Properties

Label 6001.2.a.b.1.6
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.68479 q^{2}\) \(+0.238039 q^{3}\) \(+5.20809 q^{4}\) \(-3.86690 q^{5}\) \(-0.639084 q^{6}\) \(+2.11314 q^{7}\) \(-8.61305 q^{8}\) \(-2.94334 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.68479 q^{2}\) \(+0.238039 q^{3}\) \(+5.20809 q^{4}\) \(-3.86690 q^{5}\) \(-0.639084 q^{6}\) \(+2.11314 q^{7}\) \(-8.61305 q^{8}\) \(-2.94334 q^{9}\) \(+10.3818 q^{10}\) \(-3.07520 q^{11}\) \(+1.23973 q^{12}\) \(-2.57965 q^{13}\) \(-5.67334 q^{14}\) \(-0.920473 q^{15}\) \(+12.7080 q^{16}\) \(+1.00000 q^{17}\) \(+7.90224 q^{18}\) \(+3.49754 q^{19}\) \(-20.1392 q^{20}\) \(+0.503010 q^{21}\) \(+8.25627 q^{22}\) \(-4.35397 q^{23}\) \(-2.05024 q^{24}\) \(+9.95295 q^{25}\) \(+6.92582 q^{26}\) \(-1.41474 q^{27}\) \(+11.0054 q^{28}\) \(+2.16159 q^{29}\) \(+2.47128 q^{30}\) \(-0.560311 q^{31}\) \(-16.8923 q^{32}\) \(-0.732017 q^{33}\) \(-2.68479 q^{34}\) \(-8.17132 q^{35}\) \(-15.3292 q^{36}\) \(-2.70142 q^{37}\) \(-9.39015 q^{38}\) \(-0.614057 q^{39}\) \(+33.3059 q^{40}\) \(-5.50111 q^{41}\) \(-1.35048 q^{42}\) \(+11.4089 q^{43}\) \(-16.0159 q^{44}\) \(+11.3816 q^{45}\) \(+11.6895 q^{46}\) \(-1.32999 q^{47}\) \(+3.02501 q^{48}\) \(-2.53463 q^{49}\) \(-26.7216 q^{50}\) \(+0.238039 q^{51}\) \(-13.4351 q^{52}\) \(+13.2443 q^{53}\) \(+3.79829 q^{54}\) \(+11.8915 q^{55}\) \(-18.2006 q^{56}\) \(+0.832549 q^{57}\) \(-5.80342 q^{58}\) \(+9.14063 q^{59}\) \(-4.79391 q^{60}\) \(-0.467478 q^{61}\) \(+1.50432 q^{62}\) \(-6.21969 q^{63}\) \(+19.9362 q^{64}\) \(+9.97526 q^{65}\) \(+1.96531 q^{66}\) \(-15.2370 q^{67}\) \(+5.20809 q^{68}\) \(-1.03641 q^{69}\) \(+21.9383 q^{70}\) \(+10.1439 q^{71}\) \(+25.3511 q^{72}\) \(+12.4447 q^{73}\) \(+7.25274 q^{74}\) \(+2.36919 q^{75}\) \(+18.2155 q^{76}\) \(-6.49834 q^{77}\) \(+1.64861 q^{78}\) \(-0.828583 q^{79}\) \(-49.1408 q^{80}\) \(+8.49325 q^{81}\) \(+14.7693 q^{82}\) \(+2.00151 q^{83}\) \(+2.61972 q^{84}\) \(-3.86690 q^{85}\) \(-30.6304 q^{86}\) \(+0.514543 q^{87}\) \(+26.4869 q^{88}\) \(+0.0494759 q^{89}\) \(-30.5572 q^{90}\) \(-5.45117 q^{91}\) \(-22.6759 q^{92}\) \(-0.133376 q^{93}\) \(+3.57075 q^{94}\) \(-13.5246 q^{95}\) \(-4.02103 q^{96}\) \(+12.1077 q^{97}\) \(+6.80494 q^{98}\) \(+9.05136 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68479 −1.89843 −0.949216 0.314624i \(-0.898122\pi\)
−0.949216 + 0.314624i \(0.898122\pi\)
\(3\) 0.238039 0.137432 0.0687159 0.997636i \(-0.478110\pi\)
0.0687159 + 0.997636i \(0.478110\pi\)
\(4\) 5.20809 2.60405
\(5\) −3.86690 −1.72933 −0.864666 0.502347i \(-0.832470\pi\)
−0.864666 + 0.502347i \(0.832470\pi\)
\(6\) −0.639084 −0.260905
\(7\) 2.11314 0.798693 0.399346 0.916800i \(-0.369237\pi\)
0.399346 + 0.916800i \(0.369237\pi\)
\(8\) −8.61305 −3.04517
\(9\) −2.94334 −0.981113
\(10\) 10.3818 3.28302
\(11\) −3.07520 −0.927208 −0.463604 0.886042i \(-0.653444\pi\)
−0.463604 + 0.886042i \(0.653444\pi\)
\(12\) 1.23973 0.357879
\(13\) −2.57965 −0.715467 −0.357733 0.933824i \(-0.616450\pi\)
−0.357733 + 0.933824i \(0.616450\pi\)
\(14\) −5.67334 −1.51626
\(15\) −0.920473 −0.237665
\(16\) 12.7080 3.17701
\(17\) 1.00000 0.242536
\(18\) 7.90224 1.86258
\(19\) 3.49754 0.802390 0.401195 0.915993i \(-0.368595\pi\)
0.401195 + 0.915993i \(0.368595\pi\)
\(20\) −20.1392 −4.50326
\(21\) 0.503010 0.109766
\(22\) 8.25627 1.76024
\(23\) −4.35397 −0.907866 −0.453933 0.891036i \(-0.649980\pi\)
−0.453933 + 0.891036i \(0.649980\pi\)
\(24\) −2.05024 −0.418504
\(25\) 9.95295 1.99059
\(26\) 6.92582 1.35827
\(27\) −1.41474 −0.272268
\(28\) 11.0054 2.07983
\(29\) 2.16159 0.401397 0.200699 0.979653i \(-0.435679\pi\)
0.200699 + 0.979653i \(0.435679\pi\)
\(30\) 2.47128 0.451191
\(31\) −0.560311 −0.100635 −0.0503174 0.998733i \(-0.516023\pi\)
−0.0503174 + 0.998733i \(0.516023\pi\)
\(32\) −16.8923 −2.98617
\(33\) −0.732017 −0.127428
\(34\) −2.68479 −0.460438
\(35\) −8.17132 −1.38121
\(36\) −15.3292 −2.55486
\(37\) −2.70142 −0.444110 −0.222055 0.975034i \(-0.571276\pi\)
−0.222055 + 0.975034i \(0.571276\pi\)
\(38\) −9.39015 −1.52328
\(39\) −0.614057 −0.0983278
\(40\) 33.3059 5.26612
\(41\) −5.50111 −0.859129 −0.429565 0.903036i \(-0.641333\pi\)
−0.429565 + 0.903036i \(0.641333\pi\)
\(42\) −1.35048 −0.208383
\(43\) 11.4089 1.73983 0.869917 0.493197i \(-0.164172\pi\)
0.869917 + 0.493197i \(0.164172\pi\)
\(44\) −16.0159 −2.41449
\(45\) 11.3816 1.69667
\(46\) 11.6895 1.72352
\(47\) −1.32999 −0.194000 −0.0969998 0.995284i \(-0.530925\pi\)
−0.0969998 + 0.995284i \(0.530925\pi\)
\(48\) 3.02501 0.436622
\(49\) −2.53463 −0.362090
\(50\) −26.7216 −3.77900
\(51\) 0.238039 0.0333321
\(52\) −13.4351 −1.86311
\(53\) 13.2443 1.81925 0.909624 0.415433i \(-0.136370\pi\)
0.909624 + 0.415433i \(0.136370\pi\)
\(54\) 3.79829 0.516882
\(55\) 11.8915 1.60345
\(56\) −18.2006 −2.43216
\(57\) 0.832549 0.110274
\(58\) −5.80342 −0.762026
\(59\) 9.14063 1.19001 0.595004 0.803723i \(-0.297150\pi\)
0.595004 + 0.803723i \(0.297150\pi\)
\(60\) −4.79391 −0.618891
\(61\) −0.467478 −0.0598544 −0.0299272 0.999552i \(-0.509528\pi\)
−0.0299272 + 0.999552i \(0.509528\pi\)
\(62\) 1.50432 0.191048
\(63\) −6.21969 −0.783608
\(64\) 19.9362 2.49203
\(65\) 9.97526 1.23728
\(66\) 1.96531 0.241913
\(67\) −15.2370 −1.86150 −0.930751 0.365655i \(-0.880845\pi\)
−0.930751 + 0.365655i \(0.880845\pi\)
\(68\) 5.20809 0.631574
\(69\) −1.03641 −0.124770
\(70\) 21.9383 2.62213
\(71\) 10.1439 1.20386 0.601930 0.798549i \(-0.294399\pi\)
0.601930 + 0.798549i \(0.294399\pi\)
\(72\) 25.3511 2.98766
\(73\) 12.4447 1.45654 0.728269 0.685292i \(-0.240325\pi\)
0.728269 + 0.685292i \(0.240325\pi\)
\(74\) 7.25274 0.843113
\(75\) 2.36919 0.273570
\(76\) 18.2155 2.08946
\(77\) −6.49834 −0.740555
\(78\) 1.64861 0.186669
\(79\) −0.828583 −0.0932229 −0.0466115 0.998913i \(-0.514842\pi\)
−0.0466115 + 0.998913i \(0.514842\pi\)
\(80\) −49.1408 −5.49411
\(81\) 8.49325 0.943694
\(82\) 14.7693 1.63100
\(83\) 2.00151 0.219695 0.109847 0.993948i \(-0.464964\pi\)
0.109847 + 0.993948i \(0.464964\pi\)
\(84\) 2.61972 0.285835
\(85\) −3.86690 −0.419425
\(86\) −30.6304 −3.30296
\(87\) 0.514543 0.0551647
\(88\) 26.4869 2.82351
\(89\) 0.0494759 0.00524443 0.00262222 0.999997i \(-0.499165\pi\)
0.00262222 + 0.999997i \(0.499165\pi\)
\(90\) −30.5572 −3.22101
\(91\) −5.45117 −0.571438
\(92\) −22.6759 −2.36413
\(93\) −0.133376 −0.0138304
\(94\) 3.57075 0.368295
\(95\) −13.5246 −1.38760
\(96\) −4.02103 −0.410395
\(97\) 12.1077 1.22935 0.614674 0.788782i \(-0.289288\pi\)
0.614674 + 0.788782i \(0.289288\pi\)
\(98\) 6.80494 0.687403
\(99\) 9.05136 0.909696
\(100\) 51.8359 5.18359
\(101\) 9.42112 0.937437 0.468718 0.883348i \(-0.344716\pi\)
0.468718 + 0.883348i \(0.344716\pi\)
\(102\) −0.639084 −0.0632787
\(103\) −10.5738 −1.04187 −0.520936 0.853596i \(-0.674417\pi\)
−0.520936 + 0.853596i \(0.674417\pi\)
\(104\) 22.2187 2.17872
\(105\) −1.94509 −0.189821
\(106\) −35.5582 −3.45372
\(107\) −15.3531 −1.48424 −0.742121 0.670266i \(-0.766180\pi\)
−0.742121 + 0.670266i \(0.766180\pi\)
\(108\) −7.36812 −0.708998
\(109\) −5.61058 −0.537396 −0.268698 0.963224i \(-0.586593\pi\)
−0.268698 + 0.963224i \(0.586593\pi\)
\(110\) −31.9262 −3.04404
\(111\) −0.643042 −0.0610349
\(112\) 26.8539 2.53746
\(113\) −6.10517 −0.574326 −0.287163 0.957882i \(-0.592712\pi\)
−0.287163 + 0.957882i \(0.592712\pi\)
\(114\) −2.23522 −0.209347
\(115\) 16.8364 1.57000
\(116\) 11.2578 1.04526
\(117\) 7.59278 0.701953
\(118\) −24.5407 −2.25915
\(119\) 2.11314 0.193712
\(120\) 7.92809 0.723732
\(121\) −1.54313 −0.140285
\(122\) 1.25508 0.113630
\(123\) −1.30948 −0.118072
\(124\) −2.91815 −0.262058
\(125\) −19.1526 −1.71306
\(126\) 16.6986 1.48763
\(127\) 20.8117 1.84674 0.923371 0.383908i \(-0.125422\pi\)
0.923371 + 0.383908i \(0.125422\pi\)
\(128\) −19.7399 −1.74478
\(129\) 2.71575 0.239109
\(130\) −26.7815 −2.34889
\(131\) 16.8451 1.47176 0.735881 0.677111i \(-0.236768\pi\)
0.735881 + 0.677111i \(0.236768\pi\)
\(132\) −3.81241 −0.331828
\(133\) 7.39079 0.640863
\(134\) 40.9082 3.53393
\(135\) 5.47068 0.470841
\(136\) −8.61305 −0.738563
\(137\) 18.5637 1.58600 0.793000 0.609221i \(-0.208518\pi\)
0.793000 + 0.609221i \(0.208518\pi\)
\(138\) 2.78256 0.236867
\(139\) −12.9589 −1.09916 −0.549579 0.835442i \(-0.685212\pi\)
−0.549579 + 0.835442i \(0.685212\pi\)
\(140\) −42.5570 −3.59672
\(141\) −0.316590 −0.0266617
\(142\) −27.2343 −2.28545
\(143\) 7.93295 0.663387
\(144\) −37.4041 −3.11701
\(145\) −8.35866 −0.694149
\(146\) −33.4113 −2.76514
\(147\) −0.603339 −0.0497626
\(148\) −14.0692 −1.15648
\(149\) −8.90355 −0.729407 −0.364703 0.931124i \(-0.618830\pi\)
−0.364703 + 0.931124i \(0.618830\pi\)
\(150\) −6.36077 −0.519355
\(151\) −15.2701 −1.24266 −0.621331 0.783548i \(-0.713408\pi\)
−0.621331 + 0.783548i \(0.713408\pi\)
\(152\) −30.1245 −2.44342
\(153\) −2.94334 −0.237955
\(154\) 17.4467 1.40589
\(155\) 2.16667 0.174031
\(156\) −3.19807 −0.256050
\(157\) 6.45498 0.515164 0.257582 0.966256i \(-0.417074\pi\)
0.257582 + 0.966256i \(0.417074\pi\)
\(158\) 2.22457 0.176977
\(159\) 3.15266 0.250022
\(160\) 65.3210 5.16408
\(161\) −9.20057 −0.725107
\(162\) −22.8026 −1.79154
\(163\) −6.09688 −0.477545 −0.238772 0.971076i \(-0.576745\pi\)
−0.238772 + 0.971076i \(0.576745\pi\)
\(164\) −28.6503 −2.23721
\(165\) 2.83064 0.220365
\(166\) −5.37364 −0.417076
\(167\) −16.3957 −1.26874 −0.634370 0.773029i \(-0.718740\pi\)
−0.634370 + 0.773029i \(0.718740\pi\)
\(168\) −4.33245 −0.334256
\(169\) −6.34540 −0.488108
\(170\) 10.3818 0.796249
\(171\) −10.2944 −0.787235
\(172\) 59.4184 4.53061
\(173\) 2.77710 0.211139 0.105570 0.994412i \(-0.466333\pi\)
0.105570 + 0.994412i \(0.466333\pi\)
\(174\) −1.38144 −0.104727
\(175\) 21.0320 1.58987
\(176\) −39.0798 −2.94575
\(177\) 2.17582 0.163545
\(178\) −0.132832 −0.00995620
\(179\) −5.18285 −0.387384 −0.193692 0.981062i \(-0.562046\pi\)
−0.193692 + 0.981062i \(0.562046\pi\)
\(180\) 59.2765 4.41821
\(181\) −4.53301 −0.336936 −0.168468 0.985707i \(-0.553882\pi\)
−0.168468 + 0.985707i \(0.553882\pi\)
\(182\) 14.6352 1.08484
\(183\) −0.111278 −0.00822590
\(184\) 37.5010 2.76461
\(185\) 10.4461 0.768014
\(186\) 0.358086 0.0262561
\(187\) −3.07520 −0.224881
\(188\) −6.92673 −0.505184
\(189\) −2.98956 −0.217458
\(190\) 36.3108 2.63426
\(191\) −3.88509 −0.281115 −0.140558 0.990073i \(-0.544889\pi\)
−0.140558 + 0.990073i \(0.544889\pi\)
\(192\) 4.74560 0.342484
\(193\) −4.72928 −0.340421 −0.170211 0.985408i \(-0.554445\pi\)
−0.170211 + 0.985408i \(0.554445\pi\)
\(194\) −32.5065 −2.33383
\(195\) 2.37450 0.170041
\(196\) −13.2006 −0.942898
\(197\) 7.03345 0.501113 0.250556 0.968102i \(-0.419386\pi\)
0.250556 + 0.968102i \(0.419386\pi\)
\(198\) −24.3010 −1.72700
\(199\) 22.7510 1.61277 0.806386 0.591389i \(-0.201420\pi\)
0.806386 + 0.591389i \(0.201420\pi\)
\(200\) −85.7253 −6.06169
\(201\) −3.62701 −0.255829
\(202\) −25.2937 −1.77966
\(203\) 4.56775 0.320593
\(204\) 1.23973 0.0867983
\(205\) 21.2723 1.48572
\(206\) 28.3886 1.97792
\(207\) 12.8152 0.890719
\(208\) −32.7823 −2.27305
\(209\) −10.7556 −0.743983
\(210\) 5.22216 0.360363
\(211\) 1.66136 0.114373 0.0571864 0.998364i \(-0.481787\pi\)
0.0571864 + 0.998364i \(0.481787\pi\)
\(212\) 68.9777 4.73741
\(213\) 2.41464 0.165449
\(214\) 41.2199 2.81773
\(215\) −44.1170 −3.00875
\(216\) 12.1853 0.829103
\(217\) −1.18402 −0.0803763
\(218\) 15.0632 1.02021
\(219\) 2.96231 0.200175
\(220\) 61.9321 4.17546
\(221\) −2.57965 −0.173526
\(222\) 1.72643 0.115871
\(223\) 0.425240 0.0284762 0.0142381 0.999899i \(-0.495468\pi\)
0.0142381 + 0.999899i \(0.495468\pi\)
\(224\) −35.6959 −2.38503
\(225\) −29.2949 −1.95299
\(226\) 16.3911 1.09032
\(227\) 15.9773 1.06045 0.530226 0.847856i \(-0.322107\pi\)
0.530226 + 0.847856i \(0.322107\pi\)
\(228\) 4.33599 0.287158
\(229\) −6.01238 −0.397309 −0.198655 0.980070i \(-0.563657\pi\)
−0.198655 + 0.980070i \(0.563657\pi\)
\(230\) −45.2022 −2.98054
\(231\) −1.54686 −0.101776
\(232\) −18.6179 −1.22233
\(233\) −13.6603 −0.894914 −0.447457 0.894305i \(-0.647670\pi\)
−0.447457 + 0.894305i \(0.647670\pi\)
\(234\) −20.3850 −1.33261
\(235\) 5.14296 0.335490
\(236\) 47.6052 3.09884
\(237\) −0.197235 −0.0128118
\(238\) −5.67334 −0.367748
\(239\) −3.46888 −0.224383 −0.112192 0.993687i \(-0.535787\pi\)
−0.112192 + 0.993687i \(0.535787\pi\)
\(240\) −11.6974 −0.755065
\(241\) −19.2299 −1.23871 −0.619354 0.785112i \(-0.712605\pi\)
−0.619354 + 0.785112i \(0.712605\pi\)
\(242\) 4.14298 0.266321
\(243\) 6.26596 0.401961
\(244\) −2.43467 −0.155864
\(245\) 9.80116 0.626173
\(246\) 3.51567 0.224151
\(247\) −9.02242 −0.574083
\(248\) 4.82599 0.306450
\(249\) 0.476438 0.0301930
\(250\) 51.4206 3.25212
\(251\) 16.4286 1.03697 0.518483 0.855088i \(-0.326497\pi\)
0.518483 + 0.855088i \(0.326497\pi\)
\(252\) −32.3927 −2.04055
\(253\) 13.3894 0.841781
\(254\) −55.8751 −3.50592
\(255\) −0.920473 −0.0576423
\(256\) 13.1251 0.820319
\(257\) 2.35761 0.147064 0.0735320 0.997293i \(-0.476573\pi\)
0.0735320 + 0.997293i \(0.476573\pi\)
\(258\) −7.29122 −0.453932
\(259\) −5.70848 −0.354708
\(260\) 51.9521 3.22193
\(261\) −6.36229 −0.393816
\(262\) −45.2255 −2.79404
\(263\) 9.43281 0.581652 0.290826 0.956776i \(-0.406070\pi\)
0.290826 + 0.956776i \(0.406070\pi\)
\(264\) 6.30491 0.388040
\(265\) −51.2145 −3.14608
\(266\) −19.8427 −1.21664
\(267\) 0.0117772 0.000720752 0
\(268\) −79.3559 −4.84744
\(269\) 12.1294 0.739540 0.369770 0.929123i \(-0.379436\pi\)
0.369770 + 0.929123i \(0.379436\pi\)
\(270\) −14.6876 −0.893861
\(271\) −15.1624 −0.921050 −0.460525 0.887647i \(-0.652339\pi\)
−0.460525 + 0.887647i \(0.652339\pi\)
\(272\) 12.7080 0.770539
\(273\) −1.29759 −0.0785337
\(274\) −49.8395 −3.01091
\(275\) −30.6073 −1.84569
\(276\) −5.39775 −0.324906
\(277\) −23.9052 −1.43633 −0.718163 0.695875i \(-0.755017\pi\)
−0.718163 + 0.695875i \(0.755017\pi\)
\(278\) 34.7919 2.08668
\(279\) 1.64918 0.0987340
\(280\) 70.3800 4.20601
\(281\) 4.51360 0.269259 0.134630 0.990896i \(-0.457016\pi\)
0.134630 + 0.990896i \(0.457016\pi\)
\(282\) 0.849978 0.0506154
\(283\) −5.44959 −0.323945 −0.161972 0.986795i \(-0.551786\pi\)
−0.161972 + 0.986795i \(0.551786\pi\)
\(284\) 52.8304 3.13491
\(285\) −3.21939 −0.190700
\(286\) −21.2983 −1.25939
\(287\) −11.6246 −0.686181
\(288\) 49.7198 2.92977
\(289\) 1.00000 0.0588235
\(290\) 22.4413 1.31780
\(291\) 2.88209 0.168951
\(292\) 64.8130 3.79289
\(293\) −29.9248 −1.74822 −0.874112 0.485724i \(-0.838556\pi\)
−0.874112 + 0.485724i \(0.838556\pi\)
\(294\) 1.61984 0.0944710
\(295\) −35.3459 −2.05792
\(296\) 23.2675 1.35239
\(297\) 4.35063 0.252449
\(298\) 23.9041 1.38473
\(299\) 11.2317 0.649548
\(300\) 12.3389 0.712389
\(301\) 24.1086 1.38959
\(302\) 40.9970 2.35911
\(303\) 2.24259 0.128834
\(304\) 44.4469 2.54920
\(305\) 1.80769 0.103508
\(306\) 7.90224 0.451741
\(307\) 5.85617 0.334229 0.167115 0.985937i \(-0.446555\pi\)
0.167115 + 0.985937i \(0.446555\pi\)
\(308\) −33.8440 −1.92844
\(309\) −2.51699 −0.143186
\(310\) −5.81704 −0.330386
\(311\) 2.45023 0.138940 0.0694698 0.997584i \(-0.477869\pi\)
0.0694698 + 0.997584i \(0.477869\pi\)
\(312\) 5.28891 0.299425
\(313\) 11.9936 0.677920 0.338960 0.940801i \(-0.389925\pi\)
0.338960 + 0.940801i \(0.389925\pi\)
\(314\) −17.3303 −0.978004
\(315\) 24.0510 1.35512
\(316\) −4.31534 −0.242757
\(317\) −6.38654 −0.358704 −0.179352 0.983785i \(-0.557400\pi\)
−0.179352 + 0.983785i \(0.557400\pi\)
\(318\) −8.46423 −0.474651
\(319\) −6.64733 −0.372179
\(320\) −77.0915 −4.30955
\(321\) −3.65464 −0.203982
\(322\) 24.7016 1.37657
\(323\) 3.49754 0.194608
\(324\) 44.2336 2.45742
\(325\) −25.6751 −1.42420
\(326\) 16.3688 0.906586
\(327\) −1.33554 −0.0738553
\(328\) 47.3814 2.61620
\(329\) −2.81047 −0.154946
\(330\) −7.59967 −0.418348
\(331\) 8.78069 0.482630 0.241315 0.970447i \(-0.422421\pi\)
0.241315 + 0.970447i \(0.422421\pi\)
\(332\) 10.4241 0.572095
\(333\) 7.95118 0.435722
\(334\) 44.0191 2.40862
\(335\) 58.9202 3.21915
\(336\) 6.39228 0.348727
\(337\) −2.57617 −0.140333 −0.0701664 0.997535i \(-0.522353\pi\)
−0.0701664 + 0.997535i \(0.522353\pi\)
\(338\) 17.0361 0.926639
\(339\) −1.45327 −0.0789307
\(340\) −20.1392 −1.09220
\(341\) 1.72307 0.0933094
\(342\) 27.6384 1.49451
\(343\) −20.1480 −1.08789
\(344\) −98.2651 −5.29810
\(345\) 4.00772 0.215768
\(346\) −7.45593 −0.400833
\(347\) 31.3116 1.68090 0.840448 0.541892i \(-0.182292\pi\)
0.840448 + 0.541892i \(0.182292\pi\)
\(348\) 2.67979 0.143652
\(349\) −17.6009 −0.942154 −0.471077 0.882092i \(-0.656135\pi\)
−0.471077 + 0.882092i \(0.656135\pi\)
\(350\) −56.4665 −3.01826
\(351\) 3.64955 0.194798
\(352\) 51.9473 2.76880
\(353\) 1.00000 0.0532246
\(354\) −5.84163 −0.310479
\(355\) −39.2255 −2.08187
\(356\) 0.257675 0.0136567
\(357\) 0.503010 0.0266221
\(358\) 13.9149 0.735423
\(359\) 26.7136 1.40989 0.704946 0.709261i \(-0.250971\pi\)
0.704946 + 0.709261i \(0.250971\pi\)
\(360\) −98.0304 −5.16665
\(361\) −6.76724 −0.356171
\(362\) 12.1702 0.639651
\(363\) −0.367325 −0.0192796
\(364\) −28.3902 −1.48805
\(365\) −48.1223 −2.51884
\(366\) 0.298758 0.0156163
\(367\) −9.79026 −0.511048 −0.255524 0.966803i \(-0.582248\pi\)
−0.255524 + 0.966803i \(0.582248\pi\)
\(368\) −55.3305 −2.88430
\(369\) 16.1916 0.842903
\(370\) −28.0456 −1.45802
\(371\) 27.9871 1.45302
\(372\) −0.694633 −0.0360150
\(373\) 6.60861 0.342181 0.171091 0.985255i \(-0.445271\pi\)
0.171091 + 0.985255i \(0.445271\pi\)
\(374\) 8.25627 0.426922
\(375\) −4.55905 −0.235429
\(376\) 11.4553 0.590762
\(377\) −5.57615 −0.287186
\(378\) 8.02633 0.412830
\(379\) 9.12903 0.468927 0.234463 0.972125i \(-0.424667\pi\)
0.234463 + 0.972125i \(0.424667\pi\)
\(380\) −70.4376 −3.61337
\(381\) 4.95400 0.253801
\(382\) 10.4306 0.533678
\(383\) −16.5312 −0.844704 −0.422352 0.906432i \(-0.638795\pi\)
−0.422352 + 0.906432i \(0.638795\pi\)
\(384\) −4.69887 −0.239788
\(385\) 25.1285 1.28067
\(386\) 12.6971 0.646267
\(387\) −33.5801 −1.70697
\(388\) 63.0578 3.20128
\(389\) 33.0435 1.67537 0.837685 0.546154i \(-0.183909\pi\)
0.837685 + 0.546154i \(0.183909\pi\)
\(390\) −6.37503 −0.322812
\(391\) −4.35397 −0.220190
\(392\) 21.8309 1.10263
\(393\) 4.00978 0.202267
\(394\) −18.8833 −0.951328
\(395\) 3.20405 0.161213
\(396\) 47.1403 2.36889
\(397\) 10.5817 0.531082 0.265541 0.964100i \(-0.414449\pi\)
0.265541 + 0.964100i \(0.414449\pi\)
\(398\) −61.0815 −3.06174
\(399\) 1.75930 0.0880749
\(400\) 126.483 6.32413
\(401\) −17.3473 −0.866283 −0.433141 0.901326i \(-0.642595\pi\)
−0.433141 + 0.901326i \(0.642595\pi\)
\(402\) 9.73775 0.485675
\(403\) 1.44541 0.0720008
\(404\) 49.0661 2.44113
\(405\) −32.8426 −1.63196
\(406\) −12.2634 −0.608625
\(407\) 8.30740 0.411783
\(408\) −2.05024 −0.101502
\(409\) 21.0245 1.03959 0.519796 0.854290i \(-0.326008\pi\)
0.519796 + 0.854290i \(0.326008\pi\)
\(410\) −57.1116 −2.82054
\(411\) 4.41887 0.217967
\(412\) −55.0696 −2.71308
\(413\) 19.3155 0.950451
\(414\) −34.4062 −1.69097
\(415\) −7.73966 −0.379925
\(416\) 43.5763 2.13650
\(417\) −3.08472 −0.151059
\(418\) 28.8766 1.41240
\(419\) −24.7279 −1.20804 −0.604019 0.796970i \(-0.706435\pi\)
−0.604019 + 0.796970i \(0.706435\pi\)
\(420\) −10.1302 −0.494304
\(421\) 27.1444 1.32294 0.661469 0.749972i \(-0.269933\pi\)
0.661469 + 0.749972i \(0.269933\pi\)
\(422\) −4.46041 −0.217129
\(423\) 3.91462 0.190335
\(424\) −114.074 −5.53993
\(425\) 9.95295 0.482789
\(426\) −6.48281 −0.314093
\(427\) −0.987848 −0.0478053
\(428\) −79.9604 −3.86503
\(429\) 1.88835 0.0911704
\(430\) 118.445 5.71191
\(431\) −38.2489 −1.84239 −0.921193 0.389105i \(-0.872784\pi\)
−0.921193 + 0.389105i \(0.872784\pi\)
\(432\) −17.9786 −0.864998
\(433\) 11.3162 0.543819 0.271910 0.962323i \(-0.412345\pi\)
0.271910 + 0.962323i \(0.412345\pi\)
\(434\) 3.17883 0.152589
\(435\) −1.98969 −0.0953982
\(436\) −29.2204 −1.39940
\(437\) −15.2282 −0.728463
\(438\) −7.95319 −0.380018
\(439\) −29.0056 −1.38436 −0.692181 0.721724i \(-0.743350\pi\)
−0.692181 + 0.721724i \(0.743350\pi\)
\(440\) −102.422 −4.88279
\(441\) 7.46026 0.355251
\(442\) 6.92582 0.329428
\(443\) 13.7757 0.654503 0.327251 0.944937i \(-0.393878\pi\)
0.327251 + 0.944937i \(0.393878\pi\)
\(444\) −3.34902 −0.158938
\(445\) −0.191318 −0.00906937
\(446\) −1.14168 −0.0540602
\(447\) −2.11939 −0.100244
\(448\) 42.1281 1.99037
\(449\) −29.7719 −1.40502 −0.702512 0.711672i \(-0.747938\pi\)
−0.702512 + 0.711672i \(0.747938\pi\)
\(450\) 78.6506 3.70762
\(451\) 16.9170 0.796592
\(452\) −31.7963 −1.49557
\(453\) −3.63487 −0.170781
\(454\) −42.8957 −2.01320
\(455\) 21.0792 0.988206
\(456\) −7.17079 −0.335803
\(457\) 41.3342 1.93353 0.966767 0.255659i \(-0.0822923\pi\)
0.966767 + 0.255659i \(0.0822923\pi\)
\(458\) 16.1420 0.754265
\(459\) −1.41474 −0.0660346
\(460\) 87.6855 4.08836
\(461\) −19.0366 −0.886621 −0.443310 0.896368i \(-0.646196\pi\)
−0.443310 + 0.896368i \(0.646196\pi\)
\(462\) 4.15299 0.193214
\(463\) −4.23576 −0.196852 −0.0984262 0.995144i \(-0.531381\pi\)
−0.0984262 + 0.995144i \(0.531381\pi\)
\(464\) 27.4696 1.27524
\(465\) 0.515751 0.0239174
\(466\) 36.6750 1.69893
\(467\) 15.9953 0.740173 0.370087 0.928997i \(-0.379328\pi\)
0.370087 + 0.928997i \(0.379328\pi\)
\(468\) 39.5439 1.82792
\(469\) −32.1981 −1.48677
\(470\) −13.8078 −0.636904
\(471\) 1.53654 0.0707999
\(472\) −78.7287 −3.62378
\(473\) −35.0846 −1.61319
\(474\) 0.529534 0.0243223
\(475\) 34.8108 1.59723
\(476\) 11.0054 0.504434
\(477\) −38.9825 −1.78489
\(478\) 9.31322 0.425977
\(479\) −2.05775 −0.0940211 −0.0470105 0.998894i \(-0.514969\pi\)
−0.0470105 + 0.998894i \(0.514969\pi\)
\(480\) 15.5489 0.709708
\(481\) 6.96871 0.317746
\(482\) 51.6283 2.35160
\(483\) −2.19009 −0.0996527
\(484\) −8.03678 −0.365308
\(485\) −46.8192 −2.12595
\(486\) −16.8228 −0.763097
\(487\) 31.0243 1.40584 0.702922 0.711267i \(-0.251878\pi\)
0.702922 + 0.711267i \(0.251878\pi\)
\(488\) 4.02641 0.182267
\(489\) −1.45129 −0.0656298
\(490\) −26.3140 −1.18875
\(491\) 26.5417 1.19781 0.598906 0.800820i \(-0.295602\pi\)
0.598906 + 0.800820i \(0.295602\pi\)
\(492\) −6.81988 −0.307464
\(493\) 2.16159 0.0973532
\(494\) 24.2233 1.08986
\(495\) −35.0007 −1.57317
\(496\) −7.12045 −0.319718
\(497\) 21.4355 0.961515
\(498\) −1.27914 −0.0573194
\(499\) −24.5262 −1.09794 −0.548971 0.835842i \(-0.684980\pi\)
−0.548971 + 0.835842i \(0.684980\pi\)
\(500\) −99.7483 −4.46088
\(501\) −3.90282 −0.174365
\(502\) −44.1074 −1.96861
\(503\) −14.8128 −0.660469 −0.330234 0.943899i \(-0.607128\pi\)
−0.330234 + 0.943899i \(0.607128\pi\)
\(504\) 53.5706 2.38622
\(505\) −36.4306 −1.62114
\(506\) −35.9476 −1.59807
\(507\) −1.51045 −0.0670815
\(508\) 108.389 4.80900
\(509\) 15.0841 0.668592 0.334296 0.942468i \(-0.391501\pi\)
0.334296 + 0.942468i \(0.391501\pi\)
\(510\) 2.47128 0.109430
\(511\) 26.2974 1.16333
\(512\) 4.24173 0.187460
\(513\) −4.94812 −0.218465
\(514\) −6.32970 −0.279191
\(515\) 40.8881 1.80174
\(516\) 14.1439 0.622650
\(517\) 4.09000 0.179878
\(518\) 15.3261 0.673389
\(519\) 0.661058 0.0290172
\(520\) −85.9175 −3.76773
\(521\) −20.6022 −0.902600 −0.451300 0.892372i \(-0.649040\pi\)
−0.451300 + 0.892372i \(0.649040\pi\)
\(522\) 17.0814 0.747633
\(523\) 22.2634 0.973511 0.486756 0.873538i \(-0.338180\pi\)
0.486756 + 0.873538i \(0.338180\pi\)
\(524\) 87.7308 3.83254
\(525\) 5.00643 0.218499
\(526\) −25.3251 −1.10423
\(527\) −0.560311 −0.0244075
\(528\) −9.30251 −0.404840
\(529\) −4.04291 −0.175779
\(530\) 137.500 5.97263
\(531\) −26.9040 −1.16753
\(532\) 38.4919 1.66884
\(533\) 14.1910 0.614678
\(534\) −0.0316192 −0.00136830
\(535\) 59.3690 2.56675
\(536\) 131.237 5.66860
\(537\) −1.23372 −0.0532389
\(538\) −32.5648 −1.40397
\(539\) 7.79449 0.335732
\(540\) 28.4918 1.22609
\(541\) 6.46705 0.278040 0.139020 0.990290i \(-0.455605\pi\)
0.139020 + 0.990290i \(0.455605\pi\)
\(542\) 40.7078 1.74855
\(543\) −1.07903 −0.0463057
\(544\) −16.8923 −0.724253
\(545\) 21.6956 0.929336
\(546\) 3.48376 0.149091
\(547\) 4.88597 0.208909 0.104454 0.994530i \(-0.466690\pi\)
0.104454 + 0.994530i \(0.466690\pi\)
\(548\) 96.6813 4.13002
\(549\) 1.37595 0.0587239
\(550\) 82.1742 3.50392
\(551\) 7.56024 0.322077
\(552\) 8.92670 0.379945
\(553\) −1.75091 −0.0744565
\(554\) 64.1805 2.72677
\(555\) 2.48658 0.105550
\(556\) −67.4911 −2.86226
\(557\) −17.4437 −0.739112 −0.369556 0.929208i \(-0.620490\pi\)
−0.369556 + 0.929208i \(0.620490\pi\)
\(558\) −4.42771 −0.187440
\(559\) −29.4309 −1.24479
\(560\) −103.842 −4.38811
\(561\) −0.732017 −0.0309058
\(562\) −12.1181 −0.511170
\(563\) −3.53010 −0.148776 −0.0743881 0.997229i \(-0.523700\pi\)
−0.0743881 + 0.997229i \(0.523700\pi\)
\(564\) −1.64883 −0.0694283
\(565\) 23.6081 0.993201
\(566\) 14.6310 0.614987
\(567\) 17.9474 0.753722
\(568\) −87.3700 −3.66597
\(569\) −42.0708 −1.76370 −0.881849 0.471532i \(-0.843701\pi\)
−0.881849 + 0.471532i \(0.843701\pi\)
\(570\) 8.64338 0.362031
\(571\) 18.6763 0.781579 0.390790 0.920480i \(-0.372202\pi\)
0.390790 + 0.920480i \(0.372202\pi\)
\(572\) 41.3155 1.72749
\(573\) −0.924802 −0.0386341
\(574\) 31.2097 1.30267
\(575\) −43.3349 −1.80719
\(576\) −58.6791 −2.44496
\(577\) −40.5092 −1.68642 −0.843210 0.537584i \(-0.819337\pi\)
−0.843210 + 0.537584i \(0.819337\pi\)
\(578\) −2.68479 −0.111673
\(579\) −1.12575 −0.0467847
\(580\) −43.5327 −1.80760
\(581\) 4.22949 0.175469
\(582\) −7.73781 −0.320743
\(583\) −40.7290 −1.68682
\(584\) −107.187 −4.43541
\(585\) −29.3606 −1.21391
\(586\) 80.3417 3.31889
\(587\) −38.2597 −1.57915 −0.789574 0.613655i \(-0.789698\pi\)
−0.789574 + 0.613655i \(0.789698\pi\)
\(588\) −3.14225 −0.129584
\(589\) −1.95971 −0.0807483
\(590\) 94.8964 3.90682
\(591\) 1.67423 0.0688688
\(592\) −34.3297 −1.41094
\(593\) 27.5094 1.12968 0.564838 0.825202i \(-0.308939\pi\)
0.564838 + 0.825202i \(0.308939\pi\)
\(594\) −11.6805 −0.479257
\(595\) −8.17132 −0.334991
\(596\) −46.3705 −1.89941
\(597\) 5.41561 0.221646
\(598\) −30.1548 −1.23312
\(599\) 8.53509 0.348734 0.174367 0.984681i \(-0.444212\pi\)
0.174367 + 0.984681i \(0.444212\pi\)
\(600\) −20.4059 −0.833069
\(601\) 18.6374 0.760237 0.380118 0.924938i \(-0.375883\pi\)
0.380118 + 0.924938i \(0.375883\pi\)
\(602\) −64.7264 −2.63805
\(603\) 44.8478 1.82634
\(604\) −79.5280 −3.23595
\(605\) 5.96714 0.242599
\(606\) −6.02089 −0.244582
\(607\) −21.3329 −0.865874 −0.432937 0.901424i \(-0.642523\pi\)
−0.432937 + 0.901424i \(0.642523\pi\)
\(608\) −59.0815 −2.39607
\(609\) 1.08730 0.0440597
\(610\) −4.85327 −0.196503
\(611\) 3.43092 0.138800
\(612\) −15.3292 −0.619645
\(613\) −25.1706 −1.01663 −0.508316 0.861171i \(-0.669732\pi\)
−0.508316 + 0.861171i \(0.669732\pi\)
\(614\) −15.7226 −0.634512
\(615\) 5.06363 0.204185
\(616\) 55.9706 2.25512
\(617\) −27.8906 −1.12283 −0.561416 0.827534i \(-0.689743\pi\)
−0.561416 + 0.827534i \(0.689743\pi\)
\(618\) 6.75758 0.271830
\(619\) −5.71695 −0.229784 −0.114892 0.993378i \(-0.536652\pi\)
−0.114892 + 0.993378i \(0.536652\pi\)
\(620\) 11.2842 0.453185
\(621\) 6.15976 0.247183
\(622\) −6.57834 −0.263768
\(623\) 0.104550 0.00418869
\(624\) −7.80347 −0.312389
\(625\) 24.2964 0.971856
\(626\) −32.2004 −1.28699
\(627\) −2.56026 −0.102247
\(628\) 33.6182 1.34151
\(629\) −2.70142 −0.107713
\(630\) −64.5717 −2.57260
\(631\) −20.9831 −0.835324 −0.417662 0.908602i \(-0.637150\pi\)
−0.417662 + 0.908602i \(0.637150\pi\)
\(632\) 7.13663 0.283880
\(633\) 0.395469 0.0157185
\(634\) 17.1465 0.680975
\(635\) −80.4770 −3.19363
\(636\) 16.4194 0.651070
\(637\) 6.53845 0.259063
\(638\) 17.8467 0.706557
\(639\) −29.8569 −1.18112
\(640\) 76.3325 3.01731
\(641\) −31.6807 −1.25131 −0.625655 0.780100i \(-0.715168\pi\)
−0.625655 + 0.780100i \(0.715168\pi\)
\(642\) 9.81193 0.387246
\(643\) −6.19284 −0.244222 −0.122111 0.992516i \(-0.538966\pi\)
−0.122111 + 0.992516i \(0.538966\pi\)
\(644\) −47.9174 −1.88821
\(645\) −10.5015 −0.413498
\(646\) −9.39015 −0.369450
\(647\) 33.9993 1.33665 0.668326 0.743869i \(-0.267011\pi\)
0.668326 + 0.743869i \(0.267011\pi\)
\(648\) −73.1528 −2.87371
\(649\) −28.1093 −1.10339
\(650\) 68.9323 2.70375
\(651\) −0.281842 −0.0110463
\(652\) −31.7531 −1.24355
\(653\) 0.879346 0.0344115 0.0172057 0.999852i \(-0.494523\pi\)
0.0172057 + 0.999852i \(0.494523\pi\)
\(654\) 3.58563 0.140209
\(655\) −65.1383 −2.54516
\(656\) −69.9084 −2.72946
\(657\) −36.6288 −1.42903
\(658\) 7.54551 0.294155
\(659\) −38.8054 −1.51165 −0.755823 0.654776i \(-0.772763\pi\)
−0.755823 + 0.654776i \(0.772763\pi\)
\(660\) 14.7422 0.573841
\(661\) −37.4692 −1.45738 −0.728692 0.684842i \(-0.759871\pi\)
−0.728692 + 0.684842i \(0.759871\pi\)
\(662\) −23.5743 −0.916241
\(663\) −0.614057 −0.0238480
\(664\) −17.2392 −0.669009
\(665\) −28.5795 −1.10827
\(666\) −21.3472 −0.827189
\(667\) −9.41151 −0.364415
\(668\) −85.3905 −3.30386
\(669\) 0.101224 0.00391353
\(670\) −158.188 −6.11135
\(671\) 1.43759 0.0554975
\(672\) −8.49701 −0.327779
\(673\) 24.7502 0.954050 0.477025 0.878890i \(-0.341715\pi\)
0.477025 + 0.878890i \(0.341715\pi\)
\(674\) 6.91647 0.266413
\(675\) −14.0809 −0.541973
\(676\) −33.0474 −1.27106
\(677\) −30.6194 −1.17680 −0.588399 0.808571i \(-0.700242\pi\)
−0.588399 + 0.808571i \(0.700242\pi\)
\(678\) 3.90172 0.149845
\(679\) 25.5852 0.981871
\(680\) 33.3059 1.27722
\(681\) 3.80322 0.145740
\(682\) −4.62608 −0.177142
\(683\) −30.1332 −1.15301 −0.576507 0.817092i \(-0.695585\pi\)
−0.576507 + 0.817092i \(0.695585\pi\)
\(684\) −53.6144 −2.05000
\(685\) −71.7839 −2.74272
\(686\) 54.0932 2.06529
\(687\) −1.43118 −0.0546029
\(688\) 144.984 5.52748
\(689\) −34.1657 −1.30161
\(690\) −10.7599 −0.409621
\(691\) 4.13707 0.157381 0.0786907 0.996899i \(-0.474926\pi\)
0.0786907 + 0.996899i \(0.474926\pi\)
\(692\) 14.4634 0.549816
\(693\) 19.1268 0.726568
\(694\) −84.0651 −3.19107
\(695\) 50.1108 1.90081
\(696\) −4.43178 −0.167986
\(697\) −5.50111 −0.208369
\(698\) 47.2547 1.78862
\(699\) −3.25168 −0.122990
\(700\) 109.537 4.14009
\(701\) −30.3432 −1.14605 −0.573023 0.819539i \(-0.694229\pi\)
−0.573023 + 0.819539i \(0.694229\pi\)
\(702\) −9.79827 −0.369812
\(703\) −9.44830 −0.356350
\(704\) −61.3080 −2.31063
\(705\) 1.22422 0.0461069
\(706\) −2.68479 −0.101043
\(707\) 19.9082 0.748724
\(708\) 11.3319 0.425879
\(709\) −25.7956 −0.968773 −0.484386 0.874854i \(-0.660957\pi\)
−0.484386 + 0.874854i \(0.660957\pi\)
\(710\) 105.312 3.95230
\(711\) 2.43880 0.0914622
\(712\) −0.426139 −0.0159702
\(713\) 2.43958 0.0913629
\(714\) −1.35048 −0.0505403
\(715\) −30.6760 −1.14722
\(716\) −26.9928 −1.00877
\(717\) −0.825728 −0.0308374
\(718\) −71.7205 −2.67659
\(719\) −32.4973 −1.21195 −0.605973 0.795485i \(-0.707216\pi\)
−0.605973 + 0.795485i \(0.707216\pi\)
\(720\) 144.638 5.39034
\(721\) −22.3441 −0.832136
\(722\) 18.1686 0.676166
\(723\) −4.57746 −0.170238
\(724\) −23.6084 −0.877397
\(725\) 21.5142 0.799017
\(726\) 0.986191 0.0366010
\(727\) −22.6400 −0.839673 −0.419836 0.907600i \(-0.637913\pi\)
−0.419836 + 0.907600i \(0.637913\pi\)
\(728\) 46.9512 1.74013
\(729\) −23.9882 −0.888452
\(730\) 129.198 4.78184
\(731\) 11.4089 0.421972
\(732\) −0.579546 −0.0214206
\(733\) 47.9061 1.76945 0.884726 0.466112i \(-0.154346\pi\)
0.884726 + 0.466112i \(0.154346\pi\)
\(734\) 26.2848 0.970190
\(735\) 2.33306 0.0860561
\(736\) 73.5488 2.71104
\(737\) 46.8570 1.72600
\(738\) −43.4711 −1.60019
\(739\) −27.8097 −1.02300 −0.511499 0.859284i \(-0.670910\pi\)
−0.511499 + 0.859284i \(0.670910\pi\)
\(740\) 54.4044 1.99994
\(741\) −2.14769 −0.0788973
\(742\) −75.1396 −2.75846
\(743\) −34.4759 −1.26480 −0.632399 0.774643i \(-0.717930\pi\)
−0.632399 + 0.774643i \(0.717930\pi\)
\(744\) 1.14877 0.0421160
\(745\) 34.4292 1.26139
\(746\) −17.7427 −0.649608
\(747\) −5.89113 −0.215545
\(748\) −16.0159 −0.585601
\(749\) −32.4433 −1.18545
\(750\) 12.2401 0.446945
\(751\) 19.0952 0.696794 0.348397 0.937347i \(-0.386726\pi\)
0.348397 + 0.937347i \(0.386726\pi\)
\(752\) −16.9016 −0.616339
\(753\) 3.91065 0.142512
\(754\) 14.9708 0.545204
\(755\) 59.0479 2.14897
\(756\) −15.5699 −0.566272
\(757\) −37.4154 −1.35988 −0.679942 0.733266i \(-0.737995\pi\)
−0.679942 + 0.733266i \(0.737995\pi\)
\(758\) −24.5095 −0.890226
\(759\) 3.18718 0.115687
\(760\) 116.488 4.22548
\(761\) −43.6149 −1.58104 −0.790519 0.612437i \(-0.790189\pi\)
−0.790519 + 0.612437i \(0.790189\pi\)
\(762\) −13.3004 −0.481824
\(763\) −11.8560 −0.429214
\(764\) −20.2339 −0.732037
\(765\) 11.3816 0.411503
\(766\) 44.3827 1.60361
\(767\) −23.5796 −0.851411
\(768\) 3.12429 0.112738
\(769\) 21.4223 0.772507 0.386254 0.922393i \(-0.373769\pi\)
0.386254 + 0.922393i \(0.373769\pi\)
\(770\) −67.4646 −2.43126
\(771\) 0.561204 0.0202113
\(772\) −24.6305 −0.886473
\(773\) 43.3763 1.56014 0.780068 0.625695i \(-0.215185\pi\)
0.780068 + 0.625695i \(0.215185\pi\)
\(774\) 90.1556 3.24057
\(775\) −5.57674 −0.200322
\(776\) −104.284 −3.74358
\(777\) −1.35884 −0.0487481
\(778\) −88.7147 −3.18058
\(779\) −19.2403 −0.689357
\(780\) 12.3666 0.442796
\(781\) −31.1946 −1.11623
\(782\) 11.6895 0.418016
\(783\) −3.05810 −0.109288
\(784\) −32.2102 −1.15036
\(785\) −24.9608 −0.890889
\(786\) −10.7654 −0.383990
\(787\) 30.3016 1.08013 0.540067 0.841622i \(-0.318399\pi\)
0.540067 + 0.841622i \(0.318399\pi\)
\(788\) 36.6309 1.30492
\(789\) 2.24537 0.0799374
\(790\) −8.60220 −0.306053
\(791\) −12.9011 −0.458710
\(792\) −77.9598 −2.77018
\(793\) 1.20593 0.0428238
\(794\) −28.4097 −1.00822
\(795\) −12.1910 −0.432372
\(796\) 118.489 4.19973
\(797\) 25.9160 0.917992 0.458996 0.888438i \(-0.348209\pi\)
0.458996 + 0.888438i \(0.348209\pi\)
\(798\) −4.72334 −0.167204
\(799\) −1.32999 −0.0470518
\(800\) −168.128 −5.94424
\(801\) −0.145624 −0.00514538
\(802\) 46.5738 1.64458
\(803\) −38.2699 −1.35051
\(804\) −18.8898 −0.666192
\(805\) 35.5777 1.25395
\(806\) −3.88061 −0.136689
\(807\) 2.88726 0.101636
\(808\) −81.1446 −2.85466
\(809\) −17.3893 −0.611375 −0.305687 0.952132i \(-0.598886\pi\)
−0.305687 + 0.952132i \(0.598886\pi\)
\(810\) 88.1754 3.09817
\(811\) −21.9774 −0.771731 −0.385865 0.922555i \(-0.626097\pi\)
−0.385865 + 0.922555i \(0.626097\pi\)
\(812\) 23.7893 0.834840
\(813\) −3.60924 −0.126581
\(814\) −22.3036 −0.781742
\(815\) 23.5761 0.825833
\(816\) 3.02501 0.105896
\(817\) 39.9029 1.39603
\(818\) −56.4462 −1.97360
\(819\) 16.0446 0.560645
\(820\) 110.788 3.86888
\(821\) −50.0768 −1.74769 −0.873845 0.486204i \(-0.838381\pi\)
−0.873845 + 0.486204i \(0.838381\pi\)
\(822\) −11.8637 −0.413795
\(823\) 18.9823 0.661682 0.330841 0.943687i \(-0.392668\pi\)
0.330841 + 0.943687i \(0.392668\pi\)
\(824\) 91.0731 3.17268
\(825\) −7.28573 −0.253657
\(826\) −51.8579 −1.80437
\(827\) 3.61530 0.125716 0.0628581 0.998022i \(-0.479978\pi\)
0.0628581 + 0.998022i \(0.479978\pi\)
\(828\) 66.7428 2.31947
\(829\) −12.6041 −0.437760 −0.218880 0.975752i \(-0.570240\pi\)
−0.218880 + 0.975752i \(0.570240\pi\)
\(830\) 20.7794 0.721262
\(831\) −5.69037 −0.197397
\(832\) −51.4285 −1.78296
\(833\) −2.53463 −0.0878196
\(834\) 8.28182 0.286776
\(835\) 63.4007 2.19407
\(836\) −56.0163 −1.93737
\(837\) 0.792697 0.0273996
\(838\) 66.3893 2.29338
\(839\) −7.50110 −0.258967 −0.129483 0.991582i \(-0.541332\pi\)
−0.129483 + 0.991582i \(0.541332\pi\)
\(840\) 16.7532 0.578040
\(841\) −24.3275 −0.838880
\(842\) −72.8771 −2.51151
\(843\) 1.07441 0.0370048
\(844\) 8.65253 0.297832
\(845\) 24.5370 0.844100
\(846\) −10.5099 −0.361339
\(847\) −3.26086 −0.112044
\(848\) 168.310 5.77977
\(849\) −1.29721 −0.0445203
\(850\) −26.7216 −0.916542
\(851\) 11.7619 0.403193
\(852\) 12.5757 0.430836
\(853\) −42.5662 −1.45744 −0.728719 0.684813i \(-0.759884\pi\)
−0.728719 + 0.684813i \(0.759884\pi\)
\(854\) 2.65216 0.0907552
\(855\) 39.8076 1.36139
\(856\) 132.237 4.51977
\(857\) −37.7156 −1.28834 −0.644170 0.764882i \(-0.722797\pi\)
−0.644170 + 0.764882i \(0.722797\pi\)
\(858\) −5.06982 −0.173081
\(859\) −50.6473 −1.72806 −0.864032 0.503436i \(-0.832069\pi\)
−0.864032 + 0.503436i \(0.832069\pi\)
\(860\) −229.765 −7.83493
\(861\) −2.76711 −0.0943030
\(862\) 102.690 3.49765
\(863\) 43.4209 1.47806 0.739032 0.673670i \(-0.235283\pi\)
0.739032 + 0.673670i \(0.235283\pi\)
\(864\) 23.8983 0.813038
\(865\) −10.7388 −0.365130
\(866\) −30.3815 −1.03240
\(867\) 0.238039 0.00808422
\(868\) −6.16647 −0.209304
\(869\) 2.54806 0.0864371
\(870\) 5.34189 0.181107
\(871\) 39.3063 1.33184
\(872\) 48.3242 1.63646
\(873\) −35.6369 −1.20613
\(874\) 40.8845 1.38294
\(875\) −40.4721 −1.36821
\(876\) 15.4280 0.521264
\(877\) −13.9419 −0.470784 −0.235392 0.971901i \(-0.575637\pi\)
−0.235392 + 0.971901i \(0.575637\pi\)
\(878\) 77.8739 2.62812
\(879\) −7.12326 −0.240262
\(880\) 151.118 5.09418
\(881\) 5.95846 0.200746 0.100373 0.994950i \(-0.467996\pi\)
0.100373 + 0.994950i \(0.467996\pi\)
\(882\) −20.0292 −0.674419
\(883\) −16.8840 −0.568191 −0.284096 0.958796i \(-0.591693\pi\)
−0.284096 + 0.958796i \(0.591693\pi\)
\(884\) −13.4351 −0.451870
\(885\) −8.41370 −0.282824
\(886\) −36.9848 −1.24253
\(887\) −48.0762 −1.61424 −0.807120 0.590388i \(-0.798975\pi\)
−0.807120 + 0.590388i \(0.798975\pi\)
\(888\) 5.53856 0.185862
\(889\) 43.9782 1.47498
\(890\) 0.513650 0.0172176
\(891\) −26.1185 −0.875001
\(892\) 2.21469 0.0741534
\(893\) −4.65170 −0.155663
\(894\) 5.69011 0.190306
\(895\) 20.0416 0.669916
\(896\) −41.7133 −1.39354
\(897\) 2.67359 0.0892685
\(898\) 79.9313 2.66734
\(899\) −1.21116 −0.0403945
\(900\) −152.570 −5.08568
\(901\) 13.2443 0.441232
\(902\) −45.4187 −1.51228
\(903\) 5.73877 0.190974
\(904\) 52.5842 1.74892
\(905\) 17.5287 0.582674
\(906\) 9.75887 0.324217
\(907\) 15.1734 0.503823 0.251911 0.967750i \(-0.418941\pi\)
0.251911 + 0.967750i \(0.418941\pi\)
\(908\) 83.2114 2.76147
\(909\) −27.7295 −0.919731
\(910\) −56.5931 −1.87604
\(911\) −1.95489 −0.0647684 −0.0323842 0.999475i \(-0.510310\pi\)
−0.0323842 + 0.999475i \(0.510310\pi\)
\(912\) 10.5801 0.350341
\(913\) −6.15506 −0.203703
\(914\) −110.974 −3.67068
\(915\) 0.430301 0.0142253
\(916\) −31.3130 −1.03461
\(917\) 35.5961 1.17549
\(918\) 3.79829 0.125362
\(919\) 6.19568 0.204377 0.102188 0.994765i \(-0.467416\pi\)
0.102188 + 0.994765i \(0.467416\pi\)
\(920\) −145.013 −4.78093
\(921\) 1.39400 0.0459337
\(922\) 51.1091 1.68319
\(923\) −26.1677 −0.861322
\(924\) −8.05618 −0.265029
\(925\) −26.8871 −0.884041
\(926\) 11.3721 0.373711
\(927\) 31.1224 1.02219
\(928\) −36.5143 −1.19864
\(929\) 10.1993 0.334628 0.167314 0.985904i \(-0.446491\pi\)
0.167314 + 0.985904i \(0.446491\pi\)
\(930\) −1.38468 −0.0454055
\(931\) −8.86495 −0.290537
\(932\) −71.1440 −2.33040
\(933\) 0.583249 0.0190947
\(934\) −42.9440 −1.40517
\(935\) 11.8915 0.388894
\(936\) −65.3971 −2.13757
\(937\) 38.0288 1.24235 0.621174 0.783673i \(-0.286656\pi\)
0.621174 + 0.783673i \(0.286656\pi\)
\(938\) 86.4450 2.82253
\(939\) 2.85495 0.0931677
\(940\) 26.7850 0.873631
\(941\) −21.3884 −0.697242 −0.348621 0.937264i \(-0.613350\pi\)
−0.348621 + 0.937264i \(0.613350\pi\)
\(942\) −4.12528 −0.134409
\(943\) 23.9517 0.779975
\(944\) 116.160 3.78067
\(945\) 11.5603 0.376058
\(946\) 94.1946 3.06253
\(947\) 52.7187 1.71313 0.856563 0.516042i \(-0.172595\pi\)
0.856563 + 0.516042i \(0.172595\pi\)
\(948\) −1.02722 −0.0333625
\(949\) −32.1029 −1.04210
\(950\) −93.4596 −3.03223
\(951\) −1.52024 −0.0492973
\(952\) −18.2006 −0.589885
\(953\) −34.0793 −1.10394 −0.551968 0.833865i \(-0.686123\pi\)
−0.551968 + 0.833865i \(0.686123\pi\)
\(954\) 104.660 3.38849
\(955\) 15.0233 0.486141
\(956\) −18.0663 −0.584305
\(957\) −1.58232 −0.0511492
\(958\) 5.52463 0.178493
\(959\) 39.2277 1.26673
\(960\) −18.3508 −0.592269
\(961\) −30.6861 −0.989873
\(962\) −18.7095 −0.603219
\(963\) 45.1894 1.45621
\(964\) −100.151 −3.22565
\(965\) 18.2877 0.588701
\(966\) 5.87994 0.189184
\(967\) 53.4542 1.71897 0.859485 0.511161i \(-0.170784\pi\)
0.859485 + 0.511161i \(0.170784\pi\)
\(968\) 13.2911 0.427192
\(969\) 0.832549 0.0267453
\(970\) 125.700 4.03597
\(971\) 10.6313 0.341174 0.170587 0.985343i \(-0.445434\pi\)
0.170587 + 0.985343i \(0.445434\pi\)
\(972\) 32.6337 1.04673
\(973\) −27.3840 −0.877890
\(974\) −83.2936 −2.66890
\(975\) −6.11168 −0.195730
\(976\) −5.94073 −0.190158
\(977\) 33.5430 1.07314 0.536568 0.843857i \(-0.319721\pi\)
0.536568 + 0.843857i \(0.319721\pi\)
\(978\) 3.89642 0.124594
\(979\) −0.152148 −0.00486268
\(980\) 51.0453 1.63058
\(981\) 16.5138 0.527246
\(982\) −71.2590 −2.27396
\(983\) −9.52847 −0.303911 −0.151956 0.988387i \(-0.548557\pi\)
−0.151956 + 0.988387i \(0.548557\pi\)
\(984\) 11.2786 0.359549
\(985\) −27.1977 −0.866590
\(986\) −5.80342 −0.184818
\(987\) −0.669000 −0.0212945
\(988\) −46.9896 −1.49494
\(989\) −49.6739 −1.57954
\(990\) 93.9696 2.98655
\(991\) 51.5442 1.63735 0.818677 0.574254i \(-0.194708\pi\)
0.818677 + 0.574254i \(0.194708\pi\)
\(992\) 9.46495 0.300512
\(993\) 2.09014 0.0663287
\(994\) −57.5499 −1.82537
\(995\) −87.9757 −2.78902
\(996\) 2.48133 0.0786241
\(997\) 32.0275 1.01432 0.507160 0.861852i \(-0.330695\pi\)
0.507160 + 0.861852i \(0.330695\pi\)
\(998\) 65.8475 2.08437
\(999\) 3.82182 0.120917
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 \(a_p\))