Properties

Label 8008.2.a.u.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.80136\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.80136 q^{3} -2.97899 q^{5} -1.00000 q^{7} +0.244902 q^{9} +O(q^{10})\) \(q-1.80136 q^{3} -2.97899 q^{5} -1.00000 q^{7} +0.244902 q^{9} -1.00000 q^{11} -1.00000 q^{13} +5.36624 q^{15} -3.36273 q^{17} -0.650951 q^{19} +1.80136 q^{21} -5.75145 q^{23} +3.87440 q^{25} +4.96293 q^{27} +3.84151 q^{29} +4.81258 q^{31} +1.80136 q^{33} +2.97899 q^{35} +5.38609 q^{37} +1.80136 q^{39} +0.331597 q^{41} -4.36013 q^{43} -0.729562 q^{45} +10.3033 q^{47} +1.00000 q^{49} +6.05749 q^{51} +2.85065 q^{53} +2.97899 q^{55} +1.17260 q^{57} +6.24631 q^{59} +8.41953 q^{61} -0.244902 q^{63} +2.97899 q^{65} -11.3964 q^{67} +10.3604 q^{69} -11.4219 q^{71} -4.43520 q^{73} -6.97920 q^{75} +1.00000 q^{77} +14.2508 q^{79} -9.67473 q^{81} -4.23541 q^{83} +10.0175 q^{85} -6.91995 q^{87} +7.54738 q^{89} +1.00000 q^{91} -8.66920 q^{93} +1.93918 q^{95} -7.46541 q^{97} -0.244902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.80136 −1.04002 −0.520008 0.854161i \(-0.674071\pi\)
−0.520008 + 0.854161i \(0.674071\pi\)
\(4\) 0 0
\(5\) −2.97899 −1.33225 −0.666123 0.745842i \(-0.732047\pi\)
−0.666123 + 0.745842i \(0.732047\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0.244902 0.0816340
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 5.36624 1.38556
\(16\) 0 0
\(17\) −3.36273 −0.815581 −0.407791 0.913076i \(-0.633701\pi\)
−0.407791 + 0.913076i \(0.633701\pi\)
\(18\) 0 0
\(19\) −0.650951 −0.149338 −0.0746692 0.997208i \(-0.523790\pi\)
−0.0746692 + 0.997208i \(0.523790\pi\)
\(20\) 0 0
\(21\) 1.80136 0.393089
\(22\) 0 0
\(23\) −5.75145 −1.19926 −0.599631 0.800277i \(-0.704686\pi\)
−0.599631 + 0.800277i \(0.704686\pi\)
\(24\) 0 0
\(25\) 3.87440 0.774880
\(26\) 0 0
\(27\) 4.96293 0.955116
\(28\) 0 0
\(29\) 3.84151 0.713351 0.356676 0.934228i \(-0.383910\pi\)
0.356676 + 0.934228i \(0.383910\pi\)
\(30\) 0 0
\(31\) 4.81258 0.864365 0.432183 0.901786i \(-0.357744\pi\)
0.432183 + 0.901786i \(0.357744\pi\)
\(32\) 0 0
\(33\) 1.80136 0.313577
\(34\) 0 0
\(35\) 2.97899 0.503542
\(36\) 0 0
\(37\) 5.38609 0.885467 0.442734 0.896653i \(-0.354009\pi\)
0.442734 + 0.896653i \(0.354009\pi\)
\(38\) 0 0
\(39\) 1.80136 0.288449
\(40\) 0 0
\(41\) 0.331597 0.0517868 0.0258934 0.999665i \(-0.491757\pi\)
0.0258934 + 0.999665i \(0.491757\pi\)
\(42\) 0 0
\(43\) −4.36013 −0.664914 −0.332457 0.943118i \(-0.607878\pi\)
−0.332457 + 0.943118i \(0.607878\pi\)
\(44\) 0 0
\(45\) −0.729562 −0.108757
\(46\) 0 0
\(47\) 10.3033 1.50289 0.751447 0.659793i \(-0.229356\pi\)
0.751447 + 0.659793i \(0.229356\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 6.05749 0.848218
\(52\) 0 0
\(53\) 2.85065 0.391566 0.195783 0.980647i \(-0.437275\pi\)
0.195783 + 0.980647i \(0.437275\pi\)
\(54\) 0 0
\(55\) 2.97899 0.401687
\(56\) 0 0
\(57\) 1.17260 0.155314
\(58\) 0 0
\(59\) 6.24631 0.813200 0.406600 0.913606i \(-0.366714\pi\)
0.406600 + 0.913606i \(0.366714\pi\)
\(60\) 0 0
\(61\) 8.41953 1.07801 0.539005 0.842302i \(-0.318800\pi\)
0.539005 + 0.842302i \(0.318800\pi\)
\(62\) 0 0
\(63\) −0.244902 −0.0308548
\(64\) 0 0
\(65\) 2.97899 0.369499
\(66\) 0 0
\(67\) −11.3964 −1.39229 −0.696145 0.717901i \(-0.745103\pi\)
−0.696145 + 0.717901i \(0.745103\pi\)
\(68\) 0 0
\(69\) 10.3604 1.24725
\(70\) 0 0
\(71\) −11.4219 −1.35553 −0.677763 0.735281i \(-0.737050\pi\)
−0.677763 + 0.735281i \(0.737050\pi\)
\(72\) 0 0
\(73\) −4.43520 −0.519101 −0.259551 0.965729i \(-0.583574\pi\)
−0.259551 + 0.965729i \(0.583574\pi\)
\(74\) 0 0
\(75\) −6.97920 −0.805888
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 14.2508 1.60334 0.801671 0.597766i \(-0.203945\pi\)
0.801671 + 0.597766i \(0.203945\pi\)
\(80\) 0 0
\(81\) −9.67473 −1.07497
\(82\) 0 0
\(83\) −4.23541 −0.464896 −0.232448 0.972609i \(-0.574674\pi\)
−0.232448 + 0.972609i \(0.574674\pi\)
\(84\) 0 0
\(85\) 10.0175 1.08655
\(86\) 0 0
\(87\) −6.91995 −0.741897
\(88\) 0 0
\(89\) 7.54738 0.800020 0.400010 0.916511i \(-0.369007\pi\)
0.400010 + 0.916511i \(0.369007\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −8.66920 −0.898954
\(94\) 0 0
\(95\) 1.93918 0.198956
\(96\) 0 0
\(97\) −7.46541 −0.757998 −0.378999 0.925397i \(-0.623732\pi\)
−0.378999 + 0.925397i \(0.623732\pi\)
\(98\) 0 0
\(99\) −0.244902 −0.0246136
\(100\) 0 0
\(101\) −12.5569 −1.24945 −0.624727 0.780843i \(-0.714790\pi\)
−0.624727 + 0.780843i \(0.714790\pi\)
\(102\) 0 0
\(103\) 13.6746 1.34739 0.673697 0.739008i \(-0.264705\pi\)
0.673697 + 0.739008i \(0.264705\pi\)
\(104\) 0 0
\(105\) −5.36624 −0.523692
\(106\) 0 0
\(107\) −4.07770 −0.394206 −0.197103 0.980383i \(-0.563153\pi\)
−0.197103 + 0.980383i \(0.563153\pi\)
\(108\) 0 0
\(109\) 0.162712 0.0155850 0.00779251 0.999970i \(-0.497520\pi\)
0.00779251 + 0.999970i \(0.497520\pi\)
\(110\) 0 0
\(111\) −9.70229 −0.920900
\(112\) 0 0
\(113\) −11.3896 −1.07144 −0.535721 0.844395i \(-0.679960\pi\)
−0.535721 + 0.844395i \(0.679960\pi\)
\(114\) 0 0
\(115\) 17.1335 1.59771
\(116\) 0 0
\(117\) −0.244902 −0.0226412
\(118\) 0 0
\(119\) 3.36273 0.308261
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −0.597327 −0.0538591
\(124\) 0 0
\(125\) 3.35315 0.299915
\(126\) 0 0
\(127\) 1.53467 0.136180 0.0680898 0.997679i \(-0.478310\pi\)
0.0680898 + 0.997679i \(0.478310\pi\)
\(128\) 0 0
\(129\) 7.85417 0.691521
\(130\) 0 0
\(131\) 20.0747 1.75393 0.876965 0.480554i \(-0.159564\pi\)
0.876965 + 0.480554i \(0.159564\pi\)
\(132\) 0 0
\(133\) 0.650951 0.0564446
\(134\) 0 0
\(135\) −14.7845 −1.27245
\(136\) 0 0
\(137\) 6.81319 0.582090 0.291045 0.956709i \(-0.405997\pi\)
0.291045 + 0.956709i \(0.405997\pi\)
\(138\) 0 0
\(139\) 10.8278 0.918405 0.459203 0.888331i \(-0.348135\pi\)
0.459203 + 0.888331i \(0.348135\pi\)
\(140\) 0 0
\(141\) −18.5600 −1.56303
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −11.4438 −0.950359
\(146\) 0 0
\(147\) −1.80136 −0.148574
\(148\) 0 0
\(149\) 15.5704 1.27557 0.637787 0.770213i \(-0.279850\pi\)
0.637787 + 0.770213i \(0.279850\pi\)
\(150\) 0 0
\(151\) −3.92435 −0.319359 −0.159680 0.987169i \(-0.551046\pi\)
−0.159680 + 0.987169i \(0.551046\pi\)
\(152\) 0 0
\(153\) −0.823539 −0.0665792
\(154\) 0 0
\(155\) −14.3367 −1.15155
\(156\) 0 0
\(157\) 4.52819 0.361389 0.180694 0.983539i \(-0.442165\pi\)
0.180694 + 0.983539i \(0.442165\pi\)
\(158\) 0 0
\(159\) −5.13504 −0.407236
\(160\) 0 0
\(161\) 5.75145 0.453278
\(162\) 0 0
\(163\) 15.5743 1.21987 0.609937 0.792450i \(-0.291195\pi\)
0.609937 + 0.792450i \(0.291195\pi\)
\(164\) 0 0
\(165\) −5.36624 −0.417761
\(166\) 0 0
\(167\) 2.96986 0.229815 0.114907 0.993376i \(-0.463343\pi\)
0.114907 + 0.993376i \(0.463343\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −0.159419 −0.0121911
\(172\) 0 0
\(173\) 9.74884 0.741191 0.370595 0.928794i \(-0.379154\pi\)
0.370595 + 0.928794i \(0.379154\pi\)
\(174\) 0 0
\(175\) −3.87440 −0.292877
\(176\) 0 0
\(177\) −11.2519 −0.845741
\(178\) 0 0
\(179\) 10.3831 0.776069 0.388034 0.921645i \(-0.373154\pi\)
0.388034 + 0.921645i \(0.373154\pi\)
\(180\) 0 0
\(181\) −15.6304 −1.16180 −0.580901 0.813974i \(-0.697300\pi\)
−0.580901 + 0.813974i \(0.697300\pi\)
\(182\) 0 0
\(183\) −15.1666 −1.12115
\(184\) 0 0
\(185\) −16.0451 −1.17966
\(186\) 0 0
\(187\) 3.36273 0.245907
\(188\) 0 0
\(189\) −4.96293 −0.361000
\(190\) 0 0
\(191\) −23.0063 −1.66468 −0.832340 0.554266i \(-0.812999\pi\)
−0.832340 + 0.554266i \(0.812999\pi\)
\(192\) 0 0
\(193\) −1.80559 −0.129969 −0.0649847 0.997886i \(-0.520700\pi\)
−0.0649847 + 0.997886i \(0.520700\pi\)
\(194\) 0 0
\(195\) −5.36624 −0.384285
\(196\) 0 0
\(197\) −22.0515 −1.57110 −0.785551 0.618797i \(-0.787620\pi\)
−0.785551 + 0.618797i \(0.787620\pi\)
\(198\) 0 0
\(199\) −1.13812 −0.0806792 −0.0403396 0.999186i \(-0.512844\pi\)
−0.0403396 + 0.999186i \(0.512844\pi\)
\(200\) 0 0
\(201\) 20.5290 1.44800
\(202\) 0 0
\(203\) −3.84151 −0.269621
\(204\) 0 0
\(205\) −0.987826 −0.0689928
\(206\) 0 0
\(207\) −1.40854 −0.0979006
\(208\) 0 0
\(209\) 0.650951 0.0450272
\(210\) 0 0
\(211\) 14.3439 0.987473 0.493737 0.869612i \(-0.335631\pi\)
0.493737 + 0.869612i \(0.335631\pi\)
\(212\) 0 0
\(213\) 20.5749 1.40977
\(214\) 0 0
\(215\) 12.9888 0.885829
\(216\) 0 0
\(217\) −4.81258 −0.326699
\(218\) 0 0
\(219\) 7.98940 0.539874
\(220\) 0 0
\(221\) 3.36273 0.226201
\(222\) 0 0
\(223\) 17.4436 1.16811 0.584056 0.811713i \(-0.301465\pi\)
0.584056 + 0.811713i \(0.301465\pi\)
\(224\) 0 0
\(225\) 0.948849 0.0632566
\(226\) 0 0
\(227\) −6.54401 −0.434341 −0.217170 0.976134i \(-0.569683\pi\)
−0.217170 + 0.976134i \(0.569683\pi\)
\(228\) 0 0
\(229\) −6.77490 −0.447698 −0.223849 0.974624i \(-0.571862\pi\)
−0.223849 + 0.974624i \(0.571862\pi\)
\(230\) 0 0
\(231\) −1.80136 −0.118521
\(232\) 0 0
\(233\) 10.4613 0.685341 0.342671 0.939456i \(-0.388669\pi\)
0.342671 + 0.939456i \(0.388669\pi\)
\(234\) 0 0
\(235\) −30.6935 −2.00223
\(236\) 0 0
\(237\) −25.6709 −1.66750
\(238\) 0 0
\(239\) −5.22666 −0.338084 −0.169042 0.985609i \(-0.554067\pi\)
−0.169042 + 0.985609i \(0.554067\pi\)
\(240\) 0 0
\(241\) −2.09179 −0.134744 −0.0673722 0.997728i \(-0.521461\pi\)
−0.0673722 + 0.997728i \(0.521461\pi\)
\(242\) 0 0
\(243\) 2.53890 0.162871
\(244\) 0 0
\(245\) −2.97899 −0.190321
\(246\) 0 0
\(247\) 0.650951 0.0414190
\(248\) 0 0
\(249\) 7.62950 0.483500
\(250\) 0 0
\(251\) 8.24646 0.520512 0.260256 0.965540i \(-0.416193\pi\)
0.260256 + 0.965540i \(0.416193\pi\)
\(252\) 0 0
\(253\) 5.75145 0.361591
\(254\) 0 0
\(255\) −18.0452 −1.13003
\(256\) 0 0
\(257\) −9.41326 −0.587183 −0.293591 0.955931i \(-0.594851\pi\)
−0.293591 + 0.955931i \(0.594851\pi\)
\(258\) 0 0
\(259\) −5.38609 −0.334675
\(260\) 0 0
\(261\) 0.940795 0.0582337
\(262\) 0 0
\(263\) −15.2008 −0.937324 −0.468662 0.883378i \(-0.655264\pi\)
−0.468662 + 0.883378i \(0.655264\pi\)
\(264\) 0 0
\(265\) −8.49206 −0.521663
\(266\) 0 0
\(267\) −13.5956 −0.832034
\(268\) 0 0
\(269\) −4.44135 −0.270794 −0.135397 0.990791i \(-0.543231\pi\)
−0.135397 + 0.990791i \(0.543231\pi\)
\(270\) 0 0
\(271\) 22.9282 1.39279 0.696393 0.717661i \(-0.254787\pi\)
0.696393 + 0.717661i \(0.254787\pi\)
\(272\) 0 0
\(273\) −1.80136 −0.109023
\(274\) 0 0
\(275\) −3.87440 −0.233635
\(276\) 0 0
\(277\) −7.57984 −0.455429 −0.227714 0.973728i \(-0.573125\pi\)
−0.227714 + 0.973728i \(0.573125\pi\)
\(278\) 0 0
\(279\) 1.17861 0.0705617
\(280\) 0 0
\(281\) −4.29252 −0.256070 −0.128035 0.991770i \(-0.540867\pi\)
−0.128035 + 0.991770i \(0.540867\pi\)
\(282\) 0 0
\(283\) 18.1474 1.07875 0.539375 0.842066i \(-0.318661\pi\)
0.539375 + 0.842066i \(0.318661\pi\)
\(284\) 0 0
\(285\) −3.49316 −0.206917
\(286\) 0 0
\(287\) −0.331597 −0.0195736
\(288\) 0 0
\(289\) −5.69207 −0.334828
\(290\) 0 0
\(291\) 13.4479 0.788330
\(292\) 0 0
\(293\) −22.3980 −1.30850 −0.654251 0.756277i \(-0.727016\pi\)
−0.654251 + 0.756277i \(0.727016\pi\)
\(294\) 0 0
\(295\) −18.6077 −1.08338
\(296\) 0 0
\(297\) −4.96293 −0.287978
\(298\) 0 0
\(299\) 5.75145 0.332615
\(300\) 0 0
\(301\) 4.36013 0.251314
\(302\) 0 0
\(303\) 22.6195 1.29945
\(304\) 0 0
\(305\) −25.0817 −1.43618
\(306\) 0 0
\(307\) 23.2327 1.32596 0.662979 0.748638i \(-0.269292\pi\)
0.662979 + 0.748638i \(0.269292\pi\)
\(308\) 0 0
\(309\) −24.6328 −1.40131
\(310\) 0 0
\(311\) −14.9345 −0.846859 −0.423429 0.905929i \(-0.639174\pi\)
−0.423429 + 0.905929i \(0.639174\pi\)
\(312\) 0 0
\(313\) −18.4203 −1.04118 −0.520590 0.853807i \(-0.674288\pi\)
−0.520590 + 0.853807i \(0.674288\pi\)
\(314\) 0 0
\(315\) 0.729562 0.0411062
\(316\) 0 0
\(317\) −17.3295 −0.973323 −0.486661 0.873591i \(-0.661785\pi\)
−0.486661 + 0.873591i \(0.661785\pi\)
\(318\) 0 0
\(319\) −3.84151 −0.215083
\(320\) 0 0
\(321\) 7.34542 0.409981
\(322\) 0 0
\(323\) 2.18897 0.121798
\(324\) 0 0
\(325\) −3.87440 −0.214913
\(326\) 0 0
\(327\) −0.293104 −0.0162087
\(328\) 0 0
\(329\) −10.3033 −0.568041
\(330\) 0 0
\(331\) 21.8640 1.20175 0.600876 0.799342i \(-0.294818\pi\)
0.600876 + 0.799342i \(0.294818\pi\)
\(332\) 0 0
\(333\) 1.31906 0.0722843
\(334\) 0 0
\(335\) 33.9498 1.85487
\(336\) 0 0
\(337\) −14.5332 −0.791674 −0.395837 0.918321i \(-0.629546\pi\)
−0.395837 + 0.918321i \(0.629546\pi\)
\(338\) 0 0
\(339\) 20.5167 1.11432
\(340\) 0 0
\(341\) −4.81258 −0.260616
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −30.8637 −1.66165
\(346\) 0 0
\(347\) −25.6184 −1.37527 −0.687634 0.726058i \(-0.741351\pi\)
−0.687634 + 0.726058i \(0.741351\pi\)
\(348\) 0 0
\(349\) −1.20847 −0.0646880 −0.0323440 0.999477i \(-0.510297\pi\)
−0.0323440 + 0.999477i \(0.510297\pi\)
\(350\) 0 0
\(351\) −4.96293 −0.264901
\(352\) 0 0
\(353\) 0.692068 0.0368351 0.0184175 0.999830i \(-0.494137\pi\)
0.0184175 + 0.999830i \(0.494137\pi\)
\(354\) 0 0
\(355\) 34.0256 1.80589
\(356\) 0 0
\(357\) −6.05749 −0.320596
\(358\) 0 0
\(359\) −30.5310 −1.61137 −0.805683 0.592347i \(-0.798202\pi\)
−0.805683 + 0.592347i \(0.798202\pi\)
\(360\) 0 0
\(361\) −18.5763 −0.977698
\(362\) 0 0
\(363\) −1.80136 −0.0945469
\(364\) 0 0
\(365\) 13.2124 0.691571
\(366\) 0 0
\(367\) −27.3898 −1.42973 −0.714867 0.699260i \(-0.753513\pi\)
−0.714867 + 0.699260i \(0.753513\pi\)
\(368\) 0 0
\(369\) 0.0812089 0.00422757
\(370\) 0 0
\(371\) −2.85065 −0.147998
\(372\) 0 0
\(373\) 12.5046 0.647464 0.323732 0.946149i \(-0.395062\pi\)
0.323732 + 0.946149i \(0.395062\pi\)
\(374\) 0 0
\(375\) −6.04024 −0.311917
\(376\) 0 0
\(377\) −3.84151 −0.197848
\(378\) 0 0
\(379\) −14.9991 −0.770451 −0.385225 0.922822i \(-0.625876\pi\)
−0.385225 + 0.922822i \(0.625876\pi\)
\(380\) 0 0
\(381\) −2.76449 −0.141629
\(382\) 0 0
\(383\) −26.6330 −1.36088 −0.680442 0.732802i \(-0.738212\pi\)
−0.680442 + 0.732802i \(0.738212\pi\)
\(384\) 0 0
\(385\) −2.97899 −0.151824
\(386\) 0 0
\(387\) −1.06781 −0.0542796
\(388\) 0 0
\(389\) −36.2672 −1.83882 −0.919410 0.393301i \(-0.871333\pi\)
−0.919410 + 0.393301i \(0.871333\pi\)
\(390\) 0 0
\(391\) 19.3406 0.978095
\(392\) 0 0
\(393\) −36.1617 −1.82412
\(394\) 0 0
\(395\) −42.4531 −2.13605
\(396\) 0 0
\(397\) 28.0713 1.40886 0.704429 0.709774i \(-0.251203\pi\)
0.704429 + 0.709774i \(0.251203\pi\)
\(398\) 0 0
\(399\) −1.17260 −0.0587033
\(400\) 0 0
\(401\) −4.24452 −0.211961 −0.105981 0.994368i \(-0.533798\pi\)
−0.105981 + 0.994368i \(0.533798\pi\)
\(402\) 0 0
\(403\) −4.81258 −0.239732
\(404\) 0 0
\(405\) 28.8210 1.43212
\(406\) 0 0
\(407\) −5.38609 −0.266978
\(408\) 0 0
\(409\) −8.33469 −0.412124 −0.206062 0.978539i \(-0.566065\pi\)
−0.206062 + 0.978539i \(0.566065\pi\)
\(410\) 0 0
\(411\) −12.2730 −0.605383
\(412\) 0 0
\(413\) −6.24631 −0.307361
\(414\) 0 0
\(415\) 12.6173 0.619356
\(416\) 0 0
\(417\) −19.5049 −0.955157
\(418\) 0 0
\(419\) 11.4213 0.557966 0.278983 0.960296i \(-0.410003\pi\)
0.278983 + 0.960296i \(0.410003\pi\)
\(420\) 0 0
\(421\) 23.8374 1.16176 0.580881 0.813988i \(-0.302708\pi\)
0.580881 + 0.813988i \(0.302708\pi\)
\(422\) 0 0
\(423\) 2.52331 0.122687
\(424\) 0 0
\(425\) −13.0286 −0.631978
\(426\) 0 0
\(427\) −8.41953 −0.407450
\(428\) 0 0
\(429\) −1.80136 −0.0869705
\(430\) 0 0
\(431\) −2.72332 −0.131178 −0.0655889 0.997847i \(-0.520893\pi\)
−0.0655889 + 0.997847i \(0.520893\pi\)
\(432\) 0 0
\(433\) −29.8039 −1.43228 −0.716141 0.697956i \(-0.754093\pi\)
−0.716141 + 0.697956i \(0.754093\pi\)
\(434\) 0 0
\(435\) 20.6145 0.988389
\(436\) 0 0
\(437\) 3.74392 0.179096
\(438\) 0 0
\(439\) −25.4516 −1.21474 −0.607370 0.794419i \(-0.707776\pi\)
−0.607370 + 0.794419i \(0.707776\pi\)
\(440\) 0 0
\(441\) 0.244902 0.0116620
\(442\) 0 0
\(443\) 25.7795 1.22482 0.612410 0.790540i \(-0.290200\pi\)
0.612410 + 0.790540i \(0.290200\pi\)
\(444\) 0 0
\(445\) −22.4836 −1.06582
\(446\) 0 0
\(447\) −28.0478 −1.32662
\(448\) 0 0
\(449\) 0.122520 0.00578207 0.00289103 0.999996i \(-0.499080\pi\)
0.00289103 + 0.999996i \(0.499080\pi\)
\(450\) 0 0
\(451\) −0.331597 −0.0156143
\(452\) 0 0
\(453\) 7.06918 0.332139
\(454\) 0 0
\(455\) −2.97899 −0.139657
\(456\) 0 0
\(457\) −20.7921 −0.972611 −0.486306 0.873789i \(-0.661656\pi\)
−0.486306 + 0.873789i \(0.661656\pi\)
\(458\) 0 0
\(459\) −16.6890 −0.778974
\(460\) 0 0
\(461\) −27.5042 −1.28100 −0.640500 0.767958i \(-0.721273\pi\)
−0.640500 + 0.767958i \(0.721273\pi\)
\(462\) 0 0
\(463\) 0.762117 0.0354186 0.0177093 0.999843i \(-0.494363\pi\)
0.0177093 + 0.999843i \(0.494363\pi\)
\(464\) 0 0
\(465\) 25.8255 1.19763
\(466\) 0 0
\(467\) 20.3063 0.939662 0.469831 0.882756i \(-0.344315\pi\)
0.469831 + 0.882756i \(0.344315\pi\)
\(468\) 0 0
\(469\) 11.3964 0.526236
\(470\) 0 0
\(471\) −8.15691 −0.375850
\(472\) 0 0
\(473\) 4.36013 0.200479
\(474\) 0 0
\(475\) −2.52205 −0.115719
\(476\) 0 0
\(477\) 0.698130 0.0319652
\(478\) 0 0
\(479\) 8.54857 0.390594 0.195297 0.980744i \(-0.437433\pi\)
0.195297 + 0.980744i \(0.437433\pi\)
\(480\) 0 0
\(481\) −5.38609 −0.245584
\(482\) 0 0
\(483\) −10.3604 −0.471417
\(484\) 0 0
\(485\) 22.2394 1.00984
\(486\) 0 0
\(487\) −4.60102 −0.208492 −0.104246 0.994552i \(-0.533243\pi\)
−0.104246 + 0.994552i \(0.533243\pi\)
\(488\) 0 0
\(489\) −28.0549 −1.26869
\(490\) 0 0
\(491\) 0.990276 0.0446906 0.0223453 0.999750i \(-0.492887\pi\)
0.0223453 + 0.999750i \(0.492887\pi\)
\(492\) 0 0
\(493\) −12.9180 −0.581796
\(494\) 0 0
\(495\) 0.729562 0.0327914
\(496\) 0 0
\(497\) 11.4219 0.512341
\(498\) 0 0
\(499\) −31.6376 −1.41629 −0.708147 0.706065i \(-0.750468\pi\)
−0.708147 + 0.706065i \(0.750468\pi\)
\(500\) 0 0
\(501\) −5.34979 −0.239011
\(502\) 0 0
\(503\) −1.31444 −0.0586078 −0.0293039 0.999571i \(-0.509329\pi\)
−0.0293039 + 0.999571i \(0.509329\pi\)
\(504\) 0 0
\(505\) 37.4068 1.66458
\(506\) 0 0
\(507\) −1.80136 −0.0800013
\(508\) 0 0
\(509\) 11.3782 0.504331 0.252165 0.967684i \(-0.418857\pi\)
0.252165 + 0.967684i \(0.418857\pi\)
\(510\) 0 0
\(511\) 4.43520 0.196202
\(512\) 0 0
\(513\) −3.23062 −0.142635
\(514\) 0 0
\(515\) −40.7364 −1.79506
\(516\) 0 0
\(517\) −10.3033 −0.453140
\(518\) 0 0
\(519\) −17.5612 −0.770850
\(520\) 0 0
\(521\) 8.20888 0.359638 0.179819 0.983700i \(-0.442449\pi\)
0.179819 + 0.983700i \(0.442449\pi\)
\(522\) 0 0
\(523\) −35.3039 −1.54373 −0.771866 0.635785i \(-0.780676\pi\)
−0.771866 + 0.635785i \(0.780676\pi\)
\(524\) 0 0
\(525\) 6.97920 0.304597
\(526\) 0 0
\(527\) −16.1834 −0.704960
\(528\) 0 0
\(529\) 10.0792 0.438228
\(530\) 0 0
\(531\) 1.52973 0.0663848
\(532\) 0 0
\(533\) −0.331597 −0.0143631
\(534\) 0 0
\(535\) 12.1474 0.525180
\(536\) 0 0
\(537\) −18.7037 −0.807124
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −0.679250 −0.0292032 −0.0146016 0.999893i \(-0.504648\pi\)
−0.0146016 + 0.999893i \(0.504648\pi\)
\(542\) 0 0
\(543\) 28.1561 1.20829
\(544\) 0 0
\(545\) −0.484719 −0.0207631
\(546\) 0 0
\(547\) 44.5901 1.90653 0.953267 0.302128i \(-0.0976972\pi\)
0.953267 + 0.302128i \(0.0976972\pi\)
\(548\) 0 0
\(549\) 2.06196 0.0880024
\(550\) 0 0
\(551\) −2.50064 −0.106531
\(552\) 0 0
\(553\) −14.2508 −0.606006
\(554\) 0 0
\(555\) 28.9030 1.22687
\(556\) 0 0
\(557\) −41.0257 −1.73832 −0.869158 0.494535i \(-0.835339\pi\)
−0.869158 + 0.494535i \(0.835339\pi\)
\(558\) 0 0
\(559\) 4.36013 0.184414
\(560\) 0 0
\(561\) −6.05749 −0.255747
\(562\) 0 0
\(563\) 30.8679 1.30093 0.650464 0.759537i \(-0.274575\pi\)
0.650464 + 0.759537i \(0.274575\pi\)
\(564\) 0 0
\(565\) 33.9295 1.42742
\(566\) 0 0
\(567\) 9.67473 0.406300
\(568\) 0 0
\(569\) 24.9698 1.04679 0.523394 0.852091i \(-0.324666\pi\)
0.523394 + 0.852091i \(0.324666\pi\)
\(570\) 0 0
\(571\) 36.9566 1.54659 0.773293 0.634049i \(-0.218608\pi\)
0.773293 + 0.634049i \(0.218608\pi\)
\(572\) 0 0
\(573\) 41.4427 1.73129
\(574\) 0 0
\(575\) −22.2834 −0.929284
\(576\) 0 0
\(577\) 25.9924 1.08208 0.541038 0.840998i \(-0.318032\pi\)
0.541038 + 0.840998i \(0.318032\pi\)
\(578\) 0 0
\(579\) 3.25253 0.135170
\(580\) 0 0
\(581\) 4.23541 0.175714
\(582\) 0 0
\(583\) −2.85065 −0.118062
\(584\) 0 0
\(585\) 0.729562 0.0301637
\(586\) 0 0
\(587\) 23.6105 0.974510 0.487255 0.873260i \(-0.337998\pi\)
0.487255 + 0.873260i \(0.337998\pi\)
\(588\) 0 0
\(589\) −3.13276 −0.129083
\(590\) 0 0
\(591\) 39.7227 1.63397
\(592\) 0 0
\(593\) −1.12660 −0.0462638 −0.0231319 0.999732i \(-0.507364\pi\)
−0.0231319 + 0.999732i \(0.507364\pi\)
\(594\) 0 0
\(595\) −10.0175 −0.410679
\(596\) 0 0
\(597\) 2.05016 0.0839076
\(598\) 0 0
\(599\) 28.4490 1.16239 0.581196 0.813763i \(-0.302585\pi\)
0.581196 + 0.813763i \(0.302585\pi\)
\(600\) 0 0
\(601\) 10.1591 0.414398 0.207199 0.978299i \(-0.433565\pi\)
0.207199 + 0.978299i \(0.433565\pi\)
\(602\) 0 0
\(603\) −2.79100 −0.113658
\(604\) 0 0
\(605\) −2.97899 −0.121113
\(606\) 0 0
\(607\) −4.58121 −0.185945 −0.0929727 0.995669i \(-0.529637\pi\)
−0.0929727 + 0.995669i \(0.529637\pi\)
\(608\) 0 0
\(609\) 6.91995 0.280411
\(610\) 0 0
\(611\) −10.3033 −0.416828
\(612\) 0 0
\(613\) 23.5802 0.952394 0.476197 0.879339i \(-0.342015\pi\)
0.476197 + 0.879339i \(0.342015\pi\)
\(614\) 0 0
\(615\) 1.77943 0.0717536
\(616\) 0 0
\(617\) 12.0743 0.486093 0.243047 0.970015i \(-0.421853\pi\)
0.243047 + 0.970015i \(0.421853\pi\)
\(618\) 0 0
\(619\) 3.53753 0.142185 0.0710926 0.997470i \(-0.477351\pi\)
0.0710926 + 0.997470i \(0.477351\pi\)
\(620\) 0 0
\(621\) −28.5440 −1.14543
\(622\) 0 0
\(623\) −7.54738 −0.302379
\(624\) 0 0
\(625\) −29.3610 −1.17444
\(626\) 0 0
\(627\) −1.17260 −0.0468291
\(628\) 0 0
\(629\) −18.1119 −0.722170
\(630\) 0 0
\(631\) −8.63310 −0.343678 −0.171839 0.985125i \(-0.554971\pi\)
−0.171839 + 0.985125i \(0.554971\pi\)
\(632\) 0 0
\(633\) −25.8385 −1.02699
\(634\) 0 0
\(635\) −4.57176 −0.181425
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −2.79724 −0.110657
\(640\) 0 0
\(641\) −33.8877 −1.33848 −0.669242 0.743045i \(-0.733381\pi\)
−0.669242 + 0.743045i \(0.733381\pi\)
\(642\) 0 0
\(643\) 15.2758 0.602418 0.301209 0.953558i \(-0.402610\pi\)
0.301209 + 0.953558i \(0.402610\pi\)
\(644\) 0 0
\(645\) −23.3975 −0.921277
\(646\) 0 0
\(647\) −28.9361 −1.13760 −0.568799 0.822477i \(-0.692592\pi\)
−0.568799 + 0.822477i \(0.692592\pi\)
\(648\) 0 0
\(649\) −6.24631 −0.245189
\(650\) 0 0
\(651\) 8.66920 0.339773
\(652\) 0 0
\(653\) 26.2086 1.02562 0.512811 0.858501i \(-0.328604\pi\)
0.512811 + 0.858501i \(0.328604\pi\)
\(654\) 0 0
\(655\) −59.8023 −2.33667
\(656\) 0 0
\(657\) −1.08619 −0.0423763
\(658\) 0 0
\(659\) 22.1501 0.862847 0.431424 0.902150i \(-0.358011\pi\)
0.431424 + 0.902150i \(0.358011\pi\)
\(660\) 0 0
\(661\) −0.223564 −0.00869563 −0.00434781 0.999991i \(-0.501384\pi\)
−0.00434781 + 0.999991i \(0.501384\pi\)
\(662\) 0 0
\(663\) −6.05749 −0.235253
\(664\) 0 0
\(665\) −1.93918 −0.0751982
\(666\) 0 0
\(667\) −22.0943 −0.855494
\(668\) 0 0
\(669\) −31.4223 −1.21486
\(670\) 0 0
\(671\) −8.41953 −0.325032
\(672\) 0 0
\(673\) −28.5052 −1.09879 −0.549396 0.835562i \(-0.685142\pi\)
−0.549396 + 0.835562i \(0.685142\pi\)
\(674\) 0 0
\(675\) 19.2284 0.740100
\(676\) 0 0
\(677\) −9.20819 −0.353899 −0.176950 0.984220i \(-0.556623\pi\)
−0.176950 + 0.984220i \(0.556623\pi\)
\(678\) 0 0
\(679\) 7.46541 0.286496
\(680\) 0 0
\(681\) 11.7881 0.451722
\(682\) 0 0
\(683\) 14.5445 0.556528 0.278264 0.960505i \(-0.410241\pi\)
0.278264 + 0.960505i \(0.410241\pi\)
\(684\) 0 0
\(685\) −20.2965 −0.775488
\(686\) 0 0
\(687\) 12.2040 0.465614
\(688\) 0 0
\(689\) −2.85065 −0.108601
\(690\) 0 0
\(691\) −9.08049 −0.345438 −0.172719 0.984971i \(-0.555255\pi\)
−0.172719 + 0.984971i \(0.555255\pi\)
\(692\) 0 0
\(693\) 0.244902 0.00930306
\(694\) 0 0
\(695\) −32.2561 −1.22354
\(696\) 0 0
\(697\) −1.11507 −0.0422363
\(698\) 0 0
\(699\) −18.8445 −0.712766
\(700\) 0 0
\(701\) −16.7898 −0.634141 −0.317071 0.948402i \(-0.602699\pi\)
−0.317071 + 0.948402i \(0.602699\pi\)
\(702\) 0 0
\(703\) −3.50608 −0.132234
\(704\) 0 0
\(705\) 55.2901 2.08235
\(706\) 0 0
\(707\) 12.5569 0.472250
\(708\) 0 0
\(709\) −15.3306 −0.575754 −0.287877 0.957667i \(-0.592949\pi\)
−0.287877 + 0.957667i \(0.592949\pi\)
\(710\) 0 0
\(711\) 3.49006 0.130887
\(712\) 0 0
\(713\) −27.6794 −1.03660
\(714\) 0 0
\(715\) −2.97899 −0.111408
\(716\) 0 0
\(717\) 9.41509 0.351613
\(718\) 0 0
\(719\) −0.748354 −0.0279089 −0.0139544 0.999903i \(-0.504442\pi\)
−0.0139544 + 0.999903i \(0.504442\pi\)
\(720\) 0 0
\(721\) −13.6746 −0.509267
\(722\) 0 0
\(723\) 3.76808 0.140136
\(724\) 0 0
\(725\) 14.8836 0.552762
\(726\) 0 0
\(727\) −17.7351 −0.657760 −0.328880 0.944372i \(-0.606671\pi\)
−0.328880 + 0.944372i \(0.606671\pi\)
\(728\) 0 0
\(729\) 24.4507 0.905582
\(730\) 0 0
\(731\) 14.6619 0.542291
\(732\) 0 0
\(733\) −18.4312 −0.680771 −0.340386 0.940286i \(-0.610558\pi\)
−0.340386 + 0.940286i \(0.610558\pi\)
\(734\) 0 0
\(735\) 5.36624 0.197937
\(736\) 0 0
\(737\) 11.3964 0.419791
\(738\) 0 0
\(739\) 46.5589 1.71270 0.856348 0.516400i \(-0.172728\pi\)
0.856348 + 0.516400i \(0.172728\pi\)
\(740\) 0 0
\(741\) −1.17260 −0.0430765
\(742\) 0 0
\(743\) 37.6360 1.38073 0.690366 0.723460i \(-0.257449\pi\)
0.690366 + 0.723460i \(0.257449\pi\)
\(744\) 0 0
\(745\) −46.3840 −1.69938
\(746\) 0 0
\(747\) −1.03726 −0.0379514
\(748\) 0 0
\(749\) 4.07770 0.148996
\(750\) 0 0
\(751\) −5.32903 −0.194459 −0.0972296 0.995262i \(-0.530998\pi\)
−0.0972296 + 0.995262i \(0.530998\pi\)
\(752\) 0 0
\(753\) −14.8548 −0.541341
\(754\) 0 0
\(755\) 11.6906 0.425465
\(756\) 0 0
\(757\) −41.9962 −1.52638 −0.763190 0.646175i \(-0.776368\pi\)
−0.763190 + 0.646175i \(0.776368\pi\)
\(758\) 0 0
\(759\) −10.3604 −0.376060
\(760\) 0 0
\(761\) 15.1395 0.548805 0.274402 0.961615i \(-0.411520\pi\)
0.274402 + 0.961615i \(0.411520\pi\)
\(762\) 0 0
\(763\) −0.162712 −0.00589059
\(764\) 0 0
\(765\) 2.45332 0.0886999
\(766\) 0 0
\(767\) −6.24631 −0.225541
\(768\) 0 0
\(769\) 1.54087 0.0555652 0.0277826 0.999614i \(-0.491155\pi\)
0.0277826 + 0.999614i \(0.491155\pi\)
\(770\) 0 0
\(771\) 16.9567 0.610680
\(772\) 0 0
\(773\) 7.08798 0.254937 0.127469 0.991843i \(-0.459315\pi\)
0.127469 + 0.991843i \(0.459315\pi\)
\(774\) 0 0
\(775\) 18.6459 0.669780
\(776\) 0 0
\(777\) 9.70229 0.348068
\(778\) 0 0
\(779\) −0.215854 −0.00773376
\(780\) 0 0
\(781\) 11.4219 0.408706
\(782\) 0 0
\(783\) 19.0651 0.681333
\(784\) 0 0
\(785\) −13.4894 −0.481459
\(786\) 0 0
\(787\) −27.6820 −0.986757 −0.493378 0.869815i \(-0.664238\pi\)
−0.493378 + 0.869815i \(0.664238\pi\)
\(788\) 0 0
\(789\) 27.3822 0.974832
\(790\) 0 0
\(791\) 11.3896 0.404967
\(792\) 0 0
\(793\) −8.41953 −0.298986
\(794\) 0 0
\(795\) 15.2973 0.542538
\(796\) 0 0
\(797\) 53.6390 1.89999 0.949996 0.312263i \(-0.101087\pi\)
0.949996 + 0.312263i \(0.101087\pi\)
\(798\) 0 0
\(799\) −34.6473 −1.22573
\(800\) 0 0
\(801\) 1.84837 0.0653089
\(802\) 0 0
\(803\) 4.43520 0.156515
\(804\) 0 0
\(805\) −17.1335 −0.603878
\(806\) 0 0
\(807\) 8.00048 0.281630
\(808\) 0 0
\(809\) 3.62134 0.127319 0.0636597 0.997972i \(-0.479723\pi\)
0.0636597 + 0.997972i \(0.479723\pi\)
\(810\) 0 0
\(811\) −9.07667 −0.318725 −0.159363 0.987220i \(-0.550944\pi\)
−0.159363 + 0.987220i \(0.550944\pi\)
\(812\) 0 0
\(813\) −41.3019 −1.44852
\(814\) 0 0
\(815\) −46.3957 −1.62517
\(816\) 0 0
\(817\) 2.83823 0.0992972
\(818\) 0 0
\(819\) 0.244902 0.00855757
\(820\) 0 0
\(821\) −11.6994 −0.408313 −0.204157 0.978938i \(-0.565445\pi\)
−0.204157 + 0.978938i \(0.565445\pi\)
\(822\) 0 0
\(823\) 33.7856 1.17769 0.588845 0.808246i \(-0.299583\pi\)
0.588845 + 0.808246i \(0.299583\pi\)
\(824\) 0 0
\(825\) 6.97920 0.242984
\(826\) 0 0
\(827\) 8.94379 0.311006 0.155503 0.987835i \(-0.450300\pi\)
0.155503 + 0.987835i \(0.450300\pi\)
\(828\) 0 0
\(829\) 44.3182 1.53923 0.769617 0.638506i \(-0.220447\pi\)
0.769617 + 0.638506i \(0.220447\pi\)
\(830\) 0 0
\(831\) 13.6540 0.473653
\(832\) 0 0
\(833\) −3.36273 −0.116512
\(834\) 0 0
\(835\) −8.84719 −0.306170
\(836\) 0 0
\(837\) 23.8845 0.825569
\(838\) 0 0
\(839\) −23.6729 −0.817279 −0.408640 0.912696i \(-0.633997\pi\)
−0.408640 + 0.912696i \(0.633997\pi\)
\(840\) 0 0
\(841\) −14.2428 −0.491130
\(842\) 0 0
\(843\) 7.73238 0.266317
\(844\) 0 0
\(845\) −2.97899 −0.102480
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −32.6900 −1.12192
\(850\) 0 0
\(851\) −30.9778 −1.06191
\(852\) 0 0
\(853\) −4.24737 −0.145427 −0.0727136 0.997353i \(-0.523166\pi\)
−0.0727136 + 0.997353i \(0.523166\pi\)
\(854\) 0 0
\(855\) 0.474909 0.0162416
\(856\) 0 0
\(857\) −53.6007 −1.83096 −0.915482 0.402359i \(-0.868190\pi\)
−0.915482 + 0.402359i \(0.868190\pi\)
\(858\) 0 0
\(859\) 17.7557 0.605816 0.302908 0.953020i \(-0.402042\pi\)
0.302908 + 0.953020i \(0.402042\pi\)
\(860\) 0 0
\(861\) 0.597327 0.0203568
\(862\) 0 0
\(863\) 10.8866 0.370586 0.185293 0.982683i \(-0.440677\pi\)
0.185293 + 0.982683i \(0.440677\pi\)
\(864\) 0 0
\(865\) −29.0417 −0.987448
\(866\) 0 0
\(867\) 10.2535 0.348226
\(868\) 0 0
\(869\) −14.2508 −0.483426
\(870\) 0 0
\(871\) 11.3964 0.386152
\(872\) 0 0
\(873\) −1.82830 −0.0618784
\(874\) 0 0
\(875\) −3.35315 −0.113357
\(876\) 0 0
\(877\) −5.43991 −0.183693 −0.0918463 0.995773i \(-0.529277\pi\)
−0.0918463 + 0.995773i \(0.529277\pi\)
\(878\) 0 0
\(879\) 40.3468 1.36086
\(880\) 0 0
\(881\) 19.3905 0.653282 0.326641 0.945148i \(-0.394083\pi\)
0.326641 + 0.945148i \(0.394083\pi\)
\(882\) 0 0
\(883\) 9.44681 0.317910 0.158955 0.987286i \(-0.449187\pi\)
0.158955 + 0.987286i \(0.449187\pi\)
\(884\) 0 0
\(885\) 33.5192 1.12674
\(886\) 0 0
\(887\) −24.2956 −0.815767 −0.407883 0.913034i \(-0.633733\pi\)
−0.407883 + 0.913034i \(0.633733\pi\)
\(888\) 0 0
\(889\) −1.53467 −0.0514711
\(890\) 0 0
\(891\) 9.67473 0.324116
\(892\) 0 0
\(893\) −6.70696 −0.224440
\(894\) 0 0
\(895\) −30.9312 −1.03391
\(896\) 0 0
\(897\) −10.3604 −0.345925
\(898\) 0 0
\(899\) 18.4876 0.616596
\(900\) 0 0
\(901\) −9.58595 −0.319354
\(902\) 0 0
\(903\) −7.85417 −0.261370
\(904\) 0 0
\(905\) 46.5630 1.54781
\(906\) 0 0
\(907\) 43.4805 1.44375 0.721873 0.692026i \(-0.243282\pi\)
0.721873 + 0.692026i \(0.243282\pi\)
\(908\) 0 0
\(909\) −3.07520 −0.101998
\(910\) 0 0
\(911\) −12.1619 −0.402940 −0.201470 0.979495i \(-0.564572\pi\)
−0.201470 + 0.979495i \(0.564572\pi\)
\(912\) 0 0
\(913\) 4.23541 0.140172
\(914\) 0 0
\(915\) 45.1812 1.49365
\(916\) 0 0
\(917\) −20.0747 −0.662923
\(918\) 0 0
\(919\) −46.3321 −1.52836 −0.764178 0.645006i \(-0.776855\pi\)
−0.764178 + 0.645006i \(0.776855\pi\)
\(920\) 0 0
\(921\) −41.8504 −1.37902
\(922\) 0 0
\(923\) 11.4219 0.375955
\(924\) 0 0
\(925\) 20.8679 0.686131
\(926\) 0 0
\(927\) 3.34893 0.109993
\(928\) 0 0
\(929\) 33.4516 1.09751 0.548756 0.835982i \(-0.315101\pi\)
0.548756 + 0.835982i \(0.315101\pi\)
\(930\) 0 0
\(931\) −0.650951 −0.0213341
\(932\) 0 0
\(933\) 26.9025 0.880747
\(934\) 0 0
\(935\) −10.0175 −0.327609
\(936\) 0 0
\(937\) 51.7909 1.69193 0.845967 0.533235i \(-0.179024\pi\)
0.845967 + 0.533235i \(0.179024\pi\)
\(938\) 0 0
\(939\) 33.1817 1.08284
\(940\) 0 0
\(941\) −29.5429 −0.963071 −0.481535 0.876427i \(-0.659921\pi\)
−0.481535 + 0.876427i \(0.659921\pi\)
\(942\) 0 0
\(943\) −1.90717 −0.0621059
\(944\) 0 0
\(945\) 14.7845 0.480941
\(946\) 0 0
\(947\) −34.9610 −1.13608 −0.568040 0.823001i \(-0.692298\pi\)
−0.568040 + 0.823001i \(0.692298\pi\)
\(948\) 0 0
\(949\) 4.43520 0.143973
\(950\) 0 0
\(951\) 31.2167 1.01227
\(952\) 0 0
\(953\) 6.41068 0.207662 0.103831 0.994595i \(-0.466890\pi\)
0.103831 + 0.994595i \(0.466890\pi\)
\(954\) 0 0
\(955\) 68.5357 2.21776
\(956\) 0 0
\(957\) 6.91995 0.223690
\(958\) 0 0
\(959\) −6.81319 −0.220009
\(960\) 0 0
\(961\) −7.83904 −0.252872
\(962\) 0 0
\(963\) −0.998638 −0.0321807
\(964\) 0 0
\(965\) 5.37885 0.173151
\(966\) 0 0
\(967\) −59.4885 −1.91302 −0.956510 0.291699i \(-0.905780\pi\)
−0.956510 + 0.291699i \(0.905780\pi\)
\(968\) 0 0
\(969\) −3.94313 −0.126672
\(970\) 0 0
\(971\) 34.9057 1.12018 0.560089 0.828432i \(-0.310767\pi\)
0.560089 + 0.828432i \(0.310767\pi\)
\(972\) 0 0
\(973\) −10.8278 −0.347125
\(974\) 0 0
\(975\) 6.97920 0.223513
\(976\) 0 0
\(977\) −8.31265 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(978\) 0 0
\(979\) −7.54738 −0.241215
\(980\) 0 0
\(981\) 0.0398486 0.00127227
\(982\) 0 0
\(983\) −47.2357 −1.50658 −0.753292 0.657686i \(-0.771535\pi\)
−0.753292 + 0.657686i \(0.771535\pi\)
\(984\) 0 0
\(985\) 65.6912 2.09309
\(986\) 0 0
\(987\) 18.5600 0.590772
\(988\) 0 0
\(989\) 25.0771 0.797405
\(990\) 0 0
\(991\) 46.3448 1.47219 0.736095 0.676878i \(-0.236667\pi\)
0.736095 + 0.676878i \(0.236667\pi\)
\(992\) 0 0
\(993\) −39.3849 −1.24984
\(994\) 0 0
\(995\) 3.39045 0.107485
\(996\) 0 0
\(997\) 45.0438 1.42655 0.713275 0.700884i \(-0.247211\pi\)
0.713275 + 0.700884i \(0.247211\pi\)
\(998\) 0 0
\(999\) 26.7307 0.845723
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 \(a_p\))