Properties

Label 8024.2.a.y.1.8
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.49807 q^{3}\) \(-3.21279 q^{5}\) \(-1.95127 q^{7}\) \(-0.755772 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.49807 q^{3}\) \(-3.21279 q^{5}\) \(-1.95127 q^{7}\) \(-0.755772 q^{9}\) \(+5.72693 q^{11}\) \(-6.02604 q^{13}\) \(+4.81299 q^{15}\) \(-1.00000 q^{17}\) \(+2.70399 q^{19}\) \(+2.92314 q^{21}\) \(-1.14624 q^{23}\) \(+5.32199 q^{25}\) \(+5.62643 q^{27}\) \(-2.95131 q^{29}\) \(-3.60709 q^{31}\) \(-8.57937 q^{33}\) \(+6.26900 q^{35}\) \(+1.95358 q^{37}\) \(+9.02746 q^{39}\) \(-5.74776 q^{41}\) \(+7.26683 q^{43}\) \(+2.42813 q^{45}\) \(-8.00236 q^{47}\) \(-3.19256 q^{49}\) \(+1.49807 q^{51}\) \(+13.8594 q^{53}\) \(-18.3994 q^{55}\) \(-4.05078 q^{57}\) \(-1.00000 q^{59}\) \(-12.5405 q^{61}\) \(+1.47471 q^{63}\) \(+19.3604 q^{65}\) \(+14.6152 q^{67}\) \(+1.71716 q^{69}\) \(+14.2858 q^{71}\) \(+9.36591 q^{73}\) \(-7.97274 q^{75}\) \(-11.1748 q^{77}\) \(+16.8513 q^{79}\) \(-6.16149 q^{81}\) \(-0.256775 q^{83}\) \(+3.21279 q^{85}\) \(+4.42128 q^{87}\) \(+5.77437 q^{89}\) \(+11.7584 q^{91}\) \(+5.40369 q^{93}\) \(-8.68734 q^{95}\) \(+4.67942 q^{97}\) \(-4.32825 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.49807 −0.864914 −0.432457 0.901655i \(-0.642353\pi\)
−0.432457 + 0.901655i \(0.642353\pi\)
\(4\) 0 0
\(5\) −3.21279 −1.43680 −0.718401 0.695629i \(-0.755126\pi\)
−0.718401 + 0.695629i \(0.755126\pi\)
\(6\) 0 0
\(7\) −1.95127 −0.737509 −0.368755 0.929527i \(-0.620216\pi\)
−0.368755 + 0.929527i \(0.620216\pi\)
\(8\) 0 0
\(9\) −0.755772 −0.251924
\(10\) 0 0
\(11\) 5.72693 1.72673 0.863367 0.504577i \(-0.168351\pi\)
0.863367 + 0.504577i \(0.168351\pi\)
\(12\) 0 0
\(13\) −6.02604 −1.67132 −0.835662 0.549245i \(-0.814916\pi\)
−0.835662 + 0.549245i \(0.814916\pi\)
\(14\) 0 0
\(15\) 4.81299 1.24271
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 2.70399 0.620338 0.310169 0.950681i \(-0.399614\pi\)
0.310169 + 0.950681i \(0.399614\pi\)
\(20\) 0 0
\(21\) 2.92314 0.637882
\(22\) 0 0
\(23\) −1.14624 −0.239008 −0.119504 0.992834i \(-0.538130\pi\)
−0.119504 + 0.992834i \(0.538130\pi\)
\(24\) 0 0
\(25\) 5.32199 1.06440
\(26\) 0 0
\(27\) 5.62643 1.08281
\(28\) 0 0
\(29\) −2.95131 −0.548044 −0.274022 0.961723i \(-0.588354\pi\)
−0.274022 + 0.961723i \(0.588354\pi\)
\(30\) 0 0
\(31\) −3.60709 −0.647852 −0.323926 0.946082i \(-0.605003\pi\)
−0.323926 + 0.946082i \(0.605003\pi\)
\(32\) 0 0
\(33\) −8.57937 −1.49348
\(34\) 0 0
\(35\) 6.26900 1.05965
\(36\) 0 0
\(37\) 1.95358 0.321167 0.160583 0.987022i \(-0.448662\pi\)
0.160583 + 0.987022i \(0.448662\pi\)
\(38\) 0 0
\(39\) 9.02746 1.44555
\(40\) 0 0
\(41\) −5.74776 −0.897649 −0.448824 0.893620i \(-0.648157\pi\)
−0.448824 + 0.893620i \(0.648157\pi\)
\(42\) 0 0
\(43\) 7.26683 1.10818 0.554091 0.832456i \(-0.313066\pi\)
0.554091 + 0.832456i \(0.313066\pi\)
\(44\) 0 0
\(45\) 2.42813 0.361965
\(46\) 0 0
\(47\) −8.00236 −1.16726 −0.583632 0.812018i \(-0.698369\pi\)
−0.583632 + 0.812018i \(0.698369\pi\)
\(48\) 0 0
\(49\) −3.19256 −0.456080
\(50\) 0 0
\(51\) 1.49807 0.209772
\(52\) 0 0
\(53\) 13.8594 1.90374 0.951868 0.306509i \(-0.0991610\pi\)
0.951868 + 0.306509i \(0.0991610\pi\)
\(54\) 0 0
\(55\) −18.3994 −2.48097
\(56\) 0 0
\(57\) −4.05078 −0.536539
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −12.5405 −1.60564 −0.802822 0.596219i \(-0.796669\pi\)
−0.802822 + 0.596219i \(0.796669\pi\)
\(62\) 0 0
\(63\) 1.47471 0.185796
\(64\) 0 0
\(65\) 19.3604 2.40136
\(66\) 0 0
\(67\) 14.6152 1.78553 0.892765 0.450523i \(-0.148762\pi\)
0.892765 + 0.450523i \(0.148762\pi\)
\(68\) 0 0
\(69\) 1.71716 0.206721
\(70\) 0 0
\(71\) 14.2858 1.69542 0.847708 0.530463i \(-0.177982\pi\)
0.847708 + 0.530463i \(0.177982\pi\)
\(72\) 0 0
\(73\) 9.36591 1.09620 0.548098 0.836414i \(-0.315352\pi\)
0.548098 + 0.836414i \(0.315352\pi\)
\(74\) 0 0
\(75\) −7.97274 −0.920613
\(76\) 0 0
\(77\) −11.1748 −1.27348
\(78\) 0 0
\(79\) 16.8513 1.89592 0.947959 0.318392i \(-0.103143\pi\)
0.947959 + 0.318392i \(0.103143\pi\)
\(80\) 0 0
\(81\) −6.16149 −0.684610
\(82\) 0 0
\(83\) −0.256775 −0.0281847 −0.0140924 0.999901i \(-0.504486\pi\)
−0.0140924 + 0.999901i \(0.504486\pi\)
\(84\) 0 0
\(85\) 3.21279 0.348476
\(86\) 0 0
\(87\) 4.42128 0.474011
\(88\) 0 0
\(89\) 5.77437 0.612082 0.306041 0.952018i \(-0.400996\pi\)
0.306041 + 0.952018i \(0.400996\pi\)
\(90\) 0 0
\(91\) 11.7584 1.23262
\(92\) 0 0
\(93\) 5.40369 0.560336
\(94\) 0 0
\(95\) −8.68734 −0.891302
\(96\) 0 0
\(97\) 4.67942 0.475123 0.237561 0.971373i \(-0.423652\pi\)
0.237561 + 0.971373i \(0.423652\pi\)
\(98\) 0 0
\(99\) −4.32825 −0.435006
\(100\) 0 0
\(101\) −4.76959 −0.474591 −0.237296 0.971437i \(-0.576261\pi\)
−0.237296 + 0.971437i \(0.576261\pi\)
\(102\) 0 0
\(103\) 9.80137 0.965757 0.482879 0.875687i \(-0.339591\pi\)
0.482879 + 0.875687i \(0.339591\pi\)
\(104\) 0 0
\(105\) −9.39143 −0.916510
\(106\) 0 0
\(107\) 10.4994 1.01502 0.507510 0.861646i \(-0.330566\pi\)
0.507510 + 0.861646i \(0.330566\pi\)
\(108\) 0 0
\(109\) −1.05602 −0.101148 −0.0505740 0.998720i \(-0.516105\pi\)
−0.0505740 + 0.998720i \(0.516105\pi\)
\(110\) 0 0
\(111\) −2.92661 −0.277782
\(112\) 0 0
\(113\) 3.98012 0.374419 0.187209 0.982320i \(-0.440056\pi\)
0.187209 + 0.982320i \(0.440056\pi\)
\(114\) 0 0
\(115\) 3.68263 0.343407
\(116\) 0 0
\(117\) 4.55432 0.421047
\(118\) 0 0
\(119\) 1.95127 0.178872
\(120\) 0 0
\(121\) 21.7977 1.98161
\(122\) 0 0
\(123\) 8.61057 0.776389
\(124\) 0 0
\(125\) −1.03449 −0.0925279
\(126\) 0 0
\(127\) −2.64081 −0.234334 −0.117167 0.993112i \(-0.537381\pi\)
−0.117167 + 0.993112i \(0.537381\pi\)
\(128\) 0 0
\(129\) −10.8863 −0.958481
\(130\) 0 0
\(131\) −19.0125 −1.66113 −0.830563 0.556924i \(-0.811981\pi\)
−0.830563 + 0.556924i \(0.811981\pi\)
\(132\) 0 0
\(133\) −5.27620 −0.457505
\(134\) 0 0
\(135\) −18.0765 −1.55578
\(136\) 0 0
\(137\) −14.1804 −1.21151 −0.605756 0.795651i \(-0.707129\pi\)
−0.605756 + 0.795651i \(0.707129\pi\)
\(138\) 0 0
\(139\) −3.84272 −0.325935 −0.162968 0.986631i \(-0.552107\pi\)
−0.162968 + 0.986631i \(0.552107\pi\)
\(140\) 0 0
\(141\) 11.9881 1.00958
\(142\) 0 0
\(143\) −34.5107 −2.88593
\(144\) 0 0
\(145\) 9.48191 0.787430
\(146\) 0 0
\(147\) 4.78269 0.394470
\(148\) 0 0
\(149\) −11.4575 −0.938637 −0.469319 0.883029i \(-0.655500\pi\)
−0.469319 + 0.883029i \(0.655500\pi\)
\(150\) 0 0
\(151\) −11.9601 −0.973302 −0.486651 0.873596i \(-0.661782\pi\)
−0.486651 + 0.873596i \(0.661782\pi\)
\(152\) 0 0
\(153\) 0.755772 0.0611006
\(154\) 0 0
\(155\) 11.5888 0.930835
\(156\) 0 0
\(157\) −1.31678 −0.105090 −0.0525452 0.998619i \(-0.516733\pi\)
−0.0525452 + 0.998619i \(0.516733\pi\)
\(158\) 0 0
\(159\) −20.7624 −1.64657
\(160\) 0 0
\(161\) 2.23662 0.176271
\(162\) 0 0
\(163\) −0.529471 −0.0414713 −0.0207357 0.999785i \(-0.506601\pi\)
−0.0207357 + 0.999785i \(0.506601\pi\)
\(164\) 0 0
\(165\) 27.5637 2.14583
\(166\) 0 0
\(167\) 17.9297 1.38744 0.693722 0.720243i \(-0.255970\pi\)
0.693722 + 0.720243i \(0.255970\pi\)
\(168\) 0 0
\(169\) 23.3132 1.79332
\(170\) 0 0
\(171\) −2.04360 −0.156278
\(172\) 0 0
\(173\) 2.09953 0.159624 0.0798120 0.996810i \(-0.474568\pi\)
0.0798120 + 0.996810i \(0.474568\pi\)
\(174\) 0 0
\(175\) −10.3846 −0.785004
\(176\) 0 0
\(177\) 1.49807 0.112602
\(178\) 0 0
\(179\) −16.3030 −1.21854 −0.609271 0.792962i \(-0.708538\pi\)
−0.609271 + 0.792962i \(0.708538\pi\)
\(180\) 0 0
\(181\) −1.68463 −0.125217 −0.0626086 0.998038i \(-0.519942\pi\)
−0.0626086 + 0.998038i \(0.519942\pi\)
\(182\) 0 0
\(183\) 18.7866 1.38874
\(184\) 0 0
\(185\) −6.27644 −0.461453
\(186\) 0 0
\(187\) −5.72693 −0.418794
\(188\) 0 0
\(189\) −10.9787 −0.798580
\(190\) 0 0
\(191\) 13.4006 0.969630 0.484815 0.874617i \(-0.338887\pi\)
0.484815 + 0.874617i \(0.338887\pi\)
\(192\) 0 0
\(193\) −10.8220 −0.778983 −0.389492 0.921030i \(-0.627349\pi\)
−0.389492 + 0.921030i \(0.627349\pi\)
\(194\) 0 0
\(195\) −29.0033 −2.07697
\(196\) 0 0
\(197\) −9.07170 −0.646332 −0.323166 0.946342i \(-0.604747\pi\)
−0.323166 + 0.946342i \(0.604747\pi\)
\(198\) 0 0
\(199\) 0.600055 0.0425367 0.0212684 0.999774i \(-0.493230\pi\)
0.0212684 + 0.999774i \(0.493230\pi\)
\(200\) 0 0
\(201\) −21.8946 −1.54433
\(202\) 0 0
\(203\) 5.75878 0.404187
\(204\) 0 0
\(205\) 18.4663 1.28974
\(206\) 0 0
\(207\) 0.866298 0.0602119
\(208\) 0 0
\(209\) 15.4856 1.07116
\(210\) 0 0
\(211\) −13.7246 −0.944842 −0.472421 0.881373i \(-0.656620\pi\)
−0.472421 + 0.881373i \(0.656620\pi\)
\(212\) 0 0
\(213\) −21.4012 −1.46639
\(214\) 0 0
\(215\) −23.3468 −1.59224
\(216\) 0 0
\(217\) 7.03839 0.477797
\(218\) 0 0
\(219\) −14.0308 −0.948115
\(220\) 0 0
\(221\) 6.02604 0.405355
\(222\) 0 0
\(223\) 2.68708 0.179940 0.0899702 0.995944i \(-0.471323\pi\)
0.0899702 + 0.995944i \(0.471323\pi\)
\(224\) 0 0
\(225\) −4.02222 −0.268148
\(226\) 0 0
\(227\) −12.9972 −0.862657 −0.431328 0.902195i \(-0.641955\pi\)
−0.431328 + 0.902195i \(0.641955\pi\)
\(228\) 0 0
\(229\) −5.04834 −0.333604 −0.166802 0.985990i \(-0.553344\pi\)
−0.166802 + 0.985990i \(0.553344\pi\)
\(230\) 0 0
\(231\) 16.7406 1.10145
\(232\) 0 0
\(233\) 28.0739 1.83919 0.919593 0.392873i \(-0.128519\pi\)
0.919593 + 0.392873i \(0.128519\pi\)
\(234\) 0 0
\(235\) 25.7099 1.67713
\(236\) 0 0
\(237\) −25.2445 −1.63981
\(238\) 0 0
\(239\) −12.7528 −0.824908 −0.412454 0.910978i \(-0.635328\pi\)
−0.412454 + 0.910978i \(0.635328\pi\)
\(240\) 0 0
\(241\) −9.45801 −0.609244 −0.304622 0.952473i \(-0.598530\pi\)
−0.304622 + 0.952473i \(0.598530\pi\)
\(242\) 0 0
\(243\) −7.64891 −0.490678
\(244\) 0 0
\(245\) 10.2570 0.655296
\(246\) 0 0
\(247\) −16.2944 −1.03679
\(248\) 0 0
\(249\) 0.384668 0.0243773
\(250\) 0 0
\(251\) 18.4836 1.16668 0.583338 0.812230i \(-0.301746\pi\)
0.583338 + 0.812230i \(0.301746\pi\)
\(252\) 0 0
\(253\) −6.56444 −0.412703
\(254\) 0 0
\(255\) −4.81299 −0.301401
\(256\) 0 0
\(257\) 27.3096 1.70352 0.851762 0.523928i \(-0.175534\pi\)
0.851762 + 0.523928i \(0.175534\pi\)
\(258\) 0 0
\(259\) −3.81196 −0.236864
\(260\) 0 0
\(261\) 2.23052 0.138065
\(262\) 0 0
\(263\) −23.7999 −1.46757 −0.733783 0.679384i \(-0.762247\pi\)
−0.733783 + 0.679384i \(0.762247\pi\)
\(264\) 0 0
\(265\) −44.5273 −2.73529
\(266\) 0 0
\(267\) −8.65044 −0.529398
\(268\) 0 0
\(269\) −24.2587 −1.47908 −0.739539 0.673114i \(-0.764956\pi\)
−0.739539 + 0.673114i \(0.764956\pi\)
\(270\) 0 0
\(271\) −13.1841 −0.800874 −0.400437 0.916324i \(-0.631142\pi\)
−0.400437 + 0.916324i \(0.631142\pi\)
\(272\) 0 0
\(273\) −17.6150 −1.06611
\(274\) 0 0
\(275\) 30.4787 1.83793
\(276\) 0 0
\(277\) −2.64730 −0.159061 −0.0795305 0.996832i \(-0.525342\pi\)
−0.0795305 + 0.996832i \(0.525342\pi\)
\(278\) 0 0
\(279\) 2.72614 0.163210
\(280\) 0 0
\(281\) 14.7305 0.878747 0.439374 0.898304i \(-0.355200\pi\)
0.439374 + 0.898304i \(0.355200\pi\)
\(282\) 0 0
\(283\) −25.5274 −1.51745 −0.758724 0.651412i \(-0.774177\pi\)
−0.758724 + 0.651412i \(0.774177\pi\)
\(284\) 0 0
\(285\) 13.0143 0.770900
\(286\) 0 0
\(287\) 11.2154 0.662025
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −7.01011 −0.410940
\(292\) 0 0
\(293\) −20.7539 −1.21245 −0.606227 0.795291i \(-0.707318\pi\)
−0.606227 + 0.795291i \(0.707318\pi\)
\(294\) 0 0
\(295\) 3.21279 0.187056
\(296\) 0 0
\(297\) 32.2221 1.86972
\(298\) 0 0
\(299\) 6.90730 0.399459
\(300\) 0 0
\(301\) −14.1795 −0.817294
\(302\) 0 0
\(303\) 7.14519 0.410481
\(304\) 0 0
\(305\) 40.2899 2.30699
\(306\) 0 0
\(307\) −15.1601 −0.865232 −0.432616 0.901578i \(-0.642409\pi\)
−0.432616 + 0.901578i \(0.642409\pi\)
\(308\) 0 0
\(309\) −14.6832 −0.835297
\(310\) 0 0
\(311\) −20.4302 −1.15849 −0.579245 0.815153i \(-0.696653\pi\)
−0.579245 + 0.815153i \(0.696653\pi\)
\(312\) 0 0
\(313\) 12.4702 0.704859 0.352430 0.935838i \(-0.385356\pi\)
0.352430 + 0.935838i \(0.385356\pi\)
\(314\) 0 0
\(315\) −4.73794 −0.266953
\(316\) 0 0
\(317\) 33.7622 1.89627 0.948137 0.317861i \(-0.102965\pi\)
0.948137 + 0.317861i \(0.102965\pi\)
\(318\) 0 0
\(319\) −16.9019 −0.946326
\(320\) 0 0
\(321\) −15.7290 −0.877905
\(322\) 0 0
\(323\) −2.70399 −0.150454
\(324\) 0 0
\(325\) −32.0705 −1.77895
\(326\) 0 0
\(327\) 1.58199 0.0874843
\(328\) 0 0
\(329\) 15.6147 0.860868
\(330\) 0 0
\(331\) −21.4388 −1.17838 −0.589192 0.807993i \(-0.700554\pi\)
−0.589192 + 0.807993i \(0.700554\pi\)
\(332\) 0 0
\(333\) −1.47646 −0.0809097
\(334\) 0 0
\(335\) −46.9555 −2.56545
\(336\) 0 0
\(337\) −9.75949 −0.531633 −0.265817 0.964024i \(-0.585642\pi\)
−0.265817 + 0.964024i \(0.585642\pi\)
\(338\) 0 0
\(339\) −5.96252 −0.323840
\(340\) 0 0
\(341\) −20.6575 −1.11867
\(342\) 0 0
\(343\) 19.8884 1.07387
\(344\) 0 0
\(345\) −5.51685 −0.297017
\(346\) 0 0
\(347\) −6.02034 −0.323189 −0.161594 0.986857i \(-0.551664\pi\)
−0.161594 + 0.986857i \(0.551664\pi\)
\(348\) 0 0
\(349\) 10.0742 0.539258 0.269629 0.962964i \(-0.413099\pi\)
0.269629 + 0.962964i \(0.413099\pi\)
\(350\) 0 0
\(351\) −33.9051 −1.80972
\(352\) 0 0
\(353\) −7.52141 −0.400324 −0.200162 0.979763i \(-0.564147\pi\)
−0.200162 + 0.979763i \(0.564147\pi\)
\(354\) 0 0
\(355\) −45.8973 −2.43598
\(356\) 0 0
\(357\) −2.92314 −0.154709
\(358\) 0 0
\(359\) −24.6228 −1.29954 −0.649770 0.760131i \(-0.725135\pi\)
−0.649770 + 0.760131i \(0.725135\pi\)
\(360\) 0 0
\(361\) −11.6884 −0.615181
\(362\) 0 0
\(363\) −32.6546 −1.71392
\(364\) 0 0
\(365\) −30.0907 −1.57502
\(366\) 0 0
\(367\) 26.9558 1.40708 0.703540 0.710656i \(-0.251602\pi\)
0.703540 + 0.710656i \(0.251602\pi\)
\(368\) 0 0
\(369\) 4.34400 0.226139
\(370\) 0 0
\(371\) −27.0434 −1.40402
\(372\) 0 0
\(373\) 8.96305 0.464089 0.232045 0.972705i \(-0.425458\pi\)
0.232045 + 0.972705i \(0.425458\pi\)
\(374\) 0 0
\(375\) 1.54975 0.0800286
\(376\) 0 0
\(377\) 17.7847 0.915958
\(378\) 0 0
\(379\) 8.94065 0.459250 0.229625 0.973279i \(-0.426250\pi\)
0.229625 + 0.973279i \(0.426250\pi\)
\(380\) 0 0
\(381\) 3.95613 0.202679
\(382\) 0 0
\(383\) 12.1628 0.621492 0.310746 0.950493i \(-0.399421\pi\)
0.310746 + 0.950493i \(0.399421\pi\)
\(384\) 0 0
\(385\) 35.9021 1.82974
\(386\) 0 0
\(387\) −5.49207 −0.279178
\(388\) 0 0
\(389\) −32.1374 −1.62943 −0.814716 0.579860i \(-0.803107\pi\)
−0.814716 + 0.579860i \(0.803107\pi\)
\(390\) 0 0
\(391\) 1.14624 0.0579679
\(392\) 0 0
\(393\) 28.4821 1.43673
\(394\) 0 0
\(395\) −54.1396 −2.72406
\(396\) 0 0
\(397\) −19.6205 −0.984725 −0.492362 0.870390i \(-0.663867\pi\)
−0.492362 + 0.870390i \(0.663867\pi\)
\(398\) 0 0
\(399\) 7.90415 0.395702
\(400\) 0 0
\(401\) 12.0664 0.602567 0.301284 0.953535i \(-0.402585\pi\)
0.301284 + 0.953535i \(0.402585\pi\)
\(402\) 0 0
\(403\) 21.7365 1.08277
\(404\) 0 0
\(405\) 19.7955 0.983649
\(406\) 0 0
\(407\) 11.1880 0.554570
\(408\) 0 0
\(409\) 34.4233 1.70212 0.851061 0.525067i \(-0.175960\pi\)
0.851061 + 0.525067i \(0.175960\pi\)
\(410\) 0 0
\(411\) 21.2433 1.04785
\(412\) 0 0
\(413\) 1.95127 0.0960155
\(414\) 0 0
\(415\) 0.824963 0.0404958
\(416\) 0 0
\(417\) 5.75668 0.281906
\(418\) 0 0
\(419\) 28.2261 1.37894 0.689468 0.724317i \(-0.257845\pi\)
0.689468 + 0.724317i \(0.257845\pi\)
\(420\) 0 0
\(421\) 18.3683 0.895218 0.447609 0.894229i \(-0.352276\pi\)
0.447609 + 0.894229i \(0.352276\pi\)
\(422\) 0 0
\(423\) 6.04796 0.294062
\(424\) 0 0
\(425\) −5.32199 −0.258155
\(426\) 0 0
\(427\) 24.4698 1.18418
\(428\) 0 0
\(429\) 51.6996 2.49608
\(430\) 0 0
\(431\) −24.1015 −1.16093 −0.580464 0.814286i \(-0.697129\pi\)
−0.580464 + 0.814286i \(0.697129\pi\)
\(432\) 0 0
\(433\) −5.56750 −0.267557 −0.133778 0.991011i \(-0.542711\pi\)
−0.133778 + 0.991011i \(0.542711\pi\)
\(434\) 0 0
\(435\) −14.2046 −0.681059
\(436\) 0 0
\(437\) −3.09943 −0.148266
\(438\) 0 0
\(439\) 8.13668 0.388342 0.194171 0.980968i \(-0.437798\pi\)
0.194171 + 0.980968i \(0.437798\pi\)
\(440\) 0 0
\(441\) 2.41285 0.114898
\(442\) 0 0
\(443\) −23.3667 −1.11019 −0.555094 0.831788i \(-0.687318\pi\)
−0.555094 + 0.831788i \(0.687318\pi\)
\(444\) 0 0
\(445\) −18.5518 −0.879440
\(446\) 0 0
\(447\) 17.1642 0.811840
\(448\) 0 0
\(449\) 27.6864 1.30660 0.653301 0.757098i \(-0.273384\pi\)
0.653301 + 0.757098i \(0.273384\pi\)
\(450\) 0 0
\(451\) −32.9170 −1.55000
\(452\) 0 0
\(453\) 17.9172 0.841822
\(454\) 0 0
\(455\) −37.7773 −1.77103
\(456\) 0 0
\(457\) −26.1242 −1.22204 −0.611018 0.791616i \(-0.709240\pi\)
−0.611018 + 0.791616i \(0.709240\pi\)
\(458\) 0 0
\(459\) −5.62643 −0.262619
\(460\) 0 0
\(461\) −23.3978 −1.08975 −0.544873 0.838519i \(-0.683422\pi\)
−0.544873 + 0.838519i \(0.683422\pi\)
\(462\) 0 0
\(463\) 7.74370 0.359880 0.179940 0.983678i \(-0.442410\pi\)
0.179940 + 0.983678i \(0.442410\pi\)
\(464\) 0 0
\(465\) −17.3609 −0.805092
\(466\) 0 0
\(467\) −14.7068 −0.680548 −0.340274 0.940326i \(-0.610520\pi\)
−0.340274 + 0.940326i \(0.610520\pi\)
\(468\) 0 0
\(469\) −28.5181 −1.31684
\(470\) 0 0
\(471\) 1.97263 0.0908942
\(472\) 0 0
\(473\) 41.6166 1.91353
\(474\) 0 0
\(475\) 14.3906 0.660287
\(476\) 0 0
\(477\) −10.4746 −0.479597
\(478\) 0 0
\(479\) 11.1475 0.509344 0.254672 0.967028i \(-0.418033\pi\)
0.254672 + 0.967028i \(0.418033\pi\)
\(480\) 0 0
\(481\) −11.7724 −0.536774
\(482\) 0 0
\(483\) −3.35063 −0.152459
\(484\) 0 0
\(485\) −15.0340 −0.682657
\(486\) 0 0
\(487\) 15.5242 0.703468 0.351734 0.936100i \(-0.385592\pi\)
0.351734 + 0.936100i \(0.385592\pi\)
\(488\) 0 0
\(489\) 0.793187 0.0358691
\(490\) 0 0
\(491\) −33.9751 −1.53328 −0.766638 0.642079i \(-0.778072\pi\)
−0.766638 + 0.642079i \(0.778072\pi\)
\(492\) 0 0
\(493\) 2.95131 0.132920
\(494\) 0 0
\(495\) 13.9058 0.625017
\(496\) 0 0
\(497\) −27.8755 −1.25039
\(498\) 0 0
\(499\) −32.4175 −1.45121 −0.725604 0.688112i \(-0.758440\pi\)
−0.725604 + 0.688112i \(0.758440\pi\)
\(500\) 0 0
\(501\) −26.8601 −1.20002
\(502\) 0 0
\(503\) 4.97912 0.222008 0.111004 0.993820i \(-0.464593\pi\)
0.111004 + 0.993820i \(0.464593\pi\)
\(504\) 0 0
\(505\) 15.3237 0.681894
\(506\) 0 0
\(507\) −34.9249 −1.55107
\(508\) 0 0
\(509\) 16.8969 0.748944 0.374472 0.927238i \(-0.377824\pi\)
0.374472 + 0.927238i \(0.377824\pi\)
\(510\) 0 0
\(511\) −18.2754 −0.808455
\(512\) 0 0
\(513\) 15.2138 0.671706
\(514\) 0 0
\(515\) −31.4897 −1.38760
\(516\) 0 0
\(517\) −45.8289 −2.01555
\(518\) 0 0
\(519\) −3.14525 −0.138061
\(520\) 0 0
\(521\) −5.85685 −0.256593 −0.128297 0.991736i \(-0.540951\pi\)
−0.128297 + 0.991736i \(0.540951\pi\)
\(522\) 0 0
\(523\) 39.1802 1.71323 0.856616 0.515955i \(-0.172563\pi\)
0.856616 + 0.515955i \(0.172563\pi\)
\(524\) 0 0
\(525\) 15.5569 0.678961
\(526\) 0 0
\(527\) 3.60709 0.157127
\(528\) 0 0
\(529\) −21.6861 −0.942875
\(530\) 0 0
\(531\) 0.755772 0.0327977
\(532\) 0 0
\(533\) 34.6362 1.50026
\(534\) 0 0
\(535\) −33.7325 −1.45838
\(536\) 0 0
\(537\) 24.4231 1.05393
\(538\) 0 0
\(539\) −18.2836 −0.787529
\(540\) 0 0
\(541\) −22.3784 −0.962123 −0.481061 0.876687i \(-0.659749\pi\)
−0.481061 + 0.876687i \(0.659749\pi\)
\(542\) 0 0
\(543\) 2.52369 0.108302
\(544\) 0 0
\(545\) 3.39276 0.145330
\(546\) 0 0
\(547\) −35.7646 −1.52919 −0.764593 0.644514i \(-0.777060\pi\)
−0.764593 + 0.644514i \(0.777060\pi\)
\(548\) 0 0
\(549\) 9.47775 0.404500
\(550\) 0 0
\(551\) −7.98030 −0.339972
\(552\) 0 0
\(553\) −32.8814 −1.39826
\(554\) 0 0
\(555\) 9.40257 0.399117
\(556\) 0 0
\(557\) 0.541951 0.0229632 0.0114816 0.999934i \(-0.496345\pi\)
0.0114816 + 0.999934i \(0.496345\pi\)
\(558\) 0 0
\(559\) −43.7902 −1.85213
\(560\) 0 0
\(561\) 8.57937 0.362221
\(562\) 0 0
\(563\) 12.6141 0.531621 0.265810 0.964025i \(-0.414360\pi\)
0.265810 + 0.964025i \(0.414360\pi\)
\(564\) 0 0
\(565\) −12.7873 −0.537965
\(566\) 0 0
\(567\) 12.0227 0.504906
\(568\) 0 0
\(569\) 18.7360 0.785453 0.392726 0.919655i \(-0.371532\pi\)
0.392726 + 0.919655i \(0.371532\pi\)
\(570\) 0 0
\(571\) 2.70457 0.113183 0.0565913 0.998397i \(-0.481977\pi\)
0.0565913 + 0.998397i \(0.481977\pi\)
\(572\) 0 0
\(573\) −20.0750 −0.838647
\(574\) 0 0
\(575\) −6.10029 −0.254400
\(576\) 0 0
\(577\) 14.8459 0.618042 0.309021 0.951055i \(-0.399999\pi\)
0.309021 + 0.951055i \(0.399999\pi\)
\(578\) 0 0
\(579\) 16.2121 0.673753
\(580\) 0 0
\(581\) 0.501036 0.0207865
\(582\) 0 0
\(583\) 79.3718 3.28724
\(584\) 0 0
\(585\) −14.6320 −0.604961
\(586\) 0 0
\(587\) 23.0981 0.953359 0.476679 0.879077i \(-0.341840\pi\)
0.476679 + 0.879077i \(0.341840\pi\)
\(588\) 0 0
\(589\) −9.75353 −0.401887
\(590\) 0 0
\(591\) 13.5901 0.559021
\(592\) 0 0
\(593\) −19.0834 −0.783662 −0.391831 0.920037i \(-0.628158\pi\)
−0.391831 + 0.920037i \(0.628158\pi\)
\(594\) 0 0
\(595\) −6.26900 −0.257004
\(596\) 0 0
\(597\) −0.898926 −0.0367906
\(598\) 0 0
\(599\) 0.836138 0.0341637 0.0170818 0.999854i \(-0.494562\pi\)
0.0170818 + 0.999854i \(0.494562\pi\)
\(600\) 0 0
\(601\) −38.5646 −1.57308 −0.786541 0.617538i \(-0.788130\pi\)
−0.786541 + 0.617538i \(0.788130\pi\)
\(602\) 0 0
\(603\) −11.0458 −0.449818
\(604\) 0 0
\(605\) −70.0314 −2.84718
\(606\) 0 0
\(607\) 41.0714 1.66704 0.833518 0.552492i \(-0.186323\pi\)
0.833518 + 0.552492i \(0.186323\pi\)
\(608\) 0 0
\(609\) −8.62709 −0.349587
\(610\) 0 0
\(611\) 48.2225 1.95087
\(612\) 0 0
\(613\) −33.5348 −1.35446 −0.677229 0.735773i \(-0.736819\pi\)
−0.677229 + 0.735773i \(0.736819\pi\)
\(614\) 0 0
\(615\) −27.6639 −1.11552
\(616\) 0 0
\(617\) 2.08120 0.0837861 0.0418930 0.999122i \(-0.486661\pi\)
0.0418930 + 0.999122i \(0.486661\pi\)
\(618\) 0 0
\(619\) 39.5091 1.58800 0.794002 0.607915i \(-0.207994\pi\)
0.794002 + 0.607915i \(0.207994\pi\)
\(620\) 0 0
\(621\) −6.44924 −0.258799
\(622\) 0 0
\(623\) −11.2673 −0.451416
\(624\) 0 0
\(625\) −23.2864 −0.931454
\(626\) 0 0
\(627\) −23.1985 −0.926460
\(628\) 0 0
\(629\) −1.95358 −0.0778944
\(630\) 0 0
\(631\) −9.92072 −0.394938 −0.197469 0.980309i \(-0.563272\pi\)
−0.197469 + 0.980309i \(0.563272\pi\)
\(632\) 0 0
\(633\) 20.5605 0.817207
\(634\) 0 0
\(635\) 8.48436 0.336692
\(636\) 0 0
\(637\) 19.2385 0.762257
\(638\) 0 0
\(639\) −10.7968 −0.427116
\(640\) 0 0
\(641\) −16.5956 −0.655487 −0.327743 0.944767i \(-0.606288\pi\)
−0.327743 + 0.944767i \(0.606288\pi\)
\(642\) 0 0
\(643\) 30.9337 1.21990 0.609952 0.792438i \(-0.291189\pi\)
0.609952 + 0.792438i \(0.291189\pi\)
\(644\) 0 0
\(645\) 34.9752 1.37715
\(646\) 0 0
\(647\) −18.8231 −0.740011 −0.370006 0.929030i \(-0.620644\pi\)
−0.370006 + 0.929030i \(0.620644\pi\)
\(648\) 0 0
\(649\) −5.72693 −0.224802
\(650\) 0 0
\(651\) −10.5440 −0.413253
\(652\) 0 0
\(653\) −27.7286 −1.08510 −0.542552 0.840022i \(-0.682542\pi\)
−0.542552 + 0.840022i \(0.682542\pi\)
\(654\) 0 0
\(655\) 61.0830 2.38671
\(656\) 0 0
\(657\) −7.07849 −0.276158
\(658\) 0 0
\(659\) 20.6909 0.806002 0.403001 0.915199i \(-0.367967\pi\)
0.403001 + 0.915199i \(0.367967\pi\)
\(660\) 0 0
\(661\) 10.5292 0.409538 0.204769 0.978810i \(-0.434356\pi\)
0.204769 + 0.978810i \(0.434356\pi\)
\(662\) 0 0
\(663\) −9.02746 −0.350598
\(664\) 0 0
\(665\) 16.9513 0.657344
\(666\) 0 0
\(667\) 3.38291 0.130987
\(668\) 0 0
\(669\) −4.02545 −0.155633
\(670\) 0 0
\(671\) −71.8184 −2.77252
\(672\) 0 0
\(673\) 6.54117 0.252144 0.126072 0.992021i \(-0.459763\pi\)
0.126072 + 0.992021i \(0.459763\pi\)
\(674\) 0 0
\(675\) 29.9438 1.15254
\(676\) 0 0
\(677\) 32.1324 1.23495 0.617475 0.786590i \(-0.288156\pi\)
0.617475 + 0.786590i \(0.288156\pi\)
\(678\) 0 0
\(679\) −9.13079 −0.350407
\(680\) 0 0
\(681\) 19.4708 0.746124
\(682\) 0 0
\(683\) 24.3836 0.933014 0.466507 0.884517i \(-0.345512\pi\)
0.466507 + 0.884517i \(0.345512\pi\)
\(684\) 0 0
\(685\) 45.5585 1.74070
\(686\) 0 0
\(687\) 7.56280 0.288539
\(688\) 0 0
\(689\) −83.5173 −3.18176
\(690\) 0 0
\(691\) 34.4359 1.31000 0.655001 0.755628i \(-0.272668\pi\)
0.655001 + 0.755628i \(0.272668\pi\)
\(692\) 0 0
\(693\) 8.44558 0.320821
\(694\) 0 0
\(695\) 12.3458 0.468304
\(696\) 0 0
\(697\) 5.74776 0.217712
\(698\) 0 0
\(699\) −42.0569 −1.59074
\(700\) 0 0
\(701\) −42.0630 −1.58870 −0.794348 0.607463i \(-0.792187\pi\)
−0.794348 + 0.607463i \(0.792187\pi\)
\(702\) 0 0
\(703\) 5.28246 0.199232
\(704\) 0 0
\(705\) −38.5153 −1.45057
\(706\) 0 0
\(707\) 9.30673 0.350016
\(708\) 0 0
\(709\) 30.3993 1.14167 0.570835 0.821065i \(-0.306620\pi\)
0.570835 + 0.821065i \(0.306620\pi\)
\(710\) 0 0
\(711\) −12.7357 −0.477628
\(712\) 0 0
\(713\) 4.13459 0.154842
\(714\) 0 0
\(715\) 110.876 4.14651
\(716\) 0 0
\(717\) 19.1046 0.713474
\(718\) 0 0
\(719\) 19.3758 0.722595 0.361298 0.932451i \(-0.382334\pi\)
0.361298 + 0.932451i \(0.382334\pi\)
\(720\) 0 0
\(721\) −19.1251 −0.712255
\(722\) 0 0
\(723\) 14.1688 0.526944
\(724\) 0 0
\(725\) −15.7068 −0.583337
\(726\) 0 0
\(727\) −51.0603 −1.89372 −0.946861 0.321642i \(-0.895765\pi\)
−0.946861 + 0.321642i \(0.895765\pi\)
\(728\) 0 0
\(729\) 29.9431 1.10900
\(730\) 0 0
\(731\) −7.26683 −0.268773
\(732\) 0 0
\(733\) −46.2303 −1.70755 −0.853777 0.520638i \(-0.825694\pi\)
−0.853777 + 0.520638i \(0.825694\pi\)
\(734\) 0 0
\(735\) −15.3658 −0.566775
\(736\) 0 0
\(737\) 83.7001 3.08313
\(738\) 0 0
\(739\) 23.2852 0.856559 0.428280 0.903646i \(-0.359120\pi\)
0.428280 + 0.903646i \(0.359120\pi\)
\(740\) 0 0
\(741\) 24.4102 0.896730
\(742\) 0 0
\(743\) 31.5690 1.15815 0.579077 0.815273i \(-0.303413\pi\)
0.579077 + 0.815273i \(0.303413\pi\)
\(744\) 0 0
\(745\) 36.8106 1.34864
\(746\) 0 0
\(747\) 0.194063 0.00710041
\(748\) 0 0
\(749\) −20.4872 −0.748587
\(750\) 0 0
\(751\) 10.8161 0.394687 0.197343 0.980334i \(-0.436769\pi\)
0.197343 + 0.980334i \(0.436769\pi\)
\(752\) 0 0
\(753\) −27.6898 −1.00907
\(754\) 0 0
\(755\) 38.4253 1.39844
\(756\) 0 0
\(757\) −19.8711 −0.722227 −0.361114 0.932522i \(-0.617603\pi\)
−0.361114 + 0.932522i \(0.617603\pi\)
\(758\) 0 0
\(759\) 9.83403 0.356953
\(760\) 0 0
\(761\) −5.07191 −0.183857 −0.0919283 0.995766i \(-0.529303\pi\)
−0.0919283 + 0.995766i \(0.529303\pi\)
\(762\) 0 0
\(763\) 2.06057 0.0745976
\(764\) 0 0
\(765\) −2.42813 −0.0877894
\(766\) 0 0
\(767\) 6.02604 0.217588
\(768\) 0 0
\(769\) −37.8647 −1.36544 −0.682718 0.730682i \(-0.739202\pi\)
−0.682718 + 0.730682i \(0.739202\pi\)
\(770\) 0 0
\(771\) −40.9118 −1.47340
\(772\) 0 0
\(773\) 21.1725 0.761520 0.380760 0.924674i \(-0.375662\pi\)
0.380760 + 0.924674i \(0.375662\pi\)
\(774\) 0 0
\(775\) −19.1969 −0.689573
\(776\) 0 0
\(777\) 5.71060 0.204867
\(778\) 0 0
\(779\) −15.5419 −0.556846
\(780\) 0 0
\(781\) 81.8139 2.92753
\(782\) 0 0
\(783\) −16.6053 −0.593425
\(784\) 0 0
\(785\) 4.23053 0.150994
\(786\) 0 0
\(787\) −25.1538 −0.896635 −0.448317 0.893874i \(-0.647977\pi\)
−0.448317 + 0.893874i \(0.647977\pi\)
\(788\) 0 0
\(789\) 35.6541 1.26932
\(790\) 0 0
\(791\) −7.76628 −0.276137
\(792\) 0 0
\(793\) 75.5694 2.68355
\(794\) 0 0
\(795\) 66.7052 2.36579
\(796\) 0 0
\(797\) 52.3936 1.85588 0.927939 0.372732i \(-0.121579\pi\)
0.927939 + 0.372732i \(0.121579\pi\)
\(798\) 0 0
\(799\) 8.00236 0.283103
\(800\) 0 0
\(801\) −4.36411 −0.154198
\(802\) 0 0
\(803\) 53.6379 1.89284
\(804\) 0 0
\(805\) −7.18579 −0.253266
\(806\) 0 0
\(807\) 36.3413 1.27927
\(808\) 0 0
\(809\) 37.2515 1.30969 0.654847 0.755761i \(-0.272733\pi\)
0.654847 + 0.755761i \(0.272733\pi\)
\(810\) 0 0
\(811\) −41.7528 −1.46614 −0.733069 0.680154i \(-0.761913\pi\)
−0.733069 + 0.680154i \(0.761913\pi\)
\(812\) 0 0
\(813\) 19.7507 0.692687
\(814\) 0 0
\(815\) 1.70108 0.0595861
\(816\) 0 0
\(817\) 19.6494 0.687447
\(818\) 0 0
\(819\) −8.88668 −0.310526
\(820\) 0 0
\(821\) 29.7956 1.03987 0.519937 0.854205i \(-0.325955\pi\)
0.519937 + 0.854205i \(0.325955\pi\)
\(822\) 0 0
\(823\) −6.68038 −0.232864 −0.116432 0.993199i \(-0.537146\pi\)
−0.116432 + 0.993199i \(0.537146\pi\)
\(824\) 0 0
\(825\) −45.6593 −1.58965
\(826\) 0 0
\(827\) −7.26386 −0.252589 −0.126295 0.991993i \(-0.540308\pi\)
−0.126295 + 0.991993i \(0.540308\pi\)
\(828\) 0 0
\(829\) 24.2552 0.842418 0.421209 0.906964i \(-0.361606\pi\)
0.421209 + 0.906964i \(0.361606\pi\)
\(830\) 0 0
\(831\) 3.96586 0.137574
\(832\) 0 0
\(833\) 3.19256 0.110616
\(834\) 0 0
\(835\) −57.6044 −1.99348
\(836\) 0 0
\(837\) −20.2950 −0.701498
\(838\) 0 0
\(839\) 22.3153 0.770411 0.385205 0.922831i \(-0.374131\pi\)
0.385205 + 0.922831i \(0.374131\pi\)
\(840\) 0 0
\(841\) −20.2898 −0.699648
\(842\) 0 0
\(843\) −22.0674 −0.760041
\(844\) 0 0
\(845\) −74.9003 −2.57665
\(846\) 0 0
\(847\) −42.5331 −1.46146
\(848\) 0 0
\(849\) 38.2420 1.31246
\(850\) 0 0
\(851\) −2.23928 −0.0767614
\(852\) 0 0
\(853\) −18.1541 −0.621584 −0.310792 0.950478i \(-0.600594\pi\)
−0.310792 + 0.950478i \(0.600594\pi\)
\(854\) 0 0
\(855\) 6.56565 0.224541
\(856\) 0 0
\(857\) −28.3858 −0.969640 −0.484820 0.874614i \(-0.661115\pi\)
−0.484820 + 0.874614i \(0.661115\pi\)
\(858\) 0 0
\(859\) 5.67840 0.193745 0.0968723 0.995297i \(-0.469116\pi\)
0.0968723 + 0.995297i \(0.469116\pi\)
\(860\) 0 0
\(861\) −16.8015 −0.572594
\(862\) 0 0
\(863\) −7.40600 −0.252103 −0.126052 0.992024i \(-0.540230\pi\)
−0.126052 + 0.992024i \(0.540230\pi\)
\(864\) 0 0
\(865\) −6.74533 −0.229348
\(866\) 0 0
\(867\) −1.49807 −0.0508773
\(868\) 0 0
\(869\) 96.5061 3.27375
\(870\) 0 0
\(871\) −88.0717 −2.98420
\(872\) 0 0
\(873\) −3.53657 −0.119695
\(874\) 0 0
\(875\) 2.01857 0.0682402
\(876\) 0 0
\(877\) −27.6807 −0.934710 −0.467355 0.884070i \(-0.654793\pi\)
−0.467355 + 0.884070i \(0.654793\pi\)
\(878\) 0 0
\(879\) 31.0909 1.04867
\(880\) 0 0
\(881\) −19.3864 −0.653144 −0.326572 0.945172i \(-0.605894\pi\)
−0.326572 + 0.945172i \(0.605894\pi\)
\(882\) 0 0
\(883\) 37.8774 1.27468 0.637339 0.770584i \(-0.280035\pi\)
0.637339 + 0.770584i \(0.280035\pi\)
\(884\) 0 0
\(885\) −4.81299 −0.161787
\(886\) 0 0
\(887\) 23.5198 0.789718 0.394859 0.918742i \(-0.370793\pi\)
0.394859 + 0.918742i \(0.370793\pi\)
\(888\) 0 0
\(889\) 5.15293 0.172824
\(890\) 0 0
\(891\) −35.2864 −1.18214
\(892\) 0 0
\(893\) −21.6383 −0.724098
\(894\) 0 0
\(895\) 52.3780 1.75080
\(896\) 0 0
\(897\) −10.3477 −0.345498
\(898\) 0 0
\(899\) 10.6456 0.355051
\(900\) 0 0
\(901\) −13.8594 −0.461724
\(902\) 0 0
\(903\) 21.2420 0.706889
\(904\) 0 0
\(905\) 5.41234 0.179912
\(906\) 0 0
\(907\) −45.9818 −1.52680 −0.763400 0.645926i \(-0.776471\pi\)
−0.763400 + 0.645926i \(0.776471\pi\)
\(908\) 0 0
\(909\) 3.60472 0.119561
\(910\) 0 0
\(911\) −33.4330 −1.10769 −0.553843 0.832621i \(-0.686839\pi\)
−0.553843 + 0.832621i \(0.686839\pi\)
\(912\) 0 0
\(913\) −1.47053 −0.0486675
\(914\) 0 0
\(915\) −60.3572 −1.99535
\(916\) 0 0
\(917\) 37.0984 1.22510
\(918\) 0 0
\(919\) −50.6378 −1.67039 −0.835194 0.549956i \(-0.814645\pi\)
−0.835194 + 0.549956i \(0.814645\pi\)
\(920\) 0 0
\(921\) 22.7109 0.748351
\(922\) 0 0
\(923\) −86.0870 −2.83359
\(924\) 0 0
\(925\) 10.3969 0.341849
\(926\) 0 0
\(927\) −7.40760 −0.243298
\(928\) 0 0
\(929\) 41.3793 1.35761 0.678806 0.734318i \(-0.262498\pi\)
0.678806 + 0.734318i \(0.262498\pi\)
\(930\) 0 0
\(931\) −8.63265 −0.282924
\(932\) 0 0
\(933\) 30.6060 1.00199
\(934\) 0 0
\(935\) 18.3994 0.601725
\(936\) 0 0
\(937\) −15.9353 −0.520583 −0.260291 0.965530i \(-0.583819\pi\)
−0.260291 + 0.965530i \(0.583819\pi\)
\(938\) 0 0
\(939\) −18.6813 −0.609642
\(940\) 0 0
\(941\) −15.3479 −0.500327 −0.250163 0.968204i \(-0.580484\pi\)
−0.250163 + 0.968204i \(0.580484\pi\)
\(942\) 0 0
\(943\) 6.58832 0.214545
\(944\) 0 0
\(945\) 35.2721 1.14740
\(946\) 0 0
\(947\) −27.1057 −0.880816 −0.440408 0.897798i \(-0.645166\pi\)
−0.440408 + 0.897798i \(0.645166\pi\)
\(948\) 0 0
\(949\) −56.4393 −1.83210
\(950\) 0 0
\(951\) −50.5783 −1.64011
\(952\) 0 0
\(953\) −15.7849 −0.511322 −0.255661 0.966767i \(-0.582293\pi\)
−0.255661 + 0.966767i \(0.582293\pi\)
\(954\) 0 0
\(955\) −43.0531 −1.39317
\(956\) 0 0
\(957\) 25.3203 0.818490
\(958\) 0 0
\(959\) 27.6697 0.893501
\(960\) 0 0
\(961\) −17.9889 −0.580288
\(962\) 0 0
\(963\) −7.93519 −0.255708
\(964\) 0 0
\(965\) 34.7687 1.11924
\(966\) 0 0
\(967\) 42.3601 1.36221 0.681104 0.732187i \(-0.261500\pi\)
0.681104 + 0.732187i \(0.261500\pi\)
\(968\) 0 0
\(969\) 4.05078 0.130130
\(970\) 0 0
\(971\) 8.86695 0.284554 0.142277 0.989827i \(-0.454558\pi\)
0.142277 + 0.989827i \(0.454558\pi\)
\(972\) 0 0
\(973\) 7.49817 0.240380
\(974\) 0 0
\(975\) 48.0441 1.53864
\(976\) 0 0
\(977\) −27.9338 −0.893682 −0.446841 0.894613i \(-0.647451\pi\)
−0.446841 + 0.894613i \(0.647451\pi\)
\(978\) 0 0
\(979\) 33.0694 1.05690
\(980\) 0 0
\(981\) 0.798108 0.0254816
\(982\) 0 0
\(983\) 5.63560 0.179748 0.0898739 0.995953i \(-0.471354\pi\)
0.0898739 + 0.995953i \(0.471354\pi\)
\(984\) 0 0
\(985\) 29.1454 0.928651
\(986\) 0 0
\(987\) −23.3920 −0.744576
\(988\) 0 0
\(989\) −8.32954 −0.264864
\(990\) 0 0
\(991\) −52.1910 −1.65790 −0.828951 0.559322i \(-0.811062\pi\)
−0.828951 + 0.559322i \(0.811062\pi\)
\(992\) 0 0
\(993\) 32.1170 1.01920
\(994\) 0 0
\(995\) −1.92785 −0.0611168
\(996\) 0 0
\(997\) 33.7822 1.06989 0.534946 0.844886i \(-0.320332\pi\)
0.534946 + 0.844886i \(0.320332\pi\)
\(998\) 0 0
\(999\) 10.9917 0.347761
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 \(a_p\))