Properties

Label 8008.2.a.p.1.9
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 9
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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.67186\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.67186 q^{3} -4.01631 q^{5} -1.00000 q^{7} +4.13885 q^{9} +O(q^{10})\) \(q+2.67186 q^{3} -4.01631 q^{5} -1.00000 q^{7} +4.13885 q^{9} +1.00000 q^{11} +1.00000 q^{13} -10.7310 q^{15} -6.26331 q^{17} +7.26832 q^{19} -2.67186 q^{21} -3.24359 q^{23} +11.1307 q^{25} +3.04285 q^{27} +0.715129 q^{29} +2.26456 q^{31} +2.67186 q^{33} +4.01631 q^{35} -5.56287 q^{37} +2.67186 q^{39} +6.82467 q^{41} -0.466688 q^{43} -16.6229 q^{45} -2.75113 q^{47} +1.00000 q^{49} -16.7347 q^{51} -11.5024 q^{53} -4.01631 q^{55} +19.4200 q^{57} -1.46522 q^{59} +3.04010 q^{61} -4.13885 q^{63} -4.01631 q^{65} +8.56250 q^{67} -8.66643 q^{69} -3.49753 q^{71} -0.308210 q^{73} +29.7397 q^{75} -1.00000 q^{77} +9.30138 q^{79} -4.28648 q^{81} -7.19951 q^{83} +25.1553 q^{85} +1.91073 q^{87} -12.1579 q^{89} -1.00000 q^{91} +6.05060 q^{93} -29.1918 q^{95} -8.50768 q^{97} +4.13885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) 2.67186 1.54260 0.771300 0.636471i \(-0.219607\pi\)
0.771300 + 0.636471i \(0.219607\pi\)
\(4\) 0 0
\(5\) −4.01631 −1.79615 −0.898073 0.439846i \(-0.855033\pi\)
−0.898073 + 0.439846i \(0.855033\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 4.13885 1.37962
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −10.7310 −2.77074
\(16\) 0 0
\(17\) −6.26331 −1.51907 −0.759537 0.650464i \(-0.774575\pi\)
−0.759537 + 0.650464i \(0.774575\pi\)
\(18\) 0 0
\(19\) 7.26832 1.66747 0.833734 0.552167i \(-0.186199\pi\)
0.833734 + 0.552167i \(0.186199\pi\)
\(20\) 0 0
\(21\) −2.67186 −0.583048
\(22\) 0 0
\(23\) −3.24359 −0.676335 −0.338168 0.941086i \(-0.609807\pi\)
−0.338168 + 0.941086i \(0.609807\pi\)
\(24\) 0 0
\(25\) 11.1307 2.22614
\(26\) 0 0
\(27\) 3.04285 0.585596
\(28\) 0 0
\(29\) 0.715129 0.132796 0.0663981 0.997793i \(-0.478849\pi\)
0.0663981 + 0.997793i \(0.478849\pi\)
\(30\) 0 0
\(31\) 2.26456 0.406728 0.203364 0.979103i \(-0.434813\pi\)
0.203364 + 0.979103i \(0.434813\pi\)
\(32\) 0 0
\(33\) 2.67186 0.465112
\(34\) 0 0
\(35\) 4.01631 0.678879
\(36\) 0 0
\(37\) −5.56287 −0.914531 −0.457265 0.889330i \(-0.651171\pi\)
−0.457265 + 0.889330i \(0.651171\pi\)
\(38\) 0 0
\(39\) 2.67186 0.427840
\(40\) 0 0
\(41\) 6.82467 1.06583 0.532917 0.846167i \(-0.321096\pi\)
0.532917 + 0.846167i \(0.321096\pi\)
\(42\) 0 0
\(43\) −0.466688 −0.0711692 −0.0355846 0.999367i \(-0.511329\pi\)
−0.0355846 + 0.999367i \(0.511329\pi\)
\(44\) 0 0
\(45\) −16.6229 −2.47799
\(46\) 0 0
\(47\) −2.75113 −0.401294 −0.200647 0.979664i \(-0.564304\pi\)
−0.200647 + 0.979664i \(0.564304\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −16.7347 −2.34333
\(52\) 0 0
\(53\) −11.5024 −1.57998 −0.789991 0.613118i \(-0.789915\pi\)
−0.789991 + 0.613118i \(0.789915\pi\)
\(54\) 0 0
\(55\) −4.01631 −0.541558
\(56\) 0 0
\(57\) 19.4200 2.57224
\(58\) 0 0
\(59\) −1.46522 −0.190755 −0.0953776 0.995441i \(-0.530406\pi\)
−0.0953776 + 0.995441i \(0.530406\pi\)
\(60\) 0 0
\(61\) 3.04010 0.389245 0.194622 0.980878i \(-0.437652\pi\)
0.194622 + 0.980878i \(0.437652\pi\)
\(62\) 0 0
\(63\) −4.13885 −0.521446
\(64\) 0 0
\(65\) −4.01631 −0.498161
\(66\) 0 0
\(67\) 8.56250 1.04608 0.523038 0.852309i \(-0.324799\pi\)
0.523038 + 0.852309i \(0.324799\pi\)
\(68\) 0 0
\(69\) −8.66643 −1.04332
\(70\) 0 0
\(71\) −3.49753 −0.415081 −0.207540 0.978226i \(-0.566546\pi\)
−0.207540 + 0.978226i \(0.566546\pi\)
\(72\) 0 0
\(73\) −0.308210 −0.0360733 −0.0180367 0.999837i \(-0.505742\pi\)
−0.0180367 + 0.999837i \(0.505742\pi\)
\(74\) 0 0
\(75\) 29.7397 3.43405
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.30138 1.04649 0.523243 0.852183i \(-0.324722\pi\)
0.523243 + 0.852183i \(0.324722\pi\)
\(80\) 0 0
\(81\) −4.28648 −0.476275
\(82\) 0 0
\(83\) −7.19951 −0.790249 −0.395125 0.918627i \(-0.629299\pi\)
−0.395125 + 0.918627i \(0.629299\pi\)
\(84\) 0 0
\(85\) 25.1553 2.72848
\(86\) 0 0
\(87\) 1.91073 0.204851
\(88\) 0 0
\(89\) −12.1579 −1.28874 −0.644369 0.764715i \(-0.722880\pi\)
−0.644369 + 0.764715i \(0.722880\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 6.05060 0.627418
\(94\) 0 0
\(95\) −29.1918 −2.99501
\(96\) 0 0
\(97\) −8.50768 −0.863824 −0.431912 0.901916i \(-0.642161\pi\)
−0.431912 + 0.901916i \(0.642161\pi\)
\(98\) 0 0
\(99\) 4.13885 0.415970
\(100\) 0 0
\(101\) 1.80021 0.179128 0.0895638 0.995981i \(-0.471453\pi\)
0.0895638 + 0.995981i \(0.471453\pi\)
\(102\) 0 0
\(103\) −2.77955 −0.273878 −0.136939 0.990580i \(-0.543726\pi\)
−0.136939 + 0.990580i \(0.543726\pi\)
\(104\) 0 0
\(105\) 10.7310 1.04724
\(106\) 0 0
\(107\) −20.0240 −1.93579 −0.967895 0.251357i \(-0.919123\pi\)
−0.967895 + 0.251357i \(0.919123\pi\)
\(108\) 0 0
\(109\) −8.24798 −0.790014 −0.395007 0.918678i \(-0.629258\pi\)
−0.395007 + 0.918678i \(0.629258\pi\)
\(110\) 0 0
\(111\) −14.8632 −1.41076
\(112\) 0 0
\(113\) −3.54931 −0.333891 −0.166945 0.985966i \(-0.553390\pi\)
−0.166945 + 0.985966i \(0.553390\pi\)
\(114\) 0 0
\(115\) 13.0272 1.21480
\(116\) 0 0
\(117\) 4.13885 0.382637
\(118\) 0 0
\(119\) 6.26331 0.574156
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 18.2346 1.64416
\(124\) 0 0
\(125\) −24.6228 −2.20233
\(126\) 0 0
\(127\) −19.0043 −1.68636 −0.843181 0.537629i \(-0.819320\pi\)
−0.843181 + 0.537629i \(0.819320\pi\)
\(128\) 0 0
\(129\) −1.24693 −0.109786
\(130\) 0 0
\(131\) −12.5199 −1.09387 −0.546933 0.837176i \(-0.684205\pi\)
−0.546933 + 0.837176i \(0.684205\pi\)
\(132\) 0 0
\(133\) −7.26832 −0.630243
\(134\) 0 0
\(135\) −12.2210 −1.05182
\(136\) 0 0
\(137\) 12.1671 1.03951 0.519754 0.854316i \(-0.326024\pi\)
0.519754 + 0.854316i \(0.326024\pi\)
\(138\) 0 0
\(139\) −4.65061 −0.394460 −0.197230 0.980357i \(-0.563195\pi\)
−0.197230 + 0.980357i \(0.563195\pi\)
\(140\) 0 0
\(141\) −7.35064 −0.619036
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −2.87218 −0.238521
\(146\) 0 0
\(147\) 2.67186 0.220371
\(148\) 0 0
\(149\) 18.4474 1.51127 0.755634 0.654994i \(-0.227329\pi\)
0.755634 + 0.654994i \(0.227329\pi\)
\(150\) 0 0
\(151\) −18.3430 −1.49273 −0.746367 0.665535i \(-0.768204\pi\)
−0.746367 + 0.665535i \(0.768204\pi\)
\(152\) 0 0
\(153\) −25.9229 −2.09574
\(154\) 0 0
\(155\) −9.09518 −0.730542
\(156\) 0 0
\(157\) −11.4946 −0.917370 −0.458685 0.888599i \(-0.651679\pi\)
−0.458685 + 0.888599i \(0.651679\pi\)
\(158\) 0 0
\(159\) −30.7330 −2.43728
\(160\) 0 0
\(161\) 3.24359 0.255631
\(162\) 0 0
\(163\) −12.6304 −0.989290 −0.494645 0.869095i \(-0.664702\pi\)
−0.494645 + 0.869095i \(0.664702\pi\)
\(164\) 0 0
\(165\) −10.7310 −0.835408
\(166\) 0 0
\(167\) −13.4204 −1.03850 −0.519252 0.854621i \(-0.673790\pi\)
−0.519252 + 0.854621i \(0.673790\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 30.0825 2.30046
\(172\) 0 0
\(173\) −14.7173 −1.11893 −0.559466 0.828853i \(-0.688994\pi\)
−0.559466 + 0.828853i \(0.688994\pi\)
\(174\) 0 0
\(175\) −11.1307 −0.841402
\(176\) 0 0
\(177\) −3.91486 −0.294259
\(178\) 0 0
\(179\) 15.5835 1.16476 0.582381 0.812916i \(-0.302121\pi\)
0.582381 + 0.812916i \(0.302121\pi\)
\(180\) 0 0
\(181\) −5.93317 −0.441009 −0.220505 0.975386i \(-0.570770\pi\)
−0.220505 + 0.975386i \(0.570770\pi\)
\(182\) 0 0
\(183\) 8.12273 0.600449
\(184\) 0 0
\(185\) 22.3422 1.64263
\(186\) 0 0
\(187\) −6.26331 −0.458018
\(188\) 0 0
\(189\) −3.04285 −0.221335
\(190\) 0 0
\(191\) −23.6050 −1.70800 −0.853998 0.520277i \(-0.825829\pi\)
−0.853998 + 0.520277i \(0.825829\pi\)
\(192\) 0 0
\(193\) 7.47196 0.537843 0.268922 0.963162i \(-0.413333\pi\)
0.268922 + 0.963162i \(0.413333\pi\)
\(194\) 0 0
\(195\) −10.7310 −0.768464
\(196\) 0 0
\(197\) 6.97053 0.496630 0.248315 0.968679i \(-0.420123\pi\)
0.248315 + 0.968679i \(0.420123\pi\)
\(198\) 0 0
\(199\) 19.8868 1.40974 0.704870 0.709337i \(-0.251005\pi\)
0.704870 + 0.709337i \(0.251005\pi\)
\(200\) 0 0
\(201\) 22.8778 1.61368
\(202\) 0 0
\(203\) −0.715129 −0.0501922
\(204\) 0 0
\(205\) −27.4100 −1.91439
\(206\) 0 0
\(207\) −13.4247 −0.933083
\(208\) 0 0
\(209\) 7.26832 0.502760
\(210\) 0 0
\(211\) −6.14141 −0.422792 −0.211396 0.977401i \(-0.567801\pi\)
−0.211396 + 0.977401i \(0.567801\pi\)
\(212\) 0 0
\(213\) −9.34493 −0.640304
\(214\) 0 0
\(215\) 1.87436 0.127830
\(216\) 0 0
\(217\) −2.26456 −0.153729
\(218\) 0 0
\(219\) −0.823496 −0.0556467
\(220\) 0 0
\(221\) −6.26331 −0.421315
\(222\) 0 0
\(223\) 27.6417 1.85102 0.925511 0.378720i \(-0.123636\pi\)
0.925511 + 0.378720i \(0.123636\pi\)
\(224\) 0 0
\(225\) 46.0683 3.07122
\(226\) 0 0
\(227\) 9.92405 0.658682 0.329341 0.944211i \(-0.393173\pi\)
0.329341 + 0.944211i \(0.393173\pi\)
\(228\) 0 0
\(229\) −16.5781 −1.09551 −0.547757 0.836638i \(-0.684518\pi\)
−0.547757 + 0.836638i \(0.684518\pi\)
\(230\) 0 0
\(231\) −2.67186 −0.175796
\(232\) 0 0
\(233\) 0.631312 0.0413587 0.0206793 0.999786i \(-0.493417\pi\)
0.0206793 + 0.999786i \(0.493417\pi\)
\(234\) 0 0
\(235\) 11.0494 0.720782
\(236\) 0 0
\(237\) 24.8520 1.61431
\(238\) 0 0
\(239\) 1.56651 0.101329 0.0506646 0.998716i \(-0.483866\pi\)
0.0506646 + 0.998716i \(0.483866\pi\)
\(240\) 0 0
\(241\) 16.8799 1.08733 0.543665 0.839302i \(-0.317036\pi\)
0.543665 + 0.839302i \(0.317036\pi\)
\(242\) 0 0
\(243\) −20.5814 −1.32030
\(244\) 0 0
\(245\) −4.01631 −0.256592
\(246\) 0 0
\(247\) 7.26832 0.462472
\(248\) 0 0
\(249\) −19.2361 −1.21904
\(250\) 0 0
\(251\) −11.2986 −0.713159 −0.356580 0.934265i \(-0.616057\pi\)
−0.356580 + 0.934265i \(0.616057\pi\)
\(252\) 0 0
\(253\) −3.24359 −0.203923
\(254\) 0 0
\(255\) 67.2116 4.20895
\(256\) 0 0
\(257\) 14.3554 0.895464 0.447732 0.894168i \(-0.352232\pi\)
0.447732 + 0.894168i \(0.352232\pi\)
\(258\) 0 0
\(259\) 5.56287 0.345660
\(260\) 0 0
\(261\) 2.95981 0.183208
\(262\) 0 0
\(263\) −18.5994 −1.14689 −0.573445 0.819244i \(-0.694393\pi\)
−0.573445 + 0.819244i \(0.694393\pi\)
\(264\) 0 0
\(265\) 46.1973 2.83788
\(266\) 0 0
\(267\) −32.4843 −1.98801
\(268\) 0 0
\(269\) 1.11668 0.0680850 0.0340425 0.999420i \(-0.489162\pi\)
0.0340425 + 0.999420i \(0.489162\pi\)
\(270\) 0 0
\(271\) −18.9549 −1.15143 −0.575714 0.817651i \(-0.695276\pi\)
−0.575714 + 0.817651i \(0.695276\pi\)
\(272\) 0 0
\(273\) −2.67186 −0.161708
\(274\) 0 0
\(275\) 11.1307 0.671207
\(276\) 0 0
\(277\) 22.8561 1.37329 0.686645 0.726993i \(-0.259083\pi\)
0.686645 + 0.726993i \(0.259083\pi\)
\(278\) 0 0
\(279\) 9.37269 0.561128
\(280\) 0 0
\(281\) 19.0790 1.13816 0.569078 0.822283i \(-0.307300\pi\)
0.569078 + 0.822283i \(0.307300\pi\)
\(282\) 0 0
\(283\) −26.9292 −1.60078 −0.800388 0.599483i \(-0.795373\pi\)
−0.800388 + 0.599483i \(0.795373\pi\)
\(284\) 0 0
\(285\) −77.9965 −4.62011
\(286\) 0 0
\(287\) −6.82467 −0.402847
\(288\) 0 0
\(289\) 22.2290 1.30759
\(290\) 0 0
\(291\) −22.7314 −1.33254
\(292\) 0 0
\(293\) 31.6732 1.85037 0.925183 0.379520i \(-0.123911\pi\)
0.925183 + 0.379520i \(0.123911\pi\)
\(294\) 0 0
\(295\) 5.88477 0.342624
\(296\) 0 0
\(297\) 3.04285 0.176564
\(298\) 0 0
\(299\) −3.24359 −0.187582
\(300\) 0 0
\(301\) 0.466688 0.0268994
\(302\) 0 0
\(303\) 4.80991 0.276322
\(304\) 0 0
\(305\) −12.2100 −0.699141
\(306\) 0 0
\(307\) −3.27175 −0.186729 −0.0933644 0.995632i \(-0.529762\pi\)
−0.0933644 + 0.995632i \(0.529762\pi\)
\(308\) 0 0
\(309\) −7.42659 −0.422484
\(310\) 0 0
\(311\) 3.26658 0.185231 0.0926155 0.995702i \(-0.470477\pi\)
0.0926155 + 0.995702i \(0.470477\pi\)
\(312\) 0 0
\(313\) −16.5394 −0.934861 −0.467431 0.884030i \(-0.654820\pi\)
−0.467431 + 0.884030i \(0.654820\pi\)
\(314\) 0 0
\(315\) 16.6229 0.936593
\(316\) 0 0
\(317\) −12.0198 −0.675100 −0.337550 0.941308i \(-0.609598\pi\)
−0.337550 + 0.941308i \(0.609598\pi\)
\(318\) 0 0
\(319\) 0.715129 0.0400395
\(320\) 0 0
\(321\) −53.5013 −2.98615
\(322\) 0 0
\(323\) −45.5237 −2.53301
\(324\) 0 0
\(325\) 11.1307 0.617421
\(326\) 0 0
\(327\) −22.0375 −1.21868
\(328\) 0 0
\(329\) 2.75113 0.151675
\(330\) 0 0
\(331\) 23.1228 1.27095 0.635473 0.772123i \(-0.280805\pi\)
0.635473 + 0.772123i \(0.280805\pi\)
\(332\) 0 0
\(333\) −23.0239 −1.26170
\(334\) 0 0
\(335\) −34.3896 −1.87891
\(336\) 0 0
\(337\) −33.1456 −1.80556 −0.902779 0.430104i \(-0.858477\pi\)
−0.902779 + 0.430104i \(0.858477\pi\)
\(338\) 0 0
\(339\) −9.48327 −0.515060
\(340\) 0 0
\(341\) 2.26456 0.122633
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 34.8070 1.87395
\(346\) 0 0
\(347\) −30.3053 −1.62688 −0.813438 0.581652i \(-0.802407\pi\)
−0.813438 + 0.581652i \(0.802407\pi\)
\(348\) 0 0
\(349\) −22.8831 −1.22491 −0.612453 0.790507i \(-0.709817\pi\)
−0.612453 + 0.790507i \(0.709817\pi\)
\(350\) 0 0
\(351\) 3.04285 0.162415
\(352\) 0 0
\(353\) −3.53227 −0.188004 −0.0940018 0.995572i \(-0.529966\pi\)
−0.0940018 + 0.995572i \(0.529966\pi\)
\(354\) 0 0
\(355\) 14.0472 0.745546
\(356\) 0 0
\(357\) 16.7347 0.885694
\(358\) 0 0
\(359\) −6.50637 −0.343393 −0.171697 0.985150i \(-0.554925\pi\)
−0.171697 + 0.985150i \(0.554925\pi\)
\(360\) 0 0
\(361\) 33.8285 1.78045
\(362\) 0 0
\(363\) 2.67186 0.140236
\(364\) 0 0
\(365\) 1.23787 0.0647929
\(366\) 0 0
\(367\) 7.08430 0.369798 0.184899 0.982758i \(-0.440804\pi\)
0.184899 + 0.982758i \(0.440804\pi\)
\(368\) 0 0
\(369\) 28.2463 1.47044
\(370\) 0 0
\(371\) 11.5024 0.597177
\(372\) 0 0
\(373\) 28.6160 1.48168 0.740840 0.671682i \(-0.234428\pi\)
0.740840 + 0.671682i \(0.234428\pi\)
\(374\) 0 0
\(375\) −65.7887 −3.39731
\(376\) 0 0
\(377\) 0.715129 0.0368310
\(378\) 0 0
\(379\) −22.0331 −1.13176 −0.565881 0.824487i \(-0.691464\pi\)
−0.565881 + 0.824487i \(0.691464\pi\)
\(380\) 0 0
\(381\) −50.7770 −2.60138
\(382\) 0 0
\(383\) 16.0233 0.818755 0.409377 0.912365i \(-0.365746\pi\)
0.409377 + 0.912365i \(0.365746\pi\)
\(384\) 0 0
\(385\) 4.01631 0.204690
\(386\) 0 0
\(387\) −1.93155 −0.0981863
\(388\) 0 0
\(389\) −13.3706 −0.677916 −0.338958 0.940801i \(-0.610074\pi\)
−0.338958 + 0.940801i \(0.610074\pi\)
\(390\) 0 0
\(391\) 20.3156 1.02740
\(392\) 0 0
\(393\) −33.4514 −1.68740
\(394\) 0 0
\(395\) −37.3572 −1.87964
\(396\) 0 0
\(397\) 7.94634 0.398815 0.199408 0.979917i \(-0.436098\pi\)
0.199408 + 0.979917i \(0.436098\pi\)
\(398\) 0 0
\(399\) −19.4200 −0.972214
\(400\) 0 0
\(401\) −23.4453 −1.17080 −0.585400 0.810745i \(-0.699063\pi\)
−0.585400 + 0.810745i \(0.699063\pi\)
\(402\) 0 0
\(403\) 2.26456 0.112806
\(404\) 0 0
\(405\) 17.2158 0.855460
\(406\) 0 0
\(407\) −5.56287 −0.275741
\(408\) 0 0
\(409\) 22.7946 1.12712 0.563561 0.826075i \(-0.309431\pi\)
0.563561 + 0.826075i \(0.309431\pi\)
\(410\) 0 0
\(411\) 32.5089 1.60354
\(412\) 0 0
\(413\) 1.46522 0.0720987
\(414\) 0 0
\(415\) 28.9154 1.41940
\(416\) 0 0
\(417\) −12.4258 −0.608494
\(418\) 0 0
\(419\) 17.7350 0.866412 0.433206 0.901295i \(-0.357382\pi\)
0.433206 + 0.901295i \(0.357382\pi\)
\(420\) 0 0
\(421\) −12.3004 −0.599486 −0.299743 0.954020i \(-0.596901\pi\)
−0.299743 + 0.954020i \(0.596901\pi\)
\(422\) 0 0
\(423\) −11.3865 −0.553631
\(424\) 0 0
\(425\) −69.7150 −3.38167
\(426\) 0 0
\(427\) −3.04010 −0.147121
\(428\) 0 0
\(429\) 2.67186 0.128999
\(430\) 0 0
\(431\) 24.8732 1.19810 0.599051 0.800711i \(-0.295545\pi\)
0.599051 + 0.800711i \(0.295545\pi\)
\(432\) 0 0
\(433\) −21.6722 −1.04150 −0.520750 0.853709i \(-0.674348\pi\)
−0.520750 + 0.853709i \(0.674348\pi\)
\(434\) 0 0
\(435\) −7.67406 −0.367943
\(436\) 0 0
\(437\) −23.5755 −1.12777
\(438\) 0 0
\(439\) −4.07828 −0.194646 −0.0973228 0.995253i \(-0.531028\pi\)
−0.0973228 + 0.995253i \(0.531028\pi\)
\(440\) 0 0
\(441\) 4.13885 0.197088
\(442\) 0 0
\(443\) −5.24459 −0.249178 −0.124589 0.992208i \(-0.539761\pi\)
−0.124589 + 0.992208i \(0.539761\pi\)
\(444\) 0 0
\(445\) 48.8300 2.31476
\(446\) 0 0
\(447\) 49.2889 2.33128
\(448\) 0 0
\(449\) 24.4449 1.15363 0.576814 0.816875i \(-0.304296\pi\)
0.576814 + 0.816875i \(0.304296\pi\)
\(450\) 0 0
\(451\) 6.82467 0.321361
\(452\) 0 0
\(453\) −49.0100 −2.30269
\(454\) 0 0
\(455\) 4.01631 0.188287
\(456\) 0 0
\(457\) −19.1223 −0.894505 −0.447252 0.894408i \(-0.647597\pi\)
−0.447252 + 0.894408i \(0.647597\pi\)
\(458\) 0 0
\(459\) −19.0583 −0.889564
\(460\) 0 0
\(461\) −20.9457 −0.975537 −0.487768 0.872973i \(-0.662189\pi\)
−0.487768 + 0.872973i \(0.662189\pi\)
\(462\) 0 0
\(463\) −37.9695 −1.76459 −0.882296 0.470694i \(-0.844004\pi\)
−0.882296 + 0.470694i \(0.844004\pi\)
\(464\) 0 0
\(465\) −24.3011 −1.12693
\(466\) 0 0
\(467\) −18.6235 −0.861794 −0.430897 0.902401i \(-0.641803\pi\)
−0.430897 + 0.902401i \(0.641803\pi\)
\(468\) 0 0
\(469\) −8.56250 −0.395380
\(470\) 0 0
\(471\) −30.7120 −1.41514
\(472\) 0 0
\(473\) −0.466688 −0.0214583
\(474\) 0 0
\(475\) 80.9015 3.71202
\(476\) 0 0
\(477\) −47.6069 −2.17977
\(478\) 0 0
\(479\) 1.76193 0.0805048 0.0402524 0.999190i \(-0.487184\pi\)
0.0402524 + 0.999190i \(0.487184\pi\)
\(480\) 0 0
\(481\) −5.56287 −0.253645
\(482\) 0 0
\(483\) 8.66643 0.394336
\(484\) 0 0
\(485\) 34.1694 1.55155
\(486\) 0 0
\(487\) 8.00877 0.362912 0.181456 0.983399i \(-0.441919\pi\)
0.181456 + 0.983399i \(0.441919\pi\)
\(488\) 0 0
\(489\) −33.7467 −1.52608
\(490\) 0 0
\(491\) −16.6387 −0.750896 −0.375448 0.926843i \(-0.622511\pi\)
−0.375448 + 0.926843i \(0.622511\pi\)
\(492\) 0 0
\(493\) −4.47907 −0.201727
\(494\) 0 0
\(495\) −16.6229 −0.747143
\(496\) 0 0
\(497\) 3.49753 0.156886
\(498\) 0 0
\(499\) 15.2986 0.684861 0.342430 0.939543i \(-0.388750\pi\)
0.342430 + 0.939543i \(0.388750\pi\)
\(500\) 0 0
\(501\) −35.8576 −1.60200
\(502\) 0 0
\(503\) −13.8933 −0.619471 −0.309736 0.950823i \(-0.600241\pi\)
−0.309736 + 0.950823i \(0.600241\pi\)
\(504\) 0 0
\(505\) −7.23019 −0.321739
\(506\) 0 0
\(507\) 2.67186 0.118662
\(508\) 0 0
\(509\) 33.2135 1.47216 0.736081 0.676893i \(-0.236674\pi\)
0.736081 + 0.676893i \(0.236674\pi\)
\(510\) 0 0
\(511\) 0.308210 0.0136344
\(512\) 0 0
\(513\) 22.1164 0.976462
\(514\) 0 0
\(515\) 11.1635 0.491924
\(516\) 0 0
\(517\) −2.75113 −0.120995
\(518\) 0 0
\(519\) −39.3225 −1.72607
\(520\) 0 0
\(521\) 34.8137 1.52521 0.762607 0.646862i \(-0.223919\pi\)
0.762607 + 0.646862i \(0.223919\pi\)
\(522\) 0 0
\(523\) −24.2251 −1.05929 −0.529645 0.848219i \(-0.677675\pi\)
−0.529645 + 0.848219i \(0.677675\pi\)
\(524\) 0 0
\(525\) −29.7397 −1.29795
\(526\) 0 0
\(527\) −14.1837 −0.617850
\(528\) 0 0
\(529\) −12.4791 −0.542570
\(530\) 0 0
\(531\) −6.06432 −0.263169
\(532\) 0 0
\(533\) 6.82467 0.295609
\(534\) 0 0
\(535\) 80.4223 3.47696
\(536\) 0 0
\(537\) 41.6369 1.79676
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −3.22631 −0.138710 −0.0693551 0.997592i \(-0.522094\pi\)
−0.0693551 + 0.997592i \(0.522094\pi\)
\(542\) 0 0
\(543\) −15.8526 −0.680301
\(544\) 0 0
\(545\) 33.1264 1.41898
\(546\) 0 0
\(547\) −8.38590 −0.358555 −0.179278 0.983799i \(-0.557376\pi\)
−0.179278 + 0.983799i \(0.557376\pi\)
\(548\) 0 0
\(549\) 12.5825 0.537008
\(550\) 0 0
\(551\) 5.19779 0.221433
\(552\) 0 0
\(553\) −9.30138 −0.395535
\(554\) 0 0
\(555\) 59.6953 2.53392
\(556\) 0 0
\(557\) −38.1225 −1.61530 −0.807652 0.589660i \(-0.799262\pi\)
−0.807652 + 0.589660i \(0.799262\pi\)
\(558\) 0 0
\(559\) −0.466688 −0.0197388
\(560\) 0 0
\(561\) −16.7347 −0.706539
\(562\) 0 0
\(563\) 12.7531 0.537480 0.268740 0.963213i \(-0.413393\pi\)
0.268740 + 0.963213i \(0.413393\pi\)
\(564\) 0 0
\(565\) 14.2551 0.599717
\(566\) 0 0
\(567\) 4.28648 0.180015
\(568\) 0 0
\(569\) −6.57158 −0.275495 −0.137747 0.990467i \(-0.543986\pi\)
−0.137747 + 0.990467i \(0.543986\pi\)
\(570\) 0 0
\(571\) 33.2885 1.39308 0.696540 0.717518i \(-0.254722\pi\)
0.696540 + 0.717518i \(0.254722\pi\)
\(572\) 0 0
\(573\) −63.0692 −2.63476
\(574\) 0 0
\(575\) −36.1035 −1.50562
\(576\) 0 0
\(577\) 24.2386 1.00906 0.504532 0.863393i \(-0.331665\pi\)
0.504532 + 0.863393i \(0.331665\pi\)
\(578\) 0 0
\(579\) 19.9640 0.829677
\(580\) 0 0
\(581\) 7.19951 0.298686
\(582\) 0 0
\(583\) −11.5024 −0.476383
\(584\) 0 0
\(585\) −16.6229 −0.687271
\(586\) 0 0
\(587\) 27.6928 1.14300 0.571501 0.820601i \(-0.306361\pi\)
0.571501 + 0.820601i \(0.306361\pi\)
\(588\) 0 0
\(589\) 16.4596 0.678205
\(590\) 0 0
\(591\) 18.6243 0.766102
\(592\) 0 0
\(593\) −12.1586 −0.499295 −0.249648 0.968337i \(-0.580315\pi\)
−0.249648 + 0.968337i \(0.580315\pi\)
\(594\) 0 0
\(595\) −25.1553 −1.03127
\(596\) 0 0
\(597\) 53.1349 2.17466
\(598\) 0 0
\(599\) −27.2244 −1.11236 −0.556179 0.831062i \(-0.687733\pi\)
−0.556179 + 0.831062i \(0.687733\pi\)
\(600\) 0 0
\(601\) −1.06230 −0.0433322 −0.0216661 0.999765i \(-0.506897\pi\)
−0.0216661 + 0.999765i \(0.506897\pi\)
\(602\) 0 0
\(603\) 35.4389 1.44318
\(604\) 0 0
\(605\) −4.01631 −0.163286
\(606\) 0 0
\(607\) −12.8642 −0.522143 −0.261072 0.965319i \(-0.584076\pi\)
−0.261072 + 0.965319i \(0.584076\pi\)
\(608\) 0 0
\(609\) −1.91073 −0.0774266
\(610\) 0 0
\(611\) −2.75113 −0.111299
\(612\) 0 0
\(613\) −35.4725 −1.43272 −0.716360 0.697731i \(-0.754193\pi\)
−0.716360 + 0.697731i \(0.754193\pi\)
\(614\) 0 0
\(615\) −73.2356 −2.95315
\(616\) 0 0
\(617\) −8.60699 −0.346505 −0.173252 0.984877i \(-0.555428\pi\)
−0.173252 + 0.984877i \(0.555428\pi\)
\(618\) 0 0
\(619\) 23.6484 0.950508 0.475254 0.879849i \(-0.342356\pi\)
0.475254 + 0.879849i \(0.342356\pi\)
\(620\) 0 0
\(621\) −9.86975 −0.396059
\(622\) 0 0
\(623\) 12.1579 0.487097
\(624\) 0 0
\(625\) 43.2391 1.72956
\(626\) 0 0
\(627\) 19.4200 0.775558
\(628\) 0 0
\(629\) 34.8420 1.38924
\(630\) 0 0
\(631\) −38.6976 −1.54053 −0.770263 0.637726i \(-0.779875\pi\)
−0.770263 + 0.637726i \(0.779875\pi\)
\(632\) 0 0
\(633\) −16.4090 −0.652199
\(634\) 0 0
\(635\) 76.3272 3.02895
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −14.4758 −0.572652
\(640\) 0 0
\(641\) −13.0769 −0.516505 −0.258252 0.966077i \(-0.583147\pi\)
−0.258252 + 0.966077i \(0.583147\pi\)
\(642\) 0 0
\(643\) −32.5189 −1.28242 −0.641210 0.767365i \(-0.721567\pi\)
−0.641210 + 0.767365i \(0.721567\pi\)
\(644\) 0 0
\(645\) 5.00804 0.197191
\(646\) 0 0
\(647\) 47.2402 1.85720 0.928602 0.371078i \(-0.121012\pi\)
0.928602 + 0.371078i \(0.121012\pi\)
\(648\) 0 0
\(649\) −1.46522 −0.0575149
\(650\) 0 0
\(651\) −6.05060 −0.237142
\(652\) 0 0
\(653\) 30.9958 1.21296 0.606480 0.795099i \(-0.292581\pi\)
0.606480 + 0.795099i \(0.292581\pi\)
\(654\) 0 0
\(655\) 50.2836 1.96474
\(656\) 0 0
\(657\) −1.27564 −0.0497673
\(658\) 0 0
\(659\) −22.4655 −0.875130 −0.437565 0.899187i \(-0.644159\pi\)
−0.437565 + 0.899187i \(0.644159\pi\)
\(660\) 0 0
\(661\) 35.2161 1.36975 0.684874 0.728661i \(-0.259857\pi\)
0.684874 + 0.728661i \(0.259857\pi\)
\(662\) 0 0
\(663\) −16.7347 −0.649921
\(664\) 0 0
\(665\) 29.1918 1.13201
\(666\) 0 0
\(667\) −2.31959 −0.0898147
\(668\) 0 0
\(669\) 73.8547 2.85539
\(670\) 0 0
\(671\) 3.04010 0.117362
\(672\) 0 0
\(673\) −11.7900 −0.454471 −0.227235 0.973840i \(-0.572969\pi\)
−0.227235 + 0.973840i \(0.572969\pi\)
\(674\) 0 0
\(675\) 33.8690 1.30362
\(676\) 0 0
\(677\) 44.0367 1.69247 0.846235 0.532810i \(-0.178864\pi\)
0.846235 + 0.532810i \(0.178864\pi\)
\(678\) 0 0
\(679\) 8.50768 0.326495
\(680\) 0 0
\(681\) 26.5157 1.01608
\(682\) 0 0
\(683\) 12.2850 0.470072 0.235036 0.971987i \(-0.424479\pi\)
0.235036 + 0.971987i \(0.424479\pi\)
\(684\) 0 0
\(685\) −48.8669 −1.86711
\(686\) 0 0
\(687\) −44.2945 −1.68994
\(688\) 0 0
\(689\) −11.5024 −0.438208
\(690\) 0 0
\(691\) 46.5518 1.77091 0.885457 0.464721i \(-0.153845\pi\)
0.885457 + 0.464721i \(0.153845\pi\)
\(692\) 0 0
\(693\) −4.13885 −0.157222
\(694\) 0 0
\(695\) 18.6783 0.708507
\(696\) 0 0
\(697\) −42.7450 −1.61908
\(698\) 0 0
\(699\) 1.68678 0.0637999
\(700\) 0 0
\(701\) 29.9052 1.12950 0.564752 0.825261i \(-0.308972\pi\)
0.564752 + 0.825261i \(0.308972\pi\)
\(702\) 0 0
\(703\) −40.4327 −1.52495
\(704\) 0 0
\(705\) 29.5224 1.11188
\(706\) 0 0
\(707\) −1.80021 −0.0677038
\(708\) 0 0
\(709\) 2.77574 0.104245 0.0521225 0.998641i \(-0.483401\pi\)
0.0521225 + 0.998641i \(0.483401\pi\)
\(710\) 0 0
\(711\) 38.4970 1.44375
\(712\) 0 0
\(713\) −7.34532 −0.275084
\(714\) 0 0
\(715\) −4.01631 −0.150201
\(716\) 0 0
\(717\) 4.18551 0.156311
\(718\) 0 0
\(719\) 3.04149 0.113428 0.0567141 0.998390i \(-0.481938\pi\)
0.0567141 + 0.998390i \(0.481938\pi\)
\(720\) 0 0
\(721\) 2.77955 0.103516
\(722\) 0 0
\(723\) 45.1008 1.67732
\(724\) 0 0
\(725\) 7.95989 0.295623
\(726\) 0 0
\(727\) 48.0533 1.78220 0.891099 0.453809i \(-0.149935\pi\)
0.891099 + 0.453809i \(0.149935\pi\)
\(728\) 0 0
\(729\) −42.1313 −1.56042
\(730\) 0 0
\(731\) 2.92301 0.108111
\(732\) 0 0
\(733\) −24.5812 −0.907927 −0.453964 0.891020i \(-0.649990\pi\)
−0.453964 + 0.891020i \(0.649990\pi\)
\(734\) 0 0
\(735\) −10.7310 −0.395819
\(736\) 0 0
\(737\) 8.56250 0.315404
\(738\) 0 0
\(739\) −6.71310 −0.246945 −0.123473 0.992348i \(-0.539403\pi\)
−0.123473 + 0.992348i \(0.539403\pi\)
\(740\) 0 0
\(741\) 19.4200 0.713410
\(742\) 0 0
\(743\) 0.756369 0.0277485 0.0138742 0.999904i \(-0.495584\pi\)
0.0138742 + 0.999904i \(0.495584\pi\)
\(744\) 0 0
\(745\) −74.0903 −2.71446
\(746\) 0 0
\(747\) −29.7977 −1.09024
\(748\) 0 0
\(749\) 20.0240 0.731660
\(750\) 0 0
\(751\) −5.17216 −0.188735 −0.0943675 0.995537i \(-0.530083\pi\)
−0.0943675 + 0.995537i \(0.530083\pi\)
\(752\) 0 0
\(753\) −30.1882 −1.10012
\(754\) 0 0
\(755\) 73.6712 2.68117
\(756\) 0 0
\(757\) −30.2045 −1.09780 −0.548901 0.835888i \(-0.684953\pi\)
−0.548901 + 0.835888i \(0.684953\pi\)
\(758\) 0 0
\(759\) −8.66643 −0.314571
\(760\) 0 0
\(761\) −23.6956 −0.858964 −0.429482 0.903075i \(-0.641304\pi\)
−0.429482 + 0.903075i \(0.641304\pi\)
\(762\) 0 0
\(763\) 8.24798 0.298597
\(764\) 0 0
\(765\) 104.114 3.76426
\(766\) 0 0
\(767\) −1.46522 −0.0529060
\(768\) 0 0
\(769\) −12.5749 −0.453463 −0.226732 0.973957i \(-0.572804\pi\)
−0.226732 + 0.973957i \(0.572804\pi\)
\(770\) 0 0
\(771\) 38.3556 1.38134
\(772\) 0 0
\(773\) −24.2181 −0.871065 −0.435533 0.900173i \(-0.643440\pi\)
−0.435533 + 0.900173i \(0.643440\pi\)
\(774\) 0 0
\(775\) 25.2062 0.905433
\(776\) 0 0
\(777\) 14.8632 0.533215
\(778\) 0 0
\(779\) 49.6039 1.77724
\(780\) 0 0
\(781\) −3.49753 −0.125152
\(782\) 0 0
\(783\) 2.17603 0.0777649
\(784\) 0 0
\(785\) 46.1659 1.64773
\(786\) 0 0
\(787\) 36.2407 1.29184 0.645921 0.763404i \(-0.276474\pi\)
0.645921 + 0.763404i \(0.276474\pi\)
\(788\) 0 0
\(789\) −49.6951 −1.76919
\(790\) 0 0
\(791\) 3.54931 0.126199
\(792\) 0 0
\(793\) 3.04010 0.107957
\(794\) 0 0
\(795\) 123.433 4.37771
\(796\) 0 0
\(797\) −27.9219 −0.989046 −0.494523 0.869165i \(-0.664657\pi\)
−0.494523 + 0.869165i \(0.664657\pi\)
\(798\) 0 0
\(799\) 17.2312 0.609595
\(800\) 0 0
\(801\) −50.3198 −1.77796
\(802\) 0 0
\(803\) −0.308210 −0.0108765
\(804\) 0 0
\(805\) −13.0272 −0.459150
\(806\) 0 0
\(807\) 2.98361 0.105028
\(808\) 0 0
\(809\) −47.6242 −1.67438 −0.837189 0.546913i \(-0.815803\pi\)
−0.837189 + 0.546913i \(0.815803\pi\)
\(810\) 0 0
\(811\) 45.4415 1.59567 0.797834 0.602877i \(-0.205979\pi\)
0.797834 + 0.602877i \(0.205979\pi\)
\(812\) 0 0
\(813\) −50.6449 −1.77619
\(814\) 0 0
\(815\) 50.7276 1.77691
\(816\) 0 0
\(817\) −3.39204 −0.118672
\(818\) 0 0
\(819\) −4.13885 −0.144623
\(820\) 0 0
\(821\) 26.2371 0.915680 0.457840 0.889035i \(-0.348623\pi\)
0.457840 + 0.889035i \(0.348623\pi\)
\(822\) 0 0
\(823\) 4.85077 0.169087 0.0845436 0.996420i \(-0.473057\pi\)
0.0845436 + 0.996420i \(0.473057\pi\)
\(824\) 0 0
\(825\) 29.7397 1.03540
\(826\) 0 0
\(827\) 36.4492 1.26746 0.633731 0.773553i \(-0.281523\pi\)
0.633731 + 0.773553i \(0.281523\pi\)
\(828\) 0 0
\(829\) 18.5408 0.643950 0.321975 0.946748i \(-0.395653\pi\)
0.321975 + 0.946748i \(0.395653\pi\)
\(830\) 0 0
\(831\) 61.0684 2.11844
\(832\) 0 0
\(833\) −6.26331 −0.217011
\(834\) 0 0
\(835\) 53.9006 1.86531
\(836\) 0 0
\(837\) 6.89072 0.238178
\(838\) 0 0
\(839\) 19.5846 0.676136 0.338068 0.941122i \(-0.390227\pi\)
0.338068 + 0.941122i \(0.390227\pi\)
\(840\) 0 0
\(841\) −28.4886 −0.982365
\(842\) 0 0
\(843\) 50.9764 1.75572
\(844\) 0 0
\(845\) −4.01631 −0.138165
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −71.9511 −2.46936
\(850\) 0 0
\(851\) 18.0437 0.618529
\(852\) 0 0
\(853\) −31.0957 −1.06470 −0.532349 0.846525i \(-0.678690\pi\)
−0.532349 + 0.846525i \(0.678690\pi\)
\(854\) 0 0
\(855\) −120.820 −4.13197
\(856\) 0 0
\(857\) 38.8309 1.32644 0.663218 0.748426i \(-0.269190\pi\)
0.663218 + 0.748426i \(0.269190\pi\)
\(858\) 0 0
\(859\) 50.2843 1.71568 0.857839 0.513918i \(-0.171806\pi\)
0.857839 + 0.513918i \(0.171806\pi\)
\(860\) 0 0
\(861\) −18.2346 −0.621433
\(862\) 0 0
\(863\) −5.79695 −0.197330 −0.0986652 0.995121i \(-0.531457\pi\)
−0.0986652 + 0.995121i \(0.531457\pi\)
\(864\) 0 0
\(865\) 59.1090 2.00977
\(866\) 0 0
\(867\) 59.3928 2.01709
\(868\) 0 0
\(869\) 9.30138 0.315528
\(870\) 0 0
\(871\) 8.56250 0.290129
\(872\) 0 0
\(873\) −35.2120 −1.19175
\(874\) 0 0
\(875\) 24.6228 0.832402
\(876\) 0 0
\(877\) −1.98595 −0.0670607 −0.0335304 0.999438i \(-0.510675\pi\)
−0.0335304 + 0.999438i \(0.510675\pi\)
\(878\) 0 0
\(879\) 84.6264 2.85438
\(880\) 0 0
\(881\) −14.0439 −0.473150 −0.236575 0.971613i \(-0.576025\pi\)
−0.236575 + 0.971613i \(0.576025\pi\)
\(882\) 0 0
\(883\) −28.9867 −0.975480 −0.487740 0.872989i \(-0.662179\pi\)
−0.487740 + 0.872989i \(0.662179\pi\)
\(884\) 0 0
\(885\) 15.7233 0.528532
\(886\) 0 0
\(887\) 24.0391 0.807154 0.403577 0.914946i \(-0.367767\pi\)
0.403577 + 0.914946i \(0.367767\pi\)
\(888\) 0 0
\(889\) 19.0043 0.637385
\(890\) 0 0
\(891\) −4.28648 −0.143602
\(892\) 0 0
\(893\) −19.9961 −0.669144
\(894\) 0 0
\(895\) −62.5880 −2.09208
\(896\) 0 0
\(897\) −8.66643 −0.289364
\(898\) 0 0
\(899\) 1.61946 0.0540119
\(900\) 0 0
\(901\) 72.0433 2.40011
\(902\) 0 0
\(903\) 1.24693 0.0414951
\(904\) 0 0
\(905\) 23.8294 0.792117
\(906\) 0 0
\(907\) 26.4792 0.879229 0.439615 0.898187i \(-0.355115\pi\)
0.439615 + 0.898187i \(0.355115\pi\)
\(908\) 0 0
\(909\) 7.45079 0.247127
\(910\) 0 0
\(911\) 30.6888 1.01677 0.508383 0.861131i \(-0.330243\pi\)
0.508383 + 0.861131i \(0.330243\pi\)
\(912\) 0 0
\(913\) −7.19951 −0.238269
\(914\) 0 0
\(915\) −32.6233 −1.07849
\(916\) 0 0
\(917\) 12.5199 0.413443
\(918\) 0 0
\(919\) 35.3413 1.16580 0.582900 0.812544i \(-0.301918\pi\)
0.582900 + 0.812544i \(0.301918\pi\)
\(920\) 0 0
\(921\) −8.74168 −0.288048
\(922\) 0 0
\(923\) −3.49753 −0.115123
\(924\) 0 0
\(925\) −61.9187 −2.03587
\(926\) 0 0
\(927\) −11.5042 −0.377846
\(928\) 0 0
\(929\) −1.25103 −0.0410450 −0.0205225 0.999789i \(-0.506533\pi\)
−0.0205225 + 0.999789i \(0.506533\pi\)
\(930\) 0 0
\(931\) 7.26832 0.238210
\(932\) 0 0
\(933\) 8.72787 0.285737
\(934\) 0 0
\(935\) 25.1553 0.822668
\(936\) 0 0
\(937\) 34.4687 1.12604 0.563022 0.826442i \(-0.309639\pi\)
0.563022 + 0.826442i \(0.309639\pi\)
\(938\) 0 0
\(939\) −44.1910 −1.44212
\(940\) 0 0
\(941\) 30.9394 1.00860 0.504299 0.863529i \(-0.331751\pi\)
0.504299 + 0.863529i \(0.331751\pi\)
\(942\) 0 0
\(943\) −22.1364 −0.720861
\(944\) 0 0
\(945\) 12.2210 0.397549
\(946\) 0 0
\(947\) 44.4862 1.44561 0.722804 0.691053i \(-0.242853\pi\)
0.722804 + 0.691053i \(0.242853\pi\)
\(948\) 0 0
\(949\) −0.308210 −0.0100049
\(950\) 0 0
\(951\) −32.1153 −1.04141
\(952\) 0 0
\(953\) −17.3416 −0.561748 −0.280874 0.959745i \(-0.590624\pi\)
−0.280874 + 0.959745i \(0.590624\pi\)
\(954\) 0 0
\(955\) 94.8048 3.06781
\(956\) 0 0
\(957\) 1.91073 0.0617650
\(958\) 0 0
\(959\) −12.1671 −0.392897
\(960\) 0 0
\(961\) −25.8718 −0.834573
\(962\) 0 0
\(963\) −82.8761 −2.67065
\(964\) 0 0
\(965\) −30.0097 −0.966045
\(966\) 0 0
\(967\) 15.4292 0.496170 0.248085 0.968738i \(-0.420199\pi\)
0.248085 + 0.968738i \(0.420199\pi\)
\(968\) 0 0
\(969\) −121.633 −3.90742
\(970\) 0 0
\(971\) −24.4337 −0.784115 −0.392058 0.919941i \(-0.628237\pi\)
−0.392058 + 0.919941i \(0.628237\pi\)
\(972\) 0 0
\(973\) 4.65061 0.149092
\(974\) 0 0
\(975\) 29.7397 0.952433
\(976\) 0 0
\(977\) −54.7742 −1.75238 −0.876191 0.481964i \(-0.839924\pi\)
−0.876191 + 0.481964i \(0.839924\pi\)
\(978\) 0 0
\(979\) −12.1579 −0.388569
\(980\) 0 0
\(981\) −34.1372 −1.08992
\(982\) 0 0
\(983\) −30.5983 −0.975935 −0.487967 0.872862i \(-0.662262\pi\)
−0.487967 + 0.872862i \(0.662262\pi\)
\(984\) 0 0
\(985\) −27.9958 −0.892020
\(986\) 0 0
\(987\) 7.35064 0.233973
\(988\) 0 0
\(989\) 1.51374 0.0481343
\(990\) 0 0
\(991\) 10.9390 0.347489 0.173745 0.984791i \(-0.444413\pi\)
0.173745 + 0.984791i \(0.444413\pi\)
\(992\) 0 0
\(993\) 61.7810 1.96056
\(994\) 0 0
\(995\) −79.8715 −2.53210
\(996\) 0 0
\(997\) 55.2991 1.75134 0.875670 0.482911i \(-0.160420\pi\)
0.875670 + 0.482911i \(0.160420\pi\)
\(998\) 0 0
\(999\) −16.9270 −0.535546
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 \(a_p\))