Properties

Label 1155.2.a.e.1.1
Level 1155
Weight 2
Character 1155.1
Self dual Yes
Analytic conductor 9.223
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1155.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(9.22272143346\)
Analytic rank: \(1\)
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 \(\chi\) = 1155.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(-1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+1.00000 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(-1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+1.00000 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.00000 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(-2.00000 q^{13}\) \(+1.00000 q^{14}\) \(-1.00000 q^{15}\) \(-1.00000 q^{16}\) \(-6.00000 q^{17}\) \(-1.00000 q^{18}\) \(-4.00000 q^{19}\) \(-1.00000 q^{20}\) \(+1.00000 q^{21}\) \(-1.00000 q^{22}\) \(+8.00000 q^{23}\) \(-3.00000 q^{24}\) \(+1.00000 q^{25}\) \(+2.00000 q^{26}\) \(-1.00000 q^{27}\) \(+1.00000 q^{28}\) \(+6.00000 q^{29}\) \(+1.00000 q^{30}\) \(+8.00000 q^{31}\) \(-5.00000 q^{32}\) \(-1.00000 q^{33}\) \(+6.00000 q^{34}\) \(-1.00000 q^{35}\) \(-1.00000 q^{36}\) \(+6.00000 q^{37}\) \(+4.00000 q^{38}\) \(+2.00000 q^{39}\) \(+3.00000 q^{40}\) \(-6.00000 q^{41}\) \(-1.00000 q^{42}\) \(-4.00000 q^{43}\) \(-1.00000 q^{44}\) \(+1.00000 q^{45}\) \(-8.00000 q^{46}\) \(-8.00000 q^{47}\) \(+1.00000 q^{48}\) \(+1.00000 q^{49}\) \(-1.00000 q^{50}\) \(+6.00000 q^{51}\) \(+2.00000 q^{52}\) \(-10.0000 q^{53}\) \(+1.00000 q^{54}\) \(+1.00000 q^{55}\) \(-3.00000 q^{56}\) \(+4.00000 q^{57}\) \(-6.00000 q^{58}\) \(-12.0000 q^{59}\) \(+1.00000 q^{60}\) \(-10.0000 q^{61}\) \(-8.00000 q^{62}\) \(-1.00000 q^{63}\) \(+7.00000 q^{64}\) \(-2.00000 q^{65}\) \(+1.00000 q^{66}\) \(-12.0000 q^{67}\) \(+6.00000 q^{68}\) \(-8.00000 q^{69}\) \(+1.00000 q^{70}\) \(-8.00000 q^{71}\) \(+3.00000 q^{72}\) \(-6.00000 q^{73}\) \(-6.00000 q^{74}\) \(-1.00000 q^{75}\) \(+4.00000 q^{76}\) \(-1.00000 q^{77}\) \(-2.00000 q^{78}\) \(+8.00000 q^{79}\) \(-1.00000 q^{80}\) \(+1.00000 q^{81}\) \(+6.00000 q^{82}\) \(-4.00000 q^{83}\) \(-1.00000 q^{84}\) \(-6.00000 q^{85}\) \(+4.00000 q^{86}\) \(-6.00000 q^{87}\) \(+3.00000 q^{88}\) \(+10.0000 q^{89}\) \(-1.00000 q^{90}\) \(+2.00000 q^{91}\) \(-8.00000 q^{92}\) \(-8.00000 q^{93}\) \(+8.00000 q^{94}\) \(-4.00000 q^{95}\) \(+5.00000 q^{96}\) \(-14.0000 q^{97}\) \(-1.00000 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) −1.00000 −0.377964
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 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
\(22\) −1.00000 −0.213201
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) −3.00000 −0.612372
\(25\) 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 \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.00000 0.182574
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −5.00000 −0.883883
\(33\) −1.00000 −0.174078
\(34\) 6.00000 1.02899
\(35\) −1.00000 −0.169031
\(36\) −1.00000 −0.166667
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 4.00000 0.648886
\(39\) 2.00000 0.320256
\(40\) 3.00000 0.474342
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −1.00000 −0.154303
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) −8.00000 −1.17954
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) 6.00000 0.840168
\(52\) 2.00000 0.277350
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.00000 0.134840
\(56\) −3.00000 −0.400892
\(57\) 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
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −8.00000 −1.01600
\(63\) −1.00000 −0.125988
\(64\) 7.00000 0.875000
\(65\) −2.00000 −0.248069
\(66\) 1.00000 0.123091
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 6.00000 0.727607
\(69\) −8.00000 −0.963087
\(70\) 1.00000 0.119523
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 3.00000 0.353553
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −6.00000 −0.697486
\(75\) −1.00000 −0.115470
\(76\) 4.00000 0.458831
\(77\) −1.00000 −0.113961
\(78\) −2.00000 −0.226455
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) −1.00000 −0.109109
\(85\) −6.00000 −0.650791
\(86\) 4.00000 0.431331
\(87\) −6.00000 −0.643268
\(88\) 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
\(92\) −8.00000 −0.834058
\(93\) −8.00000 −0.829561
\(94\) 8.00000 0.825137
\(95\) −4.00000 −0.410391
\(96\) 5.00000 0.510310
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −1.00000 −0.101015
\(99\) 1.00000 0.100504
\(100\) −1.00000 −0.100000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) −6.00000 −0.594089
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) −6.00000 −0.588348
\(105\) 1.00000 0.0975900
\(106\) 10.0000 0.971286
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 1.00000 0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −6.00000 −0.569495
\(112\) 1.00000 0.0944911
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −4.00000 −0.374634
\(115\) 8.00000 0.746004
\(116\) −6.00000 −0.557086
\(117\) −2.00000 −0.184900
\(118\) 12.0000 1.10469
\(119\) 6.00000 0.550019
\(120\) −3.00000 −0.273861
\(121\) 1.00000 0.0909091
\(122\) 10.0000 0.905357
\(123\) 6.00000 0.541002
\(124\) −8.00000 −0.718421
\(125\) 1.00000 0.0894427
\(126\) 1.00000 0.0890871
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 3.00000 0.265165
\(129\) 4.00000 0.352180
\(130\) 2.00000 0.175412
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 1.00000 0.0870388
\(133\) 4.00000 0.346844
\(134\) 12.0000 1.03664
\(135\) −1.00000 −0.0860663
\(136\) −18.0000 −1.54349
\(137\) −22.0000 −1.87959 −0.939793 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 8.00000 0.681005
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 1.00000 0.0845154
\(141\) 8.00000 0.673722
\(142\) 8.00000 0.671345
\(143\) −2.00000 −0.167248
\(144\) −1.00000 −0.0833333
\(145\) 6.00000 0.498273
\(146\) 6.00000 0.496564
\(147\) −1.00000 −0.0824786
\(148\) −6.00000 −0.493197
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 1.00000 0.0816497
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) −12.0000 −0.973329
\(153\) −6.00000 −0.485071
\(154\) 1.00000 0.0805823
\(155\) 8.00000 0.642575
\(156\) −2.00000 −0.160128
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −8.00000 −0.636446
\(159\) 10.0000 0.793052
\(160\) −5.00000 −0.395285
\(161\) −8.00000 −0.630488
\(162\) −1.00000 −0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 6.00000 0.468521
\(165\) −1.00000 −0.0778499
\(166\) 4.00000 0.310460
\(167\) −16.0000 −1.23812 −0.619059 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 3.00000 0.231455
\(169\) −9.00000 −0.692308
\(170\) 6.00000 0.460179
\(171\) −4.00000 −0.305888
\(172\) 4.00000 0.304997
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 6.00000 0.454859
\(175\) −1.00000 −0.0755929
\(176\) −1.00000 −0.0753778
\(177\) 12.0000 0.901975
\(178\) −10.0000 −0.749532
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) −2.00000 −0.148250
\(183\) 10.0000 0.739221
\(184\) 24.0000 1.76930
\(185\) 6.00000 0.441129
\(186\) 8.00000 0.586588
\(187\) −6.00000 −0.438763
\(188\) 8.00000 0.583460
\(189\) 1.00000 0.0727393
\(190\) 4.00000 0.290191
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) −7.00000 −0.505181
\(193\) −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
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 3.00000 0.212132
\(201\) 12.0000 0.846415
\(202\) −6.00000 −0.422159
\(203\) −6.00000 −0.421117
\(204\) −6.00000 −0.420084
\(205\) −6.00000 −0.419058
\(206\) −16.0000 −1.11477
\(207\) 8.00000 0.556038
\(208\) 2.00000 0.138675
\(209\) −4.00000 −0.276686
\(210\) −1.00000 −0.0690066
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 10.0000 0.686803
\(213\) 8.00000 0.548151
\(214\) 12.0000 0.820303
\(215\) −4.00000 −0.272798
\(216\) −3.00000 −0.204124
\(217\) −8.00000 −0.543075
\(218\) 2.00000 0.135457
\(219\) 6.00000 0.405442
\(220\) −1.00000 −0.0674200
\(221\) 12.0000 0.807207
\(222\) 6.00000 0.402694
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 5.00000 0.334077
\(225\) 1.00000 0.0666667
\(226\) 14.0000 0.931266
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) −4.00000 −0.264906
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) −8.00000 −0.527504
\(231\) 1.00000 0.0657952
\(232\) 18.0000 1.18176
\(233\) −22.0000 −1.44127 −0.720634 0.693316i \(-0.756149\pi\)
−0.720634 + 0.693316i \(0.756149\pi\)
\(234\) 2.00000 0.130744
\(235\) −8.00000 −0.521862
\(236\) 12.0000 0.781133
\(237\) −8.00000 −0.519656
\(238\) −6.00000 −0.388922
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 1.00000 0.0645497
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 10.0000 0.640184
\(245\) 1.00000 0.0638877
\(246\) −6.00000 −0.382546
\(247\) 8.00000 0.509028
\(248\) 24.0000 1.52400
\(249\) 4.00000 0.253490
\(250\) −1.00000 −0.0632456
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 1.00000 0.0629941
\(253\) 8.00000 0.502956
\(254\) 0 0
\(255\) 6.00000 0.375735
\(256\) −17.0000 −1.06250
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −4.00000 −0.249029
\(259\) −6.00000 −0.372822
\(260\) 2.00000 0.124035
\(261\) 6.00000 0.371391
\(262\) 12.0000 0.741362
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) −3.00000 −0.184637
\(265\) −10.0000 −0.614295
\(266\) −4.00000 −0.245256
\(267\) −10.0000 −0.611990
\(268\) 12.0000 0.733017
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 1.00000 0.0608581
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 6.00000 0.363803
\(273\) −2.00000 −0.121046
\(274\) 22.0000 1.32907
\(275\) 1.00000 0.0603023
\(276\) 8.00000 0.481543
\(277\) −18.0000 −1.08152 −0.540758 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) −4.00000 −0.239904
\(279\) 8.00000 0.478947
\(280\) −3.00000 −0.179284
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −8.00000 −0.476393
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 8.00000 0.474713
\(285\) 4.00000 0.236940
\(286\) 2.00000 0.118262
\(287\) 6.00000 0.354169
\(288\) −5.00000 −0.294628
\(289\) 19.0000 1.11765
\(290\) −6.00000 −0.352332
\(291\) 14.0000 0.820695
\(292\) 6.00000 0.351123
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 1.00000 0.0583212
\(295\) −12.0000 −0.698667
\(296\) 18.0000 1.04623
\(297\) −1.00000 −0.0580259
\(298\) 18.0000 1.04271
\(299\) −16.0000 −0.925304
\(300\) 1.00000 0.0577350
\(301\) 4.00000 0.230556
\(302\) −16.0000 −0.920697
\(303\) −6.00000 −0.344691
\(304\) 4.00000 0.229416
\(305\) −10.0000 −0.572598
\(306\) 6.00000 0.342997
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 1.00000 0.0569803
\(309\) −16.0000 −0.910208
\(310\) −8.00000 −0.454369
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 6.00000 0.339683
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 2.00000 0.112867
\(315\) −1.00000 −0.0563436
\(316\) −8.00000 −0.450035
\(317\) −34.0000 −1.90963 −0.954815 0.297200i \(-0.903947\pi\)
−0.954815 + 0.297200i \(0.903947\pi\)
\(318\) −10.0000 −0.560772
\(319\) 6.00000 0.335936
\(320\) 7.00000 0.391312
\(321\) 12.0000 0.669775
\(322\) 8.00000 0.445823
\(323\) 24.0000 1.33540
\(324\) −1.00000 −0.0555556
\(325\) −2.00000 −0.110940
\(326\) −20.0000 −1.10770
\(327\) 2.00000 0.110600
\(328\) −18.0000 −0.993884
\(329\) 8.00000 0.441054
\(330\) 1.00000 0.0550482
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 4.00000 0.219529
\(333\) 6.00000 0.328798
\(334\) 16.0000 0.875481
\(335\) −12.0000 −0.655630
\(336\) −1.00000 −0.0545545
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 9.00000 0.489535
\(339\) 14.0000 0.760376
\(340\) 6.00000 0.325396
\(341\) 8.00000 0.433224
\(342\) 4.00000 0.216295
\(343\) −1.00000 −0.0539949
\(344\) −12.0000 −0.646997
\(345\) −8.00000 −0.430706
\(346\) −6.00000 −0.322562
\(347\) 20.0000 1.07366 0.536828 0.843692i \(-0.319622\pi\)
0.536828 + 0.843692i \(0.319622\pi\)
\(348\) 6.00000 0.321634
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 1.00000 0.0534522
\(351\) 2.00000 0.106752
\(352\) −5.00000 −0.266501
\(353\) 34.0000 1.80964 0.904819 0.425797i \(-0.140006\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(354\) −12.0000 −0.637793
\(355\) −8.00000 −0.424596
\(356\) −10.0000 −0.529999
\(357\) −6.00000 −0.317554
\(358\) −4.00000 −0.211407
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 3.00000 0.158114
\(361\) −3.00000 −0.157895
\(362\) −6.00000 −0.315353
\(363\) −1.00000 −0.0524864
\(364\) −2.00000 −0.104828
\(365\) −6.00000 −0.314054
\(366\) −10.0000 −0.522708
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) −8.00000 −0.417029
\(369\) −6.00000 −0.312348
\(370\) −6.00000 −0.311925
\(371\) 10.0000 0.519174
\(372\) 8.00000 0.414781
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 6.00000 0.310253
\(375\) −1.00000 −0.0516398
\(376\) −24.0000 −1.23771
\(377\) −12.0000 −0.618031
\(378\) −1.00000 −0.0514344
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 4.00000 0.205196
\(381\) 0 0
\(382\) −16.0000 −0.818631
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) −3.00000 −0.153093
\(385\) −1.00000 −0.0509647
\(386\) 22.0000 1.11977
\(387\) −4.00000 −0.203331
\(388\) 14.0000 0.710742
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) −2.00000 −0.101274
\(391\) −48.0000 −2.42746
\(392\) 3.00000 0.151523
\(393\) 12.0000 0.605320
\(394\) −22.0000 −1.10834
\(395\) 8.00000 0.402524
\(396\) −1.00000 −0.0502519
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) −16.0000 −0.802008
\(399\) −4.00000 −0.200250
\(400\) −1.00000 −0.0500000
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −12.0000 −0.598506
\(403\) −16.0000 −0.797017
\(404\) −6.00000 −0.298511
\(405\) 1.00000 0.0496904
\(406\) 6.00000 0.297775
\(407\) 6.00000 0.297409
\(408\) 18.0000 0.891133
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 6.00000 0.296319
\(411\) 22.0000 1.08518
\(412\) −16.0000 −0.788263
\(413\) 12.0000 0.590481
\(414\) −8.00000 −0.393179
\(415\) −4.00000 −0.196352
\(416\) 10.0000 0.490290
\(417\) −4.00000 −0.195881
\(418\) 4.00000 0.195646
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) −1.00000 −0.0487950
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 4.00000 0.194717
\(423\) −8.00000 −0.388973
\(424\) −30.0000 −1.45693
\(425\) −6.00000 −0.291043
\(426\) −8.00000 −0.387601
\(427\) 10.0000 0.483934
\(428\) 12.0000 0.580042
\(429\) 2.00000 0.0965609
\(430\) 4.00000 0.192897
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 8.00000 0.384012
\(435\) −6.00000 −0.287678
\(436\) 2.00000 0.0957826
\(437\) −32.0000 −1.53077
\(438\) −6.00000 −0.286691
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 3.00000 0.143019
\(441\) 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 \(0.407984\pi\)
\(444\) 6.00000 0.284747
\(445\) 10.0000 0.474045
\(446\) 8.00000 0.378811
\(447\) 18.0000 0.851371
\(448\) −7.00000 −0.330719
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −6.00000 −0.282529
\(452\) 14.0000 0.658505
\(453\) −16.0000 −0.751746
\(454\) −12.0000 −0.563188
\(455\) 2.00000 0.0937614
\(456\) 12.0000 0.561951
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) 10.0000 0.467269
\(459\) 6.00000 0.280056
\(460\) −8.00000 −0.373002
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −1.00000 −0.0465242
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −6.00000 −0.278543
\(465\) −8.00000 −0.370991
\(466\) 22.0000 1.01913
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 2.00000 0.0924500
\(469\) 12.0000 0.554109
\(470\) 8.00000 0.369012
\(471\) 2.00000 0.0921551
\(472\) −36.0000 −1.65703
\(473\) −4.00000 −0.183920
\(474\) 8.00000 0.367452
\(475\) −4.00000 −0.183533
\(476\) −6.00000 −0.275010
\(477\) −10.0000 −0.457869
\(478\) 16.0000 0.731823
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 5.00000 0.228218
\(481\) −12.0000 −0.547153
\(482\) 22.0000 1.00207
\(483\) 8.00000 0.364013
\(484\) −1.00000 −0.0454545
\(485\) −14.0000 −0.635707
\(486\) 1.00000 0.0453609
\(487\) 24.0000 1.08754 0.543772 0.839233i \(-0.316996\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(488\) −30.0000 −1.35804
\(489\) −20.0000 −0.904431
\(490\) −1.00000 −0.0451754
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) −6.00000 −0.270501
\(493\) −36.0000 −1.62136
\(494\) −8.00000 −0.359937
\(495\) 1.00000 0.0449467
\(496\) −8.00000 −0.359211
\(497\) 8.00000 0.358849
\(498\) −4.00000 −0.179244
\(499\) −12.0000 −0.537194 −0.268597 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 16.0000 0.714827
\(502\) −20.0000 −0.892644
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) −3.00000 −0.133631
\(505\) 6.00000 0.266996
\(506\) −8.00000 −0.355643
\(507\) 9.00000 0.399704
\(508\) 0 0
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −6.00000 −0.265684
\(511\) 6.00000 0.265424
\(512\) 11.0000 0.486136
\(513\) 4.00000 0.176604
\(514\) 30.0000 1.32324
\(515\) 16.0000 0.705044
\(516\) −4.00000 −0.176090
\(517\) −8.00000 −0.351840
\(518\) 6.00000 0.263625
\(519\) −6.00000 −0.263371
\(520\) −6.00000 −0.263117
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 12.0000 0.524222
\(525\) 1.00000 0.0436436
\(526\) −16.0000 −0.697633
\(527\) −48.0000 −2.09091
\(528\) 1.00000 0.0435194
\(529\) 41.0000 1.78261
\(530\) 10.0000 0.434372
\(531\) −12.0000 −0.520756
\(532\) −4.00000 −0.173422
\(533\) 12.0000 0.519778
\(534\) 10.0000 0.432742
\(535\) −12.0000 −0.518805
\(536\) −36.0000 −1.55496
\(537\) −4.00000 −0.172613
\(538\) −14.0000 −0.603583
\(539\) 1.00000 0.0430730
\(540\) 1.00000 0.0430331
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −8.00000 −0.343629
\(543\) −6.00000 −0.257485
\(544\) 30.0000 1.28624
\(545\) −2.00000 −0.0856706
\(546\) 2.00000 0.0855921
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 22.0000 0.939793
\(549\) −10.0000 −0.426790
\(550\) −1.00000 −0.0426401
\(551\) −24.0000 −1.02243
\(552\) −24.0000 −1.02151
\(553\) −8.00000 −0.340195
\(554\) 18.0000 0.764747
\(555\) −6.00000 −0.254686
\(556\) −4.00000 −0.169638
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) −8.00000 −0.338667
\(559\) 8.00000 0.338364
\(560\) 1.00000 0.0422577
\(561\) 6.00000 0.253320
\(562\) −18.0000 −0.759284
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) −8.00000 −0.336861
\(565\) −14.0000 −0.588984
\(566\) 4.00000 0.168133
\(567\) −1.00000 −0.0419961
\(568\) −24.0000 −1.00702
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) −4.00000 −0.167542
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 2.00000 0.0836242
\(573\) −16.0000 −0.668410
\(574\) −6.00000 −0.250435
\(575\) 8.00000 0.333623
\(576\) 7.00000 0.291667
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −19.0000 −0.790296
\(579\) 22.0000 0.914289
\(580\) −6.00000 −0.249136
\(581\) 4.00000 0.165948
\(582\) −14.0000 −0.580319
\(583\) −10.0000 −0.414158
\(584\) −18.0000 −0.744845
\(585\) −2.00000 −0.0826898
\(586\) 18.0000 0.743573
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 1.00000 0.0412393
\(589\) −32.0000 −1.31854
\(590\) 12.0000 0.494032
\(591\) −22.0000 −0.904959
\(592\) −6.00000 −0.246598
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 1.00000 0.0410305
\(595\) 6.00000 0.245976
\(596\) 18.0000 0.737309
\(597\) −16.0000 −0.654836
\(598\) 16.0000 0.654289
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −3.00000 −0.122474
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −4.00000 −0.163028
\(603\) −12.0000 −0.488678
\(604\) −16.0000 −0.651031
\(605\) 1.00000 0.0406558
\(606\) 6.00000 0.243733
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 20.0000 0.811107
\(609\) 6.00000 0.243132
\(610\) 10.0000 0.404888
\(611\) 16.0000 0.647291
\(612\) 6.00000 0.242536
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −4.00000 −0.161427
\(615\) 6.00000 0.241943
\(616\) −3.00000 −0.120873
\(617\) 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 \(0.690240\pi\)
\(620\) −8.00000 −0.321288
\(621\) −8.00000 −0.321029
\(622\) 16.0000 0.641542
\(623\) −10.0000 −0.400642
\(624\) −2.00000 −0.0800641
\(625\) 1.00000 0.0400000
\(626\) −10.0000 −0.399680
\(627\) 4.00000 0.159745
\(628\) 2.00000 0.0798087
\(629\) −36.0000 −1.43541
\(630\) 1.00000 0.0398410
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 24.0000 0.954669
\(633\) 4.00000 0.158986
\(634\) 34.0000 1.35031
\(635\) 0 0
\(636\) −10.0000 −0.396526
\(637\) −2.00000 −0.0792429
\(638\) −6.00000 −0.237542
\(639\) −8.00000 −0.316475
\(640\) 3.00000 0.118585
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) −12.0000 −0.473602
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 8.00000 0.315244
\(645\) 4.00000 0.157500
\(646\) −24.0000 −0.944267
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 3.00000 0.117851
\(649\) −12.0000 −0.471041
\(650\) 2.00000 0.0784465
\(651\) 8.00000 0.313545
\(652\) −20.0000 −0.783260
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) −2.00000 −0.0782062
\(655\) −12.0000 −0.468879
\(656\) 6.00000 0.234261
\(657\) −6.00000 −0.234082
\(658\) −8.00000 −0.311872
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 1.00000 0.0389249
\(661\) −42.0000 −1.63361 −0.816805 0.576913i \(-0.804257\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) −28.0000 −1.08825
\(663\) −12.0000 −0.466041
\(664\) −12.0000 −0.465690
\(665\) 4.00000 0.155113
\(666\) −6.00000 −0.232495
\(667\) 48.0000 1.85857
\(668\) 16.0000 0.619059
\(669\) 8.00000 0.309298
\(670\) 12.0000 0.463600
\(671\) −10.0000 −0.386046
\(672\) −5.00000 −0.192879
\(673\) −38.0000 −1.46479 −0.732396 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(674\) −26.0000 −1.00148
\(675\) −1.00000 −0.0384900
\(676\) 9.00000 0.346154
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) −14.0000 −0.537667
\(679\) 14.0000 0.537271
\(680\) −18.0000 −0.690268
\(681\) −12.0000 −0.459841
\(682\) −8.00000 −0.306336
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 4.00000 0.152944
\(685\) −22.0000 −0.840577
\(686\) 1.00000 0.0381802
\(687\) 10.0000 0.381524
\(688\) 4.00000 0.152499
\(689\) 20.0000 0.761939
\(690\) 8.00000 0.304555
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −6.00000 −0.228086
\(693\) −1.00000 −0.0379869
\(694\) −20.0000 −0.759190
\(695\) 4.00000 0.151729
\(696\) −18.0000 −0.682288
\(697\) 36.0000 1.36360
\(698\) 10.0000 0.378506
\(699\) 22.0000 0.832116
\(700\) 1.00000 0.0377964
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) −2.00000 −0.0754851
\(703\) −24.0000 −0.905177
\(704\) 7.00000 0.263822
\(705\) 8.00000 0.301297
\(706\) −34.0000 −1.27961
\(707\) −6.00000 −0.225653
\(708\) −12.0000 −0.450988
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 8.00000 0.300235
\(711\) 8.00000 0.300023
\(712\) 30.0000 1.12430
\(713\) 64.0000 2.39682
\(714\) 6.00000 0.224544
\(715\) −2.00000 −0.0747958
\(716\) −4.00000 −0.149487
\(717\) 16.0000 0.597531
\(718\) −8.00000 −0.298557
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −16.0000 −0.595871
\(722\) 3.00000 0.111648
\(723\) 22.0000 0.818189
\(724\) −6.00000 −0.222988
\(725\) 6.00000 0.222834
\(726\) 1.00000 0.0371135
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 6.00000 0.222375
\(729\) 1.00000 0.0370370
\(730\) 6.00000 0.222070
\(731\) 24.0000 0.887672
\(732\) −10.0000 −0.369611
\(733\) 46.0000 1.69905 0.849524 0.527549i \(-0.176889\pi\)
0.849524 + 0.527549i \(0.176889\pi\)
\(734\) −8.00000 −0.295285
\(735\) −1.00000 −0.0368856
\(736\) −40.0000 −1.47442
\(737\) −12.0000 −0.442026
\(738\) 6.00000 0.220863
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −6.00000 −0.220564
\(741\) −8.00000 −0.293887
\(742\) −10.0000 −0.367112
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) −24.0000 −0.879883
\(745\) −18.0000 −0.659469
\(746\) −14.0000 −0.512576
\(747\) −4.00000 −0.146352
\(748\) 6.00000 0.219382
\(749\) 12.0000 0.438470
\(750\) 1.00000 0.0365148
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 8.00000 0.291730
\(753\) −20.0000 −0.728841
\(754\) 12.0000 0.437014
\(755\) 16.0000 0.582300
\(756\) −1.00000 −0.0363696
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 20.0000 0.726433
\(759\) −8.00000 −0.290382
\(760\) −12.0000 −0.435286
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) 2.00000 0.0724049
\(764\) −16.0000 −0.578860
\(765\) −6.00000 −0.216930
\(766\) −24.0000 −0.867155
\(767\) 24.0000 0.866590
\(768\) 17.0000 0.613435
\(769\) 26.0000 0.937584 0.468792 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 1.00000 0.0360375
\(771\) 30.0000 1.08042
\(772\) 22.0000 0.791797
\(773\) −10.0000 −0.359675 −0.179838 0.983696i \(-0.557557\pi\)
−0.179838 + 0.983696i \(0.557557\pi\)
\(774\) 4.00000 0.143777
\(775\) 8.00000 0.287368
\(776\) −42.0000 −1.50771
\(777\) 6.00000 0.215249
\(778\) 10.0000 0.358517
\(779\) 24.0000 0.859889
\(780\) −2.00000 −0.0716115
\(781\) −8.00000 −0.286263
\(782\) 48.0000 1.71648
\(783\) −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 \(0.666316\pi\)
\(788\) −22.0000 −0.783718
\(789\) −16.0000 −0.569615
\(790\) −8.00000 −0.284627
\(791\) 14.0000 0.497783
\(792\) 3.00000 0.106600
\(793\) 20.0000 0.710221
\(794\) 18.0000 0.638796
\(795\) 10.0000 0.354663
\(796\) −16.0000 −0.567105
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 4.00000 0.141598
\(799\) 48.0000 1.69812
\(800\) −5.00000 −0.176777
\(801\) 10.0000 0.353333
\(802\) −2.00000 −0.0706225
\(803\) −6.00000 −0.211735
\(804\) −12.0000 −0.423207
\(805\) −8.00000 −0.281963
\(806\) 16.0000 0.563576
\(807\) −14.0000 −0.492823
\(808\) 18.0000 0.633238
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 6.00000 0.210559
\(813\) −8.00000 −0.280572
\(814\) −6.00000 −0.210300
\(815\) 20.0000 0.700569
\(816\) −6.00000 −0.210042
\(817\) 16.0000 0.559769
\(818\) 14.0000 0.489499
\(819\) 2.00000 0.0698857
\(820\) 6.00000 0.209529
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) −22.0000 −0.767338
\(823\) −8.00000 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) 48.0000 1.67216
\(825\) −1.00000 −0.0348155
\(826\) −12.0000 −0.417533
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −8.00000 −0.278019
\(829\) 30.0000 1.04194 0.520972 0.853574i \(-0.325570\pi\)
0.520972 + 0.853574i \(0.325570\pi\)
\(830\) 4.00000 0.138842
\(831\) 18.0000 0.624413
\(832\) −14.0000 −0.485363
\(833\) −6.00000 −0.207888
\(834\) 4.00000 0.138509
\(835\) −16.0000 −0.553703
\(836\) 4.00000 0.138343
\(837\) −8.00000 −0.276520
\(838\) 36.0000 1.24360
\(839\) 16.0000 0.552381 0.276191 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 3.00000 0.103510
\(841\) 7.00000 0.241379
\(842\) −6.00000 −0.206774
\(843\) −18.0000 −0.619953
\(844\) 4.00000 0.137686
\(845\) −9.00000 −0.309609
\(846\) 8.00000 0.275046
\(847\) −1.00000 −0.0343604
\(848\) 10.0000 0.343401
\(849\) 4.00000 0.137280
\(850\) 6.00000 0.205798
\(851\) 48.0000 1.64542
\(852\) −8.00000 −0.274075
\(853\) 38.0000 1.30110 0.650548 0.759465i \(-0.274539\pi\)
0.650548 + 0.759465i \(0.274539\pi\)
\(854\) −10.0000 −0.342193
\(855\) −4.00000 −0.136797
\(856\) −36.0000 −1.23045
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) −2.00000 −0.0682789
\(859\) −44.0000 −1.50126 −0.750630 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) 4.00000 0.136399
\(861\) −6.00000 −0.204479
\(862\) 16.0000 0.544962
\(863\) −16.0000 −0.544646 −0.272323 0.962206i \(-0.587792\pi\)
−0.272323 + 0.962206i \(0.587792\pi\)
\(864\) 5.00000 0.170103
\(865\) 6.00000 0.204006
\(866\) −2.00000 −0.0679628
\(867\) −19.0000 −0.645274
\(868\) 8.00000 0.271538
\(869\) 8.00000 0.271381
\(870\) 6.00000 0.203419
\(871\) 24.0000 0.813209
\(872\) −6.00000 −0.203186
\(873\) −14.0000 −0.473828
\(874\) 32.0000 1.08242
\(875\) −1.00000 −0.0338062
\(876\) −6.00000 −0.202721
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) −32.0000 −1.07995
\(879\) 18.0000 0.607125
\(880\) −1.00000 −0.0337100
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) −12.0000 −0.403604
\(885\) 12.0000 0.403376
\(886\) −12.0000 −0.403148
\(887\) −32.0000 −1.07445 −0.537227 0.843437i \(-0.680528\pi\)
−0.537227 + 0.843437i \(0.680528\pi\)
\(888\) −18.0000 −0.604040
\(889\) 0 0
\(890\) −10.0000 −0.335201
\(891\) 1.00000 0.0335013
\(892\) 8.00000 0.267860
\(893\) 32.0000 1.07084
\(894\) −18.0000 −0.602010
\(895\) 4.00000 0.133705
\(896\) −3.00000 −0.100223
\(897\) 16.0000 0.534224
\(898\) −2.00000 −0.0667409
\(899\) 48.0000 1.60089
\(900\) −1.00000 −0.0333333
\(901\) 60.0000 1.99889
\(902\) 6.00000 0.199778
\(903\) −4.00000 −0.133112
\(904\) −42.0000 −1.39690
\(905\) 6.00000 0.199447
\(906\) 16.0000 0.531564
\(907\) 44.0000 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) −12.0000 −0.398234
\(909\) 6.00000 0.199007
\(910\) −2.00000 −0.0662994
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) −4.00000 −0.132453
\(913\) −4.00000 −0.132381
\(914\) −18.0000 −0.595387
\(915\) 10.0000 0.330590
\(916\) 10.0000 0.330409
\(917\) 12.0000 0.396275
\(918\) −6.00000 −0.198030
\(919\) −32.0000 −1.05558 −0.527791 0.849374i \(-0.676980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(920\) 24.0000 0.791257
\(921\) −4.00000 −0.131804
\(922\) −14.0000 −0.461065
\(923\) 16.0000 0.526646
\(924\) −1.00000 −0.0328976
\(925\) 6.00000 0.197279
\(926\) −16.0000 −0.525793
\(927\) 16.0000 0.525509
\(928\) −30.0000 −0.984798
\(929\) −14.0000 −0.459325 −0.229663 0.973270i \(-0.573762\pi\)
−0.229663 + 0.973270i \(0.573762\pi\)
\(930\) 8.00000 0.262330
\(931\) −4.00000 −0.131095
\(932\) 22.0000 0.720634
\(933\) 16.0000 0.523816
\(934\) −28.0000 −0.916188
\(935\) −6.00000 −0.196221
\(936\) −6.00000 −0.196116
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) −12.0000 −0.391814
\(939\) −10.0000 −0.326338
\(940\) 8.00000 0.260931
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) −2.00000 −0.0651635
\(943\) −48.0000 −1.56310
\(944\) 12.0000 0.390567
\(945\) 1.00000 0.0325300
\(946\) 4.00000 0.130051
\(947\) −28.0000 −0.909878 −0.454939 0.890523i \(-0.650339\pi\)
−0.454939 + 0.890523i \(0.650339\pi\)
\(948\) 8.00000 0.259828
\(949\) 12.0000 0.389536
\(950\) 4.00000 0.129777
\(951\) 34.0000 1.10253
\(952\) 18.0000 0.583383
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 10.0000 0.323762
\(955\) 16.0000 0.517748
\(956\) 16.0000 0.517477
\(957\) −6.00000 −0.193952
\(958\) 16.0000 0.516937
\(959\) 22.0000 0.710417
\(960\) −7.00000 −0.225924
\(961\) 33.0000 1.06452
\(962\) 12.0000 0.386896
\(963\) −12.0000 −0.386695
\(964\) 22.0000 0.708572
\(965\) −22.0000 −0.708205
\(966\) −8.00000 −0.257396
\(967\) 56.0000 1.80084 0.900419 0.435023i \(-0.143260\pi\)
0.900419 + 0.435023i \(0.143260\pi\)
\(968\) 3.00000 0.0964237
\(969\) −24.0000 −0.770991
\(970\) 14.0000 0.449513
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) 1.00000 0.0320750
\(973\) −4.00000 −0.128234
\(974\) −24.0000 −0.769010
\(975\) 2.00000 0.0640513
\(976\) 10.0000 0.320092
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 20.0000 0.639529
\(979\) 10.0000 0.319601
\(980\) −1.00000 −0.0319438
\(981\) −2.00000 −0.0638551
\(982\) 20.0000 0.638226
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 18.0000 0.573819
\(985\) 22.0000 0.700978
\(986\) 36.0000 1.14647
\(987\) −8.00000 −0.254643
\(988\) −8.00000 −0.254514
\(989\) −32.0000 −1.01754
\(990\) −1.00000 −0.0317821
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) −40.0000 −1.27000
\(993\) −28.0000 −0.888553
\(994\) −8.00000 −0.253745
\(995\) 16.0000 0.507234
\(996\) −4.00000 −0.126745
\(997\) −10.0000 −0.316703 −0.158352 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 12.0000 0.379853
\(999\) −6.00000 −0.189832
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 \(a_p\))