Properties

Label 8024.2.a.y.1.11
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.823534 q^{3}\) \(+3.63980 q^{5}\) \(+3.42292 q^{7}\) \(-2.32179 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.823534 q^{3}\) \(+3.63980 q^{5}\) \(+3.42292 q^{7}\) \(-2.32179 q^{9}\) \(-1.67000 q^{11}\) \(+1.71525 q^{13}\) \(-2.99750 q^{15}\) \(-1.00000 q^{17}\) \(-8.21569 q^{19}\) \(-2.81889 q^{21}\) \(+1.40727 q^{23}\) \(+8.24811 q^{25}\) \(+4.38268 q^{27}\) \(-9.95781 q^{29}\) \(-6.20012 q^{31}\) \(+1.37530 q^{33}\) \(+12.4587 q^{35}\) \(-1.91074 q^{37}\) \(-1.41257 q^{39}\) \(+4.14541 q^{41}\) \(-7.78851 q^{43}\) \(-8.45085 q^{45}\) \(+3.59899 q^{47}\) \(+4.71635 q^{49}\) \(+0.823534 q^{51}\) \(-9.21150 q^{53}\) \(-6.07845 q^{55}\) \(+6.76590 q^{57}\) \(-1.00000 q^{59}\) \(-9.69562 q^{61}\) \(-7.94730 q^{63}\) \(+6.24317 q^{65}\) \(-7.29905 q^{67}\) \(-1.15893 q^{69}\) \(-13.5788 q^{71}\) \(+4.25258 q^{73}\) \(-6.79260 q^{75}\) \(-5.71627 q^{77}\) \(+15.8841 q^{79}\) \(+3.35609 q^{81}\) \(-7.87799 q^{83}\) \(-3.63980 q^{85}\) \(+8.20059 q^{87}\) \(+6.32519 q^{89}\) \(+5.87116 q^{91}\) \(+5.10601 q^{93}\) \(-29.9034 q^{95}\) \(+12.2886 q^{97}\) \(+3.87739 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.823534 −0.475468 −0.237734 0.971330i \(-0.576405\pi\)
−0.237734 + 0.971330i \(0.576405\pi\)
\(4\) 0 0
\(5\) 3.63980 1.62777 0.813883 0.581029i \(-0.197350\pi\)
0.813883 + 0.581029i \(0.197350\pi\)
\(6\) 0 0
\(7\) 3.42292 1.29374 0.646870 0.762600i \(-0.276078\pi\)
0.646870 + 0.762600i \(0.276078\pi\)
\(8\) 0 0
\(9\) −2.32179 −0.773931
\(10\) 0 0
\(11\) −1.67000 −0.503524 −0.251762 0.967789i \(-0.581010\pi\)
−0.251762 + 0.967789i \(0.581010\pi\)
\(12\) 0 0
\(13\) 1.71525 0.475725 0.237863 0.971299i \(-0.423553\pi\)
0.237863 + 0.971299i \(0.423553\pi\)
\(14\) 0 0
\(15\) −2.99750 −0.773950
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −8.21569 −1.88481 −0.942405 0.334475i \(-0.891441\pi\)
−0.942405 + 0.334475i \(0.891441\pi\)
\(20\) 0 0
\(21\) −2.81889 −0.615132
\(22\) 0 0
\(23\) 1.40727 0.293436 0.146718 0.989178i \(-0.453129\pi\)
0.146718 + 0.989178i \(0.453129\pi\)
\(24\) 0 0
\(25\) 8.24811 1.64962
\(26\) 0 0
\(27\) 4.38268 0.843447
\(28\) 0 0
\(29\) −9.95781 −1.84912 −0.924559 0.381039i \(-0.875566\pi\)
−0.924559 + 0.381039i \(0.875566\pi\)
\(30\) 0 0
\(31\) −6.20012 −1.11357 −0.556787 0.830655i \(-0.687966\pi\)
−0.556787 + 0.830655i \(0.687966\pi\)
\(32\) 0 0
\(33\) 1.37530 0.239409
\(34\) 0 0
\(35\) 12.4587 2.10591
\(36\) 0 0
\(37\) −1.91074 −0.314124 −0.157062 0.987589i \(-0.550202\pi\)
−0.157062 + 0.987589i \(0.550202\pi\)
\(38\) 0 0
\(39\) −1.41257 −0.226192
\(40\) 0 0
\(41\) 4.14541 0.647405 0.323702 0.946159i \(-0.395072\pi\)
0.323702 + 0.946159i \(0.395072\pi\)
\(42\) 0 0
\(43\) −7.78851 −1.18774 −0.593868 0.804563i \(-0.702400\pi\)
−0.593868 + 0.804563i \(0.702400\pi\)
\(44\) 0 0
\(45\) −8.45085 −1.25978
\(46\) 0 0
\(47\) 3.59899 0.524967 0.262483 0.964936i \(-0.415458\pi\)
0.262483 + 0.964936i \(0.415458\pi\)
\(48\) 0 0
\(49\) 4.71635 0.673765
\(50\) 0 0
\(51\) 0.823534 0.115318
\(52\) 0 0
\(53\) −9.21150 −1.26530 −0.632649 0.774439i \(-0.718032\pi\)
−0.632649 + 0.774439i \(0.718032\pi\)
\(54\) 0 0
\(55\) −6.07845 −0.819619
\(56\) 0 0
\(57\) 6.76590 0.896166
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −9.69562 −1.24140 −0.620698 0.784050i \(-0.713151\pi\)
−0.620698 + 0.784050i \(0.713151\pi\)
\(62\) 0 0
\(63\) −7.94730 −1.00127
\(64\) 0 0
\(65\) 6.24317 0.774370
\(66\) 0 0
\(67\) −7.29905 −0.891721 −0.445861 0.895102i \(-0.647102\pi\)
−0.445861 + 0.895102i \(0.647102\pi\)
\(68\) 0 0
\(69\) −1.15893 −0.139519
\(70\) 0 0
\(71\) −13.5788 −1.61151 −0.805756 0.592248i \(-0.798241\pi\)
−0.805756 + 0.592248i \(0.798241\pi\)
\(72\) 0 0
\(73\) 4.25258 0.497727 0.248863 0.968539i \(-0.419943\pi\)
0.248863 + 0.968539i \(0.419943\pi\)
\(74\) 0 0
\(75\) −6.79260 −0.784342
\(76\) 0 0
\(77\) −5.71627 −0.651429
\(78\) 0 0
\(79\) 15.8841 1.78710 0.893552 0.448960i \(-0.148205\pi\)
0.893552 + 0.448960i \(0.148205\pi\)
\(80\) 0 0
\(81\) 3.35609 0.372899
\(82\) 0 0
\(83\) −7.87799 −0.864722 −0.432361 0.901701i \(-0.642319\pi\)
−0.432361 + 0.901701i \(0.642319\pi\)
\(84\) 0 0
\(85\) −3.63980 −0.394791
\(86\) 0 0
\(87\) 8.20059 0.879196
\(88\) 0 0
\(89\) 6.32519 0.670469 0.335235 0.942135i \(-0.391184\pi\)
0.335235 + 0.942135i \(0.391184\pi\)
\(90\) 0 0
\(91\) 5.87116 0.615465
\(92\) 0 0
\(93\) 5.10601 0.529469
\(94\) 0 0
\(95\) −29.9034 −3.06803
\(96\) 0 0
\(97\) 12.2886 1.24772 0.623861 0.781535i \(-0.285563\pi\)
0.623861 + 0.781535i \(0.285563\pi\)
\(98\) 0 0
\(99\) 3.87739 0.389692
\(100\) 0 0
\(101\) −0.139659 −0.0138966 −0.00694828 0.999976i \(-0.502212\pi\)
−0.00694828 + 0.999976i \(0.502212\pi\)
\(102\) 0 0
\(103\) −17.4212 −1.71656 −0.858282 0.513178i \(-0.828468\pi\)
−0.858282 + 0.513178i \(0.828468\pi\)
\(104\) 0 0
\(105\) −10.2602 −1.00129
\(106\) 0 0
\(107\) −11.8435 −1.14496 −0.572479 0.819919i \(-0.694018\pi\)
−0.572479 + 0.819919i \(0.694018\pi\)
\(108\) 0 0
\(109\) 5.88639 0.563814 0.281907 0.959442i \(-0.409033\pi\)
0.281907 + 0.959442i \(0.409033\pi\)
\(110\) 0 0
\(111\) 1.57356 0.149356
\(112\) 0 0
\(113\) −0.374802 −0.0352584 −0.0176292 0.999845i \(-0.505612\pi\)
−0.0176292 + 0.999845i \(0.505612\pi\)
\(114\) 0 0
\(115\) 5.12218 0.477645
\(116\) 0 0
\(117\) −3.98246 −0.368178
\(118\) 0 0
\(119\) −3.42292 −0.313778
\(120\) 0 0
\(121\) −8.21110 −0.746464
\(122\) 0 0
\(123\) −3.41389 −0.307820
\(124\) 0 0
\(125\) 11.8225 1.05743
\(126\) 0 0
\(127\) −8.86284 −0.786450 −0.393225 0.919442i \(-0.628641\pi\)
−0.393225 + 0.919442i \(0.628641\pi\)
\(128\) 0 0
\(129\) 6.41410 0.564730
\(130\) 0 0
\(131\) −21.3583 −1.86609 −0.933043 0.359764i \(-0.882857\pi\)
−0.933043 + 0.359764i \(0.882857\pi\)
\(132\) 0 0
\(133\) −28.1216 −2.43845
\(134\) 0 0
\(135\) 15.9520 1.37293
\(136\) 0 0
\(137\) −11.7961 −1.00781 −0.503903 0.863760i \(-0.668103\pi\)
−0.503903 + 0.863760i \(0.668103\pi\)
\(138\) 0 0
\(139\) −7.38315 −0.626230 −0.313115 0.949715i \(-0.601373\pi\)
−0.313115 + 0.949715i \(0.601373\pi\)
\(140\) 0 0
\(141\) −2.96389 −0.249605
\(142\) 0 0
\(143\) −2.86447 −0.239539
\(144\) 0 0
\(145\) −36.2444 −3.00993
\(146\) 0 0
\(147\) −3.88408 −0.320353
\(148\) 0 0
\(149\) 17.2514 1.41329 0.706645 0.707568i \(-0.250208\pi\)
0.706645 + 0.707568i \(0.250208\pi\)
\(150\) 0 0
\(151\) −10.7179 −0.872209 −0.436104 0.899896i \(-0.643642\pi\)
−0.436104 + 0.899896i \(0.643642\pi\)
\(152\) 0 0
\(153\) 2.32179 0.187706
\(154\) 0 0
\(155\) −22.5672 −1.81264
\(156\) 0 0
\(157\) 10.8328 0.864551 0.432276 0.901741i \(-0.357711\pi\)
0.432276 + 0.901741i \(0.357711\pi\)
\(158\) 0 0
\(159\) 7.58599 0.601608
\(160\) 0 0
\(161\) 4.81697 0.379630
\(162\) 0 0
\(163\) 13.6522 1.06932 0.534661 0.845067i \(-0.320439\pi\)
0.534661 + 0.845067i \(0.320439\pi\)
\(164\) 0 0
\(165\) 5.00581 0.389702
\(166\) 0 0
\(167\) 18.6055 1.43974 0.719869 0.694110i \(-0.244202\pi\)
0.719869 + 0.694110i \(0.244202\pi\)
\(168\) 0 0
\(169\) −10.0579 −0.773685
\(170\) 0 0
\(171\) 19.0751 1.45871
\(172\) 0 0
\(173\) 9.08486 0.690709 0.345354 0.938472i \(-0.387759\pi\)
0.345354 + 0.938472i \(0.387759\pi\)
\(174\) 0 0
\(175\) 28.2326 2.13418
\(176\) 0 0
\(177\) 0.823534 0.0619006
\(178\) 0 0
\(179\) −8.47002 −0.633079 −0.316539 0.948579i \(-0.602521\pi\)
−0.316539 + 0.948579i \(0.602521\pi\)
\(180\) 0 0
\(181\) −10.8643 −0.807537 −0.403769 0.914861i \(-0.632300\pi\)
−0.403769 + 0.914861i \(0.632300\pi\)
\(182\) 0 0
\(183\) 7.98467 0.590244
\(184\) 0 0
\(185\) −6.95470 −0.511320
\(186\) 0 0
\(187\) 1.67000 0.122122
\(188\) 0 0
\(189\) 15.0015 1.09120
\(190\) 0 0
\(191\) 9.82479 0.710897 0.355448 0.934696i \(-0.384328\pi\)
0.355448 + 0.934696i \(0.384328\pi\)
\(192\) 0 0
\(193\) 3.28013 0.236109 0.118054 0.993007i \(-0.462334\pi\)
0.118054 + 0.993007i \(0.462334\pi\)
\(194\) 0 0
\(195\) −5.14146 −0.368188
\(196\) 0 0
\(197\) 11.3655 0.809761 0.404880 0.914370i \(-0.367313\pi\)
0.404880 + 0.914370i \(0.367313\pi\)
\(198\) 0 0
\(199\) 17.8798 1.26746 0.633731 0.773554i \(-0.281523\pi\)
0.633731 + 0.773554i \(0.281523\pi\)
\(200\) 0 0
\(201\) 6.01102 0.423985
\(202\) 0 0
\(203\) −34.0847 −2.39228
\(204\) 0 0
\(205\) 15.0885 1.05382
\(206\) 0 0
\(207\) −3.26739 −0.227099
\(208\) 0 0
\(209\) 13.7202 0.949046
\(210\) 0 0
\(211\) 12.3055 0.847146 0.423573 0.905862i \(-0.360776\pi\)
0.423573 + 0.905862i \(0.360776\pi\)
\(212\) 0 0
\(213\) 11.1826 0.766221
\(214\) 0 0
\(215\) −28.3486 −1.93336
\(216\) 0 0
\(217\) −21.2225 −1.44068
\(218\) 0 0
\(219\) −3.50214 −0.236653
\(220\) 0 0
\(221\) −1.71525 −0.115380
\(222\) 0 0
\(223\) 7.01903 0.470029 0.235015 0.971992i \(-0.424486\pi\)
0.235015 + 0.971992i \(0.424486\pi\)
\(224\) 0 0
\(225\) −19.1504 −1.27669
\(226\) 0 0
\(227\) −12.0704 −0.801140 −0.400570 0.916266i \(-0.631188\pi\)
−0.400570 + 0.916266i \(0.631188\pi\)
\(228\) 0 0
\(229\) 14.8254 0.979689 0.489845 0.871810i \(-0.337053\pi\)
0.489845 + 0.871810i \(0.337053\pi\)
\(230\) 0 0
\(231\) 4.70754 0.309733
\(232\) 0 0
\(233\) −7.32389 −0.479804 −0.239902 0.970797i \(-0.577115\pi\)
−0.239902 + 0.970797i \(0.577115\pi\)
\(234\) 0 0
\(235\) 13.0996 0.854523
\(236\) 0 0
\(237\) −13.0811 −0.849710
\(238\) 0 0
\(239\) −8.14583 −0.526910 −0.263455 0.964672i \(-0.584862\pi\)
−0.263455 + 0.964672i \(0.584862\pi\)
\(240\) 0 0
\(241\) 0.717882 0.0462428 0.0231214 0.999733i \(-0.492640\pi\)
0.0231214 + 0.999733i \(0.492640\pi\)
\(242\) 0 0
\(243\) −15.9119 −1.02075
\(244\) 0 0
\(245\) 17.1666 1.09673
\(246\) 0 0
\(247\) −14.0920 −0.896652
\(248\) 0 0
\(249\) 6.48779 0.411147
\(250\) 0 0
\(251\) 31.0093 1.95729 0.978645 0.205557i \(-0.0659007\pi\)
0.978645 + 0.205557i \(0.0659007\pi\)
\(252\) 0 0
\(253\) −2.35014 −0.147752
\(254\) 0 0
\(255\) 2.99750 0.187710
\(256\) 0 0
\(257\) 22.3229 1.39247 0.696233 0.717816i \(-0.254858\pi\)
0.696233 + 0.717816i \(0.254858\pi\)
\(258\) 0 0
\(259\) −6.54030 −0.406394
\(260\) 0 0
\(261\) 23.1199 1.43109
\(262\) 0 0
\(263\) 22.6184 1.39471 0.697355 0.716726i \(-0.254360\pi\)
0.697355 + 0.716726i \(0.254360\pi\)
\(264\) 0 0
\(265\) −33.5280 −2.05961
\(266\) 0 0
\(267\) −5.20901 −0.318786
\(268\) 0 0
\(269\) 8.03588 0.489956 0.244978 0.969529i \(-0.421219\pi\)
0.244978 + 0.969529i \(0.421219\pi\)
\(270\) 0 0
\(271\) 2.90056 0.176196 0.0880982 0.996112i \(-0.471921\pi\)
0.0880982 + 0.996112i \(0.471921\pi\)
\(272\) 0 0
\(273\) −4.83510 −0.292634
\(274\) 0 0
\(275\) −13.7743 −0.830624
\(276\) 0 0
\(277\) 7.72804 0.464333 0.232167 0.972676i \(-0.425419\pi\)
0.232167 + 0.972676i \(0.425419\pi\)
\(278\) 0 0
\(279\) 14.3954 0.861830
\(280\) 0 0
\(281\) 5.90146 0.352051 0.176026 0.984386i \(-0.443676\pi\)
0.176026 + 0.984386i \(0.443676\pi\)
\(282\) 0 0
\(283\) 30.2948 1.80084 0.900419 0.435024i \(-0.143260\pi\)
0.900419 + 0.435024i \(0.143260\pi\)
\(284\) 0 0
\(285\) 24.6265 1.45875
\(286\) 0 0
\(287\) 14.1894 0.837573
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −10.1201 −0.593252
\(292\) 0 0
\(293\) 20.1311 1.17607 0.588036 0.808835i \(-0.299901\pi\)
0.588036 + 0.808835i \(0.299901\pi\)
\(294\) 0 0
\(295\) −3.63980 −0.211917
\(296\) 0 0
\(297\) −7.31906 −0.424695
\(298\) 0 0
\(299\) 2.41382 0.139595
\(300\) 0 0
\(301\) −26.6594 −1.53662
\(302\) 0 0
\(303\) 0.115014 0.00660736
\(304\) 0 0
\(305\) −35.2901 −2.02070
\(306\) 0 0
\(307\) −10.4030 −0.593729 −0.296864 0.954920i \(-0.595941\pi\)
−0.296864 + 0.954920i \(0.595941\pi\)
\(308\) 0 0
\(309\) 14.3470 0.816171
\(310\) 0 0
\(311\) −10.0866 −0.571959 −0.285979 0.958236i \(-0.592319\pi\)
−0.285979 + 0.958236i \(0.592319\pi\)
\(312\) 0 0
\(313\) −13.7156 −0.775254 −0.387627 0.921816i \(-0.626705\pi\)
−0.387627 + 0.921816i \(0.626705\pi\)
\(314\) 0 0
\(315\) −28.9265 −1.62983
\(316\) 0 0
\(317\) −32.6090 −1.83150 −0.915751 0.401745i \(-0.868404\pi\)
−0.915751 + 0.401745i \(0.868404\pi\)
\(318\) 0 0
\(319\) 16.6295 0.931074
\(320\) 0 0
\(321\) 9.75356 0.544390
\(322\) 0 0
\(323\) 8.21569 0.457133
\(324\) 0 0
\(325\) 14.1476 0.784767
\(326\) 0 0
\(327\) −4.84764 −0.268075
\(328\) 0 0
\(329\) 12.3190 0.679171
\(330\) 0 0
\(331\) −2.91630 −0.160294 −0.0801472 0.996783i \(-0.525539\pi\)
−0.0801472 + 0.996783i \(0.525539\pi\)
\(332\) 0 0
\(333\) 4.43634 0.243110
\(334\) 0 0
\(335\) −26.5671 −1.45151
\(336\) 0 0
\(337\) −7.45047 −0.405853 −0.202926 0.979194i \(-0.565045\pi\)
−0.202926 + 0.979194i \(0.565045\pi\)
\(338\) 0 0
\(339\) 0.308662 0.0167642
\(340\) 0 0
\(341\) 10.3542 0.560711
\(342\) 0 0
\(343\) −7.81673 −0.422064
\(344\) 0 0
\(345\) −4.21829 −0.227105
\(346\) 0 0
\(347\) 1.08658 0.0583307 0.0291653 0.999575i \(-0.490715\pi\)
0.0291653 + 0.999575i \(0.490715\pi\)
\(348\) 0 0
\(349\) 29.8659 1.59869 0.799344 0.600874i \(-0.205181\pi\)
0.799344 + 0.600874i \(0.205181\pi\)
\(350\) 0 0
\(351\) 7.51740 0.401249
\(352\) 0 0
\(353\) 30.3790 1.61691 0.808454 0.588559i \(-0.200305\pi\)
0.808454 + 0.588559i \(0.200305\pi\)
\(354\) 0 0
\(355\) −49.4242 −2.62316
\(356\) 0 0
\(357\) 2.81889 0.149191
\(358\) 0 0
\(359\) 28.7554 1.51765 0.758826 0.651293i \(-0.225773\pi\)
0.758826 + 0.651293i \(0.225773\pi\)
\(360\) 0 0
\(361\) 48.4976 2.55251
\(362\) 0 0
\(363\) 6.76212 0.354919
\(364\) 0 0
\(365\) 15.4785 0.810183
\(366\) 0 0
\(367\) −10.1650 −0.530609 −0.265305 0.964165i \(-0.585473\pi\)
−0.265305 + 0.964165i \(0.585473\pi\)
\(368\) 0 0
\(369\) −9.62478 −0.501046
\(370\) 0 0
\(371\) −31.5302 −1.63697
\(372\) 0 0
\(373\) −12.3167 −0.637733 −0.318866 0.947800i \(-0.603302\pi\)
−0.318866 + 0.947800i \(0.603302\pi\)
\(374\) 0 0
\(375\) −9.73620 −0.502775
\(376\) 0 0
\(377\) −17.0801 −0.879672
\(378\) 0 0
\(379\) −21.7104 −1.11519 −0.557593 0.830114i \(-0.688275\pi\)
−0.557593 + 0.830114i \(0.688275\pi\)
\(380\) 0 0
\(381\) 7.29885 0.373932
\(382\) 0 0
\(383\) −25.1847 −1.28688 −0.643438 0.765498i \(-0.722493\pi\)
−0.643438 + 0.765498i \(0.722493\pi\)
\(384\) 0 0
\(385\) −20.8060 −1.06037
\(386\) 0 0
\(387\) 18.0833 0.919225
\(388\) 0 0
\(389\) 19.3852 0.982870 0.491435 0.870914i \(-0.336472\pi\)
0.491435 + 0.870914i \(0.336472\pi\)
\(390\) 0 0
\(391\) −1.40727 −0.0711687
\(392\) 0 0
\(393\) 17.5893 0.887264
\(394\) 0 0
\(395\) 57.8150 2.90899
\(396\) 0 0
\(397\) −8.35493 −0.419322 −0.209661 0.977774i \(-0.567236\pi\)
−0.209661 + 0.977774i \(0.567236\pi\)
\(398\) 0 0
\(399\) 23.1591 1.15941
\(400\) 0 0
\(401\) −14.7173 −0.734946 −0.367473 0.930034i \(-0.619777\pi\)
−0.367473 + 0.930034i \(0.619777\pi\)
\(402\) 0 0
\(403\) −10.6348 −0.529756
\(404\) 0 0
\(405\) 12.2155 0.606992
\(406\) 0 0
\(407\) 3.19093 0.158169
\(408\) 0 0
\(409\) −15.5965 −0.771195 −0.385597 0.922667i \(-0.626005\pi\)
−0.385597 + 0.922667i \(0.626005\pi\)
\(410\) 0 0
\(411\) 9.71446 0.479179
\(412\) 0 0
\(413\) −3.42292 −0.168431
\(414\) 0 0
\(415\) −28.6743 −1.40757
\(416\) 0 0
\(417\) 6.08027 0.297752
\(418\) 0 0
\(419\) −23.7769 −1.16158 −0.580789 0.814054i \(-0.697256\pi\)
−0.580789 + 0.814054i \(0.697256\pi\)
\(420\) 0 0
\(421\) 5.13183 0.250110 0.125055 0.992150i \(-0.460089\pi\)
0.125055 + 0.992150i \(0.460089\pi\)
\(422\) 0 0
\(423\) −8.35611 −0.406288
\(424\) 0 0
\(425\) −8.24811 −0.400092
\(426\) 0 0
\(427\) −33.1873 −1.60604
\(428\) 0 0
\(429\) 2.35899 0.113893
\(430\) 0 0
\(431\) −15.5724 −0.750094 −0.375047 0.927006i \(-0.622374\pi\)
−0.375047 + 0.927006i \(0.622374\pi\)
\(432\) 0 0
\(433\) 3.35744 0.161348 0.0806742 0.996741i \(-0.474293\pi\)
0.0806742 + 0.996741i \(0.474293\pi\)
\(434\) 0 0
\(435\) 29.8485 1.43113
\(436\) 0 0
\(437\) −11.5617 −0.553071
\(438\) 0 0
\(439\) 13.2109 0.630521 0.315261 0.949005i \(-0.397908\pi\)
0.315261 + 0.949005i \(0.397908\pi\)
\(440\) 0 0
\(441\) −10.9504 −0.521447
\(442\) 0 0
\(443\) −15.8529 −0.753195 −0.376598 0.926377i \(-0.622906\pi\)
−0.376598 + 0.926377i \(0.622906\pi\)
\(444\) 0 0
\(445\) 23.0224 1.09137
\(446\) 0 0
\(447\) −14.2071 −0.671974
\(448\) 0 0
\(449\) 34.2691 1.61726 0.808630 0.588317i \(-0.200209\pi\)
0.808630 + 0.588317i \(0.200209\pi\)
\(450\) 0 0
\(451\) −6.92283 −0.325983
\(452\) 0 0
\(453\) 8.82654 0.414707
\(454\) 0 0
\(455\) 21.3698 1.00183
\(456\) 0 0
\(457\) −19.3054 −0.903068 −0.451534 0.892254i \(-0.649123\pi\)
−0.451534 + 0.892254i \(0.649123\pi\)
\(458\) 0 0
\(459\) −4.38268 −0.204566
\(460\) 0 0
\(461\) −16.8151 −0.783157 −0.391579 0.920145i \(-0.628071\pi\)
−0.391579 + 0.920145i \(0.628071\pi\)
\(462\) 0 0
\(463\) −23.5431 −1.09414 −0.547070 0.837087i \(-0.684257\pi\)
−0.547070 + 0.837087i \(0.684257\pi\)
\(464\) 0 0
\(465\) 18.5848 0.861851
\(466\) 0 0
\(467\) −20.8183 −0.963356 −0.481678 0.876348i \(-0.659972\pi\)
−0.481678 + 0.876348i \(0.659972\pi\)
\(468\) 0 0
\(469\) −24.9841 −1.15366
\(470\) 0 0
\(471\) −8.92118 −0.411066
\(472\) 0 0
\(473\) 13.0068 0.598053
\(474\) 0 0
\(475\) −67.7640 −3.10922
\(476\) 0 0
\(477\) 21.3872 0.979252
\(478\) 0 0
\(479\) −29.0694 −1.32821 −0.664107 0.747637i \(-0.731188\pi\)
−0.664107 + 0.747637i \(0.731188\pi\)
\(480\) 0 0
\(481\) −3.27740 −0.149437
\(482\) 0 0
\(483\) −3.96694 −0.180502
\(484\) 0 0
\(485\) 44.7282 2.03100
\(486\) 0 0
\(487\) −12.2714 −0.556068 −0.278034 0.960571i \(-0.589683\pi\)
−0.278034 + 0.960571i \(0.589683\pi\)
\(488\) 0 0
\(489\) −11.2430 −0.508428
\(490\) 0 0
\(491\) 19.8158 0.894277 0.447138 0.894465i \(-0.352443\pi\)
0.447138 + 0.894465i \(0.352443\pi\)
\(492\) 0 0
\(493\) 9.95781 0.448477
\(494\) 0 0
\(495\) 14.1129 0.634328
\(496\) 0 0
\(497\) −46.4792 −2.08488
\(498\) 0 0
\(499\) −6.43165 −0.287920 −0.143960 0.989584i \(-0.545984\pi\)
−0.143960 + 0.989584i \(0.545984\pi\)
\(500\) 0 0
\(501\) −15.3223 −0.684549
\(502\) 0 0
\(503\) 10.2693 0.457886 0.228943 0.973440i \(-0.426473\pi\)
0.228943 + 0.973440i \(0.426473\pi\)
\(504\) 0 0
\(505\) −0.508329 −0.0226203
\(506\) 0 0
\(507\) 8.28303 0.367862
\(508\) 0 0
\(509\) 15.6208 0.692380 0.346190 0.938164i \(-0.387475\pi\)
0.346190 + 0.938164i \(0.387475\pi\)
\(510\) 0 0
\(511\) 14.5562 0.643929
\(512\) 0 0
\(513\) −36.0067 −1.58974
\(514\) 0 0
\(515\) −63.4097 −2.79416
\(516\) 0 0
\(517\) −6.01031 −0.264333
\(518\) 0 0
\(519\) −7.48169 −0.328410
\(520\) 0 0
\(521\) 5.55808 0.243504 0.121752 0.992561i \(-0.461149\pi\)
0.121752 + 0.992561i \(0.461149\pi\)
\(522\) 0 0
\(523\) 4.22156 0.184596 0.0922980 0.995731i \(-0.470579\pi\)
0.0922980 + 0.995731i \(0.470579\pi\)
\(524\) 0 0
\(525\) −23.2505 −1.01474
\(526\) 0 0
\(527\) 6.20012 0.270082
\(528\) 0 0
\(529\) −21.0196 −0.913895
\(530\) 0 0
\(531\) 2.32179 0.100757
\(532\) 0 0
\(533\) 7.11043 0.307987
\(534\) 0 0
\(535\) −43.1081 −1.86372
\(536\) 0 0
\(537\) 6.97535 0.301009
\(538\) 0 0
\(539\) −7.87630 −0.339256
\(540\) 0 0
\(541\) −39.0422 −1.67856 −0.839278 0.543703i \(-0.817022\pi\)
−0.839278 + 0.543703i \(0.817022\pi\)
\(542\) 0 0
\(543\) 8.94712 0.383958
\(544\) 0 0
\(545\) 21.4253 0.917757
\(546\) 0 0
\(547\) −27.8232 −1.18964 −0.594818 0.803861i \(-0.702776\pi\)
−0.594818 + 0.803861i \(0.702776\pi\)
\(548\) 0 0
\(549\) 22.5112 0.960755
\(550\) 0 0
\(551\) 81.8103 3.48523
\(552\) 0 0
\(553\) 54.3700 2.31205
\(554\) 0 0
\(555\) 5.72743 0.243116
\(556\) 0 0
\(557\) −35.7360 −1.51418 −0.757092 0.653308i \(-0.773381\pi\)
−0.757092 + 0.653308i \(0.773381\pi\)
\(558\) 0 0
\(559\) −13.3593 −0.565036
\(560\) 0 0
\(561\) −1.37530 −0.0580652
\(562\) 0 0
\(563\) −36.5933 −1.54222 −0.771112 0.636700i \(-0.780299\pi\)
−0.771112 + 0.636700i \(0.780299\pi\)
\(564\) 0 0
\(565\) −1.36420 −0.0573924
\(566\) 0 0
\(567\) 11.4876 0.482435
\(568\) 0 0
\(569\) 38.6467 1.62016 0.810078 0.586323i \(-0.199425\pi\)
0.810078 + 0.586323i \(0.199425\pi\)
\(570\) 0 0
\(571\) 23.8657 0.998747 0.499374 0.866387i \(-0.333564\pi\)
0.499374 + 0.866387i \(0.333564\pi\)
\(572\) 0 0
\(573\) −8.09105 −0.338008
\(574\) 0 0
\(575\) 11.6073 0.484059
\(576\) 0 0
\(577\) 8.29767 0.345437 0.172718 0.984971i \(-0.444745\pi\)
0.172718 + 0.984971i \(0.444745\pi\)
\(578\) 0 0
\(579\) −2.70130 −0.112262
\(580\) 0 0
\(581\) −26.9657 −1.11873
\(582\) 0 0
\(583\) 15.3832 0.637107
\(584\) 0 0
\(585\) −14.4953 −0.599308
\(586\) 0 0
\(587\) −1.22441 −0.0505367 −0.0252684 0.999681i \(-0.508044\pi\)
−0.0252684 + 0.999681i \(0.508044\pi\)
\(588\) 0 0
\(589\) 50.9383 2.09888
\(590\) 0 0
\(591\) −9.35990 −0.385015
\(592\) 0 0
\(593\) 28.8137 1.18324 0.591618 0.806219i \(-0.298490\pi\)
0.591618 + 0.806219i \(0.298490\pi\)
\(594\) 0 0
\(595\) −12.4587 −0.510758
\(596\) 0 0
\(597\) −14.7246 −0.602637
\(598\) 0 0
\(599\) 35.4720 1.44935 0.724673 0.689093i \(-0.241991\pi\)
0.724673 + 0.689093i \(0.241991\pi\)
\(600\) 0 0
\(601\) −25.8542 −1.05461 −0.527307 0.849675i \(-0.676798\pi\)
−0.527307 + 0.849675i \(0.676798\pi\)
\(602\) 0 0
\(603\) 16.9469 0.690130
\(604\) 0 0
\(605\) −29.8867 −1.21507
\(606\) 0 0
\(607\) −22.6106 −0.917737 −0.458869 0.888504i \(-0.651745\pi\)
−0.458869 + 0.888504i \(0.651745\pi\)
\(608\) 0 0
\(609\) 28.0699 1.13745
\(610\) 0 0
\(611\) 6.17318 0.249740
\(612\) 0 0
\(613\) 20.9462 0.846009 0.423005 0.906128i \(-0.360975\pi\)
0.423005 + 0.906128i \(0.360975\pi\)
\(614\) 0 0
\(615\) −12.4259 −0.501059
\(616\) 0 0
\(617\) −29.7620 −1.19817 −0.599086 0.800685i \(-0.704469\pi\)
−0.599086 + 0.800685i \(0.704469\pi\)
\(618\) 0 0
\(619\) −25.5098 −1.02533 −0.512663 0.858590i \(-0.671341\pi\)
−0.512663 + 0.858590i \(0.671341\pi\)
\(620\) 0 0
\(621\) 6.16761 0.247498
\(622\) 0 0
\(623\) 21.6506 0.867413
\(624\) 0 0
\(625\) 1.79080 0.0716321
\(626\) 0 0
\(627\) −11.2990 −0.451241
\(628\) 0 0
\(629\) 1.91074 0.0761862
\(630\) 0 0
\(631\) 1.66481 0.0662751 0.0331376 0.999451i \(-0.489450\pi\)
0.0331376 + 0.999451i \(0.489450\pi\)
\(632\) 0 0
\(633\) −10.1340 −0.402790
\(634\) 0 0
\(635\) −32.2589 −1.28016
\(636\) 0 0
\(637\) 8.08974 0.320527
\(638\) 0 0
\(639\) 31.5272 1.24720
\(640\) 0 0
\(641\) −2.10967 −0.0833271 −0.0416636 0.999132i \(-0.513266\pi\)
−0.0416636 + 0.999132i \(0.513266\pi\)
\(642\) 0 0
\(643\) 0.0991497 0.00391008 0.00195504 0.999998i \(-0.499378\pi\)
0.00195504 + 0.999998i \(0.499378\pi\)
\(644\) 0 0
\(645\) 23.3460 0.919248
\(646\) 0 0
\(647\) −18.7453 −0.736956 −0.368478 0.929637i \(-0.620121\pi\)
−0.368478 + 0.929637i \(0.620121\pi\)
\(648\) 0 0
\(649\) 1.67000 0.0655532
\(650\) 0 0
\(651\) 17.4775 0.684995
\(652\) 0 0
\(653\) −30.5985 −1.19741 −0.598707 0.800968i \(-0.704318\pi\)
−0.598707 + 0.800968i \(0.704318\pi\)
\(654\) 0 0
\(655\) −77.7400 −3.03755
\(656\) 0 0
\(657\) −9.87361 −0.385206
\(658\) 0 0
\(659\) −34.2995 −1.33612 −0.668059 0.744108i \(-0.732875\pi\)
−0.668059 + 0.744108i \(0.732875\pi\)
\(660\) 0 0
\(661\) 12.6750 0.492999 0.246500 0.969143i \(-0.420720\pi\)
0.246500 + 0.969143i \(0.420720\pi\)
\(662\) 0 0
\(663\) 1.41257 0.0548596
\(664\) 0 0
\(665\) −102.357 −3.96923
\(666\) 0 0
\(667\) −14.0133 −0.542598
\(668\) 0 0
\(669\) −5.78041 −0.223484
\(670\) 0 0
\(671\) 16.1917 0.625072
\(672\) 0 0
\(673\) −11.4390 −0.440940 −0.220470 0.975394i \(-0.570759\pi\)
−0.220470 + 0.975394i \(0.570759\pi\)
\(674\) 0 0
\(675\) 36.1488 1.39137
\(676\) 0 0
\(677\) 28.5089 1.09569 0.547844 0.836581i \(-0.315449\pi\)
0.547844 + 0.836581i \(0.315449\pi\)
\(678\) 0 0
\(679\) 42.0630 1.61423
\(680\) 0 0
\(681\) 9.94038 0.380916
\(682\) 0 0
\(683\) −26.8553 −1.02759 −0.513795 0.857913i \(-0.671761\pi\)
−0.513795 + 0.857913i \(0.671761\pi\)
\(684\) 0 0
\(685\) −42.9353 −1.64047
\(686\) 0 0
\(687\) −12.2092 −0.465811
\(688\) 0 0
\(689\) −15.8001 −0.601934
\(690\) 0 0
\(691\) 40.7700 1.55096 0.775482 0.631370i \(-0.217507\pi\)
0.775482 + 0.631370i \(0.217507\pi\)
\(692\) 0 0
\(693\) 13.2720 0.504161
\(694\) 0 0
\(695\) −26.8732 −1.01936
\(696\) 0 0
\(697\) −4.14541 −0.157019
\(698\) 0 0
\(699\) 6.03148 0.228131
\(700\) 0 0
\(701\) 25.4972 0.963016 0.481508 0.876442i \(-0.340089\pi\)
0.481508 + 0.876442i \(0.340089\pi\)
\(702\) 0 0
\(703\) 15.6980 0.592063
\(704\) 0 0
\(705\) −10.7880 −0.406298
\(706\) 0 0
\(707\) −0.478040 −0.0179785
\(708\) 0 0
\(709\) 14.0923 0.529246 0.264623 0.964352i \(-0.414752\pi\)
0.264623 + 0.964352i \(0.414752\pi\)
\(710\) 0 0
\(711\) −36.8796 −1.38309
\(712\) 0 0
\(713\) −8.72525 −0.326763
\(714\) 0 0
\(715\) −10.4261 −0.389913
\(716\) 0 0
\(717\) 6.70837 0.250529
\(718\) 0 0
\(719\) 36.8851 1.37558 0.687791 0.725909i \(-0.258581\pi\)
0.687791 + 0.725909i \(0.258581\pi\)
\(720\) 0 0
\(721\) −59.6314 −2.22079
\(722\) 0 0
\(723\) −0.591200 −0.0219870
\(724\) 0 0
\(725\) −82.1331 −3.05035
\(726\) 0 0
\(727\) −27.3173 −1.01314 −0.506572 0.862198i \(-0.669087\pi\)
−0.506572 + 0.862198i \(0.669087\pi\)
\(728\) 0 0
\(729\) 3.03571 0.112434
\(730\) 0 0
\(731\) 7.78851 0.288068
\(732\) 0 0
\(733\) −6.50008 −0.240086 −0.120043 0.992769i \(-0.538303\pi\)
−0.120043 + 0.992769i \(0.538303\pi\)
\(734\) 0 0
\(735\) −14.1372 −0.521460
\(736\) 0 0
\(737\) 12.1894 0.449003
\(738\) 0 0
\(739\) 53.5474 1.96977 0.984887 0.173201i \(-0.0554109\pi\)
0.984887 + 0.173201i \(0.0554109\pi\)
\(740\) 0 0
\(741\) 11.6052 0.426329
\(742\) 0 0
\(743\) −22.3363 −0.819441 −0.409720 0.912211i \(-0.634374\pi\)
−0.409720 + 0.912211i \(0.634374\pi\)
\(744\) 0 0
\(745\) 62.7916 2.30051
\(746\) 0 0
\(747\) 18.2911 0.669235
\(748\) 0 0
\(749\) −40.5394 −1.48128
\(750\) 0 0
\(751\) 18.5529 0.677004 0.338502 0.940966i \(-0.390080\pi\)
0.338502 + 0.940966i \(0.390080\pi\)
\(752\) 0 0
\(753\) −25.5372 −0.930628
\(754\) 0 0
\(755\) −39.0109 −1.41975
\(756\) 0 0
\(757\) 26.2770 0.955054 0.477527 0.878617i \(-0.341533\pi\)
0.477527 + 0.878617i \(0.341533\pi\)
\(758\) 0 0
\(759\) 1.93542 0.0702513
\(760\) 0 0
\(761\) −36.6124 −1.32720 −0.663600 0.748088i \(-0.730972\pi\)
−0.663600 + 0.748088i \(0.730972\pi\)
\(762\) 0 0
\(763\) 20.1486 0.729429
\(764\) 0 0
\(765\) 8.45085 0.305541
\(766\) 0 0
\(767\) −1.71525 −0.0619342
\(768\) 0 0
\(769\) 42.6282 1.53721 0.768606 0.639723i \(-0.220951\pi\)
0.768606 + 0.639723i \(0.220951\pi\)
\(770\) 0 0
\(771\) −18.3837 −0.662073
\(772\) 0 0
\(773\) 4.55031 0.163663 0.0818316 0.996646i \(-0.473923\pi\)
0.0818316 + 0.996646i \(0.473923\pi\)
\(774\) 0 0
\(775\) −51.1393 −1.83698
\(776\) 0 0
\(777\) 5.38616 0.193227
\(778\) 0 0
\(779\) −34.0574 −1.22023
\(780\) 0 0
\(781\) 22.6766 0.811434
\(782\) 0 0
\(783\) −43.6418 −1.55963
\(784\) 0 0
\(785\) 39.4292 1.40729
\(786\) 0 0
\(787\) 40.8442 1.45594 0.727969 0.685610i \(-0.240464\pi\)
0.727969 + 0.685610i \(0.240464\pi\)
\(788\) 0 0
\(789\) −18.6270 −0.663139
\(790\) 0 0
\(791\) −1.28291 −0.0456152
\(792\) 0 0
\(793\) −16.6304 −0.590564
\(794\) 0 0
\(795\) 27.6114 0.979277
\(796\) 0 0
\(797\) 39.3181 1.39272 0.696359 0.717694i \(-0.254802\pi\)
0.696359 + 0.717694i \(0.254802\pi\)
\(798\) 0 0
\(799\) −3.59899 −0.127323
\(800\) 0 0
\(801\) −14.6858 −0.518897
\(802\) 0 0
\(803\) −7.10180 −0.250617
\(804\) 0 0
\(805\) 17.5328 0.617949
\(806\) 0 0
\(807\) −6.61782 −0.232958
\(808\) 0 0
\(809\) 23.0635 0.810871 0.405435 0.914124i \(-0.367120\pi\)
0.405435 + 0.914124i \(0.367120\pi\)
\(810\) 0 0
\(811\) −34.6779 −1.21770 −0.608852 0.793284i \(-0.708370\pi\)
−0.608852 + 0.793284i \(0.708370\pi\)
\(812\) 0 0
\(813\) −2.38871 −0.0837757
\(814\) 0 0
\(815\) 49.6912 1.74061
\(816\) 0 0
\(817\) 63.9880 2.23866
\(818\) 0 0
\(819\) −13.6316 −0.476327
\(820\) 0 0
\(821\) −16.0009 −0.558434 −0.279217 0.960228i \(-0.590075\pi\)
−0.279217 + 0.960228i \(0.590075\pi\)
\(822\) 0 0
\(823\) −19.6078 −0.683485 −0.341742 0.939794i \(-0.611017\pi\)
−0.341742 + 0.939794i \(0.611017\pi\)
\(824\) 0 0
\(825\) 11.3436 0.394935
\(826\) 0 0
\(827\) 0.558266 0.0194128 0.00970641 0.999953i \(-0.496910\pi\)
0.00970641 + 0.999953i \(0.496910\pi\)
\(828\) 0 0
\(829\) −42.5804 −1.47888 −0.739439 0.673224i \(-0.764909\pi\)
−0.739439 + 0.673224i \(0.764909\pi\)
\(830\) 0 0
\(831\) −6.36431 −0.220775
\(832\) 0 0
\(833\) −4.71635 −0.163412
\(834\) 0 0
\(835\) 67.7203 2.34356
\(836\) 0 0
\(837\) −27.1731 −0.939241
\(838\) 0 0
\(839\) 12.9527 0.447178 0.223589 0.974684i \(-0.428223\pi\)
0.223589 + 0.974684i \(0.428223\pi\)
\(840\) 0 0
\(841\) 70.1579 2.41924
\(842\) 0 0
\(843\) −4.86005 −0.167389
\(844\) 0 0
\(845\) −36.6087 −1.25938
\(846\) 0 0
\(847\) −28.1059 −0.965731
\(848\) 0 0
\(849\) −24.9488 −0.856240
\(850\) 0 0
\(851\) −2.68893 −0.0921752
\(852\) 0 0
\(853\) 40.7420 1.39498 0.697490 0.716594i \(-0.254300\pi\)
0.697490 + 0.716594i \(0.254300\pi\)
\(854\) 0 0
\(855\) 69.4296 2.37444
\(856\) 0 0
\(857\) −45.3564 −1.54934 −0.774672 0.632363i \(-0.782085\pi\)
−0.774672 + 0.632363i \(0.782085\pi\)
\(858\) 0 0
\(859\) −3.30053 −0.112613 −0.0563064 0.998414i \(-0.517932\pi\)
−0.0563064 + 0.998414i \(0.517932\pi\)
\(860\) 0 0
\(861\) −11.6855 −0.398239
\(862\) 0 0
\(863\) −32.4319 −1.10399 −0.551997 0.833846i \(-0.686134\pi\)
−0.551997 + 0.833846i \(0.686134\pi\)
\(864\) 0 0
\(865\) 33.0670 1.12431
\(866\) 0 0
\(867\) −0.823534 −0.0279687
\(868\) 0 0
\(869\) −26.5265 −0.899849
\(870\) 0 0
\(871\) −12.5197 −0.424215
\(872\) 0 0
\(873\) −28.5317 −0.965651
\(874\) 0 0
\(875\) 40.4673 1.36804
\(876\) 0 0
\(877\) −28.1805 −0.951587 −0.475794 0.879557i \(-0.657839\pi\)
−0.475794 + 0.879557i \(0.657839\pi\)
\(878\) 0 0
\(879\) −16.5787 −0.559184
\(880\) 0 0
\(881\) −41.2321 −1.38915 −0.694573 0.719423i \(-0.744407\pi\)
−0.694573 + 0.719423i \(0.744407\pi\)
\(882\) 0 0
\(883\) −13.8254 −0.465263 −0.232631 0.972565i \(-0.574734\pi\)
−0.232631 + 0.972565i \(0.574734\pi\)
\(884\) 0 0
\(885\) 2.99750 0.100760
\(886\) 0 0
\(887\) −14.1521 −0.475181 −0.237590 0.971365i \(-0.576358\pi\)
−0.237590 + 0.971365i \(0.576358\pi\)
\(888\) 0 0
\(889\) −30.3368 −1.01746
\(890\) 0 0
\(891\) −5.60467 −0.187763
\(892\) 0 0
\(893\) −29.5682 −0.989462
\(894\) 0 0
\(895\) −30.8291 −1.03050
\(896\) 0 0
\(897\) −1.98787 −0.0663729
\(898\) 0 0
\(899\) 61.7396 2.05913
\(900\) 0 0
\(901\) 9.21150 0.306880
\(902\) 0 0
\(903\) 21.9549 0.730614
\(904\) 0 0
\(905\) −39.5438 −1.31448
\(906\) 0 0
\(907\) 7.85160 0.260708 0.130354 0.991468i \(-0.458389\pi\)
0.130354 + 0.991468i \(0.458389\pi\)
\(908\) 0 0
\(909\) 0.324258 0.0107550
\(910\) 0 0
\(911\) 15.2329 0.504688 0.252344 0.967638i \(-0.418799\pi\)
0.252344 + 0.967638i \(0.418799\pi\)
\(912\) 0 0
\(913\) 13.1562 0.435408
\(914\) 0 0
\(915\) 29.0626 0.960779
\(916\) 0 0
\(917\) −73.1078 −2.41423
\(918\) 0 0
\(919\) −40.1711 −1.32512 −0.662561 0.749008i \(-0.730530\pi\)
−0.662561 + 0.749008i \(0.730530\pi\)
\(920\) 0 0
\(921\) 8.56720 0.282299
\(922\) 0 0
\(923\) −23.2911 −0.766637
\(924\) 0 0
\(925\) −15.7600 −0.518185
\(926\) 0 0
\(927\) 40.4484 1.32850
\(928\) 0 0
\(929\) −0.497465 −0.0163213 −0.00816065 0.999967i \(-0.502598\pi\)
−0.00816065 + 0.999967i \(0.502598\pi\)
\(930\) 0 0
\(931\) −38.7481 −1.26992
\(932\) 0 0
\(933\) 8.30666 0.271948
\(934\) 0 0
\(935\) 6.07845 0.198787
\(936\) 0 0
\(937\) −58.7000 −1.91765 −0.958823 0.284004i \(-0.908337\pi\)
−0.958823 + 0.284004i \(0.908337\pi\)
\(938\) 0 0
\(939\) 11.2953 0.368608
\(940\) 0 0
\(941\) −20.7858 −0.677598 −0.338799 0.940859i \(-0.610021\pi\)
−0.338799 + 0.940859i \(0.610021\pi\)
\(942\) 0 0
\(943\) 5.83371 0.189972
\(944\) 0 0
\(945\) 54.6025 1.77622
\(946\) 0 0
\(947\) −12.0761 −0.392421 −0.196210 0.980562i \(-0.562864\pi\)
−0.196210 + 0.980562i \(0.562864\pi\)
\(948\) 0 0
\(949\) 7.29425 0.236781
\(950\) 0 0
\(951\) 26.8546 0.870820
\(952\) 0 0
\(953\) −60.9157 −1.97325 −0.986627 0.162995i \(-0.947885\pi\)
−0.986627 + 0.162995i \(0.947885\pi\)
\(954\) 0 0
\(955\) 35.7602 1.15717
\(956\) 0 0
\(957\) −13.6950 −0.442696
\(958\) 0 0
\(959\) −40.3769 −1.30384
\(960\) 0 0
\(961\) 7.44152 0.240049
\(962\) 0 0
\(963\) 27.4982 0.886118
\(964\) 0 0
\(965\) 11.9390 0.384330
\(966\) 0 0
\(967\) −6.76303 −0.217484 −0.108742 0.994070i \(-0.534682\pi\)
−0.108742 + 0.994070i \(0.534682\pi\)
\(968\) 0 0
\(969\) −6.76590 −0.217352
\(970\) 0 0
\(971\) 7.29604 0.234141 0.117070 0.993124i \(-0.462650\pi\)
0.117070 + 0.993124i \(0.462650\pi\)
\(972\) 0 0
\(973\) −25.2719 −0.810180
\(974\) 0 0
\(975\) −11.6510 −0.373131
\(976\) 0 0
\(977\) 25.0345 0.800924 0.400462 0.916313i \(-0.368850\pi\)
0.400462 + 0.916313i \(0.368850\pi\)
\(978\) 0 0
\(979\) −10.5631 −0.337597
\(980\) 0 0
\(981\) −13.6670 −0.436353
\(982\) 0 0
\(983\) 49.9355 1.59270 0.796348 0.604838i \(-0.206762\pi\)
0.796348 + 0.604838i \(0.206762\pi\)
\(984\) 0 0
\(985\) 41.3682 1.31810
\(986\) 0 0
\(987\) −10.1452 −0.322924
\(988\) 0 0
\(989\) −10.9605 −0.348525
\(990\) 0 0
\(991\) 17.6320 0.560098 0.280049 0.959986i \(-0.409649\pi\)
0.280049 + 0.959986i \(0.409649\pi\)
\(992\) 0 0
\(993\) 2.40167 0.0762148
\(994\) 0 0
\(995\) 65.0786 2.06313
\(996\) 0 0
\(997\) −10.4382 −0.330580 −0.165290 0.986245i \(-0.552856\pi\)
−0.165290 + 0.986245i \(0.552856\pi\)
\(998\) 0 0
\(999\) −8.37415 −0.264946
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 \(a_p\))