Properties

Label 23.3.b.a.22.1
Level 23
Weight 3
Character 23.22
Self dual Yes
Analytic conductor 0.627
Analytic rank 0
Dimension 3
CM disc. -23
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 23.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.626704608029\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.621.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 22.1
Root \(-0.523976\)
Character \(\chi\) = 23.22

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.72545 q^{2}\) \(+4.24943 q^{3}\) \(+9.87897 q^{4}\) \(-15.8310 q^{6}\) \(-21.9018 q^{8}\) \(+9.05761 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.72545 q^{2}\) \(+4.24943 q^{3}\) \(+9.87897 q^{4}\) \(-15.8310 q^{6}\) \(-21.9018 q^{8}\) \(+9.05761 q^{9}\) \(+41.9799 q^{12}\) \(-21.3624 q^{13}\) \(+42.0781 q^{16}\) \(-33.7437 q^{18}\) \(-23.0000 q^{23}\) \(-93.0700 q^{24}\) \(+25.0000 q^{25}\) \(+79.5844 q^{26}\) \(+0.244826 q^{27}\) \(+55.4730 q^{29}\) \(-33.9378 q^{31}\) \(-69.1528 q^{32}\) \(+89.4799 q^{36}\) \(-90.7777 q^{39}\) \(-8.78692 q^{41}\) \(+85.6853 q^{46}\) \(+42.8975 q^{47}\) \(+178.808 q^{48}\) \(+49.0000 q^{49}\) \(-93.1362 q^{50}\) \(-211.038 q^{52}\) \(-0.912087 q^{54}\) \(-206.662 q^{58}\) \(+26.0000 q^{59}\) \(+126.433 q^{62}\) \(+89.3126 q^{64}\) \(-97.7368 q^{69}\) \(-85.6223 q^{71}\) \(-198.378 q^{72}\) \(+144.884 q^{73}\) \(+106.236 q^{75}\) \(+338.188 q^{78}\) \(-80.4782 q^{81}\) \(+32.7352 q^{82}\) \(+235.728 q^{87}\) \(-227.216 q^{92}\) \(-144.216 q^{93}\) \(-159.813 q^{94}\) \(-293.860 q^{96}\) \(-182.547 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 33q^{6} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 33q^{6} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 39q^{18} \) \(\mathstrut -\mathstrut 69q^{23} \) \(\mathstrut -\mathstrut 132q^{24} \) \(\mathstrut +\mathstrut 75q^{25} \) \(\mathstrut +\mathstrut 87q^{26} \) \(\mathstrut -\mathstrut 114q^{27} \) \(\mathstrut -\mathstrut 84q^{32} \) \(\mathstrut +\mathstrut 255q^{36} \) \(\mathstrut -\mathstrut 42q^{39} \) \(\mathstrut +\mathstrut 231q^{48} \) \(\mathstrut +\mathstrut 147q^{49} \) \(\mathstrut -\mathstrut 309q^{52} \) \(\mathstrut -\mathstrut 297q^{54} \) \(\mathstrut -\mathstrut 273q^{58} \) \(\mathstrut +\mathstrut 78q^{59} \) \(\mathstrut +\mathstrut 303q^{62} \) \(\mathstrut -\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 33q^{72} \) \(\mathstrut +\mathstrut 399q^{78} \) \(\mathstrut +\mathstrut 243q^{81} \) \(\mathstrut -\mathstrut 129q^{82} \) \(\mathstrut +\mathstrut 246q^{87} \) \(\mathstrut -\mathstrut 276q^{92} \) \(\mathstrut -\mathstrut 546q^{93} \) \(\mathstrut -\mathstrut 57q^{94} \) \(\mathstrut -\mathstrut 21q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.72545 −1.86272 −0.931362 0.364094i \(-0.881379\pi\)
−0.931362 + 0.364094i \(0.881379\pi\)
\(3\) 4.24943 1.41648 0.708238 0.705974i \(-0.249491\pi\)
0.708238 + 0.705974i \(0.249491\pi\)
\(4\) 9.87897 2.46974
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −15.8310 −2.63850
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −21.9018 −2.73772
\(9\) 9.05761 1.00640
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 41.9799 3.49833
\(13\) −21.3624 −1.64326 −0.821629 0.570023i \(-0.806934\pi\)
−0.821629 + 0.570023i \(0.806934\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 42.0781 2.62988
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −33.7437 −1.87465
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −23.0000 −1.00000
\(24\) −93.0700 −3.87792
\(25\) 25.0000 1.00000
\(26\) 79.5844 3.06094
\(27\) 0.244826 0.00906764
\(28\) 0 0
\(29\) 55.4730 1.91286 0.956431 0.291959i \(-0.0943072\pi\)
0.956431 + 0.291959i \(0.0943072\pi\)
\(30\) 0 0
\(31\) −33.9378 −1.09477 −0.547384 0.836882i \(-0.684376\pi\)
−0.547384 + 0.836882i \(0.684376\pi\)
\(32\) −69.1528 −2.16102
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 89.4799 2.48555
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −90.7777 −2.32763
\(40\) 0 0
\(41\) −8.78692 −0.214315 −0.107158 0.994242i \(-0.534175\pi\)
−0.107158 + 0.994242i \(0.534175\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 85.6853 1.86272
\(47\) 42.8975 0.912714 0.456357 0.889797i \(-0.349154\pi\)
0.456357 + 0.889797i \(0.349154\pi\)
\(48\) 178.808 3.72516
\(49\) 49.0000 1.00000
\(50\) −93.1362 −1.86272
\(51\) 0 0
\(52\) −211.038 −4.05842
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −0.912087 −0.0168905
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −206.662 −3.56313
\(59\) 26.0000 0.440678 0.220339 0.975423i \(-0.429284\pi\)
0.220339 + 0.975423i \(0.429284\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 126.433 2.03925
\(63\) 0 0
\(64\) 89.3126 1.39551
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −97.7368 −1.41648
\(70\) 0 0
\(71\) −85.6223 −1.20595 −0.602974 0.797761i \(-0.706018\pi\)
−0.602974 + 0.797761i \(0.706018\pi\)
\(72\) −198.378 −2.75525
\(73\) 144.884 1.98471 0.992354 0.123420i \(-0.0393864\pi\)
0.992354 + 0.123420i \(0.0393864\pi\)
\(74\) 0 0
\(75\) 106.236 1.41648
\(76\) 0 0
\(77\) 0 0
\(78\) 338.188 4.33574
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −80.4782 −0.993557
\(82\) 32.7352 0.399210
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 235.728 2.70952
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −227.216 −2.46974
\(93\) −144.216 −1.55071
\(94\) −159.813 −1.70013
\(95\) 0 0
\(96\) −293.860 −3.06104
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −182.547 −1.86272
\(99\) 0 0
\(100\) 246.974 2.46974
\(101\) −166.000 −1.64356 −0.821782 0.569802i \(-0.807020\pi\)
−0.821782 + 0.569802i \(0.807020\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 467.874 4.49879
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 2.41863 0.0223947
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 548.016 4.72427
\(117\) −193.492 −1.65378
\(118\) −96.8617 −0.820862
\(119\) 0 0
\(120\) 0 0
\(121\) 121.000 1.00000
\(122\) 0 0
\(123\) −37.3394 −0.303572
\(124\) −335.270 −2.70379
\(125\) 0 0
\(126\) 0 0
\(127\) −60.4714 −0.476153 −0.238076 0.971246i \(-0.576517\pi\)
−0.238076 + 0.971246i \(0.576517\pi\)
\(128\) −56.1183 −0.438424
\(129\) 0 0
\(130\) 0 0
\(131\) −71.6641 −0.547054 −0.273527 0.961864i \(-0.588190\pi\)
−0.273527 + 0.961864i \(0.588190\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 364.113 2.63850
\(139\) −277.019 −1.99294 −0.996472 0.0839253i \(-0.973254\pi\)
−0.996472 + 0.0839253i \(0.973254\pi\)
\(140\) 0 0
\(141\) 182.290 1.29284
\(142\) 318.981 2.24635
\(143\) 0 0
\(144\) 381.128 2.64672
\(145\) 0 0
\(146\) −539.757 −3.69697
\(147\) 208.222 1.41648
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −395.775 −2.63850
\(151\) 298.554 1.97718 0.988591 0.150626i \(-0.0481289\pi\)
0.988591 + 0.150626i \(0.0481289\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −896.790 −5.74866
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 299.817 1.85072
\(163\) 82.0066 0.503108 0.251554 0.967843i \(-0.419058\pi\)
0.251554 + 0.967843i \(0.419058\pi\)
\(164\) −86.8057 −0.529303
\(165\) 0 0
\(166\) 0 0
\(167\) 242.000 1.44910 0.724551 0.689221i \(-0.242047\pi\)
0.724551 + 0.689221i \(0.242047\pi\)
\(168\) 0 0
\(169\) 287.350 1.70030
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −22.0000 −0.127168 −0.0635838 0.997977i \(-0.520253\pi\)
−0.0635838 + 0.997977i \(0.520253\pi\)
\(174\) −878.194 −5.04709
\(175\) 0 0
\(176\) 0 0
\(177\) 110.485 0.624209
\(178\) 0 0
\(179\) −328.704 −1.83633 −0.918167 0.396194i \(-0.870331\pi\)
−0.918167 + 0.396194i \(0.870331\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 503.741 2.73772
\(185\) 0 0
\(186\) 537.270 2.88855
\(187\) 0 0
\(188\) 423.784 2.25417
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 379.527 1.97670
\(193\) −314.746 −1.63081 −0.815403 0.578894i \(-0.803485\pi\)
−0.815403 + 0.578894i \(0.803485\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 484.069 2.46974
\(197\) −173.650 −0.881474 −0.440737 0.897636i \(-0.645283\pi\)
−0.440737 + 0.897636i \(0.645283\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −547.545 −2.73772
\(201\) 0 0
\(202\) 618.424 3.06151
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −208.325 −1.00640
\(208\) −898.888 −4.32158
\(209\) 0 0
\(210\) 0 0
\(211\) −406.000 −1.92417 −0.962085 0.272749i \(-0.912067\pi\)
−0.962085 + 0.272749i \(0.912067\pi\)
\(212\) 0 0
\(213\) −363.845 −1.70819
\(214\) 0 0
\(215\) 0 0
\(216\) −5.36213 −0.0248247
\(217\) 0 0
\(218\) 0 0
\(219\) 615.673 2.81129
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −382.000 −1.71300 −0.856502 0.516143i \(-0.827367\pi\)
−0.856502 + 0.516143i \(0.827367\pi\)
\(224\) 0 0
\(225\) 226.440 1.00640
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1214.96 −5.23689
\(233\) 425.691 1.82700 0.913501 0.406836i \(-0.133368\pi\)
0.913501 + 0.406836i \(0.133368\pi\)
\(234\) 720.844 3.08053
\(235\) 0 0
\(236\) 256.853 1.08836
\(237\) 0 0
\(238\) 0 0
\(239\) 477.376 1.99739 0.998694 0.0510816i \(-0.0162668\pi\)
0.998694 + 0.0510816i \(0.0162668\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −450.779 −1.86272
\(243\) −344.189 −1.41642
\(244\) 0 0
\(245\) 0 0
\(246\) 139.106 0.565471
\(247\) 0 0
\(248\) 743.298 2.99717
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 225.283 0.886941
\(255\) 0 0
\(256\) −148.185 −0.578846
\(257\) −494.950 −1.92587 −0.962937 0.269725i \(-0.913067\pi\)
−0.962937 + 0.269725i \(0.913067\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 502.453 1.92511
\(262\) 266.981 1.01901
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 232.912 0.865843 0.432922 0.901432i \(-0.357483\pi\)
0.432922 + 0.901432i \(0.357483\pi\)
\(270\) 0 0
\(271\) −286.000 −1.05535 −0.527675 0.849446i \(-0.676936\pi\)
−0.527675 + 0.849446i \(0.676936\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −965.539 −3.49833
\(277\) 210.526 0.760023 0.380012 0.924982i \(-0.375920\pi\)
0.380012 + 0.924982i \(0.375920\pi\)
\(278\) 1032.02 3.71231
\(279\) −307.395 −1.10178
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −679.112 −2.40820
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −845.860 −2.97838
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −626.359 −2.17486
\(289\) 289.000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 1431.30 4.90172
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −775.720 −2.63850
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 491.334 1.64326
\(300\) 1049.50 3.49833
\(301\) 0 0
\(302\) −1112.25 −3.68294
\(303\) −705.405 −2.32807
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −214.000 −0.697068 −0.348534 0.937296i \(-0.613320\pi\)
−0.348534 + 0.937296i \(0.613320\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 91.8165 0.295230 0.147615 0.989045i \(-0.452840\pi\)
0.147615 + 0.989045i \(0.452840\pi\)
\(312\) 1988.20 6.37242
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 266.000 0.839117 0.419558 0.907728i \(-0.362185\pi\)
0.419558 + 0.907728i \(0.362185\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −795.041 −2.45383
\(325\) −534.059 −1.64326
\(326\) −305.511 −0.937151
\(327\) 0 0
\(328\) 192.449 0.586736
\(329\) 0 0
\(330\) 0 0
\(331\) −330.086 −0.997240 −0.498620 0.866821i \(-0.666160\pi\)
−0.498620 + 0.866821i \(0.666160\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −901.559 −2.69928
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −1070.51 −3.16718
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 81.9599 0.236878
\(347\) 602.000 1.73487 0.867435 0.497550i \(-0.165767\pi\)
0.867435 + 0.497550i \(0.165767\pi\)
\(348\) 2328.75 6.69182
\(349\) 617.088 1.76816 0.884081 0.467334i \(-0.154785\pi\)
0.884081 + 0.467334i \(0.154785\pi\)
\(350\) 0 0
\(351\) −5.23006 −0.0149005
\(352\) 0 0
\(353\) 453.608 1.28501 0.642504 0.766282i \(-0.277896\pi\)
0.642504 + 0.766282i \(0.277896\pi\)
\(354\) −411.606 −1.16273
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1224.57 3.42058
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) 514.180 1.41648
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −967.797 −2.62988
\(369\) −79.5885 −0.215687
\(370\) 0 0
\(371\) 0 0
\(372\) −1424.71 −3.82986
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −939.533 −2.49876
\(377\) −1185.03 −3.14332
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −256.969 −0.674458
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −238.470 −0.621017
\(385\) 0 0
\(386\) 1172.57 3.03774
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1073.19 −2.73772
\(393\) −304.531 −0.774888
\(394\) 646.925 1.64194
\(395\) 0 0
\(396\) 0 0
\(397\) −249.103 −0.627463 −0.313732 0.949512i \(-0.601579\pi\)
−0.313732 + 0.949512i \(0.601579\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1051.95 2.62988
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 724.991 1.79899
\(404\) −1639.91 −4.05918
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −800.908 −1.95821 −0.979106 0.203352i \(-0.934816\pi\)
−0.979106 + 0.203352i \(0.934816\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 776.105 1.87465
\(415\) 0 0
\(416\) 1477.27 3.55112
\(417\) −1177.17 −2.82296
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 1512.53 3.58420
\(423\) 388.549 0.918557
\(424\) 0 0
\(425\) 0 0
\(426\) 1355.49 3.18189
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 10.3018 0.0238468
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −2293.66 −5.23666
\(439\) 218.954 0.498755 0.249378 0.968406i \(-0.419774\pi\)
0.249378 + 0.968406i \(0.419774\pi\)
\(440\) 0 0
\(441\) 443.823 1.00640
\(442\) 0 0
\(443\) −279.785 −0.631568 −0.315784 0.948831i \(-0.602268\pi\)
−0.315784 + 0.948831i \(0.602268\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1423.12 3.19086
\(447\) 0 0
\(448\) 0 0
\(449\) −574.000 −1.27840 −0.639198 0.769042i \(-0.720734\pi\)
−0.639198 + 0.769042i \(0.720734\pi\)
\(450\) −843.592 −1.87465
\(451\) 0 0
\(452\) 0 0
\(453\) 1268.68 2.80063
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −916.853 −1.98883 −0.994417 0.105519i \(-0.966350\pi\)
−0.994417 + 0.105519i \(0.966350\pi\)
\(462\) 0 0
\(463\) 98.0000 0.211663 0.105832 0.994384i \(-0.466250\pi\)
0.105832 + 0.994384i \(0.466250\pi\)
\(464\) 2334.20 5.03060
\(465\) 0 0
\(466\) −1585.89 −3.40320
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −1911.50 −4.08440
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −569.447 −1.20645
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −1778.44 −3.72059
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1195.36 2.46974
\(485\) 0 0
\(486\) 1282.26 2.63839
\(487\) 937.005 1.92404 0.962018 0.272987i \(-0.0880116\pi\)
0.962018 + 0.272987i \(0.0880116\pi\)
\(488\) 0 0
\(489\) 348.481 0.712640
\(490\) 0 0
\(491\) −658.430 −1.34100 −0.670499 0.741910i \(-0.733920\pi\)
−0.670499 + 0.741910i \(0.733920\pi\)
\(492\) −368.874 −0.749745
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1428.04 −2.87911
\(497\) 0 0
\(498\) 0 0
\(499\) −863.786 −1.73103 −0.865517 0.500880i \(-0.833010\pi\)
−0.865517 + 0.500880i \(0.833010\pi\)
\(500\) 0 0
\(501\) 1028.36 2.05262
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1221.07 2.40843
\(508\) −597.395 −1.17597
\(509\) 288.744 0.567278 0.283639 0.958931i \(-0.408458\pi\)
0.283639 + 0.958931i \(0.408458\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 776.527 1.51665
\(513\) 0 0
\(514\) 1843.91 3.58737
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −93.4874 −0.180130
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1871.86 −3.58594
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −707.967 −1.35108
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) 235.498 0.443499
\(532\) 0 0
\(533\) 187.709 0.352175
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1396.80 −2.60112
\(538\) −867.701 −1.61283
\(539\) 0 0
\(540\) 0 0
\(541\) 564.021 1.04255 0.521277 0.853388i \(-0.325456\pi\)
0.521277 + 0.853388i \(0.325456\pi\)
\(542\) 1065.48 1.96583
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −145.734 −0.266424 −0.133212 0.991088i \(-0.542529\pi\)
−0.133212 + 0.991088i \(0.542529\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 2140.61 3.87792
\(553\) 0 0
\(554\) −784.305 −1.41571
\(555\) 0 0
\(556\) −2736.66 −4.92206
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 1145.19 2.05230
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 1800.84 3.19297
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 1875.28 3.30155
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −575.000 −1.00000
\(576\) 808.959 1.40444
\(577\) 1041.76 1.80547 0.902736 0.430196i \(-0.141555\pi\)
0.902736 + 0.430196i \(0.141555\pi\)
\(578\) −1076.65 −1.86272
\(579\) −1337.49 −2.31000
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −3173.21 −5.43359
\(585\) 0 0
\(586\) 0 0
\(587\) −1172.51 −1.99746 −0.998731 0.0503716i \(-0.983959\pi\)
−0.998731 + 0.0503716i \(0.983959\pi\)
\(588\) 2057.02 3.49833
\(589\) 0 0
\(590\) 0 0
\(591\) −737.914 −1.24859
\(592\) 0 0
\(593\) −286.000 −0.482293 −0.241147 0.970489i \(-0.577524\pi\)
−0.241147 + 0.970489i \(0.577524\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1830.44 −3.06094
\(599\) 1106.00 1.84641 0.923205 0.384307i \(-0.125560\pi\)
0.923205 + 0.384307i \(0.125560\pi\)
\(600\) −2326.75 −3.87792
\(601\) 608.661 1.01275 0.506374 0.862314i \(-0.330986\pi\)
0.506374 + 0.862314i \(0.330986\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2949.41 4.88313
\(605\) 0 0
\(606\) 2627.95 4.33655
\(607\) 386.000 0.635914 0.317957 0.948105i \(-0.397003\pi\)
0.317957 + 0.948105i \(0.397003\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −916.393 −1.49982
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 797.246 1.29845
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −5.63100 −0.00906764
\(622\) −342.058 −0.549932
\(623\) 0 0
\(624\) −3819.76 −6.12141
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −1725.27 −2.72554
\(634\) −990.969 −1.56304
\(635\) 0 0
\(636\) 0 0
\(637\) −1046.76 −1.64326
\(638\) 0 0
\(639\) −775.533 −1.21367
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1217.81 1.88225 0.941123 0.338065i \(-0.109772\pi\)
0.941123 + 0.338065i \(0.109772\pi\)
\(648\) 1762.62 2.72009
\(649\) 0 0
\(650\) 1989.61 3.06094
\(651\) 0 0
\(652\) 810.140 1.24255
\(653\) 1101.87 1.68739 0.843697 0.536819i \(-0.180374\pi\)
0.843697 + 0.536819i \(0.180374\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −369.737 −0.563624
\(657\) 1312.30 1.99741
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 1229.72 1.85758
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1275.88 −1.91286
\(668\) 2390.71 3.57891
\(669\) −1623.28 −2.42643
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −447.414 −0.664805 −0.332402 0.943138i \(-0.607859\pi\)
−0.332402 + 0.943138i \(0.607859\pi\)
\(674\) 0 0
\(675\) 6.12065 0.00906764
\(676\) 2838.72 4.19929
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1360.29 1.99164 0.995821 0.0913307i \(-0.0291120\pi\)
0.995821 + 0.0913307i \(0.0291120\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 554.000 0.801737 0.400868 0.916136i \(-0.368708\pi\)
0.400868 + 0.916136i \(0.368708\pi\)
\(692\) −217.337 −0.314071
\(693\) 0 0
\(694\) −2242.72 −3.23159
\(695\) 0 0
\(696\) −5162.87 −7.41792
\(697\) 0 0
\(698\) −2298.93 −3.29360
\(699\) 1808.94 2.58790
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 19.4843 0.0277555
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1689.89 −2.39362
\(707\) 0 0
\(708\) 1091.48 1.54164
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 780.569 1.09477
\(714\) 0 0
\(715\) 0 0
\(716\) −3247.25 −4.53527
\(717\) 2028.57 2.82925
\(718\) 0 0
\(719\) −862.000 −1.19889 −0.599444 0.800417i \(-0.704611\pi\)
−0.599444 + 0.800417i \(0.704611\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1344.89 −1.86272
\(723\) 0 0
\(724\) 0 0
\(725\) 1386.82 1.91286
\(726\) −1915.55 −2.63850
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −738.303 −1.01276
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1590.51 2.16102
\(737\) 0 0
\(738\) 296.503 0.401766
\(739\) −77.1950 −0.104459 −0.0522294 0.998635i \(-0.516633\pi\)
−0.0522294 + 0.998635i \(0.516633\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 3158.59 4.24542
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 1805.05 2.40033
\(753\) 0 0
\(754\) 4414.78 5.85515
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1060.71 −1.39384 −0.696921 0.717148i \(-0.745447\pi\)
−0.696921 + 0.717148i \(0.745447\pi\)
\(762\) 957.323 1.25633
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −555.421 −0.724148
\(768\) −629.699 −0.819921
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −2103.25 −2.72795
\(772\) −3109.36 −4.02767
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −848.445 −1.09477
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 13.5812 0.0173451
\(784\) 2061.83 2.62988
\(785\) 0 0
\(786\) 1134.52 1.44340
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −1715.49 −2.17701
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 928.020 1.16879
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1728.82 −2.16102
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −2700.92 −3.35101
\(807\) 989.741 1.22645
\(808\) 3635.70 4.49963
\(809\) 146.000 0.180470 0.0902349 0.995921i \(-0.471238\pi\)
0.0902349 + 0.995921i \(0.471238\pi\)
\(810\) 0 0
\(811\) 878.276 1.08295 0.541477 0.840715i \(-0.317865\pi\)
0.541477 + 0.840715i \(0.317865\pi\)
\(812\) 0 0
\(813\) −1215.34 −1.49488
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 2983.74 3.64761
\(819\) 0 0
\(820\) 0 0
\(821\) 1274.00 1.55177 0.775883 0.630877i \(-0.217305\pi\)
0.775883 + 0.630877i \(0.217305\pi\)
\(822\) 0 0
\(823\) −1593.03 −1.93564 −0.967819 0.251648i \(-0.919028\pi\)
−0.967819 + 0.251648i \(0.919028\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −2058.04 −2.48555
\(829\) −1654.00 −1.99517 −0.997587 0.0694210i \(-0.977885\pi\)
−0.997587 + 0.0694210i \(0.977885\pi\)
\(830\) 0 0
\(831\) 894.616 1.07655
\(832\) −1907.93 −2.29318
\(833\) 0 0
\(834\) 4385.50 5.25839
\(835\) 0 0
\(836\) 0 0
\(837\) −8.30886 −0.00992695
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 2236.25 2.65904
\(842\) 0 0
\(843\) 0 0
\(844\) −4010.86 −4.75221
\(845\) 0 0
\(846\) −1447.52 −1.71102
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) −3594.42 −4.21880
\(853\) −1606.00 −1.88277 −0.941383 0.337339i \(-0.890473\pi\)
−0.941383 + 0.337339i \(0.890473\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1350.48 1.57582 0.787912 0.615788i \(-0.211162\pi\)
0.787912 + 0.615788i \(0.211162\pi\)
\(858\) 0 0
\(859\) 1717.93 1.99992 0.999962 0.00876272i \(-0.00278930\pi\)
0.999962 + 0.00876272i \(0.00278930\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −182.078 −0.210982 −0.105491 0.994420i \(-0.533641\pi\)
−0.105491 + 0.994420i \(0.533641\pi\)
\(864\) −16.9304 −0.0195954
\(865\) 0 0
\(866\) 0 0
\(867\) 1228.08 1.41648
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 6082.21 6.94316
\(877\) −1558.00 −1.77651 −0.888255 0.459350i \(-0.848082\pi\)
−0.888255 + 0.459350i \(0.848082\pi\)
\(878\) −815.700 −0.929044
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1653.44 −1.87465
\(883\) 938.000 1.06229 0.531144 0.847282i \(-0.321762\pi\)
0.531144 + 0.847282i \(0.321762\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1042.32 1.17644
\(887\) −1773.23 −1.99914 −0.999568 0.0293802i \(-0.990647\pi\)
−0.999568 + 0.0293802i \(0.990647\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −3773.77 −4.23068
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2087.89 2.32763
\(898\) 2138.41 2.38130
\(899\) −1882.63 −2.09414
\(900\) 2237.00 2.48555
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) −4726.42 −5.21680
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) −1503.56 −1.65409
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −909.377 −0.987380
\(922\) 3415.69 3.70465
\(923\) 1829.09 1.98168
\(924\) 0 0
\(925\) 0 0
\(926\) −365.094 −0.394270
\(927\) 0 0
\(928\) −3836.11 −4.13374
\(929\) −1411.44 −1.51931 −0.759657 0.650324i \(-0.774633\pi\)
−0.759657 + 0.650324i \(0.774633\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 4205.39 4.51222
\(933\) 390.168 0.418186
\(934\) 0 0
\(935\) 0 0
\(936\) 4237.82 4.52759
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 202.099 0.214315
\(944\) 1094.03 1.15893
\(945\) 0 0
\(946\) 0 0
\(947\) 1287.60 1.35967 0.679833 0.733367i \(-0.262052\pi\)
0.679833 + 0.733367i \(0.262052\pi\)
\(948\) 0 0
\(949\) −3095.06 −3.26139
\(950\) 0 0
\(951\) 1130.35 1.18859
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 4715.98 4.93304
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 190.773 0.198515
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 804.337 0.831786 0.415893 0.909414i \(-0.363469\pi\)
0.415893 + 0.909414i \(0.363469\pi\)
\(968\) −2650.12 −2.73772
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −3400.24 −3.49818
\(973\) 0 0
\(974\) −3490.77 −3.58395
\(975\) −2269.44 −2.32763
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) −1298.25 −1.32745
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 2452.95 2.49791
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 817.799 0.831097
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1154.00 1.16448 0.582240 0.813017i \(-0.302176\pi\)
0.582240 + 0.813017i \(0.302176\pi\)
\(992\) 2346.89 2.36582
\(993\) −1402.68 −1.41257
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1318.00 −1.32197 −0.660983 0.750401i \(-0.729860\pi\)
−0.660983 + 0.750401i \(0.729860\pi\)
\(998\) 3217.99 3.22444
\(999\) 0 0
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 \(a_p\))