Properties

Label 174.2.a.e.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

Related objects

Downloads

Learn more about

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

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.00000 q^{10}\) \(-2.00000 q^{11}\) \(+1.00000 q^{12}\) \(+1.00000 q^{14}\) \(-1.00000 q^{15}\) \(+1.00000 q^{16}\) \(-3.00000 q^{17}\) \(+1.00000 q^{18}\) \(-1.00000 q^{19}\) \(-1.00000 q^{20}\) \(+1.00000 q^{21}\) \(-2.00000 q^{22}\) \(-4.00000 q^{23}\) \(+1.00000 q^{24}\) \(-4.00000 q^{25}\) \(+1.00000 q^{27}\) \(+1.00000 q^{28}\) \(+1.00000 q^{29}\) \(-1.00000 q^{30}\) \(+4.00000 q^{31}\) \(+1.00000 q^{32}\) \(-2.00000 q^{33}\) \(-3.00000 q^{34}\) \(-1.00000 q^{35}\) \(+1.00000 q^{36}\) \(+3.00000 q^{37}\) \(-1.00000 q^{38}\) \(-1.00000 q^{40}\) \(-7.00000 q^{41}\) \(+1.00000 q^{42}\) \(+9.00000 q^{43}\) \(-2.00000 q^{44}\) \(-1.00000 q^{45}\) \(-4.00000 q^{46}\) \(-1.00000 q^{47}\) \(+1.00000 q^{48}\) \(-6.00000 q^{49}\) \(-4.00000 q^{50}\) \(-3.00000 q^{51}\) \(-2.00000 q^{53}\) \(+1.00000 q^{54}\) \(+2.00000 q^{55}\) \(+1.00000 q^{56}\) \(-1.00000 q^{57}\) \(+1.00000 q^{58}\) \(-3.00000 q^{59}\) \(-1.00000 q^{60}\) \(+6.00000 q^{61}\) \(+4.00000 q^{62}\) \(+1.00000 q^{63}\) \(+1.00000 q^{64}\) \(-2.00000 q^{66}\) \(+12.0000 q^{67}\) \(-3.00000 q^{68}\) \(-4.00000 q^{69}\) \(-1.00000 q^{70}\) \(+16.0000 q^{71}\) \(+1.00000 q^{72}\) \(-10.0000 q^{73}\) \(+3.00000 q^{74}\) \(-4.00000 q^{75}\) \(-1.00000 q^{76}\) \(-2.00000 q^{77}\) \(+10.0000 q^{79}\) \(-1.00000 q^{80}\) \(+1.00000 q^{81}\) \(-7.00000 q^{82}\) \(+1.00000 q^{84}\) \(+3.00000 q^{85}\) \(+9.00000 q^{86}\) \(+1.00000 q^{87}\) \(-2.00000 q^{88}\) \(+6.00000 q^{89}\) \(-1.00000 q^{90}\) \(-4.00000 q^{92}\) \(+4.00000 q^{93}\) \(-1.00000 q^{94}\) \(+1.00000 q^{95}\) \(+1.00000 q^{96}\) \(-6.00000 q^{98}\) \(-2.00000 q^{99}\) \(+O(q^{100})\)

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 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) −2.00000 −0.426401
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) 1.00000 0.185695
\(30\) −1.00000 −0.182574
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.00000 −0.348155
\(34\) −3.00000 −0.514496
\(35\) −1.00000 −0.169031
\(36\) 1.00000 0.166667
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) −1.00000 −0.162221
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 1.00000 0.154303
\(43\) 9.00000 1.37249 0.686244 0.727372i \(-0.259258\pi\)
0.686244 + 0.727372i \(0.259258\pi\)
\(44\) −2.00000 −0.301511
\(45\) −1.00000 −0.149071
\(46\) −4.00000 −0.589768
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) −4.00000 −0.565685
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.00000 0.269680
\(56\) 1.00000 0.133631
\(57\) −1.00000 −0.132453
\(58\) 1.00000 0.131306
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) −1.00000 −0.129099
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 4.00000 0.508001
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.00000 −0.246183
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −3.00000 −0.363803
\(69\) −4.00000 −0.481543
\(70\) −1.00000 −0.119523
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 1.00000 0.117851
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 3.00000 0.348743
\(75\) −4.00000 −0.461880
\(76\) −1.00000 −0.114708
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −7.00000 −0.773021
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 1.00000 0.109109
\(85\) 3.00000 0.325396
\(86\) 9.00000 0.970495
\(87\) 1.00000 0.107211
\(88\) −2.00000 −0.213201
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 4.00000 0.414781
\(94\) −1.00000 −0.103142
\(95\) 1.00000 0.102598
\(96\) 1.00000 0.102062
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −6.00000 −0.606092
\(99\) −2.00000 −0.201008
\(100\) −4.00000 −0.400000
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) −3.00000 −0.297044
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) −2.00000 −0.194257
\(107\) 17.0000 1.64345 0.821726 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) 1.00000 0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 2.00000 0.190693
\(111\) 3.00000 0.284747
\(112\) 1.00000 0.0944911
\(113\) −5.00000 −0.470360 −0.235180 0.971952i \(-0.575568\pi\)
−0.235180 + 0.971952i \(0.575568\pi\)
\(114\) −1.00000 −0.0936586
\(115\) 4.00000 0.373002
\(116\) 1.00000 0.0928477
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) −3.00000 −0.275010
\(120\) −1.00000 −0.0912871
\(121\) −7.00000 −0.636364
\(122\) 6.00000 0.543214
\(123\) −7.00000 −0.631169
\(124\) 4.00000 0.359211
\(125\) 9.00000 0.804984
\(126\) 1.00000 0.0890871
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.00000 0.792406
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −2.00000 −0.174078
\(133\) −1.00000 −0.0867110
\(134\) 12.0000 1.03664
\(135\) −1.00000 −0.0860663
\(136\) −3.00000 −0.257248
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) −4.00000 −0.340503
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −1.00000 −0.0842152
\(142\) 16.0000 1.34269
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −1.00000 −0.0830455
\(146\) −10.0000 −0.827606
\(147\) −6.00000 −0.494872
\(148\) 3.00000 0.246598
\(149\) 17.0000 1.39269 0.696347 0.717705i \(-0.254807\pi\)
0.696347 + 0.717705i \(0.254807\pi\)
\(150\) −4.00000 −0.326599
\(151\) 5.00000 0.406894 0.203447 0.979086i \(-0.434786\pi\)
0.203447 + 0.979086i \(0.434786\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −3.00000 −0.242536
\(154\) −2.00000 −0.161165
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −17.0000 −1.35675 −0.678374 0.734717i \(-0.737315\pi\)
−0.678374 + 0.734717i \(0.737315\pi\)
\(158\) 10.0000 0.795557
\(159\) −2.00000 −0.158610
\(160\) −1.00000 −0.0790569
\(161\) −4.00000 −0.315244
\(162\) 1.00000 0.0785674
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) −7.00000 −0.546608
\(165\) 2.00000 0.155700
\(166\) 0 0
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 1.00000 0.0771517
\(169\) −13.0000 −1.00000
\(170\) 3.00000 0.230089
\(171\) −1.00000 −0.0764719
\(172\) 9.00000 0.686244
\(173\) −15.0000 −1.14043 −0.570214 0.821496i \(-0.693140\pi\)
−0.570214 + 0.821496i \(0.693140\pi\)
\(174\) 1.00000 0.0758098
\(175\) −4.00000 −0.302372
\(176\) −2.00000 −0.150756
\(177\) −3.00000 −0.225494
\(178\) 6.00000 0.449719
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) −4.00000 −0.294884
\(185\) −3.00000 −0.220564
\(186\) 4.00000 0.293294
\(187\) 6.00000 0.438763
\(188\) −1.00000 −0.0729325
\(189\) 1.00000 0.0727393
\(190\) 1.00000 0.0725476
\(191\) 17.0000 1.23008 0.615038 0.788497i \(-0.289140\pi\)
0.615038 + 0.788497i \(0.289140\pi\)
\(192\) 1.00000 0.0721688
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −5.00000 −0.356235 −0.178118 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) −2.00000 −0.142134
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) −4.00000 −0.282843
\(201\) 12.0000 0.846415
\(202\) 18.0000 1.26648
\(203\) 1.00000 0.0701862
\(204\) −3.00000 −0.210042
\(205\) 7.00000 0.488901
\(206\) −1.00000 −0.0696733
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) −1.00000 −0.0690066
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −2.00000 −0.137361
\(213\) 16.0000 1.09630
\(214\) 17.0000 1.16210
\(215\) −9.00000 −0.613795
\(216\) 1.00000 0.0680414
\(217\) 4.00000 0.271538
\(218\) −16.0000 −1.08366
\(219\) −10.0000 −0.675737
\(220\) 2.00000 0.134840
\(221\) 0 0
\(222\) 3.00000 0.201347
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 1.00000 0.0668153
\(225\) −4.00000 −0.266667
\(226\) −5.00000 −0.332595
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) −1.00000 −0.0662266
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 4.00000 0.263752
\(231\) −2.00000 −0.131590
\(232\) 1.00000 0.0656532
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) 0 0
\(235\) 1.00000 0.0652328
\(236\) −3.00000 −0.195283
\(237\) 10.0000 0.649570
\(238\) −3.00000 −0.194461
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 25.0000 1.61039 0.805196 0.593009i \(-0.202060\pi\)
0.805196 + 0.593009i \(0.202060\pi\)
\(242\) −7.00000 −0.449977
\(243\) 1.00000 0.0641500
\(244\) 6.00000 0.384111
\(245\) 6.00000 0.383326
\(246\) −7.00000 −0.446304
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 9.00000 0.569210
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.00000 0.0629941
\(253\) 8.00000 0.502956
\(254\) 2.00000 0.125491
\(255\) 3.00000 0.187867
\(256\) 1.00000 0.0625000
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 9.00000 0.560316
\(259\) 3.00000 0.186411
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) −8.00000 −0.494242
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) −2.00000 −0.123091
\(265\) 2.00000 0.122859
\(266\) −1.00000 −0.0613139
\(267\) 6.00000 0.367194
\(268\) 12.0000 0.733017
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 8.00000 0.482418
\(276\) −4.00000 −0.240772
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −14.0000 −0.839664
\(279\) 4.00000 0.239474
\(280\) −1.00000 −0.0597614
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) −1.00000 −0.0595491
\(283\) −10.0000 −0.594438 −0.297219 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) 16.0000 0.949425
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) −7.00000 −0.413197
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) −1.00000 −0.0587220
\(291\) 0 0
\(292\) −10.0000 −0.585206
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) −6.00000 −0.349927
\(295\) 3.00000 0.174667
\(296\) 3.00000 0.174371
\(297\) −2.00000 −0.116052
\(298\) 17.0000 0.984784
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) 9.00000 0.518751
\(302\) 5.00000 0.287718
\(303\) 18.0000 1.03407
\(304\) −1.00000 −0.0573539
\(305\) −6.00000 −0.343559
\(306\) −3.00000 −0.171499
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) −2.00000 −0.113961
\(309\) −1.00000 −0.0568880
\(310\) −4.00000 −0.227185
\(311\) −17.0000 −0.963982 −0.481991 0.876176i \(-0.660086\pi\)
−0.481991 + 0.876176i \(0.660086\pi\)
\(312\) 0 0
\(313\) −29.0000 −1.63918 −0.819588 0.572953i \(-0.805798\pi\)
−0.819588 + 0.572953i \(0.805798\pi\)
\(314\) −17.0000 −0.959366
\(315\) −1.00000 −0.0563436
\(316\) 10.0000 0.562544
\(317\) 24.0000 1.34797 0.673987 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) −2.00000 −0.112154
\(319\) −2.00000 −0.111979
\(320\) −1.00000 −0.0559017
\(321\) 17.0000 0.948847
\(322\) −4.00000 −0.222911
\(323\) 3.00000 0.166924
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −11.0000 −0.609234
\(327\) −16.0000 −0.884802
\(328\) −7.00000 −0.386510
\(329\) −1.00000 −0.0551318
\(330\) 2.00000 0.110096
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 0 0
\(333\) 3.00000 0.164399
\(334\) −14.0000 −0.766046
\(335\) −12.0000 −0.655630
\(336\) 1.00000 0.0545545
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −13.0000 −0.707107
\(339\) −5.00000 −0.271563
\(340\) 3.00000 0.162698
\(341\) −8.00000 −0.433224
\(342\) −1.00000 −0.0540738
\(343\) −13.0000 −0.701934
\(344\) 9.00000 0.485247
\(345\) 4.00000 0.215353
\(346\) −15.0000 −0.806405
\(347\) −37.0000 −1.98626 −0.993132 0.116999i \(-0.962673\pi\)
−0.993132 + 0.116999i \(0.962673\pi\)
\(348\) 1.00000 0.0536056
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −10.0000 −0.532246 −0.266123 0.963939i \(-0.585743\pi\)
−0.266123 + 0.963939i \(0.585743\pi\)
\(354\) −3.00000 −0.159448
\(355\) −16.0000 −0.849192
\(356\) 6.00000 0.317999
\(357\) −3.00000 −0.158777
\(358\) −16.0000 −0.845626
\(359\) 3.00000 0.158334 0.0791670 0.996861i \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 6.00000 0.313625
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −4.00000 −0.208514
\(369\) −7.00000 −0.364405
\(370\) −3.00000 −0.155963
\(371\) −2.00000 −0.103835
\(372\) 4.00000 0.207390
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) 6.00000 0.310253
\(375\) 9.00000 0.464758
\(376\) −1.00000 −0.0515711
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 1.00000 0.0512989
\(381\) 2.00000 0.102463
\(382\) 17.0000 0.869796
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.00000 0.101929
\(386\) −16.0000 −0.814379
\(387\) 9.00000 0.457496
\(388\) 0 0
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) −6.00000 −0.303046
\(393\) −8.00000 −0.403547
\(394\) −5.00000 −0.251896
\(395\) −10.0000 −0.503155
\(396\) −2.00000 −0.100504
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) −24.0000 −1.20301
\(399\) −1.00000 −0.0500626
\(400\) −4.00000 −0.200000
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 12.0000 0.598506
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) −1.00000 −0.0496904
\(406\) 1.00000 0.0496292
\(407\) −6.00000 −0.297409
\(408\) −3.00000 −0.148522
\(409\) 4.00000 0.197787 0.0988936 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 7.00000 0.345705
\(411\) −2.00000 −0.0986527
\(412\) −1.00000 −0.0492665
\(413\) −3.00000 −0.147620
\(414\) −4.00000 −0.196589
\(415\) 0 0
\(416\) 0 0
\(417\) −14.0000 −0.685583
\(418\) 2.00000 0.0978232
\(419\) 35.0000 1.70986 0.854931 0.518742i \(-0.173599\pi\)
0.854931 + 0.518742i \(0.173599\pi\)
\(420\) −1.00000 −0.0487950
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 23.0000 1.11962
\(423\) −1.00000 −0.0486217
\(424\) −2.00000 −0.0971286
\(425\) 12.0000 0.582086
\(426\) 16.0000 0.775203
\(427\) 6.00000 0.290360
\(428\) 17.0000 0.821726
\(429\) 0 0
\(430\) −9.00000 −0.434019
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 1.00000 0.0481125
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 4.00000 0.192006
\(435\) −1.00000 −0.0479463
\(436\) −16.0000 −0.766261
\(437\) 4.00000 0.191346
\(438\) −10.0000 −0.477818
\(439\) −29.0000 −1.38409 −0.692047 0.721852i \(-0.743291\pi\)
−0.692047 + 0.721852i \(0.743291\pi\)
\(440\) 2.00000 0.0953463
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 3.00000 0.142374
\(445\) −6.00000 −0.284427
\(446\) 0 0
\(447\) 17.0000 0.804072
\(448\) 1.00000 0.0472456
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) −4.00000 −0.188562
\(451\) 14.0000 0.659234
\(452\) −5.00000 −0.235180
\(453\) 5.00000 0.234920
\(454\) −3.00000 −0.140797
\(455\) 0 0
\(456\) −1.00000 −0.0468293
\(457\) 3.00000 0.140334 0.0701670 0.997535i \(-0.477647\pi\)
0.0701670 + 0.997535i \(0.477647\pi\)
\(458\) 13.0000 0.607450
\(459\) −3.00000 −0.140028
\(460\) 4.00000 0.186501
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) −2.00000 −0.0930484
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 1.00000 0.0464238
\(465\) −4.00000 −0.185496
\(466\) −4.00000 −0.185296
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 1.00000 0.0461266
\(471\) −17.0000 −0.783319
\(472\) −3.00000 −0.138086
\(473\) −18.0000 −0.827641
\(474\) 10.0000 0.459315
\(475\) 4.00000 0.183533
\(476\) −3.00000 −0.137505
\(477\) −2.00000 −0.0915737
\(478\) 2.00000 0.0914779
\(479\) 32.0000 1.46212 0.731059 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 0 0
\(482\) 25.0000 1.13872
\(483\) −4.00000 −0.182006
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −37.0000 −1.67663 −0.838315 0.545186i \(-0.816459\pi\)
−0.838315 + 0.545186i \(0.816459\pi\)
\(488\) 6.00000 0.271607
\(489\) −11.0000 −0.497437
\(490\) 6.00000 0.271052
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −7.00000 −0.315584
\(493\) −3.00000 −0.135113
\(494\) 0 0
\(495\) 2.00000 0.0898933
\(496\) 4.00000 0.179605
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) 38.0000 1.70111 0.850557 0.525883i \(-0.176265\pi\)
0.850557 + 0.525883i \(0.176265\pi\)
\(500\) 9.00000 0.402492
\(501\) −14.0000 −0.625474
\(502\) 0 0
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 1.00000 0.0445435
\(505\) −18.0000 −0.800989
\(506\) 8.00000 0.355643
\(507\) −13.0000 −0.577350
\(508\) 2.00000 0.0887357
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 3.00000 0.132842
\(511\) −10.0000 −0.442374
\(512\) 1.00000 0.0441942
\(513\) −1.00000 −0.0441511
\(514\) −8.00000 −0.352865
\(515\) 1.00000 0.0440653
\(516\) 9.00000 0.396203
\(517\) 2.00000 0.0879599
\(518\) 3.00000 0.131812
\(519\) −15.0000 −0.658427
\(520\) 0 0
\(521\) −38.0000 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 1.00000 0.0437688
\(523\) 34.0000 1.48672 0.743358 0.668894i \(-0.233232\pi\)
0.743358 + 0.668894i \(0.233232\pi\)
\(524\) −8.00000 −0.349482
\(525\) −4.00000 −0.174574
\(526\) −9.00000 −0.392419
\(527\) −12.0000 −0.522728
\(528\) −2.00000 −0.0870388
\(529\) −7.00000 −0.304348
\(530\) 2.00000 0.0868744
\(531\) −3.00000 −0.130189
\(532\) −1.00000 −0.0433555
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) −17.0000 −0.734974
\(536\) 12.0000 0.518321
\(537\) −16.0000 −0.690451
\(538\) 18.0000 0.776035
\(539\) 12.0000 0.516877
\(540\) −1.00000 −0.0430331
\(541\) 3.00000 0.128980 0.0644900 0.997918i \(-0.479458\pi\)
0.0644900 + 0.997918i \(0.479458\pi\)
\(542\) −8.00000 −0.343629
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) 16.0000 0.685365
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 6.00000 0.256074
\(550\) 8.00000 0.341121
\(551\) −1.00000 −0.0426014
\(552\) −4.00000 −0.170251
\(553\) 10.0000 0.425243
\(554\) 26.0000 1.10463
\(555\) −3.00000 −0.127343
\(556\) −14.0000 −0.593732
\(557\) −9.00000 −0.381342 −0.190671 0.981654i \(-0.561066\pi\)
−0.190671 + 0.981654i \(0.561066\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) −1.00000 −0.0422577
\(561\) 6.00000 0.253320
\(562\) 30.0000 1.26547
\(563\) −10.0000 −0.421450 −0.210725 0.977545i \(-0.567582\pi\)
−0.210725 + 0.977545i \(0.567582\pi\)
\(564\) −1.00000 −0.0421076
\(565\) 5.00000 0.210352
\(566\) −10.0000 −0.420331
\(567\) 1.00000 0.0419961
\(568\) 16.0000 0.671345
\(569\) 31.0000 1.29959 0.649794 0.760111i \(-0.274855\pi\)
0.649794 + 0.760111i \(0.274855\pi\)
\(570\) 1.00000 0.0418854
\(571\) −2.00000 −0.0836974 −0.0418487 0.999124i \(-0.513325\pi\)
−0.0418487 + 0.999124i \(0.513325\pi\)
\(572\) 0 0
\(573\) 17.0000 0.710185
\(574\) −7.00000 −0.292174
\(575\) 16.0000 0.667246
\(576\) 1.00000 0.0416667
\(577\) 4.00000 0.166522 0.0832611 0.996528i \(-0.473466\pi\)
0.0832611 + 0.996528i \(0.473466\pi\)
\(578\) −8.00000 −0.332756
\(579\) −16.0000 −0.664937
\(580\) −1.00000 −0.0415227
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 0.165663
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) −6.00000 −0.247436
\(589\) −4.00000 −0.164817
\(590\) 3.00000 0.123508
\(591\) −5.00000 −0.205673
\(592\) 3.00000 0.123299
\(593\) −36.0000 −1.47834 −0.739171 0.673517i \(-0.764783\pi\)
−0.739171 + 0.673517i \(0.764783\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 3.00000 0.122988
\(596\) 17.0000 0.696347
\(597\) −24.0000 −0.982255
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) −4.00000 −0.163299
\(601\) 28.0000 1.14214 0.571072 0.820900i \(-0.306528\pi\)
0.571072 + 0.820900i \(0.306528\pi\)
\(602\) 9.00000 0.366813
\(603\) 12.0000 0.488678
\(604\) 5.00000 0.203447
\(605\) 7.00000 0.284590
\(606\) 18.0000 0.731200
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 1.00000 0.0405220
\(610\) −6.00000 −0.242933
\(611\) 0 0
\(612\) −3.00000 −0.121268
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 28.0000 1.12999
\(615\) 7.00000 0.282267
\(616\) −2.00000 −0.0805823
\(617\) −33.0000 −1.32853 −0.664265 0.747497i \(-0.731255\pi\)
−0.664265 + 0.747497i \(0.731255\pi\)
\(618\) −1.00000 −0.0402259
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) −4.00000 −0.160644
\(621\) −4.00000 −0.160514
\(622\) −17.0000 −0.681638
\(623\) 6.00000 0.240385
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) −29.0000 −1.15907
\(627\) 2.00000 0.0798723
\(628\) −17.0000 −0.678374
\(629\) −9.00000 −0.358854
\(630\) −1.00000 −0.0398410
\(631\) 23.0000 0.915616 0.457808 0.889051i \(-0.348635\pi\)
0.457808 + 0.889051i \(0.348635\pi\)
\(632\) 10.0000 0.397779
\(633\) 23.0000 0.914168
\(634\) 24.0000 0.953162
\(635\) −2.00000 −0.0793676
\(636\) −2.00000 −0.0793052
\(637\) 0 0
\(638\) −2.00000 −0.0791808
\(639\) 16.0000 0.632950
\(640\) −1.00000 −0.0395285
\(641\) −37.0000 −1.46141 −0.730706 0.682692i \(-0.760809\pi\)
−0.730706 + 0.682692i \(0.760809\pi\)
\(642\) 17.0000 0.670936
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) −4.00000 −0.157622
\(645\) −9.00000 −0.354375
\(646\) 3.00000 0.118033
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 1.00000 0.0392837
\(649\) 6.00000 0.235521
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) −11.0000 −0.430793
\(653\) 10.0000 0.391330 0.195665 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) −16.0000 −0.625650
\(655\) 8.00000 0.312586
\(656\) −7.00000 −0.273304
\(657\) −10.0000 −0.390137
\(658\) −1.00000 −0.0389841
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 2.00000 0.0778499
\(661\) −24.0000 −0.933492 −0.466746 0.884391i \(-0.654574\pi\)
−0.466746 + 0.884391i \(0.654574\pi\)
\(662\) 17.0000 0.660724
\(663\) 0 0
\(664\) 0 0
\(665\) 1.00000 0.0387783
\(666\) 3.00000 0.116248
\(667\) −4.00000 −0.154881
\(668\) −14.0000 −0.541676
\(669\) 0 0
\(670\) −12.0000 −0.463600
\(671\) −12.0000 −0.463255
\(672\) 1.00000 0.0385758
\(673\) −5.00000 −0.192736 −0.0963679 0.995346i \(-0.530723\pi\)
−0.0963679 + 0.995346i \(0.530723\pi\)
\(674\) 2.00000 0.0770371
\(675\) −4.00000 −0.153960
\(676\) −13.0000 −0.500000
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) −5.00000 −0.192024
\(679\) 0 0
\(680\) 3.00000 0.115045
\(681\) −3.00000 −0.114960
\(682\) −8.00000 −0.306336
\(683\) −23.0000 −0.880071 −0.440035 0.897980i \(-0.645034\pi\)
−0.440035 + 0.897980i \(0.645034\pi\)
\(684\) −1.00000 −0.0382360
\(685\) 2.00000 0.0764161
\(686\) −13.0000 −0.496342
\(687\) 13.0000 0.495981
\(688\) 9.00000 0.343122
\(689\) 0 0
\(690\) 4.00000 0.152277
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) −15.0000 −0.570214
\(693\) −2.00000 −0.0759737
\(694\) −37.0000 −1.40450
\(695\) 14.0000 0.531050
\(696\) 1.00000 0.0379049
\(697\) 21.0000 0.795432
\(698\) 14.0000 0.529908
\(699\) −4.00000 −0.151294
\(700\) −4.00000 −0.151186
\(701\) −33.0000 −1.24639 −0.623196 0.782065i \(-0.714166\pi\)
−0.623196 + 0.782065i \(0.714166\pi\)
\(702\) 0 0
\(703\) −3.00000 −0.113147
\(704\) −2.00000 −0.0753778
\(705\) 1.00000 0.0376622
\(706\) −10.0000 −0.376355
\(707\) 18.0000 0.676960
\(708\) −3.00000 −0.112747
\(709\) −46.0000 −1.72757 −0.863783 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) −16.0000 −0.600469
\(711\) 10.0000 0.375029
\(712\) 6.00000 0.224860
\(713\) −16.0000 −0.599205
\(714\) −3.00000 −0.112272
\(715\) 0 0
\(716\) −16.0000 −0.597948
\(717\) 2.00000 0.0746914
\(718\) 3.00000 0.111959
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −1.00000 −0.0372419
\(722\) −18.0000 −0.669891
\(723\) 25.0000 0.929760
\(724\) 0 0
\(725\) −4.00000 −0.148556
\(726\) −7.00000 −0.259794
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 10.0000 0.370117
\(731\) −27.0000 −0.998631
\(732\) 6.00000 0.221766
\(733\) 34.0000 1.25582 0.627909 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) −10.0000 −0.369107
\(735\) 6.00000 0.221313
\(736\) −4.00000 −0.147442
\(737\) −24.0000 −0.884051
\(738\) −7.00000 −0.257674
\(739\) 40.0000 1.47142 0.735712 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) −3.00000 −0.110282
\(741\) 0 0
\(742\) −2.00000 −0.0734223
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) 4.00000 0.146647
\(745\) −17.0000 −0.622832
\(746\) −32.0000 −1.17160
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) 17.0000 0.621166
\(750\) 9.00000 0.328634
\(751\) −46.0000 −1.67856 −0.839282 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) −1.00000 −0.0364662
\(753\) 0 0
\(754\) 0 0
\(755\) −5.00000 −0.181969
\(756\) 1.00000 0.0363696
\(757\) 37.0000 1.34479 0.672394 0.740193i \(-0.265266\pi\)
0.672394 + 0.740193i \(0.265266\pi\)
\(758\) −12.0000 −0.435860
\(759\) 8.00000 0.290382
\(760\) 1.00000 0.0362738
\(761\) 20.0000 0.724999 0.362500 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(762\) 2.00000 0.0724524
\(763\) −16.0000 −0.579239
\(764\) 17.0000 0.615038
\(765\) 3.00000 0.108465
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 42.0000 1.51456 0.757279 0.653091i \(-0.226528\pi\)
0.757279 + 0.653091i \(0.226528\pi\)
\(770\) 2.00000 0.0720750
\(771\) −8.00000 −0.288113
\(772\) −16.0000 −0.575853
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 9.00000 0.323498
\(775\) −16.0000 −0.574737
\(776\) 0 0
\(777\) 3.00000 0.107624
\(778\) 12.0000 0.430221
\(779\) 7.00000 0.250801
\(780\) 0 0
\(781\) −32.0000 −1.14505
\(782\) 12.0000 0.429119
\(783\) 1.00000 0.0357371
\(784\) −6.00000 −0.214286
\(785\) 17.0000 0.606756
\(786\) −8.00000 −0.285351
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) −5.00000 −0.178118
\(789\) −9.00000 −0.320408
\(790\) −10.0000 −0.355784
\(791\) −5.00000 −0.177780
\(792\) −2.00000 −0.0710669
\(793\) 0 0
\(794\) −22.0000 −0.780751
\(795\) 2.00000 0.0709327
\(796\) −24.0000 −0.850657
\(797\) −56.0000 −1.98362 −0.991811 0.127715i \(-0.959236\pi\)
−0.991811 + 0.127715i \(0.959236\pi\)
\(798\) −1.00000 −0.0353996
\(799\) 3.00000 0.106132
\(800\) −4.00000 −0.141421
\(801\) 6.00000 0.212000
\(802\) 10.0000 0.353112
\(803\) 20.0000 0.705785
\(804\) 12.0000 0.423207
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 18.0000 0.633630
\(808\) 18.0000 0.633238
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 56.0000 1.96643 0.983213 0.182462i \(-0.0584065\pi\)
0.983213 + 0.182462i \(0.0584065\pi\)
\(812\) 1.00000 0.0350931
\(813\) −8.00000 −0.280572
\(814\) −6.00000 −0.210300
\(815\) 11.0000 0.385313
\(816\) −3.00000 −0.105021
\(817\) −9.00000 −0.314870
\(818\) 4.00000 0.139857
\(819\) 0 0
\(820\) 7.00000 0.244451
\(821\) 10.0000 0.349002 0.174501 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) −2.00000 −0.0697580
\(823\) −2.00000 −0.0697156 −0.0348578 0.999392i \(-0.511098\pi\)
−0.0348578 + 0.999392i \(0.511098\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 8.00000 0.278524
\(826\) −3.00000 −0.104383
\(827\) 16.0000 0.556375 0.278187 0.960527i \(-0.410266\pi\)
0.278187 + 0.960527i \(0.410266\pi\)
\(828\) −4.00000 −0.139010
\(829\) 11.0000 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(830\) 0 0
\(831\) 26.0000 0.901930
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) −14.0000 −0.484780
\(835\) 14.0000 0.484490
\(836\) 2.00000 0.0691714
\(837\) 4.00000 0.138260
\(838\) 35.0000 1.20905
\(839\) −49.0000 −1.69167 −0.845834 0.533446i \(-0.820897\pi\)
−0.845834 + 0.533446i \(0.820897\pi\)
\(840\) −1.00000 −0.0345033
\(841\) 1.00000 0.0344828
\(842\) 30.0000 1.03387
\(843\) 30.0000 1.03325
\(844\) 23.0000 0.791693
\(845\) 13.0000 0.447214
\(846\) −1.00000 −0.0343807
\(847\) −7.00000 −0.240523
\(848\) −2.00000 −0.0686803
\(849\) −10.0000 −0.343199
\(850\) 12.0000 0.411597
\(851\) −12.0000 −0.411355
\(852\) 16.0000 0.548151
\(853\) −7.00000 −0.239675 −0.119838 0.992793i \(-0.538237\pi\)
−0.119838 + 0.992793i \(0.538237\pi\)
\(854\) 6.00000 0.205316
\(855\) 1.00000 0.0341993
\(856\) 17.0000 0.581048
\(857\) −38.0000 −1.29806 −0.649028 0.760765i \(-0.724824\pi\)
−0.649028 + 0.760765i \(0.724824\pi\)
\(858\) 0 0
\(859\) −43.0000 −1.46714 −0.733571 0.679613i \(-0.762148\pi\)
−0.733571 + 0.679613i \(0.762148\pi\)
\(860\) −9.00000 −0.306897
\(861\) −7.00000 −0.238559
\(862\) 12.0000 0.408722
\(863\) 52.0000 1.77010 0.885050 0.465495i \(-0.154124\pi\)
0.885050 + 0.465495i \(0.154124\pi\)
\(864\) 1.00000 0.0340207
\(865\) 15.0000 0.510015
\(866\) 14.0000 0.475739
\(867\) −8.00000 −0.271694
\(868\) 4.00000 0.135769
\(869\) −20.0000 −0.678454
\(870\) −1.00000 −0.0339032
\(871\) 0 0
\(872\) −16.0000 −0.541828
\(873\) 0 0
\(874\) 4.00000 0.135302
\(875\) 9.00000 0.304256
\(876\) −10.0000 −0.337869
\(877\) 24.0000 0.810422 0.405211 0.914223i \(-0.367198\pi\)
0.405211 + 0.914223i \(0.367198\pi\)
\(878\) −29.0000 −0.978703
\(879\) −14.0000 −0.472208
\(880\) 2.00000 0.0674200
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) −6.00000 −0.202031
\(883\) −12.0000 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 0 0
\(885\) 3.00000 0.100844
\(886\) −4.00000 −0.134383
\(887\) 48.0000 1.61168 0.805841 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) 3.00000 0.100673
\(889\) 2.00000 0.0670778
\(890\) −6.00000 −0.201120
\(891\) −2.00000 −0.0670025
\(892\) 0 0
\(893\) 1.00000 0.0334637
\(894\) 17.0000 0.568565
\(895\) 16.0000 0.534821
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 9.00000 0.300334
\(899\) 4.00000 0.133407
\(900\) −4.00000 −0.133333
\(901\) 6.00000 0.199889
\(902\) 14.0000 0.466149
\(903\) 9.00000 0.299501
\(904\) −5.00000 −0.166298
\(905\) 0 0
\(906\) 5.00000 0.166114
\(907\) −44.0000 −1.46100 −0.730498 0.682915i \(-0.760712\pi\)
−0.730498 + 0.682915i \(0.760712\pi\)
\(908\) −3.00000 −0.0995585
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 16.0000 0.530104 0.265052 0.964234i \(-0.414611\pi\)
0.265052 + 0.964234i \(0.414611\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) 3.00000 0.0992312
\(915\) −6.00000 −0.198354
\(916\) 13.0000 0.429532
\(917\) −8.00000 −0.264183
\(918\) −3.00000 −0.0990148
\(919\) −39.0000 −1.28649 −0.643246 0.765660i \(-0.722413\pi\)
−0.643246 + 0.765660i \(0.722413\pi\)
\(920\) 4.00000 0.131876
\(921\) 28.0000 0.922631
\(922\) 0 0
\(923\) 0 0
\(924\) −2.00000 −0.0657952
\(925\) −12.0000 −0.394558
\(926\) 16.0000 0.525793
\(927\) −1.00000 −0.0328443
\(928\) 1.00000 0.0328266
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) −4.00000 −0.131165
\(931\) 6.00000 0.196642
\(932\) −4.00000 −0.131024
\(933\) −17.0000 −0.556555
\(934\) −8.00000 −0.261768
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) 7.00000 0.228680 0.114340 0.993442i \(-0.463525\pi\)
0.114340 + 0.993442i \(0.463525\pi\)
\(938\) 12.0000 0.391814
\(939\) −29.0000 −0.946379
\(940\) 1.00000 0.0326164
\(941\) −38.0000 −1.23876 −0.619382 0.785090i \(-0.712617\pi\)
−0.619382 + 0.785090i \(0.712617\pi\)
\(942\) −17.0000 −0.553890
\(943\) 28.0000 0.911805
\(944\) −3.00000 −0.0976417
\(945\) −1.00000 −0.0325300
\(946\) −18.0000 −0.585230
\(947\) 52.0000 1.68977 0.844886 0.534946i \(-0.179668\pi\)
0.844886 + 0.534946i \(0.179668\pi\)
\(948\) 10.0000 0.324785
\(949\) 0 0
\(950\) 4.00000 0.129777
\(951\) 24.0000 0.778253
\(952\) −3.00000 −0.0972306
\(953\) 16.0000 0.518291 0.259145 0.965838i \(-0.416559\pi\)
0.259145 + 0.965838i \(0.416559\pi\)
\(954\) −2.00000 −0.0647524
\(955\) −17.0000 −0.550107
\(956\) 2.00000 0.0646846
\(957\) −2.00000 −0.0646508
\(958\) 32.0000 1.03387
\(959\) −2.00000 −0.0645834
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 17.0000 0.547817
\(964\) 25.0000 0.805196
\(965\) 16.0000 0.515058
\(966\) −4.00000 −0.128698
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) −7.00000 −0.224989
\(969\) 3.00000 0.0963739
\(970\) 0 0
\(971\) −22.0000 −0.706014 −0.353007 0.935621i \(-0.614841\pi\)
−0.353007 + 0.935621i \(0.614841\pi\)
\(972\) 1.00000 0.0320750
\(973\) −14.0000 −0.448819
\(974\) −37.0000 −1.18556
\(975\) 0 0
\(976\) 6.00000 0.192055
\(977\) 12.0000 0.383914 0.191957 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) −11.0000 −0.351741
\(979\) −12.0000 −0.383522
\(980\) 6.00000 0.191663
\(981\) −16.0000 −0.510841
\(982\) 2.00000 0.0638226
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) −7.00000 −0.223152
\(985\) 5.00000 0.159313
\(986\) −3.00000 −0.0955395
\(987\) −1.00000 −0.0318304
\(988\) 0 0
\(989\) −36.0000 −1.14473
\(990\) 2.00000 0.0635642
\(991\) 19.0000 0.603555 0.301777 0.953378i \(-0.402420\pi\)
0.301777 + 0.953378i \(0.402420\pi\)
\(992\) 4.00000 0.127000
\(993\) 17.0000 0.539479
\(994\) 16.0000 0.507489
\(995\) 24.0000 0.760851
\(996\) 0 0
\(997\) 25.0000 0.791758 0.395879 0.918303i \(-0.370440\pi\)
0.395879 + 0.918303i \(0.370440\pi\)
\(998\) 38.0000 1.20287
\(999\) 3.00000 0.0949158
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 \(a_p\))