Properties

Label 26.2.a.a.1.1
Level 26
Weight 2
Character 26.1
Self dual Yes
Analytic conductor 0.208
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 26.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.207611045255\)
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 \(\chi\) = 26.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.00000 q^{5}\) \(-1.00000 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.00000 q^{5}\) \(-1.00000 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+3.00000 q^{10}\) \(+6.00000 q^{11}\) \(+1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+1.00000 q^{14}\) \(-3.00000 q^{15}\) \(+1.00000 q^{16}\) \(-3.00000 q^{17}\) \(+2.00000 q^{18}\) \(+2.00000 q^{19}\) \(-3.00000 q^{20}\) \(-1.00000 q^{21}\) \(-6.00000 q^{22}\) \(-1.00000 q^{24}\) \(+4.00000 q^{25}\) \(-1.00000 q^{26}\) \(-5.00000 q^{27}\) \(-1.00000 q^{28}\) \(+6.00000 q^{29}\) \(+3.00000 q^{30}\) \(-4.00000 q^{31}\) \(-1.00000 q^{32}\) \(+6.00000 q^{33}\) \(+3.00000 q^{34}\) \(+3.00000 q^{35}\) \(-2.00000 q^{36}\) \(-7.00000 q^{37}\) \(-2.00000 q^{38}\) \(+1.00000 q^{39}\) \(+3.00000 q^{40}\) \(+1.00000 q^{42}\) \(-1.00000 q^{43}\) \(+6.00000 q^{44}\) \(+6.00000 q^{45}\) \(+3.00000 q^{47}\) \(+1.00000 q^{48}\) \(-6.00000 q^{49}\) \(-4.00000 q^{50}\) \(-3.00000 q^{51}\) \(+1.00000 q^{52}\) \(+5.00000 q^{54}\) \(-18.0000 q^{55}\) \(+1.00000 q^{56}\) \(+2.00000 q^{57}\) \(-6.00000 q^{58}\) \(-6.00000 q^{59}\) \(-3.00000 q^{60}\) \(+8.00000 q^{61}\) \(+4.00000 q^{62}\) \(+2.00000 q^{63}\) \(+1.00000 q^{64}\) \(-3.00000 q^{65}\) \(-6.00000 q^{66}\) \(+14.0000 q^{67}\) \(-3.00000 q^{68}\) \(-3.00000 q^{70}\) \(-3.00000 q^{71}\) \(+2.00000 q^{72}\) \(+2.00000 q^{73}\) \(+7.00000 q^{74}\) \(+4.00000 q^{75}\) \(+2.00000 q^{76}\) \(-6.00000 q^{77}\) \(-1.00000 q^{78}\) \(+8.00000 q^{79}\) \(-3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+12.0000 q^{83}\) \(-1.00000 q^{84}\) \(+9.00000 q^{85}\) \(+1.00000 q^{86}\) \(+6.00000 q^{87}\) \(-6.00000 q^{88}\) \(-6.00000 q^{89}\) \(-6.00000 q^{90}\) \(-1.00000 q^{91}\) \(-4.00000 q^{93}\) \(-3.00000 q^{94}\) \(-6.00000 q^{95}\) \(-1.00000 q^{96}\) \(-10.0000 q^{97}\) \(+6.00000 q^{98}\) \(-12.0000 q^{99}\) \(+O(q^{100})\)

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
\(5\) −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 \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) 3.00000 0.948683
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) 1.00000 0.267261
\(15\) −3.00000 −0.774597
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 2.00000 0.471405
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −3.00000 −0.670820
\(21\) −1.00000 −0.218218
\(22\) −6.00000 −1.27920
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.00000 0.800000
\(26\) −1.00000 −0.196116
\(27\) −5.00000 −0.962250
\(28\) −1.00000 −0.188982
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 3.00000 0.547723
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.00000 1.04447
\(34\) 3.00000 0.514496
\(35\) 3.00000 0.507093
\(36\) −2.00000 −0.333333
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) −2.00000 −0.324443
\(39\) 1.00000 0.160128
\(40\) 3.00000 0.474342
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 1.00000 0.154303
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 6.00000 0.904534
\(45\) 6.00000 0.894427
\(46\) 0 0
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) −4.00000 −0.565685
\(51\) −3.00000 −0.420084
\(52\) 1.00000 0.138675
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 5.00000 0.680414
\(55\) −18.0000 −2.42712
\(56\) 1.00000 0.133631
\(57\) 2.00000 0.264906
\(58\) −6.00000 −0.787839
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) −3.00000 −0.387298
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 4.00000 0.508001
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) −3.00000 −0.372104
\(66\) −6.00000 −0.738549
\(67\) 14.0000 1.71037 0.855186 0.518321i \(-0.173443\pi\)
0.855186 + 0.518321i \(0.173443\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) −3.00000 −0.358569
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 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
\(75\) 4.00000 0.461880
\(76\) 2.00000 0.229416
\(77\) −6.00000 −0.683763
\(78\) −1.00000 −0.113228
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −3.00000 −0.335410
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −1.00000 −0.109109
\(85\) 9.00000 0.976187
\(86\) 1.00000 0.107833
\(87\) 6.00000 0.643268
\(88\) −6.00000 −0.639602
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −6.00000 −0.632456
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −4.00000 −0.414781
\(94\) −3.00000 −0.309426
\(95\) −6.00000 −0.615587
\(96\) −1.00000 −0.102062
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 6.00000 0.606092
\(99\) −12.0000 −1.20605
\(100\) 4.00000 0.400000
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 3.00000 0.297044
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 3.00000 0.292770
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −5.00000 −0.481125
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 18.0000 1.71623
\(111\) −7.00000 −0.664411
\(112\) −1.00000 −0.0944911
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −2.00000 −0.187317
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) −2.00000 −0.184900
\(118\) 6.00000 0.552345
\(119\) 3.00000 0.275010
\(120\) 3.00000 0.273861
\(121\) 25.0000 2.27273
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 3.00000 0.268328
\(126\) −2.00000 −0.178174
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 3.00000 0.263117
\(131\) −21.0000 −1.83478 −0.917389 0.397991i \(-0.869707\pi\)
−0.917389 + 0.397991i \(0.869707\pi\)
\(132\) 6.00000 0.522233
\(133\) −2.00000 −0.173422
\(134\) −14.0000 −1.20942
\(135\) 15.0000 1.29099
\(136\) 3.00000 0.257248
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 3.00000 0.253546
\(141\) 3.00000 0.252646
\(142\) 3.00000 0.251754
\(143\) 6.00000 0.501745
\(144\) −2.00000 −0.166667
\(145\) −18.0000 −1.49482
\(146\) −2.00000 −0.165521
\(147\) −6.00000 −0.494872
\(148\) −7.00000 −0.575396
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −4.00000 −0.326599
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) −2.00000 −0.162221
\(153\) 6.00000 0.485071
\(154\) 6.00000 0.483494
\(155\) 12.0000 0.963863
\(156\) 1.00000 0.0800641
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −8.00000 −0.636446
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) −18.0000 −1.40130
\(166\) −12.0000 −0.931381
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.00000 0.0771517
\(169\) 1.00000 0.0769231
\(170\) −9.00000 −0.690268
\(171\) −4.00000 −0.305888
\(172\) −1.00000 −0.0762493
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) −6.00000 −0.454859
\(175\) −4.00000 −0.302372
\(176\) 6.00000 0.452267
\(177\) −6.00000 −0.450988
\(178\) 6.00000 0.449719
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 6.00000 0.447214
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 1.00000 0.0741249
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) 21.0000 1.54395
\(186\) 4.00000 0.293294
\(187\) −18.0000 −1.31629
\(188\) 3.00000 0.218797
\(189\) 5.00000 0.363696
\(190\) 6.00000 0.435286
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 10.0000 0.717958
\(195\) −3.00000 −0.214834
\(196\) −6.00000 −0.428571
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 12.0000 0.852803
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) −4.00000 −0.282843
\(201\) 14.0000 0.987484
\(202\) 12.0000 0.844317
\(203\) −6.00000 −0.421117
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) 12.0000 0.830057
\(210\) −3.00000 −0.207020
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 0 0
\(213\) −3.00000 −0.205557
\(214\) −12.0000 −0.820303
\(215\) 3.00000 0.204598
\(216\) 5.00000 0.340207
\(217\) 4.00000 0.271538
\(218\) 7.00000 0.474100
\(219\) 2.00000 0.135147
\(220\) −18.0000 −1.21356
\(221\) −3.00000 −0.201802
\(222\) 7.00000 0.469809
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 1.00000 0.0668153
\(225\) −8.00000 −0.533333
\(226\) 6.00000 0.399114
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 2.00000 0.132453
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) −6.00000 −0.393919
\(233\) −27.0000 −1.76883 −0.884414 0.466702i \(-0.845442\pi\)
−0.884414 + 0.466702i \(0.845442\pi\)
\(234\) 2.00000 0.130744
\(235\) −9.00000 −0.587095
\(236\) −6.00000 −0.390567
\(237\) 8.00000 0.519656
\(238\) −3.00000 −0.194461
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) −3.00000 −0.193649
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −25.0000 −1.60706
\(243\) 16.0000 1.02640
\(244\) 8.00000 0.512148
\(245\) 18.0000 1.14998
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) 4.00000 0.254000
\(249\) 12.0000 0.760469
\(250\) −3.00000 −0.189737
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) −20.0000 −1.25491
\(255\) 9.00000 0.563602
\(256\) 1.00000 0.0625000
\(257\) 9.00000 0.561405 0.280702 0.959795i \(-0.409433\pi\)
0.280702 + 0.959795i \(0.409433\pi\)
\(258\) 1.00000 0.0622573
\(259\) 7.00000 0.434959
\(260\) −3.00000 −0.186052
\(261\) −12.0000 −0.742781
\(262\) 21.0000 1.29738
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) −6.00000 −0.369274
\(265\) 0 0
\(266\) 2.00000 0.122628
\(267\) −6.00000 −0.367194
\(268\) 14.0000 0.855186
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) −15.0000 −0.912871
\(271\) 11.0000 0.668202 0.334101 0.942537i \(-0.391567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(272\) −3.00000 −0.181902
\(273\) −1.00000 −0.0605228
\(274\) 0 0
\(275\) 24.0000 1.44725
\(276\) 0 0
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 13.0000 0.779688
\(279\) 8.00000 0.478947
\(280\) −3.00000 −0.179284
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −3.00000 −0.178647
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −3.00000 −0.178017
\(285\) −6.00000 −0.355409
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) −8.00000 −0.470588
\(290\) 18.0000 1.05700
\(291\) −10.0000 −0.586210
\(292\) 2.00000 0.117041
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 6.00000 0.349927
\(295\) 18.0000 1.04800
\(296\) 7.00000 0.406867
\(297\) −30.0000 −1.74078
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) 1.00000 0.0576390
\(302\) −17.0000 −0.978240
\(303\) −12.0000 −0.689382
\(304\) 2.00000 0.114708
\(305\) −24.0000 −1.37424
\(306\) −6.00000 −0.342997
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −6.00000 −0.341882
\(309\) −4.00000 −0.227552
\(310\) −12.0000 −0.681554
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) −14.0000 −0.790066
\(315\) −6.00000 −0.338062
\(316\) 8.00000 0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) 36.0000 2.01561
\(320\) −3.00000 −0.167705
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) 16.0000 0.886158
\(327\) −7.00000 −0.387101
\(328\) 0 0
\(329\) −3.00000 −0.165395
\(330\) 18.0000 0.990867
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 12.0000 0.658586
\(333\) 14.0000 0.767195
\(334\) 0 0
\(335\) −42.0000 −2.29471
\(336\) −1.00000 −0.0545545
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −6.00000 −0.325875
\(340\) 9.00000 0.488094
\(341\) −24.0000 −1.29967
\(342\) 4.00000 0.216295
\(343\) 13.0000 0.701934
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) 0 0
\(347\) 3.00000 0.161048 0.0805242 0.996753i \(-0.474341\pi\)
0.0805242 + 0.996753i \(0.474341\pi\)
\(348\) 6.00000 0.321634
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 4.00000 0.213809
\(351\) −5.00000 −0.266880
\(352\) −6.00000 −0.319801
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 6.00000 0.318896
\(355\) 9.00000 0.477670
\(356\) −6.00000 −0.317999
\(357\) 3.00000 0.158777
\(358\) −3.00000 −0.158555
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −6.00000 −0.316228
\(361\) −15.0000 −0.789474
\(362\) −20.0000 −1.05118
\(363\) 25.0000 1.31216
\(364\) −1.00000 −0.0524142
\(365\) −6.00000 −0.314054
\(366\) −8.00000 −0.418167
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −21.0000 −1.09174
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 18.0000 0.930758
\(375\) 3.00000 0.154919
\(376\) −3.00000 −0.154713
\(377\) 6.00000 0.309016
\(378\) −5.00000 −0.257172
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −6.00000 −0.307794
\(381\) 20.0000 1.02463
\(382\) 18.0000 0.920960
\(383\) 21.0000 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 18.0000 0.917365
\(386\) 4.00000 0.203595
\(387\) 2.00000 0.101666
\(388\) −10.0000 −0.507673
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 3.00000 0.151911
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) −21.0000 −1.05931
\(394\) −3.00000 −0.151138
\(395\) −24.0000 −1.20757
\(396\) −12.0000 −0.603023
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −2.00000 −0.100251
\(399\) −2.00000 −0.100125
\(400\) 4.00000 0.200000
\(401\) 36.0000 1.79775 0.898877 0.438201i \(-0.144384\pi\)
0.898877 + 0.438201i \(0.144384\pi\)
\(402\) −14.0000 −0.698257
\(403\) −4.00000 −0.199254
\(404\) −12.0000 −0.597022
\(405\) −3.00000 −0.149071
\(406\) 6.00000 0.297775
\(407\) −42.0000 −2.08186
\(408\) 3.00000 0.148522
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 6.00000 0.295241
\(414\) 0 0
\(415\) −36.0000 −1.76717
\(416\) −1.00000 −0.0490290
\(417\) −13.0000 −0.636613
\(418\) −12.0000 −0.586939
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 3.00000 0.146385
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 13.0000 0.632830
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 3.00000 0.145350
\(427\) −8.00000 −0.387147
\(428\) 12.0000 0.580042
\(429\) 6.00000 0.289683
\(430\) −3.00000 −0.144673
\(431\) −33.0000 −1.58955 −0.794777 0.606902i \(-0.792412\pi\)
−0.794777 + 0.606902i \(0.792412\pi\)
\(432\) −5.00000 −0.240563
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) −4.00000 −0.192006
\(435\) −18.0000 −0.863034
\(436\) −7.00000 −0.335239
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 18.0000 0.858116
\(441\) 12.0000 0.571429
\(442\) 3.00000 0.142695
\(443\) 21.0000 0.997740 0.498870 0.866677i \(-0.333748\pi\)
0.498870 + 0.866677i \(0.333748\pi\)
\(444\) −7.00000 −0.332205
\(445\) 18.0000 0.853282
\(446\) 19.0000 0.899676
\(447\) −6.00000 −0.283790
\(448\) −1.00000 −0.0472456
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 8.00000 0.377124
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 17.0000 0.798730
\(454\) 0 0
\(455\) 3.00000 0.140642
\(456\) −2.00000 −0.0936586
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 13.0000 0.607450
\(459\) 15.0000 0.700140
\(460\) 0 0
\(461\) 9.00000 0.419172 0.209586 0.977790i \(-0.432788\pi\)
0.209586 + 0.977790i \(0.432788\pi\)
\(462\) 6.00000 0.279145
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 6.00000 0.278543
\(465\) 12.0000 0.556487
\(466\) 27.0000 1.25075
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −14.0000 −0.646460
\(470\) 9.00000 0.415139
\(471\) 14.0000 0.645086
\(472\) 6.00000 0.276172
\(473\) −6.00000 −0.275880
\(474\) −8.00000 −0.367452
\(475\) 8.00000 0.367065
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) −15.0000 −0.686084
\(479\) −21.0000 −0.959514 −0.479757 0.877401i \(-0.659275\pi\)
−0.479757 + 0.877401i \(0.659275\pi\)
\(480\) 3.00000 0.136931
\(481\) −7.00000 −0.319173
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) 30.0000 1.36223
\(486\) −16.0000 −0.725775
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −8.00000 −0.362143
\(489\) −16.0000 −0.723545
\(490\) −18.0000 −0.813157
\(491\) −9.00000 −0.406164 −0.203082 0.979162i \(-0.565096\pi\)
−0.203082 + 0.979162i \(0.565096\pi\)
\(492\) 0 0
\(493\) −18.0000 −0.810679
\(494\) −2.00000 −0.0899843
\(495\) 36.0000 1.61808
\(496\) −4.00000 −0.179605
\(497\) 3.00000 0.134568
\(498\) −12.0000 −0.537733
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) 3.00000 0.134164
\(501\) 0 0
\(502\) −24.0000 −1.07117
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 20.0000 0.887357
\(509\) −18.0000 −0.797836 −0.398918 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) −9.00000 −0.398527
\(511\) −2.00000 −0.0884748
\(512\) −1.00000 −0.0441942
\(513\) −10.0000 −0.441511
\(514\) −9.00000 −0.396973
\(515\) 12.0000 0.528783
\(516\) −1.00000 −0.0440225
\(517\) 18.0000 0.791639
\(518\) −7.00000 −0.307562
\(519\) 0 0
\(520\) 3.00000 0.131559
\(521\) −9.00000 −0.394297 −0.197149 0.980374i \(-0.563168\pi\)
−0.197149 + 0.980374i \(0.563168\pi\)
\(522\) 12.0000 0.525226
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −21.0000 −0.917389
\(525\) −4.00000 −0.174574
\(526\) 12.0000 0.523225
\(527\) 12.0000 0.522728
\(528\) 6.00000 0.261116
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) −2.00000 −0.0867110
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) −36.0000 −1.55642
\(536\) −14.0000 −0.604708
\(537\) 3.00000 0.129460
\(538\) −24.0000 −1.03471
\(539\) −36.0000 −1.55063
\(540\) 15.0000 0.645497
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) −11.0000 −0.472490
\(543\) 20.0000 0.858282
\(544\) 3.00000 0.128624
\(545\) 21.0000 0.899541
\(546\) 1.00000 0.0427960
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 0 0
\(549\) −16.0000 −0.682863
\(550\) −24.0000 −1.02336
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 28.0000 1.18961
\(555\) 21.0000 0.891400
\(556\) −13.0000 −0.551323
\(557\) 3.00000 0.127114 0.0635570 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) −8.00000 −0.338667
\(559\) −1.00000 −0.0422955
\(560\) 3.00000 0.126773
\(561\) −18.0000 −0.759961
\(562\) 6.00000 0.253095
\(563\) 39.0000 1.64365 0.821827 0.569737i \(-0.192955\pi\)
0.821827 + 0.569737i \(0.192955\pi\)
\(564\) 3.00000 0.126323
\(565\) 18.0000 0.757266
\(566\) 4.00000 0.168133
\(567\) −1.00000 −0.0419961
\(568\) 3.00000 0.125877
\(569\) 15.0000 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) 6.00000 0.251312
\(571\) 5.00000 0.209243 0.104622 0.994512i \(-0.466637\pi\)
0.104622 + 0.994512i \(0.466637\pi\)
\(572\) 6.00000 0.250873
\(573\) −18.0000 −0.751961
\(574\) 0 0
\(575\) 0 0
\(576\) −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
\(579\) −4.00000 −0.166234
\(580\) −18.0000 −0.747409
\(581\) −12.0000 −0.497844
\(582\) 10.0000 0.414513
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 6.00000 0.248069
\(586\) −21.0000 −0.867502
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) −6.00000 −0.247436
\(589\) −8.00000 −0.329634
\(590\) −18.0000 −0.741048
\(591\) 3.00000 0.123404
\(592\) −7.00000 −0.287698
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 30.0000 1.23091
\(595\) −9.00000 −0.368964
\(596\) −6.00000 −0.245770
\(597\) 2.00000 0.0818546
\(598\) 0 0
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) −4.00000 −0.163299
\(601\) −19.0000 −0.775026 −0.387513 0.921864i \(-0.626666\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(602\) −1.00000 −0.0407570
\(603\) −28.0000 −1.14025
\(604\) 17.0000 0.691720
\(605\) −75.0000 −3.04918
\(606\) 12.0000 0.487467
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) −2.00000 −0.0811107
\(609\) −6.00000 −0.243132
\(610\) 24.0000 0.971732
\(611\) 3.00000 0.121367
\(612\) 6.00000 0.242536
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −2.00000 −0.0807134
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) −24.0000 −0.966204 −0.483102 0.875564i \(-0.660490\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(618\) 4.00000 0.160904
\(619\) −28.0000 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 12.0000 0.481932
\(621\) 0 0
\(622\) 30.0000 1.20289
\(623\) 6.00000 0.240385
\(624\) 1.00000 0.0400320
\(625\) −29.0000 −1.16000
\(626\) 1.00000 0.0399680
\(627\) 12.0000 0.479234
\(628\) 14.0000 0.558661
\(629\) 21.0000 0.837325
\(630\) 6.00000 0.239046
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) −8.00000 −0.318223
\(633\) −13.0000 −0.516704
\(634\) 6.00000 0.238290
\(635\) −60.0000 −2.38103
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) −36.0000 −1.42525
\(639\) 6.00000 0.237356
\(640\) 3.00000 0.118585
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −12.0000 −0.473602
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 0 0
\(645\) 3.00000 0.118125
\(646\) 6.00000 0.236067
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −36.0000 −1.41312
\(650\) −4.00000 −0.156893
\(651\) 4.00000 0.156772
\(652\) −16.0000 −0.626608
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 7.00000 0.273722
\(655\) 63.0000 2.46161
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 3.00000 0.116952
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) −18.0000 −0.700649
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) −8.00000 −0.310929
\(663\) −3.00000 −0.116510
\(664\) −12.0000 −0.465690
\(665\) 6.00000 0.232670
\(666\) −14.0000 −0.542489
\(667\) 0 0
\(668\) 0 0
\(669\) −19.0000 −0.734582
\(670\) 42.0000 1.62260
\(671\) 48.0000 1.85302
\(672\) 1.00000 0.0385758
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −23.0000 −0.885927
\(675\) −20.0000 −0.769800
\(676\) 1.00000 0.0384615
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 6.00000 0.230429
\(679\) 10.0000 0.383765
\(680\) −9.00000 −0.345134
\(681\) 0 0
\(682\) 24.0000 0.919007
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) −13.0000 −0.496342
\(687\) −13.0000 −0.495981
\(688\) −1.00000 −0.0381246
\(689\) 0 0
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 0 0
\(693\) 12.0000 0.455842
\(694\) −3.00000 −0.113878
\(695\) 39.0000 1.47935
\(696\) −6.00000 −0.227429
\(697\) 0 0
\(698\) 19.0000 0.719161
\(699\) −27.0000 −1.02123
\(700\) −4.00000 −0.151186
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 5.00000 0.188713
\(703\) −14.0000 −0.528020
\(704\) 6.00000 0.226134
\(705\) −9.00000 −0.338960
\(706\) −24.0000 −0.903252
\(707\) 12.0000 0.451306
\(708\) −6.00000 −0.225494
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) −9.00000 −0.337764
\(711\) −16.0000 −0.600047
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) −3.00000 −0.112272
\(715\) −18.0000 −0.673162
\(716\) 3.00000 0.112115
\(717\) 15.0000 0.560185
\(718\) 0 0
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 6.00000 0.223607
\(721\) 4.00000 0.148968
\(722\) 15.0000 0.558242
\(723\) −10.0000 −0.371904
\(724\) 20.0000 0.743294
\(725\) 24.0000 0.891338
\(726\) −25.0000 −0.927837
\(727\) −10.0000 −0.370879 −0.185440 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(728\) 1.00000 0.0370625
\(729\) 13.0000 0.481481
\(730\) 6.00000 0.222070
\(731\) 3.00000 0.110959
\(732\) 8.00000 0.295689
\(733\) 23.0000 0.849524 0.424762 0.905305i \(-0.360358\pi\)
0.424762 + 0.905305i \(0.360358\pi\)
\(734\) −26.0000 −0.959678
\(735\) 18.0000 0.663940
\(736\) 0 0
\(737\) 84.0000 3.09418
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 21.0000 0.771975
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) −9.00000 −0.330178 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) 4.00000 0.146647
\(745\) 18.0000 0.659469
\(746\) 4.00000 0.146450
\(747\) −24.0000 −0.878114
\(748\) −18.0000 −0.658145
\(749\) −12.0000 −0.438470
\(750\) −3.00000 −0.109545
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 3.00000 0.109399
\(753\) 24.0000 0.874609
\(754\) −6.00000 −0.218507
\(755\) −51.0000 −1.85608
\(756\) 5.00000 0.181848
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 6.00000 0.217643
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) −20.0000 −0.724524
\(763\) 7.00000 0.253417
\(764\) −18.0000 −0.651217
\(765\) −18.0000 −0.650791
\(766\) −21.0000 −0.758761
\(767\) −6.00000 −0.216647
\(768\) 1.00000 0.0360844
\(769\) 32.0000 1.15395 0.576975 0.816762i \(-0.304233\pi\)
0.576975 + 0.816762i \(0.304233\pi\)
\(770\) −18.0000 −0.648675
\(771\) 9.00000 0.324127
\(772\) −4.00000 −0.143963
\(773\) −39.0000 −1.40273 −0.701366 0.712801i \(-0.747426\pi\)
−0.701366 + 0.712801i \(0.747426\pi\)
\(774\) −2.00000 −0.0718885
\(775\) −16.0000 −0.574737
\(776\) 10.0000 0.358979
\(777\) 7.00000 0.251124
\(778\) 6.00000 0.215110
\(779\) 0 0
\(780\) −3.00000 −0.107417
\(781\) −18.0000 −0.644091
\(782\) 0 0
\(783\) −30.0000 −1.07211
\(784\) −6.00000 −0.214286
\(785\) −42.0000 −1.49904
\(786\) 21.0000 0.749045
\(787\) −40.0000 −1.42585 −0.712923 0.701242i \(-0.752629\pi\)
−0.712923 + 0.701242i \(0.752629\pi\)
\(788\) 3.00000 0.106871
\(789\) −12.0000 −0.427211
\(790\) 24.0000 0.853882
\(791\) 6.00000 0.213335
\(792\) 12.0000 0.426401
\(793\) 8.00000 0.284088
\(794\) 34.0000 1.20661
\(795\) 0 0
\(796\) 2.00000 0.0708881
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 2.00000 0.0707992
\(799\) −9.00000 −0.318397
\(800\) −4.00000 −0.141421
\(801\) 12.0000 0.423999
\(802\) −36.0000 −1.27120
\(803\) 12.0000 0.423471
\(804\) 14.0000 0.493742
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 24.0000 0.844840
\(808\) 12.0000 0.422159
\(809\) −33.0000 −1.16022 −0.580109 0.814539i \(-0.696990\pi\)
−0.580109 + 0.814539i \(0.696990\pi\)
\(810\) 3.00000 0.105409
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −6.00000 −0.210559
\(813\) 11.0000 0.385787
\(814\) 42.0000 1.47210
\(815\) 48.0000 1.68137
\(816\) −3.00000 −0.105021
\(817\) −2.00000 −0.0699711
\(818\) −32.0000 −1.11885
\(819\) 2.00000 0.0698857
\(820\) 0 0
\(821\) −3.00000 −0.104701 −0.0523504 0.998629i \(-0.516671\pi\)
−0.0523504 + 0.998629i \(0.516671\pi\)
\(822\) 0 0
\(823\) 14.0000 0.488009 0.244005 0.969774i \(-0.421539\pi\)
0.244005 + 0.969774i \(0.421539\pi\)
\(824\) 4.00000 0.139347
\(825\) 24.0000 0.835573
\(826\) −6.00000 −0.208767
\(827\) 18.0000 0.625921 0.312961 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(828\) 0 0
\(829\) 38.0000 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) 36.0000 1.24958
\(831\) −28.0000 −0.971309
\(832\) 1.00000 0.0346688
\(833\) 18.0000 0.623663
\(834\) 13.0000 0.450153
\(835\) 0 0
\(836\) 12.0000 0.415029
\(837\) 20.0000 0.691301
\(838\) −9.00000 −0.310900
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) −3.00000 −0.103510
\(841\) 7.00000 0.241379
\(842\) −17.0000 −0.585859
\(843\) −6.00000 −0.206651
\(844\) −13.0000 −0.447478
\(845\) −3.00000 −0.103203
\(846\) 6.00000 0.206284
\(847\) −25.0000 −0.859010
\(848\) 0 0
\(849\) −4.00000 −0.137280
\(850\) 12.0000 0.411597
\(851\) 0 0
\(852\) −3.00000 −0.102778
\(853\) −37.0000 −1.26686 −0.633428 0.773802i \(-0.718353\pi\)
−0.633428 + 0.773802i \(0.718353\pi\)
\(854\) 8.00000 0.273754
\(855\) 12.0000 0.410391
\(856\) −12.0000 −0.410152
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) −6.00000 −0.204837
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 3.00000 0.102299
\(861\) 0 0
\(862\) 33.0000 1.12398
\(863\) −45.0000 −1.53182 −0.765909 0.642949i \(-0.777711\pi\)
−0.765909 + 0.642949i \(0.777711\pi\)
\(864\) 5.00000 0.170103
\(865\) 0 0
\(866\) 25.0000 0.849535
\(867\) −8.00000 −0.271694
\(868\) 4.00000 0.135769
\(869\) 48.0000 1.62829
\(870\) 18.0000 0.610257
\(871\) 14.0000 0.474372
\(872\) 7.00000 0.237050
\(873\) 20.0000 0.676897
\(874\) 0 0
\(875\) −3.00000 −0.101419
\(876\) 2.00000 0.0675737
\(877\) −13.0000 −0.438979 −0.219489 0.975615i \(-0.570439\pi\)
−0.219489 + 0.975615i \(0.570439\pi\)
\(878\) −26.0000 −0.877457
\(879\) 21.0000 0.708312
\(880\) −18.0000 −0.606780
\(881\) 21.0000 0.707508 0.353754 0.935339i \(-0.384905\pi\)
0.353754 + 0.935339i \(0.384905\pi\)
\(882\) −12.0000 −0.404061
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) −3.00000 −0.100901
\(885\) 18.0000 0.605063
\(886\) −21.0000 −0.705509
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 7.00000 0.234905
\(889\) −20.0000 −0.670778
\(890\) −18.0000 −0.603361
\(891\) 6.00000 0.201008
\(892\) −19.0000 −0.636167
\(893\) 6.00000 0.200782
\(894\) 6.00000 0.200670
\(895\) −9.00000 −0.300837
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) −24.0000 −0.800445
\(900\) −8.00000 −0.266667
\(901\) 0 0
\(902\) 0 0
\(903\) 1.00000 0.0332779
\(904\) 6.00000 0.199557
\(905\) −60.0000 −1.99447
\(906\) −17.0000 −0.564787
\(907\) −37.0000 −1.22856 −0.614282 0.789086i \(-0.710554\pi\)
−0.614282 + 0.789086i \(0.710554\pi\)
\(908\) 0 0
\(909\) 24.0000 0.796030
\(910\) −3.00000 −0.0994490
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 2.00000 0.0662266
\(913\) 72.0000 2.38285
\(914\) 10.0000 0.330771
\(915\) −24.0000 −0.793416
\(916\) −13.0000 −0.429532
\(917\) 21.0000 0.693481
\(918\) −15.0000 −0.495074
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 2.00000 0.0659022
\(922\) −9.00000 −0.296399
\(923\) −3.00000 −0.0987462
\(924\) −6.00000 −0.197386
\(925\) −28.0000 −0.920634
\(926\) 40.0000 1.31448
\(927\) 8.00000 0.262754
\(928\) −6.00000 −0.196960
\(929\) 36.0000 1.18112 0.590561 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(930\) −12.0000 −0.393496
\(931\) −12.0000 −0.393284
\(932\) −27.0000 −0.884414
\(933\) −30.0000 −0.982156
\(934\) −36.0000 −1.17796
\(935\) 54.0000 1.76599
\(936\) 2.00000 0.0653720
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 14.0000 0.457116
\(939\) −1.00000 −0.0326338
\(940\) −9.00000 −0.293548
\(941\) −21.0000 −0.684580 −0.342290 0.939594i \(-0.611203\pi\)
−0.342290 + 0.939594i \(0.611203\pi\)
\(942\) −14.0000 −0.456145
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) −15.0000 −0.487950
\(946\) 6.00000 0.195077
\(947\) 6.00000 0.194974 0.0974869 0.995237i \(-0.468920\pi\)
0.0974869 + 0.995237i \(0.468920\pi\)
\(948\) 8.00000 0.259828
\(949\) 2.00000 0.0649227
\(950\) −8.00000 −0.259554
\(951\) −6.00000 −0.194563
\(952\) −3.00000 −0.0972306
\(953\) 15.0000 0.485898 0.242949 0.970039i \(-0.421885\pi\)
0.242949 + 0.970039i \(0.421885\pi\)
\(954\) 0 0
\(955\) 54.0000 1.74740
\(956\) 15.0000 0.485135
\(957\) 36.0000 1.16371
\(958\) 21.0000 0.678479
\(959\) 0 0
\(960\) −3.00000 −0.0968246
\(961\) −15.0000 −0.483871
\(962\) 7.00000 0.225689
\(963\) −24.0000 −0.773389
\(964\) −10.0000 −0.322078
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) −31.0000 −0.996893 −0.498446 0.866921i \(-0.666096\pi\)
−0.498446 + 0.866921i \(0.666096\pi\)
\(968\) −25.0000 −0.803530
\(969\) −6.00000 −0.192748
\(970\) −30.0000 −0.963242
\(971\) −3.00000 −0.0962746 −0.0481373 0.998841i \(-0.515328\pi\)
−0.0481373 + 0.998841i \(0.515328\pi\)
\(972\) 16.0000 0.513200
\(973\) 13.0000 0.416761
\(974\) 16.0000 0.512673
\(975\) 4.00000 0.128103
\(976\) 8.00000 0.256074
\(977\) −54.0000 −1.72761 −0.863807 0.503824i \(-0.831926\pi\)
−0.863807 + 0.503824i \(0.831926\pi\)
\(978\) 16.0000 0.511624
\(979\) −36.0000 −1.15056
\(980\) 18.0000 0.574989
\(981\) 14.0000 0.446986
\(982\) 9.00000 0.287202
\(983\) 39.0000 1.24391 0.621953 0.783054i \(-0.286339\pi\)
0.621953 + 0.783054i \(0.286339\pi\)
\(984\) 0 0
\(985\) −9.00000 −0.286764
\(986\) 18.0000 0.573237
\(987\) −3.00000 −0.0954911
\(988\) 2.00000 0.0636285
\(989\) 0 0
\(990\) −36.0000 −1.14416
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 4.00000 0.127000
\(993\) 8.00000 0.253872
\(994\) −3.00000 −0.0951542
\(995\) −6.00000 −0.190213
\(996\) 12.0000 0.380235
\(997\) −46.0000 −1.45683 −0.728417 0.685134i \(-0.759744\pi\)
−0.728417 + 0.685134i \(0.759744\pi\)
\(998\) 40.0000 1.26618
\(999\) 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 \(a_p\))