Properties

Label 6010.2.a.c.1.2
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 1.2
Root \(-1.45194\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.45194 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.45194 q^{6} +1.53125 q^{7} +1.00000 q^{8} +3.01199 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.45194 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.45194 q^{6} +1.53125 q^{7} +1.00000 q^{8} +3.01199 q^{9} +1.00000 q^{10} -0.396039 q^{11} -2.45194 q^{12} -1.09276 q^{13} +1.53125 q^{14} -2.45194 q^{15} +1.00000 q^{16} +3.63794 q^{17} +3.01199 q^{18} -2.31419 q^{19} +1.00000 q^{20} -3.75453 q^{21} -0.396039 q^{22} -7.59249 q^{23} -2.45194 q^{24} +1.00000 q^{25} -1.09276 q^{26} -0.0293880 q^{27} +1.53125 q^{28} -0.633968 q^{29} -2.45194 q^{30} -1.51909 q^{31} +1.00000 q^{32} +0.971063 q^{33} +3.63794 q^{34} +1.53125 q^{35} +3.01199 q^{36} -9.28972 q^{37} -2.31419 q^{38} +2.67939 q^{39} +1.00000 q^{40} -8.32601 q^{41} -3.75453 q^{42} +4.30278 q^{43} -0.396039 q^{44} +3.01199 q^{45} -7.59249 q^{46} +1.40081 q^{47} -2.45194 q^{48} -4.65526 q^{49} +1.00000 q^{50} -8.92000 q^{51} -1.09276 q^{52} -3.05413 q^{53} -0.0293880 q^{54} -0.396039 q^{55} +1.53125 q^{56} +5.67424 q^{57} -0.633968 q^{58} -3.82943 q^{59} -2.45194 q^{60} -1.88634 q^{61} -1.51909 q^{62} +4.61211 q^{63} +1.00000 q^{64} -1.09276 q^{65} +0.971063 q^{66} +0.761251 q^{67} +3.63794 q^{68} +18.6163 q^{69} +1.53125 q^{70} +10.9195 q^{71} +3.01199 q^{72} -9.16888 q^{73} -9.28972 q^{74} -2.45194 q^{75} -2.31419 q^{76} -0.606437 q^{77} +2.67939 q^{78} +12.0604 q^{79} +1.00000 q^{80} -8.96390 q^{81} -8.32601 q^{82} +5.18730 q^{83} -3.75453 q^{84} +3.63794 q^{85} +4.30278 q^{86} +1.55445 q^{87} -0.396039 q^{88} +4.52465 q^{89} +3.01199 q^{90} -1.67330 q^{91} -7.59249 q^{92} +3.72471 q^{93} +1.40081 q^{94} -2.31419 q^{95} -2.45194 q^{96} -3.00998 q^{97} -4.65526 q^{98} -1.19287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + O(q^{10}) \) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + 16q^{10} - 14q^{11} - 8q^{12} - 20q^{13} - 10q^{14} - 8q^{15} + 16q^{16} - 27q^{17} - 2q^{18} - 17q^{19} + 16q^{20} - 12q^{21} - 14q^{22} - 9q^{23} - 8q^{24} + 16q^{25} - 20q^{26} - 11q^{27} - 10q^{28} - 23q^{29} - 8q^{30} - 21q^{31} + 16q^{32} - 9q^{33} - 27q^{34} - 10q^{35} - 2q^{36} - 16q^{37} - 17q^{38} - 6q^{39} + 16q^{40} - 35q^{41} - 12q^{42} + 3q^{43} - 14q^{44} - 2q^{45} - 9q^{46} - 25q^{47} - 8q^{48} - 24q^{49} + 16q^{50} - q^{51} - 20q^{52} - 39q^{53} - 11q^{54} - 14q^{55} - 10q^{56} - 6q^{57} - 23q^{58} - 32q^{59} - 8q^{60} - 38q^{61} - 21q^{62} + q^{63} + 16q^{64} - 20q^{65} - 9q^{66} + 5q^{67} - 27q^{68} - 25q^{69} - 10q^{70} - 16q^{71} - 2q^{72} - 17q^{73} - 16q^{74} - 8q^{75} - 17q^{76} - 34q^{77} - 6q^{78} - 40q^{79} + 16q^{80} - 28q^{81} - 35q^{82} - 22q^{83} - 12q^{84} - 27q^{85} + 3q^{86} + 10q^{87} - 14q^{88} - 46q^{89} - 2q^{90} - q^{91} - 9q^{92} + 14q^{93} - 25q^{94} - 17q^{95} - 8q^{96} - 21q^{97} - 24q^{98} + 15q^{99} + O(q^{100}) \)

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
\(3\) −2.45194 −1.41563 −0.707813 0.706400i \(-0.750318\pi\)
−0.707813 + 0.706400i \(0.750318\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.45194 −1.00100
\(7\) 1.53125 0.578759 0.289380 0.957214i \(-0.406551\pi\)
0.289380 + 0.957214i \(0.406551\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.01199 1.00400
\(10\) 1.00000 0.316228
\(11\) −0.396039 −0.119410 −0.0597052 0.998216i \(-0.519016\pi\)
−0.0597052 + 0.998216i \(0.519016\pi\)
\(12\) −2.45194 −0.707813
\(13\) −1.09276 −0.303078 −0.151539 0.988451i \(-0.548423\pi\)
−0.151539 + 0.988451i \(0.548423\pi\)
\(14\) 1.53125 0.409245
\(15\) −2.45194 −0.633087
\(16\) 1.00000 0.250000
\(17\) 3.63794 0.882331 0.441166 0.897426i \(-0.354565\pi\)
0.441166 + 0.897426i \(0.354565\pi\)
\(18\) 3.01199 0.709932
\(19\) −2.31419 −0.530911 −0.265456 0.964123i \(-0.585522\pi\)
−0.265456 + 0.964123i \(0.585522\pi\)
\(20\) 1.00000 0.223607
\(21\) −3.75453 −0.819306
\(22\) −0.396039 −0.0844359
\(23\) −7.59249 −1.58314 −0.791572 0.611076i \(-0.790737\pi\)
−0.791572 + 0.611076i \(0.790737\pi\)
\(24\) −2.45194 −0.500499
\(25\) 1.00000 0.200000
\(26\) −1.09276 −0.214309
\(27\) −0.0293880 −0.00565572
\(28\) 1.53125 0.289380
\(29\) −0.633968 −0.117725 −0.0588624 0.998266i \(-0.518747\pi\)
−0.0588624 + 0.998266i \(0.518747\pi\)
\(30\) −2.45194 −0.447660
\(31\) −1.51909 −0.272837 −0.136418 0.990651i \(-0.543559\pi\)
−0.136418 + 0.990651i \(0.543559\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.971063 0.169040
\(34\) 3.63794 0.623902
\(35\) 1.53125 0.258829
\(36\) 3.01199 0.501998
\(37\) −9.28972 −1.52722 −0.763610 0.645678i \(-0.776575\pi\)
−0.763610 + 0.645678i \(0.776575\pi\)
\(38\) −2.31419 −0.375411
\(39\) 2.67939 0.429045
\(40\) 1.00000 0.158114
\(41\) −8.32601 −1.30030 −0.650152 0.759804i \(-0.725295\pi\)
−0.650152 + 0.759804i \(0.725295\pi\)
\(42\) −3.75453 −0.579337
\(43\) 4.30278 0.656167 0.328084 0.944649i \(-0.393597\pi\)
0.328084 + 0.944649i \(0.393597\pi\)
\(44\) −0.396039 −0.0597052
\(45\) 3.01199 0.449000
\(46\) −7.59249 −1.11945
\(47\) 1.40081 0.204329 0.102164 0.994768i \(-0.467423\pi\)
0.102164 + 0.994768i \(0.467423\pi\)
\(48\) −2.45194 −0.353906
\(49\) −4.65526 −0.665038
\(50\) 1.00000 0.141421
\(51\) −8.92000 −1.24905
\(52\) −1.09276 −0.151539
\(53\) −3.05413 −0.419517 −0.209758 0.977753i \(-0.567268\pi\)
−0.209758 + 0.977753i \(0.567268\pi\)
\(54\) −0.0293880 −0.00399920
\(55\) −0.396039 −0.0534020
\(56\) 1.53125 0.204622
\(57\) 5.67424 0.751571
\(58\) −0.633968 −0.0832440
\(59\) −3.82943 −0.498550 −0.249275 0.968433i \(-0.580192\pi\)
−0.249275 + 0.968433i \(0.580192\pi\)
\(60\) −2.45194 −0.316543
\(61\) −1.88634 −0.241521 −0.120760 0.992682i \(-0.538533\pi\)
−0.120760 + 0.992682i \(0.538533\pi\)
\(62\) −1.51909 −0.192925
\(63\) 4.61211 0.581072
\(64\) 1.00000 0.125000
\(65\) −1.09276 −0.135541
\(66\) 0.971063 0.119530
\(67\) 0.761251 0.0930017 0.0465008 0.998918i \(-0.485193\pi\)
0.0465008 + 0.998918i \(0.485193\pi\)
\(68\) 3.63794 0.441166
\(69\) 18.6163 2.24114
\(70\) 1.53125 0.183020
\(71\) 10.9195 1.29591 0.647955 0.761679i \(-0.275625\pi\)
0.647955 + 0.761679i \(0.275625\pi\)
\(72\) 3.01199 0.354966
\(73\) −9.16888 −1.07314 −0.536568 0.843857i \(-0.680280\pi\)
−0.536568 + 0.843857i \(0.680280\pi\)
\(74\) −9.28972 −1.07991
\(75\) −2.45194 −0.283125
\(76\) −2.31419 −0.265456
\(77\) −0.606437 −0.0691099
\(78\) 2.67939 0.303381
\(79\) 12.0604 1.35690 0.678448 0.734649i \(-0.262653\pi\)
0.678448 + 0.734649i \(0.262653\pi\)
\(80\) 1.00000 0.111803
\(81\) −8.96390 −0.995989
\(82\) −8.32601 −0.919454
\(83\) 5.18730 0.569381 0.284690 0.958620i \(-0.408109\pi\)
0.284690 + 0.958620i \(0.408109\pi\)
\(84\) −3.75453 −0.409653
\(85\) 3.63794 0.394591
\(86\) 4.30278 0.463980
\(87\) 1.55445 0.166654
\(88\) −0.396039 −0.0422179
\(89\) 4.52465 0.479612 0.239806 0.970821i \(-0.422916\pi\)
0.239806 + 0.970821i \(0.422916\pi\)
\(90\) 3.01199 0.317491
\(91\) −1.67330 −0.175409
\(92\) −7.59249 −0.791572
\(93\) 3.72471 0.386235
\(94\) 1.40081 0.144482
\(95\) −2.31419 −0.237431
\(96\) −2.45194 −0.250250
\(97\) −3.00998 −0.305617 −0.152809 0.988256i \(-0.548832\pi\)
−0.152809 + 0.988256i \(0.548832\pi\)
\(98\) −4.65526 −0.470253
\(99\) −1.19287 −0.119887
\(100\) 1.00000 0.100000
\(101\) 0.532308 0.0529667 0.0264833 0.999649i \(-0.491569\pi\)
0.0264833 + 0.999649i \(0.491569\pi\)
\(102\) −8.92000 −0.883212
\(103\) 6.08972 0.600038 0.300019 0.953933i \(-0.403007\pi\)
0.300019 + 0.953933i \(0.403007\pi\)
\(104\) −1.09276 −0.107154
\(105\) −3.75453 −0.366405
\(106\) −3.05413 −0.296643
\(107\) 13.6173 1.31644 0.658219 0.752826i \(-0.271310\pi\)
0.658219 + 0.752826i \(0.271310\pi\)
\(108\) −0.0293880 −0.00282786
\(109\) −9.80852 −0.939486 −0.469743 0.882803i \(-0.655653\pi\)
−0.469743 + 0.882803i \(0.655653\pi\)
\(110\) −0.396039 −0.0377609
\(111\) 22.7778 2.16197
\(112\) 1.53125 0.144690
\(113\) −20.8087 −1.95752 −0.978758 0.205021i \(-0.934274\pi\)
−0.978758 + 0.205021i \(0.934274\pi\)
\(114\) 5.67424 0.531441
\(115\) −7.59249 −0.708004
\(116\) −0.633968 −0.0588624
\(117\) −3.29139 −0.304289
\(118\) −3.82943 −0.352528
\(119\) 5.57062 0.510657
\(120\) −2.45194 −0.223830
\(121\) −10.8432 −0.985741
\(122\) −1.88634 −0.170781
\(123\) 20.4148 1.84074
\(124\) −1.51909 −0.136418
\(125\) 1.00000 0.0894427
\(126\) 4.61211 0.410880
\(127\) −9.69057 −0.859899 −0.429949 0.902853i \(-0.641469\pi\)
−0.429949 + 0.902853i \(0.641469\pi\)
\(128\) 1.00000 0.0883883
\(129\) −10.5501 −0.928887
\(130\) −1.09276 −0.0958418
\(131\) −21.5290 −1.88099 −0.940497 0.339803i \(-0.889640\pi\)
−0.940497 + 0.339803i \(0.889640\pi\)
\(132\) 0.971063 0.0845202
\(133\) −3.54361 −0.307270
\(134\) 0.761251 0.0657621
\(135\) −0.0293880 −0.00252932
\(136\) 3.63794 0.311951
\(137\) −12.2619 −1.04760 −0.523801 0.851841i \(-0.675486\pi\)
−0.523801 + 0.851841i \(0.675486\pi\)
\(138\) 18.6163 1.58472
\(139\) 6.79180 0.576073 0.288036 0.957619i \(-0.406998\pi\)
0.288036 + 0.957619i \(0.406998\pi\)
\(140\) 1.53125 0.129415
\(141\) −3.43469 −0.289253
\(142\) 10.9195 0.916347
\(143\) 0.432778 0.0361907
\(144\) 3.01199 0.250999
\(145\) −0.633968 −0.0526481
\(146\) −9.16888 −0.758822
\(147\) 11.4144 0.941444
\(148\) −9.28972 −0.763610
\(149\) 1.03273 0.0846047 0.0423023 0.999105i \(-0.486531\pi\)
0.0423023 + 0.999105i \(0.486531\pi\)
\(150\) −2.45194 −0.200200
\(151\) −4.34453 −0.353553 −0.176777 0.984251i \(-0.556567\pi\)
−0.176777 + 0.984251i \(0.556567\pi\)
\(152\) −2.31419 −0.187705
\(153\) 10.9574 0.885856
\(154\) −0.606437 −0.0488681
\(155\) −1.51909 −0.122016
\(156\) 2.67939 0.214523
\(157\) 5.37740 0.429163 0.214582 0.976706i \(-0.431161\pi\)
0.214582 + 0.976706i \(0.431161\pi\)
\(158\) 12.0604 0.959470
\(159\) 7.48852 0.593878
\(160\) 1.00000 0.0790569
\(161\) −11.6260 −0.916260
\(162\) −8.96390 −0.704270
\(163\) 14.9767 1.17306 0.586531 0.809927i \(-0.300493\pi\)
0.586531 + 0.809927i \(0.300493\pi\)
\(164\) −8.32601 −0.650152
\(165\) 0.971063 0.0755972
\(166\) 5.18730 0.402613
\(167\) −2.41704 −0.187037 −0.0935183 0.995618i \(-0.529811\pi\)
−0.0935183 + 0.995618i \(0.529811\pi\)
\(168\) −3.75453 −0.289669
\(169\) −11.8059 −0.908144
\(170\) 3.63794 0.279018
\(171\) −6.97030 −0.533032
\(172\) 4.30278 0.328084
\(173\) −11.4142 −0.867808 −0.433904 0.900959i \(-0.642864\pi\)
−0.433904 + 0.900959i \(0.642864\pi\)
\(174\) 1.55445 0.117842
\(175\) 1.53125 0.115752
\(176\) −0.396039 −0.0298526
\(177\) 9.38952 0.705760
\(178\) 4.52465 0.339137
\(179\) −1.20874 −0.0903458 −0.0451729 0.998979i \(-0.514384\pi\)
−0.0451729 + 0.998979i \(0.514384\pi\)
\(180\) 3.01199 0.224500
\(181\) 14.9579 1.11182 0.555908 0.831244i \(-0.312371\pi\)
0.555908 + 0.831244i \(0.312371\pi\)
\(182\) −1.67330 −0.124033
\(183\) 4.62518 0.341903
\(184\) −7.59249 −0.559726
\(185\) −9.28972 −0.682993
\(186\) 3.72471 0.273109
\(187\) −1.44077 −0.105360
\(188\) 1.40081 0.102164
\(189\) −0.0450005 −0.00327330
\(190\) −2.31419 −0.167889
\(191\) −9.94895 −0.719881 −0.359940 0.932975i \(-0.617203\pi\)
−0.359940 + 0.932975i \(0.617203\pi\)
\(192\) −2.45194 −0.176953
\(193\) 25.9678 1.86920 0.934602 0.355694i \(-0.115756\pi\)
0.934602 + 0.355694i \(0.115756\pi\)
\(194\) −3.00998 −0.216104
\(195\) 2.67939 0.191875
\(196\) −4.65526 −0.332519
\(197\) 23.4003 1.66720 0.833602 0.552366i \(-0.186275\pi\)
0.833602 + 0.552366i \(0.186275\pi\)
\(198\) −1.19287 −0.0847732
\(199\) −5.85957 −0.415374 −0.207687 0.978195i \(-0.566594\pi\)
−0.207687 + 0.978195i \(0.566594\pi\)
\(200\) 1.00000 0.0707107
\(201\) −1.86654 −0.131656
\(202\) 0.532308 0.0374531
\(203\) −0.970765 −0.0681344
\(204\) −8.92000 −0.624525
\(205\) −8.32601 −0.581514
\(206\) 6.08972 0.424291
\(207\) −22.8685 −1.58947
\(208\) −1.09276 −0.0757696
\(209\) 0.916510 0.0633963
\(210\) −3.75453 −0.259087
\(211\) −18.4089 −1.26732 −0.633660 0.773612i \(-0.718448\pi\)
−0.633660 + 0.773612i \(0.718448\pi\)
\(212\) −3.05413 −0.209758
\(213\) −26.7740 −1.83452
\(214\) 13.6173 0.930863
\(215\) 4.30278 0.293447
\(216\) −0.0293880 −0.00199960
\(217\) −2.32611 −0.157907
\(218\) −9.80852 −0.664317
\(219\) 22.4815 1.51916
\(220\) −0.396039 −0.0267010
\(221\) −3.97542 −0.267415
\(222\) 22.7778 1.52874
\(223\) −20.6115 −1.38025 −0.690124 0.723691i \(-0.742444\pi\)
−0.690124 + 0.723691i \(0.742444\pi\)
\(224\) 1.53125 0.102311
\(225\) 3.01199 0.200799
\(226\) −20.8087 −1.38417
\(227\) 1.48231 0.0983846 0.0491923 0.998789i \(-0.484335\pi\)
0.0491923 + 0.998789i \(0.484335\pi\)
\(228\) 5.67424 0.375786
\(229\) 16.8575 1.11397 0.556987 0.830521i \(-0.311957\pi\)
0.556987 + 0.830521i \(0.311957\pi\)
\(230\) −7.59249 −0.500634
\(231\) 1.48694 0.0978337
\(232\) −0.633968 −0.0416220
\(233\) 9.60557 0.629281 0.314641 0.949211i \(-0.398116\pi\)
0.314641 + 0.949211i \(0.398116\pi\)
\(234\) −3.29139 −0.215165
\(235\) 1.40081 0.0913786
\(236\) −3.82943 −0.249275
\(237\) −29.5712 −1.92086
\(238\) 5.57062 0.361089
\(239\) 16.5353 1.06958 0.534789 0.844986i \(-0.320391\pi\)
0.534789 + 0.844986i \(0.320391\pi\)
\(240\) −2.45194 −0.158272
\(241\) −12.5932 −0.811197 −0.405599 0.914051i \(-0.632937\pi\)
−0.405599 + 0.914051i \(0.632937\pi\)
\(242\) −10.8432 −0.697024
\(243\) 22.0671 1.41560
\(244\) −1.88634 −0.120760
\(245\) −4.65526 −0.297414
\(246\) 20.4148 1.30160
\(247\) 2.52886 0.160908
\(248\) −1.51909 −0.0964623
\(249\) −12.7189 −0.806030
\(250\) 1.00000 0.0632456
\(251\) −16.6158 −1.04878 −0.524389 0.851479i \(-0.675706\pi\)
−0.524389 + 0.851479i \(0.675706\pi\)
\(252\) 4.61211 0.290536
\(253\) 3.00693 0.189044
\(254\) −9.69057 −0.608040
\(255\) −8.92000 −0.558592
\(256\) 1.00000 0.0625000
\(257\) −9.19197 −0.573379 −0.286690 0.958024i \(-0.592555\pi\)
−0.286690 + 0.958024i \(0.592555\pi\)
\(258\) −10.5501 −0.656822
\(259\) −14.2249 −0.883893
\(260\) −1.09276 −0.0677704
\(261\) −1.90950 −0.118195
\(262\) −21.5290 −1.33006
\(263\) −2.49743 −0.153998 −0.0769990 0.997031i \(-0.524534\pi\)
−0.0769990 + 0.997031i \(0.524534\pi\)
\(264\) 0.971063 0.0597648
\(265\) −3.05413 −0.187614
\(266\) −3.54361 −0.217273
\(267\) −11.0942 −0.678951
\(268\) 0.761251 0.0465008
\(269\) −3.88751 −0.237026 −0.118513 0.992953i \(-0.537813\pi\)
−0.118513 + 0.992953i \(0.537813\pi\)
\(270\) −0.0293880 −0.00178850
\(271\) −30.2193 −1.83569 −0.917846 0.396936i \(-0.870073\pi\)
−0.917846 + 0.396936i \(0.870073\pi\)
\(272\) 3.63794 0.220583
\(273\) 4.10282 0.248314
\(274\) −12.2619 −0.740767
\(275\) −0.396039 −0.0238821
\(276\) 18.6163 1.12057
\(277\) −20.8024 −1.24990 −0.624949 0.780666i \(-0.714880\pi\)
−0.624949 + 0.780666i \(0.714880\pi\)
\(278\) 6.79180 0.407345
\(279\) −4.57548 −0.273927
\(280\) 1.53125 0.0915099
\(281\) −14.8183 −0.883986 −0.441993 0.897019i \(-0.645728\pi\)
−0.441993 + 0.897019i \(0.645728\pi\)
\(282\) −3.43469 −0.204533
\(283\) 16.1605 0.960640 0.480320 0.877093i \(-0.340521\pi\)
0.480320 + 0.877093i \(0.340521\pi\)
\(284\) 10.9195 0.647955
\(285\) 5.67424 0.336113
\(286\) 0.432778 0.0255907
\(287\) −12.7492 −0.752563
\(288\) 3.01199 0.177483
\(289\) −3.76536 −0.221492
\(290\) −0.633968 −0.0372279
\(291\) 7.38027 0.432639
\(292\) −9.16888 −0.536568
\(293\) −23.7155 −1.38548 −0.692738 0.721189i \(-0.743596\pi\)
−0.692738 + 0.721189i \(0.743596\pi\)
\(294\) 11.4144 0.665701
\(295\) −3.82943 −0.222958
\(296\) −9.28972 −0.539954
\(297\) 0.0116388 0.000675352 0
\(298\) 1.03273 0.0598245
\(299\) 8.29681 0.479817
\(300\) −2.45194 −0.141563
\(301\) 6.58864 0.379763
\(302\) −4.34453 −0.250000
\(303\) −1.30519 −0.0749809
\(304\) −2.31419 −0.132728
\(305\) −1.88634 −0.108011
\(306\) 10.9574 0.626395
\(307\) 8.00442 0.456837 0.228418 0.973563i \(-0.426645\pi\)
0.228418 + 0.973563i \(0.426645\pi\)
\(308\) −0.606437 −0.0345549
\(309\) −14.9316 −0.849428
\(310\) −1.51909 −0.0862785
\(311\) −0.0537748 −0.00304929 −0.00152464 0.999999i \(-0.500485\pi\)
−0.00152464 + 0.999999i \(0.500485\pi\)
\(312\) 2.67939 0.151690
\(313\) −1.40462 −0.0793941 −0.0396970 0.999212i \(-0.512639\pi\)
−0.0396970 + 0.999212i \(0.512639\pi\)
\(314\) 5.37740 0.303464
\(315\) 4.61211 0.259863
\(316\) 12.0604 0.678448
\(317\) 22.2009 1.24693 0.623464 0.781852i \(-0.285725\pi\)
0.623464 + 0.781852i \(0.285725\pi\)
\(318\) 7.48852 0.419936
\(319\) 0.251076 0.0140576
\(320\) 1.00000 0.0559017
\(321\) −33.3888 −1.86358
\(322\) −11.6260 −0.647893
\(323\) −8.41889 −0.468439
\(324\) −8.96390 −0.497994
\(325\) −1.09276 −0.0606157
\(326\) 14.9767 0.829480
\(327\) 24.0499 1.32996
\(328\) −8.32601 −0.459727
\(329\) 2.14499 0.118257
\(330\) 0.971063 0.0534553
\(331\) −9.64406 −0.530086 −0.265043 0.964237i \(-0.585386\pi\)
−0.265043 + 0.964237i \(0.585386\pi\)
\(332\) 5.18730 0.284690
\(333\) −27.9805 −1.53332
\(334\) −2.41704 −0.132255
\(335\) 0.761251 0.0415916
\(336\) −3.75453 −0.204827
\(337\) 21.3371 1.16230 0.581152 0.813795i \(-0.302602\pi\)
0.581152 + 0.813795i \(0.302602\pi\)
\(338\) −11.8059 −0.642154
\(339\) 51.0215 2.77111
\(340\) 3.63794 0.197295
\(341\) 0.601620 0.0325795
\(342\) −6.97030 −0.376911
\(343\) −17.8472 −0.963656
\(344\) 4.30278 0.231990
\(345\) 18.6163 1.00227
\(346\) −11.4142 −0.613633
\(347\) −8.03328 −0.431249 −0.215625 0.976476i \(-0.569179\pi\)
−0.215625 + 0.976476i \(0.569179\pi\)
\(348\) 1.55445 0.0833271
\(349\) −29.8503 −1.59785 −0.798925 0.601431i \(-0.794597\pi\)
−0.798925 + 0.601431i \(0.794597\pi\)
\(350\) 1.53125 0.0818489
\(351\) 0.0321142 0.00171413
\(352\) −0.396039 −0.0211090
\(353\) −17.5750 −0.935421 −0.467711 0.883882i \(-0.654921\pi\)
−0.467711 + 0.883882i \(0.654921\pi\)
\(354\) 9.38952 0.499047
\(355\) 10.9195 0.579549
\(356\) 4.52465 0.239806
\(357\) −13.6588 −0.722900
\(358\) −1.20874 −0.0638841
\(359\) −0.327073 −0.0172623 −0.00863113 0.999963i \(-0.502747\pi\)
−0.00863113 + 0.999963i \(0.502747\pi\)
\(360\) 3.01199 0.158746
\(361\) −13.6445 −0.718133
\(362\) 14.9579 0.786172
\(363\) 26.5867 1.39544
\(364\) −1.67330 −0.0877047
\(365\) −9.16888 −0.479921
\(366\) 4.62518 0.241762
\(367\) 2.12995 0.111183 0.0555913 0.998454i \(-0.482296\pi\)
0.0555913 + 0.998454i \(0.482296\pi\)
\(368\) −7.59249 −0.395786
\(369\) −25.0778 −1.30550
\(370\) −9.28972 −0.482949
\(371\) −4.67664 −0.242799
\(372\) 3.72471 0.193117
\(373\) 14.4437 0.747866 0.373933 0.927456i \(-0.378009\pi\)
0.373933 + 0.927456i \(0.378009\pi\)
\(374\) −1.44077 −0.0745004
\(375\) −2.45194 −0.126617
\(376\) 1.40081 0.0722411
\(377\) 0.692777 0.0356798
\(378\) −0.0450005 −0.00231457
\(379\) −0.670819 −0.0344576 −0.0172288 0.999852i \(-0.505484\pi\)
−0.0172288 + 0.999852i \(0.505484\pi\)
\(380\) −2.31419 −0.118715
\(381\) 23.7606 1.21729
\(382\) −9.94895 −0.509033
\(383\) 16.8074 0.858820 0.429410 0.903110i \(-0.358722\pi\)
0.429410 + 0.903110i \(0.358722\pi\)
\(384\) −2.45194 −0.125125
\(385\) −0.606437 −0.0309069
\(386\) 25.9678 1.32173
\(387\) 12.9599 0.658789
\(388\) −3.00998 −0.152809
\(389\) −12.7529 −0.646599 −0.323299 0.946297i \(-0.604792\pi\)
−0.323299 + 0.946297i \(0.604792\pi\)
\(390\) 2.67939 0.135676
\(391\) −27.6211 −1.39686
\(392\) −4.65526 −0.235126
\(393\) 52.7876 2.66278
\(394\) 23.4003 1.17889
\(395\) 12.0604 0.606822
\(396\) −1.19287 −0.0599437
\(397\) −25.8713 −1.29845 −0.649223 0.760598i \(-0.724906\pi\)
−0.649223 + 0.760598i \(0.724906\pi\)
\(398\) −5.85957 −0.293714
\(399\) 8.68870 0.434979
\(400\) 1.00000 0.0500000
\(401\) −28.6031 −1.42837 −0.714186 0.699956i \(-0.753203\pi\)
−0.714186 + 0.699956i \(0.753203\pi\)
\(402\) −1.86654 −0.0930945
\(403\) 1.66001 0.0826909
\(404\) 0.532308 0.0264833
\(405\) −8.96390 −0.445420
\(406\) −0.970765 −0.0481783
\(407\) 3.67909 0.182366
\(408\) −8.92000 −0.441606
\(409\) 14.6563 0.724705 0.362352 0.932041i \(-0.381974\pi\)
0.362352 + 0.932041i \(0.381974\pi\)
\(410\) −8.32601 −0.411192
\(411\) 30.0653 1.48301
\(412\) 6.08972 0.300019
\(413\) −5.86383 −0.288540
\(414\) −22.8685 −1.12392
\(415\) 5.18730 0.254635
\(416\) −1.09276 −0.0535772
\(417\) −16.6530 −0.815503
\(418\) 0.916510 0.0448279
\(419\) −17.9226 −0.875577 −0.437789 0.899078i \(-0.644238\pi\)
−0.437789 + 0.899078i \(0.644238\pi\)
\(420\) −3.75453 −0.183202
\(421\) −22.5700 −1.09999 −0.549997 0.835167i \(-0.685371\pi\)
−0.549997 + 0.835167i \(0.685371\pi\)
\(422\) −18.4089 −0.896130
\(423\) 4.21921 0.205145
\(424\) −3.05413 −0.148322
\(425\) 3.63794 0.176466
\(426\) −26.7740 −1.29720
\(427\) −2.88846 −0.139782
\(428\) 13.6173 0.658219
\(429\) −1.06114 −0.0512325
\(430\) 4.30278 0.207498
\(431\) −32.5987 −1.57022 −0.785112 0.619354i \(-0.787395\pi\)
−0.785112 + 0.619354i \(0.787395\pi\)
\(432\) −0.0293880 −0.00141393
\(433\) 15.0639 0.723927 0.361963 0.932192i \(-0.382107\pi\)
0.361963 + 0.932192i \(0.382107\pi\)
\(434\) −2.32611 −0.111657
\(435\) 1.55445 0.0745301
\(436\) −9.80852 −0.469743
\(437\) 17.5705 0.840509
\(438\) 22.4815 1.07421
\(439\) −14.3218 −0.683541 −0.341771 0.939783i \(-0.611027\pi\)
−0.341771 + 0.939783i \(0.611027\pi\)
\(440\) −0.396039 −0.0188804
\(441\) −14.0216 −0.667695
\(442\) −3.97542 −0.189091
\(443\) −27.0727 −1.28626 −0.643131 0.765756i \(-0.722365\pi\)
−0.643131 + 0.765756i \(0.722365\pi\)
\(444\) 22.7778 1.08099
\(445\) 4.52465 0.214489
\(446\) −20.6115 −0.975983
\(447\) −2.53219 −0.119769
\(448\) 1.53125 0.0723449
\(449\) −15.6995 −0.740906 −0.370453 0.928851i \(-0.620798\pi\)
−0.370453 + 0.928851i \(0.620798\pi\)
\(450\) 3.01199 0.141986
\(451\) 3.29743 0.155270
\(452\) −20.8087 −0.978758
\(453\) 10.6525 0.500499
\(454\) 1.48231 0.0695685
\(455\) −1.67330 −0.0784455
\(456\) 5.67424 0.265721
\(457\) −12.6625 −0.592325 −0.296162 0.955138i \(-0.595707\pi\)
−0.296162 + 0.955138i \(0.595707\pi\)
\(458\) 16.8575 0.787699
\(459\) −0.106912 −0.00499022
\(460\) −7.59249 −0.354002
\(461\) −4.40611 −0.205213 −0.102607 0.994722i \(-0.532718\pi\)
−0.102607 + 0.994722i \(0.532718\pi\)
\(462\) 1.48694 0.0691789
\(463\) −0.442044 −0.0205435 −0.0102718 0.999947i \(-0.503270\pi\)
−0.0102718 + 0.999947i \(0.503270\pi\)
\(464\) −0.633968 −0.0294312
\(465\) 3.72471 0.172729
\(466\) 9.60557 0.444969
\(467\) 9.22001 0.426651 0.213326 0.976981i \(-0.431570\pi\)
0.213326 + 0.976981i \(0.431570\pi\)
\(468\) −3.29139 −0.152145
\(469\) 1.16567 0.0538256
\(470\) 1.40081 0.0646144
\(471\) −13.1850 −0.607534
\(472\) −3.82943 −0.176264
\(473\) −1.70407 −0.0783532
\(474\) −29.5712 −1.35825
\(475\) −2.31419 −0.106182
\(476\) 5.57062 0.255329
\(477\) −9.19899 −0.421193
\(478\) 16.5353 0.756305
\(479\) −37.4477 −1.71103 −0.855514 0.517779i \(-0.826759\pi\)
−0.855514 + 0.517779i \(0.826759\pi\)
\(480\) −2.45194 −0.111915
\(481\) 10.1515 0.462867
\(482\) −12.5932 −0.573603
\(483\) 28.5063 1.29708
\(484\) −10.8432 −0.492871
\(485\) −3.00998 −0.136676
\(486\) 22.0671 1.00098
\(487\) −31.5684 −1.43050 −0.715250 0.698869i \(-0.753687\pi\)
−0.715250 + 0.698869i \(0.753687\pi\)
\(488\) −1.88634 −0.0853905
\(489\) −36.7218 −1.66062
\(490\) −4.65526 −0.210303
\(491\) 33.9877 1.53384 0.766921 0.641741i \(-0.221788\pi\)
0.766921 + 0.641741i \(0.221788\pi\)
\(492\) 20.4148 0.920371
\(493\) −2.30634 −0.103872
\(494\) 2.52886 0.113779
\(495\) −1.19287 −0.0536153
\(496\) −1.51909 −0.0682092
\(497\) 16.7206 0.750020
\(498\) −12.7189 −0.569949
\(499\) 21.0596 0.942756 0.471378 0.881931i \(-0.343757\pi\)
0.471378 + 0.881931i \(0.343757\pi\)
\(500\) 1.00000 0.0447214
\(501\) 5.92644 0.264774
\(502\) −16.6158 −0.741598
\(503\) 24.9741 1.11354 0.556770 0.830667i \(-0.312040\pi\)
0.556770 + 0.830667i \(0.312040\pi\)
\(504\) 4.61211 0.205440
\(505\) 0.532308 0.0236874
\(506\) 3.00693 0.133674
\(507\) 28.9472 1.28559
\(508\) −9.69057 −0.429949
\(509\) 16.0776 0.712629 0.356314 0.934366i \(-0.384033\pi\)
0.356314 + 0.934366i \(0.384033\pi\)
\(510\) −8.92000 −0.394984
\(511\) −14.0399 −0.621088
\(512\) 1.00000 0.0441942
\(513\) 0.0680093 0.00300269
\(514\) −9.19197 −0.405440
\(515\) 6.08972 0.268345
\(516\) −10.5501 −0.464444
\(517\) −0.554775 −0.0243990
\(518\) −14.2249 −0.625007
\(519\) 27.9870 1.22849
\(520\) −1.09276 −0.0479209
\(521\) −5.18769 −0.227277 −0.113638 0.993522i \(-0.536251\pi\)
−0.113638 + 0.993522i \(0.536251\pi\)
\(522\) −1.90950 −0.0835766
\(523\) −19.3734 −0.847141 −0.423570 0.905863i \(-0.639223\pi\)
−0.423570 + 0.905863i \(0.639223\pi\)
\(524\) −21.5290 −0.940497
\(525\) −3.75453 −0.163861
\(526\) −2.49743 −0.108893
\(527\) −5.52637 −0.240732
\(528\) 0.971063 0.0422601
\(529\) 34.6460 1.50635
\(530\) −3.05413 −0.132663
\(531\) −11.5342 −0.500541
\(532\) −3.54361 −0.153635
\(533\) 9.09836 0.394094
\(534\) −11.0942 −0.480091
\(535\) 13.6173 0.588729
\(536\) 0.761251 0.0328811
\(537\) 2.96376 0.127896
\(538\) −3.88751 −0.167602
\(539\) 1.84367 0.0794124
\(540\) −0.0293880 −0.00126466
\(541\) 19.8067 0.851557 0.425778 0.904827i \(-0.360000\pi\)
0.425778 + 0.904827i \(0.360000\pi\)
\(542\) −30.2193 −1.29803
\(543\) −36.6759 −1.57391
\(544\) 3.63794 0.155976
\(545\) −9.80852 −0.420151
\(546\) 4.10282 0.175585
\(547\) 2.93473 0.125480 0.0627399 0.998030i \(-0.480016\pi\)
0.0627399 + 0.998030i \(0.480016\pi\)
\(548\) −12.2619 −0.523801
\(549\) −5.68162 −0.242486
\(550\) −0.396039 −0.0168872
\(551\) 1.46712 0.0625014
\(552\) 18.6163 0.792362
\(553\) 18.4675 0.785316
\(554\) −20.8024 −0.883811
\(555\) 22.7778 0.966863
\(556\) 6.79180 0.288036
\(557\) −25.6017 −1.08478 −0.542389 0.840128i \(-0.682480\pi\)
−0.542389 + 0.840128i \(0.682480\pi\)
\(558\) −4.57548 −0.193695
\(559\) −4.70192 −0.198870
\(560\) 1.53125 0.0647073
\(561\) 3.53267 0.149150
\(562\) −14.8183 −0.625072
\(563\) 11.7753 0.496271 0.248135 0.968725i \(-0.420182\pi\)
0.248135 + 0.968725i \(0.420182\pi\)
\(564\) −3.43469 −0.144627
\(565\) −20.8087 −0.875427
\(566\) 16.1605 0.679275
\(567\) −13.7260 −0.576438
\(568\) 10.9195 0.458173
\(569\) −8.94237 −0.374884 −0.187442 0.982276i \(-0.560020\pi\)
−0.187442 + 0.982276i \(0.560020\pi\)
\(570\) 5.67424 0.237668
\(571\) 35.7012 1.49405 0.747025 0.664796i \(-0.231482\pi\)
0.747025 + 0.664796i \(0.231482\pi\)
\(572\) 0.432778 0.0180953
\(573\) 24.3942 1.01908
\(574\) −12.7492 −0.532142
\(575\) −7.59249 −0.316629
\(576\) 3.01199 0.125499
\(577\) 24.9421 1.03835 0.519176 0.854668i \(-0.326239\pi\)
0.519176 + 0.854668i \(0.326239\pi\)
\(578\) −3.76536 −0.156618
\(579\) −63.6714 −2.64609
\(580\) −0.633968 −0.0263241
\(581\) 7.94308 0.329534
\(582\) 7.38027 0.305922
\(583\) 1.20956 0.0500947
\(584\) −9.16888 −0.379411
\(585\) −3.29139 −0.136082
\(586\) −23.7155 −0.979680
\(587\) −17.1312 −0.707081 −0.353541 0.935419i \(-0.615022\pi\)
−0.353541 + 0.935419i \(0.615022\pi\)
\(588\) 11.4144 0.470722
\(589\) 3.51546 0.144852
\(590\) −3.82943 −0.157655
\(591\) −57.3760 −2.36014
\(592\) −9.28972 −0.381805
\(593\) 12.8189 0.526407 0.263204 0.964740i \(-0.415221\pi\)
0.263204 + 0.964740i \(0.415221\pi\)
\(594\) 0.0116388 0.000477546 0
\(595\) 5.57062 0.228373
\(596\) 1.03273 0.0423023
\(597\) 14.3673 0.588014
\(598\) 8.29681 0.339282
\(599\) 32.3387 1.32132 0.660662 0.750684i \(-0.270276\pi\)
0.660662 + 0.750684i \(0.270276\pi\)
\(600\) −2.45194 −0.100100
\(601\) −1.00000 −0.0407909
\(602\) 6.58864 0.268533
\(603\) 2.29288 0.0933732
\(604\) −4.34453 −0.176777
\(605\) −10.8432 −0.440837
\(606\) −1.30519 −0.0530195
\(607\) 20.5926 0.835829 0.417914 0.908486i \(-0.362761\pi\)
0.417914 + 0.908486i \(0.362761\pi\)
\(608\) −2.31419 −0.0938527
\(609\) 2.38025 0.0964527
\(610\) −1.88634 −0.0763756
\(611\) −1.53075 −0.0619276
\(612\) 10.9574 0.442928
\(613\) −7.15441 −0.288964 −0.144482 0.989507i \(-0.546152\pi\)
−0.144482 + 0.989507i \(0.546152\pi\)
\(614\) 8.00442 0.323032
\(615\) 20.4148 0.823205
\(616\) −0.606437 −0.0244340
\(617\) 24.3727 0.981208 0.490604 0.871383i \(-0.336776\pi\)
0.490604 + 0.871383i \(0.336776\pi\)
\(618\) −14.9316 −0.600637
\(619\) 4.67772 0.188014 0.0940068 0.995572i \(-0.470032\pi\)
0.0940068 + 0.995572i \(0.470032\pi\)
\(620\) −1.51909 −0.0610081
\(621\) 0.223128 0.00895383
\(622\) −0.0537748 −0.00215617
\(623\) 6.92839 0.277580
\(624\) 2.67939 0.107261
\(625\) 1.00000 0.0400000
\(626\) −1.40462 −0.0561401
\(627\) −2.24722 −0.0897454
\(628\) 5.37740 0.214582
\(629\) −33.7955 −1.34751
\(630\) 4.61211 0.183751
\(631\) 0.155312 0.00618288 0.00309144 0.999995i \(-0.499016\pi\)
0.00309144 + 0.999995i \(0.499016\pi\)
\(632\) 12.0604 0.479735
\(633\) 45.1374 1.79405
\(634\) 22.2009 0.881711
\(635\) −9.69057 −0.384559
\(636\) 7.48852 0.296939
\(637\) 5.08711 0.201558
\(638\) 0.251076 0.00994020
\(639\) 32.8895 1.30109
\(640\) 1.00000 0.0395285
\(641\) 48.8605 1.92988 0.964938 0.262479i \(-0.0845400\pi\)
0.964938 + 0.262479i \(0.0845400\pi\)
\(642\) −33.3888 −1.31775
\(643\) 1.16722 0.0460305 0.0230153 0.999735i \(-0.492673\pi\)
0.0230153 + 0.999735i \(0.492673\pi\)
\(644\) −11.6260 −0.458130
\(645\) −10.5501 −0.415411
\(646\) −8.41889 −0.331237
\(647\) 24.0041 0.943699 0.471849 0.881679i \(-0.343587\pi\)
0.471849 + 0.881679i \(0.343587\pi\)
\(648\) −8.96390 −0.352135
\(649\) 1.51661 0.0595320
\(650\) −1.09276 −0.0428617
\(651\) 5.70348 0.223537
\(652\) 14.9767 0.586531
\(653\) 13.4784 0.527450 0.263725 0.964598i \(-0.415049\pi\)
0.263725 + 0.964598i \(0.415049\pi\)
\(654\) 24.0499 0.940424
\(655\) −21.5290 −0.841206
\(656\) −8.32601 −0.325076
\(657\) −27.6165 −1.07742
\(658\) 2.14499 0.0836205
\(659\) 1.40035 0.0545499 0.0272750 0.999628i \(-0.491317\pi\)
0.0272750 + 0.999628i \(0.491317\pi\)
\(660\) 0.971063 0.0377986
\(661\) 21.4629 0.834811 0.417406 0.908720i \(-0.362939\pi\)
0.417406 + 0.908720i \(0.362939\pi\)
\(662\) −9.64406 −0.374827
\(663\) 9.74746 0.378560
\(664\) 5.18730 0.201306
\(665\) −3.54361 −0.137415
\(666\) −27.9805 −1.08422
\(667\) 4.81340 0.186375
\(668\) −2.41704 −0.0935183
\(669\) 50.5381 1.95391
\(670\) 0.761251 0.0294097
\(671\) 0.747064 0.0288401
\(672\) −3.75453 −0.144834
\(673\) 37.2551 1.43608 0.718038 0.696004i \(-0.245040\pi\)
0.718038 + 0.696004i \(0.245040\pi\)
\(674\) 21.3371 0.821874
\(675\) −0.0293880 −0.00113114
\(676\) −11.8059 −0.454072
\(677\) −36.9326 −1.41943 −0.709717 0.704487i \(-0.751177\pi\)
−0.709717 + 0.704487i \(0.751177\pi\)
\(678\) 51.0215 1.95947
\(679\) −4.60904 −0.176879
\(680\) 3.63794 0.139509
\(681\) −3.63454 −0.139276
\(682\) 0.601620 0.0230372
\(683\) 50.0879 1.91656 0.958280 0.285830i \(-0.0922692\pi\)
0.958280 + 0.285830i \(0.0922692\pi\)
\(684\) −6.97030 −0.266516
\(685\) −12.2619 −0.468502
\(686\) −17.8472 −0.681408
\(687\) −41.3335 −1.57697
\(688\) 4.30278 0.164042
\(689\) 3.33744 0.127146
\(690\) 18.6163 0.708710
\(691\) −42.7100 −1.62477 −0.812383 0.583124i \(-0.801830\pi\)
−0.812383 + 0.583124i \(0.801830\pi\)
\(692\) −11.4142 −0.433904
\(693\) −1.82658 −0.0693860
\(694\) −8.03328 −0.304939
\(695\) 6.79180 0.257628
\(696\) 1.55445 0.0589212
\(697\) −30.2896 −1.14730
\(698\) −29.8503 −1.12985
\(699\) −23.5522 −0.890827
\(700\) 1.53125 0.0578759
\(701\) 20.5609 0.776573 0.388287 0.921539i \(-0.373067\pi\)
0.388287 + 0.921539i \(0.373067\pi\)
\(702\) 0.0321142 0.00121207
\(703\) 21.4981 0.810818
\(704\) −0.396039 −0.0149263
\(705\) −3.43469 −0.129358
\(706\) −17.5750 −0.661443
\(707\) 0.815099 0.0306549
\(708\) 9.38952 0.352880
\(709\) 23.4133 0.879305 0.439653 0.898168i \(-0.355102\pi\)
0.439653 + 0.898168i \(0.355102\pi\)
\(710\) 10.9195 0.409803
\(711\) 36.3256 1.36232
\(712\) 4.52465 0.169568
\(713\) 11.5337 0.431940
\(714\) −13.6588 −0.511167
\(715\) 0.432778 0.0161850
\(716\) −1.20874 −0.0451729
\(717\) −40.5434 −1.51412
\(718\) −0.327073 −0.0122063
\(719\) 0.106141 0.00395838 0.00197919 0.999998i \(-0.499370\pi\)
0.00197919 + 0.999998i \(0.499370\pi\)
\(720\) 3.01199 0.112250
\(721\) 9.32490 0.347277
\(722\) −13.6445 −0.507797
\(723\) 30.8776 1.14835
\(724\) 14.9579 0.555908
\(725\) −0.633968 −0.0235450
\(726\) 26.5867 0.986725
\(727\) −24.5064 −0.908891 −0.454446 0.890774i \(-0.650163\pi\)
−0.454446 + 0.890774i \(0.650163\pi\)
\(728\) −1.67330 −0.0620166
\(729\) −27.2153 −1.00797
\(730\) −9.16888 −0.339356
\(731\) 15.6533 0.578957
\(732\) 4.62518 0.170951
\(733\) 21.9169 0.809517 0.404759 0.914424i \(-0.367356\pi\)
0.404759 + 0.914424i \(0.367356\pi\)
\(734\) 2.12995 0.0786180
\(735\) 11.4144 0.421027
\(736\) −7.59249 −0.279863
\(737\) −0.301486 −0.0111054
\(738\) −25.0778 −0.923127
\(739\) 0.152216 0.00559937 0.00279968 0.999996i \(-0.499109\pi\)
0.00279968 + 0.999996i \(0.499109\pi\)
\(740\) −9.28972 −0.341497
\(741\) −6.20060 −0.227785
\(742\) −4.67664 −0.171685
\(743\) 31.6241 1.16018 0.580089 0.814553i \(-0.303018\pi\)
0.580089 + 0.814553i \(0.303018\pi\)
\(744\) 3.72471 0.136555
\(745\) 1.03273 0.0378364
\(746\) 14.4437 0.528821
\(747\) 15.6241 0.571655
\(748\) −1.44077 −0.0526798
\(749\) 20.8516 0.761901
\(750\) −2.45194 −0.0895320
\(751\) 37.8318 1.38050 0.690251 0.723570i \(-0.257500\pi\)
0.690251 + 0.723570i \(0.257500\pi\)
\(752\) 1.40081 0.0510822
\(753\) 40.7408 1.48468
\(754\) 0.692777 0.0252295
\(755\) −4.34453 −0.158114
\(756\) −0.0450005 −0.00163665
\(757\) 44.2639 1.60880 0.804400 0.594088i \(-0.202487\pi\)
0.804400 + 0.594088i \(0.202487\pi\)
\(758\) −0.670819 −0.0243652
\(759\) −7.37279 −0.267615
\(760\) −2.31419 −0.0839444
\(761\) 9.80467 0.355419 0.177710 0.984083i \(-0.443131\pi\)
0.177710 + 0.984083i \(0.443131\pi\)
\(762\) 23.7606 0.860757
\(763\) −15.0193 −0.543736
\(764\) −9.94895 −0.359940
\(765\) 10.9574 0.396167
\(766\) 16.8074 0.607277
\(767\) 4.18467 0.151100
\(768\) −2.45194 −0.0884766
\(769\) −16.5291 −0.596053 −0.298027 0.954558i \(-0.596328\pi\)
−0.298027 + 0.954558i \(0.596328\pi\)
\(770\) −0.606437 −0.0218545
\(771\) 22.5381 0.811690
\(772\) 25.9678 0.934602
\(773\) −5.81158 −0.209028 −0.104514 0.994523i \(-0.533329\pi\)
−0.104514 + 0.994523i \(0.533329\pi\)
\(774\) 12.9599 0.465834
\(775\) −1.51909 −0.0545673
\(776\) −3.00998 −0.108052
\(777\) 34.8785 1.25126
\(778\) −12.7529 −0.457214
\(779\) 19.2679 0.690346
\(780\) 2.67939 0.0959375
\(781\) −4.32457 −0.154745
\(782\) −27.6211 −0.987728
\(783\) 0.0186310 0.000665819 0
\(784\) −4.65526 −0.166259
\(785\) 5.37740 0.191928
\(786\) 52.7876 1.88287
\(787\) 9.72019 0.346487 0.173244 0.984879i \(-0.444575\pi\)
0.173244 + 0.984879i \(0.444575\pi\)
\(788\) 23.4003 0.833602
\(789\) 6.12353 0.218004
\(790\) 12.0604 0.429088
\(791\) −31.8634 −1.13293
\(792\) −1.19287 −0.0423866
\(793\) 2.06132 0.0731997
\(794\) −25.8713 −0.918140
\(795\) 7.48852 0.265591
\(796\) −5.85957 −0.207687
\(797\) −24.3351 −0.861992 −0.430996 0.902354i \(-0.641838\pi\)
−0.430996 + 0.902354i \(0.641838\pi\)
\(798\) 8.68870 0.307576
\(799\) 5.09606 0.180286
\(800\) 1.00000 0.0353553
\(801\) 13.6282 0.481528
\(802\) −28.6031 −1.01001
\(803\) 3.63124 0.128144
\(804\) −1.86654 −0.0658278
\(805\) −11.6260 −0.409764
\(806\) 1.66001 0.0584713
\(807\) 9.53192 0.335539
\(808\) 0.532308 0.0187265
\(809\) −31.9916 −1.12477 −0.562383 0.826877i \(-0.690115\pi\)
−0.562383 + 0.826877i \(0.690115\pi\)
\(810\) −8.96390 −0.314959
\(811\) 41.0016 1.43976 0.719881 0.694098i \(-0.244197\pi\)
0.719881 + 0.694098i \(0.244197\pi\)
\(812\) −0.970765 −0.0340672
\(813\) 74.0958 2.59865
\(814\) 3.67909 0.128952
\(815\) 14.9767 0.524609
\(816\) −8.92000 −0.312263
\(817\) −9.95743 −0.348366
\(818\) 14.6563 0.512444
\(819\) −5.03995 −0.176110
\(820\) −8.32601 −0.290757
\(821\) 3.01881 0.105357 0.0526786 0.998612i \(-0.483224\pi\)
0.0526786 + 0.998612i \(0.483224\pi\)
\(822\) 30.0653 1.04865
\(823\) 22.0814 0.769711 0.384855 0.922977i \(-0.374251\pi\)
0.384855 + 0.922977i \(0.374251\pi\)
\(824\) 6.08972 0.212145
\(825\) 0.971063 0.0338081
\(826\) −5.86383 −0.204029
\(827\) 4.29652 0.149405 0.0747024 0.997206i \(-0.476199\pi\)
0.0747024 + 0.997206i \(0.476199\pi\)
\(828\) −22.8685 −0.794735
\(829\) −24.2828 −0.843375 −0.421688 0.906741i \(-0.638562\pi\)
−0.421688 + 0.906741i \(0.638562\pi\)
\(830\) 5.18730 0.180054
\(831\) 51.0062 1.76939
\(832\) −1.09276 −0.0378848
\(833\) −16.9356 −0.586783
\(834\) −16.6530 −0.576648
\(835\) −2.41704 −0.0836453
\(836\) 0.916510 0.0316981
\(837\) 0.0446430 0.00154309
\(838\) −17.9226 −0.619127
\(839\) 15.3535 0.530062 0.265031 0.964240i \(-0.414618\pi\)
0.265031 + 0.964240i \(0.414618\pi\)
\(840\) −3.75453 −0.129544
\(841\) −28.5981 −0.986141
\(842\) −22.5700 −0.777813
\(843\) 36.3335 1.25139
\(844\) −18.4089 −0.633660
\(845\) −11.8059 −0.406134
\(846\) 4.21921 0.145060
\(847\) −16.6036 −0.570507
\(848\) −3.05413 −0.104879
\(849\) −39.6244 −1.35991
\(850\) 3.63794 0.124780
\(851\) 70.5321 2.41781
\(852\) −26.7740 −0.917261
\(853\) 56.1846 1.92372 0.961861 0.273537i \(-0.0881937\pi\)
0.961861 + 0.273537i \(0.0881937\pi\)
\(854\) −2.88846 −0.0988411
\(855\) −6.97030 −0.238379
\(856\) 13.6173 0.465431
\(857\) −0.0467261 −0.00159613 −0.000798066 1.00000i \(-0.500254\pi\)
−0.000798066 1.00000i \(0.500254\pi\)
\(858\) −1.06114 −0.0362268
\(859\) 22.7705 0.776918 0.388459 0.921466i \(-0.373008\pi\)
0.388459 + 0.921466i \(0.373008\pi\)
\(860\) 4.30278 0.146723
\(861\) 31.2603 1.06535
\(862\) −32.5987 −1.11032
\(863\) −7.02499 −0.239134 −0.119567 0.992826i \(-0.538151\pi\)
−0.119567 + 0.992826i \(0.538151\pi\)
\(864\) −0.0293880 −0.000999800 0
\(865\) −11.4142 −0.388095
\(866\) 15.0639 0.511894
\(867\) 9.23241 0.313549
\(868\) −2.32611 −0.0789534
\(869\) −4.77638 −0.162027
\(870\) 1.55445 0.0527007
\(871\) −0.831868 −0.0281868
\(872\) −9.80852 −0.332158
\(873\) −9.06601 −0.306838
\(874\) 17.5705 0.594329
\(875\) 1.53125 0.0517658
\(876\) 22.4815 0.759580
\(877\) 18.7288 0.632427 0.316214 0.948688i \(-0.397588\pi\)
0.316214 + 0.948688i \(0.397588\pi\)
\(878\) −14.3218 −0.483337
\(879\) 58.1490 1.96132
\(880\) −0.396039 −0.0133505
\(881\) 14.8962 0.501867 0.250933 0.968004i \(-0.419263\pi\)
0.250933 + 0.968004i \(0.419263\pi\)
\(882\) −14.0216 −0.472131
\(883\) 4.82170 0.162263 0.0811316 0.996703i \(-0.474147\pi\)
0.0811316 + 0.996703i \(0.474147\pi\)
\(884\) −3.97542 −0.133708
\(885\) 9.38952 0.315625
\(886\) −27.0727 −0.909525
\(887\) −47.6008 −1.59828 −0.799140 0.601145i \(-0.794711\pi\)
−0.799140 + 0.601145i \(0.794711\pi\)
\(888\) 22.7778 0.764372
\(889\) −14.8387 −0.497675
\(890\) 4.52465 0.151667
\(891\) 3.55006 0.118931
\(892\) −20.6115 −0.690124
\(893\) −3.24173 −0.108480
\(894\) −2.53219 −0.0846891
\(895\) −1.20874 −0.0404039
\(896\) 1.53125 0.0511556
\(897\) −20.3432 −0.679241
\(898\) −15.6995 −0.523900
\(899\) 0.963054 0.0321197
\(900\) 3.01199 0.100400
\(901\) −11.1107 −0.370153
\(902\) 3.29743 0.109792
\(903\) −16.1549 −0.537602
\(904\) −20.8087 −0.692086
\(905\) 14.9579 0.497219
\(906\) 10.6525 0.353906
\(907\) −3.99060 −0.132506 −0.0662529 0.997803i \(-0.521104\pi\)
−0.0662529 + 0.997803i \(0.521104\pi\)
\(908\) 1.48231 0.0491923
\(909\) 1.60330 0.0531783
\(910\) −1.67330 −0.0554693
\(911\) −42.2628 −1.40023 −0.700114 0.714031i \(-0.746867\pi\)
−0.700114 + 0.714031i \(0.746867\pi\)
\(912\) 5.67424 0.187893
\(913\) −2.05438 −0.0679900
\(914\) −12.6625 −0.418837
\(915\) 4.62518 0.152904
\(916\) 16.8575 0.556987
\(917\) −32.9663 −1.08864
\(918\) −0.106912 −0.00352862
\(919\) 14.7126 0.485323 0.242662 0.970111i \(-0.421980\pi\)
0.242662 + 0.970111i \(0.421980\pi\)
\(920\) −7.59249 −0.250317
\(921\) −19.6263 −0.646709
\(922\) −4.40611 −0.145108
\(923\) −11.9325 −0.392762
\(924\) 1.48694 0.0489169
\(925\) −9.28972 −0.305444
\(926\) −0.442044 −0.0145265
\(927\) 18.3421 0.602435
\(928\) −0.633968 −0.0208110
\(929\) −38.6413 −1.26778 −0.633890 0.773423i \(-0.718543\pi\)
−0.633890 + 0.773423i \(0.718543\pi\)
\(930\) 3.72471 0.122138
\(931\) 10.7732 0.353076
\(932\) 9.60557 0.314641
\(933\) 0.131852 0.00431665
\(934\) 9.22001 0.301688
\(935\) −1.44077 −0.0471182
\(936\) −3.29139 −0.107582
\(937\) 15.2972 0.499739 0.249870 0.968279i \(-0.419612\pi\)
0.249870 + 0.968279i \(0.419612\pi\)
\(938\) 1.16567 0.0380604
\(939\) 3.44405 0.112392
\(940\) 1.40081 0.0456893
\(941\) 10.9774 0.357855 0.178927 0.983862i \(-0.442737\pi\)
0.178927 + 0.983862i \(0.442737\pi\)
\(942\) −13.1850 −0.429592
\(943\) 63.2152 2.05857
\(944\) −3.82943 −0.124637
\(945\) −0.0450005 −0.00146387
\(946\) −1.70407 −0.0554041
\(947\) −8.54937 −0.277817 −0.138909 0.990305i \(-0.544359\pi\)
−0.138909 + 0.990305i \(0.544359\pi\)
\(948\) −29.5712 −0.960428
\(949\) 10.0194 0.325244
\(950\) −2.31419 −0.0750822
\(951\) −54.4352 −1.76518
\(952\) 5.57062 0.180545
\(953\) −38.3295 −1.24161 −0.620806 0.783964i \(-0.713195\pi\)
−0.620806 + 0.783964i \(0.713195\pi\)
\(954\) −9.19899 −0.297828
\(955\) −9.94895 −0.321941
\(956\) 16.5353 0.534789
\(957\) −0.615623 −0.0199003
\(958\) −37.4477 −1.20988
\(959\) −18.7760 −0.606310
\(960\) −2.45194 −0.0791359
\(961\) −28.6924 −0.925560
\(962\) 10.1515 0.327297
\(963\) 41.0152 1.32170
\(964\) −12.5932 −0.405599
\(965\) 25.9678 0.835934
\(966\) 28.5063 0.917174
\(967\) 58.2218 1.87229 0.936144 0.351618i \(-0.114368\pi\)
0.936144 + 0.351618i \(0.114368\pi\)
\(968\) −10.8432 −0.348512
\(969\) 20.6426 0.663135
\(970\) −3.00998 −0.0966446
\(971\) −28.4335 −0.912473 −0.456237 0.889858i \(-0.650803\pi\)
−0.456237 + 0.889858i \(0.650803\pi\)
\(972\) 22.0671 0.707801
\(973\) 10.4000 0.333408
\(974\) −31.5684 −1.01152
\(975\) 2.67939 0.0858091
\(976\) −1.88634 −0.0603802
\(977\) 16.0515 0.513533 0.256766 0.966473i \(-0.417343\pi\)
0.256766 + 0.966473i \(0.417343\pi\)
\(978\) −36.7218 −1.17423
\(979\) −1.79194 −0.0572707
\(980\) −4.65526 −0.148707
\(981\) −29.5431 −0.943239
\(982\) 33.9877 1.08459
\(983\) −41.7868 −1.33279 −0.666396 0.745598i \(-0.732164\pi\)
−0.666396 + 0.745598i \(0.732164\pi\)
\(984\) 20.4148 0.650801
\(985\) 23.4003 0.745596
\(986\) −2.30634 −0.0734488
\(987\) −5.25938 −0.167408
\(988\) 2.52886 0.0804538
\(989\) −32.6688 −1.03881
\(990\) −1.19287 −0.0379117
\(991\) −7.71703 −0.245140 −0.122570 0.992460i \(-0.539114\pi\)
−0.122570 + 0.992460i \(0.539114\pi\)
\(992\) −1.51909 −0.0482312
\(993\) 23.6466 0.750403
\(994\) 16.7206 0.530344
\(995\) −5.85957 −0.185761
\(996\) −12.7189 −0.403015
\(997\) 12.5044 0.396020 0.198010 0.980200i \(-0.436552\pi\)
0.198010 + 0.980200i \(0.436552\pi\)
\(998\) 21.0596 0.666629
\(999\) 0.273006 0.00863753
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 \(a_p\))