Properties

Label 5610.2.a.q.1.1
Level 5610
Weight 2
Character 5610.1
Self dual Yes
Analytic conductor 44.796
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5610.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(44.7960755339\)
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 \(\chi\) = 5610.1

$q$-expansion

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

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
\(5\) 1.00000 0.447214
\(6\) −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
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 4.00000 1.06904
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 1.00000 0.223607
\(21\) −4.00000 −0.872872
\(22\) −1.00000 −0.213201
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) −4.00000 −0.755929
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 −0.182574
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) −4.00000 −0.676123
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 4.00000 0.648886
\(39\) 2.00000 0.320256
\(40\) −1.00000 −0.158114
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 4.00000 0.617213
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 1.00000 0.150756
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 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
\(50\) −1.00000 −0.141421
\(51\) −1.00000 −0.140028
\(52\) 2.00000 0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 1.00000 0.134840
\(56\) 4.00000 0.534522
\(57\) −4.00000 −0.529813
\(58\) 6.00000 0.787839
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 1.00000 0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −8.00000 −1.01600
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) −1.00000 −0.121268
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 10.0000 1.16248
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) −4.00000 −0.455842
\(78\) −2.00000 −0.226455
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −4.00000 −0.436436
\(85\) −1.00000 −0.108465
\(86\) 4.00000 0.431331
\(87\) −6.00000 −0.643268
\(88\) −1.00000 −0.106600
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −1.00000 −0.105409
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) −12.0000 −1.23771
\(95\) −4.00000 −0.410391
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −9.00000 −0.909137
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 1.00000 0.0990148
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −2.00000 −0.196116
\(105\) −4.00000 −0.390360
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.00000 0.0962250
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −10.0000 −0.949158
\(112\) −4.00000 −0.377964
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 2.00000 0.184900
\(118\) −12.0000 −1.10469
\(119\) 4.00000 0.366679
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −2.00000 −0.181071
\(123\) 6.00000 0.541002
\(124\) 8.00000 0.718421
\(125\) 1.00000 0.0894427
\(126\) 4.00000 0.356348
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.00000 −0.352180
\(130\) −2.00000 −0.175412
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 1.00000 0.0870388
\(133\) 16.0000 1.38738
\(134\) −8.00000 −0.691095
\(135\) 1.00000 0.0860663
\(136\) 1.00000 0.0857493
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −4.00000 −0.338062
\(141\) 12.0000 1.01058
\(142\) 12.0000 1.00702
\(143\) 2.00000 0.167248
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −2.00000 −0.165521
\(147\) 9.00000 0.742307
\(148\) −10.0000 −0.821995
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 4.00000 0.324443
\(153\) −1.00000 −0.0808452
\(154\) 4.00000 0.322329
\(155\) 8.00000 0.642575
\(156\) 2.00000 0.160128
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) −8.00000 −0.636446
\(159\) 6.00000 0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 6.00000 0.468521
\(165\) 1.00000 0.0778499
\(166\) 12.0000 0.931381
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 4.00000 0.308607
\(169\) −9.00000 −0.692308
\(170\) 1.00000 0.0766965
\(171\) −4.00000 −0.305888
\(172\) −4.00000 −0.304997
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 6.00000 0.454859
\(175\) −4.00000 −0.302372
\(176\) 1.00000 0.0753778
\(177\) 12.0000 0.901975
\(178\) 6.00000 0.449719
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 0.0745356
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 8.00000 0.592999
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) −10.0000 −0.735215
\(186\) −8.00000 −0.586588
\(187\) −1.00000 −0.0731272
\(188\) 12.0000 0.875190
\(189\) −4.00000 −0.290957
\(190\) 4.00000 0.290191
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) −2.00000 −0.143592
\(195\) 2.00000 0.143223
\(196\) 9.00000 0.642857
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −1.00000 −0.0710669
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.00000 0.564276
\(202\) −6.00000 −0.422159
\(203\) 24.0000 1.68447
\(204\) −1.00000 −0.0700140
\(205\) 6.00000 0.419058
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) −4.00000 −0.276686
\(210\) 4.00000 0.276026
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 6.00000 0.412082
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) −4.00000 −0.272798
\(216\) −1.00000 −0.0680414
\(217\) −32.0000 −2.17230
\(218\) −2.00000 −0.135457
\(219\) 2.00000 0.135147
\(220\) 1.00000 0.0674200
\(221\) −2.00000 −0.134535
\(222\) 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
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −4.00000 −0.264906
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) −4.00000 −0.263181
\(232\) 6.00000 0.393919
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) −2.00000 −0.130744
\(235\) 12.0000 0.782794
\(236\) 12.0000 0.781133
\(237\) 8.00000 0.519656
\(238\) −4.00000 −0.259281
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 1.00000 0.0645497
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) 9.00000 0.574989
\(246\) −6.00000 −0.382546
\(247\) −8.00000 −0.509028
\(248\) −8.00000 −0.508001
\(249\) −12.0000 −0.760469
\(250\) −1.00000 −0.0632456
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) −1.00000 −0.0626224
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 4.00000 0.249029
\(259\) 40.0000 2.48548
\(260\) 2.00000 0.124035
\(261\) −6.00000 −0.371391
\(262\) −12.0000 −0.741362
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 6.00000 0.368577
\(266\) −16.0000 −0.981023
\(267\) −6.00000 −0.367194
\(268\) 8.00000 0.488678
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −8.00000 −0.484182
\(274\) 18.0000 1.08742
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −20.0000 −1.19952
\(279\) 8.00000 0.478947
\(280\) 4.00000 0.239046
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −12.0000 −0.714590
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) −12.0000 −0.712069
\(285\) −4.00000 −0.236940
\(286\) −2.00000 −0.118262
\(287\) −24.0000 −1.41668
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 6.00000 0.352332
\(291\) 2.00000 0.117242
\(292\) 2.00000 0.117041
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −9.00000 −0.524891
\(295\) 12.0000 0.698667
\(296\) 10.0000 0.581238
\(297\) 1.00000 0.0580259
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 16.0000 0.922225
\(302\) −20.0000 −1.15087
\(303\) 6.00000 0.344691
\(304\) −4.00000 −0.229416
\(305\) 2.00000 0.114520
\(306\) 1.00000 0.0571662
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −4.00000 −0.227921
\(309\) 8.00000 0.455104
\(310\) −8.00000 −0.454369
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −2.00000 −0.113228
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 22.0000 1.24153
\(315\) −4.00000 −0.225374
\(316\) 8.00000 0.450035
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −6.00000 −0.336463
\(319\) −6.00000 −0.335936
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) −20.0000 −1.10770
\(327\) 2.00000 0.110600
\(328\) −6.00000 −0.331295
\(329\) −48.0000 −2.64633
\(330\) −1.00000 −0.0550482
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −12.0000 −0.658586
\(333\) −10.0000 −0.547997
\(334\) 0 0
\(335\) 8.00000 0.437087
\(336\) −4.00000 −0.218218
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 9.00000 0.489535
\(339\) 18.0000 0.977626
\(340\) −1.00000 −0.0542326
\(341\) 8.00000 0.433224
\(342\) 4.00000 0.216295
\(343\) −8.00000 −0.431959
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) −6.00000 −0.321634
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 4.00000 0.213809
\(351\) 2.00000 0.106752
\(352\) −1.00000 −0.0533002
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) −12.0000 −0.637793
\(355\) −12.0000 −0.636894
\(356\) −6.00000 −0.317999
\(357\) 4.00000 0.211702
\(358\) 12.0000 0.634220
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) −26.0000 −1.36653
\(363\) 1.00000 0.0524864
\(364\) −8.00000 −0.419314
\(365\) 2.00000 0.104685
\(366\) −2.00000 −0.104542
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 10.0000 0.519875
\(371\) −24.0000 −1.24602
\(372\) 8.00000 0.414781
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 1.00000 0.0517088
\(375\) 1.00000 0.0516398
\(376\) −12.0000 −0.618853
\(377\) −12.0000 −0.618031
\(378\) 4.00000 0.205738
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −4.00000 −0.205196
\(381\) −16.0000 −0.819705
\(382\) 0 0
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.00000 −0.203859
\(386\) −2.00000 −0.101797
\(387\) −4.00000 −0.203331
\(388\) 2.00000 0.101535
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −2.00000 −0.101274
\(391\) 0 0
\(392\) −9.00000 −0.454569
\(393\) 12.0000 0.605320
\(394\) −6.00000 −0.302276
\(395\) 8.00000 0.402524
\(396\) 1.00000 0.0502519
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) 16.0000 0.802008
\(399\) 16.0000 0.801002
\(400\) 1.00000 0.0500000
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −8.00000 −0.399004
\(403\) 16.0000 0.797017
\(404\) 6.00000 0.298511
\(405\) 1.00000 0.0496904
\(406\) −24.0000 −1.19110
\(407\) −10.0000 −0.495682
\(408\) 1.00000 0.0495074
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) −6.00000 −0.296319
\(411\) −18.0000 −0.887875
\(412\) 8.00000 0.394132
\(413\) −48.0000 −2.36193
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) −2.00000 −0.0980581
\(417\) 20.0000 0.979404
\(418\) 4.00000 0.195646
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −4.00000 −0.195180
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) −20.0000 −0.973585
\(423\) 12.0000 0.583460
\(424\) −6.00000 −0.291386
\(425\) −1.00000 −0.0485071
\(426\) 12.0000 0.581402
\(427\) −8.00000 −0.387147
\(428\) 0 0
\(429\) 2.00000 0.0965609
\(430\) 4.00000 0.192897
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 32.0000 1.53605
\(435\) −6.00000 −0.287678
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 9.00000 0.428571
\(442\) 2.00000 0.0951303
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) −10.0000 −0.474579
\(445\) −6.00000 −0.284427
\(446\) −8.00000 −0.378811
\(447\) 6.00000 0.283790
\(448\) −4.00000 −0.188982
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 6.00000 0.282529
\(452\) 18.0000 0.846649
\(453\) 20.0000 0.939682
\(454\) 0 0
\(455\) −8.00000 −0.375046
\(456\) 4.00000 0.187317
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −14.0000 −0.654177
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 4.00000 0.186097
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −6.00000 −0.278543
\(465\) 8.00000 0.370991
\(466\) −6.00000 −0.277945
\(467\) −36.0000 −1.66588 −0.832941 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 2.00000 0.0924500
\(469\) −32.0000 −1.47762
\(470\) −12.0000 −0.553519
\(471\) −22.0000 −1.01371
\(472\) −12.0000 −0.552345
\(473\) −4.00000 −0.183920
\(474\) −8.00000 −0.367452
\(475\) −4.00000 −0.183533
\(476\) 4.00000 0.183340
\(477\) 6.00000 0.274721
\(478\) −24.0000 −1.09773
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −20.0000 −0.911922
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 2.00000 0.0908153
\(486\) −1.00000 −0.0453609
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 20.0000 0.904431
\(490\) −9.00000 −0.406579
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 6.00000 0.270501
\(493\) 6.00000 0.270226
\(494\) 8.00000 0.359937
\(495\) 1.00000 0.0449467
\(496\) 8.00000 0.359211
\(497\) 48.0000 2.15309
\(498\) 12.0000 0.537733
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 4.00000 0.178174
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) −16.0000 −0.709885
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 1.00000 0.0442807
\(511\) −8.00000 −0.353899
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) −6.00000 −0.264649
\(515\) 8.00000 0.352522
\(516\) −4.00000 −0.176090
\(517\) 12.0000 0.527759
\(518\) −40.0000 −1.75750
\(519\) 6.00000 0.263371
\(520\) −2.00000 −0.0877058
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 6.00000 0.262613
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 12.0000 0.524222
\(525\) −4.00000 −0.174574
\(526\) 24.0000 1.04645
\(527\) −8.00000 −0.348485
\(528\) 1.00000 0.0435194
\(529\) −23.0000 −1.00000
\(530\) −6.00000 −0.260623
\(531\) 12.0000 0.520756
\(532\) 16.0000 0.693688
\(533\) 12.0000 0.519778
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) −8.00000 −0.345547
\(537\) −12.0000 −0.517838
\(538\) 18.0000 0.776035
\(539\) 9.00000 0.387657
\(540\) 1.00000 0.0430331
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −20.0000 −0.859074
\(543\) 26.0000 1.11577
\(544\) 1.00000 0.0428746
\(545\) 2.00000 0.0856706
\(546\) 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
\(549\) 2.00000 0.0853579
\(550\) −1.00000 −0.0426401
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) −32.0000 −1.36078
\(554\) 22.0000 0.934690
\(555\) −10.0000 −0.424476
\(556\) 20.0000 0.848189
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −8.00000 −0.338667
\(559\) −8.00000 −0.338364
\(560\) −4.00000 −0.169031
\(561\) −1.00000 −0.0422200
\(562\) −6.00000 −0.253095
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 12.0000 0.505291
\(565\) 18.0000 0.757266
\(566\) −20.0000 −0.840663
\(567\) −4.00000 −0.167984
\(568\) 12.0000 0.503509
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 4.00000 0.167542
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 2.00000 0.0836242
\(573\) 0 0
\(574\) 24.0000 1.00174
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 26.0000 1.08239 0.541197 0.840896i \(-0.317971\pi\)
0.541197 + 0.840896i \(0.317971\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 2.00000 0.0831172
\(580\) −6.00000 −0.249136
\(581\) 48.0000 1.99138
\(582\) −2.00000 −0.0829027
\(583\) 6.00000 0.248495
\(584\) −2.00000 −0.0827606
\(585\) 2.00000 0.0826898
\(586\) 6.00000 0.247858
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 9.00000 0.371154
\(589\) −32.0000 −1.31854
\(590\) −12.0000 −0.494032
\(591\) 6.00000 0.246807
\(592\) −10.0000 −0.410997
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 4.00000 0.163984
\(596\) 6.00000 0.245770
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −16.0000 −0.652111
\(603\) 8.00000 0.325785
\(604\) 20.0000 0.813788
\(605\) 1.00000 0.0406558
\(606\) −6.00000 −0.243733
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 4.00000 0.162221
\(609\) 24.0000 0.972529
\(610\) −2.00000 −0.0809776
\(611\) 24.0000 0.970936
\(612\) −1.00000 −0.0404226
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) −20.0000 −0.807134
\(615\) 6.00000 0.241943
\(616\) 4.00000 0.161165
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −8.00000 −0.321807
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 8.00000 0.321288
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 24.0000 0.961540
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) −26.0000 −1.03917
\(627\) −4.00000 −0.159745
\(628\) −22.0000 −0.877896
\(629\) 10.0000 0.398726
\(630\) 4.00000 0.159364
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.00000 −0.318223
\(633\) 20.0000 0.794929
\(634\) 18.0000 0.714871
\(635\) −16.0000 −0.634941
\(636\) 6.00000 0.237915
\(637\) 18.0000 0.713186
\(638\) 6.00000 0.237542
\(639\) −12.0000 −0.474713
\(640\) −1.00000 −0.0395285
\(641\) 6.00000 0.236986 0.118493 0.992955i \(-0.462194\pi\)
0.118493 + 0.992955i \(0.462194\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) −4.00000 −0.157378
\(647\) 36.0000 1.41531 0.707653 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 12.0000 0.471041
\(650\) −2.00000 −0.0784465
\(651\) −32.0000 −1.25418
\(652\) 20.0000 0.783260
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 12.0000 0.468879
\(656\) 6.00000 0.234261
\(657\) 2.00000 0.0780274
\(658\) 48.0000 1.87123
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 1.00000 0.0389249
\(661\) −34.0000 −1.32245 −0.661223 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) −20.0000 −0.777322
\(663\) −2.00000 −0.0776736
\(664\) 12.0000 0.465690
\(665\) 16.0000 0.620453
\(666\) 10.0000 0.387492
\(667\) 0 0
\(668\) 0 0
\(669\) 8.00000 0.309298
\(670\) −8.00000 −0.309067
\(671\) 2.00000 0.0772091
\(672\) 4.00000 0.154303
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 22.0000 0.847408
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) −18.0000 −0.691286
\(679\) −8.00000 −0.307012
\(680\) 1.00000 0.0383482
\(681\) 0 0
\(682\) −8.00000 −0.306336
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −4.00000 −0.152944
\(685\) −18.0000 −0.687745
\(686\) 8.00000 0.305441
\(687\) 14.0000 0.534133
\(688\) −4.00000 −0.152499
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 6.00000 0.228086
\(693\) −4.00000 −0.151947
\(694\) 0 0
\(695\) 20.0000 0.758643
\(696\) 6.00000 0.227429
\(697\) −6.00000 −0.227266
\(698\) −26.0000 −0.984115
\(699\) 6.00000 0.226941
\(700\) −4.00000 −0.151186
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 40.0000 1.50863
\(704\) 1.00000 0.0376889
\(705\) 12.0000 0.451946
\(706\) 18.0000 0.677439
\(707\) −24.0000 −0.902613
\(708\) 12.0000 0.450988
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 12.0000 0.450352
\(711\) 8.00000 0.300023
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) −4.00000 −0.149696
\(715\) 2.00000 0.0747958
\(716\) −12.0000 −0.448461
\(717\) 24.0000 0.896296
\(718\) 0 0
\(719\) 12.0000 0.447524 0.223762 0.974644i \(-0.428166\pi\)
0.223762 + 0.974644i \(0.428166\pi\)
\(720\) 1.00000 0.0372678
\(721\) −32.0000 −1.19174
\(722\) 3.00000 0.111648
\(723\) −10.0000 −0.371904
\(724\) 26.0000 0.966282
\(725\) −6.00000 −0.222834
\(726\) −1.00000 −0.0371135
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 8.00000 0.296500
\(729\) 1.00000 0.0370370
\(730\) −2.00000 −0.0740233
\(731\) 4.00000 0.147945
\(732\) 2.00000 0.0739221
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) −32.0000 −1.18114
\(735\) 9.00000 0.331970
\(736\) 0 0
\(737\) 8.00000 0.294684
\(738\) −6.00000 −0.220863
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) −10.0000 −0.367607
\(741\) −8.00000 −0.293887
\(742\) 24.0000 0.881068
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) −8.00000 −0.293294
\(745\) 6.00000 0.219823
\(746\) 22.0000 0.805477
\(747\) −12.0000 −0.439057
\(748\) −1.00000 −0.0365636
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 12.0000 0.437595
\(753\) 12.0000 0.437304
\(754\) 12.0000 0.437014
\(755\) 20.0000 0.727875
\(756\) −4.00000 −0.145479
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 16.0000 0.581146
\(759\) 0 0
\(760\) 4.00000 0.145095
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 16.0000 0.579619
\(763\) −8.00000 −0.289619
\(764\) 0 0
\(765\) −1.00000 −0.0361551
\(766\) 12.0000 0.433578
\(767\) 24.0000 0.866590
\(768\) 1.00000 0.0360844
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 4.00000 0.144150
\(771\) 6.00000 0.216085
\(772\) 2.00000 0.0719816
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 4.00000 0.143777
\(775\) 8.00000 0.287368
\(776\) −2.00000 −0.0717958
\(777\) 40.0000 1.43499
\(778\) −6.00000 −0.215110
\(779\) −24.0000 −0.859889
\(780\) 2.00000 0.0716115
\(781\) −12.0000 −0.429394
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) 9.00000 0.321429
\(785\) −22.0000 −0.785214
\(786\) −12.0000 −0.428026
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) 6.00000 0.213741
\(789\) −24.0000 −0.854423
\(790\) −8.00000 −0.284627
\(791\) −72.0000 −2.56003
\(792\) −1.00000 −0.0355335
\(793\) 4.00000 0.142044
\(794\) −38.0000 −1.34857
\(795\) 6.00000 0.212798
\(796\) −16.0000 −0.567105
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) −16.0000 −0.566394
\(799\) −12.0000 −0.424529
\(800\) −1.00000 −0.0353553
\(801\) −6.00000 −0.212000
\(802\) −6.00000 −0.211867
\(803\) 2.00000 0.0705785
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) −18.0000 −0.633630
\(808\) −6.00000 −0.211079
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 44.0000 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) 24.0000 0.842235
\(813\) 20.0000 0.701431
\(814\) 10.0000 0.350500
\(815\) 20.0000 0.700569
\(816\) −1.00000 −0.0350070
\(817\) 16.0000 0.559769
\(818\) −26.0000 −0.909069
\(819\) −8.00000 −0.279543
\(820\) 6.00000 0.209529
\(821\) −6.00000 −0.209401 −0.104701 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) 18.0000 0.627822
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) −8.00000 −0.278693
\(825\) 1.00000 0.0348155
\(826\) 48.0000 1.67013
\(827\) −48.0000 −1.66912 −0.834562 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) 0 0
\(829\) 38.0000 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) 12.0000 0.416526
\(831\) −22.0000 −0.763172
\(832\) 2.00000 0.0693375
\(833\) −9.00000 −0.311832
\(834\) −20.0000 −0.692543
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) 8.00000 0.276520
\(838\) 12.0000 0.414533
\(839\) 36.0000 1.24286 0.621429 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 4.00000 0.138013
\(841\) 7.00000 0.241379
\(842\) 34.0000 1.17172
\(843\) 6.00000 0.206651
\(844\) 20.0000 0.688428
\(845\) −9.00000 −0.309609
\(846\) −12.0000 −0.412568
\(847\) −4.00000 −0.137442
\(848\) 6.00000 0.206041
\(849\) 20.0000 0.686398
\(850\) 1.00000 0.0342997
\(851\) 0 0
\(852\) −12.0000 −0.411113
\(853\) −22.0000 −0.753266 −0.376633 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 8.00000 0.273754
\(855\) −4.00000 −0.136797
\(856\) 0 0
\(857\) 6.00000 0.204956 0.102478 0.994735i \(-0.467323\pi\)
0.102478 + 0.994735i \(0.467323\pi\)
\(858\) −2.00000 −0.0682789
\(859\) −28.0000 −0.955348 −0.477674 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) −4.00000 −0.136399
\(861\) −24.0000 −0.817918
\(862\) 24.0000 0.817443
\(863\) −36.0000 −1.22545 −0.612727 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 6.00000 0.204006
\(866\) −2.00000 −0.0679628
\(867\) 1.00000 0.0339618
\(868\) −32.0000 −1.08615
\(869\) 8.00000 0.271381
\(870\) 6.00000 0.203419
\(871\) 16.0000 0.542139
\(872\) −2.00000 −0.0677285
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) −4.00000 −0.135225
\(876\) 2.00000 0.0675737
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −8.00000 −0.269987
\(879\) −6.00000 −0.202375
\(880\) 1.00000 0.0337100
\(881\) 6.00000 0.202145 0.101073 0.994879i \(-0.467773\pi\)
0.101073 + 0.994879i \(0.467773\pi\)
\(882\) −9.00000 −0.303046
\(883\) −16.0000 −0.538443 −0.269221 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 12.0000 0.403376
\(886\) 12.0000 0.403148
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 10.0000 0.335578
\(889\) 64.0000 2.14649
\(890\) 6.00000 0.201120
\(891\) 1.00000 0.0335013
\(892\) 8.00000 0.267860
\(893\) −48.0000 −1.60626
\(894\) −6.00000 −0.200670
\(895\) −12.0000 −0.401116
\(896\) 4.00000 0.133631
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) −48.0000 −1.60089
\(900\) 1.00000 0.0333333
\(901\) −6.00000 −0.199889
\(902\) −6.00000 −0.199778
\(903\) 16.0000 0.532447
\(904\) −18.0000 −0.598671
\(905\) 26.0000 0.864269
\(906\) −20.0000 −0.664455
\(907\) −28.0000 −0.929725 −0.464862 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 0 0
\(909\) 6.00000 0.199007
\(910\) 8.00000 0.265197
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) −4.00000 −0.132453
\(913\) −12.0000 −0.397142
\(914\) 10.0000 0.330771
\(915\) 2.00000 0.0661180
\(916\) 14.0000 0.462573
\(917\) −48.0000 −1.58510
\(918\) 1.00000 0.0330049
\(919\) −52.0000 −1.71532 −0.857661 0.514216i \(-0.828083\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) 42.0000 1.38320
\(923\) −24.0000 −0.789970
\(924\) −4.00000 −0.131590
\(925\) −10.0000 −0.328798
\(926\) −8.00000 −0.262896
\(927\) 8.00000 0.262754
\(928\) 6.00000 0.196960
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) −8.00000 −0.262330
\(931\) −36.0000 −1.17985
\(932\) 6.00000 0.196537
\(933\) −12.0000 −0.392862
\(934\) 36.0000 1.17796
\(935\) −1.00000 −0.0327035
\(936\) −2.00000 −0.0653720
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 32.0000 1.04484
\(939\) 26.0000 0.848478
\(940\) 12.0000 0.391397
\(941\) −30.0000 −0.977972 −0.488986 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 22.0000 0.716799
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) −4.00000 −0.130120
\(946\) 4.00000 0.130051
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 8.00000 0.259828
\(949\) 4.00000 0.129845
\(950\) 4.00000 0.129777
\(951\) −18.0000 −0.583690
\(952\) −4.00000 −0.129641
\(953\) 54.0000 1.74923 0.874616 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) −6.00000 −0.193952
\(958\) −24.0000 −0.775405
\(959\) 72.0000 2.32500
\(960\) 1.00000 0.0322749
\(961\) 33.0000 1.06452
\(962\) 20.0000 0.644826
\(963\) 0 0
\(964\) −10.0000 −0.322078
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 4.00000 0.128499
\(970\) −2.00000 −0.0642161
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 1.00000 0.0320750
\(973\) −80.0000 −2.56468
\(974\) −8.00000 −0.256337
\(975\) 2.00000 0.0640513
\(976\) 2.00000 0.0640184
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) −20.0000 −0.639529
\(979\) −6.00000 −0.191761
\(980\) 9.00000 0.287494
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) −48.0000 −1.53096 −0.765481 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) −6.00000 −0.191273
\(985\) 6.00000 0.191176
\(986\) −6.00000 −0.191079
\(987\) −48.0000 −1.52786
\(988\) −8.00000 −0.254514
\(989\) 0 0
\(990\) −1.00000 −0.0317821
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) −8.00000 −0.254000
\(993\) 20.0000 0.634681
\(994\) −48.0000 −1.52247
\(995\) −16.0000 −0.507234
\(996\) −12.0000 −0.380235
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) −32.0000 −1.01294
\(999\) −10.0000 −0.316386
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))