Properties

Label 110.2.a.a.1.1
Level 110
Weight 2
Character 110.1
Self dual Yes
Analytic conductor 0.878
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 110.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.878354422234\)
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 \(\chi\) = 110.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{6}\) \(+5.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{6}\) \(+5.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+1.00000 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+2.00000 q^{13}\) \(-5.00000 q^{14}\) \(-1.00000 q^{15}\) \(+1.00000 q^{16}\) \(+3.00000 q^{17}\) \(+2.00000 q^{18}\) \(-7.00000 q^{19}\) \(-1.00000 q^{20}\) \(+5.00000 q^{21}\) \(-1.00000 q^{22}\) \(-6.00000 q^{23}\) \(-1.00000 q^{24}\) \(+1.00000 q^{25}\) \(-2.00000 q^{26}\) \(-5.00000 q^{27}\) \(+5.00000 q^{28}\) \(-3.00000 q^{29}\) \(+1.00000 q^{30}\) \(-7.00000 q^{31}\) \(-1.00000 q^{32}\) \(+1.00000 q^{33}\) \(-3.00000 q^{34}\) \(-5.00000 q^{35}\) \(-2.00000 q^{36}\) \(-7.00000 q^{37}\) \(+7.00000 q^{38}\) \(+2.00000 q^{39}\) \(+1.00000 q^{40}\) \(+6.00000 q^{41}\) \(-5.00000 q^{42}\) \(+8.00000 q^{43}\) \(+1.00000 q^{44}\) \(+2.00000 q^{45}\) \(+6.00000 q^{46}\) \(+6.00000 q^{47}\) \(+1.00000 q^{48}\) \(+18.0000 q^{49}\) \(-1.00000 q^{50}\) \(+3.00000 q^{51}\) \(+2.00000 q^{52}\) \(-3.00000 q^{53}\) \(+5.00000 q^{54}\) \(-1.00000 q^{55}\) \(-5.00000 q^{56}\) \(-7.00000 q^{57}\) \(+3.00000 q^{58}\) \(-6.00000 q^{59}\) \(-1.00000 q^{60}\) \(-1.00000 q^{61}\) \(+7.00000 q^{62}\) \(-10.0000 q^{63}\) \(+1.00000 q^{64}\) \(-2.00000 q^{65}\) \(-1.00000 q^{66}\) \(+8.00000 q^{67}\) \(+3.00000 q^{68}\) \(-6.00000 q^{69}\) \(+5.00000 q^{70}\) \(+3.00000 q^{71}\) \(+2.00000 q^{72}\) \(+2.00000 q^{73}\) \(+7.00000 q^{74}\) \(+1.00000 q^{75}\) \(-7.00000 q^{76}\) \(+5.00000 q^{77}\) \(-2.00000 q^{78}\) \(-10.0000 q^{79}\) \(-1.00000 q^{80}\) \(+1.00000 q^{81}\) \(-6.00000 q^{82}\) \(-6.00000 q^{83}\) \(+5.00000 q^{84}\) \(-3.00000 q^{85}\) \(-8.00000 q^{86}\) \(-3.00000 q^{87}\) \(-1.00000 q^{88}\) \(+9.00000 q^{89}\) \(-2.00000 q^{90}\) \(+10.0000 q^{91}\) \(-6.00000 q^{92}\) \(-7.00000 q^{93}\) \(-6.00000 q^{94}\) \(+7.00000 q^{95}\) \(-1.00000 q^{96}\) \(-4.00000 q^{97}\) \(-18.0000 q^{98}\) \(-2.00000 q^{99}\) \(+O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.00000 −0.408248
\(7\) 5.00000 1.88982 0.944911 0.327327i \(-0.106148\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −5.00000 −1.33631
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 2.00000 0.471405
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −1.00000 −0.223607
\(21\) 5.00000 1.09109
\(22\) −1.00000 −0.213201
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) −5.00000 −0.962250
\(28\) 5.00000 0.944911
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 1.00000 0.182574
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) −3.00000 −0.514496
\(35\) −5.00000 −0.845154
\(36\) −2.00000 −0.333333
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 7.00000 1.13555
\(39\) 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 \(0.344787\pi\)
\(42\) −5.00000 −0.771517
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 1.00000 0.150756
\(45\) 2.00000 0.298142
\(46\) 6.00000 0.884652
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 1.00000 0.144338
\(49\) 18.0000 2.57143
\(50\) −1.00000 −0.141421
\(51\) 3.00000 0.420084
\(52\) 2.00000 0.277350
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 5.00000 0.680414
\(55\) −1.00000 −0.134840
\(56\) −5.00000 −0.668153
\(57\) −7.00000 −0.927173
\(58\) 3.00000 0.393919
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) −1.00000 −0.129099
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 7.00000 0.889001
\(63\) −10.0000 −1.25988
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 3.00000 0.363803
\(69\) −6.00000 −0.722315
\(70\) 5.00000 0.597614
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 2.00000 0.235702
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 7.00000 0.813733
\(75\) 1.00000 0.115470
\(76\) −7.00000 −0.802955
\(77\) 5.00000 0.569803
\(78\) −2.00000 −0.226455
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 5.00000 0.545545
\(85\) −3.00000 −0.325396
\(86\) −8.00000 −0.862662
\(87\) −3.00000 −0.321634
\(88\) −1.00000 −0.106600
\(89\) 9.00000 0.953998 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) −2.00000 −0.210819
\(91\) 10.0000 1.04828
\(92\) −6.00000 −0.625543
\(93\) −7.00000 −0.725866
\(94\) −6.00000 −0.618853
\(95\) 7.00000 0.718185
\(96\) −1.00000 −0.102062
\(97\) −4.00000 −0.406138 −0.203069 0.979164i \(-0.565092\pi\)
−0.203069 + 0.979164i \(0.565092\pi\)
\(98\) −18.0000 −1.81827
\(99\) −2.00000 −0.201008
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −3.00000 −0.297044
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −2.00000 −0.196116
\(105\) −5.00000 −0.487950
\(106\) 3.00000 0.291386
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −5.00000 −0.481125
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 1.00000 0.0953463
\(111\) −7.00000 −0.664411
\(112\) 5.00000 0.472456
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 7.00000 0.655610
\(115\) 6.00000 0.559503
\(116\) −3.00000 −0.278543
\(117\) −4.00000 −0.369800
\(118\) 6.00000 0.552345
\(119\) 15.0000 1.37505
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 6.00000 0.541002
\(124\) −7.00000 −0.628619
\(125\) −1.00000 −0.0894427
\(126\) 10.0000 0.890871
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 0.704361
\(130\) 2.00000 0.175412
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 1.00000 0.0870388
\(133\) −35.0000 −3.03488
\(134\) −8.00000 −0.691095
\(135\) 5.00000 0.430331
\(136\) −3.00000 −0.257248
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 6.00000 0.510754
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −5.00000 −0.422577
\(141\) 6.00000 0.505291
\(142\) −3.00000 −0.251754
\(143\) 2.00000 0.167248
\(144\) −2.00000 −0.166667
\(145\) 3.00000 0.249136
\(146\) −2.00000 −0.165521
\(147\) 18.0000 1.48461
\(148\) −7.00000 −0.575396
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 7.00000 0.567775
\(153\) −6.00000 −0.485071
\(154\) −5.00000 −0.402911
\(155\) 7.00000 0.562254
\(156\) 2.00000 0.160128
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 10.0000 0.795557
\(159\) −3.00000 −0.237915
\(160\) 1.00000 0.0790569
\(161\) −30.0000 −2.36433
\(162\) −1.00000 −0.0785674
\(163\) 5.00000 0.391630 0.195815 0.980641i \(-0.437265\pi\)
0.195815 + 0.980641i \(0.437265\pi\)
\(164\) 6.00000 0.468521
\(165\) −1.00000 −0.0778499
\(166\) 6.00000 0.465690
\(167\) 21.0000 1.62503 0.812514 0.582941i \(-0.198098\pi\)
0.812514 + 0.582941i \(0.198098\pi\)
\(168\) −5.00000 −0.385758
\(169\) −9.00000 −0.692308
\(170\) 3.00000 0.230089
\(171\) 14.0000 1.07061
\(172\) 8.00000 0.609994
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 3.00000 0.227429
\(175\) 5.00000 0.377964
\(176\) 1.00000 0.0753778
\(177\) −6.00000 −0.450988
\(178\) −9.00000 −0.674579
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 2.00000 0.149071
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −10.0000 −0.741249
\(183\) −1.00000 −0.0739221
\(184\) 6.00000 0.442326
\(185\) 7.00000 0.514650
\(186\) 7.00000 0.513265
\(187\) 3.00000 0.219382
\(188\) 6.00000 0.437595
\(189\) −25.0000 −1.81848
\(190\) −7.00000 −0.507833
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 1.00000 0.0721688
\(193\) 23.0000 1.65558 0.827788 0.561041i \(-0.189599\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 4.00000 0.287183
\(195\) −2.00000 −0.143223
\(196\) 18.0000 1.28571
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 2.00000 0.142134
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.00000 0.564276
\(202\) 6.00000 0.422159
\(203\) −15.0000 −1.05279
\(204\) 3.00000 0.210042
\(205\) −6.00000 −0.419058
\(206\) 4.00000 0.278693
\(207\) 12.0000 0.834058
\(208\) 2.00000 0.138675
\(209\) −7.00000 −0.484200
\(210\) 5.00000 0.345033
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −3.00000 −0.206041
\(213\) 3.00000 0.205557
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 5.00000 0.340207
\(217\) −35.0000 −2.37595
\(218\) −14.0000 −0.948200
\(219\) 2.00000 0.135147
\(220\) −1.00000 −0.0674200
\(221\) 6.00000 0.403604
\(222\) 7.00000 0.469809
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) −5.00000 −0.334077
\(225\) −2.00000 −0.133333
\(226\) −12.0000 −0.798228
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) −7.00000 −0.463586
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) −6.00000 −0.395628
\(231\) 5.00000 0.328976
\(232\) 3.00000 0.196960
\(233\) 27.0000 1.76883 0.884414 0.466702i \(-0.154558\pi\)
0.884414 + 0.466702i \(0.154558\pi\)
\(234\) 4.00000 0.261488
\(235\) −6.00000 −0.391397
\(236\) −6.00000 −0.390567
\(237\) −10.0000 −0.649570
\(238\) −15.0000 −0.972306
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −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
\(243\) 16.0000 1.02640
\(244\) −1.00000 −0.0640184
\(245\) −18.0000 −1.14998
\(246\) −6.00000 −0.382546
\(247\) −14.0000 −0.890799
\(248\) 7.00000 0.444500
\(249\) −6.00000 −0.380235
\(250\) 1.00000 0.0632456
\(251\) −30.0000 −1.89358 −0.946792 0.321847i \(-0.895696\pi\)
−0.946792 + 0.321847i \(0.895696\pi\)
\(252\) −10.0000 −0.629941
\(253\) −6.00000 −0.377217
\(254\) 16.0000 1.00393
\(255\) −3.00000 −0.187867
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −8.00000 −0.498058
\(259\) −35.0000 −2.17479
\(260\) −2.00000 −0.124035
\(261\) 6.00000 0.371391
\(262\) 3.00000 0.185341
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 3.00000 0.184289
\(266\) 35.0000 2.14599
\(267\) 9.00000 0.550791
\(268\) 8.00000 0.488678
\(269\) −12.0000 −0.731653 −0.365826 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) −5.00000 −0.304290
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 3.00000 0.181902
\(273\) 10.0000 0.605228
\(274\) −12.0000 −0.724947
\(275\) 1.00000 0.0603023
\(276\) −6.00000 −0.361158
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) 4.00000 0.239904
\(279\) 14.0000 0.838158
\(280\) 5.00000 0.298807
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) −6.00000 −0.357295
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 3.00000 0.178017
\(285\) 7.00000 0.414644
\(286\) −2.00000 −0.118262
\(287\) 30.0000 1.77084
\(288\) 2.00000 0.117851
\(289\) −8.00000 −0.470588
\(290\) −3.00000 −0.176166
\(291\) −4.00000 −0.234484
\(292\) 2.00000 0.117041
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −18.0000 −1.04978
\(295\) 6.00000 0.349334
\(296\) 7.00000 0.406867
\(297\) −5.00000 −0.290129
\(298\) −15.0000 −0.868927
\(299\) −12.0000 −0.693978
\(300\) 1.00000 0.0577350
\(301\) 40.0000 2.30556
\(302\) −2.00000 −0.115087
\(303\) −6.00000 −0.344691
\(304\) −7.00000 −0.401478
\(305\) 1.00000 0.0572598
\(306\) 6.00000 0.342997
\(307\) −10.0000 −0.570730 −0.285365 0.958419i \(-0.592115\pi\)
−0.285365 + 0.958419i \(0.592115\pi\)
\(308\) 5.00000 0.284901
\(309\) −4.00000 −0.227552
\(310\) −7.00000 −0.397573
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) −2.00000 −0.113228
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 7.00000 0.395033
\(315\) 10.0000 0.563436
\(316\) −10.0000 −0.562544
\(317\) −21.0000 −1.17948 −0.589739 0.807594i \(-0.700769\pi\)
−0.589739 + 0.807594i \(0.700769\pi\)
\(318\) 3.00000 0.168232
\(319\) −3.00000 −0.167968
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 30.0000 1.67183
\(323\) −21.0000 −1.16847
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) −5.00000 −0.276924
\(327\) 14.0000 0.774202
\(328\) −6.00000 −0.331295
\(329\) 30.0000 1.65395
\(330\) 1.00000 0.0550482
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −6.00000 −0.329293
\(333\) 14.0000 0.767195
\(334\) −21.0000 −1.14907
\(335\) −8.00000 −0.437087
\(336\) 5.00000 0.272772
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) 9.00000 0.489535
\(339\) 12.0000 0.651751
\(340\) −3.00000 −0.162698
\(341\) −7.00000 −0.379071
\(342\) −14.0000 −0.757033
\(343\) 55.0000 2.96972
\(344\) −8.00000 −0.431331
\(345\) 6.00000 0.323029
\(346\) −18.0000 −0.967686
\(347\) 30.0000 1.61048 0.805242 0.592946i \(-0.202035\pi\)
0.805242 + 0.592946i \(0.202035\pi\)
\(348\) −3.00000 −0.160817
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −5.00000 −0.267261
\(351\) −10.0000 −0.533761
\(352\) −1.00000 −0.0533002
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 6.00000 0.318896
\(355\) −3.00000 −0.159223
\(356\) 9.00000 0.476999
\(357\) 15.0000 0.793884
\(358\) 12.0000 0.634220
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) −2.00000 −0.105409
\(361\) 30.0000 1.57895
\(362\) 22.0000 1.15629
\(363\) 1.00000 0.0524864
\(364\) 10.0000 0.524142
\(365\) −2.00000 −0.104685
\(366\) 1.00000 0.0522708
\(367\) −4.00000 −0.208798 −0.104399 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) −6.00000 −0.312772
\(369\) −12.0000 −0.624695
\(370\) −7.00000 −0.363913
\(371\) −15.0000 −0.778761
\(372\) −7.00000 −0.362933
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) −3.00000 −0.155126
\(375\) −1.00000 −0.0516398
\(376\) −6.00000 −0.309426
\(377\) −6.00000 −0.309016
\(378\) 25.0000 1.28586
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 7.00000 0.359092
\(381\) −16.0000 −0.819705
\(382\) 12.0000 0.613973
\(383\) −18.0000 −0.919757 −0.459879 0.887982i \(-0.652107\pi\)
−0.459879 + 0.887982i \(0.652107\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −5.00000 −0.254824
\(386\) −23.0000 −1.17067
\(387\) −16.0000 −0.813326
\(388\) −4.00000 −0.203069
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 2.00000 0.101274
\(391\) −18.0000 −0.910299
\(392\) −18.0000 −0.909137
\(393\) −3.00000 −0.151330
\(394\) 0 0
\(395\) 10.0000 0.503155
\(396\) −2.00000 −0.100504
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) −11.0000 −0.551380
\(399\) −35.0000 −1.75219
\(400\) 1.00000 0.0500000
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) −8.00000 −0.399004
\(403\) −14.0000 −0.697390
\(404\) −6.00000 −0.298511
\(405\) −1.00000 −0.0496904
\(406\) 15.0000 0.744438
\(407\) −7.00000 −0.346977
\(408\) −3.00000 −0.148522
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 6.00000 0.296319
\(411\) 12.0000 0.591916
\(412\) −4.00000 −0.197066
\(413\) −30.0000 −1.47620
\(414\) −12.0000 −0.589768
\(415\) 6.00000 0.294528
\(416\) −2.00000 −0.0980581
\(417\) −4.00000 −0.195881
\(418\) 7.00000 0.342381
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) −5.00000 −0.243975
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −5.00000 −0.243396
\(423\) −12.0000 −0.583460
\(424\) 3.00000 0.145693
\(425\) 3.00000 0.145521
\(426\) −3.00000 −0.145350
\(427\) −5.00000 −0.241967
\(428\) 0 0
\(429\) 2.00000 0.0965609
\(430\) 8.00000 0.385794
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) −5.00000 −0.240563
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 35.0000 1.68005
\(435\) 3.00000 0.143839
\(436\) 14.0000 0.670478
\(437\) 42.0000 2.00913
\(438\) −2.00000 −0.0955637
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 1.00000 0.0476731
\(441\) −36.0000 −1.71429
\(442\) −6.00000 −0.285391
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) −7.00000 −0.332205
\(445\) −9.00000 −0.426641
\(446\) −14.0000 −0.662919
\(447\) 15.0000 0.709476
\(448\) 5.00000 0.236228
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 2.00000 0.0942809
\(451\) 6.00000 0.282529
\(452\) 12.0000 0.564433
\(453\) 2.00000 0.0939682
\(454\) 18.0000 0.844782
\(455\) −10.0000 −0.468807
\(456\) 7.00000 0.327805
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −14.0000 −0.654177
\(459\) −15.0000 −0.700140
\(460\) 6.00000 0.279751
\(461\) 3.00000 0.139724 0.0698620 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) −5.00000 −0.232621
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) −3.00000 −0.139272
\(465\) 7.00000 0.324617
\(466\) −27.0000 −1.25075
\(467\) −39.0000 −1.80470 −0.902352 0.430999i \(-0.858161\pi\)
−0.902352 + 0.430999i \(0.858161\pi\)
\(468\) −4.00000 −0.184900
\(469\) 40.0000 1.84703
\(470\) 6.00000 0.276759
\(471\) −7.00000 −0.322543
\(472\) 6.00000 0.276172
\(473\) 8.00000 0.367840
\(474\) 10.0000 0.459315
\(475\) −7.00000 −0.321182
\(476\) 15.0000 0.687524
\(477\) 6.00000 0.274721
\(478\) −6.00000 −0.274434
\(479\) −36.0000 −1.64488 −0.822441 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) 1.00000 0.0456435
\(481\) −14.0000 −0.638345
\(482\) 22.0000 1.00207
\(483\) −30.0000 −1.36505
\(484\) 1.00000 0.0454545
\(485\) 4.00000 0.181631
\(486\) −16.0000 −0.725775
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 1.00000 0.0452679
\(489\) 5.00000 0.226108
\(490\) 18.0000 0.813157
\(491\) 33.0000 1.48927 0.744635 0.667472i \(-0.232624\pi\)
0.744635 + 0.667472i \(0.232624\pi\)
\(492\) 6.00000 0.270501
\(493\) −9.00000 −0.405340
\(494\) 14.0000 0.629890
\(495\) 2.00000 0.0898933
\(496\) −7.00000 −0.314309
\(497\) 15.0000 0.672842
\(498\) 6.00000 0.268866
\(499\) 44.0000 1.96971 0.984855 0.173379i \(-0.0554684\pi\)
0.984855 + 0.173379i \(0.0554684\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 21.0000 0.938211
\(502\) 30.0000 1.33897
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 10.0000 0.445435
\(505\) 6.00000 0.266996
\(506\) 6.00000 0.266733
\(507\) −9.00000 −0.399704
\(508\) −16.0000 −0.709885
\(509\) −12.0000 −0.531891 −0.265945 0.963988i \(-0.585684\pi\)
−0.265945 + 0.963988i \(0.585684\pi\)
\(510\) 3.00000 0.132842
\(511\) 10.0000 0.442374
\(512\) −1.00000 −0.0441942
\(513\) 35.0000 1.54529
\(514\) −6.00000 −0.264649
\(515\) 4.00000 0.176261
\(516\) 8.00000 0.352180
\(517\) 6.00000 0.263880
\(518\) 35.0000 1.53781
\(519\) 18.0000 0.790112
\(520\) 2.00000 0.0877058
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −6.00000 −0.262613
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −3.00000 −0.131056
\(525\) 5.00000 0.218218
\(526\) 9.00000 0.392419
\(527\) −21.0000 −0.914774
\(528\) 1.00000 0.0435194
\(529\) 13.0000 0.565217
\(530\) −3.00000 −0.130312
\(531\) 12.0000 0.520756
\(532\) −35.0000 −1.51744
\(533\) 12.0000 0.519778
\(534\) −9.00000 −0.389468
\(535\) 0 0
\(536\) −8.00000 −0.345547
\(537\) −12.0000 −0.517838
\(538\) 12.0000 0.517357
\(539\) 18.0000 0.775315
\(540\) 5.00000 0.215166
\(541\) 41.0000 1.76273 0.881364 0.472438i \(-0.156626\pi\)
0.881364 + 0.472438i \(0.156626\pi\)
\(542\) −20.0000 −0.859074
\(543\) −22.0000 −0.944110
\(544\) −3.00000 −0.128624
\(545\) −14.0000 −0.599694
\(546\) −10.0000 −0.427960
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 12.0000 0.512615
\(549\) 2.00000 0.0853579
\(550\) −1.00000 −0.0426401
\(551\) 21.0000 0.894630
\(552\) 6.00000 0.255377
\(553\) −50.0000 −2.12622
\(554\) 4.00000 0.169944
\(555\) 7.00000 0.297133
\(556\) −4.00000 −0.169638
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) −14.0000 −0.592667
\(559\) 16.0000 0.676728
\(560\) −5.00000 −0.211289
\(561\) 3.00000 0.126660
\(562\) −30.0000 −1.26547
\(563\) −6.00000 −0.252870 −0.126435 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) 6.00000 0.252646
\(565\) −12.0000 −0.504844
\(566\) −2.00000 −0.0840663
\(567\) 5.00000 0.209980
\(568\) −3.00000 −0.125877
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) −7.00000 −0.293198
\(571\) −25.0000 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(572\) 2.00000 0.0836242
\(573\) −12.0000 −0.501307
\(574\) −30.0000 −1.25218
\(575\) −6.00000 −0.250217
\(576\) −2.00000 −0.0833333
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 8.00000 0.332756
\(579\) 23.0000 0.955847
\(580\) 3.00000 0.124568
\(581\) −30.0000 −1.24461
\(582\) 4.00000 0.165805
\(583\) −3.00000 −0.124247
\(584\) −2.00000 −0.0827606
\(585\) 4.00000 0.165380
\(586\) 6.00000 0.247858
\(587\) 3.00000 0.123823 0.0619116 0.998082i \(-0.480280\pi\)
0.0619116 + 0.998082i \(0.480280\pi\)
\(588\) 18.0000 0.742307
\(589\) 49.0000 2.01901
\(590\) −6.00000 −0.247016
\(591\) 0 0
\(592\) −7.00000 −0.287698
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 5.00000 0.205152
\(595\) −15.0000 −0.614940
\(596\) 15.0000 0.614424
\(597\) 11.0000 0.450200
\(598\) 12.0000 0.490716
\(599\) 9.00000 0.367730 0.183865 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) −40.0000 −1.63028
\(603\) −16.0000 −0.651570
\(604\) 2.00000 0.0813788
\(605\) −1.00000 −0.0406558
\(606\) 6.00000 0.243733
\(607\) −49.0000 −1.98885 −0.994424 0.105453i \(-0.966371\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) 7.00000 0.283887
\(609\) −15.0000 −0.607831
\(610\) −1.00000 −0.0404888
\(611\) 12.0000 0.485468
\(612\) −6.00000 −0.242536
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 10.0000 0.403567
\(615\) −6.00000 −0.241943
\(616\) −5.00000 −0.201456
\(617\) −48.0000 −1.93241 −0.966204 0.257780i \(-0.917009\pi\)
−0.966204 + 0.257780i \(0.917009\pi\)
\(618\) 4.00000 0.160904
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 7.00000 0.281127
\(621\) 30.0000 1.20386
\(622\) 15.0000 0.601445
\(623\) 45.0000 1.80289
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) −14.0000 −0.559553
\(627\) −7.00000 −0.279553
\(628\) −7.00000 −0.279330
\(629\) −21.0000 −0.837325
\(630\) −10.0000 −0.398410
\(631\) 35.0000 1.39333 0.696664 0.717398i \(-0.254667\pi\)
0.696664 + 0.717398i \(0.254667\pi\)
\(632\) 10.0000 0.397779
\(633\) 5.00000 0.198732
\(634\) 21.0000 0.834017
\(635\) 16.0000 0.634941
\(636\) −3.00000 −0.118958
\(637\) 36.0000 1.42637
\(638\) 3.00000 0.118771
\(639\) −6.00000 −0.237356
\(640\) 1.00000 0.0395285
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 0 0
\(643\) 5.00000 0.197181 0.0985904 0.995128i \(-0.468567\pi\)
0.0985904 + 0.995128i \(0.468567\pi\)
\(644\) −30.0000 −1.18217
\(645\) −8.00000 −0.315000
\(646\) 21.0000 0.826234
\(647\) 6.00000 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.00000 −0.235521
\(650\) −2.00000 −0.0784465
\(651\) −35.0000 −1.37176
\(652\) 5.00000 0.195815
\(653\) −45.0000 −1.76099 −0.880493 0.474059i \(-0.842788\pi\)
−0.880493 + 0.474059i \(0.842788\pi\)
\(654\) −14.0000 −0.547443
\(655\) 3.00000 0.117220
\(656\) 6.00000 0.234261
\(657\) −4.00000 −0.156055
\(658\) −30.0000 −1.16952
\(659\) −21.0000 −0.818044 −0.409022 0.912525i \(-0.634130\pi\)
−0.409022 + 0.912525i \(0.634130\pi\)
\(660\) −1.00000 −0.0389249
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −8.00000 −0.310929
\(663\) 6.00000 0.233021
\(664\) 6.00000 0.232845
\(665\) 35.0000 1.35724
\(666\) −14.0000 −0.542489
\(667\) 18.0000 0.696963
\(668\) 21.0000 0.812514
\(669\) 14.0000 0.541271
\(670\) 8.00000 0.309067
\(671\) −1.00000 −0.0386046
\(672\) −5.00000 −0.192879
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) −5.00000 −0.192593
\(675\) −5.00000 −0.192450
\(676\) −9.00000 −0.346154
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −12.0000 −0.460857
\(679\) −20.0000 −0.767530
\(680\) 3.00000 0.115045
\(681\) −18.0000 −0.689761
\(682\) 7.00000 0.268044
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 14.0000 0.535303
\(685\) −12.0000 −0.458496
\(686\) −55.0000 −2.09991
\(687\) 14.0000 0.534133
\(688\) 8.00000 0.304997
\(689\) −6.00000 −0.228582
\(690\) −6.00000 −0.228416
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 18.0000 0.684257
\(693\) −10.0000 −0.379869
\(694\) −30.0000 −1.13878
\(695\) 4.00000 0.151729
\(696\) 3.00000 0.113715
\(697\) 18.0000 0.681799
\(698\) 10.0000 0.378506
\(699\) 27.0000 1.02123
\(700\) 5.00000 0.188982
\(701\) 39.0000 1.47301 0.736505 0.676432i \(-0.236475\pi\)
0.736505 + 0.676432i \(0.236475\pi\)
\(702\) 10.0000 0.377426
\(703\) 49.0000 1.84807
\(704\) 1.00000 0.0376889
\(705\) −6.00000 −0.225973
\(706\) −6.00000 −0.225813
\(707\) −30.0000 −1.12827
\(708\) −6.00000 −0.225494
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 3.00000 0.112588
\(711\) 20.0000 0.750059
\(712\) −9.00000 −0.337289
\(713\) 42.0000 1.57291
\(714\) −15.0000 −0.561361
\(715\) −2.00000 −0.0747958
\(716\) −12.0000 −0.448461
\(717\) 6.00000 0.224074
\(718\) 12.0000 0.447836
\(719\) −51.0000 −1.90198 −0.950990 0.309223i \(-0.899931\pi\)
−0.950990 + 0.309223i \(0.899931\pi\)
\(720\) 2.00000 0.0745356
\(721\) −20.0000 −0.744839
\(722\) −30.0000 −1.11648
\(723\) −22.0000 −0.818189
\(724\) −22.0000 −0.817624
\(725\) −3.00000 −0.111417
\(726\) −1.00000 −0.0371135
\(727\) −10.0000 −0.370879 −0.185440 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(728\) −10.0000 −0.370625
\(729\) 13.0000 0.481481
\(730\) 2.00000 0.0740233
\(731\) 24.0000 0.887672
\(732\) −1.00000 −0.0369611
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) 4.00000 0.147643
\(735\) −18.0000 −0.663940
\(736\) 6.00000 0.221163
\(737\) 8.00000 0.294684
\(738\) 12.0000 0.441726
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 7.00000 0.257325
\(741\) −14.0000 −0.514303
\(742\) 15.0000 0.550667
\(743\) −3.00000 −0.110059 −0.0550297 0.998485i \(-0.517525\pi\)
−0.0550297 + 0.998485i \(0.517525\pi\)
\(744\) 7.00000 0.256632
\(745\) −15.0000 −0.549557
\(746\) −2.00000 −0.0732252
\(747\) 12.0000 0.439057
\(748\) 3.00000 0.109691
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) 5.00000 0.182453 0.0912263 0.995830i \(-0.470921\pi\)
0.0912263 + 0.995830i \(0.470921\pi\)
\(752\) 6.00000 0.218797
\(753\) −30.0000 −1.09326
\(754\) 6.00000 0.218507
\(755\) −2.00000 −0.0727875
\(756\) −25.0000 −0.909241
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −26.0000 −0.944363
\(759\) −6.00000 −0.217786
\(760\) −7.00000 −0.253917
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 16.0000 0.579619
\(763\) 70.0000 2.53417
\(764\) −12.0000 −0.434145
\(765\) 6.00000 0.216930
\(766\) 18.0000 0.650366
\(767\) −12.0000 −0.433295
\(768\) 1.00000 0.0360844
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 5.00000 0.180187
\(771\) 6.00000 0.216085
\(772\) 23.0000 0.827788
\(773\) 9.00000 0.323708 0.161854 0.986815i \(-0.448253\pi\)
0.161854 + 0.986815i \(0.448253\pi\)
\(774\) 16.0000 0.575108
\(775\) −7.00000 −0.251447
\(776\) 4.00000 0.143592
\(777\) −35.0000 −1.25562
\(778\) −18.0000 −0.645331
\(779\) −42.0000 −1.50481
\(780\) −2.00000 −0.0716115
\(781\) 3.00000 0.107348
\(782\) 18.0000 0.643679
\(783\) 15.0000 0.536056
\(784\) 18.0000 0.642857
\(785\) 7.00000 0.249841
\(786\) 3.00000 0.107006
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) 0 0
\(789\) −9.00000 −0.320408
\(790\) −10.0000 −0.355784
\(791\) 60.0000 2.13335
\(792\) 2.00000 0.0710669
\(793\) −2.00000 −0.0710221
\(794\) 22.0000 0.780751
\(795\) 3.00000 0.106399
\(796\) 11.0000 0.389885
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 35.0000 1.23899
\(799\) 18.0000 0.636794
\(800\) −1.00000 −0.0353553
\(801\) −18.0000 −0.635999
\(802\) −3.00000 −0.105934
\(803\) 2.00000 0.0705785
\(804\) 8.00000 0.282138
\(805\) 30.0000 1.05736
\(806\) 14.0000 0.493129
\(807\) −12.0000 −0.422420
\(808\) 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
\(811\) −13.0000 −0.456492 −0.228246 0.973604i \(-0.573299\pi\)
−0.228246 + 0.973604i \(0.573299\pi\)
\(812\) −15.0000 −0.526397
\(813\) 20.0000 0.701431
\(814\) 7.00000 0.245350
\(815\) −5.00000 −0.175142
\(816\) 3.00000 0.105021
\(817\) −56.0000 −1.95919
\(818\) 4.00000 0.139857
\(819\) −20.0000 −0.698857
\(820\) −6.00000 −0.209529
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) −12.0000 −0.418548
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 4.00000 0.139347
\(825\) 1.00000 0.0348155
\(826\) 30.0000 1.04383
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 12.0000 0.417029
\(829\) −52.0000 −1.80603 −0.903017 0.429604i \(-0.858653\pi\)
−0.903017 + 0.429604i \(0.858653\pi\)
\(830\) −6.00000 −0.208263
\(831\) −4.00000 −0.138758
\(832\) 2.00000 0.0693375
\(833\) 54.0000 1.87099
\(834\) 4.00000 0.138509
\(835\) −21.0000 −0.726735
\(836\) −7.00000 −0.242100
\(837\) 35.0000 1.20978
\(838\) −24.0000 −0.829066
\(839\) 48.0000 1.65714 0.828572 0.559883i \(-0.189154\pi\)
0.828572 + 0.559883i \(0.189154\pi\)
\(840\) 5.00000 0.172516
\(841\) −20.0000 −0.689655
\(842\) −8.00000 −0.275698
\(843\) 30.0000 1.03325
\(844\) 5.00000 0.172107
\(845\) 9.00000 0.309609
\(846\) 12.0000 0.412568
\(847\) 5.00000 0.171802
\(848\) −3.00000 −0.103020
\(849\) 2.00000 0.0686398
\(850\) −3.00000 −0.102899
\(851\) 42.0000 1.43974
\(852\) 3.00000 0.102778
\(853\) −34.0000 −1.16414 −0.582069 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) 5.00000 0.171096
\(855\) −14.0000 −0.478790
\(856\) 0 0
\(857\) 3.00000 0.102478 0.0512390 0.998686i \(-0.483683\pi\)
0.0512390 + 0.998686i \(0.483683\pi\)
\(858\) −2.00000 −0.0682789
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) −8.00000 −0.272798
\(861\) 30.0000 1.02240
\(862\) 24.0000 0.817443
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) 5.00000 0.170103
\(865\) −18.0000 −0.612018
\(866\) 28.0000 0.951479
\(867\) −8.00000 −0.271694
\(868\) −35.0000 −1.18798
\(869\) −10.0000 −0.339227
\(870\) −3.00000 −0.101710
\(871\) 16.0000 0.542139
\(872\) −14.0000 −0.474100
\(873\) 8.00000 0.270759
\(874\) −42.0000 −1.42067
\(875\) −5.00000 −0.169031
\(876\) 2.00000 0.0675737
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 16.0000 0.539974
\(879\) −6.00000 −0.202375
\(880\) −1.00000 −0.0337100
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 36.0000 1.21218
\(883\) −1.00000 −0.0336527 −0.0168263 0.999858i \(-0.505356\pi\)
−0.0168263 + 0.999858i \(0.505356\pi\)
\(884\) 6.00000 0.201802
\(885\) 6.00000 0.201688
\(886\) −12.0000 −0.403148
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 7.00000 0.234905
\(889\) −80.0000 −2.68311
\(890\) 9.00000 0.301681
\(891\) 1.00000 0.0335013
\(892\) 14.0000 0.468755
\(893\) −42.0000 −1.40548
\(894\) −15.0000 −0.501675
\(895\) 12.0000 0.401116
\(896\) −5.00000 −0.167038
\(897\) −12.0000 −0.400668
\(898\) 30.0000 1.00111
\(899\) 21.0000 0.700389
\(900\) −2.00000 −0.0666667
\(901\) −9.00000 −0.299833
\(902\) −6.00000 −0.199778
\(903\) 40.0000 1.33112
\(904\) −12.0000 −0.399114
\(905\) 22.0000 0.731305
\(906\) −2.00000 −0.0664455
\(907\) 17.0000 0.564476 0.282238 0.959344i \(-0.408923\pi\)
0.282238 + 0.959344i \(0.408923\pi\)
\(908\) −18.0000 −0.597351
\(909\) 12.0000 0.398015
\(910\) 10.0000 0.331497
\(911\) 15.0000 0.496972 0.248486 0.968635i \(-0.420067\pi\)
0.248486 + 0.968635i \(0.420067\pi\)
\(912\) −7.00000 −0.231793
\(913\) −6.00000 −0.198571
\(914\) −17.0000 −0.562310
\(915\) 1.00000 0.0330590
\(916\) 14.0000 0.462573
\(917\) −15.0000 −0.495344
\(918\) 15.0000 0.495074
\(919\) −4.00000 −0.131948 −0.0659739 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) −6.00000 −0.197814
\(921\) −10.0000 −0.329511
\(922\) −3.00000 −0.0987997
\(923\) 6.00000 0.197492
\(924\) 5.00000 0.164488
\(925\) −7.00000 −0.230159
\(926\) 22.0000 0.722965
\(927\) 8.00000 0.262754
\(928\) 3.00000 0.0984798
\(929\) −45.0000 −1.47640 −0.738201 0.674581i \(-0.764324\pi\)
−0.738201 + 0.674581i \(0.764324\pi\)
\(930\) −7.00000 −0.229539
\(931\) −126.000 −4.12948
\(932\) 27.0000 0.884414
\(933\) −15.0000 −0.491078
\(934\) 39.0000 1.27612
\(935\) −3.00000 −0.0981105
\(936\) 4.00000 0.130744
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) −40.0000 −1.30605
\(939\) 14.0000 0.456873
\(940\) −6.00000 −0.195698
\(941\) −15.0000 −0.488986 −0.244493 0.969651i \(-0.578622\pi\)
−0.244493 + 0.969651i \(0.578622\pi\)
\(942\) 7.00000 0.228072
\(943\) −36.0000 −1.17232
\(944\) −6.00000 −0.195283
\(945\) 25.0000 0.813250
\(946\) −8.00000 −0.260102
\(947\) 3.00000 0.0974869 0.0487435 0.998811i \(-0.484478\pi\)
0.0487435 + 0.998811i \(0.484478\pi\)
\(948\) −10.0000 −0.324785
\(949\) 4.00000 0.129845
\(950\) 7.00000 0.227110
\(951\) −21.0000 −0.680972
\(952\) −15.0000 −0.486153
\(953\) −27.0000 −0.874616 −0.437308 0.899312i \(-0.644068\pi\)
−0.437308 + 0.899312i \(0.644068\pi\)
\(954\) −6.00000 −0.194257
\(955\) 12.0000 0.388311
\(956\) 6.00000 0.194054
\(957\) −3.00000 −0.0969762
\(958\) 36.0000 1.16311
\(959\) 60.0000 1.93750
\(960\) −1.00000 −0.0322749
\(961\) 18.0000 0.580645
\(962\) 14.0000 0.451378
\(963\) 0 0
\(964\) −22.0000 −0.708572
\(965\) −23.0000 −0.740396
\(966\) 30.0000 0.965234
\(967\) −13.0000 −0.418052 −0.209026 0.977910i \(-0.567029\pi\)
−0.209026 + 0.977910i \(0.567029\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −21.0000 −0.674617
\(970\) −4.00000 −0.128432
\(971\) −24.0000 −0.770197 −0.385098 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 16.0000 0.513200
\(973\) −20.0000 −0.641171
\(974\) −8.00000 −0.256337
\(975\) 2.00000 0.0640513
\(976\) −1.00000 −0.0320092
\(977\) 12.0000 0.383914 0.191957 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) −5.00000 −0.159882
\(979\) 9.00000 0.287641
\(980\) −18.0000 −0.574989
\(981\) −28.0000 −0.893971
\(982\) −33.0000 −1.05307
\(983\) −6.00000 −0.191370 −0.0956851 0.995412i \(-0.530504\pi\)
−0.0956851 + 0.995412i \(0.530504\pi\)
\(984\) −6.00000 −0.191273
\(985\) 0 0
\(986\) 9.00000 0.286618
\(987\) 30.0000 0.954911
\(988\) −14.0000 −0.445399
\(989\) −48.0000 −1.52631
\(990\) −2.00000 −0.0635642
\(991\) −40.0000 −1.27064 −0.635321 0.772248i \(-0.719132\pi\)
−0.635321 + 0.772248i \(0.719132\pi\)
\(992\) 7.00000 0.222250
\(993\) 8.00000 0.253872
\(994\) −15.0000 −0.475771
\(995\) −11.0000 −0.348723
\(996\) −6.00000 −0.190117
\(997\) −28.0000 −0.886769 −0.443384 0.896332i \(-0.646222\pi\)
−0.443384 + 0.896332i \(0.646222\pi\)
\(998\) −44.0000 −1.39280
\(999\) 35.0000 1.10735
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 \(a_p\))