.57273 −0.259203 −0.129602 0.991566i \(-0.541370\pi\)
−0.129602 + 0.991566i \(0.541370\pi\)
\(644\) 6.32029 0.249054
\(645\) 1.94739 0.0766782
\(646\) −15.1367 −0.595547
\(647\) −16.7970 −0.660359 −0.330180 0.943918i \(-0.607109\pi\)
−0.330180 + 0.943918i \(0.607109\pi\)
\(648\) 4.35366 0.171028
\(649\) −9.47622 −0.371974
\(650\) −1.20674 −0.0473321
\(651\) −5.52575 −0.216571
\(652\) −7.48872 −0.293281
\(653\) −20.2827 −0.793722 −0.396861 0.917879i \(-0.629901\pi\)
−0.396861 + 0.917879i \(0.629901\pi\)
\(654\) −5.02821 −0.196619
\(655\) −1.86617 −0.0729174
\(656\) −4.79426 −0.187184
\(657\) −18.5154 −0.722355
\(658\) 27.1547 1.05860
\(659\) 8.34781 0.325185 0.162592 0.986693i \(-0.448014\pi\)
0.162592 + 0.986693i \(0.448014\pi\)
\(660\) 2.80743 0.109279
\(661\) −17.1480 −0.666981 −0.333490 0.942754i \(-0.608226\pi\)
−0.333490 + 0.942754i \(0.608226\pi\)
\(662\) −20.8164 −0.809052
\(663\) −2.00476 −0.0778584
\(664\) 14.7455 0.572235
\(665\) 19.7499 0.765866
\(666\) 5.29264 0.205086
\(667\) 16.0747 0.622417
\(668\) 0.756944 0.0292870
\(669\) −7.41436 −0.286656
\(670\) −6.47843 −0.250284
\(671\) −8.37325 −0.323246
\(672\) −2.16761 −0.0836174
\(673\) −0.527550 −0.0203356 −0.0101678 0.999948i \(-0.503237\pi\)
−0.0101678 + 0.999948i \(0.503237\pi\)
\(674\) 13.2746 0.511319
\(675\) −4.04140 −0.155553
\(676\) −11.5438 −0.443992
\(677\) −21.8328 −0.839105 −0.419552 0.907731i \(-0.637813\pi\)
−0.419552 + 0.907731i \(0.637813\pi\)
\(678\) −9.52015 −0.365619
\(679\) 18.8779 0.724468
\(680\) 2.24040 0.0859156
\(681\) −5.95211 −0.228085
\(682\) 9.65153 0.369576
\(683\) −25.5697 −0.978398 −0.489199 0.872172i \(-0.662711\pi\)
−0.489199 + 0.872172i \(0.662711\pi\)
\(684\) 16.5538 0.632951
\(685\) 16.5456 0.632174
\(686\) 15.9458 0.608814
\(687\) −18.9923 −0.724601
\(688\) 2.62620 0.100123
\(689\) 5.11894 0.195016
\(690\) −1.60326 −0.0610349
\(691\) 39.4532 1.50087 0.750436 0.660943i \(-0.229844\pi\)
0.750436 + 0.660943i \(0.229844\pi\)
\(692\) −18.3173 −0.696321
\(693\) 27.1166 1.03008
\(694\) 2.90152 0.110140
\(695\) 17.7109 0.671814
\(696\) −5.51300 −0.208970
\(697\) −10.7411 −0.406847
\(698\) −2.22064 −0.0840526
\(699\) 6.19963 0.234491
\(700\) −2.92320 −0.110486
\(701\) 15.2977 0.577785 0.288893 0.957361i \(-0.406713\pi\)
0.288893 + 0.957361i \(0.406713\pi\)
\(702\) 4.87690 0.184067
\(703\) 14.5944 0.550438
\(704\) 3.78605 0.142692
\(705\) −6.88828 −0.259428
\(706\) 18.6751 0.702846
\(707\) −10.8027 −0.406277
\(708\) −1.85598 −0.0697519
\(709\) −8.37724 −0.314614 −0.157307 0.987550i \(-0.550281\pi\)
−0.157307 + 0.987550i \(0.550281\pi\)
\(710\) 3.13750 0.117748
\(711\) 17.5592 0.658520
\(712\) 10.3519 0.387955
\(713\) −5.51175 −0.206417
\(714\) −4.85632 −0.181743
\(715\) −4.56876 −0.170862
\(716\) 2.24990 0.0840829
\(717\) −4.40595 −0.164543
\(718\) 10.0962 0.376786
\(719\) 20.9443 0.781090 0.390545 0.920584i \(-0.372287\pi\)
0.390545 + 0.920584i \(0.372287\pi\)
\(720\) −2.45015 −0.0913116
\(721\) −18.1114 −0.674505
\(722\) 26.6470 0.991698
\(723\) −20.9580 −0.779437
\(724\) −9.62422 −0.357681
\(725\) −7.43472 −0.276119
\(726\) 2.47234 0.0917572
\(727\) −23.8660 −0.885140 −0.442570 0.896734i \(-0.645933\pi\)
−0.442570 + 0.896734i \(0.645933\pi\)
\(728\) 3.52753 0.130739
\(729\) −1.67676 −0.0621021
\(730\) 7.55686 0.279692
\(731\) 5.88376 0.217619
\(732\) −1.63995 −0.0606144
\(733\) 14.3164 0.528787 0.264394 0.964415i \(-0.414828\pi\)
0.264394 + 0.964415i \(0.414828\pi\)
\(734\) 13.3188 0.491606
\(735\) 1.14570 0.0422598
\(736\) −2.16212 −0.0796967
\(737\) −24.5277 −0.903488
\(738\) 11.7466 0.432400
\(739\) −41.9894 −1.54461 −0.772303 0.635255i \(-0.780895\pi\)
−0.772303 + 0.635255i \(0.780895\pi\)
\(740\) −2.16013 −0.0794080
\(741\) 6.04563 0.222092
\(742\) 12.4001 0.455222
\(743\) 2.19212 0.0804212 0.0402106 0.999191i \(-0.487197\pi\)
0.0402106 + 0.999191i \(0.487197\pi\)
\(744\) 1.89031 0.0693022
\(745\) −6.38704 −0.234003
\(746\) −7.01034 −0.256667
\(747\) −36.1285 −1.32187
\(748\) 8.48227 0.310143
\(749\) 12.4766 0.455886
\(750\) 0.741521 0.0270765
\(751\) −6.65765 −0.242941 −0.121470 0.992595i \(-0.538761\pi\)
−0.121470 + 0.992595i \(0.538761\pi\)
\(752\) −9.28939 −0.338749
\(753\) 1.14380 0.0416823
\(754\) 8.97175 0.326732
\(755\) −3.63992 −0.132470
\(756\) 11.8138 0.429664
\(757\) −8.18191 −0.297377 −0.148688 0.988884i \(-0.547505\pi\)
−0.148688 + 0.988884i \(0.547505\pi\)
\(758\) −11.3530 −0.412361
\(759\) −6.07000 −0.220327
\(760\) −6.75626 −0.245075
\(761\) −46.9481 −1.70187 −0.850934 0.525272i \(-0.823964\pi\)
−0.850934 + 0.525272i \(0.823964\pi\)
\(762\) −16.0046 −0.579784
\(763\) 19.8220 0.717605
\(764\) 1.03740 0.0375319
\(765\) −5.48932 −0.198467
\(766\) −1.90171 −0.0687116
\(767\) 3.02038 0.109060
\(768\) 0.741521 0.0267573
\(769\) −41.5242 −1.49740 −0.748700 0.662909i \(-0.769322\pi\)
−0.748700 + 0.662909i \(0.769322\pi\)
\(770\) −11.0674 −0.398840
\(771\) 9.07204 0.326722
\(772\) −12.0456 −0.433532
\(773\) −11.1666 −0.401635 −0.200818 0.979629i \(-0.564360\pi\)
−0.200818 + 0.979629i \(0.564360\pi\)
\(774\) −6.43459 −0.231286
\(775\) 2.54924 0.0915713
\(776\) −6.45797 −0.231828
\(777\) 4.68232 0.167977
\(778\) 16.4178 0.588608
\(779\) 32.3912 1.16054
\(780\) −0.894820 −0.0320397
\(781\) 11.8787 0.425054
\(782\) −4.84402 −0.173222
\(783\) 30.0467 1.07378
\(784\) 1.54507 0.0551810
\(785\) −3.48148 −0.124259
\(786\) −1.38381 −0.0493588
\(787\) 18.9384 0.675081 0.337540 0.941311i \(-0.390405\pi\)
0.337540 + 0.941311i \(0.390405\pi\)
\(788\) 15.0764 0.537073
\(789\) 4.48750 0.159759
\(790\) −7.16658 −0.254975
\(791\) 37.5300 1.33441
\(792\) −9.27637 −0.329621
\(793\) 2.66883 0.0947728
\(794\) 0.399823 0.0141892
\(795\) −3.14551 −0.111560
\(796\) 0.396256 0.0140449
\(797\) −45.5372 −1.61301 −0.806506 0.591226i \(-0.798644\pi\)
−0.806506 + 0.591226i \(0.798644\pi\)
\(798\) 14.6449 0.518425
\(799\) −20.8120 −0.736275
\(800\) 1.00000 0.0353553
\(801\) −25.3638 −0.896185
\(802\) 12.1723 0.429819
\(803\) 28.6106 1.00965
\(804\) −4.80390 −0.169420
\(805\) 6.32029 0.222761
\(806\) −3.07626 −0.108357
\(807\) 11.7166 0.412443
\(808\) 3.69551 0.130008
\(809\) 13.0849 0.460041 0.230021 0.973186i \(-0.426121\pi\)
0.230021 + 0.973186i \(0.426121\pi\)
\(810\) 4.35366 0.152972
\(811\) −52.3893 −1.83964 −0.919819 0.392343i \(-0.871665\pi\)
−0.919819 + 0.392343i \(0.871665\pi\)
\(812\) 21.7331 0.762684
\(813\) 4.07129 0.142786
\(814\) −8.17836 −0.286651
\(815\) −7.48872 −0.262319
\(816\) 1.66131 0.0581574
\(817\) −17.7433 −0.620760
\(818\) −33.4856 −1.17080
\(819\) −8.64295 −0.302009
\(820\) −4.79426 −0.167423
\(821\) −53.0479 −1.85138 −0.925691 0.378280i \(-0.876516\pi\)
−0.925691 + 0.378280i \(0.876516\pi\)
\(822\) 12.2689 0.427927
\(823\) 50.1815 1.74922 0.874608 0.484830i \(-0.161119\pi\)
0.874608 + 0.484830i \(0.161119\pi\)
\(824\) 6.19576 0.215840
\(825\) 2.80743 0.0977423
\(826\) 7.31656 0.254576
\(827\) −37.8153 −1.31497 −0.657483 0.753470i \(-0.728379\pi\)
−0.657483 + 0.753470i \(0.728379\pi\)
\(828\) 5.29751 0.184101
\(829\) 39.7175 1.37945 0.689723 0.724074i \(-0.257732\pi\)
0.689723 + 0.724074i \(0.257732\pi\)
\(830\) 14.7455 0.511823
\(831\) 9.41154 0.326483
\(832\) −1.20674 −0.0418361
\(833\) 3.46158 0.119937
\(834\) 13.1330 0.454760
\(835\) 0.756944 0.0261951
\(836\) −25.5795 −0.884685
\(837\) −10.3025 −0.356106
\(838\) 9.60020 0.331634
\(839\) −32.3825 −1.11797 −0.558985 0.829178i \(-0.688809\pi\)
−0.558985 + 0.829178i \(0.688809\pi\)
\(840\) −2.16761 −0.0747897
\(841\) 26.2751 0.906038
\(842\) −5.78529 −0.199374
\(843\) −8.46169 −0.291436
\(844\) 18.2045 0.626624
\(845\) −11.5438 −0.397118
\(846\) 22.7604 0.782518
\(847\) −9.74637 −0.334889
\(848\) −4.24197 −0.145670
\(849\) −1.98758 −0.0682135
\(850\) 2.24040 0.0768452
\(851\) 4.67046 0.160101
\(852\) 2.32652 0.0797052
\(853\) 4.06971 0.139344 0.0696720 0.997570i \(-0.477805\pi\)
0.0696720 + 0.997570i \(0.477805\pi\)
\(854\) 6.46496 0.221226
\(855\) 16.5538 0.566129
\(856\) −4.26814 −0.145882
\(857\) 44.2655 1.51208 0.756039 0.654526i \(-0.227132\pi\)
0.756039 + 0.654526i \(0.227132\pi\)
\(858\) −3.38783 −0.115659
\(859\) −36.6492 −1.25046 −0.625228 0.780442i \(-0.714994\pi\)
−0.625228 + 0.780442i \(0.714994\pi\)
\(860\) 2.62620 0.0895528
\(861\) 10.3921 0.354161
\(862\) 19.4632 0.662919
\(863\) −36.5565 −1.24440 −0.622198 0.782860i \(-0.713760\pi\)
−0.622198 + 0.782860i \(0.713760\pi\)
\(864\) −4.04140 −0.137491
\(865\) −18.3173 −0.622809
\(866\) −2.27704 −0.0773770
\(867\) −8.88386 −0.301712
\(868\) −7.45192 −0.252935
\(869\) −27.1330 −0.920424
\(870\) −5.51300 −0.186908
\(871\) 7.81776 0.264895
\(872\) −6.78094 −0.229632
\(873\) 15.8230 0.535527
\(874\) 14.6078 0.494117
\(875\) −2.92320 −0.0988220
\(876\) 5.60357 0.189327
\(877\) −36.0907 −1.21870 −0.609349 0.792902i \(-0.708569\pi\)
−0.609349 + 0.792902i \(0.708569\pi\)
\(878\) 4.72610 0.159498
\(879\) 15.1624 0.511416
\(880\) 3.78605 0.127628
\(881\) 32.4769 1.09417 0.547087 0.837076i \(-0.315737\pi\)
0.547087 + 0.837076i \(0.315737\pi\)
\(882\) −3.78565 −0.127469
\(883\) 28.1173 0.946223 0.473111 0.881003i \(-0.343131\pi\)
0.473111 + 0.881003i \(0.343131\pi\)
\(884\) −2.70358 −0.0909311
\(885\) −1.85598 −0.0623880
\(886\) 26.4606 0.888961
\(887\) −31.1536 −1.04604 −0.523018 0.852321i \(-0.675194\pi\)
−0.523018 + 0.852321i \(0.675194\pi\)
\(888\) −1.60178 −0.0537523
\(889\) 63.0926 2.11606
\(890\) 10.3519 0.346998
\(891\) 16.4832 0.552206
\(892\) −9.99886 −0.334787
\(893\) 62.7615 2.10023
\(894\) −4.73612 −0.158400
\(895\) 2.24990 0.0752060
\(896\) −2.92320 −0.0976571
\(897\) 1.93471 0.0645980
\(898\) 6.77324 0.226026
\(899\) −18.9529 −0.632113
\(900\) −2.45015 −0.0816716
\(901\) −9.50373 −0.316615
\(902\) −18.1513 −0.604372
\(903\) −5.69259 −0.189437
\(904\) −12.8387 −0.427008
\(905\) −9.62422 −0.319920
\(906\) −2.69908 −0.0896708
\(907\) 1.65719 0.0550262 0.0275131 0.999621i \(-0.491241\pi\)
0.0275131 + 0.999621i \(0.491241\pi\)
\(908\) −8.02690 −0.266382
\(909\) −9.05454 −0.300320
\(910\) 3.52753 0.116936
\(911\) −32.9676 −1.09227 −0.546133 0.837698i \(-0.683901\pi\)
−0.546133 + 0.837698i \(0.683901\pi\)
\(912\) −5.00990 −0.165895
\(913\) 55.8270 1.84760
\(914\) 26.8513 0.888163
\(915\) −1.63995 −0.0542152
\(916\) −25.6126 −0.846264
\(917\) 5.45519 0.180146
\(918\) −9.05436 −0.298839
\(919\) 31.2474 1.03076 0.515379 0.856963i \(-0.327651\pi\)
0.515379 + 0.856963i \(0.327651\pi\)
\(920\) −2.16212 −0.0712829
\(921\) −16.1092 −0.530817
\(922\) −5.33116 −0.175572
\(923\) −3.78613 −0.124622
\(924\) −8.20667 −0.269980
\(925\) −2.16013 −0.0710247
\(926\) 23.2851 0.765197
\(927\) −15.1805 −0.498594
\(928\) −7.43472 −0.244057
\(929\) −25.9809 −0.852404 −0.426202 0.904628i \(-0.640149\pi\)
−0.426202 + 0.904628i \(0.640149\pi\)
\(930\) 1.89031 0.0619858
\(931\) −10.4389 −0.342121
\(932\) 8.36069 0.273864
\(933\) −16.2568 −0.532224
\(934\) −3.15723 −0.103308
\(935\) 8.48227 0.277400
\(936\) 2.95668 0.0966421
\(937\) −54.3313 −1.77492 −0.887462 0.460880i \(-0.847534\pi\)
−0.887462 + 0.460880i \(0.847534\pi\)
\(938\) 18.9377 0.618339
\(939\) −10.0102 −0.326670
\(940\) −9.28939 −0.302987
\(941\) −0.654760 −0.0213446 −0.0106723 0.999943i \(-0.503397\pi\)
−0.0106723 + 0.999943i \(0.503397\pi\)
\(942\) −2.58159 −0.0841128
\(943\) 10.3658 0.337555
\(944\) −2.50293 −0.0814636
\(945\) 11.8138 0.384303
\(946\) 9.94293 0.323273
\(947\) 19.0893 0.620318 0.310159 0.950685i \(-0.399618\pi\)
0.310159 + 0.950685i \(0.399618\pi\)
\(948\) −5.31417 −0.172596
\(949\) −9.11914 −0.296020
\(950\) −6.75626 −0.219202
\(951\) 17.0114 0.551633
\(952\) −6.54914 −0.212259
\(953\) −53.7847 −1.74226 −0.871129 0.491054i \(-0.836612\pi\)
−0.871129 + 0.491054i \(0.836612\pi\)
\(954\) 10.3935 0.336500
\(955\) 1.03740 0.0335695
\(956\) −5.94177 −0.192171
\(957\) −20.8725 −0.674712
\(958\) 17.2512 0.557360
\(959\) −48.3660 −1.56182
\(960\) 0.741521 0.0239325
\(961\) −24.5014 −0.790368
\(962\) 2.60671 0.0840437
\(963\) 10.4576 0.336991
\(964\) −28.2635 −0.910307
\(965\) −12.0456 −0.387763
\(966\) 4.68663 0.150790
\(967\) −26.8623 −0.863835 −0.431917 0.901913i \(-0.642163\pi\)
−0.431917 + 0.901913i \(0.642163\pi\)
\(968\) 3.33415 0.107164
\(969\) −11.2242 −0.360574
\(970\) −6.45797 −0.207353
\(971\) 54.4207 1.74644 0.873222 0.487322i \(-0.162026\pi\)
0.873222 + 0.487322i \(0.162026\pi\)
\(972\) 15.3525 0.492432
\(973\) −51.7725 −1.65975
\(974\) 14.1137 0.452233
\(975\) −0.894820 −0.0286572
\(976\) −2.21161 −0.0707918
\(977\) 18.4818 0.591284 0.295642 0.955299i \(-0.404466\pi\)
0.295642 + 0.955299i \(0.404466\pi\)
\(978\) −5.55305 −0.177567
\(979\) 39.1929 1.25261
\(980\) 1.54507 0.0493554
\(981\) 16.6143 0.530454
\(982\) 5.58698 0.178288
\(983\) 31.3006 0.998333 0.499166 0.866506i \(-0.333640\pi\)
0.499166 + 0.866506i \(0.333640\pi\)
\(984\) −3.55504 −0.113331
\(985\) 15.0764 0.480373
\(986\) −16.6568 −0.530460
\(987\) 20.1358 0.640929
\(988\) 8.15302 0.259382
\(989\) −5.67816 −0.180555
\(990\) −9.27637 −0.294822
\(991\) 0.691328 0.0219608 0.0109804 0.999940i \(-0.496505\pi\)
0.0109804 + 0.999940i \(0.496505\pi\)
\(992\) 2.54924 0.0809383
\(993\) −15.4358 −0.489840
\(994\) −9.17151 −0.290903
\(995\) 0.396256 0.0125622
\(996\) 10.9341 0.346459
\(997\) −28.0981 −0.889877 −0.444938 0.895561i \(-0.646774\pi\)
−0.444938 + 0.895561i \(0.646774\pi\)
\(998\) 31.5338 0.998186
\(999\) 8.72995 0.276203
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 \(a_p\))