Properties

Label 6040.2.a.l.1.5
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.41589\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.0722232 q^{3}\) \(+1.00000 q^{5}\) \(-0.709626 q^{7}\) \(-2.99478 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.0722232 q^{3}\) \(+1.00000 q^{5}\) \(-0.709626 q^{7}\) \(-2.99478 q^{9}\) \(-0.425521 q^{11}\) \(+6.40956 q^{13}\) \(+0.0722232 q^{15}\) \(-4.34731 q^{17}\) \(+2.76398 q^{19}\) \(-0.0512515 q^{21}\) \(-2.37546 q^{23}\) \(+1.00000 q^{25}\) \(-0.432962 q^{27}\) \(-1.12262 q^{29}\) \(-1.10634 q^{31}\) \(-0.0307325 q^{33}\) \(-0.709626 q^{35}\) \(-7.75024 q^{37}\) \(+0.462919 q^{39}\) \(-4.05857 q^{41}\) \(-9.49867 q^{43}\) \(-2.99478 q^{45}\) \(+4.25704 q^{47}\) \(-6.49643 q^{49}\) \(-0.313977 q^{51}\) \(-5.36390 q^{53}\) \(-0.425521 q^{55}\) \(+0.199623 q^{57}\) \(+7.25935 q^{59}\) \(-3.77690 q^{61}\) \(+2.12518 q^{63}\) \(+6.40956 q^{65}\) \(+12.7000 q^{67}\) \(-0.171563 q^{69}\) \(-6.91929 q^{71}\) \(+11.6280 q^{73}\) \(+0.0722232 q^{75}\) \(+0.301961 q^{77}\) \(+10.0703 q^{79}\) \(+8.95308 q^{81}\) \(-3.42260 q^{83}\) \(-4.34731 q^{85}\) \(-0.0810794 q^{87}\) \(+1.05887 q^{89}\) \(-4.54839 q^{91}\) \(-0.0799037 q^{93}\) \(+2.76398 q^{95}\) \(-4.57137 q^{97}\) \(+1.27434 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0722232 0.0416981 0.0208490 0.999783i \(-0.493363\pi\)
0.0208490 + 0.999783i \(0.493363\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.709626 −0.268213 −0.134107 0.990967i \(-0.542816\pi\)
−0.134107 + 0.990967i \(0.542816\pi\)
\(8\) 0 0
\(9\) −2.99478 −0.998261
\(10\) 0 0
\(11\) −0.425521 −0.128299 −0.0641497 0.997940i \(-0.520434\pi\)
−0.0641497 + 0.997940i \(0.520434\pi\)
\(12\) 0 0
\(13\) 6.40956 1.77769 0.888846 0.458205i \(-0.151508\pi\)
0.888846 + 0.458205i \(0.151508\pi\)
\(14\) 0 0
\(15\) 0.0722232 0.0186479
\(16\) 0 0
\(17\) −4.34731 −1.05438 −0.527189 0.849748i \(-0.676754\pi\)
−0.527189 + 0.849748i \(0.676754\pi\)
\(18\) 0 0
\(19\) 2.76398 0.634099 0.317050 0.948409i \(-0.397308\pi\)
0.317050 + 0.948409i \(0.397308\pi\)
\(20\) 0 0
\(21\) −0.0512515 −0.0111840
\(22\) 0 0
\(23\) −2.37546 −0.495317 −0.247658 0.968847i \(-0.579661\pi\)
−0.247658 + 0.968847i \(0.579661\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −0.432962 −0.0833237
\(28\) 0 0
\(29\) −1.12262 −0.208466 −0.104233 0.994553i \(-0.533239\pi\)
−0.104233 + 0.994553i \(0.533239\pi\)
\(30\) 0 0
\(31\) −1.10634 −0.198705 −0.0993526 0.995052i \(-0.531677\pi\)
−0.0993526 + 0.995052i \(0.531677\pi\)
\(32\) 0 0
\(33\) −0.0307325 −0.00534984
\(34\) 0 0
\(35\) −0.709626 −0.119949
\(36\) 0 0
\(37\) −7.75024 −1.27413 −0.637065 0.770810i \(-0.719852\pi\)
−0.637065 + 0.770810i \(0.719852\pi\)
\(38\) 0 0
\(39\) 0.462919 0.0741264
\(40\) 0 0
\(41\) −4.05857 −0.633842 −0.316921 0.948452i \(-0.602649\pi\)
−0.316921 + 0.948452i \(0.602649\pi\)
\(42\) 0 0
\(43\) −9.49867 −1.44853 −0.724267 0.689520i \(-0.757822\pi\)
−0.724267 + 0.689520i \(0.757822\pi\)
\(44\) 0 0
\(45\) −2.99478 −0.446436
\(46\) 0 0
\(47\) 4.25704 0.620952 0.310476 0.950581i \(-0.399511\pi\)
0.310476 + 0.950581i \(0.399511\pi\)
\(48\) 0 0
\(49\) −6.49643 −0.928062
\(50\) 0 0
\(51\) −0.313977 −0.0439655
\(52\) 0 0
\(53\) −5.36390 −0.736789 −0.368395 0.929670i \(-0.620092\pi\)
−0.368395 + 0.929670i \(0.620092\pi\)
\(54\) 0 0
\(55\) −0.425521 −0.0573773
\(56\) 0 0
\(57\) 0.199623 0.0264407
\(58\) 0 0
\(59\) 7.25935 0.945087 0.472544 0.881307i \(-0.343336\pi\)
0.472544 + 0.881307i \(0.343336\pi\)
\(60\) 0 0
\(61\) −3.77690 −0.483582 −0.241791 0.970328i \(-0.577735\pi\)
−0.241791 + 0.970328i \(0.577735\pi\)
\(62\) 0 0
\(63\) 2.12518 0.267747
\(64\) 0 0
\(65\) 6.40956 0.795008
\(66\) 0 0
\(67\) 12.7000 1.55155 0.775773 0.631012i \(-0.217360\pi\)
0.775773 + 0.631012i \(0.217360\pi\)
\(68\) 0 0
\(69\) −0.171563 −0.0206538
\(70\) 0 0
\(71\) −6.91929 −0.821169 −0.410584 0.911823i \(-0.634675\pi\)
−0.410584 + 0.911823i \(0.634675\pi\)
\(72\) 0 0
\(73\) 11.6280 1.36096 0.680478 0.732768i \(-0.261772\pi\)
0.680478 + 0.732768i \(0.261772\pi\)
\(74\) 0 0
\(75\) 0.0722232 0.00833962
\(76\) 0 0
\(77\) 0.301961 0.0344116
\(78\) 0 0
\(79\) 10.0703 1.13299 0.566497 0.824064i \(-0.308298\pi\)
0.566497 + 0.824064i \(0.308298\pi\)
\(80\) 0 0
\(81\) 8.95308 0.994787
\(82\) 0 0
\(83\) −3.42260 −0.375680 −0.187840 0.982200i \(-0.560149\pi\)
−0.187840 + 0.982200i \(0.560149\pi\)
\(84\) 0 0
\(85\) −4.34731 −0.471532
\(86\) 0 0
\(87\) −0.0810794 −0.00869263
\(88\) 0 0
\(89\) 1.05887 0.112240 0.0561199 0.998424i \(-0.482127\pi\)
0.0561199 + 0.998424i \(0.482127\pi\)
\(90\) 0 0
\(91\) −4.54839 −0.476801
\(92\) 0 0
\(93\) −0.0799037 −0.00828562
\(94\) 0 0
\(95\) 2.76398 0.283578
\(96\) 0 0
\(97\) −4.57137 −0.464152 −0.232076 0.972698i \(-0.574552\pi\)
−0.232076 + 0.972698i \(0.574552\pi\)
\(98\) 0 0
\(99\) 1.27434 0.128076
\(100\) 0 0
\(101\) −14.6098 −1.45373 −0.726866 0.686779i \(-0.759024\pi\)
−0.726866 + 0.686779i \(0.759024\pi\)
\(102\) 0 0
\(103\) 6.19587 0.610497 0.305249 0.952273i \(-0.401260\pi\)
0.305249 + 0.952273i \(0.401260\pi\)
\(104\) 0 0
\(105\) −0.0512515 −0.00500163
\(106\) 0 0
\(107\) −14.3924 −1.39137 −0.695684 0.718348i \(-0.744899\pi\)
−0.695684 + 0.718348i \(0.744899\pi\)
\(108\) 0 0
\(109\) −5.52240 −0.528950 −0.264475 0.964393i \(-0.585199\pi\)
−0.264475 + 0.964393i \(0.585199\pi\)
\(110\) 0 0
\(111\) −0.559747 −0.0531288
\(112\) 0 0
\(113\) 14.9331 1.40479 0.702396 0.711787i \(-0.252114\pi\)
0.702396 + 0.711787i \(0.252114\pi\)
\(114\) 0 0
\(115\) −2.37546 −0.221512
\(116\) 0 0
\(117\) −19.1953 −1.77460
\(118\) 0 0
\(119\) 3.08496 0.282798
\(120\) 0 0
\(121\) −10.8189 −0.983539
\(122\) 0 0
\(123\) −0.293123 −0.0264300
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.72098 −0.773862 −0.386931 0.922109i \(-0.626465\pi\)
−0.386931 + 0.922109i \(0.626465\pi\)
\(128\) 0 0
\(129\) −0.686024 −0.0604011
\(130\) 0 0
\(131\) −15.1693 −1.32535 −0.662676 0.748906i \(-0.730579\pi\)
−0.662676 + 0.748906i \(0.730579\pi\)
\(132\) 0 0
\(133\) −1.96139 −0.170074
\(134\) 0 0
\(135\) −0.432962 −0.0372635
\(136\) 0 0
\(137\) −15.4998 −1.32424 −0.662118 0.749400i \(-0.730342\pi\)
−0.662118 + 0.749400i \(0.730342\pi\)
\(138\) 0 0
\(139\) 6.44923 0.547017 0.273508 0.961870i \(-0.411816\pi\)
0.273508 + 0.961870i \(0.411816\pi\)
\(140\) 0 0
\(141\) 0.307457 0.0258925
\(142\) 0 0
\(143\) −2.72740 −0.228077
\(144\) 0 0
\(145\) −1.12262 −0.0932287
\(146\) 0 0
\(147\) −0.469193 −0.0386984
\(148\) 0 0
\(149\) −9.80041 −0.802881 −0.401441 0.915885i \(-0.631490\pi\)
−0.401441 + 0.915885i \(0.631490\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) 13.0193 1.05254
\(154\) 0 0
\(155\) −1.10634 −0.0888636
\(156\) 0 0
\(157\) 1.30208 0.103917 0.0519585 0.998649i \(-0.483454\pi\)
0.0519585 + 0.998649i \(0.483454\pi\)
\(158\) 0 0
\(159\) −0.387398 −0.0307227
\(160\) 0 0
\(161\) 1.68569 0.132851
\(162\) 0 0
\(163\) −1.15240 −0.0902627 −0.0451314 0.998981i \(-0.514371\pi\)
−0.0451314 + 0.998981i \(0.514371\pi\)
\(164\) 0 0
\(165\) −0.0307325 −0.00239252
\(166\) 0 0
\(167\) −20.7287 −1.60403 −0.802016 0.597302i \(-0.796239\pi\)
−0.802016 + 0.597302i \(0.796239\pi\)
\(168\) 0 0
\(169\) 28.0825 2.16019
\(170\) 0 0
\(171\) −8.27751 −0.632997
\(172\) 0 0
\(173\) −19.9420 −1.51616 −0.758080 0.652161i \(-0.773863\pi\)
−0.758080 + 0.652161i \(0.773863\pi\)
\(174\) 0 0
\(175\) −0.709626 −0.0536427
\(176\) 0 0
\(177\) 0.524294 0.0394083
\(178\) 0 0
\(179\) 1.27486 0.0952877 0.0476439 0.998864i \(-0.484829\pi\)
0.0476439 + 0.998864i \(0.484829\pi\)
\(180\) 0 0
\(181\) −2.32402 −0.172743 −0.0863716 0.996263i \(-0.527527\pi\)
−0.0863716 + 0.996263i \(0.527527\pi\)
\(182\) 0 0
\(183\) −0.272779 −0.0201644
\(184\) 0 0
\(185\) −7.75024 −0.569809
\(186\) 0 0
\(187\) 1.84987 0.135276
\(188\) 0 0
\(189\) 0.307241 0.0223485
\(190\) 0 0
\(191\) 21.5672 1.56055 0.780275 0.625437i \(-0.215079\pi\)
0.780275 + 0.625437i \(0.215079\pi\)
\(192\) 0 0
\(193\) −23.0265 −1.65749 −0.828743 0.559629i \(-0.810944\pi\)
−0.828743 + 0.559629i \(0.810944\pi\)
\(194\) 0 0
\(195\) 0.462919 0.0331503
\(196\) 0 0
\(197\) 11.1640 0.795400 0.397700 0.917516i \(-0.369808\pi\)
0.397700 + 0.917516i \(0.369808\pi\)
\(198\) 0 0
\(199\) 13.2879 0.941955 0.470977 0.882145i \(-0.343901\pi\)
0.470977 + 0.882145i \(0.343901\pi\)
\(200\) 0 0
\(201\) 0.917232 0.0646965
\(202\) 0 0
\(203\) 0.796642 0.0559133
\(204\) 0 0
\(205\) −4.05857 −0.283463
\(206\) 0 0
\(207\) 7.11398 0.494456
\(208\) 0 0
\(209\) −1.17613 −0.0813546
\(210\) 0 0
\(211\) 10.3780 0.714449 0.357225 0.934018i \(-0.383723\pi\)
0.357225 + 0.934018i \(0.383723\pi\)
\(212\) 0 0
\(213\) −0.499733 −0.0342412
\(214\) 0 0
\(215\) −9.49867 −0.647804
\(216\) 0 0
\(217\) 0.785090 0.0532954
\(218\) 0 0
\(219\) 0.839813 0.0567493
\(220\) 0 0
\(221\) −27.8644 −1.87436
\(222\) 0 0
\(223\) −16.2413 −1.08760 −0.543799 0.839215i \(-0.683015\pi\)
−0.543799 + 0.839215i \(0.683015\pi\)
\(224\) 0 0
\(225\) −2.99478 −0.199652
\(226\) 0 0
\(227\) 15.8156 1.04972 0.524860 0.851189i \(-0.324118\pi\)
0.524860 + 0.851189i \(0.324118\pi\)
\(228\) 0 0
\(229\) −26.4248 −1.74620 −0.873101 0.487540i \(-0.837894\pi\)
−0.873101 + 0.487540i \(0.837894\pi\)
\(230\) 0 0
\(231\) 0.0218086 0.00143490
\(232\) 0 0
\(233\) 2.08510 0.136599 0.0682996 0.997665i \(-0.478243\pi\)
0.0682996 + 0.997665i \(0.478243\pi\)
\(234\) 0 0
\(235\) 4.25704 0.277698
\(236\) 0 0
\(237\) 0.727307 0.0472437
\(238\) 0 0
\(239\) −14.1081 −0.912580 −0.456290 0.889831i \(-0.650822\pi\)
−0.456290 + 0.889831i \(0.650822\pi\)
\(240\) 0 0
\(241\) 7.38114 0.475461 0.237730 0.971331i \(-0.423597\pi\)
0.237730 + 0.971331i \(0.423597\pi\)
\(242\) 0 0
\(243\) 1.94551 0.124804
\(244\) 0 0
\(245\) −6.49643 −0.415042
\(246\) 0 0
\(247\) 17.7159 1.12723
\(248\) 0 0
\(249\) −0.247191 −0.0156651
\(250\) 0 0
\(251\) −17.2947 −1.09163 −0.545817 0.837904i \(-0.683781\pi\)
−0.545817 + 0.837904i \(0.683781\pi\)
\(252\) 0 0
\(253\) 1.01081 0.0635489
\(254\) 0 0
\(255\) −0.313977 −0.0196620
\(256\) 0 0
\(257\) 0.978328 0.0610264 0.0305132 0.999534i \(-0.490286\pi\)
0.0305132 + 0.999534i \(0.490286\pi\)
\(258\) 0 0
\(259\) 5.49977 0.341739
\(260\) 0 0
\(261\) 3.36201 0.208103
\(262\) 0 0
\(263\) −25.8209 −1.59218 −0.796092 0.605175i \(-0.793103\pi\)
−0.796092 + 0.605175i \(0.793103\pi\)
\(264\) 0 0
\(265\) −5.36390 −0.329502
\(266\) 0 0
\(267\) 0.0764748 0.00468018
\(268\) 0 0
\(269\) 6.91986 0.421911 0.210956 0.977496i \(-0.432342\pi\)
0.210956 + 0.977496i \(0.432342\pi\)
\(270\) 0 0
\(271\) 16.0232 0.973338 0.486669 0.873586i \(-0.338212\pi\)
0.486669 + 0.873586i \(0.338212\pi\)
\(272\) 0 0
\(273\) −0.328499 −0.0198817
\(274\) 0 0
\(275\) −0.425521 −0.0256599
\(276\) 0 0
\(277\) −19.9286 −1.19739 −0.598696 0.800977i \(-0.704314\pi\)
−0.598696 + 0.800977i \(0.704314\pi\)
\(278\) 0 0
\(279\) 3.31326 0.198360
\(280\) 0 0
\(281\) −18.0361 −1.07594 −0.537971 0.842963i \(-0.680809\pi\)
−0.537971 + 0.842963i \(0.680809\pi\)
\(282\) 0 0
\(283\) −9.38500 −0.557880 −0.278940 0.960308i \(-0.589983\pi\)
−0.278940 + 0.960308i \(0.589983\pi\)
\(284\) 0 0
\(285\) 0.199623 0.0118247
\(286\) 0 0
\(287\) 2.88007 0.170005
\(288\) 0 0
\(289\) 1.89911 0.111712
\(290\) 0 0
\(291\) −0.330159 −0.0193542
\(292\) 0 0
\(293\) −0.207112 −0.0120996 −0.00604982 0.999982i \(-0.501926\pi\)
−0.00604982 + 0.999982i \(0.501926\pi\)
\(294\) 0 0
\(295\) 7.25935 0.422656
\(296\) 0 0
\(297\) 0.184235 0.0106904
\(298\) 0 0
\(299\) −15.2256 −0.880521
\(300\) 0 0
\(301\) 6.74050 0.388516
\(302\) 0 0
\(303\) −1.05517 −0.0606178
\(304\) 0 0
\(305\) −3.77690 −0.216264
\(306\) 0 0
\(307\) 4.53418 0.258779 0.129390 0.991594i \(-0.458698\pi\)
0.129390 + 0.991594i \(0.458698\pi\)
\(308\) 0 0
\(309\) 0.447485 0.0254566
\(310\) 0 0
\(311\) −20.3605 −1.15454 −0.577269 0.816554i \(-0.695882\pi\)
−0.577269 + 0.816554i \(0.695882\pi\)
\(312\) 0 0
\(313\) −7.35555 −0.415760 −0.207880 0.978154i \(-0.566656\pi\)
−0.207880 + 0.978154i \(0.566656\pi\)
\(314\) 0 0
\(315\) 2.12518 0.119740
\(316\) 0 0
\(317\) 13.4717 0.756645 0.378322 0.925674i \(-0.376501\pi\)
0.378322 + 0.925674i \(0.376501\pi\)
\(318\) 0 0
\(319\) 0.477700 0.0267461
\(320\) 0 0
\(321\) −1.03947 −0.0580174
\(322\) 0 0
\(323\) −12.0159 −0.668580
\(324\) 0 0
\(325\) 6.40956 0.355539
\(326\) 0 0
\(327\) −0.398846 −0.0220562
\(328\) 0 0
\(329\) −3.02090 −0.166548
\(330\) 0 0
\(331\) −5.06564 −0.278433 −0.139216 0.990262i \(-0.544458\pi\)
−0.139216 + 0.990262i \(0.544458\pi\)
\(332\) 0 0
\(333\) 23.2103 1.27192
\(334\) 0 0
\(335\) 12.7000 0.693873
\(336\) 0 0
\(337\) 5.66912 0.308817 0.154408 0.988007i \(-0.450653\pi\)
0.154408 + 0.988007i \(0.450653\pi\)
\(338\) 0 0
\(339\) 1.07852 0.0585771
\(340\) 0 0
\(341\) 0.470773 0.0254938
\(342\) 0 0
\(343\) 9.57742 0.517132
\(344\) 0 0
\(345\) −0.171563 −0.00923664
\(346\) 0 0
\(347\) −10.1912 −0.547091 −0.273546 0.961859i \(-0.588196\pi\)
−0.273546 + 0.961859i \(0.588196\pi\)
\(348\) 0 0
\(349\) −18.8306 −1.00798 −0.503990 0.863710i \(-0.668135\pi\)
−0.503990 + 0.863710i \(0.668135\pi\)
\(350\) 0 0
\(351\) −2.77510 −0.148124
\(352\) 0 0
\(353\) 8.92794 0.475187 0.237593 0.971365i \(-0.423641\pi\)
0.237593 + 0.971365i \(0.423641\pi\)
\(354\) 0 0
\(355\) −6.91929 −0.367238
\(356\) 0 0
\(357\) 0.222806 0.0117921
\(358\) 0 0
\(359\) 20.4790 1.08084 0.540419 0.841396i \(-0.318266\pi\)
0.540419 + 0.841396i \(0.318266\pi\)
\(360\) 0 0
\(361\) −11.3604 −0.597918
\(362\) 0 0
\(363\) −0.781378 −0.0410117
\(364\) 0 0
\(365\) 11.6280 0.608638
\(366\) 0 0
\(367\) 12.4178 0.648203 0.324101 0.946022i \(-0.394938\pi\)
0.324101 + 0.946022i \(0.394938\pi\)
\(368\) 0 0
\(369\) 12.1545 0.632740
\(370\) 0 0
\(371\) 3.80637 0.197617
\(372\) 0 0
\(373\) −24.4196 −1.26440 −0.632198 0.774807i \(-0.717847\pi\)
−0.632198 + 0.774807i \(0.717847\pi\)
\(374\) 0 0
\(375\) 0.0722232 0.00372959
\(376\) 0 0
\(377\) −7.19552 −0.370588
\(378\) 0 0
\(379\) 19.9830 1.02646 0.513228 0.858252i \(-0.328449\pi\)
0.513228 + 0.858252i \(0.328449\pi\)
\(380\) 0 0
\(381\) −0.629857 −0.0322686
\(382\) 0 0
\(383\) −2.98342 −0.152446 −0.0762228 0.997091i \(-0.524286\pi\)
−0.0762228 + 0.997091i \(0.524286\pi\)
\(384\) 0 0
\(385\) 0.301961 0.0153893
\(386\) 0 0
\(387\) 28.4465 1.44602
\(388\) 0 0
\(389\) 9.79740 0.496748 0.248374 0.968664i \(-0.420104\pi\)
0.248374 + 0.968664i \(0.420104\pi\)
\(390\) 0 0
\(391\) 10.3268 0.522251
\(392\) 0 0
\(393\) −1.09558 −0.0552646
\(394\) 0 0
\(395\) 10.0703 0.506691
\(396\) 0 0
\(397\) 0.268968 0.0134991 0.00674957 0.999977i \(-0.497852\pi\)
0.00674957 + 0.999977i \(0.497852\pi\)
\(398\) 0 0
\(399\) −0.141658 −0.00709176
\(400\) 0 0
\(401\) −27.5671 −1.37663 −0.688316 0.725411i \(-0.741650\pi\)
−0.688316 + 0.725411i \(0.741650\pi\)
\(402\) 0 0
\(403\) −7.09118 −0.353237
\(404\) 0 0
\(405\) 8.95308 0.444882
\(406\) 0 0
\(407\) 3.29789 0.163470
\(408\) 0 0
\(409\) −6.35099 −0.314036 −0.157018 0.987596i \(-0.550188\pi\)
−0.157018 + 0.987596i \(0.550188\pi\)
\(410\) 0 0
\(411\) −1.11944 −0.0552181
\(412\) 0 0
\(413\) −5.15143 −0.253485
\(414\) 0 0
\(415\) −3.42260 −0.168009
\(416\) 0 0
\(417\) 0.465784 0.0228096
\(418\) 0 0
\(419\) −37.8847 −1.85079 −0.925393 0.379008i \(-0.876265\pi\)
−0.925393 + 0.379008i \(0.876265\pi\)
\(420\) 0 0
\(421\) −0.950439 −0.0463216 −0.0231608 0.999732i \(-0.507373\pi\)
−0.0231608 + 0.999732i \(0.507373\pi\)
\(422\) 0 0
\(423\) −12.7489 −0.619873
\(424\) 0 0
\(425\) −4.34731 −0.210876
\(426\) 0 0
\(427\) 2.68018 0.129703
\(428\) 0 0
\(429\) −0.196982 −0.00951038
\(430\) 0 0
\(431\) −2.49509 −0.120184 −0.0600921 0.998193i \(-0.519139\pi\)
−0.0600921 + 0.998193i \(0.519139\pi\)
\(432\) 0 0
\(433\) 9.35197 0.449427 0.224713 0.974425i \(-0.427855\pi\)
0.224713 + 0.974425i \(0.427855\pi\)
\(434\) 0 0
\(435\) −0.0810794 −0.00388746
\(436\) 0 0
\(437\) −6.56570 −0.314080
\(438\) 0 0
\(439\) −16.1962 −0.773002 −0.386501 0.922289i \(-0.626316\pi\)
−0.386501 + 0.922289i \(0.626316\pi\)
\(440\) 0 0
\(441\) 19.4554 0.926448
\(442\) 0 0
\(443\) 22.2330 1.05632 0.528161 0.849144i \(-0.322882\pi\)
0.528161 + 0.849144i \(0.322882\pi\)
\(444\) 0 0
\(445\) 1.05887 0.0501951
\(446\) 0 0
\(447\) −0.707817 −0.0334786
\(448\) 0 0
\(449\) 24.4972 1.15609 0.578047 0.816004i \(-0.303815\pi\)
0.578047 + 0.816004i \(0.303815\pi\)
\(450\) 0 0
\(451\) 1.72701 0.0813216
\(452\) 0 0
\(453\) −0.0722232 −0.00339334
\(454\) 0 0
\(455\) −4.54839 −0.213232
\(456\) 0 0
\(457\) 18.1628 0.849621 0.424810 0.905282i \(-0.360341\pi\)
0.424810 + 0.905282i \(0.360341\pi\)
\(458\) 0 0
\(459\) 1.88222 0.0878546
\(460\) 0 0
\(461\) −7.11272 −0.331272 −0.165636 0.986187i \(-0.552968\pi\)
−0.165636 + 0.986187i \(0.552968\pi\)
\(462\) 0 0
\(463\) 9.63466 0.447761 0.223880 0.974617i \(-0.428128\pi\)
0.223880 + 0.974617i \(0.428128\pi\)
\(464\) 0 0
\(465\) −0.0799037 −0.00370544
\(466\) 0 0
\(467\) 8.59139 0.397562 0.198781 0.980044i \(-0.436302\pi\)
0.198781 + 0.980044i \(0.436302\pi\)
\(468\) 0 0
\(469\) −9.01222 −0.416146
\(470\) 0 0
\(471\) 0.0940401 0.00433314
\(472\) 0 0
\(473\) 4.04189 0.185846
\(474\) 0 0
\(475\) 2.76398 0.126820
\(476\) 0 0
\(477\) 16.0637 0.735508
\(478\) 0 0
\(479\) 24.6154 1.12471 0.562354 0.826896i \(-0.309896\pi\)
0.562354 + 0.826896i \(0.309896\pi\)
\(480\) 0 0
\(481\) −49.6756 −2.26501
\(482\) 0 0
\(483\) 0.121746 0.00553962
\(484\) 0 0
\(485\) −4.57137 −0.207575
\(486\) 0 0
\(487\) 31.6149 1.43261 0.716305 0.697788i \(-0.245832\pi\)
0.716305 + 0.697788i \(0.245832\pi\)
\(488\) 0 0
\(489\) −0.0832298 −0.00376378
\(490\) 0 0
\(491\) 29.4660 1.32978 0.664890 0.746941i \(-0.268478\pi\)
0.664890 + 0.746941i \(0.268478\pi\)
\(492\) 0 0
\(493\) 4.88039 0.219802
\(494\) 0 0
\(495\) 1.27434 0.0572775
\(496\) 0 0
\(497\) 4.91011 0.220248
\(498\) 0 0
\(499\) −17.2934 −0.774159 −0.387079 0.922046i \(-0.626516\pi\)
−0.387079 + 0.922046i \(0.626516\pi\)
\(500\) 0 0
\(501\) −1.49709 −0.0668851
\(502\) 0 0
\(503\) 21.9170 0.977229 0.488615 0.872500i \(-0.337502\pi\)
0.488615 + 0.872500i \(0.337502\pi\)
\(504\) 0 0
\(505\) −14.6098 −0.650129
\(506\) 0 0
\(507\) 2.02821 0.0900759
\(508\) 0 0
\(509\) −20.3000 −0.899783 −0.449891 0.893083i \(-0.648537\pi\)
−0.449891 + 0.893083i \(0.648537\pi\)
\(510\) 0 0
\(511\) −8.25154 −0.365027
\(512\) 0 0
\(513\) −1.19670 −0.0528355
\(514\) 0 0
\(515\) 6.19587 0.273023
\(516\) 0 0
\(517\) −1.81146 −0.0796679
\(518\) 0 0
\(519\) −1.44027 −0.0632210
\(520\) 0 0
\(521\) −41.0111 −1.79673 −0.898364 0.439253i \(-0.855243\pi\)
−0.898364 + 0.439253i \(0.855243\pi\)
\(522\) 0 0
\(523\) 2.08941 0.0913636 0.0456818 0.998956i \(-0.485454\pi\)
0.0456818 + 0.998956i \(0.485454\pi\)
\(524\) 0 0
\(525\) −0.0512515 −0.00223680
\(526\) 0 0
\(527\) 4.80962 0.209510
\(528\) 0 0
\(529\) −17.3572 −0.754661
\(530\) 0 0
\(531\) −21.7402 −0.943444
\(532\) 0 0
\(533\) −26.0136 −1.12678
\(534\) 0 0
\(535\) −14.3924 −0.622239
\(536\) 0 0
\(537\) 0.0920747 0.00397332
\(538\) 0 0
\(539\) 2.76437 0.119070
\(540\) 0 0
\(541\) 31.1115 1.33759 0.668795 0.743447i \(-0.266810\pi\)
0.668795 + 0.743447i \(0.266810\pi\)
\(542\) 0 0
\(543\) −0.167848 −0.00720306
\(544\) 0 0
\(545\) −5.52240 −0.236554
\(546\) 0 0
\(547\) 27.0295 1.15570 0.577849 0.816144i \(-0.303892\pi\)
0.577849 + 0.816144i \(0.303892\pi\)
\(548\) 0 0
\(549\) 11.3110 0.482741
\(550\) 0 0
\(551\) −3.10290 −0.132188
\(552\) 0 0
\(553\) −7.14613 −0.303884
\(554\) 0 0
\(555\) −0.559747 −0.0237599
\(556\) 0 0
\(557\) −7.37891 −0.312655 −0.156327 0.987705i \(-0.549965\pi\)
−0.156327 + 0.987705i \(0.549965\pi\)
\(558\) 0 0
\(559\) −60.8823 −2.57505
\(560\) 0 0
\(561\) 0.133604 0.00564075
\(562\) 0 0
\(563\) 15.0319 0.633517 0.316759 0.948506i \(-0.397405\pi\)
0.316759 + 0.948506i \(0.397405\pi\)
\(564\) 0 0
\(565\) 14.9331 0.628242
\(566\) 0 0
\(567\) −6.35334 −0.266815
\(568\) 0 0
\(569\) 3.11822 0.130722 0.0653612 0.997862i \(-0.479180\pi\)
0.0653612 + 0.997862i \(0.479180\pi\)
\(570\) 0 0
\(571\) −3.83446 −0.160467 −0.0802335 0.996776i \(-0.525567\pi\)
−0.0802335 + 0.996776i \(0.525567\pi\)
\(572\) 0 0
\(573\) 1.55765 0.0650719
\(574\) 0 0
\(575\) −2.37546 −0.0990634
\(576\) 0 0
\(577\) −3.66270 −0.152480 −0.0762401 0.997089i \(-0.524292\pi\)
−0.0762401 + 0.997089i \(0.524292\pi\)
\(578\) 0 0
\(579\) −1.66305 −0.0691140
\(580\) 0 0
\(581\) 2.42877 0.100762
\(582\) 0 0
\(583\) 2.28246 0.0945296
\(584\) 0 0
\(585\) −19.1953 −0.793626
\(586\) 0 0
\(587\) 5.97122 0.246459 0.123229 0.992378i \(-0.460675\pi\)
0.123229 + 0.992378i \(0.460675\pi\)
\(588\) 0 0
\(589\) −3.05791 −0.125999
\(590\) 0 0
\(591\) 0.806298 0.0331667
\(592\) 0 0
\(593\) 4.17424 0.171416 0.0857078 0.996320i \(-0.472685\pi\)
0.0857078 + 0.996320i \(0.472685\pi\)
\(594\) 0 0
\(595\) 3.08496 0.126471
\(596\) 0 0
\(597\) 0.959695 0.0392777
\(598\) 0 0
\(599\) −4.48902 −0.183416 −0.0917082 0.995786i \(-0.529233\pi\)
−0.0917082 + 0.995786i \(0.529233\pi\)
\(600\) 0 0
\(601\) −42.0849 −1.71668 −0.858339 0.513082i \(-0.828504\pi\)
−0.858339 + 0.513082i \(0.828504\pi\)
\(602\) 0 0
\(603\) −38.0336 −1.54885
\(604\) 0 0
\(605\) −10.8189 −0.439852
\(606\) 0 0
\(607\) 33.7422 1.36955 0.684777 0.728752i \(-0.259899\pi\)
0.684777 + 0.728752i \(0.259899\pi\)
\(608\) 0 0
\(609\) 0.0575360 0.00233148
\(610\) 0 0
\(611\) 27.2857 1.10386
\(612\) 0 0
\(613\) 15.3190 0.618729 0.309365 0.950944i \(-0.399884\pi\)
0.309365 + 0.950944i \(0.399884\pi\)
\(614\) 0 0
\(615\) −0.293123 −0.0118199
\(616\) 0 0
\(617\) 23.3517 0.940106 0.470053 0.882638i \(-0.344235\pi\)
0.470053 + 0.882638i \(0.344235\pi\)
\(618\) 0 0
\(619\) −8.96970 −0.360523 −0.180261 0.983619i \(-0.557694\pi\)
−0.180261 + 0.983619i \(0.557694\pi\)
\(620\) 0 0
\(621\) 1.02848 0.0412716
\(622\) 0 0
\(623\) −0.751400 −0.0301042
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.0849439 −0.00339233
\(628\) 0 0
\(629\) 33.6927 1.34342
\(630\) 0 0
\(631\) −21.0985 −0.839919 −0.419959 0.907543i \(-0.637956\pi\)
−0.419959 + 0.907543i \(0.637956\pi\)
\(632\) 0 0
\(633\) 0.749531 0.0297912
\(634\) 0 0
\(635\) −8.72098 −0.346082
\(636\) 0 0
\(637\) −41.6393 −1.64981
\(638\) 0 0
\(639\) 20.7218 0.819741
\(640\) 0 0
\(641\) 16.9207 0.668328 0.334164 0.942515i \(-0.391546\pi\)
0.334164 + 0.942515i \(0.391546\pi\)
\(642\) 0 0
\(643\) 3.47485 0.137035 0.0685173 0.997650i \(-0.478173\pi\)
0.0685173 + 0.997650i \(0.478173\pi\)
\(644\) 0 0
\(645\) −0.686024 −0.0270122
\(646\) 0 0
\(647\) −32.7346 −1.28693 −0.643465 0.765476i \(-0.722504\pi\)
−0.643465 + 0.765476i \(0.722504\pi\)
\(648\) 0 0
\(649\) −3.08901 −0.121254
\(650\) 0 0
\(651\) 0.0567017 0.00222232
\(652\) 0 0
\(653\) 7.51048 0.293908 0.146954 0.989143i \(-0.453053\pi\)
0.146954 + 0.989143i \(0.453053\pi\)
\(654\) 0 0
\(655\) −15.1693 −0.592715
\(656\) 0 0
\(657\) −34.8234 −1.35859
\(658\) 0 0
\(659\) −11.5988 −0.451824 −0.225912 0.974148i \(-0.572536\pi\)
−0.225912 + 0.974148i \(0.572536\pi\)
\(660\) 0 0
\(661\) 13.9039 0.540797 0.270399 0.962748i \(-0.412845\pi\)
0.270399 + 0.962748i \(0.412845\pi\)
\(662\) 0 0
\(663\) −2.01245 −0.0781572
\(664\) 0 0
\(665\) −1.96139 −0.0760594
\(666\) 0 0
\(667\) 2.66674 0.103257
\(668\) 0 0
\(669\) −1.17300 −0.0453508
\(670\) 0 0
\(671\) 1.60715 0.0620433
\(672\) 0 0
\(673\) −39.5867 −1.52595 −0.762977 0.646425i \(-0.776263\pi\)
−0.762977 + 0.646425i \(0.776263\pi\)
\(674\) 0 0
\(675\) −0.432962 −0.0166647
\(676\) 0 0
\(677\) 29.2265 1.12327 0.561633 0.827387i \(-0.310173\pi\)
0.561633 + 0.827387i \(0.310173\pi\)
\(678\) 0 0
\(679\) 3.24396 0.124492
\(680\) 0 0
\(681\) 1.14225 0.0437713
\(682\) 0 0
\(683\) 10.6734 0.408405 0.204203 0.978929i \(-0.434540\pi\)
0.204203 + 0.978929i \(0.434540\pi\)
\(684\) 0 0
\(685\) −15.4998 −0.592216
\(686\) 0 0
\(687\) −1.90849 −0.0728133
\(688\) 0 0
\(689\) −34.3803 −1.30978
\(690\) 0 0
\(691\) −5.74934 −0.218715 −0.109358 0.994002i \(-0.534879\pi\)
−0.109358 + 0.994002i \(0.534879\pi\)
\(692\) 0 0
\(693\) −0.904307 −0.0343518
\(694\) 0 0
\(695\) 6.44923 0.244633
\(696\) 0 0
\(697\) 17.6439 0.668309
\(698\) 0 0
\(699\) 0.150592 0.00569593
\(700\) 0 0
\(701\) −7.14573 −0.269890 −0.134945 0.990853i \(-0.543086\pi\)
−0.134945 + 0.990853i \(0.543086\pi\)
\(702\) 0 0
\(703\) −21.4215 −0.807926
\(704\) 0 0
\(705\) 0.307457 0.0115795
\(706\) 0 0
\(707\) 10.3675 0.389910
\(708\) 0 0
\(709\) 3.10751 0.116705 0.0583526 0.998296i \(-0.481415\pi\)
0.0583526 + 0.998296i \(0.481415\pi\)
\(710\) 0 0
\(711\) −30.1583 −1.13102
\(712\) 0 0
\(713\) 2.62807 0.0984220
\(714\) 0 0
\(715\) −2.72740 −0.101999
\(716\) 0 0
\(717\) −1.01894 −0.0380528
\(718\) 0 0
\(719\) −0.755404 −0.0281718 −0.0140859 0.999901i \(-0.504484\pi\)
−0.0140859 + 0.999901i \(0.504484\pi\)
\(720\) 0 0
\(721\) −4.39675 −0.163743
\(722\) 0 0
\(723\) 0.533089 0.0198258
\(724\) 0 0
\(725\) −1.12262 −0.0416932
\(726\) 0 0
\(727\) −35.3433 −1.31081 −0.655405 0.755278i \(-0.727502\pi\)
−0.655405 + 0.755278i \(0.727502\pi\)
\(728\) 0 0
\(729\) −26.7187 −0.989583
\(730\) 0 0
\(731\) 41.2937 1.52730
\(732\) 0 0
\(733\) −18.3054 −0.676127 −0.338064 0.941123i \(-0.609772\pi\)
−0.338064 + 0.941123i \(0.609772\pi\)
\(734\) 0 0
\(735\) −0.469193 −0.0173064
\(736\) 0 0
\(737\) −5.40410 −0.199063
\(738\) 0 0
\(739\) 39.9731 1.47044 0.735218 0.677831i \(-0.237080\pi\)
0.735218 + 0.677831i \(0.237080\pi\)
\(740\) 0 0
\(741\) 1.27950 0.0470035
\(742\) 0 0
\(743\) 49.6574 1.82175 0.910876 0.412679i \(-0.135407\pi\)
0.910876 + 0.412679i \(0.135407\pi\)
\(744\) 0 0
\(745\) −9.80041 −0.359059
\(746\) 0 0
\(747\) 10.2500 0.375026
\(748\) 0 0
\(749\) 10.2132 0.373183
\(750\) 0 0
\(751\) −52.4001 −1.91211 −0.956053 0.293193i \(-0.905282\pi\)
−0.956053 + 0.293193i \(0.905282\pi\)
\(752\) 0 0
\(753\) −1.24908 −0.0455190
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) −0.176781 −0.00642521 −0.00321261 0.999995i \(-0.501023\pi\)
−0.00321261 + 0.999995i \(0.501023\pi\)
\(758\) 0 0
\(759\) 0.0730037 0.00264987
\(760\) 0 0
\(761\) −4.65090 −0.168595 −0.0842975 0.996441i \(-0.526865\pi\)
−0.0842975 + 0.996441i \(0.526865\pi\)
\(762\) 0 0
\(763\) 3.91884 0.141872
\(764\) 0 0
\(765\) 13.0193 0.470712
\(766\) 0 0
\(767\) 46.5293 1.68007
\(768\) 0 0
\(769\) −9.07879 −0.327390 −0.163695 0.986511i \(-0.552341\pi\)
−0.163695 + 0.986511i \(0.552341\pi\)
\(770\) 0 0
\(771\) 0.0706580 0.00254468
\(772\) 0 0
\(773\) 28.3926 1.02121 0.510605 0.859815i \(-0.329421\pi\)
0.510605 + 0.859815i \(0.329421\pi\)
\(774\) 0 0
\(775\) −1.10634 −0.0397410
\(776\) 0 0
\(777\) 0.397211 0.0142499
\(778\) 0 0
\(779\) −11.2178 −0.401919
\(780\) 0 0
\(781\) 2.94431 0.105356
\(782\) 0 0
\(783\) 0.486054 0.0173701
\(784\) 0 0
\(785\) 1.30208 0.0464731
\(786\) 0 0
\(787\) 35.8995 1.27968 0.639839 0.768509i \(-0.279001\pi\)
0.639839 + 0.768509i \(0.279001\pi\)
\(788\) 0 0
\(789\) −1.86487 −0.0663910
\(790\) 0 0
\(791\) −10.5969 −0.376784
\(792\) 0 0
\(793\) −24.2083 −0.859660
\(794\) 0 0
\(795\) −0.387398 −0.0137396
\(796\) 0 0
\(797\) 5.72995 0.202965 0.101483 0.994837i \(-0.467641\pi\)
0.101483 + 0.994837i \(0.467641\pi\)
\(798\) 0 0
\(799\) −18.5067 −0.654718
\(800\) 0 0
\(801\) −3.17108 −0.112045
\(802\) 0 0
\(803\) −4.94797 −0.174610
\(804\) 0 0
\(805\) 1.68569 0.0594126
\(806\) 0 0
\(807\) 0.499775 0.0175929
\(808\) 0 0
\(809\) −19.2161 −0.675603 −0.337802 0.941217i \(-0.609683\pi\)
−0.337802 + 0.941217i \(0.609683\pi\)
\(810\) 0 0
\(811\) −10.8110 −0.379627 −0.189814 0.981820i \(-0.560788\pi\)
−0.189814 + 0.981820i \(0.560788\pi\)
\(812\) 0 0
\(813\) 1.15724 0.0405863
\(814\) 0 0
\(815\) −1.15240 −0.0403667
\(816\) 0 0
\(817\) −26.2541 −0.918515
\(818\) 0 0
\(819\) 13.6214 0.475972
\(820\) 0 0
\(821\) −7.62772 −0.266209 −0.133105 0.991102i \(-0.542495\pi\)
−0.133105 + 0.991102i \(0.542495\pi\)
\(822\) 0 0
\(823\) 15.5370 0.541587 0.270794 0.962637i \(-0.412714\pi\)
0.270794 + 0.962637i \(0.412714\pi\)
\(824\) 0 0
\(825\) −0.0307325 −0.00106997
\(826\) 0 0
\(827\) −4.22755 −0.147006 −0.0735031 0.997295i \(-0.523418\pi\)
−0.0735031 + 0.997295i \(0.523418\pi\)
\(828\) 0 0
\(829\) 18.9122 0.656849 0.328424 0.944530i \(-0.393482\pi\)
0.328424 + 0.944530i \(0.393482\pi\)
\(830\) 0 0
\(831\) −1.43930 −0.0499289
\(832\) 0 0
\(833\) 28.2420 0.978527
\(834\) 0 0
\(835\) −20.7287 −0.717345
\(836\) 0 0
\(837\) 0.479005 0.0165568
\(838\) 0 0
\(839\) −25.4110 −0.877284 −0.438642 0.898662i \(-0.644540\pi\)
−0.438642 + 0.898662i \(0.644540\pi\)
\(840\) 0 0
\(841\) −27.7397 −0.956542
\(842\) 0 0
\(843\) −1.30262 −0.0448648
\(844\) 0 0
\(845\) 28.0825 0.966067
\(846\) 0 0
\(847\) 7.67739 0.263798
\(848\) 0 0
\(849\) −0.677815 −0.0232625
\(850\) 0 0
\(851\) 18.4103 0.631099
\(852\) 0 0
\(853\) 21.2801 0.728615 0.364308 0.931279i \(-0.381306\pi\)
0.364308 + 0.931279i \(0.381306\pi\)
\(854\) 0 0
\(855\) −8.27751 −0.283085
\(856\) 0 0
\(857\) 40.9808 1.39988 0.699939 0.714202i \(-0.253210\pi\)
0.699939 + 0.714202i \(0.253210\pi\)
\(858\) 0 0
\(859\) −48.7945 −1.66485 −0.832424 0.554140i \(-0.813047\pi\)
−0.832424 + 0.554140i \(0.813047\pi\)
\(860\) 0 0
\(861\) 0.208008 0.00708888
\(862\) 0 0
\(863\) 10.5779 0.360075 0.180037 0.983660i \(-0.442378\pi\)
0.180037 + 0.983660i \(0.442378\pi\)
\(864\) 0 0
\(865\) −19.9420 −0.678048
\(866\) 0 0
\(867\) 0.137160 0.00465819
\(868\) 0 0
\(869\) −4.28512 −0.145363
\(870\) 0 0
\(871\) 81.4012 2.75817
\(872\) 0 0
\(873\) 13.6903 0.463345
\(874\) 0 0
\(875\) −0.709626 −0.0239897
\(876\) 0 0
\(877\) 43.0020 1.45207 0.726037 0.687656i \(-0.241360\pi\)
0.726037 + 0.687656i \(0.241360\pi\)
\(878\) 0 0
\(879\) −0.0149583 −0.000504532 0
\(880\) 0 0
\(881\) −34.9536 −1.17762 −0.588809 0.808273i \(-0.700403\pi\)
−0.588809 + 0.808273i \(0.700403\pi\)
\(882\) 0 0
\(883\) 54.2117 1.82437 0.912185 0.409778i \(-0.134394\pi\)
0.912185 + 0.409778i \(0.134394\pi\)
\(884\) 0 0
\(885\) 0.524294 0.0176239
\(886\) 0 0
\(887\) 15.5465 0.522002 0.261001 0.965339i \(-0.415947\pi\)
0.261001 + 0.965339i \(0.415947\pi\)
\(888\) 0 0
\(889\) 6.18864 0.207560
\(890\) 0 0
\(891\) −3.80973 −0.127631
\(892\) 0 0
\(893\) 11.7663 0.393746
\(894\) 0 0
\(895\) 1.27486 0.0426140
\(896\) 0 0
\(897\) −1.09964 −0.0367160
\(898\) 0 0
\(899\) 1.24201 0.0414232
\(900\) 0 0
\(901\) 23.3186 0.776854
\(902\) 0 0
\(903\) 0.486821 0.0162004
\(904\) 0 0
\(905\) −2.32402 −0.0772531
\(906\) 0 0
\(907\) −47.3249 −1.57140 −0.785698 0.618610i \(-0.787696\pi\)
−0.785698 + 0.618610i \(0.787696\pi\)
\(908\) 0 0
\(909\) 43.7533 1.45120
\(910\) 0 0
\(911\) −22.7348 −0.753236 −0.376618 0.926369i \(-0.622913\pi\)
−0.376618 + 0.926369i \(0.622913\pi\)
\(912\) 0 0
\(913\) 1.45639 0.0481995
\(914\) 0 0
\(915\) −0.272779 −0.00901781
\(916\) 0 0
\(917\) 10.7646 0.355477
\(918\) 0 0
\(919\) 12.5632 0.414422 0.207211 0.978296i \(-0.433561\pi\)
0.207211 + 0.978296i \(0.433561\pi\)
\(920\) 0 0
\(921\) 0.327473 0.0107906
\(922\) 0 0
\(923\) −44.3496 −1.45979
\(924\) 0 0
\(925\) −7.75024 −0.254826
\(926\) 0 0
\(927\) −18.5553 −0.609436
\(928\) 0 0
\(929\) 27.9530 0.917108 0.458554 0.888666i \(-0.348367\pi\)
0.458554 + 0.888666i \(0.348367\pi\)
\(930\) 0 0
\(931\) −17.9560 −0.588483
\(932\) 0 0
\(933\) −1.47050 −0.0481420
\(934\) 0 0
\(935\) 1.84987 0.0604973
\(936\) 0 0
\(937\) 4.67569 0.152748 0.0763740 0.997079i \(-0.475666\pi\)
0.0763740 + 0.997079i \(0.475666\pi\)
\(938\) 0 0
\(939\) −0.531241 −0.0173364
\(940\) 0 0
\(941\) 3.59574 0.117218 0.0586088 0.998281i \(-0.481334\pi\)
0.0586088 + 0.998281i \(0.481334\pi\)
\(942\) 0 0
\(943\) 9.64095 0.313953
\(944\) 0 0
\(945\) 0.307241 0.00999456
\(946\) 0 0
\(947\) −42.9876 −1.39691 −0.698454 0.715655i \(-0.746128\pi\)
−0.698454 + 0.715655i \(0.746128\pi\)
\(948\) 0 0
\(949\) 74.5305 2.41936
\(950\) 0 0
\(951\) 0.972968 0.0315506
\(952\) 0 0
\(953\) −33.4247 −1.08273 −0.541365 0.840787i \(-0.682092\pi\)
−0.541365 + 0.840787i \(0.682092\pi\)
\(954\) 0 0
\(955\) 21.5672 0.697899
\(956\) 0 0
\(957\) 0.0345010 0.00111526
\(958\) 0 0
\(959\) 10.9990 0.355178
\(960\) 0 0
\(961\) −29.7760 −0.960516
\(962\) 0 0
\(963\) 43.1022 1.38895
\(964\) 0 0
\(965\) −23.0265 −0.741250
\(966\) 0 0
\(967\) 57.6070 1.85252 0.926259 0.376888i \(-0.123006\pi\)
0.926259 + 0.376888i \(0.123006\pi\)
\(968\) 0 0
\(969\) −0.867824 −0.0278785
\(970\) 0 0
\(971\) −29.7096 −0.953426 −0.476713 0.879059i \(-0.658172\pi\)
−0.476713 + 0.879059i \(0.658172\pi\)
\(972\) 0 0
\(973\) −4.57654 −0.146717
\(974\) 0 0
\(975\) 0.462919 0.0148253
\(976\) 0 0
\(977\) 40.2087 1.28639 0.643195 0.765702i \(-0.277608\pi\)
0.643195 + 0.765702i \(0.277608\pi\)
\(978\) 0 0
\(979\) −0.450571 −0.0144003
\(980\) 0 0
\(981\) 16.5384 0.528031
\(982\) 0 0
\(983\) 29.5098 0.941216 0.470608 0.882342i \(-0.344035\pi\)
0.470608 + 0.882342i \(0.344035\pi\)
\(984\) 0 0
\(985\) 11.1640 0.355714
\(986\) 0 0
\(987\) −0.218179 −0.00694472
\(988\) 0 0
\(989\) 22.5637 0.717483
\(990\) 0 0
\(991\) 27.7388 0.881151 0.440576 0.897716i \(-0.354774\pi\)
0.440576 + 0.897716i \(0.354774\pi\)
\(992\) 0 0
\(993\) −0.365857 −0.0116101
\(994\) 0 0
\(995\) 13.2879 0.421255
\(996\) 0 0
\(997\) 39.6362 1.25529 0.627646 0.778499i \(-0.284019\pi\)
0.627646 + 0.778499i \(0.284019\pi\)
\(998\) 0 0
\(999\) 3.35556 0.106165
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 \(a_p\))