Properties

Label 186.2.a.c.1.1
Level 186
Weight 2
Character 186.1
Self dual Yes
Analytic conductor 1.485
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 186 = 2 \cdot 3 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 186.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.4852174776\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 186.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+1.00000 q^{6}\) \(-2.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+1.00000 q^{6}\) \(-2.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+1.00000 q^{10}\) \(-3.00000 q^{11}\) \(+1.00000 q^{12}\) \(-1.00000 q^{13}\) \(-2.00000 q^{14}\) \(+1.00000 q^{15}\) \(+1.00000 q^{16}\) \(+3.00000 q^{17}\) \(+1.00000 q^{18}\) \(-5.00000 q^{19}\) \(+1.00000 q^{20}\) \(-2.00000 q^{21}\) \(-3.00000 q^{22}\) \(+4.00000 q^{23}\) \(+1.00000 q^{24}\) \(-4.00000 q^{25}\) \(-1.00000 q^{26}\) \(+1.00000 q^{27}\) \(-2.00000 q^{28}\) \(+1.00000 q^{30}\) \(+1.00000 q^{31}\) \(+1.00000 q^{32}\) \(-3.00000 q^{33}\) \(+3.00000 q^{34}\) \(-2.00000 q^{35}\) \(+1.00000 q^{36}\) \(-2.00000 q^{37}\) \(-5.00000 q^{38}\) \(-1.00000 q^{39}\) \(+1.00000 q^{40}\) \(+2.00000 q^{41}\) \(-2.00000 q^{42}\) \(-6.00000 q^{43}\) \(-3.00000 q^{44}\) \(+1.00000 q^{45}\) \(+4.00000 q^{46}\) \(-7.00000 q^{47}\) \(+1.00000 q^{48}\) \(-3.00000 q^{49}\) \(-4.00000 q^{50}\) \(+3.00000 q^{51}\) \(-1.00000 q^{52}\) \(+14.0000 q^{53}\) \(+1.00000 q^{54}\) \(-3.00000 q^{55}\) \(-2.00000 q^{56}\) \(-5.00000 q^{57}\) \(+10.0000 q^{59}\) \(+1.00000 q^{60}\) \(+7.00000 q^{61}\) \(+1.00000 q^{62}\) \(-2.00000 q^{63}\) \(+1.00000 q^{64}\) \(-1.00000 q^{65}\) \(-3.00000 q^{66}\) \(-7.00000 q^{67}\) \(+3.00000 q^{68}\) \(+4.00000 q^{69}\) \(-2.00000 q^{70}\) \(-3.00000 q^{71}\) \(+1.00000 q^{72}\) \(-6.00000 q^{73}\) \(-2.00000 q^{74}\) \(-4.00000 q^{75}\) \(-5.00000 q^{76}\) \(+6.00000 q^{77}\) \(-1.00000 q^{78}\) \(+15.0000 q^{79}\) \(+1.00000 q^{80}\) \(+1.00000 q^{81}\) \(+2.00000 q^{82}\) \(-1.00000 q^{83}\) \(-2.00000 q^{84}\) \(+3.00000 q^{85}\) \(-6.00000 q^{86}\) \(-3.00000 q^{88}\) \(+10.0000 q^{89}\) \(+1.00000 q^{90}\) \(+2.00000 q^{91}\) \(+4.00000 q^{92}\) \(+1.00000 q^{93}\) \(-7.00000 q^{94}\) \(-5.00000 q^{95}\) \(+1.00000 q^{96}\) \(+13.0000 q^{97}\) \(-3.00000 q^{98}\) \(-3.00000 q^{99}\) \(+O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.00000 −0.436436
\(22\) −3.00000 −0.639602
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) −1.00000 −0.196116
\(27\) 1.00000 0.192450
\(28\) −2.00000 −0.377964
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.00000 0.182574
\(31\) 1.00000 0.179605
\(32\) 1.00000 0.176777
\(33\) −3.00000 −0.522233
\(34\) 3.00000 0.514496
\(35\) −2.00000 −0.338062
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −5.00000 −0.811107
\(39\) −1.00000 −0.160128
\(40\) 1.00000 0.158114
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −2.00000 −0.308607
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) −3.00000 −0.452267
\(45\) 1.00000 0.149071
\(46\) 4.00000 0.589768
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) −4.00000 −0.565685
\(51\) 3.00000 0.420084
\(52\) −1.00000 −0.138675
\(53\) 14.0000 1.92305 0.961524 0.274721i \(-0.0885855\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 1.00000 0.136083
\(55\) −3.00000 −0.404520
\(56\) −2.00000 −0.267261
\(57\) −5.00000 −0.662266
\(58\) 0 0
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 1.00000 0.129099
\(61\) 7.00000 0.896258 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) 1.00000 0.127000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −3.00000 −0.369274
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 3.00000 0.363803
\(69\) 4.00000 0.481543
\(70\) −2.00000 −0.239046
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) −4.00000 −0.461880
\(76\) −5.00000 −0.573539
\(77\) 6.00000 0.683763
\(78\) −1.00000 −0.113228
\(79\) 15.0000 1.68763 0.843816 0.536633i \(-0.180304\pi\)
0.843816 + 0.536633i \(0.180304\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) −1.00000 −0.109764 −0.0548821 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) −2.00000 −0.218218
\(85\) 3.00000 0.325396
\(86\) −6.00000 −0.646997
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 1.00000 0.105409
\(91\) 2.00000 0.209657
\(92\) 4.00000 0.417029
\(93\) 1.00000 0.103695
\(94\) −7.00000 −0.721995
\(95\) −5.00000 −0.512989
\(96\) 1.00000 0.102062
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) −3.00000 −0.303046
\(99\) −3.00000 −0.301511
\(100\) −4.00000 −0.400000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 3.00000 0.297044
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −2.00000 −0.195180
\(106\) 14.0000 1.35980
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 1.00000 0.0962250
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) −3.00000 −0.286039
\(111\) −2.00000 −0.189832
\(112\) −2.00000 −0.188982
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) −5.00000 −0.468293
\(115\) 4.00000 0.373002
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 10.0000 0.920575
\(119\) −6.00000 −0.550019
\(120\) 1.00000 0.0912871
\(121\) −2.00000 −0.181818
\(122\) 7.00000 0.633750
\(123\) 2.00000 0.180334
\(124\) 1.00000 0.0898027
\(125\) −9.00000 −0.804984
\(126\) −2.00000 −0.178174
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.00000 −0.528271
\(130\) −1.00000 −0.0877058
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) −3.00000 −0.261116
\(133\) 10.0000 0.867110
\(134\) −7.00000 −0.604708
\(135\) 1.00000 0.0860663
\(136\) 3.00000 0.257248
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 4.00000 0.340503
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −2.00000 −0.169031
\(141\) −7.00000 −0.589506
\(142\) −3.00000 −0.251754
\(143\) 3.00000 0.250873
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) −3.00000 −0.247436
\(148\) −2.00000 −0.164399
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) −4.00000 −0.326599
\(151\) −3.00000 −0.244137 −0.122068 0.992522i \(-0.538953\pi\)
−0.122068 + 0.992522i \(0.538953\pi\)
\(152\) −5.00000 −0.405554
\(153\) 3.00000 0.242536
\(154\) 6.00000 0.483494
\(155\) 1.00000 0.0803219
\(156\) −1.00000 −0.0800641
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 15.0000 1.19334
\(159\) 14.0000 1.11027
\(160\) 1.00000 0.0790569
\(161\) −8.00000 −0.630488
\(162\) 1.00000 0.0785674
\(163\) −21.0000 −1.64485 −0.822423 0.568876i \(-0.807379\pi\)
−0.822423 + 0.568876i \(0.807379\pi\)
\(164\) 2.00000 0.156174
\(165\) −3.00000 −0.233550
\(166\) −1.00000 −0.0776151
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) −2.00000 −0.154303
\(169\) −12.0000 −0.923077
\(170\) 3.00000 0.230089
\(171\) −5.00000 −0.382360
\(172\) −6.00000 −0.457496
\(173\) −21.0000 −1.59660 −0.798300 0.602260i \(-0.794267\pi\)
−0.798300 + 0.602260i \(0.794267\pi\)
\(174\) 0 0
\(175\) 8.00000 0.604743
\(176\) −3.00000 −0.226134
\(177\) 10.0000 0.751646
\(178\) 10.0000 0.749532
\(179\) −5.00000 −0.373718 −0.186859 0.982387i \(-0.559831\pi\)
−0.186859 + 0.982387i \(0.559831\pi\)
\(180\) 1.00000 0.0745356
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 2.00000 0.148250
\(183\) 7.00000 0.517455
\(184\) 4.00000 0.294884
\(185\) −2.00000 −0.147043
\(186\) 1.00000 0.0733236
\(187\) −9.00000 −0.658145
\(188\) −7.00000 −0.510527
\(189\) −2.00000 −0.145479
\(190\) −5.00000 −0.362738
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 1.00000 0.0721688
\(193\) −21.0000 −1.51161 −0.755807 0.654795i \(-0.772755\pi\)
−0.755807 + 0.654795i \(0.772755\pi\)
\(194\) 13.0000 0.933346
\(195\) −1.00000 −0.0716115
\(196\) −3.00000 −0.214286
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) −3.00000 −0.213201
\(199\) 15.0000 1.06332 0.531661 0.846957i \(-0.321568\pi\)
0.531661 + 0.846957i \(0.321568\pi\)
\(200\) −4.00000 −0.282843
\(201\) −7.00000 −0.493742
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 2.00000 0.139686
\(206\) 14.0000 0.975426
\(207\) 4.00000 0.278019
\(208\) −1.00000 −0.0693375
\(209\) 15.0000 1.03757
\(210\) −2.00000 −0.138013
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 14.0000 0.961524
\(213\) −3.00000 −0.205557
\(214\) −12.0000 −0.820303
\(215\) −6.00000 −0.409197
\(216\) 1.00000 0.0680414
\(217\) −2.00000 −0.135769
\(218\) 10.0000 0.677285
\(219\) −6.00000 −0.405442
\(220\) −3.00000 −0.202260
\(221\) −3.00000 −0.201802
\(222\) −2.00000 −0.134231
\(223\) 9.00000 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) −2.00000 −0.133631
\(225\) −4.00000 −0.266667
\(226\) 14.0000 0.931266
\(227\) −22.0000 −1.46019 −0.730096 0.683345i \(-0.760525\pi\)
−0.730096 + 0.683345i \(0.760525\pi\)
\(228\) −5.00000 −0.331133
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 4.00000 0.263752
\(231\) 6.00000 0.394771
\(232\) 0 0
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −7.00000 −0.456630
\(236\) 10.0000 0.650945
\(237\) 15.0000 0.974355
\(238\) −6.00000 −0.388922
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 1.00000 0.0645497
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −2.00000 −0.128565
\(243\) 1.00000 0.0641500
\(244\) 7.00000 0.448129
\(245\) −3.00000 −0.191663
\(246\) 2.00000 0.127515
\(247\) 5.00000 0.318142
\(248\) 1.00000 0.0635001
\(249\) −1.00000 −0.0633724
\(250\) −9.00000 −0.569210
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −2.00000 −0.125988
\(253\) −12.0000 −0.754434
\(254\) −12.0000 −0.752947
\(255\) 3.00000 0.187867
\(256\) 1.00000 0.0625000
\(257\) 28.0000 1.74659 0.873296 0.487190i \(-0.161978\pi\)
0.873296 + 0.487190i \(0.161978\pi\)
\(258\) −6.00000 −0.373544
\(259\) 4.00000 0.248548
\(260\) −1.00000 −0.0620174
\(261\) 0 0
\(262\) −18.0000 −1.11204
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) −3.00000 −0.184637
\(265\) 14.0000 0.860013
\(266\) 10.0000 0.613139
\(267\) 10.0000 0.611990
\(268\) −7.00000 −0.427593
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 1.00000 0.0608581
\(271\) 7.00000 0.425220 0.212610 0.977137i \(-0.431804\pi\)
0.212610 + 0.977137i \(0.431804\pi\)
\(272\) 3.00000 0.181902
\(273\) 2.00000 0.121046
\(274\) −2.00000 −0.120824
\(275\) 12.0000 0.723627
\(276\) 4.00000 0.240772
\(277\) −17.0000 −1.02143 −0.510716 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 20.0000 1.19952
\(279\) 1.00000 0.0598684
\(280\) −2.00000 −0.119523
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −7.00000 −0.416844
\(283\) 9.00000 0.534994 0.267497 0.963559i \(-0.413803\pi\)
0.267497 + 0.963559i \(0.413803\pi\)
\(284\) −3.00000 −0.178017
\(285\) −5.00000 −0.296174
\(286\) 3.00000 0.177394
\(287\) −4.00000 −0.236113
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 13.0000 0.762073
\(292\) −6.00000 −0.351123
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) −3.00000 −0.174964
\(295\) 10.0000 0.582223
\(296\) −2.00000 −0.116248
\(297\) −3.00000 −0.174078
\(298\) 5.00000 0.289642
\(299\) −4.00000 −0.231326
\(300\) −4.00000 −0.230940
\(301\) 12.0000 0.691669
\(302\) −3.00000 −0.172631
\(303\) 2.00000 0.114897
\(304\) −5.00000 −0.286770
\(305\) 7.00000 0.400819
\(306\) 3.00000 0.171499
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 6.00000 0.341882
\(309\) 14.0000 0.796432
\(310\) 1.00000 0.0567962
\(311\) 27.0000 1.53103 0.765515 0.643418i \(-0.222484\pi\)
0.765515 + 0.643418i \(0.222484\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 8.00000 0.451466
\(315\) −2.00000 −0.112687
\(316\) 15.0000 0.843816
\(317\) −17.0000 −0.954815 −0.477408 0.878682i \(-0.658423\pi\)
−0.477408 + 0.878682i \(0.658423\pi\)
\(318\) 14.0000 0.785081
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −12.0000 −0.669775
\(322\) −8.00000 −0.445823
\(323\) −15.0000 −0.834622
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) −21.0000 −1.16308
\(327\) 10.0000 0.553001
\(328\) 2.00000 0.110432
\(329\) 14.0000 0.771845
\(330\) −3.00000 −0.165145
\(331\) 32.0000 1.75888 0.879440 0.476011i \(-0.157918\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) −1.00000 −0.0548821
\(333\) −2.00000 −0.109599
\(334\) −2.00000 −0.109435
\(335\) −7.00000 −0.382451
\(336\) −2.00000 −0.109109
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −12.0000 −0.652714
\(339\) 14.0000 0.760376
\(340\) 3.00000 0.162698
\(341\) −3.00000 −0.162459
\(342\) −5.00000 −0.270369
\(343\) 20.0000 1.07990
\(344\) −6.00000 −0.323498
\(345\) 4.00000 0.215353
\(346\) −21.0000 −1.12897
\(347\) −7.00000 −0.375780 −0.187890 0.982190i \(-0.560165\pi\)
−0.187890 + 0.982190i \(0.560165\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 8.00000 0.427618
\(351\) −1.00000 −0.0533761
\(352\) −3.00000 −0.159901
\(353\) 9.00000 0.479022 0.239511 0.970894i \(-0.423013\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(354\) 10.0000 0.531494
\(355\) −3.00000 −0.159223
\(356\) 10.0000 0.529999
\(357\) −6.00000 −0.317554
\(358\) −5.00000 −0.264258
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 1.00000 0.0527046
\(361\) 6.00000 0.315789
\(362\) −18.0000 −0.946059
\(363\) −2.00000 −0.104973
\(364\) 2.00000 0.104828
\(365\) −6.00000 −0.314054
\(366\) 7.00000 0.365896
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 4.00000 0.208514
\(369\) 2.00000 0.104116
\(370\) −2.00000 −0.103975
\(371\) −28.0000 −1.45369
\(372\) 1.00000 0.0518476
\(373\) −16.0000 −0.828449 −0.414224 0.910175i \(-0.635947\pi\)
−0.414224 + 0.910175i \(0.635947\pi\)
\(374\) −9.00000 −0.465379
\(375\) −9.00000 −0.464758
\(376\) −7.00000 −0.360997
\(377\) 0 0
\(378\) −2.00000 −0.102869
\(379\) −35.0000 −1.79783 −0.898915 0.438124i \(-0.855643\pi\)
−0.898915 + 0.438124i \(0.855643\pi\)
\(380\) −5.00000 −0.256495
\(381\) −12.0000 −0.614779
\(382\) −8.00000 −0.409316
\(383\) −26.0000 −1.32854 −0.664269 0.747494i \(-0.731257\pi\)
−0.664269 + 0.747494i \(0.731257\pi\)
\(384\) 1.00000 0.0510310
\(385\) 6.00000 0.305788
\(386\) −21.0000 −1.06887
\(387\) −6.00000 −0.304997
\(388\) 13.0000 0.659975
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) −1.00000 −0.0506370
\(391\) 12.0000 0.606866
\(392\) −3.00000 −0.151523
\(393\) −18.0000 −0.907980
\(394\) −22.0000 −1.10834
\(395\) 15.0000 0.754732
\(396\) −3.00000 −0.150756
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 15.0000 0.751882
\(399\) 10.0000 0.500626
\(400\) −4.00000 −0.200000
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) −7.00000 −0.349128
\(403\) −1.00000 −0.0498135
\(404\) 2.00000 0.0995037
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 3.00000 0.148522
\(409\) 30.0000 1.48340 0.741702 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(410\) 2.00000 0.0987730
\(411\) −2.00000 −0.0986527
\(412\) 14.0000 0.689730
\(413\) −20.0000 −0.984136
\(414\) 4.00000 0.196589
\(415\) −1.00000 −0.0490881
\(416\) −1.00000 −0.0490290
\(417\) 20.0000 0.979404
\(418\) 15.0000 0.733674
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −2.00000 −0.0975900
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −8.00000 −0.389434
\(423\) −7.00000 −0.340352
\(424\) 14.0000 0.679900
\(425\) −12.0000 −0.582086
\(426\) −3.00000 −0.145350
\(427\) −14.0000 −0.677507
\(428\) −12.0000 −0.580042
\(429\) 3.00000 0.144841
\(430\) −6.00000 −0.289346
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 1.00000 0.0481125
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) −20.0000 −0.956730
\(438\) −6.00000 −0.286691
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) −3.00000 −0.143019
\(441\) −3.00000 −0.142857
\(442\) −3.00000 −0.142695
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 10.0000 0.474045
\(446\) 9.00000 0.426162
\(447\) 5.00000 0.236492
\(448\) −2.00000 −0.0944911
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) −4.00000 −0.188562
\(451\) −6.00000 −0.282529
\(452\) 14.0000 0.658505
\(453\) −3.00000 −0.140952
\(454\) −22.0000 −1.03251
\(455\) 2.00000 0.0937614
\(456\) −5.00000 −0.234146
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) −5.00000 −0.233635
\(459\) 3.00000 0.140028
\(460\) 4.00000 0.186501
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 6.00000 0.279145
\(463\) 19.0000 0.883005 0.441502 0.897260i \(-0.354446\pi\)
0.441502 + 0.897260i \(0.354446\pi\)
\(464\) 0 0
\(465\) 1.00000 0.0463739
\(466\) 4.00000 0.185296
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 14.0000 0.646460
\(470\) −7.00000 −0.322886
\(471\) 8.00000 0.368621
\(472\) 10.0000 0.460287
\(473\) 18.0000 0.827641
\(474\) 15.0000 0.688973
\(475\) 20.0000 0.917663
\(476\) −6.00000 −0.275010
\(477\) 14.0000 0.641016
\(478\) 20.0000 0.914779
\(479\) 35.0000 1.59919 0.799595 0.600539i \(-0.205047\pi\)
0.799595 + 0.600539i \(0.205047\pi\)
\(480\) 1.00000 0.0456435
\(481\) 2.00000 0.0911922
\(482\) 2.00000 0.0910975
\(483\) −8.00000 −0.364013
\(484\) −2.00000 −0.0909091
\(485\) 13.0000 0.590300
\(486\) 1.00000 0.0453609
\(487\) −17.0000 −0.770344 −0.385172 0.922845i \(-0.625858\pi\)
−0.385172 + 0.922845i \(0.625858\pi\)
\(488\) 7.00000 0.316875
\(489\) −21.0000 −0.949653
\(490\) −3.00000 −0.135526
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 2.00000 0.0901670
\(493\) 0 0
\(494\) 5.00000 0.224961
\(495\) −3.00000 −0.134840
\(496\) 1.00000 0.0449013
\(497\) 6.00000 0.269137
\(498\) −1.00000 −0.0448111
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) −9.00000 −0.402492
\(501\) −2.00000 −0.0893534
\(502\) 12.0000 0.535586
\(503\) 9.00000 0.401290 0.200645 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 2.00000 0.0889988
\(506\) −12.0000 −0.533465
\(507\) −12.0000 −0.532939
\(508\) −12.0000 −0.532414
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 3.00000 0.132842
\(511\) 12.0000 0.530849
\(512\) 1.00000 0.0441942
\(513\) −5.00000 −0.220755
\(514\) 28.0000 1.23503
\(515\) 14.0000 0.616914
\(516\) −6.00000 −0.264135
\(517\) 21.0000 0.923579
\(518\) 4.00000 0.175750
\(519\) −21.0000 −0.921798
\(520\) −1.00000 −0.0438529
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) −26.0000 −1.13690 −0.568450 0.822718i \(-0.692457\pi\)
−0.568450 + 0.822718i \(0.692457\pi\)
\(524\) −18.0000 −0.786334
\(525\) 8.00000 0.349149
\(526\) 24.0000 1.04645
\(527\) 3.00000 0.130682
\(528\) −3.00000 −0.130558
\(529\) −7.00000 −0.304348
\(530\) 14.0000 0.608121
\(531\) 10.0000 0.433963
\(532\) 10.0000 0.433555
\(533\) −2.00000 −0.0866296
\(534\) 10.0000 0.432742
\(535\) −12.0000 −0.518805
\(536\) −7.00000 −0.302354
\(537\) −5.00000 −0.215766
\(538\) 10.0000 0.431131
\(539\) 9.00000 0.387657
\(540\) 1.00000 0.0430331
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 7.00000 0.300676
\(543\) −18.0000 −0.772454
\(544\) 3.00000 0.128624
\(545\) 10.0000 0.428353
\(546\) 2.00000 0.0855921
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 7.00000 0.298753
\(550\) 12.0000 0.511682
\(551\) 0 0
\(552\) 4.00000 0.170251
\(553\) −30.0000 −1.27573
\(554\) −17.0000 −0.722261
\(555\) −2.00000 −0.0848953
\(556\) 20.0000 0.848189
\(557\) −32.0000 −1.35588 −0.677942 0.735116i \(-0.737128\pi\)
−0.677942 + 0.735116i \(0.737128\pi\)
\(558\) 1.00000 0.0423334
\(559\) 6.00000 0.253773
\(560\) −2.00000 −0.0845154
\(561\) −9.00000 −0.379980
\(562\) −18.0000 −0.759284
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −7.00000 −0.294753
\(565\) 14.0000 0.588984
\(566\) 9.00000 0.378298
\(567\) −2.00000 −0.0839921
\(568\) −3.00000 −0.125877
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) −5.00000 −0.209427
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 3.00000 0.125436
\(573\) −8.00000 −0.334205
\(574\) −4.00000 −0.166957
\(575\) −16.0000 −0.667246
\(576\) 1.00000 0.0416667
\(577\) 43.0000 1.79011 0.895057 0.445952i \(-0.147135\pi\)
0.895057 + 0.445952i \(0.147135\pi\)
\(578\) −8.00000 −0.332756
\(579\) −21.0000 −0.872730
\(580\) 0 0
\(581\) 2.00000 0.0829740
\(582\) 13.0000 0.538867
\(583\) −42.0000 −1.73946
\(584\) −6.00000 −0.248282
\(585\) −1.00000 −0.0413449
\(586\) 14.0000 0.578335
\(587\) −17.0000 −0.701665 −0.350833 0.936438i \(-0.614101\pi\)
−0.350833 + 0.936438i \(0.614101\pi\)
\(588\) −3.00000 −0.123718
\(589\) −5.00000 −0.206021
\(590\) 10.0000 0.411693
\(591\) −22.0000 −0.904959
\(592\) −2.00000 −0.0821995
\(593\) 14.0000 0.574911 0.287456 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) −3.00000 −0.123091
\(595\) −6.00000 −0.245976
\(596\) 5.00000 0.204808
\(597\) 15.0000 0.613909
\(598\) −4.00000 −0.163572
\(599\) 15.0000 0.612883 0.306442 0.951889i \(-0.400862\pi\)
0.306442 + 0.951889i \(0.400862\pi\)
\(600\) −4.00000 −0.163299
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 12.0000 0.489083
\(603\) −7.00000 −0.285062
\(604\) −3.00000 −0.122068
\(605\) −2.00000 −0.0813116
\(606\) 2.00000 0.0812444
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 7.00000 0.283422
\(611\) 7.00000 0.283190
\(612\) 3.00000 0.121268
\(613\) 19.0000 0.767403 0.383701 0.923457i \(-0.374649\pi\)
0.383701 + 0.923457i \(0.374649\pi\)
\(614\) 8.00000 0.322854
\(615\) 2.00000 0.0806478
\(616\) 6.00000 0.241747
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 14.0000 0.563163
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 1.00000 0.0401610
\(621\) 4.00000 0.160514
\(622\) 27.0000 1.08260
\(623\) −20.0000 −0.801283
\(624\) −1.00000 −0.0400320
\(625\) 11.0000 0.440000
\(626\) −26.0000 −1.03917
\(627\) 15.0000 0.599042
\(628\) 8.00000 0.319235
\(629\) −6.00000 −0.239236
\(630\) −2.00000 −0.0796819
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 15.0000 0.596668
\(633\) −8.00000 −0.317971
\(634\) −17.0000 −0.675156
\(635\) −12.0000 −0.476205
\(636\) 14.0000 0.555136
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) −3.00000 −0.118678
\(640\) 1.00000 0.0395285
\(641\) 27.0000 1.06644 0.533218 0.845978i \(-0.320983\pi\)
0.533218 + 0.845978i \(0.320983\pi\)
\(642\) −12.0000 −0.473602
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −8.00000 −0.315244
\(645\) −6.00000 −0.236250
\(646\) −15.0000 −0.590167
\(647\) 38.0000 1.49393 0.746967 0.664861i \(-0.231509\pi\)
0.746967 + 0.664861i \(0.231509\pi\)
\(648\) 1.00000 0.0392837
\(649\) −30.0000 −1.17760
\(650\) 4.00000 0.156893
\(651\) −2.00000 −0.0783862
\(652\) −21.0000 −0.822423
\(653\) −31.0000 −1.21312 −0.606562 0.795036i \(-0.707452\pi\)
−0.606562 + 0.795036i \(0.707452\pi\)
\(654\) 10.0000 0.391031
\(655\) −18.0000 −0.703318
\(656\) 2.00000 0.0780869
\(657\) −6.00000 −0.234082
\(658\) 14.0000 0.545777
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) −3.00000 −0.116775
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) 32.0000 1.24372
\(663\) −3.00000 −0.116510
\(664\) −1.00000 −0.0388075
\(665\) 10.0000 0.387783
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) −2.00000 −0.0773823
\(669\) 9.00000 0.347960
\(670\) −7.00000 −0.270434
\(671\) −21.0000 −0.810696
\(672\) −2.00000 −0.0771517
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) −32.0000 −1.23259
\(675\) −4.00000 −0.153960
\(676\) −12.0000 −0.461538
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 14.0000 0.537667
\(679\) −26.0000 −0.997788
\(680\) 3.00000 0.115045
\(681\) −22.0000 −0.843042
\(682\) −3.00000 −0.114876
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) −5.00000 −0.191180
\(685\) −2.00000 −0.0764161
\(686\) 20.0000 0.763604
\(687\) −5.00000 −0.190762
\(688\) −6.00000 −0.228748
\(689\) −14.0000 −0.533358
\(690\) 4.00000 0.152277
\(691\) −23.0000 −0.874961 −0.437481 0.899228i \(-0.644129\pi\)
−0.437481 + 0.899228i \(0.644129\pi\)
\(692\) −21.0000 −0.798300
\(693\) 6.00000 0.227921
\(694\) −7.00000 −0.265716
\(695\) 20.0000 0.758643
\(696\) 0 0
\(697\) 6.00000 0.227266
\(698\) 0 0
\(699\) 4.00000 0.151294
\(700\) 8.00000 0.302372
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 10.0000 0.377157
\(704\) −3.00000 −0.113067
\(705\) −7.00000 −0.263635
\(706\) 9.00000 0.338719
\(707\) −4.00000 −0.150435
\(708\) 10.0000 0.375823
\(709\) −35.0000 −1.31445 −0.657226 0.753693i \(-0.728270\pi\)
−0.657226 + 0.753693i \(0.728270\pi\)
\(710\) −3.00000 −0.112588
\(711\) 15.0000 0.562544
\(712\) 10.0000 0.374766
\(713\) 4.00000 0.149801
\(714\) −6.00000 −0.224544
\(715\) 3.00000 0.112194
\(716\) −5.00000 −0.186859
\(717\) 20.0000 0.746914
\(718\) −15.0000 −0.559795
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 1.00000 0.0372678
\(721\) −28.0000 −1.04277
\(722\) 6.00000 0.223297
\(723\) 2.00000 0.0743808
\(724\) −18.0000 −0.668965
\(725\) 0 0
\(726\) −2.00000 −0.0742270
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 2.00000 0.0741249
\(729\) 1.00000 0.0370370
\(730\) −6.00000 −0.222070
\(731\) −18.0000 −0.665754
\(732\) 7.00000 0.258727
\(733\) −46.0000 −1.69905 −0.849524 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) −17.0000 −0.627481
\(735\) −3.00000 −0.110657
\(736\) 4.00000 0.147442
\(737\) 21.0000 0.773545
\(738\) 2.00000 0.0736210
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 5.00000 0.183680
\(742\) −28.0000 −1.02791
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 1.00000 0.0366618
\(745\) 5.00000 0.183186
\(746\) −16.0000 −0.585802
\(747\) −1.00000 −0.0365881
\(748\) −9.00000 −0.329073
\(749\) 24.0000 0.876941
\(750\) −9.00000 −0.328634
\(751\) 22.0000 0.802791 0.401396 0.915905i \(-0.368525\pi\)
0.401396 + 0.915905i \(0.368525\pi\)
\(752\) −7.00000 −0.255264
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) −3.00000 −0.109181
\(756\) −2.00000 −0.0727393
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −35.0000 −1.27126
\(759\) −12.0000 −0.435572
\(760\) −5.00000 −0.181369
\(761\) −3.00000 −0.108750 −0.0543750 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) −12.0000 −0.434714
\(763\) −20.0000 −0.724049
\(764\) −8.00000 −0.289430
\(765\) 3.00000 0.108465
\(766\) −26.0000 −0.939418
\(767\) −10.0000 −0.361079
\(768\) 1.00000 0.0360844
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 6.00000 0.216225
\(771\) 28.0000 1.00840
\(772\) −21.0000 −0.755807
\(773\) −36.0000 −1.29483 −0.647415 0.762138i \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(774\) −6.00000 −0.215666
\(775\) −4.00000 −0.143684
\(776\) 13.0000 0.466673
\(777\) 4.00000 0.143499
\(778\) 30.0000 1.07555
\(779\) −10.0000 −0.358287
\(780\) −1.00000 −0.0358057
\(781\) 9.00000 0.322045
\(782\) 12.0000 0.429119
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 8.00000 0.285532
\(786\) −18.0000 −0.642039
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) −22.0000 −0.783718
\(789\) 24.0000 0.854423
\(790\) 15.0000 0.533676
\(791\) −28.0000 −0.995565
\(792\) −3.00000 −0.106600
\(793\) −7.00000 −0.248577
\(794\) −22.0000 −0.780751
\(795\) 14.0000 0.496529
\(796\) 15.0000 0.531661
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 10.0000 0.353996
\(799\) −21.0000 −0.742927
\(800\) −4.00000 −0.141421
\(801\) 10.0000 0.353333
\(802\) −3.00000 −0.105934
\(803\) 18.0000 0.635206
\(804\) −7.00000 −0.246871
\(805\) −8.00000 −0.281963
\(806\) −1.00000 −0.0352235
\(807\) 10.0000 0.352017
\(808\) 2.00000 0.0703598
\(809\) 15.0000 0.527372 0.263686 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) 1.00000 0.0351364
\(811\) 52.0000 1.82597 0.912983 0.407997i \(-0.133772\pi\)
0.912983 + 0.407997i \(0.133772\pi\)
\(812\) 0 0
\(813\) 7.00000 0.245501
\(814\) 6.00000 0.210300
\(815\) −21.0000 −0.735598
\(816\) 3.00000 0.105021
\(817\) 30.0000 1.04957
\(818\) 30.0000 1.04893
\(819\) 2.00000 0.0698857
\(820\) 2.00000 0.0698430
\(821\) −38.0000 −1.32621 −0.663105 0.748527i \(-0.730762\pi\)
−0.663105 + 0.748527i \(0.730762\pi\)
\(822\) −2.00000 −0.0697580
\(823\) 9.00000 0.313720 0.156860 0.987621i \(-0.449863\pi\)
0.156860 + 0.987621i \(0.449863\pi\)
\(824\) 14.0000 0.487713
\(825\) 12.0000 0.417786
\(826\) −20.0000 −0.695889
\(827\) 43.0000 1.49526 0.747628 0.664117i \(-0.231193\pi\)
0.747628 + 0.664117i \(0.231193\pi\)
\(828\) 4.00000 0.139010
\(829\) −10.0000 −0.347314 −0.173657 0.984806i \(-0.555558\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(830\) −1.00000 −0.0347105
\(831\) −17.0000 −0.589723
\(832\) −1.00000 −0.0346688
\(833\) −9.00000 −0.311832
\(834\) 20.0000 0.692543
\(835\) −2.00000 −0.0692129
\(836\) 15.0000 0.518786
\(837\) 1.00000 0.0345651
\(838\) 0 0
\(839\) 20.0000 0.690477 0.345238 0.938515i \(-0.387798\pi\)
0.345238 + 0.938515i \(0.387798\pi\)
\(840\) −2.00000 −0.0690066
\(841\) −29.0000 −1.00000
\(842\) 22.0000 0.758170
\(843\) −18.0000 −0.619953
\(844\) −8.00000 −0.275371
\(845\) −12.0000 −0.412813
\(846\) −7.00000 −0.240665
\(847\) 4.00000 0.137442
\(848\) 14.0000 0.480762
\(849\) 9.00000 0.308879
\(850\) −12.0000 −0.411597
\(851\) −8.00000 −0.274236
\(852\) −3.00000 −0.102778
\(853\) 54.0000 1.84892 0.924462 0.381273i \(-0.124514\pi\)
0.924462 + 0.381273i \(0.124514\pi\)
\(854\) −14.0000 −0.479070
\(855\) −5.00000 −0.170996
\(856\) −12.0000 −0.410152
\(857\) 28.0000 0.956462 0.478231 0.878234i \(-0.341278\pi\)
0.478231 + 0.878234i \(0.341278\pi\)
\(858\) 3.00000 0.102418
\(859\) 10.0000 0.341196 0.170598 0.985341i \(-0.445430\pi\)
0.170598 + 0.985341i \(0.445430\pi\)
\(860\) −6.00000 −0.204598
\(861\) −4.00000 −0.136320
\(862\) 32.0000 1.08992
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) 1.00000 0.0340207
\(865\) −21.0000 −0.714021
\(866\) 24.0000 0.815553
\(867\) −8.00000 −0.271694
\(868\) −2.00000 −0.0678844
\(869\) −45.0000 −1.52652
\(870\) 0 0
\(871\) 7.00000 0.237186
\(872\) 10.0000 0.338643
\(873\) 13.0000 0.439983
\(874\) −20.0000 −0.676510
\(875\) 18.0000 0.608511
\(876\) −6.00000 −0.202721
\(877\) 8.00000 0.270141 0.135070 0.990836i \(-0.456874\pi\)
0.135070 + 0.990836i \(0.456874\pi\)
\(878\) −20.0000 −0.674967
\(879\) 14.0000 0.472208
\(880\) −3.00000 −0.101130
\(881\) 7.00000 0.235836 0.117918 0.993023i \(-0.462378\pi\)
0.117918 + 0.993023i \(0.462378\pi\)
\(882\) −3.00000 −0.101015
\(883\) −26.0000 −0.874970 −0.437485 0.899226i \(-0.644131\pi\)
−0.437485 + 0.899226i \(0.644131\pi\)
\(884\) −3.00000 −0.100901
\(885\) 10.0000 0.336146
\(886\) −6.00000 −0.201574
\(887\) 8.00000 0.268614 0.134307 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 24.0000 0.804934
\(890\) 10.0000 0.335201
\(891\) −3.00000 −0.100504
\(892\) 9.00000 0.301342
\(893\) 35.0000 1.17123
\(894\) 5.00000 0.167225
\(895\) −5.00000 −0.167132
\(896\) −2.00000 −0.0668153
\(897\) −4.00000 −0.133556
\(898\) −15.0000 −0.500556
\(899\) 0 0
\(900\) −4.00000 −0.133333
\(901\) 42.0000 1.39922
\(902\) −6.00000 −0.199778
\(903\) 12.0000 0.399335
\(904\) 14.0000 0.465633
\(905\) −18.0000 −0.598340
\(906\) −3.00000 −0.0996683
\(907\) −37.0000 −1.22856 −0.614282 0.789086i \(-0.710554\pi\)
−0.614282 + 0.789086i \(0.710554\pi\)
\(908\) −22.0000 −0.730096
\(909\) 2.00000 0.0663358
\(910\) 2.00000 0.0662994
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −5.00000 −0.165567
\(913\) 3.00000 0.0992855
\(914\) −22.0000 −0.727695
\(915\) 7.00000 0.231413
\(916\) −5.00000 −0.165205
\(917\) 36.0000 1.18882
\(918\) 3.00000 0.0990148
\(919\) −20.0000 −0.659739 −0.329870 0.944027i \(-0.607005\pi\)
−0.329870 + 0.944027i \(0.607005\pi\)
\(920\) 4.00000 0.131876
\(921\) 8.00000 0.263609
\(922\) −18.0000 −0.592798
\(923\) 3.00000 0.0987462
\(924\) 6.00000 0.197386
\(925\) 8.00000 0.263038
\(926\) 19.0000 0.624379
\(927\) 14.0000 0.459820
\(928\) 0 0
\(929\) −10.0000 −0.328089 −0.164045 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) 1.00000 0.0327913
\(931\) 15.0000 0.491605
\(932\) 4.00000 0.131024
\(933\) 27.0000 0.883940
\(934\) −12.0000 −0.392652
\(935\) −9.00000 −0.294331
\(936\) −1.00000 −0.0326860
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 14.0000 0.457116
\(939\) −26.0000 −0.848478
\(940\) −7.00000 −0.228315
\(941\) 12.0000 0.391189 0.195594 0.980685i \(-0.437336\pi\)
0.195594 + 0.980685i \(0.437336\pi\)
\(942\) 8.00000 0.260654
\(943\) 8.00000 0.260516
\(944\) 10.0000 0.325472
\(945\) −2.00000 −0.0650600
\(946\) 18.0000 0.585230
\(947\) 3.00000 0.0974869 0.0487435 0.998811i \(-0.484478\pi\)
0.0487435 + 0.998811i \(0.484478\pi\)
\(948\) 15.0000 0.487177
\(949\) 6.00000 0.194768
\(950\) 20.0000 0.648886
\(951\) −17.0000 −0.551263
\(952\) −6.00000 −0.194461
\(953\) 39.0000 1.26333 0.631667 0.775240i \(-0.282371\pi\)
0.631667 + 0.775240i \(0.282371\pi\)
\(954\) 14.0000 0.453267
\(955\) −8.00000 −0.258874
\(956\) 20.0000 0.646846
\(957\) 0 0
\(958\) 35.0000 1.13080
\(959\) 4.00000 0.129167
\(960\) 1.00000 0.0322749
\(961\) 1.00000 0.0322581
\(962\) 2.00000 0.0644826
\(963\) −12.0000 −0.386695
\(964\) 2.00000 0.0644157
\(965\) −21.0000 −0.676014
\(966\) −8.00000 −0.257396
\(967\) 43.0000 1.38279 0.691393 0.722478i \(-0.256997\pi\)
0.691393 + 0.722478i \(0.256997\pi\)
\(968\) −2.00000 −0.0642824
\(969\) −15.0000 −0.481869
\(970\) 13.0000 0.417405
\(971\) 42.0000 1.34784 0.673922 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 1.00000 0.0320750
\(973\) −40.0000 −1.28234
\(974\) −17.0000 −0.544715
\(975\) 4.00000 0.128103
\(976\) 7.00000 0.224065
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −21.0000 −0.671506
\(979\) −30.0000 −0.958804
\(980\) −3.00000 −0.0958315
\(981\) 10.0000 0.319275
\(982\) −28.0000 −0.893516
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 2.00000 0.0637577
\(985\) −22.0000 −0.700978
\(986\) 0 0
\(987\) 14.0000 0.445625
\(988\) 5.00000 0.159071
\(989\) −24.0000 −0.763156
\(990\) −3.00000 −0.0953463
\(991\) 12.0000 0.381193 0.190596 0.981669i \(-0.438958\pi\)
0.190596 + 0.981669i \(0.438958\pi\)
\(992\) 1.00000 0.0317500
\(993\) 32.0000 1.01549
\(994\) 6.00000 0.190308
\(995\) 15.0000 0.475532
\(996\) −1.00000 −0.0316862
\(997\) 18.0000 0.570066 0.285033 0.958518i \(-0.407995\pi\)
0.285033 + 0.958518i \(0.407995\pi\)
\(998\) 40.0000 1.26618
\(999\) −2.00000 −0.0632772
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 \(a_p\))