Properties

Label 8015.2.a.l.1.51
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.51
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00507 q^{2} -2.97462 q^{3} +2.02029 q^{4} -1.00000 q^{5} -5.96432 q^{6} -1.00000 q^{7} +0.0406892 q^{8} +5.84839 q^{9} +O(q^{10})\) \(q+2.00507 q^{2} -2.97462 q^{3} +2.02029 q^{4} -1.00000 q^{5} -5.96432 q^{6} -1.00000 q^{7} +0.0406892 q^{8} +5.84839 q^{9} -2.00507 q^{10} -4.21808 q^{11} -6.00961 q^{12} +0.537768 q^{13} -2.00507 q^{14} +2.97462 q^{15} -3.95900 q^{16} +5.04173 q^{17} +11.7264 q^{18} -1.80467 q^{19} -2.02029 q^{20} +2.97462 q^{21} -8.45753 q^{22} +0.0595591 q^{23} -0.121035 q^{24} +1.00000 q^{25} +1.07826 q^{26} -8.47289 q^{27} -2.02029 q^{28} +3.07069 q^{29} +5.96432 q^{30} -3.60353 q^{31} -8.01944 q^{32} +12.5472 q^{33} +10.1090 q^{34} +1.00000 q^{35} +11.8155 q^{36} -10.8597 q^{37} -3.61849 q^{38} -1.59966 q^{39} -0.0406892 q^{40} -4.34933 q^{41} +5.96432 q^{42} -7.91072 q^{43} -8.52176 q^{44} -5.84839 q^{45} +0.119420 q^{46} -2.71923 q^{47} +11.7765 q^{48} +1.00000 q^{49} +2.00507 q^{50} -14.9973 q^{51} +1.08645 q^{52} -6.21568 q^{53} -16.9887 q^{54} +4.21808 q^{55} -0.0406892 q^{56} +5.36822 q^{57} +6.15693 q^{58} -3.72905 q^{59} +6.00961 q^{60} -2.31653 q^{61} -7.22533 q^{62} -5.84839 q^{63} -8.16151 q^{64} -0.537768 q^{65} +25.1580 q^{66} +1.76203 q^{67} +10.1858 q^{68} -0.177166 q^{69} +2.00507 q^{70} -6.64223 q^{71} +0.237966 q^{72} +3.46914 q^{73} -21.7745 q^{74} -2.97462 q^{75} -3.64597 q^{76} +4.21808 q^{77} -3.20742 q^{78} +16.1254 q^{79} +3.95900 q^{80} +7.65849 q^{81} -8.72069 q^{82} +9.34281 q^{83} +6.00961 q^{84} -5.04173 q^{85} -15.8615 q^{86} -9.13414 q^{87} -0.171630 q^{88} +12.1526 q^{89} -11.7264 q^{90} -0.537768 q^{91} +0.120327 q^{92} +10.7192 q^{93} -5.45224 q^{94} +1.80467 q^{95} +23.8548 q^{96} +4.40673 q^{97} +2.00507 q^{98} -24.6690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00507 1.41780 0.708898 0.705311i \(-0.249193\pi\)
0.708898 + 0.705311i \(0.249193\pi\)
\(3\) −2.97462 −1.71740 −0.858700 0.512478i \(-0.828727\pi\)
−0.858700 + 0.512478i \(0.828727\pi\)
\(4\) 2.02029 1.01015
\(5\) −1.00000 −0.447214
\(6\) −5.96432 −2.43492
\(7\) −1.00000 −0.377964
\(8\) 0.0406892 0.0143858
\(9\) 5.84839 1.94946
\(10\) −2.00507 −0.634058
\(11\) −4.21808 −1.27180 −0.635900 0.771772i \(-0.719371\pi\)
−0.635900 + 0.771772i \(0.719371\pi\)
\(12\) −6.00961 −1.73483
\(13\) 0.537768 0.149150 0.0745750 0.997215i \(-0.476240\pi\)
0.0745750 + 0.997215i \(0.476240\pi\)
\(14\) −2.00507 −0.535877
\(15\) 2.97462 0.768045
\(16\) −3.95900 −0.989750
\(17\) 5.04173 1.22280 0.611400 0.791322i \(-0.290607\pi\)
0.611400 + 0.791322i \(0.290607\pi\)
\(18\) 11.7264 2.76394
\(19\) −1.80467 −0.414020 −0.207010 0.978339i \(-0.566373\pi\)
−0.207010 + 0.978339i \(0.566373\pi\)
\(20\) −2.02029 −0.451751
\(21\) 2.97462 0.649116
\(22\) −8.45753 −1.80315
\(23\) 0.0595591 0.0124189 0.00620946 0.999981i \(-0.498023\pi\)
0.00620946 + 0.999981i \(0.498023\pi\)
\(24\) −0.121035 −0.0247062
\(25\) 1.00000 0.200000
\(26\) 1.07826 0.211464
\(27\) −8.47289 −1.63061
\(28\) −2.02029 −0.381800
\(29\) 3.07069 0.570212 0.285106 0.958496i \(-0.407971\pi\)
0.285106 + 0.958496i \(0.407971\pi\)
\(30\) 5.96432 1.08893
\(31\) −3.60353 −0.647214 −0.323607 0.946192i \(-0.604896\pi\)
−0.323607 + 0.946192i \(0.604896\pi\)
\(32\) −8.01944 −1.41765
\(33\) 12.5472 2.18419
\(34\) 10.1090 1.73368
\(35\) 1.00000 0.169031
\(36\) 11.8155 1.96924
\(37\) −10.8597 −1.78533 −0.892666 0.450719i \(-0.851168\pi\)
−0.892666 + 0.450719i \(0.851168\pi\)
\(38\) −3.61849 −0.586997
\(39\) −1.59966 −0.256150
\(40\) −0.0406892 −0.00643352
\(41\) −4.34933 −0.679250 −0.339625 0.940561i \(-0.610300\pi\)
−0.339625 + 0.940561i \(0.610300\pi\)
\(42\) 5.96432 0.920315
\(43\) −7.91072 −1.20637 −0.603187 0.797600i \(-0.706103\pi\)
−0.603187 + 0.797600i \(0.706103\pi\)
\(44\) −8.52176 −1.28470
\(45\) −5.84839 −0.871826
\(46\) 0.119420 0.0176075
\(47\) −2.71923 −0.396640 −0.198320 0.980137i \(-0.563549\pi\)
−0.198320 + 0.980137i \(0.563549\pi\)
\(48\) 11.7765 1.69980
\(49\) 1.00000 0.142857
\(50\) 2.00507 0.283559
\(51\) −14.9973 −2.10004
\(52\) 1.08645 0.150663
\(53\) −6.21568 −0.853789 −0.426895 0.904301i \(-0.640392\pi\)
−0.426895 + 0.904301i \(0.640392\pi\)
\(54\) −16.9887 −2.31187
\(55\) 4.21808 0.568766
\(56\) −0.0406892 −0.00543732
\(57\) 5.36822 0.711039
\(58\) 6.15693 0.808445
\(59\) −3.72905 −0.485482 −0.242741 0.970091i \(-0.578046\pi\)
−0.242741 + 0.970091i \(0.578046\pi\)
\(60\) 6.00961 0.775838
\(61\) −2.31653 −0.296602 −0.148301 0.988942i \(-0.547380\pi\)
−0.148301 + 0.988942i \(0.547380\pi\)
\(62\) −7.22533 −0.917618
\(63\) −5.84839 −0.736828
\(64\) −8.16151 −1.02019
\(65\) −0.537768 −0.0667019
\(66\) 25.1580 3.09673
\(67\) 1.76203 0.215266 0.107633 0.994191i \(-0.465673\pi\)
0.107633 + 0.994191i \(0.465673\pi\)
\(68\) 10.1858 1.23521
\(69\) −0.177166 −0.0213283
\(70\) 2.00507 0.239651
\(71\) −6.64223 −0.788287 −0.394144 0.919049i \(-0.628959\pi\)
−0.394144 + 0.919049i \(0.628959\pi\)
\(72\) 0.237966 0.0280446
\(73\) 3.46914 0.406033 0.203016 0.979175i \(-0.434926\pi\)
0.203016 + 0.979175i \(0.434926\pi\)
\(74\) −21.7745 −2.53124
\(75\) −2.97462 −0.343480
\(76\) −3.64597 −0.418221
\(77\) 4.21808 0.480695
\(78\) −3.20742 −0.363169
\(79\) 16.1254 1.81425 0.907126 0.420859i \(-0.138271\pi\)
0.907126 + 0.420859i \(0.138271\pi\)
\(80\) 3.95900 0.442630
\(81\) 7.65849 0.850943
\(82\) −8.72069 −0.963039
\(83\) 9.34281 1.02551 0.512754 0.858536i \(-0.328625\pi\)
0.512754 + 0.858536i \(0.328625\pi\)
\(84\) 6.00961 0.655703
\(85\) −5.04173 −0.546853
\(86\) −15.8615 −1.71039
\(87\) −9.13414 −0.979282
\(88\) −0.171630 −0.0182958
\(89\) 12.1526 1.28817 0.644087 0.764952i \(-0.277238\pi\)
0.644087 + 0.764952i \(0.277238\pi\)
\(90\) −11.7264 −1.23607
\(91\) −0.537768 −0.0563734
\(92\) 0.120327 0.0125449
\(93\) 10.7192 1.11153
\(94\) −5.45224 −0.562355
\(95\) 1.80467 0.185156
\(96\) 23.8548 2.43467
\(97\) 4.40673 0.447436 0.223718 0.974654i \(-0.428181\pi\)
0.223718 + 0.974654i \(0.428181\pi\)
\(98\) 2.00507 0.202542
\(99\) −24.6690 −2.47933
\(100\) 2.02029 0.202029
\(101\) 3.68268 0.366440 0.183220 0.983072i \(-0.441348\pi\)
0.183220 + 0.983072i \(0.441348\pi\)
\(102\) −30.0705 −2.97742
\(103\) 12.9844 1.27939 0.639694 0.768630i \(-0.279061\pi\)
0.639694 + 0.768630i \(0.279061\pi\)
\(104\) 0.0218813 0.00214564
\(105\) −2.97462 −0.290294
\(106\) −12.4628 −1.21050
\(107\) −17.6012 −1.70157 −0.850785 0.525513i \(-0.823873\pi\)
−0.850785 + 0.525513i \(0.823873\pi\)
\(108\) −17.1177 −1.64715
\(109\) −5.15431 −0.493693 −0.246846 0.969055i \(-0.579394\pi\)
−0.246846 + 0.969055i \(0.579394\pi\)
\(110\) 8.45753 0.806394
\(111\) 32.3037 3.06613
\(112\) 3.95900 0.374091
\(113\) −1.23862 −0.116520 −0.0582599 0.998301i \(-0.518555\pi\)
−0.0582599 + 0.998301i \(0.518555\pi\)
\(114\) 10.7636 1.00811
\(115\) −0.0595591 −0.00555391
\(116\) 6.20369 0.575998
\(117\) 3.14508 0.290762
\(118\) −7.47700 −0.688314
\(119\) −5.04173 −0.462175
\(120\) 0.121035 0.0110489
\(121\) 6.79220 0.617473
\(122\) −4.64481 −0.420521
\(123\) 12.9376 1.16654
\(124\) −7.28020 −0.653781
\(125\) −1.00000 −0.0894427
\(126\) −11.7264 −1.04467
\(127\) 18.8785 1.67520 0.837598 0.546287i \(-0.183959\pi\)
0.837598 + 0.546287i \(0.183959\pi\)
\(128\) −0.325496 −0.0287701
\(129\) 23.5314 2.07183
\(130\) −1.07826 −0.0945697
\(131\) −5.27999 −0.461315 −0.230658 0.973035i \(-0.574088\pi\)
−0.230658 + 0.973035i \(0.574088\pi\)
\(132\) 25.3490 2.20635
\(133\) 1.80467 0.156485
\(134\) 3.53298 0.305203
\(135\) 8.47289 0.729230
\(136\) 0.205144 0.0175909
\(137\) −0.940881 −0.0803849 −0.0401924 0.999192i \(-0.512797\pi\)
−0.0401924 + 0.999192i \(0.512797\pi\)
\(138\) −0.355229 −0.0302391
\(139\) −10.5016 −0.890731 −0.445365 0.895349i \(-0.646926\pi\)
−0.445365 + 0.895349i \(0.646926\pi\)
\(140\) 2.02029 0.170746
\(141\) 8.08869 0.681190
\(142\) −13.3181 −1.11763
\(143\) −2.26835 −0.189689
\(144\) −23.1538 −1.92948
\(145\) −3.07069 −0.255007
\(146\) 6.95587 0.575672
\(147\) −2.97462 −0.245343
\(148\) −21.9399 −1.80345
\(149\) 4.02623 0.329842 0.164921 0.986307i \(-0.447263\pi\)
0.164921 + 0.986307i \(0.447263\pi\)
\(150\) −5.96432 −0.486985
\(151\) 10.9291 0.889397 0.444698 0.895680i \(-0.353311\pi\)
0.444698 + 0.895680i \(0.353311\pi\)
\(152\) −0.0734306 −0.00595601
\(153\) 29.4860 2.38380
\(154\) 8.45753 0.681527
\(155\) 3.60353 0.289443
\(156\) −3.23178 −0.258749
\(157\) 8.20693 0.654985 0.327492 0.944854i \(-0.393796\pi\)
0.327492 + 0.944854i \(0.393796\pi\)
\(158\) 32.3326 2.57224
\(159\) 18.4893 1.46630
\(160\) 8.01944 0.633993
\(161\) −0.0595591 −0.00469391
\(162\) 15.3558 1.20646
\(163\) 3.61002 0.282758 0.141379 0.989956i \(-0.454846\pi\)
0.141379 + 0.989956i \(0.454846\pi\)
\(164\) −8.78691 −0.686143
\(165\) −12.5472 −0.976799
\(166\) 18.7330 1.45396
\(167\) 16.5517 1.28081 0.640405 0.768038i \(-0.278767\pi\)
0.640405 + 0.768038i \(0.278767\pi\)
\(168\) 0.121035 0.00933805
\(169\) −12.7108 −0.977754
\(170\) −10.1090 −0.775326
\(171\) −10.5544 −0.807117
\(172\) −15.9820 −1.21861
\(173\) 20.0193 1.52204 0.761018 0.648731i \(-0.224700\pi\)
0.761018 + 0.648731i \(0.224700\pi\)
\(174\) −18.3146 −1.38842
\(175\) −1.00000 −0.0755929
\(176\) 16.6994 1.25876
\(177\) 11.0925 0.833766
\(178\) 24.3668 1.82637
\(179\) −9.85328 −0.736469 −0.368234 0.929733i \(-0.620038\pi\)
−0.368234 + 0.929733i \(0.620038\pi\)
\(180\) −11.8155 −0.880672
\(181\) 19.1524 1.42359 0.711794 0.702389i \(-0.247883\pi\)
0.711794 + 0.702389i \(0.247883\pi\)
\(182\) −1.07826 −0.0799260
\(183\) 6.89082 0.509384
\(184\) 0.00242341 0.000178656 0
\(185\) 10.8597 0.798425
\(186\) 21.4926 1.57592
\(187\) −21.2664 −1.55516
\(188\) −5.49364 −0.400665
\(189\) 8.47289 0.616312
\(190\) 3.61849 0.262513
\(191\) 4.78905 0.346524 0.173262 0.984876i \(-0.444569\pi\)
0.173262 + 0.984876i \(0.444569\pi\)
\(192\) 24.2774 1.75207
\(193\) −6.03763 −0.434598 −0.217299 0.976105i \(-0.569725\pi\)
−0.217299 + 0.976105i \(0.569725\pi\)
\(194\) 8.83580 0.634373
\(195\) 1.59966 0.114554
\(196\) 2.02029 0.144307
\(197\) 10.1442 0.722741 0.361371 0.932422i \(-0.382309\pi\)
0.361371 + 0.932422i \(0.382309\pi\)
\(198\) −49.4630 −3.51518
\(199\) 6.70984 0.475648 0.237824 0.971308i \(-0.423566\pi\)
0.237824 + 0.971308i \(0.423566\pi\)
\(200\) 0.0406892 0.00287716
\(201\) −5.24137 −0.369698
\(202\) 7.38402 0.519538
\(203\) −3.07069 −0.215520
\(204\) −30.2989 −2.12134
\(205\) 4.34933 0.303770
\(206\) 26.0345 1.81391
\(207\) 0.348325 0.0242102
\(208\) −2.12902 −0.147621
\(209\) 7.61226 0.526551
\(210\) −5.96432 −0.411577
\(211\) −20.0259 −1.37864 −0.689321 0.724456i \(-0.742091\pi\)
−0.689321 + 0.724456i \(0.742091\pi\)
\(212\) −12.5575 −0.862452
\(213\) 19.7581 1.35380
\(214\) −35.2916 −2.41248
\(215\) 7.91072 0.539507
\(216\) −0.344755 −0.0234576
\(217\) 3.60353 0.244624
\(218\) −10.3347 −0.699956
\(219\) −10.3194 −0.697320
\(220\) 8.52176 0.574537
\(221\) 2.71128 0.182381
\(222\) 64.7710 4.34715
\(223\) 4.60789 0.308567 0.154284 0.988027i \(-0.450693\pi\)
0.154284 + 0.988027i \(0.450693\pi\)
\(224\) 8.01944 0.535821
\(225\) 5.84839 0.389893
\(226\) −2.48352 −0.165201
\(227\) −9.82621 −0.652189 −0.326094 0.945337i \(-0.605733\pi\)
−0.326094 + 0.945337i \(0.605733\pi\)
\(228\) 10.8454 0.718253
\(229\) 1.00000 0.0660819
\(230\) −0.119420 −0.00787431
\(231\) −12.5472 −0.825545
\(232\) 0.124944 0.00820295
\(233\) 26.5562 1.73975 0.869876 0.493271i \(-0.164199\pi\)
0.869876 + 0.493271i \(0.164199\pi\)
\(234\) 6.30609 0.412242
\(235\) 2.71923 0.177383
\(236\) −7.53378 −0.490408
\(237\) −47.9671 −3.11580
\(238\) −10.1090 −0.655270
\(239\) 0.0705261 0.00456196 0.00228098 0.999997i \(-0.499274\pi\)
0.00228098 + 0.999997i \(0.499274\pi\)
\(240\) −11.7765 −0.760173
\(241\) 6.36305 0.409880 0.204940 0.978774i \(-0.434300\pi\)
0.204940 + 0.978774i \(0.434300\pi\)
\(242\) 13.6188 0.875451
\(243\) 2.63753 0.169198
\(244\) −4.68008 −0.299611
\(245\) −1.00000 −0.0638877
\(246\) 25.9408 1.65392
\(247\) −0.970495 −0.0617511
\(248\) −0.146625 −0.00931068
\(249\) −27.7914 −1.76121
\(250\) −2.00507 −0.126812
\(251\) −26.6127 −1.67978 −0.839888 0.542759i \(-0.817380\pi\)
−0.839888 + 0.542759i \(0.817380\pi\)
\(252\) −11.8155 −0.744304
\(253\) −0.251225 −0.0157944
\(254\) 37.8527 2.37509
\(255\) 14.9973 0.939165
\(256\) 15.6704 0.979399
\(257\) 27.4541 1.71254 0.856271 0.516526i \(-0.172775\pi\)
0.856271 + 0.516526i \(0.172775\pi\)
\(258\) 47.1821 2.93743
\(259\) 10.8597 0.674792
\(260\) −1.08645 −0.0673787
\(261\) 17.9586 1.11161
\(262\) −10.5867 −0.654051
\(263\) −16.0791 −0.991478 −0.495739 0.868471i \(-0.665103\pi\)
−0.495739 + 0.868471i \(0.665103\pi\)
\(264\) 0.510535 0.0314213
\(265\) 6.21568 0.381826
\(266\) 3.61849 0.221864
\(267\) −36.1494 −2.21231
\(268\) 3.55981 0.217450
\(269\) 25.4706 1.55297 0.776486 0.630135i \(-0.217000\pi\)
0.776486 + 0.630135i \(0.217000\pi\)
\(270\) 16.9887 1.03390
\(271\) 19.4672 1.18255 0.591274 0.806471i \(-0.298625\pi\)
0.591274 + 0.806471i \(0.298625\pi\)
\(272\) −19.9602 −1.21027
\(273\) 1.59966 0.0968157
\(274\) −1.88653 −0.113969
\(275\) −4.21808 −0.254360
\(276\) −0.357927 −0.0215447
\(277\) −1.94385 −0.116794 −0.0583972 0.998293i \(-0.518599\pi\)
−0.0583972 + 0.998293i \(0.518599\pi\)
\(278\) −21.0563 −1.26287
\(279\) −21.0749 −1.26172
\(280\) 0.0406892 0.00243164
\(281\) 0.724470 0.0432182 0.0216091 0.999766i \(-0.493121\pi\)
0.0216091 + 0.999766i \(0.493121\pi\)
\(282\) 16.2184 0.965789
\(283\) −15.5685 −0.925449 −0.462724 0.886502i \(-0.653128\pi\)
−0.462724 + 0.886502i \(0.653128\pi\)
\(284\) −13.4192 −0.796286
\(285\) −5.36822 −0.317986
\(286\) −4.54819 −0.268940
\(287\) 4.34933 0.256733
\(288\) −46.9008 −2.76366
\(289\) 8.41906 0.495239
\(290\) −6.15693 −0.361547
\(291\) −13.1084 −0.768427
\(292\) 7.00869 0.410152
\(293\) −3.24922 −0.189822 −0.0949108 0.995486i \(-0.530257\pi\)
−0.0949108 + 0.995486i \(0.530257\pi\)
\(294\) −5.96432 −0.347846
\(295\) 3.72905 0.217114
\(296\) −0.441874 −0.0256834
\(297\) 35.7393 2.07381
\(298\) 8.07287 0.467649
\(299\) 0.0320290 0.00185228
\(300\) −6.00961 −0.346965
\(301\) 7.91072 0.455966
\(302\) 21.9136 1.26098
\(303\) −10.9546 −0.629325
\(304\) 7.14470 0.409777
\(305\) 2.31653 0.132644
\(306\) 59.1214 3.37975
\(307\) −25.7115 −1.46743 −0.733717 0.679455i \(-0.762216\pi\)
−0.733717 + 0.679455i \(0.762216\pi\)
\(308\) 8.52176 0.485572
\(309\) −38.6236 −2.19722
\(310\) 7.22533 0.410371
\(311\) −13.4262 −0.761330 −0.380665 0.924713i \(-0.624305\pi\)
−0.380665 + 0.924713i \(0.624305\pi\)
\(312\) −0.0650887 −0.00368492
\(313\) −10.9285 −0.617718 −0.308859 0.951108i \(-0.599947\pi\)
−0.308859 + 0.951108i \(0.599947\pi\)
\(314\) 16.4555 0.928635
\(315\) 5.84839 0.329519
\(316\) 32.5781 1.83266
\(317\) 34.2758 1.92512 0.962560 0.271068i \(-0.0873767\pi\)
0.962560 + 0.271068i \(0.0873767\pi\)
\(318\) 37.0723 2.07891
\(319\) −12.9524 −0.725195
\(320\) 8.16151 0.456242
\(321\) 52.3569 2.92228
\(322\) −0.119420 −0.00665501
\(323\) −9.09868 −0.506264
\(324\) 15.4724 0.859578
\(325\) 0.537768 0.0298300
\(326\) 7.23832 0.400894
\(327\) 15.3321 0.847868
\(328\) −0.176970 −0.00977155
\(329\) 2.71923 0.149916
\(330\) −25.1580 −1.38490
\(331\) 31.2613 1.71828 0.859138 0.511744i \(-0.171000\pi\)
0.859138 + 0.511744i \(0.171000\pi\)
\(332\) 18.8752 1.03591
\(333\) −63.5120 −3.48044
\(334\) 33.1873 1.81593
\(335\) −1.76203 −0.0962699
\(336\) −11.7765 −0.642463
\(337\) −19.7364 −1.07511 −0.537554 0.843229i \(-0.680652\pi\)
−0.537554 + 0.843229i \(0.680652\pi\)
\(338\) −25.4860 −1.38626
\(339\) 3.68444 0.200111
\(340\) −10.1858 −0.552401
\(341\) 15.2000 0.823126
\(342\) −21.1623 −1.14433
\(343\) −1.00000 −0.0539949
\(344\) −0.321880 −0.0173546
\(345\) 0.177166 0.00953829
\(346\) 40.1400 2.15794
\(347\) 14.2612 0.765581 0.382790 0.923835i \(-0.374963\pi\)
0.382790 + 0.923835i \(0.374963\pi\)
\(348\) −18.4536 −0.989219
\(349\) 26.0146 1.39253 0.696266 0.717784i \(-0.254843\pi\)
0.696266 + 0.717784i \(0.254843\pi\)
\(350\) −2.00507 −0.107175
\(351\) −4.55645 −0.243205
\(352\) 33.8267 1.80297
\(353\) 25.7693 1.37156 0.685781 0.727808i \(-0.259461\pi\)
0.685781 + 0.727808i \(0.259461\pi\)
\(354\) 22.2413 1.18211
\(355\) 6.64223 0.352533
\(356\) 24.5518 1.30124
\(357\) 14.9973 0.793739
\(358\) −19.7565 −1.04416
\(359\) 3.32748 0.175618 0.0878089 0.996137i \(-0.472014\pi\)
0.0878089 + 0.996137i \(0.472014\pi\)
\(360\) −0.237966 −0.0125419
\(361\) −15.7432 −0.828587
\(362\) 38.4019 2.01836
\(363\) −20.2043 −1.06045
\(364\) −1.08645 −0.0569454
\(365\) −3.46914 −0.181583
\(366\) 13.8166 0.722203
\(367\) 25.1398 1.31229 0.656144 0.754635i \(-0.272186\pi\)
0.656144 + 0.754635i \(0.272186\pi\)
\(368\) −0.235794 −0.0122916
\(369\) −25.4365 −1.32417
\(370\) 21.7745 1.13200
\(371\) 6.21568 0.322702
\(372\) 21.6558 1.12280
\(373\) 6.46116 0.334546 0.167273 0.985911i \(-0.446504\pi\)
0.167273 + 0.985911i \(0.446504\pi\)
\(374\) −42.6406 −2.20489
\(375\) 2.97462 0.153609
\(376\) −0.110643 −0.00570599
\(377\) 1.65132 0.0850471
\(378\) 16.9887 0.873805
\(379\) −34.4818 −1.77121 −0.885604 0.464440i \(-0.846256\pi\)
−0.885604 + 0.464440i \(0.846256\pi\)
\(380\) 3.64597 0.187034
\(381\) −56.1565 −2.87698
\(382\) 9.60237 0.491300
\(383\) −34.4404 −1.75982 −0.879911 0.475139i \(-0.842398\pi\)
−0.879911 + 0.475139i \(0.842398\pi\)
\(384\) 0.968230 0.0494098
\(385\) −4.21808 −0.214973
\(386\) −12.1059 −0.616172
\(387\) −46.2650 −2.35178
\(388\) 8.90290 0.451976
\(389\) −8.42958 −0.427397 −0.213698 0.976900i \(-0.568551\pi\)
−0.213698 + 0.976900i \(0.568551\pi\)
\(390\) 3.20742 0.162414
\(391\) 0.300281 0.0151859
\(392\) 0.0406892 0.00205511
\(393\) 15.7060 0.792263
\(394\) 20.3397 1.02470
\(395\) −16.1254 −0.811358
\(396\) −49.8386 −2.50448
\(397\) −2.36237 −0.118564 −0.0592820 0.998241i \(-0.518881\pi\)
−0.0592820 + 0.998241i \(0.518881\pi\)
\(398\) 13.4537 0.674372
\(399\) −5.36822 −0.268747
\(400\) −3.95900 −0.197950
\(401\) −4.92460 −0.245923 −0.122961 0.992411i \(-0.539239\pi\)
−0.122961 + 0.992411i \(0.539239\pi\)
\(402\) −10.5093 −0.524156
\(403\) −1.93787 −0.0965320
\(404\) 7.44009 0.370158
\(405\) −7.65849 −0.380553
\(406\) −6.15693 −0.305563
\(407\) 45.8073 2.27058
\(408\) −0.610226 −0.0302107
\(409\) −13.7940 −0.682067 −0.341034 0.940051i \(-0.610777\pi\)
−0.341034 + 0.940051i \(0.610777\pi\)
\(410\) 8.72069 0.430684
\(411\) 2.79877 0.138053
\(412\) 26.2322 1.29237
\(413\) 3.72905 0.183495
\(414\) 0.698414 0.0343252
\(415\) −9.34281 −0.458621
\(416\) −4.31260 −0.211443
\(417\) 31.2382 1.52974
\(418\) 15.2631 0.746542
\(419\) −5.80673 −0.283678 −0.141839 0.989890i \(-0.545301\pi\)
−0.141839 + 0.989890i \(0.545301\pi\)
\(420\) −6.00961 −0.293239
\(421\) 12.5564 0.611959 0.305980 0.952038i \(-0.401016\pi\)
0.305980 + 0.952038i \(0.401016\pi\)
\(422\) −40.1533 −1.95463
\(423\) −15.9031 −0.773236
\(424\) −0.252911 −0.0122824
\(425\) 5.04173 0.244560
\(426\) 39.6164 1.91942
\(427\) 2.31653 0.112105
\(428\) −35.5596 −1.71884
\(429\) 6.74748 0.325772
\(430\) 15.8615 0.764910
\(431\) 1.04885 0.0505211 0.0252606 0.999681i \(-0.491958\pi\)
0.0252606 + 0.999681i \(0.491958\pi\)
\(432\) 33.5442 1.61390
\(433\) −20.8286 −1.00096 −0.500480 0.865748i \(-0.666843\pi\)
−0.500480 + 0.865748i \(0.666843\pi\)
\(434\) 7.22533 0.346827
\(435\) 9.13414 0.437948
\(436\) −10.4132 −0.498702
\(437\) −0.107485 −0.00514169
\(438\) −20.6911 −0.988658
\(439\) −30.8376 −1.47180 −0.735899 0.677091i \(-0.763240\pi\)
−0.735899 + 0.677091i \(0.763240\pi\)
\(440\) 0.171630 0.00818214
\(441\) 5.84839 0.278495
\(442\) 5.43630 0.258578
\(443\) 5.46977 0.259877 0.129938 0.991522i \(-0.458522\pi\)
0.129938 + 0.991522i \(0.458522\pi\)
\(444\) 65.2629 3.09724
\(445\) −12.1526 −0.576089
\(446\) 9.23913 0.437485
\(447\) −11.9765 −0.566470
\(448\) 8.16151 0.385595
\(449\) 5.27563 0.248972 0.124486 0.992221i \(-0.460272\pi\)
0.124486 + 0.992221i \(0.460272\pi\)
\(450\) 11.7264 0.552788
\(451\) 18.3458 0.863870
\(452\) −2.50238 −0.117702
\(453\) −32.5099 −1.52745
\(454\) −19.7022 −0.924671
\(455\) 0.537768 0.0252109
\(456\) 0.218428 0.0102289
\(457\) −10.2876 −0.481235 −0.240617 0.970620i \(-0.577350\pi\)
−0.240617 + 0.970620i \(0.577350\pi\)
\(458\) 2.00507 0.0936906
\(459\) −42.7180 −1.99391
\(460\) −0.120327 −0.00561026
\(461\) 21.4763 1.00025 0.500126 0.865953i \(-0.333287\pi\)
0.500126 + 0.865953i \(0.333287\pi\)
\(462\) −25.1580 −1.17046
\(463\) −0.554878 −0.0257874 −0.0128937 0.999917i \(-0.504104\pi\)
−0.0128937 + 0.999917i \(0.504104\pi\)
\(464\) −12.1569 −0.564368
\(465\) −10.7192 −0.497089
\(466\) 53.2469 2.46661
\(467\) 13.4722 0.623418 0.311709 0.950178i \(-0.399099\pi\)
0.311709 + 0.950178i \(0.399099\pi\)
\(468\) 6.35398 0.293713
\(469\) −1.76203 −0.0813629
\(470\) 5.45224 0.251493
\(471\) −24.4125 −1.12487
\(472\) −0.151732 −0.00698403
\(473\) 33.3681 1.53426
\(474\) −96.1772 −4.41757
\(475\) −1.80467 −0.0828041
\(476\) −10.1858 −0.466864
\(477\) −36.3517 −1.66443
\(478\) 0.141410 0.00646792
\(479\) −3.22190 −0.147212 −0.0736062 0.997287i \(-0.523451\pi\)
−0.0736062 + 0.997287i \(0.523451\pi\)
\(480\) −23.8548 −1.08882
\(481\) −5.84002 −0.266282
\(482\) 12.7584 0.581127
\(483\) 0.177166 0.00806132
\(484\) 13.7222 0.623738
\(485\) −4.40673 −0.200100
\(486\) 5.28843 0.239888
\(487\) −15.6127 −0.707481 −0.353740 0.935344i \(-0.615090\pi\)
−0.353740 + 0.935344i \(0.615090\pi\)
\(488\) −0.0942578 −0.00426685
\(489\) −10.7384 −0.485609
\(490\) −2.00507 −0.0905797
\(491\) 39.8739 1.79948 0.899742 0.436422i \(-0.143755\pi\)
0.899742 + 0.436422i \(0.143755\pi\)
\(492\) 26.1378 1.17838
\(493\) 15.4816 0.697255
\(494\) −1.94591 −0.0875505
\(495\) 24.6690 1.10879
\(496\) 14.2664 0.640580
\(497\) 6.64223 0.297945
\(498\) −55.7235 −2.49703
\(499\) 36.1402 1.61786 0.808929 0.587906i \(-0.200048\pi\)
0.808929 + 0.587906i \(0.200048\pi\)
\(500\) −2.02029 −0.0903503
\(501\) −49.2351 −2.19966
\(502\) −53.3602 −2.38158
\(503\) −29.1419 −1.29937 −0.649686 0.760203i \(-0.725100\pi\)
−0.649686 + 0.760203i \(0.725100\pi\)
\(504\) −0.237966 −0.0105998
\(505\) −3.68268 −0.163877
\(506\) −0.503723 −0.0223932
\(507\) 37.8099 1.67920
\(508\) 38.1401 1.69219
\(509\) −5.02226 −0.222608 −0.111304 0.993786i \(-0.535503\pi\)
−0.111304 + 0.993786i \(0.535503\pi\)
\(510\) 30.0705 1.33154
\(511\) −3.46914 −0.153466
\(512\) 32.0712 1.41736
\(513\) 15.2908 0.675105
\(514\) 55.0474 2.42804
\(515\) −12.9844 −0.572160
\(516\) 47.5404 2.09285
\(517\) 11.4699 0.504447
\(518\) 21.7745 0.956718
\(519\) −59.5498 −2.61394
\(520\) −0.0218813 −0.000959559 0
\(521\) −25.1235 −1.10068 −0.550341 0.834940i \(-0.685502\pi\)
−0.550341 + 0.834940i \(0.685502\pi\)
\(522\) 36.0081 1.57603
\(523\) 38.1779 1.66940 0.834702 0.550702i \(-0.185640\pi\)
0.834702 + 0.550702i \(0.185640\pi\)
\(524\) −10.6671 −0.465996
\(525\) 2.97462 0.129823
\(526\) −32.2396 −1.40571
\(527\) −18.1681 −0.791413
\(528\) −49.6744 −2.16180
\(529\) −22.9965 −0.999846
\(530\) 12.4628 0.541352
\(531\) −21.8090 −0.946428
\(532\) 3.64597 0.158073
\(533\) −2.33893 −0.101310
\(534\) −72.4820 −3.13660
\(535\) 17.6012 0.760966
\(536\) 0.0716954 0.00309677
\(537\) 29.3098 1.26481
\(538\) 51.0703 2.20180
\(539\) −4.21808 −0.181686
\(540\) 17.1177 0.736629
\(541\) 35.4011 1.52201 0.761007 0.648744i \(-0.224705\pi\)
0.761007 + 0.648744i \(0.224705\pi\)
\(542\) 39.0330 1.67661
\(543\) −56.9712 −2.44487
\(544\) −40.4319 −1.73350
\(545\) 5.15431 0.220786
\(546\) 3.20742 0.137265
\(547\) −28.2855 −1.20940 −0.604699 0.796454i \(-0.706707\pi\)
−0.604699 + 0.796454i \(0.706707\pi\)
\(548\) −1.90086 −0.0812005
\(549\) −13.5480 −0.578214
\(550\) −8.45753 −0.360630
\(551\) −5.54159 −0.236079
\(552\) −0.00720873 −0.000306824 0
\(553\) −16.1254 −0.685723
\(554\) −3.89754 −0.165591
\(555\) −32.3037 −1.37121
\(556\) −21.2162 −0.899768
\(557\) 2.45585 0.104058 0.0520288 0.998646i \(-0.483431\pi\)
0.0520288 + 0.998646i \(0.483431\pi\)
\(558\) −42.2565 −1.78886
\(559\) −4.25413 −0.179931
\(560\) −3.95900 −0.167298
\(561\) 63.2596 2.67082
\(562\) 1.45261 0.0612746
\(563\) 30.2286 1.27399 0.636993 0.770870i \(-0.280178\pi\)
0.636993 + 0.770870i \(0.280178\pi\)
\(564\) 16.3415 0.688102
\(565\) 1.23862 0.0521093
\(566\) −31.2158 −1.31210
\(567\) −7.65849 −0.321626
\(568\) −0.270266 −0.0113401
\(569\) −13.8470 −0.580495 −0.290248 0.956952i \(-0.593738\pi\)
−0.290248 + 0.956952i \(0.593738\pi\)
\(570\) −10.7636 −0.450840
\(571\) −26.0706 −1.09102 −0.545511 0.838104i \(-0.683664\pi\)
−0.545511 + 0.838104i \(0.683664\pi\)
\(572\) −4.58273 −0.191614
\(573\) −14.2456 −0.595120
\(574\) 8.72069 0.363994
\(575\) 0.0595591 0.00248378
\(576\) −47.7317 −1.98882
\(577\) 43.7245 1.82027 0.910137 0.414308i \(-0.135976\pi\)
0.910137 + 0.414308i \(0.135976\pi\)
\(578\) 16.8808 0.702148
\(579\) 17.9597 0.746379
\(580\) −6.20369 −0.257594
\(581\) −9.34281 −0.387605
\(582\) −26.2832 −1.08947
\(583\) 26.2182 1.08585
\(584\) 0.141157 0.00584110
\(585\) −3.14508 −0.130033
\(586\) −6.51491 −0.269129
\(587\) 33.4838 1.38202 0.691012 0.722844i \(-0.257165\pi\)
0.691012 + 0.722844i \(0.257165\pi\)
\(588\) −6.00961 −0.247832
\(589\) 6.50320 0.267960
\(590\) 7.47700 0.307823
\(591\) −30.1751 −1.24124
\(592\) 42.9938 1.76703
\(593\) 23.6782 0.972345 0.486173 0.873863i \(-0.338393\pi\)
0.486173 + 0.873863i \(0.338393\pi\)
\(594\) 71.6597 2.94023
\(595\) 5.04173 0.206691
\(596\) 8.13417 0.333189
\(597\) −19.9593 −0.816878
\(598\) 0.0642202 0.00262616
\(599\) 1.85993 0.0759946 0.0379973 0.999278i \(-0.487902\pi\)
0.0379973 + 0.999278i \(0.487902\pi\)
\(600\) −0.121035 −0.00494123
\(601\) −9.18487 −0.374659 −0.187329 0.982297i \(-0.559983\pi\)
−0.187329 + 0.982297i \(0.559983\pi\)
\(602\) 15.8615 0.646467
\(603\) 10.3050 0.419653
\(604\) 22.0800 0.898421
\(605\) −6.79220 −0.276142
\(606\) −21.9647 −0.892254
\(607\) 28.5474 1.15870 0.579351 0.815078i \(-0.303306\pi\)
0.579351 + 0.815078i \(0.303306\pi\)
\(608\) 14.4725 0.586936
\(609\) 9.13414 0.370134
\(610\) 4.64481 0.188063
\(611\) −1.46231 −0.0591589
\(612\) 59.5704 2.40799
\(613\) −13.3492 −0.539168 −0.269584 0.962977i \(-0.586886\pi\)
−0.269584 + 0.962977i \(0.586886\pi\)
\(614\) −51.5533 −2.08052
\(615\) −12.9376 −0.521695
\(616\) 0.171630 0.00691517
\(617\) −5.06353 −0.203850 −0.101925 0.994792i \(-0.532500\pi\)
−0.101925 + 0.994792i \(0.532500\pi\)
\(618\) −77.4430 −3.11521
\(619\) 16.9850 0.682683 0.341342 0.939939i \(-0.389119\pi\)
0.341342 + 0.939939i \(0.389119\pi\)
\(620\) 7.28020 0.292380
\(621\) −0.504637 −0.0202504
\(622\) −26.9204 −1.07941
\(623\) −12.1526 −0.486884
\(624\) 6.33305 0.253525
\(625\) 1.00000 0.0400000
\(626\) −21.9125 −0.875798
\(627\) −22.6436 −0.904298
\(628\) 16.5804 0.661630
\(629\) −54.7519 −2.18310
\(630\) 11.7264 0.467191
\(631\) 11.2203 0.446673 0.223336 0.974741i \(-0.428305\pi\)
0.223336 + 0.974741i \(0.428305\pi\)
\(632\) 0.656130 0.0260994
\(633\) 59.5696 2.36768
\(634\) 68.7253 2.72943
\(635\) −18.8785 −0.749171
\(636\) 37.3538 1.48118
\(637\) 0.537768 0.0213071
\(638\) −25.9704 −1.02818
\(639\) −38.8463 −1.53674
\(640\) 0.325496 0.0128664
\(641\) −3.24683 −0.128242 −0.0641210 0.997942i \(-0.520424\pi\)
−0.0641210 + 0.997942i \(0.520424\pi\)
\(642\) 104.979 4.14320
\(643\) 27.5358 1.08590 0.542952 0.839763i \(-0.317306\pi\)
0.542952 + 0.839763i \(0.317306\pi\)
\(644\) −0.120327 −0.00474154
\(645\) −23.5314 −0.926549
\(646\) −18.2435 −0.717779
\(647\) −2.70474 −0.106334 −0.0531671 0.998586i \(-0.516932\pi\)
−0.0531671 + 0.998586i \(0.516932\pi\)
\(648\) 0.311618 0.0122415
\(649\) 15.7295 0.617435
\(650\) 1.07826 0.0422929
\(651\) −10.7192 −0.420117
\(652\) 7.29329 0.285627
\(653\) 3.77151 0.147591 0.0737954 0.997273i \(-0.476489\pi\)
0.0737954 + 0.997273i \(0.476489\pi\)
\(654\) 30.7419 1.20210
\(655\) 5.27999 0.206306
\(656\) 17.2190 0.672288
\(657\) 20.2889 0.791546
\(658\) 5.45224 0.212550
\(659\) 32.0382 1.24803 0.624015 0.781412i \(-0.285500\pi\)
0.624015 + 0.781412i \(0.285500\pi\)
\(660\) −25.3490 −0.986710
\(661\) 14.5424 0.565634 0.282817 0.959174i \(-0.408731\pi\)
0.282817 + 0.959174i \(0.408731\pi\)
\(662\) 62.6810 2.43617
\(663\) −8.06504 −0.313220
\(664\) 0.380151 0.0147527
\(665\) −1.80467 −0.0699822
\(666\) −127.346 −4.93455
\(667\) 0.182887 0.00708142
\(668\) 33.4393 1.29380
\(669\) −13.7067 −0.529933
\(670\) −3.53298 −0.136491
\(671\) 9.77133 0.377218
\(672\) −23.8548 −0.920220
\(673\) 30.4908 1.17533 0.587667 0.809103i \(-0.300046\pi\)
0.587667 + 0.809103i \(0.300046\pi\)
\(674\) −39.5728 −1.52429
\(675\) −8.47289 −0.326122
\(676\) −25.6796 −0.987675
\(677\) 5.48274 0.210719 0.105359 0.994434i \(-0.466401\pi\)
0.105359 + 0.994434i \(0.466401\pi\)
\(678\) 7.38755 0.283717
\(679\) −4.40673 −0.169115
\(680\) −0.205144 −0.00786691
\(681\) 29.2293 1.12007
\(682\) 30.4770 1.16703
\(683\) 39.2025 1.50004 0.750022 0.661413i \(-0.230043\pi\)
0.750022 + 0.661413i \(0.230043\pi\)
\(684\) −21.3230 −0.815307
\(685\) 0.940881 0.0359492
\(686\) −2.00507 −0.0765538
\(687\) −2.97462 −0.113489
\(688\) 31.3186 1.19401
\(689\) −3.34259 −0.127343
\(690\) 0.355229 0.0135233
\(691\) −10.6839 −0.406434 −0.203217 0.979134i \(-0.565140\pi\)
−0.203217 + 0.979134i \(0.565140\pi\)
\(692\) 40.4448 1.53748
\(693\) 24.6690 0.937097
\(694\) 28.5946 1.08544
\(695\) 10.5016 0.398347
\(696\) −0.371660 −0.0140877
\(697\) −21.9281 −0.830587
\(698\) 52.1611 1.97433
\(699\) −78.9946 −2.98785
\(700\) −2.02029 −0.0763599
\(701\) 0.208068 0.00785862 0.00392931 0.999992i \(-0.498749\pi\)
0.00392931 + 0.999992i \(0.498749\pi\)
\(702\) −9.13598 −0.344815
\(703\) 19.5983 0.739164
\(704\) 34.4259 1.29748
\(705\) −8.08869 −0.304638
\(706\) 51.6692 1.94460
\(707\) −3.68268 −0.138501
\(708\) 22.4102 0.842226
\(709\) −18.6005 −0.698557 −0.349278 0.937019i \(-0.613573\pi\)
−0.349278 + 0.937019i \(0.613573\pi\)
\(710\) 13.3181 0.499820
\(711\) 94.3078 3.53682
\(712\) 0.494479 0.0185314
\(713\) −0.214623 −0.00803770
\(714\) 30.0705 1.12536
\(715\) 2.26835 0.0848314
\(716\) −19.9065 −0.743941
\(717\) −0.209789 −0.00783470
\(718\) 6.67182 0.248990
\(719\) −30.8939 −1.15215 −0.576074 0.817398i \(-0.695416\pi\)
−0.576074 + 0.817398i \(0.695416\pi\)
\(720\) 23.1538 0.862891
\(721\) −12.9844 −0.483563
\(722\) −31.5661 −1.17477
\(723\) −18.9277 −0.703929
\(724\) 38.6935 1.43803
\(725\) 3.07069 0.114042
\(726\) −40.5109 −1.50350
\(727\) −33.1830 −1.23069 −0.615344 0.788259i \(-0.710983\pi\)
−0.615344 + 0.788259i \(0.710983\pi\)
\(728\) −0.0218813 −0.000810976 0
\(729\) −30.8211 −1.14152
\(730\) −6.95587 −0.257448
\(731\) −39.8837 −1.47515
\(732\) 13.9215 0.514553
\(733\) 31.8446 1.17621 0.588104 0.808785i \(-0.299874\pi\)
0.588104 + 0.808785i \(0.299874\pi\)
\(734\) 50.4070 1.86056
\(735\) 2.97462 0.109721
\(736\) −0.477630 −0.0176057
\(737\) −7.43238 −0.273775
\(738\) −51.0020 −1.87741
\(739\) 12.2176 0.449433 0.224716 0.974424i \(-0.427854\pi\)
0.224716 + 0.974424i \(0.427854\pi\)
\(740\) 21.9399 0.806526
\(741\) 2.88686 0.106051
\(742\) 12.4628 0.457526
\(743\) 10.8666 0.398658 0.199329 0.979933i \(-0.436124\pi\)
0.199329 + 0.979933i \(0.436124\pi\)
\(744\) 0.436154 0.0159902
\(745\) −4.02623 −0.147510
\(746\) 12.9551 0.474318
\(747\) 54.6404 1.99919
\(748\) −42.9644 −1.57094
\(749\) 17.6012 0.643133
\(750\) 5.96432 0.217786
\(751\) 11.8906 0.433893 0.216946 0.976184i \(-0.430390\pi\)
0.216946 + 0.976184i \(0.430390\pi\)
\(752\) 10.7654 0.392575
\(753\) 79.1627 2.88485
\(754\) 3.31100 0.120580
\(755\) −10.9291 −0.397750
\(756\) 17.1177 0.622565
\(757\) 29.1979 1.06122 0.530608 0.847618i \(-0.321964\pi\)
0.530608 + 0.847618i \(0.321964\pi\)
\(758\) −69.1382 −2.51121
\(759\) 0.747300 0.0271253
\(760\) 0.0734306 0.00266361
\(761\) −27.7343 −1.00537 −0.502684 0.864470i \(-0.667654\pi\)
−0.502684 + 0.864470i \(0.667654\pi\)
\(762\) −112.597 −4.07898
\(763\) 5.15431 0.186598
\(764\) 9.67529 0.350040
\(765\) −29.4860 −1.06607
\(766\) −69.0553 −2.49507
\(767\) −2.00537 −0.0724096
\(768\) −46.6135 −1.68202
\(769\) 4.91549 0.177257 0.0886285 0.996065i \(-0.471752\pi\)
0.0886285 + 0.996065i \(0.471752\pi\)
\(770\) −8.45753 −0.304788
\(771\) −81.6658 −2.94112
\(772\) −12.1978 −0.439008
\(773\) −28.3561 −1.01990 −0.509949 0.860205i \(-0.670336\pi\)
−0.509949 + 0.860205i \(0.670336\pi\)
\(774\) −92.7644 −3.33435
\(775\) −3.60353 −0.129443
\(776\) 0.179306 0.00643672
\(777\) −32.3037 −1.15889
\(778\) −16.9019 −0.605961
\(779\) 7.84911 0.281224
\(780\) 3.23178 0.115716
\(781\) 28.0174 1.00254
\(782\) 0.602083 0.0215304
\(783\) −26.0176 −0.929793
\(784\) −3.95900 −0.141393
\(785\) −8.20693 −0.292918
\(786\) 31.4916 1.12327
\(787\) −1.92615 −0.0686598 −0.0343299 0.999411i \(-0.510930\pi\)
−0.0343299 + 0.999411i \(0.510930\pi\)
\(788\) 20.4942 0.730075
\(789\) 47.8292 1.70276
\(790\) −32.3326 −1.15034
\(791\) 1.23862 0.0440404
\(792\) −1.00376 −0.0356671
\(793\) −1.24576 −0.0442382
\(794\) −4.73671 −0.168100
\(795\) −18.4893 −0.655748
\(796\) 13.5558 0.480474
\(797\) −10.7617 −0.381197 −0.190599 0.981668i \(-0.561043\pi\)
−0.190599 + 0.981668i \(0.561043\pi\)
\(798\) −10.7636 −0.381029
\(799\) −13.7096 −0.485012
\(800\) −8.01944 −0.283530
\(801\) 71.0732 2.51125
\(802\) −9.87415 −0.348668
\(803\) −14.6331 −0.516392
\(804\) −10.5891 −0.373449
\(805\) 0.0595591 0.00209918
\(806\) −3.88555 −0.136863
\(807\) −75.7655 −2.66707
\(808\) 0.149845 0.00527153
\(809\) −6.30481 −0.221665 −0.110833 0.993839i \(-0.535352\pi\)
−0.110833 + 0.993839i \(0.535352\pi\)
\(810\) −15.3558 −0.539547
\(811\) −7.36136 −0.258492 −0.129246 0.991613i \(-0.541256\pi\)
−0.129246 + 0.991613i \(0.541256\pi\)
\(812\) −6.20369 −0.217707
\(813\) −57.9076 −2.03091
\(814\) 91.8467 3.21922
\(815\) −3.61002 −0.126453
\(816\) 59.3742 2.07851
\(817\) 14.2763 0.499463
\(818\) −27.6578 −0.967032
\(819\) −3.14508 −0.109898
\(820\) 8.78691 0.306852
\(821\) −16.1155 −0.562435 −0.281218 0.959644i \(-0.590738\pi\)
−0.281218 + 0.959644i \(0.590738\pi\)
\(822\) 5.61172 0.195731
\(823\) 30.9022 1.07718 0.538592 0.842567i \(-0.318957\pi\)
0.538592 + 0.842567i \(0.318957\pi\)
\(824\) 0.528323 0.0184050
\(825\) 12.5472 0.436838
\(826\) 7.47700 0.260158
\(827\) −19.2827 −0.670527 −0.335263 0.942124i \(-0.608825\pi\)
−0.335263 + 0.942124i \(0.608825\pi\)
\(828\) 0.703718 0.0244559
\(829\) −31.4656 −1.09284 −0.546422 0.837510i \(-0.684010\pi\)
−0.546422 + 0.837510i \(0.684010\pi\)
\(830\) −18.7330 −0.650231
\(831\) 5.78221 0.200583
\(832\) −4.38900 −0.152161
\(833\) 5.04173 0.174686
\(834\) 62.6347 2.16886
\(835\) −16.5517 −0.572795
\(836\) 15.3790 0.531893
\(837\) 30.5323 1.05535
\(838\) −11.6429 −0.402197
\(839\) −39.9857 −1.38046 −0.690230 0.723590i \(-0.742491\pi\)
−0.690230 + 0.723590i \(0.742491\pi\)
\(840\) −0.121035 −0.00417610
\(841\) −19.5709 −0.674858
\(842\) 25.1763 0.867634
\(843\) −2.15502 −0.0742230
\(844\) −40.4582 −1.39263
\(845\) 12.7108 0.437265
\(846\) −31.8868 −1.09629
\(847\) −6.79220 −0.233383
\(848\) 24.6079 0.845038
\(849\) 46.3103 1.58937
\(850\) 10.1090 0.346736
\(851\) −0.646796 −0.0221719
\(852\) 39.9172 1.36754
\(853\) −4.62619 −0.158398 −0.0791988 0.996859i \(-0.525236\pi\)
−0.0791988 + 0.996859i \(0.525236\pi\)
\(854\) 4.64481 0.158942
\(855\) 10.5544 0.360954
\(856\) −0.716177 −0.0244784
\(857\) −19.2967 −0.659161 −0.329581 0.944127i \(-0.606907\pi\)
−0.329581 + 0.944127i \(0.606907\pi\)
\(858\) 13.5292 0.461878
\(859\) −28.1006 −0.958781 −0.479391 0.877602i \(-0.659142\pi\)
−0.479391 + 0.877602i \(0.659142\pi\)
\(860\) 15.9820 0.544981
\(861\) −12.9376 −0.440913
\(862\) 2.10301 0.0716287
\(863\) −3.26753 −0.111228 −0.0556140 0.998452i \(-0.517712\pi\)
−0.0556140 + 0.998452i \(0.517712\pi\)
\(864\) 67.9478 2.31163
\(865\) −20.0193 −0.680675
\(866\) −41.7628 −1.41916
\(867\) −25.0435 −0.850523
\(868\) 7.28020 0.247106
\(869\) −68.0183 −2.30736
\(870\) 18.3146 0.620922
\(871\) 0.947562 0.0321069
\(872\) −0.209724 −0.00710216
\(873\) 25.7723 0.872260
\(874\) −0.215514 −0.00728987
\(875\) 1.00000 0.0338062
\(876\) −20.8482 −0.704396
\(877\) −2.03846 −0.0688339 −0.0344169 0.999408i \(-0.510957\pi\)
−0.0344169 + 0.999408i \(0.510957\pi\)
\(878\) −61.8314 −2.08671
\(879\) 9.66522 0.326000
\(880\) −16.6994 −0.562936
\(881\) −59.1070 −1.99137 −0.995684 0.0928132i \(-0.970414\pi\)
−0.995684 + 0.0928132i \(0.970414\pi\)
\(882\) 11.7264 0.394849
\(883\) −10.8542 −0.365274 −0.182637 0.983180i \(-0.558463\pi\)
−0.182637 + 0.983180i \(0.558463\pi\)
\(884\) 5.47758 0.184231
\(885\) −11.0925 −0.372872
\(886\) 10.9673 0.368452
\(887\) 23.0551 0.774114 0.387057 0.922056i \(-0.373492\pi\)
0.387057 + 0.922056i \(0.373492\pi\)
\(888\) 1.31441 0.0441087
\(889\) −18.8785 −0.633165
\(890\) −24.3668 −0.816776
\(891\) −32.3041 −1.08223
\(892\) 9.30929 0.311698
\(893\) 4.90732 0.164217
\(894\) −24.0137 −0.803140
\(895\) 9.85328 0.329359
\(896\) 0.325496 0.0108741
\(897\) −0.0952741 −0.00318111
\(898\) 10.5780 0.352992
\(899\) −11.0653 −0.369049
\(900\) 11.8155 0.393849
\(901\) −31.3378 −1.04401
\(902\) 36.7846 1.22479
\(903\) −23.5314 −0.783077
\(904\) −0.0503985 −0.00167623
\(905\) −19.1524 −0.636648
\(906\) −65.1846 −2.16561
\(907\) 19.7985 0.657398 0.328699 0.944435i \(-0.393390\pi\)
0.328699 + 0.944435i \(0.393390\pi\)
\(908\) −19.8518 −0.658806
\(909\) 21.5377 0.714362
\(910\) 1.07826 0.0357440
\(911\) −20.7775 −0.688388 −0.344194 0.938899i \(-0.611848\pi\)
−0.344194 + 0.938899i \(0.611848\pi\)
\(912\) −21.2528 −0.703751
\(913\) −39.4087 −1.30424
\(914\) −20.6274 −0.682293
\(915\) −6.89082 −0.227803
\(916\) 2.02029 0.0667524
\(917\) 5.27999 0.174361
\(918\) −85.6525 −2.82695
\(919\) −17.1507 −0.565750 −0.282875 0.959157i \(-0.591288\pi\)
−0.282875 + 0.959157i \(0.591288\pi\)
\(920\) −0.00242341 −7.98974e−5 0
\(921\) 76.4821 2.52017
\(922\) 43.0615 1.41815
\(923\) −3.57198 −0.117573
\(924\) −25.3490 −0.833922
\(925\) −10.8597 −0.357066
\(926\) −1.11257 −0.0365613
\(927\) 75.9377 2.49412
\(928\) −24.6252 −0.808362
\(929\) −18.8004 −0.616821 −0.308411 0.951253i \(-0.599797\pi\)
−0.308411 + 0.951253i \(0.599797\pi\)
\(930\) −21.4926 −0.704771
\(931\) −1.80467 −0.0591458
\(932\) 53.6512 1.75740
\(933\) 39.9379 1.30751
\(934\) 27.0126 0.883879
\(935\) 21.2664 0.695487
\(936\) 0.127970 0.00418285
\(937\) 4.31292 0.140897 0.0704485 0.997515i \(-0.477557\pi\)
0.0704485 + 0.997515i \(0.477557\pi\)
\(938\) −3.53298 −0.115356
\(939\) 32.5083 1.06087
\(940\) 5.49364 0.179183
\(941\) −35.2484 −1.14906 −0.574532 0.818482i \(-0.694816\pi\)
−0.574532 + 0.818482i \(0.694816\pi\)
\(942\) −48.9488 −1.59484
\(943\) −0.259042 −0.00843556
\(944\) 14.7633 0.480506
\(945\) −8.47289 −0.275623
\(946\) 66.9052 2.17527
\(947\) 20.6912 0.672373 0.336187 0.941795i \(-0.390863\pi\)
0.336187 + 0.941795i \(0.390863\pi\)
\(948\) −96.9076 −3.14741
\(949\) 1.86559 0.0605598
\(950\) −3.61849 −0.117399
\(951\) −101.958 −3.30620
\(952\) −0.205144 −0.00664875
\(953\) −61.0154 −1.97648 −0.988241 0.152904i \(-0.951138\pi\)
−0.988241 + 0.152904i \(0.951138\pi\)
\(954\) −72.8876 −2.35982
\(955\) −4.78905 −0.154970
\(956\) 0.142483 0.00460824
\(957\) 38.5285 1.24545
\(958\) −6.46013 −0.208717
\(959\) 0.940881 0.0303826
\(960\) −24.2774 −0.783551
\(961\) −18.0145 −0.581114
\(962\) −11.7096 −0.377534
\(963\) −102.939 −3.31715
\(964\) 12.8552 0.414039
\(965\) 6.03763 0.194358
\(966\) 0.355229 0.0114293
\(967\) 24.9242 0.801508 0.400754 0.916186i \(-0.368748\pi\)
0.400754 + 0.916186i \(0.368748\pi\)
\(968\) 0.276369 0.00888284
\(969\) 27.0651 0.869458
\(970\) −8.83580 −0.283700
\(971\) 13.9355 0.447210 0.223605 0.974680i \(-0.428217\pi\)
0.223605 + 0.974680i \(0.428217\pi\)
\(972\) 5.32859 0.170915
\(973\) 10.5016 0.336664
\(974\) −31.3046 −1.00306
\(975\) −1.59966 −0.0512300
\(976\) 9.17116 0.293562
\(977\) 55.6211 1.77948 0.889738 0.456471i \(-0.150887\pi\)
0.889738 + 0.456471i \(0.150887\pi\)
\(978\) −21.5313 −0.688495
\(979\) −51.2607 −1.63830
\(980\) −2.02029 −0.0645359
\(981\) −30.1444 −0.962436
\(982\) 79.9498 2.55130
\(983\) −33.3702 −1.06435 −0.532173 0.846636i \(-0.678624\pi\)
−0.532173 + 0.846636i \(0.678624\pi\)
\(984\) 0.526420 0.0167817
\(985\) −10.1442 −0.323220
\(986\) 31.0416 0.988566
\(987\) −8.08869 −0.257466
\(988\) −1.96068 −0.0623777
\(989\) −0.471155 −0.0149819
\(990\) 49.4630 1.57204
\(991\) 17.7506 0.563867 0.281934 0.959434i \(-0.409024\pi\)
0.281934 + 0.959434i \(0.409024\pi\)
\(992\) 28.8983 0.917523
\(993\) −92.9906 −2.95097
\(994\) 13.3181 0.422425
\(995\) −6.70984 −0.212716
\(996\) −56.1467 −1.77908
\(997\) −61.4602 −1.94647 −0.973233 0.229822i \(-0.926186\pi\)
−0.973233 + 0.229822i \(0.926186\pi\)
\(998\) 72.4635 2.29379
\(999\) 92.0134 2.91118
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 \(a_p\))