Properties

Label 210.2.a.d.1.1
Level 210
Weight 2
Character 210.1
Self dual Yes
Analytic conductor 1.677
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 210.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.67685844245\)
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 \(\chi\) = 210.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.00000 q^{10}\) \(+1.00000 q^{12}\) \(+2.00000 q^{13}\) \(+1.00000 q^{14}\) \(-1.00000 q^{15}\) \(+1.00000 q^{16}\) \(-6.00000 q^{17}\) \(+1.00000 q^{18}\) \(-4.00000 q^{19}\) \(-1.00000 q^{20}\) \(+1.00000 q^{21}\) \(+1.00000 q^{24}\) \(+1.00000 q^{25}\) \(+2.00000 q^{26}\) \(+1.00000 q^{27}\) \(+1.00000 q^{28}\) \(-6.00000 q^{29}\) \(-1.00000 q^{30}\) \(-4.00000 q^{31}\) \(+1.00000 q^{32}\) \(-6.00000 q^{34}\) \(-1.00000 q^{35}\) \(+1.00000 q^{36}\) \(+2.00000 q^{37}\) \(-4.00000 q^{38}\) \(+2.00000 q^{39}\) \(-1.00000 q^{40}\) \(+6.00000 q^{41}\) \(+1.00000 q^{42}\) \(+8.00000 q^{43}\) \(-1.00000 q^{45}\) \(-12.0000 q^{47}\) \(+1.00000 q^{48}\) \(+1.00000 q^{49}\) \(+1.00000 q^{50}\) \(-6.00000 q^{51}\) \(+2.00000 q^{52}\) \(+6.00000 q^{53}\) \(+1.00000 q^{54}\) \(+1.00000 q^{56}\) \(-4.00000 q^{57}\) \(-6.00000 q^{58}\) \(-12.0000 q^{59}\) \(-1.00000 q^{60}\) \(+2.00000 q^{61}\) \(-4.00000 q^{62}\) \(+1.00000 q^{63}\) \(+1.00000 q^{64}\) \(-2.00000 q^{65}\) \(+8.00000 q^{67}\) \(-6.00000 q^{68}\) \(-1.00000 q^{70}\) \(+1.00000 q^{72}\) \(+14.0000 q^{73}\) \(+2.00000 q^{74}\) \(+1.00000 q^{75}\) \(-4.00000 q^{76}\) \(+2.00000 q^{78}\) \(-16.0000 q^{79}\) \(-1.00000 q^{80}\) \(+1.00000 q^{81}\) \(+6.00000 q^{82}\) \(+12.0000 q^{83}\) \(+1.00000 q^{84}\) \(+6.00000 q^{85}\) \(+8.00000 q^{86}\) \(-6.00000 q^{87}\) \(+6.00000 q^{89}\) \(-1.00000 q^{90}\) \(+2.00000 q^{91}\) \(-4.00000 q^{93}\) \(-12.0000 q^{94}\) \(+4.00000 q^{95}\) \(+1.00000 q^{96}\) \(+14.0000 q^{97}\) \(+1.00000 q^{98}\) \(+O(q^{100})\)

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
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) −1.00000 −0.169031
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.00000 −0.648886
\(39\) 2.00000 0.320256
\(40\) −1.00000 −0.158114
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 1.00000 0.154303
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 1.00000 0.141421
\(51\) −6.00000 −0.840168
\(52\) 2.00000 0.277350
\(53\) 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
\(56\) 1.00000 0.133631
\(57\) −4.00000 −0.529813
\(58\) −6.00000 −0.787839
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) −1.00000 −0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −4.00000 −0.508001
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 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
\(69\) 0 0
\(70\) −1.00000 −0.119523
\(71\) 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 \(0.194369\pi\)
\(74\) 2.00000 0.232495
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 1.00000 0.109109
\(85\) 6.00000 0.650791
\(86\) 8.00000 0.862662
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 −0.105409
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) −4.00000 −0.414781
\(94\) −12.0000 −1.23771
\(95\) 4.00000 0.410391
\(96\) 1.00000 0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −6.00000 −0.594089
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 2.00000 0.196116
\(105\) −1.00000 −0.0975900
\(106\) 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
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 1.00000 0.0944911
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 2.00000 0.184900
\(118\) −12.0000 −1.10469
\(119\) −6.00000 −0.550019
\(120\) −1.00000 −0.0912871
\(121\) −11.0000 −1.00000
\(122\) 2.00000 0.181071
\(123\) 6.00000 0.541002
\(124\) −4.00000 −0.359211
\(125\) −1.00000 −0.0894427
\(126\) 1.00000 0.0890871
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.00000 0.704361
\(130\) −2.00000 −0.175412
\(131\) 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
\(135\) −1.00000 −0.0860663
\(136\) −6.00000 −0.514496
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) 14.0000 1.15865
\(147\) 1.00000 0.0824786
\(148\) 2.00000 0.164399
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 1.00000 0.0816497
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −4.00000 −0.324443
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 2.00000 0.160128
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −16.0000 −1.27289
\(159\) 6.00000 0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 1.00000 0.0771517
\(169\) −9.00000 −0.692308
\(170\) 6.00000 0.460179
\(171\) −4.00000 −0.305888
\(172\) 8.00000 0.609994
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −6.00000 −0.454859
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) 6.00000 0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.00000 0.148250
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 1.00000 0.0727393
\(190\) 4.00000 0.290191
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) −22.0000 −1.58359 −0.791797 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 14.0000 1.00514
\(195\) −2.00000 −0.143223
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 1.00000 0.0707107
\(201\) 8.00000 0.564276
\(202\) −6.00000 −0.422159
\(203\) −6.00000 −0.421117
\(204\) −6.00000 −0.420084
\(205\) −6.00000 −0.419058
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) −1.00000 −0.0690066
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) −8.00000 −0.545595
\(216\) 1.00000 0.0680414
\(217\) −4.00000 −0.271538
\(218\) 14.0000 0.948200
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 2.00000 0.134231
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.00000 0.0666667
\(226\) 18.0000 1.19734
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) −4.00000 −0.264906
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 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 \(0.562969\pi\)
\(234\) 2.00000 0.130744
\(235\) 12.0000 0.782794
\(236\) −12.0000 −0.781133
\(237\) −16.0000 −1.03931
\(238\) −6.00000 −0.388922
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) −11.0000 −0.707107
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) −1.00000 −0.0638877
\(246\) 6.00000 0.382546
\(247\) −8.00000 −0.509028
\(248\) −4.00000 −0.254000
\(249\) 12.0000 0.760469
\(250\) −1.00000 −0.0632456
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) 8.00000 0.501965
\(255\) 6.00000 0.375735
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 8.00000 0.498058
\(259\) 2.00000 0.124274
\(260\) −2.00000 −0.124035
\(261\) −6.00000 −0.371391
\(262\) 12.0000 0.741362
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −4.00000 −0.245256
\(267\) 6.00000 0.367194
\(268\) 8.00000 0.488678
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −6.00000 −0.363803
\(273\) 2.00000 0.121046
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −4.00000 −0.239904
\(279\) −4.00000 −0.239474
\(280\) −1.00000 −0.0597614
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) −12.0000 −0.714590
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) 0 0
\(285\) 4.00000 0.236940
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) 6.00000 0.352332
\(291\) 14.0000 0.820695
\(292\) 14.0000 0.819288
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 1.00000 0.0583212
\(295\) 12.0000 0.698667
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 8.00000 0.461112
\(302\) −16.0000 −0.920697
\(303\) −6.00000 −0.344691
\(304\) −4.00000 −0.229416
\(305\) −2.00000 −0.114520
\(306\) −6.00000 −0.342997
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 4.00000 0.227185
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 2.00000 0.113228
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 2.00000 0.112867
\(315\) −1.00000 −0.0563436
\(316\) −16.0000 −0.900070
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) −16.0000 −0.886158
\(327\) 14.0000 0.774202
\(328\) 6.00000 0.331295
\(329\) −12.0000 −0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 12.0000 0.658586
\(333\) 2.00000 0.109599
\(334\) 12.0000 0.656611
\(335\) −8.00000 −0.437087
\(336\) 1.00000 0.0545545
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −9.00000 −0.489535
\(339\) 18.0000 0.977626
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 1.00000 0.0539949
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −6.00000 −0.321634
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 1.00000 0.0534522
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) −6.00000 −0.317554
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) 2.00000 0.105118
\(363\) −11.0000 −0.577350
\(364\) 2.00000 0.104828
\(365\) −14.0000 −0.732793
\(366\) 2.00000 0.104542
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) −2.00000 −0.103975
\(371\) 6.00000 0.311504
\(372\) −4.00000 −0.207390
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −12.0000 −0.618853
\(377\) −12.0000 −0.618031
\(378\) 1.00000 0.0514344
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 4.00000 0.205196
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) −36.0000 −1.83951 −0.919757 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) 8.00000 0.406663
\(388\) 14.0000 0.710742
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −2.00000 −0.101274
\(391\) 0 0
\(392\) 1.00000 0.0505076
\(393\) 12.0000 0.605320
\(394\) −18.0000 −0.906827
\(395\) 16.0000 0.805047
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −4.00000 −0.200502
\(399\) −4.00000 −0.200250
\(400\) 1.00000 0.0500000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 8.00000 0.399004
\(403\) −8.00000 −0.398508
\(404\) −6.00000 −0.298511
\(405\) −1.00000 −0.0496904
\(406\) −6.00000 −0.297775
\(407\) 0 0
\(408\) −6.00000 −0.297044
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) −6.00000 −0.296319
\(411\) −6.00000 −0.295958
\(412\) −16.0000 −0.788263
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 2.00000 0.0980581
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −28.0000 −1.36302
\(423\) −12.0000 −0.583460
\(424\) 6.00000 0.291386
\(425\) −6.00000 −0.291043
\(426\) 0 0
\(427\) 2.00000 0.0967868
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 1.00000 0.0481125
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −4.00000 −0.192006
\(435\) 6.00000 0.287678
\(436\) 14.0000 0.670478
\(437\) 0 0
\(438\) 14.0000 0.668946
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) −12.0000 −0.570782
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 2.00000 0.0949158
\(445\) −6.00000 −0.284427
\(446\) −16.0000 −0.757622
\(447\) 18.0000 0.851371
\(448\) 1.00000 0.0472456
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) −16.0000 −0.751746
\(454\) −12.0000 −0.563188
\(455\) −2.00000 −0.0937614
\(456\) −4.00000 −0.187317
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) 2.00000 0.0934539
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −6.00000 −0.278543
\(465\) 4.00000 0.185496
\(466\) −6.00000 −0.277945
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 2.00000 0.0924500
\(469\) 8.00000 0.369406
\(470\) 12.0000 0.553519
\(471\) 2.00000 0.0921551
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) −16.0000 −0.734904
\(475\) −4.00000 −0.183533
\(476\) −6.00000 −0.275010
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 4.00000 0.182384
\(482\) 26.0000 1.18427
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) −14.0000 −0.635707
\(486\) 1.00000 0.0453609
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 2.00000 0.0905357
\(489\) −16.0000 −0.723545
\(490\) −1.00000 −0.0451754
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 6.00000 0.270501
\(493\) 36.0000 1.62136
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 12.0000 0.536120
\(502\) 12.0000 0.535586
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 1.00000 0.0445435
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 8.00000 0.354943
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 6.00000 0.265684
\(511\) 14.0000 0.619324
\(512\) 1.00000 0.0441942
\(513\) −4.00000 −0.176604
\(514\) −6.00000 −0.264649
\(515\) 16.0000 0.705044
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 2.00000 0.0878750
\(519\) −6.00000 −0.263371
\(520\) −2.00000 −0.0877058
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) −6.00000 −0.262613
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 12.0000 0.524222
\(525\) 1.00000 0.0436436
\(526\) 0 0
\(527\) 24.0000 1.04546
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) −6.00000 −0.260623
\(531\) −12.0000 −0.520756
\(532\) −4.00000 −0.173422
\(533\) 12.0000 0.519778
\(534\) 6.00000 0.259645
\(535\) −12.0000 −0.518805
\(536\) 8.00000 0.345547
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 20.0000 0.859074
\(543\) 2.00000 0.0858282
\(544\) −6.00000 −0.257248
\(545\) −14.0000 −0.599694
\(546\) 2.00000 0.0855921
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −6.00000 −0.256307
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) −16.0000 −0.680389
\(554\) −22.0000 −0.934690
\(555\) −2.00000 −0.0848953
\(556\) −4.00000 −0.169638
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) −4.00000 −0.169334
\(559\) 16.0000 0.676728
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) −30.0000 −1.26547
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) −12.0000 −0.505291
\(565\) −18.0000 −0.757266
\(566\) 20.0000 0.840663
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 4.00000 0.167542
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 19.0000 0.790296
\(579\) −22.0000 −0.914289
\(580\) 6.00000 0.249136
\(581\) 12.0000 0.497844
\(582\) 14.0000 0.580319
\(583\) 0 0
\(584\) 14.0000 0.579324
\(585\) −2.00000 −0.0826898
\(586\) −6.00000 −0.247858
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 1.00000 0.0412393
\(589\) 16.0000 0.659269
\(590\) 12.0000 0.494032
\(591\) −18.0000 −0.740421
\(592\) 2.00000 0.0821995
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 18.0000 0.737309
\(597\) −4.00000 −0.163709
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 1.00000 0.0408248
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 8.00000 0.326056
\(603\) 8.00000 0.325785
\(604\) −16.0000 −0.651031
\(605\) 11.0000 0.447214
\(606\) −6.00000 −0.243733
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −4.00000 −0.162221
\(609\) −6.00000 −0.243132
\(610\) −2.00000 −0.0809776
\(611\) −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 \(0.487140\pi\)
\(614\) 20.0000 0.807134
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) −16.0000 −0.643614
\(619\) −28.0000 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 4.00000 0.160644
\(621\) 0 0
\(622\) 0 0
\(623\) 6.00000 0.240385
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) −10.0000 −0.399680
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −12.0000 −0.478471
\(630\) −1.00000 −0.0398410
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −16.0000 −0.636446
\(633\) −28.0000 −1.11290
\(634\) 30.0000 1.19145
\(635\) −8.00000 −0.317470
\(636\) 6.00000 0.237915
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 12.0000 0.473602
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 24.0000 0.944267
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) −4.00000 −0.156772
\(652\) −16.0000 −0.626608
\(653\) −42.0000 −1.64359 −0.821794 0.569785i \(-0.807026\pi\)
−0.821794 + 0.569785i \(0.807026\pi\)
\(654\) 14.0000 0.547443
\(655\) −12.0000 −0.468879
\(656\) 6.00000 0.234261
\(657\) 14.0000 0.546192
\(658\) −12.0000 −0.467809
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 26.0000 1.01128 0.505641 0.862744i \(-0.331256\pi\)
0.505641 + 0.862744i \(0.331256\pi\)
\(662\) −4.00000 −0.155464
\(663\) −12.0000 −0.466041
\(664\) 12.0000 0.465690
\(665\) 4.00000 0.155113
\(666\) 2.00000 0.0774984
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) −16.0000 −0.618596
\(670\) −8.00000 −0.309067
\(671\) 0 0
\(672\) 1.00000 0.0385758
\(673\) 50.0000 1.92736 0.963679 0.267063i \(-0.0860531\pi\)
0.963679 + 0.267063i \(0.0860531\pi\)
\(674\) −22.0000 −0.847408
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 18.0000 0.691286
\(679\) 14.0000 0.537271
\(680\) 6.00000 0.230089
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) −4.00000 −0.152944
\(685\) 6.00000 0.229248
\(686\) 1.00000 0.0381802
\(687\) 2.00000 0.0763048
\(688\) 8.00000 0.304997
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 4.00000 0.151729
\(696\) −6.00000 −0.227429
\(697\) −36.0000 −1.36360
\(698\) 26.0000 0.984115
\(699\) −6.00000 −0.226941
\(700\) 1.00000 0.0377964
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 2.00000 0.0754851
\(703\) −8.00000 −0.301726
\(704\) 0 0
\(705\) 12.0000 0.451946
\(706\) 18.0000 0.677439
\(707\) −6.00000 −0.225653
\(708\) −12.0000 −0.450988
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) −6.00000 −0.224544
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −16.0000 −0.595871
\(722\) −3.00000 −0.111648
\(723\) 26.0000 0.966950
\(724\) 2.00000 0.0743294
\(725\) −6.00000 −0.222834
\(726\) −11.0000 −0.408248
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 2.00000 0.0741249
\(729\) 1.00000 0.0370370
\(730\) −14.0000 −0.518163
\(731\) −48.0000 −1.77534
\(732\) 2.00000 0.0739221
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 8.00000 0.295285
\(735\) −1.00000 −0.0368856
\(736\) 0 0
\(737\) 0 0
\(738\) 6.00000 0.220863
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) −2.00000 −0.0735215
\(741\) −8.00000 −0.293887
\(742\) 6.00000 0.220267
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) −4.00000 −0.146647
\(745\) −18.0000 −0.659469
\(746\) 26.0000 0.951928
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) −1.00000 −0.0365148
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) −12.0000 −0.437595
\(753\) 12.0000 0.437304
\(754\) −12.0000 −0.437014
\(755\) 16.0000 0.582300
\(756\) 1.00000 0.0363696
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 4.00000 0.145095
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 8.00000 0.289809
\(763\) 14.0000 0.506834
\(764\) 0 0
\(765\) 6.00000 0.216930
\(766\) −36.0000 −1.30073
\(767\) −24.0000 −0.866590
\(768\) 1.00000 0.0360844
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) −22.0000 −0.791797
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 8.00000 0.287554
\(775\) −4.00000 −0.143684
\(776\) 14.0000 0.502571
\(777\) 2.00000 0.0717496
\(778\) −30.0000 −1.07555
\(779\) −24.0000 −0.859889
\(780\) −2.00000 −0.0716115
\(781\) 0 0
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) 1.00000 0.0357143
\(785\) −2.00000 −0.0713831
\(786\) 12.0000 0.428026
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) 16.0000 0.569254
\(791\) 18.0000 0.640006
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) 2.00000 0.0709773
\(795\) −6.00000 −0.212798
\(796\) −4.00000 −0.141776
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) −4.00000 −0.141598
\(799\) 72.0000 2.54718
\(800\) 1.00000 0.0353553
\(801\) 6.00000 0.212000
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −8.00000 −0.281788
\(807\) 18.0000 0.633630
\(808\) −6.00000 −0.211079
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −4.00000 −0.140459 −0.0702295 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) −6.00000 −0.210559
\(813\) 20.0000 0.701431
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) −6.00000 −0.210042
\(817\) −32.0000 −1.11954
\(818\) −22.0000 −0.769212
\(819\) 2.00000 0.0698857
\(820\) −6.00000 −0.209529
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) −6.00000 −0.209274
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) −12.0000 −0.417533
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) −12.0000 −0.416526
\(831\) −22.0000 −0.763172
\(832\) 2.00000 0.0693375
\(833\) −6.00000 −0.207888
\(834\) −4.00000 −0.138509
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) −4.00000 −0.138260
\(838\) −12.0000 −0.414533
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) −1.00000 −0.0345033
\(841\) 7.00000 0.241379
\(842\) −10.0000 −0.344623
\(843\) −30.0000 −1.03325
\(844\) −28.0000 −0.963800
\(845\) 9.00000 0.309609
\(846\) −12.0000 −0.412568
\(847\) −11.0000 −0.377964
\(848\) 6.00000 0.206041
\(849\) 20.0000 0.686398
\(850\) −6.00000 −0.205798
\(851\) 0 0
\(852\) 0 0
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 2.00000 0.0684386
\(855\) 4.00000 0.136797
\(856\) 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
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) −8.00000 −0.272798
\(861\) 6.00000 0.204479
\(862\) 24.0000 0.817443
\(863\) −48.0000 −1.63394 −0.816970 0.576681i \(-0.804348\pi\)
−0.816970 + 0.576681i \(0.804348\pi\)
\(864\) 1.00000 0.0340207
\(865\) 6.00000 0.204006
\(866\) −34.0000 −1.15537
\(867\) 19.0000 0.645274
\(868\) −4.00000 −0.135769
\(869\) 0 0
\(870\) 6.00000 0.203419
\(871\) 16.0000 0.542139
\(872\) 14.0000 0.474100
\(873\) 14.0000 0.473828
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 14.0000 0.473016
\(877\) 50.0000 1.68838 0.844190 0.536044i \(-0.180082\pi\)
0.844190 + 0.536044i \(0.180082\pi\)
\(878\) −28.0000 −0.944954
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 1.00000 0.0336718
\(883\) −40.0000 −1.34611 −0.673054 0.739594i \(-0.735018\pi\)
−0.673054 + 0.739594i \(0.735018\pi\)
\(884\) −12.0000 −0.403604
\(885\) 12.0000 0.403376
\(886\) 12.0000 0.403148
\(887\) −12.0000 −0.402921 −0.201460 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) 2.00000 0.0671156
\(889\) 8.00000 0.268311
\(890\) −6.00000 −0.201120
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) 48.0000 1.60626
\(894\) 18.0000 0.602010
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) 24.0000 0.800445
\(900\) 1.00000 0.0333333
\(901\) −36.0000 −1.19933
\(902\) 0 0
\(903\) 8.00000 0.266223
\(904\) 18.0000 0.598671
\(905\) −2.00000 −0.0664822
\(906\) −16.0000 −0.531564
\(907\) −16.0000 −0.531271 −0.265636 0.964073i \(-0.585582\pi\)
−0.265636 + 0.964073i \(0.585582\pi\)
\(908\) −12.0000 −0.398234
\(909\) −6.00000 −0.199007
\(910\) −2.00000 −0.0662994
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) −4.00000 −0.132453
\(913\) 0 0
\(914\) 2.00000 0.0661541
\(915\) −2.00000 −0.0661180
\(916\) 2.00000 0.0660819
\(917\) 12.0000 0.396275
\(918\) −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
\(921\) 20.0000 0.659022
\(922\) −30.0000 −0.987997
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) −16.0000 −0.525793
\(927\) −16.0000 −0.525509
\(928\) −6.00000 −0.196960
\(929\) 54.0000 1.77168 0.885841 0.463988i \(-0.153582\pi\)
0.885841 + 0.463988i \(0.153582\pi\)
\(930\) 4.00000 0.131165
\(931\) −4.00000 −0.131095
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 8.00000 0.261209
\(939\) −10.0000 −0.326338
\(940\) 12.0000 0.391397
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 2.00000 0.0651635
\(943\) 0 0
\(944\) −12.0000 −0.390567
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) −16.0000 −0.519656
\(949\) 28.0000 0.908918
\(950\) −4.00000 −0.129777
\(951\) 30.0000 0.972817
\(952\) −6.00000 −0.194461
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) −6.00000 −0.193750
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) 4.00000 0.128965
\(963\) 12.0000 0.386695
\(964\) 26.0000 0.837404
\(965\) 22.0000 0.708205
\(966\) 0 0
\(967\) 56.0000 1.80084 0.900419 0.435023i \(-0.143260\pi\)
0.900419 + 0.435023i \(0.143260\pi\)
\(968\) −11.0000 −0.353553
\(969\) 24.0000 0.770991
\(970\) −14.0000 −0.449513
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 1.00000 0.0320750
\(973\) −4.00000 −0.128234
\(974\) −16.0000 −0.512673
\(975\) 2.00000 0.0640513
\(976\) 2.00000 0.0640184
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −16.0000 −0.511624
\(979\) 0 0
\(980\) −1.00000 −0.0319438
\(981\) 14.0000 0.446986
\(982\) 24.0000 0.765871
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 6.00000 0.191273
\(985\) 18.0000 0.573528
\(986\) 36.0000 1.14647
\(987\) −12.0000 −0.381964
\(988\) −8.00000 −0.254514
\(989\) 0 0
\(990\) 0 0
\(991\) 56.0000 1.77890 0.889449 0.457034i \(-0.151088\pi\)
0.889449 + 0.457034i \(0.151088\pi\)
\(992\) −4.00000 −0.127000
\(993\) −4.00000 −0.126936
\(994\) 0 0
\(995\) 4.00000 0.126809
\(996\) 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
\(999\) 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 \(a_p\))