Properties

Label 8008.2.a.y.1.13
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 1.13
Root \(-2.46105\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.46105 q^{3} -1.12857 q^{5} +1.00000 q^{7} +3.05676 q^{9} +O(q^{10})\) \(q+2.46105 q^{3} -1.12857 q^{5} +1.00000 q^{7} +3.05676 q^{9} -1.00000 q^{11} -1.00000 q^{13} -2.77747 q^{15} +6.31528 q^{17} -1.83477 q^{19} +2.46105 q^{21} -8.30939 q^{23} -3.72632 q^{25} +0.139682 q^{27} -7.64782 q^{29} -5.82327 q^{31} -2.46105 q^{33} -1.12857 q^{35} +4.38927 q^{37} -2.46105 q^{39} -1.61087 q^{41} -9.78285 q^{43} -3.44977 q^{45} +3.50039 q^{47} +1.00000 q^{49} +15.5422 q^{51} +10.6895 q^{53} +1.12857 q^{55} -4.51547 q^{57} -11.5145 q^{59} +7.27639 q^{61} +3.05676 q^{63} +1.12857 q^{65} -10.5388 q^{67} -20.4498 q^{69} +13.2627 q^{71} -14.6993 q^{73} -9.17066 q^{75} -1.00000 q^{77} -8.87583 q^{79} -8.82651 q^{81} -14.7237 q^{83} -7.12725 q^{85} -18.8216 q^{87} +5.76039 q^{89} -1.00000 q^{91} -14.3313 q^{93} +2.07068 q^{95} -7.88319 q^{97} -3.05676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) 2.46105 1.42089 0.710443 0.703754i \(-0.248494\pi\)
0.710443 + 0.703754i \(0.248494\pi\)
\(4\) 0 0
\(5\) −1.12857 −0.504713 −0.252357 0.967634i \(-0.581206\pi\)
−0.252357 + 0.967634i \(0.581206\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 3.05676 1.01892
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −2.77747 −0.717140
\(16\) 0 0
\(17\) 6.31528 1.53168 0.765840 0.643032i \(-0.222324\pi\)
0.765840 + 0.643032i \(0.222324\pi\)
\(18\) 0 0
\(19\) −1.83477 −0.420926 −0.210463 0.977602i \(-0.567497\pi\)
−0.210463 + 0.977602i \(0.567497\pi\)
\(20\) 0 0
\(21\) 2.46105 0.537045
\(22\) 0 0
\(23\) −8.30939 −1.73263 −0.866314 0.499500i \(-0.833517\pi\)
−0.866314 + 0.499500i \(0.833517\pi\)
\(24\) 0 0
\(25\) −3.72632 −0.745265
\(26\) 0 0
\(27\) 0.139682 0.0268819
\(28\) 0 0
\(29\) −7.64782 −1.42016 −0.710082 0.704119i \(-0.751342\pi\)
−0.710082 + 0.704119i \(0.751342\pi\)
\(30\) 0 0
\(31\) −5.82327 −1.04589 −0.522945 0.852367i \(-0.675167\pi\)
−0.522945 + 0.852367i \(0.675167\pi\)
\(32\) 0 0
\(33\) −2.46105 −0.428413
\(34\) 0 0
\(35\) −1.12857 −0.190764
\(36\) 0 0
\(37\) 4.38927 0.721592 0.360796 0.932645i \(-0.382505\pi\)
0.360796 + 0.932645i \(0.382505\pi\)
\(38\) 0 0
\(39\) −2.46105 −0.394083
\(40\) 0 0
\(41\) −1.61087 −0.251576 −0.125788 0.992057i \(-0.540146\pi\)
−0.125788 + 0.992057i \(0.540146\pi\)
\(42\) 0 0
\(43\) −9.78285 −1.49187 −0.745936 0.666018i \(-0.767997\pi\)
−0.745936 + 0.666018i \(0.767997\pi\)
\(44\) 0 0
\(45\) −3.44977 −0.514262
\(46\) 0 0
\(47\) 3.50039 0.510584 0.255292 0.966864i \(-0.417828\pi\)
0.255292 + 0.966864i \(0.417828\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 15.5422 2.17634
\(52\) 0 0
\(53\) 10.6895 1.46832 0.734160 0.678976i \(-0.237576\pi\)
0.734160 + 0.678976i \(0.237576\pi\)
\(54\) 0 0
\(55\) 1.12857 0.152177
\(56\) 0 0
\(57\) −4.51547 −0.598088
\(58\) 0 0
\(59\) −11.5145 −1.49906 −0.749532 0.661968i \(-0.769722\pi\)
−0.749532 + 0.661968i \(0.769722\pi\)
\(60\) 0 0
\(61\) 7.27639 0.931646 0.465823 0.884878i \(-0.345758\pi\)
0.465823 + 0.884878i \(0.345758\pi\)
\(62\) 0 0
\(63\) 3.05676 0.385115
\(64\) 0 0
\(65\) 1.12857 0.139982
\(66\) 0 0
\(67\) −10.5388 −1.28752 −0.643762 0.765226i \(-0.722627\pi\)
−0.643762 + 0.765226i \(0.722627\pi\)
\(68\) 0 0
\(69\) −20.4498 −2.46187
\(70\) 0 0
\(71\) 13.2627 1.57399 0.786997 0.616957i \(-0.211635\pi\)
0.786997 + 0.616957i \(0.211635\pi\)
\(72\) 0 0
\(73\) −14.6993 −1.72042 −0.860209 0.509942i \(-0.829667\pi\)
−0.860209 + 0.509942i \(0.829667\pi\)
\(74\) 0 0
\(75\) −9.17066 −1.05894
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −8.87583 −0.998609 −0.499304 0.866427i \(-0.666411\pi\)
−0.499304 + 0.866427i \(0.666411\pi\)
\(80\) 0 0
\(81\) −8.82651 −0.980723
\(82\) 0 0
\(83\) −14.7237 −1.61614 −0.808068 0.589089i \(-0.799487\pi\)
−0.808068 + 0.589089i \(0.799487\pi\)
\(84\) 0 0
\(85\) −7.12725 −0.773059
\(86\) 0 0
\(87\) −18.8216 −2.01789
\(88\) 0 0
\(89\) 5.76039 0.610600 0.305300 0.952256i \(-0.401243\pi\)
0.305300 + 0.952256i \(0.401243\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −14.3313 −1.48609
\(94\) 0 0
\(95\) 2.07068 0.212447
\(96\) 0 0
\(97\) −7.88319 −0.800416 −0.400208 0.916424i \(-0.631062\pi\)
−0.400208 + 0.916424i \(0.631062\pi\)
\(98\) 0 0
\(99\) −3.05676 −0.307216
\(100\) 0 0
\(101\) 11.6940 1.16359 0.581797 0.813334i \(-0.302350\pi\)
0.581797 + 0.813334i \(0.302350\pi\)
\(102\) 0 0
\(103\) 14.2920 1.40824 0.704118 0.710083i \(-0.251343\pi\)
0.704118 + 0.710083i \(0.251343\pi\)
\(104\) 0 0
\(105\) −2.77747 −0.271053
\(106\) 0 0
\(107\) −17.6760 −1.70881 −0.854404 0.519610i \(-0.826077\pi\)
−0.854404 + 0.519610i \(0.826077\pi\)
\(108\) 0 0
\(109\) 13.7778 1.31967 0.659837 0.751408i \(-0.270625\pi\)
0.659837 + 0.751408i \(0.270625\pi\)
\(110\) 0 0
\(111\) 10.8022 1.02530
\(112\) 0 0
\(113\) 4.96334 0.466911 0.233456 0.972367i \(-0.424997\pi\)
0.233456 + 0.972367i \(0.424997\pi\)
\(114\) 0 0
\(115\) 9.37775 0.874480
\(116\) 0 0
\(117\) −3.05676 −0.282597
\(118\) 0 0
\(119\) 6.31528 0.578920
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −3.96444 −0.357461
\(124\) 0 0
\(125\) 9.84829 0.880858
\(126\) 0 0
\(127\) −14.9712 −1.32848 −0.664240 0.747519i \(-0.731245\pi\)
−0.664240 + 0.747519i \(0.731245\pi\)
\(128\) 0 0
\(129\) −24.0761 −2.11978
\(130\) 0 0
\(131\) 15.3791 1.34368 0.671838 0.740698i \(-0.265505\pi\)
0.671838 + 0.740698i \(0.265505\pi\)
\(132\) 0 0
\(133\) −1.83477 −0.159095
\(134\) 0 0
\(135\) −0.157642 −0.0135676
\(136\) 0 0
\(137\) −12.0238 −1.02726 −0.513632 0.858010i \(-0.671700\pi\)
−0.513632 + 0.858010i \(0.671700\pi\)
\(138\) 0 0
\(139\) 20.9661 1.77832 0.889162 0.457593i \(-0.151288\pi\)
0.889162 + 0.457593i \(0.151288\pi\)
\(140\) 0 0
\(141\) 8.61462 0.725482
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 8.63112 0.716775
\(146\) 0 0
\(147\) 2.46105 0.202984
\(148\) 0 0
\(149\) −14.6526 −1.20039 −0.600195 0.799854i \(-0.704910\pi\)
−0.600195 + 0.799854i \(0.704910\pi\)
\(150\) 0 0
\(151\) 13.0826 1.06465 0.532323 0.846542i \(-0.321319\pi\)
0.532323 + 0.846542i \(0.321319\pi\)
\(152\) 0 0
\(153\) 19.3043 1.56066
\(154\) 0 0
\(155\) 6.57198 0.527874
\(156\) 0 0
\(157\) −1.44812 −0.115572 −0.0577862 0.998329i \(-0.518404\pi\)
−0.0577862 + 0.998329i \(0.518404\pi\)
\(158\) 0 0
\(159\) 26.3075 2.08632
\(160\) 0 0
\(161\) −8.30939 −0.654872
\(162\) 0 0
\(163\) 6.97261 0.546137 0.273069 0.961995i \(-0.411961\pi\)
0.273069 + 0.961995i \(0.411961\pi\)
\(164\) 0 0
\(165\) 2.77747 0.216226
\(166\) 0 0
\(167\) 5.02380 0.388754 0.194377 0.980927i \(-0.437732\pi\)
0.194377 + 0.980927i \(0.437732\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.60846 −0.428890
\(172\) 0 0
\(173\) −12.1426 −0.923184 −0.461592 0.887092i \(-0.652722\pi\)
−0.461592 + 0.887092i \(0.652722\pi\)
\(174\) 0 0
\(175\) −3.72632 −0.281684
\(176\) 0 0
\(177\) −28.3378 −2.13000
\(178\) 0 0
\(179\) −6.10770 −0.456511 −0.228255 0.973601i \(-0.573302\pi\)
−0.228255 + 0.973601i \(0.573302\pi\)
\(180\) 0 0
\(181\) 9.69721 0.720788 0.360394 0.932800i \(-0.382642\pi\)
0.360394 + 0.932800i \(0.382642\pi\)
\(182\) 0 0
\(183\) 17.9075 1.32376
\(184\) 0 0
\(185\) −4.95361 −0.364197
\(186\) 0 0
\(187\) −6.31528 −0.461819
\(188\) 0 0
\(189\) 0.139682 0.0101604
\(190\) 0 0
\(191\) −9.52272 −0.689040 −0.344520 0.938779i \(-0.611958\pi\)
−0.344520 + 0.938779i \(0.611958\pi\)
\(192\) 0 0
\(193\) −10.1215 −0.728564 −0.364282 0.931289i \(-0.618686\pi\)
−0.364282 + 0.931289i \(0.618686\pi\)
\(194\) 0 0
\(195\) 2.77747 0.198899
\(196\) 0 0
\(197\) −7.40852 −0.527835 −0.263917 0.964545i \(-0.585015\pi\)
−0.263917 + 0.964545i \(0.585015\pi\)
\(198\) 0 0
\(199\) −3.83670 −0.271977 −0.135988 0.990710i \(-0.543421\pi\)
−0.135988 + 0.990710i \(0.543421\pi\)
\(200\) 0 0
\(201\) −25.9366 −1.82943
\(202\) 0 0
\(203\) −7.64782 −0.536771
\(204\) 0 0
\(205\) 1.81799 0.126974
\(206\) 0 0
\(207\) −25.3998 −1.76541
\(208\) 0 0
\(209\) 1.83477 0.126914
\(210\) 0 0
\(211\) −5.48435 −0.377558 −0.188779 0.982020i \(-0.560453\pi\)
−0.188779 + 0.982020i \(0.560453\pi\)
\(212\) 0 0
\(213\) 32.6402 2.23647
\(214\) 0 0
\(215\) 11.0407 0.752967
\(216\) 0 0
\(217\) −5.82327 −0.395309
\(218\) 0 0
\(219\) −36.1756 −2.44452
\(220\) 0 0
\(221\) −6.31528 −0.424811
\(222\) 0 0
\(223\) 10.6506 0.713219 0.356610 0.934254i \(-0.383933\pi\)
0.356610 + 0.934254i \(0.383933\pi\)
\(224\) 0 0
\(225\) −11.3905 −0.759364
\(226\) 0 0
\(227\) −18.0320 −1.19682 −0.598412 0.801189i \(-0.704201\pi\)
−0.598412 + 0.801189i \(0.704201\pi\)
\(228\) 0 0
\(229\) 5.70503 0.376999 0.188499 0.982073i \(-0.439638\pi\)
0.188499 + 0.982073i \(0.439638\pi\)
\(230\) 0 0
\(231\) −2.46105 −0.161925
\(232\) 0 0
\(233\) 2.49616 0.163529 0.0817645 0.996652i \(-0.473944\pi\)
0.0817645 + 0.996652i \(0.473944\pi\)
\(234\) 0 0
\(235\) −3.95044 −0.257698
\(236\) 0 0
\(237\) −21.8438 −1.41891
\(238\) 0 0
\(239\) −7.30917 −0.472791 −0.236395 0.971657i \(-0.575966\pi\)
−0.236395 + 0.971657i \(0.575966\pi\)
\(240\) 0 0
\(241\) −2.84554 −0.183297 −0.0916486 0.995791i \(-0.529214\pi\)
−0.0916486 + 0.995791i \(0.529214\pi\)
\(242\) 0 0
\(243\) −22.1415 −1.42038
\(244\) 0 0
\(245\) −1.12857 −0.0721019
\(246\) 0 0
\(247\) 1.83477 0.116744
\(248\) 0 0
\(249\) −36.2357 −2.29635
\(250\) 0 0
\(251\) −4.21343 −0.265949 −0.132975 0.991119i \(-0.542453\pi\)
−0.132975 + 0.991119i \(0.542453\pi\)
\(252\) 0 0
\(253\) 8.30939 0.522407
\(254\) 0 0
\(255\) −17.5405 −1.09843
\(256\) 0 0
\(257\) 7.22890 0.450926 0.225463 0.974252i \(-0.427610\pi\)
0.225463 + 0.974252i \(0.427610\pi\)
\(258\) 0 0
\(259\) 4.38927 0.272736
\(260\) 0 0
\(261\) −23.3775 −1.44703
\(262\) 0 0
\(263\) 31.2574 1.92742 0.963708 0.266957i \(-0.0860183\pi\)
0.963708 + 0.266957i \(0.0860183\pi\)
\(264\) 0 0
\(265\) −12.0639 −0.741080
\(266\) 0 0
\(267\) 14.1766 0.867593
\(268\) 0 0
\(269\) −6.79410 −0.414244 −0.207122 0.978315i \(-0.566410\pi\)
−0.207122 + 0.978315i \(0.566410\pi\)
\(270\) 0 0
\(271\) 3.25998 0.198029 0.0990147 0.995086i \(-0.468431\pi\)
0.0990147 + 0.995086i \(0.468431\pi\)
\(272\) 0 0
\(273\) −2.46105 −0.148949
\(274\) 0 0
\(275\) 3.72632 0.224706
\(276\) 0 0
\(277\) −2.94766 −0.177108 −0.0885539 0.996071i \(-0.528225\pi\)
−0.0885539 + 0.996071i \(0.528225\pi\)
\(278\) 0 0
\(279\) −17.8003 −1.06568
\(280\) 0 0
\(281\) 10.4355 0.622528 0.311264 0.950323i \(-0.399248\pi\)
0.311264 + 0.950323i \(0.399248\pi\)
\(282\) 0 0
\(283\) 21.3817 1.27101 0.635505 0.772097i \(-0.280792\pi\)
0.635505 + 0.772097i \(0.280792\pi\)
\(284\) 0 0
\(285\) 5.09603 0.301863
\(286\) 0 0
\(287\) −1.61087 −0.0950868
\(288\) 0 0
\(289\) 22.8827 1.34604
\(290\) 0 0
\(291\) −19.4009 −1.13730
\(292\) 0 0
\(293\) 1.12807 0.0659025 0.0329512 0.999457i \(-0.489509\pi\)
0.0329512 + 0.999457i \(0.489509\pi\)
\(294\) 0 0
\(295\) 12.9950 0.756597
\(296\) 0 0
\(297\) −0.139682 −0.00810520
\(298\) 0 0
\(299\) 8.30939 0.480545
\(300\) 0 0
\(301\) −9.78285 −0.563874
\(302\) 0 0
\(303\) 28.7794 1.65333
\(304\) 0 0
\(305\) −8.21193 −0.470214
\(306\) 0 0
\(307\) 17.8790 1.02041 0.510206 0.860052i \(-0.329569\pi\)
0.510206 + 0.860052i \(0.329569\pi\)
\(308\) 0 0
\(309\) 35.1734 2.00094
\(310\) 0 0
\(311\) −15.2644 −0.865563 −0.432782 0.901499i \(-0.642468\pi\)
−0.432782 + 0.901499i \(0.642468\pi\)
\(312\) 0 0
\(313\) 11.7555 0.664459 0.332230 0.943199i \(-0.392199\pi\)
0.332230 + 0.943199i \(0.392199\pi\)
\(314\) 0 0
\(315\) −3.44977 −0.194373
\(316\) 0 0
\(317\) −33.0135 −1.85422 −0.927110 0.374789i \(-0.877715\pi\)
−0.927110 + 0.374789i \(0.877715\pi\)
\(318\) 0 0
\(319\) 7.64782 0.428195
\(320\) 0 0
\(321\) −43.5016 −2.42802
\(322\) 0 0
\(323\) −11.5871 −0.644724
\(324\) 0 0
\(325\) 3.72632 0.206699
\(326\) 0 0
\(327\) 33.9079 1.87511
\(328\) 0 0
\(329\) 3.50039 0.192982
\(330\) 0 0
\(331\) −22.1492 −1.21743 −0.608714 0.793390i \(-0.708314\pi\)
−0.608714 + 0.793390i \(0.708314\pi\)
\(332\) 0 0
\(333\) 13.4169 0.735244
\(334\) 0 0
\(335\) 11.8938 0.649830
\(336\) 0 0
\(337\) 25.1041 1.36751 0.683755 0.729712i \(-0.260346\pi\)
0.683755 + 0.729712i \(0.260346\pi\)
\(338\) 0 0
\(339\) 12.2150 0.663428
\(340\) 0 0
\(341\) 5.82327 0.315348
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 23.0791 1.24254
\(346\) 0 0
\(347\) −24.0730 −1.29230 −0.646152 0.763209i \(-0.723623\pi\)
−0.646152 + 0.763209i \(0.723623\pi\)
\(348\) 0 0
\(349\) −19.3655 −1.03661 −0.518307 0.855195i \(-0.673437\pi\)
−0.518307 + 0.855195i \(0.673437\pi\)
\(350\) 0 0
\(351\) −0.139682 −0.00745570
\(352\) 0 0
\(353\) −5.02927 −0.267681 −0.133840 0.991003i \(-0.542731\pi\)
−0.133840 + 0.991003i \(0.542731\pi\)
\(354\) 0 0
\(355\) −14.9679 −0.794415
\(356\) 0 0
\(357\) 15.5422 0.822580
\(358\) 0 0
\(359\) −6.30526 −0.332779 −0.166389 0.986060i \(-0.553211\pi\)
−0.166389 + 0.986060i \(0.553211\pi\)
\(360\) 0 0
\(361\) −15.6336 −0.822821
\(362\) 0 0
\(363\) 2.46105 0.129172
\(364\) 0 0
\(365\) 16.5892 0.868317
\(366\) 0 0
\(367\) −2.60896 −0.136187 −0.0680933 0.997679i \(-0.521692\pi\)
−0.0680933 + 0.997679i \(0.521692\pi\)
\(368\) 0 0
\(369\) −4.92405 −0.256336
\(370\) 0 0
\(371\) 10.6895 0.554973
\(372\) 0 0
\(373\) 10.2717 0.531848 0.265924 0.963994i \(-0.414323\pi\)
0.265924 + 0.963994i \(0.414323\pi\)
\(374\) 0 0
\(375\) 24.2371 1.25160
\(376\) 0 0
\(377\) 7.64782 0.393883
\(378\) 0 0
\(379\) −25.4041 −1.30492 −0.652460 0.757823i \(-0.726263\pi\)
−0.652460 + 0.757823i \(0.726263\pi\)
\(380\) 0 0
\(381\) −36.8449 −1.88762
\(382\) 0 0
\(383\) −18.2432 −0.932183 −0.466092 0.884736i \(-0.654338\pi\)
−0.466092 + 0.884736i \(0.654338\pi\)
\(384\) 0 0
\(385\) 1.12857 0.0575174
\(386\) 0 0
\(387\) −29.9038 −1.52010
\(388\) 0 0
\(389\) −34.2961 −1.73888 −0.869441 0.494038i \(-0.835520\pi\)
−0.869441 + 0.494038i \(0.835520\pi\)
\(390\) 0 0
\(391\) −52.4761 −2.65383
\(392\) 0 0
\(393\) 37.8487 1.90921
\(394\) 0 0
\(395\) 10.0170 0.504011
\(396\) 0 0
\(397\) −4.69756 −0.235764 −0.117882 0.993028i \(-0.537610\pi\)
−0.117882 + 0.993028i \(0.537610\pi\)
\(398\) 0 0
\(399\) −4.51547 −0.226056
\(400\) 0 0
\(401\) −16.7387 −0.835889 −0.417944 0.908473i \(-0.637249\pi\)
−0.417944 + 0.908473i \(0.637249\pi\)
\(402\) 0 0
\(403\) 5.82327 0.290078
\(404\) 0 0
\(405\) 9.96135 0.494984
\(406\) 0 0
\(407\) −4.38927 −0.217568
\(408\) 0 0
\(409\) −34.0983 −1.68605 −0.843027 0.537871i \(-0.819229\pi\)
−0.843027 + 0.537871i \(0.819229\pi\)
\(410\) 0 0
\(411\) −29.5912 −1.45963
\(412\) 0 0
\(413\) −11.5145 −0.566593
\(414\) 0 0
\(415\) 16.6168 0.815685
\(416\) 0 0
\(417\) 51.5986 2.52680
\(418\) 0 0
\(419\) −18.3810 −0.897971 −0.448985 0.893539i \(-0.648214\pi\)
−0.448985 + 0.893539i \(0.648214\pi\)
\(420\) 0 0
\(421\) 6.61356 0.322325 0.161163 0.986928i \(-0.448476\pi\)
0.161163 + 0.986928i \(0.448476\pi\)
\(422\) 0 0
\(423\) 10.6998 0.520243
\(424\) 0 0
\(425\) −23.5328 −1.14151
\(426\) 0 0
\(427\) 7.27639 0.352129
\(428\) 0 0
\(429\) 2.46105 0.118821
\(430\) 0 0
\(431\) 35.9318 1.73077 0.865386 0.501105i \(-0.167073\pi\)
0.865386 + 0.501105i \(0.167073\pi\)
\(432\) 0 0
\(433\) −3.63283 −0.174583 −0.0872913 0.996183i \(-0.527821\pi\)
−0.0872913 + 0.996183i \(0.527821\pi\)
\(434\) 0 0
\(435\) 21.2416 1.01846
\(436\) 0 0
\(437\) 15.2459 0.729308
\(438\) 0 0
\(439\) 39.0982 1.86606 0.933028 0.359804i \(-0.117156\pi\)
0.933028 + 0.359804i \(0.117156\pi\)
\(440\) 0 0
\(441\) 3.05676 0.145560
\(442\) 0 0
\(443\) −9.86352 −0.468630 −0.234315 0.972161i \(-0.575285\pi\)
−0.234315 + 0.972161i \(0.575285\pi\)
\(444\) 0 0
\(445\) −6.50102 −0.308178
\(446\) 0 0
\(447\) −36.0608 −1.70562
\(448\) 0 0
\(449\) 29.8132 1.40697 0.703487 0.710708i \(-0.251625\pi\)
0.703487 + 0.710708i \(0.251625\pi\)
\(450\) 0 0
\(451\) 1.61087 0.0758531
\(452\) 0 0
\(453\) 32.1969 1.51274
\(454\) 0 0
\(455\) 1.12857 0.0529083
\(456\) 0 0
\(457\) 15.6736 0.733178 0.366589 0.930383i \(-0.380526\pi\)
0.366589 + 0.930383i \(0.380526\pi\)
\(458\) 0 0
\(459\) 0.882133 0.0411745
\(460\) 0 0
\(461\) 1.65607 0.0771310 0.0385655 0.999256i \(-0.487721\pi\)
0.0385655 + 0.999256i \(0.487721\pi\)
\(462\) 0 0
\(463\) −35.6461 −1.65661 −0.828306 0.560276i \(-0.810695\pi\)
−0.828306 + 0.560276i \(0.810695\pi\)
\(464\) 0 0
\(465\) 16.1740 0.750049
\(466\) 0 0
\(467\) 22.2596 1.03005 0.515025 0.857175i \(-0.327783\pi\)
0.515025 + 0.857175i \(0.327783\pi\)
\(468\) 0 0
\(469\) −10.5388 −0.486638
\(470\) 0 0
\(471\) −3.56388 −0.164215
\(472\) 0 0
\(473\) 9.78285 0.449816
\(474\) 0 0
\(475\) 6.83696 0.313701
\(476\) 0 0
\(477\) 32.6753 1.49610
\(478\) 0 0
\(479\) −17.2604 −0.788647 −0.394323 0.918972i \(-0.629021\pi\)
−0.394323 + 0.918972i \(0.629021\pi\)
\(480\) 0 0
\(481\) −4.38927 −0.200134
\(482\) 0 0
\(483\) −20.4498 −0.930499
\(484\) 0 0
\(485\) 8.89675 0.403981
\(486\) 0 0
\(487\) −21.1130 −0.956722 −0.478361 0.878163i \(-0.658769\pi\)
−0.478361 + 0.878163i \(0.658769\pi\)
\(488\) 0 0
\(489\) 17.1599 0.775999
\(490\) 0 0
\(491\) 10.9835 0.495678 0.247839 0.968801i \(-0.420280\pi\)
0.247839 + 0.968801i \(0.420280\pi\)
\(492\) 0 0
\(493\) −48.2981 −2.17524
\(494\) 0 0
\(495\) 3.44977 0.155056
\(496\) 0 0
\(497\) 13.2627 0.594914
\(498\) 0 0
\(499\) 19.7724 0.885132 0.442566 0.896736i \(-0.354068\pi\)
0.442566 + 0.896736i \(0.354068\pi\)
\(500\) 0 0
\(501\) 12.3638 0.552375
\(502\) 0 0
\(503\) 17.2151 0.767582 0.383791 0.923420i \(-0.374618\pi\)
0.383791 + 0.923420i \(0.374618\pi\)
\(504\) 0 0
\(505\) −13.1975 −0.587281
\(506\) 0 0
\(507\) 2.46105 0.109299
\(508\) 0 0
\(509\) −32.2352 −1.42880 −0.714400 0.699738i \(-0.753300\pi\)
−0.714400 + 0.699738i \(0.753300\pi\)
\(510\) 0 0
\(511\) −14.6993 −0.650257
\(512\) 0 0
\(513\) −0.256286 −0.0113153
\(514\) 0 0
\(515\) −16.1296 −0.710755
\(516\) 0 0
\(517\) −3.50039 −0.153947
\(518\) 0 0
\(519\) −29.8835 −1.31174
\(520\) 0 0
\(521\) 12.4244 0.544325 0.272162 0.962251i \(-0.412261\pi\)
0.272162 + 0.962251i \(0.412261\pi\)
\(522\) 0 0
\(523\) −14.8783 −0.650582 −0.325291 0.945614i \(-0.605462\pi\)
−0.325291 + 0.945614i \(0.605462\pi\)
\(524\) 0 0
\(525\) −9.17066 −0.400240
\(526\) 0 0
\(527\) −36.7755 −1.60197
\(528\) 0 0
\(529\) 46.0460 2.00200
\(530\) 0 0
\(531\) −35.1971 −1.52743
\(532\) 0 0
\(533\) 1.61087 0.0697747
\(534\) 0 0
\(535\) 19.9487 0.862457
\(536\) 0 0
\(537\) −15.0313 −0.648650
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 11.0299 0.474212 0.237106 0.971484i \(-0.423801\pi\)
0.237106 + 0.971484i \(0.423801\pi\)
\(542\) 0 0
\(543\) 23.8653 1.02416
\(544\) 0 0
\(545\) −15.5493 −0.666057
\(546\) 0 0
\(547\) −18.1982 −0.778101 −0.389050 0.921217i \(-0.627197\pi\)
−0.389050 + 0.921217i \(0.627197\pi\)
\(548\) 0 0
\(549\) 22.2422 0.949272
\(550\) 0 0
\(551\) 14.0320 0.597784
\(552\) 0 0
\(553\) −8.87583 −0.377439
\(554\) 0 0
\(555\) −12.1911 −0.517482
\(556\) 0 0
\(557\) 20.7801 0.880483 0.440241 0.897879i \(-0.354893\pi\)
0.440241 + 0.897879i \(0.354893\pi\)
\(558\) 0 0
\(559\) 9.78285 0.413771
\(560\) 0 0
\(561\) −15.5422 −0.656192
\(562\) 0 0
\(563\) −6.41182 −0.270226 −0.135113 0.990830i \(-0.543140\pi\)
−0.135113 + 0.990830i \(0.543140\pi\)
\(564\) 0 0
\(565\) −5.60149 −0.235656
\(566\) 0 0
\(567\) −8.82651 −0.370678
\(568\) 0 0
\(569\) 42.0250 1.76178 0.880889 0.473323i \(-0.156946\pi\)
0.880889 + 0.473323i \(0.156946\pi\)
\(570\) 0 0
\(571\) 21.9071 0.916785 0.458393 0.888750i \(-0.348425\pi\)
0.458393 + 0.888750i \(0.348425\pi\)
\(572\) 0 0
\(573\) −23.4359 −0.979048
\(574\) 0 0
\(575\) 30.9635 1.29127
\(576\) 0 0
\(577\) 23.2586 0.968269 0.484134 0.874994i \(-0.339135\pi\)
0.484134 + 0.874994i \(0.339135\pi\)
\(578\) 0 0
\(579\) −24.9096 −1.03521
\(580\) 0 0
\(581\) −14.7237 −0.610842
\(582\) 0 0
\(583\) −10.6895 −0.442715
\(584\) 0 0
\(585\) 3.44977 0.142631
\(586\) 0 0
\(587\) −30.4207 −1.25560 −0.627799 0.778375i \(-0.716044\pi\)
−0.627799 + 0.778375i \(0.716044\pi\)
\(588\) 0 0
\(589\) 10.6844 0.440242
\(590\) 0 0
\(591\) −18.2327 −0.749994
\(592\) 0 0
\(593\) 20.5517 0.843957 0.421979 0.906606i \(-0.361336\pi\)
0.421979 + 0.906606i \(0.361336\pi\)
\(594\) 0 0
\(595\) −7.12725 −0.292189
\(596\) 0 0
\(597\) −9.44231 −0.386448
\(598\) 0 0
\(599\) −3.38583 −0.138341 −0.0691707 0.997605i \(-0.522035\pi\)
−0.0691707 + 0.997605i \(0.522035\pi\)
\(600\) 0 0
\(601\) 33.7434 1.37642 0.688211 0.725511i \(-0.258396\pi\)
0.688211 + 0.725511i \(0.258396\pi\)
\(602\) 0 0
\(603\) −32.2147 −1.31188
\(604\) 0 0
\(605\) −1.12857 −0.0458830
\(606\) 0 0
\(607\) 26.2209 1.06427 0.532137 0.846658i \(-0.321389\pi\)
0.532137 + 0.846658i \(0.321389\pi\)
\(608\) 0 0
\(609\) −18.8216 −0.762691
\(610\) 0 0
\(611\) −3.50039 −0.141610
\(612\) 0 0
\(613\) 17.1368 0.692149 0.346075 0.938207i \(-0.387514\pi\)
0.346075 + 0.938207i \(0.387514\pi\)
\(614\) 0 0
\(615\) 4.47415 0.180415
\(616\) 0 0
\(617\) −28.7678 −1.15815 −0.579074 0.815275i \(-0.696586\pi\)
−0.579074 + 0.815275i \(0.696586\pi\)
\(618\) 0 0
\(619\) −4.70624 −0.189160 −0.0945800 0.995517i \(-0.530151\pi\)
−0.0945800 + 0.995517i \(0.530151\pi\)
\(620\) 0 0
\(621\) −1.16068 −0.0465763
\(622\) 0 0
\(623\) 5.76039 0.230785
\(624\) 0 0
\(625\) 7.51711 0.300684
\(626\) 0 0
\(627\) 4.51547 0.180330
\(628\) 0 0
\(629\) 27.7195 1.10525
\(630\) 0 0
\(631\) −9.62586 −0.383199 −0.191600 0.981473i \(-0.561368\pi\)
−0.191600 + 0.981473i \(0.561368\pi\)
\(632\) 0 0
\(633\) −13.4972 −0.536467
\(634\) 0 0
\(635\) 16.8961 0.670501
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 40.5409 1.60377
\(640\) 0 0
\(641\) −3.47126 −0.137107 −0.0685534 0.997647i \(-0.521838\pi\)
−0.0685534 + 0.997647i \(0.521838\pi\)
\(642\) 0 0
\(643\) 12.9442 0.510470 0.255235 0.966879i \(-0.417847\pi\)
0.255235 + 0.966879i \(0.417847\pi\)
\(644\) 0 0
\(645\) 27.1716 1.06988
\(646\) 0 0
\(647\) −23.2745 −0.915016 −0.457508 0.889206i \(-0.651258\pi\)
−0.457508 + 0.889206i \(0.651258\pi\)
\(648\) 0 0
\(649\) 11.5145 0.451985
\(650\) 0 0
\(651\) −14.3313 −0.561689
\(652\) 0 0
\(653\) 17.5041 0.684987 0.342493 0.939520i \(-0.388729\pi\)
0.342493 + 0.939520i \(0.388729\pi\)
\(654\) 0 0
\(655\) −17.3564 −0.678171
\(656\) 0 0
\(657\) −44.9320 −1.75297
\(658\) 0 0
\(659\) −9.94490 −0.387398 −0.193699 0.981061i \(-0.562049\pi\)
−0.193699 + 0.981061i \(0.562049\pi\)
\(660\) 0 0
\(661\) 13.0326 0.506908 0.253454 0.967347i \(-0.418433\pi\)
0.253454 + 0.967347i \(0.418433\pi\)
\(662\) 0 0
\(663\) −15.5422 −0.603609
\(664\) 0 0
\(665\) 2.07068 0.0802974
\(666\) 0 0
\(667\) 63.5487 2.46062
\(668\) 0 0
\(669\) 26.2117 1.01340
\(670\) 0 0
\(671\) −7.27639 −0.280902
\(672\) 0 0
\(673\) −34.6008 −1.33376 −0.666881 0.745165i \(-0.732371\pi\)
−0.666881 + 0.745165i \(0.732371\pi\)
\(674\) 0 0
\(675\) −0.520502 −0.0200341
\(676\) 0 0
\(677\) −31.3813 −1.20608 −0.603040 0.797711i \(-0.706044\pi\)
−0.603040 + 0.797711i \(0.706044\pi\)
\(678\) 0 0
\(679\) −7.88319 −0.302529
\(680\) 0 0
\(681\) −44.3775 −1.70055
\(682\) 0 0
\(683\) 8.50776 0.325540 0.162770 0.986664i \(-0.447957\pi\)
0.162770 + 0.986664i \(0.447957\pi\)
\(684\) 0 0
\(685\) 13.5698 0.518474
\(686\) 0 0
\(687\) 14.0403 0.535673
\(688\) 0 0
\(689\) −10.6895 −0.407239
\(690\) 0 0
\(691\) 33.2712 1.26570 0.632848 0.774276i \(-0.281886\pi\)
0.632848 + 0.774276i \(0.281886\pi\)
\(692\) 0 0
\(693\) −3.05676 −0.116117
\(694\) 0 0
\(695\) −23.6618 −0.897543
\(696\) 0 0
\(697\) −10.1731 −0.385334
\(698\) 0 0
\(699\) 6.14317 0.232356
\(700\) 0 0
\(701\) 49.2054 1.85846 0.929231 0.369500i \(-0.120471\pi\)
0.929231 + 0.369500i \(0.120471\pi\)
\(702\) 0 0
\(703\) −8.05332 −0.303737
\(704\) 0 0
\(705\) −9.72222 −0.366160
\(706\) 0 0
\(707\) 11.6940 0.439797
\(708\) 0 0
\(709\) −25.3934 −0.953671 −0.476835 0.878993i \(-0.658216\pi\)
−0.476835 + 0.878993i \(0.658216\pi\)
\(710\) 0 0
\(711\) −27.1313 −1.01750
\(712\) 0 0
\(713\) 48.3878 1.81214
\(714\) 0 0
\(715\) −1.12857 −0.0422062
\(716\) 0 0
\(717\) −17.9882 −0.671782
\(718\) 0 0
\(719\) −4.03613 −0.150522 −0.0752611 0.997164i \(-0.523979\pi\)
−0.0752611 + 0.997164i \(0.523979\pi\)
\(720\) 0 0
\(721\) 14.2920 0.532263
\(722\) 0 0
\(723\) −7.00300 −0.260444
\(724\) 0 0
\(725\) 28.4982 1.05840
\(726\) 0 0
\(727\) 36.8804 1.36782 0.683909 0.729567i \(-0.260279\pi\)
0.683909 + 0.729567i \(0.260279\pi\)
\(728\) 0 0
\(729\) −28.0118 −1.03747
\(730\) 0 0
\(731\) −61.7814 −2.28507
\(732\) 0 0
\(733\) 46.0408 1.70056 0.850278 0.526334i \(-0.176434\pi\)
0.850278 + 0.526334i \(0.176434\pi\)
\(734\) 0 0
\(735\) −2.77747 −0.102449
\(736\) 0 0
\(737\) 10.5388 0.388203
\(738\) 0 0
\(739\) −33.7700 −1.24225 −0.621124 0.783712i \(-0.713324\pi\)
−0.621124 + 0.783712i \(0.713324\pi\)
\(740\) 0 0
\(741\) 4.51547 0.165880
\(742\) 0 0
\(743\) −32.8431 −1.20490 −0.602448 0.798158i \(-0.705808\pi\)
−0.602448 + 0.798158i \(0.705808\pi\)
\(744\) 0 0
\(745\) 16.5366 0.605853
\(746\) 0 0
\(747\) −45.0068 −1.64671
\(748\) 0 0
\(749\) −17.6760 −0.645868
\(750\) 0 0
\(751\) −44.4424 −1.62172 −0.810862 0.585237i \(-0.801001\pi\)
−0.810862 + 0.585237i \(0.801001\pi\)
\(752\) 0 0
\(753\) −10.3694 −0.377883
\(754\) 0 0
\(755\) −14.7646 −0.537340
\(756\) 0 0
\(757\) 1.68206 0.0611357 0.0305678 0.999533i \(-0.490268\pi\)
0.0305678 + 0.999533i \(0.490268\pi\)
\(758\) 0 0
\(759\) 20.4498 0.742281
\(760\) 0 0
\(761\) −36.3394 −1.31730 −0.658651 0.752448i \(-0.728873\pi\)
−0.658651 + 0.752448i \(0.728873\pi\)
\(762\) 0 0
\(763\) 13.7778 0.498790
\(764\) 0 0
\(765\) −21.7863 −0.787684
\(766\) 0 0
\(767\) 11.5145 0.415766
\(768\) 0 0
\(769\) −1.81762 −0.0655449 −0.0327725 0.999463i \(-0.510434\pi\)
−0.0327725 + 0.999463i \(0.510434\pi\)
\(770\) 0 0
\(771\) 17.7907 0.640715
\(772\) 0 0
\(773\) −24.7208 −0.889146 −0.444573 0.895743i \(-0.646645\pi\)
−0.444573 + 0.895743i \(0.646645\pi\)
\(774\) 0 0
\(775\) 21.6994 0.779465
\(776\) 0 0
\(777\) 10.8022 0.387527
\(778\) 0 0
\(779\) 2.95559 0.105895
\(780\) 0 0
\(781\) −13.2627 −0.474577
\(782\) 0 0
\(783\) −1.06827 −0.0381767
\(784\) 0 0
\(785\) 1.63431 0.0583308
\(786\) 0 0
\(787\) 30.5597 1.08933 0.544667 0.838652i \(-0.316656\pi\)
0.544667 + 0.838652i \(0.316656\pi\)
\(788\) 0 0
\(789\) 76.9261 2.73864
\(790\) 0 0
\(791\) 4.96334 0.176476
\(792\) 0 0
\(793\) −7.27639 −0.258392
\(794\) 0 0
\(795\) −29.6899 −1.05299
\(796\) 0 0
\(797\) 45.7590 1.62087 0.810433 0.585831i \(-0.199232\pi\)
0.810433 + 0.585831i \(0.199232\pi\)
\(798\) 0 0
\(799\) 22.1059 0.782050
\(800\) 0 0
\(801\) 17.6081 0.622152
\(802\) 0 0
\(803\) 14.6993 0.518725
\(804\) 0 0
\(805\) 9.37775 0.330522
\(806\) 0 0
\(807\) −16.7206 −0.588593
\(808\) 0 0
\(809\) −16.5329 −0.581264 −0.290632 0.956835i \(-0.593866\pi\)
−0.290632 + 0.956835i \(0.593866\pi\)
\(810\) 0 0
\(811\) −5.39570 −0.189469 −0.0947343 0.995503i \(-0.530200\pi\)
−0.0947343 + 0.995503i \(0.530200\pi\)
\(812\) 0 0
\(813\) 8.02296 0.281377
\(814\) 0 0
\(815\) −7.86910 −0.275643
\(816\) 0 0
\(817\) 17.9493 0.627967
\(818\) 0 0
\(819\) −3.05676 −0.106812
\(820\) 0 0
\(821\) −0.478489 −0.0166994 −0.00834969 0.999965i \(-0.502658\pi\)
−0.00834969 + 0.999965i \(0.502658\pi\)
\(822\) 0 0
\(823\) 6.60949 0.230392 0.115196 0.993343i \(-0.463250\pi\)
0.115196 + 0.993343i \(0.463250\pi\)
\(824\) 0 0
\(825\) 9.17066 0.319281
\(826\) 0 0
\(827\) 12.3810 0.430530 0.215265 0.976556i \(-0.430938\pi\)
0.215265 + 0.976556i \(0.430938\pi\)
\(828\) 0 0
\(829\) −22.0788 −0.766830 −0.383415 0.923576i \(-0.625252\pi\)
−0.383415 + 0.923576i \(0.625252\pi\)
\(830\) 0 0
\(831\) −7.25434 −0.251650
\(832\) 0 0
\(833\) 6.31528 0.218811
\(834\) 0 0
\(835\) −5.66973 −0.196209
\(836\) 0 0
\(837\) −0.813408 −0.0281155
\(838\) 0 0
\(839\) 15.8007 0.545500 0.272750 0.962085i \(-0.412067\pi\)
0.272750 + 0.962085i \(0.412067\pi\)
\(840\) 0 0
\(841\) 29.4891 1.01687
\(842\) 0 0
\(843\) 25.6822 0.884542
\(844\) 0 0
\(845\) −1.12857 −0.0388241
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 52.6214 1.80596
\(850\) 0 0
\(851\) −36.4722 −1.25025
\(852\) 0 0
\(853\) −43.5280 −1.49037 −0.745185 0.666858i \(-0.767639\pi\)
−0.745185 + 0.666858i \(0.767639\pi\)
\(854\) 0 0
\(855\) 6.32955 0.216466
\(856\) 0 0
\(857\) −6.61496 −0.225963 −0.112981 0.993597i \(-0.536040\pi\)
−0.112981 + 0.993597i \(0.536040\pi\)
\(858\) 0 0
\(859\) −5.55129 −0.189408 −0.0947038 0.995505i \(-0.530190\pi\)
−0.0947038 + 0.995505i \(0.530190\pi\)
\(860\) 0 0
\(861\) −3.96444 −0.135108
\(862\) 0 0
\(863\) −12.8522 −0.437495 −0.218748 0.975781i \(-0.570197\pi\)
−0.218748 + 0.975781i \(0.570197\pi\)
\(864\) 0 0
\(865\) 13.7038 0.465943
\(866\) 0 0
\(867\) 56.3155 1.91257
\(868\) 0 0
\(869\) 8.87583 0.301092
\(870\) 0 0
\(871\) 10.5388 0.357095
\(872\) 0 0
\(873\) −24.0970 −0.815560
\(874\) 0 0
\(875\) 9.84829 0.332933
\(876\) 0 0
\(877\) −33.9578 −1.14667 −0.573337 0.819320i \(-0.694351\pi\)
−0.573337 + 0.819320i \(0.694351\pi\)
\(878\) 0 0
\(879\) 2.77623 0.0936399
\(880\) 0 0
\(881\) 39.7693 1.33986 0.669931 0.742423i \(-0.266324\pi\)
0.669931 + 0.742423i \(0.266324\pi\)
\(882\) 0 0
\(883\) 50.8579 1.71150 0.855752 0.517387i \(-0.173095\pi\)
0.855752 + 0.517387i \(0.173095\pi\)
\(884\) 0 0
\(885\) 31.9813 1.07504
\(886\) 0 0
\(887\) −19.6392 −0.659421 −0.329711 0.944082i \(-0.606951\pi\)
−0.329711 + 0.944082i \(0.606951\pi\)
\(888\) 0 0
\(889\) −14.9712 −0.502118
\(890\) 0 0
\(891\) 8.82651 0.295699
\(892\) 0 0
\(893\) −6.42241 −0.214918
\(894\) 0 0
\(895\) 6.89298 0.230407
\(896\) 0 0
\(897\) 20.4498 0.682799
\(898\) 0 0
\(899\) 44.5353 1.48533
\(900\) 0 0
\(901\) 67.5073 2.24900
\(902\) 0 0
\(903\) −24.0761 −0.801202
\(904\) 0 0
\(905\) −10.9440 −0.363791
\(906\) 0 0
\(907\) 39.9066 1.32508 0.662539 0.749028i \(-0.269479\pi\)
0.662539 + 0.749028i \(0.269479\pi\)
\(908\) 0 0
\(909\) 35.7456 1.18561
\(910\) 0 0
\(911\) −5.32300 −0.176359 −0.0881794 0.996105i \(-0.528105\pi\)
−0.0881794 + 0.996105i \(0.528105\pi\)
\(912\) 0 0
\(913\) 14.7237 0.487283
\(914\) 0 0
\(915\) −20.2100 −0.668121
\(916\) 0 0
\(917\) 15.3791 0.507862
\(918\) 0 0
\(919\) 24.7182 0.815379 0.407690 0.913121i \(-0.366335\pi\)
0.407690 + 0.913121i \(0.366335\pi\)
\(920\) 0 0
\(921\) 44.0012 1.44989
\(922\) 0 0
\(923\) −13.2627 −0.436547
\(924\) 0 0
\(925\) −16.3558 −0.537777
\(926\) 0 0
\(927\) 43.6873 1.43488
\(928\) 0 0
\(929\) −26.0883 −0.855931 −0.427965 0.903795i \(-0.640769\pi\)
−0.427965 + 0.903795i \(0.640769\pi\)
\(930\) 0 0
\(931\) −1.83477 −0.0601323
\(932\) 0 0
\(933\) −37.5663 −1.22987
\(934\) 0 0
\(935\) 7.12725 0.233086
\(936\) 0 0
\(937\) 0.787111 0.0257138 0.0128569 0.999917i \(-0.495907\pi\)
0.0128569 + 0.999917i \(0.495907\pi\)
\(938\) 0 0
\(939\) 28.9308 0.944122
\(940\) 0 0
\(941\) 2.09811 0.0683964 0.0341982 0.999415i \(-0.489112\pi\)
0.0341982 + 0.999415i \(0.489112\pi\)
\(942\) 0 0
\(943\) 13.3854 0.435888
\(944\) 0 0
\(945\) −0.157642 −0.00512809
\(946\) 0 0
\(947\) −8.80450 −0.286108 −0.143054 0.989715i \(-0.545692\pi\)
−0.143054 + 0.989715i \(0.545692\pi\)
\(948\) 0 0
\(949\) 14.6993 0.477158
\(950\) 0 0
\(951\) −81.2477 −2.63464
\(952\) 0 0
\(953\) 42.1631 1.36580 0.682899 0.730513i \(-0.260719\pi\)
0.682899 + 0.730513i \(0.260719\pi\)
\(954\) 0 0
\(955\) 10.7471 0.347767
\(956\) 0 0
\(957\) 18.8216 0.608417
\(958\) 0 0
\(959\) −12.0238 −0.388270
\(960\) 0 0
\(961\) 2.91044 0.0938850
\(962\) 0 0
\(963\) −54.0314 −1.74114
\(964\) 0 0
\(965\) 11.4229 0.367716
\(966\) 0 0
\(967\) 33.8790 1.08947 0.544737 0.838607i \(-0.316629\pi\)
0.544737 + 0.838607i \(0.316629\pi\)
\(968\) 0 0
\(969\) −28.5164 −0.916079
\(970\) 0 0
\(971\) −3.12178 −0.100183 −0.0500913 0.998745i \(-0.515951\pi\)
−0.0500913 + 0.998745i \(0.515951\pi\)
\(972\) 0 0
\(973\) 20.9661 0.672143
\(974\) 0 0
\(975\) 9.17066 0.293696
\(976\) 0 0
\(977\) −47.2461 −1.51154 −0.755768 0.654840i \(-0.772736\pi\)
−0.755768 + 0.654840i \(0.772736\pi\)
\(978\) 0 0
\(979\) −5.76039 −0.184103
\(980\) 0 0
\(981\) 42.1154 1.34464
\(982\) 0 0
\(983\) 6.17996 0.197110 0.0985551 0.995132i \(-0.468578\pi\)
0.0985551 + 0.995132i \(0.468578\pi\)
\(984\) 0 0
\(985\) 8.36105 0.266405
\(986\) 0 0
\(987\) 8.61462 0.274206
\(988\) 0 0
\(989\) 81.2896 2.58486
\(990\) 0 0
\(991\) −34.3570 −1.09139 −0.545693 0.837985i \(-0.683733\pi\)
−0.545693 + 0.837985i \(0.683733\pi\)
\(992\) 0 0
\(993\) −54.5102 −1.72983
\(994\) 0 0
\(995\) 4.33000 0.137270
\(996\) 0 0
\(997\) −17.6230 −0.558126 −0.279063 0.960273i \(-0.590024\pi\)
−0.279063 + 0.960273i \(0.590024\pi\)
\(998\) 0 0
\(999\) 0.613104 0.0193978
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 \(a_p\))