Properties

Label 8008.2.a.y.1.10
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 1.10
Root \(-1.44419\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.44419 q^{3} -3.20437 q^{5} +1.00000 q^{7} -0.914318 q^{9} +O(q^{10})\) \(q+1.44419 q^{3} -3.20437 q^{5} +1.00000 q^{7} -0.914318 q^{9} -1.00000 q^{11} -1.00000 q^{13} -4.62772 q^{15} -2.31952 q^{17} +6.29372 q^{19} +1.44419 q^{21} -3.44251 q^{23} +5.26801 q^{25} -5.65302 q^{27} +7.75096 q^{29} +7.59336 q^{31} -1.44419 q^{33} -3.20437 q^{35} +4.91871 q^{37} -1.44419 q^{39} -6.73003 q^{41} +9.09518 q^{43} +2.92982 q^{45} +1.34640 q^{47} +1.00000 q^{49} -3.34982 q^{51} -7.22970 q^{53} +3.20437 q^{55} +9.08933 q^{57} -4.77419 q^{59} -1.83923 q^{61} -0.914318 q^{63} +3.20437 q^{65} +10.8247 q^{67} -4.97163 q^{69} -3.88452 q^{71} -11.1855 q^{73} +7.60800 q^{75} -1.00000 q^{77} -0.193203 q^{79} -5.42107 q^{81} -0.916052 q^{83} +7.43259 q^{85} +11.1939 q^{87} -9.66381 q^{89} -1.00000 q^{91} +10.9663 q^{93} -20.1674 q^{95} -15.9476 q^{97} +0.914318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) 1.44419 0.833803 0.416901 0.908952i \(-0.363116\pi\)
0.416901 + 0.908952i \(0.363116\pi\)
\(4\) 0 0
\(5\) −3.20437 −1.43304 −0.716520 0.697567i \(-0.754266\pi\)
−0.716520 + 0.697567i \(0.754266\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −0.914318 −0.304773
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −4.62772 −1.19487
\(16\) 0 0
\(17\) −2.31952 −0.562565 −0.281283 0.959625i \(-0.590760\pi\)
−0.281283 + 0.959625i \(0.590760\pi\)
\(18\) 0 0
\(19\) 6.29372 1.44388 0.721940 0.691956i \(-0.243251\pi\)
0.721940 + 0.691956i \(0.243251\pi\)
\(20\) 0 0
\(21\) 1.44419 0.315148
\(22\) 0 0
\(23\) −3.44251 −0.717812 −0.358906 0.933374i \(-0.616850\pi\)
−0.358906 + 0.933374i \(0.616850\pi\)
\(24\) 0 0
\(25\) 5.26801 1.05360
\(26\) 0 0
\(27\) −5.65302 −1.08792
\(28\) 0 0
\(29\) 7.75096 1.43932 0.719659 0.694328i \(-0.244298\pi\)
0.719659 + 0.694328i \(0.244298\pi\)
\(30\) 0 0
\(31\) 7.59336 1.36381 0.681904 0.731441i \(-0.261152\pi\)
0.681904 + 0.731441i \(0.261152\pi\)
\(32\) 0 0
\(33\) −1.44419 −0.251401
\(34\) 0 0
\(35\) −3.20437 −0.541638
\(36\) 0 0
\(37\) 4.91871 0.808632 0.404316 0.914619i \(-0.367510\pi\)
0.404316 + 0.914619i \(0.367510\pi\)
\(38\) 0 0
\(39\) −1.44419 −0.231255
\(40\) 0 0
\(41\) −6.73003 −1.05105 −0.525527 0.850777i \(-0.676132\pi\)
−0.525527 + 0.850777i \(0.676132\pi\)
\(42\) 0 0
\(43\) 9.09518 1.38700 0.693501 0.720456i \(-0.256067\pi\)
0.693501 + 0.720456i \(0.256067\pi\)
\(44\) 0 0
\(45\) 2.92982 0.436751
\(46\) 0 0
\(47\) 1.34640 0.196392 0.0981961 0.995167i \(-0.468693\pi\)
0.0981961 + 0.995167i \(0.468693\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.34982 −0.469068
\(52\) 0 0
\(53\) −7.22970 −0.993076 −0.496538 0.868015i \(-0.665396\pi\)
−0.496538 + 0.868015i \(0.665396\pi\)
\(54\) 0 0
\(55\) 3.20437 0.432078
\(56\) 0 0
\(57\) 9.08933 1.20391
\(58\) 0 0
\(59\) −4.77419 −0.621547 −0.310773 0.950484i \(-0.600588\pi\)
−0.310773 + 0.950484i \(0.600588\pi\)
\(60\) 0 0
\(61\) −1.83923 −0.235490 −0.117745 0.993044i \(-0.537566\pi\)
−0.117745 + 0.993044i \(0.537566\pi\)
\(62\) 0 0
\(63\) −0.914318 −0.115193
\(64\) 0 0
\(65\) 3.20437 0.397454
\(66\) 0 0
\(67\) 10.8247 1.32245 0.661226 0.750187i \(-0.270036\pi\)
0.661226 + 0.750187i \(0.270036\pi\)
\(68\) 0 0
\(69\) −4.97163 −0.598514
\(70\) 0 0
\(71\) −3.88452 −0.461008 −0.230504 0.973071i \(-0.574038\pi\)
−0.230504 + 0.973071i \(0.574038\pi\)
\(72\) 0 0
\(73\) −11.1855 −1.30916 −0.654579 0.755993i \(-0.727154\pi\)
−0.654579 + 0.755993i \(0.727154\pi\)
\(74\) 0 0
\(75\) 7.60800 0.878496
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −0.193203 −0.0217370 −0.0108685 0.999941i \(-0.503460\pi\)
−0.0108685 + 0.999941i \(0.503460\pi\)
\(80\) 0 0
\(81\) −5.42107 −0.602341
\(82\) 0 0
\(83\) −0.916052 −0.100550 −0.0502749 0.998735i \(-0.516010\pi\)
−0.0502749 + 0.998735i \(0.516010\pi\)
\(84\) 0 0
\(85\) 7.43259 0.806178
\(86\) 0 0
\(87\) 11.1939 1.20011
\(88\) 0 0
\(89\) −9.66381 −1.02436 −0.512181 0.858878i \(-0.671162\pi\)
−0.512181 + 0.858878i \(0.671162\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 10.9663 1.13715
\(94\) 0 0
\(95\) −20.1674 −2.06914
\(96\) 0 0
\(97\) −15.9476 −1.61924 −0.809618 0.586957i \(-0.800326\pi\)
−0.809618 + 0.586957i \(0.800326\pi\)
\(98\) 0 0
\(99\) 0.914318 0.0918924
\(100\) 0 0
\(101\) −19.0368 −1.89423 −0.947117 0.320890i \(-0.896018\pi\)
−0.947117 + 0.320890i \(0.896018\pi\)
\(102\) 0 0
\(103\) 8.07416 0.795570 0.397785 0.917479i \(-0.369779\pi\)
0.397785 + 0.917479i \(0.369779\pi\)
\(104\) 0 0
\(105\) −4.62772 −0.451619
\(106\) 0 0
\(107\) −11.5277 −1.11443 −0.557214 0.830369i \(-0.688130\pi\)
−0.557214 + 0.830369i \(0.688130\pi\)
\(108\) 0 0
\(109\) −12.6152 −1.20831 −0.604157 0.796865i \(-0.706490\pi\)
−0.604157 + 0.796865i \(0.706490\pi\)
\(110\) 0 0
\(111\) 7.10355 0.674239
\(112\) 0 0
\(113\) 1.36869 0.128756 0.0643778 0.997926i \(-0.479494\pi\)
0.0643778 + 0.997926i \(0.479494\pi\)
\(114\) 0 0
\(115\) 11.0311 1.02865
\(116\) 0 0
\(117\) 0.914318 0.0845287
\(118\) 0 0
\(119\) −2.31952 −0.212630
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −9.71944 −0.876372
\(124\) 0 0
\(125\) −0.858794 −0.0768129
\(126\) 0 0
\(127\) −5.79620 −0.514330 −0.257165 0.966368i \(-0.582788\pi\)
−0.257165 + 0.966368i \(0.582788\pi\)
\(128\) 0 0
\(129\) 13.1352 1.15649
\(130\) 0 0
\(131\) −5.40661 −0.472378 −0.236189 0.971707i \(-0.575898\pi\)
−0.236189 + 0.971707i \(0.575898\pi\)
\(132\) 0 0
\(133\) 6.29372 0.545735
\(134\) 0 0
\(135\) 18.1144 1.55904
\(136\) 0 0
\(137\) −3.40955 −0.291298 −0.145649 0.989336i \(-0.546527\pi\)
−0.145649 + 0.989336i \(0.546527\pi\)
\(138\) 0 0
\(139\) 14.4035 1.22169 0.610843 0.791752i \(-0.290831\pi\)
0.610843 + 0.791752i \(0.290831\pi\)
\(140\) 0 0
\(141\) 1.94445 0.163752
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −24.8370 −2.06260
\(146\) 0 0
\(147\) 1.44419 0.119115
\(148\) 0 0
\(149\) −20.7281 −1.69811 −0.849057 0.528301i \(-0.822829\pi\)
−0.849057 + 0.528301i \(0.822829\pi\)
\(150\) 0 0
\(151\) −3.57387 −0.290838 −0.145419 0.989370i \(-0.546453\pi\)
−0.145419 + 0.989370i \(0.546453\pi\)
\(152\) 0 0
\(153\) 2.12077 0.171454
\(154\) 0 0
\(155\) −24.3320 −1.95439
\(156\) 0 0
\(157\) −24.9355 −1.99007 −0.995035 0.0995229i \(-0.968268\pi\)
−0.995035 + 0.0995229i \(0.968268\pi\)
\(158\) 0 0
\(159\) −10.4411 −0.828030
\(160\) 0 0
\(161\) −3.44251 −0.271307
\(162\) 0 0
\(163\) −8.63735 −0.676529 −0.338265 0.941051i \(-0.609840\pi\)
−0.338265 + 0.941051i \(0.609840\pi\)
\(164\) 0 0
\(165\) 4.62772 0.360268
\(166\) 0 0
\(167\) 4.69294 0.363150 0.181575 0.983377i \(-0.441880\pi\)
0.181575 + 0.983377i \(0.441880\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.75447 −0.440055
\(172\) 0 0
\(173\) 5.64279 0.429013 0.214507 0.976723i \(-0.431186\pi\)
0.214507 + 0.976723i \(0.431186\pi\)
\(174\) 0 0
\(175\) 5.26801 0.398224
\(176\) 0 0
\(177\) −6.89484 −0.518248
\(178\) 0 0
\(179\) 15.9075 1.18898 0.594491 0.804103i \(-0.297354\pi\)
0.594491 + 0.804103i \(0.297354\pi\)
\(180\) 0 0
\(181\) −3.03636 −0.225691 −0.112845 0.993613i \(-0.535996\pi\)
−0.112845 + 0.993613i \(0.535996\pi\)
\(182\) 0 0
\(183\) −2.65620 −0.196352
\(184\) 0 0
\(185\) −15.7614 −1.15880
\(186\) 0 0
\(187\) 2.31952 0.169620
\(188\) 0 0
\(189\) −5.65302 −0.411196
\(190\) 0 0
\(191\) 2.02901 0.146814 0.0734071 0.997302i \(-0.476613\pi\)
0.0734071 + 0.997302i \(0.476613\pi\)
\(192\) 0 0
\(193\) −18.6853 −1.34500 −0.672499 0.740098i \(-0.734779\pi\)
−0.672499 + 0.740098i \(0.734779\pi\)
\(194\) 0 0
\(195\) 4.62772 0.331398
\(196\) 0 0
\(197\) −2.29290 −0.163362 −0.0816811 0.996659i \(-0.526029\pi\)
−0.0816811 + 0.996659i \(0.526029\pi\)
\(198\) 0 0
\(199\) −19.8927 −1.41015 −0.705077 0.709131i \(-0.749088\pi\)
−0.705077 + 0.709131i \(0.749088\pi\)
\(200\) 0 0
\(201\) 15.6330 1.10266
\(202\) 0 0
\(203\) 7.75096 0.544011
\(204\) 0 0
\(205\) 21.5655 1.50620
\(206\) 0 0
\(207\) 3.14754 0.218769
\(208\) 0 0
\(209\) −6.29372 −0.435346
\(210\) 0 0
\(211\) −12.4066 −0.854106 −0.427053 0.904227i \(-0.640448\pi\)
−0.427053 + 0.904227i \(0.640448\pi\)
\(212\) 0 0
\(213\) −5.60999 −0.384390
\(214\) 0 0
\(215\) −29.1443 −1.98763
\(216\) 0 0
\(217\) 7.59336 0.515471
\(218\) 0 0
\(219\) −16.1539 −1.09158
\(220\) 0 0
\(221\) 2.31952 0.156027
\(222\) 0 0
\(223\) 3.84264 0.257322 0.128661 0.991689i \(-0.458932\pi\)
0.128661 + 0.991689i \(0.458932\pi\)
\(224\) 0 0
\(225\) −4.81663 −0.321109
\(226\) 0 0
\(227\) −14.2631 −0.946675 −0.473337 0.880881i \(-0.656951\pi\)
−0.473337 + 0.880881i \(0.656951\pi\)
\(228\) 0 0
\(229\) 21.2055 1.40130 0.700648 0.713507i \(-0.252894\pi\)
0.700648 + 0.713507i \(0.252894\pi\)
\(230\) 0 0
\(231\) −1.44419 −0.0950207
\(232\) 0 0
\(233\) −15.2038 −0.996037 −0.498019 0.867166i \(-0.665939\pi\)
−0.498019 + 0.867166i \(0.665939\pi\)
\(234\) 0 0
\(235\) −4.31436 −0.281438
\(236\) 0 0
\(237\) −0.279021 −0.0181244
\(238\) 0 0
\(239\) 28.1442 1.82050 0.910248 0.414063i \(-0.135891\pi\)
0.910248 + 0.414063i \(0.135891\pi\)
\(240\) 0 0
\(241\) −3.48559 −0.224527 −0.112263 0.993678i \(-0.535810\pi\)
−0.112263 + 0.993678i \(0.535810\pi\)
\(242\) 0 0
\(243\) 9.13000 0.585690
\(244\) 0 0
\(245\) −3.20437 −0.204720
\(246\) 0 0
\(247\) −6.29372 −0.400460
\(248\) 0 0
\(249\) −1.32295 −0.0838387
\(250\) 0 0
\(251\) 3.01109 0.190058 0.0950291 0.995474i \(-0.469706\pi\)
0.0950291 + 0.995474i \(0.469706\pi\)
\(252\) 0 0
\(253\) 3.44251 0.216428
\(254\) 0 0
\(255\) 10.7341 0.672193
\(256\) 0 0
\(257\) 24.4961 1.52803 0.764014 0.645200i \(-0.223226\pi\)
0.764014 + 0.645200i \(0.223226\pi\)
\(258\) 0 0
\(259\) 4.91871 0.305634
\(260\) 0 0
\(261\) −7.08685 −0.438665
\(262\) 0 0
\(263\) 18.3192 1.12961 0.564804 0.825225i \(-0.308952\pi\)
0.564804 + 0.825225i \(0.308952\pi\)
\(264\) 0 0
\(265\) 23.1667 1.42312
\(266\) 0 0
\(267\) −13.9564 −0.854115
\(268\) 0 0
\(269\) 13.8621 0.845189 0.422594 0.906319i \(-0.361119\pi\)
0.422594 + 0.906319i \(0.361119\pi\)
\(270\) 0 0
\(271\) 21.2214 1.28911 0.644555 0.764558i \(-0.277042\pi\)
0.644555 + 0.764558i \(0.277042\pi\)
\(272\) 0 0
\(273\) −1.44419 −0.0874063
\(274\) 0 0
\(275\) −5.26801 −0.317673
\(276\) 0 0
\(277\) −10.3438 −0.621497 −0.310749 0.950492i \(-0.600580\pi\)
−0.310749 + 0.950492i \(0.600580\pi\)
\(278\) 0 0
\(279\) −6.94275 −0.415652
\(280\) 0 0
\(281\) −30.5867 −1.82465 −0.912324 0.409469i \(-0.865714\pi\)
−0.912324 + 0.409469i \(0.865714\pi\)
\(282\) 0 0
\(283\) −5.97881 −0.355404 −0.177702 0.984084i \(-0.556866\pi\)
−0.177702 + 0.984084i \(0.556866\pi\)
\(284\) 0 0
\(285\) −29.1256 −1.72525
\(286\) 0 0
\(287\) −6.73003 −0.397261
\(288\) 0 0
\(289\) −11.6198 −0.683520
\(290\) 0 0
\(291\) −23.0314 −1.35012
\(292\) 0 0
\(293\) −1.92545 −0.112486 −0.0562430 0.998417i \(-0.517912\pi\)
−0.0562430 + 0.998417i \(0.517912\pi\)
\(294\) 0 0
\(295\) 15.2983 0.890701
\(296\) 0 0
\(297\) 5.65302 0.328021
\(298\) 0 0
\(299\) 3.44251 0.199085
\(300\) 0 0
\(301\) 9.09518 0.524237
\(302\) 0 0
\(303\) −27.4927 −1.57942
\(304\) 0 0
\(305\) 5.89359 0.337466
\(306\) 0 0
\(307\) −2.64519 −0.150969 −0.0754845 0.997147i \(-0.524050\pi\)
−0.0754845 + 0.997147i \(0.524050\pi\)
\(308\) 0 0
\(309\) 11.6606 0.663349
\(310\) 0 0
\(311\) 19.4111 1.10070 0.550352 0.834932i \(-0.314493\pi\)
0.550352 + 0.834932i \(0.314493\pi\)
\(312\) 0 0
\(313\) 3.05781 0.172838 0.0864188 0.996259i \(-0.472458\pi\)
0.0864188 + 0.996259i \(0.472458\pi\)
\(314\) 0 0
\(315\) 2.92982 0.165076
\(316\) 0 0
\(317\) −13.2197 −0.742491 −0.371245 0.928535i \(-0.621069\pi\)
−0.371245 + 0.928535i \(0.621069\pi\)
\(318\) 0 0
\(319\) −7.75096 −0.433971
\(320\) 0 0
\(321\) −16.6482 −0.929214
\(322\) 0 0
\(323\) −14.5984 −0.812276
\(324\) 0 0
\(325\) −5.26801 −0.292216
\(326\) 0 0
\(327\) −18.2187 −1.00750
\(328\) 0 0
\(329\) 1.34640 0.0742293
\(330\) 0 0
\(331\) −34.6991 −1.90723 −0.953617 0.301021i \(-0.902673\pi\)
−0.953617 + 0.301021i \(0.902673\pi\)
\(332\) 0 0
\(333\) −4.49727 −0.246449
\(334\) 0 0
\(335\) −34.6865 −1.89513
\(336\) 0 0
\(337\) 1.19120 0.0648890 0.0324445 0.999474i \(-0.489671\pi\)
0.0324445 + 0.999474i \(0.489671\pi\)
\(338\) 0 0
\(339\) 1.97665 0.107357
\(340\) 0 0
\(341\) −7.59336 −0.411204
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 15.9310 0.857694
\(346\) 0 0
\(347\) −1.36302 −0.0731705 −0.0365852 0.999331i \(-0.511648\pi\)
−0.0365852 + 0.999331i \(0.511648\pi\)
\(348\) 0 0
\(349\) 29.7802 1.59410 0.797050 0.603913i \(-0.206393\pi\)
0.797050 + 0.603913i \(0.206393\pi\)
\(350\) 0 0
\(351\) 5.65302 0.301736
\(352\) 0 0
\(353\) −25.1209 −1.33705 −0.668526 0.743689i \(-0.733074\pi\)
−0.668526 + 0.743689i \(0.733074\pi\)
\(354\) 0 0
\(355\) 12.4475 0.660643
\(356\) 0 0
\(357\) −3.34982 −0.177291
\(358\) 0 0
\(359\) 26.6694 1.40756 0.703779 0.710419i \(-0.251495\pi\)
0.703779 + 0.710419i \(0.251495\pi\)
\(360\) 0 0
\(361\) 20.6110 1.08479
\(362\) 0 0
\(363\) 1.44419 0.0758003
\(364\) 0 0
\(365\) 35.8424 1.87608
\(366\) 0 0
\(367\) 7.86807 0.410710 0.205355 0.978688i \(-0.434165\pi\)
0.205355 + 0.978688i \(0.434165\pi\)
\(368\) 0 0
\(369\) 6.15339 0.320333
\(370\) 0 0
\(371\) −7.22970 −0.375348
\(372\) 0 0
\(373\) 21.9264 1.13530 0.567652 0.823269i \(-0.307852\pi\)
0.567652 + 0.823269i \(0.307852\pi\)
\(374\) 0 0
\(375\) −1.24026 −0.0640468
\(376\) 0 0
\(377\) −7.75096 −0.399195
\(378\) 0 0
\(379\) −15.4705 −0.794667 −0.397333 0.917674i \(-0.630064\pi\)
−0.397333 + 0.917674i \(0.630064\pi\)
\(380\) 0 0
\(381\) −8.37081 −0.428850
\(382\) 0 0
\(383\) −19.2393 −0.983080 −0.491540 0.870855i \(-0.663566\pi\)
−0.491540 + 0.870855i \(0.663566\pi\)
\(384\) 0 0
\(385\) 3.20437 0.163310
\(386\) 0 0
\(387\) −8.31588 −0.422720
\(388\) 0 0
\(389\) 2.09352 0.106145 0.0530727 0.998591i \(-0.483098\pi\)
0.0530727 + 0.998591i \(0.483098\pi\)
\(390\) 0 0
\(391\) 7.98494 0.403816
\(392\) 0 0
\(393\) −7.80817 −0.393870
\(394\) 0 0
\(395\) 0.619093 0.0311500
\(396\) 0 0
\(397\) −2.42903 −0.121910 −0.0609549 0.998141i \(-0.519415\pi\)
−0.0609549 + 0.998141i \(0.519415\pi\)
\(398\) 0 0
\(399\) 9.08933 0.455036
\(400\) 0 0
\(401\) 37.1875 1.85706 0.928528 0.371262i \(-0.121075\pi\)
0.928528 + 0.371262i \(0.121075\pi\)
\(402\) 0 0
\(403\) −7.59336 −0.378252
\(404\) 0 0
\(405\) 17.3711 0.863178
\(406\) 0 0
\(407\) −4.91871 −0.243812
\(408\) 0 0
\(409\) −14.9890 −0.741159 −0.370579 0.928801i \(-0.620841\pi\)
−0.370579 + 0.928801i \(0.620841\pi\)
\(410\) 0 0
\(411\) −4.92404 −0.242885
\(412\) 0 0
\(413\) −4.77419 −0.234923
\(414\) 0 0
\(415\) 2.93537 0.144092
\(416\) 0 0
\(417\) 20.8013 1.01865
\(418\) 0 0
\(419\) 11.0522 0.539933 0.269967 0.962870i \(-0.412987\pi\)
0.269967 + 0.962870i \(0.412987\pi\)
\(420\) 0 0
\(421\) −16.3196 −0.795368 −0.397684 0.917522i \(-0.630186\pi\)
−0.397684 + 0.917522i \(0.630186\pi\)
\(422\) 0 0
\(423\) −1.23104 −0.0598550
\(424\) 0 0
\(425\) −12.2192 −0.592719
\(426\) 0 0
\(427\) −1.83923 −0.0890067
\(428\) 0 0
\(429\) 1.44419 0.0697261
\(430\) 0 0
\(431\) 17.8849 0.861485 0.430742 0.902475i \(-0.358252\pi\)
0.430742 + 0.902475i \(0.358252\pi\)
\(432\) 0 0
\(433\) −17.6237 −0.846939 −0.423469 0.905910i \(-0.639188\pi\)
−0.423469 + 0.905910i \(0.639188\pi\)
\(434\) 0 0
\(435\) −35.8693 −1.71980
\(436\) 0 0
\(437\) −21.6662 −1.03643
\(438\) 0 0
\(439\) −31.0473 −1.48181 −0.740903 0.671612i \(-0.765602\pi\)
−0.740903 + 0.671612i \(0.765602\pi\)
\(440\) 0 0
\(441\) −0.914318 −0.0435390
\(442\) 0 0
\(443\) −19.1022 −0.907575 −0.453787 0.891110i \(-0.649927\pi\)
−0.453787 + 0.891110i \(0.649927\pi\)
\(444\) 0 0
\(445\) 30.9664 1.46795
\(446\) 0 0
\(447\) −29.9353 −1.41589
\(448\) 0 0
\(449\) −10.0218 −0.472960 −0.236480 0.971636i \(-0.575994\pi\)
−0.236480 + 0.971636i \(0.575994\pi\)
\(450\) 0 0
\(451\) 6.73003 0.316905
\(452\) 0 0
\(453\) −5.16135 −0.242501
\(454\) 0 0
\(455\) 3.20437 0.150223
\(456\) 0 0
\(457\) −29.7473 −1.39152 −0.695760 0.718274i \(-0.744932\pi\)
−0.695760 + 0.718274i \(0.744932\pi\)
\(458\) 0 0
\(459\) 13.1123 0.612028
\(460\) 0 0
\(461\) −34.5306 −1.60825 −0.804125 0.594460i \(-0.797366\pi\)
−0.804125 + 0.594460i \(0.797366\pi\)
\(462\) 0 0
\(463\) 20.2120 0.939332 0.469666 0.882844i \(-0.344374\pi\)
0.469666 + 0.882844i \(0.344374\pi\)
\(464\) 0 0
\(465\) −35.1400 −1.62958
\(466\) 0 0
\(467\) −21.6012 −0.999585 −0.499792 0.866145i \(-0.666590\pi\)
−0.499792 + 0.866145i \(0.666590\pi\)
\(468\) 0 0
\(469\) 10.8247 0.499840
\(470\) 0 0
\(471\) −36.0116 −1.65933
\(472\) 0 0
\(473\) −9.09518 −0.418197
\(474\) 0 0
\(475\) 33.1554 1.52127
\(476\) 0 0
\(477\) 6.61025 0.302663
\(478\) 0 0
\(479\) −3.51296 −0.160511 −0.0802556 0.996774i \(-0.525574\pi\)
−0.0802556 + 0.996774i \(0.525574\pi\)
\(480\) 0 0
\(481\) −4.91871 −0.224274
\(482\) 0 0
\(483\) −4.97163 −0.226217
\(484\) 0 0
\(485\) 51.1022 2.32043
\(486\) 0 0
\(487\) 12.5414 0.568307 0.284154 0.958779i \(-0.408287\pi\)
0.284154 + 0.958779i \(0.408287\pi\)
\(488\) 0 0
\(489\) −12.4740 −0.564092
\(490\) 0 0
\(491\) 3.99406 0.180250 0.0901248 0.995930i \(-0.471273\pi\)
0.0901248 + 0.995930i \(0.471273\pi\)
\(492\) 0 0
\(493\) −17.9785 −0.809710
\(494\) 0 0
\(495\) −2.92982 −0.131685
\(496\) 0 0
\(497\) −3.88452 −0.174245
\(498\) 0 0
\(499\) −33.4341 −1.49672 −0.748358 0.663295i \(-0.769157\pi\)
−0.748358 + 0.663295i \(0.769157\pi\)
\(500\) 0 0
\(501\) 6.77749 0.302796
\(502\) 0 0
\(503\) 30.2391 1.34830 0.674148 0.738596i \(-0.264511\pi\)
0.674148 + 0.738596i \(0.264511\pi\)
\(504\) 0 0
\(505\) 61.0010 2.71451
\(506\) 0 0
\(507\) 1.44419 0.0641387
\(508\) 0 0
\(509\) −8.11821 −0.359833 −0.179917 0.983682i \(-0.557583\pi\)
−0.179917 + 0.983682i \(0.557583\pi\)
\(510\) 0 0
\(511\) −11.1855 −0.494816
\(512\) 0 0
\(513\) −35.5785 −1.57083
\(514\) 0 0
\(515\) −25.8726 −1.14008
\(516\) 0 0
\(517\) −1.34640 −0.0592145
\(518\) 0 0
\(519\) 8.14925 0.357713
\(520\) 0 0
\(521\) −1.43863 −0.0630277 −0.0315139 0.999503i \(-0.510033\pi\)
−0.0315139 + 0.999503i \(0.510033\pi\)
\(522\) 0 0
\(523\) −29.7573 −1.30119 −0.650597 0.759423i \(-0.725481\pi\)
−0.650597 + 0.759423i \(0.725481\pi\)
\(524\) 0 0
\(525\) 7.60800 0.332040
\(526\) 0 0
\(527\) −17.6129 −0.767231
\(528\) 0 0
\(529\) −11.1492 −0.484746
\(530\) 0 0
\(531\) 4.36513 0.189431
\(532\) 0 0
\(533\) 6.73003 0.291510
\(534\) 0 0
\(535\) 36.9392 1.59702
\(536\) 0 0
\(537\) 22.9734 0.991376
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 20.4480 0.879128 0.439564 0.898211i \(-0.355133\pi\)
0.439564 + 0.898211i \(0.355133\pi\)
\(542\) 0 0
\(543\) −4.38508 −0.188182
\(544\) 0 0
\(545\) 40.4237 1.73156
\(546\) 0 0
\(547\) 33.2759 1.42278 0.711388 0.702799i \(-0.248067\pi\)
0.711388 + 0.702799i \(0.248067\pi\)
\(548\) 0 0
\(549\) 1.68164 0.0717708
\(550\) 0 0
\(551\) 48.7824 2.07820
\(552\) 0 0
\(553\) −0.193203 −0.00821581
\(554\) 0 0
\(555\) −22.7624 −0.966211
\(556\) 0 0
\(557\) 3.87173 0.164050 0.0820252 0.996630i \(-0.473861\pi\)
0.0820252 + 0.996630i \(0.473861\pi\)
\(558\) 0 0
\(559\) −9.09518 −0.384685
\(560\) 0 0
\(561\) 3.34982 0.141429
\(562\) 0 0
\(563\) −14.8940 −0.627708 −0.313854 0.949471i \(-0.601620\pi\)
−0.313854 + 0.949471i \(0.601620\pi\)
\(564\) 0 0
\(565\) −4.38580 −0.184512
\(566\) 0 0
\(567\) −5.42107 −0.227663
\(568\) 0 0
\(569\) −29.9316 −1.25480 −0.627399 0.778698i \(-0.715880\pi\)
−0.627399 + 0.778698i \(0.715880\pi\)
\(570\) 0 0
\(571\) −11.1058 −0.464762 −0.232381 0.972625i \(-0.574652\pi\)
−0.232381 + 0.972625i \(0.574652\pi\)
\(572\) 0 0
\(573\) 2.93028 0.122414
\(574\) 0 0
\(575\) −18.1351 −0.756288
\(576\) 0 0
\(577\) −33.5890 −1.39833 −0.699165 0.714961i \(-0.746445\pi\)
−0.699165 + 0.714961i \(0.746445\pi\)
\(578\) 0 0
\(579\) −26.9851 −1.12146
\(580\) 0 0
\(581\) −0.916052 −0.0380042
\(582\) 0 0
\(583\) 7.22970 0.299424
\(584\) 0 0
\(585\) −2.92982 −0.121133
\(586\) 0 0
\(587\) 7.92290 0.327013 0.163507 0.986542i \(-0.447719\pi\)
0.163507 + 0.986542i \(0.447719\pi\)
\(588\) 0 0
\(589\) 47.7905 1.96917
\(590\) 0 0
\(591\) −3.31138 −0.136212
\(592\) 0 0
\(593\) 18.3912 0.755235 0.377618 0.925962i \(-0.376743\pi\)
0.377618 + 0.925962i \(0.376743\pi\)
\(594\) 0 0
\(595\) 7.43259 0.304707
\(596\) 0 0
\(597\) −28.7288 −1.17579
\(598\) 0 0
\(599\) 29.5765 1.20846 0.604232 0.796808i \(-0.293480\pi\)
0.604232 + 0.796808i \(0.293480\pi\)
\(600\) 0 0
\(601\) 12.3041 0.501895 0.250948 0.968001i \(-0.419258\pi\)
0.250948 + 0.968001i \(0.419258\pi\)
\(602\) 0 0
\(603\) −9.89725 −0.403047
\(604\) 0 0
\(605\) −3.20437 −0.130276
\(606\) 0 0
\(607\) −31.0101 −1.25866 −0.629331 0.777137i \(-0.716671\pi\)
−0.629331 + 0.777137i \(0.716671\pi\)
\(608\) 0 0
\(609\) 11.1939 0.453598
\(610\) 0 0
\(611\) −1.34640 −0.0544694
\(612\) 0 0
\(613\) −44.2716 −1.78811 −0.894056 0.447955i \(-0.852152\pi\)
−0.894056 + 0.447955i \(0.852152\pi\)
\(614\) 0 0
\(615\) 31.1447 1.25588
\(616\) 0 0
\(617\) 41.0672 1.65330 0.826651 0.562715i \(-0.190243\pi\)
0.826651 + 0.562715i \(0.190243\pi\)
\(618\) 0 0
\(619\) −25.9283 −1.04214 −0.521072 0.853513i \(-0.674468\pi\)
−0.521072 + 0.853513i \(0.674468\pi\)
\(620\) 0 0
\(621\) 19.4605 0.780924
\(622\) 0 0
\(623\) −9.66381 −0.387172
\(624\) 0 0
\(625\) −23.5881 −0.943525
\(626\) 0 0
\(627\) −9.08933 −0.362993
\(628\) 0 0
\(629\) −11.4090 −0.454908
\(630\) 0 0
\(631\) 35.3034 1.40541 0.702704 0.711483i \(-0.251976\pi\)
0.702704 + 0.711483i \(0.251976\pi\)
\(632\) 0 0
\(633\) −17.9175 −0.712156
\(634\) 0 0
\(635\) 18.5732 0.737055
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 3.55169 0.140503
\(640\) 0 0
\(641\) 44.0440 1.73963 0.869816 0.493376i \(-0.164237\pi\)
0.869816 + 0.493376i \(0.164237\pi\)
\(642\) 0 0
\(643\) −17.3413 −0.683875 −0.341937 0.939723i \(-0.611083\pi\)
−0.341937 + 0.939723i \(0.611083\pi\)
\(644\) 0 0
\(645\) −42.0899 −1.65729
\(646\) 0 0
\(647\) −8.57704 −0.337198 −0.168599 0.985685i \(-0.553924\pi\)
−0.168599 + 0.985685i \(0.553924\pi\)
\(648\) 0 0
\(649\) 4.77419 0.187403
\(650\) 0 0
\(651\) 10.9663 0.429801
\(652\) 0 0
\(653\) 4.46090 0.174569 0.0872843 0.996183i \(-0.472181\pi\)
0.0872843 + 0.996183i \(0.472181\pi\)
\(654\) 0 0
\(655\) 17.3248 0.676936
\(656\) 0 0
\(657\) 10.2271 0.398996
\(658\) 0 0
\(659\) −12.4968 −0.486805 −0.243402 0.969925i \(-0.578264\pi\)
−0.243402 + 0.969925i \(0.578264\pi\)
\(660\) 0 0
\(661\) −7.91620 −0.307905 −0.153952 0.988078i \(-0.549200\pi\)
−0.153952 + 0.988078i \(0.549200\pi\)
\(662\) 0 0
\(663\) 3.34982 0.130096
\(664\) 0 0
\(665\) −20.1674 −0.782060
\(666\) 0 0
\(667\) −26.6827 −1.03316
\(668\) 0 0
\(669\) 5.54949 0.214556
\(670\) 0 0
\(671\) 1.83923 0.0710028
\(672\) 0 0
\(673\) 49.8822 1.92282 0.961408 0.275126i \(-0.0887195\pi\)
0.961408 + 0.275126i \(0.0887195\pi\)
\(674\) 0 0
\(675\) −29.7801 −1.14624
\(676\) 0 0
\(677\) 13.7608 0.528870 0.264435 0.964404i \(-0.414815\pi\)
0.264435 + 0.964404i \(0.414815\pi\)
\(678\) 0 0
\(679\) −15.9476 −0.612014
\(680\) 0 0
\(681\) −20.5986 −0.789340
\(682\) 0 0
\(683\) −9.42960 −0.360814 −0.180407 0.983592i \(-0.557741\pi\)
−0.180407 + 0.983592i \(0.557741\pi\)
\(684\) 0 0
\(685\) 10.9255 0.417441
\(686\) 0 0
\(687\) 30.6247 1.16841
\(688\) 0 0
\(689\) 7.22970 0.275430
\(690\) 0 0
\(691\) 27.3993 1.04232 0.521159 0.853460i \(-0.325500\pi\)
0.521159 + 0.853460i \(0.325500\pi\)
\(692\) 0 0
\(693\) 0.914318 0.0347321
\(694\) 0 0
\(695\) −46.1541 −1.75072
\(696\) 0 0
\(697\) 15.6104 0.591286
\(698\) 0 0
\(699\) −21.9572 −0.830499
\(700\) 0 0
\(701\) −20.4288 −0.771587 −0.385793 0.922585i \(-0.626072\pi\)
−0.385793 + 0.922585i \(0.626072\pi\)
\(702\) 0 0
\(703\) 30.9570 1.16757
\(704\) 0 0
\(705\) −6.23075 −0.234664
\(706\) 0 0
\(707\) −19.0368 −0.715953
\(708\) 0 0
\(709\) 35.7380 1.34217 0.671085 0.741380i \(-0.265828\pi\)
0.671085 + 0.741380i \(0.265828\pi\)
\(710\) 0 0
\(711\) 0.176649 0.00662484
\(712\) 0 0
\(713\) −26.1402 −0.978958
\(714\) 0 0
\(715\) −3.20437 −0.119837
\(716\) 0 0
\(717\) 40.6455 1.51793
\(718\) 0 0
\(719\) 36.2923 1.35347 0.676737 0.736225i \(-0.263393\pi\)
0.676737 + 0.736225i \(0.263393\pi\)
\(720\) 0 0
\(721\) 8.07416 0.300697
\(722\) 0 0
\(723\) −5.03385 −0.187211
\(724\) 0 0
\(725\) 40.8321 1.51647
\(726\) 0 0
\(727\) −12.4117 −0.460326 −0.230163 0.973152i \(-0.573926\pi\)
−0.230163 + 0.973152i \(0.573926\pi\)
\(728\) 0 0
\(729\) 29.4486 1.09069
\(730\) 0 0
\(731\) −21.0964 −0.780279
\(732\) 0 0
\(733\) −53.4904 −1.97571 −0.987856 0.155372i \(-0.950342\pi\)
−0.987856 + 0.155372i \(0.950342\pi\)
\(734\) 0 0
\(735\) −4.62772 −0.170696
\(736\) 0 0
\(737\) −10.8247 −0.398734
\(738\) 0 0
\(739\) −18.7385 −0.689306 −0.344653 0.938730i \(-0.612003\pi\)
−0.344653 + 0.938730i \(0.612003\pi\)
\(740\) 0 0
\(741\) −9.08933 −0.333905
\(742\) 0 0
\(743\) −12.1809 −0.446875 −0.223438 0.974718i \(-0.571728\pi\)
−0.223438 + 0.974718i \(0.571728\pi\)
\(744\) 0 0
\(745\) 66.4207 2.43346
\(746\) 0 0
\(747\) 0.837563 0.0306448
\(748\) 0 0
\(749\) −11.5277 −0.421215
\(750\) 0 0
\(751\) −1.39702 −0.0509781 −0.0254891 0.999675i \(-0.508114\pi\)
−0.0254891 + 0.999675i \(0.508114\pi\)
\(752\) 0 0
\(753\) 4.34858 0.158471
\(754\) 0 0
\(755\) 11.4520 0.416782
\(756\) 0 0
\(757\) 28.5775 1.03867 0.519333 0.854572i \(-0.326180\pi\)
0.519333 + 0.854572i \(0.326180\pi\)
\(758\) 0 0
\(759\) 4.97163 0.180459
\(760\) 0 0
\(761\) −7.46884 −0.270745 −0.135373 0.990795i \(-0.543223\pi\)
−0.135373 + 0.990795i \(0.543223\pi\)
\(762\) 0 0
\(763\) −12.6152 −0.456700
\(764\) 0 0
\(765\) −6.79575 −0.245701
\(766\) 0 0
\(767\) 4.77419 0.172386
\(768\) 0 0
\(769\) −6.26487 −0.225917 −0.112958 0.993600i \(-0.536033\pi\)
−0.112958 + 0.993600i \(0.536033\pi\)
\(770\) 0 0
\(771\) 35.3771 1.27407
\(772\) 0 0
\(773\) 0.328063 0.0117996 0.00589980 0.999983i \(-0.498122\pi\)
0.00589980 + 0.999983i \(0.498122\pi\)
\(774\) 0 0
\(775\) 40.0019 1.43691
\(776\) 0 0
\(777\) 7.10355 0.254839
\(778\) 0 0
\(779\) −42.3570 −1.51760
\(780\) 0 0
\(781\) 3.88452 0.138999
\(782\) 0 0
\(783\) −43.8163 −1.56587
\(784\) 0 0
\(785\) 79.9027 2.85185
\(786\) 0 0
\(787\) −39.7572 −1.41719 −0.708596 0.705614i \(-0.750671\pi\)
−0.708596 + 0.705614i \(0.750671\pi\)
\(788\) 0 0
\(789\) 26.4563 0.941871
\(790\) 0 0
\(791\) 1.36869 0.0486650
\(792\) 0 0
\(793\) 1.83923 0.0653131
\(794\) 0 0
\(795\) 33.4571 1.18660
\(796\) 0 0
\(797\) −4.10621 −0.145450 −0.0727248 0.997352i \(-0.523169\pi\)
−0.0727248 + 0.997352i \(0.523169\pi\)
\(798\) 0 0
\(799\) −3.12299 −0.110483
\(800\) 0 0
\(801\) 8.83579 0.312197
\(802\) 0 0
\(803\) 11.1855 0.394726
\(804\) 0 0
\(805\) 11.0311 0.388794
\(806\) 0 0
\(807\) 20.0195 0.704721
\(808\) 0 0
\(809\) 36.6278 1.28776 0.643882 0.765125i \(-0.277323\pi\)
0.643882 + 0.765125i \(0.277323\pi\)
\(810\) 0 0
\(811\) −1.01553 −0.0356602 −0.0178301 0.999841i \(-0.505676\pi\)
−0.0178301 + 0.999841i \(0.505676\pi\)
\(812\) 0 0
\(813\) 30.6478 1.07486
\(814\) 0 0
\(815\) 27.6773 0.969493
\(816\) 0 0
\(817\) 57.2425 2.00266
\(818\) 0 0
\(819\) 0.914318 0.0319489
\(820\) 0 0
\(821\) −27.9550 −0.975636 −0.487818 0.872945i \(-0.662207\pi\)
−0.487818 + 0.872945i \(0.662207\pi\)
\(822\) 0 0
\(823\) 15.8816 0.553597 0.276798 0.960928i \(-0.410727\pi\)
0.276798 + 0.960928i \(0.410727\pi\)
\(824\) 0 0
\(825\) −7.60800 −0.264876
\(826\) 0 0
\(827\) 23.4062 0.813915 0.406957 0.913447i \(-0.366590\pi\)
0.406957 + 0.913447i \(0.366590\pi\)
\(828\) 0 0
\(829\) −2.62109 −0.0910341 −0.0455171 0.998964i \(-0.514494\pi\)
−0.0455171 + 0.998964i \(0.514494\pi\)
\(830\) 0 0
\(831\) −14.9384 −0.518206
\(832\) 0 0
\(833\) −2.31952 −0.0803664
\(834\) 0 0
\(835\) −15.0379 −0.520409
\(836\) 0 0
\(837\) −42.9254 −1.48372
\(838\) 0 0
\(839\) −34.9194 −1.20555 −0.602776 0.797910i \(-0.705939\pi\)
−0.602776 + 0.797910i \(0.705939\pi\)
\(840\) 0 0
\(841\) 31.0775 1.07164
\(842\) 0 0
\(843\) −44.1729 −1.52140
\(844\) 0 0
\(845\) −3.20437 −0.110234
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −8.63454 −0.296336
\(850\) 0 0
\(851\) −16.9327 −0.580445
\(852\) 0 0
\(853\) −18.9813 −0.649907 −0.324954 0.945730i \(-0.605349\pi\)
−0.324954 + 0.945730i \(0.605349\pi\)
\(854\) 0 0
\(855\) 18.4395 0.630616
\(856\) 0 0
\(857\) −31.9430 −1.09115 −0.545577 0.838061i \(-0.683689\pi\)
−0.545577 + 0.838061i \(0.683689\pi\)
\(858\) 0 0
\(859\) −41.8276 −1.42714 −0.713570 0.700584i \(-0.752923\pi\)
−0.713570 + 0.700584i \(0.752923\pi\)
\(860\) 0 0
\(861\) −9.71944 −0.331237
\(862\) 0 0
\(863\) −45.1376 −1.53650 −0.768250 0.640149i \(-0.778872\pi\)
−0.768250 + 0.640149i \(0.778872\pi\)
\(864\) 0 0
\(865\) −18.0816 −0.614793
\(866\) 0 0
\(867\) −16.7813 −0.569921
\(868\) 0 0
\(869\) 0.193203 0.00655395
\(870\) 0 0
\(871\) −10.8247 −0.366782
\(872\) 0 0
\(873\) 14.5812 0.493499
\(874\) 0 0
\(875\) −0.858794 −0.0290325
\(876\) 0 0
\(877\) 57.8694 1.95411 0.977055 0.212985i \(-0.0683186\pi\)
0.977055 + 0.212985i \(0.0683186\pi\)
\(878\) 0 0
\(879\) −2.78071 −0.0937912
\(880\) 0 0
\(881\) 41.5819 1.40093 0.700465 0.713687i \(-0.252976\pi\)
0.700465 + 0.713687i \(0.252976\pi\)
\(882\) 0 0
\(883\) 21.5021 0.723604 0.361802 0.932255i \(-0.382162\pi\)
0.361802 + 0.932255i \(0.382162\pi\)
\(884\) 0 0
\(885\) 22.0936 0.742669
\(886\) 0 0
\(887\) −11.9618 −0.401638 −0.200819 0.979628i \(-0.564360\pi\)
−0.200819 + 0.979628i \(0.564360\pi\)
\(888\) 0 0
\(889\) −5.79620 −0.194398
\(890\) 0 0
\(891\) 5.42107 0.181613
\(892\) 0 0
\(893\) 8.47385 0.283567
\(894\) 0 0
\(895\) −50.9735 −1.70386
\(896\) 0 0
\(897\) 4.97163 0.165998
\(898\) 0 0
\(899\) 58.8559 1.96295
\(900\) 0 0
\(901\) 16.7694 0.558670
\(902\) 0 0
\(903\) 13.1352 0.437111
\(904\) 0 0
\(905\) 9.72962 0.323424
\(906\) 0 0
\(907\) 14.1790 0.470805 0.235402 0.971898i \(-0.424359\pi\)
0.235402 + 0.971898i \(0.424359\pi\)
\(908\) 0 0
\(909\) 17.4057 0.577311
\(910\) 0 0
\(911\) 12.5401 0.415472 0.207736 0.978185i \(-0.433390\pi\)
0.207736 + 0.978185i \(0.433390\pi\)
\(912\) 0 0
\(913\) 0.916052 0.0303169
\(914\) 0 0
\(915\) 8.51145 0.281380
\(916\) 0 0
\(917\) −5.40661 −0.178542
\(918\) 0 0
\(919\) 44.3897 1.46428 0.732141 0.681153i \(-0.238521\pi\)
0.732141 + 0.681153i \(0.238521\pi\)
\(920\) 0 0
\(921\) −3.82015 −0.125878
\(922\) 0 0
\(923\) 3.88452 0.127861
\(924\) 0 0
\(925\) 25.9118 0.851975
\(926\) 0 0
\(927\) −7.38235 −0.242468
\(928\) 0 0
\(929\) −13.8764 −0.455269 −0.227634 0.973747i \(-0.573099\pi\)
−0.227634 + 0.973747i \(0.573099\pi\)
\(930\) 0 0
\(931\) 6.29372 0.206268
\(932\) 0 0
\(933\) 28.0334 0.917771
\(934\) 0 0
\(935\) −7.43259 −0.243072
\(936\) 0 0
\(937\) 51.7319 1.69001 0.845003 0.534761i \(-0.179598\pi\)
0.845003 + 0.534761i \(0.179598\pi\)
\(938\) 0 0
\(939\) 4.41605 0.144112
\(940\) 0 0
\(941\) 36.8613 1.20164 0.600821 0.799383i \(-0.294840\pi\)
0.600821 + 0.799383i \(0.294840\pi\)
\(942\) 0 0
\(943\) 23.1682 0.754459
\(944\) 0 0
\(945\) 18.1144 0.589260
\(946\) 0 0
\(947\) 17.5413 0.570014 0.285007 0.958525i \(-0.408004\pi\)
0.285007 + 0.958525i \(0.408004\pi\)
\(948\) 0 0
\(949\) 11.1855 0.363095
\(950\) 0 0
\(951\) −19.0917 −0.619091
\(952\) 0 0
\(953\) −21.5672 −0.698630 −0.349315 0.937005i \(-0.613586\pi\)
−0.349315 + 0.937005i \(0.613586\pi\)
\(954\) 0 0
\(955\) −6.50172 −0.210391
\(956\) 0 0
\(957\) −11.1939 −0.361846
\(958\) 0 0
\(959\) −3.40955 −0.110100
\(960\) 0 0
\(961\) 26.6592 0.859973
\(962\) 0 0
\(963\) 10.5400 0.339648
\(964\) 0 0
\(965\) 59.8747 1.92743
\(966\) 0 0
\(967\) −29.8799 −0.960874 −0.480437 0.877029i \(-0.659522\pi\)
−0.480437 + 0.877029i \(0.659522\pi\)
\(968\) 0 0
\(969\) −21.0828 −0.677278
\(970\) 0 0
\(971\) −16.3515 −0.524744 −0.262372 0.964967i \(-0.584505\pi\)
−0.262372 + 0.964967i \(0.584505\pi\)
\(972\) 0 0
\(973\) 14.4035 0.461754
\(974\) 0 0
\(975\) −7.60800 −0.243651
\(976\) 0 0
\(977\) −33.9649 −1.08663 −0.543317 0.839527i \(-0.682832\pi\)
−0.543317 + 0.839527i \(0.682832\pi\)
\(978\) 0 0
\(979\) 9.66381 0.308857
\(980\) 0 0
\(981\) 11.5343 0.368261
\(982\) 0 0
\(983\) −44.2905 −1.41265 −0.706324 0.707889i \(-0.749648\pi\)
−0.706324 + 0.707889i \(0.749648\pi\)
\(984\) 0 0
\(985\) 7.34730 0.234104
\(986\) 0 0
\(987\) 1.94445 0.0618926
\(988\) 0 0
\(989\) −31.3102 −0.995606
\(990\) 0 0
\(991\) 3.59295 0.114134 0.0570669 0.998370i \(-0.481825\pi\)
0.0570669 + 0.998370i \(0.481825\pi\)
\(992\) 0 0
\(993\) −50.1121 −1.59026
\(994\) 0 0
\(995\) 63.7435 2.02081
\(996\) 0 0
\(997\) 5.16274 0.163506 0.0817528 0.996653i \(-0.473948\pi\)
0.0817528 + 0.996653i \(0.473948\pi\)
\(998\) 0 0
\(999\) −27.8056 −0.879729
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 \(a_p\))