Properties

Label 1155.2.a.c.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

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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

\(f(q)\) \(=\) \(q\)\(-2.00000 q^{2}\) \(+1.00000 q^{3}\) \(+2.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.00000 q^{2}\) \(+1.00000 q^{3}\) \(+2.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{9}\) \(-2.00000 q^{10}\) \(+1.00000 q^{11}\) \(+2.00000 q^{12}\) \(-6.00000 q^{13}\) \(-2.00000 q^{14}\) \(+1.00000 q^{15}\) \(-4.00000 q^{16}\) \(-7.00000 q^{17}\) \(-2.00000 q^{18}\) \(-5.00000 q^{19}\) \(+2.00000 q^{20}\) \(+1.00000 q^{21}\) \(-2.00000 q^{22}\) \(-1.00000 q^{23}\) \(+1.00000 q^{25}\) \(+12.0000 q^{26}\) \(+1.00000 q^{27}\) \(+2.00000 q^{28}\) \(-5.00000 q^{29}\) \(-2.00000 q^{30}\) \(-8.00000 q^{31}\) \(+8.00000 q^{32}\) \(+1.00000 q^{33}\) \(+14.0000 q^{34}\) \(+1.00000 q^{35}\) \(+2.00000 q^{36}\) \(-2.00000 q^{37}\) \(+10.0000 q^{38}\) \(-6.00000 q^{39}\) \(+12.0000 q^{41}\) \(-2.00000 q^{42}\) \(-11.0000 q^{43}\) \(+2.00000 q^{44}\) \(+1.00000 q^{45}\) \(+2.00000 q^{46}\) \(+8.00000 q^{47}\) \(-4.00000 q^{48}\) \(+1.00000 q^{49}\) \(-2.00000 q^{50}\) \(-7.00000 q^{51}\) \(-12.0000 q^{52}\) \(-11.0000 q^{53}\) \(-2.00000 q^{54}\) \(+1.00000 q^{55}\) \(-5.00000 q^{57}\) \(+10.0000 q^{58}\) \(-5.00000 q^{59}\) \(+2.00000 q^{60}\) \(+7.00000 q^{61}\) \(+16.0000 q^{62}\) \(+1.00000 q^{63}\) \(-8.00000 q^{64}\) \(-6.00000 q^{65}\) \(-2.00000 q^{66}\) \(-2.00000 q^{67}\) \(-14.0000 q^{68}\) \(-1.00000 q^{69}\) \(-2.00000 q^{70}\) \(+12.0000 q^{71}\) \(+4.00000 q^{73}\) \(+4.00000 q^{74}\) \(+1.00000 q^{75}\) \(-10.0000 q^{76}\) \(+1.00000 q^{77}\) \(+12.0000 q^{78}\) \(-10.0000 q^{79}\) \(-4.00000 q^{80}\) \(+1.00000 q^{81}\) \(-24.0000 q^{82}\) \(-1.00000 q^{83}\) \(+2.00000 q^{84}\) \(-7.00000 q^{85}\) \(+22.0000 q^{86}\) \(-5.00000 q^{87}\) \(+15.0000 q^{89}\) \(-2.00000 q^{90}\) \(-6.00000 q^{91}\) \(-2.00000 q^{92}\) \(-8.00000 q^{93}\) \(-16.0000 q^{94}\) \(-5.00000 q^{95}\) \(+8.00000 q^{96}\) \(+3.00000 q^{97}\) \(-2.00000 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.00000 1.00000
\(5\) 1.00000 0.447214
\(6\) −2.00000 −0.816497
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) 1.00000 0.301511
\(12\) 2.00000 0.577350
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 0.258199
\(16\) −4.00000 −1.00000
\(17\) −7.00000 −1.69775 −0.848875 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) −2.00000 −0.471405
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 2.00000 0.447214
\(21\) 1.00000 0.218218
\(22\) −2.00000 −0.426401
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 12.0000 2.35339
\(27\) 1.00000 0.192450
\(28\) 2.00000 0.377964
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −2.00000 −0.365148
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 8.00000 1.41421
\(33\) 1.00000 0.174078
\(34\) 14.0000 2.40098
\(35\) 1.00000 0.169031
\(36\) 2.00000 0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 10.0000 1.62221
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −2.00000 −0.308607
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 2.00000 0.301511
\(45\) 1.00000 0.149071
\(46\) 2.00000 0.294884
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −4.00000 −0.577350
\(49\) 1.00000 0.142857
\(50\) −2.00000 −0.282843
\(51\) −7.00000 −0.980196
\(52\) −12.0000 −1.66410
\(53\) −11.0000 −1.51097 −0.755483 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) −2.00000 −0.272166
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −5.00000 −0.662266
\(58\) 10.0000 1.31306
\(59\) −5.00000 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) 2.00000 0.258199
\(61\) 7.00000 0.896258 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) 16.0000 2.03200
\(63\) 1.00000 0.125988
\(64\) −8.00000 −1.00000
\(65\) −6.00000 −0.744208
\(66\) −2.00000 −0.246183
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −14.0000 −1.69775
\(69\) −1.00000 −0.120386
\(70\) −2.00000 −0.239046
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 4.00000 0.464991
\(75\) 1.00000 0.115470
\(76\) −10.0000 −1.14708
\(77\) 1.00000 0.113961
\(78\) 12.0000 1.35873
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −4.00000 −0.447214
\(81\) 1.00000 0.111111
\(82\) −24.0000 −2.65036
\(83\) −1.00000 −0.109764 −0.0548821 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) 2.00000 0.218218
\(85\) −7.00000 −0.759257
\(86\) 22.0000 2.37232
\(87\) −5.00000 −0.536056
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) −2.00000 −0.210819
\(91\) −6.00000 −0.628971
\(92\) −2.00000 −0.208514
\(93\) −8.00000 −0.829561
\(94\) −16.0000 −1.65027
\(95\) −5.00000 −0.512989
\(96\) 8.00000 0.816497
\(97\) 3.00000 0.304604 0.152302 0.988334i \(-0.451331\pi\)
0.152302 + 0.988334i \(0.451331\pi\)
\(98\) −2.00000 −0.202031
\(99\) 1.00000 0.100504
\(100\) 2.00000 0.200000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 14.0000 1.38621
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 0 0
\(105\) 1.00000 0.0975900
\(106\) 22.0000 2.13683
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 2.00000 0.192450
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −2.00000 −0.190693
\(111\) −2.00000 −0.189832
\(112\) −4.00000 −0.377964
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 10.0000 0.936586
\(115\) −1.00000 −0.0932505
\(116\) −10.0000 −0.928477
\(117\) −6.00000 −0.554700
\(118\) 10.0000 0.920575
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −14.0000 −1.26750
\(123\) 12.0000 1.08200
\(124\) −16.0000 −1.43684
\(125\) 1.00000 0.0894427
\(126\) −2.00000 −0.178174
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0 0
\(129\) −11.0000 −0.968496
\(130\) 12.0000 1.05247
\(131\) 2.00000 0.174741 0.0873704 0.996176i \(-0.472154\pi\)
0.0873704 + 0.996176i \(0.472154\pi\)
\(132\) 2.00000 0.174078
\(133\) −5.00000 −0.433555
\(134\) 4.00000 0.345547
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) −22.0000 −1.87959 −0.939793 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 2.00000 0.170251
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 2.00000 0.169031
\(141\) 8.00000 0.673722
\(142\) −24.0000 −2.01404
\(143\) −6.00000 −0.501745
\(144\) −4.00000 −0.333333
\(145\) −5.00000 −0.415227
\(146\) −8.00000 −0.662085
\(147\) 1.00000 0.0824786
\(148\) −4.00000 −0.328798
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −2.00000 −0.163299
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) −7.00000 −0.565916
\(154\) −2.00000 −0.161165
\(155\) −8.00000 −0.642575
\(156\) −12.0000 −0.960769
\(157\) −17.0000 −1.35675 −0.678374 0.734717i \(-0.737315\pi\)
−0.678374 + 0.734717i \(0.737315\pi\)
\(158\) 20.0000 1.59111
\(159\) −11.0000 −0.872357
\(160\) 8.00000 0.632456
\(161\) −1.00000 −0.0788110
\(162\) −2.00000 −0.157135
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) 24.0000 1.87409
\(165\) 1.00000 0.0778499
\(166\) 2.00000 0.155230
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 14.0000 1.07375
\(171\) −5.00000 −0.382360
\(172\) −22.0000 −1.67748
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 10.0000 0.758098
\(175\) 1.00000 0.0755929
\(176\) −4.00000 −0.301511
\(177\) −5.00000 −0.375823
\(178\) −30.0000 −2.24860
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 2.00000 0.149071
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 12.0000 0.889499
\(183\) 7.00000 0.517455
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) 16.0000 1.17318
\(187\) −7.00000 −0.511891
\(188\) 16.0000 1.16692
\(189\) 1.00000 0.0727393
\(190\) 10.0000 0.725476
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −8.00000 −0.577350
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −6.00000 −0.430775
\(195\) −6.00000 −0.429669
\(196\) 2.00000 0.142857
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) −2.00000 −0.142134
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) −2.00000 −0.141069
\(202\) −4.00000 −0.281439
\(203\) −5.00000 −0.350931
\(204\) −14.0000 −0.980196
\(205\) 12.0000 0.838116
\(206\) 2.00000 0.139347
\(207\) −1.00000 −0.0695048
\(208\) 24.0000 1.66410
\(209\) −5.00000 −0.345857
\(210\) −2.00000 −0.138013
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) −22.0000 −1.51097
\(213\) 12.0000 0.822226
\(214\) 24.0000 1.64061
\(215\) −11.0000 −0.750194
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 0 0
\(219\) 4.00000 0.270295
\(220\) 2.00000 0.134840
\(221\) 42.0000 2.82523
\(222\) 4.00000 0.268462
\(223\) 9.00000 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) 8.00000 0.534522
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) 23.0000 1.52656 0.763282 0.646066i \(-0.223587\pi\)
0.763282 + 0.646066i \(0.223587\pi\)
\(228\) −10.0000 −0.662266
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 2.00000 0.131876
\(231\) 1.00000 0.0657952
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 12.0000 0.784465
\(235\) 8.00000 0.521862
\(236\) −10.0000 −0.650945
\(237\) −10.0000 −0.649570
\(238\) 14.0000 0.907485
\(239\) 5.00000 0.323423 0.161712 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) −4.00000 −0.258199
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) −2.00000 −0.128565
\(243\) 1.00000 0.0641500
\(244\) 14.0000 0.896258
\(245\) 1.00000 0.0638877
\(246\) −24.0000 −1.53018
\(247\) 30.0000 1.90885
\(248\) 0 0
\(249\) −1.00000 −0.0633724
\(250\) −2.00000 −0.126491
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 2.00000 0.125988
\(253\) −1.00000 −0.0628695
\(254\) 14.0000 0.878438
\(255\) −7.00000 −0.438357
\(256\) 16.0000 1.00000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 22.0000 1.36966
\(259\) −2.00000 −0.124274
\(260\) −12.0000 −0.744208
\(261\) −5.00000 −0.309492
\(262\) −4.00000 −0.247121
\(263\) 4.00000 0.246651 0.123325 0.992366i \(-0.460644\pi\)
0.123325 + 0.992366i \(0.460644\pi\)
\(264\) 0 0
\(265\) −11.0000 −0.675725
\(266\) 10.0000 0.613139
\(267\) 15.0000 0.917985
\(268\) −4.00000 −0.244339
\(269\) −25.0000 −1.52428 −0.762138 0.647414i \(-0.775850\pi\)
−0.762138 + 0.647414i \(0.775850\pi\)
\(270\) −2.00000 −0.121716
\(271\) −3.00000 −0.182237 −0.0911185 0.995840i \(-0.529044\pi\)
−0.0911185 + 0.995840i \(0.529044\pi\)
\(272\) 28.0000 1.69775
\(273\) −6.00000 −0.363137
\(274\) 44.0000 2.65814
\(275\) 1.00000 0.0603023
\(276\) −2.00000 −0.120386
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 0 0
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −16.0000 −0.952786
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 24.0000 1.42414
\(285\) −5.00000 −0.296174
\(286\) 12.0000 0.709575
\(287\) 12.0000 0.708338
\(288\) 8.00000 0.471405
\(289\) 32.0000 1.88235
\(290\) 10.0000 0.587220
\(291\) 3.00000 0.175863
\(292\) 8.00000 0.468165
\(293\) 29.0000 1.69420 0.847099 0.531435i \(-0.178347\pi\)
0.847099 + 0.531435i \(0.178347\pi\)
\(294\) −2.00000 −0.116642
\(295\) −5.00000 −0.291111
\(296\) 0 0
\(297\) 1.00000 0.0580259
\(298\) 20.0000 1.15857
\(299\) 6.00000 0.346989
\(300\) 2.00000 0.115470
\(301\) −11.0000 −0.634029
\(302\) −4.00000 −0.230174
\(303\) 2.00000 0.114897
\(304\) 20.0000 1.14708
\(305\) 7.00000 0.400819
\(306\) 14.0000 0.800327
\(307\) 18.0000 1.02731 0.513657 0.857996i \(-0.328290\pi\)
0.513657 + 0.857996i \(0.328290\pi\)
\(308\) 2.00000 0.113961
\(309\) −1.00000 −0.0568880
\(310\) 16.0000 0.908739
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −31.0000 −1.75222 −0.876112 0.482108i \(-0.839871\pi\)
−0.876112 + 0.482108i \(0.839871\pi\)
\(314\) 34.0000 1.91873
\(315\) 1.00000 0.0563436
\(316\) −20.0000 −1.12509
\(317\) −22.0000 −1.23564 −0.617822 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) 22.0000 1.23370
\(319\) −5.00000 −0.279946
\(320\) −8.00000 −0.447214
\(321\) −12.0000 −0.669775
\(322\) 2.00000 0.111456
\(323\) 35.0000 1.94745
\(324\) 2.00000 0.111111
\(325\) −6.00000 −0.332820
\(326\) 12.0000 0.664619
\(327\) 0 0
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) −2.00000 −0.110096
\(331\) −3.00000 −0.164895 −0.0824475 0.996595i \(-0.526274\pi\)
−0.0824475 + 0.996595i \(0.526274\pi\)
\(332\) −2.00000 −0.109764
\(333\) −2.00000 −0.109599
\(334\) −16.0000 −0.875481
\(335\) −2.00000 −0.109272
\(336\) −4.00000 −0.218218
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) −46.0000 −2.50207
\(339\) 9.00000 0.488813
\(340\) −14.0000 −0.759257
\(341\) −8.00000 −0.433224
\(342\) 10.0000 0.540738
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −1.00000 −0.0538382
\(346\) 12.0000 0.645124
\(347\) −32.0000 −1.71785 −0.858925 0.512101i \(-0.828867\pi\)
−0.858925 + 0.512101i \(0.828867\pi\)
\(348\) −10.0000 −0.536056
\(349\) −25.0000 −1.33822 −0.669110 0.743164i \(-0.733324\pi\)
−0.669110 + 0.743164i \(0.733324\pi\)
\(350\) −2.00000 −0.106904
\(351\) −6.00000 −0.320256
\(352\) 8.00000 0.426401
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 10.0000 0.531494
\(355\) 12.0000 0.636894
\(356\) 30.0000 1.59000
\(357\) −7.00000 −0.370479
\(358\) 0 0
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −44.0000 −2.31259
\(363\) 1.00000 0.0524864
\(364\) −12.0000 −0.628971
\(365\) 4.00000 0.209370
\(366\) −14.0000 −0.731792
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 4.00000 0.208514
\(369\) 12.0000 0.624695
\(370\) 4.00000 0.207950
\(371\) −11.0000 −0.571092
\(372\) −16.0000 −0.829561
\(373\) 29.0000 1.50156 0.750782 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) 14.0000 0.723923
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) 30.0000 1.54508
\(378\) −2.00000 −0.102869
\(379\) 5.00000 0.256833 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(380\) −10.0000 −0.512989
\(381\) −7.00000 −0.358621
\(382\) 16.0000 0.818631
\(383\) 34.0000 1.73732 0.868659 0.495410i \(-0.164982\pi\)
0.868659 + 0.495410i \(0.164982\pi\)
\(384\) 0 0
\(385\) 1.00000 0.0509647
\(386\) 12.0000 0.610784
\(387\) −11.0000 −0.559161
\(388\) 6.00000 0.304604
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 12.0000 0.607644
\(391\) 7.00000 0.354005
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 24.0000 1.20910
\(395\) −10.0000 −0.503155
\(396\) 2.00000 0.100504
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) −40.0000 −2.00502
\(399\) −5.00000 −0.250313
\(400\) −4.00000 −0.200000
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 4.00000 0.199502
\(403\) 48.0000 2.39105
\(404\) 4.00000 0.199007
\(405\) 1.00000 0.0496904
\(406\) 10.0000 0.496292
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −24.0000 −1.18528
\(411\) −22.0000 −1.08518
\(412\) −2.00000 −0.0985329
\(413\) −5.00000 −0.246034
\(414\) 2.00000 0.0982946
\(415\) −1.00000 −0.0490881
\(416\) −48.0000 −2.35339
\(417\) 0 0
\(418\) 10.0000 0.489116
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 2.00000 0.0975900
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) −44.0000 −2.14189
\(423\) 8.00000 0.388973
\(424\) 0 0
\(425\) −7.00000 −0.339550
\(426\) −24.0000 −1.16280
\(427\) 7.00000 0.338754
\(428\) −24.0000 −1.16008
\(429\) −6.00000 −0.289683
\(430\) 22.0000 1.06093
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) −4.00000 −0.192450
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 16.0000 0.768025
\(435\) −5.00000 −0.239732
\(436\) 0 0
\(437\) 5.00000 0.239182
\(438\) −8.00000 −0.382255
\(439\) −5.00000 −0.238637 −0.119318 0.992856i \(-0.538071\pi\)
−0.119318 + 0.992856i \(0.538071\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) −84.0000 −3.99547
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) −4.00000 −0.189832
\(445\) 15.0000 0.711068
\(446\) −18.0000 −0.852325
\(447\) −10.0000 −0.472984
\(448\) −8.00000 −0.377964
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) −2.00000 −0.0942809
\(451\) 12.0000 0.565058
\(452\) 18.0000 0.846649
\(453\) 2.00000 0.0939682
\(454\) −46.0000 −2.15889
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) 33.0000 1.54367 0.771837 0.635820i \(-0.219338\pi\)
0.771837 + 0.635820i \(0.219338\pi\)
\(458\) 40.0000 1.86908
\(459\) −7.00000 −0.326732
\(460\) −2.00000 −0.0932505
\(461\) −38.0000 −1.76984 −0.884918 0.465746i \(-0.845786\pi\)
−0.884918 + 0.465746i \(0.845786\pi\)
\(462\) −2.00000 −0.0930484
\(463\) −6.00000 −0.278844 −0.139422 0.990233i \(-0.544524\pi\)
−0.139422 + 0.990233i \(0.544524\pi\)
\(464\) 20.0000 0.928477
\(465\) −8.00000 −0.370991
\(466\) 12.0000 0.555889
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) −12.0000 −0.554700
\(469\) −2.00000 −0.0923514
\(470\) −16.0000 −0.738025
\(471\) −17.0000 −0.783319
\(472\) 0 0
\(473\) −11.0000 −0.505781
\(474\) 20.0000 0.918630
\(475\) −5.00000 −0.229416
\(476\) −14.0000 −0.641689
\(477\) −11.0000 −0.503655
\(478\) −10.0000 −0.457389
\(479\) −10.0000 −0.456912 −0.228456 0.973554i \(-0.573368\pi\)
−0.228456 + 0.973554i \(0.573368\pi\)
\(480\) 8.00000 0.365148
\(481\) 12.0000 0.547153
\(482\) 36.0000 1.63976
\(483\) −1.00000 −0.0455016
\(484\) 2.00000 0.0909091
\(485\) 3.00000 0.136223
\(486\) −2.00000 −0.0907218
\(487\) −22.0000 −0.996915 −0.498458 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 0 0
\(489\) −6.00000 −0.271329
\(490\) −2.00000 −0.0903508
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) 24.0000 1.08200
\(493\) 35.0000 1.57632
\(494\) −60.0000 −2.69953
\(495\) 1.00000 0.0449467
\(496\) 32.0000 1.43684
\(497\) 12.0000 0.538274
\(498\) 2.00000 0.0896221
\(499\) −25.0000 −1.11915 −0.559577 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) 2.00000 0.0894427
\(501\) 8.00000 0.357414
\(502\) −24.0000 −1.07117
\(503\) −11.0000 −0.490466 −0.245233 0.969464i \(-0.578864\pi\)
−0.245233 + 0.969464i \(0.578864\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 2.00000 0.0889108
\(507\) 23.0000 1.02147
\(508\) −14.0000 −0.621150
\(509\) −35.0000 −1.55135 −0.775674 0.631134i \(-0.782590\pi\)
−0.775674 + 0.631134i \(0.782590\pi\)
\(510\) 14.0000 0.619930
\(511\) 4.00000 0.176950
\(512\) −32.0000 −1.41421
\(513\) −5.00000 −0.220755
\(514\) −36.0000 −1.58789
\(515\) −1.00000 −0.0440653
\(516\) −22.0000 −0.968496
\(517\) 8.00000 0.351840
\(518\) 4.00000 0.175750
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −23.0000 −1.00765 −0.503824 0.863806i \(-0.668074\pi\)
−0.503824 + 0.863806i \(0.668074\pi\)
\(522\) 10.0000 0.437688
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 4.00000 0.174741
\(525\) 1.00000 0.0436436
\(526\) −8.00000 −0.348817
\(527\) 56.0000 2.43940
\(528\) −4.00000 −0.174078
\(529\) −22.0000 −0.956522
\(530\) 22.0000 0.955619
\(531\) −5.00000 −0.216982
\(532\) −10.0000 −0.433555
\(533\) −72.0000 −3.11867
\(534\) −30.0000 −1.29823
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) 0 0
\(538\) 50.0000 2.15565
\(539\) 1.00000 0.0430730
\(540\) 2.00000 0.0860663
\(541\) 12.0000 0.515920 0.257960 0.966156i \(-0.416950\pi\)
0.257960 + 0.966156i \(0.416950\pi\)
\(542\) 6.00000 0.257722
\(543\) 22.0000 0.944110
\(544\) −56.0000 −2.40098
\(545\) 0 0
\(546\) 12.0000 0.513553
\(547\) 3.00000 0.128271 0.0641354 0.997941i \(-0.479571\pi\)
0.0641354 + 0.997941i \(0.479571\pi\)
\(548\) −44.0000 −1.87959
\(549\) 7.00000 0.298753
\(550\) −2.00000 −0.0852803
\(551\) 25.0000 1.06504
\(552\) 0 0
\(553\) −10.0000 −0.425243
\(554\) 44.0000 1.86938
\(555\) −2.00000 −0.0848953
\(556\) 0 0
\(557\) 38.0000 1.61011 0.805056 0.593199i \(-0.202135\pi\)
0.805056 + 0.593199i \(0.202135\pi\)
\(558\) 16.0000 0.677334
\(559\) 66.0000 2.79150
\(560\) −4.00000 −0.169031
\(561\) −7.00000 −0.295540
\(562\) 36.0000 1.51857
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) 16.0000 0.673722
\(565\) 9.00000 0.378633
\(566\) −28.0000 −1.17693
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) 15.0000 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) 10.0000 0.418854
\(571\) −18.0000 −0.753277 −0.376638 0.926360i \(-0.622920\pi\)
−0.376638 + 0.926360i \(0.622920\pi\)
\(572\) −12.0000 −0.501745
\(573\) −8.00000 −0.334205
\(574\) −24.0000 −1.00174
\(575\) −1.00000 −0.0417029
\(576\) −8.00000 −0.333333
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −64.0000 −2.66205
\(579\) −6.00000 −0.249351
\(580\) −10.0000 −0.415227
\(581\) −1.00000 −0.0414870
\(582\) −6.00000 −0.248708
\(583\) −11.0000 −0.455573
\(584\) 0 0
\(585\) −6.00000 −0.248069
\(586\) −58.0000 −2.39596
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 2.00000 0.0824786
\(589\) 40.0000 1.64817
\(590\) 10.0000 0.411693
\(591\) −12.0000 −0.493614
\(592\) 8.00000 0.328798
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) −2.00000 −0.0820610
\(595\) −7.00000 −0.286972
\(596\) −20.0000 −0.819232
\(597\) 20.0000 0.818546
\(598\) −12.0000 −0.490716
\(599\) −10.0000 −0.408589 −0.204294 0.978909i \(-0.565490\pi\)
−0.204294 + 0.978909i \(0.565490\pi\)
\(600\) 0 0
\(601\) −3.00000 −0.122373 −0.0611863 0.998126i \(-0.519488\pi\)
−0.0611863 + 0.998126i \(0.519488\pi\)
\(602\) 22.0000 0.896653
\(603\) −2.00000 −0.0814463
\(604\) 4.00000 0.162758
\(605\) 1.00000 0.0406558
\(606\) −4.00000 −0.162489
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −40.0000 −1.62221
\(609\) −5.00000 −0.202610
\(610\) −14.0000 −0.566843
\(611\) −48.0000 −1.94187
\(612\) −14.0000 −0.565916
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) −36.0000 −1.45284
\(615\) 12.0000 0.483887
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 2.00000 0.0804518
\(619\) 30.0000 1.20580 0.602901 0.797816i \(-0.294011\pi\)
0.602901 + 0.797816i \(0.294011\pi\)
\(620\) −16.0000 −0.642575
\(621\) −1.00000 −0.0401286
\(622\) −24.0000 −0.962312
\(623\) 15.0000 0.600962
\(624\) 24.0000 0.960769
\(625\) 1.00000 0.0400000
\(626\) 62.0000 2.47802
\(627\) −5.00000 −0.199681
\(628\) −34.0000 −1.35675
\(629\) 14.0000 0.558217
\(630\) −2.00000 −0.0796819
\(631\) −3.00000 −0.119428 −0.0597141 0.998216i \(-0.519019\pi\)
−0.0597141 + 0.998216i \(0.519019\pi\)
\(632\) 0 0
\(633\) 22.0000 0.874421
\(634\) 44.0000 1.74746
\(635\) −7.00000 −0.277787
\(636\) −22.0000 −0.872357
\(637\) −6.00000 −0.237729
\(638\) 10.0000 0.395904
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 24.0000 0.947204
\(643\) 19.0000 0.749287 0.374643 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) −2.00000 −0.0788110
\(645\) −11.0000 −0.433125
\(646\) −70.0000 −2.75411
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) 0 0
\(649\) −5.00000 −0.196267
\(650\) 12.0000 0.470679
\(651\) −8.00000 −0.313545
\(652\) −12.0000 −0.469956
\(653\) −1.00000 −0.0391330 −0.0195665 0.999809i \(-0.506229\pi\)
−0.0195665 + 0.999809i \(0.506229\pi\)
\(654\) 0 0
\(655\) 2.00000 0.0781465
\(656\) −48.0000 −1.87409
\(657\) 4.00000 0.156055
\(658\) −16.0000 −0.623745
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 2.00000 0.0778499
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 6.00000 0.233197
\(663\) 42.0000 1.63114
\(664\) 0 0
\(665\) −5.00000 −0.193892
\(666\) 4.00000 0.154997
\(667\) 5.00000 0.193601
\(668\) 16.0000 0.619059
\(669\) 9.00000 0.347960
\(670\) 4.00000 0.154533
\(671\) 7.00000 0.270232
\(672\) 8.00000 0.308607
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) −26.0000 −1.00148
\(675\) 1.00000 0.0384900
\(676\) 46.0000 1.76923
\(677\) 13.0000 0.499631 0.249815 0.968294i \(-0.419630\pi\)
0.249815 + 0.968294i \(0.419630\pi\)
\(678\) −18.0000 −0.691286
\(679\) 3.00000 0.115129
\(680\) 0 0
\(681\) 23.0000 0.881362
\(682\) 16.0000 0.612672
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −10.0000 −0.382360
\(685\) −22.0000 −0.840577
\(686\) −2.00000 −0.0763604
\(687\) −20.0000 −0.763048
\(688\) 44.0000 1.67748
\(689\) 66.0000 2.51440
\(690\) 2.00000 0.0761387
\(691\) 42.0000 1.59776 0.798878 0.601494i \(-0.205427\pi\)
0.798878 + 0.601494i \(0.205427\pi\)
\(692\) −12.0000 −0.456172
\(693\) 1.00000 0.0379869
\(694\) 64.0000 2.42941
\(695\) 0 0
\(696\) 0 0
\(697\) −84.0000 −3.18173
\(698\) 50.0000 1.89253
\(699\) −6.00000 −0.226941
\(700\) 2.00000 0.0755929
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 12.0000 0.452911
\(703\) 10.0000 0.377157
\(704\) −8.00000 −0.301511
\(705\) 8.00000 0.301297
\(706\) 12.0000 0.451626
\(707\) 2.00000 0.0752177
\(708\) −10.0000 −0.375823
\(709\) −35.0000 −1.31445 −0.657226 0.753693i \(-0.728270\pi\)
−0.657226 + 0.753693i \(0.728270\pi\)
\(710\) −24.0000 −0.900704
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 14.0000 0.523937
\(715\) −6.00000 −0.224387
\(716\) 0 0
\(717\) 5.00000 0.186728
\(718\) 30.0000 1.11959
\(719\) −25.0000 −0.932343 −0.466171 0.884694i \(-0.654367\pi\)
−0.466171 + 0.884694i \(0.654367\pi\)
\(720\) −4.00000 −0.149071
\(721\) −1.00000 −0.0372419
\(722\) −12.0000 −0.446594
\(723\) −18.0000 −0.669427
\(724\) 44.0000 1.63525
\(725\) −5.00000 −0.185695
\(726\) −2.00000 −0.0742270
\(727\) −47.0000 −1.74313 −0.871567 0.490277i \(-0.836896\pi\)
−0.871567 + 0.490277i \(0.836896\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −8.00000 −0.296093
\(731\) 77.0000 2.84795
\(732\) 14.0000 0.517455
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 34.0000 1.25496
\(735\) 1.00000 0.0368856
\(736\) −8.00000 −0.294884
\(737\) −2.00000 −0.0736709
\(738\) −24.0000 −0.883452
\(739\) −10.0000 −0.367856 −0.183928 0.982940i \(-0.558881\pi\)
−0.183928 + 0.982940i \(0.558881\pi\)
\(740\) −4.00000 −0.147043
\(741\) 30.0000 1.10208
\(742\) 22.0000 0.807645
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) −58.0000 −2.12353
\(747\) −1.00000 −0.0365881
\(748\) −14.0000 −0.511891
\(749\) −12.0000 −0.438470
\(750\) −2.00000 −0.0730297
\(751\) 17.0000 0.620339 0.310169 0.950681i \(-0.399614\pi\)
0.310169 + 0.950681i \(0.399614\pi\)
\(752\) −32.0000 −1.16692
\(753\) 12.0000 0.437304
\(754\) −60.0000 −2.18507
\(755\) 2.00000 0.0727875
\(756\) 2.00000 0.0727393
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −10.0000 −0.363216
\(759\) −1.00000 −0.0362977
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 14.0000 0.507166
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) −7.00000 −0.253086
\(766\) −68.0000 −2.45694
\(767\) 30.0000 1.08324
\(768\) 16.0000 0.577350
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) −2.00000 −0.0720750
\(771\) 18.0000 0.648254
\(772\) −12.0000 −0.431889
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 22.0000 0.790774
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) −2.00000 −0.0717496
\(778\) −60.0000 −2.15110
\(779\) −60.0000 −2.14972
\(780\) −12.0000 −0.429669
\(781\) 12.0000 0.429394
\(782\) −14.0000 −0.500639
\(783\) −5.00000 −0.178685
\(784\) −4.00000 −0.142857
\(785\) −17.0000 −0.606756
\(786\) −4.00000 −0.142675
\(787\) 28.0000 0.998092 0.499046 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) −24.0000 −0.854965
\(789\) 4.00000 0.142404
\(790\) 20.0000 0.711568
\(791\) 9.00000 0.320003
\(792\) 0 0
\(793\) −42.0000 −1.49146
\(794\) −76.0000 −2.69714
\(795\) −11.0000 −0.390130
\(796\) 40.0000 1.41776
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 10.0000 0.353996
\(799\) −56.0000 −1.98114
\(800\) 8.00000 0.282843
\(801\) 15.0000 0.529999
\(802\) −24.0000 −0.847469
\(803\) 4.00000 0.141157
\(804\) −4.00000 −0.141069
\(805\) −1.00000 −0.0352454
\(806\) −96.0000 −3.38146
\(807\) −25.0000 −0.880042
\(808\) 0 0
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) −2.00000 −0.0702728
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) −10.0000 −0.350931
\(813\) −3.00000 −0.105215
\(814\) 4.00000 0.140200
\(815\) −6.00000 −0.210171
\(816\) 28.0000 0.980196
\(817\) 55.0000 1.92421
\(818\) 20.0000 0.699284
\(819\) −6.00000 −0.209657
\(820\) 24.0000 0.838116
\(821\) −3.00000 −0.104701 −0.0523504 0.998629i \(-0.516671\pi\)
−0.0523504 + 0.998629i \(0.516671\pi\)
\(822\) 44.0000 1.53468
\(823\) 14.0000 0.488009 0.244005 0.969774i \(-0.421539\pi\)
0.244005 + 0.969774i \(0.421539\pi\)
\(824\) 0 0
\(825\) 1.00000 0.0348155
\(826\) 10.0000 0.347945
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) −2.00000 −0.0695048
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) 2.00000 0.0694210
\(831\) −22.0000 −0.763172
\(832\) 48.0000 1.66410
\(833\) −7.00000 −0.242536
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) −10.0000 −0.345857
\(837\) −8.00000 −0.276520
\(838\) 30.0000 1.03633
\(839\) 15.0000 0.517858 0.258929 0.965896i \(-0.416631\pi\)
0.258929 + 0.965896i \(0.416631\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 46.0000 1.58526
\(843\) −18.0000 −0.619953
\(844\) 44.0000 1.51454
\(845\) 23.0000 0.791224
\(846\) −16.0000 −0.550091
\(847\) 1.00000 0.0343604
\(848\) 44.0000 1.51097
\(849\) 14.0000 0.480479
\(850\) 14.0000 0.480196
\(851\) 2.00000 0.0685591
\(852\) 24.0000 0.822226
\(853\) −36.0000 −1.23262 −0.616308 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(854\) −14.0000 −0.479070
\(855\) −5.00000 −0.170996
\(856\) 0 0
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 12.0000 0.409673
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) −22.0000 −0.750194
\(861\) 12.0000 0.408959
\(862\) 16.0000 0.544962
\(863\) 39.0000 1.32758 0.663788 0.747921i \(-0.268948\pi\)
0.663788 + 0.747921i \(0.268948\pi\)
\(864\) 8.00000 0.272166
\(865\) −6.00000 −0.204006
\(866\) 52.0000 1.76703
\(867\) 32.0000 1.08678
\(868\) −16.0000 −0.543075
\(869\) −10.0000 −0.339227
\(870\) 10.0000 0.339032
\(871\) 12.0000 0.406604
\(872\) 0 0
\(873\) 3.00000 0.101535
\(874\) −10.0000 −0.338255
\(875\) 1.00000 0.0338062
\(876\) 8.00000 0.270295
\(877\) 23.0000 0.776655 0.388327 0.921521i \(-0.373053\pi\)
0.388327 + 0.921521i \(0.373053\pi\)
\(878\) 10.0000 0.337484
\(879\) 29.0000 0.978146
\(880\) −4.00000 −0.134840
\(881\) −33.0000 −1.11180 −0.555899 0.831250i \(-0.687626\pi\)
−0.555899 + 0.831250i \(0.687626\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 84.0000 2.82523
\(885\) −5.00000 −0.168073
\(886\) 72.0000 2.41889
\(887\) 43.0000 1.44380 0.721899 0.691998i \(-0.243269\pi\)
0.721899 + 0.691998i \(0.243269\pi\)
\(888\) 0 0
\(889\) −7.00000 −0.234772
\(890\) −30.0000 −1.00560
\(891\) 1.00000 0.0335013
\(892\) 18.0000 0.602685
\(893\) −40.0000 −1.33855
\(894\) 20.0000 0.668900
\(895\) 0 0
\(896\) 0 0
\(897\) 6.00000 0.200334
\(898\) 0 0
\(899\) 40.0000 1.33407
\(900\) 2.00000 0.0666667
\(901\) 77.0000 2.56524
\(902\) −24.0000 −0.799113
\(903\) −11.0000 −0.366057
\(904\) 0 0
\(905\) 22.0000 0.731305
\(906\) −4.00000 −0.132891
\(907\) −2.00000 −0.0664089 −0.0332045 0.999449i \(-0.510571\pi\)
−0.0332045 + 0.999449i \(0.510571\pi\)
\(908\) 46.0000 1.52656
\(909\) 2.00000 0.0663358
\(910\) 12.0000 0.397796
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 20.0000 0.662266
\(913\) −1.00000 −0.0330952
\(914\) −66.0000 −2.18309
\(915\) 7.00000 0.231413
\(916\) −40.0000 −1.32164
\(917\) 2.00000 0.0660458
\(918\) 14.0000 0.462069
\(919\) 30.0000 0.989609 0.494804 0.869004i \(-0.335240\pi\)
0.494804 + 0.869004i \(0.335240\pi\)
\(920\) 0 0
\(921\) 18.0000 0.593120
\(922\) 76.0000 2.50293
\(923\) −72.0000 −2.36991
\(924\) 2.00000 0.0657952
\(925\) −2.00000 −0.0657596
\(926\) 12.0000 0.394344
\(927\) −1.00000 −0.0328443
\(928\) −40.0000 −1.31306
\(929\) −50.0000 −1.64045 −0.820223 0.572043i \(-0.806151\pi\)
−0.820223 + 0.572043i \(0.806151\pi\)
\(930\) 16.0000 0.524661
\(931\) −5.00000 −0.163868
\(932\) −12.0000 −0.393073
\(933\) 12.0000 0.392862
\(934\) −56.0000 −1.83238
\(935\) −7.00000 −0.228924
\(936\) 0 0
\(937\) 28.0000 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(938\) 4.00000 0.130605
\(939\) −31.0000 −1.01165
\(940\) 16.0000 0.521862
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) 34.0000 1.10778
\(943\) −12.0000 −0.390774
\(944\) 20.0000 0.650945
\(945\) 1.00000 0.0325300
\(946\) 22.0000 0.715282
\(947\) 23.0000 0.747400 0.373700 0.927550i \(-0.378089\pi\)
0.373700 + 0.927550i \(0.378089\pi\)
\(948\) −20.0000 −0.649570
\(949\) −24.0000 −0.779073
\(950\) 10.0000 0.324443
\(951\) −22.0000 −0.713399
\(952\) 0 0
\(953\) 34.0000 1.10137 0.550684 0.834714i \(-0.314367\pi\)
0.550684 + 0.834714i \(0.314367\pi\)
\(954\) 22.0000 0.712276
\(955\) −8.00000 −0.258874
\(956\) 10.0000 0.323423
\(957\) −5.00000 −0.161627
\(958\) 20.0000 0.646171
\(959\) −22.0000 −0.710417
\(960\) −8.00000 −0.258199
\(961\) 33.0000 1.06452
\(962\) −24.0000 −0.773791
\(963\) −12.0000 −0.386695
\(964\) −36.0000 −1.15948
\(965\) −6.00000 −0.193147
\(966\) 2.00000 0.0643489
\(967\) −47.0000 −1.51142 −0.755709 0.654907i \(-0.772708\pi\)
−0.755709 + 0.654907i \(0.772708\pi\)
\(968\) 0 0
\(969\) 35.0000 1.12436
\(970\) −6.00000 −0.192648
\(971\) −13.0000 −0.417190 −0.208595 0.978002i \(-0.566889\pi\)
−0.208595 + 0.978002i \(0.566889\pi\)
\(972\) 2.00000 0.0641500
\(973\) 0 0
\(974\) 44.0000 1.40985
\(975\) −6.00000 −0.192154
\(976\) −28.0000 −0.896258
\(977\) −7.00000 −0.223950 −0.111975 0.993711i \(-0.535718\pi\)
−0.111975 + 0.993711i \(0.535718\pi\)
\(978\) 12.0000 0.383718
\(979\) 15.0000 0.479402
\(980\) 2.00000 0.0638877
\(981\) 0 0
\(982\) −54.0000 −1.72321
\(983\) 14.0000 0.446531 0.223265 0.974758i \(-0.428328\pi\)
0.223265 + 0.974758i \(0.428328\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) −70.0000 −2.22925
\(987\) 8.00000 0.254643
\(988\) 60.0000 1.90885
\(989\) 11.0000 0.349780
\(990\) −2.00000 −0.0635642
\(991\) −33.0000 −1.04828 −0.524140 0.851632i \(-0.675613\pi\)
−0.524140 + 0.851632i \(0.675613\pi\)
\(992\) −64.0000 −2.03200
\(993\) −3.00000 −0.0952021
\(994\) −24.0000 −0.761234
\(995\) 20.0000 0.634043
\(996\) −2.00000 −0.0633724
\(997\) −22.0000 −0.696747 −0.348373 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) 50.0000 1.58272
\(999\) −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 \(a_p\))