Properties

Label 8008.2.a.y.1.12
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-2.05490\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.05490 q^{3} +0.929320 q^{5} +1.00000 q^{7} +1.22261 q^{9} +O(q^{10})\) \(q+2.05490 q^{3} +0.929320 q^{5} +1.00000 q^{7} +1.22261 q^{9} -1.00000 q^{11} -1.00000 q^{13} +1.90966 q^{15} -5.05388 q^{17} +4.52180 q^{19} +2.05490 q^{21} -3.13093 q^{23} -4.13637 q^{25} -3.65235 q^{27} -3.89235 q^{29} -0.650557 q^{31} -2.05490 q^{33} +0.929320 q^{35} -6.58094 q^{37} -2.05490 q^{39} -11.3620 q^{41} -8.86287 q^{43} +1.13620 q^{45} +7.96562 q^{47} +1.00000 q^{49} -10.3852 q^{51} -9.49550 q^{53} -0.929320 q^{55} +9.29185 q^{57} +12.4166 q^{59} -7.70412 q^{61} +1.22261 q^{63} -0.929320 q^{65} -12.8613 q^{67} -6.43374 q^{69} -10.0543 q^{71} +15.4339 q^{73} -8.49981 q^{75} -1.00000 q^{77} -10.2793 q^{79} -11.1731 q^{81} +8.85960 q^{83} -4.69667 q^{85} -7.99838 q^{87} -1.21794 q^{89} -1.00000 q^{91} -1.33683 q^{93} +4.20220 q^{95} +6.19616 q^{97} -1.22261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) 2.05490 1.18640 0.593198 0.805056i \(-0.297865\pi\)
0.593198 + 0.805056i \(0.297865\pi\)
\(4\) 0 0
\(5\) 0.929320 0.415604 0.207802 0.978171i \(-0.433369\pi\)
0.207802 + 0.978171i \(0.433369\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 1.22261 0.407537
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.90966 0.493072
\(16\) 0 0
\(17\) −5.05388 −1.22575 −0.612873 0.790181i \(-0.709986\pi\)
−0.612873 + 0.790181i \(0.709986\pi\)
\(18\) 0 0
\(19\) 4.52180 1.03737 0.518686 0.854965i \(-0.326421\pi\)
0.518686 + 0.854965i \(0.326421\pi\)
\(20\) 0 0
\(21\) 2.05490 0.448416
\(22\) 0 0
\(23\) −3.13093 −0.652843 −0.326422 0.945224i \(-0.605843\pi\)
−0.326422 + 0.945224i \(0.605843\pi\)
\(24\) 0 0
\(25\) −4.13637 −0.827273
\(26\) 0 0
\(27\) −3.65235 −0.702896
\(28\) 0 0
\(29\) −3.89235 −0.722791 −0.361395 0.932413i \(-0.617700\pi\)
−0.361395 + 0.932413i \(0.617700\pi\)
\(30\) 0 0
\(31\) −0.650557 −0.116844 −0.0584218 0.998292i \(-0.518607\pi\)
−0.0584218 + 0.998292i \(0.518607\pi\)
\(32\) 0 0
\(33\) −2.05490 −0.357712
\(34\) 0 0
\(35\) 0.929320 0.157084
\(36\) 0 0
\(37\) −6.58094 −1.08190 −0.540950 0.841055i \(-0.681935\pi\)
−0.540950 + 0.841055i \(0.681935\pi\)
\(38\) 0 0
\(39\) −2.05490 −0.329047
\(40\) 0 0
\(41\) −11.3620 −1.77444 −0.887220 0.461346i \(-0.847367\pi\)
−0.887220 + 0.461346i \(0.847367\pi\)
\(42\) 0 0
\(43\) −8.86287 −1.35158 −0.675788 0.737096i \(-0.736196\pi\)
−0.675788 + 0.737096i \(0.736196\pi\)
\(44\) 0 0
\(45\) 1.13620 0.169374
\(46\) 0 0
\(47\) 7.96562 1.16191 0.580953 0.813937i \(-0.302680\pi\)
0.580953 + 0.813937i \(0.302680\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −10.3852 −1.45422
\(52\) 0 0
\(53\) −9.49550 −1.30431 −0.652154 0.758087i \(-0.726134\pi\)
−0.652154 + 0.758087i \(0.726134\pi\)
\(54\) 0 0
\(55\) −0.929320 −0.125309
\(56\) 0 0
\(57\) 9.29185 1.23074
\(58\) 0 0
\(59\) 12.4166 1.61650 0.808251 0.588838i \(-0.200414\pi\)
0.808251 + 0.588838i \(0.200414\pi\)
\(60\) 0 0
\(61\) −7.70412 −0.986411 −0.493206 0.869913i \(-0.664175\pi\)
−0.493206 + 0.869913i \(0.664175\pi\)
\(62\) 0 0
\(63\) 1.22261 0.154035
\(64\) 0 0
\(65\) −0.929320 −0.115268
\(66\) 0 0
\(67\) −12.8613 −1.57125 −0.785626 0.618702i \(-0.787659\pi\)
−0.785626 + 0.618702i \(0.787659\pi\)
\(68\) 0 0
\(69\) −6.43374 −0.774531
\(70\) 0 0
\(71\) −10.0543 −1.19322 −0.596612 0.802530i \(-0.703487\pi\)
−0.596612 + 0.802530i \(0.703487\pi\)
\(72\) 0 0
\(73\) 15.4339 1.80640 0.903199 0.429222i \(-0.141212\pi\)
0.903199 + 0.429222i \(0.141212\pi\)
\(74\) 0 0
\(75\) −8.49981 −0.981474
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −10.2793 −1.15652 −0.578258 0.815854i \(-0.696267\pi\)
−0.578258 + 0.815854i \(0.696267\pi\)
\(80\) 0 0
\(81\) −11.1731 −1.24145
\(82\) 0 0
\(83\) 8.85960 0.972468 0.486234 0.873829i \(-0.338370\pi\)
0.486234 + 0.873829i \(0.338370\pi\)
\(84\) 0 0
\(85\) −4.69667 −0.509425
\(86\) 0 0
\(87\) −7.99838 −0.857517
\(88\) 0 0
\(89\) −1.21794 −0.129101 −0.0645506 0.997914i \(-0.520561\pi\)
−0.0645506 + 0.997914i \(0.520561\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −1.33683 −0.138623
\(94\) 0 0
\(95\) 4.20220 0.431136
\(96\) 0 0
\(97\) 6.19616 0.629125 0.314563 0.949237i \(-0.398142\pi\)
0.314563 + 0.949237i \(0.398142\pi\)
\(98\) 0 0
\(99\) −1.22261 −0.122877
\(100\) 0 0
\(101\) −4.27848 −0.425725 −0.212863 0.977082i \(-0.568279\pi\)
−0.212863 + 0.977082i \(0.568279\pi\)
\(102\) 0 0
\(103\) 17.0901 1.68393 0.841966 0.539530i \(-0.181398\pi\)
0.841966 + 0.539530i \(0.181398\pi\)
\(104\) 0 0
\(105\) 1.90966 0.186364
\(106\) 0 0
\(107\) 16.9650 1.64006 0.820032 0.572318i \(-0.193956\pi\)
0.820032 + 0.572318i \(0.193956\pi\)
\(108\) 0 0
\(109\) 14.2886 1.36860 0.684298 0.729202i \(-0.260109\pi\)
0.684298 + 0.729202i \(0.260109\pi\)
\(110\) 0 0
\(111\) −13.5232 −1.28356
\(112\) 0 0
\(113\) −5.28934 −0.497579 −0.248790 0.968558i \(-0.580033\pi\)
−0.248790 + 0.968558i \(0.580033\pi\)
\(114\) 0 0
\(115\) −2.90963 −0.271325
\(116\) 0 0
\(117\) −1.22261 −0.113031
\(118\) 0 0
\(119\) −5.05388 −0.463289
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −23.3477 −2.10519
\(124\) 0 0
\(125\) −8.49060 −0.759423
\(126\) 0 0
\(127\) 5.76890 0.511907 0.255953 0.966689i \(-0.417611\pi\)
0.255953 + 0.966689i \(0.417611\pi\)
\(128\) 0 0
\(129\) −18.2123 −1.60350
\(130\) 0 0
\(131\) −11.3283 −0.989762 −0.494881 0.868961i \(-0.664788\pi\)
−0.494881 + 0.868961i \(0.664788\pi\)
\(132\) 0 0
\(133\) 4.52180 0.392090
\(134\) 0 0
\(135\) −3.39420 −0.292127
\(136\) 0 0
\(137\) −11.6510 −0.995409 −0.497704 0.867347i \(-0.665824\pi\)
−0.497704 + 0.867347i \(0.665824\pi\)
\(138\) 0 0
\(139\) −8.37197 −0.710101 −0.355051 0.934847i \(-0.615536\pi\)
−0.355051 + 0.934847i \(0.615536\pi\)
\(140\) 0 0
\(141\) 16.3685 1.37848
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −3.61724 −0.300395
\(146\) 0 0
\(147\) 2.05490 0.169485
\(148\) 0 0
\(149\) 12.9193 1.05839 0.529196 0.848499i \(-0.322494\pi\)
0.529196 + 0.848499i \(0.322494\pi\)
\(150\) 0 0
\(151\) 13.1077 1.06669 0.533346 0.845897i \(-0.320934\pi\)
0.533346 + 0.845897i \(0.320934\pi\)
\(152\) 0 0
\(153\) −6.17894 −0.499537
\(154\) 0 0
\(155\) −0.604575 −0.0485607
\(156\) 0 0
\(157\) 8.26949 0.659978 0.329989 0.943985i \(-0.392955\pi\)
0.329989 + 0.943985i \(0.392955\pi\)
\(158\) 0 0
\(159\) −19.5123 −1.54743
\(160\) 0 0
\(161\) −3.13093 −0.246752
\(162\) 0 0
\(163\) −4.91977 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(164\) 0 0
\(165\) −1.90966 −0.148667
\(166\) 0 0
\(167\) 3.44439 0.266535 0.133267 0.991080i \(-0.457453\pi\)
0.133267 + 0.991080i \(0.457453\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 5.52841 0.422768
\(172\) 0 0
\(173\) 16.2236 1.23346 0.616729 0.787176i \(-0.288457\pi\)
0.616729 + 0.787176i \(0.288457\pi\)
\(174\) 0 0
\(175\) −4.13637 −0.312680
\(176\) 0 0
\(177\) 25.5148 1.91781
\(178\) 0 0
\(179\) 17.4581 1.30488 0.652441 0.757839i \(-0.273745\pi\)
0.652441 + 0.757839i \(0.273745\pi\)
\(180\) 0 0
\(181\) −7.20535 −0.535569 −0.267785 0.963479i \(-0.586292\pi\)
−0.267785 + 0.963479i \(0.586292\pi\)
\(182\) 0 0
\(183\) −15.8312 −1.17028
\(184\) 0 0
\(185\) −6.11580 −0.449642
\(186\) 0 0
\(187\) 5.05388 0.369576
\(188\) 0 0
\(189\) −3.65235 −0.265670
\(190\) 0 0
\(191\) −21.7213 −1.57170 −0.785848 0.618420i \(-0.787773\pi\)
−0.785848 + 0.618420i \(0.787773\pi\)
\(192\) 0 0
\(193\) 4.29040 0.308829 0.154415 0.988006i \(-0.450651\pi\)
0.154415 + 0.988006i \(0.450651\pi\)
\(194\) 0 0
\(195\) −1.90966 −0.136753
\(196\) 0 0
\(197\) −6.83071 −0.486668 −0.243334 0.969943i \(-0.578241\pi\)
−0.243334 + 0.969943i \(0.578241\pi\)
\(198\) 0 0
\(199\) 8.16560 0.578844 0.289422 0.957202i \(-0.406537\pi\)
0.289422 + 0.957202i \(0.406537\pi\)
\(200\) 0 0
\(201\) −26.4286 −1.86413
\(202\) 0 0
\(203\) −3.89235 −0.273189
\(204\) 0 0
\(205\) −10.5589 −0.737465
\(206\) 0 0
\(207\) −3.82791 −0.266058
\(208\) 0 0
\(209\) −4.52180 −0.312779
\(210\) 0 0
\(211\) 6.07057 0.417915 0.208958 0.977925i \(-0.432993\pi\)
0.208958 + 0.977925i \(0.432993\pi\)
\(212\) 0 0
\(213\) −20.6605 −1.41564
\(214\) 0 0
\(215\) −8.23644 −0.561721
\(216\) 0 0
\(217\) −0.650557 −0.0441627
\(218\) 0 0
\(219\) 31.7151 2.14310
\(220\) 0 0
\(221\) 5.05388 0.339961
\(222\) 0 0
\(223\) −11.1208 −0.744705 −0.372353 0.928091i \(-0.621449\pi\)
−0.372353 + 0.928091i \(0.621449\pi\)
\(224\) 0 0
\(225\) −5.05717 −0.337145
\(226\) 0 0
\(227\) 8.64172 0.573571 0.286786 0.957995i \(-0.407413\pi\)
0.286786 + 0.957995i \(0.407413\pi\)
\(228\) 0 0
\(229\) −23.3645 −1.54397 −0.771984 0.635642i \(-0.780735\pi\)
−0.771984 + 0.635642i \(0.780735\pi\)
\(230\) 0 0
\(231\) −2.05490 −0.135202
\(232\) 0 0
\(233\) −25.3459 −1.66046 −0.830231 0.557419i \(-0.811792\pi\)
−0.830231 + 0.557419i \(0.811792\pi\)
\(234\) 0 0
\(235\) 7.40261 0.482893
\(236\) 0 0
\(237\) −21.1230 −1.37209
\(238\) 0 0
\(239\) −22.5131 −1.45625 −0.728125 0.685444i \(-0.759608\pi\)
−0.728125 + 0.685444i \(0.759608\pi\)
\(240\) 0 0
\(241\) 16.5802 1.06803 0.534013 0.845476i \(-0.320683\pi\)
0.534013 + 0.845476i \(0.320683\pi\)
\(242\) 0 0
\(243\) −12.0024 −0.769957
\(244\) 0 0
\(245\) 0.929320 0.0593720
\(246\) 0 0
\(247\) −4.52180 −0.287715
\(248\) 0 0
\(249\) 18.2056 1.15373
\(250\) 0 0
\(251\) −10.6471 −0.672037 −0.336019 0.941855i \(-0.609080\pi\)
−0.336019 + 0.941855i \(0.609080\pi\)
\(252\) 0 0
\(253\) 3.13093 0.196840
\(254\) 0 0
\(255\) −9.65119 −0.604381
\(256\) 0 0
\(257\) 5.22557 0.325962 0.162981 0.986629i \(-0.447889\pi\)
0.162981 + 0.986629i \(0.447889\pi\)
\(258\) 0 0
\(259\) −6.58094 −0.408920
\(260\) 0 0
\(261\) −4.75883 −0.294564
\(262\) 0 0
\(263\) −8.00459 −0.493584 −0.246792 0.969068i \(-0.579376\pi\)
−0.246792 + 0.969068i \(0.579376\pi\)
\(264\) 0 0
\(265\) −8.82436 −0.542076
\(266\) 0 0
\(267\) −2.50274 −0.153165
\(268\) 0 0
\(269\) 11.9168 0.726581 0.363291 0.931676i \(-0.381653\pi\)
0.363291 + 0.931676i \(0.381653\pi\)
\(270\) 0 0
\(271\) 10.1920 0.619122 0.309561 0.950880i \(-0.399818\pi\)
0.309561 + 0.950880i \(0.399818\pi\)
\(272\) 0 0
\(273\) −2.05490 −0.124368
\(274\) 0 0
\(275\) 4.13637 0.249432
\(276\) 0 0
\(277\) 17.5066 1.05187 0.525934 0.850526i \(-0.323716\pi\)
0.525934 + 0.850526i \(0.323716\pi\)
\(278\) 0 0
\(279\) −0.795379 −0.0476181
\(280\) 0 0
\(281\) −6.56131 −0.391415 −0.195707 0.980662i \(-0.562700\pi\)
−0.195707 + 0.980662i \(0.562700\pi\)
\(282\) 0 0
\(283\) 5.00778 0.297681 0.148841 0.988861i \(-0.452446\pi\)
0.148841 + 0.988861i \(0.452446\pi\)
\(284\) 0 0
\(285\) 8.63509 0.511499
\(286\) 0 0
\(287\) −11.3620 −0.670676
\(288\) 0 0
\(289\) 8.54172 0.502454
\(290\) 0 0
\(291\) 12.7325 0.746392
\(292\) 0 0
\(293\) 16.8927 0.986883 0.493441 0.869779i \(-0.335739\pi\)
0.493441 + 0.869779i \(0.335739\pi\)
\(294\) 0 0
\(295\) 11.5390 0.671825
\(296\) 0 0
\(297\) 3.65235 0.211931
\(298\) 0 0
\(299\) 3.13093 0.181066
\(300\) 0 0
\(301\) −8.86287 −0.510847
\(302\) 0 0
\(303\) −8.79186 −0.505079
\(304\) 0 0
\(305\) −7.15959 −0.409957
\(306\) 0 0
\(307\) 5.17232 0.295200 0.147600 0.989047i \(-0.452845\pi\)
0.147600 + 0.989047i \(0.452845\pi\)
\(308\) 0 0
\(309\) 35.1183 1.99781
\(310\) 0 0
\(311\) 13.9152 0.789059 0.394530 0.918883i \(-0.370908\pi\)
0.394530 + 0.918883i \(0.370908\pi\)
\(312\) 0 0
\(313\) 15.9020 0.898831 0.449416 0.893323i \(-0.351632\pi\)
0.449416 + 0.893323i \(0.351632\pi\)
\(314\) 0 0
\(315\) 1.13620 0.0640175
\(316\) 0 0
\(317\) −14.6516 −0.822918 −0.411459 0.911428i \(-0.634981\pi\)
−0.411459 + 0.911428i \(0.634981\pi\)
\(318\) 0 0
\(319\) 3.89235 0.217930
\(320\) 0 0
\(321\) 34.8613 1.94577
\(322\) 0 0
\(323\) −22.8526 −1.27156
\(324\) 0 0
\(325\) 4.13637 0.229444
\(326\) 0 0
\(327\) 29.3616 1.62370
\(328\) 0 0
\(329\) 7.96562 0.439159
\(330\) 0 0
\(331\) 24.5219 1.34784 0.673922 0.738803i \(-0.264608\pi\)
0.673922 + 0.738803i \(0.264608\pi\)
\(332\) 0 0
\(333\) −8.04594 −0.440915
\(334\) 0 0
\(335\) −11.9522 −0.653019
\(336\) 0 0
\(337\) −0.125969 −0.00686198 −0.00343099 0.999994i \(-0.501092\pi\)
−0.00343099 + 0.999994i \(0.501092\pi\)
\(338\) 0 0
\(339\) −10.8691 −0.590327
\(340\) 0 0
\(341\) 0.650557 0.0352296
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −5.97900 −0.321899
\(346\) 0 0
\(347\) −34.1881 −1.83531 −0.917656 0.397375i \(-0.869921\pi\)
−0.917656 + 0.397375i \(0.869921\pi\)
\(348\) 0 0
\(349\) 4.95886 0.265442 0.132721 0.991153i \(-0.457629\pi\)
0.132721 + 0.991153i \(0.457629\pi\)
\(350\) 0 0
\(351\) 3.65235 0.194948
\(352\) 0 0
\(353\) −29.1296 −1.55041 −0.775207 0.631707i \(-0.782355\pi\)
−0.775207 + 0.631707i \(0.782355\pi\)
\(354\) 0 0
\(355\) −9.34364 −0.495909
\(356\) 0 0
\(357\) −10.3852 −0.549644
\(358\) 0 0
\(359\) 1.21670 0.0642150 0.0321075 0.999484i \(-0.489778\pi\)
0.0321075 + 0.999484i \(0.489778\pi\)
\(360\) 0 0
\(361\) 1.44668 0.0761411
\(362\) 0 0
\(363\) 2.05490 0.107854
\(364\) 0 0
\(365\) 14.3430 0.750747
\(366\) 0 0
\(367\) −14.4543 −0.754508 −0.377254 0.926110i \(-0.623132\pi\)
−0.377254 + 0.926110i \(0.623132\pi\)
\(368\) 0 0
\(369\) −13.8913 −0.723151
\(370\) 0 0
\(371\) −9.49550 −0.492982
\(372\) 0 0
\(373\) −22.7743 −1.17921 −0.589605 0.807692i \(-0.700716\pi\)
−0.589605 + 0.807692i \(0.700716\pi\)
\(374\) 0 0
\(375\) −17.4473 −0.900977
\(376\) 0 0
\(377\) 3.89235 0.200466
\(378\) 0 0
\(379\) 12.4702 0.640551 0.320275 0.947324i \(-0.396225\pi\)
0.320275 + 0.947324i \(0.396225\pi\)
\(380\) 0 0
\(381\) 11.8545 0.607325
\(382\) 0 0
\(383\) 21.2679 1.08674 0.543371 0.839493i \(-0.317148\pi\)
0.543371 + 0.839493i \(0.317148\pi\)
\(384\) 0 0
\(385\) −0.929320 −0.0473625
\(386\) 0 0
\(387\) −10.8359 −0.550817
\(388\) 0 0
\(389\) 31.7751 1.61106 0.805530 0.592555i \(-0.201881\pi\)
0.805530 + 0.592555i \(0.201881\pi\)
\(390\) 0 0
\(391\) 15.8233 0.800220
\(392\) 0 0
\(393\) −23.2786 −1.17425
\(394\) 0 0
\(395\) −9.55280 −0.480653
\(396\) 0 0
\(397\) −12.8096 −0.642895 −0.321448 0.946927i \(-0.604169\pi\)
−0.321448 + 0.946927i \(0.604169\pi\)
\(398\) 0 0
\(399\) 9.29185 0.465174
\(400\) 0 0
\(401\) −34.6309 −1.72939 −0.864693 0.502300i \(-0.832487\pi\)
−0.864693 + 0.502300i \(0.832487\pi\)
\(402\) 0 0
\(403\) 0.650557 0.0324066
\(404\) 0 0
\(405\) −10.3833 −0.515952
\(406\) 0 0
\(407\) 6.58094 0.326205
\(408\) 0 0
\(409\) −35.9173 −1.77600 −0.887998 0.459847i \(-0.847904\pi\)
−0.887998 + 0.459847i \(0.847904\pi\)
\(410\) 0 0
\(411\) −23.9416 −1.18095
\(412\) 0 0
\(413\) 12.4166 0.610980
\(414\) 0 0
\(415\) 8.23340 0.404162
\(416\) 0 0
\(417\) −17.2036 −0.842462
\(418\) 0 0
\(419\) −19.0102 −0.928708 −0.464354 0.885650i \(-0.653713\pi\)
−0.464354 + 0.885650i \(0.653713\pi\)
\(420\) 0 0
\(421\) 31.2677 1.52389 0.761947 0.647639i \(-0.224244\pi\)
0.761947 + 0.647639i \(0.224244\pi\)
\(422\) 0 0
\(423\) 9.73886 0.473520
\(424\) 0 0
\(425\) 20.9047 1.01403
\(426\) 0 0
\(427\) −7.70412 −0.372828
\(428\) 0 0
\(429\) 2.05490 0.0992115
\(430\) 0 0
\(431\) −14.0409 −0.676326 −0.338163 0.941088i \(-0.609805\pi\)
−0.338163 + 0.941088i \(0.609805\pi\)
\(432\) 0 0
\(433\) 19.8510 0.953980 0.476990 0.878909i \(-0.341728\pi\)
0.476990 + 0.878909i \(0.341728\pi\)
\(434\) 0 0
\(435\) −7.43305 −0.356388
\(436\) 0 0
\(437\) −14.1574 −0.677242
\(438\) 0 0
\(439\) 21.7936 1.04015 0.520076 0.854120i \(-0.325904\pi\)
0.520076 + 0.854120i \(0.325904\pi\)
\(440\) 0 0
\(441\) 1.22261 0.0582196
\(442\) 0 0
\(443\) −21.4482 −1.01903 −0.509516 0.860461i \(-0.670176\pi\)
−0.509516 + 0.860461i \(0.670176\pi\)
\(444\) 0 0
\(445\) −1.13185 −0.0536550
\(446\) 0 0
\(447\) 26.5479 1.25567
\(448\) 0 0
\(449\) 29.1215 1.37433 0.687164 0.726503i \(-0.258856\pi\)
0.687164 + 0.726503i \(0.258856\pi\)
\(450\) 0 0
\(451\) 11.3620 0.535014
\(452\) 0 0
\(453\) 26.9351 1.26552
\(454\) 0 0
\(455\) −0.929320 −0.0435672
\(456\) 0 0
\(457\) −30.7601 −1.43890 −0.719449 0.694545i \(-0.755606\pi\)
−0.719449 + 0.694545i \(0.755606\pi\)
\(458\) 0 0
\(459\) 18.4586 0.861572
\(460\) 0 0
\(461\) 7.34317 0.342006 0.171003 0.985271i \(-0.445299\pi\)
0.171003 + 0.985271i \(0.445299\pi\)
\(462\) 0 0
\(463\) 3.40181 0.158095 0.0790477 0.996871i \(-0.474812\pi\)
0.0790477 + 0.996871i \(0.474812\pi\)
\(464\) 0 0
\(465\) −1.24234 −0.0576122
\(466\) 0 0
\(467\) −2.03680 −0.0942521 −0.0471260 0.998889i \(-0.515006\pi\)
−0.0471260 + 0.998889i \(0.515006\pi\)
\(468\) 0 0
\(469\) −12.8613 −0.593877
\(470\) 0 0
\(471\) 16.9930 0.782995
\(472\) 0 0
\(473\) 8.86287 0.407515
\(474\) 0 0
\(475\) −18.7038 −0.858190
\(476\) 0 0
\(477\) −11.6093 −0.531554
\(478\) 0 0
\(479\) 12.5052 0.571379 0.285690 0.958322i \(-0.407777\pi\)
0.285690 + 0.958322i \(0.407777\pi\)
\(480\) 0 0
\(481\) 6.58094 0.300065
\(482\) 0 0
\(483\) −6.43374 −0.292745
\(484\) 0 0
\(485\) 5.75822 0.261467
\(486\) 0 0
\(487\) −14.7529 −0.668518 −0.334259 0.942481i \(-0.608486\pi\)
−0.334259 + 0.942481i \(0.608486\pi\)
\(488\) 0 0
\(489\) −10.1096 −0.457173
\(490\) 0 0
\(491\) −0.0293564 −0.00132483 −0.000662417 1.00000i \(-0.500211\pi\)
−0.000662417 1.00000i \(0.500211\pi\)
\(492\) 0 0
\(493\) 19.6715 0.885958
\(494\) 0 0
\(495\) −1.13620 −0.0510683
\(496\) 0 0
\(497\) −10.0543 −0.450996
\(498\) 0 0
\(499\) −31.6586 −1.41723 −0.708617 0.705593i \(-0.750681\pi\)
−0.708617 + 0.705593i \(0.750681\pi\)
\(500\) 0 0
\(501\) 7.07787 0.316216
\(502\) 0 0
\(503\) 6.47377 0.288651 0.144326 0.989530i \(-0.453899\pi\)
0.144326 + 0.989530i \(0.453899\pi\)
\(504\) 0 0
\(505\) −3.97608 −0.176933
\(506\) 0 0
\(507\) 2.05490 0.0912613
\(508\) 0 0
\(509\) 26.2339 1.16280 0.581400 0.813618i \(-0.302505\pi\)
0.581400 + 0.813618i \(0.302505\pi\)
\(510\) 0 0
\(511\) 15.4339 0.682754
\(512\) 0 0
\(513\) −16.5152 −0.729165
\(514\) 0 0
\(515\) 15.8821 0.699850
\(516\) 0 0
\(517\) −7.96562 −0.350328
\(518\) 0 0
\(519\) 33.3379 1.46337
\(520\) 0 0
\(521\) −2.50570 −0.109777 −0.0548883 0.998492i \(-0.517480\pi\)
−0.0548883 + 0.998492i \(0.517480\pi\)
\(522\) 0 0
\(523\) −0.325724 −0.0142429 −0.00712146 0.999975i \(-0.502267\pi\)
−0.00712146 + 0.999975i \(0.502267\pi\)
\(524\) 0 0
\(525\) −8.49981 −0.370962
\(526\) 0 0
\(527\) 3.28784 0.143220
\(528\) 0 0
\(529\) −13.1973 −0.573796
\(530\) 0 0
\(531\) 15.1807 0.658785
\(532\) 0 0
\(533\) 11.3620 0.492141
\(534\) 0 0
\(535\) 15.7659 0.681618
\(536\) 0 0
\(537\) 35.8747 1.54811
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −32.7800 −1.40932 −0.704662 0.709543i \(-0.748901\pi\)
−0.704662 + 0.709543i \(0.748901\pi\)
\(542\) 0 0
\(543\) −14.8063 −0.635398
\(544\) 0 0
\(545\) 13.2786 0.568795
\(546\) 0 0
\(547\) 22.5393 0.963710 0.481855 0.876251i \(-0.339963\pi\)
0.481855 + 0.876251i \(0.339963\pi\)
\(548\) 0 0
\(549\) −9.41915 −0.401999
\(550\) 0 0
\(551\) −17.6004 −0.749803
\(552\) 0 0
\(553\) −10.2793 −0.437122
\(554\) 0 0
\(555\) −12.5673 −0.533454
\(556\) 0 0
\(557\) −37.0145 −1.56835 −0.784177 0.620538i \(-0.786914\pi\)
−0.784177 + 0.620538i \(0.786914\pi\)
\(558\) 0 0
\(559\) 8.86287 0.374860
\(560\) 0 0
\(561\) 10.3852 0.438464
\(562\) 0 0
\(563\) 10.8927 0.459074 0.229537 0.973300i \(-0.426279\pi\)
0.229537 + 0.973300i \(0.426279\pi\)
\(564\) 0 0
\(565\) −4.91549 −0.206796
\(566\) 0 0
\(567\) −11.1731 −0.469224
\(568\) 0 0
\(569\) −10.1624 −0.426028 −0.213014 0.977049i \(-0.568328\pi\)
−0.213014 + 0.977049i \(0.568328\pi\)
\(570\) 0 0
\(571\) −22.7132 −0.950516 −0.475258 0.879846i \(-0.657645\pi\)
−0.475258 + 0.879846i \(0.657645\pi\)
\(572\) 0 0
\(573\) −44.6350 −1.86466
\(574\) 0 0
\(575\) 12.9507 0.540080
\(576\) 0 0
\(577\) −13.2471 −0.551485 −0.275743 0.961231i \(-0.588924\pi\)
−0.275743 + 0.961231i \(0.588924\pi\)
\(578\) 0 0
\(579\) 8.81633 0.366394
\(580\) 0 0
\(581\) 8.85960 0.367558
\(582\) 0 0
\(583\) 9.49550 0.393264
\(584\) 0 0
\(585\) −1.13620 −0.0469760
\(586\) 0 0
\(587\) −17.7195 −0.731361 −0.365680 0.930741i \(-0.619164\pi\)
−0.365680 + 0.930741i \(0.619164\pi\)
\(588\) 0 0
\(589\) −2.94169 −0.121210
\(590\) 0 0
\(591\) −14.0364 −0.577382
\(592\) 0 0
\(593\) 15.0647 0.618635 0.309317 0.950959i \(-0.399899\pi\)
0.309317 + 0.950959i \(0.399899\pi\)
\(594\) 0 0
\(595\) −4.69667 −0.192545
\(596\) 0 0
\(597\) 16.7795 0.686739
\(598\) 0 0
\(599\) −7.88585 −0.322207 −0.161103 0.986938i \(-0.551505\pi\)
−0.161103 + 0.986938i \(0.551505\pi\)
\(600\) 0 0
\(601\) −7.00278 −0.285649 −0.142825 0.989748i \(-0.545619\pi\)
−0.142825 + 0.989748i \(0.545619\pi\)
\(602\) 0 0
\(603\) −15.7243 −0.640344
\(604\) 0 0
\(605\) 0.929320 0.0377822
\(606\) 0 0
\(607\) 5.40076 0.219210 0.109605 0.993975i \(-0.465041\pi\)
0.109605 + 0.993975i \(0.465041\pi\)
\(608\) 0 0
\(609\) −7.99838 −0.324111
\(610\) 0 0
\(611\) −7.96562 −0.322254
\(612\) 0 0
\(613\) 27.8522 1.12494 0.562470 0.826817i \(-0.309851\pi\)
0.562470 + 0.826817i \(0.309851\pi\)
\(614\) 0 0
\(615\) −21.6975 −0.874927
\(616\) 0 0
\(617\) 33.6574 1.35499 0.677497 0.735525i \(-0.263065\pi\)
0.677497 + 0.735525i \(0.263065\pi\)
\(618\) 0 0
\(619\) −39.0524 −1.56965 −0.784824 0.619719i \(-0.787246\pi\)
−0.784824 + 0.619719i \(0.787246\pi\)
\(620\) 0 0
\(621\) 11.4353 0.458881
\(622\) 0 0
\(623\) −1.21794 −0.0487957
\(624\) 0 0
\(625\) 12.7913 0.511654
\(626\) 0 0
\(627\) −9.29185 −0.371081
\(628\) 0 0
\(629\) 33.2593 1.32613
\(630\) 0 0
\(631\) 35.8663 1.42781 0.713907 0.700240i \(-0.246924\pi\)
0.713907 + 0.700240i \(0.246924\pi\)
\(632\) 0 0
\(633\) 12.4744 0.495814
\(634\) 0 0
\(635\) 5.36115 0.212751
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −12.2925 −0.486283
\(640\) 0 0
\(641\) −20.1431 −0.795606 −0.397803 0.917471i \(-0.630227\pi\)
−0.397803 + 0.917471i \(0.630227\pi\)
\(642\) 0 0
\(643\) −40.8212 −1.60983 −0.804916 0.593389i \(-0.797790\pi\)
−0.804916 + 0.593389i \(0.797790\pi\)
\(644\) 0 0
\(645\) −16.9251 −0.666423
\(646\) 0 0
\(647\) −4.47095 −0.175771 −0.0878857 0.996131i \(-0.528011\pi\)
−0.0878857 + 0.996131i \(0.528011\pi\)
\(648\) 0 0
\(649\) −12.4166 −0.487394
\(650\) 0 0
\(651\) −1.33683 −0.0523945
\(652\) 0 0
\(653\) 8.15206 0.319015 0.159507 0.987197i \(-0.449009\pi\)
0.159507 + 0.987197i \(0.449009\pi\)
\(654\) 0 0
\(655\) −10.5276 −0.411349
\(656\) 0 0
\(657\) 18.8696 0.736175
\(658\) 0 0
\(659\) 27.7186 1.07976 0.539881 0.841741i \(-0.318469\pi\)
0.539881 + 0.841741i \(0.318469\pi\)
\(660\) 0 0
\(661\) 14.5438 0.565689 0.282845 0.959166i \(-0.408722\pi\)
0.282845 + 0.959166i \(0.408722\pi\)
\(662\) 0 0
\(663\) 10.3852 0.403328
\(664\) 0 0
\(665\) 4.20220 0.162954
\(666\) 0 0
\(667\) 12.1867 0.471869
\(668\) 0 0
\(669\) −22.8522 −0.883516
\(670\) 0 0
\(671\) 7.70412 0.297414
\(672\) 0 0
\(673\) −7.94442 −0.306235 −0.153117 0.988208i \(-0.548931\pi\)
−0.153117 + 0.988208i \(0.548931\pi\)
\(674\) 0 0
\(675\) 15.1075 0.581487
\(676\) 0 0
\(677\) −13.9244 −0.535159 −0.267579 0.963536i \(-0.586224\pi\)
−0.267579 + 0.963536i \(0.586224\pi\)
\(678\) 0 0
\(679\) 6.19616 0.237787
\(680\) 0 0
\(681\) 17.7579 0.680483
\(682\) 0 0
\(683\) −25.1515 −0.962396 −0.481198 0.876612i \(-0.659798\pi\)
−0.481198 + 0.876612i \(0.659798\pi\)
\(684\) 0 0
\(685\) −10.8275 −0.413696
\(686\) 0 0
\(687\) −48.0116 −1.83176
\(688\) 0 0
\(689\) 9.49550 0.361750
\(690\) 0 0
\(691\) −1.16034 −0.0441416 −0.0220708 0.999756i \(-0.507026\pi\)
−0.0220708 + 0.999756i \(0.507026\pi\)
\(692\) 0 0
\(693\) −1.22261 −0.0464432
\(694\) 0 0
\(695\) −7.78023 −0.295121
\(696\) 0 0
\(697\) 57.4220 2.17501
\(698\) 0 0
\(699\) −52.0832 −1.96997
\(700\) 0 0
\(701\) 20.8732 0.788370 0.394185 0.919031i \(-0.371027\pi\)
0.394185 + 0.919031i \(0.371027\pi\)
\(702\) 0 0
\(703\) −29.7577 −1.12233
\(704\) 0 0
\(705\) 15.2116 0.572902
\(706\) 0 0
\(707\) −4.27848 −0.160909
\(708\) 0 0
\(709\) 12.3585 0.464132 0.232066 0.972700i \(-0.425451\pi\)
0.232066 + 0.972700i \(0.425451\pi\)
\(710\) 0 0
\(711\) −12.5677 −0.471324
\(712\) 0 0
\(713\) 2.03685 0.0762805
\(714\) 0 0
\(715\) 0.929320 0.0347546
\(716\) 0 0
\(717\) −46.2621 −1.72769
\(718\) 0 0
\(719\) −19.2310 −0.717195 −0.358598 0.933492i \(-0.616745\pi\)
−0.358598 + 0.933492i \(0.616745\pi\)
\(720\) 0 0
\(721\) 17.0901 0.636467
\(722\) 0 0
\(723\) 34.0707 1.26710
\(724\) 0 0
\(725\) 16.1002 0.597945
\(726\) 0 0
\(727\) 9.36247 0.347235 0.173617 0.984813i \(-0.444454\pi\)
0.173617 + 0.984813i \(0.444454\pi\)
\(728\) 0 0
\(729\) 8.85535 0.327976
\(730\) 0 0
\(731\) 44.7919 1.65669
\(732\) 0 0
\(733\) −34.4130 −1.27107 −0.635537 0.772070i \(-0.719221\pi\)
−0.635537 + 0.772070i \(0.719221\pi\)
\(734\) 0 0
\(735\) 1.90966 0.0704388
\(736\) 0 0
\(737\) 12.8613 0.473750
\(738\) 0 0
\(739\) 13.6474 0.502027 0.251013 0.967984i \(-0.419236\pi\)
0.251013 + 0.967984i \(0.419236\pi\)
\(740\) 0 0
\(741\) −9.29185 −0.341344
\(742\) 0 0
\(743\) 35.7957 1.31322 0.656608 0.754232i \(-0.271991\pi\)
0.656608 + 0.754232i \(0.271991\pi\)
\(744\) 0 0
\(745\) 12.0062 0.439872
\(746\) 0 0
\(747\) 10.8319 0.396317
\(748\) 0 0
\(749\) 16.9650 0.619886
\(750\) 0 0
\(751\) −37.5922 −1.37176 −0.685879 0.727716i \(-0.740582\pi\)
−0.685879 + 0.727716i \(0.740582\pi\)
\(752\) 0 0
\(753\) −21.8787 −0.797303
\(754\) 0 0
\(755\) 12.1813 0.443322
\(756\) 0 0
\(757\) −12.4938 −0.454095 −0.227048 0.973884i \(-0.572907\pi\)
−0.227048 + 0.973884i \(0.572907\pi\)
\(758\) 0 0
\(759\) 6.43374 0.233530
\(760\) 0 0
\(761\) 32.6874 1.18492 0.592458 0.805601i \(-0.298158\pi\)
0.592458 + 0.805601i \(0.298158\pi\)
\(762\) 0 0
\(763\) 14.2886 0.517281
\(764\) 0 0
\(765\) −5.74221 −0.207610
\(766\) 0 0
\(767\) −12.4166 −0.448337
\(768\) 0 0
\(769\) −12.1192 −0.437030 −0.218515 0.975834i \(-0.570121\pi\)
−0.218515 + 0.975834i \(0.570121\pi\)
\(770\) 0 0
\(771\) 10.7380 0.386720
\(772\) 0 0
\(773\) −52.8912 −1.90236 −0.951182 0.308631i \(-0.900129\pi\)
−0.951182 + 0.308631i \(0.900129\pi\)
\(774\) 0 0
\(775\) 2.69094 0.0966615
\(776\) 0 0
\(777\) −13.5232 −0.485141
\(778\) 0 0
\(779\) −51.3765 −1.84076
\(780\) 0 0
\(781\) 10.0543 0.359770
\(782\) 0 0
\(783\) 14.2162 0.508047
\(784\) 0 0
\(785\) 7.68500 0.274290
\(786\) 0 0
\(787\) −1.99290 −0.0710392 −0.0355196 0.999369i \(-0.511309\pi\)
−0.0355196 + 0.999369i \(0.511309\pi\)
\(788\) 0 0
\(789\) −16.4486 −0.585586
\(790\) 0 0
\(791\) −5.28934 −0.188067
\(792\) 0 0
\(793\) 7.70412 0.273581
\(794\) 0 0
\(795\) −18.1332 −0.643117
\(796\) 0 0
\(797\) −23.8825 −0.845962 −0.422981 0.906139i \(-0.639016\pi\)
−0.422981 + 0.906139i \(0.639016\pi\)
\(798\) 0 0
\(799\) −40.2573 −1.42420
\(800\) 0 0
\(801\) −1.48907 −0.0526136
\(802\) 0 0
\(803\) −15.4339 −0.544650
\(804\) 0 0
\(805\) −2.90963 −0.102551
\(806\) 0 0
\(807\) 24.4879 0.862014
\(808\) 0 0
\(809\) −37.0178 −1.30148 −0.650739 0.759302i \(-0.725541\pi\)
−0.650739 + 0.759302i \(0.725541\pi\)
\(810\) 0 0
\(811\) 25.6575 0.900957 0.450478 0.892787i \(-0.351253\pi\)
0.450478 + 0.892787i \(0.351253\pi\)
\(812\) 0 0
\(813\) 20.9436 0.734524
\(814\) 0 0
\(815\) −4.57203 −0.160151
\(816\) 0 0
\(817\) −40.0761 −1.40209
\(818\) 0 0
\(819\) −1.22261 −0.0427215
\(820\) 0 0
\(821\) 23.2467 0.811316 0.405658 0.914025i \(-0.367042\pi\)
0.405658 + 0.914025i \(0.367042\pi\)
\(822\) 0 0
\(823\) −37.8583 −1.31966 −0.659829 0.751416i \(-0.729371\pi\)
−0.659829 + 0.751416i \(0.729371\pi\)
\(824\) 0 0
\(825\) 8.49981 0.295926
\(826\) 0 0
\(827\) −27.9460 −0.971778 −0.485889 0.874021i \(-0.661504\pi\)
−0.485889 + 0.874021i \(0.661504\pi\)
\(828\) 0 0
\(829\) 32.6059 1.13245 0.566225 0.824251i \(-0.308404\pi\)
0.566225 + 0.824251i \(0.308404\pi\)
\(830\) 0 0
\(831\) 35.9742 1.24793
\(832\) 0 0
\(833\) −5.05388 −0.175107
\(834\) 0 0
\(835\) 3.20094 0.110773
\(836\) 0 0
\(837\) 2.37606 0.0821288
\(838\) 0 0
\(839\) −31.4877 −1.08708 −0.543538 0.839385i \(-0.682916\pi\)
−0.543538 + 0.839385i \(0.682916\pi\)
\(840\) 0 0
\(841\) −13.8496 −0.477573
\(842\) 0 0
\(843\) −13.4828 −0.464373
\(844\) 0 0
\(845\) 0.929320 0.0319696
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 10.2905 0.353168
\(850\) 0 0
\(851\) 20.6044 0.706311
\(852\) 0 0
\(853\) 51.2557 1.75496 0.877480 0.479612i \(-0.159223\pi\)
0.877480 + 0.479612i \(0.159223\pi\)
\(854\) 0 0
\(855\) 5.13766 0.175704
\(856\) 0 0
\(857\) 29.9404 1.02275 0.511373 0.859359i \(-0.329137\pi\)
0.511373 + 0.859359i \(0.329137\pi\)
\(858\) 0 0
\(859\) 9.94140 0.339196 0.169598 0.985513i \(-0.445753\pi\)
0.169598 + 0.985513i \(0.445753\pi\)
\(860\) 0 0
\(861\) −23.3477 −0.795687
\(862\) 0 0
\(863\) 26.3903 0.898335 0.449168 0.893448i \(-0.351721\pi\)
0.449168 + 0.893448i \(0.351721\pi\)
\(864\) 0 0
\(865\) 15.0769 0.512630
\(866\) 0 0
\(867\) 17.5524 0.596110
\(868\) 0 0
\(869\) 10.2793 0.348703
\(870\) 0 0
\(871\) 12.8613 0.435787
\(872\) 0 0
\(873\) 7.57550 0.256392
\(874\) 0 0
\(875\) −8.49060 −0.287035
\(876\) 0 0
\(877\) 48.0860 1.62375 0.811875 0.583831i \(-0.198447\pi\)
0.811875 + 0.583831i \(0.198447\pi\)
\(878\) 0 0
\(879\) 34.7128 1.17083
\(880\) 0 0
\(881\) 51.5152 1.73559 0.867795 0.496922i \(-0.165536\pi\)
0.867795 + 0.496922i \(0.165536\pi\)
\(882\) 0 0
\(883\) −48.2091 −1.62236 −0.811182 0.584793i \(-0.801176\pi\)
−0.811182 + 0.584793i \(0.801176\pi\)
\(884\) 0 0
\(885\) 23.7114 0.797051
\(886\) 0 0
\(887\) 36.4825 1.22496 0.612481 0.790485i \(-0.290171\pi\)
0.612481 + 0.790485i \(0.290171\pi\)
\(888\) 0 0
\(889\) 5.76890 0.193483
\(890\) 0 0
\(891\) 11.1731 0.374311
\(892\) 0 0
\(893\) 36.0189 1.20533
\(894\) 0 0
\(895\) 16.2242 0.542315
\(896\) 0 0
\(897\) 6.43374 0.214816
\(898\) 0 0
\(899\) 2.53219 0.0844534
\(900\) 0 0
\(901\) 47.9892 1.59875
\(902\) 0 0
\(903\) −18.2123 −0.606068
\(904\) 0 0
\(905\) −6.69607 −0.222585
\(906\) 0 0
\(907\) −38.6480 −1.28329 −0.641643 0.767003i \(-0.721747\pi\)
−0.641643 + 0.767003i \(0.721747\pi\)
\(908\) 0 0
\(909\) −5.23093 −0.173499
\(910\) 0 0
\(911\) −43.0649 −1.42680 −0.713402 0.700755i \(-0.752847\pi\)
−0.713402 + 0.700755i \(0.752847\pi\)
\(912\) 0 0
\(913\) −8.85960 −0.293210
\(914\) 0 0
\(915\) −14.7122 −0.486371
\(916\) 0 0
\(917\) −11.3283 −0.374095
\(918\) 0 0
\(919\) 14.0454 0.463314 0.231657 0.972798i \(-0.425585\pi\)
0.231657 + 0.972798i \(0.425585\pi\)
\(920\) 0 0
\(921\) 10.6286 0.350224
\(922\) 0 0
\(923\) 10.0543 0.330941
\(924\) 0 0
\(925\) 27.2212 0.895027
\(926\) 0 0
\(927\) 20.8945 0.686265
\(928\) 0 0
\(929\) −11.3509 −0.372411 −0.186205 0.982511i \(-0.559619\pi\)
−0.186205 + 0.982511i \(0.559619\pi\)
\(930\) 0 0
\(931\) 4.52180 0.148196
\(932\) 0 0
\(933\) 28.5944 0.936137
\(934\) 0 0
\(935\) 4.69667 0.153598
\(936\) 0 0
\(937\) 27.2212 0.889279 0.444640 0.895710i \(-0.353332\pi\)
0.444640 + 0.895710i \(0.353332\pi\)
\(938\) 0 0
\(939\) 32.6769 1.06637
\(940\) 0 0
\(941\) 2.64879 0.0863479 0.0431740 0.999068i \(-0.486253\pi\)
0.0431740 + 0.999068i \(0.486253\pi\)
\(942\) 0 0
\(943\) 35.5735 1.15843
\(944\) 0 0
\(945\) −3.39420 −0.110413
\(946\) 0 0
\(947\) −45.8007 −1.48832 −0.744161 0.668000i \(-0.767150\pi\)
−0.744161 + 0.668000i \(0.767150\pi\)
\(948\) 0 0
\(949\) −15.4339 −0.501005
\(950\) 0 0
\(951\) −30.1076 −0.976307
\(952\) 0 0
\(953\) 15.2570 0.494224 0.247112 0.968987i \(-0.420518\pi\)
0.247112 + 0.968987i \(0.420518\pi\)
\(954\) 0 0
\(955\) −20.1860 −0.653204
\(956\) 0 0
\(957\) 7.99838 0.258551
\(958\) 0 0
\(959\) −11.6510 −0.376229
\(960\) 0 0
\(961\) −30.5768 −0.986348
\(962\) 0 0
\(963\) 20.7416 0.668387
\(964\) 0 0
\(965\) 3.98715 0.128351
\(966\) 0 0
\(967\) 1.77630 0.0571220 0.0285610 0.999592i \(-0.490908\pi\)
0.0285610 + 0.999592i \(0.490908\pi\)
\(968\) 0 0
\(969\) −46.9599 −1.50857
\(970\) 0 0
\(971\) −13.4161 −0.430544 −0.215272 0.976554i \(-0.569064\pi\)
−0.215272 + 0.976554i \(0.569064\pi\)
\(972\) 0 0
\(973\) −8.37197 −0.268393
\(974\) 0 0
\(975\) 8.49981 0.272212
\(976\) 0 0
\(977\) −10.1992 −0.326302 −0.163151 0.986601i \(-0.552166\pi\)
−0.163151 + 0.986601i \(0.552166\pi\)
\(978\) 0 0
\(979\) 1.21794 0.0389255
\(980\) 0 0
\(981\) 17.4694 0.557754
\(982\) 0 0
\(983\) −10.9526 −0.349335 −0.174667 0.984627i \(-0.555885\pi\)
−0.174667 + 0.984627i \(0.555885\pi\)
\(984\) 0 0
\(985\) −6.34792 −0.202261
\(986\) 0 0
\(987\) 16.3685 0.521017
\(988\) 0 0
\(989\) 27.7490 0.882367
\(990\) 0 0
\(991\) −39.4006 −1.25160 −0.625800 0.779983i \(-0.715228\pi\)
−0.625800 + 0.779983i \(0.715228\pi\)
\(992\) 0 0
\(993\) 50.3900 1.59908
\(994\) 0 0
\(995\) 7.58846 0.240570
\(996\) 0 0
\(997\) 27.5869 0.873687 0.436843 0.899538i \(-0.356096\pi\)
0.436843 + 0.899538i \(0.356096\pi\)
\(998\) 0 0
\(999\) 24.0359 0.760463
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 \(a_p\))