Properties

Label 174.2.a.b.1.1
Level 174
Weight 2
Character 174.1
Self dual Yes
Analytic conductor 1.389
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 174 = 2 \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 174.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.38939699517\)
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 \(\chi\) = 174.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.00000 q^{5}\) \(-1.00000 q^{6}\) \(+5.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.00000 q^{5}\) \(-1.00000 q^{6}\) \(+5.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.00000 q^{10}\) \(+6.00000 q^{11}\) \(+1.00000 q^{12}\) \(-4.00000 q^{13}\) \(-5.00000 q^{14}\) \(-3.00000 q^{15}\) \(+1.00000 q^{16}\) \(+3.00000 q^{17}\) \(-1.00000 q^{18}\) \(-1.00000 q^{19}\) \(-3.00000 q^{20}\) \(+5.00000 q^{21}\) \(-6.00000 q^{22}\) \(-1.00000 q^{24}\) \(+4.00000 q^{25}\) \(+4.00000 q^{26}\) \(+1.00000 q^{27}\) \(+5.00000 q^{28}\) \(-1.00000 q^{29}\) \(+3.00000 q^{30}\) \(-4.00000 q^{31}\) \(-1.00000 q^{32}\) \(+6.00000 q^{33}\) \(-3.00000 q^{34}\) \(-15.0000 q^{35}\) \(+1.00000 q^{36}\) \(-1.00000 q^{37}\) \(+1.00000 q^{38}\) \(-4.00000 q^{39}\) \(+3.00000 q^{40}\) \(-9.00000 q^{41}\) \(-5.00000 q^{42}\) \(-7.00000 q^{43}\) \(+6.00000 q^{44}\) \(-3.00000 q^{45}\) \(-3.00000 q^{47}\) \(+1.00000 q^{48}\) \(+18.0000 q^{49}\) \(-4.00000 q^{50}\) \(+3.00000 q^{51}\) \(-4.00000 q^{52}\) \(-6.00000 q^{53}\) \(-1.00000 q^{54}\) \(-18.0000 q^{55}\) \(-5.00000 q^{56}\) \(-1.00000 q^{57}\) \(+1.00000 q^{58}\) \(+3.00000 q^{59}\) \(-3.00000 q^{60}\) \(-10.0000 q^{61}\) \(+4.00000 q^{62}\) \(+5.00000 q^{63}\) \(+1.00000 q^{64}\) \(+12.0000 q^{65}\) \(-6.00000 q^{66}\) \(-4.00000 q^{67}\) \(+3.00000 q^{68}\) \(+15.0000 q^{70}\) \(+12.0000 q^{71}\) \(-1.00000 q^{72}\) \(+2.00000 q^{73}\) \(+1.00000 q^{74}\) \(+4.00000 q^{75}\) \(-1.00000 q^{76}\) \(+30.0000 q^{77}\) \(+4.00000 q^{78}\) \(+14.0000 q^{79}\) \(-3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+9.00000 q^{82}\) \(+5.00000 q^{84}\) \(-9.00000 q^{85}\) \(+7.00000 q^{86}\) \(-1.00000 q^{87}\) \(-6.00000 q^{88}\) \(-6.00000 q^{89}\) \(+3.00000 q^{90}\) \(-20.0000 q^{91}\) \(-4.00000 q^{93}\) \(+3.00000 q^{94}\) \(+3.00000 q^{95}\) \(-1.00000 q^{96}\) \(+8.00000 q^{97}\) \(-18.0000 q^{98}\) \(+6.00000 q^{99}\) \(+O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 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
\(7\) 5.00000 1.88982 0.944911 0.327327i \(-0.106148\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 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
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −5.00000 −1.33631
\(15\) −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 \(0.381478\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −3.00000 −0.670820
\(21\) 5.00000 1.09109
\(22\) −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
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) 5.00000 0.944911
\(29\) −1.00000 −0.185695
\(30\) 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
\(35\) −15.0000 −2.53546
\(36\) 1.00000 0.166667
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 1.00000 0.162221
\(39\) −4.00000 −0.640513
\(40\) 3.00000 0.474342
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) −5.00000 −0.771517
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 6.00000 0.904534
\(45\) −3.00000 −0.447214
\(46\) 0 0
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 1.00000 0.144338
\(49\) 18.0000 2.57143
\(50\) −4.00000 −0.565685
\(51\) 3.00000 0.420084
\(52\) −4.00000 −0.554700
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 −0.136083
\(55\) −18.0000 −2.42712
\(56\) −5.00000 −0.668153
\(57\) −1.00000 −0.132453
\(58\) 1.00000 0.131306
\(59\) 3.00000 0.390567 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) −3.00000 −0.387298
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 4.00000 0.508001
\(63\) 5.00000 0.629941
\(64\) 1.00000 0.125000
\(65\) 12.0000 1.48842
\(66\) −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
\(69\) 0 0
\(70\) 15.0000 1.79284
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 1.00000 0.116248
\(75\) 4.00000 0.461880
\(76\) −1.00000 −0.114708
\(77\) 30.0000 3.41882
\(78\) 4.00000 0.452911
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) −3.00000 −0.335410
\(81\) 1.00000 0.111111
\(82\) 9.00000 0.993884
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 5.00000 0.545545
\(85\) −9.00000 −0.976187
\(86\) 7.00000 0.754829
\(87\) −1.00000 −0.107211
\(88\) −6.00000 −0.639602
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 3.00000 0.316228
\(91\) −20.0000 −2.09657
\(92\) 0 0
\(93\) −4.00000 −0.414781
\(94\) 3.00000 0.309426
\(95\) 3.00000 0.307794
\(96\) −1.00000 −0.102062
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) −18.0000 −1.81827
\(99\) 6.00000 0.603023
\(100\) 4.00000 0.400000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −3.00000 −0.297044
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 4.00000 0.392232
\(105\) −15.0000 −1.46385
\(106\) 6.00000 0.582772
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 1.00000 0.0962250
\(109\) 8.00000 0.766261 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 18.0000 1.71623
\(111\) −1.00000 −0.0949158
\(112\) 5.00000 0.472456
\(113\) −3.00000 −0.282216 −0.141108 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) −4.00000 −0.369800
\(118\) −3.00000 −0.276172
\(119\) 15.0000 1.37505
\(120\) 3.00000 0.273861
\(121\) 25.0000 2.27273
\(122\) 10.0000 0.905357
\(123\) −9.00000 −0.811503
\(124\) −4.00000 −0.359211
\(125\) 3.00000 0.268328
\(126\) −5.00000 −0.445435
\(127\) −22.0000 −1.95218 −0.976092 0.217357i \(-0.930256\pi\)
−0.976092 + 0.217357i \(0.930256\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.00000 −0.616316
\(130\) −12.0000 −1.05247
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 6.00000 0.522233
\(133\) −5.00000 −0.433555
\(134\) 4.00000 0.345547
\(135\) −3.00000 −0.258199
\(136\) −3.00000 −0.257248
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −15.0000 −1.26773
\(141\) −3.00000 −0.252646
\(142\) −12.0000 −1.00702
\(143\) −24.0000 −2.00698
\(144\) 1.00000 0.0833333
\(145\) 3.00000 0.249136
\(146\) −2.00000 −0.165521
\(147\) 18.0000 1.48461
\(148\) −1.00000 −0.0821995
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) −4.00000 −0.326599
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 1.00000 0.0811107
\(153\) 3.00000 0.242536
\(154\) −30.0000 −2.41747
\(155\) 12.0000 0.963863
\(156\) −4.00000 −0.320256
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) −14.0000 −1.11378
\(159\) −6.00000 −0.475831
\(160\) 3.00000 0.237171
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 5.00000 0.391630 0.195815 0.980641i \(-0.437265\pi\)
0.195815 + 0.980641i \(0.437265\pi\)
\(164\) −9.00000 −0.702782
\(165\) −18.0000 −1.40130
\(166\) 0 0
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) −5.00000 −0.385758
\(169\) 3.00000 0.230769
\(170\) 9.00000 0.690268
\(171\) −1.00000 −0.0764719
\(172\) −7.00000 −0.533745
\(173\) −21.0000 −1.59660 −0.798300 0.602260i \(-0.794267\pi\)
−0.798300 + 0.602260i \(0.794267\pi\)
\(174\) 1.00000 0.0758098
\(175\) 20.0000 1.51186
\(176\) 6.00000 0.452267
\(177\) 3.00000 0.225494
\(178\) 6.00000 0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −3.00000 −0.223607
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 20.0000 1.48250
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) 3.00000 0.220564
\(186\) 4.00000 0.293294
\(187\) 18.0000 1.31629
\(188\) −3.00000 −0.218797
\(189\) 5.00000 0.363696
\(190\) −3.00000 −0.217643
\(191\) −21.0000 −1.51951 −0.759753 0.650211i \(-0.774680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) −8.00000 −0.574367
\(195\) 12.0000 0.859338
\(196\) 18.0000 1.28571
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) −6.00000 −0.426401
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −4.00000 −0.282843
\(201\) −4.00000 −0.282138
\(202\) 6.00000 0.422159
\(203\) −5.00000 −0.350931
\(204\) 3.00000 0.210042
\(205\) 27.0000 1.88576
\(206\) 13.0000 0.905753
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) −6.00000 −0.415029
\(210\) 15.0000 1.03510
\(211\) −25.0000 −1.72107 −0.860535 0.509390i \(-0.829871\pi\)
−0.860535 + 0.509390i \(0.829871\pi\)
\(212\) −6.00000 −0.412082
\(213\) 12.0000 0.822226
\(214\) 9.00000 0.615227
\(215\) 21.0000 1.43219
\(216\) −1.00000 −0.0680414
\(217\) −20.0000 −1.35769
\(218\) −8.00000 −0.541828
\(219\) 2.00000 0.135147
\(220\) −18.0000 −1.21356
\(221\) −12.0000 −0.807207
\(222\) 1.00000 0.0671156
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −5.00000 −0.334077
\(225\) 4.00000 0.266667
\(226\) 3.00000 0.199557
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) −1.00000 −0.0662266
\(229\) −7.00000 −0.462573 −0.231287 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) 30.0000 1.97386
\(232\) 1.00000 0.0656532
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 4.00000 0.261488
\(235\) 9.00000 0.587095
\(236\) 3.00000 0.195283
\(237\) 14.0000 0.909398
\(238\) −15.0000 −0.972306
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −3.00000 −0.193649
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −25.0000 −1.60706
\(243\) 1.00000 0.0641500
\(244\) −10.0000 −0.640184
\(245\) −54.0000 −3.44993
\(246\) 9.00000 0.573819
\(247\) 4.00000 0.254514
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) −3.00000 −0.189737
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 5.00000 0.314970
\(253\) 0 0
\(254\) 22.0000 1.38040
\(255\) −9.00000 −0.563602
\(256\) 1.00000 0.0625000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 7.00000 0.435801
\(259\) −5.00000 −0.310685
\(260\) 12.0000 0.744208
\(261\) −1.00000 −0.0618984
\(262\) −12.0000 −0.741362
\(263\) −3.00000 −0.184988 −0.0924940 0.995713i \(-0.529484\pi\)
−0.0924940 + 0.995713i \(0.529484\pi\)
\(264\) −6.00000 −0.369274
\(265\) 18.0000 1.10573
\(266\) 5.00000 0.306570
\(267\) −6.00000 −0.367194
\(268\) −4.00000 −0.244339
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 3.00000 0.182574
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 3.00000 0.181902
\(273\) −20.0000 −1.21046
\(274\) 6.00000 0.362473
\(275\) 24.0000 1.44725
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) −14.0000 −0.839664
\(279\) −4.00000 −0.239474
\(280\) 15.0000 0.896421
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 3.00000 0.178647
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 12.0000 0.712069
\(285\) 3.00000 0.177705
\(286\) 24.0000 1.41915
\(287\) −45.0000 −2.65627
\(288\) −1.00000 −0.0589256
\(289\) −8.00000 −0.470588
\(290\) −3.00000 −0.176166
\(291\) 8.00000 0.468968
\(292\) 2.00000 0.117041
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −18.0000 −1.04978
\(295\) −9.00000 −0.524000
\(296\) 1.00000 0.0581238
\(297\) 6.00000 0.348155
\(298\) −3.00000 −0.173785
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) −35.0000 −2.01737
\(302\) −17.0000 −0.978240
\(303\) −6.00000 −0.344691
\(304\) −1.00000 −0.0573539
\(305\) 30.0000 1.71780
\(306\) −3.00000 −0.171499
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 30.0000 1.70941
\(309\) −13.0000 −0.739544
\(310\) −12.0000 −0.681554
\(311\) 21.0000 1.19080 0.595400 0.803429i \(-0.296993\pi\)
0.595400 + 0.803429i \(0.296993\pi\)
\(312\) 4.00000 0.226455
\(313\) 11.0000 0.621757 0.310878 0.950450i \(-0.399377\pi\)
0.310878 + 0.950450i \(0.399377\pi\)
\(314\) 13.0000 0.733632
\(315\) −15.0000 −0.845154
\(316\) 14.0000 0.787562
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 6.00000 0.336463
\(319\) −6.00000 −0.335936
\(320\) −3.00000 −0.167705
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 1.00000 0.0555556
\(325\) −16.0000 −0.887520
\(326\) −5.00000 −0.276924
\(327\) 8.00000 0.442401
\(328\) 9.00000 0.496942
\(329\) −15.0000 −0.826977
\(330\) 18.0000 0.990867
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 0 0
\(333\) −1.00000 −0.0547997
\(334\) −6.00000 −0.328305
\(335\) 12.0000 0.655630
\(336\) 5.00000 0.272772
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) −3.00000 −0.163178
\(339\) −3.00000 −0.162938
\(340\) −9.00000 −0.488094
\(341\) −24.0000 −1.29967
\(342\) 1.00000 0.0540738
\(343\) 55.0000 2.96972
\(344\) 7.00000 0.377415
\(345\) 0 0
\(346\) 21.0000 1.12897
\(347\) −3.00000 −0.161048 −0.0805242 0.996753i \(-0.525659\pi\)
−0.0805242 + 0.996753i \(0.525659\pi\)
\(348\) −1.00000 −0.0536056
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −20.0000 −1.06904
\(351\) −4.00000 −0.213504
\(352\) −6.00000 −0.319801
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) −3.00000 −0.159448
\(355\) −36.0000 −1.91068
\(356\) −6.00000 −0.317999
\(357\) 15.0000 0.793884
\(358\) 0 0
\(359\) 9.00000 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) 3.00000 0.158114
\(361\) −18.0000 −0.947368
\(362\) −8.00000 −0.420471
\(363\) 25.0000 1.31216
\(364\) −20.0000 −1.04828
\(365\) −6.00000 −0.314054
\(366\) 10.0000 0.522708
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 0 0
\(369\) −9.00000 −0.468521
\(370\) −3.00000 −0.155963
\(371\) −30.0000 −1.55752
\(372\) −4.00000 −0.207390
\(373\) 20.0000 1.03556 0.517780 0.855514i \(-0.326758\pi\)
0.517780 + 0.855514i \(0.326758\pi\)
\(374\) −18.0000 −0.930758
\(375\) 3.00000 0.154919
\(376\) 3.00000 0.154713
\(377\) 4.00000 0.206010
\(378\) −5.00000 −0.257172
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 3.00000 0.153897
\(381\) −22.0000 −1.12709
\(382\) 21.0000 1.07445
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −90.0000 −4.58682
\(386\) 4.00000 0.203595
\(387\) −7.00000 −0.355830
\(388\) 8.00000 0.406138
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) −12.0000 −0.607644
\(391\) 0 0
\(392\) −18.0000 −0.909137
\(393\) 12.0000 0.605320
\(394\) −9.00000 −0.453413
\(395\) −42.0000 −2.11325
\(396\) 6.00000 0.301511
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 16.0000 0.802008
\(399\) −5.00000 −0.250313
\(400\) 4.00000 0.200000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 4.00000 0.199502
\(403\) 16.0000 0.797017
\(404\) −6.00000 −0.298511
\(405\) −3.00000 −0.149071
\(406\) 5.00000 0.248146
\(407\) −6.00000 −0.297409
\(408\) −3.00000 −0.148522
\(409\) 8.00000 0.395575 0.197787 0.980245i \(-0.436624\pi\)
0.197787 + 0.980245i \(0.436624\pi\)
\(410\) −27.0000 −1.33343
\(411\) −6.00000 −0.295958
\(412\) −13.0000 −0.640464
\(413\) 15.0000 0.738102
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) 14.0000 0.685583
\(418\) 6.00000 0.293470
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) −15.0000 −0.731925
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) 25.0000 1.21698
\(423\) −3.00000 −0.145865
\(424\) 6.00000 0.291386
\(425\) 12.0000 0.582086
\(426\) −12.0000 −0.581402
\(427\) −50.0000 −2.41967
\(428\) −9.00000 −0.435031
\(429\) −24.0000 −1.15873
\(430\) −21.0000 −1.01271
\(431\) 36.0000 1.73406 0.867029 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 1.00000 0.0481125
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 20.0000 0.960031
\(435\) 3.00000 0.143839
\(436\) 8.00000 0.383131
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) −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
\(442\) 12.0000 0.570782
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) −1.00000 −0.0474579
\(445\) 18.0000 0.853282
\(446\) 16.0000 0.757622
\(447\) 3.00000 0.141895
\(448\) 5.00000 0.236228
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) −4.00000 −0.188562
\(451\) −54.0000 −2.54276
\(452\) −3.00000 −0.141108
\(453\) 17.0000 0.798730
\(454\) −3.00000 −0.140797
\(455\) 60.0000 2.81284
\(456\) 1.00000 0.0468293
\(457\) 11.0000 0.514558 0.257279 0.966337i \(-0.417174\pi\)
0.257279 + 0.966337i \(0.417174\pi\)
\(458\) 7.00000 0.327089
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) −30.0000 −1.39573
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 12.0000 0.556487
\(466\) −24.0000 −1.11178
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −4.00000 −0.184900
\(469\) −20.0000 −0.923514
\(470\) −9.00000 −0.415139
\(471\) −13.0000 −0.599008
\(472\) −3.00000 −0.138086
\(473\) −42.0000 −1.93116
\(474\) −14.0000 −0.643041
\(475\) −4.00000 −0.183533
\(476\) 15.0000 0.687524
\(477\) −6.00000 −0.274721
\(478\) −6.00000 −0.274434
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 3.00000 0.136931
\(481\) 4.00000 0.182384
\(482\) −17.0000 −0.774329
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) −24.0000 −1.08978
\(486\) −1.00000 −0.0453609
\(487\) 23.0000 1.04223 0.521115 0.853487i \(-0.325516\pi\)
0.521115 + 0.853487i \(0.325516\pi\)
\(488\) 10.0000 0.452679
\(489\) 5.00000 0.226108
\(490\) 54.0000 2.43947
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) −9.00000 −0.405751
\(493\) −3.00000 −0.135113
\(494\) −4.00000 −0.179969
\(495\) −18.0000 −0.809040
\(496\) −4.00000 −0.179605
\(497\) 60.0000 2.69137
\(498\) 0 0
\(499\) −22.0000 −0.984855 −0.492428 0.870353i \(-0.663890\pi\)
−0.492428 + 0.870353i \(0.663890\pi\)
\(500\) 3.00000 0.134164
\(501\) 6.00000 0.268060
\(502\) 0 0
\(503\) −33.0000 −1.47140 −0.735699 0.677309i \(-0.763146\pi\)
−0.735699 + 0.677309i \(0.763146\pi\)
\(504\) −5.00000 −0.222718
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) −22.0000 −0.976092
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) 9.00000 0.398527
\(511\) 10.0000 0.442374
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 −0.0441511
\(514\) 0 0
\(515\) 39.0000 1.71855
\(516\) −7.00000 −0.308158
\(517\) −18.0000 −0.791639
\(518\) 5.00000 0.219687
\(519\) −21.0000 −0.921798
\(520\) −12.0000 −0.526235
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 1.00000 0.0437688
\(523\) 2.00000 0.0874539 0.0437269 0.999044i \(-0.486077\pi\)
0.0437269 + 0.999044i \(0.486077\pi\)
\(524\) 12.0000 0.524222
\(525\) 20.0000 0.872872
\(526\) 3.00000 0.130806
\(527\) −12.0000 −0.522728
\(528\) 6.00000 0.261116
\(529\) −23.0000 −1.00000
\(530\) −18.0000 −0.781870
\(531\) 3.00000 0.130189
\(532\) −5.00000 −0.216777
\(533\) 36.0000 1.55933
\(534\) 6.00000 0.259645
\(535\) 27.0000 1.16731
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) −6.00000 −0.258678
\(539\) 108.000 4.65189
\(540\) −3.00000 −0.129099
\(541\) −1.00000 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(542\) −20.0000 −0.859074
\(543\) 8.00000 0.343313
\(544\) −3.00000 −0.128624
\(545\) −24.0000 −1.02805
\(546\) 20.0000 0.855921
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) −6.00000 −0.256307
\(549\) −10.0000 −0.426790
\(550\) −24.0000 −1.02336
\(551\) 1.00000 0.0426014
\(552\) 0 0
\(553\) 70.0000 2.97670
\(554\) −14.0000 −0.594803
\(555\) 3.00000 0.127343
\(556\) 14.0000 0.593732
\(557\) 45.0000 1.90671 0.953356 0.301849i \(-0.0976040\pi\)
0.953356 + 0.301849i \(0.0976040\pi\)
\(558\) 4.00000 0.169334
\(559\) 28.0000 1.18427
\(560\) −15.0000 −0.633866
\(561\) 18.0000 0.759961
\(562\) 6.00000 0.253095
\(563\) −30.0000 −1.26435 −0.632175 0.774826i \(-0.717837\pi\)
−0.632175 + 0.774826i \(0.717837\pi\)
\(564\) −3.00000 −0.126323
\(565\) 9.00000 0.378633
\(566\) −14.0000 −0.588464
\(567\) 5.00000 0.209980
\(568\) −12.0000 −0.503509
\(569\) 33.0000 1.38343 0.691716 0.722170i \(-0.256855\pi\)
0.691716 + 0.722170i \(0.256855\pi\)
\(570\) −3.00000 −0.125656
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) −24.0000 −1.00349
\(573\) −21.0000 −0.877288
\(574\) 45.0000 1.87826
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −16.0000 −0.666089 −0.333044 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 8.00000 0.332756
\(579\) −4.00000 −0.166234
\(580\) 3.00000 0.124568
\(581\) 0 0
\(582\) −8.00000 −0.331611
\(583\) −36.0000 −1.49097
\(584\) −2.00000 −0.0827606
\(585\) 12.0000 0.496139
\(586\) 6.00000 0.247858
\(587\) 21.0000 0.866763 0.433381 0.901211i \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(588\) 18.0000 0.742307
\(589\) 4.00000 0.164817
\(590\) 9.00000 0.370524
\(591\) 9.00000 0.370211
\(592\) −1.00000 −0.0410997
\(593\) −24.0000 −0.985562 −0.492781 0.870153i \(-0.664020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(594\) −6.00000 −0.246183
\(595\) −45.0000 −1.84482
\(596\) 3.00000 0.122885
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) −4.00000 −0.163299
\(601\) 32.0000 1.30531 0.652654 0.757656i \(-0.273656\pi\)
0.652654 + 0.757656i \(0.273656\pi\)
\(602\) 35.0000 1.42649
\(603\) −4.00000 −0.162893
\(604\) 17.0000 0.691720
\(605\) −75.0000 −3.04918
\(606\) 6.00000 0.243733
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 1.00000 0.0405554
\(609\) −5.00000 −0.202610
\(610\) −30.0000 −1.21466
\(611\) 12.0000 0.485468
\(612\) 3.00000 0.121268
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) −20.0000 −0.807134
\(615\) 27.0000 1.08875
\(616\) −30.0000 −1.20873
\(617\) 33.0000 1.32853 0.664265 0.747497i \(-0.268745\pi\)
0.664265 + 0.747497i \(0.268745\pi\)
\(618\) 13.0000 0.522937
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 12.0000 0.481932
\(621\) 0 0
\(622\) −21.0000 −0.842023
\(623\) −30.0000 −1.20192
\(624\) −4.00000 −0.160128
\(625\) −29.0000 −1.16000
\(626\) −11.0000 −0.439648
\(627\) −6.00000 −0.239617
\(628\) −13.0000 −0.518756
\(629\) −3.00000 −0.119618
\(630\) 15.0000 0.597614
\(631\) −13.0000 −0.517522 −0.258761 0.965941i \(-0.583314\pi\)
−0.258761 + 0.965941i \(0.583314\pi\)
\(632\) −14.0000 −0.556890
\(633\) −25.0000 −0.993661
\(634\) 0 0
\(635\) 66.0000 2.61913
\(636\) −6.00000 −0.237915
\(637\) −72.0000 −2.85274
\(638\) 6.00000 0.237542
\(639\) 12.0000 0.474713
\(640\) 3.00000 0.118585
\(641\) −27.0000 −1.06644 −0.533218 0.845978i \(-0.679017\pi\)
−0.533218 + 0.845978i \(0.679017\pi\)
\(642\) 9.00000 0.355202
\(643\) −40.0000 −1.57745 −0.788723 0.614749i \(-0.789257\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) 21.0000 0.826874
\(646\) 3.00000 0.118033
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 18.0000 0.706562
\(650\) 16.0000 0.627572
\(651\) −20.0000 −0.783862
\(652\) 5.00000 0.195815
\(653\) 42.0000 1.64359 0.821794 0.569785i \(-0.192974\pi\)
0.821794 + 0.569785i \(0.192974\pi\)
\(654\) −8.00000 −0.312825
\(655\) −36.0000 −1.40664
\(656\) −9.00000 −0.351391
\(657\) 2.00000 0.0780274
\(658\) 15.0000 0.584761
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) −18.0000 −0.700649
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) −17.0000 −0.660724
\(663\) −12.0000 −0.466041
\(664\) 0 0
\(665\) 15.0000 0.581675
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) 6.00000 0.232147
\(669\) −16.0000 −0.618596
\(670\) −12.0000 −0.463600
\(671\) −60.0000 −2.31627
\(672\) −5.00000 −0.192879
\(673\) −13.0000 −0.501113 −0.250557 0.968102i \(-0.580614\pi\)
−0.250557 + 0.968102i \(0.580614\pi\)
\(674\) 10.0000 0.385186
\(675\) 4.00000 0.153960
\(676\) 3.00000 0.115385
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 3.00000 0.115214
\(679\) 40.0000 1.53506
\(680\) 9.00000 0.345134
\(681\) 3.00000 0.114960
\(682\) 24.0000 0.919007
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) −1.00000 −0.0382360
\(685\) 18.0000 0.687745
\(686\) −55.0000 −2.09991
\(687\) −7.00000 −0.267067
\(688\) −7.00000 −0.266872
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) −52.0000 −1.97817 −0.989087 0.147335i \(-0.952930\pi\)
−0.989087 + 0.147335i \(0.952930\pi\)
\(692\) −21.0000 −0.798300
\(693\) 30.0000 1.13961
\(694\) 3.00000 0.113878
\(695\) −42.0000 −1.59315
\(696\) 1.00000 0.0379049
\(697\) −27.0000 −1.02270
\(698\) −2.00000 −0.0757011
\(699\) 24.0000 0.907763
\(700\) 20.0000 0.755929
\(701\) 45.0000 1.69963 0.849813 0.527084i \(-0.176715\pi\)
0.849813 + 0.527084i \(0.176715\pi\)
\(702\) 4.00000 0.150970
\(703\) 1.00000 0.0377157
\(704\) 6.00000 0.226134
\(705\) 9.00000 0.338960
\(706\) 30.0000 1.12906
\(707\) −30.0000 −1.12827
\(708\) 3.00000 0.112747
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 36.0000 1.35106
\(711\) 14.0000 0.525041
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) −15.0000 −0.561361
\(715\) 72.0000 2.69265
\(716\) 0 0
\(717\) 6.00000 0.224074
\(718\) −9.00000 −0.335877
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) −3.00000 −0.111803
\(721\) −65.0000 −2.42073
\(722\) 18.0000 0.669891
\(723\) 17.0000 0.632237
\(724\) 8.00000 0.297318
\(725\) −4.00000 −0.148556
\(726\) −25.0000 −0.927837
\(727\) −10.0000 −0.370879 −0.185440 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(728\) 20.0000 0.741249
\(729\) 1.00000 0.0370370
\(730\) 6.00000 0.222070
\(731\) −21.0000 −0.776713
\(732\) −10.0000 −0.369611
\(733\) 50.0000 1.84679 0.923396 0.383849i \(-0.125402\pi\)
0.923396 + 0.383849i \(0.125402\pi\)
\(734\) −26.0000 −0.959678
\(735\) −54.0000 −1.99182
\(736\) 0 0
\(737\) −24.0000 −0.884051
\(738\) 9.00000 0.331295
\(739\) 8.00000 0.294285 0.147142 0.989115i \(-0.452992\pi\)
0.147142 + 0.989115i \(0.452992\pi\)
\(740\) 3.00000 0.110282
\(741\) 4.00000 0.146944
\(742\) 30.0000 1.10133
\(743\) −21.0000 −0.770415 −0.385208 0.922830i \(-0.625870\pi\)
−0.385208 + 0.922830i \(0.625870\pi\)
\(744\) 4.00000 0.146647
\(745\) −9.00000 −0.329734
\(746\) −20.0000 −0.732252
\(747\) 0 0
\(748\) 18.0000 0.658145
\(749\) −45.0000 −1.64426
\(750\) −3.00000 −0.109545
\(751\) −10.0000 −0.364905 −0.182453 0.983215i \(-0.558404\pi\)
−0.182453 + 0.983215i \(0.558404\pi\)
\(752\) −3.00000 −0.109399
\(753\) 0 0
\(754\) −4.00000 −0.145671
\(755\) −51.0000 −1.85608
\(756\) 5.00000 0.181848
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 28.0000 1.01701
\(759\) 0 0
\(760\) −3.00000 −0.108821
\(761\) −36.0000 −1.30500 −0.652499 0.757789i \(-0.726280\pi\)
−0.652499 + 0.757789i \(0.726280\pi\)
\(762\) 22.0000 0.796976
\(763\) 40.0000 1.44810
\(764\) −21.0000 −0.759753
\(765\) −9.00000 −0.325396
\(766\) 6.00000 0.216789
\(767\) −12.0000 −0.433295
\(768\) 1.00000 0.0360844
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 90.0000 3.24337
\(771\) 0 0
\(772\) −4.00000 −0.143963
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 7.00000 0.251610
\(775\) −16.0000 −0.574737
\(776\) −8.00000 −0.287183
\(777\) −5.00000 −0.179374
\(778\) 12.0000 0.430221
\(779\) 9.00000 0.322458
\(780\) 12.0000 0.429669
\(781\) 72.0000 2.57636
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 18.0000 0.642857
\(785\) 39.0000 1.39197
\(786\) −12.0000 −0.428026
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 9.00000 0.320612
\(789\) −3.00000 −0.106803
\(790\) 42.0000 1.49429
\(791\) −15.0000 −0.533339
\(792\) −6.00000 −0.213201
\(793\) 40.0000 1.42044
\(794\) −26.0000 −0.922705
\(795\) 18.0000 0.638394
\(796\) −16.0000 −0.567105
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 5.00000 0.176998
\(799\) −9.00000 −0.318397
\(800\) −4.00000 −0.141421
\(801\) −6.00000 −0.212000
\(802\) −30.0000 −1.05934
\(803\) 12.0000 0.423471
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) 6.00000 0.211210
\(808\) 6.00000 0.211079
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 3.00000 0.105409
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −5.00000 −0.175466
\(813\) 20.0000 0.701431
\(814\) 6.00000 0.210300
\(815\) −15.0000 −0.525427
\(816\) 3.00000 0.105021
\(817\) 7.00000 0.244899
\(818\) −8.00000 −0.279713
\(819\) −20.0000 −0.698857
\(820\) 27.0000 0.942881
\(821\) 54.0000 1.88461 0.942306 0.334751i \(-0.108652\pi\)
0.942306 + 0.334751i \(0.108652\pi\)
\(822\) 6.00000 0.209274
\(823\) 26.0000 0.906303 0.453152 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) 13.0000 0.452876
\(825\) 24.0000 0.835573
\(826\) −15.0000 −0.521917
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −49.0000 −1.70184 −0.850920 0.525295i \(-0.823955\pi\)
−0.850920 + 0.525295i \(0.823955\pi\)
\(830\) 0 0
\(831\) 14.0000 0.485655
\(832\) −4.00000 −0.138675
\(833\) 54.0000 1.87099
\(834\) −14.0000 −0.484780
\(835\) −18.0000 −0.622916
\(836\) −6.00000 −0.207514
\(837\) −4.00000 −0.138260
\(838\) −21.0000 −0.725433
\(839\) −3.00000 −0.103572 −0.0517858 0.998658i \(-0.516491\pi\)
−0.0517858 + 0.998658i \(0.516491\pi\)
\(840\) 15.0000 0.517549
\(841\) 1.00000 0.0344828
\(842\) −14.0000 −0.482472
\(843\) −6.00000 −0.206651
\(844\) −25.0000 −0.860535
\(845\) −9.00000 −0.309609
\(846\) 3.00000 0.103142
\(847\) 125.000 4.29505
\(848\) −6.00000 −0.206041
\(849\) 14.0000 0.480479
\(850\) −12.0000 −0.411597
\(851\) 0 0
\(852\) 12.0000 0.411113
\(853\) −19.0000 −0.650548 −0.325274 0.945620i \(-0.605456\pi\)
−0.325274 + 0.945620i \(0.605456\pi\)
\(854\) 50.0000 1.71096
\(855\) 3.00000 0.102598
\(856\) 9.00000 0.307614
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 24.0000 0.819346
\(859\) 5.00000 0.170598 0.0852989 0.996355i \(-0.472815\pi\)
0.0852989 + 0.996355i \(0.472815\pi\)
\(860\) 21.0000 0.716094
\(861\) −45.0000 −1.53360
\(862\) −36.0000 −1.22616
\(863\) −36.0000 −1.22545 −0.612727 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 63.0000 2.14206
\(866\) −26.0000 −0.883516
\(867\) −8.00000 −0.271694
\(868\) −20.0000 −0.678844
\(869\) 84.0000 2.84950
\(870\) −3.00000 −0.101710
\(871\) 16.0000 0.542139
\(872\) −8.00000 −0.270914
\(873\) 8.00000 0.270759
\(874\) 0 0
\(875\) 15.0000 0.507093
\(876\) 2.00000 0.0675737
\(877\) −16.0000 −0.540282 −0.270141 0.962821i \(-0.587070\pi\)
−0.270141 + 0.962821i \(0.587070\pi\)
\(878\) 1.00000 0.0337484
\(879\) −6.00000 −0.202375
\(880\) −18.0000 −0.606780
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) −18.0000 −0.606092
\(883\) 56.0000 1.88455 0.942275 0.334840i \(-0.108682\pi\)
0.942275 + 0.334840i \(0.108682\pi\)
\(884\) −12.0000 −0.403604
\(885\) −9.00000 −0.302532
\(886\) −12.0000 −0.403148
\(887\) 48.0000 1.61168 0.805841 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) 1.00000 0.0335578
\(889\) −110.000 −3.68928
\(890\) −18.0000 −0.603361
\(891\) 6.00000 0.201008
\(892\) −16.0000 −0.535720
\(893\) 3.00000 0.100391
\(894\) −3.00000 −0.100335
\(895\) 0 0
\(896\) −5.00000 −0.167038
\(897\) 0 0
\(898\) −15.0000 −0.500556
\(899\) 4.00000 0.133407
\(900\) 4.00000 0.133333
\(901\) −18.0000 −0.599667
\(902\) 54.0000 1.79800
\(903\) −35.0000 −1.16473
\(904\) 3.00000 0.0997785
\(905\) −24.0000 −0.797787
\(906\) −17.0000 −0.564787
\(907\) −28.0000 −0.929725 −0.464862 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 3.00000 0.0995585
\(909\) −6.00000 −0.199007
\(910\) −60.0000 −1.98898
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) −11.0000 −0.363848
\(915\) 30.0000 0.991769
\(916\) −7.00000 −0.231287
\(917\) 60.0000 1.98137
\(918\) −3.00000 −0.0990148
\(919\) 29.0000 0.956622 0.478311 0.878191i \(-0.341249\pi\)
0.478311 + 0.878191i \(0.341249\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −12.0000 −0.395199
\(923\) −48.0000 −1.57994
\(924\) 30.0000 0.986928
\(925\) −4.00000 −0.131519
\(926\) 16.0000 0.525793
\(927\) −13.0000 −0.426976
\(928\) 1.00000 0.0328266
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) −12.0000 −0.393496
\(931\) −18.0000 −0.589926
\(932\) 24.0000 0.786146
\(933\) 21.0000 0.687509
\(934\) 12.0000 0.392652
\(935\) −54.0000 −1.76599
\(936\) 4.00000 0.130744
\(937\) −49.0000 −1.60076 −0.800380 0.599493i \(-0.795369\pi\)
−0.800380 + 0.599493i \(0.795369\pi\)
\(938\) 20.0000 0.653023
\(939\) 11.0000 0.358971
\(940\) 9.00000 0.293548
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 13.0000 0.423563
\(943\) 0 0
\(944\) 3.00000 0.0976417
\(945\) −15.0000 −0.487950
\(946\) 42.0000 1.36554
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 14.0000 0.454699
\(949\) −8.00000 −0.259691
\(950\) 4.00000 0.129777
\(951\) 0 0
\(952\) −15.0000 −0.486153
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 6.00000 0.194257
\(955\) 63.0000 2.03863
\(956\) 6.00000 0.194054
\(957\) −6.00000 −0.193952
\(958\) −24.0000 −0.775405
\(959\) −30.0000 −0.968751
\(960\) −3.00000 −0.0968246
\(961\) −15.0000 −0.483871
\(962\) −4.00000 −0.128965
\(963\) −9.00000 −0.290021
\(964\) 17.0000 0.547533
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) −4.00000 −0.128631 −0.0643157 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) −25.0000 −0.803530
\(969\) −3.00000 −0.0963739
\(970\) 24.0000 0.770594
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 1.00000 0.0320750
\(973\) 70.0000 2.24410
\(974\) −23.0000 −0.736968
\(975\) −16.0000 −0.512410
\(976\) −10.0000 −0.320092
\(977\) −12.0000 −0.383914 −0.191957 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) −5.00000 −0.159882
\(979\) −36.0000 −1.15056
\(980\) −54.0000 −1.72497
\(981\) 8.00000 0.255420
\(982\) 30.0000 0.957338
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 9.00000 0.286910
\(985\) −27.0000 −0.860292
\(986\) 3.00000 0.0955395
\(987\) −15.0000 −0.477455
\(988\) 4.00000 0.127257
\(989\) 0 0
\(990\) 18.0000 0.572078
\(991\) 47.0000 1.49300 0.746502 0.665383i \(-0.231732\pi\)
0.746502 + 0.665383i \(0.231732\pi\)
\(992\) 4.00000 0.127000
\(993\) 17.0000 0.539479
\(994\) −60.0000 −1.90308
\(995\) 48.0000 1.52170
\(996\) 0 0
\(997\) −19.0000 −0.601736 −0.300868 0.953666i \(-0.597276\pi\)
−0.300868 + 0.953666i \(0.597276\pi\)
\(998\) 22.0000 0.696398
\(999\) −1.00000 −0.0316386
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 \(a_p\))