Properties

Label 114.2.a.c.1.1
Level 114
Weight 2
Character 114.1
Self dual Yes
Analytic conductor 0.910
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 114.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.910294583043\)
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 \(\chi\) = 114.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{6}\) \(-4.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{6}\) \(-4.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+1.00000 q^{12}\) \(-4.00000 q^{13}\) \(-4.00000 q^{14}\) \(+1.00000 q^{16}\) \(+6.00000 q^{17}\) \(+1.00000 q^{18}\) \(+1.00000 q^{19}\) \(-4.00000 q^{21}\) \(-6.00000 q^{23}\) \(+1.00000 q^{24}\) \(-5.00000 q^{25}\) \(-4.00000 q^{26}\) \(+1.00000 q^{27}\) \(-4.00000 q^{28}\) \(+6.00000 q^{29}\) \(+2.00000 q^{31}\) \(+1.00000 q^{32}\) \(+6.00000 q^{34}\) \(+1.00000 q^{36}\) \(-4.00000 q^{37}\) \(+1.00000 q^{38}\) \(-4.00000 q^{39}\) \(+6.00000 q^{41}\) \(-4.00000 q^{42}\) \(-4.00000 q^{43}\) \(-6.00000 q^{46}\) \(+6.00000 q^{47}\) \(+1.00000 q^{48}\) \(+9.00000 q^{49}\) \(-5.00000 q^{50}\) \(+6.00000 q^{51}\) \(-4.00000 q^{52}\) \(+6.00000 q^{53}\) \(+1.00000 q^{54}\) \(-4.00000 q^{56}\) \(+1.00000 q^{57}\) \(+6.00000 q^{58}\) \(-12.0000 q^{59}\) \(+14.0000 q^{61}\) \(+2.00000 q^{62}\) \(-4.00000 q^{63}\) \(+1.00000 q^{64}\) \(+8.00000 q^{67}\) \(+6.00000 q^{68}\) \(-6.00000 q^{69}\) \(+1.00000 q^{72}\) \(+14.0000 q^{73}\) \(-4.00000 q^{74}\) \(-5.00000 q^{75}\) \(+1.00000 q^{76}\) \(-4.00000 q^{78}\) \(-10.0000 q^{79}\) \(+1.00000 q^{81}\) \(+6.00000 q^{82}\) \(-12.0000 q^{83}\) \(-4.00000 q^{84}\) \(-4.00000 q^{86}\) \(+6.00000 q^{87}\) \(-6.00000 q^{89}\) \(+16.0000 q^{91}\) \(-6.00000 q^{92}\) \(+2.00000 q^{93}\) \(+6.00000 q^{94}\) \(+1.00000 q^{96}\) \(-10.0000 q^{97}\) \(+9.00000 q^{98}\) \(+O(q^{100})\)

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
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) −4.00000 −0.784465
\(27\) 1.00000 0.192450
\(28\) −4.00000 −0.755929
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 1.00000 0.162221
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −4.00000 −0.617213
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) −5.00000 −0.707107
\(51\) 6.00000 0.840168
\(52\) −4.00000 −0.554700
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) 1.00000 0.132453
\(58\) 6.00000 0.787839
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 2.00000 0.254000
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 6.00000 0.727607
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) −4.00000 −0.464991
\(75\) −5.00000 −0.577350
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −4.00000 −0.436436
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 16.0000 1.67726
\(92\) −6.00000 −0.625543
\(93\) 2.00000 0.207390
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 6.00000 0.594089
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 1.00000 0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) −4.00000 −0.377964
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) −4.00000 −0.369800
\(118\) −12.0000 −1.10469
\(119\) −24.0000 −2.20008
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 14.0000 1.26750
\(123\) 6.00000 0.541002
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) −4.00000 −0.356348
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −6.00000 −0.510754
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) 9.00000 0.742307
\(148\) −4.00000 −0.328798
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) −5.00000 −0.408248
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 1.00000 0.0811107
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −10.0000 −0.795557
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 24.0000 1.89146
\(162\) 1.00000 0.0785674
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −4.00000 −0.308607
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) −4.00000 −0.304997
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 6.00000 0.454859
\(175\) 20.0000 1.51186
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) −6.00000 −0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 16.0000 1.18600
\(183\) 14.0000 1.03491
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 0 0
\(188\) 6.00000 0.437595
\(189\) −4.00000 −0.290957
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 1.00000 0.0721688
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −5.00000 −0.353553
\(201\) 8.00000 0.564276
\(202\) 0 0
\(203\) −24.0000 −1.68447
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) −10.0000 −0.696733
\(207\) −6.00000 −0.417029
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −8.00000 −0.543075
\(218\) −16.0000 −1.08366
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) −4.00000 −0.268462
\(223\) −22.0000 −1.47323 −0.736614 0.676313i \(-0.763577\pi\)
−0.736614 + 0.676313i \(0.763577\pi\)
\(224\) −4.00000 −0.267261
\(225\) −5.00000 −0.333333
\(226\) −18.0000 −1.19734
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 1.00000 0.0662266
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −4.00000 −0.261488
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) −10.0000 −0.649570
\(238\) −24.0000 −1.55569
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −11.0000 −0.707107
\(243\) 1.00000 0.0641500
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −4.00000 −0.254514
\(248\) 2.00000 0.127000
\(249\) −12.0000 −0.760469
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) −4.00000 −0.249029
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 12.0000 0.741362
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.00000 −0.245256
\(267\) −6.00000 −0.367194
\(268\) 8.00000 0.488678
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 6.00000 0.363803
\(273\) 16.0000 0.968364
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 20.0000 1.19952
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 6.00000 0.357295
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) −10.0000 −0.586210
\(292\) 14.0000 0.819288
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 9.00000 0.524891
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) 24.0000 1.38796
\(300\) −5.00000 −0.288675
\(301\) 16.0000 0.922225
\(302\) −10.0000 −0.575435
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) −10.0000 −0.568880
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) −4.00000 −0.226455
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 24.0000 1.33747
\(323\) 6.00000 0.333849
\(324\) 1.00000 0.0555556
\(325\) 20.0000 1.10940
\(326\) −4.00000 −0.221540
\(327\) −16.0000 −0.884802
\(328\) 6.00000 0.331295
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −12.0000 −0.658586
\(333\) −4.00000 −0.219199
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) −4.00000 −0.218218
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 3.00000 0.163178
\(339\) −18.0000 −0.977626
\(340\) 0 0
\(341\) 0 0
\(342\) 1.00000 0.0540738
\(343\) −8.00000 −0.431959
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 24.0000 1.28839 0.644194 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) 6.00000 0.321634
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 20.0000 1.06904
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −24.0000 −1.27021
\(358\) 12.0000 0.634220
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −16.0000 −0.840941
\(363\) −11.0000 −0.577350
\(364\) 16.0000 0.838628
\(365\) 0 0
\(366\) 14.0000 0.731792
\(367\) −4.00000 −0.208798 −0.104399 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) −6.00000 −0.312772
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) −24.0000 −1.24602
\(372\) 2.00000 0.103695
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −24.0000 −1.23606
\(378\) −4.00000 −0.205738
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 18.0000 0.920960
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) −4.00000 −0.203331
\(388\) −10.0000 −0.507673
\(389\) 24.0000 1.21685 0.608424 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(390\) 0 0
\(391\) −36.0000 −1.82060
\(392\) 9.00000 0.454569
\(393\) 12.0000 0.605320
\(394\) 12.0000 0.604551
\(395\) 0 0
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 20.0000 1.00251
\(399\) −4.00000 −0.200250
\(400\) −5.00000 −0.250000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 8.00000 0.399004
\(403\) −8.00000 −0.398508
\(404\) 0 0
\(405\) 0 0
\(406\) −24.0000 −1.19110
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) −10.0000 −0.492665
\(413\) 48.0000 2.36193
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) −4.00000 −0.196116
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) −4.00000 −0.194717
\(423\) 6.00000 0.291730
\(424\) 6.00000 0.291386
\(425\) −30.0000 −1.45521
\(426\) 0 0
\(427\) −56.0000 −2.71003
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 1.00000 0.0481125
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −6.00000 −0.287019
\(438\) 14.0000 0.668946
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) −24.0000 −1.14156
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) −22.0000 −1.04173
\(447\) 12.0000 0.567581
\(448\) −4.00000 −0.188982
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −5.00000 −0.235702
\(451\) 0 0
\(452\) −18.0000 −0.846649
\(453\) −10.0000 −0.469841
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) −10.0000 −0.467269
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) −36.0000 −1.66588 −0.832941 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) −4.00000 −0.184900
\(469\) −32.0000 −1.47762
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) −10.0000 −0.459315
\(475\) −5.00000 −0.229416
\(476\) −24.0000 −1.10004
\(477\) 6.00000 0.274721
\(478\) −18.0000 −0.823301
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 0 0
\(481\) 16.0000 0.729537
\(482\) 14.0000 0.637683
\(483\) 24.0000 1.09204
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 14.0000 0.633750
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 6.00000 0.270501
\(493\) 36.0000 1.62136
\(494\) −4.00000 −0.179969
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) −12.0000 −0.536120
\(502\) 12.0000 0.535586
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) −4.00000 −0.178174
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 2.00000 0.0887357
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) −56.0000 −2.47729
\(512\) 1.00000 0.0441942
\(513\) 1.00000 0.0441511
\(514\) 18.0000 0.793946
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 16.0000 0.703000
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 6.00000 0.262613
\(523\) 8.00000 0.349816 0.174908 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 12.0000 0.524222
\(525\) 20.0000 0.872872
\(526\) −18.0000 −0.784837
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) −4.00000 −0.173422
\(533\) −24.0000 −1.03956
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) 8.00000 0.345547
\(537\) 12.0000 0.517838
\(538\) −6.00000 −0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 20.0000 0.859074
\(543\) −16.0000 −0.686626
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) 16.0000 0.684737
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) −18.0000 −0.768922
\(549\) 14.0000 0.597505
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) −6.00000 −0.255377
\(553\) 40.0000 1.70097
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) 20.0000 0.848189
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 2.00000 0.0846668
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) 6.00000 0.252646
\(565\) 0 0
\(566\) −4.00000 −0.168133
\(567\) −4.00000 −0.167984
\(568\) 0 0
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) −24.0000 −1.00174
\(575\) 30.0000 1.25109
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 19.0000 0.790296
\(579\) −10.0000 −0.415586
\(580\) 0 0
\(581\) 48.0000 1.99138
\(582\) −10.0000 −0.414513
\(583\) 0 0
\(584\) 14.0000 0.579324
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 9.00000 0.371154
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 12.0000 0.493614
\(592\) −4.00000 −0.164399
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) 20.0000 0.818546
\(598\) 24.0000 0.981433
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) −5.00000 −0.204124
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 16.0000 0.652111
\(603\) 8.00000 0.325785
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −34.0000 −1.38002 −0.690009 0.723801i \(-0.742393\pi\)
−0.690009 + 0.723801i \(0.742393\pi\)
\(608\) 1.00000 0.0405554
\(609\) −24.0000 −0.972529
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 6.00000 0.242536
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −16.0000 −0.645707
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) −10.0000 −0.402259
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) 30.0000 1.20289
\(623\) 24.0000 0.961540
\(624\) −4.00000 −0.160128
\(625\) 25.0000 1.00000
\(626\) −10.0000 −0.399680
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) −10.0000 −0.397779
\(633\) −4.00000 −0.158986
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) −36.0000 −1.42637
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.00000 −0.236986 −0.118493 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) 12.0000 0.473602
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 24.0000 0.945732
\(645\) 0 0
\(646\) 6.00000 0.236067
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 20.0000 0.784465
\(651\) −8.00000 −0.313545
\(652\) −4.00000 −0.156652
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) −16.0000 −0.625650
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 14.0000 0.546192
\(658\) −24.0000 −0.935617
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −4.00000 −0.155582 −0.0777910 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) 8.00000 0.310929
\(663\) −24.0000 −0.932083
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) −36.0000 −1.39393
\(668\) −12.0000 −0.464294
\(669\) −22.0000 −0.850569
\(670\) 0 0
\(671\) 0 0
\(672\) −4.00000 −0.154303
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 2.00000 0.0770371
\(675\) −5.00000 −0.192450
\(676\) 3.00000 0.115385
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) −18.0000 −0.691286
\(679\) 40.0000 1.53506
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 1.00000 0.0382360
\(685\) 0 0
\(686\) −8.00000 −0.305441
\(687\) −10.0000 −0.381524
\(688\) −4.00000 −0.152499
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 0 0
\(696\) 6.00000 0.227429
\(697\) 36.0000 1.36360
\(698\) 2.00000 0.0757011
\(699\) −6.00000 −0.226941
\(700\) 20.0000 0.755929
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) −4.00000 −0.150970
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) −6.00000 −0.224860
\(713\) −12.0000 −0.449404
\(714\) −24.0000 −0.898177
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −18.0000 −0.672222
\(718\) −6.00000 −0.223918
\(719\) −18.0000 −0.671287 −0.335643 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 0 0
\(721\) 40.0000 1.48968
\(722\) 1.00000 0.0372161
\(723\) 14.0000 0.520666
\(724\) −16.0000 −0.594635
\(725\) −30.0000 −1.11417
\(726\) −11.0000 −0.408248
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 16.0000 0.592999
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) 14.0000 0.517455
\(733\) 50.0000 1.84679 0.923396 0.383849i \(-0.125402\pi\)
0.923396 + 0.383849i \(0.125402\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) 6.00000 0.220863
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) −4.00000 −0.146944
\(742\) −24.0000 −0.881068
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 2.00000 0.0733236
\(745\) 0 0
\(746\) −4.00000 −0.146450
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) −48.0000 −1.75388
\(750\) 0 0
\(751\) −10.0000 −0.364905 −0.182453 0.983215i \(-0.558404\pi\)
−0.182453 + 0.983215i \(0.558404\pi\)
\(752\) 6.00000 0.218797
\(753\) 12.0000 0.437304
\(754\) −24.0000 −0.874028
\(755\) 0 0
\(756\) −4.00000 −0.145479
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) 8.00000 0.290573
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 2.00000 0.0724524
\(763\) 64.0000 2.31696
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) 48.0000 1.73318
\(768\) 1.00000 0.0360844
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −10.0000 −0.359908
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −4.00000 −0.143777
\(775\) −10.0000 −0.359211
\(776\) −10.0000 −0.358979
\(777\) 16.0000 0.573997
\(778\) 24.0000 0.860442
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 0 0
\(782\) −36.0000 −1.28736
\(783\) 6.00000 0.214423
\(784\) 9.00000 0.321429
\(785\) 0 0
\(786\) 12.0000 0.428026
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) 12.0000 0.427482
\(789\) −18.0000 −0.640817
\(790\) 0 0
\(791\) 72.0000 2.56003
\(792\) 0 0
\(793\) −56.0000 −1.98862
\(794\) 26.0000 0.922705
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) −4.00000 −0.141598
\(799\) 36.0000 1.27359
\(800\) −5.00000 −0.176777
\(801\) −6.00000 −0.212000
\(802\) 30.0000 1.05934
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −8.00000 −0.281788
\(807\) −6.00000 −0.211210
\(808\) 0 0
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) −24.0000 −0.842235
\(813\) 20.0000 0.701431
\(814\) 0 0
\(815\) 0 0
\(816\) 6.00000 0.210042
\(817\) −4.00000 −0.139942
\(818\) 14.0000 0.489499
\(819\) 16.0000 0.559085
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) −18.0000 −0.627822
\(823\) 32.0000 1.11545 0.557725 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) −10.0000 −0.348367
\(825\) 0 0
\(826\) 48.0000 1.67013
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −6.00000 −0.208514
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 0 0
\(831\) −10.0000 −0.346896
\(832\) −4.00000 −0.138675
\(833\) 54.0000 1.87099
\(834\) 20.0000 0.692543
\(835\) 0 0
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) 0 0
\(839\) 36.0000 1.24286 0.621429 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −28.0000 −0.964944
\(843\) −18.0000 −0.619953
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) 44.0000 1.51186
\(848\) 6.00000 0.206041
\(849\) −4.00000 −0.137280
\(850\) −30.0000 −1.02899
\(851\) 24.0000 0.822709
\(852\) 0 0
\(853\) 38.0000 1.30110 0.650548 0.759465i \(-0.274539\pi\)
0.650548 + 0.759465i \(0.274539\pi\)
\(854\) −56.0000 −1.91628
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 0 0
\(861\) −24.0000 −0.817918
\(862\) −12.0000 −0.408722
\(863\) 12.0000 0.408485 0.204242 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −10.0000 −0.339814
\(867\) 19.0000 0.645274
\(868\) −8.00000 −0.271538
\(869\) 0 0
\(870\) 0 0
\(871\) −32.0000 −1.08428
\(872\) −16.0000 −0.541828
\(873\) −10.0000 −0.338449
\(874\) −6.00000 −0.202953
\(875\) 0 0
\(876\) 14.0000 0.473016
\(877\) 44.0000 1.48577 0.742887 0.669417i \(-0.233456\pi\)
0.742887 + 0.669417i \(0.233456\pi\)
\(878\) 26.0000 0.877457
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 9.00000 0.303046
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −24.0000 −0.807207
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) −4.00000 −0.134231
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) −22.0000 −0.736614
\(893\) 6.00000 0.200782
\(894\) 12.0000 0.401340
\(895\) 0 0
\(896\) −4.00000 −0.133631
\(897\) 24.0000 0.801337
\(898\) −30.0000 −1.00111
\(899\) 12.0000 0.400222
\(900\) −5.00000 −0.166667
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) −18.0000 −0.598671
\(905\) 0 0
\(906\) −10.0000 −0.332228
\(907\) 8.00000 0.265636 0.132818 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) 12.0000 0.398234
\(909\) 0 0
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 1.00000 0.0331133
\(913\) 0 0
\(914\) 2.00000 0.0661541
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) −48.0000 −1.58510
\(918\) 6.00000 0.198030
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) −16.0000 −0.527218
\(922\) 12.0000 0.395199
\(923\) 0 0
\(924\) 0 0
\(925\) 20.0000 0.657596
\(926\) −4.00000 −0.131448
\(927\) −10.0000 −0.328443
\(928\) 6.00000 0.196960
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) 9.00000 0.294963
\(932\) −6.00000 −0.196537
\(933\) 30.0000 0.982156
\(934\) −36.0000 −1.17796
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −58.0000 −1.89478 −0.947389 0.320085i \(-0.896288\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(938\) −32.0000 −1.04484
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 2.00000 0.0651635
\(943\) −36.0000 −1.17232
\(944\) −12.0000 −0.390567
\(945\) 0 0
\(946\) 0 0
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) −10.0000 −0.324785
\(949\) −56.0000 −1.81784
\(950\) −5.00000 −0.162221
\(951\) 18.0000 0.583690
\(952\) −24.0000 −0.777844
\(953\) 54.0000 1.74923 0.874616 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) −18.0000 −0.582162
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) 72.0000 2.32500
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 16.0000 0.515861
\(963\) 12.0000 0.386695
\(964\) 14.0000 0.450910
\(965\) 0 0
\(966\) 24.0000 0.772187
\(967\) −28.0000 −0.900419 −0.450210 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(968\) −11.0000 −0.353553
\(969\) 6.00000 0.192748
\(970\) 0 0
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 1.00000 0.0320750
\(973\) −80.0000 −2.56468
\(974\) 38.0000 1.21760
\(975\) 20.0000 0.640513
\(976\) 14.0000 0.448129
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) −4.00000 −0.127906
\(979\) 0 0
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 36.0000 1.14881
\(983\) −48.0000 −1.53096 −0.765481 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) 6.00000 0.191273
\(985\) 0 0
\(986\) 36.0000 1.14647
\(987\) −24.0000 −0.763928
\(988\) −4.00000 −0.127257
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) 26.0000 0.825917 0.412959 0.910750i \(-0.364495\pi\)
0.412959 + 0.910750i \(0.364495\pi\)
\(992\) 2.00000 0.0635001
\(993\) 8.00000 0.253872
\(994\) 0 0
\(995\) 0 0
\(996\) −12.0000 −0.380235
\(997\) 26.0000 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) −4.00000 −0.126618
\(999\) −4.00000 −0.126554
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 \(a_p\))