Properties

Label 6010.2.a.c.1.8
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 1.8
Root \(0.293003\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.706997 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-0.706997 q^{6}\) \(-2.05365 q^{7}\) \(+1.00000 q^{8}\) \(-2.50015 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.706997 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-0.706997 q^{6}\) \(-2.05365 q^{7}\) \(+1.00000 q^{8}\) \(-2.50015 q^{9}\) \(+1.00000 q^{10}\) \(+5.00436 q^{11}\) \(-0.706997 q^{12}\) \(+1.44319 q^{13}\) \(-2.05365 q^{14}\) \(-0.706997 q^{15}\) \(+1.00000 q^{16}\) \(-5.11077 q^{17}\) \(-2.50015 q^{18}\) \(-0.185021 q^{19}\) \(+1.00000 q^{20}\) \(+1.45192 q^{21}\) \(+5.00436 q^{22}\) \(-2.44691 q^{23}\) \(-0.706997 q^{24}\) \(+1.00000 q^{25}\) \(+1.44319 q^{26}\) \(+3.88859 q^{27}\) \(-2.05365 q^{28}\) \(-2.29010 q^{29}\) \(-0.706997 q^{30}\) \(-9.99830 q^{31}\) \(+1.00000 q^{32}\) \(-3.53807 q^{33}\) \(-5.11077 q^{34}\) \(-2.05365 q^{35}\) \(-2.50015 q^{36}\) \(-5.58316 q^{37}\) \(-0.185021 q^{38}\) \(-1.02033 q^{39}\) \(+1.00000 q^{40}\) \(+2.67087 q^{41}\) \(+1.45192 q^{42}\) \(+2.86150 q^{43}\) \(+5.00436 q^{44}\) \(-2.50015 q^{45}\) \(-2.44691 q^{46}\) \(-1.49218 q^{47}\) \(-0.706997 q^{48}\) \(-2.78253 q^{49}\) \(+1.00000 q^{50}\) \(+3.61330 q^{51}\) \(+1.44319 q^{52}\) \(+9.86709 q^{53}\) \(+3.88859 q^{54}\) \(+5.00436 q^{55}\) \(-2.05365 q^{56}\) \(+0.130809 q^{57}\) \(-2.29010 q^{58}\) \(-9.79527 q^{59}\) \(-0.706997 q^{60}\) \(+1.70579 q^{61}\) \(-9.99830 q^{62}\) \(+5.13444 q^{63}\) \(+1.00000 q^{64}\) \(+1.44319 q^{65}\) \(-3.53807 q^{66}\) \(-4.31306 q^{67}\) \(-5.11077 q^{68}\) \(+1.72996 q^{69}\) \(-2.05365 q^{70}\) \(-10.7214 q^{71}\) \(-2.50015 q^{72}\) \(-1.68245 q^{73}\) \(-5.58316 q^{74}\) \(-0.706997 q^{75}\) \(-0.185021 q^{76}\) \(-10.2772 q^{77}\) \(-1.02033 q^{78}\) \(+3.43628 q^{79}\) \(+1.00000 q^{80}\) \(+4.75124 q^{81}\) \(+2.67087 q^{82}\) \(+0.478299 q^{83}\) \(+1.45192 q^{84}\) \(-5.11077 q^{85}\) \(+2.86150 q^{86}\) \(+1.61909 q^{87}\) \(+5.00436 q^{88}\) \(-7.20336 q^{89}\) \(-2.50015 q^{90}\) \(-2.96380 q^{91}\) \(-2.44691 q^{92}\) \(+7.06877 q^{93}\) \(-1.49218 q^{94}\) \(-0.185021 q^{95}\) \(-0.706997 q^{96}\) \(-4.23091 q^{97}\) \(-2.78253 q^{98}\) \(-12.5117 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.706997 −0.408185 −0.204093 0.978952i \(-0.565424\pi\)
−0.204093 + 0.978952i \(0.565424\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −0.706997 −0.288630
\(7\) −2.05365 −0.776206 −0.388103 0.921616i \(-0.626870\pi\)
−0.388103 + 0.921616i \(0.626870\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.50015 −0.833385
\(10\) 1.00000 0.316228
\(11\) 5.00436 1.50887 0.754435 0.656375i \(-0.227911\pi\)
0.754435 + 0.656375i \(0.227911\pi\)
\(12\) −0.706997 −0.204093
\(13\) 1.44319 0.400268 0.200134 0.979769i \(-0.435862\pi\)
0.200134 + 0.979769i \(0.435862\pi\)
\(14\) −2.05365 −0.548860
\(15\) −0.706997 −0.182546
\(16\) 1.00000 0.250000
\(17\) −5.11077 −1.23954 −0.619772 0.784782i \(-0.712775\pi\)
−0.619772 + 0.784782i \(0.712775\pi\)
\(18\) −2.50015 −0.589292
\(19\) −0.185021 −0.0424467 −0.0212234 0.999775i \(-0.506756\pi\)
−0.0212234 + 0.999775i \(0.506756\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.45192 0.316836
\(22\) 5.00436 1.06693
\(23\) −2.44691 −0.510217 −0.255108 0.966912i \(-0.582111\pi\)
−0.255108 + 0.966912i \(0.582111\pi\)
\(24\) −0.706997 −0.144315
\(25\) 1.00000 0.200000
\(26\) 1.44319 0.283032
\(27\) 3.88859 0.748360
\(28\) −2.05365 −0.388103
\(29\) −2.29010 −0.425260 −0.212630 0.977133i \(-0.568203\pi\)
−0.212630 + 0.977133i \(0.568203\pi\)
\(30\) −0.706997 −0.129079
\(31\) −9.99830 −1.79575 −0.897874 0.440253i \(-0.854889\pi\)
−0.897874 + 0.440253i \(0.854889\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.53807 −0.615898
\(34\) −5.11077 −0.876490
\(35\) −2.05365 −0.347130
\(36\) −2.50015 −0.416692
\(37\) −5.58316 −0.917866 −0.458933 0.888471i \(-0.651768\pi\)
−0.458933 + 0.888471i \(0.651768\pi\)
\(38\) −0.185021 −0.0300144
\(39\) −1.02033 −0.163383
\(40\) 1.00000 0.158114
\(41\) 2.67087 0.417120 0.208560 0.978010i \(-0.433122\pi\)
0.208560 + 0.978010i \(0.433122\pi\)
\(42\) 1.45192 0.224037
\(43\) 2.86150 0.436374 0.218187 0.975907i \(-0.429986\pi\)
0.218187 + 0.975907i \(0.429986\pi\)
\(44\) 5.00436 0.754435
\(45\) −2.50015 −0.372701
\(46\) −2.44691 −0.360778
\(47\) −1.49218 −0.217657 −0.108829 0.994061i \(-0.534710\pi\)
−0.108829 + 0.994061i \(0.534710\pi\)
\(48\) −0.706997 −0.102046
\(49\) −2.78253 −0.397504
\(50\) 1.00000 0.141421
\(51\) 3.61330 0.505963
\(52\) 1.44319 0.200134
\(53\) 9.86709 1.35535 0.677675 0.735362i \(-0.262988\pi\)
0.677675 + 0.735362i \(0.262988\pi\)
\(54\) 3.88859 0.529171
\(55\) 5.00436 0.674787
\(56\) −2.05365 −0.274430
\(57\) 0.130809 0.0173261
\(58\) −2.29010 −0.300704
\(59\) −9.79527 −1.27524 −0.637618 0.770353i \(-0.720080\pi\)
−0.637618 + 0.770353i \(0.720080\pi\)
\(60\) −0.706997 −0.0912730
\(61\) 1.70579 0.218404 0.109202 0.994020i \(-0.465170\pi\)
0.109202 + 0.994020i \(0.465170\pi\)
\(62\) −9.99830 −1.26979
\(63\) 5.13444 0.646878
\(64\) 1.00000 0.125000
\(65\) 1.44319 0.179005
\(66\) −3.53807 −0.435506
\(67\) −4.31306 −0.526924 −0.263462 0.964670i \(-0.584864\pi\)
−0.263462 + 0.964670i \(0.584864\pi\)
\(68\) −5.11077 −0.619772
\(69\) 1.72996 0.208263
\(70\) −2.05365 −0.245458
\(71\) −10.7214 −1.27239 −0.636196 0.771527i \(-0.719493\pi\)
−0.636196 + 0.771527i \(0.719493\pi\)
\(72\) −2.50015 −0.294646
\(73\) −1.68245 −0.196916 −0.0984579 0.995141i \(-0.531391\pi\)
−0.0984579 + 0.995141i \(0.531391\pi\)
\(74\) −5.58316 −0.649029
\(75\) −0.706997 −0.0816370
\(76\) −0.185021 −0.0212234
\(77\) −10.2772 −1.17119
\(78\) −1.02033 −0.115529
\(79\) 3.43628 0.386612 0.193306 0.981139i \(-0.438079\pi\)
0.193306 + 0.981139i \(0.438079\pi\)
\(80\) 1.00000 0.111803
\(81\) 4.75124 0.527915
\(82\) 2.67087 0.294948
\(83\) 0.478299 0.0525001 0.0262501 0.999655i \(-0.491643\pi\)
0.0262501 + 0.999655i \(0.491643\pi\)
\(84\) 1.45192 0.158418
\(85\) −5.11077 −0.554341
\(86\) 2.86150 0.308563
\(87\) 1.61909 0.173585
\(88\) 5.00436 0.533466
\(89\) −7.20336 −0.763555 −0.381777 0.924254i \(-0.624688\pi\)
−0.381777 + 0.924254i \(0.624688\pi\)
\(90\) −2.50015 −0.263539
\(91\) −2.96380 −0.310690
\(92\) −2.44691 −0.255108
\(93\) 7.06877 0.732997
\(94\) −1.49218 −0.153907
\(95\) −0.185021 −0.0189828
\(96\) −0.706997 −0.0721576
\(97\) −4.23091 −0.429584 −0.214792 0.976660i \(-0.568907\pi\)
−0.214792 + 0.976660i \(0.568907\pi\)
\(98\) −2.78253 −0.281078
\(99\) −12.5117 −1.25747
\(100\) 1.00000 0.100000
\(101\) 4.22384 0.420288 0.210144 0.977670i \(-0.432607\pi\)
0.210144 + 0.977670i \(0.432607\pi\)
\(102\) 3.61330 0.357770
\(103\) −1.25399 −0.123560 −0.0617798 0.998090i \(-0.519678\pi\)
−0.0617798 + 0.998090i \(0.519678\pi\)
\(104\) 1.44319 0.141516
\(105\) 1.45192 0.141693
\(106\) 9.86709 0.958377
\(107\) 13.0482 1.26141 0.630707 0.776021i \(-0.282765\pi\)
0.630707 + 0.776021i \(0.282765\pi\)
\(108\) 3.88859 0.374180
\(109\) −3.61976 −0.346710 −0.173355 0.984859i \(-0.555461\pi\)
−0.173355 + 0.984859i \(0.555461\pi\)
\(110\) 5.00436 0.477147
\(111\) 3.94728 0.374659
\(112\) −2.05365 −0.194051
\(113\) 6.27803 0.590588 0.295294 0.955406i \(-0.404582\pi\)
0.295294 + 0.955406i \(0.404582\pi\)
\(114\) 0.130809 0.0122514
\(115\) −2.44691 −0.228176
\(116\) −2.29010 −0.212630
\(117\) −3.60819 −0.333577
\(118\) −9.79527 −0.901728
\(119\) 10.4957 0.962141
\(120\) −0.706997 −0.0645397
\(121\) 14.0436 1.27669
\(122\) 1.70579 0.154435
\(123\) −1.88830 −0.170262
\(124\) −9.99830 −0.897874
\(125\) 1.00000 0.0894427
\(126\) 5.13444 0.457412
\(127\) 22.1156 1.96244 0.981221 0.192886i \(-0.0617848\pi\)
0.981221 + 0.192886i \(0.0617848\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.02307 −0.178121
\(130\) 1.44319 0.126576
\(131\) −11.9713 −1.04594 −0.522968 0.852352i \(-0.675175\pi\)
−0.522968 + 0.852352i \(0.675175\pi\)
\(132\) −3.53807 −0.307949
\(133\) 0.379968 0.0329474
\(134\) −4.31306 −0.372592
\(135\) 3.88859 0.334677
\(136\) −5.11077 −0.438245
\(137\) −23.0925 −1.97292 −0.986462 0.163988i \(-0.947564\pi\)
−0.986462 + 0.163988i \(0.947564\pi\)
\(138\) 1.72996 0.147264
\(139\) −13.6405 −1.15697 −0.578487 0.815691i \(-0.696357\pi\)
−0.578487 + 0.815691i \(0.696357\pi\)
\(140\) −2.05365 −0.173565
\(141\) 1.05497 0.0888444
\(142\) −10.7214 −0.899717
\(143\) 7.22222 0.603952
\(144\) −2.50015 −0.208346
\(145\) −2.29010 −0.190182
\(146\) −1.68245 −0.139241
\(147\) 1.96724 0.162255
\(148\) −5.58316 −0.458933
\(149\) −1.26679 −0.103780 −0.0518899 0.998653i \(-0.516524\pi\)
−0.0518899 + 0.998653i \(0.516524\pi\)
\(150\) −0.706997 −0.0577261
\(151\) −8.57737 −0.698017 −0.349008 0.937120i \(-0.613482\pi\)
−0.349008 + 0.937120i \(0.613482\pi\)
\(152\) −0.185021 −0.0150072
\(153\) 12.7777 1.03302
\(154\) −10.2772 −0.828159
\(155\) −9.99830 −0.803083
\(156\) −1.02033 −0.0816917
\(157\) −19.4496 −1.55225 −0.776124 0.630580i \(-0.782817\pi\)
−0.776124 + 0.630580i \(0.782817\pi\)
\(158\) 3.43628 0.273376
\(159\) −6.97601 −0.553233
\(160\) 1.00000 0.0790569
\(161\) 5.02510 0.396033
\(162\) 4.75124 0.373293
\(163\) −7.83300 −0.613528 −0.306764 0.951786i \(-0.599246\pi\)
−0.306764 + 0.951786i \(0.599246\pi\)
\(164\) 2.67087 0.208560
\(165\) −3.53807 −0.275438
\(166\) 0.478299 0.0371232
\(167\) 11.9151 0.922014 0.461007 0.887396i \(-0.347488\pi\)
0.461007 + 0.887396i \(0.347488\pi\)
\(168\) 1.45192 0.112018
\(169\) −10.9172 −0.839786
\(170\) −5.11077 −0.391978
\(171\) 0.462581 0.0353745
\(172\) 2.86150 0.218187
\(173\) 7.26378 0.552255 0.276127 0.961121i \(-0.410949\pi\)
0.276127 + 0.961121i \(0.410949\pi\)
\(174\) 1.61909 0.122743
\(175\) −2.05365 −0.155241
\(176\) 5.00436 0.377218
\(177\) 6.92523 0.520532
\(178\) −7.20336 −0.539915
\(179\) −3.07473 −0.229816 −0.114908 0.993376i \(-0.536657\pi\)
−0.114908 + 0.993376i \(0.536657\pi\)
\(180\) −2.50015 −0.186351
\(181\) −14.2293 −1.05765 −0.528827 0.848729i \(-0.677368\pi\)
−0.528827 + 0.848729i \(0.677368\pi\)
\(182\) −2.96380 −0.219691
\(183\) −1.20599 −0.0891493
\(184\) −2.44691 −0.180389
\(185\) −5.58316 −0.410482
\(186\) 7.06877 0.518307
\(187\) −25.5761 −1.87031
\(188\) −1.49218 −0.108829
\(189\) −7.98580 −0.580882
\(190\) −0.185021 −0.0134228
\(191\) −26.0360 −1.88390 −0.941949 0.335755i \(-0.891008\pi\)
−0.941949 + 0.335755i \(0.891008\pi\)
\(192\) −0.706997 −0.0510231
\(193\) −15.7653 −1.13481 −0.567407 0.823438i \(-0.692053\pi\)
−0.567407 + 0.823438i \(0.692053\pi\)
\(194\) −4.23091 −0.303762
\(195\) −1.02033 −0.0730673
\(196\) −2.78253 −0.198752
\(197\) 4.70772 0.335411 0.167706 0.985837i \(-0.446364\pi\)
0.167706 + 0.985837i \(0.446364\pi\)
\(198\) −12.5117 −0.889165
\(199\) −22.5777 −1.60049 −0.800245 0.599673i \(-0.795297\pi\)
−0.800245 + 0.599673i \(0.795297\pi\)
\(200\) 1.00000 0.0707107
\(201\) 3.04932 0.215083
\(202\) 4.22384 0.297188
\(203\) 4.70305 0.330089
\(204\) 3.61330 0.252982
\(205\) 2.67087 0.186542
\(206\) −1.25399 −0.0873698
\(207\) 6.11766 0.425207
\(208\) 1.44319 0.100067
\(209\) −0.925911 −0.0640466
\(210\) 1.45192 0.100192
\(211\) 10.5796 0.728326 0.364163 0.931335i \(-0.381355\pi\)
0.364163 + 0.931335i \(0.381355\pi\)
\(212\) 9.86709 0.677675
\(213\) 7.57998 0.519372
\(214\) 13.0482 0.891954
\(215\) 2.86150 0.195152
\(216\) 3.88859 0.264585
\(217\) 20.5330 1.39387
\(218\) −3.61976 −0.245161
\(219\) 1.18949 0.0803781
\(220\) 5.00436 0.337394
\(221\) −7.37579 −0.496149
\(222\) 3.94728 0.264924
\(223\) 2.98502 0.199892 0.0999458 0.994993i \(-0.468133\pi\)
0.0999458 + 0.994993i \(0.468133\pi\)
\(224\) −2.05365 −0.137215
\(225\) −2.50015 −0.166677
\(226\) 6.27803 0.417609
\(227\) −0.464604 −0.0308368 −0.0154184 0.999881i \(-0.504908\pi\)
−0.0154184 + 0.999881i \(0.504908\pi\)
\(228\) 0.130809 0.00866306
\(229\) 5.74517 0.379652 0.189826 0.981818i \(-0.439208\pi\)
0.189826 + 0.981818i \(0.439208\pi\)
\(230\) −2.44691 −0.161345
\(231\) 7.26594 0.478064
\(232\) −2.29010 −0.150352
\(233\) 7.46355 0.488953 0.244477 0.969655i \(-0.421384\pi\)
0.244477 + 0.969655i \(0.421384\pi\)
\(234\) −3.60819 −0.235875
\(235\) −1.49218 −0.0973392
\(236\) −9.79527 −0.637618
\(237\) −2.42944 −0.157809
\(238\) 10.4957 0.680336
\(239\) −7.74748 −0.501143 −0.250571 0.968098i \(-0.580618\pi\)
−0.250571 + 0.968098i \(0.580618\pi\)
\(240\) −0.706997 −0.0456365
\(241\) 1.98293 0.127731 0.0638657 0.997959i \(-0.479657\pi\)
0.0638657 + 0.997959i \(0.479657\pi\)
\(242\) 14.0436 0.902756
\(243\) −15.0249 −0.963848
\(244\) 1.70579 0.109202
\(245\) −2.78253 −0.177769
\(246\) −1.88830 −0.120393
\(247\) −0.267020 −0.0169901
\(248\) −9.99830 −0.634893
\(249\) −0.338156 −0.0214298
\(250\) 1.00000 0.0632456
\(251\) −6.98470 −0.440870 −0.220435 0.975402i \(-0.570748\pi\)
−0.220435 + 0.975402i \(0.570748\pi\)
\(252\) 5.13444 0.323439
\(253\) −12.2452 −0.769851
\(254\) 22.1156 1.38766
\(255\) 3.61330 0.226274
\(256\) 1.00000 0.0625000
\(257\) 6.46020 0.402976 0.201488 0.979491i \(-0.435422\pi\)
0.201488 + 0.979491i \(0.435422\pi\)
\(258\) −2.02307 −0.125951
\(259\) 11.4658 0.712453
\(260\) 1.44319 0.0895026
\(261\) 5.72560 0.354405
\(262\) −11.9713 −0.739589
\(263\) −3.54780 −0.218767 −0.109383 0.994000i \(-0.534888\pi\)
−0.109383 + 0.994000i \(0.534888\pi\)
\(264\) −3.53807 −0.217753
\(265\) 9.86709 0.606131
\(266\) 0.379968 0.0232973
\(267\) 5.09276 0.311672
\(268\) −4.31306 −0.263462
\(269\) −18.6251 −1.13559 −0.567797 0.823168i \(-0.692204\pi\)
−0.567797 + 0.823168i \(0.692204\pi\)
\(270\) 3.88859 0.236652
\(271\) −5.90574 −0.358748 −0.179374 0.983781i \(-0.557407\pi\)
−0.179374 + 0.983781i \(0.557407\pi\)
\(272\) −5.11077 −0.309886
\(273\) 2.09540 0.126819
\(274\) −23.0925 −1.39507
\(275\) 5.00436 0.301774
\(276\) 1.72996 0.104131
\(277\) −9.69772 −0.582680 −0.291340 0.956620i \(-0.594101\pi\)
−0.291340 + 0.956620i \(0.594101\pi\)
\(278\) −13.6405 −0.818105
\(279\) 24.9973 1.49655
\(280\) −2.05365 −0.122729
\(281\) 12.4748 0.744184 0.372092 0.928196i \(-0.378641\pi\)
0.372092 + 0.928196i \(0.378641\pi\)
\(282\) 1.05497 0.0628225
\(283\) 25.4177 1.51093 0.755463 0.655191i \(-0.227412\pi\)
0.755463 + 0.655191i \(0.227412\pi\)
\(284\) −10.7214 −0.636196
\(285\) 0.130809 0.00774848
\(286\) 7.22222 0.427059
\(287\) −5.48503 −0.323771
\(288\) −2.50015 −0.147323
\(289\) 9.11996 0.536468
\(290\) −2.29010 −0.134479
\(291\) 2.99124 0.175350
\(292\) −1.68245 −0.0984579
\(293\) −9.55180 −0.558022 −0.279011 0.960288i \(-0.590007\pi\)
−0.279011 + 0.960288i \(0.590007\pi\)
\(294\) 1.96724 0.114732
\(295\) −9.79527 −0.570303
\(296\) −5.58316 −0.324515
\(297\) 19.4599 1.12918
\(298\) −1.26679 −0.0733834
\(299\) −3.53135 −0.204223
\(300\) −0.706997 −0.0408185
\(301\) −5.87650 −0.338716
\(302\) −8.57737 −0.493572
\(303\) −2.98624 −0.171555
\(304\) −0.185021 −0.0106117
\(305\) 1.70579 0.0976732
\(306\) 12.7777 0.730453
\(307\) 14.7147 0.839810 0.419905 0.907568i \(-0.362063\pi\)
0.419905 + 0.907568i \(0.362063\pi\)
\(308\) −10.2772 −0.585597
\(309\) 0.886569 0.0504352
\(310\) −9.99830 −0.567865
\(311\) 5.07781 0.287936 0.143968 0.989582i \(-0.454014\pi\)
0.143968 + 0.989582i \(0.454014\pi\)
\(312\) −1.02033 −0.0577647
\(313\) −4.59432 −0.259686 −0.129843 0.991535i \(-0.541447\pi\)
−0.129843 + 0.991535i \(0.541447\pi\)
\(314\) −19.4496 −1.09761
\(315\) 5.13444 0.289293
\(316\) 3.43628 0.193306
\(317\) −20.3855 −1.14496 −0.572482 0.819917i \(-0.694019\pi\)
−0.572482 + 0.819917i \(0.694019\pi\)
\(318\) −6.97601 −0.391195
\(319\) −11.4605 −0.641662
\(320\) 1.00000 0.0559017
\(321\) −9.22502 −0.514890
\(322\) 5.02510 0.280038
\(323\) 0.945600 0.0526146
\(324\) 4.75124 0.263958
\(325\) 1.44319 0.0800536
\(326\) −7.83300 −0.433830
\(327\) 2.55916 0.141522
\(328\) 2.67087 0.147474
\(329\) 3.06442 0.168947
\(330\) −3.53807 −0.194764
\(331\) 10.6950 0.587851 0.293925 0.955828i \(-0.405038\pi\)
0.293925 + 0.955828i \(0.405038\pi\)
\(332\) 0.478299 0.0262501
\(333\) 13.9588 0.764936
\(334\) 11.9151 0.651963
\(335\) −4.31306 −0.235648
\(336\) 1.45192 0.0792089
\(337\) 22.8677 1.24569 0.622843 0.782347i \(-0.285978\pi\)
0.622843 + 0.782347i \(0.285978\pi\)
\(338\) −10.9172 −0.593818
\(339\) −4.43855 −0.241069
\(340\) −5.11077 −0.277170
\(341\) −50.0351 −2.70955
\(342\) 0.462581 0.0250135
\(343\) 20.0899 1.08475
\(344\) 2.86150 0.154282
\(345\) 1.72996 0.0931380
\(346\) 7.26378 0.390503
\(347\) 16.6582 0.894258 0.447129 0.894469i \(-0.352446\pi\)
0.447129 + 0.894469i \(0.352446\pi\)
\(348\) 1.61909 0.0867924
\(349\) −19.1618 −1.02571 −0.512853 0.858477i \(-0.671411\pi\)
−0.512853 + 0.858477i \(0.671411\pi\)
\(350\) −2.05365 −0.109772
\(351\) 5.61197 0.299545
\(352\) 5.00436 0.266733
\(353\) 1.54088 0.0820128 0.0410064 0.999159i \(-0.486944\pi\)
0.0410064 + 0.999159i \(0.486944\pi\)
\(354\) 6.92523 0.368072
\(355\) −10.7214 −0.569031
\(356\) −7.20336 −0.381777
\(357\) −7.42045 −0.392732
\(358\) −3.07473 −0.162505
\(359\) 36.2403 1.91269 0.956345 0.292240i \(-0.0944005\pi\)
0.956345 + 0.292240i \(0.0944005\pi\)
\(360\) −2.50015 −0.131770
\(361\) −18.9658 −0.998198
\(362\) −14.2293 −0.747875
\(363\) −9.92878 −0.521126
\(364\) −2.96380 −0.155345
\(365\) −1.68245 −0.0880634
\(366\) −1.20599 −0.0630380
\(367\) −34.0183 −1.77574 −0.887871 0.460092i \(-0.847817\pi\)
−0.887871 + 0.460092i \(0.847817\pi\)
\(368\) −2.44691 −0.127554
\(369\) −6.67759 −0.347621
\(370\) −5.58316 −0.290255
\(371\) −20.2635 −1.05203
\(372\) 7.06877 0.366499
\(373\) −1.57188 −0.0813891 −0.0406945 0.999172i \(-0.512957\pi\)
−0.0406945 + 0.999172i \(0.512957\pi\)
\(374\) −25.5761 −1.32251
\(375\) −0.706997 −0.0365092
\(376\) −1.49218 −0.0769534
\(377\) −3.30504 −0.170218
\(378\) −7.98580 −0.410745
\(379\) −17.1650 −0.881708 −0.440854 0.897579i \(-0.645324\pi\)
−0.440854 + 0.897579i \(0.645324\pi\)
\(380\) −0.185021 −0.00949138
\(381\) −15.6357 −0.801040
\(382\) −26.0360 −1.33212
\(383\) 13.9245 0.711508 0.355754 0.934580i \(-0.384224\pi\)
0.355754 + 0.934580i \(0.384224\pi\)
\(384\) −0.706997 −0.0360788
\(385\) −10.2772 −0.523774
\(386\) −15.7653 −0.802434
\(387\) −7.15418 −0.363668
\(388\) −4.23091 −0.214792
\(389\) −21.5436 −1.09230 −0.546152 0.837686i \(-0.683908\pi\)
−0.546152 + 0.837686i \(0.683908\pi\)
\(390\) −1.02033 −0.0516664
\(391\) 12.5056 0.632436
\(392\) −2.78253 −0.140539
\(393\) 8.46367 0.426936
\(394\) 4.70772 0.237172
\(395\) 3.43628 0.172898
\(396\) −12.5117 −0.628735
\(397\) −25.0604 −1.25775 −0.628873 0.777508i \(-0.716484\pi\)
−0.628873 + 0.777508i \(0.716484\pi\)
\(398\) −22.5777 −1.13172
\(399\) −0.268636 −0.0134486
\(400\) 1.00000 0.0500000
\(401\) 9.66917 0.482855 0.241428 0.970419i \(-0.422384\pi\)
0.241428 + 0.970419i \(0.422384\pi\)
\(402\) 3.04932 0.152086
\(403\) −14.4294 −0.718780
\(404\) 4.22384 0.210144
\(405\) 4.75124 0.236091
\(406\) 4.70305 0.233409
\(407\) −27.9401 −1.38494
\(408\) 3.61330 0.178885
\(409\) 31.5033 1.55774 0.778869 0.627187i \(-0.215794\pi\)
0.778869 + 0.627187i \(0.215794\pi\)
\(410\) 2.67087 0.131905
\(411\) 16.3263 0.805318
\(412\) −1.25399 −0.0617798
\(413\) 20.1160 0.989846
\(414\) 6.11766 0.300667
\(415\) 0.478299 0.0234788
\(416\) 1.44319 0.0707580
\(417\) 9.64382 0.472260
\(418\) −0.925911 −0.0452878
\(419\) 29.8651 1.45900 0.729502 0.683978i \(-0.239752\pi\)
0.729502 + 0.683978i \(0.239752\pi\)
\(420\) 1.45192 0.0708466
\(421\) −1.24282 −0.0605716 −0.0302858 0.999541i \(-0.509642\pi\)
−0.0302858 + 0.999541i \(0.509642\pi\)
\(422\) 10.5796 0.515005
\(423\) 3.73069 0.181392
\(424\) 9.86709 0.479188
\(425\) −5.11077 −0.247909
\(426\) 7.57998 0.367251
\(427\) −3.50309 −0.169526
\(428\) 13.0482 0.630707
\(429\) −5.10609 −0.246524
\(430\) 2.86150 0.137994
\(431\) 15.0924 0.726975 0.363488 0.931599i \(-0.381586\pi\)
0.363488 + 0.931599i \(0.381586\pi\)
\(432\) 3.88859 0.187090
\(433\) 19.3810 0.931392 0.465696 0.884945i \(-0.345804\pi\)
0.465696 + 0.884945i \(0.345804\pi\)
\(434\) 20.5330 0.985615
\(435\) 1.61909 0.0776295
\(436\) −3.61976 −0.173355
\(437\) 0.452731 0.0216570
\(438\) 1.18949 0.0568359
\(439\) 20.4014 0.973705 0.486852 0.873484i \(-0.338145\pi\)
0.486852 + 0.873484i \(0.338145\pi\)
\(440\) 5.00436 0.238573
\(441\) 6.95676 0.331274
\(442\) −7.37579 −0.350831
\(443\) 20.6581 0.981498 0.490749 0.871301i \(-0.336723\pi\)
0.490749 + 0.871301i \(0.336723\pi\)
\(444\) 3.94728 0.187330
\(445\) −7.20336 −0.341472
\(446\) 2.98502 0.141345
\(447\) 0.895620 0.0423613
\(448\) −2.05365 −0.0970257
\(449\) 24.9190 1.17600 0.588001 0.808860i \(-0.299915\pi\)
0.588001 + 0.808860i \(0.299915\pi\)
\(450\) −2.50015 −0.117858
\(451\) 13.3660 0.629380
\(452\) 6.27803 0.295294
\(453\) 6.06418 0.284920
\(454\) −0.464604 −0.0218049
\(455\) −2.96380 −0.138945
\(456\) 0.130809 0.00612571
\(457\) −13.7300 −0.642263 −0.321132 0.947035i \(-0.604063\pi\)
−0.321132 + 0.947035i \(0.604063\pi\)
\(458\) 5.74517 0.268454
\(459\) −19.8737 −0.927625
\(460\) −2.44691 −0.114088
\(461\) −13.8355 −0.644385 −0.322193 0.946674i \(-0.604420\pi\)
−0.322193 + 0.946674i \(0.604420\pi\)
\(462\) 7.26594 0.338042
\(463\) 20.7694 0.965237 0.482618 0.875831i \(-0.339686\pi\)
0.482618 + 0.875831i \(0.339686\pi\)
\(464\) −2.29010 −0.106315
\(465\) 7.06877 0.327806
\(466\) 7.46355 0.345742
\(467\) −18.1859 −0.841545 −0.420772 0.907166i \(-0.638241\pi\)
−0.420772 + 0.907166i \(0.638241\pi\)
\(468\) −3.60819 −0.166789
\(469\) 8.85751 0.409002
\(470\) −1.49218 −0.0688292
\(471\) 13.7508 0.633605
\(472\) −9.79527 −0.450864
\(473\) 14.3199 0.658432
\(474\) −2.42944 −0.111588
\(475\) −0.185021 −0.00848935
\(476\) 10.4957 0.481071
\(477\) −24.6693 −1.12953
\(478\) −7.74748 −0.354361
\(479\) 29.5437 1.34989 0.674944 0.737869i \(-0.264168\pi\)
0.674944 + 0.737869i \(0.264168\pi\)
\(480\) −0.706997 −0.0322699
\(481\) −8.05754 −0.367392
\(482\) 1.98293 0.0903198
\(483\) −3.55273 −0.161655
\(484\) 14.0436 0.638345
\(485\) −4.23091 −0.192116
\(486\) −15.0249 −0.681543
\(487\) 1.39387 0.0631622 0.0315811 0.999501i \(-0.489946\pi\)
0.0315811 + 0.999501i \(0.489946\pi\)
\(488\) 1.70579 0.0772175
\(489\) 5.53791 0.250433
\(490\) −2.78253 −0.125702
\(491\) −31.6266 −1.42729 −0.713643 0.700509i \(-0.752956\pi\)
−0.713643 + 0.700509i \(0.752956\pi\)
\(492\) −1.88830 −0.0851310
\(493\) 11.7042 0.527129
\(494\) −0.267020 −0.0120138
\(495\) −12.5117 −0.562358
\(496\) −9.99830 −0.448937
\(497\) 22.0179 0.987639
\(498\) −0.338156 −0.0151531
\(499\) 11.7470 0.525867 0.262934 0.964814i \(-0.415310\pi\)
0.262934 + 0.964814i \(0.415310\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.42391 −0.376353
\(502\) −6.98470 −0.311742
\(503\) 0.853379 0.0380503 0.0190252 0.999819i \(-0.493944\pi\)
0.0190252 + 0.999819i \(0.493944\pi\)
\(504\) 5.13444 0.228706
\(505\) 4.22384 0.187958
\(506\) −12.2452 −0.544367
\(507\) 7.71844 0.342788
\(508\) 22.1156 0.981221
\(509\) 3.73108 0.165377 0.0826886 0.996575i \(-0.473649\pi\)
0.0826886 + 0.996575i \(0.473649\pi\)
\(510\) 3.61330 0.160000
\(511\) 3.45516 0.152847
\(512\) 1.00000 0.0441942
\(513\) −0.719472 −0.0317655
\(514\) 6.46020 0.284947
\(515\) −1.25399 −0.0552575
\(516\) −2.02307 −0.0890607
\(517\) −7.46741 −0.328416
\(518\) 11.4658 0.503781
\(519\) −5.13547 −0.225422
\(520\) 1.44319 0.0632879
\(521\) −5.79178 −0.253743 −0.126871 0.991919i \(-0.540494\pi\)
−0.126871 + 0.991919i \(0.540494\pi\)
\(522\) 5.72560 0.250602
\(523\) 18.2440 0.797753 0.398876 0.917005i \(-0.369400\pi\)
0.398876 + 0.917005i \(0.369400\pi\)
\(524\) −11.9713 −0.522968
\(525\) 1.45192 0.0633671
\(526\) −3.54780 −0.154691
\(527\) 51.0990 2.22591
\(528\) −3.53807 −0.153975
\(529\) −17.0126 −0.739679
\(530\) 9.86709 0.428599
\(531\) 24.4897 1.06276
\(532\) 0.379968 0.0164737
\(533\) 3.85456 0.166960
\(534\) 5.09276 0.220385
\(535\) 13.0482 0.564121
\(536\) −4.31306 −0.186296
\(537\) 2.17383 0.0938075
\(538\) −18.6251 −0.802987
\(539\) −13.9248 −0.599783
\(540\) 3.88859 0.167338
\(541\) 17.8511 0.767478 0.383739 0.923442i \(-0.374636\pi\)
0.383739 + 0.923442i \(0.374636\pi\)
\(542\) −5.90574 −0.253673
\(543\) 10.0601 0.431719
\(544\) −5.11077 −0.219122
\(545\) −3.61976 −0.155054
\(546\) 2.09540 0.0896747
\(547\) −11.6106 −0.496432 −0.248216 0.968705i \(-0.579844\pi\)
−0.248216 + 0.968705i \(0.579844\pi\)
\(548\) −23.0925 −0.986462
\(549\) −4.26474 −0.182015
\(550\) 5.00436 0.213386
\(551\) 0.423716 0.0180509
\(552\) 1.72996 0.0736320
\(553\) −7.05691 −0.300090
\(554\) −9.69772 −0.412017
\(555\) 3.94728 0.167553
\(556\) −13.6405 −0.578487
\(557\) −0.0176112 −0.000746212 0 −0.000373106 1.00000i \(-0.500119\pi\)
−0.000373106 1.00000i \(0.500119\pi\)
\(558\) 24.9973 1.05822
\(559\) 4.12967 0.174666
\(560\) −2.05365 −0.0867825
\(561\) 18.0822 0.763433
\(562\) 12.4748 0.526218
\(563\) −0.574818 −0.0242257 −0.0121129 0.999927i \(-0.503856\pi\)
−0.0121129 + 0.999927i \(0.503856\pi\)
\(564\) 1.05497 0.0444222
\(565\) 6.27803 0.264119
\(566\) 25.4177 1.06839
\(567\) −9.75737 −0.409771
\(568\) −10.7214 −0.449859
\(569\) 40.5272 1.69899 0.849495 0.527596i \(-0.176907\pi\)
0.849495 + 0.527596i \(0.176907\pi\)
\(570\) 0.130809 0.00547900
\(571\) 4.62409 0.193512 0.0967561 0.995308i \(-0.469153\pi\)
0.0967561 + 0.995308i \(0.469153\pi\)
\(572\) 7.22222 0.301976
\(573\) 18.4074 0.768979
\(574\) −5.48503 −0.228941
\(575\) −2.44691 −0.102043
\(576\) −2.50015 −0.104173
\(577\) −13.2880 −0.553189 −0.276594 0.960987i \(-0.589206\pi\)
−0.276594 + 0.960987i \(0.589206\pi\)
\(578\) 9.11996 0.379340
\(579\) 11.1460 0.463214
\(580\) −2.29010 −0.0950911
\(581\) −0.982257 −0.0407509
\(582\) 2.99124 0.123991
\(583\) 49.3785 2.04505
\(584\) −1.68245 −0.0696203
\(585\) −3.60819 −0.149180
\(586\) −9.55180 −0.394581
\(587\) −30.1623 −1.24493 −0.622466 0.782647i \(-0.713869\pi\)
−0.622466 + 0.782647i \(0.713869\pi\)
\(588\) 1.96724 0.0811277
\(589\) 1.84990 0.0762236
\(590\) −9.79527 −0.403265
\(591\) −3.32835 −0.136910
\(592\) −5.58316 −0.229467
\(593\) −15.0331 −0.617337 −0.308668 0.951170i \(-0.599883\pi\)
−0.308668 + 0.951170i \(0.599883\pi\)
\(594\) 19.4599 0.798450
\(595\) 10.4957 0.430283
\(596\) −1.26679 −0.0518899
\(597\) 15.9624 0.653296
\(598\) −3.53135 −0.144408
\(599\) 3.79170 0.154925 0.0774623 0.996995i \(-0.475318\pi\)
0.0774623 + 0.996995i \(0.475318\pi\)
\(600\) −0.706997 −0.0288630
\(601\) −1.00000 −0.0407909
\(602\) −5.87650 −0.239508
\(603\) 10.7833 0.439131
\(604\) −8.57737 −0.349008
\(605\) 14.0436 0.570953
\(606\) −2.98624 −0.121308
\(607\) −34.5176 −1.40103 −0.700513 0.713639i \(-0.747046\pi\)
−0.700513 + 0.713639i \(0.747046\pi\)
\(608\) −0.185021 −0.00750359
\(609\) −3.32504 −0.134738
\(610\) 1.70579 0.0690654
\(611\) −2.15350 −0.0871212
\(612\) 12.7777 0.516509
\(613\) −13.7687 −0.556114 −0.278057 0.960565i \(-0.589690\pi\)
−0.278057 + 0.960565i \(0.589690\pi\)
\(614\) 14.7147 0.593835
\(615\) −1.88830 −0.0761435
\(616\) −10.2772 −0.414080
\(617\) 7.91563 0.318671 0.159336 0.987224i \(-0.449065\pi\)
0.159336 + 0.987224i \(0.449065\pi\)
\(618\) 0.886569 0.0356630
\(619\) 22.9512 0.922487 0.461243 0.887274i \(-0.347404\pi\)
0.461243 + 0.887274i \(0.347404\pi\)
\(620\) −9.99830 −0.401541
\(621\) −9.51505 −0.381826
\(622\) 5.07781 0.203602
\(623\) 14.7932 0.592676
\(624\) −1.02033 −0.0408458
\(625\) 1.00000 0.0400000
\(626\) −4.59432 −0.183626
\(627\) 0.654617 0.0261429
\(628\) −19.4496 −0.776124
\(629\) 28.5343 1.13774
\(630\) 5.13444 0.204561
\(631\) −29.6919 −1.18201 −0.591007 0.806666i \(-0.701270\pi\)
−0.591007 + 0.806666i \(0.701270\pi\)
\(632\) 3.43628 0.136688
\(633\) −7.47971 −0.297292
\(634\) −20.3855 −0.809612
\(635\) 22.1156 0.877631
\(636\) −6.97601 −0.276617
\(637\) −4.01571 −0.159108
\(638\) −11.4605 −0.453724
\(639\) 26.8051 1.06039
\(640\) 1.00000 0.0395285
\(641\) −23.7718 −0.938931 −0.469465 0.882951i \(-0.655553\pi\)
−0.469465 + 0.882951i \(0.655553\pi\)
\(642\) −9.22502 −0.364082
\(643\) −26.0809 −1.02853 −0.514266 0.857631i \(-0.671936\pi\)
−0.514266 + 0.857631i \(0.671936\pi\)
\(644\) 5.02510 0.198017
\(645\) −2.02307 −0.0796583
\(646\) 0.945600 0.0372041
\(647\) 38.8577 1.52765 0.763827 0.645421i \(-0.223318\pi\)
0.763827 + 0.645421i \(0.223318\pi\)
\(648\) 4.75124 0.186646
\(649\) −49.0190 −1.92417
\(650\) 1.44319 0.0566064
\(651\) −14.5168 −0.568957
\(652\) −7.83300 −0.306764
\(653\) 12.7761 0.499967 0.249984 0.968250i \(-0.419575\pi\)
0.249984 + 0.968250i \(0.419575\pi\)
\(654\) 2.55916 0.100071
\(655\) −11.9713 −0.467757
\(656\) 2.67087 0.104280
\(657\) 4.20638 0.164107
\(658\) 3.06442 0.119463
\(659\) 2.00349 0.0780449 0.0390225 0.999238i \(-0.487576\pi\)
0.0390225 + 0.999238i \(0.487576\pi\)
\(660\) −3.53807 −0.137719
\(661\) −25.2346 −0.981510 −0.490755 0.871298i \(-0.663279\pi\)
−0.490755 + 0.871298i \(0.663279\pi\)
\(662\) 10.6950 0.415673
\(663\) 5.21466 0.202521
\(664\) 0.478299 0.0185616
\(665\) 0.379968 0.0147345
\(666\) 13.9588 0.540891
\(667\) 5.60367 0.216975
\(668\) 11.9151 0.461007
\(669\) −2.11040 −0.0815927
\(670\) −4.31306 −0.166628
\(671\) 8.53638 0.329543
\(672\) 1.45192 0.0560092
\(673\) −22.6212 −0.871985 −0.435992 0.899950i \(-0.643603\pi\)
−0.435992 + 0.899950i \(0.643603\pi\)
\(674\) 22.8677 0.880833
\(675\) 3.88859 0.149672
\(676\) −10.9172 −0.419893
\(677\) −31.7848 −1.22159 −0.610795 0.791789i \(-0.709150\pi\)
−0.610795 + 0.791789i \(0.709150\pi\)
\(678\) −4.43855 −0.170462
\(679\) 8.68880 0.333446
\(680\) −5.11077 −0.195989
\(681\) 0.328473 0.0125871
\(682\) −50.0351 −1.91594
\(683\) 10.5366 0.403172 0.201586 0.979471i \(-0.435390\pi\)
0.201586 + 0.979471i \(0.435390\pi\)
\(684\) 0.462581 0.0176872
\(685\) −23.0925 −0.882319
\(686\) 20.0899 0.767035
\(687\) −4.06182 −0.154968
\(688\) 2.86150 0.109094
\(689\) 14.2401 0.542503
\(690\) 1.72996 0.0658585
\(691\) 40.7628 1.55069 0.775345 0.631538i \(-0.217576\pi\)
0.775345 + 0.631538i \(0.217576\pi\)
\(692\) 7.26378 0.276127
\(693\) 25.6946 0.976056
\(694\) 16.6582 0.632336
\(695\) −13.6405 −0.517415
\(696\) 1.61909 0.0613715
\(697\) −13.6502 −0.517038
\(698\) −19.1618 −0.725283
\(699\) −5.27671 −0.199583
\(700\) −2.05365 −0.0776206
\(701\) −33.0731 −1.24916 −0.624578 0.780963i \(-0.714729\pi\)
−0.624578 + 0.780963i \(0.714729\pi\)
\(702\) 5.61197 0.211810
\(703\) 1.03300 0.0389604
\(704\) 5.00436 0.188609
\(705\) 1.05497 0.0397324
\(706\) 1.54088 0.0579918
\(707\) −8.67428 −0.326230
\(708\) 6.92523 0.260266
\(709\) 9.66820 0.363097 0.181548 0.983382i \(-0.441889\pi\)
0.181548 + 0.983382i \(0.441889\pi\)
\(710\) −10.7214 −0.402366
\(711\) −8.59123 −0.322196
\(712\) −7.20336 −0.269957
\(713\) 24.4650 0.916220
\(714\) −7.42045 −0.277703
\(715\) 7.22222 0.270096
\(716\) −3.07473 −0.114908
\(717\) 5.47744 0.204559
\(718\) 36.2403 1.35248
\(719\) −36.2264 −1.35102 −0.675508 0.737353i \(-0.736076\pi\)
−0.675508 + 0.737353i \(0.736076\pi\)
\(720\) −2.50015 −0.0931753
\(721\) 2.57526 0.0959076
\(722\) −18.9658 −0.705833
\(723\) −1.40192 −0.0521381
\(724\) −14.2293 −0.528827
\(725\) −2.29010 −0.0850520
\(726\) −9.92878 −0.368491
\(727\) 23.9662 0.888859 0.444429 0.895814i \(-0.353406\pi\)
0.444429 + 0.895814i \(0.353406\pi\)
\(728\) −2.96380 −0.109846
\(729\) −3.63116 −0.134487
\(730\) −1.68245 −0.0622703
\(731\) −14.6244 −0.540905
\(732\) −1.20599 −0.0445746
\(733\) 47.4317 1.75193 0.875965 0.482374i \(-0.160225\pi\)
0.875965 + 0.482374i \(0.160225\pi\)
\(734\) −34.0183 −1.25564
\(735\) 1.96724 0.0725628
\(736\) −2.44691 −0.0901944
\(737\) −21.5841 −0.795060
\(738\) −6.67759 −0.245805
\(739\) −13.1939 −0.485347 −0.242674 0.970108i \(-0.578024\pi\)
−0.242674 + 0.970108i \(0.578024\pi\)
\(740\) −5.58316 −0.205241
\(741\) 0.188782 0.00693509
\(742\) −20.2635 −0.743898
\(743\) 24.6000 0.902488 0.451244 0.892401i \(-0.350980\pi\)
0.451244 + 0.892401i \(0.350980\pi\)
\(744\) 7.06877 0.259154
\(745\) −1.26679 −0.0464117
\(746\) −1.57188 −0.0575508
\(747\) −1.19582 −0.0437528
\(748\) −25.5761 −0.935155
\(749\) −26.7963 −0.979117
\(750\) −0.706997 −0.0258159
\(751\) −6.01528 −0.219501 −0.109750 0.993959i \(-0.535005\pi\)
−0.109750 + 0.993959i \(0.535005\pi\)
\(752\) −1.49218 −0.0544143
\(753\) 4.93816 0.179957
\(754\) −3.30504 −0.120362
\(755\) −8.57737 −0.312163
\(756\) −7.98580 −0.290441
\(757\) 13.2749 0.482485 0.241242 0.970465i \(-0.422445\pi\)
0.241242 + 0.970465i \(0.422445\pi\)
\(758\) −17.1650 −0.623461
\(759\) 8.65734 0.314242
\(760\) −0.185021 −0.00671142
\(761\) 21.9055 0.794072 0.397036 0.917803i \(-0.370039\pi\)
0.397036 + 0.917803i \(0.370039\pi\)
\(762\) −15.6357 −0.566421
\(763\) 7.43372 0.269119
\(764\) −26.0360 −0.941949
\(765\) 12.7777 0.461979
\(766\) 13.9245 0.503112
\(767\) −14.1364 −0.510436
\(768\) −0.706997 −0.0255116
\(769\) −45.5916 −1.64408 −0.822038 0.569433i \(-0.807163\pi\)
−0.822038 + 0.569433i \(0.807163\pi\)
\(770\) −10.2772 −0.370364
\(771\) −4.56734 −0.164489
\(772\) −15.7653 −0.567407
\(773\) 7.18395 0.258389 0.129194 0.991619i \(-0.458761\pi\)
0.129194 + 0.991619i \(0.458761\pi\)
\(774\) −7.15418 −0.257152
\(775\) −9.99830 −0.359150
\(776\) −4.23091 −0.151881
\(777\) −8.10632 −0.290813
\(778\) −21.5436 −0.772376
\(779\) −0.494167 −0.0177054
\(780\) −1.02033 −0.0365336
\(781\) −53.6536 −1.91988
\(782\) 12.5056 0.447200
\(783\) −8.90526 −0.318248
\(784\) −2.78253 −0.0993761
\(785\) −19.4496 −0.694187
\(786\) 8.46367 0.301889
\(787\) 3.09512 0.110329 0.0551645 0.998477i \(-0.482432\pi\)
0.0551645 + 0.998477i \(0.482432\pi\)
\(788\) 4.70772 0.167706
\(789\) 2.50828 0.0892972
\(790\) 3.43628 0.122257
\(791\) −12.8929 −0.458418
\(792\) −12.5117 −0.444583
\(793\) 2.46177 0.0874201
\(794\) −25.0604 −0.889361
\(795\) −6.97601 −0.247414
\(796\) −22.5777 −0.800245
\(797\) −26.6893 −0.945384 −0.472692 0.881228i \(-0.656718\pi\)
−0.472692 + 0.881228i \(0.656718\pi\)
\(798\) −0.268636 −0.00950963
\(799\) 7.62620 0.269796
\(800\) 1.00000 0.0353553
\(801\) 18.0095 0.636335
\(802\) 9.66917 0.341430
\(803\) −8.41958 −0.297120
\(804\) 3.04932 0.107541
\(805\) 5.02510 0.177111
\(806\) −14.4294 −0.508254
\(807\) 13.1679 0.463533
\(808\) 4.22384 0.148594
\(809\) 3.03665 0.106763 0.0533815 0.998574i \(-0.483000\pi\)
0.0533815 + 0.998574i \(0.483000\pi\)
\(810\) 4.75124 0.166942
\(811\) −19.1322 −0.671822 −0.335911 0.941894i \(-0.609044\pi\)
−0.335911 + 0.941894i \(0.609044\pi\)
\(812\) 4.70305 0.165045
\(813\) 4.17534 0.146436
\(814\) −27.9401 −0.979301
\(815\) −7.83300 −0.274378
\(816\) 3.61330 0.126491
\(817\) −0.529437 −0.0185227
\(818\) 31.5033 1.10149
\(819\) 7.40995 0.258925
\(820\) 2.67087 0.0932708
\(821\) 41.5636 1.45058 0.725290 0.688443i \(-0.241706\pi\)
0.725290 + 0.688443i \(0.241706\pi\)
\(822\) 16.3263 0.569446
\(823\) 7.20870 0.251280 0.125640 0.992076i \(-0.459902\pi\)
0.125640 + 0.992076i \(0.459902\pi\)
\(824\) −1.25399 −0.0436849
\(825\) −3.53807 −0.123180
\(826\) 20.1160 0.699926
\(827\) 26.3246 0.915397 0.457698 0.889108i \(-0.348674\pi\)
0.457698 + 0.889108i \(0.348674\pi\)
\(828\) 6.11766 0.212603
\(829\) −17.0067 −0.590667 −0.295334 0.955394i \(-0.595431\pi\)
−0.295334 + 0.955394i \(0.595431\pi\)
\(830\) 0.478299 0.0166020
\(831\) 6.85626 0.237841
\(832\) 1.44319 0.0500335
\(833\) 14.2209 0.492724
\(834\) 9.64382 0.333938
\(835\) 11.9151 0.412337
\(836\) −0.925911 −0.0320233
\(837\) −38.8793 −1.34387
\(838\) 29.8651 1.03167
\(839\) 48.0681 1.65950 0.829748 0.558138i \(-0.188484\pi\)
0.829748 + 0.558138i \(0.188484\pi\)
\(840\) 1.45192 0.0500961
\(841\) −23.7555 −0.819154
\(842\) −1.24282 −0.0428306
\(843\) −8.81965 −0.303765
\(844\) 10.5796 0.364163
\(845\) −10.9172 −0.375564
\(846\) 3.73069 0.128264
\(847\) −28.8406 −0.990974
\(848\) 9.86709 0.338837
\(849\) −17.9703 −0.616738
\(850\) −5.11077 −0.175298
\(851\) 13.6615 0.468311
\(852\) 7.57998 0.259686
\(853\) −36.5741 −1.25227 −0.626137 0.779713i \(-0.715365\pi\)
−0.626137 + 0.779713i \(0.715365\pi\)
\(854\) −3.50309 −0.119873
\(855\) 0.462581 0.0158199
\(856\) 13.0482 0.445977
\(857\) −4.13912 −0.141390 −0.0706948 0.997498i \(-0.522522\pi\)
−0.0706948 + 0.997498i \(0.522522\pi\)
\(858\) −5.10609 −0.174319
\(859\) 38.0715 1.29898 0.649491 0.760369i \(-0.274982\pi\)
0.649491 + 0.760369i \(0.274982\pi\)
\(860\) 2.86150 0.0975762
\(861\) 3.87790 0.132158
\(862\) 15.0924 0.514049
\(863\) 23.5948 0.803178 0.401589 0.915820i \(-0.368458\pi\)
0.401589 + 0.915820i \(0.368458\pi\)
\(864\) 3.88859 0.132293
\(865\) 7.26378 0.246976
\(866\) 19.3810 0.658593
\(867\) −6.44779 −0.218978
\(868\) 20.5330 0.696935
\(869\) 17.1964 0.583347
\(870\) 1.61909 0.0548924
\(871\) −6.22455 −0.210911
\(872\) −3.61976 −0.122581
\(873\) 10.5779 0.358009
\(874\) 0.452731 0.0153138
\(875\) −2.05365 −0.0694260
\(876\) 1.18949 0.0401891
\(877\) −25.7086 −0.868119 −0.434060 0.900884i \(-0.642919\pi\)
−0.434060 + 0.900884i \(0.642919\pi\)
\(878\) 20.4014 0.688513
\(879\) 6.75310 0.227776
\(880\) 5.00436 0.168697
\(881\) 27.1414 0.914417 0.457209 0.889359i \(-0.348849\pi\)
0.457209 + 0.889359i \(0.348849\pi\)
\(882\) 6.95676 0.234246
\(883\) 6.73581 0.226678 0.113339 0.993556i \(-0.463845\pi\)
0.113339 + 0.993556i \(0.463845\pi\)
\(884\) −7.37579 −0.248075
\(885\) 6.92523 0.232789
\(886\) 20.6581 0.694024
\(887\) 23.6715 0.794810 0.397405 0.917643i \(-0.369911\pi\)
0.397405 + 0.917643i \(0.369911\pi\)
\(888\) 3.94728 0.132462
\(889\) −45.4177 −1.52326
\(890\) −7.20336 −0.241457
\(891\) 23.7769 0.796556
\(892\) 2.98502 0.0999458
\(893\) 0.276085 0.00923884
\(894\) 0.895620 0.0299540
\(895\) −3.07473 −0.102777
\(896\) −2.05365 −0.0686076
\(897\) 2.49666 0.0833609
\(898\) 24.9190 0.831558
\(899\) 22.8971 0.763660
\(900\) −2.50015 −0.0833385
\(901\) −50.4284 −1.68001
\(902\) 13.3660 0.445039
\(903\) 4.15467 0.138259
\(904\) 6.27803 0.208804
\(905\) −14.2293 −0.472998
\(906\) 6.06418 0.201469
\(907\) 11.6296 0.386155 0.193078 0.981183i \(-0.438153\pi\)
0.193078 + 0.981183i \(0.438153\pi\)
\(908\) −0.464604 −0.0154184
\(909\) −10.5603 −0.350261
\(910\) −2.96380 −0.0982489
\(911\) −11.6634 −0.386426 −0.193213 0.981157i \(-0.561891\pi\)
−0.193213 + 0.981157i \(0.561891\pi\)
\(912\) 0.130809 0.00433153
\(913\) 2.39358 0.0792158
\(914\) −13.7300 −0.454149
\(915\) −1.20599 −0.0398688
\(916\) 5.74517 0.189826
\(917\) 24.5848 0.811862
\(918\) −19.8737 −0.655930
\(919\) −6.75251 −0.222745 −0.111372 0.993779i \(-0.535525\pi\)
−0.111372 + 0.993779i \(0.535525\pi\)
\(920\) −2.44691 −0.0806724
\(921\) −10.4032 −0.342798
\(922\) −13.8355 −0.455649
\(923\) −15.4729 −0.509298
\(924\) 7.26594 0.239032
\(925\) −5.58316 −0.183573
\(926\) 20.7694 0.682525
\(927\) 3.13518 0.102973
\(928\) −2.29010 −0.0751761
\(929\) −9.97770 −0.327358 −0.163679 0.986514i \(-0.552336\pi\)
−0.163679 + 0.986514i \(0.552336\pi\)
\(930\) 7.06877 0.231794
\(931\) 0.514827 0.0168728
\(932\) 7.46355 0.244477
\(933\) −3.59000 −0.117531
\(934\) −18.1859 −0.595062
\(935\) −25.5761 −0.836428
\(936\) −3.60819 −0.117937
\(937\) 41.3109 1.34957 0.674785 0.738015i \(-0.264237\pi\)
0.674785 + 0.738015i \(0.264237\pi\)
\(938\) 8.85751 0.289208
\(939\) 3.24817 0.106000
\(940\) −1.49218 −0.0486696
\(941\) 42.5318 1.38650 0.693249 0.720699i \(-0.256179\pi\)
0.693249 + 0.720699i \(0.256179\pi\)
\(942\) 13.7508 0.448026
\(943\) −6.53539 −0.212822
\(944\) −9.79527 −0.318809
\(945\) −7.98580 −0.259778
\(946\) 14.3199 0.465582
\(947\) 24.1694 0.785399 0.392700 0.919667i \(-0.371541\pi\)
0.392700 + 0.919667i \(0.371541\pi\)
\(948\) −2.42944 −0.0789046
\(949\) −2.42809 −0.0788191
\(950\) −0.185021 −0.00600288
\(951\) 14.4125 0.467357
\(952\) 10.4957 0.340168
\(953\) −39.9170 −1.29304 −0.646519 0.762898i \(-0.723776\pi\)
−0.646519 + 0.762898i \(0.723776\pi\)
\(954\) −24.6693 −0.798697
\(955\) −26.0360 −0.842505
\(956\) −7.74748 −0.250571
\(957\) 8.10251 0.261917
\(958\) 29.5437 0.954514
\(959\) 47.4238 1.53140
\(960\) −0.706997 −0.0228182
\(961\) 68.9660 2.22471
\(962\) −8.05754 −0.259786
\(963\) −32.6224 −1.05124
\(964\) 1.98293 0.0638657
\(965\) −15.7653 −0.507504
\(966\) −3.55273 −0.114307
\(967\) 32.3808 1.04130 0.520648 0.853771i \(-0.325690\pi\)
0.520648 + 0.853771i \(0.325690\pi\)
\(968\) 14.0436 0.451378
\(969\) −0.668537 −0.0214765
\(970\) −4.23091 −0.135846
\(971\) 1.62327 0.0520931 0.0260465 0.999661i \(-0.491708\pi\)
0.0260465 + 0.999661i \(0.491708\pi\)
\(972\) −15.0249 −0.481924
\(973\) 28.0129 0.898051
\(974\) 1.39387 0.0446624
\(975\) −1.02033 −0.0326767
\(976\) 1.70579 0.0546010
\(977\) 26.7430 0.855585 0.427792 0.903877i \(-0.359291\pi\)
0.427792 + 0.903877i \(0.359291\pi\)
\(978\) 5.53791 0.177083
\(979\) −36.0482 −1.15210
\(980\) −2.78253 −0.0888847
\(981\) 9.04997 0.288943
\(982\) −31.6266 −1.00924
\(983\) 29.2734 0.933677 0.466839 0.884342i \(-0.345393\pi\)
0.466839 + 0.884342i \(0.345393\pi\)
\(984\) −1.88830 −0.0601967
\(985\) 4.70772 0.150000
\(986\) 11.7042 0.372736
\(987\) −2.16653 −0.0689616
\(988\) −0.267020 −0.00849503
\(989\) −7.00183 −0.222645
\(990\) −12.5117 −0.397647
\(991\) 32.0354 1.01764 0.508820 0.860873i \(-0.330082\pi\)
0.508820 + 0.860873i \(0.330082\pi\)
\(992\) −9.99830 −0.317446
\(993\) −7.56134 −0.239952
\(994\) 22.0179 0.698366
\(995\) −22.5777 −0.715761
\(996\) −0.338156 −0.0107149
\(997\) 32.2423 1.02113 0.510563 0.859841i \(-0.329437\pi\)
0.510563 + 0.859841i \(0.329437\pi\)
\(998\) 11.7470 0.371844
\(999\) −21.7107 −0.686895
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 \(a_p\))