Properties

Label 6008.2.a.e.1.3
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.97134 q^{3}\) \(+0.343630 q^{5}\) \(-1.43593 q^{7}\) \(+5.82889 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.97134 q^{3}\) \(+0.343630 q^{5}\) \(-1.43593 q^{7}\) \(+5.82889 q^{9}\) \(-4.62084 q^{11}\) \(-0.0491454 q^{13}\) \(-1.02104 q^{15}\) \(-3.66831 q^{17}\) \(-8.44232 q^{19}\) \(+4.26665 q^{21}\) \(-7.46524 q^{23}\) \(-4.88192 q^{25}\) \(-8.40561 q^{27}\) \(+2.21104 q^{29}\) \(+0.764542 q^{31}\) \(+13.7301 q^{33}\) \(-0.493429 q^{35}\) \(+1.43564 q^{37}\) \(+0.146028 q^{39}\) \(-4.38923 q^{41}\) \(+0.508420 q^{43}\) \(+2.00298 q^{45}\) \(+1.72952 q^{47}\) \(-4.93810 q^{49}\) \(+10.8998 q^{51}\) \(-2.75864 q^{53}\) \(-1.58786 q^{55}\) \(+25.0851 q^{57}\) \(-3.37486 q^{59}\) \(+4.47668 q^{61}\) \(-8.36989 q^{63}\) \(-0.0168878 q^{65}\) \(+8.03766 q^{67}\) \(+22.1818 q^{69}\) \(-7.02723 q^{71}\) \(-12.2930 q^{73}\) \(+14.5059 q^{75}\) \(+6.63521 q^{77}\) \(-16.4658 q^{79}\) \(+7.48929 q^{81}\) \(-2.64120 q^{83}\) \(-1.26054 q^{85}\) \(-6.56976 q^{87}\) \(+4.57255 q^{89}\) \(+0.0705695 q^{91}\) \(-2.27172 q^{93}\) \(-2.90103 q^{95}\) \(+0.346939 q^{97}\) \(-26.9344 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.97134 −1.71551 −0.857753 0.514061i \(-0.828140\pi\)
−0.857753 + 0.514061i \(0.828140\pi\)
\(4\) 0 0
\(5\) 0.343630 0.153676 0.0768379 0.997044i \(-0.475518\pi\)
0.0768379 + 0.997044i \(0.475518\pi\)
\(6\) 0 0
\(7\) −1.43593 −0.542732 −0.271366 0.962476i \(-0.587475\pi\)
−0.271366 + 0.962476i \(0.587475\pi\)
\(8\) 0 0
\(9\) 5.82889 1.94296
\(10\) 0 0
\(11\) −4.62084 −1.39324 −0.696618 0.717442i \(-0.745313\pi\)
−0.696618 + 0.717442i \(0.745313\pi\)
\(12\) 0 0
\(13\) −0.0491454 −0.0136305 −0.00681524 0.999977i \(-0.502169\pi\)
−0.00681524 + 0.999977i \(0.502169\pi\)
\(14\) 0 0
\(15\) −1.02104 −0.263632
\(16\) 0 0
\(17\) −3.66831 −0.889695 −0.444848 0.895606i \(-0.646742\pi\)
−0.444848 + 0.895606i \(0.646742\pi\)
\(18\) 0 0
\(19\) −8.44232 −1.93680 −0.968401 0.249399i \(-0.919767\pi\)
−0.968401 + 0.249399i \(0.919767\pi\)
\(20\) 0 0
\(21\) 4.26665 0.931060
\(22\) 0 0
\(23\) −7.46524 −1.55661 −0.778305 0.627887i \(-0.783920\pi\)
−0.778305 + 0.627887i \(0.783920\pi\)
\(24\) 0 0
\(25\) −4.88192 −0.976384
\(26\) 0 0
\(27\) −8.40561 −1.61766
\(28\) 0 0
\(29\) 2.21104 0.410579 0.205290 0.978701i \(-0.434186\pi\)
0.205290 + 0.978701i \(0.434186\pi\)
\(30\) 0 0
\(31\) 0.764542 0.137316 0.0686579 0.997640i \(-0.478128\pi\)
0.0686579 + 0.997640i \(0.478128\pi\)
\(32\) 0 0
\(33\) 13.7301 2.39011
\(34\) 0 0
\(35\) −0.493429 −0.0834047
\(36\) 0 0
\(37\) 1.43564 0.236018 0.118009 0.993013i \(-0.462349\pi\)
0.118009 + 0.993013i \(0.462349\pi\)
\(38\) 0 0
\(39\) 0.146028 0.0233832
\(40\) 0 0
\(41\) −4.38923 −0.685482 −0.342741 0.939430i \(-0.611355\pi\)
−0.342741 + 0.939430i \(0.611355\pi\)
\(42\) 0 0
\(43\) 0.508420 0.0775334 0.0387667 0.999248i \(-0.487657\pi\)
0.0387667 + 0.999248i \(0.487657\pi\)
\(44\) 0 0
\(45\) 2.00298 0.298587
\(46\) 0 0
\(47\) 1.72952 0.252276 0.126138 0.992013i \(-0.459742\pi\)
0.126138 + 0.992013i \(0.459742\pi\)
\(48\) 0 0
\(49\) −4.93810 −0.705443
\(50\) 0 0
\(51\) 10.8998 1.52628
\(52\) 0 0
\(53\) −2.75864 −0.378928 −0.189464 0.981888i \(-0.560675\pi\)
−0.189464 + 0.981888i \(0.560675\pi\)
\(54\) 0 0
\(55\) −1.58786 −0.214107
\(56\) 0 0
\(57\) 25.0851 3.32260
\(58\) 0 0
\(59\) −3.37486 −0.439370 −0.219685 0.975571i \(-0.570503\pi\)
−0.219685 + 0.975571i \(0.570503\pi\)
\(60\) 0 0
\(61\) 4.47668 0.573180 0.286590 0.958053i \(-0.407478\pi\)
0.286590 + 0.958053i \(0.407478\pi\)
\(62\) 0 0
\(63\) −8.36989 −1.05451
\(64\) 0 0
\(65\) −0.0168878 −0.00209468
\(66\) 0 0
\(67\) 8.03766 0.981956 0.490978 0.871172i \(-0.336640\pi\)
0.490978 + 0.871172i \(0.336640\pi\)
\(68\) 0 0
\(69\) 22.1818 2.67037
\(70\) 0 0
\(71\) −7.02723 −0.833979 −0.416989 0.908911i \(-0.636915\pi\)
−0.416989 + 0.908911i \(0.636915\pi\)
\(72\) 0 0
\(73\) −12.2930 −1.43878 −0.719392 0.694605i \(-0.755579\pi\)
−0.719392 + 0.694605i \(0.755579\pi\)
\(74\) 0 0
\(75\) 14.5059 1.67499
\(76\) 0 0
\(77\) 6.63521 0.756153
\(78\) 0 0
\(79\) −16.4658 −1.85255 −0.926275 0.376847i \(-0.877008\pi\)
−0.926275 + 0.376847i \(0.877008\pi\)
\(80\) 0 0
\(81\) 7.48929 0.832143
\(82\) 0 0
\(83\) −2.64120 −0.289909 −0.144954 0.989438i \(-0.546304\pi\)
−0.144954 + 0.989438i \(0.546304\pi\)
\(84\) 0 0
\(85\) −1.26054 −0.136725
\(86\) 0 0
\(87\) −6.56976 −0.704352
\(88\) 0 0
\(89\) 4.57255 0.484690 0.242345 0.970190i \(-0.422083\pi\)
0.242345 + 0.970190i \(0.422083\pi\)
\(90\) 0 0
\(91\) 0.0705695 0.00739769
\(92\) 0 0
\(93\) −2.27172 −0.235566
\(94\) 0 0
\(95\) −2.90103 −0.297640
\(96\) 0 0
\(97\) 0.346939 0.0352263 0.0176131 0.999845i \(-0.494393\pi\)
0.0176131 + 0.999845i \(0.494393\pi\)
\(98\) 0 0
\(99\) −26.9344 −2.70701
\(100\) 0 0
\(101\) −10.1152 −1.00650 −0.503249 0.864141i \(-0.667862\pi\)
−0.503249 + 0.864141i \(0.667862\pi\)
\(102\) 0 0
\(103\) −1.76800 −0.174206 −0.0871029 0.996199i \(-0.527761\pi\)
−0.0871029 + 0.996199i \(0.527761\pi\)
\(104\) 0 0
\(105\) 1.46615 0.143081
\(106\) 0 0
\(107\) 10.2387 0.989808 0.494904 0.868948i \(-0.335203\pi\)
0.494904 + 0.868948i \(0.335203\pi\)
\(108\) 0 0
\(109\) −3.77213 −0.361304 −0.180652 0.983547i \(-0.557821\pi\)
−0.180652 + 0.983547i \(0.557821\pi\)
\(110\) 0 0
\(111\) −4.26579 −0.404891
\(112\) 0 0
\(113\) −14.6720 −1.38023 −0.690113 0.723701i \(-0.742439\pi\)
−0.690113 + 0.723701i \(0.742439\pi\)
\(114\) 0 0
\(115\) −2.56528 −0.239213
\(116\) 0 0
\(117\) −0.286463 −0.0264835
\(118\) 0 0
\(119\) 5.26744 0.482866
\(120\) 0 0
\(121\) 10.3522 0.941106
\(122\) 0 0
\(123\) 13.0419 1.17595
\(124\) 0 0
\(125\) −3.39572 −0.303722
\(126\) 0 0
\(127\) −8.81598 −0.782292 −0.391146 0.920329i \(-0.627921\pi\)
−0.391146 + 0.920329i \(0.627921\pi\)
\(128\) 0 0
\(129\) −1.51069 −0.133009
\(130\) 0 0
\(131\) 4.16118 0.363564 0.181782 0.983339i \(-0.441813\pi\)
0.181782 + 0.983339i \(0.441813\pi\)
\(132\) 0 0
\(133\) 12.1226 1.05116
\(134\) 0 0
\(135\) −2.88842 −0.248595
\(136\) 0 0
\(137\) 0.351303 0.0300138 0.0150069 0.999887i \(-0.495223\pi\)
0.0150069 + 0.999887i \(0.495223\pi\)
\(138\) 0 0
\(139\) 18.2267 1.54597 0.772983 0.634427i \(-0.218764\pi\)
0.772983 + 0.634427i \(0.218764\pi\)
\(140\) 0 0
\(141\) −5.13899 −0.432781
\(142\) 0 0
\(143\) 0.227093 0.0189905
\(144\) 0 0
\(145\) 0.759778 0.0630962
\(146\) 0 0
\(147\) 14.6728 1.21019
\(148\) 0 0
\(149\) −12.2338 −1.00223 −0.501116 0.865380i \(-0.667077\pi\)
−0.501116 + 0.865380i \(0.667077\pi\)
\(150\) 0 0
\(151\) −18.1763 −1.47916 −0.739582 0.673067i \(-0.764977\pi\)
−0.739582 + 0.673067i \(0.764977\pi\)
\(152\) 0 0
\(153\) −21.3822 −1.72865
\(154\) 0 0
\(155\) 0.262719 0.0211021
\(156\) 0 0
\(157\) −1.28430 −0.102499 −0.0512493 0.998686i \(-0.516320\pi\)
−0.0512493 + 0.998686i \(0.516320\pi\)
\(158\) 0 0
\(159\) 8.19686 0.650053
\(160\) 0 0
\(161\) 10.7196 0.844821
\(162\) 0 0
\(163\) 6.53430 0.511806 0.255903 0.966702i \(-0.417627\pi\)
0.255903 + 0.966702i \(0.417627\pi\)
\(164\) 0 0
\(165\) 4.71807 0.367301
\(166\) 0 0
\(167\) −10.4435 −0.808139 −0.404070 0.914728i \(-0.632405\pi\)
−0.404070 + 0.914728i \(0.632405\pi\)
\(168\) 0 0
\(169\) −12.9976 −0.999814
\(170\) 0 0
\(171\) −49.2094 −3.76313
\(172\) 0 0
\(173\) −20.5372 −1.56141 −0.780706 0.624899i \(-0.785140\pi\)
−0.780706 + 0.624899i \(0.785140\pi\)
\(174\) 0 0
\(175\) 7.01011 0.529914
\(176\) 0 0
\(177\) 10.0279 0.753742
\(178\) 0 0
\(179\) −13.3752 −0.999708 −0.499854 0.866110i \(-0.666613\pi\)
−0.499854 + 0.866110i \(0.666613\pi\)
\(180\) 0 0
\(181\) 25.7792 1.91615 0.958075 0.286518i \(-0.0924977\pi\)
0.958075 + 0.286518i \(0.0924977\pi\)
\(182\) 0 0
\(183\) −13.3018 −0.983294
\(184\) 0 0
\(185\) 0.493329 0.0362703
\(186\) 0 0
\(187\) 16.9507 1.23956
\(188\) 0 0
\(189\) 12.0699 0.877955
\(190\) 0 0
\(191\) 5.09149 0.368407 0.184204 0.982888i \(-0.441029\pi\)
0.184204 + 0.982888i \(0.441029\pi\)
\(192\) 0 0
\(193\) −3.05868 −0.220169 −0.110084 0.993922i \(-0.535112\pi\)
−0.110084 + 0.993922i \(0.535112\pi\)
\(194\) 0 0
\(195\) 0.0501795 0.00359343
\(196\) 0 0
\(197\) 1.74396 0.124252 0.0621261 0.998068i \(-0.480212\pi\)
0.0621261 + 0.998068i \(0.480212\pi\)
\(198\) 0 0
\(199\) −12.0399 −0.853489 −0.426744 0.904372i \(-0.640340\pi\)
−0.426744 + 0.904372i \(0.640340\pi\)
\(200\) 0 0
\(201\) −23.8826 −1.68455
\(202\) 0 0
\(203\) −3.17490 −0.222834
\(204\) 0 0
\(205\) −1.50827 −0.105342
\(206\) 0 0
\(207\) −43.5140 −3.02444
\(208\) 0 0
\(209\) 39.0106 2.69842
\(210\) 0 0
\(211\) 22.0033 1.51477 0.757385 0.652969i \(-0.226477\pi\)
0.757385 + 0.652969i \(0.226477\pi\)
\(212\) 0 0
\(213\) 20.8803 1.43070
\(214\) 0 0
\(215\) 0.174708 0.0119150
\(216\) 0 0
\(217\) −1.09783 −0.0745256
\(218\) 0 0
\(219\) 36.5267 2.46824
\(220\) 0 0
\(221\) 0.180280 0.0121270
\(222\) 0 0
\(223\) 11.6491 0.780083 0.390042 0.920797i \(-0.372461\pi\)
0.390042 + 0.920797i \(0.372461\pi\)
\(224\) 0 0
\(225\) −28.4562 −1.89708
\(226\) 0 0
\(227\) 3.04337 0.201996 0.100998 0.994887i \(-0.467796\pi\)
0.100998 + 0.994887i \(0.467796\pi\)
\(228\) 0 0
\(229\) −2.59651 −0.171582 −0.0857911 0.996313i \(-0.527342\pi\)
−0.0857911 + 0.996313i \(0.527342\pi\)
\(230\) 0 0
\(231\) −19.7155 −1.29719
\(232\) 0 0
\(233\) 19.4569 1.27466 0.637331 0.770590i \(-0.280038\pi\)
0.637331 + 0.770590i \(0.280038\pi\)
\(234\) 0 0
\(235\) 0.594314 0.0387688
\(236\) 0 0
\(237\) 48.9257 3.17806
\(238\) 0 0
\(239\) 2.34917 0.151955 0.0759776 0.997110i \(-0.475792\pi\)
0.0759776 + 0.997110i \(0.475792\pi\)
\(240\) 0 0
\(241\) 14.6402 0.943059 0.471530 0.881850i \(-0.343702\pi\)
0.471530 + 0.881850i \(0.343702\pi\)
\(242\) 0 0
\(243\) 2.96356 0.190113
\(244\) 0 0
\(245\) −1.69688 −0.108409
\(246\) 0 0
\(247\) 0.414901 0.0263995
\(248\) 0 0
\(249\) 7.84791 0.497341
\(250\) 0 0
\(251\) −5.08850 −0.321183 −0.160592 0.987021i \(-0.551340\pi\)
−0.160592 + 0.987021i \(0.551340\pi\)
\(252\) 0 0
\(253\) 34.4957 2.16872
\(254\) 0 0
\(255\) 3.74550 0.234552
\(256\) 0 0
\(257\) −21.2462 −1.32530 −0.662652 0.748927i \(-0.730569\pi\)
−0.662652 + 0.748927i \(0.730569\pi\)
\(258\) 0 0
\(259\) −2.06148 −0.128094
\(260\) 0 0
\(261\) 12.8879 0.797741
\(262\) 0 0
\(263\) 26.2830 1.62068 0.810341 0.585959i \(-0.199282\pi\)
0.810341 + 0.585959i \(0.199282\pi\)
\(264\) 0 0
\(265\) −0.947949 −0.0582321
\(266\) 0 0
\(267\) −13.5866 −0.831489
\(268\) 0 0
\(269\) −4.75172 −0.289717 −0.144859 0.989452i \(-0.546273\pi\)
−0.144859 + 0.989452i \(0.546273\pi\)
\(270\) 0 0
\(271\) 2.74968 0.167031 0.0835156 0.996506i \(-0.473385\pi\)
0.0835156 + 0.996506i \(0.473385\pi\)
\(272\) 0 0
\(273\) −0.209686 −0.0126908
\(274\) 0 0
\(275\) 22.5586 1.36033
\(276\) 0 0
\(277\) −18.7768 −1.12819 −0.564094 0.825711i \(-0.690774\pi\)
−0.564094 + 0.825711i \(0.690774\pi\)
\(278\) 0 0
\(279\) 4.45643 0.266799
\(280\) 0 0
\(281\) 18.9396 1.12984 0.564920 0.825145i \(-0.308907\pi\)
0.564920 + 0.825145i \(0.308907\pi\)
\(282\) 0 0
\(283\) −0.580094 −0.0344830 −0.0172415 0.999851i \(-0.505488\pi\)
−0.0172415 + 0.999851i \(0.505488\pi\)
\(284\) 0 0
\(285\) 8.61997 0.510603
\(286\) 0 0
\(287\) 6.30263 0.372033
\(288\) 0 0
\(289\) −3.54351 −0.208442
\(290\) 0 0
\(291\) −1.03087 −0.0604309
\(292\) 0 0
\(293\) 4.39793 0.256930 0.128465 0.991714i \(-0.458995\pi\)
0.128465 + 0.991714i \(0.458995\pi\)
\(294\) 0 0
\(295\) −1.15970 −0.0675205
\(296\) 0 0
\(297\) 38.8410 2.25378
\(298\) 0 0
\(299\) 0.366882 0.0212173
\(300\) 0 0
\(301\) −0.730057 −0.0420798
\(302\) 0 0
\(303\) 30.0557 1.72666
\(304\) 0 0
\(305\) 1.53832 0.0880839
\(306\) 0 0
\(307\) −27.5154 −1.57039 −0.785193 0.619251i \(-0.787436\pi\)
−0.785193 + 0.619251i \(0.787436\pi\)
\(308\) 0 0
\(309\) 5.25332 0.298851
\(310\) 0 0
\(311\) −4.48920 −0.254559 −0.127280 0.991867i \(-0.540625\pi\)
−0.127280 + 0.991867i \(0.540625\pi\)
\(312\) 0 0
\(313\) 17.6691 0.998719 0.499360 0.866395i \(-0.333569\pi\)
0.499360 + 0.866395i \(0.333569\pi\)
\(314\) 0 0
\(315\) −2.87614 −0.162052
\(316\) 0 0
\(317\) 20.6921 1.16218 0.581092 0.813838i \(-0.302626\pi\)
0.581092 + 0.813838i \(0.302626\pi\)
\(318\) 0 0
\(319\) −10.2169 −0.572034
\(320\) 0 0
\(321\) −30.4226 −1.69802
\(322\) 0 0
\(323\) 30.9690 1.72316
\(324\) 0 0
\(325\) 0.239924 0.0133086
\(326\) 0 0
\(327\) 11.2083 0.619820
\(328\) 0 0
\(329\) −2.48347 −0.136918
\(330\) 0 0
\(331\) −7.44499 −0.409214 −0.204607 0.978844i \(-0.565592\pi\)
−0.204607 + 0.978844i \(0.565592\pi\)
\(332\) 0 0
\(333\) 8.36820 0.458574
\(334\) 0 0
\(335\) 2.76198 0.150903
\(336\) 0 0
\(337\) 11.7620 0.640718 0.320359 0.947296i \(-0.396197\pi\)
0.320359 + 0.947296i \(0.396197\pi\)
\(338\) 0 0
\(339\) 43.5956 2.36779
\(340\) 0 0
\(341\) −3.53282 −0.191313
\(342\) 0 0
\(343\) 17.1423 0.925597
\(344\) 0 0
\(345\) 7.62232 0.410372
\(346\) 0 0
\(347\) −25.4748 −1.36756 −0.683780 0.729689i \(-0.739665\pi\)
−0.683780 + 0.729689i \(0.739665\pi\)
\(348\) 0 0
\(349\) −26.7600 −1.43243 −0.716215 0.697879i \(-0.754127\pi\)
−0.716215 + 0.697879i \(0.754127\pi\)
\(350\) 0 0
\(351\) 0.413097 0.0220495
\(352\) 0 0
\(353\) 23.1096 1.23000 0.615001 0.788527i \(-0.289156\pi\)
0.615001 + 0.788527i \(0.289156\pi\)
\(354\) 0 0
\(355\) −2.41476 −0.128162
\(356\) 0 0
\(357\) −15.6514 −0.828359
\(358\) 0 0
\(359\) −11.1174 −0.586752 −0.293376 0.955997i \(-0.594779\pi\)
−0.293376 + 0.955997i \(0.594779\pi\)
\(360\) 0 0
\(361\) 52.2728 2.75120
\(362\) 0 0
\(363\) −30.7598 −1.61447
\(364\) 0 0
\(365\) −4.22423 −0.221106
\(366\) 0 0
\(367\) 27.9175 1.45728 0.728641 0.684896i \(-0.240152\pi\)
0.728641 + 0.684896i \(0.240152\pi\)
\(368\) 0 0
\(369\) −25.5843 −1.33187
\(370\) 0 0
\(371\) 3.96121 0.205656
\(372\) 0 0
\(373\) −9.21823 −0.477302 −0.238651 0.971105i \(-0.576705\pi\)
−0.238651 + 0.971105i \(0.576705\pi\)
\(374\) 0 0
\(375\) 10.0899 0.521038
\(376\) 0 0
\(377\) −0.108662 −0.00559639
\(378\) 0 0
\(379\) 18.3495 0.942550 0.471275 0.881986i \(-0.343794\pi\)
0.471275 + 0.881986i \(0.343794\pi\)
\(380\) 0 0
\(381\) 26.1953 1.34203
\(382\) 0 0
\(383\) 18.6447 0.952698 0.476349 0.879256i \(-0.341960\pi\)
0.476349 + 0.879256i \(0.341960\pi\)
\(384\) 0 0
\(385\) 2.28006 0.116202
\(386\) 0 0
\(387\) 2.96353 0.150644
\(388\) 0 0
\(389\) −12.8384 −0.650931 −0.325465 0.945554i \(-0.605521\pi\)
−0.325465 + 0.945554i \(0.605521\pi\)
\(390\) 0 0
\(391\) 27.3848 1.38491
\(392\) 0 0
\(393\) −12.3643 −0.623696
\(394\) 0 0
\(395\) −5.65815 −0.284692
\(396\) 0 0
\(397\) −2.04334 −0.102552 −0.0512761 0.998685i \(-0.516329\pi\)
−0.0512761 + 0.998685i \(0.516329\pi\)
\(398\) 0 0
\(399\) −36.0204 −1.80328
\(400\) 0 0
\(401\) −34.7641 −1.73604 −0.868019 0.496531i \(-0.834607\pi\)
−0.868019 + 0.496531i \(0.834607\pi\)
\(402\) 0 0
\(403\) −0.0375737 −0.00187168
\(404\) 0 0
\(405\) 2.57354 0.127880
\(406\) 0 0
\(407\) −6.63387 −0.328829
\(408\) 0 0
\(409\) −21.4640 −1.06133 −0.530664 0.847582i \(-0.678057\pi\)
−0.530664 + 0.847582i \(0.678057\pi\)
\(410\) 0 0
\(411\) −1.04384 −0.0514889
\(412\) 0 0
\(413\) 4.84607 0.238460
\(414\) 0 0
\(415\) −0.907594 −0.0445520
\(416\) 0 0
\(417\) −54.1577 −2.65212
\(418\) 0 0
\(419\) 16.8700 0.824155 0.412078 0.911149i \(-0.364803\pi\)
0.412078 + 0.911149i \(0.364803\pi\)
\(420\) 0 0
\(421\) 21.8430 1.06456 0.532281 0.846568i \(-0.321335\pi\)
0.532281 + 0.846568i \(0.321335\pi\)
\(422\) 0 0
\(423\) 10.0812 0.490163
\(424\) 0 0
\(425\) 17.9084 0.868684
\(426\) 0 0
\(427\) −6.42821 −0.311083
\(428\) 0 0
\(429\) −0.674771 −0.0325783
\(430\) 0 0
\(431\) −21.2561 −1.02387 −0.511936 0.859024i \(-0.671072\pi\)
−0.511936 + 0.859024i \(0.671072\pi\)
\(432\) 0 0
\(433\) 7.83699 0.376622 0.188311 0.982109i \(-0.439699\pi\)
0.188311 + 0.982109i \(0.439699\pi\)
\(434\) 0 0
\(435\) −2.25756 −0.108242
\(436\) 0 0
\(437\) 63.0239 3.01484
\(438\) 0 0
\(439\) −13.2921 −0.634396 −0.317198 0.948359i \(-0.602742\pi\)
−0.317198 + 0.948359i \(0.602742\pi\)
\(440\) 0 0
\(441\) −28.7836 −1.37065
\(442\) 0 0
\(443\) 30.8426 1.46537 0.732687 0.680566i \(-0.238266\pi\)
0.732687 + 0.680566i \(0.238266\pi\)
\(444\) 0 0
\(445\) 1.57127 0.0744851
\(446\) 0 0
\(447\) 36.3508 1.71934
\(448\) 0 0
\(449\) −25.6520 −1.21059 −0.605296 0.796001i \(-0.706945\pi\)
−0.605296 + 0.796001i \(0.706945\pi\)
\(450\) 0 0
\(451\) 20.2819 0.955038
\(452\) 0 0
\(453\) 54.0079 2.53751
\(454\) 0 0
\(455\) 0.0242498 0.00113685
\(456\) 0 0
\(457\) −6.31909 −0.295595 −0.147797 0.989018i \(-0.547218\pi\)
−0.147797 + 0.989018i \(0.547218\pi\)
\(458\) 0 0
\(459\) 30.8344 1.43922
\(460\) 0 0
\(461\) 17.5015 0.815128 0.407564 0.913177i \(-0.366378\pi\)
0.407564 + 0.913177i \(0.366378\pi\)
\(462\) 0 0
\(463\) 24.3125 1.12990 0.564948 0.825127i \(-0.308896\pi\)
0.564948 + 0.825127i \(0.308896\pi\)
\(464\) 0 0
\(465\) −0.780629 −0.0362008
\(466\) 0 0
\(467\) −33.1917 −1.53593 −0.767964 0.640493i \(-0.778730\pi\)
−0.767964 + 0.640493i \(0.778730\pi\)
\(468\) 0 0
\(469\) −11.5415 −0.532938
\(470\) 0 0
\(471\) 3.81611 0.175837
\(472\) 0 0
\(473\) −2.34933 −0.108022
\(474\) 0 0
\(475\) 41.2147 1.89106
\(476\) 0 0
\(477\) −16.0798 −0.736243
\(478\) 0 0
\(479\) −40.9888 −1.87283 −0.936414 0.350898i \(-0.885876\pi\)
−0.936414 + 0.350898i \(0.885876\pi\)
\(480\) 0 0
\(481\) −0.0705552 −0.00321704
\(482\) 0 0
\(483\) −31.8516 −1.44930
\(484\) 0 0
\(485\) 0.119218 0.00541343
\(486\) 0 0
\(487\) 0.843153 0.0382069 0.0191035 0.999818i \(-0.493919\pi\)
0.0191035 + 0.999818i \(0.493919\pi\)
\(488\) 0 0
\(489\) −19.4157 −0.878007
\(490\) 0 0
\(491\) −20.9217 −0.944185 −0.472092 0.881549i \(-0.656501\pi\)
−0.472092 + 0.881549i \(0.656501\pi\)
\(492\) 0 0
\(493\) −8.11077 −0.365291
\(494\) 0 0
\(495\) −9.25545 −0.416001
\(496\) 0 0
\(497\) 10.0906 0.452627
\(498\) 0 0
\(499\) −24.6333 −1.10274 −0.551370 0.834261i \(-0.685895\pi\)
−0.551370 + 0.834261i \(0.685895\pi\)
\(500\) 0 0
\(501\) 31.0311 1.38637
\(502\) 0 0
\(503\) −11.6987 −0.521619 −0.260810 0.965390i \(-0.583989\pi\)
−0.260810 + 0.965390i \(0.583989\pi\)
\(504\) 0 0
\(505\) −3.47588 −0.154675
\(506\) 0 0
\(507\) 38.6203 1.71519
\(508\) 0 0
\(509\) 36.1721 1.60330 0.801651 0.597793i \(-0.203955\pi\)
0.801651 + 0.597793i \(0.203955\pi\)
\(510\) 0 0
\(511\) 17.6519 0.780873
\(512\) 0 0
\(513\) 70.9628 3.13309
\(514\) 0 0
\(515\) −0.607536 −0.0267712
\(516\) 0 0
\(517\) −7.99183 −0.351480
\(518\) 0 0
\(519\) 61.0230 2.67861
\(520\) 0 0
\(521\) 21.5527 0.944241 0.472121 0.881534i \(-0.343489\pi\)
0.472121 + 0.881534i \(0.343489\pi\)
\(522\) 0 0
\(523\) −6.50799 −0.284574 −0.142287 0.989825i \(-0.545446\pi\)
−0.142287 + 0.989825i \(0.545446\pi\)
\(524\) 0 0
\(525\) −20.8294 −0.909071
\(526\) 0 0
\(527\) −2.80457 −0.122169
\(528\) 0 0
\(529\) 32.7298 1.42303
\(530\) 0 0
\(531\) −19.6717 −0.853679
\(532\) 0 0
\(533\) 0.215710 0.00934345
\(534\) 0 0
\(535\) 3.51831 0.152110
\(536\) 0 0
\(537\) 39.7423 1.71501
\(538\) 0 0
\(539\) 22.8182 0.982848
\(540\) 0 0
\(541\) −18.8108 −0.808737 −0.404369 0.914596i \(-0.632509\pi\)
−0.404369 + 0.914596i \(0.632509\pi\)
\(542\) 0 0
\(543\) −76.5988 −3.28717
\(544\) 0 0
\(545\) −1.29621 −0.0555237
\(546\) 0 0
\(547\) 3.91680 0.167470 0.0837352 0.996488i \(-0.473315\pi\)
0.0837352 + 0.996488i \(0.473315\pi\)
\(548\) 0 0
\(549\) 26.0941 1.11367
\(550\) 0 0
\(551\) −18.6663 −0.795211
\(552\) 0 0
\(553\) 23.6438 1.00544
\(554\) 0 0
\(555\) −1.46585 −0.0622219
\(556\) 0 0
\(557\) 7.41115 0.314021 0.157010 0.987597i \(-0.449814\pi\)
0.157010 + 0.987597i \(0.449814\pi\)
\(558\) 0 0
\(559\) −0.0249865 −0.00105682
\(560\) 0 0
\(561\) −50.3663 −2.12647
\(562\) 0 0
\(563\) 8.38055 0.353198 0.176599 0.984283i \(-0.443490\pi\)
0.176599 + 0.984283i \(0.443490\pi\)
\(564\) 0 0
\(565\) −5.04174 −0.212108
\(566\) 0 0
\(567\) −10.7541 −0.451630
\(568\) 0 0
\(569\) −36.2279 −1.51875 −0.759377 0.650651i \(-0.774496\pi\)
−0.759377 + 0.650651i \(0.774496\pi\)
\(570\) 0 0
\(571\) −1.71890 −0.0719337 −0.0359668 0.999353i \(-0.511451\pi\)
−0.0359668 + 0.999353i \(0.511451\pi\)
\(572\) 0 0
\(573\) −15.1286 −0.632005
\(574\) 0 0
\(575\) 36.4447 1.51985
\(576\) 0 0
\(577\) 23.6396 0.984129 0.492065 0.870559i \(-0.336242\pi\)
0.492065 + 0.870559i \(0.336242\pi\)
\(578\) 0 0
\(579\) 9.08840 0.377701
\(580\) 0 0
\(581\) 3.79258 0.157343
\(582\) 0 0
\(583\) 12.7472 0.527936
\(584\) 0 0
\(585\) −0.0984372 −0.00406988
\(586\) 0 0
\(587\) 1.35858 0.0560748 0.0280374 0.999607i \(-0.491074\pi\)
0.0280374 + 0.999607i \(0.491074\pi\)
\(588\) 0 0
\(589\) −6.45451 −0.265953
\(590\) 0 0
\(591\) −5.18192 −0.213156
\(592\) 0 0
\(593\) 6.33616 0.260195 0.130097 0.991501i \(-0.458471\pi\)
0.130097 + 0.991501i \(0.458471\pi\)
\(594\) 0 0
\(595\) 1.81005 0.0742048
\(596\) 0 0
\(597\) 35.7748 1.46417
\(598\) 0 0
\(599\) −38.3985 −1.56892 −0.784460 0.620179i \(-0.787060\pi\)
−0.784460 + 0.620179i \(0.787060\pi\)
\(600\) 0 0
\(601\) −21.1092 −0.861062 −0.430531 0.902576i \(-0.641674\pi\)
−0.430531 + 0.902576i \(0.641674\pi\)
\(602\) 0 0
\(603\) 46.8506 1.90790
\(604\) 0 0
\(605\) 3.55731 0.144625
\(606\) 0 0
\(607\) 27.3475 1.11000 0.555000 0.831850i \(-0.312718\pi\)
0.555000 + 0.831850i \(0.312718\pi\)
\(608\) 0 0
\(609\) 9.43373 0.382274
\(610\) 0 0
\(611\) −0.0849978 −0.00343864
\(612\) 0 0
\(613\) −0.809174 −0.0326822 −0.0163411 0.999866i \(-0.505202\pi\)
−0.0163411 + 0.999866i \(0.505202\pi\)
\(614\) 0 0
\(615\) 4.48159 0.180715
\(616\) 0 0
\(617\) 14.7264 0.592863 0.296432 0.955054i \(-0.404203\pi\)
0.296432 + 0.955054i \(0.404203\pi\)
\(618\) 0 0
\(619\) −5.84706 −0.235013 −0.117507 0.993072i \(-0.537490\pi\)
−0.117507 + 0.993072i \(0.537490\pi\)
\(620\) 0 0
\(621\) 62.7499 2.51806
\(622\) 0 0
\(623\) −6.56588 −0.263056
\(624\) 0 0
\(625\) 23.2427 0.929709
\(626\) 0 0
\(627\) −115.914 −4.62916
\(628\) 0 0
\(629\) −5.26638 −0.209984
\(630\) 0 0
\(631\) −26.1832 −1.04234 −0.521168 0.853454i \(-0.674503\pi\)
−0.521168 + 0.853454i \(0.674503\pi\)
\(632\) 0 0
\(633\) −65.3794 −2.59860
\(634\) 0 0
\(635\) −3.02943 −0.120219
\(636\) 0 0
\(637\) 0.242685 0.00961552
\(638\) 0 0
\(639\) −40.9609 −1.62039
\(640\) 0 0
\(641\) −17.6223 −0.696037 −0.348019 0.937488i \(-0.613145\pi\)
−0.348019 + 0.937488i \(0.613145\pi\)
\(642\) 0 0
\(643\) −11.9812 −0.472494 −0.236247 0.971693i \(-0.575917\pi\)
−0.236247 + 0.971693i \(0.575917\pi\)
\(644\) 0 0
\(645\) −0.519119 −0.0204403
\(646\) 0 0
\(647\) −14.1539 −0.556446 −0.278223 0.960517i \(-0.589745\pi\)
−0.278223 + 0.960517i \(0.589745\pi\)
\(648\) 0 0
\(649\) 15.5947 0.612145
\(650\) 0 0
\(651\) 3.26203 0.127849
\(652\) 0 0
\(653\) 9.58530 0.375102 0.187551 0.982255i \(-0.439945\pi\)
0.187551 + 0.982255i \(0.439945\pi\)
\(654\) 0 0
\(655\) 1.42990 0.0558710
\(656\) 0 0
\(657\) −71.6544 −2.79550
\(658\) 0 0
\(659\) −2.36439 −0.0921035 −0.0460517 0.998939i \(-0.514664\pi\)
−0.0460517 + 0.998939i \(0.514664\pi\)
\(660\) 0 0
\(661\) 10.5947 0.412085 0.206043 0.978543i \(-0.433941\pi\)
0.206043 + 0.978543i \(0.433941\pi\)
\(662\) 0 0
\(663\) −0.535675 −0.0208039
\(664\) 0 0
\(665\) 4.16569 0.161538
\(666\) 0 0
\(667\) −16.5059 −0.639112
\(668\) 0 0
\(669\) −34.6136 −1.33824
\(670\) 0 0
\(671\) −20.6860 −0.798574
\(672\) 0 0
\(673\) −12.2357 −0.471652 −0.235826 0.971795i \(-0.575779\pi\)
−0.235826 + 0.971795i \(0.575779\pi\)
\(674\) 0 0
\(675\) 41.0355 1.57946
\(676\) 0 0
\(677\) 33.7430 1.29685 0.648424 0.761279i \(-0.275428\pi\)
0.648424 + 0.761279i \(0.275428\pi\)
\(678\) 0 0
\(679\) −0.498181 −0.0191184
\(680\) 0 0
\(681\) −9.04290 −0.346525
\(682\) 0 0
\(683\) 27.0033 1.03325 0.516626 0.856211i \(-0.327188\pi\)
0.516626 + 0.856211i \(0.327188\pi\)
\(684\) 0 0
\(685\) 0.120718 0.00461240
\(686\) 0 0
\(687\) 7.71513 0.294350
\(688\) 0 0
\(689\) 0.135574 0.00516497
\(690\) 0 0
\(691\) −0.194869 −0.00741317 −0.00370659 0.999993i \(-0.501180\pi\)
−0.00370659 + 0.999993i \(0.501180\pi\)
\(692\) 0 0
\(693\) 38.6759 1.46918
\(694\) 0 0
\(695\) 6.26323 0.237578
\(696\) 0 0
\(697\) 16.1010 0.609870
\(698\) 0 0
\(699\) −57.8131 −2.18669
\(700\) 0 0
\(701\) −18.2430 −0.689029 −0.344515 0.938781i \(-0.611957\pi\)
−0.344515 + 0.938781i \(0.611957\pi\)
\(702\) 0 0
\(703\) −12.1201 −0.457120
\(704\) 0 0
\(705\) −1.76591 −0.0665081
\(706\) 0 0
\(707\) 14.5247 0.546259
\(708\) 0 0
\(709\) 29.4184 1.10483 0.552416 0.833568i \(-0.313706\pi\)
0.552416 + 0.833568i \(0.313706\pi\)
\(710\) 0 0
\(711\) −95.9775 −3.59944
\(712\) 0 0
\(713\) −5.70748 −0.213747
\(714\) 0 0
\(715\) 0.0780359 0.00291838
\(716\) 0 0
\(717\) −6.98020 −0.260680
\(718\) 0 0
\(719\) 40.3065 1.50318 0.751590 0.659631i \(-0.229287\pi\)
0.751590 + 0.659631i \(0.229287\pi\)
\(720\) 0 0
\(721\) 2.53872 0.0945470
\(722\) 0 0
\(723\) −43.5011 −1.61782
\(724\) 0 0
\(725\) −10.7941 −0.400883
\(726\) 0 0
\(727\) 41.8581 1.55243 0.776216 0.630467i \(-0.217136\pi\)
0.776216 + 0.630467i \(0.217136\pi\)
\(728\) 0 0
\(729\) −31.2736 −1.15828
\(730\) 0 0
\(731\) −1.86504 −0.0689811
\(732\) 0 0
\(733\) 19.9611 0.737282 0.368641 0.929572i \(-0.379823\pi\)
0.368641 + 0.929572i \(0.379823\pi\)
\(734\) 0 0
\(735\) 5.04201 0.185977
\(736\) 0 0
\(737\) −37.1407 −1.36810
\(738\) 0 0
\(739\) 33.0715 1.21655 0.608277 0.793725i \(-0.291861\pi\)
0.608277 + 0.793725i \(0.291861\pi\)
\(740\) 0 0
\(741\) −1.23281 −0.0452886
\(742\) 0 0
\(743\) −28.9789 −1.06313 −0.531567 0.847017i \(-0.678396\pi\)
−0.531567 + 0.847017i \(0.678396\pi\)
\(744\) 0 0
\(745\) −4.20390 −0.154019
\(746\) 0 0
\(747\) −15.3952 −0.563283
\(748\) 0 0
\(749\) −14.7020 −0.537200
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 15.1197 0.550992
\(754\) 0 0
\(755\) −6.24590 −0.227312
\(756\) 0 0
\(757\) −21.0900 −0.766530 −0.383265 0.923638i \(-0.625200\pi\)
−0.383265 + 0.923638i \(0.625200\pi\)
\(758\) 0 0
\(759\) −102.499 −3.72046
\(760\) 0 0
\(761\) −3.54644 −0.128558 −0.0642791 0.997932i \(-0.520475\pi\)
−0.0642791 + 0.997932i \(0.520475\pi\)
\(762\) 0 0
\(763\) 5.41652 0.196091
\(764\) 0 0
\(765\) −7.34755 −0.265651
\(766\) 0 0
\(767\) 0.165859 0.00598882
\(768\) 0 0
\(769\) −9.73837 −0.351175 −0.175587 0.984464i \(-0.556182\pi\)
−0.175587 + 0.984464i \(0.556182\pi\)
\(770\) 0 0
\(771\) 63.1299 2.27357
\(772\) 0 0
\(773\) −26.7194 −0.961030 −0.480515 0.876987i \(-0.659550\pi\)
−0.480515 + 0.876987i \(0.659550\pi\)
\(774\) 0 0
\(775\) −3.73243 −0.134073
\(776\) 0 0
\(777\) 6.12538 0.219747
\(778\) 0 0
\(779\) 37.0553 1.32764
\(780\) 0 0
\(781\) 32.4717 1.16193
\(782\) 0 0
\(783\) −18.5851 −0.664178
\(784\) 0 0
\(785\) −0.441325 −0.0157516
\(786\) 0 0
\(787\) 27.6834 0.986807 0.493403 0.869801i \(-0.335753\pi\)
0.493403 + 0.869801i \(0.335753\pi\)
\(788\) 0 0
\(789\) −78.0960 −2.78029
\(790\) 0 0
\(791\) 21.0680 0.749092
\(792\) 0 0
\(793\) −0.220008 −0.00781271
\(794\) 0 0
\(795\) 2.81668 0.0998975
\(796\) 0 0
\(797\) −42.8043 −1.51621 −0.758104 0.652134i \(-0.773874\pi\)
−0.758104 + 0.652134i \(0.773874\pi\)
\(798\) 0 0
\(799\) −6.34440 −0.224449
\(800\) 0 0
\(801\) 26.6529 0.941735
\(802\) 0 0
\(803\) 56.8038 2.00456
\(804\) 0 0
\(805\) 3.68357 0.129829
\(806\) 0 0
\(807\) 14.1190 0.497012
\(808\) 0 0
\(809\) 36.2810 1.27557 0.637785 0.770214i \(-0.279851\pi\)
0.637785 + 0.770214i \(0.279851\pi\)
\(810\) 0 0
\(811\) 11.2274 0.394249 0.197125 0.980378i \(-0.436840\pi\)
0.197125 + 0.980378i \(0.436840\pi\)
\(812\) 0 0
\(813\) −8.17025 −0.286543
\(814\) 0 0
\(815\) 2.24538 0.0786523
\(816\) 0 0
\(817\) −4.29225 −0.150167
\(818\) 0 0
\(819\) 0.411342 0.0143734
\(820\) 0 0
\(821\) −41.2557 −1.43983 −0.719917 0.694061i \(-0.755820\pi\)
−0.719917 + 0.694061i \(0.755820\pi\)
\(822\) 0 0
\(823\) −33.5150 −1.16826 −0.584129 0.811661i \(-0.698564\pi\)
−0.584129 + 0.811661i \(0.698564\pi\)
\(824\) 0 0
\(825\) −67.0293 −2.33366
\(826\) 0 0
\(827\) 25.2127 0.876730 0.438365 0.898797i \(-0.355558\pi\)
0.438365 + 0.898797i \(0.355558\pi\)
\(828\) 0 0
\(829\) −33.1710 −1.15208 −0.576038 0.817423i \(-0.695402\pi\)
−0.576038 + 0.817423i \(0.695402\pi\)
\(830\) 0 0
\(831\) 55.7923 1.93541
\(832\) 0 0
\(833\) 18.1145 0.627629
\(834\) 0 0
\(835\) −3.58868 −0.124192
\(836\) 0 0
\(837\) −6.42644 −0.222130
\(838\) 0 0
\(839\) 17.3377 0.598562 0.299281 0.954165i \(-0.403253\pi\)
0.299281 + 0.954165i \(0.403253\pi\)
\(840\) 0 0
\(841\) −24.1113 −0.831425
\(842\) 0 0
\(843\) −56.2760 −1.93825
\(844\) 0 0
\(845\) −4.46636 −0.153647
\(846\) 0 0
\(847\) −14.8650 −0.510768
\(848\) 0 0
\(849\) 1.72366 0.0591559
\(850\) 0 0
\(851\) −10.7174 −0.367388
\(852\) 0 0
\(853\) 45.8869 1.57114 0.785568 0.618775i \(-0.212371\pi\)
0.785568 + 0.618775i \(0.212371\pi\)
\(854\) 0 0
\(855\) −16.9098 −0.578303
\(856\) 0 0
\(857\) 19.0723 0.651496 0.325748 0.945457i \(-0.394384\pi\)
0.325748 + 0.945457i \(0.394384\pi\)
\(858\) 0 0
\(859\) 6.41099 0.218740 0.109370 0.994001i \(-0.465117\pi\)
0.109370 + 0.994001i \(0.465117\pi\)
\(860\) 0 0
\(861\) −18.7273 −0.638225
\(862\) 0 0
\(863\) −9.48469 −0.322863 −0.161431 0.986884i \(-0.551611\pi\)
−0.161431 + 0.986884i \(0.551611\pi\)
\(864\) 0 0
\(865\) −7.05718 −0.239951
\(866\) 0 0
\(867\) 10.5290 0.357584
\(868\) 0 0
\(869\) 76.0860 2.58104
\(870\) 0 0
\(871\) −0.395014 −0.0133845
\(872\) 0 0
\(873\) 2.02227 0.0684434
\(874\) 0 0
\(875\) 4.87603 0.164840
\(876\) 0 0
\(877\) 10.0781 0.340313 0.170156 0.985417i \(-0.445573\pi\)
0.170156 + 0.985417i \(0.445573\pi\)
\(878\) 0 0
\(879\) −13.0678 −0.440765
\(880\) 0 0
\(881\) 27.7601 0.935262 0.467631 0.883924i \(-0.345108\pi\)
0.467631 + 0.883924i \(0.345108\pi\)
\(882\) 0 0
\(883\) −10.2389 −0.344567 −0.172283 0.985047i \(-0.555114\pi\)
−0.172283 + 0.985047i \(0.555114\pi\)
\(884\) 0 0
\(885\) 3.44588 0.115832
\(886\) 0 0
\(887\) 54.6655 1.83549 0.917745 0.397171i \(-0.130008\pi\)
0.917745 + 0.397171i \(0.130008\pi\)
\(888\) 0 0
\(889\) 12.6591 0.424574
\(890\) 0 0
\(891\) −34.6068 −1.15937
\(892\) 0 0
\(893\) −14.6011 −0.488609
\(894\) 0 0
\(895\) −4.59611 −0.153631
\(896\) 0 0
\(897\) −1.09013 −0.0363985
\(898\) 0 0
\(899\) 1.69043 0.0563790
\(900\) 0 0
\(901\) 10.1195 0.337130
\(902\) 0 0
\(903\) 2.16925 0.0721882
\(904\) 0 0
\(905\) 8.85849 0.294466
\(906\) 0 0
\(907\) −25.3279 −0.840998 −0.420499 0.907293i \(-0.638145\pi\)
−0.420499 + 0.907293i \(0.638145\pi\)
\(908\) 0 0
\(909\) −58.9603 −1.95559
\(910\) 0 0
\(911\) −32.9288 −1.09098 −0.545491 0.838117i \(-0.683657\pi\)
−0.545491 + 0.838117i \(0.683657\pi\)
\(912\) 0 0
\(913\) 12.2045 0.403912
\(914\) 0 0
\(915\) −4.57088 −0.151109
\(916\) 0 0
\(917\) −5.97517 −0.197318
\(918\) 0 0
\(919\) 0.265854 0.00876971 0.00438485 0.999990i \(-0.498604\pi\)
0.00438485 + 0.999990i \(0.498604\pi\)
\(920\) 0 0
\(921\) 81.7577 2.69401
\(922\) 0 0
\(923\) 0.345356 0.0113675
\(924\) 0 0
\(925\) −7.00869 −0.230444
\(926\) 0 0
\(927\) −10.3055 −0.338475
\(928\) 0 0
\(929\) 0.426009 0.0139769 0.00698844 0.999976i \(-0.497775\pi\)
0.00698844 + 0.999976i \(0.497775\pi\)
\(930\) 0 0
\(931\) 41.6890 1.36630
\(932\) 0 0
\(933\) 13.3390 0.436698
\(934\) 0 0
\(935\) 5.82475 0.190490
\(936\) 0 0
\(937\) 25.7808 0.842222 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(938\) 0 0
\(939\) −52.5011 −1.71331
\(940\) 0 0
\(941\) 21.4944 0.700697 0.350348 0.936619i \(-0.386063\pi\)
0.350348 + 0.936619i \(0.386063\pi\)
\(942\) 0 0
\(943\) 32.7666 1.06703
\(944\) 0 0
\(945\) 4.14757 0.134921
\(946\) 0 0
\(947\) 49.1488 1.59712 0.798560 0.601915i \(-0.205595\pi\)
0.798560 + 0.601915i \(0.205595\pi\)
\(948\) 0 0
\(949\) 0.604143 0.0196113
\(950\) 0 0
\(951\) −61.4833 −1.99373
\(952\) 0 0
\(953\) −30.2774 −0.980781 −0.490391 0.871503i \(-0.663146\pi\)
−0.490391 + 0.871503i \(0.663146\pi\)
\(954\) 0 0
\(955\) 1.74959 0.0566153
\(956\) 0 0
\(957\) 30.3578 0.981328
\(958\) 0 0
\(959\) −0.504447 −0.0162894
\(960\) 0 0
\(961\) −30.4155 −0.981144
\(962\) 0 0
\(963\) 59.6800 1.92316
\(964\) 0 0
\(965\) −1.05105 −0.0338346
\(966\) 0 0
\(967\) −26.0631 −0.838132 −0.419066 0.907956i \(-0.637642\pi\)
−0.419066 + 0.907956i \(0.637642\pi\)
\(968\) 0 0
\(969\) −92.0197 −2.95610
\(970\) 0 0
\(971\) −51.6428 −1.65730 −0.828648 0.559770i \(-0.810890\pi\)
−0.828648 + 0.559770i \(0.810890\pi\)
\(972\) 0 0
\(973\) −26.1723 −0.839045
\(974\) 0 0
\(975\) −0.712896 −0.0228310
\(976\) 0 0
\(977\) 8.61973 0.275770 0.137885 0.990448i \(-0.455970\pi\)
0.137885 + 0.990448i \(0.455970\pi\)
\(978\) 0 0
\(979\) −21.1290 −0.675287
\(980\) 0 0
\(981\) −21.9873 −0.702001
\(982\) 0 0
\(983\) −24.8716 −0.793281 −0.396641 0.917974i \(-0.629824\pi\)
−0.396641 + 0.917974i \(0.629824\pi\)
\(984\) 0 0
\(985\) 0.599278 0.0190946
\(986\) 0 0
\(987\) 7.37925 0.234884
\(988\) 0 0
\(989\) −3.79548 −0.120689
\(990\) 0 0
\(991\) −15.5601 −0.494283 −0.247142 0.968979i \(-0.579491\pi\)
−0.247142 + 0.968979i \(0.579491\pi\)
\(992\) 0 0
\(993\) 22.1216 0.702009
\(994\) 0 0
\(995\) −4.13728 −0.131161
\(996\) 0 0
\(997\) −18.3009 −0.579595 −0.289797 0.957088i \(-0.593588\pi\)
−0.289797 + 0.957088i \(0.593588\pi\)
\(998\) 0 0
\(999\) −12.0674 −0.381797
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 \(a_p\))