Properties

Label 178.2.a.b.1.1
Level 178
Weight 2
Character 178.1
Self dual Yes
Analytic conductor 1.421
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 178 = 2 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 178.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.42133715598\)
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 \(\chi\) = 178.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(-4.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(-4.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+3.00000 q^{10}\) \(-6.00000 q^{11}\) \(+1.00000 q^{12}\) \(+2.00000 q^{13}\) \(-4.00000 q^{14}\) \(+3.00000 q^{15}\) \(+1.00000 q^{16}\) \(+3.00000 q^{17}\) \(-2.00000 q^{18}\) \(+5.00000 q^{19}\) \(+3.00000 q^{20}\) \(-4.00000 q^{21}\) \(-6.00000 q^{22}\) \(-3.00000 q^{23}\) \(+1.00000 q^{24}\) \(+4.00000 q^{25}\) \(+2.00000 q^{26}\) \(-5.00000 q^{27}\) \(-4.00000 q^{28}\) \(+3.00000 q^{30}\) \(+5.00000 q^{31}\) \(+1.00000 q^{32}\) \(-6.00000 q^{33}\) \(+3.00000 q^{34}\) \(-12.0000 q^{35}\) \(-2.00000 q^{36}\) \(-10.0000 q^{37}\) \(+5.00000 q^{38}\) \(+2.00000 q^{39}\) \(+3.00000 q^{40}\) \(-4.00000 q^{42}\) \(-1.00000 q^{43}\) \(-6.00000 q^{44}\) \(-6.00000 q^{45}\) \(-3.00000 q^{46}\) \(+12.0000 q^{47}\) \(+1.00000 q^{48}\) \(+9.00000 q^{49}\) \(+4.00000 q^{50}\) \(+3.00000 q^{51}\) \(+2.00000 q^{52}\) \(+9.00000 q^{53}\) \(-5.00000 q^{54}\) \(-18.0000 q^{55}\) \(-4.00000 q^{56}\) \(+5.00000 q^{57}\) \(+12.0000 q^{59}\) \(+3.00000 q^{60}\) \(-10.0000 q^{61}\) \(+5.00000 q^{62}\) \(+8.00000 q^{63}\) \(+1.00000 q^{64}\) \(+6.00000 q^{65}\) \(-6.00000 q^{66}\) \(-4.00000 q^{67}\) \(+3.00000 q^{68}\) \(-3.00000 q^{69}\) \(-12.0000 q^{70}\) \(-6.00000 q^{71}\) \(-2.00000 q^{72}\) \(-1.00000 q^{73}\) \(-10.0000 q^{74}\) \(+4.00000 q^{75}\) \(+5.00000 q^{76}\) \(+24.0000 q^{77}\) \(+2.00000 q^{78}\) \(-10.0000 q^{79}\) \(+3.00000 q^{80}\) \(+1.00000 q^{81}\) \(-12.0000 q^{83}\) \(-4.00000 q^{84}\) \(+9.00000 q^{85}\) \(-1.00000 q^{86}\) \(-6.00000 q^{88}\) \(-1.00000 q^{89}\) \(-6.00000 q^{90}\) \(-8.00000 q^{91}\) \(-3.00000 q^{92}\) \(+5.00000 q^{93}\) \(+12.0000 q^{94}\) \(+15.0000 q^{95}\) \(+1.00000 q^{96}\) \(+17.0000 q^{97}\) \(+9.00000 q^{98}\) \(+12.0000 q^{99}\) \(+O(q^{100})\)

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 \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 3.00000 0.948683
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −4.00000 −1.06904
\(15\) 3.00000 0.774597
\(16\) 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
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 3.00000 0.670820
\(21\) −4.00000 −0.872872
\(22\) −6.00000 −1.27920
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 1.00000 0.204124
\(25\) 4.00000 0.800000
\(26\) 2.00000 0.392232
\(27\) −5.00000 −0.962250
\(28\) −4.00000 −0.755929
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 3.00000 0.547723
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.00000 −1.04447
\(34\) 3.00000 0.514496
\(35\) −12.0000 −2.02837
\(36\) −2.00000 −0.333333
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 5.00000 0.811107
\(39\) 2.00000 0.320256
\(40\) 3.00000 0.474342
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −4.00000 −0.617213
\(43\) −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
\(46\) −3.00000 −0.442326
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) 4.00000 0.565685
\(51\) 3.00000 0.420084
\(52\) 2.00000 0.277350
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) −5.00000 −0.680414
\(55\) −18.0000 −2.42712
\(56\) −4.00000 −0.534522
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 3.00000 0.387298
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 5.00000 0.635001
\(63\) 8.00000 1.00791
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) −6.00000 −0.738549
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 3.00000 0.363803
\(69\) −3.00000 −0.361158
\(70\) −12.0000 −1.43427
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −2.00000 −0.235702
\(73\) −1.00000 −0.117041 −0.0585206 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) −10.0000 −1.16248
\(75\) 4.00000 0.461880
\(76\) 5.00000 0.573539
\(77\) 24.0000 2.73505
\(78\) 2.00000 0.226455
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −4.00000 −0.436436
\(85\) 9.00000 0.976187
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −6.00000 −0.639602
\(89\) −1.00000 −0.106000
\(90\) −6.00000 −0.632456
\(91\) −8.00000 −0.838628
\(92\) −3.00000 −0.312772
\(93\) 5.00000 0.518476
\(94\) 12.0000 1.23771
\(95\) 15.0000 1.53897
\(96\) 1.00000 0.102062
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 9.00000 0.909137
\(99\) 12.0000 1.20605
\(100\) 4.00000 0.400000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 3.00000 0.297044
\(103\) 5.00000 0.492665 0.246332 0.969185i \(-0.420775\pi\)
0.246332 + 0.969185i \(0.420775\pi\)
\(104\) 2.00000 0.196116
\(105\) −12.0000 −1.17108
\(106\) 9.00000 0.874157
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) −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
\(111\) −10.0000 −0.949158
\(112\) −4.00000 −0.377964
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 5.00000 0.468293
\(115\) −9.00000 −0.839254
\(116\) 0 0
\(117\) −4.00000 −0.369800
\(118\) 12.0000 1.10469
\(119\) −12.0000 −1.10004
\(120\) 3.00000 0.273861
\(121\) 25.0000 2.27273
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) 5.00000 0.449013
\(125\) −3.00000 −0.268328
\(126\) 8.00000 0.712697
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 6.00000 0.526235
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −6.00000 −0.522233
\(133\) −20.0000 −1.73422
\(134\) −4.00000 −0.345547
\(135\) −15.0000 −1.29099
\(136\) 3.00000 0.257248
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) −3.00000 −0.255377
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) −12.0000 −1.01419
\(141\) 12.0000 1.01058
\(142\) −6.00000 −0.503509
\(143\) −12.0000 −1.00349
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −1.00000 −0.0827606
\(147\) 9.00000 0.742307
\(148\) −10.0000 −0.821995
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 4.00000 0.326599
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 5.00000 0.405554
\(153\) −6.00000 −0.485071
\(154\) 24.0000 1.93398
\(155\) 15.0000 1.20483
\(156\) 2.00000 0.160128
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −10.0000 −0.795557
\(159\) 9.00000 0.713746
\(160\) 3.00000 0.237171
\(161\) 12.0000 0.945732
\(162\) 1.00000 0.0785674
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 0 0
\(165\) −18.0000 −1.40130
\(166\) −12.0000 −0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −4.00000 −0.308607
\(169\) −9.00000 −0.692308
\(170\) 9.00000 0.690268
\(171\) −10.0000 −0.764719
\(172\) −1.00000 −0.0762493
\(173\) 3.00000 0.228086 0.114043 0.993476i \(-0.463620\pi\)
0.114043 + 0.993476i \(0.463620\pi\)
\(174\) 0 0
\(175\) −16.0000 −1.20949
\(176\) −6.00000 −0.452267
\(177\) 12.0000 0.901975
\(178\) −1.00000 −0.0749532
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) −6.00000 −0.447214
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −8.00000 −0.592999
\(183\) −10.0000 −0.739221
\(184\) −3.00000 −0.221163
\(185\) −30.0000 −2.20564
\(186\) 5.00000 0.366618
\(187\) −18.0000 −1.31629
\(188\) 12.0000 0.875190
\(189\) 20.0000 1.45479
\(190\) 15.0000 1.08821
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 1.00000 0.0721688
\(193\) −22.0000 −1.58359 −0.791797 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 17.0000 1.22053
\(195\) 6.00000 0.429669
\(196\) 9.00000 0.642857
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 12.0000 0.852803
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 4.00000 0.282843
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) 5.00000 0.348367
\(207\) 6.00000 0.417029
\(208\) 2.00000 0.138675
\(209\) −30.0000 −2.07514
\(210\) −12.0000 −0.828079
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 9.00000 0.618123
\(213\) −6.00000 −0.411113
\(214\) 18.0000 1.23045
\(215\) −3.00000 −0.204598
\(216\) −5.00000 −0.340207
\(217\) −20.0000 −1.35769
\(218\) −7.00000 −0.474100
\(219\) −1.00000 −0.0675737
\(220\) −18.0000 −1.21356
\(221\) 6.00000 0.403604
\(222\) −10.0000 −0.671156
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −4.00000 −0.267261
\(225\) −8.00000 −0.533333
\(226\) −6.00000 −0.399114
\(227\) 24.0000 1.59294 0.796468 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 5.00000 0.331133
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) −9.00000 −0.593442
\(231\) 24.0000 1.57908
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) −4.00000 −0.261488
\(235\) 36.0000 2.34838
\(236\) 12.0000 0.781133
\(237\) −10.0000 −0.649570
\(238\) −12.0000 −0.777844
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 3.00000 0.193649
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 25.0000 1.60706
\(243\) 16.0000 1.02640
\(244\) −10.0000 −0.640184
\(245\) 27.0000 1.72497
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) 5.00000 0.317500
\(249\) −12.0000 −0.760469
\(250\) −3.00000 −0.189737
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 8.00000 0.503953
\(253\) 18.0000 1.13165
\(254\) −7.00000 −0.439219
\(255\) 9.00000 0.563602
\(256\) 1.00000 0.0625000
\(257\) −3.00000 −0.187135 −0.0935674 0.995613i \(-0.529827\pi\)
−0.0935674 + 0.995613i \(0.529827\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 40.0000 2.48548
\(260\) 6.00000 0.372104
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) −6.00000 −0.369274
\(265\) 27.0000 1.65860
\(266\) −20.0000 −1.22628
\(267\) −1.00000 −0.0611990
\(268\) −4.00000 −0.244339
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) −15.0000 −0.912871
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) 3.00000 0.181902
\(273\) −8.00000 −0.484182
\(274\) 18.0000 1.08742
\(275\) −24.0000 −1.44725
\(276\) −3.00000 −0.180579
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) 8.00000 0.479808
\(279\) −10.0000 −0.598684
\(280\) −12.0000 −0.717137
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 12.0000 0.714590
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −6.00000 −0.356034
\(285\) 15.0000 0.888523
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 17.0000 0.996558
\(292\) −1.00000 −0.0585206
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 9.00000 0.524891
\(295\) 36.0000 2.09600
\(296\) −10.0000 −0.581238
\(297\) 30.0000 1.74078
\(298\) −12.0000 −0.695141
\(299\) −6.00000 −0.346989
\(300\) 4.00000 0.230940
\(301\) 4.00000 0.230556
\(302\) −16.0000 −0.920697
\(303\) 0 0
\(304\) 5.00000 0.286770
\(305\) −30.0000 −1.71780
\(306\) −6.00000 −0.342997
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 24.0000 1.36753
\(309\) 5.00000 0.284440
\(310\) 15.0000 0.851943
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 2.00000 0.113228
\(313\) 20.0000 1.13047 0.565233 0.824931i \(-0.308786\pi\)
0.565233 + 0.824931i \(0.308786\pi\)
\(314\) 14.0000 0.790066
\(315\) 24.0000 1.35225
\(316\) −10.0000 −0.562544
\(317\) −27.0000 −1.51647 −0.758236 0.651981i \(-0.773938\pi\)
−0.758236 + 0.651981i \(0.773938\pi\)
\(318\) 9.00000 0.504695
\(319\) 0 0
\(320\) 3.00000 0.167705
\(321\) 18.0000 1.00466
\(322\) 12.0000 0.668734
\(323\) 15.0000 0.834622
\(324\) 1.00000 0.0555556
\(325\) 8.00000 0.443760
\(326\) −1.00000 −0.0553849
\(327\) −7.00000 −0.387101
\(328\) 0 0
\(329\) −48.0000 −2.64633
\(330\) −18.0000 −0.990867
\(331\) −34.0000 −1.86881 −0.934405 0.356214i \(-0.884068\pi\)
−0.934405 + 0.356214i \(0.884068\pi\)
\(332\) −12.0000 −0.658586
\(333\) 20.0000 1.09599
\(334\) −12.0000 −0.656611
\(335\) −12.0000 −0.655630
\(336\) −4.00000 −0.218218
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −9.00000 −0.489535
\(339\) −6.00000 −0.325875
\(340\) 9.00000 0.488094
\(341\) −30.0000 −1.62459
\(342\) −10.0000 −0.540738
\(343\) −8.00000 −0.431959
\(344\) −1.00000 −0.0539164
\(345\) −9.00000 −0.484544
\(346\) 3.00000 0.161281
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) 0 0
\(349\) −16.0000 −0.856460 −0.428230 0.903670i \(-0.640863\pi\)
−0.428230 + 0.903670i \(0.640863\pi\)
\(350\) −16.0000 −0.855236
\(351\) −10.0000 −0.533761
\(352\) −6.00000 −0.319801
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 12.0000 0.637793
\(355\) −18.0000 −0.955341
\(356\) −1.00000 −0.0529999
\(357\) −12.0000 −0.635107
\(358\) 18.0000 0.951330
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) −6.00000 −0.316228
\(361\) 6.00000 0.315789
\(362\) −10.0000 −0.525588
\(363\) 25.0000 1.31216
\(364\) −8.00000 −0.419314
\(365\) −3.00000 −0.157027
\(366\) −10.0000 −0.522708
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) −3.00000 −0.156386
\(369\) 0 0
\(370\) −30.0000 −1.55963
\(371\) −36.0000 −1.86903
\(372\) 5.00000 0.259238
\(373\) −25.0000 −1.29445 −0.647225 0.762299i \(-0.724071\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) −18.0000 −0.930758
\(375\) −3.00000 −0.154919
\(376\) 12.0000 0.618853
\(377\) 0 0
\(378\) 20.0000 1.02869
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 15.0000 0.769484
\(381\) −7.00000 −0.358621
\(382\) −3.00000 −0.153493
\(383\) 15.0000 0.766464 0.383232 0.923652i \(-0.374811\pi\)
0.383232 + 0.923652i \(0.374811\pi\)
\(384\) 1.00000 0.0510310
\(385\) 72.0000 3.66946
\(386\) −22.0000 −1.11977
\(387\) 2.00000 0.101666
\(388\) 17.0000 0.863044
\(389\) 36.0000 1.82527 0.912636 0.408773i \(-0.134043\pi\)
0.912636 + 0.408773i \(0.134043\pi\)
\(390\) 6.00000 0.303822
\(391\) −9.00000 −0.455150
\(392\) 9.00000 0.454569
\(393\) 0 0
\(394\) 0 0
\(395\) −30.0000 −1.50946
\(396\) 12.0000 0.603023
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) −10.0000 −0.501255
\(399\) −20.0000 −1.00125
\(400\) 4.00000 0.200000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) −4.00000 −0.199502
\(403\) 10.0000 0.498135
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) 60.0000 2.97409
\(408\) 3.00000 0.148522
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) 5.00000 0.246332
\(413\) −48.0000 −2.36193
\(414\) 6.00000 0.294884
\(415\) −36.0000 −1.76717
\(416\) 2.00000 0.0980581
\(417\) 8.00000 0.391762
\(418\) −30.0000 −1.46735
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) −12.0000 −0.585540
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −4.00000 −0.194717
\(423\) −24.0000 −1.16692
\(424\) 9.00000 0.437079
\(425\) 12.0000 0.582086
\(426\) −6.00000 −0.290701
\(427\) 40.0000 1.93574
\(428\) 18.0000 0.870063
\(429\) −12.0000 −0.579365
\(430\) −3.00000 −0.144673
\(431\) −15.0000 −0.722525 −0.361262 0.932464i \(-0.617654\pi\)
−0.361262 + 0.932464i \(0.617654\pi\)
\(432\) −5.00000 −0.240563
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −20.0000 −0.960031
\(435\) 0 0
\(436\) −7.00000 −0.335239
\(437\) −15.0000 −0.717547
\(438\) −1.00000 −0.0477818
\(439\) −1.00000 −0.0477274 −0.0238637 0.999715i \(-0.507597\pi\)
−0.0238637 + 0.999715i \(0.507597\pi\)
\(440\) −18.0000 −0.858116
\(441\) −18.0000 −0.857143
\(442\) 6.00000 0.285391
\(443\) 6.00000 0.285069 0.142534 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) −10.0000 −0.474579
\(445\) −3.00000 −0.142214
\(446\) 8.00000 0.378811
\(447\) −12.0000 −0.567581
\(448\) −4.00000 −0.188982
\(449\) 39.0000 1.84052 0.920262 0.391303i \(-0.127976\pi\)
0.920262 + 0.391303i \(0.127976\pi\)
\(450\) −8.00000 −0.377124
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) −16.0000 −0.751746
\(454\) 24.0000 1.12638
\(455\) −24.0000 −1.12514
\(456\) 5.00000 0.234146
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −4.00000 −0.186908
\(459\) −15.0000 −0.700140
\(460\) −9.00000 −0.419627
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 24.0000 1.11658
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 0 0
\(465\) 15.0000 0.695608
\(466\) 6.00000 0.277945
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) −4.00000 −0.184900
\(469\) 16.0000 0.738811
\(470\) 36.0000 1.66056
\(471\) 14.0000 0.645086
\(472\) 12.0000 0.552345
\(473\) 6.00000 0.275880
\(474\) −10.0000 −0.459315
\(475\) 20.0000 0.917663
\(476\) −12.0000 −0.550019
\(477\) −18.0000 −0.824163
\(478\) 15.0000 0.686084
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 3.00000 0.136931
\(481\) −20.0000 −0.911922
\(482\) −22.0000 −1.00207
\(483\) 12.0000 0.546019
\(484\) 25.0000 1.13636
\(485\) 51.0000 2.31579
\(486\) 16.0000 0.725775
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) −10.0000 −0.452679
\(489\) −1.00000 −0.0452216
\(490\) 27.0000 1.21974
\(491\) −15.0000 −0.676941 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 10.0000 0.449921
\(495\) 36.0000 1.61808
\(496\) 5.00000 0.224507
\(497\) 24.0000 1.07655
\(498\) −12.0000 −0.537733
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −3.00000 −0.134164
\(501\) −12.0000 −0.536120
\(502\) −12.0000 −0.535586
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 8.00000 0.356348
\(505\) 0 0
\(506\) 18.0000 0.800198
\(507\) −9.00000 −0.399704
\(508\) −7.00000 −0.310575
\(509\) −33.0000 −1.46270 −0.731350 0.682003i \(-0.761109\pi\)
−0.731350 + 0.682003i \(0.761109\pi\)
\(510\) 9.00000 0.398527
\(511\) 4.00000 0.176950
\(512\) 1.00000 0.0441942
\(513\) −25.0000 −1.10378
\(514\) −3.00000 −0.132324
\(515\) 15.0000 0.660979
\(516\) −1.00000 −0.0440225
\(517\) −72.0000 −3.16656
\(518\) 40.0000 1.75750
\(519\) 3.00000 0.131685
\(520\) 6.00000 0.263117
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 0 0
\(525\) −16.0000 −0.698297
\(526\) 0 0
\(527\) 15.0000 0.653410
\(528\) −6.00000 −0.261116
\(529\) −14.0000 −0.608696
\(530\) 27.0000 1.17281
\(531\) −24.0000 −1.04151
\(532\) −20.0000 −0.867110
\(533\) 0 0
\(534\) −1.00000 −0.0432742
\(535\) 54.0000 2.33462
\(536\) −4.00000 −0.172774
\(537\) 18.0000 0.776757
\(538\) 15.0000 0.646696
\(539\) −54.0000 −2.32594
\(540\) −15.0000 −0.645497
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −22.0000 −0.944981
\(543\) −10.0000 −0.429141
\(544\) 3.00000 0.128624
\(545\) −21.0000 −0.899541
\(546\) −8.00000 −0.342368
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 18.0000 0.768922
\(549\) 20.0000 0.853579
\(550\) −24.0000 −1.02336
\(551\) 0 0
\(552\) −3.00000 −0.127688
\(553\) 40.0000 1.70097
\(554\) −1.00000 −0.0424859
\(555\) −30.0000 −1.27343
\(556\) 8.00000 0.339276
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) −10.0000 −0.423334
\(559\) −2.00000 −0.0845910
\(560\) −12.0000 −0.507093
\(561\) −18.0000 −0.759961
\(562\) −6.00000 −0.253095
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 12.0000 0.505291
\(565\) −18.0000 −0.757266
\(566\) 14.0000 0.588464
\(567\) −4.00000 −0.167984
\(568\) −6.00000 −0.251754
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 15.0000 0.628281
\(571\) 47.0000 1.96689 0.983444 0.181210i \(-0.0580014\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) −12.0000 −0.501745
\(573\) −3.00000 −0.125327
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) −2.00000 −0.0833333
\(577\) 44.0000 1.83174 0.915872 0.401470i \(-0.131501\pi\)
0.915872 + 0.401470i \(0.131501\pi\)
\(578\) −8.00000 −0.332756
\(579\) −22.0000 −0.914289
\(580\) 0 0
\(581\) 48.0000 1.99138
\(582\) 17.0000 0.704673
\(583\) −54.0000 −2.23645
\(584\) −1.00000 −0.0413803
\(585\) −12.0000 −0.496139
\(586\) −18.0000 −0.743573
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 9.00000 0.371154
\(589\) 25.0000 1.03011
\(590\) 36.0000 1.48210
\(591\) 0 0
\(592\) −10.0000 −0.410997
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 30.0000 1.23091
\(595\) −36.0000 −1.47586
\(596\) −12.0000 −0.491539
\(597\) −10.0000 −0.409273
\(598\) −6.00000 −0.245358
\(599\) −3.00000 −0.122577 −0.0612883 0.998120i \(-0.519521\pi\)
−0.0612883 + 0.998120i \(0.519521\pi\)
\(600\) 4.00000 0.163299
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) 4.00000 0.163028
\(603\) 8.00000 0.325785
\(604\) −16.0000 −0.651031
\(605\) 75.0000 3.04918
\(606\) 0 0
\(607\) 2.00000 0.0811775 0.0405887 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) 5.00000 0.202777
\(609\) 0 0
\(610\) −30.0000 −1.21466
\(611\) 24.0000 0.970936
\(612\) −6.00000 −0.242536
\(613\) 41.0000 1.65597 0.827987 0.560747i \(-0.189486\pi\)
0.827987 + 0.560747i \(0.189486\pi\)
\(614\) 2.00000 0.0807134
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 5.00000 0.201129
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 15.0000 0.602414
\(621\) 15.0000 0.601929
\(622\) 12.0000 0.481156
\(623\) 4.00000 0.160257
\(624\) 2.00000 0.0800641
\(625\) −29.0000 −1.16000
\(626\) 20.0000 0.799361
\(627\) −30.0000 −1.19808
\(628\) 14.0000 0.558661
\(629\) −30.0000 −1.19618
\(630\) 24.0000 0.956183
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −10.0000 −0.397779
\(633\) −4.00000 −0.158986
\(634\) −27.0000 −1.07231
\(635\) −21.0000 −0.833360
\(636\) 9.00000 0.356873
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 3.00000 0.118585
\(641\) 9.00000 0.355479 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(642\) 18.0000 0.710403
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 12.0000 0.472866
\(645\) −3.00000 −0.118125
\(646\) 15.0000 0.590167
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 1.00000 0.0392837
\(649\) −72.0000 −2.82625
\(650\) 8.00000 0.313786
\(651\) −20.0000 −0.783862
\(652\) −1.00000 −0.0391630
\(653\) 48.0000 1.87839 0.939193 0.343391i \(-0.111576\pi\)
0.939193 + 0.343391i \(0.111576\pi\)
\(654\) −7.00000 −0.273722
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) −48.0000 −1.87123
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) −18.0000 −0.700649
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) −34.0000 −1.32145
\(663\) 6.00000 0.233021
\(664\) −12.0000 −0.465690
\(665\) −60.0000 −2.32670
\(666\) 20.0000 0.774984
\(667\) 0 0
\(668\) −12.0000 −0.464294
\(669\) 8.00000 0.309298
\(670\) −12.0000 −0.463600
\(671\) 60.0000 2.31627
\(672\) −4.00000 −0.154303
\(673\) 29.0000 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(674\) 8.00000 0.308148
\(675\) −20.0000 −0.769800
\(676\) −9.00000 −0.346154
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) −6.00000 −0.230429
\(679\) −68.0000 −2.60960
\(680\) 9.00000 0.345134
\(681\) 24.0000 0.919682
\(682\) −30.0000 −1.14876
\(683\) 15.0000 0.573959 0.286980 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) −10.0000 −0.382360
\(685\) 54.0000 2.06323
\(686\) −8.00000 −0.305441
\(687\) −4.00000 −0.152610
\(688\) −1.00000 −0.0381246
\(689\) 18.0000 0.685745
\(690\) −9.00000 −0.342624
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 3.00000 0.114043
\(693\) −48.0000 −1.82337
\(694\) 18.0000 0.683271
\(695\) 24.0000 0.910372
\(696\) 0 0
\(697\) 0 0
\(698\) −16.0000 −0.605609
\(699\) 6.00000 0.226941
\(700\) −16.0000 −0.604743
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) −10.0000 −0.377426
\(703\) −50.0000 −1.88579
\(704\) −6.00000 −0.226134
\(705\) 36.0000 1.35584
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) −22.0000 −0.826227 −0.413114 0.910679i \(-0.635559\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) −18.0000 −0.675528
\(711\) 20.0000 0.750059
\(712\) −1.00000 −0.0374766
\(713\) −15.0000 −0.561754
\(714\) −12.0000 −0.449089
\(715\) −36.0000 −1.34632
\(716\) 18.0000 0.672692
\(717\) 15.0000 0.560185
\(718\) −24.0000 −0.895672
\(719\) 21.0000 0.783168 0.391584 0.920142i \(-0.371927\pi\)
0.391584 + 0.920142i \(0.371927\pi\)
\(720\) −6.00000 −0.223607
\(721\) −20.0000 −0.744839
\(722\) 6.00000 0.223297
\(723\) −22.0000 −0.818189
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) 25.0000 0.927837
\(727\) −1.00000 −0.0370879 −0.0185440 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(728\) −8.00000 −0.296500
\(729\) 13.0000 0.481481
\(730\) −3.00000 −0.111035
\(731\) −3.00000 −0.110959
\(732\) −10.0000 −0.369611
\(733\) 5.00000 0.184679 0.0923396 0.995728i \(-0.470565\pi\)
0.0923396 + 0.995728i \(0.470565\pi\)
\(734\) −16.0000 −0.590571
\(735\) 27.0000 0.995910
\(736\) −3.00000 −0.110581
\(737\) 24.0000 0.884051
\(738\) 0 0
\(739\) −7.00000 −0.257499 −0.128750 0.991677i \(-0.541096\pi\)
−0.128750 + 0.991677i \(0.541096\pi\)
\(740\) −30.0000 −1.10282
\(741\) 10.0000 0.367359
\(742\) −36.0000 −1.32160
\(743\) −3.00000 −0.110059 −0.0550297 0.998485i \(-0.517525\pi\)
−0.0550297 + 0.998485i \(0.517525\pi\)
\(744\) 5.00000 0.183309
\(745\) −36.0000 −1.31894
\(746\) −25.0000 −0.915315
\(747\) 24.0000 0.878114
\(748\) −18.0000 −0.658145
\(749\) −72.0000 −2.63082
\(750\) −3.00000 −0.109545
\(751\) −34.0000 −1.24068 −0.620339 0.784334i \(-0.713005\pi\)
−0.620339 + 0.784334i \(0.713005\pi\)
\(752\) 12.0000 0.437595
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) −48.0000 −1.74690
\(756\) 20.0000 0.727393
\(757\) −1.00000 −0.0363456 −0.0181728 0.999835i \(-0.505785\pi\)
−0.0181728 + 0.999835i \(0.505785\pi\)
\(758\) −1.00000 −0.0363216
\(759\) 18.0000 0.653359
\(760\) 15.0000 0.544107
\(761\) −33.0000 −1.19625 −0.598125 0.801403i \(-0.704087\pi\)
−0.598125 + 0.801403i \(0.704087\pi\)
\(762\) −7.00000 −0.253583
\(763\) 28.0000 1.01367
\(764\) −3.00000 −0.108536
\(765\) −18.0000 −0.650791
\(766\) 15.0000 0.541972
\(767\) 24.0000 0.866590
\(768\) 1.00000 0.0360844
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 72.0000 2.59470
\(771\) −3.00000 −0.108042
\(772\) −22.0000 −0.791797
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 2.00000 0.0718885
\(775\) 20.0000 0.718421
\(776\) 17.0000 0.610264
\(777\) 40.0000 1.43499
\(778\) 36.0000 1.29066
\(779\) 0 0
\(780\) 6.00000 0.214834
\(781\) 36.0000 1.28818
\(782\) −9.00000 −0.321839
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 42.0000 1.49904
\(786\) 0 0
\(787\) −1.00000 −0.0356462 −0.0178231 0.999841i \(-0.505674\pi\)
−0.0178231 + 0.999841i \(0.505674\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −30.0000 −1.06735
\(791\) 24.0000 0.853342
\(792\) 12.0000 0.426401
\(793\) −20.0000 −0.710221
\(794\) 20.0000 0.709773
\(795\) 27.0000 0.957591
\(796\) −10.0000 −0.354441
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) −20.0000 −0.707992
\(799\) 36.0000 1.27359
\(800\) 4.00000 0.141421
\(801\) 2.00000 0.0706665
\(802\) −18.0000 −0.635602
\(803\) 6.00000 0.211735
\(804\) −4.00000 −0.141069
\(805\) 36.0000 1.26883
\(806\) 10.0000 0.352235
\(807\) 15.0000 0.528025
\(808\) 0 0
\(809\) 15.0000 0.527372 0.263686 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) 3.00000 0.105409
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) −22.0000 −0.771574
\(814\) 60.0000 2.10300
\(815\) −3.00000 −0.105085
\(816\) 3.00000 0.105021
\(817\) −5.00000 −0.174928
\(818\) 14.0000 0.489499
\(819\) 16.0000 0.559085
\(820\) 0 0
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 18.0000 0.627822
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) 5.00000 0.174183
\(825\) −24.0000 −0.835573
\(826\) −48.0000 −1.67013
\(827\) 15.0000 0.521601 0.260801 0.965393i \(-0.416014\pi\)
0.260801 + 0.965393i \(0.416014\pi\)
\(828\) 6.00000 0.208514
\(829\) 20.0000 0.694629 0.347314 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) −36.0000 −1.24958
\(831\) −1.00000 −0.0346896
\(832\) 2.00000 0.0693375
\(833\) 27.0000 0.935495
\(834\) 8.00000 0.277017
\(835\) −36.0000 −1.24583
\(836\) −30.0000 −1.03757
\(837\) −25.0000 −0.864126
\(838\) 9.00000 0.310900
\(839\) 15.0000 0.517858 0.258929 0.965896i \(-0.416631\pi\)
0.258929 + 0.965896i \(0.416631\pi\)
\(840\) −12.0000 −0.414039
\(841\) −29.0000 −1.00000
\(842\) 8.00000 0.275698
\(843\) −6.00000 −0.206651
\(844\) −4.00000 −0.137686
\(845\) −27.0000 −0.928828
\(846\) −24.0000 −0.825137
\(847\) −100.000 −3.43604
\(848\) 9.00000 0.309061
\(849\) 14.0000 0.480479
\(850\) 12.0000 0.411597
\(851\) 30.0000 1.02839
\(852\) −6.00000 −0.205557
\(853\) 56.0000 1.91740 0.958702 0.284413i \(-0.0917988\pi\)
0.958702 + 0.284413i \(0.0917988\pi\)
\(854\) 40.0000 1.36877
\(855\) −30.0000 −1.02598
\(856\) 18.0000 0.615227
\(857\) 12.0000 0.409912 0.204956 0.978771i \(-0.434295\pi\)
0.204956 + 0.978771i \(0.434295\pi\)
\(858\) −12.0000 −0.409673
\(859\) −52.0000 −1.77422 −0.887109 0.461561i \(-0.847290\pi\)
−0.887109 + 0.461561i \(0.847290\pi\)
\(860\) −3.00000 −0.102299
\(861\) 0 0
\(862\) −15.0000 −0.510902
\(863\) 33.0000 1.12333 0.561667 0.827364i \(-0.310160\pi\)
0.561667 + 0.827364i \(0.310160\pi\)
\(864\) −5.00000 −0.170103
\(865\) 9.00000 0.306009
\(866\) −16.0000 −0.543702
\(867\) −8.00000 −0.271694
\(868\) −20.0000 −0.678844
\(869\) 60.0000 2.03536
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) −7.00000 −0.237050
\(873\) −34.0000 −1.15073
\(874\) −15.0000 −0.507383
\(875\) 12.0000 0.405674
\(876\) −1.00000 −0.0337869
\(877\) −4.00000 −0.135070 −0.0675352 0.997717i \(-0.521513\pi\)
−0.0675352 + 0.997717i \(0.521513\pi\)
\(878\) −1.00000 −0.0337484
\(879\) −18.0000 −0.607125
\(880\) −18.0000 −0.606780
\(881\) 6.00000 0.202145 0.101073 0.994879i \(-0.467773\pi\)
0.101073 + 0.994879i \(0.467773\pi\)
\(882\) −18.0000 −0.606092
\(883\) −19.0000 −0.639401 −0.319700 0.947519i \(-0.603582\pi\)
−0.319700 + 0.947519i \(0.603582\pi\)
\(884\) 6.00000 0.201802
\(885\) 36.0000 1.21013
\(886\) 6.00000 0.201574
\(887\) 57.0000 1.91387 0.956936 0.290298i \(-0.0937544\pi\)
0.956936 + 0.290298i \(0.0937544\pi\)
\(888\) −10.0000 −0.335578
\(889\) 28.0000 0.939090
\(890\) −3.00000 −0.100560
\(891\) −6.00000 −0.201008
\(892\) 8.00000 0.267860
\(893\) 60.0000 2.00782
\(894\) −12.0000 −0.401340
\(895\) 54.0000 1.80502
\(896\) −4.00000 −0.133631
\(897\) −6.00000 −0.200334
\(898\) 39.0000 1.30145
\(899\) 0 0
\(900\) −8.00000 −0.266667
\(901\) 27.0000 0.899500
\(902\) 0 0
\(903\) 4.00000 0.133112
\(904\) −6.00000 −0.199557
\(905\) −30.0000 −0.997234
\(906\) −16.0000 −0.531564
\(907\) 38.0000 1.26177 0.630885 0.775877i \(-0.282692\pi\)
0.630885 + 0.775877i \(0.282692\pi\)
\(908\) 24.0000 0.796468
\(909\) 0 0
\(910\) −24.0000 −0.795592
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 5.00000 0.165567
\(913\) 72.0000 2.38285
\(914\) −10.0000 −0.330771
\(915\) −30.0000 −0.991769
\(916\) −4.00000 −0.132164
\(917\) 0 0
\(918\) −15.0000 −0.495074
\(919\) 29.0000 0.956622 0.478311 0.878191i \(-0.341249\pi\)
0.478311 + 0.878191i \(0.341249\pi\)
\(920\) −9.00000 −0.296721
\(921\) 2.00000 0.0659022
\(922\) 18.0000 0.592798
\(923\) −12.0000 −0.394985
\(924\) 24.0000 0.789542
\(925\) −40.0000 −1.31519
\(926\) 20.0000 0.657241
\(927\) −10.0000 −0.328443
\(928\) 0 0
\(929\) 15.0000 0.492134 0.246067 0.969253i \(-0.420862\pi\)
0.246067 + 0.969253i \(0.420862\pi\)
\(930\) 15.0000 0.491869
\(931\) 45.0000 1.47482
\(932\) 6.00000 0.196537
\(933\) 12.0000 0.392862
\(934\) 18.0000 0.588978
\(935\) −54.0000 −1.76599
\(936\) −4.00000 −0.130744
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 16.0000 0.522419
\(939\) 20.0000 0.652675
\(940\) 36.0000 1.17419
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) 14.0000 0.456145
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) 60.0000 1.95180
\(946\) 6.00000 0.195077
\(947\) −48.0000 −1.55979 −0.779895 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) −10.0000 −0.324785
\(949\) −2.00000 −0.0649227
\(950\) 20.0000 0.648886
\(951\) −27.0000 −0.875535
\(952\) −12.0000 −0.388922
\(953\) −36.0000 −1.16615 −0.583077 0.812417i \(-0.698151\pi\)
−0.583077 + 0.812417i \(0.698151\pi\)
\(954\) −18.0000 −0.582772
\(955\) −9.00000 −0.291233
\(956\) 15.0000 0.485135
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) −72.0000 −2.32500
\(960\) 3.00000 0.0968246
\(961\) −6.00000 −0.193548
\(962\) −20.0000 −0.644826
\(963\) −36.0000 −1.16008
\(964\) −22.0000 −0.708572
\(965\) −66.0000 −2.12462
\(966\) 12.0000 0.386094
\(967\) −1.00000 −0.0321578 −0.0160789 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(968\) 25.0000 0.803530
\(969\) 15.0000 0.481869
\(970\) 51.0000 1.63751
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 16.0000 0.513200
\(973\) −32.0000 −1.02587
\(974\) −4.00000 −0.128168
\(975\) 8.00000 0.256205
\(976\) −10.0000 −0.320092
\(977\) −9.00000 −0.287936 −0.143968 0.989582i \(-0.545986\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(978\) −1.00000 −0.0319765
\(979\) 6.00000 0.191761
\(980\) 27.0000 0.862483
\(981\) 14.0000 0.446986
\(982\) −15.0000 −0.478669
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −48.0000 −1.52786
\(988\) 10.0000 0.318142
\(989\) 3.00000 0.0953945
\(990\) 36.0000 1.14416
\(991\) −19.0000 −0.603555 −0.301777 0.953378i \(-0.597580\pi\)
−0.301777 + 0.953378i \(0.597580\pi\)
\(992\) 5.00000 0.158750
\(993\) −34.0000 −1.07896
\(994\) 24.0000 0.761234
\(995\) −30.0000 −0.951064
\(996\) −12.0000 −0.380235
\(997\) 26.0000 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) −4.00000 −0.126618
\(999\) 50.0000 1.58193
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 \(a_p\))