Properties

Label 79.2.a.a.1.1
Level 79
Weight 2
Character 79.1
Self dual Yes
Analytic conductor 0.631
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 79.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.630818175968\)
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 \(\chi\) = 79.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(-1.00000 q^{4}\) \(-3.00000 q^{5}\) \(+1.00000 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(-1.00000 q^{4}\) \(-3.00000 q^{5}\) \(+1.00000 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(-2.00000 q^{9}\) \(+3.00000 q^{10}\) \(-2.00000 q^{11}\) \(+1.00000 q^{12}\) \(+3.00000 q^{13}\) \(+1.00000 q^{14}\) \(+3.00000 q^{15}\) \(-1.00000 q^{16}\) \(-6.00000 q^{17}\) \(+2.00000 q^{18}\) \(+4.00000 q^{19}\) \(+3.00000 q^{20}\) \(+1.00000 q^{21}\) \(+2.00000 q^{22}\) \(+2.00000 q^{23}\) \(-3.00000 q^{24}\) \(+4.00000 q^{25}\) \(-3.00000 q^{26}\) \(+5.00000 q^{27}\) \(+1.00000 q^{28}\) \(-6.00000 q^{29}\) \(-3.00000 q^{30}\) \(-10.0000 q^{31}\) \(-5.00000 q^{32}\) \(+2.00000 q^{33}\) \(+6.00000 q^{34}\) \(+3.00000 q^{35}\) \(+2.00000 q^{36}\) \(-2.00000 q^{37}\) \(-4.00000 q^{38}\) \(-3.00000 q^{39}\) \(-9.00000 q^{40}\) \(-10.0000 q^{41}\) \(-1.00000 q^{42}\) \(+4.00000 q^{43}\) \(+2.00000 q^{44}\) \(+6.00000 q^{45}\) \(-2.00000 q^{46}\) \(+7.00000 q^{47}\) \(+1.00000 q^{48}\) \(-6.00000 q^{49}\) \(-4.00000 q^{50}\) \(+6.00000 q^{51}\) \(-3.00000 q^{52}\) \(+8.00000 q^{53}\) \(-5.00000 q^{54}\) \(+6.00000 q^{55}\) \(-3.00000 q^{56}\) \(-4.00000 q^{57}\) \(+6.00000 q^{58}\) \(-3.00000 q^{59}\) \(-3.00000 q^{60}\) \(-4.00000 q^{61}\) \(+10.0000 q^{62}\) \(+2.00000 q^{63}\) \(+7.00000 q^{64}\) \(-9.00000 q^{65}\) \(-2.00000 q^{66}\) \(+8.00000 q^{67}\) \(+6.00000 q^{68}\) \(-2.00000 q^{69}\) \(-3.00000 q^{70}\) \(+15.0000 q^{71}\) \(-6.00000 q^{72}\) \(+2.00000 q^{73}\) \(+2.00000 q^{74}\) \(-4.00000 q^{75}\) \(-4.00000 q^{76}\) \(+2.00000 q^{77}\) \(+3.00000 q^{78}\) \(-1.00000 q^{79}\) \(+3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+10.0000 q^{82}\) \(-6.00000 q^{83}\) \(-1.00000 q^{84}\) \(+18.0000 q^{85}\) \(-4.00000 q^{86}\) \(+6.00000 q^{87}\) \(-6.00000 q^{88}\) \(-7.00000 q^{89}\) \(-6.00000 q^{90}\) \(-3.00000 q^{91}\) \(-2.00000 q^{92}\) \(+10.0000 q^{93}\) \(-7.00000 q^{94}\) \(-12.0000 q^{95}\) \(+5.00000 q^{96}\) \(-19.0000 q^{97}\) \(+6.00000 q^{98}\) \(+4.00000 q^{99}\) \(+O(q^{100})\)

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 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) −1.00000 −0.500000
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 3.00000 1.06066
\(9\) −2.00000 −0.666667
\(10\) 3.00000 0.948683
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 1.00000 0.267261
\(15\) 3.00000 0.774597
\(16\) −1.00000 −0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 2.00000 0.471405
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 3.00000 0.670820
\(21\) 1.00000 0.218218
\(22\) 2.00000 0.426401
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) −3.00000 −0.612372
\(25\) 4.00000 0.800000
\(26\) −3.00000 −0.588348
\(27\) 5.00000 0.962250
\(28\) 1.00000 0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −3.00000 −0.547723
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) −5.00000 −0.883883
\(33\) 2.00000 0.348155
\(34\) 6.00000 1.02899
\(35\) 3.00000 0.507093
\(36\) 2.00000 0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −4.00000 −0.648886
\(39\) −3.00000 −0.480384
\(40\) −9.00000 −1.42302
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) −1.00000 −0.154303
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 2.00000 0.301511
\(45\) 6.00000 0.894427
\(46\) −2.00000 −0.294884
\(47\) 7.00000 1.02105 0.510527 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) −4.00000 −0.565685
\(51\) 6.00000 0.840168
\(52\) −3.00000 −0.416025
\(53\) 8.00000 1.09888 0.549442 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) −5.00000 −0.680414
\(55\) 6.00000 0.809040
\(56\) −3.00000 −0.400892
\(57\) −4.00000 −0.529813
\(58\) 6.00000 0.787839
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) −3.00000 −0.387298
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 10.0000 1.27000
\(63\) 2.00000 0.251976
\(64\) 7.00000 0.875000
\(65\) −9.00000 −1.11631
\(66\) −2.00000 −0.246183
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 6.00000 0.727607
\(69\) −2.00000 −0.240772
\(70\) −3.00000 −0.358569
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) −6.00000 −0.707107
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 2.00000 0.232495
\(75\) −4.00000 −0.461880
\(76\) −4.00000 −0.458831
\(77\) 2.00000 0.227921
\(78\) 3.00000 0.339683
\(79\) −1.00000 −0.112509
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.00000 −0.109109
\(85\) 18.0000 1.95237
\(86\) −4.00000 −0.431331
\(87\) 6.00000 0.643268
\(88\) −6.00000 −0.639602
\(89\) −7.00000 −0.741999 −0.370999 0.928633i \(-0.620985\pi\)
−0.370999 + 0.928633i \(0.620985\pi\)
\(90\) −6.00000 −0.632456
\(91\) −3.00000 −0.314485
\(92\) −2.00000 −0.208514
\(93\) 10.0000 1.03695
\(94\) −7.00000 −0.721995
\(95\) −12.0000 −1.23117
\(96\) 5.00000 0.510310
\(97\) −19.0000 −1.92916 −0.964579 0.263795i \(-0.915026\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) 6.00000 0.606092
\(99\) 4.00000 0.402015
\(100\) −4.00000 −0.400000
\(101\) 11.0000 1.09454 0.547270 0.836956i \(-0.315667\pi\)
0.547270 + 0.836956i \(0.315667\pi\)
\(102\) −6.00000 −0.594089
\(103\) −9.00000 −0.886796 −0.443398 0.896325i \(-0.646227\pi\)
−0.443398 + 0.896325i \(0.646227\pi\)
\(104\) 9.00000 0.882523
\(105\) −3.00000 −0.292770
\(106\) −8.00000 −0.777029
\(107\) −11.0000 −1.06341 −0.531705 0.846930i \(-0.678449\pi\)
−0.531705 + 0.846930i \(0.678449\pi\)
\(108\) −5.00000 −0.481125
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) −6.00000 −0.572078
\(111\) 2.00000 0.189832
\(112\) 1.00000 0.0944911
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 4.00000 0.374634
\(115\) −6.00000 −0.559503
\(116\) 6.00000 0.557086
\(117\) −6.00000 −0.554700
\(118\) 3.00000 0.276172
\(119\) 6.00000 0.550019
\(120\) 9.00000 0.821584
\(121\) −7.00000 −0.636364
\(122\) 4.00000 0.362143
\(123\) 10.0000 0.901670
\(124\) 10.0000 0.898027
\(125\) 3.00000 0.268328
\(126\) −2.00000 −0.178174
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 3.00000 0.265165
\(129\) −4.00000 −0.352180
\(130\) 9.00000 0.789352
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) −2.00000 −0.174078
\(133\) −4.00000 −0.346844
\(134\) −8.00000 −0.691095
\(135\) −15.0000 −1.29099
\(136\) −18.0000 −1.54349
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 2.00000 0.170251
\(139\) −21.0000 −1.78120 −0.890598 0.454791i \(-0.849714\pi\)
−0.890598 + 0.454791i \(0.849714\pi\)
\(140\) −3.00000 −0.253546
\(141\) −7.00000 −0.589506
\(142\) −15.0000 −1.25877
\(143\) −6.00000 −0.501745
\(144\) 2.00000 0.166667
\(145\) 18.0000 1.49482
\(146\) −2.00000 −0.165521
\(147\) 6.00000 0.494872
\(148\) 2.00000 0.164399
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 4.00000 0.326599
\(151\) 6.00000 0.488273 0.244137 0.969741i \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 12.0000 0.973329
\(153\) 12.0000 0.970143
\(154\) −2.00000 −0.161165
\(155\) 30.0000 2.40966
\(156\) 3.00000 0.240192
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 1.00000 0.0795557
\(159\) −8.00000 −0.634441
\(160\) 15.0000 1.18585
\(161\) −2.00000 −0.157622
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 10.0000 0.780869
\(165\) −6.00000 −0.467099
\(166\) 6.00000 0.465690
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 3.00000 0.231455
\(169\) −4.00000 −0.307692
\(170\) −18.0000 −1.38054
\(171\) −8.00000 −0.611775
\(172\) −4.00000 −0.304997
\(173\) −8.00000 −0.608229 −0.304114 0.952636i \(-0.598361\pi\)
−0.304114 + 0.952636i \(0.598361\pi\)
\(174\) −6.00000 −0.454859
\(175\) −4.00000 −0.302372
\(176\) 2.00000 0.150756
\(177\) 3.00000 0.225494
\(178\) 7.00000 0.524672
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) −6.00000 −0.447214
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 3.00000 0.222375
\(183\) 4.00000 0.295689
\(184\) 6.00000 0.442326
\(185\) 6.00000 0.441129
\(186\) −10.0000 −0.733236
\(187\) 12.0000 0.877527
\(188\) −7.00000 −0.510527
\(189\) −5.00000 −0.363696
\(190\) 12.0000 0.870572
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −7.00000 −0.505181
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 19.0000 1.36412
\(195\) 9.00000 0.644503
\(196\) 6.00000 0.428571
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −4.00000 −0.284268
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 12.0000 0.848528
\(201\) −8.00000 −0.564276
\(202\) −11.0000 −0.773957
\(203\) 6.00000 0.421117
\(204\) −6.00000 −0.420084
\(205\) 30.0000 2.09529
\(206\) 9.00000 0.627060
\(207\) −4.00000 −0.278019
\(208\) −3.00000 −0.208013
\(209\) −8.00000 −0.553372
\(210\) 3.00000 0.207020
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −8.00000 −0.549442
\(213\) −15.0000 −1.02778
\(214\) 11.0000 0.751945
\(215\) −12.0000 −0.818393
\(216\) 15.0000 1.02062
\(217\) 10.0000 0.678844
\(218\) −10.0000 −0.677285
\(219\) −2.00000 −0.135147
\(220\) −6.00000 −0.404520
\(221\) −18.0000 −1.21081
\(222\) −2.00000 −0.134231
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 5.00000 0.334077
\(225\) −8.00000 −0.533333
\(226\) 0 0
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 4.00000 0.264906
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 6.00000 0.395628
\(231\) −2.00000 −0.131590
\(232\) −18.0000 −1.18176
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 6.00000 0.392232
\(235\) −21.0000 −1.36989
\(236\) 3.00000 0.195283
\(237\) 1.00000 0.0649570
\(238\) −6.00000 −0.388922
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −3.00000 −0.193649
\(241\) −15.0000 −0.966235 −0.483117 0.875556i \(-0.660496\pi\)
−0.483117 + 0.875556i \(0.660496\pi\)
\(242\) 7.00000 0.449977
\(243\) −16.0000 −1.02640
\(244\) 4.00000 0.256074
\(245\) 18.0000 1.14998
\(246\) −10.0000 −0.637577
\(247\) 12.0000 0.763542
\(248\) −30.0000 −1.90500
\(249\) 6.00000 0.380235
\(250\) −3.00000 −0.189737
\(251\) −5.00000 −0.315597 −0.157799 0.987471i \(-0.550440\pi\)
−0.157799 + 0.987471i \(0.550440\pi\)
\(252\) −2.00000 −0.125988
\(253\) −4.00000 −0.251478
\(254\) 11.0000 0.690201
\(255\) −18.0000 −1.12720
\(256\) −17.0000 −1.06250
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 4.00000 0.249029
\(259\) 2.00000 0.124274
\(260\) 9.00000 0.558156
\(261\) 12.0000 0.742781
\(262\) −6.00000 −0.370681
\(263\) 26.0000 1.60323 0.801614 0.597841i \(-0.203975\pi\)
0.801614 + 0.597841i \(0.203975\pi\)
\(264\) 6.00000 0.369274
\(265\) −24.0000 −1.47431
\(266\) 4.00000 0.245256
\(267\) 7.00000 0.428393
\(268\) −8.00000 −0.488678
\(269\) −19.0000 −1.15845 −0.579225 0.815168i \(-0.696645\pi\)
−0.579225 + 0.815168i \(0.696645\pi\)
\(270\) 15.0000 0.912871
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 6.00000 0.363803
\(273\) 3.00000 0.181568
\(274\) −12.0000 −0.724947
\(275\) −8.00000 −0.482418
\(276\) 2.00000 0.120386
\(277\) 11.0000 0.660926 0.330463 0.943819i \(-0.392795\pi\)
0.330463 + 0.943819i \(0.392795\pi\)
\(278\) 21.0000 1.25950
\(279\) 20.0000 1.19737
\(280\) 9.00000 0.537853
\(281\) 23.0000 1.37206 0.686032 0.727571i \(-0.259351\pi\)
0.686032 + 0.727571i \(0.259351\pi\)
\(282\) 7.00000 0.416844
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) −15.0000 −0.890086
\(285\) 12.0000 0.710819
\(286\) 6.00000 0.354787
\(287\) 10.0000 0.590281
\(288\) 10.0000 0.589256
\(289\) 19.0000 1.11765
\(290\) −18.0000 −1.05700
\(291\) 19.0000 1.11380
\(292\) −2.00000 −0.117041
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) −6.00000 −0.349927
\(295\) 9.00000 0.524000
\(296\) −6.00000 −0.348743
\(297\) −10.0000 −0.580259
\(298\) 6.00000 0.347571
\(299\) 6.00000 0.346989
\(300\) 4.00000 0.230940
\(301\) −4.00000 −0.230556
\(302\) −6.00000 −0.345261
\(303\) −11.0000 −0.631933
\(304\) −4.00000 −0.229416
\(305\) 12.0000 0.687118
\(306\) −12.0000 −0.685994
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) −2.00000 −0.113961
\(309\) 9.00000 0.511992
\(310\) −30.0000 −1.70389
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) −9.00000 −0.509525
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 18.0000 1.01580
\(315\) −6.00000 −0.338062
\(316\) 1.00000 0.0562544
\(317\) 31.0000 1.74113 0.870567 0.492050i \(-0.163752\pi\)
0.870567 + 0.492050i \(0.163752\pi\)
\(318\) 8.00000 0.448618
\(319\) 12.0000 0.671871
\(320\) −21.0000 −1.17394
\(321\) 11.0000 0.613960
\(322\) 2.00000 0.111456
\(323\) −24.0000 −1.33540
\(324\) −1.00000 −0.0555556
\(325\) 12.0000 0.665640
\(326\) −4.00000 −0.221540
\(327\) −10.0000 −0.553001
\(328\) −30.0000 −1.65647
\(329\) −7.00000 −0.385922
\(330\) 6.00000 0.330289
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 6.00000 0.329293
\(333\) 4.00000 0.219199
\(334\) −18.0000 −0.984916
\(335\) −24.0000 −1.31126
\(336\) −1.00000 −0.0545545
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) 4.00000 0.217571
\(339\) 0 0
\(340\) −18.0000 −0.976187
\(341\) 20.0000 1.08306
\(342\) 8.00000 0.432590
\(343\) 13.0000 0.701934
\(344\) 12.0000 0.646997
\(345\) 6.00000 0.323029
\(346\) 8.00000 0.430083
\(347\) −14.0000 −0.751559 −0.375780 0.926709i \(-0.622625\pi\)
−0.375780 + 0.926709i \(0.622625\pi\)
\(348\) −6.00000 −0.321634
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 4.00000 0.213809
\(351\) 15.0000 0.800641
\(352\) 10.0000 0.533002
\(353\) −4.00000 −0.212899 −0.106449 0.994318i \(-0.533948\pi\)
−0.106449 + 0.994318i \(0.533948\pi\)
\(354\) −3.00000 −0.159448
\(355\) −45.0000 −2.38835
\(356\) 7.00000 0.370999
\(357\) −6.00000 −0.317554
\(358\) 16.0000 0.845626
\(359\) −35.0000 −1.84723 −0.923615 0.383322i \(-0.874780\pi\)
−0.923615 + 0.383322i \(0.874780\pi\)
\(360\) 18.0000 0.948683
\(361\) −3.00000 −0.157895
\(362\) −22.0000 −1.15629
\(363\) 7.00000 0.367405
\(364\) 3.00000 0.157243
\(365\) −6.00000 −0.314054
\(366\) −4.00000 −0.209083
\(367\) −2.00000 −0.104399 −0.0521996 0.998637i \(-0.516623\pi\)
−0.0521996 + 0.998637i \(0.516623\pi\)
\(368\) −2.00000 −0.104257
\(369\) 20.0000 1.04116
\(370\) −6.00000 −0.311925
\(371\) −8.00000 −0.415339
\(372\) −10.0000 −0.518476
\(373\) −2.00000 −0.103556 −0.0517780 0.998659i \(-0.516489\pi\)
−0.0517780 + 0.998659i \(0.516489\pi\)
\(374\) −12.0000 −0.620505
\(375\) −3.00000 −0.154919
\(376\) 21.0000 1.08299
\(377\) −18.0000 −0.927047
\(378\) 5.00000 0.257172
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 12.0000 0.615587
\(381\) 11.0000 0.563547
\(382\) 15.0000 0.767467
\(383\) 2.00000 0.102195 0.0510976 0.998694i \(-0.483728\pi\)
0.0510976 + 0.998694i \(0.483728\pi\)
\(384\) −3.00000 −0.153093
\(385\) −6.00000 −0.305788
\(386\) −14.0000 −0.712581
\(387\) −8.00000 −0.406663
\(388\) 19.0000 0.964579
\(389\) −9.00000 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(390\) −9.00000 −0.455733
\(391\) −12.0000 −0.606866
\(392\) −18.0000 −0.909137
\(393\) −6.00000 −0.302660
\(394\) 6.00000 0.302276
\(395\) 3.00000 0.150946
\(396\) −4.00000 −0.201008
\(397\) −1.00000 −0.0501886 −0.0250943 0.999685i \(-0.507989\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) −11.0000 −0.551380
\(399\) 4.00000 0.200250
\(400\) −4.00000 −0.200000
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 8.00000 0.399004
\(403\) −30.0000 −1.49441
\(404\) −11.0000 −0.547270
\(405\) −3.00000 −0.149071
\(406\) −6.00000 −0.297775
\(407\) 4.00000 0.198273
\(408\) 18.0000 0.891133
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) −30.0000 −1.48159
\(411\) −12.0000 −0.591916
\(412\) 9.00000 0.443398
\(413\) 3.00000 0.147620
\(414\) 4.00000 0.196589
\(415\) 18.0000 0.883585
\(416\) −15.0000 −0.735436
\(417\) 21.0000 1.02837
\(418\) 8.00000 0.391293
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 3.00000 0.146385
\(421\) −13.0000 −0.633581 −0.316791 0.948495i \(-0.602605\pi\)
−0.316791 + 0.948495i \(0.602605\pi\)
\(422\) 12.0000 0.584151
\(423\) −14.0000 −0.680703
\(424\) 24.0000 1.16554
\(425\) −24.0000 −1.16417
\(426\) 15.0000 0.726752
\(427\) 4.00000 0.193574
\(428\) 11.0000 0.531705
\(429\) 6.00000 0.289683
\(430\) 12.0000 0.578691
\(431\) 20.0000 0.963366 0.481683 0.876346i \(-0.340026\pi\)
0.481683 + 0.876346i \(0.340026\pi\)
\(432\) −5.00000 −0.240563
\(433\) −3.00000 −0.144171 −0.0720854 0.997398i \(-0.522965\pi\)
−0.0720854 + 0.997398i \(0.522965\pi\)
\(434\) −10.0000 −0.480015
\(435\) −18.0000 −0.863034
\(436\) −10.0000 −0.478913
\(437\) 8.00000 0.382692
\(438\) 2.00000 0.0955637
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 18.0000 0.858116
\(441\) 12.0000 0.571429
\(442\) 18.0000 0.856173
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 21.0000 0.995495
\(446\) 26.0000 1.23114
\(447\) 6.00000 0.283790
\(448\) −7.00000 −0.330719
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 8.00000 0.377124
\(451\) 20.0000 0.941763
\(452\) 0 0
\(453\) −6.00000 −0.281905
\(454\) 8.00000 0.375459
\(455\) 9.00000 0.421927
\(456\) −12.0000 −0.561951
\(457\) 7.00000 0.327446 0.163723 0.986506i \(-0.447650\pi\)
0.163723 + 0.986506i \(0.447650\pi\)
\(458\) −16.0000 −0.747631
\(459\) −30.0000 −1.40028
\(460\) 6.00000 0.279751
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 2.00000 0.0930484
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) 6.00000 0.278543
\(465\) −30.0000 −1.39122
\(466\) 18.0000 0.833834
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 6.00000 0.277350
\(469\) −8.00000 −0.369406
\(470\) 21.0000 0.968658
\(471\) 18.0000 0.829396
\(472\) −9.00000 −0.414259
\(473\) −8.00000 −0.367840
\(474\) −1.00000 −0.0459315
\(475\) 16.0000 0.734130
\(476\) −6.00000 −0.275010
\(477\) −16.0000 −0.732590
\(478\) −12.0000 −0.548867
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −15.0000 −0.684653
\(481\) −6.00000 −0.273576
\(482\) 15.0000 0.683231
\(483\) 2.00000 0.0910032
\(484\) 7.00000 0.318182
\(485\) 57.0000 2.58824
\(486\) 16.0000 0.725775
\(487\) 18.0000 0.815658 0.407829 0.913058i \(-0.366286\pi\)
0.407829 + 0.913058i \(0.366286\pi\)
\(488\) −12.0000 −0.543214
\(489\) −4.00000 −0.180886
\(490\) −18.0000 −0.813157
\(491\) 13.0000 0.586682 0.293341 0.956008i \(-0.405233\pi\)
0.293341 + 0.956008i \(0.405233\pi\)
\(492\) −10.0000 −0.450835
\(493\) 36.0000 1.62136
\(494\) −12.0000 −0.539906
\(495\) −12.0000 −0.539360
\(496\) 10.0000 0.449013
\(497\) −15.0000 −0.672842
\(498\) −6.00000 −0.268866
\(499\) 10.0000 0.447661 0.223831 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) −3.00000 −0.134164
\(501\) −18.0000 −0.804181
\(502\) 5.00000 0.223161
\(503\) −13.0000 −0.579641 −0.289821 0.957081i \(-0.593596\pi\)
−0.289821 + 0.957081i \(0.593596\pi\)
\(504\) 6.00000 0.267261
\(505\) −33.0000 −1.46848
\(506\) 4.00000 0.177822
\(507\) 4.00000 0.177646
\(508\) 11.0000 0.488046
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 18.0000 0.797053
\(511\) −2.00000 −0.0884748
\(512\) 11.0000 0.486136
\(513\) 20.0000 0.883022
\(514\) 2.00000 0.0882162
\(515\) 27.0000 1.18976
\(516\) 4.00000 0.176090
\(517\) −14.0000 −0.615719
\(518\) −2.00000 −0.0878750
\(519\) 8.00000 0.351161
\(520\) −27.0000 −1.18403
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −12.0000 −0.525226
\(523\) −6.00000 −0.262362 −0.131181 0.991358i \(-0.541877\pi\)
−0.131181 + 0.991358i \(0.541877\pi\)
\(524\) −6.00000 −0.262111
\(525\) 4.00000 0.174574
\(526\) −26.0000 −1.13365
\(527\) 60.0000 2.61364
\(528\) −2.00000 −0.0870388
\(529\) −19.0000 −0.826087
\(530\) 24.0000 1.04249
\(531\) 6.00000 0.260378
\(532\) 4.00000 0.173422
\(533\) −30.0000 −1.29944
\(534\) −7.00000 −0.302920
\(535\) 33.0000 1.42671
\(536\) 24.0000 1.03664
\(537\) 16.0000 0.690451
\(538\) 19.0000 0.819148
\(539\) 12.0000 0.516877
\(540\) 15.0000 0.645497
\(541\) −29.0000 −1.24681 −0.623404 0.781900i \(-0.714251\pi\)
−0.623404 + 0.781900i \(0.714251\pi\)
\(542\) 0 0
\(543\) −22.0000 −0.944110
\(544\) 30.0000 1.28624
\(545\) −30.0000 −1.28506
\(546\) −3.00000 −0.128388
\(547\) −18.0000 −0.769624 −0.384812 0.922995i \(-0.625734\pi\)
−0.384812 + 0.922995i \(0.625734\pi\)
\(548\) −12.0000 −0.512615
\(549\) 8.00000 0.341432
\(550\) 8.00000 0.341121
\(551\) −24.0000 −1.02243
\(552\) −6.00000 −0.255377
\(553\) 1.00000 0.0425243
\(554\) −11.0000 −0.467345
\(555\) −6.00000 −0.254686
\(556\) 21.0000 0.890598
\(557\) −11.0000 −0.466085 −0.233042 0.972467i \(-0.574868\pi\)
−0.233042 + 0.972467i \(0.574868\pi\)
\(558\) −20.0000 −0.846668
\(559\) 12.0000 0.507546
\(560\) −3.00000 −0.126773
\(561\) −12.0000 −0.506640
\(562\) −23.0000 −0.970196
\(563\) 18.0000 0.758610 0.379305 0.925272i \(-0.376163\pi\)
0.379305 + 0.925272i \(0.376163\pi\)
\(564\) 7.00000 0.294753
\(565\) 0 0
\(566\) −24.0000 −1.00880
\(567\) −1.00000 −0.0419961
\(568\) 45.0000 1.88816
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) −12.0000 −0.502625
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) 6.00000 0.250873
\(573\) 15.0000 0.626634
\(574\) −10.0000 −0.417392
\(575\) 8.00000 0.333623
\(576\) −14.0000 −0.583333
\(577\) −16.0000 −0.666089 −0.333044 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) −19.0000 −0.790296
\(579\) −14.0000 −0.581820
\(580\) −18.0000 −0.747409
\(581\) 6.00000 0.248922
\(582\) −19.0000 −0.787575
\(583\) −16.0000 −0.662652
\(584\) 6.00000 0.248282
\(585\) 18.0000 0.744208
\(586\) 12.0000 0.495715
\(587\) 25.0000 1.03186 0.515930 0.856631i \(-0.327446\pi\)
0.515930 + 0.856631i \(0.327446\pi\)
\(588\) −6.00000 −0.247436
\(589\) −40.0000 −1.64817
\(590\) −9.00000 −0.370524
\(591\) 6.00000 0.246807
\(592\) 2.00000 0.0821995
\(593\) 27.0000 1.10876 0.554379 0.832265i \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) 10.0000 0.410305
\(595\) −18.0000 −0.737928
\(596\) 6.00000 0.245770
\(597\) −11.0000 −0.450200
\(598\) −6.00000 −0.245358
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) −12.0000 −0.489898
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 4.00000 0.163028
\(603\) −16.0000 −0.651570
\(604\) −6.00000 −0.244137
\(605\) 21.0000 0.853771
\(606\) 11.0000 0.446844
\(607\) 13.0000 0.527654 0.263827 0.964570i \(-0.415015\pi\)
0.263827 + 0.964570i \(0.415015\pi\)
\(608\) −20.0000 −0.811107
\(609\) −6.00000 −0.243132
\(610\) −12.0000 −0.485866
\(611\) 21.0000 0.849569
\(612\) −12.0000 −0.485071
\(613\) 6.00000 0.242338 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) −12.0000 −0.484281
\(615\) −30.0000 −1.20972
\(616\) 6.00000 0.241747
\(617\) 37.0000 1.48956 0.744782 0.667308i \(-0.232553\pi\)
0.744782 + 0.667308i \(0.232553\pi\)
\(618\) −9.00000 −0.362033
\(619\) 37.0000 1.48716 0.743578 0.668649i \(-0.233127\pi\)
0.743578 + 0.668649i \(0.233127\pi\)
\(620\) −30.0000 −1.20483
\(621\) 10.0000 0.401286
\(622\) −4.00000 −0.160385
\(623\) 7.00000 0.280449
\(624\) 3.00000 0.120096
\(625\) −29.0000 −1.16000
\(626\) 26.0000 1.03917
\(627\) 8.00000 0.319489
\(628\) 18.0000 0.718278
\(629\) 12.0000 0.478471
\(630\) 6.00000 0.239046
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −3.00000 −0.119334
\(633\) 12.0000 0.476957
\(634\) −31.0000 −1.23117
\(635\) 33.0000 1.30957
\(636\) 8.00000 0.317221
\(637\) −18.0000 −0.713186
\(638\) −12.0000 −0.475085
\(639\) −30.0000 −1.18678
\(640\) −9.00000 −0.355756
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) −11.0000 −0.434135
\(643\) 16.0000 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(644\) 2.00000 0.0788110
\(645\) 12.0000 0.472500
\(646\) 24.0000 0.944267
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 3.00000 0.117851
\(649\) 6.00000 0.235521
\(650\) −12.0000 −0.470679
\(651\) −10.0000 −0.391931
\(652\) −4.00000 −0.156652
\(653\) −7.00000 −0.273931 −0.136966 0.990576i \(-0.543735\pi\)
−0.136966 + 0.990576i \(0.543735\pi\)
\(654\) 10.0000 0.391031
\(655\) −18.0000 −0.703318
\(656\) 10.0000 0.390434
\(657\) −4.00000 −0.156055
\(658\) 7.00000 0.272888
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 6.00000 0.233550
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −20.0000 −0.777322
\(663\) 18.0000 0.699062
\(664\) −18.0000 −0.698535
\(665\) 12.0000 0.465340
\(666\) −4.00000 −0.154997
\(667\) −12.0000 −0.464642
\(668\) −18.0000 −0.696441
\(669\) 26.0000 1.00522
\(670\) 24.0000 0.927201
\(671\) 8.00000 0.308837
\(672\) −5.00000 −0.192879
\(673\) −30.0000 −1.15642 −0.578208 0.815890i \(-0.696248\pi\)
−0.578208 + 0.815890i \(0.696248\pi\)
\(674\) −31.0000 −1.19408
\(675\) 20.0000 0.769800
\(676\) 4.00000 0.153846
\(677\) −15.0000 −0.576497 −0.288248 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 0 0
\(679\) 19.0000 0.729153
\(680\) 54.0000 2.07081
\(681\) 8.00000 0.306561
\(682\) −20.0000 −0.765840
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 8.00000 0.305888
\(685\) −36.0000 −1.37549
\(686\) −13.0000 −0.496342
\(687\) −16.0000 −0.610438
\(688\) −4.00000 −0.152499
\(689\) 24.0000 0.914327
\(690\) −6.00000 −0.228416
\(691\) −23.0000 −0.874961 −0.437481 0.899228i \(-0.644129\pi\)
−0.437481 + 0.899228i \(0.644129\pi\)
\(692\) 8.00000 0.304114
\(693\) −4.00000 −0.151947
\(694\) 14.0000 0.531433
\(695\) 63.0000 2.38973
\(696\) 18.0000 0.682288
\(697\) 60.0000 2.27266
\(698\) −12.0000 −0.454207
\(699\) 18.0000 0.680823
\(700\) 4.00000 0.151186
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) −15.0000 −0.566139
\(703\) −8.00000 −0.301726
\(704\) −14.0000 −0.527645
\(705\) 21.0000 0.790906
\(706\) 4.00000 0.150542
\(707\) −11.0000 −0.413698
\(708\) −3.00000 −0.112747
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 45.0000 1.68882
\(711\) 2.00000 0.0750059
\(712\) −21.0000 −0.787008
\(713\) −20.0000 −0.749006
\(714\) 6.00000 0.224544
\(715\) 18.0000 0.673162
\(716\) 16.0000 0.597948
\(717\) −12.0000 −0.448148
\(718\) 35.0000 1.30619
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) −6.00000 −0.223607
\(721\) 9.00000 0.335178
\(722\) 3.00000 0.111648
\(723\) 15.0000 0.557856
\(724\) −22.0000 −0.817624
\(725\) −24.0000 −0.891338
\(726\) −7.00000 −0.259794
\(727\) 30.0000 1.11264 0.556319 0.830969i \(-0.312213\pi\)
0.556319 + 0.830969i \(0.312213\pi\)
\(728\) −9.00000 −0.333562
\(729\) 13.0000 0.481481
\(730\) 6.00000 0.222070
\(731\) −24.0000 −0.887672
\(732\) −4.00000 −0.147844
\(733\) 34.0000 1.25582 0.627909 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) 2.00000 0.0738213
\(735\) −18.0000 −0.663940
\(736\) −10.0000 −0.368605
\(737\) −16.0000 −0.589368
\(738\) −20.0000 −0.736210
\(739\) −13.0000 −0.478213 −0.239106 0.970993i \(-0.576854\pi\)
−0.239106 + 0.970993i \(0.576854\pi\)
\(740\) −6.00000 −0.220564
\(741\) −12.0000 −0.440831
\(742\) 8.00000 0.293689
\(743\) 20.0000 0.733729 0.366864 0.930274i \(-0.380431\pi\)
0.366864 + 0.930274i \(0.380431\pi\)
\(744\) 30.0000 1.09985
\(745\) 18.0000 0.659469
\(746\) 2.00000 0.0732252
\(747\) 12.0000 0.439057
\(748\) −12.0000 −0.438763
\(749\) 11.0000 0.401931
\(750\) 3.00000 0.109545
\(751\) 10.0000 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) −7.00000 −0.255264
\(753\) 5.00000 0.182210
\(754\) 18.0000 0.655521
\(755\) −18.0000 −0.655087
\(756\) 5.00000 0.181848
\(757\) −9.00000 −0.327111 −0.163555 0.986534i \(-0.552296\pi\)
−0.163555 + 0.986534i \(0.552296\pi\)
\(758\) 23.0000 0.835398
\(759\) 4.00000 0.145191
\(760\) −36.0000 −1.30586
\(761\) −10.0000 −0.362500 −0.181250 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) −11.0000 −0.398488
\(763\) −10.0000 −0.362024
\(764\) 15.0000 0.542681
\(765\) −36.0000 −1.30158
\(766\) −2.00000 −0.0722629
\(767\) −9.00000 −0.324971
\(768\) 17.0000 0.613435
\(769\) −36.0000 −1.29819 −0.649097 0.760706i \(-0.724853\pi\)
−0.649097 + 0.760706i \(0.724853\pi\)
\(770\) 6.00000 0.216225
\(771\) 2.00000 0.0720282
\(772\) −14.0000 −0.503871
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 8.00000 0.287554
\(775\) −40.0000 −1.43684
\(776\) −57.0000 −2.04618
\(777\) −2.00000 −0.0717496
\(778\) 9.00000 0.322666
\(779\) −40.0000 −1.43315
\(780\) −9.00000 −0.322252
\(781\) −30.0000 −1.07348
\(782\) 12.0000 0.429119
\(783\) −30.0000 −1.07211
\(784\) 6.00000 0.214286
\(785\) 54.0000 1.92734
\(786\) 6.00000 0.214013
\(787\) −26.0000 −0.926800 −0.463400 0.886149i \(-0.653371\pi\)
−0.463400 + 0.886149i \(0.653371\pi\)
\(788\) 6.00000 0.213741
\(789\) −26.0000 −0.925625
\(790\) −3.00000 −0.106735
\(791\) 0 0
\(792\) 12.0000 0.426401
\(793\) −12.0000 −0.426132
\(794\) 1.00000 0.0354887
\(795\) 24.0000 0.851192
\(796\) −11.0000 −0.389885
\(797\) −10.0000 −0.354218 −0.177109 0.984191i \(-0.556675\pi\)
−0.177109 + 0.984191i \(0.556675\pi\)
\(798\) −4.00000 −0.141598
\(799\) −42.0000 −1.48585
\(800\) −20.0000 −0.707107
\(801\) 14.0000 0.494666
\(802\) −10.0000 −0.353112
\(803\) −4.00000 −0.141157
\(804\) 8.00000 0.282138
\(805\) 6.00000 0.211472
\(806\) 30.0000 1.05670
\(807\) 19.0000 0.668832
\(808\) 33.0000 1.16094
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) 3.00000 0.105409
\(811\) 50.0000 1.75574 0.877869 0.478901i \(-0.158965\pi\)
0.877869 + 0.478901i \(0.158965\pi\)
\(812\) −6.00000 −0.210559
\(813\) 0 0
\(814\) −4.00000 −0.140200
\(815\) −12.0000 −0.420342
\(816\) −6.00000 −0.210042
\(817\) 16.0000 0.559769
\(818\) 0 0
\(819\) 6.00000 0.209657
\(820\) −30.0000 −1.04765
\(821\) 2.00000 0.0698005 0.0349002 0.999391i \(-0.488889\pi\)
0.0349002 + 0.999391i \(0.488889\pi\)
\(822\) 12.0000 0.418548
\(823\) −48.0000 −1.67317 −0.836587 0.547833i \(-0.815453\pi\)
−0.836587 + 0.547833i \(0.815453\pi\)
\(824\) −27.0000 −0.940590
\(825\) 8.00000 0.278524
\(826\) −3.00000 −0.104383
\(827\) −1.00000 −0.0347734 −0.0173867 0.999849i \(-0.505535\pi\)
−0.0173867 + 0.999849i \(0.505535\pi\)
\(828\) 4.00000 0.139010
\(829\) −4.00000 −0.138926 −0.0694629 0.997585i \(-0.522129\pi\)
−0.0694629 + 0.997585i \(0.522129\pi\)
\(830\) −18.0000 −0.624789
\(831\) −11.0000 −0.381586
\(832\) 21.0000 0.728044
\(833\) 36.0000 1.24733
\(834\) −21.0000 −0.727171
\(835\) −54.0000 −1.86875
\(836\) 8.00000 0.276686
\(837\) −50.0000 −1.72825
\(838\) −9.00000 −0.310900
\(839\) 12.0000 0.414286 0.207143 0.978311i \(-0.433583\pi\)
0.207143 + 0.978311i \(0.433583\pi\)
\(840\) −9.00000 −0.310530
\(841\) 7.00000 0.241379
\(842\) 13.0000 0.448010
\(843\) −23.0000 −0.792162
\(844\) 12.0000 0.413057
\(845\) 12.0000 0.412813
\(846\) 14.0000 0.481330
\(847\) 7.00000 0.240523
\(848\) −8.00000 −0.274721
\(849\) −24.0000 −0.823678
\(850\) 24.0000 0.823193
\(851\) −4.00000 −0.137118
\(852\) 15.0000 0.513892
\(853\) −4.00000 −0.136957 −0.0684787 0.997653i \(-0.521815\pi\)
−0.0684787 + 0.997653i \(0.521815\pi\)
\(854\) −4.00000 −0.136877
\(855\) 24.0000 0.820783
\(856\) −33.0000 −1.12792
\(857\) 41.0000 1.40053 0.700267 0.713881i \(-0.253064\pi\)
0.700267 + 0.713881i \(0.253064\pi\)
\(858\) −6.00000 −0.204837
\(859\) 45.0000 1.53538 0.767690 0.640821i \(-0.221406\pi\)
0.767690 + 0.640821i \(0.221406\pi\)
\(860\) 12.0000 0.409197
\(861\) −10.0000 −0.340799
\(862\) −20.0000 −0.681203
\(863\) 14.0000 0.476566 0.238283 0.971196i \(-0.423415\pi\)
0.238283 + 0.971196i \(0.423415\pi\)
\(864\) −25.0000 −0.850517
\(865\) 24.0000 0.816024
\(866\) 3.00000 0.101944
\(867\) −19.0000 −0.645274
\(868\) −10.0000 −0.339422
\(869\) 2.00000 0.0678454
\(870\) 18.0000 0.610257
\(871\) 24.0000 0.813209
\(872\) 30.0000 1.01593
\(873\) 38.0000 1.28611
\(874\) −8.00000 −0.270604
\(875\) −3.00000 −0.101419
\(876\) 2.00000 0.0675737
\(877\) −30.0000 −1.01303 −0.506514 0.862232i \(-0.669066\pi\)
−0.506514 + 0.862232i \(0.669066\pi\)
\(878\) 20.0000 0.674967
\(879\) 12.0000 0.404750
\(880\) −6.00000 −0.202260
\(881\) −32.0000 −1.07811 −0.539054 0.842271i \(-0.681218\pi\)
−0.539054 + 0.842271i \(0.681218\pi\)
\(882\) −12.0000 −0.404061
\(883\) −49.0000 −1.64898 −0.824491 0.565876i \(-0.808538\pi\)
−0.824491 + 0.565876i \(0.808538\pi\)
\(884\) 18.0000 0.605406
\(885\) −9.00000 −0.302532
\(886\) 4.00000 0.134383
\(887\) 38.0000 1.27592 0.637958 0.770072i \(-0.279780\pi\)
0.637958 + 0.770072i \(0.279780\pi\)
\(888\) 6.00000 0.201347
\(889\) 11.0000 0.368928
\(890\) −21.0000 −0.703922
\(891\) −2.00000 −0.0670025
\(892\) 26.0000 0.870544
\(893\) 28.0000 0.936984
\(894\) −6.00000 −0.200670
\(895\) 48.0000 1.60446
\(896\) −3.00000 −0.100223
\(897\) −6.00000 −0.200334
\(898\) 22.0000 0.734150
\(899\) 60.0000 2.00111
\(900\) 8.00000 0.266667
\(901\) −48.0000 −1.59911
\(902\) −20.0000 −0.665927
\(903\) 4.00000 0.133112
\(904\) 0 0
\(905\) −66.0000 −2.19391
\(906\) 6.00000 0.199337
\(907\) −32.0000 −1.06254 −0.531271 0.847202i \(-0.678286\pi\)
−0.531271 + 0.847202i \(0.678286\pi\)
\(908\) 8.00000 0.265489
\(909\) −22.0000 −0.729694
\(910\) −9.00000 −0.298347
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 4.00000 0.132453
\(913\) 12.0000 0.397142
\(914\) −7.00000 −0.231539
\(915\) −12.0000 −0.396708
\(916\) −16.0000 −0.528655
\(917\) −6.00000 −0.198137
\(918\) 30.0000 0.990148
\(919\) 56.0000 1.84727 0.923635 0.383274i \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) −18.0000 −0.593442
\(921\) −12.0000 −0.395413
\(922\) 10.0000 0.329332
\(923\) 45.0000 1.48119
\(924\) 2.00000 0.0657952
\(925\) −8.00000 −0.263038
\(926\) 19.0000 0.624379
\(927\) 18.0000 0.591198
\(928\) 30.0000 0.984798
\(929\) 12.0000 0.393707 0.196854 0.980433i \(-0.436928\pi\)
0.196854 + 0.980433i \(0.436928\pi\)
\(930\) 30.0000 0.983739
\(931\) −24.0000 −0.786568
\(932\) 18.0000 0.589610
\(933\) −4.00000 −0.130954
\(934\) −6.00000 −0.196326
\(935\) −36.0000 −1.17733
\(936\) −18.0000 −0.588348
\(937\) 28.0000 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(938\) 8.00000 0.261209
\(939\) 26.0000 0.848478
\(940\) 21.0000 0.684944
\(941\) −6.00000 −0.195594 −0.0977972 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) −18.0000 −0.586472
\(943\) −20.0000 −0.651290
\(944\) 3.00000 0.0976417
\(945\) 15.0000 0.487950
\(946\) 8.00000 0.260102
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) −1.00000 −0.0324785
\(949\) 6.00000 0.194768
\(950\) −16.0000 −0.519109
\(951\) −31.0000 −1.00524
\(952\) 18.0000 0.583383
\(953\) 9.00000 0.291539 0.145769 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(954\) 16.0000 0.518019
\(955\) 45.0000 1.45617
\(956\) −12.0000 −0.388108
\(957\) −12.0000 −0.387905
\(958\) 0 0
\(959\) −12.0000 −0.387500
\(960\) 21.0000 0.677772
\(961\) 69.0000 2.22581
\(962\) 6.00000 0.193448
\(963\) 22.0000 0.708940
\(964\) 15.0000 0.483117
\(965\) −42.0000 −1.35203
\(966\) −2.00000 −0.0643489
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) −21.0000 −0.674966
\(969\) 24.0000 0.770991
\(970\) −57.0000 −1.83016
\(971\) −18.0000 −0.577647 −0.288824 0.957382i \(-0.593264\pi\)
−0.288824 + 0.957382i \(0.593264\pi\)
\(972\) 16.0000 0.513200
\(973\) 21.0000 0.673229
\(974\) −18.0000 −0.576757
\(975\) −12.0000 −0.384308
\(976\) 4.00000 0.128037
\(977\) −6.00000 −0.191957 −0.0959785 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 4.00000 0.127906
\(979\) 14.0000 0.447442
\(980\) −18.0000 −0.574989
\(981\) −20.0000 −0.638551
\(982\) −13.0000 −0.414847
\(983\) −40.0000 −1.27580 −0.637901 0.770118i \(-0.720197\pi\)
−0.637901 + 0.770118i \(0.720197\pi\)
\(984\) 30.0000 0.956365
\(985\) 18.0000 0.573528
\(986\) −36.0000 −1.14647
\(987\) 7.00000 0.222812
\(988\) −12.0000 −0.381771
\(989\) 8.00000 0.254385
\(990\) 12.0000 0.381385
\(991\) −57.0000 −1.81066 −0.905332 0.424704i \(-0.860378\pi\)
−0.905332 + 0.424704i \(0.860378\pi\)
\(992\) 50.0000 1.58750
\(993\) −20.0000 −0.634681
\(994\) 15.0000 0.475771
\(995\) −33.0000 −1.04617
\(996\) −6.00000 −0.190117
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) −10.0000 −0.316544
\(999\) −10.0000 −0.316386
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 \(a_p\))