Properties

Label 8036.2.a.t.1.17
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Root \(2.36764\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.36764 q^{3}\) \(+2.42438 q^{5}\) \(+2.60574 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.36764 q^{3}\) \(+2.42438 q^{5}\) \(+2.60574 q^{9}\) \(-5.39480 q^{11}\) \(+6.20082 q^{13}\) \(+5.74007 q^{15}\) \(-2.01510 q^{17}\) \(+6.62798 q^{19}\) \(+1.84933 q^{23}\) \(+0.877626 q^{25}\) \(-0.933478 q^{27}\) \(+6.47525 q^{29}\) \(-8.80856 q^{31}\) \(-12.7730 q^{33}\) \(+3.09106 q^{37}\) \(+14.6813 q^{39}\) \(-1.00000 q^{41}\) \(+10.5582 q^{43}\) \(+6.31730 q^{45}\) \(+3.78617 q^{47}\) \(-4.77104 q^{51}\) \(-1.87169 q^{53}\) \(-13.0791 q^{55}\) \(+15.6927 q^{57}\) \(+3.79702 q^{59}\) \(+6.72660 q^{61}\) \(+15.0332 q^{65}\) \(-3.50663 q^{67}\) \(+4.37854 q^{69}\) \(+12.6539 q^{71}\) \(+1.71794 q^{73}\) \(+2.07790 q^{75}\) \(-0.277292 q^{79}\) \(-10.0273 q^{81}\) \(-6.38817 q^{83}\) \(-4.88538 q^{85}\) \(+15.3311 q^{87}\) \(-1.19988 q^{89}\) \(-20.8555 q^{93}\) \(+16.0687 q^{95}\) \(-9.32529 q^{97}\) \(-14.0574 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.36764 1.36696 0.683480 0.729969i \(-0.260466\pi\)
0.683480 + 0.729969i \(0.260466\pi\)
\(4\) 0 0
\(5\) 2.42438 1.08422 0.542108 0.840309i \(-0.317626\pi\)
0.542108 + 0.840309i \(0.317626\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 2.60574 0.868579
\(10\) 0 0
\(11\) −5.39480 −1.62659 −0.813297 0.581848i \(-0.802330\pi\)
−0.813297 + 0.581848i \(0.802330\pi\)
\(12\) 0 0
\(13\) 6.20082 1.71980 0.859899 0.510464i \(-0.170526\pi\)
0.859899 + 0.510464i \(0.170526\pi\)
\(14\) 0 0
\(15\) 5.74007 1.48208
\(16\) 0 0
\(17\) −2.01510 −0.488734 −0.244367 0.969683i \(-0.578580\pi\)
−0.244367 + 0.969683i \(0.578580\pi\)
\(18\) 0 0
\(19\) 6.62798 1.52056 0.760281 0.649594i \(-0.225061\pi\)
0.760281 + 0.649594i \(0.225061\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.84933 0.385611 0.192806 0.981237i \(-0.438241\pi\)
0.192806 + 0.981237i \(0.438241\pi\)
\(24\) 0 0
\(25\) 0.877626 0.175525
\(26\) 0 0
\(27\) −0.933478 −0.179648
\(28\) 0 0
\(29\) 6.47525 1.20242 0.601212 0.799090i \(-0.294685\pi\)
0.601212 + 0.799090i \(0.294685\pi\)
\(30\) 0 0
\(31\) −8.80856 −1.58206 −0.791032 0.611775i \(-0.790456\pi\)
−0.791032 + 0.611775i \(0.790456\pi\)
\(32\) 0 0
\(33\) −12.7730 −2.22349
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.09106 0.508167 0.254083 0.967182i \(-0.418226\pi\)
0.254083 + 0.967182i \(0.418226\pi\)
\(38\) 0 0
\(39\) 14.6813 2.35089
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 10.5582 1.61011 0.805055 0.593200i \(-0.202136\pi\)
0.805055 + 0.593200i \(0.202136\pi\)
\(44\) 0 0
\(45\) 6.31730 0.941727
\(46\) 0 0
\(47\) 3.78617 0.552270 0.276135 0.961119i \(-0.410946\pi\)
0.276135 + 0.961119i \(0.410946\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −4.77104 −0.668080
\(52\) 0 0
\(53\) −1.87169 −0.257097 −0.128548 0.991703i \(-0.541032\pi\)
−0.128548 + 0.991703i \(0.541032\pi\)
\(54\) 0 0
\(55\) −13.0791 −1.76358
\(56\) 0 0
\(57\) 15.6927 2.07855
\(58\) 0 0
\(59\) 3.79702 0.494330 0.247165 0.968973i \(-0.420501\pi\)
0.247165 + 0.968973i \(0.420501\pi\)
\(60\) 0 0
\(61\) 6.72660 0.861253 0.430627 0.902530i \(-0.358293\pi\)
0.430627 + 0.902530i \(0.358293\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 15.0332 1.86463
\(66\) 0 0
\(67\) −3.50663 −0.428403 −0.214201 0.976790i \(-0.568715\pi\)
−0.214201 + 0.976790i \(0.568715\pi\)
\(68\) 0 0
\(69\) 4.37854 0.527115
\(70\) 0 0
\(71\) 12.6539 1.50174 0.750871 0.660449i \(-0.229634\pi\)
0.750871 + 0.660449i \(0.229634\pi\)
\(72\) 0 0
\(73\) 1.71794 0.201070 0.100535 0.994934i \(-0.467945\pi\)
0.100535 + 0.994934i \(0.467945\pi\)
\(74\) 0 0
\(75\) 2.07790 0.239936
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.277292 −0.0311978 −0.0155989 0.999878i \(-0.504965\pi\)
−0.0155989 + 0.999878i \(0.504965\pi\)
\(80\) 0 0
\(81\) −10.0273 −1.11415
\(82\) 0 0
\(83\) −6.38817 −0.701193 −0.350596 0.936527i \(-0.614021\pi\)
−0.350596 + 0.936527i \(0.614021\pi\)
\(84\) 0 0
\(85\) −4.88538 −0.529894
\(86\) 0 0
\(87\) 15.3311 1.64366
\(88\) 0 0
\(89\) −1.19988 −0.127187 −0.0635936 0.997976i \(-0.520256\pi\)
−0.0635936 + 0.997976i \(0.520256\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −20.8555 −2.16262
\(94\) 0 0
\(95\) 16.0687 1.64862
\(96\) 0 0
\(97\) −9.32529 −0.946840 −0.473420 0.880837i \(-0.656981\pi\)
−0.473420 + 0.880837i \(0.656981\pi\)
\(98\) 0 0
\(99\) −14.0574 −1.41283
\(100\) 0 0
\(101\) 17.8284 1.77399 0.886996 0.461777i \(-0.152788\pi\)
0.886996 + 0.461777i \(0.152788\pi\)
\(102\) 0 0
\(103\) −0.0560307 −0.00552087 −0.00276044 0.999996i \(-0.500879\pi\)
−0.00276044 + 0.999996i \(0.500879\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.65938 0.933808 0.466904 0.884308i \(-0.345369\pi\)
0.466904 + 0.884308i \(0.345369\pi\)
\(108\) 0 0
\(109\) 17.1326 1.64101 0.820503 0.571643i \(-0.193694\pi\)
0.820503 + 0.571643i \(0.193694\pi\)
\(110\) 0 0
\(111\) 7.31852 0.694644
\(112\) 0 0
\(113\) −14.8841 −1.40018 −0.700090 0.714055i \(-0.746857\pi\)
−0.700090 + 0.714055i \(0.746857\pi\)
\(114\) 0 0
\(115\) 4.48347 0.418086
\(116\) 0 0
\(117\) 16.1577 1.49378
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 18.1039 1.64581
\(122\) 0 0
\(123\) −2.36764 −0.213483
\(124\) 0 0
\(125\) −9.99421 −0.893909
\(126\) 0 0
\(127\) −12.9367 −1.14795 −0.573974 0.818874i \(-0.694599\pi\)
−0.573974 + 0.818874i \(0.694599\pi\)
\(128\) 0 0
\(129\) 24.9980 2.20096
\(130\) 0 0
\(131\) −5.37469 −0.469589 −0.234794 0.972045i \(-0.575442\pi\)
−0.234794 + 0.972045i \(0.575442\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.26311 −0.194777
\(136\) 0 0
\(137\) −7.20652 −0.615695 −0.307847 0.951436i \(-0.599609\pi\)
−0.307847 + 0.951436i \(0.599609\pi\)
\(138\) 0 0
\(139\) −14.3439 −1.21664 −0.608319 0.793693i \(-0.708156\pi\)
−0.608319 + 0.793693i \(0.708156\pi\)
\(140\) 0 0
\(141\) 8.96431 0.754931
\(142\) 0 0
\(143\) −33.4522 −2.79741
\(144\) 0 0
\(145\) 15.6985 1.30369
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.37448 −0.276448 −0.138224 0.990401i \(-0.544139\pi\)
−0.138224 + 0.990401i \(0.544139\pi\)
\(150\) 0 0
\(151\) 4.69407 0.381998 0.190999 0.981590i \(-0.438827\pi\)
0.190999 + 0.981590i \(0.438827\pi\)
\(152\) 0 0
\(153\) −5.25082 −0.424504
\(154\) 0 0
\(155\) −21.3553 −1.71530
\(156\) 0 0
\(157\) 12.5703 1.00322 0.501609 0.865095i \(-0.332742\pi\)
0.501609 + 0.865095i \(0.332742\pi\)
\(158\) 0 0
\(159\) −4.43150 −0.351441
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −15.8637 −1.24254 −0.621272 0.783595i \(-0.713384\pi\)
−0.621272 + 0.783595i \(0.713384\pi\)
\(164\) 0 0
\(165\) −30.9666 −2.41074
\(166\) 0 0
\(167\) 12.4327 0.962070 0.481035 0.876702i \(-0.340261\pi\)
0.481035 + 0.876702i \(0.340261\pi\)
\(168\) 0 0
\(169\) 25.4502 1.95771
\(170\) 0 0
\(171\) 17.2708 1.32073
\(172\) 0 0
\(173\) −13.8812 −1.05536 −0.527682 0.849442i \(-0.676939\pi\)
−0.527682 + 0.849442i \(0.676939\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 8.98999 0.675729
\(178\) 0 0
\(179\) −15.1352 −1.13126 −0.565628 0.824660i \(-0.691366\pi\)
−0.565628 + 0.824660i \(0.691366\pi\)
\(180\) 0 0
\(181\) 1.24711 0.0926968 0.0463484 0.998925i \(-0.485242\pi\)
0.0463484 + 0.998925i \(0.485242\pi\)
\(182\) 0 0
\(183\) 15.9262 1.17730
\(184\) 0 0
\(185\) 7.49391 0.550963
\(186\) 0 0
\(187\) 10.8711 0.794972
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 24.9998 1.80892 0.904460 0.426559i \(-0.140274\pi\)
0.904460 + 0.426559i \(0.140274\pi\)
\(192\) 0 0
\(193\) 20.6634 1.48739 0.743693 0.668522i \(-0.233073\pi\)
0.743693 + 0.668522i \(0.233073\pi\)
\(194\) 0 0
\(195\) 35.5931 2.54888
\(196\) 0 0
\(197\) 11.4928 0.818828 0.409414 0.912349i \(-0.365733\pi\)
0.409414 + 0.912349i \(0.365733\pi\)
\(198\) 0 0
\(199\) 3.57078 0.253126 0.126563 0.991959i \(-0.459605\pi\)
0.126563 + 0.991959i \(0.459605\pi\)
\(200\) 0 0
\(201\) −8.30244 −0.585609
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.42438 −0.169326
\(206\) 0 0
\(207\) 4.81885 0.334933
\(208\) 0 0
\(209\) −35.7567 −2.47334
\(210\) 0 0
\(211\) 15.7479 1.08413 0.542064 0.840337i \(-0.317643\pi\)
0.542064 + 0.840337i \(0.317643\pi\)
\(212\) 0 0
\(213\) 29.9599 2.05282
\(214\) 0 0
\(215\) 25.5971 1.74571
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.06747 0.274854
\(220\) 0 0
\(221\) −12.4953 −0.840524
\(222\) 0 0
\(223\) 5.43674 0.364071 0.182035 0.983292i \(-0.441731\pi\)
0.182035 + 0.983292i \(0.441731\pi\)
\(224\) 0 0
\(225\) 2.28686 0.152457
\(226\) 0 0
\(227\) −20.0641 −1.33170 −0.665852 0.746084i \(-0.731932\pi\)
−0.665852 + 0.746084i \(0.731932\pi\)
\(228\) 0 0
\(229\) 12.3577 0.816617 0.408309 0.912844i \(-0.366119\pi\)
0.408309 + 0.912844i \(0.366119\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.65717 0.501638 0.250819 0.968034i \(-0.419300\pi\)
0.250819 + 0.968034i \(0.419300\pi\)
\(234\) 0 0
\(235\) 9.17913 0.598780
\(236\) 0 0
\(237\) −0.656528 −0.0426461
\(238\) 0 0
\(239\) 0.492584 0.0318626 0.0159313 0.999873i \(-0.494929\pi\)
0.0159313 + 0.999873i \(0.494929\pi\)
\(240\) 0 0
\(241\) 24.1779 1.55744 0.778719 0.627373i \(-0.215870\pi\)
0.778719 + 0.627373i \(0.215870\pi\)
\(242\) 0 0
\(243\) −20.9408 −1.34335
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 41.0989 2.61506
\(248\) 0 0
\(249\) −15.1249 −0.958502
\(250\) 0 0
\(251\) −24.9113 −1.57239 −0.786193 0.617981i \(-0.787951\pi\)
−0.786193 + 0.617981i \(0.787951\pi\)
\(252\) 0 0
\(253\) −9.97675 −0.627233
\(254\) 0 0
\(255\) −11.5668 −0.724343
\(256\) 0 0
\(257\) −7.95771 −0.496388 −0.248194 0.968710i \(-0.579837\pi\)
−0.248194 + 0.968710i \(0.579837\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 16.8728 1.04440
\(262\) 0 0
\(263\) −16.0497 −0.989668 −0.494834 0.868987i \(-0.664771\pi\)
−0.494834 + 0.868987i \(0.664771\pi\)
\(264\) 0 0
\(265\) −4.53770 −0.278749
\(266\) 0 0
\(267\) −2.84089 −0.173860
\(268\) 0 0
\(269\) 16.6584 1.01568 0.507840 0.861451i \(-0.330444\pi\)
0.507840 + 0.861451i \(0.330444\pi\)
\(270\) 0 0
\(271\) 2.52867 0.153605 0.0768027 0.997046i \(-0.475529\pi\)
0.0768027 + 0.997046i \(0.475529\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.73462 −0.285508
\(276\) 0 0
\(277\) 0.883573 0.0530887 0.0265444 0.999648i \(-0.491550\pi\)
0.0265444 + 0.999648i \(0.491550\pi\)
\(278\) 0 0
\(279\) −22.9528 −1.37415
\(280\) 0 0
\(281\) −4.76979 −0.284542 −0.142271 0.989828i \(-0.545440\pi\)
−0.142271 + 0.989828i \(0.545440\pi\)
\(282\) 0 0
\(283\) −23.6795 −1.40760 −0.703800 0.710398i \(-0.748515\pi\)
−0.703800 + 0.710398i \(0.748515\pi\)
\(284\) 0 0
\(285\) 38.0451 2.25360
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −12.9394 −0.761139
\(290\) 0 0
\(291\) −22.0790 −1.29429
\(292\) 0 0
\(293\) 23.2377 1.35756 0.678780 0.734342i \(-0.262509\pi\)
0.678780 + 0.734342i \(0.262509\pi\)
\(294\) 0 0
\(295\) 9.20543 0.535961
\(296\) 0 0
\(297\) 5.03593 0.292214
\(298\) 0 0
\(299\) 11.4673 0.663173
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 42.2113 2.42498
\(304\) 0 0
\(305\) 16.3078 0.933785
\(306\) 0 0
\(307\) 26.2175 1.49631 0.748155 0.663524i \(-0.230940\pi\)
0.748155 + 0.663524i \(0.230940\pi\)
\(308\) 0 0
\(309\) −0.132661 −0.00754681
\(310\) 0 0
\(311\) −20.3994 −1.15675 −0.578373 0.815772i \(-0.696312\pi\)
−0.578373 + 0.815772i \(0.696312\pi\)
\(312\) 0 0
\(313\) 11.7718 0.665381 0.332691 0.943036i \(-0.392044\pi\)
0.332691 + 0.943036i \(0.392044\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.4111 −1.03407 −0.517036 0.855964i \(-0.672965\pi\)
−0.517036 + 0.855964i \(0.672965\pi\)
\(318\) 0 0
\(319\) −34.9327 −1.95586
\(320\) 0 0
\(321\) 22.8700 1.27648
\(322\) 0 0
\(323\) −13.3561 −0.743151
\(324\) 0 0
\(325\) 5.44200 0.301868
\(326\) 0 0
\(327\) 40.5639 2.24319
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −32.6689 −1.79564 −0.897822 0.440359i \(-0.854851\pi\)
−0.897822 + 0.440359i \(0.854851\pi\)
\(332\) 0 0
\(333\) 8.05448 0.441383
\(334\) 0 0
\(335\) −8.50140 −0.464481
\(336\) 0 0
\(337\) 27.0008 1.47083 0.735413 0.677619i \(-0.236988\pi\)
0.735413 + 0.677619i \(0.236988\pi\)
\(338\) 0 0
\(339\) −35.2403 −1.91399
\(340\) 0 0
\(341\) 47.5205 2.57338
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 10.6153 0.571506
\(346\) 0 0
\(347\) −25.9286 −1.39192 −0.695959 0.718082i \(-0.745020\pi\)
−0.695959 + 0.718082i \(0.745020\pi\)
\(348\) 0 0
\(349\) −33.7455 −1.80636 −0.903178 0.429267i \(-0.858772\pi\)
−0.903178 + 0.429267i \(0.858772\pi\)
\(350\) 0 0
\(351\) −5.78833 −0.308958
\(352\) 0 0
\(353\) −37.3762 −1.98933 −0.994667 0.103142i \(-0.967110\pi\)
−0.994667 + 0.103142i \(0.967110\pi\)
\(354\) 0 0
\(355\) 30.6779 1.62821
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −33.3640 −1.76089 −0.880443 0.474153i \(-0.842754\pi\)
−0.880443 + 0.474153i \(0.842754\pi\)
\(360\) 0 0
\(361\) 24.9301 1.31211
\(362\) 0 0
\(363\) 42.8636 2.24976
\(364\) 0 0
\(365\) 4.16494 0.218003
\(366\) 0 0
\(367\) 14.1406 0.738132 0.369066 0.929403i \(-0.379678\pi\)
0.369066 + 0.929403i \(0.379678\pi\)
\(368\) 0 0
\(369\) −2.60574 −0.135649
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.6001 −0.548852 −0.274426 0.961608i \(-0.588488\pi\)
−0.274426 + 0.961608i \(0.588488\pi\)
\(374\) 0 0
\(375\) −23.6627 −1.22194
\(376\) 0 0
\(377\) 40.1519 2.06793
\(378\) 0 0
\(379\) −18.9849 −0.975190 −0.487595 0.873070i \(-0.662126\pi\)
−0.487595 + 0.873070i \(0.662126\pi\)
\(380\) 0 0
\(381\) −30.6295 −1.56920
\(382\) 0 0
\(383\) −15.1555 −0.774411 −0.387205 0.921993i \(-0.626560\pi\)
−0.387205 + 0.921993i \(0.626560\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 27.5119 1.39851
\(388\) 0 0
\(389\) −7.74145 −0.392507 −0.196254 0.980553i \(-0.562878\pi\)
−0.196254 + 0.980553i \(0.562878\pi\)
\(390\) 0 0
\(391\) −3.72658 −0.188461
\(392\) 0 0
\(393\) −12.7254 −0.641909
\(394\) 0 0
\(395\) −0.672261 −0.0338251
\(396\) 0 0
\(397\) 17.9596 0.901368 0.450684 0.892683i \(-0.351180\pi\)
0.450684 + 0.892683i \(0.351180\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 19.3204 0.964817 0.482408 0.875947i \(-0.339762\pi\)
0.482408 + 0.875947i \(0.339762\pi\)
\(402\) 0 0
\(403\) −54.6203 −2.72083
\(404\) 0 0
\(405\) −24.3101 −1.20798
\(406\) 0 0
\(407\) −16.6757 −0.826582
\(408\) 0 0
\(409\) 8.50740 0.420664 0.210332 0.977630i \(-0.432545\pi\)
0.210332 + 0.977630i \(0.432545\pi\)
\(410\) 0 0
\(411\) −17.0625 −0.841630
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −15.4874 −0.760245
\(416\) 0 0
\(417\) −33.9613 −1.66309
\(418\) 0 0
\(419\) −23.9947 −1.17222 −0.586108 0.810233i \(-0.699341\pi\)
−0.586108 + 0.810233i \(0.699341\pi\)
\(420\) 0 0
\(421\) −33.7635 −1.64553 −0.822766 0.568380i \(-0.807570\pi\)
−0.822766 + 0.568380i \(0.807570\pi\)
\(422\) 0 0
\(423\) 9.86577 0.479690
\(424\) 0 0
\(425\) −1.76851 −0.0857851
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −79.2029 −3.82395
\(430\) 0 0
\(431\) 9.44247 0.454828 0.227414 0.973798i \(-0.426973\pi\)
0.227414 + 0.973798i \(0.426973\pi\)
\(432\) 0 0
\(433\) −11.6428 −0.559516 −0.279758 0.960071i \(-0.590254\pi\)
−0.279758 + 0.960071i \(0.590254\pi\)
\(434\) 0 0
\(435\) 37.1684 1.78209
\(436\) 0 0
\(437\) 12.2573 0.586346
\(438\) 0 0
\(439\) −11.9530 −0.570486 −0.285243 0.958455i \(-0.592074\pi\)
−0.285243 + 0.958455i \(0.592074\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 24.3873 1.15868 0.579339 0.815087i \(-0.303311\pi\)
0.579339 + 0.815087i \(0.303311\pi\)
\(444\) 0 0
\(445\) −2.90897 −0.137898
\(446\) 0 0
\(447\) −7.98957 −0.377894
\(448\) 0 0
\(449\) −6.58128 −0.310590 −0.155295 0.987868i \(-0.549633\pi\)
−0.155295 + 0.987868i \(0.549633\pi\)
\(450\) 0 0
\(451\) 5.39480 0.254031
\(452\) 0 0
\(453\) 11.1139 0.522175
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −32.5508 −1.52266 −0.761331 0.648364i \(-0.775454\pi\)
−0.761331 + 0.648364i \(0.775454\pi\)
\(458\) 0 0
\(459\) 1.88105 0.0878001
\(460\) 0 0
\(461\) 26.6674 1.24203 0.621013 0.783801i \(-0.286722\pi\)
0.621013 + 0.783801i \(0.286722\pi\)
\(462\) 0 0
\(463\) 22.9214 1.06525 0.532624 0.846352i \(-0.321206\pi\)
0.532624 + 0.846352i \(0.321206\pi\)
\(464\) 0 0
\(465\) −50.5618 −2.34475
\(466\) 0 0
\(467\) 14.7685 0.683406 0.341703 0.939808i \(-0.388996\pi\)
0.341703 + 0.939808i \(0.388996\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 29.7619 1.37136
\(472\) 0 0
\(473\) −56.9594 −2.61900
\(474\) 0 0
\(475\) 5.81688 0.266897
\(476\) 0 0
\(477\) −4.87714 −0.223309
\(478\) 0 0
\(479\) −11.8208 −0.540105 −0.270053 0.962846i \(-0.587041\pi\)
−0.270053 + 0.962846i \(0.587041\pi\)
\(480\) 0 0
\(481\) 19.1671 0.873944
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −22.6081 −1.02658
\(486\) 0 0
\(487\) 16.4003 0.743167 0.371584 0.928399i \(-0.378815\pi\)
0.371584 + 0.928399i \(0.378815\pi\)
\(488\) 0 0
\(489\) −37.5597 −1.69851
\(490\) 0 0
\(491\) 30.3512 1.36973 0.684866 0.728669i \(-0.259861\pi\)
0.684866 + 0.728669i \(0.259861\pi\)
\(492\) 0 0
\(493\) −13.0483 −0.587666
\(494\) 0 0
\(495\) −34.0806 −1.53181
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 21.3568 0.956060 0.478030 0.878344i \(-0.341351\pi\)
0.478030 + 0.878344i \(0.341351\pi\)
\(500\) 0 0
\(501\) 29.4362 1.31511
\(502\) 0 0
\(503\) 12.7631 0.569079 0.284540 0.958664i \(-0.408159\pi\)
0.284540 + 0.958664i \(0.408159\pi\)
\(504\) 0 0
\(505\) 43.2229 1.92339
\(506\) 0 0
\(507\) 60.2569 2.67610
\(508\) 0 0
\(509\) −17.2326 −0.763821 −0.381911 0.924199i \(-0.624734\pi\)
−0.381911 + 0.924199i \(0.624734\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −6.18707 −0.273166
\(514\) 0 0
\(515\) −0.135840 −0.00598582
\(516\) 0 0
\(517\) −20.4257 −0.898320
\(518\) 0 0
\(519\) −32.8656 −1.44264
\(520\) 0 0
\(521\) 5.39754 0.236471 0.118235 0.992986i \(-0.462276\pi\)
0.118235 + 0.992986i \(0.462276\pi\)
\(522\) 0 0
\(523\) −44.8818 −1.96254 −0.981271 0.192633i \(-0.938297\pi\)
−0.981271 + 0.192633i \(0.938297\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 17.7502 0.773209
\(528\) 0 0
\(529\) −19.5800 −0.851304
\(530\) 0 0
\(531\) 9.89403 0.429364
\(532\) 0 0
\(533\) −6.20082 −0.268587
\(534\) 0 0
\(535\) 23.4180 1.01245
\(536\) 0 0
\(537\) −35.8347 −1.54638
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −33.3053 −1.43191 −0.715954 0.698147i \(-0.754008\pi\)
−0.715954 + 0.698147i \(0.754008\pi\)
\(542\) 0 0
\(543\) 2.95271 0.126713
\(544\) 0 0
\(545\) 41.5360 1.77920
\(546\) 0 0
\(547\) −11.1540 −0.476913 −0.238456 0.971153i \(-0.576641\pi\)
−0.238456 + 0.971153i \(0.576641\pi\)
\(548\) 0 0
\(549\) 17.5277 0.748066
\(550\) 0 0
\(551\) 42.9178 1.82836
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 17.7429 0.753144
\(556\) 0 0
\(557\) −0.446080 −0.0189010 −0.00945050 0.999955i \(-0.503008\pi\)
−0.00945050 + 0.999955i \(0.503008\pi\)
\(558\) 0 0
\(559\) 65.4695 2.76906
\(560\) 0 0
\(561\) 25.7389 1.08670
\(562\) 0 0
\(563\) −25.2991 −1.06623 −0.533116 0.846042i \(-0.678979\pi\)
−0.533116 + 0.846042i \(0.678979\pi\)
\(564\) 0 0
\(565\) −36.0848 −1.51810
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11.4740 −0.481014 −0.240507 0.970647i \(-0.577314\pi\)
−0.240507 + 0.970647i \(0.577314\pi\)
\(570\) 0 0
\(571\) 26.1564 1.09461 0.547305 0.836933i \(-0.315654\pi\)
0.547305 + 0.836933i \(0.315654\pi\)
\(572\) 0 0
\(573\) 59.1905 2.47272
\(574\) 0 0
\(575\) 1.62302 0.0676844
\(576\) 0 0
\(577\) −19.5225 −0.812733 −0.406366 0.913710i \(-0.633204\pi\)
−0.406366 + 0.913710i \(0.633204\pi\)
\(578\) 0 0
\(579\) 48.9236 2.03320
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 10.0974 0.418193
\(584\) 0 0
\(585\) 39.1724 1.61958
\(586\) 0 0
\(587\) −18.2892 −0.754875 −0.377438 0.926035i \(-0.623195\pi\)
−0.377438 + 0.926035i \(0.623195\pi\)
\(588\) 0 0
\(589\) −58.3829 −2.40563
\(590\) 0 0
\(591\) 27.2109 1.11930
\(592\) 0 0
\(593\) 5.93664 0.243788 0.121894 0.992543i \(-0.461103\pi\)
0.121894 + 0.992543i \(0.461103\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 8.45434 0.346013
\(598\) 0 0
\(599\) 11.1101 0.453945 0.226972 0.973901i \(-0.427117\pi\)
0.226972 + 0.973901i \(0.427117\pi\)
\(600\) 0 0
\(601\) 45.6877 1.86364 0.931820 0.362921i \(-0.118220\pi\)
0.931820 + 0.362921i \(0.118220\pi\)
\(602\) 0 0
\(603\) −9.13734 −0.372101
\(604\) 0 0
\(605\) 43.8908 1.78441
\(606\) 0 0
\(607\) −11.3754 −0.461713 −0.230857 0.972988i \(-0.574153\pi\)
−0.230857 + 0.972988i \(0.574153\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 23.4774 0.949793
\(612\) 0 0
\(613\) 9.53763 0.385221 0.192611 0.981275i \(-0.438305\pi\)
0.192611 + 0.981275i \(0.438305\pi\)
\(614\) 0 0
\(615\) −5.74007 −0.231462
\(616\) 0 0
\(617\) −11.5729 −0.465907 −0.232954 0.972488i \(-0.574839\pi\)
−0.232954 + 0.972488i \(0.574839\pi\)
\(618\) 0 0
\(619\) 47.1787 1.89627 0.948137 0.317863i \(-0.102965\pi\)
0.948137 + 0.317863i \(0.102965\pi\)
\(620\) 0 0
\(621\) −1.72630 −0.0692742
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −28.6179 −1.14472
\(626\) 0 0
\(627\) −84.6590 −3.38095
\(628\) 0 0
\(629\) −6.22880 −0.248359
\(630\) 0 0
\(631\) −33.0915 −1.31735 −0.658675 0.752427i \(-0.728883\pi\)
−0.658675 + 0.752427i \(0.728883\pi\)
\(632\) 0 0
\(633\) 37.2853 1.48196
\(634\) 0 0
\(635\) −31.3635 −1.24462
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 32.9727 1.30438
\(640\) 0 0
\(641\) −14.1502 −0.558898 −0.279449 0.960161i \(-0.590152\pi\)
−0.279449 + 0.960161i \(0.590152\pi\)
\(642\) 0 0
\(643\) 6.23293 0.245803 0.122901 0.992419i \(-0.460780\pi\)
0.122901 + 0.992419i \(0.460780\pi\)
\(644\) 0 0
\(645\) 60.6048 2.38631
\(646\) 0 0
\(647\) −46.0471 −1.81030 −0.905149 0.425094i \(-0.860241\pi\)
−0.905149 + 0.425094i \(0.860241\pi\)
\(648\) 0 0
\(649\) −20.4842 −0.804074
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.07124 0.0810540 0.0405270 0.999178i \(-0.487096\pi\)
0.0405270 + 0.999178i \(0.487096\pi\)
\(654\) 0 0
\(655\) −13.0303 −0.509136
\(656\) 0 0
\(657\) 4.47650 0.174645
\(658\) 0 0
\(659\) 3.83230 0.149285 0.0746427 0.997210i \(-0.476218\pi\)
0.0746427 + 0.997210i \(0.476218\pi\)
\(660\) 0 0
\(661\) 19.0169 0.739670 0.369835 0.929097i \(-0.379414\pi\)
0.369835 + 0.929097i \(0.379414\pi\)
\(662\) 0 0
\(663\) −29.5844 −1.14896
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 11.9748 0.463668
\(668\) 0 0
\(669\) 12.8723 0.497670
\(670\) 0 0
\(671\) −36.2887 −1.40091
\(672\) 0 0
\(673\) −27.0308 −1.04196 −0.520981 0.853568i \(-0.674434\pi\)
−0.520981 + 0.853568i \(0.674434\pi\)
\(674\) 0 0
\(675\) −0.819244 −0.0315327
\(676\) 0 0
\(677\) 21.8341 0.839153 0.419577 0.907720i \(-0.362179\pi\)
0.419577 + 0.907720i \(0.362179\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −47.5047 −1.82038
\(682\) 0 0
\(683\) −1.52594 −0.0583886 −0.0291943 0.999574i \(-0.509294\pi\)
−0.0291943 + 0.999574i \(0.509294\pi\)
\(684\) 0 0
\(685\) −17.4714 −0.667546
\(686\) 0 0
\(687\) 29.2585 1.11628
\(688\) 0 0
\(689\) −11.6060 −0.442155
\(690\) 0 0
\(691\) −21.3213 −0.811101 −0.405551 0.914073i \(-0.632920\pi\)
−0.405551 + 0.914073i \(0.632920\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −34.7752 −1.31910
\(696\) 0 0
\(697\) 2.01510 0.0763275
\(698\) 0 0
\(699\) 18.1294 0.685718
\(700\) 0 0
\(701\) −24.5558 −0.927460 −0.463730 0.885977i \(-0.653489\pi\)
−0.463730 + 0.885977i \(0.653489\pi\)
\(702\) 0 0
\(703\) 20.4875 0.772700
\(704\) 0 0
\(705\) 21.7329 0.818509
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 33.9389 1.27460 0.637301 0.770615i \(-0.280051\pi\)
0.637301 + 0.770615i \(0.280051\pi\)
\(710\) 0 0
\(711\) −0.722549 −0.0270977
\(712\) 0 0
\(713\) −16.2899 −0.610061
\(714\) 0 0
\(715\) −81.1009 −3.03300
\(716\) 0 0
\(717\) 1.16626 0.0435549
\(718\) 0 0
\(719\) 15.1635 0.565501 0.282751 0.959193i \(-0.408753\pi\)
0.282751 + 0.959193i \(0.408753\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 57.2448 2.12896
\(724\) 0 0
\(725\) 5.68285 0.211056
\(726\) 0 0
\(727\) 14.2238 0.527533 0.263766 0.964587i \(-0.415035\pi\)
0.263766 + 0.964587i \(0.415035\pi\)
\(728\) 0 0
\(729\) −19.4982 −0.722155
\(730\) 0 0
\(731\) −21.2759 −0.786916
\(732\) 0 0
\(733\) −4.49898 −0.166174 −0.0830869 0.996542i \(-0.526478\pi\)
−0.0830869 + 0.996542i \(0.526478\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.9176 0.696837
\(738\) 0 0
\(739\) −42.9630 −1.58042 −0.790210 0.612837i \(-0.790028\pi\)
−0.790210 + 0.612837i \(0.790028\pi\)
\(740\) 0 0
\(741\) 97.3075 3.57468
\(742\) 0 0
\(743\) 37.4336 1.37331 0.686654 0.726985i \(-0.259079\pi\)
0.686654 + 0.726985i \(0.259079\pi\)
\(744\) 0 0
\(745\) −8.18103 −0.299730
\(746\) 0 0
\(747\) −16.6459 −0.609041
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −28.7039 −1.04742 −0.523711 0.851896i \(-0.675453\pi\)
−0.523711 + 0.851896i \(0.675453\pi\)
\(752\) 0 0
\(753\) −58.9810 −2.14939
\(754\) 0 0
\(755\) 11.3802 0.414168
\(756\) 0 0
\(757\) 12.8034 0.465348 0.232674 0.972555i \(-0.425252\pi\)
0.232674 + 0.972555i \(0.425252\pi\)
\(758\) 0 0
\(759\) −23.6214 −0.857402
\(760\) 0 0
\(761\) −28.2763 −1.02501 −0.512507 0.858683i \(-0.671283\pi\)
−0.512507 + 0.858683i \(0.671283\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −12.7300 −0.460254
\(766\) 0 0
\(767\) 23.5446 0.850148
\(768\) 0 0
\(769\) 36.7877 1.32660 0.663299 0.748354i \(-0.269156\pi\)
0.663299 + 0.748354i \(0.269156\pi\)
\(770\) 0 0
\(771\) −18.8410 −0.678543
\(772\) 0 0
\(773\) −12.2330 −0.439991 −0.219996 0.975501i \(-0.570604\pi\)
−0.219996 + 0.975501i \(0.570604\pi\)
\(774\) 0 0
\(775\) −7.73062 −0.277692
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.62798 −0.237472
\(780\) 0 0
\(781\) −68.2654 −2.44273
\(782\) 0 0
\(783\) −6.04450 −0.216013
\(784\) 0 0
\(785\) 30.4752 1.08771
\(786\) 0 0
\(787\) 13.3678 0.476511 0.238256 0.971202i \(-0.423424\pi\)
0.238256 + 0.971202i \(0.423424\pi\)
\(788\) 0 0
\(789\) −38.0000 −1.35284
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 41.7104 1.48118
\(794\) 0 0
\(795\) −10.7437 −0.381038
\(796\) 0 0
\(797\) −44.5584 −1.57834 −0.789169 0.614176i \(-0.789489\pi\)
−0.789169 + 0.614176i \(0.789489\pi\)
\(798\) 0 0
\(799\) −7.62953 −0.269913
\(800\) 0 0
\(801\) −3.12657 −0.110472
\(802\) 0 0
\(803\) −9.26796 −0.327059
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 39.4411 1.38839
\(808\) 0 0
\(809\) −36.8454 −1.29542 −0.647708 0.761888i \(-0.724272\pi\)
−0.647708 + 0.761888i \(0.724272\pi\)
\(810\) 0 0
\(811\) 3.28194 0.115244 0.0576222 0.998338i \(-0.481648\pi\)
0.0576222 + 0.998338i \(0.481648\pi\)
\(812\) 0 0
\(813\) 5.98698 0.209972
\(814\) 0 0
\(815\) −38.4598 −1.34719
\(816\) 0 0
\(817\) 69.9795 2.44827
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 47.0394 1.64169 0.820843 0.571154i \(-0.193504\pi\)
0.820843 + 0.571154i \(0.193504\pi\)
\(822\) 0 0
\(823\) 14.4688 0.504350 0.252175 0.967682i \(-0.418854\pi\)
0.252175 + 0.967682i \(0.418854\pi\)
\(824\) 0 0
\(825\) −11.2099 −0.390278
\(826\) 0 0
\(827\) −24.2290 −0.842526 −0.421263 0.906939i \(-0.638413\pi\)
−0.421263 + 0.906939i \(0.638413\pi\)
\(828\) 0 0
\(829\) 7.50568 0.260683 0.130342 0.991469i \(-0.458393\pi\)
0.130342 + 0.991469i \(0.458393\pi\)
\(830\) 0 0
\(831\) 2.09198 0.0725701
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 30.1416 1.04309
\(836\) 0 0
\(837\) 8.22259 0.284214
\(838\) 0 0
\(839\) 1.05557 0.0364424 0.0182212 0.999834i \(-0.494200\pi\)
0.0182212 + 0.999834i \(0.494200\pi\)
\(840\) 0 0
\(841\) 12.9289 0.445823
\(842\) 0 0
\(843\) −11.2932 −0.388957
\(844\) 0 0
\(845\) 61.7009 2.12258
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −56.0646 −1.92413
\(850\) 0 0
\(851\) 5.71637 0.195955
\(852\) 0 0
\(853\) −30.6698 −1.05011 −0.525056 0.851067i \(-0.675956\pi\)
−0.525056 + 0.851067i \(0.675956\pi\)
\(854\) 0 0
\(855\) 41.8709 1.43195
\(856\) 0 0
\(857\) 20.5630 0.702420 0.351210 0.936297i \(-0.385770\pi\)
0.351210 + 0.936297i \(0.385770\pi\)
\(858\) 0 0
\(859\) 7.90583 0.269743 0.134872 0.990863i \(-0.456938\pi\)
0.134872 + 0.990863i \(0.456938\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 19.1040 0.650307 0.325153 0.945661i \(-0.394584\pi\)
0.325153 + 0.945661i \(0.394584\pi\)
\(864\) 0 0
\(865\) −33.6532 −1.14424
\(866\) 0 0
\(867\) −30.6358 −1.04045
\(868\) 0 0
\(869\) 1.49594 0.0507461
\(870\) 0 0
\(871\) −21.7440 −0.736766
\(872\) 0 0
\(873\) −24.2992 −0.822405
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.798972 0.0269794 0.0134897 0.999909i \(-0.495706\pi\)
0.0134897 + 0.999909i \(0.495706\pi\)
\(878\) 0 0
\(879\) 55.0185 1.85573
\(880\) 0 0
\(881\) −45.1673 −1.52172 −0.760862 0.648913i \(-0.775224\pi\)
−0.760862 + 0.648913i \(0.775224\pi\)
\(882\) 0 0
\(883\) 0.569815 0.0191758 0.00958790 0.999954i \(-0.496948\pi\)
0.00958790 + 0.999954i \(0.496948\pi\)
\(884\) 0 0
\(885\) 21.7952 0.732636
\(886\) 0 0
\(887\) −17.3283 −0.581827 −0.290913 0.956749i \(-0.593959\pi\)
−0.290913 + 0.956749i \(0.593959\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 54.0956 1.81227
\(892\) 0 0
\(893\) 25.0947 0.839761
\(894\) 0 0
\(895\) −36.6935 −1.22653
\(896\) 0 0
\(897\) 27.1506 0.906531
\(898\) 0 0
\(899\) −57.0376 −1.90231
\(900\) 0 0
\(901\) 3.77166 0.125652
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.02347 0.100503
\(906\) 0 0
\(907\) −0.570307 −0.0189367 −0.00946836 0.999955i \(-0.503014\pi\)
−0.00946836 + 0.999955i \(0.503014\pi\)
\(908\) 0 0
\(909\) 46.4561 1.54085
\(910\) 0 0
\(911\) −0.0757389 −0.00250934 −0.00125467 0.999999i \(-0.500399\pi\)
−0.00125467 + 0.999999i \(0.500399\pi\)
\(912\) 0 0
\(913\) 34.4629 1.14056
\(914\) 0 0
\(915\) 38.6112 1.27645
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 8.78886 0.289918 0.144959 0.989438i \(-0.453695\pi\)
0.144959 + 0.989438i \(0.453695\pi\)
\(920\) 0 0
\(921\) 62.0736 2.04540
\(922\) 0 0
\(923\) 78.4646 2.58269
\(924\) 0 0
\(925\) 2.71279 0.0891961
\(926\) 0 0
\(927\) −0.146001 −0.00479531
\(928\) 0 0
\(929\) −23.2132 −0.761600 −0.380800 0.924658i \(-0.624351\pi\)
−0.380800 + 0.924658i \(0.624351\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −48.2986 −1.58123
\(934\) 0 0
\(935\) 26.3557 0.861922
\(936\) 0 0
\(937\) 38.2589 1.24986 0.624931 0.780680i \(-0.285127\pi\)
0.624931 + 0.780680i \(0.285127\pi\)
\(938\) 0 0
\(939\) 27.8714 0.909549
\(940\) 0 0
\(941\) 0.504301 0.0164398 0.00821988 0.999966i \(-0.497384\pi\)
0.00821988 + 0.999966i \(0.497384\pi\)
\(942\) 0 0
\(943\) −1.84933 −0.0602223
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.1942 1.17615 0.588076 0.808805i \(-0.299885\pi\)
0.588076 + 0.808805i \(0.299885\pi\)
\(948\) 0 0
\(949\) 10.6526 0.345799
\(950\) 0 0
\(951\) −43.5910 −1.41353
\(952\) 0 0
\(953\) 19.7072 0.638378 0.319189 0.947691i \(-0.396590\pi\)
0.319189 + 0.947691i \(0.396590\pi\)
\(954\) 0 0
\(955\) 60.6090 1.96126
\(956\) 0 0
\(957\) −82.7082 −2.67358
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 46.5907 1.50293
\(962\) 0 0
\(963\) 25.1698 0.811085
\(964\) 0 0
\(965\) 50.0960 1.61265
\(966\) 0 0
\(967\) −52.6805 −1.69409 −0.847046 0.531520i \(-0.821621\pi\)
−0.847046 + 0.531520i \(0.821621\pi\)
\(968\) 0 0
\(969\) −31.6224 −1.01586
\(970\) 0 0
\(971\) 45.1542 1.44907 0.724534 0.689239i \(-0.242055\pi\)
0.724534 + 0.689239i \(0.242055\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 12.8847 0.412641
\(976\) 0 0
\(977\) 10.5637 0.337962 0.168981 0.985619i \(-0.445952\pi\)
0.168981 + 0.985619i \(0.445952\pi\)
\(978\) 0 0
\(979\) 6.47313 0.206882
\(980\) 0 0
\(981\) 44.6430 1.42534
\(982\) 0 0
\(983\) −56.1922 −1.79225 −0.896126 0.443799i \(-0.853630\pi\)
−0.896126 + 0.443799i \(0.853630\pi\)
\(984\) 0 0
\(985\) 27.8629 0.887787
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 19.5255 0.620876
\(990\) 0 0
\(991\) −0.796507 −0.0253019 −0.0126509 0.999920i \(-0.504027\pi\)
−0.0126509 + 0.999920i \(0.504027\pi\)
\(992\) 0 0
\(993\) −77.3482 −2.45457
\(994\) 0 0
\(995\) 8.65694 0.274443
\(996\) 0 0
\(997\) −26.8484 −0.850297 −0.425148 0.905124i \(-0.639778\pi\)
−0.425148 + 0.905124i \(0.639778\pi\)
\(998\) 0 0
\(999\) −2.88543 −0.0912911
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 \(a_p\))