Properties

Label 8004.2.a.d.1.4
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(3.55127\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.29538 q^{5} +2.07218 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.29538 q^{5} +2.07218 q^{7} +1.00000 q^{9} -3.34522 q^{11} +2.39646 q^{13} -1.29538 q^{15} +4.56989 q^{17} -2.47664 q^{19} +2.07218 q^{21} +1.00000 q^{23} -3.32200 q^{25} +1.00000 q^{27} +1.00000 q^{29} -10.5344 q^{31} -3.34522 q^{33} -2.68425 q^{35} -0.207606 q^{37} +2.39646 q^{39} -8.96963 q^{41} -7.63588 q^{43} -1.29538 q^{45} -0.402401 q^{47} -2.70607 q^{49} +4.56989 q^{51} -11.7012 q^{53} +4.33332 q^{55} -2.47664 q^{57} +3.18505 q^{59} -3.69207 q^{61} +2.07218 q^{63} -3.10431 q^{65} +2.52007 q^{67} +1.00000 q^{69} +8.77089 q^{71} +2.10000 q^{73} -3.32200 q^{75} -6.93191 q^{77} -2.54874 q^{79} +1.00000 q^{81} +4.26686 q^{83} -5.91972 q^{85} +1.00000 q^{87} +11.4643 q^{89} +4.96589 q^{91} -10.5344 q^{93} +3.20818 q^{95} -3.13627 q^{97} -3.34522 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} - 5q^{5} - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 8q + 8q^{3} - 5q^{5} - 4q^{7} + 8q^{9} - 5q^{11} - 4q^{13} - 5q^{15} - 3q^{17} - 5q^{19} - 4q^{21} + 8q^{23} - 5q^{25} + 8q^{27} + 8q^{29} - 2q^{31} - 5q^{33} - 15q^{35} - 10q^{37} - 4q^{39} - 11q^{41} - 7q^{43} - 5q^{45} - 14q^{47} - 18q^{49} - 3q^{51} - 15q^{53} - 17q^{55} - 5q^{57} + 4q^{59} + q^{61} - 4q^{63} - 5q^{67} + 8q^{69} - q^{71} - 21q^{73} - 5q^{75} - 8q^{79} + 8q^{81} + 3q^{83} + 8q^{87} - 20q^{89} - 7q^{91} - 2q^{93} - 3q^{95} - 7q^{97} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.29538 −0.579309 −0.289655 0.957131i \(-0.593540\pi\)
−0.289655 + 0.957131i \(0.593540\pi\)
\(6\) 0 0
\(7\) 2.07218 0.783210 0.391605 0.920133i \(-0.371920\pi\)
0.391605 + 0.920133i \(0.371920\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.34522 −1.00862 −0.504312 0.863522i \(-0.668254\pi\)
−0.504312 + 0.863522i \(0.668254\pi\)
\(12\) 0 0
\(13\) 2.39646 0.664657 0.332329 0.943164i \(-0.392166\pi\)
0.332329 + 0.943164i \(0.392166\pi\)
\(14\) 0 0
\(15\) −1.29538 −0.334464
\(16\) 0 0
\(17\) 4.56989 1.10836 0.554180 0.832397i \(-0.313032\pi\)
0.554180 + 0.832397i \(0.313032\pi\)
\(18\) 0 0
\(19\) −2.47664 −0.568181 −0.284091 0.958797i \(-0.591692\pi\)
−0.284091 + 0.958797i \(0.591692\pi\)
\(20\) 0 0
\(21\) 2.07218 0.452187
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −3.32200 −0.664401
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −10.5344 −1.89204 −0.946018 0.324113i \(-0.894934\pi\)
−0.946018 + 0.324113i \(0.894934\pi\)
\(32\) 0 0
\(33\) −3.34522 −0.582329
\(34\) 0 0
\(35\) −2.68425 −0.453721
\(36\) 0 0
\(37\) −0.207606 −0.0341302 −0.0170651 0.999854i \(-0.505432\pi\)
−0.0170651 + 0.999854i \(0.505432\pi\)
\(38\) 0 0
\(39\) 2.39646 0.383740
\(40\) 0 0
\(41\) −8.96963 −1.40082 −0.700410 0.713740i \(-0.747000\pi\)
−0.700410 + 0.713740i \(0.747000\pi\)
\(42\) 0 0
\(43\) −7.63588 −1.16446 −0.582230 0.813024i \(-0.697820\pi\)
−0.582230 + 0.813024i \(0.697820\pi\)
\(44\) 0 0
\(45\) −1.29538 −0.193103
\(46\) 0 0
\(47\) −0.402401 −0.0586962 −0.0293481 0.999569i \(-0.509343\pi\)
−0.0293481 + 0.999569i \(0.509343\pi\)
\(48\) 0 0
\(49\) −2.70607 −0.386581
\(50\) 0 0
\(51\) 4.56989 0.639912
\(52\) 0 0
\(53\) −11.7012 −1.60728 −0.803639 0.595117i \(-0.797106\pi\)
−0.803639 + 0.595117i \(0.797106\pi\)
\(54\) 0 0
\(55\) 4.33332 0.584305
\(56\) 0 0
\(57\) −2.47664 −0.328040
\(58\) 0 0
\(59\) 3.18505 0.414658 0.207329 0.978271i \(-0.433523\pi\)
0.207329 + 0.978271i \(0.433523\pi\)
\(60\) 0 0
\(61\) −3.69207 −0.472721 −0.236360 0.971665i \(-0.575955\pi\)
−0.236360 + 0.971665i \(0.575955\pi\)
\(62\) 0 0
\(63\) 2.07218 0.261070
\(64\) 0 0
\(65\) −3.10431 −0.385042
\(66\) 0 0
\(67\) 2.52007 0.307875 0.153938 0.988081i \(-0.450805\pi\)
0.153938 + 0.988081i \(0.450805\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 8.77089 1.04091 0.520457 0.853888i \(-0.325762\pi\)
0.520457 + 0.853888i \(0.325762\pi\)
\(72\) 0 0
\(73\) 2.10000 0.245786 0.122893 0.992420i \(-0.460783\pi\)
0.122893 + 0.992420i \(0.460783\pi\)
\(74\) 0 0
\(75\) −3.32200 −0.383592
\(76\) 0 0
\(77\) −6.93191 −0.789964
\(78\) 0 0
\(79\) −2.54874 −0.286756 −0.143378 0.989668i \(-0.545796\pi\)
−0.143378 + 0.989668i \(0.545796\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.26686 0.468349 0.234174 0.972195i \(-0.424761\pi\)
0.234174 + 0.972195i \(0.424761\pi\)
\(84\) 0 0
\(85\) −5.91972 −0.642084
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) 11.4643 1.21522 0.607609 0.794236i \(-0.292129\pi\)
0.607609 + 0.794236i \(0.292129\pi\)
\(90\) 0 0
\(91\) 4.96589 0.520566
\(92\) 0 0
\(93\) −10.5344 −1.09237
\(94\) 0 0
\(95\) 3.20818 0.329153
\(96\) 0 0
\(97\) −3.13627 −0.318440 −0.159220 0.987243i \(-0.550898\pi\)
−0.159220 + 0.987243i \(0.550898\pi\)
\(98\) 0 0
\(99\) −3.34522 −0.336208
\(100\) 0 0
\(101\) −6.99330 −0.695860 −0.347930 0.937521i \(-0.613115\pi\)
−0.347930 + 0.937521i \(0.613115\pi\)
\(102\) 0 0
\(103\) 0.242322 0.0238767 0.0119383 0.999929i \(-0.496200\pi\)
0.0119383 + 0.999929i \(0.496200\pi\)
\(104\) 0 0
\(105\) −2.68425 −0.261956
\(106\) 0 0
\(107\) 6.51995 0.630307 0.315154 0.949041i \(-0.397944\pi\)
0.315154 + 0.949041i \(0.397944\pi\)
\(108\) 0 0
\(109\) −3.31025 −0.317064 −0.158532 0.987354i \(-0.550676\pi\)
−0.158532 + 0.987354i \(0.550676\pi\)
\(110\) 0 0
\(111\) −0.207606 −0.0197051
\(112\) 0 0
\(113\) −2.81651 −0.264955 −0.132477 0.991186i \(-0.542293\pi\)
−0.132477 + 0.991186i \(0.542293\pi\)
\(114\) 0 0
\(115\) −1.29538 −0.120794
\(116\) 0 0
\(117\) 2.39646 0.221552
\(118\) 0 0
\(119\) 9.46963 0.868080
\(120\) 0 0
\(121\) 0.190527 0.0173206
\(122\) 0 0
\(123\) −8.96963 −0.808764
\(124\) 0 0
\(125\) 10.7801 0.964203
\(126\) 0 0
\(127\) 19.9180 1.76744 0.883720 0.468016i \(-0.155031\pi\)
0.883720 + 0.468016i \(0.155031\pi\)
\(128\) 0 0
\(129\) −7.63588 −0.672301
\(130\) 0 0
\(131\) 14.0614 1.22855 0.614274 0.789093i \(-0.289449\pi\)
0.614274 + 0.789093i \(0.289449\pi\)
\(132\) 0 0
\(133\) −5.13205 −0.445006
\(134\) 0 0
\(135\) −1.29538 −0.111488
\(136\) 0 0
\(137\) −1.50454 −0.128542 −0.0642709 0.997932i \(-0.520472\pi\)
−0.0642709 + 0.997932i \(0.520472\pi\)
\(138\) 0 0
\(139\) −0.952139 −0.0807594 −0.0403797 0.999184i \(-0.512857\pi\)
−0.0403797 + 0.999184i \(0.512857\pi\)
\(140\) 0 0
\(141\) −0.402401 −0.0338883
\(142\) 0 0
\(143\) −8.01668 −0.670389
\(144\) 0 0
\(145\) −1.29538 −0.107575
\(146\) 0 0
\(147\) −2.70607 −0.223193
\(148\) 0 0
\(149\) 10.9676 0.898498 0.449249 0.893407i \(-0.351692\pi\)
0.449249 + 0.893407i \(0.351692\pi\)
\(150\) 0 0
\(151\) −19.6627 −1.60013 −0.800064 0.599915i \(-0.795201\pi\)
−0.800064 + 0.599915i \(0.795201\pi\)
\(152\) 0 0
\(153\) 4.56989 0.369454
\(154\) 0 0
\(155\) 13.6460 1.09607
\(156\) 0 0
\(157\) −11.8999 −0.949713 −0.474856 0.880063i \(-0.657500\pi\)
−0.474856 + 0.880063i \(0.657500\pi\)
\(158\) 0 0
\(159\) −11.7012 −0.927962
\(160\) 0 0
\(161\) 2.07218 0.163311
\(162\) 0 0
\(163\) −5.26061 −0.412043 −0.206021 0.978547i \(-0.566052\pi\)
−0.206021 + 0.978547i \(0.566052\pi\)
\(164\) 0 0
\(165\) 4.33332 0.337349
\(166\) 0 0
\(167\) 7.47097 0.578121 0.289061 0.957311i \(-0.406657\pi\)
0.289061 + 0.957311i \(0.406657\pi\)
\(168\) 0 0
\(169\) −7.25700 −0.558231
\(170\) 0 0
\(171\) −2.47664 −0.189394
\(172\) 0 0
\(173\) −17.6123 −1.33904 −0.669520 0.742794i \(-0.733500\pi\)
−0.669520 + 0.742794i \(0.733500\pi\)
\(174\) 0 0
\(175\) −6.88379 −0.520366
\(176\) 0 0
\(177\) 3.18505 0.239403
\(178\) 0 0
\(179\) −25.7861 −1.92734 −0.963671 0.267092i \(-0.913937\pi\)
−0.963671 + 0.267092i \(0.913937\pi\)
\(180\) 0 0
\(181\) −24.6428 −1.83169 −0.915843 0.401537i \(-0.868476\pi\)
−0.915843 + 0.401537i \(0.868476\pi\)
\(182\) 0 0
\(183\) −3.69207 −0.272925
\(184\) 0 0
\(185\) 0.268928 0.0197720
\(186\) 0 0
\(187\) −15.2873 −1.11792
\(188\) 0 0
\(189\) 2.07218 0.150729
\(190\) 0 0
\(191\) −5.87144 −0.424843 −0.212421 0.977178i \(-0.568135\pi\)
−0.212421 + 0.977178i \(0.568135\pi\)
\(192\) 0 0
\(193\) 9.91160 0.713453 0.356726 0.934209i \(-0.383893\pi\)
0.356726 + 0.934209i \(0.383893\pi\)
\(194\) 0 0
\(195\) −3.10431 −0.222304
\(196\) 0 0
\(197\) 2.88494 0.205543 0.102772 0.994705i \(-0.467229\pi\)
0.102772 + 0.994705i \(0.467229\pi\)
\(198\) 0 0
\(199\) −3.02405 −0.214369 −0.107185 0.994239i \(-0.534184\pi\)
−0.107185 + 0.994239i \(0.534184\pi\)
\(200\) 0 0
\(201\) 2.52007 0.177752
\(202\) 0 0
\(203\) 2.07218 0.145439
\(204\) 0 0
\(205\) 11.6190 0.811509
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 8.28493 0.573081
\(210\) 0 0
\(211\) −11.0518 −0.760838 −0.380419 0.924814i \(-0.624220\pi\)
−0.380419 + 0.924814i \(0.624220\pi\)
\(212\) 0 0
\(213\) 8.77089 0.600972
\(214\) 0 0
\(215\) 9.89132 0.674583
\(216\) 0 0
\(217\) −21.8292 −1.48186
\(218\) 0 0
\(219\) 2.10000 0.141905
\(220\) 0 0
\(221\) 10.9515 0.736680
\(222\) 0 0
\(223\) −22.7076 −1.52062 −0.760308 0.649563i \(-0.774952\pi\)
−0.760308 + 0.649563i \(0.774952\pi\)
\(224\) 0 0
\(225\) −3.32200 −0.221467
\(226\) 0 0
\(227\) −4.93703 −0.327682 −0.163841 0.986487i \(-0.552388\pi\)
−0.163841 + 0.986487i \(0.552388\pi\)
\(228\) 0 0
\(229\) 0.626925 0.0414284 0.0207142 0.999785i \(-0.493406\pi\)
0.0207142 + 0.999785i \(0.493406\pi\)
\(230\) 0 0
\(231\) −6.93191 −0.456086
\(232\) 0 0
\(233\) −2.30837 −0.151227 −0.0756133 0.997137i \(-0.524091\pi\)
−0.0756133 + 0.997137i \(0.524091\pi\)
\(234\) 0 0
\(235\) 0.521260 0.0340033
\(236\) 0 0
\(237\) −2.54874 −0.165558
\(238\) 0 0
\(239\) 9.58186 0.619799 0.309900 0.950769i \(-0.399705\pi\)
0.309900 + 0.950769i \(0.399705\pi\)
\(240\) 0 0
\(241\) −22.3502 −1.43971 −0.719853 0.694127i \(-0.755791\pi\)
−0.719853 + 0.694127i \(0.755791\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 3.50538 0.223950
\(246\) 0 0
\(247\) −5.93517 −0.377646
\(248\) 0 0
\(249\) 4.26686 0.270401
\(250\) 0 0
\(251\) 22.6196 1.42774 0.713868 0.700281i \(-0.246942\pi\)
0.713868 + 0.700281i \(0.246942\pi\)
\(252\) 0 0
\(253\) −3.34522 −0.210312
\(254\) 0 0
\(255\) −5.91972 −0.370707
\(256\) 0 0
\(257\) 5.75230 0.358818 0.179409 0.983775i \(-0.442581\pi\)
0.179409 + 0.983775i \(0.442581\pi\)
\(258\) 0 0
\(259\) −0.430197 −0.0267311
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −16.8177 −1.03703 −0.518513 0.855070i \(-0.673514\pi\)
−0.518513 + 0.855070i \(0.673514\pi\)
\(264\) 0 0
\(265\) 15.1574 0.931111
\(266\) 0 0
\(267\) 11.4643 0.701606
\(268\) 0 0
\(269\) 7.31440 0.445967 0.222983 0.974822i \(-0.428420\pi\)
0.222983 + 0.974822i \(0.428420\pi\)
\(270\) 0 0
\(271\) 7.77195 0.472113 0.236056 0.971739i \(-0.424145\pi\)
0.236056 + 0.971739i \(0.424145\pi\)
\(272\) 0 0
\(273\) 4.96589 0.300549
\(274\) 0 0
\(275\) 11.1128 0.670130
\(276\) 0 0
\(277\) −13.9342 −0.837224 −0.418612 0.908165i \(-0.637483\pi\)
−0.418612 + 0.908165i \(0.637483\pi\)
\(278\) 0 0
\(279\) −10.5344 −0.630679
\(280\) 0 0
\(281\) −25.2711 −1.50755 −0.753774 0.657134i \(-0.771769\pi\)
−0.753774 + 0.657134i \(0.771769\pi\)
\(282\) 0 0
\(283\) −1.83289 −0.108954 −0.0544770 0.998515i \(-0.517349\pi\)
−0.0544770 + 0.998515i \(0.517349\pi\)
\(284\) 0 0
\(285\) 3.20818 0.190036
\(286\) 0 0
\(287\) −18.5867 −1.09714
\(288\) 0 0
\(289\) 3.88388 0.228464
\(290\) 0 0
\(291\) −3.13627 −0.183851
\(292\) 0 0
\(293\) −5.56600 −0.325169 −0.162585 0.986695i \(-0.551983\pi\)
−0.162585 + 0.986695i \(0.551983\pi\)
\(294\) 0 0
\(295\) −4.12583 −0.240215
\(296\) 0 0
\(297\) −3.34522 −0.194110
\(298\) 0 0
\(299\) 2.39646 0.138591
\(300\) 0 0
\(301\) −15.8229 −0.912017
\(302\) 0 0
\(303\) −6.99330 −0.401755
\(304\) 0 0
\(305\) 4.78261 0.273852
\(306\) 0 0
\(307\) −22.0931 −1.26092 −0.630459 0.776223i \(-0.717133\pi\)
−0.630459 + 0.776223i \(0.717133\pi\)
\(308\) 0 0
\(309\) 0.242322 0.0137852
\(310\) 0 0
\(311\) 2.65450 0.150523 0.0752613 0.997164i \(-0.476021\pi\)
0.0752613 + 0.997164i \(0.476021\pi\)
\(312\) 0 0
\(313\) 11.0163 0.622675 0.311338 0.950299i \(-0.399223\pi\)
0.311338 + 0.950299i \(0.399223\pi\)
\(314\) 0 0
\(315\) −2.68425 −0.151240
\(316\) 0 0
\(317\) 15.4677 0.868750 0.434375 0.900732i \(-0.356969\pi\)
0.434375 + 0.900732i \(0.356969\pi\)
\(318\) 0 0
\(319\) −3.34522 −0.187297
\(320\) 0 0
\(321\) 6.51995 0.363908
\(322\) 0 0
\(323\) −11.3180 −0.629750
\(324\) 0 0
\(325\) −7.96103 −0.441599
\(326\) 0 0
\(327\) −3.31025 −0.183057
\(328\) 0 0
\(329\) −0.833847 −0.0459715
\(330\) 0 0
\(331\) 24.8710 1.36703 0.683516 0.729935i \(-0.260450\pi\)
0.683516 + 0.729935i \(0.260450\pi\)
\(332\) 0 0
\(333\) −0.207606 −0.0113767
\(334\) 0 0
\(335\) −3.26443 −0.178355
\(336\) 0 0
\(337\) 26.0891 1.42116 0.710581 0.703616i \(-0.248432\pi\)
0.710581 + 0.703616i \(0.248432\pi\)
\(338\) 0 0
\(339\) −2.81651 −0.152972
\(340\) 0 0
\(341\) 35.2400 1.90835
\(342\) 0 0
\(343\) −20.1127 −1.08599
\(344\) 0 0
\(345\) −1.29538 −0.0697407
\(346\) 0 0
\(347\) −12.7184 −0.682761 −0.341381 0.939925i \(-0.610895\pi\)
−0.341381 + 0.939925i \(0.610895\pi\)
\(348\) 0 0
\(349\) −5.30296 −0.283861 −0.141930 0.989877i \(-0.545331\pi\)
−0.141930 + 0.989877i \(0.545331\pi\)
\(350\) 0 0
\(351\) 2.39646 0.127913
\(352\) 0 0
\(353\) −0.486228 −0.0258793 −0.0129397 0.999916i \(-0.504119\pi\)
−0.0129397 + 0.999916i \(0.504119\pi\)
\(354\) 0 0
\(355\) −11.3616 −0.603011
\(356\) 0 0
\(357\) 9.46963 0.501186
\(358\) 0 0
\(359\) −5.55410 −0.293134 −0.146567 0.989201i \(-0.546822\pi\)
−0.146567 + 0.989201i \(0.546822\pi\)
\(360\) 0 0
\(361\) −12.8662 −0.677170
\(362\) 0 0
\(363\) 0.190527 0.0100001
\(364\) 0 0
\(365\) −2.72028 −0.142386
\(366\) 0 0
\(367\) 26.4300 1.37963 0.689817 0.723983i \(-0.257691\pi\)
0.689817 + 0.723983i \(0.257691\pi\)
\(368\) 0 0
\(369\) −8.96963 −0.466940
\(370\) 0 0
\(371\) −24.2469 −1.25884
\(372\) 0 0
\(373\) −13.8677 −0.718041 −0.359020 0.933330i \(-0.616889\pi\)
−0.359020 + 0.933330i \(0.616889\pi\)
\(374\) 0 0
\(375\) 10.7801 0.556683
\(376\) 0 0
\(377\) 2.39646 0.123424
\(378\) 0 0
\(379\) 9.75453 0.501057 0.250528 0.968109i \(-0.419396\pi\)
0.250528 + 0.968109i \(0.419396\pi\)
\(380\) 0 0
\(381\) 19.9180 1.02043
\(382\) 0 0
\(383\) −33.2399 −1.69848 −0.849239 0.528009i \(-0.822939\pi\)
−0.849239 + 0.528009i \(0.822939\pi\)
\(384\) 0 0
\(385\) 8.97942 0.457634
\(386\) 0 0
\(387\) −7.63588 −0.388153
\(388\) 0 0
\(389\) 25.7182 1.30397 0.651983 0.758234i \(-0.273937\pi\)
0.651983 + 0.758234i \(0.273937\pi\)
\(390\) 0 0
\(391\) 4.56989 0.231109
\(392\) 0 0
\(393\) 14.0614 0.709302
\(394\) 0 0
\(395\) 3.30157 0.166120
\(396\) 0 0
\(397\) 8.87415 0.445381 0.222690 0.974889i \(-0.428516\pi\)
0.222690 + 0.974889i \(0.428516\pi\)
\(398\) 0 0
\(399\) −5.13205 −0.256924
\(400\) 0 0
\(401\) 14.9358 0.745860 0.372930 0.927859i \(-0.378353\pi\)
0.372930 + 0.927859i \(0.378353\pi\)
\(402\) 0 0
\(403\) −25.2453 −1.25756
\(404\) 0 0
\(405\) −1.29538 −0.0643677
\(406\) 0 0
\(407\) 0.694489 0.0344245
\(408\) 0 0
\(409\) 7.06303 0.349244 0.174622 0.984636i \(-0.444130\pi\)
0.174622 + 0.984636i \(0.444130\pi\)
\(410\) 0 0
\(411\) −1.50454 −0.0742136
\(412\) 0 0
\(413\) 6.59999 0.324764
\(414\) 0 0
\(415\) −5.52718 −0.271319
\(416\) 0 0
\(417\) −0.952139 −0.0466264
\(418\) 0 0
\(419\) −11.9202 −0.582339 −0.291169 0.956672i \(-0.594044\pi\)
−0.291169 + 0.956672i \(0.594044\pi\)
\(420\) 0 0
\(421\) −20.8575 −1.01653 −0.508266 0.861200i \(-0.669713\pi\)
−0.508266 + 0.861200i \(0.669713\pi\)
\(422\) 0 0
\(423\) −0.402401 −0.0195654
\(424\) 0 0
\(425\) −15.1812 −0.736396
\(426\) 0 0
\(427\) −7.65063 −0.370240
\(428\) 0 0
\(429\) −8.01668 −0.387049
\(430\) 0 0
\(431\) 14.8354 0.714596 0.357298 0.933991i \(-0.383698\pi\)
0.357298 + 0.933991i \(0.383698\pi\)
\(432\) 0 0
\(433\) −14.0717 −0.676244 −0.338122 0.941102i \(-0.609792\pi\)
−0.338122 + 0.941102i \(0.609792\pi\)
\(434\) 0 0
\(435\) −1.29538 −0.0621085
\(436\) 0 0
\(437\) −2.47664 −0.118474
\(438\) 0 0
\(439\) 14.5612 0.694970 0.347485 0.937686i \(-0.387036\pi\)
0.347485 + 0.937686i \(0.387036\pi\)
\(440\) 0 0
\(441\) −2.70607 −0.128860
\(442\) 0 0
\(443\) −6.80116 −0.323133 −0.161566 0.986862i \(-0.551655\pi\)
−0.161566 + 0.986862i \(0.551655\pi\)
\(444\) 0 0
\(445\) −14.8506 −0.703987
\(446\) 0 0
\(447\) 10.9676 0.518748
\(448\) 0 0
\(449\) −37.6453 −1.77659 −0.888295 0.459273i \(-0.848110\pi\)
−0.888295 + 0.459273i \(0.848110\pi\)
\(450\) 0 0
\(451\) 30.0054 1.41290
\(452\) 0 0
\(453\) −19.6627 −0.923834
\(454\) 0 0
\(455\) −6.43269 −0.301569
\(456\) 0 0
\(457\) 26.7498 1.25130 0.625651 0.780103i \(-0.284833\pi\)
0.625651 + 0.780103i \(0.284833\pi\)
\(458\) 0 0
\(459\) 4.56989 0.213304
\(460\) 0 0
\(461\) −35.4003 −1.64876 −0.824378 0.566040i \(-0.808475\pi\)
−0.824378 + 0.566040i \(0.808475\pi\)
\(462\) 0 0
\(463\) 15.0666 0.700205 0.350103 0.936711i \(-0.386147\pi\)
0.350103 + 0.936711i \(0.386147\pi\)
\(464\) 0 0
\(465\) 13.6460 0.632819
\(466\) 0 0
\(467\) −38.1976 −1.76757 −0.883787 0.467890i \(-0.845014\pi\)
−0.883787 + 0.467890i \(0.845014\pi\)
\(468\) 0 0
\(469\) 5.22203 0.241131
\(470\) 0 0
\(471\) −11.8999 −0.548317
\(472\) 0 0
\(473\) 25.5437 1.17450
\(474\) 0 0
\(475\) 8.22742 0.377500
\(476\) 0 0
\(477\) −11.7012 −0.535759
\(478\) 0 0
\(479\) 26.2228 1.19815 0.599074 0.800693i \(-0.295535\pi\)
0.599074 + 0.800693i \(0.295535\pi\)
\(480\) 0 0
\(481\) −0.497519 −0.0226849
\(482\) 0 0
\(483\) 2.07218 0.0942875
\(484\) 0 0
\(485\) 4.06265 0.184475
\(486\) 0 0
\(487\) 23.2431 1.05324 0.526622 0.850099i \(-0.323458\pi\)
0.526622 + 0.850099i \(0.323458\pi\)
\(488\) 0 0
\(489\) −5.26061 −0.237893
\(490\) 0 0
\(491\) 17.8054 0.803546 0.401773 0.915739i \(-0.368394\pi\)
0.401773 + 0.915739i \(0.368394\pi\)
\(492\) 0 0
\(493\) 4.56989 0.205817
\(494\) 0 0
\(495\) 4.33332 0.194768
\(496\) 0 0
\(497\) 18.1749 0.815254
\(498\) 0 0
\(499\) −2.04536 −0.0915628 −0.0457814 0.998951i \(-0.514578\pi\)
−0.0457814 + 0.998951i \(0.514578\pi\)
\(500\) 0 0
\(501\) 7.47097 0.333778
\(502\) 0 0
\(503\) 1.43371 0.0639258 0.0319629 0.999489i \(-0.489824\pi\)
0.0319629 + 0.999489i \(0.489824\pi\)
\(504\) 0 0
\(505\) 9.05895 0.403118
\(506\) 0 0
\(507\) −7.25700 −0.322295
\(508\) 0 0
\(509\) −42.0972 −1.86593 −0.932963 0.359973i \(-0.882786\pi\)
−0.932963 + 0.359973i \(0.882786\pi\)
\(510\) 0 0
\(511\) 4.35157 0.192502
\(512\) 0 0
\(513\) −2.47664 −0.109347
\(514\) 0 0
\(515\) −0.313897 −0.0138320
\(516\) 0 0
\(517\) 1.34612 0.0592024
\(518\) 0 0
\(519\) −17.6123 −0.773095
\(520\) 0 0
\(521\) 28.8944 1.26588 0.632942 0.774199i \(-0.281847\pi\)
0.632942 + 0.774199i \(0.281847\pi\)
\(522\) 0 0
\(523\) −27.6066 −1.20715 −0.603576 0.797305i \(-0.706258\pi\)
−0.603576 + 0.797305i \(0.706258\pi\)
\(524\) 0 0
\(525\) −6.88379 −0.300433
\(526\) 0 0
\(527\) −48.1411 −2.09706
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 3.18505 0.138219
\(532\) 0 0
\(533\) −21.4953 −0.931065
\(534\) 0 0
\(535\) −8.44578 −0.365143
\(536\) 0 0
\(537\) −25.7861 −1.11275
\(538\) 0 0
\(539\) 9.05241 0.389915
\(540\) 0 0
\(541\) 30.1781 1.29746 0.648728 0.761020i \(-0.275301\pi\)
0.648728 + 0.761020i \(0.275301\pi\)
\(542\) 0 0
\(543\) −24.6428 −1.05752
\(544\) 0 0
\(545\) 4.28801 0.183678
\(546\) 0 0
\(547\) −33.1654 −1.41805 −0.709026 0.705183i \(-0.750865\pi\)
−0.709026 + 0.705183i \(0.750865\pi\)
\(548\) 0 0
\(549\) −3.69207 −0.157574
\(550\) 0 0
\(551\) −2.47664 −0.105509
\(552\) 0 0
\(553\) −5.28145 −0.224590
\(554\) 0 0
\(555\) 0.268928 0.0114153
\(556\) 0 0
\(557\) −3.76297 −0.159442 −0.0797212 0.996817i \(-0.525403\pi\)
−0.0797212 + 0.996817i \(0.525403\pi\)
\(558\) 0 0
\(559\) −18.2990 −0.773967
\(560\) 0 0
\(561\) −15.2873 −0.645430
\(562\) 0 0
\(563\) 10.4214 0.439209 0.219605 0.975589i \(-0.429523\pi\)
0.219605 + 0.975589i \(0.429523\pi\)
\(564\) 0 0
\(565\) 3.64843 0.153491
\(566\) 0 0
\(567\) 2.07218 0.0870234
\(568\) 0 0
\(569\) −5.75895 −0.241428 −0.120714 0.992687i \(-0.538518\pi\)
−0.120714 + 0.992687i \(0.538518\pi\)
\(570\) 0 0
\(571\) 27.5956 1.15484 0.577420 0.816447i \(-0.304060\pi\)
0.577420 + 0.816447i \(0.304060\pi\)
\(572\) 0 0
\(573\) −5.87144 −0.245283
\(574\) 0 0
\(575\) −3.32200 −0.138537
\(576\) 0 0
\(577\) −21.1518 −0.880563 −0.440281 0.897860i \(-0.645121\pi\)
−0.440281 + 0.897860i \(0.645121\pi\)
\(578\) 0 0
\(579\) 9.91160 0.411912
\(580\) 0 0
\(581\) 8.84170 0.366815
\(582\) 0 0
\(583\) 39.1430 1.62114
\(584\) 0 0
\(585\) −3.10431 −0.128347
\(586\) 0 0
\(587\) 9.77333 0.403388 0.201694 0.979449i \(-0.435355\pi\)
0.201694 + 0.979449i \(0.435355\pi\)
\(588\) 0 0
\(589\) 26.0900 1.07502
\(590\) 0 0
\(591\) 2.88494 0.118671
\(592\) 0 0
\(593\) 17.8530 0.733134 0.366567 0.930392i \(-0.380533\pi\)
0.366567 + 0.930392i \(0.380533\pi\)
\(594\) 0 0
\(595\) −12.2667 −0.502887
\(596\) 0 0
\(597\) −3.02405 −0.123766
\(598\) 0 0
\(599\) 35.3672 1.44506 0.722532 0.691337i \(-0.242978\pi\)
0.722532 + 0.691337i \(0.242978\pi\)
\(600\) 0 0
\(601\) 2.06551 0.0842540 0.0421270 0.999112i \(-0.486587\pi\)
0.0421270 + 0.999112i \(0.486587\pi\)
\(602\) 0 0
\(603\) 2.52007 0.102625
\(604\) 0 0
\(605\) −0.246804 −0.0100340
\(606\) 0 0
\(607\) −12.6383 −0.512974 −0.256487 0.966548i \(-0.582565\pi\)
−0.256487 + 0.966548i \(0.582565\pi\)
\(608\) 0 0
\(609\) 2.07218 0.0839690
\(610\) 0 0
\(611\) −0.964336 −0.0390129
\(612\) 0 0
\(613\) −39.2427 −1.58500 −0.792498 0.609874i \(-0.791220\pi\)
−0.792498 + 0.609874i \(0.791220\pi\)
\(614\) 0 0
\(615\) 11.6190 0.468525
\(616\) 0 0
\(617\) −22.1575 −0.892027 −0.446013 0.895026i \(-0.647157\pi\)
−0.446013 + 0.895026i \(0.647157\pi\)
\(618\) 0 0
\(619\) 34.8696 1.40153 0.700765 0.713392i \(-0.252842\pi\)
0.700765 + 0.713392i \(0.252842\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 23.7562 0.951771
\(624\) 0 0
\(625\) 2.64572 0.105829
\(626\) 0 0
\(627\) 8.28493 0.330868
\(628\) 0 0
\(629\) −0.948736 −0.0378286
\(630\) 0 0
\(631\) 0.841411 0.0334960 0.0167480 0.999860i \(-0.494669\pi\)
0.0167480 + 0.999860i \(0.494669\pi\)
\(632\) 0 0
\(633\) −11.0518 −0.439270
\(634\) 0 0
\(635\) −25.8013 −1.02389
\(636\) 0 0
\(637\) −6.48497 −0.256944
\(638\) 0 0
\(639\) 8.77089 0.346971
\(640\) 0 0
\(641\) 2.96517 0.117117 0.0585586 0.998284i \(-0.481350\pi\)
0.0585586 + 0.998284i \(0.481350\pi\)
\(642\) 0 0
\(643\) −31.7424 −1.25180 −0.625900 0.779903i \(-0.715268\pi\)
−0.625900 + 0.779903i \(0.715268\pi\)
\(644\) 0 0
\(645\) 9.89132 0.389470
\(646\) 0 0
\(647\) −21.2960 −0.837233 −0.418616 0.908163i \(-0.637485\pi\)
−0.418616 + 0.908163i \(0.637485\pi\)
\(648\) 0 0
\(649\) −10.6547 −0.418233
\(650\) 0 0
\(651\) −21.8292 −0.855554
\(652\) 0 0
\(653\) 4.17578 0.163411 0.0817055 0.996657i \(-0.473963\pi\)
0.0817055 + 0.996657i \(0.473963\pi\)
\(654\) 0 0
\(655\) −18.2147 −0.711709
\(656\) 0 0
\(657\) 2.10000 0.0819287
\(658\) 0 0
\(659\) 22.2473 0.866634 0.433317 0.901242i \(-0.357343\pi\)
0.433317 + 0.901242i \(0.357343\pi\)
\(660\) 0 0
\(661\) −12.3765 −0.481389 −0.240694 0.970601i \(-0.577375\pi\)
−0.240694 + 0.970601i \(0.577375\pi\)
\(662\) 0 0
\(663\) 10.9515 0.425322
\(664\) 0 0
\(665\) 6.64794 0.257796
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) −22.7076 −0.877928
\(670\) 0 0
\(671\) 12.3508 0.476797
\(672\) 0 0
\(673\) −6.79407 −0.261892 −0.130946 0.991390i \(-0.541801\pi\)
−0.130946 + 0.991390i \(0.541801\pi\)
\(674\) 0 0
\(675\) −3.32200 −0.127864
\(676\) 0 0
\(677\) 16.2863 0.625932 0.312966 0.949764i \(-0.398677\pi\)
0.312966 + 0.949764i \(0.398677\pi\)
\(678\) 0 0
\(679\) −6.49892 −0.249406
\(680\) 0 0
\(681\) −4.93703 −0.189187
\(682\) 0 0
\(683\) −25.8757 −0.990104 −0.495052 0.868863i \(-0.664851\pi\)
−0.495052 + 0.868863i \(0.664851\pi\)
\(684\) 0 0
\(685\) 1.94895 0.0744655
\(686\) 0 0
\(687\) 0.626925 0.0239187
\(688\) 0 0
\(689\) −28.0413 −1.06829
\(690\) 0 0
\(691\) −30.7317 −1.16909 −0.584544 0.811362i \(-0.698726\pi\)
−0.584544 + 0.811362i \(0.698726\pi\)
\(692\) 0 0
\(693\) −6.93191 −0.263321
\(694\) 0 0
\(695\) 1.23338 0.0467847
\(696\) 0 0
\(697\) −40.9902 −1.55261
\(698\) 0 0
\(699\) −2.30837 −0.0873107
\(700\) 0 0
\(701\) 28.3829 1.07201 0.536003 0.844216i \(-0.319933\pi\)
0.536003 + 0.844216i \(0.319933\pi\)
\(702\) 0 0
\(703\) 0.514166 0.0193922
\(704\) 0 0
\(705\) 0.521260 0.0196318
\(706\) 0 0
\(707\) −14.4914 −0.545005
\(708\) 0 0
\(709\) 29.0589 1.09133 0.545666 0.838003i \(-0.316277\pi\)
0.545666 + 0.838003i \(0.316277\pi\)
\(710\) 0 0
\(711\) −2.54874 −0.0955852
\(712\) 0 0
\(713\) −10.5344 −0.394517
\(714\) 0 0
\(715\) 10.3846 0.388362
\(716\) 0 0
\(717\) 9.58186 0.357841
\(718\) 0 0
\(719\) 49.4207 1.84308 0.921540 0.388283i \(-0.126932\pi\)
0.921540 + 0.388283i \(0.126932\pi\)
\(720\) 0 0
\(721\) 0.502134 0.0187004
\(722\) 0 0
\(723\) −22.3502 −0.831215
\(724\) 0 0
\(725\) −3.32200 −0.123376
\(726\) 0 0
\(727\) 22.8099 0.845972 0.422986 0.906136i \(-0.360982\pi\)
0.422986 + 0.906136i \(0.360982\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −34.8951 −1.29064
\(732\) 0 0
\(733\) 3.89556 0.143886 0.0719429 0.997409i \(-0.477080\pi\)
0.0719429 + 0.997409i \(0.477080\pi\)
\(734\) 0 0
\(735\) 3.50538 0.129298
\(736\) 0 0
\(737\) −8.43019 −0.310530
\(738\) 0 0
\(739\) −14.4058 −0.529925 −0.264963 0.964259i \(-0.585360\pi\)
−0.264963 + 0.964259i \(0.585360\pi\)
\(740\) 0 0
\(741\) −5.93517 −0.218034
\(742\) 0 0
\(743\) −5.33015 −0.195544 −0.0977722 0.995209i \(-0.531172\pi\)
−0.0977722 + 0.995209i \(0.531172\pi\)
\(744\) 0 0
\(745\) −14.2071 −0.520508
\(746\) 0 0
\(747\) 4.26686 0.156116
\(748\) 0 0
\(749\) 13.5105 0.493663
\(750\) 0 0
\(751\) 20.7768 0.758157 0.379079 0.925364i \(-0.376241\pi\)
0.379079 + 0.925364i \(0.376241\pi\)
\(752\) 0 0
\(753\) 22.6196 0.824303
\(754\) 0 0
\(755\) 25.4706 0.926969
\(756\) 0 0
\(757\) 53.5790 1.94736 0.973680 0.227918i \(-0.0731917\pi\)
0.973680 + 0.227918i \(0.0731917\pi\)
\(758\) 0 0
\(759\) −3.34522 −0.121424
\(760\) 0 0
\(761\) 27.1972 0.985896 0.492948 0.870059i \(-0.335919\pi\)
0.492948 + 0.870059i \(0.335919\pi\)
\(762\) 0 0
\(763\) −6.85943 −0.248328
\(764\) 0 0
\(765\) −5.91972 −0.214028
\(766\) 0 0
\(767\) 7.63282 0.275605
\(768\) 0 0
\(769\) 42.1185 1.51883 0.759417 0.650605i \(-0.225485\pi\)
0.759417 + 0.650605i \(0.225485\pi\)
\(770\) 0 0
\(771\) 5.75230 0.207164
\(772\) 0 0
\(773\) −19.3920 −0.697483 −0.348742 0.937219i \(-0.613391\pi\)
−0.348742 + 0.937219i \(0.613391\pi\)
\(774\) 0 0
\(775\) 34.9954 1.25707
\(776\) 0 0
\(777\) −0.430197 −0.0154332
\(778\) 0 0
\(779\) 22.2146 0.795920
\(780\) 0 0
\(781\) −29.3406 −1.04989
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) 15.4148 0.550178
\(786\) 0 0
\(787\) 3.62566 0.129241 0.0646204 0.997910i \(-0.479416\pi\)
0.0646204 + 0.997910i \(0.479416\pi\)
\(788\) 0 0
\(789\) −16.8177 −0.598727
\(790\) 0 0
\(791\) −5.83631 −0.207515
\(792\) 0 0
\(793\) −8.84787 −0.314197
\(794\) 0 0
\(795\) 15.1574 0.537577
\(796\) 0 0
\(797\) −1.63466 −0.0579026 −0.0289513 0.999581i \(-0.509217\pi\)
−0.0289513 + 0.999581i \(0.509217\pi\)
\(798\) 0 0
\(799\) −1.83893 −0.0650566
\(800\) 0 0
\(801\) 11.4643 0.405073
\(802\) 0 0
\(803\) −7.02496 −0.247905
\(804\) 0 0
\(805\) −2.68425 −0.0946074
\(806\) 0 0
\(807\) 7.31440 0.257479
\(808\) 0 0
\(809\) −14.0528 −0.494069 −0.247034 0.969007i \(-0.579456\pi\)
−0.247034 + 0.969007i \(0.579456\pi\)
\(810\) 0 0
\(811\) −11.5614 −0.405976 −0.202988 0.979181i \(-0.565065\pi\)
−0.202988 + 0.979181i \(0.565065\pi\)
\(812\) 0 0
\(813\) 7.77195 0.272574
\(814\) 0 0
\(815\) 6.81446 0.238700
\(816\) 0 0
\(817\) 18.9114 0.661624
\(818\) 0 0
\(819\) 4.96589 0.173522
\(820\) 0 0
\(821\) −25.6772 −0.896141 −0.448070 0.893998i \(-0.647889\pi\)
−0.448070 + 0.893998i \(0.647889\pi\)
\(822\) 0 0
\(823\) 37.6775 1.31336 0.656678 0.754171i \(-0.271961\pi\)
0.656678 + 0.754171i \(0.271961\pi\)
\(824\) 0 0
\(825\) 11.1128 0.386900
\(826\) 0 0
\(827\) −11.8022 −0.410404 −0.205202 0.978720i \(-0.565785\pi\)
−0.205202 + 0.978720i \(0.565785\pi\)
\(828\) 0 0
\(829\) 32.4581 1.12731 0.563657 0.826009i \(-0.309394\pi\)
0.563657 + 0.826009i \(0.309394\pi\)
\(830\) 0 0
\(831\) −13.9342 −0.483372
\(832\) 0 0
\(833\) −12.3664 −0.428472
\(834\) 0 0
\(835\) −9.67771 −0.334911
\(836\) 0 0
\(837\) −10.5344 −0.364123
\(838\) 0 0
\(839\) 27.7743 0.958874 0.479437 0.877576i \(-0.340841\pi\)
0.479437 + 0.877576i \(0.340841\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −25.2711 −0.870383
\(844\) 0 0
\(845\) 9.40054 0.323388
\(846\) 0 0
\(847\) 0.394806 0.0135657
\(848\) 0 0
\(849\) −1.83289 −0.0629046
\(850\) 0 0
\(851\) −0.207606 −0.00711664
\(852\) 0 0
\(853\) −44.3405 −1.51819 −0.759095 0.650980i \(-0.774358\pi\)
−0.759095 + 0.650980i \(0.774358\pi\)
\(854\) 0 0
\(855\) 3.20818 0.109718
\(856\) 0 0
\(857\) −26.1959 −0.894833 −0.447417 0.894326i \(-0.647656\pi\)
−0.447417 + 0.894326i \(0.647656\pi\)
\(858\) 0 0
\(859\) 2.69695 0.0920186 0.0460093 0.998941i \(-0.485350\pi\)
0.0460093 + 0.998941i \(0.485350\pi\)
\(860\) 0 0
\(861\) −18.5867 −0.633433
\(862\) 0 0
\(863\) 32.2978 1.09943 0.549715 0.835352i \(-0.314736\pi\)
0.549715 + 0.835352i \(0.314736\pi\)
\(864\) 0 0
\(865\) 22.8146 0.775718
\(866\) 0 0
\(867\) 3.88388 0.131904
\(868\) 0 0
\(869\) 8.52610 0.289228
\(870\) 0 0
\(871\) 6.03923 0.204631
\(872\) 0 0
\(873\) −3.13627 −0.106147
\(874\) 0 0
\(875\) 22.3383 0.755174
\(876\) 0 0
\(877\) −58.3784 −1.97130 −0.985649 0.168807i \(-0.946009\pi\)
−0.985649 + 0.168807i \(0.946009\pi\)
\(878\) 0 0
\(879\) −5.56600 −0.187736
\(880\) 0 0
\(881\) 33.7270 1.13629 0.568145 0.822928i \(-0.307661\pi\)
0.568145 + 0.822928i \(0.307661\pi\)
\(882\) 0 0
\(883\) −24.7213 −0.831939 −0.415969 0.909379i \(-0.636558\pi\)
−0.415969 + 0.909379i \(0.636558\pi\)
\(884\) 0 0
\(885\) −4.12583 −0.138688
\(886\) 0 0
\(887\) 13.8477 0.464961 0.232480 0.972601i \(-0.425316\pi\)
0.232480 + 0.972601i \(0.425316\pi\)
\(888\) 0 0
\(889\) 41.2738 1.38428
\(890\) 0 0
\(891\) −3.34522 −0.112069
\(892\) 0 0
\(893\) 0.996604 0.0333501
\(894\) 0 0
\(895\) 33.4026 1.11653
\(896\) 0 0
\(897\) 2.39646 0.0800153
\(898\) 0 0
\(899\) −10.5344 −0.351342
\(900\) 0 0
\(901\) −53.4730 −1.78144
\(902\) 0 0
\(903\) −15.8229 −0.526553
\(904\) 0 0
\(905\) 31.9217 1.06111
\(906\) 0 0
\(907\) −45.7772 −1.52001 −0.760004 0.649918i \(-0.774803\pi\)
−0.760004 + 0.649918i \(0.774803\pi\)
\(908\) 0 0
\(909\) −6.99330 −0.231953
\(910\) 0 0
\(911\) −31.0176 −1.02766 −0.513829 0.857892i \(-0.671774\pi\)
−0.513829 + 0.857892i \(0.671774\pi\)
\(912\) 0 0
\(913\) −14.2736 −0.472387
\(914\) 0 0
\(915\) 4.78261 0.158108
\(916\) 0 0
\(917\) 29.1377 0.962211
\(918\) 0 0
\(919\) −11.6585 −0.384579 −0.192289 0.981338i \(-0.561591\pi\)
−0.192289 + 0.981338i \(0.561591\pi\)
\(920\) 0 0
\(921\) −22.0931 −0.727991
\(922\) 0 0
\(923\) 21.0191 0.691851
\(924\) 0 0
\(925\) 0.689668 0.0226761
\(926\) 0 0
\(927\) 0.242322 0.00795889
\(928\) 0 0
\(929\) −13.1735 −0.432210 −0.216105 0.976370i \(-0.569335\pi\)
−0.216105 + 0.976370i \(0.569335\pi\)
\(930\) 0 0
\(931\) 6.70197 0.219648
\(932\) 0 0
\(933\) 2.65450 0.0869043
\(934\) 0 0
\(935\) 19.8028 0.647621
\(936\) 0 0
\(937\) −26.4194 −0.863084 −0.431542 0.902093i \(-0.642030\pi\)
−0.431542 + 0.902093i \(0.642030\pi\)
\(938\) 0 0
\(939\) 11.0163 0.359502
\(940\) 0 0
\(941\) 56.9867 1.85771 0.928857 0.370439i \(-0.120793\pi\)
0.928857 + 0.370439i \(0.120793\pi\)
\(942\) 0 0
\(943\) −8.96963 −0.292091
\(944\) 0 0
\(945\) −2.68425 −0.0873187
\(946\) 0 0
\(947\) 7.07399 0.229874 0.114937 0.993373i \(-0.463333\pi\)
0.114937 + 0.993373i \(0.463333\pi\)
\(948\) 0 0
\(949\) 5.03255 0.163363
\(950\) 0 0
\(951\) 15.4677 0.501573
\(952\) 0 0
\(953\) 5.22561 0.169274 0.0846370 0.996412i \(-0.473027\pi\)
0.0846370 + 0.996412i \(0.473027\pi\)
\(954\) 0 0
\(955\) 7.60572 0.246115
\(956\) 0 0
\(957\) −3.34522 −0.108136
\(958\) 0 0
\(959\) −3.11768 −0.100675
\(960\) 0 0
\(961\) 79.9739 2.57980
\(962\) 0 0
\(963\) 6.51995 0.210102
\(964\) 0 0
\(965\) −12.8392 −0.413310
\(966\) 0 0
\(967\) −18.8964 −0.607668 −0.303834 0.952725i \(-0.598267\pi\)
−0.303834 + 0.952725i \(0.598267\pi\)
\(968\) 0 0
\(969\) −11.3180 −0.363586
\(970\) 0 0
\(971\) 41.1467 1.32046 0.660230 0.751063i \(-0.270459\pi\)
0.660230 + 0.751063i \(0.270459\pi\)
\(972\) 0 0
\(973\) −1.97300 −0.0632516
\(974\) 0 0
\(975\) −7.96103 −0.254957
\(976\) 0 0
\(977\) −26.6384 −0.852238 −0.426119 0.904667i \(-0.640119\pi\)
−0.426119 + 0.904667i \(0.640119\pi\)
\(978\) 0 0
\(979\) −38.3508 −1.22570
\(980\) 0 0
\(981\) −3.31025 −0.105688
\(982\) 0 0
\(983\) 46.8376 1.49389 0.746944 0.664887i \(-0.231520\pi\)
0.746944 + 0.664887i \(0.231520\pi\)
\(984\) 0 0
\(985\) −3.73708 −0.119073
\(986\) 0 0
\(987\) −0.833847 −0.0265417
\(988\) 0 0
\(989\) −7.63588 −0.242807
\(990\) 0 0
\(991\) −57.7917 −1.83582 −0.917908 0.396794i \(-0.870123\pi\)
−0.917908 + 0.396794i \(0.870123\pi\)
\(992\) 0 0
\(993\) 24.8710 0.789256
\(994\) 0 0
\(995\) 3.91728 0.124186
\(996\) 0 0
\(997\) 48.0535 1.52187 0.760935 0.648828i \(-0.224740\pi\)
0.760935 + 0.648828i \(0.224740\pi\)
\(998\) 0 0
\(999\) −0.207606 −0.00656836
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 \(a_p\))